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Colored diff for /texts/archimedes/xml/Attic/baldi_mecha_01_la_1621.xml between version 1.45 and 1.48

version 1.45, 2002/10/03 00:40:10

version 1.48, 2002/10/09 23:05:34

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<s id="id.000001">BERNARDINI BALDI VRBINATIS <lb/>GVASTALLÆ AB<lb/>BATIS <lb/><emph type="italics"/>IN<emph.end type="italics"/></s>

<s id="id.000002">MECHANICA ARISTOTE<lb/>LIS PROBLEMATA <lb/>EXERCITATIONES:</s>

<s id="id.000003"><emph type="italics"/>ADIECTA SVCCINCTA NAR<lb/>ratione de autoris vita & &longs;criptis.<emph.end type="italics"/></s><figure id="id.007.01.001.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.001.1.jpg"></figure>

<s id="id.000004"><emph type="italics"/><gap/>NTIAE.<emph.end type="italics"/></s>

<s id="id.000004"><emph type="italics"/>MOGVNTIAE.<emph.end type="italics"/></s>

<s id="id.000005">Typis & Sumptibus Viduæ Ioannis Albini.</s>

</section><section>

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<s id="id.000180">Centrum grauitatis <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> corporis e&longs;t pun<lb/>ctum quod dam intra po&longs;itum, à quo &longs;i graue, mente ap<lb/>pen&longs;um concipiatur, dum fertur, quie&longs;cit, & &longs;eruat eam <lb/>quam in principio habuit po&longs;itionem; neque in ip&longs;a latio<lb/>ne circumuertitur. </s>

<s id="id.000181">Commandinus verò in lib.

<s id="id.000181">Commandinus verò in lib. de centro <lb/>grauitatis &longs;olidorum hoc pacto: Centrum grauitatis v<lb/>niu&longs;cuiu&longs;que &longs;olidæ figuræ, e&longs;t punctum illud intra po&longs;i<lb/>tum, circa quod vndique partes æqualium momentorum <lb/>ad&longs;i&longs;tunt. </s>

de centro <lb/>grauitatis &longs;olidorum hoc pacto: Centrum grauitatis v<lb/>niu&longs;cuiu&longs;que &longs;olidæ figuræ, e&longs;t punctum illud intra po&longs;i<lb/>tum, circa quod vndique partes æqualium momentorum <lb/>ad&longs;i&longs;tunt. </s>

<s id="id.000182">Si enim per tale centrum ducatur planum, fi<lb/>guram quomodolibet &longs;ecans, in partes æquè ponderantes <lb/>eam diuidit. </s>

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<s id="id.001266">E&longs;to igitur &longs;cindendum quippiam ABCD, Cuneus <lb/>EFG, cuius pars HFI &longs;ci&longs;&longs;uræ in&longs;erta HI, facta igitur vali<lb/>da percu&longs;&longs;ione in EG, fiet vt cum EG fuerit in NO, H &longs;it v<lb/>bi N, A vbi P, itemque I vbi O, D verò vbi Q & facta erit <lb/>&longs;ci&longs;&longs;io NSO, toti nempe cuneo EFG, æqualis. </s>

<s id="id.001267">Vultigitur <lb/>Ari&longs;toteles, duos in cunco vectes con&longs;iderari EF, GF, quo<lb/>rum alterius, nempe EF, fulcimentum &longs;it in H, pondus ve<lb/>ro in F; alterius autem, hoc e&longs;t, GF fulcimentum quidem <lb/>&longs;it in I, pondus verò itidem &longs;it in F. </s>

<s id="id.001267">Vult igitur <lb/>Ari&longs;toteles, duos in cuneo vectes con&longs;iderari EF, GF, quo<lb/>rum alterius, nempe EF, fulcimentum &longs;it in H, pondus ve<lb/>ro in F; alterius autem, hoc e&longs;t, GF fulcimentum quidem <lb/>&longs;it in I, pondus verò itidem &longs;it in F. </s>

<s id="id.001268">His nequaquam con<lb/>&longs;entiens G. Vbald. aliam viam ingreditur. </s>

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<s id="id.001269">Ait enim EHF <lb/>vectes quidem e&longs;&longs;e, quorum commune fulcimentum F, <lb/>potentias verò mouentes in EG. </s>

<s id="id.001270">Pondera vtrinque inter <lb/>fulcimenta & potentias, vbi HI, idemque; e&longs;&longs;e ac &longs;i EF, GF, <lb/><gap/>eor&longs;um à cuneo con&longs;iderati in puncto F, adinuicem fulti <lb/>atque di&longs;tracti pondera pellerent H in NP, I verò in O, <lb/><expan abbr="q.">que</expan> Verumenimuerò quoniam cunei angulus non muta<lb/>tur, nec vertex ip&longs;e centri vllum pror&longs;us præbet v&longs;um, nec <lb/>eius latera vtrinque di&longs;tracta ad contrarias partes didu<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.134.jpg"/>cuntur, vectes in cuneo hoc pacto con&longs;iderare videtur à <lb/>veritate alienum. </s>

<s id="id.001270">Pondera vtrinque inter <lb/>fulcimenta & potentias, vbi HI, idemque; e&longs;&longs;e ac &longs;i EF, GF, <lb/>&longs;eor&longs;um à cuneo con&longs;iderati in puncto F, adinuicem fulti <lb/>atque di&longs;tracti pondera pellerent H in NP, I verò in O, <lb/><expan abbr="q.">que</expan> Verum enimuerò quoniam cunei angulus non muta<lb/>tur, nec vertex ip&longs;e centri vllum pror&longs;us præbet v&longs;um, nec <lb/>eius latera vtrinque di&longs;tracta ad contrarias partes didu<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.134.jpg"/>cuntur, vectes in cuneo hoc pacto con&longs;iderare videtur à <lb/>veritate alienum. </s>

<s id="id.001271">Ari&longs;totelis autem &longs;olutionem fal&longs;am e&longs;<lb/>&longs;e, clarè patet. </s>

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<s id="id.001274">At eiu&longs;modi operationes per contactum fieri nulli e&longs;t i<lb/>gnotum. </s>

<s id="id.001275">Solutio igitur i&longs;ta mco iudicio, tanto Philo&longs;o<lb/>pho pror&longs;us videtur indigna. </s>

<s id="id.001275">Solutio igitur i&longs;ta meo iudicio, tanto Philo&longs;o<lb/>pho pror&longs;us videtur indigna. </s>

<s id="id.001276">Porrò G. Vbald. ijs quæ de diuaricatis vectibus in <lb/>medium adduxerat non acquie&longs;cens alias quærit cau&longs;&longs;as, <lb/>cur cuneus minoris anguli validiùs &longs;cindat. </s>

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<s id="id.001292">Tales <lb/>&longs;unt orbiculares illæ cu&longs;pides, quibus ad perforandum v<lb/>timur, & ideo vernaculè Pantirolos vocamus. </s>

<s id="id.001293">Acus item <lb/>&longs;utorij, & cætera quæ nen &longs;ecus ac linea in punctum de&longs;i<lb/>nunt, & imagina<gap/>iam quandam lineam ceu axem in eo <lb/>puncto de&longs;inen<gap/>em continent. </s>

<s id="id.001293">Acus item <lb/>&longs;utorij, & cætera quæ non &longs;ecus ac linea in punctum de&longs;i<lb/>nunt, & imaginariam quandam lineam ceu axem in eo <lb/>puncto de&longs;inentem continent. </s>

<s id="id.001294">Ad lineam quoque refe<lb/>runtur lateratæ cu&longs;pides oblongæ, & &longs;ubtiles ceu&longs;ubulæ, <lb/>claui, en&longs;es, pugiones, & his &longs;imilia, quæ cum adacta vali<lb/>dam faciant partium &longs;eparationem ad cunei naturam <expan abbr="n&omacr;">non</expan> <lb/>referre magnæ videretur dementiæ. </s>

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<s id="id.001299">Ve&longs;pæ quoque, Apes, Scorpiones a<lb/>culeis i&longs;tis ceu linearibus cuneis vtuntur. </s>

<s id="id.001300">Nec refert, vt <lb/>diximus, vt um laterati &longs;int, ceu &longs;ubulæ, & claui, vel ro<lb/>tundi & vtrum plura paucioraue latera habeant, dummo<lb/>do in punctum & aculeatam aciem de&longs;inant. </s>

<s id="id.001300">Nec refert, vt <lb/>diximus, vtrum laterati &longs;int, ceu &longs;ubulæ, & claui, vel ro<lb/>tundi & vtrum plura paucioraue latera habeant, dummo<lb/>do in punctum & aculeatam aciem de&longs;inant. </s>

<s id="id.001302">obrem huc ea omnia referuntur, quæ acie ipsâ &longs;cindunt, <lb/>ceu &longs;unt cunei propriè dicti, de quibus hoc loco e&longs;t &longs;er<lb/>mo, cultra, en&longs;es, a&longs;ciæ, &longs;ecures, &longs;calpra lata, & cætera e<lb/>in&longs;modi, quibus corpora acie &longs;cinduntur. </s>

<s id="id.001301">Altera por<lb/>ro cuneorum &longs;pecies &longs;uperficiei naturam &longs;apit, acie &longs;iqui<lb/>dem in lineam de&longs;init, quæ &longs;uperficiei e&longs;t terminus, <expan abbr="quã">quam</expan>obrem huc ea omnia referuntur, quæ acie ipsâ &longs;cindunt, <lb/>ceu &longs;unt cunei propriè dicti, de quibus hoc loco e&longs;t &longs;er<lb/>mo, cultra, en&longs;es, a&longs;ciæ, &longs;ecures, &longs;calpra lata, & cætera e<lb/>iu&longs;modi, quibus corpora acie &longs;cinduntur. </s>

<s id="id.001303">Quidam his ad<lb/>dunt &longs;erras, quibus haud pror&longs;us a&longs;&longs;entimur. </s>

