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version 1.6, 2004/08/19 16:52:33 |
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| <s id="N10570"><margin.target id="marg9"/><emph type="italics"/>Liu.de bello <lb/>Punico.<emph.end type="italics"/><!-- KEEP S--></s> | <s id="N10570"><margin.target id="marg9"/><emph type="italics"/>Liu.de bello <lb/>Punico.<emph.end type="italics"/><!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N1057C" type="main"> | <p id="N1057C" type="main"> |
| <s id="N1057E">Propriè tamen hìc apud Ari&longs;totelem &longs;icut apud cœteros <lb/>omnes Philo&longs;ophos, ac Geometras, mechanica facultas tan­<lb/>tùm fignificat artem &longs;iue &longs;cientiam, quæ Geometricis princi­<lb/>pijs circa &longs;tatum & lationem grauium & leuium ver&longs;atur, hoc <lb/>e&longs;t circa grauia & leuia prout artificiosè moueri, aut quie&longs;ce­<lb/>re debent, vt clariùs infra ex Pappo, & ex tradenda<arrow.to.target n="marg10"/> defini­<lb/>tione con&longs;tabit. </s> | <s id="N1057E">Propriè tamen hìc apud Ari&longs;totelem &longs;icut apud cœteros <lb/>omnes Philo&longs;ophos, ac Geometras, mechanica facultas tan­<lb/>tùm &longs;ignificat artem &longs;iue &longs;cientiam, quæ Geometricis princi­<lb/>pijs circa &longs;tatum & lationem grauium & leuium ver&longs;atur, hoc <lb/>e&longs;t circa grauia & leuia prout artificiosè moueri, aut quie&longs;ce­<lb/>re debent, vt clariùs infra ex Pappo, & ex tradenda<arrow.to.target n="marg10"/> defini­<lb/>tione con&longs;tabit. </s> |
| </p> | </p> |
| <p id="N10591" type="margin"> | <p id="N10591" type="margin"> |
| <s id="N10593"><margin.target id="marg10"/><emph type="italics"/>Papp. <!-- REMOVE S-->lib.<emph.end type="italics"/>8. <lb/><emph type="italics"/><expan abbr="collectionũ">collectionum</expan><emph.end type="italics"/></s> | <s id="N10593"><margin.target id="marg10"/><emph type="italics"/>Papp. <!-- REMOVE S-->lib.<emph.end type="italics"/>8. <lb/><emph type="italics"/><expan abbr="collectionũ">collectionum</expan><emph.end type="italics"/></s> |
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| <s id="N10683">ADDITIO SECVNDA.<!-- KEEP S--></s> | <s id="N10683">ADDITIO SECVNDA.<!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N10687" type="main"> | <p id="N10687" type="main"> |
| <s id="N10689">Vt <expan abbr="aut&etilde;">autem</expan> Mechanicæ facultatis natura ex proprio obie­<lb/>cto, quemadmodum commune e&longs;t omnibus artibus, <lb/>atque &longs;cientijs in doctrina Ari&longs;totelis 2. de anlma text. </s> | <s id="N10689">Vt <expan abbr="aut&etilde;">autem</expan> Mechanicæ facultatis natura ex proprio obie­<lb/>cto, quemadmodum commune e&longs;t omnibus artibus, <lb/>atque &longs;cientijs in doctrina Ari&longs;totelis 2. de anima text. </s> |
| <s id="N10694">33. <lb/>præcipuè digno&longs;catur, Ob&longs;eruandum in primis e&longs;t, id quod <lb/>per mechanicam facultatem intendimus, & ad quod tanquam <lb/>ad finem con&longs;e quendum omnis mechanica contemplatio or­<lb/>dinatur, aliud non e&longs;&longs;e, quàm grauis aut leuis cuiu&longs;que cor­<lb/>poris motionem, vel quietem, quæ parua vt plurimum virtu­<lb/>te, arte ip&longs;a mirabiliter comparatur, &longs;iue motio &longs;it &longs;ecundum <lb/>naturam, &longs;iue &longs;it præter aut contra naturam ip&longs;ius corporis <lb/>grauis aut leuis. </s> | <s id="N10694">33. <lb/>præcipuè digno&longs;catur, Ob&longs;eruandum in primis e&longs;t, id quod <lb/>per mechanicam facultatem intendimus, & ad quod tanquam <lb/>ad finem con&longs;e quendum omnis mechanica contemplatio or­<lb/>dinatur, aliud non e&longs;&longs;e, quàm grauis aut leuis cuiu&longs;que cor­<lb/>poris motionem, vel quietem, quæ parua vt plurimum virtu­<lb/>te, arte ip&longs;a mirabiliter comparatur, &longs;iue motio &longs;it &longs;ecundum <lb/>naturam, &longs;iue &longs;it præter aut contra naturam ip&longs;ius corporis <lb/>grauis aut leuis. </s> |
| <s id="N106A7">Porro inductione con&longs;tat, mechanicum om­<lb/>nem conatum, <expan abbr="omnemq.">omnemque</expan> tractatum in admirabilem lationem, <lb/>aut &longs;tatum corporum ordinari ex ip&longs;ius artis proprio in&longs;titu­<lb/>to, vt ad leuanda, vel detinenda etiam exigua virtute quæ-<pb pagenum="10" xlink:href="005/01/018.jpg"/>cunque pondera, ad aerem vel aquam artificiosè pellendam, <lb/>attrahendam, aut continendam, ad mi&longs;&longs;ilia proijcienda, <expan abbr="aliaq.">aliaque</expan> <lb/>&longs;ecundum varias po&longs;itiones locanda, vel de loco ad locum, <lb/>diuer&longs;imodè transferenda, & &longs;imilia, quæ per &longs;e nota erunt <lb/>mechanicamenta omnia ad id præ&longs;tandum accomodata, ac <lb/>&longs;peculationes mechanicas recen&longs;enti. </s> | <s id="N106A7">Porro inductione con&longs;tat, mechanicum om­<lb/>nem conatum, <expan abbr="omnemq.">omnemque</expan> tractatum in admirabilem lationem, <lb/>aut &longs;tatum corporum ordinari ex ip&longs;ius artis proprio in&longs;titu­<lb/>to, vt ad leuanda, vel detinenda etiam exigua virtute quæ-<pb pagenum="10" xlink:href="005/01/018.jpg"/>cunque pondera, ad aerem vel aquam artificiosè pellendam, <lb/>attrahendam, aut continendam, ad mi&longs;&longs;ilia proijcienda, <expan abbr="aliaq.">aliaque</expan> <lb/>&longs;ecundum varias po&longs;itiones locanda, vel de loco ad locum, <lb/>diuer&longs;imodè transferenda, & &longs;imilia, quæ per &longs;e nota erunt <lb/>mechanicamenta omnia ad id præ&longs;tandum accomodata, ac <lb/>&longs;peculationes mechanicas recen&longs;enti. </s> |
| </p> | </p> |
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| <s id="N106F0">Denique ob&longs;eruandum etiam erit, prædictam quantitatem <lb/>ponderis, tum grauitatem, tum leuitatem re&longs;pectu <expan abbr="diuer&longs;orũ">diuer&longs;orum</expan> <lb/>à Mechanicis appellari. </s> | <s id="N106F0">Denique ob&longs;eruandum etiam erit, prædictam quantitatem <lb/>ponderis, tum grauitatem, tum leuitatem re&longs;pectu <expan abbr="diuer&longs;orũ">diuer&longs;orum</expan> <lb/>à Mechanicis appellari. </s> |
| <s id="N106FB">Maior enim quantitas ponderis re­<lb/>&longs;pectu minoris, ab ip&longs;is dicitur grauitas; minor vero compa­<lb/>ratione maioris, dicitur leuitas. </s> | <s id="N106FB">Maior enim quantitas ponderis re­<lb/>&longs;pectu minoris, ab ip&longs;is dicitur grauitas; minor vero compa­<lb/>ratione maioris, dicitur leuitas. </s> |
| <s id="N10702">Sicut illud corpus ab ip&longs;is <lb/>dicitur leue, quod minus habet pondus re&longs;pectu alterius; il­<lb/>lud vero graue, quod maius; etiam &longs;i per &longs;e &longs;impliciter lo­<lb/>quendo vtrumque graue &longs;it. </s> | <s id="N10702">Sicut illud corpus ab ip&longs;is <lb/>dicitur leue, quod minus habet pondus re&longs;pectu alterius; il­<lb/>lud vero graue, quod maius; etiam &longs;i per &longs;e &longs;impliciter lo­<lb/>quendo vtrumque graue &longs;it. </s> |
| <s id="N1070B">Non enim Mechanicus accipit <lb/>graue aut leue &longs;impliciter & &longs;ecundum &longs;e, quemadmodum vt <lb/>plurimum accipit Phy&longs;icus (nempe per graue intelligendo, <lb/>quod nullam habet in &longs;e leuitatem, per leue autem quod nul­<lb/>lam habet in &longs;e grauiratem;) &longs;ed &longs;emper vtrumque accipit <lb/>re&longs;pectiue; ita vt idem dicatur graue & leue re&longs;pectu diuer&longs;o­<lb/>rum, vt habetur etiam apud Ari&longs;totelem lib. | <s id="N1070B">Non enim Mechanicus accipit <lb/>graue aut leue &longs;impliciter & &longs;ecundum &longs;e, quemadmodum vt <lb/>plurimum accipit Phy&longs;icus (nempe per graue intelligendo, <lb/>quod nullam habet in &longs;e leuitatem, per leue autem quod nul­<lb/>lam habet in &longs;e grauirtatem;) &longs;ed &longs;emper vtrumque accipit <lb/>re&longs;pectiue; ita vt idem dicatur graue & leue re&longs;pectu diuer&longs;o­<lb/>rum, vt habetur etiam apud Ari&longs;totelem lib. |
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| 4. de cœlo tex. <lb/><!-- REMOVE S-->27. vbi aer & aqua re&longs;pectu terræ dicuntur leuia, re&longs;pectu ve­<lb/>ro ignis, grauia. </s> | 4. de cœlo tex. <lb/><!-- REMOVE S-->27. vbi aer & aqua re&longs;pectu terræ dicuntur leuia, re&longs;pectu ve­<lb/>ro ignis, grauia. </s> |
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| </p> | </p> |
| <p id="N10748" type="main"> | <p id="N10748" type="main"> |
| <s id="N1074A">Secundo vero non minus facile con&longs;tabit, obiectum forma­<lb/>le eiu&longs;dem facultatis e&longs;&longs;e admirabilem, & artificio&longs;am mobi­<lb/>litatem, aut quietèm ip&longs;orum grauium, & leuium, ab&longs;trahen­<lb/>do à motione & quiete naturali aut violenta, vt quæ per im­<lb/>petum impre&longs;&longs;um, aut detentionem fieri con&longs;ueuit. </s> | <s id="N1074A">Secundo vero non minus facile con&longs;tabit, obiectum forma­<lb/>le eiu&longs;dem facultatis e&longs;&longs;e admirabilem, & artificio&longs;am mobi­<lb/>litatem, aut quietèm ip&longs;orum grauium, & leuium, ab&longs;trahen­<lb/>do à motione & quiete naturali aut violenta, vt quæ per im­<lb/>petum impre&longs;&longs;um, aut detentionem fieri con&longs;ueuit. </s> |
| <s id="N10755">Con&longs;tat <lb/>autem ex eo quod obiectum formale cuiu&longs;que facultatis, aut <lb/>&longs;cientiæ, e&longs;t ip&longs;a ratio &longs;ub qua de proprio &longs;ubiecto materiali <lb/>agitur in tali &longs;cientia: ratio autem &longs;ub qua in mechanica fa­<lb/>cultate agitur de graui & leui, <expan abbr="virtuteq.">virtuteque</expan> motiua aut detentiua <lb/>eorum, e&longs;t ip&longs;a arti&longs;icio&longs;a mobilitas &longs;ecundum <expan abbr="locũ">locum</expan>, & quies <lb/>con&longs;equenda ip&longs;orum, mediantibus præceptis tradendis in <lb/>eadem &longs;cientia, vt per &longs;e patet ex fine explicato, ad quem <lb/>tota hæc &longs;cientia dirigitur, & ordinatur. </s> | <s id="N10755">Con&longs;tat <lb/>autem ex eo quod obiectum formale cuiu&longs;que facultatis, aut <lb/>&longs;cientiæ, e&longs;t ip&longs;a ratio &longs;ub qua de proprio &longs;ubiecto materiali <lb/>agitur in tali &longs;cientia: ratio autem &longs;ub qua in mechanica fa­<lb/>cultate agitur de graui & leui, <expan abbr="virtuteq.">virtuteque</expan> motiua aut detentiua <lb/>eorum, e&longs;t ip&longs;a artificio&longs;a mobilitas &longs;ecundum <expan abbr="locũ">locum</expan>, & quies <lb/>con&longs;equenda ip&longs;orum, mediantibus præceptis tradendis in <lb/>eadem &longs;cientia, vt per &longs;e patet ex fine explicato, ad quem <lb/>tota hæc &longs;cientia dirigitur, & ordinatur. </s> |
| <s id="N10770">Ea ergo admirabi­<lb/>lis, <expan abbr="artificio&longs;aq.">artificio&longs;aque</expan> mobilitas, iure cen&longs;eri debet formale obie­<lb/>ctum huius facultatis mechanicæ. </s> | <s id="N10770">Ea ergo admirabi­<lb/>lis, <expan abbr="artificio&longs;aq.">artificio&longs;aque</expan> mobilitas, iure cen&longs;eri debet formale obie­<lb/>ctum huius facultatis mechanicæ. </s> |
| </p> | </p> |
| <p id="N1077B" type="main"> | <p id="N1077B" type="main"> |
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| <s id="N107CF">ADDITIO TERTIA.<!-- KEEP S--></s> | <s id="N107CF">ADDITIO TERTIA.<!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N107D3" type="main"> | <p id="N107D3" type="main"> |
| <s id="N107D5">Hvcu&longs;que ad &longs;ignificandum habitum intellectualem <expan abbr="cõ-templationis">con­<lb/>templationis</expan> mechanicæ, vt plurimum v&longs;i &longs;umus no­<lb/>mine facultatis mechanicæ, eo quod nomen facultas ab&longs;tra­<lb/>hat à propria &longs;ignificatione artis, aut&longs;cientiæ, latiusq pateat <lb/>&longs;ecundum communem omnium conceptionem. </s> | <s id="N107D5">Hviu&longs;que ad &longs;ignificandum habitum intellectualem <expan abbr="cõ-templationis">con­<lb/>templationis</expan> mechanicæ, vt plurimum v&longs;i &longs;umus no­<lb/>mine facultatis mechanicæ, eo quod nomen facultas ab&longs;tra­<lb/>hat à propria &longs;ignificatione artis, aut &longs;cientiæ, <expan abbr="latiusq.">latiusque</expan> pateat <lb/>&longs;ecundum communem omnium conceptionem. </s> |
| <s id="N107E4">Quare de­<lb/>terminandum nunc e&longs;t, vtrum talis habitus vel facultas, &longs;it ve­<lb/>rè in &longs;e, ac propriè vocari po&longs;&longs;it tum ars, tum &longs;cientia. </s> | <s id="N107E4">Quare de­<lb/>terminandum nunc e&longs;t, vtrum talis habitus vel facultas, &longs;it ve­<lb/>rè in &longs;e, ac propriè vocari po&longs;&longs;it tum ars, tum &longs;cientia. </s> |
| <s id="N107EB">Quod <lb/>&longs;anè au&longs;picari debet à communi ratione artis atque &longs;cientiæ <lb/>ab Ari&longs;totele &longs;æpius explicata, <expan abbr="aptèq.">aptèque</expan> pa&longs;&longs;im licet non &longs;em­<lb/>per di&longs;tincta. </s> | <s id="N107EB">Quod <lb/>&longs;anè au&longs;picari debet à communi ratione artis atque &longs;cientiæ <lb/>ab Ari&longs;totele &longs;æpius explicata, <expan abbr="aptèq.">aptèque</expan> pa&longs;&longs;im licet non &longs;em­<lb/>per di&longs;tincta. </s> |
| <s id="N107F8">Nam 6 Ethicorum cap. | <s id="N107F8">Nam 6 Ethicorum cap. |
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| <s id="N1080C">Ac proinde &longs;equenti capite di&longs;tinguit artem <lb/>à &longs;cientia, eo quod &longs;cientia &longs;it de rebus quæ non po&longs;&longs;unt ali­<lb/>ter &longs;e habere. </s> | <s id="N1080C">Ac proinde &longs;equenti capite di&longs;tinguit artem <lb/>à &longs;cientia, eo quod &longs;cientia &longs;it de rebus quæ non po&longs;&longs;unt ali­<lb/>ter &longs;e habere. </s> |
| <s id="N10813">Nihilominus 1. Metaphi&longs;ices cap. | <s id="N10813">Nihilominus 1. Metaphi&longs;ices cap. |
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| 1. idem <lb/>Philo&longs;ophus artem videtur confundere cum &longs;cientia &longs;altem <lb/>practica; ait enim, artem e&longs;&longs;e de vniuer&longs;alibus, ac propter <lb/>cau&longs;am ea quæ &longs;iunt cogno&longs;cere, exemplum adhibens tum <pb pagenum="13" xlink:href="005/01/021.jpg"/>medicinæ, tum architecturæ; imò ip&longs;as mathematicas di&longs;ci­<lb/>plinas indefinitè loquendo, quas con&longs;tat e&longs;&longs;e &longs;cientias, artes <lb/>appellat. </s> | 1. idem <lb/>Philo&longs;ophus artem videtur confundere cum &longs;cientia &longs;altem <lb/>practica; ait enim, artem e&longs;&longs;e de vniuer&longs;alibus, ac propter <lb/>cau&longs;am ea quæ &longs;fiunt cogno&longs;cere, exemplum adhibens tum <pb pagenum="13" xlink:href="005/01/021.jpg"/>medicinæ, tum architecturæ; imò ip&longs;as mathematicas di&longs;ci­<lb/>plinas indefinitè loquendo, quas con&longs;tat e&longs;&longs;e &longs;cientias, artes <lb/>appellat. </s> |
| </p> | </p> |
| <p id="N10825" type="main"> | <p id="N10825" type="main"> |
| <s id="N10827">Ex quibus primò dicendum erit, mechanicam facultatem <lb/>verè & propriè e&longs;&longs;e artem, prout in hoc libello, & in explica­<lb/>to textu a&longs;&longs;umitur ab Ari&longs;totele. <!-- KEEP S--></s> | <s id="N10827">Ex quibus primò dicendum erit, mechanicam facultatem <lb/>verè & propriè e&longs;&longs;e artem, prout in hoc libello, & in explica­<lb/>to textu a&longs;&longs;umitur ab Ari&longs;totele. <!-- KEEP S--></s> |
| <s id="N1082F">Nam proculdubio huiu&longs;­<lb/>modi facultas e&longs;t habitus intellectualis vera cum ratione effe­<lb/>ctiuus; qui nimitum pro ratiocinationem ver&longs;atur circa facti­<lb/>bilia, vt &longs;unt grauia & leuia, quæ aliter atque aliter &longs;e po&longs;&longs;unt <lb/>habere &longs;ecundum artificio&longs;am motionem, aut quietem illis <lb/>tribuendam ab eodem principio in quo e&longs;t ip&longs;e habitus intel­<lb/>lectualis, ac directiuus mechanicæ operationis. </s> | <s id="N1082F">Nam procul dubio huiu&longs;­<lb/>modi facultas e&longs;t habitus intellectualis vera cum ratione effe­<lb/>ctiuus; qui nimirum pro ratiocinationem ver&longs;atur circa facti­<lb/>bilia, vt &longs;unt grauia & leuia, quæ aliter atque aliter &longs;e po&longs;&longs;unt <lb/>habere &longs;ecundum artificio&longs;am motionem, aut quietem illis <lb/>tribuendam ab eodem principio in quo e&longs;t ip&longs;e habitus intel­<lb/>lectualis, ac directiuus mechanicæ operationis. </s> |
| </p> | </p> |
| <p id="N1083E" type="main"> | <p id="N1083E" type="main"> |
| <s id="N10840">Secundò dicendum e&longs;t, eandem facultatem mechanicam <lb/>verè etiam ac propriè e&longs;&longs;e ac vocari po&longs;&longs;e &longs;cientiam. </s> | <s id="N10840">Secundò dicendum e&longs;t, eandem facultatem mechanicam <lb/>verè etiam ac propriè e&longs;&longs;e ac vocari po&longs;&longs;e &longs;cientiam. </s> |
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| 2. iure & quidem optimo mechanica facultas &longs;eu noti­<lb/>tia, &longs;cientia e&longs;&longs;e debet, ac dici: quandoquidem hæ omnes <lb/>conditiones illi proprij&longs;&longs;imè conueniunt. </s> | 2. iure & quidem optimo mechanica facultas &longs;eu noti­<lb/>tia, &longs;cientia e&longs;&longs;e debet, ac dici: quandoquidem hæ omnes <lb/>conditiones illi proprij&longs;&longs;imè conueniunt. </s> |
| <s id="N10890">In primis enim e&longs;t <lb/>intellectualis cognitio eorum quæ circa motionem localem, <lb/>aut quietem grauium ac leuium contingunt, orta ex præexi­<lb/>&longs;tenti alia cognitione principiorum, quæ &longs;iue &longs;int per &longs;e nota, <lb/>&longs;iue demon&longs;trentur in alia &longs;uperiori &longs;cientia, vt infra dicetur, <lb/>omnino tamen &longs;unt cau&longs;a eius quod a&longs;&longs;eritur in conclu&longs;ione. <lb/></s> | <s id="N10890">In primis enim e&longs;t <lb/>intellectualis cognitio eorum quæ circa motionem localem, <lb/>aut quietem grauium ac leuium contingunt, orta ex præexi­<lb/>&longs;tenti alia cognitione principiorum, quæ &longs;iue &longs;int per &longs;e nota, <lb/>&longs;iue demon&longs;trentur in alia &longs;uperiori &longs;cientia, vt infra dicetur, <lb/>omnino tamen &longs;unt cau&longs;a eius quod a&longs;&longs;eritur in conclu&longs;ione. <lb/></s> |
| <s id="N1089E">Ideo <expan abbr="namq.">namque</expan> dicimus in motu circulari, partem diametri, quæ <lb/>magis di&longs;tat à centro circuli, velocius moueri; quia hæe ma-<pb pagenum="14" xlink:href="005/01/022.jpg"/>gis participat de motu recto, ac naturali à quo prouenit ip&longs;a <lb/>maior velocitas tanquam à cau&longs;a intrin&longs;eca, & hoc ita &longs;e ha­<lb/>bere demon&longs;tratur ex principijs geometricis. </s> | <s id="N1089E">Ideo <expan abbr="namq.">namque</expan> dicimus in motu circulari, partem diametri, quæ <lb/>magis di&longs;tat à centro circuli, velocius moueri; quia hæc ma-<pb pagenum="14" xlink:href="005/01/022.jpg"/>gis participat de motu recto, ac naturali à quo prouenit ip&longs;a <lb/>maior velocitas tanquam à cau&longs;a intrin&longs;eca, & hoc ita &longs;e ha­<lb/>bere demon&longs;tratur ex principijs geometricis. </s> |
| <s id="N108B0">Similiter non <lb/>ex alio dicimus rotunda corpora &longs;uper planum, facilius mo­<lb/>ueri, ni&longs;i quia parua vel minima &longs;ui parte planum contingám, <lb/>ac minus offen&longs;ant. </s> | <s id="N108B0">Similiter non <lb/>ex alio dicimus rotunda corpora &longs;uper planum, facilius mo­<lb/>ueri, ni&longs;i quia parua vel minima &longs;ui parte planum contingám, <lb/>ac minus offen&longs;ant. </s> |
| <s id="N108B9"><expan abbr="Idq.">Idque</expan> probatur eo quòd circulus tangat in <lb/>puncto, ac miagis à plano &longs;emotum efficiat angulum. </s> | <s id="N108B9"><expan abbr="Idq.">Idque</expan> probatur eo quòd circulus tangat in <lb/>puncto, ac magis à plano &longs;emotum efficiat angulum. </s> |
| <s id="N108C1">Quæ <lb/>de&longs;umuntur ex geometricis, <expan abbr="&longs;untq.">&longs;untque</expan> veræ cau&longs;æ ip&longs;ius mobili­<lb/>taris facilioris quæ de rotundis corporibus a&longs;&longs;eueratur. </s> | <s id="N108C1">Quæ <lb/>de&longs;umuntur ex geometricis, <expan abbr="&longs;untq.">&longs;untque</expan> veræ cau&longs;æ ip&longs;ius mobili­<lb/>taris facilioris quæ de rotundis corporibus a&longs;&longs;eueratur. </s> |
| <s id="N108CC">Quod <lb/>cum in omnibus conclu&longs;ionibus mechanicis ob&longs;eruetur, vt <lb/>per &longs;e con&longs;tat, palàm conuincitur, eas con&longs;tituere notitiam <lb/>quandam rerum &longs;iue effectuum procedentem ex cognitione <lb/>cau&longs;æ illorum, ac proinde per di&longs;cur&longs;um & illationem virtute <lb/>medij, nempe ip&longs;ius cau&longs;æ præcognitæ, ex notitia <expan abbr="anteced&etilde;-tis">anteceden­<lb/>tis</expan> deueniendo in notitiam con&longs;equentis, quod e&longs;t &longs;ecundum <lb/>hanc conditionem participare propriam rationem &longs;cientiæ. </s> | <s id="N108CC">Quod <lb/>cum in omnibus conclu&longs;ionibus mechanicis ob&longs;eruetur, vt <lb/>per &longs;e con&longs;tat, palàm conuincitur, eas con&longs;tituere notitiam <lb/>quandam rerum &longs;iue effectuum procedentem ex cognitione <lb/>cau&longs;æ illorum, ac proinde per di&longs;cur&longs;um & illationem virtute <lb/>medij, nempe ip&longs;ius cau&longs;æ præcognitæ, ex notitia <expan abbr="anteced&etilde;-tis">anteceden­<lb/>tis</expan> deueniendo in notitiam con&longs;equentis, quod e&longs;t &longs;ecundum <lb/>hanc conditionem participare propriam rationem &longs;cientiæ. </s> |
| </p> | </p> |
| |
| <s id="N108E3">Deinde probatur, nam ea quæ per mechanicam notitiam <lb/>ex cau&longs;is proprijs cogno&longs;cuntur, tàm nece&longs;&longs;ario ab ip&longs;is cau­<lb/>&longs;is procedunt, vt non po&longs;&longs;int aliter &longs;e habere, quæ erat altera <lb/>conditio propriæ &longs;cientiæ. </s> | <s id="N108E3">Deinde probatur, nam ea quæ per mechanicam notitiam <lb/>ex cau&longs;is proprijs cogno&longs;cuntur, tàm nece&longs;&longs;ario ab ip&longs;is cau­<lb/>&longs;is procedunt, vt non po&longs;&longs;int aliter &longs;e habere, quæ erat altera <lb/>conditio propriæ &longs;cientiæ. </s> |
| <s id="N108EC">Neque enim contingenter pon­<lb/>dus libræ aut vectis magis grauitat in parte remotiori à fulci­<lb/>mento ex eo quòd pars diametri, quæ plus à centro circuli <lb/>di&longs;ce&longs;&longs;erit, magis ab eadem virtute moueri &longs;uapte natura <lb/>præualeat: &longs;ed nece&longs;&longs;ariò ac ineffabiliter, cùm nece&longs;&longs;ariò li­<lb/>bra aut vectis in &longs;uo proprio motu con&longs;tituatur veluti diame­<lb/>ter circuli; & hoc quod e&longs;t pondus in parte di&longs;tantiori à ful­<lb/>cimento quod e&longs;t centrum, magis grauitare &longs;eu efficaciùs de­<lb/>or&longs;um impellere e&longs;&longs;entialiter dependeat ab eo, quod e&longs;t par­<lb/>tem illam di&longs;tantiorem à centro aptiorem e&longs;&longs;e ad motum, vt <lb/>aperti&longs;&longs;imè ex geometricis principijs demon&longs;trabitur. </s> | <s id="N108EC">Neque enim contingenter pon­<lb/>dus libræ aut vectis magis grauitat in parte remotiori à fulci­<lb/>mento ex eo quòd pars diametri, quæ plus à centro circuli <lb/>di&longs;ce&longs;&longs;erit, magis ab eadem virtute moueri &longs;uapte natura <lb/>præualeat: &longs;ed nece&longs;&longs;ariò ac ineffabiliter, cùm nece&longs;&longs;ariò li­<lb/>bra aut vectis in &longs;uo proprio motu con&longs;tituatur veluti diame­<lb/>ter circuli; & hoc quod e&longs;t pondus in parte di&longs;tantiori à ful­<lb/>cimento quod e&longs;t centrum, magis grauitare &longs;eu efficaciùs de­<lb/>or&longs;um impellere e&longs;&longs;entialiter dependeat ab eo, quod e&longs;t par­<lb/>tem illam di&longs;tantiorem à centro aptiorem e&longs;&longs;e ad motum, vt <lb/>aperti&longs;&longs;imè ex geometricis principijs demon&longs;trabitur. </s> |
| <s id="N10903">Nec <lb/>per accidens e&longs;t, longiùs ferri mi&longs;&longs;ilia funda, quàm manu mi&longs;­<lb/>&longs;a, quia in motu circulari qui fit per emi&longs;&longs;ionem, &longs;eu proie­<lb/>ctionem, magis illa di&longs;tant à centro per fundæ v&longs;um, quàm &longs;i <lb/>&longs;ola manu proijcerentur, vt per &longs;e con&longs;tat; &longs;ed nece&longs;&longs;ariò ex <lb/>tali cau&longs;a talis procedit effectus, qui proinde aliter non pote&longs;t <lb/>&longs;e habere propter eandem rationem, vt in cœteris quoque <pb pagenum="15" xlink:href="005/01/023.jpg"/>facilè erit inductione probare. </s> | <s id="N10903">Nec <lb/>per accidens e&longs;t, longiùs ferri mi&longs;&longs;ilia funda, quàm manu mi&longs;­<lb/>&longs;a, quia in motu circulari qui fit per emi&longs;&longs;ionem, &longs;eu proie­<lb/>ctionem, magis illa di&longs;tant à centro per fundæ v&longs;um, quàm &longs;i <lb/>&longs;ola manu proijcerentur, vt per &longs;e con&longs;tat; &longs;ed nece&longs;&longs;ariò ex <lb/>tali cau&longs;a talis procedit effectus, qui proinde aliter non pote&longs;t <lb/>&longs;e habere propter eandem rationem, vt in cœteris quoque <pb pagenum="15" xlink:href="005/01/023.jpg"/>facilè erit inductione probare. </s> |
| <s id="N10917">Cumque ip&longs;æ cau&longs;æ ex qui­<lb/>bus mechanica facultas &longs;uas elicit conclu&longs;iones, vel &longs;int per <lb/>&longs;e notæ, vt citius ferri, quod facilius mouetur; Aequalia ab <lb/>æqualibns non moueri, & &longs;imilia; vel fundentur in principijs <lb/>demon&longs;tratis in alia &longs;uperiori &longs;cientia, de quibus habetur ve­<lb/>ra certitudo, & euidentia hinc vlterius fit, vt ip&longs;a pariter co­<lb/>gnitio mechanicarum conclu&longs;ionum, eandem participet, ac <lb/>&longs;ortiatur euidentiam, vt commune e&longs;t omnibus &longs;cientijs, quæ <lb/>nimirum euidentiam non ni&longs;i ex principijs obtinent per re&longs;o­<lb/>lutionem v&longs;que ad elementa, vt &longs;æpè docet Philo&longs;ophus in <lb/>Analiticis. </s> | <s id="N10917">Cumque ip&longs;æ cau&longs;æ ex qui­<lb/>bus mechanica facultas &longs;uas elicit conclu&longs;iones, vel &longs;int per <lb/>&longs;e notæ, vt citius ferri, quod facilius mouetur; Aequalia ab <lb/>æqualibus non moueri, & &longs;imilia; vel fundentur in principijs <lb/>demon&longs;tratis in alia &longs;uperiori &longs;cientia, de quibus habetur ve­<lb/>ra certitudo, & euidentia hinc vlterius fit, vt ip&longs;a pariter co­<lb/>gnitio mechanicarum conclu&longs;ionum, eandem participet, ac <lb/>&longs;ortiatur euidentiam, vt commune e&longs;t omnibus &longs;cientijs, quæ <lb/>nimirum euidentiam non ni&longs;i ex principijs obtinent per re&longs;o­<lb/>lutionem v&longs;que ad elementa, vt &longs;æpè docet Philo&longs;ophus in <lb/>Analiticis. </s> |
| </p> | </p> |
