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version 1.21, 2006/05/03 18:18:27 |
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| <s><lb/>Hinc domus tua floret docti&longs;simorum familiaritatibus; <lb/>hinc nulli ad tuam con&longs;uetudinem præcluditur aditus; <lb/>hinc plurimorum &longs;tudia commouentur; hinc illa &longs;apien­<lb/>tum æmulatio & admiratio: hinc omnium omnino or­<lb/>dinum ad te concur&longs;us; tanquam ad &longs;apienti&longs;simum hu­<lb/>mani <expan abbr="diuiniq;">diuinique</expan> iuris patronum, & interpretem. </s> | <s><lb/>Hinc domus tua floret docti&longs;simorum familiaritatibus; <lb/>hinc nulli ad tuam con&longs;uetudinem præcluditur aditus; <lb/>hinc plurimorum &longs;tudia commouentur; hinc illa &longs;apien­<lb/>tum æmulatio & admiratio: hinc omnium omnino or­<lb/>dinum ad te concur&longs;us; tanquam ad &longs;apienti&longs;simum hu­<lb/>mani <expan abbr="diuiniq;">diuinique</expan> iuris patronum, & interpretem. </s> |
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| <s>Quid ego <lb/>igitur quem tibi &longs;excentis eximiæ beneuolentiæ argu­<lb/>mentis obligatum volu&longs;ti, perexigiuum hunc ingenij <lb/>mei partum expo&longs;iturus, vnum te nominis & exi&longs;tima­<lb/>tionis meæ patronum non &longs;u&longs;cipiam equidem in am­<lb/>pli&longs;simi Theatri lucem &longs;apienti&longs;simorum <32> hominum <lb/>con&longs;pectum, quibus abundat hæc no&longs;tra ætas inferre me <lb/>non magnopere cogitabam. <gap/>Tu hortatus es dubitan­<lb/>tem impuli&longs;ti vel reluctantem<gap/> tuere igitur ob&longs;equen­<lb/>tem. </s> | <s>Quid ego <lb/>igitur quem tibi &longs;excentis eximiæ beneuolentiæ argu­<lb/>mentis obligatum volu&longs;ti, perexigiuum hunc ingenij <lb/>mei partum expo&longs;iturus, vnum te nominis & exi&longs;tima­<lb/>tionis meæ patronum non &longs;u&longs;cipiam equidem in am­<lb/>pli&longs;simi Theatri lucem &longs;apienti&longs;simorum <32> hominum <lb/>con&longs;pectum, quibus abundat hæc no&longs;tra ætas inferre me <lb/>non magnopere cogitabam: Tu hortatus es dubitan­<lb/>tem impuli&longs;ti vel reluctantem: tuere igitur ob&longs;equen­<lb/>tem. </s> |
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| <s>iam nunc mihi videor in exigua vel nulla &longs;pe lau­<lb/>dis ex ingenio meo; &longs;empiternam nominis immortali­<lb/>tatem ex tuo patrocinio con&longs;ecutus. </s> | <s>iam nunc mihi videor in exigua vel nulla &longs;pe lau­<lb/>dis ex ingenio meo; &longs;empiternam nominis immortali­<lb/>tatem ex tuo patrocinio con&longs;ecutus. </s> |
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| <s><emph type="italics"/>Accipiantur duo corpora D, plumbeum, E, &longs;tanneum grauitate <lb/>quacunque, &longs;it vcrbi gratia plumbi D, grauitas<emph.end type="italics"/> 23<emph type="italics"/>, &longs;tanni vero E, <lb/>grauitas<emph.end type="italics"/> 37<emph type="italics"/>, deinde duarum quantitatum aquæ, quarum vna &longs;it ma­<lb/>gnitudine æqualis plumbo D, altera stanno E, inueniantur graui­<lb/>tates, quæ &longs;int, primæ videlicet quantitatis<emph.end type="italics"/> 2<emph type="italics"/>, &longs;ecundæ vero<emph.end type="italics"/> 5<emph type="italics"/>, & fiat,<emph.end type="italics"/><pb xlink:href="029/01/026.jpg" pagenum="19"/><emph type="italics"/>ut 23, ad 2, ita 37, ad<emph.end type="italics"/> 3 5/21. <emph type="italics"/>grauitas igitur aquæ, magnitudinem <lb/>habentis æqualem plumbo, cuius grauitas est 37, erit<emph.end type="italics"/> 3 5/21. </s></p><p type="main"> | <s><emph type="italics"/>Accipiantur duo corpora D, plumbeum, E, &longs;tanneum grauitate <lb/>quacunque, &longs;it vcrbi gratia plumbi D, grauitas<emph.end type="italics"/> 