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version 1.30, 2005/09/30 12:35:03

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<?xml version="1.0" encoding="UTF-8"?>

<?xml version="1.0"?>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd">

<info>

<author>Cardano, Girolamo</author>

<title>Opus novum de proportionibus</title>

<title>De subtilitate</title>

<place>Basel</place>

<cvs_file>carda_propo_015_la_1570.xml</cvs_file>

<cvs_file>carda_subti_016_la_1663.xml</cvs_file>

<cvs_version/>

</info>

</info> <text> <front><section>

<text>

<front>

<s>Title page and dedication missing<pb xlink:href="016/01/001.jpg"/>Title page and dedication missing<pb xlink:href="016/01/002.jpg"/>Title page and dedication missing<pb xlink:href="016/01/003.jpg"/>Title page and dedication missing<pb xlink:href="016/01/004.jpg"/>Title page and dedication missing</s><pb xlink:href="016/01/005.jpg"/></section> </front> <body> <chap> <pb xlink:href="016/01/006.jpg" pagenum="357"/><figure id="id.016.01.006.1.jpg" xlink:href="016/01/006/1.jpg"/>

<s><emph type="center"/>DE SVBTILITATE.<emph.end type="center"/></s>

<s><emph type="center"/>LIBER PRIMVS.<emph.end type="center"/></s>

<s><emph type="center"/>DE PRINCIPIIS, MATERIA, FORMA, VACVO,<emph.end type="center"/></s>

<s id="id000001">HIERONYMI <lb/>CARDANI MEDIO<lb/>LANENSIS, CIVISQVE BONO<lb/>NIENSIS, PHILOSOPHI, MEDICI ET <lb/>Mathematici clari&longs;simi,</s>

<s><emph type="center"/>corporum repugnantia, motu Naturali, & Loco.<emph.end type="center"/></s>

<s id="id000002">OPVS NOVVM DE <lb/>PROPORTIONIBVS NVMERORVM, MO<lb/>TVVM, PONDERVM, SONORVM, ALIARVMQVE RERVM <lb/>men&longs;urandarum, non &longs;olùm Geometrico more &longs;tabilitum, &longs;ed etiam <lb/>uarijs experimentis & ob&longs;eruationibus rerum in natura, &longs;olerti <lb/>demon&longs;tratione illu&longs;tratum, ad multiplices u&longs;us ac<lb/>commodatum, & in <var>V</var> libros dige&longs;tum.</s>

<s>PROPOSITVM no&longs;tri ne</s>

<s><arrow.to.target n="marg1"/><lb/>gotij in hoc Opere e&longs;t, de <lb/>Subtilitate tractare. </s>

<s id="id000003">PRAETEREA.</s>

<s>E&longs;t au<lb/>tem &longs;ubtilitas ratio quædam, <lb/>qua &longs;en&longs;ibilia à &longs;en&longs;ibus, in<lb/>telligibilia ab intellectu, dif<lb/><arrow.to.target n="marg2"/><lb/>ficilè compræhenduntur. </s>

<s id="id000004">ARTIS MAGNÆ, SIVE DE REGVLIS <lb/>ALGEBRAICIS, LIBER VNVS, ABSTRVSISSIMVS <lb/>& inexhau&longs;tus plane totius Arithmeticæ the&longs;aurus, ab <lb/>authore recens multis in locis recogni<lb/>tus & auctus.</s>

<s>Ergo &longs;i &longs;ingula, qu&ecedil; <lb/>&longs;ubtilitate con&longs;tant, magnum etiam per &longs;e <lb/>exhibent negotium, &longs;untque difficillima, <lb/>quid rogo de ea tractatione dicendum erit, <lb/>in qua omnis &longs;ubtilitatis ratio explicanda <lb/>e&longs;t? </s>

<s>Idque &longs;olùm apertum & facilè videri <lb/>pote&longs;t, quod in vnaquaque di&longs;ciplina e&longs;t <lb/>ob&longs;curi&longs;&longs;imum. </s>

<s>Maiu&longs;que nobis negotium <lb/>&longs;upere&longs;t in ip&longs;ius rei tractatione, quàm in <lb/>ip&longs;a re. </s>

<s id="id000006">DE ALIZA REGVLA LIBER, HOC EST, ALGEBRAICAE <lb/>logi&longs;ticæ &longs;uæ, numeros recondita numerandi &longs;ubtilitate, &longs;ecundum Geo<lb/>metricas quantitates inquirentis, nece&longs;&longs;aria Coronis, <lb/>nunc demum in lucem edita.</s>

<s>Cum enim &longs;cribentes in quatuor <lb/>laborent generibus, rerum ob&longs;curitate, in<lb/>certorum dubitatione, cau&longs;arum inuentio<lb/>ne, rectaque earum explicatione, omnia <lb/>hæc hoc in libro cumulatiùs habentur. </s>

<s>Si <lb/>ob&longs;curitas difficultatem parit, hic liber &longs;o<lb/>lùm ob&longs;curi&longs;&longs;ima &longs;eligit. </s>

<s id="id000007">O<emph type="italics"/>pus<emph.end type="italics"/> P<emph type="italics"/>hy&longs;icis &<emph.end type="italics"/> M<emph type="italics"/>athematicis imprimis <lb/>utile & nece&longs;&longs;arium.<emph.end type="italics"/></s>

<s>Si certò &longs;cire &longs;em<lb/>per laborio&longs;um fuit: quid hoc argumento <lb/>laborio&longs;ius? </s>

<s id="id000008">Cum Cæ&longs;. </s>

<s>vbi habeam quos fugiam, vt <lb/>Plinium & Albertum, quibus nulla in hoc <lb/>genere, quòd palàm mentiantur, fides ha<lb/>betur, quos &longs;equar non habeam. </s>

<s id="id000009">Maie&longs;t. </s>

<s id="id000010">Gratia & Priuilegio.</s>

<s>Et tamen <lb/>&longs;i non omnia mihi ad vnguem fuerint ex<lb/>plorata, operam ( vt dici &longs;olet ) & oleum <lb/>perdam. </s>

<s>Quid de cau&longs;is dicam? </s>

<s id="id000011">BASILEÆ.</s>

<s>quos omni<lb/>bus intactas, velut tamen ex Oraculo quo<lb/>dam acceptas, depromere oportet. </s>

</section>

<s>At Ora<lb/>culis fides ab&longs;que demon&longs;tratione habeba<lb/>tur: nobis, &longs;i eam non addiderimus, nulla <lb/>dabitur. </s>

<s>Intentata pror&longs;us tot &longs;eculis vel res <lb/>ip&longs;as &longs;cientibus Philo&longs;ophis, quæ nunc à <lb/>me vno &longs;unt explicanda. </s>

<s id="id000012">IN LIBRVM DE <lb/>PROPORTIONIBVS HIERONYMI <lb/>CARDANI MEDIOLANENSIS, CIVISQVE <lb/>Bononien&longs;is, Medici, Præfatio ad M. A. </s>

<s>Quædam etiam <lb/>cùm de&longs;ierint, aut nuper &longs;int inuenta, nomi<lb/>nibus aut carent, aut nomina rebus ip&longs;is. <lb/></s>

<s id="id000013">Amulium <lb/>Venetum Card. </s>

<s id="id000014">Illu&longs;tri&longs;simum.</s>

<s>Porrò nomina inuenire nouis rebus, & &longs;e<lb/>ne&longs;cente lingua difficillimum e&longs;t. </s>

<s>Et &longs;i inue<lb/>nero, vt calumniam non &longs;ubeam eorum, <lb/>qui nuper de his &longs;crip&longs;erunt, iudicium ad<lb/>iicere cogor. </s>

<s id="id000015">Bene Dictum e&longs;t meo iudicio à Platone M. <lb/>A. </s>

<s id="id000016">Amuli optime, beatas fore Re&longs;pub. </s>

<s>In reliquo, ne Oedipus ip&longs;e <lb/>Lectori &longs;atisfaciat. </s>

<s id="id000017">&longs;i uel <lb/>illarum domini &longs;apientiæ amatores e&longs;&longs;ent, <lb/>aut qui &longs;apientiæ e&longs;&longs;ent amatores domina<lb/>rentur, hoc ip&longs;um clarè intelligens, &longs;tudio &longs;a<lb/>pientiæ nihil e&longs;&longs;e utilius humano generi: <lb/>quo &longs;imul & pietas, & iu&longs;titia, & mutuus <lb/>amor hominum inter &longs;e & eorum commo<lb/>da continerentur. </s>

<s id="id000018">Nempe hi&longs;ce quatuor tota no&longs;tra felicitas com<lb/>prehenditur. </s>

<s>Itaque cùm rem ad<lb/>modum laborio&longs;am aggre&longs;&longs;i &longs;imus, non ta<lb/>men pro laboris magnitudine, operi ip&longs;i <lb/>præmij vice vtilitatis & gloriæ tantundem <lb/>acceder. </s>

<s id="id000019">Si quidem pietate in Deos nihil ni&longs;i &longs;anctum, & pu<lb/>rum, & illu&longs;tre &longs;apimus: hoc ip&longs;o primum quod &longs;upra nos e&longs;t, intel<lb/>ligimus, Deos ueneramur, gratias agimus, timor cum ueneratione <lb/>no&longs;tros animos &longs;ubit, & de futura uita cogitamus, hæc ip&longs;a morta<lb/>lia &longs;i non negligentes &longs;altem paruifacientes. </s>

<s id="id000020">Iu&longs;titiam autem adeò <lb/>nece&longs;&longs;ariam humano generi e&longs;&longs;e &longs;cimus, ut &longs;ine illa neque e&longs;&longs;e, nedum <lb/>benè e&longs;&longs;e po&longs;símus, ut neque latronum c&oelig;tus ab&longs;que ea diu &longs;tare po&longs;<lb/>&longs;int. </s>

<s>Erant & quædam præter hæc ab <lb/>antiquis non rectè tractata. </s>

<s id="id000021">Porrò quid dicam de concordia, & mutua hominum beneuo<lb/>lentia, in quibus omnis uit&etail; human&etail; dulcedo repo&longs;ita e&longs;t: nec quis <lb/>&longs;u&longs;tineat uiuere, qui &longs;e omnibus odio&longs;um e&longs;&longs;e &longs;entiat. </s>

<s id="id000022">His ip&longs;is fi<lb/>lios in &longs;pem alimus, parentes fouemus, fratres tuemur, & adiuua<lb/>mus, amicis opitulamur, cum hominibus hilarem & iucundam ui<lb/>tam ducimus. </s>

<s>Sed in his non <lb/>laboro, cùm nulla &longs;it authoritas aduer&longs;us ex<lb/>perimenta &longs;cribentibus. </s>

<s id="id000023">Si quis &longs;erpentem in lecto haberet, nunquam &longs;om<lb/>num caperet: ita nihil mole&longs;tius e&longs;t in hac uita, quam e&longs;&longs;e cum quo <lb/>nolis, & priuari con&longs;uetudine eorum cum quibus maximè uiuere <lb/>cupias. </s>

<s id="id000024">Quid enim habent Principes præcipuum cum tota illa po<lb/>tentia quam habent, ni&longs;i hoc unum, quod &longs;uis quos amant bene fa<lb/>cere po&longs;sint: nam reliqua omnia exerceri, uenari, edere, bibere, dor<lb/>mire, iter agere, loca amæna inui&longs;ere multis alijs conce&longs;&longs;um e&longs;t, ma<lb/>ioreque commodo qui in uita priuata degunt. </s>

<s>Ergo tot & tanta <lb/>&longs;unt difficultatis argumenta in hac tracta<lb/>tione. </s>

<s id="id000025">Si ergo principatum <lb/>cum tot laboribus, curis, periculis, & meritò omnes appetunt: nec <lb/>e&longs;t in eo quicquam præcipuum præter hoc, cui dubium e&longs;t quin <lb/>hoc non &longs;it &longs;ummum huius uitæ hominibus bonum? </s>

<s id="id000026">propter cu<lb/>ius uel dubiam &longs;pem eorum, quæ habent obliti mortales pericli<lb/>tantur. </s>

<s>Sed vt ad rem ip&longs;am reuertar, quan<lb/>quam ob&longs;cura tenuia &longs;int plerunque, & exi<lb/>lia &longs;ubtilia, non tamen omnia neque &longs;em<lb/>per. </s>

<s id="id000027">Succedunt inde tot commoda, non &longs;olum utilia, &longs;ed pleraque<pb xlink:href="015/01/007.jpg"/>etiam nece&longs;&longs;aria, quæ nos &longs;apientia docet: huiu&longs;modi ergo omnia <lb/>cùm libris contineantur, meritò optimus qui&longs;que librorum bono<lb/>rum perpetuitati atque in columitati fauere debet. </s>

<s>Quæ enim verborum vitio potiùs quàm <lb/>arte vlla ob&longs;cura &longs;unt atque implicata, ve<lb/>lut nodi fortuitò in &longs;eip&longs;os redeuntes, tum <lb/>quæ &longs;en&longs;u tenuia videntur, haud tamen den<lb/>&longs;a, hæc &longs;ubtilitatis nomen non merentur. <lb/></s>

<s id="id000029">Caligulam exe<lb/>cramur &longs;olum ob id quod Vergilij, & T. </s>

<s id="id000030">Liuij &longs;cripta delere cogi<lb/>tauerit. </s>

<s>Talia &longs;unt gracilia hominum crura ab ini<lb/>tio praua nutritione, aliove ca&longs;u oblæ&longs;a. </s>

<s id="id000031">Quid facturi e&longs;&longs;emus, &longs;i feci&longs;&longs;et quod cogitauerat? </s>

<s id="id000032">E&longs;t in &longs;a<lb/>pientum monumentis bonum &longs;ine malo, mens &longs;ine corporea labe: <lb/>Virtutes ab&longs;que uitijs, gratiæ & iucunditas &longs;ine &longs;orde, & immundi<lb/>tia, uoluptas &longs;ine dolore, conuer&longs;atio ab&longs;que tædio, delitiæ ab&longs;que mi&longs;e<lb/>ria nuda, omnia bona præ&longs;tant, atque laudabilia ab omnibus morta<lb/>litatis exuuijs libera, tantum commodi afferunt libri. </s>

<s><margin.target id="marg1"/>Subtilitatis <lb/>definitio.</s>

<s id="id000033">Sed & in eo<lb/>rum electione ac &longs;tudijs modus, ac medio critas quædam &longs;eruanda <lb/>e&longs;t, quæ &longs;i quis neglexerit non leui incommodo afficietur: eam an<lb/>tiqui rationem alij proportionem appellarunt, non equidem etiam <lb/>in pertritis tam <expan abbr="facillimã">facillimam</expan>, ut rentur homines: nam in alijs rebus per<lb/>ob&longs;curam e&longs;&longs;e fatentur, ego difficillimam puto undique, & magis for<lb/>&longs;an ubi non exi&longs;timamus. </s>

<s id="id000034">Vnde plures decidere uidemus magnis <lb/>cum auxilijs, & euidenti &longs;pe: quid aliud e&longs;t in cau&longs;a quàm ignota <lb/>men&longs;ura rerum? </s>

<s><margin.target id="marg2"/>Difficultas <lb/>in opere <lb/>&longs;cribendo.</s>

<s id="id000035">quam tamen plerique tenere &longs;e putant. </s>

<s id="id000036">Ergo, cùm <lb/>&longs;ummum bonum in hac men&longs;ura &longs;itum e&longs;&longs;e cernerem, ut clarè o&longs;ten<lb/>dunt mu&longs;icæ uoces, quæ non ni&longs;i indiuiduo (ut ita dicam) &longs;patio <lb/>&longs;eu loco &longs;tare po&longs;&longs;unt, ita & in figuris picturarum & &longs;tatuarum, & <lb/>diebus decretorijs, & negotijs ciuilibus oper&etail; pretium me factu<lb/>rum exi&longs;timaui, &longs;i omnia hæc quæ latè patebant breuiter in unum <lb/>redegi&longs;&longs;em, <expan abbr="nõ">non</expan> tantum ne lectorem tædio afficerem, quàm ut quòd <lb/>aliàs do cui, breuibus tractationibus, & plura continerentur, & faci<lb/>lius docerentur. </s>

<s>Con&longs;tat ergo &longs;ubtilitas in tribus &longs;ub&longs;tan<lb/><arrow.to.target n="marg3"/><lb/>tiis, accidentibus, ac repræ&longs;entationibus. <lb/></s>

<s id="id000037">Cum uerò bona fortuna quædam effeci&longs;&longs;et, ut tibi <lb/>libellum dedica&longs;&longs;em de Prouidentia ex con&longs;titutione temporum, <lb/>longe meliore occa&longs;ione nominis tui typographi obliti &longs;int, indi<lb/>gnum fore putaui, ut non ærea (quemadmodum cum Glauco Dio<lb/>medes) cum aureis commutarem. </s>

<s id="id000038">Itaque infinitis licet circumuentus <lb/>negotijs totus huic operæ in cubui, atque adeò ut præter &longs;pem unius <lb/>anni penè &longs;patio liber ab&longs;olueretur. </s>

<s>Eorum enim quorum e&longs;t &longs;cientia aliqua, <lb/>quædam &longs;unt, quædam autem non, &longs;ed &longs;o<lb/>lùm e&longs;&longs;e videntur. </s>

<s id="id000039">Qui cum tibi (ut dixi) iam iurè <lb/>deberetur, eò tamen magis dedicandum putaui, quod non ego &longs;o<lb/>lum quanquam id maximè, &longs;ed communis con&longs;en&longs;us ho<lb/>minum exi&longs;timet, te &longs;ingulari uirtute omnibus <lb/>&longs;tudio&longs;is plurimum fauere, <lb/>Vale.</s>

<s>Quæ videntur, alia qui<lb/>dem nobis dormientibus, alia autem vigi<lb/>lantibus alia per interiores &longs;en&longs;us, alia verò <lb/>per externos. </s>

</section>

<s>Externi &longs;en&longs;us, quorum e&longs;t <lb/>ratio habenda, quatuor &longs;unt: tactus, vi&longs;us, <lb/>olfactus, auditus. </s>

<s>Nam gu&longs;tus qua&longs;i con<lb/>temnendus e&longs;&longs;e videtur. </s>

<s id="id000040">TABVLA PRO<lb/>POSITIONVM DE <lb/>PROPORTIONIBVS.<lb/><arrow.to.target n="table1"/></s>

<s>Horum &longs;ingulis <lb/>quadrifariam repræ&longs;entatio contingit: vel <lb/>quia non percipiunt quæ percipere debent, <lb/>velut cùm caro acu citra dolorem perfora<lb/>tur: vel quia percipiunt, quod non e&longs;t, vt <lb/>ec&longs;ta&longs;i ac &longs;omniis: vel aliter quàm &longs;int, vt <lb/>magnitudines aut colores: aut non &longs;imili <lb/>ratione, vt in imagine. </s>

<table>

<table.target id="table1"/>

<s>Videntur rur&longs;us &longs;ub <lb/>hoc genere plura e&longs;&longs;e, &longs;ed non &longs;unt. </s>

<row>

<s>Nam <lb/>oratio, auditus: pictura, &longs;culptura, vi&longs;us, &longs;pe<lb/>cies imaginantis virtutis: &longs;criptura autem <lb/>vi&longs;u & auditu con&longs;tare videtur: vtraque au<lb/>tem, tam &longs;criptura quàm oratio, auxilio in<lb/>terioris &longs;en&longs;us con&longs;tant. </s>

<cell>Proportionem <emph type="italics"/>in proportionem duci, e&longs;t &longs;uperiores numeros atque inferiores inuicem ducere.<emph.end type="italics"/></cell>

<cell><emph type="italics"/>pagina<emph.end type="italics"/> 6</cell>

<s>Quæ autem &longs;unt, <lb/>alia quidem &longs;ub&longs;tantiæ, alia accidentia. </s>

</row>

<row>

<s>Sub<lb/>&longs;tantiarum aliæ quidem corporeæ, aliæ cor<lb/>pore carent: atque hæ omnes immortales <lb/>atque incorruptibiles: carent enim contra<lb/>rio, & in &longs;eip&longs;is &longs;ub&longs;i&longs;tunt. </s>

<cell>P<emph type="italics"/>roportio extremorum producitur ex intermedijs.<emph.end type="italics"/></cell>

<s>Quæ igitur incor<lb/>poreæ, aliæ quidem à nullis pendent, &longs;ed <lb/>aliorum &longs;unt cau&longs;æ, aliæ ab aliis. </s>

</row>

<s>Quæ à <lb/>nullis pendeat, vna tantùm e&longs;t, Deus opti<lb/>mus atque immen&longs;us, cuius fabrica e&longs;t <lb/>vniuer&longs;um ip&longs;um. </s>

<row>

<s>De illius intellectu, &longs;a<lb/>pientia ac pote&longs;tate bonitatéque, inde de <lb/>vniuer&longs;i ortu, extremo loco tanquam de <lb/><arrow.to.target n="marg4"/><lb/>perfecti&longs;&longs;imo dicendum erit. </s>

<cell>S<emph type="italics"/>i proportio ex duabus proportionibus in quatuor terminis producatur, ip&longs;a uerò proportio inter duas alias quantitates fuerit con&longs;tituta: con&longs;urgent trecenti &longs;exaginta modi productionis proportionis.<emph.end type="italics"/></cell>

<s>Ad de vniuer&longs;i <lb/>ordine etiam ibidem erit con&longs;iderandum. <lb/></s>

</row>

<row>

<s>Nam vniuer&longs;um ordine con&longs;tat: ip&longs;um verò <lb/>in tempore, aut in illo tempus. </s>

<cell>S<emph type="italics"/>i fuerit proportio primi ad &longs;ecundum, producta ex proportionibus tertij ad quartum, & quinti ad &longs;extum, producetur etiam ex proportione tertij ad &longs;extum, & quinti ad quartum.<emph.end type="italics"/></cell>

<s>Septem igi<lb/>tur hæc vltimo in libro tractanda erunt. <pb xlink:href="016/01/007.jpg" pagenum="358"/>Quæ autem pendent ab aliis, & corpore ca<lb/>rent, alia aliorum &longs;unt cau&longs;æ, alia nullius. <lb/></s>

</row>

<s>Et quæ aliorum &longs;unt cau&longs;æ, vt perpetuò <lb/>cau&longs;æ &longs;int corporibus etiam immortalibus <lb/>annectuntur, vocantúrque &longs;ub&longs;tantiæ pri<lb/>mæ. </s>

<row>

<s>Quatuor igitur in his &longs;pectanda erunt, <lb/>vt intelligunt, vt producunt, vt manent <lb/>(in æuo enim e&longs;&longs;e videntur<emph type="italics"/>)<emph.end type="italics"/> vt mouent, at<lb/>que corpori a&longs;&longs;i&longs;tunt. </s>

<cell>S<emph type="italics"/>i fuerit proportio primi ad &longs;ecundum, producta ex proportione tertij ad quartum, & quinti ad &longs;extum: erit proportio tertij ad &longs;extum, producta ex proportionibus primi ad &longs;ecundum, & quarti ad quintum.<emph.end type="italics"/></cell>

<s>Plurima verò in hoc <lb/>genere & in vltima tractatione ad libros de <lb/>æternitatis arcanis reiecta &longs;unt, quòd cùm <lb/>omnia hæc &longs;upra humanam mentem &longs;int <lb/>clariora, & quæ apertiùs demon&longs;trari pote<lb/>rant, tùm generalia, tantùm huic negotio <lb/>pertinebant. </s>

</row>

<row>

<s>Quæ verò immortalia & in<lb/>corporea nullius erant cau&longs;a: mortali cor<lb/>pori annexa fuêre. </s>

<cell>E<emph type="italics"/>x trecentis &longs;exaginta modis producendarum proportionum triginta &longs;ex tantum e&longs;&longs;e nece&longs;&longs;arios.<emph.end type="italics"/></cell>

<s>Alia igitur horum ma<lb/>nife&longs;ta, alia de quibus e&longs;t dubitatio. </s>

</row>

<s>Atque <lb/>illa &longs;i &longs;int præclara magis, dæmonas quidam <lb/>vocant, de quibus ante intelligentias tra<lb/>ctabimus. </s>

<row>

<s>Tum verò ante illud de xxiv. </s>

<cell>I<emph type="italics"/>n modis qui nece&longs;&longs;ariò producuntur ex duabus proportionibus, cum duæ quantitates ex illis quæ modos conficiunt, æquales fuerint: proportio producta ad quatuor quantitates omiologas reducetur.<emph.end type="italics"/></cell>

<s>ge<lb/>neribus repræ&longs;entationum dictis, ob rei affi<lb/>nitatem: plerique enim mirabilia &longs;unt, ad <lb/>hos veluti cau&longs;as referunt. </s>

</row>

<row>

<s>Verùm cùm an <lb/>&longs;int, nondum liqueat naturam &longs;pectantibus, <lb/>de his tantùm, velut de probabilibus loque<lb/>mur, initium ab effectibus, &longs;olúmque id <lb/>cum dubitatione &longs;umentes. </s>

<cell>S<emph type="italics"/>i duarum proportionum &longs;uperiores numeri alternatim cum inferioribus multiplicentur atque coniungantur, erit proportio aggregati ad productum ex inferioribus inuicem proportio, ex primis proportionibus compo&longs;ita.<emph.end type="italics"/></cell>

<s>At de intelle<lb/>ctus immortalitate, illiú&longs;que &longs;eparatione, <lb/>aliàs dictum e&longs;t. </s>

</row>

<s>Reliquum e&longs;t igitur, vt de <lb/>propriis illius affectus loquamur. </s>

<row>

<s>Sunt au<lb/>tem artes, de quibus ante illa tractabimus, <lb/>tùm de rebus, quæ artibus ip&longs;is con&longs;tant. <lb/></s>

<cell>S<emph type="italics"/>i duarum proportionum &longs;uperiores numeri alternatim cum inferioribus multiplicentur, minusque productum ex maiore detrahatur, erit re&longs;idui ad productum ex in&longs;erioribus proportio uelut illa, quæ relinquitur detracta minore proportione ex maiore.<emph.end type="italics"/></cell>

<s>Ante artes, de &longs;cientiis atque intellectu di<lb/>cendum erit. </s>

</row>

<row>

<s>Nam de Prudentia, in libris <lb/>de Sapientia di&longs;putauimus. </s>

<cell>S<emph type="italics"/>i fuerit alicuius quantitatis ad unam partem proportio, uelut alterius partis ad &longs;ecundam quantitatem, erit proportio cuiu&longs;uis quantitatis eiu&longs;dem generis ad &longs;ecundam compo&longs;ita proportio, ex proportionibus eiu&longs;dem quantitatis, a&longs;&longs;umptæ ad utranque partem primæ quantitatis &longs;eor&longs;um.<emph.end type="italics"/></cell>

<s>At priùs de Ani<lb/>ma & Intellectu dicendum erit, quoniam <lb/>non e&longs;t &longs;cientia, neque principiorum cogni<lb/>tio ab&longs;que illis. </s>

</row>

<s>Atque po&longs;t hæc de leuioris <lb/>cuiu&longs;dam generis &longs;ubtilitatibus &longs;eu inutili<lb/>bus, quæ nec ad artem, quòd non confe<lb/>rant: nec ad &longs;cientiam, quòd non demon<lb/>&longs;trentur, referri queunt. </s>

<row>

<s>Rur&longs;us, vt anima <lb/>corpori mortali annectitur, &longs;en&longs;us fiunt: <lb/>atque inde cùm &longs;en&longs;us non &longs;int, ni&longs;i etiam <lb/>&longs;en&longs;ibilia, tum verò &longs;en&longs;u &longs;en&longs;ibilia perci<lb/>piente voluptas &longs;it, antea de his tribus di<lb/>cendum erit, &longs;cilicet de &longs;en&longs;u, &longs;en&longs;ibilibus, <lb/>ac voluptate. </s>

<cell>P<emph type="italics"/>roportio aggregati quarumlibet duarum quantitatum ad aggregatum duarum æqualium <expan abbr="quantitat&utilde;">quantitatum</expan> e&longs;t, compo&longs;ita ex proportionibus primis, & diui&longs;a per duplam.<emph.end type="italics"/></cell>

<s>Colores tamen ad luminis tra<lb/>ctationem ob commodum reiicimus. </s>

</row>

<row>

<s>Cor<lb/>porearum verò &longs;ub&longs;tantiarum aliæ quidem <lb/>immortales, vt c&oelig;lum: aliæ corruptioni <lb/>obnoxiæ. </s>

<cell>P<emph type="italics"/>ropo&longs;itis duabus proportionibus unam alteri iungere ab&longs;que multiplicatione.<emph.end type="italics"/></cell>

<s>Horum etiam quædam &longs;implices, <lb/>aliæ mixtæ. </s>

</row>

<s>Atque omnium horum &longs;unt <lb/>principia quædam, velut locus & motus, <lb/>& corporum repugnantia, & certa men&longs;u<lb/>ra &longs;ub&longs;tantiæ: neque enim di&longs;&longs;olui pote&longs;t <lb/>corpus in incorporea, neque vacuum admit<lb/>titur. </s>

<row>

<s>Tum etiam forma e&longs;t principium, at<lb/>que communis cum aliis tam generabilibus, <lb/>quàm ingenerabilibus corporibus. </s>

<cell>P<emph type="italics"/>roportio confu&longs;a aggregata primæ & tertiæ quatuor quantitatum omiologarum ad aggregatum &longs;ecundæ & quartæ, e&longs;t uelut compo&longs;ita ex ei&longs;dem diui&longs;a per duplam.<emph.end type="italics"/></cell>

<s>Igitur de <lb/>omnibus his quinque, tum de materia, pri<lb/>mo loco, atque in primo libro tractandum <lb/>erit. </s>

</row>

<row>

<s>Po&longs;t hæc de quatuor elementis <emph type="italics"/>(<emph.end type="italics"/> tot <lb/>enim exi&longs;timantur <emph type="italics"/>)<emph.end type="italics"/> inde de c&oelig;lo, pò&longs;t de <lb/>luce, lumine atque coloribus. </s>

<cell>XIIII.</cell>

<cell>P<emph type="italics"/>roportiones confu&longs;æ & coniunctæ in tribus quantitatibus inuicem commutantur.<emph.end type="italics"/></cell>

<s>Inde ad com<lb/>po&longs;ita corpora de&longs;cendendum. </s>

</row>

<s>Horum quæ<lb/>dam perfecta, quædam imperfecta, de qui<lb/>bus primò dicendum erit. </s>

<row>

<s>Con&longs;tant hæc mi<lb/>&longs;tione. </s>

<cell>S<emph type="italics"/>i fuerint quatuor quantitates proportio confu&longs;a, aggregati primæ & tertiæ, ad aggregatum &longs;ecundæ & quartæ, erit ut monadis addito prouentu, qui fit diui&longs;a differentia, differentiarum primæ & &longs;ecundæ, atque quartæ & tertiæ, per aggregatum tertiæ & quartæ ad ip&longs;am monadem.<emph.end type="italics"/></cell>

<s>De mi&longs;tione igitur quinto loco di<lb/>cendum erit. </s>

</row>

<row>

<s>Perfectorum autem corporum <lb/>& quæ viuunt, quædam vitam in &longs;eip&longs;is <lb/>habent, atque horum alia aqueæ &longs;ub&longs;tan<lb/>tiæ, quæ Metalla vocantur: quædam ter<lb/>reæ, quæ Lapides dicuntur: Cùm verò hæc <lb/>generatione & corruptione, & mutatione <lb/>qualitatum fiant, imprimis de metallis: de <lb/>mutatione qualitatum, quam barbari vo<lb/>cant Altercationem, dicendum erit: pò&longs;t <lb/>de Lapidibus. </s>

<cell>O<emph type="italics"/>mnium quatuor quantitatum propo&longs;ita prima, quæ non minorem habet proportionem ad &longs;uam corre&longs;pondentem quàm alia ad aliam, erit proportio confu&longs;a illarum,<emph.end type="italics"/></cell>

<s>Eorum autem quæ vitam <lb/>aliundè trahunt, quædam motu carent, vt <lb/>arbores, & herbæ, de quibus octauo loco <lb/>dicendum e&longs;t: pò&longs;t de his quæ motu prædi<lb/>ta &longs;unt, non tamen &longs;emine generantur. </s>

<cell/>

</row>

<s>At <lb/>de generatione tali dicendum erit: &longs;icut in <lb/>decimo de Generatione, quæ &longs;emine in ani<lb/>malibus fit. </s>

<row>

<s>Atque hæc animalia intellectu <lb/>carent. </s>

<cell/>

<cell><emph type="italics"/>ut producti ex aggregato primæ & tertiæ, in tertiam ad productum ex aggre gato tertiæ & omiotatæ ad &longs;ecundam in ip&longs;am quartam.<emph.end type="italics"/></cell>

<s>De corpore verò, quod &longs;ummam <lb/>perfectionem con&longs;ecutum e&longs;t, <emph type="italics"/>(<emph.end type="italics"/> illud autem <lb/>e&longs;t homo ) cur factum &longs;it, & de illius for<lb/>ma atque actionibus dicendum erit. </s>

</row>

<s>Duode<lb/>cimus verò ea tractat de illo, quæ ad cor<lb/>pus pertinent, atque hæc quatuor &longs;unt ge<lb/>nerum: quædam enim aliis &longs;unt communia <lb/>animalibus, quædam propria: quædam &longs;unt <lb/>actiones ex &longs;ub&longs;tantiæ propria quadam na<lb/>tura, quædam verò quæ ad illius manife<lb/>&longs;tam &longs;tructuram referuntur. </s>

<row>

<s>Iam verò & <lb/>quædam &longs;unt accidentia, de quibus dicen<lb/>dum e&longs;t, velut grauitas, leuitas: hæc au<lb/>tem in elementis, den&longs;itas, raritas, a&longs;pe<lb/>ritas, lenitas, durities, mollities: atque <lb/>hæc in mi&longs;tis, communiáque, velut genitis <lb/>nitor, per&longs;picuitas, figuráque genitis &longs;o<lb/>lùm. </s>

<cell>O<emph type="italics"/>mnes duæ proportiones conuer&longs;æ producunt æqualem proportionem.<emph.end type="italics"/></cell>

<s>Quædam verò de aliis tantùm dicun<lb/>tur, vt generatio, corruptio, nutritio, mu<lb/>tatio, auctio, attractio, retentio, conco<lb/>ctio, expul&longs;io. </s>

</row>

<row>

<s>Subtilitas verò in omnibus <lb/>his, quorum genera numerauimus. </s>

<cell>XVIII.</cell>

<cell>S<emph type="italics"/>i fuerint quotlibet quantitates in continua proportione multiplici præter, <expan abbr="ultimã">ultimam</expan> proportio uerò penultimæ ad ultimam, qualis re&longs;idui primæ ad &longs;ecundam, erit primæ ad aggregatum reliquarum, uelut penultimæ ad ultimam.<emph.end type="italics"/></cell>

<s>Quod <lb/>igitur tot &longs;int, de quibus tractandum e&longs;t, & <lb/>quòd plura e&longs;&longs;e non po&longs;&longs;int, tùm verò quæ <lb/>de illis demon&longs;tranda, & quo ordine, abun<lb/>dè me explica&longs;&longs;e reor. </s>

</row>

<s>Vnde non leuis vti<lb/><arrow.to.target n="marg5"/><lb/>litas ex tanto labore, &longs;ed quanta vnquam <lb/>alia ex tractatione po&longs;&longs;it haberi, &longs;eu ad <lb/>vnum tantùm genus, &longs;eu ad plurima refe<lb/>ratur. </s>

<row>

<s>Primùm enim ad omnem naturæ co<lb/>gnitionem confert, & ad difficilium rerum <lb/>&longs;cientiam, & ob&longs;curarum inuentionem, li<lb/>bris quoque interpretandis omnibus aliqua <lb/>in parte auxiliatur. </s>

<cell>S<emph type="italics"/>i fuerint aliquot quantitates arithmeticæ omiologæ, quarum exce&longs;&longs;us &longs;it æqualis minimè, omnibus autem deficientibus &longs;upplementa ad æqualitatem maximè adiungantur, erunt quadrata omnium quantitatum æqualium, adiecto rur&longs;us quadrato primæ cum eo quod fit ex minima primi ordinis in aggregatum omnium quantitatum eiu&longs;dem, tripla aggregato quadratorum omnium quanti tatum primi ordinis pariter acceptis.<emph.end type="italics"/></cell>

<s>Artium vires docet, ac <lb/>noua quædam &longs;citu iucunda common&longs;trat, <lb/>tum ex his etiam, quæ ad comparandas di<lb/>uitias, & opes non parùm momenti afferunt. <lb/></s>

</row>

<row>

<s>Decernit & circa antiquas, & non leues du<lb/>bitationes, quid verum &longs;it, velut in chymi<lb/>cis. </s>

<cell>C<emph type="italics"/>um fuerint quatuor quantitates, fueritque <expan abbr="&longs;ec&utilde;da">&longs;ecunda</expan> æqualis tertiæ, aut prima æqualis quartæ, erit proportio primæ ad quartam, aut tertiæ ad &longs;ecundam, producta ex proportionibus primæ ad &longs;ecundam & tertiæ ad quartam.<emph.end type="italics"/></cell>

<s>O&longs;tendit & prodigio&longs;a opera tùm natu<lb/>ræ, tùm artis. </s>

</row>

<s>Reuocat & antiqua in v&longs;um <lb/>inuenta, quæ vetu&longs;tate, vel bellis gra<lb/>ui&longs;&longs;imis excoluerunt. </s>

<row>

<s>Et quæ &longs;en&longs;ibus ad<lb/>miranda videntur, cur fiant, in omni<lb/>bus edocet. </s>

<cell>C<emph type="italics"/>um decu&longs;&longs;atim ducta fuerit prima in quartam, & &longs;ecunda in tertiam, productumque primæ in quartam, diui&longs;um fuerit per productum &longs;ecundæ in tertiam, erit proportio primæ ad &longs;ecundam, diui&longs;a per proportíonem tertiæ ad quartam.<emph.end type="italics"/> E<emph type="italics"/>t &longs;imiliter interpo&longs;ita omiologa.<emph.end type="italics"/></cell>

<s>Iam verò propo&longs;itum rem ag<lb/>grediamur. </s>

</row>

<row>

<s><margin.target id="marg3"/>Subtilitas in <lb/>quib. </s>

<cell>C<emph type="italics"/>um fuerit proportio primæ ad &longs;ecundam maior quàm tertiæ ad quartam, erit confu&longs;a ex his maior quàm tertiæ ad quartam, minor autem quàm primæ ad &longs;ecundam.<emph.end type="italics"/></cell>

<s>&longs;it. <lb/></s>

</row>

<s>Quæ <expan abbr="tractã-da">tractan<lb/>da</expan> &longs;int in <lb/>his libris.</s>

<row>

<cell>XXIII.</cell>

<s><margin.target id="marg4"/>Ordo li<lb/>brorum.</s>

<cell>O<emph type="italics"/>mnis motus naturalis ad locum &longs;uum e&longs;t: ideò per rectam lineam fit.<emph.end type="italics"/></cell>

<s><margin.target id="marg5"/>Vtilitas.</s>

</row>

<row>

<s>Hylen e&longs;&longs;e, o&longs;tendit rerum ip&longs;arum per<lb/><arrow.to.target n="marg6"/><lb/>petua generatio, quæ &longs;emper ex aliquo fit <lb/>alio. </s>

<cell>XXIIII.</cell>

<cell>O<emph type="italics"/>mnis motus circularis uoluntarius e&longs;t.<emph.end type="italics"/></cell>

<s>Etenim frumenta ex terra & humore, <lb/>& animalia ex &longs;emine, & &longs;anguine, vel <lb/>ouis, & cinis ex lignis: nec quicquam tam <lb/>pu&longs;illum e&longs;t, quòd ex nullo fiat. </s>

</row>

<s>Nec &longs;uffi<lb/>cit, vt aliquid præ&longs;it, cùm non ex arundi-<pb xlink:href="016/01/008.jpg" pagenum="359"/>ne, aut &longs;tipula multus cinis fieri po&longs;&longs;it, ex <lb/>multa verò quercu paucus nunquam cinis <lb/>euadet. </s>

<row>

<s>Itaque aliquid in generatione om<lb/>ni commune manet, quod materiam pri<lb/>mam dicimus aut hylen. </s>

<cell>T<emph type="italics"/>res &longs;unt motus omnino &longs;implices naturalis, uoluntarius, & uiolentus.<emph.end type="italics"/></cell>

<s>Cùm enim aliquid <lb/>generatur ex alio, &longs;i forma perit (aliter enim <lb/>e&longs;&longs;et idem ac non e&longs;&longs;et) manente aliquo ma<lb/>teriam illud e&longs;&longs;e, nece&longs;&longs;e e&longs;t. </s>

</row>

<row>

<s>O&longs;tendit idem <lb/>corruptio, cùm nihil pror&longs;us dum corrum<lb/>pitur, pereat. </s>

<cell>M<emph type="italics"/>otus ergo compo&longs;iti quatuor nece&longs;&longs;ariò &longs;unt &longs;pecies.<emph.end type="italics"/></cell>

<s>Nam malum putre&longs;cit, & in <lb/>vermes tran&longs;it: & ligna dum vruntur, in <lb/>cineres: & aquam in vapores calore ignis, <lb/>aut &longs;olis, vel fumum permutatur. </s>

</row>

<s>E&longs;t au<lb/>tem vapor & fumus aliquid: nam & homi<lb/>nem &longs;uffocat, & &longs;i colligatur, denuò tran<lb/>&longs;it in guttas aquæ. </s>

<row>

<cell>XXVII.</cell>

<s>Manife&longs;tum e&longs;t igitur <lb/>aliquid e&longs;&longs;e in rerum natura &longs;ub forma lati<lb/>tans, quod nec per generationem fit, nec <lb/>corruptione ip&longs;a interit: atque hoc ip&longs;um <lb/>vt primum quoddam, & quod multis &longs;ub<lb/>iicitur formis, materiam primam vocare <lb/>&longs;olemus ingenitam, & nunquam interitu<lb/>ram. </s>

<cell>M<emph type="italics"/>otus uoluntarius e&longs;t in loco: naturalis ad locum: uiolentus ex loco.<emph.end type="italics"/></cell>

<s>Manet autem atque e&longs;t: quod enim <lb/>manet e&longs;t. </s>

</row>

<row>

<s>Materia igitur actu e&longs;t talis, qua<lb/>lem de&longs;crip&longs;imus: verùm formis compara<lb/>ta, potentia e&longs;t: illas enim &longs;u&longs;cipere pote&longs;t. <lb/></s>

<cell>XXVIII.</cell>

<cell>M<emph type="italics"/>otus quilibet uoluntarius aut uiolentus in aliquo medio fit.<emph.end type="italics"/></cell>

<s>Ad formam igitur comparata materia, po<lb/>tentia e&longs;t, in &longs;eip&longs;a verò actu. </s>

</row>

<s>Quemadmo<lb/>dum f&oelig;tus cùm nondum perfectus e&longs;t, in<lb/>fans potentia e&longs;t, &longs;ed talis, qualis f&oelig;tus actu <lb/>e&longs;t: e&longs;t enim hoc quidem &longs;ic delineatum com<lb/>mi&longs;tum, ac tale quale videtur. </s>

<row>

<s>Cùm autem <lb/>ad formam infantis comparatur, potentia <lb/>e&longs;&longs;e dicitur: nam &longs;i actu e&longs;&longs;et, e&longs;&longs;et infans <lb/><arrow.to.target n="marg7"/><lb/>iam, non autem f&oelig;tus. </s>

<cell>O<emph type="italics"/>mnis motus uoluntarius æqualis e&longs;t &longs;emper: &longs;impliciter etiam quilibet alius motus.<emph.end type="italics"/></cell>

<s>Materia igitur pri<lb/>ma actu e&longs;t, atque ( vt ita dicam ) imminu<lb/>to: ad formas comparata, potentia e&longs;t: nam <lb/>ni&longs;i potentia ad illas e&longs;&longs;et, eas nunquam <lb/>&longs;u&longs;ciperet: neque enim ex lapide homo fit, <lb/>quia lapis ad hominis formam &longs;u&longs;cipiendam <lb/>potentiam non habet. </s>

</row>

<row>

<s>Complexa verò à for<lb/>ma, cui tunc &longs;ubiacet, actum con&longs;equitur <lb/>perfectiorem, non tamen perfectum: actus <lb/>enim perfectus e&longs;t, qui potentia omninò <lb/>caret. </s>

<cell>I<emph type="italics"/>n omni corpore mobili in medio partes medij re&longs;i&longs;tunt obuiæ, aliæ impellunt.<emph.end type="italics"/></cell>

<s>Dicemus igitur ficus materiam per <lb/>&longs;e con&longs;ideratam actu e&longs;&longs;e, &longs;ed tenui admo<lb/>dum: vt verò ad alienas formas compara<lb/>tur, potentia quidem ad illas: vt autem pro<lb/>priè ficus formæ &longs;ubiacet, actu con&longs;i&longs;tere. <lb/></s>

</row>

<s>Sed nec materia prima omnibus e&longs;t &longs;poliata <lb/>rebus: cùm enim <emph type="italics"/>(<emph.end type="italics"/>vt dixi ) neque ex pugil<lb/>lo paleæ, ferri pugillus ob materiæ paucita<lb/>tem, nec rur&longs;us ex ferri pugillo, paleæ pu<lb/>gillus ob illius redundantiam, &longs;equitur <lb/>vt materia prima quantitatem quandam <lb/>retineat, quam indefinitam vocamus. </s>

<row>

<s>Nam<lb/><arrow.to.target n="marg8"/><lb/>que non &longs;ibi certos de&longs;cribit limites, cùm <lb/>modò &longs;ub forma maius complendo &longs;pa<lb/>tium, modò minùs latitet. </s>

<cell>O<emph type="italics"/>mnis motus naturalis in æquali medio ualidior e&longs;t in fine quàm in principio.<emph.end type="italics"/>V<emph type="italics"/>iolentus contrà.<emph.end type="italics"/></cell>

<s>Nam &longs;i ex terra <lb/>ignis fiat, ampliorem occupat locum: qua<lb/>re materia illa prior, quæ minori &longs;ubiicie<lb/>batur quantitati, mutatione formæ maio<lb/>rem locum impleuit. </s>

</row>

<row>

<s>Circum&longs;criptos tamen <lb/>habet limites magnitudinis ac paruitatis, <lb/>intra quos ceu quidam Proteus infinitos ma<lb/>gnitudinis tèrminos &longs;ubit. </s>

<cell>XXXII.</cell>

<cell>O<emph type="italics"/>mne mobile naturaliter motum &longs;eu uiolenter uelocius mouetur in medio rariore quàm den&longs;iore.<emph.end type="italics"/> M<emph type="italics"/>aior quoque e&longs;t proportio finis motus in corpore rariore ad finem motus in corpore den&longs;iore quàm principij.<emph.end type="italics"/> I<emph type="italics"/>n uiolento autem celerius perueniret ad finem motus in corpore den&longs;iore.<emph.end type="italics"/></cell>

<s>Quúmque hæc <lb/>quantitatis certa determinatio illi actu in<lb/>hæreat, quid mirum e&longs;t ip&longs;am materiam pri<lb/>mam, propter quam magnitudo ip&longs;a e&longs;t <lb/>con&longs;tituta, actu e&longs;&longs;e, ac &longs;ub&longs;i&longs;tere? </s>

