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version 1.13, 2003/11/20 19:14:55

version 1.14, 2003/11/24 18:58:04

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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><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>

<s><lb/>Habet no&longs;tra hæc ætas, quos admitetur; habet quos ex<lb/>tollat præclaros viros, &longs;ed quos tibi anteponat, non facile <lb/>inueniet. </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>

<s>In primis enim tua vitæ integritas <lb/>elu&longs;modi e&longs;t, vt non conterita dome&longs;tico præcomo lati&longs;<lb/>&longs;ime peruagetur. </s>

<s>In primis enim tua vitæ integritas <lb/>elu&longs;modi e&longs;t, vt non contenta dome&longs;tico præcomo lati&longs;<lb/>&longs;ime peruagetur. </s>

<s>Habent omnes quod prædicent, & imi <lb/>tentur; habet quod excipiat grati&longs;sima memoria po&longs;te<lb/>ritas vniuer&longs;a. </s>

<s>Doctrinæ vero ea excellentia es, vt ea &longs;atis <lb/>omnibus clarus, & illu&longs;tris, non &longs;atis tibi, <gap/>cum a&longs;sidue <lb/>certes. </s>

<s>nec minum, qui vel à primis incunabulis ad &longs;um<lb/>ma contendebas, &longs;i prouecta iam ætate vix habeas, quo <lb/>altius contendas. </s>

<s>nec mirum, qui vel à primis incunabulis ad &longs;um<lb/>ma contendebas, &longs;i prouecta iam ætate vix habeas, quo <lb/>altius contendas. </s>

<s>Præclarum &longs;anè & eximium vno do<lb/>ctrinæ genere; &longs;ublime, atque admirabile multiplici ex<lb/>cellere. </s>

<s>Tu vero în omni genere laudem egregiam a&longs;&longs;e<lb/>cutus es ab&longs;olutam videlicet tibî gloriam propo&longs;itam <lb/>volui&longs;ti; <expan abbr="quiq;">quique</expan> intelligebas hominem ad hone&longs;ta omnia <pb xlink:href="029/01/004.jpg"/>genitum, nullam tibi rerum glorio&longs;arum partem con<lb/>temnendam puta&longs;ti. </s>

<s>Placet incredibili rerum humana<lb/>num v&longs;ui diuinarum rerum cognitionem adiungere; vt <lb/>habeat animus à caducis ad æterna, &longs;e conferendo, vnde <lb/>oblectamentum capiat, & admirationem. </s>

<s>Placet incredibili rerum humana<lb/>rum v&longs;ui diuinarum rerum cognitionem adiungere; vt <lb/>habeat animus à caducis ad æterna, &longs;e conferendo, vnde <lb/>oblectamentum capiat, & admirationem. </s>

<s>Philo&longs;ophiam <lb/>ita tenes, vt qui in maximis negocijs a&longs;sidue ver&longs;atus es, <lb/>videaris &longs;emper fui&longs;fe otio&longs;us. </s>

<s>Philo&longs;ophiam <lb/>ita tenes, vt qui in maximis negoijs a&longs;sidue ver&longs;atus es, <lb/>videaris &longs;emper fui&longs;fe otio&longs;us. </s>

<s>Quid dicam de &longs;ingulari <lb/><expan abbr="caq;">caque</expan> eximia rerum c&oelig;le&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>Exitum tuorum labor um <lb/>f&oelig;lici&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 laborum <lb/>felici&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;imos: 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>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;apientiæ, quæ vix vllos habet at ter<lb/>minos, humanitatis tuæ terminis circum&longs;cribis; & expo<lb/>nis omnibus<gap/> vt ex tanto &longs;onte perennes ad omnium or<lb/>dinum homines fluuii deducantur. </s>

<s>F&oelig;lix qui &longs;olidæ <lb/>f&oelig;licitatis 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 f&oelig;nus honorem ex honore, laudem <lb/>ex laude con&longs;equi vberiorem, hæc illa &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 xlink:href="029/01/005.jpg"/>rens vbertatis ip&longs;a &longs;uæ dominæ nunquam debilitatur, <lb/>nunquam deficit. </s>

<s>Felix qui &longs;olidæ <lb/>felicitatis cau&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 f&oelig;nus honorem ex honore, laudem <lb/>ex laude con&longs;equi vberiorem, hæc illa &longs;apienti viro non <lb/>indigna liberalitas, quæ rerum pre&longs;tanti&longs;simarum po&longs;<lb/>&longs;e&longs;sione non imminuta, in copia tenuitatem non inqui-<pb xlink:href="029/01/005.jpg"/>rens vbertatis ip&longs;a &longs;uæ dominæ nunquam debilitatur, <lb/>nunquam deficit. </s>

<s>Quin etiam i&longs;to loco con&longs;titutus bo<lb/>narum literarum &longs;tudio&longs;os complecteris, ac tueris. </s>

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<s>Ab eo &longs;imul ac Theodo&longs;io. </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. </s>

<s>Rubeo ho<lb/>mine mihi tum ex &longs;tudiorum &longs;imilitudine, tum pracipue ex <lb/>eius humanitate amici&longs;simo, ad Reuerendi&longs;simum Sera<lb/>phinum deductus &longs;um. </s>

<s>I&longs;qs me tantus Præ&longs;ul non &longs;olum <lb/>humani&longs;sime complexus est, 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>Argumentum quidem, vt <lb/>dicebam non iniucundum e&longs;t, nec ab v&longs;u alienam. </s>

<s>Huiu&longs;<lb/>medi enim comparatione Archimides mixtionem argemi <lb/>in aure deprehendit, & furtum Aurificis in corona aurea <lb/>patefecit. </s>

<s>Huiu&longs;<lb/>medi enim comparatione Archimedes mixtionem argemi <lb/>in aure deprehendit, & furtum Aurificis in corona aurea <lb/>patefecit. </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 deprehendi queat, & alte <lb/><gap/> ab alieno di&longs;cerni & &longs;imul explicabo, quo pacto ex au<lb/>ri grauitate <gap/> qualitas, <gap/>perfectio intelligi po&longs;sit. </s>

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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 & A&longs;ino <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>

<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 pronuntiatum; vnicuique enim no<lb/>tius e&longs;t duo trianguli latera reliquo e&longs;&longs;e maiora (cum & A&longs;ino <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>

