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Colored diff for /texts/archimedes/xml/gheta_promo_029_la_1603.xml between version 1.9 and 1.10

version 1.9, 2003/11/17 17:54:45 version 1.10, 2003/11/17 18:22:18
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 <s><expan abbr="Tuq;">Tuque</expan> <lb/>is es, quem non modo rudes, &longs;ed etiam docti &longs;u&longs;piciunt. </s> <s><expan abbr="Tuq;">Tuque</expan> <lb/>is es, quem non modo rudes, &longs;ed etiam docti &longs;u&longs;piciunt. </s>
  
 <s><lb/>Habetino&longs;tra b&aelig;c &aelig;tas, quos admitetur; habet quos ex&shy;<lb/>tollat pr&aelig;claros viros, &longs;ed quos tibi anteponat, non facile <lb/>inueniet. </s> <s><lb/>Habetino&longs;tra h&aelig;c &aelig;tas, quos admitetur; habet quos ex&shy;<lb/>tollat pr&aelig;claros viros, &longs;ed quos tibi anteponat, non facile <lb/>inueniet. </s>
  
 <s>Degis ea in Vrbe, qu&aelig; laudis mediocritatem <lb/>vel nunquam agnouit, vel &longs;emper contemp&longs;it: neque in <lb/>tanta maie&longs;tate, tua deficit virtus, &longs;ed bono in lumine po <lb/>&longs;ita collucet magis. </s> <s>Degis ea in Vrbe, qu&aelig; laudis mediocritatem <lb/>vel nunquam agnouit, vel &longs;emper contemp&longs;it: neque in <lb/>tanta maie&longs;tate, tua deficit virtus, &longs;ed bono in lumine po <lb/>&longs;ita collucet magis. </s>
  
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 <s>Rubeo ba <lb/>mine mihi tum ex &longs;tudiorum &longs;imilitudine, tum pracipue ex <lb/>eius humanitate amici&longs;simo, ad Reuerendi&longs;simum Sera&shy;<lb/>phinum deductus &longs;um. <!-- KEEP S--></s> <s>Rubeo ba <lb/>mine mihi tum ex &longs;tudiorum &longs;imilitudine, tum pracipue ex <lb/>eius humanitate amici&longs;simo, ad Reuerendi&longs;simum Sera&shy;<lb/>phinum deductus &longs;um. <!-- KEEP S--></s>
  
 <s>I&longs;qs me tantus Pr&aelig;&longs;ul non &longs;olum <lb/>humani&longs;sime complexus est, ver <gap/> ets am ita bo<gap/>tus ad <lb/>eualganda, que &longs;crip&longs;eram; plane vt mihi nefas putauerim <lb/>non parere. </s> <s>I&longs;qs me tantus Pr&aelig;&longs;ul non &longs;olum <lb/>humani&longs;sime complexus est, verum etiam ita bo<gap/>tus ad <lb/>eualganda, que &longs;crip&longs;eram; plane vt mihi nefas putauerim <lb/>non parere. </s>
  
 <s>Aecipeigitur &amp; tu Lactor optime amico ac be&shy;<lb/>uigno auimo laborem hunc, quem &agrave; me tali<gap/><lb/>&longs;umma benignitas expre&longs;sit. </s> <s>Aecipeigitur &amp; tu Lactor optime amico ac be&shy;<lb/>uigno auimo laborem hunc, quem &agrave; me tali<gap/><lb/>&longs;umma benignitas expre&longs;sit. </s>
  
 <s>Argumentum quidem, vt <lb/>dicob am non iniucundum e&longs;t, nec ab v&longs;u alienam. </s> <s>Argumentum quidem, vt <lb/>dicebam non iniucundum e&longs;t, nec ab v&longs;u alienam. </s>
  
 <s>Huiu&longs;&shy;<lb/>medi enim comparatione Archimides mixtionem argemi <lb/>in aure deprebeudit, &amp; furtum Auri&longs;itis in corona aurea <lb/>patefecit. </s> <s>Huiu&longs;&shy;<lb/>medi enim comparatione Archimides mixtionem argemi <lb/>in aure deprebeudit, &amp; furtum Auri&longs;itis in corona aurea <lb/>patefecit. </s>
  
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 <s>Accipiatur aliquod &longs;oli&shy;<lb/>dum corpus D, eiu&longs;dem generis cum <lb/>corpore &longs;olido A, cui &aelig;quale grauita&shy;<lb/>te accipiatur alterum E, eiu&longs;dem ge&shy;<lb/>neris cum corpore B, deinde liquidi <lb/>magnitudine &aelig;qualis corpori D,<arrow.to.target n="note28"/> *in&shy;<lb/>ueniatur grauitas, qu&aelig; &longs;it G, item li&shy;<lb/>quidi eiu&longs;dem generis, &aelig;qualis ma&shy;<lb/>gnitudine corpori E,* inueniatur grauitas, qu&aelig; &longs;it H, &amp; fiat vt H, ad<arrow.to.target n="note29"/><lb/>G, ita C, ad aliam grauitatem, qu&aelig; &longs;it F. <!-- KEEP S--></s> <s>Accipiatur aliquod &longs;oli&shy;<lb/>dum corpus D, eiu&longs;dem generis cum <lb/>corpore &longs;olido A, cui &aelig;quale grauita&shy;<lb/>te accipiatur alterum E, eiu&longs;dem ge&shy;<lb/>neris cum corpore B, deinde liquidi <lb/>magnitudine &aelig;qualis corpori D,<arrow.to.target n="note28"/> *in&shy;<lb/>ueniatur grauitas, qu&aelig; &longs;it G, item li&shy;<lb/>quidi eiu&longs;dem generis, &aelig;qualis ma&shy;<lb/>gnitudine corpori E,* inueniatur grauitas, qu&aelig; &longs;it H, &amp; fiat vt H, ad<arrow.to.target n="note29"/><lb/>G, ita C, ad aliam grauitatem, qu&aelig; &longs;it F. <!-- KEEP S--></s>
  
 <s>Quoniam igitur &longs;unt qua&shy;<lb/>tuor corpora A, B, D, E, quorum A, B, primum videlicet, &amp; &longs;ecundum <lb/>&longs;unt &aelig;qualia magnitudine, tertium vero D, &amp; E, quartum &aelig;que gra&shy;<lb/>uia, &amp; &longs;unt <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> generis &longs;olida A, D, itidem &longs;olida B, E, *erit vt<arrow.to.target n="note30"/> gra&shy;<lb/>uitas C, ad &longs;olidi B, grauitatem, ita grauitas H, ad grauitatem G, &longs;ed <pb pagenum="18"/>vt grauitas H, ad <expan abbr="grauitat&etilde;">grauitatem</expan> G, ita e&longs;t grauitas C, ad F, grauitatem; er&shy;<lb/>go grauitas F, &aelig;qualis erit grauitati &longs;olidi B, inuenta igitur e&longs;t cor&shy;<lb/>poris &longs;olidi B, grauitas F, quod &longs;acere oportebat. </s></p><p type="margin"> <s>Quoniam igitur &longs;unt qua&shy;<lb/>tuor corpora A, B, D, E, quorum A, B, primum videlicet, &amp; &longs;ecundum <lb/>&longs;unt &aelig;qualia magnitudine, tertium vero D, &amp; E, quartum &aelig;que gra&shy;<lb/>uia, &amp; &longs;unt <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> generis &longs;olida A, D, itidem &longs;olida B, E, *erit vt<arrow.to.target n="note30"/> gra&shy;<lb/>uitas C, ad &longs;olidi B, grauitatem, ita grauitas H, ad grauitatem G, &longs;ed <pb pagenum="18"/>vt grauitas H, ad <expan abbr="grauitat&etilde;">grauitatem</expan> G, ita e&longs;t grauitas C, ad F, grauitatem; er&shy;<lb/>go grauitas F, &aelig;qualis erit grauitati &longs;olidi B, inuenta igitur e&longs;t cor&shy;<lb/>poris &longs;olidi B, grauitas F, quod facere oportebat. </s></p><p type="margin">
  