</row>

<s>ob&longs;cu<lb/>riùs hæc quidem ab aliis dicta &longs;unt, non &longs;o<lb/>lùm ob rei ip&longs;ius &longs;ubtilitatem, &longs;ed quòd ple<lb/>rique dum quæ non perfectè a&longs;&longs;equebantur, <lb/>&longs;cribere vellent, &longs;ermonibus non tantùm <lb/>ob&longs;curius, &longs;ed etiam ambiguis tractationem <lb/>ip&longs;am inuoluunt. </s>

<row>

<cell>XXXIII.</cell>

<s>Porrò ad materiæ &longs;cien<lb/>tiam, imò e&longs;&longs;entiam &longs;equitur, vt cùm for<lb/>mas ip&longs;as aduenientes impedimus, prior re<lb/>maneat: atque eo modo aqua frigida in &longs;an<lb/>guineis temperantiam con&longs;eruat, bilis pro<lb/>hibendo generationem. </s>

<cell>O<emph type="italics"/>mnia duo mobilia æqualis undique magnitudinis quæ æquali in tempore æqualia &longs;pacia pertran&longs;eunt in diuer&longs;is &longs;ub&longs;tantia medijs nece&longs;&longs;e e&longs;t, ut &longs;it ponderis ad pondus, quem ad modum medij ad medium proportio duplicata.<emph.end type="italics"/></cell>

<s>Etenim cùm nece&longs;<lb/>&longs;e &longs;it materiam primam &longs;emper &longs;ub aliqua <lb/>iacere forma, &longs;i &longs;ub&longs;equens impediatur ar<lb/><arrow.to.target n="marg9"/><lb/>te, vel ca&longs;u, priorem formam manere ne<lb/>ce&longs;&longs;e e&longs;t. </s>

</row>

<row>

<s>Inde igitur tota præ&longs;eruandi me<lb/>thodus ortum habuit. </s>

<cell>XXXIIII.</cell>

<cell>P<emph type="italics"/>roportio corporis cubi ad &longs;uam &longs;uperficiem quadratam, e&longs;t uelut eiu&longs;dem &longs;uperfi ciei, ad latus eiu&longs;dem uerò ad monadem.<emph.end type="italics"/></cell>

<s>Similiter & in tran&longs;<lb/>mutationibus par materiæ quantitas requi<lb/>renda fuit, cùm maior aut minor oportuna <lb/>e&longs;&longs;e non po&longs;&longs;it. </s>

</row>

<s><expan abbr="Atq;">Atque</expan> ea ratione ex con&longs;imili<lb/>bus con&longs;imilia magis fiunt, quàm ex di&longs;&longs;imi<lb/>libus. </s>

<row>

<s>Rur&longs;us rari ac den&longs;i ratio à materiæ <lb/>multitudine, aut paucitate &longs;umpta e&longs;t: ve<lb/>rùm de his inferiùs dicemus. </s>

<cell>V<emph type="italics"/>ocum magnitudines excre&longs;cunt in acumine, non in grauitate, finis autem e&longs;t in utroque extremo.<emph.end type="italics"/> P<emph type="italics"/>ropter hoc minima facta uariatione in hypate acutæ uix ferunt.<emph.end type="italics"/></cell>

<s>Cùm itaque <lb/>materia ab initio tota fui&longs;&longs;et, imple&longs;&longs;étque <lb/>hoc concauum orbis, nec po&longs;&longs;et finiri, va<lb/>cuum e&longs;&longs;e non poterat: nam vacuo aucto, <lb/><arrow.to.target n="marg10"/><lb/>materiam tolli nece&longs;&longs;e erat. </s>

</row>

<row>

<s>Multa etiam <lb/>erant, quæ vacuum e&longs;&longs;e non po&longs;&longs;e demon<lb/>&longs;trabant, et&longs;i Heron in &longs;piritualibus illud <lb/>e&longs;&longs;e o&longs;tendere nitatur: verùm non e&longs;t &longs;a<lb/>pientis omnia ab&longs;urda refellere: nec no&longs;tri <lb/>multò minùs in&longs;tituti, quæ ab euidentibus <lb/>rationibus po&longs;&longs;unt demon&longs;trari, ob&longs;curiori<lb/>bus argumentis pro&longs;equi. </s>

<cell>XXXVI.</cell>

<cell>S<emph type="italics"/>i proportio per proportionem minorem æquali ducatur, proportio minor pro<emph.end type="italics"/></cell>

<s>Quòd igitur va<lb/>cuum non &longs;it, folles o&longs;tendunt occlu&longs;i, qui <lb/>&longs;i nimium di&longs;tendantur ac violenter fran<lb/>guntur: nam locus capacior factus, cùm <lb/>nec aëre impleri po&longs;&longs;it, tantam tenuitatem <lb/>non admittente, nec vacuum dari queat, &longs;u<lb/>pere&longs;t tertium vt folles ip&longs;i di&longs;rumpantur. <lb/></s>

<cell/>

</row>

<s>Huius igitur vacui nece&longs;&longs;itate aqua a&longs;cen<lb/>dit, dum per canalem &longs;ugimus, pronáque de<lb/>&longs;cendit, hauriens &longs;itulam ex vrceolo. </s>

<row>

<s>Hæc <lb/>autem infrà demon&longs;trabuntur. </s>

<cell/>

<cell><emph type="italics"/>ducetur.<emph.end type="italics"/> V<emph type="italics"/>nde manife&longs;tum e&longs;t duas proportiones minores æqualitate <expan abbr="inuic&etilde;">inuicem</expan> du ctas proportionem minorem unaquaque illarum producere.<emph.end type="italics"/></cell>

<s><margin.target id="marg6"/>Materiam <lb/>primam e&longs;&longs;e.</s>

</row>

<s><margin.target id="marg7"/>Materiam <lb/>primam <lb/>actu e&longs;&longs;e.</s>

<row>

<cell>XXXVII.</cell>

<s><margin.target id="marg8"/>Materiam <lb/>primam <lb/>quandam <lb/>retinere.</s>

<cell>S<emph type="italics"/>i plures homines, quorum per &longs;e nauim mouere poßint, aut pondus ferre &longs;imul iuncti eam moueant, aut pondus ferant, erunt illæ proportiones coniunctæ non productæ.<emph.end type="italics"/></cell>

<s><margin.target id="marg9"/>Præ&longs;eruandi <lb/>methodus <lb/>vnde ortum <lb/>habuerit.</s>

</row>

<row>

<s><margin.target id="marg10"/>Vacuum non <lb/>e&longs;&longs;e.</s>

<cell>XXXVIII.</cell>

<cell>O<emph type="italics"/>mne corpus tantum re&longs;i&longs;tit motui contrario &longs;uo natúrali, quantum mouetur occulto motu quie&longs;cendo.<emph.end type="italics"/></cell>

<s>Hac ratione lucerna mirabilis excogitata <lb/><arrow.to.target n="marg11"/><lb/>e&longs;t, turris formâ vndequaque conclu&longs;a, &longs;o<lb/>lóque foramine D, contenta, per quod <lb/>oleum ip&longs;um infunditur, donec tota implea<lb/>tur. </s>

</row>

<s>Solida e&longs;t ex &longs;tanno, cúmque conuer<lb/>titur, vt nunc iacet, oleum effundi per D, <lb/>non pote&longs;t.</s>

<row>

<cell>XXXIX.</cell>

<s>Nam &longs;i effunderetur, quod e&longs;t <lb/>in C, de&longs;cenderet grauis & vacui ratione ad <lb/>D: & quod e&longs;&longs;et in B, ad C: & quod e&longs;&longs;et <lb/>in A: ad B: igitur vacuum in A, relinque<lb/>retur. </s>

<cell>A<emph type="italics"/>b æquali aut minore ui quàm &longs;it impedimentum non fit motus.<emph.end type="italics"/></cell>

<s>Ne igitur vacuum in A, relinquatur, <lb/><figure id="id.016.01.008.1.jpg" xlink:href="016/01/008/1.jpg"/><lb/>manet: quare etiam in B, oleum, & in C <lb/>& in D: nihil ergo effunditur. </s>

</row>

<row>

<s>Sed quonam <lb/>pacto igitur dum accen&longs;o ellychnio in F, <lb/>oleum con&longs;umitur, per E, canalem ex ip&longs;o <lb/>D, exire pote&longs;t, itaque ad vacui rationem <pb xlink:href="016/01/009.jpg" pagenum="360"/>rur&longs;us peruenire videtur nece&longs;&longs;arium? </s>

<cell>O<emph type="italics"/>mne corpus &longs;phæricum tangens planum in puncto mouetur ad latus per quamcunque uim, quæ medium diuidere pote&longs;t.<emph.end type="italics"/></cell>

<s>Siue <lb/>enim trahatur caloris vi, &longs;eu &longs;pontè de&longs;cen<lb/>dat oleum, quantum ad vacui rationem at<lb/>tinet, nihil intere&longs;&longs;e videtur. </s>

</row>

<s>Attamen ex<lb/>perimentum edocet, ardere quidem lucer<lb/>nam, & &longs;ic &longs;en&longs;im vacuam reddi: &longs;pontè <lb/>autem oleum nequaquam de&longs;cendere. </s>

<row>

<s>Cau<lb/>&longs;a igitur e&longs;t, quòd ignis calefaciendo rariùs <lb/>ac tenuiùs efficit oleum: id rarius factum <lb/>intume&longs;cit, & per D, foramen exuberat, <lb/>leui&longs;&longs;imáque eius pars interim a&longs;cendit ad <lb/>&longs;ummum lucernæ, vbi A, &longs;crip&longs;imus: quæ <lb/>cum multo aëre referta &longs;it, locum aëre com<lb/>plet, ac &longs;ic &longs;en&longs;im augetur, dum <expan abbr="ole&utilde;">oleum</expan> effundi<lb/>tur. </s>

<cell>S<emph type="italics"/>i fuerint duæ quantitates &longs;umaturque toties <expan abbr="aggregat&utilde;">aggregatum</expan> maioris & minoris, quoties aggregatum minoris & maioris, erit proportio confu&longs;a maioris aggregati ad minus, minor quam multiplicis maioris ad multiplex minoris.<emph.end type="italics"/></cell>

<s>Quamobrem & illud diligenter cauere <lb/>nece&longs;&longs;arium e&longs;t, ne canalis D E F, iu&longs;to bre<lb/><arrow.to.target n="marg12"/><lb/>uior &longs;it, aut ellychnium in F, maius: nam <lb/>vtroque modo oleum nimio calore celeriùs <lb/>intume&longs;cit, adeò vt effundatur. </s>

</row>

<row>

<s>Hac ratione <lb/>excogitarunt Athenien&longs;es lucernam ante <lb/>Mineruæ &longs;imulachrum, quæ toto anno ar<lb/>deret. </s>

<cell>T<emph type="italics"/>rahentium nauim, aut ferentium pondera proportiones in &longs;e inuicem, quomodo ducere oporteat con&longs;iderare.<emph.end type="italics"/></cell>

<s>Nam A B C D, &longs;patium auctum erat <lb/>iuxta multitudinem dierum anni: commo<lb/>diùs for&longs;an fuerit, &longs;i &longs;ubere craticulæ ferreæ <lb/>&longs;u&longs;tententur. </s>

</row>

<s>Ideóque in va&longs;e maximo <lb/>oleum effu&longs;um, per&longs;euerante flamma el<lb/>lychnij &longs;ufficiet in totum annum. </s>

<row>

<cell>XLIII.</cell>

<s>Vt verò <lb/>per&longs;eueret flamma, ellychnium comburi non <lb/>debet. </s>

<cell>P<emph type="italics"/>roductionem ad additionem retrahere.<emph.end type="italics"/></cell>

<s>Tale fit è ligno Carpa&longs;io, hoc enim <lb/>non vritur: aut, vt inferiùs docebimus, è la<lb/>pidum cru&longs;tarum filis. <lb/><arrow.to.target n="marg13"/></s>

</row>

<row>

<s><margin.target id="marg11"/>Lucerna mi<lb/>rabilis.</s>

<cell>XLIIII.</cell>

<cell>S<emph type="italics"/>i fuerit proportio motoris ad id quod e&longs;t maximum non mouens, & &longs;patium & tempus, nota erit etiam reliquorum nota.<emph.end type="italics"/></cell>

<s><margin.target id="marg12"/>Lucernatoto <lb/>anno <expan abbr="ard&etilde;s">ardens</expan>.</s>

</row>

<s><margin.target id="marg13"/>Vbique tria <lb/>&longs;unt, mate<lb/>ria, forma <lb/>& anima.</s>

<row>

<s>Materia igitur vbique e&longs;t, illa verò &longs;ine <lb/>forma e&longs;&longs;e non pote&longs;t, quare & formam vbi<lb/>que e&longs;&longs;e nece&longs;&longs;e e&longs;t: &longs;ed & animam quan<lb/>dam, &longs;eu quòd vbique fiat generatio, &longs;eu <lb/>quod magis ad præ&longs;entem attinet tractatio<lb/>nem, in quocunque corpore, cùm extra lo<lb/>cum &longs;uum fuerit, motus principium e&longs;&longs;e vi<lb/>deatur. </s>

<cell>R<emph type="italics"/>ationem &longs;tateræ o&longs;tendere.<emph.end type="italics"/></cell>

<s>At motus non ab anima, &longs;ed à na<lb/>tura e&longs;t. </s>

</row>

<row>

<s>Mea nihil intere&longs;t, modò ( quod ad <lb/>præ&longs;entem mihi &longs;olùm tractationem nece&longs;<lb/>&longs;arium e&longs;t ) fatearis principium e&longs;&longs;e quod<lb/>dam motus: nam de anima, an omnis natu<lb/>ra anima &longs;it po&longs;teriùs con&longs;iderandum. </s>

<cell>A<emph type="italics"/>n &longs;it aliqua proportio & qualis inter animam & uitas, & &longs;ua corpora con&longs;iderare.<emph.end type="italics"/></cell>

<s>Nunc <lb/>&longs;atis &longs;it, cùm mi&longs;ta omnia &longs;int corporea aut <lb/>&longs;implicia, quædam ex his vt leuia &longs;ursùm, <lb/>alia deorsùm ferri vt grauia: neque verò <lb/>impelluntur: nam violenter ad propria re<lb/>mearent: nec trahuntur: locus enim acci<lb/>dens e&longs;t, & elementum ip&longs;um non trahit <lb/>vbique: vt cùm aqua &longs;ursùm fuerit. </s>

</row>

<s>Inti<lb/>mum igitur e&longs;t, quo mouetur elementum, <lb/>aut ab elemento mixtum. </s>

<row>

<cell>XLVII.</cell>

<s>Dico etenim mix<lb/>tum, vt lapidem, à terra, quæ in ip&longs;o e&longs;t <lb/>deorsùm moueri, aut aqua. </s>

<cell>S<emph type="italics"/>i duo mobilia æqualister in eodem circulo iuxta proprios motus moueantur, productum temporis circuituum inuicem, erit æquale producto differentiæ tempo rum circuitus ductæ in tempus coniunctionis primæ.<emph.end type="italics"/></cell>

<s>Siquidem mix<lb/>ta & ip&longs;a ab elemento, aut elementis, quæ <lb/>in ip&longs;is dominantur, moueri &longs;olent. </s>

</row>

<row>

<s>Cùm <lb/>verò corpora ip&longs;a eiu&longs;dem non fuerint ge<lb/>neris, eodem in loco e&longs;&longs;e non po&longs;&longs;unt: nam </s>

<cell>XLVIII.</cell>

<cell>S<emph type="italics"/>i tria mobilia ex eodem puncto di&longs;cedant, fuerintque duorum ac duorum coniunctiones in temporibus commen&longs;is, illa tria mobilia denuo coniungentur in tem pore producto ex denominatore diui&longs;ionis temporis maioris per minus in minus aut numeratore in maius.<emph.end type="italics"/></cell>

<s><arrow.to.target n="marg14"/><lb/>materia illa duas haberet &longs;imul formas. </s>

</row>

<s>Plus <lb/>verò e&longs;&longs;e ac minùs de eodem corpore, o&longs;ten<lb/>dunt oua vitrea, quæ cùm exuguntur, ex par<lb/>uulo foramine aquam trahunt: nam aër ille <lb/>rarior factus ob attractionem denuò cogi<lb/>tur, occupátque minorem locum quàm priùs, <lb/>atque &longs;ic ne vacuum detur, aquam ad &longs;e <lb/>trahit. </s>

<row>

<s>Igitur aër ip&longs;e cogi pote&longs;t, ac &longs;eip<lb/>&longs;um &longs;ubingredi, eadémque ratione rarior <lb/>euadere: vtque e&longs;t terminus quidam in rari<lb/>tate, qui vacui rationem habet atque &longs;ic <lb/>mouet, ita den&longs;itatis alius, quem &longs;i quis <lb/>præterire nitatur, motum excitat, qui vo<lb/>catur impul&longs;us. </s>

<cell>P<emph type="italics"/>ropofitio mobilis in circulo circuitus tempore dataque ratione di&longs;tantiæ ab illo mo bilis circuitum inuenire, quod ex <expan abbr="eod&etilde;">eodem</expan> puncto di&longs;cedens <expan abbr="c&utilde;alio">cunalio</expan> mobili in dato puncto <expan abbr="cõueniat">conueniat</expan> &longs;ub <expan abbr="quoc&utilde;que">quocunque</expan> numero <expan abbr="circuitu&utilde;">circuituum</expan> <expan abbr="t&etilde;pus">tempus</expan> quoque <expan abbr="cõiunctionis">coniunctionis</expan>.<emph.end type="italics"/></cell>

<s>Fit igitur impul&longs;us, vel cùm <lb/>corpus locum alterius &longs;ubingreditur, vel cùm <lb/>idem corpus adeò cra&longs;&longs;e&longs;cit, vt tantam cra&longs;&longs;i<lb/>tiem ferre non queat: tunc enim locum alium <lb/>atque ampliorem quærens, motum impul&longs;us <lb/>excitat: vtque à vacuo & raritate nimia attra<lb/>ctio fit, &longs;ic à den&longs;itate maiore aut corporum <lb/>coïtione in vnum, impul&longs;io, quæ attractioni <lb/>contraria e&longs;t. </s>

</row>

<row>

<s><margin.target id="marg14"/>Duo corpora <lb/>in eodem loco <lb/>e&longs;&longs;e non po&longs;<lb/>&longs;unt.</s>

<cell>O<emph type="italics"/>mnes circuituum portiones in ei&longs;dem temporibus repetuntur.<emph.end type="italics"/></cell>

<s>Igitur quòd corpora &longs;imilia coëant & ra<lb/><arrow.to.target n="marg15"/><lb/>re&longs;cant, ab experimento acceptum e&longs;t: &longs;ed <lb/>ratio non adeò clara. </s>

</row>

<s>Alexander putat ma<lb/>teriam habere potentiam ad formas diuer<lb/>&longs;as, quarum quantitates materiæ diuer&longs;æ <lb/>&longs;unt: veluti &longs;i ex aqua fiat aër, quòd aër <lb/>minorem po&longs;tulet materiam, materia illa <lb/>rare&longs;cit, quod in igne dum è puluere fit, ma<lb/>nife&longs;tè videmus. </s>

<row>

<s>At conden&longs;ari & rare&longs;ce<lb/>cere, e&longs;t formam ex parte mutare. </s>

<cell>O<emph type="italics"/>perationes dictas exemplo declarare.<emph.end type="italics"/></cell>

<s>Cúm enim <lb/>aër cogitur, ad aquæ naturam tran&longs;it. </s>

</row>

<row>

<s>Vn<lb/>de in cucurbitulis lintea madefacta cogunt <lb/>aërem, atque ideò magis trahunt. </s>

<cell>T<emph type="italics"/>ria mobilia coniuncta in <expan abbr="eod&etilde;">eodem</expan> puncto, quorum duo & duo conueniant in partib. incommen&longs;is inter &longs;e, in perpetuum in nullo unquam puncto conuenient.<emph.end type="italics"/></cell>

<s>Igitur <lb/>quæ rare&longs;cunt vel conden&longs;antur, formam <lb/>partim mutant. </s>

</row>

<s>At forma corporis, formam <lb/>elementi &longs;equitur. </s>

<row>

<s>Repugnat igitur, duo <lb/>corpora &longs;imul e&longs;&longs;e, non ob materiam, quæ <lb/>potentia tantùm in loco e&longs;t, & locum occu<lb/>pat, & decernit &longs;ibi quantitatem pote&longs;tate <lb/>quidem &longs;ola, non actu, &longs;ed ob formarum di<lb/>uer&longs;itatem. </s>

<cell>C<emph type="italics"/>irculorum &longs;e in aduer&longs;um mouentium proportionem declarare.<emph.end type="italics"/></cell>

<s>Conden&longs;ari igitur corpus po<lb/>te&longs;t, quod &longs;imiles habet partes, non autem <lb/>corpora &longs;e penetrare po&longs;&longs;unt. </s>

</row>

<row>

<s>Porrò in con<lb/>den&longs;atione videtur difflari aliquid tenuius, <lb/>aut exprimi. </s>

<cell>LIIII.</cell>

<cell>P<emph type="italics"/>roportio circuli ad &longs;uum diametrum per &longs;imilitudinem e&longs;t quarta pars peripheriæ.<emph.end type="italics"/> R<emph type="italics"/>ur&longs;usque eiu&longs;dem circuli ad peripheriam diametri quarta pars.<emph.end type="italics"/></cell>

<s>Sed &longs;i ita e&longs;t, videbitur quod <lb/>rare&longs;cit, aut conden&longs;at generari. </s>

</row>

<s>Verùm ele<lb/>mentorum mutatio adeò facilis e&longs;t in con<lb/>iuncta & &longs;imilia, vt non omninò vera <lb/>generatio videatur. </s>

<row>

<s>Nam ex aqua in le<lb/>bete aër fit ob ignis calorem: ignis au<lb/>tem nihil generat. </s>

<cell>P<emph type="italics"/>roportionem medicamentorum per ordines &longs;up po&longs;ita æquali proportione in ordinibus per quantitates & proportiones demon&longs;trare.<emph.end type="italics"/></cell>

<s>Non igitur e&longs;t hæc ge<lb/>neratio elementorum, &longs;ed tran&longs;mutatio quæ<lb/>dam ad affinia. </s>

</row>

<row>

<s>Dicemus autem de hoc in<lb/>feriùs. </s>

<cell>P<emph type="italics"/>roportio cuiu&longs;uis binomij ad &longs;uum reci&longs;um, uel ei commen&longs;um e&longs;t duplicata ei quæ ad numeri latus.<emph.end type="italics"/></cell>

<s><margin.target id="marg15"/>Corporum <lb/>vnitio quo<lb/>modo fiat.</s>

</row>

<s>Ergo in vniuer&longs;umtres erunt motus nà<lb/><arrow.to.target n="marg16"/><lb/>turales. </s>

<row>

<s>Primus quidem ac validi&longs;&longs;imus à va<lb/>cui fuga, &longs;ed veriùs à forma elementi, cùm <lb/>maiorem raritatem non admittat, nec ma<lb/>teriæ partes &longs;eparari vnquam queant. </s>

<cell>M<emph type="italics"/>otus rationem ad pondus inuenire.<emph.end type="italics"/></cell>

<s>Cùm <lb/>igitur in follibus apertio maior fit, quàm <lb/>paucus ille aër ferre po&longs;&longs;it, primùm rarior <lb/>redditus, cùm materia prima &longs;eperationem <lb/>non admittat, aër ille non &longs;u&longs;tinens maio<lb/>rem raritatem, aut aliquid ad &longs;e trahit, aut <lb/>folles omninò di&longs;rumpit. </s>

</row>

<row>

<s>Non igitur à va<lb/>cuo motus vllus, &longs;ed à formis ip&longs;is maximè <lb/>aëris, dum ampliùs diuelli nequit, nec &longs;e<lb/>parari, fieri con&longs;ueuit. </s>

<cell>LVIII.</cell>

<cell>Q<emph type="italics"/>uæ ex alto de&longs;cendunt, cur non eandem pro di&longs;tantia motus rationem in libero aëre &longs;eruent con&longs;iderare.<emph.end type="italics"/></cell>

<s>E&longs;&longs;e autem hunc mo<lb/>tum naturalem, o&longs;tendit con&longs;en&longs;us in hoc <lb/>vniuer&longs;i, & obedientia omnium corporum, <lb/>quæ relictis propriis motibus, vt huic &longs;a<lb/>tisfaciant, a&longs;cendunt &longs;pontè grauia, de&longs;cen<lb/>dúntque leuia. </s>

</row>

<s>Secundus ( vt dixi ) è directo <lb/>huic contrarius, &longs;pecie quidem vt primus <lb/>à vacuo fit. </s>

<row>

<s>Hic ne corpora &longs;e mutuò pene<lb/>trent factus videtur, &longs;ed veriùs oppo&longs;itam <lb/>priori ob rationem, ne &longs;cilicet forma plus <lb/>iu&longs;to, quàm debeat materiæ primæ con&longs;e<lb/>quatur, &longs;icut in priore ne iu&longs;to minùs. </s>

<cell>O<emph type="italics"/>mne mobile motum duobus motibus non ad idem tendentibus utroque &longs;eor&longs;um tar dius mouetur &longs;imili motu.<emph.end type="italics"/></cell>

<s>Hunc <pb xlink:href="016/01/010.jpg" pagenum="361"/>igitur ei&longs;dem rationibus quibus priorem, na<lb/>turalem e&longs;&longs;e demon&longs;trauimus à natura pro<lb/>fici&longs;ci, quamvis apud quo&longs;dam ob&longs;curius <lb/>certè con&longs;tat. </s>

</row>

<row>

<s>Neque &longs;atis liquet ex his mo<lb/>tibus, qui &longs;it validior. </s>

<cell>O<emph type="italics"/>mne mobile motu naturali de&longs;cendentis parte, de&longs;cendit grauiore &longs;ecundum gra<emph.end type="italics"/></cell>

<s>Illud tamen clarum <lb/>e&longs;t, ambos motibus omnibus violentis, tum <lb/>etiam elementorum naturalibus potentiores <lb/>multò e&longs;&longs;e, neque vbi impul&longs;us huius ge<lb/>neris, aut attractionis ratio habenda &longs;it, <lb/><arrow.to.target n="marg17"/><lb/>grauis aut leuis penè vllam e&longs;&longs;e curam. </s>

<cell/>

</row>

<s>At<lb/>que ea ratione, quam &longs;uo loco pro&longs;eque<lb/>mur, tanta vi tormenta bellica pilas illas fer<lb/>reas emittunt, cùm nulla vis alia impellen<lb/>do quicquam &longs;imile po&longs;&longs;it efficere. </s>

<row>

<s>Quòd <lb/>ni&longs;i machinæ periculum fracturæ ob&longs;ta<lb/>ret, nihil prohiberet ex Germaniis in In<lb/>diam, quoniam ex ordine e&longs;t vniuer&longs;i, im<lb/>pelli. </s>

<cell/>

<cell><emph type="italics"/>uitatis centrum.<emph.end type="italics"/></cell>

<s><margin.target id="marg16"/>Tres e&longs;&longs;e mo<lb/>tus natura<lb/>les à princi<lb/>pio.</s>

</row>

<s><margin.target id="marg17"/>Bellicæ ma<lb/>chinæ impel<lb/>lunt ordine <lb/>vniuer&longs;i.</s>

<row>

<s>Tertius autem motus grauium e&longs;t ad in<lb/>ferna, leuium ad &longs;uperna: quem planè om<lb/>nes naturalem e&longs;&longs;e fatentur, quò minùs de <lb/>eo laboro. </s>

<cell>P<emph type="italics"/>roportionum ictus ad pondus rei & di&longs;tantiam generaliter con&longs;iderare.<emph.end type="italics"/></cell>

<s>Sed nec &longs;i concedatur nobis alios <lb/>motus naturales dici debere, modò &longs;emper <lb/>his, vt dixi, contingant rationibus, quic<lb/>quam ad ea, quæ declarare propo&longs;ueramus <lb/>oberit. </s>

</row>

<row>

<s>Erat & quartum genus naturalis mo<lb/>tus, quo quædam ad alia mouentur: quod <lb/>quia generale non e&longs;t, ad locum &longs;uum trans<lb/>feretur, velut de Herculeo vocato lapide, <lb/>& ferro, electro atque fe&longs;tuca. </s>

<cell>P<emph type="italics"/>roportionem motoris in plano ad motorem, qui eleuat pondus iuxta id quod mouet, inuenire.<emph.end type="italics"/></cell>

<s>His igitur de<lb/>mon&longs;tratis tanquam principiis ratio con&longs;ur<lb/>git machinæ Cte&longs;ibicæ, quæ &longs;ic con&longs;tat. <lb/><arrow.to.target n="marg18"/></s>

</row>

<s><margin.target id="marg18"/>Machina <lb/>Ctc&longs;iaica.</s><figure id="id.016.01.010.1.jpg" xlink:href="016/01/010/1.jpg"/>

<row>

<cell>LXIII.</cell>

<s>Catinus A, æ<lb/>reus, cuius &longs;um<lb/>mum os per quod <lb/>effundi aqua de<lb/>bet B. </s>

<cell>O<emph type="italics"/>mne graue quanto proximius alligatum plano, tantò facilius trabitur.<emph.end type="italics"/></cell>

<s>In imo eius <lb/>duo foramina C, <lb/>& D, &longs;uper qui<lb/>bus axes aut coria <lb/>ita collocentur vt <lb/>in follibus: quæ <lb/>ex inferiore par<lb/>te eleuentur ver<lb/>sùs A, &longs;ed &longs;i com<lb/>primantur, occludant ob&longs;cula illa: hæreánt<lb/>que catino ex o&longs;culis C, & D, fi&longs;tulæ duæ, <lb/>dextra ac &longs;ini&longs;tra producantur E, & F, & <lb/>modiolis in&longs;erantur in G, & in H. </s>

</row>

<row>

<s>Modioli <lb/>inanes &longs;unt, & in aqua mer&longs;i, in imo haben<lb/>tes foramina K, & L, in medio: &longs;upra quæ <lb/>axes cum corio vt in catino, qui eleuari po&longs;<lb/>&longs;int ad &longs;uperiùs: cùm verò premuntur o&longs;cula, <lb/>ad vnguem concludant. </s>

<cell>LXIIII.</cell>

<cell>O<emph type="italics"/>mne mobile quantò latius tanto tardius moustur in plano.<emph.end type="italics"/></cell>

<s>In modiolis autem <lb/>emboli ma&longs;culi M, & N, torno politi, & oleo <lb/><arrow.to.target n="marg19"/><lb/>&longs;ubacti, vt modiolos ad amu&longs;&longs;im impleant: <lb/>inde vectibus & tegulis ita &longs;int aptati, vt vl<lb/>trò, citróque permeantes, cùm M, a&longs;cendit, <lb/>exinanitúrque &longs;ubiectum vas, alterna vice <lb/>N, de&longs;cendat, & impleat embolum, expri<lb/>mátque quicquid in eo continetur. </s>

</row>

<s>Hac ra<lb/>tione parata cùm ex O, trahitur M, embo<lb/>lus ma&longs;culus, locus Q, modioli exinanitur: <lb/>quare eleuatur axis & corium &longs;uprà K, aquá<lb/>que a&longs;cendit donec impleatur modiolus ex <lb/>primi motus ratione: interim verò cùm N, <lb/>pre&longs;&longs;us &longs;it, incipiat ex imo trahi alterno mo<lb/>tu, <expan abbr="de&longs;cendétq;">de&longs;cendétque</expan> M, embolus <expan abbr="cúmq;">cúmque</expan> aqua, quæ <lb/>in &longs;patio Q, continebatur non po&longs;&longs;it effluere, <lb/>M, concludente &longs;uperiùs modioli capacita<lb/>tem ad vnguem: nec de&longs;cendere per K, quo<lb/>niam axis foramen premit, & quò magis vr<lb/>getur pondere & impetu ex &longs;uperiore loco <lb/>ab aqua, ita magis exqui&longs;itè hæret K, fora<lb/>mini: &longs;equitur vt aqua per G, exeat, qua &longs;o<lb/>lùm exitus patet, a&longs;cendén&longs;que per fi&longs;tulam <lb/>E, ingreditur eleuans operculum in catinum <lb/>per C, <expan abbr="foram&etilde;">foramen</expan>, donec catinus impleatur: pò&longs;t <lb/>ce&longs;&longs;ante impul&longs;u ex E, &longs;ub&longs;idet corium, & <lb/>axis in C, vá&longs;que A, plenum manet. </s>

<row>

<s>Interim <lb/>verò dnm M, ad K, de&longs;cendit, N, ad &longs;ummum <lb/>modioli <expan abbr="a&longs;c&etilde;dit">a&longs;cendit</expan>, modiolú&longs;que impletur aqua <lb/>eadem ratione: vnde cum rur&longs;us premitur, <lb/>exprimit aquam per H, in F, & per D, eadem <lb/>ratione in modiolum, qui cùm iam plenus &longs;it <lb/>aqua, nec illa per C, regredi po&longs;&longs;it, cùm axis <lb/>& corium eò magis hæreant foramini, quò <lb/>magis ab aqua ex &longs;uperiore parte premun<lb/>tur, &longs;equitur vt ex &longs;ecundi motus naturalis <lb/>ratione, quo etiam grauia &longs;ursùm feruntur, <lb/>vt aqua per A, in B, a&longs;cendens effundatur, at<lb/>que ita alternante motu ac pleno &longs;emper ca<lb/>tino, vt effluere ex imo K, & L, in altum a&longs;<lb/>cendens, quantumlibet per B, nunquam de<lb/>&longs;inat. </s>

<cell>P<emph type="italics"/>roportionem duorum mobilium inter &longs;e cum auxilio medij inuenire.<emph.end type="italics"/></cell>

<s><margin.target id="marg19"/>Vitruuius <lb/>lib.

</row>

<row>

10. 6. 12.</s>

<cell>P<emph type="italics"/>roportionem laterum eptagoni, & &longs;ubten&longs;arum con&longs;iderare, & quæ à reflexa proportione pendent.<emph.end type="italics"/></cell>

<s>Eiu&longs;dem argumenti e&longs;t tuba nauium, qua <lb/>&longs;olent naues aqua periclitantes euacuare. <lb/></s>

</row>

<s>Cuius exemplo con&longs;tructa e&longs;t machina Bar<lb/>tholomæi Brambillæ, quam nos vidimus <lb/>Mediolani, nulla ex parte antiquis artificio <lb/>inferior. </s><figure id="id.016.01.010.2.jpg" xlink:href="016/01/010/2.jpg"/>

<row>

<cell>LXVII.</cell>

<s>Machina Brambilica.</s>

<cell>S<emph type="italics"/>i fuerint aliquot quantitates ab una quantitate aliæque totidem ab eadem analogæ, erit proportio tertiæ unius ordinis ad tertiam alterius, ut &longs;ecundæ ad &longs;ecundum duplicata, & quartæ ad quartam triplicata, quintæ ad quintam quadruplicata, atque &longs;ic de alijs.<emph.end type="italics"/></cell>

<s>BD, tuba, inanis in<lb/>tus, lignea, rotunda, ve<lb/>ctibus & regulis fixa, <lb/>latior parte &longs;uperiore <lb/>tota DM, inferiore ar<lb/>ctior: qua parte exci<lb/>pitur C, va&longs;e aquæ im<lb/>mer&longs;o, & vndique à la<lb/>teribus perforato, vt <lb/>aqua ingredi po&longs;&longs;it: la<lb/>pilli autem & arena <lb/>minimè, fundo va&longs;is C, <lb/>&longs;olido. </s>

</row>

<row>

<s>Sic fiet vt tuba <lb/>aquam ex va&longs;e puram, <lb/>cùm opus fuerit, non <lb/>lapillos aut arenam, <lb/>quibus machina impe<lb/>diretur, hauriat. </s>

<cell>LXVIII.</cell>

<cell>P<emph type="italics"/>ropo&longs;itio collectorum ab<emph.end type="italics"/> E<emph type="italics"/>uclide &<emph.end type="italics"/> A<emph type="italics"/>rchimede.<emph.end type="italics"/></cell>

<s>In loco <lb/>M, vbi arctior pars la<lb/>tiori committitur, co<lb/>rium &longs;uperiùs ex parte <lb/>M, annectitur, cui &longs;u<lb/>perimminet lamina te<lb/>nuis plumbea, vt cùm <lb/>eleuetur ex parte Q, <lb/>pondere &longs;uo denuò cadat, & integat canalem <lb/>L, exqui&longs;ite. </s>

</row>

<s>Embolus autem ma&longs;culus AE, <lb/>minor tubæ latitudine, &longs;ed <expan abbr="tam&etilde;">tamen</expan> in &longs;upremo, <lb/>vbi e&longs;t D, ad amu&longs;&longs;im ob&longs;truat tubæ <expan abbr="foram&etilde;">foramen</expan>. <lb/></s>

<row>

<s>Inane autem &longs;it OP. </s>

<cell>P<emph type="italics"/>ropo&longs;itio collectorum ex quatuor libris<emph.end type="italics"/> A<emph type="italics"/>pollonij<emph.end type="italics"/> P<emph type="italics"/>ergei &<emph.end type="italics"/> <expan abbr="q.">que</expan> S<emph type="italics"/>ereni.<emph.end type="italics"/></cell>

<s>Ex imo emboli tres vir<lb/>gæ ferreæ &longs;olidæ prodeant, ad latera tubæ in<lb/>tus pertingentes, quas corio circumue&longs;ties, <lb/>ne contactu tubam exulcerent. </s>

</row>

<row>

<s>Hæ tripodis <lb/>imaginem referunt, inferiùs latiores ac ma<lb/>gis di&longs;tantes, vbi F, quàm &longs;uperiùs vbi E. <lb/></s>

<cell>S<emph type="italics"/>i fuerint tres quantitates in continua proportione, aliæque totidem in continua proportione poterunt con&longs;tituere tres quantitates in æquali differentia peruer&longs;im copulatæ.<emph.end type="italics"/></cell>

<s>Manife&longs;tum e&longs;t igitur, totum &longs;patium iuxta <lb/>N, e&longs;&longs;e inane, nec præter virgulas aliquid <lb/>e&longs;&longs;e in eo: quo fit vt peruia &longs;it vita ex O, & <lb/>P, in N, atque vici&longs;&longs;im ex N, in O, & P: <expan abbr="tot&utilde;">totum</expan> <pb xlink:href="016/01/011.jpg" pagenum="362"/>enim &longs;patium &longs;upra F, inane e&longs;t, nec in eo <lb/>aliquid continetur præter embolum & vir<lb/>gulas. </s>

</row>

<s>In imo harum virgularum circulus F, <lb/>câpitibus earum annexus con&longs;tituatur, nec <lb/>totus inanis, &longs;ed in medio tantùm, & vbi <lb/>foramen relinquitur, corio &longs;upernè, ac &longs;u<lb/>per corium plumbi lamina tenui, vt in M, <lb/>dictum e&longs;t, integatur, &longs;ic vt cùm integitur, <lb/>ne aër po&longs;&longs;it tran&longs;ire, & corium tamen cum <lb/>plumbo eleuari po&longs;&longs;it ver&longs;us N, & foramen <lb/>ip&longs;um detegere. </s>

<row>

<s>Hoc itaque fiet, &longs;i corium <lb/>media qua&longs;i parte annexum fuerit circulo, <lb/>capita virgarum continente: reliqua parte <lb/>di&longs;iunctum, ac &longs;olùm ad amu&longs;&longs;im foramen <lb/>illud, cùm hæret, occludens. </s>

<cell>P<emph type="italics"/>roportionem leuitatis ponderis per uirgam torcularem attracti ad rectam &longs;u&longs;pen&longs;ionem inuenire.<emph.end type="italics"/></cell>

<s>Ex ip&longs;is rur&longs;us <lb/>virgarum capitibus tres aliæ virgæ rectà <lb/>prodeant, lateribus intror&longs;um tubæ hæren<lb/>tes. </s>

</row>

<row>

<s>Has corium circumambit vndequaque <lb/>ab F, &longs;uprema parte v&longs;que in G, hærens ad <lb/>amu&longs;&longs;im lateribus tubæ intror&longs;um, ne vel aër <lb/>ex K, in N, po&longs;&longs;it permeare. </s>

<cell>LXXII.</cell>

<cell>P<emph type="italics"/>roportionem ponderis &longs;phæræ pendentis ad a&longs;cendentem per accliue planum inuenire.<emph.end type="italics"/></cell>

<s>Ita fiet in H, mo<lb/>diolum, &longs;ed inuer&longs;um, videatur: e&longs;t enim fun<lb/>dus F, & corio circumue&longs;titus vndequaque <lb/>tereti forma, & in G, apertus ac patens. </s>

</row>

<s>Quo <lb/>peracto ita aptetur A, embolus, vt citrò, vl<lb/>tróque commeare modò de&longs;cendendo v&longs;que <lb/>ad M, parte G, ima modioli inuer&longs;i, modò <lb/>&longs;ursùm vbi nunc pingitur, retrahi po&longs;&longs;it. </s>

<row>

<cell>LXXIII.</cell>

<s>His <lb/>itaque &longs;ic di&longs;po&longs;itis, iaceat G, &longs;uper M Q, & <lb/>incipiat eleuari, tunc aër contentus in &longs;patio <lb/>H, rarior factus demùm trahit Q, & eleuat: <lb/>cuius &longs;ucce&longs;&longs;u a&longs;cendit aër ex L, in K, &longs;pa<lb/>tium, huius &longs;ucce&longs;&longs;u aqua a&longs;cendit ex B, in <lb/>L. </s>

<cell>P<emph type="italics"/>roportionem ponderum attractorum penes figuram in plano inuenire.<emph.end type="italics"/></cell>

<s>Cùm autem embolus de&longs;cendit aëris im<lb/>pul&longs;u, & plumbi grauitate, illicò Q, de&longs;cen<lb/>dit: quare aqua, quæ e&longs;t in L, nece&longs;&longs;ariò ma<lb/>net: nam reclu&longs;o operculo MQ, &longs;i aqua de&longs;<lb/>cenderet, conuelleretur modicus ille aër, qui <lb/>e&longs;&longs;et in &longs;uprema parte L, &longs;upra aquam, cùm <lb/>non po&longs;&longs;it alium haurire aërem ex K, pro<lb/>pter periculum MQ: aër verò qui in K, con<lb/>tinebatur, dum de&longs;cendit per G, eleuans <lb/>operculum F, effugit &longs;patium O, & per P, <lb/>foramen exit foràs: ita &longs;æpiùs repetito a&longs;cen<lb/>&longs;u, de&longs;cen&longs;úque G, & emboli, impletur lo<lb/>cus L, aqua, pò&longs;t rur&longs;us eleuato G, & ob <lb/>motus primi rationem, ne aër in K, nimis <lb/>conuellatur, eleuato Q M, operculo aqua <lb/>ingreditur, &longs;patium K, donec impleatur, & <lb/>&longs;imul cum eo &longs;patium H, quod (vt dixi) com<lb/>mune e&longs;t cum K, quia G, e&longs;t medioli os pa<lb/>tens, & nulla ex parte conclu&longs;um. </s>

</row>

<row>

<s>Sic igitur <lb/>iam plenum, & rur&longs;us embolus de&longs;cendat: <lb/>aqua igitur quæ in H, e&longs;t, eleuabit opercu<lb/>lum F, & implebit &longs;patia N, & O. </s>

<cell>LXXIIII.</cell>

<cell>P<emph type="italics"/>roportionem concutientis ad concu&longs;&longs;um in&longs;tabili inuenire.<emph.end type="italics"/></cell>

<s>Cùm au<lb/>tem &longs;ursùm trahitur embolus, ne aqua, quæ <lb/>in O. a&longs;cenderat, rursùm de&longs;cendat, prohibet <lb/>operculum in F, quod grauitate tum propria, <lb/>tum aquæ &longs;uperincumbentis, cadens obturat <lb/>foramen. </s>

</row>

<s>Itaque con&longs;tat hac machina aquam <lb/>&longs;emper a&longs;cendere, & nunquam po&longs;&longs;e de&longs;<lb/>cendere: vnde cùm peruenerit ad P, effun<lb/>ditur per P, os tubæ in locum, quem volue<lb/>ris, tuncque minimo labore quantum voles <lb/>aquæ ex B, exhauries: nam plena iam tuba <lb/><arrow.to.target n="marg20"/><lb/>facilior fit motus emboli A. </s>

<row>

<s>Tubæ verò qui<lb/>bus &longs;iccantur naues, tum fontes & &longs;caturigi<lb/>nes aquarum, &longs;impliciore con&longs;tructione con<lb/>&longs;tant. </s>

<cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> immoti in aqua, ad <expan abbr="immot&utilde;">immotum</expan> in terra in excipiendo <expan abbr="ict&utilde;">ictum</expan> inuenire.<emph.end type="italics"/></cell>

<s>Manente ratione B, & C, ne lapides <lb/>machinam impediant, embolus quatuor <lb/>habet corij fru&longs;ta in imo, & totidem iuxtà, <lb/>duorum tamen cubitorum, aut paulò plus <lb/>&longs;patio di&longs;tincta, quæ &longs;upernè alligantur. </s>

</row>

<row>

<s>Pal<lb/>mi longitudo e&longs;t eorum: & vt trahuntur, <lb/>aqua ingreditur vacui ratione: cùm de&longs;cen<lb/>dunt, dilatantur propter aëris impul&longs;um, &longs;ed <lb/>& ob celeritatem aliquid rur&longs;us permeat <lb/>aquæ &longs;uperiùs. </s>

<cell>LXXVI.</cell>

<cell>P<emph type="italics"/>roportionem <expan abbr="duor&utilde;">duorum</expan> mobilium &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> <expan abbr="concurrenti&utilde;">concurrentium</expan> per <expan abbr="rectã">rectam</expan> inuenire.<emph.end type="italics"/></cell>

<s>Itaque non &longs;olùm trahen<lb/>do, &longs;ed & premendo aqua a&longs;cendit. </s>

</row>

<s>Iam igi<lb/>tur declarauimus exemplum quietis, quæ <lb/>fit per vacui fugam, hanc tamen docui<lb/>mus potiùs debere dici raritatis violentiam: </s>

<row>

<cell>LXXVII.</cell>

<s><margin.target id="marg20"/>Tubæ <expan abbr="hauri&etilde;-tes">haurien<lb/>tes</expan> aquas.</s><figure id="id.016.01.011.1.jpg" xlink:href="016/01/011/1.jpg"/>

<cell>P<emph type="italics"/>roportionem motus obliqui ad motum rectum in nauibus inuenire.<emph.end type="italics"/></cell>

<s>Horologij <lb/>mola.<lb/>fit enim à forma elementi fu<lb/>gientis maiorem, quam ei con<lb/>uenire po&longs;&longs;it, raritatem. </s>

</row>

<row>

<s>Sic ea<lb/>dem ratione appellabimus im<lb/>pul&longs;um, &longs;eu &longs;it motus, &longs;eu quies, <lb/>à den&longs;itate, &longs;icut tertium ele<lb/>menti motum, &longs;eu grauis &longs;it, &longs;eu <lb/>leuis. </s>

<cell>LXXVIII.</cell>

<cell>P<emph type="italics"/>roportionem nauis ad triremes quotuis concurrentes demon&longs;trare.<emph.end type="italics"/></cell>

<s>Exemplo igitur lucernæ <lb/>quies olei in &longs;uprema parte <lb/>o&longs;ten&longs;a e&longs;t. </s>

</row>

<s>Secundo autem <lb/>exmplo motus attractionis ob <lb/>raritatem, & impul&longs;us ob den<lb/>&longs;itatem, in machina Cte&longs;ibica <lb/>demon&longs;tratur. </s>