<s>THEOREMA IV. PROPOS. IV.</s>

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<s>Quando vero corpus &longs;olidum fuerit leuius liquido, hoc e&longs;t <lb/>demi&longs;&longs;um in liquidum non de&longs;cendat, per adiectionem alicuius <lb/>alius &longs;olidi corporis liquido grauioris, quæ&longs;ita liquidi grauitas <lb/>inuenietur. </s>

<s><emph type="italics"/>Sit igitur propo&longs;itum aliquod ccreum corpus A, cuius grauitas &longs;it<emph.end type="italics"/><lb/>21. <emph type="italics"/>& oporteat &longs;cire quanta erit grauitas aquæ magnitudinem haben<lb/>tis æqualem ceræ A. </s>

<s><emph type="italics"/>Sit igitur propo&longs;itum aliquod cereum corpus A, cuius grauitas &longs;it<emph.end type="italics"/><lb/>21. <emph type="italics"/>& oporteat &longs;cire quanta erit grauitas aquæ magnitudinem haben<lb/>tis æqualem ceræ A. </s>

<s>Quoniam cera leuior est, quam aqua, &longs;i demitta<lb/><gap/>ur in aquam non feretur deor&longs;um, accipiatur aliquod corpus &longs;olidum <lb/>F, grauius quam aqua, ita vt corpus constans ex vtri&longs;que corporibus <lb/>A, F, demi&longs;&longs;um in aquam feratur deor&longs;um, &longs;it igitur corpus F, plum<lb/>beum, cuius grauitas &longs;it v.g.<emph.end type="italics"/> 23, <emph type="italics"/>& eiu&longs;dem in aqua ponderati<emph.end type="italics"/> 21, <lb/><emph type="italics"/><gap/>go aquæ magnitudinem habentis <expan abbr="æqual&etilde;">æqualem</expan> plumbo F, erit grauitas<emph.end type="italics"/> 2, </s>

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<s><emph type="italics"/>Dixi &longs;eta e quina corpus ponder andum debere appendi, quia fere <lb/>æque grauis e&longs;t atque aqua, & ideo nihil addet, vel minuet grauita<lb/>tis in ip&longs;o corpore ponderando.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quod &longs;i corpus ponderandum fuerit, tam graue, vt &longs;eta &longs;implici &longs;u<lb/>stineri nequeat, appendatur pluribus &longs;imul iunctis &longs;etis, & ne aliquid <lb/>grauitatis &longs;etarum coniunctio addat corpori ponderando, ponantur <lb/>in altera lance totidem &longs;etæ æquales eis, quæ ex lance, cui appen&longs;um e&longs;t <lb/>corpus pendent, v&longs;que ad corpus appen&longs;um, hac igitur &longs;etarum addi<lb/>tione æque ponderabunt lances, & quamuis illæ &longs;etæ, quibus appen<lb/>&longs;um est corpus, &longs;int longiores, quam aliæ alteri lanci addilæ, longitudi<lb/>ne partium, quibus ligatum est corpus, tamen quoniam illæ partes <lb/>æque graues &longs;unt, atque aqua, exi&longs;tentes cum ip&longs;o corpore in aqua, nul<lb/>lam grauitatem habebunt, & ideo illæ &longs;etæ, quæ alias &longs;uperant dictis <lb/>partibus, & &longs;i longiores, non erunt grauiores quam aliæ, existenti<lb/>bus, nempe, vt dictum e&longs;t, illis partibus cum ip&longs;o corpore in aqua. </s>

<s><emph type="italics"/>Quod &longs;i corpus ponderandum fuerit, tam graue, vt &longs;eta &longs;implici &longs;u<lb/>stineri nequeat, appendatur pluribus &longs;imul iunctis &longs;etis, & ne aliquid <lb/>grauitatis &longs;etarum coniunctio addat corpori ponderando, ponantur <lb/>in altera lance totidem &longs;etæ æquales eis, quæ ex lance, cui appen&longs;um e&longs;t <lb/>corpus pendent, v&longs;que ad corpus appen&longs;um, hac igitur &longs;etarum addi<lb/>tione æque ponderabunt lances, & quamuis illæ &longs;etæ, quibus appen<lb/>&longs;um est corpus, &longs;int longiores, quam aliæ alteri lanci addita, longitudi<lb/>ne partium, quibus ligatum est corpus, tamen quoniam illæ partes <lb/>æque graues &longs;unt, atque aqua, exi&longs;tentes cum ip&longs;o corpore in aqua, nul<lb/>lam grauitatem habebunt, & ideo illæ &longs;etæ, quæ alias &longs;uperant dictis <lb/>partibus, & &longs;i longiores, non erunt grauiores quam aliæ, existenti<lb/>bus, nempe, vt dictum e&longs;t, illis partibus cum ip&longs;o corpore in aqua. </s>

<s>Sic <lb/>igitur in aqua ponderanda erunt &longs;olida corpora, quod animaduerti&longs;&longs;e <lb/>fuit operæ pretium.<emph.end type="italics"/></s><pb xlink:href="029/01/018.jpg" pagenum="11"/>

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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 habentis æqualem plumbo D, inuenta graui<emph.end type="italics"/><pb xlink:href="029/01/024.jpg" pagenum="17"/><emph type="italics"/>tate 2, fiat vt<emph.end type="italics"/> 23<emph type="italics"/>, ad<emph.end type="italics"/> 2<emph type="italics"/>, ita cubus ex<emph.end type="italics"/> 10<emph type="italics"/>, hoc est<emph.end type="italics"/> 1000<emph type="italics"/>, ad alium nume<lb/>rum qui &longs;it<emph.end type="italics"/> 86 22/2<gap/><31> <emph type="italics"/>is igitur numerus erit cubus diametrs &longs;phæræ ex <lb/>plumbo, grauitatem æqualem habentis propo&longs;ite ex aqua &longs;phæræ B, <lb/>quare eius latus cubicum, quod est<emph.end type="italics"/> 4 41/100<31> <emph type="italics"/>ferè, indicabit ip&longs;am <lb/>diametrum.<emph.end type="italics"/></s>