23<emph type="italics"/>, &longs;tanni vero E, <lb/>grauitas<emph.end type="italics"/> 37<emph type="italics"/>, deinde duarum quantitatum aquæ, quarum vna &longs;it ma­<lb/>gnitudine æqualis plumbo D, altera stanno E, inueniantur graui­<lb/>tates, quæ &longs;int, primæ videlicet quantitatis<emph.end type="italics"/> 2<emph type="italics"/>, &longs;ecundæ vero<emph.end type="italics"/> 5<emph type="italics"/>, & fiat,<emph.end type="italics"/><pb xlink:href="029/01/026.jpg" pagenum="19"/><emph type="italics"/>ut 23, ad 2, ita 37, ad<emph.end type="italics"/> 3 5/21. <emph type="italics"/>grauitas igitur aquæ, magnitudinem <lb/>habentis æqualem plumbo, cuius grauitas est 37, erit<emph.end type="italics"/> 3 5/21. </s></p><p type="main"> |
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| <s><emph type="italics"/>Et quoniam aquæ, magnitudinem habentis æqualem stanno E, cu­<lb/>ius grauitas est 37, e&longs;t grauitas<emph.end type="italics"/> 5, <emph type="italics"/>erunt grauitates duarum quan­<lb/>titatum aquæ<emph.end type="italics"/> 3 5/21, & 5, <emph type="italics"/>quarum quantitatum prima e&longs;t æqualis <lb/>magnitudine corpori plumbeo, &longs;ecunda stanneo, que &longs;unt æque gra­<lb/>uia, vtriu&longs;que enim grauitas est<emph.end type="italics"/> 37. <emph type="italics"/>Fiat igitur vt<emph.end type="italics"/> 5, <emph type="italics"/>ad<emph.end type="italics"/> 3 5/21, <emph type="italics"/>it a<emph.end type="italics"/><lb/>1150, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 740, <emph type="italics"/>tanta igitur erit grauitas <lb/>&longs;tanni, magnitudinem habentis æqualem propo&longs;ito plumbo A, quanta <lb/><gap/>iam inueniebatur & &longs;upra.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Et quoniam aquæ, magnitudinem habentis æqualem stanno E, cu­<lb/>ius grauitas est 37, e&longs;t grauitas<emph.end type="italics"/> 5, <emph type="italics"/>erunt grauitates duarum quan­<lb/>titatum aquæ<emph.end type="italics"/> 3 5/21, & 5, <emph type="italics"/>quarum quantitatum prima e&longs;t æqualis <lb/>magnitudine corpori plumbeo, &longs;ecunda stanneo, que &longs;unt æque gra­<lb/>uia, vtriu&longs;que enim grauitas est<emph.end type="italics"/> 37. <emph type="italics"/>Fiat igitur vt<emph.end type="italics"/> 5, <emph type="italics"/>ad<emph.end type="italics"/> 3 5/21, <emph type="italics"/>it a<emph.end type="italics"/><lb/>1150, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 740, <emph type="italics"/>tanta igitur erit grauitas <lb/>&longs;tanni, magnitudinem habentis æqualem propo&longs;ito plumbo A, quanta <lb/>etiam inueniebatur & &longs;upra.<emph.end type="italics"/></s></p><p type="main"> |
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| <s>Quod &longs;i propo&longs;itum &longs;it cereum corpus aliquod, aut cuiu&longs;­<lb/>cunque generis &longs;olidi, &longs;iue leuioris quam aqua, &longs;iue grauio­<lb/>ris, & oporteat inuenire grauitatem alicuius &longs;olidi alterius <lb/>generis, magnitudine æqualis propo&longs;ito corpori &longs;olido. </s> | <s>Quod &longs;i propo&longs;itum &longs;it cereum corpus aliquod, aut cuiu&longs;­<lb/>cunque generis &longs;olidi, &longs;iue leuioris quam aqua, &longs;iue grauio­<lb/>ris, & oporteat inuenire grauitatem alicuius &longs;olidi alterius <lb/>generis, magnitudine æqualis propo&longs;ito corpori &longs;olido. </s> |
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| <s>Propo&longs;itis duobus &longs;olidis corporibus æque graui­<lb/>bus, data magnitudine vnius, magnitudinem alte­<lb/>rius inuenire. </s></p><p type="main"> | <s>Propo&longs;itis duobus &longs;olidis corporibus æque graui­<lb/>bus, data magnitudine vnius, magnitudinem alte­<lb/>rius inuenire. </s></p><p type="main"> |
