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version 1.7, 2003/11/17 16:44:59 |
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| <s>Et vero illis non &longs;olum nos plurimum de­<lb/>bemus, quod plurima ip&longs;i perfecere: verum etiam quod <lb/>quædam qua&longs;i fundamenta iecere, quibus dum rerum <lb/><expan abbr="nouarũ">nouarum</expan> molem conamur imponere, nos quoque experi­<lb/>ri no&longs;tras vires, exercere indu&longs;triam, remque &longs;apientiæ <lb/>publicam amplificare po&longs;simus. </s> | <s>Et vero illis non &longs;olum nos plurimum de­<lb/>bemus, quod plurima ip&longs;i perfecere: verum etiam quod <lb/>quædam qua&longs;i fundamenta iecere, quibus dum rerum <lb/><expan abbr="nouarũ">nouarum</expan> molem conamur imponere, nos quoque experi­<lb/>ri no&longs;tras vires, exercere indu&longs;triam, remque &longs;apientiæ <lb/>publicam amplificare po&longs;simus. </s> |
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| <s>Quo in genere magno­<lb/>rum ego virorum &longs;tudium potius, quam gloriam æmu­<lb/>latus &longs;uper vnum ex Archimedeis fundamentis, de ra­<lb/>tione, qua varia corporum genera inter &longs;e grauitate & <lb/>magnitudine comparantur, fabricatus nonnulla &longs;um: <pb/>quæ nunc omnium oculis expo&longs;iturus, vt eam <expan abbr="&longs;u&longs;tineã">&longs;u&longs;tineam</expan>, <lb/>per&longs;onam, quam &longs;emper recu&longs;aui, patrocinium huiu&longs;­<lb/>modi quærendum mihi exi&longs;timaui, quod & imbecillita<lb/>tem meam contra obtrectatorum, &longs;i qui forte exi&longs;terent, <lb/>calumnias &longs;u&longs;tineret; & imminentem famæ, exi&longs;timatio <lb/>ni&longs;que iacturam auerteret. </s> | <s>Quo in genere magno­<lb/>rum ego virorum &longs;tudium potius, quam gloriam æmu­<lb/>latus &longs;uper vnum ex Archimedeis fundamentis, de ra­<lb/>tione, qua varia corporum genera inter &longs;e grauitate & <lb/>magnitudine comparantur, fabricatus nonnulla &longs;um: <pb/>quæ nunc omnium oculis expo&longs;iturus, vt eam <expan abbr="&longs;u&longs;tineã">&longs;u&longs;tineam</expan>, <lb/>per&longs;onam, quam &longs;emper recu&longs;aui, patrocinium huiu&longs;­<lb/>modi quærendum miniexi&longs;timaui, quod & &longs;mbecillita <lb/>tem meam contra obtrectatorum, &longs;i qui forte exi&longs;terent, <lb/>calumnias &longs;u&longs;tineret; & imminentem famæ, exi&longs;timatio <lb/>ni&longs;que iacturam auerteret. </s> |
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| <s>Vnus igitur tu occuri&longs;ti SE­<lb/>RAPHINE qui & <expan abbr="cõmodi&longs;sime">commodi&longs;sime</expan> mihi patrocinari po&longs;­<lb/>&longs;es, & quodam qua&longs;i iure deberes. </s> | <s>Vnus igitur tu occuri&longs;ti SE­<lb/>RAPHINE qui & <expan abbr="cõmodi&longs;sime">commodi&longs;sime</expan> mihi patrocinari po&longs;­<lb/>&longs;es, & quodam qua&longs;i iure deberes. </s> |
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| <s><expan abbr="Tuq;">Tuque</expan> <lb/>is es, quem non modo rudes, &longs;ed etiam docti &longs;u&longs;piciunt. </s> | <s><expan abbr="Tuq;">Tuque</expan> <lb/>is es, quem non modo rudes, &longs;ed etiam docti &longs;u&longs;piciunt. </s> |
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| <s><lb/>Habetino&longs;tra bæc ætas, quos admitetur; habet quos ex­<lb/>tollat præclaros viros, &longs;ed quos tibi anteponat, non facile <lb/>inueniet. </s> | <s><lb/>Habetino&longs;tra hæc ætas, quos admitetur; habet quos ex­<lb/>tollat præclaros viros, &longs;ed quos tibi anteponat, non facile <lb/>inueniet. </s> |
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| <s>Degis ea in Vrbe, quæ laudis mediocritatem <lb/>vel nunquam agnouit, vel &longs;emper contemp&longs;it: neque in <lb/>tanta maie&longs;tate, tua deficit virtus, &longs;ed bono in lumine po <lb/>&longs;ita collucet magis. </s> | <s>Degis ea in Vrbe, quæ laudis mediocritatem <lb/>vel nunquam agnouit, vel &longs;emper contemp&longs;it: neque in <lb/>tanta maie&longs;tate, tua deficit virtus, &longs;ed bono in lumine po <lb/>&longs;ita collucet magis. </s> |
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| <s>Quid dicam de &longs;ingulari <lb/><expan abbr="caq;">caque</expan> eximia rerum cœle&longs;tium, <expan abbr="totiu&longs;q;">totiu&longs;que</expan> mundi cognitio­<lb/>ne quam tu tanta cum auiditate ex reconditi&longs;simis Ma­<lb/>thematicorum fontibus hau&longs;i&longs;ti, vt illud a&longs;&longs;ecutus in eo <lb/>genere iam &longs;is, quod alij in maxima tranquillitate, in <lb/>&longs;ummo otio vix au&longs;int optare? </s> | <s>Quid dicam de &longs;ingulari <lb/><expan abbr="caq;">caque</expan> eximia rerum cœle&longs;tium, <expan abbr="totiu&longs;q;">totiu&longs;que</expan> mundi cognitio­<lb/>ne quam tu tanta cum auiditate ex reconditi&longs;simis Ma­<lb/>thematicorum fontibus hau&longs;i&longs;ti, vt illud a&longs;&longs;ecutus in eo <lb/>genere iam &longs;is, quod alij in maxima tranquillitate, in <lb/>&longs;ummo otio vix au&longs;int optare? </s> |
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| <s>Exitum tuorum labor um <lb/>fœlici&longs;simum vides: gloria multiplici frueris, <gap/>eque illa <lb/>precaria &longs;ed tua & quibu&longs;dam qua&longs;i gradibus ad ampli&longs;­<lb/>&longs;<gap/>mos: honores euehendus, in ea con&longs;titueris dignitate; in <lb/>qua pro &longs;acro&longs;ancta Eccle&longs;ia <gap/>quam non excubando, <lb/>in peramplo tot illu&longs;trium vitorum Theatro non alienæ <lb/>gloriæ &longs;pectator, &longs;ed actor tuæ con&longs;i&longs;tas. </s> | <s>Exitum tuorum labor um <lb/>fœlici&longs;simum vides: gloria multiplici frueris, <gap/>eque illa <lb/>precaria &longs;od tua & quibu&longs;dam qua&longs;i gradibus ad ampli&longs;­<lb/>&longs;<gap/>mos: honores euehendus, in ea con&longs;titueris dignitate; in <lb/>qua pro &longs;acro&longs;anta Eccle&longs;ia <gap/>quam non excubando, <lb/>in peramplo tot illu&longs;trium vitorum Theatro non alienæ <lb/>gloriæ &longs;pectator, &longs;ed actor tuæ con&longs;i&longs;tas. </s> |
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| <s>Tu vero, quod <lb/>rarum e&longs;t, laudem &longs;apientiæ, quæ vix vllos habet at ter­<lb/>minos, humanitatis tuæ terminis circum&longs;cribis; & expo­<lb/>nis omnibus<gap/> vt extanto &longs;onte perennes ad omnium or­<lb/>dinum homines fiuuli deducantur. </s> | <s>Tu vero, quod <lb/>rarum e&longs;t, laudem &longs;a pientiæ, quæ vix vllos habeb at ter­<lb/>minos, humanitatis tuæ terminis circum&longs;cribis; & expo­<lb/>nis omnibus<gap/> vt extanto &longs;onte perennes ad omnium or­<lb/>dinum homines fiuuli deducantur. </s> |
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| <s>Fœlix qui &longs;olidæ <lb/>fœlicitatis car&longs;am & in&longs;tium in re con&longs;titutumita foues, <lb/>vt cum alijs illam communicando, non imminuas, &longs;ed <lb/>amplifices, prægrande videlicet non &longs;uccre&longs;centis, &longs;ed <lb/>adultæ iam virtutis fœnus honorem ex honore, laudem <lb/>ex laude con&longs;equi vberiorem, hæcilla &longs;apienti viro non <lb/>indigna liberalitas, quæ terum pre&longs;tanti&longs;simarum po&longs;­<lb/>&longs;e&longs;sione non imminuta, in copia tenuitatem non inqui-<pb/>rens vbertatis ip&longs;a&longs;uæ dominæ nunquam debilitatur, <lb/>nunquam deficit. </s> | <s>Fœlix qui &longs;olidæ <lb/>fœlicitatis car&longs;am & in&longs;tium in re con&longs;titutumita foues, <lb/>vt cum alijs illam communicando, non imminuas, &longs;ed <lb/>amplifices, prægrande videlicet non &longs;uccre&longs;centis, &longs;ed <lb/>adultæ iam virtutis fœnus honorem ex honore, laudem <lb/>ex laude con&longs;equi vberiorem, hæcilla &longs;apienti viro non <lb/>indigna liberalitas, quæ terum pre&longs;tanti&longs;simarum po&longs;­<lb/>&longs;e&longs;sione non imminuta, in copia tenuitatem non inqui-<pb/>rens vbertatis ip&longs;a&longs;uæ dominæ nunquam debilitatur, <lb/>nunquam deficit. </s> |
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| <s><lb/>Hinc domus tua floret docti&longs;simorum familiaritatibus; <lb/>hinc nulli ad tuam con&longs;uetudinom præcluditur aditus; <lb/>hinc plurimorum &longs;tudia commouentur; hinc illa &longs;apien <lb/>tum æmulatio & admiratio<gap/> hinc omnium omnino or­<lb/>dinum ad te concur&longs;us; tanquam ad &longs;apienti&longs;simum hu­<lb/>mani <expan abbr="diuiniq;">diuinique</expan> iuris paponum, & interpetem. </s> | <s><lb/>Hinc domus tua floret docti&longs;simorum familiaritatibus; <lb/>hinc nulli ad tuam con&longs;uetudinom præcluditur aditus; <lb/>hinc plurimorum &longs;tudia commouentur; hinc illa &longs;apien <lb/>tum æmulatio & admiratio<gap/> hinc omnium omnino or­<lb/>dinum ad te concur&longs;us; tanquam ad &longs;apienti&longs;simum hu­<lb/>mani <expan abbr="diuiniq;">diuinique</expan> iuris paponum, & interpetem. </s> |
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| <s>Quid ego <lb/>igitur quem tibi &longs;excentis eximiæ beneuolentiœ argu­<lb/>mentis obligatum vo<gap/>&longs;ti, perexigitum hunc ingenij <lb/>mei partum exp<gap/>&longs;uiuus, vnum te nominis & exi&longs;tima­<lb/>tionis meæ patronum non &longs;u&longs;eipiam<gap/> equide<gap/> in am­<lb/>pli&longs;simi Theatri lucern &longs;apienti&longs;simorum<32> hominum <lb/>con&longs;pectum, quibus abundat hæd no&longs;tra ætas inferre me <lb/>non magnopere cogitabam <gap/>Tu hortatus es dubitan­<lb/>tem impuli&longs;ti vel reluctamem<gap/> tuereigitur ob&longs;equen­<lb/>tem. </s> | <s>Quid ego <lb/>igitur quem tibi &longs;exœntis eximiæ beneuolentiœ argu­<lb/>mentis obligatum vo<gap/>&longs;ti, perexigitum hunc ingenij <lb/>mei partum exp<gap/>&longs;uiuus, vnum te nominis & exi&longs;tima­<lb/>tionis meæ patronum non &longs;u&longs;eipiam<gap/> equide<gap/> in am­<lb/>pli&longs;simi Theatri lucern &longs;apienti&longs;simorum<32> hominum <lb/>con&longs;pectum, quibus abundat hæd no&longs;tra ætas inferre me <lb/>non magnopere cogitabam <gap/>Tu hortatus es dubitan­<lb/>tem impuli&longs;ti vel reluctamem<gap/> tuereigitur ob&longs;equen­<lb/>tem. </s> |
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| <s>iam nunc mihi videor in exigua vel nulla &longs;pe lau­<lb/>dis ex ingenio meo; &longs;empiternam nominis immortali­<lb/>tatem ex tuo patrocinio con&longs;ecutus. </s> | <s>iam nunc mihi videor in exigua vel nulla &longs;pe lau­<lb/>dis ex ingenio meo; &longs;empiternam nominis immortali­<lb/>tatem ex tuo patrocinio con&longs;ecutus. </s> |
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| <s>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. <!-- KEEP S--></s> | <s>Rubeo ba <lb/>mine mihi tum ex &longs;tudiorum &longs;imilitudine, tum pracipue ex <lb/>eius humanitate amici&longs;simo, ad Reuerendi&longs;simum Sera­<lb/>phinum deductus &longs;um. <!-- KEEP S--></s> |
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| <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> |
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| <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> |
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| <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> |
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| <s>Huiu&longs;­<lb/>medi enim comparatione Archimides mixtionem argemi <lb/>in aure deprebeudit, & furtum Auri&longs;itis in corona aurea <lb/>patefecit. </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>de quæ re &longs;uo leco ego tractabo, & facilem mon­<lb/>strabo viam, quæ vel argentum in aure, vel quod visme­<lb/>tallum in quolibet admistum diprebeudi queat, & alte <lb/><gap/> ab aliero di&longs;rerni & &longs;imul explicabo, quo pacto ex au­<lb/>ri grauitate <gap/> qualiras, <gap/>perfectio intelligi po&longs;sit. </s> | <s>de quæ re &longs;uo leco ego tractabo, & facilem mon­<lb/>strabo viam, quæ vel argentum in aure, vel quod visme­<lb/>tallum in quolibet admistum diprebeudi queat, & alte <lb/><gap/> ab aliero di&longs;rerni & &longs;imu<gap/>, quo pacto ex au­<lb/>ri grauitate <gap/> qualiras, <gap/>perfectio intelligi po&longs;sit. </s> |
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| <s><lb/>Tati vere apu&longs;culo nomen ab Arthimede, quem Ducem &longs;e­<lb/>quer impo&longs;ui Nam cum ille, vt erat &longs;ummus Magi&longs;ter, &longs;e­<lb/>tis haliui&longs;&longs;et hunc, totem qu<gap/> fabr<gap/> pe&longs;ito fundumen­<lb/>to delineare in primo lib. | <s><lb/>Tati vere apu&longs;culo nomen ab Arthimede, quem Ducem &longs;e­<lb/>quer impo&longs;ui Nam cum ille, vt erat &longs;ummus Magi&longs;ter, &longs;e­<lb/>tis haliui&longs;&longs;et hunc, totem qua&longs; fabr<gap/> pe&longs;ito fundumen­<lb/>to delineare in primo lib. |
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| vbi agit de i&longs;s quæ vt huntur in <lb/>a quæ. </s> | vbi agit de i&longs;s quæ vt huntur in <lb/>a quæ. </s> |
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| <s><margin.target id="note8"/>10. 5. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> | <s><margin.target id="note8"/>10. 5. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>ID QVOD nos duobus præcedentibus Theorematis de­<lb/>mon&longs;trauimus, <expan abbr="nõnulli">nonnulli</expan>, vt per &longs;e notum, & vt commune quod­<lb/>dam axioma &longs;upponunt, quam bene & rationabiliter ip&longs;i vide­<lb/>rint; melius enim Euclides propo&longs;itionem 20. primi libri Ele­<lb/>mentorum &longs;uppo&longs;ui&longs;&longs;et vt pronunciatum; vnicuique enim no­<lb/>tius e&longs;t duo trianguli latera reliquo e&longs;&longs;e maiora (cum & Afino <lb/>illud &longs;it notum) quam corpora grauia ciu&longs;dem generis eandem <lb/>in grauitate rationem habere, quam in magnitudine, & tamen <lb/>illam propo&longs;itionem demon&longs;trat Euclides, non &longs;upponit, non <lb/>igitur hæc, quæ minus ad principij rationem accedit, &longs;uppo­<lb/>nenda fuit, &longs;ed demon&longs;tranda. </s></p><p type="head"> | <s>ID QVOD nos duobus præcedentibus Theorematis de­<lb/>mon&longs;trauimus, <expan abbr="nõnulli">nonnulli</expan>, vt per &longs;e notum, & vt commune quod­<lb/>dam axioma &longs;upponunt, quam bene & rationabiliter ip&longs;i vide­<lb/>rint; melius enim Euclides propo&longs;itionem 20. primi libri Ele­<lb/>mentorum &longs;uppo&longs;ui&longs;&longs;et vt pronunciatum; vnicuique enim no­<lb/>tius e&longs;t duo trianguli latera reliquo e&longs;&longs;e maiora (cum & Afino <lb/>illud &longs;it notum) quam corpora grauia eiu&longs;dem generis eandem <lb/>in grauitate rationem habere, quam in magnitudine, & tamen <lb/>illam propo&longs;itionem demon&longs;trat Euclides, non &longs;upponit, non <lb/>igitur hæc, quæ minus ad principij rationem accedit, &longs;uppo­<lb/>nenda fuit, &longs;ed demon&longs;tranda. </s></p><p type="head"> |
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| <s>THEOREMA IV. PROPOS. IV.<!-- KEEP S--></s></p><p type="main"> | <s>THEOREMA IV. PROPOS. IV.<!-- KEEP S--></s></p><p type="main"> |
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| <s><margin.target id="note10"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s></p><p type="margin"> | <s><margin.target id="note10"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s></p><p type="margin"> |
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| <s><margin.target id="note11"/>2. & 3. <lb/><emph type="italics"/>buius.<emph.end type="italics"/></s></p><p type="margin"> | <s><margin.target id="note11"/>2. & 3. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s></p><p type="margin"> |
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| <s><margin.target id="note12"/>23. 5. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head"> | <s><margin.target id="note12"/>23. 5. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="head"> |
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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></p><p type="main"> | <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></p><p type="main"> |
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| <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"/><!-- KEEP S--></s></p><p type="main"> | <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"/><!-- KEEP S--></s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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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></p><p type="main"> | <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></p><p type="main"> |
