,transcriber's ,note4    ,variable      
spelling and hyphenation have been      
retained4 ,minor punctuation            
inconsistencies have been silently      
repaired4 ,the author's corrections1    
additions and comments have been applied
 in the text4 ,changes made by  the     
transcriber can be found at the end of  
the book4 ,the original text  is printed
 in a two-column layout4 ,formatting and
 special characters are  indicated as   
follows3        italic                  
,illustration3 ,galileo ,galilei        
,,the                                   
,,life                                  
,,of                                    
,,galileo ,,galilei1                    
,,with                                  
,,illustrations ,,of ,,the ,,advancement
                                        
,,of                                    
,,experimental ,,philosophy4            
,,mdcccxxx4                             
,,london4          ,,life ,,of          
,,galileo3    ,,with ,,illustrations    

,,of ,,the ,,advancement ,,of           
,,experimental ,,philosophy4            
,,chapter ,i4        ,introduction4     
,,the knowledge which we at present     
possess of the phenomena of nature and  
of their connection has not by any means
 been regularly progressive1 as  we     
might have expected1 from the time when 
they first drew the attention  of       
mankind4 ,without entering into the     
question touching the scientific        
acquirements of eastern nations at a    
remote period1 it is certain that  some 
among the early ,greeks were in         
possession of several truths1  however  
acquired1 connected with the economy of 
the universe1 which were  afterwards    
suffered to fall into neglect and       
oblivion4 ,but the  philosophers of the 
old school appear in general to have    
confined  themselves at the best to     
observations2 very few traces remain of 
their  having instituted experiments1   
properly so called4 ,this putting of    
nature to the torture1 as ,bacon calls  

it1 has occasioned the principal  part  
of modern philosophical discoveries4    
,the experimentalist may so  order his  
examination of nature as to vary at     
pleasure the circumstances  in which it 
is made1 often to discard accidents     
which complicate the  general           
appearances1 and at once to bring any   
theory which he may form  to a decisive 
test4 ,the province of the mere observer
 is necessarily  limited3 the power of  
selection among the phenomena to be     
presented is  in great measure denied to
 him1 and he may consider himself       
fortunate if  they are such as to lead  
him readily to a knowledge of the laws  
which  they follow4    ,perhaps to this 
imperfection of method it may be        
attributed that natural  philosophy     
continued to be stationary1 or even to  
decline1 during a long  series of ages1 
until little more than two centuries    
ago4 ,within this  comparatively short  
period it has rapidly reached a degree  
of perfection  so different from its    

former degraded state1 that we can      
hardly  institute any comparison between
 the two4 ,before that epoch1 a few     
insulated facts1 such as might first    
happen to be noticed1 often             
inaccurately observed and always too    
hastily generalized1 were found         
sufficient to excite the naturalist's   
lively imagination2 and having  once    
pleased his fancy with the supposed     
fitness of his artificial  scheme1 his  
perverted ingenuity was thenceforward   
employed in forcing  the observed       
phenomena into an imaginary agreement   
with the result of  his theory2 instead 
of taking the more rational1 and it     
should seem1 the  more obvious1 method  
of correcting the theory by the result  
of his  observations1 and considering   
the one merely as the general and       
abbreviated expression of the other4    
,but natural phenomena were not then    
valued on their own account1 and for the
 proofs which they afford of a  vast and
 beneficent design in the structure of  

the universe1 so much as  for the       
fertile topics which the favourite mode 
of viewing the subject  supplied to the 
spirit of scholastic disputation3 and it
 is a  humiliating reflection that      
mankind never reasoned so ill as when   
they  most professed to cultivate the   
art of reasoning4 ,however specious the 
objects1 and alluring the announcements 
of this art1 the then prevailing  manner
 of studying it curbed and corrupted all
 that is free and noble in  the human   
mind4 ,innumerable fallacies lurked     
every where among the most  generally   
received opinions1 and crowds of        
dogmatic and self-sufficient  pedants   
fully justified the lively definition1  
that logic is the art of  talking       
unintelligibly on things of which we are
 ignorant4#a    ,the error which lay at 
the root of the philosophy of the middle
 ages was  this3--from the belief that  
general laws and universal principles   
might  be discovered1 of which the      
natural phenomena were effects1 it was  

thought that the proper order of study  
was1 first to detect the general  cause1
 and then to pursue it into its         
consequences2 it was considered  absurd 
to begin with the effect instead of the 
cause2 whereas the real  choice lay     
between proceeding from particular facts
 to general facts1  or from general     
facts to particular facts2 and it was   
under this  misrepresentation of the    
real question that all the sophistry    
lurked4 ,as  soon as it is well         
understood that the general cause is no 
other than  a single fact1 common to a  
great number of phenomena1 it is        
necessarily  perceived that an accurate 
scrutiny of these latter must precede   
any  safe reasoning with respect to the 
former4 ,but at the time of which we    
are speaking1 those who adopted this    
order of reasoning1 and who began  their
 inquiries by a minute and sedulous     
investigation of facts1 were  treated   
with disdain1 as men who degraded the   
lofty name of philosophy  by bestowing  

it upon mere mechanical operations4     
,among the earliest and  noblest of     
these was ,galileo4    ,it is common1   
especially in this country1 to name     
,bacon as the founder  of the present   
school of experimental philosophy2 we   
speak of the  ,baconian or inductive    
method of reasoning as synonimous and   
convertible  terms1 and we are apt to   
overlook what ,galileo had already done 
before  ,bacon's writings appeared4     
,certainly the ,italian did not range   
over the  circle of the sciences with   
the supreme and searching glance of the 
,english philosopher1 but we find in    
every part of his writings              
philosophical maxims which do not lose  
by comparison with those of  ,bacon2 and
 ,galileo deserves the additional       
praise1 that he himself gave  to the    
world a splendid practical illustration 
of the value of the  principles which he
 constantly recommended4 ,in support of 
this view of  the comparative deserts of
 these two celebrated men1 we are able  

to  adduce the authority of ,hume1 who  
will be readily admitted as a  competent
 judge of philosophical merit1 where his
 prejudices cannot bias  his decision4  
,discussing the character of ,bacon1 he 
says1 ,if we  consider the variety of   
talents displayed by this man1 as a     
public  speaker1 a man of business1 a   
wit1 a courtier1 a companion1 an author1
 a  philosopher1 he is justly the object
 of great admiration4 ,if we consider   
him merely as an author and philosopher1
 the light in which we view him  at     
present1 though very estimable1 he was  
yet inferior to his  contemporary       
,galileo1 perhaps even to ,kepler4      
,bacon pointed out at a  distance the   
road to true philosophy3 ,galileo both  
pointed it out to  others1 and made     
himself considerable advances in it4    
,the ,englishman was  ignorant of       
geometry3 the ,florentine revived that  
science1 excelled in  it1 and was the   
first that applied it1 together with    
experiment1 to  natural philosophy4 ,the

 former rejected with the most positive 
disdain  the system of ,copernicus3 the 
latter fortified it with new proofs     
derived both from reason and the        
senses4#b    ,if we compare them from   
another point of view1 not so much in   
respect of  their intrinsic merit1 as of
 the influence which each exercised on  
the  philosophy of his age1 ,galileo's  
superior talent or better fortune1 in   
arresting the attention of his          
contemporaries1 seems indisputable4 ,the
  fate of the two writers is directly   
opposed the one to the other2  ,bacon's 
works seem to be most studied and       
appreciated when his readers  have come 
to their perusal1 imbued with knowledge 
and a philosophical  spirit1 which1     
however1 they have attained             
independently of his  assistance4 ,the  
proud appeal to posterity which he      
uttered in his will1  ,for my name and  
memory1 ,i leave it to men's charitable 
speeches1 and to  foreign nations1 and  
the next ages1 of itself indicates a    

consciousness  of the fact that his     
contemporary countrymen were but        
slightly affected  by his philosophical 
precepts4 ,but ,galileo's personal      
exertions changed  the general character
 of philosophy in ,italy3 at the time of
 his death1  his immediate pupils had   
obtained possession of the most         
celebrated  universities1 and were      
busily engaged in practising and        
enforcing the  lessons which he had     
taught them2 nor was it then easy to    
find there a  single student of natural 
philosophy who did not readily ascribe  
the  formation of his principles to the 
direct or remote influence of           
,galileo's example4 ,unlike ,bacon's1   
his reputation1 and the value of his    
writings1 were higher among his         
contemporaries than they have since     
become4 ,this judgment perhaps awards   
the highest intellectual prize to  him  
whose disregarded services rise in      
estimation with the advance of          
knowledge2 but the praise due to        

superior usefulness belongs to him who  
succeeded in training round him a school
 of imitators1 and thereby  enabled his 
imitators to surpass himself4    ,the   
biography of men who have devoted       
themselves to philosophical  pursuits   
seldom affords so various and striking a
 succession of  incidents as that of a  
soldier or statesman4 ,the life of a man
 who is  shut up during the greater part
 of his time in his study or laboratory 
supplies but scanty materials for       
personal details2 and the lapse of  time
 rapidly removes from us the            
opportunities of preserving such        
peculiarities as might have been worth  
recording4 ,an account of it will       
therefore consist chiefly in a review of
 his works and opinions1 and of  the    
influence which he and they have        
exercised over his own and  succeeding  
ages4 ,viewed in this light1 few lives  
can be considered more  interesting than
 that of ,galileo2 and if we compare the
 state in which  he found1 with that in 

which he left1 the study of nature1 we  
shall feel  how justly an enthusiastic  
panegyric pronounced upon the age       
immediately  following him may be       
transferred to this earlier period4     
,this is the  age wherein all men's     
minds are in a kind of fermentation1 and
 the  spirit of wisdom and learning     
begins to mount and free itself from    
those  drossie and terrene impediments  
wherewith it has been so long clogged1  
and from the insipid phlegm and caput   
mortuum of useless notions in  which it 
hath endured so violent and long a      
fixation4 ,this is the age  wherein1    
methinks1 philosophy comes in with a    
spring tide1 and the  peripatetics may  
as well hope to stop the current of the 
tide1 or1 with  ,xerxes1 to fetter the  
ocean1 as hinder the overflowing of free
  philosophy4 ,methinks ,i see how all  
the old rubbish must be thrown away1    
and the rotten buildings be overthrown  
and carried away1 with so  powerful an  
inundation4 ,these are the days that    

must lay a new  foundation of a more    
magnificent philosophy1 never to be     
overthrown1  that will empirically and  
sensibly canvass the phenomena of       
nature1  deducing the causes of things  
from such originals in nature as we     
observe are producible by art1 and the  
infallible demonstration of  mechanics3 
and certainly this is the way1 and no   
other1 to build a true  and permanent   
philosophy4#c      ,,footnotes3    #a   
,mnage4    #b ,hume's ,england1 ,james  
,i4    #c ,power's ,experimental        
,philosophy1 #affc4          ,,chapter  
,,ii4        ,galileo's                 
,birth--,family--,education--,observatio
n of the                                
,pendulum--,pulsilogies--,hydrostatical 
,balance--,lecturer at ,pisa4           
,,galileo ,,galilei was born at ,pisa1  
on the #aeth day of ,february1 #aefd1 of
  a noble and ancient ,florentine       
family1 which1 in the middle of the     
fourteenth century1 adopted this surname
 instead of ,bonajuti1 under  which     

several of their ancestors filled       
distinguished offices in the            
,florentine state4 ,some misapprehension
 has occasionally existed1 in           
consequence of the identity of his      
proper name with that of his family2    
his most correct appellation would      
perhaps be ,galileo de' ,galilei1 but   
the surname usually occurs as we have   
written it4 ,he is most commonly  spoken
 of by his ,christian name1 agreeably to
 the ,italian custom2 just  as ,sanzio1 
,buonarotti1 ,sarpi1 ,reni1 ,vecelli1   
are universally known by  their         
,christian names of ,raphael1 ,michel   
,angelo1 ,fra ,paolo1 ,guido1 and       
,titian4    ,several authors have       
followed ,rossi in styling ,galileo     
illegitimate1 but  without having any   
probable grounds even when they wrote1  
and the  assertion has since been       
completely disproved by an inspection of
 the  registers at ,pisa and ,florence1 
in which are preserved the dates of his 
birth1 and of his mother's marriage1    

eighteen months previous to it4#d       
,his father1 ,vincenzo ,galilei1 was a  
man of considerable talent and          
learning1 with a competent knowledge of 
mathematics1 and particularly  devoted  
to the theory and practice of music1 on 
which he published  several esteemed    
treatises4 ,the only one which it is at 
present easy to  procure--his ,dialogue 
on ancient and modern music--exhibits   
proofs1 not  only of a thorough         
acquaintance with his subject1 but of a 
sound and  vigorous understanding       
applied to other topics incidentally    
discussed4  ,there is a passage in the  
introductory part1 which becomes        
interesting  when considered as         
affording some traces of the precepts by
 which  ,galileo was in all probability 
trained to reach his preeminent station 
in the intellectual world4 ,it appears  
to me1 says one of the speakers  in the 
dialogue1 that they who in proof of any 
assertion rely simply on  the weight of 
authority1 without adducing any argument

 in support of it1  act very absurdly3  
,i1 on the contrary1 wish to be allowed 
freely to  question and freely to answer
 you without any sort of adulation1 as  
well  becomes those who are truly in    
search of truth4 ,sentiments like these 
were of rare occurrence at the close of 
the sixteenth century1 and it is  to be 
regretted that ,vincenzo hardly lived   
long enough to witness his  idea of a   
true philosopher splendidly realized in 
the person of his son4  ,vincenzo died  
at an advanced age1 in #aeia4 ,his      
family consisted of three  sons1        
,galileo1 ,michel ,angelo1 and          
,benedetto1 and the same number of      
daughters1 ,giulia1 ,virginia1 and      
,livia4 ,after ,vincenzo's death the    
chief  support of the family devolved   
upon ,galileo1 who seems to have        
assisted  them to his utmost power4 ,in 
a letter to his mother1 dated #afjj1    
relative to the intended marriage of his
 sister ,livia with a certain  ,pompeo  
,baldi1 he agrees to the match1 but     

recommends its temporary  postponement1 
as he was at that time exerting himself 
to furnish money  to his brother ,michel
 ,angelo1 who had received the offer of 
an  advantageous settlement in ,poland4 
,as the sum advanced to his brother1    
which prevented him from promoting his  
sister's marriage1 did not exceed  #bjj 
crowns1 it may be inferred that the     
family were in a somewhat  straitened   
condition4 ,however he promises1 as soon
 as his brother should  repay him1 to   
take measures for the young lady1 since 
she too is bent  upon coming out to     
prove the miseries of this world4--,as  
,livia was at  the date of this letter  
in a convent1 the last expression seems 
to  denote that she had been destined to
 take the veil4 ,this proposed  marriage
 never took place1 but ,livia was       
afterwards married to ,taddeo           
,galletti3 her sister ,virginia married 
,benedetto ,landucci4 ,galileo  mentions
 one of his sisters1 7without naming    
her7 as living with him in  #afai at    

,bellosguardo4 ,michel ,angelo is       
probably the same brother of  ,galileo  
who is mentioned by ,liceti as having   
communicated from ,germany  some        
observations on natural history4#e ,he  
finally settled in the  service of the  
,elector of ,bavaria2 in what situation 
is not known1 but  upon his death the   
,elector granted a pension to his       
family1 who then  took up their abode at
 ,munich4 ,on the taking of that city in
 #afcf1 in  the course of the bloody    
thirty years' war1 which was then raging
  between the ,austrians and ,swedes1   
his widow and four of his children  were
 killed1 and every thing which they     
possessed was either burnt or  carried  
away4 ,galileo sent for his two nephews1
 ,alberto and a younger  brother1 to    
,arcetri near ,florence1 where he was   
then living4 ,these two  were then the  
only survivors of ,michel ,angelo's     
family2 and many of  ,galileo's letters 
about that date contain allusions to the
 assistance he  had been affording them4

 ,the last trace of ,alberto is on his  
return into  ,germany to the ,elector1  
in whose service his father had died4   
,these  details include almost every    
thing which is known of the rest of     
,vincenzo's family4    ,galileo         
exhibited early symptoms of an active   
and intelligent mind1 and  distinguished
 himself in his childhood by his skill  
in the construction  of ingenious toys  
and models of machinery1 supplying the  
deficiencies of  his information from   
the resources of his own invention2 and 
he  conciliated the universal good-will 
of his companions by the ready good     
nature with which he employed himself in
 their service and for their  amusement4
 ,it is worthy of observation1 that the 
boyhood of his great  follower ,newton1 
whose genius in many respects so closely
 resembled his  own1 was marked by a    
similar talent4 ,galileo's father was   
not opulent1  as has been already       
stated3 he was burdened with a large    
family1 and was  unable to provide      

expensive instructors for his son2 but  
,galileo's own  energetic industry      
rapidly supplied the want of better     
opportunities2  and he acquired1 under  
considerable disadvantages1 the ordinary
  rudiments of a classical education1   
and a competent knowledge of the  other 
branches of literature which were then  
usually studied4 ,his  leisure hours    
were applied to music and drawing2 for  
the former  accomplishment he inherited 
his father's talent1 being an excellent 
performer on several instruments1       
especially on the lute2 this continued  
to be a favourite recreation during the 
whole of his life4 ,he was also         
passionately fond of painting1 and at   
one time he wished to make it his       
profession3 and his skill and judgment  
of pictures were highly esteemed  by the
 most eminent contemporary artists1 who 
did not scruple to own  publicly their  
deference to young ,galileo's criticism4
    ,when he had reached his nineteenth 
year1 his father1 becoming daily more   

sensible of his superior genius1        
determined1 although at a great         
personal sacrifice1 to give him the     
advantages of an university  education4 
,accordingly1 in #aeha1 he commenced his
 academical studies in  the university  
of his native town1 ,pisa1 his father at
 this time  intending that he should    
adopt the profession of medicine4 ,in   
the  matriculation lists at ,pisa1 he is
 styled ,galileo1 the son of ,vincenzo  
,galilei1 a ,florentine1 ,scholar in    
,arts4 ,his instructor was the          
celebrated botanist1 ,andreas           
,csalpinus1 who was professor of        
medicine  at ,pisa from #aefg to #aeib4 
,hist4 ,acad4 ,pisan42 ,pisis1 #agia4   
,it is dated  #eth ,november1 #aeha4    
,viviani1 his pupil1 friend1 and        
panegyrist1 declares  that1 almost from 
the first day of his being enrolled on  
the lists of  the academy1 he was       
noticed for the reluctance with which he
 listened to  the dogmas of the         
,aristotelian philosophy1 then          

universally taught2 and  he soon became 
obnoxious to the professors from the    
boldness with which  he promulgated what
 they styled his philosophical          
paradoxes4 ,his early  habits of free   
inquiry were irreconcileable with the   
mental quietude of  his instructors1    
whose philosophic doubts1 when they     
ventured to  entertain any1 were        
speedily lulled by a quotation from     
,aristotle4  ,galileo thought himself   
capable of giving the world an example  
of a  sounder and more original mode of 
thinking2 he felt himself destined to   
be the founder of a new school of       
rational and experimental philosophy4   
,of this we are now securely enjoying   
the benefits2 and it is difficult  at   
this time fully to appreciate the       
obstacles which then presented          
themselves to free inquiry3 but we shall
 see1 in the course of this  narrative1 
how arduous their struggle was who      
happily effected this  important        
revolution4 ,the vindictive rancour with

 which the partisans of  the old        
philosophy never ceased to assail       
,galileo is of itself a  sufficient     
proof of the prominent station which he 
occupied in the  contest4    ,galileo's 
earliest mechanical discovery1 to the   
superficial observer  apparently an     
unimportant one1 occurred during the    
period of his studies  at ,pisa4 ,his   
attention was one day arrested by the   
vibrations of a lamp  swinging from the 
roof of the cathedral1 which1 whether   
great or small1  seemed to recur at     
equal intervals4 ,the instruments then  
employed for  measuring time were very  
imperfect3 ,galileo attempted to bring  
his  observation to the test before     
quitting the church1 by comparing the   
vibrations with the beatings of his own 
pulse1 and his mind being then          
principally employed upon his intended  
profession1 it occurred to him1  when he
 had further satisfied himself of their 
regularity by repeated  and varied      
experiments1 that the process he at     

first adopted might be  reversed1 and   
that an instrument on this principle    
might be usefully  employed in          
ascertaining the rate of the pulse1 and 
its variation from  day to day4 ,he     
immediately carried the idea into       
execution1 and it was  for this sole and
 limited purpose that the first pendulum
 was  constructed4 ,viviani tells us1   
that the value of the invention was     
rapidly appreciated by the physicians of
 the day1 and was in common use  in     
#afed1 when he wrote4    ,illustration3 
,instrument ,no4 #a1 ,no4 #b1 ,no4 #c   
,santorio1 who was professor of medicine
 at ,padua1 has given  representations  
of four different forms of these        
instruments1 which he  calls            
pulsilogies1 7pulsilogias17 and strongly
 recommends to medical  practitioners4#f
 ,these instruments seem to have been   
used in the  following manner3 ,no4 #a  
consists merely of a weight fastened to 
a string  and a graduated scale4 ,the   
string being gathered up into the hand  

till  the vibrations of the weight      
coincided with the beatings of the      
patient's pulse1 the length was         
ascertained from the scale1 which1 of   
course1 if great1 indicated a languid1  
if shorter1 a more lively action4  ,in  
,no4 #b the improvement is introduced of
 connecting the scale and  string1 the  
length of the latter is regulated by the
 turns of a peg at  a1 and a bead upon  
the string at b showed the measure4 ,no4
 #c is  still more compact1 the string  
being shortened by winding upon an axle 
at the back of the dial-plate4 ,the     
construction of ,no4 #d1 which ,santorio
  claims as his own improvement1 is not 
given1 but it is probable that the      
principal index1 by its motion1 shifted 
a weight to different distances  from   
the point of suspension1 and that the   
period of vibration was  still more     
accurately adjusted by a smaller weight 
connected with the  second index4       
,venturi seems to have mistaken the     
third figure for that  of a pendulum    

clock1 as he mentions this as one of the
 earliest  adaptations of ,galileo's    
principle to that purpose2#g but it is  
obvious1 from ,santorio's description1  
that it is nothing more than a  circular
 scale1 the index showing1 by the figure
 to which it points1 the  length of     
string remaining unwound upon the axis4 
,we shall1 for the  present1 postpone   
the consideration of the invention of   
pendulum clocks1  and the examination of
 the different claims to the honour of  
their first  construction4    ,at the   
time of which we are speaking1 ,galileo 
was entirely ignorant of  mathematics1  
the study of which was then at a low    
ebb1 not only in  ,italy1 but in every  
part of ,europe4 ,commandine had        
recently revived a  taste for the       
writings of ,euclid and ,archimedes1 and
 ,vieta ,tartalea and  others had made  
considerable progress in algebra1 ,guido
 ,ubaldi and  ,benedetti had done       
something towards establishing the      
principles of  statics1 which was the   

only part of mechanics as yet           
cultivated2 but  with these             
inconsiderable exceptions the           
application of mathematics to  the      
phenomena of nature was scarcely thought
 of4 ,galileo's first  inducement to    
acquire a knowledge of geometry arose   
from his partiality  for drawing and    
music1 and from the wish to understand  
their principles  and theory4 ,his      
father1 fearful lest he should relax his
 medical  studies1 refused openly to    
encourage him in this new pursuit2 but  
he  connived at the instruction which   
his son now began to receive in the     
writings of ,euclid1 from the tuition of
 an intimate friend1 named  ,ostilio    
,ricci1 who was one of the professors in
 the university4  ,galileo's whole      
attention was soon directed to the      
enjoyment of the new  sensations thus   
communicated to him1 insomuch that      
,vincenzo1 finding his  prognostics     
verified1 began to repent his indirect  
sanction1 and  privately requested      

,ricci to invent some excuse for        
discontinuing his  lessons4 ,but it was 
fortunately too late2 the impression was
 made and  could not be effaced2 from   
that time ,hippocrates and ,galen lay   
unheeded  before the young physician1   
and served only to conceal from his     
father's  sight the mathematical volumes
 on which the whole of his time was     
really  employed4 ,his progress soon    
revealed the true nature of his         
pursuits3  ,vincenzo yielded to the     
irresistible predilection of his son's  
mind1 and  no longer attempted to turn  
him from the speculations to which his  
whole  existence was thenceforward      
abandoned4    ,after mastering the      
elementary writers1 ,galileo proceeded  
to the study  of ,archimedes1 and1      
whilst perusing the ,hydrostatics of    
that author1  composed his earliest     
work1--an ,essay on the ,hydrostatical  
,balance4 ,in  this he explains the     
method probably adopted by ,archimedes  
for the  solution of ,hiero's celebrated

 question#h1 and shows himself already  
well acquainted with the true principles
 of specific gravities4 ,this  essay had
 an immediate and important influence on
 young ,galileo's  fortunes1 for it     
introduced him to the approving notice  
of ,guido ,ubaldi1  then one of the most
 distinguished mathematicians of ,italy4
 ,at his  suggestion ,galileo applied   
himself to consider the position of the 
centre of gravity in solid bodies1 a    
choice of subject that sufficiently     
showed the estimate ,ubaldi had formed  
of his talents2 for it was a  question  
on which ,commandine had recently       
written1 and which engaged at  that time
 the attention of geometricians of the  
highest order4 ,galileo  tells us       
himself that he discontinued these      
researches on meeting with  ,lucas      
,valerio's treatise on the same subject4
 ,ubaldi was so much struck  with the   
genius displayed in the essay with which
 ,galileo furnished him1  that he       
introduced him to his brother1 the      

,cardinal ,del ,monte3 by this  latter  
he was mentioned to ,ferdinand de'      
,medici1 the reigning ,duke of          
,tuscany1 as a young man of whom the    
highest expectations might be           
entertained4 ,by the ,duke's patronage  
he was nominated1 in #aehi1 to the      
lectureship of mathematics at ,pisa1    
being then in his twenty-sixth year4    
,his public salary was fixed at the     
insignificant sum of sixty crowns       
annually1 but he had an opportunity of  
greatly adding to his income by  private
 tuition4      ,,footnotes3    #d       
,erythrus1 ,pinacotheca1 vol4 i42       
,salusbury's ,life of ,galileo4 ,nelli1 
,vita di ,gal4 ,galilei4    #e ,de his  
qu diu vivunt4 ,patavii1 #afab4    #f   
,comment1 in ,avicennam4 ,venetiis1     
#afbe4    #g ,essai sur les ,ouvrages de
 ,leonard da ,vinci4 ,paris1 #agig4     
#h ,see ,treatise on ,,hydrostatics4    
,,chapter ,,iii4        ,galileo at     
,pisa--,aristotle--,leonardo da         
,vinci--,galileo becomes a              

,copernican--,urstisius--,bruno--,experi
ments on falling        bodies--,galileo
 at ,padua--,thermometer4      ,,no     
sooner was ,galileo settled in his new  
office than he renewed his  inquiries   
into the phenomena of nature with       
increased diligence4 ,he  instituted a  
course of experiments for the purpose of
 putting to the  test the mechanical    
doctrines of ,aristotle1 most of which  
he found  unsupported even by the       
pretence of experience4 ,it is to be    
regretted  that we do not more          
frequently find detailed his method of  
experimenting1 than occasionally in the 
course of his dialogues1 and it  is     
chiefly upon the references which he    
makes to the results with which  the    
experiments furnished him1 and upon the 
avowed and notorious  character of his  
philosophy1 that the truth of these     
accounts must be  made to depend4       
,venturi has found several unpublished  
papers by ,galileo  on the subject of   
motion1 in the ,grand ,duke's private   

library at  ,florence1 bearing the date 
of #aeij1 in which are many of the      
theorems  which he afterwards developed 
in his ,dialogues on ,motion4 ,these    
were not  published till fifty years    
afterwards1 and we shall reserve an     
account  of their contents till we reach
 that period of his life4    ,galileo   
was by no means the first who had       
ventured to call in question  the       
authority of ,aristotle in matters of   
science1 although he was  undoubtedly   
the first whose opinions and writings   
produced a very marked  and general     
effect4 ,nizzoli1 a celebrated scholar  
who lived in the early  part of the     
#afth century1 had condemned            
,aristotle's philosophy1  especially his
 ,physics1 in very unequivocal and      
forcible terms1  declaring that1        
although there were many excellent      
truths in his  writings1 the number was 
scarcely less of false1 useless1 and    
ridiculous  propositions4#i ,about the  
time of ,galileo's birth1 ,benedetti had

  written expressly in confutation of   
several propositions contained in       
,aristotle's mechanics1 and had         
expounded in a clear manner some of the 
doctrines of statical equilibrium4#aj   
,within the last forty years it  has    
been established that the celebrated    
painter ,leonardo da ,vinci1 who  died  
in #aeai1 amused his leisure hours in   
scientific pursuits2 and many  ideas    
appear to have occurred to him which are
 to be found in the  writings of        
,galileo at a later date4 ,it is not    
impossible 7though there  are probably  
no means of directly ascertaining the   
fact7 that ,galileo  may have been      
acquainted with ,leonardo's             
investigations1 although they  remained1
 till very lately1 almost unknown to the
 mathematical world4  ,this supposition 
is rendered more probable from the fact1
 that ,mazenta1  the preserver of       
,leonardo's manuscripts1 was1 at the    
very time of their  discovery1 a        
contemporary student with ,galileo at   

,pisa4 ,kopernik1 or1 as  he is usually 
called1 ,copernicus1 a native of ,thorn 
in ,prussia1 had  published his great   
work1 ,de ,revolutionibus1 in #aedc1    
restoring the  knowledge of the true    
theory of the solar system1 and his     
opinions were  gradually and silently   
gaining ground4    ,it is not           
satisfactorily ascertained at what      
period ,galileo embraced  the new       
astronomical theory4 ,gerard ,voss      
attributes his conversion  to a public  
lecture of ,mstlin1 the instructor of   
,kepler2 and later  writers 7among whom 
is ,laplace7 repeat the same story1 but 
without  referring to any additional    
sources of information1 and in most     
instances merely transcribing ,voss's   
words1 so as to shew indisputably       
whence they derived their account4 ,voss
 himself gives no authority1  and his   
general inaccuracy makes his mere word  
not of much weight4 ,the  assertion     
appears1 on many accounts1 destitute of 
much probability4  ,if the story were   

correct1 it seems likely that some      
degree of  acquaintance1 if not of      
friendly intercourse1 would have        
subsisted  between ,mstlin1 and his     
supposed pupil1 such as in fact we find 
subsisting between ,mstlin and his      
acknowledged pupil ,kepler1 the  devoted
 friend of ,galileo2 but1 on the        
contrary1 we find ,mstlin  writing to   
,kepler himself of ,galileo as an entire
 stranger1 and in  the most disparaging 
terms4 ,if ,mstlin could lay claim to   
the honour  of so celebrated a disciple1
 it is not likely that he could fail so 
entirely to comprehend the distinction  
it must confer upon himself as  to      
attempt diminishing it by underrating   
his pupil's reputation4 ,there  is a    
passage in ,galileo's works which more  
directly controverts the  claim advanced
 for ,mstlin1 although ,salusbury1 in   
his life of ,galileo1  having apparently
 an imperfect recollection of its tenor1
 refers to  this very passage in        
confirmation of ,voss's statement4 ,in  

the second  part of the dialogue on the 
,copernican system1 ,galileo makes      
,sagredo1  one of the speakers in it1   
give the following account3--,being very
  young1 and having scarcely finished my
 course of philosophy1 which ,i  left   
off as being set upon other employments1
 there chanced to come  into these parts
 a certain foreigner of ,rostoch1 whose 
name1 as ,i  remember1 was ,christianus 
,urstisius1 a follower of ,copernicus1  
who1  in an academy1 gave two or three  
lectures upon this point1 to whom  many 
flocked as auditors2 but ,i1 thinking   
they went more for the  novelty of the  
subject than otherwise1 did not go to   
hear him2 for ,i  had concluded with    
myself that that opinion could be no    
other than a  solemn madness2 and       
questioning some of those who had been  
there1 ,i  perceived they all made a    
jest thereof1 except one1 who told me   
that  the business was not altogether to
 be laughed at3 and because the man  was
 reputed by me to be very intelligent   

and wary1 ,i repented that ,i  was not  
there1 and began from that time forward1
 as oft as ,i met with  any one of the  
,copernican persuasion1 to demand of    
them if they had  been always of the    
same judgment4 ,of as many as ,i        
examined ,i found not  so much as one   
who told me not that he had been a long 
time of the  contrary opinion1 but to   
have changed it for this1 as convinced  
by the  strength of the reasons proving 
the same2 and afterwards questioning    
them one by one1 to see whether they    
were well possessed of the reasons  of  
the other side1 ,i found them all to be 
very ready and perfect in  them1 so that
 ,i could not truly say that they took  
this opinion out  of ignorance1 vanity1 
or to show the acuteness of their wits4 
,on the  contrary1 of as many of the    
,peripatetics and ,ptolemeans as ,i have
  asked1 7and out of curiosity ,i have  
talked with many17 what pains they  had 
taken in the book of ,copernicus1 ,i    
found very few that had so much  as     

superficially perused it1 but of those  
who ,i thought had understood  the same1
 not one3 and1 moreover1 ,i have        
inquired amongst the followers  of the  
,peripatetic doctrine1 if ever any of   
them had held the contrary  opinion1 and
 likewise found none that had4          
,whereupon1 considering that  there was 
no man who followed the opinion of      
,copernicus that had not  been first on 
the contrary side1 and that was not very
 well acquainted  with the reasons of   
,aristotle and ,ptolemy1 and1 on the    
contrary1 that  there was not one of the
 followers of ,ptolemy that had ever    
been of  the judgment of ,copernicus1   
and had left that to embrace this of    
,aristotle2--considering1 ,i say1 these 
things1 ,i began to think that  one who 
leaveth an opinion imbued with his milk 
and followed by very  many1 to take up  
another1 owned by very few1 and denied  
by all the  schools1 and that really    
seems a great paradox1 must needs have  
been  moved1 not to say forced1 by more 

powerful reasons4 ,for this cause ,i  am
 become very curious to dive1 as they   
say1 into the bottom of this  business4 
,it seems improbable that ,galileo      
should think it worth while  to give so 
detailed an account of the birth and    
growth of opinion in  any one besides   
himself2 and although ,sagredo is not   
the personage who  generally in the     
dialogue represents ,galileo1 yet as the
 real ,sagredo  was a young nobleman1 a 
pupil of ,galileo himself1 the account  
cannot  refer to him4 ,the circumstance 
mentioned of the intermission of his    
philosophical studies1 though in itself 
trivial1 agrees very well with          
,galileo's original medical destination4
 ,urstisius is not a fictitious  name1  
as possibly ,salusbury may have thought1
 when alluding to this  passage2 he was 
mathematical professor at ,ble1 about   
#aefg1 and several  treatises by him are
 still extant4 ,according to ,kstner1   
his ,german name  was ,wursteisen4 ,in  
#aefh ,voss informs us that he published

 some new  questions on ,purbach's      
,theory of the ,planets4 ,he died at    
,ble in #aehf1  when ,galileo was about 
twenty-two years old4    ,it is not     
unlikely that ,galileo also1 in part1   
owed his emancipation  from popular     
prejudices to the writings of ,giordano 
,bruno1 an  unfortunate man1 whose      
unsparing boldness in exposing fallacies
 and  absurdities was rewarded by a     
judicial murder1 and by the character of
  heretic and infidel1 with which his   
executioners endeavoured to  stigmatize 
him for the purpose of covering over    
their own atrocious  crime4 ,bruno was  
burnt at ,rome in #afjj1 but not1 as    
,montucla supposes1  on account of his  
,spaccio della ,bestia trionfante4 ,the 
title of this  book has led him to      
suppose that it was directed against the
 church of  ,rome1 to which it does not 
in the slightest degree relate4 ,bruno  
attacked the fashionable philosophy     
alternately with reason and  ridicule1  
and numerous passages in his writings1  

tedious and obscure as  they generally  
are1 show that he had completely        
outstripped the age in  which he lived4 
,among his astronomical opinions1 he    
believed that the  universe consisted of
 innumerable systems of suns with       
assemblages of  planets revolving round 
each of them1 like our own earth1 the   
smallness  of which1 alone1 prevented   
their being observed by us4 ,he remarked
  further1 that it is by no means       
improbable that there are yet other     
planets revolving round our own sun1    
which we have not yet noticed1  either  
on account of their minute size or too  
remote distance from us4  ,he declined  
asserting that all the apparently fixed 
stars are really so1  considering this  
as not sufficiently proved1 because at  
such enormous  distances the motions    
become difficult to estimate1 and it is 
only by  long observation that we can   
determine if any of these move round    
each  other1 or what other motions they 
may have4 ,he ridiculed the             

,aristotelians in no very measured      
terms--,they harden themselves1 and     
heat themselves1 and embroil themselves 
for ,aristotle2 they call  themselves   
his champions1 they hate all but        
,aristotle's friends1 they  are ready to
 live and die for ,aristotle1 and yet   
they do not understand  so much as the  
titles of ,aristotle's chapters4 ,and in
 another place he  introduces an        
,aristotelian inquiring1 ,do you take   
,plato for an  ignoramus--,aristotle for
 an ass8 to whom he answers1 ,my son1 ,i
 neither  call them asses1 nor you      
mules1--them baboons1 nor you apes1--as 
you  would have me3 ,i told you that ,i 
esteem them the heroes of the world1    
but ,i will not credit them without     
sufficient reason2 and if you were  not 
both blind and deaf1 you would          
understand that ,i must disbelieve      
their absurd and contradictory          
assertions4#aa ,bruno's works1 though in
  general considered those of a         
visionary and madman1 were in very      

extensive circulation1 probably not the 
less eagerly sought after from  being   
included among the books prohibited by  
the ,romish church2 and  although it has
 been reserved for later observations to
 furnish complete  verification of his  
most daring speculations1 yet there was 
enough1  abstractedly taken1 in the wild
 freedom of his remarks1 to attract a   
mind like ,galileo's2 and it is with    
more satisfaction that we refer the     
formation of his opinions to a man of   
undoubted though eccentric genius1  like
 ,bruno1 than to such as ,maestlin1 who1
 though a diligent and careful          
observer1 seems seldom to have taken any
 very enlarged views of the  science on 
which he was engaged4    ,with a few    
exceptions similar to those above       
mentioned1 the rest of  ,galileo's      
contemporaries well deserved the        
contemptuous epithet which he  fixed on 
them of ,paper ,philosophers1 for1 to   
use his own words1 in a  letter to      
,kepler on this subject1 this sort of   

men fancied philosophy  was to be       
studied like the neid or ,odyssey1 and  
that the true reading  of nature was to 
be detected by the collation of texts4  
,galileo's own  method of philosophizing
 was widely different2 seldom omitting  
to bring  with every new assertion the  
test of experiment1 either directly in  
confirmation of it1 or tending to show  
its probability and consistency4  ,we   
have already seen that he engaged in a  
series of experiments to  investigate   
the truth of some of ,aristotle's       
positions4 ,as fast as he  succeeded in 
demonstrating the falsehood of any of   
them1 he denounced  them from his       
professorial chair with an energy and   
success which  irritated more and more  
against him the other members of the    
academic  body4    ,there seems         
something in the stubborn opposition    
which he encountered in  establishing   
the truth of his mechanical theorems1   
still more stupidly  absurd than in the 
ill will to which1 at a later period of 

his life1 his  astronomical opinions    
exposed him3 it is intelligible that the
 vulgar  should withhold their assent   
from one who pretended to discoveries in
  the remote heavens1 which few         
possessed instruments to verify1 or     
talents to appreciate2 but it is        
difficult to find terms for             
stigmatizing the obdurate folly of those
 who preferred the evidence of  their   
books to that of their senses1 in       
judging of phenomena so obvious  as     
those1 for instance1 presented by the   
fall of bodies to the ground4           
,aristotle had asserted1 that if two    
different weights of the same  material 
were let fall from the same height1 the 
heavier one would reach  the ground     
sooner than the other1 in the proportion
 of their weights4  ,the experiment is  
certainly not a very difficult one1 but 
nobody thought  of that method of       
argument1 and consequently this         
assertion had been  long received1 upon 
his word1 among the axioms of the       

science of motion4  ,galileo ventured to
 appeal from the authority of ,aristotle
 to that of  his own senses1 and        
maintained that1 with the exception of  
an  inconsiderable difference1 which he 
attributed to the disproportionate      
resistance of the air1 they would fall  
in the same time4 ,the  ,aristotelians  
ridiculed and refused to listen to such 
an idea4 ,galileo  repeated his         
experiments in their presence from the  
famous leaning tower  at ,pisa3 and with
 the sound of the simultaneously falling
 weights still  ringing in their ears1  
they could persist in gravely           
maintaining that a  weight of ten pounds
 would reach the ground in a tenth part 
of the time  taken by one of a single   
pound1 because they were able to quote  
chapter  and verse in which ,aristotle  
assures them that such is the fact4 ,a  
temper of mind like this could not fail 
to produce ill will towards him  who    
felt no scruples in exposing their      
wilful folly2 and the watchful  malice  

of these men soon found the means of    
making ,galileo desirous of  quitting   
his situation at ,pisa4 ,don ,giovanni  
de' ,medici1 a natural son  of ,cosmo1  
who possessed a slight knowledge of     
mechanics on which he  prided himself1  
had proposed a contrivance for cleansing
 the port of  ,leghorn1 on the          
efficiency of which ,galileo was        
consulted4 ,his opinion  was            
unfavourable1 and the violence of the   
inventor's disappointment1  7for        
,galileo's judgment was verified by the 
result17 took the somewhat  unreasonable
 direction of hatred towards the man    
whose penetration had  foreseen the     
failure4 ,galileo's situation was       
rendered so unpleasant by  the          
machinations of this person1 that he    
decided on accepting overtures          
elsewhere1 which had already been made  
to him2 accordingly1 under the          
negotiation of his staunch friend ,guido
 ,ubaldi1 and with the consent of       
,ferdinand1 he procured from the        

republic of ,venice a nomination for six
  years to the professorship of         
mathematics in the university of ,padua1
  whither he removed in ,september      
#aeib4    ,galileo's predecessor in the 
mathematical chair at ,padua was        
,moleti1 who  died in #aehh1 and the    
situation had remained unfilled during  
the  intervening four years4 ,this seems
 to show that the directors attributed  
but little importance to the knowledge  
which it was the professor's duty  to   
impart4 ,this inference is strengthened 
by the fact1 that the amount  of the    
annual salary attached to it did not    
exceed #ahj florins1 whilst  the        
professors of philosophy and civil law1 
in the same university1 were  rated at  
the annual stipends of #adjj and #afhj  
florins4#ab ,galileo  joined the        
university about a year after its       
triumph over the ,jesuits1  who had     
established a school in ,padua about the
 year #aedb1 and1  increasing yearly in 
influence1 had shown symptoms of a      

design to get  the whole management of  
the public education into the hands of  
their own  body4#ac ,after several      
violent disputes it was at length       
decreed by the  ,venetian senate1 in    
#aeia1 that no ,jesuit should be allowed
 to give  instruction at ,padua in any  
of the sciences professed in the        
university4  ,it does not appear that   
after this decree they were again       
troublesome to  the university1 but this
 first decree against them was followed1
 in  #afjf1 by a second more peremptory1
 which banished them entirely from the  
,venetian territory4 ,galileo would of  
course find his fellow-professors  much 
embittered against that society1 and    
would naturally feel inclined  to make  
common cause with them1 so that it is   
not unlikely that the  hatred which the 
,jesuits afterwards bore to ,galileo on 
personal  considerations1 might be      
enforced by their recollection of the   
university to which he had belonged4    
,galileo's writings now began to follow 

each other with great rapidity1  but he 
was at this time apparently so careless 
of his reputation1 that  many of his    
works and inventions1 after a long      
circulation in manuscript  among his    
pupils and friends1 found their way into
 the hands of those  who were not       
ashamed to publish them as their own1   
and to denounce  ,galileo's claim to the
 authorship as the pretence of an       
impudent  plagiarist4 ,he was1 however1 
so much beloved and esteemed by his     
friends1 that they vied with each other 
in resenting affronts of this  nature   
offered to him1 and in more than one    
instance he was relieved1 by  their full
 and triumphant answers1 from the       
trouble of vindicating his  own         
character4    ,to this epoch of         
,galileo's life may be referred his     
re-invention of the  thermometer4 ,the  
original idea of this useful instrument 
belongs to the  ,greek mathematician    
,hero2 and ,santorio himself1 who has   
been named as  the inventor by ,italian 

writers1 and at one time claimed it     
himself1  refers it to him4 ,in #afch1  
,castelli wrote to ,cesarini that he    
remembered an experiment shown to him   
more than thirty-five years back  by    
,galileo1 who took a small glass bottle1
 about the size of a hen's  egg1 the    
neck of which was twenty-two inches     
long1 and as narrow as a  straw4 ,having
 well heated the bulb in his hands1 and 
then introducing  its mouth into a      
vessel in which was a little water1 and 
withdrawing the  heat of his hand from  
the bulb1 the water rose in the neck of 
the bottle  more than eleven inches     
above the level in the vessel1 and      
,galileo  employed this principle in the
 construction of an instrument for      
measuring heat and cold4#ad ,in #afac1 a
 ,venetian nobleman named  ,sagredo1 who
 has been already mentioned as          
,galileo's friend and pupil1  writes to 
him in the following words3 ,i have     
brought the instrument  which you       
invented for measuring heat into several

 convenient and  perfect forms1 so that 
the difference of temperature between   
two rooms  is seen as far as #ajj       
degrees4#ae ,this date is anterior to   
the claims  both of ,santorio and       
,drebbel1 a ,dutch physician1 who was   
the first to  introduce it into         
,holland4    ,galileo's thermometer1 as 
we have just seen1 consisted merely of a
 glass  tube ending in a bulb1 the air  
in which1 being partly expelled by heat1
  was replaced by water from a glass    
into which the open end of the tube  was
 plunged1 and the different degrees of  
temperature were indicated by  the      
expansion of the air which yet remained 
in the bulb1 so that the  scale would be
 the reverse of that of the thermometer 
now in use1 for  the water would stand  
at the highest level in the coldest     
weather4 ,it  was1 in truth1 a barometer
 also1 in consequence of the            
communication  between the tube and     
external air1 although ,galileo did not 
intend it  for this purpose1 and when he

 attempted to determine the relative    
weight  of the air1 employed a          
contrivance still more imperfect than   
this rude  barometer would have been4 ,a
 passage among his posthumous fragments 
intimates that he subsequently used     
spirit of wine instead of water4        
,viviani attributes an improvement of   
this imperfect instrument1 but  without 
specifying its nature1 to ,ferdinand    
,,ii41 a pupil and subsequent  patron of
 ,galileo1 and1 after the death of his  
father ,cosmo1 reigning  duke of        
,florence4 ,it was still further        
improved by ,ferdinand's younger        
brother1 ,leopold de' ,medici1 who      
invented the modern process of          
expelling all the air from the tube by  
boiling the spirit of wine in it1  and  
of hermetically sealing the end of the  
tube1 whilst the contained  liquid is in
 this expanded state1 which deprived it 
of its barometrical  character1 and     
first made it an accurate thermometer4  
,the final  improvement was the         

employment of mercury instead of spirit 
of wine1  which is recommended by ,lana 
so early as #afgj1 on account of its    
equable  expansion4#af ,for further     
details on the history and use of this  
instrument1 the reader may consult the  
,treatises on the ,,thermometer and     
,,pyrometer4      ,,footnotes3    #i    
,antibarbarus ,philosophicus4           
,francofurti1 #afgd4    #aj             
,speculationum liber4 ,venetiis1 #aehe4 
#aa ,de l',infinito ,universo4 ,dial4   
#c4 ,la ,cena de le ,cenere1 #aehd4     
#ab ,riccoboni1 ,commentarii de         
,gymnasio ,patavino1 #aeih4    #ac      
,nelli4    #ad ,nelli4    #ae ,venturi4 
,memorie e ,lettere di ,gal4 ,galilei4  
,modena1 #ahba4    #af ,prodromo all'   
,arte ,maestra4 ,brescia1 #afgj4        
,,chapter ,,iv4        ,astronomy before
                                        
,copernicus--,fracastoro--,bacon--,keple
r--,galileo's        ,treatise on the   
,sphere4      ,,this period of          
,galileo's lectureship at ,padua derives

 interest from its  including the first 
notice which we find of his having      
embraced the  doctrines of the          
,copernican astronomy4 ,most of our     
readers are aware of  the principles of 
the theory of the celestial motions     
which ,copernicus  restored2 but the    
number of those who possess much        
knowledge of the  cumbrous and unwieldy 
system which it superseded is perhaps   
more  limited4 ,the present is not a fit
 opportunity to enter into many details 
respecting it2 these will find their    
proper place in the ,history of         
,astronomy3 but a brief sketch of its   
leading principles is necessary to      
render what follows intelligible4       
,the earth was supposed to be immoveably
 fixed in the centre of the  universe1  
and immediately surrounding it the      
atmospheres of air and  fire1 beyond    
which the sun1 moon1 and planets1 were  
thought to be  carried round the earth1 
fixed each to a separate orb or heaven  
of solid  but transparent matter4 ,the  

order of distance in which they were    
supposed to be placed with regard to the
 central earth was as follows3  ,the    
,moon1 ,mercury1 ,venus1 ,the ,sun1     
,mars1 ,jupiter1 and ,saturn4 ,it became
  a question in the ages immediately    
preceding ,copernicus1 whether the ,sun 
was not nearer the ,earth than ,mercury1
 or at least than ,venus2 and this      
question was one on which the           
astronomical theorists were then chiefly
  divided4    ,we possess at this time a
 curious record of a former belief in   
this  arrangement of the ,sun and       
planets1 in the order in which the days 
of  the week have been named from them4 
,according to the dreams of  ,astrology1
 each planet was supposed to exert its  
influence in  succession1 reckoning from
 the most distant down to the nearest1  
over  each hour of the twenty-four4 ,the
 planet which was supposed to           
predominate over the first hour1 gave   
its name to that day4#ag ,the  general  
reader will trace this curious fact more

 easily with the ,french  or ,latin     
names than with the ,english1 which have
 been translated into  the titles of the
 corresponding ,saxon deities4 ,placing 
the ,sun and  planets in the following  
order1 and beginning1 for instance1 with
  ,monday1 or the ,moon's day2 ,saturn  
ruled the second hour of that day1      
,jupiter the third1 and so round till we
 come again and again to the ,moon  on  
the #hth1 #aeth1 and #bb;d hours2       
,saturn ruled the #bc;d1 ,jupiter the   
#bdth1 so that the next day would be the
 day of ,mars1 or1 as the ,saxons       
translated it1 ,tuisco's day1 or        
,tuesday4 ,in the same manner the       
following days would belong respectively
 to ,mercury or ,woden1 ,jupiter or     
,thor1 ,venus or ,frea1 ,saturn or      
,seater1 the ,sun1 and again the ,moon4 
,in  this manner the whole week will be 
found to complete the cycle of the      
seven planets4    ,illustration3 ,cycle 
of the seven planets4    ,the other     
stars were supposed to be fixed in an   

outer orb1 beyond which  were two       
crystalline spheres1 7as they were      
called17 and on the outside  of all1 the
 primum mobile or first moveable1 which 
sphere was  supposed to revolve round   
the earth in twenty-four hours1 and by  
its  friction1 or rather1 as most of the
 philosophers of that day chose to  term
 it1 by the sort of heavenly influence  
which it exercised on the  interior     
orbs1 to carry them round with a similar
 motion4 ,hence the  diversity of day   
and night4 ,but beside this principal   
and general  motion1 each orb was       
supposed to have one of its own1 which  
was intended  to account for the        
apparent changes of position of the     
planets with  respect to the fixed stars
 and to each other4 ,this supposition1  
however1  proving insufficient to       
account for all the irregularities of   
motion  observed1 two hypotheses were   
introduced4--,first1 that to each planet
  belonged several concentric spheres or
 heavens1 casing each other like  the   

coats of an onion1 and1 secondly1 that  
the centres of these solid  spheres1    
with which the planet revolved1 were    
placed in the  circumference of a       
secondary revolving sphere1 the centre  
of which  secondary sphere was situated 
at the earth4 ,they thus acquired the   
names  of ,eccentrics or ,epicycles1 the
 latter word signifying a circle upon a 
circle4 ,the whole art of astronomers   
was then directed towards inventing  and
 combining different eccentric and      
epicyclical motions1 so as to  represent
 with tolerable fidelity the ever       
varying phenomena of the  heavens4      
,aristotle had lent his powerful        
assistance in this1 as in other         
branches of natural philosophy1 in      
enabling the false system to prevail    
against and obliterate the knowledge of 
the true1 which1 as we gather  from his 
own writings1 was maintained by some    
philosophers before his  time4 ,of these
 ancient opinions1 only a few traces now
 remain1  principally preserved in the  

works of those who were adverse to them4
  ,archimedes says expressly that       
,aristarchus of ,samos1 who lived about 
#cjj  ,b4 ,c41 taught the immobility of 
the sun and stars1 and that the earth is
  carried round the central sun4#ah     
,aristotle's words are3 ,most of those  
who assert that the whole concave is    
finite1 say that the earth is  situated 
in the middle point of the universe3    
those who are called  ,pythagoreans1 who
 live in ,italy1 are of a contrary      
opinion4 ,for they say  that fire is in 
the centre1 and that the earth1 which1  
according to  them1 is one of the stars1
 occasions the change of day and night  
by its  own motion1 with which it is    
carried about the centre4 ,it might be  
doubtful1 upon this passage alone1      
whether the ,pythagorean theory         
embraced more than the diurnal motion of
 the earth1 but a little  farther1 we   
find the following passage3 ,some1 as we
 have said1 make the  earth to be one of
 the stars3 others say that it is placed

 in the centre  of the ,universe1 and   
revolves on a central axis4#ai ,from    
which1 in  conjunction with the former  
extract1 it very plainly appears that   
the  ,pythagoreans maintained both the  
diurnal and annual motions of the       
earth4    ,some idea of the             
supererogatory labour entailed upon     
astronomers by the  adoption of the     
system which places the earth in the    
centre1 may be  formed in a popular     
manner by observing1 in passing through 
a thickly  planted wood1 in how         
complicated a manner the relative       
positions of the  trees appear at each  
step to be continually changing1 and by 
considering  the difficulty with which  
the laws of their apparent motions could
 be  traced1 if we were to attempt to   
refer these changes to a real motion of 
the trees instead of the traveller4 ,the
 apparent complexity in the  heavens is 
still greater than in the case          
suggested2 because1 in  addition to the 
earth's motions1 with which all the     

stars appear to be  impressed1 each of  
the planets has also a real motion of   
its own1 which  of course greatly       
contributes to perplex and complicate   
the general  appearances4 ,accordingly  
the heavens rapidly became1 under this  
system1        ,with centric and        
eccentric scribbled o'er1      ,cycle   
and epicycle1 orb in orb2#bj    crossing
 and penetrating each other in every    
direction4 ,maestlin has  given a       
concise enumeration of the principal    
orbs which belonged to this  theory4    
,after warning the readers that they are
 not mere fictions which  have nothing  
to correspond with them out of the      
imagination1 but that  they exist       
really1 and bodily in the heavens1#ba he
 describes seven  principal spheres     
belonging to each planet1 which he      
classes as  ,eccentrics1 ,epicycles1 and
 ,concentrepicycles1 and explains their 
use in  accounting for the planet's     
revolutions1 motions of the apogee1 and 
nodes1 c4 c4 ,in what manner this       

multitude of solid and crystalline  orbs
 were secured from injuring or          
interfering with each other was not     
very closely inquired into4    ,the     
reader will cease to expect any very    
intelligible explanation of  this and   
numberless other difficulties which     
belong to this unwieldy  machinery when 
he is introduced to the reasoning by    
which it was upheld4  ,gerolamo         
,fracastoro1 who lived in the sixteenth 
century1 writes in the  following terms1
 in his work entitled ,homocentrica1    
7certainly one of  the best productions 
of the day17 in which he endeavours to  
simplify the  necessary apparatus1 and  
to explain all the phenomena 7as the    
title of  his book implies7 by          
concentric spheres round the earth4     
,there are  some1 not only of the       
ancients but also among the moderns1 who
 believe  that the stars move freely    
without any such agency2 but it is      
difficult  to conceive in what manner   
they have imbued themselves with this   

notion1  since not only reason1 but the 
very senses1 inform us that all the     
stars are carried round fastened to     
solid spheres4 ,what ideas  ,fracastoro 
entertained of the evidence of the      
senses it is not now  easy to guess1 but
 he goes on to give a specimen of the   
reasoning  which appeared to him so     
incontrovertible4 ,the planets are      
observed to  move one while forwards1   
then backwards1 now to the right1 now to
 the  left1 quicker and slower by turns2
 which variety is consistent with a     
compound structure like that of an      
animal1 which possesses in itself       
various springs and principles of       
action1 but is totally at variance  with
 our notion of a simple and undecaying  
substance like the heavens  and heavenly
 bodies4 ,for that which is simple1 is  
altogether single1 and  singleness is of
 one only nature1 and one nature can be 
the cause of  only one effect2 and      
therefore it is altogether impossible   
that the  stars of themselves should    

move with such variety of motion4 ,and  
besides1 if the stars move by           
themselves1 they either move in an empty
  space1 or in a fluid medium like the  
air4 ,but there cannot be such a  thing 
as empty space1 and if there were such a
 medium1 the motion of the  star would  
occasion condensation and rarefaction in
 different parts of  it1 which is the   
property of corruptible bodies and where
 they exist  some violent motion is     
going on2 but the heavens are           
incorruptible and  are not susceptible  
of violent motion1 and hence1 and from  
many other  similar reasons1 any one who
 is not obstinate may satisfy himself   
that  the stars cannot have any         
independent motion4    ,some persons may
 perhaps think that arguments of this   
force are  unnecessarily dragged from   
the obscurity to which they are now for 
the  most part happily consigned2 but it
 is essential1 in order to set          
,galileo's character and merits in their
 true light1 to show how low at  this   

time philosophy had fallen4 ,for we     
shall form a very inadequate  notion of 
his powers and deserts if we do not     
contemplate him in the  midst of men    
who1 though of undoubted talent and     
ingenuity1 could so far  bewilder       
themselves as to mistake such a string  
of unmeaning phrases for  argument3 we  
must reflect on the difficulty every one
 experiences in  delivering himself from
 the erroneous impressions of infancy1  
which will  remain stamped upon the     
imagination in spite of all the efforts 
of  matured reason to erase them1 and   
consider every step of ,galileo's       
course as a triumph over difficulties of
 a like nature4 ,we ought to be  fully  
penetrated with this feeling before we  
sit down to the perusal of  his works1  
every line of which will then increase  
our admiration of the  penetrating      
acuteness of his invention and          
unswerving accuracy of his  judgment4   
,in almost every page we discover an    
allusion to some new  experiment1 or the

 germ of some new theory2 and amid all  
this wonderful  fertility it is rarely  
indeed that we find the exuberance of   
his  imagination seducing him from the  
rigid path of philosophical induction4  
,this is the more remarkable as he was  
surrounded by friends and               
contemporaries of a different           
temperament and much less cautious      
disposition4 ,a disadvantageous contrast
 is occasionally furnished even  by the 
sagacious ,bacon1 who could so far      
deviate from the sound  principles of   
inductive philosophy1 as to write1 for  
instance1 in the  following strain1     
bordering upon the worst manner of the  
,aristotelians3--,motion in a circle has
 no limit1 and seems to emanate  from   
the appetite of the body1 which moves   
only for the sake of moving1  and that  
it may follow itself and seek its own   
embraces1 and put in  action and enjoy  
its own nature1 and exercise its        
peculiar operation3 on  the contrary1   
motion in a straight line seems         

transitory1 and to move  towards a limit
 of cessation or rest1 and that it may  
reach some point1  and then put off its 
motion4#bb ,bacon rejected all the      
machinery of  the primum mobile and the 
solid spheres1 the eccentrics and the   
epicycles1 and carried his dislike of   
these doctrines so far as to  assert    
that nothing short of their gross       
absurdity could have driven  theorists  
to the extravagant supposition of the   
motion of the earth1  which1 said he1 we
 know to be most false4#bc ,instances of
 extravagant  suppositions and premature
 generalizations are to be found in     
almost  every page of his other great   
contemporary1 ,kepler4    ,it is with   
pain that we observe ,delambre taking   
every opportunity1 in  his admirable    
,history of ,astronomy1 to undervalue   
and sneer at ,galileo1  seemingly for   
the sake of elevating the character of  
,kepler1 who appears  his principal     
favourite1 but whose merit as a         
philosopher cannot safely  be brought   

into competition with that of his       
illustrious contemporary4  ,delambre is 
especially dissatisfied with ,galileo1  
for taking no notice1  in his ,system of
 the ,world1 of the celebrated laws of  
the planetary  motions which ,kepler    
discovered1 and which are now           
inseparably connected  with his name4   
,the analysis of ,newton and his        
successors has now  identified those    
apparently mysterious laws with the     
general phenomena  of motion1 and has   
thus entitled them to an attention of   
which1 before  that time1 they were     
scarcely worthy2 at any rate not more   
than is at  present the empirical law   
which includes the distances of all the 
planets from the sun 7roughly taken7 in 
one algebraical formula4 ,the           
observations of ,kepler's day were      
scarcely accurate enough to prove that  
the relations which he discovered       
between the distances of the planets    
from the sun and the periods of their   
revolutions around him were  necessarily

 to be received as demonstrated truths2 
and ,galileo surely  acted most         
prudently and philosophically in holding
 himself altogether  aloof from         
,kepler's fanciful devices and numeral  
concinnities1 although1  with all the   
extravagance1 they possessed much of the
 genius of the  ,platonic reveries1 and 
although it did happen that ,galileo1 by
  systematically avoiding them1 failed  
to recognise some important truths4     
,galileo probably was thinking of those 
very laws1 when he said of  ,kepler1 ,he
 possesses a bold and free genius1      
perhaps too much so2 but  his mode of   
philosophizing is widely different from 
mine4 ,we shall have  further occasion  
in the sequel to recognise the justice  
of this remark4    ,in the treatise on  
the ,sphere which bears ,galileo's name1
 and which1 if  he be indeed the author 
of it1 was composed during the early    
part of his  residence at ,padua1 he    
also adopts the ,ptolemaic system1      
placing the  earth immoveable in the    

centre1 and adducing against its motion 
the  usual arguments1 which in his      
subsequent writings he ridicules and    
refutes4 ,some doubts have been         
expressed of its authenticity2 but1     
however this may be1 we have it under   
,galileo's own hand that he taught  the 
,ptolemaic system1 in compliance with   
popular prejudices1 for some  time after
 he had privately become a convert to   
the contrary opinions4  ,in a letter1   
apparently the first which he wrote to  
,kepler1 dated from  ,padua1 #aeig1 he  
says1 acknowledging the receipt of      
,kepler's ,mysterium  ,cosmographicum1  
,i have as yet read nothing beyond the  
preface of your  book1 from which       
however ,i catch a glimpse of your      
meaning1 and feel  great joy on meeting 
with so powerful an associate in the    
pursuit of  truth1 and consequently such
 a friend to truth itself1 for it is    
deplorable that there should be so few  
who care about truth1 and who do  not   
persist in their perverse mode of       

philosophizing2 but as this is not  the 
fit time for lamenting the melancholy   
condition of our times1 but  for        
congratulating you on your elegant      
discoveries in confirmation of  the     
truth1 ,i shall only add a promise to   
peruse your book  dispassionately1 and  
with a conviction that ,i shall find in 
it much to  admire4 ,this ,i shall do   
the more willingly because many years   
ago ,i  became a convert to the opinions
 of ,copernicus1#bd and by that theory  
have succeeded in fully explaining many 
phenomena1 which on the contrary        
hypothesis are altogether inexplicable4 
,i have arranged many arguments  and    
confutations of the opposite opinions1  
which however ,i have not yet  dared to 
publish1 fearing the fate of our master 
,copernicus1 who1  although he has      
earned immortal fame among a few1 yet by
 an infinite  number 7for so only can   
the number of fools be measured7 is     
exploded and  derided4 ,if there were   
many such as you1 ,i would venture to   

publish my  speculations2 but1 since    
that is not so1 ,i shall take time to   
consider  of it4 ,this interesting      
letter was the beginning of the         
friendship of  these two great men1     
which lasted uninterruptedly till #afcj1
 the date of  ,kepler's death4 ,that    
extraordinary genius never omitted an   
opportunity  of testifying his          
admiration of ,galileo1 although there  
were not wanting  persons envious of    
their good understanding1 who exerted   
themselves to  provoke coolness and     
quarrel between them4 ,thus ,brutius    
writes to ,kepler  in #afjb3be ,galileo 
tells me he has written to you1 and has 
got your  book1 which however he denied 
to ,magini1 and ,i abused him for       
praising  you with too many             
qualifications4 ,i know it to be a fact 
that1 both in  his lectures1 and        
elsewhere1 he is publishing your        
inventions as his  own2 but ,i have     
taken care1 and shall continue to do so1
 that all this  shall redound not to his

 credit but to yours4 ,the only notice  
which  ,kepler took of these repeated   
insinuations1 which appear to have been 
utterly groundless1 was1 by renewed     
expressions of respect and  admiration1 
to testify the value he set upon his    
friend and  fellow-labourer in          
philosophy4      ,,footnotes3    #ag    
,dion ,cassius1 lib4 #cg4    #ah ,the   
pretended translation by ,roberval of an
 ,arabic version of  ,aristarchus1 ,de  
,systemate ,mundi1 in which the         
,copernican system is  fully developed1 
is spurious4 ,menage asserts this in his
 observations on  ,diogen4 ,laert4 lib4 
#h1 sec4 #he1 tom4 ii41 p4 #chi4 7,ed4  
,amst4 #afib47 ,the  commentary contains
 many authorities well worth consulting4
 ,delambre1  ,histoire de l',astronomie1
 infers it from its not containing some 
opinions which ,archimedes tells us were
 held by ,aristarchus4 ,a more  direct  
proof may be gathered from the following
 blunder of the supposed  translator4   
,astronomers had been long aware that   

the earth in different  parts of her    
orbit is at different distances from the
 sun4 ,roberval  wished to claim for    
,aristarchus the credit of having known 
this1 and  introduced into his book1 not
 only the mention of the fact1 but an   
explanation of its cause4 ,accordingly  
he makes ,aristarchus give a reason  why
 the sun's apogee 7or place of greatest 
distance from the earth7  must always be
 at the north summer solstice4 ,in fact1
 it was there1 or  nearly so1 in        
,roberval's time1 and he knew not but   
that it had always  been there4 ,it is  
however moveable1 and1 when ,aristarchus
 lived1 was  nearly half way between the
 solstices and equinoxes4 ,he therefore 
would  hardly have given a reason for   
the necessity of a phenomenon of which1 
if he observed anything on the subject1 
he must have observed the  contrary4    
,the change in the obliquity of the     
earth's axis to the  ecliptic was known 
in the time of ,roberval1 and he        
accordingly has  introduced the proper  

value which it had in ,aristarchus's    
time4    #ai ,de ,clo4 lib4 #b4    #bj  
,paradise ,lost1 b4 viii4 v4 #hc4    #ba
 ,itaque tam circulos primi motus quam  
orbes secundorum mobilium  rever in     
clesti corpore esse concludimus1 c4 ,non
 ergo sunt mera  figmenta1 quibus extra 
mentem nihil correspondeat4 ,m4         
,maestlini1 ,de  ,astronomi             
,hypothesibus disputatio4 ,heidelberg1  
#aehb4    #bb ,opuscula ,philosophica1  
,thema ,cli4    #bc ,nobis constat      
falsissimum esse4 ,de ,aug4 ,scient4    
lib4 iii4 c4 #c1  #afbc4    #bd ,id     
autum e libentius faciam1 quod in       
,copernici sententiam multis  abhinc    
annis venerim4--,kepl4 ,epistol4    #be 
,kepleri ,epistol4          ,,chapter   
,v4        ,galileo re-elected          
,professor at ,padua--,new              
star--,compass of                       
proportion--,capra--,gilbert--,proposals
 to return to ,pisa--,lost              
writings--,cavalieri4      ,,galileo',s 
reputation was now rapidly increasing3  

his lectures were  attended by many     
persons of the highest rank2 among whom 
were the  ,archduke ,ferdinand1         
afterwards ,emperor of ,germany1 the    
,landgrave of  ,hesse1 and the ,princes 
of ,alsace and ,mantua4 ,on the         
expiration of the  first period for     
which he had been elected professor1 he 
was rechosen  for a similar period1 with
 a salary increased to #cbj florins4    
,the  immediate occasion of this        
augmentation is said by ,fabroni#bf1 to 
have  arisen out of the malice of an ill
 wisher of ,galileo1 who1 hoping to do  
him disservice1 apprized the senate that
 he was not married to ,marina  ,gamba1 
then living with him1 and the mother of 
his son ,vincenzo4 ,whether  or not the 
senate might consider themselves        
entitled to inquire into the  morality  
of his private life1 it was probably    
from a wish to mark their  sense of the 
informer's impertinence1 that they      
returned the brief  answer1 that if he  
had a family to provide for1 he stood   

the more in  need of an increased       
stipend4    ,during ,galileo's residence
 at ,padua1 and1 according to ,viviani's
  intimation1 towards the thirtieth year
 of his age1 that is to say in  #aeid1  
he experienced the first attack of a    
disease which pressed  heavily on him   
for the rest of his life4 ,he enjoyed1  
when a young man1 a  healthy and        
vigorous constitution1 but chancing to  
sleep one afternoon  near an open       
window1 through which was blowing a     
current of air cooled  artificially by  
the fall of water1 the consequences were
 most disastrous  to him4 ,he contracted
 a sort of chronic complaint1 which     
showed itself  in acute pains in his    
limbs1 chest1 and back1 accompanied with
 frequent  hmorrhages and loss of sleep 
and appetite2 and this painful disorder 
thenceforward never left him entirely1  
but recurred intermittingly1 with       
greater or less violence1 as long as he 
lived4 ,others of the party did  not    
even escape so well1 but died shortly   

after committing this  imprudence4      
,in #afjd1 the attention of astronomers 
was called to the contemplation of  a   
new star1 which appeared suddenly with  
great splendour in the  constellation   
,serpentarius1 or ,ophiuchus1 as it is  
now more commonly  called4 ,maestlin1   
who was one of the earliest to notice   
it1 relates his  observations in the    
following words3 ,how wonderful is this 
new star6 ,i  am certain that ,i did not
 see it before the #bith of ,september1 
nor  indeed1 on account of several      
cloudy nights1 had ,i a good view till  
the  #fth of ,october4 ,now that it is  
on the other side of the sun1 instead of
  surpassing ,jupiter as it did1 and    
almost rivalling ,venus1 it scarcely    
matches the ,cor ,leonis1 and hardly    
surpasses ,saturn4 ,it continues        
however to shine with the same bright   
and strongly sparkling light1 and       
changes its colours almost with every   
moment2 first tawny1 then yellow1       
presently purple and red1 and1 when it  

has risen above the vapours1 most       
frequently white4 ,this was by no means 
an unprecedented phenomenon2 and  the   
curious reader may find in ,riccioli#bg 
a catalogue of the principal  new stars 
which have at different times appeared4 
,there is a tradition  of a similar     
occurrence as early as the times of the 
,greek astronomer  ,hipparchus1 who is  
said to have been stimulated by it to   
the formation  of his catalogue of the  
stars2 and only thirty-two years before1
 in  #aegb1 the same remarkable         
phenomenon in the constellation         
,cassiopeia was  mainly instrumental in 
detaching the celebrated ,tycho ,brahe  
from the  chemical studies1 which till  
then divided his attention with         
astronomy4  ,tycho's star disappeared at
 the end of two years2 and at that time 
,galileo was a child4 ,on the present   
occasion1 he set himself earnestly  to  
consider the new phenomenon1 and        
embodied the results of his             
observations in three lectures1 which   

have been unfortunately lost4 ,only  the
 exordium of the first has been         
preserved3 in this he reproaches his    
auditors with their general             
insensibility to the magnificent wonders
 of  creation daily exposed to their    
view1 in no respect less admirable than 
the new prodigy1 to hear an explanation 
of which they had hurried in  crowds to 
his lecture room4 ,he showed1 from the  
absence of parallax1  that the new star 
could not be1 as the vulgar hypothesis  
represented1 a  mere meteor engendered  
in our atmosphere and nearer the earth  
than the  moon1 but must be situated    
among the most remote heavenly bodies4  
,this  was inconceivable to the         
,aristotelians1 whose notions of a      
perfect1  simple1 and unchangeable sky  
were quite at variance with the         
introduction of any such new body2 and  
we may perhaps consider these  lectures 
as the first public declaration of      
,galileo's hostility to the  old        
,ptolemaic and ,aristotelian astronomy4 

,in #afjf he was reappointed to the     
lectureship1 and his salary a second    
time increased1 being raised to #ebj    
florins4 ,his public lectures were at   
this period so much thronged that the   
ordinary place of meeting was  found    
insufficient to contain his auditors1   
and he was on several  occasions obliged
 to adjourn to the open air1--even from 
the school of  medicine1 which was      
calculated to contain one thousand      
persons4    ,about this time he was     
considerably annoyed by a young         
,milanese1 of the  name of ,balthasar   
,capra1 who pirated an instrument which 
,galileo had  invented some years       
before1 and had called the geometrical  
and military  compass4 ,the original    
offender was a ,german named ,simon     
,mayer1 whom we  shall meet with        
afterwards arrogating to himself the    
merit of one of  ,galileo's astronomical
 discoveries2 but on this occasion1 as  
soon as he  found ,galileo disposed to  
resent the injury done to him1 he       

hastily  quitted ,italy1 leaving his    
friend ,capra to bear alone the shame of
 the  exposure which followed4 ,the     
instrument is of simple construction1   
consisting merely of two straight       
rulers1 connected by a joint2 so that   
they can be set to any required angle4  
,this simple and useful  instrument1 now
 called the ,sector1 is to be found in  
almost every case  of mathematical      
instruments4 ,instead of the            
trigonometrical and  logarithmic lines  
which are now generally engraved upon   
it1 ,galileo's  compass merely          
contained1 on one side1 three pairs of  
lines1 divided in  simple1 duplicate1   
and triplicate proportion1 with a fourth
 pair on  which were registered the     
specific gravities of several of the    
most  common metals4 ,these were used   
for multiplications1 divisions1 and the 
extraction of roots2 for finding the    
dimensions of equally heavy balls  of   
different materials1 c4 ,on the other   
side were lines contrived for  assisting

 to describe any required polygon on a  
given line2 for finding  polygons of one
 kind equal in area to those of another2
 and a multitude  of other similar      
operations useful to the practical      
engineer4    ,unless the instrument1    
which is now called ,gunter's scale1 be 
much  altered from what it originally   
was1 it is difficult to understand on   
what grounds ,salusbury charges ,gunter 
with plagiarism from ,galileo's         
,compass4 ,he declares that he has      
closely compared the two1 and can find  
no difference between them4#bh ,there   
has also been some confusion1 by        
several writers1 between this instrument
 and what is now commonly called  the   
,proportional ,compass4 ,the latter     
consists of two slips of metal  pointed 
at each end1 and connected by a pin     
which1 sliding in a groove  through     
both1 can be shifted to different       
positions4 ,its use is to find          
proportional lines2 for it is obvious   
that the openings measured by each  pair

 of legs will be in the same proportion 
in which the slips are  divided by the  
centre4 ,the divisions usually marked on
 it are calculated  for finding the     
submultiples of straight lines1 and the 
chords of  submultiple arcs4 ,montucla  
has mentioned this mistake of one       
instrument  for the other1 and charges  
,voltaire with the more inexcusable     
error of  confounding ,galileo's with   
the ,mariner's ,compass4 ,he refers to a
  treatise by ,hulsius for his authority
 in attributing the ,proportional       
,compass to ,burgi1 a ,swiss astronomer 
of some celebrity4 ,horcher also has    
been styled the inventor2 but he did no 
more than describe its form and         
application4 ,in the frontispiece of his
 book is an engraving of this  compass  
exactly similar to those which are now  
used4#bi ,to the  description which     
,galileo published of his compass1 he   
added a short  treatise on the method of
 measuring heights and distances with   
the  quadrant and plumb line4 ,the      

treatise1 which is printed by itself at 
the  end of the first volume of the     
,padua edition of ,galileo's works1     
contains nothing more than the          
demonstrations belonging to the same    
operations4 ,they are quite elementary1 
and contain little or nothing  that was 
new even at that time4    ,such an      
instrument as ,galileo's ,compass was of
 much more importance  before the grand 
discovery of logarithms than it can now 
be considered3  however it acquires an  
additional interest from the value which
 he  himself set on it4 ,in #afjg1      
,capra1 at the instigation of ,mayer1   
published as his own invention what he  
calls the proportional hoop1  which is a
 mere copy of ,galileo's instrument4    
,this produced from ,galileo  a long    
essay1 entitled ,a ,defence of ,galileo 
against the ,calumnies and  ,impostures 
of ,balthasar ,capra4 ,his principal    
complaint seems to have  been of the    
misrepresentations which ,capra had     
published of his lectures  on the new   

star already mentioned1 but he takes    
occasion1 after pointing  out the       
blunders and falsehoods which ,capra had
 committed on that  occasion1 to add a  
complete proof of his piracy of the     
geometrical  compass4 ,he showed1 from  
the authenticated depositions of        
workmen1 and  of those for whom the     
instruments had been fabricated1 that he
 had  devised them as early as the year 
#aeig1 and had explained their          
construction and use both to ,balthasar 
himself and to his father ,aurelio      
,capra1 who was then residing in ,padua4
 ,he gives1 in the same essay1 the      
minutes of a public meeting between     
himself and ,capra1 in which he  proved1
 to the satisfaction of the university1 
that wherever ,capra had  endeavoured to
 introduce into his book propositions   
which were not to be  met with in       
,galileo's1 he had fallen into the      
greatest absurdities1 and  betrayed the 
most complete ignorance of his subject4 
,the consequence of  this public        

exposure1 and of the report of the      
famous ,fra ,paolo ,sarpi1  to whom the 
matter had been referred1 was a formal  
prohibition by the  university of       
,capra's publication1 and all copies of 
the book then on  hand were seized1 and 
probably destroyed1 though ,galileo has 
preserved  it from oblivion by          
incorporating it in his own publication4
    ,nearly at the same time1 #afjg1 or 
immediately after1 he first turned his  
attention towards the loadstone1 on     
which our countryman ,gilbert had       
already published his researches1       
conducted in the true spirit of the     
inductive method4 ,very little that is  
original is to be found in  ,galileo's  
works on this subject1 except some      
allusions to his method of  arming      
magnets1 in which1 as in most of his    
practical and mechanical  operations1 he
 appears to have been singularly        
successful4 ,sir ,kenelm  ,digby#cj     
asserts1 that the magnets armed by      
,galileo would support twice  as great a

 weight as one of ,gilbert's of the same
 size4 ,galileo was well  acquainted1 as
 appears from his frequent allusions in 
different parts of  his works1 with what
 ,gilbert had done1 of whom he says1 ,i 
extremely  praise1 admire1 and envy this
 author2--,i think him1 moreover1 worthy
 of  the greatest praise for the many   
new and true observations that he has   
made to the disgrace of so many vain and
 fabling authors1 who write1 not  from  
their own knowledge only1 but repeat    
every thing they hear from the  foolish 
vulgar1 without attempting to satisfy   
themselves of the same by  experience1  
perhaps that they may not diminish the  
size of their books4    ,galileo's      
reputation being now greatly increased1 
proposals were made to  him1 in #afji1  
to return to his original situation at  
,pisa4 ,he had been  in the habit of    
passing over to ,florence during the    
academic vacation1  for the purpose of  
giving mathematical instruction to the  
younger  members of ,ferdinand's family2

 and ,cosmo1 who had now succeeded his  
father as duke of ,tuscany1 regretted   
that so masterly a genius had been      
allowed to leave the university which he
 naturally should have graced4 ,a  few  
extracts from ,galileo's answers to     
these overtures will serve to  show the 
nature of his situation at ,padua1 and  
the manner in which his  time was there 
occupied4 ,i will not hesitate to say1  
having now  laboured during twenty      
years1 and those the best of my life1 in
 dealing  out1 as one may say1 in       
detail1 at the request of any body1 the 
little  talent which ,god has granted to
 my assiduity in my profession1 that my 
wish certainly would be to have         
sufficient rest and leisure to enable   
me1 before my life comes to its close1  
to conclude three great works  which ,i 
have in hand1 and to publish them2 which
 might perhaps bring  some credit to me1
 and to those who had favoured me in    
this undertaking1  and possibly may be  
of greater and more frequent service to 

students  than in the rest of my life ,i
 could personally afford them4 ,greater 
leisure than ,i have here ,i doubt if ,i
 could meet with elsewhere1 so long  as 
,i am compelled to support my family    
from my public and private  lectures1   
7nor would ,i willingly lecture in any  
other city than this1  for several      
reasons which would be long to mention7 
nevertheless not  even the liberty ,i   
have here is sufficient1 where ,i am    
obliged to spend  many1 and often the   
best hours of the day at the request of 
this and  that man4--,my public salary  
here is #ebj florins1 which ,i am almost
  certain will be advanced to as many   
crowns upon my re-election1 and  these  
,i can greatly increase by receiving    
pupils1 and from private  lectures1 to  
any extent that ,i please4 ,my public   
duty does not confine  me during more   
than #fj half hours in the year1 and    
even that not so  strictly but that ,i  
may1 on occasion of any business1       
contrive to get  some vacant days2 the  

rest of my time is absolutely at my own 
disposal2  but because my private       
lectures and domestic pupils are a great
  hindrance and interruption of my      
studies1 ,i wish to live entirely exempt
  from the former1 and in great measure 
from the latter3 for if ,i am to  return
 to my native country1 ,i should wish   
the first object of his  ,serene        
,highness to be1 that leisure and       
opportunity should be given me  to      
complete my works without employing     
myself in lecturing4--,and1 in  short1  
,i should wish to gain my bread from my 
writings1 which ,i would  always        
dedicate to my ,serene ,master4--,the   
works which ,i have to finish  are      
principally--two books on the system or 
structure of the ,universe1  an immense 
work1 full of philosophy1 astronomy1 and
 geometry2 three  books on ,local       
,motion1 a science entirely new1 no one1
 either ancient or  modern1 having      
discovered any of the very many         
admirable accidents which  ,i           

demonstrate in natural and violent      
motions1 so that ,i may with very  great
 reason call it a new science1 and      
invented by me from its very  first     
principles2 three books of ,mechanics1  
two on the demonstration of  principles 
and one of problems2 and although others
 have treated this  same matter1 yet all
 that has been hitherto written1 neither
 in  quantity1 nor otherwise1 is the    
quarter of what ,i am writing on it4 ,i 
have also different treatises on natural
 subjects2 ,on sound and speech2  ,on   
light and colours2 ,on the tide2 ,on the
 composition of continuous  quantity2   
,on the motions of animals2--,and others
 besides4 ,i have also  an idea of      
writing some books relating to the      
military art1 giving not  only a model  
of a soldier1 but teaching with very    
exact rules every  thing which it is his
 duty to know that depends upon         
mathematics2 as the  knowledge of       
castrametation1 drawing up battalions1  
fortifications1  assaults1 planning1    

surveying1 the knowledge of artillery1  
the use of  instruments1 c4 ,i also wish
 to reprint the ',use of my ,geometrical
  ,compass1' which is dedicated to his  
highness1 and which is no longer to  be 
met with2 for this instrument has       
experienced such favour from the        
public1 that in fact no other           
instruments of this kind are now made1  
and  ,i know that up to this time       
several thousands of mine have been     
made4--,i  say nothing as to the amount 
of my salary1 feeling convinced that as 
,i  am to live upon it1 the graciousness
 of his highness would not deprive  me  
of any of those comforts1 which1        
however1 ,i feel the want of less  than 
many others2 and therefore ,i say       
nothing more on the subject4  ,finally1 
on the title and profession of my       
service1 ,i should wish that  to the    
name of ,mathematician1 his highness    
would add that of  ,philosopher1 as ,i  
profess to have studied a greater number
 of years in  philosophy than months in 

pure mathematics2 and how ,i have       
profited by  it1 and if ,i can or ought 
to deserve this title1 ,i may let their 
highnesses see as often as it shall     
please them to give me an  opportunity  
of discussing such subjects in their    
presence with those who  are most       
esteemed in this knowledge4 ,it may     
perhaps be seen in the  expressions of  
this letter1 that ,galileo was not      
inclined to undervalue  his own merits1 
but the peculiar nature of the          
correspondence should be  taken into    
account1 which might justify his        
indulging a little more than  usual in  
self-praise1 and it would have been     
perhaps almost impossible  for him to   
have remained entirely blind to his vast
 superiority over his  contemporaries4  
,many of the treatises which ,galileo   
here mentions1 as well as another on    
dialling1 have been irrecoverably lost1 
through the superstitious  weakness of  
some of his relations1 who after his    
death suffered the  family confessor to 

examine his papers1 and to destroy      
whatever seemed  to him objectionable2 a
 portion which1 according to the notions
 then  prevalent1 was like to comprise  
the most valuable part of the papers    
submitted to this expurgation4 ,it is   
also supposed that many were burnt  by  
his infatuated grandson ,cosimo1 who    
conceived he was thus offering a  proper
 and pious sacrifice before devoting    
himself to the life of a  missionary4 ,a
 ,treatise on ,fortification1 by        
,galileo1 was found in #agic1  and is   
contained among the documents published 
by ,venturi4 ,galileo does  not profess 
in it to give much original matter1 but 
to lay before his  readers a compendium 
of the most approved principles then    
already known4  ,it has been supposed   
that ,gustavus ,adolphus of ,sweden     
attended ,galileo's  lectures on this   
subject1 whilst in ,italy2 but the fact 
is not  satisfactorily ascertained4     
,galileo himself mentions a ,prince     
,gustavus  of ,sweden to whom he gave   

instruction in mathematics1 but the     
dates  cannot well be made to agree4    
,the question deserves notice only from 
its  having been made the subject of    
controversy4    ,the loss of ,galileo's 
,essay on ,continuous ,quantity is      
particularly to be  regretted1 as it    
would be highly interesting to see how  
far he succeeded  in methodizing his    
thoughts on this important topic4 ,it is
 to his pupil  ,cavalieri 7who refused  
to publish his book so long as he hoped 
to see  ,galileo's printed7 that we owe 
,the ,method of ,indivisibles1 which is 
universally recognized as one of the    
first germs of the powerful methods  of 
modern analysis4 ,throughout ,galileo's 
works we find many indications  of his  
having thought much on the subject1 but 
his remarks are vague1  and bear little1
 if at all1 on the application of the   
method4 ,to this  the chief part of     
,cavalieri's book is devoted1 though he 
was not so  entirely regardless of the  
principles on which his method of       

measuring  spaces is founded1 as he is  
sometimes represented4 ,this method     
consisted  in considering lines as made 
up of an infinite number of points1     
surfaces in like manner as composed of  
lines1 and solids of surfaces2  but     
there is an observation at the beginning
 of the #gth book1 which  shews clearly 
that ,cavalieri had taken a much more   
profound view of the  subject than is   
implied in this superficial exposition1 
and had  approached very closely to the 
apparently more exact theories of his   
successors4 ,anticipating the objections
 to his hypothesis1 he argues1  that    
there is no necessity to suppose the    
continuous quantities made up  of these 
indivisible parts1 but only that they   
will observe the same  ratios as those  
parts do4 ,it ought not to be omitted1  
that ,kepler also  had given an impulse 
to ,cavalieri in his ,new method of     
,gauging1 which  is the earliest work   
with which we are acquainted1 where     
principles of  this sort are            

employed4#ca      ,,footnotes3    #bf   
,vit ,italorum ,illustrium4    #bg      
,almagestum ,novum1 vol4 i4    #bh      
,math4 ,coll4 vol4 ii4    #bi           
,constructio ,circini ,proportionum4    
,mogunti1 #afje4    #cj ,treatise of the
 ,nature of ,bodies4 ,london1 #affe4    
#ca ,nova ,stereometria                 
,doliorum--,lincii1 #afae4              
,,chapter ,,vi4        ,invention of the
                                        
telescope--,fracastoro--,porta--,reflect
ing        telescope--,roger            
,bacon--,digges--,de                    
,dominis--,jansen--,lipperhey--,galileo 
constructs                              
telescopes--,microscopes--,re-elected   
,professor at ,padua for life4          
,,the year #afji was signalized by      
,galileo's discovery of the telescope1  
which1 in the minds of many1 is the     
principal1 if not the sole invention    
associated with his name4 ,it cannot be 
denied that his fame1 as the  founder of
 the school of experimental philosophy1 

has been in an  unmerited degree cast   
into the shade by the splendour of his  
astronomical discoveries2 yet           
,lagrange#cb surely errs in the opposite
  extreme1 when he almost denies that   
these form any real or solid part of    
the glory of this great man2 and        
,montucla#cc omits an important         
ingredient in his merit1 when he 7in    
other respects very justly7  remarks1   
that it required far less genius to     
point a telescope towards  the heavens  
than to trace the unheeded1 because     
daily recurring1  phenomena of motion up
 to its simple and primary laws4 ,we are
 to  remember that in the days of       
,galileo a telescope could scarcely be  
pointed to the heavens with impunity1   
and that a courageous mind was  required
 to contradict1 and a strong one to bear
 down1 a party1 who1  when invited to   
look on any object in the heavens which 
,aristotle had  never suspected1        
immediately refused all credit to those 
senses1 to  which1 on other occasions1  

they so confidently appealed4 ,it surely
 is a  real and solid part of ,galileo's
 glory that he consumed his life in     
laborious and indefatigable             
observations1 and that he persevered in 
announcing his discoveries undisgusted  
by the invectives1 and undismayed  by   
the persecutions1 to which they         
subjected him4 ,plagiarist6 liar6       
impostor6 heretic6 were among the       
expressions of malignant hatred         
lavished upon him1 and although he also 
was not without some violent and        
foul-mouthed partisans1 yet it must be  
told to his credit that he  himself     
seldom condescended to notice these     
torrents of abuse1 otherwise  than by   
good-humoured retorts1 and by           
prosecuting his observations with       
renewed assiduity and zeal4    ,the use 
of single lenses in aid of the sight had
 been long known4  ,spectacles were in  
common use at the beginning of the      
fourteenth  century1 and there are      
several hints1 more or less obscure1 in 

many  early writers1 of the effects     
which might be expected from a          
combination  of glasses2 but it does not
 appear with certainty that any of these
  authors had attempted to reduce their 
ideas to practice4 ,after the  discovery
 of the telescope1 almost every country 
endeavoured to find in  the writings of 
its early philosophers traces of the    
knowledge of such  an instrument1 but in
 general with success very inadequate to
 the zeal  of their national            
prepossessions4 ,there are two authors  
especially to  whom the attention of    
,kepler and others was turned1          
immediately upon the  promulgation of   
the discovery1 as containing the germ of
 it in their  works4 ,these are         
,baptista ,porta1 and ,gerolamo         
,fracastoro4 ,we have  already had      
occasion to quote the ,homocentrica of  
,fracastoro1 who died  in #aeec2 the    
following expressions1 though they seem 
to refer to actual  experiment1 yet fall
 short of the meaning with which it has 

been  attempted to invest them4 ,after  
explaining and commenting on some       
phenomena of refraction through         
different media1 to which he was led by 
the necessity of reconciling his theory 
with the variable magnitudes of  the    
planets1 he goes on to say--,for which  
reason1 those things which  are seen at 
the bottom of water1 appear greater than
 those which are at  the top2 and if any
 one look through two eyeglasses1 one   
placed upon  the other1 he will see     
every thing much larger and nearer4#cd  
,it  should seem that this passage 7as  
,delambre has already remarked7 rather  
refers to the close application of one  
glass upon another1 and it may  fairly  
be doubted whether anything analogous to
 the composition of the  telescope was  
in the writer's thoughts4 ,baptista     
,porta writes on the  same subject more 
fully2--,concave lenses show distant    
objects most  clearly1 convex those     
which are nearer1 whence they may be    
used to  assist the sight4 ,with a      

concave glass distant objects will be   
seen1  small1 but distinct2 with a      
convex one those near at hand1 larger1  
but  confused2 if you know rightly how  
to combine one of each sort1 you  will  
see both far and near objects larger and
 clearer4#ce ,these words  show1 if     
,porta really was then unacquainted with
 the telescope1 how  close it is        
possible to pass by an invention without
 lighting on it1 for  of precisely such 
a combination of a convex and concave   
lens1 fitted to  the ends of an organ   
pipe by way of tube1 did the whole of   
,galileo's  telescope consist4 ,if      
,porta had stopped here he might more   
securely have  enjoyed the reputation of
 the invention1 but he then professes to
  describe the construction of his      
instrument1 which has no relation       
whatever to his previous remarks4 ,i    
shall now endeavour to show in what     
manner we may contrive to recognize our 
friends at the distance of  several     
miles1 and how those of weak sight may  

read the most minute  letters from a    
distance4 ,it is an invention of great  
utility1 and  grounded on optical       
principles1 nor is it at all difficult  
of execution2  but it must be so        
divulged as not to be understood by the 
vulgar1 and  yet be clear to the        
sharpsighted4 ,the description which    
follows seems  far enough removed from  
the apprehended danger of being too     
clear1 and  indeed every writer who has 
hitherto quoted it has merely given the 
passage in its original ,latin1         
apparently despairing of an intelligible
  translation4 ,with some alterations in
 the punctuation1 which appear          
necessary to bring it into any          
grammatical construction1#cf it may be  
supposed to bear something like the     
following meaning3--,let a view be      
contrived in the centre of a mirror1    
where it is most effective4 ,all the    
solar rays are exceedingly dispersed1   
and do not in the least come  together  
7in the true centre72 but there is a    

concourse of all the rays  in the       
central part of the said mirror1 half   
way towards the other  centre1 where the
 cross diameters meet4 ,this view is    
contrived in the  following manner4 ,a  
concave cylindrical mirror placed       
directly in front1  but with its axis   
inclined1 must be adapted to that focus3
 and let  obtuse angled or right angled 
triangles be cut out with two cross     
lines  on each side drawn from the      
centre1 and a glass 7specillum7 will be 
completed fit for the purposes we       
mentioned4 ,if it were not for the  word
 specillum1 which1 in the passage       
immediately preceding this1  ,porta#cg  
contrasts with speculum1 and which he   
afterwards explains  to mean a glass    
lens1 it would be very clear that the   
foregoing passage  7supposing it to have
 any meaning7 must be referred to a     
reflecting  telescope1 and it is a      
little singular that while this obscure 
passage  has attracted universal        
attention1 no one1 so far as we are     

aware1 has  taken any notice of the     
following unequivocal description of the
  principal part of ,newton's           
construction of the same instrument4 ,it
 is in  the #eth chapter of the #agth   
book1 where ,porta explains by what     
device  exceedingly minute letters may  
be read without difficulty4 ,place a    
concave mirror so that the back of it   
may lie against your breast2  opposite  
to it1 and within the burning point1    
place the writing2 put a  plane mirror  
behind it1 that may be under your eyes4 
,then the images of  the letters which  
are in the concave mirror1 and which the
 concave has  magnified1 will be        
reflected in the plane mirror1 so that  
you may read  without difficulty4    ,we
 have not been able to meet with the    
,italian translation of ,porta's        
,natural ,magic1 which was published in 
#afaa1 under his own  superintendence2  
but the ,english translator of #afeh    
would probably have  known if any       
intelligible interpretation were there  

given of the  mysterious passage above  
quoted1 and his translation is so devoid
 of  meaning as strongly to militate    
against this idea4 ,porta1 indeed1      
claimed the invention as his own1 and is
 believed to have hastened his  death1  
7which happened in #afae1 he being then 
#hj years old17 by the  fatigue of      
composing a ,treatise on the ,telescope1
 in which he had  promised to exhaust   
the subject4 ,we do not know whether    
this is the same  work which was        
published after his death by            
,stelliola1#ch but which  contains no   
allusion to ,porta's claim1 and possibly
 ,stelliola may have  thought it most   
for his friend's reputation to suppress 
it4 ,schott#ci  says1 a friend of his   
had seen ,porta's book in manuscript1   
and that it  did at that time contain   
the assertion of ,porta's title to the  
invention4 ,after all it is not         
improbable that he may have derived his 
notions of magnifying distant objects   
from our celebrated countryman  ,roger  

