| version 1.15, 2002/08/22 15:44:06 |
version 1.19, 2002/10/29 20:24:54 |
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| <translator/> | <translator/> |
| <lang>la</lang> | <lang>la</lang> |
| <cvs_file>gasse_demot_01_la_1642</cvs_file> | <cvs_file>gasse_demot_01_la_1642</cvs_file> |
| <cvs_version/> | <cvs_version>1.19</cvs_version> |
| <locator>0000000027.xml</locator> | <locator>027.xml</locator> |
| </info> <text> <front> </front> <body> <chap> <pb/><p type="main"> | </info> <text> <front> </front> <body> <chap> <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.001.jpg"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>PETRI GASSENDI<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s id="id.000001"><emph type="center"/><emph type="italics"/>PETRI GASSENDI<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/>DEMOTV IMPRESSO <lb/>A MOTORE <lb/>TRANSLATO.<emph.end type="center"/></s></p><p type="main"> | <s id="id.000002"><emph type="center"/>DEMOTV IMPRESSO <lb/>A MOTORE <lb/>TRANSLATO.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/>EPISTOLÆ DVÆ.<emph.end type="center"/></s></p><p type="main"> | <s id="id.000003"><emph type="center"/>EPISTOLÆ DVÆ.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>IN QVIBVS ALIQVOT PRÆCIPV Æ <lb/>tum de Motu vuiuersè, tum &longs;peciatim de Motu <lb/>Terræ attributo difficultates explicantur.<emph.end type="italics"/><emph.end type="center"/></s></p><figure/><p type="main"> | <s id="id.000004"><emph type="center"/><emph type="italics"/>IN QVIBVS ALIQVOT PRÆCIPV Æ <lb/>tum de Motu vuiuersè, tum &longs;peciatim de Motu <lb/>Terræ attributo difficultates explicantur.<emph.end type="italics"/><emph.end type="center"/></s></p><figure id="id.027.00.001.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.001.1.jpg"/><p type="main"> |
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| <s><emph type="center"/>PARISIIS, <lb/>Apud LVDOVICVM DE HEVQVEVILLE, via Iacobæa, &longs;ub <lb/>&longs;igno Pacis.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> | <s id="id.000005"><emph type="center"/>PARISIIS, <lb/>Apud LVDOVICVM DE HEVQVEVILLE, via Iacobæa, &longs;ub <lb/>&longs;igno Pacis.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="center"/>M. DC. XLII. <lb/><emph type="italics"/>CVM PRIVILEGIO REGIS.<emph.end type="italics"/><emph.end type="center"/></s></p><pb/><figure/><p type="main"> | <s id="id.000006"><emph type="center"/>M. DC. XLII. <lb/><emph type="italics"/>CVM PRIVILEGIO REGIS.<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.002.jpg"/><figure id="id.027.00.002.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.002.1.jpg"/><p type="main"> |
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| <s><emph type="center"/>ELENCHVS <lb/>ARTICVLORVM.<emph.end type="center"/></s></p><p type="main"> | <s id="id.000007"><emph type="center"/>ELENCHVS <lb/>ARTICVLORVM.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>EPISTOLÆ PRIORIS.<emph.end type="italics"/><emph.end type="center"/><lb/></s></p><p type="main"> | <s id="id.000008"><emph type="center"/><emph type="italics"/>EPISTOLÆ PRIORIS.<emph.end type="italics"/><emph.end type="center"/><lb/></s></p><p type="main"> |
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| <s><emph type="italics"/>I. REcen&longs;ent<gap/> compendio­<lb/>sè experiments ex aqua, <lb/>curru, & nani facta, qui­<lb/>bus comprobatur, &longs;i id <lb/>corpus, cui in&longs;istimus, <lb/>transferatur, motum rei à nobis proiectæ <lb/>perinde & &longs;ieri, & apparere nobis, ac &longs;i il­<lb/>lud quic&longs;ceret.<emph.end type="italics"/> pag.1. </s></p><p type="main"> | <s id="id.000009"><emph type="italics"/>I. REcen&longs;ent<gap/> compendio­<lb/>sè experiments ex aqua, <lb/>curru, & nani facta, qui­<lb/>bus comprobatur, &longs;i id <lb/>corpus, cui in&longs;istimus, <lb/>transferatur, motum rei à nobis proiectæ <lb/>perinde & &longs;ieri, & apparere nobis, ac &longs;i il­<lb/>lud quic&longs;ceret.<emph.end type="italics"/> pag.1. </s></p><p type="main"> |
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| <s><emph type="italics"/>II. Propo<gap/>tur experimenta &longs;acienda de pi­<lb/>ia, quæ inter ambulandum dimi&longs;&longs;a &longs;emper <lb/>procurrit; & iacta retror sùm, vel &longs;egmùs <lb/>mouetur, vel ad perpendiculum cadit, vel <lb/>etiam &longs;equitur, promotæ antr<gap/>sùm. </s> | <s id="id.000010"><emph type="italics"/>II. Propo<gap/>tur experimenta &longs;acienda de pi­<lb/>ia, quæ inter ambulandum dimi&longs;&longs;a &longs;emper <lb/>procurrit; & iacta retror sùm, vel &longs;egmùs <lb/>mouetur, vel ad perpendiculum cadit, vel <lb/>etiam &longs;equitur, promotæ antr<gap/>sùm. </s> |
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| <s>Cau&longs;a <lb/>dicitur ex motu, quem manus (&longs;eu habeat, <lb/>&longs;eu non habeat proprium) accipit à corpore, <lb/>imprimitque contactæ pilæ.<emph.end type="italics"/> p.3. </s></p><p type="main"> | <s id="id.000011">Cau&longs;a <lb/>dicitur ex motu, quem manus (&longs;eu habeat, <lb/>&longs;eu non habeat proprium) accipit à corpore, <lb/>imprimitque contactæ pilæ.<emph.end type="italics"/> p.3. </s></p><p type="main"> |
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| <s><emph type="italics"/>III. <!-- KEEP S--></s> | <s id="id.000012"><emph type="italics"/>III. <!-- KEEP S--></s> |
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| <s>Dum manus inter ambul andum liberè <lb/>pendent, non ni&longs;i pr<gap/>sùm mouentur; & <lb/>cùm videntur retro &longs;um &longs;lecti, reip&longs;â quic&longs;­<lb/>c<gap/>. </s> | <s id="id.000013">Dum manus inter ambul andum liberè <lb/>pendent, non ni&longs;i pr<gap/>sùm mouentur; & <lb/>cùm videntur retro &longs;um &longs;lecti, reip&longs;â quic&longs;­<lb/>c<gap/>. </s> |
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| <s>Ex quo dimi&longs;&longs;apila, dum manus pror­<lb/>sùm porrigitur, mouetur duplò vel<gap/>iùs <lb/>(veluti & <gap/>us) quà ncorporis truncus; <lb/>& dum manus apparet retrorsùm ire, cadit <lb/>ad perpendiculum.<emph.end type="italics"/> p.7. </s></p><p type="main"> | <s id="id.000014">Ex quo dimi&longs;&longs;apila, dum manus pror­<lb/>sùm porrigitur, mouetur duplò vel<gap/>iùs <lb/>(veluti & <gap/>us) quà ncorporis truncus; <lb/>& dum manus apparet retrorsùm ire, cadit <lb/>ad perpendiculum.<emph.end type="italics"/> p.7. </s></p><p type="main"> |
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| <s><emph type="italics"/>IV. <!-- KEEP S--></s> | <s id="id.000015"><emph type="italics"/>IV. <!-- KEEP S--></s> |
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| <s>Experimenta de pilaè curru, aut cquo <lb/>(<gap/> cuatißimè moto) directè &longs;ursùm <lb/>proiecta, recideutéque in manum, & complu-<emph.end type="italics"/><lb/><lb/><emph type="italics"/>ra alia, id<gap/>ò contingere, quòd motus cur<gap/>us, <lb/>aut equi impre&longs;&longs;us manui, componatur cum <lb/>motu ip&longs;ius manus proprio, &longs;iatque motus <lb/>reipsâ mi&longs;tus, licet ad oculum non alius, <lb/>quàm manus proprius appareat.<emph.end type="italics"/> p.10. </s></p><p type="main"> | <s id="id.000016">Experimenta de pilaè curru, aut cquo <lb/>(<gap/> cuatißimè moto) directè &longs;ursùm <lb/>proiecta, recideutéque in manum, & complu-<emph.end type="italics"/><lb/><lb/><emph type="italics"/>ra alia, id<gap/>ò contingere, quòd motus cur<gap/>us, <lb/>aut equi impre&longs;&longs;us manui, componatur cum <lb/>motu ip&longs;ius manus proprio, &longs;iatque motus <lb/>reipsâ mi&longs;tus, licet ad oculum non alius, <lb/>quàm manus proprius appareat.<emph.end type="italics"/> p.10. </s></p><p type="main"> |
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| <s><emph type="italics"/>V. <!-- KEEP S--></s> | <s id="id.000017"><emph type="italics"/>V. <!-- KEEP S--></s> |
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| <s>Experimenta varia de pila, aut alie <lb/>proi<gap/>ctili, quod, dum nauis mou<gap/>, proie­<lb/>ctum &longs;ursùm, in eandem nauis partem reci­<lb/>du: dimi&longs;&longs;um ex fa&longs;tigto mali, decidit ad <lb/>eiu&longs;dem pedem; & &longs;eu in proram, &longs;eu in <lb/>puppim pari vi adactum, æquale &longs;uprana­<lb/>uim &longs;patium con&longs;icit, licet iuæquale aëris <lb/>respectu. </s> | <s id="id.000018">Experimenta varia de pila, aut alie <lb/>proi<gap/>ctili, quod, dum nauis mou<gap/>, proie­<lb/>ctum &longs;ursùm, in eandem nauis partem reci­<lb/>du: dimi&longs;&longs;um ex fa&longs;tigto mali, decidit ad <lb/>eiu&longs;dem pedem; & &longs;eu in proram, &longs;eu in <lb/>puppim pari vi adactum, æquale &longs;uprana­<lb/>uim &longs;patium con&longs;icit, licet iuæquale aëris <lb/>respectu. </s> |
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| <s>Can&longs;adicitur ex compo&longs;itione mo­<lb/>tus n<gap/>is, & motus manus propry, oculo <lb/>intereà non alium, quàm manus proprium <lb/>ob&longs;eruante, ob motum nauis, qui &longs;it tam ip&longs;i, <lb/>quam proiectili communis.<emph.end type="italics"/> p.14. </s></p><p type="main"> | <s id="id.000019">Can&longs;adicitur ex compo&longs;itione mo­<lb/>tus n<gap/>is, & motus manus propry, oculo <lb/>intereà non alium, quàm manus proprium <lb/>ob&longs;eruante, ob motum nauis, qui &longs;it tam ip&longs;i, <lb/>quam proiectili communis.<emph.end type="italics"/> p.14. </s></p><p type="main"> |
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| <s><emph type="italics"/>VI. <!-- KEEP S--></s> | <s id="id.000020"><emph type="italics"/>VI. <!-- KEEP S--></s> |
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| <s>Ad inuc&longs;tigandum cau&longs;am motus tam <lb/>naturalis, cuius impetus continuò cre&longs;cit, <lb/>quàm proiect<gap/>, cuius decre&longs;cit; præmit­<lb/><gap/>r accelerat<gap/> grauis decidentis &longs;it <lb/>fieri, vt acqui&longs;ita &longs;patia &longs;int in duplicata <lb/>temporum, quibus acquiruntur, ratione; & <lb/>lineam, quam pro<gap/>ctum obliquè de&longs;<gap/><lb/>per aërem, e&longs;&longs;e parabolicam, re&longs;que mon&longs;ira­<lb/>tur ex &longs;<gap/>bemate ad vtrumque præmi&longs;&longs;um <lb/>intelligendum comparate.<emph.end type="italics"/> p.20. </s></p><pb/><p type="main"> | <s id="id.000021">Ad inuc&longs;tigandum cau&longs;am motus tam <lb/>naturalis, cuius impetus continuò cre&longs;cit, <lb/>quàm proiect<gap/>, cuius decre&longs;cit; præmit­<lb/><gap/>r accelerat<gap/> grauis decidentis &longs;it <lb/>fieri, vt acqui&longs;ita &longs;patia &longs;int in duplicata <lb/>temporum, quibus acquiruntur, ratione; & <lb/>lineam, quam pro<gap/>ctum obliquè de&longs;<gap/><lb/>per aërem, e&longs;&longs;e parabolicam, re&longs;que mon&longs;ira­<lb/>tur ex &longs;<gap/>bemate ad vtrumque præmi&longs;&longs;um <lb/>intelligendum comparate.<emph.end type="italics"/> p.20. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.003.jpg"/><p type="main"> |
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| <s><emph type="italics"/>VII. <!-- KEEP S--></s> | <s id="id.000022"><emph type="italics"/>VII. <!-- KEEP S--></s> |
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| <s>Ex eo elicitur lapidem è naui mota <lb/>proiectum &longs;ecundum altitudinem mali, & <lb/>recidentem &longs;ecundum eandem, de&longs;cribere <lb/>lineam, ad vi&longs;um quidem rectam, &longs;edreipsâ <lb/>tamen parabolicam; vt & dimi&longs;&longs;um è &longs;um­<lb/>mo malo &longs;emiparabolicam; compo&longs;ito motu <lb/>ex perpendiculari, qui à man<gap/>, aut granita­<lb/>te, & horizontali, qui à naui. </s> | <s id="id.000023">Ex eo elicitur lapidem è naui mota <lb/>proiectum &longs;ecundum altitudinem mali, & <lb/>recidentem &longs;ecundum eandem, de&longs;cribere <lb/>lineam, ad vi&longs;um quidem rectam, &longs;edreipsâ <lb/>tamen parabolicam; vt & dimi&longs;&longs;um è &longs;um­<lb/>mo malo &longs;emiparabolicam; compo&longs;ito motu <lb/>ex perpendiculari, qui à man<gap/>, aut granita­<lb/>te, & horizontali, qui à naui. </s> |
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| <s>Nihil ex vtro­<lb/>vis motu ob compo&longs;itionem deperdi, &longs;ed <lb/>tantundem &longs;parij & perpendieulariter, & <lb/>horizontaliter peruadi, quantum &longs;i motus &longs;e­<lb/>iuncti forent. </s> | <s id="id.000024">Nihil ex vtro­<lb/>vis motu ob compo&longs;itionem deperdi, &longs;ed <lb/>tantundem &longs;parij & perpendieulariter, & <lb/>horizontaliter peruadi, quantum &longs;i motus &longs;e­<lb/>iuncti forent. </s> |
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| <s>Tempora a&longs;cen&longs;us, & de&longs;cen­<lb/>&longs;us e&longs;&longs;e æqualia, & velocitatem qua pro­<lb/>portione in a&longs;cen&longs;u decre&longs;cit, in de&longs;cen&longs;u in­<lb/>cre&longs;cere; idque perinde, ac dum motus tran&longs;­<lb/>luitius est nullus. </s> | <s id="id.000025">Tempora a&longs;cen&longs;us, & de&longs;cen­<lb/>&longs;us e&longs;&longs;e æqualia, & velocitatem qua pro­<lb/>portione in a&longs;cen&longs;u decre&longs;cit, in de&longs;cen&longs;u in­<lb/>cre&longs;cere; idque perinde, ac dum motus tran&longs;­<lb/>luitius est nullus. </s> |
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| <s>Proportionem velocita­<lb/>tis cre&longs;centis, & decre&longs;centis &longs;ecundum li­<lb/>neam parabolicam, e&longs;&longs;e eandem, quæ &longs;ecun­<lb/>dum perpendicularem. </s> | <s id="id.000026">Proportionem velocita­<lb/>tis cre&longs;centis, & decre&longs;centis &longs;ecundum li­<lb/>neam parabolicam, e&longs;&longs;e eandem, quæ &longs;ecun­<lb/>dum perpendicularem. </s> |
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| <s>In motu compo&longs;ito <lb/>&longs;patia quidem &longs;ursùm, aut deorsùm acquiri <lb/>inæqualiter per momenta æqualia; at pror­<lb/>sùn, &longs;eu &longs;ecundum berizontem, penitùs <lb/>æqualiter. </s> | <s id="id.000027">In motu compo&longs;ito <lb/>&longs;patia quidem &longs;ursùm, aut deorsùm acquiri <lb/>inæqualiter per momenta æqualia; at pror­<lb/>sùn, &longs;eu &longs;ecundum berizontem, penitùs <lb/>æqualiter. </s> |
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| <s>Quantumcúmque apertæ, aut <lb/>contractæ &longs;int parabolicæ, &longs;emiparabolicæve <lb/>lincæ, modò altitudo eadem &longs;it, ip&longs;as tempore <lb/>a juali d<gap/>&longs;cribi. </s> | <s id="id.000028">Quantumcúmque apertæ, aut <lb/>contractæ &longs;int parabolicæ, &longs;emiparabolicæve <lb/>lincæ, modò altitudo eadem &longs;it, ip&longs;as tempore <lb/>a juali d<gap/>&longs;cribi. </s> |
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| <s>Denique quod vis proiecti­<lb/>le, etiam globum bombardicum, directè &longs;ur­<lb/>&longs;um è pede mili, dum nauis monetur, emi&longs;­<lb/>&longs;um, ad pedem mali recidere.<emph.end type="italics"/> p.23. </s></p><p type="main"> | <s id="id.000029">Denique quod vis proiecti­<lb/>le, etiam globum bombardicum, directè &longs;ur­<lb/>&longs;um è pede mili, dum nauis monetur, emi&longs;­<lb/>&longs;um, ad pedem mali recidere.<emph.end type="italics"/> p.23. </s></p><p type="main"> |
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| <s><emph type="italics"/>VIII. <!-- KEEP S--></s> | <s id="id.000030"><emph type="italics"/>VIII. <!-- KEEP S--></s> |
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| <s>Declaratur etiam, cur ex duobus in­<lb/>tra<gap/> motam colludentibus, pilamque vi <lb/>pariex prora, ac puppi remittentibus, non aut <lb/><gap/>e propiùs, aut bic remotiùs pilæ occurrat. <lb/></s> | <s id="id.000031">Declaratur etiam, cur ex duobus in­<lb/>tra<gap/> motam colludentibus, pilamque vi <lb/>pariex prora, ac puppi remittentibus, non aut <lb/><gap/>e propiùs, aut bic remotiùs pilæ occurrat. <lb/></s> |
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| <s>N<gap/>mpe quòd motus nauis vtrique commn­<lb/><gap/>s quantum virtutis addit pilæ ab boc pro­<lb/>iectæ, tantundem illum &longs;emouet: & quan­<lb/>tum adimit rejectæ ab illo, tantundem i&longs;tum <lb/>promouet, mirabili compen&longs;atione.<emph.end type="italics"/> p.31. </s></p><p type="main"> | <s id="id.000032">N<gap/>mpe quòd motus nauis vtrique commn­<lb/><gap/>s quantum virtutis addit pilæ ab boc pro­<lb/>iectæ, tantundem illum &longs;emouet: & quan­<lb/>tum adimit rejectæ ab illo, tantundem i&longs;tum <lb/>promouet, mirabili compen&longs;atione.<emph.end type="italics"/> p.31. </s></p><p type="main"> |
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| <s><emph type="italics"/>IX. <!-- KEEP S--></s> | <s id="id.000033"><emph type="italics"/>IX. <!-- KEEP S--></s> |
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| <s>Nullus motus non <gap/>uralis, vt nullus <lb/>non e&longs;t à naturalibus principi<gap/>s: Nullus non <lb/>violentus, vt nullus (&longs;eclu&longs;o primæ vo) <lb/>non ab alto e&longs;t. </s> | <s id="id.000034">Nullus motus non <gap/>uralis, vt nullus <lb/>non e&longs;t à naturalibus principi<gap/>s: Nullus non <lb/>violentus, vt nullus (&longs;eclu&longs;o primæ vo) <lb/>non ab alto e&longs;t. </s> |
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| <s>Is naturalis e&longs;t, qui ant &longs;pon­<lb/>tc, <gap/> &longs;ine repugnantia fit; is violentus, qui <lb/>p<gap/>ater <gap/>un, ant cum <expan abbr="repugnãtia">repugnantia</expan>. </s> | <s id="id.000035">Is naturalis e&longs;t, qui ant &longs;pon­<lb/>tc, <gap/> &longs;ine repugnantia fit; is violentus, qui <lb/>p<gap/>ater <gap/>un, ant cum <expan abbr="repugnãtia">repugnantia</expan>. </s> |
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| <s>Æqua­<lb/><gap/>tas character motus naturalis; inæqua­<lb/><gap/>as violenta. <gap/>uralis ergo propriè &longs;<gap/>­<lb/>les circularis, mix méque <gap/>s; violen-<emph.end type="italics"/><lb/><lb/><emph type="italics"/>tus autem rectus, qualis e&longs;t non modò rei pro­<lb/>iectæ &longs;ursùm, verum etiam rei cadentis <lb/>deorsùm.<emph.end type="italics"/> p.33. </s></p><p type="main"> | <s id="id.000036">Æqua­<lb/><gap/>tas character motus naturalis; inæqua­<lb/><gap/>as violenta. <gap/>uralis ergo propriè &longs;<gap/>­<lb/>les circularis, mix méque <gap/>s; violen-<emph.end type="italics"/><lb/><lb/><emph type="italics"/>tus autem rectus, qualis e&longs;t non modò rei pro­<lb/>iectæ &longs;ursùm, verum etiam rei cadentis <lb/>deorsùm.<emph.end type="italics"/> p.33. </s></p><p type="main"> |
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| <s><emph type="italics"/>X. <!-- KEEP S--></s> | <s id="id.000037"><emph type="italics"/>X. <!-- KEEP S--></s> |
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| <s>Cùm motus lapidis tam dimi&longs;si, quàm <lb/>recidentis ex malitran&longs;iati altitudine, com­<lb/>po&longs;itus &longs;it ex perpendiculari, & borizontali, <lb/>horizont alis potiùs, quàm perpendicularis <lb/>habendus nuuralis e&longs;t, ob iam memoratam <lb/>æquabilitatem. </s> | <s id="id.000038">Cùm motus lapidis tam dimi&longs;si, quàm <lb/>recidentis ex malitran&longs;iati altitudine, com­<lb/>po&longs;itus &longs;it ex perpendiculari, & borizontali, <lb/>horizont alis potiùs, quàm perpendicularis <lb/>habendus nuuralis e&longs;t, ob iam memoratam <lb/>æquabilitatem. </s> |
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| <s>Videtur omnis motus hori­<lb/>zontalis &longs;uapte natura æquabilis, atque per­<lb/>petuus; vt vel intelligitur exemplo globi <lb/>vniformis materiæ, qui &longs;emel motus &longs;upræ <lb/>terræ &longs;uperficiem exqui&longs;itè rotundam, poli­<lb/>tamque &longs;uppo&longs;itam, videatur vt æquabili­<lb/>ter, ita perpetuò reuoluendus.<emph.end type="italics"/> p.38. </s></p><p type="main"> | <s id="id.000039">Videtur omnis motus hori­<lb/>zontalis &longs;uapte natura æquabilis, atque per­<lb/>petuus; vt vel intelligitur exemplo globi <lb/>vniformis materiæ, qui &longs;emel motus &longs;upræ <lb/>terræ &longs;uperficiem exqui&longs;itè rotundam, poli­<lb/>tamque &longs;uppo&longs;itam, videatur vt æquabili­<lb/>ter, ita perpetuò reuoluendus.<emph.end type="italics"/> p.38. </s></p><p type="main"> |
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| <s><emph type="italics"/>XI. <!-- KEEP S--></s> | <s id="id.000040"><emph type="italics"/>XI. <!-- KEEP S--></s> |
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| <s>Si motus lapidis deorsùm violentus e&longs;t, <lb/>& ab externo principio; debet; hoc proinde <lb/>e&longs;&longs;e vel impellens, vel attrabent, vel <expan abbr="vtrũ-que">vtrun­<lb/>que</expan>. </s> | <s id="id.000041">Si motus lapidis deorsùm violentus e&longs;t, <lb/>& ab externo principio; debet; hoc proinde <lb/>e&longs;&longs;e vel impellens, vel attrabent, vel <expan abbr="vtrũ-que">vtrun­<lb/>que</expan>. </s> |
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| <s>Impellens aliud e&longs;&longs;e non pote&longs;t, quàm <lb/>aer &longs;upornè incumbens, qui vt lapidi &longs;ur­<lb/>sùm nitenti re&longs;i&longs;tit, ita deorsùm tendentem <lb/>in&longs;ectaiur. </s> | <s id="id.000042">Impellens aliud e&longs;&longs;e non pote&longs;t, quàm <lb/>aer &longs;upornè incumbens, qui vt lapidi &longs;ur­<lb/>sùm nitenti re&longs;i&longs;tit, ita deorsùm tendentem <lb/>in&longs;ectaiur. </s> |
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| <s>Quanta &longs;it <expan abbr="aēris">aerris</expan>, fluxi licet, in <lb/>impellendo vis, probatur ex variis effecti­<lb/>bus, at præ&longs;ertim in pyriis, pnenmatici&longs;que <lb/>catapultis. </s> | <s id="id.000043">Quanta &longs;it <expan abbr="aēris">aerris</expan>, fluxi licet, in <lb/>impellendo vis, probatur ex variis effecti­<lb/>bus, at præ&longs;ertim in pyriis, pnenmatici&longs;que <lb/>catapultis. </s> |
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| <s>Non &longs;ufficit tamen &longs;ola aëris vis <lb/>ad motum illum deorsùm præ&longs;tandum.<emph.end type="italics"/> p 41. </s></p><p type="main"> | <s id="id.000044">Non &longs;ufficit tamen &longs;ola aëris vis <lb/>ad motum illum deorsùm præ&longs;tandum.<emph.end type="italics"/> p 41. </s></p><p type="main"> |
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| <s><emph type="italics"/>XII. <!-- KEEP S--></s> | <s id="id.000045"><emph type="italics"/>XII. <!-- KEEP S--></s> |
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| <s>Attrabens cau&longs;a alia e&longs;&longs;e non pote&longs;t, <lb/>quàm ip&longs;amet Terra, cui &longs;it in&longs;ita (vt & <lb/>cuivis Toti) vis continendi, retrabendique <lb/>parteis &longs;ui omneis, quales enumerantur beic. <lb/></s> | <s id="id.000046">Attrabens cau&longs;a alia e&longs;&longs;e non pote&longs;t, <lb/>quàm ip&longs;amet Terra, cui &longs;it in&longs;ita (vt & <lb/>cuivis Toti) vis continendi, retrabendique <lb/>parteis &longs;ui omneis, quales enumerantur beic. <lb/></s> |
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| <s>Explicatur pancis analogia, vel eadem po­<lb/>tiùs natura Magnetis, ac Terræ. <!-- KEEP S--></s> | <s id="id.000047">Explicatur pancis analogia, vel eadem po­<lb/>tiùs natura Magnetis, ac Terræ. <!-- KEEP S--></s> |
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| <s>Non vide­<lb/>tur vtrin&longs;que actio in res attractas fieri, <lb/>ni&longs;i emißis corpu&longs;culis &longs;ubtilißimis, quæ <lb/>ip&longs;as pelliciant: quòd nulla actio phy&longs;ica &longs;i­<lb/>ne contactu, & organi &longs;altem interuemn &longs;it. <lb/></s> | <s id="id.000048">Non vide­<lb/>tur vtrin&longs;que actio in res attractas fieri, <lb/>ni&longs;i emißis corpu&longs;culis &longs;ubtilißimis, quæ <lb/>ip&longs;as pelliciant: quòd nulla actio phy&longs;ica &longs;i­<lb/>ne contactu, & organi &longs;altem interuemn &longs;it. <lb/></s> |
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| <s>Declaratur res exemplobalitus è re odorain <lb/>narets tran&longs;mißi.<emph.end type="italics"/> p.46. </s></p><p type="main"> | <s id="id.000049">Declaratur res exemplobalitus è re odorain <lb/>narets tran&longs;mißi.<emph.end type="italics"/> p.46. </s></p><p type="main"> |
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| <s><emph type="italics"/>XIII. <!-- KEEP S--></s> | <s id="id.000050"><emph type="italics"/>XIII. <!-- KEEP S--></s> |
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| <s>Idem &longs;it circa alios &longs;en&longs;us. </s> | <s id="id.000051">Idem &longs;it circa alios &longs;en&longs;us. </s> |
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| <s>Corpu&longs;cu­<lb/>la, qua &longs;en&longs;us permulcent, aliaratione figu­<lb/>rata, quàm quæ exa&longs;perant. </s> | <s id="id.000052">Corpu&longs;cu­<lb/>la, qua &longs;en&longs;us permulcent, aliaratione figu­<lb/>rata, quàm quæ exa&longs;perant. </s> |
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| <s>Arguitur id iur­<lb/>sùs ex od<gap/>e. </s> | <s id="id.000053">Arguitur id iur­<lb/>sùs ex od<gap/>e. </s> |
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| <s>Subtilitas corpu&longs;culorum inef­<lb/>fabilis probabilis fit. </s> | <s id="id.000054">Subtilitas corpu&longs;culorum inef­<lb/>fabilis probabilis fit. </s> |
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| <s>Sympatbia, & Anti­<lb/>pathia, ni&longs;i per ip&longs;a, qua&longs;i organula, non e&longs;t. <lb/></s> | <s id="id.000055">Sympatbia, & Anti­<lb/>pathia, ni&longs;i per ip&longs;a, qua&longs;i organula, non e&longs;t. <lb/></s> |
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| <s>Debent in re excipiente respondere particu­<lb/>læ analogica; vti &longs;unt, quæ in naribus (non <lb/>in partibus altis) re&longs;pect<gap/> corpu&longs;culorum<emph.end type="italics"/><pb/><lb/><emph type="italics"/>odoris. </s> | <s id="id.000056">Debent in re excipiente respondere particu­<lb/>læ analogica; vti &longs;unt, quæ in naribus (non <lb/>in partibus altis) re&longs;pect<gap/> corpu&longs;culorum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.004.jpg"/><lb/><emph type="italics"/>odoris. </s> |
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| <s>Debent & poruli analogici in iis, qu<gap/><lb/>ab ip&longs;is peruaduntur rebus; vt exemplis <lb/>o&longs;tenditur.<emph.end type="italics"/> p.50. </s></p><p type="main"> | <s id="id.000057">Debent & poruli analogici in iis, qu<gap/><lb/>ab ip&longs;is peruaduntur rebus; vt exemplis <lb/>o&longs;tenditur.<emph.end type="italics"/> p.50. </s></p><p type="main"> |
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| <s><emph type="italics"/>XIV. <!-- KEEP S--></s> | <s id="id.000058"><emph type="italics"/>XIV. <!-- KEEP S--></s> |
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| <s>Di&longs;&longs;icultas præcipua; quomodo attra­<lb/>ctio ferri à Magnete per emi&longs;&longs;a corpu&longs;cul<gap/><lb/>fiat: Fieri fortè radiis iugi illorum corpu&longs;cn­<lb/>lorum emißione creatis, refracti&longs;que in re <lb/>attracta ver&longs;us perpendicularem: vnde & <lb/>factis angulis, qua&longs;icubitis, in ferro, com­<lb/>preßio, & attractio in magnetem &longs;equatur. <lb/></s> | <s id="id.000059">Di&longs;&longs;icultas præcipua; quomodo attra­<lb/>ctio ferri à Magnete per emi&longs;&longs;a corpu&longs;cul<gap/><lb/>fiat: Fieri fortè radiis iugi illorum corpu&longs;cn­<lb/>lorum emißione creatis, refracti&longs;que in re <lb/>attracta ver&longs;us perpendicularem: vnde & <lb/>factis angulis, qua&longs;icubitis, in ferro, com­<lb/>preßio, & attractio in magnetem &longs;equatur. <lb/></s> |
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| <s>Rationem quorundam effectuum betne red­<lb/>di, & actionem electricorum po&longs;&longs;e exinde <lb/>intelligi.<emph.end type="italics"/> p.54. </s></p><p type="main"> | <s id="id.000060">Rationem quorundam effectuum betne red­<lb/>di, & actionem electricorum po&longs;&longs;e exinde <lb/>intelligi.<emph.end type="italics"/> p.54. </s></p><p type="main"> |
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| <s><emph type="italics"/>XV. <!-- KEEP S--></s> | <s id="id.000061"><emph type="italics"/>XV. <!-- KEEP S--></s> |
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| <s>Vis Terræ attractrix, perinde ac vis <lb/>magnetis ex&longs;eritur. </s> | <s id="id.000062">Vis Terræ attractrix, perinde ac vis <lb/>magnetis ex&longs;eritur. </s> |
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| <s>Propè, quàm pr<gap/>cùl, ma­<lb/>ior. </s> | <s id="id.000063">Propè, quàm pr<gap/>cùl, ma­<lb/>ior. </s> |
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| <s>Lapis in &longs;patiis imaginariis con&longs;titutus <lb/>tam con&longs;tante mundo, quàm non ex&longs;tante, ibi <lb/>quie&longs;ceret. </s> | <s id="id.000064">Lapis in &longs;patiis imaginariis con&longs;titutus <lb/>tam con&longs;tante mundo, quàm non ex&longs;tante, ibi <lb/>quie&longs;ceret. </s> |
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| <s>Etiam in medio aeris &longs;patio, &longs;i <lb/>fieret penitùs inane. </s> | <s id="id.000065">Etiam in medio aeris &longs;patio, &longs;i <lb/>fieret penitùs inane. </s> |
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| <s>Moueturiam, quiatra­<lb/>bitur. </s> | <s id="id.000066">Moueturiam, quiatra­<lb/>bitur. </s> |
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| <s>Ingens &longs;axum, cohibita attractione, <lb/>facillimè mobile. </s> | <s id="id.000067">Ingens &longs;axum, cohibita attractione, <lb/>facillimè mobile. </s> |
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| <s>Motus deorsùm initio len­<lb/>tißimus. </s> | <s id="id.000068">Motus deorsùm initio len­<lb/>tißimus. </s> |
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| <s>Vis proiectoimpre&longs;&longs;a ideò debili­<lb/>tatur, quòd attractio à Terra facta ip&longs;am <lb/>continenter re&longs;ringat. </s> | <s id="id.000069">Vis proiectoimpre&longs;&longs;a ideò debili­<lb/>tatur, quòd attractio à Terra facta ip&longs;am <lb/>continenter re&longs;ringat. </s> |
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| <s>Quare pondera &longs;en <lb/>magna, &longs;en parua (eiu&longs;dem præ&longs;ertim ma­<lb/>teriæ) æqua vdocitate cad<gap/>t.<emph.end type="italics"/> p.58. </s></p><p type="main"> | <s id="id.000070">Quare pondera &longs;en <lb/>magna, &longs;en parua (eiu&longs;dem præ&longs;ertim ma­<lb/>teriæ) æqua vdocitate cad<gap/>t.<emph.end type="italics"/> p.58. </s></p><p type="main"> |
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| <s><emph type="italics"/>XVI. <!-- KEEP S--></s> | <s id="id.000071"><emph type="italics"/>XVI. <!-- KEEP S--></s> |
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| <s>Impre&longs;&longs;us &longs;emel motus illi lapidi in <lb/>imaginariis &longs;patiis con&longs;tisuto foret æquabi­<lb/>lis, & perpetuus, attractionis refringentis <lb/>defectu. </s> | <s id="id.000072">Impre&longs;&longs;us &longs;emel motus illi lapidi in <lb/>imaginariis &longs;patiis con&longs;tisuto foret æquabi­<lb/>lis, & perpetuus, attractionis refringentis <lb/>defectu. </s> |
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| <s>Comprobatur ex dictis de aquabili­<lb/>ta<gap/>e motus horizontalis, & ex con&longs;tantia <lb/>motus rei p<gap/>n&longs;ilis, cuius excur&longs;us, & recur­<lb/>&longs;us præcipue ob &longs;<gap/>lam ip&longs;ius chordæ, par­<lb/>tium ve eius qua&longs;i &longs;arcinulas &longs;ensìm re­<lb/>fringuntur, ac dentque c<gap/>&longs;&longs;ant.<emph.end type="italics"/> p.62. </s></p><p type="main"> | <s id="id.000073">Comprobatur ex dictis de aquabili­<lb/>ta<gap/>e motus horizontalis, & ex con&longs;tantia <lb/>motus rei p<gap/>n&longs;ilis, cuius excur&longs;us, & recur­<lb/>&longs;us præcipue ob &longs;<gap/>lam ip&longs;ius chordæ, par­<lb/>tium ve eius qua&longs;i &longs;arcinulas &longs;ensìm re­<lb/>fringuntur, ac dentque c<gap/>&longs;&longs;ant.<emph.end type="italics"/> p.62. </s></p><p type="main"> |
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| <s><emph type="italics"/>XVII. <!-- KEEP S--></s> | <s id="id.000074"><emph type="italics"/>XVII. <!-- KEEP S--></s> |
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| <s>Pote&longs;t fimplex Terræ attractio & <lb/>emonere lapidem à quiete in aëre, & &longs;uperæ­<lb/>re re&longs;i&longs;tentiam &longs;uppo&longs;iti aëris. </s> | <s id="id.000075">Pote&longs;t fimplex Terræ attractio & <lb/>emonere lapidem à quiete in aëre, & &longs;uperæ­<lb/>re re&longs;i&longs;tentiam &longs;uppo&longs;iti aëris. </s> |
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| <s>Si mobile vno <lb/>ictu pul&longs;um, pluribus &longs;imilibus continenter <lb/>pu &longs;etur, ip&longs;ins velocit as continenter auge­<lb/>bitur. </s> | <s id="id.000076">Si mobile vno <lb/>ictu pul&longs;um, pluribus &longs;imilibus continenter <lb/>pu &longs;etur, ip&longs;ins velocit as continenter auge­<lb/>bitur. </s> |
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| <s>Lapis in aere, &longs;cu à Terra, &longs;eu ab aëre, <lb/>&longs;eu ab vtroque c<gap/>ntinenter ictus accipiat, <lb/>non pote&longs;t continuò non accelerari. </s> | <s id="id.000077">Lapis in aere, &longs;cu à Terra, &longs;eu ab aëre, <lb/>&longs;eu ab vtroque c<gap/>ntinenter ictus accipiat, <lb/>non pote&longs;t continuò non accelerari. </s> |
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| <s>Si ab al­<lb/>tera, &longs;implicive tantum ca<gap/>&longs;a moueretur, <lb/>v. <gap/>otuas cius incre&longs;ceret &longs;ecundum &longs;eriem <lb/>v<gap/>uatum. </s> | <s id="id.000078">Si ab al­<lb/>tera, &longs;implicive tantum ca<gap/>&longs;a moueretur, <lb/>v. <gap/>otuas cius incre&longs;ceret &longs;ecundum &longs;eriem <lb/>v<gap/>uatum. </s> |
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| <s>Atqui incre&longs;<gap/> &longs;ecundum &longs;e­<lb/><gap/>m n<gap/> ab vnitate imparium.<emph.end type="italics"/> p.66. <lb/></s></p><p type="main"> | <s id="id.000079">Atqui incre&longs;<gap/> &longs;ecundum &longs;e­<lb/><gap/>m n<gap/> ab vnitate imparium.<emph.end type="italics"/> p.66. <lb/></s></p><p type="main"> |
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| <s><emph type="italics"/>XVIII. <!-- KEEP S--></s> | <s id="id.000080"><emph type="italics"/>XVIII. <!-- KEEP S--></s> |
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| <s>Coniungenda <gap/>t. </s> | <s id="id.000081">Coniungenda <gap/>t. </s> |
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| <s>aqu<gap/>&longs;<gap/>: vt <lb/>&longs;it in primo moment<gap/>us à Terra at­<lb/>trahente: in &longs;ecundo &longs;int duo, vnus à Ter­<lb/>ra attrabente, alins ab aere imp<gap/>llente, & <lb/>con&longs;equenter &longs;ingulis momentis duo: &longs;icque, <lb/>cum impetus omnes mancmt, &longs;int in primo <lb/>momento, 1. in &longs;ecnndo 3. in tertio 5. & <gap/>quæ <lb/>e&longs;t progre&longs;sio numerorum imparium. </s> | <s id="id.000082">aqu<gap/>&longs;<gap/>: vt <lb/>&longs;it in primo moment<gap/>us à Terra at­<lb/>trahente: in &longs;ecundo &longs;int duo, vnus à Ter­<lb/>ra attrabente, alins ab aere imp<gap/>llente, & <lb/>con&longs;equenter &longs;ingulis momentis duo: &longs;icque, <lb/>cum impetus omnes mancmt, &longs;int in primo <lb/>momento, 1. in &longs;ecnndo 3. in tertio 5. & <gap/>quæ <lb/>e&longs;t progre&longs;sio numerorum imparium. </s> |
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| <s>H<gap/>int <lb/>&longs;equitur &longs;patia in fine <gap/>nin&longs;que momenti ab <lb/>v&longs;que initio qua&longs;ita e&longs;&longs;e 1. 4. 9. & <gap/>. </s> | <s id="id.000083">H<gap/>int <lb/>&longs;equitur &longs;patia in fine <gap/>nin&longs;que momenti ab <lb/>v&longs;que initio qua&longs;ita e&longs;&longs;e 1. 4. 9. & <gap/>. </s> |
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| <s>quæ <lb/>&longs;unt quadrata momentorum. </s> | <s id="id.000084">quæ <lb/>&longs;unt quadrata momentorum. </s> |
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| <s>Declaratur res <lb/>&longs;chemate. </s> | <s id="id.000085">Declaratur res <lb/>&longs;chemate. </s> |
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| <s>Cur graue proiectum tant<gap/> a&longs;<gap/>n­<lb/>dat tempore, quanto deinceps de&longs;cendit. </s> | <s id="id.000086">Cur graue proiectum tant<gap/> a&longs;<gap/>n­<lb/>dat tempore, quanto deinceps de&longs;cendit. </s> |
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| <s>Ea­<lb/>dem proportio &longs;eruatur in rebus obliquè de­<lb/>cidentibus: & in excur&longs;ibus, recur&longs;ibu&longs;que <lb/>rerum pen&longs;ilium. </s> | <s id="id.000087">Ea­<lb/>dem proportio &longs;eruatur in rebus obliquè de­<lb/>cidentibus: & in excur&longs;ibus, recur&longs;ibu&longs;que <lb/>rerum pen&longs;ilium. </s> |
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| <s>An ca&longs;urus fuerit ead<gap/><lb/>incrementi velocitatis proportione demi&longs;&longs;us <lb/>in centrum lapis à Terræ &longs;uperficie, à l una, <lb/>à Sole, à Fixis?<emph.end type="italics"/> p.69. </s></p><p type="main"> | <s id="id.000088">An ca&longs;urus fuerit ead<gap/><lb/>incrementi velocitatis proportione demi&longs;&longs;us <lb/>in centrum lapis à Terræ &longs;uperficie, à l una, <lb/>à Sole, à Fixis?<emph.end type="italics"/> p.69. </s></p><p type="main"> |
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| <s><emph type="italics"/>XIX. <!-- KEEP S--></s> | <s id="id.000089"><emph type="italics"/>XIX. <!-- KEEP S--></s> |
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| <s>Vis motrix in re proiecta non aloud, <lb/>quàm impre&longs;&longs;us motus, qui ex &longs;e in cop<gap/> &longs;e­<lb/>ueraret porpctuò, ni&longs;i facta à Terra attra­<lb/>ctione labe&longs;actaretur. </s> | <s id="id.000090">Vis motrix in re proiecta non aloud, <lb/>quàm impre&longs;&longs;us motus, qui ex &longs;e in cop<gap/> &longs;e­<lb/>ueraret porpctuò, ni&longs;i facta à Terra attra­<lb/>ctione labe&longs;actaretur. </s> |
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| <s>Imprimitur, dum mo­<lb/>uens iunctum mobili ip&longs;um &longs;ecum monet, & <lb/>aliquo v&longs;que in viam <gap/>dam comitatur. <lb/></s> | <s id="id.000091">Imprimitur, dum mo­<lb/>uens iunctum mobili ip&longs;um &longs;ecum monet, & <lb/>aliquo v&longs;que in viam <gap/>dam comitatur. <lb/></s> |
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| <s>Motus reflexus cum directo continüatus, <gap/>b <lb/>eadem cau&longs;a cum illo e&longs;t. </s> | <s id="id.000092">Motus reflexus cum directo continüatus, <gap/>b <lb/>eadem cau&longs;a cum illo e&longs;t. </s> |
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| <s>R<gap/>&longs;t<gap/>xio, & i<gap/>­<lb/>dentia ad angulos pareis, eadem leg<gap/>, qua <lb/>emer&longs;io, & precidentia in re pen&longs;ili.<emph.end type="italics"/> p.74. </s></p><p type="main"> | <s id="id.000093">R<gap/>&longs;t<gap/>xio, & i<gap/>­<lb/>dentia ad angulos pareis, eadem leg<gap/>, qua <lb/>emer&longs;io, & precidentia in re pen&longs;ili.<emph.end type="italics"/> p.74. </s></p><p type="main"> |
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| <s><emph type="italics"/>XX. <!-- KEEP S--></s> | <s id="id.000094"><emph type="italics"/>XX. <!-- KEEP S--></s> |
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| <s>Differtur tractatio de argum<gap/><lb/>motu rerum &longs;ur&longs;um proiectarum <gap/>idin­<lb/>tinmque ad quictem Terræ a&longs;&longs;erendam a&longs;­<lb/>&longs;<gap/>pto, in occa&longs;ionem aliam. </s> | <s id="id.000095">Differtur tractatio de argum<gap/><lb/>motu rerum &longs;ur&longs;um proiectarum <gap/>idin­<lb/>tinmque ad quictem Terræ a&longs;&longs;erendam a&longs;­<lb/>&longs;<gap/>pto, in occa&longs;ionem aliam. </s> |
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| <s>Epi&longs;tola<gap/>­<lb/>cludilur.<emph.end type="italics"/> p 77. </s></p><p type="main"> | <s id="id.000096">Epi&longs;tola<gap/>­<lb/>cludilur.<emph.end type="italics"/> p 77. </s></p><p type="main"> |
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| <s><emph type="center"/>EPISTOLÆ POSTERIORIS.<emph.end type="center"/></s></p><p type="main"> | <s id="id.000097"><emph type="center"/>EPISTOLÆ POSTERIORIS.<emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="italics"/>I. PRoponitur agendum de imbecillitate <lb/>argumenti, quo ab Ari&longs;tot<gap/>e v&longs;que <lb/>probatur Terram quic&longs;cere. </s> | <s id="id.000098"><emph type="italics"/>I. PRoponitur agendum de imbecillitate <lb/>argumenti, quo ab Ari&longs;tot<gap/>e v&longs;que <lb/>probatur Terram quic&longs;cere. </s> |
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| <s>Sene<gap/>a rem di&longs;­<lb/>qui&longs;rtione non indignam cen&longs;uit, mon<gap/>ur­<lb/>ne Terra, an-non. </s> | <s id="id.000099">Sene<gap/>a rem di&longs;­<lb/>qui&longs;rtione non indignam cen&longs;uit, mon<gap/>ur­<lb/>ne Terra, an-non. </s> |
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| <s>Plato eam momri opina­<lb/>tus e&longs;t. </s> | <s id="id.000100">Plato eam momri opina­<lb/>tus e&longs;t. </s> |
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| <s>Argumentum vulgare pro qui<gap/>e, <lb/>Quòd lapis &longs;ursùm directè protectus epup­<lb/>pt, dum namis mon<gap/>, non recidat in p<gap/><lb/>intereà &longs;ubductam. </s> | <s id="id.000101">Argumentum vulgare pro qui<gap/>e, <lb/>Quòd lapis &longs;ursùm directè protectus epup­<lb/>pt, dum namis mon<gap/>, non recidat in p<gap/><lb/>intereà &longs;ubductam. </s> |
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| <s>Cùm exemplam bet fal­<lb/>&longs;um &longs;it, videtur argumontum po&longs;&longs;e r<gap/>or-<emph.end type="italics"/><pb/><lb/><emph type="italics"/>quer;<emph.end type="italics"/> p.79. </s></p><p type="main"> | <s id="id.000102">Cùm exemplam bet fal­<lb/>&longs;um &longs;it, videtur argumontum po&longs;&longs;e r<gap/>or-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.005.jpg"/><lb/><emph type="italics"/>quer;<emph.end type="italics"/> p.79. </s></p><p type="main"> |
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| <s>II. <emph type="italics"/>Dedaratur &longs;chimate, quemodo lapit <lb/>&longs;u &longs;am protectus <gap/>cund<gap/> altitudtuem <lb/>Turiss, non poßit de&longs;ers à Turri, tamet&longs;i <lb/>Terra eam transfirst; quonsam lapis vnà <lb/>tranifertur, propter metum, quo Terra mo­<lb/>utns borizontaliter manum pr<gap/>cientem, <lb/><gap/> fimù lapidem<gap/>juanquam bic m<gap/>s, <lb/>quòd &longs;it tam oculo, quàm turri, lapi lique <lb/>communis, ob&longs;eruabi<gap/>isnon &longs;it, &longs;ed &longs;olus <gap/>e, <lb/><gap/> &longs;ursùm, ac deoriùm, &longs;cu porpendicularis <lb/>e&longs;t.<emph.end type="italics"/> p. </s> | <s id="id.000103">II. <emph type="italics"/>Dedaratur &longs;chimate, quemodo lapit <lb/>&longs;u &longs;am protectus <gap/>cund<gap/> altitudtuem <lb/>Turiss, non poßit de&longs;ers à Turri, tamet&longs;i <lb/>Terra eam transfirst; quonsam lapis vnà <lb/>tranifertur, propter metum, quo Terra mo­<lb/>utns borizontaliter manum pr<gap/>cientem, <lb/><gap/> fimù lapidem<gap/>juanquam bic m<gap/>s, <lb/>quòd &longs;it tam oculo, quàm turri, lapi lique <lb/>communis, ob&longs;eruabi<gap/>isnon &longs;it, &longs;ed &longs;olus <gap/>e, <lb/><gap/> &longs;ursùm, ac deoriùm, &longs;cu porpendicularis <lb/>e&longs;t.<emph.end type="italics"/> p. </s> |
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| <s>S9. </s></p><p type="main"> | <s id="id.000104">S9. </s></p><p type="main"> |
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| <s>III. <emph type="italics"/>Motus Terræinob&longs;eruabilis, ni&longs;i quis <lb/>ill<gap/> non abripiatur. </s> | <s id="id.000105">III. <emph type="italics"/>Motus Terræinob&longs;eruabilis, ni&longs;i quis <lb/>ill<gap/> non abripiatur. </s> |
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| <s>Aeridem e&longs;t Terræglo­<lb/><gap/>, quod lanugo mals catoneo. </s> | <s id="id.000106">Aeridem e&longs;t Terræglo­<lb/><gap/>, quod lanugo mals catoneo. </s> |
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| <s>Ob &longs;luiditæ­<lb/>tem non-nibil retardatur; vnde & appa­<lb/>ret in occa&longs;um moutri. </s> | <s id="id.000107">Ob &longs;luiditæ­<lb/>tem non-nibil retardatur; vnde & appa­<lb/>ret in occa&longs;um moutri. </s> |
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| <s>Inde nauigatio in <lb/>occa&longs;um, quàmin ortum facilior. </s> | <s id="id.000108">Inde nauigatio in <lb/>occa&longs;um, quàmin ortum facilior. </s> |
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| <s>Quomede <lb/><gap/>o <gap/> hori<gap/>ontalis imprimatur lapidi, quæ­<lb/>tenus Terratran sfort proiectorem? </s> | <s id="id.000109">Quomede <lb/><gap/>o <gap/> hori<gap/>ontalis imprimatur lapidi, quæ­<lb/>tenus Terratran sfort proiectorem? </s> |
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| <s>Quomo­<lb/>do volucri, dum transfert rem, à quailla <lb/>anolat, & aerem, cui de<gap/>ceps alis innititur? <lb/></s> | <s id="id.000110">Quomo­<lb/>do volucri, dum transfert rem, à quailla <lb/>anolat, & aerem, cui de<gap/>ceps alis innititur? <lb/></s> |
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| <s>Quomodo nubi, aut plumæ? </s> | <s id="id.000111">Quomodo nubi, aut plumæ? </s> |
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| <s>vente, ignea­<lb/>ve traiectioni?<emph.end type="italics"/> p.91. </s></p><p type="main"> | <s id="id.000112">vente, ignea­<lb/>ve traiectioni?<emph.end type="italics"/> p.91. </s></p><p type="main"> |
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| <s>IV. <emph type="italics"/>Di&longs;irimen inter æerem, & mundanum <lb/><gap/>tium, in quo aer. </s> | <s id="id.000113">IV. <emph type="italics"/>Di&longs;irimen inter æerem, & mundanum <lb/><gap/>tium, in quo aer. </s> |
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| <s>Spatiu<gap/> immotum; <lb/>acr cum Terra mobilis. </s> | <s id="id.000114">Spatiu<gap/> immotum; <lb/>acr cum Terra mobilis. </s> |
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| <s>Heinclapts vide­<lb/>ri pote&longs;t de&longs;eribere rectam lineam tam <lb/>a&longs;<gap/>ndendo, quàm ex&longs;cendende per aerem, <lb/>& intereà tamen de&longs;cribere lineam para­<lb/>b<gap/>am per spatium munda<gap/>m. </s> | <s id="id.000115">Heinclapts vide­<lb/>ri pote&longs;t de&longs;eribere rectam lineam tam <lb/>a&longs;<gap/>ndendo, quàm ex&longs;cendende per aerem, <lb/>& intereà tamen de&longs;cribere lineam para­<lb/>b<gap/>am per spatium munda<gap/>m. </s> |
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| <s>Pere&longs;t <lb/><gap/> viam exiguam con&longs;icere per aerem, <lb/>& conficeretamen per spatium mundanum <lb/>pro<gap/>. </s> | <s id="id.000116">Pere&longs;t <lb/><gap/> viam exiguam con&longs;icere per aerem, <lb/>& conficeretamen per spatium mundanum <lb/>pro<gap/>. </s> |
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| <s>Quid &longs;it di&longs;<gap/>riminis in motu <lb/>p<gap/> &longs;ur&longs;um lapidis, pro<gap/> &longs;pectatur <lb/><gap/> nauis, ant cum motu Terræ con­<lb/>i<gap/>.<emph.end type="italics"/> p.96. </s></p><p type="main"> | <s id="id.000117">Quid &longs;it di&longs;<gap/>riminis in motu <lb/>p<gap/> &longs;ur&longs;um lapidis, pro<gap/> &longs;pectatur <lb/><gap/> nauis, ant cum motu Terræ con­<lb/>i<gap/>.<emph.end type="italics"/> p.96. </s></p><p type="main"> |
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| <s>V. <emph type="italics"/>Declaratur non concludere, quod obli­<lb/>citur de globerum explo&longs;ione in ortum, in <lb/>oc<gap/>a&longs;um, in a<gap/>&longs;trum, in boream, & &longs;ur­<lb/>&longs;<gap/>, ex dictis à &longs;i<gap/>li de proiectis è naui: <lb/>ci<gap/>n motus Terræ glob<gap/> impre&longs;&longs;us impri­<lb/><gap/> etiam machinæ, ac proinde mot<gap/> eo­<lb/>dem communi <gap/>tente Terræ, machinæ, <lb/>ip&longs;i globo, &longs;olus explo&longs;ionis motus &longs;uper&longs;it, <lb/><gap/>utus occa&longs;ione glabus perinde recedat à <lb/>macbina, &longs;eu quie&longs;cat, &longs;eu moueatur Terra.<emph.end type="italics"/><lb/>p.99. <lb/></s></p><p type="main"> | <s id="id.000118">V. <emph type="italics"/>Declaratur non concludere, quod obli­<lb/>citur de globerum explo&longs;ione in ortum, in <lb/>oc<gap/>a&longs;um, in a<gap/>&longs;trum, in boream, & &longs;ur­<lb/>&longs;<gap/>, ex dictis à &longs;i<gap/>li de proiectis è naui: <lb/>ci<gap/>n motus Terræ glob<gap/> impre&longs;&longs;us impri­<lb/><gap/> etiam machinæ, ac proinde mot<gap/> eo­<lb/>dem communi <gap/>tente Terræ, machinæ, <lb/>ip&longs;i globo, &longs;olus explo&longs;ionis motus &longs;uper&longs;it, <lb/><gap/>utus occa&longs;ione glabus perinde recedat à <lb/>macbina, &longs;eu quie&longs;cat, &longs;eu moueatur Terra.<emph.end type="italics"/><lb/>p.99. <lb/></s></p><p type="main"> |
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| <s>VI. <emph type="italics"/>Neque quod obiicitur de apparente So­<lb/>lis motu, & Terræ quicte, ob vi&longs;us &longs;allt­<lb/>ciam. </s> | <s id="id.000119">VI. <emph type="italics"/>Neque quod obiicitur de apparente So­<lb/>lis motu, & Terræ quicte, ob vi&longs;us &longs;allt­<lb/>ciam. </s> |
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| <s>Vt cnim maris inexpertus, &longs;i non co­<lb/>gitan<gap/> con&longs;tituatur in naut tran&longs;<gap/>, iura­<lb/>bit ip&longs;am quie&longs;cere, aliam ancboris &longs;irma­<lb/>tam m<gap/>eri; ita<gap/>os non cogitantes nati is <lb/>Terra, po&longs;&longs;umus, &longs;i ea circa Solem in mun­<lb/>dano spario q<gap/> &longs;centem transferatur, exi&longs;ti­<lb/>mare ip&longs;am immotam, Solem circa ip&longs;am <lb/>moueri. </s> | <s id="id.000120">Vt cnim maris inexpertus, &longs;i non co­<lb/>gitan<gap/> con&longs;tituatur in naut tran&longs;<gap/>, iura­<lb/>bit ip&longs;am quie&longs;cere, aliam ancboris &longs;irma­<lb/>tam m<gap/>eri; ita<gap/>os non cogitantes nati is <lb/>Terra, po&longs;&longs;umus, &longs;i ea circa Solem in mun­<lb/>dano spario q<gap/> &longs;centem transferatur, exi&longs;ti­<lb/>mare ip&longs;am immotam, Solem circa ip&longs;am <lb/>moueri. </s> |
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| <s>Neque licebit illum horta<gap/>, vt <lb/>&longs;eu&longs;um ratione cerrigat, qu<gap/> nos pariiure <lb/>moneamur.<emph.end type="italics"/> p.104. </s></p><p type="main"> | <s id="id.000121">Neque licebit illum horta<gap/>, vt <lb/>&longs;eu&longs;um ratione cerrigat, qu<gap/> nos pariiure <lb/>moneamur.<emph.end type="italics"/> p.104. </s></p><p type="main"> |
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| <s>VII. <emph type="italics"/>Idem dicendum, quod attinet ad tæ­<lb/>tera &longs;idera exoriri vi&longs;a, & occidere ex con­<lb/>uer&longs;ione Terræ in ortum. </s> | <s id="id.000122">VII. <emph type="italics"/>Idem dicendum, quod attinet ad tæ­<lb/>tera &longs;idera exoriri vi&longs;a, & occidere ex con­<lb/>uer&longs;ione Terræ in ortum. </s> |
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| <s>Sic apparet attoli <lb/>Polus ex &longs;olono&longs;tri ver&longs;us ip&longs;u<gap/> progre&longs;&longs;u. <lb/></s> | <s id="id.000123">Sic apparet attoli <lb/>Polus ex &longs;olono&longs;tri ver&longs;us ip&longs;u<gap/> progre&longs;&longs;u. <lb/></s> |
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| <s>Argument a aliquot à &longs;imili. </s> | <s id="id.000124">Argument a aliquot à &longs;imili. </s> |
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| <s>Violentia ex <lb/>raptu primi mobilis &longs;ublat a ex &longs;implic<gap/> Ter­<lb/>ræ conuer &longs;ione in ortum. </s> | <s id="id.000125">Violentia ex <lb/>raptu primi mobilis &longs;ublat a ex &longs;implic<gap/> Ter­<lb/>ræ conuer &longs;ione in ortum. </s> |
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| <s>Soliditas orbium <lb/>caelig;le&longs;tium cum ab&longs;eruatis, & ratione pu­<lb/>gnans. </s> | <s id="id.000126">Soliditas orbium <lb/>caelig;le&longs;tium cum ab&longs;eruatis, & ratione pu­<lb/>gnans. </s> |
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| <s>Argumentum ex apparente Cometa­<lb/>rum & omnium &longs;ublimium in <gap/>a&longs;um mo­<lb/>tu. </s> | <s id="id.000127">Argumentum ex apparente Cometa­<lb/>rum & omnium &longs;ublimium in <gap/>a&longs;um mo­<lb/>tu. </s> |
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| <s>Ex rapidita<gap/>e, quinquagies millies in <lb/>cælo, quàm in Terra vt matore, &longs;ic ab&longs;ur­<lb/>diore. </s> | <s id="id.000128">Ex rapidita<gap/>e, quinquagies millies in <lb/>cælo, quàm in Terra vt matore, &longs;ic ab&longs;ur­<lb/>diore. </s> |
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| <s>D<gap/>tractio partium Te<gap/>æ non ti­<lb/>menda. </s> | <s id="id.000129">D<gap/>tractio partium Te<gap/>æ non ti­<lb/>menda. </s> |
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| <s>Argumentkm ex figura Terræ &longs;ua­<lb/>pte natura volubili.<emph.end type="italics"/> p.107. </s></p><p type="main"> | <s id="id.000130">Argumentkm ex figura Terræ &longs;ua­<lb/>pte natura volubili.<emph.end type="italics"/> p.107. </s></p><p type="main"> |
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| <s>VIII. <emph type="italics"/>Granitas e&longs;t partium Terræ propria, <lb/>vt vniantur; nontotius, vt ten<gap/>at in cen­<lb/>trum. </s> | <s id="id.000131">VIII. <emph type="italics"/>Granitas e&longs;t partium Terræ propria, <lb/>vt vniantur; nontotius, vt ten<gap/>at in cen­<lb/>trum. </s> |
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| <s>In <gap/>undo nibil e&longs;t ex &longs;e &longs;upremum, <lb/>aut infinum, &longs;<gap/> &longs;olùm extrem<gap/>m, <gap/> me­<lb/>dium. </s> | <s id="id.000132">In <gap/>undo nibil e&longs;t ex &longs;e &longs;upremum, <lb/>aut infinum, &longs;<gap/> &longs;olùm extrem<gap/>m, <gap/> me­<lb/>dium. </s> |
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| <s>Non t<gap/>unt grauia in centr<gap/> &longs;eu <lb/>Terræ, &longs;eu <gap/>di, ni&longs;i ex accidenti. </s> | <s id="id.000133">Non t<gap/>unt grauia in centr<gap/> &longs;eu <lb/>Terræ, &longs;eu <gap/>di, ni&longs;i ex accidenti. </s> |
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| <s>Graui­<lb/>tas e&longs;t vis non tam grauibus in&longs;ita, quàm <lb/>magneticè à Telluris mole impre&longs;&longs;a. </s> | <s id="id.000134">Graui­<lb/>tas e&longs;t vis non tam grauibus in&longs;ita, quàm <lb/>magneticè à Telluris mole impre&longs;&longs;a. </s> |
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| <s>Leuitas <lb/>nibil æliud, quàm grauit as minor. </s> | <s id="id.000135">Leuitas <lb/>nibil æliud, quàm grauit as minor. </s> |
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| <s>Compre­<lb/>batur variis exëplis, at in igne pctißimàin, <lb/>qui &longs;ur&longs;um, non vt &longs;pbæram pc<gap/>ens, &longs;ed vt <lb/>ab aere abactus contendit. </s> | <s id="id.000136">Compre­<lb/>batur variis exëplis, at in igne pctißimàin, <lb/>qui &longs;ur&longs;um, non vt &longs;pbæram pc<gap/>ens, &longs;ed vt <lb/>ab aere abactus contendit. </s> |
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| <s>Motus recti &longs;ur­<lb/>&longs;ù<gap/>, & deorsùm, t<gap/>nquam partium proprij, <lb/>m<gap/>tui circulari, tanquam proprio totius non <lb/>obstant. </s> | <s id="id.000137">Motus recti &longs;ur­<lb/>&longs;ù<gap/>, & deorsùm, t<gap/>nquam partium proprij, <lb/>m<gap/>tui circulari, tanquam proprio totius non <lb/>obstant. </s> |
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| <s>Idemiuris pote<gap/> & Luna, & aliis <lb/>glob<gap/>s competere. </s> | <s id="id.000138">Idemiuris pote<gap/> & Luna, & aliis <lb/>glob<gap/>s competere. </s> |
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| <s>Terra non minùs mobilis <lb/>per aib<gap/>rem, quàm Luna. <!-- KEEP S--></s> | <s id="id.000139">Terra non minùs mobilis <lb/>per aib<gap/>rem, quàm Luna. <!-- KEEP S--></s> |
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| <s>Cù<gap/> nibil p<gap/>­<lb/>dat, band inepta Archimedca &longs;pon&longs;io fuit.<emph.end type="italics"/><lb/>p.112. </s></p><p type="main"> | <s id="id.000140">Cù<gap/> nibil p<gap/>­<lb/>dat, band inepta Archimedca &longs;pon&longs;io fuit.<emph.end type="italics"/><lb/>p.112. </s></p><p type="main"> |
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| <s>IX. <emph type="italics"/>Orde pertium mundi Pythagericus,<emph.end type="italics"/><pb/><lb/><emph type="italics"/>&longs;eu Copernicanus. </s> | <s id="id.000141">IX. <emph type="italics"/>Orde pertium mundi Pythagericus,<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.006.jpg"/><lb/><emph type="italics"/>&longs;eu Copernicanus. </s> |
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| <s>Sol in centro, Fixæ in <lb/>circum&longs;erentia immotæ. </s> | <s id="id.000142">Sol in centro, Fixæ in <lb/>circum&longs;erentia immotæ. </s> |
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| <s>Medio in spatio <lb/>Planetæ mobiles, ac in ip&longs;is Terra iuter Ve­<lb/>nerem, & Martem. </s> | <s id="id.000143">Medio in spatio <lb/>Planetæ mobiles, ac in ip&longs;is Terra iuter Ve­<lb/>nerem, & Martem. </s> |
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| <s>Di&longs;t ant<gap/>a Fixarum tan­<lb/>ta, vt magnus orbis, cuius <gap/>emidiameter &longs;it <lb/>à sole ad Terram, pro puncto habeatur, com­<lb/>paratus ad ip&longs;am. </s> | <s id="id.000144">Di&longs;t ant<gap/>a Fixarum tan­<lb/>ta, vt magnus orbis, cuius <gap/>emidiameter &longs;it <lb/>à sole ad Terram, pro puncto habeatur, com­<lb/>paratus ad ip&longs;am. </s> |
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| <s>Duplex Terræ motus, <lb/>Diurnus <gap/>ca proprium axem, Annuns <lb/>&longs;ubZodiaci &longs;ignis, in quorum vno dum e&longs;t, <lb/>apparet Solin oppo&longs;ito e&longs;&longs;e. </s> | <s id="id.000145">Duplex Terræ motus, <lb/>Diurnus <gap/>ca proprium axem, Annuns <lb/>&longs;ubZodiaci &longs;ignis, in quorum vno dum e&longs;t, <lb/>apparet Solin oppo&longs;ito e&longs;&longs;e. </s> |
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| <s>Continetur &longs;<gap/>­<lb/>per axis Terræ in &longs;ui parallili&longs;<gap/> & duci <lb/>in F<gap/>mamentum conc<gap/>us, de&longs;cribit qui­<lb/>dem circulum tantum circa polum mundi, <lb/>quantus circulus magni orbis e&longs;t, &longs;ed qui <lb/>beinc tamen appareat vt punctum. </s> | <s id="id.000146">Continetur &longs;<gap/>­<lb/>per axis Terræ in &longs;ui parallili&longs;<gap/> & duci <lb/>in F<gap/>mamentum conc<gap/>us, de&longs;cribit qui­<lb/>dem circulum tantum circa polum mundi, <lb/>quantus circulus magni orbis e&longs;t, &longs;ed qui <lb/>beinc tamen appareat vt punctum. </s> |
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| <s>Conti­<lb/><gap/>tia hac non omninô a&longs;&longs;equnta m<gap/>tum <lb/>centri, retrabit &longs;en&longs;im æquinoctialia <gap/>nnct<gap/><lb/>in fignorum anteced<gap/>tia.<emph.end type="italics"/> p.122. </s></p><p type="main"> | <s id="id.000147">Conti­<lb/><gap/>tia hac non omninô a&longs;&longs;equnta m<gap/>tum <lb/>centri, retrabit &longs;en&longs;im æquinoctialia <gap/>nnct<gap/><lb/>in fignorum anteced<gap/>tia.<emph.end type="italics"/> p.122. </s></p><p type="main"> |
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| <s>X. <emph type="italics"/>Tran&longs;la<gap/> per Eclipticam Te<gap/>, Sol <lb/>perinde videbitur Eclipticam percurrere, <lb/>& Eclip&longs;es hand&longs;<gap/>ùscontingent, quàm &longs;i <lb/>in centro qu<gap/>&longs;ceret. </s> | <s id="id.000148">X. <emph type="italics"/>Tran&longs;la<gap/> per Eclipticam Te<gap/>, Sol <lb/>perinde videbitur Eclipticam percurrere, <lb/>& Eclip&longs;es hand&longs;<gap/>ùscontingent, quàm &longs;i <lb/>in centro qu<gap/>&longs;ceret. </s> |
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| <s>Si Terra habetur Pla­<lb/>netarum vnus, omnes tam motu, quàm ma­<lb/>gnitudinc congruunt; &longs;i non habetur, di&longs;&longs;o­<lb/>nant. </s> | <s id="id.000149">Si Terra habetur Pla­<lb/>netarum vnus, omnes tam motu, quàm ma­<lb/>gnitudinc congruunt; &longs;i non habetur, di&longs;&longs;o­<lb/>nant. </s> |
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| <s>L<gap/>a videtur altera Terra. <!-- KEEP S--></s> | <s id="id.000150">L<gap/>a videtur altera Terra. <!-- KEEP S--></s> |
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| <s>L<gap/><lb/>Terra <expan abbr="exiracentrũ">exiracentrum</expan> Firm amenti&longs;it, videtur <lb/>tamen bemi&longs;phærium, quod duæ parallelæ, <lb/>vna per centrum, alia per terræ &longs;uperficiem <lb/><gap/>aductæ, ad &longs;en&longs;um tandem <expan abbr="co&etilde;ant">coenant</expan>. </s> | <s id="id.000151">L<gap/><lb/>Terra <expan abbr="exiracentrũ">exiracentrum</expan> Firm amenti&longs;it, videtur <lb/>tamen bemi&longs;phærium, quod duæ parallelæ, <lb/>vna per centrum, alia per terræ &longs;uperficiem <lb/><gap/>aductæ, ad &longs;en&longs;um tandem <expan abbr="co&etilde;ant">coenant</expan>. </s> |
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| <s>Axis <lb/>Terræ continentia, & Fixarum di&longs;tantia <lb/><gap/>, vt vbicumque in Zodiaco Terræ &longs;it, <lb/><gap/>dem &longs;<gap/>ellæ verticales, eadem altitudo po­<lb/><gap/> appareat. </s> | <s id="id.000152">Axis <lb/>Terræ continentia, & Fixarum di&longs;tantia <lb/><gap/>, vt vbicumque in Zodiaco Terræ &longs;it, <lb/><gap/>dem &longs;<gap/>ellæ verticales, eadem altitudo po­<lb/><gap/> appareat. </s> |
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| <s>Eadem axis, at &longs;imùl æqua­<lb/><gap/>is continentia & dierum, noctiumque <lb/><gap/>qualitatem, & æ&longs;t atis, ac biemis vicißi­<lb/>tudinem parit. </s> | <s id="id.000153">Eadem axis, at &longs;imùl æqua­<lb/><gap/>is continentia & dierum, noctiumque <lb/><gap/>qualitatem, & æ&longs;t atis, ac biemis vicißi­<lb/>tudinem parit. </s> |
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| <s>Stellæ Fixæ apparent pro­<lb/><gap/>, taxta &longs;ignorum &longs;eriem, quòd &longs;ectio­<lb/><gap/> aquinectiales regrediantur adner&longs;us <lb/><gap/>Sol Apoge<gap/>s, ac Perigeius appares, <lb/><gap/> T<gap/>ra <gap/> & Peribelia &longs;iat.<emph.end type="italics"/><lb/><lb/><emph type="italics"/>Motus Planetarum circæ S<gap/>lem <gap/>llipticus, <lb/>non circularis.<emph.end type="italics"/> p.132. </s></p><p type="main"> | <s id="id.000154">Stellæ Fixæ apparent pro­<lb/><gap/>, taxta &longs;ignorum &longs;eriem, quòd &longs;ectio­<lb/><gap/> aquinectiales regrediantur adner&longs;us <lb/><gap/>Sol Apoge<gap/>s, ac Perigeius appares, <lb/><gap/> T<gap/>ra <gap/> & Peribelia &longs;iat.<emph.end type="italics"/><lb/><lb/><emph type="italics"/>Motus Planetarum circæ S<gap/>lem <gap/>llipticus, <lb/>non circularis.<emph.end type="italics"/> p.132. </s></p><p type="main"> |
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| <s>XI. <emph type="italics"/>Tran&longs;<gap/> per Z<gap/>diatum <expan abbr="Terrã">Terram</expan>, n<gap/><lb/>e&longs;t Planetarum, quinon vno tenore, ac <gap/>am <lb/>&longs;emper viam procedat. </s> | <s id="id.000155">XI. <emph type="italics"/>Tran&longs;<gap/> per Z<gap/>diatum <expan abbr="Terrã">Terram</expan>, n<gap/><lb/>e&longs;t Planetarum, quinon vno tenore, ac <gap/>am <lb/>&longs;emper viam procedat. </s> |
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| <s>Regreßiones <gap/>æ, <lb/>Station<gap/>&longs;que, quæ in vulgari &longs;ententia<gap/>an­<lb/>tæ inconciunitatis &longs;unt, non-ni&longs;i apparenter <lb/>fiunt. </s> | <s id="id.000156">Regreßiones <gap/>æ, <lb/>Station<gap/>&longs;que, quæ in vulgari &longs;ententia<gap/>an­<lb/>tæ inconciunitatis &longs;unt, non-ni&longs;i apparenter <lb/>fiunt. </s> |
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| <s>Res decl<gap/>atur in Mercurio, & Ve­<lb/>nere; itemque in Marte, Ioue, ac Saturne. <lb/><!-- KEEP S--></s> | <s id="id.000157">Res decl<gap/>atur in Mercurio, & Ve­<lb/>nere; itemque in Marte, Ioue, ac Saturne. <lb/><!-- KEEP S--></s> |
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| <s>Sol in medio omnium congruè collecatus. <lb/></s> | <s id="id.000158">Sol in medio omnium congruè collecatus. <lb/></s> |
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| <s>Con&longs;titutus in centro Sol, & nibilominùs <lb/>&longs;ibi ip&longs;i motn circiter men&longs;tiuo circumdu­<lb/>ctus (quod mon &longs;trant eins Macula) vide­<lb/>tur Pl<gap/>etas omneis &longs;uis veluti magneticis <lb/>radiis circumagcre, propiures rapiàiùs, re­<lb/>motiores &longs;egu<gap/>s.<emph.end type="italics"/> p.142. </s></p><p type="main"> | <s id="id.000159">Con&longs;titutus in centro Sol, & nibilominùs <lb/>&longs;ibi ip&longs;i motn circiter men&longs;tiuo circumdu­<lb/>ctus (quod mon &longs;trant eins Macula) vide­<lb/>tur Pl<gap/>etas omneis &longs;uis veluti magneticis <lb/>radiis circumagcre, propiures rapiàiùs, re­<lb/>motiores &longs;egu<gap/>s.<emph.end type="italics"/> p.142. </s></p><p type="main"> |
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| <s>XII. <emph type="italics"/>Ex motu Terræ attributo æ&longs;tus ma<gap/>is <lb/>deducitur, & exemplo nauiculæ aqua &longs;emi­<lb/>plenæ declaratur. </s> | <s id="id.000160">XII. <emph type="italics"/>Ex motu Terræ attributo æ&longs;tus ma<gap/>is <lb/>deducitur, & exemplo nauiculæ aqua &longs;emi­<lb/>plenæ declaratur. </s> |
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| <s>Ex motu diurno, & an­<lb/>n<gap/>o coninnct<gap/>s oritur bis in die in æqualit as, <lb/>ob quam mare quotidie bis fluat, at rifluat. <lb/></s> | <s id="id.000161">Ex motu diurno, & an­<lb/>n<gap/>o coninnct<gap/>s oritur bis in die in æqualit as, <lb/>ob quam mare quotidie bis fluat, at rifluat. <lb/></s> |
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| <s>Res mediterrance mars applicatur. </s> | <s id="id.000162">Res mediterrance mars applicatur. </s> |
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| <s>In eræ <lb/>Prouinciæ attollitur mare, ac deprimitur ad <lb/>&longs;e&longs;qui-pedem. </s> | <s id="id.000163">In eræ <lb/>Prouinciæ attollitur mare, ac deprimitur ad <lb/>&longs;e&longs;qui-pedem. </s> |
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| <s>Creata &longs;peciali inaqualitate <lb/>ctrca &longs;el&longs;titia, & æquinoctia, fit a&longs;tus v<gap/>be­<lb/>mentior, &longs;ed circa æquinoctia p<gap/>æ&longs;ersìm. <lb/></s> | <s id="id.000164">Creata &longs;peciali inaqualitate <lb/>ctrca &longs;el&longs;titia, & æquinoctia, fit a&longs;tus v<gap/>be­<lb/>mentior, &longs;ed circa æquinoctia p<gap/>æ&longs;ersìm. <lb/></s> |
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| <s>Creatâ aliâ ob con&longs;titutam in coniunctione, <lb/>ant oppo&longs;itione Lunam, fit quoque æ&longs;tus in <lb/>no<gap/>iluniiis, ac in pleniluniis maior. </s> | <s id="id.000165">Creatâ aliâ ob con&longs;titutam in coniunctione, <lb/>ant oppo&longs;itione Lunam, fit quoque æ&longs;tus in <lb/>no<gap/>iluniiis, ac in pleniluniis maior. </s> |
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| <s>Ex m<gap/><lb/>Terra æ&longs;lus maris, ex a&longs;tu maris motus <lb/>Terræ e&longs;&longs;icitur probabilis. </s> | <s id="id.000166">Ex m<gap/><lb/>Terra æ&longs;lus maris, ex a&longs;tu maris motus <lb/>Terræ e&longs;&longs;icitur probabilis. </s> |
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| <s>Declaratur res <lb/>iterum naniculæ comparatione.<emph.end type="italics"/> p.149. </s></p><p type="main"> | <s id="id.000167">Declaratur res <lb/>iterum naniculæ comparatione.<emph.end type="italics"/> p.149. </s></p><p type="main"> |
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| <s>XIII. <emph type="italics"/>Statur decreto Cardinalium de <lb/>Terra quic&longs;cente, non mota. </s> | <s id="id.000168">XIII. <emph type="italics"/>Statur decreto Cardinalium de <lb/>Terra quic&longs;cente, non mota. </s> |
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| <s>Epi&longs;t<gap/>a con­<lb/>cluditur.<emph.end type="italics"/> p.155. </s></p><p type="main"> | <s id="id.000169">Epi&longs;t<gap/>a con­<lb/>cluditur.<emph.end type="italics"/> p.155. </s></p><p type="main"> |
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| <s>Po&longs;t &longs;criptum. <emph type="italics"/>Explicatur Problema; <lb/>Quam obcan&longs;am fiat, vt res flexilis, viluti <lb/>virga, a<gap/> lamina, vbi man<gap/> diflexa<gap/>&longs;t, di­<lb/>mittente mann mo<gap/>atur, &longs;uumque &longs;itum <lb/>repetat?<emph.end type="italics"/> p.15<gap/>. </s></p><pb/><p type="main"> | <s id="id.000170">Po&longs;t &longs;criptum. <emph type="italics"/>Explicatur Problema; <lb/>Quam obcan&longs;am fiat, vt res flexilis, viluti <lb/>virga, a<gap/> lamina, vbi man<gap/> diflexa<gap/>&longs;t, di­<lb/>mittente mann mo<gap/>atur, &longs;uumque &longs;itum <lb/>repetat?<emph.end type="italics"/> p.15<gap/>. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.007.jpg"/><p type="main"> |
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| <s><emph type="center"/><emph type="italics"/>SVMMA PRIVILEGII.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s id="id.000171"><emph type="center"/><emph type="italics"/>SVMMA PRIVILEGII.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>JVxta Priuilegium à Rege Chri&longs;tiani&longs;&longs;imo conce&longs;&longs;um, cautum e&longs;t, ne quis toto regne <lb/>imprimat, alibive impre&longs;&longs;as di<gap/>endat PSTRI GASS<gap/>NDI <emph type="italics"/>De Metu impre&longs;&longs;e <gap/><lb/>Motore tran&longs;lato, Epi&longs;tolas duas<emph.end type="italics"/>, præter LVD. DI HIVQV<gap/>VILLE, Bibliopolam Pa­<lb/>ri&longs;ien&longs;em, idque in dece<gap/>nium, &longs;ub &longs;olitis p<gap/>nis, Datum Pari&longs;<gap/>s 8. April. </s> | <s id="id.000172">JVxta Priuilegium à Rege Chri&longs;tiani&longs;&longs;imo conce&longs;&longs;um, cautum e&longs;t, ne quis toto regne <lb/>imprimat, alibive impre&longs;&longs;as di<gap/>endat PSTRI GASS<gap/>NDI <emph type="italics"/>De Metu impre&longs;&longs;e <gap/><lb/>Motore tran&longs;lato, Epi&longs;tolas duas<emph.end type="italics"/>, præter LVD. DI HIVQV<gap/>VILLE, Bibliopolam Pa­<lb/>ri&longs;ien&longs;em, idque in dece<gap/>nium, &longs;ub &longs;olitis p<gap/>nis, Datum Pari&longs;<gap/>s 8. April. </s> |
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| <s>1642. Signa­<lb/>tum C<gap/>RET </s></p><pb pagenum="1"/><figure/><p type="main"> | <s id="id.000173">1642. Signa­<lb/>tum C<gap/>RET </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.008.jpg" pagenum="1"/><figure id="id.027.00.008.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.008.1.jpg"/><p type="main"> |
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| <s><emph type="center"/>DE MOTV IMPRESSO <lb/>A MOTORE TRANSLATO. <lb/><emph type="italics"/>EPISTOLA PRIMA.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s id="id.000174"><emph type="center"/>DE MOTV IMPRESSO <lb/>A MOTORE TRANSLATO. <lb/><emph type="italics"/>EPISTOLA PRIMA.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s><emph type="center"/>VIRO ERVDITO ET AMICO SINCERO <lb/>PETRO PVTEANO CLAVD I. F. <lb/>PETRVS GASSENDVS S.<emph.end type="center"/></s></p><p type="main"> | <s id="id.000175"><emph type="center"/>VIRO ERVDITO ET AMICO SINCERO <lb/>PETRO PVTEANO CLAVD I. F. <lb/>PETRVS GASSENDVS S.<emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>INSINVAVIT Luillerius no&longs;ter <lb/>po&longs;tremis &longs;uis literis, adhibui&longs;&longs;e te ægrè <lb/>fidemijs, quæ ad ip&longs;um per&longs;crip&longs;eram, <lb/>de factis à me circa motum Proje­<lb/>ctilium experimentis. </s> | <s id="id.000176">INSINVAVIT Luillerius no&longs;ter <lb/>po&longs;tremis &longs;uis literis, adhibui&longs;&longs;e te ægrè <lb/>fidemijs, quæ ad ip&longs;um per&longs;crip&longs;eram, <lb/>de factis à me circa motum Proje­<lb/>ctilium experimentis. </s> |
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| <s>Id verò miratus non &longs;um, qui <lb/>per&longs;pectum habeo nihil po&longs;&longs;e magis paradoxum &longs;a­<lb/>pere; & noui alios præclaros viros, quibus res e&longs;t <lb/>vi&longs;a non minùs improbabilis, quoadv&longs;que fuere ip­<lb/>&longs;imet experti. </s> | <s id="id.000177">Id verò miratus non &longs;um, qui <lb/>per&longs;pectum habeo nihil po&longs;&longs;e magis paradoxum &longs;a­<lb/>pere; & noui alios præclaros viros, quibus res e&longs;t <lb/>vi&longs;a non minùs improbabilis, quoadv&longs;que fuere ip­<lb/>&longs;imet experti. </s> |
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| <s>Occa&longs;ionem certè explorandi denuò <lb/>rei veritatem fecit mihi nuper Prorex optimius; cùm <lb/>profectus Ma&longs;&longs;iliam, me in comitatum adhibitum <lb/>voluit. </s> | <s id="id.000178">Occa&longs;ionem certè explorandi denuò <lb/>rei veritatem fecit mihi nuper Prorex optimius; cùm <lb/>profectus Ma&longs;&longs;iliam, me in comitatum adhibitum <lb/>voluit. </s> |