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<s id="id.001306">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 id="id.001307">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/007-01-pageimg/007.01.137.jpg"/><figure id="id.007.01.137.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.137.1.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 id="id.001307">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 confi<lb/>ciuntur, triplicem dentium qualitatem dentatis animali-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.137.jpg"/><figure id="id.007.01.137.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.137.1.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 id="id.001308">Molares KK, <lb/>CaniniL, L, Temni<lb/>ci &longs;eu &longs;ecantes M. </s>

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<s id="id.001319">Pertingente enim &longs;ci&longs;&longs;ione in <lb/>O, <expan abbr="fulcim&emacr;tum">fulcimentum</expan> fit in P. quo ca&longs;u &longs;ci&longs;&longs;ura e&longs;t facilior, quip<lb/>pe quod maiorem habeat proportionem BO ad OP, <expan abbr="quã">quam</expan> <lb/>BN ad NL. </s>

<s id="id.001320">Hoc autem experiuntur materiarij, qui primis <lb/>ictibus, &longs;ecuriculâ nondum probè adactâ, & nondum fa<lb/>ctâ notabili &longs;ci&longs;&longs;ione difficultatem &longs;entiunt, mox <expan abbr="factaiã">facta iam</expan> <lb/>&longs;eparatione faoillima paullatim fit materiæ totius &longs;epara<lb/>tio. </s>

<s id="id.001320">Hoc autem experiuntur materiarij, qui primis <lb/>ictibus, &longs;ecuriculâ nondum probè adactâ, & nondum fa<lb/>ctâ notabili &longs;ci&longs;&longs;ione difficultatem &longs;entiunt, mox <expan abbr="factaiã">facta iam</expan> <lb/>&longs;eparatione facillima paullatim fit materiæ totius &longs;epara<lb/>tio. </s>

<s id="id.001321">Hocidem & nos ab&longs;que cunei v&longs;u experimur, cum ba<lb/>culum aut quippiam tale manibus diductis &longs;cin dimus. </s>

<s id="id.001322">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 id="id.001322">à <lb/>principio enim difficultatem &longs;entimus, deinde ex ea <expan abbr="quã">quam</expan> <lb/>diximus proportione &longs;ci&longs;&longs;io ip&longs;a fit apprime facilis. </s>

<s id="id.001323">Vti-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.139.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.007.01.139.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.139.1.jpg"></figure><lb/>corporis &longs;eparatio. </s>

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<s id="id.001334">Et&longs;i de tignis eiu&longs;mo di aliud quippiam &longs;entire videa<lb/>tur Picolomineus. </s>

<s id="id.001335">Græea lectio pro tignis habet <foreign lang="greek">cu/la</foreign>, id <lb/>e&longs;t, ligna; item vbi Leoniceni ver&longs;io legit, ad &longs;e inuicem <lb/>iunctis, textus habet <foreign lang="greek">snm<gap/>ai/nousin e(autoi_s e)ranti/ws</foreign>, hoc e&longs;t, in<lb/>uicem ex oppo&longs;ito concurrunt. </s>

<s id="id.001335">Græca lectio pro tignis habet <foreign lang="greek">cu/la</foreign>, id <lb/>e&longs;t, ligna; item vbi Leoniceni ver&longs;io legit, ad &longs;e inuicem <lb/>iunctis, textus habet <foreign lang="greek">sumbai/nousin e(autoi=s e)nanti/ws</foreign>, hoc e&longs;t, in<lb/>uicem ex oppo&longs;ito concurrunt. </s>

<s id="id.001336">Certè locum totum ita <lb/>redderem: Cur &longs;i quis duas Trochleas fecerit, in duobus <lb/>lignis &longs;ibi ex oppo&longs;ito concurrentibus, ei&longs;queue Trochleis <lb/>circumpo&longs;uerit funem, cuius alterum caput alteri ligno<lb/>rum &longs;it annexum, alterum verò Trochleis cohæreat, vel <lb/>apponatur. </s>

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<s id="id.001353">de Vecte <lb/>prop.

<s id="id.001353">de Vecte <lb/>prop. 3. Po&longs;ita nempe inter fulcimentum & pondus &longs;u&longs;ti<lb/>nente potentiâ. </s>

3. Po&longs;ita nempe inter fulcimentum & pondus &longs;u&longs;ti<lb/>nente potentiâ. </s>

<s id="id.001354">Præterea quod a&longs;&longs;eruit Ari&longs;toteles, Tro<lb/>chleas ad vectem reduci, verum quidem e&longs;t, &longs;ed aptius di<lb/>xi&longs;&longs;et ad libram, etenim vectis vtcunque à fulcimento di<lb/>uiditur. </s>

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<s id="id.001360">Erunt i<lb/>gitur invniuer&longs;um <lb/>quinque, indatur pereos funis ductarius KLMNOP <lb/>QRSTVX, ex cuius extremitate pendeat pondus X, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.142.jpg"/>Trahatur funis in K. </s>

<s id="id.001361">Dico ex multiplicatione <expan abbr="orbiculor&umacr;">orbiculorum</expan>, <lb/>trahentipondus nequaquam minui. </s>

<s id="id.001361">Dico ex multiplicatione <expan abbr="orbiculor&umacr;">orbiculorum</expan>, <lb/>trahenti xspondus nequaquam minui. </s>

<s id="id.001362">Sint autem orbicu<lb/>lorum diametri, LM, NO, PQ, RS, TV, applicetur poten<lb/>tîa in S. </s>

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<s id="id.001394">Dico igitur, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.145.jpg"/><figure id="id.007.01.145.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.145.1.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 id="id.001395">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>

<s id="id.001395">Sunt <lb/>autem, hic vectes <lb/>quatuor in feriorum <lb/>cubiculorum, loco, <lb/>CD, HI, MN, QR, <lb/>quorum, 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>

<s id="id.001396">Tum potentia in K, hoc e&longs;t, in H, vna cum poten<lb/>tia in L, hoc e&longs;t, in I &longs;u&longs;tinebunt quingenta. </s>

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<s id="id.001400">Hinc colligimus, pondus totum inter <lb/>loca &longs;tabilia diuidi, nempe A, K, O, S, & ip&longs;am potentiam <lb/>quæ &longs;u&longs;tinet in T, & locis ip&longs;is &longs;tabilibus quindecim par<lb/>tes integri ponderis, potentia verò T &longs;extam decimam <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.146.jpg"/>tantùm commendari. </s>

<s id="id.001401">Itaque &longs;i ex puncto V appendere<lb/>tur AB, in X potentia, quæ in X &longs;u&longs;tineret mille, minus <lb/>&longs;exaginta duo cum dimidio, quod quidem à potentia in <lb/>T &longs;u&longs;tinetur; quod &longs;i alius adderetur orbiculus, & fierent <lb/>quinque, potentia in T &longs;u&longs;tiner et trige&longs;imam &longs;ecundam <lb/>partem integri ponderis, hoce&longs;t, dimidium librarum &longs;e<lb/>vaginta duarum cum dimidio, nempe triginta & vnam <lb/>cum quarta parte, &longs;i item textus adderetur, potentia in T <lb/>&longs;exage&longs;imam partem &longs;u&longs;tineret integri ponderis, hoc e&longs;t, <lb/>libras quindecim & <gap/> libræ vnius. </s>

<s id="id.001401">Itaque &longs;i ex puncto V appendere<lb/>tur AB, in X potentia, quæ in X &longs;u&longs;tineret mille, minus <lb/>&longs;exaginta duo cum dimidio, quod quidem à potentia in <lb/>T &longs;u&longs;tinetur; quod &longs;i alius adderetur orbiculus, & fierent <lb/>quinque, potentia in T &longs;u&longs;tineret trige&longs;imam &longs;ecundam <lb/>partem integri ponderis, hoc e&longs;t, dimidium librarum &longs;e<lb/>xaginta duarum cum dimidio, nempe triginta & vnam <lb/>cum quarta parte, &longs;i item textus adderetur, potentia in T <lb/>&longs;exage&longs;imam partem &longs;u&longs;tineret integri ponderis, hoc e&longs;t, <lb/>libras quindecim & <gap/> libræ vnius. </s>

<s id="id.001402">Vnde patet clarè pon<lb/>deris diminutionem fieri ex orbiculis inferioribus, non <lb/>autem ex&longs;uperioribus, &longs;uperiores autem addi non nece&longs;<lb/>&longs;itatis quidem, &longs;ed commoditatis gratiâ: neque enim ab&longs;<lb/>que &longs;uperioribus vnico ductario fune fieri po&longs;&longs;et attractio <lb/>& ponderis ip&longs;ius eleuatio. </s>

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<s id="id.001404">QVÆSTIO XIX.</s>

<s id="id.001405"><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, de&longs;uperque magnum adijciat pondus, ligni quippiam quod <lb/>curandum &longs;it, non diuidit; &longs;i verò &longs;ecurim extollens percutiat, illud <lb/>&longs;cindit, cum alioquin multo minus habeat ponder is id quod <lb/>percutit, quam illud quod&longs;uperiacet <lb/>& premit?<emph.end type="italics"/></s>

<s id="id.001405"><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, de&longs;uperque magnum adijciat pondus, ligni quippiam quod <lb/>curandum &longs;it, non diuidit; &longs;i verò &longs;ecurim extollens percutiat, illud <lb/>&longs;cindit, cum alioquin multo minus habeat ponderis id quod <lb/>percutit, quam illud quod s&longs;uperiacet <lb/>& premit?<emph.end type="italics"/></s>

<s id="id.001406">Poterat Ari&longs;toteles, nî fallimur, rem breuius & vniuer<lb/>&longs;alius proponere. </s>

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<s id="id.001410">Incumbens igitur connatam graui motionem non moue<lb/>tur, motum verò & &longs;ecundum hanc mouetur & &longs;ecun-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.147.jpg"/>dum eam quæ e&longs;t <expan abbr="percuti&emacr;tis">percutientis</expan>? </s>

<s id="id.001411">Hæc præclarè quidem, cæ<lb/>tera autem, quæ de cuneoiterat, nempe ad vectem eiuslo<lb/>perationem referri &longs;uperius confutauimus. </s>

