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version 1.32, 2002/09/20 00:02:43

version 1.33, 2002/09/20 00:26:18

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<s>MECHANICA ARISTOTE<lb/>LIS PROBLEMATA <lb/>EXERCITATIONES:</s>

<s><emph type="italics"/>ADIECTA SVCCINCTA NAR<lb/>ratione de autoris vita & &longs;criptis.<emph.end type="italics"/></s><figure id="id.007.00.002.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.002.1.jpg">

<s><emph type="italics"/><gap/>NTIAE.<emph.end type="italics"/></s>

<s>Typis & Sumptibus Viduæ Ioannis Albini.</s>

<s><emph type="italics"/>NOBILISSIMO AC GENE<lb/>ROSO DOMINO<emph.end type="italics"/>D. ADAMO PHILIP<lb/>PO BARONI A CRON<lb/>BERG, EQVITI, SACRÆ CÆSA<lb/>REÆ MAIESTATIS, ET SERENISSIMI Principis Archiducis Alberti Camerario intimo & c. <lb/></s>

Line 60

<s>Anno 1621.26.Martij. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.006.jpg"/><figure id="id.007.00.006.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.006.1.jpg">

<s>PRAEFATIO.</s>

Line 388

<s>Hi&longs;toriæ &longs;cribendæ leges. </s>

<s>Etalia quædam. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.020.jpg"/><figure id="id.007.00.020.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.020.1.jpg">

<s>IN MECHANICA ARISTOTE<lb/>LIS PROBLEMATAEXER CITATIONES.</s>

Line 436

<s>Sienim per tale centrum ducatur planum, fi<lb/>guram quomodolibet &longs;ecans, in partes æ què ponderantes <lb/>eam diuidit. </s>

<s>Nos verò quàm breui&longs;&longs;imè dicimus: <expan abbr="Centr&umacr;">Centrum</expan> <lb/>grauitatis, <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> magnitudinis punctum e&longs;&longs;e intra <lb/>extraue magnitudinem po&longs;itum, per quod &longs;i plano linea <lb/>punctoue diuidatur, in partes &longs;ecatur æqueponderantes. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.022.jpg"/><figure id="id.007.00.022.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.022.1.jpg">

<s>Diximus, Magnitudinis vtlineæ, plani &longs;olidique; cen<lb/>trum complecteremur. </s>

Line 444

<s>Diximus in&longs;uper, intra extraue. </s>

<s>Aliquando enim <lb/>grauitatis centrum extra molem corporis cuius corporis <lb/>centrum e&longs;t, cadit, vtin &longs;equenti figura. </s><figure id="id.007.00.022.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.022.2.jpg">

<s>E&longs;to corpus aliquod <lb/>&longs;uperficiesue ABCDE, <lb/>ducatur linea CF, <expan abbr="diuid&emacr;s">diuidens</expan> <lb/>figuras in partes hinc inde <lb/>æqueponderantes ABC, <lb/>EDC. </s>

Line 452

<s>Attamen licet hoc verum &longs;it, intra e&longs;&longs;e dici <lb/>pote&longs;t, quippe quod imaginario quodam, & vtita dicam, <lb/>virtuali ambitu ACDA contineatur. </s>

<s>Dicebamus, duplex e&longs;&longs;e grauitatis centrum, Natu<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.023.jpg"/>râ, Violentià: a&longs;firmamus modò, hæc re quidem vnum e&longs;<lb/>&longs;e, & ratione &longs;olum, non autem reip&longs;a ac&longs;i duo e&longs;&longs;ent con<lb/>&longs;iderari. </s><figure id="id.007.00.023.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.023.1.jpg">

<s>E&longs;to enim grauitatis na<lb/>turalis centrum B, corporis A, <lb/>&longs;ecundum quod dimi&longs;&longs;um, &longs;ua<lb/>pte naturâ cadet in C, &longs;i verò <lb/>corpus violenter impellatur in <lb/>D, aiiud acquiret centrum gra<lb/>uitatis ex violentia &longs;ecundum <lb/>quam fertur, motum, in D, <expan abbr="id&emacr;">idem</expan> <lb/>autem &longs;untre, nempe vnum B, <lb/>duo autem &longs;i violentia & natura &longs;eor&longs;um con&longs;ideren<lb/>tur. </s>

<s>Hæc centra, duo motus &longs;equuntur, rectus vterque, <lb/>Naturalis videlicet, & Violentus. </s>

<s>Tertius ex his mixtus, & <lb/>is quidem non rectus, &longs;ed curuus. </s><figure id="id.007.00.023.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.023.2.jpg">

<s>Proijciatur enim violen<lb/>ter corpus graue A &longs;uperante <lb/>igitur violentia, rectà feretur <lb/>in B; ea autem elangue&longs;cente <lb/>paullatim per curuam & mi<lb/>xtam <expan abbr="lineã">lineam</expan> &longs;ecetur in C, qua<lb/>tenus enim ad anteriora fer<lb/>tur, violentia e&longs;t; quatenus ve<lb/>rò ad inferiores partes, naturæ. </s>

Line 492

<s>Cuneus D. </s>

<s>Cochlea vero E. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.025.jpg"/><figure id="id.007.00.025.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.025.1.jpg">

<s>Porro, Cuneum ad libram reducere conatur Ari<lb/>&longs;toteles, quod facit & G. Vbaldus, qui cò refert & Co<lb/>chleam, quippe quod nihil aliud &longs;it Cochlea, quàm Cu<lb/>neus Cylindro inuolutus. </s>

Line 546

<s>Sit enim circulus AB, cuius centrum C, <lb/>&longs;emidiameter AC, &longs;umatur autem in ea punctum D, i<lb/>temqueue punctum E. </s>

<s>Erit itaque in ip&longs;a circulatione D <lb/>tardius E, ip&longs;um verò E tardius A, & ita citius id feretur <lb/>&longs;emper, quod remotius à mouente termino accipitur. </s><figure id="id.007.00.027.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.027.1.jpg">

<s>Hæc ex illo, quibus ne vltro a&longs;<lb/>&longs;en&longs;um præbeamus non vnica de cau<lb/>&longs;a cohibemur. </s>

Line 574

<s>Ad tertium, quod contrarijs feratur lationibus, an<lb/>tror&longs;um, retror&longs;um, &longs;ur&longs;um & deor&longs;um. </s>

<s>Dicimus, facilè <lb/>&longs;olui, Nullus enim, re bene per&longs;pectâ, affirmauerit circu<lb/>lum contrarijs lationibus moueri. </s><figure id="id.007.00.028.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.028.1.jpg">

<s>E&longs;to enim circulus ABCD, <lb/>circa centrum E; ponamus ro<lb/>tari, & A ver&longs;us B, exempli gra<lb/>tiâ, antror&longs;um, mouebitur <expan abbr="aut&emacr;">autem</expan> <lb/>& B ver&longs;us C, & C ver&longs;us D, tum <lb/>D ver&longs;us A. </s>

Line 590

<s>Circulum quidem duplici notione produci, Natu<lb/>rali videlicet altera, & altera quæ e&longs;t præter naturam, & <lb/>ideo circularem lineam in ter mixtas computari. </s>

<s>Motus mixtus ait, vel proportione &longs;eruata fit, aut <lb/>non; Si proportione &longs;eruatâ, rectam lineam; ea verò non <lb/>&longs;eruata, circularem lineam produci. </s><figure id="id.007.00.029.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.029.1.jpg">

<s>E&longs;to enim rectangu<lb/>lum ABCD, cuius late<lb/>ra in datâ &longs;int proportio<lb/>ne, AD cum AB. </s>

Line 616

<s>Cæterùm fal&longs;um <lb/>e&longs;t, a&longs;&longs;erere circulum ex mixto motu nun quam &longs;eruatâ <lb/>proportione produci. </s>

<s>&longs;eruat enim a&longs;&longs;iduè mixtus motus <lb/>quo producitur (&longs;i cum mixto motu producere velimus) <lb/>aliquam proportionem, &longs;ed non eandem. </s><figure id="id.007.00.030.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.030.1.jpg">

<s>E&longs;to enim recta AB, cui ad rectos <lb/>angulos AC. </s>

Line 640

<s>Ait autem; &longs;i duobus ab eadem potentia latis hoc <lb/>quidem plus repellatur, illud verò minus, æquum e&longs;t tar<lb/>diùs id moueri quod plus repellitur, eo quod minus. </s>

<s>De<lb/>trahi autem plus lineam, cuius extremum prepius e&longs;t cen<lb/>tro illa quæ &longs;uum habet terminum à centro remotiorem. </s><figure id="id.007.00.031.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.031.1.jpg">

<s>E&longs;to, inquit, circulus <lb/>BCDE & alter in eo minor <lb/>MNOP circa idem centrum <lb/>A. Ducanturque; Diametrima<lb/>ioris quidem CD, EB, mino<lb/>ris verò MO, NP. </s>

Line 678

<s>tunc enim dici pote&longs;t, pondus quod aliâs rectà ad <lb/>mundi centrum tenderet, à circuli centro in circulatio<lb/>ne retrahi, &longs;ed hæc ad circuli naturam, quatenus circulus <lb/>e&longs;t, ne quaquam &longs;pectant. </s><figure id="id.007.00.033.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.033.1.jpg">

<s>E&longs;to igitur circum ferentia <lb/>AFBH, cuius centrum C, dia<lb/>meter ACB, &longs;emidiameter AC. <lb/>&longs;umatur in AC punctum quod<lb/>libet, D, & centro C, &longs;patio CD, <lb/>circumferentia de&longs;cribatur <lb/>DGEI. </s>

Line 704

<s>Non enim propterea <lb/>quòd illæ magnæ &longs;int, hæ verò exiguæ, hæ &longs;unt illis exa<lb/>ctiores; &longs;ed quoniam magnæ, rudes &longs;unt, minores verò ex<lb/>qui&longs;ita diligentia elaboratæ, & à materiæ pertina cia libe<lb/>riores. </s>

<s>Cæteris ergo paribus, exactiores e&longs;&longs;e maiores, ex <lb/>Philo&longs;ophimente, ita docebimus. </s><figure id="id.007.00.034.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.034.1.jpg">

<s>E&longs;to libra maior AB, <lb/>cuius fulcimentum C. <lb/></s>

Line 714

<s>Itaque vt diameter ad <lb/>diametrum, ita portio ad portionem: maior autem dia<lb/>meter AB diametro DE: maior ergo portio AF, portio<lb/>ne DG. quod autem maius e&longs;t, minus obtutum fallit, ex<lb/>qui&longs;itius itaque tractum ex maiori AB quàm ex ip&longs;a mi<lb/>nori DE cogno &longs;cemus, quod fuerat o&longs;tendendum. </s>

<s>Cæterùm hac eadem de cau&longs;&longs;a, A&longs;tronomica in<lb/>&longs;trumenta, puta A&longs;trolabia, Armillæ, & alia eiu&longs;modi, <lb/>quo ampliora eò ex qui&longs;itiora, & certiora probantur. </s><figure id="id.007.00.035.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.035.1.jpg">

<s>E&longs;to enim A<lb/>&longs;trolabium magnum, <lb/>cuius diameter AB, <lb/>paruum autem CD, <lb/>circa idem centrum <lb/>E. </s>

Line 728

<s><emph type="italics"/>Vtrum libræ quæ ponderibus vacuæ æquilibrant, <lb/>omni pror&longs;us careant fraude?<emph.end type="italics"/></s>

<s>Videri cuipiam po&longs;&longs;et, libras, quæ ponderibus va<lb/>cuæ, æquilibrant, omm pror&longs;us fraude carere, verunta<lb/>men ita non e&longs;t, quod diligentiùs (res enim magni mo<lb/>menti e&longs;t) di&longs;quiremus. </s><figure id="id.007.00.036.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.036.1.jpg">

<s>E&longs;to enim libra AB, ita diui&longs;a <lb/>in C, vt AC &longs;it partium IS, CB ve<lb/>rò carundem &longs;it 10. apponatur parti <lb/>A lanx ponderans 10, parti vero B <lb/>lanx ponderans 15. ex permutata i<lb/>gitur proportione libra &longs;u&longs;pen&longs;a in <lb/>C, aequè ponderabit; &longs;i autem appo<lb/>natur lanci B &longs;acoma vnciarum 6, & in lance A con&longs;titua<lb/>tur purpura, quæ ita &longs;e habeat ad vncias 6, vt 10 ad 15, ite<lb/>rum æqueponderabit, &longs;ed vt 10 ad 15, ita 4 ad 6. Purpura<lb/>rius ergo fraudulentus, ponens in lance A vncias purpuræ <lb/>4, facto æquilibrio petet pretium vnciarum 6, & ita em<lb/>ptorem decipiet, quod &longs;anè innuerat, non autem demon<lb/>&longs;trauerat Ari&longs;toteles. </s>

Line 754

<s>Ari&longs;toteles primam quæ&longs;tionis partem ita &longs;oluit: An <lb/>quia &longs;ur&longs;um parte quidem exi&longs;tente, plus libræ extra per<lb/>pend culum &longs;it? </s>

<s>Spartum enim perpendiculum e&longs;t: quare <lb/>nece&longs;&longs;<gap/> e&longs;t deor&longs;um ferriid quod plus e&longs;t, donec a&longs;cendat <lb/>qua bifariam libram diuidit ad ip&longs;um perpendiculum, <lb/>cum onus in cum bat ad libræ partem &longs;ur&longs;us raptam. </s><figure id="id.007.00.037.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.037.1.jpg">

<s>Sit libra recta (hoc e&longs;t, in æquilibrio con&longs;tituta) BC, <lb/>&longs;partum autem AD, <lb/>fulcimentum autem <lb/>D, de&longs;uper: &longs;parto au<lb/>tem deor&longs;um proie<lb/>cto ad M perpendicu<lb/>laris erit vbi ADM. <lb/></s>

Line 766

<s>Nos autem cla<lb/>rius rem ob oculos ponimus. </s>

<s>Id ergo &longs;ibi vult Ari&longs;toteles, <lb/>propterea quòd pars iugi HDG maior e&longs;t parte ED q, <lb/>eam eleuatam nece&longs;&longs;e e&longs;t de&longs;cendere, & iterum à perpen<lb/>diculari ADM bifariam diui&longs;am ad æquilibrium reuer<lb/>ti, Po&longs;&longs;umus nos idem &longs;impliciori figura demon&longs;trare. </s><figure id="id.007.00.038.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.038.1.jpg">

<s>E&longs;to libra AB, bi<lb/>fariam, diui&longs;a in G, <lb/><expan abbr="fulciment&umacr;">fulcimentum</expan> verò &longs;ur<lb/>&longs;um vbi D, prod<gap/>ca<lb/>tur perpendicularis <lb/>DC in E. </s>

Line 782

<s>Si pondus circa &longs;tabile centrum conuertatur, dimi&longs;<lb/>&longs;um non &longs;tabit, ni&longs;i &longs;ecundum grauitatis centrum fuerit <lb/>in perpendiculari, quæ per centrum, circa quod conuer<lb/>titur, ad mundi centrum cadit. </s>

<s>Stabit autem in ea per<lb/>pendiculari in duobus punctis, altero à centro mundi <lb/>remoti&longs;&longs;imo; altero verò cidem quantum licuerit pro<lb/>ximo. </s><figure id="id.007.00.039.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.039.1.jpg">

<s>E&longs;to corpus A, cuius graui<lb/>tatis centrum B, nixum lineae in<lb/>flexibili BC, cum qua liberè <lb/>conuertatur circa centrum C. <lb/></s>

Line 816

<s>Ad hæc autem dubitare quis po&longs;&longs;et, cur experientiâ <lb/>docente, pondera quæ infra fulcimentum habent, vt lan<lb/>cea &longs;ari&longs;&longs;aue ad planum horizontis perpendiculariter e<lb/>recta, licet eo ca&longs;u grauitatis centrum in ip&longs;a perpendicu<lb/>lari con&longs;tituatur, non &longs;tet quidem, &longs;ed altrin&longs;ecus ca<lb/>dat? </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.041.jpg"/><figure id="id.007.00.041.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.041.1.jpg">

<s>Sit enim horizontis <lb/>planum AB, cui in puncto <lb/>C perpendiculariter ere<lb/>cta &longs;tatuatur &longs;ari&longs;&longs;a DC, <lb/>cuius grauitatis centrum <lb/>E, in ip&longs;a perpendiculari. <lb/></s>

Line 828

<s>Id certè agit, qui nutantis &longs;ari&longs;&longs;æ, digito, motum &longs;e<lb/>quitur; vt in ip&longs;o motu digitum a&longs;&longs;iduè centro grauitatis <lb/>&longs;ari&longs;&longs;æ &longs;upponat, vnde &longs;it vt nun quam extra fulcimentum <lb/>permanens, nun quam cadat. </s>

<s>Similis huic alia quo que dubitatio &longs;oluitur: Nempe, <lb/>Cur turbines, quibus pueri ludunt, dum quidem rotan<lb/>tur, &longs;tent erecti, rotationevero ce&longs;&longs;ante, cadant. </s><figure id="id.007.00.041.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.041.2.jpg">

<s>E&longs;to enim Turbo AB, cu<lb/>ius grauitatis centrum C, planum <lb/>horizontis DE, linea Horizonti <lb/>perpendicularis ABC, tran&longs;iens <lb/>per centrum grauitatis C, &longs;it au<lb/>tem fulcimentum in B. <expan abbr="Itaq;">Itaque</expan> cum <lb/>centrum grauitatis C &longs;it in ip&longs;a <lb/>perpendiculari, &longs;tabit ex demon-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.042.jpg"/>&longs;tratis, at ex vitio materiæ non &longs;tabit. </s>

Line 844

<s>De&longs;cribit au<lb/>tem in rotatione grauitatis centrum, quod in medio non <lb/>e&longs;t paruum circulum, per cuius centrum ip&longs;a perpendi<lb/>cula<gap/>is pertingit. </s>

<s>Modò redeuntes ad libram, cuius ful cimentum e&longs;t <lb/>&longs;ur&longs;um, alio principio, nempe Mechanico, cur depre&longs;&longs;a <lb/>ad æqualitatem reuertatur, demon&longs;trabimus. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.043.jpg"/><figure id="id.007.00.043.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.043.1.jpg">

<s>Sit igitur, vt &longs;u<lb/>periùs, libra AB, cu<lb/>ius centrum grauita<lb/>tis C, fulcimentum, <lb/>verò &longs;ur&longs;um, in D li<lb/>bræ quidem in C per<lb/>pendiculariter con<lb/>iunctum. </s>

Line 864

<s>Hinc colligimus &longs;ieri po&longs;&longs;e, libras illas, quæ non <gap/><lb/>quouis, quantumuis paruo pondere declinant, cas fulci-<gap/><lb/>mentum habere &longs;ur&longs;um. </s>

<s>His ad dimus, cæteris paribus, re&longs;i&longs;tentiam eò e&longs;&longs;e <lb/>maiorem, quo minus grauitatis centrum di&longs;tat à fulci<lb/>mento &longs;ur&longs;um, circa quod ip&longs;a libra aduertitur. </s><figure id="id.007.00.044.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.044.1.jpg">

<s>E&longs;to libra AB, cuius gra<lb/>uitatis centrum C, & primò <lb/>quidem eius ful cimentum <lb/>&longs;ur&longs;um &longs;it vbi D, itaque &longs;i ap<lb/>po&longs;ito pondere de clinauerit <lb/>libra ad partes B, punctum <lb/>C, dum a&longs;cendet de&longs;cribet <lb/>portionem circuli CE. fulciatur iterum &longs;ur&longs;um puncto F, <lb/>& iterum declinet ad partes B, & iterum punctum C, dum <lb/>a&longs;cendet, circuli portionem de&longs;cribet CG. </s>

Line 874

<s>E&longs;to enim iterum libra AB, cuius fulcimentum D, <lb/>centrum grauitatis C, &longs;it & alia libra, cuius brachia bre<lb/>uiora EF, idem habens centrum C, & eidem puncto &longs;u<lb/>&longs;pen&longs;a D. </s>

<s>Dico igitur, eodem pondere appo&longs;ito, faciliùs <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.045.jpg"/><figure id="id.007.00.045.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.045.1.jpg"><lb/>declinaturam libram ad <lb/>partes B, quàm &longs;i idem ap<lb/>poneretur in F. </s>

<s>Dico igitur, eodem pondere appo&longs;ito, faciliùs <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.045.jpg"/><figure id="id.007.00.045.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.045.1.jpg"></figure><lb/>declinaturam libram ad <lb/>partes B, quàm &longs;i idem ap<lb/>poneretur in F. </s>

<s>Demit<lb/>tatur enim, à puncto B <lb/>horizonti perpendicula<lb/>ris BG, & ab F item per<lb/>pendicularis FH, Tum <lb/>iuncta DB, centro D, eo<lb/>dem vero &longs;patio DB, circuli portio de&longs;cribatur BI, item <lb/>iuncta DF eodem centro D, &longs;patio DF, portio circuli de<lb/>&longs;cribatu: FK. e&longs;t autem maior DB ip&longs;a DF ex propo&longs;. <lb/></s>

Line 898

<s>Producatur perpendicularis DC, in G & fiat <lb/>CG æqualis CB, CH verò æqualis CF. </s>

<s>Sunt igitur duo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.046.jpg"/><figure id="id.007.00.046.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.046.1.jpg"><lb/>vectes DG, DH, quo<lb/>rum quidem commu<lb/>ne fulcimentum D, <lb/>pondus verò C, poten<lb/>tiæ vbi HG. </s>

<s>Sunt igitur duo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.046.jpg"/><figure id="id.007.00.046.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.046.1.jpg"></figure><lb/>vectes DG, DH, quo<lb/>rum quidem commu<lb/>ne fulcimentum D, <lb/>pondus verò C, poten<lb/>tiæ vbi HG. </s>

<s>Sunt au<lb/>tem hi vectes cius na<lb/>turæ, in quibus <expan abbr="p&omacr;dus">pondus</expan> <lb/>e&longs;t inter fulcimentum <lb/>& potentiam, itaque <lb/>vt &longs;e habet DC, ad <lb/>DG, ita potentia in G <lb/>ad pondus in C, item vt DC ad DH ita potentia in H ad <lb/>idem pondus C, &longs;ed minor e&longs;t propo&longs;itio DC, ad DG <lb/>quàm DC ad DH. minor ergo potentia requiritur in G, <lb/>hoc e&longs;t, in B, quàm in H, hoc e&longs;t in F. </s>