| <p id="N1092E" type="main"> | <p id="N1092E" type="main"> |
| <s id="N10930">Quòd &longs;i mechanica facultas &longs;imul à nobis <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> ars, <lb/>& hæc iuxta doctrinam allegatam Ari&longs;totelis 6. Ethic. <!-- REMOVE S-->cap. | <s id="N10930">Quòd &longs;i mechanica facultas &longs;imul à nobis <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> ars, <lb/>& hæc iuxta doctrinam allegatam Ari&longs;totelis 6. Ethic. <!-- REMOVE S-->cap. |
| |
| </p> | </p> |
| <p id="N10966" type="main"> | <p id="N10966" type="main"> |
| <s id="N10968">Tertio dicendum e&longs;t, mechanicam facultatem non e&longs;&longs;e <lb/>&longs;cientiam &longs;peculatiuam, &longs;ed practicam. </s> | <s id="N10968">Tertio dicendum e&longs;t, mechanicam facultatem non e&longs;&longs;e <lb/>&longs;cientiam &longs;peculatiuam, &longs;ed practicam. </s> |
| <s id="N1096D">In quo nulla pote&longs;t <lb/>e&longs;&longs;e difficultas præ&longs;ertim in doctrina Ari&longs;to<gap/>elis, nam vt ip&longs;e <lb/>docet lib. | <s id="N1096D">In quo nulla pote&longs;t <lb/>e&longs;&longs;e difficultas præ&longs;ertim in doctrina Ari&longs;totelis, nam vt ip&longs;e <lb/>docet lib. |
| | |
| 2. Met. <!-- REMOVE S-->cap. | 2. Met. <!-- REMOVE S-->cap. |
| | |
| |
| cap. | cap. |
| | |
| 1. eam diuidit in actiuam & factiuam. </s> | 1. eam diuidit in actiuam & factiuam. </s> |
| <s id="N109B7"><expan abbr="Quoniã">Quoniam</expan> <lb/>&longs;ub actiua optimè intelligitur contineri &longs;cientias, quæ ver&longs;an­<lb/>tur circa actus immanentes intellectus ac voluntatis, prout <lb/>dirigibiles per ip&longs;as met &longs;cientias; cuiu&longs;modi &longs;unt Logica, & <lb/>Philo&longs;ophia moralis, quarum finis & opus, e&longs;t ip&longs;a rectitudo <lb/>actionis internæ, &longs;eu actuum immanentium intellectus & vo­<lb/>luntatis, &longs;iuè in genere moris in ordine ad hone&longs;tatem, &longs;iuè in <lb/>genere cognitionis in ordine ad veritatem: &longs;ub factiua verò <lb/>contineri omnes illas artes, &longs;iuè &longs;cientias, quæ ver&longs;antur cir­<lb/>ca factionem aliquam &longs;eu opus extrin&longs;ccus faciendum, nem­<lb/>pe genere di&longs;tinctum ab ip&longs;o actu &longs;cientifico per quem opus <lb/>&longs;it aut dirigitur, vt quælibet operatio corporea, vel opus ex <lb/>tali operatione relictum, vt per&longs;picuè docet idem Ari&longs;toteles <lb/><gap/> Met. <!-- REMOVE S-->tex. <!-- REMOVE S-->16. & 1. magn. </s> | <s id="N109B7"><expan abbr="Quoniã">Quoniam</expan> <lb/>&longs;ub actiua optimè intelligitur contineri &longs;cientias, quæ ver&longs;an­<lb/>tur circa actus immanentes intellectus ac voluntatis, prout <lb/>dirigibiles per ip&longs;as met &longs;cientias; cuiu&longs;modi &longs;unt Logica, & <lb/>Philo&longs;ophia moralis, quarum finis & opus, e&longs;t ip&longs;a rectitudo <lb/>actionis internæ, &longs;eu actuum immanentium intellectus & vo­<lb/>luntatis, &longs;iuè in genere moris in ordine ad hone&longs;tatem, &longs;iuè in <lb/>genere cognitionis in ordine ad veritatem: &longs;ub factiua verò <lb/>contineri omnes illas artes, &longs;iuè &longs;cientias, quæ ver&longs;antur cir­<lb/>ca factionem aliquam &longs;eu opus extrin&longs;ecus faciendum, nem­<lb/>pe genere di&longs;tinctum ab ip&longs;o actu &longs;cientifico per quem opus <lb/>&longs;it aut dirigitur, vt quælibet operatio corporea, vel opus ex <lb/>tali operatione relictum, vt per&longs;picuè docet idem Ari&longs;toteles <lb/><gap/> Met. <!-- REMOVE S-->tex. <!-- REMOVE S-->16. & 1. magn. </s> |
| <s id="N109DC">moral. </s> | <s id="N109DC">moral. </s> |
| <s id="N109DF">cap. | <s id="N109DF">cap. |
| | |
| 33. Et huiu&longs;inodi <lb/>dicimus e&longs;&longs;e facultatem mechanicam, cum verè pro fine ha­<lb/>b<gap/>at opus externum, vt diximus, nempe motum localem & <lb/>arti&longs;icio&longs;um, vel quietem grauibus & leuibus impertiendam, <lb/>non &longs;ecus ac medicina con&longs;tituitur &longs;cientia practica, <lb/>co quod eius finis, ad quem ordinatur <lb/>tanquam ad proprium opus <lb/>&longs;it &longs;anitas anima­<lb/>lis ho­<lb/>minibus im­<lb/>pertien­<lb/>da. </s> | 33. Et huiu&longs;modi <lb/>dicimus e&longs;&longs;e facultatem mechanicam, cum verè pro fine ha­<lb/>beat opus externum, vt diximus, nempe motum localem & <lb/>artificio&longs;um, vel quietem grauibus & leuibus impertiendam, <lb/>non &longs;ecus ac medicina con&longs;tituitur &longs;cientia practica, <lb/>eo quod eius finis, ad quem ordinatur <lb/>tanquam ad proprium opus <lb/>&longs;it &longs;anitas anima­<lb/>lis ho­<lb/>minibus im­<lb/>pertien­<lb/>da. </s> |
| </p> | </p> |
| <pb pagenum="17" xlink:href="005/01/025.jpg"/> | <pb pagenum="17" xlink:href="005/01/025.jpg"/> |
| <p id="N109FE" type="head"> | <p id="N109FE" type="head"> |
| |
| <s id="N10A0B">ADDITIO QVARTA.</s> | <s id="N10A0B">ADDITIO QVARTA.</s> |
| </p> | </p> |
| <p id="N10A0E" type="main"> | <p id="N10A0E" type="main"> |
| <s id="N10A10">Vtrum autem Mechanica facultás portineat ad &longs;cien­<lb/>tiam phy&longs;icam, an ad mathernaticam, vel potius di­<lb/>cenda &longs;it partim phy&longs;ica, partim mathematica, non leuem <lb/>habet difficultatem. </s> | <s id="N10A10">Vtrum autem Mechanica facultás pertineat ad &longs;cien­<lb/>tiam phy&longs;icam, an ad mathematicam, vel potius di­<lb/>cenda &longs;it partim phy&longs;ica, partim mathematica, non leuem <lb/>habet difficultatem. </s> |
| <s id="N10A19">Etenim e&longs;&longs;e &longs;cientia<gap/> phy&longs;icam, illud <lb/>primoloco &longs;uadet, quia nimirumleius &longs;ubiectum e&longs;t phy&longs;i­<lb/>cum, vt graue, & leue, <expan abbr="virtusq.">virtusque</expan> moti<gap/>, ac detentiua, qua &longs;e­<lb/>cundum locum ip&longs;a cientur aut detinenti<gap/>. </s> | <s id="N10A19">Etenim e&longs;&longs;e &longs;cientia<gap/> phy&longs;icam, illud <lb/>primoloco &longs;uadet, quia nimirumleius &longs;ubiectum e&longs;t phy&longs;i­<lb/>cum, vt graue, & leue, <expan abbr="virtusq.">virtusque</expan> moti<gap/>, ac detentiua, qua &longs;e­<lb/>cundum locum ip&longs;a cientur aut detinenti<gap/>. </s> |
| <s id="N10A2C">Secundo <expan abbr="quoniã">quoniam</expan> <lb/>de huiu&longs;modi &longs;obiecto agitur&longs;ub rato<gap/>e phy&longs;ica, prout &longs;cili­<lb/>cet e&longs;t mobile &longs;ecundum locum n<gap/>a &longs;ua aut violentia; quæ <lb/>certè fit per impre&longs;&longs;ionem impetus, eleuationem, vel tractio­<lb/>nem, aut proiectionem, quæ &longs;unt operationes phy&longs;ioæ. </s> | <s id="N10A2C">Secundo <expan abbr="quoniã">quoniam</expan> <lb/>de huiu&longs;modi &longs;ubiecto agitur &longs;ub ratione phy&longs;ica, prout &longs;cili­<lb/>cet e&longs;t mobile &longs;ecundum locum n<gap/>a &longs;ua aut violentia; quæ <lb/>certè fit per impre&longs;&longs;ionem impetus, eleuationem, vel tractio­<lb/>nem, aut proiectionem, quæ &longs;unt operationes phy&longs;icæ. </s> |
| <s id="N10A3F">Ter­<lb/>tio, quia &longs;i&longs;tendo in puris principijs phy&longs;icis, fatis <expan abbr="vid&etilde;tur">videntur</expan> de­<lb/>mon&longs;trari omnia quæ pertractantur in ip&longs;a mechanica &longs;cien­<lb/>tia quoad propo&longs;itiones vniuer&longs;ales, ac propriè &longs;cientificas. <lb/></s> | <s id="N10A3F">Ter­<lb/>tio, quia &longs;i&longs;tendo in puris principijs phy&longs;icis, fatis <expan abbr="vid&etilde;tur">videntur</expan> de­<lb/>mon&longs;trari omnia quæ pertractantur in ip&longs;a mechanica &longs;cien­<lb/>tia quoad propo&longs;itiones vniuer&longs;ales, ac propriè &longs;cientificas. <lb/></s> |
| <s id="N10A4D">Vt exempli gratia, grauia æqualia ex æqualibus <expan abbr="di&longs;tãtijs">di&longs;tantijs</expan> &etail;què <lb/>ponderare, nec vnum po&longs;&longs;e in libra aliud vincere; nam ratio <lb/>huius e&longs;t, quia actio debet e&longs;&longs;e ab inæquali proportione, vt ex <lb/>Ari&longs;t. | <s id="N10A4D">Vt exempli gratia, grauia æqualia ex æqualibus <expan abbr="di&longs;tãtijs">di&longs;tantijs</expan> &etail;què <lb/>ponderare, nec vnum po&longs;&longs;e in libra aliud vincere; nam ratio <lb/>huius e&longs;t, quia actio debet e&longs;&longs;e ab inæquali proportione, vt ex <lb/>Ari&longs;t. |
| | |
| |
| <s id="N10B0D">Secundum requi&longs;itum e&longs;t, vt idem &longs;it obiectum &longs;ubalter­<lb/>natæ, ac &longs;ubalternantis &longs;ecundum aliquam rationem forma­<lb/>lem. </s> | <s id="N10B0D">Secundum requi&longs;itum e&longs;t, vt idem &longs;it obiectum &longs;ubalter­<lb/>natæ, ac &longs;ubalternantis &longs;ecundum aliquam rationem forma­<lb/>lem. </s> |
| <s id="N10B14">Quandoquidem &longs;i &longs;ubiecta e&longs;&longs;ent e&longs;&longs;entialiter diuer&longs;a <lb/>&longs;ecundum formalitatem qua cadunt &longs;ub &longs;cientiam, non dare­<lb/>tur tran&longs;itus à &longs;cientia &longs;ubalternata ad <expan abbr="&longs;ubalternant&etilde;">&longs;ubalternantem</expan>, vt do­<lb/>cet Ari&longs;toteles; hoc e&longs;t accipiendo ex illa propria principia <lb/>ac media ad probandum &longs;uas conclu&longs;iones; quia tam pa&longs;&longs;io­<lb/>nes demon&longs;trandæ de &longs;ubiecto, quàm principia quæ &longs;unt <lb/>cau&longs;æ intrin&longs;ecæ ip&longs;arum <expan abbr="pa&longs;&longs;ionũ">pa&longs;&longs;ionum</expan>, debent e&longs;&longs;e maximè pro­<lb/>pria & connexa cum ip&longs;o &longs;ubiecto: nihil autem pote&longs;t e&longs;&longs;e <lb/>maximè proprium duobus &longs;ubiectis e&longs;&longs;entialiter diuer&longs;is; ac <lb/>proinde ex connexione cum principijs vnius, inferri non po­<lb/>te&longs;t connexio alterius ad conficiendas demon&longs;trationes. </s> | <s id="N10B14">Quandoquidem &longs;i &longs;ubiecta e&longs;&longs;ent e&longs;&longs;entialiter diuer&longs;a <lb/>&longs;ecundum formalitatem qua cadunt &longs;ub &longs;cientiam, non dare­<lb/>tur tran&longs;itus à &longs;cientia &longs;ubalternata ad <expan abbr="&longs;ubalternant&etilde;">&longs;ubalternantem</expan>, vt do­<lb/>cet Ari&longs;toteles; hoc e&longs;t accipiendo ex illa propria principia <lb/>ac media ad probandum &longs;uas conclu&longs;iones; quia tam pa&longs;&longs;io­<lb/>nes demon&longs;trandæ de &longs;ubiecto, quàm principia quæ &longs;unt <lb/>cau&longs;æ intrin&longs;ecæ ip&longs;arum <expan abbr="pa&longs;&longs;ionũ">pa&longs;&longs;ionum</expan>, debent e&longs;&longs;e maximè pro­<lb/>pria & connexa cum ip&longs;o &longs;ubiecto: nihil autem pote&longs;t e&longs;&longs;e <lb/>maximè proprium duobus &longs;ubiectis e&longs;&longs;entialiter diuer&longs;is; ac <lb/>proinde ex connexione cum principijs vnius, inferri non po­<lb/>te&longs;t connexio alterius ad conficiendas demon&longs;trationes. </s> |
| <s id="N10B33">Ea­<lb/>dem ergo e&longs;&longs;entialiter debent e&longs;&longs;e &longs;ubiecta &longs;ubalternantis, ac <lb/>&longs;ubalternatæ, &longs;altem &longs;ecundum aliquam rationem formalem, <lb/>quamuis alia ratione differant inter &longs;e. </s> | <s id="N10B33">Ea­<lb/>dem ergo e&longs;&longs;entialiter debent e&longs;&longs;e &longs;ubiecta &longs;ubalternantis, ac <lb/>&longs;ubalternatæ, &longs;altem &longs;ecundum aliquam rationem formalem, <lb/>quamuis alia ratione differant inter &longs;e. </s> |
| <s id="N10B3C">Semper enim ratio <lb/>lla formalis &longs;ub qua agitur de aliquo in &longs;cientia, vniuer&longs;aliori <lb/>ac &longs;impliciori modo con&longs;ideratur in &longs;ubalternante, quàm in <lb/>&longs;ubalternata, in qua &longs;emper contrahitur ab aliqua differentia <lb/>accidentali &longs;uperaddita, vt con&longs;tat in Mu&longs;ica re&longs;pectu Arith­<lb/>meticæ, & in Per&longs;pectiua re&longs;pectu Geometriæ. </s> | <s id="N10B3C">Semper enim ratio <lb/>illa formalis &longs;ub qua agitur de aliquo in &longs;cientia, vniuer&longs;aliori <lb/>ac &longs;impliciori modo con&longs;ideratur in &longs;ubalternante, quàm in <lb/>&longs;ubalternata, in qua &longs;emper contrahitur ab aliqua differentia <lb/>accidentali &longs;uperaddita, vt con&longs;tat in Mu&longs;ica re&longs;pectu Arith­<lb/>meticæ, & in Per&longs;pectiua re&longs;pectu Geometriæ. </s> |
| <s id="N10B49">Siquidem in <lb/>Arithmetica &longs;impliciter con&longs;ideratur numerus &longs;ecundum &longs;e, <lb/>in Mu&longs;ica vero con&longs;ideratur numerus in &longs;ono. </s> | <s id="N10B49">Siquidem in <lb/>Arithmetica &longs;impliciter con&longs;ideratur numerus &longs;ecundum &longs;e, <lb/>in Mu&longs;ica vero con&longs;ideratur numerus in &longs;ono. </s> |
| <s id="N10B50"><expan abbr="Similiterq.">Similiterque</expan> in <lb/>Geometria &longs;olum con&longs;iderantur lineæ, in Per&longs;pectiua vero <lb/>con&longs;iderantur in vi&longs;u, quæ differentiæ putantur accidentales; <lb/>nam vt docet Ari&longs;toteles locis citatis, & 13 metaph. </s> | <s id="N10B50"><expan abbr="Similiterq.">Similiterque</expan> in <lb/>Geometria &longs;olum con&longs;iderantur lineæ, in Per&longs;pectiua vero <lb/>con&longs;iderantur in vi&longs;u, quæ differentiæ putantur accidentales; <lb/>nam vt docet Ari&longs;toteles locis citatis, & 13 metaph. </s> |
| <s id="N10B5C">&longs;um. <!-- REMOVE S-->1. <lb/>cap. | <s id="N10B5C">&longs;um. <!-- REMOVE S-->1. <lb/>cap. |
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| </p> | </p> |
| <p id="N10B68" type="main"> | <p id="N10B68" type="main"> |
| <s id="N10B6A">Quibus po&longs;itis, dicendum e&longs;t, Mechanicam <expan abbr="facultat&etilde;">facultatem</expan> ab­<pb pagenum="20" xlink:href="005/01/028.jpg"/>&longs;olutè ac totaliter non &longs;ubalternari Philo&longs;ophiæ naturali, &longs;ed <lb/>Mathematicæ; Ita &longs;en&longs;it expre&longs;sè Ari&longs;toteles in principio iam <lb/>explicato huius opu&longs;culi, cum ait, &longs;ubiectum quidem huius <lb/>facultatis e&longs;&longs;e Phy&longs;icum, con&longs;iderationem verò e&longs;&longs;e mathe­<lb/>maticam. </s> | <s id="N10B6A">Quibus po&longs;itis, dicendum e&longs;t, Mechanicam <expan abbr="facultat&etilde;">facultatem</expan> ab­<pb pagenum="20" xlink:href="005/01/028.jpg"/>&longs;olutè ac totaliter non &longs;ubalternari Philo&longs;ophiæ naturali, &longs;ed <lb/>Mathematicæ; Ita &longs;en&longs;it expre&longs;sè Ari&longs;toteles in principio iam <lb/>explicato huius opu&longs;culi, cum ait, &longs;ubiectum quidem huius <lb/>facultatis e&longs;&longs;e Phy&longs;icum, con&longs;iderationem verò e&longs;&longs;e mathe­<lb/>maticam. </s> |
| <s id="N10B7E">Quod po&longs;tea omnes Philo&longs;ophi, ac Mathematici <lb/>vniuer&longs;aliter &longs;upponunt in di&longs;tributione, ac &longs;ubalternatione <lb/>Mathcmaticarum di&longs;ciplinarum, &longs;ubordinando hanc &longs;cien­<lb/>tiam Geometricæ. <!-- KEEP S--></s> | <s id="N10B7E">Quod po&longs;tea omnes Philo&longs;ophi, ac Mathematici <lb/>vniuer&longs;aliter &longs;upponunt in di&longs;tributione, ac &longs;ub alternatione <lb/>Mathematicarum di&longs;ciplinarum, &longs;ubordinando hanc &longs;cien­<lb/>tiam Geometricæ. <!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N10B88" type="main"> | <p id="N10B88" type="main"> |
| <s id="N10B8A">Ratione verò probatur, nam quælibet &longs;cientia &longs;ubalterna, <lb/>illi &longs;cicntiæ dicitur &longs;ubalternari, cuius idem &longs;ubiectum &longs;ecun­<lb/>dum aliquam rationem formalem con&longs;iderat, cuiu&longs;que con­<lb/>clu&longs;ionibus vtitur tanquam principijs ad conficiendas pro­<lb/>prias demon&longs;trationes; &longs;ed &longs;cientia Mechanica circa idem <lb/>&longs;ubiectum &longs;ecundum aliquam rationem formalem ver&longs;atur <lb/>ac Geometria, ex <expan abbr="eaq.">eaque</expan> vt plurimum &longs;umit &longs;ua principia ad <lb/>demon&longs;trandas mechanicas conclu&longs;iones. </s> | <s id="N10B8A">Ratione verò probatur, nam quælibet &longs;cientia &longs;ubalterna, <lb/>illi &longs;cicntiæ dicitur &longs;ubalternari, cuius idem &longs;ubiectum &longs;ecun­<lb/>dum aliquam rationem formalem con&longs;iderat, cuiu&longs;que con­<lb/>clu&longs;ionibus vtitur tanquam principijs ad conficiendas pro­<lb/>prias demon&longs;trationes; &longs;ed &longs;cientia Mechanica circa idem <lb/>&longs;ubiectum &longs;ecundum aliquam rationem formalem ver&longs;atur <lb/>ac Geometria, ex <expan abbr="eaq.">eaque</expan> vt plurimum &longs;umit &longs;ua principia ad <lb/>demon&longs;trandas mechanicas conclu&longs;iones. </s> |
| |
| </p> | </p> |
| <p id="N10BEA" type="main"> | <p id="N10BEA" type="main"> |
| <s id="N10BEC">Quod autem Mechanica facultas vtatur principijs. </s> | <s id="N10BEC">Quod autem Mechanica facultas vtatur principijs. </s> |
| <s id="N10BEF">proba­<lb/>tis in Geometria, palam o&longs;tendunt ip&longs;æ demon&longs;trationes me­<lb/>chanicæ, quæ ferè omnes immediatè nituntur propo&longs;itioni­<lb/>bus, ac theorematibus demon&longs;tratis in illa, deinde re&longs;oluun­<lb/>tur in eadem principia geometrica; <expan abbr="&longs;iquid&etilde;">&longs;iquidem</expan> præ cipuè fundan­<lb/>tur in proprietatibus, ac pa&longs;&longs;ionibus circuli quæ &longs;anè demon­<lb/>&longs;trantur principijs geometrieis, vt pr&etail;&longs;ertim patet ex tertio ac <lb/>&longs;exto <expan abbr="elementorũ">elementorum</expan> Euclidis. <!-- KEEP S--></s> | <s id="N10BEF">proba­<lb/>tis in Geometria, palam o&longs;tendunt ip&longs;æ demon&longs;trationes me­<lb/>chanicæ, quæ ferè omnes immediatè nituntur propo&longs;itioni­<lb/>bus, ac theorematibus demon&longs;tratis in illa, deinde re&longs;oluun­<lb/>tur in eadem principia geometrica; <expan abbr="&longs;iquid&etilde;">&longs;iquidem</expan> præcipuè fundan­<lb/>tur in proprietatibus, ac pa&longs;&longs;ionibus circuli quæ &longs;anè demon­<lb/>&longs;trantur principijs geometricis, vt pr&etail;&longs;ertim patet ex tertio ac <lb/>&longs;exto <expan abbr="elementorũ">elementorum</expan> Euclidis. <!-- KEEP S--></s> |
| <s id="N10C09">Rur&longs;us principia Mechanica, quæ <lb/>traduntur ab Archimede, <expan abbr="alijsq.">alijsque</expan> Mechanicis, vel &longs;unt omninò <lb/>geometrica, vel &longs;umuntur ex geornetricis. </s> | <s id="N10C09">Rur&longs;us principia Mechanica, quæ <lb/>traduntur ab Archimede, <expan abbr="alijsq.">alijsque</expan> Mechanicis, vel &longs;unt omninò <lb/>geometrica, vel &longs;umuntur ex geometricis. </s> |
| <s id="N10C14">Vt grauia æqua­<lb/>lia ex æqualibus di&longs;tantijs æquè ponderare: Aequalia verò <lb/>grauia ex inæqualibus di&longs;tantijs, non æquè ponderare, &longs;ed <lb/>præponderare ad graue ex maiori di&longs;tantia. </s> | <s id="N10C14">Vt grauia æqua­<lb/>lia ex æqualibus di&longs;tantijs æquè ponderare: Aequalia verò <lb/>grauia ex inæqualibus di&longs;tantijs, non æquè ponderare, &longs;ed <lb/>præponderare ad graue ex maiori di&longs;tantia. </s> |
| <s id="N10C1D">Et æqualibus &longs;i­<lb/>milibusq, figuris planis inter &longs;e coaptatis, centra quoque <lb/>grauitatum inter &longs;e coaptari oportere. </s> | <s id="N10C1D">Et æqualibus &longs;i­<lb/>milibusque, figuris planis inter &longs;e coaptatis, centra quoque <lb/>grauitatum inter &longs;e coaptari oportere. </s> |
| <s id="N10C24">Et &longs;imilia vt vi­<lb/>dere e&longs;t apud ip&longs;um Archimedem, Pappum, & alios <lb/>Auctores. </s> | <s id="N10C24">Et &longs;imilia vt vi­<lb/>dere e&longs;t apud ip&longs;um Archimedem, Pappum, & alios <lb/>Auctores. </s> |
| </p> | </p> |
| <p id="N10C2B" type="main"> | <p id="N10C2B" type="main"> |
| <s id="N10C2D">Ad primum igitur argumentum in contrarium Re&longs;ponde­<lb/>tur, &longs;ubiectum Mechanicæ facultatis e&longs;&longs;e quidem phy&longs;icum <lb/>in genere entis, non tamen in genere &longs;cibilis, nempe &longs;ub ra­<lb/>tione qua de illo agitur in hac &longs;cientia. </s> | <s id="N10C2D">Ad primum igitur argumentum in contrarium Re&longs;ponde­<lb/>tur, &longs;ubiectum Mechanicæ facultatis e&longs;&longs;e quidem phy&longs;icum <lb/>in genere entis, non tamen in genere &longs;cibilis, nempe &longs;ub ra­<lb/>tione qua de illo agitur in hac &longs;cientia. </s> |
| <s id="N10C36">Quare licet <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan> <lb/>materiale huius facultatis, quod e&longs;t graue, & leue, &longs;eu quan­<lb/>titas ponderis cuiu&longs;que corporis mobilis &longs;ecundum locum, <lb/>connotet pa&longs;&longs;ionem quamdam corporis naturalis, quod con <lb/>&longs;tituitur &longs;ubiectum adæquatum Phy&longs;icæ; cum tamen non <expan abbr="cõ-&longs;ideretur">con­<lb/>&longs;ideretur</expan> hic per habitudinemad illud, pertinere non pote&longs;t <lb/>ad &longs;cientiam phy&longs;icam; &longs;icut nec ip&longs;a quantitas, quæ con&longs;ti­<lb/>tuitur &longs;ubiectum adæ quatum totius facultatis mathematicæ, <lb/>quamuis in &longs;e &longs;it affectio corporis naturalis, & pa&longs;&longs;io &longs;ub&longs;tar­<lb/>tiæ corporeæ, de <expan abbr="illaq.">illaque</expan> abundè etiam tractetur in Phy&longs;ica. <lb/></s> | <s id="N10C36">Quare licet <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan> <lb/>materiale huius facultatis, quod e&longs;t graue, & leue, &longs;eu quan­<lb/>titas ponderis cuiu&longs;que corporis mobilis &longs;ecundum locum, <lb/>connotet pa&longs;&longs;ionem quamdam corporis naturalis, quod con<lb/>&longs;tituitur &longs;ubiectum adæquatum Phy&longs;icæ; cum tamen non <expan abbr="cõ-&longs;ideretur">con­<lb/>&longs;ideretur</expan> hic per habitudinem ad illud, pertinere non pote&longs;t <lb/>ad &longs;cientiam phy&longs;icam; &longs;icut nec ip&longs;a quantitas, quæ con&longs;ti­<lb/>tuitur &longs;ubiectum adæquatum totius facultatis mathematicæ, <lb/>quamuis in &longs;e &longs;it affectio corporis naturalis, & pa&longs;&longs;io &longs;ub&longs;tan­<lb/>tiæ corporeæ, de <expan abbr="illaq.">illaque</expan> abundè etiam tractetur in Phy&longs;ica. <lb/></s> |
| <s id="N10C58"><expan abbr="Idemq.">Idemque</expan> exempli&longs;icari pote&longs;t in Mu&longs;ica & Per&longs;pectiua, quarum <pb pagenum="22" xlink:href="005/01/030.jpg"/>&longs;ubiecta materialia non minus &longs;unt phy&longs;ica, con&longs;ideratio ve­<lb/>rò mathematica. </s> | <s id="N10C58"><expan abbr="Idemq.">Idemque</expan> exemplificari pote&longs;t in Mu&longs;ica & Per&longs;pectiua, quarum <pb pagenum="22" xlink:href="005/01/030.jpg"/>&longs;ubiecta materialia non minus &longs;unt phy&longs;ica, con&longs;ideratio ve­<lb/>rò mathematica. </s> |
| <s id="N10C65">Ac tandem aperti&longs;&longs;imè con&longs;tare pote&longs;t in­<lb/>ductione partium eiu&longs;dem facultatis Mechanicæ. <!-- KEEP S--></s> | <s id="N10C65">Ac tandem aperti&longs;&longs;imè con&longs;tare pote&longs;t in­<lb/>ductione partium eiu&longs;dem facultatis Mechanicæ. <!-- KEEP S--></s> |
| <s id="N10C6B">Nam licet <lb/>Centrobarica verbigratia, vel Machinaria, non agat ni&longs;i de <lb/>&longs;ubiectis phy&longs;icis, tota tamen eorum con&longs;ideratio e&longs;t mathe­<lb/>matica, geometricè procedendo ad <expan abbr="demon&longs;trãdas">demon&longs;trandas</expan> dimen&longs;io­<lb/>nes, &longs;iguras, di&longs;tantias, pondero&longs;itatem, vires, ac motum ip­<lb/>&longs;orum. </s> | <s id="N10C6B">Nam licet <lb/>Centrobarica verbigratia, vel Machinaria, non agat ni&longs;i de <lb/>&longs;ubiectis phy&longs;icis, tota tamen eorum con&longs;ideratio e&longs;t mathe­<lb/>matica, geometricè procedendo ad <expan abbr="demon&longs;trãdas">demon&longs;trandas</expan> dimen&longs;io­<lb/>nes, &longs;iguras, di&longs;tantias, pondero&longs;itatem, vires, ac motum ip­<lb/>&longs;orum. </s> |
| <s id="N10C7C">Similites &longs;piritalis tractatio quamuis agat de aere, ac <lb/>de coniunctione aeris cum alijs elementis ad multos vitæ no­<lb/>&longs;træ v&longs;us, quæ res phy&longs;icæ in &longs;e &longs;unt, nibilominus ad mathe­<lb/>maticam contemplationem pertinet, & ab Herone mathe­<lb/>maticè cum &longs;uis demon&longs;trationibus traditur, contemplando <lb/>proportionem, numerum, magnitudinem, di&longs;tantiam, ordi­<lb/>nem, figuram, & cau&longs;as effectuum, qui ex inclu&longs;o aere profi­<lb/>ci&longs;cuntur. </s> | <s id="N10C7C">Similites &longs;piritalis tractatio quamuis agat de aere, ac <lb/>de coniunctione aeris cum alijs elementis ad multos vitæ no­<lb/>&longs;træ v&longs;us, quæ res phy&longs;icæ in &longs;e &longs;unt, nihilominus ad mathe­<lb/>maticam contemplationem pertinet, & ab Herone mathe­<lb/>maticè cum &longs;uis demon&longs;trationibus traditur, contemplando <lb/>proportionem, numerum, magnitudinem, di&longs;tantiam, ordi­<lb/>nem, figuram, & cau&longs;as effectuum, qui ex inclu&longs;o aere profi­<lb/>ci&longs;cuntur. </s> |
| <s id="N10C8D">Quorum omnium ratio e&longs;t, quia in his non atten­<lb/>ditur &longs;ubiectum materialiter &longs;umptum in e&longs;&longs;e rei, &longs;ed formali­<lb/>tas qua cadit &longs;ub &longs;cientiam, &longs;eu ratio &longs;ub que agitur de ille, <lb/>quæ dicitur &longs;ubiectum, vel obiectum formale; cumo, hoc in <lb/>propo&longs;ito pertineat ad Mathematioum, &longs;equitur, facultatem <lb/>ip&longs;am &longs;iue &longs;cientiam mechanieam, e&longs;&longs;e verè mathematicam. </s> | <s id="N10C8D">Quorum omnium ratio e&longs;t, quia in his non atten­<lb/>ditur &longs;ubiectum materialiter &longs;umptum in e&longs;&longs;e rei, &longs;ed formali­<lb/>tas qua cadit &longs;ub &longs;cientiam, &longs;eu ratio &longs;ub que agitur de ille, <lb/>quæ dicitur &longs;ubiectum, vel obiectum formale; <expan abbr="cumq.">cumque</expan>, hoc in <lb/>propo&longs;ito pertineat ad Mathematicum, &longs;equitur, facultatem <lb/>ip&longs;am &longs;iue &longs;cientiam mechanicam, e&longs;&longs;e verè mathematicam. </s> |
| </p> | </p> |
| <p id="N10C9A" type="main"> | <p id="N10C9A" type="main"> |
| <s id="N10C9C">Ad &longs;ecundum Re&longs;pondetur, motionem & quietem <expan abbr="grauiũ">grauium</expan> <lb/>& leuium, &longs;iue ex natura &longs;ua, &longs;iue ex aliqua violentia vtraque <lb/>profici&longs;catur, e&longs;&longs;e quidem pa&longs;&longs;iones phy&longs;icas eorum prout <lb/>corpora naturalia &longs;unt, non tamen con&longs;iderari à Mechanieis <lb/>vt tales pa&longs;&longs;iones &longs;unt, &longs;ed prout obtineri po&longs;&longs;une ab illis tan­<lb/>quam finis intentus, mediante aliquo artificio. </s> | <s id="N10C9C">Ad &longs;ecundum Re&longs;pondetur, motionem & quietem <expan abbr="grauiũ">grauium</expan> <lb/>& leuium, &longs;iue ex natura &longs;ua, &longs;iue ex aliqua violentia vtraque <lb/>profici&longs;catur, e&longs;&longs;e quidem pa&longs;&longs;iones phy&longs;icas eorum prout <lb/>corpora naturalia &longs;unt, non tamen con&longs;iderari à Mechanicis <lb/>vt tales pa&longs;&longs;iones &longs;unt, &longs;ed prout obtineri po&longs;&longs;um ab illis tan­<lb/>quam finis intentus, mediante aliquo artificio. </s> |
