,transcriber's ,notes ,all apparent printer's errors retained4 ,variation in punctuation are as in the original1 but missing full stops at end of paragraphs have been supplied4 ,there are inconsistencies in the use of italics1 spacing of words and use of full stop after ',,axiome'1 abbreviations etc4 ,all are retained to match text4 ,there is a great variation in spelling including multiple spellings of the same word1 all spelling has been retained to match text4 ,there are several instances of obviously missing letters or inverted n u4 ,these have been changed or obvious letters replaced1 with the changes surrounded by 4 ,all instances are detailed at the end of the text4 ,it should also be noted that in the original text there is a missing line at the end of page #bd in original text4 ,there are a number of instances in the original text where 'that' is immediately followed by a second 'that' in the sentence4 ,these could be potential printer's errors or1 since several of them make sense1 part of the author's style4 ,they have been left in the text as they appear in the original text4 ,the original text has many sidenotes1 some are true sidenotes1 introductions to paragraphs etc1 some acting as footnotes with some marked in original text with 994 ,these have been dealt with in three ways with the footnotes placed after their relevant paragraph and sidenotes place before their relevant paragraph4 #a7 ,footnotes marked with capital letter4 ,these were sidenotes in original text marked with 99 in the original text and thus acting like footnotes4 #b7 ,footnotes marked with number4 ,these were sidenotes in original text that were unmarked but acting like normal footnotes4 ,the anchor in the text was placed at the most suitable relevant place in comparison with the placement of the sidenote text in the margin1 but still should be considered only an approximate placement4 #c7 ,sidenotes placed at start of the relevant paragraph4 ,some sidenotes were considered not to be relevant as footnotes1 introductions to paragraphs etc1 and were left as sidenotes before their relevant paragraph4 99 99 99 99 99 ,a ,,discourse ,,presented ,,to ,,the ,,most ,,serene ,don ,cosimo ,,ii4 ,,great ,,duke ,,of ,,tuscany1 ,,concerning ,the ,,natation of ,,bodies ,vpon1 ,and ,,submersion ,in1 ,,the ,,water4 ,by ,,galileus ,,galilei3 ,philosopher and ,mathematician unto ,his most ,serene ,highnesse4 ,englished from the ,second ,edition of the ,,italian1 compared with the ,manuscript ,copies1 and reduced into ,,propositions3 ,by ,,thomas ,,salusbury1 ,esq2 ,,london3 ,printed by ,,william ,,leybourn3 ,m ,,dc ,,lxiii4 99 99 99 99 99 ,decoration ,a ,,discovrse ,presented to the ,most ,serene ,,don ,,cosimo ,,ii4 ,,great ,,duke of ,,tuscany3 ,,concerning ,the ,natation of ,,bodies ,upon1 or ,submersion ,in1 the ,,water4 ,considering 7,most ,serene ,prince7 that the publishing this present ,treatise1 of so different an ,argument from that which many expect1 and which according to the intentions ,i proposed in my ,a ,astronomicall ,adviso1 ,i should before this time have put forth1 might peradventure make some thinke1 either that ,i had wholly relinquished my farther imployment about the new ,celestiall ,observations1 or that1 at least1 ,i handled them very remissely2 ,i have judged fit to render an account1 aswell of my deferring that1 as of my writing1 and publishing this treatise4 ,a ,his ,nuncio ,siderio4 ,as to the first1 the last discoveries of ,saturn to be tricorporeall1 and of the mutations of ,figure in ,venus1 like to those that are seen in the ,moon1 together with the ,consequents depending thereupon1 have not so much occasioned the demur1 as the investigation of the times of the ,conversions of each of the ,four ,medicean ,planets about ,jupiter1 which ,i lighted upon in ,april the year past1 #afaa1 at my being in ,rome2 where1 in the end1 ,i assertained my selfe1 that the first and neerest to ,jupiter1 moved about #h gr4 #bi m4 of its ,sphere in an houre1 makeing its whole revolution in one naturall day1 and #ah hours1 and almost an halfe4 ,the second moves in its ,orbe #ad gr4 #ac min4 or very neer1 in an hour1 and its compleat conversion is consummate in #c dayes1 #ac hours1 and one third1 or thereabouts4 ,the third passeth in an hour1 #b gr4 #f min4 little more or less of its ,circle1 and measures it all in #g dayes1 #d hours1 or very neer4 ,the fourth1 and more remote than the rest1 goes in one houre1 #j gr #ed min4 and almost an halfe of its ,sphere1 and finisheth it all in #af dayes1 and very neer #ah hours4 ,but because the excessive velocity of their returns or restitutions1 requires a most scrupulous precisenesse to calculate their places1 in times past and future1 especially if the time be for many ,moneths or ,years2 ,i am therefore forced1 with other ,observations1 and more exact than the former1 and in times more remote from one another1 to correct the ,tables of such ,motions1 and limit them even to the shortest moment3 for such exactnesse my first ,observations suffice not2 not only in regard of the short intervals of ,time1 but because ,i had not as then found out a way to measure the distances between the said ,planets by any ,instrument3 ,i ,observed such ,intervals with simple relation to the ,diameter of the ,body of ,jupiter2 taken1 as we have said1 by the eye1 the which1 though they admit not errors of above a ,minute1 yet they suffice not for the determination of the exact greatness of the ,spheres of those ,stars4 ,but now that ,i have hit upon a way of taking such measures without failing1 scarce in a very few ,seconds1 ,i will continue the observation to the very occultation of ,,jupiter1 which shall serve to bring us to the perfect knowledge of the ,motions1 and ,magnitudes of the ,orbes of the said ,planets1 together also with some other consequences thence arising4 ,i adde to these things the observation of some obscure ,spots#a1 which are discovered in the ,solar ,body1 which changing1 position in that1 propounds to our consideration a great argument either that the ,sun revolves in it selfe1 or that perhaps other ,starrs1 in like manner as ,venus and ,mercury1 revolve about it1 invisible in other times1 by reason of their small digressions1 lesse than that of ,mercury1 and only visible when they interpose between the ,sun and our eye1 or else hint the truth of both this and that2 the certainty of which things ought not to be contemned1 nor omitted4 #a ,the ,authors ,observations of the ,solar ,spots ,continuall observation hath at last assured me that these ,spots are matters contiguous to the ,body of the ,sun1 there continually produced in great number1 and afterwards dissolved1 some in a shorter1 some in a longer time1 and to be by the ,conversion or ,revolution of the ,sun in it selfe1 which in a ,lunar ,moneth1 or thereabouts1 finisheth its ,period1 caried about in a ,circle1 an accident great of it selfe1 and greater for its ,consequences4 ,as to the other particular in the next place ,b ,many causes have moved me to write the present ,tract1 the subject whereof1 is the ,dispute which ,i held some dayes since1 with some learned men of this ,city1 about which1 as your ,highnesse knows1 have followed many ,discourses3 ,the principall of which ,causes hath been the ,intimation of your ,highnesse1 having commended to me ,writing1 as a singular means to make true known from false1 reall from apparent ,reasons1 farr better than by ,disputing vocally1 where the one or the other1 or very often both the ,disputants1 through too greate heate1 or exalting of the voyce1 either are not understood1 or else being transported by ostentation of not yeilding to one another1 farr from the first ,proposition1 with the novelty1 of the various ,proposals1 confound both themselves and their ,auditors4 ,b ,the occasion inducing the ,author to write this ,treatise4 ,moreover1 it seemed to me convenient to informe your ,highnesse of all the sequell1 concerning the ,controversie of which ,i treat1 as it hath been advertised often already by others3 and because the ,doctrine which ,i follow1 in the discussion of the point in hand1 is different from that of ,aristotle2 and interferes with his ,principles1 ,i have considered that against the ,authority of that most famous ,man1 which amongst many makes all suspected that comes not from the ,schooles of the ,peripateticks1 its farr better to give ones ,reasons by the ,pen than by word of mouth1 and therfore ,i resolved to write the present discourse3 in which yet ,i hope to demonstrate that it was not out of capritiousnesse1 or for that ,i had not read or understood ,aristotle1 that ,i sometimes swerve from his opinion1 but because severall ,reasons perswade me to it1 and the same ,aristotle hath tought me to fix my judgment on that which is grounded upon ,reason1 and not on the bare ,authority of the ,master#b2 and it is most certaine according to the sentence of ,alcinoos1 that philosophating should be free4 ,nor is the resolution of our ,question in my judgment without some benefit to the ,universall#c1 forasmuch as treating whether the figure of ,solids operates1 or not1 in their going1 or not going to the bottome in ,water1 in occurrences of building ,bridges or other ,fabricks on the ,water1 which happen commonly in affairs of grand import1 it may be of great availe to know the truth4 #b ,aristotle prefers ,reason to the ,authority ofan ,author4 #c ,the benefit of this ,argument4 ,i say therfore1 that being the last ,summer in company with certain ,learned men1 it was said in the argumentation2 ,that ,condensation was the propriety of ,cold#d1 and there was alledged for instance1 the example of ,ice3 now ,i at that time said1 that1 in my judgment1 the ,ice should be rather ,water rarified than condensed#e1 and my reason was1 because ,condensation begets diminution of ,mass1 and augmentation of gravity1 and ,rarifaction causeth greater ,lightness1 and augmentarion of ,masse3 and ,water in freezing1 encreaseth in ,masse1 and the ,ice made thereby is lighter than the ,water on which it swimmeth4 #d ,condensation the ,propriety of ,cold1 according to the ,peripateticks4 #e ,ice rather water rarified1 than condensed1 and why3 ,what ,i say1 is manifest1 because1 the medium subtracting from the whole ,gravity of ,sollids the weight of such another ,masse of the said ,medium2 as ,archimedes proves in his ,c ,first ,booke ,de ,insidentibus ,humido2 when ever the ,masse of the said ,solid encreaseth by ,distraction1 the more shall the ,medium detract from its entire ,gravity2 and lesse1 when by ,compression it shall be condensed and reduced to a lesse ,masse4 ,c ,in lib3 #a4 of ,natation of ,bodies ,prop4 #g4 ,sidenote3 ,figure operates not in the ,natation of ,sollids4 ,it was answered me1 that that proceeded not from the greater ,levity1 but from the ,figure1 large and flat1 which not being able to penetrate the ,resistance of the ,water1 is the cause that it submergeth not4 ,i replied1 that any piece of ,ice1 of whatsoever ,figure1 swims upon the ,water1 a manifest signe1 that its being never so flat and broad1 hath not any part in its floating3 and added1 that it was a manifest proofe hereof to see a piece of ,ice of very broad ,figure being thrust to the botome of the ,water1 suddenly return to flote atoppe1 which had it been more grave1 and had its swimming proceeded from its ,forme1 unable to penetrate the ,resistance of the ,medium1 that would be altogether impossible2 ,i concluded therefore1 that the ,figure was in sort a ,cause of the ,natation or ,submersion of ,bodies1 but the greater or lesse ,gravity in respect of the ,water3 and therefore all ,bodyes heavier than it of what ,figure soever they be1 indifferently go to the bottome1 and the lighter1 though of any figure1 float indifferently on the top3 and ,i suppose that those which hold otherwise1 were induced to that beliefe1 by seeing how that diversity of ,formes or ,figures1 greatly altereth the ,velosity1 and ,tardity of ,motion2 so that ,bodies of ,figure broad and thin1 descend far more leasurely into the ,water1 than those of a more compacted ,figure1 though both made of the same ,matter3 by which some might be induced to believe that the ,dilatation of the ,figure might reduce it to such amplenesse that it should not only retard but wholly impede and take away the ,motion1 which ,i hold to be false4 ,upon this ,conclusion1 in many dayes discourse1 was spoken much1 and many things1 and divers ,experiments produced1 of which your ,highnesse heard1 and saw some1 and in this discourse shall have all that which hath been produced against my ,assertion1 and what hath been suggested to my thoughts on this matter1 and for confirmation of my ,conclusion3 which if it shall suffice to remove that 7as ,i esteem hitherto false7 ,opinion1 ,i shall thinke ,i have not unprofitably spent my paynes and time4 and although that come not to passe1 yet ought ,i to promise another benefit to my selfe1 namely1 of attaining the knowledge of the truth1 by hearing my ,fallacyes confuted1 and true demonstrations produced by those of the contrary opinion4 ,and to proceed with the greatest plainness and perspicuity that ,i can possible1 it is1 ,i conceive1 necessary1 first of all to declare what is the true1 intrinsecall1 and totall ,cause1 of the ascending of some ,sollid ,bodyes in the ,water1 and therein floating2 or on the contrary1 of their sinking and so much the rather in asmuch as ,i cannot satisfie myselfe in that which ,aristotle hath left written on this ,subject4 ,sidenote3 ,the cause of the ,natation submersion of ,solids in the ,water4 ,i say then the ,cause why some ,sollid ,bodyes descend to the ,bottom of ,water1 is the excesse of their ,gravity1 above the ,gravity of the ,water2 and on the contrary1 the excess of the ,waters ,gravity above the ,gravity of those1 is the ,cause that others do not descend1 rather that they rise from the ,bottom1 and ascend to the ,surface4 ,this was subtilly demonstrated by ,archimedes in his ,book ,of the ,,natation of ,,bodies3 ,conferred afterwards by a very grave ,author1 but1 if ,i erre not invisibly1 as below for defence of him1 ,i shall endeavour to prove4 ,i1 with a different ,method1 and by other meanes1 will endeavour to demonstrate the same1 reducing the ,causes of such ,effects to more intrinsecall and immediate ,principles1 in which also are discovered the ,causes of some admirable and almost incredible ,accidents1 as that would be1 that a very little quantity of ,water1 should be able1 with its small weight1 to raise and sustain a ,solid ,body1 an hundred or a thousand times heavier than it4 ,and because demonstrative ,order so requires1 ,i shall define certain ,termes1 and afterwards explain some ,propositions1 of which1 as of things true and obvious1 ,i may make use of to my present purpose4 ,,definition ,i4 ,i then call equally ,grave in specie1 those ,matters of which equall ,masses weigh equally4 ,as if for example1 two ,balls1 one of ,wax1 and the other of some ,wood of equall ,masse1 were also equall in ,weight1 we say1 that such ,wood1 and the ,wax are in specie equally grave4 ,,definition ,,ii4 ,but equally grave in ,absolute ,gravity1 we call two ,sollids1 weighing equally1 though of ,mass they be unequall4 ,as for example1 a ,mass of ,lead1 and another of ,wood1 that weigh each ten pounds1 ,i call equall in ,absolute ,gravity1 though the ,mass of the ,wood be much greater then that of the ,lead4 ,and1 consequently1 less ,grave in specie4 ,,definition ,,iii4 ,i call a ,matter more ,grave in specie than another1 of which a ,mass1 equall to a ,mass of the other1 shall weigh more4 ,and so ,i say1 that ,lead is more grave in specie than ,tinn1 because if you take of them two equall ,masses1 that of the ,lead weigheth more4 ,,definition ,,iv4 ,but ,i call that ,body more grave absolutely than this1 if that weigh more than this1 without any respect had to the ,masses4 ,and thus a great piece of ,wood is said to weigh more than a little lump of ,lead1 though the ,lead be in specie more heavy than the ,wood4 ,and the same is to be understood of the less grave in specie1 and the less grave absolutely4 ,these ,termes defined1 ,i take from the ,mechanicks two ,principles3 the first is1 that ,,axiome4 ,i4 ,weights absolutely equall1 moved with equall ,velocity1 are of equall ,force and ,moment in their operations4 ,,definition ,v4 ,moment1 amongst ,mechanicians1 signifieth that ,vertue1 that ,force1 or that ,efficacy1 with which the ,mover moves1 and the ,moveable resists4 ,which ,vertue dependes not only on the simple ,gravity1 but on the ,velocity of the ,motion1 and on the diverse ,inclinations of the ,spaces along which the ,motion is made3 ,for a descending ,weight makes a greater ,impetus in a ,space much declining1 than in one less declining2 and in summe1 what ever is the occasion of such ,vertue1 it ever retaines the name of ,moment2 nor in my ,judgement1 is this sence new in our ,idiome1 for1 if ,i mistake not1 ,i think we often say2 ,this is a weighty businesse1 but the other is of small moment3 and we consider lighter matters and let pass those of ,moment2 a ,metaphor1 ,i suppose1 taken from the ,mechanicks4 ,as for example1 two weights equall in absolute ,gravity1 being put into a ,ballance of equall ,arms1 they stand in ,equilibrium1 neither one going down1 nor the other up3 because the equality of the ,distances of both1 from the ,centre on which the ,ballance is supported1 and about which it moves1 causeth that those weights1 the said ,ballance moving1 shall in the same ,time move equall ,spaces1 that is1 shall move with equall ,velocity1 so that there is no reason for which this ,weight should descend more than that1 or that more than this2 and therefore they make an ,equilibrium1 and their ,moments continue of semblable and equall ,vertue4 ,the second ,principle is2 ,that ,,axiome ,,ii4 ,the ,moment and ,force of the ,gravity1 is encreased by the ,velocity of the ,motion4 ,so that ,weights absolutely equall1 but conjoyned with ,velocity unequall1 are of ,force1 ,moment and ,vertue unequall3 and the more potent1 the more swift1 according to the proportion of the ,velocity of the one1 to the ,velocity of the other4 ,of this we have a very pertinent example in the ,balance or ,stiliard of unequall ,arms1 at which ,weights absolutely equall being suspended1 they do not weigh down1 and gravitate equally1 but that which is at a greater distance from the ,centre1 about which the ,beam moves1 descends1 raising the other1 and the ,motion of this which ascends is slow1 and the other swift3 and such is the ,force and ,vertue1 which from the ,velocity of the ,mover1 is conferred on the ,moveable1 which receives it1 that it can exquisitely compensate1 as much more ,weight added to the other slower ,moveable3 so that if of the ,arms of the ,balance1 one were ten times as long as the other1 whereupon in the ,beames moving about the ,centre1 the end of that would go ten times as far as the end of this1 a ,weight suspended at the greater distance1 may sustain and poyse another ten times more grave absolutely than it3 and that because the ,stiliard moving1 the lesser ,weight shall move ten times faster than the bigger4 ,it ought alwayes therefore to be understood1 that ,motions are according to the same ,inclinations1 namely1 that if one of the ,moveables move perpendicularly to the ,horizon1 then the other makes its ,motion by the like ,perpendicular2 and if the ,motion of one were to be made ,horizontally2 that then the other is made along the same ,horizontall plain3 and in summe1 alwayes both in like ,inclinations4 ,this proportion between the ,gravity and ,velocity is found in all ,mechanicall ,instruments3 and is considered by ,aristotle1 as a ,principle in his ,mechanicall ,questions2 whereupon we also may take it for a true ,assumption1 ,that ,,axiome ,,iii4 ,weights absolutely unequall1 do alternately counterpoyse and become of equall ,moments1 as oft as their ,gravities1 with contrary proportion1 answer to the ,velocity of their ,motions4 ,that is to say1 that by how much the one is less grave than the other1 by so much is it in a constitution of moving more swiftly than that4 ,having prefatically explicated these things1 we may begin to enquire1 what ,bodyes those are which totally submerge in ,water1 and go to the ,bottom1 and which those that by constraint float on the top1 so that being thrust by violence under ,water1 they return to swim1 with one part of their ,mass visible above the ,surface of the ,water3 and this we will do by considering the respective operation of the said ,solids1 and of ,water3 ,which operation followes the ,submersion and sinking2 and this it is#f1 ,that in the ,submersion that the ,solid maketh1 being depressed downwards by its proper ,gravity1 it comes to drive away the water from the place where it successively subenters1 and the water repulsed riseth and ascends above its first levell1 to which ,ascent on the other side it1 as being a grave ,body of its own nature1 resists3 ,and because the descending ,solid more and more immerging1 greater and greater quantity of ,water ascends1 till the whole ,sollid be submerged2 its necessary to compare the ,moments of the ,resistance of the water to ,ascension1 with the ,moments of the pressive ,gravity of the ,solid3 ,and if the ,moments of the ,resistance of the water1 shall equalize the ,moments of the ,solid1 before its totall ,immersion#g2 in this case doubtless there shall be made an ,equilibrium1 nor shall the ,body sink any farther4 ,but if the ,moment of the ,solid1 shall alwayes exceed the ,moments wherewith the repulsed water successively makes ,resistance#h1 that ,solid shall not only wholly submerge under water1 but shall descend to the ,bottom4 ,but if1 lastly1 in the instant of totall ,submersion1 the equality shall be made between the ,moments of the prement ,solid1 and the resisting ,water#i2 then shall rest1 ensue1 and the said ,solid shall be able to rest indifferently1 in whatsoever part of the water4 ,by this time is manifest the necessity of comparing the ,gravity of the water1 and of the ,solid#aj2 and this comparison might at first sight seem sufficient to conclude and determine which are the ,solids that float a-top1 and which those that sink to the ,bottom in the water1 asserting that those shall float which are lesse grave in specie than the water1 and those submerge1 which are in specie more grave4 ,for it seems in appearance1 that the ,sollid in sinking continually1 raiseth so much ,water in ,mass1 as answers to the parts of its own ,bulk submerged3 whereupon it is impossible1 that a ,solid less grave in specie1 than water1 should wholly sink1 as being unable to raise a weight greater than its own1 and such would a ,mass of water equall to its own ,mass be4 ,and likewise it seems necessary1 that the graver ,solids do go to the ,bottom1 as being of a ,force more than sufficient for the raising a ,masse of water1 equall to its own1 though inferiour in weight4 ,nevertheless the business succeeds otherwise3 and though the ,conclusions are true1 yet are the ,causes thus assigned deficient1 nor is it true1 that the ,solid in submerging1 raiseth and repulseth ,masses of ,water1 equall to the parts of it self submerged2 but the ,water repulsed1 is alwayes less than the parts of the ,solid submerged#aa3 and so much the more by how much the ,vessell in which the ,water is contained is narrower3 in such manner that it hinders not1 but that a ,solid may submerge all under ,water1 without raising so much ,water in ,mass1 as would equall the tenth or twentieth part of its own ,bulk3 like as on the contrary1 a very small quantity of ,water1 may raise a very great ,solid ,mass#ab1 though such ,solid should weigh absolutely a hundred times as much1 or more1 than the said ,water1 if so be that the ,matter of that same ,solid be in specie less grave than the ,water4 ,and thus a great ,beam1 as suppose of a #ajjj weight1 may be raised and born afloat by ,water1 which weighs not #ej3 and this happens when the ,moment of the ,water is compensated by the ,velocity of its ,motion4 #f ,how the submersion of ,solids in the ,water1 is effected4 #g ,what ,solids shall float on the ,water4 #h ,what ,solids shall sinke to the botome4 #i ,what ,solids shall rest in all places of the ,water4 #aj ,the ,gravitie of the ,water and ,solid must be compared in all ,problems1 of ,natation of ,bodies4 #aa ,the water repelled is ever less than the parts of the ,sollid submerged4 #ab ,a small quantity of water1 may float a very great ,solid ,mass4 ,but because such things1 propounded thus in abstract1 are somewhat difficult to be comprehended1 it would be good to demonstrate them by particular examples2 and for facility of demonstration1 we will suppose the ,vessels in which we are to put the ,water1 and place the ,solids1 to be inviron'd and included with sides erected perpendicular to the ,plane of the ,horizon1 and the ,solid that is to be put into such vessell to be either a streight ,cylinder1 or else an upright ,prisme4 ,the which proposed and declared1 ,i proceed to demonstrate the truth of what hath been hinted1 forming the ensuing ,theoreme4 ,,theoreme ,i4 ,sidenote3 ,the ,proportion of the water raised to the ,solid submerged4 ,the ,mass of the ,water which ascends in the submerging of a ,solid1 ,prisme or ,cylinder1 or that abaseth in taking it out1 is less than the ,mass of the said ,solid1 so depressed or advanced3 and hath to it the same proportion1 that the ,surface of the ,water circumfusing the ,solid1 hath to the same circumfused ,surface1 together with the ,base of the ,solid4 ,let the ,vessell be ,a ,b ,c ,d1 and in it the ,water raised up to the ,levell ,e ,f ,g1 before the ,solid ,prisme ,h ,i ,k be therein immerged2 but after that it is depressed under ,water1 let the ,water be raised as high as the ,levell ,l ,m1 the ,solid ,h ,i ,k shall then be all under ,water1 and the ,mass of the elevated ,water shall be ,l ,g1 which is less than the ,masse of the ,solid depressed1 namely of ,h ,i ,k1 being equall to the only part ,e ,i ,k1 which is contained under the first ,levell ,e ,f ,g4 ,which is manifest1 because if the ,solid ,h ,i ,k be taken out1 the ,water ,i ,g shall return into the place occupied by the ,mass ,e ,i ,k1 where it was continuate before the submersion of the ,prisme4 ,and the ,mass ,l ,g being equall to the ,mass ,e ,k3 adde thereto the ,mass ,e ,n1 and it shall be the whole ,mass ,e ,m1 composed of the parts of the ,prisme ,e ,n1 and of the ,water ,n ,f1 equall to the whole ,solid ,h ,i ,k3 ,and1 therefore1 the ,mass ,l ,g shall have the same proportion to ,e ,m1 as to the ,mass ,h ,i ,k3 ,but the ,mass ,l ,g hath the same proportion to the ,mass ,e ,m1 as the ,surface ,l ,m hath to the ,surface ,m ,h3 ,therefore it is manifest1 that the ,mass of ,water repulsed ,l ,g1 is in proportion to the ,mass of the ,solid submerged ,h ,i ,k2 as the ,surface ,l ,m1 namely1 that of the ,water ambient about the ,sollid1 to the whole ,surface ,h ,m1 compounded of the said ambient water1 and the ,base of the ,prisme ,h ,n4 ,but if we suppose the first ,levell of the ,water the according to the ,surface ,h ,m1 and the ,prisme allready submerged ,h ,i ,k2 and after to be taken out and raised to ,e ,a ,o1 and the ,water to be faln from the first ,levell ,h ,l ,m as low as ,e ,f ,g2 ,it is manifest1 that the ,prisme ,e ,a ,o being the same with ,h ,i ,k1 its superiour part ,h ,o1 shall be equall to the inferiour ,e ,i ,k3 and remove the common part ,e ,n1 and1 consequently1 the ,mass of the ,water ,l ,g is equall to the ,mass ,h ,o2 and1 therefore1 less than the ,solid1 which is without the ,water1 namely1 the whole ,prisme ,e ,a ,o1 to which likewise1 the said ,mass of ,water abated ,l ,g1 hath the same proportion1 that the ,surface of the ,waters circumfused ,l ,m hath to the same circumfused ,surface1 together with the ,base of the ,prisme ,a ,o3 which hath the same demonstration with the former case above4 ,illustration ,and from hence is inferred1 that the ,mass of the ,water1 that riseth in the immersion