<row>

<cell>LXXIX.</cell>

<s>Hoc tertio &longs;imi<lb/>liter <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> motus exemplar, <lb/>ac quietis etiam grauis præter <lb/>naturam. </s>

<cell>P<emph type="italics"/>roportionem medicamentorum purgantium inuicem declarare<emph.end type="italics"/></cell>

<s>Supere&longs;t modò, vt <lb/>motum à &longs;ola raritate, &longs;eu à va<lb/>cuo quarto exemplo doceamus: <lb/>verùm id inferiùs exponere <lb/>oportet, ratione quadam &longs;in<lb/>gulari, cùm motus elemento<lb/>rum docebimus. </s>

</row>

<row>

<s>Nunc verò <lb/>motum qui ob &longs;olam fit den&longs;i<lb/>tatem aggrediemur, cuius <lb/>exemplum in tormentis bellicis <lb/>patuit, in quibus impul&longs;us mo<lb/>tus &longs;olum apparet. </s>

<cell>P<emph type="italics"/>roportionem motus &longs;ecundum obliquum ad rectum in &longs;pacio declarare.<emph.end type="italics"/></cell>

<s>Eiu&longs;dem planè generis e&longs;t <lb/>motus, qui fit in molis horologiorum, &longs;i<lb/>cut bali&longs;tarum ex raritate, tum &longs;corpio<lb/>num, ac eiu&longs;cemodi generis tormentorum: <lb/>nam cùm nimium tenditur neruus, vt &longs;e <lb/>contrahat, impul&longs;u mouetur acriore, ac <lb/>impo&longs;itum lapidem, aut &longs;agittam impel<lb/>lit. </s>

</row>

<s>Itaque ad motum raritatis hæc ratio re<lb/>ducitur. </s>

<row>

<cell>LXXXI.</cell>

<s>Contraria igitur ( vr dixi ) ratio<lb/>ne, mola torquetur in horologio: nam <lb/>chalybs mollis redditus, in tenuem bra<lb/>cteam prolongam & &longs;trictam, vt in figu<lb/>ra vides, redigitur; inde per vim in or<lb/>bem arcti&longs;&longs;ime colligitur, cap&longs;ulæque in<lb/>cluditur. </s>

<cell>Q<emph type="italics"/>ualis &longs;it angulus, per quem pote&longs;t moueri nauis ad rectum explorare.<emph.end type="italics"/></cell>

<s>Funis autem tenuis, &longs;ed validior, <lb/>circumuoluitur cap&longs;ulæ, cuius extremum <lb/>axi rotæ latiori nectitur. </s>

</row>

<row>

<s>Ita fit, vt dum <lb/>chalybs den&longs;itate nimia pre&longs;&longs;us tenditur, <lb/>cap&longs;ulam circumuoluat, quæ trahit funem: <lb/>inde axis &longs;en&longs;im circumuolutus, rota à qua <lb/>denticulis implicatis aliæ circumaguntur, <lb/>&longs;ecum agit. </s>

<cell>LXXXII.</cell>

<cell>P<emph type="italics"/>roportionem uelorum indagare.<emph.end type="italics"/></cell>

<s>Sextum exemplum e&longs;t, quónam <lb/><arrow.to.target n="marg21"/><lb/>pacto quies ex impul&longs;u po&longs;&longs;it contingere. <lb/></s>

</row>

<s>Huius generis e&longs;t vrceus aqua plenus fi&longs;tu<lb/>lam inanem habens: cùm enim fi&longs;tula ver<lb/>titur inferiùs, aqua ip&longs;a pendere vide<lb/>tur. </s>

<row>

<cell>LXXXIII.</cell>

<s>Simili ratione lapides &longs;uper aquam <lb/>iacti re&longs;iliunt: & &longs;itula aqua plena cir<lb/>cumuelociter acta, non effundit aquam: <lb/>quia cùm tempus de&longs;it aëris diui&longs;ioni, ne <pb xlink:href="016/01/012.jpg" pagenum="363"/>nimium comprimatur, aqua &longs;ub&longs;i&longs;tit. </s>

<cell>P<emph type="italics"/>roportionem rece&longs;&longs;us à recta uia ad obliquitatem inue&longs;tigare.<emph.end type="italics"/></cell>

<s>Ea<lb/><arrow.to.target n="marg22"/><lb/>dem ratione plumbea lamina lata aquæ &longs;u<lb/>pernatat: nam de&longs;cendendo partes, quæ in <lb/>medio &longs;unt, non habentes, quò diffugiant, <lb/>nimium comprimerentur: vel &longs;i antè di<lb/>labantur, vacuum relinqui in medio ne<lb/>ce&longs;&longs;e e&longs;t: non pote&longs;t igitur vllo pacto de&longs;<lb/>cendere, ni&longs;i ad vnam partem priùs incli<lb/>netur. </s>

</row>

<row>

<s><margin.target id="marg21"/>Situla aqua <lb/>plena <expan abbr="circ&utilde;-uoluta">circun<lb/>uoluta</expan> cur <lb/>non effunda<lb/>tur.</s>

<cell>LXXXIIII.</cell>

<cell>D<emph type="italics"/><expan abbr="i&longs;tantiã">i&longs;tantiam</expan> centri terræ à centro mundi per motum lapidis<emph.end type="italics"/> H<emph type="italics"/>erculei declarare.<emph.end type="italics"/></cell>

<s><margin.target id="marg22"/>Plumbea, la<lb/>mina lata &longs;i <lb/>æqualiter <lb/>aqua in&longs;i<lb/>&longs;tat, mergi <lb/>cur non po&longs;<lb/>&longs;it.</s>

</row>

<s>Quòd igitur à raritate fiant hæc, & quo<lb/>modo, o&longs;ten&longs;um e&longs;t. </s>

<row>

<cell>LXXXV.</cell>

<s>Operæpretium autem <lb/>erit, vt demon&longs;tremus, hos motus à vacuo <lb/>nulla ratione fieri po&longs;&longs;e. </s>

<cell>P<emph type="italics"/>roportio ponderis unius grauis ad aliud &longs;ub eadem men&longs;ura e&longs;t ueluti eiu&longs;dem ad differentiam ponderis ua&longs;is repleti ex altero graui, & ex ambobus detracto priore.<emph.end type="italics"/></cell>

<s>Hoc autem infrà per <lb/>exqui&longs;itas rationes declarabitur. </s>

</row>

<row>

<s>Nunc autem <lb/>&longs;ufficiat tantum declara&longs;&longs;e &longs;en&longs;ibili quodam <lb/>experimento, quantum ad rationem in&longs;tru<lb/>mentorum docendam &longs;ufficiat. </s>

<cell>LXXXVI.</cell>

<cell>S<emph type="italics"/>i circuli in æ quales &longs;eu in &longs;phæra &longs;eu in plano &longs;e &longs;ecuerint, nunquàm oppo&longs;itos angulos æquales habent.<emph.end type="italics"/></cell>

<s>Nam &longs;i fati&longs;<lb/>cant rimis machinæ, iam nullus vacui metus <lb/>e&longs;t, & tamen trahunt, &longs;ed tantò debilius, & <lb/>maiore difficultate, quantò hiant magis. <lb/></s>

</row>

<s>Hócque fundamento machinæ omnes con<lb/>&longs;tant, quæ alioquin ab indiui&longs;ibili quadam <lb/>ratione pendêrent, e&longs;&longs;étque ob id omnes &longs;ta<lb/>tim inutiles, vel &longs;altem non diuturnæ. </s>

<row>

<cell>LXXXVII.</cell>

<s>In non <lb/>exactis ergo operibus atque vetu&longs;tis manet <lb/>etiam v&longs;us: fru&longs;tatio verò pro erroris magni<lb/>tudine. </s>

<cell>P<emph type="italics"/>roportiones craßitiei aquæ ad <expan abbr="a&etilde;r&etilde;">aerrem</expan> in <expan abbr="cõparatione">comparatione</expan> ad radios demon&longs;trare.<emph.end type="italics"/></cell>

<s>Attractio igitur à forma fit, quæ <expan abbr="d&utilde;">dum</expan> <lb/>metuit aliam con&longs;equi raritatem, ne pereat, <lb/>quantum pote&longs;t, re&longs;i&longs;tit. </s>

</row>

<row>

<s>O&longs;tendimut enim <lb/>&longs;uperiùs, mutata &longs;ub&longs;tantia atque den&longs;itate, <lb/>mutari quoque formam. </s>

<cell>LXXXVIII.</cell>

<cell>I<emph type="italics"/><expan abbr="n&longs;trument&utilde;">n&longs;trumentum</expan><emph.end type="italics"/> A<emph type="italics"/>colingen, quo momenta temporum <expan abbr="deprehendãtur">deprehendantur</expan> fabricare.<emph.end type="italics"/></cell>

<s>Quòd &longs;i metu vacui <lb/>fieret attractio, qua&longs;i con&longs;entiente vniuer&longs;o, <lb/>e&longs;&longs;et hæc attractio infinita, &longs;ed non e&longs;t, ve<lb/>rùm pro quantitate formæ, & elementi ac <lb/>in&longs;trumenti continentis. </s>

</row>

<s>Nam canalis paruus <lb/>aquam modicam haurit, nec trahit plumbi <lb/>magnam molem. </s>

<row>

<cell>LXXXIX.</cell>

<s>Indicio igitur hoc e&longs;t, à <lb/>forma fieri <expan abbr="hãc">hanc</expan> attractionem, & pro viribus <lb/><arrow.to.target n="marg23"/><lb/>eius atque magnitudine. </s>

<cell>P<emph type="italics"/>roportionem den&longs;itatis aquæ ad aërem per pondera inuenire.<emph.end type="italics"/></cell>

<s>E&longs;t & tertia conie<lb/>ctura, quòd plana quæ non fati&longs;cunt, <expan abbr="attam&etilde;">attamen</expan> <lb/>di&longs;iunguntur. </s>

</row>

<row>

<s>At hoc fieri nequiret, ni&longs;i ad<lb/>mi&longs;&longs;o vacuo. </s>

<cell>R<emph type="italics"/>ationem impetus uiolenti extra mißi ponderis ad æqualitatem reducere.<emph.end type="italics"/></cell>

<s>Inter plana igitur quæcunque <lb/>dum clauduntur, aër intercipitur, qui vetat <lb/>plana di&longs;iungi quoad licet. </s>

</row>

<s>Sed cum (vt dixi) <lb/>pro &longs;ui robore &longs;olùm impediat, maiore nixu <lb/>vincitur. </s>

<row>

<s>Solùm illud obiicies, quòd à minore <lb/>aëre minùs hæc di&longs;iunctio impediretur, at <lb/>magis tamen impeditur. </s>

<cell>P<emph type="italics"/>roportionem grauis cubi, & &longs;phærici æqualium in accliui, & de&longs;cen&longs;us eorum demon&longs;trare.<emph.end type="italics"/></cell>

<s>Vt enim magis pla<lb/>na ad vnguem coierint, eò minùs aëris inter<lb/>cipitur, & tamen eò difficilius diuelluntur. <lb/></s>

</row>

<row>

<s>Sed cau&longs;a e&longs;t, quia magis nece&longs;&longs;e e&longs;t aërem <lb/>illum à propria forma recedere, quò magis <lb/>rare&longs;cit. </s>

<cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> ponderis æqualis iuxta longitudinis <expan abbr="cõparation&etilde;">comparationem</expan> demon&longs;trare.<emph.end type="italics"/></cell>

<s><expan abbr="Cõ&longs;equitur">Con&longs;equitur</expan> enim, vt dictum e&longs;t, alia <lb/>&longs;ub&longs;tantia quædam, & noua generatio, quæ <lb/>vt à priore magis recedit, eò maiore labore <lb/><expan abbr="cõficitur">conficitur</expan>. </s>

</row>

<s>At dices: Aëre rarefacto, quid aliud <lb/>pote&longs;t generari quàm ignis? </s>

<row>

<cell>XCIII.</cell>

<s>Ignis autem ca<lb/>lidi&longs;&longs;imus: at inter plana nulla e&longs;t manife&longs;ta <lb/>caliditas, imò frigus. </s>

<cell>P<emph type="italics"/>ropter qd in <expan abbr="cõcußione">concußione</expan> <expan abbr="etiã">etiam</expan> leui nauis loco moueatar <expan abbr="o&longs;t&etilde;dere">o&longs;tendere</expan>.<emph.end type="italics"/> V<emph type="italics"/>nde manifi <expan abbr="&longs;i&utilde;">&longs;ium</expan> e&longs;t duas naues &longs;ibi <expan abbr="inuic&etilde;">inuicem</expan> occur&longs;antes retrocedere, & <expan abbr="quãt&utilde;">quantum</expan> <expan abbr="retrocedãt">retrocedant</expan> ambæ.<emph.end type="italics"/></cell>

<s>Sed non e&longs;t ignis &longs;eu <lb/>æther calidus: hoc enim inferiùs declarabi<lb/>tur. </s>

</row>

<s>Quod enim humidum e&longs;t, &longs;i attenuetur, <lb/>non in ignem, &longs;ed in ætheris tran&longs;it natu<lb/>ram: aër autem humidus, & æther minimè <lb/>calidus e&longs;t. </s>

<row>

<cell>XCIIII.</cell>

<s>Confe&longs;tim verò alio in ingredien<lb/>te aëre, fit mixtio. </s>

<cell>S<emph type="italics"/>i <expan abbr="quãtitas">quantitas</expan> aliqua nota atque proportio erit producta, <expan abbr="quãtitas">quantitas</expan> nota &longs;imiliter.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i duæ proportiones notæ fuerint, erit producta ex his atque diui&longs;a coniunctaque atque detracta nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit totius ad partem proportio nota, erit et ad aliam partem nota: & alterius partis ad <expan abbr="alterã">alteram</expan> uno minor.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit partis ad partem, erit ad totum monade minor atque nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerit unius <expan abbr="quãtitatis">quantitatis</expan> ad duas <expan abbr="quãtitates">quantitates</expan> proportio nota, erit & <expan abbr="cõfu&longs;a">confu&longs;a</expan> ex eis nota.<emph.end type="italics"/> E<emph type="italics"/>t &longs;i fuerint trium quantitatum omiologarum, aut quatuor analogarum omnes præter unam cognitæ, erunt & illa alia cognita.<emph.end type="italics"/></cell>

<s><margin.target id="marg23"/>Plana iun<lb/>cta quomodo <lb/>di&longs;iungi po&longs;<lb/>&longs;int.</s>

</row>

<row>

<s>Hæc &longs;atis &longs;int de his motibus duobus prio<lb/>ribus, tum quiete, quæ ab eis fit, exempla, <lb/>cùm hîc non &longs;it præ&longs;entis in&longs;tituti de ma<lb/>chinis loqui, &longs;ed in duodecimo libro de <expan abbr="Rer&utilde;">Rerum</expan> <lb/>varietate. </s>

<cell>C<emph type="italics"/>uiu&longs;uis trigoni rectanguli, aut cuius duo auguli &longs;int in dupla proportione, aut qui circulo in&longs;criptus &longs;it cognita quantitate unius lateris in comparatione ad dimetien <expan abbr="t&etilde;">tem</expan>, &longs;i proportio duorum laterum cognita fuerit, <expan abbr="er&utilde;t">erunt</expan> omnia eius latera cognita.<emph.end type="italics"/></cell>

<s>His ad vnguem tot exempla ex<lb/>plica&longs;&longs;e &longs;ufficiat, quot etiam modos: &longs;ex enim <lb/>modis &longs;ena &longs;ufficiunt exempla. </s>

</row>

<s>Ergo grauia <lb/>deor&longs;um moueri, leuia &longs;ursùm, palàm e&longs;t. <lb/></s>

<row>

<s>Sed &longs;uperaddunt quidam ne hoc contenti, <lb/>leuia grauibus velle &longs;upere&longs;&longs;e, vnde etiam <lb/>aër &longs;i &longs;ub aqua exi&longs;tat, quamvis in propria <lb/>regione, &longs;uperiùs tamen emergere nititur: vt <lb/>in vrceis manife&longs;tum e&longs;t, cum &longs;emipleni ver<lb/>tuntur: & in ve&longs;ica aëre plena, quæ aquæ im<lb/>mer&longs;a e&longs;t. </s>

<cell>C<emph type="italics"/>um in <expan abbr="per&longs;picu&utilde;">per&longs;picuum</expan> den&longs;um radij lumino&longs;i inciderint, quatuor fiunt luminis genera.<emph.end type="italics"/></cell>

<s>Sed non e&longs;t hic motus alius à pri<lb/>mo: nam aqua ip&longs;a cum &longs;it in &longs;ublimi, cona<lb/>tur, de&longs;cendere, & ad illius de&longs;cen&longs;um aër ne <lb/>nimium con&longs;tringatur, a&longs;cendit. </s>

</row>

<row>

<s>Sed in ve<lb/>&longs;ica, quæ in flumine e&longs;t, cum aër &longs;it in loco <lb/>aquæ, a&longs;cendere nititur: igitur &longs;ufficiet vna <lb/>ratio motus in elementis ad locum &longs;num. <lb/></s>

<cell>XCVII.</cell>

<cell>M<emph type="italics"/><expan abbr="ot&utilde;">otum</expan> inuer&longs;ionis in figuris in <expan abbr="cõparatione">comparatione</expan> ad <expan abbr="mot&utilde;">motum</expan> &longs;phæræ in plano inue&longs;tigare.<emph.end type="italics"/></cell>

<s>Quòd autem aqua ve&longs;icam impellat &longs;ursùm, <lb/>non aër a&longs;cendat, patet, quoniam ve&longs;ica &longs;ub <lb/>terra po&longs;ita non a&longs;cendit. </s>

</row>

<s>Quod verò dubitatione magis dignum e&longs;t, <lb/>id e&longs;t: Quomodo aqua tantùm a&longs;cendat, <lb/>quantùm de&longs;cendere pote&longs;t, dum à motu ra<lb/>ritatis adiuuatur: id ip&longs;um plenius exemplo <lb/>patebit. <lb/><figure id="id.016.01.012.1.jpg" xlink:href="016/01/012/1.jpg"/><lb/><arrow.to.target n="marg24"/></s>

<row>

<cell>XCVIII.</cell>

<s><margin.target id="marg24"/>Quomodo <lb/>aqua <expan abbr="tant&utilde;">tantum</expan> <lb/>a&longs;cendat, <lb/>quantum <lb/>pote&longs;t de&longs;<lb/>cendere.</s>

<cell>P<emph type="italics"/>roportionem ponderum æqualium per differentiam angulorum inuenire.<emph.end type="italics"/></cell>

<s>Vas &longs;it aqua plenum, cuius &longs;upremum E, <lb/>imum F, in quo canalis A B C. </s>

</row>

<row>

<s>Sit autem <lb/>CD, linea æqualiter à finitore di&longs;tans, &longs;ecun<lb/>dùm quem libella ducitur. </s>

<cell>P<emph type="italics"/>roportionem grauitatum per multitudinem &longs;uppo&longs;itorum orbium o&longs;tendere.<emph.end type="italics"/></cell>

<s>Impleatur autem <lb/>canalis ABC, aqua, & emittetur aqua per <lb/>C, dico, quòd exhauriet quicquid e&longs;t aquæ <lb/>&longs;upra C D, lineam: nihil autem eius quod <lb/>e&longs;t infra C D, lineam, &longs;ed canalis plenus <lb/>pendebit, & vas v&longs;que ad CD, aqua plenum <lb/>con&longs;picietur. </s>

</row>

<s>Hoc itaque &longs;ic e&longs;&longs;e, declarat <lb/>exemplum. </s>

<row>

<s>For&longs;an quis dicat, hæc ad aquæ <lb/>tractationem debui&longs;&longs;e transferri: &longs;ed non <lb/>oportuit, quandoquidem &longs;eu aqua, &longs;eu vino, <lb/>oleo, lactéve vas plenum fuerit, nihil inter<lb/>&longs;it. </s>

<cell>P<emph type="italics"/><expan abbr="roportion&etilde;">roportionem</expan> grauitatis <expan abbr="ponder&utilde;">ponderum</expan> attractorum per <expan abbr="trochlear&utilde;">trochlearum</expan> <expan abbr="numer&utilde;">numerum</expan> inue&longs;tigare.<emph.end type="italics"/></cell>

<s>Itaque huius experimenti potiùs ratio <lb/>reddenda e&longs;t. </s>

</row>

<row>

<s>Aqua igitur quæ &longs;upra C D, <lb/>e&longs;t, quum tanta ad vnguem &longs;it, quæ a&longs;cendit, <lb/>quanta e&longs;t illa, quæ ex C, effunditur, &longs;eu ca<lb/>nalis latior &longs;it in C, quàm in A, &longs;eu arctior, <lb/>quia &longs;emper totus canalis ad vnguem ple<lb/>nus e&longs;t, leuior e&longs;t aqua, quæ effunditur <lb/>per C. </s>

<cell>P<emph type="italics"/>roportionem precij gemmarum ex tribus in eodem genere cognitis inuenire.<emph.end type="italics"/></cell>

<s>Quòd verò leuior &longs;it aqua in parte <lb/>&longs;upra C D, quàm in C, cau&longs;a e&longs;t, quia <lb/>aqua &longs;upra C D, de&longs;cendere appetit, vt &longs;it <lb/>inferior illa, quæ e&longs;t in C, igitur compri<lb/>mit aquam, & in canalem impellit. </s>

</row>

<s>Quæ <lb/>autem e&longs;t infra C D, non appetit e&longs;&longs;e in C, <lb/>altiùs e&longs;t loco eius, ideo non vult a&longs;cende<lb/>re. </s>

<row>

<s>Sed aqua, quæ effluit ex C, non præ<lb/>bet con&longs;iderandi cau&longs;am, cùm tamen &longs;it hu<lb/>milior ip&longs;a aqua, quæ in va&longs;e continetur: <lb/>quia attractio illa non fit, ni&longs;i continuita<lb/>tis ratione: continuitas pendet ex ratione ra<lb/>ritatis, quæ nulla e&longs;&longs;e pote&longs;t, aqua iam <lb/>egrediente os canalis C. </s>

<cell>P<emph type="italics"/>roportionem motuum inuer&longs;ionis, & attractionis in plano inuenire.<emph.end type="italics"/></cell>

<s>Denique tota hæc <lb/>contemplatio ab&longs;oluitur hoc argumento, <pb xlink:href="016/01/013.jpg" pagenum="364"/>quòd aqua, quæ debet trahere aliam aquam <lb/>&longs;ecum, oportet vt va&longs;e contineatur, quoniam <lb/>&longs;ine illo conuelli nequit, &longs;ed ab aëre iuuatur <lb/>adueniente, & vt corpus continuum ad &ecedil;qui<lb/>librium perueniat. </s>

</row>

<row>

<s>Cùm igitur humilius e&longs;t <lb/>o&longs;culum C, ad illud perueniet: tùm autem <lb/>&longs;ublimius, non de&longs;cendet: quia quæ è directo <lb/>e&longs;t loci inferioris, vt in A, a&longs;cendere cogetur <lb/>ad C, quod e&longs;t in directo D. </s>

<cell>P<emph type="italics"/>roportionem eorundem in accliui demon&longs;trare.<emph.end type="italics"/></cell>

<s>Si autem aqua <lb/>de&longs;cendat primò, deinde a&longs;cendat, vt in figu<lb/>ra &longs;equente, ex A, in B, inde in E, & po&longs;tmo</s>

</row>

<s><arrow.to.target n="marg25"/><lb/><figure id="id.016.01.013.1.jpg" xlink:href="016/01/013/1.jpg"/><lb/>dum in C, & in D: tunc peruenire poterit, &longs;i <lb/>D, minùs di&longs;tet à linea B C, quàm A, locus, <lb/>ex quo de&longs;cendit. </s>

<row>

<cell>CIIII.</cell>

<s>Sed oportet in &longs;ingulis &longs;pa<lb/>tiis certam e&longs;&longs;e differentiam altitudinis A, & <lb/>D. </s>

<cell>P<emph type="italics"/>roportionem motus attractionis in decliui ad motum in plano determinare.<emph.end type="italics"/></cell>

<s>Quantò enim lengior via fuerit, eò maior <lb/>differentia A, & D, iuxta altitudinis men&longs;u<lb/>ram e&longs;&longs;e debet. </s>

</row>

<row>

<s>Hinc errores quorundam, qui <lb/>ad libramentum, quum conati e&longs;&longs;ent aquas <lb/>deducere, maximas iacturas impen&longs;arum &longs;u&longs;<lb/>ceperunt. </s>

<cell>P<emph type="italics"/>roportionem ferentium pondus in pertica inuenire.<emph.end type="italics"/></cell>

<s>In &longs;ingulis igitur millibus pa&longs;&longs;uum, <lb/>A, altius palmo e&longs;&longs;e debet quàm D, vt in de<lb/>cem millibus pa&longs;&longs;uum decem palmis. </s>

</row>

<s>Cau&longs;a <lb/>huius e&longs;t, aqu&ecedil; rotunditas euidens, quæ etiam <lb/>in vrceorum &longs;uperficie apparet. </s>

<row>

<s>Vnde ad li<lb/>bramentum licet A, &longs;it altius quàm D, non <lb/>tamen erit altius quandoque loco medio in<lb/>ter A & D. </s>

<cell>Q<emph type="italics"/>uales proportiones angulorum doceant laterum proportiones.<emph.end type="italics"/> A<emph type="italics"/>tque uicißim determinare.<emph.end type="italics"/></cell>

<s>Indiget etiam impetu quodam. <lb/></s>

</row>

<row>

<s>Sed hæc nunc præter intentum qua&longs;i &longs;unt: <lb/>voluit tamen ob magnitudinem periculi, & <lb/>erroris frequentiam, hæc &longs;ubieci&longs;&longs;e. </s>

<cell>S<emph type="italics"/>i in circulo duæ diametri ad rectum angulum &longs;e &longs;ecauerint: aliæ uerò ad perpendiculum ex diametro exicrint ad circum ferentiam, &longs;ingulæ &longs;upra diametrum erunt ma iores portionibus reliquis diametri &longs;uperioribus, infra autem minores.<emph.end type="italics"/> D<emph type="italics"/>imidium autem portionis &longs;uperioris re&longs;iduum ad centrum maius &longs;agitta habebit.<emph.end type="italics"/> I<emph type="italics"/>n aliqua præterea portionis &longs;uperioris parte, quæ uer&longs;us diametrum tran&longs;uer&longs;um po&longs;ita e&longs;t, maior e&longs;t differentia partis diametri ei <expan abbr="corre&longs;põdentis">corre&longs;pondentis</expan>, <expan abbr="&qtilde;">quae</expan> line æ tran&longs;uer&longs;æ.<emph.end type="italics"/></cell>

<s><margin.target id="marg25"/>Ratio <expan abbr="duc&etilde;-dæ">ducen<lb/>dæ</expan> aquæ.</s>

</row>

<s>Sed iam ad elementorum motum &longs;impli<lb/>cem veniamus exemplis explicandum. </s>

<row>

<cell>CVIII.</cell>

<s>Igitur <lb/>grauis motus exemplum præbent ponderum <lb/>horologia, quæ &longs;en&longs;im trahendo rotas ver<lb/>tunt. </s>

<cell>P<emph type="italics"/>unctum æqualitatis differentiæ de&longs;cen&longs;us & remotionis à centro inuenire.<emph.end type="italics"/></cell>

<s>Huiu&longs;ce autem generis infinita facilè <lb/>e&longs;&longs;et inuenire exempla. </s>

</row>

<row>

<s>At motus leuis hoc <lb/>vnum &longs;ubiiciatur exemplum. <lb/><arrow.to.target n="marg26"/></s>

<cell>R<emph type="italics"/>ationem libræ expendere.<emph.end type="italics"/></cell>

<s><margin.target id="marg26"/>Modus quo <lb/>naues demer<lb/>&longs;æ gurgitibus <lb/><expan abbr="recuperãtur">recuperantur</expan>.</s>

</row>

<s>Cùm naues freto merguntur, quas eruere <lb/>con&longs;ilium e&longs;t, cymbæ onu&longs;tæ &longs;axis per funes <lb/>alligantur nauigio ab vrinatoribus, &longs;ic vt <lb/>funes quantum fieri pote&longs;t, tendatur, inde <lb/>totidem cymbis vacuis lapides ex prioribus <lb/>detracti excipiuntur: quo fit vt alleuatæ <lb/>cymbæ nauigium paululùm ex profundo &longs;e<lb/>cum trahant. </s>

<row>

<s>Nam aër cymbas, quæ pondere <lb/>lapidum fermè mergebantur, cùm aquæ &longs;ub<lb/>e&longs;&longs;e nolit, in &longs;uperficiem aquæ attollit, vnde <lb/>nauigium fermè pro cymbæ altitudine &longs;upe<lb/>riùs trahitur. </s>

<cell>S<emph type="italics"/>i duæ &longs;phæræ ex eadem materia de&longs;cendant in aëre, eodem temporis momento ad planum ueniunt.<emph.end type="italics"/></cell>

<s>Trahatur igitur ex A, in B, tunc <lb/>cymbæ, quæ plenæ &longs;unt lapidibus illi anne<lb/>ctantur funibus, transfu&longs;i&longs;que lapidibus na<lb/>nigium trahetur in C. </s>

</row>

<row>

<s>Rur&longs;us priores cym<lb/>bæ, in quas lapides transfudi&longs;ti, nectuntur <lb/>ten&longs;is funibus nauigio in C, trahéntque de<lb/>ductis lapidibus ip&longs;um in D, atque perpetua <lb/>tran&longs;mutatione ad aquæ &longs;uperficiem tandem <lb/>deducetur. </s>

<cell>C<emph type="italics"/>ur ex medio tela ualidiorem ictum, & naues in &longs;calmo à remo ac malo recipiant inde ex puppi explorare.<emph.end type="italics"/></cell>

<s>Sed dices, plurimis cymbis opus <lb/>erit ad triremem educendam. </s>

</row>

<s>Verum e&longs;t, &longs;ed <lb/>ratio &longs;ic con&longs;tat: quælibet nauis aut cymba <lb/>tantùm ferre pote&longs;t ponderis, quantum e&longs;t <lb/>pondus aquæ, quam continere pote&longs;t. </s>

<row>

<s>Velut <lb/>&longs;i triremis capiat in flumine mille amphoras <lb/>aquæ, quarum pondus &longs;it decem millium ta<lb/>lentorum, triremis illa in flumine decem <lb/>millia talenta feret. </s>

<cell>C<emph type="italics"/>ur ex imo leuia longiùs ferantur declarare,<emph.end type="italics"/></cell>

<s>Quòd &longs;i eadem in mari <lb/>capiat ( vt dixi ) ea&longs;dem mille amphoras, <lb/>quarum pondus &longs;it duodecim millium talen<lb/>torum (nam aqua maris grauior e&longs;t aqua flu<lb/>minis ) eadem in mari duodecim millia ta<lb/>lenta ponderis feret. </s>

</row>

<row>

<s>Atque ea ratione mani<lb/><figure id="id.016.01.013.2.jpg" xlink:href="016/01/013/2.jpg"/><lb/>fe&longs;tum e&longs;t, cur nauigia appellare &longs;oleamus à <lb/>men&longs;ura, vt nauem mille, vel quingentarum <lb/>amphorarum: idem enim e&longs;t ac &longs;i dicas, quæ <lb/>ferre pote&longs;t mille aut quingenta ponderis ta<lb/>lenta. </s>

<cell>CXIII.</cell>

<cell>C<emph type="italics"/>ur uirga longius mittatur à puero quam à uiro inueftigare.<emph.end type="italics"/></cell>

<s>Nam qualis e&longs;t capacitas, vt dixi, nauis <lb/>ratione aquæ, tantùm e&longs;t pondus, quod ferre <lb/>pote&longs;t, &longs;cilicet quantum e&longs;t pondus aquæ <lb/>quam capit. </s>

</row>

<s>Manife&longs;tum e&longs;t igitur ex hoc, <lb/>quòd diuer&longs;a pondera eadem nauis in diuer<lb/>&longs;is aquis feret, quoniam & aquarum ip&longs;arum <lb/>diuer&longs;a &longs;unt pondera. </s>

<row>

<cell>CXIIII.</cell>

<s>Iuxta verò hanc ratio<lb/>nem liquet ponderis magnitudinem e&longs;&longs;e pro <lb/>ratione impellentis aquæ. </s>

<cell>C<emph type="italics"/>ircularis motus differentias quatuor e&longs;&longs;e, earumque rationem contemplari.<emph.end type="italics"/></cell>

<s>Nam &longs;i ( vt gratia <lb/>exempli dicam) cymba viginti amphoras &longs;u<lb/>&longs;tinet, hoc e&longs;t, quia aër inclu&longs;us ab aquæ am<lb/>phoris viginti &longs;uperiùs impellitur, vt aqua <lb/>illa &longs;cilicet, quæ in naui contineretur, locum <lb/>&longs;uum recipiat. </s>

</row>

<row>

<s>Bellè igitur conuenit hoc ex<lb/>perimentum cum ratione, quæ &longs;uperiùs dicta <lb/>e&longs;t, &longs;cilicet ve&longs;icam aëre plenam ab aqua &longs;ur<lb/>sùm pelli, quòd ve&longs;ica aquæ locum occupet: <lb/>quare pondus pro magnitudine aquæ, quam <lb/>ve&longs;ica continere pote&longs;t, in aëre &longs;u&longs;tinebit: id <lb/>e&longs;t, ita ve&longs;icæ pondere &longs;uperimpo&longs;ito, vt ip<lb/>&longs;um pondus totum in aëre &longs;it, non in aqua. <lb/></s>

<cell>P<emph type="italics"/>roportionem motuum impul&longs;ionis, & attractionis inter &longs;e, ab eadem ui declarare.<emph.end type="italics"/></cell>

<s>Verùm pondus, quod in aqua e&longs;t ( vt ad na</s>

</row>

<s><arrow.to.target n="marg27"/><lb/>uigium eruendum rur&longs;us veniam ) tantò le<lb/>uius redditur, quantò aqua ip&longs;a grauior ex<lb/>titerit: vnde paucioribus cymbis opus erit, <lb/>quàm quæ pondus demer&longs;i nauigij ferre po&longs;<lb/>&longs;ent. </s>

<row>

<s>Duplici verò ratione nauigia ex gra<lb/>uioribus aquis faciliùs extrahuntur, quàm <pb xlink:href="016/01/014.jpg" pagenum="365"/>ex leuioribus: atque ideò ex mari, quàm ex <lb/>fluminibus, vel lacubus. </s>

<cell>C<emph type="italics"/>ur machinæ oblongæ igneæ longius emittant &longs;phæram explorare.<emph.end type="italics"/></cell>

<s>Altera quòd cymbæ <lb/>in mari plus &longs;u&longs;tinent ponderis: reliqua, quòd <lb/>nauigium in ea aqua minùs graue e&longs;t. </s>

</row>

<row>

<s>Opor<lb/>tet <expan abbr="hãc">hanc</expan> <expan abbr="aut&etilde;">autem</expan> ob cau&longs;am animaduertere, cùm, <lb/>vt dictum e&longs;t, nauigium grauius reddatur in <lb/>aquæ &longs;uperficie <emph type="italics"/>(<emph.end type="italics"/> quia partim e&longs;t in aëre) <lb/>quàm in imo, vt quantò magis eleuatur à <lb/>cymbis, eò plures ac maiores cymbæ alligen<lb/>tur, ne decepti hac ratione non &longs;olùm denuò <lb/>mergatur, &longs;ed & impetu adiecto omnes <expan abbr="&longs;ec&utilde;">&longs;ecum</expan> <lb/>cymbas in profundum trahat. </s>

<cell>CXVII.</cell>

<cell>I<emph type="italics"/>n curriculis maior e&longs;t uis pulueris copio&longs;ioris ampliore in &longs;pacio, quàm paucioris in minore iuxta proportionem eandem.<emph.end type="italics"/></cell>

<s>Dubitabit au<lb/>tem aliquis, cur exoneratis cymbis B, imple<lb/>tis autem aliis, per A, &longs;ignificantur, non de&longs;<lb/>cendat nauis, quæ eleuata fuit ab A, cymbis <lb/>vacuis? </s>

</row>

<s>Non enim plenæ po&longs;&longs;unt &longs;u&longs;tinere <lb/>pondus. </s>

<row>

<cell>CXVIII.</cell>

<s>Cau&longs;a e&longs;t, quia factis iam funibus <lb/>æqualibus cymbarum A, & B, cùm iam va<lb/>cuum &longs;eu inane, vel aër, qui in cymbis con<lb/>tinetur potentior &longs;it nauis pondere, plus tra<lb/>het inane cymbarum B, quàm remittet gra<lb/>uitas aucti poderis cymbarum A. </s>

<cell>Q<emph type="italics"/>uanta proportione decedat ictus in obliquum parietem ab eo qui e&longs;t ad perpendiculum declarare.<emph.end type="italics"/></cell>

<s>Itaque hac <lb/>ratione perpetuò nauis a&longs;cendet: hoc dunta<lb/>xat ob&longs;eruato, vt plenarum cymbarum funes <lb/>eò &longs;int vacuarum cymbarum funibus breuio<lb/>res, quantò pondus lapidum eas cymbas de<lb/>primit. </s>

</row>

<row>

<s>Sed de &longs;implici leuis motu &longs;ur&longs;um &longs;a<lb/>tis, nunc de motu, qui ex graui & leui com<lb/>ponitur, dicendum erit. </s>

<cell>Q<emph type="italics"/>uantum ictus machinæ procliuis ad angulum minuatur explorare.<emph.end type="italics"/></cell>

<s>Pro cuius exemplo <lb/>mirificè &longs;e offert Heronis machina, quam <lb/>nos &longs;æpè tractauimus. </s>

</row>

<s>Ea &longs;ic &longs;e habet: A, la<lb/><arrow.to.target n="marg28"/><lb/><figure id="id.016.01.014.1.jpg" xlink:href="016/01/014/1.jpg"/><lb/>brum aqua plenum: &longs;ub quo vas B, & ip&longs;um <lb/>aqua plenum, &longs;it iunctum A, vt ex altero in <lb/>alterum aqua permeare non po&longs;&longs;it. </s>

<row>

<s>Sub B, vas <lb/>aliud, quod vocetur C, inane. </s>

<cell>P<emph type="italics"/>roportionem partium nauis ad eundem obliquum uentum explorare.<emph.end type="italics"/></cell>

<s>Fi&longs;tula D, fera<lb/>tur ex B, in C, cuius &longs;ummum os fermè ad <lb/>labrum perueniat. </s>

</row>

<row>

<s>Fi&longs;tula alia E, quæ &longs;uper <lb/>labrum non parùm a&longs;cendat, & in&longs;erta labro, <lb/>in medio penetret v&longs;que ad imum primi va<lb/>&longs;is, non tamen ip&longs;i imo iungatur. </s>

<cell>F<emph type="italics"/>labelli uires atque naturam declarare.<emph.end type="italics"/></cell>

<s>Alia fi&longs;tula <lb/>F, cuius &longs;upremum in imo labri o&longs;culum <expan abbr="&longs;it&utilde;">&longs;itum</expan> <lb/>&longs;it, inferiùs os in ip&longs;o &longs;epto inter duo va&longs;a fi<lb/>niatur, ita <expan abbr="tam&etilde;">tamen</expan> vt aqua ex labro per &longs;uperius <lb/>os in vas C, deferatur. </s>

</row>

<s>Tunc verò videmus <lb/><expan abbr="aquã">aquam</expan>, qu&ecedil; e&longs;t in B, va&longs;e, per E, fi&longs;tulam emitti, <lb/>ac eò donec finiatur labri aqua v&longs;que per&longs;e<lb/>uerare. </s>

<row>

<cell>CXXII.</cell>

<s>Id quomodo fiat ex duobus motibus <lb/>compo&longs;itis demon&longs;trandum. </s>

<cell>C<emph type="italics"/>ontemptus circa<emph.end type="italics"/> S<emph type="italics"/>olis rationem in umbris declarare.<emph.end type="italics"/></cell>

<s>Aqua de&longs;cen<lb/>dens per F, fi&longs;tulam, cùm aër in C, non po&longs;&longs;it <lb/>&longs;ub&longs;i&longs;tere, a&longs;cendit per D, fi&longs;tulam in vas B, <lb/>&longs;uperiùs. </s>

</row>

<s>At verò cum ibi locus aqua plenus <lb/>&longs;it, cogitur aqua a&longs;cendere per E, fi&longs;tulam <lb/>pre&longs;&longs;a ab aëre, atque &longs;ic effunditur. </s>

<row>

<cell>CXXIII.</cell>

<s>Manife<lb/>&longs;tum e&longs;t igitur hîc duos e&longs;&longs;e motus: vnum &longs;e<lb/>cundum naturam aquæ de&longs;cendentis ex labro <lb/>in C, vas per F, fi&longs;tulam, alterum aëris a&longs;cen<lb/><arrow.to.target n="marg29"/><lb/>dentis ex va&longs;e C, in vas B, quod <emph type="italics"/>(<emph.end type="italics"/>vt dictum <lb/>e&longs;t) ab aqua &longs;ursùm impellatur. </s>

<cell>C<emph type="italics"/>ognita ratione umbræ ad gnomonem &longs;inum, & arcum altitudinis ab horizonte, quouis tempore digno&longs;cere.<emph.end type="italics"/></cell>

<s>Ab his igitur <lb/>duobus motibus naturalibus violentius im<lb/>petus fit quo aqua ex va&longs;e B, per fi&longs;tulam <lb/>a&longs;cendit. </s>

</row>

<row>

<s>Verùm motus grauis dum repetit <lb/>alternatim folles mouet, aut alias machinas, <lb/>quòd in machina Cte&longs;ibica demon&longs;trare <lb/>oportunum erat, vt emboli ma&longs;culi vici&longs;&longs;im <lb/>in modiolis a&longs;cendere, de&longs;cenderétque po&longs;<lb/>&longs;ent. </s>

<cell>CXXIIII.</cell>

<cell>P<emph type="italics"/>roportionem umbræ uer&longs;æ e&longs;&longs;e ad gnomonem, uelut gnomonis ad umbram uer&longs;am.<emph.end type="italics"/></cell>

<s>Id autem &longs;ic fit: Rota cum pinnis iux<lb/>ta aquæ delabentis ca&longs;um ( vt &longs;olet fieri) &longs;ta<lb/>tuatur, vt ex aquæ perpetuo defluxu &longs;uper <lb/>pinnas rota circumuoluatur, in qua &longs;it axis <lb/>A, quem palàm e&longs;t nece&longs;&longs;e fore, vt & ip&longs;e <lb/>circumagatur. </s>

</row>

<s>Rotæ de&longs;criptionem, vt rem <lb/>noti&longs;&longs;imam ac in molis omnibus con&longs;pi<lb/>cuam, prætermitto. </s>

<row>

<s><margin.target id="marg27"/>Nauigia fa<lb/>ciliùs ex ma<lb/>ri, extrahi, <lb/>quàm flumi<lb/>nibus vel la<lb/>cubus.</s>

<cell>P<emph type="italics"/>roportionem dimetientis, & peripheriæ cuiuslibet circuli paralleli æquinoctiali per cognitam partem magni circuli demon&longs;trare.<emph.end type="italics"/></cell>

<s><margin.target id="marg28"/>Machina <lb/>Heronis.</s>

</row>

<row>

<s><margin.target id="marg29"/>De motu al<lb/>lernante.</s><figure id="id.016.01.014.2.jpg" xlink:href="016/01/014/2.jpg"/>

<cell>CXXVI.</cell>

<cell>C<emph type="italics"/>irculi horarij naturam declarare.<emph.end type="italics"/></cell>

<s>Trabs &longs;uperiacens tignis atque inclu&longs;a fo<lb/>raminibus rotundis vocetur B, ita vt mobilis <lb/>&longs;it, ac vt in cardinibus circumuolui po&longs;&longs;it. <lb/></s>

</row>

<s>Iuxta huius extremum E, annulus infixus, cui <lb/>alter annulus cum ferrea virga F: hæ rur&longs;us <lb/>in annulum finiatur, quem excipiat alter an<lb/>nulus G, virga H, annexus: in extrtmo H, an<lb/>nulus iunctus e&longs;t, qui vnco ita annectitur in <lb/>&longs;ummitate axis A, vt &longs;ecum moueatur, &longs;ed <lb/>redeunte axe, redit & annulus ad pri&longs;tinum <lb/>locum ac &longs;itum. </s>

<row>

<cell>CXXVII.</cell>

<s>Ex altera trabis parte duo <lb/>annuli ex aduer&longs;o collocantur C, & D. </s>

<cell>D<emph type="italics"/>ata poli altitudine ortus amplitudinem demonftrare.<emph.end type="italics"/></cell>

<s>Licet <lb/>& bis duos & tria paria &longs;ic ex aduer&longs;o collo<lb/>care. </s>

</row>

<row>

<s>Si igitur emboli aut folles alter C, fune <lb/>iungatur, alter D, circumuoluto axe, trahitur <lb/>primum trabs ver&longs;us D, túncque eleuatur <lb/>follium alter ex C, altero cadente D. </s>

<cell>CXXVIII.</cell>

<cell>N<emph type="italics"/>ota amplitudine ortus, cuiu&longs;que puncti arcum &longs;emidiurnum inuenire.<emph.end type="italics"/></cell>

<s>Quum <lb/>verò rota dimidium axis circumuertit, annu<lb/>lus in imo H, redit ad locum &longs;uperiorem & <lb/>impellit E, propter virgas, & trabs flectitur <lb/>ver&longs;us C, atque &longs;ic mutata vice folles mo<lb/>uentur. </s>

</row>

<s>Nutat enim trabs dextra ac &longs;ini&longs;tra <lb/>vici&longs;&longs;im, &longs;ed non circumuoluitur. </s>

<row>

<cell>CXXIX.</cell>

<s>Ergo licet <lb/>multa paria follium annulis multis in trabe <lb/>ex aduer&longs;o collocatis mouere, &longs;ed robu&longs;ta vi <lb/>aquæ opus e&longs;t. </s>

<cell>D<emph type="italics"/>ata altitudine<emph.end type="italics"/> S<emph type="italics"/>olis in quacunque regione, quacunque die di&longs;tantiam<emph.end type="italics"/> S<emph type="italics"/>olis à meridiano cogno&longs;cere.<emph.end type="italics"/></cell>

<s>Licet & eidem axi alteram <lb/>trabem, quod fabri facere &longs;olent à &longs;ini&longs;tra <lb/>iungere, <expan abbr="atq;">atque</expan> &longs;ic numerus <expan abbr="folli&utilde;">follium</expan> duplicabitur. <lb/></s>

</row>

<row>

<s>Nec alio opus e&longs;t auxilio, aliáve <expan abbr="quã">quam</expan> quæ in <lb/>vno patefacta e&longs;t indu&longs;tria, &longs;ed &longs;ola maiore vi. </s>

<cell>D<emph type="italics"/>ata regionis altitudine, & loco<emph.end type="italics"/> S<emph type="italics"/>olis proportionem gnomonis, tam ad umbram rectam quàm uer&longs;am, uel etiam in cylindro determinare.<emph.end type="italics"/></cell>

<s>Sed motuum tran&longs;latio, quæ &longs;olet in v&longs;u <lb/>e&longs;&longs;e, tùm in molendinis, tum horologiis, <lb/>quamvis vulgata, tamen &longs;ubtiliori con&longs;tat <lb/>ratione. <lb/><figure id="id.016.01.014.3.jpg" xlink:href="016/01/014/3.jpg"/><lb/><arrow.to.target n="marg30"/></s>