<s>Data igitur ponderis <lb/>æqualitate faciliùs &longs;uperabitur re&longs;i&longs;tentia C in B, quàm <lb/>in F: quod o&longs;tendendum fuerat. </s>

<s>Ad huius libræ naturam illæ quoque rediguntur, <lb/>quarum iugum non rectum quidem, &longs;ed curuum, vel ex <lb/>rectis &longs;ur&longs;um in angulum ad fulcimentum detinentibus, <lb/>nec refert vtrum curuitas &longs;it circuli portio quælibet, aut <lb/>ellip&longs;is &longs;ecundum alterum diametrorum; quod ita de<lb/>mon&longs;tramus. </s><figure id="id.007.00.046.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.046.2.jpg">

<s>E&longs;to libra, cuius iugum <lb/>curuum <expan abbr="angulat&umacr;ue">angulatunue</expan> ABC, <lb/>cuius fulcimentum B, æqua<lb/>lia autem brachia AB, BC, <lb/>& pondera item <expan abbr="vtrinq;">vtrinque</expan> ap<lb/>pen&longs;a æqualia. </s>

Line 926

<s>Hinc ratio pendet earum imaguncularum, quas ex <lb/>contu&longs;a papyro ligneaue leui materia compingunt, per<lb/>queue manus earum ambas, ferreum filum trajicientes, v<lb/>trinque plumbea appendunt pondera æqualia, ea <expan abbr="quid&emacr;">quidem</expan> <lb/>lege, vt centrum grauitatis infra pedes imaguncula &longs;ta<lb/>tuatur. </s>

<s>Tunc enim exten &longs;o filo imponentes ceu funam<lb/>bulos per illud, vltrò citroque; decurrere faciunt, imagun<lb/>cula interim erecta & in neutram partem cadente, quod <lb/>vt figurâ clarius fiat; </s><figure id="id.007.00.047.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.047.1.jpg">

<s>E&longs;to imaguncu<lb/>la AB, per cuius ma<lb/>nus traij ciatur filum <lb/>ferreum curuum <expan abbr="c&umacr;">cum</expan> <lb/>æ qualibus ponderi<lb/>bus hinc inde <expan abbr="app&emacr;-&longs;is">appen<lb/>&longs;is</expan> CD. </s>

Line 936

<s>Si <lb/>verò ad partes H eleuabitur in G. quare cum FG loca <lb/>&longs;intremotiora à mundi centro, quàm &longs;it E, non &longs;tabit gra<lb/>uitatis centrum in punctis FG, &longs;ed ad infimum locum re<lb/>uertecur, hoc e&longs;t, in ip&longs;a perpendiculari in E, & imagun<lb/>cula ad perpendiculum ip&longs;i H<emph type="italics"/>B<emph.end type="italics"/>E filo, hoc e&longs;t, ip&longs;i hori<lb/>zonti reuertetur. </s>

<s>Hinc etiam Arictum, T e&longs;tudinun<gap/> queue demolito<lb/>riatum Machinarum vis pendet, nempe ex ratione libra<lb/>rum, quæ fulcimentum habent &longs;ur&longs;um. </s><figure id="id.007.00.048.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.048.1.jpg">

<s>E&longs;to enim Aries A<emph type="italics"/>B<emph.end type="italics"/><lb/>funi appen&longs;us CD, cu<lb/>ius grauitatis centrum, <lb/>D, perpendicularis verò <lb/>quæ ad mundi centrum <lb/>ip&longs;a CDE. </s>

Line 966

<s>Hæc ille, qui &longs;chemate quo que rem aperit, at eo a<lb/>pud interpretes, & Picolomineum Paraphra&longs;tem, ita <expan abbr="m&emacr;-dosè">men<lb/>dosè</expan> lineato, vt inde ob&longs;curitas lucis loco, legentibus of<lb/>fundatur. </s>

<s>Nos, quod & &longs;uprà quo que fecimus, no&longs;tra fi<lb/>gurâ, &longs;ole ip&longs;o clariorem, ex Ari&longs;to telis ip&longs;ius mente rem <lb/>totam efficiemus. </s><figure id="id.007.00.049.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.049.1.jpg">

<s>Sit libra recta, (hoc <lb/>e&longs;t, in æquilibrio con<lb/>&longs;tituta) vbi NG. </s>

Line 978

<s>Incumbit enim onus ex<lb/>ce&longs;&longs;us medietatis eius, vbi e&longs;t F. </s>

<s>Sen&longs;us e&longs;t igitur, idcirco <lb/>partem iugi KLO inclinatam, ad æquilibrium non re<lb/>uerti, propterea quòd maior &longs;it ip&longs;a KLO pars quæ tra<lb/>hit, ip&longs;a<gap/> RKL, quæ trahitur & eleuatur. </s><figure id="id.007.00.050.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.050.1.jpg">

<s>Pote&longs;t hoc idem longè <lb/>&longs;impliciori themate demon<lb/>&longs;trari. </s>

Line 1018

<s>fu&longs;i&longs;&longs;imè enim ibi hac de re & ab&longs;oluti&longs;&longs;i<lb/>mè agit. </s>

<s>Nos autem quidem paucis ea, quæ ad hanc co<lb/>gnitionem pertinent, explicabimus. </s><figure id="id.007.00.051.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.051.1.jpg">

<s>E&longs;to enim libra A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius brachia æqualia, <lb/>& centrum grauitatis <lb/>in C, brachijs verò <lb/>AC, C<emph type="italics"/>B<emph.end type="italics"/> æqualibus, æ<lb/>qualia pondera hinc <lb/>inde <expan abbr="apponãtur">apponantur</expan>. </s>

Line 1038

<s>Circa hæc po&longs;&longs;et cuipiam oriri Dubium, num chor<lb/>dulæ, quibus lances appenduntur, variationem aliquam <lb/>circa ea quæ demon&longs;trata &longs;unt, inducere valeant. </s>

<s>Dicimus nullam inde fieri: E&longs;to enim libra AB, cu<lb/>ius centrum & fulcimentum C, ab cuius extremitate A <lb/>dependeat, funiculus AD, ab alia verò <emph type="italics"/>B<emph.end type="italics"/>, funiculus <emph type="italics"/>B<emph.end type="italics"/>E, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.053.jpg"/><figure id="id.007.00.053.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.053.1.jpg"><lb/>quibus appen&longs;æ &longs;int æ<lb/>qualis ponderis lances <lb/>DE. </s>

<s>Dicimus nullam inde fieri: E&longs;to enim libra AB, cu<lb/>ius centrum & fulcimentum C, ab cuius extremitate A <lb/>dependeat, funiculus AD, ab alia verò <emph type="italics"/>B<emph.end type="italics"/>, funiculus <emph type="italics"/>B<emph.end type="italics"/>E, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.053.jpg"/><figure id="id.007.00.053.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.053.1.jpg"></figure><lb/>quibus appen&longs;æ &longs;int æ<lb/>qualis ponderis lances <lb/>DE. </s>

<s>Moueatur libra, <lb/>fiatque in ICH, funi<lb/>culi verò in lancibus in <lb/>IK, HL. &longs;ecet autem fu<lb/>niculus IK libram A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>in M, LH verò produ<lb/>catur & eandem &longs;ecer <lb/>in N. quoniam igitur <lb/>IC, æqualis e&longs;t CH, pa<lb/>rallelæ autem KI, LN æquales <expan abbr="er&umacr;t">erunt</expan> alterni anguli MIC, <lb/>NHC, &longs;ed & anguli ad verticem ICH, BCH æquales <lb/>&longs;unt, quare triangulum IMC, æquale triangulo HNC, <lb/>& latera lateribus, quæ æqualibus angulis &longs;ubtenduntur. <lb/></s>

Line 1054

<s>Ari&longs;toteles ita quæ&longs;tionem proponit, vt eam R heto<lb/>rico quodam fuco admirabiliorem f<gap/>ciat. </s>

<s>Soluit au<lb/>tem hoc pacto, <expan abbr="inqui&emacr;s">inquiens</expan>, fieri po&longs;&longs;e eam e&longs;&longs;e cau&longs;&longs;am, quod <lb/>vectis &longs;it libra, eius nempe generis quod fulcimentum ha<lb/>bet deor&longs;um, atque id circo in ip&longs;a pre&longs;&longs;ione in partes in<lb/>æquales vectem diuidi. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.054.jpg"/><figure id="id.007.00.054.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.054.1.jpg">

<s>Figura quam ex<lb/>hibet, vix ferè quid &longs;i<lb/>bi velit explicat. </s>

Line 1110

<s>Cæterum videtur A riftoteles id &longs;ub<lb/>odora&longs;&longs;e, quod po&longs;tea Archimedes, Mechanicorum prin<lb/>ceps, in propo&longs;. </s>

<s>6. primi Æqueponderantium explicitè <lb/>protulit & probauit: nempe in æquilibrio ita e&longs;&longs;e pondus <lb/>ad pondus, vt brachium ad brachium, ratione permutata. </s><figure id="id.007.00.056.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.056.1.jpg">

<s>E&longs;to enim vectis <lb/>AB, quomodolibet <lb/>fulcimento diui&longs;us in <lb/>C. <expan abbr="app&emacr;datur">appendatur</expan> autem <lb/>in A, pondus D, in B <lb/>verò pondus E, ita &longs;e <lb/>habens ad pondus D, vtip&longs;a AC ad CB. </s>

Line 1130

<s>Teneo, at nondum acquie&longs;co: pe<lb/>tam enim, Cur ea rationis permutatio mirabilem illum <lb/>effectum pariat. </s>

<s>Hoc quod illi non do cent, puto nos, i<lb/>gnorantiæ &longs;omno &longs;epultos, &longs;omnia&longs;&longs;e. </s><figure id="id.007.00.056.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.056.2.jpg">

<s>Æqualitatem &longs;tatus <lb/>e&longs;&longs;e cau&longs;&longs;am, nemo, vt <lb/>puto, inficiabitur. </s>

Line 1140

<s>Datâ <lb/>igitur harum potentiarum æqualitate, linea AB, nec ad <lb/>partes A, nec ad partes B transferetur, &longs;ed pror&longs;us immo<lb/>bilis &longs;tabit. </s>

<s>His ita con&longs;titutis, Dico vecte quomodolibet diui&longs;o, <lb/>ponderibu&longs;que vtrinque appo&longs;itis, permutatâ propor<lb/>tione &longs;ibi inuicem re&longs;pondentibus, rem e&longs;&longs;e redactam ad <lb/>æqualitatem, & inde &longs;tatum fieri, hoc e&longs;t, æquilibrium. </s><figure id="id.007.00.057.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.057.1.jpg">

<s>E&longs;to enim vectis AB, quo modo libet diui&longs;us in C, & <lb/>ip&longs;i quidem C fulcimentum &longs;upponatur. </s>

Line 1160

<s>Cur igitur &longs;eruata permutatim brachiorum & <lb/>ponderum proportione fiat æquilibrium, ex his quæ de<lb/>mon&longs;trauimus, clarè patet. </s>

<s>Sed forte dicet qui&longs;piam, &longs;i brachia, pondera &longs;unt, <lb/>vel ponderibus æquipollentia, &longs;u&longs;tinenti duplicabitur <lb/>pondus. </s><figure id="id.007.00.058.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.058.1.jpg">

<s>E&longs;to enim vectis AB, <lb/>ita diui&longs;us in C, vt pars <lb/>maior CB minori AC &longs;it <lb/>in proportione quintu<lb/>pla. </s>

Line 1200

<s>Plurimum autem diuidi vbi plurima <lb/>pars remi à &longs;calmo e&longs;t. </s>

<s>Rem facilem, eo quod verbis potu<lb/>erit, &longs;chemate non declarauit, nos autem apponemus. </s><figure id="id.007.00.059.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.059.1.jpg">

<s>E&longs;to enim nauis AB, mare CD, <lb/>remorum alter, quiad proram EF, cu<lb/>ius &longs;calmus G, alterverò in medio na<lb/>uis, HI, circa &longs;calmum K. </s>

Line 1232

<s>Addimus, fal&longs;um videri quod a&longs;&longs;erit Ari&longs;toteles, <lb/>nempeillos qui in media naui &longs;unt, remiges, maximè na<lb/>uim mouere; facilius, melius dixi&longs;&longs;et. </s>

<s>Si enim maximè, <lb/>quod ait, denorat, maximo &longs;patio, & velocius pror&longs;us fal<lb/>&longs;um, etenim tardius mouent & minori &longs;patio, quod nos i<lb/>ta demon&longs;tramus. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.061.jpg"/><figure id="id.007.00.061.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.061.1.jpg">

<s>E&longs;to enim Remus AB <lb/>qui marí fulcitur in B, Scal<lb/>mus remi qui ad <expan abbr="prorã">proram</expan> pup<lb/>pimue C, qui in media naui <lb/>D, maior autem remi pars <lb/>e&longs;t à &longs;calmo Dad A quami<lb/>p&longs;ius C 2d A, Pellantur remi & &longs;tante ceu centro BA, in <lb/>E. eodem igitur tempore C eritin F, & D in G, &longs;ed maiu<gap/><lb/>e&longs;t &longs;patium CF &longs;patio DG, Ergo vnica impul&longs;ione, plus <lb/>mouit &longs;calmum, hoc e&longs;t, nauim, potentia ad puppim pro<lb/>ramue remigans, quàm ea quæ operatur in media naui vt <lb/>&longs;entire vid<gap/>batur (&longs;i modo is e&longs;t eius &longs;en&longs;us) Ari&longs;toteles. <lb/></s>

Line 1266

<s>quamobrem omnia <lb/>ferè quæ de Temone dicenda fuerant, de remo loquens <lb/>proponit. </s>

<s>Aitautem. </s><figure id="id.007.00.062.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.062.1.jpg">

<s>Aitautem. </s><figure id="id.007.00.062.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.062.1.jpg"></figure>

<s>Sit remus AB, <lb/>&longs;calmus vero C, remi <lb/>in nauigio <expan abbr="principi&umacr;">principium</expan> <lb/>A, palmula autem, <lb/>quæ in mari B. </s>

Line 1280

<s>Illud quoque <lb/>fal&longs;um e&longs;t, nauim ip&longs;am tantum moueri in aëre, quantum <lb/>e&longs;t &longs;patium AD, hoc e&longs;t, remi extremum quod e&longs;t in naui, <lb/>&longs;iquidem &longs;calmi motu, non autem manubrij remi, nauis <lb/>agatur. </s>

<s>Aliter igitur res &longs;e habet, & forte hoc pacto. </s><figure id="id.007.00.063.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.063.1.jpg">

<s>Aliter igitur res &longs;e habet, & forte hoc pacto. </s><figure id="id.007.00.063.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.063.1.jpg"></figure>

<s>Sit remus AB, cuíus <lb/>manubrium A, palmula <lb/>B, &longs;calmus C. </s>

Line 1288

<s>P o&longs;uitautem Ari&longs;toteles &longs;calmum ad medium <lb/>remi, &longs;ed non ad medium collocari &longs;olet, maior enim pars <lb/>in mare propendet puta HB, quo ca&longs;u translationis &longs;pa<lb/>tium fit maius, nempe ab H in I. fit autem motus &longs;calmi ex <lb/>centris qui &longs;unt in &longs;patio ip&longs;o BE, quatenus autem ad te<lb/>monem pertinet, quem remum ait, obliquè puppim ip&longs;am <lb/>propellentem, ita &longs;e res habet. </s>

<s>E&longs;to nauis carina AB, prora A, puppis B, Temonis <lb/>ala BC, gubernaculum BD, cardo verò fulcimentumue <lb/>B; factaitaque impul&longs;ione obliquâ gubernaculi à D in E, <lb/>minor fiet motus in mari à C in F, eritqueue temo vbi EGF, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.064.jpg"/><figure id="id.007.00.064.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.064.1.jpg"><lb/>cardo verò vbi G, translata igitur e<lb/>rit eo motu, puppis ip&longs;a à B in G. facta <lb/>itaque paruâ motione puppis ex B in <lb/>G, prora ip&longs;a quæ longè di&longs;tat à pup<lb/>pi B maiori &longs;patio &longs;uperato translata <lb/>erit in H facta proræ in contrariam <lb/>partem ab ea quæ facta e&longs;t guberna<lb/>culi motione. </s>

<s>E&longs;to nauis carina AB, prora A, puppis B, Temonis <lb/>ala BC, gubernaculum BD, cardo verò fulcimentumue <lb/>B; factaitaque impul&longs;ione obliquâ gubernaculi à D in E, <lb/>minor fiet motus in mari à C in F, eritqueue temo vbi EGF, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.064.jpg"/><figure id="id.007.00.064.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.064.1.jpg"></figure><lb/>cardo verò vbi G, translata igitur e<lb/>rit eo motu, puppis ip&longs;a à B in G. facta <lb/>itaque paruâ motione puppis ex B in <lb/>G, prora ip&longs;a quæ longè di&longs;tat à pup<lb/>pi B maiori &longs;patio &longs;uperato translata <lb/>erit in H facta proræ in contrariam <lb/>partem ab ea quæ facta e&longs;t guberna<lb/>culi motione. </s>

<s>Porrò quod & in præ<lb/>cedente quæ&longs;tione a dnotauimus, <expan abbr="l&omacr;-gè">lon<lb/>gè</expan> meliùs procedet demon&longs;tratio &longs;i <lb/><expan abbr="fulciment&umacr;">fulcimentum</expan> mare intelligatur, quàm <lb/>&longs;calmus, neque enim mare ceu pon<lb/>dus, &longs;ed &longs;calmus ip&longs;e Temonisuecardo, ponderum in&longs;tar <lb/>transferuntur. </s>

Line 1306

<s>Obliqui igitur motus qui validèin puppi &longs;it, cau&longs;&longs;a <lb/>e&longs;t non quidem ex conuer&longs;ione temonis percu&longs;&longs;io maris, <lb/>&longs;ed mare ip&longs;um, cuius fluctus naui currente obliquam te<lb/>monis alam ad eam partem quæ mari obuertitur, impel<lb/>lentes temonem cum puppiad contrariam partem vali<lb/>di&longs;&longs;imè transferunt. </s>

<s>E&longs;to nauis carina AB, prora B, puppis A, Temo AC, <lb/>gubernaculum AD; Itaque currentenaui, Temone in<lb/>terim & guberna culo in eadem carinæ linea exi&longs;tentibus, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.065.jpg"/><figure id="id.007.00.065.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.065.1.jpg"><lb/>Temo quidem mare &longs;ecat, nulla fa<lb/>ctâ in puppi, nauis ad &longs;ini&longs;tram dex<lb/>tramue translatione. </s>

<s>E&longs;to nauis carina AB, prora B, puppis A, Temo AC, <lb/>gubernaculum AD; Itaque currentenaui, Temone in<lb/>terim & guberna culo in eadem carinæ linea exi&longs;tentibus, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.065.jpg"/><figure id="id.007.00.065.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.065.1.jpg"></figure><lb/>Temo quidem mare &longs;ecat, nulla fa<lb/>ctâ in puppi, nauis ad &longs;ini&longs;tram dex<lb/>tramue translatione. </s>

<s>Si verò mouea<lb/>tur gubernaculum à D in E, co moto <lb/>mouebitur aliquantulum & puppis <lb/>ad partes E, quod voluit Ari&longs;toteles. <lb/></s>

Line 1324

<s>Pulcherrima enim res e&longs;t, & <lb/>nobis per&longs;pecti&longs;&longs;ima, qui Gua&longs;tallâ re&longs;identiæ olim no<lb/>&longs;træ oppido ad Padum, Mantuam pergentes &longs;æpi&longs;&longs;imè ad <lb/>Ca&longs;trum B<gap/>rgi Iu&longs;is ea qua diximus machinatione lati&longs;<lb/>&longs;imum eiu&longs;dem Padi aluum tran&longs;ie cimus. </s>

<s>Habet autem <lb/>&longs;e hoc pacto. </s><figure id="id.007.00.066.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.066.1.jpg">

<s>Habet autem <lb/>&longs;e hoc pacto. </s><figure id="id.007.00.066.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.066.1.jpg"></figure>

<s>E&longs;to fluminis citerior <lb/>ripa AB, vlterior CD. </s>

Line 1334

<s>Ex quibus apparet, motus cau&longs;&longs;am non <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.067.jpg"/>e&longs;&longs;e &longs;olam cam, quæ ab ala temonis fit, aquæ <expan abbr="percu&longs;&longs;ion&emacr;">percu&longs;&longs;ionem</expan>, <lb/>vt &longs;en&longs;erat Ari&longs;toteles, &longs;ed currentis a quæ temonis alam <lb/>ferientis impul&longs;ion<gap/>m: nihil autem referre, vtrum &longs;tante <lb/>naui a qua currat, vel câ currente a qua &longs;tet, vt in mari fit, <lb/>idem enim vtroque modo temo patitur. </s>

<s>Vt autem machi<lb/>næ huius & totius negotij &longs;pecies facilius animo concipia<lb/>tur, &longs;chema hoc &longs;tudio &longs;orum oculis &longs;ubijciemus. </s><figure id="id.007.00.067.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.067.1.jpg">

<s>Lembi nauiculæueideo appo&longs;itæ &longs;unt, vt oblongum <lb/>funem &longs;u&longs;tineant; id etenim nî fieret, aquæ immer&longs;us a<lb/>quam &longs;cindens machinæ motum impediret, ideo etiam <lb/>apponuntur, ne funis madens celeriter maceretur & pu<lb/>tre&longs;cat. </s>

Line 1344

<s>Diximus enim, Temonem currente naui, lateraliter <lb/>conuer&longs;um obuios fluctus ex cipientem puppim ip&longs;am ob<lb/>liquè in alteram partem transferre. </s>

<s>Porrò ea vela, de qui<lb/>bus loquimur, ventorum flatibus obliquè oppo&longs;ita can<lb/>dem ob cau&longs;&longs;am circulariter agitantur, quodvt figurâ eui<lb/>dentius fiat, </s><figure id="id.007.00.068.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.068.1.jpg">

<s>E&longs;to velum AB, brachio <lb/>CE obliquè affixum, ita vt <lb/>angulus ACE maior &longs;it an<lb/>gulo BCE, ventus obliquè <lb/>velum feriens FG. <expan abbr="Itaq;">Itaque</expan> quo<lb/>niam ventus in velum obli. <lb/></s>