of the ,solid1 or that ebbeth in elevating it1 is not equall to all the ,mass of the ,solid1 which is submerged or elevated1 but to that part only1 which in the immersion is under the first ,levell of the ,water1 and in the elevation remaines above the first ,levell3 ,which is that which was to be demonstrated4 ,we will now pursue the things that remain4 ,and first we will demonstrate that1 ,,theoreme ,,ii4 ,sidenote3 ,the proportion of the water abated1 to the ,solid raised4 ,when in one of the above said ,vessels1 of what ever breadth1 whether wide or narrow1 there is placed such a ,prisme or ,cylinder1 inviron'd with ,water1 if we elevate that ,solid perpendicularly1 the ,water circumfused shall abate1 and the ,abatement of the ,water1 shall have the same proportion to the ,elevation of the ,prisme1 as one of the ,bases of the ,prisme1 hath to the ,surface of the ,water ,circumfused4 ,illustration ,imagine in the ,vessell1 as is aforesaid1 the ,prisme ,a ,c ,d ,b to be placed1 and in the rest of the ,space the ,water to be diffused as far as the ,levell ,e ,a3 and raising the ,solid1 let it be transferred to ,g ,m1 and let the ,water be abased from ,e ,a to ,n ,o3 ,i say1 that the descent of the ,water1 measured by the ,line ,a ,o1 hath the same proportion to the rise of the ,prisme1 measured by the ,line ,g ,a1 as the ,base of the ,solid ,g ,h hath to the ,surface of the ,water ,n ,o4 ,the which is manifest3 because the ,mass of the ,solid ,g ,a ,b ,h1 raised above the first ,levell ,e ,a ,b1 is equall to the ,mass of ,water that is abased ,e ,n ,o ,a4 ,therefore1 ,e ,n ,o ,a and ,g ,a ,b ,h are two equall ,prismes2 for of equall ,prismes1 the ,bases answer contrarily to their heights3 ,therefore1 as the ,altitude ,a ,o is to the ,altitude ,a ,g1 so is the ,superficies or ,base ,g ,h to the ,surface of the ,water ,n ,o4 ,if therefore1 for example1 a ,pillar were erected in a waste ,pond full of ,water1 or else in a ,well1 capable of little more then the ,mass of the said ,pillar1 in elevating the said ,pillar1 and taking it out of the ,water1 according as it riseth1 the ,water that invirons it will gradually abate1 and the abasement of the ,water at the instant of lifting out the ,pillar1 shall have the same proportion1 that the thickness of the ,pillar hath to the excess of the breadth of the said ,pond or ,well1 above the thickness of the said ,pillar3 so that if the breadth of the ,well were an eighth part larger than the thickness of the ,pillar1 and the breadth of the ,pond twenty five times as great as the said thickness1 in the ,pillars ascending one foot1 the water in the ,well shall descend seven foot1 and that in the ,pond only #a_/be of a foot4 ,sidenote3 ,why a ,solid less grave in specie than water1 stayeth not under water1 in very small depths3 ,this ,demonstrated1 it will not be difficult to show the true cause1 how it comes to pass1 that1 ,,theoreme ,,iii4 ,a ,prisme or regular ,cylinder1 of a substance specifically less grave than ,water1 if it should be totally submerged in ,water1 stayes not underneath1 but riseth1 though the ,water circumfused be very little1 and in absolute ,gravity1 never so much inferiour to the ,gravity of the said ,prisme4 ,let then the ,prisme ,a ,e ,f ,b1 be put into the ,vessell ,c ,d ,f ,b1 the same being less grave in specie than the ,water3 and let the ,water infused rise to the height of the ,prisme3 ,i say1 that the ,prisme left at liberty1 it shall rise1 being born up by the ,water circumfused ,c ,d ,e ,a4 ,for the ,water ,c ,e being specifically more grave than the ,solid ,a ,f1 the absolute weight of the water ,c ,e1 shall have greater proportion to the absolute weight of the ,prisme ,a ,f1 than the ,mass ,c ,e hath to the ,mass ,a ,f 7in regard the ,mass hath the same proportion to the ,mass1 that the weight absolute hath to the weight absolute1 in case the ,masses are of the same ,gravity in specie47 ,but the ,mass ,c ,e is to the ,mass ,a ,f1 as the ,surface of the water ,a ,c1 is to the ,superficies1 or ,base of the ,prisme ,a ,b2 which is the same proportion as the ascent of the ,prisme when it riseth1 hath to the descent of the ,water circumfused ,c ,e4 ,illustration ,therefore1 the absolute ,gravity of the water ,c ,e1 hath greater proportion to the absolute ,gravity of the ,prisme ,a ,f2 than the ,ascent of the ,prisme ,a ,f1 hath to the descent of the said water ,c ,e4 ,the ,moment1 therefore1 compounded of the absolute ,gravity of the water ,c ,e1 and of the ,velocity of its descent1 whilst it forceably repulseth and raiseth the ,solid ,a ,f1 is greater than the ,moment compounded of the absolute ,gravity of the ,prisme ,a ,f1 and of the ,tardity of its ascent1 with which ,moment it contrasts and resists the repulse and violence done it by the ,moment of the water3 ,therefore1 the ,prisme shall be raised4 ,sidenote3 ,the ,proportion according to which the ,submersion ,natation of ,solids is made4 ,it followes1 now1 that we proceed forward to demonstrate more particularly1 how much such ,solids shall be inferiour in ,gravity to the water elevated2 namely1 what part of them shall rest submerged1 and what shall be visible above the ,surface of the water3 but first it is necessary to demonstrate the subsequent ,lemma4 ,,lemma ,i4 ,sidenote3 ,the absolute ,gravity of ,solids1 are in a proportion compounded of their ,specifick ,gravities1 and of their ,masses4 ,the absolute ,gravities of ,solids1 have a proportion compounded of the proportions of their specificall ,gravities1 and of their ,masses4 ,illustration ,let ,a and ,b be two ,solids4 ,i say1 that the ,absolute ,gravity of ,a1 hath to the ,absolute ,gravity of ,b1 a proportion compounded of the proportions of the specificall ,gravity of ,a1 to the ,specificall ,gravity of ,b1 and of the ,mass ,a to the ,mass ,b4 ,let the ,line ,d have the same proportion to ,e1 that the specifick ,gravity of ,a1 hath to the specifick ,gravity of ,b2 and let ,e be to ,f1 as the ,mass ,a to the ,mass ,b3 ,it is manifest1 that the proportion of ,d to ,f1 is compounded of the proportions ,d and ,e2 and ,e and ,f4 ,it is requisite1 therefore1 to demonstrate1 that as ,d is to ,f1 so the absolute ,gravity of ,a1 is to the absolute ,gravity of ,b4 ,take the ,solid ,c1 equall in ,mass to the ,solid ,a1 and of the same ,gravity in specie with the ,solid ,b4 ,because1 therefore1 ,a and ,c are equall in ,mass1 the absolute ,gravity of ,a1 shall have to the absolute ,gravity of ,c1 the same proportion1 as the specificall ,gravity of ,a1 hath to the specificall ,gravity of ,c1 or of ,b1 which is the same in specie2 that is1 as ,d is to ,e4 ,and1 because1 ,c and ,b are of the same ,gravity in specie1 it shall be1 that as the absolute weight of ,c1 is to the absolute weight of ,b1 so the ,mass ,c1 or the ,mass ,a1 is to the ,mass ,b2 that is1 as the ,line ,e to the ,line ,f4 ,as therefore1 the absolute ,gravity of ,a1 is to the absolute ,gravity of ,c1 so is the ,line ,d to the ,line ,e3 and1 as the absolute ,gravity of ,c1 is to the absolute ,gravity of ,b1 so is the ,line ,e to the ,line ,f3 ,therefore1 by ,equality of proportion1 the absolute ,gravity of ,a1 is to the absolute ,gravity of ,b1 as the ,line ,d to the ,line ,f3 which was to be demonstrated4 ,i proceed now to demonstrate1 how that1 ,,theoreme ,,iv4 ,sidenote3 ,the proportion of water requisite to make a ,solid swim3 ,if a ,solid1 ,cylinder1 or ,prisme1 lesse grave specifically than the ,water1 being put into a ,vessel1 as above1 of whatsoever greatnesse1 and the ,water1 be afterwards infused1 the ,solid shall rest in the bottom1 unraised1 till the ,water arrive to that part of the ,altitude1 of the said ,prisme1 to which its whole ,altitude hath the same proportion1 that the ,specificall ,gravity of the ,water1 hath to the ,specificall ,gravity of the said ,solid3 but infusing more ,water1 the ,solid shall ascend4 ,illustration ,let the ,vessell be ,m ,l ,g ,n of any bigness1 and let there be placed in it the ,solid ,prisme ,d ,f ,g ,e1 less grave in specie than the water2 and look what proportion the ,specificall ,gravity of the water1 hath to that of the ,prisme1 such let the ,altitude ,d ,f1 have to the ,altitude ,f ,b4 ,i say1 that infusing water to the ,altitude ,f ,b1 the ,solid ,d ,g shall not float1 but shall stand in ,equilibrium1 so1 that that every little quantity of water1 that is infused1 shall raise it4 ,let the water1 therefore1 be infused to the ,levell ,a ,b ,c2 and2 because the ,specifick ,gravity of the ,solid ,d ,g1 is to the ,specifick ,gravity of the water1 as the altitude ,b ,f is to the altitude ,f ,d2 that is1 as the ,mass ,b ,g to the ,mass ,g ,d2 as the proportion of the ,mass ,b ,g is to the ,mass ,g ,d1 as the proportion of the ,mass ,g ,d is to the ,mass ,a ,f1 they compose the ,proportion of the ,mass ,b ,g to the ,mass ,a ,f4 ,therefore1 the ,mass ,b ,g is to the ,mass ,a ,f1 in a proportion compounded of the proportions of the ,specifick ,gravity of the ,solid ,g ,d1 to the ,specifick ,gravity of the water1 and of the ,mass ,g ,d to the ,mass ,a ,f3 ,but the same proportions of the ,specifick ,gravity of ,g ,d1 to the ,specifick ,gravity of the water1 and of the ,mass ,g ,d to the ,mass ,a ,f1 do also by the precedent ,lemma1 compound the proportion of the absolute ,gravity of the ,solid ,d ,g1 to the absolute ,gravity of the ,mass of the water ,a ,f3 ,therefore1 as the ,mass ,b ,g is to the ,mass ,a ,f1 so is the ,absolute ,gravity of the ,solid ,d ,g1 to the ,absolute ,gravity of the ,mass of the water ,a ,f4 ,but as the ,mass ,b ,g is to the ,mass ,a ,f2 so is the ,base of the ,prisme ,d ,e1 to the ,surface of the water ,a ,b2 and so is the descent of the water ,a ,b1 to the ,elevation of the ,prisme ,d ,g2 ,therefore1 the descent of the water is to the elevation of the ,prisme1 as the absolute ,gravity of the ,prisme1 is to the absolute ,gravity of the water3 ,therefore1 the ,moment resulting from the absolute ,gravity of the water ,a ,f1 and the ,velocity of the ,motion of declination1 with which ,moment it forceth the ,prisme ,d ,g1 to rise and ascend1 is equall to the ,moment that results from the absolute ,gravity of the ,prisme ,d ,g1 and from the ,velocity of the ,motion1 wherewith being raised1 it would ascend3 with which ,moment it resists its being raised3 because1 therefore1 such ,moments are equall1 there shall be an ,equilibrium between the water and the ,solid4 ,and1 it is manifest1 that putting a little more water unto the other ,a ,f1 it will increase the ,gravity and ,moment1 whereupon the ,prisme ,d ,g1 shall be overcome1 and elevated till that the only part ,b ,f remaines submerged4 ,which is that that was to be demonstrated4 ,,corollary ,i4 ,sidenote3 ,how far ,solids less grave in specie than water1 do submerge4 ,by what hath been demonstrated1 it is manifest1 that ,solids less grave in specie than the water1 submerge only so far1 that as much water in ,mass1 as is the part of the ,solid submerged1 doth weigh absolutely as much as the whole ,solid4 ,for1 it being supposed1 that the ,specificall ,gravity of the water1 is to the ,specificall ,gravity of the ,prisme ,d ,g1 as the ,altitude ,d ,f1 is to the ,altitude ,f ,b2 that is1 as the ,solid ,d ,g is to the ,solid ,b ,g2 we might easily demonstrate1 that as much water in ,mass as is equall to the ,solid ,b ,g1 doth weigh absolutely as much as the whole ,solid ,d ,g2 ,for1 by the ,lemma foregoing1 the ,absolute ,gravity of a ,mass of water1 equall to the ,mass ,b ,g1 hath to the ,absolute ,gravity of the ,prisme ,d ,g1 a proportion compounded of the proportions1 of the ,mass ,b ,g to the ,mass ,g ,d1 and of the ,specifick ,gravity of the water1 to the ,specifick ,gravity of the ,prisme3 ,but the ,gravity in specie of the water1 to the ,gravity in specie of the ,prisme1 is supposed to be as the ,mass ,g ,d to the ,mass ,g ,b4 ,therefore1 the ,absolute ,gravity of a ,mass of water1 equall to the ,mass ,b ,g1 is to the ,absolute ,gravity of the ,solid ,d ,g1 in a proportion compounded of the proportions1 of the ,mass ,b ,g to the ,mass ,g ,d1 and of the ,mass ,d ,g to the ,mass ,g ,b2 which is a proportion of equalitie4 ,the ,absolute ,gravity1 therefore1 of a ,mass of ,water equall to the part of the ,mass of the ,prisme ,b ,g1 is equall to the ,absolute ,gravity of the whole ,solid ,d ,g4 ,,corollary ,,ii4 ,sidenote3 ,a ,rule to equilibrate ,solids in the water4 ,it followes1 moreover1 that a ,solid less grave than the water1 being put into a ,vessell of any imaginable greatness1 and water being circumfused about it to such a height1 that as much water in ,mass1 as is the part of the ,solid submerged1 do weigh absolutely as much as the whole ,solid2 it shall by that water be justly sustained1 be the circumfused ,water in quantity greater or lesser4 ,illustration ,for1 if the ,cylinder or ,prisme ,m1 less grave than the water1 v4 gra4 in ,subsequiteriall proportion1 shall be put into the capacious ,vessell ,a ,b ,c ,d1 and the water raised about it1 to three quarters of its height1 namely1 to its ,levell ,a ,d3 it shall be sustained and exactly poysed in ,equilibrium4 ,the same will happen2 if the ,vessell ,e ,n ,s ,f were very small1 so1 that between the ,vessell and the ,solid ,m1 there were but a very narrow space1 and only capable of so much water1 as the hundredth part of the ,mass ,m1 by which it should be likewise raised and erected1 as before it had been elevated to three fourths of the height of the ,solid3 which to many at the first sight1 may seem a notable ,paradox1 and beget a conceit1 that the ,demonstration of these effects1 were sophisticall and fallacious3 but1 for those who so repute it1 the ,experiment is a means that may fully satisfie them4 ,but he that shall but comprehend of what ,importance ,velocity of ,motion is1 and how it exactly compensates the defect and want of ,gravity1 will cease to wonder1 in considering that at the elevation of the ,solid ,m1 the great ,mass of water ,a ,b ,c ,d abateth very little1 but the little ,mass of water ,e ,n ,s ,f decreaseth very much1 and in an instant1 as the ,solid ,m before did rise1 howbeit for a very short space3 ,whereupon the ,moment1 compounded of the small ,absolute ,gravity of the water ,e ,n ,s ,f1 and of its great ,velocity in ebbing1 equalizeth the ,force and and ,moment1 that results from the composition of the immense ,gravity of the water ,a ,b ,c ,d1 with its great slownesse of ebbing2 since that in the ,elevation of the ,sollid ,m1 the abasement of the lesser water ,e ,s1 is performed just so much more swiftly than the great ,mass of water ,a ,c1 as this is more in ,mass than that which we thus demonstrate4 ,sidenote3 ,the proportion according to which water riseth and falls in different ,vessels at the ,immersion and ,elevation of ,solids4 ,in the rising of the ,solid ,m1 its elevation hath the same proportion to the circumfused water ,e ,n ,s ,f1 that the ,surface of the said water1 hath to the ,superficies or ,base of the said ,solid ,m2 which ,base hath the same proportion to the ,surface of the water ,a ,d1 that the abasement or ebbing of the water ,a ,c1 hath to the rise or elevation of the said ,solid ,m4 ,therefore1 by ,perturbation of proportion1 in the ascent of the said ,solid ,m1 the abasement of the water ,a ,b ,c ,d1 to the abasement of the water ,e ,n ,s ,f1 hath the same proportion1 that the ,surface of the water ,e ,f1 hath to the ,surface of the water ,a ,d2 that is1 that the whole ,mass of the water ,e ,n ,s ,f1 hath to the whole ,mass ,a ,b ,c ,d1 being equally high3 ,it is manifest1 therefore1 that in the expulsion and elevation of the ,solid ,m1 the water ,e ,n ,s ,f shall exceed in ,velocity of ,motion the water ,a ,b ,c ,d1 asmuch as it on the other side is exceeded by that in quantity3 whereupon their ,moments in such operations1 are mutually equall4 ,illustration ,and1 for ampler confirmation1 and clearer explication of this1 let us consider the present ,figure1 7which if ,i be not deceived1 may serve to detect the errors of some ,practick ,mechanitians who upon a false foundation some times attempt impossible enterprizes17 in which1 unto the large ,vessell ,e ,i ,d ,f1 the narrow ,funnell or ,pipe ,i ,c ,a ,b is continued1 and suppose water infused into them1 unto the ,levell ,l ,g ,h1 which water shall rest in this position1 not without admiration in some1 who cannot conceive how it can be1 that the heavie charge of the great ,mass of water ,g ,d1 pressing downwards1 should not elevate and repulse the little quantity of the other1 contained in the ,funnell or ,pipe ,c ,l1 by which the descent of it is resisted and hindered3 ,but such wonder shall cease1 if we begin to suppose the water ,g ,d to be abased only to ,q ,d1 and shall afterwards consider1 what the water ,c ,l hath done1 which to give place to the other1 which is descended from the ,levell ,g ,h1 to the ,levell ,q ,o1 shall of necessity have ascended in the same time1 from the ,levell ,l unto ,a ,b4 ,and the ascent ,l ,b1 shall be so much greater than the descent ,g ,q1 by how much the breadth of the ,vessell ,g ,d1 is greater than that of the ,funnell ,i ,c2 which1 in summe1 is as much as the water ,g ,d1 is more than the water ,l ,c3 but in regard that the ,moment of the ,velocity of the ,motion1 in one ,moveable1 compensates that of the ,gravity of another what wonder is it1 if the swift ascent of the lesser ,water ,c ,l1 shall resist the slow descent of the greater ,g ,d8 ,the same1 therefore1 happens in this operation1 as in rhe ,stilliard1 in which a weight of two pounds counterpoyseth an other of #bjj1 asoften as that shall move in the same time1 a space #ajj times greater than this3 which falleth out when one ,arme of the ,beam is an hundred times as long as the other4 ,let the erroneous opinion of those therefore cease1 who hold that a ,ship is better1 and easier born up in a great abundance of water1 then in a lesser quantity#ac1 7this was believed by ,aristotle in his ,problems1 ,sect4 #bc1 ,probl4 #b47 it being on the contrary true1 that its possible1 that a ,ship may as well float in ten ,tun of water1 as in an ,ocean4 #ac ,a ship flotes as well in ten ,tun of ,water as in an ,ocean4 ,sidenote3 ,a ,solid specifiaclly graver than the water1 cannot be born up by any quantity of it4 ,but following our matter1 ,i say1 that by what hath been hitherto demonstrated1 we may understand how1 that ,,corollary ,,iii4 ,one of the above named ,solids1 when more grave in specie than the water1 can never be sustained1 by any whatever quantity of it4 ,for having seen how that the ,moment wherewith such a ,solid1 as grave in specie as the water1 contrasts with the ,moment of any ,mass of water whatsoever1 is able to retain it1 even to its totall ,submersion1 without its ever ascending2 it remaineth1 manifest1 that the water is far less able to raise it up1 when it exceeds the same in specie3 so1 that though you infuse water till its totall ,submersion1 it shall still stay at the ,bottome1 and with such ,gravity1 and ,resistance to ,elevation1 as is the excess of its ,absolute ,gravity1 above the ,absolute ,gravity of a ,mass equall to it1 made of water1 or of a ,matter in specie equally grave with the water3 and1 though you should moreover adde never so much water above the ,levell of that which equalizeth the ,altitude of the ,solid1 it shall not1 for all that1 encrease the ,pression1 or ,gravitation1 of the parts circumfused about the said ,solid1 by which greater pression1 it might come to be repulsed2 because1 the ,resistance is not made1 but only by those parts of the water1 which at the ,motion of the said ,solid do also move1 and these are those only1 which are comprehended by the two ,superficies equidistant to the ,horizon1 and their parallels1 that comprehend the ,altitude of the ,solid immerged in the water4 ,i conceive1 ,i have by this time sufficiently declared and opened the way to the contemplation of the true1 intrinsecall and proper ,causes of diverse ,motions1 and of the ,rest of many ,solid ,bodies in diverse ,mediums1 and particularly in the water1 shewing how all in effect1 depend on the mutuall excesses of the ,gravity of the ,moveables and of the ,mediums3 and1 that which did highly import1 removing the ,objection1 which peradventure would have begotten much doubting1 and scruple in some1 about the verity of my ,conclusion1 namely1 how that notwithstanding1 that the excess of the ,gravity of the water1 above the ,gravity of the ,solid1 demitted into it1 be the cause of its floating and rising from the ,bottom to the ,surface1 yet a quantity of water1 that weighs not ten pounds1 can raise a ,solid that weighs above #ajj pounds3 in that we have demonstrated1 ,that it sufficeth1 that such difference be found between the ,specificall ,gravities of the ,mediums and ,moveables1 let the particular and absolute ,gravities be what they will3 insomuch1 that a ,solid1 provided that it be ,specifically less grave than the water1 although its absolute weight were #ajjj pounds1 yet may it be born up and elevated by ten pounds of water1 and less3 and on the contrary1 another ,solid1 so that it be ,specifically more grave than the water1 though in absolute ,gravity it were not above a pound1 yet all the water in the ,sea1 cannot raise it from the ,bottom1 or float it4 ,this sufficeth me1 for my present occasion1 to have1 by the above declared ,examples1 discovered and demonstrated1 without extending such matters farther1 and1 as ,i might have done1 into a long ,treatise3 yea1 but that there was a necessity of resolving the above proposed doubt1 ,i should have contented my self with that only1 which is demonstrated by ,archimedes1 in his first ,book ,de ,insidentibus humido#ad3 where in generall termes he infers and confirms the same ,conclusions1 namely1 that ,solids 7a7 less grave than water1 swim or float upon it1 the 7b7 more grave go to the ,bottom1 and the 7c7 equally grave rest indifferently in all places1 yea1 though they should be wholly under water4 #ad ,of ,natation 7a7 ,lib4 #a1 ,prop4 #d4 7b7 ,id4 ,lib4 #a4 ,prop4 #c4 7c7 ,id4 ,lib4 #a4 ,prop4 #c4 ,sidenote3 ,the ,authors defence of ,archimedes his ,doctrine1 against the oppositions of ,buonamico4 ,but1 because that this ,doctrine of ,archimedes1 perused1 transcribed and examined by ,signor ,francesco ,buonamico1 in his fifth ,book of ,motion1 ,chap4 #bi1 and afterwards by him confuted1 might by the ,authority of so renowned1 and famous a ,philosopher1 be rendered dubious1 and suspected of falsity2 ,i have judged it necessary to defend it1 if ,i am able so to do1 and to clear ,archimedes1 from those censures1 with which he appeareth to be charged4 ,buonamico rejecteth the ,doctrine of ,archimedes1 first#ae1 as not consentaneous with the ,opinion of ,aristotle1 adding1 that it was a strange thing to him1 that the ,water should exceed the ,earth in ,gravity#af1 seeing on the contrary1 that the ,gravity of water1 increaseth1 by means of the participation of ,earth4 ,and he subjoyns presently after#ag1 that he was not satisfied with the ,reasons of ,archimedes1 as not being able with that ,doctrine1 to assign the cause whence it comes1 that a ,boat and a ,vessell1 which otherwise1 floats above the water1 doth sink to the ,bottom1 if once it be filled with water2 that by reason of the equality of ,gravity1 between the water within it1 and the other water without1 it should stay a top2 but yet1 nevertheless1 we see it to go to the ,bottom4 #ae ,his first ,objection against the ,doctrine of ,archimedes4 #af ,his ,second ,objection4 #ag ,his third ,objection4 ,he farther addes#ah1 that ,aristotle had clearly confuted the ,ancients1 who said1 that light ,bodies moved upwards#ai1 driven by the impulse of the more grave ,ambient3 which if it were so1 it should seem of necessity to follow1 that all naturall ,bodies are by nature heavy1 and none light3 ,for that the same would befall the ,fire and ,air1 if put in the ,bottom of the water4 ,and1 howbeit1 ,aristotle grants a ,pulsion in the ,elements1 by which the ,earth is reduced into a ,sphericall ,figure1 yet nevertheless1 in his judgement2 it is not such that it can remove grave ,bodies from their naturall places1 but rather1 that it send them toward the ,centre1 to which 7as he somewhat obscurely continues to say17 the water principally moves1 if it in the interim meet not with something that resists it1 and1 by its ,gravity1 thrusts it out of its place3 in which case1 if it cannot directly1 yet at least as well as it can1 it tends to the ,centre3 but it happens1 that light ,bodies by such ,impulsion1 do all ascend upward3 but this properly they have by nature1 as also1 that other of swimming4 ,he concludes1 lastly#bj1 that he concurs with ,archimedes in his ,conclusions2 but not in the ,causes1 which he would referre to the facile and difficult ,separation of the ,medium1 and to the predominance of the ,elements1 so that when the ,moveable superates the power of the ,medium2 as for example1 ,lead doth the ,continuity of water1 it shall move thorow it1 else not4 #ah ,his fourth ,objection4 #ai ,the ,ancients denyed ,absolute ,levity4 #bj ,the causes of ,natation ,submersion1 according to the ,peripateticks4 ,this is all that ,i have been able to collect1 as produced against ,archimedes by ,signor ,buonamico3 who hath not well observed the ,principles and ,suppositions of ,archimedes2 which yet must be false1 if the ,doctrine be false1 which depends upon them2 but is contented to alledge therein some ,inconveniences1 and some ,repugnances to the ,doctrine and ,opinion of ,aristotle4 ,in answer to which ,objections1 ,i say1 first#ba1 ,that the being of ,archimedes ,doctrine1 simply different from the ,doctrine of ,aristotle1 ought not to move any to suspect it1 there being no cause1 why the ,authority of this should be preferred to the ,authority of the other3 but1 because1 where the decrees of ,nature are indifferently exposed to the intellectuall eyes of each1 the ,authority of the one and the other1 loseth all authenticalness of ,perswasion1 the absolute power residing in ,reason2 therefore ,i pass to that which he alledgeth in the second place#bb1 as an absurd consequent of the ,doctrine of ,archimedes1 namely1 ,that water should be more grave than ,earth4 ,but ,i really find not1 that ever ,archimedes said such a thing1 or that it can be rationally deduced from his ,conclusions3 and if that were manifest unto me1 ,i verily believe1 ,i should renounce his ,doctrine1 as most erroneous4 ,perhaps this ,deduction of ,buonamico1 is founded upon that which he citeth of the ,vessel1 which swims as long as its voyd of water1 but once full it sinks to the ,bottom1 and understanding it of a ,vessel of ,earth1 he infers against ,archimedes thus3 ,thou sayst that the ,solids which swim1 are less grave than water3 this ,vessell swimmeth3 therefore1 this ,vessell is lesse grave than water4 ,if this be the ,illation4 ,i easily answer1 granting that this ,vessell is lesse grave than water1 and denying the other consequence1 namely1 that ,earth is less ,grave than ,water4 ,the ,vessel that swims occupieth in the water1 not only a place equall to the ,mass of the ,earth1 of which it is formed2 but equall to the ,earth and to the ,air together1 contained in its concavity4 ,and1 if such a ,mass compounded of ,earth and ,air1 shall be less grave than such another quantity of water1 it shall swim1 and shall accord with the ,doctrine of ,archimedes2 but if1 again1 removing the ,air1 the ,vessell shall be filled with water1 so that the ,solid put in the water1 be nothing but ,earth1 nor occupieth other place1 than that which is only possest by ,earth1 it shall then go to the ,bottom1 by reason that the ,earth is heavier than the water3 and this corresponds well with the meaning of ,archimedes4 ,see the same effect illustrated1 with such another ,experiment1 ,in pressing a ,viall ,glass to the ,bottom of the water1 when it is full of ,air1 it will meet with great resistance1 because it is not the ,glass alone1 that is pressed under water1 but together with the ,glass a great ,mass of ,air1 and such1 that if you should take as