| <s id="N10CAD">Vnde ratio <lb/>formalis &longs;ub qua grauia & leuia con&longs;tituuntur obiecta huius <lb/>&longs;cientiæ, non e&longs;t prout mobilia &longs;unt &longs;ecundum locum, aut <lb/>quie&longs;cere po&longs;&longs;unt, ab&longs;olutè loquendo; &longs;ed prout artificiosè <lb/>moueri aut quie&longs;cere po&longs;&longs;unt, iouoluendo modum quo mo­<lb/>uenda &longs;unt, vel detinenda, & <gap/>irca quem formaliter ors ip&longs;a <lb/>ver&longs;atur ad &longs;inem intentum. </s> | <s id="N10CAD">Vnde ratio <lb/>formalis &longs;ub qua grauia & leuia con&longs;tituuntur obiecta huius <lb/>&longs;cientiæ, non e&longs;t prout mobilia &longs;unt &longs;ecundum locum, aut <lb/>quie&longs;cere po&longs;&longs;unt, ab&longs;olutè loquendo; &longs;ed prout artificiosè <lb/>moueri aut quie&longs;cere po&longs;&longs;unt, loquendo modum quo mo­<lb/>uenda &longs;unt, vel detinenda, & circa quem formaliter ors ip&longs;a <lb/>ver&longs;atur ad finem intentum. </s> |
| </p> | </p> |
| <p id="N10CBE" type="main"> | <p id="N10CBE" type="main"> |
| <s id="N10CC0">Ad tertium Re&longs;pondetur, nec omnia, nec &longs;ntis demon&longs;tra­<lb/>ri po&longs;&longs;e ex principijs phy&longs;icis in hac &longs;cientia. </s> | <s id="N10CC0">Ad tertium Re&longs;pondetur, nec omnia, nec &longs;atis demon&longs;tra­<lb/>ri po&longs;&longs;e ex principijs phy&longs;icis in hac &longs;cientia. </s> |
| <s id="N10CC5">Porrò licet non­<lb/>nulla de graui & leui &longs;npponantur, vel etiam probentur ex <lb/><gap/>is, cæteratamen vt plurimum & exactè non <expan abbr="demon&longs;trãtus">demon&longs;trantus</expan> <pb pagenum="23" xlink:href="005/01/031.jpg"/>ni&longs;i ex principijs geométricis, quare &longs;lcat de lride multa <lb/>pertractantur in Phy&longs;ica, quod ramen non tollit omnimod am <lb/>eius cognitionem ad Per&longs;pectiram refe<gap/>ita quamuis mul­<lb/>ta de graui & lem &longs;umantur ex phy&longs;ic<gap/>, hoc non ob&longs;tat quo­<lb/><gap/>s prout artificiosè mobilia &longs;unt, ex pro&longs;e&longs;&longs;o & omnino <lb/>&longs;olum cogno&longs;cantur in hac &longs;cientia ex principijs mathem ati­<lb/>cis. </s> | <s id="N10CC5">Porrò licet non­<lb/>nulla de graui & leui &longs;upponantur, vel etiam probentur ex <lb/><gap/>is, cætera tamen vt plurimum & exactè non <expan abbr="demon&longs;trãtus">demon&longs;tratus</expan> <pb pagenum="23" xlink:href="005/01/031.jpg"/>ni&longs;i ex principijs geométricis, quare ficat de lride multa <lb/>pertractantur in Phy&longs;ica, quod ramen non tollit omnimodam <lb/>eius cognitionem ad Per&longs;pectiuam referri, ita quamuis mul­<lb/>ta de graui & lem &longs;umantur ex phy&longs;icis, hoc non ob&longs;tat quo­<lb/>minus prout artificiosè mobilia &longs;unt, ex pro&longs;e&longs;&longs;o & omnino <lb/>&longs;olum cogno&longs;cantur in hac &longs;cientia ex principijs mathemati­<lb/>cis. </s> |
| <s id="N10CE7">Et &longs;ic, grauia æ qudlia ex æqualibus di&longs;tan&longs;&longs;js æ què pon­<lb/>derare, <expan abbr="vnumq.">vnumque</expan> in libra non po&longs;&longs;e aliud vincere, non &longs;atis <lb/>probatur ex illo principio phyfico, quod àctio debeat e&longs;&longs;e ab <lb/>inæquali proportione. </s> | <s id="N10CE7">Et &longs;ic, grauia æqualia ex æqualibus di&longs;tantijs æquè pon­<lb/>derare, <expan abbr="vnumq.">vnumque</expan> in libra non po&longs;&longs;e aliud vincere, non &longs;atis <lb/>probatur ex illo principio physico, quod àctio debeat e&longs;&longs;e ab <lb/>inæquali proportione. </s> |
| <s id="N10CF4">Quando qoid<gap/> inæqualitas di&longs;&longs;<gap/>­<lb/>tiæ non tollic æ qual tatera ponderis, nec proportionem illius <lb/>ad aluerum, &longs;i &longs;edundum &longs;e ac phy&longs;iec con&longs;ideretur, tollit <lb/>au<gap/>&longs;r mathematicè demon&longs;tratur, maiorem di&longs;tantiam a <lb/>centro, vbi grauia falciuntar, grauitatem, vel potiùs e&longs;&longs;e­<lb/>ctumillius, actamq ponderandi in ip&longs;is grauibus augere. <lb/></s> | <s id="N10CF4">Quando quiddem inæqualitas di&longs;&longs;<gap/>­<lb/>tiæ non tollit æqual tatera ponderis, nec proportionem illius <lb/>ad aluerum, &longs;i &longs;ecundum &longs;e ac phy&longs;icis con&longs;ideretur, tollit <lb/>autem &longs;e mathematicè demon&longs;tratur, maiorem di&longs;tantiam a <lb/>centro, vbi grauia falciuntur, grauitatem, vel potiùs effe­<lb/>ctum illius, <expan abbr="actumq.">actumque</expan> ponderandi in ip&longs;is grauibus augere. <lb/></s> |
| <s id="N10D08">Item maior velotitas, ac faci&longs;itas quam experimur in motu <lb/>circulari earum partium, quæ magis di&longs;&longs;ant à centro, non <lb/>probatur à priori, nec demon&longs;tratur ex eo quod maius &longs;pa­<lb/>cium percurrant in æ quali tempore, nam hoc e&longs;t idem pet <lb/>diuer&longs;a explicare. </s> | <s id="N10D08">Item maior velocitas, ac facilitas quam experimur in motu <lb/>circulari earum partium, quæ magis di&longs;&longs;ant à centro, non <lb/>probatur à priori, nec demon&longs;tratur ex eo quod maius &longs;pa­<lb/>tium percurrant in æquali tempore, nam hoc e&longs;t idem per <lb/>diuer&longs;a explicare. </s> |
| <s id="N10D13">Demon&longs;tratur autem per cau&longs;am, & à <lb/>priori, ex illo principio mathematico, quod quanto magis li­<lb/>neæ à centro di&longs;ce&longs;&longs;erint, magis participant de motu recto <lb/>acnaturali, <expan abbr="minusq.">minusque</expan> retranuntar in circumuolutione cil cull, <lb/>at &longs;uo lo eo explicabitur ex Ari&longs;totele qui &longs;anè in hoc <expan abbr="alijsq.">alijsque</expan> <lb/>dogmatibus mechanicis non vitur demon&longs;trationibus geo­<lb/>metricis ad exemplum, vt in logica vel phy&longs;ica, neque ad <lb/>confirmationem veritatis probatæ; &longs;ed ve ab&longs;olutè probet <lb/>quod a&longs;&longs;ump&longs;erat, <expan abbr="quodq.">quodque</expan> aliter omninò probate nequiret. </s> | <s id="N10D13">Demon&longs;tratur autem per cau&longs;am, & à <lb/>priori, ex illo principio mathematico, quod quanto magis li­<lb/>neæ à centro di&longs;ce&longs;&longs;erint, magis participant de motu recto <lb/>ac naturali, <expan abbr="minusq.">minusque</expan> retrahuntur in circumuolutione circull, <lb/>at &longs;uo lo eo explicabitur ex Ari&longs;totele qui &longs;anè in hoc <expan abbr="alijsq.">alijsque</expan> <lb/>dogmatibus mechanicis non vtitur demon&longs;trationibus geo­<lb/>metricis ad exemplum, vt in logica vel phy&longs;ica, neque ad <lb/>confirmationem veritatis probatæ; &longs;ed ve ab&longs;olutè probet <lb/>quod a&longs;&longs;ump&longs;erat, <expan abbr="quodq.">quodque</expan> aliter omninò probare nequiret. </s> |
| </p> | </p> |
| <p id="N10D32" type="main"> | <p id="N10D32" type="main"> |
| <s id="N10D34">Ex quibus fæcil<gap/> apparet quid re&longs;pandendum &longs;it ad quar­<lb/>tum & quintum argumentum, nem peprincipia mathemati­<lb/>ca non modo in mechanica &longs;oientia de&longs;eruire ad maiorem <lb/>claritatem doctrinæ, & vt hæc aptetur ad praxim circa parti­<lb/>cularia, &longs;ed ab&longs;olutè ad demon&longs;trandas &longs;uas conclu&longs;iones in <lb/>vniuer&longs;um, quas quippe aliter non po&longs;&longs;et omninò probare. <lb/></s> | <s id="N10D34">Ex quibus fæcile apparet quid re&longs;paondendum &longs;it ad quar­<lb/>tum & quintum argumentum, nempe principia mathemati­<lb/>ca non modo in mechanica &longs;cientia de&longs;eruire ad maiorem <lb/>claritatem doctrinæ, & vt hæc aptetur ad praxim circa parti­<lb/>cularia, &longs;ed ab&longs;olutè ad demon&longs;trandas &longs;uas conclu&longs;iones in <lb/>vniuer&longs;um, quas quippe aliter non po&longs;&longs;et omninò probare. <lb/></s> |
| <s id="N10D44">Id quod non &longs;olum verificatur in vni vel altera conclu&longs;ione, <lb/>&longs;ed ferè in omnibus, vt in progre&longs;&longs;u con&longs;tabit. </s> | <s id="N10D44">Id quod non &longs;olum verificatur in vni vel altera conclu&longs;ione, <lb/>&longs;ed ferè in omnibus, vt in progre&longs;&longs;u con&longs;tabit. </s> |
| </p> | </p> |
| <pb pagenum="24" xlink:href="005/01/032.jpg"/> | <pb pagenum="24" xlink:href="005/01/032.jpg"/> |
| <p id="N10D4D" type="main"> | <p id="N10D4D" type="main"> |
| <s id="N10D4F">Quod <expan abbr="tand&etilde;">tandem</expan> afferebatur de ortu Mechanices ex Phy&longs;ica, <lb/>& Mathematica ad probandum e&longs;&longs;e &longs;cientiam ex vtraque <lb/>conflatam, &longs;i rectè con&longs;ideretur, nullius e&longs;t momenti; nam <lb/>vere dicitur ex Phy&longs;ica &longs;ump&longs;i&longs;&longs;e &longs;ubiectum, & ex Geome­<lb/>tria principia quibus in &longs;uis demon&longs;trationibus procederet; <lb/>ex quo tamen non &longs;equitur, ip&longs;am veluti mixtam quandam <lb/>re&longs;ultare &longs;cientiam, partim &longs;cilicet Phy&longs;icam, partim verò <lb/>Mathematicam; tum quia &longs;peci&longs;icatio &longs;cientiarum vt diximus <lb/>non attenditur ex &longs;ubiecto materiali, &longs;ed ex obiecto formali; <lb/>tum etiam, quia nequit vna eademque &longs;cientia, pluribus &longs;cien­<lb/>tijs omnino diuer&longs;is &longs;ubalternari, cum vnitas ip&longs;ius attenda­<lb/>tur penes vnitatem eiu&longs;dem obiecti formalis, quod mutuari <lb/>debet vel ex vna, vel ex altera &longs;uperiori &longs;cientia. </s> | <s id="N10D4F">Quod <expan abbr="tand&etilde;">tandem</expan> afferebatur de ortu Mechanices ex Phy&longs;ica, <lb/>& Mathematica ad probandum e&longs;&longs;e &longs;cientiam ex vtraque <lb/>conflatam, &longs;i rectè con&longs;ideretur, nullius e&longs;t momenti; nam <lb/>vere dicitur ex Phy&longs;ica &longs;ump&longs;i&longs;&longs;e &longs;ubiectum, & ex Geome­<lb/>tria principia quibus in &longs;uis demon&longs;trationibus procederet; <lb/>ex quo tamen non &longs;equitur, ip&longs;am veluti mixtam quandam <lb/>re&longs;ultare &longs;cientiam, partim &longs;cilicet Phy&longs;icam, partim verò <lb/>Mathematicam; tum quia &longs;pecificatio &longs;cientiarum vt diximus <lb/>non attenditur ex &longs;ubiecto materiali, &longs;ed ex obiecto formali; <lb/>tum etiam, quia nequit vna eademque &longs;cientia, pluribus &longs;cien­<lb/>tijs omnino diuer&longs;is &longs;ubalternari, cum vnitas ip&longs;ius attenda­<lb/>tur penes vnitatem eiu&longs;dem obiecti formalis, quod mutuari <lb/>debet vel ex vna, vel ex altera &longs;uperiori &longs;cientia. </s> |
| <s id="N10D6E">Quare cum <lb/>Ari&longs;toteles ait, Mechanica problemata e&longs;&longs;e Mathematicarum <lb/>quæ&longs;tionum, naturaliumque communia, non intellexit e&longs;&longs;e <lb/>veluti aggregata & <expan abbr="cõflata">conflata</expan> ex illis vtri&longs;que. </s> | <s id="N10D6E">Quare cum <lb/>Ari&longs;toteles ait, Mechanica problemata e&longs;&longs;e Mathematicarum <lb/>quæ&longs;tionum, naturaliumque communia, non intellexit e&longs;&longs;e <lb/>veluti aggregata & <expan abbr="cõflata">conflata</expan> ex illis vtri&longs;que. </s> |
| <s id="N10D7B">Non enim <expan abbr="cõmu-nia">commu­<lb/>nia</expan> conflantur ex particularibus, &longs;ed particularia ex commu­<lb/>nibus ac vniuer&longs;alibus. </s> | <s id="N10D7B">Non enim <expan abbr="cõmu-nia">commu­<lb/>nia</expan> conflantur ex particularibus, &longs;ed particularia ex commu­<lb/>nibus ac vniuer&longs;alibus. </s> |
| <s id="N10D86">Vnde potius &longs;en&longs;it Philo&longs;ophus, Me­<lb/>chanicam facultatem de his rebus agere, quæ communes &longs;unt <lb/>naturalibus ac Mathematicis quæ&longs;tionibus (quamuis &longs;ub di­<lb/>uer&longs;a ratione formali) cui&longs;modi &longs;unt quantitas ponderis, &longs;eu <lb/>ip&longs;a ponderantia, quæ dicuntur grauia & leuia, ac virtus qua <lb/>ip&longs;a mouentur aut detinentur. </s> | <s id="N10D86">Vnde potius &longs;en&longs;it Philo&longs;ophus, Me­<lb/>chanicam facultatem de his rebus agere, quæ communes &longs;unt <lb/>naturalibus ac Mathematicis quæ&longs;tionibus (quamuis &longs;ub di­<lb/>uer&longs;a ratione formali) cuiu&longs;modi &longs;unt quantitas ponderis, &longs;eu <lb/>ip&longs;a ponderantia, quæ dicuntur grauia & leuia, ac virtus qua <lb/>ip&longs;a mouentur aut detinentur. </s> |
| <s id="N10D93">Siquidem de his omnibus <lb/>multa quæruntur in phy&longs;icis, prout &longs;unt affectiones corporis <lb/>naturalis, vel corpora quædam naturalia; <expan abbr="multaq.">multaque</expan> pa­<lb/>riter in mathematicis, prout dimen&longs;ionem habent <lb/>quantitatiuam, aut virtutis, ab&longs;trahendo <lb/>ab hac vel illa materia, <expan abbr="peculiaresq.">peculiaresque</expan> <lb/>fortiuntur pa&longs;&longs;iones in ordine <lb/>ad motum arti&longs;i­<lb/>cio&longs;um. </s> | <s id="N10D93">Siquidem de his omnibus <lb/>multa quæruntur in phy&longs;icis, prout &longs;unt affectiones corporis <lb/>naturalis, vel corpora quædam naturalia; <expan abbr="multaq.">multaque</expan> pa­<lb/>riter in mathematicis, prout dimen&longs;ionem habent <lb/>quantitatiuam, aut virtutis, ab&longs;trahendo <lb/>ab hac vel illa materia, <expan abbr="peculiaresq.">peculiaresque</expan> <lb/>fortiuntur pa&longs;&longs;iones in ordine <lb/>ad motum artifi­<lb/>cio&longs;um. </s> |
| </p> | </p> |
| <pb pagenum="25" xlink:href="005/01/033.jpg"/> | <pb pagenum="25" xlink:href="005/01/033.jpg"/> |
| <p id="N10DB2" type="head"> | <p id="N10DB2" type="head"> |
| |
| <s id="N10DFC">Denique <lb/>per cæteras particulas explicatur vltima differentia, ex pro­<lb/>prio obiecto ac fine de&longs;umpta, qua certè huiu&longs;modi &longs;cientia <lb/>optimè di&longs;tinguitur ab illis quæ non ver&longs;antur circa quantita­<lb/>tem aliquam; tum ab illa contemplatione Logica, aut Me­<lb/>taphi&longs;ica, quæ tantum ver&longs;atur circa quantitatem prædica­<lb/>mentalem; item à Phy&longs;ica quæ circa quantitatem &longs;olum <lb/>ver&longs;atur in quantum e&longs;t affectio corporis naturalis, & in ordi­<lb/>ne ad principium motus & quietis naturalis. </s> | <s id="N10DFC">Denique <lb/>per cæteras particulas explicatur vltima differentia, ex pro­<lb/>prio obiecto ac fine de&longs;umpta, qua certè huiu&longs;modi &longs;cientia <lb/>optimè di&longs;tinguitur ab illis quæ non ver&longs;antur circa quantita­<lb/>tem aliquam; tum ab illa contemplatione Logica, aut Me­<lb/>taphi&longs;ica, quæ tantum ver&longs;atur circa quantitatem prædica­<lb/>mentalem; item à Phy&longs;ica quæ circa quantitatem &longs;olum <lb/>ver&longs;atur in quantum e&longs;t affectio corporis naturalis, & in ordi­<lb/>ne ad principium motus & quietis naturalis. </s> |
| <s id="N10E0F">Rur&longs;us non <lb/>minus di&longs;tinguitur, eadem differentia, à reliquis di&longs;ciplinis <lb/>Mathematicis, nam licet conueniat cum illis in hoc quod e&longs;t <pb pagenum="26" xlink:href="005/01/034.jpg"/>ver&longs;ari circa quantitatem modo quodam ab&longs;tracto à materia, <lb/>illam tamen contrahit ad quantitatem ponderis grauium, & <lb/>leuium, ac virtutis qua debent moueri, &longs;icetnon determi­<lb/>net materiam ponderantem, aut virtutis mouentis. </s> | <s id="N10E0F">Rur&longs;us non <lb/>minus di&longs;tinguitur, eadem differentia, à reliquis di&longs;ciplinis <lb/>Mathematicis, nam licet conueniat cum illis in hoc quod e&longs;t <pb pagenum="26" xlink:href="005/01/034.jpg"/>ver&longs;ari circa quantitatem modo quodam ab&longs;tracto à materia, <lb/>illam tamen contrahit ad quantitatem ponderis grauium, & <lb/>leuium, ac virtutis qua debent moueri, &longs;icetnon determi­<lb/>net materiam ponderantem, aut virtutis mouentis. </s> |
| <s id="N10E21">Per <lb/>quod &longs;anè primo di&longs;tinguitur ab Arithmetica & Mu&longs;ica, quæ <lb/>ver&longs;atur circa quantitatem di&longs;cretam; non autem continuam <lb/>&longs;icut grauium ac lenium; deinde à Geometria propriè dicta, <lb/>& a Stereometria quæ ver&longs;antur circa quantitatem <expan abbr="cõtinuam">continuam</expan> <lb/>planorum ac &longs;olidorum, ab&longs;trahendo à grauitate aut &longs;euitate, <lb/>& à quocunque motu illorum. </s> | <s id="N10E21">Per <lb/>quod &longs;anè primo di&longs;tinguitur ab Arithmetica & Mu&longs;ica, quæ <lb/>ver&longs;atur circa quantitatem di&longs;cretam; non autem continuam <lb/>&longs;icut grauium ac lenium; deinde à Geometria propriè dicta, <lb/>& a Stereometria quæ ver&longs;antur circa quantitatem <expan abbr="cõtinuam">continuam</expan> <lb/>planorum ac &longs;olidorum, ab&longs;trahendo à grauitate aut &longs;euitate, <lb/>& à quocunque motu illorum. </s> |
| <s id="N10E34">Denique di&longs;tinguitur à Per­<lb/>&longs;pectiua quæ &longs;anè quantitatem con&longs;ideran in lineis vi&longs;ualibus, <lb/>& à Geode&longs;ia quæ illam con&longs;iderat in aceruis tanquam co­<lb/>nis, vel in puteis tanquam cylindris; tandem ab Aftronoinias <lb/>quæ illam con&longs;iderat in corporibus cele&longs;tibus eorumque <lb/>di&longs;tantijs, ac motibus à natura præ&longs;criptis. </s> | <s id="N10E34">Denique di&longs;tinguitur à Per­<lb/>&longs;pectiua quæ &longs;anè quantitatem con&longs;ideran in lineis vi&longs;ualibus, <lb/>& à Geode&longs;ia quæ illam con&longs;iderat in aceruis tanquam co­<lb/>nis, vel in puteis tanquam cylindris; tandem ab Astronomias <lb/>quæ illam con&longs;iderat in corporibus cele&longs;ribus eorumque <lb/>di&longs;tantijs, ac motibus à natura præ&longs;criptis. </s> |
| <s id="N10E41">Cum igitur per <lb/>idem res <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> in e&longs;&longs;e &longs;ui, per quod di&longs;tinguitur ab alijs, <lb/>vt recepti&longs;&longs;imum e&longs;t in doctrina Peripaterica, &longs;atis videtur <lb/>explicata con&longs;titutio & e&longs;&longs;entia huius &longs;eientiæ per traditam <lb/>de&longs;initionem &longs;eu quidditatiuam de&longs;criptionem, cum per eam <lb/>con&longs;tet &longs;ufficienter ab alijs &longs;cientijs ac facultatibus di&longs;tingui. </s> | <s id="N10E41">Cum igitur per <lb/>idem res <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> in e&longs;&longs;e &longs;ui, per quod di&longs;tinguitur ab alijs, <lb/>vt recepti&longs;&longs;imum e&longs;t in doctrina Peripatetica, &longs;atis videtur <lb/>explicata con&longs;titutio & e&longs;&longs;entia huius &longs;cientiæ per traditam <lb/>definitionem &longs;eu quidditatiuam de&longs;criptionem, cum per eam <lb/>con&longs;tet &longs;ufficienter ab alijs &longs;cientijs ac facultatibus di&longs;tingui. </s> |
| </p> | </p> |
| <p id="N10E52" type="head"> | <p id="N10E52" type="head"> |
| <s id="N10E54"><emph type="italics"/>De vnitate &longs;cientiæ Mechinicæ <lb/>eiu&longs;que partibus.<emph.end type="italics"/></s> | <s id="N10E54"><emph type="italics"/>De vnitate &longs;cientiæ Mechinicæ <lb/>eiu&longs;que partibus.<emph.end type="italics"/></s> |
| |
| </p> | </p> |
| <p id="N10E62" type="main"> | <p id="N10E62" type="main"> |
| <s id="N10E64">Ex peditis ijs quæ ad quæ&longs;tionem, an &longs;it, & quid &longs;it Hæc <lb/>&longs;cientia, pertinere videbantur, &longs;equitur inquirendum, <lb/>quotuplex &longs;it; vtrum &longs;cilicet &longs;it vna vel multiplex, & quas <lb/>habeat partes. </s> | <s id="N10E64">Ex peditis ijs quæ ad quæ&longs;tionem, an &longs;it, & quid &longs;it Hæc <lb/>&longs;cientia, pertinere videbantur, &longs;equitur inquirendum, <lb/>quotuplex &longs;it; vtrum &longs;cilicet &longs;it vna vel multiplex, & quas <lb/>habeat partes. </s> |
| <s id="N10E6D">Qua in re &longs;upponimus primo, &longs;crmonem e&longs;&longs;e <lb/>de &longs;cientia totali, prout e&longs;t aggregatum quoddam ex omni­<lb/>bus &longs;cientijs partialibus, &longs;iue actualibus, &longs;iue habitualibus, <lb/>nempe ex omnibus conclu&longs;ionibus demon&longs;tratis de &longs;ubiecto <lb/>adæquato, circa quod huiu&longs;modi facultas ver&longs;atur. </s> | <s id="N10E6D">Qua in re &longs;upponimus primo, &longs;ermonem e&longs;&longs;e <lb/>de &longs;cientia totali, prout e&longs;t aggregatum quoddam ex omni­<lb/>bus &longs;cientijs partialibus, &longs;iue actualibus, &longs;iue habitualibus, <lb/>nempe ex omnibus conclu&longs;ionibus demon&longs;tratis de &longs;ubiecto <lb/>adæquato, circa quod huiu&longs;modi facultas ver&longs;atur. </s> |
| <s id="N10E78">Deinde <lb/>&longs;upponimus vnitatem &longs;cientiæ totalis de &longs;umi, tùm ex vnitate <lb/>ordinis quo conclu&longs;iones ac partes illius coaptantur inter &longs;e, <pb pagenum="27" xlink:href="005/01/035.jpg"/>ad componendam integram &longs;cientiam de eodem &longs;ubiecto <lb/>materiali ac pa&longs;&longs;ionibus illios; tum ex vnitate obiecti form­<lb/>lis circa quod omnes &longs;cientiæ partiales conueniunt. </s> | <s id="N10E78">Deinde <lb/>&longs;upponimus vnitatem &longs;cientiæ totalis de &longs;umi, tùm ex vnitate <lb/>ordinis quo conclu&longs;iones ac partes illius coaptantur inter &longs;e, <pb pagenum="27" xlink:href="005/01/035.jpg"/>ad componendam integram &longs;cientiam de eodem &longs;ubiecto <lb/>materiali ac pa&longs;&longs;ionibus illius; tum ex vnitate obiecti form­<lb/>lis circa quod omnes &longs;cientiæ partiales conueniunt. </s> |
| </p> | </p> |
| <p id="N10E88" type="main"> | <p id="N10E88" type="main"> |
| <s id="N10E8A">Quibus po&longs;itis dicendum e&longs;t, Mechanicam facultatem e&longs;­<lb/>&longs;e vnicam &longs;eientiam totalem vnitate ordinis, ac obiecti for­<lb/>malis, &longs;ub quà &longs;cientia totali tanquam &longs;ub &longs;pecie atoma con­<lb/>tinentur omnes conclu&longs;iones, vel &longs;cientiæ partiales Mecha­<lb/>nicæ. </s> | <s id="N10E8A">Quibus po&longs;itis dicendum e&longs;t, Mechanicam facultatem e&longs;­<lb/>&longs;e vnicam &longs;cientiam totalem vnitate ordinis, ac obiecti for­<lb/>malis, &longs;ub quà &longs;cientia totali tanquam &longs;ub &longs;pecie atoma con­<lb/>tinentur omnes conclu&longs;iones, vel &longs;cientiæ partiales Mecha­<lb/>nicæ. </s> |
| <s id="N10E95">Id quod facile probatur ex eo, quia omnis Mechani­<lb/>ca cognitio ver&longs;atur circa eandem rationem formalem obie­<lb/>cti ad&etail;quati, nempe quantitatem ponderis artificiosè mouen­<lb/>di, aut detinendi, licet non de eodem pondere, vel de ei&longs;den<gap/><lb/>ponderantibus in qualibet parte huius &longs;cientiæ persè agatur­<lb/>Deinde probatur, quia omnes conclu&longs;iones demon&longs;tratæ in <lb/>hac &longs;cientia, <expan abbr="ordinãtur">ordinantur</expan> ad plenam cognitionem obiecti expli­<lb/>cati, &longs;iue per contemplationem partium illius, agendo de <lb/>hoc, vel illo graui, aut leui quod moueri debet, aut quie&longs;ce­<lb/>re, &longs;iue per contemplationem plurium pa&longs;&longs;ionum quas idem <lb/>&longs;ubiectum patitur, quatenus cadit &longs;ub artificio&longs;am motionem <lb/>aut quietem. </s> | <s id="N10E95">Id quod facile probatur ex eo, quia omnis Mechani­<lb/>ca cognitio ver&longs;atur circa eandem rationem formalem obie­<lb/>cti ad&etail;quati, nempe quantitatem ponderis artificiosè mouen­<lb/>di, aut detinendi, licet non de eodem pondere, vel de ei&longs;dem F<lb/>ponderantibus in qualibet parte huius &longs;cientiæ persè agatur. <lb/>Deinde probatur, quia omnes conclu&longs;iones demon&longs;tratæ in <lb/>hac &longs;cientia, <expan abbr="ordinãtur">ordinantur</expan> ad plenam cognitionem obiecti expli­<lb/>cati, &longs;iue per contemplationem partium illius, agendo de <lb/>hoc, vel illo graui, aut leui quod moueri debet, aut quie&longs;ce­<lb/>re, &longs;iue per contemplationem plurium pa&longs;&longs;ionum quas idem <lb/>&longs;ubiectum patitur, quatenus cadit &longs;ub artificio&longs;am motionem <lb/>aut quietem. </s> |
| <s id="N10EB3">Rur&longs;us plurimæ conclu&longs;iones in ea demon&longs;tra­<lb/>tæ, de&longs;eruiunt tanquam principia in demon&longs;trationibus reli­<lb/>quarum; vnde talis apparet ordo & connexio inter illas ad <lb/>inuicem, vt indubitanter ad eandem omninò &longs;cientiam tota­<lb/>lem in &longs;pecie &longs;umptam pertinere ab omnibus dicantur. </s> | <s id="N10EB3">Rur&longs;us plurimæ conclu&longs;iones in ea demon&longs;tra­<lb/>tæ, de&longs;eruiunt tanquam principia in demon&longs;trationibus reli­<lb/>quarum; vnde talis apparet ordo & connexio inter illas ad <lb/>inuicem, vt indubitanter ad eandem omninò &longs;cientiam tota­<lb/>lem in &longs;pecie &longs;umptam pertinere ab omnibus dicantur. </s> |
| </p> | </p> |
| <p id="N10EBE" type="main"> | <p id="N10EBE" type="main"> |
| |
| <s id="N10F52">Secunda verò docet quo pacto rotis, neruis, tim­<lb/>panis, <expan abbr="alijsq.">alijsque</expan> in&longs;trumentis motus veluti animatus præ&longs;tetur <pb pagenum="29" xlink:href="005/01/037.jpg"/>in&longs;en&longs;ibilibus, vt fertur de &longs;tatua Dedali ac Vulcani, de Ar­<lb/>chitæ columba, ac &longs;imilibus. </s> | <s id="N10F52">Secunda verò docet quo pacto rotis, neruis, tim­<lb/>panis, <expan abbr="alijsq.">alijsque</expan> in&longs;trumentis motus veluti animatus præ&longs;tetur <pb pagenum="29" xlink:href="005/01/037.jpg"/>in&longs;en&longs;ibilibus, vt fertur de &longs;tatua Dedali ac Vulcani, de Ar­<lb/>chitæ columba, ac &longs;imilibus. </s> |
| <s id="N10F62">Tertia modum tradit, quo ex <lb/>inclu&longs;o aere varij emittantur &longs;onitus ad morum vel percu&longs;&longs;io­<lb/>nem aqu&etail;, vt de &longs;erpentum &longs;ibilis, ac volucrum cantibus, <expan abbr="hu-manisq.">hu­<lb/>manisque</expan> vocibus imitatis, à pluribus enarratur: de que armo­<lb/>nia quam reddebant argentei remi celeberrimi illius nauigij <lb/>Cleopatræ Aegypti Reginæ cum aquam offenderent, ob &longs;pi­<lb/>ritum inter thecas eorum re&longs;eratum, qui agitatione remigum, <lb/><expan abbr="aquarumq.">aquarumque</expan> percu&longs;&longs;ione per varia <expan abbr="artificio&longs;aq.">artificio&longs;aque</expan> foramina exire <lb/>cogebatur. </s> | <s id="N10F62">Tertia modum tradit, quo ex <lb/>inclu&longs;o aere varij emittantur &longs;onitus ad morum vel percu&longs;&longs;io­<lb/>nem aqu&etail;, vt de &longs;erpentum &longs;ibilis, ac volucrum cantibus, <expan abbr="hu-manisq.">hu­<lb/>manisque</expan> vocibus imitatis, à pluribus enarratur: de que armo­<lb/>nia quam reddebant argentei remi celeberrimi illius nauigij <lb/>Cleopatræ Aegypti Reginæ cum aquam offenderent, ob &longs;pi­<lb/>ritum inter thecas eorum re&longs;eratum, qui agitatione remigum, <lb/><expan abbr="aquarumq.">aquarumque</expan> percu&longs;&longs;ione per varia <expan abbr="artificio&longs;aq.">artificio&longs;aque</expan> foramina exire <lb/>cogebatur. </s> |
