texts/archimedes/xml/gheta_promo_029_la_1603.xml - Colored diff

Main History Search Repository tree

Return to gheta_promo_029_la_1603.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/gheta_promo_029_la_1603.xml between version 1.16 and 1.17

version 1.16, 2003/12/01 12:10:20

version 1.17, 2003/12/01 12:34:16

Line 60

<s>Hæc &longs;unt firmi&longs;sima & &longs;olidi&longs;sima funda<lb/>menta ad æternam po&longs;teritatis memoriam, quam licet <lb/>profici&longs;ci iam videas ex iis quibus abundas animi orna<lb/>mentis, ne&longs;cio tamen quo pacto gratior nobis accidit, <lb/>cum ex aliorum etiam prædonio &longs;u&longs;cipit in crementum. </s>

<s><lb/>Hinc domus tua floret docti&longs;simorum familiaritatibus; <lb/>hinc nulli ad tuam con&longs;uetudinem præcluditur aditus; <lb/>hinc plurimorum &longs;tudia commouentur; hinc illa &longs;apien <lb/>tum æmulatio & admiratio<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 patronum, & interpretem. </s>

<s><lb/>Hinc domus tua floret docti&longs;simorum familiaritatibus; <lb/>hinc xnulli ad tuam con&longs;uetudinem 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 patronum, & interpretem. </s>

<s>Quid ego <lb/>igitur quem tibi &longs;excentis eximiæ beneuolentiæ argu<lb/>mentis obligatum 5, perexigiuum hunc ingenij <lb/>mei partum expo&longs;iturus, vnum te nominis & exi&longs;tima<lb/>tionis meæ patronum non &longs;u&longs;cipiam equidem in am<lb/>pli&longs;simi Theatri lucem &longs;apienti&longs;simorum <32> hominum <lb/>con&longs;pectum, quibus abundat hæc no&longs;tra ætas inferre me <lb/>non magnopere cogitabam. <gap/>Tu hortatus es dubitan<lb/>tem impuli&longs;ti vel reluctantem<gap/> tuere igitur ob&longs;equen<lb/>tem. </s>

<s>Quid ego <lb/>igitur quem tibi &longs;excentis eximiæ beneuolentiæ argu<lb/>mentis obligatum volu&longs;ti, perexigiuum hunc ingenij <lb/>mei partum expo&longs;iturus, vnum te nominis & exi&longs;tima<lb/>tionis meæ patronum non &longs;u&longs;cipiam equidem in am<lb/>pli&longs;simi Theatri lucem &longs;apienti&longs;simorum <32> hominum <lb/>con&longs;pectum, quibus abundat hæc no&longs;tra ætas inferre me <lb/>non magnopere cogitabam. <gap/>Tu hortatus es dubitan<lb/>tem impuli&longs;ti vel reluctantem<gap/> tuere igitur ob&longs;equen<lb/>tem. </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>

Line 90

<s>Mathematicis ex<lb/>cellens vir, ac Magi&longs;ter meus, cui ego plurimum debere me <lb/>fateor, ab eo enim prima elementa habui, repo&longs;cere à me pu<lb/>blicum aliquem doctrina &longs;ua fructum videretur ac Fede<lb/>ricus Saminiatus euius suorum &longs;uauitatem, & beneuol&ecedil;n<lb/>tiam erga me diu, dum &longs;imul hi&longs;ce studijs condi&longs;cipuli ope<lb/>ram dedimus, expertus &longs;um, me ut aliquid auderem tum <lb/>oratione, tum exemplo &longs;uo excitaret, c&oelig;pi minus ab ea cogi<lb/>tatione alienus e&longs;&longs;e. </s>

<s>Deinde vero &longs;ummos vivos habui <pb xlink:href="029/01/007.jpg"/>hortatores. </s>

<s>Deinde vero &longs;ummos vixos habui <pb xlink:href="029/01/007.jpg"/>hortatores. </s>

<s>Etenim cum Clauium, quod tam diu cupiebam, <lb/>vidi&longs;&longs;em <gap/> minorem tanta scientia, & fama viri beni<lb/>gnitatem <gap/>peri&longs;&longs;em. </s>

Line 274

<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/>tur 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"/>ergo aquæ magnitudinem habentis <expan abbr="æqual&etilde;">æqualem</expan> plumbo F, erit grauitas<emph.end type="italics"/> 2, </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"/>ergo aquæ magnitudinem habentis <expan abbr="æqual&etilde;">æqualem</expan> plumbo F, erit grauitas<emph.end type="italics"/> 2, </s>