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| <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. <!-- KEEP S--></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. <!-- KEEP S--></s> |
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| <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. <!-- KEEP S--></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. <!-- KEEP S--></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></p><p type="main"> | <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></p><p type="main"> |
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| <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> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <s>At vero &longs;i <expan abbr="propo&longs;itũ">propo&longs;itum</expan> fuerit inuenire <expan abbr="quãta">quanta</expan> erit grauitas ceræ, <lb/>aut ligni, aut <expan abbr="cuiu&longs;cũque">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></p><p type="main"> | <s>At vero &longs;i <expan abbr="propo&longs;itũ">propo&longs;itum</expan> fuerit inuenire <expan abbr="quãta">quanta</expan> erit grauitas ceræ, <lb/>aut ligni, aut <expan abbr="cuiu&longs;cũque">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></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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></p><p type="head"> | <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></p><p type="head"> |
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| <s>PROBLEMA III. PROPOS. X.<!-- KEEP S--></s></p><p type="main"> | <s>PROBLEMA III. PROPOS. X.<!-- KEEP S--></s></p><p type="main"> |
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| <s>Propo&longs;itis duobus corporibus æque grauibus, vno <lb/>&longs;olido, altero liquido, data &longs;olidi corporis magnitu-<pb pagenum="13"/>dine, magnitudinem liquidi inuenire. </s></p><p type="main"> | <s>Propo&longs;itis duobus corporibus æque grauibus, vno <lb/>&longs;olido, altero liquido, data &longs;olidi corporis magnitu­<pb pagenum="13"/>dine, magnitudinem liquidi inuenire. </s></p><p type="main"> |
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| <s>SINT duo propo&longs;ita corpora <lb/>æque grauia, A, quidem &longs;olidum B, <lb/>vero liquidum, &longs;it autem &longs;olidi A, da­<lb/><figure id="fig9"/><lb/>ta magnitudo C, & oporteat inuenire <lb/>quanta erit magnitudo liquidi B, Ac­<lb/>cipiatur aliquod corpus &longs;olidum D, <lb/>eiu&longs;dem generis cuni &longs;olido A, & &longs;it <lb/>eius grauitas G, & liquidi, quod &longs;it E, <lb/>eiu&longs;dem gener is cum liquido B, ma­<lb/>gnitudinem habentis æqualem &longs;olido <lb/>D,* inueniatur grauitas quæ &longs;it H, &<arrow.to.target n="note20"/><lb/>fiat vt grauitas H, ad grauitatem G, <lb/>ita magnitudo C, ad aliam magnitudinem quæ &longs;it F. <!-- KEEP S--></s> | <s>SINT duo propo&longs;ita corpora <lb/>æque grauia, A, quidem &longs;olidum B, <lb/>vero liquidum, &longs;it autem &longs;olidi A, da­<lb/><figure id="fig9"/><lb/>ta magnitudo C, & oporteat inuenire <lb/>quanta erit magnitudo liquidi B, Ac­<lb/>cipiatur aliquod corpus &longs;olidum D, <lb/>eiu&longs;dem generis cuni &longs;olido A, & &longs;it <lb/>eius grauitas G, & liquidi, quod &longs;it E, <lb/>eiu&longs;dem gener is cum liquido B, ma­<lb/>gnitudinem habentis æqualem &longs;olido <lb/>D,* inueniatur grauitas quæ &longs;it H, &<arrow.to.target n="note20"/><lb/>fiat vt grauitas H, ad grauitatem G, <lb/>ita magnitudo C, ad aliam magnitudinem quæ &longs;it F. <!-- KEEP S--></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></p><p type="main"> | <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></p><p type="main"> |
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| <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 haben­<lb/>tis æqualem propo&longs;ito plumbo A, accipiatur aliquod corpus <expan abbr="plumbeũ">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="plumbeũ">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> |
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| <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"/><!-- KEEP S--></s></p><p type="main"> | <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"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Quod &longs;i <expan abbr="propo&longs;itũ">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></p><p type="main"> | <s>Quod &longs;i <expan abbr="propo&longs;itũ">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></p><p type="main"> |
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| <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="proximũ">proximum</expan> <lb/>vero indicabit ip&longs;am diametrum.<emph.end type="italics"/></s></p><p type="main"> | <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="proximũ">proximum</expan> <lb/>vero indicabit ip&longs;am diametrum.<emph.end type="italics"/></s></p><p type="main"> |
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| <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="proximũ">proximum</expan> vero indicabit quæ&longs;itum latus eubi ex aqua.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius 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="proximũ">proximum</expan> vero indicabit quæ&longs;itum latus eubi ex aqua.<emph.end type="italics"/></s></p><p type="main"> |
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| <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></p><p type="head"> | <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></p><p type="head"> |
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| <s>SINT propo&longs;ita duo corpora æ­<lb/>quæ grauia, A, quidem &longs;olidum, B, <lb/>vero liquidum, &longs;it autem, liquidi B; <lb/><figure id="fig10"/><lb/>data magnitudo F, & oporteat &longs;olidi <lb/>A, magnitudinem inuenire. </s> | <s>SINT propo&longs;ita duo corpora æ­<lb/>quæ grauia, A, quidem &longs;olidum, B, <lb/>vero liquidum, &longs;it autem, liquidi B; <lb/><figure id="fig10"/><lb/>data magnitudo F, & oporteat &longs;olidi <lb/>A, magnitudinem inuenire. </s> |
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| <s>Accipia­<lb/>tur aliquod corpus &longs;olidum D, <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>generis cum corpore &longs;olido A, cuius <lb/>grauitas &longs;it G, deinde liquidi quod &longs;it <lb/>E, eiu&longs;dem generis cum corpore liqui <lb/>do B, magnitudinem æqualem<arrow.to.target n="note24"/> haben­<lb/>tis &longs;olido D, *inueniatur grauitas, <lb/>quæ &longs;it H, & fiat vt grauitas G; ad gra­<lb/>uitatem H, ita F, magnitudo, ad aliam magnitudinem, quæ &longs;it C; <lb/>quoniam igitur &longs;unt quatuor corpora D, E, A, B, quorum primum D, <lb/>& &longs;ecundum E, &longs;unt magnitudine æqualia, tertium vero A, & <expan abbr="quartũ">quartum</expan> <lb/>B, æquæ grauia, & &longs;unt eiu&longs;dem generis &longs;olida D, A, &longs;imiliter, & liqui­<lb/>da E, B,* erit vt grauitas G, ad grauitatem H, ita F, magnitudo ad ma<arrow.to.target n="note25"/><lb/>gnitudinem &longs;olidi A, &longs;ed vt grauitas G, ad grauitatem H, ita e&longs;t ma­<lb/>gnitudo F, ad C, magnitudinem, ergo magnitudo C, æqualis erit ma­<lb/>gnitudini corporis &longs;olidi A, inuenta igitur e&longs;t corporis &longs;olidi A, ma­<lb/>gnitudo C, quod erat faciendum. </s></p><p type="margin"> | <s>Accipia­<lb/>tur aliquod corpus &longs;olidum D, <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>generis cum corpore &longs;olido A, cuius <lb/>grauitas &longs;it G, deinde liquidi quod &longs;it <lb/>E, eiu&longs;dem generis cum corpore liqui <lb/>do B, magnitudinem æqualem<arrow.to.target n="note24"/> haben­<lb/>tis &longs;olido D, *inueniatur grauitas, <lb/>quæ &longs;it H, & fiat vt grauitas G; ad gra­<lb/>uitatem H, ita F, magnitudo, ad aliam magnitudinem, quæ &longs;it C; <lb/>quoniam igitur &longs;unt quatuor corpora D, E, A, B, quorum primum D, <lb/>& &longs;ecundum E, &longs;unt magnitudine æqualia, tertium vero A, & <expan abbr="quartũ">quartum</expan> <lb/>B, æquæ grauia, & &longs;unt eiu&longs;dem generis &longs;olida D, A, &longs;imiliter, & liqui­<lb/>da E, B,* erit vt grauitas G, ad grauitatem H, ita F, magnitudo ad ma<arrow.to.target n="note25"/><lb/>gnitudinem &longs;olidi A, &longs;ed vt grauitas G, ad grauitatem H, ita e&longs;t ma­<lb/>gnitudo F, ad C, magnitudinem, ergo magnitudo C, æqualis erit ma­<lb/>gnitudini corporis &longs;olidi A, inuenta igitur e&longs;t corporis &longs;olidi A, ma­<lb/>gnitudo C, quod erat &longs;aciendum. </s></p><p type="margin"> |
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| <s><margin.target id="note24"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> | <s><margin.target id="note24"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> |
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| <s>Qvod &longs;i propo&longs;ita duo corpora æque grauia A, B, fue<lb/>rint regularia vtpote &longs;phærica, fuerit autem liqui-<pb pagenum="16"/>dæ &longs;phæræ B, data diameter F, & oporteat inuenire quan<lb/>ta erit diameter &longs;olidæ &longs;phæræ A, ita faciendum erit. </s></p><p type="main"> | <s>Qvod &longs;i propo&longs;ita duo corpora æque grauia A, B, fue<lb/>rint regularia vtpote &longs;phærica, fuerit autem liqui-<pb pagenum="16"/>dæ &longs;phæræ B, data diameter F, & oporteat inuenire quan<lb/>ta erit diameter &longs;olidæ &longs;phæræ A, ita faciendum erit. </s></p><p type="main"> |
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| <s>Accepto vt &longs;upra corpore &longs;olido D, & liquid E, inuenta grauitate, <lb/>vt dictum e&longs;t, fiat vt grauitas G, ad prauitatem H, ita cubus ex F, ad <lb/>alium cubum, cuius latus &longs;it C, Quoniam igitur eadem ratione qua <lb/>fupra o&longs;tendetut, vt grauitas G, ad grauitatem H, ita e&longs;&longs;e magnitudi­<lb/>nem &longs;phæræ B, ad &longs;phæræ A, magnitudinem, &longs;ed magnitudo &longs;phæræ B, <lb/><arrow.to.target n="note26"/> ad magnitudinem &longs;phæræ A, *triplicatam rationem habet eius, quam <lb/>F, diameter &longs;phæræ B, ad diametrum &longs;phæræ A, &longs;imiliter, & cubus ex <lb/><arrow.to.target n="note27"/> F, ad cubum ex diametro &longs;phæræ A, <expan abbr="triplicatã*">triplicatan*</expan> rationem liabet eius, <lb/>quam F, ad diametrum &longs;phæræ A, ergo, vt grauitas G, ad <expan abbr="grauitat&etilde;">grauitatem</expan> <lb/>H, ita erit cubus ex F, ad cubum ex diametro &longs;phæræ A, &longs;ed vt graui­<lb/>tas G, ad grauitatem H, ita e&longs;t cubus ex F, ad cubum ex C, ergo cubus <lb/>ex C, æqualis erit eubo diametri &longs;phæræ A, quare, & latus C, æquabi­<lb/>tur ip&longs;ius &longs;phæræ A, diametro, inuenta igitur e&longs;t quantitas diametri <lb/>&longs;olidæ &longs;phæræ A, quod facere oportebat. </s></p><p type="margin"> | <s>Accepto vt &longs;upra corpore &longs;olido D, & liquid E, inuenta grauitate, <lb/>vt dictum e&longs;t, fiat vt grauitas G, ad prauitatem H, ita cubus ex F, ad <lb/>alium cubum, cuius latus &longs;it C, Quoniam igitur eadem ratione qua <lb/>fupra o&longs;tendetut, vt grauitas G, ad grauitatem H, ita e&longs;&longs;e magnitudi­<lb/>nem &longs;phæræ B, ad &longs;phæræ A, magnitudinem, &longs;ed magnitudo &longs;phæræ B, <lb/><arrow.to.target n="note26"/> ad magnitudinem &longs;phæræ A, *triplicatam rationem habet cius, quam <lb/>F, diameter &longs;phæræ B, ad diametrum &longs;phæræ A, &longs;imiliter, & cubus ex <lb/><arrow.to.target n="note27"/> F, ad cubum ex diametro &longs;phæræ A, <expan abbr="triplicatã*">triplicatan*</expan> rationem liabet eius, <lb/>quam F, ad diametrum &longs;phæræ A, ergo, vt grauitas G, ad <expan abbr="grauitat&etilde;">grauitatem</expan> <lb/>H, ita erit cubus ex F, ad cubum ex diametro &longs;phæræ A, &longs;ed vt graui­<lb/>tas G, ad grauitatem H, ita e&longs;t cubus ex F, ad cubum ex C, ergo cubus <lb/>ex C, æqualis erit eubo diametri &longs;phæræ A, quare, & latus C, æquabi­<lb/>tur ip&longs;ius &longs;phæræ A, diametro, inuenta igitur e&longs;t quantitas diametri <lb/>&longs;olidæ &longs;phæræ A, quod facere oportebat. </s></p><p type="margin"> |
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| <s><margin.target id="note26"/>18.12. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="margin"> | <s><margin.target id="note26"/>18.12. <lb/><emph type="italics"/>Elem.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="margin"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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="plumbeũ">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></p><p type="main"> | <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="plumbeũ">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></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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></p><p type="head"> | <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></p><p type="head"> |
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| <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>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> |
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| <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. <!-- KEEP S--></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. <!-- KEEP S--></s> |
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| <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></p><p type="margin"> | <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 facere oportebat. </s></p><p type="margin"> |
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| <s><margin.target id="note28"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> | <s><margin.target id="note28"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> |
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| <s>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></p><p type="main"> | <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></p><p type="main"> |
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| <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. <!-- KEEP S--></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. <!-- KEEP S--></s> |
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| <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"/><!-- KEEP S--></s></p><p type="main"> | <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"/><!-- KEEP S--></s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <s><emph type="italics"/>Accipiantur duo corpora D, plumbeum, E, &longs;tanneum grauitate <lb/>quacunque, &longs;it vcrbi gratia plumbi D, grauitas<emph.end type="italics"/> 23<emph type="italics"/>, &longs;tanni vero E, <lb/>grauitas<emph.end type="italics"/> 37<emph type="italics"/>, deinde duarum quantitatum aquæ, quarum vna &longs;it ma­<lb/>gnitudine æqualis plumbo D, altera stanno E, inueniantur graui­<lb/>tates, quæ &longs;int, primæ videlicet quantitatis<emph.end type="italics"/> 2<emph type="italics"/>, &longs;ecundæ vero<emph.end type="italics"/> 5<emph type="italics"/>, & fiat,<emph.end type="italics"/><pb 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></p><p type="main"> | <s><emph type="italics"/>Accipiantur duo corpora D, plumbeum, E, &longs;tanneum grauitate <lb/>quacunque, &longs;it vcrbi gratia plumbi D, grauitas<emph.end type="italics"/> 23<emph type="italics"/>, &longs;tanni vero E, <lb/>grauitas<emph.end type="italics"/> 37<emph type="italics"/>, deinde duarum quantitatum aquæ, quarum vna &longs;it ma­<lb/>gnitudine æqualis plumbo D, altera stanno E, inueniantur graui­<lb/>tates, quæ &longs;int, primæ videlicet quantitatis<emph.end type="italics"/> 2<emph type="italics"/>, &longs;ecundæ vero<emph.end type="italics"/> 5<emph type="italics"/>, & fiat,<emph.end type="italics"/><pb 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></p><p type="main"> |
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| <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></p><p type="main"> | <s><emph type="italics"/>Et quoniam aquæ, magnitudinem habentis æqualem stanno E, cu­<lb/>ius grauitas est 37, e&longs;t grauitas<emph.end type="italics"/> 5, <emph type="italics"/>erunt grauitates duarum quan­<lb/>titatum aquæ<emph.end type="italics"/> 3 5/21, & 5, <emph type="italics"/>quarum quantitatum prima e&longs;t æqualis <lb/>magnitudine corpori plumbeo, &longs;ecunda stanneo, que &longs;unt æque gra­<lb/>uia, vtriu&longs;que enim grauitas est<emph.end type="italics"/> 37. <emph type="italics"/>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></p><p type="main"> |
