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Colored diff for /texts/archimedes/xml/gheta_promo_029_la_1603.xml between version 1.1 and 1.2

version 1.1, 2003/09/26 15:37:38

version 1.2, 2003/11/11 18:49:36

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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<lb/>phinum deductus &longs;um. </s>

<s>I&longs;qs me tantus Præ&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 Præ&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 & tu Lactor optime amico ac be<lb/>uigno auimo laborem bunc, quem à me tali<gap/><lb/>&longs;umma benignitas expre&longs;sit. </s>

<s>Aecipeigitur & tu Lactor optime amico ac be<lb/>uigno auimo laborem hunc, quem à 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;<lb/>medi enim comparatione Archimides mixtionem argemi <lb/>in aure deprebeudit, & furtum Auri&longs;itis in corona aurea <lb/>patefecit. </s>

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<s><margin.target id="note10"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

<s><margin.target id="note11"/>2. & 3. <lb/><emph type="italics"/>buius.<emph.end type="italics"/></s>

<s><margin.target id="note11"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

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<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>grauitatis, & vult &longs;cire quanta erit grauitas liqui<lb/>di, magnitudinem habentis propo&longs;ito Corpori &longs;olido æ<lb/>qualem. </s>

<s><emph type="italics"/>Sit primum propo&longs;itum aliquod corpus plumbeum A, euius graui<lb/>tas &longs;it<emph.end type="italics"/> 23. <emph type="italics"/>& oporteat &longs;cire quanta erit grauitas aquæ magnitudinem <lb/>habentis æqualem propo&longs;ito plumbo A, ponderetur plumbum A, in <lb/>aqua (modum quo ponderanda &longs;int corpora &longs;olida in aqua, inferius <lb/>apponemus) & habeat grauitatem<emph.end type="italics"/> 21. <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 23. <pb pagenum="9"/><emph type="italics"/>juperat numerum<emph.end type="italics"/> 21, <emph type="italics"/>numero 2, erit grauitàs aquæ magnitudinem <lb/>babentis æqualem plumbo A, 2.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit primum propo&longs;itum aliquod corpus plumbeum A, euius graui<lb/>tas &longs;it<emph.end type="italics"/> 23. <emph type="italics"/>& oporteat &longs;cire quanta erit grauitas aquæ magnitudinem <lb/>habentis æqualem propo&longs;ito plumbo A, ponderetur plumbum A, in <lb/>aqua (modum quo ponderanda &longs;int corpora &longs;olida in aqua, inferius <lb/>apponemus) & habeat grauitatem<emph.end type="italics"/> 21. <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 23. <pb pagenum="9"/><emph type="italics"/>juperat numerum<emph.end type="italics"/> 21, <emph type="italics"/>numero 2, erit grauitàs aquæ magnitudinem <lb/>habentis æqualem plumbo A, 2.<emph.end type="italics"/></s>

<s>Eadem via omnium liquidorum inuenitur grauitas, quan<lb/>do nimirum corpus &longs;olidum &longs;it grauius liquido, cuius liquidi <lb/>quærenda e&longs;t grauitas, hoc e&longs;t quando corpus &longs;olidum demi&longs;<lb/>&longs;um in liquidum feratur deor&longs;um. </s>

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<s>Propo&longs;itis duobus corporibus magnitudine æquali<lb/>bus, vno &longs;olido, altero liquido, data corporis li<lb/>quidi grauitate, grauitatem &longs;olidi inuenire. </s>

<s>SINT duo propo&longs;ita corpora <lb/>magnitudine æqualia, A, quidem &longs;o<lb/><figure id="fig8"/><lb/>lidum, B, vero liquidum, &longs;it autem li<lb/>quidi B, data grauitas F, & oporteat <lb/>inuenire grauitatem &longs;olidi A, accipia <lb/>tur aliquod corpus &longs;olidum D, <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>generis, cum &longs;olido A, cuius grauitas <lb/>&longs;it H, deinde liquidi eiu&longs;dem generis <lb/>cum liquido B, magnitudine æqualis <lb/>&longs;olido D,* inueniatur grauitas quæ &longs;it<arrow.to.target n="note18"/><lb/>G, & &longs;iat vt G, ad H, ita F, ad aliam <lb/>grauitatem, quæ &longs;it C. </s>

<s>SINT duo propo&longs;ita corpora <lb/>magnitudine æqualia, A, quidem &longs;o<lb/><figure id="fig8"/><lb/>lidum, B, vero liquidum, &longs;it autem li<lb/>quidi B, data grauitas F, & oporteat <lb/>inuenire grauitatem &longs;olidi A, accipia <lb/>tur aliquod corpus &longs;olidum D, <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>generis, cum &longs;olido A, cuius grauitas <lb/>&longs;it H, deinde liquidi eiu&longs;dem generis <lb/>cum liquido B, magnitudine æqualis <lb/>&longs;olido D,* inueniatur grauitas quæ &longs;it<arrow.to.target n="note18"/><lb/>G, & fiat vt G, ad H, ita F, ad aliam <lb/>grauitatem, quæ &longs;it C. </s>

<s>Dico &longs;olidi A, <lb/>grauitatem e&longs;&longs;e C, accipiatur enim aliquod corpus liquidum E, eiu&longs;<lb/>dem generis cum liquido B, grauitatem habens æqualem &longs;olido D. </s>

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<s>Qvidam proponit aliquod corpus liquidum notæ <lb/>grauitatis, & vult &longs;cire quanta erit grauitas alicu<lb/>ius &longs;olidi, magnitudinem habentis propo&longs;ito Corpori li<lb/>quido æqualem. </s>

<s><emph type="italics"/>Sitpropo&longs;itum aliquod corpus aqueum B, euius grauitas &longs;it 100. &<emph.end type="italics"/><pb pagenum="12"/><emph type="italics"/>oporteat &longs;cire quanta erit grauitas plumbi magnitudinem babentis <lb/>æqualem propo&longs;itæ aquæ B, verbi gratia &longs;it vas aliquod plenum aqua, <lb/>cuius aquæ grauitas &longs;it 100, & oporteat &longs;cire, &longs;i illud <expan abbr="id&etilde;">idem</expan> vas replea<lb/>tur plumbo, quanta illius plumbi erit grauitas. </s>

<s><emph type="italics"/>Sitpropo&longs;itum aliquod corpus aqueum B, euius grauitas &longs;it 100. &<emph.end type="italics"/><pb pagenum="12"/><emph type="italics"/>oporteat &longs;cire quanta erit grauitas plumbi magnitudinem habentis <lb/>æqualem propo&longs;itæ aquæ B, verbi gratia &longs;it vas aliquod plenum aqua, <lb/>cuius aquæ grauitas &longs;it 100, & oporteat &longs;cire, &longs;i illud <expan abbr="id&etilde;">idem</expan> vas replea<lb/>tur plumbo, quanta illius plumbi erit grauitas. </s>

<s>Accipiatur aliquod <lb/>plumbeum corpus D, cuius grauitas &longs;it<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ <expan abbr="magnitudin&etilde;">magnitudinem</expan> <lb/>babentis æqualem plumbo D, inueniatur grauitas, quod quomodo fie<lb/>ri oporteat iam dictum e&longs;t in antecedentis problematis exemplo: &longs;it igi <lb/>tur ea inuenta grauitas<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita<emph.end type="italics"/> 100<emph type="italics"/>, ad alium nume<lb/>rum qui &longs;it<emph.end type="italics"/> 1150<emph type="italics"/>, is igitur numerus erit grauitas plumbi magnitu<lb/>dinem babentis propo&longs;itæ aquæ B, æqualem, boc est illius plumbi, quod <lb/>in va&longs;e continetur.<emph.end type="italics"/></s>

<s>Accipiatur aliquod <lb/>plumbeum corpus D, cuius grauitas &longs;it<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ <expan abbr="magnitudin&etilde;">magnitudinem</expan> <lb/>habentis æqualem plumbo D, inueniatur grauitas, quod quomodo fie<lb/>ri oporteat iam dictum e&longs;t in antecedentis problematis exemplo: &longs;it igi <lb/>tur ea inuenta grauitas<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita<emph.end type="italics"/> 100<emph type="italics"/>, ad alium nume<lb/>rum qui &longs;it<emph.end type="italics"/> 1150<emph type="italics"/>, is igitur numerus erit grauitas plumbi magnitu<lb/>dinem habentis propo&longs;itæ aquæ B, æqualem, hoc est illius plumbi, quod <lb/>in va&longs;e continetur.<emph.end type="italics"/></s>

<s>At vero &longs;i <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> fuerit inuenire <expan abbr="quãta">quanta</expan> erit grauitas ceræ, <lb/>aut ligni, aut <expan abbr="cuiu&longs;c&utilde;que">cuiu&longs;cunque</expan> &longs;olidi leuioris quam aqua, nihil diuer <lb/>&longs;i in opere accidet, ni&longs;i quod ratio inueniendi grauitatem <lb/>aquæ magnitudinem habentis æqualem corpori &longs;olido leuio<lb/>ri, quàm aqua, differt in aliquo à ratione, qua inuenitur graui<lb/>tas aquæ magnitudinem habentis æqualem &longs;olido corpori <lb/>grauiori, quam aqua, &longs;ed vtramque rationem exemplo ante<lb/>cedentis Problematis illu&longs;trauimus, in eo enim &longs;atis explica<lb/>tum e&longs;t de vtraque. </s>

<s><emph type="italics"/>Sed ne exemplorum inopia laborare videamur, &longs;it inuenienda gra<lb/>uitas ceræ magnitudinem babentis æqualem propo&longs;itæ aquæ B, acci<lb/>piatur aliquod cereum corpus D, cuius grauitas &longs;it<emph.end type="italics"/> 21, <emph type="italics"/>deinde aquæ <lb/>magnitudinem babentis æqualem ceræ D, inueniatur grauitas, vt in <lb/>antecedentis Problematis exemplo dictum est, quæ grauitas &longs;it<emph.end type="italics"/> 22, <emph type="italics"/>& <lb/>fiat vt<emph.end type="italics"/> 22<emph type="italics"/>, ad<emph.end type="italics"/> 21<emph type="italics"/>, ita<emph.end type="italics"/> 100<emph type="italics"/>, hoc est grauitas aquæ B, ad alium numerum <lb/>qui &longs;it<emph.end type="italics"/> 95 5/11. <emph type="italics"/>is igitur numerus indicabit quanta erit grauitas ceræ <lb/>magnitudinem habentis æqualem propo&longs;itæ aquæ B.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sed ne exemplorum inopia laborare videamur, &longs;it inuenienda gra<lb/>uitas ceræ magnitudinem habentis æqualem propo&longs;itæ aquæ B, acci<lb/>piatur aliquod cereum corpus D, cuius grauitas &longs;it<emph.end type="italics"/> 21, <emph type="italics"/>deinde aquæ <lb/>magnitudinem habentis æqualem ceræ D, inueniatur grauitas, vt in <lb/>antecedentis Problematis exemplo dictum est, quæ grauitas &longs;it<emph.end type="italics"/> 22, <emph type="italics"/>& <lb/>fiat vt<emph.end type="italics"/> 22<emph type="italics"/>, ad<emph.end type="italics"/> 21<emph type="italics"/>, ita<emph.end type="italics"/> 100<emph type="italics"/>, hoc est grauitas aquæ B, ad alium numerum <lb/>qui &longs;it<emph.end type="italics"/> 95 5/11. <emph type="italics"/>is igitur numerus indicabit quanta erit grauitas ceræ <lb/>magnitudinem habentis æqualem propo&longs;itæ aquæ B.<emph.end type="italics"/></s>

<s>Similiter &longs;i propo&longs;itum liquidum corpus B, fuerit olei, aut <lb/>vini, aut cuiu&longs;cumque liquidi, præter argenti viui, eadem om<lb/>nino via, qua ante, inuenietur quæ&longs;ita corporis &longs;olidi grauitas, <lb/>&longs;ed de argento viuo tractabimus ad finem propo&longs;itionis deci<lb/>mæ quartæ. </s>

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<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>magnitudinis, & vult &longs;cire quanta erit magnitudo <lb/>alicuius liquidi, grauitatem habentis propo&longs;ito corpori <lb/>&longs;olido æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus plumbeum A, cuius magnitudo &longs;it<emph.end type="italics"/><lb/>10<emph type="italics"/>, & oporteat &longs;cire quanta erit magnitudo aquæ grauitatem baben<lb/>tis æqualem propo&longs;ito plumbo A, accipiatur aliquod corpus <expan abbr="plumbe&utilde;">plumbeum</expan> <lb/>D, cuius grauitas<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ magnitudinem babentis æqualem <lb/>plumbo D, inueniatur grauitas, vt in exemplo propo&longs;. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus plumbeum A, cuius magnitudo &longs;it<emph.end type="italics"/><lb/>10<emph type="italics"/>, & oporteat &longs;cire quanta erit magnitudo aquæ grauitatem baben<lb/>tis æqualem propo&longs;ito plumbo A, accipiatur aliquod corpus <expan abbr="plumbe&utilde;">plumbeum</expan> <lb/>D, cuius grauitas<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ magnitudinem habentis æqualem <lb/>plumbo D, inueniatur grauitas, vt in exemplo propo&longs;. </s>