<s><emph type="italics"/>Et quoniam ceræ A, grauitas est<emph.end type="italics"/> 21, <emph type="italics"/>plumbi vero F,<emph.end type="italics"/> 23, <emph type="italics"/>erit vtro<lb/>rumque corporum A, F, ceræ nimirum, & plumbi grauitas<emph.end type="italics"/> 44, <emph type="italics"/>coniun<lb/>gatur cera, & plumbum, & ita coniuncta ponderentur in aqua, & <lb/>habeant grauitatem<emph.end type="italics"/> 20, <emph type="italics"/>quoniam igitur numerus<emph.end type="italics"/> 44, <emph type="italics"/>&longs;uperat nume<lb/>rum<emph.end type="italics"/> 20, <emph type="italics"/>numero<emph.end type="italics"/> 24, <emph type="italics"/>erit grauitas aquæ habentis magnitudinem æqua<lb/>lem vtri&longs;que corporibus ceræ & plumbi<emph.end type="italics"/> 24, <emph type="italics"/>&longs;ed grauitas aquæ magni<lb/>tudinem habentis æqualem plumbo F, est<emph.end type="italics"/> 2, <emph type="italics"/>ergo reliquum quod est<emph.end type="italics"/><lb/>22, <emph type="italics"/>erit grauitas, aquæ magnitudine æqualis propo&longs;itæ ceræ A.<emph.end type="italics"/></s>

Line 284

<s><emph type="italics"/>Similiter &longs;it aliquod cereum corpus A, cuius grauitas<emph.end type="italics"/> 2100, <emph type="italics"/>& opor<lb/>teat facere, quod imperatum e&longs;t. </s>

<s>accipiatur aliquod paruum ceræ cor<lb/>pus F, cuius grauitas &longs;it v.g.<emph.end type="italics"/> 21, <emph type="italics"/>& inuenta grauitate aquæ magni<emph.end type="italics"/><pb xlink:href="029/01/017.jpg" pagenum="10"/><emph type="italics"/>tudinem habentis æqualem ceræ F, quæ &longs;it<emph.end type="italics"/> 12, <emph type="italics"/>fiat vt<emph.end type="italics"/> 21, <emph type="italics"/>ad<emph.end type="italics"/> 22, <emph type="italics"/>ita<emph.end type="italics"/><lb/>2100, <emph type="italics"/>ad alium numerum qui &longs;it<emph.end type="italics"/> 2200; <emph type="italics"/>erit igitur grauitas aquæ ma <lb/>gnitudinem habentis æqualem ceræ A,<emph.end type="italics"/> 2200. </s>

<s>accipiatur aliquod paruum ceræ cor<lb/>pus F, cuius grauitas &longs;it v.g.<emph.end type="italics"/> 21, <emph type="italics"/>& inuenta grauitate aquæ magni-<emph.end type="italics"/><pb xlink:href="029/01/017.jpg" pagenum="10"/><emph type="italics"/>tudinem habentis æqualem ceræ F, quæ &longs;it<emph.end type="italics"/> 12, <emph type="italics"/>fiat vt<emph.end type="italics"/> 21, <emph type="italics"/>ad<emph.end type="italics"/> 22, <emph type="italics"/>ita<emph.end type="italics"/><lb/>2100, <emph type="italics"/>ad alium numerum qui &longs;it<emph.end type="italics"/> 2200; <emph type="italics"/>erit igitur grauitas aquæ ma <lb/>gnitudinem habentis æqualem ceræ A,<emph.end type="italics"/> 2200. </s>

<s>Neque nece&longs;&longs;e e&longs;t, vt illud corpus &longs;olidum magni ponderis <lb/>reip&longs;a proponatur, &longs;ufficit enim vt eius grauitas notificetur <lb/>numero tantum. </s>

Line 436

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

<s><emph type="italics"/>Accipiantur duo corpora D, plumbeum, E, &longs;tanneum grauitate <lb/>quacunque, &longs;it verbi gratia plumbi D, grauitas<emph.end type="italics"/> 23<emph type="italics"/>, &longs;tanni vero E, <lb/>grauitas<emph.end type="italics"/> 37<emph type="italics"/>, deinde duarum quantitatum aquæ, quarum vna &longs;it ma<lb/>gnitudine æqualis plumbo D, altera stanno E, inueniantur graui<lb/>tates, quæ &longs;int, primæ videlicet quantitatis<emph.end type="italics"/> 2<emph type="italics"/>, &longs;ecundæ vero<emph.end type="italics"/> 5<emph type="italics"/>, & fiat,<emph.end type="italics"/><pb xlink:href="029/01/026.jpg" pagenum="19"/><emph type="italics"/>ut 23, ad 2, ita 37, ad<emph.end type="italics"/> 3 5/21. <emph type="italics"/>grauitas igitur aquæ, magnitudinem <lb/>habentis æqualem plumbo, cuius grauitas est 37, erit<emph.end type="italics"/> 3 5/21. </s>