</row>

<s><margin.target id="marg30"/>Motuum <lb/>tra&longs;latio.</s>

<row>

<cell>CXXXI.</cell>

<s>Sit igitur rota AB, quæ circumagi po&longs;&longs;it <pb xlink:href="016/01/015.jpg" pagenum="366"/>alia rota cum paxillis, vt in molendinis fieri <lb/>&longs;olet aut manubrio C, dentes verò in eius <lb/>exteriore &longs;uperficie re&longs;picientes cylindrum <lb/>&longs;eu columnam FG, erectam ad perpendicu<lb/>lum plani F H. </s>

<cell>S<emph type="italics"/>i lineæ alicui duplum alterius adiungatur, erit proportio duarum ad primam maior quàm dupli cum prima ad primam cum una adiecta.<emph.end type="italics"/></cell>

<s>In quo plano etiam rota &longs;u<lb/>per&longs;tans fixum habet palum, cui axis infi<lb/>gigitur. </s>

</row>

<row>

<s>In FG, autem columna, DE, cur<lb/>riculum dentatum e&longs;t. </s>

<cell>CXXXII.</cell>

<cell>S<emph type="italics"/>i ad duas lineas quarum una alteri dupla &longs;it eadem linea addatur, erit aggregati ex minore, & adiecta ad ip&longs;am minorem, minor proportio quàm aggregati ex maiore, & adiecta ad ip&longs;am maiorem duplicata.<emph.end type="italics"/></cell>

<s>Itaque quum rota <lb/>A B, circumuertitur &longs;uper axe CK, motu <lb/>ex A, in B, &longs;eu A, &longs;ur&longs;um deor&longs;um, F G, <lb/>cylindrus circumuertitur ex D E, ver&longs;us <lb/>K, &longs;eu ex dextro in &longs;ini&longs;trum, quare con<lb/>tingit tran&longs;latio motus, quæ erit eò velo<lb/>cior, quò numerus dentium A B, rotæ, <lb/>plures continebit dentes circuli D E. </s>

</row>

<s>His <lb/>autem vtemur ad machinæ Augu&longs;tanæ in<lb/>tellectum. </s>

<row>

<cell>CXXXIII.</cell>

<s>His modò vi&longs;is, po&longs;tquam &longs;ermonem de <lb/>motibus omnibus generalibus fermè ab&longs;ol<lb/>uimus, quarto exemplo in libramento aqua<lb/>rum declarato, Heronis autem machina in <lb/>compo&longs;itis elementorum motibus &longs;atisfa<lb/>ciente, vt in vniuer&longs;um pro decem modis <lb/>decem exempla &longs;ubiecerim, colligere illa in <lb/>vnum breuiter operæ pretium erit. </s>

<cell>S<emph type="italics"/>i fuerint duæ quantitates, <expan abbr="quar&utilde;">quarum</expan> una alteri dupla &longs;it: minuatur à minore quædam quantitas, <expan abbr="ead&etilde;que">eadenque</expan> maiori addatur, erit minoris ad re&longs;iduum maior proportio, quàm aggregati ad maiorem duplicata.<emph.end type="italics"/> S<emph type="italics"/>i uerò minori addatur, & à maiore detrabatur, erit aggregati ad minorem minor proportio quàm maioris ad re&longs;iduum duplicata.<emph.end type="italics"/></cell>

<s>Quieti <lb/>ob raritatem lucernæ exemplum appo&longs;ui<lb/>mus. </s>

</row>

<row>

<s>Motui à raritate fi&longs;tulam in va&longs;e col<lb/>locatam, vbi de aquæ de&longs;cen&longs;u egimus. <lb/></s>

<cell>CXXXIIII.</cell>

<cell>S<emph type="italics"/>i rectangula &longs;uperficies &longs;it, cuius pars tertia quadrata &longs;it corpus, quod ex latere quadratæ in re&longs;iduum &longs;uperficiei con&longs;tat, maius e&longs;t quouis corpore ex eadem &longs;uperficies, aliter diui&longs;a con&longs;tituto.<emph.end type="italics"/></cell>

<s>Quieti ob den&longs;itatem plumbi laminam, tum <lb/>coria &longs;uper aquam &longs;par&longs;a. </s>

</row>

<s>Motui ob den&longs;i<lb/>tatem impul&longs;um bellicarum machinarum. <lb/></s>

<row>

<cell>CXXXV.</cell>

<s>Motui attractionis ob raritatem, & impul<lb/>&longs;us ob den&longs;itatem, in Cte&longs;ibica machina. <lb/></s>

<cell>S<emph type="italics"/>i linea in duas partes, quarum una fit alteri dupla diuidatur, erit quod fit ex tertia parte in quadratum re&longs;idui parallelipedum maius omni pararallelipedo, quod ex diui&longs;ione eiu&longs;dem lineæ creari poßit.<emph.end type="italics"/></cell>

<s>Vtriu&longs;que verò motus, tum etiam quietis <lb/>ob raritatem, Brambilica machina exem<lb/>plum erit. </s>

</row>

<row>

<s>Motus leuis elementi, nauigij re<lb/>cuperationem: grauis verò, &longs;implicis horo<lb/>logiorum motum &longs;ubiecimus. </s>

<cell>CXXXVI.</cell>

<cell>D<emph type="italics"/>enominationes in infinitum extendere.<emph.end type="italics"/></cell>

<s>Grauis, &longs;ed <lb/>&longs;æpiùs repetiti, follium alternam iactatio<lb/>nem. </s>

</row>

<s>Grauis ac leuis &longs;imul ad vnum finem <lb/>tendentium, Heronis machinam. </s>

<row>

<cell>CXXXVII.</cell>

<s>Ergo &longs;ic poterat videri tractatio hæc ab<lb/>&longs;oluta: &longs;ed non omnia &longs;ump&longs;imus genera. <lb/></s>

<cell>R<emph type="italics"/>ationem numerorum ex progreßione declarare.<emph.end type="italics"/></cell>

<s>Decem enim hæc exempla duobus conti<lb/>nentur generibus: altero, quòd vnum tan<lb/>tùm habet motorem, vt Heronis machina: <lb/>reliquo, quod duos, &longs;ed diuer&longs;os habet mo<lb/>tores, vt Brambilica. </s>

</row>

<row>

<s>Supere&longs;t tertium ge<lb/>nus, in quo illæ continentur machinæ, quæ <lb/>plures habent motores, &longs;ed non diuer&longs;os: <lb/>quod quidem videtur e&longs;&longs;e nobili&longs;&longs;imum, quia <lb/>motui principali, &longs;eu <foreign lang="greek">au)tokine/tw|</foreign> magis a&longs;&longs;i<lb/>milatur. </s>

<cell>CXXXVIII.</cell>

<cell>M<emph type="italics"/>odos u&longs;us horum numerorum declarare.<emph.end type="italics"/></cell>

<s>Contingit is motus, quum aqua, <lb/>gratia exempli, rotam, qua aqua effunditur </s>

</row>

<s><arrow.to.target n="marg31"/><lb/>vertetit. </s>

<row>

<cell>CXXXIX.</cell>

<s>Atque hoc in genere primum e&longs;t <lb/>Archimedis inuentum Cochlea appellata, <lb/>cuius meminit Diodorus Siculus in antiqua <lb/>hi&longs;toria bis, dicens Ægyptum &longs;iccatam <lb/>beneficio cochleæ ab Archimede inuentæ. <lb/></s>

<cell>R<emph type="italics"/>adices omnes à propo&longs;itis numeris extrahere.<emph.end type="italics"/></cell>

<s>Quod &longs;i ita e&longs;t, cùm Archimedes &longs;ecundi <lb/>belli Punici temporibus floruerit, ne&longs;cio <lb/>quo pacto antiquo tempore bene potuerit <lb/>Ægyptus habitari. </s>

</row>

<row>

<s>Vtcunque tamen res &longs;e <lb/>habeat, in&longs;trumentum id nobili&longs;&longs;imum pro<lb/>culdubio e&longs;t, atque tali artifice haud indi<lb/>gnum. </s>

<cell>R<emph type="italics"/>adices per numeros fractos determinare.<emph.end type="italics"/></cell>

<s>Meminit huius Vitruuius in fine &longs;ui <lb/>operis. </s>

</row>

<s>Sed Galeaz de Rubeis ciuis no&longs;ter, <lb/>fabérque ferrarius, cuius infrà mentionem <lb/>facturi &longs;umus, cùm iam olim inuentam ip<lb/>&longs;e, qua&longs;i primus auctor exi&longs;timaret reperi&longs;&longs;e, <lb/>præ lætitia in&longs;aniuit. </s>

<row>

<s>Vidimus illum ver&longs;an<lb/>tem tru&longs;atilem machinam, ac paulò pò&longs;t <lb/>mente excu&longs;&longs;um. </s>

<cell>N<emph type="italics"/>umeros fractos ad minores in ea <expan abbr="i&etilde;">iem</expan> proportione ualde propinqud deducere<emph.end type="italics"/></cell>

<s>Erat autem machina <lb/>talis: </s>

</row>

<row>

<s><margin.target id="marg31"/>Coclhea Ar<lb/>chimedis.</s><figure id="id.016.01.015.1.jpg" xlink:href="016/01/015/1.jpg"/>

<cell>CXLII.</cell>

<cell>D<emph type="italics"/><expan abbr="enomination&utilde;">enominationum</expan> in <expan abbr="crem&etilde;ta">crementa</expan> ex extrema cognita inuenire.<emph.end type="italics"/> E<emph type="italics"/>t <expan abbr="cõuer&longs;o">conuer&longs;o</expan> modo.<emph.end type="italics"/></cell>

<s>Lignum A H, &longs;olidum, rectum, rotun<lb/>dum, æqualéque, ac tam longum vt incli<lb/>natum ad &longs;uper&longs;iciem aquæ, infixúmque <lb/>alueo quantum opus e&longs;t, &longs;upraip&longs;am aquam <lb/>promineat, canali ( vt vides ) metallico <lb/>&longs;implici, ad cochleæ imaginem fabricato, <lb/>circumtegatur. </s>

</row>

<s>Sunt qui multiplici vtantur: <lb/>tres mihi nece&longs;&longs;arij e&longs;&longs;e videntur, quique <lb/>adeò &longs;en&longs;im a&longs;cendant, vt omnia &longs;patia com<lb/>pleantur. </s>

<row>

<cell>CXLIII.</cell>

<s>Duo ora habet canalis, inferius <lb/>quidem latius, angu&longs;tius quod &longs;uperius e&longs;t. <lb/></s>

<cell>S<emph type="italics"/>i linea in duas partes diuidatur, corpora quæ fiunt ex una parte in alterius quadratum mutuo æqualia &longs;unt corpori, quod fit ex tota linea in &longs;uperficiem unius partis in alteram.<emph.end type="italics"/></cell>

<s>Vocetur autem illud K. </s>

</row>

<row>

<s>Demon&longs;trandum <lb/>e&longs;t igitur, quòd vbi terminis A & H ti<lb/>gnum claudatur, ita vt circumuerti po&longs;&longs;it, <lb/>quod motu aquæ circumuertetur. </s>

<cell>CXLIIII.</cell>

<cell>D<emph type="italics"/>uplum cubi medietatis maius e&longs;t aggregato corporum mutuorum, cuiuslibet diui&longs;ionis quantum e&longs;t, quod fit ex tota in quadratum differentiæ.<emph.end type="italics"/></cell>

<s>Secundò, <lb/>quòd vbi circumagatur aqua a&longs;cendet, ef<lb/>fundeturque per K. </s>

</row>

<s>Nam pinnæ quæ additæ <lb/>&longs;unt B C D E F G, &longs;eu inter &longs;patia alter<lb/>utrinque, &longs;eu in coniunctionibus tigni cum <lb/>canali, occurrentes aquæ, nece&longs;&longs;ariò ver<lb/>tent illud in&longs;trumentum: quia augeri po&longs;&longs;unt <lb/>longitudine ac latitudine: pondus verò AH, <lb/>paruum e&longs;t, & longè minus etiam factum <lb/>ob inclinationem, & axes in annulis po&longs;i<lb/>tos, ita vt circumagi po&longs;&longs;int. </s>

<row>

<s>O&longs;tendunt id <lb/>etiam molæ in fluminibus Pado atque Tici<lb/>no, vbi quanquam leni&longs;&longs;imè fluant aquæ, <lb/>hoc tamen ingenio lapides molares circum<lb/>acti terunt, ac molunt triticum. </s>

<cell>S<emph type="italics"/>i linea in duas partes diuidatur quadrata ambarum partium detracto eo, quod fit ex una parte in alteram, æqualia &longs;unt producto unius in alteram cum quadrato differentiæ.<emph.end type="italics"/></cell>

<s>Sed quòd <lb/>aqua ip&longs;a a&longs;cendat ex L, in K, patet: quum <lb/>enim L, eleuatur, pars quæ &longs;uccedit fit humi<lb/>lior, igitur aqua de&longs;cendet, qua a&longs;cendente <lb/>iterum pars &longs;uccedens de&longs;cendit: eadémque <lb/>ratio &longs;emper o&longs;tendit <expan abbr="aquã">aquam</expan> ver&longs;us K, tendere: <lb/>hócque experimento pulcherrimè congruit, <lb/>& nos non &longs;emel periculum de hoc fecimus. <lb/></s>

</row>

<row>

<s>Conuer&longs;o igitur axe &longs;eu tigno in f&oelig;mineis <lb/>cardinibus A, & H, in quibus intruditur, <lb/>donec aqua canalis impletus fuerit, effun<lb/><arrow.to.target n="marg32"/><lb/>deretur per K, &longs;uper planum ripæ. </s>

<cell>CXLVI.</cell>

<cell>C<emph type="italics"/>orpus quod fit ex linea diui&longs;a in &longs;uperficiem æqualem quadratis ambarum par tium detracta &longs;uperficie unius partis in alteram, e&longs;t æquale aggregato cuborum ambarum partium.<emph.end type="italics"/></cell>

<s>Ex quo <lb/>non videtur hæc ratio concludere, aqua <lb/>perpetuò de&longs;cendit, igitur in fine erit in hu<lb/>miliore loco, quàm in initio. </s>

</row>

<s>Sed tamen non <lb/>&longs;emper de&longs;cendit, verùm pars quæ de&longs;cen<lb/>dit maior, impellit minorem, cogitque a&longs;<lb/>cendere. </s>

<row>

<cell>CXLVII.</cell>

<s>At cùm effundi c&oelig;perit, tunc tam <lb/>machina faciliùs vertetur, & aqua qua&longs;i <lb/>&longs;ponte effluet, propter ea, quæ de aquæ de&longs;<lb/>cen&longs;u iam demon&longs;trauimus. </s>

<cell>P<emph type="italics"/>ropo&longs;ita linea diui&longs;a duas ei line as adijcere, ut proportio <expan abbr="additar&utilde;">additarum</expan> &longs;ingularium<emph.end type="italics"/></cell>

<cell/>

<s>Sunt qui canali <lb/>tabulas affigant, nectántque omnia &longs;imul, <lb/>vt machina robu&longs;tior ac firmior euadat, pa<lb/>xillos tabulis, non tigno, ob commodita<lb/>tem maiorem in&longs;erentes. </s>

</row>

<s>Dubitabit autem <lb/>meritò aliquis, cur a&longs;cendente parte canalis <lb/>iuxta B, cùm tam L, quàm C, de&longs;cendant, <lb/>aqua non non redeat in L, & rur&longs;us effun<lb/>datur ( nam L, humilior e&longs;t quàm C, ) & <lb/>ex eadem parte. </s>

<row>

<cell/>

<s>Duplex huius ratio e&longs;t: al<lb/>tera, quòd aqua quæ e&longs;t in B, impellitur <pb xlink:href="016/01/016.jpg" pagenum="367"/>ab ea, quæ e&longs;t e&longs;t in L, ideo tran&longs;it ad C, <lb/>& non redit: reliqua Geometrica, o&longs;tendens <lb/>partem mediam inter L, & B, in conuer<lb/>&longs;ione altiorem e&longs;&longs;e, quàm &longs;it pars media in<lb/>ter B, & O. </s>

<cell><emph type="italics"/>& partium &longs;imul iunctarum ad additas &longs;it mutua.<emph.end type="italics"/></cell>

<s>Indicio etiam e&longs;t, quòd plum<lb/>bea &longs;phærula impo&longs;ita, cùm à nulla alia re <lb/>prematur, a&longs;cendit tamen in K. </s>

</row>

<row>

<s>Et demon<lb/>&longs;tratio hæc e&longs;t: Sit tignum A B, in plano <lb/>A C, eleuatio partis A D, tigni &longs;it D C, <lb/>eius partis cochleæ pars corre&longs;pondens AE, <lb/>& altitudo DE, &longs;it gratia exempli &longs;e&longs;quial<lb/>tera DC, & ducatur recta AE, erunt igitur <lb/>omnes lineæ inter A D, & A C, minores <lb/>lineis è directo con&longs;titutis inter AD, & AE, <lb/>ex demon&longs;tratis in &longs;exto elementorum Eu<lb/>clidis: <lb/><figure id="id.016.01.016.1.jpg" xlink:href="016/01/016/1.jpg"/><lb/><arrow.to.target n="marg33"/></s>

<cell>CXLVIII.</cell>

<cell>P<emph type="italics"/>ropo&longs;itis tribus lineis primam &longs;ic diuidere, ut adiectis duabus alijs lineis, &longs;ecundum <expan abbr="ration&etilde;">rationem</expan> mutuam &longs;ingularum &longs;ingulis, <expan abbr="aggregat&utilde;">aggregatum</expan> ex una <expan abbr="adiectar&utilde;">adiectarum</expan>, & par te ad <expan abbr="aggregat&utilde;">aggregatum</expan> ex alia parte, & adiecta &longs;e habeat, ut &longs;ecunda ad <expan abbr="tertiã">tertiam</expan>.<emph.end type="italics"/></cell>

<s><margin.target id="marg32"/>Aliquid per<lb/>petuò <expan abbr="de&longs;c&etilde;-dit">de&longs;cen<lb/>dit</expan>, quod in <lb/>fine erit al<lb/>tius.</s>

</row>

<s><margin.target id="marg33"/>Demon&longs;tratio <lb/>o&longs;tendens <lb/>quod cochlea <lb/>ver&longs;a graue <lb/>a&longs;cendit.</s>

<row>

<cell>CXLIX.</cell>

<s>Circumuertatur igitur AB, ita vt quando <lb/>E, erit in humillimo loco, pondus rotun<lb/>dum in A, po&longs;itum &longs;it in directo D. </s>

<cell>D<emph type="italics"/>atam lineam &longs;ic diuidere, ut proportio quadratorum ad dupium unius partis in alteram &longs;it, ut lineæ datæ ad lineam datam.<emph.end type="italics"/></cell>

<s>Quia <lb/>igitur D E, longior e&longs;t D C, igitur &longs;i E, <lb/>erit in oppo&longs;ito &longs;ui loci, erit infrà C: &longs;ed <lb/>C, e&longs;t in directo A, igitur pondus erit in<lb/>feriùs quàm ab initio: &longs;ed omnes lineæ &longs;er<lb/>uant eandem rationem, & &longs;unt longiores <lb/>etiam in circumferentia A E, quàm in re<lb/>cta A E, à linea A D, quia pars e&longs;t minor <lb/>toto: igitur conuer&longs;o A B, pondus de&longs;cen<lb/>det in AE. </s>

</row>

<row>

<s>Sed omne graue liberum in mo<lb/>tu de&longs;cendit, igitur pondus perueniet ad E. <lb/></s>

<cell>P<emph type="italics"/>ropo&longs;itis duabus lineis, lineam communem utrique adiungere, ut &longs;it maioris ad additam proportio, uelut quadratorum minoris, & adiectæ ad duplum unius in alteram.<emph.end type="italics"/></cell>

<s>Sed quum erit in E, circumactum de&longs;cen<lb/>det ver&longs;us F, non ver&longs;us A, tum ob impe<lb/>tum, tum quia pars quæ e&longs;t inter A, & E, <lb/>a&longs;cendit, nam in priore motu de&longs;cenderat: <lb/>pars autem E F, adhuc de&longs;cendit, igitur <lb/>pondus perueniet ex H, in A, quare ex A, in <lb/>B, multis conuer&longs;ionibus eadem ratione fa<lb/>ctis. </s>

</row>

<s>Facilè autem ligula circumdata calamo <lb/>hoc, quod tibi perdifficile for&longs;an videtur, ex<lb/>perieris. </s>

<row>

<s>Sed ad rem reuertor. </s>

<cell>P<emph type="italics"/>roportio differentiæ quadratorum partium cuiu&longs;uis lineæ, ad quadratum differentiæ illarum e&longs;t, uelut totius lineæ ad differentiam.<emph.end type="italics"/></cell>

<s>Cochlea quam Vi<lb/>truuius docet, alieno indiget auxilio, hæc <lb/>autem no&longs;tra &longs;eip&longs;am circunducit: &longs;ed eò <lb/>faciliùs, quò &longs;piræ canalis frequentiores <lb/>fuerint, & machina mollius a&longs;cenderit. </s>

</row>

<row>

<s>Quò <lb/>verò faciliùs circumagetur, eò &longs;erius: hoc <lb/>enim fermè generale e&longs;t in omnibus machi<lb/>nis. </s>

<cell>S<emph type="italics"/>i linea in duas partes æquales, duasque inæquales diuidatur, fueritque proportio aggregati ex maiore, & dimidio ad ip&longs;am maiorem, uelut ex minore, & aliqua linea ad ip&longs;am minorem, & rur&longs;us aggregati ex minore, & dimidio ad ip&longs;am minorem, uelut aggregati ex maiore, & alia addita ad ip&longs;am maiorem, erit proportio dimidij ad partem unam inæqualem, uelut alterius partis inæqualis ad &longs;uam additam mutuò, & etiam proportio additarum inuicem, uelut proportio <expan abbr="parti&utilde;">partium</expan> <expan abbr="inæquali&utilde;">inæqualium</expan> duplicata, & rur&longs;us ip&longs;um <expan abbr="dimidi&utilde;">dimidium</expan> lineæ a&longs;&longs;umptæ <expan abbr="medi&utilde;">medium</expan>, erit proportione inter additas.<emph.end type="italics"/> D<emph type="italics"/><expan abbr="em&utilde;">emum</expan> proportio dimidij <expan abbr="c&utilde;">cum</expan> addita maiore ad <expan abbr="dimidi&utilde;">dimidium</expan>, cum addita minore, uelut maioris partis ad <expan abbr="minor&etilde;">minorem</expan>.<emph.end type="italics"/></cell>

<s>Ita contrariis rationibus celeriter aquam <lb/>tran&longs;mittet, &longs;ed difficiliùs reuertetur. </s>

</row>

<s>Por<lb/>rò difficultas facit vt machinæ magis atte<lb/>rantur, & aquarum multitudine ac impetu <lb/>indigeamus. </s>

<row>

<cell>CLIII.</cell>

<s>Verùm celeritatem cum diffi<lb/>culate eligemus, vbi torrens fuerit, & ripa<lb/>rum altitudo immodica. </s>

<cell>V<emph type="italics"/>im quamcunque manus multiplicare.<emph.end type="italics"/></cell>

<s>Nam &longs;i in&longs;trumen<lb/>ti a&longs;cen&longs;us mollis fuerit, reddetur in&longs;trumen<lb/>tum ob longitudinem graui&longs;&longs;imum. </s>

</row>

<row>

<s>Eadem <lb/>in magnitudine & prauitate ratio. </s>

<cell>CLIIII.</cell>

<cell>S<emph type="italics"/>i lineæ datæ alia linea adiungatur, ab extremitatibus autem prioris lineæ duæ rectæ in unum punctum concurrant proportionem habentes, quam mediam inter tota m & adiectam, & adiectam erit punctus, concur&longs;us à puncto extremo lineæ adiectæ di&longs;tans per lineam mediam.<emph.end type="italics"/> Q<emph type="italics"/>uod &longs;i ab extremo alicuius lineæ æqua'is mediæ, &longs;eu peripheria circuli, cuius &longs;emidiameter &longs;it media linea duæ lineæ ad prædicta puncta producantur, ip&longs;æ erunt in proportione mediæ ad adiectam.<emph.end type="italics"/></cell>

<s>Nam par<lb/>uum facilè circumagitur, &longs;ed &longs;erò irrigat. <lb/></s>

</row>

<s>V&longs;us eius vbi modica terra e&longs;t irriganda, & <lb/>flumen profundum, & leniter currit, & ripæ <lb/>altiores. </s>

<row>

<s>In contrariis cau&longs;is magnis vtemur <lb/>machinis. </s>

<cell>Q<emph type="italics"/>uadr atorum numerum proportionem & inuentionem con&longs;iderare.<emph.end type="italics"/></cell>

</row>

<row>

<s><margin.target id="marg34"/>Machina <lb/>Augu&longs;tana.</s>

<cell>H<emph type="italics"/>orologiorum tempus multiplicare.<emph.end type="italics"/></cell>

<s>E&longs;t & alius machinæ modus ( vt intelli<lb/>go ) Augu&longs;tæ, qui tamen &longs;ub hoc genere <lb/>comprehenditur. </s>

</row>

<s>Columna ver&longs;atilis A B, <lb/>rota cum paxillis vertitur à flumine, iuxta <lb/><figure id="id.016.01.016.2.jpg" xlink:href="016/01/016/2.jpg"/><lb/>rationem à nobis &longs;uperiùs declaratam, dum <lb/>de motuum tran&longs;latione ageremus. </s>

<row>

<cell>CLVII.</cell>

<s>In ea <lb/>curriculi pro numero cochlearum, gratia <lb/>exempli, CDEFGHK, & cochleæ pro nu<lb/>mero va&longs;orum, & va&longs;a pro altitudine: va&longs;a <lb/>autem LMNOPQR, fixa in columna ST. <lb/></s>

<cell>H<emph type="italics"/>orologiorum molarium rationem o&longs;tendere.<emph.end type="italics"/></cell>

<s>Ver&longs;a A B, vertuntur in curriculis cochleæ <lb/>omnes, quarum infima C, haurit aquam <lb/>ex &longs;ubiecto flumine, & transfundit eam in <lb/>vas L, à quo haurit cochlea D, transfun<lb/>dens aquam in vas M, atque ita vno motu <lb/>columnæ A B, C in L, D in M, E in N, <lb/>F in O, G in P, H in Q, K in R, aquam <lb/>fundunt, haurientes è &longs;ubiectis va&longs;is. </s>

</row>

<row>

<s>R, au<lb/>tem transfert aquam per os V, in locum de<lb/>&longs;tinatum. </s>

<cell>CLVIII.</cell>

<cell>R<emph type="italics"/>ationem indicis mobilis cum rota, qua horarum numerus per ictus indicatur explicare.<emph.end type="italics"/></cell>

<s>Contingit rur&longs;us dubitatio: quia <lb/>cochleæ ore &longs;uperiore a&longs;cendente, aquam <lb/>mittere haud debent. </s>

</row>

<s>Quamobrem primam <lb/>triplicem fecimus. </s>

<row>

<s>Sed videntur &longs;ub&longs;ultem <lb/>effundere dum a&longs;cendunt: quia ( vt demon<lb/>&longs;tratum e&longs;t) partes de&longs;cendunt, & aqua tota <lb/>de&longs;cendit, quam ob cau&longs;am compre&longs;&longs;a exi<lb/>lit: &longs;ed non quemadmodum ore cochleæ <lb/>de&longs;cendente, &longs;ed pluribus circa eundem axem <lb/>cochleis po&longs;itis, fit continua non &longs;olùm, <lb/>&longs;ed æqualis aquarum effu&longs;io. </s>

<cell>N<emph type="italics"/>ullus angulus rectilineus æqualis e&longs;&longs;e pote&longs;t alicui angulo contento recta, & cir culi portione.<emph.end type="italics"/></cell>

<s>Atque hæc de <lb/>machinis iuxta prima genera, & &longs;pecies di<lb/>cta &longs;int. </s>

</row>

<row>

<s>Sed po&longs;tquàm de motibus natura<lb/>libus &longs;ermonem habuimus, qui in loco <lb/>fiunt, par e&longs;t vt quid &longs;it locus intelligamus. <lb/></s>

<cell>P<emph type="italics"/>ropo&longs;ita linea tribusque in ea &longs;ignis punctum inuenire, ex quo ductæ tres lineæ ad &longs;igna &longs;int in proportionibus datis.<emph.end type="italics"/></cell>

<s>Nam & hoc e&longs;&longs;e quintum naturalium rerum <lb/>principium &longs;uppo&longs;itum e&longs;t: &longs;uppo&longs;iiones au<lb/>tem hæ, &longs;ecundùm &longs;en&longs;um demon&longs;trationi<lb/>bus ip&longs;is &longs;unt firmiores. </s>

</row>

<s>Quid igitur &longs;it locus, <lb/>&longs;ciendum e&longs;t. </s>

<row>

<s>E&longs;t igitur locus, vltima corpo</s>

<cell>S<emph type="italics"/>i fuerint duo trianguli, quorum ba&longs;es in eadem linea &longs;int con&longs;tituti, & æquales ad unum punctum terminati, & latus unum commune inter reliqua quantitate medium nece&longs;&longs;e e&longs;t angulum à maioribus lineis <expan abbr="content&utilde;">contentum</expan> minorem e&longs;&longs;e.<emph.end type="italics"/></cell>

<s><arrow.to.target n="marg35"/><lb/>ris &longs;uperficies, corpus contentum ambiens. <lb/></s>

</row>

<row>

<s>Manet autem recedente corpore, quia ad c&oelig;<lb/>li ambitum comparata e&longs;t. </s>

<cell>CLXII.</cell>

<cell>P<emph type="italics"/>roportionem duorum orbium, quorum diametrorum conuexæ partis, & concauæ proportiones datæ &longs;int inue&longs;tigare.<emph.end type="italics"/></cell>

<s>Manife&longs;tum e&longs;t <lb/>igitur, locum quemlibet æqualem e&longs;&longs;e cor<lb/>pori in eo contento ad vnguem: & quòd om<lb/>ne corpus e&longs;t in loco, & quòd in omni loco <lb/>aliquod corpus e&longs;t. </s>

</row>

<s>Nam omne corpus &longs;uam <lb/>habet extre mam &longs;uperficiem, & illa vbi nul<lb/>lum aliud &longs;it corpus à quo contineatur vt vl<lb/>timum, c&oelig;lum e&longs;t ei locus: alia autem cor-<pb xlink:href="016/01/017.jpg" pagenum="368"/>pora ab alio continentur. </s>

<row>

<cell>CLXIII.</cell>

<s>Sed locus e&longs;&longs;e non <lb/>pote&longs;t eadem ratione &longs;ine corpore, &longs;i omnis <lb/>locus e&longs;t vltima &longs;uperficies continens cor<lb/>pus. </s>

<cell>P<emph type="italics"/>roportionem uirium &longs;tellarum per motus &longs;uos indagare.<emph.end type="italics"/></cell>

<s>E&longs;t etiam locus ip&longs;e æternus, quia or<lb/>bis c&oelig;le&longs;tis &longs;uperficies extrema immota e&longs;t, <lb/>vt corpus ip&longs;um continet atque vniuer&longs;um. <lb/></s>

</row>

<row>

<s>Locus igitur vt in vniuer&longs;o, æternus e&longs;t & <lb/>immobilis, acimmutabilis: vt autem cor<lb/>poris certi &longs;uperficies, mutatur corporum <lb/>mutatione, nec manet. </s>

<cell>CLXIIII.</cell>

<cell>S<emph type="italics"/>yderum proportionem in magnitudine o&longs;tendere.<emph.end type="italics"/></cell>

<s>Locus igitur vbi <lb/>Alexander &longs;edit in Babylonica, vel Su&longs;is, <lb/>adhuc manet, &longs;ed nunc in aëre erat in ciui<lb/>tate atque domo, nunc autem for&longs;an in <lb/>agro, atque etiam &longs;ub terra. </s>

</row>

<s>E&longs;t vbi in <lb/>Ro&longs;tris facundi&longs;&longs;imus Cicero perorauit, <lb/>locus manet, at tunc propter terram in <lb/>aëre fuit, nunc autem cre&longs;cente for&longs;itan <lb/>terra, &longs;ub ip&longs;a terra. </s>

<row>

<s>Et in quolibet loco <lb/>nunc vici&longs;&longs;itudinibus temporum id agenti<lb/>bus infiniti erunt homines, aliá&longs;que fuêre, <lb/>&longs;i vera e&longs;t opinio Ari&longs;totelis de mundi æter<lb/>nitate. </s>

<cell>P<emph type="italics"/>roportionem motuum omnium &longs;tellarum ad<emph.end type="italics"/> S<emph type="italics"/>olem con&longs;iderare.<emph.end type="italics"/></cell>

<s>Tria igitur &longs;unt &longs;emper nobi&longs;cum <lb/>æterna, mens, hyle, & locus. </s>

</row>

<row>

<s>Sed men<lb/>tem mutare, aut materiam non licet, locum <lb/>mutare licet, & alium adipi&longs;ci. </s>

<cell>CLXVI.</cell>

<cell>P<emph type="italics"/>roportiones mu&longs;icas &longs;uperpartientes in eas, quæ particulá una tantum abundant reducere.<emph.end type="italics"/></cell>

<s>Quocun<lb/>que igitur perrexerimus, ad rem æternam <lb/>imus. </s>

</row>

<s>Et nunc locus in quo &longs;cribo æternus <lb/>e&longs;t, atque in eo complures for&longs;an fuêre re<lb/><arrow.to.target n="marg36"/><lb/>ges, aut &longs;apientes. </s>

<row>

<s>Cùm enim principia <lb/>rerum naturalium &longs;int quinque, materia <lb/>&longs;eu hyle, forma, anima, locus, motus: <lb/>tempus autem non e&longs;t principium, &longs;ed mo<lb/>tum &longs;equitur: proximum autem videtur e&longs;&longs;e <lb/>principio, quia nihil &longs;ine ip&longs;o fit: de hoc au<lb/>tem po&longs;teriùs dicemus. </s>

<cell>CLXVII.</cell>

<cell>P<emph type="italics"/>roportionem mu&longs;icam ad &longs;apores & odores coaptare.<emph.end type="italics"/></cell>

<s>Quies quoquè non <lb/>e&longs;t principium, &longs;ed principij priuatio, vt <lb/>mors, frigus, &longs;iccitas. </s>

</row>

<s>Repugnantia item <lb/>corporum atque inane &longs;eu vacuum, non &longs;unt <lb/>principia, à forma enim pendêre hæc, de<lb/>mon&longs;trauimus, & aliàs etiam demon&longs;trabi<lb/>mus. </s>

<row>

<cell>CLXVIII.</cell>

<s>Horum igitur principiorum nul<lb/>lum non e&longs;t &longs;ecundùm genus æternum <lb/>& primum, aliter non po&longs;&longs;ent e&longs;&longs;e princi<lb/>pia. </s>

<cell>P<emph type="italics"/>icturarum proportiones explicare.<emph.end type="italics"/></cell>

<s>Sed per &longs;e æterna &longs;unt mens, hyle & <lb/>locus. </s>

</row>

<row>

<s>Forma & motus parte æterna in c&oelig;<lb/>le&longs;tibus, parte mortalia in his, quæ &longs;u lunæ <lb/>cælo &longs;unt con&longs;tituta. </s>

<cell>CLXIX.</cell>

<cell>P<emph type="italics"/>roportionem mu&longs;icam in in&longs;trumentis declarare iuxta compo&longs;itionis rationem.<emph.end type="italics"/></cell>

<s>Anima verò parte qua<lb/>dam, qua intelligit, æterna, reliqua mor<lb/>talis e&longs;t. </s>

</row>

<s>Expers corporis e&longs;t mens, locus & <lb/>motus. </s>

<row>

<s>Sed mens ab&longs;oluitur omninò à cor<lb/>pore, motus &longs;ine corpore non e&longs;t. </s>

<cell>C<emph type="italics"/>oniugationes cuiu&longs;uis numeri breuiter inuenire.<emph.end type="italics"/></cell>

<s>Anima <lb/>autem, hyle & forma, cum corpore nece&longs;&longs;a<lb/>riò &longs;unt. </s>

</row>

<row>

<s>Anima tamen non videtur pars il<lb/>lius. </s>

<cell>CLXXI.</cell>

<cell>P<emph type="italics"/>ropo&longs;itis duobus quibuslibet numeris, quotuis alios &longs;eu in continuum &longs;eu medios in continua proportione arithmetica, geometrica & mu&longs;ica inuenire.<emph.end type="italics"/></cell>

<s>Quòd verò plura e&longs;&longs;e non po&longs;&longs;int princi<lb/>pia, ex hoc demon&longs;tratur. </s>

</row>

<s>Nam quæ &longs;unt, <lb/>quædam viuunt, quædam non. </s>

<row>

<cell>CLXXII.</cell>

<s>Reguntur <lb/>autem omnia atque fiunt, tum manet. </s>

<cell>P<emph type="italics"/>roportiones<emph.end type="italics"/> S<emph type="italics"/>tiphelij de&longs;cribere.<emph.end type="italics"/></cell>

<s>Cor<lb/>pus igitur in loco manet. </s>

</row>

<row>

<s>Fiunt autem ex <lb/>materia atque forma. </s>

<cell>CLXXIII.</cell>

<cell>C<emph type="italics"/>irculum &longs;uper centro &longs;uo mouere æqualiter, ita quod omnia illius puncta per rectam lineam moueantur ultro citroque.<emph.end type="italics"/></cell>

<s>Reguntur autem ab <lb/>anima, quæ in nobilioribus mens e&longs;t, & à <lb/>corpore &longs;eparata: in corporibus autem, vitæ <lb/>principium. </s>

</row>

<s>Sed cau&longs;a qua manent e&longs;t motus, <lb/>item generationis, & reliquorum. </s>

<row>

<cell>CLXXIIII.</cell>

<s>Omnia <lb/>hæc cùm &longs;int quidam motus, & vt fiunt, & vt <lb/>manent, igitur motus principium e&longs;t. </s>

<cell>P<emph type="italics"/>rogre&longs;&longs;us & regre&longs;&longs;us, tam &longs;ine latitudine quàm cum latitudine in planetis per &longs;olos concentricos circulos æqualiter motos demon&longs;trare.<emph.end type="italics"/></cell>

<s>De <lb/>principiis &longs;ecundùm &longs;en&longs;um, & vt ad hanc <lb/>pertinebat tractationem, hæc docui&longs;&longs;e hacte<lb/>nus &longs;ufficiat: non enim hoc modo priuatio <lb/>principium e&longs;t. </s>

</row>

<row>

<s>Supere&longs;t nunc, vt declaremus, <lb/>vacuum non dari, præter rationes tres &longs;en&longs;i<lb/>biles &longs;uperiùs adductas, hoc diligentiùs nunc <lb/>demon&longs;trantes. </s>

<cell>CLXXV.</cell>

<cell>C<emph type="italics"/>au&longs;am uarietatis diametrorum ex &longs;uppo&longs;itis concentricis demon&longs;trare.<emph.end type="italics"/></cell>

<s>O&longs;ten&longs;um erit & pari ratio<lb/>ne de corporum repugnantia, quicquid &longs;upe<lb/>riùs &longs;uppo&longs;uimus: nam neque in eodem loco <lb/>duo corpora, nec corpus vnum in duobus <lb/>locis, nec corpore locum e&longs;&longs;e po&longs;&longs;e diximus. <lb/></s>

</row>

<s>Nunc igitur hoc vltimo denuò demon&longs;tru<lb/>to, reliqua etiam erunt manife&longs;ta: neque <lb/>enim in hoc libro &longs;ingula demon&longs;trare, &longs;ed <lb/>res per capita tractare propo&longs;itum e&longs;t. </s>

<row>

<cell>CLXXVI.</cell>

<s>Pri<lb/>múm igitur vacuum non e&longs;t: quomodo igi<lb/>tur quod non e&longs;t, efficere quicquam po<lb/>terit? </s>

<cell>R<emph type="italics"/>ationem centri grauitatis declarare.<emph.end type="italics"/></cell>

<s>Deinde &longs;i e&longs;&longs;e ponatur, &longs;ub&longs;tantia <lb/>non e&longs;t vacuum, neque à &longs;ub&longs;tantia profi<lb/><arrow.to.target n="marg37"/><lb/>ci&longs;citur, & vt vno verbo ab&longs;oluam, nihil <lb/>e&longs;t, atque ideo nullam poterit habere ope<lb/>rationem. </s>

</row>

<row>

<s><margin.target id="marg35"/>Locus quid <lb/>&longs;it.</s>

<cell>CLXXVII.</cell>

<cell>S<emph type="italics"/>i proportio aliqua ex duabus proportionibus eiu&longs;dem quantitatis ad alias duas componatur, erit proportio illarum duarum eadem proportioni producti ex proportione in primam duarum quantitatum, detracta priore illa quantitate, quæ ad duas comparatur, ad eandem priorem quantitatem.<emph.end type="italics"/></cell>

<s><margin.target id="marg36"/><expan abbr="Principior&utilde;">Principiorum</expan> <lb/>naturalium <lb/>diui&longs;io.</s>

</row>

<s><margin.target id="marg37"/>Demon&longs;tra<lb/>tio, quia nul<lb/>lus motus e&longs;t <lb/>à vacuo.</s>

<row>

<cell>CLXXVIII.</cell>

<s>For&longs;an dicet qui&longs;piam, naturam metu <lb/>vacui, &longs;eu vt illud euitet, motum ciere. </s>

<cell>P<emph type="italics"/>roportionem mi&longs;tionis metallorum, maximè auri & argenti declarare.<emph.end type="italics"/></cell>

<s>Sed <lb/>neque i&longs;tud: nam quum aër rarior aqua &longs;it, <lb/>oportuit primò antequàm fiat attractio va<lb/>cui ratione, quum aqua a&longs;cendit aquæ con<lb/>&longs;ecutione, priorem aquam in aërem verti, <lb/>húncque rur&longs;us in ignem, qui aëre rarior e&longs;t: <lb/>deinde ip&longs;um ignem attenuari, demum fieri <lb/>hanc attractionem. </s>

</row>

<row>

<s>Sed nos videmus, aquam <lb/>non verti in aërem, &longs;ed trahere: &longs;imiliter <lb/>aërem, antequam in ignem tran&longs;eat: non igi<lb/>tur metu vacui, quum adhuc &longs;uper&longs;int tot <lb/>intermedia, &longs;ed metu raritatis natura moli<lb/>tur eam attractionem, quam à vacuo appel<lb/>lant. </s>

<cell>CLXXIX.</cell>

<cell>S<emph type="italics"/>i duobus totis duæ portiones &longs;imiles ab&longs;cindantur ab ei&longs;dem denuò, & ab&longs;cißis portionibus partes eædem auferantur, denuoque ac denuò quoties libuerit à portionibus, & ù re&longs;iduis ip&longs;arum quantitatum partes eædem auferantur, erit re&longs;iduí ad re&longs;iduum, ueluti totius ad totum.<emph.end type="italics"/></cell>

<s>Nec e&longs;t vt eam cum Auerroë, violen<lb/><arrow.to.target n="marg38"/><lb/>tam dicam: nam ip&longs;a pror&longs;us e&longs;t naturalis, <lb/>&longs;icut & motus aquæ, quum in aëre fuerit & <lb/>de&longs;cendit: violenter enim quie&longs;cit, & ideo <lb/>naturaliter mouetur. </s>

</row>

<s>Sic elementum, quod <lb/>raritatis cau&longs;a trahit, violentiam patitur, à <lb/>qua motu illo &longs;e liberat. </s>

<row>

<cell>CLXXX.</cell>

<s>Quòd verò eo motu <lb/>graue &longs;ur&longs;um trahatur, contingit ca&longs;u, e&longs;t que <lb/>ei quod trahitur, quandoque violentum, & <lb/>quandoque non, velut &longs;i leue &longs;ur&longs;um traha<lb/>tur. </s>

<cell>S<emph type="italics"/>i aliqua quantitas in duas partes diuidatur, fueritque alicuius quantitatis ad partes illas compo&longs;ita proportio, non poterit eiu&longs;dem quantitatis ad partes alias quantitatis diui&longs;a, aliter proportio eadem componi.<emph.end type="italics"/></cell>

<s>Satis e&longs;t motum ex principio ip&longs;o e&longs;&longs;e <lb/>naturalem. </s>

</row>

<row>

<s><margin.target id="marg38"/>Motus at<lb/>tractionis à <lb/>raritate, non <lb/>e&longs;t <expan abbr="viol&etilde;tus">violentus</expan>.</s>

<cell>CLXXXI.</cell>

<cell>C<emph type="italics"/>um fuerit aliqua proportio, compo&longs;ita ex proportionibus primæ ad &longs;ecundam & tertiam, & rur&longs;us quartæ ad quintam & &longs;extam: ita &longs;e habebit proportio &longs;ecundæ ad tertiam, ad proportionem quintæ ad &longs;extam, uelut producti ex proportione in &longs;ecundam detracta prima ad primam ad productum ex proportione in quintam, detracta quarta ad quartam.<emph.end type="italics"/></cell>

<s>Vt inuito, vel &longs;altem non iuuante pa&longs;&longs;o <lb/>fit? </s>

</row>

<s>Imò quod mouetur ad locum, &longs;pontè <lb/>mouetur, vt elementum aut mixtum, non vt <lb/>graue, aut leue. </s>

<row>

<cell>CLXXXII.</cell>

<s>Obliui&longs;citur enim propriæ <lb/>naturæ, quòd &longs;ic mouetur con&longs;en&longs;u alterius. <lb/></s>

<cell>P<emph type="italics"/>ropo&longs;ita differentia proportionum partium &longs;imilium ad partes a&longs;&longs;umptas, propo&longs;itaque proportione totius ad re&longs;idua eadem, differentiam proportionum totius ad reliquum re&longs;idui inuenire.<emph.end type="italics"/></cell>

<s>Velut qui filium hortatur ad vitæ pericu<lb/>lum, dum muri vrbis ab ho&longs;te oppugnan<lb/>tur, pietatem exercet: vbi communis cau<lb/>&longs;a non impelleret, id agens crudelis habe<lb/>retur. </s>

</row>

<row>

<s>Sed iam ad motus grauium veniamus. </s>

<cell>CLXXXIII.</cell>

<cell>S<emph type="italics"/>pacium uitæ naturalis per &longs;pacium uitæ fortuitum declarare.<emph.end type="italics"/></cell>

<s>Hic <lb/><arrow.to.target n="marg39"/><lb/>autem liber e&longs;t, aut fit pondere alligato, vt in <lb/>libra & &longs;tatera. </s>

</row>

<s>Quæri &longs;olet, cur pondera <lb/>ponderibus magis agitantur? </s>

<row>

<cell>CLXXXIIII.</cell>

<s>nam manu<lb/>brio A, agitetur &longs;uper furculam C, pondus <lb/>B. </s>

<cell>Q<emph type="italics"/>uæcunque grauia in uorticibus aquarum, merguntur, in medio uorticis, primum uer&longs;a mergantur.<emph.end type="italics"/></cell>

<s>Con&longs;tat quòd &longs;i addatur pondus ip&longs;i ma<lb/>nubrio, vtpote plumbum v&longs;que ad certam <lb/>metam, faciliùs de&longs;cendere à lateribus ad <lb/>medium adiuuante pondere: at contrà diffi<lb/>cilius moueri à medio ad latera. </s>

</row>

<row>

<s>Ob id, pon<lb/>deris meta quædam habenda e&longs;t, v&longs;que ad <lb/>quam motus facilitas augetur. </s>