,bacon1 who died about the year #acjj4  
,he has been supposed1 not  without good
 grounds1 to have been one of the first 
who recognised the  use of single lenses
 in producing distinct vision1 and he   
has some  expressions with respect to   
their combination which promise effects 
analogous to those held out by ,porta4  
,in ,the ,admirable ,force of ,art and  
,nature1 he says1 ,physical figurations 
are far more strange1 for in  such      
manner may we frame perspects and       
looking-glasses that one thing  shall   
appear to be many1 as one man shall     
seeme a whole armie2 and  divers sunnes 
and moones1 yea1 as many as we please1  
shall appeare at  one time1 c4 ,and so  
may the perspects be framed1 that things
 most farre  off may seeme most nigh    
unto us1 and clean contrarie1 soe that  
we may  reade very small letters an     
incredible distance from us1 and behold 
things how little soever they be1 and   
make stars to appeare wheresoever  we   
will1 c4 ,and1 besides all these1 we may

 so frame perspects that any  man       
entering into a house he shall indeed   
see gold1 and silver1 and  precious     
stones1 and what else he will1 but when 
he maketh haste to the  place he shall  
find just nothing4 ,it seems plain1 that
 the author is  here speaking solely of 
mirrors1 and we must not too hastily    
draw the  conclusion1 because in the    
first and last of these assertions he   
is1 to  a certain extent1 borne out by  
facts1 that he therefore was in         
possession of a method of accomplishing 
the middle problem also4 ,in the        
previous chapter1 he gives a long list  
of notable things1 7much in the  style  
of the ,marquis of ,worcester's ,century
 of ,inventions7 which if we  can really
 persuade ourselves that he was capable 
of accomplishing1 we  must allow the    
present age to be still immeasurably    
inferior to him in  science4    ,thomas 
,digges1 in the preface to his          
,pantometria1 7published in #aeia7      
declares1 ,my father1 by his continuall 

painfull practises1 assisted  with      
demonstrations mathematicall1 was able1 
and sundry times hath by  proportionall 
glasses1 duely situate in convenient    
angles1 not only  discouered things     
farre off1 read letters1 numbered peeces
 of money1  with the verye coyne and    
superscription thereof1 cast by some of 
his  freends of purpose1 upon downes in 
open fields2 but also1 seuen miles  off1
 declared what hath beene doone at that 
instant in priuate places4  ,he hath    
also sundrie times1 by the sunne beames1
 fired powder and  dischargde ordnance  
halfe a mile and more distante2 which   
things ,i am  the boulder to report1 for
 that there are yet living diverse 7of  
these  his dooings7 occulati testes1    
7eye witnesses7 and many other matters  
farre more strange and rare1 which ,i   
omit as impertinent to this place4      
,we find another pretender to the honour
 of the discovery of the  telescope in  
the celebrated ,antonio de ,dominis1    
,archbishop of ,spalatro1  famous in the

 annals of optics for being one of the  
first to explain the  theory of the     
rainbow4 ,montucla1 following ,p4       
,boscovich1 has scarcely  done justice  
to ,de ,dominis1 whom he treats as a    
mere pretender and  ignorant person4    
,the indisposition of ,boscovich towards
 him is  sufficiently accounted for by  
the circumstance of his being a         
,catholic  prelate who had embraced the 
cause of ,protestantism4 ,his nominal   
reconciliation with the ,church of ,rome
 would probably not have saved him  from
 the stake1 had not a natural death     
released him when imprisoned on  that   
account at ,rome4 ,judgment was         
pronounced upon him notwithstanding1    
and his body and books were publicly    
burnt in the ,campo de ,fiori1 in       
#afbd4 ,his treatise1 ,de ,radiis1      
7which is very rarely to be met with7   
was  published by ,bartolo after the    
acknowledged invention of the telescope 
by ,galileo2 but ,bartolo tells us1 in  
the preface1 that the manuscript  was   

communicated to him from a collection of
 papers written #bj years  before1 on   
his inquiring the ,archbishop's opinion 
with respect to the  newly discovered   
instrument1 and that he got leave to    
publish it1 with  the addition of one or
 two chapters4 ,the treatise contains a 
complete  description of a telescope1   
which1 however1 is professed merely to  
be an  improvement on spectacles1 and if
 the author's intention had been to     
interpolate an afterwritten account1 in 
order to secure to himself the          
undeserved honour of the invention1 it  
seems improbable that he would  have    
suffered an acknowledgment of additions1
 previous to publication1  to be        
inserted in the preface4 ,besides1 the  
whole tone of the work is  that of a    
candid and truth-seeking philosopher1   
very far indeed removed  from being1 as 
,montucla calls him1 conspicuous for    
ignorance even among  the ignorant men  
of his age4 ,he gives a drawing of a    
convex and concave  lens1 and traces the

 passage of the rays through them2 to   
which he  subjoins1 that he has not     
satisfied himself with any determination
 of  the precise distance to which the  
glasses should be separated1 according  
to their convexity and concavity1 but   
recommends the proper distance to  be   
found by actual experiment1 and tells   
us1 that the effect of the  instrument  
will be to prevent the confusion arising
 from the  interference of the direct   
and refracted rays1 and to magnify the  
object  by increasing the visible angle 
under which it is viewed4 ,these1 among 
the many claimants1 are certainly the   
authors who approached the most  nearly 
to the discovery3 and the reader may    
judge1 from the passages  cited1 whether
 the knowledge of the telescope can with
 probability be  referred to a period   
earlier than the commencement of the    
#agth century4  ,at all events1 we can  
find no earlier trace of its being      
applied to any  practical use2 the      
knowledge1 if it existed1 remained      

speculative and  barren4    ,in #afji1  
,galileo1 then being on a visit to a    
friend at ,venice1 heard a  rumour of   
the recent invention1 by a ,dutch       
spectacle-maker1 of an  instrument which
 was said to represent distant objects  
nearer than they  usually appeared4     
,according to his own account1 this     
general rumour1  which was confirmed to 
him by letters from ,paris1 was all that
 he  learned on the subject2 and        
returning to ,padua1 he immediately     
applied  himself to consider the means  
by which such an effect could be        
produced4  ,fuccarius1 in an abusive    
letter which he wrote on the subject1   
asserts  that one of the ,dutch         
telescopes had been at that time        
actually brought  to ,venice1 and that  
he 7,fuccarius7 had seen it2 which1 even
 if true1 is  perfectly consistent with 
,galileo's statement2 and in fact the   
question1  whether or not ,galileo saw  
the original instrument1 becomes        
important  only from his expressly      

asserting the contrary1 and professing  
to give  the train of reasoning by which
 he discovered its principle2 so that   
any  insinuation that he had actually   
seen the ,dutch glass1 becomes a direct 
impeachment of his veracity4 ,it is     
certain1 from the following extract  of 
a letter from ,lorenzo ,pignoria to     
,paolo ,gualdo1 that one at least of    
the ,dutch glasses had been sent to     
,italy4 ,it is dated ,padua1 #cast      
,august1 #afji4dj ,we have no news1     
except the return of ,his ,serene       
,highness1 and the re-election of the   
lecturers1 among whom ,sign4 ,galileo   
has contrived to get #ajjj florins for  
life2 and it is said to be on  account  
of an eyeglass1 like the one which was  
sent from ,flanders to  ,cardinal       
,borghese4 ,we have seen some here1 and 
truly they succeed  well4    ,it is     
allowed by every one that the ,dutchman1
 or rather ,zealander1 made  his        
discovery by mere accident1 which       
greatly derogates from any honour       

attached to it2 but even this diminished
 degree of credit has been  fiercely    
disputed4 ,according to one account1    
which appears consistent  and probable1 
it had been made for sometime before its
 importance was in  the slightest degree
 understood or appreciated1 but was set 
up in the  optician's shop as a curious 
philosophical toy1 showing a large and  
inverted image of a weathercock1 towards
 which it was directed4 ,the  ,marquis  
,spinola1 chancing to see it1 was struck
 with the phenomenon1  purchased the    
instrument1 and presented it either to  
the ,archduke ,albert  of ,austria1 or  
to ,prince ,maurice of ,nassau1 whose   
name appears in every  version of the   
story1 and who first entertained the    
idea of employing it  in military       
reconnoissances4    ,zacharias ,jansen1 
and ,henry ,lipperhey1 two              
spectacle-makers1 living  close to each 
other1 near the church of ,middleburg1  
have both had  strenuous supporters of  
their title to the invention4 ,a third  

pretender  appeared afterwards in the   
person of ,james ,metius of ,alkmaer1   
who is  mentioned by ,huyghens and ,des 
,cartes1 but his claims rest upon no    
authority whatever comparable to that   
which supports the other two4  ,about   
half a century afterwards1 ,borelli was 
at the pains to collect and  publish a  
number of letters and depositions which 
he procured1 as well  on one side as on 
the other4#da ,it seems that the truth  
lies between  them1 and that one1       
probably ,jansen1 was the inventor of   
the  microscope1 which application of   
the principle was unquestionably of  an 
earlier date1 perhaps as far back as    
#aeij4 ,jansen gave one of his          
microscopes to the ,archduke1 who gave  
it to ,cornelius ,drebbel1 a  salaried  
mathematician at the court of our ,james
 the first1 where  ,william ,borelli    
7not the author above mentioned7 saw it 
many years  afterwards1 when ambassador 
from the ,united ,provinces to ,england1
 and  got from ,drebbel this account of 

the quarter whence it came4 ,lipperhey  
afterwards1 in #afji1 accidentally hit  
upon the telescope1 and on the  fame of 
this discovery it would not be difficult
 for ,jansen1 already in  possession of 
an instrument so much resembling it1 to 
perceive the  slight difference between 
them1 and to construct a telescope      
independently of ,lipperhey1 so that    
each1 with some show of reason1  might  
claim the priority of the invention4 ,a 
notion of this kind  reconciles the     
testimony of many conflicting witnesses 
on the subject1  some of whom do not    
seem to distinguish very accurately     
whether the  telescope or microscope is 
the instrument to which their evidence  
refers4 ,borelli arrives at the         
conclusion1 that ,jansen was the        
inventor2  but not satisfied with this1 
he endeavours1 with a glaring partiality
  which makes his former determination  
suspicious1 to secure for him and  his  
son the more solid reputation of having 
anticipated ,galileo in the  useful     

employment of the invention4 ,he has    
however inserted in his  collections a  
letter from ,john the son of ,zacharias1
 in which ,john1  omitting all mention  
of his father1 speaks of his own        
observation of the  satellites of       
,jupiter1 evidently seeking to insinuate
 that they were  earlier than           
,galileo's2 and in this sense the letter
 has since been  quoted1#db although it 
appears from ,john's own deposition1    
preserved in  the same collection1 that 
at the time of their discovery he could 
not  have been more than six years old4 
,an oversight of this sort throws  doubt
 on the whole of the pretended          
observations1 and indeed the letter  has
 much the air of being the production of
 a person imperfectly  informed on the  
subject on which he writes1 and probably
 was compiled to  suit ,borelli's       
purposes1 which were to make ,galileo's 
share in the  invention appear as small 
as possible4    ,galileo himself gives a
 very intelligible account of the       

process of  reasoning1 by which he      
detected the secret4--,i argued in the  
following  manner4 ,the contrivance     
consists either of one glass or of      
more--one is  not sufficient1 since it  
must be either convex1 concave1 or      
plane2 the  last does not produce any   
sensible alteration in objects1 the     
concave  diminishes them3 it is true    
that the convex magnifies1 but it       
renders  them confused and indistinct2  
consequently1 one glass is insufficient 
to  produce the desired effect4         
,proceeding to consider two glasses1 and
  bearing in mind that the plane glass  
causes no change1 ,i determined that    
the instrument could not consist of the 
combination of a plane glass  with      
either of the other two4 ,i therefore   
applied myself to make  experiments on  
combinations of the two other kinds1 and
 thus obtained  that of which ,i was in 
search4 ,it has been urged against      
,galileo that1  if he really invented   
the telescope on theoretical principles1

 the same  theory ought at once to have 
conducted him to a more perfect         
instrument  than that which he at first 
constructed2#dc but it is plain1 from   
this  statement1 that he does not       
profess to have theorized beyond the    
determination of the species of glass   
which he should employ in his           
experiments1 and the rest of his        
operations he avows to have been purely 
empirical4 ,besides1 we must take into  
account the difficulty of grinding  the 
glasses1 particularly when fit tools    
were yet to be made1 and  something must
 be attributed to ,galileo's eagerness  
to bring his results  to the test of    
actual experiment1 without waiting for  
that improvement  which a longer delay  
might and did suggest4 ,galileo's       
language bears a  resemblance to the    
first passage which we quoted from      
,baptista ,porta1  sufficiently close to
 make it not improbable that he might be
 assisted  in his inquiries by some     
recollection of it1 and the same passage

 seems1  in like manner1 to have        
recurred to the mind of ,kepler1 as soon
 as he  heard of the invention4         
,galileo's telescope consisted of a     
plano-convex  and plano-concave lens1   
the latter nearest the eye1 distant from
 each  other by the difference of their 
focal lengths1 being1 in principle1     
exactly the same with the modern        
opera-glass4 ,he seems to have thought  
that the ,dutch glass was the same1 but 
this could not be the case1 if  the     
above quoted particular of the inverted 
weathercock1 which belongs  to most     
traditions of the story1 be correct2    
because it is the  peculiarity of this  
kind of telescope not to invert objects1
 and we  should be thus furnished with a
 demonstrative proof of the falsehood of
  ,fuccarius's insinuation3 in that case
 the ,dutch glass must have been        
similar to what was afterwards called   
the astronomical telescope1  consisting 
of two convex glasses distant from each 
other by the sum of  their focal        

lengths4 ,this supposition is not       
controverted by the fact1  that this    
sort of telescope was never employed by 
astronomers till long  afterwards2 for  
the fame of ,galileo's observations1 and
 the superior  excellence of the        
instruments constructed under his       
superintendence1  induced every one in  
the first instance to imitate his       
constructions as  closely as possible4  
,the astronomical telescope was however 
eventually  found to possess superior   
advantages over that which ,galileo     
imagined1  and it is on this latter     
principle that all modern refracting    
telescopes  are constructed2 the        
inversion being counteracted in those   
which are  intended for terrestrial     
observations1 by the introduction of a  
second  pair of similar glasses1 which  
restore the inverted image to its       
original position4 ,for further details 
on the improvements which have  been    
subsequently introduced1 and on the     
reflecting telescope1 which was  not    

brought into use till the latter part of
 the century1 the reader is  referred to
 the ,treatise on ,,optical             
,,instruments4    ,galileo1 about the   
same time1 constructed microscopes on   
the same  principle1 for we find that1  
in #afab1 he presented one to           
,sigismund1  ,king of ,poland2 but his  
attention being principally devoted to  
the  employment and perfection of his   
telescope1 the microscope remained a    
long time imperfect in his hands3 twelve
 years later1 in #afbd1 he wrote  to ,p4
 ,federigo ,cesi1 that he had delayed to
 send the microscope1 the use  of which 
he there describes1 because he had only 
just brought it to  perfection1 having  
experienced some difficulty in working  
the glasses4  ,schott tells an amusing  
story1 in his ,magic of ,nature1 of a   
,bavarian  philosopher1 who1 travelling 
in the ,tyrol with one of the newly     
invented  microscopes about him1 was    
taken ill on the road and died4 ,the    
authorities of the village took         

possession of his baggage1 and were     
proceeding to perform the last duties to
 his body1 when1 on examining  the      
little glass instrument in his pocket1  
which chanced to contain a  flea1 they  
were struck with the greatest           
astonishment and terror1 and  the poor  
,bavarian1 condemned by acclamation as a
 sorcerer who was in the  habit of using
 a portable familiar1 was declared      
unworthy of ,christian  burial4         
,fortunately for his character1 some    
bold sceptic ventured to  open the      
instrument1 and discovered the true     
nature of the imprisoned  fiend4    ,as 
soon as ,galileo's first telescope was  
completed1 he returned with it  to      
,venice1 and the extraordinary sensation
 which it excited tends also  strongly  
to refute ,fuccarius's assertion that   
the ,dutch glass was  already known     
there4 ,during more than a month        
,galileo's whole time was  employed in  
exhibiting his instrument to the        
principal inhabitants of  ,venice1 who  

thronged to his house to satisfy        
themselves of the truth of  the         
wonderful stories in circulation2 and at
 the end of that time the  ,doge1       
,leonardo ,donati1 caused it to be      
intimated to him that such a  present   
would not be deemed unacceptable by the 
senate4 ,galileo took the  hint1 and his
 complaisance was rewarded by a mandate 
confirming him for  life in his         
professorship at ,padua1 at the same    
time doubling his yearly  salary1 which 
was thus made to amount to #ajjj        
florins4    ,it was long before the     
phrenzy of public curiosity abated4     
,sirturi  describes a ludicrous violence
 which was done to himself1 when1 with  
the  first telescope which he had       
succeeded in making1 he went up into the
  tower of ,st4 ,mark1 at ,venice1 in   
the vain hope of being there entirely   
unmolested4 ,unluckily he was seen by   
some idlers in the street3 a crowd  soon
 collected round him1 who insisted on   
taking possession of his  instrument1   

and1 handing it one to the other1       
detained him there for  several hours   
till their curiosity was satiated1 when 
he was allowed to  return home4 ,hearing
 them also inquire eagerly at what inn  
he lodged1 he  thought it better to quit
 ,venice early the next morning1 and    
prosecute  his observations in a less   
inquisitive neighbourhood4#dd           
,instruments of  an inferior description
 were soon manufactured1 and vended     
every where  as philosophical           
playthings1 much in the way in which1 in
 our own time1  the kaleidoscope spread 
over ,europe as fast as travellers could
 carry  them4 ,but the fabrication of a 
better sort was long confined1 almost   
solely1 to ,galileo and those whom he   
immediately instructed2 and so late  as 
the year #afcg1 we find ,gaertner1 or as
 he chose to call himself1  ,hortensius1
 assuring ,galileo that none could be   
met with in ,holland  sufficiently good 
to show ,jupiter's disc well defined2   
and in #afcd  ,gassendi begs for a      

telescope from ,galileo1 informing him  
that he was  unable to procure a good   
one either in ,venice1 ,paris1 or       
,amsterdam4    ,the instrument1 on its  
first invention1 was generally known by 
the names  of ,galileo's tube1 the      
perspective1 the double eye-glass3 the  
names of  telescope and microscope were 
suggested by ,demisiano1 as we are told 
by  ,lagalla in his treatise on the     
,moon4#de      ,,footnotes3    #cb      
,mecanique ,analytique4    #cc ,histoire
 des ,mathmatiques1 tom4 ii4    #cd ,per
 duo specilla ocularia si quis          
perspiciat1 altero alteri  superposito1 
majora multo et propinquiora videbit    
omnia4--,fracast4  ,homocentrica1  #b1  
c4 #h4    #ce ,si utrumque recte        
componere noveris1 et longinqua et      
proxima majora  et clara videbis4--,mag4
 ,nat4 lib4 #ag4    #cf ,the passage in 
the original1 which is printed alike in 
the editions  of #aeih1 #afjg1 #afai1   
and #afej1 is as follows3 ,visus        
constituatur centro  valentissimus      

speculi1 ubi fiet1 et valentissim       
universales solares  radii disperguntur1
 et coeunt minim1 sed centro prdicti    
speculi in  illius medio1 ubi diametri  
transversales1 omnium ibi concursus4    
,constituitur hoc modo speculum concavum
 columnare quidistantibus  lateribus1   
sed lateri uno obliquo sectionibus illis
 accomodetur1  trianguli vero           
obtusianguli1 vel orthogonii secentur1  
hinc inde duobus  transversalibus       
lineis1 ex-centro eductis4 ,et confectum
 erit specillum1  ad id1 quod diximus   
utile4    #cg ,diximus de ,ptolemi      
speculo1 sive specillo potius1 quo per  
sexcentena millia pervenientes naves    
conspiciebat4    #ch ,il ,telescopio1   
#afbg4    #ci ,magia ,natur et ,artis   
,herbipoli1 #afeg4    #dj ,lettre       
d',uomini illustri4 ,venezia1 #agdd4    
#da ,borelli4 ,de vero ,telescopii      
inventore1 #afee4    #db ,encyclopdia   
,britannica4 ,art4 ,,telescope4    #dc  
,ibid4    #dd ,telescopium1 ,venetiis1  
#afai4    #de ,de phnomenis in orbe     

,lun4 ,venetiis1 #afab4                 
,,chapter ,,vii4        ,discovery of   
,jupiter's                              
satellites--,kepler--,sizzi--,astrologer
s--,mstlin--,horky--,mayer4      ,,as   
soon as ,galileo had provided himself   
with a second instrument1 he  began a   
careful examination of the heavenly     
bodies1 and a series of  splendid       
discoveries soon rewarded his diligence4
 ,after considering the  beautiful      
appearances which the varied surface of 
the moon presented to  this new         
instrument1 he turned his telescope     
towards ,jupiter1 and his  attention was
 soon arrested by the singular position 
of three small  stars1 near the body of 
that planet1 which appeared almost in a 
straight  line with it1 and in the      
direction of the ecliptic4 ,the         
following  evening he was surprised to  
find that two of the three which had    
been to  the eastward of the planet1 now
 appeared on the contrary side1 which he
  could not reconcile with the apparent 

motion of ,jupiter among the fixed      
stars1 as given by the tables4          
,observing these night after night1 he  
could not fail to remark that they      
changed their relative positions4 ,a    
fourth also appeared1 and in a short    
time he could no longer refuse to       
believe that these small stars were four
 moons1 revolving round ,jupiter  in the
 same manner in which our earth is      
accompanied by its single  attendant4   
,in honour of his patron ,cosmo1 he     
named them the ,medican  stars4 ,as they
 are now hardly known by this           
appellation1 his doubts1  whether he    
should call them ,medican1 after        
,cosmo's family1 or ,cosmical1  from his
 individual name1 are become of less    
interest4    ,an extract from a letter  
which ,galileo received on this occasion
 from  the court of ,france1 will serve 
to show how highly the honour of giving 
a name to these new planets was at that 
time appreciated1 and also how  much was
 expected from ,galileo's first success 

in examining the heavens4  ,the second  
request1 but the most pressing one which
 ,i can make to you1  is1 that you      
should determine1 if you discover any   
other fine star1 to  call it by the name
 of the great star of ,france1 as well  
as the most  brilliant of all the earth2
 and1 if it seems fit to you1 call it   
rather  by his proper name of ,henri1   
than by the family name of ,bourbon3    
thus  you will have an opportunity of   
doing a thing just and due and proper in
  itself1 and at the same time will     
render yourself and your family rich    
and powerful for ever4 ,the writer then 
proceeds to enumerate the  different    
claims of ,henri ,,iv4 to this honour1  
not forgetting that he  married into the
 family of the ,medici1 c4    ,the      
result of these observations was given  
to the world1 in an ,essay  which       
,galileo entitled ,nuncius ,sidereus1 or
 the ,intelligencer of the  ,stars2 and 
it is difficult to describe the         
extraordinary sensation which  its      

publication produced4 ,many doubted1    
many positively refused to  believe1 so 
novel an announcement2 all were struck  
with the greatest  astonishment1        
according to their respective opinions1 
either at the new  view of the universe 
thus offered to them1 or at the daring  
audacity of  ,galileo in inventing such 
fables4 ,we shall proceed to extract a  
few  passages from contemporary writers 
relative to this book1 and the          
discoveries announced in it4    ,kepler 
deserves precedence1 both from his own  
celebrity1 and from the  lively and     
characteristic account which he gives of
 his first receiving  the               
intelligence3--,i was sitting idle at   
home1 thinking of you1 most  excellent  
,galileo1 and your letters1 when the    
news was brought me of the  discovery of
 four planets by the help of the double 
eye-glass4  ,wachenfels stopped his     
carriage at my door to tell me1 when    
such a fit  of wonder seized me at a    
report which seemed so very absurd1 and 

,i was  thrown into such agitation at   
seeing an old dispute between us decided
  in this way1 that between his joy1 my 
colouring1 and the laughter of  both1   
confounded as we were by such a novelty1
 we were hardly capable1  he of         
speaking1 or ,i of listening4 ,my       
amazement was increased by the          
assertion of ,wachenfels1 that those who
 sent this news from ,galileo were      
celebrated men1 far removed by their    
learning1 weight1 and character1  above 
vulgar folly2 that the book was actually
 in the press1 and would  be published  
immediately4 ,on our separating1 the    
authority of ,galileo  had the greatest 
influence on me1 earned by the accuracy 
of his  judgment1 and excellence of his 
understanding2 so ,i immediately fell to
  thinking how there could be any       
addition to the number of the planets   
without overturning my ,mysterium       
,cosmographicum1 published thirteen     
years ago1 according to which ,euclid's 
five regular solids do not allow  more  

than six planets round the sun4    ,this
 was one of the many wild notions of    
,kepler's fanciful brain1 among  which  
he was lucky enough at length to hit    
upon the real and principal  laws of the
 planetary motions4 ,his theory may be  
briefly given in his  own words3--,the  
orbit of the earth is the measure of the
 rest4 ,about it  circumscribe a        
dodecahedron4 ,the sphere including this
 will be that of  ,mars4 ,about ,mars'  
orbit describe a tetrahedron3 the sphere
 containing  this will be ,jupiter's    
orbit4 ,round ,jupiter's describe a     
cube3 the  sphere including this will be
 ,saturn's4 ,within the earth's orbit   
inscribe an icosahedron3 the sphere     
inscribed in it will be ,venus's  orbit4
 ,in ,venus inscribe an octahedron3 the 
sphere inscribed in it will  be         
,mercury's4 ,you have now the reason of 
the number of the planets3 for  as there
 are no more than the five regular      
solids here enumerated1  ,kepler        
conceived this to be a satisfactory     

reason why there could be  neither more 
nor less than six planets4 ,his letter  
continues3--,i am so  far from          
disbelieving the existence of the four  
circumjovial planets1  that ,i long for 
a telescope to anticipate you1 if       
possible1 in  discovering two round     
,mars1 7as the proportion seems to me to
 require17  six or eight round ,saturn1 
and perhaps one each round ,mercury and 
,venus4    ,the reader has here an      
opportunity of verifying ,galileo's     
observation1  that ,kepler's method of  
philosophizing differed widely from his 
own4 ,the  proper line is certainly     
difficult to hit between the mere       
theorist and  the mere observer4 ,it is 
not difficult at once to condemn the    
former1  and yet the latter will deprive
 himself of an important1 and often     
indispensable assistance1 if he neglect 
from time to time to consolidate  his   
observations1 and thence to conjecture  
the course of future  observation most  
likely to reward his assiduity4 ,this   

cannot be more  forcibly expressed than 
in the words of ,leonardo da ,vinci3#df 
,theory  is the general1 experiments are
 the soldiers4 ,the interpreter of the  
works of nature is experiment2 that is  
never wrong2 it is our judgment  which  
is sometimes deceived1 because we are   
expecting results which  experiment     
refuses to give4 ,we must consult       
experiment1 and vary the  circumstances1
 till we have deduced general rules1 for
 it alone can  furnish us with them4    
,but you will ask1 what is the use of   
these general  rules8 ,i answer1 that   
they direct us in our inquiries into    
nature and  the operations of art4 ,they
 keep us from deceiving ourselves and   
others1  by promising ourselves results 
which we can never obtain4    ,in the   
instance before us1 it is well known    
that1 adopting some of the  opinions of 
,bruno and ,brutti1 ,galileo1 even      
before he had seen the  satellites of   
,jupiter1 had allowed the possibility of
 the discovery of  new planets2 and we  

can scarcely suppose that they had      
weakened his  belief in the probability 
of further success1 or discouraged him  
from  examining the other heavenly      
bodies4 ,kepler on the contrary had     
taken  the opposite side of the         
argument2 but no sooner was the fallacy 
of his  first position undeniably       
demonstrated1 than1 passing at once from
 one  extreme to the other1 he framed an
 unsupported theory to account for the  
number of satellites which were round   
,jupiter1 and for those which he        
expected to meet with elsewhere4 ,kepler
 has been styled the legislator  of the 
skies2 his laws were promulgated rather 
too arbitrarily1 and they  often failed1
 as all laws must do which are not drawn
 from a careful  observation of the     
nature of those who are to be governed  
by them4  ,astronomers have reason to be
 grateful for the theorems which he was 
the  first to establish2 but so far as  
regards the progress of the science of  
inductive reasoning1 it is perhaps to be

 regretted1 that the seventeen  years   
which he wasted in random and           
unconnected guesses should have been    
finally rewarded1 by discoveries        
splendid enough to shed deceitful       
lustre upon the method by which he      
arrived at them4    ,galileo himself    
clearly perceived the fallacious nature 
of these  speculations on numbers and   
proportions1 and has expressed his      
sentiments concerning them very         
unequivocally4 ,how great and common an 
error appears to me the mistake of those
 who persist in making their  knowledge 
and apprehension the measure of the     
apprehension and knowledge  of ,god2 as 
if that alone were perfect1 which they  
understand to be so4  ,but ,i1 on the   
contrary1 observe that ,nature has other
 scales of  perfection1 which we cannot 
comprehend1 and rather seem disposed to 
class among imperfections4 ,for         
instance1 among the relations of        
different numbers1 those appear to us   
most perfect which exist between        

numbers nearly related to each other2 as
 the double1 the triple1 the  proportion
 of three to two1 c42 those appear less 
perfect which exist  between numbers    
remote from1 and prime to each other2 as
 #aa to #g1 #ag to  #ac1 #ec to #cg1 c42
 and most imperfect of all do those     
appear which exist  between             
incommensurable quantities1 which by us 
are nameless and  inexplicable4         
,consequently1 if the task had been     
given to a man1 of  establishing and    
ordering the rapid motions of the       
heavenly bodies1  according to his      
notions of perfect proportions1 ,i doubt
 not that he  would have arranged them  
according to the former rational        
proportions2  but1 on the contrary1     
,god1 with no regard to our imaginary   
symmetries1  has ordered them in        
proportions not only incommeasurable and
 irrational1  but altogether            
inappreciable by our intellect4 ,a man  
ignorant of  geometry may perhaps       
lament1 that the circumference of a     

circle does not  happen to be exactly   
three times the diameter1 or in some    
other  assignable proportion to it1     
rather than such that we have not yet   
been  able to explain what the ratio    
between them is2 but one who has more   
understanding will know that if they    
were other than they are1 thousands  of 
admirable conclusions would have been   
lost1 and that none of the  other       
properties of the circle would have been
 true3 the surface of the  sphere would 
not be quadruple of a great circle1 nor 
the cylinder be to  the sphere as three 
to two3 in short1 no part of geometry   
would be true1  and as it now is4 ,if   
one of our most celebrated architects   
had had to  distribute this vast        
multitude of fixed stars through the    
great vault of  heaven1 ,i believe he   
would have disposed them with beautiful 
arrangements of squares1 hexagons1 and  
octagons2 he would have dispersed  the  
larger ones among the middle sized and  
the less1 so as to correspond  exactly  

with each other2 and then he would think
 he had contrived  admirable            
proportions3 but ,god1 on the contrary1 
has shaken them out  from ,his hand as  
if by chance1 and we1 forsooth1 must    
think that ,he has  scattered them up   
yonder without any regularity1 symmetry1
 and  elegance4    ,it is worth         
remarking that the dangerous ideas of   
aptitude and  congruence of numbers had 
taken such deep and general root1 that  
long  afterwards1 when the reality of   
,jupiter's satellites was incontestably 
established1 and ,huyghens had          
discovered a similar satellite near     
,saturn1 he was so rash as to declare   
his belief1 7unwarned by the vast       
progress which astronomy had made in his
 own time17 that no more  satellites    
would be discovered1 since the one which
 he discovered near  ,saturn1 with      
,jupiter's four1 and our moon1 made up  
the number six1  exactly equal to the   
number of the principal planets4 ,every 
reader knows  that this notion1 so      

unworthy the genius of ,huyghens1 has   
been since  exploded by the discovery   
both of new planets1 and new satellites4
    ,francesco ,sizzi1 a ,florentine    
astronomer1 took the matter up in a     
somewhat different strain from          
,kepler4#dg--,there are seven windows   
given to animals in the domicile of the 
head1 through which the air is  admitted
 to the rest of the tabernacle of the   
body1 to enlighten1 to  warm1 and       
nourish it1 which are the principal     
parts of the   7or little world72 two   
nostrils1 two eyes1 two ears1 and a     
mouth2 so in  the heavens1 as in a  7or 
great world71 there are two  favourable 
stars1 two unpropitious1 two luminaries1
 and ,mercury alone  undecided and      
indifferent4 ,from which and many other 
similar phenomena  of nature1 such as   
the seven metals1 c41 which it were     
tedious to  enumerate1 we gather that   
the number of planets is necessarily    
seven4  ,moreover1 the satellites are   
invisible to the naked eye1 and         

therefore  can exercise no influence on 
the earth1 and therefore would be       
useless1  and therefore do not exist4   
,besides1 as well the ,jews and other   
ancient  nations as modern ,europeans   
have adopted the division of the week   
into  seven days1 and have named them   
from the seven planets3 now if we       
increase the number of the planets this 
whole system falls to the  ground4 ,to  
these remarks ,galileo calmly replied1  
that whatever their  force might be1 as 
a reason for believing beforehand that  
no more than  seven planets would be    
discovered1 they hardly seemed of       
sufficient  weight to destroy the new   
ones when actually seen4    ,others1    
again1 took a more dogged line of       
opposition1 without venturing  into the 
subtle analogies and arguments of the   
philosopher just cited4  ,they contented
 themselves1 and satisfied others1 with 
the simple  assertion1 that such things 
were not1 and could not be1 and the     
manner  in which they maintained        

themselves in their incredulity was     
sufficiently ludicrous4 ,oh1 my dear    
,kepler1#dh says ,galileo1 how ,i  wish 
that we could have one hearty laugh     
together4 ,here1 at ,padua1 is  the     
principal professor of philosophy1 whom 
,i have repeatedly and  urgently        
requested to look at the moon and       
planets through my glass1  which he     
pertinaciously refuses to do4 ,why are  
you not here8 what shouts  of laughter  
we should have at this glorious folly6  
and to hear the  professor of philosophy
 at ,pisa labouring before the grand    
duke with  logical arguments1 as if with
 magical incantations1 to charm the new 
planets out of the sky4    ,another     
opponent of ,galileo deserves to be     
named1 were it only for the  singular   
impudence of the charge he ventures to  
bring against him4 ,we  are not to      
think1 says ,christmann1 in the         
,appendix to his ,nodus  ,gordius1 that 
,jupiter has four satellites given him  
by nature1 in  order1 by revolving round

 him1 to immortalize the name of the    
,medici1  who first had notice of the   
observation4 ,these are the dreams of   
idle  men1 who love ludicrous ideas     
better than our laborious and           
industrious  correction of the          
heavens4--,nature abhors so horrible a  
chaos1 and to  the truly wise such      
vanity is detestable4    ,galileo was   
also urged by the astrologers to        
attribute some influence1  according to 
their fantastic notions1 to the         
satellites1 and the account  which he   
gives his friend ,dini of his answer to 
one of this class is  well worth        
extracting1 as a specimen of his method 
of uniting sarcasm  with serious        
expostulation2 ,i must1 says he1 tell   
you what ,i said a  few days back to one
 of those nativity-casters1 who believe 
that ,god1  when he created the heavens 
and the stars1 had no thoughts beyond   
what  they can themselves conceive1 in  
order to free myself from his tedious   
importunity2 for he protested1 that     

unless ,i would declare to him the      
effect of the ,medican planets1 he would
 reject and deny them as  needless and  
superfluous4 ,i believe this set of men 
to be of ,sizzi's  opinion1 that        
astronomers discovered the other seven  
planets1 not by  seeing them corporally 
in the skies1 but only from their       
effects on  earth1--much in the manner  
in which some houses are discovered to  
be  haunted by evil spirits1 not by     
seeing them1 but from the extravagant   
pranks which are played there4 ,i       
replied1 that he ought to reconsider    
the hundred or thousand opinions which1 
in the course of his life1 he  might    
have given1 and particularly to examine 
well the events which he  had predicted 
with the help of ,jupiter1 and if he    
should find that all  had succeeded     
conformably to his predictions1 ,i bid  
him prophecy merrily  on1 according to  
his old and wonted rules2 for ,i assured
 him that the  new planets would not in 
any degree affect the things which are  

already  past1 and that in future he    
would not be a less fortunate conjuror  
than  he had been3 but if1 on the       
contrary1 he should find the events     
depending on ,jupiter1 in some trifling 
particulars not to have agreed  with his
 dogmas and prognosticating aphorisms1  
he ought to set to work  to find new    
tables for calculating the constitution 
of the four ,jovial  circulators at     
every bygone moment1 and1 perhaps1 from 
the diversity of  their aspects1 he     
would be able1 with accurate            
observations and  multiplied            
conjunctions1 to discover the           
alterations and variety of  influences  
depending upon them2 and ,i reminded    
him1 that in ages past  they had not    
acquired knowledge with little labour1  
at the expense of  others1 from written 
books1 but that the first inventors     
acquired the  most excellent knowledge  
of things natural and divine with study 
and  contemplation of the vast book     
which nature holds ever open before     

those  who have eyes in their forehead  
and in their brain2 and that it was a   
more honourable and praiseworthy        
enterprize with their own watching1     
toil1 and study1 to discover something  
admirable and new among the  infinite   
number which yet remain concealed in the
 darkest depths of  philosophy1 than to 
pass a listless and lazy existence1     
labouring only  to darken the toilsome  
inventions of their neighbours1 in order
 to  excuse their own cowardice and     
inaptitude for reasoning1 while they cry
  out that nothing can be added to the  
discoveries already made4    ,the       
extract given above from ,kepler1 is    
taken from an ,essay1 published  with   
the later editions of the ,nuncius1 the 
object and spirit of which  seem to have
 been greatly misunderstood1 even by    
some of ,kepler's  intimate             
friends4--,they considered it as a      
covert attack upon ,galileo1  and1      
accordingly1 ,maestlin thus writes to   
him3--,in your ,essay 7which ,i  have   

just received7 you have plucked         
,galileo's feathers well2 ,i mean1  that
 you have shown him not to be the       
inventor of the telescope1 not to  have 
been the first who observed the         
irregularities of the moon's  surface1  
not to have been the first discoverer of
 more worlds than the  ancients were    
acquainted with1 c4 ,one source of      
exultation was still  left him1 from the
 apprehension of which ,martin ,horky   
has now entirely  delivered me4 ,it is  
difficult to discover in what part of   
,kepler's book  ,maestlin found all     
this1 for it is one continued encomium  
upon ,galileo2  insomuch that ,kepler   
almost apologizes in the preface for    
what may seem  his intemperate          
admiration of his friend4 ,some might   
wish ,i had spoken  in more moderate    
terms in praise of ,galileo1 in         
consideration of the  distinguished men 
who are opposed to his opinions1 but ,i 
have written  nothing fulsome or        
insincere4 ,i praise him1 for myself2 ,i

 leave other  men's judgments free2 and 
shall be ready to join in condemnation  
when  some one wiser than myself shall1 
by sound reasoning1 point out his       
errors4 ,however1 ,maestlin was not the 
only one who misunderstood  ,kepler's   
intentions3 the ,martin ,horky of whom  
he speaks1 a young ,german1  also       
signalized himself by a vain attack upon
 the book which he thought  his patron  
,kepler condemned4 ,he was then         
travelling in ,italy1 whence he  wrote  
to ,kepler his first undetermined       
thoughts about the new  discoveries4    
,they are wonderful2 they are           
stupendous2 whether they are  true or   
false ,i cannot tell4#di ,he seems soon 
to have decided that  most reputation   
was to be gained on the side of         
,galileo's opponents1 and  his letters  
accordingly became filled with the most 
rancorous abuse of  him4 ,at the same   
time1 that the reader may appreciate    
,horky's own  character1 we shall quote 
a short sentence at the end of one of   

his  letters1 where he writes of a      
paltry piece of dishonesty with as great
  glee as if he had solved an ingenious 
and scientific problem4 ,after          
mentioning his meeting ,galileo at      
,bologna1 and being indulged with a     
trial of his telescope1 which1 he says1 
does wonders upon the earth1  but       
represents celestial objects falsely2#ej
 he concludes with the  following       
honourable sentence3--,i must confide to
 you a theft which ,i  committed4 ,i    
contrived to take a mould of the glass  
in wax1 without the  knowledge of any   
one1 and1 when ,i get home1 ,i trust to 
make a telescope  even better than      
,galileo's own4    ,horky having        
declared to ,kepler1 ,i will never      
concede his four new  planets to that   
,italian from ,padua though ,i die for  
it1 followed up  this declaration by    
publishing a book against ,galileo1     
which is the one  alluded to by         
,maestlin1 as having destroyed the      
little credit which1  according to his  

view1 ,kepler's publication had left    
him4 ,this book  professes to contain   
the examination of four principal       
questions  touching the alleged planets2
 #ast1 ,whether they exist8 #bnd1 ,what 
they  are8 #crd1 ,what they are like8   
#dth1 ,why they are8 ,the first question
 is  soon disposed of1 by ,horky's      
declaring positively that he has        
examined  the heavens with ,galileo's   
own glass1 and that no such thing as a  
satellite about ,jupiter exists4 ,to the
 second1 he declares solemnly1  that he 
does not more surely know that he has a 
soul in his body1 than  that reflected  
rays are the sole cause of ,galileo's   
erroneous  observations4 ,in regard to  
the third question1 he says1 that these 
planets are like the smallest fly       
compared to an elephant2 and1 finally1  
concludes on the fourth1 that the only  
use of them is to gratify  ,galileo's   
thirst of gold1 and to afford himself a 
subject of  discussion4#ea    ,galileo  
did not condescend to notice this       

impertinent folly2 it was  answered by  
,roffini1 a pupil of ,magini1 and by a  
young ,scotchman of the  name of        
,wedderburn1 then a student at ,padua1  
and afterwards a physician  at the      
,court of ,vienna4 ,in the latter reply 
we find it mentioned1 that  ,galileo was
 also using his telescope for the       
examination of insects1  c4#eb ,horky   
sent his performance triumphantly to    
,kepler1 and1 as he  returned home      
before receiving an answer1 he presented
 himself before  his patron in the same 
misapprehension under which he had      
written1 but  the philosopher received  
him with a burst of indignation which   
rapidly  undeceived him4 ,the conclusion
 of the story is characteristic enough  
to  be given in ,kepler's own account of
 the matter to ,galileo1 in which1      
after venting his wrath against this    
scum of a fellow1 whose  obscurity had  
given him audacity1 he says1 that ,horky
 begged so hard  to be forgiven1 that ,i
 have taken him again into favour upon  

this  preliminary condition1 to which he
 has agreed3--that ,i am to shew him    
,jupiter's satellites1 ,,and ,,he ,,is  
,,to ,,see ,,them1 and own that they are
  there4    ,in the same letter ,kepler 
writes1 that although he has himself    
perfect  confidence in the truth of     
,galileo's assertions1 yet he wishes he 
could  furnish him with some            
corroborative testimonies1 which ,kepler
 could  quote in arguing the point with 
others4 ,this request produced the      
following reply1 from which the reader  
will also learn the new change  which   
had now taken place in ,galileo's       
fortunes1 the result of the             
correspondence with ,florence1 part of  
which we have already  extracted4#ec ,in
 the first place1 ,i return you my      
thanks that you  first1 and almost      
alone1 before the question had been     
sifted 7such is  your candour and the   
loftiness of your mind71 put faith in my
  assertions4 ,you tell me you have some
 telescopes1 but not sufficiently  good 

to magnify distant objects with         
clearness1 and that you anxiously       
expect a sight of mine1 which magnifies 
images more than a thousand  times4 ,it 
is mine no longer1 for the ,grand ,duke 
of ,tuscany has asked it  of me1 and    
intends to lay it up in his museum1     
among his most rare and  precious       
curiosities1 in eternal remembrance of  
the invention3 ,i have  made no other of
 equal excellence1 for the mechanical   
labour is very  great3 ,i have1 however1
 devised some instruments for figuring  
and  polishing them which ,i am         
unwilling to construct here1 as they    
could not  conveniently be carried to   
,florence1 where ,i shall in future     
reside4 ,you  ask1 my dear ,kepler1 for 
other testimonies3--,i produce1 for one1
 the  ,grand ,duke1 who1 after observing
 the ,medican planets several times with
  me at ,pisa during the last months1   
made me a present1 at parting1 worth    
more than a thousand florins1 and has   
now invited me to attach myself to  him 

with the annual salary of one thousand  
florins1 and with the title  of         
,philosopher and ,principal             
,mathematician to ,his ,highness2       
without the  duties of any office to    
perform1 but with the most complete     
leisure2 so  that ,i can complete my    
,treatises on ,mechanics1 on the        
,constitution of  the ,universe1 and on 
,natural and ,violent ,local ,motion1 of
 which ,i have  demonstrated            
geometrically many new and admirable    
phenomena4 ,i produce1  for another     
witness1 myself1 who1 although already  
endowed in this  college with the noble 
salary of one thousand florins1 such as 
no  professor of mathematics ever before
 received1 and which ,i might  securely 
enjoy during my life1 even if these     
planets had deceived me and  should     
disappear1 yet quit this situation1 and 
betake me where want and  disgrace will 
be my punishment should ,i prove to have
 been mistaken4    ,it is difficult not 
to regret that ,galileo should be thus  

called on to  resign his best glasses1  
but it appears probable that on becoming
 more  familiar with the ,grand ,duke1  
he ventured to suggest that this        
telescope  would be more advantageously 
employed in his own hands1 than         
pompously  laid up in a museum2 for in  
#afcg we find him saying1 in answer to a
  request from his friend ,micanzio to  
send him a telescope--,i am sorry  that 
,i cannot oblige you with the glasses   
for your friend1 but ,i am no  longer   
capable of making them1 and ,i have just
 parted with two tolerably  good ones   
which ,i had1 reserving only my old     
discoverer of celestial  novelties which
 is already promised to the ,grand      
,duke4 ,cosmo was dead  in #afcg1 and it
 is his son ,ferdinand who is here      
meant1 who appears to  have inherited   
his father's love of science4 ,galileo  
tells us1 in the  same letter1 that     
,ferdinand had been amusing himself for 
some months  with making object-glasses1
 and always carried one with him to work

 at  wherever he went4    ,when         
forwarding this telescope to ,cosmo in  
the first instance1 ,galileo  adds1 with
 a very natural feeling--,i send it to  
his highness unadorned  and unpolished1 
as ,i made it for my own use1 and beg   
that it may always  be left in the same 
state2 for none of the old parts ought  
to be  displaced to make room for new   
ones1 which will have had no share in   
the  watchings and fatigues of these    
observations4 ,a telescope was in       
existence1 though with the object glass 
broken1 at the end of the last  century1
 and probably still is in the ,museum at
 ,florence1 which was  shewn as the     
discoverer of ,jupiter's satellites4    
,nelli1 on whose  authority this is     
mentioned1 appears to question its      
genuineness4 ,the  first reflecting     
telescope1 made with ,newton's own      
hands1 and scarcely  possessing less    
interest than the first of ,galileo's1  
is preserved in  the library of the     
,royal ,society4    ,by degrees the     

enemies of ,galileo and of the new stars
 found it  impossible to persevere in   
their disbelief1 whether real or        
pretended1  and at length seemed        
resolved to compensate for the          
sluggishness of  their perception1 by   
its acuteness when brought into action4 
,simon ,mayer  published his ,mundus    
,jovialis in #afad1 in which he claims  
to have been  an original observer of   
the satellites1 but1 with an affectation
 of  candour1 allows that ,galileo      
observed them probably about the same   
time4  ,the earliest observation which  
he has recorded is dated #bith          
,december1  #afji1 but1 not to mention  
the total want of probability that      
,mayer would  not have immediately      
published so interesting a discovery1 it
 is to be  observed1 that1 as he used   
the old style1 this date of #bith       
,december  agrees with the #hth         
,january1 #afaj1 of the new style1 which
 was the date  of ,galileo's second     
observation1 and ,galileo ventured to   

declare his  opinion1 that this         
pretended observation was in fact a     
plagiarism4    ,scheiner counted five1  
,rheita nine1 and other observers1 with 
increasing  contempt for ,galileo's     
imperfect announcements1 carried the    
number as  high as twelve4#ed ,in       
imitation of ,galileo's nomenclature1   
and to  honour the sovereigns of the    
respective observers1 these supposed    
additional satellites were dignified    
with the names of ,vladislavian1        
,agrippine1 ,urbanoctavian1 and         
,ferdinandotertian planets2 but a very  
short time served to show it was as     
unsafe to exceed as to fall short of    
the number which ,galileo had fixed     
upon1 for ,jupiter rapidly removed      
himself from the neighbourhood of the   
fixed stars1 which gave rise to  these  
pretended discoveries1 carrying with him
 only his four original  attendants1    
which continued in every part of his    
orbit to revolve  regularly about him4  
,perhaps we cannot better wind up this  

account of the discovery of  ,jupiter's 
satellites1 and of the intense interest 
they have at all times  inspired1 than  
in the words of one who inherits a name 
worthy to be  ranked with that of       
,galileo in the list of astronomical    
discoverers1 and  who takes his own     
place among the most accomplished       
mathematicians of  the present times4   
,the discovery of these bodies was one  
of the first  brilliant results of the  
invention of the telescope2 one of the  
first  great facts which opened the eyes
 of mankind to the system of the        
universe1 which taught them the         
comparative insignificance of their own 
planet1 and the superior vastness and   
nicer mechanism of those other  bodies1 
which had before been distinguished from
 the stars only by their  motion1 and   
wherein none but the boldest thinkers   
had ventured to  suspect a community of 
nature with our own globe4 ,this        
discovery gave  the holding turn to the 
opinions of mankind respecting the      

,copernican  system2 the analogy        
presented by these little bodies 7little
 however  only in comparison with the   
great central body about which they     
revolve7  performing their beautiful    
revolutions in perfect harmony and order
  about it1 being too strong to be      
resisted4 ,this elegant system was      
watched with all the curiosity and      
interest the subject naturally          
inspired4 ,the eclipses of the          
satellites speedily attracted attention1
  and the more when it was discerned1 as
 it speedily was1 by ,galileo  himself1 
that they afforded a ready method of    
determining the difference  of          
longitudes of distant places on the     
earth's surface1 by observations  of the
 instants of their disappearances and   
reappearances1  simultaneously made4    
,thus the first astronomical solution of
 the great  problem of the longitude1   
the first mighty step which pointed out 
a  connection between speculative       
astronomy and practical utility1 and    

which1 replacing the fast dissipating   
dreams of astrology by nobler  visions1 
showed how the stars might really1 and  
without fiction1 be  called arbiters of 
the destinies of empires1 we owe to the 
satellites of  ,jupiter1 those atoms    
imperceptible to the naked eye1 and     
floating like  motes in the beam of     
their primary--itself an atom to our    
sight1 noticed  only by the careless    
vulgar as a large star1 and by the      
philosophers of  former ages as         
something moving among the stars1 they  
knew not what1 nor  why3 perhaps only to
 perplex the wise with fruitless        
conjectures1 and  harass the weak with  
fears as idle as their theories4#ee     
,,footnotes3    #df ,venturi4 ,essai sur
 les ouvrages de ,leo4 da ,vinci4    #dg
 ,dianoia ,astronomica1 ,venetiis1      
#afaj4    #dh ,kepleri ,epistol4    #di 
,kepleri ,epistol4    #ej ,it may seem  
extraordinary that any one could support
 an argument by  this partial disbelief 
in the instrument1 which was allowed on 

all hands  to represent terrestrial     
objects correctly4 ,a similar instance  
of  obstinacy1 in an almost identical   
case though in a more unpretending      
station1 once came under the writer's   
own observation4 ,a farmer in           
,cambridgeshire1 who had acquired some  
confused notions of the use of the      
quadrant1 consulted him on a new method 
of determining the distances and        
magnitudes of the sun and moon1 which he
 declared were far different  from the  
quantities usually assigned to them4    
,after a little  conversation1 the root 
of his error1 certainly sufficiently    
gross1  appeared to be that he had      
confounded the angular measure of a     
degree1  with #fi miles1 the linear     
measure of a degree on the earth's      
surface4  ,as a short way of showing his
 mistake1 he was desired to determine1  
in  the same manner1 the height of his  
barn which stood about #cj yards        
distant2 he lifted the quadrant to his  
eye1 but perceiving1 probably1  the     

monstrous size to which his principles  
were forcing him1 he said1  ,oh1 ,sir1  
the quadrant's only true for the sky4   
,he must have been an  objector of this 
kind1 who said to ,galileo1--,oh1 ,sir1 
the telescope's  only true for the      
earth4    #ea ,venturi4    #eb ,quatuor 
probl4 confut4 per ,j4 ,wedderbornium1  
,scotobritannum4  ,patavii1 #afaj4      
#ec ,see page #ah4    #ed ,sherburne's  
,sphere of ,manilius4 ,london1 #afge4   
#ee ,herschel's ,address to the         
,astronomical ,society1 #ahbg4          
,,chapter ,,viii4        ,observations  
on the                                  
,moon--,nebul--,saturn--,venus--,mars4  
,,there were other discoveries announced
 in ,galileo's book of great and        
unprecedented importance1 and which     
scarcely excited less discussion  than  
the controverted ,medican planets4 ,his 
observations on the moon  threw         
additional light on the constitution of 
the solar system1 and  cleared up the   
difficulties which encumbered the       

explanation of the  varied appearance of
 her surface4 ,the different theories   
current at that  day1 to account for    
these phenomena1 are collected and      
described by  ,benedetti1 and also with 
some liveliness1 in a mythological poem1
 by  ,marini4#ef ,we are told1 that1 in 
the opinion of some1 the dark shades  on
 the moon's surface arise from the      
interposition of opaque bodies  floating
 between her and the sun1 which prevents
 his light from reaching  those parts3  
others thought1 that on account of her  
vicinity to the  earth1 she was partly  
tainted with the imperfection of our    
terrestrial  and elementary nature1 and 
was not of that entirely pure and       
refined  substance of which the more    
remote heavens consist3 a third party   
looked  on her as a vast mirror1 and    
maintained that the dark parts of her   
surface were the reflected images of our
 earthly forests and mountains4         
,galileo's glass taught him to believe  
that the surface of this planet1  far   

from being smooth and polished1 as was  
generally taken for granted1  really    
resembled our earth in its structure2 he
 was able distinctly to  trace on it the
 outlines of mountains and other        
inequalities1 the  summits of which     
reflected the rays of the sun before    
these reached the  lower parts1 and the 
sides of which1 turned from his beams1  
lay buried  in deep shadow4 ,he         
recognised a distribution into something
 similar to  continents of land1 and    
oceans of water1 which reflect the sun's
 light  to us with greater or less      
vivacity1 according to their            
constitution4  ,these conclusions were  
utterly odious to the ,aristotelians2   
they had  formed a preconceived notion  
of what the moon ought to be1 and they  
loathed the doctrines of ,galileo1 who  
took delight1 as they said1 in          
distorting and ruining the fairest works
 of nature4 ,it was in vain he  argued1 
as to the imaginary perfection of the   
spherical form1 that  although the moon1

 or the earth1 were it absolutely       
smooth1 would indeed  be a more perfect 
sphere than in its present rough state1 
yet touching  the perfection of the     
earth1 considered as a natural body     
calculated for  a particular purpose1   
every one must see that absolute        
smoothness and  sphericity would make it
 not only less perfect1 but as far from 
being  perfect as possible4 ,what else1 
he demanded1 would it be but a vast     
unblessed desert1 void of animals1 of   
plants1 of cities and of men2 the  abode
 of silence and inaction2 senseless1    
lifeless1 soulless1 and stript  of all  
those ornaments which make it now so    
various and so beautiful8    ,he        
reasoned to no purpose with the slaves  
of the ancient schools3  nothing could  
console them for the destruction of     
their smooth  unalterable surface1 and  
to such an absurd length was this       
hallucination  carried1 that one        
opponent of ,galileo1 ,lodovico delle   
,colombe1  constrained to allow the     

evidence of the sensible inequalities of
 the  moon's surface1 attempted to      
reconcile the old doctrine with the new 
observations1 by asserting1 that every  
part of the moon1 which to the          
terrestrial observer appeared hollow and
 sunken1 was in fact entirely  and      
exactly filled up with a clear crystal  
substance1 perfectly  imperceptible by  
the senses1 but which restored to the   
moon her  accurately spherical and      
smooth surface4 ,galileo met the        
argument in the  manner most fitting1   
according to one of ,aristotle's own    
maxims1 that  it is foolish to refute   
absurd opinions with too much curiosity4
  ,truly1 says he1 the idea is          
admirable1 its only fault is that it is 
neither demonstrated nor demonstrable2  
but ,i am perfectly ready to  believe   
it1 provided that1 with equal courtesy1 
,i may be allowed to  raise upon your   
smooth surface1 crystal mountains 7which
 nobody can  perceive7 ten times higher 
than those which ,i have actually seen  

and  measured4 ,by threatening to       
proceed to such extremities1 he seems to
  have scared the opposite party into   
moderation1 for we do not find that  the
 crystalline theory was persevered in4  
,in the same essay1 ,galileo also       
explained at some length the cause of   
that part of the moon being visible1    
which is unenlightened directly by  the 
sun in her first and last quarter4      
,maestlin1 and before him ,leonardo  da 
,vinci1 had already declared this to    
arise from what may be called           
earthshine1 or the reflection of the    
sun's light from the terrestrial  globe1
 exactly similar to that which the moon 
affords us when we are  similarly placed
 between her and the sun2 but the notion
 had not been  favourably received1     
because one of the arguments against the
 earth  being a planet1 revolving like  
the rest round the sun1 was1 that it did
  not shine like them1 and was therefore
 of a different nature2 and this        
argument1 weak as it was in itself1 the 

theory of terrestrial reflection        
completely overturned4 ,the more popular
 opinions ascribed this feeble  light1  
some to the fixed stars1 some to ,venus1
 some to the rays of the  sun1          
penetrating and shining through the     
moon4 ,even the sagacious  ,benedetti   
adopted the notion of this light being  
caused by ,venus1 in the  same sentence 
in which he explains the true reason of 
the faint light  observed during a total
 eclipse of the moon1 pointing out that 
it is  occasioned by those rays of the  
sun1 which reach the moon1 after being  
bent round the sides of the earth by the
 action of our atmosphere4#eg           
,galileo also announced the detection of
 innumerable stars1 invisible to  the   
unassisted sight2 and those remarkable  
appearances in the heavens1  generally  
called nebul1 the most considerable of  
which is familiar to  all under the name
 of the milky way1 when examined by his 
instrument1  were found to resolve      
themselves into a vast collection of    

minute stars1  too closely congregated  
to produce a separate impression upon   
the  unassisted eye4#eh ,benedetti1 who 
divined that the dark shades on the     
moon's surface arose from the           
constitution of those parts which       
suffered  much of the light to pass into
 them1 and consequently reflected a less
  portion of it1 had maintained that the
 milky way was the result of the        
converse of the same phenomenon1 and    
declared1 in the language of his        
astronomy1 that it was a part of the    
eighth orb1 which did not1 like the     
rest1 allow the sun's light to traverse 
it freely1 but reflected a small  part  
feebly to our sight4    ,the            
,anti-,copernicans would probably have  
been well pleased1 if by these          
eternally renewed discussions and       
disputes1 they could have occupied      
,galileo's time sufficiently to detain  
his attention from his telescope  and   
astronomical observations2 but he knew  
too well where his real  strength lay1  

and they had scarcely time to compound  
any thing like an  argument against him 
and his theories1 before they found him 
in  possession of some new facts1 which 
they were unprepared to meet1  otherwise
 than by the never-failing resource of  
abuse and affected  contempt4 ,the year 
had not expired before ,galileo had new 
intelligence  to communicate of the     
highest importance4 ,perhaps he had been
 taught  caution from the numerous      
piracies which had been committed upon  
his  discoveries1 and he first announced
 his new discoveries enigmatically1     
veiling their real import by            
transpositions of the letters in the    
words  which described them1 7a practice
 then common1 and not disused even at a 
much later date17 and inviting all      
astronomers to declare1 within a        
certain time1 if they had noted any     
thing new in the heavens worthy of      
observation4 ,the transposed letters    
which he published were--               
,smaismrmilme poeta leumi bvne          

nugttaviras4    ,kepler1 in the true    
spirit of his riddling philosophy1      
endeavoured to  decypher the meaning1   
and fancied he had succeeded when he    
formed a  barbarous ,latin verse1       
,salve umbistineum geminatum ,martia    
proles1    conceiving that the          
discovery1 whatever it might be1 related
 to the  planet ,mars1 to which         
,kepler's attention had before been     
particularly  directed4 ,the reader1    
however1 need not weary himself in      
seeking a  translation of this solution1
 for at the request of the ,emperor     
,rodolph1  ,galileo speedily sent to him
 the real reading--        ,altissimum  
planetam tergeminum observavi2    that  
is1 ,i have observed that the most      
distant planet is triple1 or1  as he    
further explains the matter1 ,i have    
with great admiration  observed that    
,saturn is not a single star1 but three 
together1 which as  it were touch each  
other2 they have no relative motion1 and
 are  constituted in this form ,symbol3 

o,oo the middle being somewhat larger   
than the lateral ones4 ,if we examine   
them with an eye-glass which  magnifies 
the surface less than #ajjj times1 the  
three stars do not  appear very         
distinctly1 but ,saturn has an oblong   
appearance1 like the  appearance of an  
olive1 thus ,symbol3 horizontal #j4 ,now
 ,i have  discovered a court for        
,jupiter1 and two servants for this old 
man1 who  aid his steps and never quit  
his side4 ,galileo was1 however1 no     
match  in this style of writing for     
,kepler1 who disapproved his friend's   
metaphor1 and1 in his usual fanciful and
 amusing strain1--,i will not1  said he1
 make an old man of ,saturn1 nor slaves 
of his attendant globes1  but rather let
 this tricorporate form be ,geryon1 so  
shall ,galileo be  ,hercules1 and the   
telescope his club2 armed with which1 he
 has conquered  that distant planet1 and
 dragged him from the remotest depths of
 nature1  and exposed him to the view of
 all4 ,galileo's glass was not of       

sufficient power to shew him the real   
constitution of this extraordinary      
planet2 it was reserved for ,huyghens1  
about the year #afef1 to declare to  the
 world that these supposed attendant    
stars are in fact part of a ring  which 
surrounds1 and yet is completely        
distinct from the body of  ,saturn2#ei  
and the still more accurate observations
 of ,herschel have  ascertained that it 
consists of two concentric rings        
revolving round the  planet1 and        
separated from each other by a space    
which our most powerful  telescopes     
scarcely enable us to measure4          
,galileo's second statement concluded   
with the remark1 that in the other      
planets nothing new was to be observed2 
but a month had scarcely  elapsed1      
before he communicated to the world     
another enigma1        ,hc immatura  me 
jam frustra leguntur oy1    which1 as he
 said1 contained the announcement of a  
new phenomenon1 in  the highest degree  
important to the truth of the           

,copernican system4 ,the  interpretation
 of this is1        ,cynthi figuras     
mulatur mater amorum1    that is to     
say1--,venus rivals the appearances of  
the moon--for ,venus  being now arrived 
at that part of her orbit in which she  
is placed  between the earth and the    
sun1 and consequently1 with only a part 
of her  enlightened surface turned      
towards the earth1 the telescope shewed 
her  in a crescent form1 like the moon  
in a similar position1 and tracing her  
through the whole of her orbit round the
 sun1 or at least so long as she  was   
not invisible from his overpowering     
light1 ,galileo had the  satisfaction of
 seeing the enlightened portion in each 
position assume  the form appropriate to
 that hypothesis4 ,it was with reason1  
therefore1  that he laid stress on the  
importance of this observation1 which   
also  established another doctrine      
scarcely less obnoxious to the          
,anti-,copernicans1 namely1 that a new  
point of resemblance was here found     

between the earth and one of the        
principal planets2 and as the           
reflection from the earth upon the moon 
had shewn it to be luminous like  the   
planets when subjected to the rays of   
the sun1 so this change of  apparent    
figure demonstrated that one of the     
planets not near the earth1  and        
therefore probably all1 were in their   
own nature not luminous1 and  only      
reflected the sun's light which fell    
upon them2 an inference1 of  which the  
probability was still farther increased 
a few years later by  the observation of
 the transit of ,mercury over the sun's 
disc4    ,it is curious that only       
twenty-five years before this discovery 
of the  phases 7or appearances7 of      
,venus1 a commentator of ,aristotle1    
under the  name of ,lucillus            
,philalthus1 had advanced the doctrine  
that all the  planets except the moon   
are luminous of themselves1 and in proof
 of his  assertion had urged1 that if   
the other planets and fixed stars       

received  their light from the sun1 they
 would1 as they approached and receded  
from him1 or as he approached and       
receded from them1 assume the same      
phases as the moon1 which1 he adds1 we  
have never yet observed4--,he  further  
remarks1 that ,mercury and ,venus would1
 in the supposed case of  their being   
nearer the earth than the sun1 eclipse  
it occasionally1 just  as eclipses are  
occasioned by the moon4 ,perhaps it is  
still more  remarkable1 that these very 
passages1 in which the reasoning is so  
correct1 though the facts are too       
hastily taken for granted1 7the common  
error of that school17 are quoted by    
,benedetti1 expressly to shew the       
ignorance and presumption of the author4
 ,copernicus1 whose want of  instruments
 had prevented him from observing the   
horned appearance of  ,venus when       
between the earth and sun1 had perceived
 how formidable an  obstacle the        
non-appearance of this phenomenon       
presented to his system2  he            

endeavoured1 though unsatisfactorily1 to
 account for it by supposing  that the  
rays of the sun passed freely through   
the body of the planet1  and ,galileo   
takes occasion to praise him for not    
being deterred from  adopting the       
system1 which1 on the whole1 appeared to
 agree best with  the phenomena1 by     
meeting with some which it did not      
enable him to  explain4 ,milton1 whose  
poem is filled with allusions to        
,galileo and his  astronomy1 has not    
suffered this beautiful phenomenon to   
pass unnoticed4  ,after describing the  
creation of the ,sun1 he adds3--        
,hither1 as to their fountain1 other    
stars      ,repairing1 in their golden  
urns draw light1      ,and hence the    
morning planet gilds her horns4#fj      
,galileo also assured himself1 at the   
same time1 that the fixed stars did  not
 receive their light from the sun4 ,this
 he ascertained by comparing  the       
vividness of their light1 in all        
positions1 with the feebleness of  that 

of the distant planets1 and by observing
 the different degrees of  brightness   
with which all the planets shone at     
different distances from  the sun4 ,the 
more remote planets did not1 of course1 
afford equal  facilities with ,venus for
 so decisive an observation2 but        
,galileo  thought he observed1 that when
 ,mars was in quadratures1 7or in the   
quarters1 the middle points of his path 
on either side17 his figure  varied     
slightly from a perfect circle4 ,galileo
 concludes the letter1 in  which he     
announces these last observations to his
 pupil ,castelli1 with  the following   
expressions1 shewing how justly he      
estimated the  opposition they          
encountered3--,you almost make me laugh 
by saying that  these clear observations
 are sufficient to convince the most    
obstinate3  it seems you have yet to    
learn that long ago the observations    
were  enough to convince those who are  
capable of reasoning1 and those who     
wish to learn the truth2 but that to    

convince the obstinate1 and those  who  
care for nothing beyond the vain        
applause of the stupid and  senseless   
vulgar1 not even the testimony of the   
stars would suffice1  were they to      
descend on earth to speak for           
themselves4 ,let us then  endeavour to  
procure some knowledge for ourselves1   
and rest contented  with this sole      
satisfaction2 but of advancing in       
popular opinion1 or  gaining the assent 
of the book-philosophers1 let us abandon
 both the  hope and the desire4         
,,footnotes3    #ef ,adone di ,marini1  
,venetiis1 #afbc1 ,cant4 x4    #eg      
,speculat4 ,lib ,venetiis1 #aehe1       
,epistol4    #eh ,this opinion1 with    
respect to the milky way1 had been held 
by some  of the ancient astronomers4    
,see ,manilius4 ,lib4 i4 v4 #gec4       
,anne magis dens stellarum turba coron  
,contexit flammas1 et crasso lumine     
candet1    ,et fulgore nitet collato    
clarior orbis4    #ei ,huyghens         
announced his discovery in this form3 a 

a a a a a a c c c  c c d e e e e e g h i
 i i i i i i l l l l m m n n n n n n n n
 n o o o o  p p q r r s t t t t t u u u 
u u1 which he afterwards recomposed into
  the sentence4 ,annulo cingitur1 tenui1
 plano1 nusquam cohrente1 ad  eclipticam
 inclinato4 ,de ,saturni ,lun4 ,hag1    
#afef4    #fj ,b4 vii4 v4 #cfd4 ,other  
passages may be examined in ,b4 i4 #bhf2
 iii4  #efe-eij1 #gbb-gcc2 iv4 #ehi2 v4 
#bfa1 #dad2 vii4 #egg2 viii4 #a-agh4    
,,chapter ,,ix4        ,account of the  
,academia ,lincea--,del ,cimento--,royal
 ,society4      ,,galileo',s resignation
 of the mathematical professorship at   
,padua  occasioned much dissatisfaction 
to all those who were connected with    
that university4 ,perhaps not fully     
appreciating his desire of returning  to
 his native country1 and the importance 
to him and to the scientific  world in  
general1 of the complete leisure which  
,cosmo secured to him at  ,florence1    
7for by the terms of his diploma he was 
not even required to  reside at ,pisa1  

nor to give any lectures1 except on     
extraordinary  occasions1 to sovereign  
princes and other strangers of          
distinction17 the  ,venetians remembered
 only that they had offered him an      
honourable asylum  when almost driven   
from ,pisa2 that they had increased his 
salary to four  times the sum which any 
previous professor had enjoyed2 and1    
finally1 by  an almost unprecedented    
decree1 that they had but just secured  
him in  his post during the remainder of
 his life4 ,many took such offence as to
  refuse to have any further            
communication with him2 and ,sagredo1 a 
constant friend of ,galileo1 wrote him  
word that he had been threatened  with a
 similar desertion unless he should     
concur in the same peremptory           
resolution1 which threats1 however1     
,sagredo1 at the same time1 intimates   
his intention of braving4    ,early in  
the year #afaa1 ,galileo made his first 
appearance in ,rome1 where  he was      
received with marks of distinguished    

consideration1 and where all  ranks were
 eager to share the pleasure of         
contemplating the new  discoveries4     
,whether we consider cardinal1 prince1  
or prelate1 he found  an honourable     
reception from them all1 and had their  
palaces as open and  free to him as the 
houses of his private friends4#fa ,among
 other  distinctions he was solicited to
 become a member of the newly-formed    
philosophical society1 the once         
celebrated ,academia ,lincea1 to which  
he readily assented4 ,the founder of    
this society was ,federigo ,cesi1 the   
,marchese di ,monticelli1 a young ,roman
 nobleman1 the devotion of whose  time  
and fortune to the interests of science 
has not been by any means  rewarded with
 a reputation commensurate with his     
deserts4 ,if the energy  of his mind had
 been less worthily employed than in    
fostering the cause  of science and     
truth1 and in extending the advantages  
of his birth and  fortune to as many as 
were willing to co-operate with him1 the

 name of  ,federigo ,cesi might have    
appeared more prominently on the page of
  history4 ,cesi had scarcely completed 
his #ahth year1 when1 in #afjc1 he      
formed the plan of a philosophical      
society1 which in the first instance    
consisted only of himself and three of  
his most intimate friends1 ,hecke1  a   
,flemish physician1 ,stelluti1 and      
,anastasio de ,filiis4 ,cesi's father1  
the ,duca d',acquasparta1 who was of an 
arbitrary and extravagant temper1       
considered such pursuits and associates 
as derogatory to his son's rank2  he    
endeavoured to thwart the design by the 
most violent and  unjustifiable         
proceedings1 in consequence of which1   
,cesi in the  beginning of #afje        
privately quitted ,rome1 ,hecke was     
obliged to leave  ,italy altogether from
 fear of the ,inquisition1 which was    
excited against  him1 and the academy   
was for a time virtually dissolved4 ,the
 details of  these transactions are     
foreign to the present narrative3 it    

will be  enough to mention that1 in     
#afji1 ,cesi1 who had never altogether  
abandoned his scheme1 found the         
opposition decaying which he at first   
experienced1 and with better success he 
renewed the plan which he had  sketched 
six years before4 ,a few extracts from  
the ,regulations will  serve to shew the
 spirit in which this distinguished     
society was  conceived3--    ,the       
,lyncean ,society desires for its       
academicians1 philosophers eager  for   
real knowledge1 who will give themselves
 to the study of nature1 and  especially
 to mathematics2 at the same time it    
will not neglect the  ornaments of      
elegant literature and philology1 which 
like a graceful  garment adorn the whole
 body of science4--,in the pious love of
 wisdom1  and to the praise of the most 
good and most high ,god1 let the        
,lynceans  give their minds1 first to   
observation and reflection1 and         
afterwards to  writing and              
publishing4--,it is not within the      

,lyncean plan to find  leisure for      
recitations and declamatory assemblies2 
the meetings will  neither be frequent  
nor full1 and chiefly for transacting   
the necessary  business of the society3 
but those who wish to enjoy such        
exercises will  in no respect be        
hindered1 provided they attend them as  
accessory  studies1 decently and        
quietly1 and without making promises and
  professions of how much they are about
 to do4 ,for there is ample             
philosophical employment for every one  
by himself1 particularly if pains  are  
taken in travelling and in the          
observation of natural phenomena1 and   
in the book of nature which every one   
has at home1 that is to say1 the        
heavens and the earth2 and enough may be
 learned from the habits of  constant   
correspondence with each other1 and     
alternate offices of  counsel and       
assistance4--,let the first fruits of   
wisdom be love2 and so  let the         
,lynceans love each other as if united  

by the strictest ties1 nor  suffer any  
interruption of this sincere bond of    
love and faith1  emanating from the     
source of virtue and philosophy4--,let  
them add to  their names the title of   
,lyncean1 which has been advisedly      
chosen as a  warning and constant       
stimulus1 especially when they write on 
any  literary subject1 also in their    
private letters to their associates1 and
  in general when any work comes from   
them wisely and well performed4--,the   
,lynceans will pass over in silence all 
political controversies and  quarrels of
 every kind1 and wordy disputes1        
especially gratuitous ones1  which give 
occasion to deceit1 unfriendliness1 and 
hatred2 like men who  desire peace1 and 
seek to preserve their studies free from
 molestation1  and to avoid every sort  
of disturbance4 ,and if any one by      
command of his  superiors1 or from some 
other necessity1 is reduced to handle   
such  matters1 since they are foreign to
 physical and mathematical science1  and

 consequently alien to the object of the
 ,academy1 let them be printed  without 
the ,lyncean name4#fb    ,the society   
which was eventually organized formed   
but a very trifling  part of the        
comprehensive scheme which ,cesi        
originally proposed to  himself2 it had 
been his wish to establish a scientific 
,order which  should have corresponding 
lodges in the principal towns of        
,europe1 and  in other parts of the     
globe1 each consisting of not more than 
five nor  less than three members1      
besides an unlimited number of          
,academicians not  restricted to any    
particular residence or regulations4    
,the  mortifications and difficulties to
 which he was subjected from his        
father's unprincipled behaviour1 render 
it most extraordinary and  admirable    
that he should have ventured to         
undertake even so much as he  actually  
carried into execution4 ,he promised to 
furnish to the members  of his society  
such assistance as they might require in

 the prosecution  of their respective   
researches1 and also to defray the      
charges of  publishing such of their    
works as should be thought worthy of    
appearing  with the common sanction4    
,such liberal offers were not likely to 
meet  with an unfavourable reception3   
they were thankfully accepted by many   
well qualified to carry his design into 
execution1 and ,cesi was soon  enabled  
formally to open his academy1 the       
distinctive title of which he  borrowed 
from the ,lynx1 with reference to the   
piercing sight which that  animal has   
been supposed to possess4 ,this quality 
seemed to him an  appropriate emblem of 
those which he desired to find in his   
academicians1 for the purpose of        
investigating the secrets of nature2    
and although1 at the present day1 the   
name may appear to border on the        
grotesque1 it was conceived in the      
spirit of the age1 and the fantastic    
names of the numberless societies which 
were rapidly formed in various  parts of

 ,italy far exceed whatever degree of   
quaintness may be thought  to belong to 
the ,lyncean name4 ,the ,inflamed--the  
,transformed--the  ,uneasy--the         
,humorists--the ,fantastic--the         
,intricate--the ,indolent--the          
,senseless--the ,undeceived--the        
,valiant--the therial ,societies are    
selected from a vast number of similar  
institutions1 the names of which1  now  
almost their sole remains1 are collected
 by the industry of ,morhof  and        
,tiraboschi4#fc ,the ,humorists are     
named by ,morhof as the only  ,italian  
philosophical society anterior to the   
,lynceans2 their founder  was ,paolo    
,mancino1 and the distinctive symbol    
which they adopted was  rain dropping   
from a cloud1 with the motto ,redit     
agmine dulci2--their  title is derived  
from the same metaphor4 ,the object of  
their union  appears to have been       
similar to that of the ,lynceans1 but   
they at no  time attained to the        
celebrity to which ,cesi's society rose 

from the  moment of its incorporation4  
,cesi took the presidency for his life1 
and  the celebrated ,baptista ,porta was
 appointed vice president at ,naples4   
,stelluti acted as the legal            
representative of the society1 with the 
title of procuratore4 ,of the other two 
original members ,anastasio de  ,filiis 
was dead1 and although ,hecke returned  
to ,italy in #afad1 and  rejoined the   
,academy1 yet he was soon afterwards    
struck off the list in  consequence of  
his lapsing into insanity4 ,among the   
academicians we find  the names of      
,galileo1 ,fabio ,colonna1 ,lucas       
,valerio1 ,guiducci1 ,welser1  ,giovanni
 ,fabro1 ,terrentio1 ,virginio          
,cesarini1 ,ciampoli1 ,molitor1         
,cardinal ,barberino1 7nephew of ,pope  
,urban ,,viii47 ,stelliola1 ,salviati1  
c4    ,the principal monument still     
remaining of the zeal and industry to   
which  ,cesi incited his academicians is
 the ,phytobasanos1 a compendium of the 
natural history of ,mexico1 which must  

be considered a surprising  performance 
for the times in which it appeared4 ,it 
was written by a  ,spaniard named       
,hernandez2 and ,reccho1 who often has  
the credit of the  whole work1 made     
great additions to it4 ,during fifty    
years the  manuscript had been          
neglected1 when ,cesi discovered it1 and
 employed  ,terrentio1 ,fabro1 and      
,colonna1 all ,lynceans1 to publish it  
enriched with  their notes and          
emendations4 ,cesi himself published    
several treatises1  two of which are    
extant2 his ,tabul ,phytosophic1 and a  
,dissertation  on ,bees entitled        
,apiarium1 the only known copy of which 
last is in the  library of the ,vatican4
 ,his great work1 ,theatrum ,natur1 was 
never  printed2 a circumstance which    
tends to shew that he did not assemble  
the  society round him for the purpose  
of ministering to his own vanity1 but   
postponed the publication of his own    
productions to the labours of his       
coadjutors4 ,this1 and many other       

valuable works belonging to the academy 
existed in manuscript till lately in the
 ,albani ,library at ,rome4 ,cesi       
collected1 not a large1 but an useful   
library for the use of the  academy1    
7which was afterwards augmented on the  
premature death of  ,cesarini by the    
donation of his books72 he filled a     
botanical garden  with the rarer        
specimens of plants1 and arranged a     
museum of natural  curiosities2 his     
palace at ,rome was constantly open to  
the academicians2  his purse and his    
influence were employed with equal      
liberality in their  service4    ,cesi's
 death1 in #afcb1 put a sudden stop to  
the prosperity of the  society1 a       
consequence which may be attributed to  
the munificence with  which he had from 
the first sustained it3 no one could be 
found to fill  his place in the princely
 manner to which the academicians were  
accustomed1 and the society1 after      
lingering some years under the  nominal 
patronage of ,urban ,,viii41 gradually  

decayed1 till1 by the death  of its     
principal members1 and dispersion of the
 rest1 it became entirely  extinct4#fd  
,bianchi1 whose sketch of the academy   
was almost the only  one till the       
appearance of ,odescalchi's history1    
made an attempt to  revive it in the    
succeeding century1 but without any     
permanent effect4 ,a  society under the 
same name has been formed since #aghd1  
and is still  flourishing in ,rome4     
,before leaving the subject it may be   
mentioned1  that one of the earliest    
notices that ,bacon's works were known  
in ,italy  is to be found in a letter to
 ,cesi1 dated #afbe2 in which ,pozzo1   
who had  gone to ,paris with ,cardinal  
,barberino1 mentions having seen them   
there  with great admiration1 and       
suggests that ,bacon would be a fit     
person to  be proposed as a member of   
their society4 ,after ,galileo's death1 
three  of his principal followers1      
,viviani1 ,torricelli1 and ,aggiunti    
formed the  plan of establishing a      

similar philosophical society1 and      
though  ,aggiunti and ,torricelli died  
before the scheme could be realized1    
,viviani pressed it forward1 and1 under 
the auspices of ,ferdinand ,,ii41       
formed a society1 which1 in #afeg1      
merged in the famous ,academia del      
,cimento1 or ,experimental ,academy4    
,this latter held its occasional        
meetings at the palace of ,ferdinand's  
brother1 ,leopold de' ,medici3 it  was  
composed chiefly1 if not entirely1 of   
,galileo's pupils and friends4  ,during 
the few years that this society lasted1 
one of the principal  objects of which  
was declared to be the repetition and   
developement of  ,galileo's experiments1
 it kept up a correspondence with the   
principal  philosophers in every part of
 ,europe1 but when ,leopold was1 in     
#afff1  created a cardinal1 it appears  
to have been dissolved1 scarcely ten    
years after its institution4#fe ,this   
digression may be excused in  favour of 
so interesting an establishment as the  

,academia ,lincea1 which  preceded by   
half a century the formation of the     
,royal ,society of ,london1  and        
,acadmie ,franoise of ,paris4    ,these 
latter two are mentioned together1      
probably for the first time1 by         
,salusbury4 ,the passage is curious in  
an historical point of view1 and  worth 
extracting3--,in imitation of these     
societies1 ,paris and ,london  have     
erected theirs of ,les ,beaux ,esprits1 
and of the ,virtuosi3 the  one by the   
countenance of the most eminent         
,cardinal ,richelieu1 the other  by the 
royal encouragement of his sacred       
,majesty that now is4 ,the ,beaux       
,esprits have published sundry volumes  
of their moral and physiological        
conferences1 with the laws and history  
of their fellowship2 and ,i hope  the   
like in due time from our ,royal        
,society2 that so such as envie their   
fame and felicity1 and such as suspect  
their ability and candor1 may be        
silenced and disappointed in their      

detractions and expectations4#ff        
,,footnotes3    #fa ,salusbury1 ,math4  
,coll4    #fb ,perhaps it was to        
deprecate the hostility of the ,jesuits 
that1 at  the close of these            
,regulations1 the ,lynceans are directed
 to address  their prayers1 among other 
,saints1 especially to ,ignatius        
,loyola1 as to  one who greatly favoured
 the interests of learning4 ,odescalchi1
 ,memorie  dell',acad4 de' ,lincei1     
,roma4 #ahjf4    #fc ,polyhistor        
,literarius1 c4--,storia della          
,letterat4 ,ital4 ,the still  existing  
society of ,chaff1 more generally known 
by its ,italian title1  ,della ,crusca1 
belongs to the same period4    #fd ,f4  
,colonn ,phytobasanus ,jano ,planco     
,auctore4 ,florent1 #agdd4    #fe ,nelli
 ,saggio di ,storia ,literaria          
,fiorentina1 ,lucca1 #agei4    #ff      
,salusbury's ,math4 ,coll4 vol4 ii4     
,london1 #affd4          ,,chapter ,x4  
,spots on the ,sun--,essay on ,floating 
,bodies--,scheiner--,change in          

,saturn4      ,,galileo did not indulge 
the curiosity of his ,roman friends by  
exhibiting  only the wonders already    
mentioned1 which now began to lose the  
gloss of  novelty1 but disclosed a new  
discovery1 which appeared still more    
extraordinary1 and1 to the opposite     
faction1 more hateful than anything  of 
which he had yet spoken4 ,this was the  
discovery1 which he first made  in the  
month of ,march1 #afaa1 of dark spots on
 the body of the sun4 ,a  curious fact1 
and one which well serves to illustrate 
,galileo's  superiority in seeing things
 simply as they are1 is1 that these     
spots  had been observed and recorded   
centuries before he existed1 but1 for   
want of careful observation1 their true 
nature had been constantly              
misapprehended4 ,one of the most        
celebrated occasions was in the year    
#hjg  of our era1 in which a dark spot  
is mentioned as visible on the face of  
the sun during seven or eight days4 ,it 
was then supposed to be  ,mercury4#fg   