<s><emph type="italics"/>Accipiantur duo corpora D, plumbeum, E, &longs;tanneum grauitate <lb/>quacunque, &longs;it vcrbi gratia plumbi D, grauitas<emph.end type="italics"/> 23<emph type="italics"/>, &longs;tanni vero E, <lb/>grauitas<emph.end type="italics"/> 37<emph type="italics"/>, deinde duarum quantitatum aquæ, quarum vna &longs;it ma<lb/>gnitudine æqualis plumbo D, altera stanno E, inueniantur graui<lb/>tates, quæ &longs;int, primæ videlicet quantitatis<emph.end type="italics"/> 2<emph type="italics"/>, &longs;ecundæ vero<emph.end type="italics"/> 5<emph type="italics"/>, & fiat,<emph.end type="italics"/><pb xlink:href="029/01/026.jpg" pagenum="19"/><emph type="italics"/>ut 23, ad 2, ita 37, ad<emph.end type="italics"/> 3 5/21. <emph type="italics"/>grauitas igitur aquæ, magnitudinem <lb/>habentis æqualem plumbo, cuius grauitas est 37, erit<emph.end type="italics"/> 3 5/21. </s>

<s><emph type="italics"/>Et quoniam aquæ, magnitudinem habentis æqualem stanno E, cu<lb/>ius grauitas est 37, e&longs;t grauitas<emph.end type="italics"/> 5, <emph type="italics"/>erunt grauitates duarum quan<lb/>titatum aquæ<emph.end type="italics"/> 3 5/21, & 5, <emph type="italics"/>quarum quantitatum prima e&longs;t æqualis <lb/>magnitudine corpori plumbeo, &longs;ecunda stanneo, que &longs;unt æque gra<lb/>uia, vtriu&longs;que enim grauitas est<emph.end type="italics"/> 37. <emph type="italics"/>Fiat igitur vt<emph.end type="italics"/> 5, <emph type="italics"/>ad<emph.end type="italics"/> 3 5/21, <emph type="italics"/>it a<emph.end type="italics"/><lb/>1150, <emph type="italics"/>ad alium numerum, qui &longs;it<emph.end type="italics"/> 740, <emph type="italics"/>tanta igitur erit grauitas <lb/>&longs;tanni, magnitudinem habentis æqualem propo&longs;ito plumbo A, quanta <lb/><gap/>iam inueniebatur & &longs;upra.<emph.end type="italics"/></s>

Line 540

<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 viui, 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>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 680

<s><emph type="italics"/>Quæro, quomodo &longs;e habet in grauitate aqua ad vinum. </s>

<s>quoniam <lb/>æqua grauior est vino, intelligatur eius grauitas<emph.end type="italics"/> 100, <emph type="italics"/>& quoniam in <lb/>linea aquæ, &longs;ub titulo vini, datur vini grauitas<emph.end type="italics"/> 98 <gap/>, <emph type="italics"/>aqua ad vinum <lb/>&longs;e habebit in grauitate, vt<emph.end type="italics"/> 100, <emph type="italics"/>ad<emph.end type="italics"/> 98 <gap/>. </s>

<s>quoniam <lb/>æqua grauior est vino, intelligatur eius grauitas<emph.end type="italics"/> 100, <emph type="italics"/>& quoniam in <lb/>linea aquæ, &longs;ub titulo vint, datur vini grauitas<emph.end type="italics"/> 98 <gap/>, <emph type="italics"/>aqua ad vinum <lb/>&longs;e habebit in grauitate, vt<emph.end type="italics"/> 100, <emph type="italics"/>ad<emph.end type="italics"/> 98 <gap/>. </s>

<s><emph type="italics"/>Contra quæro quomodo &longs;e habent in magnitudine argentum, & <lb/>aurum. </s>

Line 758

<s><emph type="italics"/>Porro ad inueniendas grauitates &longs;phærarum ex reliquis metallis <lb/>vel ex quacunque alia materia, hæc erit ratio.<emph.end type="italics"/></s>