much water1 as the ,mass of the ,glass1 and of the ,air contained in it1 you would have a weight much greater than that of the ,viall1 and of its ,air3 and1 therefore1 it will not submerge without great violence3 but if we demit only the ,glass into the water1 which shall be when you shall fill the ,glass with water1 then shall the ,glass descend to the ,bottom2 as superiour in ,gravity to the water4 #ba ,the ,authors answer to the first ,objection4 #bb ,the ,authors answer to the second ,objection4 ,returning1 therefore1 to our first purpose2 ,i say1 that ,earth is more grave than water1 and that therefore1 a ,solid of ,earth goeth to the bottom of it2 but one may possibly make a composition of ,earth and ,air1 which shall be less grave than a like ,mass of ,water2 and this shall swim3 and yet both this and the other experiment shall very well accord with the ,doctrine of ,archimedes4 ,but because that in my judgment it hath nothing of difficulty in it1 ,i will not positively affirme that ,signor ,buonamico1 would by such a discourse object unto ,archimedes the absurdity of inferring by his doctrine1 that ,earth was less grave than ,water1 though ,i know not how to conceive what other accident he could have induced thence4 ,perhaps such a ,probleme 7in my judgement false7 was read by ,signor ,buonamico in some other ,author1 by whom peradventure it was attributed as a singular propertie1 of some particular ,water1 and so comes now to be used with a double errour in confutation of ,archimedes1 since he saith no such thing1 nor by him that did say it was it meant of the common ,element of ,water4 ,sidenote3 ,the ,authors answer to the third ,objection4 ,the third difficulty in the doctrine of ,archimedes was1 that he could not render a reason whence it arose1 that a piece of ,wood1 and a ,vessell of ,wood1 which otherwise floats1 goeth to the bottom1 if filled with ,water4 ,signor ,buonamico hath supposed that a ,vessell of ,wood1 and of ,wood that by nature swims1 as before is said1 goes to the bottom1 if it be filled with water2 of which he in the following ,chapter1 which is the #cj of the fifth ,book copiously discourseth3 but ,i 7speaking alwayes without diminution of his singular ,learning7 dare in defence of ,archimedes deny this experiment1 being certain that a piece of ,wood which by its nature sinks not in ,water1 shall not sinke though it be turned and converted into the forme of any ,vessell whatsoever1 and then filled with ,water3 and he that would readily see the ,experiment in some other tractable ,matter1 and that is easily reduced into several ,figures1 may take pure ,wax1 and making it first into a ,ball or other solid ,figure1 let him adde to it so much ,lead as shall just carry it to the bottome1 so that being a graine less it could not be able to sinke it1 and making it afterwards into the forme of a ,dish1 and filling it with ,water1 he shall finde that without the said ,lead it shall not sinke1 and that with the ,lead it shall descend with much slowness3 in short he shall satisfie himself1 that the ,water included makes no alteration4 ,i say not all this while1 but that its possible of ,wood to make ,barkes1 which being filled with water1 sinke2 but that proceeds not through its ,gravity1 encreased by the ,water1 but rather from the ,nailes and other ,iron ,workes1 so that it no longer hath a ,body less grave than ,water1 but one mixt of ,iron and ,wood1 more grave than a like ,masse of ,water4 ,therefore let ,signor ,buonamico desist from desiring a reason of an effect1 that is not in nature3 yea if the sinking of the ,woodden ,vessell when its full of ,water1 may call in question the ,doctrine of ,archimedes1 which he would not have you to follow1 is on the contrary consonant and agreeable to the ,doctrine of the ,peripateticks1 since it aptly assignes a reason why such a ,vessell must1 when its full of ,water1 descend to the bottom2 converting the ,argument the other way1 we may with safety say that the ,doctrine of ,archimedes is true1 since it aptly agreeth with true experiments1 and question the other1 whose ,deductions are fastened upon erroneouss ,conclusions4 ,as for the other point hinted in this same ,instance1 where it seemes that ,benonamico understands the same not only of a piece of wood1 shaped in the forme of a ,vessell1 but also of massie ,wood1 which filled1 scilicet1 as ,i believe1 he would say1 soaked and steeped in ,water1 goes finally to the bottom that happens in some porose ,woods1 which1 while their ,porosity is replenished with ,air1 or other ,matter less grave than ,water1 are ,masses specificially less grave than the said ,water1 like as is that ,viall of ,glass whilest it is full of ,air3 but when1 such light ,matter departing1 there succeedeth ,water into the same ,porosities and ,cavities1 there results a compound of ,water and ,glass more grave than a like ,mass of ,water3 but the excess of its ,gravity consists in the ,matter of the ,glass1 and not in the ,water1 which cannot be graver than it self3 so that which remaines of the ,wood1 the ,air of its ,cavities departing1 if it shall be more grave in specie than ,water1 fil but its ,porosities with ,water1 and you shall have a ,compost of ,water and of ,wood more grave than ,water1 but not by vertue of the ,water received into and imbibed by the ,porosities1 but of that ,matter of the ,wood which remains when the ,air is departed3 and being such it shall1 according to the ,doctrine of ,archimedes1 goe to the bottom1 like as before1 according to the same ,doctrine it did swim4 ,sidenote3 ,the ,authors answer to the fourth ,objection4 ,as to that finally which presents itself in the fourth place1 namely1 that the ,ancients have been heretofore confuted by ,aristotle1 who denying ,positive and ,absolute ,levity1 and truely esteeming all ,bodies to be grave1 said1 that that which moved upward was driven by the circumambient ,air1 and therefore that also the ,doctrine of ,archimedes1 as an adherent to such an ,opinion was convicted and confuted3 ,i answer first1 that ,signor ,buonamico in my judgement hath imposed upon ,archimedes1 and deduced from his words more than ever he intended by them1 or may from his ,propositions be collected1 in regard that ,archimedes neither denies1 nor admitteth ,positive ,levity1 nor doth he so much as mention it3 so that much less ought ,buonamico to inferre1 that he hath denyed that it might be the ,cause and ,principle of the ,ascension of ,fire1 and other ,light ,bodies#bc3 having but only demonstrated1 that ,solid ,bodies more grave than ,water descend in it1 according to the excess of their ,gravity above the ,gravity of that1 he demonstrates likewise1 how the less grave ascend in the same ,water#bd1 accordng to its excess of ,gravity1 above the ,gravity of them4 ,so that the most that can be gathered from the ,demonstration of ,archimedes is1 that like as the excess of the ,gravity of the ,moveable above the ,gravity of the ,water1 is the ,cause that it descends therein1 so the excess of the ,gravity of the water above that of the ,moveable1 is a sufficient ,cause why it descends not1 but rather betakes it self to swim3 not enquiring whether of moving upwards there is1 or is not any other ,cause contrary to ,gravity3 nor doth ,archimedes discourse less properly than if one should say3 ,if the ,south ,winde shall assault the ,barke with greater ,impetus than is the violence with which the ,streame of the ,river carries it towards the ,south1 the motion of it shall be towards the ,north3 but if the ,impetus of the ,water shall overcome that of the ,winde1 its motion shall be towards the ,south4 ,the discourse is excellent and would be unworthily contradicted by such as should oppose it1 saying3 ,thou mis-alledgest as ,cause of the motion of the ,bark towards the ,south1 the ,impetus of the ,stream of the ,water above that of the ,south ,winde2 mis-alledgest ,i say1 for it is the ,force of the ,north ,winde opposite to the ,south1 that is able to drive the ,bark towards the ,south4 ,such an ,objection would be superfluous1 because he which alledgeth for ,cause of the ,motion the ,stream of the ,water1 denies not but that the ,winde opposite to the ,south may do the same1 but only affirmeth that the force of the ,water prevailing over the ,south ,wind1 the ,bark shall move towards the ,south3 and saith no more than is true4 ,and just thus when ,archimedes saith1 that the ,gravity of the ,water prevailing over that by which the moveable descends to the ,bottom1 such moveable shall be raised from the ,bottom to the ,surface alledgeth a very true ,cause of such an ,accident1 nor doth he affirm or deny that there is1 or is not1 a vertue contrary to ,gravity1 called by some ,levity1 that hath also a power of moving some ,matters upwards4 ,let therefore the ,weapons of ,signor ,buonamico be directed against ,plato#be1 and other ,ancients1 who totally denying ,levity1 and taking all ,bodies to be grave1 say that the ,motion upwards is made1 not from an intrinsecal ,principle of the ,moveable1 but only by the ,impulse of the ,medium2 and let ,archimedes and his ,doctrine escape him1 since he hath given him no ,cause of quarelling with him4 ,but if this ,apologie1 produced in defence of ,archimedes1 should seem to some insufficient to free him from the ,objections and ,arguments1 produced by ,aristotle against ,plato1 and the other ,ancients1 as if they did also fight against ,archimedes1 alledging the ,impulse of the ,water as the ,cause of the swimming of some ,bodies less grave than it#bf1 ,i would not question1 but that ,i should be able to maintaine the ,doctrine of ,plato and those others to be most true1 who absolutely deny ,levity1 and affirm no other ,intrinsecal ,principle of ,motion to be in ,elementary ,bodies save only that towards the ,centre of the ,earth#bg1 nor no other ,cause of moving upwards1 speaking of that which hath the resemblance of natural ,motion1 but only the repulse of the ,medium1 fluid1 and exceeding the ,gravity of the ,moveable#bh3 and as to the ,reasons of ,aristotle on the contrary1 ,i believe that ,i could be able fully to answer them1 and ,i would assay to do it1 if it were absolutely necessary to the present ,matter1 or were it not too long a ,digression for this short ,treatise4 ,i will only say1 that if there were in some of our ,ellementary ,bodies an ,intrinsecall ,principle and ,naturall ,inclination to shun the ,centre of the ,earth1 and to move towards the ,concave of the ,moon1 such ,bodies1 without doubt1 would more swiftly ascend through those ,mediums that least oppose the ,velocity of the ,moveable1 and these are the more tenuous and subtle2 as is1 for example1 the ,air in comparison of the ,water1 we daily proving that we can with farre more expeditious ,velocity move a ,hand or a ,board to and again in one than in the other#bi3 nevertheless1 we never could finde any ,body1 that did not ascend much more swiftly in the water than in the ,air4 ,yea of ,bodies which we see continually to ascend in the ,water1 there is none that having arrived to the confines of the ,air1 do not wholly lose their ,motion#cj2 even the ,air it self1 which rising with great ,celerity through the ,water1 being once come to its ,region it loseth all #bc ,of ,natation1 ,lib4 #a4 ,prop4 #g4 #bd ,of ,natation1 ,lib4 #a4 ,prop4 #d4 #be ,plato denyeth ,positive ,levity4 #bf ,the ,authors defence of the doctrine of ,plato and the ,ancients1 who absolutely deny ,levity3 #bg ,according to ,plato there is no ,principle of the ,motion1 of descent in ,naturall ,bodies1 save that to the ,centre4 #bh ,no cause of the motion of ,ascent1 save the ,impulse of the ,medium1 exceeding the ,moveable in ,gravitie4 #bi ,bodies ascend much swifter in the ,water1 than in the ,air4 #cj ,all ,bodies ascending through ,water1 lose their ,motion1 comming to the confines of the ,air4 ,sidenote3 ,the lighter ,bodies ascend more swiftly through ,water4 ,and1 howbeit1 ,experience shewes1 that the ,bodies1 successively less grave1 do most expeditiously ascend in water1 it cannot be doubted1 but that the ,ignean ,exhalations do ascend more swiftly through the water1 than doth the ,air3 which ,air is seen by ,experience to ascend more swiftly through the ,water1 than the ,fiery ,exhalations through the ,air#ca3 ,therefore1 we must of necessity conclude1 that the said ,exhalations do much more expeditiously ascend through the ,water1 than through the ,air2 and that1 consequently1 they are moved by the ,impulse of the ,ambient ,medium1 and not by an intrinsick ,principle that is in them1 of avoiding the ,centre of the ,earth2 to which other grave ,bodies tend4 #ca ,fiery ,exhalations ascend thorow the ,water more swiftly than doth the ,air2 the ,air ascends more swiftly thorow the ,water1 than ,fire thorow the ,air4 ,sidenote3 ,the ,authors confutation of the ,peripateticks ,causes of ,natation ,submersion4 ,to that which for a finall conclusion1 ,signor ,buonamico produceth of going about to reduce the descending or not descending1 to the easie and uneasie ,division of the ,medium1 and to the predominancy of the ,elements3 ,i answer1 as to the first part1 that that cannot in any manner be admitted as a ,cause1 being that in none of the ,fluid ,mediums1 as the ,air1 the ,water1 and other ,liquids1 there is any ,resistance against ,division#cb1 but all by every the least ,force1 are divided and penetrated1 as ,i will anon demonstrate3 so1 that of such ,resistance of ,division there can be no ,act1 since it self is not in being4 ,as to the other part1 ,i say1 that the predominancy of the ,elements in ,moveables#cc1 is to be considered1 as far as to the excesse or defect of ,gravity1 in relation to the ,medium3 for in that ,action1 the ,elements operate not1 but only1 so far as they are grave or light3 therefore1 to say that the ,wood of the ,firre sinks not1 because ,air predominateth in it1 is no more than to say1 because it is less grave than the ,water4 ,yea1 even the immediate ,cause1 is its being less grave than the ,water#cd3 and it being under the predominancy of the ,air1 is the ,cause of its less ,gravity3 ,therefore1 he that alledgeth the predominancy of the ,element for a ,cause1 brings the ,cause of the ,cause1 and not the neerest and immediate ,cause4 ,now1 who knows not that the true ,cause is the immediate1 and not the mediate#ce8 ,moreover1 he that alledgeth ,gravity1 brings a ,cause most perspicuous to ,sence#cf3 ,the cause we may very easily assertain our selves2 whether ,ebony1 for example1 and ,firre1 be more or less grave than water3 but whether ,earth or ,air predominates in them1 who shall make that manifest8 ,certainly1 no ,experiment can better do it than to observe whether they swim or sink4 ,so1 that he who knows1 not whether such a ,solid swims1 unless when he knows that ,air predominates in it1 knows not whether it swim1 unless he sees it swim1 for then he knows that it swims1 when he knows that it is ,air that predominates1 but knows not that ,air hath the predominance1 unless he sees it swim3 therefore1 he knows not if it swims1 till such time as he hath seen it swim4 #cb ,water other fluids void of ,resistance against ,division4 #cc ,the predominancy of ,elements in ,moveables to be considered only in relation to their excess or defect of ,gravity in reference to the ,medium4 #cd ,the immediate ,cause of ,natation is that the ,moveable is less grave than the ,water4 #ce ,the ,peripateticks alledge for the reason of ,natation the ,cause of the ,cause4 #cf ,gravity a ,cause most perspicuous to sence4 ,let us not then despise those ,hints1 though very dark1 which ,reason1 after some contemplation1 offereth to our ,intelligence1 and lets be content to be taught by ,archimedes1 that then any ,body shall submerge in water#cg1 when it shall be specifically more grave than it1 and that if it shall be less grave#ch1 it shall of necessity swim1 and that it will rest indifferently in any place under water1 if its ,gravity be perfectly like to that of the water4 #cg ,lib #a4 of ,natation ,prop4 #g #ch ,id4 ,lib4 #a4 ,prop4 #d4 ,these things explained and proved#ci1 ,i come to consider that which offers it self1 touching what the ,diversity of figure given unto the said ,moveable hath to do with these ,motions and ,rests2 and proceed to affirme1 that1 #ci ,id4 ,lib #a4 ,prop4 #c4 ,,theoreme ,v4 ,sidenote3 ,diversity of ,figure no ,cause of its absolute ,natation or ,submersion4 ,the diversity of ,figures given to this or that ,solid1 cannot any way be a ,cause of its absolute ,sinking or ,swimming4 ,so that if a ,solid being formed1 for example1 into a ,sphericall ,figure1 doth sink or swim in the water1 ,i say1 that being formed into any other ,figure1 the same figure in the same water1 shall sink or swim3 nor can such its ,motion by the ,expansion or by other mutation of ,figure1 be impeded or taken away4 ,sidenote3 ,the ,expansion of ,figure1 retards the ,velocity of the ascent or descent of the ,moveable in the water2 but doth not deprive it of all ,motion4 ,the ,expansion of the ,figure may indeed retard its ,velocity1 aswell of ascent as descent1 and more and more according as the said ,figure is reduced to a greater breadth and thinness3 but that it may be reduced to such a form as that that same matter be wholly hindred from moving in the same water1 that ,i hold to be impossible4 ,in this ,i have met with great contradictors1 who producing some ,experiments1 and in perticular a thin ,board of ,ebony1 and a ,ball of the same ,wood1 and shewing how the ,ball in ,water descended to the bottom1 and the ,board being put lightly upon the ,water submerged not1 but rested2 have held1 and with the ,authority of ,aristotle1 confirmed themselves in their ,opinions1 that the ,cause of that ,rest was the breadth of the ,figure1 unable by its small weight to pierce and penetrate the ,resistance of the ,waters ,crassitude1 which ,resistance is readily overcome by the other ,sphericall ,figure4 ,this is the ,principal point in the present ,question1 in which ,i perswade my self to be on the right side4 ,therefore1 beginning to investigate with the examination of exquisite ,experiments that really the ,figure doth not a jot alter the descent or ,ascent of the same ,solids1 and having already demonstrated that the greater or less ,gravity of the ,solid in relation to the ,gravity of the ,medium is the cause of ,descent or ,ascent3 when ever we would make proof of that1 which about this ,effect the diversity of ,figure worketh1 its necessary to make the ,experiment with ,matter wherein variety of ,gravities hath no place4 ,for making use of ,matters which may be different in their ,specifical ,gravities1 and meeting with varieties of effects of ,ascending and ,descending1 we shall alwayes be left unsatisfied whether that diversity derive it self really from the sole ,figure1 or else from the divers ,gravity also4 ,we may remedy this by takeing one only ,matter1 that is tractable and easily reduceable into every sort of ,figure4 ,moreover1 it will be an excellent expedient to take a kinde of ,matter1 exactly alike in ,gravity unto the ,water3 for that ,matter1 as far as pertaines to the ,gravity1 is indifferent either to ,ascend or ,descend2 so that we may presently observe any the least difference that derives it self from the diversity of ,figure4 ,sidenote3 ,an ,experiment in ,wax1 that proveth ,figure to have no ,operation in ,natation ,submersion4 ,now to do this1 ,wax is most apt1 which1 besides its incapacity of receiveing any sensible alteration from its imbibing of ,water1 is ductile or pliant1 and the same piece is easily reduceable into all ,figures3 and being in ,specie a very inconsiderable matter inferiour in ,gravity to the ,water1 by mixing therewith a little of the fileings of ,lead it is reduced to a ,gravity exactly equall to that of the ,water4 ,this ,matter prepared1 and1 for example1 a ,ball being made thereof as bigge as an ,orange or biger1 and that made so grave as to sink to the bottom1 but so lightly1 that takeing thence one only ,grain of ,lead1 it returns to the top1 and being added1 it submergeth to the bottom1 let the same ,wax afterwards be made into a very broad and thin ,flake or ,cake2 and then1 returning to make the same ,experiment1 you shall see that it being put to the bottom1 it shall1 with the ,grain of ,lead rest below1 and that ,grain deducted1 it shall ascend to the very ,surface1 and added again it shall dive to the bottom4 ,and this same effect shall happen alwaies in all sort of ,figures1 as wel regular as irregular3 nor shall you ever finde any that will swim without the removall of the ,grain of ,lead1 or sinke to the bottom unless it be added3 and1 in short1 about the going or not going to the ,bottom1 you shall discover no diversity1 although1 indeed1 you shall about the quick and slow descent3 for the more expatiated and distended ,figures move more slowly aswel in the diveing to the bottom as in the rising to the top2 and the other more contracted and compact ,figures1 more speedily4 ,now ,i know not what may be expected from the diversity of ,figures1 if the most contrary to one another operate not so much as doth a very small ,grain of ,lead1 added or removed4 ,me thinkes ,i hear some of the ,adversaries to raise a doubt upon my produced ,experiment#dj4 ,and first that they offer to my consideration1 that the ,figure1 as a ,figure simply1 and disjunct from the ,matter workes not any effect1 but requires to be conjoyned with the ,matter2 and1 furthermore1 not with every ,matter1 but with those only1 wherewith it may be able to execute the desired operation4 ,like as we see it verified by ,experience1 that the ,acute and sharp ,angle is more apt to cut1 than the ,obtuse2 yet alwaies provided1 that both the one and the other1 be joyned with a ,matter apt to cut1 as for example1 with ,steel4 ,therefore1 a ,knife with a fine and sharp edge1 cuts ,bread or ,wood with much ease1 which it will not do1 if the edge be blunt and thick3 but he that will instead of ,steel1 take ,wax1 and mould it into a ,knife1 undoubtedly shall never know the effects of sharp and blunt edges3 because neither of them will cut1 the ,wax being unable by reason of its flexibility1 to overcome the hardness of the ,wood and ,bread4 ,and1 therefore1 applying the like discourse to our purpose1 they say1 that the difference of ,figure will shew different effects1 touching ,natation and ,submersion1 but not conjoyned with any kind of ,matter1 but only with those ,matters which1 by their ,gravity1 are apt to resist the ,velocity of the water1 whence he that would elect for the ,matter1 ,cork or other light wood1 unable1 through its ,levity1 to superate the ,crassitude of the water1 and of that ,matter should forme ,solids of divers ,figures1 would in vain seek to find out what operation ,figure hath in ,natation or ,submersion2 because all would swim1 and that not through any property of this or that ,figure1 but through the debility of the ,matter1 wanting so much ,gravity1 as is requisite to superate and overcome the ,density and ,crassitude of the water4 #dj ,an objection against the ,experiment in ,water4 ,its needfull1 therefore1 if wee would see the effect wrought by the ,diversity of ,figure1 first to make choice of a ,matter of its nature apt to penetrate the ,crassitude of the water4 ,and1 for this effect#da1 they have made choice of such a ,matter1 as fit1 that being readily reduced into ,sphericall ,figure1 goes to the ,bottom2 and it is ,ebony1 of which they afterwards making a small ,board or ,splinter1 as thin as a ,lath1 have illustrated how that this1 put upon the ,surface of the water1 rests there without descending to the ,bottom3 and making1 on the otherside1 of the same wood a ,ball1 no less than a hazell ,nut1 they shew1 that this swims not1 but descendes4 ,from which ,experiment1 they think they may frankly conclude1 that the ,breadth of the ,figure in the flat ,lath or ,board1 is the cause of its not descending to the ,bottom1 for as much as a ,ball of the same ,matter1 not different from the ,board in any thing but in ,figure1 submergeth in the same water to the ,bottom4 ,the discourse and the ,experiment hath really so much of probability and likelyhood of truth in it1 that it would be no wonder1 if many perswaded by a certain cursory observation1 should yield credit to it2 nevertheless1 ,i think ,i am able to discover1 how that it is not free from falacy4 #da ,an ,experiment in ,ebany1 brought to disprove the ,experiment in ,wax4 ,beginning1 therefore1 to examine one by one1 all the particulars that have been produced1 ,i say1 that ,figures1 as simple ,figures1 not only operate not in naturall things1 but neither are they ever seperated from the ,corporeall substance#db3 nor have ,i ever alledged them stript of sensible ,matter1 like as also ,i freely admit1 that in our endeavouring to examine the ,diversity of ,accidents1 dependant upon the variety of ,figures1 it is necessary to apply them to ,matters1 which obstruct not the various operations of those various ,figures3 and ,i admit and grant1 that ,i should do very ill2 if ,i would experiment the influence of ,acutenesse of edge with a ,knife of ,wax1 applying it to cut an ,oak1 because there is no ,acuteness in ,wax able to cut that very hard wood4 ,but yet such an ,experiment of this ,knife1 would not be besides the purpose1 to cut curded ,milk1 or other very yielding ,matter3 yea1 in such like ,matters1 the ,wax is more commodious than ,steel2 for finding the diversity depending upon ,angles1 more or less ,acute1 for that ,milk is indifferently cut with a ,raisor1 and with a ,knife1 that hath a blunt edge4 ,it needs1 therefore1 that regard be had1 not only to the hardness1 solidity or ,gravity of ,bodies1 which under divers figures1 are to divide and penetrate some ,matters1 but it forceth also1 that regard be had1 on the other side1 to the ,resistance of the ,matters1 to be divided and penetrated4 ,but since ,i have in making the ,experiment concerning our ,contest2 chosen a ,matter which penetrates the ,resistance of the water2 and in all figures descendes to the ,bottome1 the ,adversaries can charge me with no defect2 yea1 ,i have propounded so much a more excellent ,method than they1 in as much as ,i have removed all other ,causes1 of descending or not descending to the ,bottom1 and retained the only sole and pure variety of ,figures1 demonstrating that the same ,figures all descende with the only alteration of a ,grain in weight3 which ,grain being removed1 they return to float and swim2 it is not true1 therefore1 7resuming the ,example by them introduced7 that ,i have gone about to experiment the efficacy of ,acuteness1 in cutting with ,matters unable to cut1 but with ,matters proportioned to our occasion1 since they are subjected to no other variety1 then that alone which depends on the ,figure more or less acute4 #db ,figure is unseperable from ,corporeall ,substance4 ,sidenote3 ,the answer to the ,objection against the ,experiment of the ,wax4 ,but let us proceed a little farther1 and observe1 how that indeed the ,consideration1 which1 they say1 ought to be had about the ,election of the ,matter1 to the end1 that it may be proportionate for the making of our experiment1 is needlessly introduced1 declaring by the example of ,cutting1 that like as ,acuteness is inefficient to cut1 unless when it is in a ,matter hard and apt to superate the ,resistance of the wood or other ,matter1 which we intend to cut2 so the aptitude of descending or not descending in water1 ought and can only be known in those ,matters1 that are able to overcome the ,renitence1 and superate the ,crassitude of the water4 ,unto which1 ,i say1 that to make distinction and election1 more of this than of that ,matter1 on which to impress the ,figures for cutting or penetrating this or that ,body1 as the solidity or obdurateness of the said ,bodies shall be greater or less1 is very necessary3 but withall ,i subjoyn1 that such distinction1 election and caution would be superfluous and unprofitable1 if the ,body to be cut or penetrated1 should