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| <s>Quippe, vt e&longs;t pereruditus, & quicquid tem-<pb pagenum="2"/>poris à curis ciuilibus re&longs;iduum e&longs;t, liberalibus &longs;tu­<lb/>djis impertitur, non paucos in itinere &longs;ermones de <lb/>Motu con&longs;eruït. </s> | <s id="id.000179">Quippe, vt e&longs;t pereruditus, & quicquid tem-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.009.jpg" pagenum="2"/>poris à curis ciuilibus re&longs;iduum e&longs;t, liberalibus &longs;tu­<lb/>djis impertitur, non paucos in itinere &longs;ermones de <lb/>Motu con&longs;eruït. </s> |
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| <s>Ip&longs;e recen&longs;ui obiter tum ob&longs;erua­<lb/>ta propria, tum quæ Galileus conge&longs;&longs;it ad&longs;truen­<lb/>do illi Theoremati, <emph type="italics"/>Si id corpus, cui in&longs;i&longs;timus, trans­<lb/>ferdtur, motus omneis no&longs;tros, rerúmqne à nobis mo­<lb/>bilium perinde fieri, appareréque, ac &longs;i illud quie&longs;ceret.<emph.end type="italics"/><lb/>Cùm rem verò e&longs;&longs;e præter omnem fidem, non tam <lb/>doctus Princeps, quàm alij quidam ex comitatu <lb/>opinarentur; &longs;tupuerunt &longs;anè, cùm iu&longs;&longs;i tam cur­<lb/>ru, quàm equo periculum facere, deprehenderunt, <lb/>&longs;eu quie&longs;cerent, &longs;eu concitati&longs;&longs;imè transferrentur, <lb/>res &longs;ursùm projectas, perinde in manum redire; ma­<lb/>nu dimi&longs;&longs;as, &longs;ecundum eandem &longs;ui, equi, aut cur­<lb/>rus lineam cadere; emi&longs;&longs;as antrorsùm, nec propiùs, <lb/>nec longiùs terram petere; depul&longs;as retrorsùm, <lb/>nihilo &longs;eciùs à tergo di&longs;cedere; directas ad dex­<lb/>tram, læuam ve, intra lateralem lineam ex æquo <lb/>teneri. </s> | <s id="id.000180">Ip&longs;e recen&longs;ui obiter tum ob&longs;erua­<lb/>ta propria, tum quæ Galileus conge&longs;&longs;it ad&longs;truen­<lb/>do illi Theoremati, <emph type="italics"/>Si id corpus, cui in&longs;i&longs;timus, trans­<lb/>ferdtur, motus omneis no&longs;tros, rerúmqne à nobis mo­<lb/>bilium perinde fieri, appareréque, ac &longs;i illud quie&longs;ceret.<emph.end type="italics"/><lb/>Cùm rem verò e&longs;&longs;e præter omnem fidem, non tam <lb/>doctus Princeps, quàm alij quidam ex comitatu <lb/>opinarentur; &longs;tupuerunt &longs;anè, cùm iu&longs;&longs;i tam cur­<lb/>ru, quàm equo periculum facere, deprehenderunt, <lb/>&longs;eu quie&longs;cerent, &longs;eu concitati&longs;&longs;imè transferrentur, <lb/>res &longs;ursùm projectas, perinde in manum redire; ma­<lb/>nu dimi&longs;&longs;as, &longs;ecundum eandem &longs;ui, equi, aut cur­<lb/>rus lineam cadere; emi&longs;&longs;as antrorsùm, nec propiùs, <lb/>nec longiùs terram petere; depul&longs;as retrorsùm, <lb/>nihilo &longs;eciùs à tergo di&longs;cedere; directas ad dex­<lb/>tram, læuam ve, intra lateralem lineam ex æquo <lb/>teneri. </s> |
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| <s>Po&longs;teà, vt planè conuincerentur, deducen­<lb/>di fuere ad mare, ob&longs;eruaturi, Vtrum naui veloci&longs;­<lb/>&longs;imè tran&longs;lata, perinde atque quie&longs;cente, lapis &longs;ur­<lb/>sùm projectus, v. </s> | <s id="id.000181">Po&longs;teà, vt planè conuincerentur, deducen­<lb/>di fuere ad mare, ob&longs;eruaturi, Vtrum naui veloci&longs;­<lb/>&longs;imè tran&longs;lata, perinde atque quie&longs;cente, lapis &longs;ur­<lb/>sùm projectus, v. <!-- REMOVE S-->c. <!-- REMOVE S-->ex pede mali, &longs;ecundum mali <lb/>longitudinem, tueretur &longs;emper tam a&longs;cendendo, <lb/>quàm de&longs;cendendo eandem à malo di&longs;tantiam, & <lb/>ad pedem mali, &longs;eu in eundem locum præci&longs;è, re­<lb/>cideret Vtrum manu ad &longs;ummum malum quie&longs;cen­<lb/>te, & ab&longs;que vlla vi dimi&longs;&longs;us lapis, in eundem pe­<lb/>dem incideret. </s> |
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| <s>c. </s> | |
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| <s>ex pede mali, &longs;ecundum mali <lb/>longitudinem, tueretur &longs;emper tam a&longs;cendendo, <lb/>quàm de&longs;cendendo eandem à malo di&longs;tantiam, & <lb/>ad pedem mali, &longs;eu in eundem locum præci&longs;è, re­<lb/>cideret Vtrum manu ad &longs;ummum malum quie&longs;cen­<lb/>te, & ab&longs;que vlla vi dimi&longs;&longs;us lapis, in eundem pe­<lb/>dem incideret. </s> | |
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| <s>Vtrum pari vi ex puppi in proram, <lb/>& ex prora in puppin tran&longs;mi&longs;&longs;us, pari impetu fer­<lb/>ri appareret, parque &longs;patium conficere. </s> | |
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| <s>Vtrum actus <pb pagenum="3"/>tran&longs;uersùm, obliquè, & quacúmque demùm ra­<lb/>tione, haud di&longs;par motus exhiberetur. </s> | |
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| <s>Cæterùm res <lb/>ita &longs;ucce&longs;&longs;it, vt nihil ampliùs hæ&longs;erint; cùm acta Tri­<lb/>remi ea celeritate, vt intra horæ quadrantem, mari <lb/>aperto, tranquillóque, milliaria quatuor peruade­<lb/>ret, i&longs;ta, aliáque ob&longs;eruitârunt. </s> | <s id="id.000182">Vtrum pari vi ex puppi in proram, <lb/>& ex prora in puppin tran&longs;mi&longs;&longs;us, pari impetu fer­<lb/>ri appareret, parque &longs;patium conficere. </s> |
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| <s>Miraculo autem <lb/>poti&longs;&longs;imùm fuit, lapidem è vertice mali ab&longs;que vi, <lb/>aut jactu dimi&longs;&longs;um, tam ex parte puppis à malo non <lb/>de&longs;eri, quàm ex parte proræ ab eo non attingi: &longs;ed <lb/>in eadem &longs;emper di&longs;tantia, &longs;eu &longs;ecundum lineam ip­<lb/>&longs;i parallelam continuò delabi. </s></p><p type="main"> | <s id="id.000183">Vtrum actus <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.010.jpg" pagenum="3"/>tran&longs;uersùm, obliquè, & quacúmque demùm ra­<lb/>tione, haud di&longs;par motus exhiberetur. </s> |
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| <s>II. <!-- KEEP S--></s> | <s id="id.000184">Cæterùm res <lb/>ita &longs;ucce&longs;&longs;it, vt nihil ampliùs hæ&longs;erint; cùm acta Tri­<lb/>remi ea celeritate, vt intra horæ quadrantem, mari <lb/>aperto, tranquillóque, milliaria quatuor peruade­<lb/>ret, i&longs;ta, aliáque ob&longs;eruitârunt. </s> |
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| <s>Ac non hæreo quidem, optime virorum, <lb/>quin tu quoque dedi&longs;&longs;es manus, &longs;i quadam &longs;orte <lb/>contigi&longs;&longs;et ade&longs;&longs;e te &longs;pectaculo; verùm non propte­<lb/>reà mihi adrogo, vt (licet me virum fidei plenum <lb/>habeas) tenearis idcircò hi&longs;toriam narranti nudam <lb/>a&longs;&longs;entiri. </s> | <s id="id.000185">Miraculo autem <lb/>poti&longs;&longs;imùm fuit, lapidem è vertice mali ab&longs;que vi, <lb/>aut jactu dimi&longs;&longs;um, tam ex parte puppis à malo non <lb/>de&longs;eri, quàm ex parte proræ ab eo non attingi: &longs;ed <lb/>in eadem &longs;emper di&longs;tantia, &longs;eu &longs;ecundum lineam ip­<lb/>&longs;i parallelam continuò delabi. </s></p><p type="main"> |
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| <s>Addo potiùs cau&longs;am, quâ &longs;emel per&longs;pectâ, <lb/>te non di&longs;&longs;en&longs;urum confidam; ac prouoco &longs;imùl ad <lb/>experimenta adeò factu facilia, vt nihil nece&longs;&longs;e exi­<lb/>&longs;times mare proptereà ip&longs;um adire. </s> | <s id="id.000186">II. <!-- KEEP S--></s> |
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| <s>Et cau&longs;a quidem <lb/>generalis e&longs;t, quia, Quicquid mouetur, motum &longs;uum <lb/>imprimit rebus omnibus, quas &longs;u&longs;tentat: Re&longs;que <lb/>perinde emittuntur, &longs;iue emittens motum à &longs;e, &longs;iue <lb/>ab alio impre&longs;&longs;um habeat. </s> | <s id="id.000187">Ac non hæreo quidem, optime virorum, <lb/>quin tu quoque dedi&longs;&longs;es manus, &longs;i quadam &longs;orte <lb/>contigi&longs;&longs;et ade&longs;&longs;e te &longs;pectaculo; verùm non propte­<lb/>reà mihi adrogo, vt (licet me virum fidei plenum <lb/>habeas) tenearis idcircò hi&longs;toriam narranti nudam <lb/>a&longs;&longs;entiri. </s> |
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| <s>Experimentum verò fa­<lb/>cillimum e&longs;t, vt dum per prolixiorem illam nobili&longs;­<lb/>&longs;i<gap/> Bibliothecæ deambulabis pergulam, pilam lu­<lb/>&longs;oriam, aliumve globum manu teneas, remque ex­<lb/>plores. </s> | <s id="id.000188">Addo potiùs cau&longs;am, quâ &longs;emel per&longs;pectâ, <lb/>te non di&longs;&longs;en&longs;urum confidam; ac prouoco &longs;imùl ad <lb/>experimenta adeò factu facilia, vt nihil nece&longs;&longs;e exi­<lb/>&longs;times mare proptereà ip&longs;um adire. </s> |
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| <s>Imprimis quippe notius e&longs;t, quàm vt mo­<lb/>neri debeat, pilam tua manu &longs;u&longs;tentatam tantun­<lb/>dem moueri, quantum ip&longs;am manum; &longs;eu manum <pb pagenum="4"/>eundem pilæ motum imprimere, quem ip&longs;a habet. <lb/></s> | <s id="id.000189">Et cau&longs;a quidem <lb/>generalis e&longs;t, quia, Quicquid mouetur, motum &longs;uum <lb/>imprimit rebus omnibus, quas &longs;u&longs;tentat: Re&longs;que <lb/>perinde emittuntur, &longs;iue emittens motum à &longs;e, &longs;iue <lb/>ab alio impre&longs;&longs;um habeat. </s> |
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| <s>Quie&longs;ce deinde reliquo corpore, & agitata &longs;ola <lb/>manu, vel manu&longs;imùl cum bracchio, proijce antror­<lb/>sùm, retrorsùmve pilam; excedet illa, procurretque <lb/>quam in partem conjeceris. </s> | <s id="id.000190">Experimentum verò fa­<lb/>cillimum e&longs;t, vt dum per prolixiorem illam nobili&longs;­<lb/>&longs;i<gap/> Bibliothecæ deambulabis pergulam, pilam lu­<lb/>&longs;oriam, aliumve globum manu teneas, remque ex­<lb/>plores. </s> |
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| <s>Re&longs;ume, & pilam ma­<lb/>nu aperta tenens, nihil age ip&longs;e: &longs;ed e&longs;to alius, qui <lb/>manum, bracchiumve propellat; haud &longs;ecus excedet, <lb/>procurretque pila, ac priùs, dum ip&longs;am &longs;pontaneo <lb/>motu abijceres. </s> | <s id="id.000191">Imprimis quippe notius e&longs;t, quàm vt mo­<lb/>neri debeat, pilam tua manu &longs;u&longs;tentatam tantun­<lb/>dem moueri, quantum ip&longs;am manum; &longs;eu manum <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.011.jpg" pagenum="4"/>eundem pilæ motum imprimere, quem ip&longs;a habet. <lb/></s> |
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| <s>Tene rursùs pilam aperta manu, & <lb/>nihil perinde age nec manu, nec bracchio; &longs;ed loco <lb/>alterius, qui propellat, e&longs;to ip&longs;um-met corpus tuum, <lb/>quod emotum paulò concitatiùs bracchium, manu<gap/>­<lb/>que transferat, parivelocitate, qua alius antè propul­<lb/>&longs;arat; videbis rursùs pilam perinde excedere, pro­<lb/>curreréque. </s> | <s id="id.000192">Quie&longs;ce deinde reliquo corpore, & agitata &longs;ola <lb/>manu, vel manu&longs;imùl cum bracchio, proijce antror­<lb/>sùm, retrorsùmve pilam; excedet illa, procurretque <lb/>quam in partem conjeceris. </s> |
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| <s>Nimirùm corpus reliquum pro agente <lb/>externo e&longs;t, quod mouere manum, & bracchium, <lb/>corpore immoto, ob articulorum flexibilitatem po­<lb/>te&longs;t. </s> | <s id="id.000193">Re&longs;ume, & pilam ma­<lb/>nu aperta tenens, nihil age ip&longs;e: &longs;ed e&longs;to alius, qui <lb/>manum, bracchiumve propellat; haud &longs;ecus excedet, <lb/>procurretque pila, ac priùs, dum ip&longs;am &longs;pontaneo <lb/>motu abijceres. </s> |
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| <s>Iam, quia de his minùs dubitabis, hærebis ma­<lb/>gis quid &longs;it euenturum, vbi extento bracchio, pilam <lb/>&longs;u&longs;tentatam duobus digitis ab&longs;que vlla vi, agitatio­<lb/>néque manus propria, deambulando dimi&longs;eris. </s> | <s id="id.000194">Tene rursùs pilam aperta manu, & <lb/>nihil perinde age nec manu, nec bracchio; &longs;ed loco <lb/>alterius, qui propellat, e&longs;to ip&longs;um-met corpus tuum, <lb/>quod emotum paulò concitatiùs bracchium, manu<gap/>­<lb/>que transferat, parivelocitate, qua alius antè propul­<lb/>&longs;arat; videbis rursùs pilam perinde excedere, pro­<lb/>curreréque. </s> |
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| <s>Id <lb/>experire itaque; & peruidebis pilam &longs;equi, procur­<lb/>reréque in eandem partem, in quam ip&longs;e conce&longs;&longs;eris; <lb/>neque euenire vnquam, vt vel con&longs;tet, vel recurrat <lb/>in partem auer&longs;am. </s> | <s id="id.000195">Nimirùm corpus reliquum pro agente <lb/>externo e&longs;t, quod mouere manum, & bracchium, <lb/>corpore immoto, ob articulorum flexibilitatem po­<lb/>te&longs;t. </s> |
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| <s>An-non proinde agno&longs;ces ha­<lb/>bere pilam motum à manu, non quem ip&longs;i manus <lb/>motu poprio imprimat, &longs;ed quem imprimat motu <lb/>accepto à reliquo corpore; adeò vt cùm pila, quo <lb/>momento dimittitur, moueatur reip&longs;â, <expan abbr="impul&longs;io-nemq;">impul&longs;io­<lb/>nemque</expan> antrorsùm habeat, non po&longs;&longs;it motum non con-<pb pagenum="5"/>tinüare, & perinde perficere, ac &longs;i immoto corpore <lb/>&longs;tante, mota manus &longs;ola motum impre&longs;&longs;i&longs;&longs;et? </s> | <s id="id.000196">Iam, quia de his minùs dubitabis, hærebis ma­<lb/>gis quid &longs;it euenturum, vbi extento bracchio, pilam <lb/>&longs;u&longs;tentatam duobus digitis ab&longs;que vlla vi, agitatio­<lb/>néque manus propria, deambulando dimi&longs;eris. </s> |
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| <s>En <lb/>verò, quod magis mirere. </s> | <s id="id.000197">Id <lb/>experire itaque; & peruidebis pilam &longs;equi, procur­<lb/>reréque in eandem partem, in quam ip&longs;e conce&longs;&longs;eris; <lb/>neque euenire vnquam, vt vel con&longs;tet, vel recurrat <lb/>in partem auer&longs;am. </s> |
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| <s>Con&longs;i&longs;te primùm in per­<lb/>gulæ medio, & nunc antrorsùm, nunc retrorsum, <lb/>moderata vi pilam conijce: adeò vt ad certum v&longs;­<lb/>que &longs;patium, quod notari po&longs;&longs;it, vtrímque excurrat. <lb/></s> | <s id="id.000198">An-non proinde agno&longs;ces ha­<lb/>bere pilam motum à manu, non quem ip&longs;i manus <lb/>motu poprio imprimat, &longs;ed quem imprimat motu <lb/>accepto à reliquo corpore; adeò vt cùm pila, quo <lb/>momento dimittitur, moueatur reip&longs;â, <expan abbr="impul&longs;io-nemq;">impul&longs;io­<lb/>nemque</expan> antrorsùm habeat, non po&longs;&longs;it motum non con-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.012.jpg" pagenum="5"/>tinüare, & perinde perficere, ac &longs;i immoto corpore <lb/>&longs;tante, mota manus &longs;ola motum impre&longs;&longs;i&longs;&longs;et? </s> |
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| <s>Incede deinde, & ab vna parte ad idem medium <lb/>perueniens (nec moueri proptereà codem tenore de­<lb/>&longs;inens) pari vi pilam conijce. </s> | <s id="id.000199">En <lb/>verò, quod magis mirere. </s> |
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| <s>Videbis profectò pro­<lb/>jectam antrorsùm excurrere longiùs, quam excur­<lb/>rerit anteà; projectam verò retrorsùm, vel excur­<lb/>rere breuiùs, vel con&longs;i&longs;tere, vel etiam te &longs;equi. </s> | <s id="id.000200">Con&longs;i&longs;te primùm in per­<lb/>gulæ medio, & nunc antrorsùm, nunc retrorsum, <lb/>moderata vi pilam conijce: adeò vt ad certum v&longs;­<lb/>que &longs;patium, quod notari po&longs;&longs;it, vtrímque excurrat. <lb/></s> |
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| <s>Cau­<lb/>&longs;a nempe e&longs;t, Quia cùm antrorsùm conijcis, dupli­<lb/>cem illi imprimis vim; altera quippe e&longs;t manus pro­<lb/>pria, & qualis anteà erat, cùm &longs;tares corpore immo­<lb/>to; altera corporis ip&longs;ius, quâ eidem manui com­<lb/>municatâ, efficitur, vt manus feratur antrorsùm ce­<lb/>leriùs; quàm ip&longs;a &longs;ola, & reliquo corpore quie&longs;cente, <lb/>moueretur. </s> | <s id="id.000201">Incede deinde, & ab vna parte ad idem medium <lb/>perueniens (nec moueri proptereà codem tenore de­<lb/>&longs;inens) pari vi pilam conijce. </s> |
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| <s>Ex quo fit, vt pila accepto velociore <lb/>motu, moucatur velociùs, & procurrat vlteriùs. </s> | <s id="id.000202">Videbis profectò pro­<lb/>jectam antrorsùm excurrere longiùs, quam excur­<lb/>rerit anteà; projectam verò retrorsùm, vel excur­<lb/>rere breuiùs, vel con&longs;i&longs;tere, vel etiam te &longs;equi. </s> |
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| <s>Cùm <lb/>proijcis verò retrorsùm, vides à manu non alium <lb/>motum, quàm ip&longs;ius proprium ver&longs;us eam partem <lb/>imprimi; nam qui motus e&longs;t à reliquo corpore, in­<lb/>oppo&longs;itam tendit partem. </s> | <s id="id.000203">Cau­<lb/>&longs;a nempe e&longs;t, Quia cùm antrorsùm conijcis, dupli­<lb/>cem illi imprimis vim; altera quippe e&longs;t manus pro­<lb/>pria, & qualis anteà erat, cùm &longs;tares corpore immo­<lb/>to; altera corporis ip&longs;ius, quâ eidem manui com­<lb/>municatâ, efficitur, vt manus feratur antrorsùm ce­<lb/>leriùs; quàm ip&longs;a &longs;ola, & reliquo corpore quie&longs;cente, <lb/>moueretur. </s> |
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| <s>Con&longs;ideranda e&longs;t ergo <lb/>manus cùm duplici motu, vno &longs;ibi proprio retror­<lb/>sùm, altero ex corporis tran&longs;latione antrorsùm. </s> | <s id="id.000204">Ex quo fit, vt pila accepto velociore <lb/>motu, moucatur velociùs, & procurrat vlteriùs. </s> |
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| <s>Ex <lb/>hoc enim fit, primò, vt pila nunquam po&longs;&longs;it tantun­<lb/>dem retrorsùm excurrere, ac excurrerat anteà; quo­<lb/>niam licet manus motu proprio moueatur æqualiter; <lb/>non tantundem tamen promouetur retrorsùm, quòd <pb pagenum="6"/>motus tran&longs;latitius ip&longs;am intereà antrorsùm abripiat. <lb/></s> | <s id="id.000205">Cùm <lb/>proijcis verò retrorsùm, vides à manu non alium <lb/>motum, quàm ip&longs;ius proprium ver&longs;us eam partem <lb/>imprimi; nam qui motus e&longs;t à reliquo corpore, in­<lb/>oppo&longs;itam tendit partem. </s> |
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| <s>Deinde fit, vt &longs;i proprius quidem fuerit velocior <lb/>tran&longs;latitio, tum pila non-nihil retrorsùm excurrat, <lb/>qua&longs;i manu aliquantò magis retrorsùm, quàm an­<lb/>trorsùm promota. </s> | <s id="id.000206">Con&longs;ideranda e&longs;t ergo <lb/>manus cùm duplici motu, vno &longs;ibi proprio retror­<lb/>sùm, altero ex corporis tran&longs;latione antrorsùm. </s> |
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| <s>Sin æquè velox fuerit, tum pila <lb/>neque retrorsùm, neque antrorsùm excurrat, &longs;ed in <lb/>eodem loco con&longs;i&longs;tat, qua&longs;i in neutram partem pro­<lb/>jecta, & ad perpendiculum cadens; quòd vno motu <lb/>alium compen&longs;ante, & neutro alterum &longs;uperante, <lb/>manus eo momento veluti immota cohæreat. </s> | <s id="id.000207">Ex <lb/>hoc enim fit, primò, vt pila nunquam po&longs;&longs;it tantun­<lb/>dem retrorsùm excurrere, ac excurrerat anteà; quo­<lb/>niam licet manus motu proprio moueatur æqualiter; <lb/>non tantundem tamen promouetur retrorsùm, quòd <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.013.jpg" pagenum="6"/>motus tran&longs;latitius ip&longs;am intereà antrorsùm abripiat. <lb/></s> |
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| <s>Si <lb/>denique fuerit minùs velox; tum pila &longs;equatur, & <lb/>antror&longs;um, &longs;eu in eandem tecum partem decurrat, <lb/>qua&longs;i in illam magis acta motu tran&longs;latitio, quàm in <lb/>oppo&longs;itam proprio. </s> | <s id="id.000208">Deinde fit, vt &longs;i proprius quidem fuerit velocior <lb/>tran&longs;latitio, tum pila non-nihil retrorsùm excurrat, <lb/>qua&longs;i manu aliquantò magis retrorsùm, quàm an­<lb/>trorsùm promota. </s> |
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| <s>Et vis ip&longs;e rem &longs;pectare jucun­<lb/>diùs? </s> | <s id="id.000209">Sin æquè velox fuerit, tum pila <lb/>neque retrorsùm, neque antrorsùm excurrat, &longs;ed in <lb/>eodem loco con&longs;i&longs;tat, qua&longs;i in neutram partem pro­<lb/>jecta, & ad perpendiculum cadens; quòd vno motu <lb/>alium compen&longs;ante, & neutro alterum &longs;uperante, <lb/>manus eo momento veluti immota cohæreat. </s> |
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| <s>Iube hæc peragi ab alio; tu verò in medio per­<lb/>gulæ con&longs;i&longs;te è regione manus, qua ille pilam pro­<lb/>ijciet. </s> | <s id="id.000210">Si <lb/>denique fuerit minùs velox; tum pila &longs;equatur, & <lb/>antror&longs;um, &longs;eu in eandem tecum partem decurrat, <lb/>qua&longs;i in illam magis acta motu tran&longs;latitio, quàm in <lb/>oppo&longs;itam proprio. </s> |
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| <s>Tum illo ambulante, & antrorsùm, proijcien­<lb/>te, videbis manum vlteriùs, quam quie&longs;cente pro­<lb/>moueri, & pilam proinde majore impetu emitti, mo­<lb/>uerique velociùs, & ferri vlteriùs. </s> | <s id="id.000211">Et vis ip&longs;e rem &longs;pectare jucun­<lb/>diùs? </s> |
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| <s>Proijciente au­<lb/>tem retrorsùm, videbis manum nunc minus promo­<lb/>ueri, &longs;icque pilam &longs;egniùs eijci: nunc tantundem, &longs;ic­<lb/>que pilam ad perpendiculum cadere; nunc non mo­<lb/>dò nihil promoueri, &longs;ed antrorsùm quoque magis <lb/>pertrahi; &longs;icque pilam virum ambulantem &longs;equi. </s> | <s id="id.000212">Iube hæc peragi ab alio; tu verò in medio per­<lb/>gulæ con&longs;i&longs;te è regione manus, qua ille pilam pro­<lb/>ijciet. </s> |
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| <s>Ad­<lb/>moneo autem, vt ad alium, dum experitur, attendas: <lb/>quia dum ip&longs;emet experiris, adnotare minimè potes <lb/>velocitatis di&longs;crimina, ob motum tran&longs;latitium facta. <lb/></s> | <s id="id.000213">Tum illo ambulante, & antrorsùm, proijcien­<lb/>te, videbis manum vlteriùs, quam quie&longs;cente pro­<lb/>moueri, & pilam proinde majore impetu emitti, mo­<lb/>uerique velociùs, & ferri vlteriùs. </s> |
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| <s>Quippe, quia tuus oculus eodem &longs;imùl motu tran&longs;­<lb/>fertur, ob&longs;eruare non pote&longs;t motum, quo manus &longs;i-<pb pagenum="7"/>mùl agitut, quique vnus idemque e&longs;t, atque idcircô pro <lb/>non motu, &longs;eu, quod idem e&longs;t, pro quietereputatut: at­<lb/>tendit verò &longs;olùm ad motiones alias, quas manus in­<lb/>tereà ob flexilitatem ex&longs;erere poteft. </s> | <s id="id.000214">Proijciente au­<lb/>tem retrorsùm, videbis manum nunc minus promo­<lb/>ueri, &longs;icque pilam &longs;egniùs eijci: nunc tantundem, &longs;ic­<lb/>que pilam ad perpendiculum cadere; nunc non mo­<lb/>dò nihil promoueri, &longs;ed antrorsùm quoque magis <lb/>pertrahi; &longs;icque pilam virum ambulantem &longs;equi. </s> |
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| <s>Ex quo capite e&longs;t, <lb/>vt pila antror&longs;ùm à te inter ambulandum projecta non <lb/>videatur ire velociùs, quàm proiecta inter quie&longs;cen­<lb/>dum; quia videlicet quantum motus corporis totius <lb/>pilam promouet, tantundem etiam promouet <expan abbr="oculũ">oculum</expan>, <lb/><expan abbr="ip&longs;eq;">ip&longs;eque</expan> adeò oculus, <expan abbr="tantund&etilde;">tantundem</expan> ex motu pilæ nó agno&longs;cit. <lb/></s> | <s id="id.000215">Ad­<lb/>moneo autem, vt ad alium, dum experitur, attendas: <lb/>quia dum ip&longs;emet experiris, adnotare minimè potes <lb/>velocitatis di&longs;crimina, ob motum tran&longs;latitium facta. <lb/></s> |
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| <s>Ill. </s> | <s id="id.000216">Quippe, quia tuus oculus eodem &longs;imùl motu tran&longs;­<lb/>fertur, ob&longs;eruare non pote&longs;t motum, quo manus &longs;i-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.014.jpg" pagenum="7"/>mùl agitut, quique vnus idemque e&longs;t, atque idcircô pro <lb/>non motu, &longs;eu, quod idem e&longs;t, pro quietereputatut: at­<lb/>tendit verò &longs;olùm ad motiones alias, quas manus in­<lb/>tereà ob flexilitatem ex&longs;erere poteft. </s> |
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| <s>An Paradoxum heic interjiciam, occa&longs;ione experi­<lb/>menti, quod ab i&longs;to loco alienum non &longs;it? </s> | <s id="id.000217">Ex quo capite e&longs;t, <lb/>vt pila antror&longs;ùm à te inter ambulandum projecta non <lb/>videatur ire velociùs, quàm proiecta inter quie&longs;cen­<lb/>dum; quia videlicet quantum motus corporis totius <lb/>pilam promouet, tantundem etiam promouet <expan abbr="oculũ">oculum</expan>, <lb/><expan abbr="ip&longs;eq;">ip&longs;eque</expan> adeò oculus, <expan abbr="tantund&etilde;">tantundem</expan> ex motu pilæ nó agno&longs;cit. <lb/></s> |
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| <s>Deambula <lb/>bracchiis pa&longs;&longs;is, liberéque pendentibus; ea pror&longs;ùm, <lb/>rur&longs;umque &longs;ponte mouebuntur; & vbi pa&longs;&longs;u tanti&longs;per <lb/>grandi, animatóque ince&longs;&longs;eris, tum &longs;en&longs;ibiliùs antè, <lb/>ac ponè, re&longs;pectu trunci corporis fient. </s> | <s id="id.000218">Ill. </s> |
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| <s>Habe intereà <lb/>pilam ad manum, quam &longs;ine vlla contentione manus, <lb/>bracchiive dimittas; ac tum, &longs;i dimi&longs;eris quidem, dum <lb/>manus anteriùs contendet, non anterius modò moue­<lb/>bitur, &longs;ed duplò etiam celeriùs mouebitur, quàm cor­<lb/>poris truncus. </s> | <s id="id.000219">An Paradoxum heic interjiciam, occa&longs;ione experi­<lb/>menti, quod ab i&longs;to loco alienum non &longs;it? </s> |
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| <s>Sin dum manus po&longs;teriùs fiet, neutram <lb/>in partem mouebitur, &longs;ed ad perpendiculum &longs;emper <lb/>cadet. </s> | <s id="id.000220">Deambula <lb/>bracchiis pa&longs;&longs;is, liberéque pendentibus; ea pror&longs;ùm, <lb/>rur&longs;umque &longs;ponte mouebuntur; & vbi pa&longs;&longs;u tanti&longs;per <lb/>grandi, animatóque ince&longs;&longs;eris, tum &longs;en&longs;ibiliùs antè, <lb/>ac ponè, re&longs;pectu trunci corporis fient. </s> |
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| <s>Id mirabile: &longs;ed nihilominùs Paradoxum penes <lb/>cau&longs;am e&longs;t, quæ videbitur tibimirabilior. </s> | <s id="id.000221">Habe intereà <lb/>pilam ad manum, quam &longs;ine vlla contentione manus, <lb/>bracchiive dimittas; ac tum, &longs;i dimi&longs;eris quidem, dum <lb/>manus anteriùs contendet, non anterius modò moue­<lb/>bitur, &longs;ed duplò etiam celeriùs mouebitur, quàm cor­<lb/>poris truncus. </s> |
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| <s>An non p<gap/><lb/>tas enim bracchia ire, ac redire, & manus extremas, vt <lb/>aliquod &longs;patium antror&longs;ùm conficiunt, ita retror&longs;ùm <lb/>conficere? </s> | <s id="id.000222">Sin dum manus po&longs;teriùs fiet, neutram <lb/>in partem mouebitur, &longs;ed ad perpendiculum &longs;emper <lb/>cadet. </s> |
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| <s>Et dico tamen, Bracchia numquam redire, <lb/>flective retror&longs;ùm: ac manus extremas, quanto tempo­<lb/>re videntur &longs;patium retrò conficere, tanto con&longs;i&longs;tere <lb/>immotas. </s> | <s id="id.000223">Id mirabile: &longs;ed nihilominùs Paradoxum penes <lb/>cau&longs;am e&longs;t, quæ videbitur tibimirabilior. </s> |
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| <s>Admirationem vt eximam, velim primùm <lb/>vt deambulando incedas iuxta parietem, quem &longs;ecun-<pb pagenum="8"/>dum totum ince&longs;&longs;um extrema pars manus (vngui&longs;ve <lb/>medij digiti) qua&longs;i præter cadens leuiter contingat. <lb/></s> | <s id="id.000224">An non p<gap/><lb/>tas enim bracchia ire, ac redire, & manus extremas, vt <lb/>aliquod &longs;patium antror&longs;ùm conficiunt, ita retror&longs;ùm <lb/>conficere? </s> |
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| <s>Per&longs;enties enim manum quidem antror&longs;ùm exporrigi: <lb/>&longs;ed non tamen ex eo puncto, in quod de&longs;inet exporre­<lb/>ctio, manum retror&longs;ùm fieri; quin potiùs in eo quie&longs;­<lb/>cere, ex&longs;pectaréque donec tur&longs;ùs exporrigatur antror­<lb/>&longs;ùm. </s> | <s id="id.000225">Et dico tamen, Bracchia numquam redire, <lb/>flective retror&longs;ùm: ac manus extremas, quanto tempo­<lb/>re videntur &longs;patium retrò conficere, tanto con&longs;i&longs;tere <lb/>immotas. </s> |
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| <s>Agno&longs;oes' & bracchium ab extrema manu ad <lb/>&longs;capulam v&longs;que, po&longs;tquam exporrecta manus fuerit, <lb/>non retror&longs;ùm agi, &longs;ed extrema manu firmata, & qua­<lb/>&longs;i centro facta, promoueri antror&longs;ùm in&longs;tar radij, cuius <lb/>extremum, & qua&longs;i pars circumferentiæ &longs;it &longs;capula, <lb/>quæ cùm &longs;it manu po&longs;terior prouehetur &longs;en&longs;im, quo­<lb/>v&longs;que illi ad perpendiculum fiat, & vlteriùs prouecta <lb/>anterior euadat. </s> | <s id="id.000226">Admirationem vt eximam, velim primùm <lb/>vt deambulando incedas iuxta parietem, quem &longs;ecun-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.015.jpg" pagenum="8"/>dum totum ince&longs;&longs;um extrema pars manus (vngui&longs;ve <lb/>medij digiti) qua&longs;i præter cadens leuiter contingat. <lb/></s> |
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| <s>Ac ni&longs;i tu quidem id po&longs;&longs;is &longs;atis ani­<lb/>maduertere, iube alium id experiti, tuque intereà eius <lb/>manum, bracchium, &longs;capulamque re&longs;pecta; & manife­<lb/>&longs;ta tibi res fiet; &longs;imúlque perno&longs;ces etiam incedentem <lb/>in aëre medio extremum digitum firmare, & &longs;uper co <lb/>qua&longs;i centro bracchium, &longs;capulamque circumducere. <lb/></s> | <s id="id.000227">Per&longs;enties enim manum quidem antror&longs;ùm exporrigi: <lb/>&longs;ed non tamen ex eo puncto, in quod de&longs;inet exporre­<lb/>ctio, manum retror&longs;ùm fieri; quin potiùs in eo quie&longs;­<lb/>cere, ex&longs;pectaréque donec tur&longs;ùs exporrigatur antror­<lb/>&longs;ùm. </s> |
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| <s>Velim prætereà vt attendas e&longs;&longs;e nobïs bracchia in&longs;tar <lb/>crurum anteriorum; adeò vt, quemadmodum quadru­<lb/>pedes decu&longs;&longs;atìm incedunt, hoc e&longs;t &longs;imùl promouendo <lb/><gap/>dem anteriorem dextrum cum po&longs;teriore &longs;ini&longs;tro, & <lb/>priorem &longs;ini&longs;trum cum po&longs;teriore dextro; ita nos &longs;pon­<lb/>te, ni&longs;i potiùs nece&longs;&longs;itate quadam naturæ, promouere <lb/>&longs;imùl dextram manum cum pede fini&longs;tro, & ma­<lb/>num &longs;ini&longs;tram cum pede dextro, nec po&longs;&longs;e &longs;ecus face­<lb/>re, quandocúmque manus liberè dependent. </s> | <s id="id.000228">Agno&longs;oes' & bracchium ab extrema manu ad <lb/>&longs;capulam v&longs;que, po&longs;tquam exporrecta manus fuerit, <lb/>non retror&longs;ùm agi, &longs;ed extrema manu firmata, & qua­<lb/>&longs;i centro facta, promoueri antror&longs;ùm in&longs;tar radij, cuius <lb/>extremum, & qua&longs;i pars circumferentiæ &longs;it &longs;capula, <lb/>quæ cùm &longs;it manu po&longs;terior prouehetur &longs;en&longs;im, quo­<lb/>v&longs;que illi ad perpendiculum fiat, & vlteriùs prouecta <lb/>anterior euadat. </s> |
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| <s>Id nem­<lb/>pe vbi ob&longs;etuâris, facile erit attendere, Quemadmo­<lb/>dum quo tempore pes &longs;ini&longs;ter transfertur, & è po&longs;tico <pb pagenum="9"/>anticus fit, pes dexter non proptereà regreditur, &longs;ed ex­<lb/>&longs;pectat hærendo terræ, donec ille è terra &longs;ublatus, ter­<lb/>ram denuò contigerit; ita profectò &longs;ini&longs;tram manum, <lb/>quæ dextrum pedem imitatur, tempore eodem non re­<lb/>gredi, &longs;ed ex&longs;pectare, hærerequein aëre medio, <expan abbr="quov&longs;q;">quov&longs;que</expan> <lb/>manus dextera cum &longs;ini&longs;tro pede quietem a&longs;&longs;equatur. <lb/></s> | <s id="id.000229">Ac ni&longs;i tu quidem id po&longs;&longs;is &longs;atis ani­<lb/>maduertere, iube alium id experiti, tuque intereà eius <lb/>manum, bracchium, &longs;capulamque re&longs;pecta; & manife­<lb/>&longs;ta tibi res fiet; &longs;imúlque perno&longs;ces etiam incedentem <lb/>in aëre medio extremum digitum firmare, & &longs;uper co <lb/>qua&longs;i centro bracchium, &longs;capulamque circumducere. <lb/></s> |
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| <s>Et con&longs;equenter, Quemadmodum dextro pede con&longs;i­<lb/>&longs;tente, factoque vt centro, ip&longs;um crus dextrum ad v&longs;­<lb/>que coxendicem non retror&longs;ùm abducitur, &longs;ed &longs;en&longs;im <lb/>in&longs;tar radij, ex &longs;itu po&longs;tico anticum acquirit; ita planè <lb/>bracchio &longs;ini&longs;tro, quod exqui&longs;itè pedem dextrum imi­<lb/>tatur, contingere. </s> | <s id="id.000230">Velim prætereà vt attendas e&longs;&longs;e nobïs bracchia in&longs;tar <lb/>crurum anteriorum; adeò vt, quemadmodum quadru­<lb/>pedes decu&longs;&longs;atìm incedunt, hoc e&longs;t &longs;imùl promouendo <lb/><gap/>dem anteriorem dextrum cum po&longs;teriore &longs;ini&longs;tro, & <lb/>priorem &longs;ini&longs;trum cum po&longs;teriore dextro; ita nos &longs;pon­<lb/>te, ni&longs;i potiùs nece&longs;&longs;itate quadam naturæ, promouere <lb/>&longs;imùl dextram manum cum pede fini&longs;tro, & ma­<lb/>num &longs;ini&longs;tram cum pede dextro, nec po&longs;&longs;e &longs;ecus face­<lb/>re, quandocúmque manus liberè dependent. </s> |
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| <s>Quo loco meditare quæ&longs;o admira­<lb/>bile artificium. </s> | <s id="id.000231">Id nem­<lb/>pe vbi ob&longs;etuâris, facile erit attendere, Quemadmo­<lb/>dum quo tempore pes &longs;ini&longs;ter transfertur, & è po&longs;tico <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.016.jpg" pagenum="9"/>anticus fit, pes dexter non proptereà regreditur, &longs;ed ex­<lb/>&longs;pectat hærendo terræ, donec ille è terra &longs;ublatus, ter­<lb/>ram denuò contigerit; ita profectò &longs;ini&longs;tram manum, <lb/>quæ dextrum pedem imitatur, tempore eodem non re­<lb/>gredi, &longs;ed ex&longs;pectare, hærerequein aëre medio, <expan abbr="quov&longs;q;">quov&longs;que</expan> <lb/>manus dextera cum &longs;ini&longs;tro pede quietem a&longs;&longs;equatur. <lb/></s> |
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| <s>Videlicet pes, & coxendix duo quædam <lb/>alternis &longs;unt centra, quæ alternatim quoque duos arcus, <lb/>&longs;eu circumferentiæ portiones, eodem &longs;emper crure, vt <lb/>radio communi intercedente, de&longs;cribant. </s> | <s id="id.000232">Et con&longs;equenter, Quemadmodum dextro pede con&longs;i­<lb/>&longs;tente, factoque vt centro, ip&longs;um crus dextrum ad v&longs;­<lb/>que coxendicem non retror&longs;ùm abducitur, &longs;ed &longs;en&longs;im <lb/>in&longs;tar radij, ex &longs;itu po&longs;tico anticum acquirit; ita planè <lb/>bracchio &longs;ini&longs;tro, quod exqui&longs;itè pedem dextrum imi­<lb/>tatur, contingere. </s> |
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| <s>Et quia ni­<lb/>hilominùs coxendice non eleuata, dum pro centro e&longs;t, <lb/>pes arcum de&longs;cribens pro&longs;cindere terram non potuit; <lb/>ideò medium crus fuit articulatum; vt flexurâ ad genu, <lb/>&longs;eu poplitem factâ, pes de&longs;criberet arcum &longs;upra terram. <lb/></s> | <s id="id.000233">Quo loco meditare quæ&longs;o admira­<lb/>bile artificium. </s> |
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| <s>Quemadmodùm etiam, quia pede non depre&longs;&longs;o co­<lb/>xendix arcum de&longs;criptura, fui&longs;&longs;et nimiùm attollenda; <lb/>corpori&longs;que truncus nimiùm &longs;ubuehendus, &longs;i crusto­<lb/>tum rigidum fui&longs;&longs;et; idcircò flexura eadem interce&longs;&longs;it, <lb/>quæ temperaret huiu&longs;modi arcum: facto intereà eodem <lb/>genu nunc centro, nunc extremo radio arcus &longs;uos, re&longs;­<lb/>pectu tam tibiæ, quàm femoris, &longs;eu dum flectitur, &longs;eu <lb/>dum tenditur, de&longs;cribente. </s> | <s id="id.000234">Videlicet pes, & coxendix duo quædam <lb/>alternis &longs;unt centra, quæ alternatim quoque duos arcus, <lb/>&longs;eu circumferentiæ portiones, eodem &longs;emper crure, vt <lb/>radio communi intercedente, de&longs;cribant. </s> |
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| <s>Meditare etiam motus æ­<lb/>quabilitatem, qua corporis truncus intereâ incedit, & <lb/>ad quam aliunde tam prolixitas, quàm flexilitas pedum <pb pagenum="10"/>confert; quatenùs calce vnius terram attingente, <lb/>& priu&longs;quàm tota planta &longs;en&longs;im &longs;uccedat, digiti al­<lb/>terius (plantâ reliquâ iam elatâ) è terra attolluntur, <lb/>&longs;icque, ab&longs;que interruptione, trunci corporis motus <lb/>continuatur. </s> | <s id="id.000235">Et quia ni­<lb/>hilominùs coxendice non eleuata, dum pro centro e&longs;t, <lb/>pes arcum de&longs;cribens pro&longs;cindere terram non potuit; <lb/>ideò medium crus fuit articulatum; vt flexurâ ad genu, <lb/>&longs;eu poplitem factâ, pes de&longs;criberet arcum &longs;upra terram. <lb/></s> |
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| <s>Tamet&longs;i notandum e&longs;t truncum non <lb/>promoueri ab eo pede, qui elatus e&longs;t, proceditque <lb/>per aërem; &longs;ed ab eo, qui terræ inhæret, & &longs;upra <lb/>quem crus deferens truncum euoluitur. </s> | <s id="id.000236">Quemadmodùm etiam, quia pede non depre&longs;&longs;o co­<lb/>xendix arcum de&longs;criptura, fui&longs;&longs;et nimiùm attollenda; <lb/>corpori&longs;que truncus nimiùm &longs;ubuehendus, &longs;i crusto­<lb/>tum rigidum fui&longs;&longs;et; idcircò flexura eadem interce&longs;&longs;it, <lb/>quæ temperaret huiu&longs;modi arcum: facto intereà eodem <lb/>genu nunc centro, nunc extremo radio arcus &longs;uos, re&longs;­<lb/>pectu tam tibiæ, quàm femoris, &longs;eu dum flectitur, &longs;eu <lb/>dum tenditur, de&longs;cribente. </s> |
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| <s>Intelliges <lb/>enim ex his, quia corporis truncus æquabiliter in­<lb/>cedit, & pedes alternatìm dimidio temporis ince­<lb/>dunt, dimidio quie&longs;cunt: ideò debere motum pe­<lb/>dum e&longs;&longs;e motu trunci duplò velociorem; & parteis <lb/>crurum reliquas tantò moueri tardiùs, quàm pedes, <lb/>quantò accedunt propiús ad coxendices, quæ non <lb/>majore feruntur velocitate, quàm truncus. </s> | <s id="id.000237">Meditare etiam motus æ­<lb/>quabilitatem, qua corporis truncus intereâ incedit, & <lb/>ad quam aliunde tam prolixitas, quàm flexilitas pedum <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.017.jpg" pagenum="10"/>confert; quatenùs calce vnius terram attingente, <lb/>& priu&longs;quàm tota planta &longs;en&longs;im &longs;uccedat, digiti al­<lb/>terius (plantâ reliquâ iam elatâ) è terra attolluntur, <lb/>&longs;icque, ab&longs;que interruptione, trunci corporis motus <lb/>continuatur. </s> |
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| <s>Intelliges <lb/>etiam con&longs;equenter manus, dimidio quoque tempo­<lb/>ris quie&longs;centeis, & reliquo dimidio pror&longs;ùm expor­<lb/>rectas, moueri duplò velociùs trunco: & parteis brac­<lb/>chij reliquas tantò moueri lentiùs, quantò magis ad <lb/>&longs;capulas &longs;imùl cum trunco motas accedunt. </s> | <s id="id.000238">Tamet&longs;i notandum e&longs;t truncum non <lb/>promoueri ab eo pede, qui elatus e&longs;t, proceditque <lb/>per aërem; &longs;ed ab eo, qui terræ inhæret, & &longs;upra <lb/>quem crus deferens truncum euoluitur. </s> |
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| <s>Intelli­<lb/>ges denique ob quam cau&longs;am fiat, quod initio dixi, <lb/>pilam dimi&longs;&longs;am, quando manus antror&longs;um exporri­<lb/>gitur, duplò velociùs moueri, quàm truncum; & <lb/>dimi&longs;&longs;am quo tempore manus retrorsùm ire apparet, <lb/>ad perpendiculum &longs;emper cadere. </s> | <s id="id.000239">Intelliges <lb/>enim ex his, quia corporis truncus æquabiliter in­<lb/>cedit, & pedes alternatìm dimidio temporis ince­<lb/>dunt, dimidio quie&longs;cunt: ideò debere motum pe­<lb/>dum e&longs;&longs;e motu trunci duplò velociorem; & parteis <lb/>crurum reliquas tantò moueri tardiùs, quàm pedes, <lb/>quantò accedunt propiús ad coxendices, quæ non <lb/>majore feruntur velocitate, quàm truncus. </s> |
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| <s>Nimirùm, quia <lb/>priore ca&longs;u motum con&longs;equitur à manu duplò ve­<lb/>lociùs, quàm truncus tran&longs;lata; & po&longs;teriore, nul­<lb/>lum habet à manu (&longs;c, icet immota, con&longs;i&longs;tentéque) <lb/>impre&longs;&longs;um. </s></p><p type="main"> | <s id="id.000240">Intelliges <lb/>etiam con&longs;equenter manus, dimidio quoque tempo­<lb/>ris quie&longs;centeis, & reliquo dimidio pror&longs;ùm expor­<lb/>rectas, moueri duplò velociùs trunco: & parteis brac­<lb/>chij reliquas tantò moueri lentiùs, quantò magis ad <lb/>&longs;capulas &longs;imùl cum trunco motas accedunt. </s> |
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| <s>IV. <!-- KEEP S--></s> | <s id="id.000241">Intelli­<lb/>ges denique ob quam cau&longs;am fiat, quod initio dixi, <lb/>pilam dimi&longs;&longs;am, quando manus antror&longs;um exporri­<lb/>gitur, duplò velociùs moueri, quàm truncum; & <lb/>dimi&longs;&longs;am quo tempore manus retrorsùm ire apparet, <lb/>ad perpendiculum &longs;emper cadere. </s> |
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| <s>Iam cùm hæc ita &longs;e&longs;e habeant, facilè cau&longs;am <pb pagenum="11"/>peruidebis eorum, de quibus ad Luillerium &longs;crip&longs;e­<lb/>ram, experimentorum. </s> | <s id="id.000242">Nimirùm, quia <lb/>priore ca&longs;u motum con&longs;equitur à manu duplò ve­<lb/>lociùs, quàm truncus tran&longs;lata; & po&longs;teriore, nul­<lb/>lum habet à manu (&longs;c, icet immota, con&longs;i&longs;tentéque) <lb/>impre&longs;&longs;um. </s></p><p type="main"> |
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| <s>Ea &longs;anè &longs;unt, quæ ip&longs;e quo­<lb/>que maxima ex parte peragere facillimè po&longs;&longs;is. </s> | <s id="id.000243">IV. <!-- KEEP S--></s> |
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| <s>Vi­<lb/>delicet, cùm aliquando curru extra vrbem vehèris, <lb/>manum extra currum protende, & auriga ju&longs;&longs;o in­<lb/>&longs;tigare equos, laxaréque habenas, proijce pilam di­<lb/>rectè &longs;ur&longs;um quantacúmque voles, aut poteris vi; & <lb/>illa haud-dubiè recidet in manum. </s> | <s id="id.000244">Iam cùm hæc ita &longs;e&longs;e habeant, facilè cau&longs;am <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.018.jpg" pagenum="11"/>peruidebis eorum, de quibus ad Luillerium &longs;crip&longs;e­<lb/>ram, experimentorum. </s> |
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| <s>Cur recidat au­<lb/>tem, tibi explicabit, &longs;i quem ju&longs;&longs;eris extra currum, <lb/>ac in via con&longs;i&longs;tere è regione tui, dum proijcies pi­<lb/>lam. </s> | <s id="id.000245">Ea &longs;anè &longs;unt, quæ ip&longs;e quo­<lb/>que maxima ex parte peragere facillimè po&longs;&longs;is. </s> |
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| <s>Ille enim videbit pilam non directè &longs;ur&longs;um ten­<lb/>dere, neque ad perpendiculum deinceps recidere; <lb/>&longs;ed videbit illam tendere obliquè, & qua&longs;i arcum, <lb/>&longs;eu lineam curuam in aëre de&longs;eribere, cuius vnum <lb/>extremum &longs;it qua parte pilam proijcies, alterum qua <lb/>recipies pilam. </s> | <s id="id.000246">Vi­<lb/>delicet, cùm aliquando curru extra vrbem vehèris, <lb/>manum extra currum protende, & auriga ju&longs;&longs;o in­<lb/>&longs;tigare equos, laxaréque habenas, proijce pilam di­<lb/>rectè &longs;ur&longs;um quantacúmque voles, aut poteris vi; & <lb/>illa haud-dubiè recidet in manum. </s> |
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| <s>Quod autem tibi ip&longs;i pila videatur <lb/>&longs;emper directè &longs;ursùm, & &longs;ecundum idem perpen­<lb/>diculum imminens; cau&longs;a e&longs;t, quia quantùm illa an­<lb/>trorsùm procedit, deflexum iter peragens, tantun­<lb/>dem tu quoque antrorsùm proucheris, adeò vt illi <lb/>&longs;emper &longs;ubijciaris, ip&longs;aque e&longs;&longs;e &longs;emper appareat in <lb/>eodem perpendiculo. </s> | <s id="id.000247">Cur recidat au­<lb/>tem, tibi explicabit, &longs;i quem ju&longs;&longs;eris extra currum, <lb/>ac in via con&longs;i&longs;tere è regione tui, dum proijcies pi­<lb/>lam. </s> |
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| <s>Cau&longs;a verò cur motus pilæ à <lb/>rectitudine deflectatur, & curuam &longs;equatur, de&longs;cri­<lb/>batve lineam, illius compo&longs;itio e&longs;t, quatenus ex <lb/>duplici vi motrice originem habet. </s> | <s id="id.000248">Ille enim videbit pilam non directè &longs;ur&longs;um ten­<lb/>dere, neque ad perpendiculum deinceps recidere; <lb/>&longs;ed videbit illam tendere obliquè, & qua&longs;i arcum, <lb/>&longs;eu lineam curuam in aëre de&longs;eribere, cuius vnum <lb/>extremum &longs;it qua parte pilam proijcies, alterum qua <lb/>recipies pilam. </s> |
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| <s>Nam &longs;i pila non <lb/>projecta &longs;ursùm detineretur &longs;olùm in manu, pro­<lb/>moueretur &longs;olùm antrorsùm, videlicet ad motum <lb/>currus, ac lineam rectam de&longs;criberet: &longs;i verò quie&longs;­<lb/>cente curru proijceretur directè &longs;ursùm, tunc non­<lb/>ni&longs;i &longs;ursùm, deorsùmque moueretur, ac rectam rur-<pb pagenum="12"/>sùs de&longs;criberet; at dum proijcitur &longs;ursùm à manu, <lb/>quæ ip&longs;a intereà mouetur antrorsùm, efficitur, vt <lb/>manus neque omninô &longs;ursùm, neque omninô antror­<lb/>sùm proijciat (videlicet motus antrorsùm, quo ab­<lb/>ripitur, deflectit illam à motu &longs;ursùm, quo per &longs;e <lb/>moueretur) &longs;ed inter vtrumque, &longs;eu obliquè proijciat; <lb/>&longs;icque projecta pila curuam lineam nece&longs;&longs;ariò de&longs;cri­<lb/>bat, cuius dimidium a&longs;cendendo, & dimidium de&longs;­<lb/>cendendo perficiatur. </s> | <s id="id.000249">Quod autem tibi ip&longs;i pila videatur <lb/>&longs;emper directè &longs;ursùm, & &longs;ecundum idem perpen­<lb/>diculum imminens; cau&longs;a e&longs;t, quia quantùm illa an­<lb/>trorsùm procedit, deflexum iter peragens, tantun­<lb/>dem tu quoque antrorsùm proucheris, adeò vt illi <lb/>&longs;emper &longs;ubijciaris, ip&longs;aque e&longs;&longs;e &longs;emper appareat in <lb/>eodem perpendiculo. </s> |
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| <s>Et vis id pleniùs cogno&longs;cere? <lb/></s> | <s id="id.000250">Cau&longs;a verò cur motus pilæ à <lb/>rectitudine deflectatur, & curuam &longs;equatur, de&longs;cri­<lb/>batve lineam, illius compo&longs;itio e&longs;t, quatenus ex <lb/>duplici vi motrice originem habet. </s> |
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| <s>Iube currum con&longs;i&longs;tere, proijce pilam &longs;ursùm, &, <lb/>&longs;igno priùs aurigæ dato, excedat currus, quam pri­<lb/>mùm projeceris; non recidet illa profectò in manum, <lb/>&longs;ed longè à curru locum prætervecto; illeque idem, <lb/>qui è regione tui con&longs;titerit, de&longs;cribentem videbit, <lb/>non arcum, &longs;ed rectam, perpendicularemque li­<lb/>neam, propter motum &longs;ursùm &longs;implicem, incom­<lb/>po&longs;itumque, & qui &longs;olius manus fuit proprius, ip&longs;o <lb/>curru nihil conferente. </s> | <s id="id.000251">Nam &longs;i pila non <lb/>projecta &longs;ursùm detineretur &longs;olùm in manu, pro­<lb/>moueretur &longs;olùm antrorsùm, videlicet ad motum <lb/>currus, ac lineam rectam de&longs;criberet: &longs;i verò quie&longs;­<lb/>cente curru proijceretur directè &longs;ursùm, tunc non­<lb/>ni&longs;i &longs;ursùm, deorsùmque moueretur, ac rectam rur-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.019.jpg" pagenum="12"/>sùs de&longs;criberet; at dum proijcitur &longs;ursùm à manu, <lb/>quæ ip&longs;a intereà mouetur antrorsùm, efficitur, vt <lb/>manus neque omninô &longs;ursùm, neque omninô antror­<lb/>sùm proijciat (videlicet motus antrorsùm, quo ab­<lb/>ripitur, deflectit illam à motu &longs;ursùm, quo per &longs;e <lb/>moueretur) &longs;ed inter vtrumque, &longs;eu obliquè proijciat; <lb/>&longs;icque projecta pila curuam lineam nece&longs;&longs;ariò de&longs;cri­<lb/>bat, cuius dimidium a&longs;cendendo, & dimidium de&longs;­<lb/>cendendo perficiatur. </s> |
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| <s>Profer deinde caput extra <lb/>currum, & de&longs;ignato in parte currus inferiore puncto <lb/>aliquo, quod in eadem linea perpendiculari cum <lb/>oculo tuo &longs;it; ac tum, tran&longs;lato citati&longs;&longs;imè curru, <lb/>admoue pilam ad oculum, ip&longs;amque nulla facta vi <lb/>à manu dimitte; videbis pilam decidere &longs;ecundum il­<lb/>lam lineam, atque idcircô ca&longs;us ille apparebit tibi <lb/>perpendicularis. </s> | <s id="id.000252">Et vis id pleniùs cogno&longs;cere? <lb/></s> |
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| <s>Non perinde porrô apparebit illi, <lb/>qui extra currum fuerit, & ad ca&longs;um attenderit: ob­<lb/>&longs;eruabit &longs;cilicet pilam qua&longs;i &longs;emi-arcum, &longs;eu curuam <lb/>lineam de&longs;cribere: quoniam quamuis manus non <lb/>imprimat illi motum &longs;ibi proprium, imprimit tamen <lb/>motum, quem habet à curru, adeó vt præter mo-<pb pagenum="13"/>tum grauitatis, quo pila &longs;ponte fertur deorsùm, fe­<lb/>ratur etiam antrorsùm eodem motu, quo ip&longs;e currus; <lb/>& quia tuus oculus intereà tantundem quoque an­<lb/>trorsùm fertur, inde fit, vt pila continuò ip&longs;i &longs;ub­<lb/>jecta oculo, perpendiculariter moueri videatur. </s> | <s id="id.000253">Iube currum con&longs;i&longs;tere, proijce pilam &longs;ursùm, &, <lb/>&longs;igno priùs aurigæ dato, excedat currus, quam pri­<lb/>mùm projeceris; non recidet illa profectò in manum, <lb/>&longs;ed longè à curru locum prætervecto; illeque idem, <lb/>qui è regione tui con&longs;titerit, de&longs;cribentem videbit, <lb/>non arcum, &longs;ed rectam, perpendicularemque li­<lb/>neam, propter motum &longs;ursùm &longs;implicem, incom­<lb/>po&longs;itumque, & qui &longs;olius manus fuit proprius, ip&longs;o <lb/>curru nihil conferente. </s> |
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| <s>Lo­<lb/>co verò pilæ v&longs;urpa lapillos; & curru nunc lentè, <lb/>nunc concitatè, & quomodocúmque voles, feratur, <lb/>idem &longs;emper videbitur. </s> | <s id="id.000254">Profer deinde caput extra <lb/>currum, & de&longs;ignato in parte currus inferiore puncto <lb/>aliquo, quod in eadem linea perpendiculari cum <lb/>oculo tuo &longs;it; ac tum, tran&longs;lato citati&longs;&longs;imè curru, <lb/>admoue pilam ad oculum, ip&longs;amque nulla facta vi <lb/>à manu dimitte; videbis pilam decidere &longs;ecundum il­<lb/>lam lineam, atque idcircô ca&longs;us ille apparebit tibi <lb/>perpendicularis. </s> |
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| <s>Proijce po&longs;teà pilam antror­<lb/>sùm; illa tantundem à te di&longs;cedet, tamque procùl à <lb/>te in terram cadet, ac &longs;i ip&longs;e quie&longs;ceres, eodem mo­<lb/>do, & eadem ex cau&longs;a, quam de pila projecta intra <lb/>pergulam dixi. </s> | <s id="id.000255">Non perinde porrô apparebit illi, <lb/>qui extra currum fuerit, & ad ca&longs;um attenderit: ob­<lb/>&longs;eruabit &longs;cilicet pilam qua&longs;i &longs;emi-arcum, &longs;eu curuam <lb/>lineam de&longs;cribere: quoniam quamuis manus non <lb/>imprimat illi motum &longs;ibi proprium, imprimit tamen <lb/>motum, quem habet à curru, adeó vt præter mo-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.020.jpg" pagenum="13"/>tum grauitatis, quo pila &longs;ponte fertur deorsùm, fe­<lb/>ratur etiam antrorsùm eodem motu, quo ip&longs;e currus; <lb/>& quia tuus oculus intereà tantundem quoque an­<lb/>trorsùm fertur, inde fit, vt pila continuò ip&longs;i &longs;ub­<lb/>jecta oculo, perpendiculariter moueri videatur. </s> |
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| <s>Di&longs;crimen e&longs;t &longs;olum, quòd corpus, <lb/>cui cohæret manus, intra pergulam moueatur per &longs;e; <lb/>in via moueatur à curru. </s> | <s id="id.000256">Lo­<lb/>co verò pilæ v&longs;urpa lapillos; & curru nunc lentè, <lb/>nunc concitatè, & quomodocúmque voles, feratur, <lb/>idem &longs;emper videbitur. </s> |
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| <s>Nec &longs;pera, vt manus pilam <lb/>a&longs;&longs;equatur, projectam licet remi&longs;&longs;a vi: Nam &longs;i alius <lb/>quidem extra currum quie&longs;cens eadem vi proijceret, <lb/>po&longs;&longs;es a&longs;&longs;equi, obimpre&longs;&longs;am folùm propriam eius vim; <lb/>at dum tu proijcis, præter vim propriam, imprimis <lb/>etiam vim currus, cau&longs;am videlicet majoris illius ve­<lb/>locitatis, ob quam pilate &longs;emper tantum &longs;ugit, quan­<lb/>tum eam ip&longs;e pro&longs;equeris. </s> | <s id="id.000257">Proijce po&longs;teà pilam antror­<lb/>sùm; illa tantundem à te di&longs;cedet, tamque procùl à <lb/>te in terram cadet, ac &longs;i ip&longs;e quie&longs;ceres, eodem mo­<lb/>do, & eadem ex cau&longs;a, quam de pila projecta intra <lb/>pergulam dixi. </s> |
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| <s>Proijce deinde retrorsùm; <lb/>& eadem, eodemque modo, ac ob ea&longs;dem cau&longs;as <lb/>euenient, quas diximus antè, circa projectionem in­<lb/>tra pergulam. </s> | <s id="id.000258">Di&longs;crimen e&longs;t &longs;olum, quòd corpus, <lb/>cui cohæret manus, intra pergulam moueatur per &longs;e; <lb/>in via moueatur à curru. </s> |
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| <s>Proijce denique in latus, & ad rectum <lb/>quidem cum latere currus angulum: Proijce etiam <lb/>ad obliquum, & ad quemcúmque volueris; abeun­<lb/>tem &longs;emper pilam videbis per lineam, quæ ad finem <lb/>v&longs;que, eundem &longs;eu rectum, &longs;eu obliquum cum latere <lb/>currus angulum con&longs;tituat. </s> | <s id="id.000259">Nec &longs;pera, vt manus pilam <lb/>a&longs;&longs;equatur, projectam licet remi&longs;&longs;a vi: Nam &longs;i alius <lb/>quidem extra currum quie&longs;cens eadem vi proijceret, <lb/>po&longs;&longs;es a&longs;&longs;equi, obimpre&longs;&longs;am folùm propriam eius vim; <lb/>at dum tu proijcis, præter vim propriam, imprimis <lb/>etiam vim currus, cau&longs;am videlicet majoris illius ve­<lb/>locitatis, ob quam pilate &longs;emper tantum &longs;ugit, quan­<lb/>tum eam ip&longs;e pro&longs;equeris. </s> |
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| <s>Illud autem erit ob&longs;erua­<lb/>tu jucundum, quòd, &longs;i ad lapidem, arborem, aliquid-<pb pagenum="14"/>ve aliud non nihil di&longs;&longs;itum, quie&longs;cen&longs;que collinees, <lb/>&longs;emper à &longs;copo &longs;is aberraturus. </s> | <s id="id.000260">Proijce deinde retrorsùm; <lb/>& eadem, eodemque modo, ac ob ea&longs;dem cau&longs;as <lb/>euenient, quas diximus antè, circa projectionem in­<lb/>tra pergulam. </s> |
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| <s>Nempe, quia dum ma­<lb/>nus eò connittitur, transfertur intereà à curru ver­<lb/>&longs;us anteriora; vt proinde pila, aut lapis tantundem à <lb/>&longs;copo antror&longs;ùm feriat, quantùm promotus interà <lb/>currus à momento v&longs;que proiectionis fuerit. </s> | <s id="id.000261">Proijce denique in latus, & ad rectum <lb/>quidem cum latere currus angulum: Proijce etiam <lb/>ad obliquum, & ad quemcúmque volueris; abeun­<lb/>tem &longs;emper pilam videbis per lineam, quæ ad finem <lb/>v&longs;que, eundem &longs;eu rectum, &longs;eu obliquum cum latere <lb/>currus angulum con&longs;tituat. </s> |
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| <s>Secùs <lb/>autem e&longs;&longs;et, &longs;i fortè ade&longs;&longs;et currus alius, qui è re­<lb/>gione, ac pari velocitate cum tuo transferretur; tunc <lb/>enim, facto in illo &longs;copo, directè in ip&longs;um pila tende­<lb/>ret, quia &longs;copus tantundem, quantum tua manus <lb/>promoueretur antror&longs;ùm. </s> | <s id="id.000262">Illud autem erit ob&longs;erua­<lb/>tu jucundum, quòd, &longs;i ad lapidem, arborem, aliquid-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.021.jpg" pagenum="14"/>ve aliud non nihil di&longs;&longs;itum, quie&longs;cen&longs;que collinees, <lb/>&longs;emper à &longs;copo &longs;is aberraturus. </s> |
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| <s>Ex quo fiet, vt &longs;i collu­<lb/>dendo, coniicere pilam in famulum velis, qui aliquan­<lb/>tò procul extra currum &longs;it, illum quidem &longs;is præ­<lb/>tergre&longs;&longs;urus, &longs;i quieuerit; at &longs;i pari velocitate, qua <lb/>currus ince&longs;&longs;erit, &longs;is omninô a&longs;&longs;equuturus. </s> | <s id="id.000263">Nempe, quia dum ma­<lb/>nus eò connittitur, transfertur intereà à curru ver­<lb/>&longs;us anteriora; vt proinde pila, aut lapis tantundem à <lb/>&longs;copo antror&longs;ùm feriat, quantùm promotus interà <lb/>currus à momento v&longs;que proiectionis fuerit. </s> |
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| <s>Quod &longs;i <lb/>fortè non curru, &longs;ed equo veharis, & experimenta <lb/>eadem velis facere: eadem omninô, ac ii&longs;dem om­<lb/>ninô de cau&longs;is contingent. </s> | <s id="id.000264">Secùs <lb/>autem e&longs;&longs;et, &longs;i fortè ade&longs;&longs;et currus alius, qui è re­<lb/>gione, ac pari velocitate cum tuo transferretur; tunc <lb/>enim, facto in illo &longs;copo, directè in ip&longs;um pila tende­<lb/>ret, quia &longs;copus tantundem, quantum tua manus <lb/>promoueretur antror&longs;ùm. </s> |
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| <s>Adnoto &longs;olùm, &longs;i pilam, <lb/>aut lapidem directè &longs;ur&longs;ùm proieceris, & ab illius re­<lb/>ditu, &longs;iue ca&longs;u timueris, non eodem tenore &longs;tatìm à <lb/>jactuincedendum e&longs;&longs;e: &longs;ed vel <expan abbr="cõcitatiùs">concitatiùs</expan>, vt po&longs;terius <lb/>cadat, vel &longs;egniùs, vt anteriùs: Nam alioquin eodem <lb/>tenore, vt vbique eris &longs;ubiectus, ita ictum nu&longs;quàm <lb/>euades. </s> | <s id="id.000265">Ex quo fiet, vt &longs;i collu­<lb/>dendo, coniicere pilam in famulum velis, qui aliquan­<lb/>tò procul extra currum &longs;it, illum quidem &longs;is præ­<lb/>tergre&longs;&longs;urus, &longs;i quieuerit; at &longs;i pari velocitate, qua <lb/>currus ince&longs;&longs;erit, &longs;is omninô a&longs;&longs;equuturus. </s> |
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| <s>Quod &longs;i &longs;ur&longs;um quidem, &longs;ed cum tantilla ta­<lb/>men antror&longs;ùm obliquitate proieceris, non erit cur à <lb/>ca&longs;u timeas: quia, vt te quie&longs;cente pila &longs;ic projecta <lb/>non recideret inte, ita non recidet te tran&longs;lato; quo­<lb/>niam vis à motu equi impre&longs;&longs;a efficiet, vt quantum <lb/>tu &longs;ucce&longs;&longs;eris, tantundem illa &longs;emper antecedat. </s></p><p type="main"> | <s id="id.000266">Quod &longs;i <lb/>fortè non curru, &longs;ed equo veharis, & experimenta <lb/>eadem velis facere: eadem omninô, ac ii&longs;dem om­<lb/>ninô de cau&longs;is contingent. </s> |
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| <s>V. <!-- KEEP S--></s> | <s id="id.000267">Adnoto &longs;olùm, &longs;i pilam, <lb/>aut lapidem directè &longs;ur&longs;ùm proieceris, & ab illius re­<lb/>ditu, &longs;iue ca&longs;u timueris, non eodem tenore &longs;tatìm à <lb/>jactuincedendum e&longs;&longs;e: &longs;ed vel <expan abbr="cõcitatiùs">concitatiùs</expan>, vt po&longs;terius <lb/>cadat, vel &longs;egniùs, vt anteriùs: Nam alioquin eodem <lb/>tenore, vt vbique eris &longs;ubiectus, ita ictum nu&longs;quàm <lb/>euades. </s> |
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| <s>Re&longs;tant experimenta peracta in naui; &longs;ed cau&longs;as <pb pagenum="15"/>tamen omnium ex iam dictis intelligis. </s> | <s id="id.000268">Quod &longs;i &longs;ur&longs;um quidem, &longs;ed cum tantilla ta­<lb/>men antror&longs;ùm obliquitate proieceris, non erit cur à <lb/>ca&longs;u timeas: quia, vt te quie&longs;cente pila &longs;ic projecta <lb/>non recideret inte, ita non recidet te tran&longs;lato; quo­<lb/>niam vis à motu equi impre&longs;&longs;a efficiet, vt quantum <lb/>tu &longs;ucce&longs;&longs;eris, tantundem illa &longs;emper antecedat. </s></p><p type="main"> |
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| <s>Potes verò <lb/>& illa ip&longs;e haud incommodè ex&longs;equi, &longs;i quando &longs;u­<lb/>pra Sequanam lembo ex&longs;patiari per æ&longs;tatem lubeat. <lb/></s> | <s id="id.000269">V. <!-- KEEP S--></s> |
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| <s>Quippe vbi &longs;ecundò fluuio etiam remiges adhibiti <lb/>erunt, ita vt lembus quanta fieri poterit celeritate fe­<lb/>ratur, experiere, vbi lapillos directè &longs;ursùm pro­<lb/>ieceris, &longs;i ex puppi quidem, reca&longs;uros in puppin, &longs;i <lb/>ex prora, in proram, &longs;i ex medio lembo, in medium: <lb/>&longs;icque tamet&longs;i de&longs;tituare malo, ex erecto cuius &longs;itu <lb/>de apparente proiectionis rectitudine iudices; facilè <lb/>tamen capies, &longs;i malus e&longs;&longs;et in medio erectus ad al­<lb/>titudinem iactus, fore vt lapillus &longs;ecundum illum, <lb/>tam a&longs;cendendo, quam de&longs;cendendo moueretur; <lb/>quoniam ex quo loco e&longs;&longs;et iactus, in eundem ca&longs;us <lb/>fieret. </s> | <s id="id.000270">Re&longs;tant experimenta peracta in naui; &longs;ed cau&longs;as <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.022.jpg" pagenum="15"/>tamen omnium ex iam dictis intelligis. </s> |
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| <s>Porrô, &longs;icuti dictum e&longs;t de pila è curru pro­<lb/>iecta, apparebit quidem tibi lapis &longs;ursùm ferri: ap­<lb/>parebit & omnibus, qui in eodem nauigio erunt, re&longs;­<lb/>pectabuntque lapidem: at &longs;i quis intereà in ripa, <lb/>nauigiove alio quie&longs;cente, è regione tui, lapidi&longs;que <lb/>con&longs;titerit, is ob&longs;eruabit lapidem de&longs;cribere in aëre <lb/>&longs;peciem curuæ lineæ, cuius crus vnum incipiat ex <lb/>aëris loco vnde iactus fiet, aliud in illum de&longs;inat, <lb/>in quem erit ca&longs;us. </s> | <s id="id.000271">Potes verò <lb/>& illa ip&longs;e haud incommodè ex&longs;equi, &longs;i quando &longs;u­<lb/>pra Sequanam lembo ex&longs;patiari per æ&longs;tatem lubeat. <lb/></s> |
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| <s>Id nempe ob compo&longs;itum mo­<lb/>tum, alterum manus proprium, qui &longs;ur&longs;um, alterum <lb/>nauigii, qui prorsùm; adeò vt mixtus ex vtroque, <lb/>&longs;eu obliquus fiat, cuius quicquid e&longs;t &longs;ur&longs;um, à manu <lb/>&longs;it, quicquid pror&longs;um, à nauigio. </s> | <s id="id.000272">Quippe vbi &longs;ecundò fluuio etiam remiges adhibiti <lb/>erunt, ita vt lembus quanta fieri poterit celeritate fe­<lb/>ratur, experiere, vbi lapillos directè &longs;ursùm pro­<lb/>ieceris, &longs;i ex puppi quidem, reca&longs;uros in puppin, &longs;i <lb/>ex prora, in proram, &longs;i ex medio lembo, in medium: <lb/>&longs;icque tamet&longs;i de&longs;tituare malo, ex erecto cuius &longs;itu <lb/>de apparente proiectionis rectitudine iudices; facilè <lb/>tamen capies, &longs;i malus e&longs;&longs;et in medio erectus ad al­<lb/>titudinem iactus, fore vt lapillus &longs;ecundum illum, <lb/>tam a&longs;cendendo, quam de&longs;cendendo moueretur; <lb/>quoniam ex quo loco e&longs;&longs;et iactus, in eundem ca&longs;us <lb/>fieret. </s> |
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| <s>Heinc iam, vt <lb/>opinor, miraculum ce&longs;&longs;at, quod dixi fui&longs;&longs;e habitum, <lb/>cum illi ad lapidem attenderent, qui ex pede mali, <lb/>& &longs;ecundum eius altitudinem proiectus, neque ex-<pb pagenum="18"/>parte puppis de&longs;ereretur à malo, neque ex parte pro­<lb/>ræ attingeretur ab illo Siquidem tamet&longs;i lapis tam <lb/>a&longs;cendendo, quàm ex&longs;cendendo appareret &longs;emper in <lb/>codem perpen diculo, quia ver&longs;abatur &longs;emper in linea <lb/>crecto malo parallela; reucrâ tamen non mouebatut <lb/>per rectam, &longs;ea perpen liculatem lineam, &longs;ed de&longs;cri. <lb/></s> | <s id="id.000273">Porrô, &longs;icuti dictum e&longs;t de pila è curru pro­<lb/>iecta, apparebit quidem tibi lapis &longs;ursùm ferri: ap­<lb/>parebit & omnibus, qui in eodem nauigio erunt, re&longs;­<lb/>pectabuntque lapidem: at &longs;i quis intereà in ripa, <lb/>nauigiove alio quie&longs;cente, è regione tui, lapidi&longs;que <lb/>con&longs;titerit, is ob&longs;eruabit lapidem de&longs;cribere in aëre <lb/>&longs;peciem curuæ lineæ, cuius crus vnum incipiat ex <lb/>aëris loco vnde iactus fiet, aliud in illum de&longs;inat, <lb/>in quem erit ca&longs;us. </s> |
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| <s>bebat potiùs curuam, quam animaduetti&longs;&longs;et, &longs;i quis <lb/>ex triremi non longè quie&longs;cente lapidem &longs;pecta&longs;&longs;et. <lb/></s> | <s id="id.000274">Id nempe ob compo&longs;itum mo­<lb/>tum, alterum manus proprium, qui &longs;ur&longs;um, alterum <lb/>nauigii, qui prorsùm; adeò vt mixtus ex vtroque, <lb/>&longs;eu obliquus fiat, cuius quicquid e&longs;t &longs;ur&longs;um, à manu <lb/>&longs;it, quicquid pror&longs;um, à nauigio. </s> |
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| <s>Vidi&longs;&longs;et enim malum progtedientem, & lapidem ex <lb/>parte puppis continuò illum a&longs;&longs;ectantem, ex parte <lb/>proræ antecedentem; adeò vt neque ex parte puppis <lb/>à malo de&longs;ereretur, quia quantum malus ab&longs;cederet, <lb/>tantundem illi in&longs;i&longs;teret: neque ex parte proræ attin­<lb/>geretur à malo, quia quantum malus accederet, tan­<lb/>tundem illi prægrederetur. </s> | <s id="id.000275">Heinc iam, vt <lb/>opinor, miraculum ce&longs;&longs;at, quod dixi fui&longs;&longs;e habitum, <lb/>cum illi ad lapidem attenderent, qui ex pede mali, <lb/>& &longs;ecundum eius altitudinem proiectus, neque ex-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.023.jpg" pagenum="18"/>parte puppis de&longs;ereretur à malo, neque ex parte pro­<lb/>ræ attingeretur ab illo Siquidem tamet&longs;i lapis tam <lb/>a&longs;cendendo, quàm ex&longs;cendendo appareret &longs;emper in <lb/>codem perpen diculo, quia ver&longs;abatur &longs;emper in linea <lb/>crecto malo parallela; reucrâ tamen non mouebatut <lb/>per rectam, &longs;ea perpen liculatem lineam, &longs;ed de&longs;cri. <lb/></s> |
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| <s>Imaginare po&longs;teà virum, <lb/>qui exporrecta manu è vertice mali demittebat, &longs;eu <lb/>&longs;inebat decidere lapidem: apparebat quidem lapis ad <lb/>perpendiculum cadere tam ip&longs;i, quàm omnibus nobis, <lb/>qui vehebamur eadem triremi: at &longs;i &longs;ui&longs;&longs;et ex illa alia, <lb/>de qua diximus, quie&longs;cente &longs;pectatus, apparuï&longs;&longs;et de&longs;­<lb/>cribere expo&longs;itæ curuæ dimidium, eaque ratione ma­<lb/>lum &longs;emper, heinc &longs;equi, illeinc præcedere, vt malus nec <lb/>de&longs;erere, nec attingere illum po&longs;&longs;et. </s> | <s id="id.000276">bebat potiùs curuam, quam animaduetti&longs;&longs;et, &longs;i quis <lb/>ex triremi non longè quie&longs;cente lapidem &longs;pecta&longs;&longs;et. <lb/></s> |
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| <s>Cau&longs;a porrô no­<lb/>ta iam e&longs;t: &longs;iquidem manus lapidem tenens non impri­<lb/>mebat quidem motum &longs;ibi proprium, &longs;ed impri­<lb/>mebat tamen motum quem, habebat à malo, ip&longs;ique <lb/>erat cum tota naui communis; ex quo efficiebatur, vt <lb/>manus &longs;ita ver&longs;us puppin adduceret lapidem ver&longs;us <lb/>malum, & &longs;ita ad proram abduceret à malo; &longs;icque <lb/>lapis è manu excedens illcinc quidem proijceretur <pb pagenum="17"/>ver&longs;us malum, ip&longs;umque adeò con&longs;equeretur, heinc <lb/>verò proijceretur à malo, ip&longs;umque antecederet; & <lb/>vtrimvis (præter motum deor&longs;ùm, qui à grauitate <lb/>propria erat) haberet motum in anteriora, &longs;eu quo <lb/>triremis ferebatur. </s> | <s id="id.000277">Vidi&longs;&longs;et enim malum progtedientem, & lapidem ex <lb/>parte puppis continuò illum a&longs;&longs;ectantem, ex parte <lb/>proræ antecedentem; adeò vt neque ex parte puppis <lb/>à malo de&longs;ereretur, quia quantum malus ab&longs;cederet, <lb/>tantundem illi in&longs;i&longs;teret: neque ex parte proræ attin­<lb/>geretur à malo, quia quantum malus accederet, tan­<lb/>tundem illi prægrederetur. </s> |
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| <s>Neque e&longs;t iam mirum, &longs;i o mni­<lb/>bus nobis, qui in eadem triremi eramus, apparebat <lb/>motus perpendicularis; quippe ob&longs;eruabilis nobis <lb/>&longs;olùm erat motus lapidis deorsùm; nam ille qui­<lb/>dem ad anteriora ob&longs;eruari non poterat, quoniam <lb/>erat nobis communis cùm lapide, & quantùm lapis <lb/>promouebatur, tantundem oculus ex&longs;i&longs;tens ex parte <lb/>puppis &longs;uccedebat, ex parte proræ antecedebat. <lb/></s> | <s id="id.000278">Imaginare po&longs;teà virum, <lb/>qui exporrecta manu è vertice mali demittebat, &longs;eu <lb/>&longs;inebat decidere lapidem: apparebat quidem lapis ad <lb/>perpendiculum cadere tam ip&longs;i, quàm omnibus nobis, <lb/>qui vehebamur eadem triremi: at &longs;i &longs;ui&longs;&longs;et ex illa alia, <lb/>de qua diximus, quie&longs;cente &longs;pectatus, apparuï&longs;&longs;et de&longs;­<lb/>cribere expo&longs;itæ curuæ dimidium, eaque ratione ma­<lb/>lum &longs;emper, heinc &longs;equi, illeinc præcedere, vt malus nec <lb/>de&longs;erere, nec attingere illum po&longs;&longs;et. </s> |
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| <s>Poteris deinde in eodem tuo lembo pari vi pilam <lb/>proijcere ex puppi ad proram, & ex prora ad pup­<lb/>pim, ob&longs;eruaréque par &longs;patium projectione vtràque <lb/>peruadi. </s> | <s id="id.000279">Cau&longs;a porrô no­<lb/>ta iam e&longs;t: &longs;iquidem manus lapidem tenens non impri­<lb/>mebat quidem motum &longs;ibi proprium, &longs;ed impri­<lb/>mebat tamen motum quem, habebat à malo, ip&longs;ique <lb/>erat cum tota naui communis; ex quo efficiebatur, vt <lb/>manus &longs;ita ver&longs;us puppin adduceret lapidem ver&longs;us <lb/>malum, & &longs;ita ad proram abduceret à malo; &longs;icque <lb/>lapis è manu excedens illcinc quidem proijceretur <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.024.jpg" pagenum="17"/>ver&longs;us malum, ip&longs;umque adeò con&longs;equeretur, heinc <lb/>verò proijceretur à malo, ip&longs;umque antecederet; & <lb/>vtrimvis (præter motum deor&longs;ùm, qui à grauitate <lb/>propria erat) haberet motum in anteriora, &longs;eu quo <lb/>triremis ferebatur. </s> |
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| <s>Quod idem erit; poteris &longs;tans ip&longs;e ad pup­<lb/>pim cùm &longs;tante ad proram &longs;ic colludere, vt ob&longs;er­<lb/>uaturus &longs;is pilam pari vi vtrimque projectam æquis <lb/>omninô &longs;patijs, ac temporibus ad vtrumque perue­<lb/>nire. </s> | <s id="id.000280">Neque e&longs;t iam mirum, &longs;i o mni­<lb/>bus nobis, qui in eadem triremi eramus, apparebat <lb/>motus perpendicularis; quippe ob&longs;eruabilis nobis <lb/>&longs;olùm erat motus lapidis deorsùm; nam ille qui­<lb/>dem ad anteriora ob&longs;eruari non poterat, quoniam <lb/>erat nobis communis cùm lapide, & quantùm lapis <lb/>promouebatur, tantundem oculus ex&longs;i&longs;tens ex parte <lb/>puppis &longs;uccedebat, ex parte proræ antecedebat. <lb/></s> |
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| <s>Et videretur &longs;anè non debere; nam ex quo mo­<lb/>mento pilam projeci&longs;ti, diffugit &longs;ocius, atque adeò <lb/>pila ad eum peruentura percurrere &longs;patium longè <lb/>amplius, & prolixiore tempore debet; ex quo verò <lb/>&longs;ocius projecit, occurris tu, atque adeò pila percur­<lb/>rere debet longè breuius, contra ctioréque tempore: <lb/>& vnde hoc tamen vt pila ad vtrum que perinde per­<lb/>ueniat? </s> | <s id="id.000281">Poteris deinde in eodem tuo lembo pari vi pilam <lb/>proijcere ex puppi ad proram, & ex prora ad pup­<lb/>pim, ob&longs;eruaréque par &longs;patium projectione vtràque <lb/>peruadi. </s> |
