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| <s id="id.000008">Domino meo gratio&longs;i&longs;&longs;imo.</s></p><p type="main"> | <s id="id.000008">Domino meo gratio&longs;i&longs;&longs;imo.</s></p><p type="main"> |
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| <s id="id.000009">Opportune &longs;ub hoc ip&longs;um tem­<lb/>pus, quo in Belgium ad Scre­<lb/>ni&longs;&longs;imos Principes iter ador­<lb/>nat.</s> | <s id="id.000009">Opportune &longs;ub hoc ip&longs;um tem­<lb/>pus, quo in Belgium ad Sere­<lb/>ni&longs;&longs;imos Principes iter ador­<lb/>nat.</s> |
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| <s id="id.000010"> Nobili&longs;&longs;ima & Genero&longs;a <lb/>Dom. <!-- REMOVE S-->V.^{ra}, prodit no&longs;tris for­<lb/>mis in publicum editus Com­<lb/>mentarius Bernardini Baldi Vrbinatis Gua­<lb/>&longs;tallæ Abbatis in Ari&longs;totelis Mechanica. <!-- KEEP S--></s> | <s id="id.000010"> Nobili&longs;&longs;ima & Genero&longs;a <lb/>Dom. <!-- REMOVE S-->V.^{ra}, prodit no&longs;tris for­<lb/>mis in publicum editus Com­<lb/>mentarius Bernardini Baldi Vrbinatis Gua­<lb/>&longs;tallæ Abbatis in Ari&longs;totelis Mechanica. <!-- KEEP S--></s> |
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| <s id="id.000011">Is <lb/>virin omni &longs;cientiæ genere, at maxime inMa­<lb/>thematicis di&longs;ciplinis fuit ver&longs;ati&longs;&longs;imus, quod <lb/>multa ab eo præclare &longs;crip ta te&longs;tantur opera, <lb/>ex quibus paucula edita, reliqua vero &longs;pera­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.004.jpg"/>mus &longs;uo temporein publicam luce<gap/> produ­<lb/>cenda. </s> | <s id="id.000011">Is <lb/>virin omni &longs;cientiæ genere, at maxime inMa­<lb/>thematicis di&longs;ciplinis fuit ver&longs;ati&longs;&longs;imus, quod <lb/>multa ab eo præclare &longs;crip ta te&longs;tantur opera, <lb/>ex quibus paucula edita, reliqua vero &longs;pera­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.004.jpg"/>mus &longs;uo temporein publicam luce<gap/> produ­<lb/>cenda. </s> |
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| <s id="id.000012"> Cum vero nemini&longs;it ob&longs;curum Nobi­<lb/>li&longs;&longs;imæ ac Genero&longs;æ Dom. <!-- REMOVE S-->V.^{ræ} id &longs;emper <lb/>extiti&longs;&longs;e familiari&longs;&longs;imum, vttum dome&longs;ticum <lb/>otium, tum maxime peregtinationes, quibus <lb/>totam pæne Europam &longs;umma cum laude <lb/>circum&longs;crip&longs;it, tum variarum linguarum per­<lb/>fecto v&longs;u, tum Mathematicarum di&longs;ciplina­<lb/>rum notitia & exercitio redderet <expan abbr="iucũdiores">iucundiores</expan>, <lb/>nulla me tenet dubitatio quin & Baldum Vr­<lb/>binatem no&longs;tris typis loquentem in hoc iti­<lb/>nere, quod à Deo felici&longs;&longs;imum Nobili&longs;&longs;imæ <lb/>ac Genero&longs;æ Dom. <!-- REMOVE S-->V.^{ræ} precor, in &longs;uum comi­<lb/>tatum ac tutelam beneuolo animo &longs;it admi&longs;­<lb/>&longs;ura.</s> | <s id="id.000012"> Cum vero nemini &longs;it ob&longs;curum Nobi­<lb/>li&longs;&longs;imæ ac Genero&longs;æ Dom. <!-- REMOVE S-->V.^{ræ} id &longs;emper <lb/>extiti&longs;&longs;e familiari&longs;&longs;imum, vt tum dome&longs;ticum <lb/>otium, tum maxime peregrinationes, quibus <lb/>totam pæne Europam &longs;umma cum laude <lb/>circum&longs;crip&longs;it, tum variarum linguarum per­<lb/>fecto v&longs;u, tum Mathematicarum di&longs;ciplina­<lb/>rum notitia & exercitio redderet <expan abbr="iucũdiores">iucundiores</expan>, <lb/>nulla me tenet dubitatio quin & Baldum Vr­<lb/>binatem no&longs;tris typis loquentem in hoc iti­<lb/>nere, quod à Deo felici&longs;&longs;imum Nobili&longs;&longs;imæ <lb/>ac Genero&longs;æ Dom. <!-- REMOVE S-->V.^{ræ} precor, in &longs;uum comi­<lb/>tatum ac tutelam beneuolo animo &longs;it admi&longs;­<lb/>&longs;ura.</s> |
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| <s id="id.000026">Verum enimuero cum inge­<lb/>nuiilli fuerint homines, & nullatenus obtrecta­<lb/>tores, credendum potius est, Comment ariolum i­<lb/>&longs;tud, eorum æuo, paucis cognitum, alicubi in Bi­<lb/>bliothecis latui&longs;&longs;e: etenim cætera quoque Ari&longs;tote­<lb/>lis &longs;cripta, po&longs;t vetu&longs;tailla tempora, ante Ale­<lb/>xandrum Aphrodi&longs;ien&longs;em, àmultis fui&longs;&longs;e igno-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.008.jpg"/>rata non dubitamus. </s> | <s id="id.000026">Verum enimuero cum inge­<lb/>nuiilli fuerint homines, & nullatenus obtrecta­<lb/>tores, credendum potius est, Comment ariolum i­<lb/>&longs;tud, eorum æuo, paucis cognitum, alicubi in Bi­<lb/>bliothecis latui&longs;&longs;e: etenim cætera quoque Ari&longs;tote­<lb/>lis &longs;cripta, po&longs;t vetu&longs;tailla tempora, ante Ale­<lb/>xandrum Aphrodi&longs;ien&longs;em, àmultis fui&longs;&longs;e igno-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.008.jpg"/>rata non dubitamus. </s> |
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| <s id="id.000027">Habemus &longs;iquidem, Stra­<lb/>bone te&longs;te, lib. | <s id="id.000027">Habemus &longs;iquidem, Stra­<lb/>bone te&longs;te, lib. 13. Ari&longs;totelis, & Theophra&longs;ti bi­<lb/>bliothecam, po&longs;t ip&longs;ius Theophra&longs;ti dece&longs;&longs;um, ad <lb/>Neleum quendam Scep&longs;ium, Cori&longs;cifilium, qui <lb/>eius fuerat auditor, perueni&longs;&longs;e; po&longs;t hæc libros, <lb/>blattis olim, & humore corruptos, Apelliconi Te­<lb/>io venditos, & ab eo Athenas translatos, tum <lb/>Athenis captis in Syllæ pote&longs;tatem deacni&longs;&longs;e, eo&longs;­<lb/>que tandem à Sylla acceptos, Tyrannionem <lb/>Grammaticum, vt potuit meliùs emendatos, <lb/>promulga&longs;&longs;e. </s> |
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| 13. Ari&longs;totelis, & Theophra&longs;ti bi­<lb/>bliothecam, po&longs;t ip&longs;ius Theophra&longs;ti dece&longs;&longs;um, ad <lb/>Neleum quendam Scep&longs;ium, Cori&longs;cifilium, qui <lb/>eius fuerat auditor, perueni&longs;&longs;e; po&longs;t hæc libros, <lb/>blattis olim, & humore corruptos, Apelliconi Te­<lb/>io venditos, & ab eo Athenas translatos, tum <lb/>Athenis captis in Syllæ pote&longs;tatem deacni&longs;&longs;e, eo&longs;­<lb/>que tandem à Sylla acceptos, Tyrannionem <lb/>Grammaticum, vt potuit meliùs emendatos, <lb/>promulga&longs;&longs;e. </s> | |
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| <s id="id.000028">Exquibus colligimus, mirum non <lb/>e&longs;&longs;e, Archimedi, Heroni, & alijs qui ante Syllam <lb/>vixêre, fui&longs;&longs;e incognitos. </s> | <s id="id.000028">Exquibus colligimus, mirum non <lb/>e&longs;&longs;e, Archimedi, Heroni, & alijs qui ante Syllam <lb/>vixêre, fui&longs;&longs;e incognitos. </s> |
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| <s id="id.000032">Olympiadem floruit, quamobrem po&longs;t Ari&longs;tote­<lb/>lem Olympiadas XL. hoc est, annos ferè CLX. <lb/><!-- KEEP S--></s> | <s id="id.000032">Olympiadem floruit, quamobrem po&longs;t Ari&longs;tote­<lb/>lem Olympiadas XL. hoc est, annos ferè CLX. <lb/><!-- KEEP S--></s> |
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| <s id="id.000033">I&longs;thæc autem con&longs;iderantibus, facile e&longs;t cogno&longs;ce­<lb/>refacultatis huius nobilitatem, atque dignit atem; <lb/>quippe quod &longs;ummus Philo&longs;ophus non modo eam <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.009.jpg"/>probauerit, &longs;cd etiam &longs;uis acutissimis lucubra­<lb/>tionibus illu&longs;trauerit. </s> | <s id="id.000033">I&longs;thæc autem con&longs;iderantibus, facile e&longs;t cogno&longs;ce­<lb/>re facultatis huius nobilitatem, atque dignitatem; <lb/>quippe quod &longs;ummus Philo&longs;ophus non modo eam <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.009.jpg"/>probauerit, &longs;ed etiam &longs;uis acutissimis lucubra­<lb/>tionibus illu&longs;trauerit. </s> |
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| <s id="id.000034">Hanc porro tractationem <lb/>&longs;ubiecto quidem Phy&longs;icam e&longs;&longs;e, demon&longs;tratio­<lb/>nibus verò Geometricam, ip&longs;emet nos docuit <lb/>Ari&longs;toteles, cuius etiam naturæ &longs;unt Per&longs;pecti­<lb/>ua, Specularia, Mu&longs;ica, & cæteræ eiu&longs;dem <lb/>modi facultates, quas quidem &longs;ubalternas Peri­<lb/>patetici appellant. </s> | <s id="id.000034">Hanc porro tractationem <lb/>&longs;ubiecto quidem Phy&longs;icam e&longs;&longs;e, demon&longs;tratio­<lb/>nibus verò Geometricam, ip&longs;emet nos docuit <lb/>Ari&longs;toteles, cuius etiam naturæ &longs;unt Per&longs;pecti­<lb/>ua, Specularia, Mu&longs;ica, & cæteræ eiu&longs;dem <lb/>modi facultates, quas quidem &longs;ubalternas Peri­<lb/>patetici appellant. </s> |
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| <s id="id.000035">Vitruuius Architecturæ <lb/>membrum, vt ita dicam, & portionem quan­<lb/>dam facit, ait enim Architecturæ partes e&longs;&longs;e tres, <lb/>Ædificationem, Gnomonicam, Machinatio­<lb/>nem. </s> | <s id="id.000035">Vitruuius Architecturæ <lb/>membrum, vt ita dicam, & portionem quan­<lb/>dam facit, ait enim Architecturæ partes e&longs;&longs;e tres, <lb/>Ædificationem, Gnomonicam, Machinatio­<lb/>nem. </s> |
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| <s id="id.000036">Estautem Architectur â quideminferior, <lb/>paret enim Architecto Mechanicus; attamen &longs;i <lb/>cæteras artes &longs;pectes, Architectonica; hæc enim <lb/>omnesferè &longs;edentariæ, &longs;ellulariæue, quas banau­<lb/>&longs;as Græci appellant, ordine &longs;ubijciuntur, & &longs;a­<lb/>nè latissimos i&longs;ihæc habet fines; præcipuè autem <lb/>circa eam ver&longs;atur cognitionem, eamque inter <lb/>cæterasferè principem, quam dixere Centrobari­<lb/>cam, quæ quidem ad Centri grauitatem, eiu&longs;que <lb/>&longs;peculationem pertinet: quà in &longs;pecie inter vete­<lb/>res primum &longs;ibi vindicauit locum Archimedes, <lb/>mox Heron, deinde Pappus; inter neotericos au-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.010.jpg"/><emph type="italics"/>tem Commandinus, qui librum de Centro gra­<lb/>uitatis &longs;olidorum &longs;crip&longs;it, & po&longs;t eum G. <!-- REMOVE S-->Vbal­<lb/>dus è Marchion. <!-- REMOVE S-->Montis, qui non modò ab­<lb/>&longs;olutissimum Mechanicorum librum cum maxi­<lb/>ma ingenij &longs;ui laude con&longs;crip&longs;it, &longs;ed & Paraphra­<lb/>&longs;in in librum Æqueponderantium Archimedis <lb/>egregiè concinnauit Centrobaricam hanc, igno­<lb/>tam fui&longs;&longs;e Ari&longs;toteli, &longs;ætis patet. </s> | <s id="id.000036">Est autem Architecturâ quidem inferior, <lb/>paret enim Architecto Mechanicus; attamen &longs;i <lb/>cæteras artes &longs;pectes, Architectonica; hæc enim <lb/>omnes ferè &longs;edentariæ, &longs;ellulariæue, quas banau­<lb/>&longs;as Græci appellant, ordine &longs;ubijciuntur, & &longs;a­<lb/>nè latissimos i&longs;thæc habet fines; præcipuè autem <lb/>circa eam ver&longs;atur cognitionem, eamque inter <lb/>cæteras ferè principem, quam dixere Centrobari­<lb/>cam, quæ quidem ad Centri grauitatem, eiu&longs;que <lb/>&longs;peculationem pertinet: quà in &longs;pecie inter vete­<lb/>res primum &longs;ibi vindicauit locum Archimedes, <lb/>mox Heron, deinde Pappus; inter neotericos au-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.010.jpg"/><emph type="italics"/>tem Commandinus, qui librum de Centro gra­<lb/>uitatis &longs;olidorum &longs;crip&longs;it, & po&longs;t eum G. <!-- REMOVE S-->Vbal­<lb/>dus è Marchion. <!-- REMOVE S-->Montis, qui non modò ab­<lb/>&longs;olutissimum Mechanicorum librum cum maxi­<lb/>ma ingenij &longs;ui laude con&longs;crip&longs;it, &longs;ed & Paraphra­<lb/>&longs;in in librum Æqueponderantium Archimedis <lb/>egregiè concinnauit Centrobaricam hanc, igno­<lb/>tam fui&longs;&longs;e Ari&longs;toteli, &longs;ætis patet. </s> |
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| <s id="id.000039">Rationalis, &longs;peculationi & <expan abbr="demō&longs;trationibus">demon&longs;trationibus</expan>, ex <lb/>Geometricis, Arithmeticis & Phy&longs;icis rationi­<lb/>bus, dat operam; Chirurgica vero materiam <lb/>tractat, & &longs;e&longs;ein varias artes diffundit, Æra­<lb/>riam, Lignariam, Sculptoriam, Pictoriam, Æ­<lb/>dificatoriam, Machinariam & Thaumaturgi­<lb/>cam, cæterasque eiu&longs;modi. </s> | <s id="id.000039">Rationalis, &longs;peculationi & <expan abbr="demō&longs;trationibus">demon&longs;trationibus</expan>, ex <lb/>Geometricis, Arithmeticis & Phy&longs;icis rationi­<lb/>bus, dat operam; Chirurgica vero materiam <lb/>tractat, & &longs;e&longs;ein varias artes diffundit, Æra­<lb/>riam, Lignariam, Sculptoriam, Pictoriam, Æ­<lb/>dificatoriam, Machinariam & Thaumaturgi­<lb/>cam, cæterasque eiu&longs;modi. </s> |
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| <s id="id.000040">Machinatoriæ au­<lb/>tem &longs;unt partes Manganaria, qua ingentiæ<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.011.jpg"/><emph type="italics"/>transferuntur pondera, tum ip&longs;a Poliorcetica, <lb/>quæ bellicas Machinas ad vrbium expugnatio­<lb/>nes, quod velip&longs;o nomine profitetur, ædificat. </s> | <s id="id.000040">Machinatoriæ au­<lb/>tem &longs;unt partes Manganaria, qua ingentia <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.011.jpg"/><emph type="italics"/>transferuntur pondera, tum ip&longs;a Poliorcetica, <lb/>quæ bellicas Machinas ad vrbium expugnatio­<lb/>nes, quod vel ip&longs;o nomine profitetur, ædificat. </s> |
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| <s id="id.000041">At­<lb/>qui hac dere plura &longs;cribere &longs;uper&longs;edemus, ne a­<lb/>ctum agamus: quis quis enim minutè magis hæc <lb/>cogno&longs;cere de&longs;iderat, is Pappum adeat libro cita­<lb/>to, & Guidum Vbaldumin Præfatione quam <lb/>&longs;uo Mechanicorum Operi præpo&longs;uit. </s> | <s id="id.000041">At­<lb/>qui hac dere plura &longs;cribere &longs;uper&longs;edemus, ne a­<lb/>ctum agamus: quis quis enim minutè magis hæc <lb/>cogno&longs;cere de&longs;iderat, is Pappum adeat libro cita­<lb/>to, & Guidum Vbaldumin Præfatione quam <lb/>&longs;uo Mechanicorum Operi præpo&longs;uit. </s> |
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| <s id="id.000044">Modo, vt audio, Simon <lb/>Sticinus Hollanden&longs;is quædam edidit, quæ ad <lb/>nos minime peruenêre. </s> | <s id="id.000044">Modo, vt audio, Simon <lb/>Sticinus Hollanden&longs;is quædam edidit, quæ ad <lb/>nos minime peruenêre. </s> |
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| <s id="id.000045">Nos demum, omnium, <lb/>tum &longs;cientia, & ingenio, tum ætate, po&longs;tremi huic <lb/>operi manum admouimus; Con&longs;iderantes enim <lb/>Ari&longs;totelem aliis fecerint Mechanici, demon&longs;tra&longs;&longs;e, <lb/>morem huiu&longs;ce facultatis &longs;tudio&longs;is ge&longs;turos nos <lb/>fore arbitrati&longs;umus, &longs;i ea&longs;dem illas quæ&longs;tiones<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.012.jpg"/><emph type="italics"/>Mechanicis, hocest, Archimedeis probationi­<lb/>bus confirmaremus; dum per latissimos faculta­<lb/>tis huius campos vægantes, alias quoque i&longs;tis af­<lb/>fines dubitationes introducentes &longs;olueremus. <lb/></s> | <s id="id.000045">Nos demum, omnium, <lb/>tum &longs;cientia, & ingenio, tum ætate, po&longs;tremi huic <lb/>operi manum admouimus; Con&longs;iderantes enim <lb/>Ari&longs;totelem aliis fecerint Mechanici, demon&longs;tra&longs;&longs;e, <lb/>morem huiu&longs;ce facultatis &longs;tudio&longs;is ge&longs;turos nos <lb/>fore arbitrati &longs;umus, &longs;i ea&longs;dem illas quæ&longs;tiones<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.012.jpg"/><emph type="italics"/>Mechanicis, hoc est, Archimedeis probationi­<lb/>bus confirmaremus; dum per latissimos faculta­<lb/>tis huius campos vagantes, alias quoque i&longs;tis af­<lb/>fines dubitationes introducentes &longs;olueremus. <lb/></s> |
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| <s id="id.000046"><expan abbr="quicquidautē&longs;ecerimus">quicquidauten&longs;ecerimus</expan> profecerimu&longs;ue, Lector <lb/>optime, boni con&longs;ule, & quia fax per manus tra­<lb/>ditur, tu interim de me accipe, vt alijs tradas.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.013.jpg"/> | <s id="id.000046"><expan abbr="quicquidautē&longs;ecerimus">quicquid autem fecerimus</expan> profecerimu&longs;ue, Lector <lb/>optime, boni con&longs;ule, & quia fax per manus tra­<lb/>ditur, tu interim de me accipe, vt alijs tradas.<emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.013.jpg"/> |
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| </chap> | </chap> |
| <chap> | <chap> |
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| <s id="id.000054">Parens hac <lb/>filij laude & gloria motus anno 1573. eum ad maiorem in­<lb/>genij cultum cape&longs;&longs;endum Patauium mi&longs;it. </s> | <s id="id.000054">Parens hac <lb/>filij laude & gloria motus anno 1573. eum ad maiorem in­<lb/>genij cultum cape&longs;&longs;endum Patauium mi&longs;it. </s> |
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| <s id="id.000055">Hîcin Ema­<lb/>nuelis Margunij familiaritatem &longs;tatim venit, cui porro <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.014.jpg"/>fuit in amotibus. </s> | <s id="id.000055">Hîc in Ema­<lb/>nuelis Margunij familiaritatem &longs;tatim venit, cui porro <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.014.jpg"/>fuit in amoribus. </s> |
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| <s id="id.000056">Homeri Iliad. <!-- REMOVE S-->illo Doctore & interpre­<lb/>te diligentius quam feci&longs;&longs;et antea, euoluit. </s> | <s id="id.000056">Homeri Iliad. <!-- REMOVE S-->illo Doctore & interpre­<lb/>te diligentius quam feci&longs;&longs;et antea, euoluit. </s> |
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| <s id="id.000057">priuato autem <lb/>&longs;tudio Anacreonti, Pindaro, Æ&longs;chyli, Euripidi, Sophocli <lb/>operam dedit, &longs;ed præ cæteris Thcocriti Bucolica triuit, <lb/>ad quod &longs;criptionis genus natura magis ferri videbatur: <lb/>centenos græci alicuius poëtæver&longs;us memoriter tenebat, <lb/>&longs;æpeque habebat in ore, in oratoribus græcis ver&longs;andis <lb/>laborem &longs;ealiquem &longs;entire, in poëtis nullum. </s> | <s id="id.000057">priuato autem <lb/>&longs;tudio Anacreonti, Pindaro, Æ&longs;chyli, Euripidi, Sophocli <lb/>operam dedit, &longs;ed præ cæteris Theocriti Bucolica triuit, <lb/>ad quod &longs;criptionis genus natura magis ferri videbatur: <lb/>centenos græci alicuius poëtæ ver&longs;us memoriter tenebat, <lb/>&longs;æpeque habebat in ore, in oratoribus græcis ver&longs;andis <lb/>laborem &longs;e aliquem &longs;entire, in poëtis nullum. </s> |
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| <s id="id.000058">Scrip&longs;it Pa­<lb/>tauij libellum de Tormentis Bellicis, & eorum inuentori­<lb/>bus, & cum in Tran&longs;alpinorum amicitias incidi&longs;&longs;et, &longs;ibi <lb/>ducebat dedecori ip&longs;os &longs;ua lingua loquentes non intelli­<lb/>gere. </s> | <s id="id.000058">Scrip&longs;it Pa­<lb/>tauij libellum de Tormentis Bellicis, & eorum inuentori­<lb/>bus, & cum in Tran&longs;alpinorum amicitias incidi&longs;&longs;et, &longs;ibi <lb/>ducebat dedecori ip&longs;os &longs;ua lingua loquentes non intelli­<lb/>gere. </s> |
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| <s id="id.000059">quare incredibili celeritate Gallicam & Germani­<lb/>cam didicit. </s> | <s id="id.000059">quare incredibili celeritate Gallicam & Germani­<lb/>cam didicit. </s> |
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| <s id="id.000060">Pe&longs;tilentia ex co Gymna&longs;io exactus in Pa­<lb/>triam redijt, vbi quin quennium integrum Federico <expan abbr="Cō-mandino">Con­<lb/>mandino</expan> affixus omnes Mathe&longs;eos partes perdidicit, cui <lb/>viro in delinean dis figuris ad Euclidis, Pappi, & Heronis <lb/>monumenta manum commodauit: ex eiu&longs;dem obitu do­<lb/>lorem vix con&longs;olabilem &longs;u&longs;tinuit, &longs;u&longs;ceptoque eius vitam <lb/>&longs;cribendi con&longs;ilio, &longs;ubinde ad omnium Mathematicorum <lb/>vitas con&longs;cribendas animum adplicuit, quod & duode­<lb/>cim annorum &longs;patio præ&longs;titit felici&longs;&longs;imè. </s> | <s id="id.000060">Pe&longs;tilentia ex eo Gymna&longs;io exactus in Pa­<lb/>triam redijt, vbi quinquennium integrum Federico <expan abbr="Cō-mandino">Com­<lb/>mandino</expan> affixus omnes Mathe&longs;eos partes perdidicit, cui <lb/>viro in delineandis figuris ad Euclidis, Pappi, & Heronis <lb/>monumenta manum commodauit: ex eiu&longs;dem obitu do­<lb/>lorem vix con&longs;olabilem &longs;u&longs;tinuit, &longs;u&longs;ceptoque eius vitam <lb/>&longs;cribendi con&longs;ilio, &longs;ubinde ad omnium Mathematicorum <lb/>vitas con&longs;cribendas animum adplicuit, quod & duode­<lb/>cim annorum &longs;patio præ&longs;titit felici&longs;&longs;imè. </s> |
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| <s id="id.000061">cum vero Ma­<lb/>thematicarum di&longs;ciplinarum amore torqueretur, ami&longs;&longs;o <lb/>Commandino Præceptore, amicum nactus fuit præ&longs;tan­<lb/>ti&longs;&longs;imum & &longs;ymmy&longs;tam Guidum Vbaldum è Marchioni­<lb/>bus Montis, in cuius &longs;e con&longs;uetudinem daret: quantum <lb/>profeci&longs;&longs;et, o&longs;tendunt ij commentarij quos anno 1582. in <lb/>Ari&longs;t. Mechanica &longs;crip&longs;it. </s> | <s id="id.000061">cum vero Ma­<lb/>thematicarum di&longs;ciplinarum amore torqueretur, ami&longs;&longs;o <lb/>Commandino Præceptore, amicum nactus fuit præ&longs;tan­<lb/>ti&longs;&longs;imum & &longs;ymmy&longs;tam Guidum Vbaldum è Marchioni­<lb/>bus Montis, in cuius &longs;e con&longs;uetudinem daret: quantum <lb/>profeci&longs;&longs;et, o&longs;tendunt ij commentarij quos anno 1582. in <lb/>Ari&longs;t. Mechanica &longs;crip&longs;it. </s> |
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| <s id="id.000062">Vt po&longs;tea à grauioribus &longs;tudijs <lb/>ad amœniora animum abduceret, de re nautica poëma I­<lb/>talicè <gap/>onfecit. </s> | <s id="id.000062">Vt po&longs;tea à grauioribus &longs;tudijs <lb/>ad amœniora animum abduceret, de re nautica poëma I­<lb/>talicè confecit. </s> |
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| <s id="id.000063">quo ab&longs;oluto Paradoxa multa Mathema­<lb/>tica explicauit. </s> | <s id="id.000063">quo ab&longs;oluto Paradoxa multa Mathema­<lb/>tica explicauit. </s> |
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| <s id="id.000066">&longs;cio dixi&longs;&longs;e ali­<lb/>quando Adrianum Romanum è Polonia reuer&longs;um, vbi <lb/>Vitruuium Palatino cuidam explicauerat, &longs;i commen­<lb/>tarium Baldi in Polonia adhibere potui&longs;&longs;em, aurum quod <lb/>mecum attuli emunxi&longs;&longs;em, quia &longs;atis feci&longs;&longs;em muneri la­<lb/>borenullo. </s> | <s id="id.000066">&longs;cio dixi&longs;&longs;e ali­<lb/>quando Adrianum Romanum è Polonia reuer&longs;um, vbi <lb/>Vitruuium Palatino cuidam explicauerat, &longs;i commen­<lb/>tarium Baldi in Polonia adhibere potui&longs;&longs;em, aurum quod <lb/>mecum attuli emunxi&longs;&longs;em, quia &longs;atis feci&longs;&longs;em muneri la­<lb/>borenullo. </s> |
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| <s id="id.000067">Cum Ferrando hero &longs;uo obueni&longs;&longs;et nece&longs;&longs;i­<lb/>tas Hi&longs;panias adeundi, illud iter &longs;ine Baldo facere &longs;e po&longs;­<lb/>&longs;e non putabat, non tam vt haberet, qui erudito cloquio <lb/>viæ tæ dium leuaret, quam cui po&longs;&longs;et arcana committere, <lb/>atque adeo à quo iuuaretur con&longs;ilio. </s> | <s id="id.000067">Cum Ferrando hero &longs;uo obueni&longs;&longs;et nece&longs;&longs;i­<lb/>tas Hi&longs;panias adeundi, illud iter &longs;ine Baldo facere &longs;e po&longs;­<lb/>&longs;e non putabat, non tam vt haberet, qui erudito eloquio <lb/>viæ tæ dium leuaret, quam cui po&longs;&longs;et arcana committere, <lb/>atque adeo à quo iuuaretur con&longs;ilio. </s> |
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| <s id="id.000068">Vix viæ &longs;e dederant <lb/>cum Baldus grauem in morbum delap&longs;us itinere cogitur <lb/>de&longs;i&longs;tere: Mediolanum proinde diuertit, vbi à S. <!-- REMOVE S-->Carolo <lb/>Borromæo & benignè exceptus, & tamdiu detentus do­<lb/>nec valetudinem recuperaret. </s> | <s id="id.000068">Vix viæ &longs;e dederant <lb/>cum Baldus grauem in morbum delap&longs;us itinere cogitur <lb/>de&longs;i&longs;tere: Mediolanum proinde diuertit, vbi à S. <!-- REMOVE S-->Carolo <lb/>Borromæo & benignè exceptus, & tamdiu detentus do­<lb/>nec valetudinem recuperaret. </s> |
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| <s id="id.000069">Gua&longs;tallam po&longs;tea &longs;e re­<lb/>cepit, vbi cum ab&longs;ente Domino liberiori otio fruerctur, <lb/>libros &longs;ex de Aula eruditi&longs;&longs;imos methodo analytica con­<lb/>&longs;crip&longs;it. </s> | <s id="id.000069">Gua&longs;tallam po&longs;tea &longs;e re­<lb/>cepit, vbi cum ab&longs;ente Domino liberiori otio frueretur, <lb/>libros &longs;ex de Aula eruditi&longs;&longs;imos methodo analytica con­<lb/>&longs;crip&longs;it. </s> |
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| <s id="id.000070">alios non commemoro, quod cum otium erit, o­<lb/>mnium &longs;yllabum dabo. </s> | <s id="id.000070">alios non commemoro, quod cum otium erit, o­<lb/>mnium &longs;yllabum dabo. </s> |
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| <s id="id.000082">Compo&longs;uit & Dictionarium <lb/>Arabicum. <!-- KEEP S--></s> | <s id="id.000082">Compo&longs;uit & Dictionarium <lb/>Arabicum. <!-- KEEP S--></s> |
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| <s id="id.000083">atque cum beati&longs;&longs;imam illam vbertatem in­<lb/>genij a&longs;&longs;idue diffundi nece&longs;&longs;e e&longs;&longs;et, anno 1603. orbem vni­<lb/>uer&longs;um de&longs;eribere aggre&longs;&longs;us fuit; atque ita quidem, vt <lb/>tam quæ ad Hi&longs;toriam, quam quæ ad Geographiam per­<lb/>tinerent complecteretur: Neque illu&longs;trare &longs;olum voluit <lb/>quæ nouerunt antiqui, quemadmodum vi&longs;um Ortelio, <lb/>&longs;ed vel oppidula omnia & pagos, de quibus aliquain po­<lb/>&longs;tremis &longs;criptoribus mentio. </s> | <s id="id.000083">atque cum beati&longs;&longs;imam illam vbertatem in­<lb/>genij a&longs;&longs;idue diffundi nece&longs;&longs;e e&longs;&longs;et, anno 1603. orbem vni­<lb/>uer&longs;um de&longs;cribere aggre&longs;&longs;us fuit; atque ita quidem, vt <lb/>tam quæ ad Hi&longs;toriam, quam quæ ad Geographiam per­<lb/>tinerent complecteretur: Neque illu&longs;trare &longs;olum voluit <lb/>quæ nouerunt antiqui, quemadmodum vi&longs;um Ortelio, <lb/>&longs;ed vel oppidula omnia & pagos, de quibus aliqua in po­<lb/>&longs;tremis &longs;criptoribus mentio. </s> |
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| <s id="id.000084">& profecto totum opus ad <lb/>vmbilicum perduxit: non dige&longs;&longs;it tamen vniuer&longs;um. </s> | <s id="id.000084">& profecto totum opus ad <lb/>vmbilicum perduxit: non dige&longs;&longs;it tamen vniuer&longs;um. </s> |