have no ,resistance1 or should not at all withstand the ,cutting or ,penitration3 and if the ,knife were to be used in cutting a ,mist or ,smoak1 one of ,paper would be equally serviceable with one of ,damascus ,steel3 and so by reason the water hath not any ,resistance against the ,penitration of any ,solid ,body1 all choice of ,matter is superfluous and needless1 and the ,election which ,i said above to have been well made of a ,matter reciprocall in ,gravity to water1 was not because it was necessary1 for the overcoming of the crassitude of the water1 but its ,gravity1 with which only it resists the sinking of ,solid ,bodies3 and for what concerneth the ,resistance of the crassitude1 if we narrowly consider it1 we shall find that all ,solid ,bodies1 as well those that sink1 as those that swim1 are indifferently accomodated and apt to bring us to the knowledge of the truth in question4 ,nor will ,i be frighted out of the belief of these ,conclusions1 by the ,experiments which may be produced against me1 of many severall ,woods1 ,corks1 ,galls1 and1 moreover1 of subtle slates and plates of all sorts of ,stone and ,mettall1 apt by means of their ,naturall ,gravity1 to move towards the ,centre of the ,earth1 the which1 nevertheless1 being impotent1 either through the ,figure 7as the ,adversaries thinke7 or through ,levity1 to break and penetrate the ,continuity of the parts of the water1 and to distract its union1 do continue to swimm without submerging in the least3 nor on the other side1 shall the ,authority of ,aristotle move me1 who in more than one place1 affirmeth the contrary to this1 which ,experience shews me4 ,sidenote3 ,no ,solid of such ,levity1 nor of such ,figure1 but that it doth penetrate the ,crassitude of the ,water4 ,sidenote3 ,bodies of all ,figures1 laid upon the water1 do penetrate its ,crassitude1 and in what proportion4 ,i return1 therefore1 to assert1 that there is not any ,solid of such ,levity1 nor of such ,figure1 that being put upon the water1 doth not divide and penetrate its ,crassitude3 yea if any with a more perspicatious eye1 shall return to observe more exactly the thin ,boards of ,wood1 he shall see them to be with part of their thickness under water1 and not only with their inferiour ,superficies1 to kisse the ,superiour of the water1 as they of necessity must have believed1 who have said1 that such ,boards submerge not1 as not being able to divide the ,tenacity of the parts of the water3 and1 moreover1 he shall see1 that subtle shivers of ,ebony1 ,stone or ,metall1 when they float1 have not only broak the ,continuity of the water1 but are with all their thickness1 under the ,surface of it2 and more and more1 according as the ,matters are more grave3 so that a thin ,plate of ,lead1 shall be lower than the ,surface of the circumfused water1 by at least twelve times the thickness of the ,plate1 and ,gold shall dive below the ,levell of the water1 almost twenty times the thickness of the ,plate1 as ,i shall anon declare4 ,but let us proceed to evince1 that the water yields and suffers it self to be penetrated by every the lightest ,body2 and therewithall demonstrate1 how1 even by ,matters that submerge not1 we may come to know that ,figure operates nothing about the going or not going to the ,bottom1 seeing that the water suffers it self to be penetrated equally by every ,figure4 ,sidenote3 ,the ,experiment of a ,cone1 demitted with its ,base1 and after with its ,point downwards4 ,make a ,cone1 or a ,piramis of ,cypress1 of ,firre1 or of other ,wood of like ,gravity1 or of pure ,wax1 and let its height be somewhat great1 namely a handfull1 or more1 and put it into the water with the ,base downwards3 first1 you shall see that it will penetrate the water1 nor shall it be at all impeded by the largeness of the ,base1 nor yet shall it sink all under water1 but the part towards the point shall lye above it3 by which shall be manifest1 first1 that that ,solid forbeares not to sink out of an inability to divide the ,continuity of the water1 having already divided it with its broad part1 that in the opinion of the ,adversaries is the less apt to make the division4 ,the ,piramid being thus fixed1 note what part of it shall be submerged1 and revert it afterwards with the point downwards1 and you shall see that it shall not dive into the water more than before1 but if you observe how far it shall sink1 every person expert in ,geometry1 may measure1 that those parts that remain out of the water1 both in the one and in the other ,experiment are equall to an hair3 whence he may manifestly conclude1 that the acute ,figure which seemed most apt to part and penetrate the water1 doth not part or penetrate it more than the large and spacious4 ,and he that would have a more easie ,experiment1 let him take two ,cylinders of the same ,matter1 one long and small1 and the other short1 but very broad1 and let him put them in the water1 not distended1 but erect and endways3 he shall see1 if he diligently measure the parts of the one and of the other1 that in each of them the part submerged1 retains exactly the same proportion to that out of the water1 and that no greater part is submerged of that long and small one1 than of the other more spacious and broad3 howbeit1 this rests upon a very large1 and that upon a very little ,superficies of water3 therefore the diversity of ,figure1 occasioneth neither facility1 nor difficulty1 in parting and penetrating the ,continuity of the water1 and1 consequently1 cannot be the ,cause of the ,natation or ,submersion4 ,he may likewise discover the non operating of variety of ,figures1 in arising from the ,bottom of the water1 towards the ,surface1 by taking ,wax1 and tempering it with a competent quantity of the filings of ,lead1 so that it may become a considerable matter graver than the water3 then let him make it into a ,ball1 and thrust it unto the ,bottom of the water2 and fasten to it as much ,cork1 or other light matter1 as just serveth to raise it1 and draw it towards the ,surface3 for afterwards changing the same ,wax into a thin ,cake1 or into any other ,figure1 that same ,cork shall raise it in the same manner to a hair4 ,this silenceth not my ,antagonists1 but they say1 that all the discourse hitherto made by me little importeth to them1 and that it serves their turn1 that they have demonstrated in one only particular1 and in what matter1 and under what ,figure pleaseth them1 namely1 in a ,board and in a ,ball of ,ebony1 that this put in the water1 descends to the ,bottom1 and that stays atop to swim3 and the ,matter being the same1 and the two ,bodies differing in nothing but in ,figure1 they affirm1 that they have with all perspicuity demonstrated and sensibly manifested what they undertook2 and lastly1 that they have obtained their intent4 ,nevertheless1 ,i believe1 and thinke1 ,i can demonstrate1 that that same ,experiment proveth nothing against my ,conclusion4 ,sidenote3 ,in ,experiments of ,natation1 the ,solid is to be put into1 not upon the water4 ,and first1 it is false1 that the ,ball descends1 and the ,board not3 for the ,board shall also descend1 if you do to both the ,figures1 as the words of our ,question requireth2 that is1 if you put them both into the water4 ,sidenote3 ,the ,question of ,natation stated4 ,the words were these4 ,that the ,antagonists having an opinion1 that the ,figure would alter the ,solid ,bodies1 in relation to the descending or not descending1 ascending or not ascending in the same ,medium1 as v4 gr4 in the same water1 in such sort1 that1 for ,example1 a ,solid that being of a ,sphericall ,figure1 shall descend to the ,bottom1 being reduced into some other ,figure1 shall not descend3 ,i holding the contrary1 do affirm1 that a ,corporeall ,solid ,body1 which reduced into a ,sphericall ,figure1 or any other1 shall go to the ,bottom1 shall do the like under whatsoever other ,figure1 c4 ,sidenote3 ,place defined according to ,aristotle4 ,but to be in the water1 implies to be placed in the water1 and by ,aristotles own ,definition of place1 to be placed1 importeth to be invironed by the ,superficies of the ,ambient ,body1 therefore1 then shall the two ,figures be in the water1 when the ,superficies of the water1 shall imbrace and inviron them3 but when the ,adversaries shew the ,board of ,ebony not descending to the ,bottom1 they put it not into the water1 but upon the water1 where being by a certain impediment 7as by and by we will shew7 retained1 it is invironed1 part by water1 and part by air1 which thing is contrary to our agreement1 that was1 that the ,bodies should be in the water1 and not part in water1 and part in air4 ,the which is again made manifest1 by the questions being put as well about the things which go to the ,bottom1 as those which arise from the ,bottom to swimme1 and who sees not that things placed in the ,bottom1 must have water about them4 ,sidenote3 ,the confutation of the ,experiment in the ,ebany4 ,it is now to be noted1 that the ,board of ,ebany and the ,ball1 put into the water1 both sink1 but the ,ball more swiftly1 and the ,board more slowly2 and slower and slower1 according as it shall be more broad and thin1 and of this ,tardity the breadth of the ,figure is the true ,cause3 ,but these broad ,boards that slowly descend1 are the same1 that being put lightly upon the water1 do swimm3 ,therefore1 if that were true which the ,adversaries affirm1 the same numerical ,figure1 would in the same numericall water1 cause one while ,rest1 and another while ,tardity of ,motion1 which is impossible3 for every perticular ,figure which descends to the ,bottom#dc1 hath of necessity its own determinate ,tardity and slowness1 proper and naturall unto it1 according to which it moveth1 so that every other ,tardity1 greater or lesser is improper to its nature3 if1 therefore1 a ,board1 as suppose of a foot square1 descendeth naturally with six degrees of ,tardity1 it is impossible1 that it should descend with ten or twenty1 unless some new impediment do arrest it4 ,much less can it1 by reason of the same ,figure rest1 and wholly cease to move2 but it is necessary1 that when ever it resteth1 there do some greater impediment intervene than the breadth of the ,figure4 ,therefore1 it must be somewhat else1 and not the ,figure1 that stayeth the ,board of ,ebany above water1 of which ,figure the only ,effect is the retardment of the ,motion1 according to which it descendeth more slowly than the ,ball4 ,let it be confessed1 therefore1 rationally discoursing1 that the true and sole ,cause of the ,ebanys going to the ,bottom1 is the excess of its ,gravity above the ,gravity of the water3 and the ,cause of the greater or less ,tardity1 the breadth of this ,figure1 or the contractedness of that3 but of its ,rest1 it can by no means be allowed1 that the quallity of the ,figure1 is the ,cause thereof3 aswell1 because1 making the ,tardity greater1 according as the ,figure more dilateth1 there cannot be so immense a ,dilatation1 to which there may not be found a correspondent immence ,tardity without redusing it to ,nullity of ,motion2 as1 because the ,figures produced by the ,antagonists for effecters of ,rest1 are the self same that do also go to the ,bottom4 #dc ,every perticular ,figure hath its own peculiar ,tardity4 ,i will not omit another reason1 founded also upon ,experience1 and if ,i deceive not my self1 manifestly concluding1 how that the ,introduction of the breadth or amplitude of ,figure1 and the ,resistance of the water against penetration1 have nothing to do in the ,effect of descending1 or ascending1 or resting in the water4 ,d,take a piece of wood or other ,matter1 of which a ,ball ascends from the ,bottom of the water to the ,surface1 more slowly than a ,ball of ,ebony of the same bignesse1 so that it is manifest1 that the ,ball of ,ebony more readily divideth the water in descending1 than the other in ascending2 as for ,example1 let the ,wood be ,walnut-tree4 ,then take a ,board of ,walnut-tree1 like and equall to that of ,ebony of the ,antagonists1 which swims2 and if it be true1 that this floats above water1 by reason of the ,figure1 unable through its breadth1 to pierce the ,crassitude of the same1 the other of ,wallnut-tree1 without all question1 being thrust unto the ,bottom1 will stay there1 as less apt1 through the same impediment of ,figure1 to divide the said ,resistance of the water4 ,but if we shall find1 and by experience see1 that not only the thin ,board1 but every other ,figure of the same ,wallnut-tree will return to float1 as undoubtedly we shall1 then ,i must desier my opposers to forbear to attribute the floating of the ,ebony1 unto the ,figure of the ,board1 in regard that the ,resistance of the water is the same1 as well to the ascent1 as to the descent1 and the force of the ,wallnut-trees ascension1 is lesse than the ,ebonys force in going to the ,bottom4 ,d ,the ,figure ,resistance of the ,medium against ,division1 have nothing to do with the ,effect of ,natation or ,submersion1 by an ,experiment in ,wallnut tree4 ,sidenote3 ,an ,experiment in ,gold1 to prove the non-operating of ,figure in ,natation and ,submersion4 ,nay1 ,i will say more1 that if we shall consider ,gold in comparison of water1 we shall find1 that it exceeds it in ,gravity almost twenty times1 so that the ,force and ,impetus1 wherewith a ,ball of ,gold goes to the ,bottom1 is very great4 ,on the contrary1 there want not matters1 as ,virgins ,wax1 and some ,woods1 which are not above a fiftieth part less grave than water1 whereupon their ,ascension therein is very slow1 and a thousand times weaker than the ,impetus of the ,golds descent3 yet notwithstanding1 a plate of ,gold swims without descending to the ,bottom1 and1 on the contrary1 we cannot make a ,cake of ,wax1 or thin ,board of ,wood1 which put in the ,bottom of the ,water1 shall rest there without ascending4 ,now if the ,figure can obstruct the ,penetration1 and impede the descent of ,gold1 that hath so great an ,impetus1 how can it choose but suffice to resist the same ,penetration of the other matter in ascending1 when as it hath scarce a thousandth part of the ,impetus that the ,gold hath in descending8 ,its therefore1 necessary1 that that which suspends the thin ,plate of ,gold1 or ,board of ,ebony1 upon the water1 be some thing that is wanting to the other ,cakes and ,boards of ,matters less grave than the water2 since that being put to the ,bottom1 and left at liberty1 they rise up to the ,surface1 without any obstruction3 ,but they want not for flatness and breadth of ,figure3 ,therefore1 the spaciousnesse of the ,figure1 is not that which makes the ,gold and ,ebony to swim4 ,and1 because1 that the excess of their ,gravity above the ,gravity of the water1 is questionless the ,cause of the sinking of the flat piece of ,ebony1 and the thin ,plate of ,gold1 when they go to the ,bottom1 therefore1 of necessity1 when they float1 the ,cause of their staying above water1 proceeds from ,levity1 which in that case1 by some ,accident1 peradventure not hitherto observed1 cometh to meet with the said ,board1 rendering it no longer as it was before1 whilst it did sink more ponderous than the water1 but less4 ,now1 let us return to take the thin ,plate of ,gold1 or of ,silver1 or the thin ,board of ,ebony1 and let us lay it lightly upon the water1 so that it stay there without sinking1 and diligently observe its effect4 ,and first1 see how false the assertion of ,aristotle1 and our oponents is1 to wit1 that it stayeth above water1 through its unability to pierce and penetrate the ,resistance of the waters ,crassitude3 for it will manifestly appear1 not only that the said ,plates have penetrated the water1 but also that they are a considerable matter lower than the ,surface of the same1 the which continueth eminent1 and maketh as it were a ,rampert on all sides1 round about the said ,plates1 the profundity of which they stay swimming3 and1 according as the said ,plates shall be more grave than the water1 two1 four1 ten or twenty times1 it is necessary1 that their ,superficies do stay below the universall ,surface of the water1 so much more1 than the thickness of those ,plates1 as we shal more distinctly shew anon4 ,in the mean space1 for the more easie understanding of what ,i say1 observe with me a little the present ,scheme3 in which let us suppose the ,surface of the water to be distended1 according to the ,lines ,f ,l ,d ,b1 upon which if one shall put a board of matter specifically more grave than water1 but so lightly that it submerge not1 it shall not rest any thing above1 but shall enter with its whole thickness into the water3 and1 moreover1 shall sink also1 as we see by the ,board ,a ,i1 ,o ,i1 whose breadth is wholly sunk into the water1 the little ,ramperts of water ,l ,a and ,d ,o incompassing it1 whose ,superficies is notably higher than the ,superficies of the ,board4 ,see now whether it be true1 that the said ,board goes not to the ,bottom1 as being of ,figure unapt to penetrate the ,crassitude of the water4 ,illustration ,sidenote3 ,why solids having penitrated the ,water1 do not proceed to a totall ,submersion4 ,but1 if it hath already penetrated1 and overcome the ,continuity of the water1 is of its own nature more grave than the said water1 why doth it not proceed in its sinking1 but stop and suspend its self within that little dimple or cavitie1 which with its ponderosity it hath made in the water8 ,i answer2 because that in submerging it self1 so far as till its ,superficies come to the ,levell with that of the water1 it loseth a part of its ,gravity1 and loseth the rest of it as it submergeth descends beneath the ,surface of the water1 which maketh ,ramperts and ,banks round about it1 and it sustaines this loss by means of its drawing after it1 and carrying along with it1 the ,air that is above it1 and by ,contact adherent to it1 which ,air succeeds to fill the ,cavity that is invironed by the ,ramperts of water2 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 composition of ,ebony and ,air1 from which resulteth a ,solid no longer superiour in ,gravity to the water1 as was the simple ,ebony1 or the simple ,gold4 ,and1 if we exactly consider1 what1 and how great the ,solid is1 that in this ,experiment enters into the water1 and contrasts with the ,gravity of the same1 it will be found to be all that which we find to be beneath the ,surface of the water1 the which is an aggregate and ,compound of a ,board of ,ebony1 and of almost the like quantity of ,air1 or a ,mass compounded of a ,plate of ,lead1 and ten or twelve times as much ,air4 ,but1 ,gentlemen1 you that are my ,antagonists in our ,question1 we require the ,identity of ,matter1 and the alteration only of the ,figure2 therefore1 you must remove that ,air1 which being conjoyned with the ,board1 makes it become another ,body less grave than the ,water1 and put only the ,ebony into the ,water1 and you shall certainly see the ,board descend to the ,bottom2 and1 if that do not happen1 you have got the day4 ,and to seperate the ,air from the ,ebony#dd1 there needs no more but only to bath the ,superficies of the said ,board with the same ,water3 for the ,water being thus interposed between the ,board and the ,air1 the other circumfused ,water shall run together without any impediment1 and shall receive into it the sole and bare ,ebony1 as it was to do4 #dd ,how to seperate the ,air from ,solids in demitting them into the water4 ,but1 me thinks ,i hear some of the ,adversaries cunningly opposing this1 and telling me1 that they will not yield1 by any means1 that their ,board be wetted1 because the weight added thereto by the ,water1 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 was1 that the ,matter be the same4 ,to this1 ,i answer1 first2 that treating of the operation of ,figure in ,bodies put into the ,water1 none can suppose them to be put into the ,water without being wet2 nor do ,i desire more to be done to the ,board1 then ,i will give you leave to do to the ,ball4 ,moreover1 it is untrue1 that the ,board sinks by vertue of the new ,weight added to it by the ,water1 in the single and slight bathing of it3 for ,i will put ten or twenty drops of ,water upon the same ,board1 whilst it is sustained upon the water2 which drops1 because not conjoyned with the other ,water circumfused1 shall not so encrease the weight of it1 as to make it sink3 but if the ,board being taken out1 and all the water wiped off that was added thereto1 ,i should bath all its ,superficies with one only very small drop1 and put it again upon the water1 without doubt it shall sink1 the other ,water running to cover it1 not being retained by the superiour ,air2 which ,air by the interposition of the thin vail of water1 that takes away its ,contiguity unto the ,ebony1 shall without ,renitence be seperated1 nor doth it in the least oppose the succession of the other ,water3 but rather1 to speak better1 it shall descend freely2 because it shall be all invironed and covered with water1 as soon as its superiour ,superficies1 before vailed with water1 doth arrive to the ,levell of the universall ,surface of the said water4 ,to say1 in the next place1 that water can encrease the weight of things that are demitted into it1 is most false2 for water hath no ,gravity in water#de1 since it descends not3 yea1 if we would well consider what any immense ,mass of water doth put upon a grave ,body2 that is placed in it1 we shall find experimentally1 that it1 on the contrary1 will rather in a great part deminish the weight of it#df1 and that we may be able to lift an huge ,stone from the ,bottom of the water1 which the water being removed1 we are not able to stir4 ,nor let them tell me by way of reply1 that although the superposed water augment not the ,gravity of things that are in it1 yet it increaseth the ponderosity of those that swim1 and are part in the water and part in the ,air1 as is seen1 for ,example1 in a ,brass ,ketle#dg1 which whilst it is empty of water1 and replenished only with ,air shall swim1 but pouring of ,water therein1 it shall become so grave1 that it shall sink to the ,bottom1 and that by reason of the new weight added thereto4 ,to this ,i will return answer1 as above1 that the ,gravity of the ,water1 contained in the ,vessel is not that which sinks it to the ,bottom1 but the proper ,gravity of the ,brass1 superiour to the ,specificall ,gravity of the ,water3 for if the ,vessel were less grave than water1 the ,ocean would not suffice to submerge it#dh4 ,and1 give me leave to repeat it again1 as the fundamentall and principall point in this ,case1 that the ,air contained in this ,vessel before the infusion of the ,water1 was that which kept it a-float#di1 since that there was made of it1 and of the ,brass1 a ,composition less grave than an equall quantity of ,water3 and the place that the ,vessel occupyeth in the ,water whilst it floats1 is not equall to the ,brass alone1 but to the ,brass and to the ,air together1 which filleth that part of the ,vessel that is below the ,levell of the water3 ,moreover1 when the ,water is infused1 the ,air is removed1 and there is a composition made of ,brass and of water1 more grave in specie than the simple water1 but not by vertue of the water infused1 as having greater ,specifick ,gravity than the other water1 but through the proper ,gravity of the ,brass1 and through the alienation of the ,air4 ,now1 as he that should say that ,brass1 that by its nature goes to the ,bottom1 being formed into the ,figure of a ,ketle#ej1 acquireth from that ,figure a vertue of lying in the ,water without sinking1 would say that which is false2 because that ,brass fashioned into any whatever ,figure1 goeth always to the ,bottom1 provided1 that that which is put into the water be simple ,brass2 and it is not the ,figure of the ,vessel that makes the ,brass to float1 but it is because that that is not purely ,brass which is put into the water1 but an aggregate of ,brass and of ,air3 so is it neither more nor less false1 that a thin ,plate of ,brass or of ,ebony1 swims by vertue of its dilated broad ,figure3 for the truth is1 that it bares up without submerging1 because that that which is put in the water1 is not pure ,brass or simple ,ebony1 but an aggregate of ,brass and ,air1 or of ,ebony and ,air4 ,and1 this is not contrary unto my ,conclusion1 the which1 7having many a time seen ,vessels of ,mettall1 and thin pieces of diverse grave ,matters float1 by vertue of the ,air conjoyned with them7 did affirm1 ,that ,figure was not the ,cause of the ,natation or ,submersion of such ,solids as were placed in the water4 ,nay more1 ,i cannot omit1 but must tell my ,antagonists1 that this new conceit of denying that the ,superficies of the ,board should be bathed1 may beget in a third person an opinion of a poverty of ,arguments of defence on their part1 since that such bathing was never insisted upon by them in the beginning of our ,dispute1 and was not questioned in the least1 being that the ,originall of the discourse arose upon the swiming of ,flakes of ,ice1 wherein it would be simplicity to require that their ,superficies might bedry3 besides1 that whether these pieces of ,ice be wet or dry they alwayes swim1 and as the ,adversaries say1 by reason of the ,figure4 #de ,water hath no ,gravity in ,water4 #df ,water deminisheth the ,gravity of ,solids immerged therein4 #dg ,the ,experiment of a brass ,ketle swiming when empty1 sinking when full1 alledged to prove that water gravitates in water1 answered4 #dh ,an ,ocean sufficeth not to sink a ,vessel specifically less grave than water4 #di ,air1 the ,cause of the ,natation of empty ,vessels of ,matters graver in specie than the water4 #ej ,neither ,figure1 nor the breadth of ,figure1 is the ,cause of ,natation4 ,some peradventure1 by way of defence1 may say1 that wetting the ,board of ,ebony1 and that in the superiour ,superficies1 it would1 though of it self unable to pierce and penetrate the water1 be born downwards1 if not by the weight of the additionall water1 at least by that desire and propension that the superiour parts of the water have to re-unite and rejoyn themselves3 by the ,motion of which parts1 the said ,board cometh in a certain manner1 to be depressed downwards4 ,sidenote3 ,the ,bathed ,solid descends not out of any affectation of union in the upper parts of the water4 ,this weak ,refuge will be removed1 if we do but consider1 that the repugnancy of the inferiour parts of the water1 is as great against ,dis-union1 as the ,inclination of its superiour parts is to union3 nor can the uper unite themselves without depressing the board1 nor can it descend without disuniting the parts of the nether ,water3 so that it doth follow1 by necessary consequence1 that for those respects1 it shall not descend4 ,moreover1 the same that may be said of the upper parts of the water1 may with equall reason be said of the nether1 namely1 that desiring to unite1 they shall force the said ,board upwards4 ,happily1 some of these ,gentlemen that dissent from me1 will wonder1 that ,i affirm1 that the contiguous superiour ,air is able to sustain that ,plate of ,brass or of ,silver1 that stayeth above water2 as if ,i would in a certain sence allow the ,air#ea1 a kind of ,magnetick vertue of sustaining the grave ,bodies1 with which it is contiguous4 ,to satisfie all ,i may1 to all doubts1 ,i have been considering how by some other sensible ,experiment ,i might demonstrate1 how truly that little contiguous and superiour ,air sustaines those ,solids1 which being by nature apt to descend to the ,bottom1 being placed lightly on the water submerge not1 unless they be first thorowly bathed2 and have found1 that one of these ,bodies having descended to the ,bottom1 by conveighing to it 7without touching it in the least7 a little ,air1 which conjoyneth with the top of the same1 it becometh sufficient1 not only1 as before to sustain it1 but also to raise it1 and to carry it back to the top1 where it stays and abideth in the same manner1 till such time1 as the assistance of the conjoyned ,air is taken away4 ,and to this effect1 ,i have taken a ,ball of ,wax1 and made it with a little ,lead1 so grave1 that it leasurely descends to the ,bottom1 making with all its ,superficies very smooth and pollite3 and this being put gently into the water1 almost wholly submergeth1 there remaining vissible only a little of the very top#eb1 the which so long as it is conjoyned with the ,air1 shall retain the ,ball a-top1 but the ,contiguity of the ,air taken away by wetting it1 it shall descend to the ,bottom and there remain4 ,now to make it by vertue of the ,air1 that before sustained it to return again to the top1 and stay there1 thrust into the water a ,glass reversed with the mouth downwards1 the which shall carry with it the ,air it contains1 and move this towards the ,ball1 abasing it till such time that you see1 by the transparency of the ,glass1 that the contained ,air do arrive to the summity of the ,ball#ec3 then gently withdraw the ,glass upwards1 and you shall see the ,ball to rise1 and afterwards stay on the top of the water#ed1 if you carefully part the ,glass and the water without overmuch commoving and disturbing it4 ,there is1 therefore1 a certain affinity between the ,air and other ,bodies1 which holds them unied1 so1 that they seperate not without a kind of violence4 ,the same likewise is seen in the water#ee2 for if we shall wholly submerge some ,body in it1 so that it be thorowly bathed1 in the drawing of it afterwards gently out again1 we shall see the water follow it1 and rise notably above its ,surface1 before it seperates from it4 ,solid ,bodies1 also#ef1 if they be equall and alike in ,superficies1 so1 that they make an exact ,contact without the interposition of the least ,air1 that may part them in the seperation and yield untill that the ambient ,medium succeeds to replenish the place1 do hold very firmly conjoyned1 and are not to be seperated without great force but1 because1 the ,air1 ,water1 and other ,liquids1 very expeditiously shape themselves to contact with any ,solid ,bodies1 so that their ,superficies do exquisitely adopt themselves to that of the ,solids1 without any thing remaining between them1 therefore1 the effect of this ,conjunction and ,adherence is more manifestly and frequently observed in them1 than in hard and inflexible ,bodies1 whose ,superficies do very rarely conjoyn with exactness of ,contact#eg4 ,this is therefore that ,magnetick vertue1 which with firm ,connection conjoyneth all ,bodies1 that do touch without the interposition of flexible fluids2 and1 who knows1 but that that a ,contact1 when it is very exact1 may be a sufficient ,cause of the ,union and ,continuity of the parts of a naturall ,body8 #ea ,a ,magnetisme in the ,air1 by which it bears up those ,solids in the water1 that are contiguous with it4 #eb ,the ,effect of the ,airs ,contiguity in the ,natation of ,solids4 #ec ,the force of ,contact4 #ed ,an ,affectation of ,conjunction betwixt ,solids and the ,air contiguous to them4 #ee ,the like affectation of ,conjunction betwixt ,solids the water4 #ef ,also the like affectation and ,conjunction betwixt ,solids themselves4 #eg ,contact may be the ,cause of the ,continuity of ,naturall ,bodies4 ,now1 pursuing my purpose1 ,i say2 that it needs not1 that we have recourse to the ,tenacity1 that the parts of the water have amongst themselves1 by which they resist and oppose ,division1 ,distraction1 and ,seperation1 because there is no such ,coherence and ,resistance of ,division for if there were1 it would be no less in the internall parts than in those nearer the superiour or externall ,surface1 so that the same ,board1 finding alwayes the same ,resistance and ,renitence1 would no less stop in the middle of the water than about the ,surface1 which is false4 ,moreover1 what ,resistance can we place in the ,continuity of the water1 if we see that it is impossible to find any ,body of whatsoever ,matter1 ,figure or ,magnitude1 which being put into the water1 shall be obstructed and impeded by the ,tenacity of the parts of the water to one another1 so1 but that it is moved upwards or downwards1 according as the ,cause of their ,motion transports it8 ,and1 what greater proof of it can we desier1 than that which we daily see in ,muddy waters1 which being put into ,vessels to be drunk1 and being1 after some hours setling#eh1 still1 as we say1 thick in the end1 after four or six dayes they are wholly setled1 and become pure and clear8 ,nor can their ,resistance of ,penetration stay those impalpable and insensible ,atomes of ,sand1 which by reason of their exceeding small force1 spend six dayes in descending the space of half a yard4 #eh ,the settlement of ,muddy ,water1 proveth that that ,element hath no aversion to ,division4 ,nor let them say1 that the seeing of such small ,bodies1 consume six dayes in descending so little a way1 is a sufficient ,argument of the ,waters ,resistance of ,division2 because that is no resisting of ,division1 but a retarding of ,motion2 and it would be simplicity to say1 that a thing opposeth ,division#ei1 and that in the same instant1 it permits it self to be divided3 nor doth the ,retardation of ,motion at all favour the ,adversaries cause1 for that they are to instance in a thing that wholly prohibiteth ,motion1 and procureth ,rest2 it is necessary1 therefore1 to find out ,bodies that stay in the water1 if one would shew its repugnancy to ,division1 and not such as move in it1 howbeit but slowly4 #ei ,water cannot oppose division1 and at the same time permit it self to be divided4 ,what then is this ,crassitude of the water1 with which it resisteth ,division8 ,what1 ,i beseech you1 should it be1 if we 7as we have said above7 with all diligence attempting the reduction of a ,matter into so like a ,gravity with the water1 that forming it into a dilated ,plate it rests suspended as we have said1 between the two waters1 it be impossible to effect it1 though we bring them to such an ,equiponderance1 that as much ,lead as the fourth part of a ,grain of ,musterd-seed1 added to the same expanded ,plate1 that in ,air i4 e4 out of the water shall weigh four or six pounds1 sinketh it to the ,bottom1 and being substracted1 it ascends to the ,surface of the water8 ,i cannot see1 7if what ,i say be true1 as it is most certain7 what minute vertue and force we can possibly find or imagine1 to which the ,resistance of the water against ,division and ,penetration is not inferiour2 whereupon1 we must of necessity conclude that it is nothing3 because1 if it were of any sensible power1 some large ,plate might be found or compounded of a ,matter alike in ,gravity to the water1 which not only would stay between the two waters2 but1 moreover1 should not be able to descend or ascend without notable force4 ,we may likewise collect the same from an other ,experiment#fj1 shewing that the ,water gives way also in the same manner to transversall ,division2 for if in a setled and standing water we should place any great ,mass that goeth not to the bottom1 drawing it with a single ,womans ,hair1 we might carry it from place to place without any opposition1 and this whatever ,figure it hath1 though that it possess a great space of water1 as for instance1 a great ,beam would do moved side-ways4 ,perhaps some might oppose me and say1 that if the ,resistance of water against ,division1 as ,i affirm1 were nothing2 ,ships should not need such a force of ,oars and ,sayles for the moving of them from place to place in a tranquile ,sea1 or standing ,lake4 ,to him that should make such an objection1 ,i would reply#fa1 that the water contrasteth not against1 nor simply resisteth ,division1 but a sudden ,division1 and with so much greater ,renitence1 by how much greater the ,velocity is3 and the ,cause of this ,resistance depends not on ,crassitude1 or any other thing that absolutely opposeth ,division1 but because that the parts of the water divided1 in giving way to that ,solid that is moved in it1 are themselves also necessitated locally to move1 some to the one side1 and some to the other1 and some downwards3 and this must no less be done by the waves before the ,ship1 or other ,body swimming through the water1 than by the posteriour and subsequent2 because1 the ,ship proceeding forwards1 to make it self a way to receive its ,bulk1 it is requisite1 that with the ,prow it repulse the adjacent parts of the water1 as well on one hand as on the other1 and that it move them as much transversly1 as is the half of the breadth of the ,hull3 and the like removall must those waves make1 that succeeding the ,poump do run from the remoter parts of the ,ship towards those of the middle1 successively to replenish the places1 which the ,ship in advancing forwards1 goeth1 leaving vacant4 ,now1 because1 all ,motitions are made in ,time#fb1 and the longer in greater time3 and it being moreover true1 that those ,bodies that in a certain time are moved by a certain power such a certain space1 shall not be moved the same space1 and in a shorter ,time1 unless by a greater ,power3 therefore1 the broader ,ships move slower than the narrower1 being put on by an equall ,force3 and the same ,vessel requires so much greater force of ,wind1 or ,oars1 the faster it is to move4 #fj ,an hair will draw a great ,mass thorow the ,water2 which proveth1 that it hath no ,resistance against transversall ,division4 #fa ,how ships are moved in the water4 #fb ,bodies moved a certain space in a certain ,time1 by a certain power1 cannot be moved the same space and in a shorter time1 but by a greater power4 ,but yet for all this1 any great ,mass swimming in a standing ,lake1 may be moved by any petit force2 only it is true1 that a lesser force more slowly moves it3 but if the waters ,resistance of ,division1 were in any manner sensible1 it would follow1 that the said ,mass1 should1 notwithstanding the percussion of some sensible force1 continue immoveable1 which is not so#fc4 ,yea1 ,i will say farther1 that should we retire our selves into the more internall contemplation of the ,nature of water and other ,fluids1 perhaps we should discover the ,constitution of their parts to be such1 that they not only do not oppose ,division1 but that they have not any thing in them to be divided3 so that the ,resistance that is observed in moving through the water#fd1 is like to that which we meet with in passing through a great ,throng of ,people1 wherein we find impediment1 and not by any difficulty in the ,division1 for that none of those persons are divided whereof the ,croud is composed1 but only in moving of those persons side-ways which were before divided and disjoyned3 and thus we find ,resistance in thrusting a ,stick into an heap of ,sand1 not because any part of the ,sand is to be cut in pieces1 but only to be moved and raised#fe4 ,two manners of ,penetration1 therefore1 offer themselves to us1 one in ,bodies1 whose parts were continuall1 and here ,division seemeth necessary1 the other in the aggregates of parts not continuall1 but contiguous only#ff1 and here there is no necessity of dividing but of moving only4 ,now1 ,i am not well resolved1 whether water and other ,fluids may be esteemed to be of parts continuall or contiguous only#fg2 yet ,i find my self indeed inclined to think that they are rather contiguous 7if there be in ,nature no other manner of aggregating1 than by the union1 or by the touching of the extreams37 and ,i am induced thereto by the great difference that ,i see between the ,conjunction of the parts of an hard or ,solid ,body#fh1 and the ,conjunction of the same parts when the same ,body shall be made ,liquid and ,fluid3 for if1 for example1 ,i take a ,mass of ,silver or other ,solid and hard ,mettall1 ,i shall in dividing it into two parts1 find not only the resistance that is found in the moving of it only#fi1 but an other incomparably greater1 dependent on that vertue1 whatever it be1 which holds the parts united3 and so if we would divide again those two parts into other two1 and successively into others and others1 we should still find a like ,resistance1 but ever less by how much smaller the parts to be divided shall be2 but if1 lastly1 employing most subtile and acute ,instruments1 such as are the most tenuous parts of the ,fire1 we shall resolve it 7perhaps7 into its last and least ,particles1 there shall not be left in them any longer either ,resistance of ,division1 or so much as a capacity of being farther divided1 especially by ,instruments more grosse than the acuities of ,fire3 and what ,knife or ,rasor put into well melted ,silver can we finde1 that will divide a thing which surpasseth the separating power of ,fire8 ,certainly none3 because either the whole shall be reduced to the most minute and ultimate ,divisions1 or if there remain parts capable still of other ,subdidivisions1 they cannot receive them1 but only from acuter ,divisors than ,fire2 but a ,stick or ,rod of ,iron1 moved in the melted ,metall1 is not such a one4 ,of a like ,constitution and ,consistence1 ,i account the parts of ,water#gj1 and other ,liquids to be1 namely1 incapable of ,division by reason of their ,ienuity2 or if not absolutely indivisible1 yet at least not to be divided by a ,board1 or other ,solid ,body1 palpable unto the hand1 the ,sector being alwayes required to be more sharp than the ,solid to be cut4 ,solid ,bodies1 therefore1 do only move1 and not divide the ,water#ga1 when put into it2 whose parts being before divided to the extreamest minuity1 and therefore capable of being moved1 either many of them at once1 or few1 or very few1 they soon give place to every small ,corpuscle1 that descends in the same3 for that1 it being little and light1 descending in the ,air1 and arriving to the ,surface of the ,water1 it meets with ,particles of ,water more small1 and of less ,resistance against ,motion and ,extrusion1 than is its own prement and extrusive force2 whereupon it submergeth1 and moveth such a portion of them1 as is proportionate to its ,power4 ,there is not1 therefore1 any ,resistance in ,water against ,division1 nay1 there is not in it any divisible parts4 ,i adde2 moreover1 that in case yet there should be any small ,resistance found 7which is absolutely false7#gb haply in attempting with an ,hair to move a very great natant ,machine1 or in essaying by the addition of one small ,grain of ,lead to sink1 or by removall of it to raise a very broad ,plate of ,matter1 equall in ,gravity with ,water1 7which likewise will not happen1 in case we proceed with dexterity7 we may observe that that ,resistance is a very different thing from that which the ,adversaries produce for the ,cause of the ,natation of the ,plate of ,lead or ,board of ,ebony1 for that one may make a ,board of ,ebony1 which being put upon the ,water swimmeth1 and cannot be submerged1 no not by the addition of an hundred ,grains of ,lead put upon the same1 and afterwards being bathed1 not only sinks1 though the said ,lead be taken away1 but though moreover a quantity of ,cork1 or of some other light ,body fastened to it1 sufficeth not to hinder it from sinking unto the bottome3 so that you see1 that although it were granted that there is a certain small ,resistance of ,division found in the substance of the ,water1 yet this hath nothing to do with that ,cause which supports the ,board above the ,water1 with a ,resistance an hundred times greater than that which men can find in the parts of the ,water3 nor let them tell me1 that only the ,surface of the ,water hath such ,resistance#gc1 and not the internall parts1 or that such ,resistance is found greatest in the beginning of the ,submersion1 as it also seems that in the beginning1 ,motion meets with greater opposition1 than in the continuance of it2 because1 first1 ,i will permit1 that the ,water be stirred1 and that the superiour parts be mingled with the middle#gd1 and inferiour parts1 or that those above be wholly removed1 and those in the middle only made use off1 and yet you shall see the effect for all that1 to be still the same3 ,moreover1 that ,hair which draws a ,beam through the ,water1 is likewise to divide the upperparts1 and is also to begin the ,motion1 and yet it begins it1 and yet it divides it3 and finally1 let the ,board of ,ebony be put in the midway1 betwixt the bottome and the top of the ,water1 and let it there for awhile be suspended and setled1 and afterwards let it be left at liberty1 and it will instantly begin its ,motion1 and will continue it unto the bottome4 ,nay1 more1 the ,board so soon as it is dimitted upon the ,water1 hath not only begun to move and divide it1 but is for a good space dimerged into it4 #fc ,the parts of ,liquids1 so farre from resisting ,division1 that they contain not any thing that may be divided4 #fd ,the ,resistance a ,solid findeth in moving through the water1 like to that we meet with in passing through a throng of people3 #fe ,or in thrusting a ,stick into an heap of ,sand4 #ff ,two kinds of ,penetration1 one in ,bodies continuall1 the other in ,bodies only contiguous4 #fg ,water consists not of continuall1 but only of contiguous parts4 #fh ,see what satisfaction he hath given1 as to this point1 in ,lib4 de ,motu4 ,dial4 #b4 #fi ,great difference betwixt the ,conjunction of the parts of a ,body when ,solid1 and when fluid4 #gj ,water consists of parts that admit of no farther division4 #ga ,solids dimitted into the water1 do onely move1 and not divide it4 #gb ,if there were any ,resistance of ,division in water1 it must needs be small1 in that it is overcome by an ,hair1 a ,grain of ,lead1 or a slight bathing of the ,solid4 #gc ,the uper parts of the ,water1 do no more resist ,division than the middle or lower parts4 #gd ,waters ,resistance of division1 not greater in the beginning of the ,submersion4 ,let us receive it1 therefore1 for a true and undoubted ,conclusion1 ,that the ,water hath not any ,renitence against simple ,division1 and that it is not possible to find any ,solid ,body1 be it of what ,figure it will1 which being put into the ,water1 its ,motion upwards or downwards1 according as it exceedeth1 or shall be exceeded by the ,water in ,gravity 7although such excesse and difference be insensible7 shall be prohibited1 and taken away1 by the ,crassitude of the said ,water4 ,when1 therefore1 we see the ,board of ,ebony1 or of other ,matter1 more grave than the ,water1 to stay in the ,confines of the ,water and ,air1 without submerging1 we must have recourse to some other ,originall1 for the investing the ,cause of that ,effect1 than to the breadth of the ,figure1 unable to overcome the ,renitence with which the ,water opposeth ,division1 since there is no ,resistance2 and from that which is not in being1 we can expect no ,action4 ,it remains most true1 therefore1 as we have said before1 that this so succeds1 for that that which in such manner put upon the water1 not the same ,body with that which is put into the ,water3 because this which is put into the ,water1 is the pure ,board of ,ebony1 which for that it is more grave than the ,water1 sinketh1 and that which is put upon the ,water1 is a ,composition of ,ebony1 and of so much ,air1 that both together are specifically less grave than the ,water1 and therefore they do not descend4 ,i will farther confirm this which ,i say4 ,gentlemen1 my ,antagonists1 we are agreed1 that the excess or defect of the ,gravity of the ,solid1 unto the ,gravity of the ,water1 is the true and proper ,cause of ,natation or ,submersion4 ,sidenote3 ,great ,caution to be had in experimenting the operation of ,figure in ,natation4 ,now1 if you will shew that besides the former ,cause1 there is another which is so powerfull1 that it can hinder and remove the ,submersion of those very ,solids1 that by their ,gravity sink1 and if you will say1 that this is the breadth or ampleness of ,figure1 you are oblieged1 when ever you would shew such an ,experiment1 first to make the circumstances certain1 that that ,solid which you put into the ,water1 be not less grave in specie than it1 for if you should not do so1 any one might with reason say1 that not the ,figure1 but the ,levity was the cause of that ,natation4 ,but ,i say1 that when you shall dimit a ,board of ,ebony into the ,water1 you do not put therein a ,solid more grave in specie than the ,water1 but one lighter1 for besides the ,ebony1 there is in the ,water a ,mass of ,air1 united with the ,ebony1 and such1 and so light1 that of both there results a ,composition less grave than the ,water3 ,see1 therefore1 that you remove the ,air1 and put the ,ebony alone into the ,water1 for so you shall immerge a ,solid more grave then the ,water1 and if this shall not go to the ,bottom1 you have well ,philosophized and ,i ill4 ,now1 since we have found the true ,cause of the ,natation of those ,bodies1 which otherwise1 as being graver than the ,water1 would descend to the bottom1 ,i think1 that for the perfect and distinct knowledge of this business1 it would be good to proceed in a way of discovering demonstratively those particular ,accidents that do attend these effects1 and1 ,,probl4 ,i4 ,sidenote3 ,to finde the proportion ,figures ought to have to the waters ,gravity1 that by help of the contiguous ,air1 they may swim4 ,to finde what proportion severall ,figures of different ,matters ought to have1 unto the ,gravity of the ,water1 that so they may be able by vertue of the ,contiguous ,air to stay afloat4 ,illustration ,let1 therefore1 for better illustration1 ,d ,f ,n ,e be a ,vessell1 wherein the water is contained1 and suppose a ,plate or ,board1 whose thickness is comprehended between the ,lines ,i ,c and ,o ,s1 and let it be of ,matter exceeding the water in ,gravity1 so that being put upon the water1 it dimergeth and abaseth below the ,levell of the said water1 leaving the little ,banks ,a ,i and ,b ,c1 which are at the greatest height they can be1 so that if the ,plate ,i ,s should but descend any little space farther1 the little ,banks or ,ramparts would no longer consist1 but expulsing the ,air ,a ,i ,c ,b1 they would diffuse themselves over the ,superficies ,i ,c1 and would submerge the ,plate4 ,the height ,a ,i ,b ,c is therefore the greatest profundity that the little ,banks of water admit of4 ,now ,i say1 that from this1 and from the proportion in ,gravity1 that the ,matter of the ,plate hath to the water1 we may easily finde of what thickness1 at most1 we may make the said ,plates1 to the end1 they may be able to bear up above water3 for if the ,matter of the ,plate or ,board ,i ,s were1 for ,example1 as heavy again as the water1 a ,board of that ,matter shall be1 at the most of a thickness equall to the greatest height of the ,banks1 that is1 as thick as ,a ,i is high3 which we will thus demonstrate4 ,let the ,solid ,i ,s be double in ,gravity to the water1 and let it be a regular ,prisme1 or ,cylinder1 to wit1 that hath its two flat ,superficies1 superiour and inferiour1 alike and equall1 and at ,right ,angles with the other laterall ,superficies1 and let its thickness ,i ,o be equall to the greatest ,altitude of the ,banks of water3 ,i say1 that if it be put upon the water1 it will not submerge3 for the ,altitude ,a ,i being equall to the ,altitude ,i ,o1 the ,mass of the ,air ,a ,b ,c ,i shall be equall to the ,mass of the ,solid ,c ,i ,o ,s3 and the whole ,mass ,a ,o ,s ,b double to the ,mass ,i ,s2 ,and since the ,mass of the ,air ,a ,c1 neither encreaseth nor diminisheth the ,gravity of the ,mass ,i ,s1 and the ,solid ,i ,s was supposed double in ,gravity to the water2 ,therefore as much water as the ,mass submerged ,a ,o ,s ,b1 compounded of the ,air ,a ,i ,c ,b1 and of the ,solid ,i ,o ,s ,c1 weighs just as much as the same submerged ,mass ,a ,o ,s ,b3 but when such a ,mass of water1 as is the submerged part of the ,solid1 weighs as much as the said ,solid1 it descends not farther1 but resteth1 as by 7a7 ,archimedes#ge1 and above by us1 hath been demonstrated3 ,therefore1 ,i ,s shall descend no farther1 but shall rest4 ,and if the ,solid ,i ,s shall be ,sesquialter in ,gravity to the water1 it shall float1 as long as its thickness be not above twice as much as the greatest ,altitude of the ,ramparts of water1 that is1 of ,a ,i4 ,for ,i ,s being ,sesquialter in ,gravity to the water1 and the ,altitude ,o ,i1 being double to ,i ,a1 the ,solid submerged ,a ,o ,s ,b1 shall be also ,sesquialter in ,mass to the ,solid ,i ,s4 ,and because the ,air ,a ,c1 neither increaseth nor diminisheth the ponderosity of the ,solid ,i ,s3 ,therefore1 as much water in quantity as the submerged ,mass ,a ,o ,s ,b1 weighs as much as the said ,mass submerged3 ,and1 therefore1 that ,mass shall rest4 ,and briefly in generall4 #ge ,of ,natation ,lib4 #a4 ,prop4 #c4 ,illustration ,,theoreme4 ,,vi4 ,sidenote3 ,the proportion of the greatest thickness of ,solids1 beyond which encreased they sink4 ,when ever the excess of the ,gravity of the ,solid above the ,gravity of the ,water1 shall have the same proportion to the ,gravity of the ,water1 that the ,altitude of the ,rampart1 hath to the thickness of the ,solid1 that ,solid shall not sink1 but being never so little thicker it shall4 ,illustration ,let the ,solid ,i ,s be superior in ,gravity to the water1 and of such thickness1 that the ,altitude of the ,rampart ,a ,i1 be in proportion to the thickness of the ,solid ,i ,o1 as the excess of the ,gravity of the said ,solid ,i ,s1 above the ,gravity of a ,mass of water equall to the ,mass ,i ,s1 is to the ,gravity of the ,mass of water equall to the ,mass ,i ,s4 ,i say1 that the ,solid ,i ,s shall not sinke1 but being never so little thicker it shall go to the bottom3 ,for being that as ,a ,i is to ,i ,o1 so is the ,excess of the ,gravity of the ,solid ,i ,s1 above the ,gravity of a ,mass of water equall to the ,mass ,i ,s1 to the ,gravity of the said ,mass of water3 ,therefore1 compounding1 as ,a ,o is to ,o ,i1 so shall the ,gravity of the ,solid ,i ,s1 be to the ,gravity of a ,mass of water equall to the ,mass ,i ,s3 ,and1 converting1 as ,i ,o is to ,o ,a1 so shall the ,gravity of a ,mass of water equall to the ,mass ,i ,s1 be to the ,gravity of the ,solid ,i ,s3 ,but as ,i ,o is to ,o ,a1 so is a ,mass of water ,i ,s1 to a ,mass of water equall to the ,mass ,a ,b ,s ,o3 and so is the ,gravity of a ,mass of water ,i ,s1 to the ,gravity of a ,mass of water ,a ,s3 ,therefore as the ,gravity of a ,mass of water1 equall to the ,mass ,i ,s1 is to the ,gravity of the ,solid ,i ,s1 so is the same ,gravity of a ,mass of water ,i ,s1 to the ,gravity of a ,mass of ,water ,a ,s3 ,therefore the ,gravity of the ,solid ,i ,s1 is equall to the ,gravity of a ,mass of water equall to the ,mass ,a ,s3 ,but the ,gravity of the ,solid ,i ,s1 is the same with the ,gravity of the ,solid ,a ,s1 compounded of the ,solid ,i ,s1 and of the ,air ,a ,b ,c ,i4 ,therefore the whole compounded ,solid ,a ,o ,s ,b1 weighs as much as the water that would be comprised in the place of the said ,compound ,a ,o ,s ,b3 ,and1 therefore1 it shall make an ,equilibrium and rest1 and that same ,solid ,i ,o ,s ,c shall sinke no farther4 ,but if its thickness ,i ,o should be increased1 it would be necessary also to encrease the ,altitude of the ,rampart ,a ,i1 to maintain the due proportion3 ,but by what hath been supposed1 the ,altitude of the ,rampart ,a ,i1 is the greatest that the ,nature of the ,water and ,air do admit1 without the waters repulsing the ,air adherent to the ,superficies of the ,solid ,i ,c1 and possessing the space ,a ,i ,c ,b3 ,therefore1 a ,solid of greater thickness than ,i ,o1 and of the same ,matter with the ,solid ,i ,s1 shall not rest without submerging1 but shall descend to the bottome3 which was to be demonstrated4 ,in consequence of this that hath been demonstrated1 sundry and various ,conclusions may be gathered1 by which the truth of my principall ,proposition comes to be more and more confirmed1 and the imperfection of all former ,argumentations touching the present ,question cometh to be discovered4 ,and first we gather from the things demonstrated1 that1 ,,theoreme ,,vii4 ,sidenote3 ,the heaviest ,bodies may swimme4 ,all ,matters1 how heavy soever1 even to ,gold it self1 the heaviest of all ,bodies1 known by us1 may float upon the ,water4 ,because its ,gravity being