,illu/ration3 ,,kepl] ,pione]s ( ,progress ,m5 ( ,sci5ce ,edit$ by ,s4 ,*apman1 ,m4,a41 ,d4,sc41 ,f4,r4,s4 ,,kepl] by ,,walt] ,w4 ,,bryant ( ! ,royal ,obs]vatory1 ,gre5wi* #aibj ,,cont5ts4 ,i4 ,a/ronomy ,be=e ,kepl] ,,ii4 ,e>ly ,life ( ,kepl] ,,iii4 ,ty*o ,brahe ,,iv4 ,kepl] ,jo9s ,ty*o ,v4 ,kepl]'s ,laws ,,vi4 ,clos+ ,ye>s ,app5dix ,i4--,li/ ( ,dates ,app5dix ,,ii4--,bibliography ,gloss>y ,,*apt] ,i4 ,,a/ronomy ,,be=e ,,kepl]4 ,9 ord] to emphasise ! importance ( ! re=ms introduc$ into a/ronomy by ,kepl]1 x w be well to sket* briefly ! hi/ory ( ! !ories :i* he _h to ov]?r[4 ,9 v e>ly times x mu/ h be5 realis$ t ! sun & moon 7 cont9ually *ang+ _! places among ! />s4 ,! day1 ! mon?1 & ! ye> 7 obvi\s divisions ( "t1 & long] p]iods 7 sugge/$ by ! tabulation ( eclipses4 ,we c imag9e ! respect accord$ to ! ,*aldaean sages :o fir/ discov]$ t eclipses c\ld be pr$ict$1 & h[ ! philosoph]s ( ,mesopotamia mu/ h s\ght eag]ly = evid5ce ( fre% p]iodic laws4 ,c]ta9 ( ! />s1 :i* appe>$ to w&]1 & 7 h5ce call$ planets1 provid$ an ext5d$ field = ^! speculations4 ,among ! ,*aldaeans & ,babylonians ! k gradually acquir$ 0 probably conf9$ to ! prie/s & utilis$ ma9ly = a/rological pr$iction or ! fix+ ( religi\s obs]vances4 ,su* speculations z 7 curr5t among !m1 & also among ! ,egyptians & o!rs :o came to %>e _! k1 7 almo/ entirely devot$ to my?ology1 assign+ fanciful t]re/rial orig9s to con/ellations1 ) occasional controv]sies z to h[ ! e>? is support$ 9 space4 ,! ,greeks1 too1 _h an elaborate my?ology l>gely adapt$ f _! neighb\rs1 b !y 7 n satisfi$ ) ?is1 & made p]si/5t attempts to r$uce ! app>5t motions ( cele/ial objects to geometrical laws4 ,"s ( ! ,py?agoreans1 if n ,py?agoras himself1 held t ! e>? is a sph]e1 & t ! app>5t daily revolution ( ! sun & />s is really due to a motion ( ! e>?1 ?\gh at fir/ ?is motion ( ! e>? 0 n suppos$ to be "o ( rotation ab\t an axis4 ,^! notions1 & also t ! planets on ! :ole move r\nd f we/ to ea/ ) ref]5ce to ! />s1 7 made kn[n to a l>g] circle ?r\gh ! writ+s ( ,plato4 ,to ,plato moreov] is attribut$ ! *all5ge to a/ronom]s to repres5t all ! motions ( ! heav5ly bodies by uni=mly describ$ circles1 a *all5ge g5]ally held responsible = a va/ am\nt ( wa/$ ef=t1 & ! po/ponem5t1 = _m c5turies1 ( real progress4 ,eudoxus ( ,cnidus1 endeav\r+ to acc\nt = ! fact t ! planets1 dur+ e app>5t revolution r\nd ! e>?1 come to re/ twice1 & 9 ! %ort] int]val betwe5 ^! /ation>y po9ts1 move 9 ! opposite direction1 f\nd t he c\ld repres5t ! ph5om5a fairly well by a sy/em ( conc5tric sph]es1 ea* rotat+ ) its own velocity1 & c>ry+ its own p>ticul> planet r\nd its own equator1 ! out]mo/ sph]e c>ry+ ! fix$ />s4 ,x 0 necess>y to assume t ! axes ab\t :i* ! v>i\s sph]es revolv$ %\ld h circul> motions also1 & gradually an increas$ numb] ( sph]es 0 evolv$1 ! total numb] requir$ by ,ari/otle rea*+ fifty-five4 ,x may be reg>d$ z c\nt+ 9 ,ari/otle's fav\r t he did consid] ! e>? to be a sph]e & n a flat disc1 b he seems to h ?\ght t ! ma!matical sph]es ( ,eudoxus _h a real solid exi/5ce1 & t n only meteors1 %oot+ />s & aurora1 b also comets & ! milky way belong to ! atmosph]e4 ,8 really great s]vice to sci5ce 9 collat+ & criticis+ all t 0 kn[n ( natural sci5ce w\ld h be5 great] if s mu* ( ! discussion _h n be5 on ! exact mean+ ( words us$ to describe ph5om5a1 in/ead ( on ! facts & causes ( ! ph5om5a !mselves4 ,ari/>*us ( ,samos seems to h be5 ! fir/ to sugge/ t ! planets revolv$ n ab\t ! e>? b ab\t ! sun1 b ! idea seem$ s improbable t x 0 h>dly notic$1 especially z ,ari/>*us himself did n exp& x into a treatise4 ,ab\t ?is "t ! necessity = m accurate places ( ! sun & moon1 & ! lib]ality ( ! ,ptolemys :o rul$ ,egypt1 comb9$ to provide regul> obs]vations at ,alex&ria1 s t1 :5 ,hipp>*us came ^u ! sc5e1 !re 0 a consid]able am\nt ( mat]ial = him to use4 ,8 discov]ies m>k$ a great advance 9 ! sci5ce ( a/ronomy4 ,he not$ ! irregul> motion ( ! sun1 &1 to expla9 x1 assum$ t x revolv$ uni=mly n exactly ab\t ! e>? b ab\t a po9t "s di/ance away1 call$ ! exc5tric4#a ,! l9e jo9+ ! c5tre ( ! e>? to ! exc5tric passes ?r\gh ! apses ( ! sun's orbit1 :]e its di/ance f ! e>? is greate/ & lea/4 ,! same result he c\ld obta9 by assum+ t ! sun mov$ r\nd a small circle1 ^: c5tre describ$ a l>g] circle ab\t ! e>?2 ?is l>g] circle c>ry+ ! o!r 0 call$ ! def]5t3 s t ! actual motion ( ! sun 0 9 an epicycle4 ,( ! two me?ods ( expression ,hipp>*us ultimately pref]r$ ! second4 ,he appli$ ! same process to ! moon b f\nd t he c\ld dep5d ^u its be+ "r only at new & full moon4 ,! irregul>ity at fir/ & ?ird qu>t]s he left to be inve/igat$ by 8 successors4 ,he also consid]$ ! planet>y obs]vations at 8 disposal insuffici5t & s gave up ! attempt at a complete planet>y !ory4 ,he made improv$ det]m9ations ( "s ( ! elem5ts ( ! motions ( ! sun & moon1 & discov]$ ! ,precession ( ! ,equ9oxes1 f ! ,alex&rian obs]vations :i* %[$ t ea* ye> z ! sun came to cross ! equator at ! v]nal equ9ox x did s at a po9t ab\t fifty seconds ( arc e>li] on ! ecliptic1 ?us produc+ 9 #aej ye>s an unmi/akable *ange ( a c\ple ( degrees1 or f\r times ! sun's diamet]4 ,he also inv5t$ trigonometry4 ,8 /> catalogue 0 due to ! appe>ance ( a new /> :i* caus$ him to se>* = possible previ\s simil> ph5om5a1 & also to prep>e = *eck+ future ones4 ,no advance 0 made 9 !oretical a/ronomy = #bfj ye>s1 ! int]val betwe5 ,hipp>*us & ,ptolemy ( ,alex&ria4 ,ptolemy accept$ ! sph]ical =m ( ! e>? b d5i$ its rotation or any o!r movem5t4 ,he made no advance on ,hipp>*us 9 reg>d to ! sun1 ?\gh ! lapse ( "t _h l>gely increas$ ! errors ( ! elem5ts adopt$ by ! latt]4 ,9 ! case ( ! moon1 h[ev]1 ,ptolemy trac$ ! v>iable inequality notic$ sometimes by ,hipp>*us at fir/ & la/ qu>t]1 :i* vani%$ :5 ! moon 0 9 apogee or p]igee4 ,?is he call$ ! evection1 & introduc$ ano!r epicycle to repres5t x4 ,9 8 planet>y !ory he f\nd t ! places giv5 by 8 adopt$ exc5tric did n fit1 be+ "o way at apogee & ! o!r at p]igee2 s t ! c5tre ( di/ance mu/ be ne>] ! e>?4 ,he f\nd x be/ to assume ! c5tre ( di/ance half-way betwe5 ! c5tre ( ! e>? & ! exc5tric1 ?us bisect+ ! exc5tricity4 ,ev5 ?is did n fit 9 ! case ( ,m]cury1 & 9 g5]al ! agreem5t betwe5 !ory & obs]vation 0 spoilt by ! necessity ( mak+ all ! orbital planes pass ?r\gh ! c5tre ( ! e>?1 in/ead ( ! sun1 ?us mak+ a good accordance practically impossible4 ,footnote #a3 ,see ,gloss>y = ?is & o!r te*nical t]ms4 ,aft] ,ptolemy's "t v little 0 he>d = _m c5turies ( any fre% planet>y !ory1 ?\gh advances 9 "s po9ts ( detail 7 made1 notably by "s ( ! ,arab philosoph]s1 :o obta9$ improv$ values = "s ( ! elem5ts by us+ bett] in/rum5ts4 ,f "t to "t v>i\s modifications ( ,ptolemy's !ory 7 sugge/$1 b none ( any real value4 ,! ,moors 9 ,spa9 did _! %>e ( ! "w c>ri$ on by _! ,ea/]n co-religioni/s1 & ! fir/ indep5d5t /> catalogue s9ce ! "t ( ,hipp>*us 0 made by ano!r ,ori5tal1 ,tam]lane's gr&son1 ,ulugh ,begh1 :o built a f9e obs]vatory at ,sam>c& 9 ! fifte5? c5tury4 ,9 ,spa9 ! "w 0 n monopolis$ by ! ,moors1 = 9 ! ?irte5? c5tury ,alphonso ( ,ca/ile1 ) ! assi/ance ( ,jewi% & ,*ri/ian comput]s1 compil$ ! ,alphons9e tables1 complet$ 9 #abeb1 9 :i* ye> he asc5d$ ! ?rone z ,alphonso ,x4 ,!y 7 long circulat$ 9 ,,ms4 & 7 fir/ pr9t$ 9 #adhc1 n long be=e ! end ( ! p]iod ( /agnation4 ,cop]nicus 0 born 9 #adgc at ,?orn 9 ,poli% ,prussia4 ,9 ! c\rse ( 8 /udies at ,crac[ & at sev]al ,italian univ]sities1 he le>nt all t 0 kn[n ( ! ,ptolemaic a/ronomy & det]m9$ to re=m x4 ,8 mat]nal uncle1 ! ,bi%op ( ,erml&1 hav+ provid$ him ) a lay canonry 9 ! ,ca!dral ( ,frau5burg1 he _h leisure to devote himself to ,sci5ce4 ,review+ ! sugge/ions ( ! anci5t ,greeks1 he 0 /ruck by ! simplification t w\ld be introduc$ by reviv+ ! idea t ! annual motion %\ld be attribut$ to ! e>? itself in/ead ( hav+ a sep>ate annual epicycle = ea* planet & = ! sun4 ,( ! sev5ty odd circles or epicycles requir$ by ! late/ =m ( ! ,ptolemaic sy/em1 ,cop]nicus succe$$ 9 disp5s+ ) r m ?an half1 b he /ill requir$ ?irty-f\r1 :i* 0 ! exact numb] assum$ be=e ! "t ( ,ari/otle4 ,8 consid]ations 7 almo/ entirely ma!matical1 8 only invasion into physics be+ 9 def5ce ( ! mov+ e>? aga9/ ! /ock objection t if ! e>? mov$1 loose objects w\ld fly (f1 & t[]s fall4 ,he did n break suffici5tly away f ! old tradition ( uni=m circul> motion4 ,ptolemy's ef=ts at exactness 7 baulk$1 z we h se51 by ! suppos$ necessity ( all ! orbit planes pass+ ?r\gh ! e>?1 & if ,cop]nicus _h simply transf]r$ ?is responsibility to ! sun he w\ld h done bett]4 ,b he w\ld n sacrifice ! old feti%1 & s1 ! orbit ( ! e>? be+ cle>ly n circul> ) respect to ! sun1 he made all 8 planet>y planes pass ?r\gh ! c5tre ( ! e>?'s orbit1 in/ead ( ?r\gh ! sun1 ?us h&icapp+ himself 9 ! same way ?\gh n 9 ! same degree z ,ptolemy4 ,8 ?irty-f\r circles or epicycles compris$ f\r = ! e>?1 ?ree = ! moon1 sev5 = ,m]cury 7on acc\nt ( 8 highly ecc5tric orbit7 & five ea* = ! o!r planets4 ,x is r an exagg]ation to call ! pres5t accept$ sy/em ! ,cop]nican sy/em1 z x is really due to ,kepl]1 half a c5tury aft] ! dea? ( ,cop]nicus1 b mu* cr$it is due to ! latt] = 8 successful attempt to provide a real alt]native = ! ,ptolemaic sy/em1 in/ead ( t9k]+ ) x4 ,! old geoc5tric sy/em once %ak51 ! way 0 gradually smoo!d = ! helioc5tric sy/em1 :i* ,cop]nicus1 /ill hamp]$ by tradition1 did n q rea*4 ,he 0 h>dly a practical a/ronom] 9 ! obs]vational s5se4 ,8 fir/ record$ obs]vation1 ( an occultation ( ,aldeb>an1 0 made 9 #adig1 & he is n kn[n to h made z _m z fifty a/ronomical obs]vations1 :ile1 ( ! few he did make & use1 at lea/ "o 0 m ?an half a degree 9 error1 :i* w\ld h be5 intol]able to su* an obs]v] z ,hipp>*us4 ,cop]nicus 9 fact seems to h consid]$ accurate obs]vations unatta9able ) ! in/rum5ts at h&4 ,he refus$ to give any op9ion on ! project$ re=m ( ! cal5d>1 on ! gr\nd t ! motions ( ! sun & moon 7 n kn[n ) suffici5t accuracy4 ,x is possible t ) bett] data he might h made mu* m progress4 ,he 0 9 no hurry to publi% any?+1 p]haps on acc\nt ( possible opposition4 ,c]ta9ly ,lu!r1 ) 8 ob/9ate conviction ( ! v]bal accuracy ( ! ,scriptures1 reject$ z m]e folly ! idea ( a mov+ e>?1 & ,melan*?on ?\ght su* op9ions %\ld be prohibit$1 b ,rheticus1 a pr(essor at ! ,prote/ant ,univ]sity ( ,witt5b]g & an en?usia/ic pupil ( ,cop]nicus1 urg$ publication1 & und]took to see ! "w ?r\gh ! press4 ,?is1 h[ev]1 he 0 unable to complete & ano!r ,lu!ran1 ,osi&]1 to :om he entru/$ x1 wrote a preface1 ) ! app>5t int5tion ( dis>m+ opposition1 9 :i* he /at$ t ! pr9ciples laid d[n 7 only ab/ract hypo!ses conv5i5t = purposes ( calculation4 ,?is unau?oris$ int]polation may h _h its %>e 9 po/pon+ ! prohibition ( ! book by ! ,*ur* ( ,rome4 ,accord+ to ,cop]nicus ! e>? is only a planet l ! o!rs1 & n ev5 ! bigge/ "o1 :ile ! sun is ! mo/ important body 9 ! sy/em1 & ! />s probably too f> away = any motion ( ! e>? to affect _! app>5t places4 ,! e>? 