<s>8. dictum e&longs;t, <lb/>quæ &longs;it<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita<emph.end type="italics"/> 10<emph type="italics"/>, ad alium numerum qui&longs;it 115, is <lb/>igitur indicabit quanta erit magnitudo aquæ grauitatem babentis <lb/>æqualem propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s>8. dictum e&longs;t, <lb/>quæ &longs;it<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita<emph.end type="italics"/> 10<emph type="italics"/>, ad alium numerum qui&longs;it 115, is <lb/>igitur indicabit quanta erit magnitudo aquæ grauitatem habentis <lb/>æqualem propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s>Quod &longs;i <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> corpus plumbeum A &longs;it regulare vt po<lb/>te &longs;phæricum, cuius &longs;phæræ diameter &longs;it 10, & oporteat inue<lb/>nire quanta erit diameter &longs;phæræ ex aqua, grauitatem haben<lb/>tis æqualem propo&longs;itæ &longs;phæræ A, ita faciendum erit. </s>

<s><emph type="italics"/>Atcipiatur, vt diximus, aliquod corpus plumbeum D, cuius gra<lb/>uitas<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ babentis magnitudinem æqualem plumbo D, <lb/>inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita cubus ex<emph.end type="italics"/> 10<emph type="italics"/>, qui <lb/>e&longs;t 1000, ad alium numerum qui &longs;it<emph.end type="italics"/> 11500<emph type="italics"/>, is igitur numerus erit <lb/>cubus diametri &longs;pbæræ ex aqua grauitatem babentis æqualem propo<lb/>&longs;itæ &longs;phæræ A, quare eius latus cubicum, quod est<emph.end type="italics"/> 22 57/100. <emph type="italics"/><expan abbr="proxim&utilde;">proximum</expan> <lb/>vero indicabit ip&longs;am diametrum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Atcipiatur, vt diximus, aliquod corpus plumbeum D, cuius gra<lb/>uitas<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ habentis magnitudinem æqualem plumbo D, <lb/>inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 2<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 2<emph type="italics"/>, ad<emph.end type="italics"/> 23<emph type="italics"/>, ita cubus ex<emph.end type="italics"/> 10<emph type="italics"/>, qui <lb/>e&longs;t 1000, ad alium numerum qui &longs;it<emph.end type="italics"/> 11500<emph type="italics"/>, is igitur numerus erit <lb/>cubus diametri &longs;phæræ ex aqua grauitatem habentis æqualem propo<lb/>&longs;itæ &longs;phæræ A, quare eius latus cubicum, quod est<emph.end type="italics"/> 22 57/100. <emph type="italics"/><expan abbr="proxim&utilde;">proximum</expan> <lb/>vero indicabit ip&longs;am diametrum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius formæ regularis, eadem ratione inueniemus latus cu <lb/>bi ex aqua grauitatem babentis æqualem propo&longs;ito cubo A, nam &longs;i cu<lb/>bi A, datum &longs;it latus<emph.end type="italics"/> 10<emph type="italics"/>, erit numerus 11500, cubus ex aqua æqualis <lb/>grauitate propo&longs;ito cubo A, quare latus cubicum numeri<emph.end type="italics"/> 11500<emph type="italics"/>, quod<emph.end type="italics"/><pb pagenum="15"/><emph type="italics"/>e&longs;t<emph.end type="italics"/> 22 17/100. <emph type="italics"/><expan abbr="proxim&utilde;">proximum</expan> vero indicabit quæ&longs;itum latus eubi ex aqua.<emph.end type="italics"/></s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius formæ regularis, eadem ratione inueniemus latus cu<lb/>bi ex aqua grauitatem habentis æqualem propo&longs;ito cubo A, nam &longs;i cu<lb/>bi A, datum &longs;it latus<emph.end type="italics"/> 10<emph type="italics"/>, erit numerus 11500, cubus ex aqua æqualis <lb/>grauitate propo&longs;ito cubo A, quare latus cubicum numeri<emph.end type="italics"/> 11500<emph type="italics"/>, quod<emph.end type="italics"/><pb pagenum="15"/><emph type="italics"/>e&longs;t<emph.end type="italics"/> 22 17/100. <emph type="italics"/><expan abbr="proxim&utilde;">proximum</expan> vero indicabit quæ&longs;itum latus eubi ex aqua.<emph.end type="italics"/></s>

<s>Neque di&longs;&longs;imili ratione inuenietur magnitudo olei, aut ar<lb/>genti viui, aut cuiu&longs;cumque generis liquidi grauitatem habe<lb/>tis propo&longs;ito corpori &longs;olido æqualem, &longs;ed quomodo inuenien<lb/>da &longs;it grauitas argenti viui magnitudinem habentis æqualem <lb/>corpori &longs;olido, docebimus po&longs;t exemplum propo&longs;itionis de<lb/>cimæ quartæ. </s>

Line 394

<s>Qvidam proponit aliquod corpus liquidum notæ <lb/>magnitudinis, & vult inuenire quanta erit magni<lb/>tudo alicuius &longs;olidi grauitatem habentis propo&longs;i<lb/>to corpori liquido æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus aqueum B, cuius magnitude &longs;it 115, <lb/>& oporteat inuenire quanta erit magnitudo plumbi grauitatem ha<lb/>bentis æqualem propo&longs;itæ aquæ B, accipiatur aliquod corpus <expan abbr="plumbe&utilde;">plumbeum</expan> <lb/>D, cuius grauitas &longs;it verbi gratia<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ magnitudinem ba<lb/>bentis æqualem plumbo D, inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 2. <emph type="italics"/>id autem do<lb/>cuit propo&longs;itionis octauæ exemplum, & fiat vt<emph.end type="italics"/> 23<emph type="italics"/>, ad<emph.end type="italics"/> 2<emph type="italics"/>, ita 115, ad <lb/>alium numerum qui &longs;it<emph.end type="italics"/> 10<emph type="italics"/>, is igitur numerus indicabit quanta erit <lb/>magnitudo plumbi grauitatem babentis æqualem propo&longs;itæ aquæ B.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus aqueum B, cuius magnitude &longs;it 115, <lb/>& oporteat inuenire quanta erit magnitudo plumbi grauitatem ha<lb/>bentis æqualem propo&longs;itæ aquæ B, accipiatur aliquod corpus <expan abbr="plumbe&utilde;">plumbeum</expan> <lb/>D, cuius grauitas &longs;it verbi gratia<emph.end type="italics"/> 23<emph type="italics"/>, deinde aquæ magnitudinem ba<lb/>bentis æqualem plumbo D, inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 2. <emph type="italics"/>id autem do<lb/>cuit propo&longs;itionis octauæ exemplum, & fiat vt<emph.end type="italics"/> 23<emph type="italics"/>, ad<emph.end type="italics"/> 2<emph type="italics"/>, ita 115, ad <lb/>alium numerum qui &longs;it<emph.end type="italics"/> 10<emph type="italics"/>, is igitur numerus indicabit quanta erit <lb/>magnitudo plumbi grauitatem habentis æqualem propo&longs;itæ aquæ B.<emph.end type="italics"/></s>

<s>Quod &longs;i propo&longs;itum corpus aqueum B, &longs;it &longs;phæricum, cuius <lb/>&longs;phæræ diameter &longs;it 10, & oporteat inuenire quanta erit dia<lb/>meter &longs;phæræ ex plumbo, grauitatem habentis æqualem pro<lb/>po&longs;itæ &longs;phæræ B, ita faciendum erit. </s>

<s><emph type="italics"/>Accepto, vt diximus aliquo corpore plumbeo D, cuius grauitas<emph.end type="italics"/> 23, <lb/><emph type="italics"/>& aquæ magnitudinem babentis æqualem plumbo D, inuenta graui-<emph.end type="italics"/><pb pagenum="17"/><emph type="italics"/>tate 2, fiat vt<emph.end type="italics"/> 23<emph type="italics"/>, ad<emph.end type="italics"/> 2<emph type="italics"/>, ita cubus ex<emph.end type="italics"/> 10<emph type="italics"/>, boc est<emph.end type="italics"/> 1000<emph type="italics"/>, ad alium nume<lb/>rum qui &longs;it<emph.end type="italics"/> 86 22/2<gap/><31> <emph type="italics"/>is igitur numerus erit cubus diametrs &longs;pbæræ ex <lb/>plumbo, grauitatem æqualem babentis propo&longs;ite ex aqua &longs;pbæræ B, <lb/>quare eius latus cubicum, quod est<emph.end type="italics"/> 4 41/100<31> <emph type="italics"/>ferè, indicabit ip&longs;am <lb/>diametrum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Accepto, vt diximus aliquo corpore plumbeo D, cuius grauitas<emph.end type="italics"/> 23, <lb/><emph type="italics"/>& aquæ magnitudinem habentis æqualem plumbo D, inuenta graui-<emph.end type="italics"/><pb pagenum="17"/><emph type="italics"/>tate 2, fiat vt<emph.end type="italics"/> 23<emph type="italics"/>, ad<emph.end type="italics"/> 2<emph type="italics"/>, ita cubus ex<emph.end type="italics"/> 10<emph type="italics"/>, hoc est<emph.end type="italics"/> 1000<emph type="italics"/>, ad alium nume<lb/>rum qui &longs;it<emph.end type="italics"/> 86 22/2<gap/><31> <emph type="italics"/>is igitur numerus erit cubus diametrs &longs;phæræ ex <lb/>plumbo, grauitatem æqualem habentis propo&longs;ite ex aqua &longs;phæræ B, <lb/>quare eius latus cubicum, quod est<emph.end type="italics"/> 4 41/100<31> <emph type="italics"/>ferè, indicabit ip&longs;am <lb/>diametrum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus aqueum B, fuerit cubicum, vel alicu <lb/>las alterius formæ regularis, eadem ratione vtemur ad inueniendum <lb/>latus cubi ex plumbo, grauitatem babentis æqualem propo&longs;ito ex aqua <lb/><gap/>bo B, nam &longs;i ex aqua cubi B, datum &longs;it latus<emph.end type="italics"/> 10<emph type="italics"/>, erit numerus<emph.end type="italics"/><lb/>86 22/2<gap/><31> <emph type="italics"/>cubus ex plumbo æqualis grauitate propo&longs;ito ex aqua cubo B, <lb/>quare latus cubicum numeri<emph.end type="italics"/> 86 22/2<gap/><31> <emph type="italics"/>quod e&longs;t<emph.end type="italics"/> 4 41/100<31> <emph type="italics"/>ferè, indicabit <lb/>quæ&longs;itum latus cubi ex plumbo.<emph.end type="italics"/></s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus aqueum B, fuerit cubicum, vel alicu <lb/>las alterius formæ regularis, eadem ratione vtemur ad inueniendum <lb/>latus cubi ex plumbo, grauitatem habentis æqualem propo&longs;ito ex aqua <lb/><gap/>bo B, nam &longs;i ex aqua cubi B, datum &longs;it latus<emph.end type="italics"/> 10<emph type="italics"/>, erit numerus<emph.end type="italics"/><lb/>86 22/2<gap/><31> <emph type="italics"/>cubus ex plumbo æqualis grauitate propo&longs;ito ex aqua cubo B, <lb/>quare latus cubicum numeri<emph.end type="italics"/> 86 22/2<gap/><31> <emph type="italics"/>quod e&longs;t<emph.end type="italics"/> 4 41/100<31> <emph type="italics"/>ferè, indicabit <lb/>quæ&longs;itum latus cubi ex plumbo.<emph.end type="italics"/></s>

<s>Neque di&longs;&longs;imili ratione inuenienda erit magnitudo auri, <lb/>argenti, ceræ, aut cuiu&longs;cunque &longs;olidi, grauitatem habentis <lb/>propo&longs;ito corpori liquido æqualem. </s>

Line 410

<s>SINT propo&longs;ita duo corpora &longs;o<lb/>lida magnitudine æqualia A, B, &longs;it au<lb/><figure id="fig11"/><lb/>tem vnius, vtpote ip&longs;ius A, data gra<lb/>uitas C, & oporteat inuenire grauita<lb/>tem ip&longs;ius B. </s>

<s>Accipiatur aliquod &longs;oli<lb/>dum corpus D, eiu&longs;dem generis cum <lb/>corpore &longs;olido A, cui æquale grauita<lb/>te accipiatur alterum E, eiu&longs;dem ge<lb/>neris cum corpore B, deinde liquidi <lb/>magnitudine æqualis corpori D,<arrow.to.target n="note28"/> *in<lb/>ueniatur grauitas, quæ &longs;it G, item li<lb/>quidi eiu&longs;dem generis, æqualis ma<lb/>gnitudine corpori E,* inueniatur grauitas, quæ &longs;it H, & &longs;iat vt H, ad<arrow.to.target n="note29"/><lb/>G, ita C, ad aliam grauitatem, quæ &longs;it F. </s>