,kepler1 whose astronomical knowledge   
would not suffer him  to overlook that  
it was impossible that ,mercury could   
remain so long in  conjunction with the 
sun1 preferred to solve the difficulty  
by supposing  that1 in ,aimoin's        
original account1 the expression was not
 octo dies  7eight days71 but           
octoties--a barbarous word1 which he    
supposed to  have been written for      
octies 7eight times72 and that the other
  accounts 7in which the number of days 
mentioned is different7 copying  loosely
 from the first1 had both mistaken the  
word1 and misquoted the  time which they
 thought they found mentioned there4 ,it
 is impossible to  look on this         
explanation as satisfactory1 but        
,kepler1 who at that time  did not dream
 of spots on the sun1 was perfectly     
contented with it4 ,in  #afji1 he       
himself observed upon the sun a black   
spot1 which he in like  manner mistook  
for ,mercury1 and unluckily the day1    
being cloudy1 did  not allow him to     

contemplate it sufficiently long to     
discover his  error1 which the slowness 
of its apparent motion would soon have  
pointed  out4#fh ,he hastened to publish
 his supposed observation1 but no sooner
  was ,galileo's discovery of the solar 
spots announced1 than he1 with that     
candour which as much as his flighty    
disposition certainly characterized  him
 at all times1 retracted his former     
opinion1 and owned his belief  that he  
had been mistaken4 ,in fact it is known 
from the more accurate  theory which we 
now possess of ,mercury's motions1 that 
it did not pass  over the sun's face at 
the time when ,kepler thought he        
perceived it  there4    ,galileo's      
observations were in their consequences 
to him particularly  unfortunate1 as in 
the course of the controversy in which  
they engaged  him1 he first became      
personally embroiled with the powerful  
party1 whose  prevailing influence was  
one of the chief causes of his          
subsequent  misfortunes4 ,before we     

enter upon that discussion1 it will be  
proper to  mention another famous       
treatise which ,galileo produced soon   
after his  return from ,rome to         
,florence1 in #afab4 ,this is1 his      
,discourse on  ,floating ,bodies1 which 
restored ,archimedes' theory of         
hydrostatics1 and  has1 of course1 met  
with the opposition which few of        
,galileo's works  failed to encounter4  
,in the commencement1 he thought it     
necessary to  apologize for writing on a
 subject so different from that which   
chiefly  occupied the public attention1 
and declared that he had been too       
closely  occupied in calculating the    
periods of the revolutions of ,jupiter's
  satellites to permit him to publish   
anything earlier4 ,these periods he  had
 succeeded in determining during the    
preceding year1 whilst at ,rome1  and he
 now announced them to complete their   
circuits1 the first in about  #a day1   
#ah hours2 the second in #c days1 #ac   
hours1 #bj minutes2 the third  in #g    

days1 #d hours2 and the outermost in #af
 days1 #ah hours4 ,all these  numbers he
 gave merely as approximately true1 and 
promised to continue  his observations1 
for the purpose of correcting the       
results4 ,he then  adds an announcement 
of his recent discovery of the solar    
spots1 which1  as they change their     
situation1 offer a strong argument1     
either that the  sun revolves on itself1
 or that1 perhaps1 other stars1 like    
,venus and  ,mercury1 revolve about it1 
invisible at all other times1 on account
 of  the small distance to which they   
are removed from him4 ,to this he       
afterwards subjoined1 that1 by continued
 observation1 he had satisfied  himself 
that these solar spots were in actual   
contact with the surface  of the sun1   
where they are continually appearing and
 disappearing2 that  their figures were 
very irregular1 some being very dark1   
and others not  so black2 that one would
 often divide into three or four1 and1  
at other  times1 two1 three1 or more    

would unite into one2 besides which1    
that  they had all a common and regular 
motion1 with which they revolved round  
with the sun1 which turned upon its axis
 in about the time of a lunar  month4   
,having by these prefatory observations 
assuaged the public thirst for          
astronomical novelties1 he ventures to  
introduce the principal subject  of the 
treatise above mentioned4 ,the question 
of floating bridges had  been discussed 
at one of the scientific parties1       
assembled at the house  of ,galileo's   
friend ,salviati1 and the general       
opinion of the company  appearing to be 
that the floating or sinking of a body  
depended  principally upon its shape1   
,galileo undertook to convince them of  
their  error4 ,if he had not preferred  
more direct arguments1 he might merely  
have told them that in this instance    
they were opposed to their  favourite   
,aristotle1 whose words are very        
unequivocal on the point in  dispute4   
,form is not the cause why a body moves 

downwards rather than  upwards1 but it  
does affect the swiftness with which it 
moves2#fi  which is exactly the         
distinction which those who called      
themselves  ,aristotelians were unable  
to perceive1 and to which the opinions  
of  ,aristotle himself were not always  
true4 ,galileo states the discussion to 
have immediately arisen from the        
assertion of some one in the company1   
that condensation is the effect of cold1
 and ice was mentioned as an  instance4 
,on this1 ,galileo observed1 that ice is
 rather water rarefied  than condensed1 
the proof of which is1 that ice always  
floats upon  water4#gj ,it was replied1 
that the reason of this phenomenon was1 
not  the superior lightness of the ice1 
but its incapacity1 owing to its flat   
shape1 to penetrate and overcome the    
resistance of the water4 ,galileo       
denied this1 and asserted that ice of   
any shape would float upon water1  and  
that1 if a flat piece of ice were       
forcibly taken to the bottom1 it  would 

of itself rise again to the surface4    
,upon this assertion it  appears that   
the conversation became so clamorous1   
that ,galileo thought  it pertinent to  
commence his ,essay with the following  
observation on the  advantage of        
delivering scientific opinions in       
writing1 because in  conversational     
arguments1 either one or other party1 or
 perhaps both1  are apt to get overwarm1
 and to speak overloud1 and either do   
not suffer  each other to be heard1 or  
else1 transported with the obstinacy of 
not  yielding1 wander far away from the 
original proposition1 and confound  both
 themselves and their auditors with the 
novelty and variety of their            
assertions4 ,after this gentle rebuke he
 proceeds with his argument1 in  which  
he takes occasion to state the famous   
hydrostatical paradox1 of  which the    
earliest notice is to be found in       
,stevin's works1 a  contemporary        
,flemish engineer1 and refers it to a   
principle on which we  shall enlarge in 

another chapter4 ,he then explains the  
true theory of  buoyancy1 and refutes   
the false reasoning on which the        
contrary opinions  were founded1 with a 
variety of experiments4    ,the whole   
value and interest of experimental      
processes generally depends  on a       
variety of minute circumstances1 the    
detail of which would be  particularly  
unsuited to a sketch like the present   
one4 ,for those who  are desirous of    
becoming more familiar with ,galileo's  
mode of conducting  an argument1 it is  
fortunate that such a series of         
experiments exists as  that contained in
 this essay2 experiments which1 from    
their simplicity1  admit of being for   
the most part concisely enumerated1 and 
at the same  time possess so much       
intrinsic beauty and characteristic     
power of  forcing conviction4 ,they also
 present an admirable specimen of the   
talent for which ,galileo was so        
deservedly famous1 of inventing         
ingenious arguments in favour of his    

adversaries' absurd opinions before  he 
condescended to crush them1 shewing that
 nothing but his love of  truth stood in
 the way of his being a more subtle     
sophist than any  amongst them4 ,in     
addition to these reasons for giving    
these experiments  somewhat in detail1  
is the fact that all explanation of one 
of the  principal phenomena to which    
they allude is omitted in many more     
modern  treatises on ,hydrostatics2 and 
in some it is referred precisely to the 
false doctrines here confuted4    ,the  
marrow of the dispute is included in    
,galileo's assertion1 that ,the         
diversity of figure given to any solid  
cannot be in any way the cause of  its  
absolutely sinking or floating2 so that 
if a solid1 when formed for  example    
into a spherical figure1 sinks or floats
 in the water1 the same  body will sink 
or float in the same water1 when put    
into any other form4  ,the breadth of   
the figure may indeed retard its        
velocity1 as well of  ascent as descent1

 and more and more according as the said
 figure is  reduced to a greater breadth
 and thinness2 but that it may be       
reduced to  such a form as absolutely to
 put an end to its motion in the same   
fluid1  ,i hold to be impossible4 ,in   
this ,i have met with great             
contradictors  who1 producing some      
experiments1 and in particular a thin   
board of  ebony1 and a ball of the same 
wood1 and shewing that the ball in water
  sinks to the bottom#ga1 and that the  
board if put lightly on the  surface    
floats1 have held and confirmed         
themselves in their opinion with  the   
authority of ,aristotle1 that the cause 
of that rest is the breadth  of the     
figure1 unable by its small weight to   
pierce and penetrate the  resistance of 
the water's thickness1 which is readily 
overcome by the  other spherical        
figure4--,for the purpose of these      
experiments1 ,galileo  recommends a     
substance such as wax1 which may be     
easily moulded into any  shape1 and with

 which1 by the addition of a few filings
 of lead1 a  substance may be readily   
made of any required specific gravity4  
,he then  declares that if a ball of wax
 of the size of an orange1 or bigger1 be
  made in this manner heavy enough to   
sink to the bottom1 but so lightly  that
 if we take from it only one grain of   
lead it returns to the top2  and if the 
same wax be afterwards moulded into a   
broad and thin cake1 or  into any other 
figure1 regular or irregular1 the       
addition of the same  grain of lead will
 always make it sink1 and it will again 
rise when we  remove the lead from      
it4--,but methinks ,i hear some of the  
adversaries  raise a doubt upon my      
produced experiment3 and1 first1 they   
offer to my  consideration that the     
figure1 as a figure simply1 and disjunct
 from the  matter1 works no effect1 but 
requires to be conjoined with the       
matter2  and1 moreover1 not with every  
matter1 but with those only wherewith it
  may be able to execute the desired    

operation4 ,just as we see by           
experience that an acute and sharp angle
 is more apt to cut than an  obtuse2 yet
 always provided that both one and the  
other are joined with  a matter fit to  
cut1 as for instance1 steel4 ,therefore 
a knife with a  fine and sharp edge cuts
 bread or wood with much ease1 which it 
will not  do if the edge be blunt and   
thick2 but if1 instead of steel1 any one
  will take wax and mould it into a     
knife1 undoubtedly he will never learn  
the effects of sharp and blunt edges1   
because neither of them will cut2  the  
wax being unable1 by reason of its      
flexibility1 to overcome the  hardness  
of the wood and bread4 ,and therefore1  
applying the like  discourse to our     
argument1 they say that the difference  
of figure will  shew different effects  
with regard to floating and sinking1 but
 not  conjoined with any kind of matter1
 but only with those matters which by   
their weight are able to overcome the   
viscosity of the water 7like the  ebony 

which they have selected72 and he that  
will select cork or other  light wood to
 form solids of different figures1 would
 in vain seek to  find out what         
operation figure has in sinking or      
floating1 because all  would swim1 and  
that not through any property of this or
 that figure1  but through the debility 
of the matter4    ,when ,i begin to     
examine one by one all the particulars  
here produced1 ,i  allow not only that  
figures1 simply as such1 do not operate 
in natural  things1 but also that they  
are never separated from the corporeal  
substance1 nor have ,i ever alleged them
 to be stript of sensible matter3  and  
also ,i freely admit1 that in our       
endeavours to examine the diversity  of 
accidents which depend upon the variety 
of figures1 it is necessary  to apply   
them to matters which obstruct not the  
various operations of  those various    
figures4 ,i admit and grant that ,i     
should do very ill if ,i  were to try   
the influence of a sharp edge with a    

knife of wax1 applying  it to cut an    
oak1 because no sharpness in wax is able
 to cut that very  hard wood4 ,but yet1 
such an experiment of this knife would  
not be beside  the purpose to cut curded
 milk1 or other very yielding matter2   
nay1 in  such matters1 the wax is more  
convenient than steel for finding the   
difference depending on the acuteness of
 the angles1 because milk is cut        
indifferently with a razor1 or a blunt  
knife4 ,we must therefore have  regard  
not only to the hardness1 solidity1 or  
weight of the bodies  which1 under      
different figures1 are to divide some   
matters asunder2 but  also1 on the other
 hand1 to the resistance of the matter  
to be  penetrated4 ,and1 since ,i have  
chosen a matter which does penetrate the
  resistance of the water1 and in all   
figures descends to the bottom1 my      
antagonists can charge me with no       
defect2 nor 7to revert to their         
illustration7 have ,i attempted to test 
the efficacy of acuteness by  cutting   

with matters unable to cut4 ,i subjoin  
withal1 that all caution1  distinction1 
and election of matter would be         
superfluous and  unnecessary1 if the    
body to be cut should not at all resist 
the cutting3  if the knife were to be   
used in cutting a mist1 or smoke1 one of
 paper  would serve the purpose as well 
as one of ,damascus steel2 and ,i assert
  that this is the case with water1 and 
that there is not any solid of  such    
lightness or of such a figure1 that     
being put on the water it will  not     
divide and penetrate its thickness2 and 
if you will examine more  carefully your
 thin boards of wood1 you will see that 
they have part of  their thickness under
 water2 and1 moreover1 you will see that
 the  shavings of ebony1 stone1 or      
metal1 when they float1 have not only   
thus  broken the continuity of the      
water1 but are with all their thickness 
under the surface of it2 and that more  
and more1 according as the  floating    
substance is heavier1 so that a thin    

floating plate of lead  will be lower   
than the surface of the surrounding     
water by at least  twelve times the     
thickness of the plate1 and gold will   
dive below the  level of the water      
almost twenty times the thickness of the
 plate1 as ,i  shall shew presently4    
,in order to illustrate more clearly the
 non-resistance of water to             
penetration1 ,galileo then directs a    
cone to be made of wood or wax1 and     
asserts that when it floats1 either with
 its base or point in the water1  the   
solid content of the part immersed will 
be the same1 although the  point is1 by 
its shape1 better adapted to overcome   
the resistance of the  water to         
division1 if that were the cause of the 
buoyancy4 ,or the  experiment may be    
varied by tempering the wax with filings
 of lead1 till  it sinks in the water1  
when it will be found that in any figure
 the same  cork must be added to it to  
raise it to the surface4--,this silences
 not  my antagonists2 but they say that 

all the discourse hitherto made by me   
imports little to them1 and that it     
serves their turn1 that they have       
demonstrated in one instance1 and in    
such manner and figure as pleases  them 
best1 namely1 in a board and a ball of  
ebony1 that one1 when put  into the     
water1 sinks to the bottom1 and that the
 other stays to swim at  the top2 and   
the matter being the same1 and the two  
bodies differing in  nothing but in     
figure1 they affirm that with all       
perspicuity they have  demonstrated and 
sensibly manifested what they undertook4
 ,nevertheless ,i  believe1 and think ,i
 can prove that this very experiment    
proves nothing  against my theory4 ,and 
first it is false that the ball sinks1  
and the  board not2 for the board will  
sink too1 if you do to both the figures 
as  the words of our question require2  
that is1 if you put them both in  the   
water2 for to be in the water implies to
 be placed in the water1 and  by        
,aristotle's own definition of place1 to

 be placed imports to be  environed by  
the surface of the ambient body2 but    
when my antagonists  shew the floating  
board of ebony1 they put it not into the
 water1 but  upon the water2 where1     
being detained by a certain impediment  
7of which  more anon7 it is surrounded1 
partly with water1 partly with air1     
which  is contrary to our agreement1 for
 that was that the bodies should be in  
the water1 and not part in the water1   
part in the air4 ,i will not omit       
another reason1 founded also upon       
experience1 and1 if ,i deceive not      
myself1 conclusive against the notion   
that figure1 and the resistance of  the 
water to penetration have anything to do
 with the buoyancy of  bodies4 ,choose a
 piece of wood or other matter1 as for  
instance  walnut-wood1 of which a ball  
rises from the bottom of the water to   
the  surface more slowly than a ball of 
ebony of the same size sinks1 so that   
clearly the ball of ebony divides the   
water more readily in sinking than  does

 the walnut in rising4 ,then take a     
board of walnut-tree equal to and  like 
the floating ebony one of my            
antagonists2 and if it be true that     
this latter floats by reason of the     
figure being unable to penetrate the    
water1 the other of walnut-tree1 without
 all question1 if thrust to the  bottom 
ought to stay there1 as having the same 
impeding figure1 and  being less apt to 
overcome the said resistance of the     
water4 ,but if we  find by experience   
that not only the thin board1 but every 
other figure  of the same walnut-tree   
will return to float1 as unquestionably 
we  shall1 then ,i must desire my       
opponents to forbear to attribute the   
floating of the ebony to the figure of  
the board1 since the resistance  of the 
water is the same in rising as in       
sinking1 and the force of  ascension of 
the walnut-tree is less than the ebony's
 force for going to  the bottom4        
,now1 let us return to the thin plate of
 gold or silver1 or the thin  board of  

ebony1 and let us lay it lightly upon   
the water1 so that it may  stay there   
without sinking1 and carefully observe  
the effect4 ,it will  appear clearly    
that the plates are a considerable      
matter lower than the  surface of the   
water which rises up1 and makes a kind  
of rampart round  them on every side1 in
 the manner shewn in the annexed figure1
 in which  ,,bdlf represents the surface
 of the water1 and ,,aeio the surface of
 the  plate4 ,but if it have already    
penetrated and overcome the continuity  
of  the water1 and is of its own nature 
heavier than the water1 why does it  not
 continue to sink1 but stop and suspend 
itself in that little dimple  that its  
weight has made in the water8 ,my answer
 is1 because in sinking  till its       
surface is below the water which rises  
up in a bank round it1  it draws after  
and carries along with it the air above 
it1 so that that  which in this case    
descends and is placed in the water1 is 
not only the  board of ebony or plate of

 iron1 but a compound of ebony and air1 
from  which composition results a solid 
no longer specifically heavier than  the
 water1 as was the ebony or gold alone4 
,but1 ,gentlemen1 we want the  same     
matter2 you are to alter nothing but the
 shape1 and therefore have  the goodness
 to remove this air1 which may be done  
simply by washing the  upper surface of 
the board1 for the water having once got
 between the  board and air will run    
together1 and the ebony will go to the  
bottom2  and if it does not1 you have   
won the day4 ,but methinks ,i hear some 
of my  antagonists cunningly opposing   
this1 and telling me that they will not 
on any account allow their board to be  
wetted1 because the weight of the  water
 so added1 by making it heavier than it 
was before1 draws it to the  bottom1 and
 that the addition of new weight is     
contrary to our  agreement1 which was   
that the matter should be the same4     
,illustration    ,to this ,i answer     
first1 that nobody can suppose bodies to

 be put into  the water without their   
being wet1 nor do ,i wish to do more to 
the  board than you may do to the ball4 
,moreover1 it is not true that the      
board sinks on account of the weight of 
the water added in the washing2  for ,i 
will put ten or twenty drops on the     
floating board1 and so long as  they    
stand separate it shall not sink2 but if
 the board be taken out1  and all that  
water wiped off1 and the whole surface  
bathed with one  single drop1 and put it
 again upon the water1 there is no      
question but  it will sink1 the other   
water running to cover it1 being no     
longer  hindered by the air4 ,in the    
next place it is altogether false that  
water  can in any way increase the      
weight of bodies immersed in it1 for    
water  has no weight in water1 since it 
does not sink4 ,now1 just as he who     
should say that brass by its own nature 
sinks1 but that when formed into  the   
shape of a kettle1 it acquires from that
 figure a virtue of lying in  the water 

without sinking1 would say what is      
false1 because that is not  purely brass
 which then is put into the water1 but a
 compound of brass  and air2 so is it   
neither more nor less false1 that a thin
 plate of  brass or ebony swims by      
virtue of its dilated and broad figure4 
,also ,i  cannot omit to tell my        
opponents1 that this conceit of refusing
 to bathe  the surface of the board1    
might beget an opinion in a third person
 of a  poverty of arguments on their    
side1 especially as the conversation    
began  about flakes of ice1 in which it 
would be simple to require that the     
surfaces should be kept dry2 not to     
mention that such pieces of ice1        
whether wet or dry1 always float1 and as
 my antagonists say1 because of  their  
shape4    ,some may wonder that ,i      
affirm this power to be in the air of   
keeping  the plate of brass or silver   
above water1 as if in a certain sense ,i
  would attribute to the air a kind of  
magnetic virtue for sustaining  heavy   

bodies with which it is in contact4 ,to 
satisfy all these doubts1 ,i  have      
contrived the following experiment to   
demonstrate how truly the air  does     
support these solids2 for ,i have found1
 when one of these bodies  which floats 
when placed lightly on the water1 is    
thoroughly bathed and  sunk to the      
bottom1 that by carrying down to it a   
little air without  otherwise touching  
it in the least1 ,i am able to raise and
 carry it back  to the top1 where it    
floats as before4 ,to this effect ,i    
take a ball of  wax1 and with a little  
lead make it just heavy enough to sink  
very  slowly to the bottom1 taking care 
that its surface be quite smooth and    
even4 ,this1 if put gently into the     
water1 submerges almost entirely1  there
 remaining visible only a little of the 
very top1 which1 so long as  it is      
joined to the air1 keeps the ball       
afloat2 but if we take away the  contact
 of the air by wetting this top1 the    
ball sinks to the bottom1  and remains  

there4 ,now to make it return to the    
surface by virtue of the  air which     
before sustained it1 thrust into the    
water a glass1 with the  mouth          
downwards1 which will carry with it the 
air it contains2 and move  this down    
towards the ball1 until you see by the  
transparency of the  glass that the air 
has reached the top of it2 then gently  
draw the glass  upwards1 and you will   
see the ball rise1 and afterwards stay  
on the top  of the water1 if you        
carefully part the glass and water      
without too much  disturbing it4#gb     
,there is therefore a certain affinity  
between the air  and other bodies1 which
 holds them united1 so that they        
separate not  without a kind of         
violence1 just as between water and     
other bodies2 for  in drawing them      
wholly out of the water1 we see the     
water follow them1  and rise sensibly   
above the level before it quits them4   
,having  established this principle by  
this exceedingly ingenious and          

convincing  experiment1 ,galileo        
proceeds to shew from it what must be   
the dimensions  of a plate of any       
substance which will float as the wax   
does1 assuming  in each case that we    
know the greatest height at which the   
rampart of  water will stand round it4  
,in like manner he shows that a         
pyramidal or  conical figure may be made
 of any substance1 such that by help of 
the  air1 it shall rest upon the water  
without wetting more than its base2  and
 that we may so form a cone of any      
substance that it shall float if  placed
 gently on the surface1 with its point  
downwards1 whereas no care  or pains    
will enable it to float with its base   
downwards1 owing to the  different      
proportions of air which in the two     
positions remain connected  with it4    
,with this parting blow at his          
antagonist's theory we close our        
extracts from this admirable essay4     
,the first elements of the theory of    
running waters were reserved for        

,castelli1 an intimate friend and pupil 
of ,galileo4 ,on the present  occasion1 
,castelli appeared as the ostensible    
author of a defence  against the attacks
 made by ,vincenzio di ,grazia and by   
,lodovico delle  ,columbe 7the author of
 the crystalline composition of the     
moon7 on the  obnoxious theory4 ,after  
destroying all the objections which they
  produced1 the writer tauntingly bids  
them remember1 that he was merely       
,galileo's pupil1 and consider how much 
more effectually ,galileo himself  would
 have confuted them1 had he thought it  
worth while4 ,it was not  known till    
several years after his death1 that this
 ,essay was in fact  written by ,galileo
 himself4#gc    ,these compositions     
merely occupied the leisure time which  
he could  withhold from the controversy 
on the solar spots to which we have     
already alluded4 ,a ,german ,jesuit     
named ,christopher ,scheiner1 who was   
professor of mathematics at ,ingolstadt1
 in imitation of ,galileo had  commenced

 a series of observations on them1 but  
adopted the theory  which1 as we have   
seen1 ,galileo had examined and         
rejected1 that these  spots are planets 
circulating at some distance from the   
body of the sun4  ,the same opinion had 
been taken up by a ,french astronomer1  
who in honour  of the reigning family   
called them ,borbonian stars4 ,scheiner 
promulgated  his notions in three       
letters1 addressed to their common      
friend ,welser1  under the quaint       
signature of ,apelles latens post       
tabulam4 ,galileo  replied to           
,scheiner's letters by three others1    
also addressed to ,welser1  and although
 the dispute was carried on amid mutual 
professions of  respect and esteem1 it  
laid the foundation of the total        
estrangement  which afterwards took     
place between the two authors4          
,galileo's part of  this controversy was
 published at ,rome by the ,lyncean     
,academy in #afac4  ,to the last of his 
letters1 written in ,december1 #afab1 is

 annexed a  table of the expected       
positions of ,jupiter's satellites      
during the  months of ,march and ,april 
of the following year1 which1 imperfect 
as it  necessarily was1 cannot be looked
 upon without the greatest interest4    
,in the same letter it is mentioned that
 ,saturn presented a novel  appearance1 
which1 for an instant1 almost induced   
,galileo to mistrust  the accuracy of   
his earlier observations4 ,the lateral  
appendages of this  planet had          
disappeared1 and the accompanying       
extract will show the  uneasiness which 
,galileo could not conceal at the sight 
of this  phenomenon1 although it is     
admirable to see the contempt with      
which1  even in that trying moment1 he  
expresses his consciousness that his    
adversaries were unworthy of the triumph
 they appeared on the point of          
celebrating4--,looking on ,saturn within
 these few days1 ,i found it  solitary1 
without the assistance of its accustomed
 stars1 and in short1  perfectly round  

and defined like ,jupiter1 and such it  
still remains4 ,now  what can be said of
 so strange a metamorphosis8 are perhaps
 the two  smaller stars consumed1 like  
the spots on the sun8 have they suddenly
  vanished and fled8 or has ,saturn     
devoured his own children8 or was the   
appearance indeed fraud and illusion1   
with which the glasses have for so  long
 a time mocked me1 and so many others   
who have often observed with  me4 ,now  
perhaps the time is come to revive the  
withering hopes of those1  who1 guided  
by more profound contemplations1 have   
fathomed all the  fallacies of the new  
observations and recognised their       
impossibility6 ,i  cannot resolve what  
to say in a chance so strange1 so new1  
and so  unexpected2 the shortness of the
 time1 the unexampled occurrence1 the   
weakness of my intellect1 and the terror
 of being mistaken1 have greatly        
confounded me4 ,these first expressions 
of alarm are not to be wondered  at2    
however1 he soon recovered courage1 and 

ventured to foretel the  periods at     
which the lateral stars would again show
 themselves1  protesting at the same    
time1 that he was in no respect to be   
understood  as classing this prediction 
among the results which depend on       
certain  principles and sound           
conclusions1 but merely on some         
conjectures which  appeared to him      
probable4 ,from one of the ,dialogues on
 the ,system1 we  learn that this       
conjecture was1 that ,saturn might      
revolve upon his axis1  but the period  
which he assumed is very different from 
the true one1 as  might be expected from
 its being intended to account for a    
phenomenon of  which ,galileo had not   
rightly apprehended the character4      
,he closed this letter with renewed     
professions of courtesy and  friendship 
towards ,apelles1 enjoining ,welser not 
to communicate it  without adding his   
excuses1 if he should be thought to     
dissent too  violently from his         
antagonist's ideas1 declaring that his  

only object  was the discovery of truth1
 and that he had freely exposed his own 
opinion1 which he was still ready to    
change1 so soon as his errors  should be
 made manifest to him2 and that he would
 consider himself  under special        
obligation to any one who would be kind 
enough to discover  and correct them4   
,these letters were written from the    
villa of his  friend ,salviati at ,selve
 near ,florence1 where he passed great  
part of  his time1 particularly during  
his frequent indispositions1 conceiving 
that the air of ,florence was           
prejudicial to him4 ,cesi was very      
anxious  for their appearance1 since    
they were 7in his own words7 so hard a  
morsel for the teeth of the             
,peripatetics1 and he exhorted ,galileo1
 in  the name of the society1 to        
continue to give them1 and the nameless 
,jesuit1 something to gnaw4             
,,footnotes3    #fg ,aimoini ,hist4     
,francorum4 ,parisiis4 #aefg4    #fh    
,mercurius in sole visus4 #afji4    #fi 

,de ,clo4 lib4 #d4    #gj ,for a        
discussion of this singular phenomenon1 
see ,treatise on  ,heat1 p4 #ab2 and it 
is worth while to remark in passing1    
what an  admirable instance it affords  
of ,galileo's instantaneous abandonment 
of  a theory so soon as it became       
inconsistent with experiment4    #ga    
,ebony is one of the few woods heavier  
than water4 ,see ,treatise on           
,hydrostatics4    #gb ,in making this   
very beautiful experiment1 it is best to
 keep the  glass a few seconds in the   
water1 to give time for the surface of  
the  ball to dry4 ,it will also succeed 
with a light needle1 if carefully       
conducted4    #gc ,nelli4 ,saggio di    
,stor4 ,liter4 ,fiorent4                
,,chapter ,,xi4        ,letter to       
,christina1 ,arch-,duchess of           
,tuscany--,caccini--,galileo            
revisits ,rome--,inchoffer--,problem of 
,longitudes4      ,,the uncompromising  
boldness with which ,galileo published  
and supported  his opinions1 with little

 regard to the power and authority of   
those who  advocated the contrary       
doctrines1 had raised against him a host
 of  enemies1 who each had objections to
 him peculiar to themselves1 but who    
now began to perceive the policy of     
uniting their strength in the common    
cause1 to crush if possible so dangerous
 an innovator4 ,all the  professors of  
the old opinions1 who suddenly found the
 knowledge on  which their reputation   
was founded struck from under them1 and 
who could  not reconcile themselves to  
their new situation of learners1 were   
united  against him2 and to this        
powerful cabal was now added the still  
greater  influence of the jesuits and   
pseudo-theological party1 who fancied   
they  saw in the spirit of ,galileo's   
writings the same inquisitive temper    
which they had already found so         
inconvenient in ,luther and his         
adherents4 ,the alarm became greater    
every day1 inasmuch as ,galileo had     
succeeded in training round him a       

numerous band of followers who all      
appeared imbued with the same dangerous 
spirit of innovation1 and his  favourite
 scholars were successful candidates for
 professorships in many  of the most    
celebrated universities of ,italy4      
,at the close of #afac1 ,galileo        
addressed a letter to his pupil1 the    
,abb  ,castelli1 in which he endeavoured
 to shew that there is as much          
difficulty in reconciling the ,ptolemaic
 as the ,copernican system of the  world
 with the astronomical expressions      
contained in the ,scriptures1 and       
asserted1 that the object of the        
,scriptures not being to teach          
astronomy1 such expressions are there   
used as would be intelligible and       
conformable to the vulgar belief1       
without regard to the true structure  of
 the universe2 which argument he        
afterwards amplified in a letter        
addressed to ,christina1 ,grand ,duchess
 of ,tuscany1 the mother of his  patron 
,cosmo4 ,he discourses on this subject  

with the moderation and good  sense     
which so peculiarly characterized him4  
,i am1 says he1 inclined  to believe1   
that the intention of the sacred        
,scriptures is to give to  mankind the  
information necessary for their         
salvation1 and which1  surpassing all   
human knowledge1 can by no other means  
be accredited than  by the mouth of the 
,holy ,spirit4 ,but ,i do not hold it   
necessary to  believe1 that the same    
,god who has endowed us with senses1    
with speech1  and intellect1 intended   
that we should neglect the use of these1
 and  seek by other means for knowledge 
which they are sufficient to procure    
us2 especially in a science like        
astronomy1 of which so little notice is 
taken in the ,scriptures1 that none of  
the planets1 except the sun and  moon1  
and1 once or twice only1 ,venus under   
the name of ,lucifer1 are so  much as   
named there4 ,this therefore being      
granted1 methinks that in the           
discussion of natural problems we ought 

not to begin at the authority of  texts 
of ,scripture1 but at sensible          
experiments and necessary               
demonstrations3 for1 from the divine    
word1 the sacred ,scripture and  nature 
did both alike proceed1 and ,i conceive 
that1 concerning natural  effects1 that 
which either sensible experience sets   
before our eyes1 or  necessary          
demonstrations do prove unto us1 ought  
not upon any account to  be called into 
question1 much less condemned1 upon the 
testimony of  ,scriptural texts1 which  
may under their words couch senses      
seemingly  contrary thereto4    ,again1 
to command the very professors of       
astronomy that they of  themselves see  
to the confuting of their own           
observations and  demonstrations1 is to 
enjoin a thing beyond all possibility of
 doing2  for it is not only to command  
them not to see that which they do see1 
and not to understand that which they do
 understand1 but it is to order  them to
 seek for and to find the contrary of   

that which they happen to  meet with4 ,i
 would entreat these wise and prudent   
fathers1 that they  would with all      
diligence consider the difference that  
is between  opinionative and            
demonstrative doctrines3 to the end that
 well weighing  in their minds with what
 force necessary inferences urge us1    
they might  the better assure themselves
 that it is not in the power of the     
professors of demonstrative sciences to 
change their opinions at  pleasure1 and 
adopt first one side and then another2  
and that there is a  great difference   
between commanding a mathematician or a 
philosopher1  and the disposing of a    
lawyer or a merchant2 and that the      
demonstrated  conclusions touching the  
things of nature and of the heavens     
cannot be  changed with the same        
facility as the opinions are touching   
what is  lawful or not in a contract1   
bargain1 or bill of exchange4           
,therefore1  first let these men apply  
themselves to examine the arguments of  

,copernicus and others1 and leave the   
condemning of them as erroneous and     
heretical to whom it belongeth2 yet let 
them not hope to find such rash  and    
precipitous determinations in the wary  
and holy fathers1 or in the  absolute   
wisdom of him who cannot err1 as those  
into which they suffer  themselves to be
 hurried by some particular affection or
 interest of  their own4 ,in these and  
such other positions1 which are not     
directly  articles of faith1 certainly  
no man doubts but ,his ,holiness hath   
always  an absolute power of admitting  
or condemning them1 but it is not in the
  power of any creature to make them to 
be true or false1 otherwise than  of    
their own nature1 and in fact they are4 
,we have been more particular  in       
extracting these passages1 because it   
has been advanced by a writer  of high  
reputation1 that the treatment which    
,galileo subsequently  experienced was  
solely in consequence of his persisting 
in the endeavour  to prove that the     

,scriptures were reconcileable with the 
,copernican  theory#gd1 whereas we see  
here distinctly that1 for the reasons we
 have  briefly stated1 he regarded this 
as a matter altogether indifferent and  
beside the question4    ,galileo had not
 entered upon this discussion till      
driven to it by a most  indecent attack1
 made on him from the pulpit1 by a      
,dominican friar named  ,caccini1 who   
thought it not unbecoming his habit or  
religion to play  upon the words of a   
,scriptural text for the purpose of     
attacking ,galileo  and his partisans   
with more personality4#ge ,galileo      
complained formally  of ,caccini's      
conduct to ,luigi ,maraffi the general  
of the ,dominicans1 who  apologised     
amply to him1 adding that he himself was
 to be pitied for  finding himself      
implicated in all the brutal conduct of 
thirty or forty  thousand monks4    ,in 
the mean time1 the inquisitors at ,rome 
had taken the alarm1 and were  already1 
in #afae1 busily employed in collecting 

evidence against  ,galileo4 ,lorini1 a  
brother ,dominican of ,caccini1 had     
given them notice  of the letter to     
,castelli of which we have spoken1 and  
the utmost  address was employed to get 
the original into their hands1 which    
attempt  however was frustrated1 as     
,castelli had returned it to the writer4
  ,caccini was sent for to ,rome1       
settled there with the title of ,master 
of  the ,convent of ,st4 ,mary of       
,minerva1 and employed to put the       
depositions  against ,galileo into      
order4 ,galileo was not at this time    
fully aware of  the machinations against
 him1 but suspecting something of their 
nature1  he solicited and obtained      
permission from ,cosmo1 towards the end 
of  #afae1 to make a journey to ,rome1  
for the purpose of more directly        
confronting his enemies in that city4   
,there was a rumour at the time  that   
this visit was not voluntary1 but that  
,galileo had been cited to  appear at   
,rome4 ,a contemporary declares that he 

heard this from ,galileo  himself3 at   
any rate1 in a letter which ,galileo    
shortly afterwards wrote  to ,picchena1 
the ,grand ,duke's secretary1 he        
expresses himself well  satisfied with  
the results of this step1 whether forced
 or not1 and  ,querenghi thus describes 
to the ,cardinal d',este the public     
effect of his  appearance3 ,your        
,eminence would be delighted with       
,galileo if you heard  him holding      
forth1 as he often does1 in the midst of
 fifteen or twenty1  all violently      
attacking him1 sometimes in one house1  
sometimes in  another4 ,but he is armed 
after such fashion that he laughs all of
 them  to scorn--and even if the novelty
 of his opinions prevents entire        
persuasion1 at least he convicts of     
emptiness most of the arguments with    
which his adversaries endeavour to      
overwhelm him4 ,he was particularly     
admirable on ,monday last1 in the house 
of ,signor ,frederico ,ghisilieri2  and 
what especially pleased me was1 that    

before replying to the contrary         
arguments1 he amplified and enforced    
them with new grounds of great          
plausibility1 so as to leave his        
adversaries in a more ridiculous plight 
when he afterwards overturned them all4 
,among the malicious stories which were 
put into circulation1 it had been  said1
 that the ,grand ,duke had withdrawn his
 favour1 which emboldened  many1 who    
would not otherwise have ventured on    
such open opposition1 to  declare       
against ,galileo4 ,his appearance at    
,rome1 where he was lodged in  the      
palace of ,cosmo's ambassador1 and      
whence he kept up a close               
correspondence with the ,grand ,duke's  
family1 put an immediate stop to        
rumours of this kind4 ,in little more   
than a month he was apparently          
triumphant1 so far as regarded himself2 
but the question now began to be        
agitated whether the whole system of    
,copernicus ought not to be  condemned  
as impious and heretical4 ,galileo again

 writes to ,picchena1  so far as        
concerns the clearing of my own         
character1 ,i might return  home        
immediately2 but although this new      
question regards me no more than  all   
those who for the last eighty years have
 supported these opinions  both in      
public and private1 yet1 as perhaps ,i  
may be of some assistance  in that part 
of the discussion which depends on the  
knowledge of truths  ascertained by     
means of the sciences which ,i profess1 
,i1 as a zealous  and ,catholic         
,christian1 neither can nor ought to    
withhold that  assistance which my      
knowledge affords2 and this business    
keeps me  sufficiently employed4 ,de    
,lambre1 whose readiness to depreciate  
,galileo's merit we have already noticed
 and lamented1 sneeringly and           
ungratefully remarks on this part of his
 life1 that it was scarcely  worth while
 to compromise his tranquillity and     
reputation1 in order to  become the     
champion of a truth which could not fail

 every day to acquire  new partisans by 
the natural effect of the progress of   
enlightened  opinions4 ,we need not stop
 to consider what the natural effects   
might  have been if none had at any time
 been found who thought their           
tranquillity worthily offered up in such
 a cause4    ,it has been hinted by     
several1 and is indeed probable1 that   
,galileo's  stay at ,rome rather injured
 the cause 7so far as provoking the     
inquisitorial censures could injure it7 
which it was his earnest desire  to     
serve1 for we cannot often enough repeat
 the assertion1 that it was  not the    
doctrine itself1 so much as the free1   
unyielding manner in which  it was      
supported1 which was originally         
obnoxious4 ,copernicus had been  allowed
 to dedicate his great work to ,pope    
,paul ,,iii41 and from the time  of its 
first appearance under that sanction in 
#aedc1 to the year #afaf1  of which we  
are now writing1 this theory was left in
 the hands of  mathematicians and       

philosophers1 who alternately attacked  
and defended  it without receiving      
either support or molestation from      
ecclesiastical  decrees4 ,but this was  
henceforward no longer the case1 and a  
higher  degree of importance was given  
to the controversy from the religious   
heresies which were asserted to be      
involved in the new opinions4 ,we have  
already given specimens of the so called
 philosophical arguments brought        
against ,copernicus2 and the reader may 
be curious to know the form of  the     
theological ones4 ,those which we select
 are taken from a work1 which  indeed   
did not come forth till the time of     
,galileo's third visit to  ,rome1 but it
 is relative to the matter now before   
us1 as it professed to  be1 and its     
author's party affected to consider it1 
a complete  refutation of the letters to
 ,castelli and the ,archduchess         
,christina4#gf    ,it was the work of a 
,jesuit1 ,melchior ,inchoffer1 and it   
was greatly  extolled by his companions1

 as differing so entirely from the      
pruriency  of the ,pythagorean writings4
 ,he quotes with approbation an author  
who1  first referring to the first verse
 of ,genesis for an argument that the   
earth was not created till after the    
heavens1 observes that the whole        
question is thus reduced to the         
examination of this purely geometrical  
difficulty--,in the formation of a      
sphere1 does the centre or              
circumference first come into existence8
 ,if the latter 7which we presume       
,melchior's friend found good reason for
 deciding upon71 the consequence  is    
inevitable4 ,the earth is in the centre 
of the universe4    ,it may not be      
unprofitable to contrast the extracts   
which we have given  from ,galileo's    
letters on the same subject with the    
following passage1  which appears one of
 the most subtle and argumentative which
 is to be  found in ,melchior's book4   
,he professes to be enumerating and     
refuting  the principal arguments which 

the ,copernicans adduced for the motion 
of  the earth4 ,fifth argument4 ,hell is
 in the centre of the earth1 and in  it 
is a fire tormenting the damned2        
therefore it is absolutely necessary    
that the earth is moveable4 ,the        
antecedent is plain4 7,inchoffer then   
quotes a number of texts of ,scripture  
on which1 according to him1 the         
,copernicans relied in proof of this    
part of the argument47 ,the  consequent 
is proved3 because fire is the cause of 
motion1 for which  reason ,pythagoras1  
who1 as ,aristotle reports1 puts the    
place of  punishment in the centre1     
perceived that the earth is animate and 
endowed with action4 ,i answer1 even    
allowing that hell is in the centre  of 
the earth1 and a fire in it1 ,i deny the
 consequence3 and for proof ,i  say1 if 
the argument is worth any thing1 it     
proves also that lime-kilns1  ovens1 and
 fire-grates are animated and           
spontaneously moveable4 ,i say1  even   
allowing that hell is in the centre of  

the earth3 for ,gregory1  book #d1 dial4
 chap4 #db1 says1 that he dare not      
decide rashly on this  matter1 although 
he thinks more probable the opinion of  
those who say  that it is under the     
earth4 ,st4 ,thomas1 in ,opusc4 #aj1    
art4 #ca1 says3  ,where hell is1 whether
 in the centre of the earth or at the   
surface1  does not in my opinion1 relate
 to any article of faith2 and it is     
superfluous to be solicitous about such 
things1 either in asserting or  denying 
them4 ,and ,opusc4 #aa1 art4 #bd1 he    
says1 that it seems to him that  nothing
 should be rashly asserted on this      
matter1 particularly as  ,augustin      
thinks that nobody knows where it is2   
but ,i do not1 says he1  think that it  
is in the centre of the earth4 ,i should
 be loth1 however1  that it should be   
hence inferred by some people that hell 
is in the  earth1 that we are ignorant  
where hell is1 and therefore that the   
situation of the earth is also unknown1 
and1 in conclusion1 that it  cannot     

therefore be the centre of the universe4
 ,the argument shall be  retorted in    
another fashion3 for if the place of the
 earth is unknown1  it cannot be said to
 be in a great circle1 so as to be moved
 round the  sun4 ,finally ,i say that in
 fact it is known where the earth is4   
,it is not impossible that some persons 
adopted the ,copernican theory1  from an
 affectation of singularity and         
freethinking1 without being able  to    
give very sound reasons for their change
 of opinion1 of whom we have  an        
instance in ,origanus1 the astrological 
instructor of ,wallenstein's  famous    
attendant ,seni1 who edited his work4   
,his arguments in favour of  the earth's
 motion are quite on a level with those 
advanced on the  opposite side in favour
 of its immobility2 but we have not     
found any  traces whatever of such      
absurdities as these having been urged  
by any of  the leaders of that party1   
and it is far more probable that they   
are the  creatures of ,melchior's own   

imagination4 ,at any rate it is worth   
remarking how completely he disregards  
the real physical arguments1  which he  
ought1 in justice to his cause1 to have 
attempted to  controvert4 ,his book was 
aimed at ,galileo and his adherents1 and
 it is  scarcely possible that he could 
seriously persuade himself that he was  
stating and overturning arguments       
similar to those by which ,galileo had  
made so many converts to the opinions of
 ,copernicus4 ,whatever may be our      
judgment of his candour1 we may at least
 feel assured that if this had  indeed  
been a fair specimen of ,galileo's      
philosophy1 he might to the end  of his 
life have taught that the earth moved   
round the sun1 or if his  fancy led him 
to a different hypothesis1 he might like
 the ,abb ,baliani  have sent the earth 
spinning round the stationary moon1 and 
like him  have remained unmolested by   
pontifical censures4 ,it is true that   
,baliani  owned his opinion to be much  
shaken1 on observing it to be opposed to

  the decree of those in whose hands was
 placed the power of judging  articles  
of faith4 ,but ,galileo's uncompromising
 spirit of analytical  investigation1   
and the sober but invincible force of   
reasoning with  which he beat down every
 sophism opposed to him1 the instruments
 with  which he worked1 were more odious
 than the work itself1 and the          
condemnation which he had vainly hoped  
to avert was probably on his very       
account accelerated4    ,galileo1       
according to his own story1 had in      
,march #afaf a most gracious  audience  
of the pope1 ,paul ,v41 which lasted for
 nearly an hour1 at the  end of which   
his holiness assured him1 that the      
,congregation were no  longer in a      
humour to listen lightly to calumnies   
against him1 and that  so long as he    
occupied the papal chair1 ,galileo might
 think himself out  of all danger4 ,but 
nevertheless he was not allowed to      
return home1  without receiving formal  
notice not to teach the opinions of     

,copernicus1 that the sun is in the     
centre of the system1 and that the      
earth moves about it1 from that time    
forward1 in any manner4 ,that these     
were the literal orders given to        
,galileo will be presently proved from  
the recital of them in the famous decree
 against him1 seventeen years  later4   
,for the present1 his letters which we  
have mentioned1 as well as  one of a    
similar tendency by ,foscarini1 a       
,carmelite friar--a commentary  on the  
book of ,joshua by a ,spaniard named    
,diego ,zuniga--,kepler's ,epitome  of  
the ,copernican ,theory--and            
,copernicus's own work1 were inserted in
  the list of forbidden books1 nor was  
it till four years afterwards1 in       
#afbj1 that1 on reconsideration1        
,copernicus was allowed to be read with 
certain omissions and alterations then  
decided upon4    ,galileo quitted ,rome 
scarcely able to conceal his contempt   
and  indignation4 ,two years afterwards 
this spirit had but little subsided1    

for in forwarding to the ,archduke      
,leopold his ,theory of the ,tides1 he  
accompanied it with the following       
remarks3--,this theory occurred to me   
when in ,rome1 whilst the theologians   
were debating on the prohibition of     
,copernicus's book1 and of the opinion  
maintained in it of the motion of  the  
earth1 which ,i at that time believed2  
until it pleased those  gentlemen to    
suspend the book1 and declare the       
opinion false and  repugnant to the     
,holy ,scriptures4 ,now1 as ,i know how 
well it becomes me  to obey and believe 
the decisions of my superiors1 which    
proceed out of  more profound knowledge 
than the weakness of my intellect can   
attain to1  this theory which ,i send   
you1 which is founded on the motion of  
the  earth1 ,i now look upon as a       
fiction and a dream1 and beg your       
highness  to receive it as such4 ,but1  
as poets often learn to prize the       
creations  of their fancy1 so1 in like  
manner1 do ,i set some value on this    

absurdity of mine4 ,it is true that when
 ,i sketched this little work1 ,i  did  
hope that ,copernicus would not1 after  
#hj years1 be convicted of  error1 and  
,i had intended to develope and amplify 
it farther1 but a  voice from heaven    
suddenly awakened me1 and at once       
annihilated all my  confused and        
entangled fancies4    ,it might have    
been predicted1 from the tone of this   
letter alone1 that  it would not be long
 before ,galileo would again bring      
himself under the  censuring notice of  
the astronomical hierarchy1 and indeed  
he had1 so  early as #afaj1 collected   
some of the materials for the work which
 caused  the final explosion1 and on    
which he now employed himself with as   
little  intermission as the weak state  
of his health permitted4    ,he had been
 before this time engaged in a          
correspondence with the court  of       
,spain1 on the method of observing      
longitudes at sea1 for the solution  of 
which important problem ,philip ,,iii4  

had offered a considerable  reward1 an  
example which has since been followed in
 our own and other  countries4 ,galileo 
had no sooner discovered ,jupiter's     
satellites1 than  he recognized the use 
which might be made of them for that    
purpose1 and  devoted himself with      
peculiar assiduity to acquiring as      
perfect a  knowledge as possible of     
their revolutions4 ,the reader will     
easily  understand how they were to be  
used1 if their motion could be so well  
ascertained as to enable ,galileo at    
,florence to predict the exact times  at
 which any remarkable configurations    
would occur1 as1 for instance1  the     
times at which any one of them would be 
eclipsed by ,jupiter4 ,a  mariner who in
 the middle of the ,atlantic should     
observe the same  eclipse1 and compare  
the time of night at which he made the  
observation  7which he might know by    
setting his watch by the sun on the     
preceding  day7 with the time mentioned 
in the predictions1 would1 from the     

difference between the two1 learn the   
difference between the hour at          
,florence and the hour at the place     
where the ship at that time happened  to
 be4 ,as the earth turns uniformly round
 through #cfj of longitude in  #bd      
hours1 that is1 through #ae in each     
hour1 the hours1 minutes1 and  seconds  
of time which express this difference   
must be multiplied by #ae1  and the     
respective products will give the       
degrees1 minutes1 and seconds  of       
longitude1 by which the ship was then   
distant from ,florence4 ,this  statement
 is merely intended to give those who   
are unacquainted with  astronomy1 a     
general idea of the manner in which it  
was proposed to use  these satellites4  
,our moon had already been occasionally 
employed in the  same way1 but the      
comparative frequency of the eclipses of
 ,jupiter's  moons1 and the suddenness  
with which they disappear1 gives a      
decided  advantage to the new method4   
,both methods were embarrassed by the   

difficulty of observing the eclipses at 
sea4 ,in addition to this1 it was       
requisite1 in both methods1 that the    
sailors should be provided with         
accurate means of knowing the hour1     
wherever they might chance to be1  which
 was far from being the case1 for       
although 7in order not to  interrupt the
 explanation7 we have above spoken of   
their watches1 yet  the watches and     
clocks of that day were not such as     
could be relied on  sufficiently1 during
 the interval which must necessarily    
occur between  the two observations4    
,this consideration led ,galileo to     
reflect on the  use which might be made 
of his pendulum for this purpose2 and1  
with  respect to the other difficulty1  
he contrived a peculiar kind of         
telescope1 with which he flattered      
himself1 somewhat prematurely1 that  it 
would be as easy to observe on          
ship-board as on shore4    ,during his  
stay at ,rome1 in #afae1 and the        
following year1 he disclosed  some of   

these ideas to the ,conte di ,lemos1 the
 viceroy of ,naples1 who  had been      
president of the council of the ,spanish
 ,indies1 and was fully  aware of the   
importance of the matter4 ,galileo was  
in consequence  invited to communicate  
directly with the ,duke of ,lerma1 the  
,spanish  minister1 and instructions    
were accordingly sent by ,cosmo1 to the 
,conte  ,orso d',elci1 his ambassador at
 ,madrid1 to conduct the business there4
  ,galileo entered warmly into the      
design1 of which he had no other means  
of verifying the practicability2 for as 
he says in one of his letters to        
,spain--,your excellency may well       
believe that if this were an            
undertaking which ,i could conclude by  
myself1 ,i would never have gone  about 
begging favours from others2 but in my  
study there are neither  seas1 nor      
,indies1 nor islands1 nor ports1 nor    
shoals1 nor ships1 for  which reason ,i 
am compelled to share the enterprise    
with great  personages1 and to fatigue  

myself to procure the acceptance of     
that1  which ought with eagerness to be 
asked of me2 but ,i console myself with 
the reflection that ,i am not singular  
in this1 but that it commonly  happens1 
with the exception of a little          
reputation1 and that too often  obscured
 and blackened by envy1 that the least  
part of the advantage  falls to the     
share of the inventors of things1 which 
afterwards bring  great gain1 honours1  
and riches to others2 so that ,i will   
never cease on  my part to do every     
thing in my power1 and ,i am ready to   
leave here all  my comforts1 my country1
 my friends1 and family1 and to cross   
over into  ,spain1 to stay as long as ,i
 may be wanted in ,seville1 or ,lisbon1 
or  wherever it may be convenient1 to   
implant the knowledge of this method1   
provided that due assistance and        
diligence be not wanting on the part of 
those who are to receive it1 and who    
should solicit and foster it4 ,but  he  
could not1 with all his enthusiasm1     

rouse the attention of the  ,spanish    
court4 ,the negotiation languished1 and 
although occasionally  renewed during   
the next ten or twelve years1 was never 
brought to a  satisfactory issue4 ,some 
explanation of this otherwise           
unaccountable  apathy of the ,spanish   
court1 with regard to the solution of a 
problem  which they had certainly much  
at heart1 is given in ,nelli's life of  
,galileo2 where it is asserted1 on the  
authority of the ,florentine  records1  
that ,cosmo required privately from     
,spain1 7in return for the  permission  
granted for ,galileo to leave ,florence1
 in pursuance of this  design17 the     
privilege of sending every year from    
,leghorn two  merchantmen1 duty free1 to
 the ,spanish ,indies4      ,,footnotes3
    #gd ,ce philosophe 7,galile7 ne fut 
point persecut comme bon astronome1     
mais comme mauvais thologien4 ,c'est son
 enttement  vouloir concilier  la ,bible
 avec ,copernic qui lui donna des juges4
 ,mais vingt auteurs1  surtout parmi les

 protestans1 ont crit que ,galile fut   
persecut et  imprisonn pour avoir       
soutenu que la terre tourne autour du   
soleil1 que  ce systme a t condann par  
l'inquisition comme faux1 erron et      
contraire  la ,bible1 c4--,bergier1     
,encyclopdie ,mthodique1 ,paris1  #agij1
 ,art4 ,,sciences ,,humaines4    #ge    
,viri ,galili1 quid statis adspicientes 
in clum4 ,acts ,i4 #aa4    #gf          
,tractatus ,syllepticus4 ,rom1 #afcc4   
,the title-page of this  remarkable     
production is decorated with an         
emblematical figure1  representing the  
earth included in a triangle2 and in the
 three corners1  grasping the globe with
 their fore feet1 are placed three bees1
 the arms  of ,pope ,urban ,,viii4 who  
condemned ,galileo and his writings4    
,the motto is  ,his fixa quiescit1      
,fixed by these it is at rest4          
,,chapter ,,xii4        ,controversy on 
,comets--,saggiatore--,galileo's        
reception by ,urban        ,,viii--,his 
family4      ,,the year #afah was       

remarkable for the appearance of three  
comets1 on  which almost every          
astronomer in ,europe found something to
 say and  write4 ,galileo published some
 of his opinions with respect to them1  
through the medium of ,mario ,guiducci4 
,this astronomer delivered a  lecture   
before the ,florentine academy1 the     
heads of which he was  supposed to have 
received from ,galileo1 who1 during the 
whole time of  the appearance of these  
comets1 was confined to his bed by      
severe  illness4 ,this essay was printed
 in ,florence at the sign of ,the       
,medicean  ,stars4#gg ,what principally 
deserves notice in it1 is the opinion of
  ,galileo1 that the distance of a comet
 cannot be safely determined by its     
parallax1 from which we learn that he   
inclined to believe that comets  are    
nothing but meteors occasionally        
appearing in the atmosphere1 like       
rainbows1 parhelia1 and similar         
phenomena4 ,he points out the difference
  in this respect between a fixed       

object1 the distance of which may be    
calculated from the difference of       
direction in which two observers 7at a  
known distance from each other7 are     
obliged to turn themselves in order  to 
see it1 and meteors like the rainbow1   
which are simultaneously formed  in     
different drops of water for each       
spectator1 so that two observers  in    
different places are in fact            
contemplating different objects4 ,he    
then  warns astronomers not to engage   
with too much warmth in a discussion on 
the distance of comets before they      
assure themselves to which of these  two
 classes of phenomena they are to be    
referred4 ,the remark is in  itself     
perfectly just1 although the opinion    
which occasioned it is now  as certainly
 known to be erroneous1 but it is       
questionable whether the  observations  
which1 up to that time1 had been made   
upon comets1 were  sufficient1 either in
 number or quality1 to justify the      
censure which  has been cast on ,galileo

 for his opinion4 ,the theory1 moreover1
 is  merely introduced as an hypothesis 
in ,guiducci's essay4 ,the same opinion 
was for a short time embraced by        
,cassini1 a celebrated ,italian         
astronomer1 invited by ,louis ,,xiv4 to 
the ,observatory at ,paris1 when the    
science was considerably more advanced1 
and ,newton1 in his ,principia1  did not
 think it unworthy of him to show on    
what grounds it is  untenable4          
,galileo was become the object of       
animosity in so many quarters that none 
of his published opinions1 whether      
correct or incorrect1 ever wanted a     
ready antagonist4 ,the champion on the  
present occasion was again a  ,jesuit2  
his name was ,oratio ,grassi1 who       
published ,the ,astronomical and        
,philosophical ,balance1 under the      
disguised signature of ,lotario ,sarsi4 
,galileo and his friends were anxious   
that his reply to ,grassi should  appear
 as quickly as possible1 but his health 
had become so precarious  and his       

frequent illnesses occasioned so many   
interruptions1 that it was  not until   
the autumn of #afbc that ,il ,saggiatore
 7or ,the ,assayer7 as he  called his   
answer1 was ready for publication4 ,this
 was printed by the  ,lyncean ,academy1 
and as ,cardinal ,maffeo ,barberino1 who
 had just been  elected ,pope1 7with the
 title of ,urban ,,viii47 had been      
closely connected  with that society1   
and was also a personal friend of ,cesi 
and of  ,galileo1 it was thought a      
prudent precaution to dedicate the      
pamphlet to  him4 ,this essay enjoys a  
peculiar reputation among ,galileo's    
works1 not  only for the matter         
contained in it1 but also for the style 
in which it  is written2 insomuch that  
,andrs#gh1 when eulogizing ,galileo as  
one of  the earliest who adorned        
philosophical truths with the graces and
  ornaments of language1 expressly      
instances the ,saggiatore1 which is also
  quoted by ,frisi and ,algarotti1 as a 
perfect model of this sort of           

composition4 ,in the latter particular1 
it is unsafe to interfere with  the     
decisions of an ,italian critic2 but    
with respect to its substance1  this    
famous composition scarcely appears to  
deserve its preeminent  reputation4 ,it 
is a prolix and rather tedious          
examination of ,grassi's  ,essay2 nor do
 the arguments seem so satisfactory1 nor
 the reasonings so  compact as is       
generally the case in ,galileo's other  
writings4 ,it does  however1 like all   
his other works1 contain many very      
remarkable  passages1 and the celebrity 
of this production requires that we     
should  extract one or two of the most  
characteristic4    ,the first1 though a 
very short one1 will serve to shew the  
tone which  ,galileo had taken with     
respect to the ,copernican system since 
its  condemnation at ,rome1 in #afaf4   
,in conclusion1 since the motion        
attributed to the earth1 which ,i1 as a 
pious and ,catholic person1  consider   
most false1 and not to exist1           

accommodates itself so well to  explain 
so many and such different phenomena1 ,i
 shall not feel sure1  unless ,sarsi    
descends to more distinct considerations
 than those which  he has yet produced1 
that1 false as it is1 it may not just as
 deludingly  correspond with the        
phenomena of comets4    ,sarsi had      
quoted a story from ,suidas in support  
of his argument that  motion always     
produces heat1 how the ,babylonians used
 to cook their eggs  by whirling them in
 a sling2 to which ,galileo replies3 ,i 
cannot refrain  from marvelling that    
,sarsi will persist in proving to me1 by
  authorities1 that which at any moment 
,i can bring to the test of  experiment4
 ,we examine witnesses in things which  
are doubtful1 past1 and  not permanent1 
but not in those things which are done  
in our own  presence4 ,if discussing a  
difficult problem were like carrying a  
weight1  since several horses will carry
 more sacks of corn than one alone will1
  ,i would agree that many reasoners    

avail more than one2 but discoursing  is
 like coursing1 and not like carrying1  
and one barb by himself will  run       
farther than a hundred ,friesland       
horses4 ,when ,sarsi brings up such a   
multitude of authors1 it does not seem  
to me that he in the least degree       
strengthens his own conclusions1 but he 
ennobles the cause of ,signor  ,mario   
and myself1 by shewing that we reason   
better than many men of  established    
reputation4 ,if ,sarsi insists that ,i  
believe1 on ,suidas'  credit1 that the  
,babylonians cooked eggs by swiftly     
whirling them in a  sling1 ,i will      
believe it2 but ,i must needs say1 that 
the cause of such  an effect is very    
remote from that to which it is         
attributed1 and to  find the true cause 
,i shall reason thus4 ,if an effect does
 not follow  with us which followed with
 others at another time1 it is because1 
in  our experiment1 something is wanting
 which was the cause of the former      
success2 and if only one thing is       

wanting to us1 that one thing is the    
true cause4 ,now we have eggs1 and      
slings1 and strong men to whirl them1   
and yet they will not become cooked2    
nay1 if they were hot at first1  they   
more quickly become cold3 and since     
nothing is wanting to us but to  be     
,babylonians1 it follows that being     
,babylonians is the true cause why  the 
eggs became hard1 and not the friction  
of the air1 which is what ,i  wished to 
prove4--,is it possible that in         
travelling post1 ,sarsi has  never      
noticed what freshness is occasioned on 
the face by the continual  change of    
air8 and if he has felt it1 will he     
rather trust the relation  by others1 of
 what was done two thousand years ago at
 ,babylon1 than what  he can at this    
moment verify in his own person8 ,i at  
least will not be  so wilfully wrong1   
and so ungrateful to nature and to ,god1
 that having  been gifted with sense and
 language1 ,i should voluntarily set    
less value  on such great endowments    

than on the fallacies of a fellow man1  
and  blindly and blunderingly believe   
whatever ,i hear1 and barter the freedom
  of my intellect for slavery to one as 
liable to error as myself4    ,our final
 extract shall exhibit a sample of      
,galileo's metaphysics1 in  which may be
 observed the germ of a theory very     
closely allied to that  which was       
afterwards developed by ,locke and      
,berkeley4--,i have now only  to fulfil 
my promise of declaring my opinions on  
the proposition that  motion is the     
cause of heat1 and to explain in what   
manner it appears to  me that it may be 
true4 ,but ,i must first make some      
remarks on that which  we call heat1    
since ,i strongly suspect that a notion 
of it prevails  which is very remote    
from the truth2 for it is believed that 
there is a  true accident1 affection1   
and quality1 really inherent in the     
substance  by which we feel ourselves   
heated4 ,this much ,i have to say1 that 
so soon  as ,i conceive a material or   

corporeal substance1 ,i simultaneously  
feel  the necessity of conceiving that  
it has its boundaries1 and is of some   
shape or other2 that1 relatively to     
others1 it is great or small2 that  it  
is in this or that place1 in this or    
that time2 that it is in motion1  or at 
rest2 that it touches1 or does not touch
 another body2 that it is  unique1 rare1
 or common2 nor can ,i1 by any act of   
the imagination1  disjoin it from these 
qualities3 but ,i do not find myself    
absolutely  compelled to apprehend it as
 necessarily accompanied by such        
conditions1  as that it must be white or
 red1 bitter or sweet1 sonorous or      
silent1  smelling sweetly or            
disagreeably2 and if the senses had not 
pointed out  these qualities1 it is     
probable that language and imagination  
alone  could never have arrived at them4
 ,because1 ,i am inclined to think that 
these tastes1 smells1 colours1 c41 with 
regard to the subject in which  they    
appear to reside1 are nothing more than 

mere names1 and exist only  in the      
sensitive body2 insomuch that1 when the 
living creature is  removed1 all these  
qualities are carried off and           
annihilated2 although  we have imposed  
particular names upon them1 and         
different from those of  the other first
 and real accidents1 and would fain     
persuade ourselves  that they are truly 
and in fact distinct4 ,but ,i do not    
believe that  there exists any thing in 
external bodies for exciting tastes1    
smells1  and sounds1 but size1 shape1   
quantity1 and motion1 swift or slow2 and
 if  ears1 tongues1 and noses were      
removed1 ,i am of opinion that shape1   
number1 and motion would remain1 but    
there would be an end of smells1        
tastes1 and sounds1 which1 abstractedly 
from the living creature1 ,i take  to be
 mere words4    ,in the spring following
 the publication of the ,saggiatore1    
that is to  say1 about the time of      
,easter1 in #afbd1 ,galileo went a third
 time to  ,rome to compliment ,urban on 

his elevation to the pontifical chair4  
,he  was obliged to make this journey in
 a litter2 and it appears from his      
letters that for some years he had been 
seldom able to bear any other  mode of  
conveyance4 ,in such a state of health  
it seems unlikely that he  would have   
quitted home on a mere visit of         
ceremony1 which suspicion is            
strengthened by the beginning of a      
letter from him to ,prince ,cesi1 dated 
in ,october1 #afbc1 in which he says3 ,i
 have received the very courteous  and  
prudent advice of your excellency about 
the time and manner of my  going to     
,rome1 and shall act upon it2 and ,i    
will visit you at ,acqua  ,sparta1 that 
,i may be completely informed of the    
actual state of things  at ,rome4       
,however this may be1 nothing could be  
more gratifying than his  public        
reception there4 ,his stay in ,rome did 
not exceed two months1  7from the       
beginning of ,april till ,june17 and    
during that time he was  admitted to six

 long and satisfactory interviews with  
the ,pope1 and on  his departure        
received the promise of a pension for   
his son ,vincenzo1  and was himself     
presented with a fine painting1 two     
medals1 one of gold  and the other of   
silver1 and a good quantity of agnus    
dei4 ,he had also  much communication   
with several of the cardinals1 one of   
whom1 ,cardinal  ,hohenzoller1 told him 
that he had represented to the pope on  
the subject  of ,copernicus1 that all   
the heretics were of that opinion1 and  
considered it as undoubted2 and that it 
would be necessary to be very           
circumspect in coming to any resolution3
 to which his holiness replied1  that   
the church had not condemned it1 nor was
 it to be condemned as  heretical1 but  
only as rash2 adding1 that there was no 
fear of any one  undertaking to prove   
that it must necessarily be true4 ,urban
 also  addressed a letter to ,ferdinand1
 who had succeeded his father ,cosmo as 
,grand ,duke of ,tuscany1 expressly for 

the purpose of recommending ,galileo  to
 him4 ,for ,we find in him not only     
literary distinction1 but also the  love
 of piety1 and he is strong in those    
qualities by which pontifical  good-will
 is easily obtained4 ,and now1 when he  
has been brought to this  city to       
congratulate ,us on ,our elevation1 ,we 
have very lovingly embraced  him2--nor  
can ,we suffer him to return to the     
country whither your  liberality recalls
 him without an ample provision of      
pontifical love4  ,and that you may know
 how dear he is to ,us1 ,we have willed 
to give him  this honourable testimonial
 of virtue and piety4 ,and ,we further  
signify  that every benefit which you   
shall confer upon him1 imitating1 or    
even  surpassing your father's          
liberality1 will conduce to ,our        
gratification4  ,honoured with these    
unequivocal marks of approbation1       
,galileo returned  to ,florence4    ,his
 son ,vincenzo is soon afterwards spoken
 of as being at ,rome2 and it  is not   

improbable that ,galileo sent him       
thither on the appointment of  his      
friend and pupil1 the ,abb ,castelli1 to
 be mathematician to the  pope4         
,vincenzo had been legitimated by an    
edict of ,cosmo in #afai1 and1          
according to ,nelli1 married1 in #afbd1 
,sestilia1 the daughter of ,carlo       
,bocchineri4 ,there are no traces to be 
found of ,vincenzo's mother after       
#afaj1 and perhaps she died about that  
time4 ,galileo's family by her          
consisted of ,vincenzo and two          
daughters1 ,julia and ,polissena1 who   
both  took the veil in the convent of   
,saint ,matthew at ,arcetri1 under the  
names of ,sister ,arcangiola and ,sister
 ,maria ,celeste4 ,the latter is said   
to have possessed extraordinary talents4
 ,the date of ,vincenzo's  marriage1 as 
given by ,nelli1 appears somewhat       
inconsistent with the  correspondence   
between ,galileo and ,castelli1 in      
which1 so late as #afbi1  ,galileo is   
apparently writing of his son as a      

student under ,castelli's               
superintendence1 and intimates the      
amount of pocket-money he can afford  to
 allow him1 which he fixes at three     
crowns a month2 adding1 that he  ought  
to be contented with as many crowns1 as1
 at his age1 ,i possessed  groats4      
,castelli had given but an unfavourable 
account of ,vincenzo's  conduct1        
characterizing him as dissolute1        
obstinate1 and impudent2 in  consequence
 of which behaviour1 ,galileo seems to  
have thought that the  pension of sixty 
crowns1 which had been granted by the   
pope1 might be  turned to better account
 than by employing it on his son's      
education2  and accordingly in his reply
 he requested ,castelli to dispose of   
it1  observing that the proceeds would  
be useful in assisting him to  discharge
 a great load of debt with which he     
found himself saddled on  account of his
 brother's family4 ,besides this        
pension1 another of one  hundred crowns 
was in a few years granted by ,urban to 

,galileo himself1  but it appears to    
have been very irregularly paid1 if at  
all4    ,about the same time ,galileo   
found himself menaced either with the   
deprivation of his stipend as           
extraordinary professor at ,pisa1 or    
with  the loss of that leisure which1 on
 his removal to ,florence1 he had been  
so anxious to secure4 ,in #afbi1 the    
question was agitated by the party      
opposed to him1 whether it were in the  
power of the grand duke to assign  a    
pension out of the funds of the         
,university1 arising out of             
ecclesiastical dues1 to one who neither 
lectured nor resided there4 ,this       
scruple had slept during nineteen years 
which had elapsed since  ,galileo's     
establishment in ,florence1 but probably
 those who now raised  it reckoned upon 
finding in ,ferdinand ,,ii41 then       
scarcely of age1 a less  firm supporter 
of ,galileo than his father ,cosmo had  
been4 ,but the matter  did not proceed  
so far2 for1 after full deliberation1   

the prevalent  opinion of the           
theologians and jurists who were        
consulted appeared to be  in favour of  
this exercise of prerogative1 and       
accordingly ,galileo  retained his      
stipend and privileges4                 
,,footnotes3    #gg ,in ,firenze nella  
,stamperia di ,pietro ,cecconcelli alle 
stelle  ,medicee1 #afai4    #gh         
,dell',origine d'ogni ,literatura3      
,parma1 #aghg4          ,,chapter       
,,xiii4        ,publication of          
,galileo's ',system of the ,world'--,his
 ,condemnation        and ,abjuration4  
,,in the year #afcj1 ,galileo brought to
 its conclusion his great work1 ,the    
,dialogue on the ,ptolemaic and         
,copernican ,systems1 and began to take 
the  necessary steps for procuring      
permission to print it4 ,this was to be 
obtained in the first instance from an  
officer at ,rome1 entitled the  master  
of the sacred palace2 and after a little
 negotiation ,galileo  found it would be
 necessary for him again to return      

thither1 as his  enemies were still busy
 in thwarting his views and wishes4     
,niccolo  ,riccardi1 who at that time   
filled the office of master of the      
palace1  had been a pupil of ,galileo1  
and was well disposed to facilitate his 
plans2 he pointed out1 however1 some    
expressions in the work which he        
thought it necessary to erase1 and1 with
 the understanding that this  should be 
done1 he returned the manuscript to     
,galileo with his  subscribed           
approbation4 ,the unhealthy season was  
drawing near1 and  ,galileo1 unwilling  
to face it1 returned home1 where he     
intended to  complete the index and     
dedication1 and then to send it back to 
,rome to  be printed in that city1 under
 the superintendence of ,federigo ,cesi4
  ,this plan was disconcerted by the    
premature death of that accomplished    
nobleman1 in ,august #afcj1 in whom     
,galileo lost one of his steadiest and  
most effective friends and protectors4  
,this unfortunate event determined      

,galileo to attempt to procure          
permission to print his book at         
,florence4  ,a contagious disorder had  
broken out in ,tuscany with such        
severity as  almost to interrupt all    
communication between ,florence and     
,rome1 and  this was urged by ,galileo  
as an additional reason for granting his
  request4 ,riccardi at first seemed    
inclined to insist that the book  should
 be sent to him a second time1 but at   
last contented himself with  inspecting 
the commencement and conclusion1 and    
consented that 7on its  receiving also a
 license from the inquisitor-general at 
,florence1 and  from one or two others  
whose names appear on the title-page7 it
 might be  printed where ,galileo       
wished4    ,these protracted            
negotiations prevented the publication  
of the work till  late in #afcb2 it then
 appeared1 with a dedication to         
,ferdinand1 under  the following        
title3--,a ,dialogue1 by ,galileo       
,galilei1 ,extraordinary  ,mathematician

 of the ,university of ,pisa1 and       
,principal ,philosopher and             
,mathematician of the ,most ,serene     
,grand ,duke of ,tuscany2 in which1 in a
  conversation of four days1 are        
discussed the two principal ,systems of 
the ,world1 the ,ptolemaic and          
,copernican1 indeterminately proposing  
the  ,philosophical ,arguments as well  
on one side as on the other4 ,the       
beginning of the introduction1 which is 
addressed ,to the discreet  ,reader1 is 
much too characteristic to be passed by 
without  notice4--,some years ago1 a    
salutary edict was promulgated at ,rome1
  which1 in order to obviate the        
perilous scandals of the present age1   
enjoined an opportune silence on the    
,pythagorean opinion of the earth's     
motion4 ,some were not wanting1 who     
rashly asserted that this decree        
originated1 not in a judicious          
examination1 but in ill informed        
passion2  and complaints were heard that
 counsellors totally inexperienced in   

astronomical observations ought not by  
hasty prohibitions to clip the  wings of
 speculative minds4 ,my zeal could not  
keep silence when ,i heard  these rash  
lamentations1 and ,i thought it proper1 
as being fully  informed with regard to 
that most prudent determination1 to     
appear  publicly on the theatre of the  
world as a witness of the actual truth4 
,i  happened at that time to be in      
,rome3 ,i was admitted to the audiences1
  and enjoyed the approbation of the    
most eminent prelates of that court1    
nor did the publication of that decree  
occur without my receiving some  prior  
intimation of it4#gi ,wherefore it is my
 intention in this present  work1 to    
show to foreign nations that as much is 
known of this matter in  ,italy1 and    
particularly in ,rome1 as ultramontane  
diligence can ever have  formed any     
notion of1 and collecting together all  
my own speculations on  the ,copernican 
system1 to give them to understand that 
the knowledge of  all these preceded the

 ,roman censures1 and that from this    
country  proceed not only dogmas for the
 salvation of the soul1 but also        
ingenious discoveries for the           
gratification of the understanding4     
,with  this object1 ,i have taken up in 
the ,dialogue the ,copernican side of   
the  question1 treating it as a pure    
mathematical hypothesis2 and            
endeavouring in every artificial manner 
to represent it as having the           
advantage1 not over the opinion of the  
stability of the earth  absolutely1 but 
according to the manner in which that   
opinion is  defended by some1 who indeed
 profess to be ,peripatetics1 but retain
 only  the name1 and are contented      
without improvement to worship shadows1 
not  philosophizing with their own      
reason1 but only from the recollection  
of  four principles imperfectly         
understood4--,this very flimsy veil     
could  scarcely blind any one as to     
,galileo's real views in composing this 
work1 nor does it seem probable that he 

framed it with any expectation  of      
appearing neutral in the discussion4 ,it
 is more likely that he  flattered      
himself that1 under the new government  
at ,rome1 he was not  likely to be      
molested on account of the personal     
prohibition which he  had received in   
#afaf1 not to believe or teach the      
motion of the earth  in any manner1     
provided he kept himself within the     
letter of the limits  of the more public
 and general order1 that the ,copernican
 system was not  to be brought forward  
otherwise than as a mere mathematically 
convenient1 but in fact unreal          
supposition4 ,so long as this decree    
remained in force1 a due regard to      
consistency would compel the ,roman     
,inquisitors to notice an unequivocal   
violation of it2 and this is  probably  
what ,urban had implied in the remark   
quoted by ,hohenzoller to  ,galileo4#hj 
,there were not wanting circumstances   
which might compensate  for the loss of 
,cosmo and of ,federigo ,cesi2 ,cosmo   

had been succeeded by  his son1 who1    
though he had not yet attained his      
father's energy1 showed  himself as     
friendly as possible to ,galileo4       
,cardinal ,bellarmine1 who had  been    
mainly instrumental in procuring the    
decree of #afaf1 was dead2  ,urban on   
the contrary1 who had been among the few
 ,cardinals who then  opposed it as     
uncalled for and ill-advised1 was now   
possessed of supreme  power1 and his    
recent affability seemed to prove that  
the increased  difference in their      
stations had not caused him to forget   
their early  and long-continued         
intimacy4 ,it is probable that ,galileo 
would not have  found himself mistaken  
in this estimate of his position1 but   
for an  unlucky circumstance1 of which  
his enemies immediately saw the         
importance1 and which they were not slow
 in making available against  him4 ,the 
dialogue of ,galileo's work is conducted
 between three  personages2--,salviati  
and ,sagredo1 who were two noblemen1    

friends of  ,galileo1 and ,simplicio1 a 
name borrowed from a noted commentator  
upon  ,aristotle1 who wrote in the sixth
 century4 ,salviati is the principal    
philosopher of the work2 it is to him   
that the others apply for  solutions of 
their doubts and difficulties1 and on   
him the principal  task falls of        
explaining the tenets of the ,copernican
 theory4 ,sagredo is  only a half       
convert1 but an acute and ingenious one2
 to him are allotted  the objections    
which seem to have some real difficulty 
in them1 as well  as lively             
illustrations and digressions1 which    
might have been thought  inconsistent   
with the gravity of ,salviati's         
character4 ,simplicio1 though  candid   
and modest1 is of course a confirmed    
,ptolemaist and ,aristotelian1  and is  
made to produce successively all the    
popular arguments of that  school in    
support of his master's system4 ,placed 
between the wit and the  philosopher1 it
 may be guessed that his success is very

 indifferent1 and  in fact he is        
alternately ridiculed and confuted at   
every turn4 ,as  ,galileo racked his    
memory and invention to leave unanswered
 no argument  which was or could be     
advanced against ,copernicus1 it        
unfortunately  happened1 that he        
introduced some which ,urban himself had
 urged upon him  in their former        
controversies on this subject2 and      
,galileo's opponents  found means to    
make ,his ,holiness believe that the    
character of ,simplicio  had been       
sketched in personal derision of him4   
,we do not think it  necessary to       
exonerate ,galileo from this charge2 the
 obvious folly of  such an useless piece
 of ingratitude speaks sufficiently for 
itself4 ,but  self-love is easily       
irritated2 and ,urban1 who aspired to a 
reputation  for literature and science1 
was peculiarly sensitive on this point4 
,his  own expressions almost prove his  
belief that such had been ,galileo's    
design1 and it seems to explain the     

otherwise inexplicable change which     
took place in his conduct towards his   
old friend1 on account of a book  which 
he had himself undertaken to examine1   
and of which he had  authorised the     
publication4    ,one of the earliest    
notices of what was approaching1 is     
found in the  dispatches1 dated ,august 
#bd1 #afcb1 from ,ferdinand's minister1 
,andrea  ,cioli1 to ,francesco          
,nicolini1 the ,tuscan ambassador at the
 court of  ,rome4    ,i have orders to  
signify to ,your ,excellency that ,his  
,highness remains  greatly astonished   
that a book1 placed by the author       
himself in the  hands of the supreme    
authority in ,rome1 read and read again 
there most  attentively1 and in which   
every thing1 not only with the consent1 
but at  the request of the author1 was  
amended1 altered1 added1 or removed at  
the will of his superiors1 which was    
again subjected here to the same        
examination1 agreeably to orders from   
,rome1 and which finally was  licensed  

both there and here1 and here printed   
and published1 should now  become an    
object of suspicion at the end of two   
years1 and the author  and printer be   
prohibited from publishing any          
more4--,in the sequel is  intimated     
,ferdinand's desire that the charges1 of
 whatever nature they  might be1 either 
against ,galileo or his book1 might be  
reduced to  writing and forwarded to    
,florence1 that he might prepare for his
  justification2 but this reasonable    
demand was utterly disregarded4 ,it     
appears to have been owing to the mean  
subserviency of ,cioli to the  court of 
,rome1 that ,ferdinand refrained from   
interfering more  strenuously to protect
 ,galileo4 ,cioli's words are3 ,the     
,grand ,duke is so  enraged with this   
business of ,galileo1 that ,i do not    
know what will be  done4 ,i know1 at    
least1 that ,his ,holiness shall have no
 reason to  complain of his ministers1  
or of their bad advice4#ha    ,a letter 
from ,galileo's ,venetian friend        

,micanzio1 dated about a month  later1  
is in rather a bolder and less formal   
style3--,the efforts of  your enemies to
 get your book prohibited will occasion 
no loss either to  your reputation1 or  
to the intelligent part of the world4   
,as to  posterity1 this is just one of  
the surest ways to hand the book down to
  them4 ,but what a wretched set this   
must be to whom every good thing1 and   
all that is founded in nature1          
necessarily appears hostile and odious6 
,the world is not restricted to a single
 corner2 you will see the book  printed 
in more places and languages than one2  
and just for this reason1  ,i wish they 
would prohibit all good books4 ,my      
disgust arises from seeing  myself      
deprived of what ,i most desire of this 
sort1 ,i mean your other  dialogues2 and
 if1 from this cause1 ,i fail in having 
the pleasure of  seeing them1 ,i shall  
devote to a hundred thousand devils     
these unnatural  and godless hypocrites4
    ,at the same time1 ,thomas          

,campanella1 a monk1 who had already    
distinguished himself by an apology for 
,galileo 7published in #afbb71  wrote to
 him from ,rome3--,i learn with the     
greatest disgust1 that a  congregation  
of angry theologians is forming to      
condemn your ,dialogues1  and that no   
single member of it has any knowledge of
 mathematics1 or  familiarity with      
abstruse speculations4 ,i should advise 
you to procure a  request from the      
,grand ,duke that1 among the ,dominicans
 and ,jesuits and  ,theatins1 and       
secular priests whom they are putting on
 this congregation  against your book1  
they should admit also ,castelli and    
myself4 ,it  appears1 from subsequent   
letters both from ,campanella and       
,castelli1 that  the required letter was
 procured and sent to ,rome1 but it was 
not  thought prudent to irritate the    
opposite party by a request which it was
  then clearly seen would have been made
 in vain4 ,not only were these  friends 
of ,galileo not admitted to the         

congregation1 but1 upon some  pretext1  
,castelli was even sent away from ,rome1
 as if ,galileo's enemies  desired to   
have as few enlightened witnesses as    
possible of their  proceedings2 and on  
the contrary1 ,scipio ,chiaramonte1 who 
had been long  known for one of the     
staunchest and most bigoted defenders of
 the old  system1 and who1 as ,montucla 
says1 seems to have spent a long life in
  nothing but retarding1 as far as he   
was able1 the progress of discovery1    
was summoned from ,pisa to complete     
their number4 ,from this period we  have
 a tolerably continuous account of the  
proceedings against ,galileo  in the    
dispatches which ,nicolini sent         
regularly to his court4 ,it appears     
from them that ,nicolini had several    
interviews with the ,pope1 whom he      
found highly incensed against ,galileo1 
and in one of the earliest he  received 
an intimation to advise the ,duke not to
 engage himself in this  matter as he   
had done in the other business of       

,alidosi1#hb because he  would not get  
through it with honour4 ,finding ,urban 
in this humour1  ,nicolini thought it   
best to temporize1 and to avoid the     
appearance of  any thing like direct    
opposition4 ,on the #aeth of ,september1
 probably as  soon as the first report  
on ,galileo's book had been made1       
,nicolini  received a private notice    
from the ,pope1 in especial token of the
  esteem in which he held the ,grand    
,duke1 that he was unable to do less    
than consign the work to the            
consideration of the ,inquisition4      
,nicolini  was permitted to communicate 
this to the ,grand ,duke only1 and both 
were  declared liable to the usual      
censures of the ,inquisition in case of 
divulging the secret4    ,the next step 
was to summon ,galileo to ,rome1 and the
 only answer  returned to all           
,nicolini's representations of his      
advanced age of  seventy years1 the very
 infirm state of his health1 and the    
discomforts  which he must necessarily  

suffer in such a journey1 and in keeping
  quarantine1 was that he might come at 
leisure1 and that the quarantine  should
 be relaxed as much as possible in his  
favour1 but that it was  indispensably  
necessary that he should be personally  
examined before the  ,inquisition at    
,rome4 ,accordingly1 on the #adth of    
,february1 #afcc1  ,nicolini announces  
,galileo's arrival1 and that he had     
officially  notified his presence to the
 ,assessor and ,commissary of the ,holy 
,office4  ,cardinal ,barberino1 ,urban's
 nephew1 who seems on the whole to have 
acted  a friendly part towards ,galileo1
 intimated to him that his most prudent 
course would be to keep himself as much 
at home and as quiet as  possible1 and  
to refuse to see any but his most       
intimate friends4 ,with  this advice1   
which was repeated to him from several  
quarters1 ,galileo  thought it best to  
comply1 and kept himself entirely       
secluded in  ,nicolini's palace1 where  
he was as usual maintained at the       

expense of  the ,grand ,duke4 ,nelli    
quotes two letters1 which passed between
  ,ferdinand's minister ,cioli and      
,nicolini1 in which the former intimated
  that ,galileo's expenses were to be   
defrayed only during the first month  of
 his residence at ,rome4 ,nicolini      
returned a spirited answer1 that in     
that case1 after the time specified1 he 
should continue to treat him as  before 
at his own private cost4    ,the        
permission to reside at the ambassador's
 palace whilst his cause was  pending1  
was granted and received as an          
extraordinary indulgence on the  part of
 the ,inquisition1 and indeed if we     
estimate the proceedings  throughout    
against ,galileo by the usual practice  
of that detestable  tribunal1 it will   
appear that he was treated with unusual 
consideration4  ,even when it became    
necessary in the course of the inquiry  
to examine  him in person1 which was in 
the beginning of ,april1 although his   
removal  to the ,holy ,office was then  

insisted upon1 yet he was not committed 
to  close or strictly solitary          
confinement4 ,on the contrary1 he was   
honourably lodged in the apartments of  
the ,fiscal of the ,inquisition1  where 
he was allowed the attendance of his own
 servant1 who was also  permitted to    
sleep in an adjoining room1 and to come 
and go at pleasure4  ,his table was     
still furnished by ,nicolini4 ,but1     
notwithstanding the  distinction with   
which he was thus treated1 ,galileo was 
annoyed and  uneasy at being 7though    
little more than nominally7 within the  
walls of  the ,inquisition4 ,he became  
exceedingly anxious that the matter     
should be  brought to a conclusion1 and 
a severe attack of his constitutional   
complaints rendered him still more      
fretful and impatient4 ,on the last  day
 of ,april1 about ten days after his    
first examination1 he was  unexpectedly 
permitted to return to ,nicolini's      
house1 although the  proceedings were   
yet far from being brought to a         

conclusion4 ,nicolini  attributes this  
favour to ,cardinal ,barberino1 who1 he 
says1 liberated  ,galileo on his own    
responsibility1 in consideration of the 
enfeebled  state of his health4    ,in  
the society of ,nicolini and his family1
 ,galileo recovered something  of his   
courage and ordinary cheerfulness1      
although his return appears to  have    
been permitted on express condition of a
 strict seclusion2 for at  the latter   
end of ,may1 ,nicolini was obliged to   
apply for permission that  ,galileo     
should take that exercise in the open   
air which was necessary  for his health2
 on which occasion he was permitted to  
go into the public  gardens in a        
half-closed carriage4    ,on the evening
 of the #bjth of ,june1 rather more than
 four months after  ,galileo's arrival  
in ,rome1 he was again summoned to the  
,holy ,office1  whither he went the     
following morning2 he was detained there
 during the  whole of that day1 and on  
the next day was conducted in a         

penitential  dress#hc to the ,convent of
 ,minerva1 where the ,cardinals and     
,prelates1  his judges1 were assembled  
for the purpose of passing judgment upon
 him1  by which this venerable old man  
was solemnly called upon to renounce and
  abjure1 as impious and heretical1 the 
opinions which his whole existence  had 
been consecrated to form and strengthen4
 ,as we are not aware that  this        
remarkable record of intolerance and    
bigoted folly has ever been  printed    
entire in ,english1 we subjoin a literal
 translation of the whole  sentence and 
abjuration4      ,the ,sentence of the  
,inquisition on ,galileo4        ,we1   
the undersigned1 by the ,grace of ,god1 
,cardinals of the ,holy      ,roman     
,church1 ,inquisitors ,general          
throughout the whole ,christian         
,republic1 ,special ,deputies of the    
,holy ,apostolical ,chair against       
heretical depravity1        ,whereas    
you1 ,galileo1 son of the late ,vincenzo
 ,galilei of ,florence1      aged       

seventy years1 were denounced in #afae  
to this ,holy ,office1 for      holding 
as true a false doctrine taught by many1
 namely1 that the      sun is immoveable
 in the centre of the world1 and that   
the earth      moves1 and also with a   
diurnal motion2 also1 for having pupils 
whom      you instructed in the same    
opinions2 also1 for maintaining a       
correspondence on the same with some    
,german mathematicians2 also for        
publishing certain letters on the solar 
spots1 in which you      developed the  
same doctrine as true2 also1 for        
answering the      objections which were
 continually produced from the ,holy    
,scriptures1      by glozing the said   
,scriptures according to your own       
meaning2 and      whereas thereupon was 
produced the copy of a writing1 in form 
of a      letter1 professedly written by
 you to a person formerly your pupil1   
in which1 following the hypotheses of   
,copernicus1 you include      several   
propositions contrary to the true sense 

and authority of the      ,holy         
,scripture3 therefore this holy tribunal
 being desirous of      providing       
against the disorder and mischief which 
was thence      proceeding and          
increasing to the detriment of the holy 
faith1 by the      desire of ,his       
,holiness1 and of the ,most ,eminent    
,lords ,cardinals of      this supreme  
and universal ,inquisition1 the two     
propositions of the      stability of   
the sun1 and motion of the earth1 were  
qualified by      the ,theological      
,qualifiers as follows3        #ast4    
,the proposition that the ,sun is in the
 centre of the world      and immoveable
 from its place1 is absurd1             
philosophically false1 and      formally
 heretical2 because it is expressly     
contrary to the ,holy      ,scripture4  
#b;dly4 ,the proposition that the ,earth
 is not the centre of the      world1   
nor immoveable1 but that it moves1 and  
also with a diurnal      motion1 is also
 absurd1 philosophically false1 and1    

theologically      considered1 at least 
erroneous in faith4        ,but whereas 
being pleased at that time to deal      
mildly with you1 it      was decreed in 
the ,holy ,congregation1 held before    
,his ,holiness on      the #beth day of 
,february1 #afaf1 that ,his ,eminence   
the ,lord ,cardinal      ,bellarmine    
should enjoin you to give up altogether 
the said false      doctrine2 if you    
should refuse1 that you should be       
ordered by the      ,commissary of the  
,holy ,office to relinquish it1 not to  
teach it to      others1 nor to defend  
it1 nor ever mention it1 and in default 
of      acquiescence that you should be 
imprisoned2 and in execution of this    
decree1 on the following day at the     
palace1 in presence of ,his             
,eminence the said ,lord ,cardinal      
,bellarmine1 after you had been         
mildly admonished by the said ,lord     
,cardinal1 you were commanded by        
the acting ,commissary of the ,holy     
,office1 before a notary and            

witnesses1 to relinquish altogether the 
said false opinion1 and in      future  
neither to defend nor teach it in any   
manner1 neither      verbally nor in    
writing1 and upon your promising        
obedience you were      dismissed4      
,and in order that so pernicious a      
doctrine might be altogether      rooted
 out1 nor insinuate itself farther to   
the heavy detriment of      the         
,catholic truth1 a decree emanated from 
the ,holy ,congregation of      the     
,index#hd prohibiting the books which   
treat of this doctrine2      and it was 
declared false1 and altogether contrary 
to the ,holy and      ,divine           
,scripture4        ,and whereas a book  
has since appeared1 published at        
,florence last      year1 the title of  
which shewed that you were the author1  
which      title is3 ,the ,dialogue of  
,galileo ,galilei1 on the two principal 
systems of the world1 the ,ptolemaic and
 ,copernican2 and whereas the      ,holy
 ,congregation has heard that1 in       

consequence of the printing of      the 
said book1 the false opinion of the     
earth's motion and stability      of the
 sun is daily gaining ground2 the said  
book has been taken      into careful   
consideration1 and in it has been       
detected a glaring      violation of the
 said order1 which had been intimated to
 you2      inasmuch as in this book you 
have defended the said opinion1         
already and in your presence condemned2 
although in the said book      you      
labour with many circumlocutions to     
induce the belief that it is      left  
by you undecided1 and in express terms  
probable3 which is      equally a very  
grave error1 since an opinion can in no 
way be      probable which has been     
already declared and finally determined 
contrary to the divine ,scripture4      
,therefore by ,our order you have       
been cited to this ,holy ,office1 where1
 on your examination upon      oath1 you
 have acknowledged the said book as     
written and printed by      you4 ,you   

also confessed that you began to write  
the said book ten or      twelve years  
ago1 after the order aforesaid had been 
given4 ,also1      that you demanded    
license to publish it1 but without      
signifying to      those who granted you
 this permission that you had been      
commanded      not to hold1 defend1 or  
teach the said doctrine in any manner4  
,you      also confessed that the style 
of the said book was1 in many places1   
so composed that the reader might think 
the arguments adduced on the      false 
side to be so worded as more effectually
 to entangle the      understanding than
 to be easily solved1 alleging in       
excuse1 that you      have thus run into
 an error1 foreign 7as you say7 to your 
intention1      from writing in the form
 of a dialogue1 and in consequence of   
the      natural complacency which every
 one feels with regard to his own       
subtilties1 and in showing himself more 
skilful than the generality      of     
mankind in contriving1 even in favour of

 false propositions1      ingenious and 
apparently probable arguments4          
,and1 upon a convenient time being given
 to you for making your      defence1   
you produced a certificate in the       
hand-writing of ,his      ,eminence the 
,lord ,cardinal ,bellarmine1 procured1  
as you said1 by      yourself1 that you 
might defend yourself against the       
calumnies of      your enemies1 who     
reported that you had abjured your      
opinions1 and      had been punished by 
the ,holy ,office2 in which certificate 
it is      declared1 that you had not   
abjured1 nor had been punished1 but     
merely that the declaration made by ,his
 ,holiness1 and promulgated by      the 
,holy ,congregation of the ,index1 had  
been announced to you1 which            
declares that the opinion of the motion 
of the earth1 and stability      of the 
sun1 is contrary to the ,holy           
,scriptures1 and1 therefore1      cannot
 be held or defended4 ,wherefore1 since 
no mention is there      made of two    

articles of the order1 to wit1 the order
 'not to teach1'      and 'in any       
manner1' you argued that we ought to    
believe that1 in      the lapse of      
fourteen or sixteen years1 they had     
escaped your      memory1 and that this 
was also the reason why you were silent 
as to      the order1 when you sought   
permission to publish your book1 and    
that      this is said by you not to    
excuse your error1 but that it may be   
attributed to vain-glorious ambition1   
rather than to malice4 ,but      this   
very certificate1 produced on your      
behalf1 has greatly      aggravated your
 offence1 since it is therein declared  
that the said      opinion is contrary  
to the ,holy ,scripture1 and yet you    
have dared to      treat of it1 to      
defend it1 and to argue that it is      
probable2 nor is      there any         
extenuation in the licence artfully and 
cunningly extorted      by you1 since   
you did not intimate the command imposed
 upon you4 ,but      whereas it appeared

 to ,us that you had not disclosed the  
whole truth      with regard to your    
intentions1 ,we thought it necessary to 
proceed      to the rigorous examination
 of you1 in which 7without any prejudice
      to what you had confessed1 and    
which is above detailed against you1    
with regard to your said intention7 you 
answered like a good      ,catholic4    
,therefore1 having seen and maturely    
considered the merits of your           
cause1 with your said confessions and   
excuses1 and every thing else      which
 ought to be seen and considered1 ,we   
have come to the      underwritten final
 sentence against you4        ,invoking1
 therefore1 the most holy name of ,our  
,lord ,jesus ,christ1      and of ,his  
,most ,glorious ,virgin ,mother ,mary1  
by this ,our final      sentence1 which1
 sitting in council and judgment for the
 tribunal of      the ,reverend ,masters
 of ,sacred ,theology1 and ,doctors of  
both ,laws1      ,our ,assessors1 ,we   
put forth in this writing touching the  

matters and      controversies before   
,us1 between ,the ,magnificent ,charles 
,sincerus1      ,doctor of both ,laws1  
,fiscal ,proctor of this ,holy ,office  
of the one      part1 and you1 ,galileo 
,galilei1 an examined and confessed     
criminal      from this present writing 
now in progress as above of the other   
part1 ,we pronounce1 judge1 and declare1
 that you1 the said ,galileo1      by   
reason of these things which have been  
detailed in the course of      this     
writing1 and which1 as above1 you have  
confessed1 have rendered      yourself  
vehemently suspected by this ,holy      
,office of heresy3 that is      to say1 
that you believe and hold the false     
doctrine1 and contrary      to the ,holy
 and ,divine ,scriptures1 namely1 that  
the sun is the      centre of the world1
 and that it does not move from east to 
west1      and that the earth does move1
 and is not the centre of the world2    
also that an opinion can be held and    
supported as probable after it      has 

been declared and finally decreed       
contrary to the ,holy      ,scripture1  
and consequently that you have incurred 
all the censures      and penalties     
enjoined and promulgated in the sacred  
canons1 and      other general and      
particular constitutions against        
delinquents of      this description4   
,from which it is ,our pleasure that you
 be      absolved1 provided that1 first1
 with a sincere heart and unfeigned     
faith1 in ,our presence1 you abjure1    
curse1 and detest the said      errors  
and heresies1 and every other error and 
heresy contrary to      the ,catholic   
and ,apostolic ,church of ,rome1 in the 
form now shown to      you4        ,but1
 that your grievous and pernicious error
 and transgression may      not go      
altogether unpunished1 and that you may 
be made more cautious      in future1   
and may be a warning to others to       
abstain from      delinquencies of this 
sort1 ,we decree that the book of the   
dialogues      of ,galileo ,galilei be  

prohibited by a public edict1 and ,we   
condemn      you to the formal prison of
 this ,holy ,office for a period        
determinable at ,our pleasure2 and1 by  
way of salutary penance1 ,we      order 
you1 during the next three years1 to    
recite once a week the      seven       
penitential psalms1 reserving to        
,ourselves the power of      moderating1
 commuting1 or taking off the whole or  
part of the said      punishment and    
penance4        ,and so ,we say1        
pronounce1 and by ,our sentence declare1
 decree1 and      reserve1 in this and  
in every other better form and manner1  
which      lawfully ,we may and can use4
        ,so ,we1 the subscribing        
,cardinals1 pronounce4        ,felix1   
,cardinal di ,ascoli1      ,guido1      
,cardinal ,bentivoglio1      ,desiderio1
 ,cardinal di ,cremona1      ,antonio1  
,cardinal ,s4 ,onofrio1                 
,berlingero1 ,cardinal ,gessi1          
,fabricio1 ,cardinal ,verospi1          
,martino1 ,cardinal ,ginetti4    ,we    

cannot suppose that ,galileo1 even      
broken down as he was with age and      
infirmities1 and overawed by the        
merciless tribunal to whose power he    
was subjected1 could without extreme    
reluctance thus formally give the  lie  
to his whole life1 and call upon ,god to
 witness his renunciation of  the       
opinions which even his bigoted judges  
must have felt that he still  clung to  
in his heart4    ,we know indeed that   
his friends were unanimous in           
recommending an  unqualified            
acquiescence in whatever might be       
required1 but some persons  have not    
been able to find an adequate           
explanation of his submission1  either  
in their exhortations1 or in the mere   
dread of the alternative  which might   
await him in case of non-compliance4 ,it
 has in short been  supposed1 although  
the suspicion scarcely rests upon       
grounds  sufficiently strong to warrant 
the assertion1 that ,galileo did not    
submit to this abjuration until forced  

to it1 not merely by the  apprehension1 
but by the actual experience of personal
 violence4 ,the  arguments on which this
 horrible idea appears to be mainly     
founded are  the two following3 ,first1 
the ,inquisitors declare in their       
sentence  that1 not satisfied with      
,galileo's first confession1 they judged
 it  necessary to proceed to the        
rigorous examination of him1 in which he
  answered like a good ,catholic4#he ,it
 is pretended by those who are  more    
familiar with inquisitorial language    
than we can profess to be1  that the    
words il rigoroso esame1 form the       
official phrase for the  application of 
the torture1 and accordingly they       
interpret this passage  to mean1 that   
the desired answers and submission had  
thus been extorted  from ,galileo1 which
 his judges had otherwise failed to get 
from him4  ,and1 secondly1 the partisans
 of this opinion bring forward in       
corroboration of it1 that ,galileo      
immediately on his departure from       