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| <s id="id.000089">Membrorum ei fuit decens habitudo, & <lb/>compactum corpus. </s> | <s id="id.000089">Membrorum ei fuit decens habitudo, & <lb/>compactum corpus. </s> |
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| <s id="id.000090">Diebus fe&longs;tis omnlbus &longs;acrum facie­<lb/>bat, ieiunabat bis in hebdomada, eleemo&longs;yni&longs;que paupe­<lb/>res &longs;ubleuabat. </s> | <s id="id.000090">Diebus fe&longs;tis omnibus &longs;acrum facie­<lb/>bat, ieiunabat bis in hebdomada, eleemo&longs;yni&longs;que paupe­<lb/>res &longs;ubleuabat. </s> |
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| <s id="id.000091">In&longs;tudijs &longs;ica&longs;&longs;iduus fuit, vt &longs;æpe & legeret <lb/>& comederet. </s> | <s id="id.000091">In&longs;tudijs &longs;ica&longs;&longs;iduus fuit, vt &longs;æpe & legeret <lb/>& comederet. </s> |
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| <s id="id.000096">Sermo modicus ei fuit, <lb/>itemque cultus. </s> | <s id="id.000096">Sermo modicus ei fuit, <lb/>itemque cultus. </s> |
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| <s id="id.000097">Nullos vnquam honores petijt, qui à <lb/>Clem. <!-- KEEP S--></s> | <s id="id.000097">Nullos vnquam honores petijt, qui à <lb/>Clem. 8. ampli&longs;&longs;imi promi&longs;&longs;i fuerant; nullum emolumen­<lb/>tum quæ&longs;iuit &longs;uo centu contentus. </s> |
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| <s id="id.000098">8. ampli&longs;&longs;imi promi&longs;&longs;i fuerant; nullum emolumen­<lb/>tum quæ&longs;iuit &longs;uo ceniu contentus. </s> | |
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| <s id="id.000099">facile parcendum e&longs;&longs;e <lb/>dicebat, ijs maxime qui in re leui impegi&longs;&longs;ent, quoniam &longs;i <lb/>quos cen&longs;emus optimos, nudos con&longs;piceremus, nullum <lb/>eorum non iudicaremus multis dignum verberibus. </s> | <s id="id.000099">facile parcendum e&longs;&longs;e <lb/>dicebat, ijs maxime qui in re leui impegi&longs;&longs;ent, quoniam &longs;i <lb/>quos cen&longs;emus optimos, nudos con&longs;piceremus, nullum <lb/>eorum non iudicaremus multis dignum verberibus. </s> |
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| <s id="id.000119">De Humanitate Dialogus qui in&longs;cribitur Go&longs;elinus. </s></p><p type="main"> | <s id="id.000119">De Humanitate Dialogus qui in&longs;cribitur Go&longs;elinus. </s></p><p type="main"> |
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| <s id="id.000120">Compatatio Vitæ Mona&longs;ticæ cum &longs;eculari. </s></p><p type="main"> | <s id="id.000120">Comparatio Vitæ Mona&longs;ticæ cum &longs;eculari. </s></p><p type="main"> |
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| <s id="id.000121">De Aula libri &longs;ex. </s></p><p type="main"> | <s id="id.000121">De Aula libri &longs;ex. </s></p><p type="main"> |
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| <s id="id.000127">De vniuer&longs;ali Diluuio poemation. </s></p><p type="main"> | <s id="id.000127">De vniuer&longs;ali Diluuio poemation. </s></p><p type="main"> |
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| <s id="id.000128">Nouæ Gnomonices lib. | <s id="id.000128">Nouæ Gnomonices lib. quin que. </s></p><p type="main"> |
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| quin que. </s></p><p type="main"> | |
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| <s id="id.000129">Hieremiæ Threnos vertit, & ex Heb. <!-- REMOVE S-->fonte annotat. </s> | <s id="id.000129">Hieremiæ Threnos vertit, & ex Heb. <!-- REMOVE S-->fonte annotat. </s> |
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| <s id="id.000130">ad­<lb/>iecit. </s></p><p type="main"> | <s id="id.000130">ad­<lb/>iecit. </s></p><p type="main"> |
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| <s id="id.000131">Poemation in&longs;eriptum, Deiphobe, quod &longs;erip&longs;it æmula­<lb/>tus Lycophonem in Ca&longs;&longs;andra. </s></p><p type="main"> | <s id="id.000131">Poemation in&longs;eriptum, Deiphobe, quod &longs;crip&longs;it æmula­<lb/>tus Lycophonem in Ca&longs;&longs;andra. </s></p><p type="main"> |
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| <s id="id.000132">Scala cœle&longs;tis.1.Sermones pij & carmina. </s></p><p type="main"> | <s id="id.000132">Scala cœle&longs;tis.1.Sermones pij & carmina. </s></p><p type="main"> |
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| <s id="id.000145">Vniuer&longs;i orbis geographica & Hi&longs;torica de&longs;criptio con­<lb/>texta ex &longs;eptingentis & eo amplius &longs;criptoribus. </s></p><p type="main"> | <s id="id.000145">Vniuer&longs;i orbis geographica & Hi&longs;torica de&longs;criptio con­<lb/>texta ex &longs;eptingentis & eo amplius &longs;criptoribus. </s></p><p type="main"> |
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| <s id="id.000146">Fede ici Vrbini Ducis Vita. <!-- KEEP S--></s></p><p type="main"> | <s id="id.000146">Federici Vrbini Ducis Vita. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000147">Guidi Vbaldi Vibini Ducis Vita. <!-- KEEP S--></s></p><p type="main"> | <s id="id.000147">Guidi Vbaldi Vibini Ducis Vita. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000152">Pro Procopio contra Flauium Blondum. <!-- KEEP S--></s></p><p type="main"> | <s id="id.000152">Pro Procopio contra Flauium Blondum. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000153">Horographium vniucr&longs;ale. </s></p><p type="main"> | <s id="id.000153">Horographium vniuer&longs;ale. </s></p><p type="main"> |
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| <s id="id.000154">Epigrammata alia. </s></p><p type="main"> | <s id="id.000154">Epigrammata alia. </s></p><p type="main"> |
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| <s id="id.000163">MECHANICE, facultas quædam e&longs;t, quæ <lb/>naturalimateriâ, Geometricisque; demon­<lb/>&longs;trationibus v&longs;a, ex centrobaricâ, & <expan abbr="eorū">eorum</expan> <lb/>quæ ad vectem & libram rediguntur, &longs;pe­<lb/>culatione; humanæ con&longs;ulens nece&longs;&longs;itati, <lb/>commoditatiqueue, &longs;uapte vi, Naturam i­<lb/>p&longs;am vel &longs;ecundans, vel &longs;uperans, varia, caqueue mirabilia <lb/>operatur. </s> | <s id="id.000163">MECHANICE, facultas quædam e&longs;t, quæ <lb/>naturalimateriâ, Geometricisque; demon­<lb/>&longs;trationibus v&longs;a, ex centrobaricâ, & <expan abbr="eorū">eorum</expan> <lb/>quæ ad vectem & libram rediguntur, &longs;pe­<lb/>culatione; humanæ con&longs;ulens nece&longs;&longs;itati, <lb/>commoditatiqueue, &longs;uapte vi, Naturam i­<lb/>p&longs;am vel &longs;ecundans, vel &longs;uperans, varia, caqueue mirabilia <lb/>operatur. </s> |
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| <s id="id.000164">Hac diffinitione de&longs;criptionéue brcuiter ca fe­<lb/>rè omnia complexi &longs;umus, quæ fu&longs;i&longs;&longs;imè ab Ari&longs;totele, <lb/>Pappo, Guido Vbaldo, & alijs hac de re tradita fuêre. </s></p></subchap1> | <s id="id.000164">Hac diffinitione de&longs;criptionéue breuiter ca fe­<lb/>rè omnia complexi &longs;umus, quæ fu&longs;i&longs;&longs;imè ab Ari&longs;totele, <lb/>Pappo, Guido Vbaldo, & alijs hac de re tradita fuêre. </s></p></subchap1> |
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| <subchap1> | <subchap1> |
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| <s id="id.000167">Graue duplex, Naturâ, Violentiâ. </s></p><p type="main"> | <s id="id.000167">Graue duplex, Naturâ, Violentiâ. </s></p><p type="main"> |
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| <s id="id.000168">Graue Naturâ dicitur, quod in&longs;ita propen&longs;ione in <lb/>centrum mundifertnr. </s> | <s id="id.000168">Graue Naturâ dicitur, quod in&longs;ita propen&longs;ione in <lb/>centrum mundi fertur. </s> |
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| <s id="id.000169">Graue autem Violentiâ, quod im­<lb/>pre&longs;&longs;o extrin&longs;ecus pondere ab impellente pellitur. </s></p><p type="main"> | <s id="id.000169">Graue autem Violentiâ, quod im­<lb/>pre&longs;&longs;o extrin&longs;ecus pondere ab impellente pellitur. </s></p><p type="main"> |
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| <s id="id.000170">Leue contrà, quòd Naturâ à centro fertur. </s></p><p type="main"> | <s id="id.000170">Leue contrà, quòd Naturâ à centro fertur. </s></p><p type="main"> |
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| <s id="id.000171">Gæterùm quicquid graue e&longs;t, &longs;ecundum punctum <lb/>e&longs;t, quod Grauitatis centrum dicitur, & hoc duplex, vt <lb/>duplex e&longs;t grauitas, Naturæ, Violentiæ. <!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.021.jpg"/><p type="main"> | <s id="id.000171">Cæterùm quicquid graue e&longs;t, &longs;ecundum punctum <lb/>e&longs;t, quod Grauitatis centrum dicitur, & hoc duplex, vt <lb/>duplex e&longs;t grauitas, Naturæ, Violentiæ. <!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.021.jpg"/><p type="main"> |
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| <s id="id.000172">Grauitatis centrum in triplici magnitudine con&longs;i­<lb/>deraripote&longs;t, lineari, planà, &longs;olidâ. </s></p><p type="main"> | <s id="id.000172">Grauitatis centrum in triplici magnitudine con&longs;i­<lb/>deraripote&longs;t, lineari, planà, &longs;olidâ. </s></p><p type="main"> |
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| <s id="id.000173">De centro grauitatis linearum nemo &longs;crip&longs;it, &longs;impli­<lb/>ci&longs;&longs;imi enim illud e&longs;t contemplationis. </s></p><p type="main"> | <s id="id.000173">De centro grauitatis linearum nemo &longs;crip&longs;it, &longs;impli­<lb/>ci&longs;&longs;imi enim illud e&longs;t contemplationis. </s></p><p type="main"> |
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| <s id="id.000174">De centro grauitatis linearum egregiè tractauit Ar­<lb/>chimedes in libro Æ queponderantium, & de quadratu­<lb/>ra Parabole, tum in co quem de his quæ vehuntur in­<lb/>&longs;crip&longs;it. </s></p><p type="main"> | <s id="id.000174">De centro grauitatis linearum egregiè tractauit Ar­<lb/>chimedes in libro Æqueponderantium, & de quadratu­<lb/>ra Parabole, tum in eo quem de his quæ vehuntur in­<lb/>&longs;crip&longs;it. </s></p><p type="main"> |
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| <s id="id.000175">De centro grauitatis &longs;olidorum ipíemet olim &longs;cri­<lb/>p&longs;erat Archimedes, &longs;ed ea quæ protulit, temporis iniuriâ <lb/>deperdita, fuâ diligentiâ re&longs;tituit Iedericus Commandi­<lb/>nus. </s></p><p type="main"> | <s id="id.000175">De centro grauitatis &longs;olidorum ip&longs;emet olim &longs;cri­<lb/>p&longs;erat Archimedes, &longs;ed ea quæ protulit, temporis iniuriâ <lb/>deperdita, &longs;uâ diligentiâ re&longs;tituit Federicus Commandi­<lb/>nus. </s></p><p type="main"> |
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| <s id="id.000176">E&longs;&longs;e autem & Leuitatis centrum in rerum natura, <lb/>palam e&longs;t. </s> | <s id="id.000176">E&longs;&longs;e autem & Leuitatis centrum in rerum natura, <lb/>palam e&longs;t. </s> |
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| <s id="id.000177">Punctum enim illud e&longs;t, &longs;ecundum quod lcuia <lb/>rectà à centro &longs;ur&longs;um feruntur. </s> | <s id="id.000177">Punctum enim illud e&longs;t, &longs;ecundum quod leuia <lb/>rectà à centro &longs;ur&longs;um feruntur. </s> |
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| <s id="id.000178">Huius autem non memi­<lb/>nêre Mechanici, propterea quod aut nihil, aut parum ad <lb/>eorum rem faciat. </s></p><p type="main"> | <s id="id.000178">Huius autem non memi­<lb/>nêre Mechanici, propterea quod aut nihil, aut parum ad <lb/>eorum rem faciat. </s></p><p type="main"> |
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| <s id="id.000196">Vbi verò peruenit in C, <lb/>violentiâ ce&longs;&longs;ante, naturâ verò manente, rectà deor&longs;um <lb/>fertur DCD. <!-- KEEP S--></s></p><p type="main"> | <s id="id.000196">Vbi verò peruenit in C, <lb/>violentiâ ce&longs;&longs;ante, naturâ verò manente, rectà deor&longs;um <lb/>fertur DCD. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000197">Cæteiùm hæc centra, hiqueue motus, naturalis nem­<lb/>pe, & violentus diuer&longs;imode &longs;e habent adinuicem. </s> | <s id="id.000197">Cæterùm hæc centra, hiqueue motus, naturalis nem­<lb/>pe, & violentus diuer&longs;imode &longs;e habent adinuicem. </s> |
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| <s id="id.000198">Sie­<lb/>nim graue corpus externâ vi adhibita, centrum mundi <lb/>ver&longs;us impellatur, adiuuabunt &longs;e inuicem Natura, Vio­<lb/>lentia, Si autem contra, altera alteri re&longs;i&longs;ter, in motibus <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.024.jpg"/>autem ad latus, eo magis pugnabunt, quo magis ab infe­<lb/>rioribus ad &longs;uperiora fiet motus. </s></p> | <s id="id.000198">Si e­<lb/>nim graue corpus externâ vi adhibita, centrum mundi <lb/>ver&longs;us impellatur, adiuuabunt &longs;e inuicem Natura, Vio­<lb/>lentia, Si autem contra, altera alteri re&longs;i&longs;tet, in motibus <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.024.jpg"/>autem ad latus, eo magis pugnabunt, quo magis ab infe­<lb/>rioribus ad &longs;uperiora fiet motus. </s></p> |
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| </subchap1><subchap1> | </subchap1><subchap1> |
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| <s id="id.000199"><emph type="italics"/>Mechanices præcipua in&longs;trumenta.<emph.end type="italics"/></s></p><p type="main"> | <s id="id.000199"><emph type="italics"/>Mechanices præcipua in&longs;trumenta.<emph.end type="italics"/></s></p><p type="main"> |
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| <s id="id.000200">Hic ira con&longs;titutis dicimus, in&longs;trumenta, quibusad <lb/>varias operationes Mechanici vtuntur, e&longs;&longs;e inter &longs;e qui­<lb/>dem diuer&longs;a, multiplicia, & &longs;i varietatem &longs;pectes, penè in­<lb/>numerabilia; quod quamuis verum&longs;it, ea omnia Ari&longs;tote­<lb/>les ad vectem re ducit, & libram: quod etiam G. <!-- REMOVE S-->Vbaldus <lb/>in libris Mechanicoiumfecit. </s> | <s id="id.000200">Hic ira con&longs;titutis dicimus, in&longs;trumenta, quibus ad <lb/>varias operationes Mechanici vtuntur, e&longs;&longs;e inter &longs;e qui­<lb/>dem diuer&longs;a, multiplicia, & &longs;i varietatem &longs;pectes, penè in­<lb/>numerabilia; quod quamuis verum &longs;it, ea omnia Ari&longs;tote­<lb/>les ad vectem re ducit, & libram: quod etiam G. <!-- REMOVE S-->Vbaldus <lb/>in libris Mechanicorum fecit. </s> |
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| <s id="id.000209">Cochlea vero E. <!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.025.jpg"/><figure id="id.007.00.025.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.025.1.jpg"></figure><p type="main"> | <s id="id.000209">Cochlea vero E. <!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.025.jpg"/><figure id="id.007.00.025.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.025.1.jpg"></figure><p type="main"> |
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| <s id="id.000210">Porro, Cuneum ad libram reducere conatur Ari­<lb/>&longs;toteles, quod facit & G. Vbaldus, qui cò refert & Co­<lb/>chleam, quippe quod nihil aliud &longs;it Cochlea, quàm Cu­<lb/>neus Cylindro inuolutus. </s> | <s id="id.000210">Porro, Cuneum ad libram reducere conatur Ari­<lb/>&longs;toteles, quod facit & G. Vbaldus, qui eò refert & Co­<lb/>chleam, quippe quod nihil aliud &longs;it Cochlea, quàm Cu­<lb/>neus Cylindro inuolutus. </s> |
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| <s id="id.000211">Nos autem duas tantùm Po­<lb/>tentias ad vectem reduci po&longs;&longs;e arbitramur, Trochleam <lb/>nempe, & Axem in Peritrochio. <!-- KEEP S--></s> | <s id="id.000211">Nos autem duas tantùm Po­<lb/>tentias ad vectem reduci po&longs;&longs;e arbitramur, Trochleam <lb/>nempe, & Axem in Peritrochio. <!-- KEEP S--></s> |
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| <s id="id.000215">Ari&longs;toteles in ip&longs;o Mechanicorum ingre&longs;&longs;uita &longs;cri­<lb/>bit, Mirum videri ab exigua virtute magnum pondus mo-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.026.jpg"/>ueri, addito nimirum ponderi pondere, &longs;iquidem & vectis <lb/>e&longs;t pondus. </s> | <s id="id.000215">Ari&longs;toteles in ip&longs;o Mechanicorum ingre&longs;&longs;uita &longs;cri­<lb/>bit, Mirum videri ab exigua virtute magnum pondus mo-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.026.jpg"/>ueri, addito nimirum ponderi pondere, &longs;iquidem & vectis <lb/>e&longs;t pondus. </s> |
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| <s id="id.000216">Duplex ergo illi admiratio, &longs;cilicet quòd exi­<lb/>gua potentia moucat ingens pondus, idqueue etiam addito <lb/>vectis ip&longs;ius pondere, fiat. </s> | <s id="id.000216">Duplex ergo illi admiratio, &longs;cilicet quòd exi­<lb/>gua potentia moueat ingens pondus, idqueue etiam addito <lb/>vectis ip&longs;ius pondere, fiat. </s> |
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| <s id="id.000217">Hoc &longs;ecundum adieci&longs;&longs;e vide­<lb/>tur, amplificationis alicuius gratiâ. </s> | <s id="id.000217">Hoc &longs;ecundum adieci&longs;&longs;e vide­<lb/>tur, amplificationis alicuius gratiâ. </s> |
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| <s id="id.000218">Erenim quatenus <lb/>ad rem pertinet, &longs;i mouendis ponderibus vectis ip&longs;ius <lb/>pondus compares, nullius ferè e&longs;&longs;e momenti proculdu­<lb/>bio affirmaueris. </s> | <s id="id.000218">Etenim quatenus <lb/>ad rem pertinet, &longs;i mouendis ponderibus vectis ip&longs;ius <lb/>pondus compares, nullius ferè e&longs;&longs;e momenti procul du­<lb/>bio affirmaueris. </s> |
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| <s id="id.000219">Sed & illud quoque notandum, aliquan­<lb/>do vectis pondus mouenti auxilium ferre, quod fit vbi <lb/>fulcimento inter potentiam mouentem, & pondus ip&longs;um <lb/>collocato, vectis pars quæ à fulcimento ad potentiam e&longs;t, <lb/>premitur. </s> | <s id="id.000219">Sed & illud quoque notandum, aliquan­<lb/>do vectis pondus mouenti auxilium ferre, quod fit vbi <lb/>fulcimento inter potentiam mouentem, & pondus ip&longs;um <lb/>collocato, vectis pars quæ à fulcimento ad potentiam e&longs;t, <lb/>premitur. </s> |
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| <s id="id.000221">Contra verò accidit, cum pondus i­<lb/>p&longs;um inter fulcimentum e&longs;t & potentiam vel potentia i­<lb/>p&longs;a inter fulcimentum & pondus. </s> | <s id="id.000221">Contra verò accidit, cum pondus i­<lb/>p&longs;um inter fulcimentum e&longs;t & potentiam vel potentia i­<lb/>p&longs;a inter fulcimentum & pondus. </s> |
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| <s id="id.000222">tunc cnim vectis vnâ <lb/>cum pondere attollitur. </s> | <s id="id.000222">tunc enim vectis vnâ <lb/>cum pondere attollitur. </s> |
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| <s id="id.000223">quæ licet vera &longs;int, non tamen in­<lb/>de &longs;e quitur, vectis pondus, quicquam quod curandum &longs;it, <lb/>in operatione efficere, aut impedire. </s></p><p type="main"> | <s id="id.000223">quæ licet vera &longs;int, non tamen in­<lb/>de &longs;e quitur, vectis pondus, quicquam quod curandum &longs;it, <lb/>in operatione efficere, aut impedire. </s></p><p type="main"> |
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| <s id="id.000232">Secundam, quòd contraria in eius circumferentia <lb/>inueniantur, quippe quæ cum vnica linea &longs;it, concaua &longs;i­<lb/>mul e&longs;t & conuexa. </s> | <s id="id.000232">Secundam, quòd contraria in eius circumferentia <lb/>inueniantur, quippe quæ cum vnica linea &longs;it, concaua &longs;i­<lb/>mul e&longs;t & conuexa. </s> |
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| <s id="id.000233">Tettiam, quod contrarijs feratur mo­<lb/>tionibus, antror&longs;um nimirum, retror&longs;um, &longs;ur&longs;um, atque <lb/>deor&longs;um. </s> | <s id="id.000233">Tertiam, quod contrarijs feratur mo­<lb/>tionibus, antror&longs;um nimirum, retror&longs;um, &longs;ur&longs;um, atque <lb/>deor&longs;um. </s> |
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| <s id="id.000234">Quartam, quod vnicâ exi&longs;tente &longs;emidiametro, <lb/>nullum in ca punctum &longs;umi po&longs;&longs;it, æqualis alteri, in latio­<lb/>ne, velocitatis. </s> | <s id="id.000234">Quartam, quod vnicâ exi&longs;tente &longs;emidiametro, <lb/>nullum in ca punctum &longs;umi po&longs;&longs;it, æqualis alteri, in latio­<lb/>ne, velocitatis. </s> |
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| <s id="id.000240">Punctum autem, quod &longs;tat, &longs;emidia­<lb/>metri pars nulla e&longs;t. </s> | <s id="id.000240">Punctum autem, quod &longs;tat, &longs;emidia­<lb/>metri pars nulla e&longs;t. </s> |
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| <s id="id.000241">Et &longs;anè cur moto <lb/><expan abbr="&longs;emidiamētro">&longs;emidiamentro</expan> fiat circulus, non ideo accidit, quod <expan abbr="alterū">alterum</expan> <lb/>extremum &longs;tet, alterum verò moueatur:led ideo quòd &longs;e­<lb/>midiameter perpetuò eandem &longs;eruct longitudinem. </s> | <s id="id.000241">Et &longs;anè cur moto <lb/><expan abbr="&longs;emidiamētro">&longs;emidiametro</expan> fiat circulus, non ideo accidit, quod <expan abbr="alterū">alterum</expan> <lb/>extremum &longs;tet, alterum verò moueatur:sed ideo quòd &longs;e­<lb/>midiameter perpetuò eandem &longs;eruet longitudinem. </s> |
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| <s id="id.000242">Elli­<lb/>p&longs;is &longs;anè centrum habet, &longs;ed ab eo ad circumferentiam <lb/>quatuor tantùm &longs;emidiametri quomodolibet &longs;umpti du­<lb/>cuntur æ quales. </s> | <s id="id.000242">Elli­<lb/>p&longs;is &longs;anè centrum habet, &longs;ed ab eo ad circumferentiam <lb/>quatuor tantùm &longs;emidiametri quomodolibet &longs;umpti du­<lb/>cuntur æ quales. </s> |
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| <s id="id.000243">Si quis igitur &longs;emidiametrum daret pro­<lb/>portione cre&longs;centem & decre&longs;centem, &longs;tante altero ex­<lb/>tremoru<gap/> Ellip&longs;is de&longs;criberetur. </s> | <s id="id.000243">Si quis igitur &longs;emidiametrum daret pro­<lb/>portione cre&longs;centem & decre&longs;centem, &longs;tante altero ex­<lb/>tremorum Ellip&longs;is de&longs;criberetur. </s> |
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| <s id="id.000244">Præterea & &longs;piralis li­<lb/>nea, quæ mixta e&longs;t, altero &longs;emidiametri extremo manen­<lb/>te, altero vero moto producitur. </s> | <s id="id.000244">Præterea & &longs;piralis li­<lb/>nea, quæ mixta e&longs;t, altero &longs;emidiametri extremo manen­<lb/>te, altero vero moto producitur. </s> |
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| <s id="id.000245">Legem itaque circulo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.028.jpg"/>prælcribit, non quidem quòd hæc extremitas &longs;ter, illa ve­<lb/>rò moueatur, &longs;ed quod &longs;ua circulatione &longs;em per &longs;emidia­<lb/>meter eandem &longs;eruet longitudinem, quod vel ex ip&longs;a cir­<lb/>culi definitionc colligitur. </s></p><p type="main"> | <s id="id.000245">Legem itaque circulo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.028.jpg"/>præ&longs;cribit, non quidem quòd hæc extremitas &longs;ter, illa ve­<lb/>rò moueatur, &longs;ed quod &longs;ua circulatione &longs;emper &longs;emidia­<lb/>meter eandem &longs;eruet longitudinem, quod vel ex ip&longs;a cir­<lb/>culi definitione colligitur. </s></p><p type="main"> |
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| <s id="id.000246">Ad &longs;ecundum miraculum, &longs;cilicet, quòd in circulo <lb/>circum ferentia, quæ vacua linea e&longs;t, concaua &longs;imul&longs;it, & <lb/>conuexa. </s> | <s id="id.000246">Ad &longs;ecundum miraculum, &longs;cilicet, quòd in circulo <lb/>circum ferentia, quæ vacua linea e&longs;t, concaua &longs;imul&longs;it, & <lb/>conuexa. </s> |
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| <s id="id.000247">Diceret qui&longs;piam id, &longs;i modò mirabile e&longs;t non <lb/>circulari tantum, &longs;ed cui ibet curuæ lineæ primo compe­<lb/>tere, etenim & Elhp&longs;is & Hyperbole, & Parabolc, & &longs;pi­<lb/>ra, tum Cy&longs;&longs;ois, Conchois, & infinitæ aliæ irregulares <lb/>concauæ &longs;imul &longs;unt & conuexæ. </s> | <s id="id.000247">Diceret qui&longs;piam id, &longs;i modò mirabile e&longs;t non <lb/>circulari tantum, &longs;ed cuilibet curuæ lineæ primo compe­<lb/>tere, etenim & Elhp&longs;is & Hyperbole, & Parabolc, & &longs;pi­<lb/>ra, tum Cy&longs;&longs;ois, Conchois, & infinitæ aliæ irregulares <lb/>concauæ &longs;imul &longs;unt & conuexæ. </s> |
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| <s id="id.000248">Sed & hæcin &longs;uperficie­<lb/>bus quoque de&longs;iderantur. </s></p><p type="main"> | <s id="id.000248">Sed & hæcin &longs;uperficie­<lb/>bus quoque de&longs;iderantur. </s></p><p type="main"> |
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| <s id="id.000251">E&longs;to enim circulus ABCD, <lb/>circa centrum E; ponamus ro­<lb/>tari, & A ver&longs;us B, exempli gra­<lb/>tiâ, antror&longs;um, mouebitur <expan abbr="autē">autem</expan> <lb/>& B ver&longs;us C, & C ver&longs;us D, tum <lb/>D ver&longs;us A. <!-- KEEP S--></s> | <s id="id.000251">E&longs;to enim circulus ABCD, <lb/>circa centrum E; ponamus ro­<lb/>tari, & A ver&longs;us B, exempli gra­<lb/>tiâ, antror&longs;um, mouebitur <expan abbr="autē">autem</expan> <lb/>& B ver&longs;us C, & C ver&longs;us D, tum <lb/>D ver&longs;us A. <!-- KEEP S--></s> |
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| <s id="id.000252">Non puto <expan abbr="quenquã">quenquam</expan> <lb/>dicturum, circulum hunc an­<lb/>tror&longs;um codem tempore, & re­<lb/>tror&longs;um ferri nec &longs;ur&longs;um aut de­<lb/>or&longs;um, &longs;i enim qui&longs;piam per eius circuli circumferentiani <lb/>ambularet, is certè centrum ip&longs;um &longs;emper ad dexteram <lb/>haberet, vel ad &longs;ini&longs;tram, &longs;i ad dexteram, antror&longs;um ibit, &longs;i <lb/>ad &longs;ini&longs;tram, tetror&longs;um. </s> | <s id="id.000252">Non puto <expan abbr="quenquã">quenquam</expan> <lb/>dicturum, circulum hunc an­<lb/>tror&longs;um eodem tempore, & re­<lb/>tror&longs;um ferri nec &longs;ur&longs;um aut de­<lb/>or&longs;um, &longs;i enim qui&longs;piam per eius circuli circumferentiam <lb/>ambularet, is certè centrum ip&longs;um &longs;emper ad dexteram <lb/>haberet, vel ad &longs;ini&longs;tram, &longs;i ad dexteram, antror&longs;um ibit, &longs;i <lb/>ad &longs;ini&longs;tram, tetror&longs;um. </s> |
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| <s id="id.000253">Sed nec &longs;ur&longs;um vel deor&longs;um, e&longs;t <lb/>manife&longs;tum. </s> | <s id="id.000253">Sed nec &longs;ur&longs;um vel deor&longs;um, e&longs;t <lb/>manife&longs;tum. </s> |