<s>Accipiatur aliquod &longs;oli<lb/>dum corpus D, eiu&longs;dem generis cum <lb/>corpore &longs;olido A, cui æquale grauita<lb/>te accipiatur alterum E, eiu&longs;dem ge<lb/>neris cum corpore B, deinde liquidi <lb/>magnitudine æqualis corpori D,<arrow.to.target n="note28"/> *in<lb/>ueniatur grauitas, quæ &longs;it G, item li<lb/>quidi eiu&longs;dem generis, æqualis ma<lb/>gnitudine corpori E,* inueniatur grauitas, quæ &longs;it H, & fiat vt H, ad<arrow.to.target n="note29"/><lb/>G, ita C, ad aliam grauitatem, quæ &longs;it F. </s>

<s>Quoniam igitur &longs;unt qua<lb/>tuor corpora A, B, D, E, quorum A, B, primum videlicet, & &longs;ecundum <lb/>&longs;unt æqualia magnitudine, tertium vero D, & E, quartum æque gra<lb/>uia, & &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<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<lb/>go grauitas F, æqualis erit grauitati &longs;olidi B, inuenta igitur e&longs;t cor<lb/>poris &longs;olidi B, grauitas F, quod &longs;acere oportebat. </s>

Line 430

<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>grauitatis, & vult &longs;cire quanta erit grauitas alicu<lb/>ius &longs;olidi, alterius generis, magnitudinem habentis pro<lb/>po&longs;ito corpori &longs;olido æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus plumbeum A, cuius grauitas &longs;it<emph.end type="italics"/><lb/>1150<emph type="italics"/>, & oporteat inuenire quanta erit grauitas stanni <expan abbr="magnitudin&etilde;">magnitudinem</expan> <lb/>babentis æqualem propo&longs;ito plumbo A. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus plumbeum A, cuius grauitas &longs;it<emph.end type="italics"/><lb/>1150<emph type="italics"/>, & oporteat inuenire quanta erit grauitas stanni <expan abbr="magnitudin&etilde;">magnitudinem</expan> <lb/>habentis æqualem propo&longs;ito plumbo A. </s>

<s>Accipiantur duo corpora æque <lb/>grauia, D, plumbeum, E, stinncum, deinde duarum quantitatum, <lb/>aquæ, quarum una &longs;it æqualis magnitudine plumbo D, altera &longs;tanno <lb/>E, <expan abbr="inueniãtur">inueniantur</expan> grauitates, quæ &longs;int, primæ videlicet quantitatis aquæ<emph.end type="italics"/><lb/>74, <emph type="italics"/>&longs;ecundæ vero<emph.end type="italics"/> 115<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 115<emph type="italics"/>, ad<emph.end type="italics"/> 74<emph type="italics"/>, ita<emph.end type="italics"/> 1150<emph type="italics"/>, ad alium nume<lb/>rum, qui &longs;it<emph.end type="italics"/> 740<emph type="italics"/>, is igitur numerus indicabit grauitatem stanni, ma<lb/>gnitudinem babentis propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s>Accipiantur duo corpora æque <lb/>grauia, D, plumbeum, E, stinncum, deinde duarum quantitatum, <lb/>aquæ, quarum una &longs;it æqualis magnitudine plumbo D, altera &longs;tanno <lb/>E, <expan abbr="inueniãtur">inueniantur</expan> grauitates, quæ &longs;int, primæ videlicet quantitatis aquæ<emph.end type="italics"/><lb/>74, <emph type="italics"/>&longs;ecundæ vero<emph.end type="italics"/> 115<emph type="italics"/>, & fiat vt<emph.end type="italics"/> 115<emph type="italics"/>, ad<emph.end type="italics"/> 74<emph type="italics"/>, ita<emph.end type="italics"/> 1150<emph type="italics"/>, ad alium nume<lb/>rum, qui &longs;it<emph.end type="italics"/> 740<emph type="italics"/>, is igitur numerus indicabit grauitatem stanni, ma<lb/>gnitudinem habentis propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s>Etiam &longs;i non accipiantur duo corpora, plumbeum videlicet <lb/>& &longs;tanneum, æque grauia, &longs;ed grauitate quacunque, grauitas <lb/>&longs;tanni magnitudinem habentis æqualem propo&longs;ito plumbo <lb/>D, inuenietur &longs;ic. </s>

<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 pagenum="19"/><emph type="italics"/>ot 23, ad 2, ita 37, ad<emph.end type="italics"/> 3 5/21. <emph type="italics"/>grauitas igitur aquæ, magnitudinem <lb/>babentis æqualem plumbo, cuius grauitas est 37, erit<emph.end type="italics"/> 3 5/21. </s>

<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 pagenum="19"/><emph type="italics"/>ot 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>

<s><emph type="italics"/>Et quoniam aquæ, magnitudinem babentis 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"/>Fiatigitur 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"/>tantaigitur erit grauitas <lb/>&longs;tanni, magnitudinem babentis æqualem propo&longs;ito plumbo A, quanta <lb/><gap/>iam inueniebatur & &longs;upra.<emph.end type="italics"/></s>

<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"/>Fiatigitur 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"/>tantaigitur 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>

<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>

Line 474

<s>Qvidam proponit aliquod corpus &longs;olidum notæ <lb/>magnitudinis, & vult inuenire, quanta erit magni <lb/>tudo alicuius &longs;olidi alterius generis, grauitatem <lb/>habentis propo&longs;ito corpori &longs;olido æqualem. </s>

<s><emph type="italics"/>SIT propo&longs;itum aliquod corpus plumbeum A, cuius magnitudo<emph.end type="italics"/><lb/>740, <emph type="italics"/>& oporteat inuenire quanta erit magnitudo &longs;tanni, grauita<lb/>tem babentis æqualem propo&longs;ito plumbo A. </s>

<s><emph type="italics"/>SIT propo&longs;itum aliquod corpus plumbeum A, cuius magnitudo<emph.end type="italics"/><lb/>740, <emph type="italics"/>& oporteat inuenire quanta erit magnitudo &longs;tanni, grauita<lb/>tem habentis æqualem propo&longs;ito plumbo A. </s>

<s>Accipiatur aliquod cor<lb/>pus plumbeum D, cuius grauitas &longs;it 115, deinde stanni, magnitudi<lb/>ne æqualis plumbo D, inueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 74, <emph type="italics"/>quod quomo<lb/>do fieri oportent, dictum est in antecedentis Problematis exemplo, & <lb/>fiat vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115. <emph type="italics"/>ita<emph.end type="italics"/> 740, <emph type="italics"/>ad alium numerum qui &longs;it<emph.end type="italics"/> 1150, <emph type="italics"/>is igitur <lb/>numcrus indicabit quanta erit magnitudo &longs;tanni, grauitatem baben <lb/>tis æqualem propo&longs;ito plumbo A.<emph.end type="italics"/></s>

<s>Quod &longs;i propo&longs;itum corpus plumbeum A, &longs;it &longs;phæricum, cu <lb/>ius &longs;phæræ diameter &longs;it 10, & oporteat inuenire quanta erit <lb/>diameter &longs;phæræ ex &longs;tanno, grauitatem habentis æqualem <lb/>propo&longs;itæ &longs;phæræ A, ita faciendum erit. </s>

<s><emph type="italics"/>Accipiatur vt diximus aliquod corpus plumbeum D, cuius graui<lb/>tas &longs;it 115, & &longs;tanni, magnitudinem babentis æqualem plumbo D, in<lb/>ueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 74. <emph type="italics"/>& 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;pbæræ ex stanno, grauitatem babentis æqualem <lb/>propo&longs;itæ ex plumbo &longs;phæræ 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>

<s><emph type="italics"/>Accipiatur vt diximus aliquod corpus plumbeum D, cuius graui<lb/>tas &longs;it 115, & &longs;tanni, magnitudinem habentis æqualem plumbo D, in<lb/>ueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 74. <emph type="italics"/>& 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;phæræ ex stanno, grauitatem habentis æqualem <lb/>propo&longs;itæ ex plumbo &longs;phæræ 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>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius formæ regularis, eadem ratione inuenietur latus cu <lb/>bi ex stanno, grauitatem bab<gap/>ntis æqualem propo&longs;ito plumbto cu<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<31> <emph type="italics"/>cubus ex &longs;tanno æqualis grauitate propo&longs;ito plumbeo Cu <lb/>bo A, quare latus. </s>

Line 508

<s>Qvidam proponit aliquod corpus liquidum notæ <lb/>grauitatis, & vult &longs;cire, quanta erit grauitas alte<lb/>rius liquidi, magnitudinem habentis propo&longs;ito corpori <lb/>liquido æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod olei corpus A, cuius grauitas<emph.end type="italics"/> 550, <emph type="italics"/>& <lb/>oporteat inuenire, quanta erit grauitas aquæ, magnitudinem haben-<emph.end type="italics"/><pb pagenum="23"/><emph type="italics"/>tis æqualem propo&longs;ito oleo A, Accipiatur aliquod corpus &longs;olidum C, <lb/>vtpote plumbeum, & aquæ, magnitudinem babentis æqualem plumb<gap/><lb/>C, inueniatur grauitas, quæ &longs;it 12, vt in exemplo propo&longs;. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod olei corpus A, cuius grauitas<emph.end type="italics"/> 550, <emph type="italics"/>& <lb/>oporteat inuenire, quanta erit grauitas aquæ, magnitudinem haben-<emph.end type="italics"/><pb pagenum="23"/><emph type="italics"/>tis æqualem propo&longs;ito oleo A, Accipiatur aliquod corpus &longs;olidum C, <lb/>vtpote plumbeum, & aquæ, magnitudinem habentis æqualem plumb<gap/><lb/>C, inueniatur grauitas, quæ &longs;it 12, vt in exemplo propo&longs;. </s>

<s>8. <expan abbr="dict&utilde;">dictum</expan> e&longs;t. </s>

<s><lb/>Similiter & olei, magnitudinem æqualem babentis, eidem plumbo C, <lb/>inueniatur grauitas, quæ &longs;it 11, & fiat, vt<emph.end type="italics"/> 11, <emph type="italics"/>ad<emph.end type="italics"/> 12, <emph type="italics"/>ita 550, ad <expan abbr="ali&utilde;">alium</expan> <lb/>numerum qui &longs;it<emph.end type="italics"/> 600. <emph type="italics"/>is igitur numerus indicabit quanta erit graui<lb/>tas aquæ, magnitudinem babentis æqualem propo&longs;ito oleo A.<emph.end type="italics"/></s>

<s><lb/>Similiter & olei, magnitudinem æqualem habentis, eidem plumbo C, <lb/>inueniatur grauitas, quæ &longs;it 11, & fiat, vt<emph.end type="italics"/> 11, <emph type="italics"/>ad<emph.end type="italics"/> 12, <emph type="italics"/>ita 550, ad <expan abbr="ali&utilde;">alium</expan> <lb/>numerum qui &longs;it<emph.end type="italics"/> 600. <emph type="italics"/>is igitur numerus indicabit quanta erit graui<lb/>tas aquæ, magnitudinem habentis æqualem propo&longs;ito oleo A.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si vero propo&longs;itum &longs;it aliquod argenti viui corpus A, cuius <lb/>grauitas<emph.end type="italics"/> 95, <emph type="italics"/>& oporteat inuexire, quanta erit grauitas aquæ, magni<lb/>tudincm babentis æqualem propo&longs;ito argento viuo A. </s>

<s><emph type="italics"/>Si vero propo&longs;itum &longs;it aliquod argenti viui corpus A, cuius <lb/>grauitas<emph.end type="italics"/> 95, <emph type="italics"/>& oporteat inuexire, quanta erit grauitas aquæ, magni<lb/>tudincm habentis æqualem propo&longs;ito argento viuo A. </s>

<s>Accipiatur ali<lb/>quod vas vitreum mundum, & politum, cuius grauitas &longs;it v. g.<emph.end type="italics"/> 91. <lb/><emph type="italics"/><expan abbr="ip&longs;umq;">ip&longs;umque</expan> vas plenum aqua ponderetur in aqua, & babeat grauitatem<emph.end type="italics"/><lb/>55, <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 91, <emph type="italics"/>&longs;uperat <expan abbr="numer&utilde;">numerum</expan><emph.end type="italics"/> 55, <emph type="italics"/>numero<emph.end type="italics"/> 36, <emph type="italics"/>* erit<emph.end type="italics"/><arrow.to.target n="note37"/><lb/><emph type="italics"/>grauitas aquæ, magnitudinem babentis æqualem ip&longs;i va&longs;i, hoc est &longs;oli<lb/>ditati ip&longs;ius va&longs;is<emph.end type="italics"/> 36, <emph type="italics"/>ponatur deinde in ip&longs;um vas propo&longs;itum argen<lb/>tum <expan abbr="viu&utilde;">viuum</expan> A, nihil interest, vt vas &longs;it plenum, vel non, & quoniam ar <lb/>genti viui A, grauitas est<emph.end type="italics"/> 95, <emph type="italics"/>& va&longs;is vitrei grauitas<emph.end type="italics"/> 91, <emph type="italics"/>erit argenti <lb/>viui &longs;imul cum ip&longs;o va&longs;e, grauitas<emph.end type="italics"/> 186. <emph type="italics"/>ponderetur itaque ip&longs;um vas, <lb/>&longs;imul cum argento viuo A, in aqua, ita vt aqua repleat va&longs;is partem <lb/>vacuam, & &longs;it va&longs;is grauitas in aqua &longs;imul cum argento viuo<emph.end type="italics"/> 143, <lb/><emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 186, <emph type="italics"/>&longs;uperat numerum<emph.end type="italics"/> 143, <emph type="italics"/>numero<emph.end type="italics"/> 43, <emph type="italics"/>* erit<emph.end type="italics"/><arrow.to.target n="note38"/><lb/><emph type="italics"/>grauitas aquæ, <expan abbr="magnitudin&etilde;">magnitudinem</expan> <expan abbr="bib&etilde;tis">bibentis</expan> æqualem argento viuo, &longs;imul <expan abbr="c&utilde;">cum</expan> <lb/>va&longs;e<emph.end type="italics"/> 43, <emph type="italics"/>&longs;ed grauitas aquæ babentis magnitudinem æqualem va&longs;i est<emph.end type="italics"/><lb/>36, <emph type="italics"/>ergo reliquum quod est<emph.end type="italics"/> 7, <emph type="italics"/>erit grauitas aquæ, magnitudinem ba<lb/>bentis æqualem propo&longs;ito argento viuo A.<emph.end type="italics"/></s>