 <s><margin.target id="note28"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note28"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin">
  
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 <s><emph type="italics"/>Accipiatur vt diximus aliquod corpus plumbeum D, cuius graui&shy;<lb/>tas &longs;it 115, &amp; &longs;tanni, magnitudinem habentis &aelig;qualem plumbo D, in&shy;<lb/>ueniatur grauitas, qu&aelig; &longs;it<emph.end type="italics"/> 74. <emph type="italics"/>&amp; fiat vt 74, ad<emph.end type="italics"/> 115, <emph type="italics"/>ita cubus ex 10, <lb/>qui e&longs;t 1000, ad alium numerum qui &longs;it<emph.end type="italics"/> 1554 2/17, <emph type="italics"/>is igitur numerus <lb/>erit cubus diametri &longs;ph&aelig;r&aelig; ex stanno, grauitatem habentis &aelig;qualem <lb/>propo&longs;it&aelig; ex plumbo &longs;ph&aelig;r&aelig; A, quare eius latus cubicum, quod est<emph.end type="italics"/><lb/>11 52/100, <emph type="italics"/>vero proximum, indicabit ip&longs;am diametrum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Accipiatur vt diximus aliquod corpus plumbeum D, cuius graui&shy;<lb/>tas &longs;it 115, &amp; &longs;tanni, magnitudinem habentis &aelig;qualem plumbo D, in&shy;<lb/>ueniatur grauitas, qu&aelig; &longs;it<emph.end type="italics"/> 74. <emph type="italics"/>&amp; fiat vt 74, ad<emph.end type="italics"/> 115, <emph type="italics"/>ita cubus ex 10, <lb/>qui e&longs;t 1000, ad alium numerum qui &longs;it<emph.end type="italics"/> 1554 2/17, <emph type="italics"/>is igitur numerus <lb/>erit cubus diametri &longs;ph&aelig;r&aelig; ex stanno, grauitatem habentis &aelig;qualem <lb/>propo&longs;it&aelig; ex plumbo &longs;ph&aelig;r&aelig; A, quare eius latus cubicum, quod est<emph.end type="italics"/><lb/>11 52/100, <emph type="italics"/>vero proximum, indicabit ip&longs;am diametrum.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius form&aelig; regularis, eadem ratione inuenietur latus cu<lb/>bi ex stanno, grauitatem bab<gap/>ntis &aelig;qualem propo&longs;ito plumbto cu&shy;<lb/>bo A, &longs;i enim ip&longs;ius cubi plumbti A, datum &longs;it latus 10, erit numerus<emph.end type="italics"/><lb/>1554 2/17&lt;31&gt; <emph type="italics"/>cubus ex &longs;tanno &aelig;qualis grauitate propo&longs;ito plumbeo Cu<lb/>bo A, quare latus. </s> <s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius form&aelig; regularis, eadem ratione inuenietur latus cu<lb/>bi ex stanno, grauitatem habentis &aelig;qualem propo&longs;ito plumbto cu&shy;<lb/>bo A, &longs;i enim ip&longs;ius cubi plumbti A, datum &longs;it latus 10, erit numerus<emph.end type="italics"/><lb/>1554 2/17&lt;31&gt; <emph type="italics"/>cubus ex &longs;tanno &aelig;qualis grauitate propo&longs;ito plumbeo Cu<lb/>bo A, quare latus. </s>
  
 <s>cubitum numeri<emph.end type="italics"/> 1554 2/17&lt;31&gt; <emph type="italics"/>quod est<emph.end type="italics"/> 11 52/100&lt;31&gt; <emph type="italics"/>pro <lb/>ximum vero; indicabit qu&aelig; &longs;itum latus.<emph.end type="italics"/></s></p><p type="main"> <s>cubitum numeri<emph.end type="italics"/> 1554 2/17&lt;31&gt; <emph type="italics"/>quod est<emph.end type="italics"/> 11 52/100&lt;31&gt; <emph type="italics"/>pro <lb/>ximum vero; indicabit qu&aelig; &longs;itum latus.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><lb/>ter &amp; liquidi, quod &longs;it I, eiu&longs;d&eacute; <lb/>generis cum liquido B, magni <lb/>tudinern habentis &aelig;qualem eidem &longs;olido C, * inueniatur grauitas,<arrow.to.target n="note40"/><lb/>qu&aelig; &longs;it E, &amp; fiat vt grauitas E, ad grauitatem D, ita magnitudo G, ad <lb/>ad aliam <expan abbr="magnitadin&etilde;">magnitadinem</expan>, qu&aelig; &longs;ie F. <!-- KEEP S--></s> <s><lb/>ter &amp; liquidi, quod &longs;it I, eiu&longs;d&eacute; <lb/>generis cum liquido B, magni <lb/>tudinern habentis &aelig;qualem eidem &longs;olido C, * inueniatur grauitas,<arrow.to.target n="note40"/><lb/>qu&aelig; &longs;it E, &amp; fiat vt grauitas E, ad grauitatem D, ita magnitudo G, ad <lb/>ad aliam <expan abbr="magnitadin&etilde;">magnitadinem</expan>, qu&aelig; &longs;ie F. <!-- KEEP S--></s>
  
 <s>Quoniam igitur &longs;unt quatuor cor&shy;<lb/>pora grauia I, H, B, A, quorum primum, &amp; &longs;ecundum &longs;unt magnitu&shy;<lb/>dine &aelig;qualia, tertium vero, &amp; quartum &aelig;que grauia, &amp; &longs;unt eiu&longs;dem <lb/>generis primum videlicet, &amp; tertium, &longs;imiliter eiu&longs;dem generis &longs;e&shy;<pb pagenum="26"/><arrow.to.target n="note41"/> cundum &amp; quartum, * Erit vt grauitas E, ad grauitatem D, ita ma&shy;<lb/>gnitudo G, ad liquidi B, magnitudinem, &longs;ed vt grauitas E, ad graui&shy;<lb/>tatem D, ita e&longs;t magnitudo G, ad F, magnitudinem; ergo magnitudo <lb/>F, &aelig;qualis erit magnitudini liquidi B. inuenta igitur e&longs;t corporis li&shy;<lb/>quidi B, magnitudo F, quod &longs;acere oportebat. </s></p><p type="margin"> <s>Quoniam igitur &longs;unt quatuor cor&shy;<lb/>pora grauia I, H, B, A, quorum primum, &amp; &longs;ecundum &longs;unt magnitu&shy;<lb/>dine &aelig;qualia, tertium vero, &amp; quartum &aelig;que grauia, &amp; &longs;unt eiu&longs;dem <lb/>generis primum videlicet, &amp; tertium, &longs;imiliter eiu&longs;dem generis &longs;e&shy;<pb pagenum="26"/><arrow.to.target n="note41"/> cundum &amp; quartum, * Erit vt grauitas E, ad grauitatem D, ita ma&shy;<lb/>gnitudo G, ad liquidi B, magnitudinem, &longs;ed vt grauitas E, ad graui&shy;<lb/>tatem D, ita e&longs;t magnitudo G, ad F, magnitudinem; ergo magnitudo <lb/>F, &aelig;qualis erit magnitudini liquidi B. inuenta igitur e&longs;t corporis li&shy;<lb/>quidi B, magnitudo F, quod facere oportebat. </s></p><p type="margin">
  