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| <s id="id.000254">Nihil autem prohibet eundem motum va­<lb/>rio re&longs;pectu contrarium dici po&longs;&longs;e, id tamen profectò fie­<lb/>rinequaquam pote&longs;t, nempe A moueriver&longs;us B, hoc e&longs;t, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.029.jpg"/>antro r&longs;um, & eandem codem tempore ver&longs;us B, id e&longs;t, re­<lb/>tror&longs;um; repugnat enim naturæ. </s></p><p type="main"> | <s id="id.000254">Nihil autem prohibet eundem motum va­<lb/>rio re&longs;pectu contrarium dici po&longs;&longs;e, id tamen profectò fie­<lb/>ri nequaquam pote&longs;t, nempe A moueri ver&longs;us B, hoc e&longs;t, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.029.jpg"/>antror&longs;um, & eandem eodem tempore ver&longs;us B, id e&longs;t, re­<lb/>tror&longs;um; repugnat enim naturæ. </s></p><p type="main"> |
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| <s id="id.000255">De quarto circuli miraculo, ibi erit nobis &longs;ermo, vbi <lb/>ca perpenderimus primò, quæ Philo&longs;ophus de Circuli <lb/>productione di&longs;&longs;erens in medium profert. </s> | <s id="id.000255">De quarto circuli miraculo, ibi erit nobis &longs;ermo, vbi <lb/>ca perpenderimus primò, quæ Philo&longs;ophus de Circuli <lb/>productione di&longs;&longs;erens in medium profert. </s> |
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| 24. </s></p><p type="main"> | 24. </s></p><p type="main"> |
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| <s id="id.000265">His ita demon&longs;tratis hac vti videtur Philo&longs;ophus <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.030.jpg"/>argumentatione: Si mixtus motus proportione &longs;emotâ, <lb/>rectam producir, &longs;i nun quam &longs;emota, efficiet circulum; &longs;i <lb/>enim modo &longs;eruaretur, modo non, partim recta partim <lb/>non recta produceretur. </s> | <s id="id.000265">His ita demon&longs;tratis hac vti videtur Philo&longs;ophus <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.030.jpg"/>argumentatione: Si mixtus motus proportione &longs;emotâ, <lb/>rectam producit, &longs;i nunquam &longs;emota, efficiet circulum; &longs;i <lb/>enim modo &longs;eruaretur, modo non, partim recta partim <lb/>non recta produceretur. </s> |
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| <s id="id.000266">Ingenio&longs;a quidem argumenta­<lb/>tio, ni vitium contineret. </s> | <s id="id.000266">Ingenio&longs;a quidem argumenta­<lb/>tio, ni vitium contineret. </s> |
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| <s id="id.000267">non enim mixtus motus, qui <lb/>nun quam &longs;eruatâ proportione fit, &longs;emper ci, culum pro­<lb/>ducit, &longs;ed & Elli &longs;im pote&longs;t, & quamlibet aliam lineam, <lb/>cuius nulla pars &longs;it recta. </s> | <s id="id.000267">non enim mixtus motus, qui <lb/>nun quam &longs;eruatâ proportione fit, &longs;emper ci, culum pro­<lb/>ducit, &longs;ed & Elli &longs;im pote&longs;t, & quamlibet aliam lineam, <lb/>cuius nulla pars &longs;it recta. </s> |
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| <s id="id.000268">Hanc difficultatem vidit Pico­<lb/>lomineus in &longs;ua Paraphra&longs;i, & eam &longs;oluere conatus e&longs;t, <lb/>&longs;ed quàm bene, aliorum e&longs;to <gap/>dicium. </s> | <s id="id.000268">Hanc difficultatem vidit Pico­<lb/>lomineus in &longs;ua Paraphra&longs;i, & eam &longs;oluere conatus e&longs;t, <lb/>&longs;ed quàm bene, aliorum e&longs;to iudicium. </s> |
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| <s id="id.000269">Cæterùm fal&longs;um <lb/>e&longs;t, a&longs;&longs;erere circulum ex mixto motu nun quam &longs;eruatâ <lb/>proportione produci. </s> | <s id="id.000269">Cæterùm fal&longs;um <lb/>e&longs;t, a&longs;&longs;erere circulum ex mixto motu nun quam &longs;eruatâ <lb/>proportione produci. </s> |
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| <s id="id.000274">Sit <lb/>autem, cum AC &longs;uo motu peruenerit <lb/>in D, punctum A, &longs;imiliter &longs;uo motu per eam latum perue­<lb/>nitle in E erit ergo ex mixto motu, non quidem in D, nec <lb/>in E, &longs;ed in F, eritque punctum F in circum ferentia circu­<lb/>li, cuius e&longs;t diameter ip&longs;a linea AB, quod quidem demon­<lb/>&longs;tratur ex conuer&longs;a propo&longs;. </s> | <s id="id.000274">Sit <lb/>autem, cum AC &longs;uo motu peruenerit <lb/>in D, punctum A, &longs;imiliter &longs;uo motu per eam latum perue­<lb/>nitle in E erit ergo ex mixto motu, non quidem in D, nec <lb/>in E, &longs;ed in F, eritque punctum F in circum ferentia circu­<lb/>li, cuius e&longs;t diameter ip&longs;a linea AB, quod quidem demon­<lb/>&longs;tratur ex conuer&longs;a propo&longs;. </s> |
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| <s id="id.000275">13. lib. | <s id="id.000275">13. lib. 6. Elem. <!-- KEEP S--></s> |
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| 6. Elem. <!-- KEEP S--></s> | |
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| <s id="id.000276">E&longs;t enim AE <lb/>hoce&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>& DB. <!-- KEEP S--></s> | <s id="id.000276">E&longs;t enim AE <lb/>hoce&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>& DB. <!-- KEEP S--></s> |
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| <s id="id.000280">Ait autem; &longs;i duobus ab eadem potentia latis hoc <lb/>quidem plus repellatur, illud verò minus, æquum e&longs;t tar­<lb/>diùs id moueri quod plus repellitur, eo quod minus. </s> | <s id="id.000280">Ait autem; &longs;i duobus ab eadem potentia latis hoc <lb/>quidem plus repellatur, illud verò minus, æquum e&longs;t tar­<lb/>diùs id moueri quod plus repellitur, eo quod minus. </s> |
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| <s id="id.000281">De­<lb/>trahi autem plus lineam, cuius extremum prepius e&longs;t cen­<lb/>tro illa quæ &longs;uum habet terminum à centro remotiorem. </s></p><figure id="id.007.00.031.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.031.1.jpg"></figure><p type="main"> | <s id="id.000281">De­<lb/>trahi autem plus lineam, cuius extremum propius e&longs;t cen­<lb/>tro illa quæ &longs;uum habet terminum à centro remotiorem. </s></p><figure id="id.007.00.031.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.031.1.jpg"></figure><p type="main"> |
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| <s id="id.000282">E&longs;to, inquit, circulus <lb/>BCDE & alter in eo minor <lb/>MNOP circa idem centrum <lb/>A. Ducanturque; Diametrima­<lb/>ioris quidem CD, EB, mino­<lb/>ris verò MO, NP. </s> | <s id="id.000282">E&longs;to, inquit, circulus <lb/>BCDE & alter in eo minor <lb/>MNOP circa idem centrum <lb/>A. Ducanturque; Diametrima­<lb/>ioris quidem CD, EB, mino­<lb/>ris verò MO, NP. </s> |
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| <s id="id.000284">Tardiùs autem <lb/>fertur AM, quam AD, pro­<lb/>pterea quòd AM à centro <lb/>magis retrahatur quàm ip&longs;a AB. <!-- KEEP S--></s> | <s id="id.000284">Tardiùs autem <lb/>fertur AM, quam AD, pro­<lb/>pterea quòd AM à centro <lb/>magis retrahatur quàm ip&longs;a AB. <!-- KEEP S--></s> |
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| <s id="id.000285">Ducatur igitur ALF & <lb/>à puncto L, ip&longs;i AB perpendicularis L q, cadens in mino-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.032.jpg"/>ri circulo, & rur&longs;us ab codem L ip&longs;i AB, parailela duca­<lb/>tur LS, Ab S verò eidem perpendicularis ST, & ab F i­<lb/>tem FX. </s> | <s id="id.000285">Ducatur igitur ALF & <lb/>à puncto L, ip&longs;i AB perpendicularis L q, cadens in mino-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.032.jpg"/>ri circulo, & rur&longs;us ab eodem L ip&longs;i AB, parallela duca­<lb/>tur LS, Ab S verò eidem perpendicularis ST, & ab F i­<lb/>tem FX. </s> |
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| <s id="id.000286">Sunt ergo q L, ST, quidem æquales, nempeillæ, <lb/>per qua<gap/>, &longs;ecundum naturam, mouentur puncta BM. <!-- KEEP S--></s> | <s id="id.000286">Sunt ergo q L, ST, quidem æquales, nempe illæ, <lb/>per quæ, &longs;ecundum naturam, mouentur puncta BM. <!-- KEEP S--></s> |
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| <s id="id.000287">Mo­<lb/>tu verò retractionis ad centrum, hoc e&longs;t, præter naturam, <lb/>plus motum e&longs;t M quàm B. <!-- KEEP S--></s> | <s id="id.000287">Mo­<lb/>tu verò retractionis ad centrum, hoc e&longs;t, præter naturam, <lb/>plus motum e&longs;t M quàm B. <!-- KEEP S--></s> |
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| <s id="id.000294">Modò quod pollicebamur, nempe minorem e&longs;&longs;e <lb/>BT, quàm q M, ita demon&longs;tramus. </s> | <s id="id.000294">Modò quod pollicebamur, nempe minorem e&longs;&longs;e <lb/>BT, quàm q M, ita demon&longs;tramus. </s> |
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| <s id="id.000295"><expan abbr="quoniã">quoniam</expan> ST. ex prop. | <s id="id.000295"><expan abbr="quoniã">quoniam</expan> ST. ex prop. 13. <lb/>1. 6. media proportionalis e&longs;t inter BT & TE, erit qua­<lb/>dratum TS æquale <expan abbr="parallelogrãmo">parallelogrammo</expan> &longs;eu rectangulo BT, <lb/>TE, item, quoniam q L media proportionalis e&longs;t inter <lb/>M q, & q O. erit quadratum q L æquale rectangulo M q, <lb/>q O, æqualia ergo &longs;unt rectangula BTE, M q O, itaque <lb/>reciproca latera habent proportionalia. </s> |
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| 13. <lb/>1. 6. media proportionalis e&longs;t inter BT & TE, erit qua­<lb/>dratum TS æquale <expan abbr="parallelogrãmo">parallelogrammo</expan> &longs;eu rectangulo BT, <lb/>TE, item, quoniam q L media proportionalis e&longs;t inter <lb/>M q, & q O. erit quadratum q L æquale rectangulo M q, <lb/>q O, æqualia ergo &longs;unt rectangula BTE, M q O, itaque <lb/>reciprocalatera habent proportionalia. </s> | |
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| <s id="id.000296">quare, vt TE, ad <lb/>q O, ita M q ad TB, &longs;ed TE maior e&longs;t ip&longs;a q O, quippe <lb/>quòd pars &longs;it q O ip&longs;ius TE, maior ergo & M q ip&longs;a TB, <lb/>quod o&longs;tendendum fuerat. </s></p><p type="main"> | <s id="id.000296">quare, vt TE, ad <lb/>q O, ita M q ad TB, &longs;ed TE maior e&longs;t ip&longs;a q O, quippe <lb/>quòd pars &longs;it q O ip&longs;ius TE, maior ergo & M q ip&longs;a TB, <lb/>quod o&longs;tendendum fuerat. </s></p><p type="main"> |
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| <s id="id.000297">Cæterùm &longs;ubtilia & ingenio&longs;a i&longs;thæc e&longs;&longs;e non nega­<lb/>mus, & longè faciliori & explicatiori modo veritas hæc <lb/>demon&longs;trari pote&longs;t, reiectis nem peillis, &longs;ecundùm, & prae­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.033.jpg"/>ter naturam motibus, qui <expan abbr="quidē">quidem</expan> in &longs;implici circulo nece&longs;­<lb/>&longs;ario non cadunt: caderent autem forta&longs;&longs;e, &longs;i de circulo <lb/>res e&longs;&longs;et à <expan abbr="pōderibus">ponderibus</expan> circumlatis ex &longs;tabili centro de&longs;eri­<lb/>pto, qua de re agit G. <!-- REMOVE S-->Vbaldus in Mechanicis ttactatu de <lb/>libra. </s> | <s id="id.000297">Cæterùm &longs;ubtilia & ingenio&longs;a i&longs;thæc e&longs;&longs;e non nega­<lb/>mus, & longè faciliori & explicatiori modo veritas hæc <lb/>demon&longs;trari pote&longs;t, reiectis nempe illis, &longs;ecundùm, & prae­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.033.jpg"/>ter naturam motibus, qui <expan abbr="quidē">quidem</expan> in &longs;implici circulo nece&longs;­<lb/>&longs;ario non cadunt: caderent autem forta&longs;&longs;e, &longs;i de circulo <lb/>res e&longs;&longs;et à <expan abbr="pōderibus">ponderibus</expan> circumlatis ex &longs;tabili centro de&longs;eri­<lb/>pto, qua de re agit G. <!-- REMOVE S-->Vbaldus in Mechanicis tractatu de <lb/>libra. </s> |
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| <s id="id.000307">Prioríbus, ceu fundamentis quibu&longs;dam iactis, oppor­<lb/>tunè ad quæ&longs;tiones proponendas, eas queue diluendas &longs;e <lb/>confert Ari&longs;toteles. <!-- KEEP S--></s> | <s id="id.000307">Prioríbus, ceu fundamentis quibu&longs;dam iactis, oppor­<lb/>tunè ad quæ&longs;tiones proponendas, eas queue diluendas &longs;e <lb/>confert Ari&longs;toteles. <!-- KEEP S--></s> |
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| <s id="id.000308">Porro in propo&longs;ita quæ&longs;tione vide­<lb/>tur prima fi onte cau&longs;&longs;am quæri de re quæ non e&longs;t: etenim <lb/>quis affirmauerit vnquam, lances quibus Apothecarij & <lb/>Macellarij vtuntur, magnas eas quidem, illis exactiores <lb/>e&longs;&longs;e quibus Gemmatij, atque Argentarij &longs;iliquis, & &longs;eru­<lb/>pulis minuti&longs;&longs;ima appendunt, quæ tamen perexiguæ &longs;unt, <lb/>& &longs;i illis comparentur minimæ? </s> | <s id="id.000308">Porro in propo&longs;ita quæ&longs;tione vide­<lb/>tur prima fronte cau&longs;&longs;am quæri de re quæ non e&longs;t: etenim <lb/>quis affirmauerit vnquam, lances quibus Apothecarij & <lb/>Macellarij vtuntur, magnas eas quidem, illis exactiores <lb/>e&longs;&longs;e quibus Gemmatij, atque Argentarij &longs;iliquis, & &longs;cru­<lb/>pulis minuti&longs;&longs;ima appendunt, quæ tamen perexiguæ &longs;unt, <lb/>& &longs;i illis comparentur minimæ? </s> |
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| <s id="id.000309">Veruntamen, ita pror&longs;us <lb/>res habet, vt a&longs;&longs;erit Ari&longs;toteles. <!-- KEEP S--></s> | <s id="id.000309">Veruntamen, ita pror&longs;us <lb/>res habet, vt a&longs;&longs;erit Ari&longs;toteles. <!-- KEEP S--></s> |
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| <s id="id.000313">Minor verò libra DE, <lb/>circa idem <expan abbr="fulcimētum">fulcimentum</expan> <lb/>C, vnà cum maiori, ima­<lb/>ginatione, conuer&longs;a. </s> | <s id="id.000313">Minor verò libra DE, <lb/>circa idem <expan abbr="fulcimētum">fulcimentum</expan> <lb/>C, vnà cum maiori, ima­<lb/>ginatione, conuer&longs;a. </s> |
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| <s id="id.000314">Ap­<lb/>ponatur queduis pon­<lb/>dus maiori libræ in A, <lb/>de clinetque; exempli gratiâ in F, erit queue minor libra in G, <lb/>in eadem enim linea &longs;unt CGF. <expan abbr="Vnaq;">Vnaque</expan> igitur ex eodem <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.035.jpg"/>centro C portionem circuli de&longs;cribet GD, AF, eritqueue <lb/>ACF &longs;ector circuli, cuius diameter AB, &longs;ed DCG &longs;e­<lb/>ctor circuli, cuius diameter DE. <!-- KEEP S--></s> | <s id="id.000314">Ap­<lb/>ponatur quoduis pon­<lb/>dus maiori libræ in A, <lb/>declinetque; exempli gratiâ in F, erit queue minor libra in G, <lb/>in eadem enim linea &longs;unt CGF. <expan abbr="Vnaq;">Vnaque</expan> igitur ex eodem <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.035.jpg"/>centro C portionem circuli de&longs;cribet GD, AF, eritqueue <lb/>ACF &longs;ector circuli, cuius diameter AB, &longs;ed DCG &longs;e­<lb/>ctor circuli, cuius diameter DE. <!-- KEEP S--></s> |
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| <s id="id.000315">Itaque vt diameter ad <lb/>diametrum, ita portio ad portionem: maior autem dia­<lb/>meter AB diametro DE: maior ergo portio AF, portio­<lb/>ne DG. quod autem maius e&longs;t, minus obtutum fallit, ex­<lb/>qui&longs;itius itaque tractum ex maiori AB quàm ex ip&longs;a mi­<lb/>nori DE cogno &longs;cemus, quod fuerat o&longs;tendendum. </s></p><p type="main"> | <s id="id.000315">Itaque vt diameter ad <lb/>diametrum, ita portio ad portionem: maior autem dia­<lb/>meter AB diametro DE: maior ergo portio AF, portio­<lb/>ne DG. quod autem maius e&longs;t, minus obtutum fallit, ex­<lb/>qui&longs;itius itaque tractum ex maiori AB quàm ex ip&longs;a mi­<lb/>nori DE cogno &longs;cemus, quod fuerat o&longs;tendendum. </s></p><p type="main"> |
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| <s id="id.000319">Hinc <lb/>itaque apparet, <expan abbr="in&longs;trumēta">in&longs;trumenta</expan> quælibet quò maiora fuerint, <lb/>eò e&longs;&longs;e & exqui&longs;itiora, quod propo&longs;uerat Ari&longs;toteles, in <lb/>hac quæ&longs;tione de Libra. <!-- KEEP S--></s></p><p type="main"> | <s id="id.000319">Hinc <lb/>itaque apparet, <expan abbr="in&longs;trumēta">in&longs;trumenta</expan> quælibet quò maiora fuerint, <lb/>eò e&longs;&longs;e & exqui&longs;itiora, quod propo&longs;uerat Ari&longs;toteles, in <lb/>hac quæ&longs;tione de Libra. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000320">Quod autem addit de fraudibus Purpurariorum, <lb/>inquiens; quamobrem machinánturij qui purpuram ven­<lb/>dunt, vt <expan abbr="pēdendo">pendendo</expan> defraudent, dum ad medium, &longs;partum, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.036.jpg"/>non ponentes; tum plumbum in alterutram libræ partem <lb/>infundentes; aut ligni quod ad radicem vergebat, in eam <lb/>quam deferri volunt partem con&longs;tituentes, aut &longs;i nodum <lb/>habucrit, ligni enim grauior ea e&longs;t pars, in qua e&longs;t radix, <lb/>nodus verò radix quæ dam e&longs;t. </s> | <s id="id.000320">Quod autem addit de fraudibus Purpurariorum, <lb/>inquiens; quamobrem machinántur ij qui purpuram ven­<lb/>dunt, vt <expan abbr="pēdendo">pendendo</expan> defraudent, dum ad medium, &longs;partum, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.036.jpg"/>non ponentes; tum plumbum in alterutram libræ partem <lb/>infundentes; aut ligni quod ad radicem vergebat, in eam <lb/>quam deferri volunt partem con&longs;tituentes, aut &longs;i nodum <lb/>habuerit, ligni enim grauior ea e&longs;t pars, in qua e&longs;t radix, <lb/>nodus verò radix quæ dam e&longs;t. </s> |
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| <s id="id.000321">Hinc quæri po&longs;&longs;et: </s></p><p type="head"> | <s id="id.000321">Hinc quæri po&longs;&longs;et: </s></p><p type="head"> |
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| <s id="id.000322"><emph type="italics"/>Vtrum libræ quæ ponderibus vacuæ æquilibrant, <lb/>omni pror&longs;us careant fraude?<emph.end type="italics"/></s></p><p type="main"> | <s id="id.000322"><emph type="italics"/>Vtrum libræ quæ ponderibus vacuæ æquilibrant, <lb/>omni pror&longs;us careant fraude?<emph.end type="italics"/></s></p><p type="main"> |
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| <s id="id.000323">Videri cuipiam po&longs;&longs;et, libras, quæ ponderibus va­<lb/>cuæ, æquilibrant, omm pror&longs;us fraude carere, verunta­<lb/>men ita non e&longs;t, quod diligentiùs (res enim magni mo­<lb/>menti e&longs;t) di&longs;quiremus. </s></p><figure id="id.007.00.036.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.036.1.jpg"></figure><p type="main"> | <s id="id.000323">Videri cuipiam po&longs;&longs;et, libras, quæ ponderibus va­<lb/>cuæ, æquilibrant, omni pror&longs;us fraude carere, verunta­<lb/>men ita non e&longs;t, quod diligentiùs (res enim magni mo­<lb/>menti e&longs;t) di&longs;quiremus. </s></p><figure id="id.007.00.036.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.036.1.jpg"></figure><p type="main"> |
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| <s id="id.000324">E&longs;to enim libra AB, ita diui&longs;a <lb/>in C, vt AC &longs;it partium IS, CB ve­<lb/>rò carundem &longs;it 10. apponatur parti <lb/>A lanx ponderans 10, parti vero B <lb/>lanx ponderans 15. ex permutata i­<lb/>gitur proportione libra &longs;u&longs;pen&longs;a in <lb/>C, aequè ponderabit; &longs;i autem appo­<lb/>natur lanci B &longs;acoma vnciarum 6, & in lance A con&longs;titua­<lb/>tur purpura, quæ ita &longs;e habeat ad vncias 6, vt 10 ad 15, ite­<lb/>rum æqueponderabit, &longs;ed vt 10 ad 15, ita 4 ad 6. Purpura­<lb/>rius ergo fraudulentus, ponens in lance A vncias purpuræ <lb/>4, facto æquilibrio petet pretium vnciarum 6, & ita em­<lb/>ptorem decipiet, quod &longs;anè innuerat, non autem demon­<lb/>&longs;trauerat Ari&longs;toteles. <!-- KEEP S--></s> | <s id="id.000324">E&longs;to enim libra AB, ita diui&longs;a <lb/>in C, vt AC &longs;it partium IS, CB ve­<lb/>rò earundem &longs;it 10. apponatur parti <lb/>A lanx ponderans 10, parti vero B <lb/>lanx ponderans 15. ex permutata i­<lb/>gitur proportione libra &longs;u&longs;pen&longs;a in <lb/>C, aequè ponderabit; &longs;i autem appo­<lb/>natur lanci B &longs;acoma vnciarum 6, & in lance A con&longs;titua­<lb/>tur purpura, quæ ita &longs;e habeat ad vncias 6, vt 10 ad 15, ite­<lb/>rum æqueponderabit, &longs;ed vt 10 ad 15, ita 4 ad 6. Purpura­<lb/>rius ergo fraudulentus, ponens in lance A vncias purpuræ <lb/>4, facto æquilibrio petet pretium vnciarum 6, & ita em­<lb/>ptorem decipiet, quod &longs;anè innuerat, non autem demon­<lb/>&longs;trauerat Ari&longs;toteles. <!-- KEEP S--></s> |
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| <s id="id.000325">Hæc autem faciliora fient ex ijs, <lb/>quæ in &longs;equentibus quæ &longs;tionibus, vbi de vecte agetur, ex­<lb/>plicabuntur. </s></p><p type="main"> | <s id="id.000325">Hæc autem faciliora fient ex ijs, <lb/>quæ in &longs;equentibus quæ &longs;tionibus, vbi de vecte agetur, ex­<lb/>plicabuntur. </s></p><p type="main"> |
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| <s id="id.000334"><emph type="italics"/>De Libra &longs;ur &longs;um fulcimentum habente.<emph.end type="italics"/></s></p><p type="main"> | <s id="id.000334"><emph type="italics"/>De Libra &longs;ur &longs;um fulcimentum habente.<emph.end type="italics"/></s></p><p type="main"> |
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| <s id="id.000335">Ari&longs;toteles primam quæ&longs;tionis partem ita &longs;oluit: An <lb/>quia &longs;ur&longs;um parte quidem exi&longs;tente, plus libræ extra per­<lb/>pend culum &longs;it? </s> | <s id="id.000335">Ari&longs;toteles primam quæ&longs;tionis partem ita &longs;oluit: An <lb/>quia &longs;ur&longs;um parte quidem exi&longs;tente, plus libræ extra per­<lb/>pendiculum &longs;it? </s> |
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| <s id="id.000336">Spartum enim perpendiculum e&longs;t: quare <lb/>nece&longs;&longs;<gap/> e&longs;t deor&longs;um ferriid quod plus e&longs;t, donec a&longs;cendat <lb/>qua bifariam libram diuidit ad ip&longs;um perpendiculum, <lb/>cum onus in cum bat ad libræ partem &longs;ur&longs;us raptam. </s></p><figure id="id.007.00.037.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.037.1.jpg"></figure><p type="main"> | <s id="id.000336">Spartum enim perpendiculum e&longs;t: quare <lb/>nece&longs;&longs;e e&longs;t deor&longs;um ferri id quod plus e&longs;t, donec a&longs;cendat <lb/>qua bifariam libram diuidit ad ip&longs;um perpendiculum, <lb/>cum onus incumbat ad libræ partem &longs;ur&longs;us raptam. </s></p><figure id="id.007.00.037.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.037.1.jpg"></figure><p type="main"> |
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| <s id="id.000337">Sit libra recta (hoc e&longs;t, in æquilibrio con&longs;tituta) BC, <lb/>&longs;partum autem AD, <lb/>fulcimentum autem <lb/>D, de&longs;uper: &longs;parto au­<lb/>tem deor&longs;um proie­<lb/>cto ad M perpendicu­<lb/>laris erit vbi ADM. <lb/></s> | <s id="id.000337">Sit libra recta (hoc e&longs;t, in æquilibrio con&longs;tituta) BC, <lb/>&longs;partum autem AD, <lb/>fulcimentum autem <lb/>D, de&longs;uper: &longs;parto au­<lb/>tem deor&longs;um proie­<lb/>cto ad M perpendicu­<lb/>laris erit vbi ADM. <lb/></s> |
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| <s id="id.000338">Si igitur in ip&longs;o B po­<lb/>natur onus, erit B qui­<lb/>dem vbi E, C autem <lb/>vbi H, quamobrem <lb/>ea quæ bifariam <expan abbr="librã">libram</expan> <lb/>&longs;ecat, primo quidem erit DM, ip&longs;ius perpendiculi; in <expan abbr="cū-bente">cun­<lb/>bente</expan> <expan abbr="autē">autem</expan> onere, erit DG. quare libræ ip&longs;ius EH, quod <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.038.jpg"/>extra perpendiculum, e&longs;t AM, vbi e&longs;t q P maius e&longs;t dimi­<lb/>dio. </s> | <s id="id.000338">Si igitur in ip&longs;o B po­<lb/>natur onus, erit B qui­<lb/>dem vbi E, C autem <lb/>vbi H, quamobrem <lb/>ea quæ bifariam <expan abbr="librã">libram</expan> <lb/>&longs;ecat, primo quidem erit DM, ip&longs;ius perpendiculi; in<expan abbr="cū-bente">cum­<lb/>bente</expan> <expan abbr="autē">autem</expan> onere, erit DG. quare libræ ip&longs;ius EH, quod <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.038.jpg"/>extra perpendiculum, e&longs;t AM, vbi e&longs;t q P maius e&longs;t dimi­<lb/>dio. </s> |
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| <s id="id.000339">Si igitur amoueatur onus ab E, nece&longs;&longs;e e&longs;t deor&longs;um <lb/>ferri H, minus e&longs;t enim E: &longs;iquidem igitur habuerit &longs;par­<lb/>tum &longs;ur&longs;um, propter hoc a&longs;cendit libra. </s></p><p type="main"> | <s id="id.000339">Si igitur amoueatur onus ab E, nece&longs;&longs;e e&longs;t deor&longs;um <lb/>ferri H, minus e&longs;t enim E: &longs;iquidem igitur habuerit &longs;par­<lb/>tum &longs;ur&longs;um, propter hoc a&longs;cendit libra. </s></p><p type="main"> |
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| <s id="id.000342">Id ergo &longs;ibi vult Ari&longs;toteles, <lb/>propterea quòd pars iugi HDG maior e&longs;t parte ED q, <lb/>eam eleuatam nece&longs;&longs;e e&longs;t de&longs;cendere, & iterum à perpen­<lb/>diculari ADM bifariam diui&longs;am ad æquilibrium reuer­<lb/>ti, Po&longs;&longs;umus nos idem &longs;impliciori figura demon&longs;trare. </s></p><figure id="id.007.00.038.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.038.1.jpg"></figure><p type="main"> | <s id="id.000342">Id ergo &longs;ibi vult Ari&longs;toteles, <lb/>propterea quòd pars iugi HDG maior e&longs;t parte ED q, <lb/>eam eleuatam nece&longs;&longs;e e&longs;t de&longs;cendere, & iterum à perpen­<lb/>diculari ADM bifariam diui&longs;am ad æquilibrium reuer­<lb/>ti, Po&longs;&longs;umus nos idem &longs;impliciori figura demon&longs;trare. </s></p><figure id="id.007.00.038.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.038.1.jpg"></figure><p type="main"> |
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| <s id="id.000343">E&longs;to libra AB, bi­<lb/>fariam, diui&longs;a in G, <lb/><expan abbr="fulcimentū">fulcimentum</expan> verò &longs;ur­<lb/>&longs;um vbi D, prod<gap/>ca­<lb/>tur perpendicularis <lb/>DC in E. <!-- KEEP S--></s> | <s id="id.000343">E&longs;to libra AB, bi­<lb/>fariam, diui&longs;a in G, <lb/><expan abbr="fulcimentū">fulcimentum</expan> verò &longs;ur­<lb/>&longs;um vbi D, produca­<lb/>tur perpendicularis <lb/>DC in E. <!-- KEEP S--></s> |
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| <s id="id.000344">Stante igi­<lb/>tur libra AB, in æqui­<lb/>librio æqualis e&longs;t pars <lb/>CH, ip&longs;i parti CB <lb/>apponatur pondus in <lb/>B. <!-- KEEP S--></s> | <s id="id.000344">Stante igi­<lb/>tur libra AB, in æqui­<lb/>librio æqualis e&longs;t pars <lb/>CH, ip&longs;i parti CB <lb/>apponatur pondus in <lb/>B. <!-- KEEP S--></s> |