<s>Accipiatur ali<lb/>quod vas vitreum mundum, & politum, cuius grauitas &longs;it v. g.<emph.end type="italics"/> 91. <lb/><emph type="italics"/><expan abbr="ip&longs;umq;">ip&longs;umque</expan> vas plenum aqua ponderetur in aqua, & habeat grauitatem<emph.end type="italics"/><lb/>55, <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 91, <emph type="italics"/>&longs;uperat <expan abbr="numer&utilde;">numerum</expan><emph.end type="italics"/> 55, <emph type="italics"/>numero<emph.end type="italics"/> 36, <emph type="italics"/>* erit<emph.end type="italics"/><arrow.to.target n="note37"/><lb/><emph type="italics"/>grauitas aquæ, magnitudinem habentis æqualem ip&longs;i va&longs;i, hoc est &longs;oli<lb/>ditati ip&longs;ius va&longs;is<emph.end type="italics"/> 36, <emph type="italics"/>ponatur deinde in ip&longs;um vas propo&longs;itum argen<lb/>tum <expan abbr="viu&utilde;">viuum</expan> A, nihil interest, vt vas &longs;it plenum, vel non, & quoniam ar <lb/>genti viui A, grauitas est<emph.end type="italics"/> 95, <emph type="italics"/>& va&longs;is vitrei grauitas<emph.end type="italics"/> 91, <emph type="italics"/>erit argenti <lb/>viui &longs;imul cum ip&longs;o va&longs;e, grauitas<emph.end type="italics"/> 186. <emph type="italics"/>ponderetur itaque ip&longs;um vas, <lb/>&longs;imul cum argento viuo A, in aqua, ita vt aqua repleat va&longs;is partem <lb/>vacuam, & &longs;it va&longs;is grauitas in aqua &longs;imul cum argento viuo<emph.end type="italics"/> 143, <lb/><emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 186, <emph type="italics"/>&longs;uperat numerum<emph.end type="italics"/> 143, <emph type="italics"/>numero<emph.end type="italics"/> 43, <emph type="italics"/>* erit<emph.end type="italics"/><arrow.to.target n="note38"/><lb/><emph type="italics"/>grauitas aquæ, <expan abbr="magnitudin&etilde;">magnitudinem</expan> <expan abbr="bib&etilde;tis">bibentis</expan> æqualem argento viuo, &longs;imul <expan abbr="c&utilde;">cum</expan> <lb/>va&longs;e<emph.end type="italics"/> 43, <emph type="italics"/>&longs;ed grauitas aquæ habentis magnitudinem æqualem va&longs;i est<emph.end type="italics"/><lb/>36, <emph type="italics"/>ergo reliquum quod est<emph.end type="italics"/> 7, <emph type="italics"/>erit grauitas aquæ, magnitudinem ba<lb/>bentis æqualem propo&longs;ito argento viuo A.<emph.end type="italics"/></s>

Line 528

<s><emph type="italics"/>Sit propo&longs;itum aliquod magnum argenti viui corpus A, cuius gra<lb/>uitas<emph.end type="italics"/> 5700. <emph type="italics"/>& oporteat facere, quod imperatum e&longs;t. </s>

<s>Accipiatur ali<lb/>quod paruum argenti viui corpus C, cuius grauitas &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>& aquæ, <lb/>magnitudinem babentis æqualem argento viuo C, inueniatur graui<lb/>tas, eo modo quo dictum est, quæ &longs;it<emph.end type="italics"/> 7, <emph type="italics"/>& &longs;iat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/> 7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad <lb/>alium numerum, qui &longs;it<emph.end type="italics"/> 420, <emph type="italics"/>is igitur numerus indicabit quanta erit <lb/>grauitas aquæ, magnitudinem babentis æqualem propo&longs;ito argento <lb/>viuo A.<emph.end type="italics"/></s>

<s>Accipiatur ali<lb/>quod paruum argenti viui corpus C, cuius grauitas &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>& aquæ, <lb/>magnitudinem habentis æqualem argento viuo C, inueniatur graui<lb/>tas, eo modo quo dictum est, quæ &longs;it<emph.end type="italics"/> 7, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/> 7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad <lb/>alium numerum, qui &longs;it<emph.end type="italics"/> 420, <emph type="italics"/>is igitur numerus indicabit quanta erit <lb/>grauitas aquæ, magnitudinem habentis æqualem propo&longs;ito argento <lb/>viuo A.<emph.end type="italics"/></s>

<s><emph type="italics"/>Contra, &longs;it propo&longs;itum aliquod corpus aqueum A, cuius grauitas<emph.end type="italics"/><lb/>420, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui, magni<lb/>tudine æqualis propo&longs;itæ aquæ A. facto, vt &longs;upra, & inuenta graui<lb/>tate<emph.end type="italics"/> 7, <emph type="italics"/>aquæ &longs;cilicet magnitudinem babentis æqualem <expan abbr="arg&etilde;to">argento</expan> viuo C,<emph.end type="italics"/><pb pagenum="24"/><emph type="italics"/>flat vt<emph.end type="italics"/> 7, <emph type="italics"/>ad<emph.end type="italics"/> 95, <emph type="italics"/>ita<emph.end type="italics"/> 420, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5700, <emph type="italics"/>is igi<lb/>tur indicabit quanta erit grauitas argenti viui, magnitudine æqua<lb/>lis propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

<s><emph type="italics"/>Contra, &longs;it propo&longs;itum aliquod corpus aqueum A, cuius grauitas<emph.end type="italics"/><lb/>420, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui, magni<lb/>tudine æqualis propo&longs;itæ aquæ A. facto, vt &longs;upra, & inuenta graui<lb/>tate<emph.end type="italics"/> 7, <emph type="italics"/>aquæ &longs;cilicet magnitudinem habentis æqualem <expan abbr="arg&etilde;to">argento</expan> viuo C,<emph.end type="italics"/><pb pagenum="24"/><emph type="italics"/>flat vt<emph.end type="italics"/> 7, <emph type="italics"/>ad<emph.end type="italics"/> 95, <emph type="italics"/>ita<emph.end type="italics"/> 420, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5700, <emph type="italics"/>is igi<lb/>tur indicabit quanta erit grauitas argenti viui, magnitudine æqua<lb/>lis propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

<s>Inueniemus etiam aliter, & expeditius grauitatem <lb/>aquæ, magnitudinem habentis æqualem propo&longs;ito ar<lb/>gento viuo A. </s>

<s><emph type="italics"/>Accipiatur enim aliquod corpus aurcum, cui &longs;uperinducatur ce<lb/>rea tunica tenui&longs;&longs;ima, ne fiat argento viuo leuius, neue ab <expan abbr="eod&etilde;">eodem</expan> di&longs;&longs;ol<lb/>uatur, deinde aquæ, magnitudinem babentis æqualem ip&longs;i corpori au <lb/>reo inueniatur grauitas, vt dictum est in propo&longs;.<emph.end type="italics"/> 8. <emph type="italics"/>exemplo, quæ &longs;it<emph.end type="italics"/> 7, <lb/><emph type="italics"/>&longs;imiliter & argenti viui, vt aquæ, magnitudinem babentis æqualem <lb/>eidem corpori aureo, inueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/><lb/>7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad<emph.end type="italics"/> 420, <emph type="italics"/>grauitas igitur aquæ, magnitudinem babentis æ<lb/>qualem argento viuo A, erit<emph.end type="italics"/> 420. </s>

<s><emph type="italics"/>Accipiatur enim aliquod corpus aurcum, cui &longs;uperinducatur ce<lb/>rea tunica tenui&longs;&longs;ima, ne fiat argento viuo leuius, neue ab <expan abbr="eod&etilde;">eodem</expan> di&longs;&longs;ol<lb/>uatur, deinde aquæ, magnitudinem habentis æqualem ip&longs;i corpori au <lb/>reo inueniatur grauitas, vt dictum est in propo&longs;.<emph.end type="italics"/> 8. <emph type="italics"/>exemplo, quæ &longs;it<emph.end type="italics"/> 7, <lb/><emph type="italics"/>&longs;imiliter & argenti viui, vt aquæ, magnitudinem habentis æqualem <lb/>eidem corpori aureo, inueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/><lb/>7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad<emph.end type="italics"/> 420, <emph type="italics"/>grauitas igitur aquæ, magnitudinem habentis æ<lb/>qualem argento viuo A, erit<emph.end type="italics"/> 420. </s>

<s><emph type="italics"/>Contra. </s>

Line 544

<s>Qua ratione inuenienda &longs;it grauitas argenti viui, ma<lb/>gnitudinem habentis propo&longs;ito cuicunque corpori &longs;oli<lb/>do æqualem. </s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus &longs;olidum, vtpote plumbeum A, cuius <lb/>grauitas<emph.end type="italics"/> 161, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui <lb/>magnitudine æqualis propo&longs;ito plumbo A. inueniatur grauitas aquæ <lb/>magnitudinem babentis æqualem plumbo A, vt in exemplo propo&longs;i<lb/>tionis<emph.end type="italics"/> 8, <emph type="italics"/>dictum e&longs;t, quæ &longs;it<emph.end type="italics"/> 14, <emph type="italics"/>& inuenta grauitate argenti viui, ma<lb/>gnitudine æqualis ip&longs;i aquæ, ea erit de qua quæritur, &longs;it enim inuen <lb/>ta argenti viui grauitas<emph.end type="italics"/> 190. <emph type="italics"/><expan abbr="Quoniã">Quoniam</expan> igitur argentum viuum, cuius <lb/>grauitas est<emph.end type="italics"/> 190, <emph type="italics"/>magnitudine æquatur aquæ, cuius grauitas e&longs;t<emph.end type="italics"/> 14, <lb/><emph type="italics"/>ip&longs;ique aquæ æquatur magnitudine plumbum A, erit argentum vi<lb/>uum, cuius grauitas 190, magnitudine propo&longs;ito plumbo A, æquale; <lb/>quare inuenta est grauitas argenti viui, magnitudine æqualis propo<lb/>&longs;ito plumbo A, quod facere oportebat.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit propo&longs;itum aliquod corpus &longs;olidum, vtpote plumbeum A, cuius <lb/>grauitas<emph.end type="italics"/> 161, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui <lb/>magnitudine æqualis propo&longs;ito plumbo A. inueniatur grauitas aquæ <lb/>magnitudinem habentis æqualem plumbo A, vt in exemplo propo&longs;i<lb/>tionis<emph.end type="italics"/> 8, <emph type="italics"/>dictum e&longs;t, quæ &longs;it<emph.end type="italics"/> 14, <emph type="italics"/>& inuenta grauitate argenti viui, ma<lb/>gnitudine æqualis ip&longs;i aquæ, ea erit de qua quæritur, &longs;it enim inuen <lb/>ta argenti viui grauitas<emph.end type="italics"/> 190. <emph type="italics"/><expan abbr="Quoniã">Quoniam</expan> igitur argentum viuum, cuius <lb/>grauitas est<emph.end type="italics"/> 190, <emph type="italics"/>magnitudine æquatur aquæ, cuius grauitas e&longs;t<emph.end type="italics"/> 14, <lb/><emph type="italics"/>ip&longs;ique aquæ æquatur magnitudine plumbum A, erit argentum vi<lb/>uum, cuius grauitas 190, magnitudine propo&longs;ito plumbo A, æquale; <lb/>quare inuenta est grauitas argenti viui, magnitudine æqualis propo<lb/>&longs;ito plumbo A, quod facere oportebat.<emph.end type="italics"/></s>

<s>Quomodo inuenienda &longs;it grauitas cuiu&longs;cunque cor-<pb pagenum="25"/>poris &longs;olidi, magnitudinem habentis propo&longs;ito corpori <lb/>ex argento viuo æqualem. </s>