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| <s>Sed videlicet cau&longs;a e&longs;t, quia licet motus <lb/>manus tuæ proprius æqualis &longs;it motui manus &longs;ocij <lb/>proprio; tua tamen manus motui&longs;ibi proprio adjun­<lb/>ctum habet motum lembi, &longs;icque pilam proijciens <pb pagenum="18"/>geminata vi, imprimis illi celeriorem motum; ma­<lb/>nus verò &longs;ocij detractum habet à motu proprio mo­<lb/>tum ciu&longs;dem lembi; &longs;icque pilam proijciens demi­<lb/>nuta vi, imprimit illi motum tardiorem: propor­<lb/>tioque huiu&longs;modi e&longs;t, vt quantùm tibi lembus ad­<lb/>ijcit, tantum illi detrahat; & quantùm ille ab&longs;cedit, <lb/>tantò pila feratur à te ad illum velociùs; quantùm tu <lb/>accedis, tantò pila feratur ab illo ad te &longs;egniùs. </s> | <s id="id.000282">Quod idem erit; poteris &longs;tans ip&longs;e ad pup­<lb/>pim cùm &longs;tante ad proram &longs;ic colludere, vt ob&longs;er­<lb/>uaturus &longs;is pilam pari vi vtrimque projectam æquis <lb/>omninô &longs;patijs, ac temporibus ad vtrumque perue­<lb/>nire. </s> |
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| <s>Ex <lb/>quo fit proinde, vt compen&longs;atione motus lembi fa­<lb/>cta, qui vtrique ve&longs;trum, & pilæ à vobis projectæ <lb/>communis e&longs;t; remaneat vtrimque &longs;olus motus ma­<lb/>nus vtriu&longs;que proprius, qui, cùm &longs;it vtrimque ab <lb/>æquali vi, idcircô ex æquo ad vtrumque fiat. </s> | <s id="id.000283">Et videretur &longs;anè non debere; nam ex quo mo­<lb/>mento pilam projeci&longs;ti, diffugit &longs;ocius, atque adeò <lb/>pila ad eum peruentura percurrere &longs;patium longè <lb/>amplius, & prolixiore tempore debet; ex quo verò <lb/>&longs;ocius projecit, occurris tu, atque adeò pila percur­<lb/>rere debet longè breuius, contra ctioréque tempore: <lb/>& vnde hoc tamen vt pila ad vtrum que perinde per­<lb/>ueniat? </s> |
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| <s>Nihil <lb/>e&longs;t nece&longs;&longs;e admoneam idem euenturum, &longs;i vterque <lb/>&longs;iti obliquè, vel è regione laterali aliquid proic­<lb/>ceritis; nam cau&longs;a &longs;emper eadem e&longs;t, con&longs;tatque mo­<lb/>tu communi detracto, cætera perinde peragi, lembo <lb/>&longs;eu moto, &longs;eu quie&longs;cente. </s> | <s id="id.000284">Sed videlicet cau&longs;a e&longs;t, quia licet motus <lb/>manus tuæ proprius æqualis &longs;it motui manus &longs;ocij <lb/>proprio; tua tamen manus motui&longs;ibi proprio adjun­<lb/>ctum habet motum lembi, &longs;icque pilam proijciens <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.025.jpg" pagenum="18"/>geminata vi, imprimis illi celeriorem motum; ma­<lb/>nus verò &longs;ocij detractum habet à motu proprio mo­<lb/>tum ciu&longs;dem lembi; &longs;icque pilam proijciens demi­<lb/>nuta vi, imprimit illi motum tardiorem: propor­<lb/>tioque huiu&longs;modi e&longs;t, vt quantùm tibi lembus ad­<lb/>ijcit, tantum illi detrahat; & quantùm ille ab&longs;cedit, <lb/>tantò pila feratur à te ad illum velociùs; quantùm tu <lb/>accedis, tantò pila feratur ab illo ad te &longs;egniùs. </s> |
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| <s>Et loci quidem angu&longs;tia, <lb/>&longs;eu brcue laterum lembi inter&longs;titium non patietur <lb/>fortè hæc adeò di&longs;ertè experiri, ac intra triremim <lb/>nobis licuit; Sed e&longs;to lembus alius, qui pari veloci­<lb/>tate, & ad latus ve&longs;trum &longs;eu propè, &longs;eu procùl mo­<lb/>neatur; eadem prorsùs euenient, licebit que tibi cùm <lb/>alio ex&longs;i&longs;tente procùl in alio lembo perinde pila col­<lb/>ludere, ac &longs;i in terra quie&longs;ceretis. </s> | <s id="id.000285">Ex <lb/>quo fit proinde, vt compen&longs;atione motus lembi fa­<lb/>cta, qui vtrique ve&longs;trum, & pilæ à vobis projectæ <lb/>communis e&longs;t; remaneat vtrimque &longs;olus motus ma­<lb/>nus vtriu&longs;que proprius, qui, cùm &longs;it vtrimque ab <lb/>æquali vi, idcircô ex æquo ad vtrumque fiat. </s> |
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| <s>Secùs &longs;anè, &longs;i ille <lb/>vel quie&longs;ceret, vel moueretur celeriùs, tardiu&longs;ve; <lb/>ita enim aberraretur vtrimque à &longs;copo, eadem ra­<lb/>tione, qua dictum e&longs;t de proiiciente quidpiam ex <lb/>curru. </s> | <s id="id.000286">Nihil <lb/>e&longs;t nece&longs;&longs;e admoneam idem euenturum, &longs;i vterque <lb/>&longs;iti obliquè, vel è regione laterali aliquid proic­<lb/>ceritis; nam cau&longs;a &longs;emper eadem e&longs;t, con&longs;tatque mo­<lb/>tu communi detracto, cætera perinde peragi, lembo <lb/>&longs;eu moto, &longs;eu quie&longs;cente. </s> |
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| <s>Ex quo adiicio obiter, vt intra lembum tuum <lb/>re&longs;piciens illius motum non ob&longs;eruas, quòd oculus <pb pagenum="19"/>tuus vnà cum illo transferatur; neque proinde vl­<lb/>lam diuer&longs;itatem, locive mutationem ob&longs;eruare in <lb/>illo potes, quatenùs nihil in ip&longs;o e&longs;t, quod eiu&longs;dem <lb/>motus particeps non &longs;it; ita re&longs;piciendo in lembum <lb/>alium pari velocitate, & è regione tui tran&longs;latum, non <lb/>iri ob&longs;eruatum à te eius motum, quia vterque mo­<lb/>tus ob æqualitatem pro eodem habetur, quatenùs <lb/>oculus vnà tran&longs;latus eandem &longs;emper di&longs;tantiam, nul­<lb/>lamque &longs;itus mutationem, diuer&longs;itatemve attendit. <lb/></s> | <s id="id.000287">Et loci quidem angu&longs;tia, <lb/>&longs;eu brcue laterum lembi inter&longs;titium non patietur <lb/>fortè hæc adeò di&longs;ertè experiri, ac intra triremim <lb/>nobis licuit; Sed e&longs;to lembus alius, qui pari veloci­<lb/>tate, & ad latus ve&longs;trum &longs;eu propè, &longs;eu procùl mo­<lb/>neatur; eadem prorsùs euenient, licebit que tibi cùm <lb/>alio ex&longs;i&longs;tente procùl in alio lembo perinde pila col­<lb/>ludere, ac &longs;i in terra quie&longs;ceretis. </s> |
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| <s>Hac ratione fiet, vt &longs;i lembus ille te procedente <lb/>quie&longs;cat, tu tamen illum moueri credas, tuum verò <lb/>quie&longs;cere; quia oculus cùm tuo tran&longs;latus, motum <lb/>ip&longs;ius ob&longs;eruare non pote&longs;t; intereà verò diuer&longs;ita­<lb/>tem in &longs;itu alterius attendit; quare & moueri illum <lb/>iudicat (loquor vulgari modo de iudicio &longs;en&longs;us.) <lb/>Quòd &longs;i ille ex aduer&longs;o tibi occurrat, & pari veloci­<lb/>tate cum tuo moueatur; tum ip&longs;e videbere &longs;emper <lb/>cum tuo quie&longs;cere, ille verò apparebit ferri duplò <lb/>velociùs, quàm reuerâ feratur; quia nempe præter <lb/>motum illius, oculus tuus affingit ip&longs;i motum tui pro­<lb/>ptium; quandò apparet oculo perinde loca commu­<lb/>tare, ac &longs;i te quie&longs;cente moueretur duplò velociùs, <lb/>quàm moueatur reip&longs;a. </s> | <s id="id.000288">Secùs &longs;anè, &longs;i ille <lb/>vel quie&longs;ceret, vel moueretur celeriùs, tardiu&longs;ve; <lb/>ita enim aberraretur vtrimque à &longs;copo, eadem ra­<lb/>tione, qua dictum e&longs;t de proiiciente quidpiam ex <lb/>curru. </s> |
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| <s>Ex hoc demùm capite e&longs;t, <lb/>cur accedentibus ad portum, videatur portus ad nos <lb/>immotos accedere: cur dum portu prouehimur, ter­<lb/>ræque, vrbe&longs;que recedere videantur; cur dum ripam, <lb/>littus, immotaque alia prætergredimur, illa videan­<lb/>tur prætergredi, nobis qua&longs;i immotis: neque i&longs;ta mo­<lb/>dò euenire deprehendantur ex lembo, aut quovis <lb/>alio nauigio: &longs;ed etiam ex curru aut quacúmque re, <pb pagenum="20"/>cum qua oculus no&longs;ter transferatur. </s> | <s id="id.000289">Ex quo adiicio obiter, vt intra lembum tuum <lb/>re&longs;piciens illius motum non ob&longs;eruas, quòd oculus <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.026.jpg" pagenum="19"/>tuus vnà cum illo transferatur; neque proinde vl­<lb/>lam diuer&longs;itatem, locive mutationem ob&longs;eruare in <lb/>illo potes, quatenùs nihil in ip&longs;o e&longs;t, quod eiu&longs;dem <lb/>motus particeps non &longs;it; ita re&longs;piciendo in lembum <lb/>alium pari velocitate, & è regione tui tran&longs;latum, non <lb/>iri ob&longs;eruatum à te eius motum, quia vterque mo­<lb/>tus ob æqualitatem pro eodem habetur, quatenùs <lb/>oculus vnà tran&longs;latus eandem &longs;emper di&longs;tantiam, nul­<lb/>lamque &longs;itus mutationem, diuer&longs;itatemve attendit. <lb/></s> |
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| <s>Sed hæc obiter <lb/>memorata &longs;unto. </s></p><p type="main"> | <s id="id.000290">Hac ratione fiet, vt &longs;i lembus ille te procedente <lb/>quie&longs;cat, tu tamen illum moueri credas, tuum verò <lb/>quie&longs;cere; quia oculus cùm tuo tran&longs;latus, motum <lb/>ip&longs;ius ob&longs;eruare non pote&longs;t; intereà verò diuer&longs;ita­<lb/>tem in &longs;itu alterius attendit; quare & moueri illum <lb/>iudicat (loquor vulgari modo de iudicio &longs;en&longs;us.) <lb/>Quòd &longs;i ille ex aduer&longs;o tibi occurrat, & pari veloci­<lb/>tate cum tuo moueatur; tum ip&longs;e videbere &longs;emper <lb/>cum tuo quie&longs;cere, ille verò apparebit ferri duplò <lb/>velociùs, quàm reuerâ feratur; quia nempe præter <lb/>motum illius, oculus tuus affingit ip&longs;i motum tui pro­<lb/>ptium; quandò apparet oculo perinde loca commu­<lb/>tare, ac &longs;i te quie&longs;cente moueretur duplò velociùs, <lb/>quàm moueatur reip&longs;a. </s> |
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| <s>VI. <!-- KEEP S--></s> | <s id="id.000291">Ex hoc demùm capite e&longs;t, <lb/>cur accedentibus ad portum, videatur portus ad nos <lb/>immotos accedere: cur dum portu prouehimur, ter­<lb/>ræque, vrbe&longs;que recedere videantur; cur dum ripam, <lb/>littus, immotaque alia prætergredimur, illa videan­<lb/>tur prætergredi, nobis qua&longs;i immotis: neque i&longs;ta mo­<lb/>dò euenire deprehendantur ex lembo, aut quovis <lb/>alio nauigio: &longs;ed etiam ex curru aut quacúmque re, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.027.jpg" pagenum="20"/>cum qua oculus no&longs;ter transferatur. </s> |
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| <s>Redco ad experimenta, ac illa poti&longs;&longs;imùm, <lb/>quæ peracta &longs;unt circa malum: quippe ea eiu&longs;modi <lb/>&longs;unt, ex quibus, quantùm fieri pote&longs;t, inue&longs;tigare <lb/>liceat, ni&longs;i germanam, at qualemcúmque motus non <lb/>&longs;olùm proiectorij, &longs;ed etiam naturalis cau&longs;am. </s> | <s id="id.000292">Sed hæc obiter <lb/>memorata &longs;unto. </s></p><p type="main"> |
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| <s>Nem­<lb/>pe vi&longs;um &longs;emper mirabile e&longs;t, cur lapis &longs;pontis &longs;uæ <lb/>factus, tum per aërem decidat, naturali impetu; tum <lb/>in principio tardius, in fine velociùs prorumpat: <lb/>idemque violenter adactus, tum impre&longs;&longs;o impetu &longs;ur­<lb/>sùm efferatur, tum in principio velociùs, & in fine <lb/>tardius emergat. </s> | <s id="id.000293">VI. <!-- KEEP S--></s> |
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| <s>Cæterùm, duo quæ dam præmit­<lb/>tenda &longs;unt, quæ inter alia benè multa magno Galileo <lb/>debentur. </s> | <s id="id.000294">Redco ad experimenta, ac illa poti&longs;&longs;imùm, <lb/>quæ peracta &longs;unt circa malum: quippe ea eiu&longs;modi <lb/>&longs;unt, ex quibus, quantùm fieri pote&longs;t, inue&longs;tigare <lb/>liceat, ni&longs;i germanam, at qualemcúmque motus non <lb/>&longs;olùm proiectorij, &longs;ed etiam naturalis cau&longs;am. </s> |
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| <s>Vnum; corpus &longs;uopte decidens motu ea <lb/>ratione accelerari, vt temporibus æqualibus maiora <lb/>&longs;emper &longs;patia peruadat, iuxta proportionem, quàm <lb/>habent numeri impares inter &longs;e, initio &longs;umpto ab vni­<lb/>tate. </s> | <s id="id.000295">Nem­<lb/>pe vi&longs;um &longs;emper mirabile e&longs;t, cur lapis &longs;pontis &longs;uæ <lb/>factus, tum per aërem decidat, naturali impetu; tum <lb/>in principio tardius, in fine velociùs prorumpat: <lb/>idemque violenter adactus, tum impre&longs;&longs;o impetu &longs;ur­<lb/>sùm efferatur, tum in principio velociùs, & in fine <lb/>tardius emergat. </s> |
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| <s>Hoc e&longs;t; &longs;i lapis ex. </s> | <s id="id.000296">Cæterùm, duo quæ dam præmit­<lb/>tenda &longs;unt, quæ inter alia benè multa magno Galileo <lb/>debentur. </s> |
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| <s>gr. </s> | <s id="id.000297">Vnum; corpus &longs;uopte decidens motu ea <lb/>ratione accelerari, vt temporibus æqualibus maiora <lb/>&longs;emper &longs;patia peruadat, iuxta proportionem, quàm <lb/>habent numeri impares inter &longs;e, initio &longs;umpto ab vni­<lb/>tate. </s> |
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| <s>è præcel&longs;a turri dimi&longs;&longs;us <lb/>intra vnum arteriæ pul&longs;um vnam orgyiam decidat, <lb/>fore vt intra &longs;ecundum decidat treis, intra tertium <lb/>quinque, intra quartum &longs;eptem, intra quintum no­<lb/>uem. </s> | <s id="id.000298">Hoc e&longs;t; &longs;i lapis ex. </s> |
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| <s>Et quia aggregando, vt in fine primi pul&longs;us <lb/>peracta e&longs;t vna orgyia, ita in fine &longs;ecundi peractæ <lb/>&longs;unt quatuor, in fine tertij nouem, in fine quarti &longs;ex­<lb/>decim, in fine quinti viginti-quinque, qui numeri <lb/>quadrati &longs;unt, vt Arithmetici appellant; heic fieri, vt <lb/>&longs;patia quibu&longs;cúm que temporibus peracta, &longs;int inter &longs;e <lb/>in duplicata ratione &longs;uorum <expan abbr="temporũ">temporum</expan> (nempevt eorun­<lb/>dem temporum quadrata) veluti Geometræ loquun-<pb pagenum="21"/>tur. </s> | <s id="id.000299">gr. <!-- REMOVE S-->è præcel&longs;a turri dimi&longs;&longs;us <lb/>intra vnum arteriæ pul&longs;um vnam orgyiam decidat, <lb/>fore vt intra &longs;ecundum decidat treis, intra tertium <lb/>quinque, intra quartum &longs;eptem, intra quintum no­<lb/>uem. </s> |
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| <s>Alterum; viam &longs;iue lineam, quam imaginamur <lb/>de&longs;cribi in aëre à corpore obliquè projecto, quam­<lb/>que notum e&longs;t e&longs;&longs;e curuam, non e&longs;&longs;e circularem (&longs;eu <lb/>qualis e&longs;t arcus, portiove circuli) &longs;ed parabolicam, <lb/>vt Geometræ vocant, id e&longs;t, qualem imaginabere, <lb/>&longs;i concipias conum, turbinemve, ita obliquè ver&longs;us <lb/>ba&longs;in re&longs;ecari vt &longs;ectio parallela fiat lateri oppo&longs;ito, <lb/>integróque relicto. </s> | |
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| <s>Cùm enim area re&longs;egmenti appel­<lb/>letur parabola, ambitus illius e&longs;t linea, quam parabo­<lb/>licam appellant. </s> | |
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| <s>Attende autem ad &longs;equentem fi­<lb/>guram; ex ea &longs;iquidem non modò <expan abbr="&longs;equentiũ">&longs;equentium</expan>, &longs;ed <expan abbr="ante-cedentiũ">ante­<lb/>cedentium</expan> quoque maxima pars intelligetur. </s> | <s id="id.000300">Et quia aggregando, vt in fine primi pul&longs;us <lb/>peracta e&longs;t vna orgyia, ita in fine &longs;ecundi peractæ <lb/>&longs;unt quatuor, in fine tertij nouem, in fine quarti &longs;ex­<lb/>decim, in fine quinti viginti-quinque, qui numeri <lb/>quadrati &longs;unt, vt Arithmetici appellant; heic fieri, vt <lb/>&longs;patia quibu&longs;cúm que temporibus peracta, &longs;int inter &longs;e <lb/>in duplicata ratione &longs;uorum <expan abbr="temporũ">temporum</expan> (nempevt eorun­<lb/>dem temporum quadrata) veluti Geometræ loquun-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.028.jpg" pagenum="21"/>tur. </s> |
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| <s>Nam pri­<lb/>mùm quidem, e&longs;to A B altitudo turris 25. orgyia­<lb/>rum; vel mali nauis quie&longs;centis 25. &longs;emi-orgyia­<lb/>rum: Et lapis cadens ex B perueniat ad A intra <lb/>quinque pul&longs;us delectæ arteriæ is, iuxta iam-dicta, <lb/>intra primum pul&longs;um perueniet ad C, intra &longs;ecundum <lb/>ad D, intra tertium ad E, intra quartum ad F, in­<lb/>tra quintum ad A. </s> | <s id="id.000301">Alterum; viam &longs;iue lineam, quam imaginamur <lb/>de&longs;cribi in aëre à corpore obliquè projecto, quam­<lb/>que notum e&longs;t e&longs;&longs;e curuam, non e&longs;&longs;e circularem (&longs;eu <lb/>qualis e&longs;t arcus, portiove circuli) &longs;ed parabolicam, <lb/>vt Geometræ vocant, id e&longs;t, qualem imaginabere, <lb/>&longs;i concipias conum, turbinemve, ita obliquè ver&longs;us <lb/>ba&longs;in re&longs;ecari vt &longs;ectio parallela fiat lateri oppo&longs;ito, <lb/>integróque relicto. </s> |
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| <s>Deinde ex G, proijciatur lapis <lb/>obliquè, ita vt perueniat ad B, vnde recidere incipiens <lb/>perueniat denique in H; is de&longs;cribet in aëre curuam <lb/>illam lineam GIKLMBNOPQH, quam mox di­<lb/>cebamus e&longs;&longs;e parabolicam. </s> | <s id="id.000302">Cùm enim area re&longs;egmenti appel­<lb/>letur parabola, ambitus illius e&longs;t linea, quam parabo­<lb/>licam appellant. </s> |
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| <s>Po&longs;t-modum, non loqua­<lb/>mur ampliùs de turri, &longs;ed &longs;olùm de malo; neque de <lb/>malo quie&longs;cente, &longs;ed de moto, &longs;iue tran&longs;lato ad mo­<lb/>tum nauis, cui e&longs;t implantatus; ac e&longs;to planities, &longs;u­<lb/>perficie&longs;ve maris, per quam nauis fertur, &longs;ecundum <lb/>lineam GH, &longs;upponamu&longs;que malum e&longs;&longs;e GR, cùm <lb/>lapis ex G proijcitur &longs;ursùm directè in R, & eadem <lb/>quidem vi, qua peruenire po&longs;&longs;et præcisè ad R. quie&longs;-<pb pagenum="22"/>cente malo. <lb/><figure id="fig1"/><lb/>promoucatur <lb/><expan abbr="cõ&longs;equenter">con&longs;equenter</expan> <lb/>nauis, adeò <lb/>vt intra vnum <lb/>momentum, <lb/>&longs;eu <expan abbr="pulsũ">pulsum</expan> ar­<lb/>teriæ malus <lb/>&longs;it factus ST; <lb/>tum quia la­<lb/>pis non de&longs;e­<lb/>rit malum, ne­<lb/>que ab illo <lb/>de&longs;eritur; erit <lb/>iuxta malum <lb/>in I directè <lb/>imminens pe­<lb/>di mali, &longs;iue <lb/>proximæ na­<lb/>uis parti è qua <lb/>e&longs;t facta pro­<lb/>jectio. </s> | <s id="id.000303">Attende autem ad &longs;equentem fi­<lb/>guram; ex ea &longs;iquidem non modò <expan abbr="&longs;equentiũ">&longs;equentium</expan>, &longs;ed <expan abbr="ante-cedentiũ">ante­<lb/>cedentium</expan> quoque maxima pars intelligetur. </s> |
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| <s>promo­<lb/>ueatur rursùs <lb/>nauis &longs;ecun­<lb/>do momento, & malus &longs;it VX; erit lapis pari, qua <lb/>antè ratione, in K. </s> | <s id="id.000304">Nam pri­<lb/>mùm quidem, e&longs;to A B altitudo turris 25. orgyia­<lb/>rum; vel mali nauis quie&longs;centis 25. &longs;emi-orgyia­<lb/>rum: Et lapis cadens ex B perueniat ad A intra <lb/>quinque pul&longs;us delectæ arteriæ is, iuxta iam-dicta, <lb/>intra primum pul&longs;um perueniet ad C, intra &longs;ecundum <lb/>ad D, intra tertium ad E, intra quartum ad F, in­<lb/>tra quintum ad A. <!-- KEEP S--></s> |
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| <s>Promoueatur tertio momento, <lb/>& malus &longs;it YZ: erit lapis in L. <!-- KEEP S--></s> | <s id="id.000305">Deinde ex G, proijciatur lapis <lb/>obliquè, ita vt perueniat ad B, vnde recidere incipiens <lb/>perueniat denique in H; is de&longs;cribet in aëre curuam <lb/>illam lineam GIKLMBNOPQH, quam mox di­<lb/>cebamus e&longs;&longs;e parabolicam. </s> |
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| <s>Promoueatur quarto, <lb/>& &longs;it malus a, b; erit lapis in M. </s> | <s id="id.000306">Po&longs;t-modum, non loqua­<lb/>mur ampliùs de turri, &longs;ed &longs;olùm de malo; neque de <lb/>malo quie&longs;cente, &longs;ed de moto, &longs;iue tran&longs;lato ad mo­<lb/>tum nauis, cui e&longs;t implantatus; ac e&longs;to planities, &longs;u­<lb/>perficie&longs;ve maris, per quam nauis fertur, &longs;ecundum <lb/>lineam GH, &longs;upponamu&longs;que malum e&longs;&longs;e GR, cùm <lb/>lapis ex G proijcitur &longs;ursùm directè in R, & eadem <lb/>quidem vi, qua peruenire po&longs;&longs;et præcisè ad R. quie&longs;-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.029.jpg" pagenum="22"/>cente malo. <lb/><figure id="id.027.00.029.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.029.1.jpg"/><lb/>promoucatur <lb/><expan abbr="cõ&longs;equenter">con&longs;equenter</expan> <lb/>nauis, adeò <lb/>vt intra vnum <lb/>momentum, <lb/>&longs;eu <expan abbr="pulsũ">pulsum</expan> ar­<lb/>teriæ malus <lb/>&longs;it factus ST; <lb/>tum quia la­<lb/>pis non de&longs;e­<lb/>rit malum, ne­<lb/>que ab illo <lb/>de&longs;eritur; erit <lb/>iuxta malum <lb/>in I directè <lb/>imminens pe­<lb/>di mali, &longs;iue <lb/>proximæ na­<lb/>uis parti è qua <lb/>e&longs;t facta pro­<lb/>jectio. </s> |
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| <s>Promoueatur quin­<lb/>to, & &longs;it malus AB; erit lapis in B; Ex quo v&longs;que <lb/>tendere deorsùm, cadereve incipiet; adeò vt cùm <pb pagenum="23"/>naui promota totidem momentis malus fuerit &longs;uc­<lb/>ce&longs;&longs;iuè cd, ef, gh, 1K, Hl; lapis &longs;it etiam futurus <lb/>&longs;ucce&longs;&longs;iuè in N, O, P, Q, ac tandem in H. </s></p><p type="main"> | <s id="id.000307">promo­<lb/>ueatur rursùs <lb/>nauis &longs;ecun­<lb/>do momento, & malus &longs;it VX; erit lapis pari, qua <lb/>antè ratione, in K. <!-- KEEP S--></s> |
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| <s>VII. <!-- KEEP S--></s> | <s id="id.000308">Promoueatur tertio momento, <lb/>& malus &longs;it YZ: erit lapis in L. <!-- KEEP S--></s> |
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| <s>Iam elicio <emph type="italics"/>primò,<emph.end type="italics"/> lineam, quam motu &longs;uo <lb/>de&longs;cribit lapis, apparere quidem iis, qui in naui &longs;unt, <lb/>e&longs;&longs;e rectam, perpendicularemque, hoc e&longs;t directam <lb/>&longs;ecundum longitudinem, erectionemque mali GR, <lb/>vel ST, vel VX, &c. </s> | <s id="id.000309">Promoueatur quarto, <lb/>& &longs;it malus a, b; erit lapis in M. </s> |
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| <s>cùm nempe ab eo lapis non di&longs;­<lb/>cedat: &longs;ed e&longs;&longs;e tamen reip&longs;â curuam, parabolicamve, <lb/>& qualis planè de&longs;criberetur, &longs;i quie&longs;cente naui, & <lb/>malo ex&longs;i&longs;tente AB lapis proijceretur obliquè ex G, <lb/>ver&longs;us B, decideretque in H. </s> | <s id="id.000310">Promoueatur quin­<lb/>to, & &longs;it malus AB; erit lapis in B; Ex quo v&longs;que <lb/>tendere deorsùm, cadereve incipiet; adeò vt cùm <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.030.jpg" pagenum="23"/>naui promota totidem momentis malus fuerit &longs;uc­<lb/>ce&longs;&longs;iuè cd, ef, gh, 1K, Hl; lapis &longs;it etiam futurus <lb/>&longs;ucce&longs;&longs;iuè in N, O, P, Q, ac tandem in H. <!-- KEEP S--></s></p><p type="main"> |
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| <s>Nec te moretur, quòd <lb/>linea curua GB &longs;it longior, quàm linea recta GR, ac <lb/>major proinde virtus requiratur ad proijciendum ex <lb/>G in B, quàm ex G in R, vel, quod e&longs;t idem, ex A in <lb/>B. </s> | <s id="id.000311">VII. <!-- KEEP S--></s> |
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| <s>Nam licet naui quie&longs;cente pro; ector majorem ap­<lb/>plicet virtutem, vt ex G proiiciat in B, quàm vt ex A <lb/>proiiciat in idem B; non requiritur tamen, vt naui mo­<lb/>ta, maiorem ex &longs;e applicet, ad ita proiiciendum, vt <lb/>lapis ex G perueniat ad locum B, quàm requiratur vt <lb/>ex G lapis perueniat ad R (quò ver&longs;us proiectio fit) <lb/>vel ex A ad ip&longs;um B: quoniam quod de e&longs;t applicitæ à <lb/>proiectore virtuti propriæ, vt lapis ex G perueniat ad <lb/>B, id &longs;uppletur vi tran&longs;latitia adiecta à naui: adeò vt, <lb/>cùm lapidis motus &longs;it compo&longs;itus ex motu &longs;ursùm, & <lb/>motu prorsùm, &longs;eu ex perpendiculari, & horizontali; <lb/>ip&longs;a quoque vis proiectionis ita &longs;it compo&longs;ita ex vi <lb/>proijcientis propria, & ex vi impre&longs;&longs;a à naui, vt quic­<lb/>quid e&longs;t motus &longs;ursùm à priore &longs;it, quicquid motus <lb/>prorsùm à po&longs;teriore; &longs;icque vis adiecta à naui, dum <pb pagenum="24"/>mouetur, &longs;it æ qualis illi exce&longs;&longs;ui, quo, naui quie&longs;cen­<lb/>te, vis proiiciens ex G in B, e&longs;t maior vi proiiciente ex <lb/>A in B. </s></p><p type="main"> | <s id="id.000312">Iam elicio <emph type="italics"/>primò,<emph.end type="italics"/> lineam, quam motu &longs;uo <lb/>de&longs;cribit lapis, apparere quidem iis, qui in naui &longs;unt, <lb/>e&longs;&longs;e rectam, perpendicularemque, hoc e&longs;t directam <lb/>&longs;ecundum longitudinem, erectionemque mali GR, <lb/>vel ST, vel VX, &c. </s> |
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| <s>Elicio <emph type="italics"/>Secundò,<emph.end type="italics"/> cùm lapis ex B verticè mali dimit­<lb/>titur, de&longs;cribere quidem ad ip&longs;um &longs;en&longs;um omnibus, <lb/>qui in naui &longs;unt, perpendicularem lineam; &longs;ed de&longs;­<lb/>cribere tamen reuerâ &longs;emi-parabolicam, qualis nem­<lb/>pe e&longs;t BNOPQH. </s> | <s id="id.000313">cùm nempe ab eo lapis non di&longs;­<lb/>cedat: &longs;ed e&longs;&longs;e tamen reip&longs;â curuam, parabolicamve, <lb/>& qualis planè de&longs;criberetur, &longs;i quie&longs;cente naui, & <lb/>malo ex&longs;i&longs;tente AB lapis proijceretur obliquè ex G, <lb/>ver&longs;us B, decideretque in H. <!-- KEEP S--></s> |
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| <s>Ratio autem apparet ex dictis. <lb/></s> | <s id="id.000314">Nec te moretur, quòd <lb/>linea curua GB &longs;it longior, quàm linea recta GR, ac <lb/>major proinde virtus requiratur ad proijciendum ex <lb/>G in B, quàm ex G in R, vel, quod e&longs;t idem, ex A in <lb/>B. </s> |
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| <s>Neque pote&longs;t morarite, quòd ad motum perpendi­<lb/>cularem nulla requiratur à proiiciente vis, grauita&longs;­<lb/>que &longs;ola lapidis &longs;ufficiat; ad motum verò illum &longs;emi­<lb/>parabolicum requiratur haud-dubiè. </s> | <s id="id.000315">Nam licet naui quie&longs;cente pro; ector majorem ap­<lb/>plicet virtutem, vt ex G proiiciat in B, quàm vt ex A <lb/>proiiciat in idem B; non requiritur tamen, vt naui mo­<lb/>ta, maiorem ex &longs;e applicet, ad ita proiiciendum, vt <lb/>lapis ex G perueniat ad locum B, quàm requiratur vt <lb/>ex G lapis perueniat ad R (quò ver&longs;us proiectio fit) <lb/>vel ex A ad ip&longs;um B: quoniam quod de e&longs;t applicitæ à <lb/>proiectore virtuti propriæ, vt lapis ex G perueniat ad <lb/>B, id &longs;uppletur vi tran&longs;latitia adiecta à naui: adeò vt, <lb/>cùm lapidis motus &longs;it compo&longs;itus ex motu &longs;ursùm, & <lb/>motu prorsùm, &longs;eu ex perpendiculari, & horizontali; <lb/>ip&longs;a quoque vis proiectionis ita &longs;it compo&longs;ita ex vi <lb/>proijcientis propria, & ex vi impre&longs;&longs;a à naui, vt quic­<lb/>quid e&longs;t motus &longs;ursùm à priore &longs;it, quicquid motus <lb/>prorsùm à po&longs;teriore; &longs;icque vis adiecta à naui, dum <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.031.jpg" pagenum="24"/>mouetur, &longs;it æ qualis illi exce&longs;&longs;ui, quo, naui quie&longs;cen­<lb/>te, vis proiiciens ex G in B, e&longs;t maior vi proiiciente ex <lb/>A in B. </s></p><p type="main"> |
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| <s>Siquidem con­<lb/>&longs;tat, nullam quidem vim projectoris propriam lapidi <lb/>imprimi, &longs;eu quie&longs;cat, &longs;eu moueatur malus; &longs;ed im­<lb/>primi tamen, dum nauis mouetur, tran&longs;latitiam, &longs;eu <lb/>qui ab ip&longs;a naui &longs;it; adeò vt cùm motus ille &longs;it com­<lb/>po&longs;itus ex perpendiculari, & horizontali, quicquid <lb/>e&longs;t in eo perpendicularis, à grauitate lapidis &longs;it; quic­<lb/>quid horizontalis, à vi, &longs;eu à motu ip&longs;ius nauis. </s></p><p type="main"> | <s id="id.000316">Elicio <emph type="italics"/>Secundò,<emph.end type="italics"/> cùm lapis ex B verticè mali dimit­<lb/>titur, de&longs;cribere quidem ad ip&longs;um &longs;en&longs;um omnibus, <lb/>qui in naui &longs;unt, perpendicularem lineam; &longs;ed de&longs;­<lb/>cribere tamen reuerâ &longs;emi-parabolicam, qualis nem­<lb/>pe e&longs;t BNOPQH. </s> |
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| <s>Elicio <emph type="italics"/>Tertiò,<emph.end type="italics"/> neutram harum virium tam in <lb/>proiecto &longs;ur&longs;um, quàm in dimi&longs;&longs;o deor&longs;ùm de&longs;truere <lb/>alteram, illamve imminüere; &longs;ed deflectere dunta­<lb/>xat; adeò vt lapis neque minùs &longs;ursùm, neque minùs <lb/>pror&longs;ùm tendat, quàm &longs;i viribus &longs;eparatis, alterâ <lb/>&longs;ursùm proijceretur, altera pror&longs;ùm propelleretur: <lb/>&longs;ed impediatur duntaxat rectitudo lineæ, quam ha­<lb/>berent &longs;eor&longs;im perpendicularis, & horizontalis, <lb/>componaturque linea, quæ &longs;it quidem breuior per­<lb/>pendiculari, & horizontali, &longs;i &longs;eor&longs;im de&longs;criptæ &longs;imùl <lb/><gap/>ung<gap/>tur; verùm quæ illis æquiualoat, ob collatas <pb pagenum="25"/>vircis in idem mobile; ea proportione, qua tempus, <lb/>breuius quidem e&longs;t temporibus &longs;eor&longs;im &longs;umptis; &longs;ed <lb/>illis tamen æquiualet, propter coniunctas in eo­<lb/>dem mobili velocitates. </s></p><p type="main"> | <s id="id.000317">Ratio autem apparet ex dictis. <lb/></s> |
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| <s>Elicio <emph type="italics"/>quartò,<emph.end type="italics"/> Tempus, quo lapis a&longs;cendit, e&longs;&longs;e <lb/>æquale tempori, quo de&longs;cendit. </s> | <s id="id.000318">Neque pote&longs;t morarite, quòd ad motum perpendi­<lb/>cularem nulla requiratur à proiiciente vis, grauita&longs;­<lb/>que &longs;ola lapidis &longs;ufficiat; ad motum verò illum &longs;emi­<lb/>parabolicum requiratur haud-dubiè. </s> |
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| <s>Quippe cùm ma­<lb/>lus æquali cur&longs;u progrediatur, &longs;eu æqualibus tempo­<lb/>ribus æqualia &longs;patia conficiat; & lapis non magis in <lb/>a&longs;cen&longs;u, quàm in ex&longs;cen&longs;u illum de&longs;erat, aut ad eum <lb/>accedat, &longs;ed perinde &longs;emper re&longs;pectu illius &longs;e habeat: <lb/>nece&longs;&longs;e e&longs;t tantundem temporis in a&longs;cen&longs;u, quantùm <lb/>in ex&longs;cen&longs;u con&longs;umi; &longs;icque lapidem nec &longs;egniùs, <lb/>nec tardiùs ex G peruenire ad B, quàm ex B peruenit <lb/>ad H. </s> | <s id="id.000319">Siquidem con­<lb/>&longs;tat, nullam quidem vim projectoris propriam lapidi <lb/>imprimi, &longs;eu quie&longs;cat, &longs;eu moueatur malus; &longs;ed im­<lb/>primi tamen, dum nauis mouetur, tran&longs;latitiam, &longs;eu <lb/>qui ab ip&longs;a naui &longs;it; adeò vt cùm motus ille &longs;it com­<lb/>po&longs;itus ex perpendiculari, & horizontali, quicquid <lb/>e&longs;t in eo perpendicularis, à grauitate lapidis &longs;it; quic­<lb/>quid horizontalis, à vi, &longs;eu à motu ip&longs;ius nauis. </s></p><p type="main"> |
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| <s>Nempe vt &longs;patium ex G in A, quod pes mali <lb/>peruadit a&longs;cendente lapide, æquale e&longs;t &longs;patio ex A <lb/>in H, quod idem peruadit lapide de&longs;cendente. </s></p><p type="main"> | <s id="id.000320">Elicio <emph type="italics"/>Tertiò,<emph.end type="italics"/> neutram harum virium tam in <lb/>proiecto &longs;ur&longs;um, quàm in dimi&longs;&longs;o deor&longs;ùm de&longs;truere <lb/>alteram, illamve imminüere; &longs;ed deflectere dunta­<lb/>xat; adeò vt lapis neque minùs &longs;ursùm, neque minùs <lb/>pror&longs;ùm tendat, quàm &longs;i viribus &longs;eparatis, alterâ <lb/>&longs;ursùm proijceretur, altera pror&longs;ùm propelleretur: <lb/>&longs;ed impediatur duntaxat rectitudo lineæ, quam ha­<lb/>berent &longs;eor&longs;im perpendicularis, & horizontalis, <lb/>componaturque linea, quæ &longs;it quidem breuior per­<lb/>pendiculari, & horizontali, &longs;i &longs;eor&longs;im de&longs;criptæ &longs;imùl <lb/><gap/>ung<gap/>tur; verùm quæ illis æquiualoat, ob collatas <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.032.jpg" pagenum="25"/>vircis in idem mobile; ea proportione, qua tempus, <lb/>breuius quidem e&longs;t temporibus &longs;eor&longs;im &longs;umptis; &longs;ed <lb/>illis tamen æquiualet, propter coniunctas in eo­<lb/>dem mobili velocitates. </s></p><p type="main"> |
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| <s>Elicio <emph type="italics"/>quintò,<emph.end type="italics"/> Velocitatem motus eadem propor­<lb/>tione reciprocè accepta a&longs;cendendo decre&longs;cere, qua <lb/>de&longs;cendendo incre&longs;cit; ita vt tam initio a&longs;<gap/>s, <lb/>quàm in fine de&longs;cen&longs;us &longs;it maxima; in fine a<gap/>, <lb/>& initio de&longs;cen&longs;us, minima, & in mediis proportione <lb/>&longs;patiis, medio proportione modo &longs;e habeat. </s> | <s id="id.000321">Elicio <emph type="italics"/>quartò,<emph.end type="italics"/> Tempus, quo lapis a&longs;cendit, e&longs;&longs;e <lb/>æquale tempori, quo de&longs;cendit. </s> |
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| <s>Quippe, <lb/>cùm in ea proportione, qua lapis de&longs;cendit, &longs;it in ea­<lb/>dem &longs;emper di&longs;tantia à malo, con&longs;tat: &longs;i malo ea­<lb/>dem æquabilitate tran&longs;lato, dum lapis a&longs;cendit, ip&longs;e <lb/>lapis non tueretur proportionem expo&longs;itam, adeò <lb/>vt celerius, aut tardiùs moueretur alicubi in pari al­<lb/>titudine; con&longs;tat, inquam, fore vt lapis non eandem <lb/>&longs;imiliter tueretur di&longs;tantiam, &longs;ed magis ad malum ac­<lb/>cederet, vel ab illo de&longs;ereretur, quod tamen non <pb pagenum="26"/>facit. </s> | <s id="id.000322">Quippe cùm ma­<lb/>lus æquali cur&longs;u progrediatur, &longs;eu æqualibus tempo­<lb/>ribus æqualia &longs;patia conficiat; & lapis non magis in <lb/>a&longs;cen&longs;u, quàm in ex&longs;cen&longs;u illum de&longs;erat, aut ad eum <lb/>accedat, &longs;ed perinde &longs;emper re&longs;pectu illius &longs;e habeat: <lb/>nece&longs;&longs;e e&longs;t tantundem temporis in a&longs;cen&longs;u, quantùm <lb/>in ex&longs;cen&longs;u con&longs;umi; &longs;icque lapidem nec &longs;egniùs, <lb/>nec tardiùs ex G peruenire ad B, quàm ex B peruenit <lb/>ad H. <!-- KEEP S--></s> |
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| <s>Ex quo &longs;equitur, vt quemadmodum in primo <lb/>momento de&longs;cen&longs;us peruenit ex B ad N, ita in vltimo <lb/>a&longs;cen&longs;us perueniat ad B ex M, paris altitudinis cum N. <lb/></s> | <s id="id.000323">Nempe vt &longs;patium ex G in A, quod pes mali <lb/>peruadit a&longs;cendente lapide, æquale e&longs;t &longs;patio ex A <lb/>in H, quod idem peruadit lapide de&longs;cendente. </s></p><p type="main"> |
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| <s>Et quemadmodum in &longs;ecundo de&longs;cen&longs;us ex N per­<lb/>uenit ad O; ita in penultimo a&longs;cen&longs;us perueniat ad M <lb/>ex L, atque ita con&longs;equenter; donec vt in vltimo de&longs;­<lb/>cen&longs;us peruenit ad H ex Q, ita in primo a&longs;cen&longs;us ex <lb/>G perueniat ad I, cuius altitudo altitudini Q e&longs;t <lb/>æqualis. </s></p><p type="main"> | <s id="id.000324">Elicio <emph type="italics"/>quintò,<emph.end type="italics"/> Velocitatem motus eadem propor­<lb/>tione reciprocè accepta a&longs;cendendo decre&longs;cere, qua <lb/>de&longs;cendendo incre&longs;cit; ita vt tam initio a&longs;<gap/>s, <lb/>quàm in fine de&longs;cen&longs;us &longs;it maxima; in fine a<gap/>, <lb/>& initio de&longs;cen&longs;us, minima, & in mediis proportione <lb/>&longs;patiis, medio proportione modo &longs;e habeat. </s> |
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| <s>Elicio <emph type="italics"/>&longs;exiò,<emph.end type="italics"/> Proportionem incrementi velocitatis <lb/>de&longs;cen&longs;us per lineam BH, dum malus mouetur, e&longs;&longs;e <lb/>eandem, quæ per lineam BA, cum malus quie&longs;cit. <lb/></s> | <s id="id.000325">Quippe, <lb/>cùm in ea proportione, qua lapis de&longs;cendit, &longs;it in ea­<lb/>dem &longs;emper di&longs;tantia à malo, con&longs;tat: &longs;i malo ea­<lb/>dem æquabilitate tran&longs;lato, dum lapis a&longs;cendit, ip&longs;e <lb/>lapis non tueretur proportionem expo&longs;itam, adeò <lb/>vt celerius, aut tardiùs moueretur alicubi in pari al­<lb/>titudine; con&longs;tat, inquam, fore vt lapis non eandem <lb/>&longs;imiliter tueretur di&longs;tantiam, &longs;ed magis ad malum ac­<lb/>cederet, vel ab illo de&longs;ereretur, quod tamen non <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.033.jpg" pagenum="26"/>facit. </s> |
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| <s>Quippe cùm incre&longs;cente velocitate perueniat tam in <lb/>primo ca&longs;u ad H, quàm in &longs;ecundo ad A, patet, &longs;i <lb/>de&longs;cen&longs;us in &longs;ecundo ca&longs;u terminaretur ad altitudi­<lb/>nem F, fore vt in primo terminaretur ad altitu dinem <lb/>Q æqualem altitudini F. Et, &longs;i illeic terminaretur ad <lb/>E, fore vt heic ad P: &longs;i illeic ad D, heic ad O, &longs;i illeic <lb/>ad C, heic ad N. </s> | <s id="id.000326">Ex quo &longs;equitur, vt quemadmodum in primo <lb/>momento de&longs;cen&longs;us peruenit ex B ad N, ita in vltimo <lb/>a&longs;cen&longs;us perueniat ad B ex M, paris altitudinis cum N. <lb/><!-- KEEP S--></s> |
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| <s>Quare & progre&longs;&longs;u facto nece&longs;&longs;e <lb/>e&longs;t eadem proportione ac qui&longs;itam e&longs;&longs;e velocitatem <lb/>per parteis lineæ B, N, O, P, Q, H, ac per parteis lineæ <lb/>B, C, D, E, F, A. </s></p><p type="main"> | <s id="id.000327">Et quemadmodum in &longs;ecundo de&longs;cen&longs;us ex N per­<lb/>uenit ad O; ita in penultimo a&longs;cen&longs;us perueniat ad M <lb/>ex L, atque ita con&longs;equenter; donec vt in vltimo de&longs;­<lb/>cen&longs;us peruenit ad H ex Q, ita in primo a&longs;cen&longs;us ex <lb/>G perueniat ad I, cuius altitudo altitudini Q e&longs;t <lb/>æqualis. </s></p><p type="main"> |
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| <s>Elicio <emph type="italics"/>&longs;eptimò,<emph.end type="italics"/> Proportionem decrementi veloci­<lb/>tatis in a&longs;cen&longs;u per lineam GB, e&longs;&longs;e reciprocè ean­<lb/>dem, quæ incrementi in de&longs;cen&longs;u per lineam BA; <lb/>adeò vt, quemadmodum illeic, in primo momento <lb/>peruenitur ex B ad C, ita heic in vltimo perueniatur <lb/>ad B ex M, altitudinis æqualis ip&longs;i C; & vt illeic in <lb/>&longs;ecundo peruenitur ex C ad D; ita heic in penultimo <lb/>perueniatur ad M ex L, altitudinis eiu&longs;dem cum D: <pb pagenum="27"/>at que ita con­<lb/><figure id="fig2"/><lb/>&longs;equenter; do­<lb/>nec, vt illeic <lb/>in vltimo per­<lb/>uenitur ad A <lb/>ex F; ita heic <lb/>in primo per­<lb/>ueniatur ex G <lb/>ad I, altitudi­<lb/>nis cum F æ­<lb/>qualis. </s> | <s id="id.000328">Elicio <emph type="italics"/>&longs;exiò,<emph.end type="italics"/> Proportionem incrementi velocitatis <lb/>de&longs;cen&longs;us per lineam BH, dum malus mouetur, e&longs;&longs;e <lb/>eandem, quæ per lineam BA, cum malus quie&longs;cit. <lb/></s> |
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| <s>Quip­<lb/>pe ex Elicito <lb/>&longs;exto, eadem <lb/>e&longs;t velocitatis <lb/>proportio &longs;e­<lb/>cundú lineam <lb/>BA, quæ &longs;e­<lb/>cundum <expan abbr="lineã">lineam</expan> <lb/>BH: & ex <lb/>Elicito quin­<lb/>to, eadem e&longs;t <lb/>&longs;ecundum li­<lb/>neam BG, <lb/>quæ &longs;ecundum eandem lineam BH. </s> | <s id="id.000329">Quippe cùm incre&longs;cente velocitate perueniat tam in <lb/>primo ca&longs;u ad H, quàm in &longs;ecundo ad A, patet, &longs;i <lb/>de&longs;cen&longs;us in &longs;ecundo ca&longs;u terminaretur ad altitudi­<lb/>nem F, fore vt in primo terminaretur ad altitu dinem <lb/>Q æqualem altitudini F. Et, &longs;i illeic terminaretur ad <lb/>E, fore vt heic ad P: &longs;i illeic ad D, heic ad O, &longs;i illeic <lb/>ad C, heic ad N. <!-- KEEP S--></s> |
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| <s>Quamobrem <lb/>non pote&longs;t e&longs;&longs;e alia (reciprocè tamen accipiendo) &longs;e­<lb/>cundum lineam BG, quàm &longs;ecundum lineam BA; <lb/>cùm quæ &longs;unt eadem, æqualiave vni tertio, non po&longs;­<lb/>&longs;int non e&longs;&longs;e eadem, æqualiave inter &longs;e. </s></p><p type="main"> | <s id="id.000330">Quare & progre&longs;&longs;u facto nece&longs;&longs;e <lb/>e&longs;t eadem proportione ac qui&longs;itam e&longs;&longs;e velocitatem <lb/>per parteis lineæ B, N, O, P, Q, H, ac per parteis lineæ <lb/>B, C, D, E, F, A. <!-- KEEP S--></s></p><p type="main"> |
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| <s>Elicio <emph type="italics"/>octauò,<emph.end type="italics"/> Malo etiam quie&longs;cente, & vniuer&longs;è <lb/>in omni projectione &longs;ur&longs;ùm facta, decrementum ve-<pb pagenum="28"/>locitatis a&longs;cendendo e&longs;&longs;e eundem reciprocè cum in­<lb/>cremento velocitatis de&longs;cendendo: adeò vt, quem­<lb/>admodum in vltimo de&longs;cen&longs;us momento percurritur <lb/>&longs;patium FA, ita in primo a&longs;cen&longs;us percurratur idem <lb/>&longs;patium AF; & quemadmodum in penultimo de&longs;­<lb/>cen&longs;us percurritur EF; ita in &longs;ecundo a&longs;cen&longs;us FE, & <lb/>ita con&longs;equenter, donec: vt in primo de&longs;cen&longs;us per­<lb/>curritur BC, ita in vltimo a&longs;cen&longs;us percurratur CB. <lb/>Quippe, cùm ex iam dictis perinde &longs;e habeant AF, & <lb/>FA, ac &longs;e habent GI, & QH; & perinde quoque C <lb/>B, & BC, ac MB, & BN, & ita de aliis. </s></p><p type="main"> | <s id="id.000331">Elicio <emph type="italics"/>&longs;eptimò,<emph.end type="italics"/> Proportionem decrementi veloci­<lb/>tatis in a&longs;cen&longs;u per lineam GB, e&longs;&longs;e reciprocè ean­<lb/>dem, quæ incrementi in de&longs;cen&longs;u per lineam BA; <lb/>adeò vt, quemadmodum illeic, in primo momento <lb/>peruenitur ex B ad C, ita heic in vltimo perueniatur <lb/>ad B ex M, altitudinis æqualis ip&longs;i C; & vt illeic in <lb/>&longs;ecundo peruenitur ex C ad D; ita heic in penultimo <lb/>perueniatur ad M ex L, altitudinis eiu&longs;dem cum D: <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.034.jpg" pagenum="27"/>at que ita con­<lb/><figure id="id.027.00.034.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.034.1.jpg"/><lb/>&longs;equenter; do­<lb/>nec, vt illeic <lb/>in vltimo per­<lb/>uenitur ad A <lb/>ex F; ita heic <lb/>in primo per­<lb/>ueniatur ex G <lb/>ad I, altitudi­<lb/>nis cum F æ­<lb/>qualis. </s> |
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| <s>Elicio <emph type="italics"/>nonò,<emph.end type="italics"/> cùm lapis per lineam parabolicam mo­<lb/>tus perueniat ex puncto G pro impetu quidem, <lb/>quem habet &longs;ur&longs;um, ad B, & pro eo, quem prorsùm, <lb/>ad H: percurrerere illum quidem æqualibus tempori­<lb/>bus &longs;ecundum impetum priorem inæqualia &longs;patia; &longs;ed <lb/>&longs;ecundum po&longs;teriorem, æqualia. </s> | <s id="id.000332">Quip­<lb/>pe ex Elicito <lb/>&longs;exto, eadem <lb/>e&longs;t velocitatis <lb/>proportio &longs;e­<lb/>cundú lineam <lb/>BA, quæ &longs;e­<lb/>cundum <expan abbr="lineã">lineam</expan> <lb/>BH: & ex <lb/>Elicito quin­<lb/>to, eadem e&longs;t <lb/>&longs;ecundum li­<lb/>neam BG, <lb/>quæ &longs;ecundum eandem lineam BH. </s> |
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| <s>Con&longs;tat quippe AF <lb/>altitudinem, &longs;eu <expan abbr="portion&etilde;">portionem</expan> perpendiculi re&longs;pondentem <lb/>motui per GI, e&longs;&longs;e majorem, quàm FE altitu dinem re&longs;­<lb/>pondentem motui per IK; cùm tamen GS. latitudo, &longs;eu <lb/>portio plani horizontalis re&longs;pondens motui per <expan abbr="eand&etilde;">eandem</expan> <lb/>GI, &longs;it æqualis latitudini SV re&longs;pondenti motui per <lb/>eandem IK; atqueita de cæteris. </s> | <s id="id.000333">Quamobrem <lb/>non pote&longs;t e&longs;&longs;e alia (reciprocè tamen accipiendo) &longs;e­<lb/>cundum lineam BG, quàm &longs;ecundum lineam BA; <lb/>cùm quæ &longs;unt eadem, æqualiave vni tertio, non po&longs;­<lb/>&longs;int non e&longs;&longs;e eadem, æqualiave inter &longs;e. </s></p><p type="main"> |
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| <s>A deò vt motus quidem <lb/>&longs;ursùm, vel deorsùm inæqualis &longs;it; &longs;ed motus prorsùm, <lb/>vel &longs;ecundum horizontem &longs;it planè æquabilis, atque <lb/>vniformis. </s></p><p type="main"> | <s id="id.000334">Elicio <emph type="italics"/>octauò,<emph.end type="italics"/> Malo etiam quie&longs;cente, & vniuer&longs;è <lb/>in omni projectione &longs;ur&longs;ùm facta, decrementum ve-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.035.jpg" pagenum="28"/>locitatis a&longs;cendendo e&longs;&longs;e eundem reciprocè cum in­<lb/>cremento velocitatis de&longs;cendendo: adeò vt, quem­<lb/>admodum in vltimo de&longs;cen&longs;us momento percurritur <lb/>&longs;patium FA, ita in primo a&longs;cen&longs;us percurratur idem <lb/>&longs;patium AF; & quemadmodum in penultimo de&longs;­<lb/>cen&longs;us percurritur EF; ita in &longs;ecundo a&longs;cen&longs;us FE, & <lb/>ita con&longs;equenter, donec: vt in primo de&longs;cen&longs;us per­<lb/>curritur BC, ita in vltimo a&longs;cen&longs;us percurratur CB. <lb/>Quippe, cùm ex iam dictis perinde &longs;e habeant AF, & <lb/>FA, ac &longs;e habent GI, & QH; & perinde quoque C <lb/>B, & BC, ac MB, & BN, & ita de aliis. </s></p><p type="main"> |
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| <s>Elicio <emph type="italics"/>decimò,<emph.end type="italics"/> cùm nauis po&longs;&longs;it moueri velociùs, & <lb/>tardiùs; & mali tamen altitudo &longs;emper eadem &longs;it; &longs;ieri <lb/>po&longs;&longs;e, vt linea parabolica efficiatur diuer&longs;imodè nunc <lb/>apertior, nunc contractior; & nihilominùs percur-<pb pagenum="29"/>ratur &longs;emper æqualibus temporibus. </s> | <s id="id.000335">Elicio <emph type="italics"/>nonò,<emph.end type="italics"/> cùm lapis per lineam parabolicam mo­<lb/>tus perueniat ex puncto G pro impetu quidem, <lb/>quem habet &longs;ur&longs;um, ad B, & pro eo, quem prorsùm, <lb/>ad H: percurrerere illum quidem æqualibus tempori­<lb/>bus &longs;ecundum impetum priorem inæqualia &longs;patia; &longs;ed <lb/>&longs;ecundum po&longs;teriorem, æqualia. </s> |
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| <s>Sen&longs;us e&longs;t, cùm <lb/>&longs;patium GH, quod &longs;uppo&longs;ui à naui peruadi momen­<lb/>tis decem, po&longs;&longs;it fieri contractius, ita vt ii&longs;dem decem <lb/>momentis, &longs;eu æquali tempore non percurratur, ni&longs;i <lb/>&longs;patium Si, vel V g, vel Y e vel a c:&longs;icque lineæ parabo­<lb/>licæ ex S, in B, ad v&longs;que <gap/>; vel ex V, in B, ad v&longs;que g, & c. <lb/></s> | <s id="id.000336">Con&longs;tat quippe AF <lb/>altitudinem, &longs;eu <expan abbr="portion&etilde;">portionem</expan> perpendiculi re&longs;pondentem <lb/>motui per GI, e&longs;&longs;e majorem, quàm FE altitu dinem re&longs;­<lb/>pondentem motui per IK; cùm tamen GS. latitudo, &longs;eu <lb/>portio plani horizontalis re&longs;pondens motui per <expan abbr="eand&etilde;">eandem</expan> <lb/>GI, &longs;it æqualis latitudini SV re&longs;pondenti motui per <lb/>eandem IK; atqueita de cæteris. </s> |
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| <s>&longs;iant &longs;emper contractiores, quàm &longs;it GBH: Et cùm <lb/>è contra idem &longs;patium po&longs;&longs;it &longs;ieri amplius; ita vt ii&longs;dem <lb/>decem momentis, &longs;eu æquali tempore percurratur &longs;pa­<lb/>tium duplò, triplò, quadruplò, & <expan abbr="quantumcúmq;">quantumcúmque</expan> vo­<lb/>les, pro nauis celeritate, expan&longs;ius; &longs;icque lineæ parabo­<lb/>licæ fiant &longs;emper, &longs;emperque apertiores, quàm &longs;it ea­<lb/>dem parabolica GBH: Nihilominùs neque lapidem <lb/>per contractiores motum, perua&longs;urum illas tempore <lb/>breuiore; neque motum per appertiores, perua&longs;urum <lb/>ip&longs;as tempore longiore, quàm &longs;it tempus, quo per­<lb/>uadit memoratam GBH. Quippe, &longs;cu nauis celeriter, <lb/>&longs;eu tardè moueatur, tantundem &longs;emper temporis in­<lb/>&longs;umit lapis, vt ex pede mali A, perueniat ad verticem <lb/>B; & rursùs tantundem, vt ex vertice B, perueniat ad <lb/>pedem A. </s> | <s id="id.000337">A deò vt motus quidem <lb/>&longs;ursùm, vel deorsùm inæqualis &longs;it; &longs;ed motus prorsùm, <lb/>vel &longs;ecundum horizontem &longs;it planè æquabilis, atque <lb/>vniformis. </s></p><p type="main"> |
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| <s>Quare & cùm intereà de&longs;cribantur per aërem <lb/>lineæ parabolicæ inæquales, nece&longs;&longs;e e&longs;t &longs;emper de&longs;cri­<lb/>bant æqualibus temporibus: omnibus putà exæqua­<lb/>tis vni, eidemque tempori, quod in&longs;umitur ex A in <lb/>B, & ex B in A, communi men&longs;ura. </s></p><p type="main"> | <s id="id.000338">Elicio <emph type="italics"/>decimò,<emph.end type="italics"/> cùm nauis po&longs;&longs;it moueri velociùs, & <lb/>tardiùs; & mali tamen altitudo &longs;emper eadem &longs;it; &longs;ieri <lb/>po&longs;&longs;e, vt linea parabolica efficiatur diuer&longs;imodè nunc <lb/>apertior, nunc contractior; & nihilominùs percur-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.036.jpg" pagenum="29"/>ratur &longs;emper æqualibus temporibus. </s> |
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| <s>Elicio <emph type="italics"/>vndecimò,<emph.end type="italics"/> Si lapis dimittatur ex B, & loco <lb/>de&longs;cen&longs;us per lineam &longs;emiparabolicam BH, de&longs;cribat <lb/>etiam quantùm voles vel contractiorem, vel apertio­<lb/>rem: perua&longs;urum tamen omneis eiu&longs;cemodi &longs;emipara­<lb/>bolicas lineas æqualibus temperibus: Quippe ea om-<pb pagenum="30"/>nia exæquantur eidem tempori de&longs;cen&longs;us ex B in A: id­<lb/>q<gap/>e cùm &longs;it eadem ratio dimidiæ ad dimidiam, quæ <lb/>totius ad totam. </s> | <s id="id.000339">Sen&longs;us e&longs;t, cùm <lb/>&longs;patium GH, quod &longs;uppo&longs;ui à naui peruadi momen­<lb/>tis decem, po&longs;&longs;it fieri contractius, ita vt ii&longs;dem decem <lb/>momentis, &longs;eu æquali tempore non percurratur, ni&longs;i <lb/>&longs;patium Si, vel V g, vel Y e vel a c:&longs;icque lineæ parabo­<lb/>licæ ex S, in B, ad v&longs;que <gap/>; vel ex V, in B, ad v&longs;que g, & c. <lb/><!-- REMOVE S-->&longs;iant &longs;emper contractiores, quàm &longs;it GBH: Et cùm <lb/>è contra idem &longs;patium po&longs;&longs;it &longs;ieri amplius; ita vt ii&longs;dem <lb/>decem momentis, &longs;eu æquali tempore percurratur &longs;pa­<lb/>tium duplò, triplò, quadruplò, & <expan abbr="quantumcúmq;">quantumcúmque</expan> vo­<lb/>les, pro nauis celeritate, expan&longs;ius; &longs;icque lineæ parabo­<lb/>licæ fiant &longs;emper, &longs;emperque apertiores, quàm &longs;it ea­<lb/>dem parabolica GBH: Nihilominùs neque lapidem <lb/>per contractiores motum, perua&longs;urum illas tempore <lb/>breuiore; neque motum per appertiores, perua&longs;urum <lb/>ip&longs;as tempore longiore, quàm &longs;it tempus, quo per­<lb/>uadit memoratam GBH. Quippe, &longs;cu nauis celeriter, <lb/>&longs;eu tardè moueatur, tantundem &longs;emper temporis in­<lb/>&longs;umit lapis, vt ex pede mali A, perueniat ad verticem <lb/>B; & rursùs tantundem, vt ex vertice B, perueniat ad <lb/>pedem A. <!-- KEEP S--></s> |
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| <s>Neque id debet tam in hoc, quàm <lb/>&longs;uperiore Elicito videri mirum; quoniam, vt nulla e&longs;t <lb/>diuer&longs;itas in motu perpendiculari, &longs;eu qui e&longs;t &longs;ursùm, <lb/>ac deor&longs;um, quatenùs tantundem &longs;emper a&longs;cenditur, <lb/>de&longs;cenditurque; & di&longs;erimen &longs;olùm e&longs;t in motu hori­<lb/>zontali, &longs;iue qui e&longs;t prorsùm, quatenùs citeriùs, vlte­<lb/>riú&longs;que proceditur: ita vis impellens &longs;ur&longs;um, quæ à <lb/>proijciente, vt propria emanat, e&longs;t vniformis &longs;emper, ac <lb/>eadem; & contrà vis impellens prorsùm, quæ, vt tran&longs;la­<lb/>titia à nauis motu imprimitur, inæqualis e&longs;t, & pro rati­<lb/>one tarditatis, aut velocitatis nunc minor, nunc major. </s></p><p type="main"> | |
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| <s>Elicio <emph type="italics"/>duo decimò,<emph.end type="italics"/> quacúmque vi aliquid &longs;ursùm ex <lb/>pede mali, donec mouetur, proijciatur, id ad pedem <lb/>mali &longs;emper reca&longs;urum. </s> | |
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| <s>Quippe, &longs;eu ad &longs;ummum ma­<lb/>lum non perueniat, &longs;eu vlteriùs longè prouchatur, <lb/>de&longs;cribit &longs;emper lineam parabolicam, in qua, vbicúm­<lb/>que ex&longs;i&longs;tat, reperitur &longs;emper in eadem di&longs;tantia vel à <lb/>malo, vel à linea &longs;ur&longs;um à malo &longs;ecundum illius lon­<lb/>gitudinem produci concepta. </s> | <s id="id.000340">Quare & cùm intereà de&longs;cribantur per aërem <lb/>lineæ parabolicæ inæquales, nece&longs;&longs;e e&longs;t &longs;emper de&longs;cri­<lb/>bant æqualibus temporibus: omnibus putà exæqua­<lb/>tis vni, eidemque tempori, quod in&longs;umitur ex A in <lb/>B, & ex B in A, communi men&longs;ura. </s></p><p type="main"> |
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| <s>Nec te verò motetur <lb/>globus bellico totmento è pede mali &longs;ur&longs;um explo&longs;us; <lb/>nam par omninô ratio e&longs;t. </s> | <s id="id.000341">Elicio <emph type="italics"/>vndecimò,<emph.end type="italics"/> Si lapis dimittatur ex B, & loco <lb/>de&longs;cen&longs;us per lineam &longs;emiparabolicam BH, de&longs;cribat <lb/>etiam quantùm voles vel contractiorem, vel apertio­<lb/>rem: perua&longs;urum tamen omneis eiu&longs;cemodi &longs;emipara­<lb/>bolicas lineas æqualibus temperibus: Quippe ea om-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.037.jpg" pagenum="30"/>nia exæquantur eidem tempori de&longs;cen&longs;us ex B in A: id­<lb/>q<gap/>e cùm &longs;it eadem ratio dimidiæ ad dimidiam, quæ <lb/>totius ad totam. </s> |
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| <s>Et quamuis ob&longs;tare videa­<lb/>tur rectitudo fi&longs;tulæ; nihilominùs, quia globus, quan­<lb/>tumcúm que tempore &longs;en&longs;um fugiente fi&longs;tulam perua­<lb/>dat, peruadit tamen &longs;ucce&longs;&longs;iuè, e&longs;t que reip&longs;à priùs in <lb/>inferioribus eius partibus, quàm in &longs;uperioribus; inde <lb/>fit, vt cùm &longs;i&longs;tula per hæc priora, & po&longs;teriora mo­<lb/>menta, moueatur interim ad motum nauis; idcircô <lb/>globus, preter motum &longs;ur&longs;um, promoueatur etiam in-<pb pagenum="31"/>tereà prorsùm, &longs;ecundum illum tantillum motum, & <lb/>dum ex&longs;iliendo per &longs;i&longs;tulam tran&longs;it, incipiat de&longs;cribere <lb/>parabolicam lineam, quam deinceps per aerem de&longs;­<lb/>cribere pergat; neque huic de&longs;criptioni magis ob&longs;tet <lb/>rectitudo fi&longs;tulæ, quàm rectitudo ip&longs;ius mali. </s> | <s id="id.000342">Neque id debet tam in hoc, quàm <lb/>&longs;uperiore Elicito videri mirum; quoniam, vt nulla e&longs;t <lb/>diuer&longs;itas in motu perpendiculari, &longs;eu qui e&longs;t &longs;ursùm, <lb/>ac deor&longs;um, quatenùs tantundem &longs;emper a&longs;cenditur, <lb/>de&longs;cenditurque; & di&longs;erimen &longs;olùm e&longs;t in motu hori­<lb/>zontali, &longs;iue qui e&longs;t prorsùm, quatenùs citeriùs, vlte­<lb/>riú&longs;que proceditur: ita vis impellens &longs;ur&longs;um, quæ à <lb/>proijciente, vt propria emanat, e&longs;t vniformis &longs;emper, ac <lb/>eadem; & contrà vis impellens prorsùm, quæ, vt tran&longs;la­<lb/>titia à nauis motu imprimitur, inæqualis e&longs;t, & pro rati­<lb/>one tarditatis, aut velocitatis nunc minor, nunc major. </s></p><p type="main"> |
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| <s>Addo, <lb/>cùm e&longs;&longs;emus in ip&longs;a triremi, nobilem Vincegue<gap/>ram <lb/>recita&longs;&longs;e optimo Proregi, nobi&longs;que circon&longs;tantibus <lb/>experimentum &longs;uo iu&longs;&longs;u factum, quod heic omitti non <lb/>debeat. </s> | <s id="id.000343">Elicio <emph type="italics"/>duo decimò,<emph.end type="italics"/> quacúmque vi aliquid &longs;ursùm ex <lb/>pede mali, donec mouetur, proijciatur, id ad pedem <lb/>mali &longs;emper reca&longs;urum. </s> |
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| <s>A&longs;&longs;eruït enim &longs;e aliquando naui cuipiam <lb/>imperitantem, & cùm illa &longs;ecundo vento, ac velo­<lb/>ci&longs;&longs;imè transferretur, iu&longs;&longs;i&longs;&longs;e è fa&longs;tigio mali explodi <lb/>&longs;ursùm fi&longs;tulâ pi&longs;toleto dictâ plumbeum globulum; <lb/>ac ip&longs;um aliquantò pò&longs;t decidi&longs;&longs;e ad pedem mali. </s></p><p type="main"> | <s id="id.000344">Quippe, &longs;eu ad &longs;ummum ma­<lb/>lum non perueniat, &longs;eu vlteriùs longè prouchatur, <lb/>de&longs;cribit &longs;emper lineam parabolicam, in qua, vbicúm­<lb/>que ex&longs;i&longs;tat, reperitur &longs;emper in eadem di&longs;tantia vel à <lb/>malo, vel à linea &longs;ur&longs;um à malo &longs;ecundum illius lon­<lb/>gitudinem produci concepta. </s> |
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| <s>VIII. <!-- KEEP S--></s> | <s id="id.000345">Nec te verò motetur <lb/>globus bellico totmento è pede mali &longs;ur&longs;um explo&longs;us; <lb/>nam par omninô ratio e&longs;t. </s> |
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| <s>Prætereo po&longs;&longs;e ex eadem figura alia quo­<lb/>que ex memoratis experimentis intelligi. </s> | <s id="id.000346">Et quamuis ob&longs;tare videa­<lb/>tur rectitudo fi&longs;tulæ; nihilominùs, quia globus, quan­<lb/>tumcúm que tempore &longs;en&longs;um fugiente fi&longs;tulam perua­<lb/>dat, peruadit tamen &longs;ucce&longs;&longs;iuè, e&longs;t que reip&longs;à priùs in <lb/>inferioribus eius partibus, quàm in &longs;uperioribus; inde <lb/>fit, vt cùm &longs;i&longs;tula per hæc priora, & po&longs;teriora mo­<lb/>menta, moueatur interim ad motum nauis; idcircô <lb/>globus, preter motum &longs;ur&longs;um, promoueatur etiam in-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.038.jpg" pagenum="31"/>tereà prorsùm, &longs;ecundum illum tantillum motum, & <lb/>dum ex&longs;iliendo per &longs;i&longs;tulam tran&longs;it, incipiat de&longs;cribere <lb/>parabolicam lineam, quam deinceps per aerem de&longs;­<lb/>cribere pergat; neque huic de&longs;criptioni magis ob&longs;tet <lb/>rectitudo fi&longs;tulæ, quàm rectitudo ip&longs;ius mali. </s> |
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| <s>Nam &longs;i &longs;up­<lb/>ponas ex. </s> | <s id="id.000347">Addo, <lb/>cùm e&longs;&longs;emus in ip&longs;a triremi, nobilem Vincegue<gap/>ram <lb/>recita&longs;&longs;e optimo Proregi, nobi&longs;que circon&longs;tantibus <lb/>experimentum &longs;uo iu&longs;&longs;u factum, quod heic omitti non <lb/>debeat. </s> |
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| <s>gr. </s> | <s id="id.000348">A&longs;&longs;eruït enim &longs;e aliquando naui cuipiam <lb/>imperitantem, & cùm illa &longs;ecundo vento, ac velo­<lb/>ci&longs;&longs;imè transferretur, iu&longs;&longs;i&longs;&longs;e è fa&longs;tigio mali explodi <lb/>&longs;ursùm fi&longs;tulâ pi&longs;toleto dictâ plumbeum globulum; <lb/>ac ip&longs;um aliquantò pò&longs;t decidi&longs;&longs;e ad pedem mali. </s></p><p type="main"> |
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| <s>puppim e&longs;&longs;e in G, & proram in A; ac <lb/>te ex puppi conijcere pilam ad &longs;ocium, qui ex prora <lb/>ad te pari ni&longs;u reijciat; eueniet, vt dum pila à te con­<lb/>jecta transferetur per aërem, ille quidem cum pro­<lb/>ra perueniat, verbi cau&longs;â ad c, &longs;ed pila tamen etiam <lb/>eò perueniat, quoniam tu pilæ præter tuam vim, qua <lb/>perueni&longs;&longs;et &longs;olùm ad A, indis etiam vim tran&longs;latitiam, <lb/>&longs;eu impre&longs;&longs;am à naui, qua &longs;uperetur, ac &longs;uperad datur <lb/>&longs;patium Ac, & qua ip&longs;e intereà &longs;equaris cum puppi <lb/>per &longs;patium GS; ita vt cùm &longs;ocius, & pila fuerint in <lb/>c, tu futurus &longs;is in S. </s> | <s id="id.000349">VIII. <!-- KEEP S--></s> |
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| <s>Eueniet quoque, vt dum pila <lb/>ab illo rejecta transferetur per aërem, tu cum puppi <lb/>promotus peruenias quidem ad V; &longs;ed & pila tamen <lb/>eò &longs;olùm perueniat, quoniam ex vi &longs;ocij propria tan­<lb/>tum detrahetur à vi nauis tran&longs;latitia, quantum foret <pb pagenum="32"/>nece&longs;&longs;arium, vt ex V promouerctur in S: quod &longs;pa­<lb/>tium e&longs;t æquale ip&longs;i e g, per quod ille intereà cum <lb/>prora recedet; ita vt cum tu & pila fueritis in V, ip&longs;e <lb/>&longs;it futurus in g. </s> | <s id="id.000350">Prætereo po&longs;&longs;e ex eadem figura alia quo­<lb/>que ex memoratis experimentis intelligi. </s> |
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| <s>Quod &longs;i &longs;upponas vim tibi à naui &longs;u­<lb/>perad ditam e&longs;&longs;e duplo majorem priore; tum tu pilam <lb/>in&longs;equutus peruenies ex G ad V, cùm ille promotus <lb/>ex A ad e, pilam reijciet, cui pilæ rejectæ tu intereà <lb/>promotus, occurras ad a. </s> | <s id="id.000351">Nam &longs;i &longs;up­<lb/>ponas ex. </s> |
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| <s>& c, S in &longs;upponas tantam <lb/>nauigij celeritatem, vt vis à motu illius impre&longs;&longs;a exæ­<lb/>quetur illi, quàm tu ni&longs;u tuo proprio imprimis, &longs;icque <lb/>vis pilæ duplicata euadat; fiet, vt pila à te ex G, <lb/>qua&longs;i ad A projecta, perueniat ad H; quò &longs;ocius &longs;imùl <lb/>perueniet, perueniente te intereà ad A; & pila ex <lb/>H ad te rejecta, non ver&longs;us A accedat, &longs;ed &longs;ursùm, <lb/>deorsùmque duntaxat mota, veluti con&longs;i&longs;tat, téque <lb/>ibi, perpendiculum non egre&longs;&longs;a, ex&longs;pectet; & tu eó­<lb/>dem accedas cum puppi; &longs;ocio tantundem intereà <lb/>recedente cum prora. </s> | <s id="id.000352">gr. <!-- REMOVE S-->puppim e&longs;&longs;e in G, & proram in A; ac <lb/>te ex puppi conijcere pilam ad &longs;ocium, qui ex prora <lb/>ad te pari ni&longs;u reijciat; eueniet, vt dum pila à te con­<lb/>jecta transferetur per aërem, ille quidem cum pro­<lb/>ra perueniat, verbi cau&longs;â ad c, &longs;ed pila tamen etiam <lb/>eò perueniat, quoniam tu pilæ præter tuam vim, qua <lb/>perueni&longs;&longs;et &longs;olùm ad A, indis etiam vim tran&longs;latitiam, <lb/>&longs;eu impre&longs;&longs;am à naui, qua &longs;uperetur, ac &longs;uperad datur <lb/>&longs;patium Ac, & qua ip&longs;e intereà &longs;equaris cum puppi <lb/>per &longs;patium GS; ita vt cùm &longs;ocius, & pila fuerint in <lb/>c, tu futurus &longs;is in S. <!-- KEEP S--></s> |
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| <s>Non mirabere verò iam con­<lb/>&longs;i&longs;tere pilam; quia pari vi ad te immi&longs;&longs;a à &longs;ocio, & re­<lb/>mi&longs;&longs;a à naui, nece&longs;&longs;e e&longs;t hæreat, quemadmodum di­<lb/>xi iam antè po&longs;&longs;e à te ob&longs;eruari in pila, quam &longs;ocius <lb/>intra pergulam antrorsùm pergens, retror&longs;ùm reijciat. <lb/></s> | |
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| <s>Quin-etiam, quemadmodum adnotatum e&longs;t euenire <lb/>in pergula, vt po&longs;&longs;it pila retror&longs;um iacta antror&longs;um <lb/>redire; ita heic fieri concipies, &longs;i &longs;upponas vim à na­<lb/>ui impre&longs;&longs;am e&longs;&longs;e majorem impre&longs;&longs;a à te. </s> | |
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| <s>Ita enim <lb/>pila ex G ad &longs;ocium vltra H perueniet, & ab illo re­<lb/>jecta, non modò in loco rejectionis non con&longs;i&longs;tet, &longs;ed <lb/>ver&longs;us ip&longs;um quoque &longs;ocium tantum regredietur, <lb/>quantum vis ip&longs;ius &longs;uperabitur à motu nauis; cùm tu <pb pagenum="33"/>tamen tam citò, ac pila ad regre&longs;&longs;ionis locum <lb/>peruenturus &longs;is. </s> | <s id="id.000353">Eueniet quoque, vt dum pila <lb/>ab illo rejecta transferetur per aërem, tu cum puppi <lb/>promotus peruenias quidem ad V; &longs;ed & pila tamen <lb/>eò &longs;olùm perueniat, quoniam ex vi &longs;ocij propria tan­<lb/>tum detrahetur à vi nauis tran&longs;latitia, quantum foret <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.039.jpg" pagenum="32"/>nece&longs;&longs;arium, vt ex V promouerctur in S: quod &longs;pa­<lb/>tium e&longs;t æquale ip&longs;i e g, per quod ille intereà cum <lb/>prora recedet; ita vt cum tu & pila fueritis in V, ip&longs;e <lb/>&longs;it futurus in g. <!-- KEEP S--></s> |
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| <s>Sed i&longs;ta iam nimis inculcata &longs;unt: <lb/>idque e&longs;t &longs;olùm mente tenendum, quæeumque vis <lb/>tibi ad datur, aut adimatur &longs;ocio ab impetu nauis; ni­<lb/>hilominùs ip&longs;os pilæ jactus, rejectu&longs;que, &longs;iue itus, & <lb/>reditus inter vtrúmque interceptos, eo&longs;dem con&longs;tan­<lb/>ter apparituros; quia eiu&longs;modi impetus ex æquo & <lb/>te, & &longs;ocium, & pilam afficiet; nihilque, quod pro­<lb/>cedat ab eiu&longs;modi impetu, aut à te, aut à &longs;ocio ob­<lb/>&longs;eruari poterit; eritque ob&longs;eruabilis motus ille &longs;olus, <lb/>qui à vi propria vtriu&longs;que pendebit, quique perinde <lb/>ob&longs;eruaretur, &longs;i nauis quie&longs;ceret; ac aliunde diuer&longs;i­<lb/>tas in motu pilæ ex compo&longs;ita tua, &longs;ocijve, & na­<lb/>uigij vi, ob&longs;eruabilis &longs;olùm erit ab oculo extra naui­<lb/>gium quie&longs;cente. </s> | <s id="id.000354">Quod &longs;i &longs;upponas vim tibi à naui &longs;u­<lb/>perad ditam e&longs;&longs;e duplo majorem priore; tum tu pilam <lb/>in&longs;equutus peruenies ex G ad V, cùm ille promotus <lb/>ex A ad e, pilam reijciet, cui pilæ rejectæ tu intereà <lb/>promotus, occurras ad a. </s> |
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| <s>Ob&longs;eruabilis, inquam, & pulcro <lb/>&longs;anè &longs;pectaculo, cuius &longs;i fieri particeps velis, &longs;ta ip&longs;e <lb/>ad ripam, aut in nauigio aliàs immoto, cùm alijduo in <lb/>tran&longs;lato colludent. </s> | <s id="id.000355">& c, S in &longs;upponas tantam <lb/>nauigij celeritatem, vt vis à motu illius impre&longs;&longs;a exæ­<lb/>quetur illi, quàm tu ni&longs;u tuo proprio imprimis, &longs;icque <lb/>vis pilæ duplicata euadat; fiet, vt pila à te ex G, <lb/>qua&longs;i ad A projecta, perueniat ad H; quò &longs;ocius &longs;imùl <lb/>perueniet, perueniente te intereà ad A; & pila ex <lb/>H ad te rejecta, non ver&longs;us A accedat, &longs;ed &longs;ursùm, <lb/>deorsùmque duntaxat mota, veluti con&longs;i&longs;tat, téque <lb/>ibi, perpendiculum non egre&longs;&longs;a, ex&longs;pectet; & tu eó­<lb/>dem accedas cum puppi; &longs;ocio tantundem intereà <lb/>recedente cum prora. </s> |
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| <s>Quippe quas illi putabunt æqua­<lb/>leis vireis, quos æqualeis pilæ itus, reditu&longs;que; ani­<lb/>maduertes ip&longs;e prorsùs inæ qualeis; & non &longs;ine volup­<lb/>tate &longs;pectabis illum, qui ad puppim, vehementiorem <lb/>quidem ictum impingere, &longs;ed continuò tamen pi­<lb/>lam in&longs;equi; illum, qui ad proram, remi&longs;&longs;iorem qui­<lb/>dem; &longs;ed continuò tamen à pila aufugere: & cùm <lb/>pila inæqualiter per aërem tran&longs;luolatura &longs;it, ab illo <lb/>nempe celeriùs, ab hoc &longs;egniùs; mirabilem tamen <lb/>fieri ex illius acce&longs;&longs;u, & in&longs;equutione pilæ, cùm hu­<lb/>ius rece&longs;&longs;u, & fuga ab eadem pila, compen&longs;ationem. </s></p><p type="main"> | <s id="id.000356">Non mirabere verò iam con­<lb/>&longs;i&longs;tere pilam; quia pari vi ad te immi&longs;&longs;a à &longs;ocio, & re­<lb/>mi&longs;&longs;a à naui, nece&longs;&longs;e e&longs;t hæreat, quemadmodum di­<lb/>xi iam antè po&longs;&longs;e à te ob&longs;eruari in pila, quam &longs;ocius <lb/>intra pergulam antrorsùm pergens, retror&longs;ùm reijciat. <lb/></s> |
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| <s>IX. <!-- KEEP S--></s> | <s id="id.000357">Quin-etiam, quemadmodum adnotatum e&longs;t euenire <lb/>in pergula, vt po&longs;&longs;it pila retror&longs;um iacta antror&longs;um <lb/>redire; ita heic fieri concipies, &longs;i &longs;upponas vim à na­<lb/>ui impre&longs;&longs;am e&longs;&longs;e majorem impre&longs;&longs;a à te. </s> |
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| <s>Po&longs;tulare heic videretur occa&longs;io, vt priu&longs;quàm <lb/>di&longs;cederem longiùs, intexerem qua&longs;i parenthe&longs;in, <pb pagenum="34"/>quid colligi exinde po&longs;&longs;it circa quæ&longs;tionem celebrem, <lb/>De motu, quieteve Telluris; idque præ&longs;ertim, cùm <lb/>tu, Germanu&longs;que, & qui adfuere cæteri, ex Luille­<lb/>rio &longs;tatim requi&longs;ieritis, ex hi&longs;ce-ne experimentis quid­<lb/>piam deriuarem ad Telluris motum: verùm quia for­<lb/>ta&longs;&longs;is euagarer nimiùm, præ&longs;tat id ad calcem reijciam; <lb/>&longs;ubijciam que intereà, quæ de cau&longs;a phy&longs;ica motus <lb/>tam naturalis, quàm projectorij inue&longs;tigari ex præmi&longs;­<lb/>&longs;is po&longs;&longs;unt. </s> | <s id="id.000358">Ita enim <lb/>pila ex G ad &longs;ocium vltra H perueniet, & ab illo re­<lb/>jecta, non modò in loco rejectionis non con&longs;i&longs;tet, &longs;ed <lb/>ver&longs;us ip&longs;um quoque &longs;ocium tantum regredietur, <lb/>quantum vis ip&longs;ius &longs;uperabitur à motu nauis; cùm tu <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.040.jpg" pagenum="33"/>tamen tam citò, ac pila ad regre&longs;&longs;ionis locum <lb/>peruenturus &longs;is. </s> |
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| <s>Cùm naturalem porrô dico, modum lo­<lb/>quendi vulgarem &longs;equor, iuxta quem, vt motus re­<lb/>rum projectilium dicitur violentus, ita motus rerum <lb/>cadentium, quas & graueis dicunt, naturalis appelli­<lb/>tatur. </s> | <s id="id.000359">Sed i&longs;ta iam nimis inculcata &longs;unt: <lb/>idque e&longs;t &longs;olùm mente tenendum, quæeumque vis <lb/>tibi ad datur, aut adimatur &longs;ocio ab impetu nauis; ni­<lb/>hilominùs ip&longs;os pilæ jactus, rejectu&longs;que, &longs;iue itus, & <lb/>reditus inter vtrúmque interceptos, eo&longs;dem con&longs;tan­<lb/>ter apparituros; quia eiu&longs;modi impetus ex æquo & <lb/>te, & &longs;ocium, & pilam afficiet; nihilque, quod pro­<lb/>cedat ab eiu&longs;modi impetu, aut à te, aut à &longs;ocio ob­<lb/>&longs;eruari poterit; eritque ob&longs;eruabilis motus ille &longs;olus, <lb/>qui à vi propria vtriu&longs;que pendebit, quique perinde <lb/>ob&longs;eruaretur, &longs;i nauis quie&longs;ceret; ac aliunde diuer&longs;i­<lb/>tas in motu pilæ ex compo&longs;ita tua, &longs;ocijve, & na­<lb/>uigij vi, ob&longs;eruabilis &longs;olùm erit ab oculo extra naui­<lb/>gium quie&longs;cente. </s> |
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| <s>Imprimis certè nullus videtur non cen&longs;eri po&longs;­<lb/>&longs;e naturalis motus, quatenus nullus non e&longs;t à rerum <lb/>principiis, quæ ip&longs;orum Author eius e&longs;&longs;e naturæ vo­<lb/>luït, vt ince&longs;&longs;anter impetum, quo moueri po&longs;&longs;ent, <lb/>haberent. </s> | <s id="id.000360">Ob&longs;eruabilis, inquam, & pulcro <lb/>&longs;anè &longs;pectaculo, cuius &longs;i fieri particeps velis, &longs;ta ip&longs;e <lb/>ad ripam, aut in nauigio aliàs immoto, cùm alijduo in <lb/>tran&longs;lato colludent. </s> |
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| <s>Ex hoc nempe e&longs;&longs;e videtur, quamobrem <lb/>variè commi&longs;ceantur, & varias rerum &longs;pecies creent, <lb/>quæ inter &longs;e variè agant, & patiantur, &longs;eu mouean­<lb/>tur, & moueant. </s> | <s id="id.000361">Quippe quas illi putabunt æqua­<lb/>leis vireis, quos æqualeis pilæ itus, reditu&longs;que; ani­<lb/>maduertes ip&longs;e prorsùs inæ qualeis; & non &longs;ine volup­<lb/>tate &longs;pectabis illum, qui ad puppim, vehementiorem <lb/>quidem ictum impingere, &longs;ed continuò tamen pi­<lb/>lam in&longs;equi; illum, qui ad proram, remi&longs;&longs;iorem qui­<lb/>dem; &longs;ed continuò tamen à pila aufugere: & cùm <lb/>pila inæqualiter per aërem tran&longs;luolatura &longs;it, ab illo <lb/>nempe celeriùs, ab hoc &longs;egniùs; mirabilem tamen <lb/>fieri ex illius acce&longs;&longs;u, & in&longs;equutione pilæ, cùm hu­<lb/>ius rece&longs;&longs;u, & fuga ab eadem pila, compen&longs;ationem. </s></p><p type="main"> |