,rome1 in addition to his old           
complaints1 was found to be afflicted   
with  hernia1 and this was a common     
consequence of the torture of the cord1 
which they suppose to have been         
inflicted4 ,it is right to mention that 
no other trace can be found of this     
supposed torturing in all the  documents
 relative to the proceedings against    
,galileo1 at least ,venturi  was so     
assured by one who had inspected the    
originals at ,paris4#hf    ,although the
 arguments we have mentioned appear to  
us slight1 yet  neither can we attach   
much importance to the contrast which   
the  favourers of the opposite opinion  
profess to consider so incredible       
between the honourable manner in which  
,galileo was treated throughout  the    
rest of the inquiry1 and the suspected  
harsh proceeding against him4  ,whether 
,galileo should be lodged in a prison or
 a palace1 was a matter  of far other   
importance to the ,inquisitors and to   
their hold upon public  opinion1 than   

the question whether or not he should be
 suffered to  exhibit a persevering     
resistance to the censures which they   
were  prepared to cast upon him4 ,nor   
need we shrink from the idea1 as we     
might  from suspecting of some gross    
crime1 on trivial grounds1 one of       
hitherto  unblemished innocence and     
character4 ,the question may be         
disencumbered  of all such scruples1    
since one atrocity more or less can do  
little  towards affecting our judgment  
of the unholy ,office of the            
,inquisition4    ,delambre1 who could   
find so much to reprehend in ,galileo's 
former  uncompromising boldness1 is     
deeply penetrated with the insincerity  
of  his behaviour on the present        
occasion4 ,he seems to have forgotten   
that a  tribunal which finds it         
convenient to carry on its inquiries in 
secret1  is always liable to the        
suspicion of putting words into the     
mouth of its  victims2 and if it were   
worth while1 there is sufficient        

internal  evidence that the language    
which ,galileo is made to hold in his   
defence  and confession1 is rather to be
 read as the composition of his judges  
than his own4 ,for instance1 in one of  
the letters which we have  extracted#hg1
 it may be seen that this obnoxious work
 was already in  forward preparation as 
early as #afaj1 and yet he is made to   
confess1 and  the circumstance appears  
to be brought forward in aggravation of 
his  guilt1 that he began to write it   
after the prohibition which he had      
received in #afaf4    ,the abjuration   
was drawn up in the following terms3--  
,the ,abjuration of ,galileo4        ,i 
,galileo ,galilei1 son of the late      
,vincenzo ,galilei1 of ,florence1       
aged #gj years1 being brought personally
 to judgment1 and kneeling      before  
you1 ,most ,eminent and ,most ,reverend 
,lords ,cardinals1 ,general             
,inquisitors of the universal ,christian
 republic against heretical             
depravity1 having before my eyes the    

,holy ,gospels1 which ,i touch      with
 my own hands1 swear1 that ,i have      
always believed1 and now      believe1  
and with the help of ,god will in future
 believe1 every      article which the  
,holy ,catholic and ,apostolic ,church  
of ,rome holds1      teaches1 and       
preaches4 ,but because ,i had been      
enjoined by this ,holy      ,office     
altogether to abandon the false opinion 
which maintains that      the sun is the
 centre and immoveable1 and forbidden to
 hold1 defend1      or teach1 the said  
false doctrine in any manner1 and after 
it had      been signified to me that   
the said doctrine is repugnant with the 
,holy ,scripture1 ,i have written and   
printed a book1 in which ,i treat       
of the same doctrine now condemned1 and 
adduce reasons with great      force in 
support of the same1 without giving any 
solution1 and      therefore have been  
judged grievously suspected of heresy2  
that is      to say1 that ,i held and   
believed that the sun is the centre of  

the      world and immoveable1 and that 
the earth is not the centre and         
moveable4 ,willing1 therefore1 to remove
 from the minds of ,your                
,eminences1 and of every ,catholic      
,christian1 this vehement suspicion     
rightfully entertained towards me1 with 
a sincere heart and      unfeigned      
faith1 ,i abjure1 curse1 and detest1 the
 said errors and      heresies1 and     
generally every other error and sect    
contrary to the      said ,holy ,church2
 and ,i swear1 that ,i will never more  
in future say      or assert anything   
verbally1 or in writing1 which may give 
rise to a      similar suspicion of me3 
but if ,i shall know any heretic1 or any
 one      suspected of heresy1 that ,i  
will denounce him to this ,holy ,office1
      or to the ,inquisitor and         
,ordinary of the place in which ,i may  
be4 ,i      swear1 moreover1 and        
promise1 that ,i will fulfil1 and       
observe fully1      all the penances    
which have been1 or shall be laid on me 

by this      ,holy ,office4 ,but if it  
shall happen that ,i violate any of my  
said      promises1 oaths1 and          
protestations1 7which ,god avert67 ,i   
subject      myself to all the pains and
 punishments1 which have been decreed   
and      promulgated by the sacred      
canons1 and other general and particular
      constitutions1 against delinquents
 of this description4 ,so may ,god      
help me1 and his ,holy ,gospels1 which  
,i touch with my own hands4 ,i1      the
 above-named ,galileo ,galilei1 have    
abjured1 sworn1 promised1 and      bound
 myself1 as above1 and in witness       
thereof with my own hand have           
subscribed this present writing of my   
abjuration1 which ,i have      recited  
word for word4 ,at ,rome in the ,convent
 of ,minerva1 #bb;d ,june1      #afcc4  
,i1 ,galileo ,galilei1 have abjured as  
above with my own hand4    ,it is said  
that ,galileo1 as he rose from his      
knees1 stamped on the  ground1 and      
whispered to one of his friends1 ,e pur 

si muove--7,it does  move though74      
,copies of ,galileo's sentence and      
abjuration were immediately promulgated 
in every direction1 and the professors  
at several universities received        
directions to read them publicly4 ,at   
,florence this ceremony took place  in  
the church of ,sta4 ,croce1 whither     
,guiducci1 ,aggiunti1 and all others    
who were known in that city as firm     
adherents to ,galileo's opinions1  were 
specially summoned4 ,the triumph of the 
,paper ,philosophers was so  far        
complete1 and the alarm occasioned by   
this proof of their dying  power        
extended even beyond ,italy4 ,i have    
been told1 writes ,descartes  from      
,holland to ,mersenne at ,paris1 that   
,galileo's system was printed in  ,italy
 last year1 but that every copy has been
 burnt at ,rome1 and himself  condemned 
to some sort of penance1 which has      
astonished me so much that  ,i have     
almost determined to burn all my papers1
 or at least never to let  them be seen 

by any one4 ,i cannot collect that he1  
who is an ,italian and  even a friend of
 the ,pope1 as ,i understand1 has been  
criminated on any  other account than   
for having attempted to establish the   
motion of the  earth4 ,i know that this 
opinion was formerly censured by some   
,cardinals1  but ,i thought ,i had since
 heard1 that no objection was now made  
to its  being publicly taught1 even at  
,rome4    ,the sentiments of all who    
felt themselves secured against the     
apprehension of personal danger could   
take but one direction1 for1 as  ,pascal
 well expressed it in one of his        
celebrated letters to the  ,jesuits--,it
 is in vain that you have procured      
against ,galileo a decree  from ,rome   
condemning his opinion of the earth's   
motion4 ,assuredly1 that  will never    
prove it to be at rest2 and if we have  
unerring observations  proving that it  
turns round1 not all mankind together   
can keep it from  turning1 nor          
themselves from turning with it4    ,the

 assembly of doctors of the ,sorbonne at
 ,paris narrowly escaped from  passing a
 similar sentence upon the system of    
,copernicus4 ,the question  was laid    
before them by ,richelieu1 and it       
appears that their opinion was  for a   
moment in favour of confirming the      
,roman decree4 ,it is to be  wished that
 the name had been preserved of one of  
its members1 who1 by  his strong and    
philosophical representations1 saved    
that celebrated body  from this         
disgrace4    ,those who saw nothing in  
the punishment of ,galileo but passion  
and  blinded superstition1 took occasion
 to revert to the history of a  similar 
blunder of the ,court of ,rome in the   
middle of the eighth  century4 ,a       
,bavarian bishop1 named ,virgil1 eminent
 both as a man of  letters and          
politician1 had asserted the existence  
of ,antipodes1 which  excited in the    
ignorant bigots of his time no less     
alarm than did the  motion of the earth 
in the seventeenth century4 ,pope       

,zachary1 who was  scandalized at the   
idea of another earth1 inhabited by     
another race of  men1 and enlightened by
 another sun and moon 7for this was the 
shape  which ,virgil's system assumed in
 his eyes71 sent out positive orders to 
his legate in ,bavaria4 ,with regard to 
,virgil1 the philosopher1 7,i know  not 
whether to call him priest17 if he own  
these perverse opinions1  strip him of  
his priesthood1 and drive him from the  
church and altars of  ,god4 ,but ,virgil
 had himself occasionally acted as      
legate1 and was  moreover too necessary 
to his sovereign to be easily displaced4
 ,he  utterly disregarded these         
denunciations1 and during twenty-five   
years  which elapsed before his death1  
retained his opinions1 his bishopric of 
,salzburg1 and his political power4 ,he 
was afterwards canonized4#hh    ,even   
the most zealous advocates of the       
authority of ,rome were  embarrassed in 
endeavouring to justify the treatment   
which ,galileo  experienced4 ,tiraboschi

 has attempted to draw a somewhat subtle
  distinction between the bulls of the  
,pope and the inquisitorial decrees     
which were sanctioned and approved by   
him2 he dwells on the reflection  that  
no one1 even among the most zealous     
,catholics1 has ever claimed            
infallibility as an attribute of the    
,inquisition1 and looks upon it as a    
special mark of grace accorded to the   
,roman ,catholic ,church1 that during   
the whole period in which most          
theologians rejected the opinions of    
,copernicus1 as contrary to the         
,scriptures1 the head of that ,church   
was  never permitted to compromise his  
infallible character by formally        
condemning it4#hi    ,whatever may be   
the value of this consolation1 it can   
hardly be  conceded1 unless it be at the
 same time admitted that many scrupulous
  members of the ,church of ,rome have  
been suffered to remain in singular     
misapprehension of the nature and       
sanction of the authority to which      

,galileo had yielded4 ,the words of the 
bull of ,sixtus ,v41 by which the       
,congregation of the ,index was         
remodelled in #aehh1 are quoted by a    
professor of the ,university of         
,louvain1 a zealous antagonist of       
,galileo1  as follows3 ,they are to     
examine and expose the books which are  
repugnant to the ,catholic doctrines and
 ,christian discipline1 and after       
reporting on them to us1 they are to    
condemn them by our authority4#ij  ,nor 
does it appear that the learned editors 
of what is commonly called  the         
,jesuit's edition of ,newton's          
,principia were of opinion1 that in     
adopting the ,copernican system they    
should transgress a mandate  emanating  
from any thing short of infallible      
wisdom4 ,the remarkable  words which    
they were compelled to prefix to their  
book1 show how  sensitive the court of  
,rome remained1 even so late as #agdb1  
with regard  to this rashly condemned   
theory4 ,in their preface they say3     

,newton in  this third book supposes the
 motion of the earth4 ,we could not     
explain  the author's propositions      
otherwise than by making the same       
supposition4  ,we are therefore forced  
to sustain a character which is not our 
own2 but  we profess to pay the         
obsequious reverence which is due to the
 decrees  pronounced by the supreme     
,pontiffs against the motion of the     
earth4#ia    ,this coy reluctance to    
admit what nobody any longer doubts has 
survived  to the present time2 for      
,bailli informs us1#ib that the utmost  
endeavours of ,lalande1 when at ,rome1  
to obtain that ,galileo's work  should  
be erased from the ,index1 were entirely
 ineffectual1 in  consequence of the    
decree which had been fulminated against
 him2 and in  fact both it1 and the book
 of ,copernicus1 ,nisi ,corrigatur1 are 
still  to be seen on the forbidden list 
of #ahbh4    ,the condemnation of       
,galileo and his book was not thought   
sufficient4  ,urban's indignation also  

vented itself upon those who had been   
instrumental in obtaining the licence   
for him4 ,the ,inquisitor at  ,florence 
was reprimanded2 ,riccardi1 the master  
of the sacred palace1 and  ,ciampoli1   
,urban's secretary1 were both dismissed 
from their situations4  ,their          
punishment appears rather anomalous and 
inconsistent with the  proceedings      
against ,galileo1 in which it was       
assumed that his book was  not properly 
licensed2 yet the others suffered on    
account of granting  that very licence1 
which he was accused of having          
surreptitiously  obtained from them1 by 
concealing circumstances with which they
 were not  bound to be otherwise        
acquainted4 ,riccardi1 in exculpation of
 his  conduct1 produced a letter in the 
hand-writing of ,ciampoli1 in which was 
contained that ,his ,holiness1 in whose 
presence the letter professed to  be    
written1 ordered the licence to be      
given4 ,urban only replied that  this   
was a ,ciampolism2 that his secretary   

and ,galileo had circumvented  him2 that
 he had already dismissed ,ciampoli1 and
 that ,riccardi must  prepare to follow 
him4    ,as soon as the ceremony of     
abjuration was concluded1 ,galileo was  
consigned1 pursuant to his sentence1 to 
the prison of the ,inquisition4         
,probably it was never intended that he 
should long remain there1 for at  the   
end of four days1 he was reconducted on 
a very slight representation  of        
,nicolini to the ambassador's palace1   
there to await his further  destination4
 ,florence was still suffering under the
 before-mentioned  contagion2 and       
,sienna was at last fixed on as the     
place of his  relegation4 ,he would have
 been shut up in some convent in that   
city1 if  ,nicolini had not recommended 
as a more suitable residence1 the palace
 of  the ,archbishop ,piccolomini1 whom 
he knew to be among ,galileo's warmest  
friends4 ,urban consented to the change1
 and ,galileo finally left ,rome  for   
,sienna in the early part of ,july4     

,piccolomini received him with the      
utmost kindness1 controlled of course   
by the strict injunctions which were    
dispatched from ,rome1 not to suffer    
him on any account to quit the confines 
of the palace4 ,galileo continued  at   
,sienna in this state of seclusion till 
,december of the same year1  when the   
contagion having ceased in ,tuscany1 he 
applied for permission  to return to his
 villa at ,arcetri4 ,this was allowed1  
subject to the same  restrictions under 
which he had been residing with the     
archbishop4      ,,footnotes3    #gi    
,delambre quotes this sentence from a   
passage which is so obviously  ironical 
throughout1 as an instance of ,galileo's
 mis-statement of  facts6--,hist4 de    
l',astr4 ,mod41 vol1 i4 p4 #fff4    #hj 
,page #ed4    #ha ,galuzzi4 ,storia di  
,toscana4 ,firenze1 #ahbb4    #hb       
,alidosi was a ,florentine nobleman1    
whose estate ,urban wished to           
confiscate on a charge of               
heresy4--,galuzzi4    #hc ,s'irrito il  

,papa1 e lo fece abjurare1 comparendo il
 pover uomo con  uno straccio di camicia
 indosso1 che faceva compassione1 ,,ms4 
nella ,bibl4  ,magliab4 ,venturi4    #hd
 ,the ,index is a list of books1 the    
reading of which is prohibited to       
,roman ,catholics4 ,this list1 in the   
early periods of the ,reformation1 was  
often consulted by the curious1 who were
 enlarging their libraries2 and  a story
 is current in ,england1 that1 to       
prevent this mischief1 the ,index       
itself was inserted in its own forbidden
 catalogue4 ,the origin of this  story  
is1 that an ,index was published in     
,spain1 particularizing the             
objectionable passages in such books as 
were only partially condemned2  and     
although compiled with the best         
intentions1 this was found to be so     
racy1 that it became necessary to forbid
 the circulation of this edition  in    
subsequent lists4    #he ,giudicassimo  
esser necessario venir contro di te al  
rigoroso esame  nel quale rispondesti   

cattolicamente4    #hf ,the fate of     
these documents is curious2 after being 
long preserved  at ,rome1 they were     
carried away in #ahji1 by order of      
,buonaparte1 to  ,paris1 where they     
remained till his first abdication4     
,just before the  hundred days1 the late
 king of ,france1 wishing to inspect    
them1 ordered  that they should be      
brought to his own apartments for that  
purpose4 ,in  the hasty flight which    
soon afterwards followed1 the           
manuscripts were  forgotten1 and it is  
not known what became of them4 ,a       
,french  translation1 begun by          
,napoleon's desire1 was completed only  
down to the  #cjth of ,april1 #afcc1 the
 date of ,galileo's first return to     
,nicolini's  palace4    #hg ,page #ah4  
#hh ,annalium ,bolorum1 libri vii4      
,ingolstadii1 #aeed4    #hi ,la ,chiesa 
non ha mai dichiarati eretici i         
sostenitori del ,sistema  ,copernicano1 
e questa troppo rigorosa censura non    
usci che dal tribunale  della ,romana   

,inquisizione a cui niuno tra ,cattolici
 ancor piu zelanti ha  mai attribuito it
 diritto dell'infallibilit4 ,anzi in cio
 ancora  d'  ammirarsi la providenza di 
,dio  favor della ,chiesa1 percioche in 
un  tempo in cui la maggior parte dei   
teologi fermamente credavano che il     
,sistema ,copernicano fosse all' autorit
 delle sacre ,carte contrario1 pur  non 
permise che dalla ,chiesa si proferisse 
su cio un solenne  giudizio4--,stor4    
della ,lett4 ,ital4    #ij ,lib4        
,fromondi ,antaristarchus1 ,antwerpi1   
#afca4    #ia ,newtoni ,principia1      
,coloni1 #agfj4    #ib ,histoire de     
l',astronomie ,moderne4                 
,,chapter ,,xiv4        ,extracts from  
the ,dialogues on the ,system4          
,,after narrating the treatment to which
 ,galileo was subject on account of  his
 admirable ,dialogues1 it will not be   
irrelevant to endeavour1 by a  few      
extracts1 to convey some idea of the    
style in which they are  written4 ,it   
has been mentioned1 that he is          

considered to surpass all  other        
,italian writers 7unless we except      
,machiavelli7 in the purity and  beauty 
of his language1 and indeed his         
principal followers1 who avowedly       
imitated his style1 make a distinguished
 group among the classical  authors of  
modern ,italy4 ,he professed to have    
formed himself from the  study of       
,ariosto1 whose poems he passionately   
admired1 insomuch that he  could repeat 
the greater part of them1 as well as    
those of ,berni and  ,petrarca1 all     
which he was in the frequent habit of   
quoting in  conversation4 ,the fashion  
and almost universal practice of that   
day was  to write on philosophical      
subjects in ,latin2 and although        
,galileo wrote  very passably in that   
language1 yet he generally preferred the
 use of  ,italian1 for which he gave his
 reasons in the following characteristic
  manner3--    ,i wrote in ,italian     
because ,i wished every one to be able  
to read what ,i  wrote2 and for the same

 cause ,i have written my last treatise 
in the  same language3 the reason which 
has induced me is1 that ,i see young men
  brought together indiscriminately to  
study to become physicians1             
philosophers1 c41 and whilst many apply 
to such professions who are  most unfit 
for them1 others who would be competent 
remain occupied  either with domestic   
business1 or with other employments     
alien to  literature2 who1 although     
furnished1 as ,ruzzante might say1 with 
a  decent set of brains1 yet1 not being 
able to understand things written  in   
gibberish1 take it into their heads1    
that in these crabbed folios  there must
 be some grand hocus pocus of logic and 
philosophy much too  high up for them to
 think of jumping at4 ,i want them to   
know1 that as  ,nature has given eyes to
 them just as well as to philosophers   
for the  purpose of seeing her works1   
she has also given them brains for      
examining and understanding them4       
,the general structure of the dialogues 

has been already described2#ic  we shall
 therefore premise no more than the     
judgment pronounced on them  by a highly
 gifted writer1 to supply the           
deficiencies of our necessarily         
imperfect analysis4    ,one forms a very
 imperfect idea of ,galileo1 from       
considering the  discoveries and        
inventions1 numerous and splendid as    
they are1 of which  he was the          
undisputed author4 ,it is by following  
his reasonings1 and by  pursuing the    
train of his thoughts1 in his own       
elegant1 though somewhat  diffuse       
exposition of them1 that we become      
acquainted with the fertility  of his   
genius--with the sagacity1 penetration1 
and comprehensiveness of  his mind4 ,the
 service which he rendered to real      
knowledge is to be  estimated1 not only 
from the truths which he discovered1 but
 from the  errors which he detected--not
 merely from the sound principles which 
he  established1 but from the pernicious
 idols which he overthrew4 ,the         

dialogues on the system are written with
 such singular felicity1 that  one reads
 them at the present day1 when the      
truths contained in them are  known and 
admitted1 with all the delight of       
novelty1 and feels one's  self carried  
back to the period when the telescope   
was first directed to  the heavens1 and 
when the earth's motion1 with all its   
train of  consequences1 was proved for  
the first time4#id    ,the first        
,dialogue is opened by an attack upon   
the arguments by which  ,aristotle      
pretended to determine  priori the      
necessary motions  belonging to         
different parts of the world1 and on his
 favourite  principle that particular   
motions belong naturally to particular  
substances4 ,salviati 7representing     
,galileo7 then objects to the           
,aristotelian distinctions between the  
corruptible elements and  incorruptible 
skies1 instancing among other things the
 solar spots and  newly appearing stars1
 as arguments that the other heavenly   

bodies may  probably be subjected to    
changes similar to those which are      
continually  occurring on the earth1 and
 that it is the great distance alone    
which  prevents their being observed4   
,after a long discussion on this point1 
,sagredo exclaims1 ,i see into the heart
 of ,simplicio1 and perceive that  he is
 much moved by the force of these too   
conclusive arguments2 but  methinks ,i  
hear him say--',oh1 to whom must we     
betake ourselves to settle  our disputes
 if ,aristotle be removed from the      
chair8 ,what other author  have we to   
follow in our schools1 our studies1 and 
academies8 ,what  philosopher has       
written on all the parts of ,natural    
,philosophy1 and so  methodically as not
 to have overlooked a single conclusion8
 ,must we then  desolate this fabric1 by
 which so many travellers have been     
sheltered8  ,must we destroy this       
asylum1 this ,prytaneum wherein so many 
students  have found a convenient       
resting-place1 where without being      

exposed to  the injuries of the weather1
 one may acquire an intimate knowledge  
of  nature1 merely by turning over a few
 leaves8 ,shall we level this  bulwark1 
behind which we are safe from every     
hostile attack8' ,i pity him  no less   
than ,i do one who at great expense of  
time and treasure1 and  with the labour 
of hundreds1 has built up a very noble  
palace2 and then1  because of insecure  
foundations1 sees it ready to           
fall--unable to bear  that those walls  
be stripped that are adorned with so    
many beautiful  pictures1 or to suffer  
those columns to fall that uphold the   
stately  galleries1 or to see ruined the
 gilded roofs1 the chimney-pieces1 the  
friezes1 and marble cornices erected at 
so much cost1 he goes about it  with    
girders and props1 with shores and      
buttresses1 to hinder its  destruction4 
,salviati proceeds to point out the many
 points of similarity between the  earth
 and moon1 and among others which we    
have already mentioned1 the  following  

remark deserves especial notice3--      
,just as from the mutual and universal  
tendency of the parts of the  earth to  
form a whole1 it follows that they all  
meet together with equal  inclination1  
and that they may unite as closely as   
possible1 assume the  spherical form2   
why ought we not to believe that the    
moon1 the sun1 and  other mundane bodies
 are also of a round figure1 from no    
other reason  than from a common        
instinct and natural concourse of all   
their component  parts2 of which if by  
accident any one should be violently    
separated  from its whole1 is it not    
reasonable to believe that              
spontaneously1 and  of its natural      
instinct1 it would return8 ,it may be   
added that if any  centre of the        
universe may be assigned1 to which the  
whole terrene globe  if thence removed  
would seek to return1 we shall find most
 probable that  the sun is placed in it1
 as by the sequel you shall understand4 
,many who are but superficially         

acquainted with the ,history of         
,astronomy1  are apt to suppose that    
,newton's great merit was in his being  
the first  to suppose an attractive     
force existing in and between the       
different  bodies composing the solar   
system4 ,this idea is very erroneous2   
,newton's  discovery consisted in       
conceiving and proving the identity of  
the force  with which a stone falls1 and
 that by which the moon falls1 towards  
the  earth 7on an assumption that this  
force becomes weaker in a certain       
proportion as the distance increases at 
which it operates71 and in  generalizing
 this idea1 in applying it to all the   
visible creation1 and  tracing the      
principle of universal gravitation with 
the assistance of a  most refined and   
beautiful geometry into many of its most
 remote  consequences4 ,but the general 
notion of an attractive force between   
the  sun1 moon1 and planets1 was very   
commonly entertained before ,newton was 
born1 and may be traced back to ,kepler1

 who was probably the first  modern     
philosopher who suggested it4 ,the      
following extraordinary  passages from  
his ,astronomy will shew the nature of  
his conceptions on  this subject3--     
,the true doctrine of gravity is founded
 on these axioms3 every  corporeal      
substance1 so far forth as it is        
corporeal1 has a natural  fitness for   
resting in every place where it may be  
situated by itself  beyond the sphere of
 influence of its cognate body4 ,gravity
 is a mutual  affection between cognate 
bodies towards union or conjunction     
7similar  in kind to the magnetic       
virtue71 so that the earth attracts a   
stone much  rather than the stone seeks 
the earth4 ,heavy bodies 7if in the     
first  place we put the earth in the    
centre of the world7 are not carried to 
the centre of the world in its quality  
of centre of the world1 but as to  the  
centre of a cognate round body1 namely  
the earth4 ,so that  wheresoever the    
earth may be placed or whithersoever it 

may be carried  by its animal faculty1  
heavy bodies will always be carried     
towards it4  ,if the earth were not     
round heavy bodies would not tend from  
every side  in a straight line towards  
the centre of the earth1 but to         
different  points from different sides4 
,if two stones were placed in any part  
of  the world near each other and beyond
 the sphere of influence of a third     
cognate body1 these stones1 like two    
magnetic needles1 would come  together  
in the intermediate point1 each         
approaching the other by a  space       
proportional to the comparative mass of 
the other4 ,if the moon  and earth were 
not retained in their orbits by their   
animal force or  some other equivalent1 
the earth would mount to the moon by a  
fifty-fourth part of their distance1 and
 the moon fall towards the earth        
through the other fifty-three parts1 and
 would there meet1 assuming  however    
that the substance of both is of the    
same density4 ,if the earth  should     

cease to attract its waters to itself1  
all the waters of the sea  would be     
raised1 and would flow to the body of   
the moon4#ie    ,he also conjectured    
that the irregularities in the moon's   
motion were  caused by the joint action 
of the sun and earth1 and recognized the
  mutual action of the sun and planets1 
when he declared the mass and  density  
of the sun to be so great that the      
united attraction of the  other planets 
cannot remove it from its place4 ,among 
these bold and  brilliant ideas1 his    
temperament led him to introduce others 
which show  how unsafe it was to follow 
his guidance1 and which account for1 if 
they  do not altogether justify1 the    
sarcastic remark of ,ross1 that         
,kepler's  opinion that the planets are 
moved round by the sunne1 and that this 
is  done by sending forth a magnetic    
virtue1 and that the sun-beames are     
like the teethe of a wheele taking hold 
of the planets1 are senslesse  crotchets
 fitter for a wheeler or a miller than a

 philosopher4#if  ,roberval took up     
,kepler's notions1 especially in the    
tract which he  falsely attributed to   
,aristarchus1 and it is much to be      
regretted that  ,roberval should deserve
 credit for anything connected with that
 impudent  fraud4 ,the principle of     
universal gravitation1 though not the   
varying  proportion1 is distinctly      
assumed in it1 as the following passages
 will  sufficiently prove3 ,in every    
single particle of the earth1 and the   
terrestrial elements1 is a certain      
property or accident which we suppose   
common to the whole system of the world1
 by virtue of which all its  parts are  
forced together1 and reciprocally       
attract each other2 and this  property  
is found in a greater or less degree in 
the different  particles1 according to  
their density4 ,if the earth be         
considered by  itself1 its centres of   
magnitude and virtue1 or gravity1 as we 
usually  call it1 will coincide1 to     
which all its parts tend in a straight  

line1  as well by their own exertion or 
gravity1 as by the reciprocal           
attraction of all the rest4 ,in a       
subsequent chapter1 ,roberval repeats   
these passages nearly in the same words1
 applying them to the whole  solar      
system1 adding1 that the force of this  
attraction is not to be  considered as  
residing in the centre itself1 as some  
ignorant people  think1 but in the whole
 system whose parts are equally disposed
 round  the centre4#ig ,this very       
curious work was reprinted in the third 
volume of the ,reflexiones              
,physico-,mathematic of ,mersenne1 from 
whom  ,roberval pretended to have       
received the ,arabic manuscript1 and who
 is  thus irretrievably implicated in   
the forgery4#ih ,the last remark1       
denying the attractive force to be due  
to any property of the central  point1  
seems aimed at ,aristotle1 who1 in a no 
less curious passage1  maintaining      
exactly the opposite opinion1 says1     
,hence1 we may better  understand what  

the ancients have related1 that like    
things are wont to  have a tendency to  
each other4 ,for this is not absolutely 
true2 for if  the earth were to be      
removed to the place now occupied by the
 moon1 no  part of the earth would then 
have a tendency towards that place1 but 
would still fall towards the point which
 the earth's centre now  occupies4#ii   
,mersenne considered the consequences of
 the attractive  force of each particle 
of matter so far as to remark1 that if a
 body  were supposed to fall towards the
 centre of the earth1 it would be       
retarded by the attraction of the part  
through which it had already            
fallen4#ajj ,galileo had not altogether 
neglected to speculate on such a        
supposition1 as is plain from the       
following extract4 ,it is taken from a  
letter to ,carcaville1 dated from       
,arcetri1 in #afcg4 ,i will say farther1
  that ,i have not absolutely and       
clearly satisfied myself that a heavy   
body would arrive sooner at the centre  

of the earth1 if it began to fall  from 
the distance only of a single yard1 than
 another which should start  from the   
distance of a thousand miles4 ,i do not 
affirm this1 but ,i offer  it as a      
paradox4#aja    ,it is very difficult to
 offer any satisfactory comment upon    
this  passage2 it may be sufficient to  
observe that this paradoxical result    
was afterwards deduced by ,newton1 as   
one of the consequences of the  general 
law with which all nature is pervaded1  
but with which there is  no reason to   
believe that ,galileo had any           
acquaintance2 indeed the idea  is fully 
negatived by other passages in this same
 letter4 ,this is one of  the many      
instances from which we may learn to be 
cautious how we invest  detached        
passages of the earlier mathematicians  
with a meaning which in  many cases     
their authors did not contemplate4 ,the 
progressive  development of these ideas 
in the hands of ,wallis1 ,huyghens1     
,hook1 ,wren1  and ,newton1 would lead  

us too far from our principal subject4  
,there is  another passage in the third 
dialogue connected with this subject1   
which  it may be as well to notice in   
this place4 ,the parts of the earth have
  such a propensity to its centre1 that 
when it changes its place1  although    
they may be very distant from the globe 
at the time of the  change1 yet must    
they follow4 ,an example similar to this
 is the  perpetual sequence of the      
,medicean stars1 although always        
separated from  ,jupiter4 ,the same may 
be said of the moon1 obliged to follow  
the earth4  ,and this may serve for     
those simple ones who have difficulty in
  comprehending how these two globes1   
not being chained together1 nor  strung 
upon a pole1 mutually follow each other1
 so that on the  acceleration or        
retardation of the one1 the other also  
moves quicker or  slower4    ,the second
 ,dialogue is appropriated chiefly to   
the discussion of the  diurnal motion of
 the earth2 and the principal arguments 

urged by  ,aristotle1 ,ptolemy1 and     
others1 are successively brought forward
 and  confuted4 ,the opposers of the    
earth's diurnal motion maintained1 that 
if  it were turning round1 a stone      
dropped from the top of a tower would   
not  fall at its foot2 but1 by the      
rotation of the earth to the eastward   
carrying away the tower with it1 would  
be left at a great distance to  the     
westward2 it was common to compare this 
effect to a stone dropped  from the     
mast-head of a ship1 and without any    
regard to truth it was  boldly asserted 
that this would fall considerably nearer
 the stern than  the foot of the mast1  
if the ship were in rapid motion4 ,the  
same  argument was presented in a       
variety of forms1--such as that a       
cannon-ball shot perpendicularly upwards
 would not fall at the same  spot2 that 
if fired to the eastward it would fly   
farther than to the  westward2 that a   
mark to the east or west would never be 
hit1 because of  the rising or sinking  

of the horizon during the flight of the 
ball2 that  ladies' ringlets would all  
stand out to the westward1#ajb with     
other  conceits of the like nature3 to  
which the general reply is given1 that  
in all these cases the stone1 or ball1  
or other body1 participates  equally in 
the motion of the earth1 which1         
therefore1 so far as regards  the       
relative motion of its parts1 may be    
disregarded4 ,the manner in  which this 
is illustrated1 appears in the following
 extract from the  dialogue3--,sagredo4 
,if the nib of a writing pen which was  
in the ship  during my voyage direct    
from ,venice to ,alexandria1 had had the
 power of  leaving a visible mark of all
 its path1 what trace1 what mark1 what  
line  would it have left8--,simplicio4  
,it would have left a line stretched    
out thither from ,venice not perfectly  
straight1 or to speak more  correctly1  
not perfectly extended in an exact      
circular arc1 but here and  there more  
and less curved accordingly as the      

vessel had pitched more or  less2 but   
this variation in some places of one or 
two yards to the right  or left1 or up  
or down in a length of many hundred     
miles1 would have  occasioned but slight
 alteration in the whole course of the  
line1 so  that it would have been hardly
 sensible1 and without any great error  
we  may speak of it as a perfectly      
circular arc4--,sagred4 ,so that the    
true  and most exact motion of the point
 of the pen would also have been a      
perfect arc of a circle if the motion of
 the vessel1 abstracting from  the      
fluctuations of the waves1 had been     
steady and gentle2 and if ,i had  held  
this pen constantly in my hand1 and had 
merely moved it an inch or  two one way 
or the other1 what alteration would that
 have made in the  true and principal   
motion8--,simpl4 ,less than that which  
would be  occasioned in a line a        
thousand yards long1 by varying here and
 there  from perfect straightness by the
 quantity of a flea's eye4--,sagred4 ,if

  then a painter on our quitting the    
port had begun to draw with this pen  on
 paper1 and had continued his drawing   
till we got to ,alexandria1 he  would   
have been able by its motion1 to produce
 an accurate  representation of many    
objects perfectly shadowed1 and filled  
up on all  sides with landscapes1       
buildings1 and animals1 although all the
 true1  real1 and essential motion of   
the point of his pen would have been no 
other but a very long and very simple   
line2 and as to the peculiar work  of   
the painter1 he would have drawn it     
exactly the same if the ship had  stood 
still4 ,therefore1 of the very          
protracted motion of the pen1 there     
remain no other traces than those marks 
drawn upon the paper1 the reason  of    
this being that the great motion from   
,venice to ,alexandria was common  to   
the paper1 the pen1 and everything that 
was in the ship2 but the  trifling      
motion forwards and backwards1 to the   
right and left1  communicated by the    

painter's fingers to the pen1 and not to
 the paper1  from being peculiar to the 
pen1 left its mark upon the paper1 which
 as  to this motion was immoveable4     
,thus it is likewise true that in the   
supposition of the earth's rotation1 the
 motion of a falling stone is  really a 
long track of many hundreds and         
thousands of yards2 and if it  could    
have delineated its course in the calm  
air1 or on any other  surface1 it would 
have left behind it a very long         
transversal line2 but  that part of all 
this motion which is common to the      
stone1 the tower1  and ourselves1 is    
imperceptible by us and the same as if  
not existing1  and only that part       
remains to be observed of which neither 
we nor the  tower partake1 which in     
short is the fall of the stone along the
 tower4    ,the mechanical doctrines    
introduced into this second dialogue    
will be  noticed on another occasion2 we
 shall pass on to other extracts1       
illustrative of the general character of

 ,galileo's reasoning3--  ,salviati4 ,i 
did not say that the earth has no       
principle1 either  internal or external1
 of its motion of rotation1 but ,i do   
say that ,i  know not which of the two  
it has1 and that my ignorance has no    
power to  take its motion away2 but if  
this author knows by what principle     
other  mundane bodies1 of the motion of 
which we are certain1 are turned round1 
,i say that what moves the ,earth is    
something like that by which ,mars and  
,jupiter1 and1 as he believes1 the      
starry sphere1 are moved round2 and if  
he will satisfy me as to the cause of   
their motion1 ,i bind myself to be  able
 to tell him what moves the earth4 ,nay 
more2 ,i undertake to do the  same if he
 can teach me what it is which moves the
 parts of the earth  downwards4--,simpl4
 ,the cause of this effect is notorious1
 and every  one knows that it is        
,gravity4--,salv4 ,you are out1 ,master 
,simplicio2  you should say that every  
one knows that it is called ,gravity2   

but ,i do  not ask you the name but the 
nature of the thing1 of which nature you
 do  not know one tittle more than you  
know of the nature of the moving cause  
of the rotation of the stars1 except it 
be the name which has been given  to the
 one1 and made familiar and domestic1 by
 the frequent experience  we have of it 
many thousand times in a day2 but of the
 principle or  virtue by which a stone  
falls to the ground1 we really know no  
more than  we know of the principle     
which carries it upwards when thrown    
into the  air1 or which carries the moon
 round its orbit1 except1 as ,i have    
said1  the name of gravity which we have
 peculiarly and exclusively assigned to 
it2 whereas we speak of the other with a
 more generic term1 and talk of  the    
virtue impressed1 and call it either an 
assisting or an informing  intelligence1
 and are content to say that ,nature is 
the cause of an  infinite number of     
other motions4    ,simplicio is made to 
quote a passage from ,scheiner's book of

 ,conclusions  against ,copernicus1 to  
the following effect3--',if the whole   
earth and  water were annihilated1 no   
hail or rain would fall from the clouds1
 but  would only be naturally carried   
round in a circle1 nor would any fire or
  fiery thing ascend1 since1 according  
to the not improbable opinion of  these 
others1 there is no fire in the upper   
regions4'--,salv4 ,the  foresight of    
this philosopher is most admirable and  
praiseworthy1 for he  is not content    
with providing for things that might    
happen during the  common course of     
nature1 but persists in shewing his care
 for the  consequences of what he very  
well knows will never come to pass4     
,nevertheless1 for the sake of hearing  
some of his notable conceits1 ,i  will  
grant that if the earth and water were  
annihilated there would be  no more hail
 or rain1 nor would fiery matter ascend 
any more1 but would  continue a motion  
of revolution4 ,what is to follow8 ,what
 conclusion is  the philosopher going to

 draw8--,simpl4 ,this objection is in   
the very  next words--',which           
nevertheless 7says he7 is contrary to   
experience and  reason4'--,salv4 ,now ,i
 must yield3 since he has so great an   
advantage  over me as experience1 with  
which ,i am quite unprovided4 ,for      
hitherto ,i  have never happened to see 
the terrestrial earth and water         
annihilated1  so as to be able to       
observe what the hail and fire did in   
the confusion4  ,but does he tell us for
 our information at least what they     
did8--,simp4  ,no1 he does not say any  
thing more4--,salv4 ,i would give       
something to  have a word or two with   
this person1 to ask him whether1 when   
this globe  vanished1 it also carried   
away the common centre of gravity1 as ,i
 fancy  it did1 in which case ,i take it
 that the hail and water would remain   
stupid and confounded amongst the       
clouds1 without knowing what to do  with
 themselves4444 ,and lastly1 that ,i may
 give this philosopher a less  equivocal

 answer1 ,i tell him that ,i know as    
much of what would follow  after the    
annihilation of the terrestrial globe1  
as he could have known  what was about  
to happen in and about it1 before it was
 created4    ,great part of the third   
,dialogue is taken up with discussions  
on the  parallax of the new stars of    
#aegb and #afjd1 in which ,delambre     
notices  that ,galileo does not employ  
logarithms in his calculations1 although
  their use had been known since ,napier
 discovered them in #afaf3 the  dialogue
 then turns to the annual motion first  
taken from the ,sun and  conferred upon 
the ,earth by ,aristarchus ,samius1 and 
afterwards by  ,copernicus4 ,salviati   
speaks of his contemporary philosophers 
with great  contempt--,if you had ever  
been worn out as ,i have been many and  
many a  time with hearing what sort of  
stuff is sufficient to make the         
obstinate  vulgar unpersuadable1 ,i do  
not say to agree with1 but even to      
listen to  these novelties1 ,i believe  

your wonder at finding so few followers 
of  these opinions would greatly fall   
off4 ,but little regard in my judgment  
is to be had of those understandings who
 are convinced and immoveably  persuaded
 of the fixedness of the earth1 by      
seeing that they are not  able to       
breakfast this morning at               
,constantinople1 and sup in the evening 
in ,japan1 and who feel satisfied that  
the earth1 so heavy as it is1  cannot   
climb up above the sun1 and then come   
tumbling in a breakneck  fashion down   
again6#ajc ,this remark serves to       
introduce several  specious arguments   
against the annual motion of the earth1 
which are  successively confuted1 and it
 is shewn how readily the apparent      
stations  and retrogradations of the    
planets are accounted for on this       
supposition4    ,the following is one of
 the frequently recurring passages in   
which  ,galileo1 whilst arguing in      
favour of the enormous distances at     
which the  theory of ,copernicus        

necessarily placed the fixed stars1     
inveighs  against the arrogance with    
which men pretend to judge of matters   
removed  above their comprehension4     
,simpl4 ,all this is very well1 and it  
is  not to be denied that the heavens   
may surpass in bigness the capacity of  
our imaginations1 as also that ,god     
might have created it yet a thousand    
times larger than it really is1 but we  
ought not to admit anything to be       
created in vain1 and useless in the     
universe4 ,now whilst we see this       
beautiful arrangement of the planets1   
disposed round the earth at  distances  
proportioned to the effects they are to 
produce on us for our  benefit1 to what 
purpose should a vast vacancy be        
afterwards interposed  between the orbit
 of ,saturn and the starry spheres1     
containing not a  single star1 and      
altogether useless and unprofitable8 to 
what end8 for  whose use and            
advantage8--,salv4 ,methinks we arrogate
 too much to  ourselves1 ,simplicio1    

when we will have it that the care of us
 alone is  the adequate and sufficient  
work and bound1 beyond which the divine 
wisdom and power does and disposes of   
nothing4 ,i feel confident that  nothing
 is omitted by the ,divine ,providence  
of what concerns the  government of     
human affairs2 but that there may not be
 other things in  the universe dependant
 upon ,his supreme wisdom1 ,i cannot for
 myself1 by  what my reason holds out to
 me1 bring myself to believe4 ,so that  
when ,i  am told of the uselessness of  
an immense space interposed between the 
orbits of the planets and the fixed     
stars1 empty and valueless1 ,i reply    
that there is temerity in attempting by 
feeble reason to judge the works  of    
,god1 and in calling vain and           
superfluous every part of the universe  
which is of no use to us4--,sagr4 ,say  
rather1 and ,i believe you would  say   
better1 that we have no means of knowing
 what is of use to us2 and ,i  hold it  
to be one of the greatest pieces of     

arrogance and folly that can  be in this
 world to say1 because ,i know not of   
what use ,jupiter or  ,saturn are to me1
 that therefore these planets are       
superfluous2 nay  more1 that there are  
no such things in nature4 ,to understand
 what effect  is worked upon us by this 
or that heavenly body 7since you will   
have it  that all their use must have a 
reference to us71 it would be necessary 
to remove it for a while1 and then the  
effect which ,i find no longer  produced
 in me1 ,i may say that it depended upon
 that star4 ,besides1 who  will dare say
 that the space which they call too vast
 and useless  between ,saturn and the   
fixed stars is void of other bodies     
belonging to  the universe4 ,must it be 
so because we do not see them3 then ,i  
suppose  the four ,medicean planets1 and
 the companions of ,saturn1 came into   
the  heavens when we first began to see 
them1 and not before6 and1 by the  same 
rule1 the other innumerable fixed stars 
did not exist before men  saw them4 ,the

 nebul were till lately only white      
flakes1 till with the  telescope we have
 made of them constellations of bright  
and beautiful  stars4 ,oh presumptuous6 
rather1 ,oh rash ignorance of man6      
,after a discussion on ,gilbert's       
,theory of ,terrestrial ,magnetism1     
introduced by the parallelism of the    
earth's axis1 and of which ,galileo     
praises very highly both the method and 
results1 the dialogue proceeds  as      
follows3--,simpl4 ,it appears to me that
 ,sig4 ,salviati1 with a fine           
circumlocution1 has so clearly explained
 the cause of these effects1  that any  
common understanding1 even though       
unacquainted with science1  may         
comprehend it3 but we1 confining        
ourselves to the terms of art1  reduce  
the cause of these and other similar    
natural phenomena to  sympathy1 which is
 a certain agreement and mutual         
appetency arising  between things which 
have the same qualities1 just as1 on the
 other  hand1 that disagreement and     

aversion1 with which other things       
naturally  repel and abhor each other1  
we style antipathy4--,sagr4 ,and thus   
with  these two words they are able to  
give a reason for the great number of   
effects and accidents which we see1 not 
without admiration1 to be  produced in  
,nature4 ,but it strikes me that this   
mode of philosophising  has a great     
sympathy with the style in which one of 
my friends used to  paint3 on one part  
of the canvas he would write with       
chalk--there ,i will  have a fountain1  
with ,diana and her nymphs2 here some   
harriers2 in this  corner ,i will have a
 huntsman1 with a stag's head2 the rest 
may be a  landscape of wood and         
mountain2 and what remains to be done   
may be put  in by the colourman3 and    
thus he flattered himself that he had   
painted  the story of ,acton1 having    
contributed nothing to it beyond the    
names4    ,the fourth ,dialogue is      
devoted entirely to an examination of   
the tides1  and is a development and    

extension of the treatise already       
mentioned to  have been sent to the     
,archduke ,leopold1 in #afah4ajd        
,galileo was  uncommonly partial to his 
theory of the tides1 from which he      
thought to  derive a direct proof of the
 earth's motion in her orbit2 and       
although  his theory was erroneous1 it  
required a farther advance in the       
science  of motion than had been        
attained even at a much later period to 
point  out the insufficiency of it4 ,it 
is well known that the problem of       
explaining the cause of this alternate  
motion of the waters had been           
considered from the earliest ages one of
 the most difficult that could  be      
proposed1 and the solutions with which  
different inquirers were  obliged to    
rest contented1 shew that it long       
deserved the name given to  it1 of the  
grave of human curiosity4#aje ,riccioli 
has enumerated  several of the opinions 
which in turn had their favourers and   
supporters4 ,one party supposed the rise

 of the waters to be occasioned  by the 
influx of rivers into the sea2 others   
compared the earth to a  large animal1  
of which the tides indicated the        
respiration2 a third  theory supposed   
the existence of subterraneous fires1 by
 which the sea  was periodically made to
 boil2 others attributed the cause of a 
similar  change of temperature to the   
sun and moon4    ,there is an unfounded 
legend1 that ,aristotle drowned himself 
in despair  of being able to invent a   
plausible explanation of the            
extraordinary  tides in the ,euripus4   
,his curiosity on the subject does not  
appear to  have been so acute 7judging  
from his writings7 as this story would  
imply4 ,in one of his books he merely   
mentions a rumour1 that there are  great
 elevations or swellings of the seas1   
which recur periodically1  according to 
the course of the moon4 ,lalande1 in the
 fourth volume of  his ,astronomy1 has  
given an interesting account of the     
opinion of the  connection of the tides 

with the moon's motion4 ,pytheas of     
,marseilles1 a  contemporary of         
,aristotle1 was the first who has been  
recorded as  observing1 that the full   
tides occur at full moon1 and the ebbs  
at new  moon4#ajf ,this is not quite    
correctly stated2 for the tide of new   
moon  is known to be still higher than  
the rise at the full1 but it is likely  
enough1 that the seeming inaccuracy     
should be attributed1 not to  ,pytheas1 
but to his biographer ,plutarch1 who1 in
 many instances1  appears to have viewed
 the opinions of the old philosophers   
through the  mist of his own prejudices 
and imperfect information4 ,the fact is1
 that1  on the same day when the tide   
rises highest1 it also ebbs lowest2 and 
,pytheas1 who1 according to ,pliny1 had 
recorded a tide in ,britain of  eighty  
cubits1 could not have been ignorant of 
this4 ,posidonius1 as  quoted by        
,strabo1 maintained the existence of    
three periods of the tide1  daily1      
monthly1 and annual1 in sympathy with   

the moon4#ajg ,pliny1 in  his vast      
collection of natural observations1 not 
unaptly styled the  ,encyclopdia of the 
,antients1 has the following curious    
passages3--,the  flow and ebb of the    
tide is very wonderful2 it happens in a 
variety of  ways1 but the cause is in   
the sun and moon4#ajh ,he then very     
accurately describes the course of the  
tide during a revolution of the  moon1  
and adds3 ,the flow takes place every   
day at a different hour2  being waited  
on by the star1 which rises every day in
 a different place  from that of the day
 before1 and with greedy draught drags  
the seas with  it4#aji ,when the moon is
 in the north1 and further removed from 
the  earth1 the tides are more gentle   
than when digressing to the south1 she  
exerts her force with a closer          
effort4#aaj    ,the ,college of ,jesuits
 at ,coimbra appears to deserve the     
credit of first  clearly pointing out   
the true relation between the tides and 
the moon1  which was also maintained a  

few years later by ,antonio de ,dominis 
and  ,kepler4 ,in the ,society's        
commentary on ,aristotle's book on      
,meteors1  after refuting the notion    
that the tides are caused by the light  
of the  sun and moon1 they say1 ,it     
appears more probable to us1 without any
  rarefaction1 of which there appears no
 need or indication1 that the moon      
raises the waters by some inherent power
 of impulsion1 in the same  manner as a 
magnet moves iron2 and according to its 
different aspects  and approaches to the
 sea1 and the obtuse or acute angles of 
its  bearing1 at one time to attract and
 raise the waters along the shore1  and 
then again to leave them to sink down by
 their own weight1 and to  gather into a
 lower level4#aaa ,the theory of        
,universal ,gravitation  seems here     
within the grasp of these philosophers1 
but unfortunately it  did not occur to  
them that possibly the same attraction  
might be exerted  on the earth as well  
as the water1 and that the tide was     

merely an  effect of the diminution of  
force1 owing to the increase of         
distance1  with which the centre of the 
earth is attracted1 as compared with    
that  exerted on its surface4 ,this     
idea1 so happily seized afterwards by   
,newton1 might at once have furnished   
them with a satisfactory  explanation of
 the tide1 which is observed on the     
opposite side of the  earth as well as  
immediately under the moon4 ,they might 
have seen that  in the latter case the  
centre of the earth is pulled away from 
the  water1 just as in the former the   
water is pulled away from the centre of 
the earth1 the sensible effect to us    
being in both cases precisely the  same4
 ,for want of this generalization1 the  
inferior tide as it is called  presented
 a formidable obstacle to this theory1  
and the most plausible  explanation that
 was given was1 that this magnetic      
virtue radiated out  from the moon was  
reflected by the solid heavens1 and     
concentrated again  as in a focus on the

 opposite side of the earth4 ,the       
majority of modern  astronomers who did 
not admit the existence of any solid    
matter fit for  producing the effect    
assigned to it1 found a reasonable      
difficulty in  acquiescing in this      
explanation4 ,galileo1 who mentions the 
,archbishop of  ,spalatro's book1       
treated the theory of attraction by the 
moon as absurd4  ,this motion of the    
seas is local and sensible1 made in an  
immense mass  of water1 and cannot be   
brought to obey light1 and warmth1 and  
predominancy of occult qualities1 and   
such like vain fancies2 all which  are  
so far from being the cause of the tide1
 that on the contrary the  tide is the  
cause of them1 inasmuch as it gives rise
 to these ideas in  brains which are    
more apt for talkativeness and          
ostentation1 than for  speculation and  
inquiry into the secrets of ,nature2    
who1 rather than see  themselves driven 
to pronounce these wise1 ingenuous1 and 
modest  words--,i do not know1--will    

blurt out from their tongues and pens   
all  sorts of extravagancies4           
,galileo's own theory is introduced by  
the following illustration1 which       
indeed probably suggested it1 as he was 
in the habit of suffering no  natural   
phenomena1 however trivial in           
appearance1 to escape him4 ,he felt  the
 advantage of this custom in being      
furnished on all occasions with a  stock
 of homely illustrations1 to which the  
daily experience of his  hearers readily
 assented1 and which he could shew to be
 identical in  principle with the       
phenomena under discussion4 ,that he was
 mistaken in  applying his observations 
in the present instance cannot be urged 
against the incalculable value of such a
 habit4    ,we may explain and render   
sensible these effects by the example of
 one  of those barks which come         
continually from ,lizza ,fusina1 with   
fresh  water for the use of the city of 
,venice4 ,let us suppose one of these   
barks to come thence with moderate      

velocity along the canal1 carrying      
gently the water with which it is       
filled1 and then1 either by touching    
the bottom1 or from some other hindrance
 which is opposed to it1 let it  be     
notably retarded2 the water will not on 
that account lose like the  bark the    
impetus it has already acquired1 but    
will forthwith run on  towards the prow 
where it will sensibly rise1 and be     
depressed at the  stern4 ,if on the     
contrary the said vessel in the middle  
of its steady  course shall receive a   
new and sensible increase of velocity1  
the  contained water before giving into 
it will persevere for some time in  its 
slowness1 and will be left behind that  
is to say towards the stern  where      
consequently it will rise1 and sink at  
the head4--,now1 my masters1  that which
 the vessel does in respect of the water
 contained in it1 and  that which the   
water does in respect of the vessel     
containing it1 is the  same to a hair as
 what the ,mediterranean vase does in   

respect of the  water which it contains1
 and that the waters do in respect of   
the  ,mediterranean vase which contains 
them4 ,we have now only to demonstrate  
how1 and in what manner it is true that 
the ,mediterranean1 and all other       
gulfs1 and in short all the parts of the
 earth move with a motion  sensibly not 
uniform1 although no motion results     
thence to the whole  globe which is not 
perfectly uniform and regular4    ,this 
unequable motion is derived from a      
combination of the earth's  motion on   
her axis1 and in her orbit1 the         
consequence of which is that a  point   
under the sun is carried in the same    
direction by the annual and  diurnal    
velocities1 whereas a point on the      
opposite side of the globe is  carried  
in opposite directions by the annual and
 diurnal motions1 so  that in every     
twenty-four hours the absolute motion   
through space of  every point in the    
earth completes a cycle of varying      
swiftness4 ,those  readers who are      

unacquainted with the mathematical      
theory of motion must  be satisfied with
 the assurance that this specious       
representation is  fallacious1 and that 
the oscillation of the water does not in
 the least  result from the causes here 
assigned to it3 the reasoning necessary 
to  prove this is not elementary enough 
to be introduced here with  propriety4  
,besides the principal daily oscillation
 of the water1 there is a monthly       
inequality in the rise and fall1 of     
which the extremes are called the       
spring and neap tides3 the manner in    
which ,galileo attempted to bring  his  
theory to bear upon these phenomena is  
exceedingly curious4    ,it is a natural
 and necessary truth1 that if a body be 
made to revolve1  the time of revolution
 will be greater in a greater circle    
than in a  less3 this is universally    
allowed1 and fully confirmed by         
experiments1  such for instance as      
these3--,in wheel clocks1 especially in 
large ones1  to regulate the going1 the 

workmen fit up a bar capable of         
revolving  horizontally1 and fasten two 
leaden weights to the ends of it2 and if
  the clock goes too slow1 by merely    
approaching these weights somewhat      
towards the centre of the bar1 they make
 its vibrations more frequent1  at which
 time they are moving in smaller circles
 than before4#aab--,or1  if you fasten a
 weight to a cord which you pass round a
 pulley in the  ceiling1 and whilst the 
weight is vibrating draw in the cord    
towards  you1 the vibrations will become
 sensibly accelerated as the length of  
the string diminishes4 ,we may observe  
the same rule to hold among the         
celestial motions of the planets1 of    
which we have a ready instance in  the  
,medicean planets1 which revolve in such
 short periods round ,jupiter4  ,we may 
therefore safely conclude1 that if the  
moon for instance shall  continue to be 
forced round by the same moving power1  
and were to move  in a smaller circle1  
it would shorten the time of its        

revolution4 ,now  this very thing       
happens in fact to the moon1 which ,i   
have just advanced  on a supposition4   
,let us call to mind that we have       
already concluded  with ,copernicus1    
that it is impossible to separate the   
moon from the  earth1 round which       
without doubt it moves in a month3 we   
must also  remember that the globe of   
the earth1 accompanied always by the    
moon1  revolves in the great circle     
round the sun in a year1 in which time  
the  moon revolves round the earth about
 thirteen times1 whence it follows  that
 the moon is sometimes near the sun1    
that is to say between the  earth and   
sun1 sometimes far from it1 when she is 
on the outside of the  earth4 ,now if it
 be true that the power which moves the 
earth and the  moon round the sun       
remains of the same efficacy1 and if it 
be true that  the same moveable1 acted  
on by the same force1 passes over       
similar arcs  of circles in a time which
 is least when the circle is smallest1  

we are  forced to the conclusion that at
 new moon1 when in conjunction with the 
sun1 the moon passes over greater arcs  
of the orbit round the sun1 than  when  
in opposition at full moon2 and this    
inequality of the moon will be  shared  
by the earth also4 ,so that exactly the 
same thing happens as in  the balance of
 the clocks2 for the moon here          
represents the leaden  weight1 which at 
one time is fixed at a greater distance 
from the centre  to make the vibrations 
slower1 and at another time nearer to   
accelerate  them4    ,wallis adopted and
 improved this theory in a paper which  
he inserted in  the ,philosophical      
,transactions for #afff1 in which he    
declares1 that the  circular motion     
round the sun should be considered as   
taking place at a  point which is the   
centre of gravity of the earth and moon4
 ,to the  first objection1 that it      
appears not how two bodies that have no 
tie can  have one common centre of      
gravity1 ,i shall only answer1 that it  

is  harder to show how they have it1    
than that they have it4#aac ,as ,wallis 
was perfectly competent from the time at
 which he lived1 and his  knowledge of  
the farthest advances of science in his 
time1 to appreciate  the value of       
,galileo's writings1 we shall conclude  
this chapter with the  judgment that he 
has passed upon them in the same paper4 
,since ,galileo1  and after him         
,torricelli and others have applied     
mechanical principles  to the solving of
 philosophical difficulties1 natural    
philosophy is well  known to have been  
rendered more intelligible1 and to have 
made a much  greater progress in less   
than a hundred years than before for    
many  ages4      ,,footnotes3    #ic    
,see page #ef4    #id ,playfair's       
,dissertation1 ,supp4 ,encyc4 ,brit4    
#ie ,astronomia ,nova4 ,prag4 #afji4    
#if ,the new ,planet no ,planet1 or the 
,earth no wandering ,star1 except in    
the wandering heads of ,galileans4      
,london1 #afdf4    #ig ,aristarchi      

,samii de ,mundi ,systemate4 ,parisiis  
#afdd4    #ih ,see page #ab4    #ii ,de 
,clo1 lib4 iv4 cap4 #c4    #ajj         
,reflexiones ,physico-,mathematic1      
,parisiis1 #afdg4    #aja ,venturi4     
#ajb ,riccioli4    #ajc ,the notions    
commonly entertained of 'up' and 'down1'
 as connected  with the observer's own  
situation1 had long been a              
stumbling-block in  the way of the new  
doctrines4 ,when ,columbus held out the 
certainty of  arriving in ,india by     
sailing to the westward on account of   
the earth's  roundness1 it was gravely  
objected1 that it might be well enough  
to sail  down to ,india1 but that the   
chief difficulty would consist in       
climbing  up back again4    #ajd ,see   
page #ej4    #aje ,riccioli ,almag4     
,nov4    #ajf ,plutarch1 ,de placit4    
,philos4 lib4 iii4 c4 #ag4    #ajg   4  
,geographi1 lib4 iii4    #ajh ,historia 
,naturalis1 lib4 ii4 c1 #ig4    #aji ,ut
 ancillante sidere1 trahenteque secum   
avido haustu maria4    #aaj ,edem       

,aquiloni1 et  terris longius recedente1
 mitiores quam cum1  in ,austros        
digress1 propiore nisu vim suam exercet4
    #aaa ,commentarii ,collegii         
,conimbricensis4 ,coloni1 #afjc4    #aab
 ,see fig4 #a4 p4 #if4    #aac ,phil4   
,trans41 ,no4 #af1 ,august #afff4       
,,chapter ,,xv4        ,galileo at      
,arcetri--,becomes ,blind--,moon's      
,libration--,publication of        the  
,dialogues on ,motion4      ,,we have   
already alluded to the imperfect state  
of the knowledge  possessed with regard 
to ,galileo's domestic life and personal
 habits2  there is reason however to    
think that unpublished materials exist  
from  which these outlines might be in  
part filled up4 ,venturi informs us that
  he had seen in the collection from    
which he derived a great part of the    
substance of his ,memoirs of ,galileo1  
about one hundred and twenty  manuscript
 letters1 dated between the years #afbc 
and #afcc1 addressed to  him by his     
daughter ,maria1 who with her sister had

 attached herself to  the convent of    
,st4 ,matthew1 close to ,galileo's usual
 place of residence4  ,it is difficult  
not to think that much interesting      
information might be  obtained from     
these1 with respect to ,galileo's       
domestic character4 ,the  very few      
published extracts confirm our          
favourable impressions of it1  and      
convey a pleasing idea of this his      
favourite daughter4 ,even when1 in  her 
affectionate eagerness to soothe her    
father's wounded feelings at  the close 
of his imprisonment in ,rome1 she dwells
 with delight upon her  hopes of being  
allowed to relieve him1 by taking on    
herself the  penitential recitations    
which formed a part of his sentence1 the
  prevalent feeling excited in every one
 by the perusal must surely be  sympathy
 with the filial tenderness which it is 
impossible to  misunderstand4    ,the   
joy she had anticipated in again meeting
 her parent1 and in  compensating to him
 by her attentive affection the insults 

of his  malignant enemies1 was destined 
to be but of short duration4 ,almost in 
the same month in which ,galileo        
returned to ,arcetri she was seized with
  a fatal illness2 and already in the   
beginning of ,april1 #afcd1 we learn    
her death from the fruitless condolence 
of his friends4 ,he was deeply  and     
bitterly affected by this additional    
blow1 which came upon him when  he was  
himself in a weak and declining state of
 health1 and his answers  breathe a     
spirit of the most hopeless and gloomy  
despondency4    ,in a letter written in 
,april to ,bocchineri1 his son's        
father-in-law1 he  says3 ,the hernia has
 returned worse than at first3 my pulse 
is  intermitting1 accompanied with a    
palpitation of the heart2 an            
immeasurable sadness and melancholy2 an 
entire loss of appetite2 ,i am  hateful 
to myself2 and in short ,i feel that ,i 
am called incessantly by  my dear       
daughter4 ,in this state1 ,i do not     
think it advisable that  ,vincenzo      

should set out on his journey1 and leave
 me1 when every hour  something may     
occur1 which would make it expedient    
that he should be  here4 ,in this       
extremity of ill health1 ,galileo       
requested leave to go to  ,florence for 
the advantage of medical assistance2 but
 far from obtaining  permission1 it was 
intimated that any additional           
importunities would be  noticed by      
depriving him of the partial liberty he 
was then allowed to  enjoy4 ,after      
several years confinement at ,arcetri1  
during the whole of  which time he      
suffered from continual indisposition1  
the inquisitor  ,fariano wrote to him in
 #afch1 that the ,pope permitted his    
removal to  ,florence1 for the purpose  
of recovering his health2 requiring him 
at the  same time to present himself at 
the ,office of the ,inquisition1 where  
he  would learn the conditions on which 
this favour had been granted4 ,these    
were that he should neither quit his    
house nor receive his friends  there2   

and so closely was the letter of these  
instructions adhered to1  that he was   
obliged to obtain a special permission  
to go out to attend  mass during        
,passion week4 ,the strictness with     
which all personal  intercourse with his
 friends was interrupted1 is manifest   
from the  result of the following letter
 from the ,duke of ,tuscany's secretary 
of  state to ,nicolini1 his ambassador  
at ,rome4 ,signor ,galileo ,galilei1    
from  his great age and the illnesses   
which afflict him1 is in a condition    
soon to go to another world2 and        
although in this the eternal memory of  
his fame and value is already secured1  
yet his ,highness is greatly  desirous  
that the world should sustain as little 
loss as possible by his  death2 that his
 labours may not perish1 but for the    
public good may be  brought to that     
perfection which he will not be able to 
give them4 ,he  has in his thoughts many
 things worthy of him1 which he cannot  
be  prevailed on to communicate to any  

but ,father ,benedetto ,castelli1 in    
whom he has entire confidence4 ,his     
,highness wishes therefore that you     
should see ,castelli1 and induce him to 
procure leave to come to ,florence  for 
a few months for this purpose1 which his
 ,highness has very much at  heart2 and 
if he obtains permission1 as his        
,highness hopes1 you will  furnish him  
with money and every thing else he may  
require for his  journey4 ,castelli1 it 
will be remembered1 was at this time    
salaried by  the court of ,rome4        
,nicolini answered that ,castelli had   
been himself to  the ,pope to ask leave 
to go to ,florence4 ,urban immediately  
intimated his  suspicions that his      
design was to see ,galileo1 and upon    
,castelli's  stating that certainly it  
would be impossible for him to refrain  
from  attempting to see him1 he received
 permission to visit him in the  company
 of an officer of the ,inquisition4 ,at 
the end of some months  ,galileo was    
remanded to ,arcetri1 which he never    

again quitted4    ,in addition to his   
other infirmities1 a disorder which some
 years before  had affected the sight of
 his right eye returned in #afcf2 in the
 course  of the ensuing year the other  
eye began to fail also1 and in a few    
months he became totally blind4 ,it     
would be difficult to find any even     
among those who are the most careless to
 make a proper use of the  invaluable   
blessing of sight1 who could bear       
unmoved to be deprived of  it1 but on   
,galileo the loss fell with peculiar and
 terrible severity2 on  him who had     
boasted that he would never cease from  
using the senses  which ,god had given  
him1 in declaring the glory of his      
works1 and the  business of whose life  
had been the splendid fulfilment of that
  undertaking4 ,the noblest eye is      
darkened1 said ,castelli1 which nature  
ever made3 an eye so privileged1 and    
gifted with such rare qualities1  that  
it may with truth be said to have seen  
more than all of those who  are gone1   

and to have opened the eyes of all who  
are to come4 ,his own  patience and     
resignation under this fatal calamity   
are truly wonderful2  and if            
occasionally a word of complaint escaped
 him1 it was in the  chastened tone of  
the following expressions--,alas6 your  
dear friend and  servant ,galileo has   
become totally and irreparably blind2 so
 that this  heaven1 this earth1 this    
universe1 which with wonderful          
observations ,i  had enlarged a hundred 
and thousand times beyond the belief of 
by-gone  ages1 henceforward for me is   
shrunk into the narrow space which ,i   
myself  fill in it4--,so it pleases     
,god3 it shall therefore please me also4
  ,hopes were at first entertained by   
,galileo's friends1 that the  blindness 
was occasioned by cataracts1 and that he
 might look forward to  relief from the 
operation of couching2 but it very soon 
appeared that  the disorder was not in  
the humours of the eye1 but in a        
cloudiness of  the cornea1 the symptoms 

of which all external remedies failed to
  alleviate4    ,as long as the power   
was left him1 he had indefatigably      
continued his  astronomical             
observations4 ,just before his sight    
began to decay1 he had  observed a new  
phenomenon in the moon1 which is now    
known by the name of  the moon's        
libration1 the nature of which we will  
shortly explain4 ,a  remarkable         
circumstance connected with the moon's  
motion is1 that the  same side is always
 visible from the earth1 showing that   
the moon turns  once on her own axis in 
exactly the time of her monthly         
revolution4#aad  ,but ,galileo1 who was 
by this time familiar with the whole of 
the moon's  visible surface1 observed   
that the above-mentioned effect does not
  accurately take place1 but that a     
small part on either side comes         
alternately forward into sight1 and then
 again recedes1 according to the  moon's
 various positions in the heavens4 ,he  
was not long in detecting  one of the   

causes of this apparent libratory or    
rocking motion4 ,it is  partly          
occasioned by our distance as spectators
 from the centre of the  earth1 which is
 also the centre of the moon's motion4  
,in consequence of  this1 as the moon   
rises in the sky we get an additional   
view of the  lower half1 and lose sight 
of a small part of the upper half which 
was  visible to us while we were looking
 down upon her when low in the  horizon4
 ,the other cause is not quite so       
simple1 nor is it so certain  that      
,galileo adverted to it3 it is however  
readily intelligible even to  those who 
are unacquainted with astronomy1 if they
 will receive as a  fact that the       
monthly motion of the moon is not       
uniform1 but that she  moves quicker at 
one time than another1 whilst the motion
 of rotation on  her own axis1 like that
 of the earth1 is perfectly uniform4 ,a 
very  little reflection will show that  
the observed phenomenon will            
necessarily follow4 ,if the moon did not

 turn on her axis1 every side of  her   
would be successively presented1 in the 
course of a month1 towards  the earth2  
it is the motion of rotation which tends
 to carry the newly  discovered parts   
out of sight4    ,let us suppose the    
moon to be in that part of her orbit    
where she moves  with her average       
motion1 and that she is moving towards  
the part where  she moves most quickly4 
,if the motion in the orbit were to     
remain the  same all the way round1 the 
motion of rotation would be just        
sufficient  at every point to bring     
round the same part of the moon directly
 in  front of the earth4 ,but since1    
from the supposed point1 the moon is    
moving for some time round the earth    
with a motion continually growing       
quicker1 the motion of rotation is not  
sufficiently quick to carry out  of     
sight the entire part discovered by the 
motion of translation4 ,we  therefore   
get a glimpse of a narrow strip on the  
side from which the  moon is moving1    

which strip grows broader and broader1  
till she passes  the point where she    
moves most swiftly1 and reaches the     
point of average  swiftness on the      
opposite side of her orbit4 ,her motion 
is now  continually growing slower1 and 
therefore from this point the motion of 
rotation is too swift1 and carries too  
much out of sight1 or in other  words1  
brings into sight a strip on the side   
towards which the moon is  moving4 ,this
 increases till she passes the point of 
least swiftness1 and  arrives at the    
point from which we began to trace her  
course1 and the  phenomena are repeated 
in the same order4    ,this interesting 
observation closes the long list of     
,galileo's  discoveries in the heavens4 
,after his abjuration1 he ostensibly    
withdrew  himself in a great measure    
from his astronomical pursuits1 and     
employed  himself till #afcf principally
 with his ,dialogues on ,motion1 the    
last  work of consequence that he       
published4 ,in that year he entered into

  correspondence with the ,elzevirs1    
through his friend ,micanzio1 on the    
project of printing a complete edition  
of his writings4 ,among the  letters    
which ,micanzio wrote on the subject is 
one intimating that he  had enjoyed the 
gratification1 in his quality of        
,theologian to the  ,republic of        
,venice1 of refusing his sanction to a  
work written against  ,galileo and      
,copernicus4 ,the temper however in     
which this refusal was  announced1      
contrasts singularly with that of the   
,roman ,inquisitors4 ,a  book was       
brought to me which a ,veronese         
,capuchin has been writing1 and  wished 
to print1 denying the motion of the     
earth4 ,i was inclined to let  it go1 to
 make the world laugh1 for the ignorant 
beast entitles every  one of the twelve 
arguments which compose his book1 ',an  
irrefragable and  undeniable            
demonstration1' and then adduces nothing
 but such childish  trash as every man  
of sense has long discarded4 ,for       

instance1 this poor  animal understands 
so much geometry and mathematics1 that  
he brings  forward as a demonstration1  
that if the earth could move1 having    
nothing  to support it1 it must         
necessarily fall4 ,he ought to have     
added that  then we should catch all the
 quails4 ,but when ,i saw that he speaks
  indecently of you1 and has had the    
impudence to put down an account of     
what passed lately1 saying that he is in
 possession of the whole of your        
process and sentence1 ,i desired the man
 who brought it to me to go and  be     
hanged4 ,but you know the ingenuity of  
impertinence2 ,i suspect he will        
succeed elsewhere1 because he is so     
enamoured of his absurdities1 that  he  
believes them more firmly than his      
,bible4    ,after ,galileo's            
condemnation at ,rome1 he had been      
placed by the  ,inquisition in the list 
of authors the whole of whose writings1 
'edita  et edenda1' were strictly       
forbidden4 ,micanzio could not even     

obtain  permission to reprint the ,essay
 on ,floating ,bodies1 in spite of his  
protestations that it did not in any way
 relate to the ,copernican  theory4     
,this was the greatest stigma with which
 the ,inquisition were in  the habit of 
branding obnoxious authors2 and1 in     
consequence of it1 when  ,galileo had   
completed his ,dialogues on ,motion1 he 
found great difficulty  in contriving   
their publication1 the nature of which  
may be learned from  the account which  
,pieroni sent to ,galileo of his        
endeavours to print  them in ,germany4  
,he first took the manuscript to        
,vienna1 but found that  every book     
printed there must receive the          
approbation of the ,jesuits2  and       
,galileo's old antagonist1 ,scheiner1   
happening to be in that city1  ,pieroni 
feared lest he should interfere to      
prevent the publication  altogether1 if 
the knowledge of it should reach him4   
,through the  intervention of ,cardinal 
,dietrichstein1 he therefore got        

permission to  have it printed at       
,olmutz1 and that it should be approved 
by a  ,dominican1 so as to keep the     
whole business a secret from ,scheiner  
and  his party2 but during this         
negociation the ,cardinal suddenly died1
 and  ,pieroni being besides            
dissatisfied with the ,olmutz type1     
carried back  the manuscript to ,vienna1
 from which he heard that ,scheiner had 
gone  into ,silesia4 ,a new approbation 
was there procured1 and the work was    
just on the point of being sent to      
press1 when the dreaded ,scheiner       
re-appeared in ,vienna1 on which        
,pieroni again thought it advisable to  
suspend the impression till his         
departure4 ,in the mean time his own    
duty  as a military architect in the    
,emperor's service carried him to       
,prague1  where ,cardinal ,harrach1 on a
 former occasion1 had offered him the   
use of  the newly-erected ,university   
press4 ,but ,harrach happened not to be 
at  ,prague1 and this plan like the rest

 became abortive4 ,in the meantime      
,galileo1 wearied with these delays1 had
 engaged with ,louis ,elzevir1 who      
undertook to print the ,dialogues at    
,amsterdam4    ,it is abundantly evident
 from ,galileo's correspondence that    
this edition  was printed with his full 
concurrence1 although1 in order to      
obviate  further annoyance1 he pretended
 that it was pirated from a manuscript  
copy which he sent into ,france to the  
,comte de ,noailles1 to whom the  work  
is dedicated4 ,the same dissimulation   
had been previously thought  necessary1 
on occasion of the ,latin translation of
 ,the ,dialogues on the  ,system1 by    
,bernegger1 which ,galileo expressly    
requested through his  friend ,deodati1 
and of which he more than once privately
 signified his  approbation1 presenting 
the translator with a valuable          
telescope1  although he publicly        
protested against its appearance4 ,the  
story which  ,bernegger introduced in   
his preface1 tending to exculpate       

,galileo from  any share in the         
publication1 is by his own confession a 
mere fiction4  ,noailles had been       
ambassador at ,rome1 and1 by his conduct
 there1 well  deserved the compliment   
which ,galileo paid him on the present  
occasion4    ,as an introduction to the 
account of this work1 which ,galileo    
considered  the best he had ever        
produced1 it will become necessary to   
premise a  slight sketch of the nature  
of the mechanical philosophy which he   
found  prevailing1 nearly as it had been
 delivered by ,aristotle1 with the same 
view with which we introduced specimens 
of the astronomical opinions  current   
when ,galileo began to write on that    
subject3 they serve to show  the nature 
and objects of the reasoning which he   
had to oppose2 and1  without some       
exposition of them1 the aim and value of
 many of his  arguments would be        
imperfectly understood and appreciated4 
,,footnotes3    #aad ,frisi says that   
,galileo did not perceive this          

conclusion 7,elogio  del ,galileo72 but 
see ,the ,dial4 on the ,system1 ,dial4  
#a4 pp4 #fa1 #fb1 #he4  ,edit4 #agdd4   
,plutarch says1 7,de ,placitis ,philos4 
lib4 ii4 c4 #bh17 that  the             
,pythagoreans believed the moon to have 
inhabitants fifteen times as  large as  
men1 and that their day is fifteen times
 as long as ours4 ,it  seems probable1  
that the former of these opinions was   
engrafted on the  latter1 which is true1
 and implies a perception of the fact in
 the text4          ,,chapter ,,xvi4    
,state of the ,science of ,motion before
 ,galileo4      ,,it is generally       
difficult to trace any branch of human  
knowledge up to  its origin1 and more   
especially when1 as in the case of      
mechanics1 it is  very closely connected
 with the immediate wants of mankind4   
,little has  been told to us when we are
 informed that so soon as a man might   
wish to  remove a heavy stone1 he would 
be led1 by natural instinct1 to slide   
under it the end of some long           

instrument1 and that the same instinct  
would teach him either to raise the     
further end1 or to press it  downwards1 
so as to turn round upon some support   
placed as near to the  stone as         
possible4#aae    ,montucla's history    
would have lost nothing in value1 if1   
omitting this  philosophical view of the
 birth of the art1 he had contented     
himself  with his previous remark1 that 
there can be little doubt that men were 
familiar with the use of mechanical     
contrivances long before the idea       
occurred of enumerating or describing   
them1 or even of examining very  closely
 the nature and limits of the aid they  
are capable of affording4  ,the most    
careless observer indeed could scarcely 
overlook that the  weights heaved up    
with a lever1 or rolled along a slope   
into their  intended places1 reached    
them more slowly than those which the   
workmen  could lift directly in their   
hands2 but it probably needed a much    
longer  time to enable them to see the  

exact relation which1 in these and all  
other machines1 exists between the      
increase of the power to move1 and  the 
decreasing swiftness of the thing moved4
    ,in the preface to ,galileo's       
,treatise on ,mechanical ,science1      
published in  #aeib1 he is at some pains
 to set in a clear light the real       
advantages  belonging to the use of     
machines1 which 7says he7 ,i have       
thought it  necessary to do1 because1 if
 ,i mistake not1 ,i see almost all      
mechanics  deceiving themselves in the  
belief that1 by the help of a machine1  
they  can raise a greater weight than   
they are able to lift by the exertion of
  the same force without it4--,now if we
 take any determinate weight1 and  any  
force1 and any distance whatever1 it is 
beyond doubt that we can  move the      
weight to that distance by means of that
 force2 because even  although the force
 may be exceedingly small1 if we divide 
the weight  into a number of fragments1 
each of which is not too much for our   

force1  and carry these pieces one by   
one1 at length we shall have removed the
  whole weight2 nor can we reasonably   
say at the end of our work1 that  this  
great weight has been moved and carried 
away by a force less than  itself1      
unless we add that the force has passed 
several times over the  space through   
which the whole weight has gone but     
once4 ,from which it  appears that the  
velocity of the force 7understanding by 
velocity the  space gone through in a   
given time7 has been as many times      
greater than  that of the weight1 as the
 weight is greater than the force3 nor  
can we  on that account say that a great
 force is overcome by a small one1      
contrary to nature3 then only might we  
say that nature is overcome when  a     
small force moves a great weight as     
swiftly as itself1 which we assert  to  
be absolutely impossible with any       
machine either already or hereafter  to 
be contrived4 ,but since it may         
occasionally happen that we have but a  

small force1 and want to move a great   
weight without dividing it into  pieces1
 then we must have recourse to a machine
 by means of which we  shall remove the 
given weight1 with the given force1     
through the  required space4 ,but       
nevertheless the force as before will   
have to travel  over that very same     
space as many times repeated as the     
weight surpasses  its power1 so that1 at
 the end of our work1 we shall find that
 we have  derived no other benefit from 
our machine than that we have carried   
away  the same weight altogether1 which 
if divided into pieces we could have    
carried without the machine1 by the same
 force1 through the same space1  in the 
same time4 ,this is one of the          
advantages of a machine1 because it     
often happens that we have a lack of    
force but abundance of time1 and  that  
we wish to move great weights all at    
once4    ,this compensation of force and
 time has been fancifully personified by
  saying that ,nature cannot be cheated1

 and in scientific treatises on         
mechanics1 is called the principle of   
virtual velocities1 consisting  in the  
theorem that two weights will balance   
each other on any machine1  no matter   
how complicated or intricate the        
connecting contrivances may  be1 when   
one weight bears to the other the same  
proportion that the  space through which
 the latter would be raised bears to    
that through  which the former would    
sink1 in the first instant of their     
motion1 if  the machine were stirred by 
a third force4 ,the whole theory of     
machines  consists merely in            
generalizing and following out this     
principle into  its consequences2       
combined1 when the machines are in a    
state of motion1  with another principle
 equally elementary1 but to which our   
present  subject does not lead us to    
allude more particularly4    ,the credit
 of making known the principle of       
virtual velocities is  universally given
 to ,galileo2 and so far deservedly1    

that he undoubtedly  perceived the      
importance of it1 and by introducing it 
everywhere into  his writings succeeded 
in recommending it to others2 so that   
five and  twenty years after his death1 
,borelli1 who had been one of ,galileo's
  pupils1 calls it that mechanical      
principle with which everybody is so    
familiar#aaf1 and from that time to the 
present it has continued to be  taught  
as an elementary truth in most systems  
of mechanics4 ,but although  ,galileo   
had the merit in this1 as in so many    
other cases1 of  familiarizing and      
reconciling the world to the reception  
of truth1 there  are remarkable traces  
before his time of the employment of    
this same  principle1 some of which have
 been strangely disregarded4 ,lagrange  
asserts#aag that the ancients were      
entirely ignorant of the principle  of  
virtual velocities1 although ,galileo1  
to whom he refers it1  distinctly       
mentions that he himself found it in the
 writings of  ,aristotle4 ,montucla     

quotes a passage from ,aristotle's      
,physics1 in which  the law is stated   
generally1 but adds that he did not     
perceive its  immediate application to  
the lever1 and other machines4 ,the     
passage to  which ,galileo alludes is in
 ,aristotle's ,mechanics1 where1 in     
discussing  the properties of the lever1
 he says expressly1 the same force will 
raise a greater weight1 in proportion as
 the force is applied at a  greater     
distance from the fulcrum1 and the      
reason1 as ,i have already  said1 is    
because it describes a greater circle2  
and a weight which is  farther removed  
from the centre is made to move through 
a greater  space4#aah    ,it is true1   
that in the last mentioned treatise1    
,aristotle has given  other reasons     
which belong to a very different kind of
 philosophy1 and  which may lead us to  
doubt whether he fully saw the force of 
the one we  have just quoted4 ,it       
appeared to him not wonderful that so   
many  mechanical paradoxes 7as he called

 them7 should be connected with         
circular motion1 since the circle itself
 seemed of so paradoxical a  nature4    
,for1 in the first place1 it is made up 
of an immoveable centre1  and a moveable
 radius1 qualities which are contrary to
 each other4 #b;dly4  ,its circumference
 is both convex and concave4 #c;dly4    
,the motion by which  it is described is
 both forward and backward1 for the     
describing radius  comes back to the    
place from which it started4 #dthly4    
,the radius is  one2 but every point of 
it moves in describing the circle with a
  different degree of swiftness4        
,perhaps ,aristotle may have borrowed   
the idea of virtual velocities1         
contrasting so strongly with his other  
physical notions1 from some older       
writer2 possibly from ,archytas1 who1 we
 are told1 was the first to  reduce the 
science of mechanics to methodical      
order2#aai and who by the  testimony of 
his countrymen was gifted with          
extraordinary talents1  although none of

 his works have come down to us4 ,the   
other principles  and maxims of         
,aristotle's mechanical philosophy1     
which we shall have  occasion to cite1  
are scattered through his books on      
,mechanics1 on the  ,heavens1 and in his
 ,physical ,lectures1 and will therefore
 follow rather  unconnectedly1 though we
 have endeavoured to arrange them with  
as much  regularity as possible4        
,after defining a body to be that which 
is divisible in every direction1        
,aristotle proceeds to inquire how it   
happens that a body has only the  three 
dimensions of length1 breadth1 and      
thickness2 and seems to think  he has   
given a reason in saying that1 when we  
speak of two things1 we do  not say all1
 but both1 and three is the first number
 of which we say  all4#abj ,when he     
comes to speak of motion1 he says1 ,if  
motion is not  understood1 we cannot but
 remain ignorant of ,nature4 ,motion    
appears to  be of the nature of         
continuous quantities1 and in continuous

 quantity  infinity first makes its     
appearance2 so as to furnish some with a
  definition who say that continuous    
quantity is that which is infinitely    
divisible4--,moreover1 unless there be  
time1 space1 and a vacuum1 it is        
impossible that there should be         
motion4#aba--;,few propositions of      
,aristotle's physical philosophy are    
more notorious than his assertion  that 
nature abhors a vacuum1 on which account
 this last passage is the  more         
remarkable1 as he certainly did not go  
so far as to deny the  existence of     
motion1 and therefore asserts here the  
necessity of that of  which he          
afterwards attempts to show the         
absurdity4--,motion is the  energy of   
what exists in power so far forth as so 
existing4 ,it is that  act of a moveable
 which belongs to its power of          
moving4#abb ,after  struggling through  
such passages as the preceding we come  
at last to a  resting-place4--,it is    
difficult to understand what motion     

is4--,when  the same question was once  
proposed to another ,greek philosopher1 
he  walked away1 saying1 ,i cannot tell 
you1 but ,i will show you2 an answer    
intrinsically worth more than all the   
subtleties of ,aristotle1 who was  not  
humble-minded enough to discover that he
 was tasking his genius  beyond the     
limits marked out for human             
comprehension4    ,he labours in the    
same manner and with the same success to
 vary the idea  of space4 ,he begins the
 next book with declaring1 that those   
who say  there is a vacuum assert the   
existence of space2 for a vacuum is     
space1  in which there is no substance2 
and after a long and tedious reasoning  
concludes that1 not only what space is1 
but also whether there be such  a thing1
 cannot but be doubted4#abc ,of time he 
is content to say  merely1 that it is   
clear that time is not motion1 but that 
without  motion there would be no       
time2#abd and there is perhaps little   
fault  to be found with this remark1    

understanding motion in the general     
sense  in which ,aristotle here applies 
it1 of every description of change4     
,proceeding after these remarks on the  
nature of motion in general to the      
motion of bodies1 we are told that all  
local motion is either straight1        
circular1 or compounded of these two2   
for these two are the only simple  sorts
 of motion4 ,bodies are divided into    
simple and concrete2 simple  bodies are 
those which have naturally a principle  
of motion1 as fire and  earth1 and their
 kinds4 ,by simple motion is meant the  
motion of a simple  body4#abe ,by these 
expressions ,aristotle did not mean that
 a simple  body cannot have what he     
calls a compound motion1 but in that    
case he  called the motion violent or   
unnatural2 this division of motion into 
natural and violent runs through the    
whole of the mechanical philosophy      
founded upon his principles4 ,circular  
motion is the only one which can  be    
endless2#abf the reason of which is     

given in another place3 for  that cannot
 be doing1 which cannot be done2 and    
therefore it cannot be  that a body     
should be moving towards a point 7i4e4  
the end of an  infinite straight line7  
whither no motion is sufficient to bring
  it4#abg ,bacon seems to have had these
 passages in view when he  indulged in  
the reflections which we have quoted in 
page #ad4 ,there are  four kinds of     
motion of one thing by another3         
,drawing1 ,pushing1  ,carrying1         
,rolling4 ,of these1 ,carrying and      
,rolling may be referred to  ,drawing   
and ,pushing4#abh--,the prime mover and 
the thing moved are  always in contact4 
,the principle of the composition of    
motions is stated very plainly3  when a 
moveable is urged in two directions with
 motions bearing an  indefinitely small 
ratio to each other1 it moves           
necessarily in a  straight line1 which  
is the diameter of the figure formed by 
drawing the  two lines of direction in  
that ratio2#abi and adds1 in a          

singularly  curious passage1 but when it
 is urged for any time with two motions 
which have an indefinitely small ratio  
one to another1 the motion cannot  be   
straight1 so that a body describes a    
curve1 when it is urged by two  motions 
bearing an indefinitely small ratio one 
to another1 and lasting  an indefinitely
 small time4#acj    ,he seemed on the   
point of discovering some of the real   
laws of motion1  when he was led to     
ask--,why are bodies in motion more     
easily moved than  those which are at   
rest8--,and why does the motion cease of
 things cast  into the air8 ,is it that 
the force has ceased which sent them    
forth1 or  is there a struggle against  
the motion1 or is it through the        
disposition  to fall1 does it become    
stronger than the projectile force1 or  
is it  foolish to entertain doubts on   
this question1 when the body has quitted
  the principle of its motion8 ,a       
commentator at the close of the         
sixteenth century says on this passage3 