| <s id="N10F80">Et hæc de diui&longs;ione &longs;eu partibus Mechanicæ fa­<lb/>cultatis attigi&longs;&longs;e &longs;ufficiat, vt omittamus alias, quæ non tàm <lb/>propriè partes illius, quàm annexæ, aut mixtæ facultates vi­<lb/>dentur, vt Architectonica, quæ licet multum occupetur in <lb/>con&longs;ideratione artificio&longs;æ motionis, aut quietis grauium & <lb/>leuium, vlterius tamen huiu&longs;modi con&longs;iderationem ordinat <lb/>ad opus con&longs;truendum ex illis, tanquam ad proprium finem, <lb/>& obiectum primarium: Vnde Vitruuius potius ip&longs;am Ma­<lb/>chinariam facultatem, partem &longs;eu portionem facit Archite­<lb/>ctonicæ. </s> | <s id="N10F80">Et hæc de diui&longs;ione &longs;eu partibus Mechanicæ fa­<lb/>cultatis attigi&longs;&longs;e &longs;ufficiat, vt omittamus alias, quæ non tàm <lb/>propriè partes illius, quàm annexæ, aut mixtæ facultates vi­<lb/>dentur, vt Architectonica, quæ licet multum occupetur in <lb/>con&longs;ideratione artificio&longs;æ motionis, aut quietis grauium & <lb/>leuium, vlterius tamen huiu&longs;modi con&longs;iderationem ordinat <lb/>ad opus con&longs;truendum ex illis, tanquam ad proprium finem, <lb/>& obiectum primarium: Vnde Vitruuius potius ip&longs;am Ma­<lb/>chinariam facultatem, partem &longs;eu portionem facit Archite­<lb/>ctonicæ. </s> |
| <s id="N10F95">Item Nautica quæ licet contempletur artificio&longs;am <lb/>motionem, aut quietem nauigij ein&longs;que membrorum, quæ <lb/>certè grauia aut leuia &longs;unt; quia tamen hæc con&longs;iderat in or­<lb/>dine ad incolumem tran&longs;uectionem, inter Mechanicas ab&longs;o­<lb/>lutè, & communiter non connumeratur. </s> | <s id="N10F95">Item Nautica quæ licet contempletur artificio&longs;am <lb/>motionem, aut quietem nauigij eiu&longs;que membrorum, quæ <lb/>certè grauia aut leuia &longs;unt; quia tamen hæc con&longs;iderat in or­<lb/>dine ad incolumem tran&longs;uectionem, inter Mechanicas ab&longs;o­<lb/>lutè, & communiter non connumeratur. </s> |
| <s id="N10FA0">Verum cum talis <lb/>differentia valde accidentaria &longs;it & ab extrin&longs;eco fine de&longs;um­<lb/>pta, non minus forta&longs;&longs;e inter Mechanicas facultates propriè <lb/>poterit <expan abbr="cõputari">computari</expan>. </s> | <s id="N10FA0">Verum cum talis <lb/>differentia valde accidentaria &longs;it & ab extrin&longs;eco fine de&longs;um­<lb/>pta, non minus forta&longs;&longs;e inter Mechanicas facultates propriè <lb/>poterit <expan abbr="cõputari">computari</expan>. </s> |
| <s id="N10FAD">Non enim apparet in quo e&longs;&longs;entialiter diffe­<lb/>rat artificio&longs;a tran&longs;uectio quæ per nauim fit, ab ea, <lb/>quæ per plau&longs;trum, aut currum; neque <lb/>intere&longs;t &longs;i per aquas, an per aera <lb/>moles aut pondera tran­<lb/>sferantur. </s> | <s id="N10FAD">Non enim apparet in quo e&longs;&longs;entialiter diffe­<lb/>rat artificio&longs;a tran&longs;uectio quæ per nauim fit, ab ea, <lb/>quæ per plau&longs;trum, aut currum; neque <lb/>intere&longs;t &longs;i per aquas, an per aera <lb/>moles aut pondera tran­<lb/>sferantur. </s> |
| </p> | </p> |
| |
| 8. Topic. <!-- REMOVE S-->cap. | 8. Topic. <!-- REMOVE S-->cap. |
| | |
| 2. Inquiens, &longs;cientiam &longs;cientia e&longs;&longs;e melio­<lb/>rem, aut eo quod exactior e&longs;t, aut quod meliorum. </s> | 2. Inquiens, &longs;cientiam &longs;cientia e&longs;&longs;e melio­<lb/>rem, aut eo quod exactior e&longs;t, aut quod meliorum. </s> |
| <s id="N1101B">Per me­<lb/>liora autem intelligit tum per &longs;e nobiliora, tum etiam &longs;upe­<lb/>riora, quæ &longs;unt vuiuer&longs;aliora, ac &longs;impliciora. </s> | <s id="N1101B">Per me­<lb/>liora autem intelligit tum per &longs;e nobiliora, tum etiam &longs;upe­<lb/>riora, quæ &longs;unt vniuer&longs;aliora, ac &longs;impliciora. </s> |
| </p> | </p> |
| <p id="N11022" type="main"> | <p id="N11022" type="main"> |
| <s id="N11024">Ex quo triplici capite facile intelligemus, <expan abbr="Mechanicã">Mechanicam</expan> facul <lb/><expan abbr="tat&etilde;">tatem</expan> <expan abbr="inferior&etilde;">inferiorem</expan> <expan abbr="gradũ">gradum</expan> perfectionis obtinere inter Mathematicas <lb/>di&longs;ciplinas, ac &longs;cientias omnes merè &longs;peculatiuas &longs;ecundum <lb/>eam partem, qua merè &longs;peculatiuæ, ac demon&longs;tratiuæ &longs;cien­<lb/>tiæ &longs;unt, vt Phy&longs;ica ac Metaphy&longs;ica: perfectiorem tamen e&longs;&longs;e <lb/>multis &longs;cientijs practicis, vt Agricultura, Architectura, Nau­<lb/>tica, &longs;i modo ab illa di&longs;tinguitur, & alijs huiu&longs;modi. </s> | <s id="N11024">Ex quo triplici capite facile intelligemus, <expan abbr="Mechanicã">Mechanicam</expan> facul <lb/><expan abbr="tat&etilde;">tatem</expan> <expan abbr="inferior&etilde;">inferiorem</expan> <expan abbr="gradũ">gradum</expan> perfectionis obtinere inter Mathematicas <lb/>di&longs;ciplinas, ac &longs;cientias omnes merè &longs;peculatiuas &longs;ecundum <lb/>eam partem, qua merè &longs;peculatiuæ, ac demon&longs;tratiuæ &longs;cien­<lb/>tiæ &longs;unt, vt Phy&longs;ica ac Metaphy&longs;ica: perfectiorem tamen e&longs;&longs;e <lb/>multis &longs;cientijs practicis, vt Agricultura, Architectura, Nau­<lb/>tica, &longs;i modo ab illa di&longs;tinguitur, & alijs huiu&longs;modi. </s> |
| </p> | </p> |
| <p id="N11042" type="main"> | <p id="N11042" type="main"> |
| <s id="N11044">Id quod planum fieri pote&longs;t &longs;igillatim di&longs;currendo per &longs;in­<lb/>gulas &longs;cientias enumeratas. </s> | <s id="N11044">Id quod planum fieri pote&longs;t &longs;igillatim di&longs;currendo per &longs;in­<lb/>gulas &longs;cientias enumeratas. </s> |
| <s id="N11049">Nam quod attinet ad Mathema­<lb/>ticas, Arithmeticam, Geometriam, A&longs;trologiam, Mu&longs;icam, <lb/>ac Per&longs;pectiuam, & &longs;i quæ &longs;unt aliæ huiu&longs;modi; nulli dubium <lb/>e&longs;t, eas omnes præ&longs;tantiores e&longs;&longs;e &longs;cientia Mechanica; tum <lb/>quia &longs;unt gratia &longs;ui, hoc e&longs;t merè &longs;peculatiuæ, ac de nobilio-<pb pagenum="31" xlink:href="005/01/039.jpg"/>ribus, &longs;eu amplioribus, ac &longs;implicioribus &longs;ubiectis pertractant, <lb/>vt per &longs;e patet; tum etiam quia vel parem, vel maiorem cer­<lb/>titudinem, & euidentiam habent, præ&longs;ertim illæ, quibus ip&longs;a <lb/>Mechanica &longs;ubalternatur, & à quibus accipit &longs;ua principia, <lb/>vt Geometria ac Stereometria. </s> | <s id="N11049">Nam quod attinet ad Mathema­<lb/>ticas, Arithmeticam, Geometriam, A&longs;trologiam, Mu&longs;icam, <lb/>ac Per&longs;pectiuam, & &longs;i quæ &longs;unt aliæ huiu&longs;modi; nulli dubium <lb/>e&longs;t, eas omnes præ&longs;tantiores e&longs;&longs;e &longs;cientia Mechanica; tum <lb/>quia &longs;unt gratia &longs;ui, hoc e&longs;t merè &longs;peculatiuæ, ac de nobilio-<pb pagenum="31" xlink:href="005/01/039.jpg"/>ribus, &longs;eu amplioribus, ac &longs;implicioribus &longs;ubiectis pertractant, <lb/>vt per &longs;e patet; tum etiam quia vel parem, vel maiorem cer-<lb/>titudinem, & euidentiam habent, præ&longs;ertim illæ, quibus ip&longs;a <lb/>Mechanica &longs;ubalternatur, & à quibus accipit &longs;ua principia, <lb/>vt Geometria ac Stereometria. </s> |
| <s id="N11061">Quandoquidem immedia­<lb/>tius attingunt primam rationem a&longs;&longs;entiendi, in qua fundatur <lb/>tota euidentia. </s> | <s id="N11061">Quandoquidem immedia­<lb/>tius attingunt primam rationem a&longs;&longs;entiendi, in qua fundatur <lb/>tota euidentia. </s> |
| <s id="N11068">Vnde vniuer&longs;aliter colligit Ari&longs;toteles primo <lb/>Metaphy&longs;ices cap. | <s id="N11068">Vnde vniuer&longs;aliter colligit Ari&longs;toteles primo <lb/>Metaphy&longs;ices cap. |
| | |
| |
| <s id="N110AA">Perfe­<lb/>ctio verò cognitionis, quæ attenditur ex maiori certitudine, <lb/>aut euidentia; licet maxima &longs;it, non e&longs;t tamen e&longs;&longs;entialis, cum <lb/>&longs;upponat &longs;cientiam ip&longs;am <expan abbr="con&longs;titutã">con&longs;titutam</expan> in e&longs;&longs;e talis &longs;cientiæ cum <lb/>&longs;ufficienti certitudine, aut euidentia. </s> | <s id="N110AA">Perfe­<lb/>ctio verò cognitionis, quæ attenditur ex maiori certitudine, <lb/>aut euidentia; licet maxima &longs;it, non e&longs;t tamen e&longs;&longs;entialis, cum <lb/>&longs;upponat &longs;cientiam ip&longs;am <expan abbr="con&longs;titutã">con&longs;titutam</expan> in e&longs;&longs;e talis &longs;cientiæ cum <lb/>&longs;ufficienti certitudine, aut euidentia. </s> |
| </p> | </p> |
| <p id="N110B9" type="main"> | <p id="N110B9" type="main"> |
| <s id="N110BB">Quod &longs;i comparemus Mechanicam facultatem cum parti­<lb/>bus quibu&longs;dam, ac &longs;ubalternatis &longs;cientijs Phy&longs;icæ, præ&longs;ertim <lb/>practicis, vt Medicina, & Agricultura, alijsq annexis, mixtis, <lb/>vel &longs;ubalternatis etiam Mathematicis, vt Architectura, & <lb/>Nautica; diuer&longs;a omnino ratio e&longs;t. </s> | <s id="N110BB">Quod &longs;i comparemus Mechanicam facultatem cum parti­<lb/>bus quibu&longs;dam, ac &longs;ubalternatis &longs;cientijs Phy&longs;icæ, præ&longs;ertim <lb/>practicis, vt Medicina, & Agricultura, <expan abbr="alijsq.">alijsque</expan> annexis, mixtis, <lb/>vel &longs;ubalternatis etiam Mathematicis, vt Architectura, & <lb/>Nautica; diuer&longs;a omnino ratio e&longs;t. </s> |
| <s id="N110C6">Nam vel &longs;ubiectum illa­<lb/>rum fecundum &longs;uam rationem &longs;pecificam ignobilius e&longs;t gra­<lb/>ui, & leui, virtuteque eorum motrici in vniuer&longs;um, vt multa <lb/>de quibus tanquam de &longs;ubiectis partialibus agitur in Medici­<lb/>na, & Agricultura: Vel tanta e&longs;t incertitudo, & imperfectio <lb/>inferendi conclu&longs;iones in talibus &longs;cientijs, vt ex genere &longs;uo <lb/>vix &longs;cientiæ <expan abbr="nũcupari">nuncupari</expan> po&longs;&longs;int, potiu&longs;que ex probabilibus, <expan abbr="quã">quam</expan> <pb pagenum="32" xlink:href="005/01/040.jpg"/>ex <expan abbr="demõ&longs;tratis">demon&longs;tratis</expan> con&longs;tare <expan abbr="videãtur">videantur</expan> magna <expan abbr="&longs;alt&etilde;">&longs;altem</expan> ex parte. </s> | <s id="N110C6">Nam vel &longs;ubiectum illa­<lb/>rum fecundum &longs;uam rationem &longs;pecificam ignobilius e&longs;t gra­<lb/>ui, & leui, virtuteque eorum motrici in vniuer&longs;um, vt multa <lb/>de quibus tanquam de &longs;ubiectis partialibus agitur in Medici­<lb/>na, & Agricultura: Vel tanta e&longs;t incertitudo, & imperfectio <lb/>inferendi conclu&longs;iones in talibus &longs;cientijs, vt ex genere &longs;uo <lb/>vix &longs;cientiæ <expan abbr="nũcupari">nuncupari</expan> po&longs;&longs;int, potiu&longs;que ex probabilibus, <expan abbr="quã">quam</expan> <pb pagenum="32" xlink:href="005/01/040.jpg"/>ex <expan abbr="demõ&longs;tratis">demon&longs;tratis</expan> con&longs;tare <expan abbr="videãtur">videantur</expan> magna <expan abbr="&longs;alt&etilde;">&longs;altem</expan> ex parte. </s> |
| <s id="N110EE">Vnde <lb/>licet derebus præ&longs;tantioribus agant <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="ration&etilde;">rationem</expan> obiecti <lb/>totalis, vt e&longs;t corpus animale &longs;anabile; aut <expan abbr="vegetatiuũ">vegetatiuum</expan> germina­<lb/>bile; nullatenus tamen <expan abbr="Mechanicã">Mechanicam</expan> <expan abbr="facultat&etilde;">facultatem</expan>, quæ de familia­<lb/>rioribus omnimoda <expan abbr="cũ">cum</expan> <expan abbr="euid&etilde;tia">euidentia</expan> tractat, antecellere <expan abbr="putabũtur">putabuntur</expan>. </s> | <s id="N110EE">Vnde <lb/>licet derebus præ&longs;tantioribus agant <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="ration&etilde;">rationem</expan> obiecti <lb/>totalis, vt e&longs;t corpus animale &longs;anabile; aut <expan abbr="vegetatiuũ">vegetatiuum</expan> germina­<lb/>bile; nullatenus tamen <expan abbr="Mechanicã">Mechanicam</expan> <expan abbr="facultat&etilde;">facultatem</expan>, quæ de familia­<lb/>rioribus omnimoda <expan abbr="cũ">cum</expan> <expan abbr="euid&etilde;tia">euidentia</expan> tractat, antecellere <expan abbr="putabũtur">putabuntur</expan>. </s> |
| </p> | </p> |
| |
| </p> | </p> |
| <p id="N1112D" type="main"> | <p id="N1112D" type="main"> |
| <s id="N1112F">Accedit, quod &longs;æpe vtilitas refunditur in dignitatem obie­<lb/>cti; vtilitas enim attenditur ex fine, ad quem ordinatur &longs;cien­<lb/>tia; qui profectò in &longs;cientijs practicis coincidit cum obiecto <lb/>formali. </s> | <s id="N1112F">Accedit, quod &longs;æpe vtilitas refunditur in dignitatem obie­<lb/>cti; vtilitas enim attenditur ex fine, ad quem ordinatur &longs;cien­<lb/>tia; qui profectò in &longs;cientijs practicis coincidit cum obiecto <lb/>formali. </s> |
| <s id="N11138">Eadem namque &longs;anitas anima&longs;is, e&longs;t finis medicinæ, <lb/>& ratio, &longs;ub qua Medicina agit de &longs;uis &longs;ubiectis. </s> | <s id="N11138">Eadem namque &longs;anitas animalis, e&longs;t finis medicinæ, <lb/>& ratio, &longs;ub qua Medicina agit de &longs;uis &longs;ubiectis. </s> |
| <s id="N1113D">Eademque <lb/>directio operationum intellectus, e&longs;t finis Logicæ &longs;cientiæ, & <lb/>ratio &longs;ub qua de ip&longs;is operationibus agitur in illa. </s> | <s id="N1113D">Eademque <lb/>directio operationum intellectus, e&longs;t finis Logicæ &longs;cientiæ, & <lb/>ratio &longs;ub qua de ip&longs;is operationibus agitur in illa. </s> |
| <s id="N11144">Cum igi­<lb/>tur talis, ac tanta &longs;it vtilitas Mechanicæ &longs;cientiæ ad fines præ­<lb/>&longs;tanti&longs;&longs;imos admirabili cum artificio con&longs;equendos, vt ad le­<lb/>uanda ingentia pondera, parua, & exigua virtute, ad commo­<lb/>ditates tam plurimas, <expan abbr="vrbiumq.">vrbiumque</expan> ornatum tam varium: ad &longs;ub­<lb/>mini&longs;trandas tot machinas, & in&longs;trumenta in bello, vt belli­<lb/>gerare potius Mechanica, quam armis ip&longs;is, homines videan­<lb/>tur: ad aptius mouenda Nauigia; ingentes paruo momento <lb/>excitandas moles, <expan abbr="immaniaq.">immaniaque</expan> euertenda ædificia: ad aquas ar­<lb/>tifi cio&longs;i&longs;&longs;i<gap/>nè <expan abbr="&longs;ublimãdas">&longs;ublimandas</expan>, <expan abbr="aeremq.">aeremque</expan> perpetuis follibus emitten­<lb/>dum; voces tàm varias effingendas, concentum æquabiliter <lb/>efformandum, motum qua&longs;i animalem in&longs;en&longs;ibilibus imper­<lb/>tiendum, & &longs;imilia; ingenue fatendum e&longs;t nec e&longs;&longs;e artem, <lb/>quæ &longs;e Mechanicæ arti in dignitate valeat comparari, nec <lb/>e&longs;&longs;e &longs;cientiam practicam, quam ip&longs;a ex certitudine, & euiden­<lb/>tia, qua procedit, & ex dignitate, ac præ&longs;tantia finis, non an­<lb/>tecellat; ita vt in quo &longs;uperatur ex parte &longs;ubiecti nobilioris à <lb/>Medicina, vel Logica, comoen&longs;etur, aut vincatur ex parte <lb/>digni&longs;&longs;imi finis, & obiecti formalis, dum admirabili artificio <lb/>intendit ip&longs;os naturæ fines Naturam emulando &longs;uperare. </s> | <s id="N11144">Cum igi­<lb/>tur talis, ac tanta &longs;it vtilitas Mechanicæ &longs;cientiæ ad fines præ­<lb/>&longs;tanti&longs;&longs;imos admirabili cum artificio con&longs;equendos, vt ad le­<lb/>uanda ingentia pondera, parua, & exigua virtute, ad commo­<lb/>ditates tam plurimas, <expan abbr="vrbiumq.">vrbiumque</expan> ornatum tam varium: ad &longs;ub­<lb/>mini&longs;trandas tot machinas, & in&longs;trumenta in bello, vt belli­<lb/>gerare potius Mechanica, quam armis ip&longs;is, homines videan­<lb/>tur: ad aptius mouenda Nauigia; ingentes paruo momento <lb/>excitandas moles, <expan abbr="immaniaq.">immaniaque</expan> euertenda ædificia: ad aquas ar­<lb/>tificio&longs;i&longs;&longs;imè <expan abbr="&longs;ublimãdas">&longs;ublimandas</expan>, <expan abbr="aeremq.">aeremque</expan> perpetuis follibus emitten­<lb/>dum; voces tàm varias effingendas, concentum æquabiliter <lb/>efformandum, motum qua&longs;i animalem in&longs;en&longs;ibilibus imper­<lb/>tiendum, & &longs;imilia; ingenue fatendum e&longs;t nec e&longs;&longs;e artem, <lb/>quæ &longs;e Mechanicæ arti in dignitate valeat comparari, nec <lb/>e&longs;&longs;e &longs;cientiam practicam, quam ip&longs;a ex certitudine, & euiden­<lb/>tia, qua procedit, & ex dignitate, ac præ&longs;tantia finis, non an­<lb/>tecellat; ita vt in quo &longs;uperatur ex parte &longs;ubiecti nobilioris à <lb/>Medicina, vel Logica, compen&longs;etur, aut vincatur ex parte <lb/>digni&longs;&longs;imi finis, & obiecti formalis, dum admirabili artificio <lb/>intendit ip&longs;os naturæ fines Naturam emulando &longs;uperare. </s> |
| </p> | </p> |
| <pb pagenum="33" xlink:href="005/01/041.jpg"/> | <pb pagenum="33" xlink:href="005/01/041.jpg"/> |
| <p id="N11183" type="head"> | <p id="N11183" type="head"> |
| |
| <s id="N111DF">Præmittit autem exemplum de magno pondere quod ab exi­<lb/>gua virtute admirandum in modum, ip&longs;ius vectis adminiculo <lb/>con&longs;tat moueri. </s> | <s id="N111DF">Præmittit autem exemplum de magno pondere quod ab exi­<lb/>gua virtute admirandum in modum, ip&longs;ius vectis adminiculo <lb/>con&longs;tat moueri. </s> |
| <s id="N111E6"><expan abbr="Rationemq.">Rationemque</expan> admirationis ac dubitationis <lb/>annectit: Quia &longs;cilicet potius oppo&longs;itum ex eo &longs;equi deberet, <lb/>cum vectis adminiculo, pondus ponderi adiungatur, <expan abbr="inqui&etilde;s">inquiens</expan>. <lb/></s> | <s id="N111E6"><expan abbr="Rationemq.">Rationemque</expan> admirationis ac dubitationis <lb/>annectit: Quia &longs;cilicet potius oppo&longs;itum ex eo &longs;equi deberet, <lb/>cum vectis adminiculo, pondus ponderi adiungatur, <expan abbr="inqui&etilde;s">inquiens</expan>. <lb/></s> |
| <s id="N111F5">Quod enim &longs;ine vecte qui&longs;piam mouere non pote&longs;t, idip&longs;um <lb/>citius mouet, vectis ad illud pondus adiungens. </s> | <s id="N111F5">Quod enim &longs;ine vecte qui&longs;piam mouere non pote&longs;t, idip&longs;um <lb/>citius mouet, vectis ad illud pondus adiungens. </s> |
| <s id="N111FA">Verumenim­<lb/>uero huius ac &longs;imilium miraculorum omnium cau&longs;as refert <lb/>ad naturam circuli. </s> | <s id="N111FA">Verum enim <lb/>uero huius ac &longs;imilium miraculorum omnium cau&longs;as refert <lb/>ad naturam circuli. </s> |
| <s id="N11201">Nam vt inferius docet, quæ circa libram <lb/>fiunt, ad circulum rediguntur; quæ vero circa vectem, ad ip­<lb/>&longs;am libram; alia autem fere omnia quæ circa Mechanicas <pb pagenum="34" xlink:href="005/01/042.jpg"/>&longs;unt motiones, ad vectem. </s> | <s id="N11201">Nam vt inferius docet, quæ circa libram <lb/>fiunt, ad circulum rediguntur; quæ vero circa vectem, ad ip­<lb/>&longs;am libram; alia autem fere omnia quæ circa Mechanicas <pb pagenum="34" xlink:href="005/01/042.jpg"/>&longs;unt motiones, ad vectem. </s> |
| <s id="N1120D">Interim ex admiralibi (inquiens) <lb/>mirandum accidere quippiam non e&longs;&longs;e ab&longs;urdum. </s> | <s id="N1120D">Interim ex admirabili (inquiens) <lb/>mirandum accidere quippiam non e&longs;&longs;e ab&longs;urdum. </s> |
| <s id="N11212">Subin­<lb/>telligendo, admirabilem profecto e&longs;&longs;e ip&longs;am naturam circuli <lb/>ex qua tot admiranda procedunt, vt &longs;tatim probare aggredi­<lb/>tur in &longs;equentibus. </s> | <s id="N11212">Subin­<lb/>telligendo, admirabilem profecto e&longs;&longs;e ip&longs;am naturam circuli <lb/>ex qua tot admiranda procedunt, vt &longs;tatim probare aggredi­<lb/>tur in &longs;equentibus. </s> |
| </p> | </p> |
| <p id="N1121B" type="head"> | <p id="N1121B" type="head"> |
| |
| <s id="N11227">Textus Tertius.</s> | <s id="N11227">Textus Tertius.</s> |
| </p> | </p> |
| <p id="N1122A" type="main"> | <p id="N1122A" type="main"> |
| <s id="N1122C">M<emph type="italics"/>axime autem e&longs;t admirandum &longs;imul <lb/>contraria fieri; Circulus verò ex buiu&longs;mo­<lb/>di e&longs;t con&longs;titutus: &longs;tatim enim ex commoto <lb/>effectus e&longs;t & manente, quorum natura ad <lb/>&longs;e inuicem est contraria. </s> | <s id="N1122C">M<emph type="italics"/>axime autem e&longs;t admirandum &longs;imul <lb/>contraria fieri; Circulus verò ex huiu&longs;mo­<lb/>di e&longs;t con&longs;titutus: &longs;tatim enim ex commoto <lb/>effectus e&longs;t & manente, quorum natura ad <lb/>&longs;e inuicem est contraria. </s> |
| <s id="N1123A">Quamobrem i&longs;thæc <lb/>cernentes minùs admirari conuenit contingentes in illo con­<lb/>trarietates.<emph.end type="italics"/></s> | <s id="N1123A">Quamobrem i&longs;thæc <lb/>cernentes minùs admirari conuenit contingentes in illo con­<lb/>trarietates.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N11243" type="head"> | <p id="N11243" type="head"> |
| |
| <s id="N11272">Cum igitur admirandum valde &longs;it, &longs;i­<lb/>mul contraria fieri, aut aliquid effici ex contrarijs, & hoc con­<lb/>tingat in ip&longs;a con&longs;titutione circuli; minus admirandum e&longs;&longs;e <pb pagenum="35" xlink:href="005/01/043.jpg"/>relinquitur (concludit Ari&longs;toteles) &longs;i ex ip&longs;o circulo con&longs;ti­<lb/>tuto, aliæ po&longs;tea oriantur contrarietates, vel alia contraria in <lb/>ip&longs;o con&longs;iderentur, vt mox ex dicendis patebit. </s> | <s id="N11272">Cum igitur admirandum valde &longs;it, &longs;i­<lb/>mul contraria fieri, aut aliquid effici ex contrarijs, & hoc con­<lb/>tingat in ip&longs;a con&longs;titutione circuli; minus admirandum e&longs;&longs;e <pb pagenum="35" xlink:href="005/01/043.jpg"/>relinquitur (concludit Ari&longs;toteles) &longs;i ex ip&longs;o circulo con&longs;ti­<lb/>tuto, aliæ po&longs;tea oriantur contrarietates, vel alia contraria in <lb/>ip&longs;o con&longs;iderentur, vt mox ex dicendis patebit. </s> |
| </p> | </p> |
| <p id="N11282" type="head"> | <p id="N11282" type="head"> |
| <s id="N11284"><emph type="italics"/>De &longs;ecunda circuli proprieiate.<emph.end type="italics"/></s> | <s id="N11284"><emph type="italics"/>De &longs;ecunda circuli proprietate.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N1128B" type="head"> | <p id="N1128B" type="head"> |
| <s id="N1128D">Textus Quartus.</s> | <s id="N1128D">Textus Quartus.</s> |
| </p> | </p> |
| <p id="N11290" type="main"> | <p id="N11290" type="main"> |
| <s id="N11292">I<emph type="italics"/>n primis enim lincæ illi, quæ circuti orbem am­<lb/>plectitur, nullam habanti latitudinem contraria <lb/>quodammodo ine&longs;&longs;e apparans, concauum &longs;cilices, <lb/>& curuum. </s> | <s id="N11292">I<emph type="italics"/>n primis enim lineæ illi, quæ circuli orbem am­<lb/>plectitur, nullam habenti latitudinem contraria <lb/>quodammodo ine&longs;&longs;e apparans, concauum &longs;cilicet, <lb/>& curuum. </s> |
| <s id="N1129E">Hæc autemeo à &longs;e inuioem di&longs;tant <lb/>modo, quo magnum, & paricum, illorum etenim <lb/>medium e&longs;t æquale: horum verò rectum; quapropter cum ad <lb/>&longs;e inuicem commutantur, illa <expan abbr="quid&etilde;">quidem</expan> prius æqualia &longs;ieri nece&longs;&longs;e <lb/>est, quam extremorum vtrumlibet: lineam vero rectam, <lb/>quando e&longs;t curua, concaua, aut ex buiu&longs;modi rur &longs;um curua &longs;it, <lb/>& circularis. </s> | <s id="N1129E">Hæc autem eo à &longs;e inuicem di&longs;tant <lb/>modo, quo magnum, & paricum, illorum etenim <lb/>medium e&longs;t æquale: horum verò rectum; quapropter cum ad <lb/>&longs;e inuicem commutantur, illa <expan abbr="quid&etilde;">quidem</expan> prius æqualia fieri nece&longs;&longs;e <lb/>est, quam extremorum vtrumlibet: lineam vero rectam, <lb/>quando e&longs;t curua, concaua, aut ex huiu&longs;modi rur&longs;um curua &longs;it, <lb/>& circularis. </s> |
| <s id="N112B1">V num quidem igitur i&longs;tuc ab&longs;urdum ine&longs;t circulo.<emph.end type="italics"/></s> | <s id="N112B1">V num quidem igitur i&longs;tuc ab&longs;urdum ine&longs;t circulo.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N112B6" type="head"> | <p id="N112B6" type="head"> |
| |
| </p> | </p> |
| <p id="N112BC" type="main"> | <p id="N112BC" type="main"> |
| <s id="N112BE">Secundò admirabilem &longs;e natura circuli o&longs;tendit, &longs;i &longs;u­<lb/>matur infacto e&longs;&longs;e, quod cum in primis (inquit Ari&longs;to­<lb/>teles) linea, quæ ip&longs;ius circuli orbem complectitur, ac <lb/>peripheria, &longs;eu <expan abbr="circunfer&etilde;tia">circunferentia</expan> nuncupatur, &longs;it per &longs;e quoad la­<lb/>titudinem, & profunditatem indiui&longs;ibilis, &longs;imul tamen tan­<lb/>quam ex duobus contrarijs inter &longs;e coniunctis con&longs;tituatur <lb/>concaua, & curua, &longs;iuè conuexa. </s> | <s id="N112BE">Secundò admirabilem &longs;e natura circuli o&longs;tendit, &longs;i &longs;u­<lb/>matur infacto e&longs;&longs;e, quod cum in primis (inquit Ari&longs;to­<lb/>teles) linea, quæ ip&longs;ius circuli orbem complectitur, ac <lb/>peripheria, &longs;eu <expan abbr="circunfer&etilde;tia">circunferentia</expan> nuncupatur, &longs;it per &longs;e quoad la­<lb/>titudinem, & profunditatem indiui&longs;ibilis, &longs;imul tamen tan­<lb/>quam ex duobus contrarijs inter &longs;e coniunctis con&longs;tituatur <lb/>concaua, & curua, &longs;iuè conuexa. </s> |
| <s id="N112D1">Etenim e&longs;t verè terminus <lb/>extimus, & conuexum ip&longs;ius circuli, ac &longs;imul ambiens, & <lb/>complectens in &longs;ua concauitate ip&longs;am &longs;uper&longs;iclem circuli: <lb/>Concauum autem, & conuexum &longs;e habent &longs;icut magnum, <lb/>& paruum. </s> | <s id="N112D1">Etenim e&longs;t verè terminus <lb/>extimus, & conuexum ip&longs;ius circuli, ac &longs;imul ambiens, & <lb/>complectens in &longs;ua concauitate ip&longs;am &longs;uperficilem circuli: <lb/>Concauum autem, & conuexum &longs;e habent &longs;icut magnum, <lb/>& paruum. </s> |
| <s id="N112DC">Horum enim medium e&longs;t æquale, illorum verò <lb/>rectum. </s> | <s id="N112DC">Horum enim medium e&longs;t æquale, illorum verò <lb/>rectum. </s> |