<cell>CLXXXV.</cell>

<cell>C<emph type="italics"/>ur homo &longs;edens quanto altius &longs;edet, & quanto magis crura ad f&oelig;mora, & f&oelig;mora ad pectus reclinata habet, facilius con&longs;urgat, cum tamen hæc oppo&longs;ito modo inuicem &longs;e habeant, declarare.<emph.end type="italics"/></cell>

<s>Hanc tamen <lb/>&longs;i tran&longs;cendas, motus redditur difficilior. <lb/></s>

</row>

<s>Hac ratione capulos en&longs;ibus grauiores ad<lb/>dunt, vt en&longs;es videantur leuiores, faciliú&longs;<lb/>que tractentur. </s>

<row>

<cell>CLXXXVI.</cell>

<s>Sed & hîc modus &longs;eruan<lb/>dus e&longs;t. </s><pb xlink:href="016/01/018.jpg" pagenum="369"/>

<cell>S<emph type="italics"/>i fuerit proportio primæ & &longs;ecundæ quantitatis ad tertiam, ut primæ & quartæ ad quintam, fueritque quarta &longs;ecunda maior, erit proportio quartæ ad quintam maior quàm &longs;ecundæ ad tertiam.<emph.end type="italics"/> Q<emph type="italics"/>uod &longs;i fuerit maior<emph.end type="italics"/></cell>

<cell/>

<s><margin.target id="marg39"/>Quomode <lb/>pondera fa<lb/>cile mouean<lb/>tur.</s><figure id="id.016.01.018.1.jpg" xlink:href="016/01/018/1.jpg"/>

</row>

<s>Adiecimus hoc, quia pleraque in&longs;trumen<lb/><arrow.to.target n="marg40"/><lb/>ta hauriendis aquis idonea, hominum aut <lb/>iumentorum viribus aguntur. </s>

<row>

<cell/>

<s>Sed et&longs;i ip&longs;a<lb/>rum aquarum rapido impetu agitentur ma<lb/>chinæ, rur&longs;us addita manubriis pondera fa<lb/>ciliorum efficiunt motum. </s>

<cell><emph type="italics"/>quartæ ad quintam quàm &longs;ecundæ ad tertiam, nece&longs;&longs;e e&longs;t quartam &longs;ecunda e&longs;&longs;e maiorem.<emph.end type="italics"/></cell>

<s>Licet itaque &longs;olo <lb/>impetu aquarum defluentium, aquas ip&longs;as in <lb/>&longs;uprema loca impellere, atque ægros humi<lb/>lioribus aquis irrigare. </s>

</row>

<row>

<s>Sed hoc tantùm in <lb/>his quæ decurrunt, & impetum labendo ha<lb/>bent. </s>

<cell>CLXXXVII.</cell>

<cell>S<emph type="italics"/>i ei&longs;dem uiribus & ‘eadem’ proportione cum auxilio ponderis tertij quartum pondus moueatur quibus &longs;ecundum, auxilio primi nece&longs;&longs;e e&longs;t <expan abbr="quart&utilde;">quartum</expan> pon dus tardius & maiore cum difficultate moueri quàm &longs;ecundum.<emph.end type="italics"/></cell>

<s>Aptetur enim à latere vno Cte&longs;ibica, <lb/>aut Brambilica, aut alterius generis machi<lb/>na: nam ( vt dixi ) innumeri po&longs;&longs;unt e&longs;&longs;e <lb/>modi earum, quanquam hæ omnibus aliis, <lb/>coclea excepta, &longs;int elegantiores: & ( vtiam <lb/>docuimus ) alternus manubrij motus rota <lb/>cum pinnis agitata perficiatur, &longs;ic fiet vt <lb/>&longs;pontè aqua &longs;eip&longs;am &longs;ur&longs;um impellat: nam<lb/>que ars contra &longs;ua in&longs;tituta eam facere co<lb/>git. </s>

</row>

<s>Quod exemplum nonnullæ ciuitates quæ <lb/>editioribus à flumine locis po&longs;itæ &longs;unt, &longs;e<lb/>quuntur. <lb/><arrow.to.target n="marg41"/></s>

<row>

<cell>CLXXXVIII.</cell>

<s><margin.target id="marg40"/>Quomodo <lb/>aqua <expan abbr="&longs;eipsã">&longs;eipsam</expan> <lb/>impellat &longs;ur<lb/>&longs;um.</s>

<cell>S<emph type="italics"/>i uires aliquæ moueant cum ponderibus aliqua pondera, ut compo&longs;ita proportio &longs;it eadem proportioni uirium & duorum ponderum mouentium aggregatum æquale duorum ponderum, ubi maior fuerit partium in æqualitas, ibi erit maior difficultas.<emph.end type="italics"/></cell>

<s><margin.target id="marg41"/>De libra & <lb/>illius ratio<lb/>ne.</s>

</row>

<row>

<s>Po&longs;t hæc videndum e&longs;t de ponderibus <lb/>quæ in libra con&longs;tituuntur. </s>

<cell>CLXXXIX.</cell>

<cell>S<emph type="italics"/>i pondus minus ad longitudinem minorem &longs;ub æquali proportione coaptetar, facilius deor&longs;um trahetur quàm quod maius e&longs;t & propius.<emph.end type="italics"/></cell>

<s>Sit igitur libra, <lb/>cuius trutina &longs;it appen&longs;a in A, & finis vbi <lb/>iunguntur latera lancis B, & lanx CD, & <lb/>manife&longs;tum e&longs;t quòd CD mouetur circa B, <lb/>velut centrum quoddam, quia CD non po<lb/>te&longs;t &longs;eparari ab ip&longs;o B: & &longs;it angulus ABC, <lb/>& ABD rectus. </s>

</row>

<s>Dico quòd pondus in C <lb/>con&longs;titutum erit grauius, quàm &longs;i lanx collo<lb/>cetur in quocunque alio loco, vtpute quòd <lb/><figure id="id.016.01.018.2.jpg" xlink:href="016/01/018/2.jpg"/><lb/>con&longs;titueretur lanx in F. </s>

<row>

<s>Vt autem cogno&longs;<lb/>camus quòd C &longs;it grauius in eo &longs;itu, quam <lb/>in F, nece&longs;&longs;arium e&longs;t vt in æquali tempore <lb/>moueatur per maius &longs;patium ver&longs;us cen<lb/>trum. </s>

<cell>S<emph type="italics"/>i fuerit primum graue minus &longs;ecundo, & &longs;ecundum minus tertio, proportio autem primi ad &longs;ecundum multo maior quàm &longs;ecundi ad tertium, po&longs;ibile erit propo&longs;itis uiribus ei&longs;dem addere pondus <expan abbr="&longs;ec&utilde;do">&longs;ecundo</expan>, ut ip&longs;um & tertium moueatur faciliùs ab ei&longs;dem uiribus, & primo uel &longs;ecundo quàm antea.<emph.end type="italics"/></cell>

<s>Videmus enim grauiora pari ratione <lb/>in reliquis, velociùs ad centrum ferri. </s>

</row>

<row>

<s>Quòd <lb/>autem hoc contingat magis pondere & li<lb/>bra in C collocata quàm in F, o&longs;tendo dua<lb/>bus rationibus. </s>

<cell>C<emph type="italics"/>um fuerint duo pondera & uires, duxerisque aggregatum ex uiribus & minore pondere in maius, addiderisque in&longs;uper quantum e&longs;t productum dimidij ui rium in &longs;e latus aggregati detracto dimidio uirium, dicetur pondus auxiliare æqualis proportionis.<emph.end type="italics"/></cell>

<s>Prima, quòd &longs;i in aliquo <lb/>tempore moueatur ex C in E, & &longs;it arcus <lb/>CE æqualis FG, quod tardius de&longs;cendet ex <lb/>F in G, quàm ex C in E, & ita erit leuiùs <lb/>in F, quàm in C. Secundò, quòd po&longs;ito <lb/>quòd in æquali &longs;patio temporis moueretur <lb/>ex C in E, ex & F in G, adhuc per arcum <lb/>CE æqualem FG, magis appropinquaret <lb/>centro quàm per motum factum in arcu <lb/>FG. </s>

</row>

<s>Ideò ergo duplici ratione magis gra<lb/>uabit pondus lance po&longs;ita ad perpendicu<lb/>lum cum trutina, quàm in quoque alio <lb/>loco. </s>

<row>

<cell>CXCII.</cell>

<s>Primùm igitur &longs;ic declaratur. </s>

<cell>S<emph type="italics"/>i ex medio diametri linea ad perpendiculum erigatur ad circuli peripheriam, ex eo puncto autem quotlibet lineæ ducantur &longs;eu intus ad circun ferentiam u&longs;que, &longs;eu extra ad diametrum, erit proportio totius lineæ ad totam uelut mutuo partis ad partem.<emph.end type="italics"/></cell>

<s>Manife<lb/>&longs;tum e&longs;t in &longs;tateris, & in his, qui pondera <lb/>eleuant, quòd quantò magis pondus à tru<lb/>tina, eò magis graue videtur: &longs;ed pondus <lb/>in G di&longs;tat à trutina quantitate BC lineæ, <lb/>& in F quantitate FP, &longs;ed CB e&longs;t maior FP, <lb/>ex decimaquinta, tertij elementorum Eu<lb/>clidis: igitur lance po&longs;ita in C, grauius pon<lb/>dus videbitur quàm in F, quod erat primum. <lb/></s>

</row>

<row>

<s>Ex hac etiam demon&longs;tratione manife&longs;tum <lb/>e&longs;t, libram quantò magis di&longs;cendit ver&longs;us <lb/>C ex A, tantò grauiùs pondus reddere, & eò <lb/>velociùs moueri: at ex C ver&longs;us Q, contra<lb/>ria ratione pondus reddi leuius, & motum <lb/>&longs;egniorem, quod & experimentum docet. <lb/></s>

<cell>CXCIII.</cell>

<cell>R<emph type="italics"/>ationem ponderis triplicem explicare.<emph.end type="italics"/></cell>

<s>Secundum verò &longs;ic demon&longs;tratur. </s>

</row>

<s>Quia enim <lb/>CE e&longs;t æqualis FG, &longs;umatur CH æqualis <lb/>CE, eritque æqualis CH ip&longs;i FG, quare re<lb/>cta &longs;ubten&longs;a CH, æqualis rectæ &longs;ubten&longs;æ <lb/>FG. </s>

<row>

<cell>CXCIIII.</cell>

<s>Igitur ex octaua primi elementorum <lb/>angulus BFG, æqualis erit angulo BCH. </s>

<cell>P<emph type="italics"/>roportionem ponderis longioris in medio &longs;u&longs;pen&longs;i, ad breuius illi æquale & in medio &longs;u&longs;pen&longs;um declarare.<emph.end type="italics"/></cell>

<s>Igi<lb/>tur ductis ad perpendiculum rectis FL & <lb/>HK, minor e&longs;t angulus FGL. qui & ip&longs;e <lb/>e&longs;&longs;et pars coæqualis BFG, ex quinta primi <lb/>elementorum, angulo KCH. </s>

</row>

<row>

<s>Igitur latus <lb/>HK, maius latere FL: nam rectæ FG & HC <lb/>æquales fuerunt, & trigoni orthogonij &longs;eu <lb/>rectanguli: igitur BN maior OF, & ideo <lb/>BM maior OP. </s>

<cell>S<emph type="italics"/>i lectus fiat dupla longitudine ad latitudinem, melius &longs;uffulcietur re&longs;tibus ex medio ad angulos & eius æquidi&longs;tantibus quàm &longs;ecundum longitudinem & latitudinem.<emph.end type="italics"/></cell>

<s>Dum igitur libra mouetur ex <lb/>C in E pondus de&longs;cendit per BM lineam, &longs;eu <lb/>propinquius centro redditur quàm e&longs;&longs;et in <lb/>C, & dum mouetur per &longs;patium arcus FG, <lb/>de&longs;cenditque per OP, & BM, maior e&longs;t OP. <lb/></s>

</row>

<s>Igitur &longs;uppo&longs;ito etiam quod in æquali tem<lb/>pore tran&longs;iret ex C in K, & ex F in G, adhuc <lb/>velociùs de&longs;cendit ex C, quam ex F. </s>

<row>

<cell>CXCVI.</cell>

<s>Igitur <lb/>grauius e&longs;t in C, quàm in F. </s>

<cell>S<emph type="italics"/>i duo circuli &longs;uper eodem centro eodem motu trans feruntur, æquale &longs;pacium &longs;uperant.<emph.end type="italics"/></cell>

<s>Ex hoc autem <lb/>demon&longs;tratur quod dicit Philo&longs;ophus, quòd <lb/>&longs;i æqualia &longs;int pondera in F & R, libra ta<lb/>men &longs;pontè redit ad &longs;itum CD, vbi trutina <lb/>&longs;it AB. </s>

</row>

<row>

<s>Nec hoc demon&longs;trat Iordanus, nec <lb/>intellexit. </s>

<cell>CXCVII.</cell>

<cell>C<emph type="italics"/>ur lances ad locum &longs;uum &longs;u&longs;pen&longs;i redeant, impendentes <expan abbr="nõ">non</expan>, <expan abbr="demõ&longs;trare">demon&longs;trare</expan>.<emph.end type="italics"/></cell>

<s>Similiter cur trutina QB po&longs;ita, <lb/>atque infrà libram ip&longs;am, velut accidit con<lb/>uer&longs;a libra, vt manu trutinam teneas &longs;uper</s>

</row>

<s><arrow.to.target n="marg42"/><lb/>incumbente libra pondus quod iam de&longs;cen<lb/>derat tractum ad R, vbi æquale aliud ad <lb/>con&longs;titutum in F, vel lances omninò vacuæ <lb/>&longs;int, non &longs;olùm non reuertuntur ad &longs;itum <lb/>CD, &longs;eu perpendiculi, imò magis R de&longs;cen<lb/>dit ver&longs;us Q & F a&longs;cendit ver&longs;us A. vt expe<lb/>rimento patet. </s>

<row>

<cell>CXCVIII.</cell>

<s>Hoc etiam Iordanus non de<lb/>mon&longs;trauit. </s>

<cell>C<emph type="italics"/>ur &longs;olidum quod cubus uocatur<emph.end type="italics"/> P<emph type="italics"/>yramide &longs;tabilius &longs;it o&longs;tendere.<emph.end type="italics"/></cell>

<s>Ari&longs;toteles dicit hoc contingere, <lb/>quum trutina e&longs;t &longs;upra libram, quia angu<lb/>lus QBF metæ, maior e&longs;t angulo QBR, Et &longs;i<lb/>militer quum trutina fuerit QB, erit meta <lb/>AB, & tunc angulus RBA, maior erit angu<lb/>lo FBA, &longs;ed maior angulus reddit grauius <lb/>pondus: igitur dum trutina &longs;uperius e&longs;t F, <lb/>erit grauius R, ideo F trahet libram ver&longs;us <lb/>C, & dum fuerit inferius R, erit grauius <lb/>quàm F, ideo trahet libram ver&longs;us <expan abbr="q.">que</expan> Quòd &longs;i <lb/>quis obiiciat, igitur pondus in F, erit gra<lb/>uius quàm in C, trutina in A appen&longs;a cuius <lb/>tamen oppo&longs;itum iam e&longs;t demon&longs;tratum. <lb/></s>

</row>

<row>

<s>Re&longs;pondemus, quòd latior angulus à meta, <lb/>facit pondus grauius, quum rectæ fuerint <pb xlink:href="016/01/019.jpg" pagenum="370"/>æquales: &longs;ed vt demon&longs;tratum e&longs;t, pondus <lb/>in C, plus di&longs;tat tam à meta, quàm à trutina, <lb/>quam in E, ideo ratio anguli ibi non tenet: <lb/>&longs;ed quum comparamus pondera in F & R, <lb/>iam illa æqualiter di&longs;tant tam à trutina, <lb/>quod à meta: ideo tanc anguli ratio &longs;pectan<lb/>da e&longs;t. </s>

<cell>CXCIX.</cell>

<cell>R<emph type="italics"/>ationem remorum nauim impellentium inuenire.<emph.end type="italics"/></cell>

<s>Generalis igitur ratio hæc &longs;it: pon<lb/>dera quò plus di&longs;tant à meta &longs;eu linea de&longs;<lb/>cen&longs;us per rectam, aut obliquum, id e&longs;t, per <lb/>angulum, eò &longs;unt grauiora. </s>

</row>

<s>Sed primò rectæ <lb/>lineæ magnitudo &longs;pectanda e&longs;t: vbi rectæ li<lb/>neæ æquales &longs;int, tunc angulus quòd maior <lb/>erit, eò pondus reddetur grauius. </s>

<row>

<s>Si igitur <lb/>BC &longs;inuetur ver&longs;us QC, eleuabitur, & mi<lb/><arrow.to.target n="marg43"/><lb/>nus di&longs;tabit à B puncto, ideoque reddet pon<lb/>dera leuiora, aureu&longs;que iu&longs;ti ponderis defi<lb/>cere videbitur, & ex aduer&longs;a parte po&longs;itus <lb/>qui deficit, bonus videbitur. </s>

<cell>C<emph type="italics"/>ur temo cum paruus &longs;it, magnam nauim agere pote&longs;t, & cur cùm uarietas &longs;it in prora, ip&longs;e con&longs;tituatur in puppi.<emph.end type="italics"/> E<emph type="italics"/>t cum transuer&longs;im ab aqua prematur rectà nauim dirigat.<emph.end type="italics"/></cell>

<s>Sed vacua libe<lb/>ra delegitur fraus, aur commutatis vici&longs;&longs;im <lb/>numo & indice. </s>

</row>

<row>

<s>Sed cur pondera quærunt <lb/>ver&longs;us medium moueri? </s>

<cell>S<emph type="italics"/>i duæ lineæ non &longs;ecantes circuli peripheriam in unum punctum ex ea coeant exterius, nece&longs;&longs;e e&longs;t illas peripheria contenta e&longs;&longs;e maiores.<emph.end type="italics"/></cell>

<s>Hoc facilè di&longs;&longs;olui<lb/>tur, &longs;i quis, quæ diximus mente teneat. </s>

</row>

<s>Nam <lb/>pondus in F, dum peruenit ad C, propin<lb/>quius redditur mundi centro ad quod natu<lb/>ra fertur linea PB: & dum ex C in Q linea <lb/>BQ & ita intentum ponderis e&longs;t rectà ferri <lb/>ad centrum quia vinculo prohibetur, moue<lb/>tur eo modo, quo moueri pote&longs;t, atque ita à <lb/>dextra, vel &longs;ini&longs;tra ver&longs;us perpendiculum, & <lb/>medium. </s>

<row>

<s>Sed dices, cur igitur libra vacua C, <lb/>non mouetur ver&longs;us Q? Re&longs;pondeo, quòd <lb/>tunc D moueretur ver&longs;us A: &longs;ed vt vi&longs;um e&longs;t <lb/>ratione rectæ linæ po&longs;ito C in Q & D in A, <lb/>adhuc tantum e&longs;&longs;et ami&longs;&longs;um ex parte D, <lb/>quantum acqui&longs;itum ip&longs;i C: &longs;ed quod e&longs;&longs;et <lb/>ami&longs;&longs;um ex parte D, e&longs;&longs;et magis contra na<lb/>turam quam illud quod e&longs;&longs;et acqui&longs;itum ip&longs;i <lb/>C &longs;ecundum naturam: igitur maius e&longs;&longs;et de<lb/>trimentum quam iuuamentum. </s>

<cell>R<emph type="italics"/>ationem &longs;trepitus o&longs;tendere.<emph.end type="italics"/></cell>

<s>Quare pari<lb/>bus ponderibus in C & D, non &longs;olum non <lb/>remouebuntur ab eo &longs;itu &longs;pontè, &longs;ed vi amo<lb/>ta redibunt. </s>

</row>

<row>

<s>His rationibus con&longs;ideratis, po&longs;<lb/>&longs;umus facere libram quæ vacua ponderibus <lb/>æqua videbitur, iu&longs;ti&longs;que notis ponderum <lb/>maius rerum ip&longs;arum pondus repræ&longs;entet. <lb/></s>

<cell>CCIII.</cell>

<cell>C<emph type="italics"/>ur &longs;cytalis onera portentur faciliùs, explorare.<emph.end type="italics"/></cell>

<s>Sic enim vt Ari&longs;toteles refert, purpuram <lb/>vendentes imponebant emptoribus. </s>

</row>

<s>Cuius <lb/>ratio &longs;ic con&longs;tat: <lb/><arrow.to.target n="marg44"/></s>

<row>

<cell>CCIIII.</cell>

<s><margin.target id="marg42"/>Cur libra <lb/>vacua redit <lb/>&longs;pontè ad &longs;i<lb/>tum rectum, <lb/>vel &longs;i pon<lb/>dera æqua<lb/>lia fuerint.</s>

<cell>C<emph type="italics"/>ur pluribus trochleis, pondera facilius eleuentur o&longs;tendere.<emph.end type="italics"/></cell>

<s><margin.target id="marg43"/>Vt aurei iu<lb/>&longs;ti ponderis <lb/>leuiores vi<lb/>deantur, & <lb/>leues iu&longs;ti. <lb/></s>

</row>

<row>

<s>Cur pondera <lb/>ver&longs;us me<lb/>dium mo<lb/>uentur.</s>

<cell>S<emph type="italics"/>uper uerbis<emph.end type="italics"/> P<emph type="italics"/>latonis de fine<emph.end type="italics"/> R<emph type="italics"/>eipublicæ.<emph.end type="italics"/></cell>

<s><margin.target id="marg44"/>Modus fa<lb/>ciendi <expan abbr="librã">libram</expan>, <lb/>quæ pondera <lb/>rerum maio<lb/>ra quàm <lb/>&longs;int o&longs;tendat.</s><figure id="id.016.01.019.1.jpg" xlink:href="016/01/019/1.jpg"/>

</row>

<s>Volenti libram quæ pro vndecim vnciis <lb/>duodecim præ&longs;eferat, virga AB &longs;umatur <lb/>metallica, quæ in partes viginti tres æquas <lb/>( nam totidem con&longs;urgunt iunctis vndecim <lb/>ac duodecim ) diuidatur. </s>

<row>

<s>In fine vndecimæ <lb/>& initio duodecimæ partis figatur lingua li<lb/>bramenti & agina. </s>

<cell>R<emph type="italics"/>hombi paßiones qua&longs;dam declarare.<emph.end type="italics"/></cell>

<s>Con&longs;tat igitur DC vnde<lb/>cima parte maiorem e&longs;&longs;e AD: quumque CD <lb/>paulò maior &longs;it AD & grauior, leuiorem li<lb/>ma vel terebratione reddemus, aut lancem <lb/>leuiorem adiiciemus ip&longs;i C quàm A, adeò vt <lb/>dum lances vacuæ &longs;unt longitudinis AC, te<lb/>nuitatis pen&longs;ata ratione, trutina &longs;ub agina <lb/>iaceat, nullam in partem libra pendente: cui <lb/>tamen cùm ex parte C pondus vnciarum <lb/>vndecim adiunxerimus, & nota duodecim <lb/>vnciarum in lance A, libra æquilibrium de<lb/>mon&longs;trabit. </s>

</row>

<row>

<s>Quum ergo nec adulterinæ &longs;int <lb/>ponderum notæ, nec lancibus vacuis libra <lb/>videatur vitio&longs;a, fraus mutatis mercibus ac <lb/>notis hincinde, vt notæ &longs;unt in C, merces in <lb/>A, manife&longs;tè depræhenditur. </s>

<cell>CCVII.</cell>

<cell>P<emph type="italics"/>roportionem agentium naturalium in tran&longs;mutatione con&longs;iderare.<emph.end type="italics"/></cell>

<s>Nam C latus <lb/>infrà de&longs;cendet duplici cau&longs;a, & quia maius <lb/>lanci &longs;uæ pondus ine&longs;t, & quia CD, ip&longs;a DA <lb/>longior e&longs;t. </s>

</row>

<s>Difficilior ac ob&longs;curior e&longs;t &longs;tate<lb/>ræ ratio, de qua in Arithmeticis diximus. <lb/></s>

<row>

<cell>CCVIII.</cell>

<s>Nunc autem quum affinis &longs;it huic con&longs;ide<lb/>rationi, quantum nece&longs;&longs;arium e&longs;t huic pro<lb/>po&longs;ito, adiicere optimum erit. </s>

<cell>M<emph type="italics"/>ota res à centro grauitatis per <expan abbr="prior&etilde;">priorem</expan> motum, in reditu uelocius mouetur quam &longs;i quieuerit.<emph.end type="italics"/></cell>

<s>Ergo tota in <lb/>tribus con&longs;tat, quorum primum e&longs;t Archi<lb/>medis in Parabolis: & e&longs;t vbi regula &longs;tate<lb/>ræ, nullius ponderis cen&longs;eatur. </s><figure id="id.016.01.019.2.jpg" xlink:href="016/01/019/2.jpg"/>

</row>

<s>Stantium in æquilibrio ponderum ratio <lb/><arrow.to.target n="marg45"/><lb/>e&longs;t, vt di&longs;tantiarum à trutina mutua. </s>

<row>

<s>Velut &longs;i <lb/>D appen&longs;um ex lancula in C faciat æquili<lb/>brium cum G appen&longs;o in F, & proportio FB <lb/>ad BC &longs;it quadrupla, erit etiam D quadru<lb/>plum ad G Secundum, cùm in parte breuiore <lb/>fuerit &longs;olùm appen&longs;um pondus, & regula fue<lb/>rit pondero&longs;a, æqualis in magnitudine & <lb/>pondere, & fiat æquilibrium, erit proportio <lb/>ponderis appen&longs;i ad pondus totius regulæ, <lb/>vt differentiæ partium regulæ ad duplum <lb/>ponderis minoris. </s>

<cell>S<emph type="italics"/>i &longs;uperficies rectangula in duas partes æquales diui&longs;a intelligatur, quæ ambæ quadratæ &longs;int, itemque in duas inæquales, erit parallelipedum ex latere mediæ partis in totam &longs;uperficiem maius aggregato parallelipedorum ex partibus inæqualibus in latera alterius partis mutuo, in eo, quod fit ex dif ferentia lateris minoris partis à mediæ latere in differentiam maioris partis &longs;uperficiei à media &longs;uperficie bis, & ex differentia amborum laterum inæqualium iunctorum ad ambo latera, æqualia iuncta in minorem partem &longs;uperficiei.<emph.end type="italics"/></cell>

<s>Exemplum: D pondus in <lb/>C appen&longs;um faciat æquilibrium <expan abbr="c&utilde;">cum</expan> BL virga <lb/><expan abbr="ab&longs;q;">ab&longs;que</expan> alio pondere, & &longs;ic BL & BC, vt aixi, <lb/>fiat æqualis BK ip&longs;i BC, tunc dico quòd pro<lb/>portio D ad pondus CL, e&longs;t veluti ponderis <lb/>LK ad pondus KC. </s>

</row>

<row>

<s>Sed ex hoc habetur re<lb/>gula: cognito pondere CL & CK ha<lb/>bendi pondus D, ducemus KL, quæ &longs;it 40, <lb/>gratia exempli in &longs;e, fit 1600, diuide per pon<lb/>dus CK, quod &longs;it 16, exit 100, huic adde <expan abbr="põ-dus">pon<lb/>dus</expan> KL, quod e&longs;t 40, fit <expan abbr="põdus">pondus</expan> D, 140. Et ita <lb/>poterimus ad <expan abbr="quancunq;">quancunque</expan> men&longs;uram volueri<lb/>mus &longs;cire <expan abbr="quant&utilde;">quantum</expan> <expan abbr="põderis">ponderis</expan> refert &longs;tatera. </s>

<cell>S<emph type="italics"/>i duæ lineæ ad æquales angulos ab eodem puncto peripheriæ circuli reflectantur, nece&longs;&longs;e e&longs;t angulos cum dimetiente factos æquales e&longs;&longs;e.<emph.end type="italics"/> V<emph type="italics"/>nde manife&longs;tum e&longs;t, protractam diametrum angulum &longs;uppo&longs;itum per æqualia diuidere.<emph.end type="italics"/></cell>

<s>Ter<lb/>tium habetur ex his duobus & e&longs;t, &longs;i virgula <lb/>&longs;ine pondere cen&longs;eatur, à parte <expan abbr="aut&etilde;">autem</expan> qu&ecedil; dif<lb/>ferentia e&longs;t <expan abbr="longitudin&utilde;">longitudinum</expan> ab agina, pondus æ<lb/>quale extendatur per <expan abbr="totã">totam</expan> <expan abbr="virgã">virgam</expan>, <expan abbr="æqual&etilde;">æqualem</expan> <expan abbr="gra-uitat&etilde;">gra<lb/>uitatem</expan> habebit cum <expan abbr="eod&etilde;">eodem</expan> pondere appen&longs;o in <lb/>puncto di&longs;tante à librili per <expan abbr="medietat&etilde;">medietatem</expan> totius <lb/>virg&ecedil;. </s>

</row>

<s>Sit vt virga CL nullius &longs;it ponderis, & <lb/>&longs;it BC æqualis BK, & coexten&longs;um <expan abbr="põdus">pondus</expan> æ<lb/>qualiter, vt &longs;ub forma tetragoni faciat <expan abbr="æqui-libri&utilde;">æqui<lb/>librium</expan> <expan abbr="c&utilde;">cum</expan> D <expan abbr="app&etilde;&longs;o">appen&longs;o</expan> in C, & &longs;umatur G <expan abbr="&ecedil;qui-pondi&utilde;">&ecedil;qui<lb/>pondium</expan> &ecedil;quale <expan abbr="põderi">ponderi</expan> <expan abbr="coext&etilde;&longs;o">coexten&longs;o</expan>, & &longs;it BM <expan abbr="di-midi&utilde;">di<lb/>midium</expan> totius CL, dico quòd G <expan abbr="&longs;u&longs;pens&utilde;">&longs;u&longs;pensum</expan> in M <lb/>faciet <expan abbr="æquilibri&utilde;">æquilibrium</expan> <expan abbr="c&utilde;">cum</expan> D, & ita æqualiter gra<lb/>uabit vt <expan abbr="coextens&utilde;">coextensum</expan> toti KL. </s>

<row>

<s>Sit igitur vt in M <lb/>faciat <expan abbr="&ecedil;quilibri&utilde;">&ecedil;quilibrium</expan> <expan abbr="c&utilde;">cum</expan> D, igitur per <expan abbr="primã">primam</expan> <expan abbr="har&utilde;">harum</expan> <lb/>proportio MB ad BC, vt D ad G. <expan abbr="It&etilde;">Item</expan> quia facit <pb xlink:href="016/01/020.jpg" pagenum="371"/><expan abbr="æquilibri&utilde;">æquilibrium</expan> D cum G coëxten&longs;o K L, &longs;i igitur <lb/>adderetur æquè graue per totam CK adhuc <lb/>faceret æquilibrium, quia in BC & BK æ<lb/>quales &longs;unt, & tunc e&longs;&longs;et proportio ponde<lb/>ris D ad pondus KL, &longs;icut ponderis LC, ad <lb/>pondus CK, ex &longs;ecunda proportione permu<lb/>tata, igitur vt longitudinis LC ad CK, quia <lb/>pondus e&longs;t æqualiter di&longs;tributum. </s>

<cell>S<emph type="italics"/>i duæ lineæ ex duobus punctis peripheriam contingentes, in eandem partem protrahantur, &longs;emper magis di&longs;tabunt inuicem ea ex parte, & nunquam concurrent.<emph.end type="italics"/></cell>

<s>Sed &longs;icut <lb/>ponderis D ad pondus LK, &longs;ic D ad G, quia <lb/>&longs;uppo&longs;itum e&longs;t G & LK æqualia e&longs;&longs;e, igitur <lb/>vt LC a<gap/> CK, &longs;ic MB ad BC: quare permu<lb/>tando vt CK ad CB, &longs;ic LC ad MB: &longs;ed CB <lb/>e&longs;t dimidium CK: igitur BM e&longs;t dimdium <lb/>LC, quod crat demon&longs;trandum. </s>

</row>

<row>

<s>Quia verò <lb/>CB e&longs;t dimidium CK, & BM dimidium <lb/>CL, &longs;equitur vt MK &longs;it dimidium KL, & ita <lb/>e&longs;t ac &longs;i &longs;u&longs;pen&longs;um e&longs;&longs;et in medio loci cui <lb/>coextenditur. </s>

<cell>CCXII.</cell>

<cell>S<emph type="italics"/>i ab eodem puncto ad circuli peripheriam lineæ quotuis ducantur, tres inuenire lineas, quæ non in alium punctum reflectentur.<emph.end type="italics"/></cell>

<s>Vnumquodque igitur pondus, <lb/>iuxta Archimedem, quantumvis inæquale, <lb/><arrow.to.target n="marg46"/><lb/>vt triangulum tantum affert grauitatis, coex<lb/>ten&longs;um virgulæ, quantum &longs;i &longs;u&longs;pendatur ex <lb/>centro in loco vbi centrum grauitatis &longs;e<lb/><arrow.to.target n="marg47"/><lb/>cundum perpendiculum &longs;itum e&longs;t. </s>

</row>

<s>Hoc au<lb/>tem generaliter &longs;upponit, etiam&longs;i pondus <expan abbr="nõ">non</expan> <lb/>extendatur v&longs;que ad aginam, &longs;ed coex-ten<lb/><arrow.to.target n="marg48"/><lb/>datur, gratia exempli per L F, & centrum <lb/>eius &longs;it in directo E, tunc dicit, e&longs;t ac &longs;i &longs;u&longs;<lb/>penderetur in ip&longs;o E. </s>

<row>

<cell>CCXIII.</cell>

<s>Ex his, vt in Arithme<lb/>ticis docuimus, colligitur ratio conficien<lb/>di &longs;tateras. </s>

<cell>P<emph type="italics"/>ropo&longs;ito circulo, atque in eius peripheria puncto &longs;ignato, lineas contingentes ultra cítraque, & eam ab ip&longs;omet deducere.<emph.end type="italics"/></cell>

<s><margin.target id="marg45"/>Stateræ ra<lb/>tio.</s>

</row>

<row>

<s><margin.target id="marg46"/>Parabola <lb/>quinta.</s>

<cell>CCXIIII.</cell>

<cell>S<emph type="italics"/>i extra circulum duo puncta æqualiter à centro di&longs;tantia &longs;ignentur, erit punctum reflexionis æqualis in medio arcus intercepti inter lineas, quæ à cen tro ducuntur ad illa puncta.<emph.end type="italics"/> S<emph type="italics"/>i uerò unum centro proximius fuerit altero, punctum æqualitatis in peripheria tantò longius, uer&longs;us breuiorem lineam, quantò punctum aliud à centro magis di&longs;teterit.<emph.end type="italics"/></cell>

<s><margin.target id="marg47"/>Parabola <lb/>octaua.</s>

</row>

<s><margin.target id="marg48"/>Statera <lb/>quomodo <lb/>perfecta e&longs;&longs;e <lb/>po&longs;&longs;it.</s>

<row>

<s>Nunc &longs;olum demon&longs;trare oportet, quo<lb/>modo &longs;tatera perfecta e&longs;&longs;e po&longs;&longs;it: et&longs;i in pre<lb/>cio&longs;is mercibus mercatores libra vtantur. </s>

<cell>P<emph type="italics"/>unctum reflexionis punctorum inæqualiter di&longs;tantium à centro, æqualiter di&longs;tat à lineis, ductis à centro ad puncta æqualiter di&longs;tantia alterutrinque.<emph.end type="italics"/></cell>

<s>Sit <lb/>igitur &longs;tatera diui&longs;a tuo modo cum pondere <lb/>auxiliari, quod mobile e&longs;t G, & æquiponi<lb/>deret G in F ip&longs;i D, quia itaque D æqui<lb/>ponderat G in F, & etiam regulæ KL. </s>

</row>

<row>

<s>Po<lb/>nantur enim N pars D, quæ facit <expan abbr="æquilibri&utilde;">æquilibrium</expan> <lb/><expan abbr="c&utilde;">cum</expan> LK, & O pars reliqua D, quæ facit <expan abbr="æqui-libri&utilde;">æqui<lb/>librium</expan> cum G. </s>

<cell>CCXVI.</cell>

<cell>S<emph type="italics"/>i fuerint circuli duo inæquales, & extra utrunqúe punctum ad illud ex minore reflexè per magnam partem minoris à maiore perueuire poterunt.<emph.end type="italics"/></cell>

<s>Igitur iuxta <expan abbr="primã">primam</expan> <expan abbr="regulã">regulam</expan> pro<lb/>portio O ad G, vt FB ad BC. </s>

</row>

<s>Proportio ve<lb/>rò N ad LK, & e&longs;t vt LK &longs;u&longs;pen&longs;a in M, ex <lb/>tertia regula, vt L C ad CK ex &longs;ecunda re<lb/>gula. </s>

<row>

<cell>CCXVII.</cell>

<s>Igitur &longs;tatuemus pondus N primò in <lb/>directo D, deinde facto æquilibrio additio <lb/>O &longs;emper e&longs;t &longs;ecundum proportionem ad G, <lb/>vt partis LB ad BC. </s>

<cell>O<emph type="italics"/>culus uidet partem &longs;uperficiei<emph.end type="italics"/> L<emph type="italics"/>unæ illuminatam à<emph.end type="italics"/> S<emph type="italics"/>ole per radios reflexos à<emph.end type="italics"/> S<emph type="italics"/>olis corpore: nec tamen pote&longs;t uidere imaginem ip&longs;ius in<emph.end type="italics"/> L<emph type="italics"/>una tan quam in &longs;peculo.<emph.end type="italics"/></cell>

<s>Secundum igitur æqua<lb/>lia incrementa BL cre&longs;cet O, &longs;ed N manet <lb/>idem &longs;emper: igitur &longs;ecundum æqualia in<lb/>crementa partium B L cre&longs;cet D pondus. <lb/></s>

</row>

<row>

<s>Æqua igitur &longs;tatera fieret, &longs;i ad <expan abbr="Capponãtur">Capponantur</expan> <lb/>pondus faciens <expan abbr="equilibr&utilde;">equilibrum</expan> <expan abbr="c&utilde;">cum</expan> LK: inde diuida<lb/>mus &longs;patia ab agina ad L per æqualia. </s>

<cell>CCXVIII.</cell>

<cell>R<emph type="italics"/>ationem maculæ<emph.end type="italics"/> L<emph type="italics"/>unæ indagare.<emph.end type="italics"/></cell>

<s>Sed <lb/>quia ip&longs;i <expan abbr="nõ">non</expan> <expan abbr="appon&utilde;t">apponunt</expan> pondus in C, <expan abbr="nece&longs;&longs;ari&utilde;">nece&longs;&longs;arium</expan> <lb/>e&longs;t vt prima nota, puta P, o&longs;tendat etiam <lb/>pondus LK: vt &longs;i LK ponderis libras duas, <lb/>& D pondus duas libras æquet, nota primi <lb/>ponderis e&longs;&longs;et in K, exempli gratia: &longs;ed quia <lb/>G po&longs;itum in K, grauaret quantum quatuor <lb/>libræ, & præter id etiam LK grauitatem <lb/>efficit duarum librarum, igitur oporteret vt <lb/>D e&longs;&longs;et librarum &longs;ex, igitur pondus e&longs;&longs;et li<lb/>brarum &longs;ex, & o&longs;tenderet tantùm quatuor. <lb/></s>

</row>

<s>Ob id faciemus primam notam quatuor li<lb/>brarum in P, nam & ibi C grauitatem effi<lb/>cit duarum librarum, & LK duarum alia<lb/>rum, igitur pondus D erit quatuor librarum, <lb/>quod faciet æquilibrium: igitur nota qua<lb/>tuor librarum primarum erit in P, & multò <lb/>minus ab agina di&longs;tans, quàm reliquæ inter<lb/>&longs;e. </s>

<row>

<cell>CCXIX.</cell>

<s>At verò reliquæ inter &longs;e æquidi&longs;tabunt, <lb/>vt &longs;i &longs;ecunda fit in Q, tertia erit in H, & <lb/>quarta in M, & quinta in R, & &longs;exta in E: <lb/>ideoque po&longs;ito G in E, o&longs;tendet libras vigin<lb/>tiquatuor. </s>

<cell>R<emph type="italics"/>ationem eorum quæ apparent circa<emph.end type="italics"/> S<emph type="italics"/>olem &longs;peculo in aqua po&longs;ito declarare.<emph.end type="italics"/></cell>

<s>Manife&longs;tum e&longs;t autem ex hoc, <lb/><arrow.to.target n="marg49"/><lb/>quod commodum affert non leue, quò G <lb/>&longs;it pondus per &longs;e notum, id e&longs;t, libra, vel bi<lb/>libra, vel trilibra. </s>

</row>

<row>

<s><margin.target id="marg49"/>Media pon<lb/>derum quo<lb/>modo ha<lb/>beantur.</s>

<cell>C<emph type="italics"/>au&longs;am cur<emph.end type="italics"/> S<emph type="italics"/>ol æ&longs;tiuis diebus exoriens umbram ad meridiem, cum in meridie ad boream mittat, explorare.<emph.end type="italics"/></cell>

<s>Centra autem ponderum in circulis & <lb/>rectangulis &longs;unt in communi &longs;ectione di<lb/>metientium duarum. </s>

</row>

<s>In omnibus autem <lb/>figuris æquilateris, quæ circulo po&longs;&longs;unt <lb/>in&longs;cribi, centrum grauitatis idem e&longs;t cum <lb/>centro circuli circum&longs;cribentis. </s>

<row>

<cell>CCXXI.</cell>

<s>Supponitur <lb/>autem in omnibus, quòd pondero&longs;a hæc æ<lb/>qualem vbique habeant cra&longs;&longs;itudinem, & <lb/>quòd ex materia quæ vbique æqualem &longs;or<lb/>tiatur grauitatem, con&longs;tituantur. </s>

<cell>M<emph type="italics"/>agnitudo<emph.end type="italics"/> L<emph type="italics"/>unæ & cæterorum a&longs;trorum digno&longs;citur ex proportione aliorum ad eam iuxta di&longs;tantiam: ip&longs;ius uerò iuxta rationem pupillæ ad<emph.end type="italics"/> L<emph type="italics"/>unam di&longs;tantiæ ratione.<emph.end type="italics"/></cell>

<s>In trigonis <lb/>autem omnibus in communi &longs;ectione trium <lb/>linearum, quarum &longs;ingulæ ad &longs;ingula latera <lb/>ex angulis oppo&longs;itis venientes, ea per æqua<lb/>lia diuidunt. </s>

</row>

<row>

<s>Has verò in vnum punctum <lb/>&longs;ecando &longs;e inuicem concurrere nece&longs;&longs;e e&longs;t: <lb/>et&longs;i id Archimedes non demon&longs;trauerit. <lb/></s>

<cell>CCXXII.</cell>

<cell>Q<emph type="italics"/>uantitates quæ æquales e&longs;&longs;e non po&longs;&longs;unt in eodem genere, maius tamen & minus recipiunt, &longs;unt in proportione pote&longs;tatis.<emph.end type="italics"/></cell>

<s>Nos autem in Geometricis elementis illud <lb/>o&longs;tendimus generaliter, nunc autem pro ne<lb/>ce&longs;&longs;itate declarabitur. </s>

</row>

<s>Nam diui&longs;is per æqualia lateribus AB & <lb/>AC in D & E, & ducta CD, BE, & per <lb/>communem &longs;ectionem AGH & DE, quæ <lb/>erit æquidi&longs;tans lateri tertio, vnde BEC & <lb/>CDB erunt æquales, quia in eadem ba&longs;i <lb/>BC, &longs;ubducto BCG, communi erit CEG æ<lb/>qualis DBC, ip&longs;i autem &longs;unt æquales AGE <lb/>& AGD, quia in æquis ba&longs;ibus & inter æ<lb/>quidi&longs;tantes, quare AGE & AGD æquales. <lb/><figure id="id.016.01.020.1.jpg" xlink:href="016/01/020/1.jpg"/><lb/>Quumque &longs;int &longs;uper eandem lineam AG, <lb/>erunt æqualis altitudinis, qui altitudo e&longs;t tri<lb/>gonorum etiam FGD, & FGE, qui <expan abbr="con&longs;i&longs;t&utilde;t">con&longs;i&longs;tunt</expan> <lb/>in eadem ba&longs;i FG, igitur etiam ip&longs;i inter &longs;e <lb/>&longs;unt æquales, Quia verò BC æquidi&longs;tat DE, <lb/>erunt ex 29 primi elementorum & 25. eiu&longs;<lb/>dem, DGE & BGC æquianguli, & propor<lb/>tio BG ad GE, vt CG ad GD. ex ei&longs;dem <lb/>etiam BGH & GEF &longs;imiles, itemque GCH <lb/>& DGF. quare proportio trigoni BGH ad <lb/>EFG, vt BG ad GE dupla, & CGH ad DFG, <lb/>vt CG ad GD dupla, e&longs;t autem ( vt dictum <lb/>fuit ) CG ad GD, vt BG, ad GE, quare BGH <lb/>ad EFG, yt HCG ad DFG: quare cum DFG <lb/>& EFG æquales &longs;int, erunt BGH & CGH <lb/>æquales: quumque &longs;int inter æquidi&longs;tantes, <lb/>erunt in ba&longs;ibus æqualibus BH & HC, igi<lb/>turtrigoni omnes ABH, ACH, CDB, CDA, <lb/>BEC, BEA, erunt, medietas ABC, quare ap<lb/>pen&longs;us trigonus in G, in nullam poterit par<lb/>tem inclinari. </s>

<row>

<cell>CCXXIII.</cell>

<s>Centrum autem &longs;ectionis pa<lb/>rabol&ecedil; &longs;eu coni rectanguli e&longs;t in eius dime<lb/>tiente, quæ à &longs;ummo ad medium ba&longs;is in eo <lb/>puncto qui à &longs;ummitate coni dimidio plus <lb/>di&longs;tat quàm à ba&longs;i, quæ e&longs;t recta linea &longs;up-<pb xlink:href="016/01/021.jpg" pagenum="372"/>po&longs;ita angulo coni. </s>

<cell>Q<emph type="italics"/>uantitates quæ actu æquales e&longs;&longs;e non po&longs;&longs;unt, in nulla proportione actu e&longs;&longs;e po&longs;&longs;unt.<emph.end type="italics"/></cell>

<s>Cum itaque fuerit po&longs;ita <lb/>virga æqualis CL ponderis vnciarum 7, & <lb/>librile in B, ita quod KL &longs;it 10. & KC, 4. & G <lb/>libra vna, &longs;ic con&longs;tituemus &longs;tateram. </s>

</row>

<row>

<s>Ducam <lb/>pondus LK, quod e&longs;t 5, in &longs;e, fit 25, diuido <lb/>per pondus KC, quod e&longs;t 2, fit 12 1/2, cui ad<lb/>do vncias 5, LK, fit 17 1/2: ponam igitur CD <lb/>vinculum ferreum vncias 5 1/2, & relinque<lb/>tur pondus LK vniuslibræ. </s>

<cell>CCXXIIII.</cell>

<cell>N<emph type="italics"/>eque temporis totius, ut imaginamur, ip&longs;um e&longs;&longs;e infinitum, neque æui uitarum proportio ulla e&longs;t ad tempus, quod pote&longs;tate e&longs;t, utpotè diem<emph.end type="italics"/></cell>

<s>Cùm igitur po<lb/>&longs;uerimus G in K &ecedil;quabitur libr&ecedil;, & aliam <lb/>libram oportebit addere in D propter LK, <lb/>igitur in K o&longs;tendemus duas libras, & &longs;ic &longs;cri<lb/>bemus, deinde S 3, in T 4, in F 5. in V 6, in L, <lb/>quis &longs;patiis. </s>