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| <s>Quippe ortus quoque, & interitus, <lb/>incrementum, & decrementum, omni&longs;que altera­<lb/>tio, qua calor, frigus, humor, &longs;iccitas, itemque co­<lb/>lor, odor, &longs;apor, & qualitates aliæ gignuntur, ni­<lb/>hil e&longs;&longs;e aliud videntur, quàm motiones quædam lo­<lb/>cales, quibus rerum principia, tenui&longs;&longs;ima licet, at­<lb/>que in&longs;en&longs;ilia, variè inter &longs;e concernuntur, excer­<lb/>nuntur, accedunt, ab&longs;cedunt, tran&longs;ponuntur, &c. </s> | <s id="id.000362">IX. <!-- KEEP S--></s> |
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| <s>Ita <lb/>&longs;altem &longs;unt opinati Philo&longs;ophi celebres apud Sextum <lb/>Empiricum, dum Ari&longs;totele defendente huiu&longs;cemo­<lb/>di mutationes à motu locali di&longs;tinctas, ip&longs;i cen&longs;ue-<pb pagenum="35"/>runt nihil e&longs;&longs;e aliud, quàm &longs;pecies qua&longs;dam motuslo­<lb/>calis. </s> | <s id="id.000363">Po&longs;tulare heic videretur occa&longs;io, vt priu&longs;quàm <lb/>di&longs;cederem longiùs, intexerem qua&longs;i parenthe&longs;in, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.041.jpg" pagenum="34"/>quid colligi exinde po&longs;&longs;it circa quæ&longs;tionem celebrem, <lb/>De motu, quieteve Telluris; idque præ&longs;ertim, cùm <lb/>tu, Germanu&longs;que, & qui adfuere cæteri, ex Luille­<lb/>rio &longs;tatim requi&longs;ieritis, ex hi&longs;ce-ne experimentis quid­<lb/>piam deriuarem ad Telluris motum: verùm quia for­<lb/>ta&longs;&longs;is euagarer nimiùm, præ&longs;tat id ad calcem reijciam; <lb/>&longs;ubijciam que intereà, quæ de cau&longs;a phy&longs;ica motus <lb/>tam naturalis, quàm projectorij inue&longs;tigari ex præmi&longs;­<lb/>&longs;is po&longs;&longs;unt. </s> |
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| <s>Deinde nullusvidetur motus, qui &longs;eclu&longs;o primæ­<lb/>uo illo, non po&longs;&longs;it cen&longs;eriviolentus: quatenus nullus e&longs;t, <lb/>qui ni&longs;i cum impul&longs;ione vnius rei in a<gap/>m fiat, ex quo <lb/>effectum e&longs;t, vt Ari&longs;toteles, etiam rerum cadentium <lb/>quæ&longs;ierit motorem externum, principium nempe <lb/>generans; & in motibus animalium di&longs;tinguendas <lb/>cen&longs;uerit parteis, quarum aliæ mouerentur ab aliis, <lb/>ad v&longs;que vnam, que moueret, per &longs;e immota. </s> | <s id="id.000364">Cùm naturalem porrô dico, modum lo­<lb/>quendi vulgarem &longs;equor, iuxta quem, vt motus re­<lb/>rum projectilium dicitur violentus, ita motus rerum <lb/>cadentium, quas & graueis dicunt, naturalis appelli­<lb/>tatur. </s> |
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| <s>Ne­<lb/>que videri ab &longs;urdum debet, e&longs;&longs;e continuam aliquam <lb/>in rebus naturæ violentiam; quoniam ip&longs;a quoque <lb/>violentia ex eò cen&longs;eri naturalis pote&longs;t, quod Au­<lb/>thor naturæ illam in&longs;tituerit, quæ gignundis rebus <lb/>naturalibus in&longs;eruiret; cum con&longs;tet nihil alterari, <lb/>nihil interire, nihil exoriri, ab&longs;que motu reciproco, <lb/>&longs;iue actione, & reactione, qua vnaquæque res vim <lb/>patiatur; adeo proinde vt violentia naturas &longs;ingu­<lb/>lareis &longs;olùm, non vniuer&longs;alem attineat. </s> | <s id="id.000365">Imprimis certè nullus videtur non cen&longs;eri po&longs;­<lb/>&longs;e naturalis motus, quatenus nullus non e&longs;t à rerum <lb/>principiis, quæ ip&longs;orum Author eius e&longs;&longs;e naturæ vo­<lb/>luït, vt ince&longs;&longs;anter impetum, quo moueri po&longs;&longs;ent, <lb/>haberent. </s> |
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| <s>Prætereà <lb/>cum motus naturalis, & violenti voces non videan­<lb/>tur nobis e&longs;&longs;e confundendæ, ea mihi &longs;emper vtriu&longs;­<lb/>que notio vi&longs;a e&longs;t commodi&longs;&longs;ima, vt naturalis ap­<lb/>pelletur, qui aut &longs;ponte, aut &longs;ine vlla repugnantia <lb/>fit: violentus, qui præter naturam, aut cum aliqua <lb/>repugnantia. </s> | <s id="id.000366">Ex hoc nempe e&longs;&longs;e videtur, quamobrem <lb/>variè commi&longs;ceantur, & varias rerum &longs;pecies creent, <lb/>quæ inter &longs;e variè agant, & patiantur, &longs;eu mouean­<lb/>tur, & moueant. </s> |
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| <s>Ita ince&longs;&longs;us animalis naturalis e&longs;t, quia <lb/>&longs;ponte &longs;it: &longs;altatio violenta, quia cum aliqua repu­<lb/>gnantia. </s> | <s id="id.000367">Quippe ortus quoque, & interitus, <lb/>incrementum, & decrementum, omni&longs;que altera­<lb/>tio, qua calor, frigus, humor, &longs;iccitas, itemque co­<lb/>lor, odor, &longs;apor, & qualitates aliæ gignuntur, ni­<lb/>hil e&longs;&longs;e aliud videntur, quàm motiones quædam lo­<lb/>cales, quibus rerum principia, tenui&longs;&longs;ima licet, at­<lb/>que in&longs;en&longs;ilia, variè inter &longs;e concernuntur, excer­<lb/>nuntur, accedunt, ab&longs;cedunt, tran&longs;ponuntur, &c. </s> |
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| <s>Ita trajectio globi per aërem violenta, quia <lb/>præter naturam; volutio &longs;upra planum naturalis, <lb/>quia nihil repugnat. </s> | <s id="id.000368">Ita <lb/>&longs;altem &longs;unt opinati Philo&longs;ophi celebres apud Sextum <lb/>Empiricum, dum Ari&longs;totele defendente huiu&longs;cemo­<lb/>di mutationes à motu locali di&longs;tinctas, ip&longs;i cen&longs;ue-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.042.jpg" pagenum="35"/>runt nihil e&longs;&longs;e aliud, quàm &longs;pecies qua&longs;dam motuslo­<lb/>calis. </s> |
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| <s>Rur&longs;ùs, quia &longs;æpenumerò cau­<lb/>&longs;a &longs;eu &longs;pontanea, &longs;eu repugnans non apparet, & <lb/>quæri pote&longs;t quoddam criterium, quo di&longs;cerni va-<pb pagenum="36"/>leat, vtrum qui&longs;piam motus naturalis &longs;it, an vio­<lb/>lentus; idcircô, vel ex eo, quòd motus principiorum, <lb/>qui e&longs;t maximè naturalis, æquabili&longs;&longs;imus ex &longs;e e&longs;t; <lb/>videtur æquabilitas a&longs;&longs;umi po&longs;&longs;e, vt character, quo, <lb/>&longs;i ad&longs;it, iudicemus <expan abbr="motũ">motum</expan> e&longs;&longs;e naturalem, &longs;i ab&longs;it, violen­<lb/>tum. </s> | <s id="id.000369">Deinde nullusvidetur motus, qui &longs;eclu&longs;o primæ­<lb/>uo illo, non po&longs;&longs;it cen&longs;eriviolentus: quatenus nullus e&longs;t, <lb/>qui ni&longs;i cum impul&longs;ione vnius rei in a<gap/>m fiat, ex quo <lb/>effectum e&longs;t, vt Ari&longs;toteles, etiam rerum cadentium <lb/>quæ&longs;ierit motorem externum, principium nempe <lb/>generans; & in motibus animalium di&longs;tinguendas <lb/>cen&longs;uerit parteis, quarum aliæ mouerentur ab aliis, <lb/>ad v&longs;que vnam, que moueret, per &longs;e immota. </s> |
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| <s>Et &longs;anè cum &longs;it commune effatum, Nihil violen­<lb/>tum e&longs;&longs;e perpetuum; cui e&longs;t con&longs;entaneum, vt quod <lb/>e&longs;t naturale perpetuum &longs;it; con&longs;tat radicem perpe­<lb/>tuitatis e&longs;&longs;e æquabilitatem, ce&longs;&longs;ationis inæquabilita­<lb/>tem; quatenus id &longs;olùm, quod neque inuale&longs;cit, ne­<lb/>que debilitatur, perdurare pote&longs;t; nihilque pote&longs;t <lb/>naturæ vi aut incre&longs;cere, aut decre&longs;cere infinitè. </s> | <s id="id.000370">Ne­<lb/>que videri ab &longs;urdum debet, e&longs;&longs;e continuam aliquam <lb/>in rebus naturæ violentiam; quoniam ip&longs;a quoque <lb/>violentia ex eò cen&longs;eri naturalis pote&longs;t, quod Au­<lb/>thor naturæ illam in&longs;tituerit, quæ gignundis rebus <lb/>naturalibus in&longs;eruiret; cum con&longs;tet nihil alterari, <lb/>nihil interire, nihil exoriri, ab&longs;que motu reciproco, <lb/>&longs;iue actione, & reactione, qua vnaquæque res vim <lb/>patiatur; adeo proinde vt violentia naturas &longs;ingu­<lb/>lareis &longs;olùm, non vniuer&longs;alem attineat. </s> |
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| <s>Ad­<lb/>hæc, &longs;i quis requirat motum in hi&longs;ce rebus compo­<lb/>&longs;itis, qui &longs;it maximè naturalis, per&longs;picuum videtur <lb/>cum e&longs;&longs;e cæle&longs;tem; quatenus e&longs;t præ cæteris æquabilis, <lb/>atque perpetuus; delecta ab authore circulari forma, <lb/>&longs;ecundum quam, principiò, & fine carentem, e&longs;&longs;e <lb/>æquabilitas, & perpetuitas po&longs;&longs;et. </s> | <s id="id.000371">Prætereà <lb/>cum motus naturalis, & violenti voces non videan­<lb/>tur nobis e&longs;&longs;e confundendæ, ea mihi &longs;emper vtriu&longs;­<lb/>que notio vi&longs;a e&longs;t commodi&longs;&longs;ima, vt naturalis ap­<lb/>pelletur, qui aut &longs;ponte, aut &longs;ine vlla repugnantia <lb/>fit: violentus, qui præter naturam, aut cum aliqua <lb/>repugnantia. </s> |
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| <s>Et ne cau&longs;eris <lb/>motum animalium videri potiùs naturalem; vide vt <lb/>vel &longs;ola ip&longs;a la&longs;&longs;itudo violentiam quandam indi<gap/>et; <lb/>cùm aliunde animalium motus ea &longs;olum ratione vi­<lb/>deatur e&longs;&longs;e naturalis, qua ex circularibus componi­<lb/>tur; quippe violentus, qua ratione i&longs;ti circulares <lb/>imperfecti &longs;unt, atque impediti. </s> | <s id="id.000372">Ita ince&longs;&longs;us animalis naturalis e&longs;t, quia <lb/>&longs;ponte &longs;it: &longs;altatio violenta, quia cum aliqua repu­<lb/>gnantia. </s> |
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| <s>Paradoxum vide­<lb/>retur, non po&longs;&longs;e vllum motum ab animali ex&longs;eri, qui <lb/>&longs;impliciter rectus &longs;it; neque hominem v. </s> | <s id="id.000373">Ita trajectio globi per aërem violenta, quia <lb/>præter naturam; volutio &longs;upra planum naturalis, <lb/>quia nihil repugnat. </s> |
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| <s>c. </s> | <s id="id.000374">Rur&longs;ùs, quia &longs;æpenumerò cau­<lb/>&longs;a &longs;eu &longs;pontanea, &longs;eu repugnans non apparet, & <lb/>quæri pote&longs;t quoddam criterium, quo di&longs;cerni va-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.043.jpg" pagenum="36"/>leat, vtrum qui&longs;piam motus naturalis &longs;it, an vio­<lb/>lentus; idcircô, vel ex eo, quòd motus principiorum, <lb/>qui e&longs;t maximè naturalis, æquabili&longs;&longs;imus ex &longs;e e&longs;t; <lb/>videtur æquabilitas a&longs;&longs;umi po&longs;&longs;e, vt character, quo, <lb/>&longs;i ad&longs;it, iudicemus <expan abbr="motũ">motum</expan> e&longs;&longs;e naturalem, &longs;i ab&longs;it, violen­<lb/>tum. </s> |
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| <s>ducere <lb/>po&longs;&longs;e digito, aut &longs;tilo rectam lineam, ni&longs;i pluribus <lb/>motibus circularibus compo&longs;itis &longs;imùl: Verùm res <lb/>tam penè intelligitur ex iis, quæ paulò antè &longs;unt dicta; <lb/>& ob&longs;etuare &longs;olùm e&longs;t opus, quomodo bracchij ex-<pb pagenum="37"/>ten&longs;io inter ducendum rectam fiat, motis ex ordine <lb/>digitis, manu, cubito, bracchio &longs;uper propriis, ac <lb/>&longs;pecialibus centris. </s> | <s id="id.000375">Et &longs;anè cum &longs;it commune effatum, Nihil violen­<lb/>tum e&longs;&longs;e perpetuum; cui e&longs;t con&longs;entaneum, vt quod <lb/>e&longs;t naturale perpetuum &longs;it; con&longs;tat radicem perpe­<lb/>tuitatis e&longs;&longs;e æquabilitatem, ce&longs;&longs;ationis inæquabilita­<lb/>tem; quatenus id &longs;olùm, quod neque inuale&longs;cit, ne­<lb/>que debilitatur, perdurare pote&longs;t; nihilque pote&longs;t <lb/>naturæ vi aut incre&longs;cere, aut decre&longs;cere infinitè. </s> |
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| <s>Con&longs;idera quoque vt inter ex­<lb/>pedite ambulandum, &longs;pontaneus ille bracchiorum <lb/>motus, cuius centrum &longs;capulæ &longs;unt, non perinde &longs;it <lb/>defatigationi obnoxius, ac motus crurum, cuius <lb/>centrum coxendices, quod non perinde inhibeatur, <lb/>& multiplicari cogatur: &longs;ed i&longs;tud tamen obiter. </s> | <s id="id.000376">Ad­<lb/>hæc, &longs;i quis requirat motum in hi&longs;ce rebus compo­<lb/>&longs;itis, qui &longs;it maximè naturalis, per&longs;picuum videtur <lb/>cum e&longs;&longs;e cæle&longs;tem; quatenus e&longs;t præ cæteris æquabilis, <lb/>atque perpetuus; delecta ab authore circulari forma, <lb/>&longs;ecundum quam, principiò, & fine carentem, e&longs;&longs;e <lb/>æquabilitas, & perpetuitas po&longs;&longs;et. </s> |
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| <s>De­<lb/>nique, &longs;i quis quærat motum, qui violentus maximè <lb/>&longs;it, is e&longs;&longs;e videtur vterque, de quo heic loci agitur; <lb/>nempe qui non modò e&longs;t in re projecta, dum &longs;ursùm <lb/>contendit, &longs;ed etiam, qui in re cadente, dum fertur <lb/>deor&longs;ùm. </s> | <s id="id.000377">Et ne cau&longs;eris <lb/>motum animalium videri potiùs naturalem; vide vt <lb/>vel &longs;ola ip&longs;a la&longs;&longs;itudo violentiam quandam indi<gap/>et; <lb/>cùm aliunde animalium motus ea &longs;olum ratione vi­<lb/>deatur e&longs;&longs;e naturalis, qua ex circularibus componi­<lb/>tur; quippe violentus, qua ratione i&longs;ti circulares <lb/>imperfecti &longs;unt, atque impediti. </s> |
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| <s>Argumento e&longs;t, quòd vt ille e&longs;t ab ex­<lb/>terno principio, ita hic non po&longs;&longs;it e&longs;&longs;e ab interno, qua­<lb/>le formam dicunt, & quale per&longs;euerans vniu&longs;modi, <lb/>intelligi cau&longs;a non po&longs;&longs;it, tanti illius, ac tam inæqua­<lb/>bilis impetus; qui cùm aliunde non valeat incremen­<lb/>tum continuum infinitè accipere, ideò longè abe&longs;t, <lb/>vt durare perpetuò po&longs;&longs;it. </s> | <s id="id.000378">Paradoxum vide­<lb/>retur, non po&longs;&longs;e vllum motum ab animali ex&longs;eri, qui <lb/>&longs;impliciter rectus &longs;it; neque hominem v. <!-- REMOVE S-->c. <!-- REMOVE S-->ducere <lb/>po&longs;&longs;e digito, aut &longs;tilo rectam lineam, ni&longs;i pluribus <lb/>motibus circularibus compo&longs;itis &longs;imùl: Verùm res <lb/>tam penè intelligitur ex iis, quæ paulò antè &longs;unt dicta; <lb/>& ob&longs;etuare &longs;olùm e&longs;t opus, quomodo bracchij ex-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.044.jpg" pagenum="37"/>ten&longs;io inter ducendum rectam fiat, motis ex ordine <lb/>digitis, manu, cubito, bracchio &longs;uper propriis, ac <lb/>&longs;pecialibus centris. </s> |
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| <s>Quid dico verò perpe­<lb/>tuò? </s> | |
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| <s>cùm prolixi&longs;&longs;imus omnium vix vnico horæ mo­<lb/>mento perduret, eaque ratione peragatur, vt &longs;i ca­<lb/>dens ex alto corpus minùs benè compactum &longs;it, im­<lb/>petu ip&longs;o di&longs;&longs;ipetur; intelligamu&longs;que, &longs;i ca&longs;us in im­<lb/>men&longs;um pateret, impetu&longs;que eadem &longs;emper propor­<lb/>tione in immen&longs;um incre&longs;ceret, nullam penitùs com­<lb/>pactionem ad inex&longs;olubilitatem corporis e&longs;&longs;e &longs;uffe­<lb/>cturam. </s> | |
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| <s>Quod &longs;anè conuincit hunc motum natura­<lb/>lem propriè non e&longs;&longs;e, &longs;ed violentum potiùs, imô <lb/>eua&longs;urum tandem violenti&longs;&longs;imum, &longs;iue quo violen­<lb/>tior excogitari non valeat; cùm is, qui à natura e&longs;t, <pb pagenum="38"/>intelligatur e&longs;&longs;e debere placidus, atque vniformis, <lb/>& nihil minùs, quàm ad de&longs;tructionem eius corpo­<lb/>ris, quod attinet, tendens. </s></p><p type="main"> | |
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| <s>X. <!-- KEEP S--></s> | |
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| <s>Non repeto heic, quemadmodum lapis à <lb/>vertice mali, dum nauis mouetur, apparenter &longs;olùm <lb/>&longs;ecundum perpendiculum cadat, reip&longs;â verò obliquè <lb/>per eam, quam de&longs;crip&longs;imus lineam; innüo duntaxat <lb/>lapidem non &longs;ponte moueri, quia mouetur vi à ma­<lb/>nu impre&longs;&longs;a ex tran&longs;latione manus à naui, cui vnà <lb/>cum malo in&longs;i&longs;tit. </s> | <s id="id.000379">Con&longs;idera quoque vt inter ex­<lb/>pedite ambulandum, &longs;pontaneus ille bracchiorum <lb/>motus, cuius centrum &longs;capulæ &longs;unt, non perinde &longs;it <lb/>defatigationi obnoxius, ac motus crurum, cuius <lb/>centrum coxendices, quod non perinde inhibeatur, <lb/>& multiplicari cogatur: &longs;ed i&longs;tud tamen obiter. </s> |
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| <s>Atque id quidem &longs;eu manus in <lb/>fa&longs;tigio mali con&longs;i&longs;tens lapidem dimittat, &longs;eu lapis <lb/>ex radice mali projectus, vbi peruenerit ad &longs;ummum, <lb/>po&longs;teà recidat; vt proinde intelligas po&longs;&longs;e vel ex hoc <lb/>capite motum lapidis decidentis, recidenti&longs;ve dici <lb/>violentum. </s> | <s id="id.000380">De­<lb/>nique, &longs;i quis quærat motum, qui violentus maximè <lb/>&longs;it, is e&longs;&longs;e videtur vterque, de quo heic loci agitur; <lb/>nempe qui non modò e&longs;t in re projecta, dum &longs;ursùm <lb/>contendit, &longs;ed etiam, qui in re cadente, dum fertur <lb/>deor&longs;ùm. </s> |
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| <s>Dices, cùm hic obliquus motus mi&longs;tus, <lb/>&longs;eu compo&longs;itus &longs;it ex perpendiculari, & horizontali; <lb/>id quidem, quod e&longs;t ex horizontali, exi&longs;timari po&longs;&longs;e <lb/>violentum, at quod ex perpendiculari, id &longs;altem e&longs;&longs;e <lb/>naturale. </s> | <s id="id.000381">Argumento e&longs;t, quòd vt ille e&longs;t ab ex­<lb/>terno principio, ita hic non po&longs;&longs;it e&longs;&longs;e ab interno, qua­<lb/>le formam dicunt, & quale per&longs;euerans vniu&longs;modi, <lb/>intelligi cau&longs;a non po&longs;&longs;it, tanti illius, ac tam inæqua­<lb/>bilis impetus; qui cùm aliunde non valeat incremen­<lb/>tum continuum infinitè accipere, ideò longè abe&longs;t, <lb/>vt durare perpetuò po&longs;&longs;it. </s> |
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| <s>Nam quòd lapis quidem &longs;ursùm projectus, <lb/>& nihilominùs obliquè incedens, &longs;ecundum vtrum­<lb/>que violentus &longs;it, videri per&longs;picuum: quoniam vtriu&longs;­<lb/>que cau&longs;a externa, impellen&longs;que e&longs;t, illius nempe <lb/>ip&longs;a vis nauis, huius verò vis manus propria: at quod <lb/>deorsùm dimi&longs;&longs;us, & obliquè nihilominùs incedens, <lb/>&longs;ecundum vtrumque violentus &longs;it, non po&longs;&longs;e perin­<lb/>de e&longs;&longs;e in confe&longs;&longs;o: quippe horizontalis quidem cau­<lb/>&longs;a &longs;imiliter externa, impellen&longs;que, vis nauis e&longs;t; &longs;ed <lb/>perpendicularis cau&longs;a non e&longs;t perinde vis propria <lb/>manus. </s> | <s id="id.000382">Quid dico verò perpe­<lb/>tuò? </s> |
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| <s>Quare & nece&longs;&longs;e videri lapidem eo motu <lb/>moueri ab interno principio: e&longs;&longs;éque proinde eum <pb pagenum="39"/>motum non violentum, &longs;ed naturalem. </s> | <s id="id.000383">cùm prolixi&longs;&longs;imus omnium vix vnico horæ mo­<lb/>mento perduret, eaque ratione peragatur, vt &longs;i ca­<lb/>dens ex alto corpus minùs benè compactum &longs;it, im­<lb/>petu ip&longs;o di&longs;&longs;ipetur; intelligamu&longs;que, &longs;i ca&longs;us in im­<lb/>men&longs;um pateret, impetu&longs;que eadem &longs;emper propor­<lb/>tione in immen&longs;um incre&longs;ceret, nullam penitùs com­<lb/>pactionem ad inex&longs;olubilitatem corporis e&longs;&longs;e &longs;uffe­<lb/>cturam. </s> |
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| <s>Attamen id <lb/>videtur primum con&longs;ideratione dignum, &longs;i ex duobus <lb/>his motibus, perpendiculari nempe, & horizontali, qui <lb/>obliquum illum componunt, alter habendus natu­<lb/>ralis &longs;it, illum horizontalem potiùs, quàm perpen­<lb/>dicularem e&longs;&longs;e. </s> | <s id="id.000384">Quod &longs;anè conuincit hunc motum natura­<lb/>lem propriè non e&longs;&longs;e, &longs;ed violentum potiùs, imô <lb/>eua&longs;urum tandem violenti&longs;&longs;imum, &longs;iue quo violen­<lb/>tior excogitari non valeat; cùm is, qui à natura e&longs;t, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.045.jpg" pagenum="38"/>intelligatur e&longs;&longs;e debere placidus, atque vniformis, <lb/>& nihil minùs, quàm ad de&longs;tructionem eius corpo­<lb/>ris, quod attinet, tendens. </s></p><p type="main"> |
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| <s>Id verò patet; quia cùm projectum <lb/>pars fuerit aliqua totius, quòd &longs;ecundum horizon­<lb/>tem, &longs;eu circulariter mouebatur, ideò ad eius imi­<lb/>tationem mouetur circulariter, ac naturaliter proin­<lb/>de, & prorsùs æquabiliter; adeò vt, quantumcùm­<lb/>que motus perpendicularis incre&longs;cat &longs;emper, aut de­<lb/>cre&longs;cat; ip&longs;e tamen horizontalis vno &longs;emper tenore <lb/>fluat, inuariabiliterque procedat. </s> | <s id="id.000385">X. <!-- KEEP S--></s> |
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| <s>Ac fortè res mi­<lb/>nùs mirabilis e&longs;&longs;et, de impre&longs;&longs;ione ex motu terræ, &longs;i <lb/>quis vellet ip&longs;am &longs;upra axem &longs;uum mobilem &longs;uppo­<lb/>nere: &longs;iquidem lapis dici po&longs;&longs;et moueri vniformiter, <lb/>ob &longs;pontaneam con&longs;equutionem, ad vniformem <lb/>motum totius; &longs;eu cum eo cohærens, &longs;eu abiunctus <lb/>foret; Sed mirabile &longs;anè e&longs;t de impre&longs;&longs;ione ex naui, <lb/>equo, curru, aliave re, aut ex &longs;ola manu: quandò <lb/>lapis non habet cum rebus eiu&longs;cemodi, motibu&longs;ve <lb/>earum parem relationem. </s> | <s id="id.000386">Non repeto heic, quemadmodum lapis à <lb/>vertice mali, dum nauis mouetur, apparenter &longs;olùm <lb/>&longs;ecundum perpendiculum cadat, reip&longs;â verò obliquè <lb/>per eam, quam de&longs;crip&longs;imus lineam; innüo duntaxat <lb/>lapidem non &longs;ponte moueri, quia mouetur vi à ma­<lb/>nu impre&longs;&longs;a ex tran&longs;latione manus à naui, cui vnà <lb/>cum malo in&longs;i&longs;tit. </s> |
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| <s>Ex quo par e&longs;t exi&longs;timare, <lb/>motum horiz ontalem, à quacúmque cau&longs;a is fiat, ex <lb/>&longs;ua natura perpetuum fore, ni&longs;i cau&longs;a aliqua interue­<lb/>nerit, quæ mobile abducat, motumque exturbet. <lb/></s> | <s id="id.000387">Atque id quidem &longs;eu manus in <lb/>fa&longs;tigio mali con&longs;i&longs;tens lapidem dimittat, &longs;eu lapis <lb/>ex radice mali projectus, vbi peruenerit ad &longs;ummum, <lb/>po&longs;teà recidat; vt proinde intelligas po&longs;&longs;e vel ex hoc <lb/>capite motum lapidis decidentis, recidenti&longs;ve dici <lb/>violentum. </s> |
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| <s>Id, vt minùs ab&longs;urdum habeas, concipiendum e&longs;t <lb/>mobile, quod tantúndem &longs;e&longs;e reducat, quantùm <lb/>abductum fuerit. </s> | <s id="id.000388">Dices, cùm hic obliquus motus mi&longs;tus, <lb/>&longs;eu compo&longs;itus &longs;it ex perpendiculari, & horizontali; <lb/>id quidem, quod e&longs;t ex horizontali, exi&longs;timari po&longs;&longs;e <lb/>violentum, at quod ex perpendiculari, id &longs;altem e&longs;&longs;e <lb/>naturale. </s> |
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| <s>Huiu&longs;modi autem e&longs;&longs;e pote&longs;t ex­<lb/>qui&longs;itus, & vniformis materiæ globus, &longs;i volui ip&longs;um <lb/>imagineris &longs;upra horizontem, &longs;eu ambitum terræ, <pb pagenum="40"/>quem aliunde e&longs;&longs;e exqui&longs;itè complanatum concipas <lb/>Si &longs;upponas enim te illi vel leuiculum imprimere <lb/>motum; intelliges &longs;anè hunc motum nun quam ce&longs;&longs;a­<lb/>turum, &longs;ed globum reuolutum iri &longs;ecundum totum <lb/>ambitum, ac reuolutione peracta reuolutum iterùm <lb/>iri, & con&longs;equenter iterùm, & ita continuò per&longs;eue­<lb/>raturum. </s> | <s id="id.000389">Nam quòd lapis quidem &longs;ursùm projectus, <lb/>& nihilominùs obliquè incedens, &longs;ecundum vtrum­<lb/>que violentus &longs;it, videri per&longs;picuum: quoniam vtriu&longs;­<lb/>que cau&longs;a externa, impellen&longs;que e&longs;t, illius nempe <lb/>ip&longs;a vis nauis, huius verò vis manus propria: at quod <lb/>deorsùm dimi&longs;&longs;us, & obliquè nihilominùs incedens, <lb/>&longs;ecundum vtrumque violentus &longs;it, non po&longs;&longs;e perin­<lb/>de e&longs;&longs;e in confe&longs;&longs;o: quippe horizontalis quidem cau­<lb/>&longs;a &longs;imiliter externa, impellen&longs;que, vis nauis e&longs;t; &longs;ed <lb/>perpendicularis cau&longs;a non e&longs;t perinde vis propria <lb/>manus. </s> |
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| <s>Cau&longs;a porrô e&longs;t, quoniam globus moueri <lb/>tantillum hoc modo non pote&longs;t, quin centro ex&longs;i­<lb/>&longs;tente &longs;emper perpendiculari ad id punctum, quo glo­<lb/>bus contingit horizontale planum, tantum &longs;it molis <lb/>antè, quantum retrò, & pars anterior non po&longs;&longs;it <lb/>tendere deor&longs;um, quin pars po&longs;terior tendat &longs;ur&longs;um; <lb/>& illa &longs;emper hanc pertrahat, i&longs;ta &longs;emper illam pro­<lb/>pellat; adeò proinde, vt cùm nulla cau&longs;a po&longs;&longs;it deor­<lb/>sùm adigere globum, quin quantum ex vna parte de­<lb/>primit, tantúndem eleuet ex alia, oporteat motum <lb/>&longs;emel impre&longs;&longs;um con&longs;tare &longs;emper inter depre&longs;&longs;ionem, <lb/>& eleuationem medium: atque idcircô vniformem, <lb/>ince&longs;&longs;antemque per&longs;euerare. </s> | <s id="id.000390">Quare & nece&longs;&longs;e videri lapidem eo motu <lb/>moueri ab interno principio: e&longs;&longs;éque proinde eum <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.046.jpg" pagenum="39"/>motum non violentum, &longs;ed naturalem. </s> |
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| <s>Accedit, quòd nulla &longs;it <lb/>cau&longs;a, quamobrem &longs;uum cur&longs;um vel retardet vnquam, <lb/>vel acceleret, quatenus nunquam magis, vel minus à <lb/>centro terræ ab&longs;cedit, aut ad id accedit: neque cur <lb/>proinde vnquam debeat à motu ce&longs;&longs;are, quemadmo­<lb/>dum &longs;ieret, &longs;i &longs;upponeres ali quam in &longs;uperficie in æqua­<lb/>bilitatem. </s> | <s id="id.000391">Attamen id <lb/>videtur primum con&longs;ideratione dignum, &longs;i ex duobus <lb/>his motibus, perpendiculari nempe, & horizontali, qui <lb/>obliquum illum componunt, alter habendus natu­<lb/>ralis &longs;it, illum horizontalem potiùs, quàm perpen­<lb/>dicularem e&longs;&longs;e. </s> |
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| <s>Nam &longs;icubi decliuitas, & accliuitas foret, <lb/>acceleraret motum per locum decliuem, & retardaret <lb/>peraccliuem: &, &longs;i tanta accliuitas e&longs;&longs;et, vt emergere <lb/>&longs;upra eam non po&longs;&longs;et, cogeretur recurrere, excurreque, <lb/>& po&longs;t excur&longs;us, recur&longs;u&longs;que aliquot conquie&longs;cere <lb/>tandem in medio inter accliuitatem, & decliuitatem <pb pagenum="41"/>loco. </s> | <s id="id.000392">Id verò patet; quia cùm projectum <lb/>pars fuerit aliqua totius, quòd &longs;ecundum horizon­<lb/>tem, &longs;eu circulariter mouebatur, ideò ad eius imi­<lb/>tationem mouetur circulariter, ac naturaliter proin­<lb/>de, & prorsùs æquabiliter; adeò vt, quantumcùm­<lb/>que motus perpendicularis incre&longs;cat &longs;emper, aut de­<lb/>cre&longs;cat; ip&longs;e tamen horizontalis vno &longs;emper tenore <lb/>fluat, inuariabiliterque procedat. </s> |
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| <s>Ex quo rur&longs;us intelligis, &longs;i globus eius naturæ <lb/>&longs;it, vt per decliuem locum acceleretur, & per accli­<lb/>uem retardetur, fore vt loco neque decliui, neque <lb/>accliui ex&longs;i&longs;tente, neque accelerationem, neque re­<lb/>tardationem accipiat, &longs;ed tenorem &longs;eruet, ac inde­<lb/>&longs;inenter moueatur. </s> | <s id="id.000393">Ac fortè res mi­<lb/>nùs mirabilis e&longs;&longs;et, de impre&longs;&longs;ione ex motu terræ, &longs;i <lb/>quis vellet ip&longs;am &longs;upra axem &longs;uum mobilem &longs;uppo­<lb/>nere: &longs;iquidem lapis dici po&longs;&longs;et moueri vniformiter, <lb/>ob &longs;pontaneam con&longs;equutionem, ad vniformem <lb/>motum totius; &longs;eu cum eo cohærens, &longs;eu abiunctus <lb/>foret; Sed mirabile &longs;anè e&longs;t de impre&longs;&longs;ione ex naui, <lb/>equo, curru, aliave re, aut ex &longs;ola manu: quandò <lb/>lapis non habet cum rebus eiu&longs;cemodi, motibu&longs;ve <lb/>earum parem relationem. </s> |
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| <s>Atque hæc quidem attingo &longs;o­<lb/>lùm, vt planum faciam, &longs;i alteruter motuum haben­<lb/>dus naturalis &longs;it, illum horizontalem e&longs;&longs;e, potiu&longs;­<lb/>quàm perpendicularem. </s></p><p type="main"> | <s id="id.000394">Ex quo par e&longs;t exi&longs;timare, <lb/>motum horiz ontalem, à quacúmque cau&longs;a is fiat, ex <lb/>&longs;ua natura perpetuum fore, ni&longs;i cau&longs;a aliqua interue­<lb/>nerit, quæ mobile abducat, motumque exturbet. <lb/></s> |
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| <s>XI. <!-- KEEP S--></s> | <s id="id.000395">Id, vt minùs ab&longs;urdum habeas, concipiendum e&longs;t <lb/>mobile, quod tantúndem &longs;e&longs;e reducat, quantùm <lb/>abductum fuerit. </s> |
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| <s>Quia verò dubium &longs;upere&longs;t de perpendicu­<lb/>laris principio, non repeto quamobrem illum non <lb/>e&longs;&longs;e internum in&longs;inüauerim. </s> | <s id="id.000396">Huiu&longs;modi autem e&longs;&longs;e pote&longs;t ex­<lb/>qui&longs;itus, & vniformis materiæ globus, &longs;i volui ip&longs;um <lb/>imagineris &longs;upra horizontem, &longs;eu ambitum terræ, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.047.jpg" pagenum="40"/>quem aliunde e&longs;&longs;e exqui&longs;itè complanatum concipas <lb/>Si &longs;upponas enim te illi vel leuiculum imprimere <lb/>motum; intelliges &longs;anè hunc motum nun quam ce&longs;&longs;a­<lb/>turum, &longs;ed globum reuolutum iri &longs;ecundum totum <lb/>ambitum, ac reuolutione peracta reuolutum iterùm <lb/>iri, & con&longs;equenter iterùm, & ita continuò per&longs;eue­<lb/>raturum. </s> |
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| <s>Addo &longs;olùm, quia vi­<lb/>demus motum deor&longs;ùm eadem proportione veloci­<lb/>tatis incre&longs;cere, qua motus &longs;ursùm decre&longs;cit; ea­<lb/>propter videri omninô duo e&longs;&longs;e principia externa, <lb/>quæ mutuò qua&longs;i colluctentur, certatimque ex&longs;erant <lb/>vireis circa idem mobile. </s> | <s id="id.000397">Cau&longs;a porrô e&longs;t, quoniam globus moueri <lb/>tantillum hoc modo non pote&longs;t, quin centro ex&longs;i­<lb/>&longs;tente &longs;emper perpendiculari ad id punctum, quo glo­<lb/>bus contingit horizontale planum, tantum &longs;it molis <lb/>antè, quantum retrò, & pars anterior non po&longs;&longs;it <lb/>tendere deor&longs;um, quin pars po&longs;terior tendat &longs;ur&longs;um; <lb/>& illa &longs;emper hanc pertrahat, i&longs;ta &longs;emper illam pro­<lb/>pellat; adeò proinde, vt cùm nulla cau&longs;a po&longs;&longs;it deor­<lb/>sùm adigere globum, quin quantum ex vna parte de­<lb/>primit, tantúndem eleuet ex alia, oporteat motum <lb/>&longs;emel impre&longs;&longs;um con&longs;tare &longs;emper inter depre&longs;&longs;ionem, <lb/>& eleuationem medium: atque idcircô vniformem, <lb/>ince&longs;&longs;antemque per&longs;euerare. </s> |
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| <s>Et principium quidem ex­<lb/>ternum motus &longs;ur&longs;um con&longs;tat e&longs;&longs;e manum, aliudve <lb/>corpus proijciens; at cum principium externum mo­<lb/>tus deor&longs;um non perinde appareat, ideó-ne nullum <lb/>e&longs;t dicendum? </s> | <s id="id.000398">Accedit, quòd nulla &longs;it <lb/>cau&longs;a, quamobrem &longs;uum cur&longs;um vel retardet vnquam, <lb/>vel acceleret, quatenus nunquam magis, vel minus à <lb/>centro terræ ab&longs;cedit, aut ad id accedit: neque cur <lb/>proinde vnquam debeat à motu ce&longs;&longs;are, quemadmo­<lb/>dum &longs;ieret, &longs;i &longs;upponeres ali quam in &longs;uperficie in æqua­<lb/>bilitatem. </s> |
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| <s>Non &longs;annè, ni&longs;i fortè cùm vides ferrum, <lb/>aliàs immotum jacens, ad magnetem pellici, nullam <lb/>cau&longs;am externam cen&longs;eas, quæ pellectionem faciat; <lb/>aut cùm vides rem pendulam, aliàs quie&longs;centem, agi­<lb/>tari, ac externam cau&longs;am non vides, nullam e&longs;&longs;e <lb/>externam putes, à qua ag<gap/>tatio procedat. </s> | <s id="id.000399">Nam &longs;icubi decliuitas, & accliuitas foret, <lb/>acceleraret motum per locum decliuem, & retardaret <lb/>peraccliuem: &, &longs;i tanta accliuitas e&longs;&longs;et, vt emergere <lb/>&longs;upra eam non po&longs;&longs;et, cogeretur recurrere, excurreque, <lb/>& po&longs;t excur&longs;us, recur&longs;u&longs;que aliquot conquie&longs;cere <lb/>tandem in medio inter accliuitatem, & decliuitatem <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.048.jpg" pagenum="41"/>loco. </s> |
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| <s>C&ecedil;terùm, <lb/>cùm plures &longs;int modi, quibus cau&longs;a externa mouet, <lb/>con&longs;tat tamen omneis ad duos, tanquam pr&ecedil;cipuos <lb/>pertinere, impul&longs;ionem, & attractionem. </s> | <s id="id.000400">Ex quo rur&longs;us intelligis, &longs;i globus eius naturæ <lb/>&longs;it, vt per decliuem locum acceleretur, & per accli­<lb/>uem retardetur, fore vt loco neque decliui, neque <lb/>accliui ex&longs;i&longs;tente, neque accelerationem, neque re­<lb/>tardationem accipiat, &longs;ed tenorem &longs;eruet, ac inde­<lb/>&longs;inenter moueatur. </s> |
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| <s>Age ita­<lb/>que experiamur, an-non motus rerum caden-<pb pagenum="42"/>dentium, &longs;iue perpendicularis, aliqua e&longs;&longs;e po&longs;&longs;it <lb/>cau&longs;a &longs;eu impellens, &longs;eu attrahens, &longs;eu po­<lb/>tiùs impellens, & attrahens &longs;imùl. </s> | <s id="id.000401">Atque hæc quidem attingo &longs;o­<lb/>lùm, vt planum faciam, &longs;i alteruter motuum haben­<lb/>dus naturalis &longs;it, illum horizontalem e&longs;&longs;e, potiu&longs;­<lb/>quàm perpendicularem. </s></p><p type="main"> |
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| <s>Ac impel­<lb/>lens quidem; &longs;i aliqua &longs;it, ea non videtur e&longs;&longs;e po&longs;&longs;e <lb/>alia, quàm aer &longs;upernè incumbens, & à tergo in­<lb/>&longs;tans. </s> | <s id="id.000402">XI. <!-- KEEP S--></s> |
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| <s>Nullum certè e&longs;&longs;e videtur argumentum alte­<lb/>rius: nam & quamuis &longs;upremæ aeris regioni &longs;aper­<lb/>ex&longs;truas, vel &longs;phæram igneam, vel auram ætheream, <lb/>quæ à cælorum regionibus, motibu&longs;ve cohibita aërem <lb/>ip&longs;um circumquáque inter &longs;e, & terram cohibeat; id <lb/>tamen nihil aliud efficiet, quàm vt aer &longs;uperne pre&longs;&longs;us <lb/>premat &longs;upernè lapidem; &longs;icque aer erit &longs;emper cau&longs;a, <lb/>&longs;altem proxima lapidem impellens. </s> | <s id="id.000403">Quia verò dubium &longs;upere&longs;t de perpendicu­<lb/>laris principio, non repeto quamobrem illum non <lb/>e&longs;&longs;e internum in&longs;inüauerim. </s> |
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| <s>Aerem porrô e&longs;&longs;e <lb/>po&longs;&longs;e impellentem lapidis cau&longs;am, non diffit<gap/>bitur &longs;al­<lb/>tem Ari&longs;toteles, qui dum res pro<gap/>ectæ à motore &longs;ejun­<lb/>ctæ &longs;unt, moueri eas vult ab aere &longs;olo, qui motus à <lb/>proijciente, alium porrô moueat, à quo alius rursùm <lb/>moueatur, quov&longs;que impetu &longs;en&longs;im debilitato, mo­<lb/>tus tandem ce&longs;&longs;et, & quies &longs;equatur. </s> | <s id="id.000404">Addo &longs;olùm, quia vi­<lb/>demus motum deor&longs;ùm eadem proportione veloci­<lb/>tatis incre&longs;cere, qua motus &longs;ursùm decre&longs;cit; ea­<lb/>propter videri omninô duo e&longs;&longs;e principia externa, <lb/>quæ mutuò qua&longs;i colluctentur, certatimque ex&longs;erant <lb/>vireis circa idem mobile. </s> |
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| <s>Quoniam verò <lb/>dicere Ari&longs;toteles non pote&longs;t; ecquidnam ip&longs;um im­<lb/>petum frangat, præter aerem occurrentem, qui aeri <lb/>procedenti, proiectûmque pellenti continuò re&longs;i&longs;tat; <lb/>an non proinde fatebitur aerem &longs;upernè incumben­<lb/>tem, qua vi pote&longs;t re&longs;i&longs;tere projecto &longs;ur&longs;ùm lapidi, <lb/>po&longs;&longs;<gap/> cum deinceps trudere deor&longs;ùm? </s> | <s id="id.000405">Et principium quidem ex­<lb/>ternum motus &longs;ur&longs;um con&longs;tat e&longs;&longs;e manum, aliudve <lb/>corpus proijciens; at cum principium externum mo­<lb/>tus deor&longs;um non perinde appareat, ideó-ne nullum <lb/>e&longs;t dicendum? </s> |
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| <s>Quamcumque <lb/>vim &longs;anè manus lapidi, aerive imprimat, &longs;uperior <lb/>e&longs;&longs;e aer videtur, qui & tendenti &longs;ur&longs;ùm lapidi con­<lb/>tinenter re&longs;i&longs;tat, & vim continenter in ip&longs;um faciens, <lb/>impetum a manu impre&longs;&longs;um continuò refringat; do­<lb/>nec &longs;uperato toto impetu, ip&longs;e &longs;emper incumbens, <pb pagenum="43"/>& parem vim faciens, impetum victorem continuò <lb/>imprimat, nouúmque &longs;emper adiiciat; adeò vt in &longs;ine <lb/>motus deorsùm, tantundem &longs;it impetus ab aere, <lb/>quantùm initio motus &longs;ur&longs;ùm, impre&longs;&longs;um fuerat ab <lb/>ip&longs;a manu. </s> | <s id="id.000406">Non &longs;annè, ni&longs;i fortè cùm vides ferrum, <lb/>aliàs immotum jacens, ad magnetem pellici, nullam <lb/>cau&longs;am externam cen&longs;eas, quæ pellectionem faciat; <lb/>aut cùm vides rem pendulam, aliàs quie&longs;centem, agi­<lb/>tari, ac externam cau&longs;am non vides, nullam e&longs;&longs;e <lb/>externam putes, à qua ag<gap/>tatio procedat. </s> |
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| <s>Et quæ&longs;o te, &longs;i aliquis lapidem &longs;ur&longs;ùm ex <lb/>fundo maris pari vi, qua aliùs ex imo aere projiciat; <lb/>quare lapis nec tam altum a&longs;cendet, neque ex <gap/>am di&longs;­<lb/>&longs;ito loco deor&longs;ùm redibit? </s> | <s id="id.000407">C&ecedil;terùm, <lb/>cùm plures &longs;int modi, quibus cau&longs;a externa mouet, <lb/>con&longs;tat tamen omneis ad duos, tanquam pr&ecedil;cipuos <lb/>pertinere, impul&longs;ionem, & attractionem. </s> |
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| <s>An-non quia aqua lapidi <lb/>magis re&longs;i&longs;tet, quàm aer, impre&longs;&longs;umque impetum & <lb/>vehementiùs franget, & expugnabit citiùs, ac dein­<lb/>ceps lapidi &longs;emper imminens, proprium impetum im­<lb/>primere perget, nec &longs;inem faciet addendi nouum, <lb/>donec in fundum reduxerit? </s> | <s id="id.000408">Age ita­<lb/>que experiamur, an-non motus rerum caden-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.049.jpg" pagenum="42"/>dentium, &longs;iue perpendicularis, aliqua e&longs;&longs;e po&longs;&longs;it <lb/>cau&longs;a &longs;eu impellens, &longs;eu attrahens, &longs;eu po­<lb/>tiùs impellens, & attrahens &longs;imùl. </s> |
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| <s>Di&longs;erimen certè &longs;olum­<lb/>mo <gap/>ò e&longs;t &longs;ecundum majorem, minoremque re&longs;i&longs;ten­<lb/>tiam; cùm aërem quoque non nihil re&longs;i&longs;tere argua­<lb/>tur, vel ex eo &longs;tridore, quem edit, dum à corporibus <lb/>vehementiùs per ip&longs;um actis frangitur. </s> | <s id="id.000409">Ac impel­<lb/>lens quidem; &longs;i aliqua &longs;it, ea non videtur e&longs;&longs;e po&longs;&longs;e <lb/>alia, quàm aer &longs;upernè incumbens, & à tergo in­<lb/>&longs;tans. </s> |
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| <s>Et quamuis <lb/>præ &longs;ua tenuïtate non videatur po&longs;&longs;e impetui tanto re­<lb/>&longs;i&longs;tere; cogita tamen proportionem e&longs;&longs;e cum aquæ <lb/>re&longs;i&longs;tentia; illamque vt intelligas, compara non <lb/>modò perexiguum, ac penè nullum lapidis a&longs;cen&longs;um <lb/>ex fundo aquæ, cum incompatabi<gap/>iter altiore ex <lb/>imo aëre; &longs;ed etiam progre&longs;&longs;um penè in&longs;en&longs;ibilem <lb/>bombardici globi per aquam tran&longs;uer&longs;ùm adacti, <lb/>re&longs;pectu illius, qui per aërem fieri ob&longs;eruatur; & <lb/>agno&longs;ces, vt intra aquam propter maximam re&longs;i&longs;ten­<lb/>tiam, paruum &longs;patium peragitur; &longs;ic in aëre propter <lb/>paruam, &longs;patium maximum peragi. </s> | <s id="id.000410">Nullum certè e&longs;&longs;e videtur argumentum alte­<lb/>rius: nam & quamuis &longs;upremæ aeris regioni &longs;aper­<lb/>ex&longs;truas, vel &longs;phæram igneam, vel auram ætheream, <lb/>quæ à cælorum regionibus, motibu&longs;ve cohibita aërem <lb/>ip&longs;um circumquáque inter &longs;e, & terram cohibeat; id <lb/>tamen nihil aliud efficiet, quàm vt aer &longs;uperne pre&longs;&longs;us <lb/>premat &longs;upernè lapidem; &longs;icque aer erit &longs;emper cau&longs;a, <lb/>&longs;altem proxima lapidem impellens. </s> |
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| <s>Dices dubium <lb/>fortè non e&longs;&longs;ede re&longs;i&longs;tentia aëris, dum aliquid agitur <lb/>&longs;ursùm; &longs;ed de impetu, qui imprimatur ab aëre, <pb pagenum="44"/>dum idem corpus fertur deor&longs;ùm; quoniam videmus <lb/>parietem, pauimentum, & alia &longs;ic re&longs;i&longs;tere, vt non <lb/>proptereà vim vllam faciant, impetumve corporibus <lb/>incurrentibus imprimant. </s> | <s id="id.000411">Aerem porrô e&longs;&longs;e <lb/>po&longs;&longs;e impellentem lapidis cau&longs;am, non diffit<gap/>bitur &longs;al­<lb/>tem Ari&longs;toteles, qui dum res pro<gap/>ectæ à motore &longs;ejun­<lb/>ctæ &longs;unt, moueri eas vult ab aere &longs;olo, qui motus à <lb/>proijciente, alium porrô moueat, à quo alius rursùm <lb/>moueatur, quov&longs;que impetu &longs;en&longs;im debilitato, mo­<lb/>tus tandem ce&longs;&longs;et, & quies &longs;equatur. </s> |
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| <s>Sed vt hoc e&longs;t verùm dè <lb/>rebus immotis, quæque di&longs;tracta in &longs;e non red<gap/>unt, <lb/>neque rur&longs;ùs coëunt; ita dici planè non pote&longs;t de iis, <lb/>quæ aut mouentur, aut à &longs;uo &longs;itu deductæ illum <lb/>repetunt. </s> | <s id="id.000412">Quoniam verò <lb/>dicere Ari&longs;toteles non pote&longs;t; ecquidnam ip&longs;um im­<lb/>petum frangat, præter aerem occurrentem, qui aeri <lb/>procedenti, proiectûmque pellenti continuò re&longs;i&longs;tat; <lb/>an non proinde fatebitur aerem &longs;upernè incumben­<lb/>tem, qua vi pote&longs;t re&longs;i&longs;tere projecto &longs;ur&longs;ùm lapidi, <lb/>po&longs;&longs;<gap/> cum deinceps trudere deor&longs;ùm? </s> |
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| <s>Abduc certè arboris ramum, ille non mo­<lb/>dò tibi re&longs;i&longs;tet, &longs;ed po&longs;tea quoque cùm vehementia <lb/>&longs;itum &longs;uum ita repetet, vt &longs;i quidpiam occurrerit, <lb/>impetu magno illud propellat; qua ratione &longs;it &longs;agit­<lb/>tarum jactus. </s> | <s id="id.000413">Quamcumque <lb/>vim &longs;anè manus lapidi, aerive imprimat, &longs;uperior <lb/>e&longs;&longs;e aer videtur, qui & tendenti &longs;ur&longs;ùm lapidi con­<lb/>tinenter re&longs;i&longs;tat, & vim continenter in ip&longs;um faciens, <lb/>impetum a manu impre&longs;&longs;um continuò refringat; do­<lb/>nec &longs;uperato toto impetu, ip&longs;e &longs;emper incumbens, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.050.jpg" pagenum="43"/>& parem vim faciens, impetum victorem continuò <lb/>imprimat, nouúmque &longs;emper adiiciat; adeò vt in &longs;ine <lb/>motus deorsùm, tantundem &longs;it impetus ab aere, <lb/>quantùm initio motus &longs;ur&longs;ùm, impre&longs;&longs;um fuerat ab <lb/>ip&longs;a manu. </s> |
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| <s>Diffinde quoque ramum in dua<gap/> par­<lb/>teis, quæ in trunco tamen cohæreant; eæ partes non <lb/>&longs;olùm diducenti re&longs;i&longs;tent, &longs;ed reducent prætereà &longs;e­<lb/>&longs;e eâ vehementiâ, eóque impetu, cui ne vires qui­<lb/>dem Milonis &longs;int pares. </s> | <s id="id.000414">Et quæ&longs;o te, &longs;i aliquis lapidem &longs;ur&longs;ùm ex <lb/>fundo maris pari vi, qua aliùs ex imo aere projiciat; <lb/>quare lapis nec tam altum a&longs;cendet, neque ex <gap/>am di&longs;­<lb/>&longs;ito loco deor&longs;ùm redibit? </s> |
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| <s>Itaque ip&longs;e quoque aër, <lb/>tamet&longs;i aliàs immotus &longs;it, ita tamen à corpore præ­<lb/>teruadente di&longs;trahi pote&longs;t, vt partes di&longs;tractæ ma­<lb/>gna cum vehementia &longs;e&longs;e inuicem repetant, locum­<lb/>que à corpore occupatum, & iam iam relictum de­<lb/>nuò repleant, &longs;ieque corpus ip&longs;um non &longs;ine facto <lb/>impetu vlteriùs propellant. </s> | <s id="id.000415">An-non quia aqua lapidi <lb/>magis re&longs;i&longs;tet, quàm aer, impre&longs;&longs;umque impetum & <lb/>vehementiùs franget, & expugnabit citiùs, ac dein­<lb/>ceps lapidi &longs;emper imminens, proprium impetum im­<lb/>primere perget, nec &longs;inem faciet addendi nouum, <lb/>donec in fundum reduxerit? </s> |
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| <s>Et res quidem videretur <lb/>&longs;ide propè de&longs;titui; &longs;ed experimenta tot &longs;unt, ac ea <lb/>præ&longs;ertìm, quæ circa vacuum impediendum com­<lb/>memorantur, vt cùm telatere non po&longs;&longs;int, comme­<lb/>morare &longs;uper&longs;luum &longs;it. </s> | <s id="id.000416">Di&longs;erimen certè &longs;olum­<lb/>mo <gap/>ò e&longs;t &longs;ecundum majorem, minoremque re&longs;i&longs;ten­<lb/>tiam; cùm aërem quoque non nihil re&longs;i&longs;tere argua­<lb/>tur, vel ex eo &longs;tridore, quem edit, dum à corporibus <lb/>vehementiùs per ip&longs;um actis frangitur. </s> |
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| <s>Velim &longs;olùm, ne hæreas, <lb/>quomodò res adeò fluxa, ac e&longs;t aër; tantam vim <lb/>propellendi habeat; cogites & ventorum vim, qua <lb/>f<gap/>ag<gap/>antur arbores, qua trans&longs;eruntur nauigia, qua <lb/>cuertuntur ædificia, qua &longs;u&longs;que deque mare moue-<pb pagenum="45"/>tur; & impetum, quo aër compre&longs;&longs;us catapultis il­<lb/>lis pneumaticis recens adinuentis, globulum plum­<lb/>beum, &longs;agittamve laxatis habenis non &longs;ecùs explodit, <lb/>ac in bombardis facit puluis pyrius. </s> | <s id="id.000417">Et quamuis <lb/>præ &longs;ua tenuïtate non videatur po&longs;&longs;e impetui tanto re­<lb/>&longs;i&longs;tere; cogita tamen proportionem e&longs;&longs;e cum aquæ <lb/>re&longs;i&longs;tentia; illamque vt intelligas, compara non <lb/>modò perexiguum, ac penè nullum lapidis a&longs;cen&longs;um <lb/>ex fundo aquæ, cum incompatabi<gap/>iter altiore ex <lb/>imo aëre; &longs;ed etiam progre&longs;&longs;um penè in&longs;en&longs;ibilem <lb/>bombardici globi per aquam tran&longs;uer&longs;ùm adacti, <lb/>re&longs;pectu illius, qui per aërem fieri ob&longs;eruatur; & <lb/>agno&longs;ces, vt intra aquam propter maximam re&longs;i&longs;ten­<lb/>tiam, paruum &longs;patium peragitur; &longs;ic in aëre propter <lb/>paruam, &longs;patium maximum peragi. </s> |
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| <s>Quin etiam in <lb/>his, quæ&longs;o te, quid pote&longs;t e&longs;&longs;e admirabilius, quàm <lb/>&longs;lammulam impetu tanto, ac tam procùl abigere glo­<lb/>bum adeò den&longs;um, atque pondero&longs;um? </s> | <s id="id.000418">Dices dubium <lb/>fortè non e&longs;&longs;ede re&longs;i&longs;tentia aëris, dum aliquid agitur <lb/>&longs;ursùm; &longs;ed de impetu, qui imprimatur ab aëre, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.051.jpg" pagenum="44"/>dum idem corpus fertur deor&longs;ùm; quoniam videmus <lb/>parietem, pauimentum, & alia &longs;ic re&longs;i&longs;tere, vt non <lb/>proptereà vim vllam faciant, impetumve corporibus <lb/>incurrentibus imprimant. </s> |
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| <s>Non-ne ip­<lb/>&longs;a quoque flammula e&longs;t admodùm fluxa? </s> | <s id="id.000419">Sed vt hoc e&longs;t verùm dè <lb/>rebus immotis, quæque di&longs;tracta in &longs;e non red<gap/>unt, <lb/>neque rur&longs;ùs coëunt; ita dici planè non pote&longs;t de iis, <lb/>quæ aut mouentur, aut à &longs;uo &longs;itu deductæ illum <lb/>repetunt. </s> |
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| <s>Et quis cre­<lb/>deret eius vi, non globum modò antror&longs;ùm agi; &longs;ed <lb/>machinam etiam tormentariam adeò magnam, adeó­<lb/>que grauem retror&longs;ùm pelli? </s> | <s id="id.000420">Abduc certè arboris ramum, ille non mo­<lb/>dò tibi re&longs;i&longs;tet, &longs;ed po&longs;tea quoque cùm vehementia <lb/>&longs;itum &longs;uum ita repetet, vt &longs;i quidpiam occurrerit, <lb/>impetu magno illud propellat; qua ratione &longs;it &longs;agit­<lb/>tarum jactus. </s> |
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| <s>Quid verò, &longs;i id &longs;ine <lb/>aere vnà accurrente non &longs;iat? </s> | <s id="id.000421">Diffinde quoque ramum in dua<gap/> par­<lb/>teis, quæ in trunco tamen cohæreant; eæ partes non <lb/>&longs;olùm diducenti re&longs;i&longs;tent, &longs;ed reducent prætereà &longs;e­<lb/>&longs;e eâ vehementiâ, eóque impetu, cui ne vires qui­<lb/>dem Milonis &longs;int pares. </s> |
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| <s>videlicet fieri videtur, <lb/>dum &longs;lamma in &longs;ui creatione ampliorem locum quæ­<lb/>ritans, tum in po&longs;ticam machinæ partem impetum <lb/>conuertit, tum in globum ant<gap/>iùs &longs;itum, qui ob li­<lb/>bertatem canalis ex&longs;iliens, fl<gap/>mmam in&longs;tantem ita <lb/>habet, vt ea di&longs;percunte, & inanem locum relinquen­<lb/>te, conuolet aër, ex aduer&longs;a parte, ac tanto quidem <lb/>impetu, vt & machinam retror&longs;ùm compellat, & <lb/>impactus tonitru excitet, & commoto aere circum­<lb/>vicino, ctiam ingenteis ædeis concutiat. </s> | <s id="id.000422">Itaque ip&longs;e quoque aër, <lb/>tamet&longs;i aliàs immotus &longs;it, ita tamen à corpore præ­<lb/>teruadente di&longs;trahi pote&longs;t, vt partes di&longs;tractæ ma­<lb/>gna cum vehementia &longs;e&longs;e inuicem repetant, locum­<lb/>que à corpore occupatum, & iam iam relictum de­<lb/>nuò repleant, &longs;ieque corpus ip&longs;um non &longs;ine facto <lb/>impetu vlteriùs propellant. </s> |
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| <s>T<gap/>ta igitur <lb/>e&longs;&longs;e pote&longs;t vehementia aëris; vt intelligas ip&longs;um po&longs;&longs;e <lb/>non lapidi modò fur&longs;ùm ni<gap/>ti re&longs;i&longs;tere, &longs;ed ip&longs;um <lb/>etiam impetu facto, impre&longs;&longs;óque, pellere deorsùm. <lb/></s> | <s id="id.000423">Et res quidem videretur <lb/>&longs;ide propè de&longs;titui; &longs;ed experimenta tot &longs;unt, ac ea <lb/>præ&longs;ertìm, quæ circa vacuum impediendum com­<lb/>memorantur, vt cùm telatere non po&longs;&longs;int, comme­<lb/>morare &longs;uper&longs;luum &longs;it. </s> |
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| <s>At, inquies, cùm lapis &longs;ursùm nititur, nonne aër quo­<lb/>que di&longs;trahitur, & in locum à lapide relictum infernè <lb/>&longs;uccedit? </s> | <s id="id.000424">Velim &longs;olùm, ne hæreas, <lb/>quomodò res adeò fluxa, ac e&longs;t aër; tantam vim <lb/>propellendi habeat; cogites & ventorum vim, qua <lb/>f<gap/>ag<gap/>antur arbores, qua trans&longs;eruntur nauigia, qua <lb/>cuertuntur ædificia, qua &longs;u&longs;que deque mare moue-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.052.jpg" pagenum="45"/>tur; & impetum, quo aër compre&longs;&longs;us catapultis il­<lb/>lis pneumaticis recens adinuentis, globulum plum­<lb/>beum, &longs;agittamve laxatis habenis non &longs;ecùs explodit, <lb/>ac in bombardis facit puluis pyrius. </s> |
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| <s>An non impetum ergo imprimet, & mo­<lb/>tum impre&longs;&longs;um à manu juuabit? </s> | <s id="id.000425">Quin etiam in <lb/>his, quæ&longs;o te, quid pote&longs;t e&longs;&longs;e admirabilius, quàm <lb/>&longs;lammulam impetu tanto, ac tam procùl abigere glo­<lb/>bum adeò den&longs;um, atque pondero&longs;um? </s> |
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| <s>An-non proinde <lb/>tantum aberit, vt impetus decre&longs;cere debeat, quin <lb/>debeat potius incre&longs;cere, ac lapis ferri &longs;ur&longs;um duplò <pb pagenum="46"/>velociùs, quàm deor&longs;um, cum &longs;ur&longs;um agatur geminæ <lb/>vi, & deor&longs;um vna duntaxat? </s> | <s id="id.000426">Non-ne ip­<lb/>&longs;a quoque flammula e&longs;t admodùm fluxa? </s> |
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| <s>Nam opponi quidem <lb/>non pote&longs;t re&longs;i&longs;tentia aëris, dum lapis &longs;ur&longs;um niti­<lb/>tur; &longs;imilis enim infernè fit, cum lapis prorumpit <lb/>deor&longs;um. </s> | <s id="id.000427">Et quis cre­<lb/>deret eius vi, non globum modò antror&longs;ùm agi; &longs;ed <lb/>machinam etiam tormentariam adeò magnam, adeó­<lb/>que grauem retror&longs;ùm pelli? </s> |
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| <s>Accidit, quòd cadente quidem lapide, vi­<lb/>detur aër accurrere ad locum iam relictum po&longs;&longs;e; at <lb/>dum lapide quie&longs;cente fulcrum &longs;u&longs;tentans &longs;ubducitur, <lb/>non e&longs;t cur aër &longs;upernè accurrat; & cum accurrat po­<lb/>tius infernè, an non deberet lapis &longs;ur&longs;um, potiu&longs;quam <lb/>deor&longs;ùm propelli? </s> | <s id="id.000428">Quid verò, &longs;i id &longs;ine <lb/>aere vnà accurrente non &longs;iat? </s> |
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| <s>Dum etiam lapis projectus &longs;ur­<lb/>&longs;um, punctum &longs;upremum attigit, in quo quædam e&longs;t <lb/>veiuti libratio, exæquatis momentis virium tam mo­<lb/>uentium, quàm re&longs;i&longs;tentium; an-non deberet lapis <lb/>in eo penitùs conquie&longs;cere, vt non ex&longs;i&longs;tente in aëre <lb/>cau&longs;a, quæ lapidem magis adigat deor&longs;ùm, quàm, <lb/>&longs;ur&longs;um? </s> | <s id="id.000429">videlicet fieri videtur, <lb/>dum &longs;lamma in &longs;ui creatione ampliorem locum quæ­<lb/>ritans, tum in po&longs;ticam machinæ partem impetum <lb/>conuertit, tum in globum ant<gap/>iùs &longs;itum, qui ob li­<lb/>bertatem canalis ex&longs;iliens, fl<gap/>mmam in&longs;tantem ita <lb/>habet, vt ea di&longs;percunte, & inanem locum relinquen­<lb/>te, conuolet aër, ex aduer&longs;a parte, ac tanto quidem <lb/>impetu, vt & machinam retror&longs;ùm compellat, & <lb/>impactus tonitru excitet, & commoto aere circum­<lb/>vicino, ctiam ingenteis ædeis concutiat. </s> |
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| <s>Vt verum fatear, hæc difficultas videtur euin­<lb/>cere, aërem quidem e&longs;&longs;e po&longs;&longs;e cau&longs;am aliquam ad­<lb/>juuantem, adaugentemque motus deorsùm velo­<lb/>citatem; at non e&longs;&longs;e tamen &longs;olam vel &longs;u&longs;ficientem; <lb/>&longs;ed exigi prætereà aliam, quæ lapidi faciat motus <lb/>deor&longs;um initium, quæque re&longs;i&longs;tentiam aëris inferio­<lb/>ris vincat, vt cœptum &longs;emel motum aër &longs;uperior <lb/>promoueat, lapidem velut &longs;ollicitans, & continuò <lb/>magis, magi&longs;que in&longs;tigans. </s></p><p type="main"> | <s id="id.000430">T<gap/>ta igitur <lb/>e&longs;&longs;e pote&longs;t vehementia aëris; vt intelligas ip&longs;um po&longs;&longs;e <lb/>non lapidi modò fur&longs;ùm ni<gap/>ti re&longs;i&longs;tere, &longs;ed ip&longs;um <lb/>etiam impetu facto, impre&longs;&longs;óque, pellere deorsùm. <lb/></s> |
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| <s>XII. <!-- KEEP S--></s> | <s id="id.000431">At, inquies, cùm lapis &longs;ursùm nititur, nonne aër quo­<lb/>que di&longs;trahitur, & in locum à lapide relictum infernè <lb/>&longs;uccedit? </s> |
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| <s>Itaque præter cau&longs;am impellentem, videtur <lb/>e&longs;&longs;e nece&longs;&longs;arium ad attrahentem recurrere, quæ id <lb/>muneris ex&longs;equatur. </s> | <s id="id.000432">An non impetum ergo imprimet, & mo­<lb/>tum impre&longs;&longs;um à manu juuabit? </s> |
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| <s>Cæterùm, hæc vis quænam <lb/>alia &longs;it, quàm quæ totius globi Telluris propria &longs;it, <lb/>& magnetica dici po&longs;&longs;it? </s> | <s id="id.000433">An-non proinde <lb/>tantum aberit, vt impetus decre&longs;cere debeat, quin <lb/>debeat potius incre&longs;cere, ac lapis ferri &longs;ur&longs;um duplò <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.053.jpg" pagenum="46"/>velociùs, quàm deor&longs;um, cum &longs;ur&longs;um agatur geminæ <lb/>vi, & deor&longs;um vna duntaxat? </s> |
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| <s>Profecto cum globus tel­<lb/>luris totum quodpiam &longs;it, notum e&longs;t nullum e&longs;&longs;e <pb pagenum="47"/>totum à natura in&longs;titutum, cui non &longs;it in&longs;ita vis <lb/>&longs;ui ip&longs;ius con&longs;eruatrix, ac proinde qua parteis &longs;ui <lb/>cohærenteis contineat, &longs;eparationique illarum re&longs;i­<lb/>&longs;tat. </s> | <s id="id.000434">Nam opponi quidem <lb/>non pote&longs;t re&longs;i&longs;tentia aëris, dum lapis &longs;ur&longs;um niti­<lb/>tur; &longs;imilis enim infernè fit, cum lapis prorumpit <lb/>deor&longs;um. </s> |
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| <s>Ex hoc autem fit, vt &longs;i partes Terræ aliquo ca­<lb/>&longs;u auellantur, re&longs;i&longs;tat ip&longs;a, & vi &longs;ua, &longs;eu hamulis, <lb/>catenuli&longs;que in&longs;en&longs;ilibus retrahat, vt dum quis ma­<lb/>num à &longs;e abduci extento bracchio non patitur, & <lb/>abductam vi &longs;ua, &longs;eu &longs;piritibus per neruos tran&longs;mi&longs;­<lb/>&longs;is retrahit in &longs;e ip&longs;um. </s> | <s id="id.000435">Accidit, quòd cadente quidem lapide, vi­<lb/>detur aër accurrere ad locum iam relictum po&longs;&longs;e; at <lb/>dum lapide quie&longs;cente fulcrum &longs;u&longs;tentans &longs;ubducitur, <lb/>non e&longs;t cur aër &longs;upernè accurrat; & cum accurrat po­<lb/>tius infernè, an non deberet lapis &longs;ur&longs;um, potiu&longs;quam <lb/>deor&longs;ùm propelli? </s> |
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| <s>Terrem autem globi parteis, <lb/>&longs;eu terrena corpora voco, non modo parteis terræ, <lb/>& aquæ (quæ e&longs;t globi terreni pars liquida, & qua­<lb/>&longs;i &longs;anguis in animali) verùm etiam tam lapides, me­<lb/>talla, cætera fo&longs;&longs;ilia, plantas, animalia, & quæcùm­<lb/>que terræ, & aquæ manife&longs;tam originem debent, in <lb/>quibus habeo etiam pluuiam, rorem, niucm, gran­<lb/>dinem, & meteora cætera, itemque vapores, & ex­<lb/>halationes; quàm ip&longs;um quoque aërem, quo tellus <lb/>qua&longs;i circumve&longs;titur, vt malum cotoneum &longs;ua lanu­<lb/>gine (quoniam &longs;i ex hoc circum terram &longs;patio de­<lb/>mas vapores, halitu&longs;que, ac vniuer&longs;è omneis fumos, <lb/>& corpu&longs;cula, quæ ex terra, & aqua continuò ex­<lb/>primuntur, a&longs;cenduntque, & de&longs;cendunt, varieque <lb/>mouentur, aut quie&longs;cunt; quod &longs;upererit nihil aliud <lb/>fore intelligitur, quàm inane &longs;patium) denique ip­<lb/>&longs;um etiam ignem; quem manife&longs;tum e&longs;t non gigni <lb/>ni&longs;i ex terrena materia, &longs;eu ea &longs;it lignum, oleum, <lb/>adeps, &longs;eu alia pinguis &longs;ub&longs;tantia. </s> | <s id="id.000436">Dum etiam lapis projectus &longs;ur­<lb/>&longs;um, punctum &longs;upremum attigit, in quo quædam e&longs;t <lb/>veiuti libratio, exæquatis momentis virium tam mo­<lb/>uentium, quàm re&longs;i&longs;tentium; an-non deberet lapis <lb/>in eo penitùs conquie&longs;cere, vt non ex&longs;i&longs;tente in aëre <lb/>cau&longs;a, quæ lapidem magis adigat deor&longs;ùm, quàm, <lb/>&longs;ur&longs;um? </s> |
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| <s>Itaque hæc cor­<lb/>pora &longs;unt, quæ, qua&longs;i &longs;ui parteis, Terra continet, <lb/>neque auelli patitur, aut dum auelluntur, repetit: <lb/>tamet&longs;i, quia corpora plura in eodem &longs;imùl loco <pb pagenum="48"/>e&longs;&longs;e virtute naturæ non po&longs;&longs;unt, efficiatur, vt plu­<lb/>ribus corporibus &longs;imùl repetitis, attracti&longs;que à Ter­<lb/>ra, ea, quæ terrena magis fuerint, propiùs admoue­<lb/>antur, quæ minùs remotiùs con&longs;i&longs;tant; & vbi con­<lb/>tigerit i&longs;ta illorum locum, &longs;eu majorem terræ vici­<lb/>niam occupare, tum illis accedentibus, ab iis expel­<lb/>lantur, coganturque &longs;ecedere, & tendere &longs;ursùm; <lb/>ex quo illa grauia, hæc leuia dicuntur, vt fortè <lb/>occurret dicendum inferiùs. </s> | <s id="id.000437">Vt verum fatear, hæc difficultas videtur euin­<lb/>cere, aërem quidem e&longs;&longs;e po&longs;&longs;e cau&longs;am aliquam ad­<lb/>juuantem, adaugentemque motus deorsùm velo­<lb/>citatem; at non e&longs;&longs;e tamen &longs;olam vel &longs;u&longs;ficientem; <lb/>&longs;ed exigi prætereà aliam, quæ lapidi faciat motus <lb/>deor&longs;um initium, quæque re&longs;i&longs;tentiam aëris inferio­<lb/>ris vincat, vt cœptum &longs;emel motum aër &longs;uperior <lb/>promoueat, lapidem velut &longs;ollicitans, & continuò <lb/>magis, magi&longs;que in&longs;tigans. </s></p><p type="main"> |
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| <s>Heic &longs;olùm dico, de­<lb/>fendi po&longs;&longs;e ine&longs;&longs;e Terræ magneticam vim, quam cir­<lb/>cumquáque diffundat, quáque &longs;ui parteis conjunctas <lb/>contineat, & &longs;ejunctas ad &longs;e reducat, eo modo, quo <lb/>magnes fragmenta, &longs;eu parteis magnetis, atque <lb/>etiam ferri (quod magnetica quædam proles e&longs;t, vt <lb/>fit ex fodinis per&longs;picuum) & junctas cohibet, & cor­<lb/>ripit &longs;ejunctas. </s> | <s id="id.000438">XII. <!-- KEEP S--></s> |
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| <s>Addere po&longs;&longs;em globum hunc Terræ <lb/>nihil e&longs;&longs;e aliud, quàm grandem magnetem, vel eo <lb/>argumento, quòd magnes parua terra &longs;it, & à Gil­<lb/>berto proptereà <foreign lang="greek">imxvognh\</foreign> vocetur; cùm nempe vtri­<lb/>que &longs;ui &longs;int poli, &longs;uus axis, &longs;uus æquator, &longs;ui me­<lb/>ridiani, &longs;ui paralleli; cùm &longs;epo&longs;ita alteratione qua­<lb/>rumdam Terræ partium in ip&longs;a eius &longs;uperficie, cæ­<lb/>teræ habeant magneticam, &longs;eu ferri ip&longs;ius attractri­<lb/>cem vim, licet quædam manife&longs;tiorem, quædam <lb/>ob&longs;curiorem &longs;ortiantur, vtiargilla, lateres, alia: cùm <lb/>magnes eas &longs;ui parteis conuertat ad polos, quas in <lb/>minera (&longs;eu dum Terræ inh&ecedil;reret) conuer&longs;as ad po­<lb/>los pr&ecedil;habuerit: cùm ille proinde argumentetur præ­<lb/>ter hanc Terræ qua&longs;i cru&longs;tam, non multas orgyiarum <lb/>centurias infra &longs;uperficiem, proten&longs;am, reliquum <pb pagenum="49"/>Terræ qua&longs;i nucleum e&longs;&longs;e &longs;uâ naturâ, & &longs;ub&longs;tantia­<lb/>liter magnetem, ac huiu&longs;modi alia; Nihilominùs <lb/>placet &longs;olùm habere Terram, qua&longs;i magnetem, qua­<lb/>tenùs vt magnes emittit ex &longs;e corpu&longs;cula quædam, <lb/>&longs;eu radios, quibus corpora magnetica ad &longs;e alliciat; <lb/>ita videtur Terra emittere, quibus ad &longs;e alliciat, <lb/>pertrahatque corpora terrena. </s> | <s id="id.000439">Itaque præter cau&longs;am impellentem, videtur <lb/>e&longs;&longs;e nece&longs;&longs;arium ad attrahentem recurrere, quæ id <lb/>muneris ex&longs;equatur. </s> |
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| <s>Scilicet concipien­<lb/>dum e&longs;t effluere continuò ex Terra non modò vapo­<lb/>res, exhalationes, & vniuer&longs;è corpu&longs;cula, ex quibus <lb/>meteora gignuntur; aut ex quibus aëris corpus <lb/>contexi intelligitur; verùm etiam alia longè in&longs;en­<lb/>&longs;ibiliora, nec minùs &longs;ubtilia, quàm quæ ex ma­<lb/>gnete emanantia po&longs;&longs;unt etiam marmor præ &longs;ubtili­<lb/>tate &longs;ua penetrare. </s> | <s id="id.000440">Cæterùm, hæc vis quænam <lb/>alia &longs;it, quàm quæ totius globi Telluris propria &longs;it, <lb/>& magnetica dici po&longs;&longs;it? </s> |
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| <s>Ac emitti quidem ex Terra ali­<lb/>quid eiu&longs;cemodi improbabile magis foret, ni&longs;i (quod <lb/>antè inuimus) vel ip&longs;um magnetis exemplum &longs;uc­<lb/>curreret, ex quo emitti aliquid, tamet&longs;i in&longs;en&longs;en&longs;ibile, <lb/>ip&longs;a ferri attractio arguit. </s> | <s id="id.000441">Profecto cum globus tel­<lb/>luris totum quodpiam &longs;it, notum e&longs;t nullum e&longs;&longs;e <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.054.jpg" pagenum="47"/>totum à natura in&longs;titutum, cui non &longs;it in&longs;ita vis <lb/>&longs;ui ip&longs;ius con&longs;eruatrix, ac proinde qua parteis &longs;ui <lb/>cohærenteis contineat, &longs;eparationique illarum re&longs;i­<lb/>&longs;tat. </s> |
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| <s>Nam quamuis po&longs;&longs;is di­<lb/>cere non tam vi magnetis ferrum attrahi, quàm vi <lb/>&longs;ibi propria tendere ad ip&longs;um; &longs;altem, cùm ferrum <lb/>non ex quacúmque di&longs;tantiâ ad magnetem tendat, <lb/>&longs;ed &longs;olùm cùm vicinum e&longs;t; manife&longs;tum e&longs;t debere <lb/>aliquid ex magnete in ferrum emitti, quo vis ferri <lb/>propria velut admoneatur, & &longs;ollicitetur ad peten­<lb/>dum magnetem. </s> | <s id="id.000442">Ex hoc autem fit, vt &longs;i partes Terræ aliquo ca­<lb/>&longs;u auellantur, re&longs;i&longs;tat ip&longs;a, & vi &longs;ua, &longs;eu hamulis, <lb/>catenuli&longs;que in&longs;en&longs;ilibus retrahat, vt dum quis ma­<lb/>num à &longs;e abduci extento bracchio non patitur, & <lb/>abductam vi &longs;ua, &longs;eu &longs;piritibus per neruos tran&longs;mi&longs;­<lb/>&longs;is retrahit in &longs;e ip&longs;um. </s> |
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| <s>Et fac loco magnetis, emi&longs;&longs;ionem <lb/>&longs;ieri ex ferro, fac ex vtróque, perinde erit; &longs;atis e&longs;t <lb/>&longs;ieri aliquod effluuium, quod &longs;it infra &longs;en&longs;um, & quo <lb/>intercedente vnum corpus pelliciatur ad aliud. </s> | <s id="id.000443">Terrem autem globi parteis, <lb/>&longs;eu terrena corpora voco, non modo parteis terræ, <lb/>& aquæ (quæ e&longs;t globi terreni pars liquida, & qua­<lb/>&longs;i &longs;anguis in animali) verùm etiam tam lapides, me­<lb/>talla, cætera fo&longs;&longs;ilia, plantas, animalia, & quæcùm­<lb/>que terræ, & aquæ manife&longs;tam originem debent, in <lb/>quibus habeo etiam pluuiam, rorem, niucm, gran­<lb/>dinem, & meteora cætera, itemque vapores, & ex­<lb/>halationes; quàm ip&longs;um quoque aërem, quo tellus <lb/>qua&longs;i circumve&longs;titur, vt malum cotoneum &longs;ua lanu­<lb/>gine (quoniam &longs;i ex hoc circum terram &longs;patio de­<lb/>mas vapores, halitu&longs;que, ac vniuer&longs;è omneis fumos, <lb/>& corpu&longs;cula, quæ ex terra, & aqua continuò ex­<lb/>primuntur, a&longs;cenduntque, & de&longs;cendunt, varieque <lb/>mouentur, aut quie&longs;cunt; quod &longs;upererit nihil aliud <lb/>fore intelligitur, quàm inane &longs;patium) denique ip­<lb/>&longs;um etiam ignem; quem manife&longs;tum e&longs;t non gigni <lb/>ni&longs;i ex terrena materia, &longs;eu ea &longs;it lignum, oleum, <lb/>adeps, &longs;eu alia pinguis &longs;ub&longs;tantia. </s> |
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| <s>Quid­<lb/>ni verò nece&longs;&longs;e &longs;it aliquid intercedere, cùm nulla <lb/>actio phy&longs;ica &longs;it &longs;ine agente phy&longs;ico; neque phy&longs;i-<pb pagenum="50"/>cum vllum agens, ni&longs;i in&longs;trumento intercedente, age­<lb/>re po&longs;&longs;it in rem di&longs;tantem? </s> | <s id="id.000444">Itaque hæc cor­<lb/>pora &longs;unt, quæ, qua&longs;i &longs;ui parteis, Terra continet, <lb/>neque auelli patitur, aut dum auelluntur, repetit: <lb/>tamet&longs;i, quia corpora plura in eodem &longs;imùl loco <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.055.jpg" pagenum="48"/>e&longs;&longs;e virtute naturæ non po&longs;&longs;unt, efficiatur, vt plu­<lb/>ribus corporibus &longs;imùl repetitis, attracti&longs;que à Ter­<lb/>ra, ea, quæ terrena magis fuerint, propiùs admoue­<lb/>antur, quæ minùs remotiùs con&longs;i&longs;tant; & vbi con­<lb/>tigerit i&longs;ta illorum locum, &longs;eu majorem terræ vici­<lb/>niam occupare, tum illis accedentibus, ab iis expel­<lb/>lantur, coganturque &longs;ecedere, & tendere &longs;ursùm; <lb/>ex quo illa grauia, hæc leuia dicuntur, vt fortè <lb/>occurret dicendum inferiùs. </s> |
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| <s>Neque &longs;u&longs;ficit dicere <lb/>emitti ex magnete v&longs;que qualitatem quandam in <lb/>ferrum; ni&longs;i dicantur &longs;imùl emitti in&longs;en&longs;ilia cor­<lb/>pu&longs;cula, quæ &longs;int qua&longs;i vehiculum eiu&longs;cemodi qua­<lb/>litatis. </s> | <s id="id.000445">Heic &longs;olùm dico, de­<lb/>fendi po&longs;&longs;e ine&longs;&longs;e Terræ magneticam vim, quam cir­<lb/>cumquáque diffundat, quáque &longs;ui parteis conjunctas <lb/>contineat, & &longs;ejunctas ad &longs;e reducat, eo modo, quo <lb/>magnes fragmenta, &longs;eu parteis magnetis, atque <lb/>etiam ferri (quod magnetica quædam proles e&longs;t, vt <lb/>fit ex fodinis per&longs;picuum) & junctas cohibet, & cor­<lb/>ripit &longs;ejunctas. </s> |
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| <s>Nempe qualitas, quod accidens &longs;it, ince­<lb/>dere &longs;olitarie non pote&longs;t, neque dici pote&longs;t alterari <lb/>à magnete acrem, lignum, chartam, qu<gap/>dlibet in­<lb/>terpo&longs;itum, à quo denique ferrum alteretur: &longs;iqui­<lb/>dem nulla fit alteratio in corporibus interpo&longs;itis; <lb/>per quæ &longs;i ferrum alteratum attraheretur, deberent <lb/>&longs;anè ip&longs;a quoque alterata attrahi magis. </s> | <s id="id.000446">Addere po&longs;&longs;em globum hunc Terræ <lb/>nihil e&longs;&longs;e aliud, quàm grandem magnetem, vel eo <lb/>argumento, quòd magnes parua terra &longs;it, & à Gil­<lb/>berto proptereà <foreign lang="greek">imxvognh\</foreign> vocetur; cùm nempe vtri­<lb/>que &longs;ui &longs;int poli, &longs;uus axis, &longs;uus æquator, &longs;ui me­<lb/>ridiani, &longs;ui paralleli; cùm &longs;epo&longs;ita alteratione qua­<lb/>rumdam Terræ partium in ip&longs;a eius &longs;uperficie, cæ­<lb/>teræ habeant magneticam, &longs;eu ferri ip&longs;ius attractri­<lb/>cem vim, licet quædam manife&longs;tiorem, quædam <lb/>ob&longs;curiorem &longs;ortiantur, vtiargilla, lateres, alia: cùm <lb/>magnes eas &longs;ui parteis conuertat ad polos, quas in <lb/>minera (&longs;eu dum Terræ inh&ecedil;reret) conuer&longs;as ad po­<lb/>los pr&ecedil;habuerit: cùm ille proinde argumentetur præ­<lb/>ter hanc Terræ qua&longs;i cru&longs;tam, non multas orgyiarum <lb/>centurias infra &longs;uperficiem, proten&longs;am, reliquum <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.056.jpg" pagenum="49"/>Terræ qua&longs;i nucleum e&longs;&longs;e &longs;uâ naturâ, & &longs;ub&longs;tantia­<lb/>liter magnetem, ac huiu&longs;modi alia; Nihilominùs <lb/>placet &longs;olùm habere Terram, qua&longs;i magnetem, qua­<lb/>tenùs vt magnes emittit ex &longs;e corpu&longs;cula quædam, <lb/>&longs;eu radios, quibus corpora magnetica ad &longs;e alliciat; <lb/>ita videtur Terra emittere, quibus ad &longs;e alliciat, <lb/>pertrahatque corpora terrena. </s> |
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| <s>Emitti ergo <lb/>ex magnete corpu&longs;cula in ferrum debent, quæ agere <lb/>in ip&longs;um po&longs;&longs;int; eo modò, quo ex re odorata non <lb/>qualitas nuda odoris aut &longs;olitariè emittitur, aut <lb/>aërem alterat; &longs;ed effunditur &longs;imùl vapor, contex­<lb/>turave aliqua corpu&longs;culorum tenui&longs;&longs;imorum, quæ <lb/>vbi ad olfactus organum peruenerint, in ip&longs;um agant, <lb/>odori que, &longs;eu rei odoratæ &longs;en&longs;ionem faciant. </s> | <s id="id.000447">Scilicet concipien­<lb/>dum e&longs;t effluere continuò ex Terra non modò vapo­<lb/>res, exhalationes, & vniuer&longs;è corpu&longs;cula, ex quibus <lb/>meteora gignuntur; aut ex quibus aëris corpus <lb/>contexi intelligitur; verùm etiam alia longè in&longs;en­<lb/>&longs;ibiliora, nec minùs &longs;ubtilia, quàm quæ ex ma­<lb/>gnete emanantia po&longs;&longs;unt etiam marmor præ &longs;ubtili­<lb/>tate &longs;ua penetrare. </s> |