 <s><margin.target id="note39"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note39"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin">
  
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 <s>SINT duo eiu&longs;dem generis, &amp; grauitatis corpora A, B, grauiora <lb/>quam aqua, &amp; &longs;int di&longs;&longs;imilia, dico ip&longs;a corpora &aelig;qualem in aqua <lb/>grauitatem habere. </s> <s>SINT duo eiu&longs;dem generis, &amp; grauitatis corpora A, B, grauiora <lb/>quam aqua, &amp; &longs;int di&longs;&longs;imilia, dico ip&longs;a corpora &aelig;qualem in aqua <lb/>grauitatem habere. </s>
  
 <s>&longs;it enim &longs;i &longs;ieri pote&longs;t corpus A, leuius corpore B, <pb pagenum="29"/>&amp; accipiatur aliquod corpus L, leuius quam aqua, ita vt cum ip&longs;i <lb/>corpori L, appendatur, corpus B, &amp; ambo &longs;imul demittantur in <expan abbr="aqu&atilde;">aquam</expan>, <lb/>&longs;int &aelig;que grauia atque aqua, neque &longs;ur&longs;um, neque deor&longs;um &longs;eran&shy;<lb/>tur, &longs;imiliter accipiatur alterum corpus M, eiu&longs;dem generis cum <lb/>corpore L, ip&longs;ique &longs;imile, &amp; <lb/><figure id="fig13"/><lb/>&aelig;quale, &amp; 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 pagenum="29"/>&amp; accipiatur aliquod corpus L, leuius quam aqua, ita vt cum ip&longs;i <lb/>corpori L, appendatur, corpus B, &amp; ambo &longs;imul demittantur in <expan abbr="aqu&atilde;">aquam</expan>, <lb/>&longs;int &aelig;que grauia atque aqua, neque &longs;ur&longs;um, neque deor&longs;um &longs;eran&shy;<lb/>tur, &longs;imiliter accipiatur alterum corpus M, eiu&longs;dem generis cum <lb/>corpore L, ip&longs;ique &longs;imile, &amp; <lb/><figure id="fig13"/><lb/>&aelig;quale, &amp; corpori M, appen <lb/>datur corpus A. <!-- KEEP S--></s>
  
 <s>Deinde in&shy;<lb/>teligatur aqua con&longs;i&longs;tens, &amp; <lb/>manens, eiu&longs;que &longs;uper&longs;i&shy;<lb/>cies &longs;ph&aelig;rica C D E, cuius <lb/>&longs;ph&aelig;r&aelig; centrum K, aqu&aelig; <lb/>enim con&longs;i&longs;tentis, atque <lb/>manentis &longs;uper&longs;icies &longs;ph&aelig;&shy;<lb/>rica e&longs;t, cui <gap/> &longs;ph&aelig;r&aelig; cen&shy;<lb/>trum idem <gap/>, quod <expan abbr="centr&utilde;">centrum</expan> <lb/>terr&aelig;, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib.  <s>Deinde in&shy;<lb/>teligatur aqua con&longs;i&longs;tens, &amp; <lb/>manens, eiu&longs;que &longs;uper&longs;i&shy;<lb/>cies &longs;ph&aelig;rica C D E, cuius <lb/>&longs;ph&aelig;r&aelig; centrum K, aqu&aelig; <lb/>enim con&longs;i&longs;tentis, atque <lb/>manentis &longs;uper&longs;icies &longs;ph&aelig;&shy;<lb/>rica e&longs;t, cui <gap/> &longs;ph&aelig;r&aelig; cen&shy;<lb/>trum idem <gap/>, quod <expan abbr="centr&utilde;">centrum</expan> <lb/>terr&aelig;, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib.
  
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 <s>intelligatur argentum, vt leuius auro, magnitudinem balere<emph.end type="italics"/><lb/>100, <emph type="italics"/>&amp; in linea auri &longs;ub titulo argenti, qu&aelig;ratur 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 &aelig;que 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"/>&amp; in linea auri &longs;ub titulo argenti, qu&aelig;ratur 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 &aelig;que 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><emph type="italics"/>Qu&aelig;ro denique quomodo &longs;e bab <gap/> in magnitudine aqua &amp; ar&shy;<lb/>gentum viuum. </s> <s><emph type="italics"/>Qu&aelig;ro denique quomodo &longs;e habent in magnitudine aqua &amp; ar&shy;<lb/>gentum viuum. </s>
  
 <s>quoniam aqua leu<gap/> est argento viuo, intelligatur <lb/>eius magnitudo<emph.end type="italics"/> 100, <emph type="italics"/>&amp; in linea argenti viui, &longs;ub titulo aqu&aelig;, qu&aelig;&shy;<lb/>ratur argenti viui magnitudo, &amp; reperietur<emph.end type="italics"/> 7 7/29, <emph type="italics"/>aqua igitur ad <lb/>argentum viuum &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 7 7/29. </s></p><p type="main"> <s>quoniam aqua leu<gap/> est argento viuo, intelligatur <lb/>eius magnitudo<emph.end type="italics"/> 100, <emph type="italics"/>&amp; in linea argenti viui, &longs;ub titulo aqu&aelig;, qu&aelig;&shy;<lb/>ratur argenti viui magnitudo, &amp; reperietur<emph.end type="italics"/> 7 7/29, <emph type="italics"/>aqua igitur ad <lb/>argentum viuum &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 7 7/29. </s></p><p type="main">
  
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 <s><emph type="italics"/>Ponderibus autem vtimur hac nostra tempe&longs;tate v&longs;itatis, <gap/>bram <lb/>enim diuidimus in<emph.end type="italics"/> 12, <emph type="italics"/>vncias vnciam vero in<emph.end type="italics"/> 24, <emph type="italics"/>&longs;crupula, &amp; &longs;cru&shy;<lb/>pulum in<emph.end type="italics"/> 24, <emph type="italics"/>grana. </s> <s><emph type="italics"/>Ponderibus autem vtimur hac nostra tempe&longs;tate v&longs;itatis, <gap/>bram <lb/>enim diuidimus in<emph.end type="italics"/> 12, <emph type="italics"/>vncias vnciam vero in<emph.end type="italics"/> 24, <emph type="italics"/>&longs;crupula, &amp; &longs;cru&shy;<lb/>pulum in<emph.end type="italics"/> 24, <emph type="italics"/>grana. </s>
  