considered to be almost twenty times greater than that of the water1 and1 moreover1 the greatest ,altitude that the ,rampart of water can be extended to1 without breaking the ,contiguity of the ,air1 adherent to the ,surface of the ,solid1 that is put upon the water being predetermined1 if we should make a ,plate of ,gold so thin1 that it exceeds not the nineteenth part of the ,altitude of the said ,rampart1 this put lightly upon the water shall rest1 without going to the bottom3 and if ,ebony shall chance to be in sesquiseptimall proportion more grave than the water1 the greatest thickness that can be allowed to a ,board of ,ebony1 so that it may be able to stay above water without sinking1 would be seaven times more than the height of the ,rampart ,tinn1 v4 gr4 eight times more grave than water1 shall swimm as oft as the thickness of its ,plate1 exceeds not the #gth part of the ,altitude of the ,rampart4 ,sidenote3 ,he elsewhere cites this as a ,proposition1 therefore ,i make it of that number4 ,and here ,i will not omit to note1 as a second ,corrollary dependent upon the things demonstrated1 that1 ,,theoreme ,,viii4 ,sidenote3 ,natation and ,submersion1 collected from the thickness1 excluding the length and breadth of ,plates4 ,the ,expansion of ,figure not only is not the ,cause of the ,natation of those grave ,bodies1 which otherwise do submerge1 but also the determining what be those ,boards of ,ebony1 or ,plates of ,iron or ,gold that will swimme1 depends not on it1 rather that same determination is to be collected from the only thickness of those ,figures of ,ebony or ,gold1 wholly excluding the consideration of length and breadth1 as having no wayes any share in this ,effect4 ,it hath already been manifested1 that the only cause of the ,natation of the said ,plates1 is the reduction of them to be less grave than the water1 by means of the connexion of that ,air1 which descendeth together with them1 and possesseth place in the water2 which place so occupyed1 if before the circumfused water diffuseth it self to fill it1 it be capable of as much water1 as shall weigh equall with the ,plate1 the ,plate shall remain suspended1 and sinke no farther4 ,now let us see on which of these three dimensions of the ,solid depends the terminating1 what and how much the ,mass of that ought to be1 that so the assistance of the ,air contiguous unto it1 may suffice to render it specifically less grave than the water1 whereupon it may rest without ,submersion4 ,it shall undoubtedly be found1 that the length and breadth have not any thing to do in the said determination1 but only the height1 or if you will the thickness3 for1 if we take a ,plate or ,board1 as for ,example1 of ,ebony1 whose ,altitude hath unto the greatest possible ,altitude of the ,rampart1 the proportion above declared1 for which cause it swims indeed1 but yet not if we never so little increase its thickness2 ,i say1 that retaining its thickness1 and encreasing its ,superficies to twice1 four times1 or ten times its bigness1 or dminishing it by dividing it into four1 or six1 or twenty1 or a hundred parts1 it shall still in the same manner continue to float3 but encreasing its thickness only a ,hairs breadth1 it will alwaies submerge1 although we should multiply the ,superficies a hundred and a hundred times4 ,now forasmuch as that this is a ,cause1 which being added1 we adde also the ,effect1 and being removed1 it is removed2 and by augmenting or lessening the length or breadth in any manner1 the effect of going1 or not going to the bottom1 is not added or removed3 ,i conclude1 that the greatness and smalness of the ,superficies hath no influence upon the ,natation or ,submersion4 ,and that the proportion of the ,altitude of the ,ramparts of ,water1 to the ,altitude of the ,solid1 being constituted in the manner aforesaid1 the greatness or smalness of the ,superficies1 makes not any variation1 is manifest from that which hath been above demonstrated1 and from this1 that1 ,the ,prisms and ,cylinders which have the same ,base1 are in proportion to one another as their heights4 ,whence ,cylinders or ,prismes#gf1 namely1 the ,board1 be they great or little1 so that they be all of equall thickness1 have the same proportion to their ,conterminall ,air1 which hath for ,base the said ,superficies of the ,board1 and for height the ,ramparts of water2 so that alwayes of that ,air1 and of the ,board1 ,solids1 are compounded1 that in ,gravity equall a ,mass of water equall to the ,mass of the ,solids1 compounded of ,air1 and of the ,board3 whereupon all the said ,solids do in the same manner continue afloat4 ,we will conclude in the third place1 that1 #gf ,prismes and ,cylinders having the same ,base1 are to one another as their heights4 ,,theoreme4 ,,ix4 ,sidenote3 ,all ,figures of all ,matters1 float by hep of the ,rampart replenished with ,air1 and some but only touch the water4 ,all sorts of ,figures of whatsoever ,matter1 albeit more grave than the ,water1 do by ,benefit of the said ,rampart1 not only float1 but some ,figures1 though of the gravest ,matter1 do stay wholly above ,water1 wetting only the inferiour ,surface that toucheth the ,water4 ,and these shall be all ,figures1 which from the inferiour ,base upwards1 grow lesser and lesser2 the which we shall exemplifie for this time in ,piramides or ,cones1 of which ,figures the passions are common4 ,we will demonstrate therefore1 that1 ,it is possible to form a ,piramide1 of any whatsoever ,matter preposed1 which being put with its ,base upon the ,water1 rests not only without submerging1 but without wetting it more then its ,base4 ,for the explication of which it is requisite1 that we first demonstrate the subsequent ,lemma1 namely1 that1 ,,lemma ,,ii4 ,sidenote3 ,solids whose ,masses are in contrary proportion to their ,specifick ,gravities are equall in absolute ,gravity4 ,solids whose ,masses answer in proportion contrarily to their ,specificall ,gravities1 are equall in ,absolute ,gravities4 ,illustration ,let ,a ,c and ,b be two ,solids1 and let the ,mass ,a ,c be to the ,mass ,b1 as the ,specificall ,gravity of the ,solid ,b1 is to the ,specificall ,gravity of the ,solid ,a ,c3 ,i say1 the ,solids ,a ,c and ,b are equall in absolute weight1 that is1 equally grave4 ,for if the ,mass ,a ,c be equall to the ,mass ,b1 then1 by the ,assumption1 the ,specificall ,gravity of ,b1 shall be equall to the ,specificall ,gravity of ,a ,c1 and being equall in ,mass1 and of the same ,specificall ,gravity they shall absolutely weigh one as much as another4 ,but if their ,masses shall be unequall1 let the ,mass ,a ,c be greater1 and in it take the part ,c1 equall to the ,mass ,b4 ,and1 because the ,masses ,b and ,c are equall2 the ,absolute weight of ,b1 shall have the same proportion to the ,absolute weight of ,c1 that the ,specificall ,gravity of ,b1 hath to the ,specificall ,gravity of ,c2 or of ,c ,a1 which is the same in specie3 ,but look what proportion the ,specificall ,gravity of ,b1 hath to the ,specificall ,gravity of ,c ,a1 the like proportion1 by the ,assumption1 hath the ,mass ,c ,a1 to the ,mass ,b1 that is1 to the ,mass ,c3 ,therefore1 the absolute weight of ,b1 to the absolute weight of ,c1 is as the ,mass ,a ,c to the ,mass ,c3 ,but as the ,mass ,a ,c1 is to the ,mass ,c1 so is the absolute weight of ,a ,c1 to the absolute weight of ,c3 ,therefore the absolute weight of ,b1 hath the same proportion to the absolute weight of ,c1 that the absolute weight of ,a ,c1 hath to the absolute weight of ,c3 ,therefore1 the two ,solids ,a ,c and ,b are equall in absolute ,gravity3 which was to be demonstrated4 ,having demonstrated this1 ,i say1 ,,theoreme ,x4 ,sidenote3 ,there may be ,cones and ,piramides of any ,matter1 which demitted into the water1 rest only their ,bases4 ,that it is possible of any assigned ,matter1 to form a ,piramide or ,cone upon any ,base1 which being put upon the ,water shall not submerge1 nor wet any more than its ,base4 ,illustration ,let the greatest possible ,altitude of the ,rampart be the ,line ,d ,b1 and the ,diameter of the ,base of the ,cone to be made of any ,matter assigned ,b ,c1 at right angles to ,d ,b3 ,and as the ,specificall ,gravity of the ,matter of the ,piramide or ,cone to be made1 is to the ,specificall ,gravity of the water1 so let the ,altitude of the ,rampart ,d ,b1 be to the third part of the ,piramide or ,cone ,a ,b ,c1 described upon the ,base1 whose ,diameter is ,b ,c3 ,i say1 that the said ,cone ,a ,b ,c1 and any other ,cone1 lower then the same1 shall rest upon the ,surface of the water ,b ,c without sinking4 ,draw ,d ,f parallel to ,b ,c1 and suppose the ,prisme or ,cylinder ,e ,c1 which shall be tripple to the ,cone ,a ,b ,c4 ,and1 because the ,cylinder ,d ,c hath the same proportion to the ,cylinder ,c ,e1 that the ,altitude ,d ,b1 hath to the ,altitude ,b ,e3 ,but the ,cylinder ,c ,e1 is to the ,cone ,a ,b ,c1 as the ,altitude ,e ,b is to the third part of the ,altitude of the ,cone3 ,therefore1 by ,equality of proportion1 the ,cylinder ,d ,c is to the ,cone ,a ,b ,c1 as ,d ,b is to the third part of the ,altitude ,b ,e3 ,but as ,d ,b is to the third part of ,b ,e1 so is the ,specificall ,gravity of the ,cone ,a ,b ,c1 to the ,specificall ,gravity of the water3 ,therefore1 as the ,mass of the ,solid ,d ,c1 is to the ,mass of the ,cone ,a ,b ,c1 so is the ,specificall ,gravity of the said ,cone1 to the ,specificall ,gravity of the water3 ,therefore1 by the precedent ,lemma1 the ,cone ,a ,b ,c weighs in absolute ,gravity1 as much as a ,mass of ,water equall to the ,mass ,d ,c3 ,but the water which by the imposition of the ,cone ,a ,b ,c1 is driven out of its place1 is as much as would precisely lie in the place ,d ,c1 and is equall in weight to the ,cone that displaceth it3 ,therefore1 there shall be an ,equilibrium1 and the ,cone shall rest without farther submerging4 ,and its manifest1 ,,corolary ,i4 ,sidenote3 ,amongst ,cones of the same ,base1 those of least ,altitude shall sink the least4 ,that making upon the same ,basis1 a ,cone of a less ,altitude1 it shall be also less grave1 and shall so much the more rest without ,submersion4 ,,corolary ,,ii4 ,sidenote3 ,there may be ,cones and ,piramides of any ,matter1 which demitted with the ,point downwards do float atop4 ,it is manifest1 also1 that one may make ,cones and ,piramids of any ,matter whatsoever1 more grave than the water1 which being put into the water1 with the ,apix or ,point downwards1 rest without ,submersion4 ,because if we reassume what hath been above demonstrated1 of ,prisms and ,cylinders1 and that on ,bases equall to those of the said ,cylinders1 we make ,cones of the same ,matter1 and three times as high as the ,cylinders1 they shall rest afloat1 for that in ,mass and ,gravity they shall be equall to those ,cylinders1 and by having their ,bases equall to those of the ,cylinders1 they shall leave equall ,masses of ,air included within the ,ramparts4 ,this1 which for ,example sake hath been demonstrated1 in ,prisms1 ,cylinders1 ,cones and ,piramids1 might be proved in all other ,solid ,figures1 but it would require a whole ,volume 7such is the multitude and variety of their ,symptoms and ,accidents7 to comprehend the particuler demonstration of them all1 and of their severall ,segments3 but ,i will to avoid prolixity in the present ,discourse1 content my self1 that by what ,i have declared every one of ordinary ,capacity may comprehend1 that there is not any ,matter so grave1 no not ,gold it self1 of which one may not form all sorts of ,figures1 which by vertue of the superiour ,air adherent to them1 and not by the ,waters ,resistance of ,penetration1 do remain afloat1 so that they sink not4 ,nay1 farther1 ,i will shew1 for removing that ,error1 that1 ,,theoreme ,,xi4 ,sidenote3 ,a ,piramide or ,cone1 demitted with the ,point downwards shal swim1 with its ,base downward shall sink4 ,a ,piramide or ,cone put into the ,water1 with the ,point downward shall swimme1 and the same put with the ,base downwards shall sinke1 and it shall be impossible to make it float4 ,now the quite contrary would happen1 if the difficulty of ,penetrating the water1 were that which had hindred the descent1 for that the said ,cone is far apter to pierce and penetrate with its sharp ,point1 than with its broad and spacious ,base4 ,and1 to demonstrate this1 let the ,cone be ,a ,b ,c1 twice as grave as the water1 and let its height be tripple to the height of the ,rampart ,d ,a ,e ,c3 ,i say1 first1 that being put lightly into the water with the ,point downwards1 it shall not descend to the bottom3 for the ,aeriall ,cylinder contained betwixt the ,ramparts ,d ,a ,c ,e1 is equall in ,mass to the ,cone ,a ,b ,c2 so that the whole ,mass of the ,solid compounded of the ,air ,d ,a ,c ,e1 and of the ,cone ,a ,b ,c1 shall be double to the ,cone ,a ,c ,b3 ,and1 because the ,cone ,a ,b ,c is supposed to be of ,matter double in ,gravity to the water1 therefore as much water as the whole ,masse ,d ,a ,b ,c ,e1 placed beneath the ,levell of the water1 weighs as much as the ,cone ,a ,b ,c3 and1 therefore1 there shall be an ,equilibrium1 and the ,cone ,a ,b ,c shall descend no lower4 ,now1 ,i say farther1 that the same ,cone placed with the ,base downwards1 shall sink to the bottom1 without any possibility of returning again1 by any means to swimme4 ,illustration ,let1 therefore1 the ,cone be ,a ,b ,d1 double in ,gravity to the water1 and let its height be tripple the height of the ,rampart of water ,l ,b3 ,it is already manifest1 that it shall not stay wholly out of the water1 because the ,cylinder being comprehended betwixt the ,ramparts ,l ,b ,d ,p1 equall to the ,cone ,a ,b ,d1 and the ,matter of the ,cone1 beig double in ,gravity to the water1 it is evident that the weight of the said ,cone shall be double to the weight of the ,mass of water equall to the ,cylinder ,l ,b ,d ,p3 ,therefore it shall not rest in this state1 but shall descend4 ,illustration ,,corolary ,i4 ,sidenote3 ,much less shall the said ,cone swim1 if one immerge a part thereof4 ,i say farther2 that much lesse shall the said ,cone stay afloat1 if one immerge a part thereof4 ,which you may see1 comparing with the water as well the part that shall immerge as the other above water4 ,let us therefore of the ,cone ,a ,b ,d1 submergeth part ,n ,t ,o ,s1 and advance the ,point ,n ,s ,f above water4 ,the ,altitude of the ,cone ,f ,n ,s1 shall either be more than half the whole ,altitude of the ,cone ,f ,t ,o1 or it shall not be more3 if it shall be more than half1 the ,cone ,f ,n ,s shall be more than half of the ,cylinder ,e ,n ,s ,c3 for the ,altitude of the ,cone ,f ,n ,s1 shall be more than ,sesquialter of the ,altitude of the ,cylinder ,e ,n ,s ,c3 ,and1 because the ,matter of the ,cone is supposed to be double in ,specificall ,gravity to the water1 the water which would be contained within the ,rampart ,e ,n ,s ,c1 would be less grave absolutely than the ,cone ,f ,n ,s2 so that the whole ,cone ,f ,n ,s cannot be sustained by the ,rampart3 ,but the part immerged ,n ,t ,o ,s1 by being double in ,specificall ,gravity to the water1 shall tend to the bottom3 ,therefore1 the whole ,cone ,f ,t ,o1 as well in respect of the part submerged1 as the part above water shall descend to the bottom4 ,but if the ,altitude of the ,point ,f ,n ,s1 shall be half the ,altitude of the whole ,cone ,f ,t ,o1 the same ,altitude of the said ,cone ,f ,n ,s shall be ,sesquialter to the ,altitude ,e ,n3 and1 therefore1 ,e ,n ,s ,c shall be double to the ,cone ,f ,n ,s2 and as much water in ,mass as the ,cylinder ,e ,n ,s ,c1 would weigh as much as the part of the ,cone ,f ,n ,s4 ,but1 because the other immerged part ,n ,t ,o ,s1 is double in ,gravity to the water1 a ,mass of water equall to that compounded of the ,cylinder ,e ,n ,s ,c1 and of the ,solid ,n ,t ,o ,s1 shall weigh less than the ,cone ,f ,t ,o1 by as much as the weight of a ,mass of water equall to the ,solid ,n ,t ,o ,s3 ,therefore1 the ,cone shall also descend4 ,again1 because the ,solid ,n ,t ,o ,s1 is septuple to the ,cone ,f ,n ,s1 to which the ,cylinder ,e ,s is double1 the proportion of the ,solid ,n ,t ,o ,s1 shall be to the ,cylinder ,e ,n ,s ,c1 as seaven to two3 ,therefore1 the whole ,solid compounded of the ,cylinder ,e ,n ,s ,c1 and of the ,solid ,n ,t ,o ,s1 is much less than double the ,solid ,n ,t ,o ,s3 ,therefore1 the single ,solid ,n ,t ,o ,s1 is much graver than a ,mass of water equall to the ,mass1 compounded of the ,cylinder ,e ,n ,s ,c1 and of ,n ,t ,o ,s4 ,,corolary ,,ii4 ,sidenote3 ,part of the ,cones towards the ,cuspis removed1 it shall still sink4 ,from whence it followeth1 that though one should remove and take away the part of the ,cone ,f ,n ,s1 the sole remainder ,n ,t ,o ,s would go to the bottom4 ,,corolary ,,iii4 ,sidenote3 ,the more the ,cone is immerged1 the more impossible is its floating4 ,and if we should more depress the ,cone ,f ,t ,o1 it would be so much the more impossible that it should sustain it self afloat1 the part submerged ,n ,t ,o ,s still encreasing1 and the ,mass of ,air contained in the ,rampart diminishing1 which ever grows less1 the more the ,cone submergeth4 ,that ,cone1 therefore1 that with its ,base upwards1 and its ,cuspis downwards doth swimme1 being dimitted with its ,base downward must of necessity sinke4 ,they have argued farre from the truth1 therefore1 who have ascribed the cause of ,natation to waters resistance of ,division1 as to a passive principle1 and to the breadth of the ,figure1 with which the division is to be made1 as the ,efficient4 ,i come in the fourth place1 to collect and conclude the reason of that which ,i have proposed to the ,adversaries1 namely1 ,,theoreme ,,xii4 ,sidenote3 ,solids of any ,figure greatnesse1 that naturally sink1 may by help of the ,air in the ,rampart swimme4 ,that it is possible to form ,solid ,bodies1 of what ,figure and greatness soever1 that of their own ,nature goe to the ,bottome2 ,but by the help of the ,air contained in the ,rampart1 rest without submerging4 ,illustration ,the truth of this ,proposition is sufficiently manifest in all those ,solid ,figures1 that determine in their uppermost part in a plane ,superficies3 for making such ,figures of some ,matter specifically as grave as the water1 putting them into the water1 so that the whole ,mass be covered1 it is manifest1 that they shall rest in all places1 provided1 that such a ,matter equall in weight to the water1 may be exactly adjusted3 and they shall by consequence1 rest or lie even with the ,levell of the water1 without making any ,rampart4 ,if1 therefore1 in respect of the ,matter1 such ,figures are apt to rest without submerging1 though deprived of the help of the ,rampart1 it is manifest1 that they may admit so much encrease of ,gravity1 7without encreasing their ,masses7 as is the weight of as much water as would be contained within the ,rampart1 that is made about their upper plane ,surface3 by the help of which being sustained1 they shall rest afloat1 but being bathed1 they shall descend1 having been made graver than the water4 ,in ,figures1 therefore1 that determine above in a plane1 we may cleerly comprehend1 that the ,rampart added or removed1 may prohibit or permit the descent3 but in those ,figures that go lessening upwards towards the top1 some ,persons may1 and that not without much seeming ,reason1 doubt whether the same may be done1 and especially by those which terminate in a very acute ,point1 such as are your ,cones and small ,piramids4 ,touching these1 therefore1 as more dubious than the rest1 ,i will endeavour to demonstrate1 that they also lie under the same ,accident of going1 or not going to the ,bottom1 be they of any whatever bigness4 ,let therefore the ,cone be ,a ,b ,d1 made of a matter specifically as grave as the water2 it is manifest that being put all under water1 it shall rest in all places 7alwayes provided1 that it shall weigh exactly as much as the water1 which is almost impossible to effect7 and that any small weight being added to it1 it shall sink to the bottom3 but if it shall descend downwards gently1 ,i say1 that it shall make the ,rampart ,e ,s ,t ,o1 and that there shall stay out of the water the point ,a ,s ,t1 tripple in height to the ,rampart ,e ,s3 which is manifest1 for the ,matter of the ,cone weighing equally with the water1 the part submerged ,s ,b ,d ,t1 becomes indifferent to move downwards or upwards2 and the ,cone ,a ,s ,t1 being equall in ,mass to the water that would be contained in the concave of the ,rampart ,e ,s ,t ,o1 shall be also equall unto it in ,gravity3 and1 therefore1 there shall be a perfect ,equilibrium1 and1 consequently1 a ,rest4 ,now here ariseth a doubt1 whether the ,cone ,a ,b ,d may be made heavier1 in such sort1 that when it is put wholly under water1 it goes to the bottom1 but yet not in such sort1 as to take from the ,rampart the vertue of sustaining it that it sink not1 and1 the reason of the doubt is this3 that although at such time as the ,cone ,a ,b ,d is specifically as grave as the water1 the ,rampart ,e ,s ,t ,o sustaines it1 not only when the point ,a ,s ,t is tripple in height to the ,altitude of the ,rampart ,e ,s1 but also when a lesser part is above water2 for although in the ,descent of the ,cone the ,point ,a ,s ,t by little and little diminisheth1 and so likewise the ,rampart ,e ,s ,t ,o1 yet the ,point diminisheth in greater proportion than the ,rampart1 in that it diminisheth according to all the three ,dimensions1 but the ,rampart according to two only1 the ,altitude still remaining the same2 or1 if you will1 because the ,cone ,s ,a ,t goes diminishing1 according to the proportion of the cubes of the ,lines that do successively become the ,diameters of the ,bases of emergent ,cones1 and the ,ramparts diminish according to the proportion of the ,squares of the same ,lines2 whereupon the proportions of the ,points are alwayes ,sesquialter of the proportions of the ,cylinders1 contained within the ,rampart2 so that if1 for ,example1 the height of the emergent ,point were double1 or equall to the height of the ,rampart1 in these cases1 the ,cylinder contained within the ,rampart1 would be much greater than the said ,point1 because it would be either sesquialter or tripple1 by reason of which it would perhaps serve over and above to sustain the whole ,cone1 since the part submerged would no longer weigh any thing2 yet1 nevertheless1 when any ,gravity is added to the whole ,mass of the ,cone1 so that also the part submerged is not without some excesse of ,gravity above the ,gravity of the water1 it is not manifest1 whether the ,cylinder contained within the ,rampart1 in the descent that the ,cone shall make1 can be reduced to such a proportion unto the emergent ,point1 and to such an excesse of ,mass above the ,mass of it1 as to compensate the excesse of the ,cones ,specificall ,gravity above the ,gravity of the water3 and the ,scruple ariseth1 because that howbeit in the descent made by the ,cone1 the emergent ,point ,a ,s ,t diminisheth1 whereby there is also a diminution of the excess of the ,cones ,gravity above the ,gravity of the water1 yet the case stands so1 that the ,rampart doth also contract it self1 and the ,cylinder contained in it doth deminish4 ,nevertheless it shall be demonstrated1 how that the ,cone ,a ,b ,d being of any supposed bignesse1 and made at the first of a ,matter exactly equall in ,gravity to the ,water1 if there may be affixed to it some ,weight1 by means of which it may descend to the bottom1 when submerged under water1 it may also by vertue of the ,rampart stay above without sinking4 ,illustration ,illustration ,let1 therefore1 the ,cone ,a ,b ,d be of any supposed greatnesse1 and alike in specificall ,gravity to the water4 ,it is manifest1 that being put lightly into the water1 it shall rest without descending2 and it shall advance above water1 the ,point ,a ,s ,t1 tripple in height to the height of the ,rampart ,e ,s3 ,now1 suppose the ,cone ,a ,b ,d more depressed1 so that it advance above water1 only the ,point ,a ,i ,r1 higher by half than the ,point ,a ,s ,t1 with the ,rampart about it ,c ,i ,r ,n4 ,and1 because1 the ,cone ,a ,b ,d is to the ,cone ,a ,i ,r1 as the cube of the ,line ,s ,t is to the cube of the ,line ,i ,r1 but the ,cylinder ,e ,s ,t ,o1 is to the ,cylinder ,c ,i ,r ,n1 as the ,square of ,s ,t to the ,square of ,i ,r1 the ,cone ,a ,s ,t shall be ,octuple to the ,cone ,a ,i ,r1 and the ,cylinder ,e ,s ,t ,o1 quadruple to the ,cylinder ,c ,i ,r ,n3 ,but the ,cone ,a ,s ,t1 is equall to the ,cylinder ,e ,s ,t ,o3 ,therefore1 the ,cylinder ,c ,i ,r ,n1 shall be double to the ,cone ,a ,i ,r3 and the water which might be contained in the ,rampart ,c ,i ,r ,n1 would be double in ,mass and in ,weight to the ,cone ,a ,i ,r1 and1 therefore1 would be able to sustain the double of the ,weight of the ,cone ,a ,i ,r3 ,therefore1 if to the whole ,cone ,a ,b ,d1 there be added as much ,weight as the ,gravity of the ,cone ,a ,i ,r1 that is to say1 the eighth part of the weight of the ,cone ,a ,s ,t1 it also shall be sustained by the ,rampart ,c ,i ,r ,n1 but without that it shall go to the bottome3 the ,cone ,a ,b ,d1 being1 by the addition of the eighth part of the weight of the ,cone ,a ,s ,t1 made specifically more grave than the water4 ,but if the ,altitude of the ,cone ,a ,i ,r1 were two thirds of the ,altitude of the ,cone ,a ,s ,t1 the ,cone ,a ,s ,t would be to the ,cone ,a ,i ,r1 as twenty seven to eight2 and the ,cylinder ,e ,s ,t ,o1 to the ,cylinder ,c ,i ,r ,n1 as nine to four1 that is1 as twenty seven to twelve2 and1 therefore1 the ,cylinder ,c ,i ,r ,n1 to the ,cone ,a ,i ,r1 as twelve to eight2 and the excess of the ,cylinder ,c ,i ,r ,n1 above the ,cone ,a ,i ,r1 to the ,cone ,a ,s ,t1 as four to twenty seven3 therefore if to the ,cone ,a ,b ,d be added so much weight as is the four twenty sevenths of the weight of the ,cone ,a ,s ,t1 which is a little more then its seventh part1 it also shall continue to swimme1 and the height of the emergent ,point shall be double to the height of the ,rampart4 ,this that hath been demonstrated in ,cones1 exactly holds in ,piramides1 although the one or the other should be very sharp in their ,point or ,cuspis#gg3 ,from whence we conclude1 that the same ,accident shall so much the more easily happen in all other ,figures1 by how much the less sharp the ,tops shall be1 in which they determine1 being assisted by more spacious ,ramparts4 #gg ,natation easiest effected in ,figures broad toward the top4 ,,theoreme ,,xiii4 ,sidenote3 ,all ,figures sink or swim1 upon bathing or not bathing of their tops4 ,all ,figures1 therefore1 of whatever greatnesse1 may go1 and not go1 to the ,bottom1 according as their ,sumities or ,tops shall be bathed or not bathed4 ,and this ,accident being common to all sorts of ,figures1 without exception of so much as one4 ,figure hath1 therefore1 no part in the production of this ,effect1 of sometimes sinking1 and sometimes again not sinking1 but only the being sometimes conjoyned to1 and sometimes seperated from1 the supereminent ,air3 which cause1 in fine1 who so shall rightly1 and1 as we say1 with both his ,eyes1 consider this business1 will find that it is reduced to1 yea1 that it really is the same with1 the true1 ,naturall and primary cause of ,natation or ,submersion2 to wit1 the excess or deficiency of the ,gravity of the water1 in relation to the ,gravity of that ,solid ,magnitude1 that is demitted into the water4 ,for like as a ,plate of ,lead1 as thick as the back of a ,knife1 which being put into the water by it self alone goes to the bottom1 if upon it you fasten a piece of ,cork four fingers thick1 doth continue afloat1 for that now the ,solid that is demitted in the water1 is not1 as before1 more grave than the water1 but less1 so the ,board of ,ebony1 of its own nature more grave than water2 and1 therefore1 descending to the bottom1 when it is demitted by it self alone into the water1 if it shall be put upon the water1 conjoyned with an ,expanded vail of ,air1 that together with the ,ebony doth descend1 and that it be such1 as that it doth make with it a compound