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| <s>Quod &longs;i propo&longs;itum &longs;it cereum corpus aliquod, aut cuiu&longs;­<lb/>cunque generis &longs;olidi, &longs;iue leuioris quam aqua, &longs;iue grauio­<lb/>ris, & oporteat inuenire grauitatem alicuius &longs;olidi alterius <lb/>generis, magnitudine æqualis propo&longs;ito corpori &longs;olido. </s> | <s>Quod &longs;i propo&longs;itum &longs;it cereum corpus aliquod, aut cuiu&longs;­<lb/>cunque generis &longs;olidi, &longs;iue leuioris quam aqua, &longs;iue grauio­<lb/>ris, & oporteat inuenire grauitatem alicuius &longs;olidi alterius <lb/>generis, magnitudine æqualis propo&longs;ito corpori &longs;olido. </s> |
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| <s>Propo&longs;itis duobus &longs;olidis corporibus æque graui­<lb/>bus, data magnitudine vnius, magnitudinem alte­<lb/>rius inuenire. </s></p><p type="main"> | <s>Propo&longs;itis duobus &longs;olidis corporibus æque graui­<lb/>bus, data magnitudine vnius, magnitudinem alte­<lb/>rius inuenire. </s></p><p type="main"> |
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| <s>SINT propo&longs;ita duo corpora &longs;olida æque grauia A, B, &longs;it au­<lb/><gap/>m vnius, vtpote ip&longs;ius A, data magnitudo C, & oporteat inueni­<lb/>re magnitudinem ip&longs;ius B, Accipiatur aliquod &longs;olidum corpus D, <lb/>ciu&longs;dem generis cum &longs;olido A, & &longs;it eius grauitas G, deinde &longs;olidi <lb/>corporis quod &longs;it E, eiu&longs;dem generis cum &longs;olido B, magnitudine <lb/>æqualis ip&longs;i D, inueniatur grauitas, quæ &longs;it H, hoc autem, Proble­<lb/>ma antecedens docuit, & fiat vt grauitas H, ad grauitatem G, ita <lb/>magnitudo C, ad aliam magnitudinem, quæ &longs;it F. <!-- KEEP S--></s> | <s>SINT propo&longs;ita duo corpora &longs;olida æque grauia A, B, &longs;it au­<lb/><gap/>m vnius, vtpote ip&longs;ius A, data magnitudo C, & oporteat inueni­<lb/>re magnitudinem ip&longs;ius B, Accipiatur aliquod &longs;olidum corpus D, <lb/>eiu&longs;dem generis cum &longs;olido A, & &longs;it eius grauitas G, deinde &longs;olidi <lb/>corporis quod &longs;it E, eiu&longs;dem generis cum &longs;olido B, magnitudine <lb/>æqualis ip&longs;i D, inueniatur grauitas, quæ &longs;it H, hoc autem, Proble­<lb/>ma antecedens docuit, & fiat vt grauitas H, ad grauitatem G, ita <lb/>magnitudo C, ad aliam magnitudinem, quæ &longs;it F. <!-- KEEP S--></s> |
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| <s>Quoniam igitur <pb pagenum="20"/>&longs;unt quatuor corpora grauia E, D, B, <lb/>A, quorum E, D, primum videlicet, <lb/><figure id="fig12"/><lb/>& &longs;ecundum, &longs;unt æqualia magnitu­<lb/>dine, tertium vero B, & quartum A, <lb/>æquegrauia, & &longs;unt eiu&longs;dem generis <lb/>corpora E, B, &longs;imiliter & corpora <lb/><arrow.to.target n="note31"/> D, A, * erit vt grauitas H, ad graui­<lb/>tatem G, ita magnitudo C, ad corpo­<lb/>ris B, magnitudinem, &longs;ed vt grauitas <lb/>H, ad grauitatem G, ita e&longs;t magnitu­<lb/>do C, ad F, magnitudinem, ergo ma­<lb/>gnitudo F, æqualis erit magnitudini <lb/>corporis B. inuenta igitur e&longs;t corporis B, magnitudo F, quod facere <lb/>oportebat. </s></p><p type="margin"> | <s>Quoniam igitur <pb pagenum="20"/>&longs;unt quatuor corpora grauia E, D, B, <lb/>A, quorum E, D, primum videlicet, <lb/><figure id="fig12"/><lb/>& &longs;ecundum, &longs;unt æqualia magnitu­<lb/>dine, tertium vero B, & quartum A, <lb/>æquegrauia, & &longs;unt eiu&longs;dem generis <lb/>corpora E, B, &longs;imiliter & corpora <lb/><arrow.to.target n="note31"/> D, A, * erit vt grauitas H, ad graui­<lb/>tatem G, ita magnitudo C, ad corpo­<lb/>ris B, magnitudinem, &longs;ed vt grauitas <lb/>H, ad grauitatem G, ita e&longs;t magnitu­<lb/>do C, ad F, magnitudinem, ergo ma­<lb/>gnitudo F, æqualis erit magnitudini <lb/>corporis B. inuenta igitur e&longs;t corporis B, magnitudo F, quod facere <lb/>oportebat. </s></p><p type="margin"> |
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| <s>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></p><p type="main"> | <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></p><p type="main"> |
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| <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. <!-- KEEP S--></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. <!-- KEEP S--></s> |
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| <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 haben<lb/>tis æqualem propo&longs;ito plumbo A.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> | <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"/><!-- KEEP S--></s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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> | <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> |
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| <s>SINT propo&longs;ita duo cor­<lb/>ra liquida, magnitudine æqualia <lb/>A, B, &longs;it autem vnius, vtpote li­<lb/>quidi A, data grauitas G, & <lb/>oporteat alterius liquidi B, gra­<lb/>uitatem inuenire. </s> | <s>SINT propo&longs;ita duo cor­<lb/>ra liquida, magnitudine æqualia <lb/>A, B, &longs;it autem vnius, vtpote li­<lb/>quidi A, data grauitas G, & <lb/>oporteat alterius liquidi B, gra­<lb/>uitatem inuenire. </s> |
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| <s>Accipiatur <lb/>aliquod corpus &longs;olidum C, & li­<lb/>quidi, quod &longs;it H, eiu&longs;dem ge­<lb/>neris cum liquido A, magnitu­<lb/><arrow.to.target n="note34"/> dine æqualis &longs;olido C, *inuenia­<lb/>tur grauitas, quæ &longs;it D, &longs;imiliter <lb/>& liquidl, quod &longs;it I, ciu&longs;dem <lb/>generis cum liquido B, magni­<lb/>tudine æqualis eidem &longs;olido C, <lb/><arrow.to.target n="note35"/> * inueniatur grauitas, quæ &longs;it E, <lb/>& fiat vt D, ad E, ita G, ad aliam grauitatem, quæ &longs;it F. <!-- KEEP S--></s> | <s>Accipiatur <lb/>aliquod corpus &longs;olidum C, & li­<lb/>quidi, quod &longs;it H, eiu&longs;dem ge­<lb/>neris cum liquido A, magnitu­<lb/><arrow.to.target n="note34"/> dine æqualis &longs;olido C, *inuenia­<lb/>tur grauitas, quæ &longs;it D, &longs;imiliter <lb/>& liquidl, quod &longs;it I, eiu&longs;dem <lb/>generis cum liquido B, magni­<lb/>tudine æqualis eidem &longs;olido C, <lb/><arrow.to.target n="note35"/> * inueniatur grauitas, quæ &longs;it E, <lb/>& fiat vt D, ad E, ita G, ad aliam grauitatem, quæ &longs;it F. <!-- KEEP S--></s> |
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| <s>Quoniam <lb/>igitur e&longs;t vt A, ad B, ita H, ad I, æquale videlicet ad æquale, erit per­<lb/>mutando vt A, ad H, ita B, ad I, & quoniam eiu&longs;dem &longs;unt generis cor­<lb/><arrow.to.target n="note36"/> pora A, H, &longs;imiliter & corpora B, I, * erit vt grauitas G, ad grauita­<lb/>tem D, ita liquidi B, grauitas, ad grauitatem E, & permutando vt <lb/>grauitas G, ad grauitatem liquidi B, ita D, grauitas, ad grauitatem <lb/>E, &longs;ed vt grauitas D, ad grauitatem E, ita e&longs;t grauitas G, ad graui­<lb/>tatem F; ergo grauitas F, æqualis erit grauitati liquidi B. inuenta <lb/>igitur e&longs;t liquidi corporis B, grauitas F, quod facere oportebat. </s></p><p type="margin"> | <s>Quoniam <lb/>igitur e&longs;t vt A, ad B, ita H, ad I, æquale videlicet ad æquale, erit per­<lb/>mutando vt A, ad H, ita B, ad I, & quoniam eiu&longs;dem &longs;unt generis cor­<lb/><arrow.to.target n="note36"/> pora A, H, &longs;imiliter & corpora B, I, * erit vt grauitas G, ad grauita­<lb/>tem D, ita liquidi B, grauitas, ad grauitatem E, & permutando vt <lb/>grauitas G, ad grauitatem liquidi B, ita D, grauitas, ad grauitatem <lb/>E, &longs;ed vt grauitas D, ad grauitatem E, ita e&longs;t grauitas G, ad graui­<lb/>tatem F; ergo grauitas F, æqualis erit grauitati liquidi B. inuenta <lb/>igitur e&longs;t liquidi corporis B, grauitas F, quod facere oportebat. </s></p><p type="margin"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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> |
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| <s>8. <expan abbr="dictũ">dictum</expan> e&longs;t. </s> | <s>8. <expan abbr="dictũ">dictum</expan> e&longs;t. </s> |
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| <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="aliũ">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"/><!-- KEEP S--></s></p><p type="main"> | <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="aliũ">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"/><!-- KEEP S--></s></p><p type="main"> |
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| <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. <!-- KEEP S--></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. <!-- KEEP S--></s> |
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| <s>Accipiatur ali­<lb/>quod vas vitreum mundum, & politum, cuius grauitas &longs;it v. <!-- REMOVE S-->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="numerũ">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="viuũ">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="cũ">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"/><!-- KEEP S--></s> | <s>Accipiatur ali­<lb/>quod vas vitreum mundum, & politum, cuius grauitas &longs;it v. <!-- REMOVE S-->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="numerũ">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="viuũ">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="cũ">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"/><!-- KEEP S--></s> |
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| </p><p type="margin"> | </p><p type="margin"> |
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| <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><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> |
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| <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"/><!-- KEEP S--></s></p><p type="main"> | <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"/><!-- KEEP S--></s></p><p type="main"> |
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| <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"/><!-- KEEP S--></s></p><p type="main"> | <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"/><!-- KEEP S--></s></p><p type="main"> |
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| <s>Inueniemus etiam aliter, & expeditius grauitatem <lb/>aquæ, magnitudinem habentis æqualem propo&longs;ito ar­<lb/>gento viuo A. <!-- KEEP S--></s></p><p type="main"> | <s>Inueniemus etiam aliter, & expeditius grauitatem <lb/>aquæ, magnitudinem habentis æqualem propo&longs;ito ar­<lb/>gento viuo A. <!-- KEEP S--></s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <s><emph type="italics"/>Contra. <!-- KEEP S--></s> | <s><emph type="italics"/>Contra. <!-- KEEP S--></s> |
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| <s>Qua ratione inuenienda &longs;it grauitas argenti viui, ma­<lb/>gnitudinem habentis propo&longs;ito cuicunque corpori &longs;oli­<lb/>do æqualem. </s></p><p type="main"> | <s>Qua ratione inuenienda &longs;it grauitas argenti viui, ma­<lb/>gnitudinem habentis propo&longs;ito cuicunque corpori &longs;oli­<lb/>do æqualem. </s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <s><lb/>ter & liquidi, quod &longs;it I, eiu&longs;dé <lb/>generis cum liquido B, magni <lb/>tudinern habentis æqualem eidem &longs;olido C, * inueniatur grauitas,<arrow.to.target n="note40"/><lb/>quæ &longs;it E, & fiat vt grauitas E, ad grauitatem D, ita magnitudo G, ad <lb/>ad aliam <expan abbr="magnitadin&etilde;">magnitadinem</expan>, quæ &longs;ie F. <!-- KEEP S--></s> | <s><lb/>ter & liquidi, quod &longs;it I, eiu&longs;dé <lb/>generis cum liquido B, magni <lb/>tudinern habentis æqualem eidem &longs;olido C, * inueniatur grauitas,<arrow.to.target n="note40"/><lb/>quæ &longs;it E, & fiat vt grauitas E, ad grauitatem D, ita magnitudo G, ad <lb/>ad aliam <expan abbr="magnitadin&etilde;">magnitadinem</expan>, quæ &longs;ie F. <!-- KEEP S--></s> |
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| <s>Quoniam igitur &longs;unt quatuor cor­<lb/>pora grauia I, H, B, A, quorum primum, & &longs;ecundum &longs;unt magnitu­<lb/>dine æqualia, tertium vero, & quartum æque grauia, & &longs;unt eiu&longs;dem <lb/>generis primum videlicet, & tertium, &longs;imiliter eiu&longs;dem generis &longs;e­<pb pagenum="26"/><arrow.to.target n="note41"/> cundum & quartum, * Erit vt grauitas E, ad grauitatem D, ita ma­<lb/>gnitudo G, ad liquidi B, magnitudinem, &longs;ed vt grauitas E, ad graui­<lb/>tatem D, ita e&longs;t magnitudo G, ad F, magnitudinem; ergo magnitudo <lb/>F, æqualis erit magnitudini liquidi B. inuenta igitur e&longs;t corporis li­<lb/>quidi B, magnitudo F, quod &longs;acere oportebat. </s></p><p type="margin"> | <s>Quoniam igitur &longs;unt quatuor cor­<lb/>pora grauia I, H, B, A, quorum primum, & &longs;ecundum &longs;unt magnitu­<lb/>dine æqualia, tertium vero, & quartum æque grauia, & &longs;unt eiu&longs;dem <lb/>generis primum videlicet, & tertium, &longs;imiliter eiu&longs;dem generis &longs;e­<pb pagenum="26"/><arrow.to.target n="note41"/> cundum & quartum, * Erit vt grauitas E, ad grauitatem D, ita ma­<lb/>gnitudo G, ad liquidi B, magnitudinem, &longs;ed vt grauitas E, ad graui­<lb/>tatem D, ita e&longs;t magnitudo G, ad F, magnitudinem; ergo magnitudo <lb/>F, æqualis erit magnitudini liquidi B. inuenta igitur e&longs;t corporis li­<lb/>quidi B, magnitudo F, quod facere oportebat. </s></p><p type="margin"> |
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| <s><margin.target id="note39"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> | <s><margin.target id="note39"/>8.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="margin"> |
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| <s>habentis propo&longs;ito corpori liquido æqualem.</s></p><p type="main"> | <s>habentis propo&longs;ito corpori liquido æqualem.</s></p><p type="main"> |
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| <s><emph type="italics"/>Sit propo&longs;itum aliquod olei corpus A, cuius magnitudo<emph.end type="italics"/> 600. <emph type="italics"/>& <lb/>oporteat inuenire quanta srit magnitudo aquæ, grauitatem habentis <lb/>æqualem propo&longs;ito oleo A, accipiatur aliquod &longs;olidum corpus C, vt <lb/>pote plumbeum, & aquæ magnitudinem habentis æqualem plumbo <lb/>C, inueniatur grauitas, vt in exemplo prop.<emph.end type="italics"/> 8, <emph type="italics"/>dictum e&longs;t, quæ &longs;it<emph.end type="italics"/> 12. <lb/><emph type="italics"/>&longs;imiliter & olei æqualem habentis magnitudinem eidem plumbo C, <lb/>inueniatur grauitas quæ &longs;it 11, & fiat vt 12, ad<emph.end type="italics"/> 11, <emph type="italics"/>ita<emph.end type="italics"/> 600, <emph type="italics"/>ad alium <lb/><expan abbr="numerũ">numerum</expan> qui &longs;it<emph.end type="italics"/> 550. <emph type="italics"/>is igitur numerus indicabit quanta erit magni­<lb/>tudo aquæ grauitatem habentis æqualem propo&longs;ito oleo A.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> | <s><emph type="italics"/>Sit propo&longs;itum aliquod olei corpus A, cuius magnitudo<emph.end type="italics"/> 600. <emph type="italics"/>& <lb/>oporteat inuenire quanta srit magnitudo aquæ, grauitatem habentis <lb/>æqualem propo&longs;ito oleo A, accipiatur aliquod &longs;olidum corpus C, vt <lb/>pote plumbeum, & aquæ magnitudinem habentis æqualem plumbo <lb/>C, inueniatur grauitas, vt in exemplo prop.<emph.end type="italics"/> 8, <emph type="italics"/>dictum e&longs;t, quæ &longs;it<emph.end type="italics"/> 12. <lb/><emph type="italics"/>&longs;imiliter & olei æqudlem habentis magnitudinem eidem plumbo C, <lb/>inueniatur grauitas quæ &longs;it 11, & fiat vt 12, ad<emph.end type="italics"/> 11, <emph type="italics"/>ita<emph.end type="italics"/> 600, <emph type="italics"/>ad alium <lb/><expan abbr="numerũ">numerum</expan> qui &longs;it<emph.end type="italics"/> 550. <emph type="italics"/>is igitur numerus indicabit quanta erit magni­<lb/>tudo aquæ grauitatem habentis æqualem propo&longs;ito oleo A.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>Similiter &longs;i <expan abbr="propo&longs;itũ">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. <!-- KEEP S--></s> | <s><emph type="italics"/>Similiter &longs;i <expan abbr="propo&longs;itũ">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. <!-- KEEP S--></s> |