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| <s>Et <lb/>certè quemadmodum odor cum vapore, &longs;eu halitu <lb/>&longs;uo ex re odorata tandem euane&longs;cit, atque exhau­<lb/>ritur; ita contingere videmus & in magnete, & in <lb/>ferro, quod ex affrictu cum magnete vim attrahen­<lb/>di contraxerit; nempe i&longs;ta vis &longs;en&longs;im elangue&longs;cit; <lb/>neque id pote&longs;t contingere, ni&longs;i effluxu continuo ip­<lb/>&longs;a corpu&longs;cula exhauria<gap/>tur. </s></p><p type="main"> | <s id="id.000448">Ac emitti quidem ex Terra ali­<lb/>quid eiu&longs;cemodi improbabile magis foret, ni&longs;i (quod <lb/>antè inuimus) vel ip&longs;um magnetis exemplum &longs;uc­<lb/>curreret, ex quo emitti aliquid, tamet&longs;i in&longs;en&longs;en&longs;ibile, <lb/>ip&longs;a ferri attractio arguit. </s> |
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| <s>XIII. <!-- KEEP S--></s> | <s id="id.000449">Nam quamuis po&longs;&longs;is di­<lb/>cere non tam vi magnetis ferrum attrahi, quàm vi <lb/>&longs;ibi propria tendere ad ip&longs;um; &longs;altem, cùm ferrum <lb/>non ex quacúmque di&longs;tantiâ ad magnetem tendat, <lb/>&longs;ed &longs;olùm cùm vicinum e&longs;t; manife&longs;tum e&longs;t debere <lb/>aliquid ex magnete in ferrum emitti, quo vis ferri <lb/>propria velut admoneatur, & &longs;ollicitetur ad peten­<lb/>dum magnetem. </s> |
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| <s>An forte dices corpora alia, vt objecta <lb/>&longs;unt vi&longs;us, vel auditus, agere in ip&longs;a &longs;en&longs;uum or­<lb/>gana, ab&longs;que huiu&longs;modi effluxu, &longs;eu emi&longs;&longs;ione cor­<lb/>pu&longs;culorum? </s> | <s id="id.000450">Et fac loco magnetis, emi&longs;&longs;ionem <lb/>&longs;ieri ex ferro, fac ex vtróque, perinde erit; &longs;atis e&longs;t <lb/>&longs;ieri aliquod effluuium, quod &longs;it infra &longs;en&longs;um, & quo <lb/>intercedente vnum corpus pelliciatur ad aliud. </s> |
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| <s>Verùm cùm hoc ip&longs;um in que&longs;tione <pb pagenum="51"/>&longs;it, probabilitate quoque &longs;ua non caret, emitti quæ­<lb/>dem &longs;pecialia lucis, colotis, &longs;oni corpu&longs;cula, quæ <lb/>organa &longs;en&longs;uum afficiant; idque vel ip&longs;a demul­<lb/>cendo, attrahendoque ad &longs;e mellitis qua&longs;i catenu­<lb/>lis, vt quæ ex rebus pulcris, con&longs;onantibu&longs;que pro­<lb/>cedunt; vel eadem di&longs;cerpendo, abigendoque &longs;ca­<lb/>bris, acuti&longs;que quibu&longs;dam qua&longs;i contulis, &longs;piculi&longs;­<lb/>que, vt quæ ex rebus deformibus, di&longs;&longs;onantibu&longs;que <lb/>oriuntur. </s> | <s id="id.000451">Quid­<lb/>ni verò nece&longs;&longs;e &longs;it aliquid intercedere, cùm nulla <lb/>actio phy&longs;ica &longs;it &longs;ine agente phy&longs;ico; neque phy&longs;i-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.057.jpg" pagenum="50"/>cum vllum agens, ni&longs;i in&longs;trumento intercedente, age­<lb/>re po&longs;&longs;it in rem di&longs;tantem? </s> |
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| <s>Ridebis forta&longs;&longs;e, quia hæc in&longs;trumenta ne­<lb/>que di&longs;cerni oculis, neque attrectari manibus po&longs;­<lb/>&longs;ent; &longs;ed peruidebis facilè vel ex ip&longs;o &longs;en&longs;u olfa­<lb/>ctus in&longs;trumenta quædam eiu&longs;modi e&longs;&longs;e, quæ tamen <lb/>neque ad oculum, neque ad manum exigi po&longs;&longs;int: <lb/>Quæ&longs;o, dum prope cloacam tran&longs;is, quid e&longs;t, quod <lb/>inde te abigit? </s> | <s id="id.000452">Neque &longs;u&longs;ficit dicere <lb/>emitti ex magnete v&longs;que qualitatem quandam in <lb/>ferrum; ni&longs;i dicantur &longs;imùl emitti in&longs;en&longs;ilia cor­<lb/>pu&longs;cula, quæ &longs;int qua&longs;i vehiculum eiu&longs;cemodi qua­<lb/>litatis. </s> |
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| <s>An vides quidpiam oculis, aut tan­<lb/>gis quidpiam manibus, quod te cogat ab&longs;cedere<gap/><lb/>Non &longs;anè; &longs;ed e&longs;t tamen quidpiam, nempe halitus <lb/>teter, qui cùm impactus in oculum, aut manum &longs;ui <lb/>&longs;en&longs;um non faciat, facit tamen impactus in intimas <lb/>nareis, in quibus quæ re&longs;idet pars, &longs;iue facultas &longs;en­<lb/>tiens offenditur, ac refugit, corpu&longs;que tuum inde <lb/>auertit: eodem planè modo, quo, &longs;i manus, aut <lb/>alia pars corporis examine quodam ve&longs;parum, vibra­<lb/>tis aculeis in&longs;ectantium, compungeretur. </s> | <s id="id.000453">Nempe qualitas, quod accidens &longs;it, ince­<lb/>dere &longs;olitarie non pote&longs;t, neque dici pote&longs;t alterari <lb/>à magnete acrem, lignum, chartam, qu<gap/>dlibet in­<lb/>terpo&longs;itum, à quo denique ferrum alteretur: &longs;iqui­<lb/>dem nulla fit alteratio in corporibus interpo&longs;itis; <lb/>per quæ &longs;i ferrum alteratum attraheretur, deberent <lb/>&longs;anè ip&longs;a quoque alterata attrahi magis. </s> |
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| <s>Di&longs;crimen <lb/>e&longs;t &longs;olùm, quòd fœtoris aculei &longs;int incomparabi­<lb/>liter &longs;ubtiliores ve&longs;parum aculeis, qui ip&longs;i iam &longs;ub­<lb/>tiles &longs;unt; idque &longs;ubinnuo, vt intelligas, quantò <lb/>&longs;en&longs;us vi&longs;us (idemque proportione dico de auditu) <lb/>e&longs;t incomparabiliter olfactu &longs;ubtilior; tantò aculeos <lb/>ex re deformi emi&longs;&longs;os, e&longs;&longs;e adhûc po&longs;&longs;e incompara-<pb pagenum="52"/>biliter &longs;ubtiliores iis, qui à re fœtida emittuntur; <lb/>vtque ex effectu oppo&longs;ito intelligas, radios illos, & <lb/>qua&longs;i catenulas, vncinulo&longs;que rei pulcræ e&longs;&longs;e po&longs;&longs;e <lb/>incomparabiliter &longs;ubtiliores iis, quibus ro&longs;a nareis <lb/>ad &longs;e pellicit. </s> | <s id="id.000454">Emitti ergo <lb/>ex magnete corpu&longs;cula in ferrum debent, quæ agere <lb/>in ip&longs;um po&longs;&longs;int; eo modò, quo ex re odorata non <lb/>qualitas nuda odoris aut &longs;olitariè emittitur, aut <lb/>aërem alterat; &longs;ed effunditur &longs;imùl vapor, contex­<lb/>turave aliqua corpu&longs;culorum tenui&longs;&longs;imorum, quæ <lb/>vbi ad olfactus organum peruenerint, in ip&longs;um agant, <lb/>odori que, &longs;eu rei odoratæ &longs;en&longs;ionem faciant. </s> |
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| <s>Vnum reperies difficile; videlicet <lb/>imaginari tenuïtatem illam incredibilem huiu&longs;modi <lb/>corpu&longs;culorum: &longs;ed quia iam legi&longs;ti, opinor, in <lb/>exemplo epi&longs;tolæ &longs;uperiore Augu&longs;to ad Licetum <lb/>&longs;criptæ, quod e&longs;t Luillerio præ manibus, vnde <lb/>po&longs;&longs;is exi&longs;timare difficultatem e&longs;&longs;e &longs;ubmotam, ideò <lb/>&longs;ubmouere non aggredior heic. </s> | <s id="id.000455">Et <lb/>certè quemadmodum odor cum vapore, &longs;eu halitu <lb/>&longs;uo ex re odorata tandem euane&longs;cit, atque exhau­<lb/>ritur; ita contingere videmus & in magnete, & in <lb/>ferro, quod ex affrictu cum magnete vim attrahen­<lb/>di contraxerit; nempe i&longs;ta vis &longs;en&longs;im elangue&longs;cit; <lb/>neque id pote&longs;t contingere, ni&longs;i effluxu continuo ip­<lb/>&longs;a corpu&longs;cula exhauria<gap/>tur. </s></p><p type="main"> |
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| <s>Velim &longs;olùm con­<lb/>&longs;ideres eam e&longs;&longs;e &longs;en&longs;uum no&longs;trorum hebetudinem, <lb/>eam naturæ &longs;ubtilitatem, vt vbi &longs;ubtilitas no&longs;tra de­<lb/>&longs;init, &longs;uam explicare natura incipiat; veluti dum ex&longs;ol­<lb/>uit, aut compingit animalculum A cari ex innumeris <lb/>prope illis myriadibus particularum, &longs;ine quibus id <lb/>animal con&longs;tare omninô non pote&longs;t; & in cuius tamen <lb/>paruitatem acuties no&longs;tra de&longs;init: aut dum ex cor­<lb/>poris &longs;uper&longs;icie continenter deradit vi&longs;ibileis &longs;pe­<lb/>cies, & qua&longs;i membranulas (ni&longs;i malis has totas e&longs;&longs;e <lb/>à lucidis corporibus ex &longs;uperficiebus corporum re­<lb/>flexas) quæ vix tandem po&longs;t multa &longs;æcula coaduna­<lb/>tæ, vnius telæ araneæ cra&longs;&longs;itudini exæquari po&longs;&longs;int. <lb/></s> | <s id="id.000456">XIII. <!-- KEEP S--></s> |
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| <s>Heinc &longs;anè minùs mirabere, minu&longs;que ridiculum <lb/>duces, quod propono tibi de illa ineffabili, aut in­<lb/>excogitabili potiùs tenuitate organulorum, quibus <lb/>agentia naturalia in eliciendis illis &longs;uis planè admi­<lb/>rabilibus operationibus vtuntur. </s> | <s id="id.000457">An forte dices corpora alia, vt objecta <lb/>&longs;unt vi&longs;us, vel auditus, agere in ip&longs;a &longs;en&longs;uum or­<lb/>gana, ab&longs;que huiu&longs;modi effluxu, &longs;eu emi&longs;&longs;ione cor­<lb/>pu&longs;culorum? </s> |
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| <s>Vtcúmque &longs;it &longs;anè, <lb/>ip&longs;e non percipio, quomodo quicquid per &longs;ympa­<lb/>thiam, aut antipathiam perhibetur agere, agat reip&longs;â, <pb pagenum="53"/>ni&longs;i immittendo in eam rem, quam allicit, abigit, aut <lb/>quo modo cúmque mouet, tenui&longs;&longs;ima organula, qui­<lb/>bus illam excitet, & ad motum compellat. </s> | <s id="id.000458">Verùm cùm hoc ip&longs;um in que&longs;tione <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.058.jpg" pagenum="51"/>&longs;it, probabilitate quoque &longs;ua non caret, emitti quæ­<lb/>dem &longs;pecialia lucis, colotis, &longs;oni corpu&longs;cula, quæ <lb/>organa &longs;en&longs;uum afficiant; idque vel ip&longs;a demul­<lb/>cendo, attrahendoque ad &longs;e mellitis qua&longs;i catenu­<lb/>lis, vt quæ ex rebus pulcris, con&longs;onantibu&longs;que pro­<lb/>cedunt; vel eadem di&longs;cerpendo, abigendoque &longs;ca­<lb/>bris, acuti&longs;que quibu&longs;dam qua&longs;i contulis, &longs;piculi&longs;­<lb/>que, vt quæ ex rebus deformibus, di&longs;&longs;onantibu&longs;que <lb/>oriuntur. </s> |
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| <s>Id &longs;olùm <lb/>notandum, non excitari, aut moueri rem ab hi&longs;ce <lb/>organulis, ni&longs;i eæ particulæ, quibus illa excipit, ana­<lb/>logiam quandam, &longs;eu proportionem cùm ip&longs;is ha­<lb/>beant; hoc e&longs;t, vt &longs;i illa &longs;int v.c. </s> | <s id="id.000459">Ridebis forta&longs;&longs;e, quia hæc in&longs;trumenta ne­<lb/>que di&longs;cerni oculis, neque attrectari manibus po&longs;­<lb/>&longs;ent; &longs;ed peruidebis facilè vel ex ip&longs;o &longs;en&longs;u olfa­<lb/>ctus in&longs;trumenta quædam eiu&longs;modi e&longs;&longs;e, quæ tamen <lb/>neque ad oculum, neque ad manum exigi po&longs;&longs;int: <lb/>Quæ&longs;o, dum prope cloacam tran&longs;is, quid e&longs;t, quod <lb/>inde te abigit? </s> |
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| <s>vncinuli, res an&longs;ulas <lb/>habeat ip&longs;is re&longs;pondenteis; &longs;i aculei, res habeat <lb/>particulas, quæ ab ip&longs;is premi, configique po&longs;&longs;int: <lb/>&longs;i figuram certam habentia, res &longs;patiola habeat vel <lb/>pari modo configurata, vnde accommodatio, ac <lb/>lenitas; vel di&longs;pari, vnde laceratio, ac a&longs;peritas, & <lb/>ita de aliis. </s> | <s id="id.000460">An vides quidpiam oculis, aut tan­<lb/>gis quidpiam manibus, quod te cogat ab&longs;cedere<gap/><lb/>Non &longs;anè; &longs;ed e&longs;t tamen quidpiam, nempe halitus <lb/>teter, qui cùm impactus in oculum, aut manum &longs;ui <lb/>&longs;en&longs;um non faciat, facit tamen impactus in intimas <lb/>nareis, in quibus quæ re&longs;idet pars, &longs;iue facultas &longs;en­<lb/>tiens offenditur, ac refugit, corpu&longs;que tuum inde <lb/>auertit: eodem planè modo, quo, &longs;i manus, aut <lb/>alia pars corporis examine quodam ve&longs;parum, vibra­<lb/>tis aculeis in&longs;ectantium, compungeretur. </s> |
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| <s>Atque ex hac quidem cau&longs;a e&longs;&longs;e po­<lb/>te&longs;t, cur præ cæteris ip&longs;a magnetis organula reperire <lb/>particulas analogicas debeant, vt vim in illas expri­<lb/>mant &longs;uam. </s> | <s id="id.000461">Di&longs;crimen <lb/>e&longs;t &longs;olùm, quòd fœtoris aculei &longs;int incomparabi­<lb/>liter &longs;ubtiliores ve&longs;parum aculeis, qui ip&longs;i iam &longs;ub­<lb/>tiles &longs;unt; idque &longs;ubinnuo, vt intelligas, quantò <lb/>&longs;en&longs;us vi&longs;us (idemque proportione dico de auditu) <lb/>e&longs;t incomparabiliter olfactu &longs;ubtilior; tantò aculeos <lb/>ex re deformi emi&longs;&longs;os, e&longs;&longs;e adhûc po&longs;&longs;e incompara-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.059.jpg" pagenum="52"/>biliter &longs;ubtiliores iis, qui à re fœtida emittuntur; <lb/>vtque ex effectu oppo&longs;ito intelligas, radios illos, & <lb/>qua&longs;i catenulas, vncinulo&longs;que rei pulcræ e&longs;&longs;e po&longs;&longs;e <lb/>incomparabiliter &longs;ubtiliores iis, quibus ro&longs;a nareis <lb/>ad &longs;e pellicit. </s> |
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| <s>Nimirùm paleam, papyrum, lignum, <lb/>lapidem, quidvis aliud illibatum prætereunt, &longs;olum­<lb/>modóque &longs;iue ferrum, &longs;iue magnetem alium affice­<lb/>re deprehenduntur. </s> | <s id="id.000462">Vnum reperies difficile; videlicet <lb/>imaginari tenuïtatem illam incredibilem huiu&longs;modi <lb/>corpu&longs;culorum: &longs;ed quia iam legi&longs;ti, opinor, in <lb/>exemplo epi&longs;tolæ &longs;uperiore Augu&longs;to ad Licetum <lb/>&longs;criptæ, quod e&longs;t Luillerio præ manibus, vnde <lb/>po&longs;&longs;is exi&longs;timare difficultatem e&longs;&longs;e &longs;ubmotam, ideò <lb/>&longs;ubmouere non aggredior heic. </s> |
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| <s>Hac certè ratione vapor odora­<lb/>tus præterit, quod dicebam mox, manum, oculum, <lb/>cæteras parteis corporis; afficitque &longs;olùm intra na­<lb/>ries ip&longs;um olfactus organum, quòd in eo &longs;olo re­<lb/>ceptacula analogica inueniat. </s> | <s id="id.000463">Velim &longs;olùm con­<lb/>&longs;ideres eam e&longs;&longs;e &longs;en&longs;uum no&longs;trorum hebetudinem, <lb/>eam naturæ &longs;ubtilitatem, vt vbi &longs;ubtilitas no&longs;tra de­<lb/>&longs;init, &longs;uam explicare natura incipiat; veluti dum ex&longs;ol­<lb/>uit, aut compingit animalculum A cari ex innumeris <lb/>prope illis myriadibus particularum, &longs;ine quibus id <lb/>animal con&longs;tare omninô non pote&longs;t; & in cuius tamen <lb/>paruitatem acuties no&longs;tra de&longs;init: aut dum ex cor­<lb/>poris &longs;uper&longs;icie continenter deradit vi&longs;ibileis &longs;pe­<lb/>cies, & qua&longs;i membranulas (ni&longs;i malis has totas e&longs;&longs;e <lb/>à lucidis corporibus ex &longs;uperficiebus corporum re­<lb/>flexas) quæ vix tandem po&longs;t multa &longs;æcula coaduna­<lb/>tæ, vnius telæ araneæ cra&longs;&longs;itudini exæquari po&longs;&longs;int. <lb/></s> |
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| <s>Sed difficile fortè erit <lb/>captu organula hæc, corpu&longs;culave magnetica pene­<lb/>trare non modò pannum, chartam, lignum, corpo­<lb/>rave alia laxiora; verùm etiam marmor, quod antè <lb/>dicebam, aliquot cra&longs;&longs;um digitis, vltra quod ma­<lb/>gnes commouere ferri ramenta, & fragminula ob­<lb/>&longs;eruatur Attamen reuoca in mentem, illam, cuius <lb/>iam memini, &longs;ubtilitatem naturæ. </s> | <s id="id.000464">Heinc &longs;anè minùs mirabere, minu&longs;que ridiculum <lb/>duces, quod propono tibi de illa ineffabili, aut in­<lb/>excogitabili potiùs tenuitate organulorum, quibus <lb/>agentia naturalia in eliciendis illis &longs;uis planè admi­<lb/>rabilibus operationibus vtuntur. </s> |
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| <s>Con&longs;idera etiam <pb pagenum="54"/>nullum e&longs;&longs;e corpus adeò &longs;olidum, quod non &longs;it in­<lb/>numeris poris, meatuli&longs;que peruium; quanquam per <lb/>illos corpu&longs;cula cuiu&longs;cumque generis traijci non po&longs;­<lb/>&longs;int. </s> | <s id="id.000465">Vtcúmque &longs;it &longs;anè, <lb/>ip&longs;e non percipio, quomodo quicquid per &longs;ympa­<lb/>thiam, aut antipathiam perhibetur agere, agat reip&longs;â, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.060.jpg" pagenum="53"/>ni&longs;i immittendo in eam rem, quam allicit, abigit, aut <lb/>quo modo cúmque mouet, tenui&longs;&longs;ima organula, qui­<lb/>bus illam excitet, & ad motum compellat. </s> |
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| <s>Scilicet corpu&longs;cula olei corpora peruadunt, <lb/>quæ corpu&longs;cula aquæ penetrare non po&longs;&longs;unt; &, &longs;i <lb/>accipias vas terreum optimè illitum, id quidem ne­<lb/>que aquæ, neque olei penetrabunt corpu&longs;cula; &longs;ed <lb/>penetrabunt tamen corpu&longs;cula &longs;alis, atque adeò vias <lb/>&longs;ibi patulas, quæ aliis &longs;uerant cæcæ, imperviæque, <lb/>reperient. </s> | <s id="id.000466">Id &longs;olùm <lb/>notandum, non excitari, aut moueri rem ab hi&longs;ce <lb/>organulis, ni&longs;i eæ particulæ, quibus illa excipit, ana­<lb/>logiam quandam, &longs;eu proportionem cùm ip&longs;is ha­<lb/>beant; hoc e&longs;t, vt &longs;i illa &longs;int v.c. </s> |
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| <s>Sic corpu&longs;cula i&longs;ta non tran&longs;eunt per vi­<lb/>trum, per quod tran&longs;eunt tamen corpu&longs;cula lucis, <lb/>& aliunde tamen corpu&longs;cula lucis ea non pertran­<lb/>&longs;eunt, quæ corpu&longs;cula aquæ, olei, &longs;alis. </s> | <s id="id.000467">vncinuli, res an&longs;ulas <lb/>habeat ip&longs;is re&longs;pondenteis; &longs;i aculei, res habeat <lb/>particulas, quæ ab ip&longs;is premi, configique po&longs;&longs;int: <lb/>&longs;i figuram certam habentia, res &longs;patiola habeat vel <lb/>pari modo configurata, vnde accommodatio, ac <lb/>lenitas; vel di&longs;pari, vnde laceratio, ac a&longs;peritas, & <lb/>ita de aliis. </s> |
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| <s>Quippe <lb/>ni&longs;i proportio &longs;it magnitudinis, & figuræ inter mea­<lb/>tulos, & corpu&longs;cula, quæ non po&longs;&longs;unt non e&longs;&longs;e in­<lb/>ter &longs;e & inæqualis cra&longs;&longs;itudinis, & diuer&longs;imodè figu­<lb/>rata, &longs;ieri pertran&longs;itio non pote&longs;t. </s> | <s id="id.000468">Atque ex hac quidem cau&longs;a e&longs;&longs;e po­<lb/>te&longs;t, cur præ cæteris ip&longs;a magnetis organula reperire <lb/>particulas analogicas debeant, vt vim in illas expri­<lb/>mant &longs;uam. </s> |
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| <s>Itaque mirum non <lb/>e&longs;t, &longs;i magnetis corpu&longs;cula meatulos &longs;ubeant, per­<lb/>uadantque, per quos alia non traijciuntur, cùm ea <lb/>præ&longs;ertim &longs;ubtilitate e&longs;&longs;e valeant, vt in paucos, aut <lb/>etiam nullos non &longs;atis patulos incurrant. </s></p><p type="main"> | <s id="id.000469">Nimirùm paleam, papyrum, lignum, <lb/>lapidem, quidvis aliud illibatum prætereunt, &longs;olum­<lb/>modóque &longs;iue ferrum, &longs;iue magnetem alium affice­<lb/>re deprehenduntur. </s> |
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| <s>XIV. <!-- KEEP S--></s> | <s id="id.000470">Hac certè ratione vapor odora­<lb/>tus præterit, quod dicebam mox, manum, oculum, <lb/>cæteras parteis corporis; afficitque &longs;olùm intra na­<lb/>ries ip&longs;um olfactus organum, quòd in eo &longs;olo re­<lb/>ceptacula analogica inueniat. </s> |
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| <s>Verùm vbi conce&longs;&longs;um fuerit corpu&longs;cula <lb/>quædam ex magnete procedere, quæ ferrum ad ip­<lb/>&longs;um pelliciant; intelligi-ne tamen pote&longs;t, aut qua <lb/>formâ &longs;int, vt attractionis organa fiant; aut quomo­<lb/>do, quave ratione attractio per illa po&longs;&longs;it peragi? <lb/></s> | <s id="id.000471">Sed difficile fortè erit <lb/>captu organula hæc, corpu&longs;culave magnetica pene­<lb/>trare non modò pannum, chartam, lignum, corpo­<lb/>rave alia laxiora; verùm etiam marmor, quod antè <lb/>dicebam, aliquot cra&longs;&longs;um digitis, vltra quod ma­<lb/>gnes commouere ferri ramenta, & fragminula ob­<lb/>&longs;eruatur Attamen reuoca in mentem, illam, cuius <lb/>iam memini, &longs;ubtilitatem naturæ. </s> |
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| <s>Heic &longs;anè pr&ecedil;&longs;ertìm conjectandum e&longs;t, cùm non mo­<lb/>do difficile, &longs;ed impo&longs;&longs;ibile etiam &longs;it agno&longs;cere ger­<lb/>manum modum, quo intima rerum natura admira­<lb/>bileis illas &longs;uas operationes ex&longs;equitur. </s> | <s id="id.000472">Con&longs;idera etiam <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.061.jpg" pagenum="54"/>nullum e&longs;&longs;e corpus adeò &longs;olidum, quod non &longs;it in­<lb/>numeris poris, meatuli&longs;que peruium; quanquam per <lb/>illos corpu&longs;cula cuiu&longs;cumque generis traijci non po&longs;­<lb/>&longs;int. </s> |
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| <s>An-non <pb pagenum="55"/>proinde e&longs;t, quòd condones, &longs;i vt ob&longs;curè &longs;olùm <lb/>conijcio, ita confu&longs;è &longs;olùm balbutiam? </s> | <s id="id.000473">Scilicet corpu&longs;cula olei corpora peruadunt, <lb/>quæ corpu&longs;cula aquæ penetrare non po&longs;&longs;unt; &, &longs;i <lb/>accipias vas terreum optimè illitum, id quidem ne­<lb/>que aquæ, neque olei penetrabunt corpu&longs;cula; &longs;ed <lb/>penetrabunt tamen corpu&longs;cula &longs;alis, atque adeò vias <lb/>&longs;ibi patulas, quæ aliis &longs;uerant cæcæ, imperviæque, <lb/>reperient. </s> |
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| <s>&longs;i nihil tan­<lb/>quam ratum, exploratúmque, & de quo dubitare <lb/>non liceat, diuendam, neque velim vnquam pr&ecedil;ju­<lb/>dicium factum per&longs;crutantibus, excogitantibu&longs;que <lb/>meliora? </s> | <s id="id.000474">Sic corpu&longs;cula i&longs;ta non tran&longs;eunt per vi­<lb/>trum, per quod tran&longs;eunt tamen corpu&longs;cula lucis, <lb/>& aliunde tamen corpu&longs;cula lucis ea non pertran­<lb/>&longs;eunt, quæ corpu&longs;cula aquæ, olei, &longs;alis. </s> |
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| <s>Nullum non ver&longs;o lapidem, vt experiar, &longs;i <lb/>fortè quidpiam occurrat veri&longs;imile; & cum ingenuè <lb/>profitear e&longs;&longs;e vbique angu&longs;tias, videor mihi e&longs;&longs;e ex­<lb/>cu&longs;atione non indignus, dum recantare &longs;emper pa­<lb/>ratus, illud interim profero, quod videatur præ <lb/>cæteris &longs;imilitudinem habere cum vero. </s> | <s id="id.000475">Quippe <lb/>ni&longs;i proportio &longs;it magnitudinis, & figuræ inter mea­<lb/>tulos, & corpu&longs;cula, quæ non po&longs;&longs;unt non e&longs;&longs;e in­<lb/>ter &longs;e & inæqualis cra&longs;&longs;itudinis, & diuer&longs;imodè figu­<lb/>rata, &longs;ieri pertran&longs;itio non pote&longs;t. </s> |
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| <s>In hoc <lb/>negotio, cum videatur e&longs;&longs;e &longs;atis per&longs;picuum, non <lb/>po&longs;&longs;e vnum corpus attrahere aliud, ni&longs;i tran&longs;mittat <lb/>aliquid, quo illud ad &longs;e pertrahat; ecquis e&longs;t tamen <lb/>adeo &longs;olers, qui conijciat, aut explicet, cuiu&longs;modi <lb/>id &longs;it, quod magnes, qua&longs;i organum, vt ferrum ad &longs;e <lb/>accer&longs;at, tran&longs;mittit? </s> | <s id="id.000476">Itaque mirum non <lb/>e&longs;t, &longs;i magnetis corpu&longs;cula meatulos &longs;ubeant, per­<lb/>uadantque, per quos alia non traijciuntur, cùm ea <lb/>præ&longs;ertim &longs;ubtilitate e&longs;&longs;e valeant, vt in paucos, aut <lb/>etiam nullos non &longs;atis patulos incurrant. </s></p><p type="main"> |
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| <s>A&longs;&longs;erere fortè po&longs;&longs;emus, id <lb/>e&longs;&longs;e qua&longs;i &longs;peciem &longs;en&longs;ibilis rei, qua animal pellicitur; <lb/>at durum fortè nimis e&longs;&longs;et animam quandam cum <lb/>Thalete, &longs;iue in magnete &longs;iue in ferro ponere Cùm <lb/>verò poni &longs;altem id debeat vt continuatum aliquid ex <lb/>magnete in ferrum v&longs;que; quònam modo habere <lb/>pote&longs;t harpagonis vim, &longs;i ex corpu&longs;culis di&longs;&longs;ociatis <lb/>con&longs;tat? </s> | <s id="id.000477">XIV. <!-- KEEP S--></s> |
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| <s>&longs;i, cum emittitur, non vno extremo tene­<lb/>tur, &longs;ed dimittitur? </s> | <s id="id.000478">Verùm vbi conce&longs;&longs;um fuerit corpu&longs;cula <lb/>quædam ex magnete procedere, quæ ferrum ad ip­<lb/>&longs;um pelliciant; intelligi-ne tamen pote&longs;t, aut qua <lb/>formâ &longs;int, vt attractionis organa fiant; aut quomo­<lb/>do, quave ratione attractio per illa po&longs;&longs;it peragi? <lb/></s> |
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| <s>&longs;i &longs;acta extremi alterius in an&longs;u­<lb/>las ferri injectione, non &longs;ubinde reducitur, &longs;ed con­<lb/>tinenter impellitur<gap/> & complura &longs;imilia non exiguæ <lb/>difficultatis? </s> | <s id="id.000479">Heic &longs;anè pr&ecedil;&longs;ertìm conjectandum e&longs;t, cùm non mo­<lb/>do difficile, &longs;ed impo&longs;&longs;ibile etiam &longs;it agno&longs;cere ger­<lb/>manum modum, quo intima rerum natura admira­<lb/>bileis illas &longs;uas operationes ex&longs;equitur. </s> |
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| <s>Et admitte concur&longs;us, complexu&longs;que <lb/>corpu&longs;culorum, cum Empedocle; adhibe vacui inter­<lb/>ceptionem cum Democrito, fugam cum Platone, <pb pagenum="56"/>& quidvis aliud cum cæteris; pares difficultates <lb/>crunt. </s> | <s id="id.000480">An-non <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.062.jpg" pagenum="55"/>proinde e&longs;t, quòd condones, &longs;i vt ob&longs;curè &longs;olùm <lb/>conijcio, ita confu&longs;è &longs;olùm balbutiam? </s> |
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| <s>An ergo præter cæterorum conjecturas, di­<lb/>cere liceat concipi po&longs;&longs;e magneticos radios, ob con­<lb/>tinentem emi&longs;&longs;ionem, eam rigiditatem tueri, vt fiant <lb/>qua&longs;i virgulæ, aut &longs;altem qua&longs;i chordulæ ten&longs;æ? <lb/></s> | <s id="id.000481">&longs;i nihil tan­<lb/>quam ratum, exploratúmque, & de quo dubitare <lb/>non liceat, diuendam, neque velim vnquam pr&ecedil;ju­<lb/>dicium factum per&longs;crutantibus, excogitantibu&longs;que <lb/>meliora? </s> |
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| <s>Nempe tamet&longs;i ex contiguis duntaxat particulis con­<lb/>&longs;tent; pote&longs;t nihilominùs continua &longs;uccedentium &longs;uf­<lb/>fectio, inde&longs;inen&longs;que in&longs;tantia, ac vehemens propul­<lb/>&longs;io rigiditatem illam creare; vt in aquæ ex&longs;ilitione <lb/>per angu&longs;tos tubulos manife&longs;tum e&longs;t fieri. </s> | <s id="id.000482">Nullum non ver&longs;o lapidem, vt experiar, &longs;i <lb/>fortè quidpiam occurrat veri&longs;imile; & cum ingenuè <lb/>profitear e&longs;&longs;e vbique angu&longs;tias, videor mihi e&longs;&longs;e ex­<lb/>cu&longs;atione non indignus, dum recantare &longs;emper pa­<lb/>ratus, illud interim profero, quod videatur præ <lb/>cæteris &longs;imilitudinem habere cum vero. </s> |
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| <s>Certè & <lb/>ip&longs;os lucis radios non videmur po&longs;&longs;e alia ratione <lb/>concipere, &longs;iue vibratos, &longs;iue repul&longs;os? </s> | <s id="id.000483">In hoc <lb/>negotio, cum videatur e&longs;&longs;e &longs;atis per&longs;picuum, non <lb/>po&longs;&longs;e vnum corpus attrahere aliud, ni&longs;i tran&longs;mittat <lb/>aliquid, quo illud ad &longs;e pertrahat; ecquis e&longs;t tamen <lb/>adeo &longs;olers, qui conijciat, aut explicet, cuiu&longs;modi <lb/>id &longs;it, quod magnes, qua&longs;i organum, vt ferrum ad &longs;e <lb/>accer&longs;at, tran&longs;mittit? </s> |
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| <s>An proinde vt <lb/>lucis radij ex vno quodam puncto prodeuntes, vbi <lb/>impinguntur in aquæ planitiem, quacúmque occur­<lb/>runt poruli, meatulique, pertran&longs;eunt (quippe ana­<lb/>logici &longs;unt) &longs;ed vnus directè, perpendiculariterve, <lb/>cæteri refractè, &longs;eu cum deflexione ad illum; ita <lb/>radij magnetici, quos in orbem effundi con&longs;tat (tan­<lb/>quam ex vno centro prodeuntes) vbi impingun­<lb/>tur in ferrum, quacúmque ip&longs;is poruli, meatulique <lb/>occurrerint, penetrant (&longs;cilicet analogici) &longs;ed vnus <lb/>directe (is nempe, qui per mediam molem, ac velu­<lb/>ti axem grauitatis traijcitur) cæteri refractè, defle­<lb/>xéque ad ip&longs;um? </s> | <s id="id.000484">A&longs;&longs;erere fortè po&longs;&longs;emus, id <lb/>e&longs;&longs;e qua&longs;i &longs;peciem &longs;en&longs;ibilis rei, qua animal pellicitur; <lb/>at durum fortè nimis e&longs;&longs;et animam quandam cum <lb/>Thalete, &longs;iue in magnete &longs;iue in ferro ponere Cùm <lb/>verò poni &longs;altem id debeat vt continuatum aliquid ex <lb/>magnete in ferrum v&longs;que; quònam modo habere <lb/>pote&longs;t harpagonis vim, &longs;i ex corpu&longs;culis di&longs;&longs;ociatis <lb/>con&longs;tat? </s> |
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| <s>Quæcúmque certe e&longs;t in aqua &longs;o­<lb/>lidiu&longs;cularum particularum di&longs;po&longs;itio, quæ radio­<lb/>rum lucis refractionem faciat; eadem radiorum ma­<lb/>gneticorum, proportione adhibita, facere refractio­<lb/>nem pote&longs;t. </s> | <s id="id.000485">&longs;i, cum emittitur, non vno extremo tene­<lb/>tur, &longs;ed dimittitur? </s> |
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| <s>An cùm vtrique radij &longs;olidas particu­<lb/>las vrgeant, illas nempe, quæ ver&longs;us medium, per­<lb/>pendicularemve &longs;unt radium, vt pote in quas defle-<pb pagenum="57"/>ctantur, & in quas ni&longs;um faciant, magnetici tamen <lb/>robu&longs;tiores &longs;unt, & parteis magnetis vehementiùs <lb/>premunt? </s> | <s id="id.000486">&longs;i &longs;acta extremi alterius in an&longs;u­<lb/>las ferri injectione, non &longs;ubinde reducitur, &longs;ed con­<lb/>tinenter impellitur<gap/> & complura &longs;imilia non exiguæ <lb/>difficultatis? </s> |
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| <s>Cum radij certè ita refracti, &longs;int qua&longs;i chor­<lb/>dulæ deflexæ, &, vt mox dicebamus, ten&longs;æ, non <lb/>po&longs;&longs;unt non premere, & vrgere parteis, quæ intra <lb/>ip&longs;um angulum deflexionis comprehenduntur. </s> | <s id="id.000487">Et admitte concur&longs;us, complexu&longs;que <lb/>corpu&longs;culorum, cum Empedocle; adhibe vacui inter­<lb/>ceptionem cum Democrito, fugam cum Platone, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.063.jpg" pagenum="56"/>& quidvis aliud cum cæteris; pares difficultates <lb/>crunt. </s> |
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| <s>An <lb/>ex hac pre&longs;&longs;ione intelligi pote&longs;t adigi ferrum ver&longs;us <lb/>magnetem, vt pote omnibus chordulis factis qua&longs;i <lb/>bracchiis, quorum qua&longs;i cubiti, & articuli &longs;int in <lb/>ip&longs;is deflexionibus; quæque con&longs;pirent omnia in <lb/>adigendo ad ip&longs;um ferro? </s> | <s id="id.000488">An ergo præter cæterorum conjecturas, di­<lb/>cere liceat concipi po&longs;&longs;e magneticos radios, ob con­<lb/>tinentem emi&longs;&longs;ionem, eam rigiditatem tueri, vt fiant <lb/>qua&longs;i virgulæ, aut &longs;altem qua&longs;i chordulæ ten&longs;æ? <lb/></s> |
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| <s>Parem profectò adactio­<lb/>nem experiri licet, &longs;i firmati &longs;imùl ad parietem ali­<lb/>quot funiculi traijciantur per foraminula in globo, <lb/>aut cra&longs;&longs;iu&longs;culo a&longs;&longs;ere ita comparata, vt medium <lb/>&longs;it directo ductu, cæteri à parte citeriore in vlte­<lb/>riorem non nihil deflexum ver&longs;us medium habeant. <lb/></s> | <s id="id.000489">Nempe tamet&longs;i ex contiguis duntaxat particulis con­<lb/>&longs;tent; pote&longs;t nihilominùs continua &longs;uccedentium &longs;uf­<lb/>fectio, inde&longs;inen&longs;que in&longs;tantia, ac vehemens propul­<lb/>&longs;io rigiditatem illam creare; vt in aquæ ex&longs;ilitione <lb/>per angu&longs;tos tubulos manife&longs;tum e&longs;t fieri. </s> |
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| <s>Nempe &longs;i funiculo medio inten&longs;o manente, ductum­<lb/>que &longs;olùm dirigente, cæteri ponè conducantur, &longs;i­<lb/>mùlque tendantur, globum, a&longs;&longs;eremve &longs;ic prement, <lb/>vt ip&longs;um compellant in locum parietis, vnde ortum <lb/>habent. </s> | <s id="id.000490">Certè & <lb/>ip&longs;os lucis radios non videmur po&longs;&longs;e alia ratione <lb/>concipere, &longs;iue vibratos, &longs;iue repul&longs;os? </s> |
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| <s>An hac ratione intelligi licet, non allici <lb/>ferrum, ni&longs;i ex certa di&longs;tantia, quod ex radiis in or­<lb/>bem fu&longs;is, ac magis, magi&longs;que continuò rare&longs;cen­<lb/>tibus, aut nulli, aut nimis pauci, quibus &longs;uperetur <lb/>ponderis re&longs;i&longs;tentia, ad ferrum pertingant? </s> | <s id="id.000491">An proinde vt <lb/>lucis radij ex vno quodam puncto prodeuntes, vbi <lb/>impinguntur in aquæ planitiem, quacúmque occur­<lb/>runt poruli, meatulique, pertran&longs;eunt (quippe ana­<lb/>logici &longs;unt) &longs;ed vnus directè, perpendiculariterve, <lb/>cæteri refractè, &longs;eu cum deflexione ad illum; ita <lb/>radij magnetici, quos in orbem effundi con&longs;tat (tan­<lb/>quam ex vno centro prodeuntes) vbi impingun­<lb/>tur in ferrum, quacúmque ip&longs;is poruli, meatulique <lb/>occurrerint, penetrant (&longs;cilicet analogici) &longs;ed vnus <lb/>directe (is nempe, qui per mediam molem, ac velu­<lb/>ti axem grauitatis traijcitur) cæteri refractè, defle­<lb/>xéque ad ip&longs;um? </s> |
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| <s>attrahi <lb/>ferrum tantò potentiùs, quantò propinquius fuerit; <lb/>quòd crebriores &longs;int radij, atque adeò chordulæ plu­<lb/>res, &longs;eu plura qua&longs;i bracchiola, quibus corripiatur, <lb/>atque pertrahatur? </s> | <s id="id.000492">Quæcúmque certe e&longs;t in aqua &longs;o­<lb/>lidiu&longs;cularum particularum di&longs;po&longs;itio, quæ radio­<lb/>rum lucis refractionem faciat; eadem radiorum ma­<lb/>gneticorum, proportione adhibita, facere refractio­<lb/>nem pote&longs;t. </s> |
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| <s>teneri ferrum ip&longs;i magneti ar­<lb/>cti&longs;&longs;imè junctum, quod &longs;ingulæ chordulæ, & qua&longs;i <pb pagenum="58"/>bracchiola &longs;tringant, reuinctumque contineant<gap/> ac <lb/>eiu&longs;modi cætera? </s> | <s id="id.000493">An cùm vtrique radij &longs;olidas particu­<lb/>las vrgeant, illas nempe, quæ ver&longs;us medium, per­<lb/>pendicularemve &longs;unt radium, vt pote in quas defle-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.064.jpg" pagenum="57"/>ctantur, & in quas ni&longs;um faciant, magnetici tamen <lb/>robu&longs;tiores &longs;unt, & parteis magnetis vehementiùs <lb/>premunt? </s> |
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| <s>An licet quoque intelligi &longs;ucci­<lb/>num, ceram ob&longs;ignatoriam, electricaque cætera ideò <lb/>attrahere fe&longs;tucas, filamenta, papyracea fragminula, <lb/>&longs;imilei&longs;que alias leuiculas res; quòd pinguem ex &longs;e <lb/>halitum emittant, con&longs;tantem ex radiolis, quirerum <lb/>porulos &longs;ubeuntes, pariratione deflectantur, & qua&longs;i <lb/>decu&longs;&longs;entur, re&longs;que ip&longs;as ver&longs;us id, vnde proflu­<lb/>xerunt, diuergere faciant, premant, compellant, <lb/>perducant; de&longs;umpto indicio vel ex eo, quòd ele­<lb/>ctrica i&longs;ta corpora non trahant, ni&longs;i priùs affricta ve­<lb/>&longs;ti, tapeti, alijverei; vt eo &longs;cilicet affrictu excitetur, <lb/>ex&longs;iliatque pinguis halitus, &longs;uam qua&longs;i prædam re­<lb/>portaturus? </s></p><p type="main"> | <s id="id.000494">Cum radij certè ita refracti, &longs;int qua&longs;i chor­<lb/>dulæ deflexæ, &, vt mox dicebamus, ten&longs;æ, non <lb/>po&longs;&longs;unt non premere, & vrgere parteis, quæ intra <lb/>ip&longs;um angulum deflexionis comprehenduntur. </s> |
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| <s>XV. <!-- KEEP S--></s> | <s id="id.000495">An <lb/>ex hac pre&longs;&longs;ione intelligi pote&longs;t adigi ferrum ver&longs;us <lb/>magnetem, vt pote omnibus chordulis factis qua&longs;i <lb/>bracchiis, quorum qua&longs;i cubiti, & articuli &longs;int in <lb/>ip&longs;is deflexionibus; quæque con&longs;pirent omnia in <lb/>adigendo ad ip&longs;um ferro? </s> |
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| <s>Quor&longs;ùm verò i&longs;ta tam multa? </s> | <s id="id.000496">Parem profectò adactio­<lb/>nem experiri licet, &longs;i firmati &longs;imùl ad parietem ali­<lb/>quot funiculi traijciantur per foraminula in globo, <lb/>aut cra&longs;&longs;iu&longs;culo a&longs;&longs;ere ita comparata, vt medium <lb/>&longs;it directo ductu, cæteri à parte citeriore in vlte­<lb/>riorem non nihil deflexum ver&longs;us medium habeant. <lb/></s> |
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| <s>Nimirùm <lb/>vt intelligamus, quomodo e&longs;&longs;e in Terra po&longs;&longs;it ma­<lb/>gnetica vis, qua corpora omnia, quæ dicuntur gra­<lb/>uia, trahantur deor&longs;ùm, perpendiculariterve in ip­<lb/>&longs;am. </s> | <s id="id.000497">Nempe &longs;i funiculo medio inten&longs;o manente, ductum­<lb/>que &longs;olùm dirigente, cæteri ponè conducantur, &longs;i­<lb/>mùlque tendantur, globum, a&longs;&longs;eremve &longs;ic prement, <lb/>vt ip&longs;um compellant in locum parietis, vnde ortum <lb/>habent. </s> |
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| <s>Ac e&longs;&longs;e quidem in ip&longs;a Terra aliquam eiu&longs;mo­<lb/>divim, confirmari aliunde melius, quàm ex effectu <lb/>ip&longs;o non pote&longs;t; quare, vt quæ e&longs;t in magnete, non <lb/>aliunde, quam ex ip&longs;a ferri attractione conuincitur; <lb/>ita, quæ e&longs;&longs;e in Terra &longs;upponitur, non aliunde, quàm <lb/>ex attractione lapidum, cæterorumque pote&longs;t con­<lb/>uinci. </s> | <s id="id.000498">An hac ratione intelligi licet, non allici <lb/>ferrum, ni&longs;i ex certa di&longs;tantia, quod ex radiis in or­<lb/>bem fu&longs;is, ac magis, magi&longs;que continuò rare&longs;cen­<lb/>tibus, aut nulli, aut nimis pauci, quibus &longs;uperetur <lb/>ponderis re&longs;i&longs;tentia, ad ferrum pertingant? </s> |
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| <s>Quod ad modum verò attractionis &longs;pectat, <lb/>idem plane dicendum e&longs;t, proportione tamen &longs;er­<lb/>uata, quod de magnete iam diximus. </s> | <s id="id.000499">attrahi <lb/>ferrum tantò potentiùs, quantò propinquius fuerit; <lb/>quòd crebriores &longs;int radij, atque adeò chordulæ plu­<lb/>res, &longs;eu plura qua&longs;i bracchiola, quibus corripiatur, <lb/>atque pertrahatur? </s> |
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| <s>Subijcio pro­<lb/>inde veri&longs;imile e&longs;&longs;e, quemadmodum virtus magne­<lb/>tis ita in orbem diffunditur, vt corpu&longs;cula radio&longs;è <lb/>ex&longs;ilientia tantò rariora fiant, quantò procedunt <pb pagenum="59"/>longiùs, &longs;icque minùs conferta minùs polleant, & <lb/>&longs;uperatâ quadam di&longs;tantiâ, attractioni imparia, ac <lb/>tandem nulla &longs;int; eodem modo Telluris globum <lb/>itaillam &longs;uam attractricem vim in orbem diffundere, <lb/>vt corpu&longs;culorum emi&longs;&longs;orum radij &longs;ummoperè tan­<lb/>dem rare&longs;cant, neque ex quacúmque di&longs;tantia (vt, &longs;i <lb/>velis, &longs;upra-lunari, aut extra-mundana) attrahere la­<lb/>pidem po&longs;&longs;int. </s> | <s id="id.000500">teneri ferrum ip&longs;i magneti ar­<lb/>cti&longs;&longs;imè junctum, quod &longs;ingulæ chordulæ, & qua&longs;i <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.065.jpg" pagenum="58"/>bracchiola &longs;tringant, reuinctumque contineant<gap/> ac <lb/>eiu&longs;modi cætera? </s> |
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| <s>Concipe certè lapidem in &longs;patiis illis <lb/>imaginaris, quæ &longs;unt proten&longs;a vltra hunc mundum, <lb/>& in quibus po&longs;&longs;et Deus alios mundos condere; an <lb/>cen&longs;eas ip&longs;um illicô vbicon&longs;titutus illeic fuerit, ver­<lb/>&longs;us hanc Terram conuolaturum, & non potiùs vbi <lb/>fuerit &longs;emel po&longs;itus, immotum man&longs;urum, vt putà <lb/>qua&longs;i non habentem neque &longs;ur&longs;ùm, neque deor&longs;ùm, <lb/>quò tendere, aut vnde recedere valeat? </s> | <s id="id.000501">An licet quoque intelligi &longs;ucci­<lb/>num, ceram ob&longs;ignatoriam, electricaque cætera ideò <lb/>attrahere fe&longs;tucas, filamenta, papyracea fragminula, <lb/>&longs;imilei&longs;que alias leuiculas res; quòd pinguem ex &longs;e <lb/>halitum emittant, con&longs;tantem ex radiolis, quirerum <lb/>porulos &longs;ubeuntes, pariratione deflectantur, & qua&longs;i <lb/>decu&longs;&longs;entur, re&longs;que ip&longs;as ver&longs;us id, vnde proflu­<lb/>xerunt, diuergere faciant, premant, compellant, <lb/>perducant; de&longs;umpto indicio vel ex eo, quòd ele­<lb/>ctrica i&longs;ta corpora non trahant, ni&longs;i priùs affricta ve­<lb/>&longs;ti, tapeti, alijverei; vt eo &longs;cilicet affrictu excitetur, <lb/>ex&longs;iliatque pinguis halitus, &longs;uam qua&longs;i prædam re­<lb/>portaturus? </s></p><p type="main"> |
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| <s>Si cen&longs;eas <lb/>fore, vt hûc feratur; imaginare non modò Terram, <lb/>verùm etiam totum mundum e&longs;&longs;e in nihilum reda­<lb/>ctum, &longs;patiáque hæc e&longs;&longs;e perinde inania, ac ante­<lb/>quàm Deus mundum conderet; tunc &longs;altem, quia <lb/>centrum non erit, &longs;patiáque omnia erunt &longs;imilia; <lb/>cen&longs;ebis lapidem non hûc acce&longs;&longs;urum, &longs;ed in loco <lb/>illo fixum perman&longs;urum. </s> | <s id="id.000502">XV. <!-- KEEP S--></s> |
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| <s>Re&longs;tituatur mundus, & <lb/>in ip&longs;o Terra, an lapis &longs;tatim hûc contendet? </s> | <s id="id.000503">Quor&longs;ùm verò i&longs;ta tam multa? </s> |
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| <s>Si fieri <lb/>dicas, oportet &longs;anè &longs;entiri Terram à lapide, deberé­<lb/>que proinde Terram tran&longs;mittere in ip&longs;um vim <lb/>quandam, atque adeò corpu&longs;cula, quibus &longs;ui &longs;en&longs;um <lb/>illi imprimat, &longs;e&longs;eque re&longs;titutam, ac in eodem loco <lb/>denuò ex&longs;i&longs;tentem veluti renunciet. </s> | <s id="id.000504">Nimirùm <lb/>vt intelligamus, quomodo e&longs;&longs;e in Terra po&longs;&longs;it ma­<lb/>gnetica vis, qua corpora omnia, quæ dicuntur gra­<lb/>uia, trahantur deor&longs;ùm, perpendiculariterve in ip­<lb/>&longs;am. </s> |
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| <s>Secùs enim <lb/>quomodo capis po&longs;&longs;e lapidem allici ad Terram? <lb/><!-- KEEP S--></s> | <s id="id.000505">Ac e&longs;&longs;e quidem in ip&longs;a Terra aliquam eiu&longs;mo­<lb/>divim, confirmari aliunde melius, quàm ex effectu <lb/>ip&longs;o non pote&longs;t; quare, vt quæ e&longs;t in magnete, non <lb/>aliunde, quam ex ip&longs;a ferri attractione conuincitur; <lb/>ita, quæ e&longs;&longs;e in Terra &longs;upponitur, non aliunde, quàm <lb/>ex attractione lapidum, cæterorumque pote&longs;t con­<lb/>uinci. </s> |
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| <s>ld verò &longs;i ita futurum &longs;it, quid-nam aliud arguitur <pb pagenum="60"/>quàm & lapidem, & alia corpora terrena Terram pe­<lb/>tere, quòd corpu&longs;culis ab illa tran&longs;mi&longs;&longs;is ad eam alli­<lb/>ciantur. </s> | <s id="id.000506">Quod ad modum verò attractionis &longs;pectat, <lb/>idem plane dicendum e&longs;t, proportione tamen &longs;er­<lb/>uata, quod de magnete iam diximus. </s> |
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| <s>Et fac iam certum aliquod aëris nos am­<lb/>bientis &longs;patium fierià Deo pror&longs;ùs inane, adeò vt ne­<lb/>que ex Terra, neque aliunde aliquid in ip&longs;um perue­<lb/>niat: an con&longs;titutus in eo lapis feretur in Terram, <lb/>centrumve ip&longs;ius? </s> | <s id="id.000507">Subijcio pro­<lb/>inde veri&longs;imile e&longs;&longs;e, quemadmodum virtus magne­<lb/>tis ita in orbem diffunditur, vt corpu&longs;cula radio&longs;è <lb/>ex&longs;ilientia tantò rariora fiant, quantò procedunt <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.066.jpg" pagenum="59"/>longiùs, &longs;icque minùs conferta minùs polleant, & <lb/>&longs;uperatâ quadam di&longs;tantiâ, attractioni imparia, ac <lb/>tandem nulla &longs;int; eodem modo Telluris globum <lb/>itaillam &longs;uam attractricem vim in orbem diffundere, <lb/>vt corpu&longs;culorum emi&longs;&longs;orum radij &longs;ummoperè tan­<lb/>dem rare&longs;cant, neque ex quacúmque di&longs;tantia (vt, &longs;i <lb/>velis, &longs;upra-lunari, aut extra-mundana) attrahere la­<lb/>pidem po&longs;&longs;int. </s> |
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| <s>Certè non magis, quàm con&longs;titu­<lb/>tus in &longs;patiis illis vltra-mundanis; quia ip&longs;i nihil ne­<lb/>que cùm Terra, neque cum alia re quacumque mun­<lb/>di ip&longs;ius communicanti, perinde erit, ac &longs;i Mundus, <lb/>Terraque, aut centrum non e&longs;&longs;et, nihilque retum <lb/>ex&longs;i&longs;teret. </s> | <s id="id.000508">Concipe certè lapidem in &longs;patiis illis <lb/>imaginaris, quæ &longs;unt proten&longs;a vltra hunc mundum, <lb/>& in quibus po&longs;&longs;et Deus alios mundos condere; an <lb/>cen&longs;eas ip&longs;um illicô vbicon&longs;titutus illeic fuerit, ver­<lb/>&longs;us hanc Terram conuolaturum, & non potiùs vbi <lb/>fuerit &longs;emel po&longs;itus, immotum man&longs;urum, vt putà <lb/>qua&longs;i non habentem neque &longs;ur&longs;ùm, neque deor&longs;ùm, <lb/>quò tendere, aut vnde recedere valeat? </s> |
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| <s>An-non igitur, &longs;i in Terram iam fettur, <lb/>ideò ferri putandum e&longs;t, quòd aliquid ip&longs;um circum­<lb/>&longs;tet, quicum communicationem habeat, & maximè <lb/>ex parte Terræ, à quo pertrahatur; &longs;i id quidem non <lb/>&longs;ufficit, quod &longs;upernè e&longs;t, vt ab eo pellatur? </s> | <s id="id.000509">Si cen&longs;eas <lb/>fore, vt hûc feratur; imaginare non modò Terram, <lb/>verùm etiam totum mundum e&longs;&longs;e in nihilum reda­<lb/>ctum, &longs;patiáque hæc e&longs;&longs;e perinde inania, ac ante­<lb/>quàm Deus mundum conderet; tunc &longs;altem, quia <lb/>centrum non erit, &longs;patiáque omnia erunt &longs;imilia; <lb/>cen&longs;ebis lapidem non hûc acce&longs;&longs;urum, &longs;ed in loco <lb/>illo fixum perman&longs;urum. </s> |
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| <s>Nec te <lb/>moretur, quòd tanta moles, quantaingentis Saxi e&longs;t, <lb/>non videatur compelli po&longs;&longs;e tenuïbus adeò chordu­<lb/>lis; nam con&longs;idera etiam quam tenüibus magna ferri <lb/>moles ad magneticum lapillum trahatur. </s> | <s id="id.000510">Re&longs;tituatur mundus, & <lb/>in ip&longs;o Terra, an lapis &longs;tatim hûc contendet? </s> |
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| <s>Addo &longs;a­<lb/>xa, & cætera corpora, quæ dicuntur grauia, non <lb/>eam habere ad motum re&longs;i&longs;tentiam, quam vulgò <lb/>concipimus. </s> | <s id="id.000511">Si fieri <lb/>dicas, oportet &longs;anè &longs;entiri Terram à lapide, deberé­<lb/>que proinde Terram tran&longs;mittere in ip&longs;um vim <lb/>quandam, atque adeò corpu&longs;cula, quibus &longs;ui &longs;en&longs;um <lb/>illi imprimat, &longs;e&longs;eque re&longs;titutam, ac in eodem loco <lb/>denuò ex&longs;i&longs;tentem veluti renunciet. </s> |
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| <s>Vides quippe &longs;i ingens moles appen­<lb/>datur funiculo, quàm leuicula vi &longs;it opus, vt è loco <lb/>dimoueatur, & pror&longs;ùm, retro: &longs;ùmque eat. </s> | <s id="id.000512">Secùs enim <lb/>quomodo capis po&longs;&longs;e lapidem allici ad Terram? <lb/><!-- KEEP S--></s> |
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| <s>Cur <lb/>maiore ergo opus &longs;it, vt cieri deor&longs;ùm po&longs;&longs;it? </s> | <s id="id.000513">ld verò &longs;i ita futurum &longs;it, quid-nam aliud arguitur <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.067.jpg" pagenum="60"/>quàm & lapidem, & alia corpora terrena Terram pe­<lb/>tere, quòd corpu&longs;culis ab illa tran&longs;mi&longs;&longs;is ad eam alli­<lb/>ciantur. </s> |
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| <s>Nec <lb/>dicas verò e&longs;&longs;e majorem, ob motum magis perni­<lb/>cem; etenim cùm primum deor&longs;ùm<gap/>ontendit, mo­<lb/>tus illius pernix non e&longs;t, &longs;ed lenti&longs;&longs;imus potiùs, cau­<lb/>&longs;áque dicenda mox e&longs;t, ob quam deinceps accelere-<pb pagenum="61"/>tur. </s> | <s id="id.000514">Et fac iam certum aliquod aëris nos am­<lb/>bientis &longs;patium fierià Deo pror&longs;ùs inane, adeò vt ne­<lb/>que ex Terra, neque aliunde aliquid in ip&longs;um perue­<lb/>niat: an con&longs;titutus in eo lapis feretur in Terram, <lb/>centrumve ip&longs;ius? </s> |
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| <s>Adnoto intereà vim illam quæ ex chordularum <lb/>in&longs;en&longs;ilium &longs;ingularibus viribus conflatur, & con&longs;tat, <lb/>comptobari tantam, quantam &longs;uperari oportet, vt <lb/>manus, aut res alia grauitantem rem, velut lapidem, <lb/>abducat à Terra. <!-- KEEP S--></s> | <s id="id.000515">Certè non magis, quàm con&longs;titu­<lb/>tus in &longs;patiis illis vltra-mundanis; quia ip&longs;i nihil ne­<lb/>que cùm Terra, neque cum alia re quacumque mun­<lb/>di ip&longs;ius communicanti, perinde erit, ac &longs;i Mundus, <lb/>Terraque, aut centrum non e&longs;&longs;et, nihilque retum <lb/>ex&longs;i&longs;teret. </s> |
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| <s>Et vides profectò quid fieri videa­<lb/>tur, dum lapis tibi ip&longs;um è Terra attollere conanti <lb/>re&longs;i&longs;tir. </s> | <s id="id.000516">An-non igitur, &longs;i in Terram iam fettur, <lb/>ideò ferri putandum e&longs;t, quòd aliquid ip&longs;um circum­<lb/>&longs;tet, quicum communicationem habeat, & maximè <lb/>ex parte Terræ, à quo pertrahatur; &longs;i id quidem non <lb/>&longs;ufficit, quod &longs;upernè e&longs;t, vt ab eo pellatur? </s> |
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| <s>Nempe tot illæ chordulæ &longs;uis deflexioni­<lb/>bus, & qua&longs;i decu&longs;&longs;ationibus illum implexum de­<lb/>tinent; & ni&longs;i vis maior interueniat, quæ eas defle­<lb/>xiones, decu&longs;&longs;atione&longs;que promoueat, &longs;trictione&longs;que <lb/>fieri vlteriùs cogat, nunquam à Terra lapis tolletur. <lb/></s> | <s id="id.000517">Nec te <lb/>moretur, quòd tanta moles, quantaingentis Saxi e&longs;t, <lb/>non videatur compelli po&longs;&longs;e tenuïbus adeò chordu­<lb/>lis; nam con&longs;idera etiam quam tenüibus magna ferri <lb/>moles ad magneticum lapillum trahatur. </s> |
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| <s>Heinc fit, vt quantò vis externa, &longs;eu quæ a manu, <lb/>aliave re extrin&longs;ecùs imprimitur, pluribus gradibus <lb/>vim illam chordularum &longs;uperauerit, tantò lapis ef­<lb/>feratur &longs;ublimiùs; quantò paucioribus, tantò humi­<lb/>liùs. </s> | <s id="id.000518">Addo &longs;a­<lb/>xa, & cætera corpora, quæ dicuntur grauia, non <lb/>eam habere ad motum re&longs;i&longs;tentiam, quam vulgò <lb/>concipimus. </s> |
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| <s>Fit eriam, vt impre&longs;&longs;a vis initio pollens vehe­<lb/>menter pellat, quia nondum refracta e&longs;t; deinceps <lb/>verò &longs;egniùs, &longs;egniu&longs;que, quoniam ip&longs;i &longs;emperaliqui <lb/>gradus adimuntur: donec ille &longs;olus &longs;upei&longs;it, quo <lb/>exæquetur vichordularum. </s> | <s id="id.000519">Vides quippe &longs;i ingens moles appen­<lb/>datur funiculo, quàm leuicula vi &longs;it opus, vt è loco <lb/>dimoueatur, & pror&longs;ùm, retro: &longs;ùmque eat. </s> |
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| <s>Idque ad eum penè mo­<lb/>dum, quo, &longs;i aduer&longs;us torrentem nitaris, poteris <lb/>quidem aliquov&longs;que, vigente conatu, occurrenteis <lb/>vndas pro&longs;cindere; &longs;ed quòd interim tamen vnda <lb/>impellente vndam conatus &longs;en&longs;im refiingatur (quia <lb/>quod ab vna &longs;upere&longs;t, à &longs;uccedente detrahitur) co­<lb/>gê<gap/>is tandem de&longs;i&longs;tere, abripieri&longs;que &longs;ecundum tor­<lb/>rentem. </s> | <s id="id.000520">Cur <lb/>maiore ergo opus &longs;it, vt cieri deor&longs;ùm po&longs;&longs;it? </s> |
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| <s>Fit denique, vt &longs;i duo lapides, duove <lb/>globi ex eadem materia veluti ex plumbo, vnus pu­<lb/>&longs;illus alius ingens, &longs;imùl dimittantur ex eadem altitu­<lb/>dine, codem momento ad Terram perueniant, ac <pb pagenum="62"/>pu&longs;illus, tamet&longs;i vnâ vnciâ pondero&longs;ior non &longs;it, non <lb/>minore velocitate, quàm ingens, tamet&longs;i &longs;it cen­<lb/>tum, & plurium librarum. </s> | <s id="id.000521">Nec <lb/>dicas verò e&longs;&longs;e majorem, ob motum magis perni­<lb/>cem; etenim cùm primum deor&longs;ùm<gap/>ontendit, mo­<lb/>tus illius pernix non e&longs;t, &longs;ed lenti&longs;&longs;imus potiùs, cau­<lb/>&longs;áque dicenda mox e&longs;t, ob quam deinceps accelere-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.068.jpg" pagenum="61"/>tur. </s> |
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| <s>Videlicet pluribus qui­<lb/>dem chordulis attrahitur ingens, &longs;ed plureis etiam par­<lb/>ticulas attrahendas habet; adeò vt fiat commen&longs;ura­<lb/>tio inter vim, ac molem, & ex vtraque vtrobique <lb/>tantum &longs;it, quantum ad motum &longs;ufficit eodem tem­<lb/>pore peragendum. </s> | <s id="id.000522">Adnoto intereà vim illam quæ ex chordularum <lb/>in&longs;en&longs;ilium &longs;ingularibus viribus conflatur, & con&longs;tat, <lb/>comptobari tantam, quantam &longs;uperari oportet, vt <lb/>manus, aut res alia grauitantem rem, velut lapidem, <lb/>abducat à Terra. <!-- KEEP S--></s> |
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| <s>Id permirum; &longs;i globi fuerint ex <lb/>diuer&longs;a materia, vt alter plumbeus, alter ligneus, <lb/>vix quicquam tardiùs attingi Terram ab vno, quàm <lb/>ab alio, hoc e&longs;t à ligneo, quàm à plumbeo; quo­<lb/>niam pari modo fit commen&longs;uratio, dum totidem <lb/>particulis totidem chordulæ de&longs;tinantur. </s> | <s id="id.000523">Et vides profectò quid fieri videa­<lb/>tur, dum lapis tibi ip&longs;um è Terra attollere conanti <lb/>re&longs;i&longs;tir. </s> |
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| <s>Et e&longs;t nihil­<lb/>ominùs tantillum, tamet&longs;i prope modùm in&longs;en&longs;ibile <lb/>di&longs;crimen; quòd ob raritatem materiæ majorem, <lb/>aër &longs;e non-nihil magis intermi&longs;ceat, non nihilque <lb/>magis ad motum deorsùm re&longs;i&longs;tat. </s></p><p type="main"> | <s id="id.000524">Nempe tot illæ chordulæ &longs;uis deflexioni­<lb/>bus, & qua&longs;i decu&longs;&longs;ationibus illum implexum de­<lb/>tinent; & ni&longs;i vis maior interueniat, quæ eas defle­<lb/>xiones, decu&longs;&longs;atione&longs;que promoueat, &longs;trictione&longs;que <lb/>fieri vlteriùs cogat, nunquam à Terra lapis tolletur. <lb/></s> |
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| <s>XVI. <!-- KEEP S--></s> | <s id="id.000525">Heinc fit, vt quantò vis externa, &longs;eu quæ a manu, <lb/>aliave re extrin&longs;ecùs imprimitur, pluribus gradibus <lb/>vim illam chordularum &longs;uperauerit, tantò lapis ef­<lb/>feratur &longs;ublimiùs; quantò paucioribus, tantò humi­<lb/>liùs. </s> |
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| <s>Quæres obiter, quid-nam eueniret illi lapi­<lb/>di, quem a&longs;&longs;ump&longs;i concipi po&longs;&longs;e in &longs;patiis illis inani­<lb/>bus, &longs;i à quiete exturbatus aliqua vi impelleretur? <lb/></s> | <s id="id.000526">Fit eriam, vt impre&longs;&longs;a vis initio pollens vehe­<lb/>menter pellat, quia nondum refracta e&longs;t; deinceps <lb/>verò &longs;egniùs, &longs;egniu&longs;que, quoniam ip&longs;i &longs;emperaliqui <lb/>gradus adimuntur: donec ille &longs;olus &longs;upei&longs;it, quo <lb/>exæquetur vichordularum. </s> |
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| <s>Re&longs;pondeo probabile e&longs;&longs;e, fore, vt æquabiliter, in­<lb/>de&longs;inenter que moueretur; & lentè quidem, celeriter­<lb/>ve, proüt &longs;emel paruus, aut magnus impre&longs;&longs;us foret <lb/>impetus. </s> | <s id="id.000527">Idque ad eum penè mo­<lb/>dum, quo, &longs;i aduer&longs;us torrentem nitaris, poteris <lb/>quidem aliquov&longs;que, vigente conatu, occurrenteis <lb/>vndas pro&longs;cindere; &longs;ed quòd interim tamen vnda <lb/>impellente vndam conatus &longs;en&longs;im refiingatur (quia <lb/>quod ab vna &longs;upere&longs;t, à &longs;uccedente detrahitur) co­<lb/>gê<gap/>is tandem de&longs;i&longs;tere, abripieri&longs;que &longs;ecundum tor­<lb/>rentem. </s> |
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| <s>Argumentum verò de&longs;umo ex æquabilita­<lb/>te illa motus horizontalis iam expo&longs;ita; cùm ille vi­<lb/>deatur aliunde non de&longs;inere, ni&longs;i ex admi&longs;tione mo­<lb/>tus perpendicularis; adeò vt, quia in illis &longs;patiis nul­<lb/>la e&longs;&longs;et perpendicularis admi&longs;tio, in quamcúmque <lb/>partem foret motus inceptus, horizontalis in&longs;tar e&longs;­<lb/>&longs;et, & neque acceleraretur, retardareturve, neque <pb pagenum="63"/>proinde vnquam de&longs;ineret. </s> | <s id="id.000528">Fit denique, vt &longs;i duo lapides, duove <lb/>globi ex eadem materia veluti ex plumbo, vnus pu­<lb/>&longs;illus alius ingens, &longs;imùl dimittantur ex eadem altitu­<lb/>dine, codem momento ad Terram perueniant, ac <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.069.jpg" pagenum="62"/>pu&longs;illus, tamet&longs;i vnâ vnciâ pondero&longs;ior non &longs;it, non <lb/>minore velocitate, quàm ingens, tamet&longs;i &longs;it cen­<lb/>tum, & plurium librarum. </s> |
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| <s>Et vis aliquod (quale <lb/>certè haberi pote&longs;t) experimentum? </s> | <s id="id.000529">Videlicet pluribus qui­<lb/>dem chordulis attrahitur ingens, &longs;ed plureis etiam par­<lb/>ticulas attrahendas habet; adeò vt fiat commen&longs;ura­<lb/>tio inter vim, ac molem, & ex vtraque vtrobique <lb/>tantum &longs;it, quantum ad motum &longs;ufficit eodem tem­<lb/>pore peragendum. </s> |
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| <s>Appende &longs;ilo <lb/>plumbum, lapidemve, qui in perpendiculo con­<lb/>quie&longs;cat, ac po&longs;teà illum pror&longs;ùm impelle; concipies <lb/>hunc motum, ex &longs;e, æquabilem, perpetuumque e&longs;&longs;e. <lb/></s> | <s id="id.000530">Id permirum; &longs;i globi fuerint ex <lb/>diuer&longs;a materia, vt alter plumbeus, alter ligneus, <lb/>vix quicquam tardiùs attingi Terram ab vno, quàm <lb/>ab alio, hoc e&longs;t à ligneo, quàm à plumbeo; quo­<lb/>niam pari modo fit commen&longs;uratio, dum totidem <lb/>particulis totidem chordulæ de&longs;tinantur. </s> |
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| <s>Cùm tantulam enim impre&longs;&longs;eris vim, vnde &longs;it, vt <lb/>lapis totics excurrat, recurratque, ac excurrendo, <lb/>recurendóque tantum in&longs;umat temporis? </s> | <s id="id.000531">Et e&longs;t nihil­<lb/>ominùs tantillum, tamet&longs;i prope modùm in&longs;en&longs;ibile <lb/>di&longs;crimen; quòd ob raritatem materiæ majorem, <lb/>aër &longs;e non-nihil magis intermi&longs;ceat, non nihilque <lb/>magis ad motum deorsùm re&longs;i&longs;tat. </s></p><p type="main"> |
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| <s>Non exi­<lb/>&longs;tima&longs;&longs;es profectò motum tanti corporis ex tantula <lb/>vi tandiù duraturum. </s> | <s id="id.000532">XVI. <!-- KEEP S--></s> |
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| <s>Sed nempe lapidis attractio, <lb/>quæ à Terra fit, à fi o cohibetur, &longs;ieque lapis inter <lb/>duas oppo&longs;itas vireis veluti indifferens manet; vnde <lb/>&longs;i illum tran&longs;uer&longs;ùm pellas, motum imprimas, ad <lb/>quem non habeat re&longs;i&longs;tentiam; &longs;icque, ni&longs;i aliud in­<lb/>terueniat, tueri illum con&longs;tanter po&longs;&longs;it. </s> | <s id="id.000533">Quæres obiter, quid-nam eueniret illi lapi­<lb/>di, quem a&longs;&longs;ump&longs;i concipi po&longs;&longs;e in &longs;patiis illis inani­<lb/>bus, &longs;i à quiete exturbatus aliqua vi impelleretur? <lb/></s> |
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| <s>Neque ob­<lb/>&longs;tat, quòd motus omninô tran&longs;uer&longs;us, &longs;iue &longs;ecun­<lb/>dum horizontem non &longs;it, &longs;ed fiat obliquè, ac &longs;ur­<lb/>&longs;um; nam quia licet filum retineat, tum tamen etiam <lb/>Terra retrahit; vt & quando Terra deor&longs;ùm redu­<lb/>cit, tunc quoque filum retinet; heinc e&longs;t, cur facta <lb/>i&longs;tarum v<gap/>ium oppo&longs;itarum compen&longs;atione, non ex <lb/>hoc capite tollatur impre&longs;&longs;i motus con&longs;tantia. </s> | <s id="id.000534">Re&longs;pondeo probabile e&longs;&longs;e, fore, vt æquabiliter, in­<lb/>de&longs;inenter que moueretur; & lentè quidem, celeriter­<lb/>ve, proüt &longs;emel paruus, aut magnus impre&longs;&longs;us foret <lb/>impetus. </s> |
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| <s>Et <lb/>quamuis tolli videatur æqu bilitas, quatenùs lapis in <lb/>tran&longs;cur&longs;u per infimum punctum, &longs;iue perpendicu­<lb/>lum, celerrimè mouetur, tardi&longs;&longs;imè verò in a&longs;cen­<lb/>&longs;<gap/> fine, & ex&longs;cen&longs;us initio; ac proportione in cæteris <lb/>locis; nihilominùs ea&longs;emper æquabilitas per&longs;euerat, <lb/>vt omnium excur&longs;uum, recur&longs;uumque durationes <lb/>æquales &longs;int; hoc e&longs;t, &longs;ub initium fint quidem ma­<lb/>joies, &longs;ub finem minores: &longs;ed non proptercà vn-<pb pagenum="64"/>quam magis, vel minùs diuturnæ; ob per&longs;eueran­<lb/>tem &longs;emper attractionem, retractionemque æqua­<lb/>lem; & quòd aliunde continenter fiat compen&longs;atio <lb/>inter vim mouentem re&longs;iduam, & percurrendum re­<lb/>&longs;iduum &longs;patium. </s> | <s id="id.000535">Argumentum verò de&longs;umo ex æquabilita­<lb/>te illa motus horizontalis iam expo&longs;ita; cùm ille vi­<lb/>deatur aliunde non de&longs;inere, ni&longs;i ex admi&longs;tione mo­<lb/>tus perpendicularis; adeò vt, quia in illis &longs;patiis nul­<lb/>la e&longs;&longs;et perpendicularis admi&longs;tio, in quamcúmque <lb/>partem foret motus inceptus, horizontalis in&longs;tar e&longs;­<lb/>&longs;et, & neque acceleraretur, retardareturve, neque <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.070.jpg" pagenum="63"/>proinde vnquam de&longs;ineret. </s> |
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| <s>Quî fit ergo vt vis continuò mi­<lb/>nüatur, decurtenturque continuò &longs;patia, ac motus <lb/>ille denique ce&longs;&longs;et? </s> | <s id="id.000536">Et vis aliquod (quale <lb/>certè haberi pote&longs;t) experimentum? </s> |
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| <s>Cau&longs;am duplicem Galileus a&longs;&longs;i­<lb/>gnat. </s> | <s id="id.000537">Appende &longs;ilo <lb/>plumbum, lapidemve, qui in perpendiculo con­<lb/>quie&longs;cat, ac po&longs;teà illum pror&longs;ùm impelle; concipies <lb/>hunc motum, ex &longs;e, æquabilem, perpetuumque e&longs;&longs;e. <lb/></s> |
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| <s>Altera e&longs;t aër, qui in omni vibratione lapidi <lb/>nonnihil re&longs;i&longs;tat, atque idcircô impre&longs;&longs;am vim, &longs;iue <lb/>impetum nonnihil continuò refringat. </s> | <s id="id.000538">Cùm tantulam enim impre&longs;&longs;eris vim, vnde &longs;it, vt <lb/>lapis totics excurrat, recurratque, ac excurrendo, <lb/>recurendóque tantum in&longs;umat temporis? </s> |
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| <s>Altera pon­<lb/>dus ip&longs;ius fili, omniumve eius particularum. </s> | <s id="id.000539">Non exi­<lb/>&longs;tima&longs;&longs;es profectò motum tanti corporis ex tantula <lb/>vi tandiù duraturum. </s> |
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| <s>Nam <lb/>quia quò filum e&longs;t breuius, eò vibrationes, &longs;iue ex­<lb/>cur&longs;us, recur&longs;u&longs;que frequentiores &longs;unt; fac in longio­<lb/>re illo filo, quo appendi&longs;ti lapidem, appen&longs;os e&longs;&longs;e &longs;in­<lb/>gulos lapillos ad &longs;ingulos digitos; agno&longs;ces illum, qui <lb/>erit appen&longs;us ad primum digitum: niti vt recurrat, dum <lb/>qui erit appen&longs;us ad &longs;ecundum adhûc excurret; quare <lb/>& huius excur&longs;um non-nihil decurtatum <gap/>ri, propter <lb/>renitentiam, quæ ab illo fit; ac pari ratione decur­<lb/>tatum iri excur&longs;um tertij, & con&longs;equenter excur&longs;um <lb/>quarti, ac cæterorum; adeò vt denique lapis infi­<lb/>mus ex&longs;i&longs;tens, cogatur etiam nonnihil excur&longs;um &longs;uum <lb/>decurtare, ob factam re&longs;i&longs;tentiam à lapillis &longs;ingulis, <lb/>qui etiam tantò frequentiùs renitentur, quantò al­<lb/>tiores fuerint; videbi&longs;que lapidem qua&longs;i laborare, vt <lb/>&longs;eriem huiu&longs;cemodi qua&longs;i &longs;arcinularum non &longs;ponte <lb/>abductarum, trahat. </s> | <s id="id.000540">Sed nempe lapidis attractio, <lb/>quæ à Terra fit, à fi o cohibetur, &longs;ieque lapis inter <lb/>duas oppo&longs;itas vireis veluti indifferens manet; vnde <lb/>&longs;i illum tran&longs;uer&longs;ùm pellas, motum imprimas, ad <lb/>quem non habeat re&longs;i&longs;tentiam; &longs;icque, ni&longs;i aliud in­<lb/>terueniat, tueri illum con&longs;tanter po&longs;&longs;it. </s> |
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| <s>Non &longs;unto deinde lapilli, &longs;ed <lb/>illorum loco habe totidem fili particulas: profectò <lb/>& illæ, cùm non-nihil pendant, lapillorum in&longs;tar <lb/>&longs;unt, & pro &longs;arcinulis habentur; quæ impetum la-<pb pagenum="65"/>pidis perparùm quidem, &longs;ed non-nihil tamen con­<lb/>tinuò refringant. </s> | <s id="id.000541">Neque ob­<lb/>&longs;tat, quòd motus omninô tran&longs;uer&longs;us, &longs;iue &longs;ecun­<lb/>dum horizontem non &longs;it, &longs;ed fiat obliquè, ac &longs;ur­<lb/>&longs;um; nam quia licet filum retineat, tum tamen etiam <lb/>Terra retrahit; vt & quando Terra deor&longs;ùm redu­<lb/>cit, tunc quoque filum retinet; heinc e&longs;t, cur facta <lb/>i&longs;tarum v<gap/>ium oppo&longs;itarum compen&longs;atione, non ex <lb/>hoc capite tollatur impre&longs;&longs;i motus con&longs;tantia. </s> |
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| <s>Quod per&longs;picuè magis vt nôris, <lb/>appende eundem lapidem ad eiu&longs;dem quidem lon­<lb/>gitudinis, &longs;ed in æqualis tamen cra&longs;&longs;itudinis, ac pro­<lb/>inde ponderis filum; & deprehendes, quò id cra&longs;­<lb/>&longs;ius erit, eo citiùs motum de&longs;iturum, tanquam vi­<lb/>brationibus &longs;ingulis &longs;en&longs;ibiliùs decurtatis; ita vt <lb/>v&longs;urpata cra&longs;&longs;iore chorda, aut etiam virga, catenáve <lb/>ferrea, per paucas omninò vibrationes habiturus &longs;is, <lb/>ac motum parùm duraturum. </s> | <s id="id.000542">Et <lb/>quamuis tolli videatur æqu bilitas, quatenùs lapis in <lb/>tran&longs;cur&longs;u per infimum punctum, &longs;iue perpendicu­<lb/>lum, celerrimè mouetur, tardi&longs;&longs;imè verò in a&longs;cen­<lb/>&longs;<gap/> fine, & ex&longs;cen&longs;us initio; ac proportione in cæteris <lb/>locis; nihilominùs ea&longs;emper æquabilitas per&longs;euerat, <lb/>vt omnium excur&longs;uum, recur&longs;uumque durationes <lb/>æquales &longs;int; hoc e&longs;t, &longs;ub initium fint quidem ma­<lb/>joies, &longs;ub finem minores: &longs;ed non proptercà vn-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.071.jpg" pagenum="64"/>quam magis, vel minùs diuturnæ; ob per&longs;eueran­<lb/>tem &longs;emper attractionem, retractionemque æqua­<lb/>lem; & quòd aliunde continenter fiat compen&longs;atio <lb/>inter vim mouentem re&longs;iduam, & percurrendum re­<lb/>&longs;iduum &longs;patium. </s> |
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| <s>Heinc, quia quò erit <lb/>aër purior, & filum tenuïus, eò vibrationes plures <lb/>erunt, & motus prolixior, finge aërem ad v&longs;que ina­<lb/>nis tenuïtatem e&longs;&longs;e redactum, atque idcircô nihil re­<lb/>&longs;i&longs;tentem; finge & non filum, &longs;ed radium incorpo­<lb/>reum, qui nullius &longs;it ponderis, neque partibus &longs;uis <lb/>renitatur; an-non capis fore vt lapis appen&longs;us im­<lb/>pre&longs;&longs;um &longs;emel motum con&longs;tanti&longs;&longs;imè tueatur; &longs;cili­<lb/>cet omneis vibrationes non æqualibus modò tem­<lb/>poribus peragens, &longs;ed æqualibus etiam arcubus con­<lb/>tinuò perficiens? </s> | <s id="id.000543">Quî fit ergo vt vis continuò mi­<lb/>nüatur, decurtenturque continuò &longs;patia, ac motus <lb/>ille denique ce&longs;&longs;et? </s> |
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| <s>Hæc porrô omnia aliò non tendunt, <lb/>quàm vt intelligamus motum per &longs;patium inane im­<lb/>pre&longs;&longs;um, vbi nihil neque attrahit, neque retinet, ne­<lb/>que omninô renititur, æquabilem fore, ac perpe­<lb/>tuum; atque exinde colligamus, omnem pror&longs;ùs mo­<lb/>tum, qui lapidi imprimitur, e&longs;&longs;e ex &longs;e huiu&longs;modi; adeò <lb/>vt in quamcúmque partem lapidem conjeceris, &longs;i <lb/>quo momento à manu emittitur, &longs;upponas omnia <lb/>vi diuina, lapide excepto, in nihilum redigi; euen­<lb/>turum &longs;it, vt lapis motum &longs;uum perpetuò, ac in <lb/>eandem partem, in quam manus ip&longs;um direxerit, <pb pagenum="66"/>moueatur. </s> | <s id="id.000544">Cau&longs;am duplicem Galileus a&longs;&longs;i­<lb/>gnat. </s> |
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| <s>Ni&longs;i iam faciat, cau&longs;am videri admi­<lb/>&longs;tionem motus perpendicularis, ob attractionem à <lb/>Terra factam interuenientis, quæ diuergere illum à <lb/>tramite faciat (neque ce&longs;&longs;et, quov&longs;que ip&longs;um ad <lb/>Terram v&longs;que perduxerit) vt dum ramenta ferri <lb/>prope magnetem tran&longs;iecta non rectà pergunt, &longs;ed <lb/>ver&longs;us magnetem diuertuntur; aut dum vniuer&longs;e rei, <lb/>quæ mouetur, oblique occurrimus, ip&longs;amque in obli­<lb/>quam deflectimus plagam. </s></p><p type="main"> | <s id="id.000545">Altera e&longs;t aër, qui in omni vibratione lapidi <lb/>nonnihil re&longs;i&longs;tat, atque idcircô impre&longs;&longs;am vim, &longs;iue <lb/>impetum nonnihil continuò refringat. </s> |
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| <s>XVII. Nunc, tandem, cùm præter cau&longs;am impel­<lb/>lentem, etiam attrahens excogitata fuerit; ea-ne po­<lb/>tis e&longs;t id præ&longs;tare quod priùs de&longs;iderabatur? </s> | <s id="id.000546">Altera pon­<lb/>dus ip&longs;ius fili, omniumve eius particularum. </s> |
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| <s>Vide­<lb/>tur e&longs;&longs;e; neque id modò, &longs;ed & videtur attrahens <lb/>vnà cum impellente euadere integra cau&longs;a eius pro­<lb/>portionis, qua velocitas continuò incre&longs;cit. </s> | <s id="id.000547">Nam <lb/>quia quò filum e&longs;t breuius, eò vibrationes, &longs;iue ex­<lb/>cur&longs;us, recur&longs;u&longs;que frequentiores &longs;unt; fac in longio­<lb/>re illo filo, quo appendi&longs;ti lapidem, appen&longs;os e&longs;&longs;e &longs;in­<lb/>gulos lapillos ad &longs;ingulos digitos; agno&longs;ces illum, qui <lb/>erit appen&longs;us ad primum digitum: niti vt recurrat, dum <lb/>qui erit appen&longs;us ad &longs;ecundum adhûc excurret; quare <lb/>& huius excur&longs;um non-nihil decurtatum <gap/>ri, propter <lb/>renitentiam, quæ ab illo fit; ac pari ratione decur­<lb/>tatum iri excur&longs;um tertij, & con&longs;equenter excur&longs;um <lb/>quarti, ac cæterorum; adeò vt denique lapis infi­<lb/>mus ex&longs;i&longs;tens, cogatur etiam nonnihil excur&longs;um &longs;uum <lb/>decurtare, ob factam re&longs;i&longs;tentiam à lapillis &longs;ingulis, <lb/>qui etiam tantò frequentiùs renitentur, quantò al­<lb/>tiores fuerint; videbi&longs;que lapidem qua&longs;i laborare, vt <lb/>&longs;eriem huiu&longs;cemodi qua&longs;i &longs;arcinularum non &longs;ponte <lb/>abductarum, trahat. </s> |