less grave than so much water in ,mass1 as equalleth the ,mass already submerged and depressed beneath the ,levell of the waters ,surface1 it shall not descend any farther1 but shall rest1 for no other than the universall and most common cause1 which is that ,solid ,magnitudes1 less grave in specie than the water1 go not to the bottom4 ,so that if one should take a ,plate of ,lead1 as for ,example1 a finger thick1 and an handfull broad every way1 and should attempt to make it swimme1 with putting it lightly on the water1 he would lose his ,labour1 because that if it should be depressed an ,hairs breadth beyond the possible ,altitude of the ,ramparts of water1 it would dive and sink2 but if whilst it is going downwards1 one should make certain ,banks or ,ramparts about it1 that should hinder the defusion of the water upon the said ,plate1 the which ,banks should rise so high1 as that they might be able to contain as much water1 as should weigh equally with the said ,plate1 it would1 without all ,question1 descend no lower1 but would rest1 as being sustained by vertue of the ,air contained within the aforesaid ,ramparts3 and1 in short1 there would be a ,vessell by this means formed with the bottom of ,lead4 ,but if the thinness of the ,lead shall be such1 that a very small height of ,rampart would suffice to contain so much ,air1 as might keep it afloat1 it shall also rest without the ,artificiall ,banks or ,ramparts1 but yet not without the ,air1 because the ,air by it self makes ,banks sufficient for a small height1 to resist the ,superfusion of the water3 so that that which in this case swimmes1 is as it were a ,vessell filled with ,air1 by vertue of which it continueth afloat4 ,i will1 in the last place1 with an other ,experiment1 attempt to remove all difficulties1 if so be there should yet be any doubt left in any one1 touching the opperation of this ,e,continuity of the ,air1 with the thin ,plate which swims1 and afterwards put an end to this part of my discourse4 ,e ,or rather ,contiguity1 ,i suppose my self to be questioning with some of my ,oponents4 ,whether ,figure have any influence upon the encrease or diminution of the ,resistance in any ,weight against its being raised in the ,air#gh2 and ,i suppose1 that ,i am to maintain the ,affirmative1 asserting that a ,mass of ,lead1 reduced to the ,figure of a ,ball1 shall be raised with less force1 then if the same had been made into a thinne and broad ,plate1 because that it in this spacious ,figure1 hath a great quantity of ,air to penetrate1 and in that other1 more compacted and contracted very little3 and to demonstrate the truth of such my ,opinion1 ,i will hang in a small thred first the ,ball or ,bullet1 and put that into the water1 tying the thred that upholds it to one end of the ,ballance that ,i hold in the ,air1 and to the other end ,i by degrees adde so much ,weight1 till that at last it brings up the ,ball of ,lead out of the water3 to do which1 suppose a ,gravity of thirty ,ounces sufficeth2 ,i afterwards reduce the said ,lead into a flat and thinne ,plate1 the which ,i likewise put into the water1 suspended by three threds1 which hold it parallel to the ,surface of the water1 and putting in the same manner1 ,weights to the other end1 till such time as the ,plate comes to be raised and drawn out of the water3 ,i finde that thirty six ounces will not suffice to seperate it from the water1 and raise it thorow the ,air3 and arguing from this ,experiment1 ,i affirm1 that ,i have fully demonstrated the truth of my ,proposition4 ,here my ,oponents desires me to look down1 shewing me a thing which ,i had not before observed1 to wit1 that in the ,ascent of the ,plate out of the water1 it draws after it another ,plate 7if ,i may so call it7 of water1 which before it divides and parts from the inferiour ,surface of the ,plate of ,lead1 is raised above the ,levell of the other water1 more than the thickness of the back of a ,knife3 ,then he goeth to repeat the ,experiment with the ,ball1 and makes me see1 that it is but a very small quantity of water1 which cleaves to its compacted and contracted ,figure3 and then he subjoynes1 that its no wonder1 if in seperating the thinne and broad ,plate from the water1 we meet with much greater ,resistance1 than in seperating the ,ball1 since together with the ,plate1 we are to raise a great quantity of water1 which occurreth not in the ,ball3 ,he telleth me moreover1 how that our ,question is1 whether the ,resistance of ,elevation be greater in a dilated ,plate of ,lead1 than in a ,ball1 and not whether more resisteth a ,plate of ,lead with a great quantity of water1 or a ,ball with a very little water3 ,he sheweth me in the close1 that the putting the ,plate and the ,ball first into the water1 to make proofe thereby of their ,resistance in the ,air1 is besides our case1 which treats of ,elivating in the ,air1 and of things placed in the ,air1 and not of the ,resistance that is made in the ,confines of the ,air and water1 and by things which are part in ,air and part in water3 and lastly1 they make me feel with my hand1 that when the thinne ,plate is in the ,air1 and free from the weight of the water1 it is raised with the very same ,force that raiseth the ,ball4 ,seeing1 and understanding these things1 ,i know not what to do1 unless to grant my self convinced1 and to thank such a ,friend1 for having made me to see that which ,i never till then observed3 and1 being advertised by this same ,accident1 to tell my ,adversaries1 that our ,question is1 whether a ,board and a ,ball of ,ebony1 equally go to the bottom in water1 and not a ,ball of ,ebony and a ,board of ,ebony1 joyned with another flat ,body of ,air3 and1 farthermore1 that we speak of sinking1 and not sinking to the bottom1 in water1 and not of that which happeneth in the ,confines of the water and ,air to ,bodies that be part in the ,air1 and part in the water2 nor much less do we treat of the greater or lesser ,force requisite in seperating this or that ,body from the ,air2 not omitting to tell them1 in the last place1 that the ,air doth resist1 and gravitate downwards in the water1 just so much as the water 7if ,i may so speak7 gravitates and resists upwards in the ,air1 and that the same ,force is required to sinke a ,bladder under water1 that is full of ,air1 as to raise it in the ,air1 being full of water1 removing the consideration of the weight of that ,filme or ,skinne1 and considering the water and the ,air only4 ,and it is likewise true1 that the same ,force is required to sink a ,cup or such like ,vessell under water1 whilst it is full of ,air1 as to raise it above the ,superficies of the water1 keeping it with the mouth downwards2 whilst it is full of water1 which is constrained in the same manner to follow the ,cup which contains it1 and to rise above the other water into the ,region of the ,air1 as the ,air is forced to follow the same ,vessell under the ,surface of the water1 till that in this case the water1 surmounting the brimme of the ,cup1 breaks in1 driving thence the ,air1 and in that case1 the said brimme coming out of the water1 and arriving to the ,confines of the ,air1 the water falls down1 and the ,air sub-enters to fill the cavity of the ,cup3 upon which ensues1 that he no less transgresses the ,articles of the ,convention1 who produceth a ,plate conjoyned with much ,air1 to see if it descend to the bottom in water1 then he that makes proof of the ,resistance against ,elevation in ,air with a ,plate of ,lead1 joyned with a like quantity of water4 #gh ,an ,experiment of the operation of ,figures1 in encreasing or lessening of the ,airs ,resistance of ,division4 ,sidenote3 ,aristotles opinion touching the ,operation of ,figure examined4 ,i have said all that ,i could at present think of1 to maintain the ,assertion ,i have undertook4 ,it remains1 that ,i examine that which ,aristotle hath writ of this matter towards the end of his ,book ,de ,caelo#gi2 wherein ,i shall note two things3 the one that it being true as hath been demonstrated1 that ,figure hath nothing to do about the moving or not moving it self upwards or downwards1 its seemes that ,aristotle at his first falling upon this ,speculation1 was of the same opinion1 as in my opinion may be collected from the examination of his words4 ',tis true1 indeed1 that in essaying afterwards to render a reason of such effect1 as not having in my conceit hit upon the right1 7which in the second place ,i will examine7 it seems that he is brought to admit the largenesse of ,figure1 to be interessed in this operation4 ,as to the first particuler1 hear the precise words of ,aristotle4 #gi ,aristot4 de ,caelo ,lib4 #d4 ,cap #f4 ,figures are not the ,causes of moving simply upwards or downwards1 but of moving more slowly or swiftly#hjha1 and by what means this comes to pass1 it is not difficult to see4 #hj ,aristotle makes not ,figure the cause of ,motion absolutely1 but of swift or slow motion1 #ha ,lib4 #d4 ,cap4 #f3 ,text4 #db4 ,here first ,i note1 that the terms being four1 which fall under the present consideration1 namely1 ,motion1 ,rest1 ,slowly and ,swiftly3 ,and ,aristotle naming figures as ,causes of ,tardity and ,velocity1 excluding them from being the ,cause of absolute and simple ,motion1 it seems necessary1 that he exclude them on the other side1 from being the ,cause of ,rest1 so that his meaning is this4 ,figures are not the ,causes of moving or not moving absolutely1 but of moving quickly or slowly3 and1 here1 if any should say the mind of ,aristotle is to exclude ,figures from being ,causes of ,motion1 but yet not from being ,causes of ,rest1 so that the sence would be to remove from ,figures1 there being the ,causes of moving simply1 but yet not there being ,causes of ,rest1 ,i would demand1 whether we ought with ,aristotle to understand1 that all ,figures universally1 are1 in some manner1 the causes of ,rest in those ,bodies1 which otherwise would move1 or else some particular ,figures only1 as for ,example1 broad and thinne ,figures3 ,if all indifferently1 then every ,body shall rest3 because every ,body hath some ,figure1 which is false2 but if some particular ,figures only may be in some manner a ,cause of ,rest1 as1 for ,example1 the broad1 then the others would be in some manner the ,causes of ,motion3 for if from seeing some ,bodies of a contracted ,figure move1 which after dilated into ,plates rest1 may be inferred1 that the ,amplitude of ,figure hath a part in the ,cause of that ,rest2 so from seeing such like ,figures rest1 which afterwards contracted move1 it may with the same reason be affirmed1 that the united and contracted ,figure1 hath a part in causing ,motion1 as the remover of that which impeded it3 ,the which again is directly opposite to what ,aristotle saith1 namely1 that ,figures are not the ,causes of ,motion4 ,besides1 if ,aristotle had admitted and not excluded ,figures from being ,causes of not moving in some ,bodies1 which moulded into another ,figure would move1 he would have impertinently propounded in a dubitative manner1 in the words immediately following1 whence it is1 that the large and thinne ,plates of ,lead or ,iron1 rest upon the water1 since the ,cause was apparent1 namely1 the ,amplitude of ,figure4 ,let us conclude1 therefore1 that the meaning of ,aristotle in this place is to affirm1 that ,figures are not the ,causes of absolutely moving or not moving1 but only of moving swiftly or slowly3 which we ought the rather to believe1 in regard it is indeed a most true conceipt and opinion4 ,now the mind of ,aristotle being such1 and appearing by consequence1 rather contrary at the first sight1 then favourable to the assertion of the ,oponents1 it is necessary1 that their ,interpretation be not exactly the same with that1 but such1 as being in part understood by some of them1 and in part by others1 was set down3 and it may easily be indeed so1 being an ,interpretation consonent to the sence of the more famous ,interpretors1 which is1 that the ,adverbe ,simply or ,absolutely1 put in the ,text1 ought not to be joyned to the ,verbe to ,move1 but with the ,noun ,causes3 so that the purport of ,aristotles words1 is to affirm1 ,that ,figures are not the ,causes absolutely of moving or not moving1 but yet are ,causes ,secundum quid1 viz4 in some sort2 by which means1 they are called ,auxiliary and ,concomitant ,causes3 and this ,proposition is received and asserted as true by ,signor ,buonamico ,lib4 #e4 ,cap4 #bh4 where he thus writes4 ,there are other ,causes concomitant1 by which some things float1 and others sink1 among which the ,figures of ,bodies hath the first place1 c4 ,concerning this ,proposition1 ,i meet with many doubts and difficulties1 for which me thinks the words of ,aristotle are not capable of such a construction and sence1 and the difficulties are these4 ,first in the order and disposure of the words of ,aristotle1 the particle ,simpliciter1 or if you will absolute1 is conjoyned with the ,verb to move1 and seperated from the ,noun ,causes1 the which is a great presumption in my favour1 seeing that the writing and the ,text saith1 ,figures are not the ,cause of moving simply upwards or downwards1 but of quicker or slower ,motion3 and1 saith not1 ,figures are not simply the ,causes of moving upwards or downwards1 and when the words of a ,text receive1 transposed1 a sence different from that which they sound1 taken in the order wherein the ,author disposeth them1 it is not convenient to inverte them4 ,and who will affirm that ,aristotle desiring to write a ,proposition1 would dispose the words in such sort1 that they should import a different1 nay1 a contrary sence8 contrary1 ,i say1 because understood as they are written2 they say1 that ,figures are not the ,causes of ,motion1 but inverted1 they say1 that ,figures are the ,causes of ,motion1 c4 ,moreover1 if the intent of ,aristotle had been to say1 that ,figures are not simply the ,causes of moving upwards or downwards1 but only ,causes ,secundum quid1 he would not have adjoyned those words1 but they are ,causes of the more swift or slow ,motion2 yea1 the subjoining this would have been not only superfluous but false1 for that the whole tenour of the ,proposition would import thus much4 ,figures are not the absolute ,causes of moving upwards or downwards1 but are the absolute ,cause of the swift or slow ,motion2 which is not true3 because the primary ,causes of greater or lesser ,velocity1 are by ,aristotle in the #dth of his ,physicks1 ,text4 #ga4 attributed to the greater or lesser ,gravity of ,moveables1 compared among themselves1 and to the greater or lesser ,resistance of the ,medium's1 depending on their greater or less ,crassitude3 and these are inserted by ,aristotle as the primary ,causes2 and these two only are in that place nominated3 and ,figure comes afterwards to be considered1 ,text4 #gd4 rather as an ,instrumentall ,cause of the force of the ,gravity1 the which divides either with the ,figure1 or with the ,impetus2 and1 indeed1 ,figure by it self without the force of ,gravity or ,levity1 would opperate nothing4 ,i adde1 that if ,aristotle had an opinion that ,figure had been in some sort the ,cause of moving or not moving1 the inquisition which he makes immediately in a doubtfull manner1 whence it comes1 that a ,plate of ,lead flotes1 would have been impertinent2 for if but just before he had said1 that ,figure was in a certain sort the ,cause of moving or not moving1 he needed not to call in ,question1 by what ,cause the ,plate of ,lead swims1 and then ascribing the ,cause to its ,figure2 and framing a discourse in this manner4 ,figure is a ,cause ,secundum quid of not sinking3 but1 now1 if it be doubted1 for what ,cause a thin ,plate of ,lead goes not to the bottom2 it shall be answered1 that that proceeds from its ,figure3 a discourse which would be indecent in a ,child1 much more in ,aristotle2 ,for where is the occasion of doubting8 ,and who sees not1 that if ,aristotle had held1 that ,figure was in some sort a ,cause of ,natation1 he would without the least ,hesitation have writ2 ,that ,figure is in a certain sort the ,cause of ,natation1 and therefore the ,plate of ,lead in respect of its large and expatiated ,figure swims2 but if we take the proposition of ,aristotle as ,i say1 and as it is written1 and as indeed it is true1 the ensuing words come in very oppositely1 as well in the introduction of swift and slow1 as in the question1 which very pertinently offers it self1 and would say thus much4 ,figures are not the ,cause of moving or not moving simply upwards or downwards1 but of moving more quickly or slowly3 ,but if it be so1 the ,cause is doubtfull1 whence it proceeds1 that a ,plate of ,lead or of ,iron broad and thin doth swim1 c4 ,and the occasion of the doubt is obvious1 because it seems at the first glance1 that the ,figure is the ,cause of this ,natation1 since the same ,lead1 or a less quantity1 but in another ,figure1 goes to the bottom1 and we have already affirmed1 that the ,figure hath no share in this effect4 ,lastly1 if the intent of ,aristotle in this place had been to say1 that ,figures1 although not absolutely1 are at least in some measure the ,cause of moving or not moving3 ,i would have it considered1 that he names no less the ,motion upwards1 than the other downwards3 and because in exemplifying it afterwards1 he produceth no other ,experiments than of a ,plate of ,lead1 and ,board of ,ebony1 ,matters that of their own ,nature go to the bottom1 but by vertue 7as our ,adversaries say7 of their ,figure1 rest afloat2 it is fit that they should produce some other ,experiment of those ,matters1 which by their ,nature swims1 but retained by their ,figure rest at the bottom4 ,but since this is impossible to be done1 we conclude1 that ,aristotle in this place1 hath not attributed any action to the ,figure of simply moving or not moving4 ,but though he hath exquisitely ,philosophiz'd1 in investigating the solution of the doubts he proposeth1 yet will ,i not undertake to maintain1 rather various difficulties1 that present themselves unto me1 give me occasion of suspecting that he hath not entirely displaid unto us1 the true ,cause of the present ,conclusion3 which difficulties ,i will propound one by one1 ready to change opinion1 whenever ,i am shewed1 that the ,truth is different from what ,i say2 to the confession whereof ,i am much more inclinable than to contradiction4 ,sidenote3 ,aristotle erred in affirming a ,needle dimitted long wayes to sink4 ,aristotle having propounded the ,question1 whence it proceeds1 that broad ,plates of ,iron or ,lead1 float or swim2 he addeth 7as it were strengthening the occasion of doubting7 forasmuch as other things1 less1 and less grave1 be they round or long1 as for instance a ,needle go to the bottom4 ,now ,i here doubt1 or rather am certain that a ,needle put lightly upon the water1 rests afloat1 no less than the thin ,plates of ,iron or ,lead4 ,i cannot believe1 albeit it hath been told me1 that some to defend ,aristotle should say1 that he intends a ,needle demitted not longwayes but endwayes1 and with the ,point downwards2 nevertheless1 not to leave them so much as this1 though very weak refuge1 and which in my judgement ,aristotle himself would refuse1 ,i say it ought to be understood1 that the ,needle must be demitted1 according to the ,dimension named by ,aristotle1 which is the length3 because1 if any other ,dimension than that which is named1 might or ought to be taken1 ,i would say1 that even the ,plates of ,iron and ,lead1 sink to the bottom1 if they be put into the water edgewayes and not flatwayes4 ,but because ,aristotle saith1 broad ,figures go not to the bottom1 it is to be understood1 being demitted broadwayes3 and1 therefore1 when he saith1 long ,figures as a ,needle1 albeit light1 rest not afloat1 it ought to be understood of them when demitted longwayes4 ,moreover1 to say that ,aristotle is to be understood of the ,needle demitted with the ,point downwards1 is to father upon him a great impertinency2 for in this place he saith1 that little ,particles of ,lead or ,iron1 if they be round or long as a ,needle1 do sink to the bottome2 so that by his ,opinion1 a ,particle or small ,grain of ,iron cannot swim3 and if he thus believed1 what a great folly would it be to subjoyn1 that neither would a ,needle demitted endwayes swim8 ,and what other is such a ,needle1 but many such like ,graines accumulated one upon another8 ,it was too unworthy of such a man to say1 that one single ,grain of ,iron could not swim1 and that neither can it swim1 though you put a hundred more upon it4 ,lastly1 either ,aristotle believed1 that a ,needle demitted longwayes upon the water1 would swim1 or he believed that it would not swim3 ,if he believed it would not swim1 he might well speak as indeed he did2 but if he believed and knew that it would float1 why1 together with the dubious ,problem of the ,natation of broad ,figures1 though of ponderous ,matter1 hath he not also introduced the ,question2 whence it proceeds1 that even long and slender ,figures1 howbeit of ,iron or ,lead do swim8 ,and the rather1 for that the occasion of doubting seems greater in long and narrow ,figures1 than in broad and thin1 as from ,aristotles not having doubted of it1 is manifested4 ,no lesser an inconvenience would they fasten upon ,aristotle1 who in his defence should say1 that he means a ,needle pretty thick1 and not a small one2 for take it for granted to be intended of a small one2 and it shall suffice to reply1 that he believed that it would swim2 and ,i will again charge him with having avoided a more wonderfull and intricate ,probleme1 and introduced the more facile and less wonderfull4 ,we say freely therefore1 that ,aristotle did hold1 that only the broad ,figure did swim1 but the long and slender1 such as a ,needle1 not4 ,the which nevertheless is false1 as it is also false in round ,bodies3 because1 as from what hath been predemonstrated1 may be gathered1 little ,balls of ,lead and ,iron1 do in like manner swim4 ,sidenote3 ,aristotle affirmeth some ,bodies volatile for their ,minuity1 ,text4 #db4 ,he proposeth likewise another ,conclusion1 which likewise seems different from the truth1 and it is1 ,that some things1 by reason of their littleness fly in the ,air1 as the small dust of the ,earth1 and the thin leaves of beaten ,gold3 but in my ,opinion1 ,experience shews us1 that that happens not only in the ,air1 but also in the water1 in which do descend1 even those ,particles or ,atomes of ,earth1 that disturbe it1 whose minuity is such1 that they are not deservable1 save only when they are many hundreds together4 ,therefore1 the dust of the ,earth1 and beaten ,gold1 do not any way sustain themselves in the ,air1 but descend downwards1 and only fly to and again in the same1 when strong ,windes raise them1 or other agitations of the ,air commove them3 and this also happens in the commotion of the water1 which raiseth its ,sand from the bottom1 and makes it muddy4 ,but ,aristotle cannot mean this impediment of the commotion1 of which he makes no mention1 nor names other than the lightness of such ,minutiae or ,atomes1 and the ,resistance of the ,crassitudes of the ,water and ,air1 by which we see1 that he speakes of a calme1 and not disturbed and agitated ,air3 but in that case1 neither ,gold nor ,earth1 be they never so small1 are sustained1 but speedily descend4 ,sidenote3 ,democritus placed the ,cause of ,natation in certain fiery ,atomes4 ,he passeth next to confute ,democritus#hb1 which1 by his ,testimony would have it1 that some ,fiery ,atomes1 which continually ascend through the water1 do spring upwards1 and sustain those grave ,bodies1 which are very broad1 and that the narrow descend to the bottom1 for that but a small quantity of those ,atomes1 encounter and resist them4 #hb ,aristot4 ,de ,caelo lib4 #d4 cap4 #f4 text4 #dc4 ,i say1 ,aristotle confutes this position#hc1 saying1 that that should much more occurre in the ,air1 as the same ,democritus instances against himself1 but after he had moved the objection1 he slightly resolves it1 with saying1 that those ,corpuscles which ascend in the ,air1 make not their ,impetus conjunctly4 ,here ,i will not say1 that the reason alledged by ,democritus is true#hd1 but ,i will only say1 it seems in my judgement1 that it is not wholly confuted by ,aristotle1 whilst he saith1 that were it true1 that the calid ascending ,atomes1 should sustain ,bodies grave1 but very broad1 it would much more be done in the ,air1 than in ,water1 for that haply in the ,opinion of ,aristotle1 the said calid ,atomes ascend with much greater ,force and ,velocity through the ,air1 than through the water4 ,and if this be so1 as ,i verily believe it is1 the ,objection of ,aristotle in my judgement seems to give occasion of suspecting1 that he may possibly be deceived in more than one particular3 ,first1 because those calid ,atomes1 7whether they be ,fiery ,corpuscles1 or whether they be ,exhalations1 or in short1 whatever other matter they be1 that ascends upwards through the ,air7 cannot be believed to mount faster through ,air1 than through water3 but rather on the contrary1 they peradventure move more impetuously through the water1 than through the ,air1 as hath been in part demonstrated above4 ,and here ,i cannot finde the reason1 why ,aristotle seeing1 that the descending ,motion of the same ,moveable1 is more swift in ,air1 than in water1 hath not advertised us1 that from the contrary ,motion1 the contrary should necessarily follow2 to wit1 that it is more swift in the water1 than in the ,air3 for since that the ,moveable which descendeth1 moves swifter through the ,air1 than through the water1 if we should suppose its ,gravity gradually to diminish1 it would first become such1 that descending swiftly through the ,air1 it would descend but slowly through the water3 and then again1 it might be such1 that descending in the ,air1 it should ascend in the water3 and being made yet less grave1 it shall ascend swiftly through the water1 and yet descend likewise through the ,air3 and in short1 before it can begin to ascend1 though but slowly through the ,air1 it shall ascend swiftly through the water3 how then is it true1 that ascending ,moveables move swifter through the ,air1 than through the water8 #hc ,democritus confuted by ,aristotle1 text #dc4 #hd ,aristotles confutation of ,democritus refuted by the ,author4 ,that which hath made ,aristotle believe1 the ,motion of ,ascent to be swifter in ,air1 than in water1 was first1 the having referred the ,causes of slow and quick1 as well in the ,motion of ,ascent1 as of ,descent1 only to the diversity of the ,figures of the ,moveable1 and to the more or less ,resistance of the greater or lesser ,crassitude1 or ,rarity of the ,medium2 not regarding the comparison of the ,excesses of the ,gravities of the ,moveables1 and of the ,mediums3 the which notwithstanding1 is the most principal point in this affair3 for if the augmentation and diminution of the ,tardity or ,velocity1 should have only respect to the ,density or ,rarity of the ,medium1 every ,body that descends in ,air1 would descend in water3 because whatever difference is found between the ,crassitude of the water1 and that of the ,air1 may well be found between the ,velocity of the same ,moveable in the ,air1 and some other ,velocity3 and this should be its proper ,velocity in the water1 which is absolutely false4 ,the other occasion is1 that he did believe1 that like as there is a positive and intrinsecall ,quality1 whereby ,elementary ,bodies have a propension of moving towards the ,centre of the ,earth1 so there is another likewise intrinsecall#he1 whereby some of those ,bodies have an ,impetus of flying the ,centre1 and moving upwards3 by ,vertue of which intrinsecall ,principle1 called by him ,levity1 the ,moveables which have that same ,motion more easily penetrate the more subtle ,medium1 than the more dense3 but such a ,proposition appears likewise uncertain1 as ,i have above hinted in part1 and as with ,reasons and ,experiments1 ,i could demonstrate1 did not the present ,argument importune me1 or