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| <s>SINT propo&longs;ita duo corpora &longs;olida æque grauia A, B, &longs;it au­<lb/><gap/>m vnius, vtpote ip&longs;ius A, data magnitudo C, & oporteat inueni­<lb/>re magnitudinem ip&longs;ius B, Accipiatur aliquod &longs;olidum corpus D, <lb/>eiu&longs;dem generis cum &longs;olido A, & &longs;it eius grauitas G, deinde &longs;olidi <lb/>corporis quod &longs;it E, eiu&longs;dem generis cum &longs;olido B, magnitudine <lb/>æqualis ip&longs;i D, inueniatur grauitas, quæ &longs;it H, hoc autem, Proble­<lb/>ma antecedens docuit, & fiat vt grauitas H, ad grauitatem G, ita <lb/>magnitudo C, ad aliam magnitudinem, quæ &longs;it F. <!-- KEEP S--></s> | <s>SINT propo&longs;ita duo corpora &longs;olida æque grauia A, B, &longs;it au­<lb/>tem vnius, vtpote ip&longs;ius A, data magnitudo C, & oporteat inueni­<lb/>re magnitudinem ip&longs;ius B, Accipiatur aliquod &longs;olidum corpus D, <lb/>eiu&longs;dem generis cum &longs;olido A, & &longs;it eius grauitas G, deinde &longs;olidi <lb/>corporis quod &longs;it E, eiu&longs;dem generis cum &longs;olido B, magnitudine <lb/>æqualis ip&longs;i D, inueniatur grauitas, quæ &longs;it H, hoc autem, Proble­<lb/>ma antecedens docuit, & fiat vt grauitas H, ad grauitatem G, ita <lb/>magnitudo C, ad aliam magnitudinem, quæ &longs;it F. <!-- KEEP S--></s> |
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| <s>Quoniam igitur <pb xlink:href="029/01/027.jpg" pagenum="20"/>&longs;unt quatuor corpora grauia E, D, B, <lb/>A, quorum E, D, primum videlicet, <lb/><figure id="id.029.01.027.1.jpg" xlink:href="029/01/027/1.jpg"/><lb/>& &longs;ecundum, &longs;unt æqualia magnitu­<lb/>dine, tertium vero B, & quartum A, <lb/>æquegrauia, & &longs;unt eiu&longs;dem generis <lb/>corpora E, B, &longs;imiliter & corpora <lb/><arrow.to.target n="note31"/> D, A, * erit vt grauitas H, ad graui­<lb/>tatem G, ita magnitudo C, ad corpo­<lb/>ris B, magnitudinem, &longs;ed vt grauitas <lb/>H, ad grauitatem G, ita e&longs;t magnitu­<lb/>do C, ad F, magnitudinem, ergo ma­<lb/>gnitudo F, æqualis erit magnitudini <lb/>corporis B. inuenta igitur e&longs;t corporis B, magnitudo F, quod facere <lb/>oportebat. </s></p><p type="margin"> | <s>Quoniam igitur <pb xlink:href="029/01/027.jpg" pagenum="20"/>&longs;unt quatuor corpora grauia E, D, B, <lb/>A, quorum E, D, primum videlicet, <lb/><figure id="id.029.01.027.1.jpg" xlink:href="029/01/027/1.jpg"/><lb/>& &longs;ecundum, &longs;unt æqualia magnitu­<lb/>dine, tertium vero B, & quartum A, <lb/>æquegrauia, & &longs;unt eiu&longs;dem generis <lb/>corpora E, B, &longs;imiliter & corpora <lb/><arrow.to.target n="note31"/> D, A, * erit vt grauitas H, ad graui­<lb/>tatem G, ita magnitudo C, ad corpo­<lb/>ris B, magnitudinem, &longs;ed vt grauitas <lb/>H, ad grauitatem G, ita e&longs;t magnitu­<lb/>do C, ad F, magnitudinem, ergo ma­<lb/>gnitudo F, æqualis erit magnitudini <lb/>corporis B. inuenta igitur e&longs;t corporis B, magnitudo F, quod facere <lb/>oportebat. </s></p><p type="margin"> |
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| <s>&longs;it enim &longs;i fieri pote&longs;t corpus A, leuius corpore B, <pb xlink:href="029/01/036.jpg" pagenum="29"/>& accipiatur aliquod corpus L, leuius quam aqua, ita vt cum ip&longs;i <lb/>corpori L, appendatur, corpus B, & ambo &longs;imul demittantur in <expan abbr="aquã">aquam</expan>, <lb/>&longs;int æque grauia atque aqua, neque &longs;ur&longs;um, neque deor&longs;um &longs;eran­<lb/>tur, &longs;imiliter accipiatur alterum corpus M, eiu&longs;dem generis cum <lb/>corpore L, ip&longs;ique &longs;imile, & <lb/><figure id="id.029.01.036.1.jpg" xlink:href="029/01/036/1.jpg"/><lb/>æquale, & corpori M, appen<lb/>datur corpus A. <!