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| <s id="id.000349">Si pondus circa &longs;tabile centrum conuertatur, dimi&longs;­<lb/>&longs;um non &longs;tabit, ni&longs;i &longs;ecundum grauitatis centrum fuerit <lb/>in perpendiculari, quæ per centrum, circa quod conuer­<lb/>titur, ad mundi centrum cadit. </s> | <s id="id.000349">Si pondus circa &longs;tabile centrum conuertatur, dimi&longs;­<lb/>&longs;um non &longs;tabit, ni&longs;i &longs;ecundum grauitatis centrum fuerit <lb/>in perpendiculari, quæ per centrum, circa quod conuer­<lb/>titur, ad mundi centrum cadit. </s> |
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| <s id="id.000350">Stabit autem in ea per­<lb/>pendiculari in duobus punctis, altero à centro mundi <lb/>remoti&longs;&longs;imo; altero verò cidem quantum licuerit pro­<lb/>ximo. </s></p><figure id="id.007.00.039.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.039.1.jpg"></figure><p type="main"> | <s id="id.000350">Stabit autem in ea per­<lb/>pendiculari in duobus punctis, altero à centro mundi <lb/>remoti&longs;&longs;imo; altero verò eidem quantum licuerit pro­<lb/>ximo. </s></p><figure id="id.007.00.039.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.039.1.jpg"></figure><p type="main"> |
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| <s id="id.000351">E&longs;to corpus A, cuius graui­<lb/>tatis centrum B, nixum lineae in­<lb/>flexibili BC, cum qua liberè <lb/>conuertatur circa centrum C. <lb/><!-- KEEP S--></s> | <s id="id.000351">E&longs;to corpus A, cuius graui­<lb/>tatis centrum B, nixum lineae in­<lb/>flexibili BC, cum qua liberè <lb/>conuertatur circa centrum C. <lb/><!-- KEEP S--></s> |
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| <s id="id.000355">Po&longs;t hæc verò in F, hoc <lb/>e&longs;t iterum in ip&longs;a perpendiculari <lb/>infra centrum C. <!-- KEEP S--></s> | <s id="id.000355">Po&longs;t hæc verò in F, hoc <lb/>e&longs;t iterum in ip&longs;a perpendiculari <lb/>infra centrum C. <!-- KEEP S--></s> |
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| <s id="id.000356">De&longs;cribet er­<lb/>go circulum ex centro C, nem­<lb/>pe BEF &longs;ecantem perpendicu­<lb/>larem in duobus punctis oppo­<lb/>&longs;itis BF, dico, pondus libe è di-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.040.jpg"/>mi&longs;&longs;um in duobus tantum punctis &longs;uapte naturâ perman­<lb/>&longs;urum, BF, in B, primò, quoniam cum corpus ip&longs;um A à <lb/>perpendiculari, quæ &longs;upei ficiei loco intelligitur ABCD <lb/>per centrum grauitatis diuidatur, in partes diuiditur æ­<lb/>queponderantes, quare in neutram partem inclinabit. <lb/></s> | <s id="id.000356">De&longs;cribet er­<lb/>go circulum ex centro C, nem­<lb/>pe BEF &longs;ecantem perpendicu­<lb/>larem in duobus punctis oppo­<lb/>&longs;itis BF, dico, pondus libe è di-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.040.jpg"/>mi&longs;&longs;um in duobus tantum punctis &longs;uapte naturâ perman­<lb/>&longs;urum, BF, in B, primò, quoniam cum corpus ip&longs;um A à <lb/>perpendiculari, quæ &longs;uperficiei loco intelligitur ABCD <lb/>per centrum grauitatis diuidatur, in partes diuiditur æ­<lb/>queponderantes, quare in neutram partem inclinabit. <lb/></s> |
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| <s id="id.000357">Stabit igitur erectum, lineæ ip&longs;i fultum, inflexibili BC, <lb/>quæ nititur puncto C. <!-- KEEP S--></s> | <s id="id.000357">Stabit igitur erectum, lineæ ip&longs;i fultum, inflexibili BC, <lb/>quæ nititur puncto C. <!-- KEEP S--></s> |
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| <s id="id.000360">E&longs;t igitur re&longs;pectu B, ip&longs;um <lb/>punctum C, ful cimentum deor&longs;um, re&longs;pectu verò F, ful­<lb/>cimentum &longs;ur&longs;um. </s> | <s id="id.000360">E&longs;t igitur re&longs;pectu B, ip&longs;um <lb/>punctum C, ful cimentum deor&longs;um, re&longs;pectu verò F, ful­<lb/>cimentum &longs;ur&longs;um. </s> |
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| <s id="id.000361">At quia linea DFCB, à centro mundi, <lb/>quod e&longs;t extra circulum, BEF, circulum ip&longs;um per cen­<lb/>trum C &longs;ecat, erit pars eius DF quidem breui&longs;&longs;ima, ip&longs;a <lb/>verò DB longi&longs;&longs;ima, ex propo&longs;. </s> | <s id="id.000361">At quia linea DFCB, à centro mundi, <lb/>quod e&longs;t extra circulum, BEF, circulum ip&longs;um per cen­<lb/>trum C &longs;ecat, erit pars eius DF quidem breui&longs;&longs;ima, ip&longs;a <lb/>verò DB longi&longs;&longs;ima, ex propo&longs;. 8. lib. 3. Elem. <!-- KEEP S--></s> |
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| <s id="id.000362">8. lib. | |
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| <s id="id.000363">Pondus igi­<lb/>tur A conuer&longs;um &longs;eu liberè motum circa centrum C, in <lb/>duobus tantum locis perpendicularis lineæ &longs;tabit remo­<lb/>ti&longs;&longs;imo altero, vt e&longs;t B, altero verò cidem quamproximo, <lb/>vt e&longs;t F. <!-- KEEP S--></s></p><p type="main"> | <s id="id.000363">Pondus igi­<lb/>tur A conuer&longs;um &longs;eu liberè motum circa centrum C, in <lb/>duobus tantum locis perpendicularis lineæ &longs;tabit remo­<lb/>ti&longs;&longs;imo altero, vt e&longs;t B, altero verò eidem quamproximo, <lb/>vt e&longs;t F. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000364">Hoc idem egregiè demon&longs;trauit G. Vbald. <!-- REMOVE S-->in &longs;uis <lb/>Mechanicis, Tractatu de Libra prop.1.<gap/></s> | <s id="id.000364">Hoc idem egregiè demon&longs;trauit G. Vbald. <!-- REMOVE S-->in &longs;uis <lb/>Mechanicis, Tractatu de Libra prop.1.</s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s id="id.000387">Sin autem tam parui momenti <lb/>&longs;it, vt eam re&longs;i&longs;tentiam non vincat, &longs;tante circa locum in­<lb/>fimum centro C, non mouebitur aut &longs;altem parum, ip&longs;a <lb/>libra. </s></p><p type="main"> | <s id="id.000387">Sin autem tam parui momenti <lb/>&longs;it, vt eam re&longs;i&longs;tentiam non vincat, &longs;tante circa locum in­<lb/>fimum centro C, non mouebitur aut &longs;altem parum, ip&longs;a <lb/>libra. </s></p><p type="main"> |
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| <s id="id.000388">Hinc colligimus &longs;ieri po&longs;&longs;e, libras illas, quæ non <gap/><lb/>quouis, quantumuis paruo pondere declinant, cas fulci-<gap/><lb/>mentum habere &longs;ur&longs;um. </s></p><p type="main"> | <s id="id.000388">Hinc colligimus &longs;ieri po&longs;&longs;e, libras illas, quæ non <gap/><lb/>quouis, quantumuis paruo pondere declinant, eas fulci-<gap/><lb/>mentum habere &longs;ur&longs;um. </s></p><p type="main"> |
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| <s id="id.000389">His ad dimus, cæteris paribus, re&longs;i&longs;tentiam eò e&longs;&longs;e <lb/>maiorem, quo minus grauitatis centrum di&longs;tat à fulci­<lb/>mento &longs;ur&longs;um, circa quod ip&longs;a libra aduertitur. </s></p><figure id="id.007.00.044.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.044.1.jpg"></figure><p type="main"> | <s id="id.000389">His ad dimus, cæteris paribus, re&longs;i&longs;tentiam eò e&longs;&longs;e <lb/>maiorem, quo minus grauitatis centrum di&longs;tat à fulci­<lb/>mento &longs;ur&longs;um, circa quod ip&longs;a libra aduertitur. </s></p><figure id="id.007.00.044.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.044.1.jpg"></figure><p type="main"> |
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| <s id="id.000399">Maior autem DFC ex <lb/>iam citata propo&longs;. </s> | <s id="id.000399">Maior autem DFC ex <lb/>iam citata propo&longs;. </s> |
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| <s id="id.000400"><expan abbr="quã">quam</expan> DBC, erit igitur re&longs;iduum CFK, <lb/>multo minus re&longs;iduo FBI, &longs;ed recti &longs;unt CFH, FBG, ex <lb/>quibus &longs;i detrahantur CFK, FBI, erit re&longs;iduum KFH, <lb/>maius re&longs;iduo IBG, plus ergo retra hitur à perpendicula­<lb/>ri po<gap/>dus de&longs;cendens per FK quàm per BI, minus igitur <lb/>præ<gap/>alebit re&longs;i&longs;tentiæ in C pondus appen&longs;um in F, quàm <lb/>&longs;i appendatur in B. quod fuerat demon&longs;trandum. </s></p><p type="main"> | <s id="id.000400"><expan abbr="quã">quam</expan> DBC, erit igitur re&longs;iduum CFK, <lb/>multo minus re&longs;iduo FBI, &longs;ed recti &longs;unt CFH, FBG, ex <lb/>quibus &longs;i detrahantur CFK, FBI, erit re&longs;iduum KFH, <lb/>maius re&longs;iduo IBG, plus ergo retrahitur à perpendicula­<lb/>ri pondus de&longs;cendens per FK quàm per BI, minus igitur <lb/>præ<gap/>alebit re&longs;i&longs;tentiæ in C pondus appen&longs;um in F, quàm <lb/>&longs;i appendatur in B. quod fuerat demon&longs;trandum. </s></p><p type="main"> |
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| <s id="id.000401">Po&longs;&longs;<gap/>mus & idem quoque aliter o&longs;tendere. </s></p><p type="main"> | <s id="id.000401">Po&longs;&longs;umus & idem quoque aliter o&longs;tendere. </s></p><p type="main"> |
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| <s id="id.000402">Sint enim &longs;eor&longs;um duæ libræ, maior AB, mïnor EF, <lb/>quàm commune grauitatis centrum C, fulcimentum ve­<lb/>rò &longs;ur&longs;um D. <!-- KEEP S--></s> | <s id="id.000402">Sint enim &longs;eor&longs;um duæ libræ, maior AB, mïnor EF, <lb/>quàm commune grauitatis centrum C, fulcimentum ve­<lb/>rò &longs;ur&longs;um D. <!-- KEEP S--></s> |
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| <s id="id.000404">Sunt igitur duo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.046.jpg"/><figure id="id.007.00.046.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.046.1.jpg"></figure><lb/>vectes DG, DH, quo­<lb/>rum quidem commu­<lb/>ne fulcimentum D, <lb/>pondus verò C, poten­<lb/>tiæ vbi HG. <!-- KEEP S--></s> | <s id="id.000404">Sunt igitur duo <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.046.jpg"/><figure id="id.007.00.046.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.046.1.jpg"></figure><lb/>vectes DG, DH, quo­<lb/>rum quidem commu­<lb/>ne fulcimentum D, <lb/>pondus verò C, poten­<lb/>tiæ vbi HG. <!-- KEEP S--></s> |
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| <s id="id.000405">Sunt au­<lb/>tem hi vectes cius na­<lb/>turæ, in quibus <expan abbr="pōdus">pondus</expan> <lb/>e&longs;t inter fulcimentum <lb/>& potentiam, itaque <lb/>vt &longs;e habet DC, ad <lb/>DG, ita potentia in G <lb/>ad pondus in C, item vt DC ad DH ita potentia in H ad <lb/>idem pondus C, &longs;ed minor e&longs;t propo&longs;itio DC, ad DG <lb/>quàm DC ad DH. minor ergo potentia requiritur in G, <lb/>hoc e&longs;t, in B, quàm in H, hoc e&longs;t in F. <!-- KEEP S--></s> | <s id="id.000405">Sunt au­<lb/>tem hi vectes eius na­<lb/>turæ, in quibus <expan abbr="pōdus">pondus</expan> <lb/>e&longs;t inter fulcimentum <lb/>& potentiam, itaque <lb/>vt &longs;e habet DC, ad <lb/>DG, ita potentia in G <lb/>ad pondus in C, item vt DC ad DH ita potentia in H ad <lb/>idem pondus C, &longs;ed minor e&longs;t propo&longs;itio DC, ad DG <lb/>quàm DC ad DH. minor ergo potentia requiritur in G, <lb/>hoc e&longs;t, in B, quàm in H, hoc e&longs;t in F. <!-- KEEP S--></s> |
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| <s id="id.000406">Data igitur ponderis <lb/>æqualitate faciliùs &longs;uperabitur re&longs;i&longs;tentia C in B, quàm <lb/>in F: quod o&longs;tendendum fuerat. </s></p><p type="main"> | <s id="id.000406">Data igitur ponderis <lb/>æqualitate faciliùs &longs;uperabitur re&longs;i&longs;tentia C in B, quàm <lb/>in F: quod o&longs;tendendum fuerat. </s></p><p type="main"> |
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| <s id="id.000412">Centrum igitur grauitatis E per <lb/>portionem EH, erit in H. <!-- KEEP S--></s> | <s id="id.000412">Centrum igitur grauitatis E per <lb/>portionem EH, erit in H. <!-- KEEP S--></s> |
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| <s id="id.000413">A&longs;cendit ergo centrum graui­<lb/>tatis in H, hoc e&longs;t, &longs;ur&longs;um, id e&longs;t, contra cius naturam; a­<lb/>moto igitur pondere ex C, grauitatis centrum extra per­<lb/>pendicularem con&longs;titutum rur&longs;us de&longs;cendet, & iterum <lb/>libra ABC ad æquilibrium reuertetur. </s> | <s id="id.000413">A&longs;cendit ergo centrum graui­<lb/>tatis in H, hoc e&longs;t, &longs;ur&longs;um, id e&longs;t, contra eius naturam; a­<lb/>moto igitur pondere ex C, grauitatis centrum extra per­<lb/>pendicularem con&longs;titutum rur&longs;us de&longs;cendet, & iterum <lb/>libra ABC ad æquilibrium reuertetur. </s> |
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| <s id="id.000414">Hoc idem egre­<lb/>giè o&longs;tendit G. Vbald. <!-- REMOVE S-->in tractatu de libra, propo&longs;. </s> | <s id="id.000414">Hoc idem egre­<lb/>giè o&longs;tendit G. Vbald. <!-- REMOVE S-->in tractatu de libra, propo&longs;. 4. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000415">4. <!-- KEEP S--></s></p><p type="main"> | |
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| <s id="id.000416">Hinc ratio pendet earum imaguncularum, quas ex <lb/>contu&longs;a papyro ligneaue leui materia compingunt, per­<lb/>queue manus earum ambas, ferreum filum trajicientes, v­<lb/>trinque plumbea appendunt pondera æqualia, ea <expan abbr="quidē">quidem</expan> <lb/>lege, vt centrum grauitatis infra pedes imaguncula &longs;ta­<lb/>tuatur. </s> | <s id="id.000416">Hinc ratio pendet earum imaguncularum, quas ex <lb/>contu&longs;a papyro ligneaue leui materia compingunt, per­<lb/>queue manus earum ambas, ferreum filum trajicientes, v­<lb/>trinque plumbea appendunt pondera æqualia, ea <expan abbr="quidē">quidem</expan> <lb/>lege, vt centrum grauitatis infra pedes imaguncula &longs;ta­<lb/>tuatur. </s> |
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| <s id="id.000420">Itaque in­<lb/>clinata imaguncula, & conuer&longs;a circa punctum <emph type="italics"/>B<emph.end type="italics"/>, &longs;i de-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.048.jpg"/>clinet ad partes I, centrum grauitatis eleuabitur in F. <!-- KEEP S--></s> | <s id="id.000420">Itaque in­<lb/>clinata imaguncula, & conuer&longs;a circa punctum <emph type="italics"/>B<emph.end type="italics"/>, &longs;i de-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.048.jpg"/>clinet ad partes I, centrum grauitatis eleuabitur in F. <!-- KEEP S--></s> |
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| <s id="id.000421">Si <lb/>verò ad partes H eleuabitur in G. quare cum FG loca <lb/>&longs;intremotiora à mundi centro, quàm &longs;it E, non &longs;tabit gra­<lb/>uitatis centrum in punctis FG, &longs;ed ad infimum locum re­<lb/>uertecur, hoc e&longs;t, in ip&longs;a perpendiculari in E, & imagun­<lb/>cula ad perpendiculum ip&longs;i H<emph type="italics"/>B<emph.end type="italics"/>E filo, hoc e&longs;t, ip&longs;i hori­<lb/>zonti reuertetur. </s></p><p type="main"> | <s id="id.000421">Si <lb/>verò ad partes H eleuabitur in G. quare cum FG loca <lb/>&longs;int remotiora à mundi centro, quàm &longs;it E, non &longs;tabit gra­<lb/>uitatis centrum in punctis FG, &longs;ed ad infimum locum re­<lb/>uertetur, hoc e&longs;t, in ip&longs;a perpendiculari in E, & imagun­<lb/>cula ad perpendiculum ip&longs;i H<emph type="italics"/>B<emph.end type="italics"/>E filo, hoc e&longs;t, ip&longs;i hori­<lb/>zonti reuertetur. </s></p><p type="main"> |
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| <s id="id.000422">Hinc etiam Arictum, T e&longs;tudinun<gap/> queue demolito­<lb/>riatum Machinarum vis pendet, nempe ex ratione libra­<lb/>rum, quæ fulcimentum habent &longs;ur&longs;um. </s></p><figure id="id.007.00.048.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.048.1.jpg"></figure><p type="main"> | <s id="id.000422">Hinc etiam Arictum, Te&longs;tudinumqueue demolito­<lb/>riatum Machinarum vis pendet, nempe ex ratione libra­<lb/>rum, quæ fulcimentum habent &longs;ur&longs;um. </s></p><figure id="id.007.00.048.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.048.1.jpg"></figure><p type="main"> |
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| <s id="id.000423">E&longs;to enim Aries A<emph type="italics"/>B<emph.end type="italics"/> <lb/>funi appen&longs;us CD, cu­<lb/>ius grauitatis centrum, <lb/>D, perpendicularis verò <lb/>quæ ad mundi centrum <lb/>ip&longs;a CDE. <!-- KEEP S--></s> | <s id="id.000423">E&longs;to enim Aries A<emph type="italics"/>B<emph.end type="italics"/> <lb/>funi appen&longs;us CD, cu­<lb/>ius grauitatis centrum, <lb/>D, perpendicularis verò <lb/>quæ ad mundi centrum <lb/>ip&longs;a CDE. <!-- KEEP S--></s> |
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| <s id="id.000427">Di­<lb/>mi&longs;&longs;a itaque Machina centrum F vtpote graue, non &longs;tabit, <lb/>&longs;ed &longs;uapte naturâ reuertetur in D. <!-- KEEP S--></s> | <s id="id.000427">Di­<lb/>mi&longs;&longs;a itaque Machina centrum F vtpote graue, non &longs;tabit, <lb/>&longs;ed &longs;uapte naturâ reuertetur in D. <!-- KEEP S--></s> |
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| <s id="id.000428">Quadruplici autem <lb/>de cau&longs;&longs;a motus Arietis violenti&longs;&longs;imus e&longs;t ex vi naturalis <lb/>ponderis, quo deor&longs;um fertur, tum velocitate naturalis <lb/>motus in de&longs;cendendo auctæ, tum ex vi pote<gap/> tiæ impel­<lb/>lentis, & naturalem motum adiuuantis, tum ex velocita­<lb/>te ex motu violento deor&longs;um & antror&longs;um impellente <lb/>acqui&longs;itâ. </s> | <s id="id.000428">Quadruplici autem <lb/>de cau&longs;&longs;a motus Arietis violenti&longs;&longs;imus e&longs;t ex vi naturalis <lb/>ponderis, quo deor&longs;um fertur, tum velocitate naturalis <lb/>motus in de&longs;cendendo auctæ, tum ex vi potentiæ impel­<lb/>lentis, & naturalem motum adiuuantis, tum ex velocita­<lb/>te ex motu violento deor&longs;um & antror&longs;um impellente <lb/>acqui&longs;itâ. </s> |
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| <s id="id.000429">Id etiam addimus, eo validiores fore ictus, quò <lb/>grauior fuerit Machina, & maius &longs;patium, quo retrotra­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.049.jpg"/>hitur, grauitate ip&longs;a & &longs;patio tum virium vnione opera<gap/><lb/>tionem mirum in modum adiuuantibus. </s></p><p type="main"> | <s id="id.000429">Id etiam addimus, eo validiores fore ictus, quò <lb/>grauior fuerit Machina, & maius &longs;patium, quo retrotra­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.049.jpg"/>hitur, grauitate ip&longs;a & &longs;patio tum virium vnione opera<gap/><lb/>tionem mirum in modum adiuuantibus. </s></p><p type="main"> |
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| <s id="id.000446">Apponatur pondus in B, de­<lb/>clinabitque; puta ad GH, cen­<lb/>trum verò C, ex &longs;tabili fulci­<lb/>mento D, circuli portionem de&longs;cribet CI, libra autem <lb/>&longs;ecabit EF perpendicularem in K. Æquales autem &longs;unt <lb/>IG, IH, at ex parte HI de&longs;umpta e&longs;t KI, addita queue ip&longs;i <lb/>IG, maior e&longs;t ergo tota KG, torâ KH. </s> | <s id="id.000446">Apponatur pondus in B, de­<lb/>clinabitque; puta ad GH, cen­<lb/>trum verò C, ex &longs;tabili fulci­<lb/>mento D, circuli portionem de&longs;cribet CI, libra autem <lb/>&longs;ecabit EF perpendicularem in K. Æquales autem &longs;unt <lb/>IG, IH, at ex parte HI de&longs;umpta e&longs;t KI, addita queue ip&longs;i <lb/>IG, maior e&longs;t ergo tota KG, torâ KH. </s> |
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| <s id="id.000447">Non igitur KH <lb/>habet KG, &longs;ed libra, ni&longs;i impedita fuerit, cum centro C <lb/>de&longs;cendente per <gap/>in M, ad ip&longs;am perpendicularem dela­<lb/>ta, ad in feriorem partem, mutatis vicibus quie&longs;cet, facto <lb/>nempe fulcimento &longs;ur&longs;um, fietque; horizonti æque di&longs;tans <lb/>iuxta po&longs;itionem LMN. <!-- KEEP S--></s></p><p type="main"> | <s id="id.000447">Non igitur KH <lb/>habet KG, &longs;ed libra, ni&longs;i impedita fuerit, cum centro C <lb/>de&longs;cendente per I in M, ad ip&longs;am perpendicularem dela­<lb/>ta, ad in feriorem partem, mutatis vicibus quie&longs;cet, facto <lb/>nempe fulcimento &longs;ur&longs;um, fietque; horizonti æque di&longs;tans <lb/>iuxta po&longs;itionem LMN. <!-- KEEP S--></s></p><p type="main"> |
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| <s id="id.000448">Demon&longs;tratio <expan abbr="quidē">quidem</expan> e&longs;t hæc, &longs;ed non ex proprijs prin­<lb/>cipijs Mechanicis, <expan abbr="nēpe">nempe</expan> ex ratione <expan abbr="cēt">cent</expan><gap/>i grauitatis petitâ. <lb/></s> | <s id="id.000448">Demon&longs;tratio <expan abbr="quidē">quidem</expan> e&longs;t hæc, &longs;ed non ex proprijs prin­<lb/>cipijs Mechanicis, <expan abbr="nēpe">nempe</expan> ex ratione <expan abbr="cēt">cent</expan>ri grauitatis petitâ. <lb/></s> |
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| <s id="id.000449">Ii&longs;dem enim &longs;tantibus, <expan abbr="cū">cum</expan> centrum grauitatis C fiat extra <lb/>perpendicularem, de&longs;cendens ad I, nun quam reuert<gap/> tur <lb/>in C, a&longs;cen deret enim; &longs;ed &longs;i liberè circa centrum D con­<lb/>uerteretur, de&longs;cendens vt dictum e&longs;t per circulum CIM <lb/>pondus B, fieret in L, A vero in N adepta po&longs;itione <lb/>LMN. <!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.051.jpg"/><p type="main"> | <s id="id.000449">Ii&longs;dem enim &longs;tantibus, <expan abbr="cū">cum</expan> centrum grauitatis C fiat extra <lb/>perpendicularem, de&longs;cendens ad I, nunquam reuertetur <lb/>in C, a&longs;cenderet enim; &longs;ed &longs;i liberè circa centrum D con­<lb/>uerteretur, de&longs;cendens vt dictum e&longs;t per circulum CIM <lb/>pondus B, fieret in L, A vero in N adepta po&longs;itione <lb/>LMN. <!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.051.jpg"/><p type="main"> |
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| <s id="id.000450">Cur autem huius libræ, quæ aliàs inutilis e&longs;t, memi­<lb/>nerit Philo&longs;ophus, ea videtur cau&longs;&longs;a, quòd inde vectis vir­<lb/>tutem eliciat, vt &longs;uo loco videbimus. </s> | <s id="id.000450">Cur autem huius libræ, quæ aliàs inutilis e&longs;t, memi­<lb/>nerit Philo&longs;ophus, ea videtur cau&longs;&longs;a, quòd inde vectis vir­<lb/>tutem eliciat, vt &longs;uo loco videbimus. </s> |
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| <s id="id.000463">Dico eam <lb/>dimi&longs;&longs;am permanere, etenim cum grauitatis centrum &longs;it <lb/>in ip&longs;a perpendiculari, in neutram partem verget, &longs;ed nec <lb/>vergere pote&longs;t, quippe quod non circa fulcimentum ceu <lb/>centrum motus, moueatur grauitatis centrum, &longs;ed in ip&longs;o <lb/>&longs;it ful cimento; &longs;itum ergo non mutat. </s> | <s id="id.000463">Dico eam <lb/>dimi&longs;&longs;am permanere, etenim cum grauitatis centrum &longs;it <lb/>in ip&longs;a perpendiculari, in neutram partem verget, &longs;ed nec <lb/>vergere pote&longs;t, quippe quod non circa fulcimentum ceu <lb/>centrum motus, moueatur grauitatis centrum, &longs;ed in ip&longs;o <lb/>&longs;it ful cimento; &longs;itum ergo non mutat. </s> |
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| <s id="id.000464">Præterea cum per­<lb/>pendicularis DCE per grauitatis centrum ducatur, cor­<lb/>pus ip&longs;um ex ponderibus & libra con&longs;tans ab ea in partes <lb/>çque ponderantes &longs;ecatur, & ideo ex centri grauitatis dif­<lb/>finitione, quam protulit Pappus, corpus ip&longs;um centro <lb/>grauitatis appen&longs;um, dum fertur quie&longs;cit, & &longs;eruat eam, <lb/>quam à principio habuit po&longs;ition<gap/>. </s> | <s id="id.000464">Præterea cum per­<lb/>pendicularis DCE per grauitatis centrum ducatur, cor­<lb/>pus ip&longs;um ex ponderibus & libra con&longs;tans ab ea in partes <lb/>çque ponderantes &longs;ecatur, & ideo ex centri grauitatis dif­<lb/>finitione, quam protulit Pappus, corpus ip&longs;um centro <lb/>grauitatis appen&longs;um, dum fertur quie&longs;cit, & &longs;eruat eam, <lb/>quam à principio habuit po&longs;itione. </s> |
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| <s id="id.000465">Et &longs;anè &longs;i partes quo­<lb/>modo libet librâ per grauitatis centrum diuisâ, &longs;untæ­<lb/>queponderantes nec trahent inuicem, nec trahentur, &longs;ta­<lb/>bit ergo libra, & quam adepta fuerat po&longs;itionem, eam &longs;er­<lb/>uabit. </s> | <s id="id.000465">Et &longs;anè &longs;i partes quo­<lb/>modo libet librâ per grauitatis centrum diuisâ, &longs;untæ­<lb/>queponderantes nec trahent inuicem, nec trahentur, &longs;ta­<lb/>bit ergo libra, & quam adepta fuerat po&longs;itionem, eam &longs;er­<lb/>uabit. </s> |
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| <s id="id.000466">Id tamen non negamus, difficile e&longs;&longs;e libras eiu&longs;ce­<lb/>modi ex materia fabricare, quippe quod non omnia quæ <lb/>vera &longs;unt, & euidenti&longs;&longs;imis demon&longs;trationibus patent, <lb/>commodè ad praxim, ex artis & materiæ imperfectione, <lb/>reducuntur. </s></p><p type="main"> | <s id="id.000466">Id tamen non negamus, difficile e&longs;&longs;e libras eiu&longs;ce­<lb/>modi ex materia fabricare, quippe quod non omnia quæ <lb/>vera &longs;unt, & euidenti&longs;&longs;imis demon&longs;trationibus patent, <lb/>commodè ad praxim, ex artis & materiæ imperfectione, <lb/>reducuntur. </s></p><p type="main"> |
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| <s id="id.000467">Cæterùm harum librarum ea e&longs;t virtus, vt vel mini­<lb/>mo pondere altrin&longs;ecus appo&longs;ito, declinet; quod illis quæ <lb/>centrum &longs;u &longs;um habent, non euenire, demon&longs;trauimus. </s></p><p type="main"> | <s id="id.000467">Cæterùm harum librarum ea e&longs;t virtus, vt vel mini­<lb/>mo pondere altrin&longs;ecus appo&longs;ito, declinet; quod illis quæ <lb/>centrum &longs;ur&longs;um habent, non euenire, demon&longs;trauimus. </s></p><p type="main"> |
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| <s id="id.000468">Circa hæc po&longs;&longs;et cuipiam oriri Dubium, num chor­<lb/>dulæ, quibus lances appenduntur, variationem aliquam <lb/>circa ea quæ demon&longs;trata &longs;unt, inducere valeant. </s></p><p type="main"> | <s id="id.000468">Circa hæc po&longs;&longs;et cuipiam oriri Dubium, num chor­<lb/>dulæ, quibus lances appenduntur, variationem aliquam <lb/>circa ea quæ demon&longs;trata &longs;unt, inducere valeant. </s></p><p type="main"> |
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| <s id="id.000475"><emph type="italics"/>Cur exiguæ vires (quod etiam à principio dixerat) vecte magna <lb/>mouent pondera, vectes in&longs;uper onus accipientes, cum facilius <lb/>&longs;it, minorem mouere grauitatem, minor est au­<lb/>tem &longs;ine vecte?<emph.end type="italics"/></s></p><p type="main"> | <s id="id.000475"><emph type="italics"/>Cur exiguæ vires (quod etiam à principio dixerat) vecte magna <lb/>mouent pondera, vectes in&longs;uper onus accipientes, cum facilius <lb/>&longs;it, minorem mouere grauitatem, minor est au­<lb/>tem &longs;ine vecte?<emph.end type="italics"/></s></p><p type="main"> |
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| <s id="id.000476">Ari&longs;toteles ita quæ&longs;tionem proponit, vt eam Rheto­<lb/>rico quodam fuco admirabiliorem f<gap/>ciat. </s> | <s id="id.000476">Ari&longs;toteles ita quæ&longs;tionem proponit, vt eam Rheto­<lb/>rico quodam fuco admirabiliorem faciat. </s> |