 <s>Ad inueniendas igitur &longs;ph&aelig;rarum grauitates ex <lb/>data diametrorum magnitudine, b&aelig;c erit ratio.<emph.end type="italics"/></s></p><p type="main"> <s>Ad inueniendas igitur &longs;ph&aelig;rarum grauitates ex <lb/>data diametrorum magnitudine, h&aelig;c erit ratio.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Qu&aelig;ris grauitatem &longs;ph&aelig;r&aelig; plumbe&aelig;, diametrum habentis<emph.end type="italics"/> 3, <emph type="italics"/>vn&shy;<lb/>ciarum, in&longs;pice tabulam, &amp; in linea trium vnciarum, &longs;ub titulo gra&shy;<lb/>uitatis plumbe&aelig; &longs;ph&aelig;r&aelig;, deprebendes ip&longs;am &longs;ph&aelig;ram grauit&aelig;tem ba&shy;<lb/>bere lib.<emph.end type="italics"/> 7, <emph type="italics"/>vnc.<emph.end type="italics"/> 4, <emph type="italics"/>&longs;eru.<emph.end type="italics"/> 13, <emph type="italics"/>gran.<emph.end type="italics"/> 22 29/57. </s></p><p type="main"> <s><emph type="italics"/>Qu&aelig;ris grauitatem &longs;ph&aelig;r&aelig; plumbe&aelig;, diametrum habentis<emph.end type="italics"/> 3, <emph type="italics"/>vn&shy;<lb/>ciarum, in&longs;pice tabulam, &amp; in linea trium vnciarum, &longs;ub titulo gra&shy;<lb/>uitatis plumbe&aelig; &longs;ph&aelig;r&aelig;, deprebendes ip&longs;am &longs;ph&aelig;ram grauit&aelig;tem ba&shy;<lb/>bere lib.<emph.end type="italics"/> 7, <emph type="italics"/>vnc.<emph.end type="italics"/> 4, <emph type="italics"/>&longs;eru.<emph.end type="italics"/> 13, <emph type="italics"/>gran.<emph.end type="italics"/> 22 29/57. </s></p><p type="main">
  
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 <s>Qua ratione hanc Tabulam compo&longs;uimus. </s></p><p type="main"> <s>Qua ratione hanc Tabulam compo&longs;uimus. </s></p><p type="main">
  
 <s><emph type="italics"/>Primum inueniendam curauimus grauitatem alicuius &longs;ph&aelig;r&aelig;, da&shy;<lb/>tem habentis diametrum, &amp; ad hoc faciendum, oportebat aliquam <lb/>&longs;pb&aelig;ram efficere, &longs;ed quoniam ad illam efficiendam, exactam buman<gap/><lb/>diligentia non &longs;ufficit, fieri curauimus Cylindrum ex &longs;tanno, altitu&shy;<lb/>dine aqualem diametro circuli, qui ba&longs;is e&longs;t ip&longs;ius Cylindri, is enim <lb/>torno &longs;ieri pote&longs;t multo exactior quam &longs;pb&aelig;ra, &amp; facilius. </s> <s><emph type="italics"/>Primum inueniendam curauimus grauitatem alicuius &longs;ph&aelig;r&aelig;, da&shy;<lb/>tem habentis diametrum, &amp; ad hoc faciendum, oportebat aliquam <lb/>&longs;pb&aelig;ram efficere, &longs;ed quoniam ad illam efficiendam, exactam buman<gap/><lb/>diligentia non &longs;ufficit, fieri curauimus Cylindrum ex &longs;tanno, altitu&shy;<lb/>dine aqualem diametro circuli, qui ba&longs;is e&longs;t ip&longs;ius Cylindri, is enim <lb/>torno fieri pote&longs;t multo exactior quam &longs;ph&aelig;ra, &amp; facilius. </s>
  
 <s>huius au&shy;<lb/>tem Cylindri altitudo, vel diameter ip&longs;ius ba&longs;is, erat duarum vncia&shy;<lb/>rum pr&aelig;dicti pedis Romani, grauitas vero duarum librarum, cum <lb/>vna vncia, &amp; octo &longs;crupulis, &longs;iue vt hoc pondus ad grana reducamus, <lb/>Cylindri grauitas erat Gran. <!-- REMOVE S-->14592. abstulimns ab hac Cylindri <lb/>grauitate partem tertiam. </s> <s>huius au&shy;<lb/>tem Cylindri altitudo, vel diameter ip&longs;ius ba&longs;is, erat duarum vncia&shy;<lb/>rum pr&aelig;dicti pedis Romani, grauitas vero duarum librarum, cum <lb/>vna vncia, &amp; octo &longs;crupulis, &longs;iue vt hoc pondus ad grana reducamus, <lb/>Cylindri grauitas erat Gran. <!-- REMOVE S-->14592. abstulimns ab hac Cylindri <lb/>grauitate partem tertiam. </s>
  
  
  
 <s>id est<emph.end type="italics"/> 4864, <emph type="italics"/>reliquum, quod est<emph.end type="italics"/> 9728. <emph type="italics"/>&longs;er&shy;<lb/>uauimus, pro grauitate &longs;ph&aelig;r&aelig;, diametrum habentis &aelig;qualem altitu&shy;<lb/>dini Cylindri, o&longs;ten&longs;um enim est ab Arcbimede propo&longs;.<emph.end type="italics"/> 32, <emph type="italics"/>lib.<emph.end type="italics"/> 1, <emph type="italics"/>de <lb/>&longs;pb&aelig;ra, &amp; Cylindro, Cylindrum, qui ba&longs;im habeat maximo in &longs;pb&aelig;ra <lb/>circulo equalem, &amp; altitudinem &aelig;qualem diametro &longs;ph&aelig;r&aelig;, ad ip&longs;am <lb/>&longs;pb&aelig;ram &longs;e&longs;quialterum e&longs;&longs;e; itaque grauitatem &longs;ph&aelig;r&aelig;, diametrum <lb/>habentis duarum vnciarum inuenimus e&longs;&longs;e gran.<emph.end type="italics"/> 9728. </s></p><p type="main"> <s>id est<emph.end type="italics"/> 4864, <emph type="italics"/>reliquum, quod est<emph.end type="italics"/> 9728. <emph type="italics"/>&longs;er&shy;<lb/>uauimus, pro grauitate &longs;ph&aelig;r&aelig;, diametrum habentis &aelig;qualem altitu&shy;<lb/>dini Cylindri, o&longs;ten&longs;um enim est ab Arcbimede propo&longs;.<emph.end type="italics"/> 32, <emph type="italics"/>lib.<emph.end type="italics"/> 1, <emph type="italics"/>de <lb/>&longs;ph&aelig;ra, &amp; Cylindro, Cylindrum, qui ba&longs;im habeat maximo in &longs;ph&aelig;ra <lb/>circulo equalem, &amp; altitudinem &aelig;qualem diametro &longs;ph&aelig;r&aelig;, ad ip&longs;am <lb/>&longs;pb&aelig;ram &longs;e&longs;quialterum e&longs;&longs;e; itaque grauitatem &longs;ph&aelig;r&aelig;, diametrum <lb/>habentis duarum vnciarum inuenimus e&longs;&longs;e gran.<emph.end type="italics"/> 9728. </s></p><p type="main">
  