-- KEEP S--></s> | <s>&longs;it enim &longs;i fieri pote&longs;t corpus A, leuius corpore B, <pb xlink:href="029/01/036.jpg" pagenum="29"/>& accipiatur aliquod corpus L, leuius quam aqua, ita vt cum ip&longs;i <lb/>corpori L, appendatur, corpus B, & ambo &longs;imul demittantur in <expan abbr="aquã">aquam</expan>, <lb/>&longs;int æque grauia atque aqua, neque &longs;ur&longs;um, neque deor&longs;um &longs;eran­<lb/>tur, &longs;imiliter accipiatur alterum corpus M, eiu&longs;dem generis cum <lb/>corpore L, ip&longs;ique &longs;imile, & <lb/><figure id="id.029.01.036.1.jpg" xlink:href="029/01/036/1.jpg"/><lb/>æquale, & corpori M, appen<lb/>datur corpus A. <!-- KEEP S--></s> |
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| <s>Deinde in­<lb/>teligatur aqua con&longs;i&longs;tens, & <lb/>manens, eiu&longs;que &longs;uper&longs;i­<lb/>cies &longs;phærica C D E, cuius <lb/>&longs;phæræ centrum K, aquæ <lb/>enim con&longs;i&longs;tentis, atque <lb/>manentis &longs;uperficies &longs;phæ­<lb/>rica e&longs;t, cui <gap/> &longs;phæræ cen­<lb/>trum idem <gap/>, quod <expan abbr="centrũ">centrum</expan> <lb/>terræ, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib. | <s>Deinde in­<lb/>teligatur aqua con&longs;i&longs;tens, & <lb/>manens, eiu&longs;que &longs;uperfi­<lb/>cies &longs;phærica C D E, cuius <lb/>&longs;phæræ centrum K, aquæ <lb/>enim con&longs;i&longs;tentis, atque <lb/>manentis &longs;uperficies &longs;phæ­<lb/>rica e&longs;t, cuius &longs;phæræ cen­<lb/>trum idem e&longs;t, quod <expan abbr="centrũ">centrum</expan> <lb/>terræ, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib. |
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| 1. de <lb/>ijs, quæ vehuntur in aqua. </s> | 1. de <lb/>ijs, quæ vehuntur in aqua. </s> |
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| <s><emph type="italics"/>Quæro exempli gratia, quam habet rationem in grauitate plumbum ad aurum. </s> | <s><emph type="italics"/>Quæro exempli gratia, quam habet rationem in grauitate plumbum ad aurum. </s> |
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| <s>In­<lb/>teligatur plumbum, quoniam leuius est auro, grauitatem habere 1, & in linea plumbi, <lb/>in prima columna nominati &longs;ub titulo auri, quæratur auri grauitas, ea erit<emph.end type="italics"/> 1 11/21. <emph type="italics"/>plum<lb/>bum igitur ad aurum rationem habebit in grauitate vt 1, ad 1 1<gap/>/21, &longs;i enim &longs;umantur <lb/>duo corpora magnitudine æqualia, vnum plumbeum alterum aureum, &longs;it autem plum<lb/>bei corporis grauitas<emph.end type="italics"/> 1, <emph type="italics"/>aurei erit<emph.end type="italics"/> 1 1<gap/>/21, <emph type="italics"/>quare corpus plumbeum ad corpus aureum <lb/>eiu&longs;dem magnitudinis rationem habebit in grauitate vt 1, ad 1 1<gap/>/21. comparantur au­<lb/>tem inter &longs;e genera diuer&longs;a grauitate, in corporibus magnitudine æqualibus.<emph.end type="italics"/></s></p><p type="main"> | <s>In­<lb/>teligatur plumbum, quoniam leuius est auro, grauitatem habere 1, & in linea plumbi, <lb/>in prima columna nominati &longs;ub titulo auri, quæratur auri grauitas, ea erit<emph.end type="italics"/> 1 15/23. <emph type="italics"/><!--neuer Satz-->plum<lb/>bum igitur ad aurum rationem habebit in grauitate vt 1, ad 1 15/23, &longs;i enim &longs;umantur <lb/>duo corpora magnitudine æqualia, vnum plumbeum alterum aureum, &longs;it autem plum<lb/>bei corporis grauitas<emph.end type="italics"/> 1, <emph type="italics"/>aurei erit<emph.end type="italics"/> 1 15/23, <emph type="italics"/>quare corpus plumbeum ad corpus aureum <lb/>eiu&longs;dem magnitudinis rationem habebit in grauitate vt 1, ad 1 15/23. comparantur au­<lb/>tem inter &longs;e genera diuer&longs;a grauitate, in corporibus magnitudine æqualibus.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Rur&longs;us, quæro quam habet rationem in grauitate aqua ad argentum viuum. </s> | <s><emph type="italics"/>Rur&longs;us, quæro quam habet rationem in grauitate aqua ad argentum viuum. </s> |