<cell/>

</row>

<s>Ex hoc patet quòd omnia hæc <lb/>&longs;patia per vncias di&longs;tribui poterunt, præter <lb/>primum BK. </s>

<row>

<s>Po&longs;&longs;emus tamen & ip&longs;um di<lb/>uidere, vt in B libra intelligatur, & AB in <lb/>K vnci&ecedil; per æqua &longs;patia addit&ecedil; <expan abbr="&longs;ignificab&utilde;t">&longs;ignificabunt</expan>, <lb/><arrow.to.target n="marg50"/><lb/>prima 13. &longs;ecunda 14. tertia 15. & ita de aliis. </s>

<cell/>

<cell><emph type="italics"/>uel men&longs;em.<emph.end type="italics"/></cell>

<s><margin.target id="marg50"/>Cur libræ <lb/>&longs;unt plerum<lb/>que exactio<lb/>ves &longs;tateris.</s>

</row>

<s>Patet autem cau&longs;a ex his, quare libr&ecedil; tri<lb/>bus cau&longs;is &longs;tateris &longs;int exactiores. </s>

<row>

<cell>CCXXV.</cell>

<s>Hoc au<lb/>tem ab initio propo&longs;itum fuit. </s>

<cell>P<emph type="italics"/>roportio media non e&longs;t ex ratione agentis, &longs;ed patientis.<emph.end type="italics"/></cell>

<s>Nam in &longs;ta<lb/>tera difficile e&longs;t virgulam adeò exactam in <lb/>magnitudine con&longs;tituere: & &longs;i etiam &longs;it in <lb/>magnitudine, non erit in pondere: vix enim <lb/>hoc a&longs;&longs;equi po&longs;&longs;umus. </s>

</row>

<row>

<s>Secundò difficillimum <lb/>e&longs;t per æqualia interualla omninò ad amu&longs;<lb/>&longs;im diuidere LB. </s>

<cell>CCXXVI.</cell>

<cell>P<emph type="italics"/>roportio &longs;ublimis non con&longs;i&longs;tit in magnitudine, &longs;ed ordine, iuxta quem differentia e&longs;t eius quod e&longs;t ante & po&longs;t.<emph.end type="italics"/></cell>

<s>Tertiò pondus rarò in ex<lb/>tremo C appendi &longs;olet, quod cùm citra <lb/>appenditur, confu&longs;ionem parit. </s>

</row>

<s><expan abbr="S&utilde;t">Sunt</expan> & additamenta multa quæ <expan abbr="vitiãt">vitiant</expan> &longs;tate<lb/>ram, horum nullum in libra e&longs;t. </s>

<row>

<cell>CCXXVII.</cell>

<s>Ob id præ<lb/>cio&longs;a non in &longs;tatera &longs;ed libra &longs;olent exami<lb/>nari. </s>

<cell>V<emph type="italics"/>itæ iuxta numerum perfectionum in comparatione ad cogitationem no&longs;tram proportionem quand am habent.<emph.end type="italics"/></cell>

<s>Multum autem refert ad exactam &longs;ta<lb/>ter&ecedil; &longs;tructuram, vt G leue &longs;it, tum etiam <lb/>LC, & quod LB tripla &longs;it BC. nam &longs;ic LK <lb/>æqualis erit KC, & quòd vincula CD in ex<lb/>tremo &longs;int LC, & &ecedil;qualis ponderis cum LK. <lb/><arrow.to.target n="marg51"/><lb/>Hoc enim &longs;tater&ecedil; genus, libr&ecedil; <expan abbr="proxim&utilde;">proximum</expan> erit. </s>

</row>

<row>

<s><margin.target id="marg51"/>Vtres quan<lb/>tum ponderis <lb/>in aqua &longs;u<lb/>&longs;tineant. <lb/></s>

<cell>CCXXVIII.</cell>

<cell>P<emph type="italics"/>roportionem &longs;cientiæ futurorum & cæterorum occultorum con&longs;iderare.<emph.end type="italics"/></cell>

<s>Quomodo <lb/>homo aquæ <lb/>immobilis ac <lb/>&longs;upinus &longs;u<lb/>per&longs;tet.</s>

</row>

<s>Quantum verò ponderis vtres in aqua <lb/>&longs;u&longs;tineant pro pontibus con&longs;truendis, expe<lb/>rimentum docet. </s>

<row>

<cell>CCXXIX.</cell>

<s>Nam ve&longs;ica plena aëre, <lb/>qu&ecedil; capax fuit quinque librarum aqu&ecedil; & <lb/>vnci&ecedil;, pondus librarum quatuordecim ac &longs;e<lb/>mis laterum &longs;u&longs;tinebat: quo fit vt in flumi<lb/>num aqua triplum fermè ponderis aquæ, <lb/>cuius &longs;unt capaces vtres, continere po&longs;&longs;int. <lb/></s>

<cell>I<emph type="italics"/>ncorporea omnia unum &longs;unt, neque numerus e&longs;t eorum.<emph.end type="italics"/></cell>

<s>Illud etiam non pr&ecedil;termittendum, ex den&longs;i<lb/>tatis ratione oriri, vt homines cùm ita &longs;e <lb/>continuerint &longs;upini in aqua, vt velut iacula<lb/>tores in funibus nullam penitùs in partem <lb/>flectantur immobiles, tum nequaquam mer<lb/>gi. </s>

</row>

<row>

<s>Hoc tamen cùm per &longs;e &longs;it difficillimum, <lb/>ob motum etiam & aquæ in&ecedil;qualitatem <lb/>etiam redditur difficiliùs. </s>

<cell>CCXXX.</cell>

<cell>P<emph type="italics"/>roportio incorporeorum a&longs;cendentium &longs;emper maior e&longs;t.<emph.end type="italics"/></cell>

<s>Atque hacte<lb/>nus de rerum mortalium principiis di<lb/>ctum &longs;it. </s><figure id="id.016.01.021.1.jpg" xlink:href="016/01/021/1.jpg"/>

</row>

<s><emph type="center"/>LIBER SECVNDVS.<emph.end type="center"/></s>

<row>

<cell>CCXXXI.</cell>

<s><emph type="center"/>De Elementis & eorum motibus & <lb/>actionibus.<emph.end type="center"/><lb/><arrow.to.target n="marg52"/></s>

<cell>T<emph type="italics"/>res e&longs;&longs;e mundos atque inter ip&longs;os nullam e&longs;&longs;e proportionem: nec numero cos definiri.<emph.end type="italics"/></cell>

<s><margin.target id="marg52"/>De elemen<lb/>torum nu.</s>

</row>

<row>

<s>NVNC verò de Elementis aga<lb/>mus, quæ forma & materia <lb/>prima con&longs;tant, & animata <lb/>qua&longs;i videntur: ea Græcis <lb/><foreign lang="greek">soix<gap/>_a</foreign> vocant. </s>

<cell>CCXXXII.</cell>

<cell>O<emph type="italics"/>mnis motus naturalis quanto uelocior e&longs;t tanto propior e&longs;t & magis &longs;imil limus quieti.<emph.end type="italics"/></cell>

<s>Perdi&longs;cere au<lb/>tem primum oportet, quot & quænam &longs;int. <lb/></s>

</row>

<s>Ari&longs;toteles quatuor exiftimat, terram, <expan abbr="aquã">aquam</expan>, <lb/>aërem, atque ignem. </s>

<row>

<cell>CCXXXIII.</cell>

<s>Primùm enim quatuor <lb/>qualitates primæ &longs;unt. </s>

<cell>Q<emph type="italics"/>uod e&longs;t in mundo incorporeo æternum e&longs;t, beatum, &longs;ecurum, immutabile &longs;ecundum locum, &longs;olum iuxta e&longs;&longs;entiam fit: iuxta quod uelut à leui &longs;u&longs;urro aquæ & aura æ&longs;tiua demulcetur.<emph.end type="italics"/></cell>

<s>Hæ &longs;olæ non con&longs;ti<lb/>tuunt elementum, quia vim non haberent <lb/>agendi ac patiendi: nec plu&longs;quam duæ &longs;i<lb/>mul e&longs;&longs;e po&longs;&longs;unt, quin contraria &longs;imul &longs;int. <lb/></s>

</row>

</table>

<s>Nam calidi, frigidi, &longs;icci atque humidi, &longs;i <lb/>tria quomodolibet acceperis, contraria ac<lb/>cipere nece&longs;&longs;e e&longs;t. </s>

<s id="id000041">FINIS.</s>

<s>Sed nec calidum cum fri<lb/>gido, nec &longs;iccum cum humido iungi pote&longs;t. <lb/></s>

<s>Igitur binis iunctis qualitatibus neque con<lb/>trariis, &longs;imul tantùm quatuor fient coniu<lb/>gationes, quæ quatuor elementa con&longs;ti<lb/>tuent. </s>

</section>

</front>

<s>Inter imum etiam locum atque &longs;u<lb/>premum, &longs;impliciter duo loca intercidere <lb/>nece&longs;&longs;e e&longs;t, imum non exqui&longs;itè, atque &longs;u<lb/>premum: atque eo totidem &longs;implicia cor<lb/>pora. </s>

<body>

<chap>

<s>Videmus etiam, & &longs;i quid probabilia <lb/>argumenta faciunt, in mi&longs;tis ip&longs;is quatuor <lb/>elementa: nam de terra, aëre & aqua, nemo <lb/>dubitare pote&longs;t ob magnitudinem, & maxi<lb/>mas moles, vt mare aquarum, aëris & terræ <lb/>in vniuer&longs;o: ignis verò incrementa, & po<lb/>tentiam, ac &longs;implicitatem, cuius etiam fons <lb/>in Lunæ concauo e&longs;&longs;e creditur. </s>

<s>Plures etiam <lb/>exi&longs;timant in di&longs;tilationibus hæc quatuor <lb/>videri: & humores totidem in animalibus <lb/>&longs;en&longs;us depræhendi. </s>

<s id="id000042">HIERONYMI CAR<lb/>DANI MEDIOLANENSIS, CI<lb/>VISQVE BONONIENSIS, MEDICI <lb/>de Proportionibus, &longs;eu Ope<lb/>ris Perfecti <lb/>LIBER QVINTVS.</s>

<s>Quinetiam multi arbi<lb/>trantur ob hoc Cometes fieri, quòd &longs;ub c&oelig;<lb/>lo ab ignis elemento vapores accendantur. <lb/></s>

<s id="id000043">Prima diffinitio.</s>

<s>Sed certè &longs;ub c&oelig;lo Lunæ nullus e&longs;t ignis: <lb/>nam quum c&oelig;lum puri&longs;&longs;ima res &longs;it, non <lb/>decuit &longs;ub omnis qualitatis experte re, ar<lb/>denti&longs;&longs;imam colloca&longs;&longs;e. </s>

<s>Natura enim &longs;em<lb/>per extrema mediis iungit. </s>

<s id="id000044">Proportio ab Euclide &longs;ic de&longs;cribitur, Quòd <lb/>&longs;it duarum quantitatum eiu&longs;dem generis, <lb/>quod ad magnitudinem attinet, compara<lb/>tio certa.</s>

<s>Inter carnem <lb/>enim & os, membranam: inter os & liga<lb/>menta, cartilagines: inter os & cerebrum, <lb/>quòd carne cerebrum e&longs;&longs;et mollius, dupli<lb/>cem membranam, ac duriorem o&longs;&longs;i pro<lb/>pinquiorem collocauit. </s>

<s id="id000045">Secunda diffinitio.</s>

<s>Nec motus veloci<lb/>tas, caloris aut cau&longs;a, aut argumentum e&longs;&longs;e <lb/>pote&longs;t. </s>

<s>Nanque ea quæ con&longs;tant, et&longs;i motu <lb/>accendantur, vt lapides, plumbum & anima<lb/>lia, quæ tamen di&longs;&longs;ipantur, quò celerius mo<lb/>uentur, eò fiunt frigidiora, vt aqua & aër: <lb/>venti enim validi omnes frigidi, & flumina <lb/>celeriter fluentia frigidi&longs;&longs;imas habent aquas. <lb/></s>

<s id="id000046">Proportiones per &longs;imilitudinem <expan abbr="dic&utilde;tur">dicuntur</expan>, <lb/>cùm quantitas quantitati <expan abbr="compara&ttilde;">comparatur</expan> alterius <lb/>generis, cui fingitur æqualis e&longs;&longs;e pote&longs;tate.</s>

<s>E&longs;t etiam aliud non leue argumentum huius <pb xlink:href="016/01/022.jpg" pagenum="373"/>rei, quòd Cometes, aut faces calores his ac<lb/>cendunt intolerabiles: quid igitur fiet &longs;i tan<lb/>ta regio & vniuer&longs;us orbe igne ambiatur? <lb/></s>

<s id="id000047">Velut &longs;i a b fingatur monas in comparatione <lb/>ad b c erit rectangulum a c æquale lineæ b c.</s>

<s>Quid enim prohibebit, ne aërem ip&longs;um ac<lb/>cendat, inde hæc omnia reliqua, tum maxi<lb/>mè quòd calor &longs;iderum adiuuabit. </s>

<s>Omnem <lb/>enim lucem Auerroës calidam e&longs;&longs;e exi&longs;timat. <lb/></s>

<s id="id000048">Tertia diffinitio.</s>

<s>Aërem etiam calidum maximè e&longs;&longs;e volunt: <lb/>humida autem qualitas omnium minimè re<lb/>&longs;i&longs;tit. </s>

<s>Quomodo igitur violenti&longs;&longs;imo & ma<lb/>ximo, & acerrimo elementorum aër ip&longs;e re<lb/>pugnabit? </s>

<s id="id000049">Proportio æqualis proportioni e&longs;t, cùm eodem modo termini <lb/>&longs;e habent inuicem in utraque</s>

<s>Itaque Auerroës ip&longs;e hoc videns </s>

<s id="id000050">Quarta diffinitio.</s>

<s><arrow.to.target n="marg53"/><lb/>dixit, aliquando ignem <expan abbr="nõ">non</expan> e&longs;&longs;e calidum actu: <lb/>&longs;ed &longs;i calidus non e&longs;t actu, quæ potentia hæc <lb/>e&longs;t: Potentia dicimus medicamenta talia, <lb/>quòd deuorata calefaciunt: an verò hic ignis <lb/>ab aliquo <expan abbr="ing&etilde;ti">ingenti</expan> animali deuorabitur? </s>

<s>Dein<lb/>de, &longs;i ignis calidus non e&longs;t, nec aqua pari ra<lb/>tione frigida (hoc autem e&longs;t confundere or<lb/>dinem vniuer&longs;i <emph type="italics"/>)<emph.end type="italics"/> quid etiam prohibet ne lu<lb/>ceat? </s>

<s id="id000051">Proportiones &longs;ecundum genus notæ dicuntur, cùm nouimus, <lb/>quòd &longs;int maiores, aut minores. </s>

<s id="id000052">Nam cùm æquales &longs;unt, &longs;imul ne<lb/>ceffe e&longs;t, ut cogno&longs;camus genus, & &longs;peciem.</s>

<s>quanquam hoc eludant vt leue argu<lb/>mentum. </s>

<s>Si etiam ibi ignis e&longs;t, cur quantò <lb/>altius a&longs;cendimus, cuncta frigidiora appa<lb/>rent, vt etiam &longs;ub torrida zona in montium <lb/>cacuminibus niues abundare <expan abbr="affirm&etilde;t">affirment</expan>? </s>

<s id="id000053">Quinta diffinitio.</s>

<s>Quod <lb/>minus mirum e&longs;t, &longs;i quis con&longs;ideret non &longs;o<lb/>lùm hyeme niues, &longs;ed media etiam æ&longs;tate fri<lb/>gidi&longs;&longs;imas grandines generari. </s>

<s id="id000054">Datum po&longs;itione e&longs;t: quod nece&longs;&longs;ariò ex po&longs;itis certam habet <lb/>quantitatem.</s>

<s>Sed dicunt <lb/>abe&longs;&longs;e ea loca à radiorum repercu&longs;&longs;u: &longs;ed hoc <lb/>minoris caliditatis argumentum e&longs;&longs;e pote&longs;t, <lb/>non autem frigiditatis. </s>

<s>Denique &longs;i ibi e&longs;&longs;et, <lb/>maximè ob generationem e&longs;&longs;et: verùm non <lb/>ob hoc e&longs;&longs;e pote&longs;t, cùm calor c&oelig;le&longs;tis &longs;it qui <lb/>generet, vel ip&longs;o te&longs;te philo&longs;opho, & leui&longs;&longs;i<lb/>ma res tam procul de&longs;cendere haud queat. <lb/></s>

<s id="id000055">Sexta diffinitio.</s>

<s>For&longs;an quis ignem ferri hunc &longs;ur&longs;um dicet, <lb/>atque ex eo coniectabitur ibi locum illius <lb/>e&longs;&longs;e. </s>

<s id="id000056">Datum &longs;impliciter dicitur, quod ex propo&longs;itis cogno&longs;ci pote&longs;t, <lb/>quantum &longs;it.</s>

<s>Sed primùm argumenta hæc rhetorica, <lb/>indigna &longs;unt vt in rebus &longs;eriis adducantur: <lb/>neque hic ignis illius naturæ e&longs;t, cuius &longs;u<lb/>periorem e&longs;&longs;e ferunt, cùm hic vrat, &longs;plen<lb/>deat, corrumpat, quorum nullum illi ine&longs;&longs;e <lb/>ferunt. </s>

<s>Dicemus etiam po&longs;t hæc, cur id con<lb/>tingat: & quòd non &longs;emper eriam contin<lb/>gat docebimus. </s>

<s id="id000057">Septima diffinitio.</s>

<s>Necillud argumenta <expan abbr="probãt">probant</expan>, <lb/>imò potius oppo&longs;itum. </s>

<s id="id000058">Proportiones pote&longs;tate <expan abbr="dicun&ttilde;">dicuntur</expan>, quæ &longs;ub comparatione aliarum <lb/><expan abbr="quantitat&utilde;">quantitatum</expan> nece&longs;&longs;ariam habentium <expan abbr="cõnexionem">connexionem</expan> <expan abbr="&longs;ol&utilde;">&longs;olum</expan> <expan abbr="cogno&longs;cun&ttilde;">cogno&longs;cuntur</expan>.</s>

<s>Nam inter duo ex<lb/>trema, non duo, &longs;ed tantùm vnum &longs;olet a&longs;&longs;i<lb/>gnari medium. </s>

<s>Quòd &longs;i &longs;tatuatur, non qua<lb/>tuor, &longs;ed tria tantùm erunt elementa. </s>

<s id="id000059">Hæ autem &longs;unt aliquando eiu&longs;dem generis, cum primis ut nu<lb/>meri: aliquandò alterius, ut linearum & &longs;uperficierum, angulorum, <lb/>& arcuum: aliquando eiu&longs;dem generis, & diuer&longs;arum &longs;pecierum, <lb/>ut arcuum per &longs;inus, qua utuntur A&longs;tronomi.</s>

<s>Quòd &longs;i <lb/>hoc non demon&longs;trat, multò minus quatuor <lb/>e&longs;&longs;e demon&longs;trabit. </s>

<s id="id000060">Octaua diffinitio.</s>

<s>Nec faces aut cometes <lb/>nobis in&longs;inuant e&longs;&longs;e ibi ignem, cùm ip&longs;e <lb/>Philo&longs;ophus &longs;ub igne aciuxta terram in aë<lb/>re fieri affirmet hæc ip&longs;a, vt ignis penitùs in<lb/>digna non &longs;int. </s>

<s>Sed neque in mi&longs;tis videtur <lb/>ignis. </s>

<s id="id000061">Proportio homonyma dicitur duarum quantitatum diuer&longs;i ge</s>

<s>Nam &longs;i modò e&longs;&longs;et, in euforbio & pi<lb/>pere potius e&longs;&longs;et, quorum vis calida e&longs;t, ac <lb/>&longs;icca non mediocriter, quàm in frigidi&longs;&longs;imis <lb/>lapidibus. </s>

<s id="id000062"><arrow.to.target n="marg1"/><lb/>neris, &longs;ed alterius a b altero dependentium, uelut motus ad tem

<s>De&longs;tillationes etiam, tres &longs;ub&longs;tan<lb/>tias tantùm docent, aquam pro aqua, oleum <lb/>vice aëris, & terram quæ in imo &longs;ub&longs;idet. <lb/></s>

<s>Quòd &longs;i dicas, olei partem rubicundiorem <lb/>ignem referre quòd acuti&longs;&longs;ima &longs;it, re&longs;ponde<lb/>mus & &longs;erò, hanc acuitatem, acremque &longs;apo<lb/>rem ex ignis vi acriote profici&longs;ci. </s>

<s>Indicio <lb/>e&longs;t, quòd metallicorum olei nulla e&longs;t pars <lb/>expers acerrimi &longs;aporis. </s>

<s>Quare &longs;i hoc totum <lb/>quod acerrimum e&longs;t ignem refert, acris ni<lb/>hil omninò ine&longs;&longs;e oportet. </s>

<s id="id000063">Dicimus enim motum tardum, uel uelocem in comparatione <lb/>ad tempus.</s>

<s>Quate etiam ad <lb/>tria tantùm redimus elementa. </s>

<s>Humores <lb/>in animalibus quatuor &longs;unt: &longs;ed quid hoc <lb/>ad elementa? </s>

<s>quid &longs;i tantùm tria cum <lb/>Thru&longs;iano expo&longs;itore artis medicæ Galeni <lb/>e&longs;&longs;e dicam? </s>

<s id="id000065">Nona diffinitio.</s>

<s>Sed tamen &longs;en&longs;us o&longs;tendit e&longs;&longs;e <lb/>quatuor? </s>

<s id="id000066">Proportionum aliæ dicuntur rhete, aliæ alogæ, rhetæ quæ &longs;unt <lb/>ut numeri ad numerum, alogæ quæ non &longs;unt numeri ad numerum.</s>

<s>Nequaquam: nam nec ip&longs;i faten<lb/>tur hunc ignem elementum e&longs;&longs;<gap/>. </s>

<s>Quare po<lb/>tius tria declarat nobis &longs;en&longs;us, quàm qua<lb/>tuor. </s>

<s id="id000067">Decima diffinitio</s>

<s>Neque quod celeriter exedat omnia, <lb/>ideo dicendum elementum: nam &longs;ic etiam <lb/>motus elementum e&longs;&longs;et: nec quia celeriter <lb/>cre&longs;cat, nam mures & ip&longs;i elementum e&longs;<lb/>&longs;ent. </s>

<s id="id000068">Proportio rhete alia æqualis, alia multiplex, uel &longs;ubmultiplex: <lb/>alia unius partis exce&longs;&longs;us, aut defectus, alia plurium, quam &longs;uper<lb/>partientem, aut &longs;upartientem uocant.</s>

<s>Sed horum neutrum terræ ine&longs;t, quam <lb/>tamen omnes vno ore elementum e&longs;&longs;e fa<lb/>tentur. </s>

<s>Omnia igitur ad hæc, ad demon<lb/>&longs;trandum quatuor e&longs;&longs;e elementa, tum etiam <lb/>ignem elementum e&longs;&longs;e, parum habent fidei: <lb/>quinimò vt ab initio propo&longs;uimus, oppo&longs;i<lb/>tum potius o&longs;tendunt. </s>

<s id="id000069">Vndecima diffinitio.</s>

<s>Supererat illud ma<lb/>ximum à qualitatum coniugationibus at <lb/>non vident hoc in mi&longs;tis o&longs;tendere: calida <lb/>enim quædam &longs;unt & humida, alia calida <lb/>& &longs;icca, atque &longs;ic deinceps. </s>

<s id="id000070">Cum diui&longs;o denominatore per numeratorem exit quantitas alo<lb/>ga, proportio dicitur aloga: &longs;i autem numerus integer, aut pars nu<lb/>meri nota dicitur rhete.</s>

<s>At in elemen<lb/>tis quoniam calor & &longs;iccitas tam immodica <lb/>ad interitum omnia erant traductura, pro <lb/>elemento c&oelig;le&longs;tem calorem ac bene tem<lb/>peratum &longs;ub&longs;tituit, ex quo omnia genera<lb/>rentur. </s>

<s>Hoc quidem ac putredine tum motu <lb/>generari &longs;olet materia, quam ignem vocant. <lb/></s>

<s id="id000071">Duodecima diffinitio.</s>

<s>Ignis <expan abbr="itaq;">itaque</expan> &longs;it, &longs;ed elementorum <expan abbr="nequaquã">nequaquam</expan>. </s>

<s id="id000072">Proportionem in proportionem duci e&longs;t, quoties recto ordine <lb/>tres quantitates in ei&longs;dem collo<expan abbr="can&ttilde;">cantur</expan>: ut &longs;int tres quan<lb/><figure id="id.015.01.021.1.jpg" xlink:href="015/01/021/1.jpg"/><lb/>titates a b c dicetur proportio a ad c producta ex pro <lb/>portione a ad b & b ad c, & &longs;imiliter proportio c ad <lb/>a producitur ex proportione b ad a, & c ad b.</s>

<s><margin.target id="marg53"/>Primo Can<lb/>ticæ com<lb/>mente 15.</s>

<s>Iam &longs;cio quid dicturi &longs;int nonnulli. </s>

<s id="id000073">Tertia decima diffinitio.</s>

<s>Quis <lb/>tu es tam audax, qui aduer&longs;us Philo&longs;ophum <lb/>&longs;entire audes? </s>

<s id="id000074">Proportionem per proportionem diuidi e&longs;t, quoties ad eandem <lb/>quantitatem duæ quantitates comparantur, tunc illarum propor<lb/>tio e&longs;t, quæ prodit una per alteram diui&longs;a.</s>

<s>præ&longs;ertim in tam confirmata, <lb/>atque antiqua rerum &longs;ententia. </s>

<s>Deinde, quo<lb/>nam pacto grandinum & niuis generatio <lb/>o&longs;tendet ignem ibi non e&longs;&longs;e, quum etiam&longs;i <lb/>nullus ad&longs;it ignis, attamen non par e&longs;t regio<lb/>nem illam e&longs;&longs;e &longs;rigidi&longs;&longs;imam, cùm radiis &longs;y<lb/>derum illu&longs;tretur, & nihilominus aërip&longs;e, in <lb/>quo &longs;ita ea e&longs;t regio, calidi&longs;&longs;imus &longs;it? </s>

<s id="id000075">Sint proportiones a & b ad c & interponatur b inter a & c, dico <lb/>proportionem a ad c diui&longs;am per proportionem a ad b, & prodire <lb/>proportionem b ad c, con&longs;tat ex conuer&longs;a præcedentis.</s>

<s>Ignem <lb/>quoque cùm dicimus atque elementum, rem <lb/>pror&longs;us calidi&longs;&longs;imam ac &longs;icci&longs;&longs;imam intelli<lb/>gimus: hic no&longs;ter ignis calidi&longs;&longs;imus e&longs;t ac <lb/>&longs;icci&longs;&longs;imus, quo fit vt immi&longs;tus etiam &longs;it: <lb/>nam &longs;i mi&longs;tus e&longs;&longs;et, talis e&longs;&longs;e non po&longs;&longs;et, <lb/>quare hic ignis elementum e&longs;t. </s>

<s id="id000076">Quarta decima diffinitio.</s>

<s>Hæc &longs;unt qu&ecedil; tamet&longs;i non mihi <expan abbr="obiiciãtur">obiiciantur</expan>, <lb/>obiici tamen po&longs;&longs;e &longs;entio. </s>

<s>Ergo vt ad <expan abbr="Ari&longs;to-tel&etilde;">Ari&longs;to<lb/>telem</expan> <expan abbr="deueniã">deueniam</expan>, homoille fuit, & in di&longs;&longs;ectione <lb/>ac &longs;ingularibus in multis aberrauit. </s>

<s id="id000077">Additio proportionum intelligitur quotiens duarum quanti<lb/>tatum ad unam tertiam, proportiones per aggregatum ip&longs;arum <lb/>quantitatum ad eandem coniunguntur.</s>

<s><expan abbr="Quin-etiã">Quin<lb/>etiam</expan> illo po&longs;teriores & Theophra&longs;tus, & Ga<lb/>lenus plura perperàm &longs;cripsêre, <expan abbr="itaq;">itaque</expan> &longs;i licuit <lb/>illi Platonem ob veritatem relinquere, cur <lb/>etiam ob <expan abbr="eand&etilde;">eandem</expan> illum nobis de&longs;erere non li<lb/>cebit? </s>

<s id="id000078">Velut &longs;i comparentur a b & b c ad d, inde tota <lb/><figure id="id.015.01.021.2.jpg" xlink:href="015/01/021/2.jpg"/><lb/>a c ad d dicemus proportionem, ac ad d e&longs;&longs;e con<lb/><expan abbr="iunctã">iunctam</expan> ex duabus proportionibus a b ad d & b c <lb/>ad <expan abbr="eand&etilde;">eandem</expan> d. </s>

<s>Propo&longs;itiones qua&longs;dam conatus e&longs;t ge<lb/>nerales a&longs;truere, quas experimentum fal&longs;as <lb/>e&longs;&longs;e docet: vt, quòd <expan abbr="null&utilde;">nullum</expan> animal bene oleat, <lb/>quodque graue non po&longs;&longs;it, vtrinque promi<lb/>nere, atque ideo terra non ex vtraque parte <lb/>aquis promineat, quæ tamen experimento <lb/>fal&longs;a e&longs;&longs;e depræhenduntur. </s>

<s id="id000079">Hoc & duo &longs;equentes &longs;icut & du&etail; <expan abbr="anteced&etilde;tes">antecedentes</expan> demon<lb/>&longs;trabitur e&longs;&longs;e. </s>

<s id="id000080">nunc &longs;olum quomodo <expan abbr="intelligend&utilde;">intelligendum</expan> &longs;it proponimus.</s>

<s><expan abbr="Itaq;">Itaque</expan> &longs;i inter mil<lb/>le propo&longs;itiones, in duabus, aut tribus aber<lb/>ra&longs;&longs;e illum fateamur, haud rem homine indi<lb/>gnam etiam &longs;apienti&longs;&longs;imo feci&longs;&longs;e illum di<lb/>cemus. </s>

<s>Nam & ab Auerroë ip&longs;o in paucis <lb/>de&longs;eritur, in nonnullis coarguitur, in pluri<lb/>bus verò &longs;en&longs;u tran&longs;po&longs;ito defenditur. </s>

<s id="id000081">Quinta decima diffinitio.</s>

<s>Hoc <lb/>autem verè e&longs;t etiam ip&longs;um confutare, non <lb/>tueri. </s>

<s id="id000082">Detractionem proportionis à proportione intelligimus fieri <lb/>per <expan abbr="detraction&etilde;">detractionem</expan> minoris quantitatis à maiore, comparatam ad ean<lb/>dem quantitatem.</s>

<s>Sed <expan abbr="neq;">neque</expan> in hoc di&longs;&longs;entimus ab Ari&longs;to<lb/>tele: <expan abbr="nã">nam</expan> in <expan abbr="cõcauo">concauo</expan> orbis Lunæ, nec <expan abbr="ign&etilde;">ignem</expan> e&longs;&longs;e <lb/>vult, nec rem <expan abbr="calidi&longs;&longs;imã">calidi&longs;&longs;imam</expan>. </s>

<s>Quod ad regionem <pb xlink:href="016/01/023.jpg" pagenum="374"/>aëris attinet, palàm e&longs;t illam e&longs;&longs;e frigidi&longs;&longs;i<lb/><arrow.to.target n="marg54"/><lb/>mam: quia (vt o&longs;tendemus) omnia elemen<lb/>ta talia &longs;unt. </s>

<s id="id000083">Velut in exemplo &longs;uperiore detracta proportione b c ad d ex

<s>Nam quod de vaporibus dici<lb/>tur, & vocata anti&longs;pa&longs;i, fabulæ &longs;imilius e&longs;t, <lb/>quàm hi&longs;toriæ rei naturalis. </s>

<pb pagenum="3" xlink:href="015/01/022.jpg"/>proportione a c ad d, relinquetur proportio a b ad d. </s>

<s>Quamobrem &longs;i <lb/>ignis in concauo Lunæ ponatur, ac ocy&longs;<lb/>&longs;imè ibi circumuolui, erit hic frigidi&longs;&longs;imus. <lb/></s>

<s id="id000084">& probatur <lb/>ex conuer&longs;ione præcedentis.</s>

<s>Ergo nos illud oppugnamus, non experi<lb/>mentum de&longs;erimus. </s>

<s id="id000085">Sexta decima diffinitio.</s>

<s>Quippe luce manife&longs;tius <lb/>e&longs;t aërem illic e&longs;&longs;e frigidi&longs;&longs;imum, tum verò <lb/>magis eum qui in concauo Lunæ e&longs;t: &longs;ed <lb/>temperatur propinquitate &longs;yderum, & ma<lb/>ximè Lunæ. </s>

<s>Et quanquam Luna tantum vni <lb/>parti paruæ è directo &longs;it, quia tamen totum <lb/>mi&longs;cetur &longs;imul ac tenui&longs;&longs;imæ e&longs;t &longs;ub&longs;tantiæ, <lb/>ideo aër ille e&longs;t temperati&longs;&longs;imus, idem etiam <lb/>puri&longs;&longs;imus ac limpidi&longs;&longs;imus, ac totus &longs;ynce<lb/>rus: qua de cau&longs;a æthera ip&longs;um antiqui, & re<lb/>ctè, imò & philo&longs;ophus ip&longs;e quandoque ap<lb/>pellauit. </s>

<s id="id000086">Extractio radicum alicuius proportionis fit per extractionem <lb/>radicum quantitatum illius iuxta unam, & eandem rationem.</s>

<s>Congruit hic belli&longs;&longs;imè loco ac c&oelig;<lb/>li naturæ, vt qui tenuitate & qualitatis tem<lb/><arrow.to.target n="marg55"/><lb/>peramento fermè &longs;it &longs;imilis. </s>

<s id="id000087">Velut quadratæ, uel cubæ, uel pronicæ, uel uniner&longs;alis, uel alte<lb/>rius modi.</s>

<s>Neque enim æ<lb/>ther ideò temperatus e&longs;t, quia æqualiter <lb/>commi&longs;tus ex calido & frigido, &longs;ed quia <lb/>vtriu&longs; que &longs;it expers qualitatis. </s>

<s>Similiter nec <lb/>&longs;iccus dici pote&longs;t, qui fluit: nee humidus, <lb/>quia non madefacit: &longs;ed purus ( vt dixi ) ac <lb/>limpidus, atque hic ad generationem apti&longs;&longs;i<lb/>mus, de quo inferiùs dicemus. <lb/><arrow.to.target n="marg56"/></s>

<s id="id000088">Decima &longs;eptima diffinitio.</s>

<s><margin.target id="marg54"/>1. Meteoro <lb/>rum c.4.</s>

<s id="id000089">Cùm fuerint duæ proportiones &longs;imiles in tribus terminis con<lb/>tinuatæ, dicetur proportio primæ quantitatis ad tertiam ueluti <lb/>primæ ad &longs;ecundam duplicata. </s>

<s><margin.target id="marg55"/>Ætber quid <lb/>&longs;it, & vbi.</s>

<s id="id000090">Et &longs;i &longs;int tres proportiones &longs;imiles <lb/>in quatuor terminis, dicetur proportio primæ quantitatis ad quar<lb/>tam triplicatà ei, quæ e&longs;t primæ ad &longs;ecundam,</s>

<s><margin.target id="marg56"/>Aër frigidus <lb/>e&longs;t natura, <lb/>non calidus.</s>

<s id="id000091">Decima octaua diffinitio.</s>

<s>Quòd verò aër calidi&longs;&longs;imus &longs;it, hoc nullum <lb/>experimentum dolet, nulla ratio cogit, imò <lb/>&longs;pontè quidem frigidi&longs;&longs;imus: atque hæc om<lb/>nia experimentis quidem con&longs;entiunt. </s>

<s>Chi<lb/>mærica illa Ari&longs;totelicorum, ne illum accu<lb/>&longs;are videar, <expan abbr="cõmenta">commenta</expan> in inexplicabiles quæ<lb/>&longs;tiones, quæ adhuc &longs;ub iudice &longs;unt, <expan abbr="terminã-tur">terminan<lb/>tur</expan>. </s>

<s id="id000092">Confu&longs;a proportio dicitur &longs;implicis, aut compo&longs;itæ quantitatis <lb/>ad compo&longs;itam in comparatione ad proportiones ad partes.</s>

<s>Itaque melius e&longs;t paucis immutatis tue<lb/>ri veritatem atque experimenta ip&longs;a, quàm <lb/>in perpetuum cum illis nugantes de rerum <lb/>natura nihil &longs;cire. </s>

<s id="id000093">Decimanona diffinitio.</s>

<s>Quis enim ni&longs;i amens au<lb/>diat di&longs;&longs;erentem atque affirmantem, aërem <lb/>e&longs;&longs;e calidum in extremo ac &longs;ummo, deinde <lb/>ob &longs;olum motum, aut vapores ab&longs;que motu, <lb/>vt &longs;ub &longs;eptentrione, adeò fieri frigidum, vt <lb/>glaciem, niuem ac grandinem gignat, nemo<lb/>que citra Solis vim de aëris calore conque<lb/>&longs;tus &longs;it, de frigore omnes quærantur, & ta<lb/>men audeant aëri non aliam fermè quam <lb/>igni tribuere caliditatem. </s>

<s>Cur ignis cùm te<lb/>nuiore &longs;it &longs;ub&longs;tantia quàm aër, nunquam à <lb/>&longs;uo immen&longs;o calore de&longs;tituitur, aut illius na<lb/>tura ac feruor mite&longs;cit? </s>

<s id="id000094">Quantitates qu&etail; in continua &longs;unt proportione Analogæ <expan abbr="uocan&ttilde;">uocantur</expan>.</s>

<s>non dicam vt frigi<lb/>dus euadat. </s>

<s id="id000095">Dictum e&longs;t hoc ad fugiendum nomen barbarum, etiam ut bre<lb/>uiter tamen po&longs;&longs;emus &longs;ententiam explicare.</s>

<s>Quòd &longs;i dicant, aërem hunc non <lb/>e&longs;&longs;e aërem qui mouetur, aut qui vapores ex<lb/>cipiat, impo&longs;&longs;ibile enim e&longs;t tanta facta tran&longs;<lb/>mutatione ex calidi&longs;&longs;imo in frigidi&longs;&longs;imum, <lb/>vel Ari&longs;totele iudice, manere &longs;ub&longs;tantiam: <lb/>palàm e&longs;t, cùm totus aër frigidus &longs;it, qui nos <lb/>ambit, aut &longs;altem temperatus, vt qui iuxta <lb/>c&oelig;lum Lunæ &longs;itus e&longs;t: nam vniuer&longs;a aëris <lb/>moles vt ex æthereis flammis &longs;æpius depre<lb/>hen&longs;um e&longs;t, motus c&oelig;li in viginti quatuor <lb/>horis circumfertur, quod etiam admittit ip&longs;e <lb/>Ari&longs;toteles vniuer&longs;am aëris machinam hanc <lb/>frigidam e&longs;&longs;e, aut temperatam: quæ &longs;i non &longs;it <lb/>aër, alius nobis quærendus aër, for&longs;an &longs;upra <lb/>c&oelig;lum, aut in imo terræ. </s>

<s id="id000096">Vige&longs;ima diffinitio.</s>

<s><margin.target id="marg57"/>Elemento<lb/>rum nume<lb/>rus.</s>

<s id="id000097">Reflexa proportio dicitur cum trium quantitatum aggregatum <lb/>primæ, & tertiæ &longs;e habet ad &longs;ecundam uelut &longs;ecunda ad tertiam,</s>

<s>Tria igitur &longs;unt elementa: terra, quæ den<lb/>&longs;i&longs;&longs;ima e&longs;t atque graui&longs;&longs;ima, in imoque po&longs;i<lb/>ta: aër, qui rari&longs;&longs;imus, leui&longs;&longs;imus, in &longs;uprema <lb/>parte collocatur: & aqua, quæ medium in <lb/>omnibus his inter hæc po&longs;&longs;idet. </s>

<s>Communia <lb/>omnibus &longs;unt, quòd expertia &longs;int imnatæ ca<lb/>liditatis, nullus enim calor ni&longs;i à c&oelig;lo, atque <lb/>ideo ab anima vel luce. </s>

<s id="id000098">Vige&longs;ima prima diffinitio.</s>

<s>Terra quòd nimis <lb/>cra&longs;&longs;a, aër quòd nimis tenuis, minus frigida </s>

<s id="id000099">Trium quantitatum analogarum aliæ quidem Geometricæ, <lb/>cùm proportio &longs;imilis e&longs;t: Aliæ Arithmeticæ, cum fuerit æqualis <lb/>exce&longs;&longs;us huc indè: Aliæ mu&longs;icæ cum fuerit proportio primæ ad ter<lb/>tiam multiplex, aut &longs;implex, aut compo&longs;ita exce&longs;&longs;us quæ &longs;implici <lb/>iuncta &longs;it ad multiplicis perfectionem: eadem autem &longs;it proportio <lb/>exce&longs;&longs;us primæ, & &longs;ecundæ ad exce&longs;&longs;um &longs;ecundæ &longs;upra tertiam.</s>

<s><arrow.to.target n="marg58"/><lb/>e&longs;&longs;e videntur: &longs;ed aqua cum media &longs;it &longs;ub<lb/>&longs;tantia, frigidi&longs;&longs;ima apparet. </s>

<s>Aër igitur cum <lb/>ingraue&longs;cit, frigidior videtur. </s>

<s id="id000100">Velut proportio 6. 4. 3. dupla e&longs;t utrinque, & 6. 3. 2 tripla. </s>

<s id="id000101">& 28. 24. <lb/>21. & 45. 40. 36. Geometrica uerò & arithmetica facilius continuan<lb/>tur in quotquot quantitatibus, &longs;ed & mu&longs;ica uelut 12. 8. 6. 4. 3. & <lb/>proportio 8 ad 5 mu&longs;ica e&longs;t: quia proportio 5 ad 4 mu&longs;ica e&longs;t, & <lb/>bene &longs;onans, igitur con&longs;titutis 8. 5. 4. cum 8 ad 4 benè &longs;onet, & 5 <lb/>ad 4, & 4 &longs;it extrema non media inde 8. & 5 benè <expan abbr="&longs;onãt">&longs;onant</expan>. </s>

<s>Sed &longs;i non af<lb/>ficiatur, ob tenuitatem qua&longs;i temperatus exi<lb/>&longs;timatur. </s>

<s id="id000102">nam in me<lb/>dijs <expan abbr="nõ">non</expan> e&longs;t <expan abbr="uer&utilde;">uerum</expan>, ut in 9. 6. 4 bis diapente, & 16. 12. 9 bis diate&longs;&longs;aron.</s>

<s>Porrò frigida iam &longs;pontè cùm den<lb/>&longs;antur, frigidiora fiunt, veluti glacies. </s>

<s id="id000103">Vige&longs;ima &longs;ecunda diffinitio.</s>

<s>Terra <lb/>autem ob raritatem calorem admittit, <expan abbr="atq;">atque</expan> <lb/>ideò minus frigida e&longs;&longs;e creditur: ob id &longs;axa <lb/>&longs;unt ip&longs;a longè frigidiora. </s>

<s>Aër autem ob lu<lb/>cem qua&longs;i temperatus, & ob raritatem faci<lb/>lè mutatus, non &longs;olùm minimè frigidus, &longs;ed <lb/>& calidus iudicatur, cum omnia elementa <lb/>ex æquo natura propria &longs;int frigidi&longs;&longs;ima. <lb/></s>

<s id="id000104">Quantitates quæ &longs;imilem habent proportionem non continua<lb/>tam, omiologæ appellantur.</s>

<s>Indicio &longs;unt regiones &longs;ub Vr&longs;a, & noctes & <lb/>montium cacumina: &longs;ed & ratio id o&longs;tendit. <lb/></s>

<s id="id000105">Vige&longs;ima tertia diffinitio.</s>

<s>Omnis enim calor ab a&longs;tris e&longs;t. </s>

<s><expan abbr="Elem&etilde;ta">Elementa</expan> au<lb/>tem <expan abbr="c&utilde;">cum</expan> pura &longs;int, caloris ab a&longs;tris &longs;unt exper<lb/>tia. </s>

<s id="id000106">Prima operatione con&longs;i&longs;tere dicuntur proportiones, cùm inter <lb/>primo conflatas quantitates con&longs;titerint.</s>

<s>Calor enim a&longs;trorum illicò mutat: & <lb/>quod mutatur, di&longs;&longs;imile e&longs;t ei ex quo muta<lb/>tum e&longs;t: quare mi&longs;tum erit elementum ex <lb/>puro atque mutato, non autem &longs;implex. </s>

<s>Om<lb/>nia igitur elementa &longs;unt frigidi&longs;&longs;ima, id e&longs;t, <lb/>caloris omnis expertia. </s>

<s id="id000107">PRIMA Animi communis &longs;ententia.</s>

<s>Siquidem nihil aliud <lb/>e&longs;t frigiditas, quam caloris priuatio. </s>

<s id="id000108">Omnis Proportio e&longs;t, aut æqualitatis, aut maior inæqualis, <lb/>aut minor.</s>

<s>In hu<lb/>mido etiam di&longs;&longs;ident: <expan abbr="nã">nam</expan> terra e&longs;t &longs;icci&longs;&longs;ima, <lb/>vt aër humidi&longs;&longs;imus, & aqua in medio collo<lb/>catur. </s>

<s>Siccum dico humido priuatum, atque <lb/>ideo graue, quia <expan abbr="nõ">non</expan> e&longs;t exten&longs;um. </s>

<s id="id000109">Secunda animi communis &longs;ententia.</s>

<s>Cùm enim <lb/>materia prima &longs;eu hyle non extenditur, mul<lb/><arrow.to.target n="marg59"/><lb/>ta e&longs;t, & ideo formæ multum & grauitatis. <lb/></s>

<s id="id000110">Quilibet numerus tantus dicitur, quanta e&longs;t illius proportio ad <lb/>monadem.</s>

<s>Ideò aqua media in omnibus etiam his e&longs;t. <lb/></s>

<s>Con&longs;tat igitur ex hoc &longs;ydera omnia e&longs;&longs;e ca<lb/>lida: nam &longs;i omnia &longs;ydera habent lucem, om<lb/>nia etiam mi&longs;cent. </s>

<s id="id000111">Dicimus enim quatuor, quod monadem quater contineat. </s>

<s id="id000112">Et <lb/>duo cum dimidio cùm monadem bis & &longs;emis contineat.</s>

<s>Elementa autem natura <lb/>&longs;ua expertia &longs;unt omnis caloris ac lucis: ni<lb/>hil autem minus e&longs;&longs;e pote&longs;t eo quòd nihil <lb/>e&longs;t. </s>

<s>Omnis igitur lux calida e&longs;t & mi&longs;cet, & <lb/>omne a&longs;trum ob id calidum. </s>

<s id="id000113">Tertia animi communis &longs;ententia.</s>

<s>Dicitur autem <lb/>Saturnus frigidus <expan abbr="tãtum">tantum</expan> comparatione, quia <lb/>non tantum mi&longs;cet vt generationem in ho<lb/>nibus iuuet, &longs;ed impedit, velut aqua tepida <lb/>feruenti mi&longs;ta, minus efficit calidam. </s>