,they fall because every thing  recurs  
to its nature2 for if you throw a stone 
a thousand times into the  air1 it will 
never accustom itself to move upwards4  
,perhaps we shall  now find it difficult
 not to smile at the idea we may form of
 this  luckless experimentalist1        
teaching stones to fly2 yet it may be   
useful  to remember that it is only     
because we have already collected an    
opinion  from the results of a vast     
number of observations in the daily     
experience of life1 that our ridicule   
would not be altogether misplaced1  and 
that we are totally unable to determine 
by any kind of reasoning1  unaccompanied
 by experiment1 whether a stone thrown  
into the air would  fall again to the   
earth1 or move for ever upwards1 or in  
any other  conceivable manner and       
direction4    ,the opinion which        
,aristotle held1 that motion must be    
caused by  something in contact with the
 body moved1 led him to his famous      
theory  that falling bodies are         

accelerated by the air through which    
they pass4  ,we will show how it was    
attempted to explain this process when  
we come  to speak of more modern        
authors4 ,he classed natural bodies into
 heavy  and light1 remarking at the same
 time that it is clear that there are   
some bodies possessing neither gravity  
nor levity4#aca ,by light bodies  he    
understood those which have a natural   
tendency to move from the  earth1       
observing that that which is lighter is 
not always light4#acb  ,he maintained   
that the heavenly bodies were altogether
 devoid of  gravity2 and we have already
 had occasion to mention his assertion1 
that  a large body falls faster than a  
small one in proportion to its          
weight4#acc ,with this opinion may be   
classed another great mistake1 in       
maintaining that the same bodies fall   
through different mediums1 as air  or   
water1 with velocities reciprocally     
proportional to their densities4  ,by a 
singular inversion of experimental      

science1 ,cardan1 relying on this       
assertion1 proposed in the sixteenth    
century to determine the densities  of  
air and water by observing the different
 times taken by a stone in  falling     
through them4#acd ,galileo inquired     
afterwards why the  experiment should   
not be made with a cork1 which pertinent
 question put  an end to the theory4    
,there are curious traces still         
preserved in the poem of ,lucretius of a
  mechanical philosophy1 of which the   
credit is in general given to           
,democritus1 where many principles are  
inculcated strongly at variance  with   
,aristotle's notions4 ,we find absolute 
levity denied1 and not only  the        
assertion that in a vacuum all things   
would fall1 but that they  would fall   
with the same velocity2 and the         
inequalities which we observe  are      
attributed to the right cause1 the      
impediment of the air1 although  the    
error remains of believing the velocity 
of bodies falling through  the air to be

 proportional to their weight4#ace ,such
 specimens of this  earlier philosophy  
may well indispose us towards           
,aristotle1 who was as  successful in   
the science of motion as he was in      
astronomy in  suppressing the knowledge 
of a theory so much sounder than that   
which he  imposed so long upon the      
credulity of his blinded admirers4      
,an agreeable contrast to ,aristotle's  
mystical sayings and fruitless          
syllogisms is presented in ,archimedes' 
book on ,equilibrium1 in which he       
demonstrates very satisfactorily1 though
 with greater cumbrousness of  apparatus
 than is now thought necessary1 the     
principal properties of the  lever4     
,this and the ,treatise on the          
,equilibrium of ,floating ,bodies are   
the only mechanical works which have    
reached us of this writer1 who was  by  
common consent one of the most          
accomplished mathematicians of          
antiquity4 ,ptolemy the astronomer wrote
 also a ,treatise on ,mechanics1  now   

lost1 which probably contained much that
 would be interesting in the  history of
 mechanics2 for ,pappus says1 in the    
,preface to the ,eighth ,book  of his   
,mathematical ,collections3 ,there is no
 occasion for me to explain  what is    
meant by a heavy1 and what by a light   
body1 and why bodies are  carried up and
 down1 and in what sense these very     
words 'up' and 'down'  are to be taken1 
and by what limits they are bounded2 for
 all this is  declared in ,ptolemy's    
,mechanics4#acf ,this book of ,ptolemy's
 appears to  have been also known by    
,eutocius1 a commentator of ,archimedes1
 who lived  about the end of the fifth  
century of our era2 he intimates that   
the  doctrines contained in it are      
grounded upon ,aristotle's2 if so1 its  
loss  is less to be lamented4 ,pappus's 
own book deserves attention for the     
enumeration which he makes of the       
mechanical powers1 namely1 the wheel    
and axle1 the lever1 pullies1 the wedge 
and the screw4 ,he gives the  credit to 

,hero and ,philo of having shown1 in    
works which have not  reached us1 that  
the theory of all these machines is the 
same4 ,in ,pappus  we also find the     
first attempt to discover the force     
necessary to  support a given weight on 
an inclined plane4 ,this in fact is     
involved in  the theory of the screw2   
and the same vicious reasoning which    
,pappus  employs on this occasion was   
probably found in those treatises which 
he  quotes with so much approbation4    
,numerous as are the faults of his      
pretended demonstration1 it was received
 undoubtingly for a long period4        
,illustration3 ,chain4    ,the credit of
 first giving the true theory of        
equilibrium on the  inclined plane is   
usually ascribed to ,stevin1 although1  
as we shall  presently show1 with very  
little reason4 ,stevin supposed a chain 
to be  placed over two inclined planes1 
and to hang down in the manner          
represented in the figure4 ,he then     
urged that the chain would be in        

equilibrium2 for otherwise1 it would    
incessantly continue in motion1 if      
there were any cause why it should begin
 to move4 ,this being conceded1  he     
remarks further1 that the parts ,,ad and
 ,,bd are also in equilibrium1  being   
exactly similar to each other2 and      
therefore if they are taken  away1 the  
remaining parts ,,ac and ,,bc will also 
be in equilibrium4 ,the  weights of     
these parts are proportional to the     
lengths ,,ac and ,,bc2 and  hence       
,stevin concluded that two weights would
 balance on two inclined  planes1 which 
are to each other as the lengths of the 
planes included  between the same       
parallels to the horizon4#acg ,this     
conclusion is the  correct one1 and     
there is certainly great ingenuity in   
this contrivance  to facilitate the     
demonstration2 it must not however be   
mistaken for an   priori proof1 as it   
sometimes seems to have been3 we should 
remember  that the experiments which led
 to the principle of virtual velocities 

are also necessary to show the absurdity
 of supposing a perpetual  motion1 which
 is made the foundation of this theorem4
 ,that principle had  been applied      
directly to determine the same          
proportion in a work written  long      
before1 where it has remained singularly
 concealed from the notice  of most who 
have written on this subject4 ,the book 
bears the name of  ,jordanus1 who lived 
at ,namur in the thirteenth century2 but
 ,commandine1  who refers to it in his  
,commentary on ,pappus1 considers it as 
the work  of an earlier period4 ,the    
author takes the principle of virtual   
velocities for the groundwork of his    
explanations1 both of the lever and     
inclined plane2 the latter will not     
occupy much space1 and in an  historical
 point of view is too curious to be     
omitted4    ,qust4 #aj4--;,if two       
weights descend by paths of different   
obliquities1 and the proportion be the  
same of the weights and the             
inclinations taken in the same order1   

they will have the same descending      
force4 ,by the inclinations1 ,i do not  
mean the angles1 but the paths up  to   
the point in which both meet the same   
perpendicular4#ach ,let1  therefore1 e  
be the weight upon dc1 and h upon da1   
and let e  be to h as dc to da4 ,i say  
these weights1 in this situation1 are   
equally effective4 ,take dk equally     
inclined with dc1 and upon it a  weight 
equal to e1 which call #f4 ,if possible 
let e descend to l1  so as to raise h to
 m1 and take #fn equal to hm or el1 and 
draw  the horizontal and perpendicular  
lines as in the figure4    ,illustration
      ,then nz3n#f 33 db3dk    and mh3mx
 33 da3db    therefore nz3mx 33 da3dk 33
 h3#f1 and therefore since er is  not   
able to raise #f to n1 neither will it  
be able to raise h to m2  therefore they
 will remain as they are4#aci ,the      
passage in ,italics  tacitly assumes the
 principle in question4 ,tartalea1 who  
edited  ,jordanus's book in #aefe1 has  
copied this theorem verbatim into one of

  his own treatises1 and from that time 
it appears to have attracted no  further
 attention4 ,the rest of the book is of 
an inferior description4  ,we find      
,aristotle's doctrine repeated1 that the
 velocity of a falling  body is         
proportional to its weight2 that the    
weight of a heavy body  changes with its
 form2 and other similar opinions4 ,the 
manner in which  falling bodies are     
accelerated by the air is given in      
detail4 ,by its  first motion the heavy 
body will drag after it what is behind1 
and move  what is just below it2 and    
these when put in motion move what is   
next to  them1 so that by being set in  
motion they less impede the falling     
body4  ,in this manner it has the effect
 of being heavier1 and impels still more
  those which give way before it1 until 
at last they are no longer  impelled1   
but begin to drag4 ,and thus it happens 
that its gravity is  increased by their 
attraction1 and their motion by its     
gravity1 whence  we see that its        

velocity is continually multiplied4     
,in this short review of the state of   
mechanical science before ,galileo1  the
 name of ,guido ,ubaldi ought not to be 
omitted1 although his works  contain    
little or nothing original4 ,we have    
already mentioned ,benedetti  as having 
successfully attacked some of           
,aristotle's statical doctrines1  but it
 is to be noticed that the laws of      
motion were little if at all  examined  
by any of these writers4 ,there are a   
few theorems connected  with this latter
 subject in ,cardan's extraordinary book
 ,on  ,proportions1 but for the most    
part false and contradictory4 ,in the   
seventy-first proposition of his fifth  
book1 he examines the force of  the     
screw in supporting a given weight1 and 
determines it accurately on  the        
principle of virtual velocities2 namely1
 that the power applied at  the end of  
the horizontal lever must make a        
complete circuit at that  distance from 
the centre1 whilst the weight rises     

through the  perpendicular height of the
 thread4 ,the very next proposition in  
the  same page is to find the same      
relation between the power and weight on
  an inclined plane2 and although the   
identity of principle in these two      
mechanical aids was well known1 yet     
,cardan declares the necessary          
sustaining force to vary as the angle of
 inclination of the plane1 for  no      
better reason than that such an         
expression will properly represent it   
at the two limiting angles of           
inclination1 since the force is nothing 
when the plane is horizontal1 and equal 
to the weight when  perpendicular4 ,this
 again shows how cautious we should be  
in attributing  the full knowledge of   
general principles to these early       
writers1 on  account of occasional      
indications of their having employed    
them4      ,,footnotes3    #aae         
,histoire des ,mathmatiques1 vol4 i4 p4 
#ig4    #aaf ,de vi ,percussionis1      
,bononi1 #affg4    #aag ,mec4 ,analyt4  

#aah ,mechanica4    #aai ,diog4 ,laert4 
,in vit4 ,archyt4    #abj ,de ,clo1 lib4
 i4 c4 #a4    #aba ,phys4 lib4 i4 c4 #c4
    #abb ,lib4 iii4 c4 #b4 ,the         
,aristotelians distinguished between    
things as  existing in act or energy 77 
and things in capacity or power  774    
,for the advantage of those who may     
think the distinction  worth attending  
to1 we give an illustration of          
,aristotle's meaning1 from  a very acute
 and learned commentator3--,it 7motion7 
is something more  than dead capacity2  
something less than perfect actuality2  
capacity  roused1 and striving to quit  
its latent character2 not the capable   
brass1 nor yet the actual statue1 but   
the capacity in energy2 that is to  say1
 the brass in fusion while it is        
becoming the statue and is not yet      
become4--,the bow moves not because it  
may be bent1 nor because it is  bent2   
but the motion lies between2 lies in an 
imperfect and obscure  union of the two 
together2 is the actuality 7if ,i may so

 say7 even of  capacity itself3         
imperfect and obscure1 because such is  
capacity to  which it belongs4--,harris1
 ,philosophical ,arrangements4    #abc  
,lib4 iv4 c4 #a4    #abd ,lib4 iv4 c4   
#aa4    #abe ,de ,clo1 lib4 i4 c4 #b4   
#abf ,phys4 lib4 vii4 c4 #h4    #abg ,de
 ,clo1 lib4 i4 c4 #f4    #abh ,phys4    
lib4 vii4 c4 #b4    #abi ,mechanica4    
#acj           1      4                 
1             4--i4e4 v  ds_/dt    #aca 
,de ,clo1 lib4 i4 c4 #c4    #acb ,lib4  
iv4 c4 #b4    #acc ,phys41 lib4 iv4 c4  
#h4    #acd ,de ,proport4 ,basile1      
#aegj4    #ace        ,nunc locus est1  
ut opinor1 in his illud quoque rebus    
,confirmare tibi1 nullam rem posse su vi
      ,corpoream sursum ferri1 sursumque
 meare4--      ,nec quom subsiliunt     
ignes ad tecta domorum1      ,et celeri 
flamm degustant tigna trabeisque        
,sponte su facere id sine vi subicente  
putandum est4      --,nonne vides etiam 
quant vi tigna trabeisque      ,respuat 
humor aqu8 ,nam quod magi' mersimus     

altum      ,direct et magn vi multi     
pressimus gre3--      ,tam cupide sursum
 revomit magis atque remittit      ,plus
 ut parte foras emergant1 exsiliantque3 
--,nec tamen hc1 quantu'st in           
sedubitamus1 opinor1      ,quinvacuum   
per inane deorsum cuncta ferantur1      
,sic igitur debent flamm quoque posse   
per auras      ,aeris express sursum    
subsidere1 quamquam      ,pondera       
quantum in se est deorsum deducere      
pugnent4      --,quod si forte aliquis  
credit ,graviora potesse      ,corpora1 
quo citius rectum per ,inane feruntur1  
--,avius a ver longe ratione recedit4   
,nam per ,aquas qucunque cadunt atque   
,aera deorsum      ,hc pro ponderibus   
casus celerare necesse 'st              
,propterea quia corpus ,aqu1 naturaque  
tenuis      ,aeris haud possunt que rem 
quamque morari3      ,sed citius cedunt 
,gravioribus exsuperata4      ,at contra
 nulli de null parte1 neque ullo        
,tempore ,inane potest ,vacuum          
subsistere reii      ,quin1 sua quod    

natura petit1 considere pergat3         
,omnia qu propter debent per ,inane     
quietum      que ponderibus non quis    
concita ferri4                          
,de ,rerum ,natura1 lib4 ii1 v4         
#ahd-bci4    #acf ,math4 ,coll4 ,pisani1
 #affb4    #acg uvres ,mathmatiques4    
,leyde1 #afcd4    #ach ,this is not a   
literal translation1 but by what        
follows1 is  evidently the ,author's    
meaning4 ,his words are1 ,proportionem  
igitur  declinationum dico non          
angulorum1 sed linearum usque ad        
quidistantem  resecationem in qu        
qualiter sumunt de directo4    #aci     
,opusculum ,de ,ponderositate4          
,venetiis1 #aefe4          ,,chapter    
,,xvii4        ,galileo's theory of     
,motion--,extracts from the ,dialogues4 
,,during ,galileo's residence at        
,sienna1 when his recent persecution had
  rendered astronomy an ungrateful1 and 
indeed an unsafe occupation for  his    
ever active mind1 he returned with      
increased pleasure to the  favourite    

employment of his earlier years1 an     
inquiry into the laws and  phenomena of 
motion4 ,his manuscript treatises on    
motion1 written about  #aeij1 which are 
mentioned by ,venturi to be in the      
,ducal library at  ,florence1 seem1 from
 the published titles of the chapters1  
to consist  principally of objections to
 the theory of ,aristotle2 a few only   
appear  to enter on a new field of      
speculation4 ,the #aath1 #acth1 and     
#agth  chapters relate to the motion of 
bodies on variously inclined planes1    
and of projectiles4 ,the title of the   
#adth implies a new theory of           
accelerated motion1 and the assertion in
 that of the #afth1 that a body  falling
 naturally for however great a time     
would never acquire more than  an       
assignable degree of velocity1 shows    
that at this early period  ,galileo had 
formed just and accurate notions of the 
action of a  resisting medium4 ,it is   
hazardous to conjecture how much he     
might have  then acquired of what we    

should now call more elementary         
knowledge2 a  safer course will be to   
trace his progress through existing     
documents in  their chronological order4
 ,in #afjb we find ,galileo apologizing 
in a  letter addressed to his early     
patron the ,marchese ,guido ,ubaldi1 for
  pressing again upon his attention the 
isochronism of the pendulum1 which      
,ubaldi had rejected as false and       
impossible4 ,it may not be superfluous  
to observe that ,galileo's results are  
not quite accurate1 for there is a      
perceptible increase in the time        
occupied by the oscillations in larger  
arcs2 it is therefore probable that he  
was induced to speak so  confidently of 
their perfect equality1 from attributing
 the increase of  time which he could   
not avoid remarking to the increased    
resistance of  the air during the larger
 vibrations4 ,the analytical methods    
then known  would not permit him to     
discover the curious fact1 that the time
 of a  total vibration is not sensibly  

altered by this cause1 except so far as 
it diminishes the extent of the swing1  
and thus in fact1 7paradoxical as  it   
may sound7 renders each oscillation     
successively more rapid1 though  in a   
very small degree4 ,he does indeed make 
the same remark1 that the  resistance of
 the air will not affect the time of the
 oscillation1 but  that assertion was a 
consequence of his erroneous belief that
 the time  of vibration in all arcs is  
the same4 ,had he been aware of the     
variation1 there is no reason to think  
that he could have perceived that  this 
result is not affected by it4 ,in this  
letter is the first mention  of the     
theorem1 that the times of fall down all
 the chords drawn from  the lowest point
 of a circle are equal2 and another1    
from which ,galileo  afterwards deduced 
the curious result1 that it takes less  
time to fall  down the curve than down  
the chord1 notwithstanding the latter is
 the  direct and shortest course4 ,in   
conclusion he says1 ,up to this point ,i

  can go without exceeding the limits of
 mechanics1 but ,i have not yet  been   
able to demonstrate that all arcs are   
passed in the same time1  which is what 
,i am seeking4 ,in #afjd he addressed   
the following letter  to ,sarpi1        
suggesting the false theory sometimes   
called ,baliani's1 who  took it from    
,galileo4     ,illustration3      ,a-   
,b-                ,c-                  
,d-     ,returning to the subject of    
motion1 in which ,i was entirely without
 a  fixed principle1 from which to      
deduce the phenomena ,i have observed1  
,i  have hit upon a proposition1 which  
seems natural and likely enough2 and  if
 ,i take it for granted1 ,i can show    
that the spaces passed in natural       
motion are in the double proportion of  
the times1 and consequently that  the   
spaces passed in equal times are as the 
odd numbers beginning from  unity1 and  
the rest4 ,the principle is this1 that  
the swiftness of the  moveable increases
 in the proportion of its distance from 

the point  whence it began to move2 as  
for instance1--if a heavy body drop from
 ,a  towards ,d1 by the line ,,abcd1 ,i 
suppose the degree of velocity which it 
has at ,b to bear to the velocity at ,c 
the ratio of ,,ab to ,,ac4 ,i shall be  
very glad if your ,reverence will       
consider this1 and tell me your opinion 
of it4 ,if we admit this principle1 not 
only1 as ,i have said1 shall we         
demonstrate the other conclusions1 but  
we have it in our power to show  that a 
body falling naturally1 and another     
projected upwards1 pass  through the    
same degrees of velocity4 ,for if the   
projectile be cast up  from ,d to ,a1 it
 is clear that at ,d it has force enough
 to reach ,a1 and  no farther2 and when 
it has reached ,c and ,b1 it is equally 
clear that it  is still joined to a     
degree of force capable of carrying it  
to ,a3 thus  it is manifest that the    
forces at ,d1 ,c and ,b decrease in the 
proportion  of ,,ab1 ,,ac1 and ,,ad2 so 
that if1 in falling1 the degrees of     

velocity  observe the same proportion1  
that is true which ,i have hitherto     
maintained and believed4    ,we have no 
means of knowing how early ,galileo     
discovered the fallacy of  this         
reasoning4 ,in his ,dialogues on        
,motion1 which contain the correct      
theory1 he has put this erroneous       
supposition in the mouth of ,sagredo1   
on which ,salviati remarks1 ,your       
discourse has so much likelihood in it1 
that our author himself did not deny to 
me when ,i proposed it to him1  that he 
also had been for some time in the same 
mistake4 ,but that which  ,i afterwards 
extremely wondered at1 was to see       
discovered in four plain  words1 not    
only the falsity1 but the impossibility 
of a supposition  carrying with it so   
much of seeming truth1 that although ,i 
proposed it  to many1 ,i never met with 
any one but did freely admit it to be   
so2 and  yet it is as false and         
impossible as that motion is made in an 
instant3  for if the velocities are as  

the spaces passed1 those spaces will be 
passed in equal times1 and consequently 
all motion must be  instantaneous4 ,the 
following manner of putting this        
reasoning will  perhaps make the        
conclusion clearer4 ,the velocity at any
 point is the  space that would be      
passed in the next moment of time1 if   
the motion be  supposed to continue the 
same as at that point4 ,at the beginning
 of the  time1 when the body is at rest1
 the motion is none2 and therefore1 on  
this theory1 the space passed in the    
next moment is none1 and thus it  will  
be seen that the body cannot begin to   
move according to the  supposed law4    
,a curious fact1 noticed by ,guido      
,grandi in his commentary on ,galileo's 
,dialogues on ,motion1 is that this     
false law of acceleration is precisely  
that which would make a circular arc the
 shortest line of descent  between two  
given points2 and although in general   
,galileo only declared  that the fall   
down the arc is made in less time than  

down the chord 7in  which he is quite   
correct71 yet in some places he seems to
 assert that  the circular arc is       
absolutely the shortest line of descent1
 which is  not true4 ,it has been       
thought possible that the law1 which on 
reflection  he perceived to be          
impossible1 might have originally       
recommended itself  to him from his     
perception that it satisfied his        
prejudice in this  respect4    ,john    
,bernouilli1 one of the first           
mathematicians in ,europe at the        
beginning of the last century1 has given
 us a proof that such a reason  might   
impose even on a strong understanding1  
in the following argument  urged by him 
in favour of ,galileo's second and      
correct theory1 that the  spaces vary as
 the squares of the times4 ,he had been 
investigating the  curve of swiftest    
descent1 and found it to be a cycloid1  
the same curve  in which ,huyghens had  
already proved that all oscillations are
 made in  accurately equal times4 ,i    

think it1 says he1 worthy of remark that
  this identity only occurs on          
,galileo's supposition1 so that this    
alone  might lead us to presume it to be
 the real law of nature4 ,for nature1   
which always does everything in the very
 simplest manner1 thus makes one  line  
do double work1 whereas on any other    
supposition1 we must have had  two      
lines1 one for equal oscillations1 the  
other for the shortest  descent4#adj    
,venturi mentions a letter addressed to 
,galileo in ,may #afji by ,luca         
,valerio1 thanking him for his          
experiments on the descent of bodies on 
inclined planes4 ,his method of making  
these experiments is detailed in  the   
,dialogues on ,motion3--,in a rule1 or  
rather plank of wood1 about  twelve     
yards long1 half a yard broad one way1  
and three inches the  other1 we made    
upon the narrow side or edge a groove of
 little more than  an inch wide3 we cut 
it very straight1 and1 to make it very  
smooth and  sleek1 we glued upon it a   

piece of vellum1 polished and smoothed  
as  exactly as possible1 and in that we 
let fall a very hard1 round1 and  smooth
 brass ball1 raising one of the ends of 
the plank a yard or two at  pleasure    
above the horizontal plane4 ,we         
observed1 in the manner that ,i  shall  
tell you presently1 the time which it   
spent in running down1 and  repeated the
 same observation again and again to    
assure ourselves of the  time1 in which 
we never found any difference1 no1 not  
so much as the  tenth part of one beat  
of the pulse4 ,having made and settled  
this  experiment1 we let the same ball  
descend through a fourth part only of   
the length of the groove1 and found the 
measured time to be exactly half  the   
former4 ,continuing our experiments with
 other portions of the  length1         
comparing the fall through the whole    
with the fall through half1  two-thirds1
 three-fourths1 in short1 with the fall 
through any part1 we  found by many     
hundred experiments that the spaces     

passed over were as  the squares of the 
times1 and that this was the case in all
 inclinations  of the plank2 during     
which1 we also remarked that the times  
of descent1  on different inclinations1 
observe accurately the proportion       
assigned to  them farther on1 and       
demonstrated by our author4 ,as to the  
estimation of  the time1 we hung up a   
great bucket full of water1 which by a  
very small  hole pierced in the bottom  
squirted out a fine thread of water1    
which we  caught in a small glass during
 the whole time of the different        
descents3  then weighing from time to   
time1 in an exact pair of scales1 the   
quantity of water caught in this way1   
the differences and proportions of      
their weights gave the differences and  
proportions of the times2 and  this with
 such exactness that1 as ,i said before1
 although the  experiments were repeated
 again and again1 they never differed in
 any  degree worth noticing4 ,in order  
to get rid of the friction1 ,galileo    

afterwards substituted experiments with 
the pendulum2 but with all his  care he 
erred very widely in his determination  
of the space through  which a body would
 fall in #a1 if the resistance of the   
air and all  other impediments were     
removed4 ,he fixed it at #d braccia3    
,mersenne has  engraved the length of   
the 'braccia' used by ,galileo1 in his  
,harmonie  ,universelle1 from which it  
appears to be about #bc ,english inches1
 so  that ,galileo's result is rather   
less than eight feet4 ,mersenne's own   
result from direct observation was      
thirteen feet3 he also made  experiments
 in ,st4 ,peter's at ,rome1 with a      
pendulum #cbe feet long1 the  vibrations
 of which were made in #aj2 from this   
the fall in #a might  have been deduced 
rather more than sixteen feet1 which is 
very close to  the truth4    ,from      
another letter also written in the early
 part of #afji1 we learn  that ,galileo 
was then busied with examining the      
strength and resistance  of beams of    

different sizes and forms1 and how much 
weaker they are in  the middle than at  
the ends1 and how much greater weight   
they can  support laid along their whole
 length1 than if sustained on a single  
point1 and of what form they should be  
so as to be equally strong  throughout4 
,he was also speculating on the motion  
of projectiles1 and  had satisfied      
himself that their motion in a vertical 
direction is  unaffected by their       
horizontal velocity2 a conclusion which1
 combined  with his other experiments1  
led him afterwards to determine the path
 of  a projectile in a non-resisting    
medium to be parabolical4    ,tartalea  
is supposed to have been the first to   
remark that no bullet  moves in a       
horizontal line2 but his theory beyond  
this point was very  erroneous1 for he  
supposed the bullet's path through the  
air to be made  up of an ascending and  
descending straight line1 connected in  
the middle  by a circular arc4          
,thomas ,digges1 in his treatise on the 

,newe ,science of ,great ,artillerie1   
came much nearer the truth2 for he      
remarked#ada1 that ,the bullet          
violentlye throwne out of the peece by  
the furie of the poulder hath two       
motions3 the one violent1 which         
endeuoreth to carry the bullet right out
  in his line diagonall1 according to   
the direction of the peece's axis1  from
 whence the violent motion proceedeth2  
the other naturall in the  bullet       
itselfe1 which endeuoreth still to      
carrye the same directlye  downeward by 
a right line perpendiculare to the      
horizon1 and which dooth  though        
insensiblye euen from the beginning by  
little and little drawe it  from that   
direct and diagonall course4 ,and a     
little farther he observes  that ,these 
middle curve arkes of the bullet's      
circuite1 compounded of  the violent and
 naturall motions of the bullet1 albeit 
they be indeed  mere helicall1 yet have 
they a very great resemblance of the    
,arkes  ,conical4 ,and in randons above 

#de they doe much resemble the          
,hyperbole1  and in all vnder the       
,ellepsis4 ,but exactlye they neuer     
accorde1 being  indeed ,spirall mixte   
and ,helicall4    ,perhaps ,digges      
deserves no greater credit from this    
latter passage than  the praise of a    
sharp and accurate eye1 for he does not 
appear to have  founded this            
determination of the form of the curve  
on any theory of the  direct fall of    
bodies2 but ,galileo's arrival at the   
same result was  preceded1 as we have   
seen1 by a careful examination of the   
simplest  phenomena into which this     
compound motion may be resolved4 ,but it
 is  time to proceed to the analysis of 
his ,dialogues on ,motion1 these        
preliminary remarks on their subject    
matter having been merely intended  to  
show how long before their publication  
,galileo was in possession of  the      
principal theories contained in them4   
,descartes1 in one of his letters to    
,mersenne1 insinuates that ,galileo  had

 taken many things in these ,dialogues  
from him3 the two which he  especially  
instances are the isochronism of the    
pendulum1 and the law of  the spaces    
varying as the squares of the times4#adb
 ,descartes was born  in #aeif3 we have 
shown that ,galileo observed the        
isochronism of the  pendulum in #aehc1  
and knew the law of the spaces in #afjd1
 although he  was then attempting to    
deduce it from an erroneous principle4  
,as  ,descartes on more than one        
occasion has been made to usurp the     
credit  due to ,galileo1 7in no instance
 more glaringly so than when he has been
  absurdly styled the forerunner of     
,newton17 it will not be misplaced to   
mention a few of his opinions on these  
subjects1 recorded in his letters  to   
,mersenne in the collection of his      
letters just cited3--,i am  astonished  
at what you tell me of having found by  
experiment that bodies  thrown up in the
 air take neither more nor less time to 
rise than to  fall again2 and you will  

excuse me if ,i say that ,i look upon   
the  experiment as a very difficult one 
to make accurately4 ,this proportion  of
 increase according to the odd numbers  
#a1 #c1 #e1 #g1 c41 which is in         
,galileo1 and which ,i think ,i wrote to
 you some time back1 cannot be  true1 as
 ,i believe ,i intimated at the same    
time1 unless we make two or  three      
suppositions which are entirely false4  
,one is ,galileo's opinion1  that motion
 increases gradually from the slowest   
degree2 and the other  is1 that the air 
makes no resistance4 ,in a later letter 
to the same  person he says1 apparently 
with some uneasiness1 ,i have been      
revising  my notes on ,galileo1 in which
 ,i have not said expressly1 that       
falling  bodies do not pass through     
every degree of slowness1 but ,i said   
that  this cannot be determined without 
knowing what weight is2 which comes  to 
the same thing4 ,as to your example1 ,i 
grant that it proves that  every degree 
of velocity is infinitely divisible1 but

 not that a falling  body actually      
passes through all these divisions4--,it
 is certain that a  stone is not equally
 disposed to receive a new motion or    
increase of  velocity1 when it is       
already moving very quickly1 and when it
 is moving  slowly4 ,but ,i believe that
 ,i am now able to determine in what    
proportion  the velocity of a stone     
increases1 not when falling in a vacuum1
 but in  this substantial               
atmosphere4--,however ,i have now got my
 mind full of  other things1 and ,i     
cannot amuse myself with hunting this   
out1 nor is  it a matter of much        
utility4 ,he afterwards returns once    
more to the  same subject3--,as to what 
,galileo says1 that falling bodies pass 
through every degree of velocity1 ,i do 
not believe that it generally  happens1 
but ,i allow it is not impossible that  
it may happen  occasionally4 ,after this
 the reader will know what value to     
attach to  the following assertion by   
the same ,descartes3--,i see nothing in 

,galileo's books to envy him1 and hardly
 any thing which ,i would own as  mine2 
and then may judge how far ,salusbury's 
blunt declaration is borne  out1 ,where 
or when did any one appear that durst   
enter the lists with  our ,galileus8    
save only one bold and unfortunate      
,frenchman1 who yet no  sooner came     
within the ring but he was hissed out   
again4#adc    ,the principal merit of   
,descartes must undoubtedly be derived  
from the  great advances he made in what
 are generally termed ,abstract or ,pure
  ,mathematics2 nor was he slow to point
 out to ,mersenne and his other  friends
 the acknowledged inferiority of        
,galileo to himself in this  respect4   
,we have not sufficient proof that this 
difference would have  existed if       
,galileo's attention had been equally   
directed to that object2  the singular  
elegance of some of his geometrical     
constructions indicates  great talent   
for this as well as for his own more    
favourite  speculations4 ,but he was far

 more profitably employed3 geometry and 
pure  mathematics already far           
outstripped any useful application of   
their  results to physical science1 and 
it was the business of ,galileo's life  
to bring up the latter to the same      
level4 ,he found abstract theorems      
already demonstrated in sufficient      
number for his purpose1 nor was there   
occasion to task his genius in search of
 new methods of inquiry1 till  all was  
exhausted which could be learned from   
those already in use4 ,the  result of   
his labours was that in the age         
immediately succeeding  ,galileo1 the   
study of nature was no longer in arrear 
of the abstract  theories of number and 
measure2 and when the genius of ,newton 
pressed it  forward to a still higher   
degree of perfection1 it became         
necessary to  discover at the same time 
more powerful instruments of            
investigation4  ,this alternating       
process has been successfully continued 
to the present  time2 the analyst acts  

as the pioneer of the naturalist1 so    
that the  abstract researches1 which at 
first have no value but in the eyes of  
those to whom an elegant formula1 in its
 own beauty1 is a source of  pleasure as
 real and as refined as a painting or a 
statue1 are often  found to furnish the 
only means for penetrating into the most
 intricate  and concealed phenomena of  
natural philosophy4    ,descartes and   
,delambre agree in suspecting that      
,galileo preferred the  dialogistic form
 for his treatises1 because it afforded 
a ready  opportunity for him to praise  
his own inventions3 the reason which he 
himself gave is1 the greater facility   
for introducing new matter and          
collateral inquiries1 such as he seldom 
failed to add each time that he         
reperused his work4 ,we shall select in 
the first place enough to show  the     
extent of his knowledge on the principal
 subject1 motion1 and shall  then allude
 as well as our limits will allow to the
 various other points  incidentally     

brought forward4    ,the dialogues are  
between the same speakers as in the     
,system of the  ,world2 and in the first
 ,simplicio gives ,aristotle's          
proof1#add that  motion in a vacuum is  
impossible1 because according to him    
bodies move  with velocities in the     
compound proportion of their weights and
 the  rarities of the mediums through   
which they move4 ,and since the density 
of a vacuum bears no assignable ratio to
 that of any medium in which  motion has
 been observed1 any body which should   
employ time in moving  through the      
latter1 would pass through the same     
distance in a vacuum  instantaneously1  
which is impossible4 ,salviati replies  
by denying the  axioms1 and asserts that
 if a cannon ball weighing #bjj lbs41   
and a  musket ball weighing half a      
pound1 be dropped together from a tower 
#bjj  yards high1 the former will not   
anticipate the latter by so much as a   
foot2 and ,i would not have you do as   
some are wont1 who fasten upon  some    

saying of mine that may want a hair's   
breadth of the truth1 and  under this   
hair they seek to hide another man's    
blunder as big as a  cable4 ,aristotle  
says that an iron ball weighing #ajj    
lbs4 will fall from  the height of #ajj 
yards while a weight of one pound falls 
but one yard3  ,i say they will reach   
the ground together4 ,they find the     
bigger to  anticipate the less by two   
inches1 and under these two inches they 
seek  to hide ,aristotle's #ii yards4   
,in the course of his reply to this     
argument ,salviati formally announces   
the principle which is the  foundation  
of the whole of ,galileo's theory of    
motion1 and which must  therefore be    
quoted in his own words3--,a heavy body 
has by nature an  intrinsic principle of
 moving towards the common centre of    
heavy things2  that is to say1 to the   
centre of our terrestrial globe1 with a 
motion  continually accelerated in such 
manner that in equal times there are    
always equal additions of velocity4     

,this is to be understood as holding    
true only when all accidental and       
external impediments are removed1       
amongst which is one that we cannot     
obviate1 namely1 the resistance of  the 
medium4 ,this opposes itself1 less or   
more1 accordingly as it is to  open more
 slowly or hastily to make way for the  
moveable1 which being by  its own       
nature1 as ,i have said1 continually    
accelerated1 consequently  encounters a 
continually increasing resistance in the
 medium1 until at  last the velocity    
reaches that degree1 and the resistance 
that power1  that they balance each     
other2 all further acceleration is      
prevented1 and  the moveable continues  
ever after with an uniform and equable  
motion4  ,that such a limiting velocity 
is not greater than some which may be   
exhibited may be proved as ,galileo     
suggested by firing a bullet upwards1   
which will in its descent strike the    
ground with less force than it  would   
have done if immediately from the mouth 

of the gun2 for he argued  that the     
degree of velocity which the air's      
resistance is capable of  diminishing   
must be greater than that which could   
ever be reached by a  body falling      
naturally from rest4 ,i do not think the
 present occasion a  fit one for        
examining the cause of this acceleration
 of natural motion1  on which the       
opinions of philosophers are much       
divided2 some referring  it to the      
approach towards the centre1 some to the
 continual diminution  of that part of  
the medium remaining to be divided1 some
 to a certain  extrusion of the ambient 
medium1 which uniting again behind the  
moveable  presses and hurries it        
forwards4 ,all these fancies1 with      
others of the  like sort1 we might spend
 our time in examining1 and with little 
to gain  by resolving them4 ,it is      
enough for our author at present that we
  understand his object to be the       
investigation and examination of some   
phenomena of a motion so accelerated1   

7no matter what may be the cause17  that
 the momenta of velocity1 from the      
beginning to move from rest1  increase  
in the simple proportion in which the   
time increases1 which is  as much as to 
say1 that in equal times are equal      
additions of velocity4  ,and if it shall
 turn out that the phenomena            
demonstrated on this  supposition are   
verified in the motion of falling and   
naturally  accelerated weights1 we may  
thence conclude that the assumed        
definition  does describe the motion of 
heavy bodies1 and that it is true that  
their  acceleration varies in the ratio 
of the time of motion4    ,when ,galileo
 first published these ,dialogues on    
,motion1 he was obliged  to rest his    
demonstrations upon another principle   
besides1 namely1 that  the velocity     
acquired in falling down all inclined   
planes of the same  perpendicular height
 is the same4 ,as this result was       
derived directly  from experiment1 and  
from that only1 his theory was so far   

imperfect  till he could show its       
consistency with the above supposed law 
of  acceleration4 ,when ,viviani was    
studying with ,galileo1 he expressed his
  dissatisfaction at this chasm in the  
reasoning2 the consequence of which     
was1 that ,galileo1 as he lay the same  
night1 sleepless through  indisposition1
 discovered the proof which he had long 
sought in vain1  and introduced it into 
the subsequent editions4 ,the third     
dialogue is  principally taken up with  
theorems on the direct fall of bodies1  
their  times of descent down differently
 inclined planes1 which in planes of    
the same height he determined to be as  
the lengths1 and with other  inquiries  
connected with the same subject1 such as
 the straight lines of  shortest descent
 under different data1 c4               
,illustration    ,the fourth dialogue is
 appropriated to projectile motion1     
determined  upon the principle that the 
horizontal motion will continue the same
 as  if there were no vertical motion1  

and the vertical motion as if there     
were no horizontal motion4 ,let ,,ab    
represent a horizontal line or plane    
placed on high1 on which let a body be  
carried with an equable motion  from ,a 
towards ,b1 and the support of the plane
 being taken away at ,b1  let the       
natural motion downwards due to the     
body's weight come upon it  in the      
direction of the perpendicular ,,bn4    
,moreover let the straight line  ,,be   
drawn in the direction ,,ab be taken to 
represent the flow1 or measure1  of the 
time1 on which let any number of equal  
parts ,,bc1 ,,cd1 ,,de1 c4 be  marked at
 pleasure1 and from the points ,c1 ,d1  
,e1 let lines be drawn  parallel to     
,,bn2 in the first of these let any part
 ,,ci be taken1 and let  ,,df be taken  
four times as great as ,,ci1 ,,eh nine  
times as great1 and so  on1             
proportionally to the squares of the    
lines ,,bc1 ,,bd1 ,,be1 c41 or1 as  we  
say1 in the double proportion of these  
lines4 ,now if we suppose that  whilst  

by its equable horizontal motion the    
body moves from ,b to ,c1 it  also      
descends by its weight through ,,ci1 at 
the end of the time denoted  by ,,bc it 
will be at ,i4 ,moreover in the time    
,,bd1 double of ,,bc1 it will  have     
fallen four times as far1 for in the    
first part of the ,treatise it  has been
 shewn that the spaces fallen through by
 a heavy body vary as  the squares of   
the times4 ,similarly at the end of the 
time ,,be1 or three  times ,,bc1 it will
 have fallen through ,,eh1 and will be  
at ,h4 ,and it is  plain that the points
 ,i1 ,f1 ,h1 are in the same parabolical
 line ,,bifh4  ,the same demonstration  
will apply if we take any number of     
equal  particles of time of whatever    
duration4    ,the curve called here a   
,parabola by ,galileo1 is one of those  
which  results from cutting straight    
through a ,cone1 and therefore is called
  also one of the ,conic ,sections1 the 
curious properties of which curves  had 
drawn the attention of geometricians    

long before ,galileo thus began  to     
point out their intimate connexion with 
the phenomena of motion4  ,after the    
proposition we have just extracted1 he  
proceeds to anticipate  some objections 
to the theory1 and explains that the    
course of a  projectile will not be     
accurately a parabola for two reasons2  
partly on  account of the resistance of 
the air1 and partly because a horizontal
  line1 or one equidistant from the     
earth's centre1 is not straight1 but    
circular4 ,the latter cause of          
difference will1 however1 as he says1 be
  insensible in all such experiments as 
we are able to make4 ,the rest of  the  
,dialogue is taken up with different    
constructions for determining  the      
circumstances of the motion of          
projectiles1 as their range1 greatest   
height1 c42 and it is proved that1 with 
a given force of projection1  the range 
will be greatest when a ball is         
projected at an elevation of  #de1      
ranges of all angles equally inclined   

above and below #de  corresponding      
exactly to each other4    ,illustration 
,one of the most interesting subjects   
discussed in these dialogues is the     
famous notion of ,nature's horror of a  
vacuum or empty space1 which the  old   
school of philosophy considered as      
impossible to be obtained4  ,galileo's  
notions of it were very different2 for  
although he still  unadvisedly adhered  
to the old phrase to denote the         
resistance  experienced in endeavouring 
to separate two smooth surfaces1 he was 
so  far from looking upon a vacuum as an
 impossibility1 that he has  described  
an apparatus by which he endeavoured to 
measure the force  necessary to produce 
one4 ,this consisted of a cylinder1 into
 which is  tightly fitted a piston2     
through the centre of the piston passes 
a rod  with a conical valve1 which1 when
 drawn down1 shuts the aperture         
closely1 supporting a basket4 ,the space
 between the piston and cylinder  being 
filled full of water poured in through  

the aperture1 the valve is  closed1 the 
vessel reversed1 and weights are added  
till the piston is  drawn forcibly      
downwards4 ,galileo concluded that the  
weight of the  piston1 rod1 and added   
weights1 would be the measure of the    
force of  resistance to the vacuum which
 he supposed would take place between   
the  piston and lower surface of the    
water4 ,the defects in this apparatus   
for  the purpose intended are of no     
consequence1 so far as regards the      
present argument1 and it is perhaps     
needless to observe that he was         
mistaken in supposing the water would   
not descend with the piston4 ,this      
experiment occasions a remark from      
,sagredo1 that he had observed that a   
lifting-pump would not work when the    
water in the cistern had sunk to  the   
depth of thirty-five feet below the     
valve2 that he thought the pump  was    
injured1 and sent for the maker of it1  
who assured him that no pump  upon that 
construction would lift water from so   

great a depth4 ,this  story is sometimes
 told of ,galileo1 as if he had said    
sneeringly on this  occasion that       
,nature's horror of a vacuum does not   
extend beyond  thirty-five feet2 but it 
is very plain that if he had made such  
an  observation1 it would have been     
seriously2 and in fact by such a        
limitation he deprived the notion of the
 principal part of its  absurdity4 ,he  
evidently had adopted the common notion 
of suction1 for he  compares the column 
of water to a rod of metal suspended    
from its upper  end1 which may be       
lengthened till it breaks with its own  
weight4 ,it is  certainly very          
extraordinary that he failed to observe 
how simply these  phenomena may be      
explained by a reference to the weight  
of the elastic  atmosphere1 which he was
 perfectly well acquainted with1 and    
endeavoured  by the following ingenious 
experiment to determine3--,take a large 
glass  flask with a bent neck1 and round
 its mouth tie a leathern pipe with a   

valve in it1 through which water may be 
forced into the flask with a  syringe   
without suffering any air to escape1 so 
that it will be  compressed within the  
bottle4 ,it will be found difficult to  
force in  more than about three-fourths 
of what the flask will hold1 which must 
be  carefully weighed4 ,the valve must  
then be opened1 and just so much air    
will rush out as would in its natural   
density occupy the space now  filled by 
the water4 ,weigh the vessel again2 the 
difference will show  the weight of that
 quantity of air4#ade ,by these means1  
which the  modern experimentalist will  
see were scarcely capable of much       
accuracy1  ,galileo found that air was  
four hundred times lighter than water1  
instead of ten times1 which was the     
proportion fixed on by ,aristotle4  ,the
 real proportion is about #hcj times4   
,the true theory of the rise of water in
 a lifting-pump is commonly dated  from 
,torricelli's famous experiment with a  
column of mercury1 in #afdd1  when he   

found that the greatest height at which 
it would stand is  fourteen times less  
than the height at which water will     
stand1 which is  exactly the proportion 
of weight between water and mercury4    
,the  following curious letter from     
,baliani1 in #afcj1 shows that the      
original  merit of suggesting the real  
cause belongs to him1 and renders it    
still  more unaccountable that ,galileo1
 to whom it was addressed1 should not at
  once have adopted the same view of the
 subject3--,i have believed that a      
vacuum may exist naturally ever since ,i
 knew that the air has sensible  weight1
 and that you taught me in one of your  
letters how to find its  weight exactly1
 though ,i have not yet succeeded with  
that experiment4  ,from that moment ,i  
took up the notion that it is not       
repugnant to the  nature of things that 
there should be a vacuum1 but merely    
that it is  difficult to produce4 ,to   
explain myself more clearly3 if we allow
 that  the air has weight1 there is no  

difference between air and water except 
in degree4 ,at the bottom of the sea the
 weight of the water above me           
compresses everything round my body1 and
 it strikes me that the same  thing must
 happen in the air1 we being placed at  
the bottom of its  immensity2 we do not 
feel its weight1 nor the compression    
round us1  because our bodies are made  
capable of supporting it4 ,but if we    
were in  a vacuum1 then the weight of   
the air above our heads would be felt4  
,it  would be felt very great1 but not  
infinite1 and therefore determinable1   
and it might be overcome by a force     
proportioned to it4 ,in fact ,i         
estimate it to be such that1 to make a  
vacuum1 ,i believe we require a  force  
greater than that of a column of water  
thirty feet high4#adf    ,illustration  
,this subject is introduced by some     
observations on the force of  cohesion1 
,galileo seeming to be of opinion that1 
although it cannot be  adequately       
accounted for by the great and principal

 resistance to a  vacuum1 yet that      
perhaps a sufficient cause may be found 
by considering  every body as composed  
of very minute particles1 between every 
two of  which is exerted a similar      
resistance4 ,this remark serves to lead 
to a  discussion on indivisibles and    
infinite quantities1 of which we shall  
merely extract what ,galileo gives as a 
curious paradox suggested in the  course
 of it4 ,he supposes a basin to be      
formed by scooping a hemisphere  out of 
a cylinder1 and a cone to be taken of   
the same depth and base as  the         
hemisphere4 ,it is easy to show1 if the 
cone and scooped cylinder be  both      
supposed to be cut by the same plane1   
parallel to the one on which  both      
stand1 that the area of the ring ,,cdef 
thus discovered in the  cylinder is     
equal to the area of the corresponding  
circular section ,,ab  of the cone1     
wherever the cutting plane is supposed  
to be4#adg ,he then  proceeds with these
 remarkable words3--,if we raise the    

plane higher and  higher1 one of these  
areas terminates in the circumference of
 a circle1  and the other in a point1   
for such are the upper rim of the basin 
and  the top of the cone4 ,now since in 
the diminution of the two areas they  to
 the very last maintain their equality  
to one another1 it is in my  thoughts   
proper to say that the highest and      
ultimate terms#adh of such  diminutions 
are equal1 and not one infinitely bigger
 than the other4 ,it  seems therefore   
that the circumference of a large circle
 may be said to  be equal to one single 
point4 ,and why may not these be called 
equal if  they be the last remainders   
and vestiges left by equal              
magnitudes#adi8    ,we think no one can 
refuse to admit the probability1 that   
,newton may  have found in such passages
 as these the first germ of the idea of 
his  prime and ultimate ratios1 which   
afterwards became in his hands an       
instrument of such power4 ,as to the    
paradoxical result1 ,descartes          

undoubtedly has given the true answer to
 it in saying that it only  proves that 
the line is not a greater area than the 
point is4 ,whilst on  this subject1 it  
may not be uninteresting to remark that 
something  similar to the doctrine of   
fluxions seems to have been lying       
dormant in  the minds of the            
mathematicians of ,galileo's era1 for   
,inchoffer  illustrates his argument in 
the treatise we have already mentioned1 
that  the ,copernicans may deduce some  
true results from what he terms their   
absurd hypothesis1 by observing1 that   
mathematicians may deduce the  truth    
that a line is length without breadth1  
from the false and  physically          
impossible supposition that a point     
flows1 and that a line is  the fluxion  
of a point4#aej    ,a suggestion that   
perhaps fire dissolves bodies by        
insinuating itself  between their minute
 particles1 brings on the subject of the
 violent  effects of heat and light2 on 
which ,sagredo inquires1 whether we are 

to  take for granted that the effect of 
light does or does not require time4    
,simplicio is ready with an answer1 that
 the discharge of artillery  proves the 
transmission of light to be             
instantaneous1 to which ,sagredo        
cautiously replies1 that nothing can be 
gathered from that experiment  except   
that light travels more swiftly than    
sound2 nor can we draw any  decisive    
conclusion from the rising of the sun4  
,who can assure us that  he is not in   
the horizon before his rays reach our   
sight8 ,salviati then  mentions an      
experiment by which he endeavoured to   
examine this question4  ,two observers  
are each to be furnished with a lantern3
 as soon as the  first shades his light1
 the second is to discover his1 and this
 is to be  repeated at a short distance 
till the observers are perfect in the   
practice4 ,the same thing is to be tried
 at the distance of several  miles1 and 
if the first observer perceive any delay
 between shading his  own light and the 

appearance of his companion's1 it is to 
be attributed  to the time taken by the 
light in traversing twice the distance  
between  them4 ,he allows that he could 
discover no perceptible interval at the 
distance of a mile1 at which he had     
tried the experiment1 but recommends    
that with the help of a telescope it    
should be tried at much greater         
distances4 ,sir ,kenelm ,digby remarks  
on this passage3 ,it may be objected    
7if there be some observable tardity in 
the motion of light7 that the  sunne    
would never be truly in that place in   
which unto our eyes he  appeareth to be2
 because that it being seene by means of
 the light which  issueth from it1 if   
that light required time to move in1 the
 sunne  7whose motion is so swifte7     
would be removed from the place where   
the  light left it1 before it could be  
with us to give tidings of him4 ,to     
this ,i answer1 allowing peradventure   
that it may be so1 who knoweth the      
contrary8 ,or what inconvenience would  

follow if it be admitted#aea8    ,the   
principal thing remaining to be noticed 
is the application of the  theory of the
 pendulum to musical concords and       
dissonances1 which are  explained1 in   
the same manner as by ,kepler in his    
,harmonices ,mundi1 to  result from the 
concurrence or opposition of vibrations 
in the air  striking upon the drum of   
the ear4 ,it is suggested that these    
vibrations  may be made manifest by     
rubbing the finger round a glass set in 
a large  vessel of water2 and if by     
pressure the note is suddenly made to   
rise  to the octave above1 every one of 
the undulations which will be seen      
regularly spreading round the glass1    
will suddenly split into two1  proving  
that the vibrations that occasion the   
octave are double those  belonging to   
the simple note4 ,galileo then describes
 a method he  discovered by accident of 
measuring the length of these waves more
  accurately than can be done in the    
agitated water4 ,he was scraping a      

brass plate with an iron chisel1 to take
 out some spots1 and moving the  tool   
rapidly upon the plate1 he occasionally 
heard a hissing and  whistling sound1   
very shrill and audible1 and whenever   
this occurred1  and then only1 he       
observed the light dust on the plate to 
arrange itself  in a long row of small  
parallel streaks equidistant from each  
other4 ,in  repeated experiments he     
produced different tones by scraping    
with  greater or less velocity1 and     
remarked that the streaks produced by   
the  acute sounds stood closer together 
than those from the low notes4 ,among   
the sounds produced were two1 which by  
comparison with a viol he  ascertained  
to differ by an exact fifth2 and        
measuring the spaces  occupied by the   
streaks in both experiments1 he found   
thirty of the one  equal to forty-five  
of the other1 which is exactly the known
 proportion  of the lengths of strings  
of the same material which sound a fifth
 to  each other4#aeb    ,salviati also  

remarks1 that if the material be not the
 same1 as for  instance if it be        
required to sound an octave to a note on
 catgut1 on a  wire of the same length1 
the weight of the wire must be made four
 times  as great1 and so for other      
intervals4 ,the immediate cause of the  
forms  of musical intervals is neither  
the length1 the tension1 nor the        
thickness1 but the proportion of the    
numbers of the undulations of the  air  
which strike upon the drum of the ear1  
and make it vibrate in the  same        
intervals4 ,hence we may gather a       
plausible reason of the different       
sensations occasioned to us by different
 couples of sounds1 of which we  hear   
some with great pleasure1 some with     
less1 and call them accordingly         
concords1 more or less perfect1 whilst  
some excite in us great                 
dissatisfaction1 and are called         
discords4 ,the disagreeable sensation   
belonging to the latter probably arises 
from the disorderly manner in  which the

 vibrations strike the drum of the ear2 
so that for instance a  most cruel      
discord would be produced by sounding   
together two strings1  of which the     
lengths are to each other as the side   
and diagonal of a  square1 which is the 
discord of the false fifth4 ,on the     
contrary1  agreeable consonances will   
result from those strings of which the  
numbers of vibrations made in the same  
time are commensurable1 to the  end that
 the cartilage of the drum may not      
undergo the incessant torture  of a     
double inflexion from the disagreeing   
percussions4 ,something  similar may be 
exhibited to the eye by hanging up      
pendulums of different  lengths3 if     
these be proportioned so that the times 
of their vibrations  correspond with    
those of the musical concords1 the eye  
will observe with  pleasure their       
crossings and interweavings still       
recurring at  appreciable intervals2 but
 if the times of vibration be           
incommensurate1  the eye will be wearied

 and worn out with following them4      
,the second dialogue is occupied        
entirely with an investigation of the   
strength of beams1 a subject which does 
not appear to have been examined  by any
 one before ,galileo beyond ,aristotle's
 remark1 that long beams are  weaker1   
because they are at once the weight1 the
 lever1 and the fulcrum2  and it is in  
the development of this observation that
 the whole theory  consists4 ,the       
principle assumed by ,galileo as the    
basis of his inquiries  is1 that the    
force of cohesion with which a beam     
resists a cross  fracture in any section
 may all be considered as acting at the 
centre of  gravity of the section1 and  
that it breaks always at the lowest     
point3  from this he deduced that the   
effect of the weight of a prismatic beam
  in overcoming the resistance of one   
end by which it is fastened to a  wall1 
varies directly as the square of the    
length1 and inversely as the  side of   
the base4 ,from this it immediately     

follows1 that if for instance  the bone 
of a large animal be three times as long
 as the corresponding  one in a smaller 
beast1 it must be nine times as thick to
 have the same  strength1 provided we   
suppose in both cases that the materials
 are of  the same consistence4 ,an      
elegant result which ,galileo also      
deduced from  this theory1 is that the  
form of such a beam1 to be equally      
strong in  every part1 should be that of
 a parabolical prism1 the vertex of the 
parabola being the farthest removed from
 the wall4 ,as an easy mode of          
describing the parabolic curve for this 
purpose1 he recommends tracing  the line
 in which a heavy flexible string hangs4
 ,this curve is not an  accurate        
parabola3 it is now called a catenary2  
but it is plain from the  description of
 it in the fourth dialogue1 that        
,galileo was perfectly  aware that this 
construction is only approximately true4
 ,in the same  place he makes the       
remark1 which to many is so paradoxical1

 that no  force1 however great1 exerted 
in a horizontal direction1 can stretch a
  heavy thread1 however slender1 into an
 accurately straight line4    ,the fifth
 and sixth dialogues were left          
unfinished1 and annexed to the  former  
ones by ,viviani after ,galileo's death3
 the fragment of the fifth1  which is on
 the subject of ,euclid's ,definition of
 ,ratio1 was at first  intended to have 
formed a part of the third1 and followed
 the first  proposition on equable      
motion3 the sixth was intended to have  
embodied  ,galileo's researches on the  
nature and laws of ,percussion1 on which
 he  was employed at the time of his    
death4 ,considering these solely as     
fragments1 we shall not here make any   
extracts from them4      ,,footnotes3   
#adj ,joh4 ,bernouilli1 ,opera ,omnia1  
,lausann1 #agdd4 tom4 i4 p4 #aib4       
#ada ,pantometria1 #aeia4    #adb       
,lettres de ,descartes4 ,paris1 #afeg4  
#adc ,math4 ,coll4 vol4 ii4    #add     
,phys4 ,lib4 iv4 c4 #h4    #ade ,it has 

been recently proposed to determine the 
density of  high-pressure steam by a    
process analogous to this4    #adf      
,venturi1 vol4 ii4    #adg ,galileo also
 reasons in the same way on the equality
 of the solids  standing on the cutting 
plane1 but one is sufficient for our    
present  purpose4    #adh ,gli altissimi
 e ultimi termini4    #adi ,le ultime   
reliquie e vestigie lasciate da         
grandezze eguali4    #aej ,punctum      
fluere1 et lineam esse fluxum puncti4   
,tract4 ,syllept4  ,rom1 #afcc4    #aea 
,treatise of the ,nature of ,bodies4    
,london1 #affe4    #aeb ,this beautiful 
experiment is more easily tried by      
drawing the bow  of a violin across the 
edge of glass strewed with fine dry     
sand4 ,those  who wish to see more on   
the subject may consult ,chladni's      
',acoustique4'          ,,chapter       
,,xviii4        ,correspondence on      
,longitudes4--,pendulum ,clock4         
,,in the spring of #afcf1 having        
finished his ,dialogues on ,motion1     

,galileo  resumed the plan of           
determining the longitude by means of   
,jupiter's  satellites4 ,perhaps he     
suspected something of the private      
intrigue which  thwarted his former     
expectations from the ,spanish          
government1 and this  may have induced  
him on the present occasion to negotiate
 the matter  without applying for       
,ferdinand's assistance and             
recommendation4  ,accordingly he        
addressed himself to ,lorenz ,real1 who 
had been ,governor  ,general of the     
,dutch possessions in ,india1 freely and
 unconditionally  offering the use of   
his theory to the ,states ,general of   
,holland4 ,not  long before1 his opinion
 had been requested by the commissioners
  appointed at ,paris to examine and    
report on the practicability of  another
 method proposed by ,morin1#aec which   
consisted in observing the  distance of 
the moon from a known star4 ,morin was a
 ,french philosopher1  principally known
 as an astrologer and zealous           

,anti-,copernican2 but his  name        
deserves to be recorded as undoubtedly  
one of the first to  recommend a method1
 which1 under the name of a ,lunar      
distance1 is now in  universal practice4
    ,the monthly motion of the moon is  
so rapid1 that her distance from a      
given star sensibly varies in a few     
minutes even to the unassisted eye2  and
 with the aid of the telescope1 we can  
of course appreciate the  change more   
accurately4 ,morin proposed that the    
distances of the moon  from a number of 
fixed stars lying near her path in the  
heavens should  be beforehand calculated
 and registered for every day in the    
year1 at a  certain hour1 in the place  
from which the longitudes were to be    
reckoned1 as for instance at ,paris4    
,just as in the case of the eclipses  of
 ,jupiter's satellites1 the observer1   
when he saw that the moon had  arrived  
at the registered distance1 would know  
the hour at ,paris3 he  might also make 
allowance for intermediate distances4   

,observing at the  same instant the hour
 on board his ship1 the difference      
between the two  would show his position
 in regard of longitude4 ,in using this 
method as  it is now practised1 several 
modifications are to be attended to1    
without which it would be wholly        
useless1 in consequence of the          
refraction of the atmosphere1 and the   
proximity of the moon to the  earth4    
,owing to the latter cause1 if two      
spectators should at the same  instant  
of time1 but in different places1       
measure the distance of the  moon in the
 ,east1 from a star still more to the   
eastward1 it would  appear greater to   
the more easterly spectator than to the 
other  observer1 who as seen from the   
star would be standing more directly    
behind the moon4 ,the mode of allowing  
for these alterations is taught by      
trigonometry and astronomy4    ,the     
success of this method depends          
altogether upon the exact knowledge     
which we now have of the moon's course1 

and till that knowledge was  perfected  
it would have been found altogether     
illusory4 ,such in fact was  the        
judgment which ,galileo pronounced upon 
it4 ,as to ,morin's book on  the method 
of finding the longitude by means of the
 moon's motion1 ,i say  freely that ,i  
conceive this idea to be as accurate in 
theory1 as  fallacious and impossible in
 practice4 ,i am sure that neither you  
nor  any one of the other four gentlemen
 can doubt the possibility of finding   
the difference of longitude between two 
meridians by means of the moon's        
motion1 provided we are sure of the     
following requisites3 ,first1 an        
,ephemeris of the moon's motion exactly 
calculated for the first meridian  from 
which the others are to be reckoned2    
secondly1 exact instruments1  and       
convenient to handle1 in taking the     
distance between the moon and a  fixed  
star2 thirdly1 great practical skill in 
the observer2 fourthly1  not less       
accuracy in the scientific calculations1

 and astronomical  computations2        
fifthly1 very perfect clocks to number  
the hours1 or other  means of knowing   
them exactly1 c4 ,supposing1 ,i say1 all
 these elements  free from error1 the   
longitude will be accurately found2 but 
,i reckon it  more easy and likely to   
err in all of these together1 than to be
  practically right in one alone4 ,morin
 ought to require his judges to  assign1
 at their pleasure1 eight or ten moments
 of different nights  during four or six
 months to come1 and pledge himself to  
predict and  assign by his calculations 
the distances of the moon at those      
determined  instants from some star     
which would then be near her4 ,if it is 
found  that the distances assigned by   
him agree with those which the quadrant 
or sextant#aed will actually show1 the  
judges would be satisfied of his        
success1 or rather of the truth of the  
matter1 and nothing would remain  but to
 show that his operations were such as  
could be performed by men  of moderate  

skill1 and also practicable at sea as   
well as on land4 ,i  incline much to    
think that an experiment of this kind   
would do much  towards abating the      
opinion and conceit which ,morin has of 
himself1  which appears to me so lofty1 
that ,i should consider myself the      
eighth  sage1 if ,i knew the half of    
what ,morin presumes to know4    ,it is 
probable that ,galileo was biassed by a 
predilection for his own  method1 on    
which he had expended so much time and  
labour2 but the  objections which he    
raises against ,morin's proposal in the 
foregoing  letter are no other than     
those to which at that period it was    
undoubtedly open4 ,with regard to his   
own1 he had already1 in #afab1 given  a 
rough prediction of the course of       
,jupiter's satellites1 which had been   
found to agree tolerably well with      
subsequent observations2 and since  that
 time1 amid all his other employments1  
he had almost  unintermittingly during  
twenty-four years continued his         

observations1  for the sake of bringing 
the tables of their motions to as high a
 state  of perfection as possible4 ,this
 was the point to which the inquiries of
  the ,states in their answer to        
,galileo's frank proposal were          
principally  directed4 ,they immediately
 appointed commissioners to communicate 
with  him1 and report the various points
 on which they required information4    
,they also sent him a golden chain1 and 
assured him that in the case of  the    
design proving successful1 he should    
have no cause to complain of  their want
 of gratitude and generosity4 ,the      
commissioners immediately  commenced an 
active correspondence with him1 in the  
course of which he  entered into more   
minute details with regard to the       
methods by which he  proposed to obviate
 the practical difficulties of the      
necessary  observations4    ,it is worth
 noticing that the secretary to the     
,prince of ,orange1 who was  mainly     
instrumental in forming this commission1

 was ,constantine  ,huyghens1 father of 
the celebrated mathematician of that    
name1 of whom  it has been said that he 
seemed destined to complete the         
discoveries of  ,galileo2 and it is not 
a little remarkable1 that ,huyghens     
nowhere in his  published works makes   
any allusion to this connexion between  
his father  and ,galileo1 not even      
during the discussion that arose some   
years later  on the subject of the      
pendulum clock1 which must necessarily  
have forced  it upon his recollection4  
,the ,dutch commissioners had chosen one
 of their number to go into ,italy  for 
the purpose of communicating personally 
with ,galileo1 but he  discouraged this 
scheme1 from a fear of its giving       
umbrage at ,rome4 ,the  correspondence  
being carried on at so great a distance 
necessarily  experienced many tedious   
delays1 till in the very midst of       
,galileo's  labours to complete his     
tables1 he was seized with the blindness
 which  we have already mentioned4 ,he  

then resolved to place all the papers   
containing his observations and         
calculations for this purpose in the    
hands of ,renieri1 a former pupil of    
his1 and then professor of  mathematics 
at ,pisa1 who undertook to finish and to
 forward them into  ,holland4 ,before   
this was done1 a new delay was          
occasioned by the deaths  which speedily
 followed each other of every one of the
 four  commissioners2 and for two or    
three years the correspondence with     
,holland was entirely interrupted4      
,constantine ,huyghens1 who was capable 
of appreciating the value of the scheme1
 succeeded after some trouble in        
renewing it1 but only just before the   
death of ,galileo himself1 by which  of 
course it was a second time broken off2 
and to complete the singular  series of 
obstacles by which the trial of this    
method was impeded1 just  as ,renieri1  
by order of the ,duke of ,tuscany1 was  
about to publish the  ephemeris and     
tables which ,galileo had entrusted to  

him1 and which the  ,duke told ,viviani 
he had seen in his possession1 he also  
was attacked  with a mortal malady2 and 
upon his death the manuscripts were     
nowhere to  be found1 nor has it since  
been discovered what became of them4    
,montucla  has intimated his suspicions 
that ,renieri himself destroyed them1   
from a  consciousness that they were    
insufficient for the purpose to which it
  was intended to apply them2 a bold    
conjecture1 and one which ought to  rest
 upon something more than mere surmise3 
for although it may be  considered      
certain1 that the practical value of    
these tables would be  very             
inconsiderable in the present advanced  
state of knowledge1 yet it  is nearly as
 sure that they were unique at that     
time1 and ,renieri was  aware of the    
value which ,galileo himself had set    
upon them1 and should  not be lightly   
accused of betraying his trust in so    
gross a manner4 ,in  #affe1 ,borelli    
calculated the places of the satellites 

for every day in  the ensuing year1     
which he professed to have deduced 7by  
desire of the  ,grand ,duke7 from       
,galileo's tables2#aee but he does not  
say whether or  not these tables were   
the same that had been in ,renieri's    
possession4    ,we have delayed till    
this opportunity to examine how far the 
invention  of the pendulum clock belongs
 to ,galileo4 ,it has been asserted that
 the  isochronism of the pendulum had   
been noticed by ,leonardo da ,vinci1 but
  the passage on which this assertion is
 founded 7as translated from his        
manuscripts by ,venturi7 scarcely       
warrants this conclusion4 ,a rod which  
engages itself in the opposite teeth of 
a spur-wheel can act like the  arm of   
the balance in clocks1 that is to say1  
it will act alternately1  first on one  
side of the wheel1 then on the opposite 
one1 without  interruption4 ,if ,da     
,vinci had constructed a clock on this  
principle1  and recognized the          
superiority of the pendulum over the old

 balance1 he  would surely have done    
more than merely mention it as affording
 an  unintermitted motion like the arm  
of the balance4 ,the use of the  balance
 is supposed to have been introduced at 
least as early as the  fourteenth       
century4 ,venturi mentions the drawing  
and description of a  clock in one of   
the manuscripts of the ,king's ,library 
at ,paris1 dated  about the middle of   
the fifteenth century1 which as he says 
nearly  resembles a modern watch4 ,the  
balance is there called ,the circle     
fastened to the stem of the pallets1 and
 moved by the force with  it4#aef ,in   
that singularly wild and extravagant    
book1 entitled ,a  ,history of both     
,worlds1 by ,robert ,flud1 are given two
 drawings of the  wheel-work of the     
clocks and watches in use before the    
application of  the pendulum4 ,an       
inspection of them will show how little 
remained to be  done when the           
isochronism of the pendulum was         
discovered4 ,fig4 #a4  represents the   

large clocks moved by a weight1 such as 
are put up in  churches and turrets2    
fig4 #b4 the small ones moved by a      
spring1 such  as are worn round the     
neck1 or placed on a shelf or table4    
,the use of  the chain is to equalize   
the spring1 which is strongest at the   
beginning  of its motion4#aeg ,this     
contrivance of the chain is mentioned by
  ,cardan1 in #aegj1 and is probably    
still older4 ,in both figures the name  
given to the cross bar1 with the weight 
attached to it1 is the time or  balance 
7tempus seu libratio7 by which the      
motion is equalized4 ,the  manner in    
which ,huyghens first applied the       
pendulum is shown in fig4  #c4aeh ,the  
action in the old clocks of the balance1
 or rake1 as it  was also called1 was by
 checking the motion of the descending  
weight  till its inertia was overcome2  
it was then forced round till the       
opposite pallet engaged in the toothed  
wheel4 ,the balance was thus  suddenly  
and forcibly reduced to a state of rest1

 and again set in  motion in the        
opposite direction4 ,it will be observed
 that these  balances wanted the spiral 
spring introduced in all modern watches1
  which has a property of isochronism   
similar to that of the pendulum4  ,hooke
 is generally named as the discoverer of
 this property of springs1  and as the  
author of its application to the        
improvement of watches1 but  the        
invention is disputed with him by       
,huyghens4 ,lahire asserts#aei that  the
 isochronism of springs was communicated
 to ,huyghens at ,paris by              
,hautefeuille1 and that this was the    
reason why ,huyghens failed to obtain   
the patent he solicited for the         
construction of spring watches4 ,a great
  number of curious contrivances at this
 early period in the history of         
,horology1 may be seen in ,schott's     
,magia ,natur1 published at ,nuremberg  
in #affd4    ,illustration3 ,fig4 #b4   
,fig4 #a4 ,fig4 #c4    ,galileo was     
early convinced of the importance of his

 pendulum to the  accuracy of           
astronomical observations2 but the      
progress of invention is  such that the 
steps which on looking back seem the    
easiest to make1 are  often those which 
are the longest delayed4 ,galileo       
recognized the  principle of the        
isochronism of the pendulum1 and        
recommended it as a  measurer of time in
 #aehc2 yet fifty years later1 although 
constantly  using it1 he had not devised
 a more convenient method of doing so1  
than  is contained in the following     
description taken from his ,astronomical
  ,operations4    ,a very exact         
time-measurer for minute intervals of   
time1 is a heavy  pendulum of any size  
hanged by a fine thread1 which1 if      
removed from the  perpendicular and     
allowed to swing freely1 always         
completes its  vibrations1 be they great
 or small1 in exactly the same time4#afj
    ,the mode of finding exactly by     
means of this the quantity of any time  
reduced to hours1 minutes1 seconds1 c41 

which are the divisions  commonly used  
among astronomers1 is this3--,fit up a  
pendulum of any  length1 as for instance
 about a foot long1 and count patiently 
7only for  once7 the number of          
vibrations during a natural day4 ,our   
object will be  attained if we know the 
exact revolution of the natural day4    
,the  observer must then fix a telescope
 in the direction of any star1 and      
continue to watch it till it disappears 
from the field of view4 ,at that        
instant he must begin to count the      
vibrations of the pendulum1  continuing 
all night and the following day till the
 return of the same  star within the    
field of view of the telescope1 and its 
second  disappearance1 as on the first  
night4 ,bearing in recollection the     
total  number of vibrations thus made in
 twenty-four hours1 the time            
corresponding to any other number of    
vibrations will be immediately  given by
 the ,golden ,rule4    ,a second extract
 out of ,galileo's ,dutch               

correspondence1 in #afcg1 will  show the
 extent of his improvements at that     
time3--,i come now to the  second       
contrivance for increasing immensely the
 exactness of  astronomical             
observations4 ,i allude to my           
time-measurer1 the precision  of which  
is so great1 and such1 that it will give
 the exact quantity of  hours1 minutes1 
seconds1 and even thirds1 if their      
recurrence could be  counted2 and its   
constancy is such that two1 four1 or six
 such  instruments will go on together  
so equably that one will not differ from
  another so much as the beat of a      
pulse1 not only in an hour1 but even in 
a day or a month4--,i do not make use of
 a weight hanging by a thread1  but a   
heavy and solid pendulum1 made for      
instance of brass or copper1 in  the    
shape of a circular sector of twelve or 
fifteen degrees1 the radius  of which   
may be two or three palms1 and the      
greater it is the less  trouble will    
there be in attending it4 ,this sector1 

such as ,i have  described1 ,i make     
thickest in the middle radius1 tapering 
gradually  towards the edges1 where ,i  
terminate it in a tolerably sharp line1 
to  obviate as much as possible the     
resistance of the air1 which is the sole
  cause of its retardation4--,these last
 words deserve notice1 because1  in a   
previous discussion1 ,galileo had       
observed that the parts of the  pendulum
 nearest the point of suspension have a 
tendency to vibrate  quicker than those 
at the other end1 and seems to have     
thought  erroneously that the stoppage  
of the pendulum is partly to be         
attributed  to this cause4--,this is    
pierced in the centre1 through which is 
passed  an iron bar shaped like those on
 which steelyards hang1 terminated below
  in an angle1 and placed on two bronze 
supports1 that they may wear away  less 
during a long motion of the sector4 ,if 
the sector 7when accurately  balanced7  
be removed several degrees from its     
perpendicular position1 it  will        

continue a reciprocal motion through a  
very great number of  vibrations before 
it will stop2 and in order that it may  
continue its  motion as long as is      
wanted1 the attendant must occasionally 
give it a  smart push1 to carry it back 
to large vibrations4 ,galileo then      
describes as before the method of       
counting the vibrations in the course   
of a day1 and gives the rule that the   
lengths of two similar pendulums  will  
have the same proportion as the squares 
of their times of  vibration4 ,he then  
continues3 ,now to save the fatigue of  
the assistant  in continually counting  
the vibrations1 this is a convenient    
contrivance3 ,a very small and delicate 
needle extends out from the  middle of  
the circumference of the sector1 which  
in passing strikes a  rod fixed at one  
end2 this rod rests upon the teeth of a 
wheel as light  as paper1 placed in a   
horizontal plane near the pendulum1     
having round  it teeth cut like those of
 a saw1 that is to say1 with one side of

 each  tooth perpendicular to the rim of
 the wheel and the other inclined       
obliquely4 ,the rod striking against the
 perpendicular side of the tooth  moves 
it1 but as the same rod returns against 
the oblique side1 it does  not move it  
the contrary way1 but slips over it and 
falls at the foot of  the following     
tooth1 so that the motion of the wheel  
will be always in  the same direction4  
,and by counting the teeth you may see  
at will the  number of teeth passed1 and
 consequently the number of vibrations  
and of  particles of time elapsed4 ,you 
may also fit to the axis of this first  
wheel a second1 with a small number of  
teeth1 touching another greater  toothed
 wheel1 c4 ,but it is superfluous to    
point out this to you1 who  have by you 
men very ingenious and well skilled in  
making clocks and  other admirable      
machines2 and on this new principle1    
that the pendulum  makes its great and  
small vibrations in the same time       
exactly1 they will  invent contrivances 

more subtle than any ,i can suggest2 and
 as the error  of clocks consists       
principally in the disability of workmen
 hitherto to  adjust what we call the   
balance of the clock1 so that it may    
vibrate  regularly1 my very simple      
pendulum1 which is not liable to any    
alteration1 affords a mean of           
maintaining the measures of time always 
equal4 ,the contrivance thus described  
would be somewhat similar to the        
annexed representation1 but it is almost
 certain that no such instrument  was   
actually constructed4    ,illustration  
,it must be owned that ,galileo greatly 
overrated the accuracy of his           
timekeeper2 and in asserting so         
positively that which he had certainly  
not experienced1 he seems to depart from
 his own principles of  philosophizing4 
,it will be remarked that in this       
passage he still is of  the erroneous   
opinion1 that all the vibrations great  
or small of the  same pendulum take     
exactly the same time2 and we have not  

been able to  find any trace of his     
having ever held a different opinion1   
unless  perhaps in the ,dialogues1 where
 he says1 ,if the vibrations are not    
exactly equal1 they are at least        
insensibly different4 ,this is very     
much at variance with the statement in  
the ,memoirs of the ,academia del       
,cimento1 edited by their secretary     
,magalotti1 on the credit of which      
,galileo's claim to the pendulum-clock  
chiefly rests4 ,it is there said  that  
experience shows that the smallest      
vibrations are rather the  quickest1 as 
,galileo announced after the            
observation1 which in #aehc he  was the 
first to make of their approximate      
equality4 ,it is not possible           
immediately in connexion with so glaring
 a misstatement1 to give  implicit      
credence to the assertion in the next   
sentence1 that to  obviate this         
inconvenience ,galileo was the first to 
contrive a clock1  constructed in #afdi1
 by his son ,vincenzo1 in which1 by the 

action of a  weight or spring1 the      
pendulum was constrained to move always 
from the  same height4 ,indeed it       
appears as if ,magalotti did not always 
tell this  story in the same manner1 for
 he is referred to as the author of the 
account given by ,becher1 that ,galileo 
himself made a pendulum-clock one  of   
which was sent to ,holland1 plainly     
insinuating that ,huyghens was a  mere  
copyist4#afa ,these two accounts        
therefore serve to invalidate each      
other's credibility4 ,tiraboschi#afb    
asserts that1 at the time he wrote1  the
 mathematical professor at ,pisa was in 
possession of the identical  clock      
constructed by ,treffler under          
,vincenzo's directions2 and quotes a    
letter from ,campani1 to whom it was    
shown by ,ferdinand1 old1 rusty1 and    
unfinished as ,galileo's son made it    
before #afdi4 ,viviani on the other     
hand says that ,treffler constructed    
this same clock some time after         
,vincenzo's death 7which happened in    

#afdi71 on a different principle from   
,vincenzo's ideas1 although he says     
distinctly that he heard ,galileo       
describe an application of the pendulum 
to a clock similar to ,huyghens'        
contrivance4 ,campani did not actually  
see this clock till #afei1 which  was   
three years after ,huyghens' invention1 
so that perhaps ,huyghens was  too      
easily satisfied when1 on occasion of   
the answer which ,ferdinand  sent to his
 complaints of the ,memorie del ,cimento
 he wrote to ,bouillaud1  ,i must       
however believe1 since such a prince    
assures me1 that ,galileo  had this idea
 before me4    ,there is another        
circumstance almost amounting to a proof
 that it was an  afterthought to        
attribute the merit of constructing the 
pendulum-clock  to ,galileo1 for on the 
reverse of a medal struck by ,viviani1  
and  inscribed to the memory of his     
excellent instructor1#afc is a rude     
exhibition of the principal objects to  
which ,galileo's attention was          

directed4 ,the pendulum is represented  
simply by a weight attached to a  string
 hanging on the face of a rock4 ,it is  
probable that1 in a design  expressly   
intended to commemorate ,galileo's      
inventions1 ,viviani would  have        
introduced the timekeeper in the most   
perfect form to which it had  been      
brought by him4 ,riccioli1#afd whose    
industry was unwearied in  collecting   
every fact and argument which related in
 any way to the  astronomical and       
mechanical knowledge and opinions of his
 time1  expressly recommends swinging a 
pendulum1 or perpendicular as it was    
often called 7only a few years before   
,huyghens' publication71 as much  more  
accurate than any clock4#afe ,join to   
all these arguments  ,huyghens' positive
 assertion1 that if ,galileo had        
conceived any such  idea1 he at least   
was entirely ignorant of it1#aff and no 
doubt can  remain that the merit of the 
original invention 7such as it was7     
rests  entirely with ,huyghens4 ,the    

step indeed seems simple enough for a   
less  genius than his3 for the property 
of the pendulum was known1 and the      
conversion of a rotatory into a         
reciprocating motion was known2 but the 
connexion of the one with the other     
having been so long delayed1 we must    
suppose that difficulties existed where 
we are not now able to perceive  them1  
for ,huyghens' improvement was received 
with universal admiration4    ,there may
 be many who will consider the pendulum 
as undeserving so long  a discussion2   
who do not know or remember that the    
telescope itself has  hardly done more  
for the precision of astronomical       
observations than  this simple          
instrument1 not to mention the          
invaluable convenience of an  uniform   
and accurate timekeeper in the daily    
intercourse of life4 ,the  patience and 
industry of modern observers are often  
the theme of  well-merited praise1 but  
we must look with a still higher degree 
of  wonder on such men as ,tycho ,brahe 

and his contemporaries1 who were  driven
 by the want of any timekeeper on which 
they could depend to the  most laborious
 expedients1 and who nevertheless       
persevered to the best  of their        
ability1 undisgusted either by the      
tedium of such processes1 or  by the    
discouraging consciousness of the       
necessary imperfection of their  most   
approved methods and instruments4       
,the invariable regularity of the       
pendulum's motion was soon made         
subservient to ulterior purposes beyond 
that of merely registering time4  ,we   
have seen the important assistance it   
afforded in establishing the  laws of   
motion2 and when the theory founded on  
those laws was extended  and improved1  
the pendulum was again instrumental1 by 
a species of  approximate reasoning     
familiar to all who are acquainted with 
physical  inquiries1 in pointing out by 
its minute irregularities in different  
parts of the earth1 a corresponding     
change in the weight of all bodies  in  

those different situations1 supposed to 
be the consequence of a  greater        
distance from the axis of the earth's   
rotation2 since that would  occasion the
 force of attraction to be              
counterbalanced by an increased         
centrifugal force4 ,the theory which    
kept pace with the constantly           
increasing accuracy of such             
observations1 proving consistent in all 
trials of it1 has left little room for  
future doubts2 and in this manner  the  
pendulum in intelligent hands became the
 simplest instrument for  ascertaining  
the form of the globe which we inhabit4 
,an ,english  astronomer1 who           
corresponded with ,kepler under the     
signature of ,brutius  7whose real name 
perhaps might be ,bruce71 had already   
declared his  belief in #afjc1 that the 
earth on which we tread is neither round
 nor  globular1 but more nearly of an   
oval figure4#afg ,there is nothing to   
guide us to the grounds on which he     
formed this opinion1 which was  perhaps 

only a lucky guess4 ,kepler's note upon 
it is3 ,this is not  altogether to be   
contemned4    ,a farther use of the     
pendulum is in furnishing a general and 
unperishing  standard of measure4 ,this 
application is suggested in the third   
volume  of the ',reflections' of        
,mersenne1 published in #afdg1 where he 
observes  that it may be best for the   
future not to divide time into hours1   
minutes1 and seconds1 but to express its
 parts by the number of  vibrations of a
 pendulum of given length1 swinging     
through a given arc4  ,it was soon seen 
that it would be more convenient to     
invert this  process1 and to choose as  
an unit of length the pendulum which    
should  make a certain number of        
vibrations in the unit of time1         
naturally  determined by the revolution 
of the earth on its axis4 ,our ,royal   
,society took an active part in these   
experiments1 which seem1                
notwithstanding their utility1 to have  
met from the first with much of  the    

same ridicule which was lavished upon   
them by the ignorant1 when  recently    
repeated for the same purpose4 ,i       
contend1 says ,graunt#afh in  a         
dedication to the ,royal ,society1 dated
 #affb1 against the envious  schismatics
 of your society 7who think you do      
nothing unless you  presently transmute 
metals1 make butter and cheese without  
milk1 and1 as  their own ballad hath it1
 make leather without hides71 by        
asserting the  usefulness of even all   
your preparatory and luciferous         
experiments1  being not the ceremonies1 
but the substance and principles of     
useful  arts4 ,for ,i find in trade the 
want of an universal measure1 and have  
heard musicians wrangle about the just  
and uniform keeping of time in  their   
consorts1 and therefore cannot with     
patience hear that your  labours about  
vibrations1 eminently conducing to both1
 should be  slighted1 nor your pendula  
called swing-swangs with scorn4#afi     
,,footnotes3    #aec ,one of the        

,commissioners was the father of ,blaise
 ,pascal4    #aed ,these instruments    
were very inferior to those now in use  
under the  same name4 ,see ,treatise on 
,opt4 ,instrum4    #aee ,theoric        
,mediceorum ,planetarum1 ,florenti1     
#afff4    #aef ,circulus affixus virg   
paletorum qui cum e de vi movetur4      
#aeg ,utriusque ,cosmi ,historia4       
,oppenhemii1 #afag4    #aeh ,huygenii   
,opera4 ,lugduni1 #agbd4    #aei        
,mmoires de l',academie1 #agag4    #afj 
,see page #hd4    #afa ,de nova         
,temporis dimetiendi ratione4 ,londini1 
#afhj4    #afb ,storia della ,lett4     
,ital4    #afc ,museum ,mazuchellianum1 
vol4 ii4 ,tab4 cvii4 p4 #bi4    #afd    
,almagestum ,novum1 vol4 i4    #afe     
,quovis horologio accuratius4    #aff   
,clarorum ,belgarum ad ,ant4            
,magliabech4 ,epistol4 ,florence1 #agde1
  tom4 i4 p4 #bce4    #afg ,kepleri     
,epistol4    #afh ,natural and          
,political ,observations4 ,london1      
#affe4    #afi ,see also ,hudibras1     