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| <s><emph type="italics"/>Contra, quæro quomodo &longs;e habent in magnitudine aurum, & plumbum. </s> | <s><emph type="italics"/>Contra, quæro quomodo &longs;e habent in magnitudine aurum, & plumbum. </s> |
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| <s>inteligatur <lb/>aurum, quoniam grauius e&longs;t plumbo, magnitudinem habere 1, & in linea plumbi, &longs;ub ti­<lb/>tulo auri, quæratur plumbi magnitudo, ea erit 1 1<gap/>/21, aurum igitur ad plumbum &longs;e ba-<emph.end type="italics"/><pb xlink:href="029/01/040.jpg" pagenum="33"/><emph type="italics"/><gap/>bit in magnitudine vt 1, ad 1 19/21, &longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>aureum, alterum plumbeum, &longs;it autem corporis aurei magnitudo 1, plumbei erit 1 1<gap/>/21, <lb/>quare corpus aureum ad corpus plumbeum eiu&longs;dem grauitatis &longs;e habebit in magnitudi­<lb/>ne vt 1, ad 1 19/21, comparantur autem inter &longs;e genera diuer&longs;a magnitudine, in corpori­<lb/>bus æque grauibus.<emph.end type="italics"/></s></p><p type="main"> | <s>inteligatur <lb/>aurum, quoniam grauius e&longs;t plumbo, magnitudinem habere 1, & in linea plumbi, &longs;ub ti­<lb/>tulo auri, quæratur plumbi magnitudo, ea erit 1 15/23, aurum igitur ad plumbum &longs;e ba-<emph.end type="italics"/><pb xlink:href="029/01/040.jpg" pagenum="33"/><emph type="italics"/><gap/>bit in magnitudine vt 1, ad 1 19/21, &longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>aureum, alterum plumbeum, &longs;it autem corporis aurei magnitudo 1, plumbei erit 1 1<gap/>/21, <lb/>quare corpus aureum ad corpus plumbeum eiu&longs;dem grauitatis &longs;e habebit in magnitudi­<lb/>ne vt 1, ad 1 19/21, comparantur autem inter &longs;e genera diuer&longs;a magnitudine, in corpori­<lb/>bus æque grauibus.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Quæro denique quomodo &longs;e habent in magnitudine ferrum, & aqua, ponatur ferrum, <lb/>vt grauius aqua, magnitudinem habere 1, & in linea aquæ, &longs;ub titulo ferri, quæratur <lb/>aquæ magnitudo, ea erit<emph.end type="italics"/> 8, <emph type="italics"/>ferrum igitur ad aquam &longs;e habebit in magnitudine vt 1, ad<emph.end type="italics"/> 8. </s></p><p type="head"> | <s><emph type="italics"/>Quæro denique quomodo &longs;e habent in magnitudine ferrum, & aqua, ponatur ferrum, <lb/>vt grauius aqua, magnitudinem habere 1, & in linea aquæ, &longs;ub titulo ferri, quæratur <lb/>aquæ magnitudo, ea erit<emph.end type="italics"/> 8, <emph type="italics"/>ferrum igitur ad aquam &longs;e habebit in magnitudine vt 1, ad<emph.end type="italics"/> 8. </s></p><p type="head"> |
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| <s><emph type="italics"/>Quæro, quomodo &longs;e habet in grauitate aqua ad vinum. </s> | <s><emph type="italics"/>Quæro, quomodo &longs;e habet in grauitate aqua ad vinum. </s> |