 <s><emph type="italics"/>Inuenta igitur grauitate &longs;ph&aelig;r&aelig;, cuius diameter est duarum vn&shy;<lb/>ciarum, facile inuenientur reliquarum <expan abbr="&longs;pb&aelig;rar&utilde;">&longs;ph&aelig;rarum</expan> grauitates, &longs;i enim <lb/>inuenienda &longs;it grauitas &longs;ph&aelig;r&aelig; stannea habentis diametrum<emph.end type="italics"/> 1/4. <emph type="italics"/>vn&shy;<lb/>ci&aelig;, fiat vt cubus ex<emph.end type="italics"/> 2, <emph type="italics"/>ad cubum ex<emph.end type="italics"/> 1/4, <emph type="italics"/>hoc est vt<emph.end type="italics"/> 512, <emph type="italics"/>ad 1, ita<emph.end type="italics"/> 9728, <lb/><emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 19, <emph type="italics"/>&longs;ph&aelig;r&aelig; igitur cuius diameter e&longs;t<emph.end type="italics"/> 1/4, <lb/><emph type="italics"/>vnci&aelig;, grauitas erit gran. <!-- REMOVE S-->19, osten&longs;um enim est prop.  <s><emph type="italics"/>Inuenta igitur grauitate &longs;ph&aelig;r&aelig;, cuius diameter est duarum vn&shy;<lb/>ciarum, facile inuenientur reliquarum <expan abbr="&longs;pb&aelig;rar&utilde;">&longs;ph&aelig;rarum</expan> grauitates, &longs;i enim <lb/>inuenienda &longs;it grauitas &longs;ph&aelig;r&aelig; stannea habentis diametrum<emph.end type="italics"/> 1/4. <emph type="italics"/>vn&shy;<lb/>ci&aelig;, fiat vt cubus ex<emph.end type="italics"/> 2, <emph type="italics"/>ad cubum ex<emph.end type="italics"/> 1/4, <emph type="italics"/>hoc est vt<emph.end type="italics"/> 512, <emph type="italics"/>ad 1, ita<emph.end type="italics"/> 9728, <lb/><emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 19, <emph type="italics"/>&longs;ph&aelig;r&aelig; igitur cuius diameter e&longs;t<emph.end type="italics"/> 1/4, <lb/><emph type="italics"/>vnci&aelig;, grauitas erit gran. <!-- REMOVE S-->19, osten&longs;um enim est prop.
  
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 <s><emph type="italics"/>Sit aliquod corpus aureum, exempli gratia<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum, quod <lb/>expurgatum &amp; ad aurum purum reductum, ami&longs;erit ex pri&longs;tina <lb/>grauitate nempe ex<emph.end type="italics"/> 24, <emph type="italics"/>vncys, quatuor vncias, ita vt reman&longs;erint <lb/>tantum<emph.end type="italics"/> 20, <emph type="italics"/>vnci&aelig; auri puri, reliquum vero vel euanuerit in fumum, <lb/>vel fuerit alterius metalli. </s> <s><emph type="italics"/>Sit aliquod corpus aureum, exempli gratia<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum, quod <lb/>expurgatum &amp; ad aurum purum reductum, ami&longs;erit ex pri&longs;tina <lb/>grauitate nempe ex<emph.end type="italics"/> 24, <emph type="italics"/>vncys, quatuor vncias, ita vt reman&longs;erint <lb/>tantum<emph.end type="italics"/> 20, <emph type="italics"/>vnci&aelig; auri puri, reliquum vero vel euanuerit in fumum, <lb/>vel fuerit alterius metalli. </s>
  
 <s>Totum igitur illud corpus aureum ab <lb/>initio propo&longs;itum, &longs;i adbuc intelligatur tale quale fuit ante expurga&shy;<lb/>tionem, appellabitur<emph.end type="italics"/> 20. <emph type="italics"/>partium, &longs;eu, (vt vulgo dicitur) di<emph.end type="italics"/> 20. <emph type="italics"/>ca&shy;<lb/>ratti. </s> <s>Totum igitur illud corpus aureum ab <lb/>initio propo&longs;itum, &longs;i adhuc intelligatur tale quale fuit ante expurga&shy;<lb/>tionem, appellabitur<emph.end type="italics"/> 20. <emph type="italics"/>partium, &longs;eu, (vt vulgo dicitur) di<emph.end type="italics"/> 20. <emph type="italics"/>ca&shy;<lb/>ratti. </s>
  
 <s>eo quod tota illa ma&lt;32&gt;a mista,<emph.end type="italics"/> 20. <emph type="italics"/>tantum vncias auri puri con&shy;<lb/>tinuerit. </s> <s>eo quod tota illa ma&lt;32&gt;a mista,<emph.end type="italics"/> 20. <emph type="italics"/>tantum vncias auri puri con&shy;<lb/>tinuerit. </s>
  
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 <s>Non enim purificant totum corpus propo&longs;itum, &longs;ed ali&shy;<lb/>quam eius particulam etiam perexiguam, quam &longs;olam ad aurum pu&shy;<lb/>rum reducunt. </s> <s>Non enim purificant totum corpus propo&longs;itum, &longs;ed ali&shy;<lb/>quam eius particulam etiam perexiguam, quam &longs;olam ad aurum pu&shy;<lb/>rum reducunt. </s>
  
 <s>hac enim reducta, non &longs;olum recte definiunt cuius <lb/>fuerit qualitatis particula illa purificata ante purificationem; ve&shy;<lb/>rum etiam cuius fuerit qualitatis, &amp; quot partium fuerit illud cor&shy;<lb/>pus, &agrave; quo eadem particula detracta fuit, &amp; illud, quod adbuc &longs;u&shy;<lb/>pere&longs;t, diminutum &longs;cilicet illa parte purificata, vt in eodem exemplo <lb/>propo&longs;ito, corporis aurei<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum apparet. </s> <s>hac enim reducta, non &longs;olum recte definiunt cuius <lb/>fuerit qualitatis particula illa purificata ante purificationem; ve&shy;<lb/>rum etiam cuius fuerit qualitatis, &amp; quot partium fuerit illud cor&shy;<lb/>pus, &agrave; quo eadem particula detracta fuit, &amp; illud, quod adhuc &longs;u&shy;<lb/>pere&longs;t, diminutum &longs;cilicet illa parte purificata, vt in eodem exemplo <lb/>propo&longs;ito, corporis aurei<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum apparet. </s>
  
 <s>Eius enim quali&shy;<lb/>tatem &longs;i forte aurifices inuestigare velint, detrabent ex eo particu&shy;<lb/>lam, verbi gratia, vnius vnci&aelig;, vel qued idem est particulam<emph.end type="italics"/> 24. <pb pagenum="61"/><emph type="italics"/>&longs;<gap/>puforam; &amp; banc particulam exeoquent ad qualitatem o&longs;que <lb/>c<gap/>ripuri. </s> <s>Eius enim quali&shy;<lb/>tatem &longs;i forte aurifices inuestigare velint, detrabent ex eo particu&shy;<lb/>lam, verbi gratia, vnius vnci&aelig;, vel qued idem est particulam<emph.end type="italics"/> 24. <pb pagenum="61"/><emph type="italics"/>&longs;<gap/>puforam; &amp; banc particulam exeoquent ad qualitatem o&longs;que <lb/>c<gap/>ripuri. </s>
  