9 fact is v small 9 comp>ison ) ! di/ance ( ! />s1 z evid5c$ by ! fact t an obs]v] any:]e on ! e>? appe>s to be 9 ! middle ( ! univ]se4 ,he %[s t ! revolution ( ! e>? w acc\nt = ! seasons1 & = ! /ation>y po9ts & retrograde motions ( ! planets4 ,he corrects def9itely ! ord] ( ! planets outw>ds f ! sun1 a matt] :i* _h be5 9 dispute4 ,a notable defect is due to ! idea t a body c only revolve ab\t ano!r body or a po9t1 z if rigidly connect$ ) x1 s t1 9 ord] to keep ! e>?'s axis 9 a con/ant direction 9 space1 he has to inv5t a ?ird motion4 ,8 discussion ( precession1 :i* he rightly attributes to a sl[ motion ( ! e>?'s axis1 is m>r$ by ! idea t ! precession is v>iable4 ,) all its defects1 p>tly due to reliance on bad obs]vations1 ! "w %[$ a great advance 9 ! int]pretation ( ! motions ( ! planets2 & 8 det]m9ations ( ! p]iods bo? 9 relation to ! e>? & to ! />s 7 adopt$ by ,re9hold1 ,pr(essor ( ,a/ronomy at ,witt5b]g1 = ! new ,prut5ic or ,prussian ,tables1 :i* 7 to sup]s$e ! obsolete ,alphons9e ,tables ( ! ?irte5? c5tury4 ,9 comp>ison ) ! "q ( ! motion ( ! e>?1 no o!r a/ronomical detail ( ! "t seems to be ( mu* consequ5ce4 ,comets1 su* z f "t to "t appe>$1 bright en\gh = nak$ eye obs]vation1 7 /ill reg>d$ z atmosph]ic ph5om5a1 & _! pr9cipal int]e/1 z well z t ( eclipses & planet>y conjunctions1 0 9 relation to a/rology4 ,re=m1 h[ev]1 0 obvi\sly 9 ! air4 ,! doctr9e ( ,cop]nicus 0 de/9$ v soon to divide o!rs besides ! ,lu!ran lead]s4 ,! leav5 ( inquiry 0 work+1 & n long aft] ! dea? ( ,cop]nicus real advances 7 to come1 fir/ 9 ! accuracy ( obs]vations1 &1 z a necess>y result ( ^!1 9 ! planet>y !ory itself4 ,,*apt] ,,ii4 ,,e>ly ,,life ,,( ,,kepl]4 ,on #ba/ ,decemb]1 #aega1 at ,weil 9 ! ,du*y ( ,wurtemb]g1 0 born a weak & sickly sev5-mon?s' *ild1 to :om 8 p>5ts ,h5ry & ,ca!r9e ,kepl] gave ! "n ( ,john4 ,h5ry ,kepl] 0 a petty (fic] 9 ! s]vice ( ! reign+ ,duke1 & 9 #aegf jo9$ ! army s]v+ 9 ! ,ne!rl&s4 ,8 wife foll[$ him1 leav+ h] "y son 9 8 gr&fa!r's c>e at ,leonb]g1 :]e he b>ely recov]$ f a sev]e attack ( smallpox4 ,x 0 f ?is place t ,john d]iv$ ! ,lat9is$ "n ( ,leonmontanus1 9 accordance ) ! common practice ( ! "t1 b he 0 n kn[n by x to any great ext5t4 ,he 0 s5t to s*ool 9 #aegg1 b 9 ! foll[+ ye> 8 fa!r return$ to ,g]many1 almo/ ru9$ by ! abscond+ ( an acqua9tance = :om he _h become surety4 ,h5ry ,kepl] 0 oblig$ to sell 8 h\se & mo/ ( 8 belong+s1 & to keep a tav]n at ,elm5d+51 )draw+ 8 son f s*ool to help him ) ! r\gh "w4 ,9 #aehc "y ,kepl] 0 s5t to ! s*ool at ,elm5d+51 & 9 #aehd _h ano!r n>r[ escape f dea? by a viol5t illness4 ,9 #aehf he 0 s5t1 at ! *>ges ( ! ,duke1 to ! mona/ic s*ool ( ,maulbronn2 f :5ce1 9 accordance ) ! s*ool regulations1 he pass$ at ! end ( 8 fir/ ye> ! exam9ation = ! ba*elor's degree at ,tb+51 return+ = two m ye>s z a vet]an to ,maulbronn be=e be+ admitt$ z a resid5t /ud5t at ,tb+54 ,! ?ree ye>s ?us sp5t at ,maulbronn 7 m>k$ by recurr5ces ( sev]al ( ! diseases f :i* he _h suff]$ 9 *ildhood1 & also by family tr\bles at 8 home4 ,8 fa!r w5t away aft] a qu>rel ) 8 wife ,ca!r9e1 & di$ abroad4 ,ca!r9e h]self1 :o seems to h be5 ( a v unamiable disposition1 next qu>rell$ ) h] own relatives4 ,x is n surpris+ !re=e t ,kepl] aft] tak+ 8 ,m4,a4 degree 9 ,augu/1 #aeia1 com+ out second 9 ! exam9ation li/s1 0 ready to accept ! fir/ appo9tm5t (f]$ him1 ev5 if x %\ld involve leav+ home4 ,?is happ5$ to be ! lecture%ip 9 a/ronomy at ,gratz1 ! *ief t[n 9 ,/yria4 ,kepl]'s k ( a/ronomy 0 limit$ to ! compulsory s*ool c\rse1 nor _h he z yet any p>ticul> lean+ t[>ds ! sci5ce2 ! po/1 moreov]1 0 a meagre & unimportant "o4 ,on ! o!r h& he _h frequ5tly express$ disgu/ at ! way 9 :i* "o aft] ano!r ( 8 companions _h refus$ =eign appo9tm5ts :i* _h be5 arrang$ = !m "u ! ,duke's s*eme ( education4 ,8 tutors also /rongly urg$ him to accept ! lecture%ip1 & he _h n ! usual reluctance to leave home4 ,he !re=e proce$$ to ,gratz1 prote/+ t he did n !reby =feit 8 claim to a m promis+ op5+1 :5 su* %\ld appe>4 ,8 a/ronomical tutor1 ,mae/l91 enc\rag$ him to devote himself to 8 newly adopt$ sci5ce1 & ! fir/ result ( ?is advice appe>$ be=e v long 9 ,kepl]'s ,my/]ium ,cosmographicum4 ,! b5t ( 8 m9d 0 t[>ds philosophical speculation1 to :i* he _h be5 attract$ 9 8 y\?ful /udies ( ,scalig]'s ,exot]ic ,ex]cises4 ,he says he devot$ mu* "t to ! exam9ation ( ! nature ( heav51 ( s\ls1 ( g5ii1 ( ! elem5ts1 ( ! ess5ce ( fire1 ( ! cause ( f\nta9s1 ! ebb & fl[ ( ! tides1 ! %ape ( ! cont95ts & inl& seas1 & ?+s ( ?is sort4 ,foll[+ 8 tutor 9 8 admiration = ! ,cop]nican !ory1 he wrote an essay on ! prim>y motion1 attribut+ x to ! rotation ( ! e>?1 & ?is n = ! ma!matical reasons br\ght =w>d by ,cop]nicus1 b1 z he himself says1 on physical or metaphysical gr\nds4 ,9 #aeie1 hav+ m leisure f lectures1 he turn$ 8 speculative m9d to ! numb]1 size1 & motion ( ! planet>y orbits4 ,he fir/ tri$ simple num]ical relations1 b none ( !m appe>$ to be twice1 ?rice1 or f\r times z great z ano!r1 al?\gh he felt conv9c$ t !re 0 "s relation betwe5 ! motions & ! di/ances1 see+ t :5 a gap appe>$ 9 "o s]ies1 !re 0 a correspond+ gap 9 ! o!r4 ,^! gaps he attempt$ to fill by hypo!tical planets betwe5 ,m>s & ,jupit]1 & betwe5 ,m]cury & ,v5us1 b ?is me?od also fail$ to provide ! regul> proportion :i* he s\ght1 besides be+ op5 to ! objection t on ! same pr9ciple !re might be _m m equally invisible planets at ei!r end ( ! s]ies4 ,he 0 nev]!less unwill+ to adopt ! op9ion ( ,rheticus t ! numb] six 0 sacr$1 ma9ta9+ t ! sacr$ness ( ! numb] 0 ( mu* m rec5t date ?an ! creation ( ! worlds1 & c\ld n !re=e acc\nt = x4 ,he next tri$ an +5i\s idea1 comp>+ ! p]p5dicul>s f diff]5t po9ts ( a quadrant ( a circle on a tang5t at its extremity4 ,! greate/ ( ^!1 ! tang5t1 n be+ cut by ! quadrant1 he call$ ! l9e ( ! sun1 & associat$ ) inf9ite =ce4 ,! %orte/1 be+ ! po9t at ! o!r end ( ! quadrant1 ?us correspond$ to ! fix$ />s or z]o =ce2 int]m$iate ones 7 to be f\nd proportional to ! =ces ( ! six planets4 ,aft] a great am\nt ( unf9i%$ trial calculations1 :i* took ne>ly a :ole summ]1 he conv9c$ himself t success did n lie t way4 ,9 ,july1 #aeie1 :ile lectur+ on ! great planet>y conjunctions1 he drew quasi-triangles 9 a circul> zodiac %[+ ! sl[ progression ( ^! po9ts ( conjunction at int]vals ( j ov] #bdj or eight signs4 ,! successive *ords m>k$ out a small] circle to :i* !y 7 tang5ts1 ab\t half ! diamet] ( ! zodiacal circle z drawn1 & ,kepl] at once saw a simil>ity to ! orbits ( ,saturn & ,jupit]1 ! radius ( ! inscrib$ circle ( an equilat]al triangle be+ half t ( ! circumscrib$ circle4 ,8 natural sequ5ce ( ideas impell$ him to try a squ>e1 9 ! hope t ! circumscrib$ & inscrib$ circles might give him a simil> analogy = ! orbits ( ,jupit] & ,m>s4 ,he next tri$ a p5tagon & s on1 b he soon not$ t he w\ld nev] rea* ! sun t way1 nor w\ld he f9d any su* limitation z six1 ! numb] ( possibles be+ obvi\sly inf9ite4 ,! actual planets moreov] 7 n ev5 six b only five1 s f> z he knew1 s he next pond]$ ! "q ( :at sort ( ?+s ^! c\ld be ( :i* only five diff]5t figures 7 possible & sudd5ly ?\ght ( ! five regul> solids4#b ,he imm$iately p\nc$ ^u ?is idea & ultimately evolv$ ! foll[+ s*eme4 ,! e>? is ! sph]e1 ! measure ( all2 r\nd x describe a dodecah$ron2 ! sph]e includ+ ?is w be ,m>s4 ,r\nd ,m>s describe a tetrah$ron2 ! sph]e includ+ ?is w be ,jupit]4 ,describe a cube r\nd ,jupit]2 ! sph]e includ+ ?is w be ,saturn4 ,n[1 inscribe 9 ! e>? an icosah$ron1 ! sph]e inscrib$ 9 x w be ,v5us3 inscribe an octah$ron 9 ,v5us3 ! circle inscrib$ 9 x w be ,m]cury4 ,) ?is result ,kepl] 0 inord9ately pleas$1 & regrett$ n a mom5t ( ! "t sp5t 9 obta9+ x1 ?\gh to u ?is ,my/]ium ,cosmographicum c only appe> useless1 ev5 )\t ! m rec5t additions to ! kn[n planets4 ,he admitt$ t a c]ta9 ?ickness mu/ be assign$ to ! int]v5+ sph]es to cov] ! greate/ & lea/ di/ances ( ! sev]al planets f ! sun1 b ev5 !n "s ( ! numb]s obta9$ are n a v close fit = ! correspond+ planet>y orbits4 ,kepl]'s own sugge/$ explanation ( ! discordances 0 t !y mu/ be due to errone\s measures ( ! planet>y di/ances1 & ?is1 9 ^? days ( crude & infrequ5t obs]vations1 c\ld n easily be disprov$4 ,he next ?\ght ( a v>iety ( reasons :y ! five regul> solids %\ld occur 9 precisely ! ord] giv5 & 9 no o!r1 div]g+ f ?is into a subtle & n v intelligible process ( reason+ to acc\nt = ! division ( ! zodiac into #cfj4 ,! next subject 0 m important1 & dealt ) ! relation betwe5 ! di/ances ( ! planets & _! times ( revolution r\nd ! sun4 ,x 0 obvi\s t ! p]iod 0 n simply proportional to ! di/ance1 z ! out] planets 7 all too sl[ = ?is1 & he conclud$ ei!r t ! mov+ intellig5ces ( ! planets are weake/ 9 ^? t are f>!/ f ! sun1 or t !re is "o mov+ intellig5ce 9 ! sun1 ! common c5tre1 =c+ !m all r\nd1 b ^? mo/ viol5tly :i* are ne>e/1 & t x langui%es 9 "s sort & gr[s weak] at ! mo/ di/ant1 because ( ! remot5ess & ! att5uation ( ! virtue4 ,?is is n s ne> a guess at ! !ory ( gravitation z might be suppos$1 = ,kepl] imag9$ t a repulsive =ce 0 necess>y to acc\nt = ! planets be+ sometimes fur!r f ! sun1 & s laid aside ! idea ( a con/ant attractive =ce4 ,he made sev]al o!r attempts to f9d a law connect+ ! di/ances & p]iods ( ! planets1 b )\t success at t "t1 & only desi/$ :5 by unconsci\sly argu+ 9 a circle he appe>$ to get ! same result f two totally diff]5t hypo!ses4 ,he s5t copies ( 8 book to sev]al lead+ a/ronom]s1 ( :om ,galileo prais$ 8 +5uity & good fai?1 :ile ,ty*o ,brahe 0 evid5tly mu* /ruck ) ! "w & advis$ him to adapt some?+ simil> to ! ,ty*onic sy/em in/ead ( ! ,cop]nican4 ,he also intimat$ t 8 ,uraniborg obs]vations w\ld provide m accurate det]m9ations ( ! planet>y orbits1 & ?us made ,kepl] eag] to visit him1 a project :i* z we %all see 0 m ?an fulfill$4 ,ano!r copy ( ! book ,kepl] s5t to ,reym]s ! ,imp]ial a/ronom] ) a mo/ fulsome lett]1 :i* ,ty*o1 :o ass]t$ t ,reym]s _h simply plagi>is$ 8 "w1 v /rongly res5t$1 ?us draw+ f ,kepl] a long lett] ( apology4 ,ab\t ! same "t ,kepl] _h m>ri$ a lady already twice wid[$1 & become involv$ 9 difficulties ) h] relatives on f9ancial gr\nds1 & ) ! ,/yrian au?orities 9 connection ) ! religi\s disputes !n com+ to a head4 ,on acc\nt ( ^! latt] he ?