texts/archimedes/xml/baldi_mecha_01_la_1621.xml - Colored diff

Main History Search Repository tree

Return to baldi_mecha_01_la_1621.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/Attic/baldi_mecha_01_la_1621.xml between version 1.45 and 1.47

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

version 1.47, 2002/10/06 04:00:11

Line 456

<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>

Line 2786

Line 2784

<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>

Line 2794

Line 2792

<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>

Line 2804

Line 2802

<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>

Line 2845

Line 2843

<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>

Line 2859

Line 2857

<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>

Line 2874

Line 2870

<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>

Line 2905

Line 2901

<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>

Line 2942

Line 2938

<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>

Line 2981

Line 2977

<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>

Line 3000

Line 2994

<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>

Line 3073

Line 3067

<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>

Line 3085

Line 3079

<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>

Line 3097

Line 3091

<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>

Line 3110

Line 3104

<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>

Line 3155

Line 3149

<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>

Line 3221

Line 3215

<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>

Line 3270

Line 3264

<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>

Line 3282

Line 3276

<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>

Line 3322

Line 3316

<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>

Line 3353

Line 3347

<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.

1. Elem.

<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>

&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>

Line 3401

Line 3391

<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>

Line 3485

Line 3475

<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>

Line 3493

Line 3483

<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>

Line 3516

Line 3504

<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>

Line 3579

Line 3567

<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>

Line 3596

Line 3584

<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 mouc<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>

Line 3628

Line 3616

<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>

Line 3670

Line 3656

<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>

Line 3712

Line 3698

<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.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>

Legend:

Removed from v.1.45
changed lines
	Added in v.1.47