 <s>Bt &longs;t quidem inuenerint, ex priori grauitate<emph.end type="italics"/> 24. <emph type="italics"/>&longs;or<gap/><lb/>pulorum, deperi&longs;&longs;e nibil: pronunciabunt aurum sllud, hoc est, non <lb/>&longs;olum partieulam illam excoctam, &longs;ed etiam illud d quo fuit dotr<gap/><lb/>sta, nec non &amp; illud quod reman&longs;it post &longs;ubiractionim e&longs;&longs;e vel &longs;ui&longs;<gap/><lb/>&longs;e aurum prima qualitatis &longs;eu<emph.end type="italics"/> 24, <emph type="italics"/>partiam; vel quod idem est au&shy;<lb/>tum purum. </s> <s>Bt &longs;t quidem inuenerint, ex priori grauitate<emph.end type="italics"/> 24. <emph type="italics"/>&longs;or<gap/><lb/>pulorum, deperi&longs;&longs;e nihil: pronunciabunt aurum sllud, hoc est, non <lb/>&longs;olum partieulam illam excoctam, &longs;ed etiam illud d quo fuit dotr<gap/><lb/>sta, nec non &amp; illud quod reman&longs;it post &longs;ubiractionim e&longs;&longs;e vel &longs;ui&longs;<gap/><lb/>&longs;e aurum prima qualitatis &longs;eu<emph.end type="italics"/> 24, <emph type="italics"/>partiam; vel quod idem est au&shy;<lb/>tum purum. </s>
  
 <s>Sivero deprebendirine gra<gap/>m diminuta<gap/>, ver&shy;<lb/>bi gratia, n<gap/>e e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>&longs;crupulorum, qu&aelig; ante def&aelig;cationem fuit<emph.end type="italics"/> 24. <lb/><emph type="italics"/>dicturi &longs;unt aurum propo&longs;itam<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum fui&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium &amp; <lb/>illud quod teman&longs;it e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium &amp; d<gap/>nique particul<gap/> expur&shy;<lb/>gatam nunc quidem e&longs;&longs;e aurum purum, fui&longs;&longs;e vero particulam auri<emph.end type="italics"/><lb/>20. <emph type="italics"/>partium.<emph.end type="italics"/></s></p><p type="main"> <s>Sivero deprebendirine gra<gap/>m diminuta<gap/>, ver&shy;<lb/>bi gratia, n<gap/>e e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>&longs;crupulorum, qu&aelig; ante def&aelig;cationem fuit<emph.end type="italics"/> 24. <lb/><emph type="italics"/>dicturi &longs;unt aurum propo&longs;itam<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum fui&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium &amp; <lb/>illud quod teman&longs;it e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium &amp; d<gap/>nique particul<gap/> expur&shy;<lb/>gatam nunc quidem e&longs;&longs;e aurum purum, fui&longs;&longs;e vero particulam auri<emph.end type="italics"/><lb/>20. <emph type="italics"/>partium.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><emph type="italics"/>Deinde inueniatur grauitas aqu&aelig; magnitudine &aelig;qualis aur<gap/><lb/>puro<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum: hoc e&longs;t vt 19, ad 1, ita fiat<emph.end type="italics"/> 24, <emph type="italics"/>ad alium, nempe ad <lb/>vnciam<emph.end type="italics"/> 1 9/19, <emph type="italics"/>hic enim numerus erit grauitas illius aqu&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Deinde inueniatur grauitas aqu&aelig; magnitudine &aelig;qualis aur<gap/><lb/>puro<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum: hoc e&longs;t vt 19, ad 1, ita fiat<emph.end type="italics"/> 24, <emph type="italics"/>ad alium, nempe ad <lb/>vnciam<emph.end type="italics"/> 1 9/19, <emph type="italics"/>hic enim numerus erit grauitas illius aqu&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>Fiat denique ot<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita <gap/>ur&longs;ue<emph.end type="italics"/> 24, <emph type="italics"/>vnti&aelig;, ad alium, numi&shy;<lb/>rus enim quartus, nempe vnc.<emph.end type="italics"/> 2<gap/> <emph type="italics"/>erit grauitas aqu&aelig;, magnitu&shy;<lb/><gap/>ine &aelig;qualis corport mi&longs;to ex argento &amp; &aelig;re, euius grauitas est in <lb/>&aelig;r&egrave; vnc.<emph.end type="italics"/> 24, <emph type="italics"/>corp<gap/>s enim ita mi&longs;tum, ad corpus aqueum eiu&longs;dem ma&shy;<lb/><gap/> nitudin<gap/> rationem babet in grauitate vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29. </s></p><p type="main"> <s><emph type="italics"/>Fiat denique ot<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita <gap/>ur&longs;ue<emph.end type="italics"/> 24, <emph type="italics"/>vnti&aelig;, ad alium, numi&shy;<lb/>rus enim quartus, nempe vnc.<emph.end type="italics"/> 2<gap/> <emph type="italics"/>erit grauitas aqu&aelig;, magnitu&shy;<lb/><gap/>ine &aelig;qualis corport mi&longs;to ex argento &amp; &aelig;re, euius grauitas est in <lb/>&aelig;r&egrave; vnc.<emph.end type="italics"/> 24, <emph type="italics"/>corp<gap/>s enim ita mi&longs;tum, ad corpus aqueum eiu&longs;dem ma&shy;<lb/><gap/> nitudin<gap/> rationem habet in grauitate vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29. </s></p><p type="main">
  
 <s><emph type="italics"/>Atque ita habebuntur tres gravitates <gap/> aqu&aelig; quantitatum, <lb/>quarum prima &aelig;quatur auro puro<emph.end type="italics"/> 24, <emph type="italics"/>vuctarum, &longs;<gap/>unda ma&longs;&longs;<gap/><lb/>propo&longs;it&aelig;<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum, &amp; reliqua corpori mi&longs;to ex argento &amp; <gap/><lb/>&longs;imiliter<emph.end type="italics"/> 24, <emph type="italics"/><gap/>vnciarum qu&aelig; quidem tres grauitates in numeris di&shy;<lb/>&longs;ponantur co ordine, quo &longs;equitur.<emph.end type="italics"/></s></p><p type="table"> <s><emph type="italics"/>Atque ita habebuntur tres gravitates <gap/> aqu&aelig; quantitatum, <lb/>quarum prima &aelig;quatur auro puro<emph.end type="italics"/> 24, <emph type="italics"/>vuctarum, &longs;<gap/>unda ma&longs;&longs;<gap/><lb/>propo&longs;it&aelig;<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum, &amp; reliqua corpori mi&longs;to ex argento &amp; <gap/><lb/>&longs;imiliter<emph.end type="italics"/> 24, <emph type="italics"/><gap/>vnciarum qu&aelig; quidem tres grauitates in numeris di&shy;<lb/>&longs;ponantur eo ordine, quo &longs;equitur.<emph.end type="italics"/></s></p><p type="table">
  
 <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main"> <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main">
  
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 <s><emph type="italics"/>Et quia inpropo&longs;ito exemplo b&aelig; partes, nempe vnc.<emph.end type="italics"/> 20, <emph type="italics"/>&longs;unt par&shy;<lb/>tes vige&longs;<gap/> quart&aelig;<emph.end type="italics"/> 24, <emph type="italics"/>onciarum, qu&aelig; constituunt grauitatem to&shy;<lb/>tius ma&longs;&longs;&aelig;. </s> <s><emph type="italics"/>Et quia inpropo&longs;ito exemplo b&aelig; partes, nempe vnc.<emph.end type="italics"/> 20, <emph type="italics"/>&longs;unt par&shy;<lb/>tes vige&longs;<gap/> quart&aelig;<emph.end type="italics"/> 24, <emph type="italics"/>onciarum, qu&aelig; constituunt grauitatem to&shy;<lb/>tius ma&longs;&longs;&aelig;. </s>
  