\ght x exp$i5t1 ! ye> aft] 8 m>riage1 to )draw to ,hung>y1 f :5ce he s5t %ort treatises to ,tb+51 ,on ! magnet 7foll[+ ! ideas ( ,gilb]t ( ,col*e/]71 ,on ! cause ( ! obliquity ( ! ecliptic & ,on ! ,div9e wisdom z %[n 9 ! ,creation4 ,8 next important /ep makes x desirable to devote a *apt] to a %ort notice ( ,ty*o ,brahe4 ,footnote #b3 ,s9ce ! sum ( ! plane angles at a corn] ( a regul> solid mu/ be less ?an f\r "r angles1 x is easily se5 t few regul> solids are possible4 ,hexagonal faces are cle>ly impossible1 or any polygonal faces ) m ?an five sides4 ,! possible =ms are ! dodecah$ron ) twelve p5tagonal faces1 ?ree meet+ at ea* corn]2 ! cube1 six squ>e faces1 ?ree meet+ at ea* corn]2 & ?ree figures ) triangul> faces1 ! tetrah$ron ( f\r faces1 ?ree meet+ at ea* corn]2 ! octah$ron ( eight faces1 f\r meet+ at ea* corn]2 & ! icosah$ron ( tw5ty faces1 five meet+ at ea* corn]4 ,,*apt] ,,iii4 ,,ty*o ,,brahe4 ,! age foll[+ t ( ,cop]nicus produc$ ?ree out/&+ figures associat$ ) ! sci5ce ( a/ronomy1 !n rea*+ ! close ( :at ,pr(essor ,=bes s aptly /yles ! geometrical p]iod4 ,^! ?ree ,sir ,david ,brew/] has t]m$ ,m>tyrs ( ,sci5ce2 ,galileo1 ! great ,italian philosoph]1 has 8 own place among ! ,pione]s ( ,sci5ce2 & invaluable ?\gh ,ty*o ,brahe's "w 01 ! latt] c h>dly be claim$ z a pione] 9 ! same s5se z ! o!r two4 ,nev]!less1 ,kepl]1 ! ?ird memb] ( ! trio1 c\ld n h made 8 mo/ valuable discov]ies )\t ,ty*o's obs]vations4 ,( noble family1 born a tw9 on #ad? ,decemb]1 #aedf1 at ,knud/rup 9 ,scania 7! s\!rnmo/ "p ( ,sw$51 !n =m+ "p ( ! k+dom ( ,d5m>k71 ,ty*o 0 kidnapp$ a ye> lat] by a *ildless uncle4 ,?is uncle br\ght him up z 8 own son1 provid$ him at ! age ( sev5 ) a tutor1 & s5t him 9 #aeei to ! ,univ]sity ( ,cop5hag51 to /udy = a political c>e] by tak+ c\rses 9 rhetoric & philosophy4 ,on #ba/ ,augu/1 #aefj1 h[ev]1 a sol> eclipse took place1 total 9 ,portugal1 & !re=e ( small proportions 9 ,d5m>k1 & ,ty*o's ke5 int]e/ 0 awak5$1 n s mu* by ! ph5om5on1 z by ! fact t x _h occurr$ accord+ to pr$iction4 ,soon aft]w>ds he pur*as$ an edition ( ,ptolemy 9 ord] to read up ! subject ( a/ronomy1 to :i*1 & to ma!matics1 he devot$ mo/ ( ! rema9d] ( 8 ?ree ye>s' c\rse at ,cop5hag54 ,8 uncle next s5t him to ,leipzig to /udy law1 b he manag$ to cont9ue 8 a/ronomical rese>*es4 ,he obta9$ ! ,alphons9e & ! new ,prut5ic ,tables1 b soon f\nd t ! latt]1 ?\gh m accurate ?an ! =m]1 fail$ to repres5t ! true positions ( ! planets1 & grasp$ ! fact t cont9u\s obs]vation 0 ess5tial 9 ord] to det]m9e ! true motions4 ,he began by obs]v+ a conjunction ( ,jupit] & ,saturn 9 ,augu/1 #aefc1 & f\nd ! ,prut5ic ,tables sev]al days 9 error1 & ! ,alphons9e a :ole mon?4 ,he provid$ himself ) a cross-/aff = det]m9+ ! angul> di/ance betwe5 />s or o!r objects1 &1 f9d+ ! divisions ( ! scale inaccurate1 con/ruct$ a table ( corrections1 an improvem5t t seems to h be5 a decid$ innovation1 ! previ\s practice hav+ be5 to use ! be/ available in/rum5t & ignore its errors4 ,ab\t ?is "t w> broke out betwe5 ,d5m>k & ,sw$51 & ,ty*o return$ to 8 uncle1 :o 0 vice-admiral & atta*$ to ! k+'s suite4 ,! uncle di$ 9 ! foll[+ mon?1 & e>ly 9 ! next ye> ,ty*o w5t abroad aga91 ?is "t to ,witt5b]g4 ,aft] five mon?s1 h[ev]1 an outbreak ( plague drove him away1 & he matriculat$ at ,ro/ock1 :]e he f\nd little a/ronomy b a good deal ( a/rology4 ,:ile !re he f\ght a duel 9 ! d>k & lo/ "p ( 8 nose1 :i* he replac$ by a composition ( gold & silv]4 ,he c>ri$ on regul> obs]vations ) 8 cross-/aff & p]sev]$ ) 8 a/ronomical /udies 9 spite ( ! objections & want ( sympa?y ( 8 fell[-c\ntrym54 ,! ,k+ ( ,d5m>k1 h[ev]1 hav+ a high] op9ion ( ! value ( sci5ce1 promis$ ,ty*o ! fir/ canonry t %\ld fall vacant 9 ! ca!dral *apt] ( ,roskilde1 s t he might be assur$ ( an income :ile devot+ himself to f9ancially unproductive "w4 ,9 #aefh ,ty*o left ,ro/ock1 & matriculat$ at ,basle1 b soon mov$ on to ,augsburg1 :]e he f\nd m en?usiasm = a/ronomy1 & induc$ "o ( 8 new fri5ds to ord] ! con/ruction ( a l>ge #ai-;foot quadrant ( heavy oak beams4 ,?is 0 ! fir/ ( ! s]ies ( great in/rum5ts associat$ ) ,ty*o's "n1 & x rema9$ 9 use = five ye>s1 be+ de/roy$ by a great /orm 9 #aegd4 ,ty*o mean:ile _h left ,augsburg 9 #aegj & return$ to live ) 8 fa!r1 n[ gov]nor ( ,hels+borg ,ca/le1 until ! latt]'s dea? 9 ! foll[+ ye>4 ,ty*o !n jo9$ 8 "m's bro!r1 ,/e5 ,bille1 ! only "o ( 8 relatives :o %[$ any sympa?y ) 8 desire = a sci5tific c>e]4 ,on #aa? ,novemb]1 #aegb1 ,ty*o notic$ an unfamili> bright /> 9 ! con/ellation ( ,cassiopeia1 & cont9u$ to obs]ve x ) a sextant4 ,x 0 a v brilliant object1 equal to ,v5us at its brighte/ = ! re/ ( ,novemb]1 n fall+ bel[ ! fir/ magnitude = ano!r f\r mon?s1 & rema9+ visible = m ?an a ye> aft]w>ds4 ,ty*o wrote a little book on ! new />1 ma9ta9+ t x _h practically no p>allax1 & !re=e c\ld n be1 z "s suppos$1 a comet4 ,deem+ au?or%ip b5ea? ! dignity ( a noble he 0 v reluctant to publi%1 b he 0 conv9c$ ( ! importance ( increas+ ! numb] & accuracy ( obs]vations1 ?\gh he 0 by no means free f all ! errone\s ideas ( 8 "t4 ,! little book conta9$ a c]ta9 am\nt ( a/rology1 b ,ty*o evid5tly did n reg>d ?is z ( v great importance4 ,he adopt$ ! view t ! v r>ity ( ! ph5om5on ( a new /> mu/ prev5t ! =mulation & adoption ( def9ite rules = det]m9+ its significance4 ,we ga!r f lectures :i* he 0 p]suad$ to deliv] at ! ,univ]sity ( ,cop5hag5 t1 ?\gh 9 agreem5t ) ! accept$ canons ( a/rology z to ! influ5ce ( planet>y conjunctions & su* ph5om5a on ! c\rse ( human ev5ts1 he did n consid] ! fate pr$ict$ by anyone's horoscope to be unavoidable1 b ?\ght ! great value ( a/rology lay 9 ! w>n+s d]iv$ f su* computations1 :i* %\ld enable ! believ] to avoid ?reat5$ calamities4 ,9 #aege he left ,d5m>k once m & made 8 way to ,cassel1 :]e he f\nd a k9dr$ _s 9 ! /udi\s ,l&grave1 ,william ,,iv4 ( ,hesse1 ^: a/ronomical pursuits _h be5 int]rupt$ by 8 accession to ! gov]nm5t ( ,hesse1 9 #aefg4 ,ty*o obs]v$ ) him = "s "t1 ! two =m+ a firm fri5d%ip1 & !n visit$ successively ,frank=t1 ,basle1 & ,v5ice1 return+ by way ( ,augsburg1 ,ratisbon1 & ,saalfeld to ,witt5b]g2 on ! way he acquir$ v>i\s a/ronomical manuscripts1 made fri5ds among practical a/ronom]s1 & exam9$ new in/rum5ts4 ,he seem$ to h consid]$ ! advantages ( ! sev]al places ?us visit$ & decid$ on ,basle1 b on 8 return to ,d5m>k to fet* 8 family ) ! object ( transf]r+ !m to ,basle1 he f\nd t 8 fri5d ! ,l&grave _h writt5 to ,k+ ,fr$]ick on 8 behalf1 urg+ him to provide ! means to enable ,ty*o to pursue 8 a/ronomical "w1 promis+ t n only %\ld cr$it result = ! k+ & = ,d5m>k b t sci5ce itself w\ld be greatly advanc$4 ,! ultimate result ( ?is lett] 0 t aft] refus+ v>i\s (f]s1 ,ty*o accept$ f ! k+ a grant ( ! small isl& ( ,hve51 9 ! ,s\nd1 ) a gu>ante$ income1 9 addition to a l>ge sum f ! treasury = build+ an obs]vatory on ! isl&1 f> remov$ f ! di/ractions ( c\rt life4 ,"h ,ty*o built 8 celebrat$ obs]vatory ( ,uraniborg & began obs]vations 9 ,decemb]1 #aegf1 us+ ! l>ge in/rum5ts !n f\nd necess>y 9 ord] to atta9 ! accuracy ( obs]vation :i* )9 ! next half-c5tury 0 to be s greatly facilitat$ by ! inv5tion ( ! telescope4 ,"h also he built sev]al small] obs]v+ rooms1 s t 8 pupils %\ld be able to obs]ve indep5d5tly4 ,= m ?an tw5ty ye>s he cont9u$ 8 obs]vations at ,uraniborg1 surr\nd$ by 8 family1 & attract+ num]\s pupils4 ,8 con/ant aim 0 to accumulate a l>ge /ore ( obs]vations ( a high ord] ( accuracy1 & ?us to provide data = ! complete re=m ( a/ronomy4 ,z we h se51 few ( ! ,dani% nobles _h any sympa?y ) ,ty*o's pursuits1 & mo/ ( !m /rongly res5t$ ! cont9ual exp5se borne by ! ,k+'s treasury4 ,ty*o moreov] 0 s absorb$ 9 8 sci5tific pursuits t he w\ld n take ! tr\ble to be a good l&lord1 nor to c>ry out all ! duties laid ^u him 9 return = c]ta9 ( 8 grants ( income4 ,8 build+s includ$ a *emical laboratory1 & he 0 9 ! habit ( mak+ up elixirs = v>i\s m$ical purposes2 ^! 7 q popul>1 p>ticul>ly z he made no *>ge = !m4 ,he seems to h be5 some?+ ( a homoeopa?i/1 = he recomm5ds sulphur to cure infecti\s diseases br\ght on by ! sulphur\s vap\rs ( ! ,aurora ,borealis6 ,k+ ,fr$]ick1 9 consid]ation ( v>i\s grants to ,ty*o1 reli$ ^u 8 assi/ance 9 sci5tific matt]s1 & especially 9 a/rological calculations2 su* z ! horoscope ( ! heir app>5t1 ,pr9ce ,*ri/ian1 born 9 #aegg1 :i* has be5 pres]v$ among ,ty*o's writ+s4 ,!re is1 h[ev]1 no kn[n copy 9 exi/5ce ( any ( ! s]ies ( annual almanacs ) pr$ictions :i* he prep>$ = ! ,k+4 ,9 ,novemb]1 #aegg1 appe>$ a bright comet1 :i* ,ty*o c>efully obs]v$ ) 8 sextant1 prov+ t x _h no p]ceptible p>allax1 & mu/ !re=e be fur!r (f ?an ! moon4 ,he ?us def9itely ov]?rew ! common belief 9 ! atmosph]ic orig9 ( comets1 :i* he _h himself hi!rto %>$4 ,) increas+ accuracy he obs]v$ sev]al o!r comets1 notably "o 9 #aehe1 :5 he _h a full equipm5t ( in/rum5ts & a l>ge /aff ( assi/ants4 ,! ye> #aehh1 :i* saw ! dea? ( 8 royal b5efactor1 saw also ! publication ( a volume ( ,ty*o's great "w ,introduction to ! ,new ,a/ronomy4 ,! fir/ volume1 devot$ to ! new /> ( #aegb1 0 n ready1 because ! r$uction ( ! obs]vations involv$ s mu* rese>* to correct ! /> places = refraction1 precession1 etc42 x 0 n complet$ 9 fact until ,ty*o's dea?1 b ! second volume1 deal+ ) ! comet ( #aegg1 0 pr9t$ at ,uraniborg & "s copies 7 issu$ 9 #aehh4 ,besides ! comet obs]vations x includ$ an acc\nt ( ,ty*o's sy/em ( ! _w4 ,he w\ld n accept ! ,cop]nican sy/em1 z he consid]$ ! e>? too heavy & sluggi% to move1 & also t ! au?ority ( ,scripture 0 aga9/ su* an hypo!sis4 ,he !re=e assum$ t ! o!r planets revolv$ ab\t ! sun1 :ile ! sun1 moon1 & />s revolv$ ab\t ! e>? z a c5tre4 ,geometrically ?is is mu* ! same z ! ,cop]nican sy/em1 b physically x involves ! grotesque dem& t ! :ole sy/em ( />s revolves r\nd our insignificant little e>? e tw5ty-f\r h\rs4 ,s9ce 8 previ\s small book on ! comet1 ,ty*o _h evid5tly consid]$ m fully its possible a/rological significance1 = he =etold a religi\s w>1 giv+ ! date ( its comm5cem5t1 & also ! ris+ ( a great ,prote/ant *ampion4 ,^! pr$ictions 7 app>5tly fulfill$ almo/ to ! lett] by ! great religi\s w>s t broke out t[>ds ! end ( ! sixte5? c5tury1 & 9 ! p]son ( ,gu/avus ,adolphus4 ,k+ ,fr$]ick's dea? did n at fir/ affect ,ty*o's position1 = ! new k+1 ,*ri/ian1 0 only elev5 ye>s old1 & = "s ye>s ! c\ncil ( reg5ts includ$ two ( 8 support]s4 ,aft] _! dea?s1 h[ev]1 8 emolum5ts began to be cut d[n on ! plea ( economy1 & z he took v little tr\ble to c>ry out any o!r ?an sci5tific duties x 0 easy en\gh = 8 enemies to f9d fault4 ,"o aft] ano!r s\rce ( income 0 cut (f1 b he p]sev]$ ) 8 sci5tific "w1 includ+ a catalogue ( />s4 ,he _h obta9$ pl5ty ( good obs]vations ( #ggg />s1 b ?\ght 8 catalogue %\ld conta9 #ajjj />s1 s he ha/ily obs]v$ z _m m z he c\ld up to ! "t ( 8 leav+ ,hve51 ?