| <s id="N112E1">Quarè &longs;icut cum magnum, & paruum inuicem, <lb/>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb/>magnum con&longs;tituatur paruum, & paruum con&longs;tituatur ma­<pb pagenum="36" xlink:href="005/01/044.jpg"/>gnum: ita quælibet linea curua, &longs;eu conuexa antequam &longs;iat <lb/>concaua, prius debet fieri recta: ab&longs;urdum igitur apparet, ean­<lb/>dem omnino circuli periferiam, &longs;imul con&longs;titui concauam, <lb/>& conuexam. </s> | <s id="N112E1">Quarè &longs;icut cum magnum, & paruum inuicem, <lb/>commutantur, prius perueniunt ad æquale, quàm ad hoc vt <lb/>magnum con&longs;tituatur paruum, & paruum con&longs;tituatur ma­<pb pagenum="36" xlink:href="005/01/044.jpg"/>gnum: ita quælibet linea curua, &longs;eu conuexa antequam fiat <lb/>concaua, prius debet fieri recta: ab&longs;urdum igitur apparet, ean­<lb/>dem omnino circuli periferiam, &longs;imul con&longs;titui concauam, <lb/>& conuexam. </s> |
| </p> | </p> |
| <p id="N112F3" type="main"> | <p id="N112F3" type="main"> |
| <s id="N112F5">Nec difficultatem euadunt, qui dicunt, concauum, & con­<lb/>uexum realiter non e&longs;&longs;e idem in circulo, &longs;eu curuitatem, & <lb/>concauitatem non reperiri in eadem linea, &longs;ed in diuer&longs;is, ità <lb/>vt in circunferentia &longs;it tantum curuitas, &longs;eù conuexum, con­<lb/>cauitas verò &longs;it potius in corpore extrin&longs;eco ambiente per li­<lb/>neam illi corre&longs;pondentem. </s> | <s id="N112F5">Nec difficultatem euadunt, qui dicunt, concauum, & con­<lb/>uexum realiter non e&longs;&longs;e idem in circulo, &longs;eu curuitatem, & <lb/>concauitatem non reperiri in eadem linea, &longs;ed in diuer&longs;is, ità <lb/>vt in circunferentia &longs;it tantum curuitas, &longs;eù conuexum, con­<lb/>cauitas verò &longs;it potius in corpore extrin&longs;eco ambiente per li­<lb/>neam illi corre&longs;pondentem. </s> |
| <s id="N11302">Etenim cum linea corporis con­<lb/>tinentis ambiens circulum, penetretur in eodem &longs;pacio cum <lb/>cir cunferentia ip&longs;ius circuli, <expan abbr="con&longs;idereturq.">con&longs;idereturque</expan> &longs;ola quantitas <lb/>ab&longs;tracta, & figura vtriu&longs;que lineæ coincidentis, eadem &longs;em­<lb/>per difficultas ob&longs;tabit; nempè quo pacto fieri po&longs;&longs;it, vt <expan abbr="ead&etilde;">eadem</expan> <lb/>longitudo latitudinis expers, circulum terminans, &longs;eù circu­<lb/>lariter exten&longs;a, &longs;imul &longs;it concaua, & conuexa. </s> | <s id="N11302">Etenim cum linea corporis con­<lb/>tinentis ambiens circulum, penetretur in eodem &longs;pacio cum <lb/>cir cunferentia ip&longs;ius circuli, <expan abbr="con&longs;idereturq.">con&longs;idereturque</expan> &longs;ola quantitas <lb/>ab&longs;tracta, & figura vtriu&longs;que lineæ coincidentis, eadem &longs;em­<lb/>per difficultas ob&longs;tabit; nempè quo pacto fieri po&longs;&longs;it, vt <expan abbr="ead&etilde;">eadem</expan> <lb/>longitudo latitudinis expers, circulum terminans, &longs;eù circu­<lb/>lariter exten&longs;a, &longs;imul &longs;it concaua, & conuexa. </s> |
| <s id="N11319">Sed nihil pro­<lb/>hibet eandem circumferentiam indiuifibilem quoad latitudi­<lb/>nem, & profunditatem, &longs;imul e&longs;&longs;e concauam, & conuexam <lb/>re&longs;pectu diuer&longs;orum, vt in alijs etiam lineatum figuris, ac &longs;u­<lb/>per&longs;iciebus poterit exemplificari: & vt eadem via dicitur <lb/>acliuis, & decliuis; idemque magnum, & paruum reipectu di­<lb/>uer&longs;orum, quæ cum illo comparantur. </s> | <s id="N11319">Sed nihil pro­<lb/>hibet eandem circumferentiam indiuisibilem quoad latitudi­<lb/>nem, & profunditatem, &longs;imul e&longs;&longs;e concauam, & conuexam <lb/>re&longs;pectu diuer&longs;orum, vt in alijs etiam linearum figuris, ac &longs;u­<lb/>perficiebus poterit exemplificari: & vt eadem via dicitur <lb/>acliuis, & decliuis; idemque magnum, & paruum rei pectu di­<lb/>uer&longs;orum, quæ cum illo comparantur. </s> |
| <s id="N11328">Quo fit, vt admiran­<lb/>dam quidem e&longs;&longs;e huiu&longs;modi proprietatem circuli iure dica­<lb/>mus, nullam tamen in &longs;e <expan abbr="repugnantiã">repugnantiam</expan> inuoluere admittamus. </s> | <s id="N11328">Quo fit, vt admiran­<lb/>dam quidem e&longs;&longs;e huiu&longs;modi proprietatem circuli iure dica­<lb/>mus, nullam tamen in &longs;e <expan abbr="repugnantiã">repugnantiam</expan> inuoluere admittamus. </s> |
| </p> | </p> |
| <p id="N11333" type="head"> | <p id="N11333" type="head"> |
| |
| <s id="N1133E">Textus Quintus.</s> | <s id="N1133E">Textus Quintus.</s> |
| </p> | </p> |
| <p id="N11341" type="main"> | <p id="N11341" type="main"> |
| <s id="N11343">A<emph type="italics"/>ltervm autem, quod &longs;imul contrarÿi <lb/>mouetur motionibus: &longs;imul enim ad anterio­<lb/>rem mouetur locum, & ad po&longs;teriorem. </s> | <s id="N11343">A<emph type="italics"/>ltervm autem, quod &longs;imul contrarijs <lb/>mouetur motionibus: &longs;imul enim ad anterio­<lb/>rem mouetur locum, & ad po&longs;teriorem. </s> |
| <s id="N1134D">Et <lb/>ea, quæ circulum de&longs;cribit, linea eodem &longs;e <lb/>babet modo: Ex que enim incipit loco, illius <lb/>extremum, ad eundem rur&longs;us redit: Illa <lb/>enim continuò commota, extremum rur&longs;us efficitur primum.<emph.end type="italics"/><pb pagenum="37" xlink:href="005/01/045.jpg"/><emph type="italics"/>Quamobrem manife&longs;tum, quod inde muiatum e&longs;t. </s> | <s id="N1134D">Et <lb/>ea, quæ circulum de&longs;cribit, linea eodem &longs;e <lb/>habet modo: Ex que enim incipit loco, illius <lb/>extremum, ad eundem rur&longs;us redit: Illa <lb/>enim continuò commota, extremum rur&longs;us efficitur primum.<emph.end type="italics"/><pb pagenum="37" xlink:href="005/01/045.jpg"/><emph type="italics"/>Quamobrem manife&longs;tum, quod inde mutatum e&longs;t. </s> |
| <s id="N11361">Quaprop­<lb/>ter (vt dictum e&longs;t prius) non e&longs;t inconueniens, ip&longs;um miracutc­<lb/>rum omnium e&longs;&longs;e principium.<emph.end type="italics"/></s> | <s id="N11361">Quaprop­<lb/>ter (vt dictum e&longs;t prius) non e&longs;t inconueniens, ip&longs;um miraculo­<lb/>rum omnium e&longs;&longs;e principium.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N1136A" type="main"> | <p id="N1136A" type="main"> |
| <s id="N1136C"><emph type="italics"/>Ea igitur, quæ circa libram fiunt, ad virculum referuntur: <lb/>“quæ verocirca vectem, ad ip&longs;am libram; alia autem ferè om-<emph.end type="italics"/><arrow.to.target n="marg13"/><lb/><emph type="italics"/>nia, quæ circa Menbanicas &longs;unt motiones, ad vectem. </s> | <s id="N1136C"><emph type="italics"/>Ea igitur, quæ circa libram fiunt, ad circulum referuntur: <lb/>“quæ vero circa vectem, ad ip&longs;am libram; alia autem ferè om-<emph.end type="italics"/><arrow.to.target n="marg13"/><lb/><emph type="italics"/>nia, quæ circa Menbanicas &longs;unt motiones, ad vectem. </s> |
| <s id="N1137C">Pra­<lb/>tereà etiam quoniam vnica exi&longs;tente, quæ ex centro e&longs;t linea, <lb/>nullum aliud alij, quæ in illa &longs;unt, punctorum æqua velocitate <lb/>feratur; &longs;ed citius &longs;emper, quod à manente termino e&longs;t remo­<lb/>tius, <expan abbr="pleraq.">pleraque</expan> miratulorum accidunt in circuli motionibus: de <lb/>quibus in ÿs, quæ po&longs;thac adducentur, quæ&longs;tionibus erit ma­<lb/>nife&longs;tam.”<emph.end type="italics"/></s> | <s id="N1137C">Prae­<lb/>tereà etiam quoniam vnica exi&longs;tente, quæ ex centro e&longs;t linea, <lb/>nullum aliud alij, quæ in illa &longs;unt, punctorum æqua velocitate <lb/>feratur; &longs;ed citius &longs;emper, quod à manente termino e&longs;t remo­<lb/>tius, <expan abbr="pleraq.">pleraque</expan> miraculorum accidunt in circuli motionibus: de <lb/>quibus in ijs, quæ po&longs;thac adducentur, quæ&longs;tionibus erit ma­<lb/>nife&longs;tam.”<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N11391" type="margin"> | <p id="N11391" type="margin"> |
| <s id="N11393"><margin.target id="marg13"/>Verba re­<lb/>&longs;ecanda.</s> | <s id="N11393"><margin.target id="marg13"/>Verba re­<lb/>&longs;ecanda.</s> |
| </p> | </p> |
| <p id="N1139A" type="main"> | <p id="N1139A" type="main"> |
| <s id="N1139C"><emph type="italics"/>Quoniam autem fecundum contrarias &longs;imul motiones mo­<lb/>uetur circulus; & alierum quidem diametri ex tremum, vbi A, <lb/>in ante mouctur, alserum verò vbi B, ad retro; efficiunt non­<lb/>nulli, vt ab vnica motione multi contrario &longs;imul moueantur <lb/>circuli; que madmodum &longs;unt illi, quos in locis proponunt &longs;acris, <lb/>æneos, & ferreos fabricantes orbiculos. </s> | <s id="N1139C"><emph type="italics"/>Quoniam autem secundum contrarias &longs;imul motiones mo­<lb/>uetur circulus; & alienum quidem diametri extremum, vbi A, <lb/>in ante mouetur, alterum verò vbi B, ad retro; efficiunt non­<lb/>nulli, vt ab vnica motione multi contrario &longs;imul moueantur <lb/>circuli; quemadmodum &longs;unt illi, quos in locis proponunt &longs;acris, <lb/>æneos, & ferreos fabricantes orbiculos. </s> |
| <s id="N113AB">Si enim AB, circu­<lb/>lum alier contingerit, circulus in quo CD, mota circuli, in quo <lb/>AB, diametro in ante, mouebitur CD, ad retro diametro cir­<lb/>culi, vbi e&longs;t A, circà idem mota, In contrarium igitur moue­<lb/>bitur circulus vbi CD, ad illum, vbi AB, El rur&longs;us ip&longs;e con­<lb/>tiguum vbi EF, in contrarium &longs;ibi ip&longs;i mouebitur propter ean­<lb/>dem cau&longs;am. </s> | <s id="N113AB">Si enim AB, circu­<lb/>lum alier contingerit, circulus in quo CD, mota circuli, in quo <lb/>AB, diametro in ante, mouebitur CD, ad retro diametro cir­<lb/>culi, vbi e&longs;t A, circà idem mota, In contrarium igitur moue­<lb/>bitur circulus vbi CD, ad illum, vbi AB, El rur&longs;us ip&longs;e con­<lb/>tiguum vbi EF, in contrarium &longs;ibi ip&longs;i mouebitur propter ean­<lb/>dem cau&longs;am. </s> |
| <s id="N113BA">Eodem etiam modo &longs;i plures fuerint, idem <lb/>facient, vno &longs;olo commoto. </s> | <s id="N113BA">Eodem etiam modo &longs;i plures fuerint, idem <lb/>facient, vno &longs;olo commoto. </s> |
| <s id="N113BF">Hanc lgitur in circulo exi&longs;tentem <lb/>animaduertens naturam Arcbitecti, in&longs;trumentum fabricant, <lb/>celantes principium, vt macbinæ &longs;olum mani&longs;e&longs;tum &longs;it illud, <lb/>quod admirationem præ&longs;tat, cau&longs;a verò lateat.<emph.end type="italics"/></s> | <s id="N113BF">Hanc lgitur in circulo exi&longs;tentem <lb/>animaduertens naturam Architecti, in&longs;trumentum fabricant, <lb/>celantes principium, vt machinæ &longs;olum manife&longs;tum &longs;it illud, <lb/>quod admirationem præ&longs;tat, cau&longs;a verò lateat.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N113CA" type="head"> | <p id="N113CA" type="head"> |
| <s id="N113CC">COMMENTARIVS.<!-- KEEP S--></s> | <s id="N113CC">COMMENTARIVS.<!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N113D0" type="main"> | <p id="N113D0" type="main"> |
| <s id="N113D2">Tertio illud quoque admiratione dignum &longs;e&longs;e o&longs;&longs;ert in <lb/>circulo, quod, inquit Ari&longs;toteles, contrarijs &longs;imul fe­<lb/>ratur motionibus, antror&longs;um videlicet, ac retror&longs;um, <lb/>&longs;ur&longs;um, ac deor&longs;um. </s> | <s id="N113D2">Tertio illud quoque admiratione dignum &longs;e&longs;e offert in <lb/>circulo, quod, inquit Ari&longs;toteles, contrarijs &longs;imul fe­<lb/>ratur motionibus, antror&longs;um videlicet, ac retror&longs;um, <lb/>&longs;ur&longs;um, ac deor&longs;um. </s> |
| <s id="N113DB">Dum enim pars circuli &longs;uperior de&longs;cen­<lb/>dit, ac mouetur antror&longs;um, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ad dexteram, altera pars illi <pb pagenum="38" xlink:href="005/01/046.jpg"/>oppo&longs;ita, quæ e&longs;t inferior, a&longs;cendit, ac mouetur retror&longs;um ad <lb/>leuam. </s> | <s id="N113DB">Dum enim pars circuli &longs;uperior de&longs;cen­<lb/>dit, ac mouetur antror&longs;um, v. <!-- REMOVE S-->g. <!-- REMOVE S-->ad dexteram, altera pars illi <pb pagenum="38" xlink:href="005/01/046.jpg"/>oppo&longs;ita, quæ e&longs;t inferior, a&longs;cendit, ac mouetur retror&longs;um ad <lb/>leuam. </s> |
| <s id="N113EB">Quod &longs;i huiu&longs;modi po&longs;itiones formaliter non con­<lb/>&longs;tituantur ni&longs;i in quadam relatione, ac re&longs;pectu vnius partis ad <lb/>alteram, hoc parumrefert, cum fundamentaliter &longs;emper im­<lb/>portent realem oppo&longs;itionem, ac diuer&longs;itatem loci, in quo <lb/>ip&longs;e partes relatæ con&longs;tituuntur, vel ad quem tendunt <expan abbr="tanquã">tanquam</expan> <lb/>ad terminum &longs;ui motus. </s> | <s id="N113EB">Quod &longs;i huiu&longs;modi po&longs;itiones formaliter non con­<lb/>&longs;tituantur ni&longs;i in quadam relatione, ac re&longs;pectu vnius partis ad <lb/>alteram, hoc parumrefert, cum fundamentaliter &longs;emper im­<lb/>portent realem oppo&longs;itionem, ac diuer&longs;itatem loci, in quo <lb/>ip&longs;e partes relatæ con&longs;tituuntur, vel ad quem tendunt <expan abbr="tanquã">tanquam</expan> <lb/>ad terminum &longs;ui motus. </s> |
| <s id="N113FC">Quapropter idem Philo&longs;ophus &longs;u­<lb/><figure id="id.005.01.046.1.jpg" xlink:href="005/01/046/1.jpg"/><lb/>biungit ex hac contra­<lb/>rietate fieri, vt vnius <lb/>circuli motione, alij cir­<lb/>culi in contrarium mo­<lb/>ueantur. </s> | <s id="N113FC">Quapropter idem Philo&longs;ophus &longs;u­<lb/><figure id="id.005.01.046.1.jpg" xlink:href="005/01/046/1.jpg"/><lb/>biungit ex hac contra­<lb/>rietate fieri, vt vnius <lb/>circuli motione, alij cir­<lb/>culi in contrarium mo­<lb/>ueantur. </s> |
| <s id="N1140F">Vt &longs;i con&longs;ti­<lb/>tuatur circulus, qui pri­<lb/>mò moueri debeat in­<lb/>ter alios quaruor, <expan abbr="&longs;intq.">&longs;intque</expan> <lb/>omnes denticulati, <lb/>quem admodum videre <lb/>e&longs;t in horologijs, <expan abbr="alijsq.">alijsque</expan> <lb/>&longs;imilibus machinis, vt <lb/>in hac &longs;igura: Nam pars <lb/>&longs;uperor medij circuli, <lb/>quæ de&longs;cendit, impellit partem inferiorem &longs;uperioris circuli, <lb/>facitque eam a&longs;cendere. </s> | <s id="N1140F">Vt &longs;i con&longs;ti­<lb/>tuatur circulus, qui pri­<lb/>mò moueri debeat in­<lb/>ter alios quaruor, <expan abbr="&longs;intq.">&longs;intque</expan> <lb/>omnes denticulati, <lb/>quem admodum videre <lb/>e&longs;t in horologijs, <expan abbr="alijsq.">alijsque</expan> <lb/>&longs;imilibus machinis, vt <lb/>in hac figura: Nam pars <lb/>&longs;uperor medij circuli, <lb/>quæ de&longs;cendit, impellit partem inferiorem &longs;uperioris circuli, <lb/>facitque eam a&longs;cendere. </s> |
| <s id="N11430">Et pars inferior eiu&longs;dem medij cir­<lb/>culi, a&longs;cendendo facit de&longs;cendere partem &longs;uperiorem circuli <lb/>inferioris. </s> | <s id="N11430">Et pars inferior eiu&longs;dem medij cir­<lb/>culi, a&longs;cendendo facit de&longs;cendere partem &longs;uperiorem circuli <lb/>inferioris. </s> |
| <s id="N11437">Deinde &longs;imiliter idem circulus medius dum dex­<lb/>tror&longs;um mouetur, mouet circulum dexterum &longs;ini&longs;tror&longs;um, & <lb/>&longs;ini&longs;trum dextror&longs;um. </s> | <s id="N11437">Deinde &longs;imiliter idem circulus medius dum dex­<lb/>tror&longs;um mouetur, mouet circulum dexterum &longs;ini&longs;tror&longs;um, & <lb/>&longs;ini&longs;trum dextror&longs;um. </s> |
| </p> | </p> |
| |
| <pb pagenum="39" xlink:href="005/01/047.jpg"/> | <pb pagenum="39" xlink:href="005/01/047.jpg"/> |
| <p id="N1147B" type="main"> | <p id="N1147B" type="main"> |
| <s id="N1147D">Quæ autem de libra ac vatia punctorum &longs;emidiametri ve­<lb/>locitate hìc docet Ari&longs;toteles, fru&longs;tra interpo&longs;ita &longs;unt ac præ­<lb/>ter Auctoris intentum, cum ad rem de qua agitur non perti­<lb/>neant, ac alibi proprijs in locis repetantur. </s> | <s id="N1147D">Quæ autem de libra ac vatia punctorum &longs;emidiametri ve­<lb/>locitate hìc docet Ari&longs;toteles, fru&longs;tra interpo&longs;ita &longs;unt ac præ­<lb/>ter Auctoris intentum, cum ad rem de qua agitur non perti­<lb/>neant, ac alibi proprijs in locis repetantur. </s> |
| <s id="N11486">Quare ex hoc <lb/>textu re&longs;ecanda e&longs;&longs;ent, incipiendo à particula (Ea igitur) <lb/>v&longs;que ad (erit manife&longs;tum) inclu&longs;iue, prout lineis confi­<lb/>gnauimus. </s> | <s id="N11486">Quare ex hoc <lb/>textu re&longs;ecanda e&longs;&longs;ent, incipiendo à particula (Ea igitur) <lb/>v&longs;que ad (erit manife&longs;tum) inclu&longs;iue, prout lineis consi­<lb/>gnauimus. </s> |
| </p> | </p> |
| <p id="N1148F" type="head"> | <p id="N1148F" type="head"> |
| <s id="N11491"><emph type="italics"/>De Quarta Circuli Proprietate.<emph.end type="italics"/><!-- KEEP S--></s> | <s id="N11491"><emph type="italics"/>De Quarta Circuli Proprietate.<emph.end type="italics"/><!-- KEEP S--></s> |
| |
| </p> | </p> |
| <p id="N1149E" type="main"> | <p id="N1149E" type="main"> |
| <s id="N114A0">I<emph type="italics"/>n primis igitur quæ accidunt circa libram du­<lb/>bitare faciunt, quam nam obcau&longs;am exactio­<lb/>res minoribus maiores &longs;unt libræ. </s> | <s id="N114A0">I<emph type="italics"/>n primis igitur quæ accidunt circa libram du­<lb/>bitare faciunt, quam nam obcau&longs;am exactio­<lb/>res minoribus maiores &longs;unt libræ. </s> |
| <s id="N114AA">IIuius au­<lb/>tem rei principium est quamobrem in ip&longs;o cir­<lb/>culo, quæ plus à centro di&longs;tat linea eadem vi <lb/>commota, citius fertur, quàm illa quæ minus distat. </s> | <s id="N114AA">Huius au­<lb/>tem rei principium est quamobrem in ip&longs;o cir­<lb/>culo, quæ plus à centro di&longs;tat linea eadem vi <lb/>commota, citius fertur, quàm illa quæ minus distat. </s> |
| <s id="N114B3">Citius <lb/>enim bifariam dicitur: &longs;iue enim in minori tempore æqualem <lb/>pertran&longs;it locum, citius feci&longs;&longs;e dicimus: &longs;eu in æquali maio­<lb/>rem. </s> | <s id="N114B3">Citius <lb/>enim bifariam dicitur: &longs;iue enim in minori tempore æqualem <lb/>pertran&longs;it locum, citius feci&longs;&longs;e dicimus: &longs;eu in æquali maio­<lb/>rem. </s> |
| <s id="N114BC">Maior autem in æquali tempore, maiorem de&longs;cribit cir­<lb/>culum: qui enim extra e&longs;t, maior eo qui intus e&longs;t. </s> | <s id="N114BC">Maior autem in æquali tempore, maiorem de&longs;cribit cir­<lb/>culum: qui enim extra e&longs;t, maior eo qui intus e&longs;t. </s> |
| <s id="N114C1">Horum <lb/>autem cau&longs;a, quoniam duas fertur lationes ea quæ circulum <lb/>de&longs;cribit linea. </s> | <s id="N114C1">Horum <lb/>autem cau&longs;a, quoniam duas fertur lationes ea quæ circulum <lb/>de&longs;cribit linea. </s> |
| <s id="N114C8">Quandoquidem igitur in proportione fertur <lb/>aliqua id quod fertur, &longs;uper rectam ferri nece&longs;&longs;e: Et bæc dia­<lb/>meter efficitur &longs;iguræ quam faciunt illæ quæ in buiu&longs;modi pro­<lb/>portione coaptantur lineæ. </s> | <s id="N114C8">Quandoquidem igitur in proportione fertur <lb/>aliqua id quod fertur, &longs;uper rectam ferri nece&longs;&longs;e: Et hæc dia­<lb/>meter efficitur figuræ quam faciunt illæ quæ in huiu&longs;modi pro­<lb/>portione coaptantur lineæ. </s> |
| <s id="N114D1">Sit enim proportio &longs;eoundum quam <lb/>latum fertur, quam habet AB ad AC. & A quidem fertur <lb/>ver&longs;us B: A B vero &longs;ubter&longs;eratur ver&longs;us MC: latum au­<lb/>tem &longs;it A quidem ad D. <!-- KEEP S--></s> | <s id="N114D1">Sit enim proportio &longs;ecundum quam <lb/>latum fertur, quam habet AB ad AC. & A quidem fertur <lb/>ver&longs;us B: A B vero &longs;ubter&longs;eratur ver&longs;us MC: latum au­<lb/>tem &longs;it A quidem ad D. <!-- KEEP S--></s> |
| <s id="N114DB">Vbi autem est A B ver&longs;us E: quo­<lb/>niam igitur lationis erat proportio, quam A B habet ad A C, <lb/>nece&longs;&longs;e e&longs;t & A D ad A E hanc habere proportionem. </s> | <s id="N114DB">Vbi autem est A B ver&longs;us E: quo­<lb/>niam igitur lationis erat proportio, quam A B habet ad A C, <lb/>nece&longs;&longs;e e&longs;t & A D ad A E hanc habere proportionem. </s> |
| <s id="N114E2">Simile <lb/>igitur est proportione paruum quadrilaterum maiori: quam­<lb/>obrem & eadem illorum e&longs;t diameter, & A erit ad F. <!-- KEEP S--></s> | <s id="N114E2">Simile <lb/>igitur est proportione paruum quadrilaterum maiori: quam­<lb/>obrem & eadem illorum e&longs;t diameter, & A erit ad F. <!-- KEEP S--></s> |
| <s id="N114EA">Eodem <lb/>etiam o&longs;tendetur modo, vbicunque latio deprabendatur; &longs;em-<emph.end type="italics"/><pb pagenum="40" xlink:href="005/01/048.jpg"/><emph type="italics"/>per enim &longs;upra diametrum erit. </s> | <s id="N114EA">Eodem <lb/>etiam o&longs;tendetur modo, vbicunque latio deprahendatur; &longs;em-<emph.end type="italics"/><pb pagenum="40" xlink:href="005/01/048.jpg"/><emph type="italics"/>per enim &longs;upra diametrum erit. </s> |
| <s id="N114F8">Manife&longs;tum igitur, quod id <lb/>quod &longs;ecundum diametrum duabus fertur lationibus, nece&longs;&longs;a­<lb/>riò &longs;ecundum laterum proportionem fertur. </s> | <s id="N114F8">Manife&longs;tum igitur, quod id <lb/>quod &longs;ecundum diametrum duabus fertur lationibus, nece&longs;&longs;a­<lb/>riò &longs;ecundum laterum proportionem fertur. </s> |
| <s id="N114FF">Si enim &longs;ecun­<lb/>dum aliam quampiam, non fertur &longs;ecundam diametrum. <lb/></s> | <s id="N114FF">Si enim &longs;ecun­<lb/>dum aliam quampiam, non fertur &longs;ecundam diametrum. <lb/></s> |
| <s id="N11505">Si autem in nulla fertur proportione &longs;ecundum duas lationes <lb/>nullo in tempore, rectam e&longs;&longs;e lationem, e&longs;t impo&longs;&longs;ibile. </s> | <s id="N11505">Si autem in nulla fertur proportione &longs;ecundum duas lationes <lb/>nullo in tempore, rectam e&longs;&longs;e lationem, e&longs;t impo&longs;&longs;ibile. </s> |
| <s id="N1150A">Sit enim <lb/>recta. </s> | <s id="N1150A">Sit enim <lb/>recta. </s> |
| <s id="N1150F">Po&longs;ita igitur bac pro diametro, & circumrepletis late­<lb/>ribus, illud quod fertur, &longs;ecundum laterum proportionem fer­<lb/>ri nece&longs;&longs;e e&longs;t: hoc enim demon&longs;tratum e&longs;t prius. </s> | <s id="N1150F">Po&longs;ita igitur hac pro diametro, & circumrepletis late­<lb/>ribus, illud quod fertur, &longs;ecundum laterum proportionem fer­<lb/>ri nece&longs;&longs;e e&longs;t: hoc enim demon&longs;tratum e&longs;t prius. </s> |
| <s id="N11516">Non igitur <lb/>restam efficiet id quod &longs;ecundum nullam proportionem, in nul­<lb/>lo &longs;ertur tempore. </s> | <s id="N11516">Non igitur <lb/>rectam efficiet id quod &longs;ecundum nullam proportionem, in nul­<lb/>lo fertur tempore. </s> |
| <s id="N1151D">Si autem &longs;ecundum quampiam feratur <lb/>proportionem, & in tempore quopiam, hoc nece&longs;&longs;e est tempus <lb/>rectam e<32>e lationem, per ea quæ retro &longs;unt dicta. </s> | <s id="N1151D">Si autem &longs;ecundum quampiam feratur <lb/>proportionem, & in tempore quopiam, hoc nece&longs;&longs;e est tempus <lb/>rectam e<32>e lationem, per ea quæ retro &longs;unt dicta. </s> |
| <s id="N11524">Quamob­<lb/>remcirculare e&longs;t id, quod &longs;ecundum nullam proportionem nul­<lb/>lo in tempore duas fertur lationes.<emph.end type="italics"/></s> | <s id="N11524">Quamob­<lb/>remcirculare e&longs;t id, quod &longs;ecundum nullam proportionem nul­<lb/>lo in tempore duas fertur lationes.<emph.end type="italics"/></s> |
| </p> | </p> |
| |
| <s id="N11555">Quod ita &longs;e habere <lb/>o&longs;tendit ex eo, quia dupliciter aliquid intelligimus velocius <lb/>alio moueri; nempe, vel quia in minori tempore, æquale <lb/>&longs;patium pertran&longs;it; vel quia eodem tempore, maius interual­<lb/>lum percurrit. </s> | <s id="N11555">Quod ita &longs;e habere <lb/>o&longs;tendit ex eo, quia dupliciter aliquid intelligimus velocius <lb/>alio moueri; nempe, vel quia in minori tempore, æquale <lb/>&longs;patium pertran&longs;it; vel quia eodem tempore, maius interual­<lb/>lum percurrit. </s> |
| <s id="N11560">Et hoc pacto inquit in de&longs;criptione circuli <lb/>contingere vt puncta quæ magis à centro di&longs;tant, velocius <lb/>moueantur. </s> | <s id="N11560">Et hoc pacto inquit in de&longs;criptione circuli <lb/>contingere vt puncta quæ magis à centro di&longs;tant, velocius <lb/>moueantur. </s> |
| <s id="N11567">Siquidem eodem tempore maiorem de&longs;cribunt <pb pagenum="41" xlink:href="005/01/049.jpg"/>ambitum. </s> | <s id="N11567">Siquidem eodem tempore maiorem de&longs;cribunt <pb pagenum="41" xlink:href="005/01/049.jpg"/>ambitum. </s> |
| <s id="N1156F">Maior enim e&longs;t circum &longs;erentia cireuli continentis, <lb/>quàm contenti. </s> | <s id="N1156F">Maior enim e&longs;t circum &longs;erentia circuli continentis, <lb/>quàm contenti. </s> |
| <s id="N11574">Si autem circaidem centrum plures cir culi <lb/>ducantur, &longs;emper ille qui coeteros continet, à remotiori pun­<lb/>cto &longs;emidiametri de&longs;cribetur, <expan abbr="proindeq.">proindeque</expan> quò remotiora erunt <lb/>ip&longs;a puncta &longs;emidiametri à centro, eò velocius mouebuntur. </s> | <s id="N11574">Si autem circaidem centrum plures cir culi <lb/>ducantur, &longs;emper ille qui coeteros continet, à remotiori pun­<lb/>cto &longs;emidiametri de&longs;cribetur, <expan abbr="proindeq.">proindeque</expan> quò remotiora erunt <lb/>ip&longs;a puncta &longs;emidiametri à centro, eò velocius mouebuntur. </s> |
| </p> | </p> |
| <p id="N11581" type="main"> | <p id="N11581" type="main"> |
| <s id="N11583">Horum autem cau&longs;am e&longs;&longs;e inquit Ari&longs;toteles, quoniam &longs;e­<lb/>midiameter circulum de&longs;cribens mouetur motu quodam <lb/>mixto ex duabus lationibus, nempe naturali, ac præternatu­<lb/>rali, vt infra &longs;equenti textu probabitur; quam duplicem la­<lb/>tionem partes &longs;emidiametri non æquè participant, hoc e&longs;t <lb/>non participant &longs;ecundum eandem proportionem. </s> | <s id="N11583">Horum autem cau&longs;am e&longs;&longs;e inquit Ari&longs;toteles, quoniam &longs;e­<lb/>midiameter circulum de&longs;cribens mouetur motu quodam <lb/>mixto ex duabus lationibus, nempe naturali, ac præternatu­<lb/>rali, vt infra &longs;equenti textu probabitur; quam duplicem la­<lb/>tionem partes &longs;emidiametri non æquè participant, hoc e&longs;t <lb/>non participant &longs;ecundum eandem proportionem. </s> |