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

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

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

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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 habentis æqualem plumbo D, in<lb/>ueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 74. <emph type="italics"/>& fiat vt 74, ad<emph.end type="italics"/> 115, <emph type="italics"/>ita cubus ex 10, <lb/>qui e&longs;t 1000, ad alium numerum qui &longs;it<emph.end type="italics"/> 1554 2/17, <emph type="italics"/>is igitur numerus <lb/>erit cubus diametri &longs;phæræ ex stanno, grauitatem habentis æqualem <lb/>propo&longs;itæ ex plumbo &longs;phæræ A, quare eius latus cubicum, quod est<emph.end type="italics"/><lb/>11 52/100, <emph type="italics"/>vero proximum, indicabit ip&longs;am diametrum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Similiter &longs;i propo&longs;itum corpus plumbeum A, fuerit cubicum, vel <lb/>alicuius alterius formæ regularis, eadem ratione inuenietur latus cu<lb/>bi ex stanno, grauitatem habentis 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 habentis æqualem propo&longs;ito plumbeo cu<lb/>bo A, &longs;i enim ip&longs;ius cubi plumbei 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>cubitum numeri<emph.end type="italics"/> 1554 2/17<31> <emph type="italics"/>quod est<emph.end type="italics"/> 11 52/100<31> <emph type="italics"/>pro <lb/>ximum vero; indicabit quæ &longs;itum latus.<emph.end type="italics"/></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 habentis æqualem argento viuo C, inueniatur graui<lb/>tas, eo modo quo dictum est, quæ &longs;it<emph.end type="italics"/> 7, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/> 7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad <lb/>alium numerum, qui &longs;it<emph.end type="italics"/> 420, <emph type="italics"/>is igitur numerus indicabit quanta erit <lb/>grauitas aquæ, magnitudinem habentis æqualem propo&longs;ito argento <lb/>viuo A.<emph.end type="italics"/></s>

<s><emph type="italics"/>Contra, &longs;it propo&longs;itum aliquod corpus aqueum A, cuius grauitas<emph.end type="italics"/><lb/>420, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui, magni<lb/>tudine æqualis propo&longs;itæ aquæ A. facto, vt &longs;upra, & inuenta graui<lb/>tate<emph.end type="italics"/> 7, <emph type="italics"/>aquæ &longs;cilicet magnitudinem habentis æqualem <expan abbr="arg&etilde;to">argento</expan> viuo C,<emph.end type="italics"/><pb xlink:href="029/01/031.jpg" pagenum="24"/><emph type="italics"/>flat vt<emph.end type="italics"/> 7, <emph type="italics"/>ad<emph.end type="italics"/> 95, <emph type="italics"/>ita<emph.end type="italics"/> 420, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5700, <emph type="italics"/>is igi<lb/>tur indicabit quanta erit grauitas argenti viui, magnitudine æqua<lb/>lis propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

<s><emph type="italics"/>Contra, &longs;it propo&longs;itum aliquod corpus aqueum A, cuius grauitas<emph.end type="italics"/><lb/>420, <emph type="italics"/>& oporteat inuenire quanta erit grauitas argenti viui, magni<lb/>tudine æqualis propo&longs;itæ aquæ A. facto, vt &longs;upra, & inuenta graui<lb/>tate<emph.end type="italics"/> 7, <emph type="italics"/>aquæ &longs;cilicet magnitudinem habentis æqualem <expan abbr="arg&etilde;to">argento</expan> viuo C,<emph.end type="italics"/><pb xlink:href="029/01/031.jpg" pagenum="24"/><emph type="italics"/>fiat vt<emph.end type="italics"/> 7, <emph type="italics"/>ad<emph.end type="italics"/> 95, <emph type="italics"/>ita<emph.end type="italics"/> 420, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 5700, <emph type="italics"/>is igi<lb/>tur indicabit quanta erit grauitas argenti viui, magnitudine æqua<lb/>lis propo&longs;itæ aquæ A.<emph.end type="italics"/></s>

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

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

<s><emph type="italics"/>Accipiatur enim aliquod corpus aureum, 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 an <lb/>reo inueniatur grauitas, vt dictum est in propo&longs;.<emph.end type="italics"/> 8. <emph type="italics"/>exemplo, quæ &longs;it<emph.end type="italics"/> 7, <lb/><emph type="italics"/>&longs;imiliter & argenti viui, vt aquæ, magnitudinem habentis æqualem <lb/>eidem corpori aureo, inueniatur grauitas, quæ &longs;it<emph.end type="italics"/> 95, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 95, <emph type="italics"/>ad<emph.end type="italics"/><lb/>7, <emph type="italics"/>ita<emph.end type="italics"/> 5700, <emph type="italics"/>ad<emph.end type="italics"/> 420, <emph type="italics"/>grauitas igitur aquæ, magnitudinem habentis æ<lb/>qualem argento viuo A, erit<emph.end type="italics"/> 420. </s>

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

<s>&longs;it propo&longs;itum aliquod corpus aqueum, 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. </s>

<s>Superinducta corpori aureo cerea <lb/>tunica, vt &longs;upra, & inuentis grauitatibus<emph.end type="italics"/> 7, & 95, <emph type="italics"/>aquæ nimirum, & <lb/>argenti viut, magnitudine æqualium prædicto aureo corpori, fiat vt<emph.end type="italics"/><lb/>7, <emph type="italics"/>ad 95, ita<emph.end type="italics"/> 430, <emph type="italics"/>ad<emph.end type="italics"/> 5700 <emph type="italics"/>grauitas igitur argenti viui, magnitudin<gap/><lb/>æqualis propo&longs;ito corpori aqueo A, erit<emph.end type="italics"/> 5700. </s>

<s>Superinducta corpori aureo cerea <lb/>tunica, vt &longs;upra, & inuentis grauitatibus<emph.end type="italics"/> 7, & 95, <emph type="italics"/>aquæ nimirum, & <lb/>argenti viut, magnitudine æqualium prædicto aureo corpori, fiat vt<emph.end type="italics"/><lb/>7, <emph type="italics"/>ad 95, ita<emph.end type="italics"/> 430, <emph type="italics"/>ad<emph.end type="italics"/> 5700 <emph type="italics"/>grauitas igitur argenti viui, magnitudine<lb/>æqualis propo&longs;ito corpori aqueo A, erit<emph.end type="italics"/> 5700. </s>

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

Line 658

<s><emph type="italics"/>Quæro exempli gratia, quam habet rationem in grauitate plumbum ad aurum. </s>