,part ,,ii4 ,cant4 ,,iii4               
,they're guilty by their own confessions
      ,of felony1 and at the ,sessions  
,upon the bench ,i will so handle 'em1  
,that the vibration of this pendulum    
,shall make all taylors' yards of one   
,unanimous opinion2      ,a thing he    
long has vaunted of1      ,but now shall
 make it out of proof4    ,hudibras was 
certainly written before #affc3 ten     
years later ,huyghens  speaks of the    
idea of so employing the pendulum as a  
common one4          ,,chapter ,,xix4   
,character of ,galileo--,miscellaneous  
details--his      ,death--,conclusion4  
,,the remaining years of ,galileo's life
 were spent at ,arcetri1 where  indeed1 
even if the ,inquisition had granted his
 liberty1 his increasing  age and       
infirmities would probably have detained
 him4 ,the rigid caution  with which he 
had been watched in ,florence was in    
great measure relaxed1  and he was      
permitted to see the friends who crowded
 round him to express  their respect and

 sympathy4 ,the ,grand ,duke visited him
 frequently1 and  many distinguished    
strangers1 such as ,gassendi and        
,deodati1 came into  ,italy solely for  
the purpose of testifying their         
admiration of his  character4 ,among    
other visitors the name of ,milton will 
be read with  interest3 we may probably 
refer to the effects of this interview  
the  allusions to ,galileo's            
discoveries1 so frequently introduced   
into his  poem4 ,milton mentions in his 
',areopagitica1' that he saw ,galileo   
whilst  in ,italy1 but enters into no   
details of his visit4    ,galileo was   
fond of society1 and his cheerful and   
popular manners  rendered him an        
universal favourite among those who were
 admitted to his  intimacy4 ,among      
these1 ,viviani1 who formed one of his  
family during the  three last years of  
his life1 deserves particular notice1 on
 account of  the strong attachment and  
almost filial veneration with which he  
ever  regarded his master and           

benefactor4 ,his long life1 which was   
prolonged  to the completion of his     
#hast year in #agjc1 enabled him to see 
the  triumphant establishment of the    
truths on account of which ,galileo had 
endured so many insults2 and even in his
 old age1 when in his turn he  had      
acquired a claim to the reverence of a  
younger generation1 our ,royal          
,society1 who invited him among them in 
#afif1 felt that the complimentary      
language in which they addressed him as 
the first mathematician of the  age     
would have been incomplete and          
unsatisfactory without an allusion to   
the friendship that gained him the      
cherished title of ,the last pupil of   
,galileo4#agj    ,torricelli1 another of
 ,galileo's most celebrated followers1  
became a  member of his family in       
,october1 #afda3 he first learned       
mathematics from  ,castelli1 and        
occasionally lectured for him at ,rome1 
in which manner he  was employed when   
,galileo1 who had seen his book ',on    

,motion1' and  augured the greatest     
success from such a beginning1 invited  
him to his  house--an offer which       
,torricelli eagerly embraced1 although  
he enjoyed  the advantages of it but for
 a short time4 ,he afterwards succeeded 
,galileo in his situation at the court  
of ,florence1#aga but survived him  only
 a few years4    ,it is from the        
accounts of ,viviani and ,gherardini    
that we principally  draw the following 
particulars of ,galileo's person and    
character3--,signor  ,galileo was of a  
cheerful and pleasant countenance1      
especially in his  old age1 square      
built1 and well proportioned in stature1
 and rather  above the middle size4 ,his
 complexion was fair and sanguine1 his  
eyes  brilliant1 and his hair of a      
reddish cast4 ,his constitution was     
naturally strong1 but worn out by       
fatigue of mind and body1 so as         
frequently to be reduced to a state of  
the utmost weakness4 ,he was  subject to
 attacks of hypochondria1 and often     

molested by severe and  dangerous       
illnesses1 occasioned in great measure  
by his sleepless  nights1 the whole of  
which he frequently spent in            
astronomical  observations4 ,during     
upwards of forty-eight years of his     
life1 he was  tormented with acute      
rheumatic pains1 suffering particularly 
on any  change of weather4 ,he found    
himself most free from these pains      
whilst  residing in the country1 of     
which consequently he became very fond3 
besides1 he used to say that in the     
country he had greater freedom to  read 
the book of ,nature1 which lay there    
open before him4 ,his library  was very 
small1 but well chosen1 and open to the 
use of the friends whom  he loved to see
 assembled round him1 and whom he was   
accustomed to  receive in the most      
hospitable manner4 ,he ate sparingly    
himself2 but was  particularly choice in
 the selection of his wines1 which in   
the latter  part of his life were       
regularly supplied out of the ,grand    

,duke's  cellars4 ,this taste gave an   
additional stimulus to his agricultural 
pursuits1 and many of his leisure hours 
were spent in the cultivation  and      
superintendence of his vineyards4 ,it   
should seem that he was  considered a   
good judge of wine2 for ,viviani has    
preserved one of his  receipts in a     
collection of miscellaneous experiments4
 ,in it he strongly  recommends that for
 wine of the first quality1 that juice  
only should be  employed1 which is      
pressed out by the mere weight of the   
heaped grapes1  which would probably be 
that of the ripest fruit4 ,the following
 letter1  written in his #gdth year1 is 
dated1 ,from my prison at ,arcetri4--,i 
am  forced to avail myself of your      
assistance and favour1 agreeably to your
  obliging offers1 in consequence of the
 excessive chill of the weather1  and of
 old age1 and from having drained out my
 grand stock of a hundred  bottles1     
which ,i laid in two years ago2 not to  
mention some minor  particulars during  

the last two months1 which ,i received  
from my ,serene  ,master1 the ,most     
,eminent ,lord ,cardinal1 their         
,highnesses the ,princes1  and the ,most
 ,excellent ,duke of ,guise1 besides    
cleaning out two barrels  of the wine of
 this country4 ,now1 ,i beg that with   
all due diligence and  industry1 and    
with consideration1 and taking counsel  
with the most  refined palates1 you will
 provide me with two cases1 that is to  
say1  with forty flasks of different    
wines1 the most exquisite that you can  
find3 take no thought of the expense1   
because ,i stint myself so much in  all 
other pleasures that ,i can afford to   
lay out something at the  request of    
,bacchus1 without giving offence to his 
two companions ,ceres  and ,venus4 ,you 
must be careful to leave out neither    
,scillo nor ,carino 7,i  believe they   
meant to call them ,scylla and          
,charybdis71 nor the country  of my     
master1 ,archimedes of ,syracuse1 nor   
,greek wines1 nor clarets1 c4  c4 ,the  

expense ,i shall easily be able to      
satisfy1 but not the infinite           
obligation4    ,in his expenditure      
,galileo observed a just mean between   
avarice and  profusion3 he spared no    
cost necessary for the success of his   
many and  various experiments1 and spent
 large sums in charity and hospitality1 
and in assisting those in whom he       
discovered excellence in any art or     
profession1 many of whom he maintained  
in his own house4 ,his temper was       
easily ruffled1 but still more easily   
pacified4 ,he seldom conversed on       
mathematical or philosophical topics    
except among his intimate friends2  and 
when such subjects were abruptly brought
 before him1 as was often  the case by  
the numberless visitors he was in the   
habit of receiving1 he  showed great    
readiness in turning the conversation   
into more popular  channels1 in such    
manner however that he often contrived  
to introduce  something to satisfy the  
curiosity of the inquirers4 ,his memory 

was  uncommonly tenacious1 and stored   
with a vast variety of old songs and    
stories1 which he was in the constant   
habit of quoting and alluding to4  ,his 
favourite ,italian authors were         
,ariosto1 ,petrarca1 and ,berni1 great  
part of whose poems he was able to      
repeat4 ,his excessive admiration of    
,ariosto determined the side which he   
took against ,tasso in the virulent  and
 unnecessary controversy which has      
divided ,italy so long on the           
respective merits of these two great    
poets2 and he was accustomed to say     
that reading ,tasso after ,ariosto was  
like tasting cucumbers after  melons4   
,when quite a youth1 he wrote a great   
number of critical remarks  on ,tasso's 
,gerusalemme ,liberata1 which one of his
 friends borrowed1 and  forgot to       
return4 ,for a long time it was thought 
that the manuscript had  perished1 till 
the ,abb ,serassi discovered it1 whilst 
collecting  materials for his ,life of  
,tasso1 published at ,rome in #aghe4    

,serassi  being a violent partizan of   
,tasso1 but also unwilling to lose the  
credit  of the discovery1 copied the    
manuscript1 but without any intention of
  publishing it1 till he could find     
leisure for replying properly to the    
sophistical and unfounded attacks of a  
critic so celebrated on other  accounts4
 ,he announced his discovery as having  
been made in one of the  famous         
libraries at ,rome1 which vague         
indication he with some reason          
considered insufficient to lead to a    
second discovery4 ,on ,serassi's  death 
his copy was found1 containing a        
reference to the situation of the       
original2 the criticisms were published1
 and form the greatest part of  the last
 volume of the ,milan edition of        
,galileo's works4 ,the manuscript  was  
imperfect at the time of this second    
discovery1 several leaves  having been  
torn out1 it is not known by whom4      
,the opinion of the most judicious      
,italian critics appears to be1 that it 

would have been more for ,galileo's     
credit if these remarks had never  been 
made public3 they are written in a      
spirit of flippant violence1  such as   
might not be extraordinary in a common  
juvenile critic1 but  which it is       
painful to notice from the pen of       
,galileo4 ,two or three  sonnets are    
extant written by ,galileo himself1 and 
in two instances he  has not scrupled to
 appropriate the conceits of the poet he
 affected to  undervalue4#agb ,it should
 be mentioned that ,galileo's matured   
taste  rather receded from the violence 
of his early prejudices1 for at a later 
period of his life he used to shun      
comparing the two2 and when forced to   
give an opinion he said1 that ,tasso's  
appeared the finer poem1 but that       
,ariosto gave him the greater pleasure4 
,besides these sonnets1 there is  extant
 a short burlesque poem written by him1 
,in abuse of ,gowns1 when1  on his first
 becoming ,professor at ,pisa1 he found 
himself obliged by  custom to wear his  

professional habit in every company4 ,it
 is written  not without humour1 but    
does not bear comparison with ,berni1   
whom he  imitated4    ,there are several
 detached subjects treated of by        
,galileo1 which may be  noticed in this 
place4 ,a letter by him containing the  
solution of a  problem in ,chances is   
probably the earliest notice extant of  
the  application of mathematics to that 
interesting subject3 the  correspondence
 between ,pascal and ,fermat1 with which
 its history is  generally made to      
begin1 not having taken place till at   
least twelve  years later4 ,there can be
 little doubt after the clear account of
 ,carlo  ,dati1 that ,galileo was the   
first to examine the curve called the   
,cycloid1 described by a point in the   
rim of a wheel rolling on a  straight   
line1 which he recommended as a graceful
 form for the arch of a  bridge at      
,pisa4 ,he even divined that the area   
contained between it and  its base is   
exactly three times that of the         

generating circle4 ,he seems  to have   
been unable to verify this guess by     
strict geometrical  reasoning1 for      
,viviani tells an odd story1 that in    
order to satisfy his  doubts he cut out 
several large cycloids of pasteboard1   
but finding the  weight in every trial  
to be rather less than three times that 
of the  circle1 he suspected the        
proportion to be irrational1 and that   
there was  some error in his estimation2
 the inquiry he abandoned was afterwards
  resumed with success by his pupil     
,torricelli4#agc    ,the account which  
,lagalla gives of an experiment shown in
 his presence  by ,galileo1 carries the 
observation of the phosphorescence of   
the  ,bologna stone at least as far back
 as #afab4agd ,other writers mention    
the name of an alchymist1 who according 
to them discovered it  accidentally in  
#afjc4 ,cesi1 ,lagalla1 and one or two  
others1 had passed  the night at        
,galileo's house1 with the intention of 
observing ,venus and  ,saturn2 but1 the 

night being cloudy1 the conversation    
turned on other  matters1 and especially
 on the nature of light1 on which       
,galileo took a  small wooden box at    
daybreak before sunrise1 and showed us  
some small  stones in it1 desiring us to
 observe that they were not in the least
  degree luminous4 ,having then exposed 
them for some time to the twilight1  he 
shut the window again2 and in the midst 
of the dark room showed us  the stones1 
shining and glistening with a faint     
light1 which we saw  presently decay and
 become extinguished4 ,in #afdj1 ,liceti
 attempted to  refer the effect of the  
earthshine upon the moon to a similar   
phosphorescent quality of that luminary1
 to which ,galileo1 then aged #gf1      
replied by a long and able letter1      
enforcing the true explanation he had   
formerly given4    ,although quite      
blind1 and nearly deaf1 the intellectual
 powers of  ,galileo remained to the end
 of his life2 but he occasionally felt  
that  he was overworking himself1 and   

used to complain to his friend ,micanzio
  that he found his head too busy for   
his body4 ,i cannot keep my restless    
brain from grinding on1 although with   
great loss of time2 for whatever  idea  
comes into my head with respect to any  
novelty1 drives out of it  whatever ,i  
had been thinking of just before4 ,he   
was busily engaged in  considering the  
nature of the force of percussion1 and  
,torricelli was  employed in arranging  
his investigations for a continuation of
 the  ',dialogues on ,motion1' when he  
was seized with an attack of fever and  
palpitation of the heart1 which1 after  
an illness of two months1 put an  end to
 his long1 laborious1 and useful life1  
on the #hth of ,january1  #afdb1 just   
one year before his great successor     
,newton was born4    ,the malice of his 
enemies was scarcely allayed by his     
death4 ,his right  of making a will was 
disputed1 as having died a prisoner to  
the  ,inquisition1 as well as his right 
to burial in consecrated ground4 ,these 

were at last conceded1 but ,urban       
anxiously interfered to prevent the     
design of erecting a monument to him in 
the church of ,santa ,croce1 in         
,florence1 for which a large sum had    
been subscribed4 ,his body was          
accordingly buried in an obscure corner 
of the church1 which for upwards  of    
thirty years after his death was        
unmarked even by an inscription to  his 
memory4 ,it was not till a century later
 that the splendid monument  was erected
 which now covers his and ,viviani's    
remains4 ,when their  bodies were       
disinterred in #agcg for the purpose of 
being removed to  their new             
resting-place1 ,capponi1 the president  
of the ,florentine  ,academy1 in a      
spirit of spurious admiration1 mutilated
 ,galileo's body1  by removing the thumb
 and forefinger of the right-hand1 and  
one of the  vertebr of the back1 which  
are still preserved in some of the      
,italian  museums4 ,the monument was put
 up at the expense of his biographer1   

,nelli1 to whom ,viviani's property     
descended1 charged with the condition   
of erecting it4 ,nor was this the only  
public testimony which ,viviani  gave of
 his attachment4 ,the medal which he    
struck in honour of ,galileo  has       
already been mentioned2 he also1 as soon
 as it was safe to do so1  covered every
 side of the house in which he lived    
with laudatory  inscriptions to the same
 effect4 ,a bust of ,galileo was placed 
over the  door1 and two bas-reliefs on  
each side representing some of his      
principal discoveries4 ,not less than   
five other medals were struck in  honour
 of him during his residence at ,padua  
and ,florence1 which are all  engraved  
in ,venturi's ,memoirs4    ,there are   
several good portraits of ,galileo      
extant1 two of which1 by  ,titi and     
,subtermanns1 are engraved in ,nelli's  
,life of ,galileo4 ,another  by         
,subtermanns is in the ,florentine      
,gallery1 and an engraving from a  copy 
of this is given by ,venturi4 ,there is 

also a very fine engraving  from the    
original picture4 ,an engraving from    
another original picture is  in the     
frontispiece of the ,padua edition of   
his works4 ,salusbury seems  in the     
following passage to describe a portrait
 of ,galileo painted by  himself3 ,he   
did not contemn the other inferior arts1
 for he had a good  hand in sculpture   
and carving2 but his particular care was
 to paint  well4 ,by the pencil he      
described what his telescope discovered2
 in one  he exceeded art1 in the other1 
nature4 ,osorius1 the eloquent bishop of
  ,sylva1 esteems one piece of ,mendoza 
the wise ,spanish minister's  felicity1 
to have been this1 that he was          
contemporary to ,titian1 and  that by   
his hand he was drawn in a fair tablet4 
,and ,galilus1 lest he  should want the 
same good fortune1 made so great a      
progress in this  curious art1 that he  
became his own ,buonarota2 and because  
there was  no other copy worthy of his  
pencil1 drew himself4 ,no other author  

makes  the slightest allusion to such a 
painting2 and it appears more likely    
that ,salusbury should be mistaken than 
that so interesting a portrait  should  
have been entirely lost sight of4       
,galileo's house at ,arcetri was        
standing in #ahba1 when ,venturi visited
  it1 and found it in the same state in 
which ,galileo might be supposed to     
have left it4 ,it is situated nearly a  
mile from ,florence1 on the             
south-eastern side1 and about a gun-shot
 to the north-west of the  convent of   
,st4 ,matthew4 ,nelli placed a suitable 
inscription over the  door of the house1
 which belonged in #ahba to a ,signor   
,alimari4#age    ,although ,nelli's     
,life of ,galileo disappointed the      
expectations that had  been formed of   
it1 it is impossible for any admirer of 
,galileo not to  feel the greatest      
degree of gratitude towards him1 for the
 successful  activity with which he     
rescued so many records of the          
illustrious  philosopher from           

destruction4 ,after ,galileo's death1   
the principal part  of his books1       
manuscripts1 and instruments1 were put  
into the charge of  ,viviani1 who was   
himself at that time an object of great 
suspicion2 most  of them he thought it  
prudent to conceal1 till the            
superstitious  outcries against ,galileo
 should be silenced4 ,at ,viviani's     
death1 he left  his library1 containing 
a very complete collection of the works 
of all  the mathematicians who had      
preceded him 7and amongst them those of 
,galileo1 ,torricelli1 and ,castelli1   
all which were enriched with notes  and 
additions by himself71 to the hospital  
of ,st4 ,mary at ,florence1  where an   
extensive library already existed4 ,the 
directors of the  hospital sold this    
unique collection in #agha1 when it     
became entirely  dispersed4 ,the        
manuscripts in ,viviani's possession    
passed to his nephew1  the ,abb         
,panzanini1 together with the portraits 
of the chief personages  of the         

,galilean school1 ,galileo's            
instruments1 and1 among other           
curiosities1 the emerald ring which he  
wore as a member of the ,lyncean        
,academy4 ,a great number of these books
 and manuscripts were purchased at      
different times by ,nelli1 after the    
death of ,panzanini1 from his           
relations1 who were ignorant or         
regardless of their value4 ,one of his  
chief acquisitions was made by an       
extraordinary accident1 related by      
,tozzetti with the following details1   
which we repeat1 as they seem to        
authenticate the story3--,in the spring 
of #agci1 the famous ,doctor ,lami  went
 out according to his custom to         
breakfast with some of his friends  at  
the inn of the ,bridge1 by the          
starting-place2 and as he and ,sig4     
,nelli were passing through the market1 
it occurred to them to buy some         
,bologna sausages from the pork-butcher1
 ,cioci1 who was supposed to excel  in  
making them4 ,they went into the shop1  

had their sausages cut off and  rolled  
in paper1 which ,nelli put into his hat4
 ,on reaching the inn1 and  calling for 
a plate to put them in1 ,nelli observed 
that the paper in  which they had been  
rolled was one of ,galileo's letters4   
,he cleaned it  as well as he could with
 his napkin1 and put it into his pocket 
without  saying a word to ,lami2 and as 
soon as he returned into the city1 and  
could get clear of him1 he flew to the  
shop of ,cioci1 who told him that  a    
servant whom he did not know brought him
 from time to time similar  letters1    
which he bought by weight as waste      
paper4 ,nelli bought all that  remained1
 and on the servant's next reappearance 
in a few days1 he  learned the quarter  
whence they came1 and after some time   
succeeded at a  small expense in getting
 into his own possession an old         
corn-chest1  containing all that still  
remained of the precious treasures which
  ,viviani had concealed in it ninety   
years before4#agf    ,the earliest      

biographical notice of ,galileo is that 
in the ,obituary of  the ,mercurio      
,italico1 published at ,venice in #afdg1
 by ,vittorio ,siri4 ,it  is very short1
 but contains an exact enumeration of   
his principal works  and discoveries4   
,rossi1 who wrote under the name of     
,janus ,nicius  ,erythrus1 introduced an
 account of ,galileo in his ,pinacotheca
 ,imaginum  ,illustrium1 in which the   
story of his illegitimacy first made its
  appearance4 ,in #affd1 ,salusbury     
published a life of ,galileo in the     
second  volume of his ,mathematical     
,collections1 the greater part of which 
is a  translation of ,galileo's         
principal works4 ,almost the whole      
edition of  the second volume of        
,salusbury's book was burnt in the great
 fire of  ,london4 ,chauffepi says that 
only one copy is known to be extant in  
,england3 this is now in the well-known 
library of the ,earl of  ,macclesfield1 
to whose kindness the author is much    
indebted for the use  he has been       

allowed to make of this unique volume4  
,a fragment of this  second volume is in
 the ,bodleian ,library at ,oxford4 ,the
 translations in  the preceding pages   
are mostly founded upon ,salusbury's    
version4  ,salusbury's account1 although
 that of an enthusiastic admirer of     
,galileo1 is too prolix to be           
interesting3 the general style of the   
performance may be guessed from the     
title of the first chapter--',of ,man   
in general1 and how he excelleth all the
 other ,animals4' ,after informing  his 
readers that ,galileo was born at ,pisa1
 he proceeds3--,italy is  affirmed to   
have been the first that peopled the    
world after the  universal deluge1 being
 governed by ,janus1 ,cameses1 and      
,saturn1 c4 ,his  description of        
,galileo's childhood is somewhat quaint4
 ,before others  had left making of dirt
 pyes1 he was framing of diagrams2 and  
whilst  others were whipping of toppes1 
he was considering the cause of their   
motion4 ,it is on the whole tolerably   

correct1 especially if we take  into    
account that ,salusbury had not yet seen
 ,viviani's ,life1 though  composed some
 years earlier4    ,the ,life of        
,galileo by ,viviani was first written  
as an outline of an  intended larger    
work1 but this latter was never         
completed4 ,this sketch  was published  
in the ,memoirs of the ,florentine      
,academy1 of which ,galileo  had been   
one of the annual presidents1 and       
afterwards prefixed to the  complete    
editions of ,galileo's works2 it is     
written in a very agreeable  and flowing
 style1 and has been the groundwork of  
most subsequent  accounts4 ,another     
original memoir by ,niccol ,gherardini1 
was published  by ,tozzetti4 ,a great   
number of references to authors who have
 treated of  ,galileo is given by ,sach 
in his ,onomasticon4 ,an approved ,latin
 memoir by  ,brenna is in the first     
volume of ,fabroni's ,vit ,italorum     
,illustrium2 he  has however fallen into
 several errors3 this same work contains

 the  lives of several of his principal 
followers4    ,the article in           
,chauffepi's ,continuation of ,bayle's  
,dictionary does not  contain anything  
which is not in the earlier accounts4   
,andrs wrote an essay entitled ',saggio 
sulla ,filosofia del ,galileo1'         
published at ,mantua #aggf2 and         
,jagemann published his ',geschichte des
  ,leben des ,galileo' at ,leipzig1 in  
#aghg2agg neither of these the author   
has been able to meet with4 ,an analysis
 of the latter may be seen in  ,kstner's
 ',geschichte der ,mathematik1          
,gttingen1 #ahjj1' from which it  does  
not appear to contain any additional    
details4 ,the ',elogio del  ,galileo' by
 ,paolo ,frisi1 first published at      
,leghorn in #agge1 is1 as its  title    
expresses1 rather in the nature of a    
panegyric than of a  continuous         
biographical account4 ,it is written    
with very great elegance  and intimate  
knowledge of the subjects of which it   
treats4 ,nelli gave  several curious    

particulars with respect to ,galileo in 
his ',saggio di  ,storia ,letteraria    
,fiorentina1 ,lucca1 #agei2' and in     
#agic published his  large work entitled
 ',vita e ,commercio ,letterario di     
,galileo ,galilei4' ,so  uninteresting a
 book was probably never written from   
such excellent  materials4 ,two thick   
quarto volumes are filled with          
repetitions of the  accounts that were  
already in print1 the bulky preparation 
of which  compelled the author to forego
 the publication of the vast collection 
of  original documents which his        
unwearied zeal and industry had         
collected4  ,this defect has been in    
great measure supplied by ,venturi in   
#ahah and  #ahba1 who has not only      
incorporated in his work many of        
,nelli's  manuscripts1 but has brought  
together a number of scattered notices  
of  ,galileo and his writings from a    
variety of outlying sources--a service  
which the writer is able to appreciate  
from having gone through the  greatest  

part of the same labour before he was   
fortunate enough to meet  with          
,venturi's book4 ,still there are many  
letters cited by ,nelli1 which  do not  
appear either in his book or ,venturi's4
 ,carlo ,dati1 in #affc1  quotes the    
registers of ,galileo's correspondence  
arranged in  alphabetical order1 in ten 
large volumes4#agh ,the writer has no   
means  of ascertaining what collection  
this may have been2 it is difficult to  
suppose that one so arranged should have
 been lost sight of4 ,it is  understood 
that a life of ,galileo is preparing at 
this moment in  ,florence1 by desire of 
the present ,grand ,duke1 which will    
probably throw  much additional light on
 the character and merits of this great 
and  useful philosopher4    ,the first  
editions of his various treatises1 as   
mentioned by ,nelli1 are  given below4  
,clement1 in his ',bibliothque          
,curieuse1' has pointed out  such among 
them1 and the many others which have    
been printed1 as have  become rare4     

,the ,florentine edition is the one used
 by the ,academia della ,crusca for     
their references2 for which reason its  
paging is marked in the margin of  the  
edition of ,padua1 which is much more   
complete1 and is the one which  has been
 on the present occasion principally    
consulted4    ,the latter contains the  
,dialogue on the ,system1 which was not 
suffered  to be printed in the former   
editions4 ,the twelve first volumes of  
the  last edition of ,milan are a mere  
transcript of that of ,padua3 the       
thirteenth contains in addition the     
,letter to the ,grand ,duchess1 the     
,commentary on ,tasso1 with some minor  
pieces4 ,a complete edition is still    
wanted1 embodying all the recently      
discovered documents1 and omitting  the 
verbose commentaries1 which1 however    
useful when they were written1  now     
convey little information that cannot be
 more agreeably and more  profitably    
learned in treatises of a later date4   
,such was the life1 and such were the   

pursuits1 of this extraordinary  man4   
,the numberless inventions of his acute 
industry2 the use of the  telescope1 and
 the brilliant discoveries to which it  
led2 the patient  investigation of the  
laws of weight and motion2 must all be  
looked upon  as forming but a part of   
his real merits1 as merely particular   
demonstrations of the spirit in which he
 everywhere withstood the  despotism of 
ignorance1 and appealed boldly from     
traditional opinions to  the judgments  
of reason and common sense4 ,he claimed 
and bequeathed to  us the right of      
exercising our faculties in examining   
the beautiful  creation which surrounds 
us4 ,idolized by his friends1 he        
deserved their  affection by numberless 
acts of kindness2 by his good humour1   
his  affability1 and by the benevolent  
generosity with which he devoted        
himself and a great part of his limited 
income to advance their talents  and    
fortunes4 ,if an intense desire of being
 useful is everywhere worthy  of honour2

 if its value is immeasurably increased1
 when united to genius  of the highest  
order2 if we feel for one who1          
notwithstanding such  titles to regard1 
is harassed by cruel persecution1--then 
none deserve  our sympathy1 our         
admiration1 and our gratitude1 more than
 ,galileo4      ,list of ,galileo's     
,works4      ,le ,operazioni del        
,compasso ,geom4 e ,milit4              
,padova1 #afjf4    ,fol4 ,difesa di     
,gal4 ,galilei contr4 all4 cal4 et      
impost4 di ,bald4 ,capra                
,venezza1 #afjg4 #dto4    ,sydereus     
,nuncius                                
,venetiis1 #afaj4 #dto4    ,discorso    
int4 alle cose che stanno in su l',acqua
                                        
,firenze1 #afab4 #dto4    ,novantiqua   
,,ss4 ,,pp4 ,doctrina de ,s4 ,scriptur  
,testimoniis                            
,argent1 #afab4 #dto4    ,istoria e     
,demostr4 int4 alle ,macchie ,solari    
,roma1 #afac4 #dto4    ,risp4 alle      
oppos4 del ,s4 ,lod4 delle ,colombe e   

del ,s4 ,vinc4 di ,grazia               
,firenze1 #afae4 #dto4    ,discorso     
delle ,comete di ,mario ,guiducci       
,firenze1 #afai4 #dto4    ,dialogo sopra
 i due ,massimi ,sistemi del ,mondo     
,firenze1 #afcb4 #dto4    ,discorso e   
,demostr4 intorno alle due nuove        
,scienze                                
,leida1 #afch4 #dto4    ,della ,scienza 
,meccanica                   ,ravenna1  
#afdi4 #dto4    ,trattato della ,sfera  
,roma1 #afee4 #dto4    ,discorso sopra  
il ,flusso e ,reflusso4 7,scienze       
,fisiche di ,tozzetti47                 
,firenze1 #aghj4 #dto4                  
,considerazioni sul ,tasso              
,roma1 #agic4    ,trattato della        
,fortificazione4 7,memorie di ,venturi47
                                        
,modena1 #ahah4 #dto4    ,the editions  
of his collected works 7in which is     
contained much that was  never published
 separately7 are--      ,opere di ,gal4 
,galilei1 ,linc4 ,nob4 ,fior4 c4        
,bologna1 #afef4 #b vols4 #dto4         

,opere di ,gal4 ,galilei1 ,nob4 ,fior4  
,accad4 ,linc4 c4                       
,firenze1 #agah4 #c vols4 #dto4         
,opere di ,gal4 ,galilei                
,padova1 #agdd4 #d vols4 #dto4    ,opere
 di ,gal4 ,galilei                      
,milano1 #ahaa4 #ac vols4 #hvo4         
,,corrections4      ,page ,co4 ,line4   
#e    #a   #b1        ,add3 ,his        
instructor was the celebrated botanist1 
,andreas        ,csalpinus1 who was     
professor of medicine at ,pisa from     
#aefg to #aeib4        ,hist4 ,acad4    
,pisan42 ,pisis1 #agia4        #h    #b 
#ah1        ,add3 ,according to ,kstner1
 his ,german name was ,wursteisen4      
#h    #b    #ba1 for #aehh read #aehf4  
#ae    #a    #eg1 for #afcb read #afcj4 
#ag    #a    #bi1        ,salusbury     
alludes to the instrument described and 
figured in ,the        ,use of the      
,sector1 ,crosse ,staffe1 and other     
,instruments4 ,london1        #afbd4 ,it
 is exactly ,galileo's ,compass4        
#ag    #a    #eb1 for ,burg1 a ,german1 

read ,burgi1 a ,swiss4     #bg    #b    
#ag1        ,the author here called     
,brutti was an ,englishman3 his real    
name1        perhaps1 was ,bruce4 ,see  
p4 #ii4       #ej    #a    #ad1         
,kepler's ,epitome was not published    
till #afai3 it was then inserted        
in the ,index4       #gc    #a    #fj1  
for under read turned from4     #hj     
#b    #dd1 for any read an indefinitely 
small4      ,,footnotes3    #agj ,the   
words of his diploma are3 ,galili in    
mathematicis disciplinis  discipulus1 in
 rumnis socius1 ,italicum ingenium ita  
perpolivit optimis  artibus ut inter    
mathematicos sculi nostri facile        
princeps per orbem  litterarium         
numeretur4--,tiraboschi4    #aga ,on    
this occasion the taste of the time     
showed itself in the  following         
anagram3--        ,evangelista          
,torricellieus1      ,en virescit       
,galilus alter4    #agb ,compare ,son4  
ii4 v4 #h  #i2 and ,son4 iii4 v4 #b  #c1
 with ,ger4 ,lib4  c4 iv4 st4 #gf1 and  

c4 vii4 st4 #ai4--,the author gladly    
owns his  obligation for these remarks  
to the kindness of ,sig4 ,panizzi1      
,professor  of ,italian in the          
,university of ,london4    #agc ,lettera
 di ,timauro ,antiate4 ,firenze1 #affc4 
#agd ,de phnomenis in orbe ,lun4        
,venetiis1 #afab4    #age ,venturi4     
#agf ,notizie sul ,ingrandimento delle  
,scienze ,fisiche4 ,firenze1 #aghj4     
#agg ,venturi4    #agh ,lettera di      
,timauro ,antiate4          ,,life ,,of 
,,kepler4          ,,chapter ,i4        
,introduction--,birth and ,education of 
,kepler--,he is appointed               
,astronomical ,professor at             
,gratz--,publishes the ',mysterium      
,cosmographicum4'      ,,in the account 
of the life and discoveries of ,galileo1
 we have  endeavoured to inculcate the  
safety and fruitfulness of the method   
followed by that great reformer in his  
search after physical truth4 ,as  his   
success furnishes the best instance of  
the value of the inductive  process1 so 

the failures and blunders of his        
adversaries supply equally  good        
examples of the dangers and the         
barrenness of the opposite course4  ,the
 history of ,,john ,,kepler might1 at   
the first view1 suggest conclusions     
somewhat inconsistent with this remark4 
,every one who is but moderately        
acquainted with astronomy is familiar   
with the discoveries which that  science
 owes to him2 the manner in which he    
made them is1 perhaps1 not  so generally
 known4 ,this extraordinary man pursued1
 almost invariably1  the hypothetical   
method4 ,his life was passed in         
speculating on the  results of a few    
principles assumed by him1 from very    
precarious  analogies1 as the causes of 
the phenomena actually observed in      
,nature4  ,we nevertheless find that he 
did1 in spite of this unphilosophical   
method1 arrive at discoveries which have
 served as guides to some of the  most  
valuable truths of modern science4      
,the difficulty will disappear if we    

attend more closely to the details  of  
,kepler's investigations4 ,we shall     
perceive that to an unusual degree  of  
rashness in the formation of his        
systems1 he added a quality very  rarely
 possessed by philosophers of the       
hypothetical school4 ,one of the        
greatest intellectual vices of the      
latter was a wilful blindness to the    
discrepancy of facts from their creed1 a
 perverse and obstinate  resistance to  
physical evidence1 leading not          
unfrequently to an attempt  at          
disguising the truth4 ,from this        
besetting sin of the school1 which  from
 an intellectual fault often degenerated
 into a moral one1 ,kepler  was         
absolutely free4 ,scheme after scheme1  
resting originally upon little  beyond  
his own glowing imagination1 but        
examined and endeared by the  ceaseless 
labour of years1 was unhesitatingly     
sacrificed1 as soon as its              
insufficiency became indisputable1 to   
make room for others as little          

deserving support4 ,the history of      
philosophy affords no more remarkable   
instance of sincere uncompromising love 
of truth4 ,to this virtue he owed  his  
great discoveries3 it must be attributed
 to his unhappy method that  he made no 
more4    ,in considering this opinion   
upon the real nature of ,kepler's title 
to  fame1 it ought not to be forgotten  
that he has exposed himself at a        
disadvantage on which certainly very few
 philosophers would venture4 ,his       
singular candour allowed him to comment 
upon his own errors with the  same      
freedom as if scrutinizing the work of a
 stranger2 careless whether  the        
impression on his readers were          
favourable or otherwise to himself1     
provided it was instructive4 ,few       
writers have spoken so much1 and so     
freely of themselves1 as ,kepler4 ,he   
records1 on almost every occasion1  the 
train of thought by which he was led to 
each of the discoveries that  eventually
 repaid his perseverance2 and he has    

thus given us a most  curious and       
interesting view of the workings of a   
mind of great1 though  eccentric power4 
,in what follows1 says he 7when         
introducing a long  string of           
suppositions1 of which he had already   
discovered the fallacy71  let the reader
 pardon my credulity1 whilst working out
 all these  matters by my own ingenuity4
 ,for it is my opinion that the         
occasions by  which men have acquired a 
knowledge of celestial phenomena are not
 less  admirable than the discoveries   
themselves4 ,agreeing altogether with   
this opinion in its widest application1 
we have not scrupled1 in the  following 
sketch1 to introduce at some length an  
account even of  ,kepler's erroneous    
speculations2 they are in themselves    
very amusing1  and will have the        
additional utility of proving the       
dangerous tendency  of his method2 they 
will show by how many absurd theories1  
and how many  years of wasted labour1   
his real discoveries and services to    

science lie  surrounded4    ,,john      
,,kepler was born 7as we are assured by 
his earliest biographer  ,hantsch7 in   
long4 #bi #g1 lat4 #dh #ed1 on the #bast
 day of ,december1  #aega4 ,on this spot
 stands the imperial city of ,weil1 in  
the duchy of  ,wirtemberg4 ,his parents 
were ,henry ,kepler and ,catherine      
,guldenmann1 both  of noble1 though     
decayed families4 ,henry ,kepler1 at the
 time of his  marriage1 was a petty     
officer in the ,duke of ,wirtemberg's   
service2 and a  few years after the     
birth of his eldest son ,john1 he joined
 the army  then serving in the          
,netherlands4 ,his wife followed him1   
leaving their  son1 then in his fifth   
year1 at ,leonberg1 under the care of   
his  grandfather4 ,he was a seven months
 child1 very weak and sickly2 and  after
 recovering with difficulty from a      
severe attack of small-pox1 he  was sent
 to school in #aegg4 ,henry ,kepler's   
limited income was still  farther       
reduced on his return into ,germany1 the

 following year1 in  consequence of the 
absconding of one of his acquaintance1  
for whom he  had incautiously become    
surety4 ,his circumstances were so much 
narrowed  by this misfortune1 that he   
was obliged to sell his house1 and      
nearly  all that he possessed1 and for  
several years he supported his family by
  keeping a tavern at ,elmendingen4     
,this occasioned great interruption to  
young ,kepler's education2 he was taken 
from school1 and employed in  menial    
services till his twelfth year1 when he 
was again placed in the  school at      
,elmendingen4 ,in the following year he 
was again seized with a  violent        
illness1 so that his life was almost    
despaired of4 ,in #aehf1 he  was        
admitted into the monastic school of    
,maulbronn1 where the cost of  his      
education was defrayed by the ,duke of  
,wirtemberg4 ,this school was  one of   
those established on the suppression of 
the monasteries at the  ,reformation1   
and the usual course of education       

followed there required  that the       
students1 after remaining a year in the 
superior classes1  should offer         
themselves for examination at the       
college of ,tubingen for  the degree of 
bachelor3 they then returned to their   
school with the  title of veterans2 and 
after completing the studies taught     
there1 they  were admitted as resident  
students at ,tubingen1 proceeded in     
about a  year to the degree of master1  
and were then allowed to commence their 
course of theology4 ,the three years of 
,kepler's life following his  admission 
to ,maulbronn1 were marked by periodical
 returns of several of  the disorders   
which had well nigh proved fatal to him 
in his childhood4  ,during the same time
 disagreements arose between his        
parents1 in  consequence of which his   
father quitted his home1 and soon after 
died  abroad4 ,after his father's       
departure1 his mother also quarrelled   
with  her relations1 having been        
treated1 says ,hantsch1 with a degree of

  barbarity by her husband and          
brother-in-law that was hardly exceeded 
even by her own perverseness3 one of his
 brothers died1 and the  family-affairs 
were in the greatest confusion4         
,notwithstanding these  disadvantages1  
,kepler took his degree of master in    
,august #aeia1  attaining the second    
place in the annual examination4 ,the   
first name on  the list was ,john       
,hippolytus ,brentius4    ,whilst he was
 thus engaged at ,tubingen1 the         
astronomical lectureship at  ,gratz1 the
 chief town of ,styria1 became vacant by
 the death of ,george  ,stadt1 and the  
situation was offered to ,kepler4 ,of   
this first occasion  of turning his     
thoughts towards astronomy1 he has      
himself given the  following account3   
,as soon as ,i was of an age to feel the
 charms of  philosophy1 ,i embraced     
every part of it with intense desire1   
but paid no  especial regard to         
astronomy4 ,i had indeed capacity enough
 for it1 and  learned without difficulty

 the geometrical and astronomical       
theorems  occurring in the usual course 
of the school1 being well grounded in   
figures1 numbers1 and proportions4 ,but 
those were compulsory  studies--there   
was nothing to show a particular turn   
for astronomy4 ,i  was educated at the  
expense of the ,duke of ,wirtemberg1 and
 when ,i saw  such of my companions as  
the duke selected to send abroad shrink 
in  various ways from their employments1
 out of fondness for home1 ,i1 who  was 
more callous1 had early made up my mind 
to go with the utmost  readiness        
whithersoever ,i might be sent4 ,the    
first offering itself was  an           
astronomical post1 which ,i was in fact 
forced to accept by the  authority of my
 tutors2 not that ,i was alarmed1 in the
 manner ,i had  condemned in others1 by 
the remoteness of the situation1 but by 
the  unexpected and contemptible nature 
of the office1 and by the slightness  of
 my information in this branch of       
philosophy4 ,i entered on it1           

therefore1 better furnished with talent 
than knowledge3 with many  protestations
 that ,i was not abandoning my claim to 
be provided for in  some other more     
brilliant profession4 ,what progress ,i 
made in the first  two years of my      
studies1 may be seen in my ',mysterium  
,cosmographicum2'  and the encouragement
 given me by my tutor1 ,mstlin1 to take 
up the  science of astronomy1 may be    
read in the same book1 and in his letter
  which is prefixed to the ',narrative  
of ,rheticus4' ,i looked on that        
discovery as of the highest importance1 
and still more so1 because ,i saw  how  
greatly it was approved by ,mstlin4     
,the nature of the singular work to     
which ,kepler thus refers with so much  
complacency1 will be best shown by      
quoting some of the most remarkable     
parts of it1 and especially the preface1
 in which he briefly details  some of   
the theories he successively examined   
and rejected1 before  detecting 7as he  
imagined he had here done7 the true     

cause of the number  and order of the   
heavenly bodies4 ,the other branches of 
philosophy with  which he occupied      
himself in his younger years1 were those
 treated by  ,scaliger in his ',exoteric
 ,exercises1' to the study of which book
 ,kepler  attributed the formation of   
many of his opinions2 and he tells us   
that  he devoted much time to the       
examination of the nature of heaven1 of 
souls1 of genii1 of the elements1 of the
 essence of fire1 of the cause  of      
fountains1 the ebb and flow of the tide1
 the shape of the continents1  and      
inland seas1 and things of this sort4   
,he also says1 that by his  first       
success with the heavens1 his hopes were
 greatly inflamed of  discovering       
similar analogies in the rest of the    
visible world1 and for  this reason1    
named his book merely a ,prodromus1 or  
,forerunner1 meaning1  at some future   
period1 to subjoin the ,aftercomer1 or  
,sequel4 ,but this  intention was never 
fulfilled2 either his imagination failed

 him1 or1  what is more likely1 the     
laborious calculations in which his     
astronomical theories engaged him1 left 
him little time for turning his         
attention to objects unconnected with   
his first pursuit4    ,it is seldom that
 we are admitted to trace the progress  
of thought in  those who have           
distinguished themselves by talent and  
originality2 and  although the whole of 
the following speculations begin and end
 in error1  yet they are so             
characteristic1 and exhibit such an     
extraordinary  picture of the           
extravagances into which ,kepler's      
lively imagination was  continually     
hurrying him1 that we cannot refrain    
from citing nearly the  whole preface4  
,from it1 better than from any          
enumeration of  peculiarities1 the      
reader will at once apprehend the nature
 of his  disposition4    ,when ,i was   
attending the celebrated ,mstlin1 six   
years ago1 at  ,tubingen1 ,i was        
disturbed by the manifold inconveniences

 of the common  theory of the universe1 
and so delighted with ,copernicus1 whom 
,mstlin  was frequently in the habit of 
quoting with great respect1 that ,i not 
only often defended his propositions in 
the physical disputations of the        
candidates1 but also wrote a correct    
essay on the primary motion1            
maintaining1 that it is caused by the   
rotation of the earth4 ,and ,i was  then
 at that point that ,i attributed to the
 earth the motion of the sun  on        
physical 7or1 if you will1 on           
metaphysical7 grounds1 as ,copernicus   
had done for mathematical reasons4 ,and1
 by this practice1 ,i came by  degrees1 
partly from ,mstlin's instructions1 and 
partly from my own  efforts1 to         
understand the superior mathematical    
convenience of the  system of           
,copernicus beyond ,ptolemy's4 ,this    
labour might have been  spared me1 by   
,joachim ,rheticus1 who has shortly and 
clearly explained  everything in his    
first ,narrative4 ,while incidentally   

engaged in these  labours1 in the       
intermission of my theology1 it happened
 conveniently  that ,i succeeded ,george
 ,stadt in his situation at ,gratz1     
where the  nature of my office connected
 me more closely with these studies4    
,everything ,i had learned from ,mstlin1
 or had acquired of myself1 was  there  
of great service to me in explaining the
 first elements of  astronomy4 ,and1 as 
in ,virgil1 ',fama mobilitate viget1    
viresque acquirit  eundo1' so it was    
with me1 that the diligent thought on   
these things  was the occasion of still 
further thinking3 until1 at last1 in the
 year  #aeie1 when ,i had some          
intermission of my lectures allowed me1 
,i brooded  with the whole energy of my 
mind on this subject4 ,there were three 
things in particular1 of which ,i       
pertinaciously sought the causes why    
they are not other than they are3 the   
number1 the size1 and the motion  of the
 orbits4 ,i attempted the thing at first
 with numbers1 and  considered whether  

one of the orbits might be double1      
triple1 quadruple1  or any other        
multiple of the others1 and how much1   
according to  ,copernicus1 each differed
 from the rest4 ,i spent a great deal of
 time in  that labour1 as if it were    
mere sport1 but could find no equality  
either  in the proportions or the       
differences1 and ,i gained nothing from 
this  beyond imprinting deeply in my    
memory the distances as assigned by     
,copernicus2 unless1 perhaps1 reader1   
this record of my various attempts  may 
force your assent1 backwards and        
forwards1 as the waves of the sea2      
until tired at length1 you will         
willingly repose yourself1 as in a safe 
haven1 on the reasons explained in this 
book4 ,however1 ,i was comforted  in    
some degree1 and my hopes of success    
were supported as well by other  reasons
 which will follow presently1 as by     
observing that the motions in  every    
case seemed to be connected with the    
distances1 and that where  there was a  

great gap between the orbits1 there was 
the same between the  motions4 ,and ,i  
reasoned1 that if ,god had adapted      
motions to the orbits  in some relation 
to the distances1 it was probable that  
he had also  arrayed the distances      
themselves in relation to something     
else4    ,finding no success by this    
method1 ,i tried another1 of singular   
audacity4 ,i inserted a new planet      
between ,mars and ,jupiter1 and another 
between ,venus and ,mercury1 both of    
which ,i supposed invisible1 perhaps  on
 account of their smallness1 and ,i     
attributed to each a certain period  of 
revolution4#agi ,i thought that ,i could
 thus contrive some equality  of        
proportions1 increasing between every   
two1 from the sun to the fixed  stars4  
,for instance1 the ,earth is nearer     
,venus in parts of the  terrestrial     
orbit1 than ,mars is to the ,earth in   
parts of the orbit of  ,mars4 ,but not  
even the interposition of a new planet  
sufficed for the  enormous gap between  

,mars and ,jupiter2 for the proportion  
of ,jupiter to  the new planet was still
 greater than that of ,saturn to        
,jupiter4 ,and  although1 by this       
supposition1 ,i got some sort of a      
proportion1 yet  there was no reasonable
 conclusion1 no certain determination of
 the  number of the planets either      
towards the fixed stars1 till we should 
get  as far as them1 nor ever towards   
the ,sun1 because the division in this  
proportion of the residuary space within
 ,mercury might be continued  without   
end4 ,nor could ,i form any conjecture1 
from the mobility of  particular        
numbers1 why1 among an infinite number1 
so few should be  moveable4 ,the opinion
 advanced by ,rheticus in his ,narrative
 is  improbable1 where he reasons from  
the sanctity of the number six to the   
number of the six moveable heavens2 for 
he who is inquiring of the frame  of the
 world itself1 must not derive reasons  
from these numbers1 which  have gained  
importance from things of later date4   

,i sought again1 in another way1 whether
 the distance of every planet is  not as
 the residuum of a sine2 and its motion 
as the residuum of the  sine of the     
complement in the same quadrant4        
,illustration    ,conceive the square   
,,ab to be constructed1 whose side ,,ac 
is equal to the  semidiameter of the    
universe4 ,from the angle ,b opposite to
 ,a the place  of the sun1 or centre of 
the world1 describe the quadrant ,,dc   
with the  radius ,,bc4 ,then in ,,ac1   
the true radius of the world1 let the   
sun1 fixed  stars1 and planets be marked
 at their respective distances1 and from
  these points draw lines parallel to   
,,bc1 meeting the quadrant4 ,i imagined 
the moving force acting on each of the  
planets to be in the proportion  of     
these parallels4 ,in the line of the sun
 is infinity1 because ,,ad is  touched1 
and not cut1 by the quadrant3 therefore 
the moving force is  infinite in the    
sun1 as deriving no motion except from  
its own act4 ,in  ,mercury the infinite 

line is cut off at ,k1 and therefore at 
this point  the motion is comparable    
with the others4 ,in the fixed stars the
 line is  altogether lost1 and          
compressed into a mere point ,c2        
therefore at that  point there is no    
moving force4 ,this was the theorem1    
which was to be  tried by calculation2  
but if any one will reflect that two    
things were  wanting to me1 first1 that 
,i did not know the size of the ,sinus  
,totus1  that is1 the radius of the     
proposed quadrant2 secondly1 that the   
energies of the motions were not thus   
expressed otherwise than in  relation   
one to another2 whoever1 ,i say1 well   
considers this1 will  doubt1 not without
 reason1 as to the progress ,i was      
likely to make in  this difficult       
course4 ,and yet1 with unremitting      
labour1 and an infinite  reciprocation  
of sines and arcs1 ,i did get so far as 
to be convinced  that this theory could 
not hold4    ,almost the whole summer   
was lost in these annoying labours2 at  

last1 by  a trifling accident1 ,i       
lighted more nearly on the truth4 ,i    
looked on it  as an interposition of    
,providence1 that ,i should obtain by   
chance1 what  ,i had failed to discover 
with my utmost exertions2 and ,i        
believed this  the more1 because ,i     
prayed constantly that ,i might succeed1
 if  ,copernicus had really spoken the  
truth4 ,it happened on the #ith or      
#aith#ahj day of ,july1 in the year     
#aeie1 that1 having occasion to show1   
in my lecture-room1 the passages of the 
great conjunctions through eight  signs1
 and how they pass gradually from one   
trine aspect to another1 ,i  inscribed  
in a circle a great number of triangles1
 or quasi-triangles1  so that the end of
 one was made the beginning of another4 
,in this manner  a smaller circle was   
shadowed out by the points in which the 
lines  crossed each other4              
,illustration3 ,a ,scheme of the great  
,conjunctions of ,,saturn  ,,jupiter1   
their leaps through eight ,signs1 and   

their passages through all the four     
,triplicities of the ,zodiac4    ,the   
radius of a circle inscribed in a       
triangle is half the radius of  that    
described about it2 therefore the       
proportion between these two  circles   
struck the eye as almost identical with 
that between ,saturn and  ,jupiter1 and 
the triangle is the first figure1 just  
as ,saturn and  ,jupiter are the first  
planets4 ,on the spot ,i tried the      
second distance  between ,jupiter and   
,mars with a square1 the third with a   
pentagon1 the  fourth with a hexagon4   
,and as the eye again cried out against 
the second  distance between ,jupiter   
and ,mars1 ,i combined the square with a
 triangle  and a pentagon4 ,there would 
be no end of mentioning every trial4    
,the  failure of this fruitless attempt 
was the beginning of the last  fortunate
 one2 for ,i reflected1 that in this way
 ,i should never reach  the sun1 if ,i  
wished to observe the same rule         
throughout2 nor should ,i  have any     

reason why there were six1 rather than  
twenty or a hundred  moveable orbits4   
,and yet figures pleased me1 as being   
quantities1 and as  having existed      
before the heavens2 for quantity was    
created with matter1  and the heavens   
afterwards4 ,but if 7this was the       
current of my  thoughts71 in relation to
 the quantity and proportion of the six 
orbits1  as ,copernicus has determined  
them among the infinite other figures1  
five  only could be found having        
peculiar properties above the rest1 my  
business would be done4 ,and then again 
it struck me1 what have plane  figures  
to do among solid orbits8 ,solid bodies 
ought rather to be  introduced4 ,this1  
reader1 is the invention and the whole  
substance of  this little work2 for if  
any one1 though but moderately skilled  
in  geometry1 should hear these words   
hinted1 the five regular solids will    
directly occur to him with the          
proportions of their circumscribed and  
inscribed spheres3 he has immediately   

before his eyes that scholium of        
,euclid to the #ahth proposition of his 
#acth ,book1 in which it is proved  to  
be impossible that there should be1 or  
be imagined1 more than five  regular    
bodies4    ,what is worthy of admiration
 7since ,i had then no proof of any     
prerogatives of the bodies with regard  
to their order7 is1 that  employing a   
conjecture which was far from being     
subtle1 derived from the  distances of  
the planets1 ,i should at once attain my
 end so happily in  arranging them1 that
 ,i was not able to change anything     
afterwards with  the utmost exercise of 
my reasoning powers4 ,in memory of the  
event1 ,i  write down here for you the  
sentence1 just as it fell from me1 and  
in  the words in which it was that      
moment conceived3--,the ,earth is the   
circle1 the measurer of all2 round it   
describe a dodecahedron1 the  circle    
including this will be ,mars4 ,round    
,mars describe a tetrahedron1  the      
circle including this will be ,jupiter4 

,describe a cube round  ,jupiter1 the   
circle including this will be ,saturn4  
,now1 inscribe in the  ,earth an        
icosahedron1 the circle inscribed in it 
will be ,venus4 ,inscribe  an octahedron
 in ,venus1 the circle inscribed in it  
will be ,mercury4 ,this  is the reason  
of the number of the planets4           
,illustration    ,this was the cause1   
and such the success1 of my labour3 now 
read my  propositions in this book4 ,the
 intense pleasure ,i have received from 
this discovery never can be told in     
words4 ,i regretted no more the time    
wasted2 ,i tired of no labour2 ,i       
shunned no toll of reckoning2 days and  
nights ,i spent in calculations2 until  
,i could see whether this opinion  would
 agree with the orbits of ,copernicus1  
or whether my joy was to  vanish into   
air4 ,i willingly subjoin that sentiment
 of ,archytas1 as  given by ,cicero3    
',if ,i could mount up into heaven1 and 
thoroughly  perceive the nature of the  
world1 and beauty of the stars1 that    

admiration would be without a charm for 
me1 unless ,i had some one like  you1   
reader1 candid1 attentive1 and eager for
 knowledge1 to whom to  describe it4'   
,if you acknowledge this feeling1 and   
are candid1 you will  refrain from      
blame1 such as not without cause ,i     
anticipate2 but if1  leaving that to    
itself1 you fear lest these things be   
not ascertained1  and that ,i have      
shouted triumph before victory1 at least
 approach these  pages1 and learn the   
matter in consideration3 you will not   
find1 as just  now1 new and unknown     
planets interposed2 that boldness of    
mine is not  approved1 but those old    
ones very little loosened1 and so       
furnished by  the interposition 7however
 absurd you may think it7 of rectilinear
  figures1 that in future you may give a
 reason to the rustics when they  ask   
for the hooks which keep the skies from 
falling4--,farewell4    ,in the third   
chapter ,kepler mentions1 that a        
thickness must be allowed  to each orb  

sufficient to include the greatest and  
least distance of  the planet from the  
sun4 ,the form and result of his        
comparison with the  real distances are 
as follows3--                           
,book ,v4    ,if the   ,saturn  be taken
 ,jupiter  #egg              #fce ,ch4  
#i    inner    ,jupiter at #ajjj  ,mars 
#ccc ,according to #ccc--ad    ,surface 
,mars    then the ,earth    #gie        
,copernicus   #geg--ai    of the        
,earth   outer    ,venus    #gie  they  
are    #gid--ba1 #bb    orbit of ,venus 
one of   ,mercury  #egg                 
#gbc--bg    ,it will be observed1 that  
,kepler's results were far from being   
entirely  satisfactory2 but he seems to 
have flattered himself1 that the        
differences might be attributed to      
erroneous measurements4 ,indeed1 the    
science of observation was then so much 
in its infancy1 that such an  assertion 
might be made without incurring much    
risk of decisive  refutation4    ,kepler
 next endeavoured to determine why the  

regular solids followed in  this rather 
than any other order2 and his           
imagination soon created a  variety of  
essential distinctions between the cube1
 pyramid1 and  dodecahedron1 belonging  
to the superior planets1 and the other  
two4    ,the next question examined in  
the book1 is the reason why the zodiac  
is  divided into #cfj degrees2 and on   
this subject1 he soon becomes enveloped 
in a variety of subtle considerations1  
7not very intelligible in the  original1
 and still more difficult to explain    
shortly to others  unacquainted with    
it17 in relation to the divisions of the
 musical  scale2 the origin of which he 
identifies with his five favourite      
solids4  ,the twentieth chapter is      
appropriated to a more interesting      
inquiry1  containing the first traces of
 his finally successful researches into 
the proportion between the distances of 
the planets1 and the times of  their    
motions round the sun4 ,he begins with  
the generally admitted fact1  that the  

more distant planets move more slowly2  
but in order to show  that the          
proportion1 whatever it may be1 is not  
the simple one of the  distances1 he    
exhibits the following little ,table3-- 
----------      ,d4 ,scr4               
-------------------     #ajgei4ab ,d4   
,scr4        ---------------------------
      #faei    #dccb4cg ,d4 ,scr4       
----------------------------------      
#aghe    #abhb     #fhf4ei ,d4 ,scr4    
----------------------------------------
-      #aagd     #hdc     #deb          
#cfe4ae ,d4 ,scr4                       
----------------------------------------
----------       #hdd     #fjf     #cbe 
#bfb4cj #bbd4db  ,d4 ,scr4              
----------------------------------------
----------       #dcd     #cab     #afg 
#ace    #aae      #hg4eh      ,at the   
head of each vertical column is placed  
the real time 7in days and  sexagesimal 
parts7 of the revolution of the planet  
placed above it1 and  underneath the    
days due to the other inferior planets1 

if they observed  the proportion of     
distance4 ,hence it appears that this   
proportion in  every case gives a time  
greater than the truth2 as for instance1
 if the  earth's rate of revolution were
 to ,jupiter's in the proportion of     
their  distances1 the second column     
shows that the time of her period would 
be  #hdc instead of #cfe days2 so of the
 rest4 ,his next attempt was to  compare
 them by two by two1 in which he found  
that he arrived at a  proportion        
something like the proportion of the    
distances1 although as  yet far from    
obtaining it exactly4 ,this process     
amounts to taking the  quotients        
obtained by dividing the period of each 
planet by the period  of the one next   
beyond4                                 
#ajgei4bg be successively taken to      
#djc                         #dccb4cg   
consist of #ajjj equal      #aei        
#fhf4ei   parts1 the planet next        
#ecb    ,for if each of the   #cfe4ae   
below will contain         #fae         

periods of           #bdd4db   of those 
parts in          #cib      ,but if the 
distance of each planet in      #egb    
succession be taken to consist of       
#bij      #ajjj equal parts1 the        
distance of        #feh      the next   
below will contain1 according   #gai    
to ,copernicus1 in                      
#ejj    ,from this table he argued that 
to make the proportions agree1 we must  
assume one of two things1 either that   
the moving intelligences of the  planets
 are weakest in those which are farthest
 from the ,sun1 or that  there is one   
moving intelligence in the ,sun1 the    
common centre forcing  them all round1  
but those most violently which are      
nearest1 and that it  languishes in some
 sort1 and grows weaker at the most     
distant1 because  of the remoteness and 
the attenuation of the virtue4    ,we   
stop here to insert a note added by     
,kepler to the later editions1 and      
shall take advantage of the same        
interruption to warn the reader not to  

confound this notion of ,kepler with the
 theory of a gravitating force  towards 
the ,sun1 in the sense in which we now  
use those words4 ,according  to our     
theory1 the effect of the presence of   
the ,sun upon the planet is  to pull it 
towards the centre in a straight line1  
and the effect of the  motion thus      
produced combined with the motion of the
 planet1 which if  undisturbed would be 
in a straight line inclined to the      
direction of the  radius1 is1 that it   
describes a curve round the ,sun4       
,kepler considered  his planets as      
perfectly quiet and unwilling to move   
when left alone2  and that this virtue  
supposed by him to proceed in every     
direction out  of the ,sun1 swept them  
round1 just as the sails of a windmill  
would  carry round anything which became
 entangled in them4 ,in other parts of  
his works ,kepler mentions having       
speculated on a real attractive force   
in the centre2 but as he knew that the  
planets are not always at the  same     

distance from the ,sun1 and conceived   
erroneously1 that to remove  them from  
their least to their greatest distance a
 repulsive force must  be supposed      
alternating with an attractive one1 he  
laid aside this  notion as improbable4  
,in a note he acknowledges that when he 
wrote the  passage just quoted1 imbued  
as he then was with ,scaliger's notions 
on  moving intelligences1 he literally  
believed that each planet was moved  by 
a living spirit1 but afterwards came to 
look on the moving cause as a  corporeal
 though immaterial substance1 something 
in the nature of light  which is        
observed to diminish similarly at       
increased distances4 ,he then  proceeds 
as follows in the original text4    ,let
 us then assume1 as is very probable1   
that motion is dispensed by  the sun in 
the same manner as light4 ,the          
proportion in which light  emanating    
from a centre is diminished1 is taught  
by optical writers3 for  there is the   
same quantity of light1 or of the solar 

rays1 in the small  circles as in the   
large2 and therefore1 as it is more     
condensed in the  former1 more          
attenuated in the latter1 a measure of  
the attenuation may  be derived from the
 proportion of the circles themselves1  
both in the  case of light and of the   
moving virtue4 ,therefore1 by how much  
the orbit  of ,venus is greater than    
that of ,mercury1 in the same proportion
 will  the motion of the latter be      
stronger1 or more hurried1 or more      
swift1 or  more powerful1 or by whatever
 other word you like to express the     
fact1  than that of the former4 ,but a  
larger orbit would require a            
proportionably longer time of           
revolution1 even though the moving force
  were the same4 ,hence it follows that 
the one cause of a greater distance  of 
the planet from the ,sun1 produces a    
double effect in increasing the  period1
 and conversely the increase of the     
periods will be double the  difference  
of the distances4 ,therefore1 half the  

increment added to the  shorter period  
ought to give the true proportion of the
 distances1 so  that the sum should     
represent the distance of the superior  
planet1 on  the same scale on which the 
shorter period represents the distance  
of  the interior one4 ,for instance1 the
 period of ,mercury is nearly #hh days2 
that of ,venus is #bbd1 the difference  
is #acf3 half of this is #fh1  which1   
added to #hh1 gives #aef4 ,the mean     
distance of ,venus ought1  therefore1 to
 be1 in proportion to that of ,mercury1 
as #aef to #hh4 ,if  this be done with  
all the planets1 we get the following   
results1 taking  successively1 as       
before1 the distance of each planet at  
#ajjj4      ,the distance in parts of   
which   #egd  ,but according  #egb      
the distance of the next         #bgd   
to ,copernicus  #bij    superior planet 
contains #ajjj1   #fid  they are        
#feh    is at                           
#gfb  respectively   #gai               
#efc                 #ejj    ,as you    

see1 we have now got nearer the truth4  
,finding that this theory of the rate of
 diminution would not bring him  quite  
close to the result he desired to find1 
,kepler immediately  imagined another4  
,this latter occasioned him a great deal
 of perplexity1  and affords another of 
the frequently recurring instances of   
the waste  of time and ingenuity        
occasioned by his impetuous and         
precipitate  temperament4 ,assuming the 
distance of any planet1 as for instance 
of  ,mars1 to be the unit of space1 and 
the virtue at that distance to be the   
unit of force1 he supposed that as many 
particles as the virtue at the  ,earth  
gained upon that of ,mars1 so many      
particles of distance did the  ,earth   
lose4 ,he endeavoured to determine the  
respective positions of the  planets    
upon this theory1 by the rules of false 
position1 but was much  astonished at   
finding the same exactly as on his      
former hypothesis4 ,the  fact was1 as he
 himself discovered1 although not until 

after several  years1 that he had become
 confused in his calculation2 and when  
half  through the process1 had retraced 
his steps so as of course to arrive     
again at the numbers from which he      
started1 and which he had taken from    
his former results4 ,this was the real  
secret of the identity of the two       
methods2 and if1 when he had taken the  
distance of ,mars at #ajjj1 instead  of 
assuming the distance of the earth at   
#fid1 as he did1 he had taken  any other
 number1 and operated upon it in the    
same manner1 he would  have had the same
 reason for relying on the accuracy of  
his supposition4  ,as it was1 the result
 utterly confounded him2 and he was     
obliged to  leave it with the remark1   
that the two theories are thus proved to
 be  the same in fact1 and only         
different in form2 although how that can
  possibly be1 ,i have never to this day
 been able to understand4--,his         
perplexity was very reasonable2 they are
 by no means the same2 it was  only his 

method of juggling with the figures     
which seemed to connect  them4          
,notwithstanding all its faults1 the    
genius and unwearied perseverance       
displayed by ,kepler in this book1      
immediately ranked him among            
astronomers of the first class2 and he  
received the most flattering  encomiums 
from many of the most celebrated2 among 
others1 from ,galileo  and ,tycho       
,brahe1 whose opinion he invited upon   
his performance4 ,galileo  contented    
himself with praising in general terms  
the ingenuity and good  faith which     
appeared so conspicuously in it4 ,tycho 
,brahe entered into a  more detailed    
criticism of the work1 and1 as ,kepler  
shrewdly remarked1  showed how highly he
 thought of it by advising him to try to
 adapt  something of the same kind to   
the ,tychonic system4 ,kepler also sent 
a  copy of his book to the imperial     
astronomer1 ,raimar1 with a             
complimentary letter1 in which he       
exalted him above all other  astronomers

 of the age4 ,raimar had surreptitiously
 acquired a notion of  ,tycho ,brahe's  
theory1 and published it as his own2 and
 ,tycho1 in his  letter1 complained of  
,kepler's extravagant flattery4 ,this   
drew a long  apologetical reply from    
,kepler1 in which he attributed the     
admiration he  had expressed of ,raimar 
to his own want of information at that  
time1  having since met with many things
 in ,euclid and ,regiomontanus1 which he
  then believed original in ,raimar4    
,with this explanation1 ,tycho professed
  himself perfectly satisfied4          
,,footnotes3    #agi ,the following     
scrupulous note added by ,kepler in     
#afba to a  subsequent edition of this  
work1 deserves to be quoted4 ,it shows  
how  entirely superior he was to the    
paltriness of attempting to appropriate 
the discoveries of others1 of which many
 of his contemporaries had  exhibited   
instances even on slighter pretences    
than this passage might  have afforded  
him4 ,the note is as follows3 ,not      

circulating round  ,jupiter like the    
,medican stars4 ,be not deceived4 ,i    
never had them in my  thoughts1 but1    
like the other primary planets1         
including the sun in the  centre of the 
system within their orbits4    #ahj     
,this inconvenient mode of dating was   
necessary before the new or  ,gregorian 
style was universally adopted4          
,,chapter ,,ii4        ,kepler's        
,marriage--,he joins ,tycho ,brahe at   
,prague--,is appointed        ,imperial 
,mathematician--,treatise on the ,new   
,star4      ,,the publication of this   
extraordinary book1 early as it occurs  
in the  history of ,kepler's life1 was  
yet preceded by his marriage4 ,he had   
contemplated this step so early as      
#aeib2 but that suit having been  broken
 off1 he paid his addresses1 in #aeif1  
to ,barbara ,muller von  ,muhleckh4     
,this lady was already a widow for the  
second time1 although  two years younger
 than ,kepler himself4 ,on occasion of  
this alliance he  was required to prove 

the nobility of his family1 and the     
delay  consequent upon the inquiry      
postponed the marriage till the         
following  year4 ,he soon became        
involved in difficulties in consequence 
of this  inconsiderate engagement3 his  
wife's fortune was less than he had been
  led to expect1 and he became embroiled
 on that account with her  relations4   
,still more serious inconvenience       
resulted to him from the  troubled state
 in which the province of ,styria was at
 that time1 arising  out of the disputes
 in ,bohemia and the two great religious
 parties into  which the empire was now 
divided1 the one headed by ,rodolph1 the
 feeble  minded emperor1--the other by  
,matthias1 his ambitious and            
enterprising  brother4    ,in the year  
following his marriage1 he thought it   
prudent1 on account of  some opinions he
 had unadvisedly promulgated1 7of what  
nature does not  very distinctly        
appear17 to withdraw himself from ,gratz
 into ,hungary4  ,thence he transmitted 

several short treatises to his friend   
,zehentmaier1  at ,tubingen--,on the    
,magnet1 ,on the ,cause of the          
,obliquity of the  ,ecliptic1 and ,on   
the ,divine ,wisdom1 as shown in the    
,creation4 ,little  is known of these   
works beyond the notice taken of them in
 ,zehentmaier's  answers4 ,kepler has   
himself told us1 that his magnetic      
philosophy was  built upon the          
investigations of ,gilbert1 of whom he  
always justly spoke  with the greatest  
respect4    ,about the same time a more 
violent persecution had driven ,tycho   
,brahe  from his observatory of         
,uraniburg1 in the little island of     
,hueen1 at the  entrance of the ,baltic4
 ,this had been bestowed on him by the  
munificence  of ,frederick ,i4 of       
,denmark1 who liberally furnished him   
with every means  of prosecuting his    
astronomical observations4 ,after       
,frederick's death1  ,tycho found       
himself unable to withstand the party   
which had constantly  opposed him1 and  

was forced1 at a great loss and much    
inconvenience1 to  quit his favourite   
island4 ,on the invitation of the       
emperor1 ,rudolph  ,,ii41 he then betook
 himself1 after a short stay at         
,hamburg1 to the  castle of ,benach1    
near ,prague1 which was assigned to him 
with an annual  pension of three        
thousand florins1 a truly munificent    
provision in those  times and that      
country4    ,kepler had been eager to   
see ,tycho ,brahe since the latter had  
intimated  that his observations had led
 him to a more accurate determination of
  the excentricities of the orbits of   
the planets4 ,by help of this1 ,kepler  
hoped that his theory might be made to  
accord more nearly with the  truth2 and 
on learning that ,tycho was in ,bohemia1
 he immediately set out  to visit him1  
and arrived at ,prague in ,january1     
#afjj4 ,from thence he  wrote a second  
letter to ,tycho1 not having received   
the answer to his  former apology1 again
 excusing himself for the part he had   

appeared to  take with ,raimar against  
him4 ,tycho replied immediately in the  
kindest  manner1 and begged he would    
repair to him directly3--,come not as a 
stranger1 but as a very welcome friend2 
come and share in my  observations with 
such instruments as ,i have with me1 and
 as a dearly  beloved associate4 ,during
 his stay of three or four months at    
,benach1  it was settled that ,tycho    
should apply to the emperor1 to procure 
him  the situation of assistant in the  
observatory4 ,kepler then returned to   
,gratz1 having previously received an   
intimation1 that he might do so in      
safety4 ,the plan1 as it had been       
arranged between them was1 that a       
letter should be procured from the      
emperor to the states of ,styria1       
requesting that ,kepler might join      
,tycho ,brahe for two years1 and retain 
his salary during that time3 a hundred  
florins were to be added annually  by   
the emperor1 on account of the greater  
dearness of living at ,prague4  ,but    

before everything was concluded1 ,kepler
 finally threw up his  situation at     
,gratz1 in consequence of new           
dissensions4 ,fearing that this  would  
utterly put an end to his hopes of      
connecting himself with ,tycho1  he     
determined to revive his claims on the  
patronage of the ,duke of  ,wirtemberg4 
,with this view he entered into         
correspondence with ,mstlin  and some of
 his other friends at ,tubingen1        
intending to prosecute his  medical     
studies1 and offer himself for the      
professorship of medicine in  that      
university4 ,he was dissuaded from this 
scheme by the pressing  instances of    
,tycho1 who undertook to exert himself  
in procuring a  permanent settlement for
 him from the emperor1 and assured him1 
even if  that attempt should fail1 that 
the language he had used when formerly  
inviting him to visit him at ,hamburg1  
should not be forgotten4 ,in            
consequence of this encouragement1      
,kepler abandoned his former scheme1    

and travelled again with his wife to    
,prague4 ,he was detained a long time   
on the road by violent illness1 and his 
money became entirely exhausted4  ,on   
this he wrote complainingly to ,tycho1  
that he was unable without  assistance  
to travel even the short distance which 
still separated them1  far less to await
 much longer the fulfilment of the      
promises held out to  him4    ,by his   
subsequent admissions1 it appears that  
for a considerable time he  lived       
entirely on ,tycho's bounty1 and by way 
of return1 he wrote an  essay against   
,raimar1 and against a ,scotchman named 
,liddell1 professor  at ,rostoch and    
,helmstadt1 who1 like ,raimar1 had      
appropriated to himself  the credit of  
the ,tychonic system4 ,kepler never     
adopted this theory1 and  indeed1 as the
 question merely regarded priority of   
invention1 there  could be no occasion1 
in the discussion1 for an examination of
 its  principles4    ,this was followed 
by a transaction1 not much to ,kepler's 

credit1 who in  the course of the       
following year1 and during a second     
absence from  ,prague1 fancied that he  
had some reason to complain of ,tycho's 
behaviour1 and wrote him a violent      
letter1 filled with reproaches and      
insults4 ,tycho appears to have behaved 
in this affair with great  moderation3  
professing to be himself occupied with  
the marriage of his  daughter1 he gave  
the care of replying to ,kepler's       
charges1 to ,ericksen1  one of his      
assistants1 who1 in a very kind and     
temperate letter1 pointed  out to him   
the ingratitude of his behaviour1 and   
the groundlessness of  his              
dissatisfaction4 ,his principal         
complaint seems to have been1 that      
,tycho had not sufficiently supplied his
 wife with money during his  absence4   
,ericksen's letter produced an immediate
 and entire change in  ,kepler's temper1
 and it is only from the humble         
recantation which he  instantaneously   
offered that we learn the extent of his 

previous  violence4 ,most noble ,tycho1 
these are the words of his letter1 how  
shall ,i enumerate or rightly estimate  
your benefits conferred on me6 ,for  two
 months you have liberally and          
gratuitously maintained me1 and my      
whole family2 you have provided for all 
my wishes2 you have done me  every      
possible kindness2 you have communicated
 to me everything you hold  most dear2  
no one1 by word or deed1 has            
intentionally injured me in  anything3  
in short1 not to your children1 your    
wife1 or yourself have  you shown more  
indulgence than to me4 ,this being so1  
as ,i am anxious to  put upon record1 ,i
 cannot reflect without consternation   
that ,i should  have been so given up by
 ,god to my own intemperance1 as to shut
 my eyes  on all these benefits2 that1  
instead of modest and respectful        
gratitude1  ,i should indulge for three 
weeks in continual moroseness towards   
all  your family1 in headlong passion1  
and the utmost insolence towards        

yourself1 who possess so many claims on 
my veneration from your noble  family1  
your extraordinary learning1 and        
distinguished reputation4  ,whatever ,i 
have said or written against the person1
 the fame1 the  honour1 and the learning
 of your excellency2 or whatever1 in any
 other  way1 ,i have injuriously spoken 
or written1 7if they admit no other more
  favourable interpretation17 as to my  
grief ,i have spoken and written  many  
things1 and more than ,i can remember2  
all and everything ,i recant1  and      
freely and honestly declare and profess 
to be groundless1 false1 and  incapable 
of proof4 ,hoffmann1 the president of   
the states of ,styria1  who had taken   
,kepler to ,prague on his first visit1  
exerted himself to  perfect the         
reconciliation1 and this hasty quarrel  
was entirely passed  over4    ,on       
,kepler's return to ,prague1 in         
,september1 #afja1 he was presented to  
the ,emperor by ,tycho1 and honoured    
with the title of ,imperial             

,mathematician1 on condition of         
assisting ,tycho in his calculations4   
,kepler desired nothing more than this  
condition1 since ,tycho was at that     
time probably the only person in the    
world who possessed observations        
sufficient for the reform which he now  
began to meditate in the theory  of     
astronomy4 ,rudolph appears to have     
valued both ,tycho ,brahe and ,kepler   
as astrologers rather than astronomers2 
but although unable to  appreciate      
rightly the importance of the task they 
undertook1 of  compiling a new set of   
astronomical tables founded upon        
,tycho's  observations1 yet his vanity  
was flattered with the prospect of his  
name  being connected with such a work1 
and he made liberal promises to defray  
the expense of the new ,rudolphine      
,tables4 ,tycho's principal assistant at
  this time was ,longomontanus1 who     
altered his name to this form1          
according to the prevalent fashion of   
giving to every name a ,latin           

termination4 ,lomborg or ,longbierg was 
the name1 not of his family1 but  of the
 village in ,denmark1 where he was born1
 just as ,mller was seldom  called by   
any other name than ,regiomontanus1 from
 his native town  ,knigsberg1 as ,george
 ,joachim ,rheticus was so surnamed from
 ,rhetia1 the  country of the ,grisons1 
and as ,kepler himself was sometimes    
called  ,leonmontanus1 from ,leonberg1  
where he passed his infancy4 ,it was    
agreed  between ,longomontanus and      
,kepler1 that in discussing ,tycho's    
observations1 the former should apply   
himself especially to the ,moon1  and   
the latter to ,mars1 on which planet1   
owing to its favourable  position1      
,tycho was then particularly engaged4   
,the nature of these  labours will be   
explained when we come to speak of the  
celebrated book  ,on the ,motions of    
,mars4    ,this arrangement was         
disturbed by the return of              
,longomontanus into  ,denmark1 where he 
had been offered an astronomical        

professorship1 and  still more by the   
sudden death of ,tycho ,brahe himself in
 the following  ,october4 ,kepler       
attended him during his illness1 and    
after his death  undertook to arrange   
some of his writings4 ,but1 in          
consequence of a  misunderstanding      
between him and ,tycho's family1 the    
manuscripts were  taken out of his      
hands2 and when1 soon afterwards1 the   
book appeared1  ,kepler complained      
heavily that they had published1 without
 his consent  or knowledge1 the notes   
and interlineations added by him for his
 own  private guidance whilst preparing 
it for publication4    ,on ,tycho's     
death1 ,kepler succeeded him as         
principal mathematician to the  emperor2
 but although he was thus nominally     
provided with a liberal  salary1 it was 
almost always in arrear4 ,the pecuniary 
embarrassments in  which he constantly  
found himself involved1 drove him to the
 resource of  gaining a livelihood by   
casting nativities4 ,his peculiar       

temperament  rendered him not averse    
from such speculations1 and he enjoyed  
considerable reputation in this line1   
and received ample remuneration  for his
 predictions4 ,but although he did not  
scruple1 when consulted1 to  avail      
himself in this manner of the credulity 
of his contemporaries1 he  passed over  
few occasions in his works of protesting
 against the  futility of this          
particular genethliac astrology4 ,his   
own astrological  creed was in a        
different strain1 more singular1 but not
 less  extravagant4 ,we shall defer     
entering into any details concerning it1
  till we come to treat of his book on  
,harmonics1 in which he has  collected  
and recapitulated the substance of his  
scattered opinions on  this strange     
subject4    ,his next works deserving   
notice are those published on occasion  
of the  new star which shone out with   
great splendour in #afjd1 in the        
constellation ,cassiopeia4#aha          
,immediately on its appearance1 ,kepler 

wrote a short account of it in ,german1 
marked with all the oddity which        
characterises most of his productions4  
,we shall see enough of his             
astronomical calculations when we come  
to his book on ,mars2 the  following    
passage will probably be found more     
amusing4    ,after comparing this star  
with that of #aegb1 and mentioning that 
many  persons who had seen it maintained
 this to be the brighter of the two1    
since it was nearly twice the size of   
its nearest neighbour1 ,jupiter1 he     
proceeds as follows3--,yonder one chose 
for its appearance a time no way        
remarkable1 and came into the world     
quite unexpectedly1 like an enemy       
storming a town1 and breaking into the  
market-place before the citizens  are   
aware of his approach2 but ours has come
 exactly in the year of  which          
astrologers have written so much about  
the fiery trigon that  happens in       
it2#ahb just in the month in which      
7according to ,cyprian7  ,mars comes up 

to a very perfect conjunction with the  
other two superior  planets2 just in the
 day when ,mars has joined ,jupiter1 and
 just in the  place where this          
conjunction has taken place4 ,therefore 
the apparition  of this star is not like
 a secret hostile irruption1 as was that
 one of  #aegb1 but the spectacle of a  
public triumph1 or the entry of a mighty
  potentate2 when the couriers ride in  
some time before1 to prepare his        
lodgings1 and the crowd of young urchins
 begin to think the time  over-long to  
wait3 then roll in1 one after another1  
the ammunition1 and  money1 and baggage 
waggons1 and presently the trampling of 
horse1 and  the rush of people from     
every side to the streets and windows2  
and when  the crowd have gazed with     
their jaws all agape at the troops of   
knights2  then at last1 the trumpeters1 
and archers1 and lackeys1 so distinguish
  the person of the monarch1 that there 
is no occasion to point him out1  but   
every one cries out of his own          

accord--',here we have him6'--,what it  
may portend is hard to determine1 and   
thus much only is certain1 that it      
comes to tell mankind either nothing at 
all1 or high and weighty news1  quite   
beyond human sense and understanding4   
,it will have an important  influence on
 political and social relations2 not    
indeed by its own  nature1 but1 as it   
were1 accidentally through the          
disposition of  mankind4 ,first1 it     
portends to the booksellers great       
disturbances1 and  tolerable gains2 for 
almost every ,theologus1 ,philosophicus1
  ,medicus1 and ,mathematicus1 or       
whoever else1 having no laborious       
occupation intrusted to him1 seeks his  
pleasure in studiis1 will make          
particular remarks upon it1 and will    
wish to bring these remarks to the      
light4 ,just so will others1 learned and
 unlearned1 wish to know its  meaning1  
and they will buy the authors who       
profess to tell them4 ,i  mention these 
things merely by way of example1        

because1 although thus  much can be     
easily predicted without great skill1   
yet may it happen just  as easily1 and  
in the same manner1 that the vulgar1 or 
whoever else is  of easy faith1 or it   
may be1 crazy1 may wish to exalt himself
 into a  great prophet2 or it may even  
happen that some powerful lord1 who has 
good foundation and beginning of great  
dignities1 will be cheered on by  this  
phenomenon to venture on some new       
scheme1 just as if ,god had set up  this
 star in the darkness merely to         
enlighten them4    ,it would hardly be  
supposed1 from the tenor of this last   
passage1 that  the writer of it was not 
a determined enemy to astrological      
predictions  of every description4 ,in  
#afjb he had published a disputation1   
not now  easily met with1 ,on the       
,principles of ,astrology1 in which it  
seems  that he treated the professed    
astrologers with great severity4 ,the   
essence of this book is probably        
contained in the second treatise on the 

new star1 which he published in         
#afjf4ahc ,in this volume he inveighs   
repeatedly against the vanity and       
worthlessness of ordinary astrology1    
declaring at the same time1 that the    
professors of that art know that  this  
judgment is pronounced by one well      
acquainted with its principles4  ,for if
 the vulgar are to pronounce who is the 
best astrologer1 my  reputation is known
 to be of the highest order2 if they    
prefer the  judgment of the learned1    
they are already condemned4 ,whether    
they stand  with me in the eyes of the  
populace1 or ,i fall with them before   
the  learned1 in both cases ,i am in    
their ranks2 ,i am on a level with them2
 ,i  cannot be renounced4    ,the theory
 which ,kepler proposed to substitute is
 intimated shortly in  the following    
passage3 ,i maintain that the colours   
and aspects1 and  conjunctions of the   
planets1 are impressed on the natures or
 faculties  of sublunary things1 and    
when they occur1 that these are excited 

as well  in forming as in moving the    
body over whose motion they preside4    
,now let  no one conceive a prejudice   
that ,i am anxiously seeking to mend the
  deplorable and hopeless cause of      
astrology by far-fetched subtilties and 
miserable quibbling4 ,i do not value it 
sufficiently1 nor have ,i ever  shunned 
having astrologers for my enemies4 ,but 
a most unfailing  experience 7as far as 
can be hoped in natural phenomena7 of   
the  excitement of sublunary natures by 
the conjunctions and aspects of the     
planets1 has instructed and compelled my
 unwilling belief4    ,after exhausting 
other topics suggested by this new star1
 he examines  the different opinions on 
the cause of its appearance4 ,among     
others he  mentions the ,epicurean      
notion1 that it was a fortuitous        
concourse of  atoms1 whose appearance in
 this form was merely one of the        
infinite  number of ways in which1 since
 the beginning of time1 they have been  
combined4 ,having descanted for some    

time on this opinion1 and declared      
himself altogether hostile to it1       
,kepler proceeds as follows3--,when ,i  
was a youth1 with plenty of idle time on
 my hands1 ,i was much taken with  the  
vanity1 of which some grown men are not 
ashamed1 of making anagrams1  by        
transposing the letters of my name1     
written in ,greek1 so as to make        
another sentence3 out of   ,i made      
2#ahd  in ,latin1 out of ,joannes       
,keplerus came ,serpens in akuleo4#ahe  
,but  not being satisfied with the      
meaning of these words1 and being unable
 to  make another1 ,i trusted the thing 
to chance1 and taking out of a pack of  
playing cards as many as there were     
letters in the name1 ,i wrote one  upon 
each1 and then began to shuffle them1   
and at each shuffle to read  them in the
 order they came1 to see if any meaning 
came of it4 ,now1 may  all the          
,epicurean gods and goddesses confound  
this same chance1 which1  although ,i   
spent a good deal of time over it1 never

 showed me anything  like sense even    
from a distance4#ahf ,so ,i gave up my  
cards to the  ,epicurean eternity1 to be
 carried away into infinity1 and1 it is 
said1  they are still flying about      
there1 in the utmost confusion among the
  atoms1 and have never yet come to any 
meaning4 ,i will tell these  disputants1
 my opponents1 not my own opinion1 but  
my wife's4 ,yesterday1  when weary with 
writing1 and my mind quite dusty with   
considering these  atoms1 ,i was called 
to supper1 and a salad ,i had asked for 
was set  before me4 ,it seems then1 said
 ,i aloud1 that if pewter dishes1 leaves
 of  lettuce1 grains of salt1 drops of  
water1 vinegar1 and oil1 and slices of  
egg1 had been flying about in the air   
from all eternity1 it might at  last    
happen by chance that there would come a
 salad4 ,yes1 says my wife1  but not so 
nice and well dressed as this of mine   
is4      ,,footnotes3    #aha ,see ,life
 of ,galileo1 p4 #af4    #ahb ,the fiery
 trigon occurs about once in every #hjj 

years1 when  ,saturn1 ,jupiter1 and     
,mars are in the three fiery signs1     
,aries1 ,leo1 and  ,sagittarius4    #ahc
 ,the copy of this work in the ,british 
,museum is ,kepler's  presentation copy 
to our ,james ,i4 ,on the blank leaf1   
opposite the  title-page1 is the        
following inscription1 apparently in the
 author's  hand-writing3--,regi         
philosophanti1 philosophus serviens1    
,platoni  ,diogenes1 ,britannias        
tenenti1 ,prag stipem mendicans ab      
,alexandro1 e  dolio conductitio1 hoc   
suum philosophema misit et commendavit4 
#ahd ,the tapster of the ,sirens4       
#ahe ,a serpent in his sting4    #ahf   
,in one of his anonymous writings       
,kepler has anagrammatized his  name1   
,joannes ,keplerus1 in a variety of     
other forms1 probably selected  from the
 luckiest of his shuffles3--,kleopas    
,herennius1 ,helenor  ,kapuensis1       
,raspinus ,enkeleo1 ,kanones ,pueriles4 
,,chapter ,,iii4        ,kepler         
publishes his ,supplement to            

,vitellion--,theory of                  
,refraction4      ,,during several years
 ,kepler remained1 as he himself        
forcibly expressed  it1 begging his     
bread from the emperor at ,prague1 and  
the splendour of  his nominal income    
served only to increase his irritation1 
at the real  neglect under which he     
nevertheless persevered in his labours4 
,his  family was increasing1 and he had 
little wherewith to support them  beyond
 the uncertain proceeds of his writings 
and nativities4 ,his salary  was charged
 partly on the states of ,silesia1      
partly on the imperial  treasury2 but it
 was in vain that repeated orders were  
procured for the  payment of the arrears
 due to him4 ,the resources of the      
empire were  drained by the constant    
demands of an engrossing war1 and       
,kepler had not  sufficient influence to
 enforce his claims against those who   
thought  even the smallest sum bestowed 
upon him ill spent1 in fostering        
profitless speculations4 ,in consequence

 of this niggardliness1 ,kepler  was    
forced to postpone the publication of   
the ,rudolphine ,tables1 which  he was  
engaged in constructing from his own and
 ,tycho ,brahe's  observations1 and     
applied himself to other works of a less
 costly  description4 ,among these may  
be mentioned a ,treatise on ,comets1    
written on occasion of one which        
appeared in #afjg3 in this he suggests  
that they are planets moving in straight
 lines4 ,the book published in  #afjd1  
which he entitles ,a ,supplement to     
,vitellion1 may be considered  as       
containing the first reasonable and     
consistent theory of optics1  especially
 in that branch of it usually termed    
dioptrics1 which relates  to the theory 
of vision through transparent           
substances4 ,in it was first  explained 
the true use of the different parts of  
the eye1 to the  knowledge of which     
,baptista ,porta had already approached 
very nearly1  though he stopped short of
 the accurate truth4 ,kepler remarked   

the  identity of the mechanism in the   
eye with that beautiful invention of    
,porta's1 the camera obscura2 showing1  
that the light which falls from         
external objects on the eye is refracted
 through a transparent  substance1      
called1 from its form and composition1  
the crystalline lens1  and makes a      
picture on the fine net-work of nerves1 
called the retina1  which lies at the   
back of the eye4 ,the manner in which   
the existence of  this coloured picture 
on the retina causes to the individual  
the  sensation of sight1 belongs to a   
theory not purely physical2 and beyond  
this point ,kepler did not attempt to   
go4    ,the direction into which rays of
 light 7as they are usually called7 are 
bent or refracted in passing through the
 air and other transparent  substances  
or mediums1 is discussed in this        
treatise at great length4  ,tycho ,brahe
 had been the first astronomer who      
recognized the necessity  of making some
 allowance on this account in the       

observed heights of the  stars4 ,a long 
controversy arose on this subject       
between ,tycho ,brahe and  ,rothman1 the
 astronomer at ,hesse ,cassel1 a man of 
unquestionable talent1  but of odd and  
eccentric habits4 ,neither was          
altogether in the right1  although      
,tycho had the advantage in the         
argument4 ,he failed however to         
establish the true law of refraction1   
and ,kepler has devoted a chapter  to an
 examination of the same question4 ,it  
is marked by precisely the  same        
qualities as those appearing so         
conspicuously in his astronomical       
writings3--great ingenuity2 wonderful   
perseverance2 bad philosophy4 ,that     
this may not be taken solely upon       
assertion1 some samples of it are       
subjoined4 ,the writings of the authors 
of this period are little read or  known
 at the present day2 and it is only by  
copious extracts that any  accurate     
notion can be formed of the nature and  
value of their labours4  ,the following 

tedious specimen of ,kepler's mode of   
examining physical  phenomena is        
advisedly selected to contrast with his 
astronomical  researches3 though the    
luck and consequently the fame that     
attended his  divination were widely    
different on the two occasions1 the     
method  pursued was the same4 ,after    
commenting on the points of difference  
between ,rothman and ,tycho ,brahe1     
,kepler proceeds to enumerate his own   
endeavours to discover the law of       
refraction4    ,i did not leave untried 
whether1 by assuming a horizontal       
refraction  according to the density of 
the medium1 the rest would correspond   
with  the sines of the distances from   
the vertical direction1 but calculation 
proved that it was not so3 and indeed   
there was no occasion to have  tried it1
 for thus the refractions would increase
 according to the same  law in all      
mediums1 which is contradicted by       
experiment4    ,the same kind of        
objection may be brought against the    

cause of  refraction alleged by ,alhazen
 and ,vitellion4 ,they say that the     
light  seeks to be compensated for the  
loss sustained at the oblique impact2 so
  that in proportion as it is enfeebled 
by striking against the denser  medium1 
in the same degree does it restore its  
energy by approaching the               
perpendicular1 that it may strike the   
bottom of the denser medium with        
greater force2 for those impacts are    
most forcible which are direct4 ,and    
they add some subtle notions1 ,i know   
not what1 how the motion of  obliquely  
incident light is compounded of a motion
 perpendicular and a  motion parallel to
 the dense surface1 and that this       
compound motion is  not destroyed1 but  
only retarded by meeting the denser     
medium4    ,illustration    ,i tried    
another way of measuring the refraction1
 which should include  the density of   
the medium and the incidence3 for1 since
 a denser medium  is the cause of       
refraction1 it seems to be the same     

thing as if we were  to prolong the     
depth of the medium in which the rays   
are refracted into  as much space as    
would be filled by the denser medium    
under the force of  the rarer one4      
,let ,a be the place of the light1 ,,bc 
the surface of the denser medium1  ,,de 
its bottom4 ,let ,,ab1 ,,ag1 ,,af be    
rays falling obliquely1 which would     
arrive at ,d1 ,i1 ,h1 if the medium were
 uniform4 ,but because it is denser1    
suppose the bottom to be depressed to   
,,kl1 determined by this that there  is 
as much of the denser matter contained  
in the space ,,dc as of the  rarer in   
,,lc3 and thus1 on the sinking of the   
whole bottom ,,de1 the points  ,d1 ,i1  
,h1 ,e will descend vertically to ,l1   
,m1 ,n1 ,k4 ,join the points ,,bl1      
,,gm1 ,,fn1 cutting ,,de in ,o1 ,p1 ,q2 
the refracted rays will be ,,abo1 ,,agp1
  ,,afq4--,this method is refuted by    
experiment2 it gives the refractions    
near the perpendicular ,,ac too great in
 respect of those near the  horizon4    