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| <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"/><!-- KEEP S--></s></p><p type="main"> | <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"/><!-- KEEP S--></s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <s>Hoc argumentum <lb/>licet primo a&longs;pectu probabile videatur, tamen fal&longs;o concludit. </s> | <s>Hoc argumentum <lb/>licet primo a&longs;pectu probabile videatur, tamen fal&longs;o concludit. </s> |
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| <s><lb/>verum e&longs;t quod aqua &longs;u&longs;tentat magis corpus planum, quam <lb/>conum, ip&longs;um tamen &longs;u&longs;tentat, netanta velocitate feratur <lb/>deor&longs;um, non ideo ip&longs;ius grauitati aliquid detrahit, neque <lb/>enim ex velociori motu &longs;impliciter inferri pote&longs;t maior gra­<lb/>uitas, illud enim valeret etiam in aere, quod e&longs;t fal&longs;um, &longs;ed <lb/>ne huiu&longs;modi dubitatio veritatis &longs;pecie aliquem decipiat, &longs;e­<lb/>quenti Theoremate eam de&longs;truere agrediar. </s></p><p type="head"> | <s><lb/>verum e&longs;t quod aqua &longs;u&longs;tentat magis corpus planum, quam <lb/>conum, ip&longs;um tamen &longs;u&longs;tentat, netanta velocitate feratur <lb/>deor&longs;um, non ideo ip&longs;ius grauitati aliquid detrahit, neque <lb/>enim ex velociori motu &longs;impliciter inferri pote&longs;t maior gra­<lb/>uitas, illud enim valeret etiam in aere, quod e&longs;t fal&longs;um, &longs;ed <lb/>ne huiu&longs;modi dubitatio veritatis &longs;pccie aliquem decipiat, &longs;e­<lb/>quenti Theoremate eam de&longs;truere agrediar. </s></p><p type="head"> |
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| <s>THEOR EMA VIII. PROPOS. XVI.<!-- KEEP S--></s></p><p type="main"> | <s>THEOR EMA VIII. PROPOS. XVI.<!-- KEEP S--></s></p><p type="main"> |
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| <s>SINT duo eiu&longs;dem generis, & grauitatis corpora A, B, grauiora <lb/>quam aqua, & &longs;int di&longs;&longs;imilia, dico ip&longs;a corpora æqualem in aqua <lb/>grauitatem habere. </s> | <s>SINT duo eiu&longs;dem generis, & grauitatis corpora A, B, grauiora <lb/>quam aqua, & &longs;int di&longs;&longs;imilia, dico ip&longs;a corpora æqualem in aqua <lb/>grauitatem habere. </s> |
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| <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. <!-- KEEP S--></s> | <s>&longs;it enim &longs;i fieri 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. <!-- KEEP S--></s> |
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| <s>Deinde in­<lb/>teligatur aqua con&longs;i&longs;tens, & <lb/>manens, eiu&longs;que &longs;uper&longs;i­<lb/>cies &longs;phærica C D E, cuius <lb/>&longs;phæræ centrum K, aquæ <lb/>enim con&longs;i&longs;tentis, atque <lb/>manentis &longs;uper&longs;icies &longs;phæ­<lb/>rica e&longs;t, cui <gap/> &longs;phæræ cen­<lb/>trum idem <gap/>, quod <expan abbr="centrũ">centrum</expan> <lb/>terræ, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib. | <s>Deinde in­<lb/>teligatur aqua con&longs;i&longs;tens, & <lb/>manens, eiu&longs;que &longs;uperfi­<lb/>cies &longs;phærica C D E, cuius <lb/>&longs;phæræ centrum K, aquæ <lb/>enim con&longs;i&longs;tentis, atque <lb/>manentis &longs;uperficies &longs;phæ­<lb/>rica e&longs;t, cui <gap/> &longs;phæræ cen­<lb/>trum idem <gap/>, quod <expan abbr="centrũ">centrum</expan> <lb/>terræ, hoc autem demon&longs;tratum e&longs;t ab Archimede Prop. 2. lib. |
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| 1. de <lb/>ijs, quæ vehuntur in aqua. </s> | 1. de <lb/>ijs, quæ vehuntur in aqua. </s> |
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| <s>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> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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, <!-- KEEP S--></s></p><p type="main"> | <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, <!-- KEEP S--></s></p><p type="main"> |
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| <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> |
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| <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></p><p type="head"> | <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></p><p type="head"> |
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| <s>intelligatur argentum, vt leuius auro, magnitudinem balere<emph.end type="italics"/><lb/>100, <emph type="italics"/>& in linea auri &longs;ub titulo argenti, quæratur auri magnitudo, <gap/><lb/>erit<emph.end type="italics"/> 54 22/57, <emph type="italics"/>argentum igitur ad aurum &longs;e habebit in magnitudine, vt<emph.end type="italics"/><lb/>100, <emph type="italics"/>ad<emph.end type="italics"/> 54 22/57, <emph type="italics"/>&longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>argenteum, alterum aureum, &longs;it autem argentei corporis magnitudo<emph.end type="italics"/><lb/>100, <emph type="italics"/>erit aurei<emph.end type="italics"/> 54 22/57, <emph type="italics"/>quare corpus argenteum, ad corpus aureum <lb/>eiu&longs;dem grauitatis, &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 54 22/57. </s></p><p type="main"> | <s>intelligatur argentum, vt leuius auro, magnitudinem balere<emph.end type="italics"/><lb/>100, <emph type="italics"/>& in linea auri &longs;ub titulo argenti, quæratur auri magnitudo, <gap/><lb/>erit<emph.end type="italics"/> 54 22/57, <emph type="italics"/>argentum igitur ad aurum &longs;e habebit in magnitudine, vt<emph.end type="italics"/><lb/>100, <emph type="italics"/>ad<emph.end type="italics"/> 54 22/57, <emph type="italics"/>&longs;i enim &longs;umantur duo corpora æque grauia, vnum <lb/>argenteum, alterum aureum, &longs;it autem argentei corporis magnitudo<emph.end type="italics"/><lb/>100, <emph type="italics"/>erit aurei<emph.end type="italics"/> 54 22/57, <emph type="italics"/>quare corpus argenteum, ad corpus aureum <lb/>eiu&longs;dem grauitatis, &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 54 22/57. </s></p><p type="main"> |
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| <s><emph type="italics"/>Quæro denique quomodo &longs;e bab <gap/> in magnitudine aqua & ar­<lb/>gentum viuum. </s> | <s><emph type="italics"/>Quæro denique quomodo &longs;e habent in magnitudine aqua & ar­<lb/>gentum viuum. </s> |
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| <s>quoniam aqua leu<gap/> est argento viuo, intelligatur <lb/>eius magnitudo<emph.end type="italics"/> 100, <emph type="italics"/>& in linea argenti viui, &longs;ub titulo aquæ, quæ­<lb/>ratur argenti viui magnitudo, & reperietur<emph.end type="italics"/> 7 7/29, <emph type="italics"/>aqua igitur ad <lb/>argentum viuum &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 7 7/29. </s></p><p type="main"> | <s>quoniam aqua leu<gap/> est argento viuo, intelligatur <lb/>eius magnitudo<emph.end type="italics"/> 100, <emph type="italics"/>& in linea argenti viui, &longs;ub titulo aquæ, quæ­<lb/>ratur argenti viui magnitudo, & reperietur<emph.end type="italics"/> 7 7/29, <emph type="italics"/>aqua igitur ad <lb/>argentum viuum &longs;e habebit in magnitudine, vt 100, ad<emph.end type="italics"/> 7 7/29. </s></p><p type="main"> |
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| <s>Hic &longs;equitur tabula, ad inueniendas &longs;phærarum grauita­<lb/>tes, ex data diametrorum magnitudine, cuius hæc e&longs;t <lb/>explicatio. </s></p><p type="main"> | <s>Hic &longs;equitur tabula, ad inueniendas &longs;phærarum grauita­<lb/>tes, ex data diametrorum magnitudine, cuius hæc e&longs;t <lb/>explicatio. </s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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> |
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| <s>Ad inueniendas igitur &longs;pbærarum grauitates ex <lb/>data diametrorum magnitudine, bæc erit ratio.<emph.end type="italics"/></s></p><p type="main"> | <s>Ad inueniendas igitur &longs;phærarum grauitates ex <lb/>data diametrorum magnitudine, hæc erit ratio.<emph.end type="italics"/></s></p><p type="main"> |
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| <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;phæram grauitætem ba­<lb/>bere lib.<emph.end type="italics"/> 7, <emph type="italics"/>vnc.<emph.end type="italics"/> 4, <emph type="italics"/>&longs;eru.<emph.end type="italics"/> 13, <emph type="italics"/>gran.<emph.end type="italics"/> 22 29/57. </s></p><p type="main"> | <s><emph type="italics"/>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></p><p type="main"> |
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| <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> |
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| <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> |
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| <s>19, gran.<emph.end type="italics"/> 11 1/17. </s></p><p type="main"> | <s>19, gran.<emph.end type="italics"/> 11 1/17. </s></p><p type="main"> |
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| <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> |
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| <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> |
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| <s>Atque ita reliquarum &longs;pbærarum in tabula nominatarum, ex <lb/>data diametrorum magnitudine, grauitates inuenies.<emph.end type="italics"/></s></p><p type="main"> | <s>Atque ita reliquarum &longs;phærarum in tabula nominatarum, ex <lb/>data diametrorum magnitudine, grauitates inuenies.<emph.end type="italics"/></s></p><p type="main"> |
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| <s>Qua ratione hanc Tabulam compo&longs;uimus. </s></p><p type="main"> | <s>Qua ratione hanc Tabulam compo&longs;uimus. </s></p><p type="main"> |
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| <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 fieri pote&longs;t multo exactior quam &longs;phæra, & facilius. </s> |
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| <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. <!-- REMOVE S-->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. <!-- REMOVE S-->14592. abstulimns ab bah Cylindri <lb/>grauitate partem tertiam. </s> |
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| <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></p><p type="main"> | <s>id est<emph.end type="italics"/> 4864, <emph type="italics"/>reliquum, quod est<emph.end type="italics"/> 9728. <emph type="italics"/>&longs;er­<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;phæra, & Cylindro, Cylindrum, qui ba&longs;im habeat maximo in &longs;phæra <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></p><p type="main"> |
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| <s><emph type="italics"/>Inuenta igitur grauitate &longs;pbæræ, cuius diameter est duarum vn­<lb/>ciarum, facile inuenientur reliquarum <expan abbr="&longs;pbærarũ">&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. <!-- REMOVE S-->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;pbærarũ">&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. <!-- REMOVE S-->19, osten&longs;um enim est prop. |
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| 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> | 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> |
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| <s><emph type="italics"/>Porro ad inueniendas grauitates &longs;phærarum ex reliquis metallis <lb/>vel ex quacunquæ alia materia, hæc erit ratio.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Porro ad inueniendas grauitates &longs;phærarum ex reliquis metallis <lb/>vel ex quacunquæ alia materia, hæc erit ratio.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Fiat vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, (<emph type="italics"/>&longs;i degrauitate &longs;phæræ<lb/><expan abbr="plūbeæ">plumbeæ</expan> quæritur cuius diameter est<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ) ita 19. grauitas vi<gap/><lb/>licet &longs;phæræ stanneæ <expan abbr="diametrū">diametrum</expan> habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, ad <expan abbr="aliū">alium</expan> numer<gap/><lb/>qui &longs;it<emph.end type="italics"/> 29 19/74, <emph type="italics"/>grauitas igitur &longs;phæræ plumbeæ, diametrum haben<lb/>tis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, erit gran.<emph.end type="italics"/> 29 39/74. <emph type="italics"/>&longs;tannum enim ad plumbum ration<gap/><lb/>habet in grauitate vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>vt con&longs;picitur in prima tabelle <lb/>quam ad comparandum inter &longs;e duodecim corporum genera, grauita<lb/>te, & magnitudine, appo&longs;uimus.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Fiat vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, (<emph type="italics"/>&longs;i degrauitate &longs;ph<gap/><lb/><expan abbr="plūbeæ">plumbeæ</expan> quæritur cuius diameter est<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ) ita 19. grauitas vi<gap/><lb/>licet &longs;phæræ stanneæ <expan abbr="diametrū">diametrum</expan> habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, ad <expan abbr="aliū">alium</expan> numer<gap/><lb/>qui &longs;it<emph.end type="italics"/> 29 19/74, <emph type="italics"/>grauitas igitur &longs;phæræ plumbeæ, diametrum hab<gap/><lb/>tis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, erit gran.<emph.end type="italics"/> 29 39/74. <emph type="italics"/>&longs;tannum enim ad plumbum ration<gap/><lb/>habet in grauitate vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>vt con&longs;picitur in prima tabelle <lb/>quam ad comparandum inter &longs;e duodecim corporum genera, grauit <lb/>te, & magnitudine, appo&longs;uimus.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Si vero quæratur de grauitate &longs;phæræ plumbeæ, diametrum <lb/>habentis<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, fiat vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, <emph type="italics"/>ita<emph.end type="italics"/> 9728, <emph type="italics"/>id est gra<gap/><emph.end type="italics"/></s></p><pb pagenum="41"/><p type="table"> | <s><emph type="italics"/>Si vero quæratur de grauitate &longs;phæræ plumbeæ, diametrum <lb/>habentis<emph.end type="italics"/> 2, <emph type="italics"/>vnciarum, fiat vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, <emph type="italics"/>ita<emph.end type="italics"/> 9728, <emph type="italics"/>id est gra<gap/><emph.end type="italics"/></s></p><pb pagenum="41"/><p type="table"> |
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| <s><emph type="italics"/>Huius tabulæ compo&longs;itio pendet ex præcedenti tabula, & ex pro­<lb/>po&longs;.<emph.end type="italics"/> 17, <emph type="italics"/>huius, &longs;i enim fiat vt grauitas &longs;phæræ stanneæ, diametrum <lb/>habentis vnius vnciæ, id est, vt grana<emph.end type="italics"/> 1216, <emph type="italics"/>ad grauitatem &longs;phæræ <lb/>vnius libræ, idest, adgrana<emph.end type="italics"/> 6912, <emph type="italics"/>ita cubus diametri vnius vnciæ, <lb/>hoc e&longs;t, ita<emph.end type="italics"/> 1, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5 11/19 <emph type="italics"/>is erit cubus diametri <lb/>&longs;phæræ stanneæ, grauitatem habentis 1, lib. | <s><emph type="italics"/>Huius tabulæ compo&longs;itio pendet ex præcedenti tabula, & ex pro­<lb/>po&longs;.<emph.end type="italics"/> 17, <emph type="italics"/>huius, &longs;i enim fiat vt grauitas &longs;phæræ stanneæ, diametrum <lb/>habentis vnius vnciæ, id est, vt grana<emph.end type="italics"/> 1216, <emph type="italics"/>ad grauitatem &longs;phæræ <lb/>vnius libræ, idest, adgrana<emph.end type="italics"/> 6912, <emph type="italics"/>ita cubus diametri vnius vnciæ, <lb/>hoc e&longs;t, ita<emph.end type="italics"/> 1, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5 11/19 <emph type="italics"/>is erit cubus diametri <lb/>&longs;phæræ stanneæ, grauitatem habentis 1, lib. |