<s id="id.001411">Hæc præclarè quidem, cæ<lb/>tera autem, quæ de cuneo iterat, nempe ad vectem eius o<lb/>perationem referri &longs;uperius confutauimus. </s>

<s id="id.001412">Porrò effe<lb/>ctus huius, de quo agitur, di&longs;putatio illuc &longs;pectat, videli<lb/>cet ad cadentium atque proiectorum naturam. </s>

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<s id="id.001431">Certè va<lb/>lidius, & certius fieri &longs;ci&longs;&longs;ionem ex cuneo & malleo, ea ra<lb/>tio e&longs;t, quod cuneus adactus, nec inde remotus eam inte <lb/>rim &longs;eruat, quam antea fecerat partium &longs;eparationem, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.149.jpg"/>quod quidem &longs;ecuri non accidit, quæ adacta ad nouam <lb/>percu&longs;&longs;ionem faciendam extrahitur. </s>

<s id="id.001432">Hoc etiam con&longs;ideramus, &longs;ecuris in circulo motum, <lb/>ex A in D, e&longs;&longs;e videndum, id e&longs;t, non &longs;ecundum naturam, <lb/>&longs;ur&longs;um enim fertur quod e&longs;t graue, ex D verq in F <expan abbr="mixt&umacr;">mixtum</expan>: <lb/>magis autem ad naturalem accedere qui fit ex F in E. </s>

<s id="id.001432">Hoc etiam con&longs;ideramus, &longs;ecuris in circulo motum, <lb/>ex A in D, e&longs;&longs;e videndum, id e&longs;t, non &longs;ecundum naturam, <lb/>&longs;ur&longs;um enim fertur quod e&longs;t graue, ex D verò in F <expan abbr="mixt&umacr;">mixtum</expan>: <lb/>magis autem ad naturalem accedere qui fit ex F in E. </s>

<s id="id.001433">Tar<lb/>dior ergo ex A in D, velocior ex D, in F, veloci&longs;&longs;imus ex F <lb/>in E; quæ dam quæ ad hanc rem faciunt, egregiè con&longs;ide<lb/>rat Guid, Vbald. in calce Tractatus, De Cuneo; ip&longs;um <lb/>con&longs;ule. </s>

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<s id="id.001454">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>

<s id="id.001455">Intelligatur autem & aliud fulcimentum D, &longs;it<lb/>queue maius &longs;pacium AD, quam AC. </s>

<s id="id.001455">Intelligatur autem & aliud fulcimentum D, &longs;it<lb/>queue maius &longs;patium AD, quam AC. </s>

<s id="id.001456">Porrò ita &longs;e habeat <lb/>pondus in E ad appendiculi F pondus, vt CF &longs;patium, ad <lb/>&longs;patium AC, quo ca&longs;u &longs;eruata, permutatim, ponderum & <lb/>brachiorum proportione, fiet ae quilibrium. </s>

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<s id="id.001459">Ita que vt it e<lb/>rum fiat æquilibrium, nece&longs;&longs;e e&longs;t <expan abbr="iter&umacr;">iterum</expan> proportiones bra<lb/>chiorum &longs;eu &longs;patiorum proportionibus ponderum æqua<lb/>re. </s>

<s id="id.001460">Transferatur igitur (lancis interim immoto pondeie) <lb/>ip&longs;um appendiculum in B, fiatque vt FC ad CA, ita BD ad <lb/>DA. </s>

<s id="id.001460">Transferatur igitur (lancis interim immoto pondere) <lb/>ip&longs;um appendiculum in B, fiatque vt FC ad CA, ita BD ad <lb/>DA. </s>

<s id="id.001461">Stabit autem iterum &longs;tatera ad eam redacta quam <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.152.jpg"/>diximus brachiorum & ponderum permutatam propor<lb/>tionem. </s>

<s id="id.001462">Nos &longs;tateris vtimur ex duplici fulcimento, altero <lb/>propiori, altero à lance &longs;eu loco, vbi lanx appenditur, re<lb/>motiori, illa grauiora appendimus pondera, & non per <lb/>vncias & libras, &longs;ed per libras tantum & &longs;elibra ponde<lb/>ramus; & hoc &longs;tateræ latus eo quod minus minutè &longs;it di<lb/>ui&longs;um; vulgo no&longs;trates Gro&longs;&longs;um, hoc e&longs;t, rude & cra&longs;&longs;um <lb/>appellant. </s>

<s id="id.001463">Aliud verò, cum fulcimentum e&longs;t loco appen<lb/>&longs;ionis lancis vicinius, & per libras, &longs;elibras & vncias diui<lb/>ditur, quo quidem minora appendimus pondera, cò quod <lb/><expan abbr="exqui&longs;itior&emacr;">exqui&longs;itiorem</expan> contineat diui&longs;ionem, &longs;ubtile dicunt. </s>

<s id="id.001463">Aliud verò, cum fulcimentum e&longs;t loco appen<lb/>&longs;ionis lancis vicinius, & per libras, &longs;elibras & vncias diui<lb/>ditur, quo quidem minora appendimus pondera, eò quod <lb/><expan abbr="exqui&longs;itior&emacr;">exqui&longs;itiorem</expan> contineat diui&longs;ionem, &longs;ubtile dicunt. </s>

<s id="id.001464">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 appendiculi, è locoin locum translationes, totidem <lb/>ex proportionum variatione fiant libræ. </s>

<s id="id.001464">Rectè <lb/>igitur dicebat Philo&longs;ophus, in &longs;tatera plures e&longs;&longs;e libras, <lb/>quamquam & ea quoque de cau&longs;&longs;a dici po&longs;&longs;it, quod, quot <lb/>&longs;unt appendiculi, è loco in locum translationes, totidem <lb/>ex proportionum variatione fiant libræ. </s>

<s id="id.001465">Et hoc quidem <lb/>&longs;en&longs;i&longs;&longs;e videtur Ari&longs;toteles. </s>

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<s id="id.001480">Si Græca ad <lb/>verbum reddas ita habent: An magis ip&longs;a manu labile e&longs;t <lb/>ferrum, & ip&longs;um vndique (dentemnempe) non comple<lb/>ctitur, caro autem digitorum cum mollis &longs;it, adhæret ma<lb/>gis, & vndique congruit. </s>

<s id="id.001481">Certè vt &longs;ententia non &longs;it con<lb/>traria propo&longs;itioni, Græca ver&longs;io ita videtur concinnan<lb/>da: Vel magis è m n<gap/>bitur, mollis enim e&longs;t digitorum <lb/>caro, ferrum autem circumplectitur, & haeret magis. </s>

<s id="id.001481">Certè vt &longs;ententia non &longs;it con<lb/>traria propo&longs;itioni, Græca ver&longs;io ita videtur concinnan<lb/>da: Vel magis è manu elabitur, mollis enim e&longs;t digitorum <lb/>caro, ferrum autem circumplectitur, & haeret magis. </s>

<s id="id.001482">quic<lb/>quid &longs;it, Græcam lectionem contrarium ei quod quæri-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.154.jpg"/>tur, affirmare certum e&longs;t. </s>

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<s id="id.001486">Hoc igitur ad ex<lb/>tractionem vtuntur^{**}, vt facilius moueant. </s>

<s id="id.001487">Figuram hoc <lb/>pactto proponit Philo&longs;ophus. </s>

<s id="id.001487">Figuram hoc <lb/>pacto proponit Philo&longs;ophus. </s>

<s id="id.001488">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>

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<s id="id.001504">Porro quod in calce quæ&longs;tionis addit Philo&longs;ophus, <lb/>Dentes commotos facilius manu extrahi quam in&longs;tru<lb/>mento, nulla ratione probat. </s>

<s id="id.001505">Ego autem arbitror, huc <lb/>pertinere ea verba, quæ &longs;uperius habentur, videlicet fer<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.156.jpg"/>rum quidem non vndique dentem <expan abbr="compreh&emacr;dere">comprehendere</expan>, quod <lb/>mollisfacit digitorum caro, quæ id circo adhæret & <gap/>om<lb/>plectitur magis. </s>

<s id="id.001505">Ego autem arbitror, huc <lb/>pertinere ea verba, quæ &longs;uperius habentur, videlicet fer<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.156.jpg"/>rum quidem non vndique dentem <expan abbr="compreh&emacr;dere">comprehendere</expan>, quod <lb/>mollis facit digitorum caro, quæ id circo adhæret & com<lb/>plectitur magis. </s>

<s id="id.001506">An autem ita &longs;it, alij videant, nobis enim <lb/>digito rem o&longs;tendi&longs;&longs;e fuerit &longs;atis. </s>

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<s id="id.001516">eo autem magis &longs;up erabit, quo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.157.jpg"/>maior fuerit pars vectis quæ à potentia ad fulcimentum. </s>

<s id="id.001517">Quod autem addit Ari&longs;toteles, eo maiorem fieri <lb/>vectium eleuationem, hoc e&longs;t, in&longs;trumenti aperitionem, <lb/>quo magis nux quæ frangitur, fuerit propior fulcimento, <lb/>hoc e&longs;t, ip&longs;i vertebræ, facile o&longs;tenditur ex conuer&longs;a 21. <lb/>propo&longs;. </s>

<s id="id.001518">lib.