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| <s>Nam <lb/>primùm &longs;i id repetas, quod paulò ante dicebamus <lb/>de inani facto, quod &longs;upra Terram e&longs;t, &longs;patio in <lb/>quo po&longs;itus &longs;emel lapis con&longs;i&longs;teret; concipe corpus <lb/>aëris ita à Deo reftitui, lapidemque circumam­<lb/>bire, vt nulla tamen vis attractrix ex Terra ad eum <lb/>perueniat; & peruidebis non fore cur lapis ab im­<lb/>motò aëre in vnam partem potius moueatur, quàm <lb/>in aliam. </s> | <s id="id.000548">Non &longs;unto deinde lapilli, &longs;ed <lb/>illorum loco habe totidem fili particulas: profectò <lb/>& illæ, cùm non-nihil pendant, lapillorum in&longs;tar <lb/>&longs;unt, & pro &longs;arcinulis habentur; quæ impetum la-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.072.jpg" pagenum="65"/>pidis perparùm quidem, &longs;ed non-nihil tamen con­<lb/>tinuò refringant. </s> |
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| <s>Finge quippe cætera de&longs;trui, & nihil &longs;uper­<lb/>e&longs;&longs;e præter lapidem, cum circum&longs;tante aëre; agno&longs;­<lb/>ces profectò aërem ex &longs;e non e&longs;&longs;e lapidem in vnam <gap/><lb/>potiù&longs;quàm in aliam partem impul&longs;urum. </s> | <s id="id.000549">Quod per&longs;picuè magis vt nôris, <lb/>appende eundem lapidem ad eiu&longs;dem quidem lon­<lb/>gitudinis, &longs;ed in æqualis tamen cra&longs;&longs;itudinis, ac pro­<lb/>inde ponderis filum; & deprehendes, quò id cra&longs;­<lb/>&longs;ius erit, eo citiùs motum de&longs;iturum, tanquam vi­<lb/>brationibus &longs;ingulis &longs;en&longs;ibiliùs decurtatis; ita vt <lb/>v&longs;urpata cra&longs;&longs;iore chorda, aut etiam virga, catenáve <lb/>ferrea, per paucas omninò vibrationes habiturus &longs;is, <lb/>ac motum parùm duraturum. </s> |
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| <s>Concipe <lb/>deinde re&longs;titui non aerem, &longs;ed &longs;olum effluuium ma­<lb/>gneticorum radiorum ex Terra; & peruidebis e&longs;&longs;e <lb/>cur lapis po&longs;&longs;it à quiete exturbari, & ver&longs;us Teriam <lb/>attrahi. </s> | <s id="id.000550">Heinc, quia quò erit <lb/>aër purior, & filum tenuïus, eò vibrationes plures <lb/>erunt, & motus prolixior, finge aërem ad v&longs;que ina­<lb/>nis tenuïtatem e&longs;&longs;e redactum, atque idcircô nihil re­<lb/>&longs;i&longs;tentem; finge & non filum, &longs;ed radium incorpo­<lb/>reum, qui nullius &longs;it ponderis, neque partibus &longs;uis <lb/>renitatur; an-non capis fore vt lapis appen&longs;us im­<lb/>pre&longs;&longs;um &longs;emel motum con&longs;tanti&longs;&longs;imè tueatur; &longs;cili­<lb/>cet omneis vibrationes non æqualibus modò tem­<lb/>poribus peragens, &longs;ed æqualibus etiam arcubus con­<lb/>tinuò perficiens? </s> |
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| <s>Itaque vis Terræ attractrix e&longs;&longs;e ea cau&longs;a po-<pb pagenum="67"/>terit, quæ motus initium in lapide faciat. </s> | <s id="id.000551">Hæc porrô omnia aliò non tendunt, <lb/>quàm vt intelligamus motum per &longs;patium inane im­<lb/>pre&longs;&longs;um, vbi nihil neque attrahit, neque retinet, ne­<lb/>que omninô renititur, æquabilem fore, ac perpe­<lb/>tuum; atque exinde colligamus, omnem pror&longs;ùs mo­<lb/>tum, qui lapidi imprimitur, e&longs;&longs;e ex &longs;e huiu&longs;modi; adeò <lb/>vt in quamcúmque partem lapidem conjeceris, &longs;i <lb/>quo momento à manu emittitur, &longs;upponas omnia <lb/>vi diuina, lapide excepto, in nihilum redigi; euen­<lb/>turum &longs;it, vt lapis motum &longs;uum perpetuò, ac in <lb/>eandem partem, in quam manus ip&longs;um direxerit, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.073.jpg" pagenum="66"/>moueatur. </s> |
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| <s>Concipe <lb/>denique re&longs;titui aërem &longs;imùl cu<gap/>ffluuio; & per­<lb/>uidebis lapidem po&longs;&longs;e adhûc à quie&longs;cendo de&longs;i&longs;te­<lb/>re, ac ver&longs;us Terram allici, quòd tamet&longs;i aër inferior <lb/>(&longs;eu qui &longs;ub ip&longs;o) nonnihil re&longs;i&longs;tat, propter qualem­<lb/>cúmque corpulentiam; nihilo minùs vis attractrix tan­<lb/>ta e&longs;&longs;e valeat, quæ & ciendo lapidi, & &longs;uperandæ <lb/>aëris re&longs;i&longs;tentiæ &longs;ufficia<gap/>. </s> | <s id="id.000552">Ni&longs;i iam faciat, cau&longs;am videri admi­<lb/>&longs;tionem motus perpendicularis, ob attractionem à <lb/>Terra factam interuenientis, quæ diuergere illum à <lb/>tramite faciat (neque ce&longs;&longs;et, quov&longs;que ip&longs;um ad <lb/>Terram v&longs;que perduxerit) vt dum ramenta ferri <lb/>prope magnetem tran&longs;iecta non rectà pergunt, &longs;ed <lb/>ver&longs;us magnetem diuertuntur; aut dum vniuer&longs;e rei, <lb/>quæ mouetur, oblique occurrimus, ip&longs;amque in obli­<lb/>quam deflectimus plagam. </s></p><p type="main"> |
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| <s>Igitur cau&longs;a hæc attrahens <lb/>habere pote&longs;tvnde id &longs;uppleat, quod vi&longs;um e&longs;t im­<lb/>pellenti dee&longs;&longs;e. </s> | <s id="id.000553">XVII. Nunc, tandem, cùm præter cau&longs;am impel­<lb/>lentem, etiam attrahens excogitata fuerit; ea-ne po­<lb/>tis e&longs;t id præ&longs;tare quod priùs de&longs;iderabatur? </s> |
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| <s>Secundò, &longs;i id repetas, quod di­<lb/>ctum e&longs;t de lapide in &longs;patiis illis imaginariis, &longs;eu in <lb/>inani con&longs;tituto; concipis iam, &longs;i cau&longs;a quæpiam le­<lb/>uiculo ictu eum pellat, fore vt moueatur æquabili <lb/>planè, ac perpetuo motu, ni&longs;i obex occurrerit. <lb/></s> | <s id="id.000554">Vide­<lb/>tur e&longs;&longs;e; neque id modò, &longs;ed & videtur attrahens <lb/>vnà cum impellente euadere integra cau&longs;a eius pro­<lb/>portionis, qua velocitas continuò incre&longs;cit. </s> |
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| <s>Concipe deinde, cùm ita mouetur, pelli ictu con­<lb/>&longs;imili; tunc quia motus præcedens non de&longs;truetur, <lb/>coïbunt duo motus in vnum, qui &longs;it priore velocior <lb/>duplò, quique pari modo &longs;it futurus ex &longs;e æquabi­<lb/>lis, atque perpetuus. </s> | <s id="id.000555">Nam <lb/>primùm &longs;i id repetas, quod paulò ante dicebamus <lb/>de inani facto, quod &longs;upra Terram e&longs;t, &longs;patio in <lb/>quo po&longs;itus &longs;emel lapis con&longs;i&longs;teret; concipe corpus <lb/>aëris ita à Deo reftitui, lapidemque circumam­<lb/>bire, vt nulla tamen vis attractrix ex Terra ad eum <lb/>perueniat; & peruidebis non fore cur lapis ab im­<lb/>motò aëre in vnam partem potius moueatur, quàm <lb/>in aliam. </s> |
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| <s>Concipe rur&longs;ùs pelli tertio, & <lb/>con&longs;imili ictu; tunc quia prior motus ex duobus <lb/>qua&longs;i gradibus compo&longs;itus per&longs;euerabit, fiet coa­<lb/>litio noui motus &longs;eu gradus; &longs;iue erit deinceps mo­<lb/>tus, qui &longs;it triplò velocior primo. </s> | <s id="id.000556">Finge quippe cætera de&longs;trui, & nihil &longs;uper­<lb/>e&longs;&longs;e præter lapidem, cum circum&longs;tante aëre; agno&longs;­<lb/>ces profectò aërem ex &longs;e non e&longs;&longs;e lapidem in vnam <gap/><lb/>potiù&longs;quàm in aliam partem impul&longs;urum. </s> |
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| <s>Concipe po&longs;teà <lb/>pelli quarto, pelli quinto, & aliis; agno&longs;ce&longs;que fore, <lb/>vt velocitas tantùm, ac tandiu incrementum accipiat, <lb/>quantùm, & quandiùictus repetentur. </s> | <s id="id.000557">Concipe <lb/>deinde re&longs;titui non aerem, &longs;ed &longs;olum effluuium ma­<lb/>gneticorum radiorum ex Terra; & peruidebis e&longs;&longs;e <lb/>cur lapis po&longs;&longs;it à quiete exturbari, & ver&longs;us Teriam <lb/>attrahi. </s> |
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| <s>Ni&longs;i facilèid <lb/>concipias, con&longs;titue exqui&longs;itum globum &longs;upra ex­<lb/>qui&longs;itam, libellatámque planitiem, & leui primum <lb/>ictu eum impelle; deprehendes moueri ip&longs;um peni­<lb/>tùs æquabiliter. </s> | <s id="id.000558">Itaque vis Terræ attractrix e&longs;&longs;e ea cau&longs;a po-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.074.jpg" pagenum="67"/>terit, quæ motus initium in lapide faciat. </s> |
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| <s>Impelle alio pari ictu; deprehendes <pb pagenum="68"/>motum fieri velociorem; impelle tertio, adhûc ve­<lb/>lociorem; impelle quarto, adhûc magis; atque ita <lb/>porrô; adeò vt clarum e&longs;&longs;e videatur, velocitatem <lb/>motus non aliunde incre&longs;cere, quàm ex eo, quòd mo­<lb/>bile dum in motu e&longs;t, de nouo mouetur, &longs;eu nouum <lb/>impul&longs;um accipit à cau&longs;a externa. </s> | <s id="id.000559">Concipe <lb/>denique re&longs;titui aërem &longs;imùl cu<gap/>ffluuio; & per­<lb/>uidebis lapidem po&longs;&longs;e adhûc à quie&longs;cendo de&longs;i&longs;te­<lb/>re, ac ver&longs;us Terram allici, quòd tamet&longs;i aër inferior <lb/>(&longs;eu qui &longs;ub ip&longs;o) nonnihil re&longs;i&longs;tat, propter qualem­<lb/>cúmque corpulentiam; nihilo minùs vis attractrix tan­<lb/>ta e&longs;&longs;e valeat, quæ & ciendo lapidi, & &longs;uperandæ <lb/>aëris re&longs;i&longs;tentiæ &longs;ufficia<gap/>. </s> |
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| <s>Neque verò, cùm <lb/>impul&longs;um dico, attractum non intelligo: quippe <lb/>cùm attrahere nihil aliud &longs;it, quàm recuruato in&longs;tru­<lb/>mento ver&longs;um &longs;e impellere; & per&longs;picuum &longs;it lapi­<lb/>dem, globumve memoratum tam impelli vno, plu­<lb/>ribu&longs;ve ictibus po&longs;&longs;e, &longs;i quis ip&longs;um antecedendo cur­<lb/>uis digitis adigat, quàm &longs;i &longs;ub&longs;equendo deuexis <lb/>propellat. </s> | <s id="id.000560">Igitur cau&longs;a hæc attrahens <lb/>habere pote&longs;tvnde id &longs;uppleat, quod vi&longs;um e&longs;t im­<lb/>pellenti dee&longs;&longs;e. </s> |
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| <s>Tertiò, cùm de motus deor&longs;ùm accele­<lb/>ratione agatur, con&longs;tat iam, &longs;iue aër &longs;olus &longs;upernè <lb/>impellat, &longs;iue Terra &longs;ola infernè accer&longs;at, &longs;iue aër, <lb/>& Terra &longs;imùl vireis conferant, non e&longs;&longs;e &longs;atis, vt la­<lb/>pidi vnicus initio ictus imprimatur; &longs;ed e&longs;&longs;e nece&longs;&longs;a­<lb/>rium, vt noui, nouique imprimantur continuò; alio­<lb/>quin enim lapis non acceleraret gradum, &longs;ed ferre­<lb/>tur motu vt æquabili, ita imperceptibili; &longs;egni&longs;&longs;imo <lb/>videlicet, propter tenuïtatem &longs;implicis conatus, <lb/>&longs;eu vniciictus penè nullam vim. </s> | <s id="id.000561">Secundò, &longs;i id repetas, quod di­<lb/>ctum e&longs;t de lapide in &longs;patiis illis imaginariis, &longs;eu in <lb/>inani con&longs;tituto; concipis iam, &longs;i cau&longs;a quæpiam le­<lb/>uiculo ictu eum pellat, fore vt moueatur æquabili <lb/>planè, ac perpetuo motu, ni&longs;i obex occurrerit. <lb/></s> |
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| <s>Cùm verò &longs;eu &longs;ola <lb/>impul&longs;io, &longs;eu &longs;ola attractio ad accelerationem &longs;uffi­<lb/>ciat; quid-nam cau&longs;æ e&longs;&longs;e putabis, cur cen&longs;eam <lb/>vtramque e&longs;&longs;e con<gap/>ungendam? </s> | <s id="id.000562">Concipe deinde, cùm ita mouetur, pelli ictu con­<lb/>&longs;imili; tunc quia motus præcedens non de&longs;truetur, <lb/>coïbunt duo motus in vnum, qui &longs;it priore velocior <lb/>duplò, quique pari modo &longs;it futurus ex &longs;e æquabi­<lb/>lis, atque perpetuus. </s> |
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| <s>Nempe in cau&longs;a pro­<lb/>portio e&longs;t, qua dictum e&longs;t antè accelerationem fieri, <lb/>Nam fac vnicam e&longs;&longs;e cau&longs;am, exempli gratiâ attra­<lb/>ctionem; concipies quidem ex dictis &longs;equi, vt quia <lb/>radij magnetici, qua&longs;i &longs;tringentes chordulæ, con­<lb/>tinentem motum, &longs;iue impetum lapidi imprimunt, <pb pagenum="69"/>talem imprimant in primo momento, qui non delea­<lb/>tur, &longs;ed per&longs;eueret in &longs;ecundo, in quo alius &longs;imilis <lb/>imprimitur, qui priori junctus per&longs;eueret vnà cum <lb/>illo in tertio; in quo alius &longs;imilis adjungitur, atque <lb/>ita con&longs;equenter; adeò vt impetus ex continua illa <lb/>adjectione continuò incre&longs;cat, motu&longs;que &longs;emper ve­<lb/>locior fiat. </s> | <s id="id.000563">Concipe rur&longs;ùs pelli tertio, & <lb/>con&longs;imili ictu; tunc quia prior motus ex duobus <lb/>qua&longs;i gradibus compo&longs;itus per&longs;euerabit, fiet coa­<lb/>litio noui motus &longs;eu gradus; &longs;iue erit deinceps mo­<lb/>tus, qui &longs;it triplò velocior primo. </s> |
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| <s>Verùm facile erit peruidere <expan abbr="cõ&longs;equi">con&longs;equi</expan> exhac <lb/>adjectione incrementuum celeritatis &longs;ecundum vni­<lb/>tatum &longs;eriem; nempe ita vt in primo momento &longs;it vnus <lb/>velocitatis gradus, in &longs;ecundo &longs;int duo, in tertio tres, <lb/>in quarto quatuor; & in primo momento, lapis de&longs;­<lb/>cendat vnum v.c. </s> | <s id="id.000564">Concipe po&longs;teà <lb/>pelli quarto, pelli quinto, & aliis; agno&longs;ce&longs;que fore, <lb/>vt velocitas tantùm, ac tandiu incrementum accipiat, <lb/>quantùm, & quandiùictus repetentur. </s> |
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| <s>orgyiam, in &longs;ecundo duas, in ter­<lb/>tio treis, in quarto quatuor; vnde & aggregando <lb/>dici po&longs;&longs;it in fine primi momenti ca&longs;um e&longs;&longs;e factum <lb/>vnius orgyiæ, in fine &longs;ecundi trium, in fine tertij <lb/>&longs;ex, in fine quarti decem. </s> | <s id="id.000565">Ni&longs;i facilèid <lb/>concipias, con&longs;titue exqui&longs;itum globum &longs;upra ex­<lb/>qui&longs;itam, libellatámque planitiem, & leui primum <lb/>ictu eum impelle; deprehendes moueri ip&longs;um peni­<lb/>tùs æquabiliter. </s> |
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| <s>Cæterùm con&longs;tat ex &longs;u­<lb/>pra dictis, talem &longs;eriem non ob&longs;eruari; &longs;ed ob&longs;erua­<lb/>ri potiùs &longs;eriem numerorum imparium ab vnitate <lb/>incipientium; & aggregando numerum orgyiarum <lb/>in fine cuiu&longs;que momenti deprehendi quadratum; <lb/>nempe non vnum, tria, &longs;ex, decem; &longs;ed vnum, qua­<lb/>tuor, nouem &longs;exdecim, &c. </s> | <s id="id.000566">Impelle alio pari ictu; deprehendes <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.075.jpg" pagenum="68"/>motum fieri velociorem; impelle tertio, adhûc ve­<lb/>lociorem; impelle quarto, adhûc magis; atque ita <lb/>porrô; adeò vt clarum e&longs;&longs;e videatur, velocitatem <lb/>motus non aliunde incre&longs;cere, quàm ex eo, quòd mo­<lb/>bile dum in motu e&longs;t, de nouo mouetur, &longs;eu nouum <lb/>impul&longs;um accipit à cau&longs;a externa. </s> |
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| <s>Et loco attractionis <lb/>v&longs;urpa impul&longs;ionem: v&longs;urpa grauitatem, vt vulgò <lb/>accipitur; v&longs;urpa quamcúm que cau&longs;am &longs;implicem; <lb/>idem penitùs con&longs;equetur. </s></p><p type="main"> | <s id="id.000567">Neque verò, cùm <lb/>impul&longs;um dico, attractum non intelligo: quippe <lb/>cùm attrahere nihil aliud &longs;it, quàm recuruato in&longs;tru­<lb/>mento ver&longs;um &longs;e impellere; & per&longs;picuum &longs;it lapi­<lb/>dem, globumve memoratum tam impelli vno, plu­<lb/>ribu&longs;ve ictibus po&longs;&longs;e, &longs;i quis ip&longs;um antecedendo cur­<lb/>uis digitis adigat, quàm &longs;i &longs;ub&longs;equendo deuexis <lb/>propellat. </s> |
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| <s>XVIII. <!-- KEEP S--></s> | <s id="id.000568">Tertiò, cùm de motus deor&longs;ùm accele­<lb/>ratione agatur, con&longs;tat iam, &longs;iue aër &longs;olus &longs;upernè <lb/>impellat, &longs;iue Terra &longs;ola infernè accer&longs;at, &longs;iue aër, <lb/>& Terra &longs;imùl vireis conferant, non e&longs;&longs;e &longs;atis, vt la­<lb/>pidi vnicus initio ictus imprimatur; &longs;ed e&longs;&longs;e nece&longs;&longs;a­<lb/>rium, vt noui, nouique imprimantur continuò; alio­<lb/>quin enim lapis non acceleraret gradum, &longs;ed ferre­<lb/>tur motu vt æquabili, ita imperceptibili; &longs;egni&longs;&longs;imo <lb/>videlicet, propter tenuïtatem &longs;implicis conatus, <lb/>&longs;eu vniciictus penè nullam vim. </s> |
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| <s>Itaque experiundum re&longs;tat, an conjungendo <lb/>vtramque cau&longs;am, quæ e&longs;t ob&longs;eruata &longs;equatur pro­<lb/>portio. </s> | <s id="id.000569">Cùm verò &longs;eu &longs;ola <lb/>impul&longs;io, &longs;eu &longs;ola attractio ad accelerationem &longs;uffi­<lb/>ciat; quid-nam cau&longs;æ e&longs;&longs;e putabis, cur cen&longs;eam <lb/>vtramque e&longs;&longs;e con<gap/>ungendam? </s> |
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| <s>Dictum e&longs;t iam initium motus e&longs;&longs;e non po&longs;&longs;e <lb/>ab aëre; itaque nece&longs;&longs;arium e&longs;t in primo momento <lb/>&longs;ola Terra agat, vnicu&longs;que, & &longs;implex ictus impri-<pb pagenum="70"/>matur lapidi, quo & motus incipiat, & re&longs;i&longs;ientlæ <lb/>aëris infernè jacentis vincatur. </s> | <s id="id.000570">Nempe in cau&longs;a pro­<lb/>portio e&longs;t, qua dictum e&longs;t antè accelerationem fieri, <lb/>Nam fac vnicam e&longs;&longs;e cau&longs;am, exempli gratiâ attra­<lb/>ctionem; concipies quidem ex dictis &longs;equi, vt quia <lb/>radij magnetici, qua&longs;i &longs;tringentes chordulæ, con­<lb/>tinentem motum, &longs;iue impetum lapidi imprimunt, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.076.jpg" pagenum="69"/>talem imprimant in primo momento, qui non delea­<lb/>tur, &longs;ed per&longs;eueret in &longs;ecundo, in quo alius &longs;imilis <lb/>imprimitur, qui priori junctus per&longs;eueret vnà cum <lb/>illo in tertio; in quo alius &longs;imilis adjungitur, atque <lb/>ita con&longs;equenter; adeò vt impetus ex continua illa <lb/>adjectione continuò incre&longs;cat, motu&longs;que &longs;emper ve­<lb/>locior fiat. </s> |
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| <s>Subnoto autem ean­<lb/>dem proportionem, qua percurruntur orgyiæ, & <lb/>percurrerentur &longs;tadia, ac milliaria, &longs;itantùm ex alto <lb/>po&longs;&longs;et aliquid cadere, eádem percurri pedes, digitos, <lb/>grana, & &longs;patia quælibet in&longs;en&longs;ilia, ad ip&longs;a v&longs;que <lb/>minima: Quare po&longs;&longs;e quoque accipi momenta non <lb/>&longs;olùm cuiu&longs;inodi &longs;unt interualla pul&longs;ationum arteriæ, <lb/>&longs;ed etiam minora, minoraque, & minimis quibu&longs;que <lb/>illis &longs;patij partibus re&longs;pondentia: Ac eadem ratione <lb/>po&longs;&longs;e accipinon modo majores, & compo&longs;itos ve­<lb/>locitatis gradus; &longs;ed minimos etiam, atque &longs;impli­<lb/>ces, quorum nempe vnus &longs;ufficere po&longs;&longs;it mobili ci­<lb/>endo per vnum ex illis &longs;patiis minimis, & in mini­<lb/>mo vno momentorum. </s> | <s id="id.000571">Verùm facile erit peruidere <expan abbr="cõ&longs;equi">con&longs;equi</expan> exhac <lb/>adjectione incrementuum celeritatis &longs;ecundum vni­<lb/>tatum &longs;eriem; nempe ita vt in primo momento &longs;it vnus <lb/>velocitatis gradus, in &longs;ecundo &longs;int duo, in tertio tres, <lb/>in quarto quatuor; & in primo momento, lapis de&longs;­<lb/>cendat vnum v.c. </s> |
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| <s>Igitur cùm primum mo­<lb/>mentum accipio, minimum intelligo, in quo vnus, <lb/>& &longs;implex ictus per attractionem imprimatur, per­<lb/>agaturque minimum &longs;patium, motu ex&longs;i&longs;tente &longs;im­<lb/>plici, & cui deinceps accedere, ex repetitis icti­<lb/>bus, gradus celeritatis po&longs;&longs;int. </s> | <s id="id.000572">orgyiam, in &longs;ecundo duas, in ter­<lb/>tio treis, in quarto quatuor; vnde & aggregando <lb/>dici po&longs;&longs;it in fine primi momenti ca&longs;um e&longs;&longs;e factum <lb/>vnius orgyiæ, in fine &longs;ecundi trium, in fine tertij <lb/>&longs;ex, in fine quarti decem. </s> |
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| <s>Porrô quia aër <lb/>infernè pre&longs;&longs;us circum&longs;tantem premit, neque v&longs;­<lb/>quam patet &longs;uccedendi libertas, ni&longs;i quà &longs;upernè <lb/>&longs;patium intereà de&longs;eritur, ideò fit, vt aër &longs;ecun­<lb/>dum latera re&longs;iliens in &longs;uperiorem locum concurrat; <lb/>derelictumque locum inuadat. </s> | <s id="id.000573">Cæterùm con&longs;tat ex &longs;u­<lb/>pra dictis, talem &longs;eriem non ob&longs;eruari; &longs;ed ob&longs;erua­<lb/>ri potiùs &longs;eriem numerorum imparium ab vnitate <lb/>incipientium; & aggregando numerum orgyiarum <lb/>in fine cuiu&longs;que momenti deprehendi quadratum; <lb/>nempe non vnum, tria, &longs;ex, decem; &longs;ed vnum, qua­<lb/>tuor, nouem &longs;exdecim, &c. </s> |
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| <s>Et quoniam non po­<lb/>te&longs;t hæc inua&longs;io fieri, quin aer accurrens vrgeat la­<lb/>pidem; idcircô fit, vt &longs;ecundo momento duplex de <lb/>nouo imprimatut ictus, vnus à Terra, quæ pergit <lb/>attrahere, alius ab aere, qui incipit vrgere. </s> | <s id="id.000574">Et loco attractionis <lb/>v&longs;urpa impul&longs;ionem: v&longs;urpa grauitatem, vt vulgò <lb/>accipitur; v&longs;urpa quamcúm que cau&longs;am &longs;implicem; <lb/>idem penitùs con&longs;equetur. </s></p><p type="main"> |
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| <s>I&longs;ti <lb/>autem &longs;unt duo motus, &longs;iue celeritatis gradus, qui <pb pagenum="71"/>cum primo non de&longs;tructo, &longs;ed per&longs;euerante iuncti, <lb/>&longs;int tres. </s> | <s id="id.000575">XVIII. <!-- KEEP S--></s> |
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| <s>In tertio autem momento pergente Terra <lb/>attrahere, & aere impellere, imprimuntur rur&longs;us <lb/>duo ictus noui, qui cum tribus prioribus, & per­<lb/>&longs;euerantibus juncti &longs;int quinque. </s> | <s id="id.000576">Itaque experiundum re&longs;tat, an conjungendo <lb/>vtramque cau&longs;am, quæ e&longs;t ob&longs;eruata &longs;equatur pro­<lb/>portio. </s> |
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| <s>Ita in quarto mo­<lb/>mento imprimuntur alij duo, qui cum prioribus &longs;int <lb/>&longs;eptem; in quinto duo qui cum prioribus &longs;int no­<lb/>uem, atque ita con&longs;equenter &longs;ecundum &longs;eriem nu­<lb/>merorum, qui ab vnitate cœperint, imparium: cùm <lb/>interim &longs;patia acqui&longs;ita in fine cuiu&longs;que momenti, <lb/>&longs;int &longs;emper inter &longs;e eadem proportione, qua mo­<lb/>mentorum ip&longs;orum quadrata, veluti iam attigimus. <lb/></s> | <s id="id.000577">Dictum e&longs;t iam initium motus e&longs;&longs;e non po&longs;&longs;e <lb/>ab aëre; itaque nece&longs;&longs;arium e&longs;t in primo momento <lb/>&longs;ola Terra agat, vnicu&longs;que, & &longs;implex ictus impri-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.077.jpg" pagenum="70"/>matur lapidi, quo & motus incipiat, & re&longs;i&longs;ientlæ <lb/>aëris infernè jacentis vincatur. </s> |
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| <s>Hæc ergo demùm mihi videtur exi&longs;timari po&longs;&longs;e cau­<lb/>&longs;a tum motus deor&longs;ùm, tum accelerationis eiu&longs;dem, <lb/>tum proportionis, qua acceleratur. </s> | <s id="id.000578">Subnoto autem ean­<lb/>dem proportionem, qua percurruntur orgyiæ, & <lb/>percurrerentur &longs;tadia, ac milliaria, &longs;itantùm ex alto <lb/>po&longs;&longs;et aliquid cadere, eádem percurri pedes, digitos, <lb/>grana, & &longs;patia quælibet in&longs;en&longs;ilia, ad ip&longs;a v&longs;que <lb/>minima: Quare po&longs;&longs;e quoque accipi momenta non <lb/>&longs;olùm cuiu&longs;inodi &longs;unt interualla pul&longs;ationum arteriæ, <lb/>&longs;ed etiam minora, minoraque, & minimis quibu&longs;que <lb/>illis &longs;patij partibus re&longs;pondentia: Ac eadem ratione <lb/>po&longs;&longs;e accipinon modo majores, & compo&longs;itos ve­<lb/>locitatis gradus; &longs;ed minimos etiam, atque &longs;impli­<lb/>ces, quorum nempe vnus &longs;ufficere po&longs;&longs;it mobili ci­<lb/>endo per vnum ex illis &longs;patiis minimis, & in mini­<lb/>mo vno momentorum. </s> |
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| <s>Vt verò &longs;imul <lb/>facilè capias quomodo vniformitas incrementi per <lb/>æqualia momen­<lb/><figure id="fig3"/><lb/>ta fiat, huiu&longs;ce­<lb/>modi concipe fi­<lb/>guram. </s> | <s id="id.000579">Igitur cùm primum mo­<lb/>mentum accipio, minimum intelligo, in quo vnus, <lb/>& &longs;implex ictus per attractionem imprimatur, per­<lb/>agaturque minimum &longs;patium, motu ex&longs;i&longs;tente &longs;im­<lb/>plici, & cui deinceps accedere, ex repetitis icti­<lb/>bus, gradus celeritatis po&longs;&longs;int. </s> |
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| <s>Intelliga­<lb/>tur in puncto A <lb/>fieri angulum ex <lb/>ductis ab eo dua­<lb/>bus lineis AB, <lb/>AC; eæ comple­<lb/>ctentur interual­<lb/>lum continuò, <expan abbr="vni-formiterq;">vni­<lb/>formiterque</expan> incre&longs; <lb/>cens. </s> | <s id="id.000580">Porrô quia aër <lb/>infernè pre&longs;&longs;us circum&longs;tantem premit, neque v&longs;­<lb/>quam patet &longs;uccedendi libertas, ni&longs;i quà &longs;upernè <lb/>&longs;patium intereà de&longs;eritur, ideò fit, vt aër &longs;ecun­<lb/>dum latera re&longs;iliens in &longs;uperiorem locum concurrat; <lb/>derelictumque locum inuadat. </s> |
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| <s>Diuidantur &longs;ineæ in parteis aliquot æqua­<lb/>leis, ducanturque per puncta diui&longs;ionnm qua&longs;i ba&longs;es <pb pagenum="72"/>quædam angulo oppo&longs;itæ, DE, FG, HI, KL, & <lb/>plures, &longs;i velis; itemque diui&longs;a in totidem parteis <lb/>KL, ducantur parallelæ DM, FN, HO; & EO, <lb/>GN, IM: di&longs;pe&longs;cetur &longs;patium in eos, quos vides <lb/>triangulos, inter &longs;e&longs;e omninò pareis. </s> | <s id="id.000581">Et quoniam non po­<lb/>te&longs;t hæc inua&longs;io fieri, quin aer accurrens vrgeat la­<lb/>pidem; idcircô fit, vt &longs;ecundo momento duplex de <lb/>nouo imprimatut ictus, vnus à Terra, quæ pergit <lb/>attrahere, alius ab aere, qui incipit vrgere. </s> |
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| <s>Concipe iam <lb/>lineas ab angulo incipientes repræ&longs;entare tempus ab <lb/>aliquo puncto æquabiliter fluens, & parteis linearum <lb/>æqualeis repræ&longs;entare æqualeis parteis, &longs;iue mo­<lb/>menta temporis. </s> | <s id="id.000582">I&longs;ti <lb/>autem &longs;unt duo motus, &longs;iue celeritatis gradus, qui <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.078.jpg" pagenum="71"/>cum primo non de&longs;tructo, &longs;ed per&longs;euerante iuncti, <lb/>&longs;int tres. </s> |
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| <s>Concipe rur&longs;ùs interuallum vnifor­<lb/>miter cre&longs;cens repræ&longs;entare velocitatem vniformi­<lb/>ter incre&longs;centem, & quos pareis triangulos vides, <lb/>totidem gradus velocitatis, & con&longs;equenter parteis <lb/>&longs;patij, quod graue decidens percurrit. </s> | <s id="id.000583">In tertio autem momento pergente Terra <lb/>attrahere, & aere impellere, imprimuntur rur&longs;us <lb/>duo ictus noui, qui cum tribus prioribus, & per­<lb/>&longs;euerantibus juncti &longs;int quinque. </s> |
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| <s>Tunc agno&longs;­<lb/>ces &longs;anè, cùm in primo momento &longs;it vnus gradus <lb/>impetus, &longs;eu velocitatis, acquiri in &longs;ecundo treis, in <lb/>tertio quinque, in quarto &longs;eptem, qui progre&longs;&longs;us e&longs;t <lb/>numerorum ab vnitate imparium. </s> | <s id="id.000584">Ita in quarto mo­<lb/>mento imprimuntur alij duo, qui cum prioribus &longs;int <lb/>&longs;eptem; in quinto duo qui cum prioribus &longs;int no­<lb/>uem, atque ita con&longs;equenter &longs;ecundum &longs;eriem nu­<lb/>merorum, qui ab vnitate cœperint, imparium: cùm <lb/>interim &longs;patia acqui&longs;ita in fine cuiu&longs;que momenti, <lb/>&longs;int &longs;emper inter &longs;e eadem proportione, qua mo­<lb/>mentorum ip&longs;orum quadrata, veluti iam attigimus. <lb/></s> |
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| <s>Et aiiunde, &longs;i du­<lb/>cas lineam, quæ diui&longs;a in &longs;exdecim parteis referat <lb/>orgyiarum &longs;exdecim altitudinem; agno&longs;ces cur gra­<lb/>ue in fine primi momenti de&longs;cenderit vnam orgyiam, <lb/>in fine &longs;ecundi quatuor, in fine tertij nouem, in fine <lb/>quarti &longs;exdecim: quia nempe ita &longs;e habere aggre­<lb/>gando intelliguntur memorati trianguli in fine <lb/>cuiu&longs;que repræ&longs;entati momenti. </s> | <s id="id.000585">Hæc ergo demùm mihi videtur exi&longs;timari po&longs;&longs;e cau­<lb/>&longs;a tum motus deor&longs;ùm, tum accelerationis eiu&longs;dem, <lb/>tum proportionis, qua acceleratur. </s> |
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| <s>Agno&longs;ces quoque, <lb/>cur idem graue &longs;ur&longs;ùm projectum &longs;ecundum ean­<lb/>dem lineam tanto tempore a&longs;cendat, quanto de&longs;­<lb/>cendit, & velocitas motus eius eadem ratione a&longs;cen­<lb/>dendo decre&longs;cat, qua de&longs;cendendo incre&longs;cit Quia <lb/>&longs;i &longs;upponas vim proiectricem indidi&longs;&longs;e illi &longs;eptem ve­<lb/>locitatis gradus, vt &longs;unt &longs;eptem trianguli ad infi-<pb pagenum="73"/>&longs;imam ba&longs;im; vis oppo&longs;ita &longs;ic retundet, vt cùm in <lb/>primo momento &longs;eptem fuerint, in &longs;ecuhdo &longs;int tan­<lb/>tùm quinque, in tertio tantùm tres, in primo tan­<lb/>tùm vnus. </s> | <s id="id.000586">Vt verò &longs;imul <lb/>facilè capias quomodo vniformitas incrementi per <lb/>æqualia momen­<lb/><figure id="id.027.00.078.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.078.1.jpg"/><lb/>ta fiat, huiu&longs;ce­<lb/>modi concipe fi­<lb/>guram. </s> |
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| <s>Memorià autem tenendum e&longs;t, loqui nos <lb/>&longs;emper tantùm de eo, quod e&longs;t perpendiculare in <lb/>motu; cùm id quidem, quod e&longs;t horizontale, e&longs;&longs;e <lb/>ex &longs;e æquabile, aliquoties dam inculcatum &longs;it. </s> | <s id="id.000587">Intelliga­<lb/>tur in puncto A <lb/>fieri angulum ex <lb/>ductis ab eo dua­<lb/>bus lineis AB, <lb/>AC; eæ comple­<lb/>ctentur interual­<lb/>lum continuò, <expan abbr="vni-formiterq;">vni­<lb/>formiterque</expan> incre&longs; <lb/>cens. </s> |
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| <s>Præ­<lb/>tereò &longs;eruari eandem proportionem, &longs;igraue decidat <lb/>non ad perpendiculum, &longs;ed &longs;upra planum horizonti <lb/>obliquum; nam &longs;egniùs id quidem pro ratione obli­<lb/>quitatis, &longs;ed facto nihilominùs eadem ratione incre­<lb/>mento, vt experiri licet globulis demi&longs;&longs;is per tubulos <lb/>vitreos, cuiu&longs;modi confici plureis in hunc v&longs;um cura­<lb/>uimus. </s> | <s id="id.000588">Diuidantur &longs;ineæ in parteis aliquot æqua­<lb/>leis, ducanturque per puncta diui&longs;ionnm qua&longs;i ba&longs;es <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.079.jpg" pagenum="72"/>quædam angulo oppo&longs;itæ, DE, FG, HI, KL, & <lb/>plures, &longs;i velis; itemque diui&longs;a in totidem parteis <lb/>KL, ducantur parallelæ DM, FN, HO; & EO, <lb/>GN, IM: di&longs;pe&longs;cetur &longs;patium in eos, quos vides <lb/>triangulos, inter &longs;e&longs;e omninò pareis. </s> |
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| <s>Prætereo eandem quoque &longs;eruari circa nu­<lb/>merum vibrationum, &longs;iue excur&longs;uum, recur&longs;uúmque <lb/>vt diximas, rerum pen&longs;ilium, quatenus chordatum, <lb/>quibus appenduntur, longitudines &longs;unt vt quadra­<lb/>ta vibrationum: adeò vt, &longs;i ex quatuor chordis prima <lb/>&longs;it vnius pedis, &longs;ecunda quatuor, tertia nouem, quar­<lb/>ta &longs;exdecim, quo tempore quartum pen&longs;ile peraget <lb/>vnam vibrationem, tertium peragat duas, &longs;ecundum <lb/>treis, & primum quatuor. </s> | <s id="id.000589">Concipe iam <lb/>lineas ab angulo incipientes repræ&longs;entare tempus ab <lb/>aliquo puncto æquabiliter fluens, & parteis linearum <lb/>æqualeis repræ&longs;entare æqualeis parteis, &longs;iue mo­<lb/>menta temporis. </s> |
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| <s>Prætercò tandem exinde <lb/>e&longs;&longs;e, vnde tam Galileus, quàm Mer&longs;ennus no&longs;ter, & <lb/>alij definiant quanto tempore lapis ca&longs;urus in cen­<lb/>trum v&longs;que (&longs;i perforatam Terram concedas) ex &longs;uper­<lb/>ficie fuerit, quanto ex Luna, quanto ex Sole, quanto <lb/>ex &longs;ideribus fixis. </s> | <s id="id.000590">Concipe rur&longs;ùs interuallum vnifor­<lb/>miter cre&longs;cens repræ&longs;entare velocitatem vniformi­<lb/>ter incre&longs;centem, & quos pareis triangulos vides, <lb/>totidem gradus velocitatis, & con&longs;equenter parteis <lb/>&longs;patij, quod graue decidens percurrit. </s> |
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| <s>Supponunt quippe eandem acce­<lb/>lerationis proportionem &longs;eruari; tamet&longs;i cx eo ca­<lb/>pite non videatur eadem futura; quòd eadem vbique <lb/>impellens, attrahen&longs;que vis futura non &longs;it. </s></p><pb pagenum="74"/><p type="main"> | <s id="id.000591">Tunc agno&longs;­<lb/>ces &longs;anè, cùm in primo momento &longs;it vnus gradus <lb/>impetus, &longs;eu velocitatis, acquiri in &longs;ecundo treis, in <lb/>tertio quinque, in quarto &longs;eptem, qui progre&longs;&longs;us e&longs;t <lb/>numerorum ab vnitate imparium. </s> |
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| <s>XIX. <!-- KEEP S--></s> | <s id="id.000592">Et aiiunde, &longs;i du­<lb/>cas lineam, quæ diui&longs;a in &longs;exdecim parteis referat <lb/>orgyiarum &longs;exdecim altitudinem; agno&longs;ces cur gra­<lb/>ue in fine primi momenti de&longs;cenderit vnam orgyiam, <lb/>in fine &longs;ecundi quatuor, in fine tertij nouem, in fine <lb/>quarti &longs;exdecim: quia nempe ita &longs;e habere aggre­<lb/>gando intelliguntur memorati trianguli in fine <lb/>cuiu&longs;que repræ&longs;entati momenti. </s> |
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| <s>Vnum addo; nempe licere ex i&longs;tis in­<lb/>telligi, quid &longs;entiendum &longs;it de difficultate vulgò <lb/>excitatata circa vim impre&longs;&longs;am projectinbus. </s> | <s id="id.000593">Agno&longs;ces quoque, <lb/>cur idem graue &longs;ur&longs;ùm projectum &longs;ecundum ean­<lb/>dem lineam tanto tempore a&longs;cendat, quanto de&longs;­<lb/>cendit, & velocitas motus eius eadem ratione a&longs;cen­<lb/>dendo decre&longs;cat, qua de&longs;cendendo incre&longs;cit Quia <lb/>&longs;i &longs;upponas vim proiectricem indidi&longs;&longs;e illi &longs;eptem ve­<lb/>locitatis gradus, vt &longs;unt &longs;eptem trianguli ad infi-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.080.jpg" pagenum="73"/>&longs;imam ba&longs;im; vis oppo&longs;ita &longs;ic retundet, vt cùm in <lb/>primo momento &longs;eptem fuerint, in &longs;ecuhdo &longs;int tan­<lb/>tùm quinque, in tertio tantùm tres, in primo tan­<lb/>tùm vnus. </s> |
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| <s>Re­<lb/>quiritur quippe quid nam hæc vis &longs;it in re mobili? <lb/></s> | <s id="id.000594">Memorià autem tenendum e&longs;t, loqui nos <lb/>&longs;emper tantùm de eo, quod e&longs;t perpendiculare in <lb/>motu; cùm id quidem, quod e&longs;t horizontale, e&longs;&longs;e <lb/>ex &longs;e æquabile, aliquoties dam inculcatum &longs;it. </s> |
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| <s>quomodo in ea imprimatur? </s> | <s id="id.000595">Præ­<lb/>tereò &longs;eruari eandem proportionem, &longs;igraue decidat <lb/>non ad perpendiculum, &longs;ed &longs;upra planum horizonti <lb/>obliquum; nam &longs;egniùs id quidem pro ratione obli­<lb/>quitatis, &longs;ed facto nihilominùs eadem ratione incre­<lb/>mento, vt experiri licet globulis demi&longs;&longs;is per tubulos <lb/>vitreos, cuiu&longs;modi confici plureis in hunc v&longs;um cura­<lb/>uimus. </s> |
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| <s>quomodo perduret? <lb/></s> | <s id="id.000596">Prætereo eandem quoque &longs;eruari circa nu­<lb/>merum vibrationum, &longs;iue excur&longs;uum, recur&longs;uúmque <lb/>vt diximas, rerum pen&longs;ilium, quatenus chordatum, <lb/>quibus appenduntur, longitudines &longs;unt vt quadra­<lb/>ta vibrationum: adeò vt, &longs;i ex quatuor chordis prima <lb/>&longs;it vnius pedis, &longs;ecunda quatuor, tertia nouem, quar­<lb/>ta &longs;exdecim, quo tempore quartum pen&longs;ile peraget <lb/>vnam vibrationem, tertium peragat duas, &longs;ecundum <lb/>treis, & primum quatuor. </s> |
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| <s>quomodo euane&longs;cat? </s> | <s id="id.000597">Prætercò tandem exinde <lb/>e&longs;&longs;e, vnde tam Galileus, quàm Mer&longs;ennus no&longs;ter, & <lb/>alij definiant quanto tempore lapis ca&longs;urus in cen­<lb/>trum v&longs;que (&longs;i perforatam Terram concedas) ex &longs;uper­<lb/>ficie fuerit, quanto ex Luna, quanto ex Sole, quanto <lb/>ex &longs;ideribus fixis. </s> |
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| <s>Enimverò, cùm haberi &longs;oleat <lb/>vt vis actiua lapidem mouens; videtur tamen vis <lb/>actiua, quæ projectionis cau&longs;a e&longs;t, e&longs;&longs;e in ip&longs;o pro­<lb/>ijciente, non verò in projectare, quæ merè pa&longs;&longs;iuè <lb/>&longs;e habet. </s> | <s id="id.000598">Supponunt quippe eandem acce­<lb/>lerationis proportionem &longs;eruari; tamet&longs;i cx eo ca­<lb/>pite non videatur eadem futura; quòd eadem vbique <lb/>impellens, attrahen&longs;que vis futura non &longs;it. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.081.jpg" pagenum="74"/><p type="main"> |
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| <s>Id, quod in re projecta e&longs;t, motus e&longs;t, <lb/>quilicet interdum nominetur vis, impetus, &c. (vt <lb/>etiam aliquoties à nobis factitatum e&longs;t, dum, vt fa­<lb/>ciliùs intelligamur, familares voces, quantum po&longs;­<lb/>&longs;umus, retinemus) non proptereà tamen aliud quid­<lb/>piam e&longs;t reip&longs;â, quàm ip&longs;emet motus. </s> | <s id="id.000599">XIX. <!-- KEEP S--></s> |
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| <s>Et &longs;anè vnus, <lb/>idemque motus, vel per Ari&longs;totelem, actio &longs;imùl, <lb/>& pa&longs;&longs;io e&longs;t; actio proüt e&longs;t à mouente, pa&longs;&longs;io, proüt <lb/>in mobili: quare vt in mouente e&longs;t vis actiua, qua, <lb/>moueat; ita in mobili vis pa&longs;&longs;iua, qua moueatur: <lb/>& dum mobile reip&longs;â mouetur, non in eo quærenda <lb/>e&longs;t vis actiua, quæ in mouente &longs;olo nece&longs;&longs;aria fuit, <lb/>&longs;ed pa&longs;&longs;iua &longs;olùm, quæ in eo e&longs;t, & redacta quidem, <lb/>vt vocant, ad actum. </s> | <s id="id.000600">Vnum addo; nempe licere ex i&longs;tis in­<lb/>telligi, quid &longs;entiendum &longs;it de difficultate vulgò <lb/>excitatata circa vim impre&longs;&longs;am projectinbus. </s> |
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| <s>Neque ob&longs;tat, quòd mouens <lb/>&longs;eparatum &longs;it, aut interii&longs;&longs;e etiam, con&longs;tante motu <lb/>accepto, po&longs;&longs;it; nam non proptereà requiritur, vt <lb/>aliam, præter motum, vim à &longs;eip&longs;o tran&longs;mi&longs;erit, <lb/>quæ motum deinceps efficiat; &longs;ed &longs;ufficit vt motum <lb/>&longs;emel in mobili fecerit, qui continuari ab&longs;que ip­<lb/>&longs;o po&longs;&longs;it. </s> | <s id="id.000601">Re­<lb/>quiritur quippe quid nam hæc vis &longs;it in re mobili? <lb/></s> |
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| <s>Pote&longs;t autem; quoniam e&longs;t eius naturæ <lb/>accidens, vt modò &longs;ubjectum per&longs;euerans habeat, <pb pagenum="75"/>neque contrarium quidpiam occurrat; per&longs;euerate <lb/>ab&longs;que continüa cau&longs;æ &longs;uæ actione valeat. </s> | <s id="id.000602">quomodo in ea imprimatur? </s> |
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| <s>Et quan­<lb/>quam principia mobilis interna dici po&longs;&longs;int habere <lb/>vim non pa&longs;&longs;iuam modo, &longs;ed etiam actiuam, qua <lb/>talem motum continü<gap/>: huiu&longs;cemodi tamen vis non <lb/>tam à mouente impre&longs;&longs;a, quàm excitata dici pote&longs;t; <lb/>planiu&longs;que e&longs;t, vt à mouente nihil imprimi aliud, <lb/>quàm motum dicamus. </s> | <s id="id.000603">quomodo perduret? <lb/></s> |
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| <s>Imprimi, inquam, qualem <lb/>mouens habet donec mobile e&longs;t ip&longs;i conjunctum, <lb/>& qualis continuandus e&longs;&longs;et, futuru&longs;que perpetuus, <lb/>ni&longs;i à motu aliquo aduer&longs;o labefactarerur. </s> | <s id="id.000604">quomodo euane&longs;cat? </s> |
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| <s>Vt nô­<lb/>ris autem quemadmodum impre&longs;&longs;io huiu&longs;modi fiat, <lb/>con&longs;idera, priu&longs;quàm lapis transferatur per aërem, <lb/>e&longs;&longs;e ip&longs;um aliquanti&longs;per conjunctum cum manu, & <lb/>haberi qua&longs;i vnum, idemque, hoc e&longs;t integrum mo­<lb/>bile cum illa; quatenùs vnus, idemque motus vtri­<lb/>que <gap/>unctìm conuenit, &longs;eu quatenùs manus eodem <lb/>ip&longs;o motu mouet lapidem, quo &longs;eip<gap/>am. </s> | <s id="id.000605">Enimverò, cùm haberi &longs;oleat <lb/>vt vis actiua lapidem mouens; videtur tamen vis <lb/>actiua, quæ projectionis cau&longs;a e&longs;t, e&longs;&longs;e in ip&longs;o pro­<lb/>ijciente, non verò in projectare, quæ merè pa&longs;&longs;iuè <lb/>&longs;e habet. </s> |
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| <s>Ex hoc <lb/>enim fit, vt manu vel &longs;ur&longs;ùm, vel tran&longs;uer&longs;ùm. <lb/></s> | <s id="id.000606">Id, quod in re projecta e&longs;t, motus e&longs;t, <lb/>quilicet interdum nominetur vis, impetus, &c. (vt <lb/>etiam aliquoties à nobis factitatum e&longs;t, dum, vt fa­<lb/>ciliùs intelligamur, familares voces, quantum po&longs;­<lb/>&longs;umus, retinemus) non proptereà tamen aliud quid­<lb/>piam e&longs;t reip&longs;â, quàm ip&longs;emet motus. </s> |
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| <s>vel quo <gap/>over&longs;ùm voles, mota, lapis in eandem <lb/>partem moueatur; & quia tamen manus à corpore <lb/>retenta, ip&longs;ive innixa &longs;e&longs;e interim &longs;ubducit à lapi­<lb/>de, fit vt lapis manui non cohærens, ac &longs;olùm con­<lb/>tiguus pergat, cœptam que cum manu non d<gap/>at <lb/>viam. </s> | <s id="id.000607">Et &longs;anè vnus, <lb/>idemque motus, vel per Ari&longs;totelem, actio &longs;imùl, <lb/>& pa&longs;&longs;io e&longs;t; actio proüt e&longs;t à mouente, pa&longs;&longs;io, proüt <lb/>in mobili: quare vt in mouente e&longs;t vis actiua, qua, <lb/>moueat; ita in mobili vis pa&longs;&longs;iua, qua moueatur: <lb/>& dum mobile reip&longs;â mouetur, non in eo quærenda <lb/>e&longs;t vis actiua, quæ in mouente &longs;olo nece&longs;&longs;aria fuit, <lb/>&longs;ed pa&longs;&longs;iua &longs;olùm, quæ in eo e&longs;t, & redacta quidem, <lb/>vt vocant, ad actum. </s> |
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| <s>Quòd &longs;i perpetuò viam non teneat, &longs;i co­<lb/>gatur deflectere, &longs;i po&longs;tremò quie&longs;cere, dicta iam e&longs;t <lb/>cau&longs;a non &longs;emel. </s> | <s id="id.000608">Neque ob&longs;tat, quòd mouens <lb/>&longs;eparatum &longs;it, aut interii&longs;&longs;e etiam, con&longs;tante motu <lb/>accepto, po&longs;&longs;it; nam non proptereà requiritur, vt <lb/>aliam, præter motum, vim à &longs;eip&longs;o tran&longs;mi&longs;erit, <lb/>quæ motum deinceps efficiat; &longs;ed &longs;ufficit vt motum <lb/>&longs;emel in mobili fecerit, qui continuari ab&longs;que ip­<lb/>&longs;o po&longs;&longs;it. </s> |
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| <s>Id &longs;olùm nota, quod dico &longs;e <lb/>manu, de quolibet alio phy&longs;ico mouente intelligi <lb/>po&longs;&longs;e. </s> | <s id="id.000609">Pote&longs;t autem; quoniam e&longs;t eius naturæ <lb/>accidens, vt modò &longs;ubjectum per&longs;euerans habeat, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.082.jpg" pagenum="75"/>neque contrarium quidpiam occurrat; per&longs;euerate <lb/>ab&longs;que continüa cau&longs;æ &longs;uæ actione valeat. </s> |
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| <s>Quippe nullum e&longs;t naturale mouens quod <lb/>non ip&longs;um quoque moueatur, vt aliquo v&longs;que mo-<pb pagenum="76"/>bile deducat, in viam tenendam dirigat, & qua&longs;i <lb/>tyrocinio aliquo in&longs;tituens, promoueat: neque enim <lb/>nudo contactu, & ab&longs;que huiu&longs;cemodi promotione <lb/>propelleret vnquam. </s> | <s id="id.000610">Et quan­<lb/>quam principia mobilis interna dici po&longs;&longs;int habere <lb/>vim non pa&longs;&longs;iuam modo, &longs;ed etiam actiuam, qua <lb/>talem motum continü<gap/>: huiu&longs;cemodi tamen vis non <lb/>tam à mouente impre&longs;&longs;a, quàm excitata dici pote&longs;t; <lb/>planiu&longs;que e&longs;t, vt à mouente nihil imprimi aliud, <lb/>quàm motum dicamus. </s> |
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| <s>Inductionem facere nihil e&longs;t <lb/>nece&longs;&longs;e; cùm propo&longs;ito quolibet exemplo, atten­<lb/>tione &longs;olùm &longs;it opus; & aliunde con&longs;tet, quò mo­<lb/>uens rapidiùs mouetur, dum contingit, & aliquo­<lb/>v&longs;que in&longs;equitur mobile, eò celeriùs mobile ferri, <lb/>& quo &longs;egniùs, eò tardiùs. </s> | <s id="id.000611">Imprimi, inquam, qualem <lb/>mouens habet donec mobile e&longs;t ip&longs;i conjunctum, <lb/>& qualis continuandus e&longs;&longs;et, futuru&longs;que perpetuus, <lb/>ni&longs;i à motu aliquo aduer&longs;o labefactarerur. </s> |
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| <s>Difficultas e&longs;&longs;e po&longs;&longs;et <lb/>de motu reflexo; nam pila impacta in parietem ita re­<lb/>&longs;ilit, vt moueri ab eo debere videatur, cùm immo­<lb/>tus tamen &longs;it, neque aliquov&longs;que con&longs;equatur pilam. <lb/></s> | <s id="id.000612">Vt nô­<lb/>ris autem quemadmodum impre&longs;&longs;io huiu&longs;modi fiat, <lb/>con&longs;idera, priu&longs;quàm lapis transferatur per aërem, <lb/>e&longs;&longs;e ip&longs;um aliquanti&longs;per conjunctum cum manu, & <lb/>haberi qua&longs;i vnum, idemque, hoc e&longs;t integrum mo­<lb/>bile cum illa; quatenùs vnus, idemque motus vtri­<lb/>que <gap/>unctìm conuenit, &longs;eu quatenùs manus eodem <lb/>ip&longs;o motu mouet lapidem, quo &longs;eip<gap/>am. </s> |
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| <s>Verùm ea re&longs;ilitio, motu&longs;que reflexus non tam à <lb/>pariete, corporevealio re&longs;&longs;ectente efficitur, quàm ab <lb/>ip&longs;o netimpingente: euenitque &longs;olùm, vt qui motus <lb/>directò continüaretur, ob&longs;taculo facto continüetur <lb/>reflexè. </s> | <s id="id.000613">Ex hoc <lb/>enim fit, vt manu vel &longs;ur&longs;ùm, vel tran&longs;uer&longs;ùm. <lb/></s> |
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| <s>Atque id quidem dicere cum ip&longs;o Ari&longs;totele <lb/>malo, quàm motus quidpiam tribuere vel paricti, <lb/>vel parti ip&longs;ius; quoniam licet res probabilitate &longs;ua <lb/>non carcat (vt arguit leui&longs;&longs;imus ictus, qui vni ex­<lb/>tremo longi&longs;&longs;imæ, cra&longs;&longs;i&longs;&longs;imæque trabis impactus, <lb/>exauditur in alio, tanquam &longs;ucce&longs;&longs;iuè in omneis <lb/>parteis, & vltrá per aërem, ad aurem v&longs;que propa­<lb/>gatus; itemque ictus ianuæ in limen, à quo totas <lb/>concuti ædeis, fene&longs;tralia vitra, dum tremunt, de­<lb/>mon&longs;trant, cæteiáque &longs;imilia) attamen res longio­<lb/>ris e&longs;t, quàm locus ferat, di qui&longs;itionis. </s> | <s id="id.000614">vel quo <gap/>over&longs;ùm voles, mota, lapis in eandem <lb/>partem moueatur; & quia tamen manus à corpore <lb/>retenta, ip&longs;ive innixa &longs;e&longs;e interim &longs;ubducit à lapi­<lb/>de, fit vt lapis manui non cohærens, ac &longs;olùm con­<lb/>tiguus pergat, cœptam que cum manu non d<gap/>at <lb/>viam. </s> |
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| <s>Quin­<lb/>etiam non alienum foret di&longs;quirere, quor&longs;ùm re­<lb/>&longs;&longs;exio ad parcis &longs;emper angulos fiat (quantùm ex <lb/>eius natura e&longs;t) cum ip&longs;a incidentia: &longs;ed quónam <pb pagenum="77"/>tandem prouelierer? </s> | <s id="id.000615">Quòd &longs;i perpetuò viam non teneat, &longs;i co­<lb/>gatur deflectere, &longs;i po&longs;tremò quie&longs;cere, dicta iam e&longs;t <lb/>cau&longs;a non &longs;emel. </s> |
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| <s>cum id explicare poui&longs;&longs;imùm <lb/>&longs;olcam ex emer&longs;ione rei pen&longs;rlis à &longs;uo perpendi­<lb/>culo <gap/> quæ non ab&longs;imiliter &longs;iat ip&longs;i in idem pro­<lb/>cidentiæ: neque po&longs;&longs;im dedu<gap/>re, quin explicem <lb/>&longs;imùl ob quam cau&longs;am fiat, vt ex&longs;i&longs;tente eadem <lb/>pen&longs;ilis longitudine, omnes procidentiæ, arque <lb/>emer&longs;iones, omne&longs;que adeò excur&longs;iones, recur&longs;io­<lb/>ne&longs;que, de quibus dictum quidpiam iam e&longs;t, &longs;int <lb/>pror&longs;ùs æqui-temporaneæ? </s></p><p type="main"> | <s id="id.000616">Id &longs;olùm nota, quod dico &longs;e <lb/>manu, de quolibet alio phy&longs;ico mouente intelligi <lb/>po&longs;&longs;e. </s> |
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| <s>XX. <!-- KEEP S--></s> | <s id="id.000617">Quippe nullum e&longs;t naturale mouens quod <lb/>non ip&longs;um quoque moueatur, vt aliquo v&longs;que mo-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.083.jpg" pagenum="76"/>bile deducat, in viam tenendam dirigat, & qua&longs;i <lb/>tyrocinio aliquo in&longs;tituens, promoueat: neque enim <lb/>nudo contactu, & ab&longs;que huiu&longs;cemodi promotione <lb/>propelleret vnquam. </s> |
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| <s>An non magis congruum putabis me­<lb/>mini&longs;&longs;e me pollicitationis, qua recepi &longs;uperiùs <lb/>declaraturum me ad calcem, quid ex factis ex­<lb/>perimentis, dicendum mon&longs;tretur de iis, quæ <lb/>&longs;olent vulgò obijci ad impugnandum motum <lb/>Telluris? </s> | <s id="id.000618">Inductionem facere nihil e&longs;t <lb/>nece&longs;&longs;e; cùm propo&longs;ito quolibet exemplo, atten­<lb/>tione &longs;olùm &longs;it opus; & aliunde con&longs;tet, quò mo­<lb/>uens rapidiùs mouetur, dum contingit, & aliquo­<lb/>v&longs;que in&longs;equitur mobile, eò celeriùs mobile ferri, <lb/>& quo &longs;egniùs, eò tardiùs. </s> |
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| <s>verùm cùm videas qua hactenùs ver­<lb/>borum mole obruerim te, æquum profectò ri­<lb/>uos iam claudam, & quod hue v&longs;que dilatum <lb/>e&longs;t, differatur adhûc in proximam v&longs;que ad te <lb/>&longs;cribendi occa&longs;ionem. </s> | <s id="id.000619">Difficultas e&longs;&longs;e po&longs;&longs;et <lb/>de motu reflexo; nam pila impacta in parietem ita re­<lb/>&longs;ilit, vt moueri ab eo debere videatur, cùm immo­<lb/>tus tamen &longs;it, neque aliquov&longs;que con&longs;equatur pilam. <lb/></s> |
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| <s>Erit heic intereà plus æquo, <lb/>quàm vt pellegendo debeas e&longs;&longs;e patiens; &longs;ed nom­<lb/>pe illa bonitas tua, quam præconceptam habui, vt <lb/>permitterem <gap/>alamo ex&longs;patiandi licentiam, fecit. </s> | <s id="id.000620">Verùm ea re&longs;ilitio, motu&longs;que reflexus non tam à <lb/>pariete, corporevealio re&longs;&longs;ectente efficitur, quàm ab <lb/>ip&longs;o netimpingente: euenitque &longs;olùm, vt qui motus <lb/>directò continüaretur, ob&longs;taculo facto continüetur <lb/>reflexè. </s> |
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| <s>Præ­<lb/>&longs;ump&longs;i quoque te pro tuo vericogno&longs;cendi ardore, <lb/>próque ea, quam de me habes, quainque non <lb/>mereor, opinione, fui&longs;&longs;e haud dubiè quidpiam <lb/>ampliùs, quàm nudas illas circa motum ob&longs;er­<lb/>uationes ex&longs;pectaturum. </s> | <s id="id.000621">Atque id quidem dicere cum ip&longs;o Ari&longs;totele <lb/>malo, quàm motus quidpiam tribuere vel paricti, <lb/>vel parti ip&longs;ius; quoniam licet res probabilitate &longs;ua <lb/>non carcat (vt arguit leui&longs;&longs;imus ictus, qui vni ex­<lb/>tremo longi&longs;&longs;imæ, cra&longs;&longs;i&longs;&longs;imæque trabis impactus, <lb/>exauditur in alio, tanquam &longs;ucce&longs;&longs;iuè in omneis <lb/>parteis, & vltrá per aërem, ad aurem v&longs;que propa­<lb/>gatus; itemque ictus ianuæ in limen, à quo totas <lb/>concuti ædeis, fene&longs;tralia vitra, dum tremunt, de­<lb/>mon&longs;trant, cæteiáque &longs;imilia) attamen res longio­<lb/>ris e&longs;t, quàm locus ferat, di qui&longs;itionis. </s> |
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| <s>Vtcùmque &longs;it, confi­<lb/>do &longs;altem te pro &longs;ingulari candoie, amoréque <lb/>erga me tuo, id, quodcùmque e&longs;t, excepturum, <pb pagenum="78"/>h biturumque tanquam à viro, qui &longs;it ob&longs;eruan­<lb/>tu&longs;i nus tui. </s> | <s id="id.000622">Quin­<lb/>etiam non alienum foret di&longs;quirere, quor&longs;ùm re­<lb/>&longs;&longs;exio ad parcis &longs;emper angulos fiat (quantùm ex <lb/>eius natura e&longs;t) cum ip&longs;a incidentia: &longs;ed quónam <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.084.jpg" pagenum="77"/>tandem prouelierer? </s> |
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| <s>Salutem lacobo Fratri optimo, toti­<lb/>que erudito con&longs;e&longs;&longs;ui nunciari exopto. </s> | <s id="id.000623">cum id explicare poui&longs;&longs;imùm <lb/>&longs;olcam ex emer&longs;ione rei pen&longs;rlis à &longs;uo perpendi­<lb/>culo <gap/> quæ non ab&longs;imiliter &longs;iat ip&longs;i in idem pro­<lb/>cidentiæ: neque po&longs;&longs;im dedu<gap/>re, quin explicem <lb/>&longs;imùl ob quam cau&longs;am fiat, vt ex&longs;i&longs;tente eadem <lb/>pen&longs;ilis longitudine, omnes procidentiæ, arque <lb/>emer&longs;iones, omne&longs;que adeò excur&longs;iones, recur&longs;io­<lb/>ne&longs;que, de quibus dictum quidpiam iam e&longs;t, &longs;int <lb/>pror&longs;ùs æqui-temporaneæ? </s></p><p type="main"> |
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| <s>Vale. <lb/><!-- KEEP S--></s> | <s id="id.000624">XX. <!-- KEEP S--></s> |
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| <s>Aquis-Sextus XII. Kal. </s> | <s id="id.000625">An non magis congruum putabis me­<lb/>mini&longs;&longs;e me pollicitationis, qua recepi &longs;uperiùs <lb/>declaraturum me ad calcem, quid ex factis ex­<lb/>perimentis, dicendum mon&longs;tretur de iis, quæ <lb/>&longs;olent vulgò obijci ad impugnandum motum <lb/>Telluris? </s> |
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| <s>Decemb. </s> | <s id="id.000626">verùm cùm videas qua hactenùs ver­<lb/>borum mole obruerim te, æquum profectò ri­<lb/>uos iam claudam, & quod hue v&longs;que dilatum <lb/>e&longs;t, differatur adhûc in proximam v&longs;que ad te <lb/>&longs;cribendi occa&longs;ionem. </s> |
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| <s>C<gap/>C, XL. <lb/><figure id="fig4"/><!-- KEEP S--></s></p><pb pagenum="79"/><figure/><p type="main"> | <s id="id.000627">Erit heic intereà plus æquo, <lb/>quàm vt pellegendo debeas e&longs;&longs;e patiens; &longs;ed nom­<lb/>pe illa bonitas tua, quam præconceptam habui, vt <lb/>permitterem <gap/>alamo ex&longs;patiandi licentiam, fecit. </s> |
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| <s><emph type="center"/>EPISTOLA SECVNDA.<emph.end type="center"/></s></p><p type="main"> | <s id="id.000628">Præ­<lb/>&longs;ump&longs;i quoque te pro tuo vericogno&longs;cendi ardore, <lb/>próque ea, quam de me habes, quainque non <lb/>mereor, opinione, fui&longs;&longs;e haud dubiè quidpiam <lb/>ampliùs, quàm nudas illas circa motum ob&longs;er­<lb/>uationes ex&longs;pectaturum. </s> |
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| <s><emph type="center"/><emph type="italics"/>EIDEM.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> | <s id="id.000629">Vtcùmque &longs;it, confi­<lb/>do &longs;altem te pro &longs;ingulari candoie, amoréque <lb/>erga me tuo, id, quodcùmque e&longs;t, excepturum, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.085.jpg" pagenum="78"/>h biturumque tanquam à viro, qui &longs;it ob&longs;eruan­<lb/>tu&longs;i nus tui. </s> |
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| <s>I. MORAM non traho, Vir eximie, <lb/>&longs;ed mox ob&longs;ignatis, mi&longs;&longs;i&longs;que, quas <lb/>peruidebis, literis, ha&longs;ce occipio, vt <lb/>liberem de propo&longs;ita Parenthe&longs;i fi­<lb/>dem. </s> | <s id="id.000630">Salutem lacobo Fratri optimo, toti­<lb/>que erudito con&longs;e&longs;&longs;ui nunciari exopto. </s> |
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| <s>Quippe intertexturus fueram <lb/>(quod adtexere præ&longs;titit) videri ex iis ob&longs;eruatis, <lb/>quæ circa motum a motore tran&longs;lato impre&longs;&longs;om <lb/>memorata &longs;unt, infirmum reddi argumentum, quo <lb/>&longs;olemus vulgò quietem a&longs;&longs;erere globo Telluris. <!-- KEEP S--></s> | <s id="id.000631">Vale. <lb/><!-- KEEP S--></s> |
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| <s>Non <lb/>quòd exinde pronunciem moueri haud dubiè I el­<lb/>lurem, vt Pythagoreis olim vi&longs;um e&longs;t, & nunc Co­<lb/>pernicanis placer; &longs;ed quòd amore veritatis, & con­<lb/>&longs;equenter ad ea, quæ deducta &longs;unt, nihil proh bere <lb/>exi&longs;timem, quò minùs in&longs;inüem conquirendam e&longs;&longs;e <lb/>rationem veri&longs;imiliorem. </s> | <s id="id.000632">Aquis-Sextus XII. Kal. </s> |
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| <s>Videlicet hæc di&longs;qui&longs;itio <lb/>non videtur e&longs;&longs;e ad eos releganda, qui laborant ver­<lb/>tigine, vt familiare e&longs;t obijci; quandò & &longs;apientum <lb/>non po&longs;tremus Seneca dignam rem duxit contem­<lb/>platione, vt &longs;ciamus, in quo rerum &longs;tatu &longs;imus; pi­<lb/>gerrimam &longs;ortiti, an veloci&longs;&longs;imam &longs;edem; circa nos <lb/>Dcus omnia, an nos agat: & Plato, qui Philo&longs;ophi <pb pagenum="80"/>diuini cognomentum tulit, Telluri attribuit tum <lb/>junior reuolutionem diurnam circa proprium axem, <lb/>tum ætate maturior etiam tran&longs;lationem per zo­<lb/>diacum. </s> | <s id="id.000633">Decemb. </s> |
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| <s>No&longs;ti enim, cùm in Timæo &longs;en&longs;i&longs;&longs;et Tel­<lb/>lurem in vniuer&longs;i centro degentem, vna &longs;ui circum­<lb/>ductione ver&longs;us ortum, diem, noctemque efficere, <lb/>dum intereà Sol, cæteráque a&longs;tra apparerent oriri, <lb/>ac deferri ver&longs;us occa&longs;um; po&longs;t-modum tamen, vt <lb/>ex Theophra&longs;to apud Plutarchum intelligitur, eum <lb/>colloca&longs;&longs;e Solem in centro, & Terræ præter mo­<lb/>tum diurnum, a&longs;&longs;ignaui&longs;&longs;e etiam annuum, quem dum <lb/>circa Solem, & &longs;ub &longs;ignis zodiaci peragerct, Sol <lb/>appareret intereà oppo&longs;ita &longs;igna peragrare. </s> | <s id="id.000634">C<gap/>C, XL. <lb/><figure id="id.027.00.085.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.085.1.jpg"/><!-- KEEP S--></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.086.jpg" pagenum="79"/><figure id="id.027.00.086.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.086.1.jpg"/><p type="main"> |
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| <s>Sed <lb/>hi&longs;ce dimi&longs;&longs;is, ecquod-nam e&longs;t illud, de quo dicere <lb/>volo, argumentum è Nempe illud e&longs;t, quod ab ip&longs;o <lb/>v&longs;que Ari&longs;totele &longs;olet obijci, dum neminem ferè <lb/>non vides, qui diurnum motum oppugnans, non <lb/>in&longs;tet fore, vt &longs;i Terra circumvolueretur in ortum, <lb/>lapis directè &longs;ur&longs;ùm projectus, non in eundem, è quo <lb/>foret projectus, locum recideret, &longs;ed caderet pro­<lb/>cùl ad parteis occiduas; quòd eo ver&longs;ante per <lb/>aerem, locus e&longs;&longs;et interea ver&longs;us ortum procùl <lb/>&longs;ubductus: eo modo, inquiunt, quo &longs;agitta &longs;ur&longs;ùm <lb/>euibrata è puppi, dum nauis mouetur, non in puppim <lb/>recidit, &longs;ed in aquam à tergo puppis, quæ intereà <lb/>&longs;ubducta e&longs;t. </s> | <s id="id.000635"><emph type="center"/>EPISTOLA SECVNDA.<emph.end type="center"/></s></p><p type="main"> |
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| <s>Enimverò quis non miretur neminem <lb/>ex tanta obijcientium <gap/>urba rem fui&longs;&longs;e expertum <lb/>adeò facilem; o'nnei&longs;que exemplum in re &longs;imili <lb/>v&longs;urpare, non quod ip&longs;i probauerint, aut ab exper­<lb/>tis acceperint; &longs;ed quòd aliunde &longs;ic &longs;e habere, aut <pb pagenum="89"/>debere &longs;e habere &longs;int rati? </s> | <s id="id.000636"><emph type="center"/><emph type="italics"/>EIDEM.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> |
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| <s>Siquidem ex iis, quæ de­<lb/>ducta &longs;unt, manife&longs;tum e&longs;t po&longs;&longs;e omninô Coperni­<lb/>canos tale exemplum retorquere, atque adeò ar­<lb/>gumentari, tam po&longs;&longs;e lapidem in eundem Terræ <lb/>locum recidere, quàm &longs;agittam in eandem pup­<lb/>pim. </s></p><p type="main"> | <s id="id.000637">I. MORAM non traho, Vir eximie, <lb/>&longs;ed mox ob&longs;ignatis, mi&longs;&longs;i&longs;que, quas <lb/>peruidebis, literis, ha&longs;ce occipio, vt <lb/>liberem de propo&longs;ita Parenthe&longs;i fi­<lb/>dem. </s> |
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| <s>II. <!-- KEEP S--></s> | <s id="id.000638">Quippe intertexturus fueram <lb/>(quod adtexere præ&longs;titit) videri ex iis ob&longs;eruatis, <lb/>quæ circa motum a motore tran&longs;lato impre&longs;&longs;om <lb/>memorata &longs;unt, infirmum reddi argumentum, quo <lb/>&longs;olemus vulgò quietem a&longs;&longs;erere globo Telluris. <!-- KEEP S--></s> |
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| <s>Sufficere po&longs;&longs;et ad hoc demon&longs;trandum <lb/>quod in&longs;crip&longs;i Schema &longs;u<gap/><lb/><gap/> iliud importunè reuocem, &longs;ubijcere heic <lb/>i&longs;tud præ&longs;tat. </s> | <s id="id.000639">Non <lb/>quòd exinde pronunciem moueri haud dubiè I el­<lb/>lurem, vt Pythagoreis olim vi&longs;um e&longs;t, & nunc Co­<lb/>pernicanis placer; &longs;ed quòd amore veritatis, & con­<lb/>&longs;equenter ad ea, quæ deducta &longs;unt, nihil proh bere <lb/>exi&longs;timem, quò minùs in&longs;inüem conquirendam e&longs;&longs;e <lb/>rationem veri&longs;imiliorem. </s> |
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| <s>E&longs;to exempli gratiâ Turris AB, è <lb/><figure id="fig5"/><lb/>cuius pede proijciatur &longs;ur&longs;ùm lapis ad v&longs;que fa&longs;ti­<lb/>gium B, & donec lapis e&longs;t in aëre, &longs;upponatur <lb/>moueri Terra ver&longs;us parteis orientaleis CDEFG <lb/>HIK; turris profectò vnà mouebitur: putas verò <lb/>lapis de&longs;eretur à turri? </s> | <s id="id.000640">Videlicet hæc di&longs;qui&longs;itio <lb/>non videtur e&longs;&longs;e ad eos releganda, qui laborant ver­<lb/>tigine, vt familiare e&longs;t obijci; quandò & &longs;apientum <lb/>non po&longs;tremus Seneca dignam rem duxit contem­<lb/>platione, vt &longs;ciamus, in quo rerum &longs;tatu &longs;imus; pi­<lb/>gerrimam &longs;ortiti, an veloci&longs;&longs;imam &longs;edem; circa nos <lb/>Dcus omnia, an nos agat: & Plato, qui Philo&longs;ophi <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.087.jpg" pagenum="80"/>diuini cognomentum tulit, Telluri attribuit tum <lb/>junior reuolutionem diurnam circa proprium axem, <lb/>tum ætate maturior etiam tran&longs;lationem per zo­<lb/>diacum. </s> |
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| <s>De&longs;ereretur &longs;anè, &longs;i is, <lb/>qui proijcit, non inhæreret ip&longs;i Terræ; eodem <lb/>modo, quo &longs;i quis extra nauim con&longs;i&longs;tens lapidem <lb/>&longs;ur&longs;ùm proijciat, dum malus è regione tran&longs;it; <lb/>talis quippe lapis non &longs;equetur malum, &longs;ed ab il­<lb/>lo de&longs;eretur. </s> | <s id="id.000641">No&longs;ti enim, cùm in Timæo &longs;en&longs;i&longs;&longs;et Tel­<lb/>lurem in vniuer&longs;i centro degentem, vna &longs;ui circum­<lb/>ductione ver&longs;us ortum, diem, noctemque efficere, <lb/>dum intereà Sol, cæteráque a&longs;tra apparerent oriri, <lb/>ac deferri ver&longs;us occa&longs;um; po&longs;t-modum tamen, vt <lb/>ex Theophra&longs;to apud Plutarchum intelligitur, eum <lb/>colloca&longs;&longs;e Solem in centro, & Terræ præter mo­<lb/>tum diurnum, a&longs;&longs;ignaui&longs;&longs;e etiam annuum, quem dum <lb/>circa Solem, & &longs;ub &longs;ignis zodiaci peragerct, Sol <lb/>appareret intereà oppo&longs;ita &longs;igna peragrare. </s> |
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| <s>At quemadmodum &longs;i naui inhæreat, <lb/>qui lapidem &longs;ur&longs;ùm &longs;ecundum malum proijcit, tunc <lb/>lapis malum &longs;equitur, neque ab illo de&longs;eritur; ita <lb/>quia Terræ inhæret qui lapidem &longs;ur&longs;ùm &longs;ecundum <pb pagenum="90"/>turrim proijcit, nece&longs;&longs;e e&longs;t lapidem &longs;equi, ac nu&longs;­<lb/>quàm de&longs;eri à turri. </s> | <s id="id.000642">Sed <lb/>hi&longs;ce dimi&longs;&longs;is, ecquod-nam e&longs;t illud, de quo dicere <lb/>volo, argumentum è Nempe illud e&longs;t, quod ab ip&longs;o <lb/>v&longs;que Ari&longs;totele &longs;olet obijci, dum neminem ferè <lb/>non vides, qui diurnum motum oppugnans, non <lb/>in&longs;tet fore, vt &longs;i Terra circumvolueretur in ortum, <lb/>lapis directè &longs;ur&longs;ùm projectus, non in eundem, è quo <lb/>foret projectus, locum recideret, &longs;ed caderet pro­<lb/>cùl ad parteis occiduas; quòd eo ver&longs;ante per <lb/>aerem, locus e&longs;&longs;et interea ver&longs;us ortum procùl <lb/>&longs;ubductus: eo modo, inquiunt, quo &longs;agitta &longs;ur&longs;ùm <lb/>euibrata è puppi, dum nauis mouetur, non in puppim <lb/>recidit, &longs;ed in aquam à tergo puppis, quæ intereà <lb/>&longs;ubducta e&longs;t. </s> |
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| <s>Cau&longs;a manife&longs;ta iam e&longs;t. <lb/></s> | <s id="id.000643">Enimverò quis non miretur neminem <lb/>ex tanta obijcientium <gap/>urba rem fui&longs;&longs;e expertum <lb/>adeò facilem; o'nnei&longs;que exemplum in re &longs;imili <lb/>v&longs;urpare, non quod ip&longs;i probauerint, aut ab exper­<lb/>tis acceperint; &longs;ed quòd aliunde &longs;ic &longs;e habere, aut <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.088.jpg" pagenum="89"/>debere &longs;e habere &longs;int rati? </s> |
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| <s>Nam vt lapidi &longs;ecundum malum projecto non &longs;ola <lb/>impre&longs;&longs;a e&longs;t vis ip&longs;ius proijcientis propria, &longs;ed etiam <lb/>alia ex motu nauis, quo manus &longs;imùl adacta fuit; <lb/>ita projecto &longs;ecundum turrim non &longs;ola vis pro­<lb/>iicientis propria impre&longs;&longs;a e&longs;t, &longs;ed alia etiam ex mo­<lb/>tu <gap/> &longs;imùl correpta. </s> | <s id="id.000644">Siquidem ex iis, quæ de­<lb/>ducta &longs;unt, manife&longs;tum e&longs;t po&longs;&longs;e omninô Coperni­<lb/>canos tale exemplum retorquere, atque adeò ar­<lb/>gumentari, tam po&longs;&longs;e lapidem in eundem Terræ <lb/>locum recidere, quàm &longs;agittam in eandem pup­<lb/>pim. </s></p><p type="main"> |
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| <s>Et vt <lb/>lapis &longs;ecundum malum vi&longs;us a&longs;cendere, de&longs;cendere­<lb/>que ad perpendiculum, de&longs;cribit nihilominùs li­<lb/>neam, quam parabolicam diximus: ita lapis &longs;ecun­<lb/>dum turrim contineri vi&longs;us in eodem perpendiculo, <lb/>de&longs;cribit tamen in &longs;patio mundano lineam &longs;imiliter <lb/>parabolicam; &longs;ed paraboles longè obtu&longs;ioris. </s> | <s id="id.000645">II. <!-- KEEP S--></s> |
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| <s>Nem­<lb/>pe vt illeic motus e&longs;t compo&longs;itus ex perpendiculari, <lb/>& horizontali; ita ex vtróque compo&longs;itus heic:adeò <lb/>vt, quicquid e&longs;t ex vi proijcientis propria, id explice­<lb/>tur v&longs;que ad fa&longs;tigium turris, ad quod lapis per­<lb/>uenit; & quicquid à vi, &longs;eu motu Telluris, id ex­<lb/>plicetur ad punctum v&longs;que horizontalis lineæ, quod <lb/>lapis decidens attingit. </s> | <s id="id.000646">Sufficere po&longs;&longs;et ad hoc demon&longs;trandum <lb/>quod in&longs;crip&longs;i Schema &longs;u<gap/><lb/><gap/> iliud importunè reuocem, &longs;ubijcere heic <lb/>i&longs;tud præ&longs;tat. </s> |
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| <s>Itaque, cùm Turris ex A <lb/>B, peruenerit ad CL, rectè concipis lapidem per­<lb/>ueni&longs;&longs;e ad M; cùm ad DN, perueni&longs;&longs;e ad O; cùm <lb/>ad EP, perueni&longs;&longs;e ad Q: cùm ad FR, perueni&longs;&longs;e ad ip­<lb/>&longs;um-met R, quod fa&longs;tigium e&longs;t; & con&longs;equenter, cùm <lb/>ad GS, perueni&longs;&longs;ead T: cum ad HV, perueni&longs;&longs;e ad X: <lb/>cùm ad IY, perueni&longs;&longs;e ad Z; cùm denique ad K <gap/>, per­<lb/>ueni&longs;&longs;e ad ip&longs;um K. ita vt vbicúmque lapis in aëre, vel <lb/>per &longs;patium mundanum fuerit, extiterit &longs;emper in li­<lb/>nea ip&longs;i Turri parallela, eidemque Turris pedi, <pb pagenum="91"/>punctove vicino perpendicularis. </s> | <s id="id.000647">E&longs;to exempli gratiâ Turris AB, è <lb/><figure id="id.027.00.088.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.088.1.jpg"/><lb/>cuius pede proijciatur &longs;ur&longs;ùm lapis ad v&longs;que fa&longs;ti­<lb/>gium B, & donec lapis e&longs;t in aëre, &longs;upponatur <lb/>moueri Terra ver&longs;us parteis orientaleis CDEFG <lb/>HIK; turris profectò vnà mouebitur: putas verò <lb/>lapis de&longs;eretur à turri? </s> |
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| <s>Nec verò iam <lb/>tibi videbitur mirum oculos omnium, qui ad lapi­<lb/>dem attendent, &longs;olum illum motum perpendicula­<lb/>rem ob&longs;eruare, nullo autem modo horizontalem, qui <lb/>perpendicularem tamen ex&longs;uperat tantoperè; &longs;i­<lb/>quidem omnium oculi vnà & cum turri, & cum <lb/>lapide, eodem horizontali motu transferuntur; <lb/>adeò vt quemadmodum ex&longs;i&longs;tentes in naui omnes <lb/>&longs;olum perpendicularem, nullo verò modò hori­<lb/>zontalem, cuius &longs;unt participes, ob&longs;eruant; ita heic <lb/>fieri nece&longs;&longs;um &longs;it. </s> | <s id="id.000648">De&longs;ereretur &longs;anè, &longs;i is, <lb/>qui proijcit, non inhæreret ip&longs;i Terræ; eodem <lb/>modo, quo &longs;i quis extra nauim con&longs;i&longs;tens lapidem <lb/>&longs;ur&longs;ùm proijciat, dum malus è regione tran&longs;it; <lb/>talis quippe lapis non &longs;equetur malum, &longs;ed ab il­<lb/>lo de&longs;eretur. </s> |
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| <s>Vnum di&longs;crimen e&longs;t, quòd qui&longs;­<lb/>piam vel in alia naui quie&longs;cente, vel in littore con­<lb/>&longs;i&longs;tere po&longs;&longs;it, vnde ad motum lapidis horizontalem <lb/>attendat; non po&longs;&longs;it verò alicubi extra Terram fi­<lb/>gere pedem, vnde pari modo progre&longs;&longs;um hori­<lb/>zontalem percipiat. </s></p><p type="main"> | <s id="id.000649">At quemadmodum &longs;i naui inhæreat, <lb/>qui lapidem &longs;ur&longs;ùm &longs;ecundum malum proijcit, tunc <lb/>lapis malum &longs;equitur, neque ab illo de&longs;eritur; ita <lb/>quia Terræ inhæret qui lapidem &longs;ur&longs;ùm &longs;ecundum <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.089.jpg" pagenum="90"/>turrim proijcit, nece&longs;&longs;e e&longs;t lapidem &longs;equi, ac nu&longs;­<lb/>quàm de&longs;eri à turri. </s> |