<s id="id000114">Proportionem defectus, &longs;eu detractæ quantitatis ad defectum <lb/>e&longs;&longs;e po&longs;&longs;e, ut quantitatis ad quantitatem dicuntur communes ani<lb/>mi &longs;ententiæ, quæ ex intellectu &longs;olo terminorum, quod ueræ &longs;int, <lb/>cogno&longs;cuntur. </s>

<s>Ob id <lb/>&longs;atis magis <expan abbr="cõducit">conducit</expan> Saturnus quàm Iupiter, <lb/>quia &longs;ata moderatiore calore <expan abbr="indig&etilde;t">indigent</expan>, qualis <lb/>e&longs;t in Saturno, non in Ioue. </s>

<s id="id000115">Si ergo defectus e&longs;t quantitas, & quantitas eiu&longs;dem <lb/>&longs;peciei, quia detrahitur, & defectus non e&longs;t &longs;implicitur, &longs;ed detra<lb/>cto ergo per quartam petitionem: uel primam diffinitionem erit <lb/>proportio inter illas. </s>

<s id="id000116">Sunt enim ambæ detractæ.</s>

<s>Non tamen mo<lb/>deratus e&longs;t pro hominum propagatione. </s>

<s>Om<lb/>nia igitur a&longs;tra calida, omnia elementa fri<lb/>gida. </s>

<s id="id000117">Quarta animi communis &longs;ententia.</s>

<s>Rur&longs;us c&oelig;lum <expan abbr="neq;">neque</expan> calidum, neque fri<lb/>gidum. </s>

<s id="id000118">Inter quantitatem, & defectum minorem quantitate, cuius e&longs;t de<lb/>fectus, e&longs;t proportio, quatenus e&longs;t quantitas. </s>

<s>Decipiuntur plurimi in elementis ob <lb/>calorem violentum, aut impre&longs;&longs;um. </s>

<s id="id000119">Sit a b linea, & detra<lb/>cta quantitas b c, non maior a b & d &longs;it alia quæuis quantitas eiu&longs;<lb/><figure id="id.015.01.023.1.jpg" xlink:href="015/01/023/1.jpg"/><lb/><expan abbr="d&etilde;">dem</expan> generis, dico quòd inter d & b c e&longs;t propor<lb/>tio quatenus b c e&longs;t quantitas, quia &longs;unt eiu&longs;<lb/>dem generis ideo &longs;unt in aliqua proportione <lb/>per primam diffinitionem. </s>

<s id="id000120">Sed ut b c e&longs;t defectus, nulla e&longs;t propor<lb/>tio: quia quanto b c augetur, tanto augetur proportio d ad b c, & <lb/>hoc e&longs;t contra demon&longs;trata ab Euclide.</s>

<s>Nam ex <lb/>actione a&longs;trorum elementorum partes ad <lb/>mi&longs;tionem veniunt, fiuntque potentia tales, <lb/>vt piper <expan abbr="calid&utilde;">calidum</expan>: &longs;ed hoc non e&longs;t <expan abbr="element&utilde;">elementum</expan>, &longs;ed <lb/><expan abbr="mi&longs;t&utilde;">mi&longs;tum</expan>. </s>

<s>Ignis <expan abbr="etiã">etiam</expan> qui <expan abbr="lapid&utilde;">lapidum</expan> colli&longs;ione accen<lb/>ditur, e&longs;t caliditas <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> in corpore rarefa<lb/>cto. </s>

<s id="id000121">Quinta animi communis &longs;ententia.</s>

<s>Violenta igitur caliditate mi&longs;ta profundi <lb/>po&longs;&longs;unt, alia corrupta, vt in putridis: alia po<lb/>tentia, vt in &longs;atis & &longs;eminibus maximè: alia <lb/>impre&longs;&longs;a, vt in aëre æ&longs;tatis tempore: alia na<lb/>turali, vt in animalibus. </s>

<s id="id000122">Cum proportio producitur ex proportionibus quælibet illa<lb/>rum dicetur producta diui&longs;a per alteram.</s>

<s>Manife&longs;tum e&longs;t igi<lb/>tur cur vita in montium iugis &longs;it perennis, <lb/><arrow.to.target n="marg60"/><lb/>ob puritatem aëris: non autem in Æthiopia, <lb/>ob calorem: neque in vallibus, quia aër &longs;im<lb/>plex non e&longs;t, &longs;ed calidus ac mi&longs;tus e&longs;&longs;e po&longs;&longs;it. <pb xlink:href="016/01/024.jpg" pagenum="375"/>In temperata igitur regione vbi venti orien<lb/>tales &longs;pirant, vita &longs;alubris ac diuturna. </s>

<s>Sed <lb/>de his aliàs. </s>

<s id="id000123">Sexta animi communis &longs;ententia.</s>

<s>Nunc &longs;olum &longs;cire &longs;ufficiat, quòd <lb/>duæ tantùm &longs;int qualitates, calor c&oelig;li, & <lb/>humidum elementorum: &longs;iccum autem & <lb/>frigus horum &longs;unt priuationes. </s>

<s id="id000124">Æqualium quantitatum &longs;eu proportionum ad tertiam compa<lb/>rabilium eadem e&longs;t proportio atque uici&longs;sim. </s>

<s>Sed & de his <lb/>po&longs;teriùs agemus. </s>

<s id="id000125">Hæc et&longs;i demon&longs;tre<lb/>tur ab Euclide, e&longs;t tamen hic generalior: & &longs;atis per &longs;e nota. </s>

<s id="id000126">Vt &longs;it <lb/>propior animi communi &longs;ententiæ, quàm rei demon&longs;trandæ.</s>

<s>Vt verò ad in&longs;titutum re<lb/><arrow.to.target n="marg61"/><lb/>uertar, elementum non voco rem calidi&longs;&longs;i<lb/>mam, vel frigidi&longs;&longs;imam, quandoquidem <lb/>vix eam liceat reperire: &longs;ed illud elemen<lb/>tum nunc dico, quod nec pabulo indiget, <lb/>nec &longs;pontè corrumpitur, nec vagatur, &longs;ed <lb/>certam tenet &longs;edem, maximam habens mo<lb/>lem, eamque &longs;ecundum naturam, ac ad gene<lb/>rationem paratum e&longs;t. </s>

<s>Cumque nullum ho<lb/>rum igni conueniat, hunc, elementum haud <lb/>quaquam appellabimus. </s>

<s id="id000127">Septima animi communis &longs;ententia.</s>

<s>Mouetur autem hic, <lb/>impotens, viuere ab&longs;que alimento, aëremque <lb/>proximum adurit: hicque ardens flamma <lb/><arrow.to.target n="marg62"/><lb/>vocatur. </s>

<s id="id000128">Ad quod quantitas proportionem habet infinitam, id in genere <lb/>illius quantitatis non comprehenditur.</s>

<s>E&longs;t enim flamma nihil aliud, quam <lb/>aër accen&longs;us. </s>

<s>Hæc autem perpetuò moue<lb/>tur, nec vnquam quie&longs;cit. </s>

<s id="id000129">Nam proportio e&longs;t duarum quantitatum eiu&longs;dem generis com<lb/>paratio certa: at hæc comparatio certa non e&longs;t: non igitur quantita<lb/>tes ambæ &longs;unt, aut non eiu&longs;dem generis.</s>

<s>Ignis enim &longs;ub<lb/>&longs;tantia cum tenui&longs;&longs;ima &longs;it, & quod &longs;ubie<lb/>ctum e&longs;t illi &longs;emper vrat, perpetuò etiam <lb/>mouetur. </s>

<s>Ob &longs;ubtilitatem igitur per angu<lb/>&longs;ti&longs;&longs;ima foramina ingreditur, ob motum ve<lb/>rò diuidit ac &longs;cindit, di&longs;ci&longs;&longs;a calore immen<lb/>&longs;o vrit, ac in propriam conuertit &longs;ub&longs;tan<lb/>tiam. </s>

<s id="id000130">PRIMA Petitio.</s>

<s>Ergo flamma non eadem vnquam <lb/>manet, &longs;ed perpetua generatione altera al<lb/>teri &longs;uccedit, & ob id moueri eam &longs;emper <lb/>videri nece&longs;&longs;arium e&longs;t. </s>

<s id="id000131">Si fuerit primi ad &longs;ecundum, ut tertij ad quartum, & ex primo in <lb/>&longs;ecundum producatur æquale, aut maius, aut minus primo, uel <lb/>&longs;ecundo, producetur eodem modo ex tertio in quartum &etail;quale aut <lb/>maius, aut minus tertio, uel quarto eadem ratione & ordine.</s>

<s>Nam quæ genita <lb/>iam e&longs;t, aëris proximam partem inuadit, <lb/>humidumque eius depa&longs;citur, & moriendo <lb/>aliam nouam excitat flammam. </s>

<s>Cum igitur <lb/>humidum quod prius erat in flammam ver<lb/>titur, aucta ex hac mutatione in immen&longs;um <lb/>quantitate, nec po&longs;&longs;it quod illi &longs;ubiectum <lb/>e&longs;t pabulum ob duritiem pellere, nece&longs;&longs;a<lb/>riò in &longs;uperiorem partem vehementer a&longs;<lb/>cendit, & eam quæ iam &longs;uprà ip&longs;am erat <lb/>accen&longs;a impellit: vnde &longs;it vt &longs;ur&longs;um ple<lb/>rumque magno impetu flamma feratur ac <lb/>feriat. </s>

<s id="id000132">Secunda petitio.</s>

<s>Si tamen tigna vrantur &longs;upernè, flam<lb/>mam eadem ratione deor&longs;um ferri nece&longs;&longs;e <lb/><arrow.to.target n="marg63"/><lb/>e&longs;t. </s>

<s id="id000133">Proportiones po&longs;&longs;unt duci, diuidi, iungi, & auferri, & &longs;umi radix <lb/>in eis cuiu&longs;cunque generis, atque earum quantitatis, ut libet, po&longs;&longs;e <lb/>tran&longs;ponere.</s>

<s>Non igitur flamma &longs;emper &longs;ur&longs;um fer<lb/>tur, &longs;ed ob id plerunque, quòd pabulum in <lb/>imo po&longs;itum e&longs;t. </s>

<s>Cùm tamen in imum fer<lb/>tur, adeò vrit, vt &longs;i humidum e&longs;t quod vri<lb/>tur, repentè colliquatum &longs;uffocet ignem: ob <lb/>idque cerei conuer&longs;a flamma inferius &longs;pontè <lb/>extinguuntur. </s>

<s id="id000134">Tertia petitio.</s>

<s>Ligna autem non &longs;ic, quòd <lb/>humidum colliquari non queat. </s>

<s id="id000135">Proportionis cuiu&longs;uis nomen à denominatore &longs;uprà &longs;cripto, & <lb/>numeratore infrà &longs;cripto &longs;umitur.</s>

<s>Extinguun<lb/><arrow.to.target n="marg64"/><lb/>tur etiam ob aliam rationem, quòd <emph type="italics"/>(<emph.end type="italics"/> vt di<lb/>xi) &longs;emper &longs;uperior pars flammæ ab inferio<lb/>re, quæ nutrimento proximior e&longs;t, propelli<lb/>tur: vnde &longs;uprema flammæ pars continuò <lb/>tran&longs;itu extincta in fumum vertitur. </s>

<s>E&longs;t <lb/><arrow.to.target n="marg65"/><lb/>enim fumus medium inter flammam & aë<lb/>rem, atque ideò duplex. </s>

<s id="id000136">Quarta petitio.</s>

<s>Quidam qui flam<lb/>mæ &longs;uccedit, & hic tenuis ac nece&longs;&longs;arius. <lb/></s>

<s id="id000137">Diui&longs;a quauis quantitate per aliam eiu&longs;dem generis, quod exit <lb/>proportio dicitur.</s>

<s>Omnis enim flamma in fumum vertitur: &longs;ed <lb/>hic cum tenui&longs;&longs;imus &longs;it, in aërem celeriter <lb/>tran&longs;it, atque ob id nec &longs;uffocat, nec oculos <lb/>vrit, &longs;ed &longs;olum calefacit ac &longs;iccat. </s>

<s>Alter e&longs;t <lb/>fumus qui flammæ præit generationem, at<lb/>que humidior e&longs;t, ac oculos vrit & &longs;uffocat, <lb/>quòd in aërem non facilè conuertatur. </s>

<s id="id000138">Quinta petitio.</s>

<s>Idem <lb/>plærunque ex carbonibus prauis ac humi<lb/>dioribus lignis excitari &longs;olet. </s>

<s id="id000139">Qu&etail;libet proportio e&longs;t uel inter duas quantitates, uel per unam <lb/>&longs;ignificatur.</s>

<s>Primus igitur <lb/>cùm flamma de&longs;cendit in cereis conuer&longs;is, <lb/>dum a&longs;cendere nititur, flammæ ip&longs;i occurrit, <lb/>eamque celerrimè &longs;uffocat. </s>

<s>Declarauimus <lb/>enim quòd huius quantitas gignatur im<lb/>men&longs;a, cùm fingulis momentis flamma quæ <lb/>maximè à nutrimento remota e&longs;t, & in am<lb/>bitu aëri vicina, in fumum tran&longs;eat, cuius <lb/>copia nihil mirum e&longs;t ignem illi occurren<lb/>tem celerrimè &longs;uffocari. </s>

<s id="id000140">Nam per tertiam petitionem &longs;i &longs;int duæ quantitates, quæ non ha<lb/>beant unius rationem, nomen &longs;umit proportio à duobus numeris, <lb/>&longs;in autem &longs;it altera monas, erit per &longs;ecundam animi communem &longs;en<lb/>tentiam, proportio numerus ip&longs;e Ideò patet, quod dicitur.</s>

<s>Huius igitur motus <lb/><arrow.to.target n="marg66"/><lb/>tam rapidi cau&longs;a, flamma cuncta corrumpit, <lb/>non &longs;olius immen&longs;æ caliditatis ratione. </s>

<s id="id000141">Sexta petitio.</s>

<s>Sed <lb/>tamen motus hic in flamma interior, quia <lb/>&longs;en&longs;im fit, nos latet. </s>

<s>Nec flamma tota illicò <lb/>perit, &longs;ed quæ &longs;olùm e&longs;t in ambitu: nam quæ <lb/>in medio e&longs;t, tandiu manet, donec ad extre<lb/>mum in contactu aëris perueniat, aliter in <lb/>flammæ medio non e&longs;&longs;et. </s>

<s id="id000142">Propo&longs;ita proportione quacunque, & monade quantitatem inue<lb/>nire, quæ &longs;e habeat ad monadem in proportione propo&longs;ita.</s>

<s>Sed fumus retrò <lb/>quandoque agitur, vel ob impetum, vel re<lb/>pul&longs;us, vel prohibitus. </s>

<s id="id000143">Nam cùm per quartam petitionem diui&longs;a quantitate per quan<lb/>titatem exeat proportio, & numerus ad <expan abbr="monad&etilde;">monadem</expan> &longs;e habeat, ut pro<lb/>portio, ideo &longs;umpta monade &longs;ecundum illum numerum, ille nume <lb/>rus e&longs;t quantitas quæ&longs;ita.</s>

<s>Impetus fit vel ob <lb/>multitudinem, vel ob celeritatem motus. </s>

<s>Li<lb/>gna igitur viridia & multitudo flammæ, re<lb/>plent cubicula fumo. </s>

<s id="id000144">Septima petitio.</s>

<s>Venti quoque repel<lb/>lunt fumum, & angu&longs;tia camini prohibet <lb/>exitum, vel &longs;i angu&longs;tior &longs;it in vno, vt non re<lb/>cipiat. </s>

<s id="id000145">Quamlibet quantitatem per aliam eiu&longs;dem generis diuidere <lb/>po&longs;&longs;e.</s>

<s>Maxima autem cau&longs;a e&longs;t à ventis. </s>

<s>Nam <lb/>fumus altius &longs;emper a&longs;cendit, tum ob impe<lb/>tum à flamma conceptum, tum ob leuita<lb/>tem. </s>

<s id="id000146">Octaua petitio.</s>

<s>Vbi ventis occurrat, maximè vbi copia <lb/><figure id="id.016.01.024.1.jpg" xlink:href="016/01/024/1.jpg"/><lb/>viridium lignorum ad&longs;it, retrogreditur: & <lb/>qui ex quatuor partibus foramina habet, ab <lb/>omni vento impeditur: nam vndique patet. <lb/></s>

<s id="id000147">Proportionem in proportionem ducere po&longs;&longs;e: quamuis &longs;int in<lb/>ter quantitates diuer&longs;i generis.</s>

<s>Auxilium à nobis ratione excogitatum. </s>

<s>In <lb/>quatuor partibus, oriente, occidente, meri<lb/>die, &longs;eptentrione binos colloca canales ficti<lb/>les ex aduer&longs;o po&longs;itos, ita vt alter &longs;ur&longs;um fe<lb/>ratur, reliquus deor&longs;um: nam impo&longs;&longs;ibile e&longs;t <lb/>octo ventos, quatuor inferius <expan abbr="t&etilde;dentes">tendentes</expan>, qua<lb/>tuor autem &longs;uperiùs, à quatuor c&oelig;li princi<lb/>palibus regionibus &longs;pirare. </s>

<s id="id000148">Quod dicitur de multiplicatione intelligendum e&longs;t de alijs ope<lb/>rationibus &longs;uprà enumeratis.</s>

<s>Quod ni fiat, fu<lb/>mus minimè pote&longs;t retrò pelli: atque id <lb/>etiam experimento ad amu&longs;&longs;im comproba<lb/>tum e&longs;t. </s>

<s id="id000149">Nona petitio.</s>

<s>Adiuuat autem non parum latitudo <lb/>faucium in imo. </s>

<s>Plerunque etiam tutiores <lb/>canales decliues tantum. </s>

<s id="id000150">Monadem &longs;emper &longs;umere in quo cunque genere po&longs;&longs;e propo&longs;i<lb/>ta proportione.</s>

<s>Sed tutior omnibus <lb/>e&longs;t qui vagina circumcingitur, quæ inferiùs <lb/>non cohæret tecto. </s>

<s><margin.target id="marg58"/>Demon&longs;tra<lb/>tio o&longs;tendens <lb/>quòd omnia <lb/>elementa <lb/>&longs;unt frigi<lb/>di&longs;&longs;ima.</s>

<s id="id000151">Nam licet diuidere per &longs;eptimam petitionem quantitatem per <lb/>quantitatem proportionis: & quod exit, e&longs;t proportio per quar<lb/>tam petitionem, & per &longs;ecundam animi communem &longs;ententiam <lb/>illa proportio e&longs;t numero æqualis: ergo diui&longs;a proportione, per &longs;i<lb/>milem numerum &longs;tatuetur monas.</s>

<s><margin.target id="marg59"/>Sidera om<lb/>nia calida. <lb/></s>

<s id="id000152">Decima petitio.</s>

<s>e&longs;&longs;e.</s>

<s><margin.target id="marg60"/>Aër vitæ &longs;a<lb/>lubrior.</s>

<s id="id000153">In quouis genere quantitatum &longs;umere po&longs;&longs;e quantitatem, quæ <lb/><arrow.to.target n="marg2"/><lb/>&longs;e habeat ad monadem in proportione data. </s>

<s id="id000154">Similem huic propo<lb/>nit Euclides in lineis generaliter: nos autem contrà generaliter in <lb/>omnibus quantitatibus, &longs;ed de monade tantum.</s>

<s><margin.target id="marg61"/>Ignem hunc <lb/>non e&longs;&longs;e ele<lb/>mentum.</s>

<s><margin.target id="marg62"/>Flamma <lb/>quid &longs;it. <lb/></s>

<s id="id000155"><margin.target id="marg2"/>D<emph type="italics"/>uodecima <lb/>&longs;exti<emph.end type="italics"/> E<emph type="italics"/>lem.<emph.end type="italics"/>Vndecima petitio.</s>

<s>Cur flamma <lb/>nunquam <lb/>quie&longs;cat. <lb/></s>

<s id="id000156">Monadem in quancunque quantitatem ductam æquale ip&longs;i pro<lb/>ducere. </s>

<s>Ignis quo<lb/>modo vrat. <lb/></s>

<s id="id000157">Similiter & proportionem æqualem.</s>

<s>Flamma non <lb/>eadem ma<lb/>net. <lb/></s>

<s id="id000158">Nam cum aliqua quantitas augeat ducta aliqua minuat, nece&longs;&longs;e <lb/>e&longs;t aliquam e&longs;&longs;e, quæ nec augeat, nec minuat, & hæc e&longs;t monas. <lb/></s>

<s>Cur flamma <lb/>plerunque <lb/>a&longs;cendat.</s>

<s id="id000159">Idem dico de diui&longs;ione. </s>

<s id="id000160">Aequalitas etiam ducta, uel diuidens non <lb/><arrow.to.target n="marg3"/><lb/>mutat proportionem: nec quantitatem ip&longs;am, igitur monas æqua<lb/>litatem refert. </s>

<s><margin.target id="marg63"/>Cur cerei <lb/>conuer&longs;i ex<lb/>tinguæntur.</s>

<s id="id000161">Quod etiam e&longs;t per&longs;picuum ex &longs;upradictis.</s>

<s><margin.target id="marg64"/>Fumus quo<lb/>modo geue<lb/>retur.</s>

<s id="id000162"><margin.target id="marg3"/>S<emph type="italics"/>ecunda ani <lb/>mi <expan abbr="cõmunis">communis</expan> <lb/>&longs;ententia.<emph.end type="italics"/></s>

<s><margin.target id="marg65"/>Fumus du<lb/>plex.</s>

<s><margin.target id="marg66"/>Cau&longs;æ cur <lb/>cubicula fu<lb/>mo replean<lb/>tur. <lb/></s>

<s id="id000163">Duodecima petitio.</s>

<s>Caminus fu<lb/>mum non re<lb/>mittens.</s>

<s id="id000164">Cum fuerint quatuor quantitates & ad primam, & tertiam æquè <lb/>multiplicibus a&longs;&longs;umptis, item que ad &longs;ecundam & quartam, & &longs;i mul<lb/>tiplex primæ maius e&longs;t multiplici &longs;ecundæ, multiplex tertiæ &longs;it ma<lb/>ius multiplici quartæ, & &longs;i minus minus, & &longs;i æquale æquale, idque<lb/> &longs;emper quouis modo a&longs;&longs;umptis his proportionibus ad primam & <lb/>tertiam, & ad &longs;ecundam & quartam erit proportio primæ ad &longs;ecun<lb/>dam, ut tertiæ ad quartam. </s>

<s>Cùm igitur ad hoc vt ignis vrat tria &longs;int <lb/><arrow.to.target n="marg67"/><lb/>nece&longs;&longs;aria, pabulum, motus, & quod pene<lb/>tret, cùm in flamma motus maior &longs;it ac ma<lb/>nife&longs;tior, atque ideò etiam introitus qui ad <lb/>motum con&longs;equitur maior, minimè ob&longs;cu<lb/>rum e&longs;t cur flamma reliquo igne &longs;it viua<lb/>tior: ideoque cerei dum flamma viget tan<lb/><arrow.to.target n="marg68"/><lb/>diu ardent donec &longs;uppetit alimentum: cùm <lb/>flamma de&longs;init, &longs;pontè vel momento peni<lb/>tus extinguuntur. </s>

<s id="id000165">Hæc etiam a&longs;&longs;umitur ab Euclide. </s>

<s id="id000166">Et per <lb/><arrow.to.target n="marg4"/><lb/>hanc intelligimus etiam conuer&longs;am.</s>

<s>Quia tamen flamma <pb xlink:href="016/01/025.jpg" pagenum="376"/>multum ab&longs;umit alimenti, ideò per&longs;æpe mi<lb/>nus durat prunis: &longs;ed hoc non merito &longs;ui <lb/>e&longs;t, &longs;ed quia celerius alimentum finitur. </s>

<s>His <lb/>de cau&longs;is & à pingui humido flammæ diu<lb/>turnæ, & à tenui atque &longs;icca &longs;ub&longs;tantia im<lb/>men&longs;æ creantur. </s>

<s id="id000167"><margin.target id="marg4"/>Q<emph type="italics"/>uinto<emph.end type="italics"/> E<emph type="italics"/>le. <lb/>diff.<emph.end type="italics"/> 6.</s>

<s>Nam in tenui & arida <lb/>&longs;ub&longs;tantia celeriter flamma flammæ &longs;ucce<lb/>dit, atque ob id in maximam molem cre&longs;cit. <lb/></s>

<s id="id000168">Tertiadecima petitio.</s>

<s>Quòd &longs;i hæc ambo iungantur, & arida, te<lb/>nui&longs;que &longs;ub&longs;tantia, & pingue ac plurimum <lb/>humidum, velut in bitumine, tunc flam<lb/>mæ maximæ, & diuturnæ excitantur. </s>

<s>Ob <lb/><arrow.to.target n="marg69"/><lb/>id verò manife&longs;tum &longs;it, cur bitumini ar<lb/>denti aqua iniecta maiores excitet flam<lb/>mas, quod etiam Georgius Agricola, vir <lb/>no&longs;træ tempe&longs;tatis memoria dignus, narrat: <lb/>e&longs;&longs;e &longs;cilicet in I&longs;landia in&longs;ula montem, no<lb/>mine Heclam, ex quo ignis emi&longs;&longs;us &longs;iccis <lb/>extinguatur, aqua verò alitur. </s>

<s id="id000169">Quantitates æquales, atque proportiones in qua&longs;uis quanti<lb/>tates ductæ eandem &longs;eruant rationem. </s>

<s id="id000170">Euclides hanc demon&longs;trat, <lb/>nos autem ad uitandum tædium petimus concedi, &longs;ub qua in<lb/><arrow.to.target n="marg5"/><lb/>cluduntur diui&longs;io etiam additio, detractio, laterum omnium in<lb/>uentio.</s>

<s>Id autem fer<lb/>mè commune e&longs;t omnibus validioribus <lb/>flammis: vnde etiam fabri in&longs;per&longs;a aqua <lb/>ignes excitare &longs;olent: cùm enim ardentior <lb/>fuerit ignis, à frigido incitatur, & ab hu<lb/>mido alitur, quorum vtrunque aquæ ine&longs;t. <lb/><arrow.to.target n="marg70"/><lb/>Ea de cau&longs;a etiam ignis qui follibus accen<lb/>ditur, cùm validus &longs;it, aqua modica non <lb/>extinguitur, &longs;ed robu&longs;tior euadit. </s>

<s>Folles <lb/>namque ignes accendunt, quoniam mo<lb/>tum concitant: inde ex motu penetrat <lb/>vis & exurit. </s>

<s id="id000171"><margin.target id="marg5"/>Q<emph type="italics"/>uarta quin<lb/>ti<emph.end type="italics"/> E<emph type="italics"/>lem.<emph.end type="italics"/></s>

<s>Nece&longs;&longs;arij autem &longs;unt in me<lb/>tallis, quoniam à paruo igne non lique&longs;<lb/>cunt, &longs;ed &longs;erò, ideò prius exuruntur quàm <lb/>lique&longs;cant. </s>

<s id="id000172">Quartadecima petitio.</s>

<s>Sed à follibus ignis accen&longs;us <lb/>mouetur & penetrat, ac colliquat metalla. <lb/></s>

<s>Vnde non paruum compendium in celeri <lb/>exitu, & quòd minus impen&longs;æ perit, & <lb/>metalli portio minor vritur. </s>

<s id="id000173">Cùm termini alicuius quantitatis eandem &longs;eruant rationem in <lb/>omnibus, & firmi &longs;unt ac &longs;tabiles eiu&longs;dem rationis comparatione <lb/>contentæ partes æqualem &longs;eruant exce&longs;&longs;um, &longs;eu proportionem.</s>

<s>Folles igi<lb/>tur ad accendendum ignem atque mollien<lb/>dum ac liquandum apti&longs;&longs;imi &longs;unt. </s>

<s id="id000174">PROPOSITIO prima.</s>

<s><margin.target id="marg67"/>Flamma cur <lb/>igne alio vi<lb/>uacior.</s>

<s><margin.target id="marg68"/>Cau&longs;æ ma<lb/>gnarum <expan abbr="flã-marum">flan<lb/>marum</expan>.</s>

<s id="id000175">Proportionem in proportionem duci e&longs;t &longs;uperiores nume<lb/>ros atque inferiores inuicem ducere.</s>

<s><margin.target id="marg69"/>Cur aqua <lb/>quandoque <lb/>ignes exci<lb/>tet.</s>

<s><margin.target id="marg70"/>Folles cur <lb/>accendant <lb/>ignem, & <lb/>vbi magis <lb/>nece&longs;&longs;arij.</s>

<s id="id000176">Sit proportio lineæ a ad lineam b, ut anguli c ad angulum d, &longs;ta<lb/><arrow.to.target n="marg6"/><lb/>tuatur e monas in genere a <lb/><figure id="id.015.01.026.1.jpg" xlink:href="015/01/026/1.jpg"/><lb/>b, & fiat f ad e, ut c ad d, & du<lb/><arrow.to.target n="marg7"/><lb/>catur a in f & b in e, & pro<lb/>ducantur g & h. </s>

<s id="id000177">Quia ergo <lb/><arrow.to.target n="marg8"/><lb/>f e&longs;t proportio ip&longs;a, erit g ad <lb/><arrow.to.target n="marg9"/><lb/>a ut c ad d, &longs;ed h e&longs;t æqualis <lb/>b, igitur a ad h ut ad b. </s>

<s>Itaque vt ad in&longs;titutum reuertar, aqua <lb/><arrow.to.target n="marg71"/><lb/>&longs;olet vehementes accendere ignes, quoniam <lb/>humidum ip&longs;um quod exhalat, pinguius <lb/>redditur, nec à circumfu&longs;o fumo ab&longs;umi<lb/>tur, &longs;ed totum ignis ip&longs;e depa&longs;citur, quo <lb/>purior inde factus, & &longs;imul collectus à <lb/>frigido alacrior in&longs;urgit. </s>

<s id="id000178">Du<lb/>cta ergo dicetur proportio a <lb/><arrow.to.target n="marg10"/><lb/>ad b in proportionem c ad d <lb/>ducendo terminos proportionis, &longs;eu quantitatis recta &longs;cilicet &longs;u<lb/>periores cum &longs;uperioribus, & inferiores cum inferioribus. </s>

<s id="id000179">Nam &longs;i <lb/><arrow.to.target n="marg11"/><lb/>rur&longs;um con&longs;tituantur f ad e ut a ad b cùm f &longs;it proportio, & k ad f ut <lb/><arrow.to.target n="marg12"/><lb/>c ad d, erit k ad e, ut g ad h, k autem fit ex ductu proportionis a ad b, <lb/>quæ e&longs;t fin proportionem c ad d, liquet igitur propo&longs;itum.</s>

<s>Vnde etiam ignes <lb/>qui aqua excitantur & accenduntur: con&longs;tat <lb/>autem pice nauali & Græca, &longs;ulphure, vini <lb/>fæce, quàm vocant tartarum, &longs;arcocolla, ha<lb/>linitro, bituminis &longs;pecie, illa quam vocant <lb/>petroleum. </s>

<s>Relatum hoc ad Marcum Grac<lb/>cum. </s>

<s>Additur igitur calx viua duplo pon<lb/>dere, & cum ouorum luteis pariter mi&longs;cen<lb/>tur omnia, & in fimo equino &longs;epeliuntur. <lb/></s>

<s>Aliud: Sulphurei olei, petrolei, iuniperini <lb/>olei, & halinitri æquales &longs;ingulorum par<lb/>tes: nigræ picis, pinguedinum an&longs;eris, & <lb/>anatis, &longs;tercoris columini, eius liquoris, <lb/>quam vocant liquidam vernicem con&longs;tant <lb/>autem oleo &longs;eminis lini, rur&longs;us &longs;ingulorum <lb/>tantundem: a&longs;phalti partes quinque: exci<lb/>pe ardente aqua, & in fimo equino &longs;epeli. <lb/></s>

<s>Aliud etiam: Vernicis liquidæ, &longs;ulphurei <lb/>olei, & iuniperini, & eius quod fit ex lini <lb/>&longs;emine, & petrolei, & lachrymæ lariginæ <lb/>partes æquas &longs;ingulorum; aquæ ardentis <lb/>tres ac mediam, tum halinitri, ligni lau<lb/>rini &longs;icci vi puluerem redactorum quan<lb/>tum &longs;ufficit, vt omnia &longs;imul mi&longs;ta, luti <lb/>&longs;pi&longs;&longs;itudinem recipiant. </s>

<s>Hæc omnia vitreo <lb/>va&longs;e excipe, & in fimo equino tribus men<lb/>&longs;ibus &longs;epeli. </s>

<s>Si igitur ex his pilæ lignis h&ecedil;<lb/>reant, &longs;pontè imbribus accenduntur: &longs;ed <lb/>hoc non omninò &longs;emper euenit. </s>

<s>Illud au<lb/>tem &longs;emper euenit, vt iam accen&longs;us nul<lb/>lis aquis extinguatur. </s>

<s id="id000184"><margin.target id="marg10"/>P<emph type="italics"/>er<emph.end type="italics"/> 2. A<emph type="italics"/>ni<lb/>mi &longs;entent.<emph.end type="italics"/></s>

<s>Puluis autem qui fa<lb/>cillimè ardet, & cuius flamma vehementer <lb/>exurit, con&longs;tat pyrio puluere, & tertia &longs;ul<lb/>phuris ac Græcæ picis parte. </s>

<s>Porrò plu<lb/>ra his in libris de rerum Varietate &longs;crip<lb/>&longs;imus: hi autem exercitationem omnium <lb/>continent locupletem, quæ hîe ratione <lb/><arrow.to.target n="marg72"/><lb/>explicantur. </s>

<s>Quonam pacto verò aquâ non <lb/>extinguantur hi ignes, facilè patet con&longs;i<lb/>deranti, quòd motum adeò vehementem <lb/>ciunt, vt flamma flammæ follium loco &longs;it. <lb/></s>

<s>Ob id igitur paruam flammam facilè e&longs;t <lb/>extinguere, magnam autem difficillimum. <lb/><arrow.to.target n="marg73"/><lb/>Non &longs;olùm enim quòd maior &longs;it, diffici<lb/>liùs extinguitur parua, &longs;ed quòd motum <lb/>excitet vehementem, à quo ( vt dixi ) <lb/>flamma fouetur. </s>

<s id="id000187">Propo&longs;itio <expan abbr="&longs;ec&utilde;nda">&longs;ecunda</expan>.</s>

<s>Ab magnitudine autem <lb/>motus & flammæ procul abe&longs;&longs;e coguntur <lb/><arrow.to.target n="marg74"/><lb/>homines: vnde etiam auxilium primò dee&longs;t, <lb/>inde fumo abundante &longs;ubit de&longs;peratio. </s>

<s>In <lb/>his ca&longs;ibus tria auxilia &longs;olùm &longs;uper&longs;unt: vt <lb/>detrahatur materia ardere apta, vel vt <lb/>murus ex lapidibus erigatur, lapide&longs;que &longs;u<lb/>per incendium proiiciantur, quo quidam <lb/>amici no&longs;tri vicinam &longs;uam domum ab in<lb/>cendio &longs;eruauerunt: vel quo vti &longs;olemus <lb/>dum luci ardent, aut &longs;egetes, vt pars in <lb/>quam ignis fertur accendatur. </s>

<s id="id000188">Proportio extremorum producitur ex intermedijs.<lb/><arrow.to.target n="marg13"/></s>

<s>Nam &longs;ic <lb/>extincto eo igne, vel etiam nondum ex<lb/>tincto, maiori &longs;ubtracta materia, peri<lb/>culo&longs;o, &longs;ed vtili tamen inuento, &longs;erua<lb/>mus reliquum. </s>

<s>Hoc autem auxilij gene<lb/>re &longs;eruati &longs;unt luci no&longs;tri in Nouarien&longs;i <lb/>agro, non multum ab&longs;imili, quo loci <lb/>dominus &longs;æpe &longs;eip&longs;um à periculo libe<lb/>rauit. </s>

<s><margin.target id="marg71"/>Ignes qui <lb/>aqua non ex <lb/>tinguuntur <lb/>artificio&longs;i.</s>

<s id="id000190">Sint a b c quantitates dico proportio<lb/><figure id="id.015.01.026.2.jpg" xlink:href="015/01/026/2.jpg"/><lb/>nem a ad c, produci ex proportione a ad b </s>

<s><margin.target id="marg72"/>Libri de re<lb/>rum Varie<lb/>tate &longs;unt <lb/>praxis hu<lb/>ius.</s>

<s id="id000191"><arrow.to.target n="marg14"/><lb/>& b ad c, &longs;tatuantur totidem à monade d e <lb/>f, erúntque ex demon&longs;trantis ab Euclide in <lb/>quinto <expan abbr="Elem&etilde;torum">Elementorum</expan> in eadem proportio<lb/>ne, &longs;tatuatur ergo d prima quantitas e &longs;e<lb/>cunda & tertia f quarta. </s>

<s><margin.target id="marg73"/>Magna <expan abbr="flã-ma">flan<lb/>ma</expan> tribus <lb/>cau&longs;is diffi<lb/>cile extin<lb/>guitur.</s>

<s id="id000192">eritqúe per præce<lb/><arrow.to.target n="marg15"/><lb/>dentem proportio productorum ex d in e <lb/>& &longs;it g, & in f & &longs;it h, producta ex propor<lb/>tionibus d ad e & e ad f, quare ex propor<lb/>tionibus a ad b & b ad e, &longs;ed ex dictis cum <lb/>e &longs;it eadem, erit proportio d ad f, ut g ad h & proportio, d ad f per <lb/>æquam proportionem ab Euclide demon&longs;tratam, ut a ad c, igitur <lb/><arrow.to.target n="marg16"/><lb/>proportio a ad c producitur ex proportionibus a ad b & b ad c, & <lb/>e&longs;t proportio ip&longs;a a ad c d numerus, ut o&longs;ten&longs;um e&longs;t.</s>

<s><margin.target id="marg74"/>Auxilia ex<lb/>tinguendi <lb/>magna in<lb/>cendia.</s>

<s>Sunt igitur bitumine loca abundantia, <lb/><arrow.to.target n="marg75"/><lb/>vel &longs;ulphure, quæ &longs;pontè ardent, & aqua <lb/>minimè extinguuntur. </s>

<s>Ætnæ in Sicilia <lb/>montis famo&longs;i&longs;&longs;imum e&longs;t incendium. </s>

<s>Cra<lb/>teres duo, inferior in putei formam an<lb/>gu&longs;tus, angu&longs;to labro lapideo circumcin<lb/>gente: &longs;uperior verò ab imo ( vt referunt) <lb/>fundæ iactu di&longs;tat, quatuor habens in am<lb/>bitu &longs;tadia ad centum M. pa&longs;&longs;uum: cineres <lb/>circumquaque effundit, &longs;umma caligine <lb/>cuncta biduo offu&longs;cans, quod etiam Pli<lb/>nius affirmat. </s>

<s>Sed no&longs;tris temporibus re<lb/>mi&longs;&longs;um videtur. </s>

<s>Puteolis verò parum an<lb/>tequàm hæc &longs;criberemus (XX. M. pa&longs;&longs;uum, <lb/>vt audio, à Neapoli di&longs;tant ) maxima ex <lb/>incendio iactura contigit. </s>

<s id="id000196">Ex hoc &longs;equitur, quòd cùm fuerit quantitas tertia monas ex pro<lb/><arrow.to.target n="marg17"/><lb/>portionibus inuicem ductis producetur prima quantitas.<lb/><arrow.to.target n="marg18"/></s>

<s>Fiunt igitur hi <lb/>ignes vbi &longs;ulphur aut bitumen gignitur, <lb/>plerunque autem iuxta mare, quòd bitu<lb/>men, & &longs;ulphur à marinis &longs;ordibus ac ca<lb/>lore fomentum accipiant. </s>

<s><margin.target id="marg75"/>Loca quæ <lb/>ardent.</s>

<s>Quomodo autem accendatur parata mate<lb/><arrow.to.target n="marg76"/><lb/>ria, inferius dicemus. </s>

<s>Ignis autem qui inter<lb/>diu latet, & &longs;olùm noctu videtur, quemadmo<lb/>dum in Apennini Mugellano videmus, inno<lb/>xius e&longs;t arboribus <expan abbr="atq;">atque</expan> etiam herbis. </s>

<s id="id000199">Ex hoc &longs;equitur, quòd conuer&longs;a proportio producitur ex con<lb/>uer&longs;is proportionibus.</s>

<s>Duplex <lb/>hic: alius ignis verè, &longs;ed à vaporibus qui &longs;uc<lb/>ce&longs;&longs;u <expan abbr="t&etilde;poris">temporis</expan> cùm <expan abbr="materiã">materiam</expan> &longs;ube&longs;&longs;e &longs;ignificet, <lb/><expan abbr="iacturã">iacturam</expan> affert. </s>

<s>Alius e&longs;t omninò innoxius, qu<gap/><lb/>non verè ignis, &longs;ed velut materia putrida li-<pb xlink:href="016/01/026.jpg" pagenum="377"/><expan abbr="gnor&utilde;">gnorum</expan> ignem noctu &longs;olo &longs;plendore, &longs;ed <expan abbr="ab&longs;q;">ab&longs;que</expan> <lb/><arrow.to.target n="marg77"/><lb/>calore refert. </s>

<s id="id000200">Propo&longs;itio tertia.</s>

<s><expan abbr="Eiu&longs;d&etilde;">Eiu&longs;dem</expan> fermè generis ignis ve<lb/>ri e&longs;t Helenæ &longs;idus circa malum nauis, quod <lb/>cadens etiam ænea va&longs;a colliquat, certus <lb/>&longs;ubmer&longs;ionis nuncius. </s>

<s id="id000201">Si proportio ex duabus proportionibus in quatuor terminis <lb/>producatur, ip&longs;a uerò proportio inter duas alias quantitates fue

<s>Nam &longs;olùm in gra<lb/>uibus accidit tempe&longs;tatibus, nec ni&longs;i cra&longs;&longs;i&longs;<lb/>&longs;imo &longs;piritu & magna ventorum vi vapor <lb/>ille cogi pote&longs;t in naui, & ardere &longs;imul vn<lb/>de etiam imminentem nunciat perniciem. <lb/></s>

<s>Velut è diuer&longs;o Ca&longs;toris olim ac Pollucis, <lb/>nunc Petri & Nicolai diuorum numina, &longs;eu <lb/>potiùs lumina gemina. </s>

<pb pagenum="8" xlink:href="015/01/027.jpg"/>rit con&longs;tituta: con&longs;urgent trecenti &longs;exaginta modi productionis <lb/>proportionis.</s>

<s><expan abbr="Nonnunquã">Nonnunquam</expan> in Ocea <lb/>no terna, imò ibi frequentius quàm gemina, <lb/>ob maioremc <expan abbr="oncu&longs;&longs;ion&etilde;">oncu&longs;&longs;ionem</expan>. </s>

<s>Vocant tunc ea, <lb/>Diui Nicolai, Helenæ, & Claræ, fignificato <lb/>deducto à claritate, ab antiqua &longs;uper&longs;titione <lb/>&longs;ideris Helenæ, & quòd Nicolaus ex qua<lb/>dam hi&longs;toria nauigantibus præe&longs;&longs;e credatur. <lb/></s>

<s>In mediterraneo autem mari &longs;olùm gemi<lb/>na, & plerunque in rudentibus, ex vnoque <lb/>in alterum, velut aues cum quodam &longs;ono <lb/>&longs;alientia, finem tempe&longs;tatis, nec non &longs;e<lb/>curitatem o&longs;tendunt. </s>

<s>Sunt enim vapores <lb/>rudentibus hærentes, qui &longs;ucce&longs;&longs;u temporis, <lb/>igne ex altero in alterum tran&longs;eunte, &longs;pe<lb/>ciem cerei accen&longs;i præbent. </s>

<s id="id000204">H&etail;c propo&longs;itio ut præcedens & <expan abbr="&longs;equ&etilde;tes">&longs;equentes</expan> tres ab Alchindo &longs;um<lb/>ptæ &longs;unt, & ab eo demon&longs;trantur. </s>

<s>Indicant autem <lb/>&longs;alutem, quòd parui &longs;int, quòd minimè len<lb/>ti, in vnum enim coi&longs;&longs;ent, quodque breui <lb/>ab&longs;umantur &longs;inguli: quanquam fal&longs;a ima<lb/>gine &longs;aliendi, qui plures &longs;unt, plerun<lb/>que duos referant, cùm &longs;ucce&longs;&longs;u multi <lb/>continuò &longs;peciem vnius diuturnioris effi<lb/>ciant. <lb/><arrow.to.target n="marg78"/></s>

<s id="id000205">Sit ergo proportio a ad b, pro<lb/><arrow.to.target n="table2"/><lb/><figure id="id.015.01.027.1.jpg" xlink:href="015/01/027/1.jpg"/>ducta ex proportione c ad d & e ad f, con&longs;tat <lb/>quòd cum &longs;int &longs;ex quantitates, quòd fieri pote<lb/>runt quindecim coniugationes, quas po&longs;ui à la<lb/>tere facilitatis gratia, quibus re&longs;pondent totidem <lb/><arrow.to.target n="table3"/><lb/>conuer&longs;æ: erunt ergo triginta. </s>

<s id="id000206">Singulæ autem ha <lb/>rum produci po&longs;&longs;unt duodecim modis: ductis <lb/><figure id="id.015.01.027.2.jpg" xlink:href="015/01/027/2.jpg"/>duodecim in triginta, fiunt trecenti &longs;exaginta mo <lb/>di. </s>

<s><margin.target id="marg76"/>Ignis inno<lb/>xius plan<lb/>tis.</s>

<s id="id000207">Et hoc e&longs;t clarum per&longs;e, modo <expan abbr="demõ&longs;tremus">demon&longs;tremus</expan>, <lb/>quod &longs;inguli horum modorum po&longs;sint produ<lb/>ci duodecim modis, & capiamus ab primam qu&etail; <lb/>pote&longs;t produci ex c d & e f: Item ambabus con<lb/>uer&longs;is d c & fe: & rur&longs;us altera recta altera con<lb/>uer&longs;a: & hoc bifariam c d & f e, & d c & e f, &longs;unt er<lb/>go iam quatuor modi. </s>

<s id="id000208">Totidem ex c e & d f, toti<lb/>demque ex c f & d e, igitur erunt duodecim mo<lb/>di, quibus produci po&longs;&longs;e intelligitur propor<lb/>tio a ad b.</s>

<s><margin.target id="marg77"/>Helenæ &longs;idus <lb/>quòd &longs;ub<lb/>mer&longs;ionem <lb/>nauium <lb/>nunciat.</s>

<table>

<s><margin.target id="marg78"/>Folium mo<lb/>tus quomo<lb/>do.</s>

<table.target id="table2"/>

<row>

<s>Diximus hucu&longs;que de igne, folliumque <lb/>interim vtilitatem adiunximus: par verò <lb/>videtur vt etiam motus rationem adiicia<lb/>mus: &longs;iquidem, vt diximus, nihil egregium <lb/>fit ab igne qui follibus non iuuetur. </s>

<s>Du<lb/>plures illos e&longs;&longs;e oportet, &longs;eu duo &longs;int, &longs;eu <lb/>quatuor, &longs;eu plures, vt opera nunquam in<lb/>termittatur. </s>

</row>

<row>

<s>Horum motus alternis vicibus <lb/>variatur, ac mi&longs;tus planè e&longs;t, ex violento, <lb/>quo aperiuntur, & aërem trahunt: & na<lb/>turali, quo &longs;pontè decidentes conceptum <lb/>iam aërem exprimunt. </s>