<s id="001518">&longs;i enim ab extremitatibus vnius lineæ <lb/>ad ea&longs;dem partes con&longs;tituantur duæ lineæ maiores con<lb/>currentes in angulo, & ab ij&longs;dem extremitatibus duæ a<lb/>liæ minores, quæ intra triangulum à maioribus con&longs;titu<lb/>tum cadant, maiorem angulum continebunt. </s>

1. Elem.

&longs;i enim ab extremitatibus vnius line æ <lb/>ad ea&longs;dem partes con&longs;tituantur duæ line æ maiores con<lb/>currentes in angulo, & ab ij&longs;dem extremitatibus duæ a<lb/>liæ minores, quæ intra triangulum à maioribus con&longs;titu<lb/>tum cadant, maiorem angulum continebunt. </s>

<s id="id.001519">At talis e&longs;t <lb/>angulus qui fit in in &longs;trumento, cum partes vectis à verte<lb/>bra ad nucem fuerint breuiores. </s>

<s id="id.001520">magìs ergo dilatantur <lb/>vectes, & magis dilatati magis comprimuntur, magis au<lb/>tem compre&longs;li validius frangunt, quod dixerat Ari&longs;to<lb/>teles. </s>

<s id="id.001520">magìs ergo dilatantur <lb/>vectes, & magis dilatati magis comprimuntur, magis au<lb/>tem compre&longs;&longs;i validius frangunt, quod dixerat Ari&longs;to<lb/>teles. </s>

<s id="id.001521">Cæterum & illud quod &longs;cribit, ex grauiori & durio<lb/>ri materia in&longs;trumentum citius fractionem facere, quam <lb/>ex leuiori & minus dura, ex parte quidem materiæ verum <lb/>e&longs;t, nec pertinet ad proportionem, quæ &longs;ane in <expan abbr="huiu&longs;mod&imacr;">huiu&longs;modim</expan> <lb/>in&longs;trumentis formæ ferè habent rationem. </s>

<s id="id.001521">Cæterum & illud quod &longs;cribit, ex grauiori & durio<lb/>ri materia in&longs;trumentum citius fractionem facere, quam <lb/>ex leuiori & minus dura, ex parte quidem materiæ verum <lb/>e&longs;t, nec pertinet ad proportionem, quæ &longs;ane in <expan abbr="huiu&longs;mod&imacr;">huiu&longs;modi</expan> <lb/>in&longs;trumentis formæ ferè habent rationem. </s>

<s id="id.001522">Nos hi&longs;ce in<lb/>&longs;trumentisnon vtimur. </s>

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<s id="id.001534">Sunt <expan abbr="aut&emacr;">autem</expan> ex ip&longs;ius Rhom<lb/>binatura latera æqualia & parallela, <lb/>Angulorum vero qui maiori diame<lb/>tro opponuntur, recto maiores, qui <lb/>vero minori minores. </s>

<s id="id.001535">His igitur con<lb/>&longs;ideratis, intelligatur punctum A mo<lb/>ueri peculiari & &longs;im plici motu, per li<lb/>neam AB, ab A ver&longs;us B, & eodem <expan abbr="t&emacr;-pore">ten<lb/>pore</expan> moueri totam lineam AB, ver&longs;us lineam DC, hac ta<lb/>men lege, vt &longs;emper eidem DC feratur parallela, & eius <lb/>alterum extremorum feratur per AC, alterum vero per <lb/>BD, Intelligatur etiam punctum B moueri eodem tem<lb/>pore proprio motu, eoque &longs;implici, per eandem rectam <lb/>BA, ver&longs;us A, & cum eadem, vt dictum e&longs;t, mota; ferri ver-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.159.jpg"/>&longs;us CD. </s>

<s id="id.001535">His igitur con<lb/>&longs;intelligatur, id eratis punctum A mo<lb/>ueri peculiari & &longs;implici motu, per li<lb/>neam AB, ab A ver&longs;us B, & eodem <expan abbr="t&emacr;-pore">tem<lb/>pore</expan> moueri totam lineam AB, ver&longs;us lineam DC, hac ta<lb/>men lege, vt &longs;emper eidem DC feratur parallela, & eius <lb/>alterum extremorum feratur per AC, alterum vero per <lb/>BD, Intelligatur etiam punctum B moueri eodem tem<lb/>pore proprio motu, eoque &longs;implici, per eandem rectam <lb/>BA, ver&longs;us A, & cum eadem, vt dictum e&longs;t, mota; ferri ver-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.159.jpg"/>&longs;us CD. </s>

<s id="id.001536">Erunt autem &longs;emper AB puncta in eadem linea <lb/>quæ mouetur, &longs;ibi inuicem ex contrarijs partibus occur<lb/>rentia. </s>

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<s id="id.001573">Velocior enim qui per longiorem diametrum, tardior <lb/>quiperbreuiorem. </s>

<s id="id.001574">Itaque &longs;implices motus punctorum <lb/>per latera ad eum qui fit per diametrosinon eodem pacto <lb/>&longs;e habent. </s>

<s id="id.001574">Itaque &longs;implices motus punctorum <lb/>per latera ad eum qui fit per diametros non eodem pacto <lb/>&longs;e habent. </s>

<s id="id.001575">Porro cum Rhomboides variæ &longs;int <expan abbr="diametror&umacr;">diametrorum</expan> <lb/>ad latera habitudines, varia quoque dari pote&longs;t propor<lb/>tio. </s>

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<s id="id.001577">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 id="id.001578">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>

<s id="id.001578">His igitur hoc pacto non perfun<lb/>ctoriè con&longs;ideratis, facile ex proprijs cau&longs;&longs;is, nî fallimur, <lb/>hocce Ari&longs;totelicum & mirabile Problema &longs;oluitur. </s>

<s id="id.001579">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>

<s id="id.001580">Ducatur queue ip&longs;is AB, <lb/>CD, parallela FG &longs;ecans longiorem <lb/>diametrum AD, in H, breuiorem ve<lb/>ro BC in I. & per I ip&longs;is BD AC paral<lb/>lela ducatur KIL, Cum ergo B mixto <lb/>motu per diametrum BC erit in I & <lb/>A per diametrum AD, mixto &longs;imili<lb/>ter motu erit in H, & quia motus mi<lb/>xti fiunt per diametros, vt dictum e&longs;t, <lb/>vt &longs;e habet AD ad BC, ita AE ad EB, per 15. propol. </s>

<s id="id.001582">item vt AE ad EB, ita per 4. propo&longs;. </s>

<s id="id.001582">item vt AE ad EB, ita per 4. propo&longs;. 6. AH ad BI. e&longs;t enim <lb/>IH ip&longs;i AB parallela. </s>

<s id="id.001583">6. AH ad BI. e&longs;t enim <lb/>IH ip&longs;i AB parallela. </s>

<s id="id.001584">Longior e&longs;t autem AH ip&longs;a BI, quip<lb/>pe quod AE longior &longs;it ip&longs;a EB. motus igitur mixtus pun<lb/>cti A per diametrum AD v&longs;que ad H velocior e&longs;t motu B, <lb/>per diametrum BC v&longs;quead I. </s>

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<s id="id.001588">Si enim Rhombus detur, ex duobus æquilateris <lb/>triangulis con&longs;tans, breuior diameter lateribus erit aequa<lb/>lis, quare non mouebitur citius motu &longs;implici punctum <lb/>per latus ac faciat mixto per minorem diametrum, quod <lb/>vt mirum propo&longs;uerat A ri&longs;toteles. </s>

<s id="id.001589">Si autem latus ip&longs;um <lb/>breuiori diametro &longs;it <expan abbr="l&omacr;gius">longius</expan>, nec mirum quoque erit &longs;im<lb/>plici motu moucri velocius quam mixto, quippe quod, vt <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.164.jpg"/>dictum e&longs;t, motus i&longs;ti à proportionibus linearum, per quas <lb/>mouentur, legem velocitatis atque tarditatis accipiant. <lb/></s>

<s id="id.001589">Si autem latus ip&longs;um <lb/>breuiori diametro &longs;it <expan abbr="l&omacr;gius">longius</expan>, nec mirum quoque erit &longs;im<lb/>plici motu moueri velocius quam mixto, quippe quod, vt <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.164.jpg"/>dictum e&longs;t, motus i&longs;ti à proportionibus linearum, per quas <lb/>mouentur, legem velocitatis atque tarditatis accipiant. <lb/></s>

<s id="id.001590">Hæc igitur nos circa hoc mirabile Ari&longs;totelicum proble<lb/>ma con&longs;iderare &longs;it &longs;atis. </s>

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<s id="id.001616">Tuncautem facto motu centrum E erit vbi P, <lb/>exi&longs;tente EP, ip&longs;i HM æquali, demittatur autem ex P per <lb/>M, ip&longs;is HL CK perpendicularis PMN. </s>

<s id="id.001617">Et quoniam in <lb/>eadem linea &longs;unt DIE, vbi E fuerit in Pleritin M, & D in <lb/>N. quamobrem rotata quarta minori<gap/> circuli parte, ma<lb/>ioris interim circuli quadrans confecit &longs;patium CN æ<lb/>quale ip&longs;i HM, hoc minus circuli quadranti HI, quod vti<lb/>que e&longs;t admirabile. </s>

<s id="id.001617">Et quoniam in <lb/>eadem linea &longs;unt DIE, vbi E fuerit in PI erit in M, & D in <lb/>N. quamobrem rotata quarta minoris circuli parte, ma<lb/>ioris interim circuli quadrans confecit &longs;patium CN æ<lb/>quale ip&longs;i HM, hoc minus circuli quadranti HI, quod vti<lb/>que e&longs;t admirabile. </s>

<s id="id.001618">Porro cau&longs;&longs;am effectus huius mirifici diligenter quæ<lb/>rit Philo&longs;ophus, & inuenram accurate explicat. </s>

<s id="id.001618">Porro cau&longs;&longs;am effectus huius mirifici diligenter quæ<lb/>rit Philo&longs;ophus, & inueneram accurate explicat. </s>

<s id="id.001619">Occur<lb/>rit autem primo ab&longs;urdæ cuidam opinioni. </s>

<s id="id.001620">Diceret enim <lb/>qui&longs;piam, ideo tardius moueri maiorem circulum, ad mo<lb/>tum minoris, quod interim <expan abbr="d&umacr;">dum</expan> minor moucretur, aliquas <lb/>inter rotan dum moras interponeret, minor vero ad mo<lb/>tum maioris &longs;patia aliqua tran&longs;iliret, & ita &longs;patiorum fieri <lb/>ad æquationem. </s>