| <s id="N11590">Quando­<lb/>quidem, vt infra pariter ip&longs;e Philo&longs;ophus o&longs;tendit, partes quæ <lb/>remotiores &longs;unt à centro, magis participant de latione natu­<lb/>rali: contra verò quæ centro &longs;unt viciniores, magis partici­<lb/>pant de motione præternaturali. </s> | <s id="N11590">Quando­<lb/>quidem, vt infra pariter ip&longs;e Philo&longs;ophus o&longs;tendit, partes quæ <lb/>remotiores &longs;unt à centro, magis participant de latione natu­<lb/>rali: contra verò quæ centro &longs;unt viciniores, magis partici­<lb/>pant de motione præternaturali. </s> |
| <s id="N1159B">Si enim &longs;ecundum eandem <lb/>aliquam proportionem, duplicem illam lationem omnes ip­<lb/>fæ participarent, non vtique mouerentur motu circulari, &longs;ed <lb/>recto, vt &longs;tatim ip&longs;e demon&longs;trat. </s> | <s id="N1159B">Si enim &longs;ecundum eandem <lb/>aliquam proportionem, duplicem illam lationem omnes ip­<lb/>sæ participarent, non vtique mouerentur motu circulari, &longs;ed <lb/>recto, vt &longs;tatim ip&longs;e demon&longs;trat. </s> |
| <s id="N115A4">Quare &longs;uppo&longs;ito quòd mo­<lb/>bile tanto velocius monetur, quanto magis participat de mo­<lb/>tu naturali, vt ex dicendis etiam tex. <!-- REMOVE S-->8. con&longs;tabit, a primo ad <lb/>vltimum conuincitur, puncta vel partes &longs;emidiametri quò <lb/>plus à centro di&longs;tauerint in de&longs;criptione circuli, eò cœlerius <lb/>moueri, quò vero minus, co tardius. </s> | <s id="N115A4">Quare &longs;uppo&longs;ito quòd mo­<lb/>bile tanto velocius monetur, quanto magis participat de mo­<lb/>tu naturali, vt ex dicendis etiam tex. <!-- REMOVE S-->8. con&longs;tabit, a primo ad <lb/>vltimum conuincitur, puncta vel partes &longs;emidiametri quò <lb/>plus à centro di&longs;tauerint in de&longs;criptione circuli, eò cœlerius <lb/>moueri, quò vero minus, eo tardius. </s> |
| </p> | </p> |
| <p id="N115B3" type="main"> | <p id="N115B3" type="main"> |
| <s id="N115B5">Et confirmari pote&longs;t argumento quod idem Philo&longs;ophus, <lb/>alijs interpo&longs;itis, &longs;equenti textu adiecit; niminum, quia &longs;i <lb/>duobus (inquit) ab eadem potentia latis, hoc quidem plus <lb/>repellatur vel impediatur ab aliquo, illud verò minus; ratio­<lb/>ni con&longs;entancum e&longs;t, tardius moueri id quod plus præpedi­<lb/>tur, aut repellit ur: Sed lineæ circumductæ in circulo, vel pun­<lb/>cta quæ &longs;unt in eius diametro, quò magis appropinquantur <lb/>centro, eò magis repelluntur in motu circulari ac impediun­<lb/>tur ab ip&longs;o centro; ergo tardius mouentur. </s> | <s id="N115B5">Et confirmari pote&longs;t argumento quod idem Philo&longs;ophus, <lb/>alijs interpo&longs;itis, &longs;equenti textu adiecit; nimirum, quia &longs;i <lb/>duobus (inquit) ab eadem potentia latis, hoc quidem plus <lb/>repellatur vel impediatur ab aliquo, illud verò minus; ratio­<lb/>ni con&longs;entaneum e&longs;t, tardius moueri id quod plus præpedi­<lb/>tur, aut repellitur: Sed lineæ circumductæ in circulo, vel pun­<lb/>cta quæ &longs;unt in eius diametro, quò magis appropinquantur <lb/>centro, eò magis repelluntur in motu circulari ac impediun­<lb/>tur ab ip&longs;o centro; ergo tardius mouentur. </s> |
| <s id="N115C8">Minor propo&longs;itio <lb/>huius argumenti probatur; quia cum centrum &longs;it fixum & <lb/>immotum, <expan abbr="eiq.">eique</expan> colligatæ &longs;int omnes partes diametri per lon­<lb/>gitudinem exten&longs;æ, illæ quæ magis ei appropinquantur, ma­<lb/>gis vinciuntur ac detinentur nè moueantur: quæ verò magis <pb pagenum="42" xlink:href="005/01/050.jpg"/>ab eo di&longs;tant, magis relaxantur, <expan abbr="magisq.">magisque</expan> &longs;oluuntur à princi­<lb/>pio detinente, ac propterea minus impediuntur nè ad im­<lb/>pul&longs;um vel motum alterius moueantur, & &longs;ic velocius fe­<lb/>runtur. </s> | <s id="N115C8">Minor propo&longs;itio <lb/>huius argumenti probatur; quia cum centrum &longs;it fixum & <lb/>immotum, <expan abbr="eiq.">eique</expan> colligatæ &longs;int omnes partes diametri per lon­<lb/>gitudinem exten&longs;æ, illæ quæ magis ei appropinquantur, ma­<lb/>gis vinciuntur ac detinentur nè moueantur: quæ verò magis <pb pagenum="42" xlink:href="005/01/050.jpg"/>ab eo di&longs;tant, magis relaxantur, <expan abbr="magisq.">magisque</expan> &longs;oluuntur à princi­<lb/>pio detinente, ac propterea minus impediuntur nè ad im­<lb/>pul&longs;um vel motum alterius moueantur, & &longs;ic velocius fe­<lb/>runtur. </s> |
| </p> | </p> |
| <p id="N115E6" type="main"> | <p id="N115E6" type="main"> |
| |
| <p id="N1162F" type="main"> | <p id="N1162F" type="main"> |
| <s id="N11631">Rur&longs;us antequam ad exactam eius probationem ex Geo­<lb/>metricis principijs accedamus, idem prælibare licebit exem­<lb/>plo huius figuræ, quod non parum ad dilucidationem textus, <lb/><expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis conducet. </s> | <s id="N11631">Rur&longs;us antequam ad exactam eius probationem ex Geo­<lb/>metricis principijs accedamus, idem prælibare licebit exem­<lb/>plo huius figuræ, quod non parum ad dilucidationem textus, <lb/><expan abbr="doctrinæq.">doctrinæque</expan> Ari&longs;totelis conducet. </s> |
| <s id="N1163D">Sit enim corpus &longs;eu pon­<lb/>dus quod moueri debeat con&longs;titutum &longs;uper planum vbi A, <lb/>mouentia verò vbi B, C. <!-- KEEP S--></s> | <s id="N1163D">Sit enim corpus &longs;eu pon­<lb/>dus quod moueri debeat con&longs;titutum &longs;uper planum vbi A, <lb/>mouentia verò vbi B, C. <!-- KEEP S--></s> |
| <s id="N11645">Deinde &longs;upponamus æquali virtu­<lb/>te & æquali &longs;imul tempore vtrumque mouens ad &longs;e pondus <pb pagenum="43" xlink:href="005/01/051.jpg"/><figure id="id.005.01.051.1.jpg" xlink:href="005/01/051/1.jpg"/><lb/>ip&longs;um trahere; quod e&longs;t, eandem &longs;emper proportionem ad <lb/>inuicem &longs;eruare, vt bene&longs;icio trochlearum vel alterius in&longs;tru­<lb/>menti. </s> | <s id="N11645">Deinde &longs;upponamus æquali virtu­<lb/>te & æquali &longs;imul tempore vtrumque mouens ad &longs;e pondus <pb pagenum="43" xlink:href="005/01/051.jpg"/><figure id="id.005.01.051.1.jpg" xlink:href="005/01/051/1.jpg"/><lb/>ip&longs;um trahere; quod e&longs;t, eandem &longs;emper proportionem ad <lb/>inuicem &longs;eruare, vt beneficio trochlearum vel alterius in&longs;tru­<lb/>menti. </s> |
| <s id="N11659">Tunc enim dicimus primo, corpus ip&longs;um mobile A <lb/>moueri motu quodam mixto ex duabus lationibus, nempe <lb/>qua appropinquatur ad B, & qua appropinquantur ad C. <lb/><!-- KEEP S--></s> | <s id="N11659">Tunc enim dicimus primo, corpus ip&longs;um mobile A <lb/>moueri motu quodam mixto ex duabus lationibus, nempe <lb/>qua appropinquatur ad B, & qua appropinquantur ad C. <lb/><!-- KEEP S--></s> |
| <s id="N11662">Quia durante huiu&longs;modi motu, non datur in&longs;tans in quo non <lb/>magis ip&longs;um pondus A appropinquetur ad B, ac &longs;imul ad C. <lb/><!-- KEEP S--></s> | <s id="N11662">Quia durante huiu&longs;modi motu, non datur in&longs;tans in quo non <lb/>magis ip&longs;um pondus A appropinquetur ad B, ac &longs;imul ad C. <lb/><!-- KEEP S--></s> |
| <s id="N11669">Præterea dicimus, huiu&longs;modi motum nece&longs;&longs;ariò e&longs;&longs;e rectum, <lb/>non verò circularem, &longs;eu pondus non ni&longs;i &longs;uper rectam tunc <lb/>&longs;emper moueri. </s> | <s id="N11669">Præterea dicimus, huiu&longs;modi motum nece&longs;&longs;ariò e&longs;&longs;e rectum, <lb/>non verò circularem, &longs;eu pondus non ni&longs;i &longs;uper rectam tunc <lb/>&longs;emper moueri. </s> |
| <s id="N11670">Ftenim &longs;eruata eadem proportione, pon­<lb/>dus ip&longs;um, & quælibet eius pars æqualiter vtrique mouenti in <lb/>æquali tempore deberet appropinquari: quia non e&longs;&longs;et maiot <lb/>ratio cur magis aut citius appropinquaretur ad B, quàm ad C. <lb/><!-- KEEP S--></s> | <s id="N11670">Etenim &longs;eruata eadem proportione, pon­<lb/>dus ip&longs;um, & quælibet eius pars æqualiter vtrique mouenti in <lb/>æquali tempore deberet appropinquari: quia non e&longs;&longs;et maior <lb/>ratio cur magis aut citius appropinquaretur ad B, quàm ad C. <lb/><!-- KEEP S--></s> |
| <s id="N1167B">At non po&longs;&longs;et æqualiter vtrique appropinquari, ni&longs;i feratur <pb pagenum="44" xlink:href="005/01/052.jpg"/>per diamctrom quadranguli A B C D, quæ e&longs;t recta A D; <lb/>&longs;iquidem in nulla alia parte interiecti &longs;pacij, di&longs;tantia e&longs;&longs;et <lb/>æqualis, vt &longs;en&longs;u con&longs;tat: Ergo &longs;eruata eadem proportione in <lb/>ip&longs;a duplici latione re&longs;pectu mobilis & cuiu&longs;que partis ip&longs;ius, <lb/>motus nece&longs;&longs;ariò erit rectus, &longs;eu <expan abbr="põdus">pondus</expan> & quælibet eius pars, <lb/>nonni&longs;i per rectam lineam poterit moueri. </s> | <s id="N1167B">At non po&longs;&longs;et æqualiter vtrique appropinquari, ni&longs;i feratur <pb pagenum="44" xlink:href="005/01/052.jpg"/>per diametrem quadranguli A B C D, quæ e&longs;t recta A D; <lb/>&longs;iquidem in nulla alia parte interiecti &longs;patij, di&longs;tantia e&longs;&longs;et <lb/>æqualis, vt &longs;en&longs;u con&longs;tat: Ergo &longs;eruata eadem proportione in <lb/>ip&longs;a duplici latione re&longs;pectu mobilis & cuiu&longs;que partis ip&longs;ius, <lb/>motus nece&longs;&longs;ariò erit rectus, &longs;eu <expan abbr="põdus">pondus</expan> & quælibet eius pars, <lb/>non ni&longs;i per rectam lineam poterit moueri. </s> |
| </p> | </p> |
| <p id="N11691" type="main"> | <p id="N11691" type="main"> |
| <s id="N11693">Deinde quod infert Ari&longs;toteles, circulare e&longs;&longs;e id quod &longs;e­<lb/>cundum nullam proportionem, nullo in tempore duas pati­<lb/>tur lationes, fal&longs;um e&longs;&longs;et etiam iuxta præfatam explicationé <lb/>proportionis; ni&longs;i per circulare intelligeremus lato modo, id <lb/>quod e&longs;t curuum. </s> | <s id="N11693">Deinde quod infert Ari&longs;toteles, circulare e&longs;&longs;e id quod &longs;e­<lb/>cundum nullam proportionem, nullo in tempore duas pati­<lb/>tur lationes, fal&longs;um e&longs;&longs;et etiam iuxta præfatam explicationé <lb/>proportionis; ni&longs;i per circulare intelligeremus lato modo, id <lb/>quod e&longs;t curuum. </s> |
| |
| <s id="N116C1">Sit inquit proportio ip&longs;arum lationum <lb/><figure id="id.005.01.052.1.jpg" xlink:href="005/01/052/1.jpg"/><lb/>quam habent inter <lb/>&longs;e latera A B & AC <lb/>in dato rectangulo <lb/>A B C D. <!-- KEEP S--></s> | <s id="N116C1">Sit inquit proportio ip&longs;arum lationum <lb/><figure id="id.005.01.052.1.jpg" xlink:href="005/01/052/1.jpg"/><lb/>quam habent inter <lb/>&longs;e latera A B & AC <lb/>in dato rectangulo <lb/>A B C D. <!-- KEEP S--></s> |
| <s id="N116D3">Et A <lb/><expan abbr="quid&etilde;">quidem</expan> duplici motu <lb/>feratur, vno quo <lb/><expan abbr="t&etilde;dat">tendat</expan> ver&longs;us B, qua­<lb/>&longs;i ex &longs;e incedendo <lb/>&longs;uper lineam A B: <lb/>altero verò, quo &longs;imul cum ip&longs;a linea A B &longs;ubterferatur ver­<lb/>&longs;us C, &longs;eu ver&longs;us lineam C D cum eadem &longs;emper proportio­<lb/>ne. </s> | <s id="N116D3">Et A <lb/><expan abbr="quid&etilde;">quidem</expan> duplici motu <lb/>feratur, vno quo <lb/><expan abbr="t&etilde;dat">tendat</expan> ver&longs;us B, qua­<lb/>&longs;i ex &longs;e incedendo <lb/>&longs;uper lineam A B: <lb/>altero verò, quo &longs;imul cum ip&longs;a linea A B &longs;ubterferatur ver­<lb/>&longs;us C, &longs;eu ver&longs;us lineam C D cum eadem &longs;emper proportio­<lb/>ne. </s> |
| <s id="N116EC">Tunc dicimus punctum A motu ip&longs;o mixto, nece&longs;&longs;ariò <lb/>ferriper rectam A D, quæ e&longs;t diameter eiu&longs;dem quadrilateri <lb/>A B C D. <!-- KEEP S--></s> | <s id="N116EC">Tunc dicimus punctum A motu ip&longs;o mixto, nece&longs;&longs;ariò <lb/>ferriper rectam A D, quæ e&longs;t diameter eiu&longs;dem quadrilateri <lb/>A B C D. <!-- KEEP S--></s> |
| <s id="N116F4">Etcnim &longs;i <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> rectangulus minor A E F G <pb pagenum="45" xlink:href="005/01/053.jpg"/>proportionalis maiori A B C D, ac per motum proprium <lb/>ver&longs;us B, ip&longs;um punctum A peragrauerit quantum e&longs;t v&longs;que <lb/>ad E; & per motum totius lineæ A B, ver&longs;us lineam C D, <lb/>peragrauerit quantum e&longs;t ab A, v&longs;que ad F, &longs;eruata eadem <lb/>proportione ip&longs;orum laterum; certe punctum A reperiri non <lb/>po&longs;&longs;et in E, neque in F; &longs;iquidem non fui&longs;&longs;et latum duabus <lb/>lationibus, nec peragra&longs;&longs;et &longs;pacium &longs;ecundum vtramque po­<lb/>&longs;itionem, &longs;imul accedendo quantum &longs;ieri pote&longs;t ad B & ad <lb/>C; &longs;ed vna tantùm latione, alterum &longs;olum &longs;pacium percur­<lb/>ri&longs;&longs;et. </s> | <s id="N116F4">Etenim &longs;i <expan abbr="cõ&longs;tituatur">con&longs;tituatur</expan> rectangulus minor A E F G <pb pagenum="45" xlink:href="005/01/053.jpg"/>proportionalis maiori A B C D, ac per motum proprium <lb/>ver&longs;us B, ip&longs;um punctum A peragrauerit quantum e&longs;t v&longs;que <lb/>ad E; & per motum totius lineæ A B, ver&longs;us lineam C D, <lb/>peragrauerit quantum e&longs;t ab A, v&longs;que ad F, &longs;eruata eadem <lb/>proportione ip&longs;orum laterum; certe punctum A reperiri non <lb/>po&longs;&longs;et in E, neque in F; &longs;iquidem non fui&longs;&longs;et latum duabus <lb/>lationibus, nec peragra&longs;&longs;et &longs;pacium &longs;ecundum vtramque po­<lb/>&longs;itionem, &longs;imul accedendo quantum fieri pote&longs;t ad B & ad <lb/>C; &longs;ed vna tantùm latione, alterum &longs;olum &longs;pacium percur­<lb/>ri&longs;&longs;et. </s> |
| <s id="N11712">Reperietur ergo ip&longs;um. </s> | <s id="N11712">Reperietur ergo ip&longs;um. </s> |
| <s id="N11715">punctum A vbi vtraque pro­<lb/>gre&longs;&longs;io pote&longs;t verificari, vt in puncto G. <!-- KEEP S--></s> | <s id="N11715">punctum A vbi vtraque pro­<lb/>gre&longs;&longs;io pote&longs;t verificari, vt in puncto G. <!-- KEEP S--></s> |
| <s id="N1171B">Quia nimirum F G <lb/>e&longs;t æqualis ip&longs;i A E, & E G æqualis ip&longs;i A F, cum &longs;int latera <lb/>oppo&longs;ita eiu&longs;dem rectanguli, vt patet per 34. primi Elemen­<lb/>torum Euclidis. <!-- KEEP S--></s> | <s id="N1171B">Quia nimirum F G <lb/>e&longs;t æqualis ip&longs;i A E, & E G æqualis ip&longs;i A F, cum &longs;int latera <lb/>oppo&longs;ita eiu&longs;dem rectanguli, vt patet per 34. primi Elemen­<lb/>torum Euclidis. <!-- KEEP S--></s> |
| |
| <p id="N11791" type="main"> | <p id="N11791" type="main"> |
| <s id="N11793">Q<emph type="italics"/>vod quidem igitur ea quæ circulum de&longs;cri­<lb/>bit, duas &longs;imul feratur lationes, manifestum <lb/>e&longs;t cùm ex istis, tùm quia &longs;ecundum rectum <lb/>lata ad perpendiculum peruenit, vt &longs;it rur&longs;us <lb/>ip&longs;a à centro <expan abbr="perpendiculũ">perpendiculum</expan>. </s> | <s id="N11793">Q<emph type="italics"/>vod quidem igitur ea quæ circulum de&longs;cri­<lb/>bit, duas &longs;imul feratur lationes, manifestum <lb/>e&longs;t cùm ex istis, tùm quia &longs;ecundum rectum <lb/>lata ad perpendiculum peruenit, vt &longs;it rur&longs;us <lb/>ip&longs;a à centro <expan abbr="perpendiculũ">perpendiculum</expan>. </s> |
| <s id="N117A5">Sit circulus ABCD, <lb/>extremum autem vbi e&longs;t B. feratur ad ip&longs;um <lb/>D, peruenit &longs;ane aliquando ad ip&longs;um C. <!-- KEEP S--></s> | <s id="N117A5">Sit circulus ABCD, <lb/>extremum autem vbi e&longs;t B. feratur ad ip&longs;um <lb/>D, peruenit &longs;ane aliquando ad ip&longs;um C. <!-- KEEP S--></s> |
| <s id="N117AD">Siquidem igitur in <lb/>propurtione feratur, quam babet BE, EC, fertur vtique &longs;ecun­<lb/>dum diametrum BC. <!-- KEEP S--></s> | <s id="N117AD">Siquidem igitur in <lb/>proportione feratur, quam habet BE, EC, fertur vtique &longs;ecun­<lb/>dum diametrum BC. <!-- KEEP S--></s> |
| <s id="N117B5">N unc autem, <expan abbr="quoniã">quoniam</expan> in nulla proportione, <lb/>in circunferentia certè fertur vbi BEC. </s> | <s id="N117B5">N unc autem, <expan abbr="quoniã">quoniam</expan> in nulla proportione, <lb/>in circunferentia certè fertur vbi BEC. </s> |
| <s id="N117BE">Si autem duobus ab <lb/><expan abbr="ead&etilde;">eadem</expan> potentia latis, hoc <expan abbr="quid&etilde;">quidem</expan> plus repellatur, illud vero minus, <lb/>rationi <expan abbr="con&longs;entaneũ">con&longs;entaneum</expan> e&longs;t, tardius moueri id quod plus repellitur <lb/>eo quod repellitur minus. </s> | <s id="N117BE">Si autem duobus ab <lb/><expan abbr="ead&etilde;">eadem</expan> potentia latis, hoc <expan abbr="quid&etilde;">quidem</expan> plus repellatur, illud vero minus, <lb/>rationi <expan abbr="con&longs;entaneũ">con&longs;entaneum</expan> e&longs;t, tardius moueri id quod plus repellitur <lb/>eo quod repellitur minus. </s> |
| <s id="N117D2">Quod videtur acctdere maiori & mi­<lb/>nori illarum quæ ex centro circulos de&longs;cribunt. </s> | <s id="N117D2">Quod videtur accidere maiori & mi­<lb/>nori illarum quæ ex centro circulos de&longs;cribunt. </s> |
| <s id="N117D7"><expan abbr="Quoniã">Quoniam</expan> enim <lb/>propius e&longs;t manenti, eius quæ minor e&longs;t, <expan abbr="extremũ">extremum</expan>, quam id quod <lb/>e&longs;t maioris, veluti rectum in contrarium, ad medium, tardius <lb/>fertur minoris extremum. </s> | <s id="N117D7"><expan abbr="Quoniã">Quoniam</expan> enim <lb/>propius e&longs;t manenti, eius quæ minor e&longs;t, <expan abbr="extremũ">extremum</expan>, quam id quod <lb/>e&longs;t maioris, veluti rectum in contrarium, ad medium, tardius <lb/>fertur minoris extremum. </s> |
| <s id="N117E7">Omne quidem igitur circulum de­<lb/>&longs;cribenti i&longs;tud accidi<gap/>: <expan abbr="ferturq.">ferturque</expan> eam quæ &longs;ecundum naturam <lb/>e&longs;t lationem, &longs;ecundum circumferentiam: illam vero quæ præ­<lb/>ter naturam, in tran&longs;uer&longs;um & &longs;ecundum centrum. </s> | <s id="N117E7">Omne quidem igitur circulum de­<lb/>&longs;cribenti i&longs;tud accidi<gap/>: <expan abbr="ferturq.">ferturque</expan> eam quæ &longs;ecundum naturam <lb/>e&longs;t lationem, &longs;ecundum circumferentiam: illam vero quæ præ­<lb/>ter naturam, in tran&longs;uer&longs;um & &longs;ecundum centrum. </s> |
| <s id="N117F6">Maio-<emph.end type="italics"/><pb pagenum="47" xlink:href="005/01/055.jpg"/><emph type="italics"/>tem autem &longs;emper eam quæ præter naturam e&longs;t ip&longs;a minor <lb/>fertur: quia enim centro e&longs;t vicinior quod trahit, vincitur <lb/>magis.<emph.end type="italics"/></s> | <s id="N117F6">Maio-<emph.end type="italics"/><pb pagenum="47" xlink:href="005/01/055.jpg"/><emph type="italics"/>rem autem &longs;emper eam quæ præter naturam e&longs;t ip&longs;a minor <lb/>fertur: quia enim centro e&longs;t vicinior quod trahit, vincitur <lb/>magis.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N11808" type="head"> | <p id="N11808" type="head"> |
| <s id="N1180A">COMMENTARIVS.<!-- KEEP S--></s> | <s id="N1180A">COMMENTARIVS.<!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N1180E" type="main"> | <p id="N1180E" type="main"> |
| <s id="N11810">Qvamuis Philo&longs;ophus &longs;uperiori textu &longs;emel atque <lb/>iterum a&longs;&longs;ump&longs;erit, &longs;ernidiametrum, &longs;eu lineam <lb/>circulum de&longs;cribentem, duabus ferri lationibus, <lb/>prout explicuimus; huc tamen illud probandum <lb/>reliquit, & ex dictis etiam de motu antror&longs;um & retror&longs;um <lb/>manife&longs;tum e&longs;&longs;e docet. </s> | <s id="N11810">Qvamuis Philo&longs;ophus &longs;uperiori textu &longs;emel atque <lb/>iterum a&longs;&longs;ump&longs;erit, &longs;emidiametrum, &longs;eu lineam <lb/>circulum de&longs;cribentem, duabus ferri lationibus, <lb/>prout explicuimus; huc tamen illud probandum <lb/>reliquit, & ex dictis etiam de motu antror&longs;um & retror&longs;um <lb/>manife&longs;tum e&longs;&longs;e docet. </s> |
| <s id="N1181D">Id igitur hic probat ex eo. </s> | <s id="N1181D">Id igitur hic probat ex eo. </s> |
| <s id="N11820">Nam &longs;i <lb/>in de&longs;criptione circuli, &longs;emidiameter vnam tantum lationem <lb/>pateretur, vt verbi gratia naturalem, qua rectà tenderet ver­<lb/>&longs;us, vnam aliquam differentiam &longs;itus, nunquam ad ip&longs;ius dia­<lb/>metri perpendiculum perueniret. </s> | <s id="N11820">Nam &longs;i <lb/>in de&longs;criptione circuli, &longs;emidiameter vnam tantum lationem <lb/>pateretur, vt verbi gratia naturalem, qua rectà tenderet ver­<lb/>&longs;us, vnam aliquam differentiam &longs;itus, nunquam ad ip&longs;ius dia­<lb/>metri perpendiculum perueniret. </s> |
| <s id="N1182B">Implicat enim vnica la­<lb/>tione, aliquid &longs;imul rectà tendere, ac in tran&longs;uer&longs;um, quem­<lb/>admodum &longs;e habet perpendiculum ad diametrum à qua pro­<lb/>pendit: At &longs;emidiameter circulum de&longs;cribendo, aliquando <lb/>peruenit ad &longs;uum perpendiculum, ita vt coincidat cum illo: <lb/>Ergo non vnica, &longs;ed duplici latione conuincitur ferri. </s> | <s id="N1182B">Implicat enim vnica la­<lb/>tione, aliquid &longs;imul rectà tendere, ac in tran&longs;uer&longs;um, quem­<lb/>admodum &longs;e habet perpendiculum ad diametrum à qua pro­<lb/>pendit: At &longs;emidiameter circulum de&longs;cribendo, aliquando <lb/>peruenit ad &longs;uum perpendiculum, ita vt coincidat cum illo: <lb/>Ergo non vnica, &longs;ed duplici latione conuincitur ferri. </s> |
| |
| <s id="N11851">Si igitur ip&longs;a recta <lb/>A E, altero eius extremo <lb/>manente in centro E, al­<lb/>tero vero nempè A, cir­<lb/>cumferatur, aliquando <lb/>ab&longs;que dubio erit in ED, <lb/>quæ e&longs;t perpendicularis <lb/>diametro AC. <!-- KEEP S--></s> | <s id="N11851">Si igitur ip&longs;a recta <lb/>A E, altero eius extremo <lb/>manente in centro E, al­<lb/>tero vero nempè A, cir­<lb/>cumferatur, aliquando <lb/>ab&longs;que dubio erit in ED, <lb/>quæ e&longs;t perpendicularis <lb/>diametro AC. <!-- KEEP S--></s> |
| <s id="N11863">Per <expan abbr="motũ">motum</expan> <lb/>autem naturalem ip&longs;a AE, de&longs;cendi&longs;&longs;et in FD, vel aliò rectè <lb/>tran&longs;lata fui&longs;&longs;et. </s> | <s id="N11863">Per <expan abbr="motũ">motum</expan> <lb/>autem naturalem ip&longs;a AE, de&longs;cendi&longs;&longs;et in FD, vel aliò rectè <lb/>tran&longs;lata fui&longs;&longs;et. </s> |
| <s id="N1186E">Non ergo linea circulum de&longs;cribens fertur, <pb pagenum="48" xlink:href="005/01/056.jpg"/>vnico tantummodo motu ver&longs;us vnicam differentiam &longs;itus, <lb/>&longs;ed duplici motu, nempe mixto ex naturali & præternaturali; <lb/>ver&longs;us duplicem differentiam &longs;itus. </s> | <s id="N1186E">Non ergo linea circulum de&longs;cribens fertur, <pb pagenum="48" xlink:href="005/01/056.jpg"/>vnico tantummodo motu ver&longs;us vnicam differentiam &longs;itus, <lb/>&longs;ed duplici motu, nempe mixto ex naturali & præternaturali; <lb/>ver&longs;us duplicem differentiam &longs;itus. </s> |
| <s id="N1187A">Naturali quippe, quo in <lb/>propo&longs;ita figura fertur ver&longs;us latus F D, præternaturali verò, <lb/>quo retrahitur in tran&longs;uer&longs;um ver&longs;us latus E D, co quòd alte­<lb/>rum eius extremum detineatur in centro E, vt clarius infra <lb/>patebit. </s> | <s id="N1187A">Naturali quippe, quo in <lb/>propo&longs;ita figura fertur ver&longs;us latus F D, præternaturali verò, <lb/>quo retrahitur in tran&longs;uer&longs;um ver&longs;us latus E D, eo quòd alte­<lb/>rum eius extremum detineatur in centro E, vt clarius infra <lb/>patebit. </s> |
| </p> | </p> |
| <p id="N11885" type="main"> | <p id="N11885" type="main"> |
| <s id="N11887">Quibus ita con&longs;titutis, reuertitur Ari&longs;toteles ad <expan abbr="probandũ">probandum</expan>, <lb/>partes vel puncta &longs;emidiamet<gap/>i, eò velocius moueri, quò plus <lb/>à centro di&longs;tauerint; cò verò tardius, quò magis ad centrum <lb/>acce&longs;&longs;erint. </s> | <s id="N11887">Quibus ita con&longs;titutis, reuertitur Ari&longs;toteles ad <expan abbr="probandũ">probandum</expan>, <lb/>partes vel puncta &longs;emidiametri, eò velocius moueri, quò plus <lb/>à centro di&longs;tauerint; eò verò tardius, quò magis ad centrum <lb/>acce&longs;&longs;erint. </s> |
| <s id="N11896">Quod cum ad doctrinam in &longs;uperiori textu tra­<lb/>ditam &longs;pectet, <expan abbr="illucq.">illucque</expan> propterea à nobis tran&longs;lat um &longs;it, ac &longs;a­<lb/>tis expo&longs;itum, non e&longs;t cur hic rur&longs;us idem repetatur ac denuo <lb/>exponatur. </s> | <s id="N11896">Quod cum ad doctrinam in &longs;uperiori textu tra­<lb/>ditam &longs;pectet, <expan abbr="illucq.">illucque</expan> propterea à nobis tran&longs;lat um &longs;it, ac &longs;a­<lb/>tis expo&longs;itum, non e&longs;t cur hic rur&longs;us idem repetatur ac denuo <lb/>exponatur. </s> |
| <s id="N118A3">Acceptionem autem & explicationem motus <lb/>naturalis ac præternaturalis, qua v&longs;i &longs;umus, &longs;ump&longs;imus ex co­<lb/>dem Philo&longs;opho textu &longs;equenti, & lib. | <s id="N118A3">Acceptionem autem & explicationem motus <lb/>naturalis ac præternaturalis, qua v&longs;i &longs;umus, &longs;ump&longs;imus ex co­<lb/>dem Philo&longs;opho textu &longs;equenti, & lib. |
| | |
| |
| </p> | </p> |
| <pb pagenum="49" xlink:href="005/01/057.jpg"/> | <pb pagenum="49" xlink:href="005/01/057.jpg"/> |
| <p id="N118DA" type="head"> | <p id="N118DA" type="head"> |
| <s id="N118DC"><emph type="italics"/>Qua ratione partes diametri a oentro remotio­<lb/>res magis participent de motu naturali, <lb/>propinquiores verò magis de præ­<lb/>ternaturali.<emph.end type="italics"/></s> | <s id="N118DC"><emph type="italics"/>Qua ratione partes diametri a centro remotio­<lb/>res magis participent de motu naturali, <lb/>propinquiores verò magis de præ­<lb/>ternaturali.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N118E9" type="head"> | <p id="N118E9" type="head"> |
| <s id="N118EB">Textus Octauus</s> | <s id="N118EB">Textus Octauus</s> |
| </p> | </p> |
| <p id="N118EE" type="main"> | <p id="N118EE" type="main"> |