<s>In<lb/>teligatur plumbum, quoniam leuius est auro, grauitatem habere 1, & in linea plumbi, <lb/>in prima columna nominati &longs;ub titulo auri, quæratur aurt grauitas, ea erit<emph.end type="italics"/> 1 11/21. <emph type="italics"/>plum<lb/>bum igitur ad aurum rationem habebit in grauitate vt 1, ad 1 1<gap/>/21, &longs;i enim &longs;umantur <lb/>duo corpora magnitudine æqualia, vnum plumbeum alterum aureum, &longs;it autem plum<lb/>bei corporis grauitas<emph.end type="italics"/> 1, <emph type="italics"/>aurei erit<emph.end type="italics"/> 1 1<gap/>/21, <emph type="italics"/>quare corpus plumbeum ad corpus aureum <lb/>eiu&longs;dem magnitudinis rationem habebit in grauitate vt 1, ad 1 1<gap/>/21. comparantur an<lb/>tem inter &longs;e genera diuer&longs;a grauitate, in corporibus magnitudine æqualibus.<emph.end type="italics"/></s>

<s>In<lb/>teligatur plumbum, quoniam leuius est auro, grauitatem habere 1, & in linea plumbi, <lb/>in prima columna nominati &longs;ub titulo auri, quæratur auri grauitas, ea erit<emph.end type="italics"/> 1 11/21. <emph type="italics"/>plum<lb/>bum igitur ad aurum rationem habebit in grauitate vt 1, ad 1 1<gap/>/21, &longs;i enim &longs;umantur <lb/>duo corpora magnitudine æqualia, vnum plumbeum alterum aureum, &longs;it autem plum<lb/>bei corporis grauitas<emph.end type="italics"/> 1, <emph type="italics"/>aurei erit<emph.end type="italics"/> 1 1<gap/>/21, <emph type="italics"/>quare corpus plumbeum ad corpus aureum <lb/>eiu&longs;dem magnitudinis rationem habebit in grauitate vt 1, ad 1 1<gap/>/21. comparantur au<lb/>tem inter &longs;e genera diuer&longs;a grauitate, in corporibus magnitudine æqualibus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Rur&longs;us, quæro quam habet rationem in grauitate aqua ad argentum viuum. </s>

Line 692

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

<s><emph type="italics"/>In dimetiendis &longs;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 hodie vtimur, men&longs;uram vt 4, ad 3, buiu&longs;modipe<lb/>dem diuidimus in duodecim partes æquales, &longs;eu vncias, quas inutnies <lb/>in prima Columna &longs;ub titulo magnitudinis.<emph.end type="italics"/></s>

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

<s><emph type="italics"/>Ponderibus autem vtimur hac nostra tempe&longs;tate v&longs;itatis, <gap/>bram <lb/>enim diuidimus in<emph.end type="italics"/> 12, <emph type="italics"/>vncias vnciam vero in<emph.end type="italics"/> 24, <emph type="italics"/>&longs;crupula, & &longs;cru<lb/>pulum in<emph.end type="italics"/> 24, <emph type="italics"/>grana. </s>

<s><emph type="italics"/>Ponderibus autem vtimur hac nostra tempe&longs;tate v&longs;itatis, libram <lb/>enim diuidimus in<emph.end type="italics"/> 12, <emph type="italics"/>vncias vnciam vero in<emph.end type="italics"/> 24, <emph type="italics"/>&longs;crupula, & &longs;cru<lb/>pulum in<emph.end type="italics"/> 24, <emph type="italics"/>grana. </s>

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

Line 714

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

<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 humana <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>

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

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

Line 880

<s>eodem pondere ma&longs;&longs;am, & <lb/>ita ex eo quod plus defluxerat aquæ in corona, quam in ma&longs;&longs;a ratio<lb/>cinatus, deprehendit argenti in auro mixtionem, & manifestum fur<lb/>tum redemptoris.<emph.end type="italics"/></s><s> Hactenus Vitruuius. </s>

<s>Mirum certe Archimedis fuit inuentum, ip&longs;ius tamen <lb/>modus ad inueniendam illam aquæ men&longs;uram, quæ ad <lb/>certum pondus auri, vel argenti, vel coronæ re&longs;ponderet, <lb/>maiori diligentia indiget, quam quæ ab hominibus adhiberi <lb/>pote&longs;t, impo&longs;&longs;ibile enim e&longs;t, exempta corona, vel aurea ma&longs;&longs;a, <lb/>vel argentea, tantum aquæ refundere, quantum è va&longs;e efflu<lb/>xerat ad vnguem, nam repo&longs;ita aqua in va&longs;e, non po&longs;&longs;umus <pb xlink:href="029/01/060.jpg" pagenum="53"/>affirmare ip&longs;um vas e&longs;&longs;e plenum, ni&longs;i aqua incipiat effluere, <lb/>cum autem incipit, effiuit aliquando totus ferè cumulus, ita<lb/>que vel plus aquæ additur eo, quod deficit, vel minus, ni&longs;i <lb/>coniectura a&longs;&longs;equatur: at vero conicctura pro veritate non ac<lb/>cipitur. </s>

<s>Mirum certe Archimedis fuit inuentum, ip&longs;ius tamen <lb/>modus ad inueniendam illam aquæ men&longs;uram, quæ ad <lb/>certum pondus auri, vel argenti, vel coronæ re&longs;ponderet, <lb/>maiori diligentia indiget, quam quæ ab hominibus adhiberi <lb/>pote&longs;t, impo&longs;&longs;ibile enim e&longs;t, exempta corona, vel aurea ma&longs;&longs;a, <lb/>vel argentea, tantum aquæ refundere, quantum è va&longs;e efflu<lb/>xerat ad vnguem, nam repo&longs;ita aqua in va&longs;e, non po&longs;&longs;umus <pb xlink:href="029/01/060.jpg" pagenum="53"/>affirmare ip&longs;um vas e&longs;&longs;e plenum, ni&longs;i aqua incipiat effluere, <lb/>cum autem incipit, effluit aliquando totus ferè cumulus, ita<lb/>que vel plus aquæ additur eo, quod deficit, vel minus, ni&longs;i <lb/>coniectura a&longs;&longs;equatur: at vero conicctura pro veritate non ac<lb/>cipitur. </s>