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| demonstratum enim <lb/>est prop.<emph.end type="italics"/> 17, <emph type="italics"/>huius, &longs;phæras eiu&longs;dem generis inter &longs;e e&longs;&longs;e in grauitate, <lb/>vt diametrorum cubi in magnitudine; quare radix cubica numeri<emph.end type="italics"/><lb/>5 13/19, <emph type="italics"/>dabit ip&longs;am diametrum, &longs;ed quoniam numerus<emph.end type="italics"/> 5 13/19, <emph type="italics"/>non est <lb/>præci&longs;e cubus, eius radix non explicabitur accurata, &longs;ed vt explicetur <lb/>veræ bene proxima, multiplicetur<emph.end type="italics"/> 5 13/19, <emph type="italics"/>per<emph.end type="italics"/> 1000000. <emph type="italics"/>& ex producto<emph.end type="italics"/><lb/>5684210 10/19, <emph type="italics"/>neglecto fracto<emph.end type="italics"/> 10/19, <emph type="italics"/>eruatur radix, tanquam ex accu­<lb/>rato numero cubo, ea erit<emph.end type="italics"/> 173. <emph type="italics"/>proxime, & erit centupla radicis nu­<lb/>meri<emph.end type="italics"/> 5 13/19, <emph type="italics"/>nam numerus<emph.end type="italics"/> 1000000, <emph type="italics"/>per quem fuit multiplicatus<emph.end type="italics"/><lb/>5 13/19, <emph type="italics"/>cubus e&longs;t ex<emph.end type="italics"/> 100<emph type="italics"/>; magnitudo igitur diametri &longs;phæræ &longs;tanneæ, <lb/>grauitatem habentis 1, lib. | demonstratum enim <lb/>est prop.<emph.end type="italics"/> 17, <emph type="italics"/>huius, &longs;phæras eiu&longs;dem generis inter &longs;e e&longs;&longs;e in grauitate, <lb/>vt diametrorum cubi in magnitudine; quare radix cubica numeri<emph.end type="italics"/><lb/>5 13/19, <emph type="italics"/>dabit ip&longs;am diametrum, &longs;ed quoniam numerus<emph.end type="italics"/> 5 13/19, <emph type="italics"/>non est <lb/>præci&longs;e cubus, cius radix non explicabitur accurata, &longs;ed vt explicetur <lb/>veræ bene proxima, multiplicetur<emph.end type="italics"/> 5 13/19, <emph type="italics"/>per<emph.end type="italics"/> 1000000. <emph type="italics"/>& ex producto<emph.end type="italics"/><lb/>5684210 10/19, <emph type="italics"/>neglecto fracto<emph.end type="italics"/> 10/19, <emph type="italics"/>eruatur radix, tanquam ex accu­<lb/>rato numero cubo, ea erit<emph.end type="italics"/> 173. <emph type="italics"/>proxime, & erit centupla radicis nu­<lb/>meri<emph.end type="italics"/> 5 13/19, <emph type="italics"/>nam numerus<emph.end type="italics"/> 1000000, <emph type="italics"/>per quem fuit multiplicatus<emph.end type="italics"/><lb/>5 13/19, <emph type="italics"/>cubus e&longs;t ex<emph.end type="italics"/> 100<emph type="italics"/>; magnitudo igitur diametri &longs;phæræ &longs;tanneæ, <lb/>grauitatem habentis 1, lib. |
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| erit<emph.end type="italics"/> 1 78/100. <emph type="italics"/>reliquarum autem ex &longs;tanno <lb/>&longs;phærarum, grauitatem habentium duplam primæ, triplam, quadru­<lb/>plam &c. </s> | erit<emph.end type="italics"/> 1 78/100. <emph type="italics"/>reliquarum autem ex &longs;tanno <lb/>&longs;phærarum, grauitatem habentium duplam primæ, triplam, quadru­<lb/>plam &c. </s> |
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| <s>Sed vt etiam euitetur labor multiplicandi prædi­<lb/>ctum numerum<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>hac ratione inuenientur eius multi­<lb/>plicia.<emph.end type="italics"/></s></p><p type="main"> | <s>Sed vt etiam euitetur labor multiplicandi prædi­<lb/>ctum numerum<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>hac ratione inuenientur eius multi­<lb/>plicia.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Prædicto numero<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>addatur eius duplum, id est,<emph.end type="italics"/><lb/>11368421 1/19, <emph type="italics"/>&longs;umma<emph.end type="italics"/> 17052631 11/19, <emph type="italics"/>dabit eius triplum, &longs;i vero ei <lb/>addatur eius triplum, id e&longs;t,<emph.end type="italics"/> 17052631 11/19, <emph type="italics"/>&longs;umma<emph.end type="italics"/> 22736842 2/19, <lb/><emph type="italics"/>dabit eius quadruplum, & &longs;i eius quadruplum ei addatur, &longs;umma <lb/>dabit eius quintuplum, & &longs;ic &longs;ola additione inuenientur eius quot­<lb/>cunque multiplicia.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Prædicto numero<emph.end type="italics"/> 5684210 10/19, <emph type="italics"/>addatur eius duplum, id est,<emph.end type="italics"/><lb/>11368421 1/19, <emph type="italics"/>&longs;umma<emph.end type="italics"/> 17052631 11/19, <emph type="italics"/>dabit cius triplum, &longs;i vero ei <lb/>addatur eius triplum, id e&longs;t,<emph.end type="italics"/> 17052631 11/19, <emph type="italics"/>&longs;umma<emph.end type="italics"/> 22736842 2/19, <lb/><emph type="italics"/>dabit eius quadruplum, & &longs;i eius quadruplum ei addatur, &longs;umma <lb/>dabit eius quintuplum, & &longs;ic &longs;ola additione inuenientur eius quot­<lb/>cunque multiplicia.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Eadem ratione inuenientur diametri &longs;phærarum ex quacunque <lb/>alia materia, &longs;i enim quæratur de magnitudine diametri verbi gra­<lb/>tia &longs;phæræ ferreæ, grauitatem habentis 1, lib. | <s><emph type="italics"/>Eadem ratione inuenientur diametri &longs;phærarum ex quacunque <lb/>alia materia, &longs;i enim quæratur de magnitudine diametri verbi gra­<lb/>tia &longs;phæræ ferreæ, grauitatem habentis 1, lib. |
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| fiat vt grana<emph.end type="italics"/> 1314 22/37, <lb/><emph type="italics"/>id est vt grauitas &longs;phæræ ferreæ, cuius diameter e&longs;t vnius vnciæ, ad <lb/>grauitatem vnius libræ, id est ad grana 6912, ita cubus diametri <lb/>vnius vnciæ, hoc e&longs;t ita 1, ad alium numerum qui &longs;it<emph.end type="italics"/> 5 49/190, <emph type="italics"/>is igi­<lb/>tur numerus * erit cubus diametri &longs;phæræ ferreæ, grauitatem haben­<emph.end type="italics"/><arrow.to.target n="note48"/><lb/><emph type="italics"/>tis<emph.end type="italics"/> 1, <emph type="italics"/>lib. | fiat vt grana<emph.end type="italics"/> 1314 22/37, <lb/><emph type="italics"/>id est vt grauitas &longs;phæræ ferreæ, cuius diameter e&longs;t vnius vnciæ, ad <lb/>grauitatem vnius libræ, id est ad grana 6912, ita cubus diametri <lb/>vnius vnciæ, hoc e&longs;t ita 1, ad alium numerum qui &longs;it<emph.end type="italics"/> 5 49/190, <emph type="italics"/>is igi­<lb/>tur numerus * erit cubus diametri &longs;phæræ ferreæ, grauitatem haben-<emph.end type="italics"/><arrow.to.target n="note48"/><lb/><emph type="italics"/>tis<emph.end type="italics"/> 1, <emph type="italics"/>lib. |
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| quare radix cubica numeri<emph.end type="italics"/> 5 49/190, <emph type="italics"/>dabit quæ&longs;itam dia­<lb/>metrum, & quoniam numerus<emph.end type="italics"/> 5 49/190, <emph type="italics"/>non e&longs;t præci&longs;e cubus, & ideo <lb/>non explicabitur eius radix accurate, multiplicetur per 1000000, & <lb/>ex producto<emph.end type="italics"/> 5257894 14/19, <emph type="italics"/>neglecto fracto<emph.end type="italics"/> 14/19, <emph type="italics"/>eruatur radix, tan­<lb/>quam ex accurato numero cubo, ea erit<emph.end type="italics"/> 174: <emph type="italics"/>ferè, & erit centupla ra­<lb/>dicis numeri<emph.end type="italics"/> 5 49/190, <emph type="italics"/>quia numerus<emph.end type="italics"/> 5 49/190, <emph type="italics"/>multiplicatus fuit per <lb/>cubum ex 100; diameter igitur &longs;phæræ ferreæ, grauitatem habentis <lb/>1, lib. | quare radix cubica numeri<emph.end type="italics"/> 5 49/190, <emph type="italics"/>dabit quæ&longs;itam dia­<lb/>metrum, & quoniam numerus<emph.end type="italics"/> 5 49/190, <emph type="italics"/>non e&longs;t præci&longs;e cubus, & ideo <lb/>non explicabitur cius radix accurate, multiplicetur per 1000000, & <lb/>ex producto<emph.end type="italics"/> 5257894 14/19, <emph type="italics"/>neglecto fracto<emph.end type="italics"/> 14/19, <emph type="italics"/>eruatur radix, tan­<lb/>quam ex accurato numero cubo, ea erit<emph.end type="italics"/> 174: <emph type="italics"/>ferè, & erit centupla ra­<lb/>dicis numeri<emph.end type="italics"/> 5 49/190, <emph type="italics"/>quia numerus<emph.end type="italics"/> 5 49/190, <emph type="italics"/>multiplicatus fuit per <lb/>cubum ex 100; diameter igitur &longs;phæræ ferreæ, grauitatem habentis <lb/>1, lib. |
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| erit<emph.end type="italics"/> 1 74/100: <emph type="italics"/>deinde &longs;i duplicetur<emph.end type="italics"/> 5257894 24/19, <emph type="italics"/>& ex ita du­<lb/>plicato eruatur radix cubica<emph.end type="italics"/> 219, <emph type="italics"/>ea dabit centuplum diametri &longs;phæ­<lb/>ra ferreæ, grauitatem habentis<emph.end type="italics"/> 2, <emph type="italics"/>lib. | erit<emph.end type="italics"/> 1 74/100: <emph type="italics"/>deinde &longs;i duplicetur<emph.end type="italics"/> 5257894 24/19, <emph type="italics"/>& ex ita du­<lb/>plicato eruatur radix cubica<emph.end type="italics"/> 219, <emph type="italics"/>ea dabit centuplum diametri &longs;phæ­<lb/>ra ferreæ, grauitatem habentis<emph.end type="italics"/> 2, <emph type="italics"/>lib. |
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| <s>Neque per collectionem quæ&longs;ita aquæ men&longs;ura inueniri <lb/>pote&longs;t: æquè enim impo&longs;&longs;ibile e&longs;t vniuer&longs;am illam æquam col­<lb/>ligere, quæ extra vas effluit, quando corona, vel aurea ma&longs;&longs;a <lb/>vel argentea in ip&longs;o va&longs;e deprimitur, cum enim aqua è va&longs;e <lb/>effluat, pars ip&longs;ius aquæ va&longs;i, ex quo effluit, pars va&longs;i in quod <lb/>influit adhæret, & &longs;i vniuer&longs;a omnino &longs;emper non colligatur, <lb/>erit non parui erroris cau&longs;a, præter quam quod, non &longs;emper <lb/>adeo facile inuenitur par auri, argentique ma&longs;&longs;a, quando co­<lb/>rona, vel alia auri ma&longs;&longs;a, quæ examinanda proponitur, medio­<lb/>crem excederet magnitudinem. </s></p><p type="main"> | <s>Neque per collectionem quæ&longs;ita aquæ men&longs;ura inueniri <lb/>pote&longs;t: æquè enim impo&longs;&longs;ibile e&longs;t vniuer&longs;am illam æquam col­<lb/>ligere, quæ extra vas effluit, quando corona, vel aurea ma&longs;&longs;a <lb/>vel argentea in ip&longs;o va&longs;e deprimitur, cum enim aqua è va&longs;e <lb/>effluat, pars ip&longs;ius aquæ va&longs;i, ex quo effluit, pars va&longs;i in quod <lb/>influit adhæret, & &longs;i vniuer&longs;a omnino &longs;emper non colligatur, <lb/>erit non parui erroris cau&longs;a, præter quam quod, non &longs;emper <lb/>adeo facile inuenitur par auri, argentique ma&longs;&longs;a, quando co­<lb/>rona, vel alia auri ma&longs;&longs;a, quæ examinanda proponitur, medio­<lb/>crem excederet magnitudinem. </s></p><p type="main"> |
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| <s>Neque præterea pote&longs;t di&longs;cerni prædicta argenti portio in <lb/>aliqua auri parua ma&longs;&longs;a, differentiæ enim aquarum, quæ ex­<lb/>tra vas effluunt, &longs;unt adeo exiguæ, vt ne cogno&longs;ci quidem <lb/>po&longs;&longs;int, quod &longs;i cogno&longs;cerentur, non &longs;emper erunt veræ, <lb/>&longs;iquidem non &longs;emper in va&longs;is medio in cumulum cre&longs;cens <lb/>æqualis aquæ copia remanet, &longs;ed maior interdum, inter­<lb/>dum minor, vt con&longs;picitur. </s> | <s>Neque præterea pote&longs;t di&longs;cerni prædicta argenti portio in <lb/>aliqua auri parua ma&longs;&longs;a, differentiæ enim aquarum, quæ ex­<lb/>tra vas effluunt, &longs;unt adeo exiguæ, vt ne cogno&longs;ci quidem <lb/>po&longs;&longs;int, quod &longs;i cogno&longs;cerentur, non &longs;emper erunt veræ, <lb/>&longs;iquidem non &longs;emper in va&longs;is medio in cumulum cre&longs;cens <lb/>æqualis aquæ co<gap/>ia remanet, &longs;ed maior interdum, inter­<lb/>dum minor, vt con&longs;picitur. </s> |
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| <s>fit enim vt aliquando cumulus <lb/>ille frangatur pluribus in locis, & ideo aqua diffundatur, vt <lb/>ferè nihilip&longs;ius cumuli &longs;uper&longs;it, aliquando vero frangatur <lb/>in vno tantum loco, & aqua colligens &longs;e in cumulum, parum <lb/>diffluat. </s></p><p type="main"> | <s>fit enim vt aliquando cumulus <lb/>ille frangatur pluribus in locis, & ideo aqua diffundatur, vt <lb/>ferè nihilip&longs;ius cumuli &longs;uper&longs;it, aliquando vero frangatur <lb/>in vno tantum loco, & aqua colligens &longs;e in cumulum, parum <lb/>diffluat. </s></p><p type="main"> |
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| & oporteat facere quod imperatum e&longs;t. </s> | & oporteat facere quod imperatum e&longs;t. </s> |
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| <s><lb/>Intelligantur duo corpora, vnum aureum, alterum argenteum, æque <lb/>grauia atque corona, deinde trium corporum ex aqua, magnitudine <lb/>æqualium, aureo &longs;cilicet corporivnum, alterum coronæ, tertium cor­<lb/>pori argenteo, inueniantur grauitates, vt in exemplo prop.<emph.end type="italics"/> 8. <emph type="italics"/>dictum <lb/>est, quæ &longs;int primi nimirum corporis aquei<emph.end type="italics"/> 5, <emph type="italics"/>&longs;ecundi vero 6, & terty<emph.end type="italics"/><lb/>9 6/31, <emph type="italics"/>& fiat vt differentia inter<emph.end type="italics"/> 5, & 9 6/32, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 4 6/31, <emph type="italics"/>ad<emph.end type="italics"/> 95, <lb/><emph type="italics"/>grauitatem videlicet coronæ, ita differentia inter<emph.end type="italics"/> 5, & 6, <emph type="italics"/>hoc est 1, ad<emph.end type="italics"/><lb/>22 17/26, <emph type="italics"/>ergo<emph.end type="italics"/> 22 17/26, <emph type="italics"/>erit grauitas portionis argenti quod est in coro­<lb/>na, qua detracta ex totali grauitate coronæ, reliquum<emph.end type="italics"/> 72 9/26, <emph type="italics"/>erit <lb/>grauitas portionis auri.<emph.end type="italics"/></s></p><p type="main"> | <s><lb/>Intelligantur duo corpora, vnum aureum, alterum argenteum, æque <lb/>grauia atque corona, deinde trium corporum ex aqua, magnitudine <lb/>æqualium, aureo &longs;eilicet corporivnum, alterum coronæ, tertium cor­<lb/>pori argenteo, inueniantur grauitates, vt in exemplo prop.<emph.end type="italics"/> 8. <emph type="italics"/>dictum <lb/>est, quæ &longs;int primi nimirum corporis aquei<emph.end type="italics"/> 5, <emph type="italics"/>&longs;ecundi vero 6, & terty<emph.end type="italics"/><lb/>9 6/31, <emph type="italics"/>& fiat vt differentia inter<emph.end type="italics"/> 5, & 9 6/32, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 4 6/31, <emph type="italics"/>ad<emph.end type="italics"/> 95, <lb/><emph type="italics"/>grauitatem videlicet coronæ, ita differentia inter<emph.end type="italics"/> 5, & 6, <emph type="italics"/>hoc est 1, ad<emph.end type="italics"/><lb/>22 17/26, <emph type="italics"/>ergo<emph.end type="italics"/> 22 17/26, <emph type="italics"/>erit grauitas portionis argenti quod est in coro­<lb/>na, qua detracta ex totali grauitate coronæ, reliquum<emph.end type="italics"/> 72 9/26, <emph type="italics"/>erit <lb/>grauitas portionis auri.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Vel &longs;i pro tertio proportionis termino &longs;umatur differentia inter<emph.end type="italics"/> 6, <lb/>& 9 6/31, <emph type="italics"/>quæ e&longs;t<emph.end type="italics"/> 3 6/31, <emph type="italics"/>quartus terminus<emph.end type="italics"/> 72 9/26, <emph type="italics"/>erit grauitas por­<lb/>tionis auri, quæ &longs;i dematur ex totali grauitate coronæ, remanebit<emph.end type="italics"/><lb/>22 17/26, <emph type="italics"/>pro grauitate portionis argenti.<emph.end type="italics"/></s></p><p type="head"> | <s><emph type="italics"/>Vel &longs;i pro tertio proportionis termino &longs;umatur differentia inter<emph.end type="italics"/> 6, <lb/>& 9 6/31, <emph type="italics"/>quæ e&longs;t<emph.end type="italics"/> 3 6/31, <emph type="italics"/>quartus terminus<emph.end type="italics"/> 72 9/26, <emph type="italics"/>erit grauitas por­<lb/>tionis auri, quæ &longs;i dematur ex totali grauitate coronæ, remanebit<emph.end type="italics"/><lb/>22 17/26, <emph type="italics"/>pro grauitate portionis argenti.<emph.end type="italics"/></s></p><p type="head"> |
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| <s><emph type="italics"/>Sit aliquod corpus mistum ex auro. </s> | <s><emph type="italics"/>Sit aliquod corpus mistum ex auro. </s> |
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| <s>& ære, & babeat grauitatem <lb/>171. lib. | <s>& ære, & habeat grauitatem <lb/>171. lib. |
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| & oporteat inuenire quanta erit portio æris in ip&longs;o corpore,<emph.end type="italics"/><pb pagenum="56"/><emph type="italics"/>& quanta auri. </s> | & oporteat inuenire quanta erit portio æris in ip&longs;o corpore,<emph.end type="italics"/><pb pagenum="56"/><emph type="italics"/>& quanta auri. </s> |