\gh ev5 !n he _h n complet$ 8 programme4 ,ab\t ! "t t ,k+ ,*ri/ian rea*$ ! age ( eighte51 ,ty*o began to look ab\t = a new patron1 & to consid] ! prospects (f]$ by transf]r+ himself ) 8 in/rum5ts & activities to ! patronage ( ! ,emp]or ,rudolph ,,ii4 ,9 #aeig1 :5 ev5 8 p5sion f ! ,royal treasury 0 cut (f1 he hurri$ly pack$ up 8 in/rum5ts & libr>y1 & aft] a few weeks' soj\rn at ,cop5hag51 proce$$ to ,ro/ock1 9 ,meckl5burg1 :5ce he s5t an appeal to ,k+ ,*ri/ian4 ,x is possible t _h he done ?is be=e leav+ ,hve5 x might h _h m effect1 b x c be readily se5 f ! tone ( ! k+'s unfav\rable reply t 8 dep>ture 0 reg>d$ z an aggravation ( previ\s %ortcom+s4 ,driv5 f ,ro/ock by ! plague1 ,ty*o settl$ tempor>ily at ,w&sbeck1 9 ,hol/e91 b t[>ds ! end ( #aeih set out to meet ! ,emp]or at ,prague4 ,once m plague int]v5$ & he sp5t "s "t at ,dresd51 aft]w>ds go+ to ,witt5b]g = ! w9t]4 ,he ultimately rea*$ ,prague 9 ,june1 #aeii4 ,rudolph grant$ him a sal>y ( at lea/ #cjjj flor9s1 promis+ also to settle on him ! fir/ h]$it>y e/ate t %\ld lapse to ! ,cr[n4 ,he (f]$1 moreov]1 ! *oice betwe5 ?ree ca/les outside ,prague1 ( :i* ,ty*o *ose ,b5atek4 ,!re he set ab\t alt]+ ! build+s 9 read9ess = 8 in/rum5ts1 = :i* he s5t to ,uraniborg4 ,be=e !y rea*$ him1 aft] _m vexati\s delays1 he _h giv5 up wait+ = ! funds promis$ = 8 build+ exp5ses1 & remov$ f ,b5atek to ,prague4 ,x 0 dur+ ?is int]val t aft] consid]able negotiation1 ,kepl]1 :o _h be5 9 correspond5ce ) ,ty*o1 cons5t$ to jo9 him z an assi/ant4 ,ano!r assi/ant1 ,longomontanus1 :o _h be5 ) ,ty*o at ,uraniborg1 0 f9d+ difficulty ) ! long s]ies ( ,m>s obs]vations1 & x 0 arrang$ t he %\ld transf] 8 en]gies to ! lun> obs]vations1 leav+ ^? ( ,m>s = ,kepl]4 ,be=e v mu* c\ld be done ) !m1 h[ev]1 ,ty*o di$ at ! end ( ,octob]1 #afja4 ,he may h regrett$ ! peaceful isl& ( ,hve51 consid]+ ! tr\bles 9 :i* ,bohemia 0 rapidly becom+ involv$1 b !re is little d\bt t _h x n be5 = 8 self-impos$ exile1 8 obs]vations w\ld n h come into ,kepl]'s h&s1 & _! great value might h be5 lo/4 ,9 any case x 0 at ,uraniborg t ! mass ( obs]vations 0 produc$ ^u :i* ! fame ( ,ty*o ,brahe re/s4 ,8 own discov]ies1 ?\gh 9 !mselves ! mo/ important made 9 a/ronomy = _m c5turies1 are f> less valuable ?an ^? = :i* 8 obs]vations furni%$ ! mat]ial4 ,he discov]$ ! ?ird & f\r? inequalities ( ! moon 9 longitude1 call$ respectively ! v>iation & ! annual equation1 also ! v>iability ( ! motion ( ! moon's nodes & ! incl9ation ( its orbit to ! ecliptic4 ,he obta9$ an improv$ value ( ! con/ant ( precession1 & did good s]vice by reject+ ! idea t x 0 v>iable1 an idea :i*1 "u ! "n ( trepidation1 _h = _m c5turies be5 accept$4 ,he discov]$ ! effect ( refraction1 ?\gh only approximately its am\nt1 & det]m9$ improv$ values ( _m o!r a/ronomical con/ants1 b s+ul>ly en\gh made no det]m9ation ( ! di/ance ( ! sun1 adopt+ in/ead ! anci5t & errone\s value giv5 by ,hipp>*us4 ,8 magnific5t ,obs]vatory ( ,uraniborg1 ! f9e/ build+ = a/ronomical purposes t ! _w _h hi!rto se51 0 all[$ to fall into decay1 & sc>cely m ?an m]e indications ( ! site may n[ be se54 ,,*apt] ,,iv4 ,,kepl] ,,jo9s ,,ty*o4 ,! association ( ,kepl] ) ,ty*o 0 "o ( ! mo/ important l&m>ks 9 ! hi/ory ( a/ronomy4 ,! y\ng] man hop$1 by ! aid ( ,ty*o's planet>y obs]vations1 to obta9 bett] support = "s ( 8 fanciful speculative !ories1 :ile ! latt]1 :o _h c]ta9ly n ga9$ 9 pre/ige by leav+ ,d5m>k1 0 9 great ne$ ( a compet5t /aff ( assi/ants4 ,( ! two x w\ld almo/ seem t ,ty*o ?\ght himself ! great] ga9]1 = 9 spite ( 8 reputation = brusqu5ess & want ( consid]ation1 he n only made light ( ,kepl]'s apology 9 ! matt] ( ,reym]s1 b treat$ him ) uni=m k9dness 9 ! face ( great rud5ess & +ratitude4 ,he begg$ him to come z a welcome fri5d1 ?\gh ,kepl]1 v t\*y on ! subject ( 8 own a/ronomical p[]s1 0 afraid he might be reg>d$ z simply a subord9ate assi/ant4 ,an arrangem5t _h be5 sugge/$ by :i* ,kepl] %\ld obta9 two ye>s' leave ( abs5ce f ,gratz on full pay1 :i*1 because ( ! high] co/ ( liv+ 9 ,prague1 %\ld be supplem5t$ by ! ,emp]or2 b be=e ?is c\ld be conclud$1 ,kepl] ?rew up 8 pr(essor%ip1 & ?9k+ he _h !reby also lo/ ! *ance ( go+ to ,prague1 appli$ to ,mae/l9 & o!rs ( 8 ,tb+5 fri5ds to make int]e/ = him ) ! ,duke ( ,wurtemb]g & secure ! pr(essor%ip ( m$ic9e4 ,ty*o1 h[ev]1 /ill urg$ him to come to ,prague1 promis+ to d 8 utmo/ to secure = him a p]man5t appo9tm5t1 or 9 any ev5t to see t he 0 n ! los] by com+4 ,kepl] 0 delay$ by illness on ! way1 b ultimately rea*$ ,prague1 accompani$ by 8 wife1 & = "s "t liv$ entirely at ,ty*o's exp5se1 writ+ by way ( return essays aga9/ ,reym]s & ano!r man1 :o _h claim$ ! cr$it ( ! ,ty*onic sy/em4 ,?is ,kepl] c\ld d ) a cle> consci5ce1 z x 0 only a "q ( priority & did n involve any support ( ! sy/em1 :i* he deem$ f> inf]ior to t ( ,cop]nicus4 ,! foll[+ ye> saw friction betwe5 ! two a/ronom]s1 & we le>n f ,kepl]'s abject lett] ( apology t he 0 entirely 9 ! wrong4 ,x 0 ab\t money matt]s1 :i* 9 "o way or ano!r embitt]$ ! re/ ( ,kepl]'s life1 & x arose dur+ 8 abs5ce f ,prague4 ,on 8 return 9 ,septemb]1 #afja1 ,ty*o pres5t$ him to ! ,emp]or1 :o gave him ! title ( ,imp]ial ,ma!matician1 on condition ( assi/+ ,ty*o 9 8 calculations1 ! v ?+ ,kepl] 0 mo/ anxi\s to be all[$ to d3 = n[h]e else 9 ! _w 0 !re su* a collection ( good obs]vations suffici5t = 8 purpose ( re=m+ ! :ole !ory ( a/ronomy4 ,! ,emp]or's int]e/ 0 /ill ma9ly ) a/rology1 b he lik$ to ?9k t 8 "n w\ld be h&$ d[n to po/]ity 9 connection ) ! new ,planet>y ,tables 9 ! same way z t ( ,alphonso ( ,ca/ile1 & he made lib]al promises to pay ! exp5ses4 ,ty*o's o!r pr9cipal assi/ant1 ,longomontanus1 did n /ay long aft] giv+ up ! ,m>s obs]vations to ,kepl]1 b in/ead ( work+ at ! new lun> !ory1 sudd5ly left to take up a pr(essor%ip ( a/ronomy 9 8 native ,d5m>k4 ,v %ortly aft]w>ds ,ty*o himself di$ ( acute di/emp]2 ,kepl] began to prep>e ! mass ( manuscripts = publication1 b1 z ev]y?+ 0 claim$ by ! ,brahe family1 he 0 n all[$ to f9i% ! "w4 ,he succe$$ to ,ty*o's po/ ( pr9cipal ma!matician to ! ,emp]or1 at a r$uc$ (ficial sal>y1 :i* ow+ to ! empt9ess ( ! ,imp]ial treasury 0 almo/ always 9 arre>4 ,9 ord] to meet 8 exp5ses he _h rec\rse to ! ca/+ ( nativities1 = :i* he ga9$ consid]able reputation & receiv$ v good pay4 ,he work$ by ! conv5tional rules ( a/rology1 & 0 q prep>$ to take fees = s do+1 al?\gh he _h v little fai? 9 !m1 pref]r+ 8 own fanciful ideas4 ,9 #afjd ! con/ellation ( ,cassiopeia 0 once m tempor>ily enri*$ by ! appe>ance ( a new />1 said by "s to be bright] ?an ,ty*o's nova1 & by o!rs to be twice z bright z ,jupit]4 ,kepl] at once wrote a %ort acc\nt ( x1 f :i* may be ga!r$ "s idea ( 8 attitude t[>ds a/rology4 ,contra/+ ! two novae1 he says3 ,yond] "o *ose = its appe>ance a "t no way rem>kable1 & came into ! _w q unexpect$ly1 l an enemy /orm+ a t[n & break+ into ! m>ket-place be=e ! citiz5s are aw>e ( 8 approa*2 b ours has come exactly 9 ! ye> ( :i* a/rolog]s h writt5 s mu* ab\t ! fi]y trigon t happ5s 9 x2 j 9 ! mon? 9 :i* 7accord+ to ,cyprian71 ,m>s comes up to a v p]fect conjunction ) ! o!r two sup]ior planets2 j 9 ! day :5 ,m>s has jo9$ ,jupit]1 & j 9 ! region :]e ?is conjunction has tak5 place4 ,!re=e ! app>ition ( ?is /> is n l a secret ho/ile irruption1 z 0 t "o ( #aegb1 b ! spectacle ( a public triumph1 or ! entry ( a mighty pot5tate2 :5 ! c\ri]s ride 9 "s "t be=e to prep>e 8 lodg+s1 & ! cr[d ( "y ur*9s beg9 to ?9k ! "t ov] long to wait1 !n roll 91 "o aft] ano!r1 ! ammunition & money1 & baggage waggons1 & pres5tly ! trampl+ ( horse & ! ru% ( p f e side to ! /reets & w9d[s2 & :5 ! cr[d h gaz$ ) _! jaws all agape at ! troops ( knights2 !n at la/ ! trumpet]s & ar*]s & lackeys s di/+ui% ! p]son ( ! mon>*1 t !re is no occasion to po9t him out1 b e "o cries ( 8 own accord--',"h we h him'4 ,:at x may port5d is h>d to det]m9e1 & ?is mu* only is c]ta91 t x comes to tell mank9d ei!r no?+ at all or high & mighty news1 q beyond human s5se & und]/&+4 ,x w h an important influ5ce on political & social relations2 n inde$ by its own nature1 b z x 7 accid5tally ?r\gh ! disposition ( mank9d4 ,fir/1 x port5ds to ! booksell]s great di/urbances & tol]able ga9s2 = almo/ e ,!ologus1 ,philosophicus1 ,m$icus1 & ,ma!maticus1 or :oev] else1 hav+ no labori\s occupation entru/$ to him1 seeks 8 pleasure 9 /udiis1 w make p>ticul> rem>ks ^u x1 & w wi% to br+ ^! rem>ks to ! light4 ,j s w o!rs1 le>n$ & unle>n$1 wi% to "k its mean+1 & !y w buy ! au?ors :o pr(ess to tell !m4 ,i m5tion ^! ?+s m]ely by way ( example1 because al?\gh ?us mu* c be easily pr$ict$ )\t great skill1 yet may x happ5 j z easily1 & 9 ! same mann]1 t ! vulg>1 or :oev] else is ( easy fai?1 or1 x may be1 crazy1 may wi% to exalt himself into a great prophet2 or x may ev5 happ5 t "s p[]ful "l1 :o has good f\ndation & beg9n+ ( great dignities1 w be *e]$ on by ?is ph5om5on to v5ture on "s new s*eme1 j z if ,god _h set up ?is /> 9 ! d>kness m]ely to enlight5 !m4 ,he made no secret ( 8 views on conv5tional a/rology1 z to :i* he claim$ to speak ) ! au?ority ( "o fully conv]sant ) its pr9ciples1 b he nev]!less express$ 8 s9c]e conviction t ! conjunctions & aspects ( ! planets c]ta9ly did affect ?+s on ! e>?1 ma9ta9+ t he 0 driv5 to ?is belief aga9/ 8 w by mo/ unfail+ exp]i5ces4 ,mean:ile ! project$ ,rudolph9e ,tables 7 cont9ually delay$ by ! want ( money4 ,kepl]'s nom9al sal>y %\ld h be5 ample = 8 exp5ses1 increas$ ?\gh !y 7 by 8 gr[+ family1 b 9 ! deplet$ /ate ( ! treasury !re 7 _m :o object$ to any paym5t = su* unpractical purposes4 ,?is p>ticul> attitude has n be5 conf9$ to any special epo* or c\ntry1 b ! obvi\s result 9 ,kepl]'s case 0 to compel him to apply himself to less exp5sive matt]s ?an ! ,planet>y ,tables1 & among ^! mu/ be includ$ n only ! horoscopes or nativities1 :i* ow+ to 8 reputation 7 always 9 dem&1 b also o!r writ+s :i* probably did n pay s well4 ,9 #afjd he publi%$ ,a ,supplem5t to ,vitellion1 conta9+ ! e>lie/ kn[n reasonable !ory ( optics1 & especially ( dioptrics or vision ?r\gh l5ses4 ,he comp>$ ! me*anism ( ! eye ) t ( ,porta's ,cam]a ,obscura1 b made no attempt to expla9 h[ ! image =m$ on ! ret9a is und]/ood by ! bra94 ,he w5t c>efully into ! "q ( refraction1 ! importance ( :i* ,ty*o _h be5 ! fir/ a/ronom] to recognise1 ?\gh he only appli$ x at l[ altitudes1 & _h n arriv$ at a true !ory or accurate values4 ,kepl] wa/$ a good deal ( "t & +5uity on trial !ories4 ,he w\ld inv>iably />t ) "s hypo!sis1 & "w out ! effect4 ,he w\ld !n te/ x by exp]im5t1 & :5 x fail$ w\ld at once recognise t 8 hypo!sis 0 a priori b\nd to fail4 ,he r>ely seems to h notic$ ! fatal objections 9 "t to save himself tr\ble4 ,he w\ld !n at once />t aga9 on a new hypo!sis1 equally gratuit\s & equally unf\nd$4 ,x nev] seems to h occurr$ to him t !re might be a bett] way ( approa*+ a problem4 ,among ! l9es he foll[$ 9 ?is p>ticul> inve/igation 71 fir/1 t refraction dep5ds only on ! angle ( incid5ce1 :i*1 he says1 _c be correct z x w\ld ?us be ! same = all refract+ sub/ances2 next1 t x dep5d$ also on ! d5sity ( ! m$ium4 ,?is 0 a good %ot1 b he un=tunately assum$ t all rays pass+ into a d5s] m$ium w\ld app>5tly p5etrate x to a dep? dep5d+ only on ! m$ium1 :i* means t !re is a con/ant ratio betwe5 ! tang5ts1 in/ead ( ! s9es1 ( ! incl9ation ( ! incid5t & refract$ rays to ! normal4 ,exp]im5t prov$ t ?is gave too high values = refraction ne> ! v]tical comp>$ ) ^? ne> ! horizon1 s ,kepl] w5t (f at a tang5t & tri$ a totally new set ( ideas1 :i* all r$uc$ to ! absurdity ( a refraction :i* vani%$ at ! horizon4 ,^! 