Line 592

<s><emph type="italics"/>Similiter &longs;i <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> &longs;it aliquod corpus aqueum A, cuius magnitu <lb/>do<emph.end type="italics"/> 5700, <emph type="italics"/>& oporteat inuenire, quanta erit magnitudo argenti viui, <lb/>grauitatem habentis æqualem propo&longs;itæ aquæ A. </s>

<s>Accipiatur aliquod <lb/>corpus &longs;olidum C &longs;i aureum, &longs;uper inducatur ei cerea tunica propter <lb/>iam <expan abbr="dictã">dictam</expan> rationem, deinde argenti viui, magnitudine æqualis ip&longs;i C, <lb/>inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>&longs;imiliter & aquæ <expan abbr="magnitudin&etilde;">magnitudinem</expan> ha<lb/>bentis equalem eidem C, inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 7, <emph type="italics"/>& &longs;iat vt<emph.end type="italics"/> 95, <lb/><emph type="italics"/>ad<emph.end type="italics"/> 7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 420, <emph type="italics"/>is igitur numerus in<lb/>dicabit quanta erit magnitudo argenti viui grauitatem habentis <lb/>æqualem propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

<s>Accipiatur aliquod <lb/>corpus &longs;olidum C &longs;i aureum, &longs;uper inducatur ei cerea tunica propter <lb/>iam <expan abbr="dictã">dictam</expan> rationem, deinde argenti viui, magnitudine æqualis ip&longs;i C, <lb/>inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>&longs;imiliter & aquæ <expan abbr="magnitudin&etilde;">magnitudinem</expan> ha<lb/>bentis equalem eidem C, inueniatur grauitas quæ &longs;it<emph.end type="italics"/> 7, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <lb/><emph type="italics"/>ad<emph.end type="italics"/> 7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 420, <emph type="italics"/>is igitur numerus in<lb/>dicabit quanta erit magnitudo argenti viui grauitatem habentis <lb/>æqualem propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

<s>Quod &longs;i propo&longs;itum corpus aqueum A, &longs;it &longs;phæricum, culus <lb/>&longs;phæræ diameter &longs;it 10, & oporteat inuenire quanta erit dia<lb/>meter &longs;phæræ ex argento viuo, grauitatem habentis æqualem <lb/>propo&longs;itæ &longs;phæræ A, ità faciendum erit. </s>

Line 618

<s>&longs;it enim &longs;i &longs;ieri pote&longs;t corpus A, leuius corpore B, <pb 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="fig13"/><lb/>æquale, & corpori M, appen <lb/>datur corpus A. </s>

<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;uper&longs;icies &longs;phæ<lb/>rica e&longs;t, cui <gap/> &longs;phæræ cen<lb/>trum idem <gap/>, quod <expan abbr="centr&utilde;">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, cui <gap/> &longs;phæræ cen<lb/>trum idem <gap/>, quod <expan abbr="centr&utilde;">centrum</expan> <lb/>terræ, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib.

1. de <lb/>ijs, quæ vehuntur in aqua. </s>

<s>Inteligantur etiam duæ pyramides con<lb/>iunctæ, & continuatæ, æquales, & &longs;imiles KCD, KDE, pro ba&longs;ibus <lb/>habentes in &longs;uper&longs;icie aquæ parallelogramma, vertices autem pun<lb/>ctum K, & corpora L, B, comprehendantur à pyramide KDE, corpo<lb/>ra vero M, A, à pyramide KCD, & &longs;ub corporibus L, B, de&longs;cribatur <lb/>quædam alterius &longs;phæræ &longs;uper&longs;icies FGH, in aqua, circa centrum K, <lb/>poterit autem huiu&longs;modi &longs;uper&longs;icies &longs;ub corporibus L, B, de&longs;cribi, <lb/>quoniam & &longs;i ip&longs;i corpora demerguntur tota, non ideo feruntur <lb/>deor&longs;um, ponuntur enim æque grauia atque aqua. </s>

<s>Inteligantur etiam duæ pyramides con<lb/>iunctæ, & continuatæ, æquales, & &longs;imiles KCD, KDE, pro ba&longs;ibus <lb/>habentes in &longs;uperficie aquæ parallelogramma, vertices autem pun<lb/>ctum K, & corpora L, B, comprehendantur à pyramide KDE, corpo<lb/>ra vero M, A, à pyramide KCD, & &longs;ub corporibus L, B, de&longs;cribatur <lb/>quædam alterius &longs;phæræ &longs;uperficies FGH, in aqua, circa centrum K, <lb/>poterit autem huiu&longs;modi &longs;uperficies &longs;ub corporibus L, B, de&longs;cribi, <lb/>quoniam & &longs;i ip&longs;i corpora demerguntur tota, non ideo feruntur <lb/>deor&longs;um, ponuntur enim æque grauia atque aqua. </s>

<s>Quoniam <lb/>igitur eiu&longs;dem generis ponuntur corpora M, L, & æqualia, & &longs;imilia, <lb/>erunt æque grauia, cum in aqua, tum in aere, & quoniam corpus <lb/>A, leuins e&longs;t in aqua, corpore B, erunt corpora M, A, &longs;imul, in aqua <lb/>leuiora corporibus L, B, &longs;ed corpora L, B, &longs;imul, æque grauia &longs;unt at<lb/>que aqua, ergo corpora M, A, &longs;imul, leuiora erunt quam aqua; quare <lb/>corpus M, non demergetur totum, &longs;ed aliqua pars ip&longs;ius ex aquæ &longs;u<lb/>per&longs;icie extabit. </s>

<s>Et quoniam eiu&longs;dem generis, & grauitatis ponuntur corpora A, B, <lb/>erunt magnitudine æqualia, & per additionem æqualium æquali<lb/>bus, corpora M, A, erunt æqualia corporibus L, B, </s>

<s>Quoniam igitur corpora M, A, æqualia &longs;unt corporibus L, B, pars <lb/>autem corporis M, extat ex aquæ &longs;uper&longs;icie, & corpora L, B, tota de<lb/>merguntur, minus loci ocupabunt in aqua corpora M, A, quam cor<lb/>pora L, B, quare maior erit grauitas corporum M, A, & aquæ conti<lb/>nentis ip&longs;a corpora, quæ e&longs;t in loco pyramidis CDGF, quam corpo<lb/>rum L, B, & aquæ ip&longs;a corpora <expan abbr="contin&etilde;tis">continentis</expan> in loco pyramidis DEHG, <pb pagenum="30"/>magis igitur aquæ pars premetur, quæ e&longs;t &longs;ub &longs;uper&longs;icie FG, quam <lb/>ca quæ e&longs;t &longs;ub &longs;uper&longs;icie GH; quare expellet partem minus pre&longs;&longs;am, <lb/>(æqualiter enim & continuatæ iacent inter &longs;e&longs;e) & <expan abbr="nõ">non</expan> manebit aqua, <lb/>quod e&longs;t ab&longs;urdum, ponebatur enim manens. </s>

<s>Quoniam igitur corpora M, A, æqualia &longs;unt corporibus L, B, pars <lb/>autem corporis M, extat ex aquæ &longs;uperficie, & corpora L, B, tota de<lb/>merguntur, minus loci ocupabunt in aqua corpora M, A, quam cor<lb/>pora L, B, quare maior erit grauitas corporum M, A, & aquæ conti<lb/>nentis ip&longs;a corpora, quæ e&longs;t in loco pyramidis CDGF, quam corpo<lb/>rum L, B, & aquæ ip&longs;a corpora <expan abbr="contin&etilde;tis">continentis</expan> in loco pyramidis DEHG, <pb pagenum="30"/>magis igitur aquæ pars premetur, quæ e&longs;t &longs;ub &longs;uperficie FG, quam <lb/>ca quæ e&longs;t &longs;ub &longs;uperficie GH; quare expellet partem minus pre&longs;&longs;am, <lb/>(æqualiter enim & continuatæ iacent inter &longs;e&longs;e) & <expan abbr="nõ">non</expan> manebit aqua, <lb/>quod e&longs;t ab&longs;urdum, ponebatur enim manens. </s>

<s>non igitur corpus A, <lb/>leuius e&longs;t in aqua corpore B. eadem ratione o&longs;tendetur neque corpus <lb/>B, leuius e&longs;&longs;e in aqua corpore A, quare con&longs;tat propo&longs;itum. </s>

Line 692

<s>Hic &longs;equitur tabula, ad inueniendas &longs;phærarum grauita<lb/>tes, ex data diametrorum magnitudine, cuius hæc e&longs;t <lb/>explicatio. </s>

<s><emph type="italics"/>In dimetiendis &longs;pbærarum diametris vtimur pede Romano anti<lb/>quo, cuius men&longs;uram in margine appo&longs;uimus, eaque re&longs;pondet ad Ro<lb/>mani palmi, quo bodie vtimur, men&longs;uram vt 4, ad 3, buiu&longs;modipe<lb/>dem diuidimus in duodeeim partes æquales, &longs;eu vncias, quas inutnies <lb/>in prima Columna &longs;ub titulo magnitudinis.<emph.end type="italics"/></s>

<s><emph type="italics"/>In dimetiendis &longs;phærarum diametris vtimur pede Romano anti<lb/>quo, cuius men&longs;uram in margine appo&longs;uimus, eaque re&longs;pondet ad Ro<lb/>mani palmi, quo bodie vtimur, men&longs;uram vt 4, ad 3, buiu&longs;modipe<lb/>dem diuidimus in duodeeim partes æquales, &longs;eu vncias, quas inutnies <lb/>in prima Columna &longs;ub titulo magnitudinis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ponderibus autem vtimur bac 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, & &longs;cru<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, & &longs;cru<lb/>pulum in<emph.end type="italics"/> 24, <emph type="italics"/>grana. </s>

<s>Ad inueniendas igitur &longs;pbærarum grauitates ex <lb/>data diametrorum magnitudine, bæc erit ratio.<emph.end type="italics"/></s>

<s>Ad inueniendas igitur &longs;phærarum grauitates ex <lb/>data diametrorum magnitudine, bæc erit ratio.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quæris grauitatem &longs;pbæræ plumbeæ, diametrum habentis<emph.end type="italics"/> 3, <emph type="italics"/>vn<lb/>ciarum, in&longs;pice tabulam, & in linea trium vnciarum, &longs;ub titulo gra<lb/>uitatis plumbeæ &longs;pbæræ, deprebendes ip&longs;am &longs;pbæram grauitætem ba<lb/>bere lib.<emph.end type="italics"/> 7, <emph type="italics"/>vne.<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>

<s><emph type="italics"/>Quæris grauitatem &longs;phæræ plumbeæ, diametrum habentis<emph.end type="italics"/> 3, <emph type="italics"/>vn<lb/>ciarum, in&longs;pice tabulam, & in linea trium vnciarum, &longs;ub titulo gra<lb/>uitatis plumbeæ &longs;phæræ, deprebendes ip&longs;am &longs;pbæram grauitætem ba<lb/>bere lib.<emph.end type="italics"/> 7, <emph type="italics"/>vne.<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>

<s><emph type="italics"/>Rur&longs;us, quæris grauitatem &longs;pbæræ aureæ, diametrum habentis<emph.end type="italics"/> 6, <lb/><emph type="italics"/>vnciarum. </s>

<s><emph type="italics"/>Rur&longs;us, quæris grauitatem &longs;phæræ aureæ, diametrum habentis<emph.end type="italics"/> 6, <lb/><emph type="italics"/>vnciarum. </s>

<s>in linea<emph.end type="italics"/> 6, <emph type="italics"/>vnciarum, &longs;ub titulo grauitatis aureæ &longs;pbæræ<emph.end type="italics"/><pb pagenum="35"/><emph type="italics"/>datur quæ&longs;ita grauitas lib.<emph.end type="italics"/> 97, <emph type="italics"/>vnc.<emph.end type="italics"/> 6, <emph type="italics"/>&longs;crup. </s>

<s>in linea<emph.end type="italics"/> 6, <emph type="italics"/>vnciarum, &longs;ub titulo grauitatis aureæ &longs;phæræ<emph.end type="italics"/><pb pagenum="35"/><emph type="italics"/>datur quæ&longs;ita grauitas lib.<emph.end type="italics"/> 97, <emph type="italics"/>vnc.<emph.end type="italics"/> 6, <emph type="italics"/>&longs;crup. </s>

<s><emph type="italics"/>Quæris denique grauitatem &longs;pbæræ stanneæ, diametrum habentis <lb/>vnius pedis. </s>

<s><emph type="italics"/>Quæris denique grauitatem &longs;phæræ stanneæ, diametrum habentis <lb/>vnius pedis. </s>

<s>in linea vnius pedis, &longs;eu 12, vnciarum, &longs;ub titulo graui<lb/>tatis &longs;pbæræ &longs;tanneæ, datur quæ&longs;ita &longs;pbæræ grauitas lib.<emph.end type="italics"/> 304, <emph type="italics"/>adun<lb/>quem. </s>