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| <s>Intelligantur duo corpori, vnum ex auro puro, al­<lb/>terum ex ære, æque grauia atque corpus mistum, & trium corporum <lb/>ex aqua, quorum vnum &longs;it æquale corpori aureo magnitudine, alte­<lb/>rum misto, tertium aureo, inueniantur grauitates, vt in exemplo pro­<lb/>po&longs;.<emph.end type="italics"/>8.<emph type="italics"/>dictum est, quæ &longs;int<emph.end type="italics"/> 9, 11, <emph type="italics"/>& 19, & fiat vt differentia inter<emph.end type="italics"/> 9, & <lb/>19, <emph type="italics"/>ad<emph.end type="italics"/> 171, <emph type="italics"/>grauitatem videlicet corporis misti, ita differentia inter<emph.end type="italics"/><lb/>9, & 11, <emph type="italics"/>ad<emph.end type="italics"/> 34 1/5, <emph type="italics"/>portio igitur corporis mi&longs;ti ærea grauitatem babebit<emph.end type="italics"/><lb/>34 1/5, <emph type="italics"/>quæ &longs;i auferatur ex totali corporis misti grauitate, remanebit<emph.end type="italics"/><lb/>136 4/5, <emph type="italics"/>pro grauitate portionis auri.<emph.end type="italics"/></s></p><p type="main"> | <s>Intelligantur duo corpo<gap/>i, vnum ex auro puro, al­<lb/>terum ex ære, æque grauia atque corpus mistum, & trium corporum <lb/>ex aqua, quorum vnum &longs;it æquale corpori aureo magnitudine, alte­<lb/>rum misto, tertium ærco, inueniantur grauitates, vt in exemplo pro­<lb/>po&longs;.<emph.end type="italics"/>8.<emph type="italics"/>dictum est, quæ &longs;int<emph.end type="italics"/> 9, 11, <emph type="italics"/>& 19, & fiat vt differentia inter<emph.end type="italics"/> 9, & <lb/>19, <emph type="italics"/>ad<emph.end type="italics"/> 171, <emph type="italics"/>grauitatem videlicet corporis misti, ita differentia inter<emph.end type="italics"/><lb/>9, & 11, <emph type="italics"/>ad<emph.end type="italics"/> 34 1/5, <emph type="italics"/>portio igitur corporis mi&longs;ti ærea grauitatem babebit<emph.end type="italics"/><lb/>34 1/5, <emph type="italics"/>quæ &longs;i auferatur ex totali corporis misti grauitate, remanebit<emph.end type="italics"/><lb/>136 4/5, <emph type="italics"/>pro grauitate portionis auri.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Vel &longs;i pro tertio proportionis termino &longs;umatur differentia inter<emph.end type="italics"/> 11, <lb/><emph type="italics"/>& 19, quartus terminus<emph.end type="italics"/> 136 4/5, <emph type="italics"/>erit grauitas portionis auri, qua ab­<lb/>lata ex totali corporis mi&longs;ti grauitate, reliquum<emph.end type="italics"/> 34 1/5, <emph type="italics"/>dabit grauita­<lb/>tem portionis æreæ.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Vel &longs;i pro tertio proportionis termino &longs;umatur differentia inter<emph.end type="italics"/> 11, <lb/><emph type="italics"/>& 19, quartus terminus<emph.end type="italics"/> 136 4/5, <emph type="italics"/>erit grauitas portionis auri, qua ab­<lb/>lata ex totali corporis mi&longs;ti grauitate, reliquum<emph.end type="italics"/> 34 1/5, <emph type="italics"/>dabit grauita­<lb/>tem portionis æreæ.<emph.end type="italics"/></s></p><p type="main"> |
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| <s>Dico quoque vt differentia grauitatum H, G, ad grauitatem EK, <lb/>ita e&longs;&longs;e differenti <gap/> grauitatum H, FV, ad grauitatem E. <!-- KEEP S--></s> | <s>Dico quoque vt differentia grauitatum H, G, ad grauitatem EK, <lb/>ita e&longs;&longs;e differenti <gap/> grauitatum H, FV, ad grauitatem E. <!-- KEEP S--></s> |
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| <s>Quoniam <lb/>enim o&longs;ten&longs;um e&longs;t, quod fit ex EK, & FV, æquale e&longs;&longs;e ei quod ex G. fit <lb/>& E, vna cum eo quod ex H, & K; quod autem fit ex H, & K, æquat<gap/><lb/><gap/>i quod, ex H, fit & EK, minus eo quod ex H, & E, quod onim additur <lb/>idem & minuitur: ergo quod fit ex EK, & FV, æquale erit ei quod fit <lb/>ex H, & EK, vna cum eo quod ex G, & E, minus eo quod ex H, & E. <lb/>addatur vtrin que quod ex H, fit & E, & &longs;ubducantur ea quæ fiunt ex <lb/>G, & E, & ox EK, & FV; quod igitur fit ex H, & E, minus eo quod ex <lb/>G, & E, æquabitur ei quod ex H, fit & EK, minus eo quod ex FV, & <lb/>EK, &longs;ed quod fit ex H, & E, minus eo quod ex G, & E, æquale e&longs;t ei <lb/>quod ex, differ entia ip&longs;arum H, G, fit & E, &longs;imiliter, & quod ex H, fit <lb/>& EK, minus eo quod ex FV, & EK, æquale e&longs;t eiquod ex differentia <lb/>ip&longs;arum H, FV, fit & EK; ergo quod ex differentia ip&longs;arum H, G, fit <lb/>& E, æquabitur ei quod ex differentia ip&longs;arum H, FV, fit & EK; qua­<lb/>re æqualitatem ad <expan abbr="proportion&etilde;">proportionem</expan> reuocando erit v<gap/> differen tia graui<pb pagenum="59"/>tatum H, G, ad grauitatem EK, ita differentia gra<gap/>tatum H, FV, <lb/>zd grauitatem E. quod &longs;ecundo loco fuit demon&longs;trandum. </s></p><p type="main"> | <s>Quoniam <lb/>enim o&longs;ten&longs;um e&longs;t, quod fit ex EK, & FV, æquale e&longs;&longs;e ei quod ex G. fit <lb/>& E, vna cum eo quod ex H, & K; quod autem fit ex H, & K, æquat<gap/><lb/><gap/>i quod, ex H, fit & EK, minus eo quod ex H, & E, quod onim additur <lb/>idem & minuitur: ergo quod fit ex EK, & FV, æquale erit ei quod fit <lb/>ex H, & EK, vna cum eo quod ex G, & E, minus eo quod ex H, & E. <lb/>addatur vtrin que quod ex H, fit & E, & &longs;ubducantur ea quæ fiunt ex <lb/>G, & E, & ox EK, & FV; quod igitur fit ex H, & E, minus eo quod ex <lb/>G, & E, æquabitur ei quod ex H, fit & EK, minus eo quod ex FV, & <lb/>EK, &longs;ed quod fit ex H, & E, minus eo quod ex G, & E, æquale e&longs;t ei <lb/>quod ex, differ entia ip&longs;arum H, G, fit & E, &longs;imiliter, & quod ex H, fit <lb/>& EK, minus eo quod ex FV, & EK, æquale e&longs;t eiquod ex differentia <lb/>ip&longs;arum H, FV, fit & EK; ergo quod ex differentia ip&longs;arum H, G, fit <lb/>& E, æquabitur ei quod ex differentia ip&longs;arum H, FV, fit & EK; qua­<lb/>re æqualitatem ad <expan abbr="proportion&etilde;">proportionem</expan> reuocando erit v<gap/> differen ti a grauis <pb pagenum="59"/>tatum H, G, ad grauitatem EK, ita differentia gra<gap/>tatum H, FV, <lb/>zd grauitatem E. quod &longs;ecundo loco fuit demon&longs;trandum. </s></p><p type="main"> |
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| <s>Alia breuior Theorematis demon&longs;tratio. </s></p><p type="main"> | <s>Alia breuior Theorematis demon&longs;tratio. </s></p><p type="main"> |
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| <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. <!-- KEEP S--></s></p><p type="margin"> | <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. <!-- KEEP S--></s></p><p type="margin"> |
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| <s><margin.target id="note52"/>4.<emph type="italics"/>buius<emph.end type="italics"/></s></p><p type="main"> | <s><margin.target id="note52"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="main"> |
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| <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></p><p type="margin"> | <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></p><p type="margin"> |
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| <s><margin.target id="note53"/>4.<emph type="italics"/>buius<emph.end type="italics"/></s></p><p type="main"> | <s><margin.target id="note53"/>4.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="main"> |
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| <s>Dico quoque vt H, minus G, ad EK, ita e&longs;&longs;e H, minus FV, ad E. <!-- KEEP S--></s> | <s>Dico quoque vt H, minus G, ad EK, ita e&longs;&longs;e H, minus FV, ad E. <!-- KEEP S--></s> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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> |
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| <s>Sed ante <lb/>omnia, duo nobis &longs;unt præmittenda, & explicanda. </s> | <s>Sed ante <lb/>omnia, duo nobis &longs;unt præmittenda, & explicanda. </s> |
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| <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>& 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> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <s><emph type="italics"/>Sit aliquod corpus aureum, exempli gratia<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum, quod <lb/>expurgatum & ad aurum purum reductum, ami&longs;erit ex pri&longs;tina <lb/>grauitate nempe ex<emph.end type="italics"/> 24, <emph type="italics"/>vncys, quatuor vncias, ita vt reman&longs;erint <lb/>tantum<emph.end type="italics"/> 20, <emph type="italics"/>vnciæ auri puri, reliquum vero vel euanuerit in fumum, <lb/>vel fuerit alterius metalli. </s> | <s><emph type="italics"/>Sit aliquod corpus aureum, exempli gratia<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum, quod <lb/>expurgatum & 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> |
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| <s>Totum igitur illud corpus aureum ab <lb/>initio propo&longs;itum, &longs;i adbuc intelligatur tale quale fuit ante expurga­<lb/>tionem, appellabitur<emph.end type="italics"/> 20. <emph type="italics"/>partium, &longs;eu, (vt vulgo dicitur) di<emph.end type="italics"/> 20. <emph type="italics"/>ca­<lb/>ratti. </s> | <s>Totum igitur illud corpus aureum ab <lb/>initio propo&longs;itum, &longs;i adhuc intelligatur tale quale fuit ante expurga­<lb/>tionem, appellabitur<emph.end type="italics"/> 20. <emph type="italics"/>partium, &longs;eu, (vt vulgo dicitur) di<emph.end type="italics"/> 20. <emph type="italics"/>ca­<lb/>ratti. </s> |
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| <s>eo quod tota illa ma<32>a mista,<emph.end type="italics"/> 20. <emph type="italics"/>tantum vncias auri puri con­<lb/>tinuerit. </s> | <s>eo quod tota illa ma<32>a mista,<emph.end type="italics"/> 20. <emph type="italics"/>tantum vncias auri puri con­<lb/>tinuerit. </s> |
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| <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>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> |
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| <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 adhuc &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> |
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| <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>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> |
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| <s>Bt &longs;t quidem inuenerint, ex priori grauitate<emph.end type="italics"/> 24. <emph type="italics"/>&longs;or<gap/><lb/>pulorum, deperi&longs;&longs;e nibil: pronunciabunt aurum sllud, boc est, non <lb/>&longs;olum partieulam illam excoctam, &longs;ed etiam illud d quo fuit 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 nihil: 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> |
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| <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 fuit<emph.end type="italics"/> 24. <lb/><emph type="italics"/>dicturi &longs;unt aurum propo&longs;itam<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum fui&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium & <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></p><p type="main"> | <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></p><p type="main"> |
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| <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><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> |
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| <s>Nam cum in bac comparatione qualitatum, &longs;eor&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 grauita<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> |
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| <s>bao enim ratione <gap/>dem numero exprimunt vnam <lb/>quamque qualitatem auri cuiuslibet ma&longs;&longs;æ propo&longs;itæ. </s> | <s>bao enim ratione <gap/>dem numero exprimunt vnam <lb/>quamque qualitatem auri cuiuslibet ma&longs;&longs;æ propo&longs;itæ. </s> |
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| <s>quem ydem ob&longs;eruant <lb/>breuiter adnotemus.<emph.end type="italics"/></s></p><p type="main"> | <s>quem ydem ob&longs;eruant <lb/>breuiter adnotemus.<emph.end type="italics"/></s></p><p type="main"> |
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| <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 deprehenderunt 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><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> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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> | <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>Et quoniam <lb/>non prodiret <gap/>ale pror&longs;us quale facere intendunt, &longs;ed paulo perfe­<lb/>ctius; propterea quod <gap/> quidem partes in wixtione <gap/>antant, ex <lb/>argenta vero & are aliquid deperdatur, &longs;olen<gap/> Aucifices tanto plue <lb/><gap/>i&longs;cere argenti & aris quantum perdi po&longs;&longs;e deprehenderunt.<emph.end type="italics"/></s></p><p type="main"> | <s>Et quoniam <lb/>non prodiret <gap/>ale pror&longs;us quale &longs;acore intendunt, &longs;ed paulo perfe­<lb/>ctius; propterea quod <gap/> quidem partes in wixtione <gap/>antant, ex <lb/>argenta vero & are aliquid deperdatur, &longs;olen<gap/> Aucifices tanto plue <lb/><gap/>i&longs;cere argenti & aris quantum perdi po&longs;&longs;e deprebenderunt.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Veru<gap/> nostra iutentio non est omnia quæ ad ciu&longs;modi mixtione <lb/>pertinent hoc loco expon<gap/>e; &longs;ed illud tantum vt recept<gap/> apud o<gap/><lb/><gap/>es ad ferre voluimus, ex quo manifeste constat, qu<gap/> metallorum <lb/>mixtio in &longs;ingulis qualitatum generibus statuatur: quaquidem e&longs;t <lb/>illa quam add<gap/>ximus <gap/>mpe in auro<emph.end type="italics"/> 23, <emph type="italics"/>partium, partes<emph.end type="italics"/> 23, <emph type="italics"/>e&longs;&longs;e <lb/>auripuri & reliquamq <gap/>deest ad<emph.end type="italics"/> 24, <emph type="italics"/>partes con&longs;tare dimidia <lb/>parte argenti, & dimidia <gap/>ris in grauitate. </s> | <s><emph type="italics"/>Veru<gap/> nostra iutentio non est omnia quæ ad ciu&longs;modi mixtione <lb/>pertinent hoc loco expon<gap/>e; &longs;ed illud tantum vt recept<gap/> apud o<gap/><lb/><gap/>es ad ferre voluimus, ex quo manifeste constat, qua metallorum <lb/>mixtio in &longs;ingulis qualitatum generibus statuatur: quaquidem e&longs;t <lb/>illa quam add<gap/>ximus <gap/>mpe in auro<emph.end type="italics"/> 23, <emph type="italics"/>partium, partes<emph.end type="italics"/> 23, <emph type="italics"/>e&longs;&longs;e <lb/>auripuri & reliquamq <gap/>deest ad<emph.end type="italics"/> 24, <emph type="italics"/>partes con&longs;tare dimidia <lb/>parte arg<gap/>ti, & dimidia <gap/>ris in grauitate. </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>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> |
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| <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: & quia 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></p><p type="main"> | <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, quo <lb/>quidem ita &longs;e habet vt &longs;equitur.<emph.end type="italics"/></s></p><p type="main"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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. <!-- KEEP S--></s></p><p type="main"> | <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. <!-- KEEP S--></s></p><p type="main"> |
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| <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 iuncta mixtionem prædi­<lb/>ctam, quæ etiam &longs;ubinte<gap/>genda erit in &longs;equantibus, in aere fuerit<emph.end type="italics"/><lb/>18, <emph type="italics"/>erit id 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></p><p type="margin"> | <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></p><p type="margin"> |
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| <s><margin.target id="note54"/>5. <emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="main"> | <s><margin.target id="note54"/>5. <emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="main"> |