<s id="id.001620">Diceret enim <lb/>qui&longs;piam, ideo tardius moueri maiorem circulum, ad mo<lb/>tum minoris, quod interim <expan abbr="d&umacr;">dum</expan> minor moueretur, aliquas <lb/>inter rotandum moras interponeret, minor vero ad mo<lb/>tum maioris &longs;patia aliqua tran&longs;iliret, & ita &longs;patiorum fieri <lb/>ad æquationem. </s>

<s id="id.001621">Porro demon&longs;trationem aggre&longs;&longs;urus haec <lb/>a&longs;&longs;umit principia. </s>

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<s id="id.001624">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>

<s id="id.001625">Praeterea quod non&longs;uo, &longs;ed alieno motu mo<lb/>uetur, impo&longs;&longs;ibile e&longs;&longs;e plus eo moueri qui <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.167.jpg"/>mouet, &longs;iquidem non &longs;uo, &longs;ed alieno motu mouctur. </s>

<s id="id.001625">Praeterea quod non &longs;uo, &longs;ed alieno motu mo<lb/>uetur, impo&longs;&longs;ibile e&longs;&longs;e plus eo moueri qui <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.167.jpg"/>mouet, &longs;iquidem non &longs;uo, &longs;ed alieno motu mouetur. </s>

<s id="id.001626">Mo<lb/>to igitur &longs;uo motu maiori circulo, minor non &longs;uo mouc<lb/>tur, &longs;ed motu maioris circuli^{1}, & ideo non plus mouetur <lb/>quam ille moueatur, mouetur autem maiori &longs;patio quam <lb/>ex &longs;e moueretur, propterea quod maior &longs;it maioris circu<lb/>li, à quo &longs;imul defertur, circumferentia. </s>

<s id="id.001626">Mo<lb/>to igitur &longs;uo motu maiori circulo, minor non &longs;uo moue<lb/>tur, &longs;ed motu maioris circuli, & ideo non plus mouetur <lb/>quam ille moueatur, mouetur autem maiori &longs;patio quam <lb/>ex &longs;e moueretur, propterea quod maior &longs;it maioris circu<lb/>li, à quo &longs;imul defertur, circumferentia. </s>

<s id="id.001627">Item &longs;i minor &longs;uo <lb/>motu circumuoluatur, maiorem feret &longs;ecum, & ideo non <lb/>plus in &longs;ua rotatione mouebitur maior, quam ip&longs;e minor <lb/>circulus moueatur. </s>

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<s id="id.001639">Rotetur itaque &longs;ecundum ab&longs;idem integri quadrantis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.168.jpg"/><figure id="id.007.01.168.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.168.1.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 id="id.001640">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/>tio mouebitur RS, <lb/>quod &longs;i intra QR, circa centrum E alij infiniti imaginen<lb/>tur circuli, quo propio es centro fuerint, eo maioris rotæ <lb/>progre&longs;&longs;us erit minor, donec ad centrum deueniatur, vbi <lb/>cum non &longs;it circulus, nullus fiet progre&longs;&longs;iuus motus, &longs;ed <lb/>circa ip&longs;um centrum nulla facta loci mutatione rotabi<lb/>tur. </s>

<s id="id.001641">tio mouebitur RS, <lb/>quod &longs;i intra QR, circa centrum E alij infiniti imaginen<lb/>tur circuli, quo propio es centro fuerint, eo maioris rotæ <lb/>progre&longs;&longs;us erit minor, donec ad centrum deueniatur, vbi <lb/>cum non &longs;it circulus, nullus fiet progre&longs;&longs;iuus motus, &longs;ed <lb/>circa ip&longs;um centrum nulla facta loci mutatione rotabi<lb/>tur. </s>

<s id="id.001642">At cum nulla materialis rota circa lineam punctumue <lb/>imaginarium conuerti po&longs;&longs;it, ideo axi ferreo alteriu&longs;ue <lb/>materiæ circa quem & cum quo circumuoluatur rota, ca<lb/>uum &longs;emirotundum incidere oportet, in quo in&longs;ertus axis <lb/>dum conuertitur à loco in quo conuertitur, non recedat. </s>

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<s id="id.001656">Sane vt veritatem hocloco vindicaret in lu<lb/>cem, egregie laborauit Picolomineus nec parum profe<lb/>cit. </s>

<s id="id.001657">Cæterum curre&longs;tes non &longs;ecundum diametrum extru<lb/>dantur, triplicem affert Philo&longs;ophus rationem. </s>

<s id="id.001657">Cæterum currentes non &longs;ecundum diametrum extru<lb/>dantur, triplicem affert Philo&longs;ophus rationem. </s>

<s id="id.001658">Prima e&longs;t <lb/>vt &longs;pondarum ligna, minus di&longs;trahantur. </s>

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<s id="id.001674">Po&longs;t hæc alterius funis principium per <lb/>foramen traij citur, quod e&longs;t in angulo B. </s>

<s id="id.001675">Deinde per E, in<lb/>de per L, N, O, M, D, F & in F probe vincitur, & nodo fa<lb/>cto ob&longs;irmatur. </s>

<s id="id.001675">Deinde per E, in<lb/>de per L, N, O, M, D, F & in F probe vincitur, & nodo fa<lb/>cto obfirmatur. </s>

<s id="id.001676">Erunt igitur aliæ quatuor alterius funis <lb/>partes, tum inter&longs;e, tum etiam &longs;upradictis æquales, nem<lb/>pe BE, NL, OM, FD, quibus il<gap/>æ pa iter adijciuntur par<lb/>ticulæ, quæ caduat extra, videlicet EL, NO, MD. <expan abbr="quoniã">quoniam</expan> <lb/>igitur quadratis ex BA, AE æquale e&longs;t quadratum BE, erit <lb/>BE quadratum 18. cuius latus radixue 4 1/3 quam proxime. <lb/></s>

<s id="id.001676">Erunt igitur aliæ quatuor alterius funis <lb/>partes, tum inter &longs;e, tum etiam &longs;upra dictis æquales, nem<lb/>pe BE, NL, OM, FD, quibus illæ pariter adijciuntur par<lb/>ticulæ, quæ cadat extra, videlicet EL, NO, MD. <expan abbr="quoniã">quoniam</expan> <lb/>igitur quadratis ex BA, AE æquale e&longs;t quadratum BE, erit <lb/>BE quadratum 18. cuius latus radixue 4 1/3 quam proxime. <lb/></s>

<s id="id.001677">Sunt autem huius longitud n s funes æquales octo. </s>

<s id="id.001677">Sunt autem huius longitudinis funes æquales octo. </s>

<s id="id.001678">Ea<lb/>rum igitur &longs;imul &longs;umptarum longitudo erit pedum 34 2/3 vel <lb/>circiter, quibus &longs;i ad dantur pedes &longs;ex funium qui cadunt <lb/>extra, erit re&longs;tis totius longitudo expan&longs;a pedum 40 2/3 plus <lb/>minu&longs;ue. </s>

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<s id="id.001685">Nos interim ne inutilem ferè &longs;peculationem ni<lb/>mia diligentia, eaque forta&longs;&longs;e fru&longs;tranea pro&longs;equamur, a<lb/>lijs difficultatem hanc di&longs;&longs;oluendam aut ceu Gordij no<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.172.jpg"/>dum gladio &longs;cindendo relinquemus. </s>

<s id="id.001686">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 id="id.001686">Sed interim &longs;ubit <lb/>mirari, cur veteres vtiliori modo prætermi&longs;&longs;o, <expan abbr="inutilioi&emacr;">inutiliorem</expan> <lb/>fuerint amplexati. </s>

<s id="id.001687">Poterant enim reticulatim hoc per li<lb/>neas lateribus æ quidi&longs;tantes intexere. </s>

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<s id="id.001697">Dvo hîc con&longs;iderat, vibrationem, & pondus. </s>

<s id="id.001698">Ait enim <lb/>primo fieri po&longs;&longs;c, procera ligna vibratione impedien<lb/>te, difficilius ferri. </s>

<s id="id.001698">Ait enim <lb/>primo fieri po&longs;&longs;e, procera ligna vibratione impedien<lb/>te, difficilius ferri. </s>

<s id="id.001699">Quærerer autem qui&longs;piam, (ip&longs;e enim <lb/>id reticet) curvibratio hæc ferenti &longs;it nocua. </s>

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<s id="id.001708">Cur autem ex medio facilius eleuetur, cau&longs;&longs;am e&longs;&longs;e ait, <lb/>quod eleuato medio ligno extrema &longs;e&longs;e inuicem &longs;u&longs;pen<lb/>dant, & altera pars alteram bene &longs;ubleuet. </s>

<s id="id.001709">Medium enim <lb/>fieri velut centrum, vbi is &longs;upponit humerum qui cleuat <lb/>aut fert. </s>

<s id="id.001709">Medium enim <lb/>fieri velut centrum, vbi is &longs;upponit humerum qui eleuat <lb/>aut fert. </s>

<s id="id.001710">Extremorum autem interim altero depre&longs;&longs;o al<lb/>terum &longs;u&longs;tolli. </s>

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<s id="id.001719">Intelligatur e<lb/>nim ij&longs;dem &longs;uppo&longs;itis, vectem quidem e&longs;&longs;e AB, cuius ful-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.175.jpg"/>cimentum quidem B, pondus A, potentia &longs;u&longs;tinens in C, <lb/>nempe inter fulcimentum & pondus. </s>

<s id="id.001720">Res igitur ad eum <lb/>vectis v&longs;um reducitur, de quo G. Vbaldus tractatu de Ve<lb/>cte, propo&longs;. </s>

<s id="id.001720">Res igitur ad eum <lb/>vectis v&longs;um reducitur, de quo G. Vbaldus tractatu de Ve<lb/>cte, propo&longs;. 3.</s>

<s id="id.001721">Quare vtile o&longs;tendit, ita &longs;e habere oporter <lb/>potentiam &longs;u&longs;tinentem ad pondus, vttotus vectis ad par<lb/>tem eius quæ à potentia ad fulcimentum. </s>

<s id="id.001721">3. Quare vtille o&longs;ten dit, ita &longs;e habere oporter <lb/>potentiam &longs;u&longs;tinentem ad pondus, vttotus vectis ad par<lb/>tem eius quæ à potentia ad fulcimentum. </s>