Line 1358

<s>Si autem nece&longs;<lb/>&longs;e ei fuerit ad dextram &longs;ini&longs;tramqueue conuerti non pote<lb/>rit, ni&longs;i cauda ip&longs;a iuuetur. </s>

<s>Omnis enim motus progre&longs;&longs;i<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.069.jpg"/><figure id="id.007.00.069.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.069.1.jpg"><lb/>pote&longs;t, quod in libris de ani<lb/>malium ince&longs;&longs;u docetip&longs;e<lb/>met Philo&longs;ophus. </s>

<s>Omnis enim motus progre&longs;&longs;i<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.069.jpg"/><figure id="id.007.00.069.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.069.1.jpg"></figure><lb/>pote&longs;t, quod in libris de ani<lb/>malium ince&longs;&longs;u docetip&longs;e<lb/>met Philo&longs;ophus. </s>

<s>Sit igitur, <lb/>pi&longs;cem conuerti velle, & fie<lb/>ri capite in D, deflectet illi<lb/>co caudam in E, caque; aquam <lb/>ceu &longs;tabile quippiam <expan abbr="feri&emacr;s">feriens</expan> <lb/>eiqueue quod<gap/>mmodo fultus, <lb/>reliquum corpus CA refle<lb/>ctet in D, &longs;i autem conuerti <lb/>velit in F, caudam defle ctet in G, & eadem ratione <gap/> cte<lb/>tur in F. </s>

Line 1378

<s>Hæcille. </s>

<s>quæ &longs;ic figurâ explicamus. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.070.jpg"/><figure id="id.007.00.070.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.070.1.jpg">

<s>E&longs;to nauis AB, malus CD, <lb/>mali &longs;edes D, locus antennæ <lb/>&longs;ublimior C, depre&longs;&longs;ior E: ita<lb/>que quoniam CD vectis e&longs;t, <lb/>quo mouens remotior fuerit à <lb/>fulcimento D, co citiùs & vio<lb/>lentiùs pellet, velocius ergo <lb/>nauis mouebitur antenna in <lb/>C, quàm in E, con&longs;tituta. </s>

Line 1404

<s>Cætcrùm quod ad puppis faciliorem <lb/>eleuationem ex mali ip&longs;ius altitudine pertinet, ad vectis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.071.jpg"/>contemplationem reducimus. </s>

<s>e&longs;t enim quæ dam vectium <lb/>&longs;pecies ab alijs non con&longs;iderata, cuius brachia in angu<lb/>lum de&longs;inunt, vtip&longs;e angulus in operatione &longs;it fulcimen<lb/>tum. </s><figure id="id.007.00.071.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.071.1.jpg">

<s>E&longs;to enim vectis, de quo agimus, <lb/>ABC, cuius brachia AB, BC. iuncta <lb/>ad angulum B, &longs;itqueue B in operatione <lb/>fulc mentum. </s>

Line 1428

<s>Ad huius vectis naturam referuntur fabrorum mal<lb/>lei, quibus clauos reuellunt, forcipes item quæ tenaci <lb/>mor&longs;u clauorum capita vmbellasue apprendentes, vio<lb/>lenterè tabulis extrahunt. </s>

<s>In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars quæ à fulcimento ad <lb/>potentiam; ac verò quæ à fulcimento ad pondus, ponderi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.072.jpg"/><figure id="id.007.00.072.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.072.1.jpg"><lb/>&longs;iquidem æquiparatur re&longs;i<lb/>&longs;tentia quae fit in C. </s>

<s>In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars quæ à fulcimento ad <lb/>potentiam; ac verò quæ à fulcimento ad pondus, ponderi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.072.jpg"/><figure id="id.007.00.072.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.072.1.jpg"></figure><lb/>&longs;iquidem æquiparatur re&longs;i<lb/>&longs;tentia quae fit in C. </s>

<s>I dem ob<lb/>&longs;eruamus in forcipe, in quo <lb/>duo quidem brachia AD, <lb/>CB, quatenus ad appren&longs;io<lb/>nem pertinet, fulcimentum, <lb/>habentin ip&longs;o <expan abbr="c&emacr;tro">centro</expan> &longs;eu ver<lb/>rebra, & ideo quo longiores <lb/>fuerint, eo tenaciùs appre<lb/>hendunt & retinent. </s>

Line 1438

<s>His igitur hoc pacto examinatis, ad nauim & malum <lb/>reuertentes, dicimus, tunc facillimam fieri puppis eleua<lb/>tionem, proræ verò demer&longs;ionem, cum maxima fuerit <lb/>proportio, quam habet altitudo mali, ad eam nauis <expan abbr="part&emacr;">partem</expan> <lb/>quæ à malo ad ip&longs;am puppis extremitatem, pertingit. <lb/></s>

<s>Quamobrem prudentes nauium fabri, vt huic difficultati <lb/>occurrant, malum non in medio quidem nauis, &longs;ed in ter<lb/>tia ferè parte longitudinis quæ à prora e&longs;t, puppim ver&longs;us <lb/>con&longs;tituunt. </s><figure id="id.007.00.072.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.072.2.jpg">

<s>E&longs;to enim nauis AB; cuius <lb/>malus CD: prora A: puppis B; <expan abbr="v&emacr;-to">ven<lb/>to</expan> igitur velum impellente, <expan abbr="mal&umacr;">malum</expan> <lb/>ad partem contrariam vergit, pu<lb/>ta in FD. </s>

Line 1462

<s>Nos autem vt rem lucidiorem <lb/>faciamus, &longs;chema, quod necip&longs;e fecit, nec Philo&longs;ophus, <lb/>proponemus. </s>

<s>E&longs;to nauis A <emph type="italics"/>B<emph.end type="italics"/>, cuius prora A, puppis verò D, guber<lb/>naculum C<emph type="italics"/>B<emph.end type="italics"/>, temonis ala <emph type="italics"/>B<emph.end type="italics"/>D, veli &longs;inus EF, velum vero <lb/>ita con&longs;titutum, vt directè ex puppi flantem ventum exci-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.074.jpg"/><figure id="id.007.00.074.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.074.1.jpg"><lb/>piat. </s>

<s>Hoc vbi euenerit, naui<lb/>gium, rectâ è puppi mouetur <lb/>in proram; Si autem ventus la<lb/>teraliter &longs;pirat, puta à parte <lb/>G ver&longs;us H & nihilo &longs;ecius na<lb/>uigium, ac &longs;i ventus ex pup<lb/>pi e&longs;&longs;et antror&longs;um propelle<lb/>re volunt, velum quidem obli<lb/>quant partem cius infimam, <lb/>pedem nempe, quæ e&longs;t in F <lb/>contrahentes, Cornu verò <lb/>antennæ vbi E, proram ver&longs;us <lb/>laxantes ventumque; ip&longs;um obliquè ex cipientesid <expan abbr="effici&umacr;t">efficiunt</expan>, <lb/>vt ventus minus violenter feriat, & minori &longs;ui parte <expan abbr="vel&umacr;">velum</expan> <lb/>impleat, & quoniam ventus velum pellit in partem con<lb/>trariam, nempe in H, ip&longs;ivt vento re&longs;i&longs;tant conuer&longs;o gu<lb/>bernaculo ex C in L, & temone <emph type="italics"/>B<emph.end type="italics"/>D, in <emph type="italics"/>B<emph.end type="italics"/>M compellunt <lb/>proram ad partem à qua ventu<gap/> ip&longs;e &longs;pirat. </s>

Line 1478

<s>Tunc enim in rectum mouebitur nauis, cum &longs;ibi inui<lb/>cem æ quatæ vires, qua&longs;i libramentum con&longs;tituerint. </s>

<s>Hæc <lb/>ille, cuius &longs;en&longs;um figurâ propo&longs;itâ facilè aperiemus. </s><figure id="id.007.00.075.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.075.1.jpg">

<s>E&longs;to carina AB, cuius prora <lb/>A, puppis, B temo BC, ventus verò <lb/>obliquè feriens H. </s>

Line 1504

<s>Hæc ferè Philo&longs;ophus, cuius rationes ad eum &longs;olum<lb/>modo circularem motum faciunt, qui fit &longs;e cundum ab&longs;i<lb/>dem, vt in carrorum rotis v&longs;u venit, nec aptantur rotis fi<lb/>gulorum trochlei&longs;queue, cuiu&longs;modi &longs;unt illæ, quæ &longs;upra <lb/>puteos appenduntur. </s>

<s>Nos igitur, ad Ari&longs;totelis mentem, <lb/>primam rotationis &longs;peciem, quæ e&longs;t &longs;ecundum ab&longs;idem, <lb/>examinabimus. </s><figure id="id.007.00.076.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.076.1.jpg">

<s>E&longs;to rota &longs;phæ<lb/>raue AB, cuius cen<lb/>trum C; Horizontis <lb/>planum DE; conta<lb/>ctus circuli in plano <lb/>B. <expan abbr="perp&emacr;">perpem</expan> dicularis ho<lb/>rizonti à puncto <expan abbr="c&omacr;-tactus">con<lb/>tactus</expan> B ip&longs;a <emph type="italics"/>B<emph.end type="italics"/>CA, <lb/>tran&longs;iens per <expan abbr="centr&umacr;">centrum</expan> <lb/>C, partes rotæ circa <lb/>perpendicularem AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, angulus contactus G<emph type="italics"/>B<emph.end type="italics"/>E. <lb/></s>

Line 1538

<s>Angulos autem hî c&longs;ectores ip&longs;os vocat; oportet <lb/>enim circulos tum maiores tum minores circa idein cen<lb/>trum e&longs;&longs;e con&longs;titutos. </s>

<s>Hæc autem non ab&longs;imili ab eo <lb/>quod &longs;uprà po&longs;uimus &longs;chemate explicantur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.078.jpg"/><figure id="id.007.00.078.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.078.1.jpg">

<s>E&longs;to enim circulus <lb/>AB circa centrum, C, <lb/>Horizontis planum DE, <lb/>tangens circulum in B, <lb/>linea verò perpendicu<lb/>laris per centrum BCA. <lb/></s>

Line 1550

<s>Si enim in figura producatur ad oppo&longs;i<lb/>tam partem &longs;emidiameter HC in K &longs;ecans minorem cir<lb/>culum in L, duos alios &longs;ectores angulosue habebimus, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> KCB, LCG, ip&longs;is ACHFCI æ quales. </s>

<s><expan abbr="Itaq;">Itaque</expan> quan<lb/>tum adiuu at motum anguli ACH maioris nutus, in de<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus (vtita appellem) in <expan abbr="a&longs;cend&emacr;-do">a&longs;cenden<lb/>do</expan> ad partes A. & &longs;anè quatenus ad reinaturam pertinet <lb/>& ad ip&longs;um æquilibrium, non differunt maiores circuli à <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex ali quaratione minores videntur fore ad motum faci<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.079.jpg"/>liores, tum quia data materiæ æqualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planuin <lb/>circum ferentiae minoris quàm maioris circuli, vt in &longs;ubie<lb/><figure id="id.007.00.079.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.079.1.jpg"><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>quæ tam in maioribus quàm in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examin abimus. </s>

<s><expan abbr="Itaq;">Itaque</expan> quan<lb/>tum adiuu at motum anguli ACH maioris nutus, in de<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus (vtita appellem) in <expan abbr="a&longs;cend&emacr;-do">a&longs;cenden<lb/>do</expan> ad partes A. & &longs;anè quatenus ad reinaturam pertinet <lb/>& ad ip&longs;um æquilibrium, non differunt maiores circuli à <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex ali quaratione minores videntur fore ad motum faci<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.079.jpg"/>liores, tum quia data materiæ æqualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planuin <lb/>circum ferentiae minoris quàm maioris circuli, vt in &longs;ubie<lb/><figure id="id.007.00.079.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.079.1.jpg"></figure><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>quæ tam in maioribus quàm in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examin abimus. </s>

<s>Cæterùm vt aliquid de motu qui &longs;e cundum ab&longs;idem <lb/>fit, ex no&longs;tro penu promamus, Dicimus, Circulos, rota&longs;ue, <lb/>quæ hoc pacto mouentur, vel per horizontis planum mo<lb/>ueri, vel per accliue, aut decliue. </s>

<s>Siautem perhorizontis <lb/>planum, ideo facilem e&longs;&longs;e motum, quòd nunquam, cæte<lb/>ris paribus, centrum grauitatis ip&longs;ius corporis à centro <lb/>mundi, in ip&longs;a rotatione, fiat remotius. </s><figure id="id.007.00.079.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.079.2.jpg">

<s>E&longs;to enim planum, <lb/>horizontis AB, cui circu<lb/>lus in&longs;i&longs;tat AD, circa cen<lb/>trum C, diui&longs;us per <expan abbr="centr&umacr;">centrum</expan> <lb/>ip&longs;um à perpendiculari <lb/>ACD; Ducatur autem per <lb/>centrum C recta linea ho<lb/>rizonti æquidi&longs;tans, ECFG: dum diuidatur circulus vt<lb/><gap/>unque in partes AH, HF, FI, ID, & CI, CH iungan<lb/>tur. </s>

Line 1566

<s>Centrum ergo circuli, quod idem & grauitatis e&longs;t <expan abbr="centr&umacr;">centrum</expan>, <lb/>feretur per rectam CPQRS, &longs;unt enim KP, LQ, NR, <lb/>OS ip&longs;i AC &longs;emidiam etro æquales, <expan abbr="n&umacr;quam">nunquam</expan> igitur cen<lb/>trum ip&longs;um C in circuli rotatione ab horizontis plano e<lb/>leuabitur, nec à mundi centro fietremotius. </s>

<s>Hoc autem longè aliter cæteris figuris contingit, <lb/>quarum motus ideo in æ qualis, quòd non &longs;em per in rota<lb/>tione centium grauitatis eandem &longs;eruet à mundi centro <lb/>di&longs;tantiam. </s><figure id="id.007.00.080.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.080.1.jpg">

<s>E&longs;to enim Ellip&longs;is <lb/>ABCD, cuius <expan abbr="c&emacr;trum">centrum</expan> <lb/>E, diameter longior <lb/>BED, breuior AEC, <lb/>Horizontis planum, <lb/>FCG. locus contactus <lb/>C perpendicularis à <lb/>contactu per centrum i<lb/>p&longs;a CEA diuidens El<lb/>lip&longs;im in partes æquales, & æqueponderantes ABC, <lb/>ADC. </s>

Line 1582

<s>ibi enim centrum grauitatis fertur <lb/>per æquidi&longs;tantem horizonti, hic verò modò attollitur, <lb/>modò deprimitur, quod &longs;anè mole&longs;tiam & difficultatem <lb/>facit. </s>

<s>Sed idem alijs figuris contingere, & maximè latera<lb/>tis, ita docebimus. </s><figure id="id.007.00.081.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.081.1.jpg">

<s>E&longs;to enim triangulum <lb/>æquilaterum ABC, cuius <lb/>grauitatis centrum E hori<lb/>zontis planum BD. </s>

Line 1602

<s>Ad hanc quæ&longs;tionem illud quoque facit, cur per de<lb/>cliue planum grauiora corpora, & rotunda maximè; ma<lb/>gno impetu dimi&longs;&longs;a, delabantur. </s>

<s>E&longs;to enim rota &longs;phæraue aut Cylindrus CD, cuius <lb/>centrum E, tangens decliue planum AB in D, quæritur <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.082.jpg"/>cur dimi&longs;&longs;a hæc magno impetu deferantur ad partes B, <lb/>Ducatur per grauitatis centrum E ad horizontem, BK <lb/>perpendicularis FEL &longs;ecans decliue planum in G, cir<lb/>cum ferentiam verò in H. opponitur autem EG angulo <lb/>recto EDG, maior ergo EG ip&longs;a ED, hoc e&longs;t, EH, inter <lb/><figure id="id.007.00.082.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.082.1.jpg"><lb/>circumferentiam igitur & pla<lb/>num decliue, &longs;patium interce<lb/>dit HG. </s>

<s>E&longs;to enim rota &longs;phæraue aut Cylindrus CD, cuius <lb/>centrum E, tangens decliue planum AB in D, quæritur <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.082.jpg"/>cur dimi&longs;&longs;a hæc magno impetu deferantur ad partes B, <lb/>Ducatur per grauitatis centrum E ad horizontem, BK <lb/>perpendicularis FEL &longs;ecans decliue planum in G, cir<lb/>cum ferentiam verò in H. opponitur autem EG angulo <lb/>recto EDG, maior ergo EG ip&longs;a ED, hoc e&longs;t, EH, inter <lb/><figure id="id.007.00.082.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.082.1.jpg"></figure><lb/>circumferentiam igitur & pla<lb/>num decliue, &longs;patium interce<lb/>dit HG. </s>

<s>Ducatur item DI ip&longs;i <lb/>FG æquidi&longs;tans. </s>

Line 1622

<s>ci&longs;catur. </s>

<s>Po&longs;&longs;umus etiam Rota &longs;phæraue in plano decliui <lb/>collocata, datam potentiam inuenire, quæ extremitati <lb/>diametri ad eam partem quavergit applicata ip&longs;am rotam <lb/>&longs;phæramue impediatne delabatur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.083.jpg"/><figure id="id.007.00.083.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.083.1.jpg">

<s>E&longs;to planum in clinatum <lb/>AB, cui Rota &longs;phæraue in&longs;i<lb/>&longs;tat tangatque; illud in C. </s>

Line 1650

<s>Quæritur, Cur maiores <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.084.jpg"/>rotae impingentes, facilius offendicula &longs;uperent quàm mi<lb/>nores. </s>

<s>Neque enim &longs;atisfacere videtur quod ait Ari&longs;tote<lb/>les, ex contactu in puncto eo anguli à plano eleuationeid <lb/>fieri, alijs ergo principijs dubitatio &longs;oluitur. </s><figure id="id.007.00.084.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.084.1.jpg">

<s>E&longs;to rota quidem maior <lb/>AB, circa centrum C minor <lb/>vero DB circa centrum, E, <lb/><expan abbr="tãgentes">tangentes</expan> horizontis planum <lb/>in B. </s>

Line 1668

<s>Rota verò minor FD, tangens itidem <lb/>planum in D. rotæ autem centrum G, offendiculi verò re<lb/>ctitudo DH. </s>

<s>Ducatur per Hip&longs;i AB horizonti æquidi<lb/>&longs;tans HI &longs;ecans minorem circulum in K, maiorem verò <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.085.jpg"/><figure id="id.007.00.085.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.085.1.jpg"><lb/>in I. </s>

<s>Ducantur etiam dia<lb/>metri maioris quidem <lb/>LEM, minoris NGO, <lb/>Tum à puncto K perpen<lb/>dicularis ducatur ad <lb/>GO, ip&longs;a KP, item à pun<lb/>cto I ad EM perpendi<lb/>cularis <expan abbr="Iq.">Ique</expan> Dico EQ ad <lb/>QL, minorem habere <lb/>proportionem quam GP, <lb/>ad PN. </s>

Line 1698

<s>Minor ergo potentia requiritur <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.086.jpg"/>ad transferendam maiorem retam CD vltra offendicu<lb/>lum IV, hoc e&longs;t, DH, quàm requiratur ad trans ferendam <lb/>minorem vltra offendiculum KT, hoc e&longs;t HD, quod fue<lb/>rat o&longs;ten dendum. </s>

<s>Ad hæc, quæri pote&longs;t, quo pacto plau&longs;trorum rotæ <lb/>in ip&longs;a plau&longs;tri conuer&longs;ione &longs;e habeant, nempe quæ &longs;it li<lb/>neailla curua, quam in conuer&longs;ione de&longs;cribunt. </s><figure id="id.007.00.086.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.086.1.jpg">

<s>E&longs;to rotarum in <lb/>plano orbita, <expan abbr="d&umacr;">dum</expan> plau<lb/>&longs;trum rectâ procedit <lb/>AB, CD, Sunt autemi<lb/>p&longs;æ lineæ, quod o&longs;ten<lb/>demus po&longs;tea, æquedi<lb/>&longs;tantes. </s>

Line 1720

<s>Hoc etiam <lb/>theorema probamus. </s>

<s>Cylindros, quorum ba&longs;es axi &longs;unt perpendiculares, <lb/>dum in æquato plano conuoluuntur, rectâ incedere & <lb/>per parallelas, quarum di&longs;tantia axis &longs;eu latoris longitudi<lb/>ne præfinitur. </s><figure id="id.007.00.087.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.087.1.jpg">

<s>E&longs;to enim Cylin<lb/>drus ABCD, cuius a<lb/>xis GH, <expan abbr="horiz&omacr;tis">horizontis</expan> pla<lb/>no in&longs;i&longs;tens &longs;ecundum <lb/>latus AB, cui latus op<lb/>po&longs;itum & aequale CD. <lb/></s>

Line 1744

<s>E&longs;to enim Cylindrus ABCD, cuius ba&longs;es ellip&longs;es <expan abbr="inuic&emacr;">inuicem</expan> <lb/><expan abbr="æquedi&longs;tãtes">æquedi&longs;tantes</expan>, quarum axes longiores AB, CD, Commu<lb/>nis autem &longs;ectio cylindri & plani ad axem & horizontem <lb/>planum perpendicularis EHF. </s>

<s>Diuidatur autem &longs;emicir-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.088.jpg"/>culus EHF in partes æquales quatuor FI, IH, HG, GE. <lb/><figure id="id.007.00.088.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.088.1.jpg"><lb/>Tum per diui&longs;ionum puncta lateri parallelae, rectæ ducan<lb/>tur KGL, M<emph type="italics"/>H<emph.end type="italics"/>N, OIP, quæ quidem <expan abbr="c&umacr;">cum</expan> ba&longs;es AMB, DNC <lb/>parallelæ &longs;int, eruntinuicem æ quales, cumqueue circum<lb/>ferentia E<emph type="italics"/>H<emph.end type="italics"/>F æquales, eosqueue rectos angulos <expan abbr="c&omacr;&longs;tituent">con&longs;tituent</expan>. <lb/></s>

<s>Diuidatur autem &longs;emicir-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.088.jpg"/>culus EHF in partes æquales quatuor FI, IH, HG, GE. <lb/><figure id="id.007.00.088.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.088.1.jpg"></figure><lb/>Tum per diui&longs;ionum puncta lateri parallelae, rectæ ducan<lb/>tur KGL, M<emph type="italics"/>H<emph.end type="italics"/>N, OIP, quæ quidem <expan abbr="c&umacr;">cum</expan> ba&longs;es AMB, DNC <lb/>parallelæ &longs;int, eruntinuicem æ quales, cumqueue circum<lb/>ferentia E<emph type="italics"/>H<emph.end type="italics"/>F æquales, eosqueue rectos angulos <expan abbr="c&omacr;&longs;tituent">con&longs;tituent</expan>. <lb/></s>