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| <s>quoniam <lb/>æqua grauior est vino, intelligatur eius grauitas<emph.end type="italics"/> 100, <emph type="italics"/>& quoniam in <lb/>linea aquæ, &longs;ub titulo vint, datur vini grauitas<emph.end type="italics"/> 98 <gap/>, <emph type="italics"/>aqua ad vinum <lb/>&longs;e habebit in grauitate, vt<emph.end type="italics"/> 100, <emph type="italics"/>ad<emph.end type="italics"/> 98 <gap/>. </s></p><p type="main"> | <s>quoniam <lb/>æqua grauior est vino, intelligatur eius grauitas<emph.end type="italics"/> 100, <emph type="italics"/>& quoniam in <lb/>linea aquæ, &longs;ub titulo vint, datur vini grauitas<emph.end type="italics"/> 98 1/3, <emph type="italics"/>aqua ad vinum <lb/>&longs;e habebit in grauitate, vt<emph.end type="italics"/> 100, <emph type="italics"/>ad<emph.end type="italics"/> 98 1/3. </s></p><p type="main"> |
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| <s><emph type="italics"/>Contra quæro quomodo &longs;e habent in magnitudine argentum, & <lb/>aurum. </s> | <s><emph type="italics"/>Contra quæro quomodo &longs;e habent in magnitudine argentum, & <lb/>aurum. </s> |
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| <s>intelligatur argentum, vt leuius auro, magnitudinem balere<emph.end type="italics"/><lb/>100, <emph type="italics"/>& in linea auri &longs;ub titulo argenti, quæratur auri magnitudo, <gap/><lb/>erit<emph.end type="italics"/> 54 22/57, <emph type="italics"/>argentum igitur ad aurum &longs;e habebit in magnitudine, vt<emph.end type="italics"/><lb/>100, <emph type="italics"/>ad<emph.end type="italics"/> 54 22/57, <emph type="italics"/>&longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>argenteum, alterum aureum, &longs;it autem argentei corporis magnitudo<emph.end type="italics"/><lb/>100, <emph type="italics"/>erit aurei<emph.end type="italics"/> 54 22/57, <emph type="italics"/>quare corpus argenteum, ad corpus aureum <lb/>eiu&longs;dem grauitatis, &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 54 22/57. </s></p><p type="main"> | <s>intelligatur argentum, vt leuius auro, magnitudinem balere<emph.end type="italics"/><lb/>100, <emph type="italics"/>& in linea auri &longs;ub titulo argenti, quæratur auri magnitudo, ea <lb/>erit<emph.end type="italics"/> 54 22/39, <emph type="italics"/>argentum igitur ad aurum &longs;e habebit in magnitudine, vt<emph.end type="italics"/><lb/>100, <emph type="italics"/>ad<emph.end type="italics"/> 54 22/39, <emph type="italics"/>&longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>argenteum, alterum aureum, &longs;it autem argentei corporis magnitudo<emph.end type="italics"/><lb/>100, <emph type="italics"/>erit aurei<emph.end type="italics"/> 54 22/39, <emph type="italics"/>quare corpus argenteum, ad corpus aureum <lb/>eiu&longs;dem grauitatis, &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 54 22/39. </s></p><p type="main"> |
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| <s><emph type="italics"/>Quæro denique quomodo &longs;e habent in magnitudine aqua & ar­<lb/>gentum viuum. </s> | <s><emph type="italics"/>Quæro denique quomodo &longs;e habent in magnitudine aqua & ar­<lb/>gentum viuum. </s> |
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| <s>TABELLE WAR HIER<!-- KEEP S--></s></p><pb xlink:href="029/01/047.jpg" pagenum="40"/><p type="table"> | <s>TABELLE WAR HIER<!-- KEEP S--></s></p><pb xlink:href="029/01/047.jpg" pagenum="40"/><p type="table"> |
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| <s>TABELLE WAR HIER<lb/><emph type="italics"/>erit gran. <!-- REMOVE S-->513. & &longs;ic reliquarum &longs;phærarum ex &longs;tanno, diametros <gap/><lb/>bentium magnitudine quacunque, inuenientur grauitates.<emph.end type="italics"/></s> | <s>TABELLE WAR HIER<lb/><emph type="italics"/>erit gran. <!-- REMOVE S-->513. & &longs;ic reliquarum &longs;phærarum ex &longs;tanno, diametros ha­<lb/>bentium magnitudine quacunque, inuenientur grauitates.<emph.end type="italics"/></s> |
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| </p><p type="main"> | </p><p type="main"> |