<s id="id.001722">Ita igitur &longs;e ha<lb/>bebit pre&longs;&longs;io, quæ fit in C ad pondus in A, vt totus vectis <lb/>AB ad partem eius CB, quæ à potentia ad fulcimentum. <lb/></s>

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<s id="id.001730">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>

<s id="id.001731">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>

<s id="id.001731">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/>ci manus 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>

</subchap1><subchap1>

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<s id="id.001737">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 id="id.001738">Sit enim oblongum lignum AB, quod humero me-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.177.jpg"/><figure id="id.007.01.177.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.177.1.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 id="id.001739">Illud <lb/>autem &longs;ubtiliter con&longs;ideramus, portantem ex vibratione <lb/>per inter ualla deprimi & &longs;ubleuari. </s>

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<s id="id.001750">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>

<s id="id.001751">Vectis diui&longs;i, &longs;itulæ, ac <lb/>ponderis, ad hoc vt fiat æ quili<lb/>brium, ca debet e&longs;&longs;e propor<lb/>tio, vt quema dmodum &longs;e habet AB ad BC, ita &longs;e habeat <lb/>plenæ &longs;itulæ pondus E ad ip&longs;um pondus A, &longs;uperabit ergo <lb/>pondus in A &longs;itulam vacuam in E nec fiet æquilibrium, i<lb/>taque vt vacua &longs;itula demittatur, tanta vis adhibenda c&longs;t <lb/>quantum e&longs;t ip&longs;ius aquæ, qua &longs;itulaimpl<gap/>tur pondus, quæ <lb/>vis dum apponitur difficilem, vt dicebamus, efficit &longs;itulæ <lb/>vacuæ demi&longs;&longs;ionem. </s>

<s id="id.001751">Vectis diui&longs;i, &longs;itulæ, ac <lb/>ponderis, ad hoc vt fiat æquili<lb/>brium, ca debet e&longs;&longs;e propor<lb/>tio, vt quemadmodum &longs;e habet AB ad BC, ita &longs;e habeat <lb/>plenæ &longs;itulæ pondus E ad ip&longs;um pondus A, &longs;uperabit ergo <lb/>pondus in A &longs;itulam vacuam in E nec fiet æquilibrium, i<lb/>taque vt vacua &longs;itula demittatur, tanta vis adhibenda e&longs;t <lb/>quantum e&longs;t ip&longs;ius aquæ, qua &longs;itula impletur pondus, quæ <lb/>vis dum apponitur difficilem, vt dicebamus, efficit &longs;itulæ <lb/>vacuæ demi&longs;&longs;ionem. </s>

<s id="id.001752">Plena vero &longs;itula &longs;it æquilibrium, vn<lb/>de quantumuis pu&longs;illa vi adhibita, &longs;itula extrahitur, qua&longs;i <lb/>ex &longs;emetip&longs;a ponderis appen&longs;i virtute a&longs;cendens. </s>

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<s id="id.001759">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/007-01-pageimg/007.01.179.jpg"/>&longs;itula &longs;u&longs;penditur FCABG, &longs;itula vero G. </s>

<s id="id.001760">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.007.01.179.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.179.1.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 id="id.001760">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.007.01.179.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-01-figures/007.01.179.1.jpg"></figure><lb/>pondere &longs;itulæ aqua plenæ, itaque extra<lb/>hens proprijs viribus <expan abbr="corpor&imacr;s">corporis</expan> pondus ad<lb/>ijciens facile &longs;itulam aqua plenam extra<lb/>hit, ex qua re magna extrahentibus fit <lb/>commoditas. </s>

<s id="id.001761">Patet autem diuer&longs;o modo <lb/>extrahentes iuuare Celonium. </s>

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<s id="id.001778">Dicimus enim, pondus quidem vere e&longs;<lb/>&longs;e pondus, non autem fulcimentum, vt &longs;ibi fingebat Ari<lb/>&longs;toteles: lignum vero vectem, duo autem qui pondus &longs;u<lb/>&longs;tinent pro duplici fulcimento haberi, vtri&longs;que enim ve<lb/>ctis cum appen&longs;o pondere innititur. </s>

<s id="id.001779">Pote&longs;t etiam alter <lb/>eorum pro porentia mouente, alter vero pro fulcimen<lb/>to, & &longs;ic vici&longs;&longs;im. </s>

<s id="id.001779">Pote&longs;t etiam alter <lb/>eorum pro potentia mouente, alter vero pro fulcimen<lb/>to, & &longs;ic vici&longs;&longs;im. </s>

<s id="id.001780">E&longs;t autem, quomodocunque res accipia<lb/>tur, pondus inter fulcimentum. </s>

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<s id="id.001810">quo igitur minor fue<lb/>rit proportio partis vectis quæ à centro grauitatis ad i<lb/>p&longs;um fulcimentum, ad totum vectem eo facilius pondus <lb/>eleuabitur. </s>

<s id="id.001811">Cur autem difficilime hæ per accliue horizonti pla<lb/>num pellantur, duplici fit de cau&longs;&longs;a, tum quia grauitatis <lb/>centrum ad ip&longs;um portantem &longs;eu pellentem vergit, & id<lb/>co pars quæ a fulcimento ad centrum grauitatis ponderis <lb/>fit maior, tum etiam quoniam ip&longs;um graue contra &longs;ui na<lb/>turam &longs;ur&longs;us pellitur ferturque. </s>

<s id="id.001811">Cur autem difficilime hæ per accliue horizonti pla<lb/>num pellantur, duplici fit de cau&longs;&longs;a, tum quia grauitatis <lb/>centrum ad ip&longs;um portantem &longs;eu pellentem vergit, & id<lb/>eo pars quæ a fulcimento ad centrum grauitatis ponderis <lb/>fit maior, tum etiam quoniam ip&longs;um graue contra &longs;ui na<lb/>turam &longs;ur&longs;us pellitur ferturque. </s>

<s id="id.001812">Quærere ad hæc qui&longs;piam po&longs;&longs;et, Cur Baiuli ma<lb/>gna ferentes pondera, curui in cedant? </s>

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<s id="id.001819"><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>

<s id="id.001820">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>

<s id="id.001820">E&longs;to enim &longs;tans AB hori<lb/>zonti IBK perpendicularis, cù<lb/>ius caput A, pedes vero B, &longs;edeat <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>

<s id="id.001821">Surgere itaque non po<lb/>terit &longs;edens, propterea quod <lb/>partes omnes corporìs non &longs;int <lb/>horizonti perpendiculares. </s>

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<s id="id.001836">Reclinetur autem pe<lb/>ctus ad anteriora, & cum f&oelig;more acutum angulum faciat <lb/>&longs;itque vbi GO, erit igitur grauitatis centrum vbi P, hoc <lb/>e&longs;t, in ip&longs;a perpendiculari NM, fretigitur inde commoda <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.187.jpg"/>&longs;urrectio, propterea quod in eadem linea facta &longs;int, graui<lb/>tatis centrum P, & fulcimentum ip&longs;um M. </s>

<s id="id.001837">Acutum vero <lb/>angulum in &longs;urrectione nece&longs;&longs;arium e&longs;&longs;e clare patet, non <lb/>autem eff<gap/>us ip&longs;ius e&longs;&longs;e cau&longs;&longs;am, vt videtur &longs;en&longs;i&longs;&longs;e Ari<lb/>&longs;toteles; ni<gap/>i dicamus, cau&longs;&longs;am e&longs;&longs;e cau&longs;&longs;æ, &longs;iquidem acuti <lb/>qui fiunt anguli centrum & pedes in eadem linea collo<lb/>cant, quicquid tamen &longs;it, nos ideo &longs;urrectionem fieri dici<lb/>mus, quod immutatis angulis centrum grauitatis &longs;upra <lb/>fulcimentum, fulcimento vero &longs;ub ip&longs;o grauitatis centro <lb/>collocetur, & hæc e&longs;t cau&longs;&longs;a proxima. </s>

<s id="id.001837">Acutum vero <lb/>angulum in &longs;urrectione nece&longs;&longs;arium e&longs;&longs;e clare patet, non <lb/>autem effectus ip&longs;ius e&longs;&longs;e cau&longs;&longs;am, vt videtur &longs;en&longs;i&longs;&longs;e Ari<lb/>&longs;toteles; nisi dicamus, cau&longs;&longs;am e&longs;&longs;e cau&longs;&longs;æ, &longs;iquidem acuti <lb/>qui fiunt anguli centrum & pedes in eadem linea collo<lb/>cant, quicquid tamen &longs;it, nos ideo &longs;urrectionem fieri dici<lb/>mus, quod immutatis angulis centrum grauitatis &longs;upra <lb/>fulcimentum, fulcimento vero &longs;ub ip&longs;o grauitatis centro <lb/>collocetur, & hæc e&longs;t cau&longs;&longs;a proxima. </s>

<s id="id.001838">Hæc nos ad Ari&longs;to<lb/>telem. </s>

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<s id="id.001848">Hinc etiam ceu con&longs;ectarium habemus, cur homi<lb/>nes &longs;i impellantur, magis ad ca&longs;um in po&longs;teriora quam in <lb/>anteriora &longs;int proni. </s>

<s id="id.001849">Necnon etiam cur &longs;imiæ, vr&longs;i, & &longs;i <lb/>quæ cætera eiu&longs;modi animalia diutius erecto corpore <lb/>ambulare nequeant, nempe ideo quod eorum corporum <lb/>moles valde in anteriora propendeat, necita commodo, <lb/>vt humanis cuenit corporibus, pedum ip&longs;orum ba&longs;ibus <lb/>fulciantur. </s>

<s id="id.001849">Nec non etiam cur &longs;imiæ, vr&longs;i, & &longs;i <lb/>quæ cætera eiu&longs;modi animalia diutius erecto corpore <lb/>ambulare nequeant, nempe ideo quod eorum corporum <lb/>moles valde in anteriora propendeat, nec ita commodo, <lb/>vt humanis euenit corporibus, pedum ip&longs;orum ba&longs;ibus <lb/>fulciantur. </s>