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| <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>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> |
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| <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></p><p type="margin"> | <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 haben<emph.end type="italics"/><arrow.to.target n="note55"/><lb/><emph type="italics"/>tis <gap/>qualem propo&longs;itæ ma&longs;&longs;æ erit vnc.<emph.end type="italics"/> 1 2431/5301. </s></p><p type="margin"> |
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| <s><margin.target id="note55"/>5.<emph type="italics"/>buius<emph.end type="italics"/></s></p><p type="main"> | <s><margin.target id="note55"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="main"> |
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| <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 enim numerus erit grauitas illius aquæ.<emph.end type="italics"/></s></p><p type="main"> | <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></p><p type="main"> |
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| <s><emph type="italics"/>Fiat denique ot<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita <gap/>ur&longs;ue<emph.end type="italics"/> 24, <emph type="italics"/>vntiæ, ad alium, numi­<lb/>rus enim quartus, nempe vnc.<emph.end type="italics"/> 2<gap/> <emph type="italics"/>erit grauitas aquæ, magnitu­<lb/><gap/>ine æqualis corport mi&longs;to ex argento & ære, euius grauitas est in <lb/>ærè vnc.<emph.end type="italics"/> 24, <emph type="italics"/>corp<gap/>s enim ita mi&longs;tum, ad corpus aqueum eiu&longs;dem ma­<lb/><gap/> nitudin<gap/> rationem babet in grauitate vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29. </s></p><p type="main"> | <s><emph type="italics"/>Fiat denique ot<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita <gap/>ur&longs;ue<emph.end type="italics"/> 24, <emph type="italics"/>vntiæ, ad alium, numi­<lb/>rus enim quartus, nempe vnc.<emph.end type="italics"/> 2<gap/> <emph type="italics"/>erit grauitas aquæ, magnitu­<lb/><gap/>ine æqualis corport mi&longs;to ex argento & ære, euius grauitas est in <lb/>ærè vnc.<emph.end type="italics"/> 24, <emph type="italics"/>corp<gap/>s enim ita mi&longs;tum, ad corpus aqueum eiu&longs;dem ma­<lb/><gap/> nitudin<gap/> rationem habet in grauitate vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29. </s></p><p type="main"> |
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| <s><emph type="italics"/>Atque ita habebuntur tres gravitates <gap/> aquæ quantitatum, <lb/>quarum prima æquatur auro puro<emph.end type="italics"/> 24, <emph type="italics"/>vuctarum, &longs;<gap/>unda ma&longs;&longs;<gap/><lb/>propo&longs;itæ<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum, & reliqua corpori mi&longs;to ex argento & <gap/><lb/>&longs;imiliter<emph.end type="italics"/> 24, <emph type="italics"/><gap/>vnciarum quæ quidem tres grauitates in numeris di­<lb/>&longs;ponantur co ordine, quo &longs;equitur.<emph.end type="italics"/></s></p><p type="table"> | <s><emph type="italics"/>Atque ita habeb<gap/>tur tres gra<gap/>tate<gap/> aquæ quantitatum, <lb/>quarum prima æquatur auto pu<gap/>o<emph.end type="italics"/> 24, <emph type="italics"/>vuctarum, &longs;<gap/>unda ma&longs;&longs;<gap/><lb/>propo&longs;itæ<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum, & reliqua corpori mi&longs;to ex argento & <gap/><lb/>&longs;imiliter<emph.end type="italics"/> 24, <emph type="italics"/><gap/>vnciarum quæ quidem tres grauitates in numeris di­<lb/>&longs;ponantur eo ordine, quo &longs;equitur.<emph.end type="italics"/></s></p><p type="table"> |
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| <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main"> | <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/>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"/>quart<gap/> enim proportionalium terminus nempe<emph.end type="italics"/> 20, </s></p><pb pagenum="64"/><p type="table"> | <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></p><pb pagenum="64"/><p type="table"> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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> | <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> |
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| <s>binc fit quod eædem<emph.end type="italics"/> 20. <emph type="italics"/>vnc. </s> | <s>hinc fit quod eædem<emph.end type="italics"/> 20. <emph type="italics"/>vnc. </s> |
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| <s>immediate denominent au­<lb/>rum propo&longs;itum e<32>e<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s> | <s>immediate denominent au­<lb/>rum propo&longs;itum e<32>e<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s> |
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| <s>Quando vero grauitas totius ma&longs;­<lb/>&longs;anon exprimitur per numerum<emph.end type="italics"/> 24, <emph type="italics"/>tunc opus erit inquirere quot <lb/>partes vige&longs;imas quartas totius grauitatis efficiat quartus ille pro­<lb/>portionis terminus vt in &longs;equenti <gap/>mplo clarius appar<gap/>bit.<emph.end type="italics"/></s></p><p type="main"> | <s>Quando vero grauitas totius ma&longs;­<lb/>&longs;anon exprimitur per numerum<emph.end type="italics"/> 24, <emph type="italics"/>tunc opus erit inquirere quot <lb/>partes vige&longs;imas quartas totius grauitatis efficiat quartus ille pro­<lb/>portionis terminus vt in &longs;equ<gap/>nti <gap/>mplo clarius appar<gap/>bit.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Sit euim propo&longs;ita a lia auri ma&longs;&longs;a cuius grauitas in aere &longs;it<emph.end type="italics"/> 5301 <lb/><emph type="italics"/>in aqua vero<emph.end type="italics"/> 4988, <emph type="italics"/>&longs;i igitur hic <gap/>erus &longs;ubtrabatur ex numero to<emph.end type="italics"/><lb/><arrow.to.target n="note56"/><emph type="italics"/>tius grauitatis<emph.end type="italics"/> 5301, <emph type="italics"/>r<gap/>liquus numerus<emph.end type="italics"/> 313, * <emph type="italics"/>erit grauitas aquæ <lb/>propo&longs;itæ ma&longs;&longs;æ magnitudine æqualis. </s> | <s><emph type="italics"/>Sit euim propo&longs;ita a lia auri ma&longs;&longs;a cuius grauitas in aere &longs;it<emph.end type="italics"/> 5301 <lb/><emph type="italics"/>in aqua vero<emph.end type="italics"/> 4988, <emph type="italics"/>&longs;i igitur hic <gap/>erus &longs;ubtrabatur ex numero to<emph.end type="italics"/><lb/><arrow.to.target n="note56"/><emph type="italics"/>tius grauitatis<emph.end type="italics"/> 5301, <emph type="italics"/>r<gap/>liquus numerus<emph.end type="italics"/> 313, * <emph type="italics"/>erit grauitas aquæ <lb/>propo&longs;itæ ma&longs;&longs;æ magnitudine æqualis. </s> |
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| <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<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>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> |
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| <s>hoc e&longs;t primo fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 1, <emph type="italics"/>ita<emph.end type="italics"/><lb/>5301, <emph type="italics"/>ad<emph.end type="italics"/> 279, <emph type="italics"/>hic enim numerus erit grauitas 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> |
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| <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></p><p type="margin"> | <s>Atque ba tre<gap/> grauitates aquæ &longs;criban­<lb/>tur eo ordine quo &longs;upra; inuenti&longs;que differentys inter primam &<emph.end type="italics"/></s></p><p type="margin"> |
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| <s><margin.target id="note56"/>5.<emph type="italics"/>buius<emph.end type="italics"/></s></p><p type="table"> | <s><margin.target id="note56"/>5.<emph type="italics"/>huius<emph.end type="italics"/></s></p><p type="table"> |
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| <s>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></p><p type="table"> | <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></p><p type="table"> |
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| <s>Vnde inposterum &longs;olum opus erit inuenire tertium pro­<lb/>portionis terminum, hoc est differentiam inter grauitates &longs;ecundæ <lb/>& tertiæ aquæ.<emph.end type="italics"/></s></p><p type="main"> | <s>Vnde inposterum &longs;olum opus erit inuenire tertium pro­<lb/>portionis terminum, hoc est differentiam inter grauitates &longs;ecundæ <lb/>& tertiæ aquæ.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Sed vt hoc etiam exemplo illustretur, proponatur aliqua ma&longs;&longs;a <lb/>auri, cuius <expan abbr="inue&longs;tigãda">inue&longs;tiganda</expan> &longs;it qualitas, & &longs;it ip&longs;ius ma&longs;&longs;æ grauitas qui­<lb/>dem in aere<emph.end type="italics"/> 837, <emph type="italics"/>in aqua vero<emph.end type="italics"/> 784, <emph type="italics"/>ergo * grauitas aquæ magnitu-<emph.end type="italics"/><arrow.to.target n="note58"/><lb/><emph type="italics"/>dinem habentis æqualem propo&longs;itæ ma&longs;&longs;æ erit<emph.end type="italics"/> 53, <emph type="italics"/>differentia enim <lb/>inter primam, & &longs;ecundam grauitatem est<emph.end type="italics"/> 53. </s></p><p type="margin"> | <s><emph type="italics"/>Sed vt hoc etiam exemplo illustretur, proponatur aliqua ma&longs;&longs;a <lb/>auri, cuius <expan abbr="inue&longs;tigãda">inue&longs;tiganda</expan> &longs;it qualitas, & &longs;it ip&longs;ius ma&longs;&longs;æ grauitas qui­<lb/>dem in aere<emph.end type="italics"/> 837, <emph type="italics"/>in aqua vero<emph.end type="italics"/> 784, <emph type="italics"/>ergo * grauitas aquæ magnitu­<emph.end type="italics"/><arrow.to.target n="note58"/><lb/><emph type="italics"/>dinem habentis æqualem propo&longs;itæ ma&longs;&longs;æ erit<emph.end type="italics"/> 53, <emph type="italics"/>differentia enim <lb/>inter primam, & &longs;ecundam grauitatem est<emph.end type="italics"/> 53. </s></p><p type="margin"> |
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| <s><margin.target id="note58"/>5.<emph type="italics"/>hui<gap/><emph.end type="italics"/></s></p><p type="main"> | <s><margin.target id="note58"/>5.<emph type="italics"/>hui<gap/><emph.end type="italics"/></s></p><p type="main"> |
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| <s>Reuocetur primum <lb/>ptopo&longs;itæ ma&longs;&longs;æ grauitas<emph.end type="italics"/> 837, <emph type="italics"/>ad grauitatem<emph.end type="italics"/> 5301, <emph type="italics"/>hoc est intelli­<lb/>gatur ip&longs;a ma&longs;&longs;a grauitatem babere<emph.end type="italics"/> 5301. <emph type="italics"/>deinde fiat vt<emph.end type="italics"/> 837, <emph type="italics"/>ad<emph.end type="italics"/> 53, <lb/><emph type="italics"/>grauitatem vidclicet aquæ ip&longs;i ma&longs;&longs;æ æqualis, ita<emph.end type="italics"/> 5301, <emph type="italics"/>ad<emph.end type="italics"/> 335 2/3, <lb/><emph type="italics"/>ergo<emph.end type="italics"/> 335 2/3, <emph type="italics"/>erit grauitas aquæ magnitudinem habentis æqualem <lb/>aureæ ma<32>æ, cuius grauitas<emph.end type="italics"/> 837, <emph type="italics"/>reuocata est ad grauitatem<emph.end type="italics"/> 5301; <lb/><emph type="italics"/>quare grauitas &longs;ecundæ aquæ erit<emph.end type="italics"/> 335 2/1, <emph type="italics"/>& con&longs;equenter differen-<emph.end type="italics"/></s></p><p type="table"> | <s>Reuocetur primum <lb/>ptopo&longs;itæ ma&longs;&longs;æ grauitas<emph.end type="italics"/> 837, <emph type="italics"/>ad grauitatem<emph.end type="italics"/> 5301, <emph type="italics"/>hoc est intelli­<lb/>gatur ip&longs;a ma&longs;&longs;a grauitatem babere<emph.end type="italics"/> 5301. <emph type="italics"/>deinde fiat vt<emph.end type="italics"/> 837, <emph type="italics"/>ad<emph.end type="italics"/> 53, <lb/><emph type="italics"/>grauitatem vidclicet aquæ ip&longs;i ma&longs;&longs;æ æqualis, ita<emph.end type="italics"/> 5301, <emph type="italics"/>ad<emph.end type="italics"/> 335 2/3, <lb/><emph type="italics"/>ergo<emph.end type="italics"/> 335 2/3, <emph type="italics"/>erit grauitas aquæ magnitudinem habentis æqualem <lb/>aureæ ma<32>æ, cuius grauitas<emph.end type="italics"/> 837, <emph type="italics"/>reuocata est ad grauitatem<emph.end type="italics"/> 5301; <lb/><emph type="italics"/>quare grauitas &longs;ecundæ aquæ erit<emph.end type="italics"/> 335 2/1, <emph type="italics"/>& con&longs;equenter differen-<emph.end type="italics"/></s></p><p type="table"> |
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| <s>TABELLE WAR HIER<lb/><emph type="italics"/>tia inter ip&longs;am grauitatem &longs;ecundæ aquæ & grauitatem tertiæ<emph.end type="italics"/> 551, <lb/><emph type="italics"/>erit<emph.end type="italics"/> 215 1/1, <emph type="italics"/>&longs;ed ip&longs;a differentia ponitur pro tertio proportionis ter­<lb/>mino; crgo<emph.end type="italics"/> 215 1/3, <emph type="italics"/>erit quæ&longs;itus terminus, nempe proportionis ter­<emph.end type="italics"/></s></p><pb pagenum="66"/><p type="table"> | <s>TABELLE WAR HIER<lb/><emph type="italics"/>tia inter ip&longs;am grauitatem &longs;ecundæ aquæ & grauitatem tertiæ<emph.end type="italics"/> 551, <lb/><emph type="italics"/>erit<emph.end type="italics"/> 215 1/1, <emph type="italics"/>&longs;ed ip&longs;a differentia ponitur pro tertio proportionis ter­<lb/>mino; crgo<emph.end type="italics"/> 215 1/3, <emph type="italics"/>erit quæ&longs;itus terminus, nempe proportionis ter-<emph.end type="italics"/></s></p><pb pagenum="66"/><p type="table"> |
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| <s>TABELLE WAR HIER<lb/><emph type="italics"/>tius. </s> | <s>TABELLE WAR HIER<lb/><emph type="italics"/>tius. </s> |
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| <s>Quartus autem terminus<emph.end type="italics"/> 4196 25/116, <emph type="italics"/>indicabit grauitatcm <lb/>auri puri, quod est in ma&longs;&longs;a propo&longs;ita, eam tamen indicabit in par­<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></p><p type="main"> | <s>Quartus autem terminus<emph.end type="italics"/> 4196 25/116, <emph type="italics"/>indicabit grauitatcm <lb/>auri puri, quod est in ma&longs;&longs;a propo&longs;ita, eam tamen indicabit in par­<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;i enim 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></p><p type="main"> |
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| <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> | <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 nihil 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> |
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| <s>Quod &longs;i con&longs;taret plura alia a&longs;&longs;umpta e&longs;&longs;e, etiam in <lb/>quauis alia ratione, facile erit cuiuis ad &longs;imilitudinem huius, for­<lb/>mare alium modum, &longs;ed nos, ne longiores &longs;imus, ad v&longs;um &longs;equentis <lb/>tabulæ nos conferamus, qua illis con&longs;ultum volumus qui minus in <lb/>præceptis Aritbmeticis &longs;unt exercitati, velillis, qui alias ob cau&longs;as <lb/>tabulis vti malunt, quam calculis.<emph.end type="italics"/></s></p><p type="main"> | <s>Quod &longs;i con&longs;taret plura alia a&longs;&longs;umpta e&longs;&longs;e, etiam in <lb/>quauis alia ratione, facile erit cuiuis ad &longs;imilitudinem huius, for­<lb/>mare alium modum, &longs;ed nos, ne longiores &longs;imus, ad v&longs;um &longs;equentis <lb/>tabulæ nos conferamus, qua illis con&longs;ultum volumus qui minus in <lb/>præceptis Aritbmeticis &longs;unt exercitati, velillis, qui alias ob cau&longs;as <lb/>tabulis vti malunt, quam calculis.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Porro in area tabulæ &longs;ub titulo grauitatis auri in aqua po&longs;ita est <lb/>grauitas auri cuiuslibet qualitatis quam obtinet in aqua, quæ qua <lb/>ratione inueniatur, dicetur inferius vbi agetur de compo&longs;itione <lb/>eiu&longs;dem tabulæ.<emph.end type="italics"/></s></p><p type="main"> | <s><emph type="italics"/>Porro in area tabulæ &longs;ub titulo grauitatis auri in aqua po&longs;ita est <lb/>grauitas auri cuiuslibet qualitatis quam obtinet in aqua, quæ qua <lb/>ratione inueniatur, dicetur inferius vbi agetur de compo&longs;itione <lb/>eiu&longs;dem tabulæ.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>V&longs;us eius &longs;unt duo, quorum alterum titulus indicat, nimirum vt <lb/>tabulæ beneficio reperiatur ex grauitate auri quam babet in aere & <lb/>aqua, eius qualitas. </s> | <s><emph type="italics"/>V&longs;us eius &longs;unt duo, quorum alterum titulus indicat, nimirum vt <lb/>tabulæ beneficio reperiatur ex grauitate auri quam habet in aere & <lb/>aqua, eius qualitas. </s> |