<s>in linea vnius pedis, &longs;eu 12, vnciarum, &longs;ub titulo graui<lb/>tatis &longs;phæræ &longs;tanneæ, datur quæ&longs;ita &longs;phæræ grauitas lib.<emph.end type="italics"/> 304, <emph type="italics"/>adun<lb/>quem. </s>

<s>Atque ita reliquarum &longs;pbærarum in tabula nominatarum, ex <lb/>data diametrorum magnitudine, grauitates inuenies.<emph.end type="italics"/></s>

<s>Atque ita reliquarum &longs;phærarum in tabula nominatarum, ex <lb/>data diametrorum magnitudine, grauitates inuenies.<emph.end type="italics"/></s>

<s>Qua ratione hanc Tabulam compo&longs;uimus. </s>

<s><emph type="italics"/>Primum inueniendam curauimus grauitatem alicuius &longs;pbæræ, da<lb/>tem habentis diametrum, & ad boc faciendum, oportebat aliquam <lb/>&longs;pbæram efficere, &longs;ed quoniam ad illam efficiendam, exactam buman<gap/><lb/>diligentia non &longs;ufficit, fieri curauimus Cylindrum ex &longs;tanno, altitu<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;pbæra, & facilius. </s>

<s><emph type="italics"/>Primum inueniendam curauimus grauitatem alicuius &longs;phæræ, da<lb/>tem habentis diametrum, & ad hoc faciendum, oportebat aliquam <lb/>&longs;pbæram efficere, &longs;ed quoniam ad illam efficiendam, exactam buman<gap/><lb/>diligentia non &longs;ufficit, fieri curauimus Cylindrum ex &longs;tanno, altitu<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;pbæra, & facilius. </s>

<s>huius au<lb/>tem Cylindri altitudo, vel diameter ip&longs;ius ba&longs;is, erat duarum vncia<lb/>rum prædicti pedis Romani, grauitas vero duarum librarum, cum <lb/>vna vncia, & octo &longs;crupulis, &longs;iue vt boc pondus ad grana reducamus, <lb/>Cylindri grauitas erat Gran. 14592. abstulimns ab bac Cylindri <lb/>grauitate partem tertiam. </s>

<s>huius au<lb/>tem Cylindri altitudo, vel diameter ip&longs;ius ba&longs;is, erat duarum vncia<lb/>rum prædicti pedis Romani, grauitas vero duarum librarum, cum <lb/>vna vncia, & octo &longs;crupulis, &longs;iue vt hoc pondus ad grana reducamus, <lb/>Cylindri grauitas erat Gran. 14592. abstulimns ab bah 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<lb/>uauimus, pro grauitate &longs;pbæræ, diametrum habentis æqualem altitu<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;pbæra, & Cylindro, Cylindrum, qui ba&longs;im habeat maximo in &longs;pbæra <lb/>circulo equalem, & altitudinem æqualem diametro &longs;pbæræ, ad ip&longs;am <lb/>&longs;pbæram &longs;e&longs;quialterum e&longs;&longs;e; itaque grauitatem &longs;pbæræ, diametrum <lb/>habentis duarum vnciarum inuenimus e&longs;&longs;e gran.<emph.end type="italics"/> 9728. </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<lb/>uauimus, pro grauitate &longs;phæræ, diametrum habentis æqualem altitu<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;pbæra, & Cylindro, Cylindrum, qui ba&longs;im habeat maximo in &longs;pbæra <lb/>circulo equalem, & altitudinem æqualem diametro &longs;phæræ, ad ip&longs;am <lb/>&longs;pbæram &longs;e&longs;quialterum e&longs;&longs;e; itaque grauitatem &longs;phæræ, diametrum <lb/>habentis duarum vnciarum inuenimus e&longs;&longs;e gran.<emph.end type="italics"/> 9728. </s>

<s><emph type="italics"/>Inuenta igitur grauitate &longs;pbæræ, cuius diameter est duarum vn<lb/>ciarum, facile inuenientur reliquarum <expan abbr="&longs;pbærar&utilde;">&longs;pbærarum</expan> grauitates, &longs;i enim <lb/>inuenienda &longs;it grauitas &longs;pbæræ stannea habentis diametrum<emph.end type="italics"/> 1/4. <emph type="italics"/>vn<lb/>ciæ, 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;phæræ igitur cuius diameter e&longs;t<emph.end type="italics"/> 1/4, <lb/><emph type="italics"/>vnciæ, grauitas erit gran. 19, osten&longs;um enim est prop.

<s><emph type="italics"/>Inuenta igitur grauitate &longs;phæræ, cuius diameter est duarum vn<lb/>ciarum, facile inuenientur reliquarum <expan abbr="&longs;pbærar&utilde;">&longs;phærarum</expan> grauitates, &longs;i enim <lb/>inuenienda &longs;it grauitas &longs;phæræ stannea habentis diametrum<emph.end type="italics"/> 1/4. <emph type="italics"/>vn<lb/>ciæ, 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;phæræ igitur cuius diameter e&longs;t<emph.end type="italics"/> 1/4, <lb/><emph type="italics"/>vnciæ, grauitas erit gran. 19, osten&longs;um enim est prop.

17, huius, &longs;phæ<lb/>ras eiu&longs;dem generis inter &longs;e e&longs;&longs;e in grauitate, vt diametrorum cubi in <lb/>magritudine.<emph.end type="italics"/></s>

Line 938

<s><emph type="italics"/>Sit aliquod corpus mistum ex auro. </s>

<s>& ære, & babeat grauitatem <lb/>171. lib.

<s>& ære, & habeat grauitatem <lb/>171. lib.

& oporteat inuenire quanta erit portio æris in ip&longs;o corpore,<emph.end type="italics"/><pb pagenum="56"/><emph type="italics"/>& quanta auri. </s>

Line 980

<s>Qhoniam igitur <lb/>corpus D, æquale e&longs;t corpori Q, magnitudine, & portio C, æqualis <lb/>portioni Lerit vt D, ad Q, ita C, ad L, & permutando vt D, ad C, ita <lb/>Q, ad L, & quoniam eiu&longs;dem &longs;unt genoris D, C, &longs;imiliter & Q, L, * erit<arrow.to.target n="note52"/><lb/>vt grauitas corporis D, hoc e&longs;t vt EK; ad K, ita H, ad V. </s>

<s><margin.target id="note52"/>4.<emph type="italics"/>buius<emph.end type="italics"/></s>

<s><margin.target id="note52"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s>Similiter quoniam ponuntur æqualia magnitudine corpora A, P, <lb/>& æquales quoque portiones B, O, erit vt A, ad P, ita B, ad O, & per<lb/>mutando vt A, ad B, ita P, ad O, &longs;ed eiu&longs;dem &longs;unt generis A, B, &longs;imili<lb/>ter & P, O, * vt igitur grauitas corporis A, id e&longs;t vt EK, ad E, ita erit<arrow.to.target n="note53"/><lb/>G, ad F, & per conuer&longs;ionem rationis erit vt EK, ad K, ita G, ad G, <lb/>minus F, &longs;ed demon&longs;tratum e&longs;t, vt EK, ad K, ita e&longs;&longs;e H, ad V, ergo vt <lb/>H, ad V, ita erit G, ad G, minus F, & permutando vt H, ad G, ita V, <lb/>ad G, minus F, & diuidendo vt H, minus G, ad G, ita erit FV, minus <lb/>G, ad G, minus F, rur&longs;us permutando erit vt H, minus G, ad FV, mi<lb/>nus G, ita G, ad G, minus F, &longs;ed vt EK, ad K, ita e&longs;t G, ad G, minus F, <lb/>vt e&longs;t demon&longs;tratum, ergo vt H, minus G, ad FV, minus G, ita erit <lb/>EK, ad K, quare permutando vt H, minus G, ad EK, ita erit FV, mi<lb/>nus G, ad K, quod e&longs;tò primum. </s>

<s><margin.target id="note53"/>4.<emph type="italics"/>buius<emph.end type="italics"/></s>

<s><margin.target id="note53"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s>Dico quoque vt H, minus G, ad EK, ita e&longs;&longs;e H, minus FV, ad E. </s>

<s><lb/>Quoniam enim o&longs;ten&longs;um e&longs;t vt EK, ad K, ita e&longs;&longs;e H, ad V, erit per <lb/>conuer&longs;ionem rationis vt EK, ad E, ita H, ad H, minus V, &longs;ed demon<lb/>&longs;tratum e&longs;t vt EK, ad E, ita e&longs;&longs;e G, ad F, ergo vt H, ad H, minus V, ita <lb/>erit G, ad F, & permutando vt H, ad G, ita H, minus V, ad F, & diui<lb/>dendo vt H, minus G, ad G, ita erit H, minus FV, ad F, & permutan<lb/>do vt H, minus G, ad H, minus FV, ita G, ad F, &longs;ed vt EK, ad E, ita e&longs;t <lb/>G, ad F, vt e&longs;t demon&longs;tratum, ergo vt H, minus G, ad H, minus FV, <lb/>ita erit EK, ad E, quare permutando, erit vt H, minus G, ad EK, ita <lb/>H, minus FV, ad E, quod erat &longs;ecundo loco demon&longs;trandum. </s>

<s>Svpere&longs;t igitur vt dicamus, qua ratione ex grauitate aúri <lb/>cogno&longs;ci po&longs;&longs;it eius qualitas; id quod ex ijs, quæ dicta <lb/>&longs;unt facilè colligitur; &longs;i videlicet nota &longs;iat cuiu&longs;uis ma&longs;&longs;æ auri <lb/>grauitas, quam habet tum in aere, tum in aqua. </s>

<s>Svpere&longs;t igitur vt dicamus, qua ratione ex grauitate aúri <lb/>cogno&longs;ci po&longs;&longs;it eius qualitas; id quod ex ijs, quæ dicta <lb/>&longs;unt facilè colligitur; &longs;i videlicet nota fiat cuiu&longs;uis ma&longs;&longs;æ auri <lb/>grauitas, quam habet tum in aere, tum in aqua. </s>

<s>Sed ante <lb/>omnia, duo nobis &longs;unt præmittenda, & explicanda. </s>

Line 1004

<s>& quia hæc affectio multiplex e&longs;t, ide<gap/> etiam auri qualitas, <lb/>qua ex varia mixtione na&longs;citur, varia &longs;it est nece&longs;&longs;au quamuis vna <lb/>tantum&longs;it qualitas auri puri. </s>

<s>Qualitas enim auri in quouis cor <lb/>pore propo&longs;ito, exprimitur partibus auripuri, qua &longs;unt in ip&longs;o corpo<lb/>re, non in magnitudine, &longs;ed in grauitate &longs;umptis, qualibus totum cor<lb/>pus constat<emph.end type="italics"/> 24<emph type="italics"/>: vel quod idem est, auri qualitas exprimitur in ra<lb/>tione quam babent illæ partes in grauitate ad totum corpas: quod <lb/>exemplo clarius explicabitur in bunc modum.<emph.end type="italics"/></s>

<s>Qualitas enim auri in quouis cor <lb/>pore propo&longs;ito, exprimitur partibus auripuri, qua &longs;unt in ip&longs;o corpo<lb/>re, non in magnitudine, &longs;ed in grauitate &longs;umptis, qualibus totum cor<lb/>pus constat<emph.end type="italics"/> 24<emph type="italics"/>: vel quod idem est, auri qualitas exprimitur in ra<lb/>tione quam babent illæ partes in grauitate ad totum corpas: quod <lb/>exemplo clarius explicabitur in hunc modum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit aliquod corpus aureum, exempli gratia<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum, quod <lb/>expurgatum & ad aurum purum red<gap/>ctum, 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"/>vnciæ auri puri, reliquum vero vel euanuerit in fumum, <lb/>vel fuerit alterius metalli. </s>

Line 1020

<s>Non enim purificant totum corpus propo&longs;itum, &longs;ed ali<lb/>quam eius particulam etiam perexiguam, quam &longs;olam ad aurum pu<lb/>rum reducunt. </s>

<s>bac enim reducta, non &longs;olum recte definiunt cuius <lb/>fuerit qualitatis particula illa purificata ante purificationem; ve<lb/>rum etiam cuius fuerit qualitatis, & quot partium fuerit illud cor<lb/>pus, à quo eadem particula detracta fuit, & illud, quod adbuc &longs;u<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<lb/>rum etiam cuius fuerit qualitatis, & quot partium fuerit illud cor<lb/>pus, à quo eadem particula detracta fuit, & illud, quod adbuc &longs;u<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<lb/>tatem &longs;i forte aurifices inuestigare velint, detrabent ex eo particu<lb/>lam, verbi gratia, vnius vnciæ, vel qued idem est particulam<emph.end type="italics"/> 24. <pb pagenum="61"/><emph type="italics"/>&longs;<gap/>puforam; & banc particulam exeoquent ad qualitatem o&longs;que <lb/>c<gap/>ripuri. </s>

<s>Bt &longs;t quidem inuenerint, ex priori gr<gap/>uitate<emph.end type="italics"/> 24. <emph type="italics"/>&longs;or<gap/><lb/>pulorum, deperi&longs;&longs;e nibil: pronunciabunt aurum sllud, boc est, non <lb/>&longs;olum partieulam illam excoctam, &longs;ed ctiam illud d quo fait dotr<gap/><lb/>sta, nec non & 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<lb/>tum purum. </s>