<s>præterea exempta corona, vel aurea ma&longs;&longs;a, vel argen<lb/>tea, eximitur etiam &longs;imul cum ip&longs;a aliquantum aquæ, quæ cir<lb/>cum ip&longs;am remanet, atque huiu&longs;modi defectus errorem indu<lb/>cit &longs;en&longs;ibilem. </s>

Line 978

<s>RESVMATVR eadem figuta vt &longs;upra. </s>

<s>Quoniam 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 generis D, C, &longs;imiliter & Q, L, * erit<arrow.to.target n="note52"/><lb/>vt grauitas corporis D, hoc e&longs;t vt EK; ad K, ita H, ad V. </s>

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

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

Line 1022

<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>

<s>Eius enim quali<lb/>tatem &longs;i forte aurifices inuestigare velint, detrahent ex eo particu<lb/>lam, verbi gratia, vnius vnciæ, vel qued idem est particulam<emph.end type="italics"/> 24. <pb xlink:href="029/01/068.jpg" pagenum="61"/><emph type="italics"/>&longs;<gap/>puforam; & hanc particulam exeoquent ad qualitatem o&longs;que <lb/>c<gap/>ripuri. </s>

<s>Eius enim quali<lb/>tatem &longs;i forte aurifices inuestigare velint, detrahent ex eo particu<lb/>lam, verbi gratia, vnius vnciæ, vel qued idem est particulam<emph.end type="italics"/> 24. <pb xlink:href="029/01/068.jpg" pagenum="61"/><emph type="italics"/>&longs;crupulorum; & hanc particulam excoquent ad qualitatem o&longs;que <lb/>c<gap/>ripuri. </s>

<s>Est &longs;i quidem inuenerint, ex priori grauitate<emph.end type="italics"/> 24. <emph type="italics"/>&longs;or<gap/><lb/>pulorum, deperi&longs;&longs;e nihil: pronunciabunt aurum illud, hoc 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;ubtractionem 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>Est &longs;i quidem inuenerint, ex priori grauitate<emph.end type="italics"/> 24. <emph type="italics"/>&longs;ru<lb/>pulorum, deperi&longs;&longs;e nihil: pronuntiabunt aurum illud, hoc est, non <lb/>&longs;olum particulam illam excoctam, &longs;ed etiam illud d quo fuit detra<lb/>cta, nec non & illud quod reman&longs;it post &longs;ubtractionem e&longs;&longs;e vel &longs;ui&longs;<gap/><lb/>&longs;e aurum prima qualitatis &longs;eu<emph.end type="italics"/> 24, <emph type="italics"/>partiam; vel quod idem est au<lb/>tum purum. </s>

<s>Sivero deprebendirine gra<gap/>m diminuta<gap/>, ver<lb/>bi gratia, n<gap/>e e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>&longs;crupulorum, quæ ante defæcationem 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>

<s>Si vero deprehenderine grauitatem diminutant, ver<lb/>bi gratia, nunc 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 reman&longs;it e&longs;&longs;e<emph.end type="italics"/> 20. <emph type="italics"/>partium & denique particul<gap/> expur<lb/>gatam nunc quidem e&longs;&longs;e aurum purum, fui&longs;&longs;e vero particulam auri<emph.end type="italics"/><lb/>20. <emph type="italics"/>partium.<emph.end type="italics"/></s>

<s><emph type="italics"/>Et eodem modo pronunclabunt de quibu&longs;eunque 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 pronuntiabunt de quibu&longs;cunque alijs auri qualit<lb/>atibus, &longs;ecundum partes auri puri, quas in qualibet ma&longs;&longs;a auri in<lb/>uenerint, ea&longs;que vige&longs;imas quartas tutius grauitatis, non magnitu<lb/>dinis. </s>

<s>Nam cum in hac 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;eor&longs;im habe a<lb/>tur 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/>æquales, ex quibus<emph.end type="italics"/> 20. <emph type="italics"/>&longs;int auri, duæ argenti, & duæ æris; quamli<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;um as, vt constat experienties<lb/>atque hinc constat quam apte ac conuenienter Aurifices vtantur <lb/>vocabulo partium. </s>

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

<s>Sed nunc ad <lb/>&longs;<gap/>undum veniamus & modum alligationis. </s>

<s>Sed nunc ad <lb/>&longs;ecundum veniamus & modum alligationis. </s>

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

<s>Et quidem <lb/>&longs;ipartes auri excipias, aris atque 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&longs;se mixtionis modum <lb/>longe optimum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quando ergo aurifices volunt producere aurum cuiu&longs;cunque <lb/>qualitatis, accipiunt tot partes auri puri æquales, quot partium fu<lb/>turum e&longs;t aurum producendum, pauciores tamen partibus<emph.end type="italics"/> 24, & <pb xlink:href="029/01/069.jpg" 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 auri puri 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 xlink:href="029/01/069.jpg" pagenum="62"/><emph type="italics"/>reliquas partes quæ d &longs;unt ad<emph.end type="italics"/> 24, <emph type="italics"/>explent argento & <gap/>e, &longs;umendo <lb/>ex otroque metallo partes aquales in grauitate; atque bis rite inter &longs;e <lb/>permixtis componunt aurum de&longs;ideratæ qualitatis: eamque deno<lb/>minant à partibus auri puri in mixtione a&longs;umptis. </s>

<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/> Aurifices tanto plue <lb/><gap/>i&longs;cere argenti & aris quantum perdi po&longs;&longs;e deprehenderunt.<emph.end type="italics"/></s>

<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 mixtione maneant, ex <lb/>argenta vero & are aliquid deperdatur, &longs;olent Aurifices tanto plus <lb/>mi&longs;cere argenti & aris quantum perdi po&longs;&longs;e deprehenderunt.<emph.end type="italics"/></s>