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| <s id="id.000477">Soluit au­<lb/>tem hoc pacto, <expan abbr="inquiēs">inquiens</expan>, fieri po&longs;&longs;e eam e&longs;&longs;e cau&longs;&longs;am, quod <lb/>vectis &longs;it libra, eius nempe generis quod fulcimentum ha­<lb/>bet deor&longs;um, atque id circo in ip&longs;a pre&longs;&longs;ione in partes in­<lb/>æquales vectem diuidi. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.054.jpg"/><figure id="id.007.00.054.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.054.1.jpg"></figure><p type="main"> | <s id="id.000477">Soluit au­<lb/>tem hoc pacto, <expan abbr="inquiēs">inquiens</expan>, fieri po&longs;&longs;e eam e&longs;&longs;e cau&longs;&longs;am, quod <lb/>vectis &longs;it libra, eius nempe generis quod fulcimentum ha­<lb/>bet deor&longs;um, atque id circo in ip&longs;a pre&longs;&longs;ione in partes in­<lb/>æquales vectem diuidi. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.054.jpg"/><figure id="id.007.00.054.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.054.1.jpg"></figure><p type="main"> |
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| <s id="id.000489">Videtur autem ip&longs;e quoque Ari&longs;toteles non &longs;ibi <lb/>pror&longs;us in a&longs;&longs;ignata ratione &longs;atis feci&longs;&longs;e, & ideo &longs;ubiungit: <lb/>quoniam ab æquali pondere celerius mouetur maior ca­<lb/>rum quæ à centro &longs;unt duo verò pondera; quod mouet & <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.055.jpg"/>quod mouetur, quod igitur motum pondus ad mouens <lb/>longitudo patitur ad longitudinem, &longs;emper autem <expan abbr="quã-tum">quan­<lb/>tum</expan> ab hypomochlio (id e&longs;t, fulcimento) di&longs;tabit magis, <lb/>tanto facilius mouebit. </s> | <s id="id.000489">Videtur autem ip&longs;e quoque Ari&longs;toteles non &longs;ibi <lb/>pror&longs;us in a&longs;&longs;ignata ratione &longs;atis feci&longs;&longs;e, & ideo &longs;ubiungit: <lb/>quoniam ab æquali pondere celerius mouetur maior ca­<lb/>rum quæ à centro &longs;unt duo verò pondera; quod mouet & <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.055.jpg"/>quod mouetur, quod igitur motum pondus ad mouens <lb/>longitudo patitur ad longitudinem, &longs;emper autem <expan abbr="quã-tum">quan­<lb/>tum</expan> ab hypomochlio (id e&longs;t, fulcimento) di&longs;tabit magis, <lb/>tanto facilius mouebit. </s> |
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| <s id="id.000490">Cau&longs;&longs;a autem <gap/>, quæ retro com­<lb/>memorata e&longs;t, quoniam quæ plus à centro di&longs;tat <expan abbr="maiorē">maiorem</expan> <lb/>de&longs;cribit circulum. </s> | <s id="id.000490">Cau&longs;&longs;a autem est, quæ retro com­<lb/>memorata e&longs;t, quoniam quæ plus à centro di&longs;tat <expan abbr="maiorē">maiorem</expan> <lb/>de&longs;cribit circulum. </s> |
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| <s id="id.000491">quare ab eadem potentia plus &longs;upera­<lb/>biturid quod mouetur, quæ plus à fulcimento di&longs;&longs;at. </s> | <s id="id.000491">quare ab eadem potentia plus &longs;upera­<lb/>bitur id quod mouetur, quæ plus à fulcimento di&longs;tat. </s> |
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| <s id="id.000492">H&ucedil;c <lb/>ille, qui a&longs;&longs;erit duo pondera in vecte con&longs;iderari, Pondus <lb/>nempe motum, & mouentem Potentiam (hanc enim <expan abbr="pō-deris">pon­<lb/>deris</expan> habere vim <expan abbr="atq;">atque</expan> rationem certum e&longs;t) Vires autem <lb/>potentiam acquirere ex brachij longitudine, & ex inde <lb/>con&longs;equenti velocitate, quo enim brachia longiora, eo <lb/>in extremitate velociora, atque idcirco ita &longs;e habere mo­<lb/>tum pondus ad potentiam mouentem, vt brachij longi­<lb/>tudo ad brachij longitudinem: brachia autem vocamus, <lb/>partes illas vectis, quæ à fulcimento ad vtranque vectis <lb/>extremitatem pertingunt, & ideo quantum à fulcimento <lb/>potentia di&longs;tabit magis, eo faciliùs pondus mouebit. </s></p><p type="main"> | <s id="id.000492">H&ucedil;c <lb/>ille, qui a&longs;&longs;erit duo pondera in vecte con&longs;iderari, Pondus <lb/>nempe motum, & mouentem Potentiam (hanc enim <expan abbr="pō-deris">pon­<lb/>deris</expan> habere vim <expan abbr="atq;">atque</expan> rationem certum e&longs;t) Vires autem <lb/>potentiam acquirere ex brachij longitudine, & ex inde <lb/>con&longs;equenti velocitate, quo enim brachia longiora, eo <lb/>in extremitate velociora, atque idcirco ita &longs;e habere mo­<lb/>tum pondus ad potentiam mouentem, vt brachij longi­<lb/>tudo ad brachij longitudinem: brachia autem vocamus, <lb/>partes illas vectis, quæ à fulcimento ad vtranque vectis <lb/>extremitatem pertingunt, & ideo quantum à fulcimento <lb/>potentia di&longs;tabit magis, eo faciliùs pondus mouebit. </s></p><p type="main"> |
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| <s id="id.000503">At brachia in ip&longs;o æquilibrio &longs;u&longs;tinent actu quidem, <lb/>&longs;ed non mouentur. </s> | <s id="id.000503">At brachia in ip&longs;o æquilibrio &longs;u&longs;tinent actu quidem, <lb/>&longs;ed non mouentur. </s> |
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| <s id="id.000504">Cæterum videtur A riftoteles id &longs;ub­<lb/>odora&longs;&longs;e, quod po&longs;tea Archimedes, Mechanicorum prin­<lb/>ceps, in propo&longs;. </s> | <s id="id.000504">Cæterum videtur Ari&longs;toteles id &longs;ub­<lb/>odora&longs;&longs;e, quod po&longs;tea Archimedes, Mechanicorum prin­<lb/>ceps, in propo&longs;. </s> |
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| <s id="id.000505">6. primi Æqueponderantium explicitè <lb/>protulit & probauit: nempe in æquilibrio ita e&longs;&longs;e pondus <lb/>ad pondus, vt brachium ad brachium, ratione permutata. </s></p><figure id="id.007.00.056.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.056.1.jpg"></figure><p type="main"> | <s id="id.000505">6. primi Æqueponderantium explicitè <lb/>protulit & probauit: nempe in æquilibrio ita e&longs;&longs;e pondus <lb/>ad pondus, vt brachium ad brachium, ratione permutata. </s></p><figure id="id.007.00.056.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.056.1.jpg"></figure><p type="main"> |
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| <s id="id.000543">Ibi enim nauem <lb/>e&longs;&longs;e lati&longs;&longs;imam. </s> | <s id="id.000543">Ibi enim nauem <lb/>e&longs;&longs;e lati&longs;&longs;imam. </s> |
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| <s id="id.000544">Moueri autem nauim, quoniam <expan abbr="appellē-te">appellen­<lb/>te</expan> mariremo, <expan abbr="extremū">extremum</expan> illius quod intus e&longs;t anterius pro­<lb/>mouctur, cuius motum nauis &longs;equitur, cui &longs;calmus alliga­<lb/>tur. </s> | <s id="id.000544">Moueri autem nauim, quoniam <expan abbr="appellē-te">appellen­<lb/>te</expan> mari remo, <expan abbr="extremū">extremum</expan> illius quod intus e&longs;t anterius pro­<lb/>mouetur, cuius motum nauis &longs;equitur, cui &longs;calmus alliga­<lb/>tur. </s> |
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| <s id="id.000545">Vbiautem plurimum maris diuidit remus, eo maximè <lb/>nece&longs;&longs;e e&longs;&longs;e propelli. </s> | <s id="id.000545">Vbiautem plurimum maris diuidit remus, eo maximè <lb/>nece&longs;&longs;e e&longs;&longs;e propelli. </s> |
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| <s id="id.000551">Contra autem remiad <lb/>proram, nempe EF pars minor EG <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.060.jpg"/>intra nauim, pars verò maior GF extra nauim e&longs;t. </s> | <s id="id.000551">Contra autem remiad <lb/>proram, nempe EF pars minor EG <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.060.jpg"/>intra nauim, pars verò maior GF extra nauim e&longs;t. </s> |
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| <s id="id.000552">Pondus <lb/>autem cò faciliùs mouctur, quo maior e&longs;t vectis pars, quæ <lb/>à fulcimento e&longs;t ad mouentem potentiam. </s></p><p type="main"> | <s id="id.000552">Pondus <lb/>autem eò faciliùs mouetur, quo maior e&longs;t vectis pars, quæ <lb/>à fulcimento e&longs;t ad mouentem potentiam. </s></p><p type="main"> |
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| <s id="id.000553">Acutè &longs;anè Philo&longs;ophus. <!-- KEEP S--></s> | <s id="id.000553">Acutè &longs;anè Philo&longs;ophus. <!-- KEEP S--></s> |
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| <s id="id.000554">Ego autem &longs;i per mode&longs;tiam <lb/>liceret, dicerem, non quidem e&longs;&longs;e fulcimentum <expan abbr="&longs;calmū">&longs;calmum</expan>, <lb/>&longs;ed mare ip&longs;um, pondus vero nauim, ad locum &longs;calmi, <expan abbr="nē-pe">nen­<lb/>pe</expan> inter mouentem potentiam, & fulcimentum po&longs;itum, <lb/>etenim & eo pacto po&longs;&longs;umus vti vecte, quod ob&longs;eruat & <lb/>demon&longs;trat G. <!-- REMOVE S-->Vbaldus tractatu de vecte propo&longs;. </s> | <s id="id.000554">Ego autem &longs;i per mode&longs;tiam <lb/>liceret, dicerem, non quidem e&longs;&longs;e fulcimentum <expan abbr="&longs;calmū">&longs;calmum</expan>, <lb/>&longs;ed mare ip&longs;um, pondus vero nauim, ad locum &longs;calmi, <expan abbr="nē-pe">nem­<lb/>pe</expan> inter mouentem potentiam, & fulcimentum po&longs;itum, <lb/>etenim & eo pacto po&longs;&longs;umus vti vecte, quod ob&longs;eruat & <lb/>demon&longs;trat G. <!-- REMOVE S-->Vbaldus tractatu de vecte propo&longs;. </s> |
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| <s id="id.000561">Addimus, fal&longs;um videri quod a&longs;&longs;erit Ari&longs;toteles, <lb/>nempeillos qui in media naui &longs;unt, remiges, maximè na­<lb/>uim mouere; facilius, melius dixi&longs;&longs;et. </s> | <s id="id.000561">Addimus, fal&longs;um videri quod a&longs;&longs;erit Ari&longs;toteles, <lb/>nempeillos qui in media naui &longs;unt, remiges, maximè na­<lb/>uim mouere; facilius, melius dixi&longs;&longs;et. </s> |
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| <s id="id.000562">Si enim maximè, <lb/>quod ait, denorat, maximo &longs;patio, & velocius pror&longs;us fal­<lb/>&longs;um, etenim tardius mouent & minori &longs;patio, quod nos i­<lb/>ta demon&longs;tramus. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.061.jpg"/><figure id="id.007.00.061.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.061.1.jpg"></figure><p type="main"> | <s id="id.000562">Si enim maximè, <lb/>quod ait, denotat, maximo &longs;patio, & velocius pror&longs;us fal­<lb/>&longs;um, etenim tardius mouent & minori &longs;patio, quod nos i­<lb/>ta demon&longs;tramus. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.061.jpg"/><figure id="id.007.00.061.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.061.1.jpg"></figure><p type="main"> |
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| <s id="id.000563">E&longs;to enim Remus AB <lb/>qui marí fulcitur in B, Scal­<lb/>mus remi qui ad <expan abbr="prorã">proram</expan> pup­<lb/>pimue C, qui in media naui <lb/>D, maior autem remi pars <lb/>e&longs;t à &longs;calmo Dad A quami­<lb/>p&longs;ius C 2d A, Pellantur remi & &longs;tante ceu centro BA, in <lb/>E. eodem igitur tempore C eritin F, & D in G, &longs;ed maiu<gap/><lb/>e&longs;t &longs;patium CF &longs;patio DG, Ergo vnica impul&longs;ione, plus <lb/>mouit &longs;calmum, hoc e&longs;t, nauim, potentia ad puppim pro­<lb/>ramue remigans, quàm ea quæ operatur in media naui vt <lb/>&longs;entire vid<gap/>batur (&longs;i modo is e&longs;t eius &longs;en&longs;us) Ari&longs;toteles. <lb/><!-- KEEP S--></s> | <s id="id.000563">E&longs;to enim Remus AB <lb/>qui marí fulcitur in B, Scal­<lb/>mus remi qui ad <expan abbr="prorã">proram</expan> pup­<lb/>pimue C, qui in media naui <lb/>D, maior autem remi pars <lb/>e&longs;t à &longs;calmo Dad A quam i­<lb/>p&longs;ius C 2d A, Pellantur remi & &longs;tante ceu centro BA, in <lb/>E. eodem igitur tempore C eritin F, & D in G, &longs;ed maius <lb/>e&longs;t &longs;patium CF &longs;patio DG, Ergo vnica impul&longs;ione, plus <lb/>mouit &longs;calmum, hoc e&longs;t, nauim, potentia ad puppim pro­<lb/>ramue remigans, quàm ea quæ operatur in media naui vt <lb/>&longs;entire videbatur (&longs;i modo is e&longs;t eius &longs;en&longs;us) Ari&longs;toteles. <lb/><!-- KEEP S--></s> |
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| <s id="id.000564">Nece&longs;&longs;arium igitur e&longs;t, quodait, maximè intelligendum, <lb/>faciliùs, Veritatem hanc cogno&longs;centes Triremium præ­<lb/>fecti robu&longs;tiores quidem remiges ad proram & puppim, <lb/>inualidiores vcrò circa mediam triremem collocant. </s></p> | <s id="id.000564">Nece&longs;&longs;arium igitur e&longs;t, quod ait, maximè intelligendum, <lb/>faciliùs, Veritatem hanc cogno&longs;centes Triremium præ­<lb/>fecti robu&longs;tiores quidem remiges ad proram & puppim, <lb/>inualidiores verò circa mediam triremem collocant. </s></p> |
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| </subchap1><subchap1> | </subchap1><subchap1> |
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| <s id="id.000571">illud autem &longs;equitur <lb/>nauis quæ illi e&longs;t alligata & remus quidem &longs;ecundum la­<lb/>titudinem onus propellens & ab eodem repul&longs;us in re-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.062.jpg"/>ctum propellit, Gubernaculum verò, vt obliquum iacet <lb/>hinc inde in obliquum motionem facit. </s> | <s id="id.000571">illud autem &longs;equitur <lb/>nauis quæ illi e&longs;t alligata & remus quidem &longs;ecundum la­<lb/>titudinem onus propellens & ab eodem repul&longs;us in re-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.062.jpg"/>ctum propellit, Gubernaculum verò, vt obliquum iacet <lb/>hinc inde in obliquum motionem facit. </s> |
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| <s id="id.000572">in extremo <expan abbr="autē">autem</expan>, <lb/>non in medio iacet, quoniam mouenti fa cillimum e&longs;t mo­<lb/>tum moucre: prima enim pars celerrimè fertur, & quo­<lb/>niam, quemadmodum in ijs quæ feruntur in fine deficit <lb/>latio, &longs;ic ip&longs;ius continui in finem, imbecillima e&longs;t latio. <lb/></s> | <s id="id.000572">in extremo <expan abbr="autē">autem</expan>, <lb/>non in medio iacet, quoniam mouenti facillimum e&longs;t mo­<lb/>tum mouere: prima enim pars celerrimè fertur, & quo­<lb/>niam, quemadmodum in ijs quæ feruntur in fine deficit <lb/>latio, &longs;ic ip&longs;ius continui in finem, imbecillima e&longs;t latio. <lb/></s> |
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| <s id="id.000573">Imbecillima autem ad expellendum e&longs;t facilis. </s> | <s id="id.000573">Imbecillima autem ad expellendum e&longs;t facilis. </s> |
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| <s id="id.000574">Propter <lb/>hæc igitur in puppi gubernaculum ponitur, nec minus, <lb/>quoniam paruaibi motione facta, multo maior fit in vlti­<lb/>mo, quia æqualis angulus &longs;emper maiorem ad&longs;pectat, <expan abbr="tã-to">tan­<lb/>to</expan> queue magis, quanto maiores fuerint illæ, quæ continent. <lb/></s> | <s id="id.000574">Propter <lb/>hæc igitur in puppi gubernaculum ponitur, nec minus, <lb/>quoniam paruaibi motione facta, multo maior fit in vlti­<lb/>mo, quia æqualis angulus &longs;emper maiorem ad&longs;pectat, <expan abbr="tã-to">tan­<lb/>to</expan> queue magis, quanto maiores fuerint illæ, quæ continent. <lb/></s> |
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| <s id="id.000575">Exijs ctiam manife&longs;tum e&longs;t, quam ob cau&longs;&longs;am magis in <lb/>contrarium procedit nauigium, quam remi ip&longs;ius palmu­<lb/>la, eadem enim magnitudo ij&longs;dem mota viribus in aëre <lb/>plus quàm in aqua progreditur. </s> | <s id="id.000575">Ex ijs etiam manife&longs;tum e&longs;t, quam ob cau&longs;&longs;am magis in <lb/>contrarium procedit nauigium, quam remi ip&longs;ius palmu­<lb/>la, eadem enim magnitudo ij&longs;dem mota viribus in aëre <lb/>plus quàm in aqua progreditur. </s> |
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| <s id="id.000576">Hæc Philo&longs;ophus, qui <lb/>haudquaquam ex more &longs;uo, quod duobus ferè poterat, <lb/>&longs;excentis verbis expo&longs;uit. </s> | <s id="id.000576">Hæc Philo&longs;ophus, qui <lb/>haudquaquam ex more &longs;uo, quod duobus ferè poterat, <lb/>&longs;excentis verbis expo&longs;uit. </s> |
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| <s id="id.000583">Hæc <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.063.jpg"/>demon&longs;tratio licet vera videatur, rei ta men, de qua e&longs;t <lb/>&longs;ermo, minimè aptatur. </s> | <s id="id.000583">Hæc <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.063.jpg"/>demon&longs;tratio licet vera videatur, rei ta men, de qua e&longs;t <lb/>&longs;ermo, minimè aptatur. </s> |
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| <s id="id.000584">Si enim aptaretur in ip&longs;ius remi <lb/>motu, cum palmula e&longs;&longs;et in F, &longs;calmus ficret in G, excur­<lb/>reretergo vel &longs;calmus per remum, vel remus per <expan abbr="&longs;calmū">&longs;calmum</expan>, <lb/>facta nempe ciu&longs;modi translatione de C in G, & &longs;ic intra <lb/>nauim modo e&longs;&longs;et pars remi DC, modò verò GD, quod <lb/>tamen non &longs;ieri ipsâ experientia docemur. </s> | <s id="id.000584">Si enim aptaretur in ip&longs;ius remi <lb/>motu, cum palmula e&longs;&longs;et in F, &longs;calmus ficret in G, excur­<lb/>reret ergo vel &longs;calmus per remum, vel remus per <expan abbr="&longs;calmū">&longs;calmum</expan>, <lb/>facta nempe eiu&longs;modi translatione de C in G, & &longs;ic intra <lb/>nauim modo e&longs;&longs;et pars remi DC, modò verò GD, quod <lb/>tamen non fieri ipsâ experientia docemur. </s> |
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| <s id="id.000585">Illud quoque <lb/>fal&longs;um e&longs;t, nauim ip&longs;am tantum moueri in aëre, quantum <lb/>e&longs;t &longs;patium AD, hoc e&longs;t, remi extremum quod e&longs;t in naui, <lb/>&longs;iquidem &longs;calmi motu, non autem manubrij remi, nauis <lb/>agatur. </s> | <s id="id.000585">Illud quoque <lb/>fal&longs;um e&longs;t, nauim ip&longs;am tantum moueri in aëre, quantum <lb/>e&longs;t &longs;patium AD, hoc e&longs;t, remi extremum quod e&longs;t in naui, <lb/>&longs;iquidem &longs;calmi motu, non autem manubrij remi, nauis <lb/>agatur. </s> |
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| <s id="id.000587">Sit remus AB, cuíus <lb/>manubrium A, palmula <lb/>B, &longs;calmus C. <!-- KEEP S--></s> | <s id="id.000587">Sit remus AB, cuíus <lb/>manubrium A, palmula <lb/>B, &longs;calmus C. <!-- KEEP S--></s> |
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| <s id="id.000588">Pellatur an­<lb/>tror&longs;us A, fiatque; in D, tunc <lb/>&longs;i æqualiter mouerentur <lb/>manubrium & palmula, i­<lb/>p&longs;a palmula ficret in G, at <lb/>minus mouetur: fiet ergo <lb/>in E. ip&longs;e verò &longs;calmus C <lb/>translatus erit in F, motaque; erit nauis à C in F, non autem <lb/>ab A in D. <!-- KEEP S--></s> | <s id="id.000588">Pellatur an­<lb/>tror&longs;us A, fiatque; in D, tunc <lb/>&longs;i æqualiter mouerentur <lb/>manubrium & palmula, i­<lb/>p&longs;a palmula fieret in G, at <lb/>minus mouetur: fiet ergo <lb/>in E. ip&longs;e verò &longs;calmus C <lb/>translatus erit in F, motaque; erit nauis à C in F, non autem <lb/>ab A in D. <!-- KEEP S--></s> |
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| <s id="id.000589">P o&longs;uitautem Ari&longs;toteles &longs;calmum ad medium <lb/>remi, &longs;ed non ad medium collocari &longs;olet, maior enim pars <lb/>in mare propendet puta HB, quo ca&longs;u translationis &longs;pa­<lb/>tium fit maius, nempe ab H in I. fit autem motus &longs;calmi ex <lb/>centris qui &longs;unt in &longs;patio ip&longs;o BE, quatenus autem ad te­<lb/>monem pertinet, quem remum ait, obliquè puppim ip&longs;am <lb/>propellentem, ita &longs;e res habet. </s></p><p type="main"> | <s id="id.000589">P o&longs;uitautem Ari&longs;toteles &longs;calmum ad medium <lb/>remi, &longs;ed non ad medium collocari &longs;olet, maior enim pars <lb/>in mare propendet puta HB, quo ca&longs;u translationis &longs;pa­<lb/>tium fit maius, nempe ab H in I. fit autem motus &longs;calmi ex <lb/>centris qui &longs;unt in &longs;patio ip&longs;o BE, quatenus autem ad te­<lb/>monem pertinet, quem remum ait, obliquè puppim ip&longs;am <lb/>propellentem, ita &longs;e res habet. </s></p><p type="main"> |
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| <s id="id.000604">Illud quoque nota­<lb/>mus, carinam in nauis conuer&longs;ione vectis in&longs;tar &longs;e habere, <lb/>cuius pars mota ad puppim, & mouens potentia e&longs;t; fulci­<lb/>mentum verò circa proram, potentia autem mouens ma­<lb/>reip&longs;um, temonem in nauis cur&longs;u oblique feriens. </s> | <s id="id.000604">Illud quoque nota­<lb/>mus, carinam in nauis conuer&longs;ione vectis in&longs;tar &longs;e habere, <lb/>cuius pars mota ad puppim, & mouens potentia e&longs;t; fulci­<lb/>mentum verò circa proram, potentia autem mouens ma­<lb/>reip&longs;um, temonem in nauis cur&longs;u oblique feriens. </s> |
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| <s id="id.000605">Vnde <lb/>colligimus naues, quo longiores &longs;unt in mouente ad Te­<lb/>monem adhibita maiori facilitate ad dextram &longs;ini&longs;tram­<lb/>ue propelli: quod &longs;anè ip&longs;emet con&longs;iderauit Ari&longs;toteles, <lb/>quì idcirco inquir, in extremo, non autem in medio temo­<lb/>nem poni eo quod mouenti facilimum &longs;it ab extremo <lb/>motum mouere. </s></p><p type="main"> | <s id="id.000605">Vnde <lb/>colligimus naues, quo longiores &longs;unt in mouente ad Te­<lb/>monem adhibita maiori facilitate ad dextram &longs;ini&longs;tram­<lb/>ue propelli: quod &longs;anè ip&longs;emet con&longs;iderauit Ari&longs;toteles, <lb/>quì idcirco inquit, in extremo, non autem in medio temo­<lb/>nem poni eo quod mouenti facilimum &longs;it ab extremo <lb/>motum mouere. </s></p><p type="main"> |
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| <s id="id.000606">Ex hac no&longs;trâ &longs;peculatione ratio habetur eius ma-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.066.jpg"/>chinationis, quâ in magnis fluminibus, ceu Pado, Abdua <lb/>& &longs;imilibus, Portitores, equos, currus, viatore&longs;que; ip&longs;os, è <lb/>ripa in ripam transferunt. </s> | <s id="id.000606">Ex hac no&longs;trâ &longs;peculatione ratio habetur eius ma-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.066.jpg"/>chinationis, quâ in magnis fluminibus, ceu Pado, Abdua <lb/>& &longs;imilibus, Portitores, equos, currus, viatore&longs;que; ip&longs;os, è <lb/>ripa in ripam transferunt. </s> |
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| <s id="id.000607">Pulcherrima enim res e&longs;t, & <lb/>nobis per&longs;pecti&longs;&longs;ima, qui Gua&longs;tallâ re&longs;identiæ olim no­<lb/>&longs;træ oppido ad Padum, Mantuam pergentes &longs;æpi&longs;&longs;imè ad <lb/>Ca&longs;trum B<gap/>rgi Iu&longs;is ea qua diximus machinatione lati&longs;­<lb/>&longs;imum eiu&longs;dem Padi aluum tran&longs;ie cimus. </s> | <s id="id.000607">Pulcherrima enim res e&longs;t, & <lb/>nobis per&longs;pecti&longs;&longs;ima, qui Gua&longs;tallâ re&longs;identiæ olim no­<lb/>&longs;træ oppido ad Padum, Mantuam pergentes &longs;æpi&longs;&longs;imè ad <lb/>Ca&longs;trum Borgi Iu&longs;is ea qua diximus machinatione lati&longs;­<lb/>&longs;imum eiu&longs;dem Padi aluum tran&longs;iecimus. </s> |
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| <s id="id.000608">Habet autem <lb/>&longs;e hoc pacto. </s></p><figure id="id.007.00.066.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.066.1.jpg"></figure><p type="main"> | <s id="id.000608">Habet autem <lb/>&longs;e hoc pacto. </s></p><figure id="id.007.00.066.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.066.1.jpg"></figure><p type="main"> |
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| <s id="id.000611">Vnde iterum temone in contrariam partem conuer&longs;o, <lb/>aquâ &longs;imiliter temonem propellente, per eandem circuli <lb/>portionem ad ripam citeriorem reuertitur, à qua paullo <lb/>antè di&longs;ce&longs;&longs;erat. </s> | <s id="id.000611">Vnde iterum temone in contrariam partem conuer&longs;o, <lb/>aquâ &longs;imiliter temonem propellente, per eandem circuli <lb/>portionem ad ripam citeriorem reuertitur, à qua paullo <lb/>antè di&longs;ce&longs;&longs;erat. </s> |
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| <s id="id.000612">Ex quibus apparet, motus cau&longs;&longs;am non <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.067.jpg"/>e&longs;&longs;e &longs;olam cam, quæ ab ala temonis fit, aquæ <expan abbr="percu&longs;&longs;ionē">percu&longs;&longs;ionem</expan>, <lb/>vt &longs;en&longs;erat Ari&longs;toteles, &longs;ed currentis a quæ temonis alam <lb/>ferientis impul&longs;ion<gap/>m: nihil autem referre, vtrum &longs;tante <lb/>naui a qua currat, vel câ currente a qua &longs;tet, vt in mari fit, <lb/>idem enim vtroque modo temo patitur. </s> | <s id="id.000612">Ex quibus apparet, motus cau&longs;&longs;am non <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.067.jpg"/>e&longs;&longs;e &longs;olam cam, quæ ab ala temonis fit, aquæ <expan abbr="percu&longs;&longs;ionē">percu&longs;&longs;ionem</expan>, <lb/>vt &longs;en&longs;erat Ari&longs;toteles, &longs;ed currentis a quæ temonis alam <lb/>ferientis impul&longs;ionem: nihil autem referre, vtrum &longs;tante <lb/>naui a qua currat, vel câ currente a qua &longs;tet, vt in mari fit, <lb/>idem enim vtroque modo temo patitur. </s> |
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| <s id="id.000613">Vt autem machi­<lb/>næ huius & totius negotij &longs;pecies facilius animo concipia­<lb/>tur, &longs;chema hoc &longs;tudio &longs;orum oculis &longs;ubijciemus. </s></p><figure id="id.007.00.067.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.067.1.jpg"></figure><p type="main"> | <s id="id.000613">Vt autem machi­<lb/>næ huius & totius negotij &longs;pecies facilius animo concipia­<lb/>tur, &longs;chema hoc &longs;tudio &longs;orum oculis &longs;ubijciemus. </s></p><figure id="id.007.00.067.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.067.1.jpg"></figure><p type="main"> |
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| <s id="id.000615">Huic &longs;peculationi affinis e&longs;t ea, velorum eorum, <lb/>quæ obliquè ventum, excipientia frumentarijs molis <lb/>dant motum, item verticillorum ex papyro, quibus con­<lb/>tra ventum currentes per lu&longs;um pueri vtuntur. </s> | <s id="id.000615">Huic &longs;peculationi affinis e&longs;t ea, velorum eorum, <lb/>quæ obliquè ventum, excipientia frumentarijs molis <lb/>dant motum, item verticillorum ex papyro, quibus con­<lb/>tra ventum currentes per lu&longs;um pueri vtuntur. </s> |
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| <s id="id.000616">vnicum <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.068.jpg"/>enim horum emnium principium, & eadem, ratio. </s></p><p type="main"> | <s id="id.000616">vnicum <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.068.jpg"/>enim horum omnium principium, & eadem, ratio. </s></p><p type="main"> |