could ,i dispatch it in few words4 #he ,lib4 #d4 ,cap4 #e4 ,the ,objection therefore of ,aristotle against ,democritus1 whilst he saith1 that if the ,fiery ascending ,atomes should sustain ,bodies grave1 but of a distended ,figure1 it would be more observable in the ,air than in the water1 because such ,corpuscles move swifter in that1 than in this1 is not good2 yea the contrary would evene1 for that they ascend more slowly through the ,air3 and1 besides their moving slowly1 they ascend1 not united together1 as in the water1 but discontinue1 and1 as we say1 scatter3 ,and1 therefore1 as ,democritus well replyes1 resolving the instance they make not their push or ,impetus conjunctly4 ,aristotle1 in the second place1 deceives himself1 whilst he will have the said grave ,bodies to be more easily sustained by the said ,fiery ascending ,atomes in the ,air than in the ,water3 not observing1 that the said ,bodies are much more grave in that1 than in this1 and that such a ,body weighs ten pounds in the ,air1 which will not in the water weigh #a_/b an ounce2 how can it then be more easily sustained in the ,air1 than in the ,water8 ,sidenote3 ,democritus confuted by the ,authour4 ,let us conclude1 therefore1 that ,democritus hath in this particular better ,philosophated than ,aristotle4 ,but yet will not ,i affirm1 that ,democritus hath reason'd rightly1 but ,i rather say1 that there is a manifest ,experiment that overthrows his ,reason1 and this it is1 ,that if it were true1 that calid ascending ,atomes should uphold a ,body1 that if they did not hinder1 would go to the bottom1 it would follow1 that we may find a ,matter very little superiour in ,gravity to the water1 the which being reduced into a ,ball1 or other contracted ,figure1 should go to the bottom1 as encountring but few ,fiery ,atomes2 and which being distended afterwards into a dilated and thin ,plate1 should come to be thrust upwards by the impulsion of a great ,multitude of those ,corpuscles1 and at last carried to the very ,surface of the water3 which wee see not to happen2 ,experience shewing us1 that a ,body v4 gra4 of a ,sphericall ,figure1 which very hardly1 and with very great leasure goeth to the bottom1 will rest there1 and will also descend thither1 being reduced into whatsoever other distended ,figure4 ,we must needs say then1 either that in the water1 there are no such ascending ,fiery ,atoms1 or if that such there be1 that they are not able to raise and lift up any ,plate of a ,matter1 that without them would go to the bottom3 ,of which two ,positions1 ,i esteem the second to be true1 understanding it of water1 constituted in its naturall ,coldness4 ,but if we take a ,vessel of ,glass1 or ,brass1 or any other hard matter1 full of cold water1 within which is put a ,solid of a flat or concave ,figure1 but that in ,gravity exceeds the water so little1 that it goes slowly to the bottom2 ,i say1 that putting some burning ,coals under the said ,vessel1 as soon as the new ,fiery ,atomes shall have penetrated the substance of the ,vessel1 they shall without doubt1 ascend through that of the water1 and thrusting against the foresaid ,solid1 they shall drive it to the ,superficies1 and there detain it1 as long as the incursions of the said ,corpuscles shall last1 which ceasing after the removall of the ,fire1 the ,solid being abandoned by its supporters1 shall return to the bottom4 ,but ,democritus notes1 that this ,cause only takes place when we treat of raising and sustaining of ,plates of ,matters1 but very little heavier than the water1 or extreamly thin3 but in ,matters very grave1 and of some thickness1 as ,plates of ,lead or other ,mettal1 that same ,effect wholly ceaseth3 ,in ,testimony of which1 let's observe that such ,plates1 being raised by the ,fiery ,atomes1 ascend through all the depth of the water1 and stop at the ,confines of the ,air1 still staying under water3 but the ,plates of the ,opponents stay not1 but only when they have their upper ,superficies dry1 nor is there any means to be used1 that when they are within the water1 they may not sink to the bottom4 ,the cause1 therefore1 of the ,supernatation of the things of which ,democritus speaks is one1 and that of the ,supernatation of the things of which we speak is another4 ,but1 returning to ,aristotle#hf1 methinks that he hath more weakly confuted ,democritus1 than ,democritus himself hath done3 ,for ,aristotle having propounded the ,objection which he maketh against him1 and opposed him with saying1 that if the calid ascendent ,corpuscles were those that raised the thin ,plate1 much more then would such a ,solid be raised and born upwards through the ,air1 it sheweth that the desire in ,aristotle to detect ,democritus1 was predominate over the exquisiteness of ,solid ,philosophizing3 which desire of his he hath discovered in other occasions1 and that we may not digress too far from this place1 in the ,text precedent to this ,chapter which we have in hand#hg2 where he attempts to confute the same ,democritus for that he1 not contenting himself with names only1 had essayed more particularly to declare what things ,gravity and ,levity were2 that is1 the ,causes of descending and ascending1 7and had introduced ,repletion and ,vacuity7 ascribing this to ,fire1 by which it moves upwards1 and that to the ,earth1 by which it descends2 afterwards attributing to the ,air more of ,fire1 and to the water more of ,earth4 ,but ,aristotle desiring a positive ,cause1 even of ascending ,motion1 and not as ,plato1 or these others1 a simple negation1 or privation1 such as ,vacuity would be in reference to ,repletion#hh1 argueth against ,democritus and saith3 ,if it be true1 as you suppose1 then there shall be a great ,mass of water1 which shall have more of ,fire1 than a small ,mass of ,air1 and a great ,mass of ,air1 which shall have more of ,earth than a little ,mass of water1 whereby it would ensue1 that a great ,mass of ,air1 should come more swiftly downwards1 than a little quantity of water3 ,but that is never in any case soever3 ,therefore ,democritus discourseth erroneously4 #hf ,aristotle shews his desire of finding ,democritus in an ,error1 to exceed that of discovering ,truth4 #hg ,cap4 #e4 ,text #da4 #hh ,id4 ibid4 ,but in my opinion1 the ,doctrine of ,democritus is not by this allegation overthrown1 but if ,i erre not1 the manner of ,aristotle deduction either concludes not1 or if it do conclude any thing1 it may with equall force be restored against himself4 ,democritus will grant to ,aristotle1 that there may be a great ,mass of ,air taken1 which contains more ,earth1 than a small quantity of water1 but yet will deny1 that such a ,mass of ,air1 shall go faster downwards than a little water1 and that for many reasons4 ,first1 because if the greater quantity of ,earth1 contained in the great ,mass of ,air1 ought to cause a greater ,velocity than a less quantity of ,earth1 contained in a little quantity of water1 it would be necessary1 first1 that it were true1 that a greater ,mass of pure ,earth1 should move more swiftly than a less3 ,but this is false1 though ,aristotle in many places affirms it to be true3 because not the greater absolute1 but the greater specificall ,gravity1 is the cause of greater ,velocity#hi3 nor doth a ,ball of ,wood1 weighing ten pounds1 descend more swiftly than one weighing ten ,ounces1 and that is of the same ,matter3 but indeed a ,bullet of ,lead of four ,ounces1 descendeth more swiftly than a ,ball of ,wood of twenty ,pounds3 because the ,lead is more grave in specie than the ,wood4 ,therefore1 its not necessary1 that a great ,mass of ,air1 by reason of the much ,earth contained in it1 do descend more swiftly than a little ,mass of water#ij1 but on the contrary1 any whatsoever ,mass of water1 shall move more swiftly than any other of ,air1 by reason the participation of the terrene parts in specie is greater in the water1 than in the ,air4 ,let us note1 in the second place1 how that in multiplying the ,mass of the ,air1 we not only multiply that which is therein of terrene1 but its ,fire also3 whence the ,cause of ascending1 no less encreaseth1 by vertue of the ,fire1 than that of descending on the account of its multiplied ,earth4 ,it was requisite in increasing the greatness of the ,air1 to multiply that which it hath of terrene only1 leaving its ,fire in its first state1 for then the terrene parts of the augmented ,air1 overcoming the terrene parts of the small quantity of water1 it might with more probability have been pretended1 that the great quantity of ,air1 ought to descend with a greater ,impetus1 than the little quantity of water4 #hi ,the greater ,specificall1 not the greater absolute ,gravity1 is the ,cause of ,velocity4 #ij ,any ,mass of water shal move more swiftly1 than any of ,air1 and why4 ,therefore1 the ,fallacy lyes more in the ,discourse of ,aristotle1 than in that of ,democritus1 who with severall other ,reasons might oppose ,aristotle1 and alledge2 ,if it be true1 that the extreame ,elements be one simply grave1 and the other simply light1 and that the mean ,elements participate of the one1 and of the other ,nature2 but the ,air more of ,levity1 and the water more of ,gravity1 then there shall be a great ,mass of ,air1 whose ,gravity shall exceed the ,gravity of a little quantity of water1 and therefore such a ,mass of ,air shall descend more swiftly than that little water3 ,but that is never seen to occurr3 ,therefore its not true1 that the mean ,elements do participate of the one1 and the other quality4 ,this argument is fallacious1 no less than the other against ,democritus4 ,lastly1 ,aristotle having said1 that if the ,position of ,democritus were true1 it would follow1 that a great ,mass of ,air should move more swiftly than a small ,mass of water1 and afterwards subjoyned1 that that is never seen in any ,case3 methinks others may become desirous to know of him in what place this should evene1 which he deduceth against ,democritus1 and what ,experiment teacheth us1 that it never falls out so4 ,to suppose to see it in the ,element of water1 or in that of the ,air is vain1 because neither doth water through water1 nor ,air through ,air move1 nor would they ever by any whatever participation others assign them1 of ,earth or of ,fire3 the ,earth1 in that it is not a ,body fluid1 and yielding to the mobility of other ,bodies1 is a most improper place and ,medium for such an ,experiment3 ,vacuum1 according to the same ,aristotle himself1 there is none1 and were there1 nothing would move in it3 there remains the ,region of ,fire1 but being so far distant from us1 what ,experiment can assure us1 or hath assertained ,aristotle in such sort1 that he should as of a thing most obvious to sence1 affirm what he produceth in confutation of ,democritus1 to wit1 that a great ,mass of ,air1 is moved no swifter than a little one of water8 ,but ,i will dwell no longer upon this matter1 whereon ,i have spoke sufficiently3 but leaving ,democritus1 ,i return to the ,text of ,aristotle1 wherein he goes about to render the true reason1 how it comes to pass1 that the thin ,plates of ,iron or ,lead do swim on the water2 and1 moreover1 that ,gold it self being beaten into thin ,leaves1 not only swims in water1 but flyeth too and again in the ,air4 ,he supposeth that of ,continualls#ia1 some are easily divisible1 others not3 and that of the easily divisible1 some are more so1 and some less3 and these he affirms we should esteem the ,causes4 ,he addes that that is easily divisible1 which is well terminated1 and the more the more divisible1 and that the ,air is more so1 than the water1 and the water than the ,earth4 ,and1 lastly1 supposeth that in each kind1 the lesse quantity is easlyer divided and broken than the greater4 #ia ,de ,caelo l4 #d4 c4 #f4 t4 #dd4 ,here ,i note1 that the ,conclusions of ,aristotle in generall are all true1 but methinks1 that he applyeth them to particulars1 in which they have no place1 as indeed they have in others1 as for ,example1 ,wax is more easily divisible than ,lead1 and ,lead than ,silver1 inasmuch as ,wax receives all the terms more easlier than ,lead1 and ,lead than ,silver4 ,its true1 moreover1 that a little quantity of ,silver is easlier divided than a great ,mass3 and all these ,propositions are true1 because true it is1 that in ,silver1 ,lead and ,wax1 there is simply a ,resistance against ,division1 and where there is the absolute1 there is also the respective4 ,but if as well in water as in ,air1 there be no ,renitence against simple ,division1 how can we say1 that the water is easlier divided than the ,air8 ,we know not how to extricate our selves from the ,equivocation3 whereupon ,i return to answer1 that ,resistance of absolute ,division is one thing1 and ,resistance of ,division made with such and such ,velocity is another4 ,but to produce ,rest1 and to abate the ,motion1 the ,resistance of absolute ,division is necessary2 and the ,resistance of speedy ,division1 causeth not ,rest1 but slowness of ,motion4 ,but that as well in the ,air1 as in water1 there is no ,resistance of simple ,division1 is manifest1 for that there is not found any ,solid ,body which divides not the ,air1 and also the water3 and that beaten ,gold1 or small dust1 are not able to superate the ,resistance of the ,air1 is contrary to that which ,experience shews us1 for we see ,gold and ,dust to go waving to and again in the ,air1 and at last to descend downwards1 and to do the same in the water1 if it be put therein1 and separated from the ,air4 ,and1 because1 as ,i say1 neither the water1 nor the ,air do resist simple ,division1 it cannot be said1 that the water resists more than the ,air4 ,nor let any object unto me1 the ,example of most light ,bodies1 as a ,feather1 or a little of the pith of ,elder1 or water-reed that divides the ,air and not the water1 and from this infer1 that the ,air is easlier divisible than the water2 for ,i say unto them1 that if they do well observe1 they shall see the same ,body likewise divide the ,continuity of the water#ib1 and submerge in part1 and in such a part1 as that so much water in ,mass would weigh as much as the whole ,solid4 ,and if they shal yet persist in their doubt1 that such a ,solid sinks not through inability to divide the water1 ,i will return them this reply1 that if they put it under water1 and then let it go1 they shall see it divide the water1 and presently ascend with no less celerity1 than that with which it divided the ,air in descending3 so that to say that this ,solid ascends in the ,air1 but that coming to the water1 it ceaseth its ,motion1 and therefore the water is more difficult to be divided1 concludes nothing3 for ,i1 on the contrary1 will propose them a piece of ,wood1 or of ,wax1 which riseth from the bottom of the water1 and easily divides its ,resistance1 which afterwards being arrived at the ,air1 stayeth there1 and hardly toucheth it2 whence ,i may aswell say1 that the water is more easier divided than the ,air4 #ib ,archimed4 ,de ,insident4 humi lib4 #b4 prop4 #a4 ,i will not on this occasion forbear to give warning of another fallacy of these persons1 who attribute the reason of sinking or swimming to the greater or lesse ,resistance of the ,crassitude of the water against ,division1 making use of the example of an ,egg1 which in sweet water goeth to the bottom1 but in salt water swims2 and alledging for the cause thereof1 the faint ,resistance of fresh water against ,division1 and the strong ,resistance of salt water4 ,but if ,i mistake not1 from the same ,experiment1 we may aswell deduce the quite contrary2 namely1 that the fresh water is more dense1 and the salt more tenuous and subtle1 since an ,egg from the bottom of salt water speedily ascends to the top1 and divides its ,resistance1 which it cannot do in the fresh1 in whose bottom it stays1 being unable to rise upwards4 ,into such like perplexities1 do false ,principles ,lead men3 but he that rightly ,philosophating1 shall acknowledge the excesses of the ,gravities of the ,moveables and of the ,mediums1 to be the ,causes of those effects1 will say1 that the ,egg sinks to the bottom in fresh water1 for that it is more grave than it1 and swimeth in the salt1 for that its less grave than it3 and shall without any absurdity1 very solidly establish his ,conclusions4 ,therefore the reason totally ceaseth1 that ,aristotle subjoyns in the ,text saying#ic2 ,the things1 therefore1 which have great breadth remain above1 because they comprehend much1 and that which is greater1 is not easily divided4 ,such discoursing ceaseth1 ,i say1 because its not true1 that there is in water or in ,air any ,resistance of ,division2 besides that the ,plate of ,lead when it stays1 hath already divided and penetrated the ,crassitude of the water1 and profounded it self ten or twelve times more than its own thickness3 besides that such ,resistance of ,division1 were it supposed to be in the water1 could not rationally be affirmed to be more in its superiour parts than in the middle1 and lower3 but if there were any difference1 the inferiour should be the more dense1 so that the ,plate would be no less unable to penetrate the lower1 than the superiour parts of the water2 nevertheless we see that no sooner do we wet the superiour ,superficies of the ,board or thin ,piece of ,wood1 but it precipitatly1 and without any retension1 descends to the bottom4 #ic ,text #de4 ,i believe not after all this1 that any 7thinking perhaps thereby to defend ,aristotle7 will say1 that it being true1 that the much water resists more than the little1 the said ,board being put lower descendeth1 because there remaineth a less ,mass of water to be divided by it3 because if after the having seen the same ,board swim in four ,inches of water1 and also after that in the same to sink1 he shall try the same ,experiment upon a profundity of ten or twenty fathom water1 he shall see the very self same effect4 ,and here ,i will take occasion to remember1 for the removall of an ,error that is too common2 ,that that ,ship or other whatsoever ,body1 that on the depth of an hundred or a thousand fathom1 swims with submerging only six fathom of its own height1 or in the ,sea dialect1 that draws six fathom water shall swim in the same manner in water1 that hath but six fathom and half an ,inch of depth#id4 ,nor do ,i on the other side1 think that it can be said1 that the superiour parts of the water are the more dense1 although a most grave ,authour hath esteemed the superiour water in the ,sea to be so1 grounding his opinion upon its being more salt1 than that at the bottom3 but ,i doubt the ,experiment1 whether hitherto in taking the water from the bottom1 the ,observatour did not light upon some spring of fresh water there spouting up3 but we plainly see on the contrary1 the fresh ,waters of ,rivers to dilate themselves for some miles beyond their place of meeting with the salt water of the ,sea1 without descending in it1 or mixing with it1 unless by the intervention of some commotion or turbulency of the ,windes4 #id ,a ,ship that in #ajj ,fathome water draweth #f ,fathome1 shall float in #f ,fathome and #a_/b an ,inch of depth4 ,but returning to ,aristotle1 ,i say1 that the breadth of ,figure hath nothing to do in this business more or less1 because the said ,plate of ,lead1 or other ,matter1 cut into long ,slices1 swim neither more nor less#ie2 and the same shall the ,slices do1 being cut anew into little pieces1 because its not the breadth but the thickness that operates in this business4 ,i say farther1 that in case it were really true1 that the ,renitence to ,division were the proper ,cause of swimming#if1 the ,figures more narrow and short1 would much better swim than the more spacious and broad1 so that augmenting the breadth of the ,figure1 the facility of supernatation will be deminished1 and decreasing1 that this will encrease4 #ie ,thickness not breadth of ,figure to be respected in ,natation4 #if ,were ,renitence the cause of ,natation1 breadth of ,figure would hinder the swiming of ,bodies4 ,and for declaration of what ,i say1 consider that when a thin ,plate of ,lead descends1 dividing the water1 the ,division and discontinuation is made between the parts of the water1 invironing the perimeter or ,circumference of the said ,plate1 and according to the bigness greater or lesser of that circuit1 it hath to divide a greater or lesser quantity of water1 so that if the circuit1 suppose of a ,board1 be ten ,feet in sinking it flatways1 it is to make the seperation and division1 and to so speak1 an incission upon ten ,feet of water2 and likewise a lesser ,board that is four ,feet in ,perimeter1 must make an incession of four ,feet4 ,this granted1 he that hath any knowledge in ,geometry1 will comprehend1 not only that a ,board sawed in many long thin pieces1 will much better float than when it was entire1 but that all ,figures1 the more short and narrow they be1 shall so much the better swim4 ,let the ,board ,a ,b ,c ,d be1 for ,example1 eight ,palmes long1 and five broad1 its circuit shall be twenty six ,palmes2 and so many must the incession be1 which it shall make in the water to descend therein3 but if we do saw ir1 as suppose into eight little pieces1 according to the ,lines ,e ,f1 ,g ,h1 c4 making seven ,segments1 we must adde to the twenty six ,palmes of the circuit of the whole ,board1 seventy others2 whereupon the eight little pieces so cut and seperated1 have to cut ninty six ,palmes of water4 ,and1 if moreover1 we cut each of the said pieces into five parts1 reducing them into ,squares1 to the circuit of ninty six ,palmes1 with four cuts of eight ,palmes apiece2 we shall adde also sixty four ,palmes1 whereupon the said ,squares to descend in the water1 must divide one hundred and sixty ,palmes of water1 but the ,resistance is much greater than that of twenty six2 therefore to the lesser ,superficies1 we shall reduce them1 so much the more easily will they float3 and the same will happen in all other ,figures1 whose ,superficies are simular amongst themselves1 but different in bigness3 because the said ,superficies1 being either deminished or encreased1 always diminish or encrease their ,perimeters in subduple proportion2 to wit1 the ,resistance that they find in penetrating the water2 therefore the little pieces gradually swim1 with more and more facility as their breadth is lessened4 ,illustration ,this is manifest2 for keeping still the same height of the ,solid1 with the same proportion as the ,base encreaseth or deminisheth1 doth the said ,solid also encrease or diminish2 whereupon the ,solid more diminishing than the ,circuit1 the ,cause of ,submersion more diminisheth than the ,cause of ,natation3 ,and on the contrary1 the ,solid more encreasing than the ,circuit1 the ,cause of ,submersion encreaseth more1 that of ,natation less4 ,and this may all be deduced out of the ,doctrine of ,aristotle against his own ,doctrine4 ,lastly1 to that which we read in the latter part of the ,text#ig1 that is to say1 that we must compare the ,gravity of the ,moveable with the ,resistance of the ,medium against ,division1 because if the force of the ,gravity exceed the ,resistance of the ,medium1 the ,moveable will descend1 if not it will float4 ,i need not make any other answer1 but that which hath been already delivered2 namely1 that its not the ,resistance of absolute ,division1 7which neither is in ,water nor ,air7 but the ,gravity of the ,medium that must be compared with the ,gravity of the ,moveables2 and if that of the ,medium be greater1 the ,moveable shall not descend1 nor so much as make a totall ,submersion1 but a partiall only2 because in the place which it would occupy in the water1 there must not remain a ,body that weighs less than a like quantity of water3 but if the ,moveable be more grave1 it shall descend to the bottom1 and possess a place where it is more conformable for it to remain1 than another ,body that is less grave4 ,and this is the only true proper and absolute ,cause of ,natation and ,submersion1 so that nothing else hath part therein3 and the ,board of the ,adversaries swimmeth1 when it is conjoyned with as much ,air1 as1 together with it1 doth form a ,body less grave than so much water as would fill the place that the said ,compound occupyes in the water2 but when they shall demit the simple ,ebony into the water1 according to the ,tenour of our ,question1 it shall alwayes go to the bottom1 though it were as thin as a ,paper4 #ig ,lib4 #d4 c4 #f4 ,text #de4 ,decoration ,,finis4 ,decoration 99 99 99 99 99 ,detailed ,transcriber's ,notes ,the text has been made to match the original text as much as possible including variation in spelling1 punctuation1 italics etc4 ,the following1 details apparent printer's errors as well as changes or additions to aid readability of text4 ,page #a1 missing full stop after abbreviation gr4 '#j gr #ed min4'4 ,page #c1 sidenote1 missing space between words 'the ,authority ofan ,author4'4 ,page #c1 printer's error1 augmentarion for augmentation 'and augmentarion of ,masse'4 ,page #d1 missing letter t 'that that proceeded not'4 ,page #d1 printer's error or inconsistent punctuation1 'my paynes and time4 and although'4 ,page #f1 inconsistent punctuation1 full stop after axiome where as there are none after those following ',,axiome4 ,i4'4 ,page #i1 missing full stop added to end of paragraph 'or else an upright ,prisme4'4 ,page #aa1 printer's error1 missing letter ,c in illustration1 'the ,prisme ,a ,c ,d ,b to be placed'4 ,page #ae1 printer's error or archaic lettering1 final y looking like a #g in original text'and of the ,specifick ,gravity'4 ,page #af1 printer's error1 letter ,n for ,t in text to refer to illustration1 'if the ,vessell ,e ,n ,s ,f'4 ,page #af1 printer's error1 duplicate word in text 'equalizeth the ,force and and ,moment1'4 ,page #ag1 printer's error1 rhe for the 'as in rhe ,stilliard1'4 ,page #ag1 missing space between words 'asoften as that'4 ,page #ah1 sidenote1 printer's error1 specifiaclly for specifically ',a ,solid specifiaclly graver'4 ,page #bj1 potential printer's error1 properly for property1 'but this properly they have'4 ,page #bj1 printer's error1 n for u 'loseth all authenticalness'4 ,page #bb1 printer's error or variation in spelling1 ,benonamico for ,buonamico 'it seemes that ,benonamico'4 ,page #bc1 printer's error1 missing i 'accordng to its excess'4 ,page #bd1 missing line at the end of page in original text 'its ,region it loseth all'4 ,page #bf1 missing letter n 'unable by its small weight'4 ,page #bi1 missing letter e 'that ,i have gone about'4 ,page #cb1 unclear symbol in original text 'other ,figure1 c4'4 ,page #cg1 potential printer's error1 comma in unusual position 'whatever ,figure1 goeth always'4 ,page #ch1 missing space between words ',superficies might bedry3'4 ,page #ci1 missing letter t1 unied for united 'which holds them unied'4 ,page #da1 printer's error1 ,motitions for ,motions 'all ,motitions are made'4 ,page #db1 sidenote1 possible missing letter e1 ',see what satisfaction'4 ,page #dc1 printer's error1 ,subdidivisions for ,subdivisions1 'other ,subdidivisions1'4 ,page #di1 missing letter i1 dminishing for diminishing 'or dminishing it by dividing'4 ,page #ej1 sidenote1 printer's error1 missing letter l1 hep for help 'float by hep of'4 ,page #ec1 printer's error1 missing letter n1 beig for being 'beig double in ,gravity'4 ,page #ed1 printer's error1 missing letter l1 'shall also descend4'4 ,page #ee1 printer's error1 missing letter r1 'to form ,solid ,bodies'4 ,page #ef1 printer's error1 missing letter ,a1 ',cone ,s ,a ,t'4 ,page #eg1 printer's error1 missing letter t1 'of which it may descend'4 ,page #eh1 sidenote1 printer's error1 inverted n1 ',natation easiest effected'4 ,page #ei1 missing letter u1 'without all ,question1'4 ,page #ei1 printer's error1 inverted n1 'with an other ,experiment'4 ,page #ei1 potential printer's error1 sidenote ends with comma1 ',or rather ,contiguity1'4 ,page #fa1 missing letter a1 'that in this case the water1'4 ,page #gd1 printer's error1 ir for it1 'but if we do saw ir1'4 ,page #ge1 unclear symbol in original text 'c4 making seven ,segments'4