<s><emph type="italics"/>Veru<gap/> nostra iutentio non est omnia quæ ad eiu&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/>auri puri & 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"/>Verum nostra intentio non est omnia quæ ad eiu&longs;modi mixtione <lb/>pertinent hoc loco exponere; &longs;ed illud tantum vt receptum apud om<lb/>nes ad ferre voluimus, ex quo manifeste constat, qua metallorum <lb/>mixtio in &longs;ingulis qualitatum generibus statuatur: quaquidem e&longs;t <lb/>illa quam adduximus, nempe 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/>auri puri & 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>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;umma omnium partium est<emph.end type="italics"/> 24, <emph type="italics"/>eademque est ratio de reliquis ita <lb/>ut numerus partium auri, &longs;emper denominet qualitatem auri, & <lb/>vna medietas reliquarum partium, quæ partibus a<gap/>ri de&longs;unt ad <lb/>complendas partes<emph.end type="italics"/> 24, <emph type="italics"/>&longs;it argenti, & reliqua medietas &longs;it æris. </s>

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

<s>hac <lb/>enim &longs;atis est &longs;uppo&longs;ui&longs;&longs;e, ad nouum illud artificium, quo paulo po&longs;t <lb/>inuestigaturi &longs;umus auri qualitatem ex &longs;ola grauitate quam habet<lb/>in aere & aqua, eamque qualitatem duplici via inuestigabimus, <lb/>vna per calculum, per tabellam altera: & quia ad calculum &longs;pe<lb/>ctant ea, quæ &longs;uperi<gap/> inuenimus, de grauitate metallorum huc re<lb/>ferenda cen&longs;uimus quæ hic &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>

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

<s><emph type="italics"/>Argenti grauitas, quæ in aert e&longs;t<emph.end type="italics"/> 31, <emph type="italics"/>erit in aqua<emph.end type="italics"/> 28. </s>

<s><emph type="italics"/>Argenti grauitas, quæ in aere e&longs;t<emph.end type="italics"/> 31, <emph type="italics"/>erit in aqua<emph.end type="italics"/> 28. </s>

<s><emph type="italics"/>Aeris grauitas; quæ in aere est<emph.end type="italics"/> 9, <emph type="italics"/>erit in aqua<emph.end type="italics"/> 8. </s>

Line 1066

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

<s><emph type="italics"/>Ex quibus clari&longs;&longs;ime colligitur, &longs;i aliquod corpus mistum con<lb/>stet partibus æqualibus argenti, & aeris in grauitate, quantam <lb/>grauitatem 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 xlink:href="029/01/070.jpg" 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 eiu&longs;dem magnitudi<lb/><gap/>is, rationem habe<gap/>it <gap/> grauitate vt<emph.end type="italics"/> 18, <emph type="italics"/>ad<emph.end type="italics"/> 1 22/11, <emph type="italics"/>vel vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/><lb/><gap/>, <emph type="italics"/>vet <gap/> nique in numerit integrinvt<emph.end type="italics"/> 299, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>omnium enim <lb/>i&longs;torum numerorum eadem e&longs;t ratie.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ex quibus clari&longs;&longs;ime colligitur, &longs;i aliquod corpus mistum con<lb/>stet partibus æqualibus argenti, & aeris in grauitate, quantam <lb/>grauitatem habeat in aqua & que &longs;it ratio in grauitate ip&longs;ius mi<lb/>sti ad aquam &longs;i enim grauitas aeris in aere &longs;it<emph.end type="italics"/> 9, <emph type="italics"/>eius grauitas in <lb/>aqua erit<emph.end type="italics"/> 8, <emph type="italics"/>& &longs;i grauitas argenti in aere &longs;it quoque<emph.end type="italics"/> 9, <emph type="italics"/>erit eius gra<gap/><emph.end type="italics"/><pb xlink:href="029/01/070.jpg" 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;ubintelligenda 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;equenter * grauitas aquæ magnitu<emph.end type="italics"/><arrow.to.target n="note54"/><lb/><emph type="italics"/>dinem habentis æqualem <gap/> corpori misto<gap/><emph.end type="italics"/> <gap/>; <emph type="italics"/>quare corpus <lb/>mi&longs;tum ex argento & are ad corpus aqueum eiu&longs;dem magnitudi<lb/><gap/>is, rationem habebit <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"/>vel denique in numeris integris vt<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 ratio.<emph.end type="italics"/></s>

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

Line 1078

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

<s><emph type="italics"/>Deinde inueniatur grauitas aquæ magnitudine æqualis aur<gap/><lb/>puro<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum: hoc e&longs;t vt 19, ad 1, ita fiat<emph.end type="italics"/> 24, <emph type="italics"/>ad alium, nempe ad <lb/>vnciam<emph.end type="italics"/> 1 9/19, <emph type="italics"/>hic enim numerus erit grauitas illius aquæ.<emph.end type="italics"/></s>

<s><emph type="italics"/>Deinde inueniatur grauitas aquæ magnitudine æqualis auro <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>

<s><emph type="italics"/>Fiat denique ut<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/>dine æqualis corpori 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>

Line 1090

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

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

<s><emph type="italics"/>Et quia inpropo&longs;ito exemplo <gap/> 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"/>unciarum, quæ constituunt grauitatem to<lb/>tius ma&longs;&longs;æ. </s>

<s>hinc fit quod eædem<emph.end type="italics"/> 20. <emph type="italics"/>vnc. </s>

<s>immediate denominent au<lb/>rum propo&longs;itum e<32>e<emph.end type="italics"/> 20, <emph type="italics"/>partium. </s>

<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>

<s>Quando vero grauitas totius ma&longs;<lb/>&longs;a non 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 exemplo clarius apparebit.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit enim 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 numerus &longs;ubtrahatur 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"/>reliquus numerus<emph.end type="italics"/> 313, * <emph type="italics"/>erit grauitas aquæ <lb/>propo&longs;itæ ma&longs;&longs;æ magnitudine æqualis. </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<lb/>ri, tum corporis misti &longs;it eadem quæ ma&longs;&longs;æ propo&longs;itæ, non &longs;ecus ac in <lb/>præcedenti exemplo factitatum est. </s>

<s>hoc e&longs;t primo fiat vt<emph.end type="italics"/> 19, <emph type="italics"/>ad<emph.end type="italics"/> 1, <emph type="italics"/>ita<emph.end type="italics"/><lb/>5301, <emph type="italics"/>ad<emph.end type="italics"/> 279, <emph type="italics"/>hic enim numerus erit grauitas aquæ magnitudinem <lb/>habentis æqualem auro puro, <gap/>uius grauitas e&longs;t<emph.end type="italics"/> 5301. <emph type="italics"/>Deinde fia<gap/><lb/>vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29, <emph type="italics"/>ita rur&longs;um grauitas<emph.end type="italics"/> 5301, <emph type="italics"/>ad aliam, hac enim ratione <lb/>producetur nu<gap/>erus<emph.end type="italics"/> 551, <emph type="italics"/>debitus grauitati aquæ, magnitudine <lb/>aqualis corpori mi&longs;to ex argento & ære grauitatem habenti eandem <lb/>cum eadem ma<32>a propo&longs;ita. </s>