| <s id="N118F0">Q<emph type="italics"/>vod autem magis quod præter naturam <lb/>e&longs;t mouetur ip&longs;a minor, quam maior illarum, <lb/>quæ ex centro circulos de&longs;cribunt, ex ÿs est <lb/>manifestum. </s> | <s id="N118F0">Q<emph type="italics"/>vod autem magis quod præter naturam <lb/>e&longs;t mouetur ip&longs;a minor, quam maior illarum, <lb/>quæ ex centro circulos de&longs;cribunt, ex ijs est <lb/>manifestum. </s> |
| <s id="N118FC">Sit circulus vbi B C D E, & <lb/>alter in hoc minor, vbi M N O P, circà <lb/>idem centrum A, & proÿciantur diametri <lb/>in magno quidem, in quibus C D, B E, in minori verò ip&longs;æ <lb/>M O, N P: & altera parte longius quadratum &longs;uppleatur <lb/>D K R C: &longs;iquidem A B circulum de&longs;cribens ad id perue­<lb/>niet, vnde e&longs;t egre&longs;&longs;a; manife&longs;tum e&longs;t, quod ad ip&longs;am fertur <lb/>AB. <!-- KEEP S--></s> | <s id="N118FC">Sit circulus vbi B C D E, & <lb/>alter in hoc minor, vbi M N O P, circà <lb/>idem centrum A, & projiciantur diametri <lb/>in magno quidem, in quibus C D, B E, in minori verò ip&longs;æ <lb/>M O, N P: & altera parte longius quadratum &longs;uppleatur <lb/>D K R C: &longs;iquidem A B circulum de&longs;cribens ad id perue­<lb/>niet, vnde e&longs;t egre&longs;&longs;a; manife&longs;tum e&longs;t, quod ad ip&longs;am fertur <lb/>AB. <!-- KEEP S--></s> |
| <s id="N1190E">Similiter etiam A M adip&longs;am A M perueniet. </s> | <s id="N1190E">Similiter etiam A M adip&longs;am A M perueniet. </s> |
| <s id="N11911">T ardiùs <lb/>autem fertur A M, quam A B quemadmodum dictum <lb/>e&longs;t: quia maior fit repul&longs;io, & magis retrabitur A M. </s> | <s id="N11911">T ardiùs <lb/>autem fertur A M, quam A B quemadmodum dictum <lb/>e&longs;t: quia maior fit repul&longs;io, & magis retrabitur A M. </s> |
| <s id="N11918">Du­<lb/>catur igitur ip&longs;a A L F, & abip&longs;o L perpendiculum ad ip­<lb/>&longs;am AB, ip&longs;a LQ in minore circulo: & rur&longs;um ab L du­<lb/>casur iuxtà A B L S, & S T adip&longs;am A B perpendicu­<lb/>lum, & ip&longs;a FX: ip&longs;æ igitur vbi &longs;unt ST, & LQ, æqua­<lb/>les: ip&longs;a ergò B T minor est, quam M <expan abbr="q.">que</expan> Aequales enim <lb/>rectæ lineæ in &etail;qualibus coniecta circulis perpendiculares à <lb/>diametro, minorem diametri re&longs;ecant &longs;ectionem in maioribus <lb/>circulis. </s> | <s id="N11918">Du­<lb/>catur igitur ip&longs;a A L F, & ab ip&longs;o L perpendiculum ad ip­<lb/>&longs;am AB, ip&longs;a LQ in minore circulo: & rur&longs;um ab L du­<lb/>catur iuxtà A B L S, & S T ad ip&longs;am A B perpendicu­<lb/>lum, & ip&longs;a FX: ip&longs;æ igitur vbi &longs;unt ST, & LQ, æqua­<lb/>les: ip&longs;a ergò B T minor est, quam M <expan abbr="q.">que</expan> Aequales enim <lb/>rectæ lineæ in &etail;qualibus coniecta circulis perpendiculares à <lb/>diametro, minorem diametri re&longs;ecant &longs;ectionem in maioribus <lb/>circulis. </s> |
| <s id="N1192F">Est autem ip&longs;a S T æqualis ip&longs;i L <expan abbr="q.">que</expan> In quan­<lb/>to autem tempore ip&longs;a AL ip&longs;am ML lata e&longs;t, in tanto tem­<lb/>poris &longs;patio in maiori circulo, maiorem, quam &longs;it B S, latum <lb/>erit extremum ip&longs;is AB. <!-- KEEP S--></s> | <s id="N1192F">Est autem ip&longs;a S T æqualis ip&longs;i L <expan abbr="q.">que</expan> In quan­<lb/>to autem tempore ip&longs;a AL ip&longs;am ML lata e&longs;t, in tanto tem­<lb/>poris &longs;patio in maiori circulo, maiorem, quam &longs;it B S, latum <lb/>erit extremum ip&longs;is AB. <!-- KEEP S--></s> |
| <s id="N1193D">Latio quidem igit ur &longs;ecundum na­<lb/>turam æqualis: Ea autem, quæ præter naturam e&longs;t minor, <lb/>videlicet B T, quam M <expan abbr="q.">que</expan> Oportet autem proportiona-<emph.end type="italics"/><pb pagenum="50" xlink:href="005/01/058.jpg"/><emph type="italics"/>biliter e&longs;&longs;e, &longs;icut quod est fecundum naturam, ita quod est <lb/>præter naturam, ad id, quod est præter naturan; maiorem <lb/>igitur circumferentiam pertran&longs;iuit, quam &longs;it ip&longs;a S B. </s> | <s id="N1193D">Latio quidem igit ur &longs;ecundum na­<lb/>turam æqualis: Ea autem, quæ præter naturam e&longs;t minor, <lb/>videlicet B T, quam M <expan abbr="q.">que</expan> Oportet autem proportiona-<emph.end type="italics"/><pb pagenum="50" xlink:href="005/01/058.jpg"/><emph type="italics"/>biliter e&longs;&longs;e, &longs;icut quod est fecundum naturam, ita quod est <lb/>præter naturam, ad id, quod est præter naturan; maiorem <lb/>igitur circumferentiam pertran&longs;iuit, quam &longs;it ip&longs;a S B. </s> |
| <s id="N11955">Ne­<lb/>ce&longs;&longs;e autem e&longs;t ip&longs;am F B. in hoc tempore pertran&longs;i<32>e: bic <lb/>enim erit, quando proportion abiliter vtrinque accidis, quod e&longs;t <lb/>præter naturam, ad id quod e&longs;t &longs;ecundum naturam. </s> | <s id="N11955">Ne­<lb/>ce&longs;&longs;e autem e&longs;t ip&longs;am F B. in hoc tempore pertran&longs;i<32>e: hic <lb/>enim erit, quando proportionabiliter vtrinque accidis, quod e&longs;t <lb/>præter naturam, ad id quod e&longs;t &longs;ecundum naturam. </s> |
| <s id="N1195E">Si igi­<lb/>tur maius e&longs;t, quod &longs;ecundum naturam in maiori, & quod e&longs;t <lb/>præter naturam, magis vtique bic coincidit vno modo: ita <lb/>quod B &longs;it latum per ip&longs;am B F in tanto tempore, in quo <lb/>M punctum per ip&longs;am M L. <!-- KEEP S--></s> | <s id="N1195E">Si igi­<lb/>tur maius e&longs;t, quod &longs;ecundum naturam in maiori, & quod e&longs;t <lb/>præter naturam, magis vtique hic coincidit vno modo: ita <lb/>quod B &longs;it latum per ip&longs;am B F in tanto tempore, in quo <lb/>M punctum per ip&longs;am M L. <!-- KEEP S--></s> |
| <s id="N1196A">Hic enim &longs;eeundum naturam <lb/>quidem &longs;igno B fit X F: e&longs;t enim ab ip&longs;o F perpendiculum: <lb/>præter naturam verò ad ip&longs;am X B. </s> | <s id="N1196A">Hic enim &longs;eeundum naturam <lb/>quidem &longs;igno B fit X F: e&longs;t enim ab ip&longs;o F perpendiculum: <lb/>præter naturam verò ad ip&longs;am X B. </s> |
| <s id="N11971">E&longs;t autem quem ad­<lb/>modum FX ad X B, &longs;ic L Q ad M <expan abbr="q.">que</expan> Manife&longs;tum <lb/>autem &longs;i coniunguntur ab ip&longs;a B M ad FL. </s> | <s id="N11971">E&longs;t autem quem ad­<lb/>modum FX ad X B, &longs;ic L Q ad M <expan abbr="q.">que</expan> Manife&longs;tum <lb/>autem &longs;i coniunguntur ab ip&longs;a B M ad FL. </s> |
| <s id="N1197C">Si autem mi­<lb/>nor, aut mator, quam &longs;it FB erit illa, quam latum e&longs;t B, <lb/>non &longs;imiliter erit, neque proportionale in vtri&longs;que quod e&longs;t &longs;e­<lb/>cundum naturam ad id quod e&longs;t præter naturam. </s> | <s id="N1197C">Si autem mi­<lb/>nor, aut maior, quam &longs;it FB erit illa, quam latum e&longs;t B, <lb/>non &longs;imiliter erit, neque proportionale in vtri&longs;que quod e&longs;t &longs;e­<lb/>cundum naturam ad id quod e&longs;t præter naturam. </s> |
| <s id="N11985">Quam igi­<lb/>tur ob cau&longs;am ab eadem potentia celerius fertur id quod plus <lb/>à centro di&longs;tat punctum ex ÿs, quæ dicta &longs;unt e&longs;t mani­<lb/>fe&longs;tum.<emph.end type="italics"/></s> | <s id="N11985">Quam igi­<lb/>tur ob cau&longs;am ab eadem potentia celerius fertur id quod plus <lb/>à centro di&longs;tat punctum ex ijs, quæ dicta &longs;unt e&longs;t mani­<lb/>fe&longs;tum.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p id="N11990" type="head"> | <p id="N11990" type="head"> |
| <s id="N11992">COMMENTARIVS.<!-- KEEP S--></s> | <s id="N11992">COMMENTARIVS.<!-- KEEP S--></s> |
| </p> | </p> |
| <p id="N11996" type="main"> | <p id="N11996" type="main"> |
| <s id="N11998">Ex a&longs;&longs;umptis ab Ari&longs;totele in illo priori argumento <lb/>iam &longs;upra textu 6. à nobis expo&longs;ito ad o&longs;tenden­<lb/>dum in ip&longs;o circulo, quæ plus à centro di&longs;tat linea <lb/>eadem vi commota citius ferri quàm illa, quæ minus di&longs;tat; <lb/>illud du<gap/>taxat ci probandum reman&longs;erat, videlicet partes <lb/>lineæ circulum de&longs;cribentis, quò viciniores centro &longs;unt, eò <lb/>magis detrahi à motu naturali, <expan abbr="magisq.">magisque</expan> participare de motu <lb/>præternaturali; E contrà verò quo remotiores &longs;unt à cen­<lb/>tro, magis participare de motu naturali, vt inde inferatur ve­<lb/>locius moueri. </s> | <s id="N11998">Ex a&longs;&longs;umptis ab Ari&longs;totele in illo priori argumento <lb/>iam &longs;upra textu 6. à nobis expo&longs;ito ad o&longs;tenden­<lb/>dum in ip&longs;o circulo, quæ plus à centro di&longs;tat linea <lb/>eadem vi commota citius ferri quàm illa, quæ minus di&longs;tat; <lb/>illud dumtaxat ci probandum reman&longs;erat, videlicet partes <lb/>lineæ circulum de&longs;cribentis, quò viciniores centro &longs;unt, eò <lb/>magis detrahi à motu naturali, <expan abbr="magisq.">magisque</expan> participare de motu <lb/>præternaturali; E contrà verò quo remotiores &longs;unt à cen­<lb/>tro, magis participare de motu naturali, vt inde inferatur ve­<lb/>locius moueri. </s> |
| <s id="N119B3">Probat autem hoc modo; &longs;it enim, inquit, <lb/>Circulus B C D E; & alter in hoc minor vbi M N O P <lb/>circà idem centrum A. <expan abbr="Sintq.">Sintque</expan> Diametri maioris quidem C. <lb/>D, & B E; minoris verò M O, & N P. <!-- KEEP S--></s> | <s id="N119B3">Probat autem hoc modo; &longs;it enim, inquit, <lb/>Circulus B C D E; & alter in hoc minor vbi M N O P <lb/>circà idem centrum A. <expan abbr="Sintq.">Sintque</expan> Diametri maioris quidem C. <lb/>D, & B E; minoris verò M O, & N P. <!-- KEEP S--></s> |
| <s id="N119C1">Deinde complea-<pb pagenum="51" xlink:href="005/01/059.jpg"/><figure id="id.005.01.059.1.jpg" xlink:href="005/01/059/1.jpg"/><lb/>tur quadrangu'um rectangulum D K R C nempe ducen­<lb/>do lineam K R. paralellam, & æqualem ip&longs;i D C. per pun­<lb/>ctum B, & claudendo ip&longs;as K R & D C per lineas D K <lb/>& C R. <!-- KEEP S--></s> | <s id="N119C1">Deinde complea-<pb pagenum="51" xlink:href="005/01/059.jpg"/><figure id="id.005.01.059.1.jpg" xlink:href="005/01/059/1.jpg"/><lb/>tur quadrangulum rectangulum D K R C nempe ducen­<lb/>do lineam K R. paralellam, & æqualem ip&longs;i D C. per pun­<lb/>ctum B, & claudendo ip&longs;as K R & D C per lineas D K <lb/>& C R. <!-- KEEP S--></s> |
| <s id="N119D6">Cum igitur motus naturalis cuiu&longs;libet lineæ dica­<lb/>tur ille, quo recta fertur ver&longs;us eam partem in quam tendit, <lb/>&longs;i linea A B &longs;tantis circuli de&longs;cripti deo<gap/>&longs;um tenderet &longs;im­<lb/>plici motu naturali, ab&longs;que dubio rectè, ac perpendiculari­<lb/>ter tota &longs;imul caderet, & coincid et cum C R. <!-- KEEP S--></s> | <s id="N119D6">Cum igitur motus naturalis cuiu&longs;libet lineæ dica­<lb/>tur ille, quo recta fertur ver&longs;us eam partem in quam tendit, <lb/>&longs;i linea A B &longs;tantis circuli de&longs;cripti deor&longs;um tenderet &longs;im­<lb/>plici motu naturali, ab&longs;que dubio rectè, ac perpendiculari­<lb/>ter tota &longs;imul caderet, & coincid<gap/>et cum C R. <!-- KEEP S--></s> |
| <s id="N119E4">Quoniam <lb/>vero non pote&longs;t ita ferri &longs;implici motu naturali, eò quod al­<lb/>terum eius extremum detineatur in centro, illæ partes ip­<lb/>&longs;ius dicentur magis participare de motu naturali, quæ re­<lb/>ctius tendunt in ip&longs;am C R; hoc e&longs;t per lineam magis appro­<lb/>pinquantem ad perpendiculum; &longs;icut è contrà illæ dicentur <lb/>magis detrahi à motu naturali, quæ magis incuruantur ten­<lb/>dendo ver&longs;us lineam C D. <!-- KEEP S--></s> | <s id="N119E4">Quoniam <lb/>vero non pote&longs;t ita ferri &longs;implici motu naturali, eò quod al­<lb/>terum eius extremum detineatur in centro, illæ partes ip­<lb/>&longs;ius dicentur magis participare de motu naturali, quæ re­<lb/>ctius tendunt in ip&longs;am C R; hoc e&longs;t per lineam magis appro­<lb/>pinquantem ad perpendiculum; &longs;icut è contrà illæ dicentur <lb/>magis detrahi à motu naturali, quæ magis incuruantur ten­<lb/>dendo ver&longs;us lineam C D. <!-- KEEP S--></s> |
| <s id="N119F6">Itaque progre&longs;&longs;as perpendicu­<lb/>laris ver&longs;us C R erit motus naturalis, ver&longs;us autem C D erit <lb/>præternaturalis Quod certè videtur &longs;upponere Ari&longs;toteles. <lb/><!-- KEEP S--></s> | <s id="N119F6">Itaque progre&longs;&longs;as perpendicu­<lb/>laris ver&longs;us C R erit motus naturalis, ver&longs;us autem C D erit <lb/>præternaturalis Quod certè videtur &longs;upponere Ari&longs;toteles. <lb/><!-- KEEP S--></s> |
| <s id="N119FF">Nunc autem &longs;ic procedit ad o&longs;tenden lum propo&longs;itum, <lb/>nempè partem dia necri propinquiorem centro, vt A M <pb pagenum="52" xlink:href="005/01/060.jpg"/>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb/>M B quæ magis di&longs;tat ab illo. </s> | <s id="N119FF">Nunc autem &longs;ic procedit ad o&longs;tenden lum propo&longs;itum, <lb/>nempè partem diametri propinquiorem centro, vt A M <pb pagenum="52" xlink:href="005/01/060.jpg"/>magis detrahi à motu naturali, ac tardiùs moueri, quàm <lb/>M B quæ magis di&longs;tat ab illo. </s> |
| <s id="N11A0B">Ducatur inquit à centro li­<lb/>nea A L F; & à puncto L perpendicularis ip&longs;i A B quæ <lb/>&longs;it L Q, & rur&longs;us ab eodem L ducatur L S paralella ei­<lb/>dem A B. </s> | <s id="N11A0B">Ducatur inquit à centro li­<lb/>nea A L F; & à puncto L perpendicularis ip&longs;i A B quæ <lb/>&longs;it L Q, & rur&longs;us ab eodem L ducatur L S paralella ei­<lb/>dem A B. </s> |
| <s id="N11A14">Deinde à puncto S excitetur alia perpendicu­<lb/>laris eidem AB. <expan abbr="Sitq.">Sitque</expan> ST; & ab F item eidem perpendicu­<lb/>laris F X. <!-- KEEP S--></s> | <s id="N11A14">Deinde à puncto S excitetur alia perpendicu­<lb/>laris eidem AB. <expan abbr="Sitq.">Sitque</expan> ST; & ab F item eidem perpendicu­<lb/>laris F X. <!-- KEEP S--></s> |
| <s id="N11A20">His po&longs;itis linea QL erit æqualis lineæ T S, vt <lb/>patet ex 34. primi Euclidis, cum &longs;int latera oppo&longs;ita rectan­<lb/>guli T L. <!-- KEEP S--></s> | <s id="N11A20">His po&longs;itis linea QL erit æqualis lineæ T S, vt <lb/>patet ex 34. primi Euclidis, cum &longs;int latera oppo&longs;ita rectan­<lb/>guli T L. <!-- KEEP S--></s> |
| |
| <s id="N11A6A">Id quod <lb/>primo loco erat probandum. </s> | <s id="N11A6A">Id quod <lb/>primo loco erat probandum. </s> |
| </p> | </p> |
| <p id="N11A6F" type="main"> | <p id="N11A6F" type="main"> |
| <s id="N11A71">Vlterius verò quod punctum B magis moueatur motu <lb/>&longs;ecundum naturam, quam ip&longs;um punctum M probatur ex <lb/>co; Nam quo tempore punctum M latum fuerit v&longs;que ad <lb/>L; punctum B eodem tempore perueniet v&longs;que ad F. <!-- KEEP S--></s> | <s id="N11A71">Vlterius verò quod punctum B magis moueatur motu <lb/>&longs;ecundum naturam, quam ip&longs;um punctum M probatur ex <lb/>eo; Nam quo tempore punctum M latum fuerit v&longs;que ad <lb/>L; punctum B eodem tempore perueniet v&longs;que ad F. <!-- KEEP S--></s> |
| <s id="N11A7B">Ete­<lb/>nim cum ita &longs;e habere debeat motus naturalis ip&longs;ius B ad <lb/>motum præter naturam eiu&longs;dem B quemadmodum &longs;e ha­<lb/>bet motus naturalis ip&longs;ius M ad motum præter naturam <pb pagenum="53" xlink:href="005/01/061.jpg"/>eiu&longs;dem M talis proportio &longs;olum verificari pote&longs;t in F, <lb/>nam proportio, quam habet linea F X referens &longs;pacium <lb/>tran&longs;actum &longs;ecundum naturam ad B X, quod ab eodem <lb/>puncto B tran&longs;actum e&longs;t præter naturam in maiori circulo, <lb/>eadem e&longs;t, ac proportio lineæ QL tran&longs;actæ &longs;ecundum <lb/>naturam ad lineam M Q tran&longs;actam præter naturam in mi­<lb/>nori circulo. </s> | <s id="N11A7B">Ete­<lb/>nim cum ita &longs;e habere debeat motus naturalis ip&longs;ius B ad <lb/>motum præter naturam eiu&longs;dem B quemadmodum &longs;e ha­<lb/>bet motus naturalis ip&longs;ius M ad motum præter naturam <pb pagenum="53" xlink:href="005/01/061.jpg"/>eiu&longs;dem M talis proportio &longs;olum verificari pote&longs;t in F, <lb/>nam proportio, quam habet linea F X referens &longs;pacium <lb/>tran&longs;actum &longs;ecundum naturam ad B X, quod ab eodem <lb/>puncto B tran&longs;actum e&longs;t præter naturam in maiori circulo, <lb/>eadem e&longs;t, ac proportio lineæ QL tran&longs;actæ &longs;ecundum <lb/>naturam ad lineam M Q tran&longs;actam præter naturam in mi­<lb/>nori circulo. </s> |
| <s id="N11A95">Quod inde patere pote&longs;t, nam &longs;i ducantur re­<lb/>ctæ B F, & M L efficientur duo triangula æquiangula <lb/>B X F, & M Q L quæ per 4. &longs;exti habebunt latera pro­<lb/>portionalia circà æquales angulos: Vnde &longs;icut &longs;e habet F X <lb/>ad X B circa angulum. </s> | <s id="N11A95">Quod inde patere pote&longs;t, nam &longs;i ducantur re­<lb/>ctæ B F, & M L efficientur duo triangula æquiangula <lb/>B X F, & M Q L quæ per 4. &longs;exti habebunt latera pro­<lb/>portionalia circà æquales angulos: Vnde &longs;icut &longs;e habet F X <lb/>ad X B circa angulum. </s> |
| <s id="N11AA0">rectum X, ita &longs;e habet L Q ad <lb/>QM circà angulum rectum <expan abbr="q.">que</expan> Et permutando, &longs;icut &longs;e <lb/>habet F X ad L Q, ità X B ad QM per 16. Quinti. </s> | <s id="N11AA0">rectum X, ita &longs;e habet L Q ad <lb/>QM circà angulum rectum <expan abbr="q.">que</expan> Et permutando, &longs;icut &longs;e <lb/>habet F X ad L Q, ità X B ad QM per 16. Quinti. </s> |
| |
| <s id="N11ADB">Attenta natura circuli cum &longs;uis proprietatibus modò <lb/>explicatis ad hoc acumen humani ingenij iam pridem <lb/>peruenit, vt machinas qua&longs;dam excogitaret, quæ naturam <lb/>ip&longs;ius circuli participantes, motricem potentiam in motu <lb/>grauium ac leuium iuuarent. </s> | <s id="N11ADB">Attenta natura circuli cum &longs;uis proprietatibus modò <lb/>explicatis ad hoc acumen humani ingenij iam pridem <lb/>peruenit, vt machinas qua&longs;dam excogitaret, quæ naturam <lb/>ip&longs;ius circuli participantes, motricem potentiam in motu <lb/>grauium ac leuium iuuarent. </s> |
| <s id="N11AE6">Huiu&longs;modi autem machinas <lb/>in&longs;trumenta mechanica communiter appellamus, vtpotè <lb/>quæ mechanica &longs;peculatione adinuenta &longs;unt, <expan abbr="eademq.">eademque</expan> arte <pb pagenum="54" xlink:href="005/01/062.jpg"/>adhibentur tanquam in&longs;trumenta ad leuanda pondera, vel <lb/>quomodolibet mouenda grauia, quæ re&longs;pectiuè dicuntur <lb/>etiam leuia. </s> | <s id="N11AE6">Huiu&longs;modi autem machinas <lb/>in&longs;trumenta mechanica communiter appellamus, vtpotè <lb/>quæ mechanica &longs;peculatione adinuenta &longs;unt, <expan abbr="eademq.">eademque</expan> arte <pb pagenum="54" xlink:href="005/01/062.jpg"/>adhibentur tanquam in&longs;trumenta ad leuanda pondera, vel <lb/>quomodolibet mouenda grauia, quæ re&longs;pectiuè dicuntur <lb/>etiam leuia. </s> |
| <s id="N11AFA">Sunt autem hæc in&longs;trumenta præcipua &longs;ex, ad <lb/>quæ cætera omniareducuntur: nempè Libra. <!-- KEEP S--></s> | <s id="N11AFA">Sunt autem hæc in&longs;trumenta præcipua &longs;ex, ad <lb/>quæ cætera omniareducuntur: nempè Libra. <!-- KEEP S--></s> |
| <s id="N11B00">Vectis, Tro­<lb/>chlea, Axis in Peritrochio, Cuneus, & Cochlea Et licet Ari­<lb/>&longs;toteles di&longs;tinciam eorum tractationem prætermi&longs;erit, ac <lb/>nonni&longs;i quatuor ex ip&longs;is hic, vel in &longs;equentibus quæ&longs;tionibus <lb/>pro opportunitate meminerit, &longs;upponit nihilominus <expan abbr="tanquã">tanquam</expan> <lb/>certum, illa omnia ac &longs;imilia participare naturam circuli, <lb/>eorumque vim qua motricem augent potentiam in hoc ip­<lb/>&longs;o con&longs;i&longs;tere, vt circuli proprietatem &longs;apiendo, faciliùs & <lb/>mouerentur, & motum præ&longs;tarent oneribus ac ponderibus <lb/>mouendis, cum circularis &longs;ine orbicularis figura &longs;it omnium <lb/>mouenti&longs;&longs;ima. </s> | <s id="N11B00">Vectis, Tro­<lb/>chlea, Axis in Peritrochio, Cuneus, & Cochlea Et licet Ari­<lb/>&longs;toteles di&longs;tinctam eorum tractationem prætermi&longs;erit, ac <lb/>non ni&longs;i quatuor ex ip&longs;is hic, vel in &longs;equentibus quæ&longs;tionibus <lb/>pro opportunitate meminerit, &longs;upponit nihilominus <expan abbr="tanquã">tanquam</expan> <lb/>certum, illa omnia ac &longs;imilia participare naturam circuli, <lb/>eorumque vim qua motricem augent potentiam in hoc ip­<lb/>&longs;o con&longs;i&longs;tere, vt circuli proprietatem &longs;apiendo, faciliùs & <lb/>mouerentur, & motum præ&longs;tarent oneribus ac ponderibus <lb/>mouendis, cum circularis &longs;ine orbicularis figura &longs;it omnium <lb/>mouenti&longs;&longs;ima. </s> |
| <s id="N11B1B">Ait enim &longs;upra tex. <!-- REMOVE S-->5. Ea igitur quæ circa <lb/>libram fiunt, ad circulum referuntur: quæ verò circa vectem, <lb/>ad ip&longs;am libram: alia autem ferè omnia, quæ circamecha­<lb/>nicas &longs;unt motiones, ad vectem. </s> | <s id="N11B1B">Ait enim &longs;upra tex. <!-- REMOVE S-->5. Ea igitur quæ circa <lb/>libram fiunt, ad circulum referuntur: quæ verò circa vectem, <lb/>ad ip&longs;am libram: alia autem ferè omnia, quæ circamecha­<lb/>nicas &longs;unt motiones, ad vectem. </s> |
| <s id="N11B26">Ex quibus infertur &longs;iue im­<lb/>mediate, &longs;iue mediante, alia quadam ab&longs;tracta ratione quam <lb/>ip&longs;a participent, mechanica penè omnia in&longs;trumenta in &longs;uis <lb/>motionibus ad circuli naturam referri. </s> | <s id="N11B26">Ex quibus infertur &longs;iue im­<lb/>mediate, &longs;iue mediante, alia quadam ab&longs;tracta ratione quam <lb/>ip&longs;a participent, mechanica penè omnia in&longs;trumenta in &longs;uis <lb/>motionibus ad circuli naturam referri. </s> |
| <s id="N11B2F">Quod vt clarius te­<lb/>neatur, pauca &longs;altem de &longs;ingulis ip&longs;is in&longs;trumentis hic adij­<lb/>cere operepretium putauimus, ea &longs;cilicet tantummo­<lb/>do, quæ ad in&longs;titutam textus dilucidationem no­<lb/>uerimus pertinere, Cum exacta huiu&longs;modi <lb/>in&longs;trumentum tractatio habeatur apud <lb/>Heronem, Pappum, & alios ve­<lb/>teres, noui&longs;simè verò & <lb/>accurati&longs;simè apud <lb/>Guidum Vbal­<lb/>dum <lb/><gap/> Marchionibus Montis, qui &longs;i­<lb/>gillatim de illis præcla <lb/>rum librum in­<lb/>&longs;tituit. </s> | <s id="N11B2F">Quod vt clarius te­<lb/>neatur, pauca &longs;altem de &longs;ingulis ip&longs;is in&longs;trumentis hic adij­<lb/>cere opere pretium putauimus, ea &longs;cilicet tantum mo­<lb/>do, quæ ad in&longs;titutam textus dilucidationem no­<lb/>uerimus pertinere, Cum exacta huiu&longs;modi <lb/>in&longs;trumentum tractatio habeatur apud <lb/>Heronem, Pappum, & alios ve­<lb/>teres, noui&longs;simè verò & <lb/>accurati&longs;simè apud <lb/>Guidum Vbal-<lb/>dum <lb/><gap/> Marchionibus Montis, qui &longs;i­<lb/>gillatim de illis præcla<lb/>rum librum in­<lb/>&longs;tituit. </s> |
| </p> | </p> |
| <pb pagenum="55" xlink:href="005/01/063.jpg"/> | <pb pagenum="55" xlink:href="005/01/063.jpg"/> |
| <p id="N11B53" type="head"> | <p id="N11B53" type="head"> |
| <s id="N11B55">DE LIBRA.</s> | <s id="N11B55">DE LIBRA.</s> |
| </p> | </p> |
| <p id="N11B58" type="main"> | <p id="N11B58" type="main"> |
| <s id="N11B5A">Libra, quæ inter mechanica in&longs;trumenta iure <lb/>primum &longs;ibi vendicat locum, co quod imme­<lb/>diatius, ac magis participet <expan abbr="naturã">naturam</expan> circuli in <lb/>&longs;uis motionibus, e&longs;t <expan abbr="iugũ">iugum</expan> <expan abbr="quoddã">quoddam</expan> ex medio <lb/>liberè &longs;u&longs;pen&longs;um, <expan abbr="axeq.">axeque</expan> <expan abbr="&longs;uffultũ">&longs;uffultum</expan>, ac plano ho­<lb/>rizontis <expan abbr="parallelũ">parallelum</expan>, ex cuius <expan abbr="vtraq;">vtraque</expan> extremitate gemina lanx <lb/>pendet, <expan abbr="cuiusq.">cuiusque</expan> conuer&longs;ione circa ip&longs;um axem, dum altera <lb/>eleuatur, altera deprimitur, pódus vel exce&longs;&longs;us <expan abbr="põderis">ponderis</expan> cu <lb/>iu&longs;libet, deprehenditur, ac men&longs;uratur. </s> | <s id="N11B5A">Libra, quæ inter mechanica in&longs;trumenta iure <lb/>primum &longs;ibi vendicat locum, eo quod imme­<lb/>diatius, ac magis participet <expan abbr="naturã">naturam</expan> circuli in <lb/>&longs;uis motionibus, e&longs;t <expan abbr="iugũ">iugum</expan> <expan abbr="quoddã">quoddam</expan> ex medio <lb/>liberè &longs;u&longs;pen&longs;um, <expan abbr="axeq.">axeque</expan> <expan abbr="&longs;uffultũ">&longs;uffultum</expan>, ac plano ho­<lb/>rizontis <expan abbr="parallelũ">parallelum</expan>, ex cuius <expan abbr="vtraq;">vtraque</expan> extremitate gemina lanx <lb/>pendet, <expan abbr="cuiusq.">cuiusque</expan> conuer&longs;ione circa ip&longs;um axem, dum altera <lb/>eleuatur, altera deprimitur, póndus vel exce&longs;&longs;us <expan abbr="põderis">ponderis</expan> cu<lb/>iu&longs;libet, deprehenditur, ac men&longs;uratur. </s> |
| <s id="N11B91">Qua in de&longs;criptione <lb/>&longs;upponitur <expan abbr="iugũ">iugum</expan> ex medio, trutina, &longs;eu axe &longs;u&longs;pen&longs;um, con&longs;ti­<lb/>tui, ac manere parallelum plano horizontis propter <expan abbr="æqui-ponderantiã">æqui­<lb/>ponderantiam</expan> vtriu&longs;que medietatis: <expan abbr="motumq.">motumque</expan> circularem, &longs;eu <lb/><expan abbr="conuer&longs;ion&etilde;">conuer&longs;ionem</expan> circa fulcimentum tanquam circa <expan abbr="centrũ">centrum</expan> im­<lb/>motum, nonni&longs;i ratione <expan abbr="inæqualiũ">inæqualium</expan> <expan abbr="ponderũ">ponderum</expan> in gemina lance <lb/>vtrinque pendentium illi competere: vnde &longs;i pondera &longs;int <lb/>æqualia, libra &longs;emper maneat, & in æquilibrio con&longs;tituatur, <lb/>&longs;eu æquidi&longs;tans à plano horizontis. </s> | <s id="N11B91">Qua in de&longs;criptione <lb/>&longs;upponitur <expan abbr="iugũ">iugum</expan> ex medio, trutina, &longs;eu axe &longs;u&longs;pen&longs;um, con&longs;ti­<lb/>tui, ac manere parallelum plano horizontis propter <expan abbr="æqui-ponderantiã">æqui­<lb/>ponderantiam</expan> vtriu&longs;que medietatis: <expan abbr="motumq.">motumque</expan> circularem, &longs;eu <lb/><expan abbr="conuer&longs;ion&etilde;">conuer&longs;ionem</expan> circa fulcimentum tanquam circa <expan abbr="centrũ">centrum</expan> im­<lb/>motum, nonni&longs;i ratione <expan abbr="inæqualiũ">inæqualium</expan> <expan abbr="ponderũ">ponderum</expan> in gemina lance <lb/>vtrinque pendentium illi competere: vnde &longs;i pondera &longs;int <lb/>æqualia, libra &longs;emper maneat, & in æquilibrio con&longs;tituatur, <lb/>&longs;eu æquidi&longs;tans à plano horizontis. </s> |