7 foll[$ by ano!r set1 involv+ ei!r a con/ant am\nt ( refraction or "o becom+ inf9ite4 ,he !n came to ! conclusion t ^! geometrical me?ods mu/ fail because ! refract$ image is n real1 & det]m9$ to try by analogy only1 comp>+ ! equally unreal image =m$ by a mirror ) t =m$ by refraction 9 wat]4 ,he notic$ h[ ! bottom ( a vessel conta9+ wat] appe>s to rise m & m away f ! v]tical1 & at once jump$ to ! analogy ( a concave mirror1 :i* magnifies ! image1 :ile a convex mirror 0 lik5$ to a r>] m$ium4 ,?is l9e ( attack also fail$ him1 z did v>i\s attempts to f9d relations betwe5 8 measurem5ts ( refraction & conic sections1 & he broke (f sudd5ly ) a diatribe aga9/ ,ty*o's critics1 :om he lik5$ to bl9d m5 disput+ ab\t col\rs4 ,n _m ye>s lat] ,snell discov]$ ! true law ( refraction1 b ,kepl]'s contribution to ! subject1 ?\gh he fail$ to discov] ! actual law1 includes sev]al ( ! adopt$ by-laws4 ,he not$ t atmosph]ic refraction w\ld alt] ) ! height ( ! atmosph]e & ) temp]ature1 & also recognis$ ! fact t ra9b[ col\rs dep5d on ! angle ( refraction1 :e!r se5 9 ! ra9b[ itself1 or 9 dew1 glass1 wat]1 or any simil> m$ium4 ,he ?us came ne> to anticipat+ ,newton4 ,be=e leav+ ! subject ( ,kepl]'s optics x w be well to recall t a few ye>s lat] aft] he>+ ( ,galileo's telescope1 ,kepl] sugge/$ t = a/ronomical purposes two convex l5ses %\ld be us$1 s t !re %\ld be a real image :]e measur+ wires c\ld be plac$ = ref]5ce4 ,he did n c>ry out ! idea himself1 & x 0 left to ! ,engli%man ,gascoigne to produce ! fir/ in/rum5t on ?is ,kepl]ian pr9ciple1 univ]sally kn[n z ! ,a/ronomical ,telescope4 ,9 #afjf came a second treatise on ! new />1 discuss+ v>i\s !ories to acc\nt = its appe>ance1 & refus+ to accept ! notion t x 0 a =tuit\s conc\rse ( atoms4 ,?is 0 foll[$ 9 #afjg by a treatise on comets1 sugge/$ by ! comet appe>+ t ye>1 kn[n z ,halley's comet aft] its next return4 ,he reg>d$ comets z planets mov+ 9 /raight l9es1 nev] hav+ exam9$ suffici5t obs]vations ( any comet to conv9ce himself t _! pa?s are curv$4 ,if he _h n assum$ t !y 7 ext]nal to ! sy/em & s c\ld n be expect$ to return1 he might h anticipat$ ,halley's discov]y4 ,ano!r sugge/ive rem>k ( 8 0 to ! effect t ! planets mu/ be self-lum9\s1 z o!rwise ,m]cury & ,v5us1 at any rate1 ought to %[ phases4 ,?is 0 put to ! te/ n long aft]w>ds by means ( ,galileo's telescope4 ,9 #afjg ,kepl] ru%$ into pr9t ) an alleg$ obs]vation ( ,m]cury cross+ ! sun1 b aft] ,galileo's discov]y ( sun-spots1 ,kepl] at once *e]fully retract$ 8 obs]vation ( ,m]cury1 & s f> 0 he f be+ annoy$ or bigot$ 9 8 views1 t he w>mly adopt$ ,galileo's side1 9 contra/ to mo/ ( ^? ^: op9ions 7 liable to be ov]?r[n by ! new discov]ies4 ,mae/l9 & o!rs ( ,kepl]'s fri5ds took ! opposite view4 ,,*apt] ,v4 ,,kepl]',s ,,laws4 ,:5 ,gilb]t ( ,col*e/]1 9 8 ,new ,philosophy1 f\nd$ on 8 rese>*es 9 magnetism1 0 deal+ ) tides1 he did n sugge/ t ! moon attract$ ! wat]1 b t subt]ranean spirits & hum\rs1 ris+ 9 sympa?y ) ! moon1 cause ! sea also to rise & fl[ to ! %ores & up riv]s4 ,x appe>s t an idea1 pres5t$ 9 "s su* way z ?is1 0 m readily receiv$ ?an a pla9 /atem5t4 ,?is s-call$ philosophical me?od 01 9 fact1 v g5]ally appli$1 & ,kepl]1 :o %>$ ,galileo's admiration = ,gilb]t's "w1 adopt$ x 9 8 own attempt to ext5d ! idea ( magnetic attraction to ! planets4 ,! g5]al idea ( gravity oppos$ ! hypo!sis ( ! rotation ( ! e>? on ! gr\nd t loose objects w\ld fly (f3 moreov]1 ! late/ ref9em5ts ( ! old sy/em ( planet>y motions necessitat$ _! orbits be+ describ$ ab\t a m]e empty po9t4 ,kepl] v /rongly combat$ ^! notions1 po9t+ out ! absurdity ( ! conclusions to :i* !y t5d$1 & proce$$ 9 set t]ms to describe 8 own !ory4 ,e corporeal sub/ance1 s f> =? z x is corporeal1 has a natural fitness = re/+ 9 e place :]e x may be situat$ by itself beyond ! sph]e ( influ5ce ( a body cognate ) x4 ,gravity is a mutual affection betwe5 cognate bodies t[>ds union or conjunction 7simil> 9 k9d to ! magnetic virtue71 s t ! e>? attracts a /one mu* r ?an ! /one seeks ! e>?4 ,heavy bodies 7if we beg9 by assum+ ! e>? to be 9 ! c5tre ( ! _w7 are n c>ri$ to ! c5tre ( ! _w 9 its quality ( c5tre ( ! _w1 b z to ! c5tre ( a cognate r\nd body1 namely1 ! e>?2 s t :]esoev] ! e>? may be plac$1 or :i!rsoev] x may be c>ri$ by its animal faculty1 heavy bodies w always be c>ri$ t[>ds x4 ,if ! e>? 7 n r\nd1 heavy bodies w\ld n t5d f e side 9 a /raight l9e t[>ds ! c5tre ( ! e>?1 b to diff]5t po9ts f diff]5t sides4 ,if two /ones 7 plac$ 9 any "p ( ! _w ne> ea* o!r1 & beyond ! sph]e ( influ5ce ( a ?ird cognate body1 ^! /ones1 l two magnetic ne$les1 w\ld come toge!r 9 ! int]m$iate po9t1 ea* approa*+ ! o!r by a space proportional to ! comp>ative mass ( ! o!r4 ,if ! moon & e>? 7 n reta9$ 9 _! orbits by _! animal =ce or "s o!r equival5t1 ! e>? w\ld m\nt to ! moon by a fifty-f\r? "p ( _! di/ance1 & ! moon fall t[>ds ! e>? ?r\gh ! o!r fifty-?ree p>ts1 & !y w\ld !re meet1 assum+1 h[ev]1 t ! sub/ance ( bo? is ( ! same d5sity4 ,if ! e>? %\ld cease to attract its wat]s to itself all ! wat]s ( ! sea w\ld he rais$ & w\ld fl[ to ! body ( ! moon4 ,! sph]e ( ! attractive virtue :i* is 9 ! moon ext5ds z f> z ! e>?1 & entices up ! wat]s2 b z ! moon flies rapidly across ! z5i?1 & ! wat]s _c foll[ s quickly1 a fl[ ( ! ocean is occasion$ 9 ! torrid zone t[>ds ! we/w>d4 ,if ! attractive virtue ( ! moon ext5ds z f> z ! e>?1 x foll[s ) great] reason t ! attractive virtue ( ! e>? ext5ds z f> z ! moon & mu* f>!r2 &1 9 %ort1 no?+ :i* consi/s ( e>?ly sub/ance anyh[ con/itut$ al?\gh ?r[n up to any height1 c ev] escape ! p[]ful op]ation ( ?is attractive virtue4 ,no?+ :i* consi/s ( corporeal matt] is absolutely light1 b t is comp>atively light] :i* is r>]1 ei!r by its own nature1 or by accid5tal heat4 ,& x is n to be ?\ght t light bodies are escap+ to ! surface ( ! univ]se :ile !y are c>ri$ upw>ds1 or t !y are n attract$ by ! e>?4 ,!y are attract$1 b 9 a less degree1 & s are driv5 outw>ds by ! heavy bodies2 :i* be+ done1 !y /op1 & are kept by ! e>? 9 _! own place4 ,b al?\gh ! attractive virtue ( ! e>? ext5ds upw>ds1 z has be5 said1 s v f>1 yet if any /one %\ld be at a di/ance great en\gh to become s5sible comp>$ ) ! e>?'s diamet]1 x is true t on ! motion ( ! e>? su* a /one w\ld n foll[ altoge!r2 its own =ce ( resi/ance w\ld be comb9$ ) ! attractive =ce ( ! e>?1 & ?us x w\ld extricate itself 9 "s degree f ! motion ( ! e>?4 ,! above passage f ! ,introduction to ,kepl]'s ,comm5t>ies on ! ,motion ( ,m>s1 always reg>d$ z 8 mo/ valuable "w1 mu/ h be5 kn[n to ,newton1 s t no su* incid5t z ! fall ( an apple 0 requir$ to provide a necess>y & suffici5t explanation ( ! g5esis ( 8 ,!ory ( ,univ]sal ,gravitation4 ,kepl]'s glimpse at su* a !ory c\ld h be5 no m ?an a glimpse1 = he w5t no fur!r ) x4 ,?is seems a pity1 z x is f> less fanciful ?an _m ( 8 ideas1 ?\gh n free f ! virtues & animal faculties1 t correspond to ,gilb]t's spirits & hum\rs4 ,we mu/1 h[ev]1 proce$ to ! subject ( ,m>s1 :i* 01 z be=e not$1 ! fir/ important inve/igation entru/$ to ,kepl] on 8 arrival at ,prague4 ,! "t tak5 f "o opposition ( ,m>s to ! next is decid$ly unequal at diff]5t p>ts ( 8 orbit1 s t _m oppositions mu/ be us$ to det]m9e ! mean motion4 ,! anci5ts _h notic$ t :at 0 call$ ! second inequality1 due z we n[ "k to ! orbital motion ( ! e>?1 only vani%$ :5 e>?1 sun1 & planet 7 9 l9e1 i4e4 at ! planet's opposition2 !re=e !y us$ oppositions to det]m9e ! mean motion1 b deem$ x necess>y to apply a correction to ! true opposition to r$uce to mean opposition1 ?us sacrific+ "p ( ! advantage ( us+ oppositions4 ,ty*o & ,longomontanus _h foll[$ ?is me?od 9 _! calculations f ,ty*o's tw5ty ye>s' obs]vations4 ,_! aim 0 to f9d a position ( ! equant1 su* t ^! obs]vations w\ld %[ a con/ant angul> motion ab\t x2 & t ! comput$ positions w\ld agree 9 latitude & longitude ) ! actual obs]v$ positions4 ,:5 ,kepl] arriv$ he 0 told t _! longitudes agre$ )9 a c\ple ( m9utes ( arc1 b t some?+ 0 wrong ) ! latitudes4 ,he f\nd1 h[ev]1 t ev5 9 longitude _! positions %[$ discordances t5 times z great z !y admitt$1 & s1 to cle> ! gr\nd ( assumptions z f> z possible1 he det]m9$ to use true oppositions4 ,to ?is ,ty*o object$1 & ,kepl] _h great difficulty 9 conv9c+ him t ! new move w\ld be any improvem5t1 b und]took to prove to him by actual examples t a false position ( ! orbit c\ld by adju/+ ! equant be made to fit ! longitudes )9 five m9utes ( arc1 :ile giv+ q errone\s values ( ! latitudes & second inequalities4 ,to avoid ! possibility ( fur!r objection he c>ri$ out ?is demon/ration sep>ately = ea* ( ! sy/ems ( ,ptolemy1 ,cop]nicus1 & ,ty*o4 ,= ! new me?od he notic$ t great accuracy 0 requir$ 9 ! r$uction ( ! obs]v$ places ( ,m>s to ! ecliptic1 & = ?is purpose ! value obta9$ = ! p>allax by ,ty*o's assi/ants fell f> %ort ( ! requisite accuracy4 ,kepl] !re=e 0 oblig$ to recompute ! p>allax f ! orig9al obs]vations1 z also ! position ( ! l9e ( nodes & ! incl9ation ( ! orbit4 ,! la/ he f\nd to be con/ant1 ?us corroborat+ 8 !ory t ! plane ( ! orbit pass$ ?r\gh ! sun4 ,he repeat$ 8 calculations no few] ?an sev5ty times 7& t be=e ! inv5tion ( log>i?ms71 & at l5g? adopt$ values = ! mean longitude & longitude ( aphelion4 ,he f\nd no discordance great] ?an two m9utes ( arc 9 ,ty*o's obs]v$ longitudes 9 opposition1 b ! latitudes1 & also longitudes 9 o!r p>ts ( ! orbit 7 mu* m discordant1 & he f\nd to 8 *agr9 t f\r ye>s' "w 0 practically wa/$4 ,be=e mak+ a fre% />t he look$ = "s simplification ( ! lab\r2 & det]m9$ to adopt ,ptolemy's assumption kn[n z ! pr9ciple ( ! bisection ( ! exc5tricity4 ,hi!rto1 s9ce ,ptolemy _h giv5 no reason = ?is assumption1 ,kepl] _h pref]r$ n to make x1 only tak+ = grant$ t ! c5tre 0 at "s po9t on ! l9e call$ ! exc5tricity 7see ,figs4 #a1 #b74 ,a m>k$ improvem5t 9 residuals 0 ! result ( ?is /ep1 prov+1 s f>1 ! correctness ( ,ptolemy's pr9ciple1 b !re /ill rema9$ discordances am\nt+ to eight m9utes ( arc4 ,cop]nicus1 :o _h no idea ( ! accuracy obta9able 9 obs]vations1 w\ld probably h reg>d$ su* an agreem5t z rem>kably good2 b ,kepl] refus$ to admit ! possibility ( an error ( eight m9utes 9 any ( ,ty*o's obs]vations4 ,he !reupon v[$ to con/ruct f ^! eight m9utes a new planet>y !ory t %\ld acc\nt = !m all4 ,8 repeat$ failures _h by ?is "t conv9c$ him t no uni=mly describ$ circle c\ld possibly repres5t ! motion ( ,m>s4 ,ei!r ! orbit c\ld n be circul>1 or else ! angul> velocity c\ld n be con/ant ab\t any po9t :atev]4 ,he det]m9$ to attack ! second inequality1 i4e4 ! optical illusion caus$ by ! e>?'s annual motion1 b fir/ reviv$ an old idea ( 8 own t = ! sake ( uni=mity ! sun1 or z he pref]r$ to reg>d x1 ! e>?1 %\ld h an equant