,whoever has leisure may verify this1   
either by calculation or  compasses4 ,it
 may be added that the reasoning itself 
is not very  sure-footed1 and1 whilst   
seeking to measure other things1        
scarcely takes  in and comprehends      
itself4 ,this reflection must not be    
mistaken for the  dawn of suspicion that
 his examination of philosophical       
questions began  not altogether at the  
right end3 it is merely an              
acknowledgment that he  had not yet     
contrived a theory with which he was    
quite satisfied before  it was disproved
 by experiment4    ,after some          
experience of ,kepler's miraculous good 
fortune in seizing  truths across the   
wildest and most absurd theories1 it is 
not easy to  keep clear of the opposite 
feeling of surprise whenever any of his 
extravagancies fail to discover to him  
some beautiful law of nature4 ,but  we  
must follow him as he plunges deeper in 
this unsuccessful inquiry2  and the     
reader must remember1 in order fully to 

appreciate this method  of              
philosophizing1 that it is almost       
certain that ,kepler laboured upon      
every one of the gratuitous suppositions
 that he makes1 until positive          
experiment satisfied him of their       
incorrectness4    ,i go on to other     
methods4 ,since density is clearly      
connected with the  cause of the        
refractions1 and refraction itself seems
 a kind of  compression of light1 as it 
were1 towards the perpendicular1 it     
occurred  to me to examine whether there
 was the same proportion between the    
mediums in respect of density and the   
parts of the bottom illuminated by  the 
light1 when let into a vessel1 first    
empty1 and afterwards filled  with      
water4 ,this mode branches out into     
many3 for the proportion may be         
imagined1 either in the straight lines1 
as if one should say that the  line     
,,eq1 illuminated by refraction1 is to  
,,eh illuminated directly1 as  the      
density of the one medium is to that of 

the other--,or another may  suppose the 
proportion to be between ,,fc and       
,,fh--,or it may be conceived  to exist 
among surfaces1 or so that some power of
 ,,eq should be to some  power of ,,eh  
in this proportion1 or the circles or   
similar figures  described on them4 ,in 
this manner the proportion of ,,eq to   
,,ep would be  double that of ,,eh to   
,,ei--,or the proportion may be         
conceived existing  among the solidities
 of the pyramidal frustums ,,fhec1      
,,fqec--,or1 since the  proportion of   
the mediums involves a threefold        
consideration1 since they  have density 
in length1 breadth1 and thickness1 ,i   
proceeded also to  examine the cubic    
proportions among the lines ,,eq1 ,,eh4 
,i also considered other lines4 ,from   
any of the points of refraction as  ,g1 
let a perpendicular ,,gy be dropped upon
 the bottom4 ,it may become a  question 
whether possibly the triangle ,,igy1    
that is1 the base ,,iy1 is  divided by  
the refracted ray ,,gp1 in the          

proportion of the densities of  the     
mediums4    ,i have put all these       
methods here together1 because the same 
remark  disproves them all4 ,for1 in    
whatever manner1 whether as line1 plane1
 or  pyramid1 ,,ei observes a given     
proportion to ,,ep1 or the abbreviated  
line  ,,yi to ,,yp1 namely1 the         
proportion of the mediums1 it is sure   
that ,,ei1 the  tangent of the distance 
of the point ,a from the vertex1 will   
become  infinite1 and will1 therefore   
make ,,ep or ,,yp1 also infinite4       
,therefore1  ,,igp1 the angle of        
refraction1 will be entirely lost2 and1 
as it  approaches the horizon1 will     
gradually become less and less1 which is
  contrary to experiment4    ,i tried   
again whether the images are equally    
removed from their points  of           
refraction1 and whether the ratio of the
 densities measures the least  distance4
 ,for instance1 supposing ,e to be the  
image1 ,c the surface of  the water1 ,k 
the bottom1 and ,,ce to ,,ck in the     

proportion of the densities  of the     
mediums4 ,now1 let ,f1 ,g1 ,b1 be three 
other points of refraction  and images  
at ,s1 ,t1 ,v1 and let ,,ce be equal to 
,,fs1 ,,gt1 and ,,bv4 ,but  according to
 this rule an image ,e would still be   
somewhat raised in the  perpendicular   
,,ak1 which is contrary to experiment1  
not to mention other  contradictions4   
,thirdly1 whether the proportion of the 
mediums holds  between ,,fh and ,,fx1   
supposing ,h to be the place of the     
image8 ,not at all4  ,for so1 ,,ce would
 be in the same proportion to ,,ck1 so  
that the height of  the image would     
always be the same1 which we have just  
refuted4  ,fourthly1 whether the raising
 of the image at ,e is to the raising at
 ,h1  as ,,ce to ,,fh8 ,not in the      
least2 for so the images either would   
never  begin to be raised1 or1 having   
once begun1 would at last be infinitely 
raised1 because ,,fh at last becomes    
infinite4 ,fifthly1 whether the images  
rise in proportion to the sines of the  

inclinations8 ,not at all2 for so  the  
proportion of ascent would be the same  
in all mediums4 ,sixthly1 are  then the 
images raised at first1 and in          
perpendicular radiation1  according to  
the proportion of the mediums1 and do   
they subsequently  rise more and more   
according to the sines of the           
inclinations8 ,for so  the proportion   
would be compound1 and would become     
different in  different mediums4 ,there 
is nothing in it3 for the calculation   
disagreed  with experiment4 ,and        
generally it is in vain to have regard  
to the image  or the place of the image1
 for that very reason1 that it is       
imaginary4  ,for there is no connexion  
between the density of the medium or any
 real  quality or refraction of the     
light1 and an accident of vision1 by an 
error of which the image happens4    ,up
 to this point1 therefore1 ,i had       
followed a nearly blind mode of         
inquiry1 and had trusted to good        
fortune2 but now ,i opened the other    

eye1 and hit upon a sure method1 for ,i 
pondered the fact1 that the image  of a 
thing seen under water approaches       
closely to the true ratio of the        
refraction1 and almost measures it2 that
 it is low if the thing is  viewed      
directly from above2 that by degrees it 
rises as the eye passes  towards the    
horizon of the water4 ,yet1 on the other
 hand1 the reason  alleged above1 proves
 that the measure is not to be sought in
 the image1  because the image is not a 
thing actually existing1 but arises from
 a  deception of vision which is purely 
accidental4 ,by a comparison of these   
conflicting arguments1 it occurred to me
 at length1 to seek the causes          
themselves of the existence of the image
 under water1 and in these  causes the  
measure of the refractions4 ,this       
opinion was strengthened in  me by      
seeing that opticians had not rightly   
pointed out the cause of the  image     
which appears both in mirrors and in    
water4 ,and this was the  origin of that

 labour which ,i undertook in the third 
chapter4 ,nor1  indeed1 was that labour 
trifling1 whilst hunting down false     
opinions of  all sorts among the        
principles1 in a matter rendered so     
intricate by the  false traditions of   
optical writers2 whilst striking out    
half a dozen  different paths1 and      
beginning anew the whole business4 ,how 
often did it  happen that a rash        
confidence made me look upon that which 
,i sought with  such ardour1 as at      
length discovered6    ,at length ,i cut 
this worse than ,gordian knot of        
catoptrics by analogy  alone1 by        
considering what happens in mirrors1 and
 what must happen  analogically in      
water4 ,in mirrors1 the image appears at
 a distance from  the real place of the 
object1 not being itself material1 but  
produced  solely by reflection at the   
polished surface4 ,whence it followed in
  water also1 that the images rise and  
approach the surface1 not according  to 
the law of the greater or less density  

in the water1 as the view is  less or   
more oblique1 but solely because of the 
refraction of the ray of  light passing 
from the object to the eye4 ,on which   
assumption1 it is  plain that every     
attempt ,i had hitherto made to measure 
refractions by  the image1 and its      
elevation1 must fall to the ground4 ,and
 this became  more evident when ,i      
discovered the true reason why the image
 is in the  same perpendicular line with
 the object both in mirrors and in dense
  mediums4 ,when ,i had succeeded thus  
far by analogy in this most difficult   
investigation1 as to the place of the   
image1 ,i began to follow out the       
analogy further1 led on by the strong   
desire of measuring refraction4  ,for ,i
 wished to get hold of some measure of  
some sort1 no matter how  blindly1      
having no fear but that so soon as the  
measure should be  accurately known1 the
 cause would plainly appear4 ,i went to 
work as  follows4 ,in convex mirrors the
 image is diminished1 and just so in    

rarer  mediums2 in denser mediums it is 
magnified1 as in concave mirrors4 ,in   
convex mirrors the central parts of the 
image approach1 and recede in  concave  
farther than towards the circumference2 
the same thing happens  in different    
mediums1 so that in water the bottom    
appears depressed1 and  the surrounding 
parts elevated4 ,hence it appears that a
 denser medium  corresponds with a      
concave reflecting surface1 and a rarer 
one with a  convex one3 it was clear1 at
 the same time1 that the plane surface  
of  the water affects a property of     
curvature4 ,i was1 therefore1 to        
excogitate causes consistent with its   
having this effect of curvature1  and to
 see if a reason could be given1 why the
 parts of the water  surrounding the    
incident perpendicular should represent 
a greater  density than the parts just  
under the perpendicular4 ,and so the    
thing  came round again to my former    
attempts1 which being refuted by reason 
and experiment1 ,i was forced to abandon

 the search after a cause4 ,i then      
proceeded to measurements4    ,kepler   
then endeavoured to connect his         
measurements of different  quantities of
 refraction with the conic sections1 and
 was tolerably well  pleased with some  
of his results4 ,they were however not  
entirely  satisfactory1 on which he     
breaks off with the following sentence3 
,now1  reader1 you and ,i have been     
detained sufficiently long whilst ,i    
have  been attempting to collect into   
one faggot the measure of different     
refractions3 ,i acknowledge that the    
cause cannot be connected with this     
mode of measurement3 for what is there  
in common between refractions  made at  
the plane surfaces of transparent       
mediums1 and mixtilinear conic          
sections8 ,wherefore1 quod ,deus bene   
vortat1 we will now have had  enough of 
the causes of this measure2 and         
although1 even now1 we are  perhaps     
erring something from the truth1 yet it 
is better1 by working  on1 to show our  

industry1 than our laziness by neglect4 
,notwithstanding the great length of    
this extract1 we must add the           
concluding paragraph of the ,chapter1   
directed1 as we are told in the  margin1
 against the ,tychonomasticks3--    ,i  
know how many blind men at this day     
dispute about colours1 and how  they    
long for some one to give some          
assistance by argument to their rash    
insults of ,tycho1 and attacks upon this
 whole matter of refractions2  who1 if  
they had kept to themselves their       
puerile errors and naked  ignorance1    
might have escaped censure2 for that may
 happen to many great  men4 ,but since  
they venture forth publicly1 and with   
thick books and  sounding titles1 lay   
baits for the applause of the unwary1   
7for  now-a-days there is more danger   
from the abundance of bad books1 than   
heretofore from the lack of good ones17 
therefore let them know that a  time is 
set for them publicly to amend their own
 errors4 ,if they longer  delay doing   

this1 it shall be open1 either to me or 
any other1 to do to  these unhappy      
meddlers in geometry as they have taken 
upon themselves to  do with respect to  
men of the highest reputation4 ,and     
although this  labour will be           
despicable1 from the vile nature of the 
follies against  which it will be       
directed1 yet so much more necessary    
than that which  they have undertaken   
against others1 as he is a greater      
public nuisance1  who endeavours to     
slander good and necessary inventions1  
than he who  fancies he has found what  
is impossible to discover4 ,meanwhile1  
let them  cease to plume themselves on  
the silence which is another word for   
their  own obscurity4    ,although      
,kepler failed1 as we have seen1 to     
detect the true law of  refraction1     
7which was discovered some years later  
by ,willibrord ,snell1  a ,flemish      
mathematician17 there are many things   
well deserving notice in  his           
investigations4 ,he remarked1 that the  

quantity of refraction would  alter1 if 
the height of the atmosphere should     
vary2 and also1 that it  would be       
different at different temperatures4    
,both these sources of  variation are   
now constantly taken into account1 the  
barometer and  thermometer giving exact 
indications of these changes4 ,there is 
also a  very curious passage in one of  
his letters to ,bregger1 written in     
#afje1  on the subject of the colours in
 the rainbow4 ,it is in these           
words3--,since every one sees a         
different rainbow1 it is possible that  
some one may see a rainbow in the very  
place of my sight4 ,in this case1  the  
medium is coloured at the place of my   
vision1 to which the solar ray  comes to
 me through water1 rain1 or aqueous     
vapours4 ,for the rainbow is  seen when 
the sun is shining between rain1 that is
 to say1 when the sun  also is visible4 
,why then do ,i not see the sun green1  
yellow1 red1 and  blue1 if vision takes 
place according to the mode of          

illumination8 ,i  will say something for
 you to attack or examine4 ,the sun's   
rays are not  coloured1 except with a   
definite quantity of refraction4        
,whether you are  in the optical        
chamber1 or standing opposite glass     
globes1 or walking in  the morning dew1 
everywhere it is obvious that a certain 
and definite  angle is observed1 under  
which1 when seen in dew1 in glass1 in   
water1  the sun's splendour appears     
coloured1 and under no other angle4     
,there is  no colouring by mere         
reflexion1 without the refraction of a  
denser  medium4 ,how closely does       
,kepler appear1 in this passage1 to     
approach  the discovery which forms not 
the least part of ,newton's fame6    ,we
 also find in this work a defence of the
 opinion that the planets are  luminous 
of themselves2 on the ground that the   
inferior planets would1  on the contrary
 supposition1 display phases like those 
of the moon when  passing between us and
 the sun4 ,the use of the telescope was 

not then  known2 and1 when some years   
later the form of the disk of the       
planets  was more clearly defined with  
their assistance1 ,kepler had the       
satisfaction of finding his assertions  
verified by the discoveries of          
,galileo1 that these changes do actually
 take place4 ,in another of his         
speculations1 connected with the same   
subject1 he was less fortunate4 ,in     
#afjg a black spot appeared on the face 
of sun1 such as may almost always  be   
seen with the assistance of the         
telescope1 although they are seldom     
large enough to be visible to the       
unassisted eye4 ,kepler saw it for a    
short time1 and mistook it for the      
planet ,mercury1 and with his usual     
precipitancy hastened to publish an     
account of his observation of this  rare
 phenomenon4 ,a few years later1        
,galileo discovered with his glasses1  a
 great number of similar spots2 and     
,kepler immediately retracted the       
opinion announced in his treatise1 and  

acknowledged his belief that  previous  
accounts of the same occurrence which he
 had seen in old  authors1 and which he 
had found great difficulty in           
reconciling with his  more accurate     
knowledge of the motions of ,mercury1   
were to be referred  to a like mistake4 
,on this occasion of the invention of   
the telescope1  ,kepler's candour and   
real love of truth appeared in a most   
favourable  light4 ,disregarding        
entirely the disagreeable necessity1 in 
consequence  of the discoveries of this 
new instrument1 of retracting several   
opinions which he had maintained with   
considerable warmth1 he ranged  himself 
at once on the side of ,galileo1 in     
opposition to the bitter and  determined
 hostility evinced by most of those     
whose theories were  endangered by the  
new views thus offered of the heavens4  
,kepler's  quarrel with his pupil1      
,horky1 on this account1 has been       
mentioned in  the ,life of ,galileo2 and
 this is only a selected instance from  

the  numerous occasions on which he     
espoused the same unpopular side of the 
argument4 ,he published a dissertation  
to accompany ,galileo's  ,intelligencer 
of the ,stars1 in which he warmly       
expressed his  admiration of that       
illustrious inquirer into nature4 ,his  
conduct in this  respect was the more   
remarkable1 as some of his most intimate
 friends  had taken a very opposite view
 of ,galileo's merit1 and seem to have  
laboured much to disturb their mutual   
regard2 ,mstlin especially1  ,kepler's  
early instructor1 seldom mentioned to   
him the name of ,galileo1  without some 
contemptuous expression of dislike4     
,these statements have  rather disturbed
 the chronological order of the account 
of ,kepler's  works4 ,we now return to  
the year #afji1 in which he published   
his great  and extraordinary book1 ,on  
the ,motions of ,mars2 a work which     
holds the  intermediate place1 and is in
 truth the connecting link1 between the 
discoveries of ,copernicus and ,newton4 

,,chapter ,,iv4        ,sketch of the   
,astronomical ,theories before ,kepler4 
,,kepler had begun to labour upon these 
commentaries from the moment when  he   
first made ,tycho's acquaintance2 and it
 is on this work that his  reputation   
should be made mainly to rest4 ,it is   
marked in many places  with his         
characteristic precipitancy1 and indeed 
one of the most  important discoveries  
announced in it 7famous among           
astronomers by the  name of the ,equable
 ,description of ,areas7 was blundered  
upon by a lucky  compensation of errors1
 of the nature of which ,kepler remained
 ignorant  to the very last4 ,yet there 
is more of the inductive method in this 
than  in any of his other publications2 
and the unwearied perseverance with     
which he exhausted years in hunting down
 his often renewed theories1  till at   
length he seemed to arrive at the true  
one1 almost by having  previously       
disproved every other1 excites a feeling
 of astonishment  nearly approaching to 

awe4 ,it is wonderful how he contrived  
to retain  his vivacity and creative    
fancy amongst the clouds of figures     
which he  conjured up round him2 for the
 slightest hint or shade of probability 
was sufficient to plunge him into the   
midst of the most laborious             
computations4 ,he was by no means an    
accurate calculator1 according to  the  
following character which he has given  
of himself3--,something of  these delays
 must be attributed to my own temper1   
for non omnia  possumus omnes1 and ,i am
 totally unable to observe any order2   
what ,i do  suddenly1 ,i do confusedly1 
and if ,i produce any thing well        
arranged1 it  has been done ten times   
over4 ,sometimes an error of calculation
  committed by hurry1 delays me a great 
length of time4 ,i could indeed  publish
 an infinity of things1 for though my   
reading is confined1 my  imagination is 
abundant1 but ,i grow dissatisfied with 
such confusion3 ,i  get disgusted and   
out of humour1 and either throw them    

away1 or put them  aside to be looked at
 again2 or1 in other words1 to be       
written again1  for that is generally   
the end of it4 ,i entreat you1 my       
friends1 not to  condemn me for ever to 
grind in the mill of mathematical       
calculations3  allow me some time for   
philosophical speculations1 my only     
delight4    ,he was very seldom able to 
afford the expense of maintaining an    
assistant1 and was forced to go through 
most of the drudgery of his             
calculations by himself2 and the most   
confirmed and merest arithmetician      
could not have toiled more doggedly than
 ,kepler did in the work of which  we   
are about to speak4    ,in order that   
the language of his astronomy may be    
understood1 it is  necessary to mention 
briefly some of the older theories4     
,when it had  been discovered that the  
planets did not move regularly round the
 earth1  which was supposed to be fixed 
in the centre of the world1 a mechanism 
was contrived by which it was thought   

that the apparent irregularity  could be
 represented1 and yet the principle of  
uniform motion1 which was  adhered to   
with superstitious reverence1 might be  
preserved4 ,this1 in  its simplest form1
 consisted in supposing the planet to   
move uniformly  in a small circle1      
called an epicycle1 the centre of which 
moved with  an equal angular motion in  
the opposite direction round the        
earth4#ahg  ,the circle ,dd1 described  
by ,d1 the centre of the epicycle1 was  
called  the deferent4 ,for instance1 if 
the planet was supposed to be at ,a when
  the centre of the epicycle was at ,d1 
its position1 when the centre of  the   
epicycle had removed to d1 would be at  
p1 found by drawing dp  parallel to     
,,da4 ,thus1 the angle adp1 measuring   
the motion of the  planet in its        
epicycle1 would be equal to ,,ded1 the  
angle described by  the centre of the   
epicycle in the deferent4 ,the angle    
p,ed between  ,ep1 the direction in     
which a planet so moving would be seen  

from the  earth1 supposed to be at ,e1  
and ,ed the direction in which it would 
have been seen had it been moving in the
 centre of the deferent1 was  called the
 equation of the orbit1 the word        
equation1 in the language of  astronomy1
 signifying what must be added or taken 
from an irregularly  varying quantity to
 make it vary uniformly4                
,illustration    ,as the accuracy of    
observations increased1 minor           
irregularities were  discovered1 which  
were attempted to be accounted for by   
making a second  deferent of the        
epicycle1 and making the centre of a    
second epicycle  revolve in the         
circumference of the first1 and so on1  
or else by  supposing the revolution in 
the epicycle not to be completed in     
exactly  the time in which its centre is
 carried round the deferent4 ,hipparchus
  was the first to make a remark by     
which the geometrical representation  of
 these inequalities was considerably    
simplified4 ,in fact1 if ,,ec be  taken 

equal to pd1 ,cd will be a              
parallelogram1 and consequently  ,cp    
equal to ,ed1 so that the machinery of  
the first deferent and  epicycle amounts
 to supposing that the planet revolves  
uniformly in a  circle round the point  
,c1 not coincident with the place of the
 earth4  ,this was consequently called  
the excentric theory1 in opposition to  
the  former or concentric one1 and was  
received as a great improvement4 ,as    
the point d is not represented by this  
construction1 the equation to  the orbit
 was measured by the angle ,cp,e1 which 
is equal to p,ed4 ,it  is not necessary 
to give any account of the manner in    
which the old  astronomers determined   
the magnitudes and positions of these   
orbits1  either in the concentric or    
excentric theory1 the present object    
being  little more than to explain the  
meaning of the terms it will be         
necessary to use in describing ,kepler's
 investigations4    ,to explain the     
irregularities observed in the other    

planets1 it became  necessary to        
introduce another hypothesis1 in        
adopting which the  severity of the     
principle of uniform motion was somewhat
 relaxed4 ,the  machinery consisted     
partly of an excentric deferent round   
,e1 the earth1  and on it an epicycle1  
in which the planet revolved uniformly2 
but the  centre of the epicycle1 instead
 of revolving uniformly round ,c1 the   
centre of the deferent1 as it had       
hitherto been made to do1 was  supposed 
to move in its circumference with an    
uniform angular motion  round a third   
point1 ,q2 the necessary effect of which
 supposition was1  that the linear      
motion of the centre of the epicycle    
ceased to be  uniform4 ,there were thus 
three points to be considered within the
  deferent2 ,e1 the place of the earth2 
,c1 the centre of the deferent1 and     
sometimes called the centre of the      
orbit2 and ,q1 called the centre of  the
 equant1 because1 if any circle were    
described round ,q1 the planet  would   

appear to a spectator at ,q1 to be      
moving equably in it4 ,it was  long     
uncertain what situation should be      
assigned to the centre of the  equant1  
so as best to represent the             
irregularities to a spectator on the    
earth1 until ,ptolemy decided on placing
 it 7in every case but that of          
,mercury1 the observations on which were
 very doubtful7 so that ,c1 the  centre 
of the orbit1 lay just half way in the  
straight line1 joining ,q1  the centre  
of equable motion1 and ,e1 the place of 
the earth4 ,this is the  famous         
principle1 known by the name of the     
bisection of the  excentricity4         
,illustration    ,the first equation    
required for the planet's motion was    
thus supposed to  be due to the         
displacement of ,e1 the earth1 from ,q1 
the centre of  uniform motion1 which was
 called the excentricity of the equant3 
it  might be represented by the angle   
d,,em1 drawing ,,em parallel to ,qd2    
for clearly ,m would have been the place

 of the centre of the epicycle at  the  
end of a time proportional to ,dd1 had  
it moved with an equable  angular motion
 round ,e instead of ,q4 ,this angle    
d,,em1 or its equal  ,ed,q1 was called  
the equation of the centre 7i4e4 of the 
centre of  the epicycle72 and is clearly
 greater than if ,,eq1 the excentricity 
of  the equant1 had been no greater than
 ,,ec1 called the excentricity of the   
orbit4 ,the second equation was measured
 by the angle subtended at ,e by  d1 the
 centre of the epicycle1 and p the      
planet's place in its  circumference3 it
 was called indifferently the equation  
of the orbit1 or  of the argument4 ,in  
order to account for the apparent       
stations and  retrogradations of the    
planets1 it became necessary to suppose 
that many  revolutions in the latter    
were completed during one of the former4
 ,the  variations of latitude of the    
planets were exhibited by supposing not 
only that the planes of their deferents 
were oblique to the plane of the        

ecliptic1 and that the plane of the     
epicycle was also oblique to that of    
the deferent1 but that the inclination  
of the two latter was continually       
changing1 although ,kepler doubts       
whether this latter complication was    
admitted by ,ptolemy4 ,in the inferior  
planets1 it was even thought  necessary 
to give to the plane of the epicycle two
 oscillatory motions  on axes at right  
angles to each other4    ,the           
astronomers at this period were much    
struck with a remarkable  connexion     
between the revolutions of the superior 
planets in their  epicycles1 and the    
apparent motion of the sun2 for when in 
conjunction  with the sun1 as seen from 
the earth1 they were always found to be 
in  the apogee1 or point of greatest    
distance from the earth1 of their       
epicycle2 and when in opposition to the 
,sun1 they were as regularly in  the    
perigee1 or point of nearest approach of
 the epicycle4 ,this  correspondence    
between two phenomena1 which1 according 

to the old  astronomy1 were entirely    
unconnected1 was very perplexing1 and it
 seems  to have been one of the facts   
which led ,copernicus to substitute the 
theory of the earth's motion round the  
sun4    ,as time wore on1 the           
superstructure of excentrics and        
epicycles1 which  had been strained into
 representing the appearances of the    
heavens at a  particular moment1 grew   
out of shape1 and the natural           
consequence of  such an artificial      
system was1 that it became next to      
impossible to  foresee what ruin might  
be produced in a remote part of it by   
any  attempt to repair the derangements 
and refit the parts to the changes1  as 
they began to be remarked in any        
particular point4 ,in the ninth  century
 of our era1 ,ptolemy's tables were     
already useless1 and all those  that    
were contrived with unceasing toil to   
supply their place1 rapidly  became as  
unserviceable as they4 ,still the       
triumph of genius was seen in  the      

veneration that continued to be paid to 
the assumptions of ,ptolemy  and        
,hipparchus2 and even when the great    
reformer1 ,copernicus1 appeared1  he did
 not for a long time intend to do more  
than slightly modify their  principles4 
,that which he found difficult in the   
,ptolemaic system1 was  none of the     
inconveniences by which1 since the      
establishment of the new  system1 it has
 become common to demonstrate the       
inferiority of the old  one2 it was the 
displacement of the centre of the equant
 from the centre  of the orbit that     
principally indisposed him against it1  
and led him to  endeavour to represent  
the appearances by some other           
combinations of  really uniform circular
 motions4    ,there was an old system1  
called the ,egyptian1 according to which
 ,saturn1  ,jupiter1 ,mars1 and the ,sun
 circulated round the earth1 the sun    
carrying  with it1 as two moons or      
satellites1 the other two planets1      
,venus and  ,mercury4 ,this system had  

never entirely lost credit3 it had been 
maintained in the fifth century by      
,martianus ,capella#ahh1 and indeed it  
was almost sanctioned1 though not       
formally taught1 by ,ptolemy himself1   
when he made the mean motion of the sun 
the same as that of the centres  of the 
epicycles of both these planets4 ,the   
remark which had also been  made by the 
old astronomers1 of the connexion       
between the motion of the  sun and the  
revolutions of the superior planets in  
their epicycles1 led  him straight to   
the expectation that he might1 perhaps1 
produce the  uniformity he sought by    
extending the ,egyptian system to these 
also1 and  this appears to have been the
 shape in which his reform was          
originally  projected4 ,it was already  
allowed that the centre of the orbits of
 all  the planets was not coincident    
with the earth1 but removed from it by  
the space ,,ec4 ,this first change      
merely made ,,ec the same for all the   
planets1 and equal to the mean distance 

of the earth from the sun4 ,this  system
 afterwards acquired great celebrity    
through its adoption by ,tycho  ,brahe1 
who believed it originated with himself4
 ,it might perhaps have  been at this   
period of his researches1 that          
,copernicus was struck with  the        
passages in the ,latin and ,greek       
authors1 to which he refers as          
testifying the existence of an old      
belief in the motion of the earth  round
 the sun4 ,he immediately recognised how
 much this alteration would  further his
 principles of uniformity1 by referring 
all the planetary  motions to one       
centre1 and did not hesitate to embrace 
it4 ,the idea of  explaining the daily  
and principal apparent motions of the   
heavenly  bodies by the revolution of   
the earth on its axis1 would be the     
concluding change1 and became almost a  
necessary consequence of his  previous  
improvements1 as it was manifestly at   
variance with his  principles to give to
 all the planets and starry worlds a    

rapid daily  motion round the centre of 
the earth1 now that the latter was      
removed  from its former supposed post  
in the centre of the universe1 and was  
itself carried with an annual motion    
round another fixed point4              
,illustration    ,the reader would1     
however1 form an inaccurate notion of   
the system of  ,copernicus1 if he       
supposed that it comprised no more than 
the theory  that each planet1 including 
the earth among them1 revolved in a     
simple  circular orbit round the sun4   
,copernicus was too well acquainted with
  the motions of the heavenly bodies1   
not to be aware that such orbits  would 
not accurately represent them2 the      
motion he attributed to the  earth round
 the sun1 was at first merely intended  
to account for those  which were called 
the second inequalities of the planets1 
according to  which they appear one     
while to move forwards1 then backwards1 
and at  intermediate periods1           
stationary1 and which thenceforward were

 also  called the optical equations1 as 
being merely an optical illusion4 ,with 
regard to what were called the first    
inequalities1 or physical  equations1   
arising from a real inequality of       
motion1 he still retained  the machinery
 of the deferent and epicycle2 and all  
the alteration he  attempted in the     
orbits of the superior planets was an   
extension of the  concentric theory to  
supply the place of the equant1 which he
 considered  the blot of the system4    
,his theory for this purpose is shown in
 the  accompanying diagram1 where ,s    
represents the sun1 ,dd1 the deferent or
  mean orbit of the planet1 on which    
revolves the centre of the great        
epicycle1 whose radius1 ,,df1 was taken 
at  of ,ptolemy's excentricity of  the  
equant2 and round the circumference of  
this revolved1 in the  opposite         
direction1 the centre of the little     
epicycle1 whose radius1 ,,fp1  was made 
equal to the remaining  of the          
excentricity of the equant4    ,the     

planet ,p revolved in the circumference 
of the little epicycle1 in  the same    
direction with the centre of the great  
epicycle in the  circumference of the   
deferent1 but with a double angular     
velocity4 ,the  planet was supposed to  
be in the perigee of the little         
epicycle1 when  its centre was in the   
apogee of the greater2 and whilst1 for  
instance1 ,d  moved equably though the  
angle ,,dsd1 ,f moved through hdf       
,,dsd1 and  ,p through rfp  #b ,,dsd4   
,it is easy to show that this           
construction gives nearly the same      
result  as ,ptolemy's2 for the deferent 
and great epicycle have been already    
shown exactly equivalent to an excentric
 circle round ,s1 and indeed            
,copernicus latterly so represented it3 
the effect of his construction1  as     
given above1 may therefore be reproduced
 in the following simpler  form1 in     
which only the smaller epicycle is      
retained3    ,illustration    ,in this  
construction1 the place of the planet is

 found at the end of any  time          
proportional to ,f f by drawing fr      
parallel to ,,sf1 and taking  rfp  #b;,f
 of4 ,hence it is plain1 if we take     
,,oq1 equal to ,,fp1 7already  assumed  
equal to  of ,ptolemy's excentricity of 
the equant17 since ,,so is  equal to  of
 the same1 that ,,sq is the whole of    
,ptolemy's excentricity  of the equant2 
and therefore1 that ,q is the position  
of the centre of  his equant4 ,it is    
also plain if we join ,qp1 since rfp    
#b;,f of1 and  o,q  fp1 that p,q is     
parallel to fo1 and1 therefore1 p,,qp is
  proportional to the time2 so that the 
planet moves uniformly about the  same  
point ,q1 as in ,ptolemy's theory2 and  
if we bisect ,,sq in ,c1 which is  the  
position of the centre of ,ptolemy's    
deferent1 the planet will1  according to
 ,copernicus1 move very nearly1 though  
not exactly1 in the  same circle1 whose 
radius is ,,cp1 as that given by the    
simple excentric  theory4    ,the       
explanation offered by ,copernicus1 of  

the motions of the inferior  planets1   
differed again in form from that of the 
others4 ,he here  introduced what was   
called a hypocycle1 which1 in fact1 was 
nothing  but a deferent not including   
the sun1 round which the centre of the  
orbit revolved4 ,an epicycle in addition
 to the hypocycle was introduced  into  
,mercury's orbit4 ,in this epicycle he  
was not supposed to revolve1  but to    
librate1 or move up and down in its     
diameter4 ,copernicus had  recourse to  
this complication to satisfy an         
erroneous assertion of  ,ptolemy with   
regard to some of ,mercury's            
inequalities4 ,he also retained  the    
oscillatory motions ascribed by ,ptolemy
 to the planes of the  epicycles1 in    
order to explain the unequal latitudes  
observed at the  same distance from the 
nodes1 or intersections of the orbit of 
the  planet with the ecliptic4 ,into    
this intricacy1 also1 he was led by     
placing too much confidence in          
,ptolemy's observations1 which he was   

unable to satisfy by an unvarying       
obliquity4 ,other very important        
errors1 such as his belief that the line
 of nodes always coincided with  the    
line of apsides1 or places of greatest  
and least distance from the  central    
body1 7whereas1 at that time1 in the    
case of ,mars1 for instance1  they were 
nearly #ij asunder17 prevented him from 
accurately  representing many of the    
celestial phenomena4    ,these brief    
details may serve to show that the      
adoption or rejection of  the theory of 
,copernicus was not altogether so simple
 a question as  sometimes it may have   
been considered4 ,it is1 however1 not a 
little  remarkable1 while it is strongly
 illustrative of the spirit of the      
times1 that these very intricacies1 with
 which ,kepler's theories have  enabled 
us to dispense1 were the only parts of  
the system of ,copernicus  that were at 
first received with approbation4 ,his   
theory of ,mercury1  especially1 was    
considered a masterpiece of subtle      

invention4 ,owing to  his dread of the  
unfavourable judgment he anticipated on 
the main  principles of his system1 his 
work remained unpublished during forty  
years1 and was at last given to the     
world only just in time to allow        
,copernicus to receive the first copy of
 it a few hours before his  death4      
,,footnotes3    #ahg ,by the opposite   
direction is meant1 that while the      
motion in the  circumference of one     
circle appeared1 as viewed from its     
centre1 to be  from left to right1 the  
other1 viewed from its centre1 appeared 
from  right to left4 ,this must be      
understood whenever these or similar    
expressions are repeated4    #ahh ,venus
 ,mercuriusque1 licet ortus occasusque  
quotidianos ostendunt1  tamen eorum     
circuli terras omnino non ambiunt1 sed  
circa solem laxiore  ambitu circulantur4
 ,denique circulorum suorum centron in  
sole  constituunt4--,de ,nuptiis        
,philologi et ,mercurii4 ,vicenti4      
#adii4          ,,chapter ,v4           

,account of the ,commentaries on the    
motions of ,mars--,discovery of         
the ,law of the equable description of  
,areas1 and of ,elliptic        ,orbits4
      ,,we may now proceed to examine   
,kepler's innovations1 but it would be  
doing injustice to one of the brightest 
points of his character1 not to  preface
 them by his own animated exhortation to
 his readers4 ,if any one  be too dull  
to comprehend the science of astronomy1 
or too feeble-minded  to believe in     
,copernicus without prejudice to his    
piety1 my advice to  such a one is1 that
 he should quit the astronomical        
schools1 and  condemning1 if he has a   
mind1 any or all of the theories of     
philosophers1 let him look to his own   
affairs1 and leaving this worldly       
travail1 let him go home and plough his 
fields3 and as often as he lifts  up to 
this goodly heaven those eyes with which
 alone he is able to see1  let him pour 
out his heart in praises and            
thanksgiving to ,god the  ,creator2 and 

let him not fear but he is offering a   
worship not less  acceptable than his to
 whom ,god has granted to see yet more  
clearly with  the eyes of his mind1 and 
who both can and will praise his ,god   
for what  he has so discovered4         
,kepler did not by any means underrate  
the importance of his labours1 as  is   
sufficiently shewn by the sort of       
colloquial motto which he prefixed  to  
his work4 ,it consists in the first     
instance of an extract from the         
writings of the celebrated and          
unfortunate ,peter ,ramus4 ,this        
distinguished philosopher was professor 
of mathematics in ,paris1 and in  the   
passage in question1 after calling on   
his contemporaries to turn  their       
thoughts towards the establishment of a 
system of ,astronomy  unassisted by any 
hypothesis1 he promised as an additional
 inducement to  vacate his own chair in 
favour of any one who should succeed in 
this  object4 ,ramus perished in the    
massacre of ,st4 ,bartholomew1 and      

,kepler  apostrophizes him as           
follows3--,it is well1 ,ramus1 that you 
have  forfeited your pledge1 by quitting
 your life and professorship together3  
for if you still held it1 ,i would      
certainly claim it as of right          
belonging to me on account of this work1
 as ,i could convince you even  with    
your own logic4 ,it was rather bold in  
,kepler to assert his claim  to a reward
 held out for a theory resting on no    
hypothesis1 by right of  a work filled  
with hypotheses of the most startling   
description2 but of  the vast importance
 of this book there can be no doubt2 and
 throughout  the many wild and eccentric
 ideas to which we are introduced in the
  course of it1 it is fit always to bear
 in mind that they form part of a  work 
which is almost the basis of modern     
,astronomy4    ,the introduction        
contains a curious criticism of the     
commonly-received  theory of gravity1   
accompanied with a declaration of       
,kepler's own  opinions on the same     

subject4 ,some of the most remarkable   
passages in it  have been already quoted
 in the life of ,galileo2 but1          
nevertheless1 they  are too important to
 ,kepler's reputation to be omitted     
here1 containing  as they do a distinct 
and positive enunciation of the law of  
universal  gravitation4 ,it does not    
appear1 however1 that ,kepler estimated 
rightly  the importance of the theory   
here traced out by him1 since on every  
other occasion he advocated principles  
with which it is scarcely               
reconcileable4 ,the discussion is       
introduced in the following terms3--    
,the motion of heavy bodies hinders many
 from believing that the earth  is moved
 by an animal motion1 or rather a       
magnetic one4 ,let such  consider the   
following propositions4 ,a mathematical 
point1 whether the  centre of the       
universe or not1 has no power1 either   
effectively or  objectively1 to move    
heavy bodies to approach it4 ,let       
physicians prove  if they can1 that such

 power can be possessed by a point1     
which1 neither  is a body1 nor is       
conceived unless by relation alone4 ,it 
is impossible  that the form#ahi of a   
stone should1 by moving its own body1   
seek a  mathematical point1 or in other 
words1 the centre of the universe1      
without regard of the body in which that
 point exists4 ,let physicians  prove if
 they can1 that natural things have any 
sympathy with that which  is nothing4   
,neither do heavy bodies tend to the    
centre of the universe  by reason that  
they are avoiding the extremities of the
 round universe2  for their distance    
from the centre is insensible1 in       
proportion to their  distance from the  
extremities of the universe4 ,and what  
reason could  there be for this hatred8 
,how strong1 how wise must those heavy  
bodies  be1 to be able to escape so     
carefully from an enemy lying on all    
sides  of them3 what activity in the    
extremities of the world to press their 
enemy so closely6 ,neither are heavy    

bodies driven into the centre by the    
whirling of the first moveable1 as      
happens in revolving water4 ,for if we  
assume such a motion1 either it would   
not be continued down to us1 or         
otherwise we should feel it1 and be     
carried away with it1 and the earth     
also with us2 nay1 rather1 we should be 
hurried away first1 and the  earth would
 follow2 all which conclusions are      
allowed by our opponents  to be absurd4 
,it is therefore plain that the vulgar  
theory of gravity is  erroneous4    ,the
 true theory of gravity is founded on   
the following axioms3--,every  corporeal
 substance1 so far forth as it is       
corporeal1 has a natural  fitness for   
resting in every place where it may be  
situated by itself  beyond the sphere of
 influence of a body cognate with it4   
,gravity is a  mutual affection between 
cognate bodies towards union or         
conjunction  7similar in kind to the    
magnetic virtue71 so that the earth     
attracts a  stone much rather than the  

stone seeks the earth4 ,heavy bodies 7if
 we  begin by assuming the earth to be  
in the centre of the world7 are not     
carried to the centre of the world in   
its quality of centre of the  world1 but
 as to the centre of a cognate round    
body1 namely1 the earth2  so that       
wheresoever the earth may be placed1 or 
whithersoever it may be  carried by its 
animal faculty1 heavy bodies will always
 be carried  towards it4 ,if the earth  
were not round1 heavy bodies would not  
tend  from every side in a straight line
 towards the centre of the earth1 but   
to different points from different      
sides4 ,if two stones were placed in    
any part of the world near each other1  
and beyond the sphere of  influence of a
 third cognate body1 these stones1 like 
two magnetic  needles1 would come       
together in the intermediate point1 each
 approaching  the other by a space      
proportional to the comparative mass of 
the other4  ,if the moon and earth were 
not retained in their orbits by their   

animal  force or some other equivalent1 
the earth would mount to the moon by a  
fifty-fourth part of their distance1 and
 the moon fall towards the earth        
through the other fifty-three parts and 
they would there meet2 assuming  however
 that the substance of both is of the   
same density4 ,if the earth  should     
cease to attract its waters to itself1  
all the waters of the sea  would be     
raised and would flow to the body of the
 moon4 ,the sphere of  the attractive   
virtue which is in the moon extends as  
far as the earth1  and entices up the   
waters2 but as the moon flies rapidly   
across the  zenith1 and the waters      
cannot follow so quickly1 a flow of the 
ocean is  occasioned in the torrid zone 
towards the westward4 ,if the attractive
  virtue of the moon extends as far as  
the earth1 it follows with greater      
reason that the attractive virtue of the
 earth extends as far as the  moon1 and 
much farther2 and in short1 nothing     
which consists of earthly  substance any

 how constituted1 although thrown up to 
any height1 can  ever escape the        
powerful operation of this attractive   
virtue4 ,nothing  which consists of     
corporeal matter is absolutely light1   
but that is  comparatively lighter which
 is rarer1 either by its own nature1 or 
by  accidental heat4 ,and it is not to  
be thought that light bodies are        
escaping to the surface of the universe 
while they are carried upwards1  or that
 they are not attracted by the earth4   
,they are attracted1 but in  a less     
degree1 and so are driven outwards by   
the heavy bodies2 which  being done1    
they stop1 and are kept by the earth in 
their own place4 ,but  although the     
attractive virtue of the earth extends  
upwards1 as has been  said1 so very far1
 yet if any stone should be at a        
distance great enough  to become        
sensible1 compared with the earth's     
diameter1 it is true that  on the motion
 of the earth such a stone would not    
follow altogether2 its  own force of    

resistance would be combined with the   
attractive force of  the earth1 and thus
 it would extricate itself in some      
degree from the  motion of the earth4   
,who1 after perusing such passages in   
the works of an author1 whose  writings 
were in the hands of every student of   
astronomy1 can believe  that ,newton    
waited for the fall of an apple to set  
him thinking for the  first time on the 
theory which has immortalized his name8 
,an apple may  have fallen1 and ,newton 
may have seen it2 but such speculations 
as those  which it is asserted to have  
been the cause of originating in him had
  been long familiar to the thoughts of 
every one in ,europe pretending to  the 
name of natural philosopher4    ,as     
,kepler always professed to have derived
 his notion of a magnetic  attraction   
among the planetary bodies from the     
writings of ,gilbert1 it  may be worth  
while to insert here an extract from the
 ,new ,philosophy  of that author1 to   
show in what form he presented a similar

 theory of  the tides1 which affords the
 most striking illustration of that     
attraction4 ,this work was not published
 till the middle of the  seventeenth    
century1 but a knowledge of its contents
 may1 in several  instances1 be traced  
back to the period in which it was      
written3--    ,there are two primary    
causes of the motion of the seas--the   
moon1 and  the diurnal revolution4 ,the 
moon does not act on the seas by its    
rays or  its light4 ,how then8          
,certainly by the common effort of the  
bodies1 and  7to explain it by something
 similar7 by their magnetic attraction4 
,it  should be known1 in the first      
place1 that the whole quantity of water 
is  not contained in the sea and rivers1
 but that the mass of earth 7,i mean    
this globe7 contains moisture and spirit
 much deeper even than the sea4  ,the   
moon draws this out by sympathy1 so that
 they burst forth on the  arrival of the
 moon1 in consequence of the attraction 
of that star2 and  for the same reason1 

the quicksands which are in the sea open
 themselves  more1 and perspire their   
moisture and spirits during the flow of 
the  tide1 and the whirlpools in the sea
 disgorge copious waters2 and as the    
star retires1 they devour the same      
again1 and attract the spirits and      
moisture of the terrestrial globe4      
,hence the moon attracts1 not so much   
the sea as the subterranean spirits and 
humours2 and the interposed  earth has  
no more power of resistance than a table
 or any other dense  body has to resist 
the force of a magnet4 ,the sea rises   
from the  greatest depths1 in           
consequence of the ascending humours and
 spirits2  and when it is raised up1 it 
necessarily flows on to the shores1 and 
from the shores it enters the           
rivers4#aij    ,this passage sets in the
 strongest light one of the most        
notorious  errors of the older          
philosophy1 to which ,kepler himself was
 remarkably  addicted4 ,if ,gilbert had 
asserted1 in direct terms1 that the moon

  attracted the water1 it is certain    
that the notion would have been         
stigmatized 7as it was for a long time  
in ,newton's hands7 as arbitrary1       
occult1 and unphilosophical3 the idea of
 these subterranean humours was  likely 
to be treated with much more indulgence4
 ,a simple statement1 that  when the    
moon was over the water the latter had a
 tendency to rise  towards it1 was      
thought to convey no instruction2 but   
the assertion that  the moon draws out  
subterranean spirits by sympathy1       
carried with it a  more imposing        
appearance of theory4 ,the farther      
removed these humours  were from common 
experience1 the easier it became to     
discuss them in  vague and general      
language2 and those who called          
themselves philosophers  could endure to
 hear attributes bestowed on these      
fictitious elements  which revolted     
their imaginations when applied to      
things of whose  reality at least some  
evidence existed4    ,it is not         

necessary to dwell upon the system of   
,tycho ,brahe1 which was  identical1 as 
we have said1 with one rejected by      
,copernicus1 and  consisted in making   
the sun revolve about the earth1        
carrying with it  all the other planets 
revolving about him4 ,tycho went so far 
as to deny  the rotation of the earth to
 explain the vicissitudes of day and    
night1  but even his favourite assistant
 ,longomontanus differed from him in    
this  part of his theory4 ,the great    
merit of ,tycho ,brahe1 and the service 
he  rendered to astronomy1 was entirely 
independent of any theory2  consisting  
in the vast accumulation of observations
 made by him during a  residence of     
fifteen years at ,uraniburg1 with the   
assistance of  instruments1 and with a  
degree of care1 very far superior to    
anything  known before his time in      
practical astronomy4 ,kepler is careful 
repeatedly to remind us1 that without   
,tycho's observations he could have     
done nothing4 ,the degree of reliance   

that might be placed on the results     
obtained by observers who acknowledged  
their inferiority to ,tycho ,brahe1     
maybe gathered from an incidental remark
 of ,kepler to ,longomontanus4 ,he  had 
been examining ,tycho's registers1 and  
had occasionally found a  difference    
amounting sometimes to #d in the right  
ascensions of the same  planet1 deduced 
from different stars on the same night4 
,longomontanus  could not deny the fact1
 but declared that it was impossible to 
be  always correct within such limits4  
,the reader should never lose sight of  
this uncertainty in the observations1   
when endeavouring to estimate the       
difficulty of finding a theory that     
would properly represent them4    ,when 
,kepler first joined ,tycho ,brahe at   
,prague1 he found him and               
,longomontanus very busily engaged in   
correcting the theory of ,mars1 and     
accordingly it was this planet to which 
he also first directed his  attention4  
,they had formed a catalogue of the mean

 oppositions of ,mars  during twenty    
years1 and had discovered a position of 
the equant1 which  7as they said7       
represented them with tolerable         
exactness4 ,on the other  hand1 they    
were much embarrassed by the unexpected 
difficulties they met  in applying a    
system which seemed on the one hand so  
accurate1 to the  determination of the  
latitudes1 with which it could in no way
 be made to  agree4 ,kepler had already 
suspected the cause of this             
imperfection1 and  was confirmed in the 
view he took of their theory1 when1 on a
 more  careful examination1 he found    
that they overrated the accuracy even of
  their longitudes4 ,the errors in      
these1 instead of amounting as they     
said1 nearly to #b1 rose sometimes above
 #ba4 ,in fact they had reasoned  ill on
 their own principles1 and even if the  
foundations of their theory  had been   
correctly laid1 could not have arrived  
at true results4 ,but  ,kepler had      
satisfied himself of the contrary1 and  

the following diagram  shews the nature 
of the first alteration he introduced1  
not perhaps so  celebrated as some of   
his later discoveries1 but at least of  
equal  consequence to astronomy1 which  
could never have been extricated from   
the confusion into which it had fallen1 
till this important change had  been    
effected4    ,illustration    ,the      
practice of ,tycho ,brahe1 indeed of all
 astronomers till the time of  ,kepler1 
had been to fix the position of the     
planet's orbit and equant  from         
observations on its mean oppositions1   
that is to say1 on the times  when it   
was precisely six signs or half a circle
 distant from the mean  place of the    
sun4 ,in the annexed figure1 let ,s     
represent the sun1 ,c the  centre of the
 earth's orbit1 ,tt4 ,tycho ,brahe's    
practice amounted to  this1 that if ,q  
were supposed the place of the centre of
 the planet's  equant1 the centre of ,pp
 its orbit was taken in ,,qc1 and not in
 ,,qs1 as  ,kepler suggested that it    

ought to be taken4 ,the consequence of  
this  erroneous practice was1 that the  
observations were deprived of the       
character for which oppositions were    
selected1 of being entirely free  from  
the second inequalities4 ,it followed   
therefore that as part of the  second   
inequalities were made conducive towards
 fixing the relative  position of the   
orbit and equant1 to which they did not 
naturally  belong1 there was an         
additional perplexity in accounting for 
the  remainder of them by the size and  
motion of the epicycle4 ,as the line of 
nodes of every planet was also made to  
pass through ,c instead of ,s1  there   
could not fail to be corresponding      
errors in the latitudes4 ,it  would only
 be in the rare case of an opposition of
 the planet in the  line ,,cs1 that the 
time of its taking place would be the   
same1 whether ,o1  the centre of the    
orbit1 was placed in ,,cq or ,,sq4      
,every other opposition  would involve  
an error1 so much the greater as it was 

observed at a  greater distance from the
 line ,,cs4    ,it was long however     
before ,tycho ,brahe could be made to   
acquiesce in the  propriety of the      
proposed alteration2 and1 in order to   
remove his doubts  as to the possibility
 that a method could be erroneous which1
 as he  still thought1 had given him    
such accurate longitudes1 ,kepler       
undertook  the ungrateful labour of the 
first part of his ,commentaries4 ,he    
there  shewed1 in the three systems of  
,copernicus1 ,tycho ,brahe1 and         
,ptolemy1  and in both the concentric   
and excentric theories1 that though a   
false  position were given to the orbit1
 the longitudes of a planet might be so 
represented1 by a proper position of the
 centre of the equant1 as never  to err 
in oppositions above #e from those given
 by observation2 though  the second     
inequalities and the latitudes would    
thereby be very greatly  deranged4      
,the change ,kepler introduced1 of      
observing apparent instead of mean      

oppositions1 made it necessary to be    
very accurate in his reductions of  the 
planet's place to the ecliptic2 and in  
order to be able to do this1  a previous
 knowledge of the parallax of ,mars     
became indispensable4 ,his  next labour 
was therefore directed to this point2   
and finding that the  assistants to whom
 ,tycho ,brahe had previously committed 
this labour had  performed it in a      
negligent and imperfect manner1 he began
 afresh with  ,tycho's original         
observations4 ,having satisfied himself 
as to the  probable limits of his errors
 in the parallax on which he finally    
fixed1  he proceeded to determine the   
inclination of the orbit and the        
position  of the line of nodes4 ,in all 
these operations his talent for         
astronomical inquiries appeared         
pre-eminent in a variety of new methods 
by which he combined and availed himself
 of the observations2 but it  must be   
sufficient merely to mention this fact1 
without entering into  any detail4 ,one 

important result may be mentioned1 at   
which he arrived  in the course of them1
 the constancy of the inclination of the
 planet's  orbit1 which naturally       
strengthened him in his new theory4     
,having gone through these preliminary  
inquiries1 he came at last to fix  the  
proportions of the orbit2 and1 in doing 
so1 he determined1 in the  first        
instance1 not to assume1 as ,ptolemy    
appeared to have done  arbitrarily1 the 
bisection of the excentricity1 but to   
investigate its  proportion along with  
the other elements of the orbit1 which  
resolution  involved him in much more   
laborious calculations4 ,after he had   
gone over  all the steps of his theory  
no less than seventy times--an appalling
  labour1 especially if we remember that
 logarithms were not then  invented--his
 final result was1 that in #aehg1 on the
 #fth of ,march1 at #g  #bc1 the        
longitude of the aphelion of ,mars was  
#d #bh #dh #ee2 that the  planet's mean 
longitude was #f #j #ea #ce2 that if the

 semidiameter of  the orbit was taken at
 #ajjjjj1 the excentricity was #aaccb2  
and the  excentricity of the equant     
#ahefd4 ,he fixed the radius of the     
greater  epicycle at #adihh1 and that of
 the smaller at #cfbh4    ,when he came 
to compare the longitudes as given by   
this1 which he  afterwards called the   
vicarious theory1 with the observations 
at  opposition1 the result seemed to    
promise him the most brilliant success4 
,his greatest error did not exceed #b2  
but1 notwithstanding these  flattering  
anticipations1 he soon found by a       
comparison of longitudes  out of        
opposition and of latitudes1 that it was
 yet far from being so  complete as he  
had imagined1 and to his infinite       
vexation he soon found  that the labour 
of four years1 which he had expended on 
this theory1  must be considered almost 
entirely fruitless4 ,even his favourite 
principle of dividing the excentricity  
in a different ratio from  ,ptolemy1 was
 found to lead him into greater error   

than if he had  retained the old        
bisection4 ,by restoring that1 he made  
his latitudes  more accurate1 but       
produced a corresponding change for the 
worse in his  longitudes2 and although  
the errors of #h1 to which they now     
amounted1  would probably have been     
disregarded by former theorists1 ,kepler
 could  not remain satisfied till they  
were accounted for4 ,accordingly he     
found  himself forced to the conclusion 
that one of the two principles on which 
this theory rested must be erroneous2   
either the orbit of the planet is  not a
 perfect circle1 or there is no fixed   
point within it round which  it moves   
with an uniform angular motion4 ,he had 
once before admitted the  possibility of
 the former of these facts1 conceiving  
it possible that  the motion of the     
planets is not at all curvilinear1 but  
that they move  in polygons round the   
sun1 a notion to which he probably      
inclined in  consequence of his         
favourite harmonics and geometrical     

figures4    ,in consequence of the      
failure of a theory conducted with such 
care in  all its practical details1     
,kepler determined that his next trial  
should  be of an entirely different     
complexion4 ,instead of first satisfying
 the  first inequalities of the planet1 
and then endeavouring to account for    
the second inequalities1 he resolved to 
reverse the process1 or1 in  other      
words1 to ascertain as accurately as    
possible what part of the  planet's     
apparent motion should be referred      
solely to the optical  illusion produced
 by the motion of the earth1 before     
proceeding to any  inquiry of the real  
inequality of the planet's proper       
motion4 ,it had  been hitherto taken for
 granted1 that the earth moved equably  
round the  centre of its orbit2 but     
,kepler1 on resuming the consideration  
of it1  recurred to an opinion he had   
entertained very early in his           
astronomical  career 7rather from his   
conviction of the existence of general  

laws1  than that he had then felt the   
want of such a supposition71 that it    
required an equant distinct from its    
orbit no less than the other  planets4  
,he now saw1 that if this were admitted1
 the changes it would  everywhere       
introduce in the optical part of the    
planet's irregularities  might perhaps  
relieve him from the perplexity in which
 the vicarious  theory had involved him4
 ,accordingly he applied himself with   
renewed  assiduity to the examination of
 this important question1 and the result
  of his calculations 7founded          
principally on observations of ,mars'   
parallax7 soon satisfied him not only   
that the earth's orbit does  require    
such an equant1 but that its centre is  
placed according to the  general law of 
the bisection of the excentricity which 
he had previously  found indispensable  
in the other planets4 ,this was an      
innovation of the  first magnitude1 and 
accordingly ,kepler did not venture to  
proceed  farther in his theory1 till by 

evidence of the most varied and         
satisfactory nature1 he had established 
it beyond the possibility of  cavil4    
,it may be here remarked1 that this     
principle of the bisection of the       
eccentricity1 so familiar to the        
,ptolemaic astronomers1 is identical    
with the theory afterwards known by the 
name of the simple elliptic  hypothesis1
 advocated by1 ,seth ,ward and others4  
,that hypothesis  consisted in supposing
 the sun to be placed in one focus of   
the elliptic  orbit of the planet1 whose
 angular motion was uniform round the   
other  focus4 ,in ,ptolemaic            
phraseology1 that other focus was the   
centre of the  equant1 and it is well   
known that the centre of the ellipse    
lies in the  middle point between the   
two foci4    ,it was at this period     
also1 that ,kepler first ventured upon  
the new  method of representing         
inequalities which terminated in one of 
his most  celebrated discoveries4 ,we   
have already seen1 in the account of the

  ,mysterium ,cosmographicum1 that he   
was speculating1 even at that time1  on 
the effects of a whirling force exerted 
by the sun on the planets  with         
diminished energy at increased          
distances1 and on the proportion        
observed between the distances of the   
planets from the sun1 and their  periods
 of revolution4 ,he seems even then to  
have believed in the  possibility of    
discovering a relation between the times
 and distances in  different planets4   
,another analogous consequence of his   
theory of the  radiation of the whirling
 force would be1 that if the same planet
 should  recede to a greater distance   
from the central body1 it would be acted
 on  by a diminished energy of          
revolution1 and consequently1 a relation
 might  be found between the velocity at
 any point of its orbit1 and its        
distance at that point from the sun4    
,hence he expected to derive a more     
direct and natural method of calculating
 the inequalities1 than from the        

imaginary equant4 ,but these ingenious  
ideas had been checked in the  outset by
 the erroneous belief which ,kepler1 in 
common with other  astronomers1 then    
entertained of the coincidence of the   
earth's equant  with its orbit2 in other
 words1 by the belief that the earth's  
linear  motion was uniform1 though it   
was known not to remain constantly at   
the  same distance from the sun4 ,as    
soon as this prejudice was removed1 his 
former ideas recurred to him with       
increased force1 and he set himself     
diligently to consider what relation    
could be found between the velocity  and
 distance of a planet from the sun4 ,the
 method he adopted in the  beginning of 
this inquiry was to assume as           
approximately correct  ,ptolemy's       
doctrine of the bisection of the        
excentricity1 and to  investigate some  
simple relation nearly representing the 
same effect4    ,in the annexed figure1 
,s is the place of the sun1 ,c the      
centre of the  planet's orbit ,,abab1 ,q

 the centre of the equant represented by
 the  equal circle ,,dede1 ,,ab1 ab1 two
 equal small arcs described by the      
planet at the apsides of its orbit3     
then1 according to ,ptolemy's           
principles1 the arc ,,de of the equant  
would be proportional to the time  of   
passing along ,,ab1 on the same scale on
 which de would represent the  time of  
passing through the equal arc ab4       
,illustration    ,,qd3,,qa 33 ,,de3,,ab1
 nearly2 and because ,,qs is bisected in
 ,c1 ,,qa1 ,,ca or ,,qd1  and ,,sa1 are 
in arithmetical proportion3 and1        
therefore1 since an  arithmetical mean1 
when the difference is small1 does not  
differ much  from a geometrical mean1   
,,qd3,,qa 33 ,,sa3,,qd1 nearly4         
,therefore1 ,,de3,,ab 33 ,s  ,a3,,qd1   
nearly1 and in the same manner de3ab 33 
,sa3,qd nearly2 and  therefore ,,de3de  
33 ,,sa3,sa nearly4 ,therefore at the   
apsides1 the  times of passing over     
equal spaces1 on ,ptolemy's theory1 are 
nearly as  the distances from the sun1  

and ,kepler1 with his usual hastiness1  
immediately concluded that this was the 
accurate and general law1 and  that the 
errors of the old theory arose solely   
from having departed from  it4    ,it   
followed immediately from this          
assumption1 that after leaving the      
point ,a1 the time in which the planet  
would arrive at any point ,p of  its    
orbit would be proportional to1 and     
might be represented by1 the  sums of   
all the lines that could be drawn from  
,s to the arc ,,ap1 on the  same scale  
that the whole period of revolution     
would be denoted by the  sum of all the 
lines drawn to every point of the orbit4
 ,kepler's first  attempt to verify this
 supposition approximately1 was made by 
dividing  the whole circumference of the
 orbit into #cfj equal parts1 and       
calculating the distances at every one  
of the points of division4 ,then        
supposing the planet to move uniformly1 
and to remain at the same  distance from
 the sun during the time of passing each

 one of these  divisions1 7a supposition
 which manifestly would not differ much 
from  the former one1 and would coincide
 with it more nearly1 the greater was   
the number of divisions taken7 he       
proceeded to add together these         
calculated distances1 and hoped to find 
that the time of arriving at any  one of
 the divisions bore the same ratio to   
the whole period1 as the sum  of the    
corresponding set of distances did to   
the sum of the whole #cfj4    ,this     
theory was erroneous2 but by almost     
miraculous good fortune1 he was  led by 
it in the following manner to the true  
measure4 ,the discovery was  a          
consequence of the tediousness of his   
first method1 which required1 in  order 
to know the time of arriving at any     
point1 that the circle should  be       
subdivided1 until one of the points of  
division fell exactly upon the  given   
place4 ,kepler therefore endeavoured to 
discover some shorter  method of        
representing these sums of the          

distances4 ,the idea then  occurred to  
him of employing for that purpose the   
area inclosed between  the two          
distances1 ,,sa1 ,,sp1 and the arc ,,ap1
 in imitation of the manner in  which he
 remembered that ,archimedes had found  
the area of the circle1 by  dividing it 
into an infinite number of small        
triangles by lines drawn  from the      
centre4 ,he hoped therefore to find1    
that the time of passing  from ,a to ,p 
bore nearly the same ratio to the whole 
period of revolution  that the area     
,,asp bore to the whole circle4    ,this
 last proportion is in fact accurately  
observed in the revolution of  one body 
round another1 in consequence of an     
attractive force in the  central body4  
,newton afterwards proved this1         
grounding his demonstration  upon laws  
of motion altogether irreconcileable    
with ,kepler's opinions2  and it is     
impossible not to admire ,kepler's      
singular good fortune in  arriving at   
this correct result in spite1 or rather 

through the means1  of his erroneous    
principles4 ,it is true that the labour 
which he  bestowed unsparingly upon     
every one of his successive guesses1    
joined  with his admirable candour1     
generally preserved him from long       
retaining  a theory altogether at       
variance with observations2 and if any  
relation  subsisted between the times   
and distances which could any way be    
expressed by any of the geometrical     
quantities under consideration1 he      
could scarcely have failed--it might be 
twenty years earlier or twenty  years   
later1--to light upon it at last1 having
 once put his  indefatigable fancy upon 
this scent4 ,but in order to prevent an 
over-estimate of his merit in detecting 
this beautiful law of nature1  let us   
for a moment reflect what might have    
been his fate had he  endeavoured in the
 same manner1 and with the same         
perseverance1 to  discover a relation1  
where1 in reality1 none existed4 ,let us
 take for  example the inclinations or  

the excentricities of the planetary     
orbits1  among which no relation has yet
 been discovered2 and if any exists1 it 
is probably of too complicated a nature 
to be hit at a venture4 ,if  ,kepler had
 exerted his ingenuity in this          
direction1 he might have wasted  his    
life in fruitless labour1 and whatever  
reputation he might have left  behind   
him as an industrious calculator1 it    
would have been very far  inferior to   
that which has procured for him the     
proud title of the  ,legislator of the  
,heavens4    ,however this may be1 the  
immediate consequence of thus lighting  
upon the  real law observed by the earth
 in its passage round the sun was1 that 
he  found himself in possession of a    
much more accurate method of            
representing its inequalities than had  
been reached by any of his              
predecessors2 and with renewed hopes he 
again attacked the planet ,mars1  whose 
path he was now able to consider        
undistorted by the illusions  arising   

out of the motion of the earth4 ,had the
 path of ,mars been  accurately         
circular1 or even as nearly approaching 
a circle as that of  the earth1 the     
method he chose of determining its      
position and size by  means of three    
distances carefully calculated from his 
observed  parallaxes1 would have given a
 satisfactory result2 but finding1 as he
  soon did1 that almost every set of    
three distances led him to a  different 
result1 he began to suspect another     
error in the long-received  opinion1    
that the orbits of the planets must     
consist of a combination  of circles2 he
 therefore1 determined1 in the first    
instance1 to fix the  distances of the  
planet at the apsides without any       
reference to the form  of the           
intermediate orbit4 ,half the difference
 between these would1 of  course1 be the
 excentricity of the orbit2 and as this 
quantity came out  very nearly the same 
as had been determined on the vicarious 
theory1 it  seemed clear that the error 

of that theory1 whatever it might be1   
did  not lie in these elements4         
,kepler also found that in the case of  
this planet likewise1 the times of      
describing equal arcs at the apsides    
were proportional to its distances  from
 the sun1 and he naturally expected that
 the method of areas would  measure the 
planet's motion with as much accuracy as
 he had found in the  case of the earth4
 ,this hope was disappointed3 when he   
calculated the  motion of the planet by 
this method1 he obtained places too much
  advanced when near the apsides1 and   
too little advanced at the mean         
distances4 ,he did not1 on that account1
 immediately reject the opinion  of     
circular orbits1 but was rather inclined
 to suspect the principle of            
measurement1 at which he felt that he   
had arrived in rather a precarious      
manner4 ,he was fully sensible that his 
areas did not accurately  represent the 
sums of any distances except those      
measured from the  centre of the circle2

 and for some time he abandoned the hope
 of being  able to use this             
substitution1 which he always considered
 merely as an  approximate              
representation of the true measure1 the 
sum of the  distances4 ,but on          
examination he found that the errors of 
this  substitution were nearly          
insensible1 and those it did in fact    
produce1  were in the contrary direction
 of the errors he was at this time      
combating4 ,as soon as he had satisfied 
himself of this1 he ventured once  more 
on the supposition1 which by this time  
had1 in his eyes1 almost  acquired the  
force of demonstration1 that the orbits 
of the planets are  not circular1 but of
 an oval form1 retiring within the      
circle at the  mean distances1 and      
coinciding with it at the apsides4      
,this notion was not altogether new2 it 
had been suggested in the case of       
,mercury1 by ,purbach1 in his ,theories 
of the ,planets4 ,in the edition of     
this work published by ,reinhold1 the   

pupil of ,copernicus1 we read the       
following passage4 ,sixthly1 it appears 
from what has been said1 that  the      
centre of ,mercury's epicycle1 by reason
 of the motions  above-mentioned1 does  
not1 as is the case with the other      
planets1  describe the circumference of 
a circular deferent1 but rather the     
periphery of a figure resembling a plane
 oval4 ,to this is added the  following 
note by ,reinhold4 ,the centre of the   
,moon's epicycle describes  a path of a 
lenticular shape2 ,mercury's on the     
contrary is egg-shaped1  the big end    
lying towards his apogee1 and the little
 end towards his  perigee4#aia ,the     
excentricity of ,mercury's orbit is1 in 
fact1 much  greater than that of any of 
the other planets1 and the merit of     
making  this first step cannot          
reasonably be withheld from ,purbach and
 his  commentator1 although they did not
 pursue the inquiry so far as ,kepler   
found himself in a condition to do4     
,before proceeding to the consideration 

of the particular oval which  ,kepler   
fixed upon in the first instance1 it    
will be necessary1 in order  to render  
intelligible the source of many of his  
doubts and  difficulties1 to make known 
something more of his theory of the     
moving  force by which he supposed the  
planets to be carried round in their    
orbits4 ,in conformity with the plan    
hitherto pursued1 this shall be done  as
 much as possible in his own words4     
,it is one of the commonest axioms in   
natural philosophy1 that if two  things 
always happen together and in the same  
manner1 and admit the same  measure1    
either the one is the cause of the      
other1 or both are the  effect of a     
common cause4 ,in the present case1 the 
increase or languor  of motion          
invariably corresponds with an approach 
to or departure from  the centre of the 
universe4 ,therefore1 either the languor
 is the cause  of the departure of the  
star1 or the departure of the languor1  
or both  have a common cause4 ,but no   

one can be of opinion that there is a   
concurrence of any third thing to be a  
common cause of these two  effects1 and 
in the following chapters it will be    
made clear that there  is no occasion to
 imagine any such third thing1 since the
 two are of  themselves sufficient4     
,now1 it is not agreeable to the nature 
of things  that activity or languor in  
linear motion should be the cause of    
distance from the centre4 ,for1 distance
 from the centre is conceived           
anteriorly to linear motion4 ,in fact   
linear motion cannot exist without      
distance from the centre1 since it      
requires space for its  accomplishment1 
but distance from the centre can be     
conceived without  motion4 ,therefore   
distance is the cause of the activity of
 motion1 and a  greater or less distance
 of a greater or less delay4 ,and since 
distance  is of the kind of relative    
quantities1 whose essence consists in   
boundaries1 7for there is no efficacy in
 relation per se without  regard to     

bounds17 it follows that the cause of   
the varying activity of  motion rests in
 one of the boundaries4 ,but the body of
 the planet  neither becomes heavier by 
receding1 nor lighter by approaching4   
,besides1 it would perhaps be absurd on 
the very mention of it1 that an  animal 
force residing in the moveable body of  
the planet for the purpose  of moving   
it1 should exert and relax itself so    
often without weariness  or decay4 ,it  
remains1 therefore1 that the cause of   
this activity and  languor resides at   
the other boundary1 that is1 in the very
 centre of  the world1 from which the   
distances are computed4--,let us        
continue our  investigation of this     
moving virtue which resides in the sun1 
and we  shall presently recognize its   
very close analogy to light4 ,and       
although  this moving virtue cannot be  
identical with the light of the sun1 let
  others look to it whether the light is
 employed as a sort of instrument1  or  
vehicle1 to convey the moving virtue4   

,there are these seeming                
contradictions3--first1 light is        
obstructed by opaque bodies1 for which  
reason if the moving virtue travelled on
 the light1 darkness would be  followed 
by a stoppage of the moveable bodies4   
,again1 light flows out in  right lines 
spherically1 the moving virtue in right 
lines also1 but  cylindrically2 that is1
 it turns in one direction only1 from   
west to  east2 not in the opposite      
direction1 not towards the poles1 c4    
,but  perhaps we shall be able presently
 to reply to these objections4 ,in      
conclusion1 since there is as much      
virtue in a large and remote circle  as 
in a narrow and close one1 nothing of   
the virtue perishes in the  passage from
 its source1 nothing is scattered       
between the source and the  moveable4   
,therefore the efflux1 like that of     
light1 is not material1 and  is unlike  
that of odours1 which are accompanied by
 a loss of substance1  unlike heat from 
a raging furnace1 unlike every other    

emanation by which  mediums are filled4 
,it remains1 therefore1 that as light   
which  illuminates all earthly things1  
is the immaterial species of that fire  
which is in the body of the sun1 so this
 virtue1 embracing and moving  all the  
planetary bodies1 is the immaterial     
species of that virtue which  resides in
 the sun itself1 of incalculable energy1
 and so the primary  act of all mundane 
motion4--,i should like to know who ever
 said that  there was anything material 
in light6--,guided by our notion of the 
efflux of this species 7or archetype71  
let us contemplate the more  intimate   
nature of the source itself4 ,for it    
seems as if something  divine were      
latent in the body of the sun1 and      
comparable to our own  soul1 whence that
 species emanates which drives round the
 planets2 just  as from the mind of a   
slinger the species of motion sticks to 
the  stones1 and carries them forward1  
even after he who cast them has drawn   
back his hand4 ,but to those who wish to

 proceed soberly1 reflections  differing
 a little from these will be offered4   
,our readers will1 perhaps1 be satisfied
 with the assurance1 that these  sober  
considerations will not enable them to  
form a much more accurate  notion of    
,kepler's meaning than the passages     
already cited4 ,we shall  therefore     
proceed to the various opinions he      
entertained on the motion  of the       
planets4    ,he considered it as        
established by his theory1 that the     
centre ,e of the  planet's epicycle 7see
 fig4 p4 #cc47 moved round the          
circumference of the  deferent ,dd1     
according to the law of the planet's    
distances2 the point  remaining to be   
settled was the motion of the planet in 
the epicycle4 ,if  it were made to move 
according to the same law1 so that when 
the centre  of the epicycle reached ,e1 
the planet should be at ,f1 taking the  
angle  ,,bef equal to ,,bsa1 it has been
 shewn 7p4 #ai7 that the path of ,f     
would  still be a circle1 excentric from

 ,dd by ,,da the radius of the epicycle4
    ,but ,kepler fancied that he saw    
many sound reasons why this could not be
  the true law of motion in the         
epicycle1 on which reasons he relied    
much  more firmly than on the           
indisputable fact1 which he mentions as 
a  collateral proof1 that it was        
contradicted by the observations4 ,some 
of  these reasons are subjoined3 ,in the
 beginning of the work it has been      
declared to be most absurd1 that a      
planet 7even though we suppose it       
endowed with mind7 should form any      
notion of a centre1 and a distance  from
 it1 if there be no body in that centre 
to serve for a  distinguishing mark4    
,and although you should say1 that the  
planet has  respect to the sun1 and     
knows beforehand1 and remembers the     
order in  which the distances from the  
sun are comprised1 so as to make a      
perfect  excentric2 in the first place1 
this is rather far-fetched1 and         
requires1  in any mind1 means for       

connecting the effect of an accurately  
circular  path with the sign of an      
increasing and diminishing diameter of  
the sun4  ,but there are no such means1 
except the position of the centre of the
  excentric at a given distance from the
 sun2 and ,i have already said1  that   
this is beyond the power of a mere mind4
 ,i do not deny that a  centre may be   
imagined1 and a circle round it2 but    
this ,i do say1 if the  circle exists   
only in imagination1 with no external   
sign or division1  that it is not       
possible that the path of a moveable    
body should be  really ordered round it 
in an exact circle4 ,besides1 if the    
planet  chooses from memory its just    
distances from the sun1 so as exactly to
  form a circle1 it must also take from 
the same source1 as if out of the       
,prussian or ,alphonsine tables1 equal  
excentric arcs1 to be described in      
unequal times1 and to be described by a 
force extraneous from the sun2  and thus
 would have1 from its memory1 a         

foreknowledge of what effects a  virtue1
 senseless and extraneous from the sun1 
was about to produce3 all  these        
consequences are absurd4    ,it is      
therefore more agreeable to reason that 
the planet takes no  thought1 either of 
the excentric or epicycle2 but that the 
work which it  accomplishes1 or joins in
 effecting1 is a libratory path in the  
diameter  ,bb of the epicycle1 in the   
direction towards the sun4 ,the law is  
now  to be discovered1 according to     
which the planet arrives at the proper  
distances in any time4 ,and indeed in   
this inquiry1 it is easier to say  what 
the law is not than what it is4--,here1 
according to his custom1  ,kepler       
enumerates several laws of motion by    
which the planet might  choose to       
regulate its energies1 each of which is 
successively  condemned4 ,only one of   
them is here mentioned1 as a specimen of
 the  rest4 ,what then if we were to say
 this8 ,although the motions of the     
planet are not epicyclical1 perhaps the 

libration is so arranged that  the      
distances from the sun are equal to what
 they would have been in a  real        
epicyclical motion4--,this leads to more
 incredible consequences  than the      
former suppositions1 and yet in the     
dearth of better opinions1  let us for  
the present content ourselves with this4
 ,the greater number  of absurd         
conclusions it will be found to involve1
 the more ready will a  physician be1   
when we come to the fifty-second        
chapter1 to admit what  the observations
 testify1 that the path of the planet is
 not circular4    ,the first oval path  
on which ,kepler was induced to fix1 by 
these and  many other similar           
considerations1 was in the first        
instance very  different from the true  
elliptical form4 ,most authors would    
have thought  it unnecessary to detain  
their readers with a theory which they  
had once  entertained and rejected2 but 
,kepler's work was written on a         
different  plan4 ,he thus introduces an 

explanation of his first oval4 ,as soon 
as ,i  was thus taught by ,brahe's very 
accurate observations that the orbit of 
a planet is not circular1 but more      
compressed at the sides1 on the  instant
 ,i thought that ,i understood the      
natural cause of this  deflection4 ,but 
the old proverb was verified in my      
case2--the more haste  the less         
speed4--,for having violently laboured  
in the #cith chapter1 in  consequence of
 my inability to find a sufficiently    
probable cause why  the orbit of the    
planet should be a perfect circle1 7some
 absurdities  always remaining with     
respect to that virtue which resides in 
the body  of the planet17 and having now
 discovered from the observations1 that 
the orbit is not a perfect circle1 ,i   
felt furiously inclined to believe  that
 if the theory which had been recognized
 as absurd1 when employed in  the #cith 
chapter for the purpose of fabricating a
 circle1 were modulated  into a more    
probable form1 it would produce an      

accurate orbit agreeing  with the       
observations4 ,if ,i had entered on this
 course a little more  warily1 ,i might 
have detected the truth immediately4    
,but1 being blinded  by my eagerness1   
and not sufficiently regardful of every 
part of the  #cith chapter1 and clinging
 to my first opinion1 which offered     
itself to  me with a wonderful show of  
probability1 on account of the equable  
motion in the epicycle1 ,i got entangled
 in new perplexities1 with which  we    
shall now have to struggle in this #deth
 chapter and the following  ones as far 
as the #ejth chapter4    ,in this       
theory1 ,kepler supposed that whilst the
 centre of the epicycle  was moving     
round a circular deferent according to  
the law of the  planets' distances 7or  
areas7 the planet itself moved equably  
in the  epicycle1 with the mean angular 
velocity of its centre in the deferent4 
,in consequence of this supposition1    
since at ,d1 when the planet is at ,a   
the aphelion1 the motion in the deferent

 is less than the mean motion1  the     
planet will have advanced through an    
angle ,,bep greater than ,,bef or       
,,bsa1 through which the centre of the  
epicycle has moved2 and  consequently1  
the path will lie everywhere within the 
circle ,aa1  except at the apsides4     
,here was a new train of laborious      
calculations to  undergo for the purpose
 of drawing the curve ,,apa according to
 this  law1 and of measuring the area of
 any part of it4 ,after a variety of    
fruitless attempts1 for this curve is   
one of singular complexity1 he was      
reduced1 as a last resource1 to suppose 
it insensibly different from an  ellipse
 on the same principal axes1 as an      
approximate means of  estimating its    
area4 ,not content even with the results
 so obtained1 and  not being able to see
 very clearly what might be the effect  
of his  alteration in substituting the  
ellipse for the oval1 and in other      
simplifications introduced by him1 he   
had courage enough to obtain the  sums  

of the #cfj distances by direct         
calculation1 as he had done in the  old 
circular theory4    ,illustration    ,in
 the preface to his book he had spoken  
of his labours under the  allegory of a 
war carried on by him against the       
planet2 and when  exulting in the early 
prospects of success this calculation   
seemed to  offer1 he did not omit once  
more to warn his readers1 in his        
peculiar  strain1 that this exultation  
was premature4    ,allow me1 gentle     
reader1 to enjoy so splendid a triumph  
for one little  day 7,i mean through the
 five next chapters71 meantime be all   
rumours  suppressed of new rebellion1   
that our preparations may not perish1   
yielding us no delight4 ,hereafter if   
anything shall come to pass1 we  will go
 through it in its own time and season2 
now let us be merry1 as  then we will be
 bold and vigorous4 ,at the time        
foretold1 that is to  say1 at the end of
 the five merry chapters1 the bad news  
could no longer  be kept a secret4 ,it  

is announced in the following           
bulletin3--,while  thus triumphing over 
,mars1 and preparing for him1 as for one
 altogether  vanquished1 tabular        
prisons1 and equated eccentric fetters1 
it is buzzed  here and there that the   
victory is vain1 and that the war is    
raging anew  as violently as before4    
,for the enemy1 left at home a despised 
captive1  has burst all the chains of   
the equations1 and broken forth of the  
prisons of the tables4 ,for no method of
 geometrically administering the  theory
 of the #deth chapter was able to come  
near the accuracy of  approximation of  
the vicarious theory of the #afth       
chapter1 which gave me  true equations  
derived from false principles4          
,skirmishers1 disposed all  round the   
circuit of the excentric1 7,i mean the  
true distances17 routed  my forces of   
physical causes levied out of the #deth 
chapter1 and shaking  off the yoke1     
regained their liberty4 ,and now there  
was little to  prevent the fugitive     

enemy from effecting a junction with his
 rebellious  supporters1 and reducing me
 to despair1 had ,i not suddenly sent   
into the  field a reserve of new        
physical reasonings on the rout and     
dispersion of  the veterans1 and        
diligently followed1 without allowing   
him the  slightest respite1 in the      
direction in which he had broken out4   
,in plainer terms1 ,kepler found1 after 
this labour was completed1 that  the    
errors in longitude he was still subject
 to were precisely of an  opposite      
nature to those he had found with the   
circle2 instead of being  too quick at  
the apsides1 the planet was now too slow
 there1 and too  much accelerated in the
 mean distances2 and the distances      
obtained from  direct observation were  
everywhere greater1 except at the       
apsides1 than  those furnished by this  
oval theory4 ,it was in the course of   
these  tedious investigations that he   
established1 still more satisfactorily  
than he had before done1 that the       

inclinations of the planets' orbits  are
 invariable1 and that the lines of their
 nodes pass through the  centre of the  
,sun1 and not1 as before his time had   
been supposed1  through the centre of   
the ecliptic4    ,when ,kepler found    
with certainty that this oval from which
 he expected  so much would not satisfy 
the observations1 his vexation was      
extreme1  not merely from the           
mortification of finding a theory       
confuted on which  he had spent such    
excessive labour1 for he was accustomed 
to  disappointments of that kind1 but   
principally from many anxious and       
fruitless speculations as to the real   
physical causes why the planet did  not 
move in the supposed epicycle1 that     
being the point of view1 as has  been   
already shewn1 from which he always     
preferred to begin his  inquiries4 ,one 
part of the reasoning by which he       
reconciled himself to  the failure      
exhibits much too curious a view of the 
state of his mind to  be passed over in 

silence4 ,the argument is founded on the
 difficulty  which he met with1 as above
 mentioned1 in calculating the          
proportions of  the oval path he had    
imagined4 ,in order that you may see the
 cause of  the impracticability of this 
method which we have just gone through1 
consider on what foundations it rests4  
,the planet is supposed to move  equably
 in the epicycle1 and to be carried by  
the ,sun unequably in the  proportion of
 the distances4 ,but by this method it  
is impossible to be  known how much of  
the oval path corresponds to any given  
time1 although  the distance at that    
part is known1 unless we first know the 
length of  the whole oval4 ,but the     
length of the oval cannot be known1     
except from  the law of the entry of the
 planet within the sides of the circle4 
,but  neither can the law of this entry 
be known before we know how much of  the
 oval path corresponds to any given     
time4 ,here you see that there is  a    
petitio principii2 and in my operations 

,i was assuming that of which  ,i was in
 search1 namely1 the length of the oval4
 ,this is at least not  the fault of my 
understanding1 but it is also most alien
 to the primary  ,ordainer of the       
planetary courses3 ,i have never yet    
found so  ungeometrical a contrivance in
 his other works4 ,therefore we must    
either  hit upon some other method of   
reducing the theory of the #deth chapter
 to  calculation2 or if that cannot be  
done1 the theory itself1 suspected on   
account of this petitio principii1 will 
totter4 ,whilst his mind was  thus      
occupied1 one of those extraordinary    
accidents which it has been  said never 
occur but to those capable of deriving  
advantage from them  7but which1 in     
fact1 are never noticed when they occur 
to any one else71  fortunately put him  
once more upon the right path4 ,half the
 extreme  breadth between the oval and  
the circle nearly represented the errors
 of  his distances at the mean point1   
and he found that this half was #dbi    

parts of a radius1 consisting of #ajjjjj
 parts2 and happening to advert  to the 
greatest optical inequality of ,mars1   
which amounts to about #e  #ah1 it      
struck him that #dbi was precisely the  
excess of the secant of #e  #ah above   
the radius taken at #ajjjjj4 ,this was a
 ray of light1 and1 to  use his own     
words1 it roused him as out of sleep4   
,in short1 this single  observation was 
enough to produce conviction in his     
singularly  constituted mind1 that      
instead of the distances ,,sf1 he should
 everywhere  substitute ,,fv1 determined
 by drawing ,,sv perpendicular on the   
line ,,fc1  since the excess of ,,sf    
above ,,fv is manifestly that of the    
secant above  the radius in the optical 
equation ,,sfc at that point4 ,it is    
still more  extraordinary that a        
substitution made for such a reason     
should have the  luck1 as is again the  
case1 to be the right one4 ,this        
substitution in  fact amounted to       
supposing that the planet1 instead of   

being at the  distance ,,sp or ,,sf1 was
 at ,sn2 or1 in other words1 that       
instead of  revolving in the            
circumference1 it librated in the       
diameter of the  epicycle1 which was to 
him an additional recommendation4 ,upon 
this new  supposition a fresh set of    
distances was rapidly calculated1 and to
  ,kepler's inexpressible joy1 they were
 found to agree with the  observations  
within the limits of the errors to which
 the latter were  necessarily subject4  
,notwithstanding this success1 he had to
 undergo1  before arriving at the       
successful termination of his labours1  
one more  disappointment4 ,although the 
distance corresponding to a time from   
the  aphelion represented approximately 
by the area ,,asf1 was thus found to be 
accurately represented by the line ,sn1 
there was still an error with  regard to
 the direction in which that distance   
was to be measured4  ,kepler's first    
idea was to set it off in the direction 
,,sf1 but this he  found to lead to     

inaccurate longitudes2 and it was not   
until after much  perplexity1 driving   
him1 as he tells us1 almost to insanity1
 that he  satisfied himself that the    
distance ,,sq equal to ,,fv ought to be 
taken  terminating in ,fm1 the line from
 ,f perpendicular to ,aa1 the line of   
apsides1 and that the curve so traced   
out by ,q would be an accurate  ellipse4
    ,illustration    ,he then found to  
his equal gratification and amazement1 a
 small part of  which he endeavoured to 
express by a triumphant figure on the   
side of  his diagram1 that the error he 
had committed in taking the area ,,asf  
to  represent the sums of the distances 
,,sf1 was exactly counterbalanced2 for  
this area does accurately represent the 
sums of the distances ,,fv or ,,sq4     
,this compensation1 which seemed to     
,kepler the greatest confirmation of    
his theory1 is altogether accidental and
 immaterial1 resulting from the         
relation between the ellipse and circle4
 ,if the laws of planetary  attraction  

had chanced to have been any other than 
those which cause  them to describe     
ellipses1 this last singular            
confirmation of an  erroneous theory    
could not have taken place1 and ,kepler 
would have been  forced either to       
abandon the theory of the areas1 which  
even then would  have continued to      
measure and define their motions1 or to 
renounce the  physical opinions from    
which he professed to have deduced it as
 an  approximative truth4    ,these are 
two of the three celebrated theorems    
called ,kepler's laws3 the  first is1   
that the planets move in ellipses round 
the sun1 placed in the  focus2 the      
second1 that the time of describing any 
arc is proportional  in the same orbit  
to the area included between the arc and
 the two  bounding distances from the   
sun4 ,the third will be mentioned on    
another  occasion1 as it was not        
discovered till twelve years later4 ,on 
the  establishment of these two         
theorems1 it became important to        

discover a  method of measuring such    
elliptic areas1 but this is a problem   
which  cannot be accurately solved4     
,kepler1 in offering it to the attention
 of  geometricians1 stated his belief   
that its solution was unattainable by   
direct processes1 on account of the     
incommensurability of the arc and  sine1
 on which the measurement of the two    
parts ,,aqm1 ,,sqm depends4  ,this1 says
 he in conclusion1 this is my belief1   
and whoever shall  shew my mistake1 and 
point out the true solution1            
,is erit mihi magnus ,apollonius4       
,,footnotes3    #ahi ,it is not very    
easy to carry the understanding aright  
among these  ,aristotelian ideas4 ,many 
at the present day might think they     
understood  better what is meant1 if for
 form had been written nature4    #aij  
,de mundo nostro sublunari1 ,philosphia 
,nova4 ,amstelodami1 #afea4    #aia     
,theoric nov planetarum4 ,g4 ,purbachii1
 ,parisiis1 #aeec4          ,,chapter   
,,vi4        ,kepler appointed          