| <s id="N11BBF">Deinde ita &longs;upponitur, <lb/>pondera in lancibus impo&longs;ita, ex vtraque iugi extremitate <lb/><expan abbr="p&etilde;dere">pendere</expan>, vt hoc non &longs;it <expan abbr="nece&longs;&longs;ariũ">nece&longs;&longs;arium</expan>, <expan abbr="neq;">neque</expan> e&longs;&longs;entialiter pertineat <lb/>ad <expan abbr="con&longs;titution&etilde;">con&longs;titutionem</expan> libræ, &longs;ed potius ad <expan abbr="commoditat&etilde;">commoditatem</expan> ponde­<lb/>randi, cum &longs;atis intelligatur libra e&longs;&longs;entialiter con&longs;tituta <lb/>etiam ab&longs;que lancibus, ponderibus in ip&longs;is iugi extremita­<lb/>tibus, adiacentibus, vt cernere e&longs;t in &longs;equentibus figuris. </s> | <s id="N11BBF">Deinde ita &longs;upponitur, <lb/>pondera in lancibus impo&longs;ita, ex vtraque iugi extremitate <lb/><expan abbr="p&etilde;dere">pendere</expan>, vt hoc non &longs;it <expan abbr="nece&longs;&longs;ariũ">nece&longs;&longs;arium</expan>, <expan abbr="neq;">neque</expan> e&longs;&longs;entialiter pertineat <lb/>ad <expan abbr="con&longs;titution&etilde;">con&longs;titutionem</expan> libræ, &longs;ed potius ad <expan abbr="commoditat&etilde;">commoditatem</expan> ponde­<lb/>randi, cum &longs;atis intelligatur libra e&longs;&longs;entialiter con&longs;tituta <lb/>etiam ab&longs;que lancibus, ponderibus in ip&longs;is iugi extremita­<lb/>tibus, adiacentibus, vt cernere e&longs;t in &longs;equentibus figuris. </s> |
| </p> | </p> |
| <p id="N11BE1" type="main"> | <p id="N11BE1" type="main"> |
| <s id="N11BE3">Quo autem pacto libra in &longs;ui motione participet natu­<lb/>ram circuli per &longs;e con&longs;tat con&longs;ideranti, iugum, diametri vi­<lb/>cem gerere, axem verò &longs;eu trutinam, aut <expan abbr="fulcimentũ">fulcimentum</expan> quod­<lb/>libet, centri locum tenere, circa quod immotum, ip&longs;a dia­<lb/>meter vertitur dum circulum de&longs;cribit; &longs;iquidem immoto <lb/>axe, &longs;eu fulcimento ip&longs;ius libræ, iugum, alterius extremita­<lb/>tis depre&longs;sione ob exuperantiam <expan abbr="põderis">ponderis</expan>, alterius verò ele­<lb/>uatione, circumagitur, non &longs;ecus ac diameter circulum <lb/>con&longs;iciendo. </s> | <s id="N11BE3">Quo autem pacto libra in &longs;ui motione participet natu­<lb/>ram circuli per &longs;e con&longs;tat con&longs;ideranti, iugum, diametri vi­<lb/>cem gerere, axem verò &longs;eu trutinam, aut <expan abbr="fulcimentũ">fulcimentum</expan> quod­<lb/>libet, centri locum tenere, circa quod immotum, ip&longs;a dia­<lb/>meter vertitur dum circulum de&longs;cribit; &longs;iquidem immoto <lb/>axe, &longs;eu fulcimento ip&longs;ius libræ, iugum, alterius extremita­<lb/>tis depre&longs;sione ob exuperantiam <expan abbr="põderis">ponderis</expan>, alterius verò ele­<lb/>uatione, circumagitur, non &longs;ecus ac diameter circulum <lb/>conficiendo. </s> |
| <s id="N11BFE">Quod &longs;i partes iugi vtrinque à centro produ­<lb/>ctæ, non &longs;int inter &longs;e <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon­<lb/>derantes; tunc quidem in ip&longs;is iugi conuer&longs;ione, ac circum­<pb pagenum="56" xlink:href="005/01/064.jpg"/>latione duo circuli de&longs;cribentur alter altero malor, <expan abbr="tanquã">tanquam</expan> <lb/>à duplici &longs;emidiametro circumlato, vt hic erit in&longs;picere. </s> | <s id="N11BFE">Quod &longs;i partes iugi vtrinque à centro produ­<lb/>ctæ, non &longs;int inter &longs;e <expan abbr="lõgitudine">longitudine</expan> æquales, quamuis æquipon­<lb/>derantes; tunc quidem in ip&longs;is iugi conuer&longs;ione, ac circum­<pb pagenum="56" xlink:href="005/01/064.jpg"/>latione duo circuli de&longs;cribentur alter altero maior, <expan abbr="tanquã">tanquam</expan> <lb/>à duplici &longs;emidiametro circumlato, vt hic erit in&longs;picere. </s> |
| </p> | </p> |
| <figure id="id.005.01.064.1.jpg" xlink:href="005/01/064/1.jpg"/> | <figure id="id.005.01.064.1.jpg" xlink:href="005/01/064/1.jpg"/> |
| <p id="N11C19" type="head"> | <p id="N11C19" type="head"> |
| <s id="N11C1B">DE VECTE.</s> | <s id="N11C1B">DE VECTE.</s> |
| </p> | </p> |
| <p id="N11C1E" type="main"> | <p id="N11C1E" type="main"> |
| <s id="N11C20">Vectis &longs;implex <expan abbr="quoddã">quoddam</expan> <expan abbr="in&longs;trumentũ">in&longs;trumentum</expan> e&longs;t ligneum, <lb/>vel <expan abbr="ferreũ">ferreum</expan> &longs;atis oblongum veluti palus, aut fu&longs;ti<gap/><lb/>grandior, ad promouenda pondera; cuius vt <expan abbr="plu-rimũ">plu­<lb/>rimum</expan> altera extremitas <expan abbr="põderi">ponderi</expan> eleuando &longs;ubijci­<lb/>tur, altera verò manu, &longs;eu <expan abbr="pot&etilde;tia">potentia</expan> præmitur, &longs;ub­<lb/>&longs;trato inter <expan abbr="vtramq;">vtramque</expan> aliquo fulcimento, cui inni­<lb/>tatur, quòd græcè hypomochilion appellatur, quodq <expan abbr="quãto">quanto</expan> pro­<lb/>pinquius ponderi locatur, tanto facilius ip&longs;o vecte leuatur. </s> | <s id="N11C20">Vectis &longs;implex <expan abbr="quoddã">quoddam</expan> <expan abbr="in&longs;trumentũ">in&longs;trumentum</expan> e&longs;t ligneum, <lb/>vel <expan abbr="ferreũ">ferreum</expan> &longs;atis oblongum veluti palus, aut fu&longs;ti<gap/><lb/>grandior, ad promouenda pondera; cuius vt <expan abbr="plu-rimũ">plu­<lb/>rimum</expan> altera extremitas <expan abbr="põderi">ponderi</expan> eleuando &longs;ubijci­<lb/>tur, altera verò manu, &longs;eu <expan abbr="pot&etilde;tia">potentia</expan> præmitur, &longs;ub­<lb/>&longs;trato inter <expan abbr="vtramq;">vtramque</expan> aliquo fulcimento, cui inni­<lb/>tatur, quòd græcè hypomochilion appellatur, <expan abbr="quodq">quoque</expan> <expan abbr="quãto">quanto</expan> pro­<lb/>pinquius ponderi locatur, tanto facilius ip&longs;o vecte leuatur. </s> |
| <s id="N11C52">Ali­<lb/>quando verò altera extremitas <expan abbr="nõ">non</expan> ponderi, &longs;ed fulcimento &longs;ubij­<lb/>citur, vel ei quoquomodo innititur <expan abbr="tanquã">tanquam</expan> manenti valido, pon-<pb pagenum="57" xlink:href="005/01/065.jpg"/><expan abbr="dusq.">dusque</expan> eleuatur, aut deprimitur per vectis <expan abbr="part&etilde;">partem</expan> mediam, quæ e&longs;t <lb/>inter <expan abbr="vtramq.">vtramque</expan> <expan abbr="extremitat&etilde;">extremitatem</expan> iuxta <expan abbr="eleuation&etilde;">eleuationem</expan>, aut <expan abbr="depre&longs;&longs;ion&etilde;">depre&longs;&longs;ionem</expan> al­<lb/>terius extremitatis vbi applicatur <expan abbr="pot&etilde;tia">potentia</expan>: vel certè <expan abbr="põdus">pondus</expan> ele­<lb/>uatur per <expan abbr="alterã">alteram</expan> extremitatem, &longs;i in illa locetur, <expan abbr="manusq.">manusque</expan> aut po­<lb/>tentia in medio adhibeatur. </s> | <s id="N11C52">Ali­<lb/>quando verò altera extremitas <expan abbr="nõ">non</expan> ponderi, &longs;ed fulcimento &longs;ubij­<lb/>citur, vel ei quoquomodo innititur <expan abbr="tanquã">tanquam</expan> manenti valido, pon-<pb pagenum="57" xlink:href="005/01/065.jpg"/><expan abbr="dusq.">dusque</expan> eleuatur, aut deprimitur per vectis <expan abbr="part&etilde;">partem</expan> mediam, quæ e&longs;t <lb/>inter <expan abbr="vtramq.">vtramque</expan> <expan abbr="extremitat&etilde;">extremitatem</expan> iuxta <expan abbr="eleuation&etilde;">eleuationem</expan>, aut <expan abbr="depre&longs;&longs;ion&etilde;">depre&longs;&longs;ionem</expan> al­<lb/>terius extremitatis vbi applicatur <expan abbr="pot&etilde;tia">potentia</expan>: vel certè <expan abbr="põdus">pondus</expan> ele­<lb/>uatur per <expan abbr="alterã">alteram</expan> extremitatem, &longs;i in illa locetur, <expan abbr="manusq.">manusque</expan> aut po­<lb/>tentia in medio adhibeatur. </s> |
| <s id="N11C95">Vnde tres nonnulli &longs;pecies <expan abbr="vectiũ">vectium</expan> di­<lb/>&longs;tinguunt, quas iuxta prædicta figuris <expan abbr="etiã">etiam</expan> hic &longs;tuduimus expri­<lb/>mere; Illud interim admonendo, eas omnes facilè in &longs;uis motio­<lb/>nibus ad <expan abbr="circulũ">circulum</expan> referri, cum ip&longs;æ nonni&longs;i <expan abbr="diametrũ">diametrum</expan>, vel <expan abbr="&longs;emidia-metrũ">&longs;emidia­<lb/>metrum</expan> <expan abbr="circulũ">circulum</expan> circa <expan abbr="immotũ">immotum</expan> <expan abbr="fulcimentũ">fulcimentum</expan> <expan abbr="de&longs;cribent&etilde;">de&longs;cribentem</expan> referant, vt <lb/>per &longs;e patet, ac prima quæ &longs;anè vtilior & frequentius in v&longs;u e&longs;t, <lb/>ad <expan abbr="librã">libram</expan> à <expan abbr="fulcim&etilde;to">fulcimento</expan> inæquales vtrinque partes <expan abbr="habent&etilde;">habentem</expan> eniden­<lb/>ti&longs;simè reducatur, vt amplius deinceps <expan abbr="cõ&longs;tabit">con&longs;tabit</expan>. </s> | <s id="N11C95">Vnde tres nonnulli &longs;pecies <expan abbr="vectiũ">vectium</expan> di­<lb/>&longs;tinguunt, quas iuxta prædicta figuris <expan abbr="etiã">etiam</expan> hic &longs;tuduimus expri­<lb/>mere; Illud interim admonendo, eas omnes facilè in &longs;uis motio­<lb/>nibus ad <expan abbr="circulũ">circulum</expan> referri, cum ip&longs;æ non ni&longs;i <expan abbr="diametrũ">diametrum</expan>, vel <expan abbr="&longs;emidia-metrũ">&longs;emidia­<lb/>metrum</expan> <expan abbr="circulũ">circulum</expan> circa <expan abbr="immotũ">immotum</expan> <expan abbr="fulcimentũ">fulcimentum</expan> <expan abbr="de&longs;cribent&etilde;">de&longs;cribentem</expan> referant, vt <lb/>per &longs;e patet, ac prima quæ &longs;anè vtilior & frequentius in v&longs;u e&longs;t, <lb/>ad <expan abbr="librã">libram</expan> à <expan abbr="fulcim&etilde;to">fulcimento</expan> inæquales vtrinque partes <expan abbr="habent&etilde;">habentem</expan> euiden­<lb/>ti&longs;simè reducatur, vt amplius deinceps <expan abbr="cõ&longs;tabit">con&longs;tabit</expan>. </s> |
| <s id="N11CDA"><expan abbr="Nã">Nam</expan> hoc quod e&longs;t <lb/>fulciri per <expan abbr="&longs;u&longs;pen&longs;ion&etilde;">&longs;u&longs;pen&longs;ionem</expan> beneficio trutinæ, vel per <expan abbr="&longs;ubiection&etilde;">&longs;ubiectionem</expan> al­<lb/>terius corporis, quod non minus axis, ac centri <expan abbr="vic&etilde;">vicem</expan> &longs;ubeat, e&longs;t <lb/>differentia valde accidentalis. </s> | <s id="N11CDA"><expan abbr="Nã">Nam</expan> hoc quod e&longs;t <lb/>fulciri per <expan abbr="&longs;u&longs;pen&longs;ion&etilde;">&longs;u&longs;pen&longs;ionem</expan> beneficio trutinæ, vel per <expan abbr="&longs;ubiection&etilde;">&longs;ubiectionem</expan> al­<lb/>terius corporis, quod non minus axis, ac centri <expan abbr="vic&etilde;">vicem</expan> &longs;ubeat, e&longs;t <lb/>differentia valde accidentalis. </s> |
| </p> | </p> |
| <figure id="id.005.01.065.1.jpg" xlink:href="005/01/065/1.jpg"/> | <figure id="id.005.01.065.1.jpg" xlink:href="005/01/065/1.jpg"/> |
| |
| <figure id="id.005.01.066.1.jpg" xlink:href="005/01/066/1.jpg"/> | <figure id="id.005.01.066.1.jpg" xlink:href="005/01/066/1.jpg"/> |
| <p id="N11D2E" type="main"> | <p id="N11D2E" type="main"> |
| <s id="N11D30">Reducitur autem Trochlea ad Vectem, & con&longs;equen­<lb/>ter ad libram, quia vnu&longs;qui&longs;que orbiculus illius per diame­<lb/>trum nititur proprio axiculo tanquam fulcimento, quod in­<lb/>ter onus leuandum, aut &longs;u&longs;tinendum, & potentiam eleuan­<lb/>tem locatur, ita vt ad depre&longs;sionem vnius extremitatis dia-<pb pagenum="59" xlink:href="005/01/067.jpg"/>metri, vbi mouentis potentia applicatur, altera extremitas, <lb/>quæ onus &longs;u&longs;tinet, eleuetur; licet hoc nonimmediatè fiat; <lb/>&longs;ed mediante fune ductario, vt hic ad oculos &longs;pectandum <lb/>proponetur ac infra fu&longs;iùs explicabitur quæ&longs;t. </s> | <s id="N11D30">Reducitur autem Trochlea ad Vectem, & con&longs;equen­<lb/>ter ad libram, quia vnu&longs;qui&longs;que orbiculus illius per diame­<lb/>trum nititur proprio axiculo tanquam fulcimento, quod in­<lb/>ter onus leuandum, aut &longs;u&longs;tinendum, & potentiam eleuan­<lb/>tem locatur, ita vt ad depre&longs;sionem vnius extremitatis dia-<pb pagenum="59" xlink:href="005/01/067.jpg"/>metri, vbi mouentis potentia applicatur, altera extremitas, <lb/>quæ onus &longs;u&longs;tinet, eleuetur; licet hoc nonimmediatè fiat; <lb/>&longs;ed mediante fune ductario, vt hic ad oculos &longs;pectandum <lb/>proponetur ac infra fu&longs;iùs explicabitur quæ&longs;t. </s> |
| <s id="N11D46">18. Sit enim <lb/>trochleç orbiculus ABC, dia­<lb/><figure id="id.005.01.067.1.jpg" xlink:href="005/01/067/1.jpg"/><lb/>meter verò orbiculi linea ho­<lb/>rizonti parallela AB, & axicu­<lb/>lus C, tanquam centrum lo­<lb/>catum in medio: Deinde per <lb/>funem ductarium ab extremo <lb/>A propendeat onus D, & ab <lb/>extremo B idem funis demit­<lb/>tatur, cui applicara &longs;it poten­<lb/>tia motiua in E. <!-- KEEP S--></s> | <s id="N11D46">18. Sit enim <lb/>trochleae orbiculus ABC, dia­<lb/><figure id="id.005.01.067.1.jpg" xlink:href="005/01/067/1.jpg"/><lb/>meter verò orbiculi linea ho­<lb/>rizonti parallela AB, & axicu­<lb/>lus C, tanquam centrum lo­<lb/>catum in medio: Deinde per <lb/>funem ductarium ab extremo <lb/>A propendeat onus D, & ab <lb/>extremo B idem funis demit­<lb/>tatur, cui applicata &longs;it poten­<lb/>tia motiua in E. <!-- KEEP S--></s> |
| <s id="N11D64">Dicimus er­<lb/>go totum orbiculum incum­<lb/>bere, ac niti axiculo C tan­<lb/>quam fulcimento per diame­<lb/>trum eius AB in cuius medio <lb/>axiculus e&longs;t locatus, & in cuius <lb/>extremis AB, vtrinque &longs;it tota <lb/>compre&longs;sio, nempe oneris ac potentiæ; <expan abbr="proindeq.">proindeque</expan> ip&longs;am <lb/>diametrum AB, vectis vicem in motione gerere, qua­<lb/>tenus nixa in præfato fulcimento C, ad depre&longs;­<lb/>&longs;ionem extremimitatis B per vim trahen­<lb/>tem in E, extremitas A nece&longs;&longs;ario <lb/>eleuatur, ac &longs;imul cum illa <lb/>pondus D pendens ex <lb/>ip&longs;a, vt per &longs;e <lb/>patet. </s> | <s id="N11D64">Dicimus er­<lb/>go totum orbiculum incum­<lb/>bere, ac niti axiculo C tan­<lb/>quam fulcimento per diame­<lb/>trum eius AB in cuius medio <lb/>axiculus e&longs;t locatus, & in cuius <lb/>extremis AB, vtrinque &longs;it tota <lb/>compre&longs;sio, nempe oneris ac potentiæ; <expan abbr="proindeq.">proindeque</expan> ip&longs;am <lb/>diametrum AB, vectis vicem in motione gerere, qua­<lb/>tenus nixa in præfato fulcimento C, ad depre&longs;­<lb/>&longs;ionem extreminitatis B per vim trahen­<lb/>tem in E, extremitas A nece&longs;&longs;ario <lb/>eleuatur, ac &longs;imul cum illa <lb/>pondus D pendens ex <lb/>ip&longs;a, vt per &longs;e <lb/>patet. </s> |
| </p> | </p> |
| <pb pagenum="60" xlink:href="005/01/068.jpg"/> | <pb pagenum="60" xlink:href="005/01/068.jpg"/> |
| <p id="N11D8D" type="head"> | <p id="N11D8D" type="head"> |
| <s id="N11D8F">DE AXE IN PERITROCHIO.</s> | <s id="N11D8F">DE AXE IN PERITROCHIO.</s> |
| </p> | </p> |
| <p id="N11D92" type="main"> | <p id="N11D92" type="main"> |
| <s id="N11D94">Axis in Peritrochio e&longs;t oblongus quidam <lb/>cylindrus Peritrochio firmiter in&longs;ixus, ac pa­<lb/>rallelus horizontis plano locatus, cuius ex­<lb/>trema in rotundis foraminibus immoti peg­<lb/>matis expeditè vertuntur. </s> | <s id="N11D94">Axis in Peritrochio e&longs;t oblongus quidam <lb/>cylindrus Peritrochio firmiter infixus, ac pa­<lb/>rallelus horizontis plano locatus, cuius ex­<lb/>trema in rotundis foraminibus immoti peg­<lb/>matis expeditè vertuntur. </s> |
| <s id="N11D9F">Peritrochium ve­<lb/>rò, e&longs;t machina rotunda, ad rotæ &longs;eu tympani &longs;imilitudi­<lb/>nem efformata, in cuius conuexa peripheria &longs;tipites qui & <lb/>Scytalæ vocantur, tanquam radij infinguntur; quibus admo­<lb/>ta manu tota machina &longs;imul cum axe ver&longs;atur, ac funibus <lb/>circa axem conuolutis, trahuntur pondera illis alligata; vt <lb/>hic licebit in&longs;picere. </s> | <s id="N11D9F">Peritrochium ve­<lb/>rò, e&longs;t machina rotunda, ad rotæ &longs;eu tympani &longs;imilitudi­<lb/>nem efformata, in cuius conuexa peripheria &longs;tipites qui & <lb/>Scytalæ vocantur, tanquam radij infinguntur; quibus admo­<lb/>ta manu tota machina &longs;imul cum axe ver&longs;atur, ac funibus <lb/>circa axem conuolutis, trahuntur pondera illis alligata; vt <lb/>hic licebit in&longs;picere. </s> |
| </p> | </p> |
| <figure id="id.005.01.068.1.jpg" xlink:href="005/01/068/1.jpg"/> | <figure id="id.005.01.068.1.jpg" xlink:href="005/01/068/1.jpg"/> |
| <p id="N11DB3" type="main"> | <p id="N11DB3" type="main"> |
| <s id="N11DB5">Reducitur <expan abbr="aut&etilde;">autem</expan> <lb/>tota huiu&longs;modi ma <lb/>china, &longs;eu in&longs;tru­<lb/>mentum ad <expan abbr="vect&etilde;">vectem</expan>; <lb/>Nam &longs;i con&longs;idere­<lb/>mus <expan abbr="con&longs;titutũ">con&longs;titutum</expan> ex <lb/>diametro axis, ac <lb/>&longs;emidiametro Pe­<lb/>ritrochij <expan abbr="coincid&etilde;-te">coinciden­<lb/>te</expan> cum illa non ali­<lb/>ter in circumuolu­<lb/>tione &longs;e habere <expan abbr="cõ-perimus">con­<lb/>perimus</expan>, ac <expan abbr="Vect&etilde;">Vectem</expan>, <lb/>qui circa &longs;uum ful­<lb/>cimentum vertitur, <lb/>tanquam circa pro­<lb/>prium centrum. <lb/></s> | <s id="N11DB5">Reducitur <expan abbr="aut&etilde;">autem</expan> <lb/>tota huiu&longs;modi ma <lb/>china, &longs;eu in&longs;tru­<lb/>mentum ad <expan abbr="vect&etilde;">vectem</expan>; <lb/>Nam &longs;i con&longs;idere­<lb/>mus <expan abbr="con&longs;titutũ">con&longs;titutum</expan> ex <lb/>diametro axis, ac <lb/>&longs;emidiametro Pe­<lb/>ritrochij <expan abbr="coincid&etilde;-te">coinciden­<lb/>te</expan> cum illa non ali­<lb/>ter in circumuolu­<lb/>tione &longs;e habere <expan abbr="cõ-perimus">com­<lb/>perimus</expan>, ac <expan abbr="Vect&etilde;">Vectem</expan>, <lb/>qui circa &longs;uum ful­<lb/>cimentum vertitur, <lb/>tanquam circa pro­<lb/>prium centrum. <lb/></s> |
| <s id="N11DF1">E&longs;to enim Axis &longs;imul, ac Peritrochij immobile centrum <lb/>A, circa quod vtriu&longs;que circumferentia de&longs;cripta &longs;it, nem­<lb/>pe tàm Axis, quàm Tympani ip&longs;ius Peritrochij cum &longs;cyta­<lb/>lis; Diameter verò Axis &longs;it linea BC; ac &longs;emidiameter Pe­<lb/>titrochij AD, con&longs;tituentes integram lineam BD. <!-- KEEP S--></s> | <s id="N11DF1">E&longs;to enim Axis &longs;imul, ac Peritrochij immobile centrum <lb/>A, circa quod vtriu&longs;que circumferentia de&longs;cripta &longs;it, nem­<lb/>pe tàm Axis, quàm Tympani ip&longs;ius Peritrochij cum &longs;cyta­<lb/>lis; Diameter verò Axis &longs;it linea BC; ac &longs;emidiameter Pe­<lb/>titrochij AD, con&longs;tituentes integram lineam BD. <!-- KEEP S--></s> |
| <s id="N11DFD">Tum <pb pagenum="61" xlink:href="005/01/069.jpg"/>ex Axe per funem BE propendeat onus F; <expan abbr="virtusq.">virtusque</expan> mo­<lb/>uentis applicetur in &longs;cytala vbi e&longs;t ip&longs;um D. <!-- KEEP S--></s> | <s id="N11DFD">Tum <pb pagenum="61" xlink:href="005/01/069.jpg"/>ex Axe per funem BE propendeat onus F; <expan abbr="virtusq.">virtusque</expan> mo­<lb/>uentis applicetur in &longs;cytala vbi e&longs;t ip&longs;um D. <!-- KEEP S--></s> |
| <s id="N11E0C">Ad motum <lb/>igitur deor&longs;um ip&longs;ius D, linea BD, non aliter &longs;e pote&longs;t <lb/>habere, ac vectis firmiter innixa immobili centro A, tan­<lb/>quam fulcimento, ac dum pars AD deprimitur, altera. <lb/></s> | <s id="N11E0C">Ad motum <lb/>igitur deor&longs;um ip&longs;ius D, linea BD, non aliter &longs;e pote&longs;t <lb/>habere, ac vectis firmiter innixa immobili centro A, tan­<lb/>quam fulcimento, ac dum pars AD deprimitur, altera. <lb/></s> |
| |
| <s id="N11E22">DE CVNEO.</s> | <s id="N11E22">DE CVNEO.</s> |
| </p> | </p> |
| <p id="N11E25" type="main"> | <p id="N11E25" type="main"> |
| <s id="N11E27">Cvnevs e&longs;t &longs;implex quoddam in&longs;trumen­<lb/>tum ad findenda, &longs;eu &longs;cindéda corpora apti&longs;­<lb/>&longs;imum accedente percu&longs;&longs;ione. </s> | <s id="N11E27">Cvnevs e&longs;t &longs;implex quoddam in&longs;trumen­<lb/>tum ad findenda, &longs;eu &longs;cindénda corpora apti&longs;­<lb/>&longs;imum accedente percu&longs;&longs;ione. </s> |
| <s id="N11E2E">E&longs;t enim &longs;oli­<lb/>dum, quod ex quadrangulari ba&longs;e <expan abbr="con&longs;urg&etilde;s">con&longs;urgens</expan>, <lb/>quatuor &longs;uperficiebus in peracutam aciem <lb/>terminantibus, clauditur. </s> | <s id="N11E2E">E&longs;t enim &longs;oli­<lb/>dum, quod ex quadrangulari ba&longs;e <expan abbr="con&longs;urg&etilde;s">con&longs;urgens</expan>, <lb/>quatuor &longs;uperficiebus in peracutam aciem <lb/>terminantibus, clauditur. </s> |
| <s id="N11E3B">Duabus videlicet &longs;ibi oppo&longs;itis <lb/>quadrangularibus, ac altera parte longioribus; duabus verò <lb/>&longs;imiliter oppo&longs;itis, &longs;ed triangularibus in prædictam acutam, <lb/>& oblongam aciem terminantibus. </s> | <s id="N11E3B">Duabus videlicet &longs;ibi oppo&longs;itis <lb/>quadrangularibus, ac altera parte longioribus; duabus verò <lb/>&longs;imiliter oppo&longs;itis, &longs;ed triangularibus in prædictam acutam, <lb/>& oblongam aciem terminantibus. </s> |
| <s id="N11E44">Quæ &longs;anè acies cum in <lb/>timulam quamlibet <expan abbr="&longs;cind&etilde;dæ">&longs;cindendæ</expan> molis &longs;e in&longs;inuare præualeat, <pb pagenum="62" xlink:href="005/01/070.jpg"/>adueniente valida percu&longs;&longs;ione, vt quæ per malleú &longs;uper ba­<lb/>&longs;im adactum fieri con&longs;ueuit, facilè totum cuneum cogit ad­<lb/>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem &longs;ecedere, quod <lb/>e&longs;t molem<gap/>p&longs;am &longs;cindi, ac diuidi. </s> | <s id="N11E44">Quæ &longs;anè acies cum in <lb/>rimulam quamlibet <expan abbr="&longs;cind&etilde;dæ">&longs;cindendæ</expan> molis &longs;e in&longs;inuare præualeat, <pb pagenum="62" xlink:href="005/01/070.jpg"/>adueniente valida percu&longs;&longs;ione, vt quæ per malleúm &longs;uper ba­<lb/>&longs;im adactum fieri con&longs;ueuit, facilè totum cuneum cogit ad­<lb/>mittere, <expan abbr="proindeq.">proindeque</expan> partes molis ab inuicem &longs;ecedere, quod <lb/>e&longs;t molem ip&longs;am &longs;cindi, ac diuidi. </s> |
| <s id="N11E5E">Cunei ergo figura &longs;ic de­<lb/>lineanda cen&longs;uimus ex quadrata ba&longs;i ABCD, excitando <lb/>&longs;operficiem quadrangularem DBEF, ac aliam triangula­<lb/>rem CDE, quæ &longs;imul cum &longs;uis oppo&longs;itis omnes quatuor <lb/>de&longs;inant, ac terminentur in aciem EF. </s> | <s id="N11E5E">Cunei ergo figura &longs;ic de­<lb/>lineanda cen&longs;uimus ex quadrata ba&longs;i ABCD, excitando <lb/>&longs;uperficiem quadrangularem DBEF, ac aliam triangula­<lb/>rem CDE, quæ &longs;imul cum &longs;uis oppo&longs;itis omnes quatuor <lb/>de&longs;inant, ac terminentur in aciem EF. </s> |
| </p> | </p> |
| <figure id="id.005.01.070.1.jpg" xlink:href="005/01/070/1.jpg"/> | <figure id="id.005.01.070.1.jpg" xlink:href="005/01/070/1.jpg"/> |
| <p id="N11E6E" type="main"> | <p id="N11E6E" type="main"> |
| <s id="N11E70">Refertur auté hoc quoque in&longs;tru­<lb/>mentum ad vecté, eo quod ex duplici <lb/>vecte videatur con&longs;tare, vt infra qu&etail;&longs;t. <lb/></s> | <s id="N11E70">Refertur auté hoc quoque in&longs;tru­<lb/>mentum ad vecté, eo quod ex duplici <lb/>vecte videatur con&longs;tare, vt infra qu&etail;&longs;t. <lb/></s> |
| <s id="N11E78">17. ex Ari&longs;totele magis ex profe&longs;&longs;o <lb/>probabitur. </s> | <s id="N11E78">17. ex Ari&longs;totele magis ex profe&longs;&longs;o <lb/>probabitur. </s> |
| <s id="N11E7D">Etenim &longs;i con&longs;iderentur <lb/>duo eius latera, quæ ex ba&longs;i in aciem <lb/>terminantur, vt CE, & DE non &longs;e­<lb/>cus ac duo vectes &longs;ibi inuicem obuer­<lb/>&longs;i, & cótra conantes reperientur, quo­<lb/>rum <expan abbr="vtiq;">vtique</expan> fulc menta &longs;unt partes &longs;cin­<lb/>dendi corporis vtrinque con&longs;titutæ vt <lb/>GH, quibus intrando cuneus innititur. </s> | <s id="N11E7D">Etenim &longs;i con&longs;iderentur <lb/>duo eius latera, quæ ex ba&longs;i in aciem <lb/>terminantur, vt CE, & DE non &longs;e­<lb/>cus ac duo vectes &longs;ibi inuicem obuer­<lb/>&longs;i, & cóntra conantes reperientur, quo­<lb/>rum <expan abbr="vtiq;">vtique</expan> fulc menta &longs;unt partes &longs;cin­<lb/>dendi corporis vtrinque con&longs;titutæ vt <lb/>GH, quibus intrando cuneus innititur. </s> |
| <s id="N11E92">Onera verò &longs;unt re­<lb/><figure id="id.005.01.070.2.jpg" xlink:href="005/01/070/2.jpg"/><lb/>reliquæ eiu&longs;dem corporis partes <lb/>&longs;ucce&longs;siuè dimouend&etail;, & adinui­<lb/>cem &longs;eparádæ per aciem intran­<lb/>tem vbi E, vt in propo&longs;ita figu <lb/>ra e&longs;t l, & K. <!-- KEEP S--></s> | <s id="N11E92">Onera verò &longs;unt re­<lb/><figure id="id.005.01.070.2.jpg" xlink:href="005/01/070/2.jpg"/><lb/>reliquæ eiu&longs;dem corporis partes <lb/>&longs;ucce&longs;siuè dimouend&etail;, & adinui­<lb/>cem &longs;eparádæ per aciem intran­<lb/>tem vbi E, vt in propo&longs;ita figu <lb/>ra e&longs;t l, & K. <!-- KEEP S--></s> |
| <s id="N11EA6">Nam pars vbi K <lb/>e&longs;t onus re&longs;pectu vectis CE in­<lb/>nixæ in G; & pars vbi I, e&longs;t <lb/>onus re&longs;pectu vectis DE innixæ <lb/>in H. <!-- KEEP S--></s> | <s id="N11EA6">Nam pars vbi K <lb/>e&longs;t onus re&longs;pectu vectis CE in­<lb/>nixæ in G; & pars vbi I, e&longs;t <lb/>onus re&longs;pectu vectis DE innixæ <lb/>in H. <!-- KEEP S--></s> |
| <s id="N11EB2">Et extrema in quibus ap­<lb/>plicatur potentia &longs;unt initia ip&longs;o­<lb/>rum laterum ex parte ba&longs;is vbi <lb/>fit tota percu&longs;&longs;io, nempe vbi C <lb/>& D, quæ omnia aperti&longs;&longs;imè <lb/>citata quæ&longs;tione amplius con&longs;ta­<lb/>bunt. </s> | <s id="N11EB2">Et extrema in quibus ap­<lb/>plicatur potentia &longs;unt initia ip&longs;o­<lb/>rum laterum ex parte ba&longs;is vbi <lb/>fit tota percu&longs;&longs;io, nempe vbi C <lb/>& D, quæ omnia aperti&longs;&longs;imè <lb/>citata quæ&longs;tione amplius con&longs;ta­<lb/>bunt. </s> |
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