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| <s id="id.000617">Diximus enim, Temonem currente naui, lateraliter <lb/>conuer&longs;um obuios fluctus ex cipientem puppim ip&longs;am ob­<lb/>liquè in alteram partem transferre. </s> | <s id="id.000617">Diximus enim, Temonem currente naui, lateraliter <lb/>conuer&longs;um obuios fluctus ex cipientem puppim ip&longs;am ob­<lb/>liquè in alteram partem transferre. </s> |
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| <s id="id.000618">Porrò ea vela, de qui­<lb/>bus loquimur, ventorum flatibus obliquè oppo&longs;ita can­<lb/>dem ob cau&longs;&longs;am circulariter agitantur, quodvt figurâ eui­<lb/>dentius fiat, </s></p><figure id="id.007.00.068.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.068.1.jpg"></figure><p type="main"> | <s id="id.000618">Porrò ea vela, de qui­<lb/>bus loquimur, ventorum flatibus obliquè oppo&longs;ita ean­<lb/>dem ob cau&longs;&longs;am circulariter agitantur, quod vt figurâ eui­<lb/>dentius fiat, </s></p><figure id="id.007.00.068.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.068.1.jpg"></figure><p type="main"> |
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| <s id="id.000619">E&longs;to velum AB, brachio <lb/>CE obliquè affixum, ita vt <lb/>angulus ACE maior &longs;it an­<lb/>gulo BCE, ventus obliquè <lb/>velum feriens FG. <expan abbr="Itaq;">Itaque</expan> quo­<lb/>niam ventus in velum obli. <lb/></s> | |
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| <s id="id.000620">quum incidit, elabitur velum, <lb/>& circa centrum E vnà cum <lb/>brachio circumuertitur, in <lb/>cuius locum &longs;uccedit velum <lb/>HI, ex qua a&longs;&longs;idua velorum <lb/>&longs;ucce&longs;&longs;ione, brachiorum & a­<lb/>xis cui adhærent, rotatio fit <lb/>perpetua. </s> | <s id="id.000619">E&longs;to velum AB, brachio <lb/>CE obliquè affixum, ita vt <lb/>angulus ACE maior &longs;it an­<lb/>gulo BCE, ventus obliquè <lb/>velum feriens FG. <expan abbr="Itaq;">Itaque</expan> quo­<lb/>niam ventus in velum obli­<lb/>quum incidit, elabitur velum, <lb/>& circa centrum E vnà cum <lb/>brachio circumuertitur, in <lb/>cuius locum &longs;uccedit velum <lb/>HI, ex qua a&longs;&longs;idua velorum <lb/>&longs;ucce&longs;&longs;ione, brachiorum & a­<lb/>xis cui adhærent, rotatio fit <lb/>perpetua. </s> |
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| <s id="id.000621">Sed enim de Te­<lb/>mone agentes non e&longs;t interim cur de caudis auium pi&longs;ci­<lb/>umque taceamus, in&longs;tar enim remonum &longs;unt à Naturai­<lb/>p&longs;a opportunis animalium partibus, po&longs;tremis videlicet, <lb/>appo&longs;iti, quanquam nec&longs;olum Temonis v&longs;um præ&longs;tent, <lb/>vt videbimus. </s></p><p type="main"> | <s id="id.000621">Sed enim de Te­<lb/>mone agentes non e&longs;t interim cur de caudis auium pi&longs;ci­<lb/>umque taceamus, in&longs;tar enim remonum &longs;unt à Naturai­<lb/>p&longs;a opportunis animalium partibus, po&longs;tremis videlicet, <lb/>appo&longs;iti, quanquam nec&longs;olum Temonis v&longs;um præ&longs;tent, <lb/>vt videbimus. </s></p><p type="main"> |
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| <s id="id.000625">Omnis enim motus progre&longs;&longs;i­<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.069.jpg"/><figure id="id.007.00.069.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.069.1.jpg"></figure><lb/>pote&longs;t, quod in libris de ani­<lb/>malium ince&longs;&longs;u docet ip&longs;e­<lb/>met Philo&longs;ophus. <!-- KEEP S--></s> | <s id="id.000625">Omnis enim motus progre&longs;&longs;i­<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.069.jpg"/><figure id="id.007.00.069.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.069.1.jpg"></figure><lb/>pote&longs;t, quod in libris de ani­<lb/>malium ince&longs;&longs;u docet ip&longs;e­<lb/>met Philo&longs;ophus. <!-- KEEP S--></s> |
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| <s id="id.000626">Sit igitur, <lb/>pi&longs;cem conuerti velle, & fie­<lb/>ri capite in D, deflectet illi­<lb/>co caudam in E, caque; aquam <lb/>ceu &longs;tabile quippiam <expan abbr="feriēs">feriens</expan> <lb/>eiqueue quod<gap/>mmodo fultus, <lb/>reliquum corpus CA refle­<lb/>ctet in D, &longs;i autem conuerti <lb/>velit in F, caudam defle ctet in G, & eadem ratione <gap/> cte­<lb/>tur in F. <!-- KEEP S--></s> | <s id="id.000626">Sit igitur, <lb/>pi&longs;cem conuerti velle, & fie­<lb/>ri capite in D, deflectet illi­<lb/>co caudam in E, caque; aquam <lb/>ceu &longs;tabile quippiam <expan abbr="feriēs">feriens</expan> <lb/>eiqueue quoddammodo fultus, <lb/>reliquum corpus CA refle­<lb/>ctet in D, &longs;i autem conuerti <lb/>velit in F, caudam defle ctet in G, & eadem ratione <gap/> cte­<lb/>tur in F. <!-- KEEP S--></s> |
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| <s id="id.000627">Sed & Temonis quoque v&longs;um præ&longs;tat natatili­<lb/>bus & volatilibus cauda. </s> | <s id="id.000627">Sed & Temonis quoque v&longs;um præ&longs;tat natatili­<lb/>bus & volatilibus cauda. </s> |
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| <s id="id.000635">quæ &longs;ic figurâ explicamus. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.070.jpg"/><figure id="id.007.00.070.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.070.1.jpg"></figure><p type="main"> | <s id="id.000635">quæ &longs;ic figurâ explicamus. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.070.jpg"/><figure id="id.007.00.070.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.070.1.jpg"></figure><p type="main"> |
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| <s id="id.000636">E&longs;to nauis AB, malus CD, <lb/>mali &longs;edes D, locus antennæ <lb/>&longs;ublimior C, depre&longs;&longs;ior E: ita­<lb/>que quoniam CD vectis e&longs;t, <lb/>quo mouens remotior fuerit à <lb/>fulcimento D, co citiùs & vio­<lb/>lentiùs pellet, velocius ergo <lb/>nauis mouebitur antenna in <lb/>C, quàm in E, con&longs;tituta. </s></p><p type="main"> | <s id="id.000636">E&longs;to nauis AB, malus CD, <lb/>mali &longs;edes D, locus antennæ <lb/>&longs;ublimior C, depre&longs;&longs;ior E: ita­<lb/>que quoniam CD vectis e&longs;t, <lb/>quo mouens remotior fuerit à <lb/>fulcimento D, eo citiùs & vio­<lb/>lentiùs pellet, velocius ergo <lb/>nauis mouebitur antenna in <lb/>C, quàm in E, con&longs;tituta. </s></p><p type="main"> |
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| <s id="id.000637">Plau&longs;ibilia &longs;unt hæc, at certè per veritatem ip&longs;am, <lb/>non vera. </s> | <s id="id.000637">Plau&longs;ibilia &longs;unt hæc, at certè per veritatem ip&longs;am, <lb/>non vera. </s> |
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| <s id="id.000646">Videmus enim, & turres <lb/>quo &longs;ublimiores fuerint, eo magis à ventorum impetuo&longs;is <lb/>flatibus infe&longs;tari, quod &longs;anè ad vectis longitudinem refer­<lb/>re, e&longs;&longs;et ridiculum. </s> | <s id="id.000646">Videmus enim, & turres <lb/>quo &longs;ublimiores fuerint, eo magis à ventorum impetuo&longs;is <lb/>flatibus infe&longs;tari, quod &longs;anè ad vectis longitudinem refer­<lb/>re, e&longs;&longs;et ridiculum. </s> |
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| <s id="id.000647">Cætcrùm quod ad puppis faciliorem <lb/>eleuationem ex mali ip&longs;ius altitudine pertinet, ad vectis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.071.jpg"/>contemplationem reducimus. </s> | <s id="id.000647">Cæterùm quod ad puppis faciliorem <lb/>eleuationem ex mali ip&longs;ius altitudine pertinet, ad vectis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.071.jpg"/>contemplationem reducimus. </s> |
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| <s id="id.000648">e&longs;t enim quæ dam vectium <lb/>&longs;pecies ab alijs non con&longs;iderata, cuius brachia in angu­<lb/>lum de&longs;inunt, vtip&longs;e angulus in operatione &longs;it fulcimen­<lb/>tum. </s></p><figure id="id.007.00.071.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.071.1.jpg"></figure><p type="main"> | <s id="id.000648">e&longs;t enim quæ dam vectium <lb/>&longs;pecies ab alijs non con&longs;iderata, cuius brachia in angu­<lb/>lum de&longs;inunt, vtip&longs;e angulus in operatione &longs;it fulcimen­<lb/>tum. </s></p><figure id="id.007.00.071.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.071.1.jpg"></figure><p type="main"> |
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| <s id="id.000660">In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars quæ à fulcimento ad <lb/>potentiam; ac verò quæ à fulcimento ad pondus, ponderi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.072.jpg"/><figure id="id.007.00.072.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.072.1.jpg"></figure><lb/>&longs;iquidem æquiparatur re&longs;i­<lb/>&longs;tentia quae fit in C. <!-- KEEP S--></s> | <s id="id.000660">In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars quæ à fulcimento ad <lb/>potentiam; ac verò quæ à fulcimento ad pondus, ponderi <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.072.jpg"/><figure id="id.007.00.072.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.072.1.jpg"></figure><lb/>&longs;iquidem æquiparatur re&longs;i­<lb/>&longs;tentia quae fit in C. <!-- KEEP S--></s> |
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| <s id="id.000661">I dem ob­<lb/>&longs;eruamus in forcipe, in quo <lb/>duo quidem brachia AD, <lb/>CB, quatenus ad appren&longs;io­<lb/>nem pertinet, fulcimentum, <lb/>habent in ip&longs;o <expan abbr="cētro">centro</expan> &longs;eu ver­<lb/>rebra, & ideo quo longiores <lb/>fuerint, eo tenaciùs appre­<lb/>hendunt & retinent. </s> | <s id="id.000661">I dem ob­<lb/>&longs;eruamus in forcipe, in quo <lb/>duo quidem brachia AD, <lb/>CB, quatenus ad appren&longs;io­<lb/>nem pertinet, fulcimentum, <lb/>habent in ip&longs;o <expan abbr="cētro">centro</expan> &longs;eu ver­<lb/>tebra, & ideo quo longiores <lb/>fuerint, eo tenaciùs appre­<lb/>hendunt & retinent. </s> |
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| <s id="id.000662">quate­<lb/>nus autem ad extractionem, <lb/>facit, pro vnico forceps totus habetur vecte, cuius <expan abbr="quidē">quidem</expan> <lb/>pars à potentia ad fulcimentum AB. quæ verò à <expan abbr="fulcimē-to">fulcimen­<lb/>to</expan> ad hoc e&longs;t clauum ip&longs;um qui reuellitur AC. <!-- KEEP S--></s> | <s id="id.000662">quate­<lb/>nus autem ad extractionem, <lb/>facit, pro vnico forceps totus habetur vecte, cuius <expan abbr="quidē">quidem</expan> <lb/>pars à potentia ad fulcimentum AB. quæ verò à <expan abbr="fulcimē-to">fulcimen­<lb/>to</expan> ad hoc e&longs;t clauum ip&longs;um qui reuellitur AC. <!-- KEEP S--></s> |
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| <s id="id.000666">E&longs;to enim nauis AB; cuius <lb/>malus CD: prora A: puppis B; <expan abbr="vē-to">ven­<lb/>to</expan> igitur velum impellente, <expan abbr="malū">malum</expan> <lb/>ad partem contrariam vergit, pu­<lb/>ta in FD. </s> | <s id="id.000666">E&longs;to enim nauis AB; cuius <lb/>malus CD: prora A: puppis B; <expan abbr="vē-to">ven­<lb/>to</expan> igitur velum impellente, <expan abbr="malū">malum</expan> <lb/>ad partem contrariam vergit, pu­<lb/>ta in FD. </s> |
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| <s id="id.000667">At <expan abbr="quoniã">quoniam</expan> ca<gap/>che&longs;ium <lb/>funi ad puppim vnitur in B, nauim, <lb/>hoc e&longs;t, ip&longs;am puppim trahatne­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.073.jpg"/>ce&longs;&longs;e e&longs;t. </s> | <s id="id.000667">At <expan abbr="quoniã">quoniam</expan> catche&longs;ium <lb/>funi ad puppim vnitur in B, nauim, <lb/>hoc e&longs;t, ip&longs;am puppim trahat ne­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.073.jpg"/>ce&longs;&longs;e e&longs;t. </s> |
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| <s id="id.000668">non pote&longs;t autem; quoniam &longs;uburræ grauitas & <lb/>onera, quæ naui impo&longs;ita inter D. & <emph type="italics"/>B.<emph.end type="italics"/> grauitatis centrum <lb/>circa punctum E con&longs;tituunt, quod quidem vi ventorum <lb/>inclinante malo ab E, in G eleuaretur, quo igitur minor <lb/>fuerit proportio CD ad DE & maius pondus ip&longs;um cu­<lb/>ius grauitatis centrum in E minus præualebit potentia <lb/>pellens in C ad eleu<gap/>tionem partis nauigij, quæ à mali &longs;e­<lb/>de ad puppim intercedit, An igitur malus &longs;it vectis, pesve­<lb/>rò fulcimentum, pondus autem quodvecte mouetur, <expan abbr="ipsū">ipsum</expan> <lb/>nauigium, vt placuit Ari&longs;toteli, & qua item ratione malus <lb/>in nauim vt vectis operetur, exijs quae dicta &longs;unt, facilè pa­<lb/>tet. </s></p> | <s id="id.000668">non pote&longs;t autem; quoniam &longs;uburræ grauitas & <lb/>onera, quæ naui impo&longs;ita inter D. & <emph type="italics"/>B.<emph.end type="italics"/> grauitatis centrum <lb/>circa punctum E con&longs;tituunt, quod quidem vi ventorum <lb/>inclinante malo ab E, in G eleuaretur, quo igitur minor <lb/>fuerit proportio CD ad DE & maius pondus ip&longs;um cu­<lb/>ius grauitatis centrum in E minus præualebit potentia <lb/>pellens in C ad eleuationem partis nauigij, quæ à mali &longs;e­<lb/>de ad puppim intercedit, An igitur malus &longs;it vectis, pes ve­<lb/>rò fulcimentum, pondus autem quod vecte mouetur, <expan abbr="ipsū">ipsum</expan> <lb/>nauigium, vt placuit Ari&longs;toteli, & qua item ratione malus <lb/>in nauim vt vectis operetur, exijs quae dicta &longs;unt, facilè pa­<lb/>tet. </s></p> |
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| </subchap1><subchap1> | </subchap1><subchap1> |
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| <s id="id.000669">QVÆSTIO VII.<!-- KEEP S--></s></p><p type="head"> | <s id="id.000669">QVÆSTIO VII.<!-- KEEP S--></s></p><p type="head"> |
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| <s id="id.000670"><emph type="italics"/>Quaritur, Cur quando ex puppi nauigare voluerint, non flante ex <lb/>puppi vento, veli quidem partem, quæ ad gubernatorem vergit, <lb/>con&longs;tringunt; illam verò quæ proram ver&longs;us e&longs;t, pedem <lb/>facientes, relaxant?<emph.end type="italics"/></s></p><p type="main"> | <s id="id.000670"><emph type="italics"/>Quæritur, Cur quando ex puppi nauigare voluerint, non flante ex <lb/>puppi vento, veli quidem partem, quæ ad gubernatorem vergit, <lb/>con&longs;tringunt; illam verò quæ proram ver&longs;us e&longs;t, pedem <lb/>facientes, relaxant?<emph.end type="italics"/></s></p><p type="main"> |
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| <s id="id.000671">Mirabilis huius effectionis cau&longs;&longs;am explicat Ari&longs;tote­<lb/>les. </s> | <s id="id.000671">Mirabilis huius effectionis cau&longs;&longs;am explicat Ari&longs;tote­<lb/>les. </s> |
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| <s id="id.000677">E&longs;to nauis A <emph type="italics"/>B<emph.end type="italics"/>, cuius prora A, puppis verò D, guber­<lb/>naculum C<emph type="italics"/>B<emph.end type="italics"/>, temonis ala <emph type="italics"/>B<emph.end type="italics"/>D, veli &longs;inus EF, velum vero <lb/>ita con&longs;titutum, vt directè ex puppi flantem ventum exci-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.074.jpg"/><figure id="id.007.00.074.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.074.1.jpg"></figure><lb/>piat. </s> | <s id="id.000677">E&longs;to nauis A <emph type="italics"/>B<emph.end type="italics"/>, cuius prora A, puppis verò D, guber­<lb/>naculum C<emph type="italics"/>B<emph.end type="italics"/>, temonis ala <emph type="italics"/>B<emph.end type="italics"/>D, veli &longs;inus EF, velum vero <lb/>ita con&longs;titutum, vt directè ex puppi flantem ventum exci-<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.074.jpg"/><figure id="id.007.00.074.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.074.1.jpg"></figure><lb/>piat. </s> |
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| <s id="id.000678">Hoc vbi euenerit, naui­<lb/>gium, rectâ è puppi mouetur <lb/>in proram; Si autem ventus la­<lb/>teraliter &longs;pirat, puta à parte <lb/>G ver&longs;us H & nihilo &longs;ecius na­<lb/>uigium, ac &longs;i ventus ex pup­<lb/>pi e&longs;&longs;et antror&longs;um propelle­<lb/>re volunt, velum quidem obli­<lb/>quant partem cius infimam, <lb/>pedem nempe, quæ e&longs;t in F <lb/>contrahentes, Cornu verò <lb/>antennæ vbi E, proram ver&longs;us <lb/>laxantes ventumque; ip&longs;um obliquè ex cipientesid <expan abbr="efficiūt">efficiunt</expan>, <lb/>vt ventus minus violenter feriat, & minori &longs;ui parte <expan abbr="velū">velum</expan> <lb/>impleat, & quoniam ventus velum pellit in partem con­<lb/>trariam, nempe in H, ip&longs;ivt vento re&longs;i&longs;tant conuer&longs;o gu­<lb/>bernaculo ex C in L, & temone <emph type="italics"/>B<emph.end type="italics"/>D, in <emph type="italics"/>B<emph.end type="italics"/>M compellunt <lb/>proram ad partem à qua ventu<gap/> ip&longs;e &longs;pirat. </s> | <s id="id.000678">Hoc vbi euenerit, naui­<lb/>gium, rectâ è puppi mouetur <lb/>in proram; Si autem ventus la­<lb/>teraliter &longs;pirat, puta à parte <lb/>G ver&longs;us H & nihilo &longs;ecius na­<lb/>uigium, ac &longs;i ventus ex pup­<lb/>pi e&longs;&longs;et antror&longs;um propelle­<lb/>re volunt, velum quidem obli­<lb/>quant partem eius infimam, <lb/>pedem nempe, quæ e&longs;t in F <lb/>contrahentes, Cornu verò <lb/>antennæ vbi E, proram ver&longs;us <lb/>laxantes ventumque; ip&longs;um obliquè excipientes id <expan abbr="efficiūt">efficiunt</expan>, <lb/>vt ventus minus violenter feriat, & minori &longs;ui parte <expan abbr="velū">velum</expan> <lb/>impleat, & quoniam ventus velum pellit in partem con­<lb/>trariam, nempe in H, ip&longs;i vt vento re&longs;i&longs;tant conuer&longs;o gu­<lb/>bernaculo ex C in L, & temone <emph type="italics"/>B<emph.end type="italics"/>D, in <emph type="italics"/>B<emph.end type="italics"/>M compellunt <lb/>proram ad partem à qua ventu<gap/> ip&longs;e &longs;pirat. </s> |
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| <s id="id.000679">Sit igitur inter <lb/>ventum & temonem pugna, illo proram in dextram, hoc <lb/>verò eandem in &longs;ini&longs;tram pellente, <expan abbr="itaq;">itaque</expan> cum neuter præ­<lb/>ualeat, nece&longs;&longs;ario nauis mediam viam, quæ inter <expan abbr="vtramq;">vtramque</expan> <lb/>e&longs;t, &longs;uo cur&longs;u tenet. </s> | <s id="id.000679">Sit igitur inter <lb/>ventum & temonem pugna, illo proram in dextram, hoc <lb/>verò eandem in &longs;ini&longs;tram pellente, <expan abbr="itaq;">itaque</expan> cum neuter præ­<lb/>ualeat, nece&longs;&longs;ario nauis mediam viam, quæ inter <expan abbr="vtramq;">vtramque</expan> <lb/>e&longs;t, &longs;uo cur&longs;u tenet. </s> |
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| <s id="id.000698">Nos igitur, ad Ari&longs;totelis mentem, <lb/>primam rotationis &longs;peciem, quæ e&longs;t &longs;ecundum ab&longs;idem, <lb/>examinabimus. </s></p><figure id="id.007.00.076.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.076.1.jpg"></figure><p type="main"> | <s id="id.000698">Nos igitur, ad Ari&longs;totelis mentem, <lb/>primam rotationis &longs;peciem, quæ e&longs;t &longs;ecundum ab&longs;idem, <lb/>examinabimus. </s></p><figure id="id.007.00.076.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.076.1.jpg"></figure><p type="main"> |
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| <s id="id.000699">E&longs;to rota &longs;phæ­<lb/>raue AB, cuius cen­<lb/>trum C; Horizontis <lb/>planum DE; conta­<lb/>ctus circuli in plano <lb/>B. <expan abbr="perpē">perpem</expan> dicularis ho­<lb/>rizonti à puncto <expan abbr="cō-tactus">con­<lb/>tactus</expan> B ip&longs;a <emph type="italics"/>B<emph.end type="italics"/>CA, <lb/>tran&longs;iens per <expan abbr="centrū">centrum</expan> <lb/>C, partes rotæ circa <lb/>perpendicularem AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, angulus contactus G<emph type="italics"/>B<emph.end type="italics"/>E. <lb/></s> | <s id="id.000699">E&longs;to rota &longs;phæ­<lb/>raue AB, cuius cen­<lb/>trum C; Horizontis <lb/>planum DE; conta­<lb/>ctus circuli in plano <lb/>B. <expan abbr="perpēdicularis">perpendicularis</expan> ho­<lb/>rizonti à puncto <expan abbr="cō-tactus">con­<lb/>tactus</expan> B ip&longs;a <emph type="italics"/>B<emph.end type="italics"/>CA, <lb/>tran&longs;iens per <expan abbr="centrū">centrum</expan> <lb/>C, partes rotæ circa <lb/>perpendicularem AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, angulus contactus G<emph type="italics"/>B<emph.end type="italics"/>E. <lb/></s> |
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| <s id="id.000700">Primo itaque id con&longs;tat, circulum in puncto planum, &longs;eu <lb/>lineam contingere. </s> | <s id="id.000700">Primo itaque id con&longs;tat, circulum in puncto planum, &longs;eu <lb/>lineam contingere. </s> |
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| <s id="id.000702">Angulum porro, quem à <lb/>terra &longs;emotum dicit, ip&longs;e angulus e&longs;t contingentiae. </s> | <s id="id.000702">Angulum porro, quem à <lb/>terra &longs;emotum dicit, ip&longs;e angulus e&longs;t contingentiae. </s> |
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| <s id="id.000703">cleua­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.077.jpg"/>tur enim ex <emph type="italics"/>B<emph.end type="italics"/> in G. <!-- KEEP S--></s> | <s id="id.000703">eleua­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.077.jpg"/>tur enim ex <emph type="italics"/>B<emph.end type="italics"/> in G. <!-- KEEP S--></s> |
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| <s id="id.000704">Si autem corpus quodpiam in plano <lb/>fuerit, puta HI in puncto illud tanget ci culus ei occur­<lb/>rens, exempli gratiâ in K. <!-- KEEP S--></s> | <s id="id.000704">Si autem corpus quodpiam in plano <lb/>fuerit, puta HI in puncto illud tanget ci culus ei occur­<lb/>rens, exempli gratiâ in K. <!-- KEEP S--></s> |
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| <s id="id.000706">In lateratis autem &longs;ecus fit, quippe quænec in <expan abbr="pū-cto">pun­<lb/>cto</expan> &longs;eu &longs;ecundum paruam &longs;ui partem, planum tangunt, <lb/>nec &longs;emotum vt circulus à plano habent angulum, nec <lb/>impingentes offen diculum in puncto tangunt. </s> | <s id="id.000706">In lateratis autem &longs;ecus fit, quippe quænec in <expan abbr="pū-cto">pun­<lb/>cto</expan> &longs;eu &longs;ecundum paruam &longs;ui partem, planum tangunt, <lb/>nec &longs;emotum vt circulus à plano habent angulum, nec <lb/>impingentes offen diculum in puncto tangunt. </s> |
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| <s id="id.000707">Cæterùm <lb/>poti&longs;&longs;imam facilitatis motus in rotatione quæ fit &longs;ecun­<lb/>dum ab&longs;idem, e&longs;&longs;e cau&longs;&longs;am dixit, nempe quò nutat pon­<lb/>dus cò à mouente impelli ac moueri. </s> | <s id="id.000707">Cæterùm <lb/>poti&longs;&longs;imam facilitatis motus in rotatione quæ fit &longs;ecun­<lb/>dum ab&longs;idem, e&longs;&longs;e cau&longs;&longs;am dixit, nempe quò nutat pon­<lb/>dus eò à mouente impelli ac moueri. </s> |
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| <s id="id.000708">Primò igitu circu­<lb/>laris &longs;phæricaue figura in æquilibrio &longs;tat; æquales enim <lb/>&longs;unt partes quæ circa perpendicularem: ceu &longs;unt AF<emph type="italics"/>B<emph.end type="italics"/>, <lb/>AG<emph type="italics"/>B.<emph.end type="italics"/> &longs;i enim impul&longs;us fiat ex parte F, pars oppo&longs;ita nuta­<lb/>bit, & propendet in pa<gap/>tem G, & &longs;uo nutu motuque; &longs;ecum <lb/>trahet partem AF<emph type="italics"/>B<emph.end type="italics"/>, fietqueue progre&longs;&longs;us. </s> | <s id="id.000708">Primò igitur circu­<lb/>laris &longs;phæricaue figura in æquilibrio &longs;tat; æquales enim <lb/>&longs;unt partes quæ circa perpendicularem: ceu &longs;unt AF<emph type="italics"/>B<emph.end type="italics"/>, <lb/>AG<emph type="italics"/>B.<emph.end type="italics"/> &longs;i enim impul&longs;us fiat ex parte F, pars oppo&longs;ita nuta­<lb/>bit, & propendet in partem G, & &longs;uo nutu motuque; &longs;ecum <lb/>trahet partem AF<emph type="italics"/>B<emph.end type="italics"/>, fietqueue progre&longs;&longs;us. </s> |
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| <s id="id.000709">Si enim ducatur <lb/>FCG diameter, ip&longs;i horizonti æ que di&longs;tans, erit veluti li­<lb/>bra, cuius pondera vtrinque AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, brachia verò <lb/>æqualia CF, CG. <!-- KEEP S--></s> | <s id="id.000709">Si enim ducatur <lb/>FCG diameter, ip&longs;i horizonti æ que di&longs;tans, erit veluti li­<lb/>bra, cuius pondera vtrinque AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, brachia verò <lb/>æqualia CF, CG. <!-- KEEP S--></s> |
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| <s id="id.000710">Potentia autem quâ trahitur pellitur­<lb/>ue ad in&longs;tar ponderis &longs;e habet, quo addito partium alteri, <lb/>facto queue rece&longs;&longs;u ab æquilibrio, &longs;equetur motus. </s> | <s id="id.000710">Potentia autem quâ trahitur pellitur­<lb/>ue ad in&longs;tar ponderis &longs;e habet, quo addito partium alteri, <lb/>facto queue rece&longs;&longs;u ab æquilibrio, &longs;equetur motus. </s> |
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| <s id="id.000711">Putauêre <lb/>quidam, vt refert Philo&longs;ophus, <expan abbr="circularē">circularem</expan> lineam, ita per­<lb/>peti motu ver&longs;atumiri, vt manentia, propte<gap/> contrarium <lb/>nixum, manent, neque enim circulus in plano contrarium <lb/>nixum habet, cum &longs;it, veluti dicebamus, in æquilibrio & <lb/>facilis in vtramuis partem moueri. </s> | <s id="id.000711">Putauêre <lb/>quidam, vt refert Philo&longs;ophus, <expan abbr="circularē">circularem</expan> lineam, ita per­<lb/>peti motu ver&longs;atum iri, vt manentia, propter contrarium <lb/>nixum, manent, neque enim circulus in plano contrarium <lb/>nixum habet, cum &longs;it, veluti dicebamus, in æquilibrio & <lb/>facilis in vtramuis partem moueri. </s> |
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| <s id="id.000712">Veruntamen perpe­<lb/>tuum e&longs;&longs;e non po&longs;&longs;e horum corporum motum, ea e&longs;t cau&longs;­<lb/>&longs;a, quod violentum accidat naturæ, & ideo non durabile. <lb/></s> | <s id="id.000712">Veruntamen perpe­<lb/>tuum e&longs;&longs;e non po&longs;&longs;e horum corporum motum, ea e&longs;t cau&longs;­<lb/>&longs;a, quod violentum accidat naturæ, & ideo non durabile. <lb/></s> |
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| <s id="id.000713">Ad hæc, addit Philo&longs;ophus, Maiores circulos ad minores <lb/>nutum habere <expan abbr="quēdam">quendam</expan>; & nutum maioris ad minoris nu­<lb/>tum, &longs;e habere vt angulos ad angulos, & <expan abbr="diametrū">diametrum</expan> ad dia­<lb/>metrum. </s> | <s id="id.000713">Ad hæc, addit Philo&longs;ophus, Maiores circulos ad minores <lb/>nutum habere <expan abbr="quēdam">quendam</expan>; & nutum maioris ad minoris nu­<lb/>tum, &longs;e habere vt angulos ad angulos, & <expan abbr="diametrū">diametrum</expan> ad dia­<lb/>metrum. </s> |