<s>Ducatur po&longs;t hæc &longs;eor&longs;um recta QR, & eidem perpendi<lb/>cularis ST eam &longs;ecans in V. applicetur autem rectæ ST <lb/>æqualis Cylindri lateri BC, ip&longs;a <foreign lang="greek">hz. </foreign></s>

Line 1766

<s>Hæc quo que &longs;peculatio ad motum qui &longs;ecundum <lb/>ab&longs;idem fit, manife&longs;tè pertinet. </s>

<s>Coni, quorum ba&longs;es cir<lb/>culi &longs;unt, &longs;i in plano &longs;ecundum latus rotentur, ba&longs;i circu<lb/>lum de&longs;cribunt, cuius centrum immobile coni ip&longs;ius e&longs;t <lb/>vertex, &longs;emidiameter verò ip&longs;um latus. </s><figure id="id.007.00.089.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.089.1.jpg">

<s>E&longs;to conus ABC cu<lb/>ius vertex C ba&longs;is AB, axis <lb/>DC, ba&longs;is verò centrum, <lb/>D, latus quo planum tan<lb/>git BC, &longs;ecatur itaque Co<lb/>nus per latus BC & axem <lb/>DE à plano horizonti per<lb/>pendiculari, cuius & coni <lb/>communis &longs;ectio e&longs;t ABC <lb/>triangulum, & quoniam coni grauitatis centrum e&longs;t in <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.090.jpg"/>axe ip&longs;o, conus in partes æque <expan abbr="p&omacr;derantes">ponderantes</expan> &longs;ecatur AEBC, <lb/>AFBC, &longs;tat ergo conus &longs;ibimet æquili bris. </s>

Line 1802

<s>Ad hæc circa axem ita libratur rota, vt <lb/>quantumuis exigua potentia alteri parti applicetur, alte<lb/>raillico &longs;uperata moueatur. </s>

<s>Licet enim propliè ea <expan abbr="tant&umacr;">tantum</expan> <lb/>corpora æquilibrare dicantur, quæ ob ponderis hinc in de <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.092.jpg"/>æqualitatem horizonti fiunt æquidi&longs;tantes, nihilominus <lb/>& hic aliquam e&longs;&longs;e æquilibrij &longs;imilitudinem patebit. </s><figure id="id.007.00.092.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.092.1.jpg">

<s>E&longs;to enim rota ABCD, <lb/>cuius axis horizonti perpendi<lb/>cularis FEG tran&longs;iens per cen<lb/>trum E, tangens autem planum <lb/>in puncto G. </s>

Line 1818

<s>Quærimus igitur primò; Cur ea quæ hoc pacto <expan abbr="ro-tãtur">ro<lb/>tantur</expan>, in ip&longs;a rotatione locum non mutent, ni&longs;i extrin&longs;eca <lb/>aliqua id fiat ex cau&longs;&longs;a. </s>

<s>E&longs;to enim rota aut aliud quippiam rotundum ccu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.093.jpg"/><figure id="id.007.00.093.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.093.1.jpg"><lb/>rizonti perpendicularem mo<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. </s>

<s>E&longs;to enim rota aut aliud quippiam rotundum ccu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.093.jpg"/><figure id="id.007.00.093.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.093.1.jpg"></figure><lb/>rizonti perpendicularem mo<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. </s>

<s>Modò circa <lb/>centrum E in finiti imagin entur <lb/>circuli, alij alijs minores v&longs;que <lb/>ad <expan abbr="centr&umacr;">centrum</expan> ip&longs;um, vti &longs;unt FGH; <lb/>ibi enim circuli e&longs;&longs;e de&longs;inunt, <lb/>vbi nullum amplius e&longs;t &longs;patium. <lb/></s>

Line 1848

<s>quo igitur figura ijs partibus, <lb/>quæ longius à centro ab&longs;unt, abundauerit magis, eo faci<lb/>lius, & velocius in circulum rotata mouebitur. </s>

<s>Modò o<lb/>&longs;tendemus, circularem cæteras omnes ea qua diximus <lb/>partium à centro remoti&longs;&longs;imarum copiâ abundare. </s><figure id="id.007.00.094.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.094.1.jpg">

<s>E&longs;to triangulum puta æqui<lb/>iaterum, ABC circa centrum D. <lb/></s>

Line 1866

<s>Quæri etiam pote&longs;t, Num axe in clinato, rotæ motus ali<lb/>qualiter impediatur? </s>

<s>Nos negatiuam partem amplecti<lb/>mur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.095.jpg"/><figure id="id.007.00.095.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.095.1.jpg">

<s>E&longs;to enim tota ABCD, cuius cen<lb/>trum E axis inclin itus, circa quem <lb/>conuertitur EGF. </s>

Line 1914

<s>Ad id autem quod dixit, quo <expan abbr="maior&emacr;s">maiorens</expan> fuerint tro<lb/>chleæ, eo faciliùs mouere, non e&longs;t, vt dicebamus, &longs;impli<lb/>citer verum, quod facilè o&longs;tendemus. </s><figure id="id.007.00.096.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.096.1.jpg">

<s>Efto enim trochlea AB circa centrum C, appen&longs;a in <lb/>puncto D, perpendicularis quæ ad mundi centrum DCE, <lb/>pondera æqualia vtrinque appen&longs;a FG. </s>

Line 1936

<s>Dico igitur, Axium, circa quos tro<lb/>chleæ rotæue conuertuntur ad rotas ip&longs;as, varias habere <lb/>proportiones. </s>

<s>O&longs;tendemus autem <expan abbr="rotã">rotam</expan> illam, trochleam<lb/>ue faciliùs moueri, & mouere pondera, quo rotæ diame<lb/>ter ad axis diametrum maiorem habuerit proportionem, <lb/>& ideo fieri po&longs;&longs;e rotam maiorem ad &longs;uum axem <expan abbr="minor&emacr;">minorem</expan> <lb/>habere proportionem quam rotam minorem ad &longs;uum. </s><figure id="id.007.00.097.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.097.1.jpg">

<s>E&longs;to enim <lb/>trochlea AB cir<lb/>ca centrum C, <lb/>cuius diameter <lb/>DCE &longs;it in ip&longs;a <lb/>quæ ad mundi <lb/>centrum <expan abbr="perp&emacr;-diculari">perpen<lb/>diculari</expan>: &longs;it au<lb/>tem appen&longs;a in D. </s>

Line 1984

<s>Duabus autem partibus con&longs;tant, alterâ, quæ ab <lb/>axe ad angulum; quæ verè vectis e&longs;t; alterâ, cui manusi<lb/>p&longs;a admouetur, ex qua res tota manubrium dicitur. </s>

<s>Fiunt <lb/>autem manubria hæc vt plurimum amouibilia, &longs;unt <expan abbr="tam&emacr;">tamen</expan> <lb/>ceu rotarum ip&longs;arum partes, & rotis ip&longs;is commodè affi<lb/>gerentur, ni&longs;i in rotatione à tran&longs;uer&longs;arijs, quibus rotæ &longs;u<lb/>&longs;tinentur, impedimentum fieret. </s><figure id="id.007.00.099.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.099.1.jpg">

<s>E&longs;to enim rota AB, cu<lb/>ius axis E, terebretur autem <lb/>in F, ibiqueue paxillus affigatur <lb/>FK. </s>

Line 2002

<s>Sunt autem eorum circulorum &longs;emidiametri, qui <lb/>à punctis FL, in ip&longs;a rotatione de&longs;cribuntur. </s>

<s>Ita igitur &longs;e <lb/>habebit potentia applicata in L ad diametrum &longs;emidia<lb/>metrumue axis rotæ CD, vt &longs;e habet potentia applicata <lb/>in F, ad diametrum &longs;emidiame trumue axis E rotæ AB, &longs;ed <lb/>&longs;patia &longs;unt æqualia & potentiæ æquales, quare nihil re<lb/>fert, vtrum manubrium lateria ffigatur, vel axi à latere ro<lb/>tæ &longs;eparatum applicetur. </s><figure id="id.007.00.100.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.100.1.jpg">

<s>Duplex autem e&longs;t ma<lb/>nubriorum forma; altera e<lb/>nim rectis partibus con&longs;tat, <lb/>altera verò curua e&longs;t tota, <lb/>&longs;ed rectis vtimur vt mani<lb/>bus apprendamus, curuis <lb/>verò vt locum illis appona<lb/>mus, & pedis pre&longs;&longs;ione ceu <lb/>in molis lapideis, quibus <lb/>gladij acuuntur, fieri a&longs;&longs;olet, conuertantnr. </s>

Line 2030

<s>In <lb/>obliquum autem haudqua quam vergit. </s>

<s>Nos quod ip&longs;e <lb/>non fecit figurâ ip&longs;a appo&longs;itâ rem clariorem faciemus. </s><figure id="id.007.00.101.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.101.1.jpg">

<s>Efto libra AB, cuius ful<lb/>cimentum C, pondera vtrin<lb/>que appen&longs;a AB, quorum v<lb/>trumque ponderet 10. Item <lb/>libra DE, cuius fulcimentum <lb/>F pondere vero appen&longs;a D, E, <lb/>ip&longs;is A, B, dimidio leuiora, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> S. </s>

Line 2050

<s>quo enim maius e&longs;t pondus cæteris <lb/>paribus, quod nos in præ cedente quæ&longs;tione demon&longs;tra<lb/>uimus, eò maiìor fit ip&longs;a collifio. </s>

<s>Porrò huius <expan abbr="quoq;">quoque</expan> &longs;peculationis e&longs;t, Cur æqualia & <lb/>&longs;imilia corpora in æqualibus &longs;imilibu&longs;queue bafibus con&longs;ti<lb/>tuta eodem &longs;imiliqueue plano fulta, ponderibus tamen in<lb/>æqualia, non eâdem facilitate euertantur, &longs;ed horum gra<lb/>uiora difficilius. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.103.jpg"/><figure id="id.007.00.103.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.103.1.jpg">

<s>Sit enim Pri&longs;ma &longs;eu <lb/>Cylindrus ABCD, cuius <lb/>grauitatis centrum E in <lb/>plano Cl, ba&longs;i fultus CD. <lb/></s>

Line 2094

8. & à no&longs;tris Me<lb/>chanicis pa&longs;&longs;im ab&longs;que rotis Cylindrica &longs;implici videli<lb/>cet, & tereti formâ ad v&longs;um adhiberi. </s>

<s>E&longs;to igitur Ari<lb/><figure id="id.007.00.104.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.104.1.jpg"><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi verò &longs;eu vul<lb/>garis, & communis CD. <lb/></s>

<s>E&longs;to igitur Ari<lb/><figure id="id.007.00.104.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.104.1.jpg"></figure><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi verò &longs;eu vul<lb/>garis, & communis CD. <lb/></s>

<s>His non modò lapicidæ <lb/>pa&longs;&longs;im, &longs;ed & nautæ na<lb/>uiumqueue fabri &longs;ubdu<lb/>cendis & mari inducen<lb/>dis nauibus vtuntur, quod varare dicunt vernaculè, Hi<lb/>&longs;panico, vt arbitror, vocabulo. </s>

Line 2106

<s>Quatenus autem ad v&longs;um pertinet. </s>

<s>E&longs;to horizontis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.105.jpg"/><figure id="id.007.00.105.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.105.1.jpg"><lb/>planum AB, &longs;cytalae duae<lb/>CD, EF, Pondus verò <lb/>eis impo&longs;itum G, tan<lb/>gens ip&longs;as in <expan abbr="p&umacr;ctis">punctis</expan> CE, <lb/>&longs;cytalæ autem planum <lb/>in punctis D, F, Pellatur <lb/>à potentia quapiam <expan abbr="p&omacr;-dus">pon<lb/>dus</expan> Gad anteriora, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytalæ & pars quædam <lb/>&longs;cytalæ D, in qua &longs;it contactus a&longs;cendet in I, C verò de<lb/>&longs;cendetin H, nulla re motum impediente, quippe quòd <lb/>nulla ponderis &longs;cytalarum, & plani ad inuicem fiat offen<lb/>&longs;atio. </s>

<s>E&longs;to horizontis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.105.jpg"/><figure id="id.007.00.105.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.105.1.jpg"></figure><lb/>planum AB, &longs;cytalae duae<lb/>CD, EF, Pondus verò <lb/>eis impo&longs;itum G, tan<lb/>gens ip&longs;as in <expan abbr="p&umacr;ctis">punctis</expan> CE, <lb/>&longs;cytalæ autem planum <lb/>in punctis D, F, Pellatur <lb/>à potentia quapiam <expan abbr="p&omacr;-dus">pon<lb/>dus</expan> Gad anteriora, <expan abbr="n&emacr;-pe">nen<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytalæ & pars quædam <lb/>&longs;cytalæ D, in qua &longs;it contactus a&longs;cendet in I, C verò de<lb/>&longs;cendetin H, nulla re motum impediente, quippe quòd <lb/>nulla ponderis &longs;cytalarum, & plani ad inuicem fiat offen<lb/>&longs;atio. </s>

<s>Præterea cum &longs;cytalarum centra ab horizontis pla<lb/>no æqualiter di&longs;tent, pondus quidem horizonti æquidi<lb/>&longs;tanter mouetur, & ideo cius centrum grauitatis nequa<lb/>quam, in motu qui &longs;it, eleuatur. </s>

<s>Cæterùm materiæ imperfectione remota nihil re<lb/>fert ad facilitatem, vtrum maioris minorisue diametri <lb/>&longs;int&longs;cytalæ, vt ea po&longs;ita eo quod maiores circuli faciliùs <lb/>offendicula &longs;uperent, quod demon&longs;tratum e&longs;t in quæ&longs;tio<lb/>ne 8. eo vtiliores &longs;unt &longs;cytalæ, quo cra&longs;&longs;iores. </s>

<s>Quatenus <lb/>autem ad plau&longs;tri naturam &longs;pectat, cuius ad &longs;cytalas Phi<lb/>lo&longs;ophus fecit comparationem, vt o&longs;ten da mus difficilius <lb/>ex eo moueri pondera. </s><figure id="id.007.00.105.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.105.2.jpg">

<s>E&longs;to plau&longs;tri rota <lb/>KL, cuius centrum M, a<lb/>xis verò NO circa quem <lb/>rotaip&longs;a conuertiturKL. <lb/></s>

Line 2124

<s>Cætetùm quod ip&longs;e reticuit, n<gap/>s dicemus, nempe <lb/>validi&longs;&longs;imè enormia pondera per &longs;cytalas moueri, &longs;i &longs;cy<lb/>talis ip&longs;is vectes adiungantur. </s>

<s>Et &longs;anè motus erit tar di&longs;&longs;i<lb/>mus, veruntamen tar ditas ip&longs;a facilitate, quæ in de fit, v<lb/>berrimè compen&longs;atur. </s><figure id="id.007.00.106.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.106.1.jpg">

<s>E&longs;to igitur horizontis planum AB, &longs;cytalæ CD, fo<lb/>ramina in &longs;cytalis EFGH, vectes foraminibus in&longs;erti IE, <lb/>KF, LG, MH. </s>

Line 2164

<s>Quamobrem con&longs;iderandum e&longs;t, quo pacto fiat à tardi<lb/>tate velocitas. </s>

<s>Re&longs;pondemus, velocitatem acquirinon ex <lb/>&longs;implici, quæ circa funditoris caput &longs;it, rotatione, &longs;ed ex <lb/>co impetu qui fit in ip&longs;a lapidis emi&longs;&longs;ione, qui quidem im<lb/>petus &longs;i ante vel po&longs;t illud tempus fiat, quod à funditore <lb/>captatur, ca&longs;&longs;a pror&longs;us & inualida fit ip&longs;a iaculatio. </s><figure id="id.007.00.108.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.108.1.jpg">

<s>E&longs;to funda AB, manus <lb/>B, brachium BC. </s>

Line 2180

<s>quippe quod ab ea dem vi plus <expan abbr="trã&longs;-feratur">tran&longs;<lb/>feratur</expan> illud extremum quod longius à centro di&longs;tat. </s>

<s>In <lb/>gracilioribus verò &longs;uculis datâ collopum paritate plus e&longs;<lb/>&longs;e id quod à ligno di&longs;tat. </s><figure id="id.007.00.109.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.109.1.jpg">

<s>E&longs;to iugum &longs;ucu<lb/>laue maior, AB circa <lb/>centrum C, minor verò <lb/>circa idem <expan abbr="centr&umacr;">centrum</expan> DE. <lb/></s>

Line 2222

<s>E&longs;to lignum quod frangi debet AB, genu vel pedis <lb/>locus C, manuum latè diductarum &longs;itus DE, minus didu<lb/>ctarum FG; ltaque quoniam DE magis à centro C di&longs;tant <lb/>quàm FG, velocius mouebuntur puncta DE ip&longs;is FG, er<lb/>go inde facilius fiet fractio quam ex FG. </s>

<s>Hæcille ex &longs;uis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.111.jpg"/><figure id="id.007.00.111.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.111.1.jpg"><lb/>principijs. </s>

<s>Nos dili<lb/>gentius, &longs;i fieri poterit, <lb/>effectus huius cau&longs;&longs;am <lb/>per&longs;crutemur. </s>

Line 2258

<s>Id &longs;anè explorati&longs;&longs;imum e&longs;t, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.113.jpg"/>angulos omnes, & emin entias quaslibet in corporibus e&longs;<lb/>&longs;e infirmiores, offen&longs;ionibus enim expo&longs;itæ &longs;unt, necre&longs;i<lb/>&longs;ten di habent facultatem. </s>

<s>Itaque in attritione quæ fit in <lb/>eorum agitatione perpetua, eminentiæ contunduntur, & <lb/>&longs;uperficies ip&longs;a paullatim leuigatur. </s><figure id="id.007.00.113.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.113.1.jpg">

<s>E&longs;to angulatus lapis ABCD. <lb/></s>

Line 2294

<s>Si igitur flexilis <lb/>fuerit vectis, ip&longs;um inflectimagis cum extollitur nece&longs;&longs;e <lb/>e&longs;t, quod longis accidit lignis, in breuibus autem quod vl<lb/>timum e&longs;t, quie&longs;centi hypomochlio depropè fit. </s>

<s>Hæc <lb/>&longs;ubiectâ figurâ ob oculos ponimus. </s><figure id="id.007.00.114.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.114.1.jpg">

<s>Hæc <lb/>&longs;ubiectâ figurâ ob oculos ponimus. </s><figure id="id.007.00.114.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.114.1.jpg"></figure>

<s>E&longs;to longum ac fle<lb/>xile lignum AB, manu ele<lb/>uetur in A, fle ctetur <expan abbr="itaq;">itaque</expan> <lb/>in B, & declinabit in C. et<lb/>enim manus quæ &longs;u&longs;tin et <lb/>in A, fulcimenti loco &longs;uccedit: longitudo vero AB ponde<lb/>ris vices refert, at que vectis, quare quo longius abfuerit à <lb/>fulcimento, id e&longs;t, manu extremum B, eo magis flectetur; <lb/>&longs;i autem lignum breuius fuerit, nempe terminatum in D, <lb/>nequaquam fle ctetur, eò quòd eius extremum D minus à <lb/>fulcimento quod e&longs;t in A &longs;it remotum. </s>

Line 2302

<s>Dicimus autem materiam, <lb/>quatenus ad hanc contemplationem &longs;pectat, in duplici <lb/>e&longs;&longs;e differentia. </s>

<s>aut enim rarefactionis & con&longs;tipationis <lb/>e&longs;t incapax, vt in chalybe videmus, nitro, metallo, mar<lb/>more, aut capax quidem, & hæc duplex: Vel enim natura <lb/>nata e&longs;t ad rectitudinem quandam, vt ar borum flagella <lb/>virgæque, autnon item, ceu &longs;tannum, plumbum, & cæte<lb/>ra eiu&longs;modi. </s><figure id="id.007.00.115.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.115.1.jpg">

<s>E&longs;to primò vitreum <lb/>corpus gracile, procerum, <lb/>teres AB, manu capiaturin <lb/>A, <expan abbr="itaq.">itaque</expan> pondere ip&longs;ius cor<lb/>poris præualente ad partes <lb/>B, quia in C puncto, quod <lb/>circa medium e&longs;t, ex parte <lb/>&longs;uperiori non fit rarefactio, <lb/>nec in in feriori con&longs;tipatio, <lb/>nec interim datur penetra<lb/>tio corporum, fit fractio à <lb/>&longs;uperiori parte, & pars CB à <lb/>reliqua parte AC, auul&longs;a & <lb/>&longs;eparata cadit in D, &longs;uccedit autem ip&longs;a &longs;eparatio rarefa<lb/>ctioni. </s>

Line 2320

<s>Modò &longs;u&longs;pendatur in <lb/>medio vt AB, in C. eo igitur ca&longs;u cum fulcimentum &longs;it in <lb/>C, <expan abbr="vtrinq;">vtrinque</expan> fit flexio in D, & E, & id quidem &longs;i materia fle<lb/>xionem patitur: &longs;in minus, fractio fit in C. </s>

<s>Si autem ab ex<lb/><figure id="id.007.00.116.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.116.1.jpg"><lb/>tremis fiat &longs;u&longs;pen&longs;io, vt in <lb/>AB, tunc ceu duo vectes <lb/>fient, quorum fulcimenta in <lb/>extremis AB. </s>

<s>Si autem ab ex<lb/><figure id="id.007.00.116.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.116.1.jpg"></figure><lb/>tremis fiat &longs;u&longs;pen&longs;io, vt in <lb/>AB, tunc ceu duo vectes <lb/>fient, quorum fulcimenta in <lb/>extremis AB. </s>

<s>Pondera au<lb/>tem communia in medio vbi <lb/>Cremoti&longs;&longs;ima enim ea pars e&longs;t ab extremis AB. </s>

<s>Cedente <lb/><figure id="id.007.00.116.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.116.2.jpg"><lb/>igitur materia &longs;uomet pon<lb/>deri, &longs;iquidein in flexibilis fu<lb/>erit, frangetur, & fiet <expan abbr="parti&umacr;">partium</expan> <lb/>&longs;eparatio in C, duoque in de <lb/>corpora AD, BE. </s>