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| <s>III. Dices, quid &longs;i aliquis intra ci&longs;tam à gry­<lb/>phe abreptam detineatur per aërem? </s> | <s id="id.000650">Cau&longs;a manife&longs;ta iam e&longs;t. <lb/></s> |
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| <s>Re&longs;ponde­<lb/>bitur, neque illum quidem po&longs;&longs;e eum motum ob­<lb/>&longs;eruare; quoniam & ip&longs;e vna cum ci&longs;ta, gryphe, <lb/>aereque, eodem illo motu &longs;imul transferetur; <lb/>oporteretque illum con&longs;titui vltra regionem <lb/>aëream, motuque ip&longs;o non corripi, vt eius ob&longs;er­<lb/>uandi euaderet capax. </s> | <s id="id.000651">Nam vt lapidi &longs;ecundum malum projecto non &longs;ola <lb/>impre&longs;&longs;a e&longs;t vis ip&longs;ius proijcientis propria, &longs;ed etiam <lb/>alia ex motu nauis, quo manus &longs;imùl adacta fuit; <lb/>ita projecto &longs;ecundum turrim non &longs;ola vis pro­<lb/>iicientis propria impre&longs;&longs;a e&longs;t, &longs;ed alia etiam ex mo­<lb/>tu <gap/> &longs;imùl correpta. </s> |
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| <s>Quo loco te minimè latet <lb/>placere Copernicanis id, quod in&longs;inuaui &longs;uperiore <lb/>Epi&longs;tola, aerem hunc no&longs;trum nihil e&longs;&longs;e aliud, quàm <lb/>halituo&longs;am quandam contexturam ex omnibus va­<lb/>poribus, fumis, tenuï&longs;&longs;imi&longs;ve corpu&longs;culis, quæ ex <lb/>&longs;olidiore Terræ, & aquæ globo continuò, & in <lb/>omnem partem circumquáque exhalantur. </s> | <s id="id.000652">Et vt <lb/>lapis &longs;ecundum malum vi&longs;us a&longs;cendere, de&longs;cendere­<lb/>que ad perpendiculum, de&longs;cribit nihilominùs li­<lb/>neam, quam parabolicam diximus: ita lapis &longs;ecun­<lb/>dum turrim contineri vi&longs;us in eodem perpendiculo, <lb/>de&longs;cribit tamen in &longs;patio mundano lineam &longs;imiliter <lb/>parabolicam; &longs;ed paraboles longè obtu&longs;ioris. </s> |
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| <s>Neque <pb pagenum="92"/>porrô longè abire à &longs;olidiore i&longs;to globo vapores <lb/>ciu&longs;cemodi; quippè quòd den&longs;iores infernè re&longs;i­<lb/>dant, &longs;ubtiliores vix &longs;upra vnum, alterumve mil­<lb/>liare emergant, parúmque omninò excedant edi­<lb/>ti&longs;&longs;imorum montium vertices. </s> | <s id="id.000653">Nem­<lb/>pe vt illeic motus e&longs;t compo&longs;itus ex perpendiculari, <lb/>& horizontali; ita ex vtróque compo&longs;itus heic:adeò <lb/>vt, quicquid e&longs;t ex vi proijcientis propria, id explice­<lb/>tur v&longs;que ad fa&longs;tigium turris, ad quod lapis per­<lb/>uenit; & quicquid à vi, &longs;eu motu Telluris, id ex­<lb/>plicetur ad punctum v&longs;que horizontalis lineæ, quod <lb/>lapis decidens attingit. </s> |
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| <s>Talis e&longs;t ergo illis <lb/>aer, &longs;iue regio aerea; e&longs;tque proinde terrenum <lb/>quid, totamque terram circumambit, eo modo, quo <lb/>epidermis totum animal, vel (vt &longs;imilitudinem re­<lb/>petam) quo lanugo malum cotoncum. </s> | <s id="id.000654">Itaque, cùm Turris ex A <lb/>B, peruenerit ad CL, rectè concipis lapidem per­<lb/>ueni&longs;&longs;e ad M; cùm ad DN, perueni&longs;&longs;e ad O; cùm <lb/>ad EP, perueni&longs;&longs;e ad Q: cùm ad FR, perueni&longs;&longs;e ad ip­<lb/>&longs;um-met R, quod fa&longs;tigium e&longs;t; & con&longs;equenter, cùm <lb/>ad GS, perueni&longs;&longs;ead T: cum ad HV, perueni&longs;&longs;e ad X: <lb/>cùm ad IY, perueni&longs;&longs;e ad Z; cùm denique ad K <gap/>, per­<lb/>ueni&longs;&longs;e ad ip&longs;um K. ita vt vbicúmque lapis in aëre, vel <lb/>per &longs;patium mundanum fuerit, extiterit &longs;emper in li­<lb/>nea ip&longs;i Turri parallela, eidemque Turris pedi, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.090.jpg" pagenum="91"/>punctove vicino perpendicularis. </s> |
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| <s>Ex quo fit, <lb/>vt quemadmodum malo cotoneo circumvoluto <lb/>non conuoluitur modò ip&longs;um malum, &longs;eu quod in <lb/>illo intimius, &longs;olidiu&longs;que e&longs;t; &longs;ed vnà etiam con­<lb/>uoluitur lanugo circumue&longs;tiens, ip&longs;ique extrin&longs;ecus <lb/>lcuiter cohærens; ita illi dicant non modò &longs;oli­<lb/>diorem hunc globum ex terra, & aqua con&longs;tantem <lb/>ver&longs;us ortum circumagi; &longs;ed &longs;imùl etiam circum­<lb/>duci regionem aëream ip&longs;i &longs;euiter circumquáque <lb/>cohærentem. </s> | <s id="id.000655">Nec verò iam <lb/>tibi videbitur mirum oculos omnium, qui ad lapi­<lb/>dem attendent, &longs;olum illum motum perpendicula­<lb/>rem ob&longs;eruare, nullo autem modo horizontalem, qui <lb/>perpendicularem tamen ex&longs;uperat tantoperè; &longs;i­<lb/>quidem omnium oculi vnà & cum turri, & cum <lb/>lapide, eodem horizontali motu transferuntur; <lb/>adeò vt quemadmodum ex&longs;i&longs;tentes in naui omnes <lb/>&longs;olum perpendicularem, nullo verò modò hori­<lb/>zontalem, cuius &longs;unt participes, ob&longs;eruant; ita heic <lb/>fieri nece&longs;&longs;um &longs;it. </s> |
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| <s>Adeò proinde, vt quemadmodum <lb/>acari aliudve animalculum intra lanuginem con­<lb/>tentum vnà cum illa ad motum mali cotonei cir­<lb/>cumraperetur: ita nece&longs;&longs;arium &longs;it quicquid conti­<lb/>netur intra aerem, vnà cum ip&longs;o aere ad motum <lb/>Terræ circumferri. </s> | <s id="id.000656">Vnum di&longs;crimen e&longs;t, quòd qui&longs;­<lb/>piam vel in alia naui quie&longs;cente, vel in littore con­<lb/>&longs;i&longs;tere po&longs;&longs;it, vnde ad motum lapidis horizontalem <lb/>attendat; non po&longs;&longs;it verò alicubi extra Terram fi­<lb/>gere pedem, vnde pari modo progre&longs;&longs;um hori­<lb/>zontalem percipiat. </s></p><p type="main"> |
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| <s>Quanquam di&longs;crimen e&longs;t, quòd <lb/>aer, ob fluxilitatem, non videatur cohæ&longs;ione adeò <lb/>vehemente &longs;olidiori globo connecti, &longs;ed retardari <lb/>nonnihil; atque adeò lenti&longs;&longs;imè quidem, &longs;ed ali­<lb/>quantulùm tamen promoueri in parteis occiduas. <lb/></s> | <s id="id.000657">III. Dices, quid &longs;i aliquis intra ci&longs;tam à gry­<lb/>phe abreptam detineatur per aërem? </s> |
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| <s>Patere id dicunt, non tam in conuallibus, intra <lb/>quas aër heinc inde cohibetur, neque liber e&longs;t, <lb/>quàm in planitiebus, & apertis campis, vbi ob&longs;er-<pb pagenum="93"/>uantur flabella, quoties viget tranquillitas, con­<lb/>uer&longs;a e&longs;&longs;e in occa&longs;um. </s> | <s id="id.000658">Re&longs;ponde­<lb/>bitur, neque illum quidem po&longs;&longs;e eum motum ob­<lb/>&longs;eruare; quoniam & ip&longs;e vna cum ci&longs;ta, gryphe, <lb/>aereque, eodem illo motu &longs;imul transferetur; <lb/>oporteretque illum con&longs;titui vltra regionem <lb/>aëream, motuque ip&longs;o non corripi, vt eius ob&longs;er­<lb/>uandi euaderet capax. </s> |
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| <s>Patere verò maximè in mari; <lb/>ac &longs;ub ip&longs;o quidem Æquatore poti&longs;&longs;imùm, vbivela <lb/>nauium &longs;unt vno tenore, vniformiterque inflata ab <lb/>ortu; atque idcircô nautæ experiuntur &longs;e&longs;e idem iter <lb/>& longè facilius, & breuiore tempore in occa&longs;um, <lb/>quàm in ortum emetiri. </s> | <s id="id.000659">Quo loco te minimè latet <lb/>placere Copernicanis id, quod in&longs;inuaui &longs;uperiore <lb/>Epi&longs;tola, aerem hunc no&longs;trum nihil e&longs;&longs;e aliud, quàm <lb/>halituo&longs;am quandam contexturam ex omnibus va­<lb/>poribus, fumis, tenuï&longs;&longs;imi&longs;ve corpu&longs;culis, quæ ex <lb/>&longs;olidiore Terræ, & aquæ globo continuò, & in <lb/>omnem partem circumquáque exhalantur. </s> |
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| <s>Neque verò nece&longs;&longs;e e&longs;t <lb/>ventum proptereà percipi adeò validum, ac obijci <lb/>&longs;olet, qua&longs;i aër con&longs;i&longs;teret, & tantundem ferri in oc­<lb/>ca&longs;um, quantum Terra in ortum apparere, aut &longs;en­<lb/>tiri deberet. </s> | <s id="id.000660">Neque <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.091.jpg" pagenum="92"/>porrô longè abire à &longs;olidiore i&longs;to globo vapores <lb/>ciu&longs;cemodi; quippè quòd den&longs;iores infernè re&longs;i­<lb/>dant, &longs;ubtiliores vix &longs;upra vnum, alterumve mil­<lb/>liare emergant, parúmque omninò excedant edi­<lb/>ti&longs;&longs;imorum montium vertices. </s> |
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| <s>Siquidem non con&longs;i&longs;tit aër, &longs;ed nonni­<lb/>hil &longs;olùm retardatur, lentiu&longs;ve in eandem regio­<lb/>nem procedit, hæcque retardatio, quæ haberi po&longs;­<lb/>&longs;it pro motu in occa&longs;um, nulla propemodùm pars <lb/>e&longs;t citati&longs;&longs;imi eius motus quo aër intereà promo­<lb/>uctur cum Terra in ortum. </s> | <s id="id.000661">Talis e&longs;t ergo illis <lb/>aer, &longs;iue regio aerea; e&longs;tque proinde terrenum <lb/>quid, totamque terram circumambit, eo modo, quo <lb/>epidermis totum animal, vel (vt &longs;imilitudinem re­<lb/>petam) quo lanugo malum cotoncum. </s> |
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| <s>Di&longs;crimen aliunde e&longs;t, <lb/>quòd illa animalcula à lanugine abripiantur, cor­<lb/>pora verò &longs;olidiora non abripiantur ab aëre (is nem­<lb/>pe e&longs;t nimiùm tenuis, fluidu&longs;que) &longs;ed motum &longs;or­<lb/>tiantur ab ip&longs;amet Terra, quæ dum mouetur, &longs;imùl <lb/>moueat corpora omnia &longs;ibi innixa. </s> | <s id="id.000662">Ex quo fit, <lb/>vt quemadmodum malo cotoneo circumvoluto <lb/>non conuoluitur modò ip&longs;um malum, &longs;eu quod in <lb/>illo intimius, &longs;olidiu&longs;que e&longs;t; &longs;ed vnà etiam con­<lb/>uoluitur lanugo circumue&longs;tiens, ip&longs;ique extrin&longs;ecus <lb/>lcuiter cohærens; ita illi dicant non modò &longs;oli­<lb/>diorem hunc globum ex terra, & aqua con&longs;tantem <lb/>ver&longs;us ortum circumagi; &longs;ed &longs;imùl etiam circum­<lb/>duci regionem aëream ip&longs;i &longs;euiter circumquáque <lb/>cohærentem. </s> |
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| <s>Et quia tamen <lb/>videtur aer quidpiam conferre aliquibus; ideò, vt <lb/>di&longs;tinctiùs rem dicam; <emph type="italics"/>Si<emph.end type="italics"/>talia quidem corpora &longs;int, <lb/>cuiu&longs;inodi lapis, &longs;agitta, aliave id genus; i&longs;ta non <lb/>mouentur cum aere, qua&longs;i ip&longs;o ea propellente; &longs;ed <lb/>ideò mouentur, quia cùm exce&longs;&longs;ere è Terra, cor­<lb/>poreve Terræ innixo, quod ea propulit, impre&longs;&longs;it <lb/>Terra &longs;imùl &longs;uum motum, eo modo, quo imprimit <lb/>nauis, dum ex ea, aut malo ip&longs;i innixo aliquid pro­<lb/>pellitur. <emph type="italics"/>Sin<emph.end type="italics"/> verò talia corpora &longs;int, cuiu&longs;modiaues, <pb pagenum="94"/>mu&longs;cæ, & &longs;imilia; habent & ea motum ab ip&longs;amet <lb/>Terra, aut certe à turri, arbore, men&longs;a, manu, <lb/>corporeve alio, cui Terræ hærenti, quando auo­<lb/>lant, innituntur; vti dum aliquis ex puppi, aut &longs;cam­<lb/>no, quod in ea, ver&longs;us proram &longs;alit. </s> | <s id="id.000663">Adeò proinde, vt quemadmodum <lb/>acari aliudve animalculum intra lanuginem con­<lb/>tentum vnà cum illa ad motum mali cotonei cir­<lb/>cumraperetur: ita nece&longs;&longs;arium &longs;it quicquid conti­<lb/>netur intra aerem, vnà cum ip&longs;o aere ad motum <lb/>Terræ circumferri. </s> |
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| <s>Contingit autem <lb/>volucres non ad perpendiculum &longs;ubinde decidere <lb/>(quod &longs;i facerent, non proptereà motum horizon­<lb/>talem minùs haberent, vt dictum e&longs;t de lapide &longs;e­<lb/>cundum turrim decidente) &longs;ed po&longs;&longs;e alarum bene­<lb/>ficio eiu&longs;modi motum variare, quantum aer vnà <lb/>tran&longs;latus pote&longs;t e&longs;&longs;e &longs;ub&longs;idio. </s> | <s id="id.000664">Quanquam di&longs;crimen e&longs;t, quòd <lb/>aer, ob fluxilitatem, non videatur cohæ&longs;ione adeò <lb/>vehemente &longs;olidiori globo connecti, &longs;ed retardari <lb/>nonnihil; atque adeò lenti&longs;&longs;imè quidem, &longs;ed ali­<lb/>quantulùm tamen promoueri in parteis occiduas. <lb/></s> |
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| <s>Nam &longs;inullus quidem <lb/>e&longs;&longs;et &longs;uppo&longs;itus aër, aut aues alas non explicarent, <lb/>rum lapidum in&longs;tar caderent in Terram; at quià <lb/>aer&longs;ube&longs;t, corpulentiamque aliquam habet, quæ <lb/>alis verberata tantum re&longs;i&longs;tat, quantum &longs;atis e&longs;t, vt <lb/>volatilia vel &longs;u&longs;tententur, vel etiam magis euehantur; <lb/>heinc fit, vt pro repul&longs;u à re&longs;i&longs;tente aere facto, mo­<lb/>tus per aerem varietur, neque ille generalis, hori­<lb/>zontali&longs;que ip&longs;i magis ob&longs;tet, quàm ob&longs;tat perpen­<lb/>diculari. </s> | <s id="id.000665">Patere id dicunt, non tam in conuallibus, intra <lb/>quas aër heinc inde cohibetur, neque liber e&longs;t, <lb/>quàm in planitiebus, & apertis campis, vbi ob&longs;er-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.092.jpg" pagenum="93"/>uantur flabella, quoties viget tranquillitas, con­<lb/>uer&longs;a e&longs;&longs;e in occa&longs;um. </s> |
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| <s>Nempe illa pars aeris verberata, ali&longs;que <lb/>re&longs;i&longs;tens comparari pote&longs;t illi parti funis intra na­<lb/>uim ten&longs;i, quam funambulus inter &longs;aliendum pede <lb/>pul&longs;et. </s> | <s id="id.000666">Patere verò maximè in mari; <lb/>ac &longs;ub ip&longs;o quidem Æquatore poti&longs;&longs;imùm, vbivela <lb/>nauium &longs;unt vno tenore, vniformiterque inflata ab <lb/>ortu; atque idcircô nautæ experiuntur &longs;e&longs;e idem iter <lb/>& longè facilius, & breuiore tempore in occa&longs;um, <lb/>quàm in ortum emetiri. </s> |
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| <s>Quin etiam comparari pote&longs;t cuilibet parti <lb/>nauis, è qua quis ip&longs;am pedibus pul&longs;ans, &longs;alire in <lb/>quamcumque valeat. </s> | <s id="id.000667">Neque verò nece&longs;&longs;e e&longs;t <lb/>ventum proptereà percipi adeò validum, ac obijci <lb/>&longs;olet, qua&longs;i aër con&longs;i&longs;teret, & tantundem ferri in oc­<lb/>ca&longs;um, quantum Terra in ortum apparere, aut &longs;en­<lb/>tiri deberet. </s> |
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| <s>Q<gap/>ppe motus nauis, qui il­<lb/>lum & in&longs;i&longs;tentem, & per aerem &longs;aliendo tran&longs;la­<lb/>tum &longs;emper deuehet, nihil pror&longs;ùs impediet, quò <lb/>minùs ex vna parte nauis in aliam in&longs;iliat, &longs;itumque, <lb/>vt volet, commutet. </s> | <s id="id.000668">Siquidem non con&longs;i&longs;tit aër, &longs;ed nonni­<lb/>hil &longs;olùm retardatur, lentiu&longs;ve in eandem regio­<lb/>nem procedit, hæcque retardatio, quæ haberi po&longs;­<lb/>&longs;it pro motu in occa&longs;um, nulla propemodùm pars <lb/>e&longs;t citati&longs;&longs;imi eius motus quo aër intereà promo­<lb/>uctur cum Terra in ortum. </s> |
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| <s>Declararem in pi&longs;ce, animali­<lb/>ve alio natante; cùm aquam po&longs;&longs;e & vnà transferri, <pb pagenum="95"/>& magis re&longs;i&longs;tere per&longs;picuum &longs;it; &longs;ed res, vt mihi <lb/>quidem videtur, non e&longs;t difficilis intellectu. </s> | <s id="id.000669">Di&longs;crimen aliunde e&longs;t, <lb/>quòd illa animalcula à lanugine abripiantur, cor­<lb/>pora verò &longs;olidiora non abripiantur ab aëre (is nem­<lb/>pe e&longs;t nimiùm tenuis, fluidu&longs;que) &longs;ed motum &longs;or­<lb/>tiantur ab ip&longs;amet Terra, quæ dum mouetur, &longs;imùl <lb/>moueat corpora omnia &longs;ibi innixa. </s> |
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| <s>Quan­<lb/>quam, &longs;i hæreas vel tantillum, habeto intra nauim <lb/>cuppam aqua plenam, & in ea pi&longs;ceis; ac deprehen­<lb/>des, qua ratione motus generalis nauis, quo aqua, <lb/>& pi&longs;ces conuehentur, nihil &longs;it penitùs ob&longs;titurus, <lb/>quò minùs pi&longs;ces eo&longs;dem motus &longs;ur&longs;ùm, deor&longs;ùm, <lb/>obliquè habeant, ac haberent, &longs;i cuppa, & aqua <lb/>penitùs conquie&longs;cerent, illóque motu de&longs;tituerentur. <lb/></s> | <s id="id.000670">Et quia tamen <lb/>videtur aer quidpiam conferre aliquibus; ideò, vt <lb/>di&longs;tinctiùs rem dicam; <emph type="italics"/>Si<emph.end type="italics"/>talia quidem corpora &longs;int, <lb/>cuiu&longs;inodi lapis, &longs;agitta, aliave id genus; i&longs;ta non <lb/>mouentur cum aere, qua&longs;i ip&longs;o ea propellente; &longs;ed <lb/>ideò mouentur, quia cùm exce&longs;&longs;ere è Terra, cor­<lb/>poreve Terræ innixo, quod ea propulit, impre&longs;&longs;it <lb/>Terra &longs;imùl &longs;uum motum, eo modo, quo imprimit <lb/>nauis, dum ex ea, aut malo ip&longs;i innixo aliquid pro­<lb/>pellitur. <emph type="italics"/>Sin<emph.end type="italics"/> verò talia corpora &longs;int, cuiu&longs;modiaues, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.093.jpg" pagenum="94"/>mu&longs;cæ, & &longs;imilia; habent & ea motum ab ip&longs;amet <lb/>Terra, aut certe à turri, arbore, men&longs;a, manu, <lb/>corporeve alio, cui Terræ hærenti, quando auo­<lb/>lant, innituntur; vti dum aliquis ex puppi, aut &longs;cam­<lb/>no, quod in ea, ver&longs;us proram &longs;alit. </s> |
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| <s>Quod inculco, vt intelligas, po&longs;&longs;e aerem, aues, & <lb/>omnia volantia generali illo, & horizontali motu <lb/>Telluris transferri; & motum tamen i&longs;tum nihil ob­<lb/>&longs;tare, quò minùs illa volent &longs;ur&longs;um, deor&longs;ùm, obli­<lb/>què, & quocúmque collibitum fuerit. <emph type="italics"/>Sin<emph.end type="italics"/> autem ta­<lb/>lia corpora &longs;int, cuiu&longs;modi nubes, pulueres, plumæ, <lb/>lanæ, &c. </s> | <s id="id.000671">Contingit autem <lb/>volucres non ad perpendiculum &longs;ubinde decidere <lb/>(quod &longs;i facerent, non proptereà motum horizon­<lb/>talem minùs haberent, vt dictum e&longs;t de lapide &longs;e­<lb/>cundum turrim decidente) &longs;ed po&longs;&longs;e alarum bene­<lb/>ficio eiu&longs;modi motum variare, quantum aer vnà <lb/>tran&longs;latus pote&longs;t e&longs;&longs;e &longs;ub&longs;idio. </s> |
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| <s>Imprimis, cùm i&longs;ta è terra, <lb/> corporéve <lb/>Terræ innixo procedunt, motum inde impre&longs;&longs;um <lb/>habent, tuenturque; & quòd &longs;int non-nihil grauiora <lb/>&longs;uppo&longs;ito aere, haud-dubiè perpendiculariter (tam­<lb/>et&longs;i paulò lentiùs) apparerent decidere, ni&longs;i ven­<lb/>tus &longs;uccureret, auerteretque i&longs;tum motum, cum <lb/>quo vna generalis, & horizontalis ille perinde co­<lb/>pularetur, ac in lapide fieri dictum e&longs;t Deinde ven­<lb/>tus &longs;uperueniens, &longs;ur&longs;umque, aut aliò abigens, im­<lb/>pellen&longs;que nihil aliud præ&longs;tat, quàm quod dictum <lb/>e&longs;t præ&longs;tari ab aere alis volucrum re&longs;i&longs;tente: di&longs;­<lb/>crimen enim &longs;olummodò e&longs;t, quòd volucris qua&longs;i <lb/>repellatur, nubes verò, & cætera à vento duntaxat <lb/>pellantur; cùm ad motum tamen perinde &longs;it, &longs;eu <lb/>manus è pauimento pilam &longs;ui&longs;ùm proijciat, &longs;eu pila <pb pagenum="96"/>in pauimentum impacta ex illo re&longs;iliat. <emph type="italics"/>Sin<emph.end type="italics"/> demùm <lb/>talia corpora &longs;int, cuiu&longs;modi ventus, ignea trajectio, <lb/>&c. </s> | <s id="id.000672">Nam &longs;inullus quidem <lb/>e&longs;&longs;et &longs;uppo&longs;itus aër, aut aues alas non explicarent, <lb/>rum lapidum in&longs;tar caderent in Terram; at quià <lb/>aer&longs;ube&longs;t, corpulentiamque aliquam habet, quæ <lb/>alis verberata tantum re&longs;i&longs;tat, quantum &longs;atis e&longs;t, vt <lb/>volatilia vel &longs;u&longs;tententur, vel etiam magis euehantur; <lb/>heinc fit, vt pro repul&longs;u à re&longs;i&longs;tente aere facto, mo­<lb/>tus per aerem varietur, neque ille generalis, hori­<lb/>zontali&longs;que ip&longs;i magis ob&longs;tet, quàm ob&longs;tat perpen­<lb/>diculari. </s> |
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| <s>tum quoque & motus ille generalis imprimitur <lb/>ip&longs;is in ea Terræ parte, è qua prodeunt; & qui pro­<lb/>prius prætereà motus ip&longs;is competit, perinde cum <lb/>illo cohæret, ac cohærent motus projectorum, vo­<lb/>lucrum, aliorum; cùm & ventus antecedens à &longs;uc­<lb/>cedente propellatur, & ignis in pabulum agens illum <lb/>&longs;ua vi pellat, & ob cohæ&longs;ionem &longs;equatur; & vtrique <lb/>aër partìm &longs;u&longs;tentaculo, partim ob&longs;taculo e&longs;&longs;e po&longs;&longs;it; <lb/>atque adeò cau&longs;a deflexionis, re&longs;ilitionis, & &longs;imi­<lb/>lium. </s></p><p type="main"> | <s id="id.000673">Nempe illa pars aeris verberata, ali&longs;que <lb/>re&longs;i&longs;tens comparari pote&longs;t illi parti funis intra na­<lb/>uim ten&longs;i, quam funambulus inter &longs;aliendum pede <lb/>pul&longs;et. </s> |
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| <s>IV. <!-- KEEP S--></s> | <s id="id.000674">Quin etiam comparari pote&longs;t cuilibet parti <lb/>nauis, è qua quis ip&longs;am pedibus pul&longs;ans, &longs;alire in <lb/>quamcumque valeat. </s> |
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| <s>Scrupulus fortè &longs;upererit ex eo, quod dixi pa­<lb/>rabolicam lineam à corporibus projectis de&longs;criptam <lb/>accipiendam e&longs;&longs;e in &longs;patio mundano, non in aere: & <lb/>cùm vnum eius extremum &longs;upponatur ad pedem tur­<lb/>ris, vnde lapis proijcitur, aliud e&longs;&longs;e accipiendum in <lb/>alio puncto horizontalis lineæ, in quod lapis decidit: <lb/>qua&longs;i aut horizon non &longs;it de&longs;cribendus in ip&longs;a Terræ <lb/>&longs;uperficie; aut punctum, in quod lapis recidit, non <lb/>&longs;it illud idem id hac &longs;uperficie, è quo lapis fuit pro­<lb/>jectus. </s> | <s id="id.000675">Q<gap/>ppe motus nauis, qui il­<lb/>lum & in&longs;i&longs;tentem, & per aerem &longs;aliendo tran&longs;la­<lb/>tum &longs;emper deuehet, nihil pror&longs;ùs impediet, quò <lb/>minùs ex vna parte nauis in aliam in&longs;iliat, &longs;itumque, <lb/>vt volet, commutet. </s> |
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| <s>Verùm non erit tibi imprimis difficile ima­<lb/>ginari aliud e&longs;&longs;e aërem, aliud &longs;patium in quo e&longs;t <lb/>aër. </s> | <s id="id.000676">Declararem in pi&longs;ce, animali­<lb/>ve alio natante; cùm aquam po&longs;&longs;e & vnà transferri, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.094.jpg" pagenum="95"/>& magis re&longs;i&longs;tere per&longs;picuum &longs;it; &longs;ed res, vt mihi <lb/>quidem videtur, non e&longs;t difficilis intellectu. </s> |
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| <s>Nam aër corpus mobile e&longs;t: &longs;patium incor­<lb/>poreus, & immobilis locus. </s> | <s id="id.000677">Quan­<lb/>quam, &longs;i hæreas vel tantillum, habeto intra nauim <lb/>cuppam aqua plenam, & in ea pi&longs;ceis; ac deprehen­<lb/>des, qua ratione motus generalis nauis, quo aqua, <lb/>& pi&longs;ces conuehentur, nihil &longs;it penitùs ob&longs;titurus, <lb/>quò minùs pi&longs;ces eo&longs;dem motus &longs;ur&longs;ùm, deor&longs;ùm, <lb/>obliquè habeant, ac haberent, &longs;i cuppa, & aqua <lb/>penitùs conquie&longs;cerent, illóque motu de&longs;tituerentur. <lb/></s> |
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| <s>Tu, verbi cau&longs;â, intra <lb/>mu&longs;æum, &longs;patium quoddam occupas, & tantùm qui­<lb/>dem, quantus es ip&longs;e, etiam cum tuis ve&longs;tibus. </s> | <s id="id.000678">Quod inculco, vt intelligas, po&longs;&longs;e aerem, aues, & <lb/>omnia volantia generali illo, & horizontali motu <lb/>Telluris transferri; & motum tamen i&longs;tum nihil ob­<lb/>&longs;tare, quò minùs illa volent &longs;ur&longs;um, deor&longs;ùm, obli­<lb/>què, & quocúmque collibitum fuerit. <emph type="italics"/>Sin<emph.end type="italics"/> autem ta­<lb/>lia corpora &longs;int, cuiu&longs;modi nubes, pulueres, plumæ, <lb/>lanæ, &c. </s> |
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| <s>Cùm <lb/>autem vno, aut altero pa&longs;&longs;u ab illo recedis; non <lb/>illud te &longs;equitur, &longs;ed ab aëre confluente occupatur. <lb/></s> | <s id="id.000679">Imprimis, cùm i&longs;ta è terra, <lb/> corporéve <lb/>Terræ innixo procedunt, motum inde impre&longs;&longs;um <lb/>habent, tuenturque; & quòd &longs;int non-nihil grauiora <lb/>&longs;uppo&longs;ito aere, haud-dubiè perpendiculariter (tam­<lb/>et&longs;i paulò lentiùs) apparerent decidere, ni&longs;i ven­<lb/>tus &longs;uccureret, auerteretque i&longs;tum motum, cum <lb/>quo vna generalis, & horizontalis ille perinde co­<lb/>pularetur, ac in lapide fieri dictum e&longs;t Deinde ven­<lb/>tus &longs;uperueniens, &longs;ur&longs;umque, aut aliò abigens, im­<lb/>pellen&longs;que nihil aliud præ&longs;tat, quàm quod dictum <lb/>e&longs;t præ&longs;tari ab aere alis volucrum re&longs;i&longs;tente: di&longs;­<lb/>crimen enim &longs;olummodò e&longs;t, quòd volucris qua&longs;i <lb/>repellatur, nubes verò, & cætera à vento duntaxat <lb/>pellantur; cùm ad motum tamen perinde &longs;it, &longs;eu <lb/>manus è pauimento pilam &longs;ui&longs;ùm proijciat, &longs;eu pila <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.095.jpg" pagenum="96"/>in pauimentum impacta ex illo re&longs;iliat. <emph type="italics"/>Sin<emph.end type="italics"/> demùm <lb/>talia corpora &longs;int, cuiu&longs;modi ventus, ignea trajectio, <lb/>&c. </s> |
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| <s>Reponatur in eo trabs; pelletur aer, &longs;ed non pelletur <pb pagenum="97"/>&longs;patium quod proinde manet immotum, quicquid <lb/>in ip&longs;o collocetur, quicquid per ip&longs;um tran&longs;eat: <lb/>imô non &longs;it domus, non &longs;it Terra, non &longs;it Mundus; <lb/>illud &longs;patium nihilominùs immobile, inalterabile. <lb/></s> | <s id="id.000680">tum quoque & motus ille generalis imprimitur <lb/>ip&longs;is in ea Terræ parte, è qua prodeunt; & qui pro­<lb/>prius prætereà motus ip&longs;is competit, perinde cum <lb/>illo cohæret, ac cohærent motus projectorum, vo­<lb/>lucrum, aliorum; cùm & ventus antecedens à &longs;uc­<lb/>cedente propellatur, & ignis in pabulum agens illum <lb/>&longs;ua vi pellat, & ob cohæ&longs;ionem &longs;equatur; & vtrique <lb/>aër partìm &longs;u&longs;tentaculo, partim ob&longs;taculo e&longs;&longs;e po&longs;&longs;it; <lb/>atque adeò cau&longs;a deflexionis, re&longs;ilitionis, & &longs;imi­<lb/>lium. </s></p><p type="main"> |
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| <s>idem omninó per&longs;euerabit. </s> | <s id="id.000681">IV. <!-- KEEP S--></s> |
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| <s>Eodem modo, loco mu­<lb/>&longs;æi, intelligito cœli fornicem; & loco tui, tuarum­<lb/>que ve&longs;tium intellige Terram cum aëre circumve­<lb/>&longs;tiente: capis profectò Terram intra hunc fornicem <lb/>certum aliquod &longs;patium occupare. </s> | <s id="id.000682">Scrupulus fortè &longs;upererit ex eo, quod dixi pa­<lb/>rabolicam lineam à corporibus projectis de&longs;criptam <lb/>accipiendam e&longs;&longs;e in &longs;patio mundano, non in aere: & <lb/>cùm vnum eius extremum &longs;upponatur ad pedem tur­<lb/>ris, vnde lapis proijcitur, aliud e&longs;&longs;e accipiendum in <lb/>alio puncto horizontalis lineæ, in quod lapis decidit: <lb/>qua&longs;i aut horizon non &longs;it de&longs;cribendus in ip&longs;a Terræ <lb/>&longs;uperficie; aut punctum, in quod lapis recidit, non <lb/>&longs;it illud idem id hac &longs;uperficie, è quo lapis fuit pro­<lb/>jectus. </s> |
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| <s>Finge Terram <lb/>ex eo moueri, non illud proptereà emouebitur, &longs;ed <lb/>con&longs;tabit planè immotum, Terraque intereà occu­<lb/>pabit aliud. </s> | <s id="id.000683">Verùm non erit tibi imprimis difficile ima­<lb/>ginari aliud e&longs;&longs;e aërem, aliud &longs;patium in quo e&longs;t <lb/>aër. </s> |
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| <s>Finge non moueri Terram ex &longs;patio, <lb/>&longs;ed conuolui tamen intra &longs;patium, veluti globus, <lb/>dum tornatur; concipies parteis quidem Terræ mu­<lb/>tare &longs;ucce&longs;&longs;iue parteis &longs;patij; &longs;ed non proptereà par­<lb/>teis &longs;patij vlla ratione aut moueri, aut mutationem <lb/>accipere. </s> | <s id="id.000684">Nam aër corpus mobile e&longs;t: &longs;patium incor­<lb/>poreus, & immobilis locus. </s> |
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| <s>Dico igitur, &longs;i in Telluris circumvolutio­<lb/>ne &longs;upponamus AB turrim moúeri in CL; &longs;patium, <lb/>quod illeic occupabatur, reman&longs;i&longs;&longs;e illeic im­<lb/>motum, vt etiam totum illud per quod tran&longs;ijt, A <lb/>BLC, in quo qui erat aer tran&longs;iit intereà in CL <lb/>ND, &longs;uccedente interim alio, qui erat ponè locum <lb/>AB. <gap/>t moueatur con&longs;equenter turris à CL, in <lb/>in DN, &longs;patium ad CL remanebit immotum, vt <lb/>etiam illud, per quod turris tran&longs;iit, & in quo qui priùs <lb/>continebatur aer, tran&longs;ijt intereà in &longs;patium DN <lb/>PE Imaginare idem ex ordine, quov&longs;que turris erit <lb/>in K<gap/>; capies profectò pedem turris ex parte &longs;patij <lb/>immota A, tran&longs;ij&longs;&longs;e in partem &longs;patij immotam K; <lb/>& de&longs;crip&longs;i&longs;&longs;e in &longs;patio intermedio, immoto manen-<pb pagenum="98"/><figure id="fig6"/><lb/>te lineam ACDEFGHIK, quam horizontalem <lb/>ideo diximus, quia re&longs;pondet horizonti, &longs;eu &longs;uper­<lb/>ficiei ip&longs;ius Terræ. <!-- KEEP S--></s> | <s id="id.000685">Tu, verbi cau&longs;â, intra <lb/>mu&longs;æum, &longs;patium quoddam occupas, & tantùm qui­<lb/>dem, quantus es ip&longs;e, etiam cum tuis ve&longs;tibus. </s> |
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| <s>Nam & cùm pes turris e&longs;&longs;et in A <lb/>illa &longs;patij linea AK occupabatur à portione &longs;uper­<lb/>ficiei Terræ antecedente; & cùm pes turris per­<lb/>uenit ad K, eadem linea occupatur à portione <lb/>con&longs;equente. </s> | <s id="id.000686">Cùm <lb/>autem vno, aut altero pa&longs;&longs;u ab illo recedis; non <lb/>illud te &longs;equitur, &longs;ed ab aëre confluente occupatur. <lb/></s> |
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| <s>Deinde, &longs;i &longs;upponamus lapidem non <lb/>quieui&longs;&longs;e in pede turris, &longs;ed a&longs;cendi&longs;&longs;e, & de&longs;­<lb/>cendi&longs;&longs;e &longs;ecundum turrim, dum turris ex AB, tran­<lb/>&longs;iret in K <gap/>, adeò vt de&longs;crip&longs;erit parabolicam lineam <lb/>AMOQRTXZK, capis &longs;anè hanc lineam de&longs;­<lb/>criptam e&longs;&longs;e in immoto &longs;patio, quod ab aere Ter­<lb/>ram circumabiente, ac vnà tran&longs;lato &longs;ucce&longs;&longs;iuè oc­<lb/>cupatur; non verò in aere ip&longs;o, qui circa turrim <lb/>tran&longs;latam idem per&longs;euerat, eamque &longs;equitur; & <lb/>in quo de&longs;cribitur &longs;olùm apparens recta linea, &longs;e­<lb/>cundum longitudinem videlicet turris. </s> | <s id="id.000687">Reponatur in eo trabs; pelletur aer, &longs;ed non pelletur <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.096.jpg" pagenum="97"/>&longs;patium quod proinde manet immotum, quicquid <lb/>in ip&longs;o collocetur, quicquid per ip&longs;um tran&longs;eat: <lb/>imô non &longs;it domus, non &longs;it Terra, non &longs;it Mundus; <lb/>illud &longs;patium nihilominùs immobile, inalterabile. <lb/></s> |
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| <s>Heinc ergo <lb/>agno&longs;cis me ideò dixi&longs;&longs;e de&longs;cribi lineam in &longs;patio <lb/>mundano, potiu&longs;quàm in aere; vt ob&longs;eruaretur <lb/>di&longs;crimen huius lineæ de&longs;criptæ propter motum <lb/>Terræ, cum linea de&longs;cripta propter motum nauis. <lb/></s> | <s id="id.000688">idem omninó per&longs;euerabit. </s> |
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| <s>Nam de&longs;cripta ob motum nauis benè intelligitur ex <lb/>diuer&longs;itate partium aëris, qui motum nauis non &longs;e-<pb pagenum="99"/>quitur, &longs;ed re&longs;pectu illius permanet immotus: de&longs;­<lb/>cripta verò ob motum Terræ intelligi non pote&longs;t <lb/>ex diuer&longs;itate partium aëris, qui ip&longs;am Terram &longs;e­<lb/>quitar; &longs;ed ex diuer&longs;itate partium mundani &longs;patij, <lb/>quod immotum per&longs;euerat. </s> | <s id="id.000689">Eodem modo, loco mu­<lb/>&longs;æi, intelligito cœli fornicem; & loco tui, tuarum­<lb/>que ve&longs;tium intellige Terram cum aëre circumve­<lb/>&longs;tiente: capis profectò Terram intra hunc fornicem <lb/>certum aliquod &longs;patium occupare. </s> |
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| <s>Dico autem aërem re&longs;­<lb/>pectu nauis manere immotum; quia dum motus il­<lb/>los intra nauim con&longs;ideramus, &longs;eponimus motum <lb/>Telluris, qui aliunde &longs;it naui, aëri, omnibu&longs;que re­<lb/>bus communis; quique ob &longs;ui communitatem re­<lb/>linquat ob&longs;eruabile inter res propriis viribus motas, <lb/>quie&longs;centei&longs;que, di&longs;crimen. </s></p><p type="main"> | <s id="id.000690">Finge Terram <lb/>ex eo moueri, non illud proptereà emouebitur, &longs;ed <lb/>con&longs;tabit planè immotum, Terraque intereà occu­<lb/>pabit aliud. </s> |
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| <s>V. <!-- KEEP S--></s> | <s id="id.000691">Finge non moueri Terram ex &longs;patio, <lb/>&longs;ed conuolui tamen intra &longs;patium, veluti globus, <lb/>dum tornatur; concipies parteis quidem Terræ mu­<lb/>tare &longs;ucce&longs;&longs;iue parteis &longs;patij; &longs;ed non proptereà par­<lb/>teis &longs;patij vlla ratione aut moueri, aut mutationem <lb/>accipere. </s> |
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| <s>Ex hoc proinde intelliges, quàm parùm con­<lb/>cludant argumenta illa, quæ ex globorum explo­<lb/>&longs;ione à bellicis tormentis petuntur. </s> | <s id="id.000692">Dico igitur, &longs;i in Telluris circumvolutio­<lb/>ne &longs;upponamus AB turrim moúeri in CL; &longs;patium, <lb/>quod illeic occupabatur, reman&longs;i&longs;&longs;e illeic im­<lb/>motum, vt etiam totum illud per quod tran&longs;ijt, A <lb/>BLC, in quo qui erat aer tran&longs;iit intereà in CL <lb/>ND, &longs;uccedente interim alio, qui erat ponè locum <lb/>AB. <gap/>t moueatur con&longs;equenter turris à CL, in <lb/>in DN, &longs;patium ad CL remanebit immotum, vt <lb/>etiam illud, per quod turris tran&longs;iit, & in quo qui priùs <lb/>continebatur aer, tran&longs;ijt intereà in &longs;patium DN <lb/>PE Imaginare idem ex ordine, quov&longs;que turris erit <lb/>in K<gap/>; capies profectò pedem turris ex parte &longs;patij <lb/>immota A, tran&longs;ij&longs;&longs;e in partem &longs;patij immotam K; <lb/>& de&longs;crip&longs;i&longs;&longs;e in &longs;patio intermedio, immoto manen-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.097.jpg" pagenum="98"/><figure id="id.027.00.097.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.097.1.jpg"/><lb/>te lineam ACDEFGHIK, quam horizontalem <lb/>ideo diximus, quia re&longs;pondet horizonti, &longs;eu &longs;uper­<lb/>ficiei ip&longs;ius Terræ. <!-- KEEP S--></s> |
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| <s>Nam, inqui­<lb/>unt, globus in ortum explo&longs;us ferctur longè vlteriùs, <lb/>quàm explo&longs;us in occa&longs;um; quoniam ille præter <lb/>motum proprium, habebit etiam motum à Ter­<lb/>ra; hic verò habebit &longs;olùm motum proprium: <lb/>atque idcircò &longs;i motus Telluris &longs;upponatur tantus, <lb/>quantus e&longs;t motus globi proprius, efficietur motus in <lb/>ortum duplò velocior, quàm in occa&longs;um; &longs;icque <lb/>&longs;copus ad ortum duplò longiùs, quàm ad occa&longs;um <lb/>attingetur. </s> | <s id="id.000693">Nam & cùm pes turris e&longs;&longs;et in A <lb/>illa &longs;patij linea AK occupabatur à portione &longs;uper­<lb/>ficiei Terræ antecedente; & cùm pes turris per­<lb/>uenit ad K, eadem linea occupatur à portione <lb/>con&longs;equente. </s> |
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| <s>Quin-etiam globus in occa&longs;um explo­<lb/>&longs;us non exibit è fi&longs;tula, &longs;ed qua&longs;i immotus con&longs;i­<lb/>&longs;tet; quia nempe quantum motu proprio in occi­<lb/>dentem connitetur, tantum impetus à Terra factus <lb/>illum in ortum re<gap/>imet. </s> | <s id="id.000694">Deinde, &longs;i &longs;upponamus lapidem non <lb/>quieui&longs;&longs;e in pede turris, &longs;ed a&longs;cendi&longs;&longs;e, & de&longs;­<lb/>cendi&longs;&longs;e &longs;ecundum turrim, dum turris ex AB, tran­<lb/>&longs;iret in K <gap/>, adeò vt de&longs;crip&longs;erit parabolicam lineam <lb/>AMOQRTXZK, capis &longs;anè hanc lineam de&longs;­<lb/>criptam e&longs;&longs;e in immoto &longs;patio, quod ab aere Ter­<lb/>ram circumabiente, ac vnà tran&longs;lato &longs;ucce&longs;&longs;iuè oc­<lb/>cupatur; non verò in aere ip&longs;o, qui circa turrim <lb/>tran&longs;latam idem per&longs;euerat, eamque &longs;equitur; & <lb/>in quo de&longs;cribitur &longs;olùm apparens recta linea, &longs;e­<lb/>cundum longitudinem videlicet turris. </s> |
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| <s>Addunt, &longs;i globus diriga­<lb/>tur &longs;eu in boream, &longs;eu in meridiem, aberrationem <lb/>&longs;emper à &longs;copo futuram; quia du<gap/> globus feretur <lb/>per aërem, &longs;copus intereà in ortum promouebitur, <pb pagenum="100"/>locu&longs;que ferietur procùl ad acca&longs;um. </s> | <s id="id.000695">Heinc ergo <lb/>agno&longs;cis me ideò dixi&longs;&longs;e de&longs;cribi lineam in &longs;patio <lb/>mundano, potiu&longs;quàm in aere; vt ob&longs;eruaretur <lb/>di&longs;crimen huius lineæ de&longs;criptæ propter motum <lb/>Terræ, cum linea de&longs;cripta propter motum nauis. <lb/></s> |
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| <s>Verumtamen <lb/>experimenta de colludentibus pilâ intra nauim à <lb/>&longs;imili &longs;umpta rem per&longs;picuè &longs;oluunt. </s> | <s id="id.000696">Nam de&longs;cripta ob motum nauis benè intelligitur ex <lb/>diuer&longs;itate partium aëris, qui motum nauis non &longs;e-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.098.jpg" pagenum="99"/>quitur, &longs;ed re&longs;pectu illius permanet immotus: de&longs;­<lb/>cripta verò ob motum Terræ intelligi non pote&longs;t <lb/>ex diuer&longs;itate partium aëris, qui ip&longs;am Terram &longs;e­<lb/>quitar; &longs;ed ex diuer&longs;itate partium mundani &longs;patij, <lb/>quod immotum per&longs;euerat. </s> |
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| <s>Loco enim <lb/>manus intellige fi&longs;tulam; loco pilæ globum; loco <lb/>nauis Terram; loco aëris mundanum ipatrum; nihil <lb/>&longs;upererit laboris. </s> | <s id="id.000697">Dico autem aërem re&longs;­<lb/>pectu nauis manere immotum; quia dum motus il­<lb/>los intra nauim con&longs;ideramus, &longs;eponimus motum <lb/>Telluris, qui aliunde &longs;it naui, aëri, omnibu&longs;que re­<lb/>bus communis; quique ob &longs;ui communitatem re­<lb/>linquat ob&longs;eruabile inter res propriis viribus motas, <lb/>quie&longs;centei&longs;que, di&longs;crimen. </s></p><p type="main"> |
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| <s>Enimverò animi gratiâ repete ex­<lb/>po&longs;itum &longs;chema, & &longs;uppone AFK e&longs;&longs;e lineam in <lb/><figure id="fig7"/><lb/>&longs;uperficie globi Telluris vnâ cum tota Tellure mo­<lb/>bilem, &longs;ed pro tempore tamen, hoc e&longs;t, dum globus <lb/>exploditur, re&longs;pondentem parti immobilis &longs;patij A <lb/>FK, eo modo, quo iam dictum e&longs;t. </s> | <s id="id.000698">V. <!-- KEEP S--></s> |
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| <s>Suppone etiam <lb/>globum explodi ex puncto Terræ A ea tormenti vi, <lb/>vt peruenite po&longs;&longs;it ad F; & rur<gap/>us pari vi ex F, vt <lb/>peruenire po&longs;&longs;it ad A, etiam globo Terræ penitùs <lb/>quie&longs;cente; dico, licet Terra moueatur, globum <lb/>vttimque explo&longs;um nihilo &longs;eciùs pernenturum ad <lb/>cadem &longs;uperficiei Terræ puncta, hoc e&longs;t, heinc ad <lb/>F, illeinc ad A. </s> | <s id="id.000699">Ex hoc proinde intelliges, quàm parùm con­<lb/>cludant argumenta illa, quæ ex globorum explo­<lb/>&longs;ione à bellicis tormentis petuntur. </s> |
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| <s>Nam &longs;it, proüt obijcitur, motus <lb/>Telluris tantus, quantus e&longs;t globi proprius (vt<gap/>&longs;&longs;e <lb/>debet tantus circiter &longs;altem, in ve&longs;tro parallelo) erit <lb/>quidem vis globi explo&longs;i ex A in F geminata; &longs;ic­<lb/>que ex A immobili &longs;patij puncto perueniet in K <lb/>etiam immobile; at quia dum globus transferetur, <pb pagenum="101"/>punctum &longs;uperficiei Terræ A non manebit immotum, <lb/>&longs;ed po&longs;t globum ibit; neque punctum &longs;uperficiei K <lb/>immotum con&longs;i&longs;tet, &longs;ed globum antecodet: inde <lb/>cueniet, vt cùm globus ex puncto mundani &longs;patij <lb/>immobili A, peruentet ad punctum clu&longs;dem &longs;pa­<lb/>tij itidem immobile K, punctum mobile &longs;uperficiei <lb/>Terræ A perueniat ad punctum &longs;patij immobile F; <lb/>& punctum mobile &longs;uperficiei F petueniat ad pun­<lb/>ctum &longs;pati<gap/> immobile K; &longs;icque globus percurrat <lb/>quidem ex mundano &longs;patio lineam AK, &longs;ed ex &longs;u­<lb/>perficie tamen Telluris &longs;olummodo lineam AF; <lb/>quemadmodum faceret Terra quie&longs;cente. </s> | <s id="id.000700">Nam, inqui­<lb/>unt, globus in ortum explo&longs;us ferctur longè vlteriùs, <lb/>quàm explo&longs;us in occa&longs;um; quoniam ille præter <lb/>motum proprium, habebit etiam motum à Ter­<lb/>ra; hic verò habebit &longs;olùm motum proprium: <lb/>atque idcircò &longs;i motus Telluris &longs;upponatur tantus, <lb/>quantus e&longs;t motus globi proprius, efficietur motus in <lb/>ortum duplò velocior, quàm in occa&longs;um; &longs;icque <lb/>&longs;copus ad ortum duplò longiùs, quàm ad occa&longs;um <lb/>attingetur. </s> |
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| <s>Explo­<lb/>datur deinde globus ex F in A; quia dum erit per <lb/>aërem, neque punctum F, neque punctum A &longs;uper­<lb/>ficiei terrenæ erunt immota; &longs;ed interim punctum <lb/>F perueniet ad punctum immobile &longs;patij K, & pun­<lb/>ctum A ad punctum immobile F, & aliunde quantum <lb/>globus vi impre&longs;&longs;a à tormento feretur ex puncto <lb/>immobili F ver&longs;us A, tantum vi impre&longs;&longs;a à Terra <lb/>referetur ex A ver&longs;us F; fiet, vt re&longs;pectu &longs;patij im­<lb/>motus con&longs;i&longs;tat, donec cadat in punctum mobile &longs;u­<lb/>perficiei A, quod intereà ad punctum F immobile <lb/>perueniet. </s> | <s id="id.000701">Quin-etiam globus in occa&longs;um explo­<lb/>&longs;us non exibit è fi&longs;tula, &longs;ed qua&longs;i immotus con&longs;i­<lb/>&longs;tet; quia nempe quantum motu proprio in occi­<lb/>dentem connitetur, tantum impetus à Terra factus <lb/>illum in ortum re<gap/>imet. </s> |
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| <s>Neque iam debet videri mirum, mo­<lb/>ueri globum per aërem, & non moueri tamen per <lb/>mundanum <gap/>patium. </s> | <s id="id.000702">Addunt, &longs;i globus diriga­<lb/>tur &longs;eu in boream, &longs;eu in meridiem, aberrationem <lb/>&longs;emper à &longs;copo futuram; quia du<gap/> globus feretur <lb/>per aërem, &longs;copus intereà in ortum promouebitur, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.099.jpg" pagenum="100"/>locu&longs;que ferietur procùl ad acca&longs;um. </s> |
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| <s>Videlicet præter iam dicta (ex <lb/>quibus con&longs;tat non tam globum transferri per aërem, <lb/>quàm aërem ferri præter globum; & motum globo <lb/>à vi&longs;u tribui, qui tamen e&longs;t aëris) con&longs;tat rem aliun­<lb/>de ita &longs;e habere, ac dum vides hominem cont<gap/>in &longs;luuij <lb/>fundum defixo, aut fune ponti illigato impellere lem-<pb pagenum="102"/>bum &longs;uis pedibus. </s> | <s id="id.000703">Verumtamen <lb/>experimenta de colludentibus pilâ intra nauim à <lb/>&longs;imili &longs;umpta rem per&longs;picuè &longs;oluunt. </s> |
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| <s>Ille quippe nihilo &longs;ecùs mutat <lb/>pedes, inambulatque, ac fac<gap/> et &longs;upra ip&longs;am Ter­<lb/>ram; & nihilominùs vides ip&longs;um non mutare locum, <lb/>&longs;i comparetur ad aërem, ripam, &longs;uppo&longs;itum fun­<lb/>dum, quidpiamve aliud immobile; &longs;ed mutare &longs;o­<lb/>lùm locum re&longs;pectu partium lembi, qui intereà &longs;ub <lb/>ip&longs;o mouetur, quatenus ex puppi aut prora oppo­<lb/>&longs;itam partem attingit. </s> | <s id="id.000704">Loco enim <lb/>manus intellige fi&longs;tulam; loco pilæ globum; loco <lb/>nauis Terram; loco aëris mundanum ipatrum; nihil <lb/>&longs;upererit laboris. </s> |
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| <s>Nimitum re&longs;pectu aëris, aut <lb/>ripæ immobilis e&longs;t, quia præter motum proprium, <lb/>quo fertur ver&longs;us vnam partem, afficitur etiam motu <lb/>alio, qui ip&longs;um tantundem refert in partem oppo­<lb/>&longs;itam. </s> | <s id="id.000705">Enimverò animi gratiâ repete ex­<lb/>po&longs;itum &longs;chema, & &longs;uppone AFK e&longs;&longs;e lineam in <lb/><figure id="id.027.00.099.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/027-00-figures/027.00.099.1.jpg"/><lb/>&longs;uperficie globi Telluris vnâ cum tota Tellure mo­<lb/>bilem, &longs;ed pro tempore tamen, hoc e&longs;t, dum globus <lb/>exploditur, re&longs;pondentem parti immobilis &longs;patij A <lb/>FK, eo modo, quo iam dictum e&longs;t. </s> |
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| <s>Idem eueniet, &longs;i quis in medio flumine, aut <lb/>etiam in mari ab&longs;que conto, aut fune, tanta volo­<lb/>citate moueatur à prora in puppim, quanta nauis <lb/>ip&longs;a mouetur. </s> | <s id="id.000706">Suppone etiam <lb/>globum explodi ex puncto Terræ A ea tormenti vi, <lb/>vt peruenite po&longs;&longs;it ad F; & rur<gap/>us pari vi ex F, vt <lb/>peruenire po&longs;&longs;it ad A, etiam globo Terræ penitùs <lb/>quie&longs;cente; dico, licet Terra moueatur, globum <lb/>vttimque explo&longs;um nihilo &longs;eciùs pernenturum ad <lb/>cadem &longs;uperficiei Terræ puncta, hoc e&longs;t, heinc ad <lb/>F, illeinc ad A. <!-- KEEP S--></s> |
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| <s>Nam mouebitur quidem per nauim, <lb/>mutabit que &longs;ucce&longs;&longs;iuè parteis nauis varias; &longs;ed quod <lb/>ad ip&longs;um aërem, aquamve, aut fundum &longs;uppo&longs;itum <lb/>&longs;pectat, con&longs;i&longs;tet qua&longs;i immobilis, neque reuerâ <lb/>locum mutabit. </s> | <s id="id.000707">Nam &longs;it, proüt obijcitur, motus <lb/>Telluris tantus, quantus e&longs;t globi proprius (vt<gap/>&longs;&longs;e <lb/>debet tantus circiter &longs;altem, in ve&longs;tro parallelo) erit <lb/>quidem vis globi explo&longs;i ex A in F geminata; &longs;ic­<lb/>que ex A immobili &longs;patij puncto perueniet in K <lb/>etiam immobile; at quia dum globus transferetur, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.100.jpg" pagenum="101"/>punctum &longs;uperficiei Terræ A non manebit immotum, <lb/>&longs;ed po&longs;t globum ibit; neque punctum &longs;uperficiei K <lb/>immotum con&longs;i&longs;tet, &longs;ed globum antecodet: inde <lb/>cueniet, vt cùm globus ex puncto mundani &longs;patij <lb/>immobili A, peruentet ad punctum clu&longs;dem &longs;pa­<lb/>tij itidem immobile K, punctum mobile &longs;uperficiei <lb/>Terræ A perueniat ad punctum &longs;patij immobile F; <lb/>& punctum mobile &longs;uperficiei F petueniat ad pun­<lb/>ctum &longs;pati<gap/> immobile K; &longs;icque globus percurrat <lb/>quidem ex mundano &longs;patio lineam AK, &longs;ed ex &longs;u­<lb/>perficie tamen Telluris &longs;olummodo lineam AF; <lb/>quemadmodum faceret Terra quie&longs;cente. </s> |
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| <s>Pari igitur modo globus feretur <lb/>quidem impetu proprio, &longs;iue à machina impre&longs;&longs;o ab <lb/>oriente in occidentem, reip&longs;áque mouebitur per Ter­<lb/>ræ &longs;uperficiem, eiu&longs;que parteis commutabit: at re&longs;­<lb/>pectu mundani &longs;patij per&longs;euerabit qua&longs;i immotus, <lb/>quia quantum motu proprio in occa&longs;um feretur, <lb/>tantundem motu à Terra impre&longs;&longs;o referetur in or­<lb/>tum. </s> | <s id="id.000708">Explo­<lb/>datur deinde globus ex F in A; quia dum erit per <lb/>aërem, neque punctum F, neque punctum A &longs;uper­<lb/>ficiei terrenæ erunt immota; &longs;ed interim punctum <lb/>F perueniet ad punctum immobile &longs;patij K, & pun­<lb/>ctum A ad punctum immobile F, & aliunde quantum <lb/>globus vi impre&longs;&longs;a à tormento feretur ex puncto <lb/>immobili F ver&longs;us A, tantum vi impre&longs;&longs;a à Terra <lb/>referetur ex A ver&longs;us F; fiet, vt re&longs;pectu &longs;patij im­<lb/>motus con&longs;i&longs;tat, donec cadat in punctum mobile &longs;u­<lb/>perficiei A, quod intereà ad punctum F immobile <lb/>perueniet. </s> |
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| <s>Eadem porrô, proportione, euenient, &longs;eu <lb/>motum Terræ velociorem, &longs;eu tardiorem habeas <lb/>motu globi proprio. </s> | <s id="id.000709">Neque iam debet videri mirum, mo­<lb/>ueri globum per aërem, & non moueri tamen per <lb/>mundanum <gap/>patium. </s> |
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| <s>Quemadmodum à pari intel­<lb/>ligitur ex dictis &longs;uperiùs de projectione, & rejectione <lb/>pilæ &longs;ecundum longitudinem nauis; cùm nihil &longs;it ne-<pb pagenum="103"/>ce&longs;&longs;e explicare ampliùs quemadmodum fiat adjectio, <lb/>aut detractio virtutis communis comparatæ cum <lb/>propria: quandò, vt iam dictum e&longs;t, &longs;imili ratione &longs;e <lb/>habent pila, & globus; manus, & fi&longs;tula; nauis, & <lb/>Terra; aër, & &longs;patium. </s> | <s id="id.000710">Videlicet præter iam dicta (ex <lb/>quibus con&longs;tat non tam globum transferri per aërem, <lb/>quàm aërem ferri præter globum; & motum globo <lb/>à vi&longs;u tribui, qui tamen e&longs;t aëris) con&longs;tat rem aliun­<lb/>de ita &longs;e habere, ac dum vides hominem cont<gap/>in &longs;luuij <lb/>fundum defixo, aut fune ponti illigato impellere lem-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.101.jpg" pagenum="102"/>bum &longs;uis pedibus. </s> |
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| <s>Heine, quod dicitur de glo­<lb/>bo projecto &longs;eu in boream, &longs;eu in meridiem ex iis <lb/>&longs;oluitur, quæ dicta &longs;unt de projectis ex naui, aut <lb/>etiam ex curru. </s> | <s id="id.000711">Ille quippe nihilo &longs;ecùs mutat <lb/>pedes, inambulatque, ac fac<gap/> et &longs;upra ip&longs;am Ter­<lb/>ram; & nihilominùs vides ip&longs;um non mutare locum, <lb/>&longs;i comparetur ad aërem, ripam, &longs;uppo&longs;itum fun­<lb/>dum, quidpiamve aliud immobile; &longs;ed mutare &longs;o­<lb/>lùm locum re&longs;pectu partium lembi, qui intereà &longs;ub <lb/>ip&longs;o mouetur, quatenus ex puppi aut prora oppo­<lb/>&longs;itam partem attingit. </s> |
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| <s>Etenim, dum globus è fi&longs;tula exit, <lb/>non tantum habet motum &longs;ecundum longitudinem <lb/>fi&longs;tulæ; &longs;ed etiam &longs;ecundum horizontalem lineam; <lb/>incipitque proinde ex hoc duplici mo<gap/>u de&longs;cribi li­<lb/>nea media, &longs;ecundum quam tendere pergat, poft­<lb/>quàm exiit è fi&longs;tula; adeò vt quantùm fi&longs;tula, tan­<lb/>tundem ip&longs;e tendat in ortum, fitque &longs;emper è re­<lb/>gione orificij fi&longs;tulæ, per quod fuit trajectus; & in­<lb/>tereà tamen promoueatur vltra id orificium, & v&longs;­<lb/>que ad &longs;copum tandem directè perueniat, qui ip&longs;e <lb/>quoque e&longs;t intereà tantundem promotus in ortum, <lb/>quantum fi&longs;tula, inque cádem &longs;ecundum Terræ &longs;u­<lb/>perficiem linea perman&longs;it. </s> | <s id="id.000712">Nimitum re&longs;pectu aëris, aut <lb/>ripæ immobilis e&longs;t, quia præter motum proprium, <lb/>quo fertur ver&longs;us vnam partem, afficitur etiam motu <lb/>alio, qui ip&longs;um tantundem refert in partem oppo­<lb/>&longs;itam. </s> |
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| <s>Dicerem etiam de globo <lb/>&longs;ur&longs;ùm directè explo&longs;o, recidentéque ad perpen­<lb/>diculum: &longs;ed ratio eadem plane e&longs;t, & d fficultas ma­<lb/>net &longs;oluta ex iis, quæ circa explo&longs;ionem è naui me­<lb/>morata &longs;unt. </s> | <s id="id.000713">Idem eueniet, &longs;i quis in medio flumine, aut <lb/>etiam in mari ab&longs;que conto, aut fune, tanta volo­<lb/>citate moueatur à prora in puppim, quanta nauis <lb/>ip&longs;a mouetur. </s> |
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| <s>Quin-etiam hoc loco videtur res e&longs;&longs;e <lb/>tantò insellectu facilior, quantò per id tempus, quo <lb/>globus exit è fi&longs;tula, intelligitur &longs;imùl moueri &longs;en­<lb/>&longs;ibiliùs ver&longs;us ortum; &longs;icque ex motu &longs;ur&longs;ùm, & <lb/>motu in orientem de&longs;cribere lineam inter verticalem, <lb/>& horizontalem mediam, &longs;ecundum quam deinceps <lb/>tran&longs;latus, ita &longs;ur&longs;ùm emoueatur à fi&longs;tula, vt tamen <pb pagenum="104"/>etiam in ortum tantundem, ac ip&longs;a promo ueatur, <lb/>&longs;icque directè illi &longs;emper immineat, &longs;eu ad perpen­<lb/>diculum &longs;it, recidatque tandem in ip&longs;am. </s></p><p type="main"> | <s id="id.000714">Nam mouebitur quidem per nauim, <lb/>mutabit que &longs;ucce&longs;&longs;iuè parteis nauis varias; &longs;ed quod <lb/>ad ip&longs;um aërem, aquamve, aut fundum &longs;uppo&longs;itum <lb/>&longs;pectat, con&longs;i&longs;tet qua&longs;i immobilis, neque reuerâ <lb/>locum mutabit. </s> |
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| <s>VI. <!-- KEEP S--></s> | <s id="id.000715">Pari igitur modo globus feretur <lb/>quidem impetu proprio, &longs;iue à machina impre&longs;&longs;o ab <lb/>oriente in occidentem, reip&longs;áque mouebitur per Ter­<lb/>ræ &longs;uperficiem, eiu&longs;que parteis commutabit: at re&longs;­<lb/>pectu mundani &longs;patij per&longs;euerabit qua&longs;i immotus, <lb/>quia quantum motu proprio in occa&longs;um feretur, <lb/>tantundem motu à Terra impre&longs;&longs;o referetur in or­<lb/>tum. </s> |
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| <s>Neque verò allata modò argumenta nulla <lb/>videntur; &longs;ed illa etiam nihil concludunt, quæ ex ap­<lb/>parente rerum motu, quieteve &longs;olent obijci. </s> | <s id="id.000716">Eadem porrô, proportione, euenient, &longs;eu <lb/>motum Terræ velociorem, &longs;eu tardiorem habeas <lb/>motu globi proprio. </s> |
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| <s>Vi­<lb/>demus enim, inquiunt, Solem, cæteraque &longs;idera <lb/>oriri, occidere, citca nos moueri; videmus & hanc <lb/>ip&longs;am Terram, cui in&longs;i&longs;timus, pror&longs;ùs quie&longs;cere: an­<lb/>non igitur omnia ibunt naturæ legi præpo&longs;tera, &longs;i <lb/>&longs;idera quie&longs;cant, & Terra moueatur? </s> | <s id="id.000717">Quemadmodum à pari intel­<lb/>ligitur ex dictis &longs;uperiùs de projectione, & rejectione <lb/>pilæ &longs;ecundum longitudinem nauis; cùm nihil &longs;it ne-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.102.jpg" pagenum="103"/>ce&longs;&longs;e explicare ampliùs quemadmodum fiat adjectio, <lb/>aut detractio virtutis communis comparatæ cum <lb/>propria: quandò, vt iam dictum e&longs;t, &longs;imili ratione &longs;e <lb/>habent pila, & globus; manus, & fi&longs;tula; nauis, & <lb/>Terra; aër, & &longs;patium. </s> |
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| <s>Sed piget cram­<lb/>bem à Copernicanis toties repetitam heic repetere; <lb/>cùm præ&longs;ertìm con&longs;tet ex iam antè dictis, &longs;eu na­<lb/>uis alia moueatur ad no&longs;tram immotam: &longs;eu no&longs;tra <lb/>moueatur ad immotam aliam, motum tamen &longs;emper <lb/>nobis apparere non no&longs;træ, &longs;ed alterius nauis: adeò <lb/>vt, &longs;i in medio mari &longs;imus, & nihil &longs;it, ni&longs;i cælum <lb/>vndique, & vndique pontus, videamur ip&longs;i nobis <lb/>ip&longs;is immoti planè con&longs;i&longs;tere; quantumcúmque & <lb/>&longs;ecundo vento moueamur; & ad nauim aliam an­<lb/>choris firmatam feramur: quæ proinde tantum ap­<lb/>parebit accedere ad nos, quantum reuerâ nos accede­<lb/>mus ad ip&longs;am. </s> | <s id="id.000718">Heine, quod dicitur de glo­<lb/>bo projecto &longs;eu in boream, &longs;eu in meridiem ex iis <lb/>&longs;oluitur, quæ dicta &longs;unt de projectis ex naui, aut <lb/>etiam ex curru. </s> |
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| <s>Cæterùm quia nos longo v&longs;u, expe­<lb/>rientiá que edocti &longs;en&longs;um, &longs;eu imaginationem mente, <lb/>&longs;eu ratione enitimur corrigere, ac reip&longs;a corrigimus, <lb/>& rem &longs;ecùs &longs;e habere, quàm nobis appareat, nobis <lb/>per&longs;uademus; finge tamen, ni&longs;i hominem natum, <lb/>educatumque in media naui, &longs;altem mediterraneum, <lb/>qui nauigium nunquam viderit, & dormiens, oculi&longs;­<lb/>ve clau&longs;is, ac nihil tale cogitans, in nauim tran&longs;la-<pb pagenum="105"/>tus, deducatur in medium mare, vbi, quemadmo­<lb/>dum dixi, nihil &longs;it præter cælum, pontumque, & na­<lb/>uis alia ad anchoram. </s> | <s id="id.000719">Etenim, dum globus è fi&longs;tula exit, <lb/>non tantum habet motum &longs;ecundum longitudinem <lb/>fi&longs;tulæ; &longs;ed etiam &longs;ecundum horizontalem lineam; <lb/>incipitque proinde ex hoc duplici mo<gap/>u de&longs;cribi li­<lb/>nea media, &longs;ecundum quam tendere pergat, poft­<lb/>quàm exiit è fi&longs;tula; adeò vt quantùm fi&longs;tula, tan­<lb/>tundem ip&longs;e tendat in ortum, fitque &longs;emper è re­<lb/>gione orificij fi&longs;tulæ, per quod fuit trajectus; & in­<lb/>tereà tamen promoueatur vltra id orificium, & v&longs;­<lb/>que ad &longs;copum tandem directè perueniat, qui ip&longs;e <lb/>quoque e&longs;t intereà tantundem promotus in ortum, <lb/>quantum fi&longs;tula, inque cádem &longs;ecundum Terræ &longs;u­<lb/>perficiem linea perman&longs;it. </s> |
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| <s>Tum, &longs;i aperiat oculos, & <lb/>naui, in qua erit, veloci&longs;&longs;imè præter aliam mota, ex <lb/>illo requiras, vtri motum, vtri quietem conuenire <lb/>exi&longs;timet; re&longs;pondebit haud-dubiè, nauim in qua <lb/>erit, quie&longs;cere, & aliam moueri. </s> | <s id="id.000720">Dicerem etiam de globo <lb/>&longs;ur&longs;ùm directè explo&longs;o, recidentéque ad perpen­<lb/>diculum: &longs;ed ratio eadem plane e&longs;t, & d fficultas ma­<lb/>net &longs;oluta ex iis, quæ circa explo&longs;ionem è naui me­<lb/>morata &longs;unt. </s> |
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| <s>Et iubeto, quan­<lb/>tum voles, vt attendat; fieri enim po&longs;&longs;e, vt nauis, <lb/>in qua erit, moueatur, immotaque &longs;it alia; iurabit <lb/>&longs;e non decipi; ac tantò magis &longs;ecurus erit nauim <lb/>&longs;uam quie&longs;cere, quantò ob&longs;eruabit omneis eius par­<lb/>teis in eodem &longs;emper &longs;itu manere; non di&longs;cedere <lb/>puppim in vnam partem, & proram in aliam; non <lb/>accedere etiam ad &longs;e mutuò; non parteìs item late­<lb/>raleis; non tran&longs;tra; non malos, non quicquid at­<lb/>tinet ad nauim; & intereà nautas variè per foros <lb/>cur&longs;it<gap/>re, malos &longs;candere, &longs;entinam exhaurire, & <lb/>omnia pror&longs;us peragere, vt &longs;i nauis con&longs;tituta e&longs;&longs;et, <lb/>con&longs;i&longs;teretque in medio foro, mediove agro oppidi. <lb/></s> | <s id="id.000721">Quin-etiam hoc loco videtur res e&longs;&longs;e <lb/>tantò insellectu facilior, quantò per id tempus, quo <lb/>globus exit è fi&longs;tula, intelligitur &longs;imùl moueri &longs;en­<lb/>&longs;ibiliùs ver&longs;us ortum; &longs;icque ex motu &longs;ur&longs;ùm, & <lb/>motu in orientem de&longs;cribere lineam inter verticalem, <lb/>& horizontalem mediam, &longs;ecundum quam deinceps <lb/>tran&longs;latus, ita &longs;ur&longs;ùm emoueatur à fi&longs;tula, vt tamen <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.103.jpg" pagenum="104"/>etiam in ortum tantundem, ac ip&longs;a promo ueatur, <lb/>&longs;icque directè illi &longs;emper immineat, &longs;eu ad perpen­<lb/>diculum &longs;it, recidatque tandem in ip&longs;am. </s></p><p type="main"> |
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| <s>Iam verò globus Terræ e&longs;t, in quem, qua&longs;i dor­<lb/>mientes tran&longs;lati, vel potiùs in quo non cogitantes <lb/>nati &longs;umus. </s> | <s id="id.000722">VI. <!-- KEEP S--></s> |
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| <s>Ex quo autem oculos aperuïmus, & <lb/>præter hunc globum, contemplati &longs;umus alium, <lb/>videlicet Solem, in eodem cum Terra qua&longs;i æquore, <lb/>&longs;eu &longs;patio mundano; quæ&longs;itum e&longs;t vtri i&longs;torum glo­<lb/>borum competeret quies, vtri motus? </s> | <s id="id.000723">Neque verò allata modò argumenta nulla <lb/>videntur; &longs;ed illa etiam nihil concludunt, quæ ex ap­<lb/>parente rerum motu, quieteve &longs;olent obijci. </s> |
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| <s>nos verò <lb/>incunctanter pronunciauimus competere haud-du­<lb/>biè quietem Terræ, & motum Soli. <!-- KEEP S--></s> | <s id="id.000724">Vi­<lb/>demus enim, inquiunt, Solem, cæteraque &longs;idera <lb/>oriri, occidere, citca nos moueri; videmus & hanc <lb/>ip&longs;am Terram, cui in&longs;i&longs;timus, pror&longs;ùs quie&longs;cere: an­<lb/>non igitur omnia ibunt naturæ legi præpo&longs;tera, &longs;i <lb/>&longs;idera quie&longs;cant, & Terra moueatur? </s> |
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| <s>Admonüere Py­<lb/>thagoras, Plato, Ari&longs;tarchus, antiquiores alij; <lb/>itemque Copernicus, Galileus, Kepplerus, recen-<pb pagenum="106"/>tiores plures, forta&longs;&longs;is nos decipi, & quie&longs;cere So­<lb/>lem, Terramque moueri: nos tamen contrà in&longs;ti­<lb/>timus; ac tantò ob&longs;tinatiores facti &longs;umus, quantò <lb/>magis attendentes, ob&longs;eruauimus parteis Terræ à &longs;e <lb/>mutuò non di&longs;trahi; &longs;ed illum quidem montem e&longs;&longs;e <lb/>&longs;emper ad boream, hanc vrbem ad au&longs;trum, illum <lb/>fluuium ad ortum, hanc in&longs;ulam ad occa&longs;um; ac <lb/>nos intereà &longs;upra Terram perinde di&longs;currere, ac <lb/>di&longs;currimus per domum, &longs;iue ciuitatem, in qua na­<lb/>ti &longs;umus: adeò vt, quema dmodum neque domus <lb/>per ciuitatem, neque ciuitas per prouinciam, Ter­<lb/>ramve di&longs;currit; ita ip&longs;a quoque Terra non videa­<lb/>tur per &longs;patia mundi di&longs;currere. </s> | <s id="id.000725">Sed piget cram­<lb/>bem à Copernicanis toties repetitam heic repetere; <lb/>cùm præ&longs;ertìm con&longs;tet ex iam antè dictis, &longs;eu na­<lb/>uis alia moueatur ad no&longs;tram immotam: &longs;eu no&longs;tra <lb/>moueatur ad immotam aliam, motum tamen &longs;emper <lb/>nobis apparere non no&longs;træ, &longs;ed alterius nauis: adeò <lb/>vt, &longs;i in medio mari &longs;imus, & nihil &longs;it, ni&longs;i cælum <lb/>vndique, & vndique pontus, videamur ip&longs;i nobis <lb/>ip&longs;is immoti planè con&longs;i&longs;tere; quantumcúmque & <lb/>&longs;ecundo vento moueamur; & ad nauim aliam an­<lb/>choris firmatam feramur: quæ proinde tantum ap­<lb/>parebit accedere ad nos, quantum reuerâ nos accede­<lb/>mus ad ip&longs;am. </s> |
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| <s>Atque ita quidem <lb/>&longs;e habet ab exortu v&longs;que no&longs;tra imaginatio; neque <lb/>animaduertimus, Terram e&longs;&longs;e fortè in&longs;tar nauis, <lb/>fierique po&longs;&longs;e, vt ex&longs;i&longs;tentes in Terra perinde fal­<lb/>lamur, ac Mediterraneus ille, dum in naui e&longs;t. <lb/></s> | <s id="id.000726">Cæterùm quia nos longo v&longs;u, expe­<lb/>rientiá que edocti &longs;en&longs;um, &longs;eu imaginationem mente, <lb/>&longs;eu ratione enitimur corrigere, ac reip&longs;a corrigimus, <lb/>& rem &longs;ecùs &longs;e habere, quàm nobis appareat, nobis <lb/>per&longs;uademus; finge tamen, ni&longs;i hominem natum, <lb/>educatumque in media naui, &longs;altem mediterraneum, <lb/>qui nauigium nunquam viderit, & dormiens, oculi&longs;­<lb/>ve clau&longs;is, ac nihil tale cogitans, in nauim tran&longs;la-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.104.jpg" pagenum="105"/>tus, deducatur in medium mare, vbi, quemadmo­<lb/>dum dixi, nihil &longs;it præter cælum, pontumque, & na­<lb/>uis alia ad anchoram. </s> |
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| <s>Quippe quod-nam erit di&longs;crimen? </s> | <s id="id.000727">Tum, &longs;i aperiat oculos, & <lb/>naui, in qua erit, veloci&longs;&longs;imè præter aliam mota, ex <lb/>illo requiras, vtri motum, vtri quietem conuenire <lb/>exi&longs;timet; re&longs;pondebit haud-dubiè, nauim in qua <lb/>erit, quie&longs;cere, & aliam moueri. </s> |
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| <s>aut quæ ratio <lb/>di&longs;criminis? </s> | <s id="id.000728">Et iubeto, quan­<lb/>tum voles, vt attendat; fieri enim po&longs;&longs;e, vt nauis, <lb/>in qua erit, moueatur, immotaque &longs;it alia; iurabit <lb/>&longs;e non decipi; ac tantò magis &longs;ecurus erit nauim <lb/>&longs;uam quie&longs;cere, quantò ob&longs;eruabit omneis eius par­<lb/>teis in eodem &longs;emper &longs;itu manere; non di&longs;cedere <lb/>puppim in vnam partem, & proram in aliam; non <lb/>accedere etiam ad &longs;e mutuò; non parteìs item late­<lb/>raleis; non tran&longs;tra; non malos, non quicquid at­<lb/>tinet ad nauim; & intereà nautas variè per foros <lb/>cur&longs;it<gap/>re, malos &longs;candere, &longs;entinam exhaurire, & <lb/>omnia pror&longs;us peragere, vt &longs;i nauis con&longs;tituta e&longs;&longs;et, <lb/>con&longs;i&longs;teretque in medio foro, mediove agro oppidi. <lb/></s> |
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| <s>& quis modus &longs;eu veritatem, &longs;eu erro­<lb/>rem interno&longs;cendi? </s> | <s id="id.000729">Iam verò globus Terræ e&longs;t, in quem, qua&longs;i dor­<lb/>mientes tran&longs;lati, vel potiùs in quo non cogitantes <lb/>nati &longs;umus. </s> |
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| <s>Ac non dico quidem proptereà <lb/>moueri Terram, quie&longs;cere Solem; &longs;ed quærendas <lb/>dico rationes meliores, quàm quæ ex &longs;en&longs;u ip&longs;o pe­<lb/>tuntur. </s> | <s id="id.000730">Ex quo autem oculos aperuïmus, & <lb/>præter hunc globum, contemplati &longs;umus alium, <lb/>videlicet Solem, in eodem cum Terra qua&longs;i æquore, <lb/>&longs;eu &longs;patio mundano; quæ&longs;itum e&longs;t vtri i&longs;torum glo­<lb/>borum competeret quies, vtri motus? </s> |
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| <s>Et ni&longs;i fui&longs;&longs;emus quidem vnquam experti <lb/>vi&longs;us no&longs;tri fallaciam, excu&longs;abiles videremur, <lb/>po&longs;&longs;emu&longs;que obijcere, nihil e&longs;&longs;e vi&longs;u mani­<lb/>fe&longs;tius, aut certius; detractáque oculis fide nihil <lb/>fieri per&longs;ua&longs;ione dignum: at quia nos experientia <lb/>docuit vi&longs;um falli tantoperè, neque fidem &longs;emper <lb/>adhibendam oculis e&longs;&longs;e, idque cùm de motu po­<lb/>ti&longs;&longs;imùm agitur; quidnam re&longs;ponderi pote&longs;t aliud, <pb pagenum="107"/>quàm & vi&longs;um, & &longs;en&longs;us alios e&longs;&longs;e ratione corri­<lb/>gendos? </s> | <s id="id.000731">nos verò <lb/>incunctanter pronunciauimus competere haud-du­<lb/>biè quietem Terræ, & motum Soli. <!-- KEEP S--></s> |
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| <s>Si ratione porrô vi&longs;um corrigamus, quid <lb/>Mediterraneo illi per&longs;uadebimus, ni&longs;i moueri nauim, <lb/>in qua e&longs;t, quie&longs;cere nauim, ver&longs;us quàm accedit? <lb/></s> | <s id="id.000732">Admonüere Py­<lb/>thagoras, Plato, Ari&longs;tarchus, antiquiores alij; <lb/>itemque Copernicus, Galileus, Kepplerus, recen-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.105.jpg" pagenum="106"/>tiores plures, forta&longs;&longs;is nos decipi, & quie&longs;cere So­<lb/>lem, Terramque moueri: nos tamen contrà in&longs;ti­<lb/>timus; ac tantò ob&longs;tinatiores facti &longs;umus, quantò <lb/>magis attendentes, ob&longs;eruauimus parteis Terræ à &longs;e <lb/>mutuò non di&longs;trahi; &longs;ed illum quidem montem e&longs;&longs;e <lb/>&longs;emper ad boream, hanc vrbem ad au&longs;trum, illum <lb/>fluuium ad ortum, hanc in&longs;ulam ad occa&longs;um; ac <lb/>nos intereà &longs;upra Terram perinde di&longs;currere, ac <lb/>di&longs;currimus per domum, &longs;iue ciuitatem, in qua na­<lb/>ti &longs;umus: adeò vt, quema dmodum neque domus <lb/>per ciuitatem, neque ciuitas per prouinciam, Ter­<lb/>ramve di&longs;currit; ita ip&longs;a quoque Terra non videa­<lb/>tur per &longs;patia mundi di&longs;currere. </s> |
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| <s>Et cùm ita fecerimus, quid, pari ratione per&longs;uade­<lb/>bimus aliud nobis ip&longs;is, quàm moueri Terram, cui <lb/>in&longs;i&longs;timus, quie&longs;cere Solem, ver&longs;us quem mouemur? </s></p><p type="main"> | <s id="id.000733">Atque ita quidem <lb/>&longs;e habet ab exortu v&longs;que no&longs;tra imaginatio; neque <lb/>animaduertimus, Terram e&longs;&longs;e fortè in&longs;tar nauis, <lb/>fierique po&longs;&longs;e, vt ex&longs;i&longs;tentes in Terra perinde fal­<lb/>lamur, ac Mediterraneus ille, dum in naui e&longs;t. <lb/></s> |
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| <s>VII. <!-- KEEP S--></s> | <s id="id.000734">Quippe quod-nam erit di&longs;crimen? </s> |
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| <s>Quod dictum porrô e&longs;t de Sole, videtur <lb/>&longs;imùl quoque dicendum de &longs;ideribus cæteris. </s> | <s id="id.000735">aut quæ ratio <lb/>di&longs;criminis? </s> |
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| <s>Nam <lb/>pari modo, &longs;i nos cum Terra ver&longs;us ortum conuerti­<lb/>mur, nece&longs;&longs;e e&longs;t nobis &longs;emper, continuóque, aliæ, <lb/>aliæque partes vi&longs;ibiles mundi aut cœli, vt putà Lu­<lb/>na, &longs;tellæque tam errantes, quàm inerrantes ver&longs;us <lb/>ortum retegantur, totidemque intereà ver&longs;us oc­<lb/>ca&longs;um occultentur; & quæ exortæ fuerint, appa­<lb/>reant continuò ad meridianum a&longs;cendere, præter­<lb/>gredique, & in occa&longs;um de&longs;cendere, ac &longs;ub Terram <lb/>quoque, &longs;eu infra horizontem pergere, donec vna <lb/>reuolutione intra horas viginti quatuor ab&longs;oluta, <lb/>appareant rur&longs;ùs exoriri, a&longs;cendere, &c. </s> | <s id="id.000736">& quis modus &longs;eu veritatem, &longs;eu erro­<lb/>rem interno&longs;cendi? </s> |
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| <s>Cur non id <lb/>verò potiùs appareat ex conuer&longs;ione no&longs;tri oculi ad <lb/>parteis cæli orientaliores, quàm ex conuer&longs;ione tot, <lb/><expan abbr="tantarumq;">tantarumque</expan> partium ver&longs;us oculum: quemadmodum <lb/>nobis eleuatio poli apparet, non toto cælo conuer­<lb/>&longs;o in meridiem; &longs;ed oculo &longs;olo promoto in boream? <lb/></s> | <s id="id.000737">Ac non dico quidem proptereà <lb/>moueri Terram, quie&longs;cere Solem; &longs;ed quærendas <lb/>dico rationes meliores, quàm quæ ex &longs;en&longs;u ip&longs;o pe­<lb/>tuntur. </s> |
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| <s>Nam in hac quidem ciuitate polus boreus attolli­<lb/>tur &longs;olum gradibus quadraginta tribus cum &longs;emi&longs;&longs;e; <lb/>& vbi tamen immoto cælo ad ciuitatem v&longs;que ve­<lb/>&longs;tram iter in&longs;tituimus, ita paulatìm parteis inferio­<lb/>res, inferiore&longs;que, &longs;ub ip&longs;o polo detegimus, vt de-<pb pagenum="108"/>nique i&longs;teic polus attollatur gradibus proximè qua­<lb/>draginta nouem. </s> | <s id="id.000738">Et ni&longs;i fui&longs;&longs;emus quidem vnquam experti <lb/>vi&longs;us no&longs;tri fallaciam, excu&longs;abiles videremur, <lb/>po&longs;&longs;emu&longs;que obijcere, nihil e&longs;&longs;e vi&longs;u mani­<lb/>fe&longs;tius, aut certius; detractáque oculis fide nihil <lb/>fieri per&longs;ua&longs;ione dignum: at quia nos experientia <lb/>docuit vi&longs;um falli tantoperè, neque fidem &longs;emper <lb/>adhibendam oculis e&longs;&longs;e, idque cùm de motu po­<lb/>ti&longs;&longs;imùm agitur; quidnam re&longs;ponderi pote&longs;t aliud, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.106.jpg" pagenum="107"/>quàm & vi&longs;um, & &longs;en&longs;us alios e&longs;&longs;e ratione corri­<lb/>gendos? </s> |