,professor at ,linz--,his second        
marriage--,publishes        his new     
,method of ,gauging--,refuses a         
,professorship at ,bologna4      ,,when 
presenting this celebrated book to the  
emperor1 ,kepler gave notice  that he   
contemplated a farther attack upon      
,mars's relations1 father  ,jupiter1    
brother ,mercury1 and the rest2 and     
promised that he would be  successful1  
provided the emperor would not forget   
the sinews of war1 and  order him to be 
furnished anew with means for recruiting
 his army4 ,the  death of his unhappy   
patron1 the ,emperor ,rodolph1 which    
happened in  #afab1 barely in time to   
save him from the last disgrace of      
deposition  from the ,imperial throne1  
seemed to put additional difficulties in
 the  way of ,kepler's receiving the    
arrears so unjustly denied to him2 but  
on  the accession of ,rodolph's brother1
 ,matthias1 he was again named to his   
post of ,imperial ,mathematician1 and   
had also a permanent professorship      

assigned to him in the ,university of   
,linz4 ,he quitted ,prague without  much
 regret1 where he had struggled against 
poverty during eleven years4  ,whatever 
disinclination he might feel to depart1 
arose from his  unwillingness to loosen 
still more the hold he yet retained upon
 the  wreck of ,tycho ,brahe's          
instruments and observations4           
,tengnagel1  son-in-law of ,tycho1 had  
abandoned astronomy for a political     
career1 and  the other members of his   
family1 who were principally females1   
suffered  the costly instruments to lie 
neglected and forgotten1 although they  
had  obstructed with the utmost jealousy
 ,kepler's attempts to continue their   
utility4 ,the only two instruments      
,kepler possessed of his own property1  
were ,an iron sextant of #b feet        
diameter1 and a brass azimuthal         
quadrant1 of #c feet diameter1 both     
divided into minutes of a degree4       
,these were the gift of his friend and  
patron1 ,hoffman1 the ,president of     

,styria1 and with these he made all the 
observations which he added to  those of
 ,tycho ,brahe4 ,his constitution was   
not favourable to these  studies1 his   
health being always delicate1 and       
suffering much from  exposure to the    
night air2 his eyes also were very weak1
 as he mentions  himself in several     
places4 ,in the summary of his character
 which he drew  up when proposing to    
become ,tycho ,brahe's assistant1 he    
describes  himself as follows3--,for    
observations my sight is dull2 for      
mechanical  operations my hand is       
awkward2 in politics and domestic       
matters my  nature is troublesome and   
choleric2 my constitution will not allow
 me1  even when in good health1 to      
remain a long time sedentary            
7particularly  for an extraordinary time
 after dinner72 ,i must rise often and  
walk  about1 and in different seasons am
 forced to make corresponding changes   
in my diet4    ,the year preceding his  
departure to ,linz was denounced by him 

as  pregnant with misfortune and misery4
 ,in the first place ,i could get no    
money from the court1 and my wife1 who  
had for a long time been  suffering     
under low spirits and despondency1 was  
taken violently ill  towards the end of 
#afaj1 with the ,hungarian fever1       
epilepsy1 and  phrenitis4 ,she was      
scarcely convalescent when all my three 
children were  at once attacked with    
small-pox4 ,leopold with his army       
occupied the town  beyond the river1    
just as ,i lost the dearest of my sons1 
him whose  nativity you will find in my 
book on the new star4 ,the town on this 
side  of the river where ,i lived was   
harassed by the ,bohemian troops1 whose 
new levies were insubordinate and       
insolent3 to complete the whole1 the    
,austrian army brought the plague with  
them into the city4 ,i went into        
,austria1 and endeavoured to procure the
 situation which ,i now hold4           
,returning in ,june1 ,i found my wife in
 a decline from her grief at the  death 

of her son1 and on the eve of an        
infectious fever2 and ,i lost her  also1
 within eleven days after my return4    
,then came fresh annoyance1 of  course1 
and her fortune was to be divided with  
my step-sisters4 ,the  ,emperor ,rodolph
 would not agree to my departure2 vain  
hopes were given  me of being paid from 
,saxony2 my time and money were wasted  
together1  till on the death of the     
emperor1 in #afab1 ,i was named again by
 his  successor1 and suffered to depart 
to ,linz4 ,these1 methinks1 were reasons
  enough why ,i should have overlooked  
not only your letters1 but even         
astronomy itself4    ,kepler's first    
marriage had not been a happy one2 but  
the necessity in  which he felt himself 
of providing some one to take charge of 
his two  surviving children1 of whom the
 eldest1 ,susanna1 was born in #afjb1   
and  ,louis in #afjg1 determined him on 
entering a second time into the married 
state4 ,the account he has left us of   
the various negotiations which  preceded

 his final choice1 does not1 in any     
point1 belie the oddity of  his         
character4 ,his friends seem to have    
received a general commission to  look  
out for a suitable match1 and in a long 
and most amusing letter to  the ,baron  
,strahlendorf1 we are made acquainted   
with the pretensions and  qualifications
 of no less than eleven ladies among    
whom his inclinations  wavered4    ,the 
first on the list was a widow1 an       
intimate friend of his first  wife's1   
and who1 on many accounts1 appeared a   
most eligible match4 ,at  first she     
seemed favourably inclined to the       
proposal2 it is certain that  she took  
time to consider it1 but at last she    
very quietly excused  herself4 ,it must 
have been from a recollection of this   
lady's good  qualities that ,kepler was 
induced to make his offer2 for we learn 
rather  unexpectedly1 after being       
informed of her decision1 that when he  
soon  afterwards paid his respects to   
her1 it was for the first time that he  

had seen her during the last six years2 
and he found1 to his great  relief1 that
 there was no single pleasing point     
about her4 ,the truth  seems to be that 
he was nettled by her answer1 and he is 
at greater  pains than appear necessary1
 considering this last discovery1 to    
determine why she would not accept his  
offered hand4 ,among other reasons  he  
suggested her children1 among whom were 
two marriageable daughters2  and it is  
diverting afterwards to find them also  
in the catalogue which  ,kepler appeared
 to be making of all his female         
acquaintance4 ,he seems to  have been   
much perplexed in attempting to         
reconcile his astrological  theory with 
the fact of his having taken so much    
trouble about a  negotiation not        
destined to succeed4 ,have the stars    
exercised any  influence here8 ,for just
 about this time the direction of the   
,mid-,heaven  is in hot opposition to   
,mars1 and the passage of ,saturn1      
through the  ascending point of the     

zodiac1 in the scheme of my nativity1   
will happen  again next ,november and   
,december4 ,but if these are the causes1
 how do  they act8 ,is that explanation 
the true one which ,i have elsewhere    
given8  ,for ,i can never think of      
handing over to the stars the office of 
deities  to produce effects4 ,let us    
therefore suppose it accounted for by   
the  stars1 that at this season ,i am   
violent in my temper and affections1 in 
rashness of belief1 in a shew of pitiful
 tender-heartedness2 in catching  at    
reputation by new and paradoxical       
notions1 and the singularity of my      
actions2 in busily inquiring into1 and  
weighing and discussing1 various        
reasons2 in the uneasiness of my mind   
with respect to my choice4 ,i thank     
,god that that did not happen which     
might have happened2 that this  marriage
 did not take place3 now for the others4
 ,of these others1 one  was too old1    
another in bad health1 another too proud
 of her birth and  quarterings2 a fourth

 had learned nothing but shewy          
accomplishments1  not at all suitable to
 the sort of life she would have to lead
 with  me4 ,another grew impatient1 and 
married a more decided admirer1 whilst  
he was hesitating4 ,the mischief 7says  
he7 in all these attachments was1  that 
whilst ,i was delaying1 comparing1 and  
balancing conflicting  reasons1 every   
day saw me inflamed with a new passion4 
,by the time he  reached the eighth1 he 
found his match in this respect4        
,fortune at  length has avenged herself 
on my doubtful inclinations4 ,at first  
she was  quite complying1 and her       
friends also3 presently1 whether she did
 or did  not consent1 not only ,i1 but  
she herself did not know4 ,after the    
lapse  of a few days1 came a renewed    
promise1 which however had to be        
confirmed  a third time2 and four days  
after that1 she again repented her      
confirmation1 and begged to be excused  
from it4 ,upon this ,i gave her up1  and
 this time all my counsellors were of   

one opinion4 ,this was the  longest     
courtship in the list1 having lasted    
three whole months2 and  quite          
disheartened by its bad success1        
,kepler's next attempt was of a  more   
timid complexion4 ,his advances to ,no4 
#i1 were made by confiding to  her the  
whole story of his recent               
disappointment1 prudently determining   
to be guided in his behaviour1 by       
observing whether the treatment he had  
experienced met with a proper degree of 
sympathy4 ,apparently the  experiment   
did not succeed2 and almost reduced to  
despair1 ,kepler betook  himself to the 
advice of a friend1 who had for some    
time past complained  that she was not  
consulted in this difficult negotiation4
 ,when she  produced ,no4 #aj1 and the  
first visit was paid1 the report upon   
her was  as follows3--,she has1         
undoubtedly1 a good fortune1 is of good 
family1  and of economical habits3 but  
her physiognomy is most horribly ugly2  
she  would be stared at in the streets1 

not to mention the striking             
disproportion in our figures4 ,i am     
lank1 lean1 and spare2 she is short  and
 thick3 in a family notorious for       
fatness she is considered  superfluously
 fat4 ,the only objection to ,no4 #aa   
seems to have been her  excessive youth2
 and when this treaty was broken of on  
that account1  ,kepler turned his back  
upon all his advisers1 and chose for    
himself one  who had figured as ,no4 #e 
in the list1 to whom he professes to    
have felt  attached throughout1 but from
 whom the representations of his friends
  had hitherto detained him1 probably on
 account of her humble station4    ,the 
following is ,kepler's summary of her   
character4 ,her name is  ,susanna1 the  
daughter of ,john ,reuthinger and       
,barbara1 citizens of the  town of      
,eferdingen2 the father was by trade a  
cabinet-maker1 but both  her parents are
 dead4 ,she has received an education   
well worth the  largest dowry1 by favour
 of the ,lady of ,stahrenberg1 the      

strictness of  whose household is famous
 throughout the province4 ,her person   
and  manners are suitable to mine2 no   
pride1 no extravagance2 she can bear to 
work2 she has a tolerable knowledge how 
to manage a family2 middle-aged1  and of
 a disposition and capability to acquire
 what she still wants4 ,her  ,i shall   
marry by favour of the noble baron of   
,stahrenberg at twelve  o'clock on the  
#cjth of next ,october1 with all        
,eferdingen assembled to  meet us1 and  
we shall eat the marriage-dinner at     
,maurice's at the ,golden  ,lion4       
,hantsch has made an absurd mistake with
 regard to this marriage1 in  stating   
that the bride was only twelve years    
old4 ,kstner and other  biographers have
 been content to repeat the same        
assertion without any  comment1         
notwithstanding its evident             
improbability4 ,the origin of the       
blunder is to be found in ,kepler's     
correspondence with ,bernegger1 to      
whom1 speaking of his wife1 he says ,she

 has been educated for twelve  years by 
the ,lady of ,stahrenberg4 ,this is by  
no means a single instance  of          
carelessness in ,hantsch2 ,kstner has   
pointed out others of greater           
consequence4 ,it was owing to this      
marriage1 that ,kepler took occasion to 
write his new method of gauging1 for as 
he tells us in his own peculiar  style  
last ,november ,i brought home a new    
wife1 and as the whole course  of       
,danube was then covered with the       
produce of the ,austrian vineyards1  to 
be sold at a reasonable rate1 ,i        
purchased a few casks1 thinking it my   
duty as a good husband and a father of a
 family1 to see that my  household was  
well provided with drink4 ,when the     
seller came to  ascertain the quantity1 
,kepler objected to his method of       
gauging1 for  he allowed no difference1 
whatever might be the proportion of the 
bulging parts4 ,the reflections to which
 this incident gave rise1  terminated in
 the publication of the above-mentioned 

treatise1 which  claims a place among   
the earliest specimens of what is now   
called the  modern analysis4 ,in it he  
extended several properties of plane    
figures  to segments of cones and       
cylinders1 from the consideration that  
these  solids are incorporated circles1 
and1 therefore1 that those properties   
are true of the whole which belong to   
each component part4 ,that the book     
might end as oddly as it began1 ,kepler 
concluded it with a parody of           
,catullus3        ,et cum pocula mille  
mensi ermus      ,conturbabimus illa1 ne
 sciamus4    ,his new residence at ,linz
 was not long undisturbed4 ,he          
quarrelled there1  as he had done in the
 early part of his life at ,gratz1 with 
the ,roman  ,catholic party1 and was    
excommunicated4 ,judge1 says he to      
,peter  ,hoffman1 how far ,i can assist 
you1 in a place where the priest and    
school-inspector have combined to brand 
me with the public stigma of  heresy1   
because in every question ,i take that  

side which seems to me to  be consonant 
with the word of ,god4 ,the particular  
dogma which  occasioned his             
excommunication1 was connected with the 
doctrine of  transubstantiation4 ,he    
published his creed in a copy of ,latin 
verses1  preserved by his biographer    
,hantsch4    ,before this occurrence1   
,kepler had been called to the diet at  
,ratisbon  to give his opinion on the   
propriety of adopting the ,gregorian    
reformation of the calendar1 and he     
published a short essay1 pointing  out  
the respective convenience of doing so1 
or of altering the old  ,julian         
,calendar in some other manner4         
,notwithstanding the readiness of  the  
diet to avail themselves of his talents 
for the settlement of a  difficult      
question1 the arrears of his salary were
 not paid much more  regularly than they
 had been in ,rodolph's time1 and he was
 driven to  provide himself with money  
by the publication of his almanac1 of   
which  necessity he heavily and justly  

complained4 ,in order to pay the expense
  of the ,ephemeris for these two years1
 ,i have also written a vile            
prophesying almanac1 which is scarcely  
more respectable than begging2  unless  
it be because it saves the emperor's    
credit1 who abandons me  entirely2 and  
with all his frequent and recent orders 
in council1 would  suffer me to perish  
with hunger4 ,kepler published this     
,ephemeris  annually till #afbj2 ten    
years later he added those belonging to 
the  years from #afbj to #afbh4    ,in  
#afag ,kepler was invited into ,italy1  
to succeed ,magini as ,professor of     
,mathematics at ,bologna4 ,the offer    
tempted him2 but1 after mature          
consideration1 he rejected it1 on       
grounds which he thus explained to      
,roffini3--,by birth and spirit ,i am a 
,german1 imbued with ,german            
principles1 and bound by such family    
ties1 that even if the emperor  should  
consent1 ,i could not1 without the      
greatest difficulty1 remove my          

dwelling-place from ,germany into       
,italy4 ,and although the glory of      
holding so distinguished a situation    
among the venerable professors of       
,bologna stimulates me1 and there       
appears great likelihood of notably     
increasing my fortune1 as well from the 
great concourse to the public  lectures1
 as from private tuition2 yet1 on the   
other hand1 that period  of my life is  
past which was once excited by novelty1 
or which might  promise itself a long   
enjoyment of these advantages4 ,besides1
 from a boy  up to my present years1    
living a ,german among ,germans1 ,i am  
accustomed  to a degree of freedom in my
 speech and manners1 which1 if          
persevered in  on my removal to         
,bologna1 seems likely to draw upon me1 
if not danger1  at least notoriety1 and 
might expose me to suspicion and party  
malice4  ,notwithstanding this answer1  
,i have yet hopes that your most        
honourable  invitation will be of       
service to me1 and may make the imperial

 treasurer  more ready than he has      
hitherto been to fulfil his master's    
intentions  towards me4 ,in that case ,i
 shall the sooner be able to publish the
  ,rudolphine ,tables and the           
,ephemerides1 of which you had the      
scheme so  many years back2 and in this 
manner you and your advisers may have no
  reason to regret this invitation1     
though for the present it seems         
fruitless4    ,in #afai1 the ,emperor   
,matthias died1 and was succeeded by    
,ferdinand ,,iii41  who retained ,kepler
 in the post he had filled under his two
 predecessors  on the imperial throne4  
,kstner1 in his ,history of             
,mathematics1 has  corrected a gross    
error of ,hantsch1 in asserting that    
,kepler  prognosticated ,matthias's     
death4 ,the letter to which ,hantsch    
refers1 in  support of his statement1   
does indeed mention the emperor's death1
 but  merely as a notorious event1 for  
the purpose of recalling a date to the  
memory of his correspondent4            

,,chapter ,,vii4        ,kepler         
publishes his ,harmonics--,account of   
his ,astrological        ,opinions and  
,discovery of the ,law of the ,periods  
of the ,planetary                       
,revolutions--,sketch of ,newton's proof
 of ,kepler's ,laws4      ,,the         
,cosmographical ,mystery was written1 as
 has been already mentioned1  when      
,kepler was only twenty-six1 and the    
wildness of its theories might  be      
considered as due merely to the vivacity
 of a young man2 but as if  purposely to
 shew that his maturer age did not      
renounce the creations of  his youthful 
fancy1 he reprinted the ,mystery in     
#afai1 nearly at the  same time when he 
published his celebrated work on        
,harmonics2 and the  extravagance of the
 latter publication does not at all lose
 in  comparison with its predecessor4   
,it is dedicated to ,james ,i4 of       
,england1  and divided into five books3 
,the first1 ,geometrical1 on the origin 
and  demonstration of the laws of the   

figures which produce harmonious        
proportions2--the second1               
,architectonical1 on figurate geometry1 
and the  congruence of plane and solid  
regular figures2--the third1 properly   
,harmonic1 on the derivation of musical 
proportions from figures1 and on  the   
nature and distinction of things        
relating to song1 in opposition to  the 
old theories2--the fourth1              
,metaphysical1 ,psychological1 and      
,astrological1 on the mental essence of 
harmonies1 and of their kinds in  the   
world1 especially on the harmony of rays
 emanating on the earth from  the       
heavenly bodies1 and on their effect in 
nature1 and on the sublunary  and human 
soul2--the fifth1 ,astronomical and     
,metaphysical1 on the very  exquisite   
harmonies of the celestial motions1 and 
the origin of the  excentricities in    
harmonious proportions4    ,the two     
first books are almost strictly1 as     
,kepler styles them1  geometrical1      
relating in great measure to the        

inscription of regular  polygons in a   
circle4 ,the following passage is       
curious1 presenting an  analogous idea  
to that contained in one of the extracts
 already given  from the ,commentaries  
on ,mars4 ,the heptagon1 and all other  
polygons and  stars beyond it1 which    
have a prime number of sides1 and all   
other  figures derived from them1 cannot
 be inscribed geometrically in a        
circle2 although their sides have a     
necessary magnitude1 it is equally a    
matter of necessity that we remain      
ignorant of it4 ,this is a question of  
great importance1 for on this account is
 it that the heptagon1 and other        
figures of this kind1 have not been     
employed by ,god in the adornment of    
the world1 as the other intelligible    
figures are employed which have  been   
already explained4 ,kepler then         
introduces the algebraical  equation1 on
 the solution of which this problem     
depends1 and makes a  remark which is   
curious at this period of the history of

 algebra--that  the root of an equation 
which cannot be accurately found1 may   
yet be  found within any degree of      
approximation by an expert calculator4  
,in  conclusion he again remarks that   
the side of the heptagon has no place   
among scientific existences1 since its  
formal description is impossible1  and  
therefore it cannot be known by the     
human mind1 since the  possibility of   
description precedes the possibility of 
knowledge2 nor is  it known even by the 
simple eternal act of an omniscient     
mind1 because  its nature belongs to    
things which cannot be known4 ,and yet  
this  scientific nonentity has some     
scientific properties1 for if a heptagon
  were described in a circle1 the       
proportion of its sides would have      
analogous proportions4    ,the third    
book is a treatise on music1 in the     
confined and ordinary  sense in which we
 now use that word1 and apparently a    
sober and rational  one1 at least as    
nearly so as ,kepler could be trusted to

 write on a  subject so dangerous to his
 discretion4 ,all the extravagance of   
the work  seems reserved for the fourth 
book1 the title of which already conveys
  some notion of the nature of its      
contents4 ,in this book he has collected
  the substance of the astrological     
opinions scattered through his other    
works4 ,we shall content ourselves with 
merely citing his own words1  without   
any attempt to explain the difference   
between the astrology  which he         
believed1 and that which he             
contemptuously rejected4 ,the           
distinctive line seems very finely      
drawn1 and as both one and the other    
are now discarded by all who enjoy the  
full use of their reasoning  powers1 it 
is not of much consequence that it      
should be accurately  traced4    ,it is 
to be observed1 that he does not in this
 treatise modify or recant  anything of 
his earlier opinions1 but refers to the 
favourable judgment  of his contemporary
 philosophers as a reason for embodying 

them in a  regular form4 ,since many    
very celebrated professors of philosophy
 and  medicine are of opinion that ,i   
have created a new and most true        
philosophy1 this tender plant1 like all 
novelties1 ought to be carefully  nursed
 and cherished1 so that it may strike   
root in the minds of  philosophers1 and 
not be choked by the excessive humours  
of vain  sophistications1 or washed away
 by the torrents of vulgar prejudices1  
or  frozen by the chill of public       
neglect2 and if ,i succeed in guarding  
it  from these dangers1 ,i have no fear 
that it will be crushed by the storms   
of calumny1 or parched by the sun of    
sterling criticism4    ,one thing is    
very remarkable in ,kepler's creed1 that
 he whose candour is  so indisputable in
 every other part of his conduct1       
professed to have  been forced to adopt 
his astrological opinions from direct   
and positive  observation4--,it is now  
more than twenty years since ,i began to
  maintain opinions like these on the   

predominant nature of the elements1     
which1 adopting the common name1 ,i call
 sublunary4 ,i have been driven to  this
 not by studying or admiring ,plato1 but
 singly and solely by  observing        
seasons1 and noting the aspects by which
 they are produced4 ,i  have seen the   
state of the atmosphere almost uniformly
 disturbed as  often as the planets are 
in conjunction1 or in the other         
configurations  so celebrated among     
astrologers4 ,i have noticed its        
tranquil state1  either when there are  
none or few such aspects1 or when they  
are  transitory and of short duration4  
,i have not formed an opinion on this   
matter without good grounds1 like the   
common herd of prophesiers1 who         
describe the operations of the stars as 
if they were a sort of deities1  the    
lords of heaven and earth1 and producing
 everything at their  pleasure4 ,they   
never trouble themselves to consider    
what means the stars  have of working   
any effects among us on the earth1      

whilst they remain in  the sky1 and send
 down nothing to us which is obvious to 
the senses  except rays of light4 ,this 
is the principal source of the filthy   
astrological superstitions of that      
vulgar and childish race of dreamers1   
the prognosticators4    ,the real manner
 in which the configurations of the     
stars operate1  according to ,kepler1 is
 as follows3--,like one who listens to a
 sweet  melodious song1 and by the      
gladness of his countenance1 by his     
voice1  and by the beating of his hand  
or foot attuned to the music1 gives     
token  that he perceives and approves   
the harmony3 just so does sublunary     
nature1 with the notable and evident    
emotion of the bowels of the earth1     
bear like witness to the same feelings1 
especially at those times when  the rays
 of the planets form harmonious         
configurations on the  earth4--,i have  
been confirmed in this theory by that   
which might have  deterred others2 ,i   
mean1 by observing that the emotions do 

not agree  nicely with the instants of  
the configurations2 but the earth       
sometimes  appears lazy and obstinate1  
and at another time 7after important and
  long-continued configurations7 she    
becomes exasperated1 and gives way to   
her passion1 even without the           
continuation of aspects4 ,for in fact   
the  earth is not an animal like a dog1 
ready at every nod2 but more like a     
bull1 or an elephant1 slow to become    
angry1 and so much the more furious     
when incensed4    ,this singular        
doctrine must not be mistaken for one of
 ,kepler's  favourite allegories2 he    
actually and literally professed to     
believe  that the earth was an enormous 
living animal2 and he has enumerated1   
with a particularity of details into    
which we forbear to follow him1 the     
analogies he recognized between its     
habits and those of men and other       
animals4 ,a few samples of these may    
speak for the rest4 ,if any one who  has
 climbed the peaks of the highest       

mountains throw a stone down their  very
 deep clefts1 a sound is heard from     
them2 or if he throw it into one  of the
 mountain lakes1 which beyond doubt are 
bottomless1 a storm will  immediately   
arise1 just as when you thrust a straw  
into the ear or nose  of a ticklish     
animal1 it shakes its head1 or runs     
shuddering away4 ,what  so like         
breathing1 especially of those fish who 
draw water into their  mouths and spout 
it out again through their gills1 as    
that wonderful  tide6 ,for although it  
is so regulated according to the course 
of the  moon1 that1 in the preface to my
 ',commentaries on ,mars1' ,i have      
mentioned it as probable that the waters
 are attracted by the moon as  iron is  
by the loadstone2 yet1 if any one uphold
 that the earth  regulates its breathing
 according to the motion of the sun and 
moon1 as  animals have daily and nightly
 alternations of sleep and waking1 ,i   
shall  not think his philosophy unworthy
 of being listened to2 especially if    

any flexible parts should be discovered 
in the depths of the earth to  supply   
the functions of lungs or gills4        
,from the next extract1 we must leave   
the reader to learn as well as he  may1 
how much ,kepler did1 and how much he   
did not believe on the  subject of      
genethliac astrology4--,hence it is that
 human spirits1 at  the time of         
celestial aspects1 are particularly     
urged to complete the  matters which    
they have in hand4 ,what the goad is to 
the ox1 what the  spur or the rowel is  
to the horse1 to the soldier the bell   
and trumpet1  an animated speech to an  
audience1 to a crowd of rustics a       
performance  on the fife and bagpipes1  
that to all1 and especially in the      
aggregate1  is a heavenly configuration 
of suitable planets2 so that every      
single  one is excited in his thoughts  
and actions1 and all become more ready  
to  unite and associate their efforts4  
,for instance1 in war you may see that  
tumults1 battles1 fights1 invasions1    

assaults1 attacks1 and panic fears1     
generally happen at the time of the     
aspects of ,mars and ,mercury1 ,mars    
and ,jupiter1 ,mars and the ,sun1 ,mars 
and ,saturn1 c4 ,in epidemic  diseases1 
a greater number of persons are attacked
 at the times of the  powerful aspects1 
they suffer more severely1 or even die1 
owing to the  failure of nature in her  
strife with the disease1 which strife   
7and not  the death7 is occasioned by   
the aspect4 ,it is not the sky which    
does all  these things immediately1 but 
the faculty of the vital soul1          
associating  its operation with the     
celestial harmonies1 is the principal   
agent in  this so-called influence of   
the heavens4 ,indeed this word influence
 has  so fascinated some philosophers   
that they prefer raving with the        
senseless vulgar1 to learning the truth 
with me4 ,this essential property  is   
the principal foundation of that        
admirable genethliac art4 ,for when     
anything begins to have its being when  

that is working harmonies1 the  sensible
 harmony of the rays of the planets has 
peculiar influence on  it4 ,this then is
 the cause why those who are born under 
a season of many  aspects among the     
planets1 generally turn out busy and    
industrious1  whether they accustom     
themselves from childhood to amass      
wealth1 or are  born or chosen to direct
 public affairs1 or finally1 have given 
their  attention to study4 ,if any one  
think that ,i might be taken as an      
instance of this last class1 ,i do not  
grudge him the knowledge of my          
nativity4 ,i am not checked by the      
reproach of boastfulness1               
notwithstanding those who1 by speech or 
conduct1 condemn as folly all  kinds of 
writing on this subject2 the idiots1 the
 half-learned1 the  inventors of titles 
and trappings1 to throw dust in the eyes
 of the  people1 and those whom ,picus  
calls the plebeian theologians3 among   
the  true lovers of wisdom1 ,i easily   
clear myself of this imputation1 by the 

advantage of my reader2 for there is no 
one whose nativity or whose  internal   
disposition and temper ,i can learn so  
well as ,i know my own4  ,well then1    
,jupiter nearest the nonagesimal had    
passed by four degrees  the trine of    
,saturn2 the ,sun and ,venus1 in        
conjunction1 were moving from  the      
latter towards the former1 nearly in    
sextiles with both3 they were  also     
removing from quadratures with ,mars1 to
 which ,mercury was closely             
approaching3 the moon drew near the     
trine of the same planet1 close to  the 
,bull's ,eye1 even in latitude4 ,the    
#beth degree of ,gemini was rising1  and
 the #bb;d of ,aquarius culminating4    
,that there was this triple             
configuration on that day--namely1 the  
sextile of ,saturn and the ,sun1  the   
sextile of ,mars and ,jupiter1 the      
quadrature of ,mercury and ,mars1 is    
proved by the change of weather2 for1   
after a frost of some days1 that  very  
day became warmer1 there was a thaw and 

a fall of rain4#aib    ,i do not wish   
this single instance to be taken as a   
defence and proof  of all the aphorisms 
of astrologers1 nor do ,i attribute to  
the heavens  the government of human    
affairs3 what a vast interval still     
separates  these philosophical          
observations from that folly or madness 
as it should  rather be called4 ,for1   
following up this example1 ,i knew a    
lady#aic1  born under nearly the same   
aspects1 whose disposition1 indeed1 was 
exceedingly restless1 but who not only  
makes no progress in literature  7that  
is not strange in a woman71 but troubles
 her whole family1 and is  the cause to 
herself of deplorable misery4 ,what1 in 
my case1 assisted  the aspects          
was--firstly1 the fancy of my mother    
when pregnant with me1  a great admirer 
of her mother-in-law1 my grandmother1   
who had some  knowledge of medicine1 my 
grandfather's profession2 a second cause
 is1  that ,i was born a male1 and not a
 female1 for astrologers have sought  in

 vain to distinguish sexes in the sky2  
thirdly1 ,i derive from my  mother a    
habit of body1 more fit for study than  
other kinds of life2  fourthly1 my      
parents' fortune was not large1 and     
there was no landed  property to which  
,i might succeed and become attached2   
fifthly1 there  were the schools1 and   
the liberality of the magistracy towards
 such boys  as were apt for learning4   
,but now if ,i am to speak of the result
 of my  studies1 what ,i pray can ,i    
find in the sky1 even remotely alluding 
to  it4 ,the learned confess that       
several not despicable branches of      
philosophy have been newly extricated or
 amended or brought to  perfection by   
me3 but here my constellations were1 not
 ,mercury from the  east1 in the angle  
of the seventh1 and in quadratures with 
,mars1 but  ,copernicus1 but ,tycho     
,brahe1 without whose books of          
observations  everything now set by me  
in the clearest light must have remained
 buried  in darkness2 not ,saturn       

predominating ,mercury1 but my ,lords   
the ,emperors  ,rodolph and ,matthias2  
not ,capricorn1 the house of ,saturn1   
but ,upper  ,austria1 the home of the   
,emperor1 and the ready and unexampled  
bounty of  his nobles to my petition4   
,here is that corner1 not the western   
one of  the horoscope1 but on the       
,earth1 whither1 by permission of my    
imperial  master1 ,i have betaken myself
 from a too uneasy court2 and whence1   
during these years of my life1 which now
 tends towards its setting1  emanate    
these ,harmonies1 and the other matters 
on which ,i am engaged4    ,however1 it 
may be owing to ,jupiter's ascendancy   
that ,i take greater  delight in the    
application of geometry to physics1 than
 in that abstract  pursuit which        
partakes of the dryness of ,saturn2 and 
it is perhaps the  gibbous moon1 in the 
bright constellation of the ,bull's     
forehead1 which  fills my mind with     
fantastic images4    ,the most          
remarkable thing contained in the #eth  

,book1 is the announcement  of the      
celebrated law connecting the mean      
distances of the planets with  the      
periods of their revolution about the   
,sun4 ,this law is expressed in         
mathematical language1 by saying that   
the squares of the times vary as  the   
cubes of the distances4#aid ,kepler's   
rapture on detecting it was  unbounded1 
as may be seen from the exulting        
rhapsody with which he  announced it4   
,what ,i prophecied two-and-twenty years
 ago1 as soon as ,i  discovered the five
 solids among the heavenly orbits--what 
,i firmly  believed long before ,i had  
seen ,ptolemy's ',harmonics'--what ,i   
had  promised my friends in the title of
 this book1 which ,i named before ,i    
was sure of my discovery--what1 sixteen 
years ago1 ,i urged as a thing to  be   
sought--that for which ,i joined ,tycho 
,brahe1 for which ,i settled in         
,prague1 for which ,i have devoted the  
best part of my life to  astronomical   
contemplations1 at length ,i have       

brought to light1 and have  recognized  
its truth beyond my most sanguine       
expectations4 ,great as is  the absolute
 nature of ,harmonics with all its      
details1 as set forth in  my third book1
 it is all found among the celestial    
motions1 not indeed  in the manner which
 ,i imagined1 7that is not the least    
part of my  delight17 but in another    
very different1 and yet most perfect and
  excellent4 ,it is now eighteen months 
since ,i got the first glimpse of       
light1 three months since the dawn1 very
 few days since the unveiled  sun1 most 
admirable to gaze on1 burst out upon me4
 ,nothing holds me2 ,i  will indulge in 
my sacred fury2 ,i will triumph over    
mankind by the  honest confession1 that 
,i have stolen the golden vases of the  
,egyptians#aie1 to build up a tabernacle
 for my ,god far away from the  confines
 of ,egypt4 ,if you forgive me1 ,i      
rejoice2 if you are angry1 ,i can  bear 
it3 the die is cast1 the book is        
written2 to be read either now or  by   

posterity1 ,i care not which3 it may    
well wait a century for a reader1  as   
,god has waited six thousand years for  
an observer4    ,he has told1 with his  
usual particularity1 the manner and     
precise moment  of the discovery4       
,another part of my ',cosmographical    
,mystery1'  suspended twenty-two years  
ago1 because it was then undetermined1  
is  completed and introduced here1 after
 ,i had discovered the true intervals   
of the orbits1 by means of ,brahe's     
observations1 and had spent the         
continuous toil of a long time in       
investigating the true proportion of    
the periodic times to the orbits1       
,sera quidem respexit inertem1          
,respexit tamen1 et longo post tempore  
venit4    ,if you would know the precise
 moment1 the first idea came across me  
on  the #hth ,march of this year1 #afah2
 but chancing to make a mistake in the  
calculation1 ,i rejected it as false4 ,i
 returned again to it with new  force on
 the #aeth ,may1 and it has dissipated  

the darkness of my mind by  such an     
agreement between this idea and my      
seventeen years' labour on  ,brahe's    
observations1 that at first ,i thought  
,i must be dreaming1 and  had taken my  
result for granted in my first          
assumptions4 ,but the fact is  perfect1 
the fact is certain1 that the proportion
 existing between the  periodic times of
 any two planets is exactly the         
sesquiplicate  proportion of the mean   
distances of the orbits4    ,there is   
high authority for not attempting over  
anxiously to understand  the rest of the
 work4 ,delambre sums it up as          
follows3--,in the music of  the         
celestial bodies it appears that ,saturn
 and ,jupiter take the bass1  ,mars the 
tenor1 the ,earth and ,venus the        
counter-tenor1 and ,mercury the  treble4
 ,if the patience of this indefatigable 
historian gave way1 as he  confesses1 in
 the perusal1 any further notice of it  
here may be well  excused4 ,kepler      
became engaged1 in consequence of this  

publication1 in  an angry controversy   
with the eccentric ,robert ,fludd1 who  
was at least  ,kepler's match in wild   
extravagance and mysticism1 if far      
inferior to  him in genius4 ,it is      
diverting to hear each reproaching the  
other with  obscurity4    ,in the       
,epitome of the ,copernican ,astronomy1 
which ,kepler published  about the same 
time1 we find the manner in which he    
endeavoured to  deduce the beautiful law
 of periodic times1 from his principles 
of  motion and radiation of whirling    
forces4 ,this work is in fact a summary 
of all his astronomical opinions1 drawn 
up in a popular style in the  form of   
question and answer4 ,we find there a   
singular argument against  believing1 as
 some did1 that each planet is carried  
round by an angel1  for in that case1   
says ,kepler1 the orbits would be       
perfectly circular2  but the elliptic   
form1 which we find in them1 rather     
smacks of the  nature of the lever and  
material necessity4    ,the             

investigation of the relation between   
the periodic times and  distances of the
 planets is introduced by a query       
whether or not they  are to be          
considered heavy4 ,the answer is given  
in the following  terms3--,although none
 of the celestial globes are heavy1 in  
the sense  in which we say on earth that
 a stone is heavy1 nor light as fire is 
light with us1 yet have they1 by reason 
of their materiality1 a natural         
inability to move from place to place3  
they have a natural inertness or        
quietude1 in consequence of which they  
remain still in every situation  where  
they are placed alone4    ,p4 ,is it    
then the sun1 which by its turning      
carries round the  planets8 ,how can the
 sun do this1 having no hands to seize  
the planet at  so great a distance1 and 
force it round along with itself8--,its 
bodily  virtue1 sent forth in straight  
lines into the whole space of the world1
  serves instead of hands2 and this     
virtue1 being a corporeal species1      

turns with the body of the sun like a   
very rapid vortex1 and travels  over the
 whole of that space which it fills as  
quickly as the sun  revolves in its very
 confined space round the centre4    ,p4
 ,explain what this virtue is1 and      
belonging to what class of  things8--,as
 there are two bodies1 the mover and the
 moved1 so are there  two powers by     
which the motion is obtained4 ,the one  
is passive1 and  rather belonging to    
matter1 namely1 the resemblance of the  
body of the  planet to the body of the  
sun in its corporeal form1 and so that  
part of  the planetary body is friendly1
 the opposite part hostile to the sun4  
,the other power is active1 and bearing 
more relation to form1 namely1  the body
 of the sun has a power of attracting   
the planet by its friendly  part1 of    
repelling it by the hostile part1 and   
finally1 of retaining it  if it be      
placed so that neither the one nor the  
other be turned directly  towards the   
sun4    ,p4 ,how can it be that the     

whole body of the planet should be like 
or  cognate to the body of the sun1 and 
yet part of the planet friendly1  part  
hostile to the sun8--,just as when one  
magnet attracts another1 the  bodies are
 cognate2 but attraction takes place    
only on one side1  repulsion on the     
other4    ,p4 ,whence1 then1 arises that
 difference of opposite parts in the    
same  body8--,in magnets the diversity  
arises from the situation of the parts  
with respect to the whole4 ,in the      
heavens the matter is a little          
differently arranged1 for the sun does  
not1 like the magnet1 possess  only on  
one side1 but in all the parts of its   
substance1 this active and  energetic   
faculty of attracting1 repelling1 or    
retaining the planet4 ,so  that it is   
probable that the centre of the solar   
body corresponds to one  extremity or   
pole of the magnet1 and its whole       
surface to the other  pole4    ,p4 ,if  
this were so1 all the planets would be  
restored#aif in the  same time with the 

sun8--,true1 if this were all3 but it   
has been said  already that1 besides    
this carrying power of the sun1 there is
 also in  the planets a natural         
inertness to motion1 which causes that1 
by reason  of their material substance1 
they are inclined to remain each in its 
place4 ,the carrying power of the sun1  
and the impotence or material  inertness
 of the planet1 are thus in opposition4 
,each shares the  victory2 the sun moves
 the planet from its place1 although in 
some  degree it escapes from the chains 
with which it was held by the sun1 and  
so is taken hold of successively by     
every part of this circular virtue1  or1
 as it may be called1 solar             
circumference1 namely1 by the parts     
which  follow those from which it has   
just extricated itself4    ,p4 ,but how 
does one planet extricate itself more   
than another from  this                 
violence--,first1 because the virtue    
emanating from the sun has the  same    
degree of weakness at different         

distances1 as the distances or the      
width of the circles described on these 
distances4#aig ,this is the  principal  
reason4 ,secondly1 the cause is partly  
in the greater or less  inertness or    
resistance of the planetary globes1     
which reduces the  proportions to       
one-half2 but of this more hereafter4   
,p4 ,how can it be that the virtue      
emanating from the sun becomes  weaker  
at a greater distance8 ,what is there to
 hurt or weaken  it8--,because that     
virtue is corporeal1 and partaking of   
quantity1 which  can be spread out and  
rarefied4 ,then1 since there is as much 
virtue  diffused in the vast orb of     
,saturn as is collected in the very     
narrow  one of ,mercury1 it is very rare
 and therefore weak in ,saturn's orbit1 
very dense and therefore powerful at    
,mercury4    ,p4 ,you said1 in the      
beginning of this inquiry into motion1  
that the  periodic times of the planets 
are exactly in the sesquiplicate        
proportion of their orbits or circles3  

pray what is the cause of  this8--,four 
causes concur for lengthening the       
periodic time4 ,first1 the  length of   
the path2 secondly1 the weight or       
quantity of matter to be  carried2      
thirdly1 the degree of strength of the  
moving virtue2 fourthly1  the bulk or   
space into which is spread out the      
matter to be moved4 ,the  circular paths
 of the planets are in the simple ratio 
of the distances2  the weights or       
quantities of matter in different       
planets are in the  subduplicate ratio  
of the same distances1 as has been      
already proved2 so  that with every     
increase of distance1 a planet has more 
matter1 and  therefore is moved more    
slowly1 and accumulates more time in its
  revolution1 requiring already as it   
did more time by reason of the  length  
of the way4 ,the third and fourth causes
 compensate each other in  a comparison 
of different planets3 the simple and    
subduplicate  proportion compound the   
sesquiplicate proportion1 which         

therefore is the  ratio of the periodic 
times4    ,three of the four            
suppositions here made by ,kepler to    
explain the  beautiful law he had       
detected1 are now indisputably known to 
be false4  ,neither the weights nor the 
sizes of the different planets observe  
the  proportions assigned by him1 nor is
 the force by which they are retained   
in their orbits in any respect similar  
in its effects to those  attributed by  
him to it4 ,the wonder which might      
naturally be felt that  he should       
nevertheless reach the desired          
conclusion1 will be  considerably abated
 on examining the mode in which he      
arrived at and  satisfied himself of the
 truth of these three suppositions4 ,it 
has been  already mentioned that his    
notions on the existence of a whirling  
force  emanating from the sun1 and      
decreasing in energy at increased       
distances1  are altogether inconsistent 
with all the experiments and            
observations we  are able to collect4   

,his reason for asserting that the sizes
 of the  different planets are          
proportional to their distances from the
 sun1 was  simply because he chose to   
take for granted that either their      
solidities1 surfaces1 or diameters1 must
 necessarily be in that  proportion1 and
 of the three1 the solidities appeared  
to him least  liable to objection4 ,the 
last element of his precarious reasoning
 rested  upon equally groundless        
assumptions4 ,taking as a principle1    
that where  there is a number of        
different things they must be different 
in every  respect1 he declared that it  
was quite unreasonable to suppose all   
the  planets of the same density4 ,he   
thought it indisputable that they must  
be rarer as they were farther from the  
sun1 and yet not in the  proportion of  
their distances1 for thus we should sin 
against the law of  variety in another  
way1 and make the quantity of matter    
7according to  what he had just said of 
their bulk7 the same in all4 ,but if we 

assume  the ratio of the quantities of  
matter to be half that of the distances1
  we shall observe the best mean of all2
 for thus ,saturn will be half as  heavy
 again as ,jupiter1 and ,jupiter half   
again as dense as ,saturn4 ,and  the    
strongest argument of all is1 that      
unless we assume this proportion  of the
 densities1 the law of the periodic     
times will not answer4 ,this  is the    
proof alluded to1 and it is clear that  
by such reasoning any  required result  
might be deduced from any given         
principles4    ,it may not be           
uninstructive to subjoin a sketch of the
 manner in which  ,newton established   
the same celebrated results1 starting   
from principles  of motion diametrically
 opposed to ,kepler's1 and it need      
scarcely be  added1 reasoning upon them 
in a manner not less different4 ,for    
this  purpose1 a very few prefatory     
remarks will be found sufficient4       
,the different motions seen in nature   
are best analysed and classified by     

supposing that every body in motion1 if 
left to itself1 will continue to  move  
forward at the same rate in a straight  
line1 and by considering all  the       
observed deviations from this manner of 
moving1 as exceptions and  disturbances 
occasioned by some external cause4 ,to  
this supposed cause  is generally given 
the name of ,force1 and it is said to be
 the first law  of motion1 that1 unless 
acted on by some force1 every body at   
rest  remains at rest1 and every body in
 motion proceeds uniformly in a         
straight line4 ,many employ this        
language1 without perceiving that it    
involves a definition of force1 on the  
admission of which1 it is reduced  to a 
truism4 ,we see common instances of     
force in a blow1 or a pull from  the end
 of a string fastened to the body3 we   
shall also have occasion  presently to  
mention some forces where no visible    
connexion exists  between the moving    
body and that towards which the motion  
takes place1  and from which the force  

is said to proceed4    ,illustration3   
c           ,c    -------------         
_/                _/                 _/ 
_/                   _/                 
_/                      -------------   
,b             ,c'     ,a second law of 
motion1 founded upon experiment1 is     
this3 if a body have  motion            
communicated to it in two directions1 by
 one of which motions  alone it would   
have passed through a given space in a  
given time1 as for  instance1 through   
,,bc in one second1 and by the other    
alone through any  other space ,bc in   
the same time1 it will1 when both are   
given to it at  the same instant1 pass  
in the same time 7in the present        
instance in one  second7 through ,,bc   
the diagonal of the parallelogram of    
which ,,bc and  ,bc are sides4          
,illustration3                      _/  
,s                    _/ _/             
_/ _/                    _/ _/          
_/ _/                      _/ _/        
_/ _/                                   

----------------------             ,a ,b
      ,c      ,d ,e     ,let a body1    
acted upon by no force1 be moving along 
the line ,,ae2 that  means1 according to
 what has been said1 let it pass over   
the equal  straight lines ,,ab1 ,,bc1   
,,cd1 ,,de1 c41 in equal times4 ,if we  
take any point  ,s not in the line ,,ae1
 and join ,,as1 ,,bs1 c41 the triangles 
,,asb1 ,,bsc1 c4  are also equal1 having
 a common altitude and standing on equal
 bases1 so  that if a string were       
conceived reaching from ,s to the moving
 body  7being lengthened or shortened in
 each position to suit its distance     
from ,s71 this string1 as the body moved
 along ,,ae1 would sweep over equal     
triangular areas in equal times4        
,illustration    ,let us now examine how
 far these conclusions will be altered  
if the body  from time to time is forced
 towards ,s4 ,we will suppose it moving 
uniformly from ,a to ,b as before1 no   
matter for the present how it got to    
,a1 or into the direction ,,ab4 ,if left

 to itself it would1 in an equal  time  
7say #a7 go through ,,bc in the same    
straight line with and equal  to ,,ab4  
,but just as it reaches ,b1 and is      
beginning to move along ,,bc1 let  it be
 suddenly pulled towards ,s with a      
motion which1 had it been at  rest1     
would have carried it in the same time1 
#a through any other  space ,bc4        
,according to the second law of motion1 
its direction during  this #a1 in       
consequence of the two motions combined1
 will be along ,,bc1  the diagonal of   
the parallelogram of which ,,bc1 ,bc1   
are sides4 ,in  this case1 as this      
figure is drawn1 ,,bc1 though passed in 
the same time1  is longer than ,,ab2    
that is to say1 the body is moving      
quicker than at  first4 ,how is it with 
the triangular areas1 supposed as before
 to be  swept by a string constantly    
stretched between ,s and the body8 ,it  
will  soon be seen that these still     
remain equal1 notwithstanding the change
  of direction1 and increased swiftness4

 ,for since ,,cc is parallel to  ,bc1   
the triangles ,,scb1 ,,sc,b are equal1  
being on the same base ,,sb1 and        
between the same parallels ,,sb1 ,,cc1  
and ,,sc,b is equal to ,,sba as before1 
therefore ,,scb1 ,,sba are equal4 ,the  
body is now moving uniformly 7though    
quicker than along ,,ab7 along ,,bc4 ,as
 before1 it would in a time equal to    
the time of passing along ,,bc1 go      
through an equal space ,,cd in the same 
straight line4 ,but if at ,c it has a   
second pull towards ,s1 strong enough   
to carry it to d in the same time1 its  
direction will change a second  time to 
,,cd1 the diagonal of the parallelogram1
 whose sides are ,,cd1  ,cd2 and the    
circumstances being exactly similar to  
those at the first  pull1 it is shewn in
 the same manner that the triangular    
area ,,sdc  ,,scb   ,,sba4    ,thus it  
appears1 that in consequence of these   
intermitting pulls towards  ,s1 the body
 may be moving round1 sometimes faster1 
sometimes slower1 but  that the         

triangles formed by any of the straight 
portions of its path  7which are all    
described in equal times71 and the lines
 joining ,s to the  ends of that        
portion1 are all equal4 ,the path it    
will take depends of  course1 in other  
respects1 upon the frequency and        
strength of the  different pulls1 and it
 might happen1 if they were duly        
proportionate1  that when at ,h1 and    
moving off in the direction ,,ha1 the   
pull ,ha  might be such as just to carry
 the body back to ,a1 the point from    
which  it started1 and with such a      
motion1 that after one pull more1 ,ab1  
at  ,a1 it might move along ,,ab as it  
did at first4 ,if this were so1 the body
  would continue to move round in the   
same polygonal path1 alternately        
approaching and receding from ,s1 as    
long as the same pulls were repeated  in
 the same order1 and at the same        
intervals4    ,it seems almost          
unnecessary to remark1 that the same    
equality which  subsists between any two

 of these triangular areas subsists also
 between  an equal number of them1 from 
whatever part of the path taken2 so     
that1  for instance1 the four paths     
,,ab1 ,,bc1 ,,cd1 ,,de1 corresponding to
 the four  areas ,,asb1 ,,bsc1 ,,csd1   
,,dse1 that is1 to the area ,,abcdes1   
are passed in the  same time as the four
 ,,ef1 ,,fg1 ,,gh1 ,,ha1 corresponding  
to the equal area  ,,efghas4 ,hence it  
may be seen1 if the whole time of       
revolution from ,a  round to ,a again be
 called a year1 that in half a year the 
body will  have got to ,e1 which in the 
present figure is more than half way    
round1  and so of any other periods4    
,the more frequently the pulls are      
supposed to recur1 the more frequently  
will the body change its direction2 and 
if the pull were supposed  constantly   
exerted in the direction towards ,s1 the
 body would move in a  curve round ,s1  
for no three successive positions of it 
could be in a  straight line4 ,those who
 are not familiar with the methods of   

measuring  curvilinear spaces must here 
be contented to observe1 that the law   
holds1 however close the pulls are      
brought together1 and however closely   
the polygon is consequently made to     
resemble a curve3 they may1 if they     
please1 consider the minute portions    
into which the curve is so divided1  as 
differing insensibly from little        
rectilinear triangles1 any equal  number
 of which1 according to what has been   
said above1 wherever taken  in the      
curve1 would be swept in equal times4   
,the theorem admits1 in this  case also1
 a rigorous proof2 but it is not easy to
 make it entirely  satisfactory1 without
 entering into explanations which would 
detain us  too long from our principal  
subject4    ,the proportion in which the
 pull is strong or weak at different    
distances from the central spot1 is     
called the law of the central or        
centripetal force1 and it may be        
observed1 that after assuming the  laws 
of motion1 our investigations cease to  

have anything hypothetical  or          
experimental in them2 and that if we    
wish1 according to these  principles of 
motion1 to determine the law of force   
necessary to make a  body move in a     
curve of any required form1 or          
conversely to discover the  form of the 
curve described1 in consequence of any  
assumed law of force1  the inquiry is   
purely geometrical1 depending upon the  
nature and  properties of geometrical   
quantities only4 ,this distinction      
between what  is hypothetical1 and what 
necessary truth1 ought never to be lost 
sight  of4    ,as the object of the     
present treatise is not to teach        
geometry1 we shall  describe1 in very   
general terms1 the manner in which      
,newton1 who was  the first who         
systematically extended the laws of     
motion to the heavenly  bodies1         
identified their results with the two   
remaining laws of ,kepler4  ,his        
,principles of ,natural ,philosophy     
contain general propositions with       

regard to any law of centripetal force1 
but that which he supposed to be  the   
true one in our system1 is expressed in 
mathematical language1 by  saying that  
the centripetal force varies inversely  
as the square of the  distance1 which   
means1 that if the force at any distance
 be taken for  the unit of force1 at    
half that distance1 it is two times     
twice1 or four  times as strong2 at     
one-third the distance1 three times     
thrice1 or nine  times as strong1 and so
 for other distances4 ,he shewed the    
probability  of this law in the first   
instance by comparing the motion of the 
moon  with that of heavy bodies at the  
surface of the earth4 ,taking ,,lp to   
represent part of the moon's orbit      
described in one minute1 the line ,,pm  
between the orbit and the tangent at ,l 
would shew the space through  which the 
central force at the earth 7assuming the
 above principles of  motion to be      
correct7 would draw the moon4 ,from the 
known distance and  motion of the moon1 

this line ,,pm is found to be about     
sixteen feet4 ,the  distance of the moon
 is about sixty times the radius of the 
earth1 and  therefore if the law of the 
central force in this instance were such
 as  has been supposed1 the force at the
 earth's surface would be #fj times     
#fj1 or #cfjj times stronger1 and at the
 earth's surface1 the central  force    
would make a body fall through #cfjj    
times #af feet in one minute4  ,galileo 
had already taught that the spaces      
through which a body would be  made to  
fall1 by the constant action of the same
 unvarying force1 would  be proportional
 to the squares of the times during     
which the force was  exerted1 and       
therefore according to these laws1 a    
body at the earth's  surface ought      
7since there are sixty seconds in a     
minute7 to fall  through #af feet in one
 second1 which was precisely the space  
previously  established by numerous     
experiments4    ,illustration    ,with  
this confirmation of the supposition1   

,newton proceeded to the  purely        
geometrical calculation of the law of   
centripetal#aih force  necessary to make
 a moving body describe an ellipse round
 its focus1  which ,kepler's            
observations had established to be the  
form of the orbits  of the planets round
 the sun4 ,the result of the inquiry    
shewed that this  curve required the    
same law of the force1 varying inversely
 as the  square of the distance1 which  
therefore of course received additional 
confirmation4 ,his method of doing this 
may1 perhaps1 be understood by          
referring to the last figure but one1 in
 which ,cd1 for instance1  representing 
the space fallen from any point ,c      
towards ,s1 in a given  time1 and the   
area ,,csd being proportional to the    
corresponding time1 the  space through  
which the body would have fallen at ,c  
in any other time  7which would be      
greater1 by ,galileo's law1 in          
proportion to the squares  of the       
times71 might be represented by a       

quantity varying directly as  ,cd1 and  
inversely in the duplicate proportion of
 the triangular area  ,,csd1 that is to 
say1 proportional to ,cd_/7,,sc  ,dk71  
if ,dk be drawn  from ,d perpendicular  
on ,,sc4 ,if this polygon represent an  
ellipse1 so  that ,,cd represents a     
small arc of the curve1 of which ,s is  
the focus1 it  is found by the nature of
 that curve1 that ,cd_/7,dk7 is the same
 at  all points of the curve1 so that   
the law of variation of the force in    
the same ellipse is represented solely  
by #a_/7,,sc74 ,if ,cd1 c4 are  drawn so
 that ,cd_/7,dk7 is not the same at     
every point1 the curve  ceases to be an 
ellipse whose focus is at ,s1 as ,newton
 has shewn in the  same work4 ,the line 
to which 7,dk7_/,cd is found to be      
equal1 is one drawn  through the focus  
at right angles to the longest axis of  
the ellipse  till it meets the          
curve2--this line is called the latus   
rectum1 and is  a third proportional to 
the two principal axes4    ,kepler's    

third law follows as an immediate       
consequence of this  determination2 for1
 according to what has been already     
shown1 the time  of revolution round the
 whole ellipse1 or1 as it is commonly   
called1  the periodic time1 bears the   
same ratio to the unit of time as the   
whole  area of the ellipse does to the  
area described in that unit4 ,the area  
of  the whole ellipse is proportional in
 different ellipses to the rectangle    
contained by the two principal axes1 and
 the area described in an unit  of time 
is proportional to ,,sc  ,dk1 that is to
 say1 is in the  subduplicate ratio of  
,,sc  ,dk1 or ,dk_/,cd1 when the force  
varies  inversely as the square of the  
distance ,,sc2 and in the ellipse1 as we
  have said already1 this is equal to a 
third proportional to the  principal    
axes2 consequently the periodic times in
 different ellipses1  which are         
proportional to the whole areas of the  
ellipses directly1 and  the areas       
described in the unit of time inversely1

 are in the compound  ratio of the      
rectangle of the axes directly1 and     
subduplicately as a  third proportional 
to the axes inversely2 that is to say1  
the squares of  these times are         
proportional to the cubes of the longest
 axes1 which is  ,kepler's law4         
,,footnotes3    #aib ,this mode of      
verifying configurations1 though        
something of the  boldest1 was by no    
means unusual4 ,on a former occasion    
,kepler1 wishing  to cast the nativity  
of his friend ,zehentmaier1 and being   
unable to  procure more accurate        
information than that he was born about 
three  o'clock in the afternoon of the  
#bast of ,october1 #agea1 supplied the  
deficiency by a record of fevers and    
accidents at known periods of his  life1
 from which he deduced a more exact     
horoscope4    #aic ,kepler probably     
meant his own mother1 whose horoscope he
 in many  places declared to be nearly  
the same as his own4    #aid ,see       
,preliminary ,treatise1 p4 #ac4    #aie 

,in allusion to the ,harmonics of       
,ptolemy4    #aif ,this is a word       
borrowed from the ,ptolemaic astronomy1 
according to  which the sun and planets 
are hurried from their places by the    
daily  motion of the primum mobile1 and 
by their own peculiar motion seek to    
regain or be restored to their former   
places4    #aig ,in other parts of his  
works1 ,kepler assumes the diminution to
 be  proportional to the circles        
themselves1 not to the diameters4       
#aih ,in many curves1 as in the circle  
and ellipse1 there is a point to  which 
the name of centre is given1 on account 
of peculiar properties  belonging to it3
 but the term centripetal force always  
refers to the  place towards which the  
force is directed1 whether or not       
situated in  the centre of the curve4   
,,chapter ,,viii4        ,the ,epitome  
prohibited at ,rome--,logarithmic       
,tables--,trial of        ,catharine    
,kepler--,kepler invited to             
,england--,rudolphine                   

,tables--,death--,conclusion4           
,,kepler',s ,epitome1 almost immediately
 on its appearance1 enjoyed the  honour 
of being placed by the side of the work 
of ,copernicus1 on the  list of books   
prohibited by the congregation of the   
,index at ,rome4 ,he  was considerably  
alarmed on receiving this intelligence1 
anticipating  that it might occasion    
difficulties in publishing his future   
writings4  ,his words to ,remus1 who had
 communicated the news to him1 are as   
follows3--,i learn from your letter1 for
 the first time1 that my book is        
prohibited at ,rome and ,florence4 ,i   
particularly beg of you1 to send me  the
 exact words of the censure1 and that   
you will inform me whether that  censure
 would be a snare for the author1 if he 
were caught in ,italy1 or  whether1 if  
taken1 he would be enjoined a           
recantation4 ,it is also of  consequence
 for me to know whether there is any    
chance of the same  censure being       
extended into ,austria4 ,for if this be 

so1 not only shall ,i  never again find 
a printer there1 but also the copies    
which the  bookseller has left in       
,austria at my desire will be           
endangered1 and the  ultimate loss will 
fall upon me4 ,it will amount to giving 
me to  understand1 that ,i must cease to
 profess ,astronomy1 after ,i have grown
  old in the belief of these opinions1  
having been hitherto gainsayed by  no   
one1--and1 in short1 ,i must give up    
,austria itself1 if room is no  longer  
to be left in it for philosophical      
liberty4 ,he was1 however1              
tranquillized1 in a great degree1 by the
 reply of his friend1 who told  him that
 the book is only prohibited as contrary
 to the decree  pronounced by the holy  
office two years ago4 ,this has been    
partly  occasioned by a ,neapolitan monk
 7,foscarini71 who was spreading these  
notions by publishing them in ,italian1 
whence were arising dangerous           
consequences and opinions3 and besides1 
,galileo was at the same time  pleading 

his cause at ,rome with too much        
violence4 ,copernicus has been          
corrected in the same manner for some   
lines1 at least in the beginning  of his
 first book4 ,but by obtaining a        
permission1 they may be read 7and1  as  
,i suppose1 this ,epitome also7 by the  
learned and skilful in this  science1   
both at ,rome and throughout all ,italy4
 ,there is therefore no  ground for your
 alarm1 either in ,italy or ,austria2   
only keep yourself  within bounds1 and  
put a guard upon your own passions4     
,we shall not dwell upon ,kepler's      
different works on comets1 beyond       
mentioning that they were divided1 on   
the plan of many of his other           
publications1 into three parts1         
,astronomical1 ,physical1 and           
,astrological4 ,he maintained that      
comets move in straight lines1 with a   
varying degree of velocity4 ,later      
theories have shewn that they obey the  
same laws of motion as the planets1     
differing from them only in the  extreme

 excentricity of their orbits4 ,in the  
second book1 which contains  the        
,physiology of ,comets1 there is a      
passing remark that comets come out     
from the remotest parts of ether1 as    
whales and monsters from the depth  of  
the sea2 and the suggestion is thrown   
out that perhaps comets are  something  
of the nature of silkworms1 and are     
wasted and consumed in  spinning their  
own tails4    ,among his other laborious
 employments1 ,kepler yet found time to 
calculate tables of logarithms1 he      
having been one of the first in         
,germany to appreciate the full         
importance of the facilities they afford
  to the numerical calculator4 ,in #afah
 he wrote to his friend ,schickhard3    
,there is a ,scottish ,baron 7whose name
 has escaped my memory71 who has  made a
 famous contrivance1 by which all need  
of multiplication and  division is      
supplied by mere addition and           
subtraction2 and he does it  without    
sines4 ,but even he wants a table of    

tangents#aii1 and the  variety1         
frequency1 and difficulty of the        
additions and subtractions1 in  some    
cases1 is greater than the labour of    
multiplying and dividing4    ,kepler    
dedicated his ,ephemeris for #afbj to   
the author of this  celebrated          
invention1 ,baron ,napier1 of           
,merchistoun2 and in #afbd1  published  
what he called ,chilias ,logarithmorum1 
containing the  ,napierian logarithms of
 the quotients of #ajj1jjj divided by   
the first  ten numbers1 then proceeding 
by the quotients of every ten to #ajj1  
and  by hundreds to #ajj1jjj4 ,in the   
supplement published the following year1
  is a curious notice of the manner in  
which this subtle contrivance was  at   
first received3 ,in the year #afba1 when
 ,i had gone into ,upper  ,austria1 and 
had conferred everywhere with those     
skilled in mathematics1  on the subject 
of ,napier's logarithms1 ,i found that  
those whose prudence  had increased1 and
 whose readiness had diminished1 through

 age1 were  hesitating whether to adopt 
this new sort of numbers1 instead of a  
table  of sines2 because they said it   
was disgraceful to a professor of       
mathematics to exult like a child at    
some compendious method of working1  and
 meanwhile to admit a form of           
calculation1 resting on no legitimate   
proof1 and which at some time might     
entangle us in error1 when we least     
feared it4 ,they complained that        
,napier's demonstration rested on a     
fiction of geometrical motion1 too loose
 and slippery for a sound method  of    
reasonable demonstration to be founded  
on it4#bjj ,this led me  forthwith to   
conceive the germ of a legitimate       
demonstration1 which  during that same  
winter ,i attempted1 without reference  
to lines or  motion1 or flow1 or any    
other which ,i may call sensible        
quality4    ,now to answer the question2
 what is the use of logarithms8 ,exactly
 what  ten years ago was announced by   
their author1 ,napier1 and which may be 

told in these words4--,wheresoever in   
common arithmetic1 and in the ,rule  of 
,three1 come two numbers to be          
multiplied together1 there the sum of   
the logarithms is to be taken2 where one
 number is to be divided by  another1   
the difference2 and the number          
corresponding to this sum or            
difference1 as the case may be1 will be 
the required product or  quotient4      
,this1 ,i say1 is the use of logarithms4
 ,but in the same work in  which ,i gave
 the demonstration of the principles1 ,i
 could not satisfy  the unfledged       
arithmetical chickens1 greedy of        
facilities1 and gaping  with their beaks
 wide open1 at the mention of this use1 
as if to bolt  down every particular    
gobbet1 till they are crammed with my   
precepticles4    ,the year #afbb was    
marked by the catastrophe of a singular 
adventure  which befell ,kepler's       
mother1 ,catharine1 then nearly seventy 
years old1  and by which he had been    
greatly harassed and annoyed during     

several  years4 ,from her youth she had 
been noted for a rude and passionate    
temper1 which on the present occasion   
involved her in serious  difficulties4  
,one of her female acquaintance1 whose  
manner of life had  been by no means    
unblemished1 was attacked after a       
miscarriage by  violent headaches1 and  
,catharine1 who had often taken occasion
 to sneer  at her notorious reputation1 
was accused with having produced these  
consequences1 by the administration of  
poisonous potions4 ,she repelled  the   
charge with violence1 and instituted an 
action of scandal against  this person1 
but was unlucky 7according to ,kepler's 
statement7 in the  choice of a young    
doctor1 whom she employed as her        
advocate4 ,considering  the suit to be  
very instructive1 he delayed its        
termination during five  years1 until   
the judge before whom it was tried was  
displaced4 ,he was  succeeded by        
another1 already indisposed against     
,catharine ,kepler1 who  on some        

occasion had taunted him with his sudden
 accession to wealth  from a very       
inferior situation4 ,her opponent1 aware
 of this advantage1  turned the tables  
on her1 and in her turn became the      
accuser4 ,the end  of the matter was1   
that in ,july1 #afbj1 ,catharine was    
imprisoned1 and  condemned to the       
torture4 ,kepler was then at ,linz1 but 
as soon as he  learned his mother's     
danger1 hurried to the scene of trial4  
,he found the  charges against her      
supported only by evidence which never  
could have  been listened to1 if her own
 intemperate conduct had not given      
advantage  to her adversaries4 ,he      
arrived in time to save her from the    
question1  but she was not finally      
acquitted and released from prison till 
,november  in the following year4       
,kepler then returned to ,linz1 leaving 
behind him  his mother1 whose spirit    
seemed in no degree broken by the       
unexpected  turn in the course of her   
litigation4 ,she immediately commenced a

 new  action for costs and damages      
against the same antagonist1 but this   
was  stopped by her death1 in ,april    
#afbb1 in her seventy-fifth year4    ,in
 #afbj ,kepler was visited by ,sir      
,henry ,wotton1 the ,english ambassador 
at ,venice1 who finding him1 as indeed  
he might have been found at every       
period of his life1 oppressed by        
pecuniary difficulties1 urged him to go 
over to ,england1 where he assured him  
of a welcome and honourable  reception2 
but ,kepler could not resolve upon the  
proposed journey1  although in his      
letters he often returned to the        
consideration of it4 ,in  one of them1  
dated a year later1 he says1 ,the fires 
of civil war are  raging in             
,germany--they who are opposed to the   
honour of the empire are  getting the   
upper hand--everything in my            
neighbourhood seems abandoned  to flame 
and destruction4 ,shall ,i then cross   
the sea1 whither ,wotton  invites me8   
,i1 a ,german8 a lover of firm land8 who

 dread the confinement  of an island8   
who presage its dangers1 and must drag  
along with me my  little wife and flock 
of children8 ,besides my son ,louis1 now
 thirteen  years old1 ,i have a         
marriageable daughter1 a two-year old   
son by my  second marriage1 an infant   
daughter1 and its mother but just       
recovering  from her confinement4 ,six  
years later1 he says again1--,as soon as
 the  ,rudolphine ,tables are published1
 my desire will be to find a place where
  ,i can lecture on them to a           
considerable assembly2 if possible1 in  
,germany2 if not1 why then in ,italy1   
,france1 the ,netherlands1 or ,england1 
provided the salary is adequate for a   
traveller4    ,in the same year in which
 he received this invitation an affront 
was put  upon ,kepler by his early      
patrons1 the ,states of ,styria1 who    
ordered all  the copies of his          
,calendar1 for #afbd1 to be publicly    
burnt4 ,kepler  declares that the reason
 of this was1 that he had given         

precedence in  the title-page to the    
,states of ,upper ,ens1 in whose service
 he then was1  above ,styria4 ,as this  
happened during his absence in          
,wirtemberg1 it was  immediately coupled
 by rumour with his hasty departure from
 ,linz3 it was  said that he had        
incurred the ,emperor's displeasure1 and
 that a large  sum was set upon his     
head4 ,at this period ,matthias had been
 succeeded by  ,ferdinand ,,iii41 who   
still continued to ,kepler his barren   
title of  imperial mathematician4    ,in
 #afbd ,kepler went to ,vienna1 in the  
hopes of getting money to complete  the 
,rudolphine ,tables1 but was obliged to 
be satisfied with the sum of  #fjjj     
florins and with recommendatory letters 
to the ,states of ,suabia1  from whom he
 also collected some money due to the   
emperor4 ,on his return  he revisited   
the ,university of ,tubingen1 where he  
found his old  preceptor1 ,mstlin1 still
 alive1 but almost worn out with old    
age4  ,mstlin had well deserved the     

regard ,kepler always appears to have   
entertained for him2 he had treated him 
with great liberality whilst at  the    
,university1 where he refused to receive
 any remuneration for his  instruction4 
,kepler took every opportunity of       
shewing his gratitude2  even whilst he  
was struggling with poverty he contrived
 to send his old  master a handsome     
silver cup1 in acknowledging the receipt
 of which  ,mstlin says1--,your mother  
had taken it into her head that you owed
 me  two hundred florins1 and had       
brought fifteen florins and a chandelier
  towards reducing the debt1 which ,i   
advised her to send to you4 ,i asked    
her to stay to dinner1 which she        
refused3 however1 we handselled your    
cup1 as you know she is of a thirsty    
temperament4    ,the publication of the 
,rudolphine ,tables1 which ,kepler      
always had so  much at heart1 was again 
delayed1 notwithstanding the recent     
grant1 by  the disturbances arising out 
of the two parties into which the       

,reformation had divided the whole of   
,germany4 ,kepler's library was  sealed 
up by desire of the ,jesuits1 and       
nothing but his connexion with  the     
,imperial ,court secured to him his own 
personal indemnity4 ,then  followed a   
popular insurrection1 and the peasantry 
blockaded ,linz1 so  that it was not    
until #afbg that these celebrated tables
 finally made  their appearance1 the    
earliest calculated on the supposition  
that the  planets move in elliptic      
orbits4 ,ptolemy's tables had been      
succeeded by  the ,alphonsine1 so called
 from ,alphonso1 ,king of ,castile1 who1
 in the  thirteenth century1 was an     
enlightened patron of astronomy4 ,after 
the  discoveries of ,copernicus1 these  
again made way for the ,prussian1 or    
,prutenic tables1 calculated by his     
pupils ,reinhold and ,rheticus4 ,these  
remained in use till the observations of
 ,tycho ,brahe showed their             
insufficiency1 and ,kepler's new        
theories enabled him to improve upon    

them4 ,the necessary types for these    
tables were cast at ,kepler's own       
expense4 ,they are divided into four    
parts1 the first and third  containing a
 variety of logarithmic and other       
tables1 for the purpose of  facilitating
 astronomical calculations4 ,in the     
second are tables of the  elements of   
the sun1 moon1 and planets4 ,the fourth 
gives the places of  #ajjj stars as     
determined by ,tycho1 and also at the   
end his table of  refractions1 which    
appears to have been different for the  
sun1 moon1 and  stars4 ,tycho ,brahe    
assumed the horizontal refraction of the
 sun to be #g  #cj1 of the moon #h1 and 
of the other stars #c4 ,he considered   
all  refraction of the atmosphere to be 
insensible above #de of altitude1 and   
even at half that altitude in the case  
of the fixed stars4 ,a more  detailed   
account of these tables is here         
obviously unsuitable3 it will  be       
sufficient to say merely1 that if       
,kepler had done nothing in the  course 

of his whole life but construct these1  
he would have well earned  the title of 
a most useful and indefatigable         
calculator4    ,some copies of these    
tables have prefixed to them a very     
remarkable map1  divided by hour lines1 
the object of which is thus explained3--
    ,the use of this nautical map is1   
that if at a given hour the place of    
the moon is known by its edge being     
observed to touch any known star1 or    
the edges of the sun1 or the shadow of  
the earth2 and if that place  shall 7if 
necessary7 be reduced from apparent to  
real by clearing it of  parallax2 and if
 the hour at ,uraniburg be computed by  
the ,rudolphine  tables1 when the moon  
occupied that true place1 the difference
 will show  the observer's meridian1    
whether the picture of the shores be    
accurate  or not1 for by this means it  
may come to be corrected4    ,this is   
probably one of the earliest            
announcements of the method of          
determining longitudes by occultations2 

the imperfect theory of the moon  long  
remained a principal obstacle to its    
introduction in practice4  ,another     
interesting passage connected with the  
same object may be  introduced here4 ,in
 a letter to his friend ,cruger1 dated  
in #afaf1 ,kepler  says3 ,you propose a 
method of observing the distances of    
places by  sundials and automata4 ,it is
 good1 but needs a very accurate        
practice1  and confidence in those who  
have the care of the clocks4 ,let there 
be  only one clock1 and let it be       
transported2 and in both places let     
meridian lines be drawn with which the  
clock may be compared when  brought4    
,the only doubt remaining is1 whether a 
greater error is likely  from the       
unequal tension in the automaton1 and   
from its motion1 which  varies with the 
state of the air1 or from actually      
measuring the  distances4 ,for if we    
trust the latter1 we can easily         
determine the  longitudes by observing  
the differences of the height of the    

pole4    ,in an ,appendix to the        
,rudolphine ,tables1 or1 as ,kepler     
calls it1 an  alms doled out to the     
nativity casters1 he has shown how they 
may use  his tables for their           
astrological predictions4 ,everything in
 his hands  became an allegory2 and on  
this occasion he says1--,astronomy is   
the  daughter of ,astrology1 and this   
modern ,astrology1 again1 is the        
daughter  of ,astronomy1 bearing        
something of the lineaments of her      
grandmother2  and1 as ,i have already   
said1 this foolish daughter1 ,astrology1
 supports  her wise but needy mother1   
,astronomy1 from the profits of a       
profession  not generally considered    
creditable4    ,soon after the          
publication of these tables1 the ,grand 
,duke of ,tuscany  sent him a golden    
chain2 and if we remember the high      
credit in which  ,galileo stood at this 
time in ,florence1 it does not seem too 
much to  attribute this honourable mark 
of approbation to his representation of 

the value of ,kepler's services to      
astronomy4 ,this was soon followed by a 
new and final change in his fortunes4   
,he received permission from the        
emperor to attach himself to the        
celebrated ,duke of ,friedland1 ,albert 
,wallenstein1 one of the most remarkable
 men in the history of that  time4      
,wallenstein was a firm believer in     
astrology1 and the reception  ,kepler   
experienced by him was probably due1 in 
great measure1 to his  reputation in    
that art4 ,however that may be1 ,kepler 
found in him a more  munificent patron  
than any one of his three emperors2 but 
he was not  destined long to enjoy the  
appearance of better fortune4 ,almost   
the last  work which he published was a 
commentary on the letter addressed1 by  
the  missionary ,terrentio1 from ,china1
 to the ,jesuits at ,ingolstadt4 ,the   
object of this communication was to     
obtain from ,europe means for  carrying 
into effect a projected scheme for      
improving the ,chinese  calendar4 ,in   

this essay ,kepler maintains the        
opinion1 which has been  discussed with 
so much warmth in more modern times1    
that the pretended  ancient observations
 of the ,chinese were obtained by       
computing them  backwards from a much   
more recent date4 ,wallenstein furnished
 him with  an assistant for his         
calculations1 and with a printing press2
 and  through his influence nominated   
him to the professorship in the         
,university of ,rostoch1 in the ,duchy  
of ,mecklenburg4 ,his claims on the     
imperial treasury1 which amounted at    
this time to #hjjj crowns1 and which    
,ferdinand would gladly have transferred
 to the charge of ,wallenstein1  still  
remained unsatisfied4 ,kepler made a    
last attempt to obtain them at          
,ratisbon1 where the imperial meeting   
was held1 but without success4 ,the     
fatigue and vexation occasioned by his  
fruitless journey brought on a  fever1  
which unexpectedly put an end to his    
life1 in the early part of  ,november1  

#afcj1 in his fifty-ninth year4 ,his old
 master1 ,mstlin1  survived him for     
about a year1 dying at the age of       
eighty-one4    ,kepler left behind him  
two children by his first wife1 ,susanna
 and  ,louis2 and three sons and two    
daughters1 ,sebald1 ,cordelia1          
,friedman1  ,hildebert1 and ,anna       
,maria1 by his widow4 ,susanna married1 
a few months  before her father's death1
 a physician named ,jacob ,bartsch1 the 
same who  latterly assisted ,kepler in  
preparing his ,ephemeris4 ,he died very 
shortly after ,kepler himself4 ,louis   
studied medicine1 and died in #affc1    
whilst practising as a physician at     
,konigsberg4 ,the other children died   
young4    ,upon ,kepler's death the     
,duke of ,friedland caused an inventory 
to be  taken of his effects1 when it    
appeared that near #bd1jjj florins were 
due  to him1 chiefly on account of his  
salary from the emperor4 ,his daughter  
,susanna1 ,bartsch's widow1 managed to  
obtain a part of these arrears by       

refusing to give up ,tycho ,brahe's     
observations till her claims were       
satisfied4 ,the widow and younger       
children were left in very straightened 
circumstances1 which induced ,louis1    
,kepler's eldest son1 to print1 for     
their relief1 one of his father's works1
 which had been left by him             
unpublished4 ,it was not without much   
reluctance1 in consequence of a         
superstitious feeling which he did not  
attempt to conceal or deny4  ,kepler    
himself1 and his son-in-law1 ,bartsch1  
had been employed in  preparing it for  
publication at the time of their        
respective deaths2 and  ,louis confessed
 that he did not approach the task      
without apprehension  that he was       
incurring some risk of a similar fate4  
,this little rhapsody  is entitled a    
,dream on ,lunar ,astronomy2 and was    
intended to illustrate  the appearances 
which would present themselves to an    
astronomer living  upon the moon4       
,the narrative in the dream is put into 

the mouth of a personage1 named         
,duracoto1 the son of an ,icelandic     
enchantress1 of the name of             
,fiolxhildis4 ,kepler tells us that he  
chose the last name from an old map  of 
,europe in his house1 in which ,iceland 
was called ,fiolx3 ,duracoto  seemed to 
him analogous to the names he found in  
the history of  ,scotland1 the          
neighbouring country4 ,fiolxhildis was  
in the habit of  selling winds to       
mariners1 and used to collect herbs to  
use in her  incantations on the sides of
 ,mount ,hecla1 on the ,eve of ,st4     
,john4  ,duracoto cut open one of his   
mother's bags1 in punishment of which   
she  sold him to some traders1 who      
brought him to ,denmark1 where he became
  acquainted with ,tycho ,brahe4 ,on his
 return to ,iceland1 ,fiolxhildis       
received him kindly1 and was delighted  
with the progress he had made in        
astronomy4 ,she then informed him of the
 existence of certain spirits1 or       
demons1 from whom1 although no traveller

 herself1 she acquired a  knowledge of  
other countries1 and especially of a    
very remarkable  country1 called        
,livania4 ,duracoto requesting further  
information1 the  necessary ceremonies  
were performed for invoking the demon2  
,duracoto and  his mother enveloped     
their heads in their clothing1 and      
presently the  screaking of a harsh     
dissonant voice began to speak in the   
,icelandic  tongue4 ,the island of      
,livania is situated in the depths of   
ether1 at  the distance of about #bejjjj
 miles2 the road thence or thither is   
very  seldom open1 and even when it is  
passable1 mankind find the journey a    
most difficult and dangerous one4 ,the  
demon describes the method  employed by 
his fellow spirits to convey such       
travellers as are thought  fit for the  
undertaking3 ,we bring no sedentary     
people into our company1  no corpulent  
or delicate persons2 but we pick out    
those who waste their  life in the      
continual use of post-horses1 or who    

sail frequently to the  ,indies2 who are
 accustomed to live upon biscuit1       
garlic1 dried fish1 and  such abominable
 feeding4 ,those withered old hags are  
exactly fit for us1  of whom the story  
is familiar that they travel immense    
distances by  night on goats1 and forks1
 and old petticoats4 ,the ,germans do   
not suit  us at all2 but we do not      
reject the dry ,spaniards4 ,this extract
 will  probably be sufficient to show   
the style of the work4 ,the inhabitants 
of  ,livania are represented to be      
divided into two classes1 the           
,privolvans  and ,subvolvans1 by whom   
are meant those supposed to live in the 
hemisphere facing the earth1 which is   
called the ,volva1 and those on the     
opposite half of the moon3 but there is 
nothing very striking in the  account   
given of the various phenomena as       
respects these two classes4 ,in  some   
notes which were added some time after  
the book was first written1  are some   
odd insights into ,kepler's method of   

composing4 ,fiolxhildis had  been made  
to invoke the dmon with twenty-one      
characters2 ,kepler  declares1 in a     
note1 that he cannot remember why he    
fixed on this  number1 except because   
that is the number of letters in        
,astronomia  ,copernicana1 or because   
there are twenty-one combinations of the
  planets1 two together1 or because     
there are twenty-one different throws   
upon two dice4 ,the dream is abruptly   
terminated by a storm1 in which1  says  
,kepler1 ,i suddenly waked2 the ,demon1 
,duracoto1 and ,fiolxhildis  were gone1 
and instead of their covered heads1 ,i  
found myself rolled up  among the       
blankets4    ,besides this trifle1      
,kepler left behind him a vast mass of  
unpublished  writings1 which came at    
last into the hands of his biographer1  
,hantsch4  ,in #agad1 ,hantsch issued a 
prospectus for publishing them by       
subscription1 in twenty-two folio       
volumes4 ,the plan met no               
encouragement1 and nothing was published

 but a single folio volume of  letters  
to and from ,kepler1 which seem to have 
furnished the principal  materials for  
the memoir prefixed to them4 ,after     
various unavailing  attempts to interest
 different learned bodies in their      
appearance1 the  manuscripts were       
purchased for the library at ,st4       
,petersburg1 where  ,euler1 ,lexell1 and
 ,kraft1 undertook to examine them1 and 
select the most  interesting parts for  
publication4 ,the result of this        
examination does  not appear4           
,kepler's body was buried in ,st4       
,peter's churchyard at ,ratisbon1 and a 
simple inscription was placed on his    
tombstone4 ,this appears to have  been  
destroyed not long after1 in the course 
of the wars which still  desolated the  
country4 ,in #aghf1 a proposal was made 
to erect a marble  monument to his      
memory1 but nothing was done4 ,kstner1  
on whose  authority it is mentioned1    
says upon this1 rather bitterly1 that it
  matters little whether or not         

,germany1 having almost refused him     
bread  during his life1 should1 a       
century and a half after his death1     
offer him  a stone4    ,delambre        
mentions1 in his ,history of ,astronomy1
 that this design was  resumed in #ahjc 
by the ,prince ,bishop of ,constance1   
and that a monument  has been erected in
 the ,botanical ,garden at ,ratisbon1   
near the place of  his interment4 ,it is
 built in the form of a temple1         
surmounted by a  sphere2 in the centre  
is placed a bust of ,kepler1 in ,carrara
 marble4  ,delambre does not mention the
 original of the bust2 but says it is   
not  unlike the figure engraved in the  
frontispiece of the ,rudolphine ,tables4
  ,that frontispiece consists of a      
portico of ten pillars1 supporting a    
cupola covered with astronomical        
emblems4 ,copernicus1 ,tycho ,brahe1    
,ptolemy1 ,hipparchus1 and other        
astronomers1 are seen among them4 ,in   
one  of the compartments of the common  
pedestal is a plan of the observatory   

at ,uraniburg2 in another1 a printing   
press2 in a third is the figure of  a   
man1 meant for ,kepler1 seated at a     
table4 ,he is identified by the  titles 
of his works1 which are round him2 but  
the whole is so small as  to convey very
 little idea of his figure or           
countenance4 ,the only  portrait known  
of ,kepler was given by him to his      
assistant ,gringallet1  who presented it
 to ,bernegger2 and it was placed by the
 latter in the  library at ,strasburg4  
,hantsch had a copy taken for the       
purpose of  engraving it1 but died      
before it was completed4 ,a portrait of 
,kepler is  engraved in the seventh part
 of ,boissard's ,bibliotheca            
,chalcographica4  ,it is not known      
whence this was taken1 but it may1      
perhaps1 be a copy of  that which was   
engraved by desire of ,bernegger in     
#afbj4 ,the likeness is  said not to    
have been well preserved4 ,his heart and
 genius1 says  ,kstner1 are faithfully  
depicted in his writings2 and that may  

console  us1 if we cannot entirely trust
 his portrait4 ,in the preceding pages1 
it has been endeavoured to select such  
passages from his writings as  might    
throw the greatest light on his         
character1 with a subordinate  reference
 only to the importance of the subjects 
treated4 ,in conclusion1  it may be well
 to support the opinion which has been  
ventured on the  real nature of his     
triumphs1 and on the danger of          
attempting to follow  his method in the 
pursuit of truth1 by the judgment       
pronounced by  ,delambre1 as well on his
 failures as on his success4            
,considering these  matters in another  
point of view1 it is not impossible to  
convince  ourselves that ,kepler may    
have been always the same4 ,ardent1     
restless1  burning to distinguish       
himself by his discoveries1 he attempted
  everything2 and having once obtained a
 glimpse of one1 no labour was too  hard
 for him in following or verifying it4  
,all his attempts had not the  same     

success1 and1 in fact1 that was         
impossible4 ,those which have failed    
seem to us only fanciful2 those which   
have been more fortunate appear         
sublime4 ,when in search of that which  
really existed1 he has sometimes  found 
it2 when he devoted himself to the      
pursuit of a chimera1 he could  not but 
fail2 but even there he unfolded the    
same qualities1 and that  obstinate     
perseverance that must triumph over all 
difficulties but those  which are       
insurmountable4#bja      ,list of       
,kepler's published ,works4      ,ein   
,calender                               
,gratz1 #aeid    ,prodromus ,dissertat4 
,cosmograph4           ,tubing1 #aeif1  
#dto4    ,de fundamentis ,astrologi     
,prag1 #afjb1 #dto4    ,paralipomena ad 
,vitellionem                            
,francofurti1 #afjd1 #dto4    ,epistola 
de ,solis deliquio                 #afje
    ,de stell nov                       
,prag1 #afjf1 #dto4    ,vom ,kometen    
,halle1 #afjh1 #dto4    ,antwort an     

,rslin                          ,prag1  
#afji1 #dto4    ,astronomia ,nova       
,prag1 #afji1 fol4    ,tertius          
interveniens                            
,frankfurt1 #afaj1 #dto4    ,dissertatio
 cum ,nuncio ,sidereo                   
,francofurti1 #afaj1 #dto4    ,strena1  
seu ,de dive sexangul                   
,frankfurt1 #afaa1 #dto4    ,dioptrica  
,francofurti1 #afaa1 #dto4    ,vom      
,geburts ,jahre des ,heylandes          
,strasburg1 #afac1 #dto4    ,respons4 ad
 epist ,s4 ,calvisiii                   
,francofurti1 #afad1 #dto4    ,eclog    
,chronic                                
,frankfurt1 #afae1 #dto4    ,nova       
,stereometria                           
,lincii1 #afae1 #dto4    ,ephemerides   
#afag-afbj                      ,lincii1
 #afaf1 #dto4    ,epitomes ,astron4     
,copern4 ,libri i4 ii4 iii4 ,lentiis1   
#afah1 #hvo4    ,de ,cometis            
,aug4 ,vindelic4 #afai1 #dto4           
,harmonice ,mundi                       
,lincii1 #afai1 fol4    ,kanones        

,pueriles                               
,ulm1 #afbj    ,epitomes ,astron4       
,copern4 ,liber iv4         ,lentiis1   
#afbb1 #hvo4    ,epitomes ,astron4      
,copern4 ,libri v4 vi4 vii4             
,francofurti1 #afbb1 #hvo4    ,discurs  
von der grossen ,conjunction            
,linz4 #afbc1 #dto4    ,chilias         
,logarithmorum                          
,marpurgi1 #afbd1 fol4    ,supplementum 
,lentiis1 #afbe1 #dto4    ,hyperaspistes
                                        
,francofurti1 #afbe1 #hvo4    ,tabul    
,rudolphin                              
,ulm1 #afbg1 fol4    ,resp4 ad epist4   
,j4 ,bartschii               ,sagani1   
#afbi1 #dto4    ,de anni #afca phnomenis
                    ,lips1 #afbi1 #dto4 
,terrentii epistolium cum               
commentatiuncul  ,sagani1 #afcj1 #dto4  
,ephemerides4                           
,sagani1 #afcj1 #dto4      ,somnium     
,francofurti1 #afcd1 #dto4    ,tabul    
mannales                                
,argentorati1 #agjj1 #abmo4             

,,footnotes3    #aii ,the meaning of    
this passage is not very clear3 ,kepler 
evidently  had seen and used logarithms 
at the time of writing this letter2 yet 
there is nothing in the method to       
justify this expression1--,at tamen     
opus est ipsi ,tangentium canone4       
#bjj ,this was the objection originally 
made to ,newton's ,fluxions1 and  in    
fact1 ,napier's idea of logarithms is   
identical with that method of           
conceiving quantities4 ,this may be seen
 at once from a few of his  definitions1
        #a ,def4 ,a line is said to     
increase uniformly1 when the point by   
which      it is described passes       
through equal intervals1 in equal times4
        #b ,def4 ,a line is said to     
diminish to a shorter one               
proportionally1      when the point     
passing along it cuts off in equal times
 segments      proportional to the      
remainder4        #f ,def4 ,the         
logarithm of any sine is the number most
 nearly denoting      the line1 which   

has increased uniformly1 whilst the     
radius has      diminished to that sine 
proportionally1 the initial velocity    
being      the same in both motions4    
7,mirifici logarithmorum canonis        
descriptio1 ,edinburgi #afad47    ,this 
last definition contains what we should 
now call the differential  equation     
between a number and the logarithm of   
its reciprocal4    #bja ,histoire       
del',astronomie ,moderne1 ,paris1 #ahba4
          ,transcriber's ,notes4        
,corrections4    ,the first line        
indicates the original1 the second the  
correction4      ,life of ,galileo      
,galilei    p4 #bj3      success very   
inadeqnate to the zeal    success very  
inadequate to the zeal    p4 #bj3       
,new method of ,guaging1   ,new method  
of ,gauging1    p4 #bc3      the        
knowlege1 if it existed    the          
knowledge1 if it existed    p4 #cj1     
note3      to represent terrestial      
objects correctly4    to represent      
terrestrial objects correctly4    p4    

#fd3      the palace of the ,archishop  
,piccolomini    the palace of the       
,archbishop ,piccolomini    p4 #fh3     
that ladies ringlets    that ladies'    
ringlets    p4 #fi3      ,for hitherto  
,i have never happened to see the       
terrestial earth    ,for hitherto ,i    
have never happened to see the          
terrestrial earth    p4 #ajf3      #hj  
#a    #ej1 for any read an indefinitely 
small4    #hj   #b    #dd1 for any read 
an indefinitely small4      ,life of    
,kepler    p4 #f3      ,now1 inscribe in
 the ,earth an icosaedron1 the circle   
inscribed in it    will be ,venus4      
,now1 inscribe in the ,earth an         
icosahedron1 the circle inscribed in    
it will be ,venus4      ,inscribe an    
octaedron in ,venus1 the circle         
inscribed in it will be    ,mercury4    
,inscribe an octahedron in ,venus1 the  
circle inscribed in it will be          
,mercury4    p4 #cb3      ,butthere are 
no such means    ,but there are no such 
means    p4 #dh3      the compound ratio

 of the rectangle of the axes directly1 
and    subduplicatly      the compound  
ratio of the rectangle of the axes      
directly1 and    subduplicately    p4   
#eb3      and was in-intended to        
illustrate the appearances    and was   
intended to illustrate the appearances