z well z ! planets4 ,f ! irregul>ities ( ! sol> motion he soon f\nd t ?is 0 ! case1 & t ! motion 0 uni=m ab\t a po9t on ! l9e f ! sun to ! c5tre ( ! e>?'s orbit1 su* t ! c5tre bisect$ ! di/ance f ! sun to ! ,equant2 ?is fully support$ ,ptolemy's pr9ciple4 ,cle>ly !n ! e>?'s l9e> velocity c\ld n be con/ant1 & ,kepl] 0 enc\rag$ to revive ano!r ( 8 speculations z to a =ce :i* 0 weak] at great] di/ances4 ,he f\nd ! velocity great] at ! ne>] apse1 s t ! "t ov] an equal arc at ei!r apse 0 proportional to ! di/ance4 ,he conjectur$ t ?is might prove to be true = arcs at all p>ts ( ! orbit1 & to te/ ?is he divid$ ! orbit into #cfj equal p>ts1 & calculat$ ! di/ances to ! po9ts ( division4 ,ar*im$es _h obta9$ an approximation to ! area ( a circle by divid+ x radially into a v l>ge numb] ( triangles1 & ,kepl] _h ?is device 9 m9d4 ,he f\nd t ! sums ( successive di/ances f 8 #cfj po9ts 7 approximately proportional to ! times f po9t to po9t1 & 0 ?us enabl$ to repres5t mu* m accurately ! annual motion ( ! e>? :i* produc$ ! second inequality ( ,m>s1 to ^: motion he n[ return$4 ,?ree po9ts are suffici5t to def9e a circle1 s he took ?ree obs]v$ positions ( ,m>s & f\nd a circle2 he !n took ?ree o!r positions1 b obta9$ a diff]5t circle1 & a ?ird set gave yet ano!r4 ,x ?us began to appe> t ! orbit c\ld n be a circle4 ,he next tri$ to divide into #cfj equal p>ts1 z he _h 9 ! case ( ! e>?1 b ! sums ( di/ances fail$ to fit ! times1 & he realis$ t ! sums ( di/ances 7 n a good measure ( ! area ( successive triangles4 ,he not$1 h[ev]1 t ! errors at ! apses 7 n[ small] ?an ) a c5tral circul> orbit1 & ( ! opposite sign1 s he det]m9$ to try :e!r an oval orbit w\ld fit bett]1 foll[+ a sugge/ion made by ,purba* 9 ! case ( ,m]cury1 ^: orbit is ev5 m ecc5tric ?an t ( ,m>s1 ?\gh obs]vations 7 too scanty to =m ! f\ndation ( any !ory4 ,kepl] gave 8 fancy play 9 ! *oice ( an oval1 great] at "o end ?an ! o!r1 endeav\r+ to satisfy "s ideas ab\t epicyclic motion1 b c\ld n f9d a satisfactory curve4 ,he !n _h ! =tunate idea ( try+ an ellipse ) ! same axis z 8 t5tative oval4 ,m>s n[ appe>$ too sl[ at ! apses in/ead ( too quick1 s obvi\sly "s int]m$iate ellipse mu/ be s\ght betwe5 ! trial ellipse & ! circle on ! same axis4 ,at ?is po9t ! long arm ( co9cid5ce came into play4 ,half-way betwe5 ! apses lay ! mean di/ance1 & at ?is position ! error 0 half ! di/ance betwe5 ! ellipse & ! circle1 am\nt+ to 4#jjdbi ( a radius4 ,) ^! figures 9 8 m9d1 ,kepl] look$ up ! greate/ optical inequality ( ,m>s1 ! angle betwe5 ! /raight l9es f ,m>s to ! ,sun & to ! c5tre ( ! circle4#c ,! secant ( ?is angle 0 #a4jjdbi1 s t he not$ t an ellipse r$uc$ f ! circle 9 ! ratio ( #a4jjdbi to #a w\ld fit ! motion ( ,m>s at ! mean di/ance z well z ! apses4 ,footnote #c3 ,?is is cle>ly a maximum at ,,amc 9 ,fig4 #b1 :5 its tang5t ,,ac_/,,cm ! ecc5tricity4 ,x is (t5 said t a co9cid5ce l ?is only happ5s to somebody :o des]ves 8 luck1 b ?is simply means t recognition is ess5tial to ! co9cid5ce4 ,9 ! same way ! appe>ance ( "o ( a l>ge numb] ( p m5tion$ is hail$ z a case ( ! old adage ,talk ( ! devil1 etc41 ignor+ all ! p :o fail$ to appe>4 ,no "o1 h[ev]1 w consid] ,kepl] unduly fav\r$4 ,8 g5ius1 9 8 case c]ta9ly an inf9ite capacity = tak+ pa9s1 enabl$ him out ( 8 m$ley ( hypo!ses1 ma9ly uns\nd1 by d9t ( enorm\s lab\r & pati5ce1 to arrive ?us at ! fir/ two ( ! laws :i* e/abli%$ 8 title ( ,legislator ( ! ,heav5s4 ,,figures ,,explanatory ,,( ,,kepl]',s ,,!ory ,,( ,,! ,,motion ,,( ,,m>s4 ,illu/ration3 ,,fig4 #a4 _/ _/ ,q ,e ,c ,a ,p _/ _/ ,illu/ration3 ,,fig4 #b4 ,m _/ _/_/ ,n _/ ,q ,e ,c ,a ,p _/ _/_/ _/ ,transcrib]'s ,note3 ,approximate r5ditions ( ^! figures are provid$4 ,fig4 #a is a circle4 ,fig4 #b is a circle :i* conta9s an ellipse1 tang5t to ! circle at ,q & ,p4 ,l9e segm5ts f ,m 7on ! circle7 & ,n 7on ! ellipse7 meet at po9t ,a4 ,,fig4 #a4--;,9 ,ptolemy's exc5tric !ory1 ,a may be tak5 to repres5t ! e>?1 ,c ! c5tre ( a planet's orbit1 & ,e ! equant1 ,p 7p]igee7 & ,q 7apogee7 be+ ! apses ( ! orbit4 ,ptolemy's idea 0 t uni=m motion 9 a circle mu/ be provid$1 & s9ce ! motion 0 n uni=m ab\t ! e>?1 ,a c\ld n co9cide ) ,c2 & s9ce ! motion /ill fail$ to be uni=m ab\t ,a or ,c1 "s po9t ,e mu/ be f\nd ab\t :i* ! motion %\ld be uni=m4 ,,fig4 #b4--,?is is n drawn to scale1 b is int5d$ to illu/rate ,kepl]'s modification ( ,ptolemy's exc5tric4 ,kepl] f\nd velocities at ,p & ,q proportional n to ,,ap & ,,aq b to ,,aq & ,,ap1 or to ,,ep & ,,eq if ,,ec ,,ca 7bisection ( ! exc5tricity74 ,! velocity at ,m 0 wrong1 & ,,am appe>$ too great4 ,kepl]'s fir/ ellipse _h ,m mov$ too ne> ,c4 ,! di/ance ,,ac is mu* exagg]at$ 9 ! figure1 z also is ,,mn4 ,,an ,,cp1 ! radius ( ! circle4 ,,mn %\ld be 4#jjdbi ( ! radius1 & ,,mc_/,,nc %\ld be #a4jjdbi4 ,! velocity at ,n appe>$ to be proportional to ,,en 7 ,,an74 ,kepl] conclud$ t ,m>s mov$ r\nd ,,pnq1 s t ! area describ$ ab\t ,a 7! sun7 0 equal 9 equal times1 ,a be+ ! focus ( ! ellipse ,,pnq4 ,! angul> velocity is n q con/ant ab\t ,e1 ! equant or empty focus1 b ! diff]5ce c\ld h>dly h be5 detect$ 9 ,kepl]'s "t4 ,kepl]'s improv$ det]m9ation ( ! e>?'s orbit 0 obta9$ by plott+ ! diff]5t positions ( ! e>? correspond+ to successive rotations ( ,m>s1 i4e4 int]vals ( #fhg days4 ,at ea* ( ^! ! date ( ! ye> w\ld give ! angle ,,mse 7,m>s-,sun-,e>?71 & ,ty*o's obs]vation ! angle ,,mes4 ,s ! triangle c\ld be solv$ except = scale1 & ! ratio ( ,,se to ,,sm w\ld give ! di/ance ( ,m>s f ! sun 9 t]ms ( t ( ! e>?4 ,measur+ f a fix$ position ( ,m>s 7e4g4 p]ihelion71 ?is gave ! v>iation ( ,,se1 %[+ ! e>?'s inequality4 ,measur+ f a fix$ position ( ! e>?1 x w\ld give simil>ly a s]ies ( positions ( ,m>s1 :i*1 ?\gh ly+ n f> f ! circle ^: diamet] 0 ! axis ( ,m>s' orbit1 jo9+ p]ihelion & aphelion1 always fell inside ! circle except at ^? two po9ts4 ,x 0 a long "t be=e x dawn$ ^u ,kepl] t ! simple/ figure fall+ )9 ! circle except at ! two extremities ( ! diamet]1 0 an ellipse1 & x is n cle> :y 8 fir/ attempt ) an ellipse %\ld h be5 j z mu* too n>r[ z ! circle 0 too wide4 ,! fact rema9s t he recognis$ sudd5ly t halv+ ?is error 0 tantam\nt to r$uc+ ! circle to ! ellipse ^: ecc5tricity 0 t ( ! old !ory1 i4e4 t 9 :i* ! sun w\ld be 9 "o focus & ! equant 9 ! o!r4 ,hav+ n[ fitt$ ! ends ( bo? major & m9or axes ( ! ellipse1 he leap$ to ! conclusion t ! orbit w\ld fit ev]y:]e4 ,! practical effect ( 8 cle>+ ( ! second inequality 0 to ref] ! orbit ( ,m>s directly to ! sun1 & he f\nd t ! area betwe5 successive di/ances ( ,m>s f ! sun 7in/ead ( ! sum ( ! di/ances7 0 /rictly proportional to ! "t tak51 9 %ort1 equal areas 7 describ$ 9 equal times 7#bnd ,law7 :5 ref]r$ to ! sun 9 ! focus ( ! ellipse 7#a/ ,law74 ,he ann\nc$ t 7#a7 ,! planet describes an ellipse1 ! sun be+ 9 "o focus2 & 7#b7 ,! /raight l9e jo9+ ! planet to ! sun sweeps out equal areas 9 any two equal int]vals ( "t4 ,^! are ,kepl]'s fir/ & second ,laws ?\gh n discov]$ 9 t ord]1 & x 0 at once cle> t ,ptolemy's bisection ( ! exc5tricity simply am\nt$ to ! fact t ! c5tre ( an ellipse bisects ! di/ance betwe5 ! foci1 ! sun be+ 9 "o focus & ! angul> velocity be+ uni=m ab\t ! empty focus4 ,= s _m c5turies _h ! feti% ( circul> motion po/pon$ discov]y4 ,x 0 natural t ,kepl] %\ld assume t 8 laws w\ld apply equally to all ! planets1 b ! pro( ( ?is1 z well z ! reason und]ly+ ! laws1 0 only giv5 by ,newton1 :o approa*$ ! subject f a totally diff]5t /&po9t4 ,?is comm5t>y on ,m>s 0 publi%$ 9 #afji1 ! ye> ( ! inv5tion ( ! telescope1 & ,kepl] petition$ ! ,emp]or = fur!r funds to enable him to complete ! /udy ( ! o!r planets1 b once m !re 0 delay2 9 #afab ,rudolph di$1 & 8 bro!r ,mat?ias :o succe$$ him1 c>$ v little = a/ronomy or ev5 a/rology1 ?\gh ,kepl] 0 reappo9t$ to 8 po/ ( ,imp]ial ,ma!matician4 ,he left ,prague to take up a p]man5t pr(essor%ip at ! ,univ]sity ( ,l9z4 ,8 own acc\nt ( ! circum/ances is gloomy en\gh4 ,he says1 ,9 ! fir/ place ,i c\ld get no money f ! ,c\rt1 & my wife1 :o _h = a long "t be5 suff]+ f l[ spirits & despond5cy1 0 tak5 viol5tly ill t[>ds ! end ( #afaj1 ) ! ,hung>ian fev]1 epilepsy & phr5itis4 ,%e 0 sc>cely convalesc5t :5 all my ?ree *ildr5 7 at once attack$ ) smallpox4 ,leopold ) 8 army occupi$ ! t[n beyond ! riv] j z ,i lo/ ! de>e/ ( my sons1 him ^: nativity y w f9d 9 my book on ! new />4 ,! t[n on ?is side ( ! riv] :]e ,i liv$ 0 h>ass$ by ! ,bohemian troops1 ^: new levies 7 insubord9ate & insol5t2 to complete ! :ole1 ! ,au/rian army br\ght ! plague ) !m into ! city4 ,i w5t into ,au/ria & endeav\r$ to procure ! situation :i* ,i n[ hold4 ,return+ 9 ,june1 ,i f\nd my wife 9 a decl9e f h] grief at ! dea? ( h] son1 & on ! eve ( an infecti\s fev]1 & ,i lo/ h] also )9 elev5 days ( my return4 ,!n came fre% annoyance1 ( c\rse1 & h] =tune 0 to be divid$ ) my /ep-si/]s4 ,! ,emp]or ,rudolph w\ld n agree to my dep>ture2 va9 hopes 7 giv5 me ( be+ paid f ,saxony2 my "t & money 7 wa/$ toge!r1 till on ! dea? ( ! ,emp]or 9 #afab1 ,i 0 nam$ aga9 by 8 successor1 & suff]$ to dep>t to ,l9z4 ,be+ ?us left a wid[] ) a t5-ye>-old daught] ,susanna1 & a boy ,l\is ( half h] age1 he look$ = a second wife to take *>ge ( !m4 ,he has giv5 an acc\nt ( elev5 ladies ^: suitability he consid]$4 ,! fir/1 an intimate fri5d ( 8 fir/ wife1 ultimately decl9$2 "o 0 too old1 ano!r an invalid1 ano!r too pr\d ( h] bir? & qu>t]+s1 ano!r c\ld d no?+ useful1 & s on4 ,numb] eight kept him guess+ = ?ree mon?s1 until he tir$ ( h] con/ant indecision1 & confid$ 8 disappo9tm5t to numb] n9e1 :o 0 n impress$4 ,numb] t51 introduc$ by a fri5d1 ,kepl] f\nd exce$+ly ugly & enorm\sly fat1 & numb] elev5 app>5tly too "y4 ,kepl] !n reconsid]$ "o ( ! e>li] ones1 disreg>d+ ! advice ( 8 fri5ds :o object$ to h] l[ly /ation4 ,%e 0 ! orphan daught] ( a cab9etmak]1 educat$ = twelve ye>s by fav\r ( ! ,lady ( ,/ahr5burg1 & ,kepl] writes ( h]3 ,h] p]son & mann]s are suitable to m9e2 no pride1 no extravagance2 %e c be> to "w2 %e has a tol]able k ( h[ to manage a family2 middle-ag$ & ( a disposition & capability to acquire :at %e /ill wants4 ,w9e f ! ,au/rian v9ey>ds 0 pl5tiful & *eap at ! "t ( ! m>riage1 & ,kepl] b\ght a few casks = 8 h\sehold4 ,:5 ! sell] came to asc]ta9 ! quantity1 ,kepl] notic$ t no prop] all[ance 0 made = ! bulg+ p>ts1 & ! up%ot ( 8 objections 0 t he wrote a book on a new me?od ( gaug+--"o ( ! e>lie/ specim5s ( mod]n analysis1 ext5d+ ! prop]ties ( plane figures to segm5ts ( cones & cyl9d]s z be+ incorporat$ circles4 ,he 0 summon$ be=e ! ,diet at ,ratisbon to give 8 op9ion on ! ,gregorian ,re=m ( ! ,cal5d>1 & soon aft]w>ds 0 excommunicat$1 hav+ fall5 f\l ( ! ,roman ,ca?olic p>ty at ,l9z j z he _h previ\sly at ,gratz1 ! reason app>5tly be+ t he desir$ to ?9k = himself4 ,mean:ile 8 sal>y 0 n paid any m regul>ly ?an be=e1 & he 0 =c$ to supplem5t x by publi%+ :at he call$ a vile prophesy+ almanac :i* is sc>cely m respectable ?an begg+ unless x be because x saves ! ,emp]or's cr$it1 :o ab&ons me entirely1 & ) all 8 frequ5t & rec5t ord]s 9 c\ncil1 w\ld suff] me to p]i% ) hung]4 ,9 #afag he 0 invit$ to ,italy to succe$ ,mag9i z ,pr(essor ( ,ma!matics at ,bologna4 ,galileo urg$ him to accept ! po/1 b he excus$ himself on ! gr\nd t he 0 a ,g]man & br\ght up among ,g]mans ) su* lib]ty ( spee* z he ?