 <s>binc fit quod e&aelig;dem<emph.end type="italics"/> 20. <emph type="italics"/>vnc. </s> <s>hinc fit quod e&aelig;dem<emph.end type="italics"/> 20. <emph type="italics"/>vnc. </s>
  
 <s>immediate denominent au&shy;<lb/>rum propo&longs;itum e&lt;32&gt;e<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s> <s>immediate denominent au&shy;<lb/>rum propo&longs;itum e&lt;32&gt;e<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s>
  
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 <s>hoc e&longs;t primo fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 1, <emph type="italics"/>ita<emph.end type="italics"/><lb/>5301, <emph type="italics"/>ad<emph.end type="italics"/> 279, <emph type="italics"/>hic enim numerus erit grauitas aqu&aelig; magnitudinem <lb/>habentis &aelig;qualem auro puro, <gap/>uius grauitas e&longs;t<emph.end type="italics"/> 5301. <emph type="italics"/>Deinde fia<gap/><lb/>vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita rur&longs;um grauitas<emph.end type="italics"/> 5301, <emph type="italics"/>ad aliam, hac enim ratione <lb/>producetur nu<gap/>erus<emph.end type="italics"/> 551, <emph type="italics"/>debitus grauitati aqu&aelig;, magnitudine <lb/>aqualis corpori mi&longs;to ex argento &amp; &aelig;re grauitatem habenti eandem <lb/>cum eadem ma&lt;32&gt;a propo&longs;ita. </s> <s>hoc e&longs;t primo fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 1, <emph type="italics"/>ita<emph.end type="italics"/><lb/>5301, <emph type="italics"/>ad<emph.end type="italics"/> 279, <emph type="italics"/>hic enim numerus erit grauitas aqu&aelig; magnitudinem <lb/>habentis &aelig;qualem auro puro, <gap/>uius grauitas e&longs;t<emph.end type="italics"/> 5301. <emph type="italics"/>Deinde fia<gap/><lb/>vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita rur&longs;um grauitas<emph.end type="italics"/> 5301, <emph type="italics"/>ad aliam, hac enim ratione <lb/>producetur nu<gap/>erus<emph.end type="italics"/> 551, <emph type="italics"/>debitus grauitati aqu&aelig;, magnitudine <lb/>aqualis corpori mi&longs;to ex argento &amp; &aelig;re grauitatem habenti eandem <lb/>cum eadem ma&lt;32&gt;a propo&longs;ita. </s>
  
 <s>Atque ba tre<gap/> grauitates aqu&aelig; &longs;criban&shy;<lb/>tur co ordine quo &longs;upra; inuenti&longs;que differentys inter primam &amp;<emph.end type="italics"/></s></p><p type="margin"> <s>Atque ba tre<gap/> grauitates aqu&aelig; &longs;criban&shy;<lb/>tur eo ordine quo &longs;upra; inuenti&longs;que differentys inter primam &amp;<emph.end type="italics"/></s></p><p type="margin">
  
 <s><margin.target id="note56"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="table"> <s><margin.target id="note56"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="table">
  
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 <s>Quartus autem terminus<emph.end type="italics"/> 4196 25/116, <emph type="italics"/>indicabit grauitatcm <lb/>auri puri, quod est in ma&longs;&longs;a propo&longs;ita, eam tamen indicabit in par&shy;<lb/>tibus, qualibus tota ma&longs;&longs;a constat<emph.end type="italics"/> 5301, <emph type="italics"/>qu&aelig; quidem grauitas vt <lb/>auri qualitatem indicet, reuocanda erit ad partes qualium tot&aelig; <lb/>ma&longs;&longs;a propo&longs;ita est<emph.end type="italics"/> 24. <emph type="italics"/>&longs;ienim fiat vt<emph.end type="italics"/> 5301, <emph type="italics"/>ad<emph.end type="italics"/> 4196<gap/>, <emph type="italics"/>ita<emph.end type="italics"/> 24, <lb/><emph type="italics"/>ad<emph.end type="italics"/> 19, <emph type="italics"/>aurum propo&longs;it&aelig; ma&longs;&longs;&aelig; appellabitur partium<emph.end type="italics"/> 19. </s></p><p type="main"> <s>Quartus autem terminus<emph.end type="italics"/> 4196 25/116, <emph type="italics"/>indicabit grauitatcm <lb/>auri puri, quod est in ma&longs;&longs;a propo&longs;ita, eam tamen indicabit in par&shy;<lb/>tibus, qualibus tota ma&longs;&longs;a constat<emph.end type="italics"/> 5301, <emph type="italics"/>qu&aelig; quidem grauitas vt <lb/>auri qualitatem indicet, reuocanda erit ad partes qualium tot&aelig; <lb/>ma&longs;&longs;a propo&longs;ita est<emph.end type="italics"/> 24. <emph type="italics"/>&longs;ienim fiat vt<emph.end type="italics"/> 5301, <emph type="italics"/>ad<emph.end type="italics"/> 4196<gap/>, <emph type="italics"/>ita<emph.end type="italics"/> 24, <lb/><emph type="italics"/>ad<emph.end type="italics"/> 19, <emph type="italics"/>aurum propo&longs;it&aelig; ma&longs;&longs;&aelig; appellabitur partium<emph.end type="italics"/> 19. </s></p><p type="main">
  
 <s><emph type="italics"/>Denique &longs;i quis hunc modum conferat cum illo, quem &longs;upra tradi&shy;<lb/>dimus, cum argentum explorauimus, quod miftum in aurea corona <lb/>credebatur; is liquido intelliget hic nibil aliud acce&longs;&longs;i&lt;32&gt;e, ni&longs;i quod <lb/>loco argenti, a&longs;&longs;umptum &longs;it corpus ex argento &amp; &aelig;re mistum, eo <lb/>quod h&aelig;c duo metalla tantum in alligationibus auri &longs;oleant adbibe&shy;<lb/>ri, vt diximus. </s> <s><emph type="italics"/>Denique &longs;i quis hunc modum conferat cum illo, quem &longs;upra tradi&shy;<lb/>dimus, cum argentum explorauimus, quod miftum in aurea corona <lb/>credebatur; is liquido intelliget hic nihil aliud acce&longs;&longs;i&lt;32&gt;e, ni&longs;i quod <lb/>loco argenti, a&longs;&longs;umptum &longs;it corpus ex argento &amp; &aelig;re mistum, eo <lb/>quod h&aelig;c duo metalla tantum in alligationibus auri &longs;oleant adbibe&shy;<lb/>ri, vt diximus. </s>
  