<s>Cedente <lb/><figure id="id.007.00.116.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.116.2.jpg"></figure><lb/>igitur materia &longs;uomet pon<lb/>deri, &longs;iquidein in flexibilis fu<lb/>erit, frangetur, & fiet <expan abbr="parti&umacr;">partium</expan> <lb/>&longs;eparatio in C, duoque in de <lb/>corpora AD, BE. </s>

<s>Si autem fle<lb/>xionis capax, vt AB in po&longs;tre<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.117.jpg"/>ma figura, facta ex contrario, nempe in in feriori parte cir<lb/>ca C rarefactione, in &longs;uperiori verò conden&longs;atione, pon<lb/>dere præualente curuabitur, fietque; lignum quidue aliud <lb/>huiu&longs;modi, vt ADB, nec amplius pondere &longs;uapte naturâ <lb/>inferiùs vergente ad rectitudinem reuertetur. </s>

Line 2344

<s>E&longs;to horizontis planum, illudqueue &longs;olidi&longs;&longs;imum, & <lb/>impenetrabile AB, trabs eidem adperpendiculum erecta <lb/>CD fulta ba&longs;i vbi C grauitatis centrum F. pondus &longs;uper<lb/>impo&longs;itum FG, cuius grauitatis centrum H: Sint autem <lb/>H & E in eadem perpendiculari, quæ ad mun di centrum <lb/>HEC. </s>

<s>Itaque eo quod tum penderis tum trabis centra <lb/>grauitent in perpendiculari, illa verò fulciatur in C, to-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.118.jpg"/><figure id="id.007.00.118.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.118.1.jpg"><lb/>tius ponderis moles recumbet <lb/>in C: non de&longs;cendet autem in I, <lb/>propterea quod &longs;upponatur i<lb/>p&longs;um planum AB, impenetrabi<lb/>le. </s>

<s>Itaque eo quod tum penderis tum trabis centra <lb/>grauitent in perpendiculari, illa verò fulciatur in C, to-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.118.jpg"/><figure id="id.007.00.118.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.118.1.jpg"></figure><lb/>tius ponderis moles recumbet <lb/>in C: non de&longs;cendet autem in I, <lb/>propterea quod &longs;upponatur i<lb/>p&longs;um planum AB, impenetrabi<lb/>le. </s>

<s>Igitur vt pondus H de&longs;cen<lb/>dat in C, alterum duorum e&longs;t <lb/>nece&longs;&longs;arium, nempe vel trabem <lb/>&longs;ubiectam comminui, aut eius <lb/>partes &longs;e&longs;e penetrare, & plura <lb/>corpora e&longs;&longs;e in eodem loco, pu<lb/>ta KC, quorum hoc &longs;ecun dum <lb/>naturæ penitus repugnat, illud <lb/>vero primum, penè impo&longs;&longs;ibile. </s>

Line 2358

<s>Præterea in præcedenti quæ&longs;tione mon&longs;trauimus <lb/>tunc facilem e&longs;&longs;e gracilis & oblongi ligni fractionem, <expan abbr="c&umacr;">cum</expan> <lb/>maxima e&longs;t longitudinis ad cra&longs;&longs;itudinem proportio. </s>

<s>Hîc <lb/>verò contrà accidit, etenim MD pars vectis quæ à fulci<lb/>mento e&longs;t ad potentiam minimam habet proportionem <lb/>ad rectam DC, quæ à fulcimento ad locum fractionis ex<lb/>tenditur, vbi C, quod vt euidentius pateat, </s><figure id="id.007.00.118.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.118.2.jpg">

<s>E&longs;to &longs;eor&longs;umtrabs AB, <lb/>cuius medium C. </s>

Line 2382

<s>Præterea, quoniam pondus, cuifulcrum re&longs;i<lb/>&longs;tit, vel ex natura premit, vel ex violentia, illud quidem <lb/>per lincam perpen dicularem, quæ ad mundi <expan abbr="c&emacr;trum">centrum</expan>, hoc <lb/>autem lateraliter & diuer&longs;imodè, varia fit fulcrorum di&longs;<lb/>po&longs;itio. </s>

<s>Cuius rei &longs;umma hæce&longs;t, vt &longs;emper contra impe<lb/>tum &longs;upponantur. </s><figure id="id.007.00.119.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.119.1.jpg">

<s>E&longs;to enim horizontis planum <lb/>AB, <expan abbr="eid&emacr;">eidem</expan> perpendiculares CADB, <lb/>ítaque &longs;i naturaliter pondus pre<lb/>matex C, fulcrum &longs;upponetur AE. <lb/></s>

Line 2392

<s>Hæc nos de arrectarijs fulcrisue; <lb/>nunc de tran&longs;uer&longs;arijs, & inclinatis agemus, & primum <lb/>de tran&longs;uer&longs;arijs, quatenus ad tectorum trabeationes &longs;pe<lb/>ctat. </s>

<s>E&longs;to tran&longs;uer&longs;aria trabs AB, muris <expan abbr="vtrinq;">vtrinque</expan> fulta CD, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.120.jpg"/><figure id="id.007.00.120.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.120.1.jpg"><lb/>cuius grauitatis centrum <lb/>E, in <expan abbr="perp&emacr;diculari">perpendiculari</expan> FEG, <lb/>quæ quidem ad mundi <lb/>centrum vergit. </s>

<s>E&longs;to tran&longs;uer&longs;aria trabs AB, muris <expan abbr="vtrinq;">vtrinque</expan> fulta CD, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.120.jpg"/><figure id="id.007.00.120.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.120.1.jpg"></figure><lb/>cuius grauitatis centrum <lb/>E, in <expan abbr="perp&emacr;diculari">perpendiculari</expan> FEG, <lb/>quæ quidem ad mundi <lb/>centrum vergit. </s>

<s><expan abbr="Itaq;">Itaque</expan> eo<lb/>dem tendente grauitatis <lb/>contro, &longs;i pondus quod <lb/>premit in E, non præua<lb/>leat vnioni <expan abbr="parti&umacr;">partium</expan> ip&longs;ius <lb/>materiæ quæ e&longs;t in E, re&longs;i&longs;tet trabs &longs;uomet ponderi, nec <lb/>frangetur. </s>

Line 2402

<s>Si autem non præualuerit ea, quam diximus, pro<lb/>portio, &longs;u&longs;pen&longs;æ remanebunt vtrin que trabes vt AHBI. </s>

<s>Huic difficultati egregiè occurrunt Architecti, ali<lb/>quando autem hoc modo: </s><figure id="id.007.00.120.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.120.2.jpg">

<s>E&longs;to tran&longs;uer&longs;aria <lb/>trabs &longs;uâ gracilitate, alia<lb/>ue de cau&longs;&longs;a imbecilla <lb/>AB, muri quibus <expan abbr="vtrinq;">vtrinque</expan> <lb/>&longs;u&longs;tinetur CD, Trabis i<lb/>p&longs;ius grauitatis centrum <lb/>G. </s>

Line 2418

<s>Po&longs;&longs;unt etiam to<lb/>tius trabis tres partes con&longs;iderari AE, EF, FB, quarum ful<lb/>cimenta quatuor A, E, F, B, Diui&longs;o igitur pondere & mul<lb/>tiplicatis fulcimentis impo&longs;&longs;ibile e&longs;t trabem conuelli & <lb/>vitium facere. </s>

<s>Sed & tectorum contignationes imbecillaque; tran&longs;<lb/>uer&longs;aria Mechanici corroborare &longs;olent, additis nempe <lb/>arrectaria trabe atque cauterijs. </s><figure id="id.007.00.121.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.121.1.jpg">

<s>E&longs;to enim tran&longs;<lb/>uer&longs;aria trabs AB <lb/>parietibus vtrinque <lb/>fulta I, K, <expan abbr="arrectari&umacr;">arrectarium</expan> <lb/>CD. </s>

Line 2434

<s>Stabit ergo compa<lb/>ges tota & &longs;uapte vi robu&longs;ti&longs;&longs;imè connexa totius tecti <lb/>pondus &longs;u&longs;tinebit. </s>

<s>Quoniam autem v&longs;u venire &longs;olet, cauterios nimia <lb/>longitudine debiles, aliquando tum proprio tum extra<lb/>neo cedentes ponderi deor&longs;um vergentes pandare, Ar<lb/>chitecti capreolis hinc inde &longs;uppo&longs;itis, ceu fulcris, huic <lb/>medentur infirmitati. </s><figure id="id.007.00.122.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.122.1.jpg">

<s>Sint enim cauterij <lb/>debiles hinc inde AB, <lb/>AC, media trabs arre<lb/>ctaria, quam <expan abbr="Monach&umacr;">Monachum</expan> <lb/>dicimus AD. </s>

Line 2472

<s>Ducatur hori<lb/>zonti æquidi&longs;tans CD, iuxta quam lateres lapide&longs;ue non <lb/>cuneati, &longs;eriatim collocentur EF. </s>

<s>Dicimus amoto arma-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.124.jpg"/><figure id="id.007.00.124.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.124.1.jpg"><lb/>mento, hoc e&longs;t, pro<lb/>hibente ip&longs;o lateres <lb/>ruere. </s>

<s>Dicimus amoto arma-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.124.jpg"/><figure id="id.007.00.124.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.124.1.jpg"></figure><lb/>mento, hoc e&longs;t, pro<lb/>hibente ip&longs;o lateres <lb/>ruere. </s>

<s>Producantur <lb/>enim AC in G, BD <lb/>verò in H, cum ip&longs;is <lb/>CG, DH, æquales <lb/>fiant CI, DK, & recta <lb/>IK iungatur, crit igi<lb/>tur GD &longs;patium ip&longs;i <lb/>CK &longs;patio &longs;imile qui<lb/>dem & æquale, quod <lb/>cùm ita &longs;it, nihil prohibet quin tota laterum GD moles in <lb/>&longs;patium CK transferatur, & corruat. </s>

<s>Si autem cunei ip&longs;i latere&longs;ue, cuneatim di&longs;po&longs;iti, ita <lb/>&longs;int vt ad vnum centrum tendant, licet ad rectam lineam <lb/>collocentur, non delabentur, &longs;ed &longs;tabunt; quod ita o&longs;ten<lb/>demus. </s><figure id="id.007.00.124.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.124.2.jpg">

<s>Sint cunci latere&longs;ue <lb/>cuneatim di&longs;po&longs;iti ABCD, <lb/>tendentes ad centrum, &longs;eu <lb/>commune punctum E, Du<lb/>cantur CAE, DBE, &longs;intqueue <lb/>muri vtrinque ponderire&longs;i<lb/>&longs;tentes CL, DM, Demitta<lb/>tur perpendicularis, quæ ad <lb/>mundi centrum FGE &longs;ecans AB, in G. </s>

Line 2504

<s>Vtilis tamen e&longs;&longs;c pote&longs;t <lb/>ad portarum & fene&longs;trarum, quæ in medijs muris &longs;unt, & <lb/>mediocri vano aperiuntur, &longs;uperliminaria. </s>

<s>Si verò ad minorem circuli portionem curuetur Ca<lb/>mera, vtilior quidem erit &longs;tructura ea ip&longs;a, de qua locuti <lb/>&longs;umus; non tamen omninò &longs;ine vitio. </s><figure id="id.007.00.125.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.125.1.jpg">

<s>E&longs;to fornix ex minori <lb/>circuli portione AB, cuius in<lb/>cumbæ AF, BH muris fultæ <lb/>AC, BD. </s>

Line 2536

<s>Circinantur autem hoc pacto, diui&longs;a nempe <lb/>&longs;ubten&longs;a, in partes tres, ea&longs;que æquales, ponitur circini <lb/>pes in altero diui&longs;ionum puncto & pars circuli de&longs;cribi<lb/>tur, mox in altero puncto circini pede collocato alia cir<lb/>culi portio lineatur, quibus arcus ip&longs;e integratur. </s>

<s>Appel<lb/>lant autem tertium acutum, eo quod ex &longs;ubten&longs;a in tres <lb/>partes diui&longs;a, arcus non fiatrotundus, &longs;ed in acutum an<lb/>gulum ex duabus circuli portionibus de&longs;inens. </s><figure id="id.007.00.126.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.126.1.jpg">

<s>Sint igitur muri <lb/>AC, BD, in quibus v<lb/>trinque incumbæ KA, <lb/>BI. </s>

Line 2550

<s>Si quid tamen <expan abbr="hab&emacr;t">habent</expan> <lb/>vitij, illud e&longs;t quod grauitatis centra momentum haben<lb/>tia ad interiorem partem ver&longs;us PQ vim faciant, & nifi <lb/>partes magno &longs;uperimpo&longs;ito pondere comprimantur, <lb/>partes quæ &longs;unt circa HG, &longs;ur&longs;um pellentes aliquali &longs;ibi <lb/>rectitudine comparata corruunt, facta nempe circa L, M, <lb/>coniunctarum partium &longs;eparatione. </s>

<s>His hoc pacto explicatis de &longs;emicirculari fornice a<lb/>gemus, quæ cæteris omnibus vtilior e&longs;t, & longè pulcher<lb/>rima, quamobrem Antiquis Architectis omnibus inpri<lb/>mis admodum familiaris: </s><figure id="id.007.00.127.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.127.1.jpg">

<s>E&longs;to vanum <lb/>ABCD, muris v<lb/>trinque clau&longs;um. <lb/></s>

Line 2588

<s>Tertio denique modo huic infirmitati me dentur, <lb/>vt videre e&longs;t in &longs;equenti figura, in qua vanum ADBC, mu<lb/>ri vtrinque AF, BH, fornix verò FGH. </s>

<s>Itaque dum muros <lb/><figure id="id.007.00.129.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.129.1.jpg"><lb/>ex&longs;truunt, arre<lb/>ctarias trabes, ro<lb/>bore aliaue mate<lb/>ria firmi&longs;&longs;ima, illis <lb/>in&longs;erunt, quales <lb/>&longs;unt IF<emph type="italics"/>K<emph.end type="italics"/> LHM, <lb/>ea proceritate vt <lb/>futuri fornicis &longs;u<lb/>perent &longs;ummita<lb/>tem. </s>

<s>Itaque dum muros <lb/><figure id="id.007.00.129.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.129.1.jpg"></figure><lb/>ex&longs;truunt, arre<lb/>ctarias trabes, ro<lb/>bore aliaue mate<lb/>ria firmi&longs;&longs;ima, illis <lb/>in&longs;erunt, quales <lb/>&longs;unt IF<emph type="italics"/>K<emph.end type="italics"/> LHM, <lb/>ea proceritate vt <lb/>futuri fornicis &longs;u<lb/>perent &longs;ummita<lb/>tem. </s>

<s>Con&longs;umma<lb/>to enim fornice, <lb/>nondum tamen, <lb/>exarmato, tran&longs;<lb/>uer&longs;ariam <expan abbr="trab&emacr;">trabem</expan> à <lb/>&longs;ummo fornicis <lb/>dor&longs;o parumper <lb/>eminentem in punctis I, L, arrectarijs trabibus validi&longs;&longs;i<lb/>mis clauibus connectunt, tum punctis NP, Oq, capreolos <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.130.jpg"/>tran&longs;uer&longs;ario, & arrectarijs ferreis, clauis affigunt. </s>

Line 2604

<s>Cum <lb/>enim PQ proxima &longs;int punctis FH, quæ cum arrectarijs à <lb/>muro di&longs;tinentur, magna in ijs fit vtrobique re&longs;i&longs;tentia. </s>

<s>Rebus igitur ita &longs;e habentibus cum ob&longs;erua&longs;&longs;ent Ar<lb/>chitecti, ob enormitatem ponderis fornices in tertia illa <lb/><figure id="id.007.00.130.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.130.1.jpg"><lb/>parte quæ &longs;umma e&longs;t <lb/>laborare, <expan abbr="quãtum">quantum</expan> ter<lb/>tijs vtrinque partibus <lb/>&longs;oliditatis addunt, tan<lb/>tundem ex illa parte <lb/>&longs;uprema demere <expan abbr="&longs;ol&emacr;t">&longs;olent</expan>, <lb/>vt videre e&longs;t in &longs;ubie<lb/>cta figura, in qua par<lb/>tes A, B, &longs;olidæ & cra&longs;<lb/>&longs;iores, quibus hærent <lb/>partes, quæ CE, DG <lb/>cra&longs;&longs;æ quidem & illæ, <lb/>tum vero &longs;umma EFG, <lb/>alijs &longs;ubtilior. </s>

<s>Rebus igitur ita &longs;e habentibus cum ob&longs;erua&longs;&longs;ent Ar<lb/>chitecti, ob enormitatem ponderis fornices in tertia illa <lb/><figure id="id.007.00.130.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.130.1.jpg"></figure><lb/>parte quæ &longs;umma e&longs;t <lb/>laborare, <expan abbr="quãtum">quantum</expan> ter<lb/>tijs vtrinque partibus <lb/>&longs;oliditatis addunt, tan<lb/>tundem ex illa parte <lb/>&longs;uprema demere <expan abbr="&longs;ol&emacr;t">&longs;olent</expan>, <lb/>vt videre e&longs;t in &longs;ubie<lb/>cta figura, in qua par<lb/>tes A, B, &longs;olidæ & cra&longs;<lb/>&longs;iores, quibus hærent <lb/>partes, quæ CE, DG <lb/>cra&longs;&longs;æ quidem & illæ, <lb/>tum vero &longs;umma EFG, <lb/>alijs &longs;ubtilior. </s>

<s>Minus <lb/>igitur grauante ponde<lb/>re in F, minor fit ad in cumbas pre&longs;&longs;io, aut &longs;i qua fit, à <expan abbr="parti&umacr;">partium</expan> <lb/>ACE, BDG &longs;oliditate haud inualidè &longs;u&longs;tinetur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.131.jpg"/>

<s>Cæterùm admonet nos locus, vt aliquid de forni<lb/>cum di&longs;&longs;olutionibus in medium afferamus: cau&longs;&longs;is enim <lb/>morborum cognitis, facilius periti medici adhibere &longs;o<lb/>lent remedia. </s><figure id="id.007.00.131.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.131.1.jpg">

<s>E&longs;to enim &longs;emicircula<lb/>ris fornix ABC, cuius cen<lb/>trum E, perpendicularis ve<lb/>rò quæ per centrum DBE, &longs;e<lb/>micirculi ABC, diameter <lb/>AEC, incumbæ <expan abbr="vtrinq;">vtrinque</expan> A, C. <lb/></s>

<s>Itaque &longs;i nulla fiat incumba<lb/>rum repul&longs;io, &longs;tabit fornix; &longs;i verò fiat, ruinam facict. </s>

<s>Pellanturitaque ad exteriores partes, vt in &longs;ecunda <lb/><figure id="id.007.00.131.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.131.2.jpg"><lb/>figura, H in F, & C in G, <lb/>ex qua pul&longs;ione cum ma<lb/>ius fiat &longs;patium quod in<lb/>tegro fornice impleba<lb/>tur, iam di&longs;tractis <expan abbr="vtrinq;">vtrinque</expan> <lb/>fornicis partibus <expan abbr="n&omacr;">non</expan> im<lb/>pletur, Diuiditur igitur <lb/>locus maior factus in tres partes, quarum hincinde duas <lb/>replent fornicis partes, tertiam verò quæ media e&longs;t, re<lb/>plet in&longs;ertus, ne vacuum detur, aër, vt in figura videre e&longs;t, <lb/>in qua &longs;olutæ vtrinque fornicis partes HIKF, PMNG, aër <lb/>autem medius &longs;patium replens IKMN. </s>

<s>Pellanturitaque ad exteriores partes, vt in &longs;ecunda <lb/><figure id="id.007.00.131.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.131.2.jpg"></figure><lb/>figura, H in F, & C in G, <lb/>ex qua pul&longs;ione cum ma<lb/>ius fiat &longs;patium quod in<lb/>tegro fornice impleba<lb/>tur, iam di&longs;tractis <expan abbr="vtrinq;">vtrinque</expan> <lb/>fornicis partibus <expan abbr="n&omacr;">non</expan> im<lb/>pletur, Diuiditur igitur <lb/>locus maior factus in tres partes, quarum hincinde duas <lb/>replent fornicis partes, tertiam verò quæ media e&longs;t, re<lb/>plet in&longs;ertus, ne vacuum detur, aër, vt in figura videre e&longs;t, <lb/>in qua &longs;olutæ vtrinque fornicis partes HIKF, PMNG, aër <lb/>autem medius &longs;patium replens IKMN. </s>

<s>Diuidantur &longs;in<lb/>guli qua drantes FK, GN, in partes tres, quarum duæ &longs;int <lb/>hincinde FQ, GR, & à centris, quæ &longs;eparatis quadranti<lb/>bus facta &longs;untin ST, rectæ ducantur SQV. TRX. </s>

Line 2628

<s>tangant tautem &longs;e in <expan abbr="p&umacr;-cto">pun<lb/>cto</expan> Z. quo pacto igitur fornices incumbis cedentibus in <lb/>medio aperti, <expan abbr="di&longs;&longs;oluãtur">di&longs;&longs;oluantur</expan> & ruinam faciant, ex i&longs;tis patet. </s>

<s>Ex demon&longs;tratis qua&longs;i ex con&longs;ectario habemus for<lb/>nices quo fuerint cra&longs;&longs;iores dato pari in cum barum &longs;ece&longs;<lb/>&longs;u, ruinæ minus e&longs;&longs;e obnoxios quàm tenuiores, hoc e&longs;t, <lb/>maiori aperitione indigere ad ruinam cra&longs;&longs;iores quam te<lb/>nuiores, quod licet ex iam dictis re&longs;ultet, nos tamen cla<lb/>rius ex &longs;ubiecto &longs;chemate demon&longs;trabimus. </s><figure id="id.007.00.132.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.132.1.jpg">

<s>E&longs;to enim cra&longs;&longs;ioris <lb/>fornicis pars <expan abbr="quid&emacr;">quidem</expan> ABCD, <lb/>tenuioris EFCD circa <expan abbr="id&emacr;">idem</expan> <lb/>centrum R. </s>

Line 2650

<s>Quæritur adhuc, quare grauiores fornices in &longs;um<lb/>mis ædificijs non &longs;ine vitio fiant? </s>