\ght might get him into tr\ble 9 ,italy4 ,9 #afai ,mat?ias di$ & 0 succe$$ by ,f]d9& ,,iii1 :o aga9 reta9$ ,kepl] 9 8 po/4 ,9 ! same ye> ,kepl] repr9t$ 8 ,my/]ium ,cosmographicum1 & also publi%$ 8 ,h>monics 9 five books d$icat$ to ,james ,i ( ,engl&4 ,! fir/ geometrical1 on ! orig9 & demon/ration ( ! laws ( ! figures :i* produce h>moni\s proportions2 ! second1 ar*itectonical1 on figurate geometry & ! congru5ce ( plane & solid regul> figures2 ! ?ird1 prop]ly ,h>monic1 on ! d]ivation ( musical proportions f figures1 & on ! nature & di/9ction ( ?+s relat+ to song1 9 opposition to ! old !ories2 ! f\r?1 metaphysical1 psy*ological1 & a/rological1 on ! m5tal ess5ce ( ,h>monics1 & ( _! k9ds 9 ! _w1 especially on ! h>mony ( rays emanat+ on ! e>? f ! heav5ly bodies1 & on _! effect 9 nature & on ! sublun>y & human s\l2 ! fif?1 a/ronomical & metaphysical1 on ! v exquisite ,h>monics ( ! cele/ial motions & ! orig9 ( ! exc5tricities 9 h>moni\s proportions4 ,! extravagance ( 8 fancies does n appe> until ! f\r? book1 9 :i* he reit]ates ! /atem5t t he 0 =c$ to adopt 8 a/rological op9ions f direct & positive obs]vation4 ,he despises ,! common h]d ( prophesi]s :o describe ! op]ations ( ! />s z if !y 7 a sort ( deities1 ! lords ( heav5 & e>?1 & produc+ ev]y?+ at _! pleasure4 ,!y nev] tr\ble !mselves to consid] :at means ! />s h ( work+ any effects among u on ! e>? :il/ !y rema9 9 ! sky & s5d d[n no?+ to u :i* is obvi\s to ! s5ses1 except rays ( light4 ,8 own notion is ,l "o :o li/5s to a sweet melodi\s song1 & by ! gladness ( 8 c\nt5ance1 by 8 voice1 & by ! beat+ ( 8 h& or foot attun$ to ! music1 gives tok5 t he p]ceives & approves ! h>mony3 j s does sublun>y nature1 ) ! notable & evid5t emotion ( ! b[els ( ! e>?1 be> l witness to ! same feel+s1 especially at ^? times :5 ! rays ( ! planets =m h>moni\s configurations on ! e>?1 & aga9 ,! e>? is n an animal l a dog1 ready at e nod2 b m l a bull or an elephant1 sl[ to become angry1 & s mu* ! m furi\s :5 inc5s$4 ,he seems to h believ$ ! e>? to be actually a liv+ animal1 z witness ! foll[+3 ,if anyone :o has climb$ ! peaks ( ! highe/ m\nta9s1 ?r[ a /one d[n _! v deep clefts1 a s\nd is he>d f !m2 or if he ?r[ x into "o ( ! m\nta9 lakes1 :i* beyond d\bt are bottomless1 a /orm w imm$iately arise1 j z :5 y ?ru/ a /raw into ! e> or nose ( a tickli% animal1 x %akes its head1 or runs %udd]+ly away4 ,:at s l brea?+1 especially ( ^? fi% :o draw wat] into _! m\?s & sp\t x out aga9 ?r\gh _! gills1 z t wond]ful tide6 ,= al?\gh x is s regulat$ accord+ to ! c\rse ( ! moon1 t1 9 ! preface to my ',comm5t>ies on ,m>s1' ,i h m5tion$ x z probable t ! wat]s are attract$ by ! moon1 z iron by ! load/one1 yet if anyone uphold t ! e>? regulates its brea?+ accord+ to ! motion ( ! sun & moon1 z animals h daily & nightly alt]nations ( sleep & wak+1 ,i %all n ?9k 8 philosophy unwor?y ( be+ li/5$ to2 especially if any flexible p>ts %\ld be discov]$ 9 ! dep?s ( ! e>?1 to supply ! functions ( lungs or gills4 ,9 ! same book ,kepl] enl>ges aga9 on 8 views 9 ref]5ce to ! basis ( a/rology z conc]n$ ) nativities & ! importance ( planet>y conjunctions4 ,he gives p>ticul>s ( 8 own nativity4 ,jupit] ne>e/ ! nonagesimal _h pass$ by f\r degrees ! tr9e ( ,saturn2 ! ,sun & ,v5us 9 conjunction 7 mov+ f ! latt] t[>ds ! =m]1 ne>ly 9 sextiles ) bo?3 !y 7 also remov+ f quadratures ) ,m>s1 to :i* ,m]cury 0 closely approa*+3 ! moon drew ne> to ! tr9e ( ! same planet1 close to ! ,bull's ,eye ev5 9 latitude4 ,! #be? degree ( ,gem9i 0 ris+1 & ! #bbnd ( ,aqu>ius culm9at+4 ,t !re 0 ?is triple configuration on t day--namely ! sextile ( ,saturn & ! ,sun1 ! sextile ( ,m>s & ,jupit]1 & ! quadrature ( ,m]cury & ,m>s1 is prov$ by ! *ange ( wea!r2 = aft] a fro/ ( "s days1 t v day became w>m]1 !re 0 a ?aw & a fall ( ra94 ,?is alleg$ pro( is int]e/+ z x relies on ! same pr9ciple :i* 0 held to ju/ify ! correction ( an unc]ta9 bir?-"t1 by ref]5ce to illnesses1 etc41 met ) lat]4 ,kepl] h[ev] goes on to say1 ,if ,i am to speak ( ! results ( my /udies1 :at1 ,i pray1 c ,i f9d 9 ! sky1 ev5 remotely allud+ to x8 ,! le>n$ confess t sev]al n despicable bran*es ( philosophy h be5 newly extricat$ or am5d$ or br\ght to p]fection by me3 b "h my con/ellations 71 n ,m]cury f ! ,ea/ 9 ! angle ( ! sev5?1 & 9 quadratures ) ,m>s1 b ,cop]nicus1 b ,ty*o ,brahe1 )\t ^: books ( obs]vations ev]y?+ n[ set by me 9 ! cle>e/ light mu/ h rema9$ buri$ 9 d>kness2 n ,saturn pr$om9at+ ,m]cury1 b my lords ! ,emp]ors ,rudolph & ,mat?ias1 n ,capricorn ! h\se ( ,saturn b ,upp] ,au/ria1 ! h\se ( ! ,emp]or1 & ! ready & unexampl$ b\nty ( 8 nobles to my petition4 ,"h is t corn]1 n ! we/]n "o ( ! horoscope1 b on ! e>? :i!r1 by p]mission ( my ,imp]ial ma/]1 ,i h betak5 myself f a too uneasy ,c\rt2 & :5ce1 dur+ ^! ye>s ( my life1 :i* n[ t5ds t[>ds its sett+1 emanate ^! ,h>monics & ! o!r matt]s on :i* ,i am engag$4 ,! fif? book conta9s a great deal ( nons5se ab\t ! h>mony ( ! sph]es2 ! notes contribut$ by ! sev]al planets are gravely set d[n1 t ( ,m]cury hav+ ! greate/ resemblance to a melody1 ?\gh p]haps m rem9isc5t ( a bugle-call4 ,yet ! book is n all wor?less = x includes ,kepl]'s ,?ird ,law1 :i* he _h dilig5tly s\ght = ye>s4 ,9 8 own words1 ,! proportion exi/+ betwe5 ! p]iodic times ( any two planets is exactly ! sesquiplicate proportion ( ! mean di/ances ( ! orbits1 or z g5]ally giv51 ! squ>es ( ! p]iodic times are proportional to ! cubes ( ! mean di/ances4 ,kepl] 0 evid5tly transport$ ) delight & wrote1 ,:at ,i prophesi$ two & tw5ty ye>s ago1 z soon z ,i discov]$ ! five solids among ! heav5ly orbits1--:at ,i firmly believ$ long be=e ,i _h se5 ,ptolemy's ',h>monics'--:at ,i _h promis$ my fri5ds 9 ! title ( ?is book1 :i* ,i nam$ be=e ,i 0 sure ( my discov]y1--:at sixte5 ye>s ago ,i urg$ z a ?+ to be s\ght1--t = :i* ,i jo9$ ,ty*o ,brahe1 = :i* ,i settl$ 9 ,prague1 = :i* ,i h devot$ ! be/ "p ( my life to a/ronomical computations1 at l5g? ,i h br\ght to light1 & h recognis$ its tru? beyond my mo/ sangu9e expectations4 ,great z is ! absolute nature ( ,h>monics1 ) all its details z set =? 9 my ?ird book1 x is all f\nd among ! cele/ial motions1 n inde$ 9 ! mann] :i* ,i imag9$ 7t is n ! lea/ "p ( my delight71 b 9 ano!r v diff]5t1 & yet mo/ p]fect & excell5t4 ,x is n[ eighte5 mon?s s9ce ,i got ! fir/ glimpse ( light1 ?ree mon?s s9ce ! dawn1 v few days s9ce ! unveil$ sun1 mo/ admirable to gaze on1 bur/ out ^u me4 ,no?+ holds me2 ,i w indulge 9 my sacr$ fury2 ,i w triumph ov] mank9d by ! hone/ confession t ,i h /ol5 ! gold5 vases ( ! ,egyptians to build up a tab]nacle = my ,god f> away f ! conf9es ( ,egypt4 ,if y =give me1 ,i rejoice1 if y are angry1 ,i c be> x2 ! die is ca/1 ! book is writt52 to be read ei!r n[ or by po/]ity1 ,i c>e n :i*2 x may well wait a c5tury = a read]1 z ,god has wait$ six ?\s& ye>s = an obs]v]4 ,he gives ! date #ae? ,may1 #afah1 = ! completion ( 8 discov]y4 ,9 8 ,epitome ( ! ,cop]nican ,a/ronomy1 he gives 8 own idea z to ! reason = ?is ,?ird ,law4 ,f\r causes concur = l5g!n+ ! p]iodic "t4 ,fir/1 ! l5g? ( ! pa?2 secondly1 ! weight or quantity ( matt] to be c>ri$2 ?irdly1 ! degree ( /r5g? ( ! mov+ virtue2 f\r?ly1 ! bulk or space into :i* is spread out ! matt] to be mov$4 ,! orbital pa?s ( ! planets are 9 ! simple ratio ( ! di/ances2 ! weights or quantities ( matt] 9 diff]5t planets are 9 ! subduplicate ratio ( ! same di/ances1 z has be5 already prov$2 s t ) e increase ( di/ance a planet has m matt] & !re=e is mov$ m sl[ly1 & accumulates m "t 9 its revolution1 requir+ already1 z x did1 m "t by reason ( ! l5g? ( ! way4 ,! ?ird & f\r? causes comp5sate ea* o!r 9 a comp>ison ( diff]5t planets2 ! simple & subduplicate proportion comp\nd ! sesquiplicate proportion1 :i* !re=e is ! ratio ( ! p]iodic times4 ,! only "p ( ?is explanation t is true is t ! pa?s are 9 ! simple ratio ( ! di/ances1 ! pro( s confid5tly claim$ be+ ( ! circul> k9d commonly kn[n z begg+ ! "q4 ,x 0 res]v$ = ,newton to e/abli% ! ,laws ( ,motion1 to f9d ! law ( =ce t w\ld con/ra9 a planet to obey ,kepl]'s fir/ & second ,laws1 & to prove t x mu/ !re=e also obey ! ?ird4 ,,*apt] ,,vi4 ,,clos+ ,,ye>s4 ,soon aft] its publication ,kepl]'s ,epitome 0 plac$ along ) ! book ( ,cop]nicus1 on ! li/ ( books prohibit$ by ! ,congregation ( ! ,index at ,rome1 & he fe>$ t ?is might prev5t ! publication or sale ( 8 books 9 ,au/ria also1 b 0 told t ?\gh ,galileo's viol5ce 0 gett+ him into tr\ble1 !re w\ld be no difficulty 9 obta9+ p]mission = le>n$ m5 to read any prohibit$ books1 & t he 7,kepl]7 ne$ fe> no?+ s long z he rema9$ quiet4 ,9 8 v>i\s works on ,comets1 he adh]$ to ! op9ion t !y travell$ 9 /raight l9es ) v>y+ velocity4 ,he sugge/$ t comets come f ! remote/ p>ts ( e!r1 z :ales & mon/]s f ! dep? ( ! sea1 & t p]haps !y are some?+ ( ! nature ( silkworms1 & are wa/$ & consum$ 9 sp9n+ _! own tails4 ,napi]'s inv5tion ( log>i?ms at once attract$ ,kepl]'s att5tion4 ,he mu/ h regrett$ t ! discov]y 0 n made e>ly en\gh to save him a va/ am\nt ( lab\r 9 computations1 b he manag$ to f9d "t to compute "s log>i?m tables = himself1 ?\gh he does n seem to h und]/ood q :at ,napi] _h done1 & ?\gh ) 8 usual hone/y he gave full cr$it to ! ,scotti% b>on = 8 inv5tion4 ,?\gh ,eug5i/s may f9d a difficulty 9 reconcil+ ,napi]'s brilliancy ) ! extreme y\? ( 8 p>5ts1 !y may at any rate attribute ,kepl]'s occasional fits ( bad temp] to h]$ity4 ,8 cantank]\s "m1 ,ca!r9e ,kepl]1 _h = "s ye>s be5 c>ry+ on an action = sl&] aga9/ a woman :o _h accus$ h] ( adm9i/]+ a poison\s potion4 ,dame ,kepl] employ$ a "y advocate :o = reasons ( 8 own nurs$ ! case s long t aft] five ye>s _h elaps$ )\t any conclusion be+ rea*$ ano!r judge 0 appo9t$1 :o _h himself suff]$ f ! cau/ic tongue ( ! prosecutrix1 & s 0 already prejudic$ aga9/ h]4 ,! def5dant1 kn[+ ?is1 turn$ ! tables on h] oppon5t by br++ an accusation ( wit*craft aga9/ h]1 & ,ca!r9e ,kepl] 0 imprison$ & condemn$ to ! torture 9 ,july1 #afbj4 ,kepl]1 he>+ ( ! s5t5ce1 hurri$ back f ,l9z1 & succe$$ 9 /opp+ ! completion ( ! s5t5ce1 secur+ 8 "m's release ! foll[+ ye>1 z x 0 made cle> t ! only support = ! case aga9/ h] 0 h] own intemp]ate language4 ,kepl] return$ to ,l9z1 & 8 "m at once br\ght ano!r action = co/s & damages aga9/ h] late oppon5t1 b di$ be=e ! case c\ld be tri$4 ,a few mon?s be=e ?is ,sir ,h5ry ,wotton1 ,engli% ,ambassador to ,v5ice1 visit$ ,kepl]1 & f9d+ him z usual1 almo/ p5niless1 urg$ him to g to ,engl&1 promis+ him a w>m welcome !re4 ,kepl]1 h[ev]1 w\ld n at t "t leave ,g]many1 giv+ sev]al reasons1 "o ( :i* 0 t he dread$ ! conf9em5t ( an isl&4 ,lat] on he express$ 8 will+ness to g z soon z 8 ,rudolph9e ,tables 7 publi%$1 & lecture on !m1 ev5 9 ,engl&1 if he c\ld n d x 9 ,g]many1 & if a good en\gh sal>y 7 =?com+4 ,9 #afbd he w5t to ,vi5na1 & manag$ to extract f ! ,treasury #fjjj flor9s on acc\nt ( exp5ses connect$ ) ! ,tables1 b1 in/ead ( a fur!r grant1 0 giv5 lett]s to ! ,/ates ( ,swabia1 :i* ow$ money to ! ,imp]ial treasury4 ,"s ( ?is he succe$$ 9 collect+1 b ! ,tables 7 /ill fur!r delay$ by ! religi\s di/urbances !n becom+ viol5t4 ,! ,jesuits contriv$ to h ,kepl]'s libr>y seal$ up1 &1 b = ! ,imp]ial protection1 w\ld h imprison$ him also2 moreov] ! peasants revolt$ & blockad$ ,l9z4 ,9 #afbg1 h[ev]1 ! long promis$ ,tables1 ! fir/ to disc>d ! conv5tional circul> motion1 7 at la/ publi%$ at ,ulm 9 f\r p>ts4 ,two ( ^! p>ts consi/$ ( subsidi>y ,tables1 ( log>i?ms & o!r comput+ devices1 ano!r conta9$ ,tables ( ! elem5ts ( ! sun1 moon1 & planets1 & ! f\r? gave ! places ( a ?