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| <s id="id.000714">Angulos autem hî c&longs;ectores ip&longs;os vocat; oportet <lb/>enim circulos tum maiores tum minores circa idein cen­<lb/>trum e&longs;&longs;e con&longs;titutos. </s> | <s id="id.000714">Angulos autem hîc &longs;ectores ip&longs;os vocat; oportet <lb/>enim circulos tum maiores tum minores circa idem cen­<lb/>trum e&longs;&longs;e con&longs;titutos. </s> |
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| <s id="id.000715">Hæc autem non ab&longs;imili ab eo <lb/>quod &longs;uprà po&longs;uimus &longs;chemate explicantur. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.078.jpg"/><figure id="id.007.00.078.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.078.1.jpg"></figure><p type="main"> | <s id="id.000715">Hæc autem non ab&longs;imili ab eo <lb/>quod &longs;uprà po&longs;uimus &longs;chemate explicantur. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.078.jpg"/><figure id="id.007.00.078.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.078.1.jpg"></figure><p type="main"> |
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| <s id="id.000716">E&longs;to enim circulus <lb/>AB circa centrum, C, <lb/>Horizontis planum DE, <lb/>tangens circulum in B, <lb/>linea verò perpendicu­<lb/>laris per centrum BCA. <lb/><!-- KEEP S--></s> | <s id="id.000716">E&longs;to enim circulus <lb/>AB circa centrum, C, <lb/>Horizontis planum DE, <lb/>tangens circulum in B, <lb/>linea verò perpendicu­<lb/>laris per centrum BCA. <lb/><!-- KEEP S--></s> |
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| <s id="id.000717">Sit autem circa idem <expan abbr="cē-trum">cen­<lb/>trum</expan> C, minor circulus <lb/>FG, ducatur queue CH &longs;e­<lb/>cu<gap/> minorem circulum in I, tangens verò maiorem in H, <lb/>con&longs;tituen&longs;queue cum AC linea angulum ACH, duos an­<lb/>gulos, ex Ari&longs;totelis mente comprehendentem, hoc e&longs;t, <lb/>duos &longs;ectores ACH, FCI. quoniam igitur &longs;ector &longs;eu an­<lb/>gulus ACH, &longs;uo &longs;patio &longs;uperat angulum &longs;eu &longs;ectorem <lb/>FGI, facilè ex nutu quem maior &longs;upra minorem habet, <lb/>maior ip&longs;e mìnorem mouet. </s> | <s id="id.000717">Sit autem circa idem <expan abbr="cē-trum">cen­<lb/>trum</expan> C, minor circulus <lb/>FG, ducatur queue CH &longs;e­<lb/>cus minorem circulum in I, tangens verò maiorem in H, <lb/>con&longs;tituen&longs;queue cum AC linea angulum ACH, duos an­<lb/>gulos, ex Ari&longs;totelis mente comprehendentem, hoc e&longs;t, <lb/>duos &longs;ectores ACH, FCI. quoniam igitur &longs;ector &longs;eu an­<lb/>gulus ACH, &longs;uo &longs;patio &longs;uperat angulum &longs;eu &longs;ectorem <lb/>FGI, facilè ex nutu quem maior &longs;upra minorem habet, <lb/>maior ip&longs;e mìnorem mouet. </s> |
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| <s id="id.000718">Videtur autem tacitè Philo­<lb/>&longs;ophus hæc ad vectis naturam referre, cuius altera extre­<lb/>mitatum in centro &longs;it, altera verò in ab &longs;ide, & ita &longs;e habe­<lb/>renutum maioris &longs;upra minorem, vt vectis ad vectem, hoc <lb/>e&longs;t, &longs;emid<gap/>ameter ad &longs;emidiametrum, &longs;eu &longs;ector ad &longs;ecto­<lb/>rem, quos quidem &longs;ectores, vt vidimus, angulos appellat. <lb/></s> | <s id="id.000718">Videtur autem tacitè Philo­<lb/>&longs;ophus hæc ad vectis naturam referre, cuius altera extre­<lb/>mitatum in centro &longs;it, altera verò in ab &longs;ide, & ita &longs;e habe­<lb/>re nutum maioris &longs;upra minorem, vt vectis ad vectem, hoc <lb/>e&longs;t, &longs;emidiameter ad &longs;emidiametrum, &longs;eu &longs;ector ad &longs;ecto­<lb/>rem, quos quidem &longs;ectores, vt vidimus, angulos appellat. <lb/></s> |
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| <s id="id.000719">Hæc autem quæ de nutu refert, licet &longs;ubtilia &longs;int, vera e&longs;­<lb/>&longs;e non videntur. </s> | <s id="id.000719">Hæc autem quæ de nutu refert, licet &longs;ubtilia &longs;int, vera e&longs;­<lb/>&longs;e non videntur. </s> |
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| <s id="id.000720">Si enim in figura producatur ad oppo&longs;i­<lb/>tam partem &longs;emidiameter HC in K &longs;ecans minorem cir­<lb/>culum in L, duos alios &longs;ectores angulosue habebimus, <expan abbr="nē-pe">nen­<lb/>pe</expan> KCB, LCG, ip&longs;is ACHFCI æ quales. </s> | <s id="id.000720">Si enim in figura producatur ad oppo&longs;i­<lb/>tam partem &longs;emidiameter HC in K &longs;ecans minorem cir­<lb/>culum in L, duos alios &longs;ectores angulosue habebimus, <expan abbr="nē-pe">nem­<lb/>pe</expan> KCB, LCG, ip&longs;is ACHFCI æquales. </s> |
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| <s id="id.000721"><expan abbr="Itaq;">Itaque</expan> quan­<lb/>tum adiuuat motum anguli ACH maioris nutus, in de­<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus (vtita appellem) in <expan abbr="a&longs;cendē-do">a&longs;cenden­<lb/>do</expan> ad partes A. & &longs;anè quatenus ad reinaturam pertinet <lb/>& ad ip&longs;um æquilibrium, non differunt maiores circuli à <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex ali quaratione minores videntur fore ad motum faci­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.079.jpg"/>liores, tum quia data materiæ æqualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planuin <lb/>circum ferentiae minoris quàm maioris circuli, vt in &longs;ubie­<lb/><figure id="id.007.00.079.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.079.1.jpg"></figure><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i­<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu­<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>quæ tam in maioribus quàm in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examin abimus. </s></p><p type="main"> | <s id="id.000721"><expan abbr="Itaq;">Itaque</expan> quan­<lb/>tum adiuuat motum anguli ACH maioris nutus, in de­<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus (vt ita appellem) in <expan abbr="a&longs;cendē-do">a&longs;cenden­<lb/>do</expan> ad partes A. & &longs;anè quatenus ad rei naturam pertinet <lb/>& ad ip&longs;um æquilibrium, non differunt maiores circuli à <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex aliqua ratione minores videntur fore ad motum faci­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.079.jpg"/>liores, tum quia data materiæ æqualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planum <lb/>circumferentiae minoris quàm maioris circuli, vt in &longs;ubie­<lb/><figure id="id.007.00.079.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.079.1.jpg"></figure><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i­<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu­<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>quæ tam in maioribus quàm in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examinabimus. </s></p><p type="main"> |
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| <s id="id.000722">Cæterùm vt aliquid de motu qui &longs;e cundum ab&longs;idem <lb/>fit, ex no&longs;tro penu promamus, Dicimus, Circulos, rota&longs;ue, <lb/>quæ hoc pacto mouentur, vel per horizontis planum mo­<lb/>ueri, vel per accliue, aut decliue. </s> | <s id="id.000722">Cæterùm vt aliquid de motu qui &longs;e cundum ab&longs;idem <lb/>fit, ex no&longs;tro penu promamus, Dicimus, Circulos, rota&longs;ue, <lb/>quæ hoc pacto mouentur, vel per horizontis planum mo­<lb/>ueri, vel per accliue, aut decliue. </s> |
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| <s id="id.000723">Siautem perhorizontis <lb/>planum, ideo facilem e&longs;&longs;e motum, quòd nunquam, cæte­<lb/>ris paribus, centrum grauitatis ip&longs;ius corporis à centro <lb/>mundi, in ip&longs;a rotatione, fiat remotius. </s></p><figure id="id.007.00.079.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.079.2.jpg"></figure><p type="main"> | <s id="id.000723">Siautem perhorizontis <lb/>planum, ideo facilem e&longs;&longs;e motum, quòd nunquam, cæte­<lb/>ris paribus, centrum grauitatis ip&longs;ius corporis à centro <lb/>mundi, in ip&longs;a rotatione, fiat remotius. </s></p><figure id="id.007.00.079.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.079.2.jpg"></figure><p type="main"> |
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| <s id="id.000724">E&longs;to enim planum, <lb/>horizontis AB, cui circu­<lb/>lus in&longs;i&longs;tat AD, circa cen­<lb/>trum C, diui&longs;us per <expan abbr="centrū">centrum</expan> <lb/>ip&longs;um à perpendiculari <lb/>ACD; Ducatur autem per <lb/>centrum C recta linea ho­<lb/>rizonti æquidi&longs;tans, ECFG: dum diuidatur circulus vt­<lb/><gap/>unque in partes AH, HF, FI, ID, & CI, CH iungan­<lb/>tur. </s> | <s id="id.000724">E&longs;to enim planum, <lb/>horizontis AB, cui circu­<lb/>lus in&longs;i&longs;tat AD, circa cen­<lb/>trum C, diui&longs;us per <expan abbr="centrū">centrum</expan> <lb/>ip&longs;um à perpendiculari <lb/>ACD; Ducatur autem per <lb/>centrum C recta linea ho­<lb/>rizonti æquidi&longs;tans, ECFG: dum diuidatur circulus vt­<lb/>cunque in partes AH, HF, FI, ID, & CI, CH iungan­<lb/>tur. </s> |
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| <s id="id.000725">Po&longs;thæc intelligatur circulum &longs;ecundum ab&longs;idem <lb/>moueri ad partes G, erit igitur aliquando punctum H, <lb/>rangens horizontis planum, tangat autem in K, tum F in <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.080.jpg"/>L, I in N. <!-- REMOVE S-->D verò in O. <!-- KEEP S--></s> | <s id="id.000725">Po&longs;thæc intelligatur circulum &longs;ecundum ab&longs;idem <lb/>moueri ad partes G, erit igitur aliquando punctum H, <lb/>tangens horizontis planum, tangat autem in K, tum F in <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.080.jpg"/>L, I in N. <!-- REMOVE S-->D verò in O. <!-- KEEP S--></s> |
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| <s id="id.000727">Centrum ergo circuli, quod idem & grauitatis e&longs;t <expan abbr="centrū">centrum</expan>, <lb/>feretur per rectam CPQRS, &longs;unt enim KP, LQ, NR, <lb/>OS ip&longs;i AC &longs;emidiam etro æquales, <expan abbr="nūquam">nunquam</expan> igitur cen­<lb/>trum ip&longs;um C in circuli rotatione ab horizontis plano e­<lb/>leuabitur, nec à mundi centro fietremotius. </s></p><p type="main"> | <s id="id.000727">Centrum ergo circuli, quod idem & grauitatis e&longs;t <expan abbr="centrū">centrum</expan>, <lb/>feretur per rectam CPQRS, &longs;unt enim KP, LQ, NR, <lb/>OS ip&longs;i AC &longs;emidiam etro æquales, <expan abbr="nūquam">nunquam</expan> igitur cen­<lb/>trum ip&longs;um C in circuli rotatione ab horizontis plano e­<lb/>leuabitur, nec à mundi centro fietremotius. </s></p><p type="main"> |
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| <s id="id.000728">Hoc autem longè aliter cæteris figuris contingit, <lb/>quarum motus ideo in æ qualis, quòd non &longs;em per in rota­<lb/>tione centium grauitatis eandem &longs;eruet à mundi centro <lb/>di&longs;tantiam. </s></p><figure id="id.007.00.080.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.080.1.jpg"></figure><p type="main"> | <s id="id.000728">Hoc autem longè aliter cæteris figuris contingit, <lb/>quarum motus ideo in æqualis, quòd non &longs;emper in rota­<lb/>tione centrum grauitatis eandem &longs;eruet à mundi centro <lb/>di&longs;tantiam. </s></p><figure id="id.007.00.080.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.080.1.jpg"></figure><p type="main"> |
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| <s id="id.000729">E&longs;to enim Ellip&longs;is <lb/>ABCD, cuius <expan abbr="cētrum">centrum</expan> <lb/>E, diameter longior <lb/>BED, breuior AEC, <lb/>Horizontis planum, <lb/>FCG. locus contactus <lb/>C perpendicularis à <lb/>contactu per centrum i­<lb/>p&longs;a CEA diuidens El­<lb/>lip&longs;im in partes æquales, & æqueponderantes ABC, <lb/>ADC. <!-- KEEP S--></s> | <s id="id.000729">E&longs;to enim Ellip&longs;is <lb/>ABCD, cuius <expan abbr="cētrum">centrum</expan> <lb/>E, diameter longior <lb/>BED, breuior AEC, <lb/>Horizontis planum, <lb/>FCG. locus contactus <lb/>C perpendicularis à <lb/>contactu per centrum i­<lb/>p&longs;a CEA diuidens El­<lb/>lip&longs;im in partes æquales, & æqueponderantes ABC, <lb/>ADC. <!-- KEEP S--></s> |
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| <s id="id.000731">Rotetur ellip&longs;is &longs;ecun dum ab&longs;i­<lb/>dem, fiet igitur punctum H in K, & à puncto K horizonti <lb/>perpendicularis erigatur KL, quæ fiat æ qualis EH. <!-- KEEP S--></s> | <s id="id.000731">Rotetur ellip&longs;is &longs;ecun dum ab&longs;i­<lb/>dem, fiet igitur punctum H in K, & à puncto K horizonti <lb/>perpendicularis erigatur KL, quæ fiat æ qualis EH. <!-- KEEP S--></s> |
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| <s id="id.000732">P o&longs;t <lb/>hæc punctum I eritin M, & ab M perpen dicularis, æqua­<lb/>lis EI. rui&longs;us D fiat in O, & ip&longs;i ED, æqualis perpendicu­<lb/>laris OP. <!-- KEEP S--></s> | <s id="id.000732">P o&longs;t <lb/>hæc punctum I erit in M, & ab M perpendicularis, æqua­<lb/>lis EI. rur&longs;us D fiat in O, & ip&longs;i ED, æqualis perpendicu­<lb/>laris OP. <!-- KEEP S--></s> |
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| <s id="id.000733">Mota igitur ellip&longs;ià C in K, haud ita difficilis e­<lb/>rit motus, quippe quod haud multum EH &longs;uperet EC, at <lb/>difficilior erit translatio in M, difficillima verò in O. Val<gap/><lb/>de enim à &longs;itu E, ibi attollitur grauitatis centrum, a&longs;cen­<lb/>dens nempe vbi P. <!-- KEEP S--></s> | <s id="id.000733">Mota igitur ellip&longs;ià C in K, haud ita difficilis e­<lb/>rit motus, quippe quod haud multum EH &longs;uperet EC, at <lb/>difficilior erit translatio in M, difficillima verò in O. Val<lb/>de enim à &longs;itu E, ibi attollitur grauitatis centrum, a&longs;cen­<lb/>dens nempe vbi P. <!-- KEEP S--></s> |
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| <s id="id.000734">Videmus igitur ex his eandem poten­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.081.jpg"/>tiam in mouendo ellip&longs;im, haud pariter &longs;e habere, vt in <lb/>mouendo circulum. </s> | <s id="id.000734">Videmus igitur ex his eandem poten­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.081.jpg"/>tiam in mouendo ellip&longs;im, haud pariter &longs;e habere, vt in <lb/>mouendo circulum. </s> |
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| <s id="id.000749">Dimi&longs;&longs;a igitur <lb/>rota, contingit quidem planum decliue in puncto D. <!-- KEEP S--></s> | <s id="id.000749">Dimi&longs;&longs;a igitur <lb/>rota, contingit quidem planum decliue in puncto D. <!-- KEEP S--></s> |
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| <s id="id.000750">At <lb/>centrum grauitatis premit &longs;e cun dam per lineam perpen­<lb/>dicularem FG, non &longs;u&longs;tentatur autem in H, quippe quod <lb/>inter planum & circum <expan abbr="ferentiã">ferentiam</expan> intercedat &longs;patium HG, <lb/>nec H locum habeat cui innitatur, corpus autem ita per <lb/>lineam DI e&longs;t diui&longs;um, vt longè maior &longs;it pars IFCHD <lb/>ip&longs;a DI, & centrum in ea parte eadat quæ non fulcitur. </s> | <s id="id.000750">At <lb/>centrum grauitatis premit &longs;ecundam per lineam perpen­<lb/>dicularem FG, non &longs;u&longs;tentatur autem in H, quippe quod <lb/>inter planum & circum <expan abbr="ferentiã">ferentiam</expan> intercedat &longs;patium HG, <lb/>nec H locum habeat cui innitatur, corpus autem ita per <lb/>lineam DI e&longs;t diui&longs;um, vt longè maior &longs;it pars IFCHD <lb/>ip&longs;a DI, & centrum in ea parte cadat quæ non fulcitur. </s> |
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| <s id="id.000751">i. <lb/></s> | <s id="id.000751">i­<lb/>taque &longs;uopte nutu, cum extra fulcimentum &longs;it D & per­<lb/>pendicularem DI ad inferiores partes rapidè rotans de­<lb/>labitur. </s> |
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| <s id="id.000752">taque &longs;uopte nutu, cum extra ful cimentum &longs;it D & per­<lb/>pendicularem DI ad inferiores partes rapidè rotans de­<lb/>labitur. </s> | |
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| <s id="id.000753">Ducatur autem perpen dicularis GL, parallela <lb/>MN, & quoniam BN breuior e&longs;t BL, erit MN ip&longs;a GL <lb/>breuior. </s> | <s id="id.000753">Ducatur autem perpen dicularis GL, parallela <lb/>MN, & quoniam BN breuior e&longs;t BL, erit MN ip&longs;a GL <lb/>breuior. </s> |
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| <s id="id.000754">E&longs;t igitur punctum M mundi centro propius <lb/>quàm D & G, quare eò non impedita rota ip&longs;a &longs;uo nutu <lb/>feretur, nec&longs;tabit donec in fimum <expan abbr="locū">locum</expan> vbi quie&longs;catnan. <lb/></s> | <s id="id.000754">E&longs;t igitur punctum M mundi centro propius <lb/>quàm D & G, quare eò non impedita rota ip&longs;a &longs;uo nutu <lb/>feretur, nec &longs;tabit donec in fimum <expan abbr="locū">locum</expan> vbi quie&longs;cat nan­<lb/>ci&longs;catur. </s> |
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| <s id="id.000755">ci&longs;catur. </s> | |
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| <s id="id.000756">Po&longs;&longs;umus etiam Rota &longs;phæraue in plano decliui <lb/>collocata, datam potentiam inuenire, quæ extremitati <lb/>diametri ad eam partem quavergit applicata ip&longs;am rotam <lb/>&longs;phæramue impediatne delabatur. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.083.jpg"/><figure id="id.007.00.083.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.083.1.jpg"></figure><p type="main"> | <s id="id.000756">Po&longs;&longs;umus etiam Rota &longs;phæraue in plano decliui <lb/>collocata, datam potentiam inuenire, quæ extremitati <lb/>diametri ad eam partem quavergit applicata ip&longs;am rotam <lb/>&longs;phæramue impediatne delabatur. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.083.jpg"/><figure id="id.007.00.083.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.083.1.jpg"></figure><p type="main"> |
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| <s id="id.000759">Ducatur per C ip&longs;i hori­<lb/>zonti perpendiculatis FCG <lb/>circulum <expan abbr="&longs;ecãs">&longs;ecans</expan> in G tum per <lb/>E ip&longs;i CG perpendicularis, ip&longs;i verò BF horizonti æ qui­<lb/>di&longs;tans HEI ceu vectis, cuius fulcimentum I re&longs;pondens <lb/>ip&longs;i C, pondus verò in E, vbi grauitatis e&longs;t centrum. </s> | <s id="id.000759">Ducatur per C ip&longs;i hori­<lb/>zonti perpendiculatis FCG <lb/>circulum <expan abbr="&longs;ecãs">&longs;ecans</expan> in G tum per <lb/>E ip&longs;i CG perpendicularis, ip&longs;i verò BF horizonti æ qui­<lb/>di&longs;tans HEI ceu vectis, cuius fulcimentum I re&longs;pondens <lb/>ip&longs;i C, pondus verò in E, vbi grauitatis e&longs;t centrum. </s> |
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| <s id="id.000760">Ap­<lb/>plicata igitur potentia in H erit pondus inter fulcimen­<lb/>tum & potentiam, quare vt IE ad IH ita potentla &longs;u&longs;ti­<lb/>nens in H ad pondus in E, quod demon&longs;trandum fuerat. </s></p><p type="main"> | <s id="id.000760">Ap­<lb/>plicata igitur potentia in H erit pondus inter fulcimen­<lb/>tum & potentiam, quare vt IE ad IH ita potentia &longs;u&longs;ti­<lb/>nens in H ad pondus in E, quod demon&longs;trandum fuerat. </s></p><p type="main"> |
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| <s id="id.000761">Quippiam &longs;imile o&longs;ten dit Pappus 1. 8. prop. | |
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| 9. alijs <lb/>tamen &longs;uppo&longs;itis & con&longs;ideratis. </s> | <s id="id.000761">Quippiam &longs;imile o&longs;tendit Pappus 1. 8. prop. 9. alijs <lb/>tamen &longs;uppo&longs;itis & con&longs;ideratis. </s> |
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| <s id="id.000762">Dico præterea, ij&longs;dem <lb/>&longs;tantibus angulum ECI æqualem e&longs;&longs;e angulo inclinatio­<lb/>nis CBF. </s> | <s id="id.000762">Dico præterea, ij&longs;dem <lb/>&longs;tantibus angulum ECI æqualem e&longs;&longs;e angulo inclinatio­<lb/>nis CBF. </s> |
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| <s id="id.000763">Producatur HI concurrens cum ip&longs;a AB in K, <lb/>concurret autem propterea, quod CIK rectus &longs;it, ICA <lb/>minorrecto, & quoniam HK parallela e&longs;t horizonti BF <lb/>alterni anguli IKC, CBF, æquales erunt. </s> | <s id="id.000763">Producatur HI concurrens cum ip&longs;a AB in K, <lb/>concurret autem propterea, quod CIK rectus &longs;it, ICA <lb/>minorrecto, & quoniam HK parallela e&longs;t horizonti BF <lb/>alterni anguli IKC, CBF, æquales erunt. </s> |
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| <s id="id.000764">Similes autem <lb/>&longs;unt ECI, ECK, trianguli, e&longs;tqueue ECI angulus æqualis <lb/>angulo EKC, hoc e&longs;t, ip&longs;i CBF. vnde &longs;equitur, quo mi­<lb/>nor fuerit inclinationis angulus, eo facilius rotam &longs;phæ­<lb/>ramue in piano inclinato &longs;u&longs;tineri. </s> | <s id="id.000764">Similes autem <lb/>&longs;unt ECI, ECK, trianguli, e&longs;tqueue ECI angulus æqualis <lb/>angulo EKC, hoc e&longs;t, ip&longs;i CBF. vnde &longs;equitur, quo mi­<lb/>nor fuerit inclinationis angulus, eo facilius rotam &longs;phæ­<lb/>ramue in plano inclinato &longs;u&longs;tineri. </s> |
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| <s id="id.000765">quo enim minor fuerit <lb/>angulus ECI, eo minus latus EI & minor proportio EI <lb/>ad IH, & ideo minor potentia &longs;u&longs;tinens requiratur in H. <lb/><!-- KEEP S--></s> | <s id="id.000765">quo enim minor fuerit <lb/>angulus ECI, eo minus latus EI & minor proportio EI <lb/>ad IH, & ideo minor potentia &longs;u&longs;tinens requiratur in H. <lb/><!-- KEEP S--></s> |
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| <s id="id.000818">Tum fiant VX, XY, YZ, Z<foreign lang="greek">a</foreign> æ quales ip&longs;is EG, <lb/>G<emph type="italics"/>H<emph.end type="italics"/>, <emph type="italics"/>H<emph.end type="italics"/>I, IF, & per puncta X, Y, Z, <foreign lang="greek">a</foreign> & paralleli ip&longs;i ST du­<lb/>cantur <foreign lang="greek">o a p, n *z c, l g m, k x q</foreign>, tum & his ex altera parte re­<lb/>&longs;pondentes parallelæ per puncta <foreign lang="greek">b, g, d, e. </foreign></s> | <s id="id.000818">Tum fiant VX, XY, YZ, Z<foreign lang="greek">a</foreign> æ quales ip&longs;is EG, <lb/>G<emph type="italics"/>H<emph.end type="italics"/>, <emph type="italics"/>H<emph.end type="italics"/>I, IF, & per puncta X, Y, Z, <foreign lang="greek">a</foreign> & paralleli ip&longs;i ST du­<lb/>cantur <foreign lang="greek">o a p, n *z c, l g m, k x q</foreign>, tum & his ex altera parte re­<lb/>&longs;pondentes parallelæ per puncta <foreign lang="greek">b, g, d, e. </foreign></s> |
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| <s id="id.000819">Sit autem <foreign lang="greek">o a</foreign> æ­<lb/>qualis AF, <foreign lang="greek">a</foreign> <11> æqualis FD, item <foreign lang="greek">e</foreign> <10>, æqualis EC, <foreign lang="greek">e s</foreign> æqualis <lb/>EB, &longs;ed & <foreign lang="greek">n *z</foreign> aequalis OI, <foreign lang="greek">*z c</foreign> ip&longs;i P, <foreign lang="greek">l</foreign>yi<gap/> &longs;i MH, y <foreign lang="greek">m</foreign> verò ip&longs;i <lb/>HN, <expan abbr="tū">tum</expan> <foreign lang="greek">k x</foreign> ip&longs;i KG. & <foreign lang="greek">x q</foreign>, ip&longs;i GL & ip&longs;is æquales & aequa­<lb/>liter po&longs;itæ ad partes R, aliæ paralle læ <expan abbr="aptētur">aptentur</expan> per <foreign lang="greek">b, g, d, c</foreign>, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.089.jpg"/>quibusita di&longs;po&longs;itis per puncta <foreign lang="greek">o, n, l, k, h</foreign>, item per <foreign lang="greek">p, c, m, q, z</foreign>. <lb/></s> | <s id="id.000819">Sit autem <foreign lang="greek">o a</foreign> æ­<lb/>qualis AF, <foreign lang="greek">a</foreign> <11> æqualis FD, item <foreign lang="greek">e</foreign> <10>, æqualis EC, <foreign lang="greek">e s</foreign> æqualis <lb/>EB, &longs;ed & <foreign lang="greek">n *z</foreign> aequalis OI, <foreign lang="greek">*z c</foreign> ip&longs;i P, <foreign lang="greek">l</foreign>y ip&longs;i MH, y <foreign lang="greek">m</foreign> verò ip&longs;i <lb/>HN, <expan abbr="tū">tum</expan> <foreign lang="greek">k x</foreign> ip&longs;i KG. & <foreign lang="greek">x q</foreign>, ip&longs;i GL & ip&longs;is æquales & aequa­<lb/>liter po&longs;itæ ad partes R, aliæ parallelæ <expan abbr="aptētur">aptentur</expan> per <foreign lang="greek">b, g, d, c</foreign>, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.089.jpg"/>quibusita di&longs;po&longs;itis per puncta <foreign lang="greek">o, n, l, k, h</foreign>, item per <foreign lang="greek">p, c, m, q, z</foreign>. <lb/></s> |
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| <s id="id.000820">ducantur lineæ <foreign lang="greek">oh, pz</foreign>, curuæ quidern & codem pacto a­<lb/>liæ curuæ illis re&longs;pondentes <foreign lang="greek">h <10>, zs</foreign>, Erunt igitur <foreign lang="greek">o, h, <10>, <lb/>p, z, s</foreign>, parallelæ quidem eo quod lincae quæ inter ip&longs;as du­<lb/>cuntur, parallelæ &longs;int & æquales, non tamen rectæ illæ, <lb/>&longs;ed curuæ. </s> | <s id="id.000820">ducantur lineæ <foreign lang="greek">oh, pz</foreign>, curuæ quidem & eodem pacto a­<lb/>liæ curuæ illis re&longs;pondentes <foreign lang="greek">h <10>, zs</foreign>, Erunt igitur <foreign lang="greek">o, h, <10>, <lb/>p, z, s</foreign>, parallelæ quidem eo quod lineae quæ inter ip&longs;as du­<lb/>cuntur, parallelæ &longs;int & æquales, non tamen rectæ illæ, <lb/>&longs;ed curuæ. </s> |
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| <s id="id.000821">Moto igitur Cylindro circulus EHF rectam <lb/>de&longs;cribet<foreign lang="greek">ae</foreign>, ellip&longs;is verò AMB, curuam <foreign lang="greek">ohr</foreign>, ellip&longs;is au­<lb/>rem DNC, ip&longs;am curuam <foreign lang="greek">pzs. </foreign></s> | <s id="id.000821">Moto igitur Cylindro circulus EHF rectam <lb/>de&longs;cribet<foreign lang="greek">ae</foreign>, ellip&longs;is verò AMB, curuam <foreign lang="greek">ohr</foreign>, ellip&longs;is au­<lb/>rem DNC, ip&longs;am curuam <foreign lang="greek">pzs. </foreign></s> |
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| <s id="id.000822">In hoc <expan abbr="autē">autem</expan> Cylindri mo­<lb/>tuillud mirabile, velociores nempe, in ip&longs;a rotatione e&longs;&longs;e <lb/>ellip&longs;es ip&longs;o circulo EHF. <!-- KEEP S--></s> | <s id="id.000822">In hoc <expan abbr="autē">autem</expan> Cylindri mo­<lb/>tuillud mirabile, velociores nempe, in ip&longs;a rotatione e&longs;&longs;e <lb/>ellip&longs;es ip&longs;o circulo EHF. <!-- KEEP S--></s> |