<s>E&longs;to ædificium ABGH, cuius <expan abbr="vtrinq;">vtrinque</expan> muri ABCD, <lb/>EFGH, maiorum &longs;ummitates AD, EH, mediæ murorum <lb/>partes KL, fornicum &longs;ummus quidem DIE, medius verò <lb/><figure id="id.007.00.133.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.133.1.jpg"><lb/>KML. Dico, magis cedere pul<lb/>&longs;os muros &longs;ummos circa DE, <lb/>quam in medio circa KL. </s>

<s>E&longs;to ædificium ABGH, cuius <expan abbr="vtrinq;">vtrinque</expan> muri ABCD, <lb/>EFGH, maiorum &longs;ummitates AD, EH, mediæ murorum <lb/>partes KL, fornicum &longs;ummus quidem DIE, medius verò <lb/><figure id="id.007.00.133.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.133.1.jpg"></figure><lb/>KML. Dico, magis cedere pul<lb/>&longs;os muros &longs;ummos circa DE, <lb/>quam in medio circa KL. </s>

<s>Sunt <lb/>enim muri BA, GH ceu vectes <lb/>quidam, <expan abbr="quor&umacr;">quorum</expan> extremis par<lb/>tibus à fulcimentis BG remo<lb/>ti&longs;&longs;imis potentia admouetur, <lb/>hoc e&longs;t, ip&longs;ius fornicis DIE ad <lb/>DE in cumbans repul&longs;io; lon<lb/>gior e&longs;t autem pars à <expan abbr="fulcim&emacr;-to">fulcimen<lb/>to</expan> ad potentiam AB, ip&longs;a BK. <lb/></s>

Line 2668

<s>Etenim quæ&longs;tio hæc <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.134.jpg"/>clari&longs;&longs;imorum virorum ingenia magnopere fatigauit. </s>

<s>Ex <lb/>quibus Ari&longs;toteles inter veteres, Guid. Vbald. inter re<lb/>centiores ad vectis naturam (ne quid in Mechanicis ad <lb/>vectem non reduci putaretur) cuneum ip&longs;um trahere co<lb/><figure id="id.007.00.134.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.134.1.jpg"><lb/>nati &longs;unt. </s>

Line 2706

<s>Idque; ex quo<lb/>dam lemmate demon&longs;trare conatur, figura autem eius ita <lb/>ferè &longs;e habet. </s><figure id="id.007.00.135.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.135.1.jpg">

<s>E&longs;to cuneus ABC, <lb/>item alius DEF. <expan abbr="Dem&omacr;-&longs;trauit">Demon<lb/>&longs;trauit</expan> igitur ex a&longs;&longs;um<lb/>pto, quo acutior fuerit <lb/>angulus BIM, eo facilius <lb/>pondera moueri, & ideo <lb/>facilius ceu vecte AB <lb/>moueri pondus I quàm <lb/>vecte DE pondus <expan abbr="q.">que</expan> In<lb/>geniosè quidem. </s>

Line 2766

<s>Ex quibus o<lb/>mnibus, nî fallimur, clarè patet, curacutiores angulo cu<lb/>nei obtu&longs;ioribus facilius &longs;cindant, quæ quidem ratio lon<lb/>gè ab ea di&longs;tat, ex qua cæteri ferè omnes Cuneum ad ve<lb/>ctis naturam referre hactenus contenderunt. </s>

<s>Cæterùm vtramque eorum quos diximus, <expan abbr="cuneor&umacr;">cuneorum</expan> <lb/>&longs;peciem &longs;olerti&longs;&longs;ima cognouit Natura, & ideo quoniam <lb/>res vel contu&longs;ione vel perforatione, vel &longs;ecatione con&longs;i<lb/>ciuntur, triplicem dentium qualitatem dentatis animali-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.138.jpg"/><figure id="id.007.00.138.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.138.1.jpg"><lb/>bus dedit, Molares, <lb/>qui & Maxillares ap<lb/>pellantur, quibus <lb/>cibus contunditur, <lb/>Canini, quibus fit <lb/>perforatio, Anterio<lb/>res, quibus cibus <lb/>&longs;cinditur, quos ideo <lb/><foreign lang="greek">temnikou\s</foreign>, id e&longs;t, &longs;ecan<lb/>tes appellant Graeci. </s>

<s>Cæterùm vtramque eorum quos diximus, <expan abbr="cuneor&umacr;">cuneorum</expan> <lb/>&longs;peciem &longs;olerti&longs;&longs;ima cognouit Natura, & ideo quoniam <lb/>res vel contu&longs;ione vel perforatione, vel &longs;ecatione con&longs;i<lb/>ciuntur, triplicem dentium qualitatem dentatis animali-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.138.jpg"/><figure id="id.007.00.138.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.138.1.jpg"></figure><lb/>bus dedit, Molares, <lb/>qui & Maxillares ap<lb/>pellantur, quibus <lb/>cibus contunditur, <lb/>Canini, quibus fit <lb/>perforatio, Anterio<lb/>res, quibus cibus <lb/>&longs;cinditur, quos ideo <lb/><foreign lang="greek">temnikou\s</foreign>, id e&longs;t, &longs;ecan<lb/>tes appellant Graeci. </s>

<s>Molares KK, <lb/>CaniniL, L, Temni<lb/>ci &longs;eu &longs;ecantes M. </s>

Line 2782

<s>Ve<lb/>runtamen cùm de hac &longs;pecie egregiè di&longs;&longs;erat G. Vbaldus, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.139.jpg"/>con&longs;ultò hanc di&longs;putationem omittimus; idque hac quo<lb/>que de cau&longs;&longs;a, quod nihil de cochlea, ac &longs;i eam non noui&longs;<lb/>&longs;et, locutus &longs;it Ari&longs;toteles. </s>

<s>Po&longs;&longs;umus autem in actu &longs;ci&longs;&longs;ionis, quæ cuneo fit, a<lb/>liâ tamen ratione vectem con&longs;iderare, nempe non in cu<lb/>neo quidem, &longs;ed in ip&longs;a re quæ &longs;cinditur. </s><figure id="id.007.00.139.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.139.1.jpg">

<s>E&longs;to enim quip<lb/>piam &longs;ci&longs;&longs;ile ABCD, <lb/>cui alteri extremita<lb/>tum, puta BD, cuneus <lb/>adigatur EFG, <expan abbr="fiatq;">fiatque</expan> <lb/>&longs;ci&longs;&longs;io per longitudi<lb/>nem &longs;ecundum <expan abbr="lineã">lineam</expan> <lb/>EH. facta igitur ex <lb/>cunei ingre&longs;&longs;u <expan abbr="parti&umacr;">partium</expan> &longs;eparatione B, expelletur in I, D ve<lb/>rò in K. fient igitur materiæ &longs;ci&longs;&longs;æ partes AIBH, CKDH, <lb/>ceu duo vectes, quorum hinc inde in corpore ip&longs;o fulci<lb/>menta L, M potentiæ vtrinque dilatantes BD, pondus ve<lb/>rò materiæ re&longs;i&longs;tentia, in &longs;eparationis loco vbi N. </s>

Line 2798

<s>à <lb/>principio enim difficultatem &longs;entimus, deinde ex ea <expan abbr="quã">quam</expan> <lb/>diximus proportionc &longs;ci&longs;&longs;io ip&longs;a fit apprime facilis. </s>

<s>Vti-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.140.jpg"/>mur etiam vecte cuneato ad &longs;cindendum & aperiendum: <lb/>adacto enim &longs;ci&longs;&longs;uræ cuneo, idqueue manu malleoue, tum <lb/>ab altera extremitate pre&longs;&longs;o, valida fit ex vectis vi <expan abbr="c&omacr;tinui">continui</expan> <lb/><figure id="id.007.00.140.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.140.1.jpg"><lb/>corporis &longs;eparatio. </s>

<s>Ma<lb/>teria &longs;ci&longs;&longs;ilis AB <expan abbr="&longs;calpr&umacr;">&longs;calprum</expan> <lb/>ceu vectis cuneatus CD, <lb/>cuius fulcimentum, E, <lb/>pondus verò vbi C, po<lb/>tentia vbi D, quo ca&longs;u <lb/>quo maior e&longs;t proportio <lb/>DE ad EC, eo e&longs;t ip&longs;a &longs;ci&longs;&longs;io leuior & facilior. </s>

Line 2828

<s>Si quis alterum funis principium trahat, ma<lb/>gna trahat pondera, et&longs;i trahens potentia &longs;it exigua? </s>

<s>Nos <lb/>verbis figuram, & figurâ verba ip&longs;a elucidabimus. </s><figure id="id.007.00.141.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.141.1.jpg">

<s>Sint duo ligna ex oppo&longs;ito concurrentia, <lb/>in quibus Trochleæ, hoc e&longs;t, orbiculi AB, fu<lb/>nis ductarius DABC, cuius alterum caput re<lb/>ligatum e&longs;t ligno trochleæ A, vbi e&longs;t C. </s>

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<s>Si enim, ait, <lb/>vnicâ Trochleâ pondus facile trahitur, id multo validius <lb/>pluribus fiet. </s>

<s>Veruntamen non ab&longs;olutè ex orbiculorum <lb/>multiplicationeid fieriita o&longs;tendemus. </s><figure id="id.007.00.142.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.142.1.jpg">

<s>Sint duæ op<lb/>po&longs;itæ lineae rectae, <lb/>vtpote trabes AB, <lb/>CD, <expan abbr="inuic&emacr;">inuicem</expan> æqui<lb/>di&longs;tantes & ip&longs;æ <lb/>&longs;tabiles: &longs;uperiori <lb/>tres appendantur <lb/>orbiculi ex <expan abbr="p&umacr;ctis">punctis</expan> <lb/>E, F, G, <expan abbr="n&emacr;pe">nempe</expan> ML, <lb/>PQ, TV. inferiori <lb/><expan abbr="aut&emacr;">autem</expan> duobus pun<lb/>ctis IH, nempe <lb/>NO, RS. </s>

Line 2892

<s>Probabimus autem, nullam <lb/>ex &longs;uperioribus orbiculis fieri ponderum imminutionem, <lb/>&longs;ed totam vim in inferioribus con&longs;i&longs;tere. </s>

<s>At nos interim <lb/>quippiam quod ad rem faciat, proponamus. </s><figure id="id.007.00.143.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.143.1.jpg">

<s>E&longs;to punctum A, cuirectæ ap<lb/>pendantur lineæ BAC, diui&longs;æ qui<lb/>dem in A, &longs;it autem lineæ BA caput <lb/>B, ip&longs;ius verò CA caput C. </s>

Line 2918

<s>Videmus igitur illam appen&longs;ionem <lb/>quidem pondus nullatenus imminuere, hanc verò pon<lb/>dus ip&longs;um, bifariam diui&longs;um, &longs;u&longs;tinentibus potentijs im<lb/>partiri. </s>

<s>Hæ cin lineis, Mathematicâ v&longs;i ab&longs;tractione, con<lb/>&longs;iderauimus, nunc verò eadem mechanicè perpenda<lb/>mus. </s><figure id="id.007.00.144.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.144.1.jpg">

<s>Sit igitur <lb/>punctum A, vt <lb/>in &longs;e quenti figu<lb/>ra clauus paxil<lb/>lu&longs;ue, cui appen<lb/>&longs;us funiculus <lb/>BAC, & funicu<lb/>li capitibus pon<lb/>dera BC, &longs;it quo<lb/>que anulus D, <lb/>per quem traìe<lb/>ctus funiculus <lb/>EDF. </s>

Line 2944

<s>Commendetur loco &longs;tabili <lb/>in S, & alteri vectis extremo R funis alligetur RT, cui <lb/>quidem potentia &longs;u&longs;tinens applicetur in T. </s>

<s>Dico igitur, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.146.jpg"/><figure id="id.007.00.146.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.146.1.jpg"><lb/>rebus ita di&longs;po&longs;itis, <lb/>potentiam in T ita <lb/>&longs;e habere ad pondus <lb/>F, vt vnum ad &longs;ex de<lb/>cim, hoc e&longs;t, in pro<lb/>portione e&longs;&longs;e &longs;ub<lb/>&longs;exdecupla. </s>

<s>Dico igitur, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.146.jpg"/><figure id="id.007.00.146.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.146.1.jpg"></figure><lb/>rebus ita di&longs;po&longs;itis, <lb/>potentiam in T ita <lb/>&longs;e habere ad pondus <lb/>F, vt vnum ad &longs;ex de<lb/>cim, hoc e&longs;t, in pro<lb/>portione e&longs;&longs;e &longs;ub<lb/>&longs;exdecupla. </s>

<s>Sunt <lb/>autem, hic vectes <lb/>quatuor in feriorum <lb/>cubiculorum, loco, <lb/>CD, HI, MN, QR, <lb/>qucrum, centra E, <lb/>G, L, P. quoniam e<lb/>nim A hoc e&longs;t, C, v<lb/>nà cum potentia G, <lb/>hoc e&longs;t, D, &longs;u&longs;tinet <lb/>pondus F alterum, <lb/>ponderis dimidium <lb/>&longs;u&longs;tinebit C, <expan abbr="alter&umacr;">alterum</expan> <lb/>vero D. erunt igitur <lb/>vtrinque librae quin<lb/>gentæ. </s>

Line 2982

<s>Porrò effe<lb/>ctus huius, de quo agitur, di&longs;putatio illuc &longs;pectat, videli<lb/>cet ad cadentium atque proiectorum naturam. </s>

<s>Ad maio<lb/>rem autem rei euidentiam hæc addimus. </s><figure id="id.007.00.148.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.148.1.jpg">

<s>Ad maio<lb/>rem autem rei euidentiam hæc addimus. </s><figure id="id.007.00.148.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.148.1.jpg"></figure>

<s>E&longs;to libra AB, cu<lb/>ius centrum C, libra<lb/>ta æqualibus ponde<lb/>ribus DE, apponatur <lb/>ponderi E pondus F, <lb/>item ponderi D pon<lb/>dus G ip&longs;i ponderi F <lb/>æquale, æquilibrabit <lb/>itidem, Modò non apponatur &longs;impliciter pondus G &longs;ex <lb/>ex H in lancem A dimittatur, tunc &longs;anè non æquilibrabit, <lb/>&longs;ed libram deprimet. </s>

Line 3000

<s>Cæterùm cur mallei & &longs;ecuris ictus &longs;it violenti&longs;&longs;i<lb/>mus, ideo fit quod non ex vnico neque duplici, &longs;ed ex tri<lb/>plici grauitate operetur. </s>

<s>E&longs;to enim &longs;ecuris A, cuius manu<lb/>brium AB, brachium vero &longs;ecuri vtentis BC, erit igitur C <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.149.jpg"/><figure id="id.007.00.149.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.149.1.jpg"><lb/>locus vbi humero <lb/>brachium iungi<lb/>tur, motus ip&longs;ius <lb/>centrum, attollit <lb/>autem &longs;ecurim is <lb/>qui percutit, & re<lb/>tro ad &longs;capulas re<lb/>ducens totis viri<lb/>bus ex centro C <lb/>&longs;ecurim vibrat, <lb/>portionem circuli <lb/>de&longs;cribens ADE <lb/>ictumqueue faciens <lb/>in E. </s>

<s>E&longs;to enim &longs;ecuris A, cuius manu<lb/>brium AB, brachium vero &longs;ecuri vtentis BC, erit igitur C <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.149.jpg"/><figure id="id.007.00.149.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.149.1.jpg"></figure><lb/>locus vbi humero <lb/>brachium iungi<lb/>tur, motus ip&longs;ius <lb/>centrum, attollit <lb/>autem &longs;ecurim is <lb/>qui percutit, & re<lb/>tro ad &longs;capulas re<lb/>ducens totis viri<lb/>bus ex centro C <lb/>&longs;ecurim vibrat, <lb/>portionem circuli <lb/>de&longs;cribens ADE <lb/>ictumqueue faciens <lb/>in E. </s>

<s>Vires igitur acquirit &longs;ecuris, tum ex naturali grauita<lb/>te, cadens ex D, in E, tum ex proprio pondere, tum etiam <lb/>ex violentia eidem à percutiente impre&longs;&longs;a. </s>

Line 3046

<s>Si enim en&longs;is iterum vt vectis con&longs;ideretur, e<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.151.jpg"/>runt AB. duo fulcimenta &longs;u&longs;tinentía pondus in C, vbi gra<lb/>uitatis e&longs;t centrum. </s>

<s>Si igitur paria fuerint &longs;patia BC, CA, <lb/><figure id="id.007.00.151.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.151.1.jpg"><lb/>in B erit dìmidium <lb/>ponderis C, quantum <lb/>ergo velocitate præ<lb/>ualetictus in B, <expan abbr="tant&umacr;">tantum</expan> <lb/>ponderis amittit. </s>

<s>Si igitur paria fuerint &longs;patia BC, CA, <lb/><figure id="id.007.00.151.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.151.1.jpg"></figure><lb/>in B erit dìmidium <lb/>ponderis C, quantum <lb/>ergo velocitate præ<lb/>ualetictus in B, <expan abbr="tant&umacr;">tantum</expan> <lb/>ponderis amittit. </s>

<s>D <lb/>verò plus quidem de <lb/>pondere participat, <lb/>&longs;ed velocitatis habet <lb/>minimum, in C verò <lb/>velocitas e&longs;t medio<lb/>cris, tota tamen ip&longs;ius <lb/>ex grauitatis centro <lb/>ponderis fit impre&longs;<lb/>&longs;io. </s>

Line 3064

<s>Ait igitur, appendiculum licet parui <expan abbr="p&omacr;-deris">pon<lb/>deris</expan> &longs;it, ideo maiori ponderi virtute æquari, quod lon<lb/>gius à centro, hoc e&longs;t, ab ip&longs;o fulcimento &longs;i&longs;tatur. </s>

<s>quic<lb/>quid tamen &longs;it, &longs;tateram e&longs;&longs;e vectem, res e&longs;t explorati&longs;<lb/>&longs;ima. </s><figure id="id.007.00.152.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.152.1.jpg">

<s>E&longs;to igitur &longs;tatera AB, <lb/>cuius appendiculum cur<lb/>rens F, fulcimentum cen<lb/>trumue C, lanx quæ cate<lb/>na &longs;u&longs;penditur E &longs;patium <lb/>à loco fulcimenti ad ap<lb/>pendiculum CF. quod ve<lb/>rò à fulcimento ad cate<lb/>nam, ex qua lanx appen<lb/>ditur AC. </s>

Line 3088

<s>Rectè <lb/>igitur dicebat Philo&longs;ophus, in &longs;tatera plures e&longs;&longs;e libras, <lb/>quanquam & ea quoque de cau&longs;&longs;a dici po&longs;&longs;it, quod, quot <lb/>&longs;unt appen diculi, è locoin locum translationes, totidem <lb/>ex proportionum variatione fiant libræ. </s>

<s>Et hoc quidem <lb/>&longs;en&longs;i&longs;&longs;e videtur Ari&longs;toteles. </s><figure id="id.007.00.153.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.153.1.jpg">

<s>Po&longs;&longs;emus & alio <lb/>modo &longs;tatera vti, nempe <lb/>&longs;tabili appendiculo, mo<lb/>bili autem fulcimento. <lb/></s>

Line 3132

<s>Hoc igitur ad ex<lb/>tractionem vtuntur^{**}, vt facilius moueant. </s>

<s>Figuram hoc <lb/>pactto proponit Philo&longs;ophus. </s><figure id="id.007.00.155.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.155.1.jpg">

<s>E&longs;to dentiforcipis alterum <lb/>quidem extremum vbi A, alte<lb/>rum autem quod extrahit B, ve<lb/>ctis vbi ADF, alter vectis, vbi <lb/>BCE, fulcimentum verò CGD <lb/>connexio vbi G. </s>

Line 3154

<s>Dicimus igitur, tum dentem ip&longs;um, tum dentifor<lb/>cipem vectes e&longs;&longs;e, varia tamen ratione & &longs;atis &longs;ane diuer<lb/>&longs;a. </s>

<s>Dens enim fit vectis eius nempe naturæ quæ fulcimen<lb/>tum habet in angulo, quo ca&longs;u ip&longs;ius Dentiforcipis <expan abbr="parti&umacr;">partium</expan>, <lb/>quibus Dens apprehenditur, ea quæ longior e&longs;t poten<lb/>tiæ mouentis loco &longs;uccedit, breuior vero fulcimentum <lb/>facit, Dentis vero re&longs;i&longs;tentia ponderis vices refert. </s><figure id="id.007.00.156.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.156.1.jpg">

<s>E&longs;to enim dens qui<lb/>dem A, cuius diameter <lb/>BC, longitudo v&longs;que ad <lb/>extremas radices CD, <lb/>pars dentiforcipis breui<lb/>or CG, longior BG. </s>

Line 3182

<s>ma<lb/>ius verò quod à vertebra ad extremitates, quæ confrin<lb/>gentis manu comprimuntur. </s>

<s>Ait igitur, & id quam oppo<lb/>fite, vim ex vectibus ictus loco &longs;uccedere & idem operari. </s><figure id="id.007.00.157.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.157.1.jpg">

<s>E&longs;to igitur in &longs;trumentum, <lb/>de quo agimus CDBF, ex duo<lb/>bus vectibus con&longs;tans, quorum <lb/>alter CAF, alter vero DAB ver<lb/>tebra &longs;eu connexio A locus v<lb/>bi nux frangitur K, manubria <lb/>vero BF. quo igitur prolixiores <lb/>erunt AB, AF, breuiores vero ACAD, violentius fiet <expan abbr="c&omacr;-fractio">con<lb/>fractio</expan>. </s>

Line 3226

<s>Difficile hoc intellectu prima fronte, & &longs;ane admi<lb/>rabile, itaque in tentam con templationem requirit. </s>

<s>Nos <lb/>primo cum Ari&longs;totele, rem totam explicabimus, tum ali<lb/>quid forta&longs;&longs;e non p&oelig;nitendum no&longs;tro de promptuario <lb/>proferemus. </s><figure id="id.007.00.159.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.159.1.jpg">

<s>E&longs;to itaque Rhombus ABCD, <lb/>cuius latera AB, BD, DC, CA, diame<lb/>trorum maior AD, minor BC, &longs;ecan<lb/>tes &longs;e inuicem in puncto &longs;eu figuræ <lb/>centro K. </s>

Line 3276

<s>Futilem igitur e&longs;&longs;e rationem hanc ip&longs;ius Ari&longs;totelis <lb/>pace, hoc pacto o&longs;tendemus. </s>