<s>Bt &longs;t quidem inuenerint, ex priori gr<gap/>uitate<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 ctiam illud d quo fait dotr<gap/><lb/>sta, nec non & 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<lb/>tum purum. </s>

<s>Sivero deprebendirine gra<gap/>m diminuta<gap/>, ver<lb/>bi gratia, n<gap/>e e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>&longs;crupulorum, quæ ante defæcationem fait<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 &longs;ni&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium & <lb/>illud quod teman&longs;it e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium & d<gap/>nique particul<gap/> expur<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>

<s><emph type="italics"/>Et eodem modo pronunclabunt de quibafeunque alys auri quali<lb/>atibus, &longs;ecundum partes auri puri, quas in qualibet ma&longs;&longs;a auri in<lb/>uenerint, ea&longs;que vige&longs;imas quartai tutius grauitatis, non magnita<lb/>dinis. </s>

<s>Nam cum in bac comparatione qualitatum, &longs;epr&longs;im habe a<lb/>tar ratio partium auri, & &longs;eor&longs;im metallorum alligatorum; manife<lb/>stum est &longs;i grauitas totius corporis intelligatur diui&longs;a in<emph.end type="italics"/> 24. <emph type="italics"/>partes <lb/>equales, ex quibus<emph.end type="italics"/> 20. <emph type="italics"/>&longs;int auri, duæ argenti, & duæ æris; quumli<lb/>bet partem auri cum qualibet parte argenti & æris collatam, magni<lb/>tudine e&longs;&longs;e minorem; & &longs;imiliter partem argenti minorem parte <lb/>aris; propterea quod aurum omnia reliqua metalla &longs;uperet grauit<gap/><lb/>te quemadmodum & argentum ip&longs;uon as, vt constat experi<gap/>nt<gap/><lb/>atque hinc constat quam apte ac conuenienter Aurifices vtantur <lb/>voeabulo parlium. </s>

<s>Nam cum in hac comparatione qualitatum, &longs;epr&longs;im habe a<lb/>tar ratio partium auri, & &longs;eor&longs;im metallorum alligatorum; manife<lb/>stum est &longs;i grauitas totius corporis intelligatur diui&longs;a in<emph.end type="italics"/> 24. <emph type="italics"/>partes <lb/>equales, ex quibus<emph.end type="italics"/> 20. <emph type="italics"/>&longs;int auri, duæ argenti, & duæ æris; quumli<lb/>bet partem auri cum qualibet parte argenti & æris collatam, magni<lb/>tudine e&longs;&longs;e minorem; & &longs;imiliter partem argenti minorem parte <lb/>aris; propterea quod aurum omnia reliqua metalla &longs;uperet grauit<gap/><lb/>te quemadmodum & argentum ip&longs;uon as, vt constat experi<gap/>nt<gap/><lb/>atque hinc constat quam apte ac conuenienter Aurifices vtantur <lb/>voeabulo parlium. </s>

<s>bao enim ratione <gap/>dem numero exprimunt vnam <lb/>quamque qualitatem auri cuiuslibet ma&longs;&longs;æ propo&longs;itæ. </s>

Line 1040

<s><emph type="italics"/>Inter varias autem & multiplices auri compo&longs;itiones quibus <lb/>cum alys metallis alligari potest, eam retinuere aurifices, quam diu<lb/>turna experientia deprebenderunt omnibus alys e&longs;&longs;e commodiorem, <lb/>eam nimirum quæ ab auri &longs;imilitudine vel minimum di&longs;cedat; qua<lb/>lis e&longs;t quæ &longs;olius argenti atque æris mixtione perficitur. </s>

<s>Et quidem <lb/>&longs;ipartes auri excipias, aris atquo argenti partes, quæ auro &longs;unt per<lb/>mi&longs;cendæ &longs;emper volunte&longs;&longs;e æquales in grauitate: propterea quod <lb/>eadem experientia Magi&longs;tra didicerunt bunc e<32>e mixtionis modum <lb/>longe optimum.<emph.end type="italics"/></s>

<s>Et quidem <lb/>&longs;ipartes auri excipias, aris atquo argenti partes, quæ auro &longs;unt per<lb/>mi&longs;cendæ &longs;emper volunte&longs;&longs;e æquales in grauitate: propterea quod <lb/>eadem experientia Magi&longs;tra didicerunt hunc e<32>e mixtionis modum <lb/>longe optimum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quando ergo aurifices volunt producere aurum cuiu&longs;cunque <lb/>qualitatis, accipiunt tot partes auri puri æquales, quot partium fu<lb/>turum e&longs;t aurum producendum, pauciores tamen partibus<emph.end type="italics"/> 24, & <pb pagenum="62"/><emph type="italics"/>veliquas partes quæ d &longs;unt ad<emph.end type="italics"/> 24, <emph type="italics"/>explent argento & <gap/>e, &longs;umendo <lb/>exvtreque metallo parles aquales in grauite; atque bis rite inter&longs;e <lb/>permixtis componunt aurum de&longs;ideratæ qualitatis: eamque deno<lb/>minant à partibus auripuri in mixtione a&longs;umptis. </s>

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<s>In auro vero<emph.end type="italics"/> 22, <emph type="italics"/>par<lb/>tium, auri e&longs;&longs;e<emph.end type="italics"/> 23, <emph type="italics"/>argenti vnam, & æris vnam, &longs;ie enim iterum <lb/>&longs;amma omnium partium est<emph.end type="italics"/> 240 <emph type="italics"/>cademqus est ratio de reliquis ita <lb/><gap/>t numerus partium auri, &longs;e<gap/>per denovinet qualitatem auri, & <lb/>vna medietas reliquarum partium, quæ partibus a<gap/>ri de&longs;unt ad <lb/><gap/>omplendas partes<emph.end type="italics"/> 24, <emph type="italics"/>&longs;it argenti, & reliqua medictas &longs;it æris. </s>

<s>bac <lb/>enim &longs;atis est &longs;uppo&longs;ui&longs;&longs;e, ad nouum illud artificium, quo paulo po&longs;t <lb/>inuestig aturi &longs;umus auri qualitat<gap/> ex &longs;ola grauitate quam babe<gap/><lb/>in aere & aqua, eamque qualitatem dupliei via inuestigabimus <gap/><lb/>vnape<gap/> calculum, par tabellam altera: & <gap/>ia ad calculum &longs;pe<lb/>stant ea, quæ &longs;uperi<gap/> inu<gap/>imus, de grauitate metallorum bucre<lb/>ferenda cen&longs;uimus quæ bic &longs;unt nece&longs;&longs;aria, cuiu&longs;modi &longs;unt auri, <lb/>argenti, atque æris grauitas, quam obtinent in aere, & aqua, qu<gap/><lb/>quidem ita &longs;e habet vt &longs;equitur.<emph.end type="italics"/></s>

<s>hac <lb/>enim &longs;atis est &longs;uppo&longs;ui&longs;&longs;e, ad nouum illud artificium, quo paulo po&longs;t <lb/>inuestig aturi &longs;umus auri qualitat<gap/> ex &longs;ola grauitate quam babe<gap/><lb/>in aere & aqua, eamque qualitatem dupliei via inuestigabimus <gap/><lb/>vnape<gap/> calculum, par tabellam altera: & <gap/>ia ad calculum &longs;pe<lb/>stant ea, quæ &longs;uperi<gap/> inu<gap/>imus, de grauitate metallorum bucre<lb/>ferenda cen&longs;uimus quæ bic &longs;unt nece&longs;&longs;aria, cuiu&longs;modi &longs;unt auri, <lb/>argenti, atque æris grauitas, quam obtinent in aere, & aqua, qu<gap/><lb/>quidem ita &longs;e habet vt &longs;equitur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Auripuri grauitas, quæ in aere e&longs;t<emph.end type="italics"/> 19, <emph type="italics"/>erit in aqua<emph.end type="italics"/> 18. </s>

Line 1066

<s><emph type="italics"/>Aes ad aquam &longs;e habet in grauitate vt<emph.end type="italics"/> 9, <emph type="italics"/>ad<emph.end type="italics"/> 1. </s>

<s><emph type="italics"/>Ex quibus clari&longs;&longs;ime colligitur, &longs;i aliquod corpus mistum con<lb/>stet partibus æqualibus argenti, & aeris in grauitate, quantam <lb/>grauitatem babeat in aqua & que &longs;it ratio in grauitate ip&longs;ius mi<lb/>sti ad aquam &longs;i enim grauitas aeris in aere &longs;it<emph.end type="italics"/> 9, <emph type="italics"/>eius grauitas in <lb/>aqua erit<emph.end type="italics"/> 8, <emph type="italics"/>& &longs;i grauitas argenti in aere &longs;it quoque<emph.end type="italics"/> 9, <emph type="italics"/>erit eius gra<gap/><emph.end type="italics"/><pb pagenum="63"/><emph type="italics"/>vitas in àqua<emph.end type="italics"/> 8 4/11, <emph type="italics"/>est enim vt 9, ad<emph.end type="italics"/> 8 4/11 <emph type="italics"/>vt<emph.end type="italics"/> 31, <emph type="italics"/>ad<emph.end type="italics"/> 28: <emph type="italics"/>Quare &longs;i <lb/>grauitas corporis mi&longs;ti ex argento, & ære iu<gap/>ta mixtionem prædi<lb/>ctam, quæ etiam &longs;ubinte<gap/>genda erit in &longs;iq<gap/>bus, in aere fuerit<emph.end type="italics"/><lb/>18, <emph type="italics"/>erit iu aqua<emph.end type="italics"/> 16<gap/> <emph type="italics"/>& còn&longs;eq<gap/> grauitas aquæ magnitu-<emph.end type="italics"/><arrow.to.target n="note54"/><lb/><emph type="italics"/>dinem habentis æqualem <gap/> eor por<gap/> misto<gap/><emph.end type="italics"/> <gap/>; <emph type="italics"/>quare corpus <lb/><gap/>stum ex argento & are ad carpui aqueum eia&longs;dem magnitudi<lb/><gap/>is, rationem habe<gap/>it <gap/> grauitate vt<emph.end type="italics"/> 18, <emph type="italics"/>ad<emph.end type="italics"/> 1 22/11, <emph type="italics"/>vel vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/><lb/><gap/>, <emph type="italics"/>vet <gap/> nique in numerit integrinvt<emph.end type="italics"/> 299, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>omnium enim <lb/>i&longs;torum numerorum eadem e&longs;t ratie.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ex quibus clari&longs;&longs;ime colligitur, &longs;i aliquod corpus mistum con<lb/>stet partibus æqualibus argenti, & aeris in grauitate, quantam <lb/>grauitatem habeat in aqua & que &longs;it ratio in grauitate ip&longs;ius mi<lb/>sti ad aquam &longs;i enim grauitas aeris in aere &longs;it<emph.end type="italics"/> 9, <emph type="italics"/>eius grauitas in <lb/>aqua erit<emph.end type="italics"/> 8, <emph type="italics"/>& &longs;i grauitas argenti in aere &longs;it quoque<emph.end type="italics"/> 9, <emph type="italics"/>erit eius gra<gap/><emph.end type="italics"/><pb pagenum="63"/><emph type="italics"/>vitas in àqua<emph.end type="italics"/> 8 4/11, <emph type="italics"/>est enim vt 9, ad<emph.end type="italics"/> 8 4/11 <emph type="italics"/>vt<emph.end type="italics"/> 31, <emph type="italics"/>ad<emph.end type="italics"/> 28: <emph type="italics"/>Quare &longs;i <lb/>grauitas corporis mi&longs;ti ex argento, & ære iu<gap/>ta mixtionem prædi<lb/>ctam, quæ etiam &longs;ubinte<gap/>genda erit in &longs;iq<gap/>bus, in aere fuerit<emph.end type="italics"/><lb/>18, <emph type="italics"/>erit iu aqua<emph.end type="italics"/> 16<gap/> <emph type="italics"/>& còn&longs;eq<gap/> grauitas aquæ magnitu-<emph.end type="italics"/><arrow.to.target n="note54"/><lb/><emph type="italics"/>dinem habentis æqualem <gap/> eor por<gap/> misto<gap/><emph.end type="italics"/> <gap/>; <emph type="italics"/>quare corpus <lb/><gap/>stum ex argento & are ad carpui aqueum eia&longs;dem magnitudi<lb/><gap/>is, rationem habe<gap/>it <gap/> grauitate vt<emph.end type="italics"/> 18, <emph type="italics"/>ad<emph.end type="italics"/> 1 22/11, <emph type="italics"/>vel vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/><lb/><gap/>, <emph type="italics"/>vet <gap/> nique in numerit integrinvt<emph.end type="italics"/> 299, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>omnium enim <lb/>i&longs;torum numerorum eadem e&longs;t ratie.<emph.end type="italics"/></s>

<s><margin.target id="note54"/>5. <emph type="italics"/>huius<emph.end type="italics"/></s>