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| <s id="id.000823">Ducatur enim recta<foreign lang="greek">o<10></foreign> quæ oc­<lb/>currat ip&longs;i VS in S, & <foreign lang="greek">oh</foreign> iungatur, fietqueue triangulum <lb/><foreign lang="greek">oh</foreign>S. c&longs;t autem, angulus <foreign lang="greek">o</foreign> S <foreign lang="greek">h</foreign> rectus, maior erg. <foreign lang="greek">oh</foreign> i­<lb/>p&longs;a <foreign lang="greek">o</foreign> S, &longs;ed recta <foreign lang="greek">o</foreign> S æqualis e&longs;t ip&longs;i<foreign lang="greek">an</foreign>, hoc e&longs;t, &longs;emicircu­<lb/>lo FHE. multo maior e&longs;t autem curua, <foreign lang="greek">o, n, l, k, h</foreign>, ip&longs;a recta <lb/><foreign lang="greek">oh</foreign>, &longs;ed eodem tempore quo &longs;emicirculus EHF conficit <lb/>in rotatione <expan abbr="&longs;patiū">&longs;patium</expan> <foreign lang="greek">a</foreign> V, eodem dimidia ellip&longs;is BMA me­<lb/>titur curuam <foreign lang="greek">onlkh. </foreign></s> | <s id="id.000823">Ducatur enim recta<foreign lang="greek">o<10></foreign> quæ oc­<lb/>currat ip&longs;i VS in S, & <foreign lang="greek">oh</foreign> iungatur, fietqueue triangulum <lb/><foreign lang="greek">oh</foreign>S. e&longs;t autem, angulus <foreign lang="greek">o</foreign> S <foreign lang="greek">h</foreign> rectus, maior erg. <foreign lang="greek">oh</foreign> i­<lb/>p&longs;a <foreign lang="greek">o</foreign> S, &longs;ed recta <foreign lang="greek">o</foreign> S æqualis e&longs;t ip&longs;i<foreign lang="greek">an</foreign>, hoc e&longs;t, &longs;emicircu­<lb/>lo FHE. multo maior e&longs;t autem curua, <foreign lang="greek">o, n, l, k, h</foreign>, ip&longs;a recta <lb/><foreign lang="greek">oh</foreign>, &longs;ed eodem tempore quo &longs;emicirculus EHF conficit <lb/>in rotatione <expan abbr="&longs;patiū">&longs;patium</expan> <foreign lang="greek">a</foreign> V, eodem dimidia ellip&longs;is BMA me­<lb/>titur curuam <foreign lang="greek">onlkh. </foreign></s> |
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| <s id="id.000824">velocior igitur e&longs;t ellip&longs;is ip&longs;o cir­<lb/>culo. </s></p><p type="main"> | <s id="id.000824">velocior igitur e&longs;t ellip&longs;is ip&longs;o cir­<lb/>culo. </s></p><p type="main"> |
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| <s id="id.000830">Quoniam igitur lateris BC, punctum C &longs;tat, B verò <lb/>circa ip&longs;um mouetur, in ip&longs;o motu circulus de&longs;cribitur <lb/>BHIK, cuius &longs;emidiameter BC, & eodem pacto alij cir­<lb/>culi in cono, qui ba&longs;i HEBF &longs;unt æquedi&longs;tantes, circulos <lb/>in plano circa idem centrum de&longs;cribent, vt facile videre <lb/>e&longs;t in obiecto &longs;chemate. </s> | <s id="id.000830">Quoniam igitur lateris BC, punctum C &longs;tat, B verò <lb/>circa ip&longs;um mouetur, in ip&longs;o motu circulus de&longs;cribitur <lb/>BHIK, cuius &longs;emidiameter BC, & eodem pacto alij cir­<lb/>culi in cono, qui ba&longs;i HEBF &longs;unt æquedi&longs;tantes, circulos <lb/>in plano circa idem centrum de&longs;cribent, vt facile videre <lb/>e&longs;t in obiecto &longs;chemate. </s> |
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| <s id="id.000831">Huic &longs;imilem demon &longs;trationem <lb/>affert Heron in libello Automatum, quem nos Tyrones <lb/>adhuc vernacule è Græco translatum, Ven<gap/>e tijs prælo <lb/>&longs;ubiecimus. </s></p><p type="main"> | <s id="id.000831">Huic &longs;imilem demon&longs;trationem <lb/>affert Heron in libello Automatum, quem nos Tyrones <lb/>adhuc vernacule è Græco translatum, Venetijs prælo <lb/>&longs;ubiecimus. </s></p><p type="main"> |
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| <s id="id.000832">Porrò &longs;i conus rotundus pro ba&longs;i ellip&longs;im habeat, <lb/>&longs;ectionem videlicet per planum axi non perpendiculare, <lb/>in ip&longs;a rotatione, &longs;tante vertice, ellip&longs;is ba&longs;is, ellip&longs;im de­<lb/>&longs;cribit in plano, cuius maior diameter à puncto quod co­<lb/>nivertex e&longs;t, ita diuiditur, vt diametri pars maior æqualis <lb/>&longs;it lateri maximo; minor verò æqualis lateri minimo. </s> | <s id="id.000832">Porrò &longs;i conus rotundus pro ba&longs;i ellip&longs;im habeat, <lb/>&longs;ectionem videlicet per planum axi non perpendiculare, <lb/>in ip&longs;a rotatione, &longs;tante vertice, ellip&longs;is ba&longs;is, ellip&longs;im de­<lb/>&longs;cribit in plano, cuius maior diameter à puncto quod co­<lb/>nivertex e&longs;t, ita diuiditur, vt diametri pars maior æqualis <lb/>&longs;it lateri maximo; minor verò æqualis lateri minimo. </s> |
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| <s id="id.000835">Modò de tertia motus &longs;pecie nobis erit &longs;ermo; in <lb/>qua quidem &longs;pecienonnulla perpendemus, quæ omi&longs;it A­<lb/>ri&longs;toteles. <!-- KEEP S--></s> | <s id="id.000835">Modò de tertia motus &longs;pecie nobis erit &longs;ermo; in <lb/>qua quidem &longs;pecienonnulla perpendemus, quæ omi&longs;it A­<lb/>ri&longs;toteles. <!-- KEEP S--></s> |
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| <s id="id.000836">Agitur autem hîc de rotundorum corporum <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.091.jpg"/>motu, qui fit çirca axem horizonti perpendicularem, axis <lb/>altera extremitate in codem horizontis plano manente, <lb/>vti videre e&longs;t in ip&longs;is figulorum rotis. </s></p><p type="main"> | <s id="id.000836">Agitur autem hîc de rotundorum corporum <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.091.jpg"/>motu, qui fit çirca axem horizonti perpendicularem, axis <lb/>altera extremitate in eodem horizontis plano manente, <lb/>vti videre e&longs;t in ip&longs;is figulorum rotis. </s></p><p type="main"> |
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| <s id="id.000837">Hanc motus &longs;peciem in extrema quæ&longs;tionis parte <lb/>cum duabus alijs &longs;peciebus comparans ait, cam quæ in <lb/>obliquo fit motionem (ita enim hanc, de qua agimus, ap­<lb/>pellat) ip&longs;am impellere mouentem, hoc e&longs;t, nullum ex&longs;e <lb/>ad motum propen&longs;ionem habere, nutumue, & omnia illi <lb/>e&longs;&longs;e à motore, &longs;ecundum verò eam motionem, quæ &longs;upra <lb/>diametrum e&longs;t, &longs;e ip&longs;um mouere circulum. </s> | <s id="id.000837">Hanc motus &longs;peciem in extrema quæ&longs;tionis parte <lb/>cum duabus alijs &longs;peciebus comparans ait, cam quæ in <lb/>obliquo fit motionem (ita enim hanc, de qua agimus, ap­<lb/>pellat) ip&longs;am impellere mouentem, hoc e&longs;t, nullum ex&longs;e <lb/>ad motum propen&longs;ionem habere, nutumue, & omnia illi <lb/>e&longs;&longs;e à motore, &longs;ecundum verò eam motionem, quæ &longs;upra <lb/>diametrum e&longs;t, &longs;e ip&longs;um mouere circulum. </s> |
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| <s id="id.000838">Dixerat enim, <lb/>ea referens quæ &longs;uperiùs circa principium de circulo ver­<lb/>ba faciens, examinauerat, circulum ex duabus fieri latio­<lb/>nibus, altera præter, altera verò &longs;ecundum naturam, & <lb/>ideo hanc &longs;emper nutum habere, & ceu continuo motam <lb/>ab eo moueri quimouet. </s> | <s id="id.000838">Dixerat enim, <lb/>ea referens quæ &longs;uperiùs circa principium de circulo ver­<lb/>ba faciens, examinauerat, circulum ex duabus fieri latio­<lb/>nibus, altera præter, altera verò &longs;ecundum naturam, & <lb/>ideo hanc &longs;emper nutum habere, & ceu continuo motam <lb/>ab eo moueri quimouet. </s> |
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| <s id="id.000839">Videtur autem clarè profiteri, <lb/>ideo difficiliorem e&longs;&longs;e huius terriæ &longs;peciei motum, eo <lb/>quòd nutu <gap/>areat proprio & t<gap/>m ab alieno, vt ita di­<lb/>cam, motore, moueatur. </s></p><p type="main"> | <s id="id.000839">Videtur autem clarè profiteri, <lb/>ideo difficiliorem e&longs;&longs;e huius terræ &longs;peciei motum, eo <lb/>quòd nutu careat proprio & t<gap/>m ab alieno, vt ita di­<lb/>cam, motore, moueatur. </s></p><p type="main"> |
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| <s id="id.000840">Veruntamen motum hunc facilitate alijs illis duo­<lb/>bus nequaquam cedere, facilè ex &longs;equentibus o&longs;tende­<lb/>mus. </s></p><p type="main"> | <s id="id.000840">Veruntamen motum hunc facilitate alijs illis duo­<lb/>bus nequaquam cedere, facilè ex &longs;equentibus o&longs;tende­<lb/>mus. </s></p><p type="main"> |
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| <s id="id.000843">Ad hæc circa axem ita libratur rota, vt <lb/>quantumuis exigua potentia alteri parti applicetur, alte­<lb/>ra illico &longs;uperata moueatur. </s> | <s id="id.000843">Ad hæc circa axem ita libratur rota, vt <lb/>quantumuis exigua potentia alteri parti applicetur, alte­<lb/>ra illico &longs;uperata moueatur. </s> |
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| <s id="id.000844">Licet enim propliè ea <expan abbr="tantū">tantum</expan> <lb/>corpora æquilibrare dicantur, quæ ob ponderis hinc in de <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.092.jpg"/>æqualitatem horizonti fiunt æquidi&longs;tantes, nihilominus <lb/>& hic aliquam e&longs;&longs;e æquilibrij &longs;imilitudinem patebit. </s></p><figure id="id.007.00.092.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.092.1.jpg"></figure><p type="main"> | <s id="id.000844">Licet enim propriè ea <expan abbr="tantū">tantum</expan> <lb/>corpora æquilibrare dicantur, quæ ob ponderis hinc in de <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.092.jpg"/>æqualitatem horizonti fiunt æquidi&longs;tantes, nihilominus <lb/>& hic aliquam e&longs;&longs;e æquilibrij &longs;imilitudinem patebit. </s></p><figure id="id.007.00.092.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.092.1.jpg"></figure><p type="main"> |
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| <s id="id.000845">E&longs;to enim rota ABCD, <lb/>cuius axis horizonti perpendi­<lb/>cularis FEG tran&longs;iens per cen­<lb/>trum E, tangens autem planum <lb/>in puncto G. <!-- KEEP S--></s> | <s id="id.000845">E&longs;to enim rota ABCD, <lb/>cuius axis horizonti perpendi­<lb/>cularis FEG tran&longs;iens per cen­<lb/>trum E, tangens autem planum <lb/>in puncto G. <!-- KEEP S--></s> |
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| <s id="id.000848">At alteri partium potentiâ quauis <lb/>licet exigua appo&longs;itâ, puta in C, præualebit pars BCD, & <lb/>partem BAD vel impellet vel rapiet, alterâ interim eius <lb/>motui ob&longs;equente. </s> | <s id="id.000848">At alteri partium potentiâ quauis <lb/>licet exigua appo&longs;itâ, puta in C, præualebit pars BCD, & <lb/>partem BAD vel impellet vel rapiet, alterâ interim eius <lb/>motui ob&longs;equente. </s> |
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| <s id="id.000849">Potentia igitur quæ in C, nullam rem <lb/>quæ impediat inueniens, veloci&longs;&longs;imè rotam mouet, quod <lb/>eo faciliùs velocius queue fit, quo magis rota e&longs;t in motu, e­<lb/>ius verò diameter maior & potentia mouens à centro re­<lb/>motior, & &longs;anè motus <expan abbr="facilitatē">facilitatem</expan> inde cogno&longs;cimus, quòd <lb/>ip&longs;o impul&longs;ore ab impul&longs;u ce&longs;&longs;ante, diuti&longs;<gap/>è rota im­<lb/>pre&longs;&longs;um motum &longs;eruet, nec ni&longs;i po&longs;t longam rotationem <lb/>omnino quie&longs;cat. </s></p><p type="main"> | <s id="id.000849">Potentia igitur quæ in C, nullam rem <lb/>quæ impediat inueniens, veloci&longs;&longs;imè rotam mouet, quod <lb/>eo faciliùs velocius queue fit, quo magis rota e&longs;t in motu, e­<lb/>ius verò diameter maior & potentia mouens à centro re­<lb/>motior, & &longs;anè motus <expan abbr="facilitatē">facilitatem</expan> inde cogno&longs;cimus, quòd <lb/>ip&longs;o impul&longs;ore ab impul&longs;u ce&longs;&longs;ante, diuti&longs;&longs;imè rota im­<lb/>pre&longs;&longs;um motum &longs;eruet, nec ni&longs;i po&longs;t longam rotationem <lb/>omnino quie&longs;cat. </s></p><p type="main"> |
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| <s id="id.000850">Cæterùm quia &longs;icco, vtaiunt, pede Ari&longs;toteles quæ <lb/>ad hunc motum <expan abbr="pertinēt">pertinent</expan> pertran&longs;ijt, nos quædam quæ ad <lb/>hanc rem faciunt, diligentiùs expendemus. </s></p><p type="main"> | <s id="id.000850">Cæterùm quia &longs;icco, vtaiunt, pede Ari&longs;toteles quæ <lb/>ad hunc motum <expan abbr="pertinēt">pertinent</expan> pertran&longs;ijt, nos quædam quæ ad <lb/>hanc rem faciunt, diligentiùs expendemus. </s></p><p type="main"> |
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| <s id="id.000851">Quærimus igitur primò; Cur ea quæ hoc pacto <expan abbr="ro-tãtur">ro­<lb/>tantur</expan>, in ip&longs;a rotatione locum non mutent, ni&longs;i extrin&longs;eca <lb/>aliqua id fiat ex cau&longs;&longs;a. </s></p><p type="main"> | <s id="id.000851">Quærimus igitur primò; Cur ea quæ hoc pacto <expan abbr="ro-tãtur">ro­<lb/>tantur</expan>, in ip&longs;a rotatione locum non mutent, ni&longs;i extrin&longs;eca <lb/>aliqua id fiat ex cau&longs;&longs;a. </s></p><p type="main"> |
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| <s id="id.000852">E&longs;to enim rota aut aliud quippiam rotundum ccu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.093.jpg"/><figure id="id.007.00.093.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.093.1.jpg"></figure><lb/>rizonti perpendicularem mo­<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. <!-- KEEP S--></s> | <s id="id.000852">E&longs;to enim rota aut aliud quippiam rotundum ceu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho­<pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.093.jpg"/><figure id="id.007.00.093.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.093.1.jpg"></figure><lb/>rizonti perpendicularem mo­<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. <!-- KEEP S--></s> |
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| <s id="id.000853">Modò circa <lb/>centrum E in finiti imagin entur <lb/>circuli, alij alijs minores v&longs;que <lb/>ad <expan abbr="centrū">centrum</expan> ip&longs;um, vti &longs;unt FGH; <lb/>ibi enim circuli e&longs;&longs;e de&longs;inunt, <lb/>vbi nullum amplius e&longs;t &longs;patium. <lb/></s> | <s id="id.000853">Modò circa <lb/>centrum E in finiti imagin entur <lb/>circuli, alij alijs minores v&longs;que <lb/>ad <expan abbr="centrū">centrum</expan> ip&longs;um, vti &longs;unt FGH; <lb/>ibi enim circuli e&longs;&longs;e de&longs;inunt, <lb/>vbi nullum amplius e&longs;t &longs;patium. <lb/></s> |
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| <s id="id.000854">Applicetur itaque potentia in <lb/>B, quæ rotam v. <!-- REMOVE S-->geat ver&longs;us A. <lb/>codem igitur tempore & in&longs;imul A ver&longs;us D, D ver&longs;us C, <lb/>& Cver&longs;us B mouebitur. </s> | <s id="id.000854">Applicetur itaque potentia in <lb/>B, quæ rotam v. <!-- REMOVE S-->geat ver&longs;us A. <lb/>eodem igitur tempore & in&longs;imul A ver&longs;us D, D ver&longs;us C, <lb/>& C ver&longs;us B mouebitur. </s> |
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| <s id="id.000870">Minus igitur a­<lb/>pta e&longs;t motui huic triangularis figura, quam quadrata, in <lb/>qua partes à centro remoti&longs;&longs;imè, & ideo veloci&longs;&longs;imè &longs;unt <lb/>quatuor. </s> | <s id="id.000870">Minus igitur a­<lb/>pta e&longs;t motui huic triangularis figura, quam quadrata, in <lb/>qua partes à centro remoti&longs;&longs;imè, & ideo veloci&longs;&longs;imè &longs;unt <lb/>quatuor. </s> |
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| <s id="id.000871"><expan abbr="Itaq;">Itaque</expan> quo <gap/>agis laterata figura angulis abunda­<lb/>bit, eo magis erit ad hunc, & cæteros omnes circulares <lb/>motus aptior. </s> | <s id="id.000871"><expan abbr="Itaq;">Itaque</expan> quo magis laterata figura angulis abunda­<lb/>bit, eo magis erit ad hunc, & cæteros omnes circulares <lb/>motus aptior. </s> |
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| <s id="id.000872">At circulus infinitas, vt ita dicam, partes à <lb/>centro remoti&longs;&longs;imas habet, itaque nulla figura e&longs;t circu­<lb/>lari, in ip&longs;a rotatione, commodior atque velocior. </s> | <s id="id.000872">At circulus infinitas, vt ita dicam, partes à <lb/>centro remoti&longs;&longs;imas habet, itaque nulla figura e&longs;t circu­<lb/>lari, in ip&longs;a rotatione, commodior atque velocior. </s> |
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| <s id="id.000873">Alia <lb/>quoque de cau&longs;&longs;a id fit, quod dum circularis figura mo­<lb/>uetur, nullis eminentibus angulis aërem verberet <expan abbr="circū-&longs;tãtem">circun­<lb/>&longs;tantem</expan>, ex qua verberatione motus impeditus &longs;it tardior. <lb/></s> | <s id="id.000873">Alia <lb/>quoque de cau&longs;&longs;a id fit, quod dum circularis figura mo­<lb/>uetur, nullis eminentibus angulis aërem verberet <expan abbr="circū-&longs;tãtem">circum­<lb/>&longs;tantem</expan>, ex qua verberatione motus impeditus &longs;it tardior. <lb/></s> |
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| <s id="id.000874">Quæri etiam pote&longs;t, Num axe in clinato, rotæ motus ali­<lb/>qualiter impediatur? </s> | <s id="id.000874">Quæri etiam pote&longs;t, Num axe in clinato, rotæ motus ali­<lb/>qualiter impediatur? </s> |
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| <s id="id.000992">E&longs;to horizontis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.105.jpg"/><figure id="id.007.00.105.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.105.1.jpg"></figure><lb/>planum AB, &longs;cytalae duae<lb/>CD, EF, Pondus verò <lb/>eis impo&longs;itum G, tan­<lb/>gens ip&longs;as in <expan abbr="pūctis">punctis</expan> CE, <lb/>&longs;cytalæ autem planum <lb/>in punctis D, F, Pellatur <lb/>à potentia quapiam <expan abbr="pō-dus">pon­<lb/>dus</expan> Gad anteriora, <expan abbr="nē-pe">nen­<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytalæ & pars quædam <lb/>&longs;cytalæ D, in qua &longs;it contactus a&longs;cendet in I, C verò de­<lb/>&longs;cendetin H, nulla re motum impediente, quippe quòd <lb/>nulla ponderis &longs;cytalarum, & plani ad inuicem fiat offen­<lb/>&longs;atio. </s> | <s id="id.000992">E&longs;to horizontis <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.105.jpg"/><figure id="id.007.00.105.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/007-00-figures/007.00.105.1.jpg"></figure><lb/>planum AB, &longs;cytalae duae<lb/>CD, EF, Pondus verò <lb/>eis impo&longs;itum G, tan­<lb/>gens ip&longs;as in <expan abbr="pūctis">punctis</expan> CE, <lb/>&longs;cytalæ autem planum <lb/>in punctis D, F, Pellatur <lb/>à potentia quapiam <expan abbr="pō-dus">pon­<lb/>dus</expan> Gad anteriora, <expan abbr="nē-pe">nen­<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytalæ & pars quædam <lb/>&longs;cytalæ D, in qua &longs;it contactus a&longs;cendet in I, C verò de­<lb/>&longs;cendetin H, nulla re motum impediente, quippe quòd <lb/>nulla ponderis &longs;cytalarum, & plani ad inuicem fiat offen­<lb/>&longs;atio. </s> |
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| <s id="id.000993">Præterea cum &longs;cytalarum centra ab horizontis pla­<lb/>no æqualiter di&longs;tent, pondus quidem horizonti æquidi­<lb/>&longs;tanter mouetur, & ideo cius centrum grauitatis nequa­<lb/>quam, in motu qui &longs;it, eleuatur. </s></p><p type="main"> | <s id="id.000993">Præterea cum &longs;cytalarum centra ab horizontis pla­<lb/>no æqualiter di&longs;tent, pondus quidem horizonti æquidi­<lb/>&longs;tanter mouetur, & ideo eius centrum grauitatis nequa­<lb/>quam, in motu qui &longs;it, eleuatur. </s></p><p type="main"> |
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| <s id="id.000994">Cæterùm materiæ imperfectione remota nihil re­<lb/>fert ad facilitatem, vtrum maioris minorisue diametri <lb/>&longs;int&longs;cytalæ, vt ea po&longs;ita eo quod maiores circuli faciliùs <lb/>offendicula &longs;uperent, quod demon&longs;tratum e&longs;t in quæ&longs;tio­<lb/>ne 8. eo vtiliores &longs;unt &longs;cytalæ, quo cra&longs;&longs;iores. </s> | <s id="id.000994">Cæterùm materiæ imperfectione remota nihil re­<lb/>fert ad facilitatem, vtrum maioris minorisue diametri <lb/>&longs;int&longs;cytalæ, vt ea po&longs;ita eo quod maiores circuli faciliùs <lb/>offendicula &longs;uperent, quod demon&longs;tratum e&longs;t in quæ&longs;tio­<lb/>ne 8. eo vtiliores &longs;unt &longs;cytalæ, quo cra&longs;&longs;iores. </s> |
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| <s id="id.000997">Funis quo rota ex axis <lb/>centro M trahitur MP, <lb/>pondus vero QR. </s> | <s id="id.000997">Funis quo rota ex axis <lb/>centro M trahitur MP, <lb/>pondus vero QR. </s> |
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| <s id="id.000998">Quo­<lb/>niam igitur pondus axem <lb/>premit in N, axis autem rotæ modiolum in O, & codem, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.106.jpg"/>tempore potentia quæ trahitin P, axem admouet modio­<lb/>lo in parte V. duplex itaque fit ex fricatione &longs;eu offen&longs;a­<lb/>tione impedimentum, in fra nempe, vbi O, & ad latus vbi <lb/>V. quæ quidem offen&longs;iones currus motum reddunt diffi­<lb/>ciliorem, quæ quidem difficultas eo maior erit, quo ma­<lb/>ior fuerit pondus axem premens, & minor proportio &longs;e­<lb/>midiametri rotæ KM, ad axis &longs;emidiametrum MO. </s> | <s id="id.000998">Quo­<lb/>niam igitur pondus axem <lb/>premit in N, axis autem rotæ modiolum in O, & eodem, <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.106.jpg"/>tempore potentia quæ trahitin P, axem admouet modio­<lb/>lo in parte V. duplex itaque fit ex fricatione &longs;eu offen&longs;a­<lb/>tione impedimentum, in fra nempe, vbi O, & ad latus vbi <lb/>V. quæ quidem offen&longs;iones currus motum reddunt diffi­<lb/>ciliorem, quæ quidem difficultas eo maior erit, quo ma­<lb/>ior fuerit pondus axem premens, & minor proportio &longs;e­<lb/>midiametri rotæ KM, ad axis &longs;emidiametrum MO. </s> |
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| <s id="id.000999">Cur <lb/>igitur &longs;cytalis facilius pondera transferantur quam plau­<lb/>&longs;tris, apertè ex dictis ad Ari&longs;to telis mentem demon&longs;tra­<lb/>uimus. </s></p><p type="main"> | <s id="id.000999">Cur <lb/>igitur &longs;cytalis facilius pondera transferantur quam plau­<lb/>&longs;tris, apertè ex dictis ad Ari&longs;to telis mentem demon&longs;tra­<lb/>uimus. </s></p><p type="main"> |
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| <s id="id.001702">Nuteti­<lb/>gitur & vibretur, in ip&longs;a vibratione, ad partem A. <!-- KEEP S--></s> | <s id="id.001702">Nuteti­<lb/>gitur & vibretur, in ip&longs;a vibratione, ad partem A. <!-- KEEP S--></s> |
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| <s id="id.001703">Sit au­<lb/>tem centrum grauitatis eius D, Lignum igitur in ip&longs;a vi­<lb/>bratione de&longs;cendet &longs;ua pre&longs;&longs;us grauitate in E, tum facta <lb/>ligni con&longs;tipatione in ea parte quæ e&longs;t inferius inter C & <lb/>D, & inde re&longs;i&longs;tentia, codem fere impetu quo de&longs;cende­<lb/>rat, repul&longs;um per D, nec enim in &longs;ua rectitudine &longs;tabit, a­<lb/>&longs;cendet in F, facta iterum materiæ con&longs;ti patione inter C <lb/>& F. <!-- KEEP S--></s> | <s id="id.001703">Sit au­<lb/>tem centrum grauitatis eius D, Lignum igitur in ip&longs;a vi­<lb/>bratione de&longs;cendet &longs;ua pre&longs;&longs;us grauitate in E, tum facta <lb/>ligni con&longs;tipatione in ea parte quæ e&longs;t inferius inter C & <lb/>D, & inde re&longs;i&longs;tentia, eodem fere impetu quo de&longs;cende­<lb/>rat, repul&longs;um per D, nec enim in &longs;ua rectitudine &longs;tabit, a­<lb/>&longs;cendet in F, facta iterum materiæ con&longs;ti patione inter C <lb/>& F. <!-- KEEP S--></s> |
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| <s id="id.001704">Mouebitur igitur lignum &longs;ua grauitate, motu fre­<lb/>quenti&longs;&longs;imo, &longs;ur&longs;um deor&longs;um, & is interim qui lignum hu­<lb/>mero fert, procedit antror&longs;um, impedit igitur motus i&longs;te, <lb/>qui fit &longs;ur&longs;um deor&longs;um lationem, quæ fit ad anteriora; La­<lb/>torem ip&longs;um quodammodo retrahens. </s> | <s id="id.001704">Mouebitur igitur lignum &longs;ua grauitate, motu fre­<lb/>quenti&longs;&longs;imo, &longs;ur&longs;um deor&longs;um, & is interim qui lignum hu­<lb/>mero fert, procedit antror&longs;um, impedit igitur motus i&longs;te, <lb/>qui fit &longs;ur&longs;um deor&longs;um lationem, quæ fit ad anteriora; La­<lb/>torem ip&longs;um quodammodo retrahens. </s> |
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| <s id="id.002053">E&longs;to enim vortex AB, cu­<lb/>ius centrum C, &longs;emidiameter <lb/>CA, fiatautem rotatio totius a­<lb/>quæ CA ad partes D, in linea <lb/>autem AC, &longs;it corpus aliquod a­<lb/>quæ rotatione <expan abbr="circumlatū">circumlatum</expan> AE, <lb/>inter circulos maiorem ADB, <lb/>minorem EFG. velocius autem <lb/>mouetur ADB, ip&longs;o EFG, citius <lb/>ergo fertur pars &longs;uperior ip&longs;ius <lb/>corporis vbi A, quam inferior <lb/>vbi E. <!-- KEEP S--></s> | <s id="id.002053">E&longs;to enim vortex AB, cu­<lb/>ius centrum C, &longs;emidiameter <lb/>CA, fiatautem rotatio totius a­<lb/>quæ CA ad partes D, in linea <lb/>autem AC, &longs;it corpus aliquod a­<lb/>quæ rotatione <expan abbr="circumlatū">circumlatum</expan> AE, <lb/>inter circulos maiorem ADB, <lb/>minorem EFG. velocius autem <lb/>mouetur ADB, ip&longs;o EFG, citius <lb/>ergo fertur pars &longs;uperior ip&longs;ius <lb/>corporis vbi A, quam inferior <lb/>vbi E. <!-- KEEP S--></s> |
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| <s id="id.002054">At id nec A repellit, nec E retrahit, &longs;iquidem eodem <lb/>tempore quo A permeauit <expan abbr="circulū">circulum</expan> ADB, codem & E per­<lb/>currit circulum EFG. <expan abbr="Itaq;">Itaque</expan> A reuer&longs;o in A & E, punctum <lb/>reuer&longs;um erit in E, nulla facta corporis E quoad &longs;itum, <lb/>muratione quod voluit Ari&longs;toteles. <!-- KEEP S--></s></p> | <s id="id.002054">At id nec A repellit, nec E retrahit, &longs;iquidem eodem <lb/>tempore quo A permeauit <expan abbr="circulū">circulum</expan> ADB, eodem & E per­<lb/>currit circulum EFG. <expan abbr="Itaq;">Itaque</expan> A reuer&longs;o in A & E, punctum <lb/>reuer&longs;um erit in E, nulla facta corporis E quoad &longs;itum, <lb/>muratione quod voluit Ari&longs;toteles. <!-- KEEP S--></s></p> |
| <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.208.jpg"/><p type="main"> | <pb xlink:href="http://archimedes.fas.harvard.edu/images/007-00-pageimg/007.00.208.jpg"/><p type="main"> |
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| <s id="id.002055">Ad &longs;ecundam vero dicimus, non ideo quod omnes <lb/>circuli æqualiter circa centrum &longs;erantur, ni&longs;i alia <expan abbr="quæpiã">quæpiam</expan> <lb/>extranea vis interce&longs;&longs;erit, quæ ea ab exterioribus circulis <lb/>pellens agat in medium. </s></p> | <s id="id.002055">Ad &longs;ecundam vero dicimus, non ideo quod omnes <lb/>circuli æqualiter circa centrum &longs;erantur, ni&longs;i alia <expan abbr="quæpiã">quæpiam</expan> <lb/>extranea vis interce&longs;&longs;erit, quæ ea ab exterioribus circulis <lb/>pellens agat in medium. </s></p> |
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