<s><emph type="italics"/>Fiat vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, (<emph type="italics"/>&longs;i de grauitate &longs;phæræ<lb/><expan abbr="pl&umacr;beæ">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="diametr&umacr;">diametrum</expan> habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, ad <expan abbr="ali&umacr;">alium</expan> numerum<lb/>qui &longs;it<emph.end type="italics"/> 29 19/74, <emph type="italics"/>grauitas igitur &longs;phæræ plumbeæ, diametrum haben<lb/>tis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, erit gran.<emph.end type="italics"/> 29 39/74. <emph type="italics"/>&longs;tannum enim ad plumbum ration<gap/><lb/>habet in grauitate vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>vt con&longs;picitur in prima tabello <lb/>quam ad comparandum inter &longs;e duodecim corporum genera, grauita<lb/>te, & magnitudine, appo&longs;uimus.<emph.end type="italics"/></s>

<s><emph type="italics"/>Fiat vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>hoc e&longs;t vt<emph.end type="italics"/> 74, <emph type="italics"/>ad<emph.end type="italics"/> 115, (<emph type="italics"/>&longs;i de grauitate &longs;phæræ<lb/><expan abbr="pl&umacr;beæ">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="diametr&umacr;">diametrum</expan> habentis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, ad <expan abbr="ali&umacr;">alium</expan> numerum<lb/>qui &longs;it<emph.end type="italics"/> 29 19/74, <emph type="italics"/>grauitas igitur &longs;phæræ plumbeæ, diametrum haben<lb/>tis<emph.end type="italics"/> 1/4, <emph type="italics"/>vnciæ, erit gran.<emph.end type="italics"/> 29 39/74. <emph type="italics"/>&longs;tannum enim ad plumbum ration<gap/><lb/>habet in grauitate vt<emph.end type="italics"/> 1, <emph type="italics"/>ad<emph.end type="italics"/> 1 41/74, <emph type="italics"/>vt con&longs;picitur in prima tabelle <lb/>quam ad comparandum inter &longs;e duodecim corporum genera, grauita<lb/>te, & magnitudine, appo&longs;uimus.<emph.end type="italics"/></s>

<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><pb xlink:href="029/01/048.jpg" pagenum="41"/>

Line 968

<s>Sed o&longs;ten&longs;um e&longs;t id quod ex EK, fit & F. æquale e&longs;&longs;e ei quod fit ex <lb/>G, & E, ergo quo<gap/> fit ex EK, & F, vna cum eo, quod ex BK, & V, hoc <lb/>e&longs;t id quod fit ex EK, & FV, æquale erit ei quod ex G, fit & E, vna <lb/>eum eo quod ex H, & K, &longs;ed quod ex G, fit & E, æquale e&longs;t ei quod fit <lb/>ex G, & EK, minus eo quod ex G, & K, quod enim additur, idem & <pb xlink:href="029/01/065.jpg" pagenum="58"/>minuitur; ergo quod fit ex EK, & FV. æquale erit ei quod fit ex G, & <lb/>EK, vna cum eo quod ex H, & K, minus eo quod fit ex G, & K. aufe<lb/>ratur vtrinque id quod fit ex G, & EK, quod igitur fit ex FV, & EK, <lb/><figure id="id.029.01.065.1.jpg" xlink:href="029/01/065/1.jpg"/><lb/>minus eo quod ex G, & <lb/>EK, æquabitur ei quod <lb/>ex H, & K, minus eo <lb/>quod fit ex G, & K, &longs;ed <lb/>quod fit ex H, & K, <lb/>minus eo quod fit ex <lb/>G, & K, æquale e&longs;t ei <lb/>quod ex differentia ip<lb/>&longs;arum H, G, fit & K, <lb/>&longs;imiliter, & quod fit ex <lb/>FV, & EK, minus eo <lb/>quod ex G, & EK, <lb/>æquale e&longs;t ei quod ex <lb/>differentia ip&longs;arum <lb/>FV, G, fit & EK, ergo <lb/>quod ex differentia <lb/>ip&longs;acum H, G, fit & K, æquale erit ei quod ex differentia ip&longs;arum <lb/>FV, G, fit & EK; æqualitatem ad proportionem reuocando, erit vt <lb/>differentia grauitatum. </s>

<s>H, G, ad grauitatem EK, ita differentia <lb/>grauitatum FV, G, ad grauitatem K, quod erat primo loco: demon<lb/>&longs;trandum. </s>

<s>H, G, ad grauitatem EK, ita differentia <lb/>grauitatum FV, G, ad graui<gap/> tom K, quod erat primo loco: demon<lb/>&longs;trandum. </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. </s>