<s>E&longs;to quadratum ABCD, cuius diametri ACBD &longs;e<lb/>cantes &longs;e&longs;e in E, moueatur eodem pacto BA, ver&longs;us CD, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.162.jpg"/><figure id="id.007.00.162.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.162.1.jpg"><lb/>item A, ver&longs;us B, & B ver&longs;us A, ita<lb/>que punctum A tum proprio tum <lb/>alieno, hoc e&longs;t lineæ illud <expan abbr="defer&emacr;-tis">deferen<lb/>tis</expan> motu deor&longs;um trudet, hoc e&longs;t, <lb/>ver&longs;us CD. </s>

<s>E&longs;to quadratum ABCD, cuius diametri ACBD &longs;e<lb/>cantes &longs;e&longs;e in E, moueatur eodem pacto BA, ver&longs;us CD, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.162.jpg"/><figure id="id.007.00.162.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.162.1.jpg"></figure><lb/>item A, ver&longs;us B, & B ver&longs;us A, ita<lb/>que punctum A tum proprio tum <lb/>alieno, hoc e&longs;t lineæ illud <expan abbr="defer&emacr;-tis">deferen<lb/>tis</expan> motu deor&longs;um trudet, hoc e&longs;t, <lb/>ver&longs;us CD. </s>

<s>Motus ergo velocior <lb/>erit motu puncti B, quod lationi<lb/>bus fertur ferè contrarijs, hoc e&longs;t, <lb/>ex B ver&longs;us A &longs;ur&longs;um, cum linea <lb/>autem BA ver&longs;us C deor&longs;um. </s>

Line 3284

<s>Stante igitur cau&longs;<lb/>&longs;a &longs;equi debui&longs;&longs;et effectus; non &longs;equitur autem, Ari&longs;tote<lb/>lis igitur cau&longs;&longs;a non e&longs;t cau&longs;&longs;a. </s>

<s>Rhombo quoque inuer&longs;o <lb/>idem clarius o&longs;tendemus hoc pacto: Sit Rhombus ABCD, <lb/><figure id="id.007.00.162.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.162.2.jpg"><lb/>cuius diametri AC, BD &longs;ecan<lb/>tes &longs;e&longs;e in E. </s>

<s>Rhombo quoque inuer&longs;o <lb/>idem clarius o&longs;tendemus hoc pacto: Sit Rhombus ABCD, <lb/><figure id="id.007.00.162.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.162.2.jpg"></figure><lb/>cuius diametri AC, BD &longs;ecan<lb/>tes &longs;e&longs;e in E. </s>

<s>Mota igitur linea <lb/>AB ver&longs;us CD, nempe deor&longs;um <lb/>& A quoque deor&longs;um ver&longs;us B, <lb/>contra vero B quidem &longs;ur<lb/>&longs;um ver&longs;us A, deor&longs;um vero <lb/>ver&longs;us C, erit B tardior A, &longs;ed <lb/>contrarium fit, quippe quod <lb/>longior &longs;it BD, per quam mouetur B ip&longs;a AC, per quam <lb/>mouetur A. </s>

Line 3318

<s>Si autem Rhombus in <lb/>duos &longs;oluatur triangulos, alter diametrorum datur æqua<lb/>lis æqualibus lateribus æquicrurium triangulorum; <expan abbr="itaq;">itaque</expan> <lb/>in i&longs;tis mixti motus per diametros aequeveloces erunt &longs;im<lb/>plicibus, qui per latera longiora, velociores autem illis <lb/>qui per latera breuiora. </s>

<s>His igitur hoc pacto non perfun<lb/>ctoriè con&longs;ideratis, facile ex proprijs cau&longs;&longs;is, nî fallimu<gap/>, <lb/>hocce Ari&longs;totelicum & mirabile Problema &longs;oluitur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.164.jpg"/><figure id="id.007.00.164.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.164.1.jpg">

<s>E&longs;to enim Rhombus ABDC, <lb/>cuius diameter longior AD maior &longs;it <lb/>tum lateribus, tum etiam altera dia<lb/>metro BC. &longs;ecent autem &longs;e inuicem <lb/>diametri in E. </s>

Line 3372

<s>Ob&longs;curiu&longs;culè, hæc &longs;ua figura o&longs;tendit Ari&longs;to<lb/>teles. </s>

<s>Nos igitur claritatem amantibus, no&longs;tram aliquan<lb/>to, nî fallimur, clariorem, proponemus. </s><figure id="id.007.00.166.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.166.1.jpg">

<s>E&longs;to circulus <lb/>maior ABCD, mi<lb/>nor FGHI, circa i<lb/>dem, & commune <lb/><expan abbr="c&emacr;trum">centrum</expan> E. </s>

Line 3408

<s>Eandemaequalemue potentiam, <expan abbr="aliquã">aliquam</expan> <lb/>magnitudinem tardius quidem mouere, aliquam vero <lb/>celerius. </s>

<s>quod autem natum e&longs;t aptum moueri, tardius <lb/>moueri, &longs;i &longs;imul cum non apto nato moueri, moueatur, <lb/>quam &longs;i &longs;eparatim moueretur, celerius autem &longs;i non &longs;imul <lb/><figure id="id.007.00.167.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.167.1.jpg"><lb/>cum eo moueatur. </s>

<s>E&longs;to enim corpus A leue <lb/>quidem & aptum natum moueri&longs;ur&longs;um, cui <lb/>connectatur B, aptum natum moueri deor<lb/>&longs;um, Si quis igitur mouere conetur corpus A <lb/>&longs;ur&longs;um difficilius mouebit, & tardius <expan abbr="iunct&umacr;">iunctum</expan> <lb/>nempeip&longs;i B, quam &longs;i ab ip&longs;o e&longs;&longs;et <expan abbr="&longs;ei&umacr;ctum">&longs;eiunctum</expan>. <lb/></s>

Line 3440

<s>E&longs;to enim rota ABCD, cuius centrum E, diametri <lb/>AEC, BED, e&longs;to alia minor rota GH, item minor KL, tum <lb/>minor NO, & adhuc minor QR, circaidem centrum E. <lb/></s>

<s>Rotetur itaque &longs;ecundum ab&longs;idem integri quadrantis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.169.jpg"/><figure id="id.007.00.169.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.169.1.jpg"><lb/>&longs;patium CD, eritque <lb/>D, in F, item &longs;i ex rota <lb/>GH, ex quadrante <lb/>HT, erit T in I. </s>

<s>Rotetur itaque &longs;ecundum ab&longs;idem integri quadrantis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.169.jpg"/><figure id="id.007.00.169.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.169.1.jpg"></figure><lb/>&longs;patium CD, eritque <lb/>D, in F, item &longs;i ex rota <lb/>GH, ex quadrante <lb/>HT, erit T in I. </s>

<s>Ex a<lb/>lijs item minoribus in <lb/>M, P, S. erit <expan abbr="itaq;">itaque</expan> <expan abbr="lon-gi&longs;&longs;im&umacr;">lon<lb/>gi&longs;&longs;imum</expan> &longs;patium CF, <lb/><expan abbr="breui&longs;&longs;im&umacr;">breui&longs;&longs;imum</expan> vero RS, <lb/>Mota igitur rota cir<lb/>ca <expan abbr="circul&umacr;">circulum</expan> &longs;eu axem, <lb/>QR, maior rota &longs;pa. <lb/></s>

Line 3488

<s>Ego autem demon&longs;trarem hoc pacto. </s>

<s>E&longs;to &longs;ponda ABCD, cuius longitudo AB, cra&longs;&longs;itudo <lb/>AC, in ea foramen vtrin que pertinens EF, re&longs;tis per fora-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.171.jpg"/><figure id="id.007.00.171.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.171.1.jpg"><lb/>men inditus GFE, &longs;itque Epars &longs;eu ca<lb/>put exterius, quodnodo in E di&longs;tine<lb/>tur. </s>

<s>E&longs;to &longs;ponda ABCD, cuius longitudo AB, cra&longs;&longs;itudo <lb/>AC, in ea foramen vtrin que pertinens EF, re&longs;tis per fora-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.171.jpg"/><figure id="id.007.00.171.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.171.1.jpg"></figure><lb/>men inditus GFE, &longs;itque Epars &longs;eu ca<lb/>put exterius, quodnodo in E di&longs;tine<lb/>tur. </s>

<s>Sit autem &longs;pondæ lignum iuxta <lb/>longitudinem vt natura a&longs;&longs;olet &longs;ci&longs;&longs;ile. <lb/></s>

Line 3504

<s>quo enim fu<lb/>nis <expan abbr="l&omacr;gior">longior</expan>, eodebilior, & pre&longs;&longs;io quæ in medio fit, ea vide<lb/>licet parte quæ ab extremis e&longs;t remoti&longs;&longs;ima, magis funem <lb/>fatigat. </s>

<s>Longiores autem funes &longs;unt quæ diametraliter <lb/>extenduntur. </s><figure id="id.007.00.171.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.171.2.jpg">

<s>Quatenus ad <expan abbr="tertiã">tertiam</expan> <lb/>rationem pertinet, hoc <lb/>pacto funes intexit <lb/>Philo&longs;oph^{9}. E&longs;to lectu<lb/>lus cum &longs;uis <expan abbr="&longs;p&omacr;dis">&longs;pondis</expan> AB <lb/>CD, cuius &longs;ponda AD, <lb/>&longs;it pedum &longs;ex, AB vero <lb/><expan abbr="tri&umacr;">trium</expan>, Diuidatur AD bi<lb/>faríam in E & BC in F. item AE in tres AG, GH, HE & in <lb/>totidem ED, nempe EL, LM, MD. </s>

Line 3536

<s>Sed interim &longs;ubit <lb/>mirari, cur veteres vtiliori modo prætermi&longs;&longs;o, <expan abbr="inutilioi&emacr;">inutilioiem</expan> <lb/>fuerint amplexati. </s>

<s>Poterant enim reticulatim hoc per li<lb/>neas lateribus æ quidi&longs;tantes intexere. </s><figure id="id.007.00.173.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.173.1.jpg">

<s>E&longs;to enim lectulus <lb/>eiu&longs;dem dimen&longs;ionis <lb/>ABCD, in cuius latere <lb/>AD &longs;int foramina quin<lb/>que E, F, G, H, I, totidem <lb/>in latere oppo&longs;ito QP, <lb/>ONM. </s>

Line 3562

<s>Quærerer autem qui&longs;piam, (ip&longs;e enim <lb/>id reticet) curvibratio hæc ferenti &longs;it nocua. </s>

<s>Nos itaque <lb/>id expliçare conabimur. </s><figure id="id.007.00.174.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.174.1.jpg">

<s>Nos itaque <lb/>id expliçare conabimur. </s><figure id="id.007.00.174.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.174.1.jpg"></figure>

<s>E&longs;to igitur lignum <lb/>oblongum, flexile, & vt <lb/>ita dicam, vibrabile <lb/>AB, imponatur hume<lb/>ro<gap/> eique hæreat in C, <lb/>manu vero &longs;u&longs;tineatur facta compre&longs;&longs;ione in B. </s>

Line 3588

<s>E&longs;to enim oblongum lignum AB, cui humerus &longs;up<lb/>ponatur in B, manus vero premendo &longs;u&longs;tinens in B. &longs;it au<lb/>tem ligni pars maxima AC, minima CB, inaioris autem ad <lb/>minorem proportio exempli gratia &longs;it &longs;excupla. </s>

<s>Ad hoc i<lb/>gitur vt fiat æquilibrium inter potentiam &longs;u&longs;tinentem in <lb/>B, & pondus comprimens in A, ita &longs;e habere oportet po<lb/>tentiam in B, ad pondus in A, vt &longs;e habet pars ligni AC ad <lb/><figure id="id.007.00.175.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.175.1.jpg"><lb/>partem CD. </s>

<s>E&longs;to igitur pon<lb/>dus in A, puta librarum &longs;ex. <lb/></s>

Line 3614

<s>quod fuerat o<lb/>&longs;tendendum. </s>

<s>Hinc alia quæ&longs;tio huic affinis &longs;oluitur, Cur ha&longs;ta &longs;a<lb/>ri&longs;&longs;aue &longs;olo iacens manu ad alteram extremitatum ap<lb/>pren&longs;a di&longs;ficillime extollatur? </s><figure id="id.007.00.176.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.176.1.jpg">

<s>E&longs;to igitur &longs;ari&longs;&longs;a ha<lb/>&longs;taue iacens AB, cuius ex<lb/>tremitati A manus ad &longs;u<lb/>&longs;tollendum applicetur, &longs;it <lb/>autem pars quæ digitis capitur AC, quæritur cur pars re<lb/>liqua CB difficillime &longs;u&longs;tollatur? </s>

Line 3624

<s>E&longs;tigitur AB <lb/>vectis, cuius fulcimentum C, pondus B, potentia A, <expan abbr="Itaq;">Itaque</expan> <lb/>quoniam maxima e&longs;t proportio BA ad AC, maximam e&longs;<lb/>&longs;e oportet potentiam pondus &longs;u&longs;tollentem in C. </s>

<s>Huc etiam illud pertinet, Cur ha&longs;ta &longs;olo iacente, &longs;i <lb/>alterum extremorum manu &longs;u&longs;tollatur, alterum vero ve<lb/>lo ci&longs;&longs;ime &longs;ur&longs;um vibretur, & eodem tempore manus ha<lb/>&longs;tæ &longs;ic vibratæ &longs;upponatur, haud magna difficultate ha&longs;tæ <lb/>ad perpendiculum fit erectio. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.177.jpg"/><figure id="id.007.00.177.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.177.1.jpg">

<s>Sit enim ha&longs;ta AB, quæ <lb/>manu ex B capta eleuetur in <lb/>C, & fiat in AC, tum facta ex <lb/>C partis A veloci vibratione, <lb/>ip&longs;a extremitas A transferatur <lb/>in D, &longs;itque vbi CD, tum velo<lb/><gap/>imanus depre&longs;&longs;ione extremi<lb/>tas C transferatur in E, <expan abbr="fiatq;">fiatque</expan> <lb/>EF horizonti perpendicuiaris; <lb/>quod vbi factum fuerit, erunt <lb/>in eadem linea quæ ad centrum mundi, manus ip&longs;a quæ <lb/>&longs;u&longs;tinet, & grauitatis ip&longs;ius centrum G, quare manus ip&longs;a <lb/>facta vibratione tantum portat, quantum præci&longs;e ip&longs;ius <lb/>e&longs;t ha&longs;tæ pondus. </s>

Line 3640

<s>Dupliciter autem vibratione ip&longs;a, portans offenditur, <lb/>tum ex cau&longs;&longs;a quam in &longs;uperiori quæ&longs;tione con&longs;ideraui<lb/>mus, nempe quod motus &longs;ur&longs;um deor&longs;um a&longs;&longs;iduus, pro<lb/>gredientis motum impediat, tum etiam quod duplici <lb/>pre&longs;&longs;ione grauetur ferentis humerus, quod Philo&longs;ophus <lb/>non animaduertit. </s>

<s>Sit enim oblongum lignum AB, quod humero me-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.178.jpg"/><figure id="id.007.00.178.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.178.1.jpg"><lb/>dio loco &longs;u&longs;tineatur in C. <lb/>nutabunt ergo extrema AB, <lb/>à centro C, valde remota, <lb/>cadent autem &longs;imul A m D, <lb/>& B in E trahere &longs;ecum conantes medium C, quare is qui <lb/>in C &longs;u&longs;tinet, non modo ligni &longs;u&longs;tinet pondus ex grauita<lb/>tis centro quod e&longs;t in C, &longs;ed impetum quoque in ip&longs;a ex<lb/>tremorum depre&longs;&longs;ione acqui&longs;itum ex ipia violentia. </s>

<s>Sit enim oblongum lignum AB, quod humero me-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.178.jpg"/><figure id="id.007.00.178.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.178.1.jpg"></figure><lb/>dio loco &longs;u&longs;tineatur in C. <lb/>nutabunt ergo extrema AB, <lb/>à centro C, valde remota, <lb/>cadent autem &longs;imul A m D, <lb/>& B in E trahere &longs;ecum conantes medium C, quare is qui <lb/>in C &longs;u&longs;tinet, non modo ligni &longs;u&longs;tinet pondus ex grauita<lb/>tis centro quod e&longs;t in C, &longs;ed impetum quoque in ip&longs;a ex<lb/>tremorum depre&longs;&longs;ione acqui&longs;itum ex ipia violentia. </s>

<s>Illud <lb/>autem &longs;ubtiliter con&longs;ideramus, portantem ex vibratione <lb/>per inter ualla deprimi & &longs;ubleuari. </s>

Line 3662

<s>Nos autem luci <lb/>ip&longs;i lucem aliquam adhuc afferre conabimur. </s>

<s>E&longs;to Celomum (Latine Tolenonem appellant) ABC, <lb/>cuius arrectarium BD, tran&longs;uer&longs;um lignum AC, quod <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.179.jpg"/><figure id="id.007.00.179.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.179.1.jpg"><lb/>conuertitur, circa <expan abbr="p&umacr;ctum">punctum</expan> &longs;eu <lb/>fulcimentum B, pondus, plum<lb/>bumue, vbi A, &longs;itula E, funi ap<lb/>pen&longs;a CE. </s>

<s>E&longs;to Celomum (Latine Tolenonem appellant) ABC, <lb/>cuius arrectarium BD, tran&longs;uer&longs;um lignum AC, quod <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.179.jpg"/><figure id="id.007.00.179.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.179.1.jpg"></figure><lb/>conuertitur, circa <expan abbr="p&umacr;ctum">punctum</expan> &longs;eu <lb/>fulcimentum B, pondus, plum<lb/>bumue, vbi A, &longs;itula E, funi ap<lb/>pen&longs;a CE. </s>

<s>Dico rebus ita con<lb/>&longs;titutis difficilem quidem e&longs;&longs;e <lb/>vacuæ &longs;itulæ demi&longs;&longs;ion em, fa<lb/>cile vero eiu&longs;dem extractio<lb/>nem. </s>

Line 3684

<s>Sit enim trochlea puteo imminens <lb/>ABCD, cuius centrum E &longs;u&longs;pen&longs;a quidem in A, funis, cui <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.180.jpg"/>&longs;itula &longs;u&longs;penditur FCABG, &longs;itula vero G. </s>

<s>E&longs;t igitur dia<lb/>meter CED, in&longs;tar libræ, quare vt fiat æquilibrium nece&longs;<lb/>&longs;e e&longs;t capiti funis F, potentiam applicare, quæ &longs;it æqualis <lb/><figure id="id.007.00.180.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.180.1.jpg"><lb/>pondere &longs;itulæ aqua plenæ, itaque extra<lb/>hens proprijs viribus <expan abbr="corpor&imacr;s">corporins</expan> pondus ad<lb/>ijciens facile &longs;itulam aqua plenam extra<lb/>hit, ex qua re magna extrahentibus fit <lb/>commoditas. </s>

<s>E&longs;t igitur dia<lb/>meter CED, in&longs;tar libræ, quare vt fiat æquilibrium nece&longs;<lb/>&longs;e e&longs;t capiti funis F, potentiam applicare, quæ &longs;it æqualis <lb/><figure id="id.007.00.180.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.180.1.jpg"></figure><lb/>pondere &longs;itulæ aqua plenæ, itaque extra<lb/>hens proprijs viribus <expan abbr="corpor&imacr;s">corporins</expan> pondus ad<lb/>ijciens facile &longs;itulam aqua plenam extra<lb/>hit, ex qua re magna extrahentibus fit <lb/>commoditas. </s>

<s>Patet autem diuer&longs;o modo <lb/>extrahentes iuuare Celonium. </s>

Line 3708

<s>Soluit Ari&longs;toteles, inquiens, lignum e&longs;&longs;e vectem, pon<lb/>dus vero fulcimentum; res quæ mouetur is qui ponde<lb/>ri e&longs;t proximior: mouens vero qui remotior. </s>

<s>Itaque quo <lb/>magis remotus e&longs;t à pondere, hoc e&longs;t, à fulcimento is qui <lb/>mouet, eo violentius is premitur qui altera vectis parte <lb/>eaque breuiori, mouetur. </s><figure id="id.007.00.181.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.181.1.jpg">

<s>E&longs;to lignum AB, pondus <lb/>C appen&longs;um in E, vicinius ex<lb/>tremo B quamip&longs;i A, &longs;it <expan abbr="aut&emacr;">autem</expan> <lb/><expan abbr="portãtium">portantium</expan> alter quidem AF, <lb/>alter vero BG, Imaginemur <lb/>itaquelocum E à pondere ita <lb/>figi & deprimi, vt&longs;ur&longs;um qui<lb/>dem ferri nequaquam po&longs;&longs;it, <lb/>circa vero punctum E, ceu <lb/>circa centrum fulcimentum<lb/>ne ip&longs;um vectem conuerti. </s>

Line 3736

<s>Hinc colligimus, pondere in medio vecte appen&longs;o <lb/>ferentes æqualiter &longs;u&longs;tinere, propterea quod totius vectis <lb/>ad partes ip&longs;as proportio &longs;it eadem, vel æqualis. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.183.jpg"/>

<s>Pulchre autem dubitari pote&longs;t, an idem pror&longs;us con<lb/>tingat, &longs;i alterum eorum qui &longs;u&longs;tinent, &longs;it &longs;tatura quidem <lb/>procerior, alterv<gap/>ro humilior. </s><figure id="id.007.00.183.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.183.1.jpg">

<s>Sit enim vectis AB, in cuius <lb/>medio pondus H libere appen<lb/>&longs;um ex C, alter portantium pro<lb/>cerior AD, humilior vero BE. &longs;it <lb/>autem horizontis planum DE, <lb/>demittatur à puncto Cad <expan abbr="horiz&omacr;-tem">horizon<lb/>tem</expan> perpendicularis, ip&longs;is vero <lb/>AD, BE, æquidi&longs;tans CF. </s>

Line 3754

<s>E&longs;to enim vectis AB, cuius medium C, pondus vecti <lb/>in C alligatum CFG, cuius grauitatis centrum H eorum <lb/>qui portant procerior AB, humilior BE, horizontis <expan abbr="plan&umacr;">planum</expan> <lb/>DE. </s>

<s>Demittatur per centrum H horizonti perpendicu<lb/>laris IHK, &longs;ecans vectem quidem in I, horizontis vero pla-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.184.jpg"/><figure id="id.007.00.184.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.184.1.jpg"><lb/>num in K. </s>