<s id="id.001850">Quærereitem haud importune po&longs;&longs;umus, Curgral<lb/>latores non &longs;tent erecti, ni&longs;i a&longs;&longs;idue moueantur? </s>

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<s id="id.001853">quamobrem grauitatis centrum fit extra ful<lb/>cimentum, & ideo coguntur grallatores a&longs;&longs;iduo motu <lb/>grauitatis centro fulcimentum &longs;upponere, quod dum fit, <lb/>à ca&longs;u prohibentur. </s>

<s id="id.001854">Pote&longs;t autem id quod fulcitur, tripliciter fulciri, <expan abbr="n&emacr;-peaut">nen<lb/>peaut</expan> puncto, aut linea, aut &longs;uperficie. </s>

<s id="id.001854">Pote&longs;t autem id quod fulcitur, tripliciter fulciri, <expan abbr="n&emacr;-peaut">nem<lb/>pe aut</expan> puncto, aut linea, aut &longs;uperficie. </s>

<s id="id.001855">Quod puncto fulcitur, nulla reimpediente ad quam<lb/>uis partem cadere pote&longs;t, centrum &longs;iquidem, motus, pun<lb/>ctum e&longs;t. </s>

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<s id="id.001870">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>

<s id="id.001871">l<gap/>em quo<lb/>que in auium pedibus ob&longs;erua<lb/>tur, ex quibus concludimus, bi<lb/>pedum omnium fulcimentum e&longs;<lb/>&longs;e quadruplex. </s>

<s id="id.001871">Idem quo<lb/>que in auium pedibus ob&longs;erua<lb/>tur, ex quibus concludimus, bi<lb/>pedum omnium fulcimentum e&longs;<lb/>&longs;e quadruplex. </s>

<s id="id.001872">Porro quadrupe<lb/>dia eo quod tota co<gap/>poris mole <lb/>ad in feriora vergant, quatuor ful<lb/>cimenta, eaque di&longs;tincta, & commode ab inuicem remo<lb/>ta eademmet Natura præparauit. </s>

<s id="id.001872">Porro quadrupe<lb/>dia eo quod tota corporis mole <lb/>ad in feriora vergant, quatuor ful<lb/>cimenta, eaque di&longs;tincta, & commode ab inuicem remo<lb/>ta eademmet Natura præparauit. </s>

<s id="id.001873">Eadem quoque in artificialibus con&longs;ideramus. </s>

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<s id="id.001879">Si <lb/>autem duobus tantum; non &longs;tabit. </s>

<s id="id.001880">ducta enim IK &longs;i pun<lb/>ctis tantum IK innitatur, con&longs;tituto grauitatis centro <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.191.jpg"/>extra fulcimentum IK, verget cedens ver&longs;<gap/>s partes, L, Si <lb/>autem innitatur punctis IL, cadet ad partes K. </s>

<s id="id.001880">ducta enim IK &longs;i pun<lb/>ctis tantum IK innitatur, con&longs;tituto grauitatis centro <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.191.jpg"/>extra fulcimentum IK, verget cedens ver&longs;is partes, L, Si <lb/>autem innitatur punctis IL, cadet ad partes K. </s>

<s id="id.001881">Sivero ip&longs;is <lb/>KL, cadet ad partes I.Ex quibus apparet, inanimata cor<lb/>pora aut vnico pede plurium virtutem habente, aut &longs;al<lb/>tem tribus actu, vt &longs;u&longs;tineantur, indigere. </s>

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<s id="id.001892">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 id="id.001893">Quæritur et<gap/>am, Cur ij 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>

<s id="id.001893">Quæritur etiam, Cur ij 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">nem<lb/>pe ver&longs;us</expan> manum ip&longs;am, quam porrigunt, extendant? </s>

<s id="id.001894">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>

<s id="id.001894">E&longs;to enim qui&longs;piam ABCD, <lb/>cuius crura BC, BD, grauitatis <lb/>centrum E, velitautem quippiam <lb/>à &longs;olo tollere quod &longs;it in F. &longs;it per<lb/>pendicularis, quæ pergrauitatis <lb/>centrum GEH. </s>

<s id="id.001895">Dum igitur ad <lb/>anteriora ínclinatur, centrum a<lb/>mouet à perpendiculari, quam<lb/>obrem docente Natura, crus BC <lb/>ad centrum ip&longs;um fulciendum. <lb/></s>

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<s id="id.001897">Huius quoque &longs;peculationis e&longs;t inue&longs;tigare, Cur <lb/>quadrupedia dum gradiuntur, pedes diametraliter mo<lb/>ueant. </s>

<s id="id.001898">Cuius rei verba fecit ip&longs;e quoque Philo&longs;ophus lib. <lb/>

<s id="id.001898">Cuius rei verba fecit ip&longs;e quoque Philo&longs;ophus lib. <lb/> de animalium ince&longs;&longs;u cap. 12. </s>

de animalium in ce&longs;&longs;u cap.

12. Nos autem ad maiorem de<lb/>clarationem, quodip&longs;e Phy&longs;icis principijs fecit, mecha<lb/>nicis demon&longs;trabimus. </s>

<s>Nos autem ad maiorem de<lb/>clarationem, quod ip&longs;e Phy&longs;icis principijs fecit, mecha<lb/>nicis demon&longs;trabimus. </s>

<s id="id.001899">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>

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<s id="id.001914">Sed <lb/>nec in anteriora corruet, quandoquidem ruinam factu<lb/>ras, nece&longs;&longs;e e&longs;t vt grauitatis centrum &longs;ecum trahat in per<lb/>pendiculari BF, & demum in eam quæ vltra perpendicu<lb/>larem e&longs;t BG, facta nempe circa B, ceu circa centrum, <expan abbr="c&omacr;-uer&longs;ione">con<lb/>uer&longs;ione</expan>. </s>

<s id="id.001915">Moueatur autem & ex &longs;emidiametro BE cen<lb/>tro B portio circuli de&longs;cribatur EH, quæ &longs;ecet BG in H, <lb/>& BF in I; Et quia EM &longs;emidiametro BK perpendicularis <lb/>per B, centrum non tran&longs;it, erit EM ip&longs;a BK, hoc e&longs;t, BI <lb/>bre<gap/>ior. </s>

<s id="id.001916">Ab&longs;cindatur ex BI, ip&longs;i EM æqualis LB. </s>

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<s id="id.001918">Nece&longs;&longs;e igitur erit ad hoc vt murus corruat, <lb/>centrum grauitatis E facta circa B, conuer&longs;ione aliquan<lb/>do fieri in I, vt demum transferri po&longs;&longs;it in H, &longs;ed I remo<lb/>tius e&longs;t à mundi centro ip&longs;is E, L, a&longs;cendet igitur graue <lb/>contra &longs;ui naturam ex E in I, at hoc e&longs;t impo&longs;&longs;ibile; quod <lb/>fuerat demon&longs;tran dum. </s>

<s id="id.001919">Ex his ij&longs;dem principijs alia &longs;oluitur quæ&longs;tio, Cur <lb/>&longs;cilicet Campanaria turris quæ Pi&longs;is vi&longs;itu<gap/>, nec non alia <lb/>Bononiæ in foro prope A &longs;ellorum turrim, quam à nobili <lb/>olim Cari&longs;endorum familia ex&longs;tructam, Cari&longs;endam vo<lb/>cant, cuius meminit & Dantes Poeta &longs;ummus in &longs;ua Co<lb/>m&oelig;dia. </s>

<s id="id.001919">Ex his ij&longs;dem principijs alia &longs;oluitur quæ&longs;tio, Cur <lb/>&longs;cilicet Campanaria turris quæ Pi&longs;is vi&longs;itur, nec non alia <lb/>Bononiæ in foro prope A &longs;ellorum turrim, quam à nobili <lb/>olim Cari&longs;endorum familia ex&longs;tructam, Cari&longs;endam vo<lb/>cant, cuius meminit & Dantes Poeta &longs;ummus in &longs;ua Co<lb/>m&oelig;dia. </s>

<s id="id.001920">Propendet autem hæc in latus, & ita propendet <lb/>vt perpendicularis, quæ à &longs;ummo inclinatæ partis in &longs;o<lb/>lum demittitur, longe cadat ab ip&longs;a, cui nititur, ba&longs;i, quod <lb/>&longs;ane mirabile videtur, muros nempe, in ruinam pronos, <lb/>ruinam non facere. </s>

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<s id="id.001940">E&longs;to horizontis pla<lb/>num AB, cui moles quæ<lb/>dam in&longs;i&longs;tat, CD. </s>

<s id="id.001941">Modo <lb/>potentia quædam appli<lb/>cetur vbi E, quæ molem in <lb/>anteriora propellat, id <lb/>e&longs;t, ver&longs;us B. Primum igitur, quoniam à quiete ad motum <lb/>fit tran&longs;itus, te&longs;i&longs;tit &longs;ua quiere corpus graue, potentiæ im<lb/>pellenti, &longs;uperata demum re&longs;i&longs;tentia moles quæ moueri <lb/>c&oelig;pit, fertur in F & mouetur, quare potentia quæ à prin<lb/>cipio re&longs;i&longs;tentiam rei non motæ &longs;uperauerat, pellendo <lb/>rem motam pergens facilius pellit: Duo enim &longs;unt quo<lb/>dammodo motores, mouens videlicet ip&longs;e, & motus quo <lb/>res mota mouetur. </s>

<s id="id.001941">Modo <lb/>potentia quædam appli<lb/>cetur vbi E, quæ molem in <lb/>anteriora propellat, id <lb/>e&longs;t, ver&longs;us B. Primum igitur, quoniam à quiete ad motum <lb/>fit tran&longs;itus, re&longs;i&longs;tit &longs;ua quiere corpus graue, potentiæ im<lb/>pellenti, &longs;uperata demum re&longs;i&longs;tentia moles quæ moueri <lb/>c&oelig;pit, fertur in F & mouetur, quare potentia quæ à prin<lb/>cipio re&longs;i&longs;tentiam rei non motæ &longs;uperauerat, pellendo <lb/>rem motam pergens facilius pellit: Duo enim &longs;unt quo<lb/>dammodo motores, mouens videlicet ip&longs;e, & motus quo <lb/>res mota mouetur. </s>

<s id="id.001942">facilius ergo pelletur ex F in G, quam <lb/>ex D in F, & ex G in B, quam ex F in G, & eo motus fiet in <lb/>progre&longs;&longs;u facilior atque in ip&longs;a velocitate velocior, quo <lb/>magis in ip&longs;a motione mouetur. </s>

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<s id="id.001945">Certe cau&longs;&longs;am velocitatis auctæ eam e&longs;&longs;e, quod <lb/>potentia mouens rem motam in motu ip&longs;o moueat, nemo <lb/>vtarbitror, inficias ibit, acquirit enim corpus motum <expan abbr="p&omacr;-">pon-</expan><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.197.jpg"/>dero&longs;itatem quan dam accidentalem, quæ cum ex motu <lb/>perinde augeatur, ip&longs;um motum faciliorem, eoque velo<lb/>ciorem facit. </s>

<s id="id.001946">Di&longs;putat hæc & Simplicius lib.