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| <s>Alter vero est vt cogno&longs;catur grauitas in aqua, <lb/>quando vnà cum grauitate quam aliquod aurum habet in aere da­<lb/>tur ip&longs;ius qualitas. </s> | <s>Alter vero est vt cogno&longs;catur grauitas in aqua, <lb/>quando vnà cum grauitate quam aliquod aurum habet in aere da­<lb/>tur ip&longs;ius qualitas. </s> |
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| <s>fiat vt lib. | <s>fiat vt lib. |
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| 1. ad vnc <lb/>11, Scrup.<emph.end type="italics"/> 5, <emph type="italics"/>Gran.<emph.end type="italics"/> 3 963/1767, <emph type="italics"/>ita lib.<emph.end type="italics"/> 3. <emph type="italics"/>ad alium numerum, is erit <lb/>lib.<emph.end type="italics"/> 2, <emph type="italics"/>vnc. </s> | 1. ad vne <lb/>11, Scrup.<emph.end type="italics"/> 5, <emph type="italics"/>Gran.<emph.end type="italics"/> 3 963/1767, <emph type="italics"/>ita lib.<emph.end type="italics"/> 3. <emph type="italics"/>ad alium numerum, is erit <lb/>lib.<emph.end type="italics"/> 2, <emph type="italics"/>vnc. </s> |
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| <s>9, Scrup. <!-- REMOVE S-->15, Gran.<emph.end type="italics"/> 10 1122/1767. <emph type="italics"/>& tanta erit grauitas au­<lb/>ri propo &longs;iti in aqua. </s> | <s>9, Scrup. <!-- REMOVE S-->15, Gran.<emph.end type="italics"/> 10 1122/1767. <emph type="italics"/>& tanta erit grauitas au­<lb/>ri propo &longs;iti in aqua. </s> |
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| <s><emph type="italics"/>Quando vero grauitas auri in aere quiaem e&longs;t vnius lib. | <s><emph type="italics"/>Quando vero grauitas auri in aere quiaem e&longs;t vnius lib. |
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| 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></p><p type="main"> | 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></p><p type="main"> |
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| <s><emph type="italics"/>Proponatur aurum vnius libræ in aqua habens grauitatem vnc. </s> | <s><emph type="italics"/>Proponatur aurum vnius libræ in aqua habens grauitatem vnc. </s> |
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| <s><emph type="italics"/>Denique &longs;i proponatur aurum non vnius libræ &longs;ed vel plurium, <lb/>vel &longs;olum aliquot vnciarum. </s> | <s><emph type="italics"/>Denique &longs;i proponatur aurum non vnius libræ &longs;ed vel plurium, <lb/>vel &longs;olum aliquot vnciarum. </s> |
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| <s>Reducenda erit eius grauitas quam <lb/>babet maqua, ad grauitatem quam haberet &longs;i e<32>et vnius libræ, id <lb/>quod ab&longs;oluetur per proportionis ratiocinationem, &longs;i pro termino <lb/>primo ponatur vera grauitas auri propo&longs;iti, pro &longs;ecundo, e iu&longs;dem <lb/>grauitas in aqua, & pro tertio lib. | <s>Reducenda erit eius grauitas quam <lb/>habet maqua, ad grauitatem quam haberet &longs;i e<32>et vnius libræ, id <lb/>quod ab&longs;oluetur per proportionis ratiocinationem, &longs;i pro termino <lb/>primo ponatur vera grauitas auri propo&longs;iti, pro &longs;ecundo, e iu&longs;dem <lb/>grauitas in aqua, & pro tertio lib. |
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| 1, quartus enim terminus indica­<lb/>bit grauitatem in aqua re&longs;pondentem vni libræ auri propo&longs;iti. </s> | 1, quartus enim terminus indica­<lb/>bit grauitatem in aqua re&longs;pondentem vni libræ auri propo&longs;iti. </s> |
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| <s>& <lb/>bac inuenta reliqua expedientur vt prius.<emph.end type="italics"/></s></p><p type="main"> | <s>& <lb/>hac inuenta reliqua expedientur vt prius.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Exemplum huius ca&longs;us hic non affero, quod per &longs;e res &longs;it clara. </s> | <s><emph type="italics"/>Exemplum huius ca&longs;us hic non affero, quod per &longs;e res &longs;it clara. </s> |
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| <s><lb/>Sed illud tantum obiter aduertere placet, quod videtur pertinere <lb/>ad commodiorem v&longs;um tabulæ, videlicet vt ys in ca&longs;ibus in quibus <lb/>nece<32>arius cst calculus, fractiones granorum ommittantur quando <lb/>minus valent quam<emph.end type="italics"/> 1/2, <emph type="italics"/>& quando valent plus, eorum loco, addatur <lb/>vnum granum reliquis granis, & &longs;i quando accidat binc procreari <lb/>grana<emph.end type="italics"/> 24. <emph type="italics"/>tunc etiam grana ommittantur addita prius vnitate ad <lb/>&longs;crupula in tabula inuenta. </s> | <s><lb/>Sed illud tantum obiter aduertere placet, quod videtur pertinere <lb/>ad commodiorem v&longs;um tabulæ, videlicet vt ys in ca&longs;ibus in quibus <lb/>nece<32>arius cst calculus, fractiones granorum ommittantur quando <lb/>minus valent quam<emph.end type="italics"/> 1/2, <emph type="italics"/>& quando valent plus, eorum loco, addatur <lb/>vnum granum reliquis granis, & &longs;i quando accidat hinc procreari <lb/>grana<emph.end type="italics"/> 24. <emph type="italics"/>tunc etiam grana ommittantur addita prius vnitate ad <lb/>&longs;crupula in tabula inuenta. </s> |
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| <s>hac enim ratione calculus erit expedi­<lb/>tior & error qui hinc oborietur erit in&longs;en&longs;ibilis.<emph.end type="italics"/></s></p><pb pagenum="70"/><p type="head"> | <s>hac enim ratione calculus erit expedi­<lb/>tior & error qui hinc oborietur erit in&longs;en&longs;ibilis.<emph.end type="italics"/></s></p><pb pagenum="70"/><p type="head"> |
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| <s>Compo&longs;itio eiu&longs;dem tabulæ.</s></p><p type="main"> | <s>Compo&longs;itio eiu&longs;dem tabulæ.</s></p><p type="main"> |
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| <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> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <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><emph type="italics"/>Et primum &longs;it propo&longs;itum aurum purum, &longs;eu<emph.end type="italics"/> 24, <emph type="italics"/>partium. </s> |
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| <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></p><p type="main"> | <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></p><p type="main"> |
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| <s><emph type="italics"/>Sit deinde propo&longs;itum quod vis aliud corpus aureum vnius libræ, <lb/>&longs;itque exemp. </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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| <s>gratia illud aurum<emph.end type="italics"/> 20, <emph type="italics"/>partium, patet igitur ex defi­<lb/>nitione qualitatis, ex<emph.end type="italics"/> 24, <emph type="italics"/>&longs;emiunciis totius grauitatis,<emph.end type="italics"/> 20, <emph type="italics"/>&longs;emiuncias <lb/>e&longs;&longs;e auri puri, duas argenti, & reliquas duas æris & quoniam gra­<lb/>uitas misti in aere, ad grauitatem eiu&longs;dem in aqua rationem habet <lb/>vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 250, <emph type="italics"/>vt exiam dictis patet, fiat vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 250, <emph type="italics"/>ita qua­<lb/>tuor &longs;emiunciæ, vel potius <gap/>, vnciæ misti quod componit qualitatem <lb/>auri<emph.end type="italics"/> 20, <emph type="italics"/>partium, paulo ante propo&longs;itam ad alias vncias. </s> | <s>gratia illud aurum<emph.end type="italics"/> 20, <emph type="italics"/>partium, patet igitur ex defi­<lb/>nitione qualitatis, ex<emph.end type="italics"/> 24, <emph type="italics"/>&longs;emiuncys totius grauitatis,<emph.end type="italics"/> 20, <emph type="italics"/>&longs;emiuncias <lb/>e&longs;&longs;e auri puri, duas argenti, & reliquas duas æris & quoniam gra­<lb/>uitas misti in aere, ad grauitatem eiu&longs;dem in aqua rationem habet <lb/>vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 250, <emph type="italics"/>vt exiam dictis patet, fiat vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 250, <emph type="italics"/>ita qua­<lb/>tuor &longs;emiunciæ, vel potius <gap/>, vnciæ misti quod componit qualitatem <lb/>auri<emph.end type="italics"/> 20, <emph type="italics"/>partium, paulo ante propo&longs;itam ad alias vncias. </s> |
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| <s>inuenien­<lb/>tur enim pro grauitate illius mi&longs;ti in aqua vnc.<emph.end type="italics"/> 1 221/274. <emph type="italics"/>Est autem <lb/>grauitas auri puri<emph.end type="italics"/> 20, <emph type="italics"/>&longs;emiunciarum vel<emph.end type="italics"/> 10, <emph type="italics"/>vnciarum in aqua vnc.<emph.end type="italics"/><lb/>9 9/19, <emph type="italics"/>eo quod ita &longs;e habeant<emph.end type="italics"/> 10, <emph type="italics"/>ad<emph.end type="italics"/> 9 9/29, <emph type="italics"/>vt 19, ad<emph.end type="italics"/> 18, <emph type="italics"/>Quare &longs;i hæ <lb/>duæ grauitates inuentæ colligantur in vnam &longs;ummam, inueniemus <lb/>totam ma&longs;&longs;am auri propo&longs;itam, cuius grauitas in aere ponebatur lib. <!-- REMOVE S--><lb/>1, in aqua babere grauitatem vnc.<emph.end type="italics"/> 11 1409/5301. <emph type="italics"/>& facta reductione <lb/>fractionis ad &longs;crupula, & grana, vnc. </s> | <s>inuenien­<lb/>tur enim pro grauitate illius mi&longs;ti in aqua vnc.<emph.end type="italics"/> 1 221/274. <emph type="italics"/>Est autem <lb/>grauitas auri puri<emph.end type="italics"/> 20, <emph type="italics"/>&longs;emiunciarum vel<emph.end type="italics"/> 10, <emph type="italics"/>vnciarum in aqua vnc.<emph.end type="italics"/><lb/>9 9/19, <emph type="italics"/>eo quod ita &longs;e habeant<emph.end type="italics"/> 10, <emph type="italics"/>ad<emph.end type="italics"/> 9 9/29, <emph type="italics"/>vt 19, ad<emph.end type="italics"/> 18, <emph type="italics"/>Quare &longs;i hæ <lb/>duæ grauitates inuentæ colligantur in vnam &longs;ummam, inueniemus <lb/>totam ma&longs;&longs;am auri propo&longs;itam, cuius grauitas in aere ponebatur lib. <!-- REMOVE S--><lb/>1, in aqua babere grauitatem vnc.<emph.end type="italics"/> 11 1409/5301. <emph type="italics"/>& facta reductione <lb/>fractionis ad &longs;crupula, & grana, vnc. </s> |
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| <s>grauitates auri<emph.end type="italics"/> 20, <emph type="italics"/>&<emph.end type="italics"/> 19, <emph type="italics"/>partium. </s> | <s>grauitates auri<emph.end type="italics"/> 20, <emph type="italics"/>&<emph.end type="italics"/> 19, <emph type="italics"/>partium. </s> |
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| <s>Quo­<lb/>niam igitur in auro<emph.end type="italics"/> 20, <emph type="italics"/>partium &longs;unt auri puri<emph.end type="italics"/> 20. <emph type="italics"/>&longs;emiunciæ, misti <lb/>vero<emph.end type="italics"/> 4, <emph type="italics"/>& in auro<emph.end type="italics"/> 29, <emph type="italics"/>partium &longs;unt auri puri<emph.end type="italics"/> 19. <emph type="italics"/>&longs;emiunciæ, misti <lb/>vero<emph.end type="italics"/> 5, <emph type="italics"/>erit in auro<emph.end type="italics"/> 20. <emph type="italics"/><expan abbr="partiũ">partium</expan> vna &longs;emiuncia auri puri plu&longs;quam in <lb/>auro<emph.end type="italics"/> 19, <emph type="italics"/>partium, in auro autem 19, partium erit vna &longs;emiuncia <lb/>misti plus quam in auro<emph.end type="italics"/> 20, <emph type="italics"/>partium; quare grauitas auri<emph.end type="italics"/> 20, <emph type="italics"/>par­<lb/>tium in aqua &longs;uperabit in aqua grauitatem auri<emph.end type="italics"/> 19, <emph type="italics"/>partium gra­<lb/>uitate, qua &longs;emiuncia auri puri &longs;uperat &longs;emiunciam mi&longs;li. </s> | <s>Quo­<lb/>niam igitur in auro<emph.end type="italics"/> 20, <emph type="italics"/>partium &longs;unt auri puri<emph.end type="italics"/> 20. <emph type="italics"/>&longs;emiuneiæ, misti <lb/>vero<emph.end type="italics"/> 4, <emph type="italics"/>& in auro<emph.end type="italics"/> 29, <emph type="italics"/>partium &longs;unt auri puri<emph.end type="italics"/> 19. <emph type="italics"/>&longs;emiunciæ, misti <lb/>vero<emph.end type="italics"/> 5, <emph type="italics"/>erit in auro<emph.end type="italics"/> 20. <emph type="italics"/><expan abbr="partiũ">partium</expan> vna &longs;emiuncia auri puri plu&longs;quam in <lb/>auro<emph.end type="italics"/> 19, <emph type="italics"/>partium, in auro autem 19, partium erit vna &longs;emiuncia <lb/>misti plus quam in auro<emph.end type="italics"/> 20, <emph type="italics"/>partium; quare grauitas auri<emph.end type="italics"/> 20, <emph type="italics"/>par­<lb/>tium in aqua &longs;uperabit in aqua grauitatem auri<emph.end type="italics"/> 19, <emph type="italics"/>partium gra­<lb/>uitate, qua &longs;emiuncia auri puri &longs;uperat &longs;emiunciam mi&longs;li. </s> |
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| <s>Quod <lb/>erat demon&longs;trandum. </s> | <s>Quod <lb/>erat demon&longs;trandum. </s> |
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| <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main"> | <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main"> |
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| <s><emph type="italics"/><expan abbr="Contractior&etilde;">Contractiorem</expan> <expan abbr="quoq.">quoque</expan> ad inuenies dimidij pedis <expan abbr="men&longs;urã">men&longs;uram</expan> in margine pag. </s> | <s><emph type="italics"/><expan abbr="Contractior&etilde;">Contractiorem</expan> <expan abbr="quoq.">quoque</expan> ad inuenies dimidy pedis <expan abbr="men&longs;urã">men&longs;uram</expan> in margine pag. </s> |
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| <s>34. <expan abbr="appo&longs;itã">appo&longs;itam</expan>, <lb/>quia mad facta papyrus, <expan abbr="dũ">dum</expan> imprimeretur recipiebat <expan abbr="verã">veram</expan> <expan abbr="men&longs;urã">men&longs;uram</expan>, ex&longs;iccata <lb/>breuiorem reddidit. </s> | <s>34. <expan abbr="appo&longs;itã">appo&longs;itam</expan>, <lb/>quia mad facta papyrus, <expan abbr="dũ">dum</expan> imprimeretur recipiebat <expan abbr="verã">veram</expan> <expan abbr="men&longs;urã">men&longs;uram</expan>, ex&longs;iccata <lb/>breuiorem reddidit. </s> |
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| <s>Ita que &longs;i quartadecima pars vnius vncia addatur ip&longs;i men <lb/>&longs;ura componetur dimidij pedis men&longs;ura; vel &longs;i ip&longs;a men&longs;ura duplicetur, & ei ad­<lb/>datur &longs;eptima pars vnius vncia fiet men&longs;ura vnius pedis, ad cuius rationem em <lb/>nes calculi in tabulas optime re&longs;pond ebunt.<emph.end type="italics"/></s></p><p type="main"> | <s>Ita que &longs;i quartadecima pars vnius vncia addatur ip&longs;i men <lb/>&longs;ura componetur dimidy pedis men&longs;ura; vel &longs;i ip&longs;a men&longs;ura duplicetur, & ei ad­<lb/>datur &longs;eptima pars vnius vncia fiet men&longs;ura vnius pedis, ad cuius rationem em <lb/>nes calculi in tabulas optime re&longs;pond ebunt.<emph.end type="italics"/></s></p><p type="main"> |
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| <s><emph type="italics"/>Denique pagina<emph.end type="italics"/> 38. <emph type="italics"/>&<emph.end type="italics"/> 39. <emph type="italics"/>tabularum prapo&longs;terus e&longs;t ordo. </s> | <s><emph type="italics"/>Denique pagina<emph.end type="italics"/> 38. <emph type="italics"/>&<emph.end type="italics"/> 39. <emph type="italics"/>tabularum prapo&longs;terus e&longs;t ordo. </s> |
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| <s>ex quo tamen nibil sr­<lb/>reris &longs;equitur &longs;i tituli recte accipiantur.<emph.end type="italics"/></s></p> </chap> </body> <back/> </text></archimedes> | <s>ex quo tamen nihil sr­<lb/>reris &longs;equitur &longs;i tituli recte accipiantur.<emph.end type="italics"/></s></p> </chap> </body> <back/> </text></archimedes> |
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