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| <s><emph type="italics"/>Aliter quoque & expeditius reliquarum &longs;phærarum ex &longs;tanno i<gap/><lb/>uenientur grauitates.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Aliter quoque & expeditius reliquarum &longs;phærarum ex &longs;tanno in­<lb/>uenientur grauitates.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Inuenta grauitate &longs;phæræ, diametrum habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, &longs;im<gap/><lb/>tiplicetur ip&longs;a grauitas, per<emph.end type="italics"/> 8, <emph type="italics"/>hoc est per cubum ex<emph.end type="italics"/> 2, <emph type="italics"/>numerus pro <lb/>ductus dabit grauitatem &longs;phæræ, diametrum habentis<emph.end type="italics"/> 2/4, <emph type="italics"/>vnciæ, b<gap/><emph.end type="italics"/><lb/><arrow.to.target n="note47"/> <emph type="italics"/>e&longs;t<emph.end type="italics"/> 1/2, <emph type="italics"/>&longs;phæræ {*} enim inter &longs;e in triplicata &longs;unt ratione &longs;uarum di<gap/><lb/>metrorum. </s> | <s><emph type="italics"/>Inuenta grauitate &longs;phæræ, diametrum habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, mul­<lb/>tiplicetur ip&longs;a grauitas, per<emph.end type="italics"/> 8, <emph type="italics"/>hoc est per cubum ex<emph.end type="italics"/> 2, <emph type="italics"/>numerus pro <lb/>ductus dabit grauitatem &longs;phæræ, diametrum habentis<emph.end type="italics"/> 2/4, <emph type="italics"/>vnciæ, hoc<emph.end type="italics"/><lb/><arrow.to.target n="note47"/> <emph type="italics"/>e&longs;t<emph.end type="italics"/> 1/2, <emph type="italics"/>&longs;phæræ {*} enim inter &longs;e in triplicata &longs;unt ratione &longs;uarum di<gap/><lb/>metrorum. </s> |
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| <s>deinde &longs;i multiplicetur eadem grauitas per<emph.end type="italics"/> 27, <emph type="italics"/>hoc est p<gap/><lb/>cubum ex<emph.end type="italics"/> 3, <emph type="italics"/>numerus productus dabit grauitatem &longs;phæræ, habent<gap/><lb/>diametrum<emph.end type="italics"/> 3/4, <emph type="italics"/>vnciæ, & &longs;i multiplicetur per<emph.end type="italics"/> 64, <emph type="italics"/>hoc est per cub<gap/><lb/>ex<emph.end type="italics"/> 4, <emph type="italics"/>numerus productus dabit grauitatem &longs;phæræ, cuius diameter<gap/><emph.end type="italics"/><lb/>4/4, <emph type="italics"/>hoc est vnius vnciæ, & eo deinceps continuo ordine,<emph.end type="italics"/></s></p><p type="margin"> | <s>deinde &longs;i multiplicetur eadem grauitas per<emph.end type="italics"/> 27, <emph type="italics"/>hoc est per <lb/>cubum ex<emph.end type="italics"/> 3, <emph type="italics"/>numerus productus dabit grauitatem &longs;phæræ, habentis <lb/>diametrum<emph.end type="italics"/> 3/4, <emph type="italics"/>vnciæ, & &longs;i multiplicetur per<emph.end type="italics"/> 64, <emph type="italics"/>hoc est per cubum <lb/>ex<emph.end type="italics"/> 4, <emph type="italics"/>numerus productus dabit grauitatem &longs;phæræ, cuius diameter e&longs;t <emph.end type="italics"/><lb/>4/4, <emph type="italics"/>hoc est vnius vnciæ, & eo deinceps continuo ordine,<emph.end type="italics"/></s></p><p type="margin"> |