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| <s>Dicent non totam Terram in bo­<lb/>ream, &longs;ed nos duntaxat progredi; verùm id adfer­<lb/>tur &longs;olùm in exemplum, vt o&longs;tendam, &longs;eu oculus &longs;o­<lb/>lus, &longs;eu oculus vnà cum Terra progrediatur ver&longs;us <lb/>ortum, po&longs;&longs;e &longs;idera videri attolli; neque, vt hoc <lb/>appareat, e&longs;&longs;e nece&longs;&longs;arium, conuerti ip&longs;a ver&longs;us oc­<lb/>ca&longs;um. </s> | <s id="id.000739">Si ratione porrô vi&longs;um corrigamus, quid <lb/>Mediterraneo illi per&longs;uadebimus, ni&longs;i moueri nauim, <lb/>in qua e&longs;t, quie&longs;cere nauim, ver&longs;us quàm accedit? <lb/></s> |
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| <s>Addo, &longs;i iudicant facilius moueri &longs;olum <lb/>oculum, quàm totam Terram in boream; cur non <lb/>facilius quoque iudicent moueri &longs;olam Terram in <lb/>ortum, quàm &longs;idera omnia, machinamque cælorum <lb/>vniuer&longs;am moueri in occa&longs;um? </s> | <s id="id.000740">Et cùm ita fecerimus, quid, pari ratione per&longs;uade­<lb/>bimus aliud nobis ip&longs;is, quàm moueri Terram, cui <lb/>in&longs;i&longs;timus, quie&longs;cere Solem, ver&longs;us quem mouemur? </s></p><p type="main"> |
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| <s>Non definio &longs;anè <lb/>vtrum fiat: &longs;ed cùm, quod &longs;pectat ad oculum, po&longs;­<lb/>&longs;it vtrumque æquè præ&longs;tari; innuo &longs;olùm e&longs;&longs;e ra­<lb/>tione agendum, vt mens in eam partem propendeat, <lb/>quam ratio fecerit veri&longs;imiliorem. </s> | <s id="id.000741">VII. <!-- KEEP S--></s> |
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| <s>Hoc verò po&longs;ito, <lb/>cùm ratione &longs;uadente &longs;it vero&longs;imilius moueri nauim <lb/>ver&longs;us portum, quàm portum, ac naueis, & domos, <lb/>terra&longs;que attiguas moueri ver&longs;us ip&longs;am nauim; & <lb/>&longs;pectante aliquo ex edita turri totam ciuitatem <lb/>circumpo&longs;itam, probabilius &longs;it hominem in fa&longs;ti­<lb/>gium turris emergere, &longs;e&longs;eque in omnem circum <lb/>partem conuertere, quàm ciuitatem totam deprimi, <lb/>ac circa ip&longs;um conuerti; & oratore pro &longs;ugge&longs;tu <lb/>perorante, con&longs;entaneum magis &longs;it ip&longs;ius vultum <lb/>ad omneis circùm auditorij parteis ex ordine dirigi, <lb/>quàm totum auditorium circa vultum immobilem, <lb/>atque id genus &longs;imilia: Cur non ratione eadem &longs;ua­<lb/>dente fiat vero&longs;imilius, probabilius, magis con&longs;en­<lb/>taneum moueri Terram ver&longs;us ortum, ac totam <pb pagenum="109"/>mundi machinam, &longs;ideraque omnia &longs;alutare ex or­<lb/>dine; quàm tantam illam machinam, totque, & <lb/>tanta &longs;idera circum ip&longs;am ire, eamque &longs;alutare? <lb/></s> | <s id="id.000742">Quod dictum porrô e&longs;t de Sole, videtur <lb/>&longs;imùl quoque dicendum de &longs;ideribus cæteris. </s> |
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| <s>Profectò nauis e&longs;t aliqua &longs;en&longs;ibilis portio, &longs;iue po­<lb/>tiùs e&longs;t alicuius &longs;en&longs;ibilis magnitudinis re&longs;pectu <lb/>portus, totiu&longs;que oppo&longs;itæ oræ; homo re&longs;pectu ci­<lb/>uitatis, vultus re&longs;pectu auditorij: Terra verò com­<lb/>parata ad tantæ illius machinæ amplitudinem, non <lb/>modò punctum e&longs;t, &longs;ed etiam, &longs;i quid fingi pote&longs;t <lb/>in&longs;en&longs;ibilius, ac minus puncto. </s> | <s id="id.000743">Nam <lb/>pari modo, &longs;i nos cum Terra ver&longs;us ortum conuerti­<lb/>mur, nece&longs;&longs;e e&longs;t nobis &longs;emper, continuóque, aliæ, <lb/>aliæque partes vi&longs;ibiles mundi aut cœli, vt putà Lu­<lb/>na, &longs;tellæque tam errantes, quàm inerrantes ver&longs;us <lb/>ortum retegantur, totidemque intereà ver&longs;us oc­<lb/>ca&longs;um occultentur; & quæ exortæ fuerint, appa­<lb/>reant continuò ad meridianum a&longs;cendere, præter­<lb/>gredique, & in occa&longs;um de&longs;cendere, ac &longs;ub Terram <lb/>quoque, &longs;eu infra horizontem pergere, donec vna <lb/>reuolutione intra horas viginti quatuor ab&longs;oluta, <lb/>appareant rur&longs;ùs exoriri, a&longs;cendere, &c. </s> |
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| <s>Quanquam res po&longs;­<lb/>&longs;et fortè videri vtcùmque tolerabilis, &longs;i tota illa ma­<lb/>china vnico, ac &longs;implici motu circumferretur ver­<lb/>&longs;us occa&longs;um; &longs;ed cùm aliunde tot Planetæ circum­<lb/>ferantur quoque ver&longs;us ortum; quid potuit fieri <lb/>ab&longs;urdius, quàm fingi &longs;upra Planetas, &longs;upraque <lb/>omneis &longs;tellas fixas, ac &longs;phæras etiam cry&longs;tallinas, <lb/><expan abbr="va&longs;ti&longs;&longs;imã">va&longs;ti&longs;&longs;imam</expan> &longs;phæram Primi mobilis, quæ aduer&longs;us infe­<lb/>riores nitenteis in ortum &longs;uis ac lentis motibus, con­<lb/>tranitatur ip&longs;a, & ver&longs;us occa&longs;um incredibili ce­<lb/>leritate omneis abripiat? </s> | <s id="id.000744">Cur non id <lb/>verò potiùs appareat ex conuer&longs;ione no&longs;tri oculi ad <lb/>parteis cæli orientaliores, quàm ex conuer&longs;ione tot, <lb/><expan abbr="tantarumq;">tantarumque</expan> partium ver&longs;us oculum: quemadmodum <lb/>nobis eleuatio poli apparet, non toto cælo conuer­<lb/>&longs;o in meridiem; &longs;ed oculo &longs;olo promoto in boream? <lb/></s> |
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| <s>An pote&longs;t e&longs;&longs;e quidpiam <lb/>violentius; & cogitari tamen e&longs;&longs;e in rerum natura <lb/>perpetuum? </s> | <s id="id.000745">Nam in hac quidem ciuitate polus boreus attolli­<lb/>tur &longs;olum gradibus quadraginta tribus cum &longs;emi&longs;&longs;e; <lb/>& vbi tamen immoto cælo ad ciuitatem v&longs;que ve­<lb/>&longs;tram iter in&longs;tituimus, ita paulatìm parteis inferio­<lb/>res, inferiore&longs;que, &longs;ub ip&longs;o polo detegimus, vt de-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.107.jpg" pagenum="108"/>nique i&longs;teic polus attollatur gradibus proximè qua­<lb/>draginta nouem. </s> |
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| <s>An e&longs;&longs;e quidpiam amfractuo&longs;ius; & at­<lb/>tribui tamen naturæ, quæ quò tendit, procedit &longs;em­<lb/>per per breui&longs;&longs;imam, & complanati&longs;&longs;imam viam? <lb/></s> | <s id="id.000746">Dicent non totam Terram in bo­<lb/>ream, &longs;ed nos duntaxat progredi; verùm id adfer­<lb/>tur &longs;olùm in exemplum, vt o&longs;tendam, &longs;eu oculus &longs;o­<lb/>lus, &longs;eu oculus vnà cum Terra progrediatur ver&longs;us <lb/>ortum, po&longs;&longs;e &longs;idera videri attolli; neque, vt hoc <lb/>appareat, e&longs;&longs;e nece&longs;&longs;arium, conuerti ip&longs;a ver&longs;us oc­<lb/>ca&longs;um. </s> |
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| <s>Terrâ profecto in ortum conuer&longs;â, quo compen­<lb/>dio&longs;iùs nihil e&longs;t, &longs;ui, lentique in ortum motus re­<lb/>linquentur ip&longs;is Planetis; & qui tam ip&longs;is, quam &longs;tel­<lb/>lis fixis ver&longs;us occa&longs;um ine&longs;&longs;e apparet, ex vnica Ter­<lb/>ræ in ortum conuer&longs;ione apparebit; adeò vt hæc <lb/>&longs;ola, &longs;implexque conuer&longs;io æqui<gap/>aleat illi primo mo-<pb pagenum="110"/>bili; intereáque rapiditate, violentia, intricatione il­<lb/>la tanta liberet orbeis inferiores. </s> | <s id="id.000747">Addo, &longs;i iudicant facilius moueri &longs;olum <lb/>oculum, quàm totam Terram in boream; cur non <lb/>facilius quoque iudicent moueri &longs;olam Terram in <lb/>ortum, quàm &longs;idera omnia, machinamque cælorum <lb/>vniuer&longs;am moueri in occa&longs;um? </s> |
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| <s>Quanquam aliunde <lb/>&longs;olidi orbes, qui in&longs;itos &longs;ibi Planetas deuehentes, <lb/>debuerunt e&longs;&longs;e contigui, vt inferiores abripi à &longs;u­<lb/>perioribus po&longs;&longs;ent, nulli planè &longs;unt; vt vel explorati <lb/>motus Veneris, & Mercurij &longs;upra, ac infra Solem, <lb/>& Cometarum traiectiones per &longs;patia illa &longs;atis con­<lb/>uincunt. </s> | <s id="id.000748">Non definio &longs;anè <lb/>vtrum fiat: &longs;ed cùm, quod &longs;pectat ad oculum, po&longs;­<lb/>&longs;it vtrumque æquè præ&longs;tari; innuo &longs;olùm e&longs;&longs;e ra­<lb/>tione agendum, vt mens in eam partem propendeat, <lb/>quam ratio fecerit veri&longs;imiliorem. </s> |
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| <s>Quare nec motus ille raptus pote&longs;t iam <lb/>ampliùs peragi; quandò Planetarum quidem glo­<lb/>bos per libera, fluxáque &longs;patia abripi non po&longs;&longs;e e&longs;t <lb/>&longs;atis per&longs;picuum; & retentis etiam &longs;olidis &longs;phæris, <lb/>manife&longs;tum e&longs;t, &longs;i &longs;uperficies inferiorum convexæ, <lb/>& &longs;uperiorum concauæ politi&longs;&longs;imæ fuerint (vt nece&longs;­<lb/>&longs;ariò, & vulgò cen&longs;ent) non po&longs;&longs;e planè inferiores <lb/>à &longs;uperioribus abripi, quippe de&longs;tituræ an&longs;is, qui­<lb/>bus in orbem impellantur, motumque accipiant; <lb/>ac po&longs;&longs;e ad &longs;ummum impul&longs;ionem pror&longs;ùm, &longs;eu in <lb/>rectum accipere, qualis profectò non admittetur. <lb/></s> | <s id="id.000749">Hoc verò po&longs;ito, <lb/>cùm ratione &longs;uadente &longs;it vero&longs;imilius moueri nauim <lb/>ver&longs;us portum, quàm portum, ac naueis, & domos, <lb/>terra&longs;que attiguas moueri ver&longs;us ip&longs;am nauim; & <lb/>&longs;pectante aliquo ex edita turri totam ciuitatem <lb/>circumpo&longs;itam, probabilius &longs;it hominem in fa&longs;ti­<lb/>gium turris emergere, &longs;e&longs;eque in omnem circum <lb/>partem conuertere, quàm ciuitatem totam deprimi, <lb/>ac circa ip&longs;um conuerti; & oratore pro &longs;ugge&longs;tu <lb/>perorante, con&longs;entaneum magis &longs;it ip&longs;ius vultum <lb/>ad omneis circùm auditorij parteis ex ordine dirigi, <lb/>quàm totum auditorium circa vultum immobilem, <lb/>atque id genus &longs;imilia: Cur non ratione eadem &longs;ua­<lb/>dente fiat vero&longs;imilius, probabilius, magis con&longs;en­<lb/>taneum moueri Terram ver&longs;us ortum, ac totam <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.108.jpg" pagenum="109"/>mundi machinam, &longs;ideraque omnia &longs;alutare ex or­<lb/>dine; quàm tantam illam machinam, totque, & <lb/>tanta &longs;idera circum ip&longs;am ire, eamque &longs;alutare? <lb/></s> |
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| <s>Noto intereà propter Cometas; cùm præter pro­<lb/>prias trajectiones, quæ &longs;unt nunc in boream, nunc <lb/>in au&longs;trum, nunc aliò; appareant etiam conuer&longs;ione <lb/>diurna ab ortu in occa&longs;um ferri; quid vero&longs;imilius <lb/>cogitari po&longs;&longs;it, quàm moueri illos motu vnico, &longs;eu <lb/>trajectione propria; circumductionem verò illam in <lb/>occa&longs;um e&longs;&longs;e duntaxat apparentem, ex conuer&longs;ione <lb/>Terræ diurna in ortum? </s> | <s id="id.000750">Profectò nauis e&longs;t aliqua &longs;en&longs;ibilis portio, &longs;iue po­<lb/>tiùs e&longs;t alicuius &longs;en&longs;ibilis magnitudinis re&longs;pectu <lb/>portus, totiu&longs;que oppo&longs;itæ oræ; homo re&longs;pectu ci­<lb/>uitatis, vultus re&longs;pectu auditorij: Terra verò com­<lb/>parata ad tantæ illius machinæ amplitudinem, non <lb/>modò punctum e&longs;t, &longs;ed etiam, &longs;i quid fingi pote&longs;t <lb/>in&longs;en&longs;ibilius, ac minus puncto. </s> |
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| <s>Hæc &longs;anè conuer&longs;io eiu&longs;­<lb/>modi e&longs;t, vt quicquid &longs;ur&longs;ùm, vltrave Terram, ac <lb/>per mundana &longs;patia &longs;eu e&longs;t, &longs;eu na&longs;citur, &longs;eu tran&longs;it, <lb/>a&longs;&longs;ingat illi, vt & apparet, conuer&longs;ionem ver&longs;us oc­<lb/>ca&longs;um. </s> | <s id="id.000751">Quanquam res po&longs;­<lb/>&longs;et fortè videri vtcùmque tolerabilis, &longs;i tota illa ma­<lb/>china vnico, ac &longs;implici motu circumferretur ver­<lb/>&longs;us occa&longs;um; &longs;ed cùm aliunde tot Planetæ circum­<lb/>ferantur quoque ver&longs;us ortum; quid potuit fieri <lb/>ab&longs;urdius, quàm fingi &longs;upra Planetas, &longs;upraque <lb/>omneis &longs;tellas fixas, ac &longs;phæras etiam cry&longs;tallinas, <lb/><expan abbr="va&longs;ti&longs;&longs;imã">va&longs;ti&longs;&longs;imam</expan> &longs;phæram Primi mobilis, quæ aduer&longs;us infe­<lb/>riores nitenteis in ortum &longs;uis ac lentis motibus, con­<lb/>tranitatur ip&longs;a, & ver&longs;us occa&longs;um incredibili ce­<lb/>leritate omneis abripiat? </s> |
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| <s>Ni&longs;i verò id non videtur e&longs;&longs;e captui accom-<pb pagenum="111"/>modatius, quàm raptum primi mobilis ad aërem <lb/>v&longs;que nobis vicinum extendere, vt &longs;eu Cometa, <lb/>&longs;eu quid aliud in eo fuerit, ver&longs;us occa&longs;um abripi <lb/>po&longs;&longs;it? </s> | <s id="id.000752">An pote&longs;t e&longs;&longs;e quidpiam <lb/>violentius; & cogitari tamen e&longs;&longs;e in rerum natura <lb/>perpetuum? </s> |
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| <s>Stupendum profectò, punctulum hoc &longs;olum <lb/>immotum con&longs;tare: & tantam circùm machinam ro­<lb/>tatione intereà illa incredibiliter celeri inde&longs;inen­<lb/>ter circumductam! Quare neque e&longs;t, cur Coperni­<lb/>canis vt ab&longs;urdum obijciant, fore vt nos in parte <lb/>quadam &longs;uperficiei terrenæ ex&longs;i&longs;tentes tanta mo­<lb/>ueamur celeritate, vt vix globus bombardicus cele­<lb/>ritatem tantam a&longs;&longs;equatur: &longs;iquidem retorquebi­<lb/>tur, quàm videatur e&longs;&longs;e incomparabiliter ab&longs;urdius <lb/>eiu&longs;dem circumductionis celeritatem transferre in <lb/>partem &longs;uperficiei &longs;phæræ Lunæ, Solis, Firmamen­<lb/>ti, Primi mobilis? </s> | <s id="id.000753">An e&longs;&longs;e quidpiam amfractuo&longs;ius; & at­<lb/>tribui tamen naturæ, quæ quò tendit, procedit &longs;em­<lb/>per per breui&longs;&longs;imam, & complanati&longs;&longs;imam viam? <lb/></s> |
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| <s>Nam nece&longs;&longs;e e&longs;t quidem in vno <lb/>horæ &longs;ecundo, &longs;eu in inter&longs;titio, quod e&longs;t ab vna me­<lb/>diocri pul&longs;atione arteriæ ad aliam, punctum terrenæ <lb/>&longs;uperficiei percurrere &longs;ub Aequatore, vbi motus e&longs;t <lb/>rapidi&longs;&longs;imus, orgyias, &longs;eu toi&longs;as circiter ducentas; <lb/>& à nobis, ver&longs;us dimidium latitudinis borealis ex­<lb/>&longs;i&longs;tentibus, circiter centum; at cùm vel ip&longs;ius Fir­<lb/>mamenti ambitus iuxta communem &longs;ententiam &longs;it <lb/>major Terræ ambitu plu&longs;quàm quinquagies millies, <lb/>nece&longs;&longs;e e&longs;t in vno horæ &longs;ecundo punctum ambitus <lb/>Firmamenti percurrere quinquagies millies tantun­<lb/>dem orgyiarum. </s> | <s id="id.000754">Terrâ profecto in ortum conuer&longs;â, quo compen­<lb/>dio&longs;iùs nihil e&longs;t, &longs;ui, lentique in ortum motus re­<lb/>linquentur ip&longs;is Planetis; & qui tam ip&longs;is, quam &longs;tel­<lb/>lis fixis ver&longs;us occa&longs;um ine&longs;&longs;e apparet, ex vnica Ter­<lb/>ræ in ortum conuer&longs;ione apparebit; adeò vt hæc <lb/>&longs;ola, &longs;implexque conuer&longs;io æqui<gap/>aleat illi primo mo-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.109.jpg" pagenum="110"/>bili; intereáque rapiditate, violentia, intricatione il­<lb/>la tanta liberet orbeis inferiores. </s> |
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| <s>Itaque dum vnum ab&longs;urdum de­<lb/>uitant, incidunt in aliud, quod &longs;it quinquagies mil­<lb/>lies ab&longs;urdius. </s> | <s id="id.000755">Quanquam aliunde <lb/>&longs;olidi orbes, qui in&longs;itos &longs;ibi Planetas deuehentes, <lb/>debuerunt e&longs;&longs;e contigui, vt inferiores abripi à &longs;u­<lb/>perioribus po&longs;&longs;ent, nulli planè &longs;unt; vt vel explorati <lb/>motus Veneris, & Mercurij &longs;upra, ac infra Solem, <lb/>& Cometarum traiectiones per &longs;patia illa &longs;atis con­<lb/>uincunt. </s> |
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| <s>Quantùm putas verò occurret ad­<lb/>augenda ab&longs;urditas, cùm acceptum fuerit punctum <lb/>in ambitu Primi mobilis, ac interpo&longs;ito pre&longs;ertìm <pb pagenum="112"/>vno, alterove cry&longs;tallino cælo? </s> | <s id="id.000756">Quare nec motus ille raptus pote&longs;t iam <lb/>ampliùs peragi; quandò Planetarum quidem glo­<lb/>bos per libera, fluxáque &longs;patia abripi non po&longs;&longs;e e&longs;t <lb/>&longs;atis per&longs;picuum; & retentis etiam &longs;olidis &longs;phæris, <lb/>manife&longs;tum e&longs;t, &longs;i &longs;uperficies inferiorum convexæ, <lb/>& &longs;uperiorum concauæ politi&longs;&longs;imæ fuerint (vt nece&longs;­<lb/>&longs;ariò, & vulgò cen&longs;ent) non po&longs;&longs;e planè inferiores <lb/>à &longs;uperioribus abripi, quippe de&longs;tituræ an&longs;is, qui­<lb/>bus in orbem impellantur, motumque accipiant; <lb/>ac po&longs;&longs;e ad &longs;ummum impul&longs;ionem pror&longs;ùm, &longs;eu in <lb/>rectum accipere, qualis profectò non admittetur. <lb/></s> |
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| <s>Et obijciant præ­<lb/>tereà parteis Terræ præ tanta illa vertigine di&longs;tra­<lb/>ctum iri: quàm erit magis di&longs;tractio timenda par­<lb/>tibus Primi mobilis, vt abreptis vertigine incom­<lb/>parabiliter rapidiore? </s> | <s id="id.000757">Noto intereà propter Cometas; cùm præter pro­<lb/>prias trajectiones, quæ &longs;unt nunc in boream, nunc <lb/>in au&longs;trum, nunc aliò; appareant etiam conuer&longs;ione <lb/>diurna ab ortu in occa&longs;um ferri; quid vero&longs;imilius <lb/>cogitari po&longs;&longs;it, quàm moueri illos motu vnico, &longs;eu <lb/>trajectione propria; circumductionem verò illam in <lb/>occa&longs;um e&longs;&longs;e duntaxat apparentem, ex conuer&longs;ione <lb/>Terræ diurna in ortum? </s> |
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| <s>Tamet&longs;i ip&longs;is partibus Terræ <lb/>nihil &longs;ube&longs;t periculi, quæ, quòd cohæreant omnes <lb/>inter &longs;e, motúque &longs;emper naturali, æquabilique fe­<lb/>rantur, perinde &longs;e habent, ac &longs;i quie&longs;cerent; &longs;olu&longs;­<lb/>que foret ca&longs;us timendus, &longs;i Terra impingeretur in <lb/>corpus ob&longs;i&longs;tens, aut aliàs quiete repentina con&longs;i­<lb/>&longs;teret; quod magis tamen timendum non e&longs;t, quàm <lb/>ne &longs;ecundum communem &longs;ententiam Mundus impin­<lb/>gatur, aut repentè conquie&longs;cat. </s> | <s id="id.000758">Hæc &longs;anè conuer&longs;io eiu&longs;­<lb/>modi e&longs;t, vt quicquid &longs;ur&longs;ùm, vltrave Terram, ac <lb/>per mundana &longs;patia &longs;eu e&longs;t, &longs;eu na&longs;citur, &longs;eu tran&longs;it, <lb/>a&longs;&longs;ingat illi, vt & apparet, conuer&longs;ionem ver&longs;us oc­<lb/>ca&longs;um. </s> |
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| <s>Quo loco id vi­<lb/>detur e&longs;&longs;e con&longs;ideratione dignum, &longs;i Terra fui&longs;&longs;et <lb/>&longs;uápte naturâ ad quie&longs;cendum in&longs;tituta, &longs;ortituram <lb/>hand-dubiè fui&longs;&longs;e aut pyramidalem, aut cubicam <lb/>formam, non, vt habet, orbicularem; cuius cau&longs;à <lb/>vti ad motum e&longs;t comparati&longs;&longs;ima, ita videtur peni­<lb/>tùs moueri &longs;uapte naturâ. </s> | <s id="id.000759">Ni&longs;i verò id non videtur e&longs;&longs;e captui accom-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.110.jpg" pagenum="111"/>modatius, quàm raptum primi mobilis ad aërem <lb/>v&longs;que nobis vicinum extendere, vt &longs;eu Cometa, <lb/>&longs;eu quid aliud in eo fuerit, ver&longs;us occa&longs;um abripi <lb/>po&longs;&longs;it? </s> |
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| <s>Neque obijcias Solem <lb/>quoque, imô etiam Firmamentum, atque adeò Mun­<lb/>dum &longs;ecundum Copernicanos orbicularis e&longs;&longs;e fi­<lb/>guræ nam & Soli ip&longs;i in centro circumvolutionem <lb/>non negant, quæ eadem po&longs;&longs;it conuenire Firmamen­<lb/>ti &longs;ideribus, circa proprios nempe axeis reuolutis, <lb/>vnde e&longs;&longs;e &longs;cintillatio à plæri&longs;que putatur; & quod ad <lb/>ip&longs;am Firmamenti, &longs;eu Mundi conuexitatem attinet, <lb/>&longs;it ne orbicularis an non; id neque ad illorum hy­<lb/>pothe&longs;in nece&longs;&longs;arium e&longs;t, neque pote&longs;t humanæ <lb/>menti innote&longs;cere vllâ conjecturâ </s></p><p type="main"> | <s id="id.000760">Stupendum profectò, punctulum hoc &longs;olum <lb/>immotum con&longs;tare: & tantam circùm machinam ro­<lb/>tatione intereà illa incredibiliter celeri inde&longs;inen­<lb/>ter circumductam! Quare neque e&longs;t, cur Coperni­<lb/>canis vt ab&longs;urdum obijciant, fore vt nos in parte <lb/>quadam &longs;uperficiei terrenæ ex&longs;i&longs;tentes tanta mo­<lb/>ueamur celeritate, vt vix globus bombardicus cele­<lb/>ritatem tantam a&longs;&longs;equatur: &longs;iquidem retorquebi­<lb/>tur, quàm videatur e&longs;&longs;e incomparabiliter ab&longs;urdius <lb/>eiu&longs;dem circumductionis celeritatem transferre in <lb/>partem &longs;uperficiei &longs;phæræ Lunæ, Solis, Firmamen­<lb/>ti, Primi mobilis? </s> |
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| <s>VIII. <!-- KEEP S--></s> | <s id="id.000761">Nam nece&longs;&longs;e e&longs;t quidem in vno <lb/>horæ &longs;ecundo, &longs;eu in inter&longs;titio, quod e&longs;t ab vna me­<lb/>diocri pul&longs;atione arteriæ ad aliam, punctum terrenæ <lb/>&longs;uperficiei percurrere &longs;ub Aequatore, vbi motus e&longs;t <lb/>rapidi&longs;&longs;imus, orgyias, &longs;eu toi&longs;as circiter ducentas; <lb/>& à nobis, ver&longs;us dimidium latitudinis borealis ex­<lb/>&longs;i&longs;tentibus, circiter centum; at cùm vel ip&longs;ius Fir­<lb/>mamenti ambitus iuxta communem &longs;ententiam &longs;it <lb/>major Terræ ambitu plu&longs;quàm quinquagies millies, <lb/>nece&longs;&longs;e e&longs;t in vno horæ &longs;ecundo punctum ambitus <lb/>Firmamenti percurrere quinquagies millies tantun­<lb/>dem orgyiarum. </s> |
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| <s>Obiter verò, ne id moretur, quòd circulari <pb pagenum="113"/>motui ob&longs;tare videatur Terræ grauitas, cuius propri­<lb/>um &longs;it id corpus, cui ine&longs;t, deor&longs;ùm rectà pellere; <lb/>ideò &longs;ciendum e&longs;t grauitatem affectionem e&longs;&longs;e non <lb/>totius Terræ, &longs;ed partium ip&longs;ius, donec ab ip&longs;a auel­<lb/>luntur. </s> | <s id="id.000762">Itaque dum vnum ab&longs;urdum de­<lb/>uitant, incidunt in aliud, quod &longs;it quinquagies mil­<lb/>lies ab&longs;urdius. </s> |
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| <s>Declarata penè res manet ex iis, quæ dixi <lb/>&longs;uperiore Epi&longs;tola, cùm de corporum terrenorum <lb/>attractione ab ip&longs;a Terra. <!-- KEEP S--></s> | <s id="id.000763">Quantùm putas verò occurret ad­<lb/>augenda ab&longs;urditas, cùm acceptum fuerit punctum <lb/>in ambitu Primi mobilis, ac interpo&longs;ito pre&longs;ertìm <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.111.jpg" pagenum="112"/>vno, alterove cry&longs;tallino cælo? </s> |
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| <s>Nam globus quidem ip&longs;e <lb/>Terræ &longs;ecundum &longs;e totum &longs;pectatùs nullo indiget <lb/>motu recto, quo &longs;e in locum &longs;uum recipiat, è quo <lb/>nunquàm egreditur; indigent verò eius partes, vt <lb/>&longs;e in <gap/>p&longs;um globum recipiant, à quo contingit illas <lb/>inter dum emoüeri, ac &longs;eparari. </s> | <s id="id.000764">Et obijciant præ­<lb/>tereà parteis Terræ præ tanta illa vertigine di&longs;tra­<lb/>ctum iri: quàm erit magis di&longs;tractio timenda par­<lb/>tibus Primi mobilis, vt abreptis vertigine incom­<lb/>parabiliter rapidiore? </s> |
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| <s>Quamobrem nihil <lb/>fuit nece&longs;&longs;e indere toti ip&longs;i globo grauitatem, &longs;eu <lb/>vìm, impetumque, quo rectà ferretur in locum, ex­<lb/>tra quem con&longs;titutus foret; &longs;ed &longs;atis fuit inderevim, <lb/>qua contineret &longs;uas parteis, ea&longs;demque retraheret, <lb/>&longs;i contingeret eas diuelli. </s> | <s id="id.000765">Tamet&longs;i ip&longs;is partibus Terræ <lb/>nihil &longs;ube&longs;t periculi, quæ, quòd cohæreant omnes <lb/>inter &longs;e, motúque &longs;emper naturali, æquabilique fe­<lb/>rantur, perinde &longs;e habent, ac &longs;i quie&longs;cerent; &longs;olu&longs;­<lb/>que foret ca&longs;us timendus, &longs;i Terra impingeretur in <lb/>corpus ob&longs;i&longs;tens, aut aliàs quiete repentina con&longs;i­<lb/>&longs;teret; quod magis tamen timendum non e&longs;t, quàm <lb/>ne &longs;ecundum communem &longs;ententiam Mundus impin­<lb/>gatur, aut repentè conquie&longs;cat. </s> |
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| <s>Scilicet motus i&longs;te rectus, <lb/>quem grauitatis dicimus, vnitiuus e&longs;t, vt &longs;ic dicam, <lb/>& congregatiuus omnium Terræ partium; indició­<lb/>que e&longs;t, quòd tam ex parte no&longs;tri, quàm ex parte <lb/>antipodum, & vndequáque in idem con&longs;piret; &longs;ed <lb/>cùm &longs;it congregatiuus partium relatarum in ip&longs;um <lb/>globum, non e&longs;t tamen congregatiuus ip&longs;ius globi <lb/>cum re alia, vt &longs;i Terra e&longs;&longs;et cum Luna, orbibu&longs;ve <lb/>aliis mundi congreganda. </s> | <s id="id.000766">Quo loco id vi­<lb/>detur e&longs;&longs;e con&longs;ideratione dignum, &longs;i Terra fui&longs;&longs;et <lb/>&longs;uápte naturâ ad quie&longs;cendum in&longs;tituta, &longs;ortituram <lb/>hand-dubiè fui&longs;&longs;e aut pyramidalem, aut cubicam <lb/>formam, non, vt habet, orbicularem; cuius cau&longs;à <lb/>vti ad motum e&longs;t comparati&longs;&longs;ima, ita videtur peni­<lb/>tùs moueri &longs;uapte naturâ. </s> |
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| <s>Neque dici pote&longs;t gra­<lb/>uitatem, &longs;eu vim ad hunc motum, conce&longs;&longs;am e&longs;&longs;e <lb/>toti Terræ, vt vel &longs;e recipiat in locum mundi infimum, <lb/>vel recepta, &longs;e in illo <expan abbr="cõtineat">contineat</expan>. </s> | <s id="id.000767">Neque obijcias Solem <lb/>quoque, imô etiam Firmamentum, atque adeò Mun­<lb/>dum &longs;ecundum Copernicanos orbicularis e&longs;&longs;e fi­<lb/>guræ nam & Soli ip&longs;i in centro circumvolutionem <lb/>non negant, quæ eadem po&longs;&longs;it conuenire Firmamen­<lb/>ti &longs;ideribus, circa proprios nempe axeis reuolutis, <lb/>vnde e&longs;&longs;e &longs;cintillatio à plæri&longs;que putatur; & quod ad <lb/>ip&longs;am Firmamenti, &longs;eu Mundi conuexitatem attinet, <lb/>&longs;it ne orbicularis an non; id neque ad illorum hy­<lb/>pothe&longs;in nece&longs;&longs;arium e&longs;t, neque pote&longs;t humanæ <lb/>menti innote&longs;cere vllâ conjecturâ </s></p><p type="main"> |
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| <s>Siquidem in mundo ni­<lb/>hil <expan abbr="infimũ">infimum</expan>, aut &longs;upremum e&longs;t, ni&longs;i comparatè ad &longs;itum <lb/>animalis, ac poti&longs;&longs;imùm hominis, cuius vna e&longs;t pars <pb pagenum="114"/>quæ dicitur &longs;uprema, videlicet caput, alia, quæ in­<lb/>fima, videlicet pedes; eo modo, quo non e&longs;t etiam <lb/>in mundo aliquid dextrum, aut &longs;ini&longs;trum, &longs;ed com­<lb/>paratè duntaxat ad &longs;itum eiu&longs;dem animalis, cuius <lb/>partes dextra, ac &longs;ini&longs;tra &longs;unt propriæ. </s> | <s id="id.000768">VIII. <!-- KEEP S--></s> |
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| <s>Ex quo fit, <lb/>vt quemadmodum pars mundi oriens tibi dextra non <lb/>dicitur, ni&longs;i quatenùs partem dextram ad ip&longs;um con­<lb/>uertis; cùm &longs;i conuerteris &longs;ini&longs;tram, &longs;ini&longs;tra ex&longs;ti­<lb/>tura &longs;it; ita pars mundi verticalis non dicatur e&longs;&longs;e &longs;u­<lb/>prema, ni&longs;i quatenùs partem tui &longs;upremam ip&longs;i ob­<lb/>uer&longs;am habes; cùm &longs;i ad antipodas tran&longs;iens obuer­<lb/>teris infimam, eadem &longs;it infima futura. </s> | <s id="id.000769">Obiter verò, ne id moretur, quòd circulari <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.112.jpg" pagenum="113"/>motui ob&longs;tare videatur Terræ grauitas, cuius propri­<lb/>um &longs;it id corpus, cui ine&longs;t, deor&longs;ùm rectà pellere; <lb/>ideò &longs;ciendum e&longs;t grauitatem affectionem e&longs;&longs;e non <lb/>totius Terræ, &longs;ed partium ip&longs;ius, donec ab ip&longs;a auel­<lb/>luntur. </s> |
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| <s>Dices in&longs;i­<lb/>mum accipiendum non e&longs;&longs;e in mundi extremo, &longs;ed <lb/>&longs;olùm in centro, &longs;eu in medio, quod idem &longs;it cen­<lb/>trum, &longs;eu medium Telluris. <!-- KEEP S--></s> | <s id="id.000770">Declarata penè res manet ex iis, quæ dixi <lb/>&longs;uperiore Epi&longs;tola, cùm de corporum terrenorum <lb/>attractione ab ip&longs;a Terra. <!-- KEEP S--></s> |
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| <s>At primùm, licet con­<lb/>cedatur habere mundum centrum, &longs;eu medium; <lb/>non &longs;equitur nihilominùs po&longs;&longs;e illud infimum dici; <lb/>vt neque licet vnbilicus &longs;it media in homine pars, di­<lb/>ci proptereà infima pote&longs;t Et &longs;anè, quod opponi­<lb/>tur medio, non &longs;upremum e&longs;t, &longs;ed extremum, &longs;unt­<lb/>que &longs;upremum, & infimum oppo&longs;itæ partes in eo­<lb/>dem extremo; etiam in ip&longs;a Terra; cuius locum me­<lb/>dium non alia ratione infimum habemus, quam vt <lb/>ip&longs;am (&longs;ic loqui liceat) infimitatem bipartiamur, qua <lb/>nos antipodibus, antipodes nobis infimi videntur. <lb/></s> | <s id="id.000771">Nam globus quidem ip&longs;e <lb/>Terræ &longs;ecundum &longs;e totum &longs;pectatùs nullo indiget <lb/>motu recto, quo &longs;e in locum &longs;uum recipiat, è quo <lb/>nunquàm egreditur; indigent verò eius partes, vt <lb/>&longs;e in <gap/>p&longs;um globum recipiant, à quo contingit illas <lb/>inter dum emoüeri, ac &longs;eparari. </s> |
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| <s>Deinde, ecquis dicere valeat, an, & qualis &longs;it pars mun­<lb/>di extrema, ac proindean, & vbi &longs;it illius centrum, <lb/>&longs;eu medium; præ&longs;ertìm verò cùm videamus non abs <lb/>ratione controuerti, moueantur-ne fixæ circa Ter­<lb/>ram, an-non; & &longs;int-ne omnes in eadem &longs;uperficie, <pb pagenum="115"/>vel potiùs (in&longs;tar planetarum, qui in eadem e&longs;&longs;e ap­<lb/>parent, neque tamen &longs;unt) longiùs, & remotiùs in <lb/>immen&longs;um di&longs;per&longs;æ? </s> | <s id="id.000772">Quamobrem nihil <lb/>fuit nece&longs;&longs;e indere toti ip&longs;i globo grauitatem, &longs;eu <lb/>vìm, impetumque, quo rectà ferretur in locum, ex­<lb/>tra quem con&longs;titutus foret; &longs;ed &longs;atis fuit inderevim, <lb/>qua contineret &longs;uas parteis, ea&longs;demque retraheret, <lb/>&longs;i contingeret eas diuelli. </s> |
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| <s>Nimirúm ex quo tanta e&longs;t di­<lb/>&longs;tantia, vt vi&longs;us no&longs;ter di&longs;cernere intercepta &longs;patia <lb/>non po&longs;&longs;it, apparent ip&longs;i omnia eiu&longs;dem e&longs;&longs;e di&longs;tan­<lb/>tiæ, omnia in eadem circumferentia, cuius ip&longs;e cen­<lb/>trum &longs;it, vbi &longs;e conuertens ea circum&longs;pectârit: adeò <lb/>vt, &longs;iue in Luna, &longs;iue in Sole, &longs;iue in quacumque <lb/>parte immen&longs;i huius &longs;patij te con&longs;titutum e&longs;&longs;e fingas, <lb/>perinde &longs;is judicaturus & Mundum e&longs;&longs;e &longs;phæricum, <lb/>& ex&longs;i&longs;tere te in centro eius circumferentiæ, in qua <lb/>& omnia &longs;idera, & quæcumque demùm procùl vi­<lb/>deris, imaginére con&longs;tituta. </s> | <s id="id.000773">Scilicet motus i&longs;te rectus, <lb/>quem grauitatis dicimus, vnitiuus e&longs;t, vt &longs;ic dicam, <lb/>& congregatiuus omnium Terræ partium; indició­<lb/>que e&longs;t, quòd tam ex parte no&longs;tri, quàm ex parte <lb/>antipodum, & vndequáque in idem con&longs;piret; &longs;ed <lb/>cùm &longs;it congregatiuus partium relatarum in ip&longs;um <lb/>globum, non e&longs;t tamen congregatiuus ip&longs;ius globi <lb/>cum re alia, vt &longs;i Terra e&longs;&longs;et cum Luna, orbibu&longs;ve <lb/>aliis mundi congreganda. </s> |
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| <s>Dignum e&longs;t certè admi­<lb/>ratione ip&longs;os Planetas, ex quibus &longs;olis, vt nobis vi­<lb/>cinioribus, conjecturam quandam licet capere, ad­<lb/>mitti à non-nemine habere motus excentricos, &longs;eu <lb/>quorum centrum alibi, quàm in centro Telluris &longs;it; <lb/>& Terræ tamen centrum id vulgò haberi, circa quod <lb/>globorum cæle&longs;tium circumductiones peragantur? <lb/></s> | <s id="id.000774">Neque dici pote&longs;t gra­<lb/>uitatem, &longs;eu vim ad hunc motum, conce&longs;&longs;am e&longs;&longs;e <lb/>toti Terræ, vt vel &longs;e recipiat in locum mundi infimum, <lb/>vel recepta, &longs;e in illo <expan abbr="cõtineat">contineat</expan>. </s> |
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| <s>Heinc proinde dico ne&longs;ciri à nobis, an dum terrena <lb/>corpora, vbi &longs;emota fuerint, referuntur in ip&longs;am <lb/>Terram, ferantur &longs;imùl in centrum Mundi; & <lb/>quamuis forta&longs;&longs;è ferantur, e&longs;&longs;e id tamen ex acci­<lb/>denti; vti e&longs;t etiam ex accidenti, quod in centrum <lb/>Terræ ip&longs;ius ferantur, in quo, tanquam in mero <lb/>puncto neque recipi, neque quietem a&longs;&longs;equi va­<lb/>leant. </s> | <s id="id.000775">Siquidem in mundo ni­<lb/>hil <expan abbr="infimũ">infimum</expan>, aut &longs;upremum e&longs;t, ni&longs;i comparatè ad &longs;itum <lb/>animalis, ac poti&longs;&longs;imùm hominis, cuius vna e&longs;t pars <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.113.jpg" pagenum="114"/>quæ dicitur &longs;uprema, videlicet caput, alia, quæ in­<lb/>fima, videlicet pedes; eo modo, quo non e&longs;t etiam <lb/>in mundo aliquid dextrum, aut &longs;ini&longs;trum, &longs;ed com­<lb/>paratè duntaxat ad &longs;itum eiu&longs;dem animalis, cuius <lb/>partes dextra, ac &longs;ini&longs;tra &longs;unt propriæ. </s> |
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| <s>Scilicet tendunt per &longs;e in Terram, veluti in <lb/>totum, ac principium &longs;uum, ip&longs;amque a&longs;&longs;equutæ <lb/>ita conquie&longs;cunt, vt peruenire pr&ecedil;terà ad v&longs;que cen­<lb/>trum non magis curent, quàm infans, vbi &longs;e recepit <pb pagenum="116"/>in &longs;uæ nutricis gremium, petere prætereà eius inte­<lb/>ranea. </s> | <s id="id.000776">Ex quo fit, <lb/>vt quemadmodum pars mundi oriens tibi dextra non <lb/>dicitur, ni&longs;i quatenùs partem dextram ad ip&longs;um con­<lb/>uertis; cùm &longs;i conuerteris &longs;ini&longs;tram, &longs;ini&longs;tra ex&longs;ti­<lb/>tura &longs;it; ita pars mundi verticalis non dicatur e&longs;&longs;e &longs;u­<lb/>prema, ni&longs;i quatenùs partem tui &longs;upremam ip&longs;i ob­<lb/>uer&longs;am habes; cùm &longs;i ad antipodas tran&longs;iens obuer­<lb/>teris infimam, eadem &longs;it infima futura. </s> |
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| <s>Ex accidenti verò e&longs;t, quòd dirigantur &longs;i­<lb/>mùl in centrum, quatenus tendentes in Terram per <lb/>breui&longs;&longs;imam lineam, contingit hanc lineam, &longs;i pro­<lb/>ducta intelligatur, tran&longs;ire per centrum; vti ex acci­<lb/>denti e&longs;t, quòd dum ego heinc contendo Pari&longs;ios, <lb/>Caletum ver&longs;us dirigar, de quo tamen non cogito, <lb/>quatenùs eadem via e&longs;t, quæ continüata perducit <lb/>Caletum. </s> | <s id="id.000777">Dices in&longs;i­<lb/>mum accipiendum non e&longs;&longs;e in mundi extremo, &longs;ed <lb/>&longs;olùm in centro, &longs;eu in medio, quod idem &longs;it cen­<lb/>trum, &longs;eu medium Telluris. <!-- KEEP S--></s> |
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| <s>Non repeto porrô quæ &longs;unt circa attra­<lb/>ctionem deducta; elicio &longs;olum grauitatem, quæ e&longs;t <lb/>in ip&longs;is partibus Terræ, terreni&longs;ve corporibus, non <lb/>tam e&longs;&longs;e vim in&longs;itam, quàm ex attractu Terræ im­<lb/>pre&longs;&longs;am; idque po&longs;&longs;e intelligi adjuncto exemplo ip­<lb/>&longs;ius magnetis. </s> | <s id="id.000778">At primùm, licet con­<lb/>cedatur habere mundum centrum, &longs;eu medium; <lb/>non &longs;equitur nihilominùs po&longs;&longs;e illud infimum dici; <lb/>vt neque licet vnbilicus &longs;it media in homine pars, di­<lb/>ci proptereà infima pote&longs;t Et &longs;anè, quod opponi­<lb/>tur medio, non &longs;upremum e&longs;t, &longs;ed extremum, &longs;unt­<lb/>que &longs;upremum, & infimum oppo&longs;itæ partes in eo­<lb/>dem extremo; etiam in ip&longs;a Terra; cuius locum me­<lb/>dium non alia ratione infimum habemus, quam vt <lb/>ip&longs;am (&longs;ic loqui liceat) infimitatem bipartiamur, qua <lb/>nos antipodibus, antipodes nobis infimi videntur. <lb/></s> |
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| <s>Accipito enim, & contineto manu la­<lb/>minulam ferri paucarum vnciarum. </s> | <s id="id.000779">Deinde, ecquis dicere valeat, an, & qualis &longs;it pars mun­<lb/>di extrema, ac proindean, & vbi &longs;it illius centrum, <lb/>&longs;eu medium; præ&longs;ertìm verò cùm videamus non abs <lb/>ratione controuerti, moueantur-ne fixæ circa Ter­<lb/>ram, an-non; & &longs;int-ne omnes in eadem &longs;uperficie, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.114.jpg" pagenum="115"/>vel potiùs (in&longs;tar planetarum, qui in eadem e&longs;&longs;e ap­<lb/>parent, neque tamen &longs;unt) longiùs, & remotiùs in <lb/>immen&longs;um di&longs;per&longs;æ? </s> |
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| <s>Si &longs;upponatur <lb/>deinde manui magnes aliquis robu&longs;ti&longs;&longs;imus, expe­<lb/>riere pondus non iam vnciarum, &longs;ed librarum aliquot <lb/>e&longs;&longs;e. </s> | <s id="id.000780">Nimirúm ex quo tanta e&longs;t di­<lb/>&longs;tantia, vt vi&longs;us no&longs;ter di&longs;cernere intercepta &longs;patia <lb/>non po&longs;&longs;it, apparent ip&longs;i omnia eiu&longs;dem e&longs;&longs;e di&longs;tan­<lb/>tiæ, omnia in eadem circumferentia, cuius ip&longs;e cen­<lb/>trum &longs;it, vbi &longs;e conuertens ea circum&longs;pectârit: adeò <lb/>vt, &longs;iue in Luna, &longs;iue in Sole, &longs;iue in quacumque <lb/>parte immen&longs;i huius &longs;patij te con&longs;titutum e&longs;&longs;e fingas, <lb/>perinde &longs;is judicaturus & Mundum e&longs;&longs;e &longs;phæricum, <lb/>& ex&longs;i&longs;tere te in centro eius circumferentiæ, in qua <lb/>& omnia &longs;idera, & quæcumque demùm procùl vi­<lb/>deris, imaginére con&longs;tituta. </s> |
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| <s>Et quia fatebere hoc pondus non tam e&longs;&longs;e in&longs;i­<lb/>rum ferro, quàm impre&longs;&longs;um ex attractione magne­<lb/>tis manui &longs;uppo&longs;iti; idcircô vbi agitur de pondere <lb/>&longs;eu grauitate lapidis, alteriu&longs;ve corporis terreni, in­<lb/>telligi pote&longs;t ea grauitas non tam conuenire huiu&longs;­<lb/>modi corpori ex &longs;e, quàm ex attractione &longs;uppo&longs;itæ <lb/>Terræ. <!-- KEEP S--></s> | <s id="id.000781">Dignum e&longs;t certè admi­<lb/>ratione ip&longs;os Planetas, ex quibus &longs;olis, vt nobis vi­<lb/>cinioribus, conjecturam quandam licet capere, ad­<lb/>mitti à non-nemine habere motus excentricos, &longs;eu <lb/>quorum centrum alibi, quàm in centro Telluris &longs;it; <lb/>& Terræ tamen centrum id vulgò haberi, circa quod <lb/>globorum cæle&longs;tium circumductiones peragantur? <lb/></s> |
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| <s>Quippe & finge quoties ferrum manu &longs;u­<lb/>&longs;tenta&longs;ti fui&longs;&longs;e magnetem &longs;uppo&longs;itum, quod &longs;uppo­<lb/>&longs;itum tamen ignorares, crederes omninô eiu&longs;modi <lb/>pondus e&longs;&longs;e in&longs;itum ip&longs;i ferro, quod e&longs;&longs;et tamen at­<lb/>tractitium: quid ni igitur idem po&longs;&longs;is de lapide <lb/>credere, quòd illum nunquam &longs;u&longs;tentâtis &longs;ine Terra <lb/>&longs;uppo&longs;ita, quam ne&longs;cieris e&longs;&longs;e magnetem ingentem? <pb pagenum="117"/>Vt hoc obiter heic attingam; dum vides maiorem <lb/>grauitatem, &longs;iue attractionem imprimi &longs;erro à ma­<lb/>gnete, quàm ab ip&longs;a Terra (à qua etiam magnes, <lb/>dum &longs;u&longs;penditur, ferrum abducit) non id videtur <lb/>e&longs;&longs;e aliunde, quàm ex eo, quòd virtus attractrix e&longs;t <lb/>in magnete collectior, atque adeò inten&longs;ior pro mo­<lb/>dulo corporis, quàm in ip&longs;o corpore Terræ, in quo <lb/>exten&longs;ior e&longs;t, neque in &longs;ingulis partibus, &longs;ed in to­<lb/>to &longs;olùm explicatur quanta e&longs;t tota; co modo, quo <lb/>&longs;i linguam grano &longs;alis admoueas, id ip&longs;am poten­<lb/>tius a&longs;&longs;iciet, quàm occanus; non quod totus ocea­<lb/>nus &longs;al&longs;edinis amplius non habeat, &longs;ed quòd &longs;al­<lb/>&longs;edo in oceano diffa&longs;ior &longs;it, neque, quà linguam ad­<lb/>moues, adeò collecta, & explicita, ac in grano <lb/>vnico &longs;alis. </s> | <s id="id.000782">Heinc proinde dico ne&longs;ciri à nobis, an dum terrena <lb/>corpora, vbi &longs;emota fuerint, referuntur in ip&longs;am <lb/>Terram, ferantur &longs;imùl in centrum Mundi; & <lb/>quamuis forta&longs;&longs;è ferantur, e&longs;&longs;e id tamen ex acci­<lb/>denti; vti e&longs;t etiam ex accidenti, quod in centrum <lb/>Terræ ip&longs;ius ferantur, in quo, tanquam in mero <lb/>puncto neque recipi, neque quietem a&longs;&longs;equi va­<lb/>leant. </s> |
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| <s>Magnetem, & ferrum vt mittam, cùm <lb/>grauitas lapidis in Terram cadentis intendatur, & ex <lb/>nouorum graduum acce&longs;&longs;ione maior euadat; ac i&longs;ta <lb/>inten&longs;io, &longs;eu graduum acce&longs;&longs;io non videatur aliun­<lb/>de e&longs;&longs;e, quàm ex ip&longs;a Terræ attractione (adjuncta <lb/>modo expo&longs;ito impal&longs;ione aëris) ecquid nam pro­<lb/>babilius e&longs;t, quàm gradum grauitatis primum, la­<lb/>pidique nondum moto conuenientem, ex eadem e&longs;&longs;e <lb/>attractione? </s> | <s id="id.000783">Scilicet tendunt per &longs;e in Terram, veluti in <lb/>totum, ac principium &longs;uum, ip&longs;amque a&longs;&longs;equutæ <lb/>ita conquie&longs;cunt, vt peruenire pr&ecedil;terà ad v&longs;que cen­<lb/>trum non magis curent, quàm infans, vbi &longs;e recepit <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.115.jpg" pagenum="116"/>in &longs;uæ nutricis gremium, petere prætereà eius inte­<lb/>ranea. </s> |
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| <s>Eadem &longs;anè e&longs;t grauitatis &longs;pecies, neque <lb/>qualitas vlla meliùs, quàm à congenea intenditur. <lb/></s> | <s id="id.000784">Ex accidenti verò e&longs;t, quòd dirigantur &longs;i­<lb/>mùl in centrum, quatenus tendentes in Terram per <lb/>breui&longs;&longs;imam lineam, contingit hanc lineam, &longs;i pro­<lb/>ducta intelligatur, tran&longs;ire per centrum; vti ex acci­<lb/>denti e&longs;t, quòd dum ego heinc contendo Pari&longs;ios, <lb/>Caletum ver&longs;us dirigar, de quo tamen non cogito, <lb/>quatenùs eadem via e&longs;t, quæ continüata perducit <lb/>Caletum. </s> |
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| <s>An interim forte hærebis, quòd de leuitate grauita­<lb/>ti oppo&longs;ita, nonnulli&longs;que corporibus conueniente <lb/>nihil intermi&longs;ceam? </s> | <s id="id.000785">Non repeto porrô quæ &longs;unt circa attra­<lb/>ctionem deducta; elicio &longs;olum grauitatem, quæ e&longs;t <lb/>in ip&longs;is partibus Terræ, terreni&longs;ve corporibus, non <lb/>tam e&longs;&longs;e vim in&longs;itam, quàm ex attractu Terræ im­<lb/>pre&longs;&longs;am; idque po&longs;&longs;e intelligi adjuncto exemplo ip­<lb/>&longs;ius magnetis. </s> |
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| <s>Sed facio nempe, quòd leuitas <lb/>nihil aliud &longs;it quàm grauitas minor; &longs;icque hæ duæ <lb/>&longs;int <expan abbr="quālitates">quallitates</expan>, &longs;eu proprietates corporum non ab­<lb/>&longs;olutæ, &longs;ed re&longs;pectiuæ; quatenùs nempe vnum cor-<pb pagenum="118"/>pus dicitur graue re&longs;pectu leuioris, & leue re&longs;pectu <lb/>grauioris, &longs;icque leue e&longs;t, quod e&longs;t minùs graue, <lb/>& graue, quod e&longs;t minùs leue. </s> | <s id="id.000786">Accipito enim, & contineto manu la­<lb/>minulam ferri paucarum vnciarum. </s> |
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| <s>Vt exemplo dicam, <lb/>comparentur lapis, aqua, oleum, aër, ignis, quæ <lb/>terrena e&longs;&longs;e corpora priùs diximus. </s> | <s id="id.000787">Si &longs;upponatur <lb/>deinde manui magnes aliquis robu&longs;ti&longs;&longs;imus, expe­<lb/>riere pondus non iam vnciarum, &longs;ed librarum aliquot <lb/>e&longs;&longs;e. </s> |
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| <s>Ob&longs;eruabis aquam <lb/>&longs;upra Terræ &longs;uperficiem, vt in lacu, fo&longs;&longs;a, aut, &longs;i <lb/>velis, intra lebetem planè quie&longs;cere: verùm &longs;i la­<lb/>pis immittatur, is ad imum ita de&longs;cendet, vt aqua <lb/>cedens locum, a&longs;cendat. </s> | <s id="id.000788">Et quia fatebere hoc pondus non tam e&longs;&longs;e in&longs;i­<lb/>rum ferro, quàm impre&longs;&longs;um ex attractione magne­<lb/>tis manui &longs;uppo&longs;iti; idcircô vbi agitur de pondere <lb/>&longs;eu grauitate lapidis, alteriu&longs;ve corporis terreni, in­<lb/>telligi pote&longs;t ea grauitas non tam conuenire huiu&longs;­<lb/>modi corpori ex &longs;e, quàm ex attractione &longs;uppo&longs;itæ <lb/>Terræ. <!-- KEEP S--></s> |
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| <s>Sic oleum in eodem va­<lb/>&longs;e optimè quie&longs;cet: &longs;ed infundatur aqua, ea petet <lb/>fundum, & oleum &longs;ummum. </s> | <s id="id.000789">Quippe & finge quoties ferrum manu &longs;u­<lb/>&longs;tenta&longs;ti fui&longs;&longs;e magnetem &longs;uppo&longs;itum, quod &longs;uppo­<lb/>&longs;itum tamen ignorares, crederes omninô eiu&longs;modi <lb/>pondus e&longs;&longs;e in&longs;itum ip&longs;i ferro, quod e&longs;&longs;et tamen at­<lb/>tractitium: quid ni igitur idem po&longs;&longs;is de lapide <lb/>credere, quòd illum nunquam &longs;u&longs;tentâtis &longs;ine Terra <lb/>&longs;uppo&longs;ita, quam ne&longs;cieris e&longs;&longs;e magnetem ingentem? <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.116.jpg" pagenum="117"/>Vt hoc obiter heic attingam; dum vides maiorem <lb/>grauitatem, &longs;iue attractionem imprimi &longs;erro à ma­<lb/>gnete, quàm ab ip&longs;a Terra (à qua etiam magnes, <lb/>dum &longs;u&longs;penditur, ferrum abducit) non id videtur <lb/>e&longs;&longs;e aliunde, quàm ex eo, quòd virtus attractrix e&longs;t <lb/>in magnete collectior, atque adeò inten&longs;ior pro mo­<lb/>dulo corporis, quàm in ip&longs;o corpore Terræ, in quo <lb/>exten&longs;ior e&longs;t, neque in &longs;ingulis partibus, &longs;ed in to­<lb/>to &longs;olùm explicatur quanta e&longs;t tota; co modo, quo <lb/>&longs;i linguam grano &longs;alis admoueas, id ip&longs;am poten­<lb/>tius a&longs;&longs;iciet, quàm occanus; non quod totus ocea­<lb/>nus &longs;al&longs;edinis amplius non habeat, &longs;ed quòd &longs;al­<lb/>&longs;edo in oceano diffa&longs;ior &longs;it, neque, quà linguam ad­<lb/>moues, adeò collecta, & explicita, ac in grano <lb/>vnico &longs;alis. </s> |
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| <s>In eodem va&longs;e non <lb/>&longs;it liquor, quie&longs;cet in illo optimè aër: &longs;ubeat oleum; <lb/>id deor&longs;ùm tendet, & aër &longs;ur&longs;ùm. </s> | <s id="id.000790">Magnetem, & ferrum vt mittam, cùm <lb/>grauitas lapidis in Terram cadentis intendatur, & ex <lb/>nouorum graduum acce&longs;&longs;ione maior euadat; ac i&longs;ta <lb/>inten&longs;io, &longs;eu graduum acce&longs;&longs;io non videatur aliun­<lb/>de e&longs;&longs;e, quàm ex ip&longs;a Terræ attractione (adjuncta <lb/>modo expo&longs;ito impal&longs;ione aëris) ecquid nam pro­<lb/>babilius e&longs;t, quàm gradum grauitatis primum, la­<lb/>pidique nondum moto conuenientem, ex eadem e&longs;&longs;e <lb/>attractione? </s> |
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| <s>Denique ignis <lb/>&longs;uápte naturâ ip&longs;i Terræ incumberet; at quia immi­<lb/>net, circum&longs;tatque aër; ideò is viciniam Terræ appe­<lb/>tit, & cogitur ignis ex Terra abire. </s> | <s id="id.000791">Eadem &longs;anè e&longs;t grauitatis &longs;pecies, neque <lb/>qualitas vlla meliùs, quàm à congenea intenditur. <lb/></s> |
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| <s>Ita corpora i&longs;ta <lb/>omnia dicentur grauia, & leuia comparatè, &longs;eu re&longs;­<lb/>pectiuè; & lapis quidem graui&longs;&longs;imus, quia maximè <lb/>omnium attrahitur; &longs;iue minimè omnium leuis, quia <lb/>minimùm abducitur: aqua verò, quæ re&longs;pectu la­<lb/>pidis leuis e&longs;t, grauis erit re&longs;pectu olei; & oleum le­<lb/>ue re&longs;pectu aquæ, erit graue re&longs;pectu aëris; & aër le­<lb/>uis re&longs;pectu olei, grauis erit re&longs;pectu ignis: ignis <lb/>po&longs;tremò omnium leui&longs;&longs;imus cen&longs;ebitur, quia ma­<lb/>ximè omnium attollitur; &longs;iue omnium minimè gra­<lb/>uis, quia ex omnibus, quæ attrahuntur à Terra, <lb/>trahitur ip&longs;e minimùm. </s> | <s id="id.000792">An interim forte hærebis, quòd de leuitate grauita­<lb/>ti oppo&longs;ita, nonnulli&longs;que corporibus conueniente <lb/>nihil intermi&longs;ceam? </s> |
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| <s>Heinc quia difficultas e&longs;t de <lb/>&longs;olo igne; non e&longs;t, cur dum &longs;ur&longs;ùm contendit, exi­<lb/>&longs;times illum &longs;uam, vt vulgò dicunt, quærere &longs;phæ­<lb/>ram (ad quam non ignis ex omnibus &longs;iluis perue-<pb pagenum="119"/>nire vnquam potis &longs;it) quippe &longs;ur&longs;ùm non tam vi <lb/>propria, quàm ab aëre impul&longs;us contendit. </s> | <s id="id.000793">Sed facio nempe, quòd leuitas <lb/>nihil aliud &longs;it quàm grauitas minor; &longs;icque hæ duæ <lb/>&longs;int <expan abbr="quālitates">quallitates</expan>, &longs;eu proprietates corporum non ab­<lb/>&longs;olutæ, &longs;ed re&longs;pectiuæ; quatenùs nempe vnum cor-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.117.jpg" pagenum="118"/>pus dicitur graue re&longs;pectu leuioris, & leue re&longs;pectu <lb/>grauioris, &longs;icque leue e&longs;t, quod e&longs;t minùs graue, <lb/>& graue, quod e&longs;t minùs leue. </s> |
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| <s>Ni&longs;i <lb/>forta&longs;&longs;is vbio leum in fundo maris fuerit, dicasillud <lb/>&longs;ur&longs;ùm conniti, vt quærat &longs;phæram oleagineam, <lb/>quæ &longs;it &longs;upra aquam; potiù&longs;quàm ab aqua &longs;ur­<lb/>&longs;ùm adigi, &longs;eu à vicinia Terræ expelli, à qua &longs;anè non <lb/>emergeret, ni&longs;i aqua &longs;ubterueniret? </s> | <s id="id.000794">Vt exemplo dicam, <lb/>comparentur lapis, aqua, oleum, aër, ignis, quæ <lb/>terrena e&longs;&longs;e corpora priùs diximus. </s> |
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| <s>Aut ni&longs;i in le­<lb/>betem aqua &longs;emi plenum, & in vertice montis edi­<lb/>ti&longs;&longs;imi con&longs;titutum lapillos inijciens, dicas aquam <lb/>a&longs;cendere, vt &longs;ur&longs;ùm inueniat &longs;phæram aqueam, <lb/>potiù&longs;quàm à lapide abigi, propellique à lebetis <lb/>fundo? </s> | <s id="id.000795">Ob&longs;eruabis aquam <lb/>&longs;upra Terræ &longs;uperficiem, vt in lacu, fo&longs;&longs;a, aut, &longs;i <lb/>velis, intra lebetem planè quie&longs;cere: verùm &longs;i la­<lb/>pis immittatur, is ad imum ita de&longs;cendet, vt aqua <lb/>cedens locum, a&longs;cendat. </s> |
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| <s>Aut ni&longs;i, cùm ignis inuolat in pabulum <lb/>&longs;uppo&longs;itum, dicas illum in &longs;uam de&longs;cendere &longs;phæ­<lb/>ram, &longs;imiliterque aerem in &longs;uam, quoties puteus <lb/>effoditur, tubulu&longs;ve vacuus in Terram defigitur per <lb/>tran&longs;uer&longs;am aquam? </s> | <s id="id.000796">Sic oleum in eodem va­<lb/>&longs;e optimè quie&longs;cet: &longs;ed infundatur aqua, ea petet <lb/>fundum, & oleum &longs;ummum. </s> |
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| <s>Aut ni&longs;i potiùs ip&longs;e aër non <lb/>tam naturaliter &longs;upra Terram, quàm &longs;upra aquam <lb/>requie&longs;cit; puta&longs;que &longs;phæram aëris ita e&longs;&longs;e nece&longs;&longs;a­<lb/>riò &longs;upra aquam, vt in tot i&longs;tis regionibus, in qui­<lb/>bus &longs;upra aquam non e&longs;t, cum violentia detinea­<lb/>tur? </s> | <s id="id.000797">In eodem va&longs;e non <lb/>&longs;it liquor, quie&longs;cet in illo optimè aër: &longs;ubeat oleum; <lb/>id deor&longs;ùm tendet, & aër &longs;ur&longs;ùm. </s> |
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| <s>Sed &longs;i probari tibi requiras, quomodò ignis <lb/>pellatur &longs;ur&longs;ùm ab aëre; con&longs;idera vt ignis in cami­<lb/>no non ardeat, &longs;i tam ianuas, quam fene&longs;tras omneis <lb/>ita perfectè occlu&longs;eris, vt ne per minimam quidem <lb/>rimulam &longs;ubingredi aër in cameram po&longs;&longs;it. </s> | <s id="id.000798">Denique ignis <lb/>&longs;uápte naturâ ip&longs;i Terræ incumberet; at quia immi­<lb/>net, circum&longs;tatque aër; ideò is viciniam Terræ appe­<lb/>tit, & cogitur ignis ex Terra abire. </s> |
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| <s>Nempe <lb/>ni&longs;i aër &longs;it, qui &longs;uccedat in locum illius, qui ignem <lb/>&longs;ur&longs;ùm abigit, nulla fiet (vnde & ignis extinguetur) <lb/>abactio; fiet autem vbi libertate ingrediendi aëri ex­<lb/>terno facta, aër interior habebit ponè alium, qui &longs;i­<lb/>bi ignem in&longs;equenti &longs;uccedat, & cameram compleat; <pb pagenum="120"/>Permirumque e&longs;t, &longs;i cubiculum &longs;it contiguum, <lb/>quod o&longs;tiolo, rimuli&longs;ve cum camera communicet, <lb/>& clau&longs;is fene&longs;tris caminum &longs;olùm apertum habeat, <lb/>&longs;uccedere aërem ex illo in camer<gap/>m, dum alius in­<lb/>tereà &longs;upernè, atque deforis in ip&longs;ius cubiculi cami­<lb/>num inducitur, cuius ductus &longs;i &longs;it angu&longs;tior, & &longs;ub­<lb/>jectus ignis igne camera inualidior, aër de&longs;cendens <lb/>fumum repellet, cubiculumque fumo complebit. <lb/></s> | <s id="id.000799">Ita corpora i&longs;ta <lb/>omnia dicentur grauia, & leuia comparatè, &longs;eu re&longs;­<lb/>pectiuè; & lapis quidem graui&longs;&longs;imus, quia maximè <lb/>omnium attrahitur; &longs;iue minimè omnium leuis, quia <lb/>minimùm abducitur: aqua verò, quæ re&longs;pectu la­<lb/>pidis leuis e&longs;t, grauis erit re&longs;pectu olei; & oleum le­<lb/>ue re&longs;pectu aquæ, erit graue re&longs;pectu aëris; & aër le­<lb/>uis re&longs;pectu olei, grauis erit re&longs;pectu ignis: ignis <lb/>po&longs;tremò omnium leui&longs;&longs;imus cen&longs;ebitur, quia ma­<lb/>ximè omnium attollitur; &longs;iue omnium minimè gra­<lb/>uis, quia ex omnibus, quæ attrahuntur à Terra, <lb/>trahitur ip&longs;e minimùm. </s> |
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| <s>Clarum e&longs;t aliunde vt per hiemen &longs;edenti ad ignem <lb/>pedes antror&longs;um incale&longs;cant, ad calcem verò refri­<lb/>gerentur; impetente &longs;cilicet calcem ip&longs;o aere frigido, <lb/>qui extrin&longs;ecus ad ignem contendit. </s> | <s id="id.000800">Heinc quia difficultas e&longs;t de <lb/>&longs;olo igne; non e&longs;t, cur dum &longs;ur&longs;ùm contendit, exi­<lb/>&longs;times illum &longs;uam, vt vulgò dicunt, quærere &longs;phæ­<lb/>ram (ad quam non ignis ex omnibus &longs;iluis perue-<pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.118.jpg" pagenum="119"/>nire vnquam potis &longs;it) quippe &longs;ur&longs;ùm non tam vi <lb/>propria, quàm ab aëre impul&longs;us contendit. </s> |
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| <s>Con&longs;idera <lb/>etiam quemadmodum ignis vehementius ardeat, &longs;i­<lb/>ligna, aut carbones crate ferrea &longs;u&longs;tententur, quàm <lb/>&longs;i focario lapidi, cineribu&longs;ve in&longs;i&longs;tant: quia videlicet <lb/>pote&longs;t aër &longs;e&longs;e meliûs &longs;upponere, & inter abigendum <lb/>&longs;ur&longs;ùm ignem, ligna, carbone&longs;ve perflare: vnde & <lb/>Chymicorum fornax, quàm flatuo&longs;am vocant, non <lb/>aliis eget follibus, quàm aëre &longs;ubter appellente, & <lb/>&longs;uperex&longs;tanteis carbones validi&longs;&longs;imo flatu ventilante. <lb/></s> | <s id="id.000801">Ni&longs;i <lb/>forta&longs;&longs;is vbio leum in fundo maris fuerit, dicasillud <lb/>&longs;ur&longs;ùm conniti, vt quærat &longs;phæram oleagineam, <lb/>quæ &longs;it &longs;upra aquam; potiù&longs;quàm ab aqua &longs;ur­<lb/>&longs;ùm adigi, &longs;eu à vicinia Terræ expelli, à qua &longs;anè non <lb/>emergeret, ni&longs;i aqua &longs;ubterueniret? </s> |
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| <s>Atque ex his denique dico, e&longs;&longs;e quidem in Terra <lb/>motus rectos &longs;ur&longs;ùm, & deor&longs;ùm; &longs;ed illos e&longs;&longs;e par­<lb/>tium proprios (vt &longs;unt etiam propriæ grauitas, & <lb/><gap/>uitas) non verò proprios totius Terræ, ip&longs;ique po­<lb/>tiùs tam grauitatis, quàm leuitatis experti, &longs;phæ­<lb/>ricáque fotmâ tornatæ, circularem motum aut com­<lb/>petere, aut non repugnare. </s> | <s id="id.000802">Aut ni&longs;i in le­<lb/>betem aqua &longs;emi plenum, & in vertice montis edi­<lb/>ti&longs;&longs;imi con&longs;titutum lapillos inijciens, dicas aquam <lb/>a&longs;cendere, vt &longs;ur&longs;ùm inueniat &longs;phæram aqueam, <lb/>potiù&longs;quàm à lapide abigi, propellique à lebetis <lb/>fundo? </s> |
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| <s>Rem declararem exem­<lb/>plo nauis, in qua qui a&longs;cendunt, ex&longs;cenduntque, & <lb/>quæ attolluntur, deprimunturque omnia non ob­<lb/>&longs;tant, quò minùs nauis &longs;uum cur&longs;um eat; verum res <pb pagenum="121"/>e&longs;t iam &longs;atis inculcata, p<gap/>æ&longs;tat que vt à pari intelliga­<lb/>tur in Luna, aut quouis alio Mundano globo, in <lb/>quo centrum &longs;it, & extremum, & in quo partes re­<lb/>ctà moueri ab&longs;que impedimento circulatis, ac ge­<lb/>neralis motus po&longs;&longs;int. </s> | <s id="id.000803">Aut ni&longs;i, cùm ignis inuolat in pabulum <lb/>&longs;uppo&longs;itum, dicas illum in &longs;uam de&longs;cendere &longs;phæ­<lb/>ram, &longs;imiliterque aerem in &longs;uam, quoties puteus <lb/>effoditur, tubulu&longs;ve vacuus in Terram defigitur per <lb/>tran&longs;uer&longs;am aquam? </s> |
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| <s>Nemo certè neget in Luna <lb/>e&longs;&longs;e vim continentem partium, atque adeò ip&longs;a, <lb/><gap/>um met, &longs;i &longs;ejungantur, retrahentem &longs;it que ad­<lb/>mitti po&longs;&longs;e in partibus Lunæ grauitatem, & leui­<lb/>tatem, ac motus &longs;ur&longs;ùm, deor&longs;ùmque, ab&longs;que eo, <lb/>quòd Luna &longs;ecundum &longs;e totam &longs;it grauis, aut leuis, <lb/>& recto feratur, non circulari motu. </s> | <s id="id.000804">Aut ni&longs;i potiùs ip&longs;e aër non <lb/>tam naturaliter &longs;upra Terram, quàm &longs;upra aquam <lb/>requie&longs;cit; puta&longs;que &longs;phæram aëris ita e&longs;&longs;e nece&longs;&longs;a­<lb/>riò &longs;upra aquam, vt in tot i&longs;tis regionibus, in qui­<lb/>bus &longs;upra aquam non e&longs;t, cum violentia detinea­<lb/>tur? </s> |
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| <s>Quæ&longs;o porrô, <lb/>&longs;i nihil Lunam æthere &longs;olo circum datam mou<gap/> in <lb/>orbem repugnat; quid repugnare po&longs;&longs;it, quò mi­<lb/>nùs ip&longs;a quoque Terra in orbem feratur, quam præ­<lb/>ter ætherem (aut &longs;i velis, ip&longs;um aërem) nihil cir­<lb/>cumambit? </s> | <s id="id.000805">Sed &longs;i probari tibi requiras, quomodò ignis <lb/>pellatur &longs;ur&longs;ùm ab aëre; con&longs;idera vt ignis in cami­<lb/>no non ardeat, &longs;i tam ianuas, quam fene&longs;tras omneis <lb/>ita perfectè occlu&longs;eris, vt ne per minimam quidem <lb/>rimulam &longs;ubingredi aër in cameram po&longs;&longs;it. </s> |
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| <s>An-non, &longs;i ingens globus plumbeus, <lb/>vbi fuerit funi prælongo appen&longs;us, nullo negotio <lb/>moueri pote&longs;t, quòd vis illum de or &longs;ùm ferens &longs;it <lb/>á fune edomita, ac velutinulla; poterit ip&longs;e globus <lb/>Telluris moueri longè faciliùs, nulla inex&longs;i&longs;tente vi, <lb/>quæ ip&longs;um aliquorsùm ferat? </s> | <s id="id.000806">Nempe <lb/>ni&longs;i aër &longs;it, qui &longs;uccedat in locum illius, qui ignem <lb/>&longs;ur&longs;ùm abigit, nulla fiet (vnde & ignis extinguetur) <lb/>abactio; fiet autem vbi libertate ingrediendi aëri ex­<lb/>terno facta, aër interior habebit ponè alium, qui &longs;i­<lb/>bi ignem in&longs;equenti &longs;uccedat, & cameram compleat; <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.119.jpg" pagenum="120"/>Permirumque e&longs;t, &longs;i cubiculum &longs;it contiguum, <lb/>quod o&longs;tiolo, rimuli&longs;ve cum camera communicet, <lb/>& clau&longs;is fene&longs;tris caminum &longs;olùm apertum habeat, <lb/>&longs;uccedere aërem ex illo in camer<gap/>m, dum alius in­<lb/>tereà &longs;upernè, atque deforis in ip&longs;ius cubiculi cami­<lb/>num inducitur, cuius ductus &longs;i &longs;it angu&longs;tior, & &longs;ub­<lb/>jectus ignis igne camera inualidior, aër de&longs;cendens <lb/>fumum repellet, cubiculumque fumo complebit. <lb/></s> |
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| <s>Quòd &longs;i putes ip&longs;um <lb/>à centro teneri; finge Intelligentiam &longs;ubuexi&longs;&longs;e illum <lb/>à centro, & congruo fune &longs;u&longs;pendi&longs;&longs;e; an non tunc <lb/>&longs;altem fune edomante illius in centrum propenden<gap/><lb/>tiam, foret motu facillimus, &longs;i modo qui<gap/>e&longs;&longs;et, <lb/>qui extra ip&longs;um con&longs;i&longs;tens impellere po&longs;&longs;et à Ec­<lb/>quam verò pote&longs;t majorem habere ad motum re&longs;i­<lb/>&longs;tentiam, &longs;i in centro fuerit &longs;u&longs;pen&longs;a per &longs;e, quàm <lb/>&longs;i extra centrum &longs;u&longs;pendatur ab alio? </s> | <s id="id.000807">Clarum e&longs;t aliunde vt per hiemen &longs;edenti ad ignem <lb/>pedes antror&longs;um incale&longs;cant, ad calcem verò refri­<lb/>gerentur; impetente &longs;cilicet calcem ip&longs;o aere frigido, <lb/>qui extrin&longs;ecus ad ignem contendit. </s> |
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| <s>An centro, <lb/>quod merum e&longs;t punctum, quòd que vt maguitudine, <pb pagenum="122"/>&longs;ic omni agendi vi caret, &longs;ube&longs;&longs;e pote&longs;t vnde re­<lb/>uinciat, cohibeat que molem hanc tantam? </s> | <s id="id.000808">Con&longs;idera <lb/>etiam quemadmodum ignis vehementius ardeat, &longs;i­<lb/>ligna, aut carbones crate ferrea &longs;u&longs;tententur, quàm <lb/>&longs;i focario lapidi, cineribu&longs;ve in&longs;i&longs;tant: quia videlicet <lb/>pote&longs;t aër &longs;e&longs;e meliûs &longs;upponere, & inter abigendum <lb/>&longs;ur&longs;ùm ignem, ligna, carbone&longs;ve perflare: vnde & <lb/>Chymicorum fornax, quàm flatuo&longs;am vocant, non <lb/>aliis eget follibus, quàm aëre &longs;ubter appellente, & <lb/>&longs;uperex&longs;tanteis carbones validi&longs;&longs;imo flatu ventilante. <lb/></s> |
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| <s>Et non­<lb/>ne iure Archimedes depopo&longs;cit &longs;olùm extra Ter­<lb/>ram locum, in quo po&longs;&longs;et &longs;e &longs;i&longs;tere, ratus &longs;e ex eo <lb/><gap/>moturum Terram? <!-- KEEP S--></s> | <s id="id.000809">Atque ex his denique dico, e&longs;&longs;e quidem in Terra <lb/>motus rectos &longs;ur&longs;ùm, & deor&longs;ùm; &longs;ed illos e&longs;&longs;e par­<lb/>tium proprios (vt &longs;unt etiam propriæ grauitas, & <lb/><gap/>uitas) non verò proprios totius Terræ, ip&longs;ique po­<lb/>tiùs tam grauitatis, quàm leuitatis experti, &longs;phæ­<lb/>ricáque fotmâ tornatæ, circularem motum aut com­<lb/>petere, aut non repugnare. </s> |
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| <s>Quanquam, vt præmonui, i&longs;ta <lb/>obiter. </s></p><p type="main"> | <s id="id.000810">Rem declararem exem­<lb/>plo nauis, in qua qui a&longs;cendunt, ex&longs;cenduntque, & <lb/>quæ attolluntur, deprimunturque omnia non ob­<lb/>&longs;tant, quò minùs nauis &longs;uum cur&longs;um eat; verum res <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.120.jpg" pagenum="121"/>e&longs;t iam &longs;atis inculcata, p<gap/>æ&longs;tat que vt à pari intelliga­<lb/>tur in Luna, aut quouis alio Mundano globo, in <lb/>quo centrum &longs;it, & extremum, & in quo partes re­<lb/>ctà moueri ab&longs;que impedimento circulatis, ac ge­<lb/>neralis motus po&longs;&longs;int. </s> |
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| <s>IX. <!-- KEEP S--></s> | <s id="id.000811">Nemo certè neget in Luna <lb/>e&longs;&longs;e vim continentem partium, atque adeò ip&longs;a, <lb/><gap/>um met, &longs;i &longs;ejungantur, retrahentem &longs;it que ad­<lb/>mitti po&longs;&longs;e in partibus Lunæ grauitatem, & leui­<lb/>tatem, ac motus &longs;ur&longs;ùm, deor&longs;ùmque, ab&longs;que eo, <lb/>quòd Luna &longs;ecundum &longs;e totam &longs;it grauis, aut leuis, <lb/>& recto feratur, non circulari motu. </s> |
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| <s>Multa &longs;unt prætereà, quæ obijci &longs;olent ex <lb/>apparente ip&longs;ius Solis, Planetarumque aliorum mo­<lb/>tu per Zodiacum, &longs;iue &longs;ub Zodiaco, vt impugnetur <lb/>annuus, quo moueri Terram per Zodiacum Co­<lb/>pernicani a&longs;&longs;euerant. </s> | <s id="id.000812">Quæ&longs;o porrô, <lb/>&longs;i nihil Lunam æthere &longs;olo circum datam mou<gap/> in <lb/>orbem repugnat; quid repugnare po&longs;&longs;it, quò mi­<lb/>nùs ip&longs;a quoque Terra in orbem feratur, quam præ­<lb/>ter ætherem (aut &longs;i velis, ip&longs;um aërem) nihil cir­<lb/>cumambit? </s> |
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| <s>Atque hoc quidem loco ex­<lb/>pli<gap/>dum forer illud ip&longs;orum Sy&longs;tema, quo præ­<lb/>cipuarum Mundi partium, ac in iis Telluris &longs;itus con­<lb/>tinetur. </s> | <s id="id.000813">An-non, &longs;i ingens globus plumbeus, <lb/>vbi fuerit funi prælongo appen&longs;us, nullo negotio <lb/>moueri pote&longs;t, quòd vis illum de or &longs;ùm ferens &longs;it <lb/>á fune edomita, ac velutinulla; poterit ip&longs;e globus <lb/>Telluris moueri longè faciliùs, nulla inex&longs;i&longs;tente vi, <lb/>quæ ip&longs;um aliquorsùm ferat? </s> |
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| <s>Verumtamen habes tu i&longs;teic Philolaüm rediui­<lb/>u<gap/>m, qui illud nupernon modoexpo&longs;uit, &longs;ed quantùm <lb/>etiam fieri pote&longs;t, geometrico more probauit. <lb/></s> | <s id="id.000814">Quòd &longs;i putes ip&longs;um <lb/>à centro teneri; finge Intelligentiam &longs;ubuexi&longs;&longs;e illum <lb/>à centro, & congruo fune &longs;u&longs;pendi&longs;&longs;e; an non tunc <lb/>&longs;altem fune edomante illius in centrum propenden<gap/><lb/>tiam, foret motu facillimus, &longs;i modo qui<gap/>e&longs;&longs;et, <lb/>qui extra ip&longs;um con&longs;i&longs;tens impellere po&longs;&longs;et à Ec­<lb/>quam verò pote&longs;t majorem habere ad motum re&longs;i­<lb/>&longs;tentiam, &longs;i in centro fuerit &longs;u&longs;pen&longs;a per &longs;e, quàm <lb/>&longs;i extra centrum &longs;u&longs;pendatur ab alio? </s> |
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| <s>Quare & mihi &longs;u&longs;&longs;<gap/>it illa hoc loco attingere, quæ <lb/>ad o&longs;tendendum argumenti propo&longs;iti imbecillitatem <lb/>conducunt. </s> | <s id="id.000815">An centro, <lb/>quod merum e&longs;t punctum, quòd que vt maguitudine, <pb xlink:href="http://archimedes.fas.harvard.edu/images/027-00-pageimg/027.00.121.jpg" pagenum="122"/>&longs;ic omni agendi vi caret, &longs;ube&longs;&longs;e pote&longs;t vnde re­<lb/>uinciat, cohibeat que molem hanc tantam? </s> |
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| <s>Primum igitur &longs;upponendum iuxta il­<lb/>lorum &longs;ententiam e&longs;t, e&longs;&longs;e, aut appatere Mun­<lb/>dum &longs;phæricæ &longs;iguræ; Solem e&longs;&longs;e in eius centro, <lb/>ex cóque non digredi: Fixas, vt vocant, &longs;tellas e&longs;&longs;e <lb/>in eiu&longs;dem circumferentia, con&longs;taréque etiam im­<lb/>motas. </s> | <s id="id.000816">Et non­<lb/>ne iure Archimedes depopo&longs;cit &longs;olùm extra Ter­<lb/>ram locum, in quo po&longs;&longs;et &longs;e &longs;i&longs;tere, ratus &longs;e ex eo <lb/><gap/>moturum Terram? <!-- KEEP S--></s> |
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| <s>In &longs;patiointermedio e&longs;&longs;e, ac moueri Plane­<lb/>tas, & co quidem ordine, vt proximè circa So­<lb/>lem vertatur Mercurij &longs;idus intra men&longs;eis circiter <lb/>treis; &longs;uccedat Venus, quæ intra nouem; tertio <lb/>loco &longs;it Tellus, quæ intra duodecim, &longs;iue annum <lb/>vnum; &longs;equatur Mars, qui intra annos proximè duos; <lb/>tum Iupiter; qui intra duodecim; ac po&longs;tremò Sa-<pb pagenum="123"/><figure id="fig8"/><lb/>turnus, qui intra triginta. </s> | <s id="id.000817">Quanquam, vt præmonui, i&longs;ta <lb/>obiter. </s></p><p type="main"> |
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| <s>Cùmque circulus à Ter­<lb/>ra de&longs;criptus &longs;atis amplo inter&longs;titio heinc à circulo <lb/>Veneris, heinc à circulo Martis di&longs;tet; idcircô in <lb/>hoc inter&longs;titio &longs;patium accipi, magnum orbem di­<lb/>ctum, in quo circulus qua&longs;i in&longs;ertus concipiatur, <lb/>cuius Terra centrum &longs;it, & &longs;ecundum cuius ambi­<lb/>tum Luna Terræ circumducatur men&longs;truo tempore; <lb/>dum intereà vna cum Terra circumducitur Soli in­<lb/>tra annum. </s> | <s id="id.000818">IX. <!-- KEEP S--></s> |
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| <s>Et cum etiam circulus Iouis &longs;atis am­<lb/>plo interuallo heinc à Martis, heinc à Saturni cir­<lb/>culis di&longs;tet; ideò concipi in hoc interuallo circellos <lb/>quatuor, &longs;ecundum quos, & circa Iouem, vt circa <pb pagenum="124"/>&longs;uum centrum, ferantur quatuor qua&longs;i Lunæ, &longs;iue <lb/>&longs;telllulæ, &longs;idera Medicea dictæ, &longs;uis quæque perio­<lb/>dis; dum intereà vnà cum Ioue conficiunt circa So­<lb/>lem periodum duodecim annorum. </s> | <s id="id.000819">Multa &longs;unt prætereà, quæ obijci &longs;olent ex <lb/>apparente ip&longs;ius Solis, Planetarumque aliorum mo­<lb/>tu per Zodiacum, &longs;iue &longs;ub Zodiaco, vt impugnetur <lb/>annuus, quo moueri Terram per Zodiacum Co­<lb/>pernicani a&longs;&longs;euerant. </s> |
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| <s>Atque id qui­<lb/>dem, ne memorem duas veluti Lunulas, &longs;iue an&longs;u­<lb/>las, quæ Saturni formam exhibent oblongam, <lb/>qua&longs;que &longs;ejungi ab eo, vt &longs;uas à Ioue Lunulas, <lb/>nondum planè con&longs;tat. <emph type="italics"/>Secundò,<emph.end type="italics"/> eam debere Mun­<lb/>di amplitudinem concipi, vt quod &longs;patium e&longs;t à <lb/>Saturno v&longs;que ad Fixas, &longs;it penè immen&longs;um; tantum <lb/>&longs;cilicet, vt complexus omnium Planetatum cum So­<lb/>le in medio, &longs;i in orbem formatum concipias, pun­<lb/>ctum penè &longs;it re&longs;pectu illius, appariturus nempe <lb/>ex Fixis qua&longs;i vna aliqua &longs;tella; veluti complexus <lb/>quatuor Lunularum, &longs;eu Planetularum Iouialium <lb/>cum &longs;oue in medio, pro vna &longs;tella heinc reputatur. <lb/></s> | <s id="id.000820">Atque hoc quidem loco ex­<lb/>pli<gap/>dum forer illud ip&longs;orum Sy&longs;tema, quo præ­<lb/>cipuarum Mundi partium, ac in iis Telluris &longs;itus con­<lb/>tinetur. </s> |
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| <s>Saltem complexus Telluris per circulum annuum <lb/>tran&longs;latæ cum comprehen&longs;is. </s> | |
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