Line 1006

<s>Qualitas enim auri in quouis cor <lb/>pore propo&longs;ito, exprimitur partibus auri puri, 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 habent illæ partes in grauitate ad totum corpus: quod <lb/>exemplo clarius explicabitur in hunc modum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Sit aliquod corpus aureum, exempli gratia<emph.end type="italics"/> 24. <emph type="italics"/>vnciarum, quod <lb/>expurgatum & ad aurum purum reductum, ami&longs;erit ex pri&longs;tina <lb/>grauitate nempe ex<emph.end type="italics"/> 24, <emph type="italics"/>vncijs, 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 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>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>

Line 1036

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

<s>quem ijdem ob&longs;eruant <lb/>breuiter adnotemus.<emph.end type="italics"/></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><emph type="italics"/>Inter varias autem & multiplices auri compo&longs;itiones quibus <lb/>cum alijs metallis alligari potest, eam retinuere aurifices, quam diu<lb/>turna experientia deprehenderunt omnibus alijs 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 volunt e&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"/>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><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 utroque 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 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>

Line 1080

<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 rur&longs;us<emph.end type="italics"/> 24, <emph type="italics"/>vnciæ, 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"/>corpus enim ita mi&longs;tum, ad corpus aqueum eiu&longs;dem ma<lb/>gnitudinis rationem habet in grauitate vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29. </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"/>corpus enim ita mi&longs;tum, ad corpus aqueum eiu&longs;dem ma<lb/>gnitudinis rationem habet in grauitate vt<emph.end type="italics"/> 279, <emph type="italics"/>ad<emph.end type="italics"/> 29. </s>

<s><emph type="italics"/>Atque ita habebuntur tres gravitates trium aquæ quantitatum, <lb/>quarum prima æquatur auro puro<emph.end type="italics"/> 24, <emph type="italics"/>unciarum, &longs;ecunda ma&longs;&longs;a <lb/>propo&longs;itæ<emph.end type="italics"/> 24, <emph type="italics"/>vnciarum, & reliqua corpori mi&longs;to ex argento & ære<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>

Line 1088

<s><emph type="italics"/>Deinde quæratur 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"/>quartus enim proportionalium terminus nempe<emph.end type="italics"/> 20, </s><pb xlink:href="029/01/071.jpg" pagenum="64"/>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>erit denominator qualitatis auri de qua queritur 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 demonstratum e&longs;t prop.<emph.end type="italics"/> 19, <emph type="italics"/>huius.<emph.end type="italics"/></s>

<s>TABELLE WAR HIER<lb/><emph type="italics"/>erit denominator 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 demonstratum 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 <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>immediate denominent au<lb/>rum propo&longs;itum e&ligsz;e<emph.end type="italics"/> 20, <emph type="italics"/>partium. </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>

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 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.

<s>Reducenda erit eius grauitas quam <lb/>habet in aqua, ad grauitatem quam haberet &longs;i e&ligsz;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 1242

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

<s><lb/>Sed illud tantum obiter aduertere placet, quod videtur pertinere <lb/>ad commodiorem v&longs;um tabulæ, videlicet vt ijs in ca&longs;ibus in quibus <lb/>nece<32>arius est 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>

<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 est 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>

<s>hac enim ratione calculus erit expedi<lb/>tior & error qui hinc oborietur erit in&longs;en&longs;ibilis.<emph.end type="italics"/></s><pb xlink:href="029/01/077.jpg" pagenum="70"/>

Line 1280

<s>Quod <lb/>erat demon&longs;trandum. </s>

<s>Et eadem est ratio de alys grauitatibus, non <lb/>&longs;olum quæ in hac tabula de&longs;cribuntur, &longs;ed etiam de illis, quæ de&longs;cri<lb/>bentur in alys, copio&longs;ioribus, in quibus videlicet denominatores non <lb/>e&longs;&longs;ent partes integræ, &longs;ed partes partiam; dummodo etiam illæ partes <lb/>per vnam eandemque differentiam progrederentur.<emph.end type="italics"/></s>

<s>Et eadem est ratio de alijs grauitatibus, non <lb/>&longs;olum quæ in hac tabula de&longs;cribuntur, &longs;ed etiam de illis, quæ de&longs;cri<lb/>bentur in alijs, copio&longs;ioribus, in quibus videlicet denominatores non <lb/>e&longs;&longs;ent partes integræ, &longs;ed partes partiam; dummodo etiam illæ partes <lb/>per vnam eandemque differentiam progrederentur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Quibus in hunc modum præ osten&longs;is, &longs;i construenda fuerit tabula <lb/>per continuam additionem eiu&longs;dem numeri, &longs;ic erit progrediendum. </s>

Legend:

Removed from v.1.16
changed lines
	Added in v.1.17