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| <s><margin.target id="note47"/>18.12. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> | <s><margin.target id="note47"/>18.12. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Fiat vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, (<emph type="italics"/>&longs;i de grauitate &longs;phæræ<lb/><expan abbr="plūbeæ">plumbeæ</expan> quæritur cuius diameter est<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ) ita 19. grauitas vi<gap/><lb/>licet &longs;phæræ stanneæ <expan abbr="diametrū">diametrum</expan> habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, ad <expan abbr="aliū">alium</expan> numerum<lb/>qui &longs;it<emph.end type="italics"/> 29 19/74, <emph type="italics"/>grauitas igitur &longs;phæræ plumbeæ, diametrum haben<lb/>tis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, erit gran.<emph.end type="italics"/> 29 39/74. <emph type="italics"/>&longs;tannum enim ad plumbum ration<gap/><lb/>habet in grauitate vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>vt con&longs;picitur in prima tabelle <lb/>quam ad comparandum inter &longs;e duodecim corporum genera, grauita<lb/>te, & magnitudine, appo&longs;uimus.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Fiat vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, (<emph type="italics"/>&longs;i de grauitate &longs;phæræ<lb/><expan abbr="plūbeæ">plumbeæ</expan> quæritur cuius diameter est<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ) ita 19. grauitas vi<gap/><lb/>licet &longs;phæræ stanneæ <expan abbr="diametrū">diametrum</expan> habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, ad <expan abbr="aliū">alium</expan> numerum<lb/>qui &longs;it<emph.end type="italics"/> 29 19/74, <emph type="italics"/>grauitas igitur &longs;phæræ plumbeæ, diametrum haben<lb/>tis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, erit gran.<emph.end type="italics"/> 29 39/74. <emph type="italics"/>&longs;tannum enim ad plumbum ration<gap/><lb/>habet in grauitate vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>vt con&longs;picitur in prima tabelle <lb/>quam ad comparandum inter &longs;e duodecim corporum genera, grauita<lb/>te, & magnitudine, appo&longs;uimus.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si vero quæratur de grauitate &longs;phæræ plumbeæ, diametrum <lb/>habentis<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, fiat vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, <emph type="italics"/>ita<emph.end type="italics"/> 9728, <emph type="italics"/>id est gra<gap/><emph.end type="italics"/></s></p><pb xlink:href="029/01/048.jpg" pagenum="41"/><p type="table"> | <s><emph type="italics"/>Si vero quæratur de grauitate &longs;phæræ plumbeæ, diametrum <lb/>habentis<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, fiat vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, <emph type="italics"/>ita<emph.end type="italics"/> 9728, <emph type="italics"/>id est grauia<emph.end type="italics"/></s></p><pb xlink:href="029/01/048.jpg" pagenum="41"/><p type="table"> |
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| <s>TABELLE WAR HIER<lb/><emph type="italics"/>&longs;phæræ stanneæ, cuius diameter est<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, ad alium numerum, <lb/>qui &longs;it<emph.end type="italics"/> 15 117 <gap/>, <emph type="italics"/>&longs;phæra igitur plumbea, cuius diameter est<emph.end type="italics"/> 2, <emph type="italics"/>vn­<lb/>ciarum grauitatem habebit gran. <!-- REMOVE S-->15 117 <gap/>, atque hæc erit ob&longs;er­<lb/>uanda in reliquis ratio.<emph.end type="italics"/></s> | <s>TABELLE WAR HIER<lb/><emph type="italics"/>&longs;phæræ stanneæ, cuius diameter est<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, ad alium numerum, <lb/>qui &longs;it<emph.end type="italics"/> 15 117 <gap/>, <emph type="italics"/>&longs;phæra igitur plumbea, cuius diameter est<emph.end type="italics"/> 2, <emph type="italics"/>vn­<lb/>ciarum grauitatem habebit gran. <!-- REMOVE S-->15 117 <gap/>, atque hæc erit ob&longs;er­<lb/>uanda in reliquis ratio.<emph.end type="italics"/></s> |
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