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

<s>Atque hæ tres grauitates aquæ &longs;criban<lb/>tur eo ordine quo &longs;upra; inuenti&longs;que differentijs inter primam &<emph.end type="italics"/></s>

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

<s>TABELLE WAR HIER<lb/><emph type="italics"/>tertiam, nec non inter &longs;ecundam & 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>

<s>TABELLE WAR HIER<lb/><arrow.to.target n="note57"/> <emph type="italics"/>&longs;enti examp<gap/>o e&longs;t<emph.end type="italics"/> 4638 51/<gap/>, <emph type="italics"/>is enim indicabit grauitatem auri <lb/>puri in ma&longs;&longs;a propo&longs;ita. </s>

<s>TABELLE WAR HIER<lb/><arrow.to.target n="note57"/> <emph type="italics"/>&longs;enti examploo e&longs;t<emph.end type="italics"/> 4638 51/<gap/>, <emph type="italics"/>is enim indicabit grauitatem auri <lb/>puri in ma&longs;&longs;a propo&longs;ita. </s>

<s>Sed quoniam <gap/>c grauitas non est expre&longs;<lb/>&longs;a in partibus vige&longs;imis quartis totius grauitatis, id quod ad g<gap/>,<emph.end type="italics"/></s><pb xlink:href="029/01/072.jpg" pagenum="65"/>

<s><margin.target id="note57"/>19. <lb/><emph type="italics"/>huius.<emph.end type="italics"/></s>

<s><emph type="italics"/>manam qualitatis auri pronunciationem requiritur, vt &longs;upra mul<lb/>tis o&longs;tendimus, reuocanda erit ad partes vige&longs;imas quartas hoc est <lb/>adpartes, qualium tota propo&longs;ita ma&longs;&longs;a est<emph.end type="italics"/> 24, <emph type="italics"/>quod factu non est <lb/>difficile. </s>

<s><emph type="italics"/>manam qualitatis auri pronuntiationem requiritur, vt &longs;upra mul<lb/>tis o&longs;tendimus, reuocanda erit ad partes vige&longs;imas quartas hoc est <lb/>ad partes, qualium tota propo&longs;ita ma&longs;&longs;a est<emph.end type="italics"/> 24, <emph type="italics"/>quod factu non est <lb/>difficile. </s>

<s>Nam &longs;i fiat vt tota grauitas ma&longs;&longs;æ propo&longs;itæ<emph.end type="italics"/> 5301, <emph type="italics"/>al gra<lb/>uitatem auri puri<emph.end type="italics"/> 4638 45/116, <emph type="italics"/>velvt<emph.end type="italics"/> 272, <emph type="italics"/>ad<emph.end type="italics"/> 238, <emph type="italics"/>cum vtrobique <lb/>eadem &longs;it ratio ita<emph.end type="italics"/> 24, <emph type="italics"/>ad alium numerum. </s>

<s>Nam &longs;i fiat vt tota grauitas ma&longs;&longs;æ propo&longs;itæ<emph.end type="italics"/> 5301, <emph type="italics"/>at gra<lb/>uitatem auri puri<emph.end type="italics"/> 4638 45/116, <emph type="italics"/>velvt<emph.end type="italics"/> 272, <emph type="italics"/>ad<emph.end type="italics"/> 238, <emph type="italics"/>cum vtrobique <lb/>eadem &longs;it ratio ita<emph.end type="italics"/> 24, <emph type="italics"/>ad alium numerum. </s>

<s>proculdubio quartus nu<lb/>merus proportionalis, erit ille qui quæritur. </s>

Line 1142

<s>Quartus autem terminus<emph.end type="italics"/> 4196 25/116, <emph type="italics"/>indicabit grauitatem <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>

<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>

<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;iße, 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>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 Arithmeticis &longs;unt exercitati, velillis, qui alias ob cau&longs;as <lb/>tabulis vti malunt, quam calculis.<emph.end type="italics"/></s>

Line 1196

<s>Et &longs;ic de alys.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quod vero ad priorem v&longs;um attinct, is per&longs;imilis est præcedenti, <lb/>& æquè facilis quando grauitas auri quam in aere & aqua habet, in <lb/>tabula reperitur precisè. </s>

<s><emph type="italics"/>Quod vero ad priorem v&longs;um attinet, is per&longs;imilis est præcedenti, <lb/>& æquè facilis quando grauitas auri quam in aere & aqua habet, in <lb/>tabula reperitur precisè. </s>

<s>Nam &longs;i proponatur exemp. </s>

Line 1214

<s>1<emph.end type="italics"/> 1. <emph type="italics"/>Scrup. 6, Gran.<emph.end type="italics"/> 23 1551/1767, <lb/><emph type="italics"/>re&longs;pondens auro 21, partium, & grauitas proxime minor e&longs;t vnc.<emph.end type="italics"/> 11, <lb/><emph type="italics"/>Scrup. 6, Gran.<emph.end type="italics"/> 9 177/1767, <emph type="italics"/><expan abbr="earumq;">earumque</expan> differentia e&longs;t Gran.<emph.end type="italics"/> 14 1374/1767, <lb/><emph type="italics"/>quem admodum & inter qua&longs;cunque duas alias grauitates proxi<emph.end type="italics"/><pb xlink:href="029/01/076.jpg" pagenum="69"/><emph type="italics"/>mas eadem e&longs;t differentia, propterta quod omnes grauitates in tabu<lb/>la procedunt per æqualem exce&longs;&longs;um, vel defectum, vt inferius de<lb/>mon&longs;trabitur. </s>