 <s>Quod &longs;i con&longs;taret plura alia a&longs;&longs;umpta e&longs;&longs;e, etiam in <lb/>quauis alia ratione, facile erit cuiuis ad &longs;imilitudinem huius, for&shy;<lb/>mare alium modum, &longs;ed nos, ne longiores &longs;imus, ad v&longs;um &longs;equentis <lb/>tabul&aelig; nos conferamus, qua illis con&longs;ultum volumus qui minus in <lb/>pr&aelig;ceptis Aritbmeticis &longs;unt exercitati, velillis, qui alias ob cau&longs;as <lb/>tabulis vti malunt, quam calculis.<emph.end type="italics"/></s></p><p type="main"> <s>Quod &longs;i con&longs;taret plura alia a&longs;&longs;umpta e&longs;&longs;e, etiam in <lb/>quauis alia ratione, facile erit cuiuis ad &longs;imilitudinem huius, for&shy;<lb/>mare alium modum, &longs;ed nos, ne longiores &longs;imus, ad v&longs;um &longs;equentis <lb/>tabul&aelig; nos conferamus, qua illis con&longs;ultum volumus qui minus in <lb/>pr&aelig;ceptis Aritbmeticis &longs;unt exercitati, velillis, qui alias ob cau&longs;as <lb/>tabulis vti malunt, quam calculis.<emph.end type="italics"/></s></p><p type="main">
  
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 <s><emph type="italics"/>Porro in area tabul&aelig; &longs;ub titulo grauitatis auri in aqua po&longs;ita est <lb/>grauitas auri cuiuslibet qualitatis quam obtinet in aqua, qu&aelig; qua <lb/>ratione inueniatur, dicetur inferius vbi agetur de compo&longs;itione <lb/>eiu&longs;dem tabul&aelig;.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Porro in area tabul&aelig; &longs;ub titulo grauitatis auri in aqua po&longs;ita est <lb/>grauitas auri cuiuslibet qualitatis quam obtinet in aqua, qu&aelig; qua <lb/>ratione inueniatur, dicetur inferius vbi agetur de compo&longs;itione <lb/>eiu&longs;dem tabul&aelig;.<emph.end type="italics"/></s></p><p type="main">
  
 <s><emph type="italics"/>V&longs;us eius &longs;unt duo, quorum alterum titulus indicat, nimirum vt <lb/>tabul&aelig; beneficio reperiatur ex grauitate auri quam babet in aere &amp; <lb/>aqua, eius qualitas. </s> <s><emph type="italics"/>V&longs;us eius &longs;unt duo, quorum alterum titulus indicat, nimirum vt <lb/>tabul&aelig; beneficio reperiatur ex grauitate auri quam habet in aere &amp; <lb/>aqua, eius qualitas. </s>
  
 <s>Alter vero est vt cogno&longs;catur grauitas in aqua, <lb/>quando vn&agrave; cum grauitate quam aliquod aurum habet in aere da&shy;<lb/>tur ip&longs;ius qualitas. </s> <s>Alter vero est vt cogno&longs;catur grauitas in aqua, <lb/>quando vn&agrave; cum grauitate quam aliquod aurum habet in aere da&shy;<lb/>tur ip&longs;ius qualitas. </s>
  
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 <s><emph type="italics"/>Denique &longs;i proponatur aurum non vnius libr&aelig; &longs;ed vel plurium, <lb/>vel &longs;olum aliquot vnciarum. </s> <s><emph type="italics"/>Denique &longs;i proponatur aurum non vnius libr&aelig; &longs;ed vel plurium, <lb/>vel &longs;olum aliquot vnciarum. </s>
  
 <s>Reducenda erit eius grauitas quam <lb/>babet maqua, ad grauitatem quam haberet &longs;i e&lt;32&gt;et vnius libr&aelig;, id <lb/>quod ab&longs;oluetur per proportionis ratiocinationem, &longs;i pro termino <lb/>primo ponatur vera grauitas auri propo&longs;iti, pro &longs;ecundo, e iu&longs;dem <lb/>grauitas in aqua, &amp; pro tertio lib.  <s>Reducenda erit eius grauitas quam <lb/>habet maqua, ad grauitatem quam haberet &longs;i e&lt;32&gt;et vnius libr&aelig;, id <lb/>quod ab&longs;oluetur per proportionis ratiocinationem, &longs;i pro termino <lb/>primo ponatur vera grauitas auri propo&longs;iti, pro &longs;ecundo, e iu&longs;dem <lb/>grauitas in aqua, &amp; pro tertio lib.
  
 1, quartus enim terminus indica&shy;<lb/>bit grauitatem in aqua re&longs;pondentem vni libr&aelig; auri propo&longs;iti. </s> 1, quartus enim terminus indica&shy;<lb/>bit grauitatem in aqua re&longs;pondentem vni libr&aelig; auri propo&longs;iti. </s>
  
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 <s><emph type="italics"/>Exemplum huius ca&longs;us hic non affero, quod per &longs;e res &longs;it clara. </s> <s><emph type="italics"/>Exemplum huius ca&longs;us hic non affero, quod per &longs;e res &longs;it clara. </s>
  
 <s><lb/>Sed illud tantum obiter aduertere placet, quod videtur pertinere <lb/>ad commodiorem v&longs;um tabul&aelig;, videlicet vt ys in ca&longs;ibus in quibus <lb/>nece&lt;32&gt;arius cst calculus, fractiones granorum ommittantur quando <lb/>minus valent quam<emph.end type="italics"/> 1/2, <emph type="italics"/>&amp; quando valent plus, eorum loco, addatur <lb/>vnum granum reliquis granis, &amp; &longs;i quando accidat binc procreari <lb/>grana<emph.end type="italics"/> 24. <emph type="italics"/>tunc etiam grana ommittantur addita prius vnitate ad <lb/>&longs;crupula in tabula inuenta. </s> <s><lb/>Sed illud tantum obiter aduertere placet, quod videtur pertinere <lb/>ad commodiorem v&longs;um tabul&aelig;, videlicet vt ys in ca&longs;ibus in quibus <lb/>nece&lt;32&gt;arius cst calculus, fractiones granorum ommittantur quando <lb/>minus valent quam<emph.end type="italics"/> 1/2, <emph type="italics"/>&amp; quando valent plus, eorum loco, addatur <lb/>vnum granum reliquis granis, &amp; &longs;i quando accidat hinc procreari <lb/>grana<emph.end type="italics"/> 24. <emph type="italics"/>tunc etiam grana ommittantur addita prius vnitate ad <lb/>&longs;crupula in tabula inuenta. </s>
  
 <s>hac enim ratione calculus erit expedi&shy;<lb/>tior &amp; error qui hinc oborietur erit in&longs;en&longs;ibilis.<emph.end type="italics"/></s></p><pb pagenum="70"/><p type="head"> <s>hac enim ratione calculus erit expedi&shy;<lb/>tior &amp; error qui hinc oborietur erit in&longs;en&longs;ibilis.<emph.end type="italics"/></s></p><pb pagenum="70"/><p type="head">
  
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 <s><emph type="italics"/>Denique pagina<emph.end type="italics"/> 38. <emph type="italics"/>&amp;<emph.end type="italics"/> 39. <emph type="italics"/>tabularum prapo&longs;terus e&longs;t ordo. </s> <s><emph type="italics"/>Denique pagina<emph.end type="italics"/> 38. <emph type="italics"/>&amp;<emph.end type="italics"/> 39. <emph type="italics"/>tabularum prapo&longs;terus e&longs;t ordo. </s>
  
 <s>ex quo tamen nibil sr&shy;<lb/>reris &longs;equitur &longs;i tituli recte accipiantur.<emph.end type="italics"/></s></p>                     </chap>                </body>                <back/>        </text></archimedes> <s>ex quo tamen nihil sr&shy;<lb/>reris &longs;equitur &longs;i tituli recte accipiantur.<emph.end type="italics"/></s></p>                     </chap>                </body>                <back/>        </text></archimedes>

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