\s& />s z det]m9$ by ,ty*o1 ) ,ty*o's refraction ,tables1 :i* _h ! peculi>ity ( us+ diff]5t values = ! refraction ( ! sun1 moon1 & />s4 ,f a map prefix$ to "s copies ( ! ,tables1 we may inf] t ,kepl] 0 "o ( ! fir/1 if n actually ! fir/1 to sugge/ ! me?od ( det]m9+ diff]5ces ( longitude by occultations ( />s at ! moon's limb4 ,9 an ,app5dix1 he %[$ h[ 8 ,tables c\ld be us$ by a/rolog]s = _! pr$ictions1 say+ ,a/ronomy is ! daught] ( ,a/rology1 & ?is mod]n ,a/rology aga9 is ! daught] ( ,a/ronomy1 be>+ some?+ ( ! l9eam5ts ( h] gr&mo!r2 &1 z ,i h already said1 ?is fooli% daught]1 ,a/rology1 supports h] wise b ne$y "m1 ,a/ronomy1 f ! pr(its ( a pr(ession n g5]ally consid]$ cr$itable4 ,!re is no d\bt t ,kepl] /rongly res5t$ hav+ to dep5d s mu* = 8 income on su* me?ods :i* he c]ta9ly did n consid] cr$itable4 ,x 0 probably ,galileo ^: praise ( ! new ,tables induc$ ! ,gr& ,duke ( ,tuscany to s5d ,kepl] a gold *a9 soon aft] _! publication1 & we may p]haps reg>d x z a m>k ( fav\r f ! ,emp]or ,f]d9& t he p]mitt$ ,kepl] to atta* himself to ! great ,wall5/e91 n[ ,duke ( ,fri$l&1 & a firm believ] 9 ,a/rology4 ,! ,duke 0 a bett] payma/] ?an ei!r ( ! ?ree successive ,emp]ors4 ,he furni%$ ,kepl] ) an assi/ant & a pr9t+ press2 & obta9$ = him ! ,pr(essor%ip ( ,a/ronomy at ! ,univ]sity ( ,ro/ock 9 ,meckl5burg4 ,app>5tly1 h[ev]1 ! ,emp]or c\ld n induce ,wall5/e9 to take ov] ! responsibility ( ! #hjjj cr[ns1 /ill ow+ f ! ,imp]ial treasury on acc\nt ( ! ,rudolph9e ,tables4 ,kepl] made a la/ attempt to secure paym5t at ,ratisbon1 b 8 j\rney ?i!r br\ght disappo9tm5t & fatigue & left him 9 su* a condition t he rapidly succumb$ to an attack ( fev]1 dy+ 9 ,novemb]1 #afcj1 9 8 fifty-n9? ye>4 ,8 body 0 buri$ at ,ratisbon1 b ! tomb/one 0 de/roy$ dur+ ! w> !n rag+4 ,8 daught]1 ,susanna1 ! wife ( ,jacob ,b>ts*1 a physician :o _h help$ ,kepl] ) 8 ,ephem]is1 lo/ h] husb& soon aft] h] fa!r's dea?1 & succe$$ 9 obta9+ "p ( ,kepl]'s arre>s ( sal>y by ?reat5+ to keep ,ty*o's manuscripts1 b h] /epmo!r 0 left almo/ p5niless ) five "y *ildr54 ,= _! b5efit ,l\is ,kepl] pr9t$ a ,dream ( ,lun> ,a/ronomy1 :i* fir/ 8 fa!r & !n 8 bro!r-9-law _h be5 prep>+ = publication at ! "t ( _! respective dea?s4 ,x is a curi\s mixture ( saga & fairy tale ) a little sci5ce 9 ! way ( a/ronomy /udi$ f ! moon1 & ca/ 9 ! =m ( a dream to ov]come ! practical difficulties ( ! hypo!sis ( visit+ ! moon4 ,o!r writ+s 9 l>ge numb]s 7 left unpubli%$4 ,no attempt at a complete edition ( ,kepl]'s works 0 made = a long "t4 ,"o 0 project$ 9 #agad by 8 biograph]1 ,hants*1 b all t appe>$ 0 "o volume ( lett]s4 ,aft] v>i\s le>n$ bodies _h decl9$ to move 9 ! matt] ! manuscripts 7 pur*as$ = ! ,imp]ial ,russian libr>y4 ,an edition 0 at l5g? br\ght out at ,frank=t by ,c4 ,fris*1 9 eight volumes1 appe>+ at int]vals f #aheh-ahgj4 ,kepl]'s fame does n re/ ^u 8 volum9\s works4 ,) 8 peculi> me?od ( approa*+ problems !re 0 b\nd to be an inord9ate am\nt ( *aff mix$ ) ! gra91 & he us$ no w9n[+ ma*9e4 ,8 simplicity & transp>5t hone/y induc$ him to include ev]y?+1 9 fact he seem$ to glory 9 ! numb] ( false trails he labori\sly foll[$4 ,he 0 "o :o might be expect$ to f9d ! prov]bial ne$le 9 a hay/ack1 b un=tunately ! ne$le 0 n always !re4 ,delambre says1 ,ard5t1 re/less1 burn+ to di/+ui% himself by 8 discov]ies he attempt$ ev]y?+1 & hav+ once obta9$ a glimpse ( "o1 no lab\r 0 too h>d = him 9 foll[+ or v]ify+ x4 ,all 8 attempts _h n ! same success1 & 9 fact t 0 impossible4 ,^? :i* h fail$ seem to u only fanciful2 ^? :i* h be5 m =tunate appe> sublime4 ,:5 9 se>* ( t :i* really exi/$1 he has sometimes f\nd x2 :5 he devot$ himself to ! pursuit ( a *im]a1 he c\ld n b fail1 b ev5 !n he unfold$ ! same qualities1 & t ob/9ate p]sev]ance t mu/ triumph ov] all difficulties b ^? :i* are insurm\ntable4 ,b]ry1 9 8 ,%ort ,hi/ory ( ,a/ronomy1 says z "o reads *apt] aft] *apt] )\t a lucid1 /ill less a correct idea1 x is impossible to refra9 f regrets t ! intellig5ce ( ,kepl] %\ld h be5 s wa/$1 & x is difficult n to suspect at times t "s ( ! valuable results :i* lie emb$d$ 9 ?is great mass ( t$i\s speculation 7 arriv$ at by a m]e accid5t4 ,on ! o!r h& x mu/ n be =gott5 t su* accid5ts h a habit ( happ5+ only to great m51 & t if ,kepl] lov$ to give re9s to 8 imag9ation he 0 equally impress$ ) ! necessity ( scrupul\sly comp>+ speculative results ) obs]v$ facts1 & ( surr5d]+ )\t demur ! mo/ belov$ ( 8 fancies if x 0 unable to /& ?is te/4 ,if ,kepl] _h burnt ?ree-qu>t]s ( :at he pr9t$1 we %\ld 9 all probability h =m$ a high] op9ion ( 8 intellectual grasp & sobriety ( judgm5t1 b we %\ld h lo/ to a great ext5t ! impression ( extraord9>y en?usiasm & indu/ry1 & ( almo/ unequall$ intellectual hone/y :i* we n[ get f a /udy ( 8 works4 ,pr(essor ,=bes is m en?usia/ic4 ,9 8 ,hi/ory ( ,a/ronomy1 he ref]s to ,kepl] z ! man ^: place1 z is g5]ally agre$1 w\ld h be5 ! mo/ difficult to fill among all ^? :o h contribut$ to ! advance ( a/ronomical k1 & aga9 propos ( ,kepl]'s great book1 x mu/ be obvi\s t he _h at t "t "s inkl+ ( ! mean+ ( 8 laws--univ]sal gravitation4 ,f t mom5t ! idea ( univ]sal gravitation 0 9 ! air1 & h9ts & guesses 7 ?r[n out by _m2 & 9 "t ! law ( gravitation w\ld d\btless h be5 discov]$1 ?\gh probably n by ! "w ( "o man1 ev5 if ,newton _h n liv$4 ,b1 if ,kepl] _h n liv$1 :o else c\ld h discov]$ 8 ,laws8 ,,app5dix ,i4 ,,li/ ,,( ,,dates4 ,johann ,kepl]1 born #aega2 s*ool at ,maulbronn1 #aehf2 ,univ]sity ( ,tb+51 #aehi2 ,m4,a4 ( ,tb+51 #aeia2 ,pr(essor at ,gratz1 #aeid2 ,prodromus1 ) ,my/]ium ,cosmographicum1 publi%$ #aeif2 fir/ m>riage1 #aeig2 jo9s ,ty*o ,brahe at ,prague1 #afjj2 dea? ( ,ty*o1 #afja2 ,kepl]'s optics1 #afjc2 ,nova1 #afjd2 on ,comets1 #afjg2 ,comm5t>y on ,m>s1 includ+ ,fir/ & ,second ,laws1 #afji2 ,pr(essor at ,l9z1 #afab2 second m>riage1 #afac2 ,?ird ,law discov]$1 #afah2 ,epitome ( ,cop]nican ,a/ronomy1 #afah-afba2 ,rudolph9e ,tables publi%$1 #afbg2 di$1 #afcj4 ,,app5dix ,,ii4 ,,bibliography4 ,= a full acc\nt ( ! v>i\s sy/ems ( ,kepl] & 8 pr$ecessors ! read] _c d bett] ?an consult ! ,hi/ory ( ! ,planet>y ,sy/ems1 f ,?ales to ,kepl]1 by ,dr4 ,j4,l4,e4 ,drey] 7,cambridge ,univ4 ,press1 #aijf74 ,! same au?or's ,ty*o ,brahe gives a weal? ( detail ab\t t ,pho5ix ( ,a/ronom]s1 z ,kepl] /yles him4 ,a great proportion ( ! lit]ature relat+ to ,kepl] is ,g]man1 b he has 8 place 9 ! hi/ories ( a/ronomy1 f ,delambre & ! m mod]n ,r4 ,wolfs ,ges*i*te to ^? ( ,a4 ,b]ry1 ,hi/ory ( ,a/ronomy 7,univ]sity ,ext5sion ,manuals1 ,murray1 #ahih71 & ,pr(essor ,g4 ,=bes1 ,hi/ory ( ,a/ronomy 7,hi/ory ( ,sci5ce ,s]ies1 ,watts1 #aiji74 ,,gloss>y4 ,apogee3 ,! po9t 9 ! orbit ( a cele/ial body :5 x is fur!/ f ! e>?4 ,apse3 ,an extremity ( ! major axis ( ! orbit ( a body2 a body is at its greate/ & lea/ di/ances f ! body ab\t :i* x revolves1 :5 at "o or o!r apse4 ,conjunction3 ,:5 a plane conta9+ ! e>?'s axis & pass+ ?r\gh ! c5tre ( ! sun also passes ?r\gh t ( ! moon or a planet1 at ! same side ( ! e>?1 ! moon or planet is 9 conjunction1 or if on opposite sides ( ! e>?1 ! moon or planet is 9 opposition4 ,m]cury & ,v5us _c be 9 opposition1 b are 9 inf]ior or sup]ior conjunction accord+ z !y are ne>] or fur!r ?an ! sun4 ,def]5t3 ,9 ! epicyclic !ory1 unev5 motion is repres5t$ by motion r\nd a circle ^: c5tre travels r\nd ano!r circle1 ! latt] is call$ ! def]5t4 ,ecliptic3 ,! plane ( ! e>?'s orbital motion ab\t ! sun1 :i* cuts ! heav5s 9 a great circle4 ,x is s call$ because obvi\sly eclipses c only occur :5 ! moon is also approximately 9 ?is plane1 besides be+ 9 conjunction or opposition ) ! sun4 ,epicycle3 ,a po9t mov+ on ! circumf]5ce ( a circle ^: c5tre describes ano!r circle1 traces an epicycle ) ref]5ce to ! c5tre ( ! second circle4 ,equant3 ,9 ,ptolemy's exc5tric !ory1 :5 a planet is describ+ a circle ab\t a c5tre :i* is n ! e>?1 9 ord] to satisfy ! conv5tion t ! motion mu/ be uni=m1 a po9t 0 f\nd ab\t :i* ! motion 0 app>5tly uni=m1#d & ?is po9t 0 call$ ! equant4 ,footnote #d3 ,i4e4 ! angul> motion ab\t ! equant 0 uni=m4 ,equ9ox3 ,:5 ! sun is 9 ! plane ( ! e>?'s equator ! l5g?s ( day & night are equal4 ,?is happ5s twice a ye>1 & ! times :5 ! sun passes ! equator are call$ ! v]nal or spr+ equ9ox & ! autumnal equ9ox respectively4 ,evection3 ,! second inequality ( ! moon1 :i* vani%es at new & full moon & is a maximum at fir/ & la/ qu>t]4 ,exc5tric3 ,z an alt]native to epicycles1 planets ^: motion r\nd ! e>? 0 n uni=m c\ld be repres5t$ z mov+ r\nd a po9t "s di/ance f ! e>? call$ ! exc5tric4 ,geoc5tric3 ,ref]r$ to ! c5tre ( ! e>?2 e4g4 ,ptolemy's !ory4 ,helioc5tric3 ,ref]r$ to ! c5tre ( ! sun2 e4g4 ! !ory commonly call$ ,cop]nican4 ,inequality3 ,! diff]5ce betwe5 ! actual position ( a planet & its !oretical position on ! hypo!sis ( uni=m circul> motion4 ,node3 ,! po9ts :]e ! orbit ( ! moon or a planet int]sect ! plane ( ! ecliptic4 ,! asc5d+ node is ! "o :5 ! planet is mov+ nor?w>ds1 & ! l9e ( int]section ( ! orbital plane ) ! ecliptic is ! l9e ( nodes4 ,occultation3 ,usually means :5 a planet or /> is hidd5 by ! moon1 b x also includes occultation ( a /> by a planet or ( a satellite by a planet or ( "o planet by ano!r4 ,opposition v4 ,conjunction4 ,p>allax3 ,! error introduc$ by obs]v+ f "s po9t o!r ?an t requir$ 9 !ory1 e4g4 9 geoc5tric places because ! obs]vations are made f ! surface ( ! e>? in/ead ( ! c5tre1 or 9 helioc5tric places because obs]vations are made f ! e>? & n f ! sun4 ,p]igee3 ,! po9t 9 ! orbit ( a cele/ial body :5 x is ne>e/ to ! e>?4 ,precession3 ,ow+ to ! sl[ motion ( ! e>?'s pole ar\nd ! pole ( ! ecliptic1 ! equator cuts ! ecliptic a little e>li] e ye>1 s t ! equ9ox ea* ye> slightly prec$es1 ) ref]5ce to ! />s1 t ( ! previ\s ye>4