<s id="id.001946">Di&longs;putat hæc & Simplicius lib. 7. Phy&longs;ic. c. <lb/>11. Ari&longs;totelis de Natura libros exponens. </s>

7. Phy&longs;ic. c. <lb/>11. Ari&longs;totelis de Natura libros exponens. </s>

</subchap1><subchap1>

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<s id="id.001947">QVAESTIO XXXII.</s>

<s id="id.001948"><emph type="italics"/>Quæritur hic, Cur caquæproijciuntur, ce&longs;&longs;ent <lb/>à latione?<emph.end type="italics"/></s>

<s id="id.001948"><emph type="italics"/>Quæritur hic, Cur ea quæ proijciuntur, ce&longs;&longs;ent <lb/>à latione?<emph.end type="italics"/></s>

<s id="id.001949">Hocitidem problema e&longs;t mere Phy&longs;icum. </s>

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<s id="id.001952">Quicquid dicat Philo&longs;ophus, id vtique explorati&longs;<lb/>&longs;imum e&longs;t. </s>

<s id="id.001953">Proicctaideo à motu ce&longs;&longs;are, propterea quod <lb/>impre&longs;&longs;io, cuius impetu & virtute feruntur, non &longs;it proie<lb/>ctus quidem naturalis, &longs;ed mere accidentalis & violenta, <lb/>at nullum accidentale & violentum quodque, non natu<lb/>rale e&longs;t, perpetuum e&longs;t. </s>

<s id="id.001953">Proiecta ideo à motu ce&longs;&longs;are, propterea quod <lb/>impre&longs;&longs;io, cuius impetu & virtute feruntur, non &longs;it proie<lb/>ctus quidem naturalis, &longs;ed mere accidentalis & violenta, <lb/>at nullum accidentale & violentum quodque, non natu<lb/>rale e&longs;t, perpetuum e&longs;t. </s>

<s id="id.001954">Ce&longs;&longs;at ergo accidentalis illa im<lb/>pre&longs;&longs;io, eaque paullatim ce&longs;&longs;ante proiecti motus elan<lb/>gue&longs;cit, donec quietem pror&longs;us adipi&longs;catur. </s>

<s id="id.001955">Illud quoque <lb/>notamus, quod à multis vidimus non ob&longs;eruatum, nempe <lb/>violentum mo<gap/>m violentia præualente non differre à <lb/>naturali, & ideo tardiorem e&longs;&longs;e à principio po&longs;t hæc, in i<lb/>p&longs;o motu fieri velociotem, remittente demum paullatim <lb/>impre&longs;&longs;a violentia, tardiorem, donec impetus, & cum im<lb/>petu motus euane&longs;cat, & res ip&longs;a mota quietem adipi&longs;ca<lb/>tur. </s>

<s id="id.001955">Illud quoque <lb/>notamus, quod à multis vidimus non ob&longs;eruatum, nempe <lb/>violentum motum violentia præualente non differre à <lb/>naturali, & ideo tardiorem e&longs;&longs;e à principio po&longs;t hæc, in i<lb/>p&longs;o motu fieri velociorem, remittente demum paullatim <lb/>impre&longs;&longs;a violentia, tardiorem, donec impetus, & cum im<lb/>petu motus euane&longs;cat, & res ip&longs;a mota quietem adipi&longs;ca<lb/>tur. </s>

<s id="id.001956">Vnde etiam experientia docemur, ictum ex proiectis <lb/>violentius fieri, &longs;i fiat paullo remotior à principio, & tunc <lb/>demum e&longs;&longs;e innocenti&longs;&longs;imum, cum ibi fit, vbi proie ctum <lb/>ex motu plene acqui&longs;ito, &longs;ummam adeptum e&longs;t velocita<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.198.jpg"/>tem. </s>

<s id="id.001957">Hin evidemus, vel pueros ip&longs;os, docente Natura <expan abbr="c&umacr;">cum</expan> <lb/>nuces, vel aliud quippiam, parieti alli&longs;um frangere <expan abbr="conã-tur">conan<lb/>tur</expan>, à pariete moderato aliquo &longs;patio recedere. </s>

<s id="id.001957">Hinc videmus, vel pueros ip&longs;os, docente Natura <expan abbr="c&umacr;">cum</expan> <lb/>nuces, vel aliud quippiam, parieti alli&longs;um frangere <expan abbr="conã-tur">conan<lb/>tur</expan>, à pariete moderato aliquo &longs;patio recedere. </s>

<s id="id.001958">Si autem <lb/>eos interroges, cur id faciant, re&longs;pondebunt, vt inde ictus <lb/>valentius fiat atque efficacius. </s>

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<s id="id.001986">fa<lb/>cto enim molis &longs;eu magnitudinis centro vbi L, grauior <lb/>pars fiet in MNO; quæ cunque igitur &longs;unt corporaita <expan abbr="c&omacr;-&longs;tituta">con<lb/>&longs;tituta</expan>, vt in illis non &longs;it idem molis & grauitatis centrum <lb/>in ip&longs;a latione conuertentur, & eorum pars grauior an<lb/>tror&longs;us fiet. </s>

<s id="id.001987">Sonitus porro in ip&longs;o motu editi ea e&longs;t cau&longs;&longs;a, <lb/>quod irregulare corpus à principio incipit conuerti, & in <lb/>ip&longs;a conuer&longs;ione dum fertur aërem verberat, & ab eodem <lb/>vici&longs;&longs;im reuerberatur, ex qua reuerberatione fit corporis <lb/>rotatio dum fertur, & ip&longs;e &longs;onitus, quem Græci <foreign lang="greek">roicon</foreign><lb/>Rh&oelig;zum appellant. </s>

<s id="id.001988">Ad hanc quoque &longs;peculationem pertinet, Cur lapi<lb/>des ad &longs;uperfi ciem aquæ proiecti non &longs;tatim demergan<lb/>tur, &longs;ed aliquot vicibus a quæ &longs;uperficiem radentes, abea, <lb/>dem re&longs;iliant. </s>

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<s id="id.002000">Dico eam ab eodem in<lb/>clinato plano ad pares angulos re&longs;ilire non tamen rectos. <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-01-pageimg/007.01.202.jpg"/>Vtique pila cadens, planum non tanget in E. e&longs;&longs;et enim <lb/>GH, vbi AB, Tangat autem in I, & à centro F ad contin<lb/>gentiæ punctum I, recta ducatur FI. </s>

<s id="id.002001">Erit igitur FI (prop. <lb/></s>

<s id="id.002001">Erit igitur FI (prop. <lb/>18. lib. 3. elem.) ip&longs;i GH plano perpendicularis. </s>

<s id="id.002002">18. lib.

3. elem.) ip&longs;i GH plano perpendicularis. </s>

<s id="id.002003">Ducatur <lb/>item peri, ip&longs;i EC, parallela IK, &longs;ecans pilæ circumferen<lb/>tiam in K. </s>

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<s id="id.002104">Quod autem in no&longs;tra Praxi diximus, <lb/>QL e&longs;&longs;etertiam, earatio e&longs;t, quod LR vt in prima figura <lb/>e&longs;t, &longs;it æqualis ip&longs;i LM &longs;ecundæ figuræ, in demon&longs;tratio<lb/>ne Pappi, ex quibus demptis QR & LA, quæ &longs;unt æqua<lb/>les, reliqua QL primæ figuræ æqualis e&longs;t AM &longs;ecundæ fi<lb/>guræ, hoc e&longs;t, ip&longs;i tertiæ proportionali: E&longs;t igitur, vt in pri<lb/>ma figura dicebamus, AB prima, kR &longs;ecunda, QL tertia, <lb/>BC quarta. </s>

<s id="id.002105">Vides igitur tu quilegis, nos ex Nicomedis demon<lb/>&longs;tratione (quatenus ad praxin pertinet) &longs;uperflua re&longs;eca&longs;<lb/>&longs;e, & ab&longs;que Conchoidis in&longs;trumento lineaue rem ip&longs;am <lb/>confeci&longs;&longs;e, idque non rentantes, vtalij, &longs;ed progre<lb/>dientes, & qua&longs;i manuductos quæ&longs;i<lb/>tum inue&longs;tiga&longs;&longs;e. </s>

<s id="id.002105">Vides igitur tu qui legis, nos ex Nicomedis demon<lb/>&longs;tratione (quatenus ad praxin pertinet) &longs;uperflua re&longs;eca&longs;<lb/>&longs;e, & ab&longs;que Conchoidis in&longs;trumento lineaue rem ip&longs;am <lb/>confeci&longs;&longs;e, idque non tentantes, vt alij, &longs;ed progre<lb/>dientes, & qua&longs;i manuductos quæ&longs;i<lb/>tum inue&longs;tiga&longs;&longs;e. </s>

<s id="id.002106">FINIS.<lb/> </s>

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