Line 1074

<s>Sit <gap/>xemp: gratia propo&longs;ita aliqua <gap/> e&longs;&longs;a aurea, cuius gra<lb/>uitas in aere &longs;it vnc<emph.end type="italics"/> 24, <emph type="italics"/>& oporte at in<gap/> euius qualitatis &longs;it ip<lb/>su<gap/> aurum. </s>

<s>Ponderetur ea ma&longs;&longs;a in aqua & babeat grauitatem <lb/>vnciarum<emph.end type="italics"/> 22 2<gap/>/5301, <emph type="italics"/>ergo * grauitas aquæ magnitudinem babe <gap/><emph.end type="italics"/><arrow.to.target n="note55"/><lb/><emph type="italics"/><gap/>is <gap/>qualem propo&longs;itæ ma&longs;&longs;æ erit vnc.<emph.end type="italics"/> 1 2431/5301. </s>

<s>Ponderetur ea ma&longs;&longs;a in aqua & habeat grauitatem <lb/>vnciarum<emph.end type="italics"/> 22 2<gap/>/5301, <emph type="italics"/>ergo * grauitas aquæ magnitudinem babe <gap/><emph.end type="italics"/><arrow.to.target n="note55"/><lb/><emph type="italics"/><gap/>is <gap/>qualem propo&longs;itæ ma&longs;&longs;æ erit vnc.<emph.end type="italics"/> 1 2431/5301. </s>

<s><margin.target id="note55"/>5.<emph type="italics"/>buius<emph.end type="italics"/></s>

<s><margin.target id="note55"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s><emph type="italics"/>Deinde inueniatur grauitas aquæ magnitudine æqualis 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 eni<gap/> numerus erit grauitas illius aquæ.<emph.end type="italics"/></s>

Line 1088

<s><emph type="italics"/>Deinde quteratur differentia inter primam & tertiam aquæ gra<lb/>uitatem, quæ est vnc.<emph.end type="italics"/> 1 1227/5302, <emph type="italics"/>& hæc differentia statuatur pro <lb/>primo proportionis termino, pro &longs;ecundo termino ponatur grauitas <lb/><gap/>a&longs;&longs;æ propo&longs;itæ idest vnc.<emph.end type="italics"/> 24, <emph type="italics"/>& protertio denique termino ponatur <lb/>different<gap/> inter &longs;ecundam aquæ grauitatem & tertiam, quæ est <lb/>vnc.<emph.end type="italics"/> 1 <gap/> <emph type="italics"/>qua<gap/> eni<gap/> proportionalium ter <gap/>inus nempe<emph.end type="italics"/> 20, </s><pb pagenum="64"/>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>erit de<gap/>ominator qualitatis auri de qua <gap/>uaritur quia ille termi<lb/><gap/>ut indicat partes auri pari i<gap/> grauitate, qualibus ma&longs;&longs;a propo&longs;ita <lb/>constat<emph.end type="italics"/> 24. <emph type="italics"/>Hoc autem de<gap/>onstratum e&longs;t prop.<emph.end type="italics"/> 19, <emph type="italics"/>buius.<emph.end type="italics"/></s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>erit de<gap/>ominator qualitatis auri de qua <gap/>uaritur quia ille termi<lb/><gap/>ut indicat partes auri pari i<gap/> grauitate, qualibus ma&longs;&longs;a propo&longs;ita <lb/>constat<emph.end type="italics"/> 24. <emph type="italics"/>Hoc autem de<gap/>onstratum e&longs;t prop.<emph.end type="italics"/> 19, <emph type="italics"/>huius.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et quia inpropo&longs;ito exemplo bæ partes, nempe vnc.<emph.end type="italics"/> 20, <emph type="italics"/>&longs;unt par<lb/>tes vige&longs;<gap/> quartæ<emph.end type="italics"/> 24, <emph type="italics"/>onciarum, quæ constituunt grauitatem to<lb/>tius ma&longs;&longs;æ. </s>

Line 1102

<s>Inueniantur <expan abbr="quoq;">quoque</expan> duæ aliæ <lb/>grauitates aquæ, vna re&longs;pondentis auro puro magnitudine, altera <lb/>corpori mi&longs;to ex argento & ære, ita tamen vt grauitas tum auri pu<gap/><lb/>ri, tum corporis misti &longs;it eadem quæ ma&longs;&longs;æ propo&longs;itæ, non &longs;ecus ac in <lb/>præcedenti oxemplo factitatum est. </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 aquæ magnitudinem <lb/>babentis æqualem 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, bac enim ratione <lb/>producetur nu<gap/>erus<emph.end type="italics"/> 551, <emph type="italics"/>debitus grauitati aquæ, magnitudine <lb/>aqualis corpori mi&longs;to ex argento & ære grauitatem habenti eandem <lb/>cum eadem ma<32>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 aquæ magnitudinem <lb/>habentis æqualem 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 aquæ, magnitudine <lb/>aqualis corpori mi&longs;to ex argento & ære grauitatem habenti eandem <lb/>cum eadem ma<32>a propo&longs;ita. </s>

<s>Atque ba tre<gap/> grauitates aquæ &longs;criban<lb/>tur co ordine quo &longs;upra; inuenti&longs;que differentys inter primam &<emph.end type="italics"/></s>

<s><margin.target id="note56"/>5.<emph type="italics"/>buius<emph.end type="italics"/></s>

<s><margin.target id="note56"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>tertiam, nec noninter &longs;ecund am & tertiam, quæ &longs;unt<emph.end type="italics"/> 272, 238; <emph type="italics"/>sta<lb/>tuatur pro primo proportionis termino prior differentia<emph.end type="italics"/> 272, <emph type="italics"/>& pro <lb/>tertio posterior<emph.end type="italics"/> 238. <emph type="italics"/>grauitas vero ma&longs;&longs;æ propo&longs;itæ<emph.end type="italics"/> 5301, <emph type="italics"/>ponatur <lb/>pro&longs;ecundo termino, & quæratur terminus quartus, qui in præ-<emph.end type="italics"/></s>

Line 1140

<s>TABELLE WAR HIER<lb/><emph type="italics"/>tius. </s>

<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<lb/>tibus, qualibus tota ma&longs;&longs;a constat<emph.end type="italics"/> 5301, <emph type="italics"/>quæ quidem grauitas vt <lb/>auri qualitatem indicet, reuocanda erit ad partes qualium totæ <lb/>ma&longs;&longs;a propo&longs;ita est<emph.end type="italics"/> 24. <emph type="italics"/>&longs;ienim &longs;iat 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;itæ ma&longs;&longs;æ appellabitur partium<emph.end type="italics"/> 19. </s>

<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<lb/>tibus, qualibus tota ma&longs;&longs;a constat<emph.end type="italics"/> 5301, <emph type="italics"/>quæ quidem grauitas vt <lb/>auri qualitatem indicet, reuocanda erit ad partes qualium totæ <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;itæ ma&longs;&longs;æ appellabitur partium<emph.end type="italics"/> 19. </s>

<s><emph type="italics"/>Denique &longs;i quis hunc modum conferat cum illo, quem &longs;upra tradi<lb/>dimus, cum argentum explorauimus, quod miftum in aurea corona <lb/>credebatur; is liquido intelliget hic nibil aliud acce&longs;&longs;i<32>e, ni&longs;i quod <lb/>loco argenti, a&longs;&longs;umptum &longs;it corpus ex argento & ære mistum, eo <lb/>quod hæc duo metalla tantum in alligationibus auri &longs;oleant adbibe<lb/>ri, vt diximus. </s>

Line 1206

<s><emph type="italics"/>Quando vero grauitas auri in aere quiaem e&longs;t vnius lib.

in aqua <lb/>vero grauitatem habet, quæ in tabula non reperuur, indicium erit <lb/>aurum propo&longs;itum non e&longs;&longs;e aliquot partium præcisè, &longs;ed annexam <lb/>habere aliquam fractionem, quæ per partem proportionalem inue<lb/>nietur boc modo.<emph.end type="italics"/></s>

in aqua <lb/>vero grauitatem habet, quæ in tabula non reperuur, indicium erit <lb/>aurum propo&longs;itum non e&longs;&longs;e aliquot partium præcisè, &longs;ed annexam <lb/>habere aliquam fractionem, quæ per partem proportionalem inue<lb/>nietur hoc modo.<emph.end type="italics"/></s>

<s><emph type="italics"/>Proponatur aurum vnius libræ in aqua habens grauitatem vnc. </s>

Line 1238

1, quartus enim terminus indica<lb/>bit grauitatem in aqua re&longs;pondentem vni libræ auri propo&longs;iti. </s>

<s>& <lb/>bac inuenta reliqua expedientur vt prius.<emph.end type="italics"/></s>

<s>& <lb/>hac inuenta reliqua expedientur vt prius.<emph.end type="italics"/></s>

<s><emph type="italics"/>Exemplum huius ca&longs;us hic non affero, quod per &longs;e res &longs;it clara. </s>

Line 1248

<s>Compo&longs;itio eiu&longs;dem tabulæ.</s>

<s><emph type="italics"/>Si ea quæ bactenus &longs;unt dicta rectè intelligantur liquido appare<lb/>bit compo&longs;itionem tabulæ in eo con&longs;istere, vt inuoniatur grauitas <lb/>quam aurum cuiu&longs;uis qualitatis habet in aqua, hoc e&longs;t &longs;i intelligan<lb/>tur propo&longs;itæ plures ma&longs;&longs;æ auri, &longs;ingulæ &longs;ingularum librarum, & <lb/>alia &longs;it qualitatis<emph.end type="italics"/> 24, <emph type="italics"/>partium alia<emph.end type="italics"/> 23, <emph type="italics"/>alia<emph.end type="italics"/> 22, <emph type="italics"/>&c. </s>

<s><emph type="italics"/>Si ea quæ hactenus &longs;unt dicta rectè intelligantur liquido appare<lb/>bit compo&longs;itionem tabulæ in eo con&longs;istere, vt inuoniatur grauitas <lb/>quam aurum cuiu&longs;uis qualitatis habet in aqua, hoc e&longs;t &longs;i intelligan<lb/>tur propo&longs;itæ plures ma&longs;&longs;æ auri, &longs;ingulæ &longs;ingularum librarum, & <lb/>alia &longs;it qualitatis<emph.end type="italics"/> 24, <emph type="italics"/>partium alia<emph.end type="italics"/> 23, <emph type="italics"/>alia<emph.end type="italics"/> 22, <emph type="italics"/>&c. </s>

<s>quanta &longs;it gra<lb/>uitas vniu&longs;cuiu&longs;que in aqua, id quod hoc extremo loco inuestigare <lb/>docebimus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et primum &longs;it propo&longs;itum aurum purum, &longs;eu<emph.end type="italics"/> 24, <emph type="italics"/>partium. </s>

<s>quo<lb/>niam igitur grauitas auri in aere, ad grauitatem eiu&longs;dem in aqua <lb/>&longs;e habet vt 19, ad<emph.end type="italics"/> 18, <emph type="italics"/>&longs;iat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 18, <emph type="italics"/>ita lib.<emph.end type="italics"/> 1, <emph type="italics"/>auri puri ad aliam <lb/>grauitatem nempe lib.<emph.end type="italics"/> 1<gap/>/19, <emph type="italics"/>quæ grauitas ad vncias, &longs;crupula, & <lb/>grana reuocata valet vnc.<emph.end type="italics"/> 11, <emph type="italics"/>Scrup.8. Gran.<emph.end type="italics"/> 20 4/19, <emph type="italics"/>atque hæc est <lb/>grauitas auri puri in aqua, quam in tabula è regione denominaioris<emph.end type="italics"/><lb/>24, <emph type="italics"/>po&longs;uimus; fractione excepta cuius loco &longs;ub&longs;tituta est fractio<emph.end type="italics"/><lb/>372/1767, <emph type="italics"/>propter cau&longs;am &longs;uperius allatam.<emph.end type="italics"/></s>

<s>quo<lb/>niam igitur grauitas auri in aere, ad grauitatem eiu&longs;dem in aqua <lb/>&longs;e habet vt 19, ad<emph.end type="italics"/> 18, <emph type="italics"/>fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 18, <emph type="italics"/>ita lib.<emph.end type="italics"/> 1, <emph type="italics"/>auri puri ad aliam <lb/>grauitatem nempe lib.<emph.end type="italics"/> 1<gap/>/19, <emph type="italics"/>quæ grauitas ad vncias, &longs;crupula, & <lb/>grana reuocata valet vnc.<emph.end type="italics"/> 11, <emph type="italics"/>Scrup.8. Gran.<emph.end type="italics"/> 20 4/19, <emph type="italics"/>atque hæc est <lb/>grauitas auri puri in aqua, quam in tabula è regione denominaioris<emph.end type="italics"/><lb/>24, <emph type="italics"/>po&longs;uimus; fractione excepta cuius loco &longs;ub&longs;tituta est fractio<emph.end type="italics"/><lb/>372/1767, <emph type="italics"/>propter cau&longs;am &longs;uperius allatam.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit deinde propo&longs;itum quod vis aliud corpus aureum vnius libræ, <lb/>&longs;itque exemp. </s>

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