<s>1<emph.end type="italics"/> 1. <emph type="italics"/>Scrup. 6, Gran.<emph.end type="italics"/> 23 1551/1767, <lb/><emph type="italics"/>re&longs;pondens auro 21, partium, & grauitas proxime minor e&longs;t vnc.<emph.end type="italics"/> 11, <lb/><emph type="italics"/>Scrup. 6, Gran.<emph.end type="italics"/> 9 177/1767, <emph type="italics"/><expan abbr="earumq;">earumque</expan> differentia e&longs;t Gran.<emph.end type="italics"/> 14 1374/1767, <lb/><emph type="italics"/>quem admodum & inter qua&longs;cunque duas alias grauitates proxi<emph.end type="italics"/><pb xlink:href="029/01/076.jpg" pagenum="69"/><emph type="italics"/>mas eadem e&longs;t differentia, propterea quod omnes grauitates in tabu<lb/>la procedunt per æqualem exce&longs;&longs;um, vel defectum, vt inferius de<lb/>mon&longs;trabitur. </s>

<s>Inueniatur quoque differentia inter eandem gra<lb/>uitatem proxime minorem & inter grauitatem auri propo&longs;iti quam <lb/>habet in aqua, quæ <expan abbr="quid&etilde;">quidem</expan> e&longs;t Gran.<emph.end type="italics"/> 7 687/1767, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 14 1374/1767, <lb/><emph type="italics"/>ad 1, ita<emph.end type="italics"/> 7 687/1767, <emph type="italics"/>ad alium numerum & inuenietur hæc fractio<emph.end type="italics"/><lb/>1/2, <emph type="italics"/>eademque adycienda erit ad denominatorem 20, partium, vt <lb/>componatur totus denominator auri propo&longs;iti partium<emph.end type="italics"/> 20 1/2, <emph type="italics"/>& eo<lb/>dem modo mueniendus erit denominator <expan abbr="cuiu&longs;cunq;">cuiu&longs;cunque</expan> alterius auri, <lb/>cuius grauitas in aqua, in tabula non reperitur.<emph.end type="italics"/></s>

<s>Inueniatur quoque differentia inter eandem gra<lb/>uitatem proxime minorem & inter grauitatem auri propo&longs;iti quam <lb/>habet in aqua, quæ <expan abbr="quid&etilde;">quidem</expan> e&longs;t Gran.<emph.end type="italics"/> 7 687/1767, <emph type="italics"/>& fiat vt<emph.end type="italics"/> 14 1374/1767, <lb/><emph type="italics"/>ad 1, ita<emph.end type="italics"/> 7 687/1767, <emph type="italics"/>ad alium numerum & inuenietur hæc fractio<emph.end type="italics"/><lb/>1/2, <emph type="italics"/>eademque adijcienda erit ad denominatorem 20, partium, vt <lb/>componatur totus denominator auri propo&longs;iti partium<emph.end type="italics"/> 20 1/2, <emph type="italics"/>& eo<lb/>dem modo inueniendus erit denominator <expan abbr="cuiu&longs;cunq;">cuiu&longs;cunque</expan> alterius auri, <lb/>cuius grauitas in aqua, in tabula non reperitur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ceterum qui volet contentus e&longs;&longs;e partibus vige&longs;imis quartis de<lb/>nominatorum auri, is multo breuius a&longs;&longs;equetur quod quæritur, per <lb/>tabellam partis proportionalis. </s>

Line 1234

<s><emph type="italics"/>Denique &longs;i proponatur aurum non vnius libræ &longs;ed vel plurium, <lb/>vel &longs;olum aliquot vnciarum. </s>

<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.

<s>Reducenda erit eius grauitas quam <lb/>habet in aqua, 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, eiu&longs;dem <lb/>grauitas in aqua, & pro tertio lib.

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

Line 1270

<s><emph type="italics"/>Quia vero permolestum videri po&longs;&longs;et omnes grauitates totius <lb/>tabulæ hac via eruere; ob&longs;eruari quidem poterit prædicta Methodus <lb/>quando &longs;eor&longs;im inuestiganda fuerit alicuius auri grauitas in aqua, <lb/>in <expan abbr="cõpo&longs;itione">compo&longs;itione</expan> vero tabulæ &longs;ic forta&longs;&longs;is <expan abbr="cõpendio&longs;ius">compendio&longs;ius</expan> quis proce&longs;&longs;erit.<emph.end type="italics"/></s>

<s><emph type="italics"/>Equidem, cum huius tabulæ con&longs;tructionem diligentius mecum<emph.end type="italics"/><pb xlink:href="029/01/078.jpg" pagenum="71"/><emph type="italics"/>pertracto, video grauitates illas, quæ in eius area de&longs;criptæ &longs;unt ne<lb/>ce&longs;&longs;ario eadem differentia procedere, &longs;icut & denominatores quali<lb/>tatum eadem differentia procedunt; atque adco differentiam illam <lb/>e&longs;&longs;e eam, qua grauitas &longs;emiunciæ auri puri in aqua &longs;uperat in aqua <lb/><expan abbr="grauitat&etilde;">grauitatem</expan> &longs;emiunciæ mi&longs;ti, quæ <expan abbr="quid&etilde;">quidem</expan> differentia e&longs;t Gra.<emph.end type="italics"/> 14 1174/1767. <lb/><emph type="italics"/>Con&longs;iderentur enim quæcunque duæ grauitates proximæ in tabula <lb/>expre<32>æ, vt exemp. </s>

<s><emph type="italics"/>Equidem, cum huius tabulæ con&longs;tructionem diligentius mecum<emph.end type="italics"/><pb xlink:href="029/01/078.jpg" pagenum="71"/><emph type="italics"/>pertracto, video grauitates illas, quæ in eius area de&longs;criptæ &longs;unt ne<lb/>ce&longs;&longs;ario eadem differentia procedere, &longs;icut & denominatores quali<lb/>tatum eadem differentia procedunt; atque adeo differentiam illam <lb/>e&longs;&longs;e eam, qua grauitas &longs;emiunciæ auri puri in aqua &longs;uperat in aqua <lb/><expan abbr="grauitat&etilde;">grauitatem</expan> &longs;emiunciæ mi&longs;ti, quæ <expan abbr="quid&etilde;">quidem</expan> differentia e&longs;t Gra.<emph.end type="italics"/> 14 1174/1767. <lb/><emph type="italics"/>Con&longs;iderentur enim quæcunque duæ grauitates proximæ in tabula <lb/>expre<32>æ, vt exemp. </s>

<s>gratia. </s>

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