<s>Po&longs;t hæc intelligatur pon<lb/>dus &longs;olutum quidem à puncto C, ap<lb/>pen&longs;um vero ex puncto I. </s>

Line 3804

<s>Ait Philo&longs;ophus, forte id fieri, quod æqualitas &longs;it o<lb/>mnino quietis cau&longs;&longs;a, rectum vero angulum quietis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.186.jpg"/>angulum e&longs;&longs;e, & &longs;tationem facere, nec alia de cau&longs;&longs;a &longs;tan<lb/>tem ip&longs;i terræ e&longs;&longs;e perpendicularem, & ideo caput & pe<lb/>des in eadem linea habere, &longs;edentem vero non item. </s>

<s><expan abbr="T&umacr;c">Tunc</expan> <lb/>autem à &longs;e&longs;&longs;ione &longs;urrectionem fieri, cum caput & pedes in <lb/>vna linea collocantur, quod &longs;ane fit cum pectus & crura <lb/>acutum cum ip&longs;o f&oelig;more angulum faciunt. </s><figure id="id.007.00.186.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.186.1.jpg">

<s>E&longs;to enim &longs;tans AB hori<lb/>zonti IBK perpendicularis, cù<lb/>ius caput A, pedes vero B, &longs;edcat <lb/>modo &longs;itque eius cum capite <lb/>Thorax CD, f&oelig;mur DE, crura <lb/>EF, &longs;intque CDE, DEF anguli <lb/>recti, quibus ita con&longs;titutis non <lb/>&longs;unt in eadem linea caput C & <lb/>pedes F. </s>

Line 3822

<s>Natura autem ideo commodam hominibus <lb/>&longs;e&longs;&longs;ionem facere volui&longs;&longs;e inde apparet, quod clunes, qui<lb/>bus tota &longs;uperior pars, & grauior nititur, carno&longs;am fece<lb/>rit, & ceruicalis cuiu&longs;dam in&longs;tar mollem & facilem. </s>

<s>Sed <lb/>nos ad quæ&longs;tionem. </s><figure id="id.007.00.187.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.187.1.jpg">

<s>Sed <lb/>nos ad quæ&longs;tionem. </s><figure id="id.007.00.187.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.187.1.jpg"></figure>

<s>E&longs;to enim &longs;tans AB, cuius caput A, <lb/>Thorax AC, f&oelig;mora CD, crura DB, pe<lb/>des vero B, centrum vero grauitatis in i<lb/>p&longs;o Thorace E. </s>

Line 3848

<s>Primum igitur quærimus, Curhominum & cætero<lb/>rum animalium, quæ aliquando erecto corpore incedunt, <lb/>pedes non quidem breues &longs;int & rotundi, &longs;ed longiores <lb/>potius, & in inferiorem partem porrecti? </s>

<s>Item cur magis <lb/>ad digitos quam ad cal caneum porrigantur? </s><figure id="id.007.00.188.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.188.1.jpg">

<s>E&longs;to <gap/>homo animalue quodpiam &longs;tans <lb/>AB, cuius pes CD, pedis pars quæ ad digitos <lb/>BC. quae vero ad cal caneum BD f&oelig;moris ver<lb/>tebra E, centrum vero grauitatis ip&longs;ius cor<lb/>poris F. </s>

Line 3880

<s>Quod linea fulcitur ad duas tantum partes, ea&longs;que <lb/>oppo&longs;itas, habet ca&longs;um. </s>

<s>&longs;itillud &longs;uperficies, corpu&longs;ue in <lb/>latus con&longs;titutum. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.190.jpg"/><figure id="id.007.00.190.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.190.1.jpg">

<s>E&longs;to horizontis pla<lb/>num ABCD, cui ad re<lb/>ctos angulos in&longs;i&longs;tat &longs;u<lb/>perficies EFGH, &longs;ecun<lb/>dum latus FG. </s>

Line 3896

<s>Si vero ad partes AB, fiet vbi L. </s>

<s>Sunt autem LKM <expan abbr="p&umacr;-cta">pun<lb/>cta</expan> in recta LKM, quæ quidem communis &longs;ectio e&longs;t plani <lb/>horizontis, & plani per IKLM, tran&longs;euntis. </s><figure id="id.007.00.190.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.190.2.jpg">

<s>Idem quoque de cor<lb/>pore dicimus in latus col<lb/>locato. </s>

Line 3906

<s>Hincanimaduertere licet, Cur prouidi&longs;&longs;ima Natu<lb/>ranulli animantium vnicum dederit pedem, &longs;ed aut qua<lb/>ternos, aut &longs;altem binos, & binos quidem ip&longs;os virtute <lb/>quaternos, &longs;iquidem in quolibet animantium bipedum <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.191.jpg"/>pede duo &longs;altem puncta con&longs;iderantur, quibus ip&longs;um ani. <lb/></s>

<s>mal fulcitur. </s><figure id="id.007.00.191.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.191.1.jpg">

<s>mal fulcitur. </s><figure id="id.007.00.191.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.191.1.jpg"></figure>

<s>Sint enim humani pedis ve<lb/>&longs;tigia A, B, C, D, in vtroque igitur <lb/>duo puncta con&longs;iderantur, A, B, <lb/>C, D, illa quidem ad digitos, hæc <lb/>autem ad calcaneum. </s>

Line 3918

<s>Sit <lb/>enim vas quo dpiam ABC, cuius pes vnicus, i&longs;que rotun<lb/>dus BC, grauitatis vero centrum D. </s>

<s>Quoniam igitur in <lb/>pedis ip&longs;ius peripheria, infinita puncta intelligantur, dici <lb/>quo dammodo pote&longs;t vas ip&longs;um infinitis fere punctis, licet <lb/><figure id="id.007.00.191.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.191.2.jpg"><lb/>pesvnicus &longs;it, &longs;u&longs;tineri. </s>

<s>Quoniam igitur in <lb/>pedis ip&longs;ius peripheria, infinita puncta intelligantur, dici <lb/>quo dammodo pote&longs;t vas ip&longs;um infinitis fere punctis, licet <lb/><figure id="id.007.00.191.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.191.2.jpg"></figure><lb/>pesvnicus &longs;it, &longs;u&longs;tineri. </s>

<s>Non<lb/>nulla autem corpora artifi<lb/>cialia. </s>

Line 3940

<s>Siautem vnico tantum genu qui&longs;piam nitatur, dif<lb/>ficultatem &longs;entiet longe minorem. </s>

<s>Triplici enim fulci<lb/><figure id="id.007.00.192.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.192.1.jpg"><lb/>mento eo ca&longs;u ingeniculatus <lb/>fulcitur. </s>

<s>Triplici enim fulci<lb/><figure id="id.007.00.192.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.192.1.jpg"></figure><lb/>mento eo ca&longs;u ingeniculatus <lb/>fulcitur. </s>

<s>Sit enim ingenicula<lb/>tus ABCDE, cuius grauitatis <lb/>centrum F. dextrum vero ge<lb/>nu, cuinititur D, &longs;ini&longs;trum ve<lb/>ro, quod eleuatur B. </s>

Line 3954

<s>Cur <lb/>id Natura docente faciant, eam puto e&longs;&longs;e cau&longs;&longs;am, quod <lb/>dum dormiunt, caput &longs;ini&longs;træ alæ, vt naturali calore iu<lb/>uentur, &longs;upponunt, quapropter ad eam partem declinan<lb/>tes, vt interim æquilibrium faciant, pedem &longs;ubleuant, & <lb/>eo ca&longs;u ceu inutilem retrahunt atque &longs;u&longs;pendunt: addita <lb/>item alia cau&longs;&longs;a, nempe vt pedem ip&longs;um dormientes nati<lb/>uo calore confoueant. </s>

<s>Quæritur et<gap/>am, Curij qui inclinantur, vt <expan abbr="r&emacr;">rem</expan> quam<lb/>piam à &longs;olo &longs;u&longs;tollant, alterum crurium ad anteriora, <expan abbr="n&emacr;-pever&longs;us">nen<lb/>pever&longs;us</expan> manum ip&longs;am, quam porrigunt, extendant? </s><figure id="id.007.00.193.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.193.1.jpg">

<s>E&longs;to enim qui&longs;piam ABCD, <lb/>cuius crura BC, BD, grauitatis <lb/>centrum E, vclitautem quippiam <lb/>à &longs;olo tollere quod &longs;it in F. &longs;it per<lb/>pendicularis, quæ pergrauitatis <lb/>centrum GEH. </s>

Line 3972

<s>Sint duæ in plano parallelæ AB, CD, in quibus qua<lb/>drupedis pedes E, F, B, D, quorum EF, anteriores, BD vero <lb/>po&longs;teriores. </s>

<s>iungantur BDEF, eritque EBDF parallelo<lb/>grammum altera parte longius, cuius diametri ducantur <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.194.jpg"/><figure id="id.007.00.194.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.194.1.jpg"><lb/>ED, BF, &longs;ecantes &longs;e&longs;e in G, vbi & grauitatis <lb/>centrum. </s>

<s>iungantur BDEF, eritque EBDF parallelo<lb/>grammum altera parte longius, cuius diametri ducantur <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.194.jpg"/><figure id="id.007.00.194.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.194.1.jpg"></figure><lb/>ED, BF, &longs;ecantes &longs;e&longs;e in G, vbi & grauitatis <lb/>centrum. </s>

<s>Moto igitur po&longs;teriori &longs;ini&longs;tro pe<lb/>de B in K, &longs;i anteriorem E, eodem tempore <lb/>moueret in I, &longs;tantibus interim DF, ceu ful<lb/>cimentis, centrum Gextra fulcimenta &longs;ieret <lb/>ad partes BE. </s>

Line 3988

<s>Dum enim dextrum crus e<lb/>leuatur, centrum &longs;ini&longs;tro fulcitur, & econtra. </s>

<s>Naturalia i&longs;thæc &longs;unt; in artifi cialibus autem quæri <lb/>po&longs;&longs;et, Cur Architecti, Arcium muros non ad perpendi<lb/>culum erectos, &longs;ed intror&longs;um inclinatos con&longs;tituant? </s><figure id="id.007.00.194.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.194.2.jpg">

<s>Vtique hoc faciunt, vt minus <lb/>&longs;int ad ruinam proni. </s>

Line 4018

<s>Propendeat autem ad partes DC ex angulo <lb/>DCF. </s>

<s>Ita autem con&longs;tituta intelligatur vt perpendicula<lb/>ris ab A, in planum horizontis demi&longs;&longs;a per grauitatis cen-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.196.jpg"/><figure id="id.007.00.196.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.196.1.jpg"><lb/>trum E extra ba&longs;im BC, non cadat, <lb/>cadat autem in C. </s>

<s>Ita autem con&longs;tituta intelligatur vt perpendicula<lb/>ris ab A, in planum horizontis demi&longs;&longs;a per grauitatis cen-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.196.jpg"/><figure id="id.007.00.196.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.196.1.jpg"></figure><lb/>trum E extra ba&longs;im BC, non cadat, <lb/>cadat autem in C. </s>

<s>Quoniam igitur <lb/>ABCD moles per E grauitatis cen<lb/>trum diuiditur, in partes &longs;ecatur æ<lb/>queponderantes, &longs;ed & centrum. <lb/></s>

Line 4050

<s>Auget autem res mota <lb/>quodammodo mouentis potentiam. </s>

<s>quod enim à mouen<lb/>te pateretur, ex &longs;e ip&longs;a agit res quæ mouetur. </s><figure id="id.007.00.197.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.197.1.jpg">

<s>E&longs;to horizontis pla<lb/>num AB, cui moles quæ<lb/>dam in&longs;i&longs;tat, CD. </s>

Line 4144

<s>Cur proiecta corpora non &longs;ibimet ip&longs;is &longs;ecun dum, <lb/>partes æ quegrauia, &longs;i fuerint irregularis figuræ in ip&longs;o mo<lb/>tu, &longs;ecundum grauiorem partem antror&longs;us inuiolento, & <lb/>deor&longs;um in naturali ferantur, & dum in latione conuer<lb/>tuntur, &longs;onitum edant. </s>

<s>E&longs;to pila ABCD, cuius centrum E concinnata ex <lb/>di&longs;pari materia leui, nempe BCD, & graui ABD. non ergo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.201.jpg"/><figure id="id.007.00.201.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.201.1.jpg"><lb/>erit <expan abbr="centr&umacr;">centrum</expan> grauitatis & cen<lb/>trum molis, &longs;it autem grauita<lb/>tis centrum F. </s>

<s>E&longs;to pila ABCD, cuius centrum E concinnata ex <lb/>di&longs;pari materia leui, nempe BCD, & graui ABD. non ergo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.201.jpg"/><figure id="id.007.00.201.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.201.1.jpg"></figure><lb/>erit <expan abbr="centr&umacr;">centrum</expan> grauitatis & cen<lb/>trum molis, &longs;it autem grauita<lb/>tis centrum F. </s>

<s>De&longs;cendat cor<lb/>pus prohibente remoto per <lb/>rectam AG. </s>

Line 4160

<s>E&longs;to aquæ &longs;uper&longs;icies AB, lapis proiectus C, tangens <lb/>aquæ &longs;uperficiem in D, & inde re&longs;iliens in E, mox iterum <lb/>eandem tangens in F, & re&longs;iliens in G, donec <expan abbr="viol&emacr;to">violento</expan> mo<lb/>tu ce&longs;&longs;ante demergatur. </s>

<s>Vtique lapis C, proiectus in D, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.202.jpg"/><figure id="id.007.00.202.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.202.1.jpg"><lb/>ni&longs;i medio den&longs;iori, aqua vi<lb/>delicet, repelleretur, pene<lb/>traret per D, in H. </s>

<s>Vtique lapis C, proiectus in D, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.202.jpg"/><figure id="id.007.00.202.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.202.1.jpg"></figure><lb/>ni&longs;i medio den&longs;iori, aqua vi<lb/>delicet, repelleretur, pene<lb/>traret per D, in H. </s>

<s>At eo re&longs;i<lb/>&longs;tente, & adhuc vigente im<lb/>petu, fertur in E ad angulos <lb/>fere pares. </s>

Line 4168

<s>Durante <lb/>igitur impetu quo pellitur antror&longs;um, fiuntip&longs;æ re&longs;ilitio<lb/>nes, & eo ce&longs;&longs;ante, re&longs;ilitiones ce&longs;&longs;ant, & lapis &longs;uapte gra<lb/>uitate demergitur. </s>

<s>Huc quoque &longs;pectat, Cur pila lu&longs;oria in horizontis <lb/>planum proiecta ad pares re&longs;iliat, angulos nempe rectos? </s><figure id="id.007.00.202.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.202.2.jpg">

<s>E&longs;to horizontis planum <lb/>AB, in quod à puncto C per <lb/>lineam perpendicularem CE <lb/>cadat proijciaturue pila DE, <lb/>cuius grauitatis centrum F. <lb/></s>

Line 4232

<s>Et quo<lb/>niam maior velocior e&longs;t, magnitudo media, non æquali<lb/>ter fertur, &longs;ed à maiori quidem pellitur, à minori vero re<lb/>trahitur, vnde transuer&longs;us fit magnitudinis motus, & ip&longs;a <lb/>magnitudo ad interiorem propellitur circulum, itaque <lb/>eodem pacto, è maiori in minorem propul&longs;a in centrum. <lb/></s>

<s>tantum fertur, & ibi quie&longs;cit. </s><figure id="id.007.00.204.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.204.1.jpg">

<s>tantum fertur, & ibi quie&longs;cit. </s><figure id="id.007.00.204.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.204.1.jpg"></figure>

<s>E&longs;to vortex AB, cuius cen<lb/>trum C, magnitudo quæ fer<lb/>tur AD, maior circulus AFB, <lb/>minor DHEG. </s>

Line 4258

<s>qua veritate cognita, omnis pror&longs;us difficultas tollitur, <lb/>Cum enim ea quæ feruntur, ab aqua ferantur, aqua vero <lb/>feratur &longs;piraliter, ea quoque &longs;piraliter ferri, e&longs;t nece&longs;&longs;a-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.206.jpg"/>rium. </s>

<s>Hæc autem clariora erunt &longs;i quo pacto vortices <lb/>fiant, qui&longs;piam con&longs;iderauerit. </s><figure id="id.007.00.206.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.206.1.jpg">

<s>E&longs;to fluminis cuiu&longs;piam curua <lb/>eademque profunda ripa ABCD. <lb/></s>

Line 4266

<s>Alia quoque de cau&longs;&longs;a, ex quie&longs;cente nimirum, & <lb/>mota aqua fiunt &longs;piræ vorticesue. </s>

<s>E&longs;to enim fluminis ripa <lb/><figure id="id.007.00.206.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.206.2.jpg"><lb/>ABC, &longs;inum efficiens, qui a quam ex <lb/>ripæ ip&longs;ius obiectu contineat quie<lb/>&longs;centem, Cur&longs;us vero fluminis liber & <lb/>rectus, &longs;it inter lineas AC, DE. </s>

<s>E&longs;to enim fluminis ripa <lb/><figure id="id.007.00.206.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.206.2.jpg"></figure><lb/>ABC, &longs;inum efficiens, qui a quam ex <lb/>ripæ ip&longs;ius obiectu contineat quie<lb/>&longs;centem, Cur&longs;us vero fluminis liber & <lb/>rectus, &longs;it inter lineas AC, DE. </s>

<s>Itaque <lb/>dum aqua AC rapide fertur ad partes <lb/>A, quie&longs;centem ABC iuxta lineam. <lb/></s>

Line 4288

<s>Sed nos hi&longs;ce explicatis commode ad ea quæ <lb/>dixerat Ari&longs;toteles, reuertemur. </s>

<s>Dicimus igitur, priman eius rationem haud magni <lb/>videri ponderis, &longs;iquidem non per circulos actu di&longs;tinctos <lb/>aqua circumfertur, &longs;ed ip&longs;amet &longs;ua mole tota &longs;imul. </s><figure id="id.007.00.207.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.207.1.jpg">

<s>E&longs;to enim vortex AB, cu<lb/>ius centrum C, &longs;emidiameter <lb/>CA, fiatautem rotatio totius a<lb/>quæ CA ad partes D, in linea <lb/>autem AC, &longs;it corpus aliquod a<lb/>quæ rotatione <expan abbr="circumlat&umacr;">circumlatum</expan> AE, <lb/>inter circulos maiorem ADB, <lb/>minorem EFG. velocius autem <lb/>mouetur ADB, ip&longs;o EFG, citius <lb/>ergo fertur pars &longs;uperior ip&longs;ius <lb/>corporis vbi A, quam inferior <lb/>vbi E. </s>

<s>Atidnec A repellit, nec E retrahit, &longs;iquidem eodem <lb/>tempore quo A permeauit <expan abbr="circul&umacr;">circulum</expan> ADB, codem & E per<lb/>currit circulum EFG. <expan abbr="Itaq;">Itaque</expan> A reuer&longs;o in A & E, punctum <lb/>reuer&longs;um erit in E, nulla facta corporis E quoad &longs;itum, <lb/>muratione quod voluit Ari&longs;toteles. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.208.jpg"/>

<s>Ad &longs;ecundam vero dicimus, non ideo quod omnes <lb/>circuli æqualiter circa centrum &longs;erantur, ni&longs;i alia <expan abbr="quæpiã">quæpiam</expan> <lb/>extranea vis interce&longs;&longs;erit, quæ ea ab exterioribus circulis <lb/>pellens agat in medium. </s><figure id="id.007.00.208.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.208.1.jpg">

<s>Tertia quoque ratio la<lb/>borare videtur. </s>

Line 4344

<s>His ita con&longs;titutis pare<lb/>tur &longs;eor&longs;um &longs;cheda regulaue quæpiam NO, in cuius late<lb/>re accipiatur OP, æqualis medietati primæ datarum &longs;eu <lb/>ip&longs;i KL. </s>

<s>Tum regulæ latus aptetur puncto L, extremum <lb/>vero O, feratur a&longs;&longs;idue per rectam EK, ver&longs;us K, nunquam <lb/><figure id="id.007.00.210.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.210.1.jpg"><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.211.jpg"/>interim regulæ latere ON amoto à puncto L, idque do<lb/>nec punctum P, obuians incidat in lineam KM, puta vbi <lb/>Qextremum vero O inueniatur in R, notato igitur in li<lb/>nea EK puncto R habebitur, quod quærebatur. </s>

<s>Tum regulæ latus aptetur puncto L, extremum <lb/>vero O, feratur a&longs;&longs;idue per rectam EK, ver&longs;us K, nunquam <lb/><figure id="id.007.00.210.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.210.1.jpg"></figure><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.211.jpg"/>interim regulæ latere ON amoto à puncto L, idque do<lb/>nec punctum P, obuians incidat in lineam KM, puta vbi <lb/>Qextremum vero O inueniatur in R, notato igitur in li<lb/>nea EK puncto R habebitur, quod quærebatur. </s>

<s>Erunti<lb/>gitur AB prima, RK &longs;ecunda, QL tertia, BC quarta. </s>

Line 4372

<s>Quoniam enim BC <lb/>bifariam &longs;ecta e&longs;t in E, & ip&longs;i adijcitur CK. </s>

<s>Rectangulum <lb/>BKC per 6. &longs;ecundi: vna cum quadrato ex CE, æquale e&longs;t <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.212.jpg"/><figure id="id.007.00.212.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.212.1.jpg"><lb/>quadrato ex EK. commune apponatur ex EF quadratum, <lb/>ergo rectangulum BKC vna cum quadrato CF æquale <lb/>e&longs;t quadratis ex KE, EF, hoce&longs;t, quadrato ex FK. </s>

<s>Rectangulum <lb/>BKC per 6. &longs;ecundi: vna cum quadrato ex CE, æquale e&longs;t <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.212.jpg"/><figure id="id.007.00.212.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.212.1.jpg"></figure><lb/>quadrato ex EK. commune apponatur ex EF quadratum, <lb/>ergo rectangulum BKC vna cum quadrato CF æquale <lb/>e&longs;t quadratis ex KE, EF, hoce&longs;t, quadrato ex FK. </s>

<s>Et quo<lb/>niam vt MA ad AB, ita e&longs;t MD ad DK, vt autem MD ad <lb/>DK per 2. &longs;exti, ita BC ad C<emph type="italics"/>K<emph.end type="italics"/> erit vt MA ad AB, ita BC <lb/>ad C<emph type="italics"/>K<emph.end type="italics"/>. </s>

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