<s>Manife&longs;tum e&longs;t au<lb/>tem, quòd quò celerius expre&longs;&longs;erint, eò <lb/>acrius ignem impellere: ob hoc ponderi<lb/>bus ea onerant. </s>

</row>

<row>

<s>Sed quia quæ grauia &longs;unt <lb/>non facilè nec celeriter attolluntur, ideò </s>

<s><arrow.to.target n="marg79"/><lb/>magnis rotis & magno aquarum impetu <lb/>machina illorum voluenda e&longs;t. </s>

</row>

<row>

<s>His igitur <lb/>cau&longs;is manife&longs;tum e&longs;t, non po&longs;&longs;e glaciem, <lb/>et&longs;i frigidi&longs;&longs;ima &longs;it, tantùm lædere frigidita<lb/>te, quantum ignis calore. </s>

<s>Nam vt ignis mo<lb/>tu omnia penetrat, introituque prius di&longs;&longs;i<lb/>pat ip&longs;a, quàm vrat, &longs;ic glacies quiete qua<lb/>dam con&longs;tat & cra&longs;&longs;a &longs;ub&longs;tantia, quibus fit, <lb/>ne omninò po&longs;&longs;it penetrare quicquam. <lb/></s>

</row>

<row>

<s>Quòd enim glacies non minus frigida &longs;it <lb/>quàm calidus ignis, o&longs;tendit experimen<lb/>tum. </s>

<s>Nam &longs;i ligno aut lateri ardenti, glaciei <lb/>tantundem imponas, non celeriùs glacies <lb/>di&longs;&longs;oluetur, quàm extinguatur ex toto ignis. <lb/></s>

</row>

<row>

<s>Nam vt ignis motu & tenuitate magis pe<lb/>netrat, ac facilius corrumpit & depa&longs;citur <lb/>quàm glacies: indicioque e&longs;t, introitum & <lb/>&longs;ubtilitatem horum effectuum mirabilium <lb/>e&longs;&longs;e cau&longs;as, quòd quæ penetrabilia non &longs;unt, <lb/>vt aurum & adamas, ab igni non ab&longs;umun<lb/>tur neque vtuntur, nec omninò verè ignea <lb/>dici po&longs;&longs;unt: ita glacies den&longs;itate &longs;ua & <lb/>quiete magis re&longs;i&longs;tit, & diutius permanet. <lb/><arrow.to.target n="marg80"/><lb/>Vt enim ignis &longs;emper fit, &longs;ic glacies eadem <lb/>manet, & multis annis quandoque durat in <lb/>gelidis &longs;ub Vr&longs;a montibus, &longs;icut & nix. </s>

<s>Ergo <lb/>glacies ac ignis penitus contraria &longs;unt. </s>

</row>

</table>

<s>Ignis <lb/>enim calidi&longs;&longs;imus, tenui&longs;&longs;imus, celerrimi mo<lb/>tus, ac qui facilè omnia inuadat, & momen<lb/>to maneat &longs;olùm: at glacies frigidi&longs;&longs;ima, <lb/>den&longs;i&longs;&longs;ima, quieta omninò, lenti progre&longs;&longs;us, <lb/>& maximè diuturna. </s>

<table>

<table.target id="table3"/>

<s><margin.target id="marg79"/>Ignis cur <lb/>magis calore <lb/>lædat, quàm <lb/>glacies fri<lb/>gore.</s>

<row>

<s><margin.target id="marg80"/>Ignis & <lb/>glacies pe<lb/>nitùs con<lb/>traria.</s>

</row>

<s>Ergo magnæ quæ&longs;tionis iam &longs;olutio ex <lb/><arrow.to.target n="marg81"/><lb/>his emergit, &longs;cilicet, an ignis hic no&longs;ter &longs;ub<lb/>&longs;tantia &longs;it, an accidens. </s>

<row>

<s>Si enim &longs;ub&longs;tantia <lb/>foret, videbatur durum, quonam pacto in <lb/>candenti ferro duæ e&longs;&longs;ent &longs;imul &longs;ub&longs;tantiæ <lb/>mutuò penetrabiles, ignea atque ferrea: tum <lb/>verò &longs;i altera di&longs;&longs;oluatur, vtpote ferrea &longs;ub<lb/>&longs;tantia, dum ignem concipit, fiet corruptio, <lb/>dum extinguitur ignis generatio fieri dice<lb/>tur, quod perab&longs;urdum e&longs;t. </s>

</row>

<s>Si verò aerem <lb/>&longs;olùm qui intus e&longs;t ardere latere ardente di<lb/>cas, non di&longs;&longs;olueretur &longs;ub&longs;tantia ligni in <lb/>cineres, nec &longs;errum deterius adeò euaderet: <lb/>igitur humidum proprium ferri, dum later <lb/>ferreus accen&longs;us e&longs;t, ardet. </s>

<row>

<s>Quòd &longs;i omni<lb/>nò ignis accidens e&longs;t, quomodo &longs;ub&longs;tan<lb/>tiam immutat lignorum in cinerem, ac fer<lb/>rum omniaque fermè ab&longs;umit? </s>

</row>

<s>Itaque ( vt <lb/>dixi ) hic ignis nihil aliud e&longs;t, quàm &longs;um<lb/>ma caliditas cum &longs;iccitate iuncta. </s>

<row>

<s>Nec &longs;ub<lb/>&longs;tantia dici pote&longs;t, ni&longs;i vt glacies, &longs;i pro re, <lb/>qu&ecedil; gelu <expan abbr="cõcreta">concreta</expan> e&longs;t intelligatur, ita ignis pro <lb/>re ip&longs;a quæ ardet. </s>

</row>

<s>Ignis igitur accidens om<lb/>nino e&longs;t, atque caliditas cum &longs;iccitate &longs;um<lb/>ma, inhæretque &longs;ub&longs;tantiæ &longs;emper quemad<lb/>modum reliqua accidentia: non igitur ele<lb/>mentum e&longs;&longs;e pote&longs;t, quod & &longs;uperius de<lb/>mon&longs;trauimus. </s>

<row>

<s>Nam naturæ principium ca<lb/>&longs;u quodam con&longs;taret, ac pabulo incerto cir<lb/>cumferri oporteret, imò eadem ratione gla<lb/>cies aliud e&longs;&longs;et elementum. </s>

</row>

<s>Quòd &longs;i elemen<lb/>tum aliud e&longs;t ignis, &longs;iquidem æqualiter cali<lb/>dus e&longs;t ac hic, aut magis, igitur & ille pa<lb/>bulò indigebit, quoniam pa&longs;ci nece&longs;&longs;e erit: <lb/>vnde igitur tantæ moli pabulum? </s>

<row>

<s>Si verò <lb/>minus calidus e&longs;t, ce&longs;&longs;at ratio ob quam &longs;ta<lb/>tuebatur elementum. </s>

</row>

<s>Siquidem ob hoc ele<lb/>mentum ignis po&longs;itus fuit, quòd e&longs;&longs;et &longs;ub<lb/>&longs;tantia calidi&longs;&longs;ima quædam ac &longs;icci&longs;&longs;ima, <lb/>vtranque habens harum qualitatum, vel al<lb/>teram &longs;altem perfectam: at non habebit, <lb/>cùm iam con&longs;tet hunc ignem illo e&longs;&longs;o longè <lb/>calidiorem, &longs;icciorem, ardentiorem, ac ma<lb/>gis penetrabilem. </s>

<row>

<s><margin.target id="marg81"/>Ignis quid <lb/>&longs;it.</s>

</row>

<s>Sed & alterius dubitationis clara &longs;olutio <lb/><arrow.to.target n="marg82"/><lb/>emergit, an &longs;cilicet ignis igne calidior &longs;it? <lb/></s>

<row>

<s>Con&longs;tat autem, quòd non ob &longs;olam mate<lb/>riam ignis calidior euadit, vt qui in ferro <lb/>e&longs;t, eo qui in palea, & qui in quercus lignis, <lb/>eo qui in &longs;alíginis, &longs;ed velut in glacie quæ<lb/>dam vix coacta e&longs;t, alia dura, alia prædura, <lb/>ita ignis quidam vix e&longs;t ignis, vt cùm cande<lb/>re ferrum incipit: alius candidor, alius &longs;plen<lb/>didi&longs;&longs;imus. </s>

</row>

<s>Cùm enim accidens &longs;it, augeri ac <lb/>minui pote&longs;t. </s>

<row>

<s>Itaque ignis igne validior <lb/><arrow.to.target n="marg83"/><lb/>euadit &longs;ex modis. </s>

</row>

<s>Natura, vt diximus: <lb/>ardentior enim celerius exurit ac ma<lb/>gis. </s>

<row>

<s>Materia, vt qui in ferro &longs;edem ha<lb/>bet, eo qui in &longs;tipulis. </s>

</row>

<s>Motu, nam magis <pb xlink:href="016/01/027.jpg" pagenum="378"/>fit penetrabilis: Magnitudine, &longs;eu propria, <lb/>&longs;eu diuturnitate temporis: hoc enim nemini <lb/>ob&longs;curum e&longs;&longs;e pote&longs;t. </s>

<row>

<s>Denique re&longs;pirationis <lb/><arrow.to.target n="marg84"/><lb/>impedimento: non ignorant hoc nautæ, qui <lb/>exiguo foculo ollam &longs;uperponentes oll&ecedil;, om<lb/>nes feruere cogunt, vnde paupertati con<lb/>&longs;ultum. </s>

</row>

<s>Sed oportet <emph type="italics"/>(<emph.end type="italics"/> vt dixi ) ne proprio <lb/><arrow.to.target n="marg85"/><lb/>fumo extinguatur igniculus, paululum illum <lb/>re&longs;pirare. </s>

<row>

<s>Ob id qui impen&longs;æ con&longs;ulunt, fur<lb/>nos exiguos ollæ in modum ex ære confi<lb/>ciunt, clatratos in imo &longs;trictè ex ferro, vt <lb/>cinis excidere po&longs;&longs;it. </s>

</row>

<s>Vltimus modus e&longs;t, <lb/>cum cogitur ignis, atque ob id calx aqua ac<lb/>cenditur: nam calor in fornace acqui&longs;itus <lb/>ac latitans, cùm (vt dixi) ex genere ignis &longs;it, <lb/>exiguæ aquæ frigore intus concluditur, <lb/>tum motu, tum coitione ip&longs;a in ignem <lb/>euadit. <lb/><arrow.to.target n="marg86"/></s>

<row>

<s><margin.target id="marg82"/>Ignis igne <lb/>calidior e&longs;t.</s>

</row>

<s><margin.target id="marg83"/>Ignis &longs;ex <lb/>modis vali<lb/>dior euadit.</s>

<row>

<s><margin.target id="marg84"/>Modus co<lb/>quendi cum <lb/>modico igne.</s>

</row>

<s><margin.target id="marg85"/>Cur calx <lb/>aqua accen<lb/>datur.</s>

<row>

<s><margin.target id="marg86"/>Calx quæ <lb/>optima.</s>

</row>

<s>Optima igitur calx e&longs;t, quæ &longs;uperfu&longs;a <lb/>aqua maximos edit &longs;trepitus, & ignem <lb/>concipit, ligna accendens proxima. </s>

<row>

<cell>direc.</cell>

<s>E&longs;t h&ecedil;c <lb/>plerunque coloris cinerei: nam in candida <lb/>iam ignis exhalauit, quia aër ingre&longs;&longs;us e&longs;t: <lb/>candor enim fit ingrediente nece&longs;&longs;ariò aë<lb/>re. </s>

<cell>conuer.</cell>

</row>

<s>Talis autem ex &longs;olidioribus lapidibus fit: <lb/>nam lapides, vt &longs;olidiores extiterint, maio<lb/>rem & diuturniorem calorem retinent. </s>

</table>

<s>Quo<lb/>modo verò calor in his quæ ardent relin<lb/>quatur, & motu ac coitione ignis accen<lb/>datur, inferius o&longs;tendemus. </s>

<s id="id000209">Propo&longs;itio quarta.</s>

<s>Verùm motus <lb/>non &longs;olùm penetrare magis cogit, &longs;ed & ca</s>

<s id="id000210">Si fuerit proportio primi ad &longs;ecundum produ<lb/>cta ex proportionibus tertij ad quartum, & quin <lb/>ti ad &longs;extum, producetur etiam ex proportione <lb/>tertij ad &longs;extum, & quinti ad quartum.</s>

<s><arrow.to.target n="marg87"/><lb/>lorem ip&longs;um accendit, atque ( vt dixi ignem <lb/>igne calidiorem reddit. </s>

<s>Nihil mirum igitur <lb/>e&longs;t fulmini tantam ine&longs;&longs;e vim, ac ignem <lb/>illum, qua&longs;i ab aliorum ignium natura alie<lb/>num miracula quædam efficere. </s>

<s id="id000211">Sit proportio a b producta ex proportioni<lb/><arrow.to.target n="table4"/><lb/><figure id="id.015.01.027.3.jpg" xlink:href="015/01/027/3.jpg"/>bus c ad d, & e ad f, dico quod etiam erit produ</s>

<s>Namque ob <lb/>motum celerem non &longs;olùm magis penetrat, <lb/>&longs;ed ignis ille multò calidior reliquo omni <lb/>igne exi&longs;tit. </s>

<table>

<table.target id="table4"/>

<s>Itaque omnia animalia præter <lb/>hominem &longs;olo contactu occidit, hominem <lb/>verò vix vnquam euadere licet. </s>

<row>

<s>Eua&longs;it tamen <lb/><arrow.to.target n="marg88"/><lb/>Ioannes Maria Cardanus, & &longs;uperuixit raro <lb/>miraculo. </s>

<cell/>

<s>Quis verò e&longs;t alius ignis, qui &longs;olo <lb/>contactu occidat ( hoc igitur ei <emph type="italics"/>)<emph.end type="italics"/> proprium <lb/>e&longs;t, quòd calidi&longs;&longs;imus &longs;it calidi&longs;&longs;imorum, at<lb/>que ( vt ita dicere liceat <emph type="italics"/>)<emph.end type="italics"/> ignis ignium. <lb/></s>

</row>

<row>

<s>Quamobrem & multum refert, an procul, & <lb/>& ex alto veniat, aut prope. </s>

<s>Itaque illæ&longs;a <lb/>quandoque crumena pecunias colliquat: ne<lb/>que e&longs;t enim hoc aut fabulo&longs;um, aut mirum. <lb/></s>

</row>

<s>Namque quod lædit, aut mole, aut mora <lb/>corrumpit: hic cùm tenui&longs;&longs;imus &longs;it, crume<lb/>nam non di&longs;cerpit: cùm verò veloci&longs;&longs;imè <lb/>moueatur, non hæret, atque ob id crumenæ <lb/>innoxium. </s>

<row>

<s>Tran&longs;ire autem nec hærere ob <lb/>&longs;ubtilitatem in crumenam docet aër, qui & <lb/>ip&longs;e vacua diducta crumena ingreditur, at<lb/>que illam implet: quod fieri non po&longs;&longs;et, ni <lb/>per abditos meatus ingrederetur, quando<lb/><arrow.to.target n="marg89"/><lb/>quidem ip&longs;ius os diligenter ob&longs;tructum &longs;it. <lb/></s>

<s>Ergo ignis &longs;cintilla, fulmini&longs;que pars aëre <lb/>ip&longs;o longè tenuior, po&longs;tquàm ingre&longs;&longs;a fue<lb/>rit, metallo infigitur, ac præ&longs;tanti&longs;&longs;ima illa <lb/>vi, tum impetu, ip&longs;um repentè liquat. </s>

</row>

<row>

<s>Hanc <lb/>tam excellentem caloris ac &longs;iccitatis ïmmo<lb/>dicæ vim, velut raram, & ob raritatem oc<lb/>cultam, quidam turpiter proprietatem ap<lb/>pellarunt, cùm con&longs;tet immodicum e&longs;&longs;e ca<lb/>lorem, ac ( vt dixi ) ignis ignium. </s>

<s>Mirum <lb/>autem minimè e&longs;&longs;e debet, ignem hunc, aut <lb/>alium quempiam, lapides accendere po&longs;&longs;e. <lb/></s>

</row>

<s>Nam ferrum haud candens, tamen accen<lb/>dit lignum & ardere facit, & lignum &longs;ul<lb/>phur, quamvis lignum non ardeat & &longs;ul<lb/>phur vitæ aquam vocatam: quod enim &longs;o<lb/>lidius e&longs;t, quod potentia tenuius e&longs;t euincit. <lb/></s>

<row>

<s>In &longs;olidi&longs;&longs;ima igitur materia ignis feruen<lb/>tior lapides accendere poterit. </s>

<s>Latet autem <lb/>hoc, quod magno v&longs;ui e&longs;&longs;e pote&longs;t ad vr<lb/>bium expugnationem. </s>

</row>

<row>

<s>Oportet autem cùm <lb/>magno motu hoc ignium genus nece&longs;&longs;ariò <lb/>coniunctum e&longs;&longs;e, & ( vt dixi) in &longs;olidi&longs;&longs;ima <lb/>materia. </s>

<s>Sed cur fulmen columnas non fe<lb/><arrow.to.target n="marg90"/><lb/>rit, non carinas? </s>

</row>

<s>Rarò quidem hæc ferit, non <lb/>tamen nunquam: nam Florentiæ in æde <lb/>maxima, &longs;eu potius in ædis ambitu, vidi<lb/>mus columnam fulgure percu&longs;&longs;am ac viola<lb/>tam: non tamen ferit frequunter, nec adeò <lb/>di&longs;iicit, quòd ob rotunditatem ictus labatur. <lb/></s>

</table>

<s>Carinas non ferit eadem ratione, ni&longs;i rarò: <lb/><arrow.to.target n="marg91"/><lb/>nam vltra quinque cubitos &longs;ub terra de&longs;cen<lb/>dere negatur. </s>

<s id="id000212"><arrow.to.target n="marg20"/><lb/>cta ex proportionibus c ad f, & e ad d, di&longs;ponan<lb/>tur ut in figura & fiat ex c in e g, & ex d in fh, ergo <lb/><arrow.to.target n="marg21"/><lb/>per primam harum g ad h ut a ad b, &longs;ed per præ<lb/>&longs;uppo&longs;ita in &longs;ecunda productione etiam prode<lb/>unt g & h, igitur per primam propo&longs;itionem ha<lb/>rum a ad b proportio producitur ex proportionibus c ad f tertiæ <lb/>&longs;cilicet ad &longs;extam, & e ad d quint&etail; ad quartam, quod fuit <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan>.</s>

<s>Humilis autem e&longs;t carina na<lb/>uis, ac cel&longs;a maius, quam frequenter tangit. <lb/></s>

<s id="id000213"><margin.target id="marg20"/>P<emph type="italics"/>er<emph.end type="italics"/> 8. <emph type="italics"/>petit.<emph.end type="italics"/></s>

<s>Ergo certum e&longs;t contra fulgura auxilium, <lb/>profundis &longs;pecubus &longs;e abdere: tutiùs enim <lb/>hoc quàm vel lauro coronari, aut vituli ma<lb/>rini pelle tegi, aut æquilæ, aut hyacinthum <lb/>lapidem ge&longs;tare: nam negant hæc fulmine <lb/>tangi. </s>

<s>Quidam ficum pro lauro &longs;crip&longs;erunt: <lb/>laurum cohibere comitiales & dæmonas, id <lb/>e&longs;t, per&longs;ua&longs;ionem illam meticulo&longs;am. </s>

<s id="id000214"><margin.target id="marg21"/>I<emph type="italics"/>n<emph.end type="italics"/> 13. <emph type="italics"/>petit.<emph.end type="italics"/></s>

<s>At de <lb/>hyacintho inferius di&longs;putabimus: nam non <lb/>leues &longs;unt autores, qui hoc affirmant. </s>

<s id="id000215">Propo&longs;itio quinta.</s>

<s>Fulmi<lb/><arrow.to.target n="marg92"/><lb/>nis admiranda vis olim fuit, &longs;ed de&longs;iit e&longs;&longs;e, <lb/>bellicorum tormentorum nunc effectibus & <lb/>copia: parum enim abe&longs;&longs;e videntur à fulmi<lb/>nis violentia. </s>

<s>Illud vnde veniat, & quam <lb/>procul, ne&longs;cimus, neque quantum &longs;ecum <lb/>ponderis ferat. </s>

<s id="id000216">Si fuerit proportio primi ad &longs;ecundum producta ex proportio<lb/>ne tertij ad quartum, & quinta ad &longs;extum: erit proportio tertij ad <lb/>&longs;extum producta ex proportionibus primi ad &longs;ecundum, & quar<lb/>ti ad quintum.</s>

<s>Sunt etiam qui affirment <lb/>&longs;olum ignem e&longs;&longs;e cum impetu, lapidem nul<lb/>lum. </s>

<s>Hoc &longs;olùm certò &longs;cimus, turres inte<lb/>gras quandoque vno ictu di&longs;iici. </s>

<s id="id000217">Sit proportio a ad b producta ex proportio<lb/><arrow.to.target n="marg22"/><lb/><arrow.to.target n="table5"/><lb/>nibus c ad d, & e ad f, dico quod proportio c ad <lb/>f producitur ex proportione a ad b & d ad e. </s>

<s>Cardani è <lb/>turre vnica, quæ &longs;ola &longs;upere&longs;t, &longs;ed antiqua <lb/>tamen, laterum plu&longs;quàm 12000. vno ictu <lb/>excu&longs;&longs;it, ac di&longs;iecit. </s>

<s id="id000218">In<lb/>terponam d e inter c & f, eritque ex &longs;ecunda pro<lb/>po&longs;itione repetita proportio c ad f producta ex <lb/>tribus proportionibus c ad d, d ad e, e ad f, &longs;ed <lb/>proportiones c ad d, & e ad f producunt pro<lb/><figure id="id.015.01.028.2.jpg" xlink:href="015/01/028/2.jpg"/>portionem a ad b, igitur proportio c ad f produ<lb/>citur ex proportionibus a ad b, & e ad f.<lb/><arrow.to.target n="table6"/></s>

<s>At machinæ hæ 60. <lb/>pleræque pondo ferri per 5000. pa&longs;&longs;uum <lb/>( mirabile certè dictu, ni dicto experientia <lb/>fidem faceret ) ferunt: eædem muros qua<lb/>tiunt, excutiuntque turritas vrbes, nec vlla <lb/>vis tanto malo re&longs;i&longs;tere pote&longs;t. </s>

<s>Leui&longs;&longs;ima <lb/>ære ex Cyprio factitio tubæ in modum ca<lb/>nalis efficitur. </s>

<table>

<s>Neque arctiores, aut latiores <lb/>in imo e&longs;&longs;e decet, quippe latiores à pila non <lb/>exactè cluduntur, & ideò minus habent im<lb/>petus. </s>

<table.target id="table5"/>

<row>

<s>Quòd &longs;i cludantur, periculum fracturæ <lb/><arrow.to.target n="marg93"/><lb/>&longs;ubeunt, ob pulueris multitudinem: Arctio<lb/>res autem ni longiores efficiantur, quantum <lb/>oportet pulueris minimè &longs;u&longs;cipiunt. </s>

<s>Si lon<lb/>giores in imo fiant, breuiores euadunt &longs;upe<lb/>riùs, ob idque multum virium. </s>

</row>

<row>

<s>Quòd &longs;i non <lb/>quantum oportet pila de&longs;cendat ferrea, reli<lb/>cto vacuo debiliorem ictum reddunt, & ma<lb/>chinam agitant, ac etiam quandoque fran<lb/>gunt. </s>

<s>Et tamen artifices, magno Principum <lb/>malo, ne aperti&longs;&longs;ima ratio vilior videatur, <lb/>men&longs;uras qua&longs;dam fingunt arctiores, alij <lb/>in imo, alij latiores facientes perperam, <lb/>cùm vna &longs;it ratio, vt vndique æquales <lb/>&longs;int, optima & &longs;ecuri&longs;&longs;ima. </s>

</row>

<row>

<s>Machinæ ad <lb/>&longs;phærulam ponderis ratio centupla, vt <pb xlink:href="016/01/028.jpg" pagenum="379"/>&longs;i &longs;phæra quam emittere debet, &longs;it pon<lb/>do XX. erit machina pondo MM. </s>

<s>Cra&longs;&longs;itu<lb/>do in imo, vbi pulueris locus e&longs;t, dodrans <lb/>dimetientis &longs;phærulæ. </s>

</row>

<row>

<s>Licet autem & pon<lb/>dus, & men&longs;uram cum eo machinæ augere; <lb/>&longs;ed minuere citra periculum fracturæ haud <lb/>licet. </s>

<s>In &longs;ummo cra&longs;&longs;itudo labri machinæ <lb/>non minor triente dimetientis &longs;phærulæ. <lb/></s>

</row>

<row>

<s>Canalis dimetientis ( vt dixi ) æqualis dime<lb/>tienti &longs;phærulæ & pulueris pyrij pondus <expan abbr="põ-deri">pon<lb/>deri</expan> ip&longs;ius &longs;phærulæ. </s>

<s>In minoribus <expan abbr="tam&etilde;">tamen</expan> tor<lb/>mentis machinæ pondus ac cra&longs;&longs;itudo maio<lb/>rem ad &longs;phærulam proportionem habere de<lb/>bet ob &longs;ecuritatem, atque eadem ratione <lb/>pulueris pondus minus e&longs;&longs;e quàm &longs;pærulæ. <lb/></s>

</row>

<row>

<s>Patet ex hoc ratio quantum &longs;patij imum <lb/>debeat capere, nempe quantum &longs;atis e&longs;t ad <lb/>continendum puluerem, qui pondus &longs;phæ<lb/>rulæ æquet. </s>

<s>Foramen vbi ignis accenditur, <lb/>fundi partem etiam obtineat: nam machi<lb/>na non adeò retrò agitur, cùm ignis &longs;olùm <lb/>pror&longs;um accendatur: ob id rectius collima<lb/>re ictu licet, & minore periculo. </s>

</row>

</table>

<s>Nam cùm <lb/>multum retrò aguntur, paruæ lædunt mili<lb/>tes, qui eis vtuntur: magnæ, &longs;i non conti<lb/>neantur, incertos edunt ictus, & labefa<lb/><arrow.to.target n="marg94"/><lb/>ctant currus quibus in&longs;ident: &longs;i vi con&longs;i&longs;tere <lb/>cogantur, fracturæ periculum &longs;ubetint. </s>

<table>

<table.target id="table6"/>

<s>E&longs;t <lb/>igitur hoc vnum fracturæ &longs;ignum, vt vehe<lb/>menter retrò agatur: aliud, &longs;i men&longs;ura non <lb/>conueniat, vt cùm tenuior fuerit, aut ar<lb/>ctior quàm oporteat, vel inæqualis vel obli<lb/>qua, quo nil fermè e&longs;t deterius. </s>

<row>

<s>Tertium &longs;i<lb/>gnum e&longs;t, cum materia ip&longs;a fuerit &longs;quamo<lb/>&longs;a aut minimè tenax, aut ve&longs;icis plena, aut <lb/>rimam obduxerit. </s>

</row>

<row>

<s>Quartum, cùm æruginem <lb/>contraxerit, aut aqua maduerit: quo errore <lb/>dum pompa Papiæ, anno M. D. X L V I. <lb/>&longs;olemnis corporis Chri&longs;ti ageretur, quin<lb/>que aut &longs;ex viri ex his qui pompam &longs;eque<lb/>bantur, fractis tormentis perierunt. </s>

</row>

<row>

<s>Quin<lb/>tum e&longs;t, &longs;i plus pulueris, aut tenuiorem pro <lb/>cra&longs;&longs;iore immi&longs;eris. </s>

</row>

<row>

<s>Nimis enim aucto ig<lb/>ne, nec moram ad exitum inueniente, fran<lb/><arrow.to.target n="marg95"/><lb/>gitur machina. </s>

</row>

<s>Accidit & fractura, dum <lb/>&longs;phærula nimis violenter intruditur. </s>

<row>

<s>Auxi<lb/>lium præ&longs;tat ne frangatur &longs;u&longs;pecta iam ma<lb/>china, &longs;i dum excutere &longs;phærulam debet, <lb/>in terra iacet: nam ea libertate in eam par<lb/>tem agitur, ad quam ignis impellit: &longs;ed <lb/>tum valde incerto ictu & exitu. </s>

</row>

<row>

<s>Ob id ma<lb/>gnas machinas in curribus mobilibus ita <lb/>collocant, vt &longs;olo ac finitori æquidi&longs;tan<lb/>tes &longs;int: atque &longs;ic dum ignem concepe<lb/>rint, recta retrò, citráque periculum agantur. <lb/><arrow.to.target n="marg96"/></s>

</row>

<s><margin.target id="marg87"/>Fulmen cur <lb/>tantam ha<lb/>beat vim.</s>

<row>

<s><margin.target id="marg88"/><expan abbr="Fulm&etilde;">Fulmen</expan> quo<lb/>modo cru <lb/>mena illæ&longs;a <lb/>pecunias li<lb/>quet.</s>

</row>

<row>

<s><margin.target id="marg89"/>Ignis lateres <lb/>vrens.</s>

</row>

<s><margin.target id="marg90"/>Fulmen ra<lb/>rò columnas <lb/>ferit, & cur.</s>

</table>

<s><margin.target id="marg91"/>Aduer&longs;us <lb/>fulgura <lb/>cautio.</s>

<s id="id000220">Propo&longs;itio &longs;exta.</s>

<s><margin.target id="marg92"/><expan abbr="Machinar&utilde;">Machinarum</expan> <lb/>ignearum <lb/>vis.</s>

<s id="id000221">Ex trecentis &longs;exaginta modis producenda<lb/>rum proportionum triginta &longs;ex tantum e&longs;&longs;e ne<lb/>ce&longs;&longs;arios.<lb/><arrow.to.target n="table7"/></s>

<s><margin.target id="marg93"/>Modus ma<lb/>chinas igneas <lb/>faciendi.</s>

<table>

<s><margin.target id="marg94"/>Signa machi<lb/>næ quæ fra<lb/><gap/>uræ obno<lb/>xia &longs;it.</s>

<table.target id="table7"/>

<row>

<s><margin.target id="marg95"/>Auxilium <lb/>machinarum <lb/>ne frangan<lb/>tur.</s>

<s><margin.target id="marg96"/><expan abbr="Machinar&utilde;">Machinarum</expan> <lb/>bellicarum <lb/>duo genera <lb/>noua.</s>

</row>

<row>

<s>E&longs;t & aliud genus ignei tormenti nouum, <lb/>cubiti & &longs;emis longitudine, pondere libra<lb/>rum LXX. v&longs;que ad LXXX. </s>

<s>Canalis capit <lb/>&longs;phæram pilæ paruæ magnitudine. </s>

</row>

<row>

<s>Ferreo <lb/>baculo dum exoneratur, &longs;u&longs;tinetur, caudá<lb/>que continetur: vnius hominis onus ac ma<lb/>china: cæterùm ob cra&longs;&longs;itudinem mirum in <lb/>modum valida, nec minus tuta. </s>

<s>Aliud, in <lb/>quo cauitas ampla iuxta foramen: varij mo<lb/>dioli cauitati imponuntur, omnes eiu&longs;dem <lb/>magnitudinis, quorum canales canalibus <lb/>machinæ è directo corre&longs;pondent, vt muta<lb/>tis modiolis non concale&longs;cat machina. </s>

</row>

<row>

<s><arrow.to.target n="marg97"/><lb/>dimus hæc Papi&ecedil; Principis Saxoniæ inuen<lb/>ta. </s>

</row>

<row>

<s>Fiunt <emph type="italics"/>(<emph.end type="italics"/> vt dixi) è Cyprio ære maiores, &longs;ed <lb/>tuti&longs;&longs;imæ è ferro, vnde nunc minores om<lb/>nes: maiores tamen ex ferro efficere opero<lb/>&longs;um e&longs;t, ob id pleræque è Cyprio ære. </s>

<s>Tor<lb/>no minores, maiores liquato metallo pla<lb/>&longs;tices opera: inde etiam torno. </s>

</row>

<row>

<s>Fiunt au<lb/>tem typi pro fingendis machinis plerunque <lb/>è tribus fru&longs;tis, quoniam ex vno fingere ni<lb/>mis e&longs;&longs;et difficile, quando vel &longs;ic etiam gra<lb/>ue &longs;it. </s>

<s>Pars vna canalis, &longs;ecunda embolus <lb/>ma&longs;culus, tertia &longs;edes. </s>

</row>

</table>

<s>Ip&longs;a verò machina <lb/>plerunque ex vno con&longs;tat fru&longs;to. </s>

<s>Vidi etiam <lb/>ex duobus con&longs;tantem, ac tornatili vitæ al<lb/>teram altera ab imo alligatam. </s>

<s id="id000222">Per quartam enim proportio a ad b produ<lb/><arrow.to.target n="marg23"/><lb/>citur bifariam, & ex c ad d, & e ad f, & ex c ad f, & <lb/>e ad d. </s>

<s id="id000223">& per præcedentem c ad f producitur ex <lb/>a ad b, & d ad e, & per quartam rur&longs;us ex a ad e, <lb/>& d ad b. </s>

<s>Materia (vt <lb/>dixi) æs Cyprium factitium. </s>

<s id="id000224">Et per præcedentem rur&longs;us a ad e ex c <lb/>ad f & b ad d, igitur per quartam eadem produ<lb/>cetur ex c ad d & b ad f. </s>

<s id="id000225">Quare per præceden<lb/>tem c ad f ex a ad e, & d ad b, & ita di&longs;ponemus <lb/>hos modos in tabula. </s>

<s>Con&longs;tat ære <lb/>ip&longs;o, & &longs;eptima fermè parte plumbi nigri <lb/>vel candidi, vel aurichalco. </s>

<s id="id000226">Vides etiam <lb/><arrow.to.target n="table8"/><lb/><figure id="id.015.01.028.4.jpg" xlink:href="015/01/028/4.jpg"/>aliquos modos non produci, ut pri<lb/>mi ad quartum nec ad &longs;extum, & li<lb/>quet, quòd cùm &longs;int quindecim o<lb/>mnes modi qui produci po&longs;&longs;e intelli<lb/>guntur, & nouem tantum producan<lb/>tur &longs;ex e&longs;&longs;e, qui non producuntur, quos <lb/>&longs;eor&longs;um in tabula coniunxi. </s>

<s id="id000227">Et con<lb/>&longs;tat etiam, quod totidem conuer&longs;i &longs;ci<lb/>licet decem octo <expan abbr="produc&utilde;tur">producuntur</expan>, de qui<lb/>bus diximus, ut &longs;int omnes triginta <lb/>&longs;ex, qui con&longs;tat ex duabus propo&longs;i<lb/>tionibus præmi&longs;sis, & hac tertia, <expan abbr="quã">quam</expan> <lb/>adiungemus &longs;cilicet, quòd propor<lb/>tio primi ad tertium producatur ex <lb/>proportionibus <expan abbr="&longs;ec&utilde;di">&longs;ecundi</expan> ad quartum, <lb/>& quinti ad <expan abbr="&longs;ext&utilde;">&longs;extum</expan>. </s>

<s>Sed impetus <lb/><arrow.to.target n="marg98"/><lb/>tanti ratio in pyrio puluere e&longs;t. </s>

<s id="id000228">Hoc enim ex præ<lb/>cedentibus non liquet: benè liquet <lb/>permutatis ordinibus, quod &longs;i pro<lb/>portio primi ad tertium producitur,

<s>Hic con&longs;tat <lb/>ex tribus partibus halinitri, & duabus &longs;ali<lb/>gnei carbonis, atque vna &longs;ulphuris: conue<lb/>nitque magnis machinis. </s>

<pb pagenum="9 [=10]" xlink:href="015/01/029.jpg"/>quod etiam propor<lb/><figure id="id.015.01.029.1.jpg" xlink:href="015/01/029/1.jpg"/><arrow.to.target n="marg24"/><lb/>tio primi ad <expan abbr="quint&utilde;">quintum</expan>. <lb/></s>

<s>Sed mediocribus <lb/>halinitri partes decem, &longs;alignei carboni <lb/>tres, &longs;ulphuris duæ. </s>

<s id="id000229">Nam tertium, & quin <lb/>tum, item que quartum, <lb/>& &longs;extum non <expan abbr="differ&utilde;t">diffe<lb/>runt</expan> ni&longs;i ordine uolun<lb/>tario. </s>

<s id="id000230">Ergo interpo&longs;i<lb/>to e inter a, & c per &longs;e<lb/>cundam propo&longs;itio<lb/>nem proportio a ad c <lb/>producitur ex proportionibus a ad <lb/>e, & e ad c, ut ex demon&longs;tratis in præ<lb/>&longs;enti proportio a ad c producitur ex <lb/>c ad f & b ad d. </s>

<s>Paruis verò halinitri <lb/>partes decem, carbonis lignorum nucis <lb/>auellanæ ab&longs;que nodis, tum &longs;ulphuris, par<lb/>tem vnam &longs;ingulorum. </s>

<s id="id000231">Proportio ergo a ad <lb/>c producitur ex proportionibus e <lb/>ad c & c ad f & b ad d, at e ad c & c ad <lb/>f producunt eam, quæ e&longs;t e ad f per <lb/><expan abbr="&longs;ec&utilde;dam">&longs;ecundam</expan> propo&longs;itionem. </s>

<s id="id000232">Igitur pro<lb/>portio a ad c producitur ex propor<lb/>tionibus b ad d &longs;ecundi ad quartum, <lb/>& e ad f quinti ad &longs;extum. </s>

<s>Contundantur hæc <lb/>ligneo malleo, madefacta priùs aqua putei, <lb/>ne ignem dum tunduntur concipiant. </s>

<s id="id000233">Hæc Al<lb/>chindus in &longs;uo libello: &longs;ed licet inge<lb/>nio &longs;a ualde: parum <expan abbr="tam&etilde;">tamen</expan> utilia olim <lb/><expan abbr="erãt">erant</expan> nece&longs;&longs;aria ad intelligendum ma<lb/>gnam <expan abbr="cõpo&longs;itionem">compo&longs;itionem</expan> Ptolem&etail;i, nunc <lb/>po&longs;tquam Heber has &longs;ex quantita<lb/>tes traduxit ad quatuor, pror&longs;us hæc <lb/>&longs;cientia ulli u&longs;ui e&longs;&longs;e de&longs;ijt.<lb/><arrow.to.target n="table9"/></s>

<s>Sunt <lb/>qui acetum addant, qui ardentem aquam, <lb/>ac &longs;iccent in &longs;ole, &longs;ed non tundunt tunc: fa<lb/>cilè enim ignem po&longs;&longs;ent concipere. </s>

<s>Verùm <lb/>tota cura e&longs;t, vt omnia &longs;ic à terrena parte <lb/>expurgata &longs;int, maximè halinitrum, vt to<lb/>tum ardeat, nec quicquam &longs;uper&longs;it. </s>

<s>Dein<lb/>de, vt ad tenui&longs;&longs;imas partes redigatur, &longs;ic <lb/>enim partes partibus optimè hærebunt: hoc <lb/>fiet, &longs;i &longs;æpiùs contundatur, made&longs;cat, &longs;ic<lb/>cetúrque. </s>

<s id="id000235"><margin.target id="marg24"/>Modi qui <expan abbr="nõ">non</expan> <lb/>producuntur <lb/>pri. ad quartu <lb/>pri. ad &longs;extum <lb/>&longs;ec. ad <expan abbr="terti&utilde;">tertium</expan> <lb/>&longs;ec. ad <expan abbr="quint&utilde;">quintum</expan> <lb/>tert. </s>

<s id="id000236">ad quint. <lb/></s>

<s>Tertiò, vt cùm perfectus fuerit, <lb/>in &longs;ole &longs;iccetur: nam iuxta ignem apponere <lb/>periculo&longs;i&longs;&longs;imum e&longs;t. </s>

<s id="id000237">quart. </s>

<s id="id000238">ad &longs;ext.</s>

<s>Ergo iam ta <gap/>ti effectus <lb/><arrow.to.target n="marg99"/><lb/>cau&longs;a quæratur. </s>

<table>

<s>Impo&longs;itus hic p<gap/>is in ma<lb/>chinam, &longs;phæruláque obducta, adiecto ab <lb/>imo machinæ extrin&longs;ecus igne illicò fermè <lb/>totus àccenditur, ac maius quàm centuplum <lb/>&longs;patium occupare nititur: quòd enim exi<lb/>guus puluis in vola manus non minus quàm <lb/>centuplum &longs;patij occupet, experimentum <lb/>o&longs;tendet, cùm &longs;i quantum e&longs;t granum milij, <lb/>ex hoc puluere accendatur, locum nucis ig<lb/>ne compleat. </s>

<table.target id="table8"/>

<row>

<s>O&longs;tendit & ratio: nam ignis <lb/>rara materia ac tenuis magnis limitibus <lb/>continetur, cùm terra & puluis &longs;olida &longs;int <lb/>ac den&longs;a. </s>

<cell/>

<cell>Primi ad &longs;ecundum.</cell>

<s>Itaque accen&longs;us iam puluis cùm <lb/>in arcto &longs;it, violenter excutit machinam <lb/>vndique, nec aliubi faciliorem exitum in<lb/>ueniens, quàm vbi &longs;phærula vi inclu&longs;a fuit, <lb/>eam magno conatu elidit, primò per canalis <lb/>&longs;patium, inde ea &longs;eruata vehementia foràs <lb/>expellit, & continuato inde impetu &longs;patia <lb/>terrarum longa &longs;uperat, & obuia quæque <lb/>euertit ac diruit. </s>

</row>

<row>

<s>Par e&longs;t etiam cum magno <lb/>&longs;trepitu hæc fieri, cùm ignis ille affatim & <lb/>tanto impetu exeat, & aërem repentè con<lb/>cutiat. </s>

<cell>tertij ad <expan abbr="quart&utilde;">quartum</expan>, & quin</cell>

<s>Ip&longs;a quoque &longs;phærula &longs;tridulum <lb/><arrow.to.target n="marg100"/><lb/>quendam &longs;onum, dum aërem velox diuidit, <lb/>excitat. </s>

</row>

<row>

<s>Tum verò halinitrum, & omne &longs;a<lb/>lis genus, &longs;pontè etiam in libero igne po<lb/>&longs;itum non leuem crepitum excitat. </s>

<cell/>

<cell>ti ad &longs;extum.</cell>

<s>His tri<lb/>bus cau&longs;is, &longs;ed prima præcipuè, dum exo<lb/>neratur machina, fragor tantus, ac tonitru <lb/>non ab&longs;imilis excitatur. </s>

</row>

<row>

<s>Sed &longs;i puluis non <pb xlink:href="016/01/029.jpg" pagenum="380"/>confertim ardeat, aut quia lentus, aut im<lb/>purus, vel non elaboratus, vel quia parum <lb/>habeat halinitri, lentè emittit, debiliter, <lb/>& paruo cum &longs;onitu. </s>

<cell>tertij ad &longs;extum, & quin</cell>

<s>At &longs;i iu&longs;to tenuior fue<lb/>rit, tota &longs;imul ardens frangit machinam. <lb/></s>

</row>

<row>

<s>Manife&longs;tum e&longs;t igitur, quòd cùm celeritas <lb/>tran&longs;itus in ignem ex proportione pendeat, <lb/>caloris ad pulueris repugnantiam attenuato <lb/>autem puluere repugnantia minuatur, quòd <lb/>in infinitum hæc perfectio pulueris progre<lb/>di pote&longs;t, &longs;ic vt momento tota accendatur. <lb/></s>

<cell/>

<cell>ti ad quartum.</cell>

<s>Tunc verò cum repentè non inuenire exi<lb/>tum po&longs;&longs;it, quippe cùm motus omnis tem<lb/>pus po&longs;tulet, machinam franget. </s>

</row>

<row>

<s>Igitur non <lb/>&longs;olùm puluerem licebit conficere, qui om<lb/>nes machinas effringet, &longs;ed tenuiore impo<lb/>&longs;ito maioribus machinis illæ peribunt: & <lb/>rur&longs;us cra&longs;&longs;iore tenuibus ac paruis, vix &longs;phæ<lb/>rulam excutere poterunt. </s>

<cell/>

<cell>Primi ad tertium.</cell>

<s>Igitur intra limites <lb/>certos atque angu&longs;tos po&longs;ita hæc e&longs;t ra<lb/>tio, quæ cum tractantium machinas peri<lb/>culo cnniuncta e&longs;t. </s>

</row>

<row>

<s>Ille autem tutò & ma<lb/>ximo cum impetu tractabit eas, & ictus di<lb/>riget, qui qualem oportebit pro <expan abbr="machinar&utilde;">machinarum</expan> <lb/>ratione puluerem efficiet & admini&longs;trabit. </s>

<cell>&longs;ecundi ad quartum, &</cell>

<s><margin.target id="marg97"/>Machinæ <lb/>bebbicæ è qua <lb/>materia <expan abbr="fiãt">fiant</expan>.</s>

</row>

<row>

<s><margin.target id="marg98"/>Pyrij pulue<lb/>ris compo&longs;i<lb/>tio.</s>

<cell/>

<cell>quinti ad &longs;extum.</cell>

<s><margin.target id="marg99"/>Cur puluis <lb/>pyrius à ma<lb/>china tanto <lb/>impetu <expan abbr="&longs;phe-rulã">&longs;phe<lb/>rulam</expan> mittat.</s>

</row>

<row>

<s><margin.target id="marg100"/>Cau&longs;a &longs;oni<lb/>tus magni <lb/>machinarum <lb/>dum exone<lb/>rantur.</s>

<cell>&longs;ecundi ad &longs;extum, &</cell>

<s>Porrò eadem quæ machinarum, &longs;ed ad<lb/><arrow.to.target n="marg101"/><lb/>mirabilior cuniculorum ratio e&longs;t. </s>

</row>

<row>

<s>Huius tam <lb/>atrocis inuenti auctor fuit Franci&longs;cus Geor<lb/>gius Senen&longs;is. </s>

<cell/>

<cell>quinti ad quartum.</cell>

<s>Docuit hic Hi&longs;panos arcem <lb/>Lucullianam iuxta Neapolim, quam Galli <lb/>tuebantur, nunc Ouum vocatam, euerte<lb/>re, æde illius &longs;acra cum Gallis, qui intus <lb/>erant, etiam in mare ex monte tran&longs;lata. <lb/></s>

</row>

<row>

<s>Ergo cùm arx maximè in monte iacet, vi<lb/>detúrque ob &longs;itum inexpugnabilis, cu<lb/>niculum effodiunt obliquum, altitudi<lb/>nis quatuor cubitorum, latitudinis duo<lb/>rum: nec multum refert obliquitas, dum <lb/>procul fueris: &longs;ed cùm ad locum quem &longs;u<lb/>bruere de&longs;tinas perueneris, obliquum &longs;pe<lb/>cum e&longs;&longs;e oportet, vt iuxta A, tum verò ibi <lb/>etiam &longs;olidam montis &longs;ub&longs;tantiam, ne vis <lb/><figure id="id.016.01.029.1.jpg" xlink:href="016/01/029/1.jpg"/><lb/>ignis conclu&longs;i raritate loci euane&longs;cat: inde <lb/>locus ille puluere totus fermè completur py<lb/>rio, eóque tenui&longs;&longs;imo. </s>

<cell/>

<cell>Primi ad quintum.</cell>

<s>Funis verò deduci<lb/>tur ex A, v&longs;que ad &longs;pecus o&longs;tium B, hic iux<lb/>ta A, vbi puluis e&longs;t, cra&longs;&longs;us ac latus in mo<lb/>dum flocci. </s>

</row>

<row>

<s>Totus autem funis aceto, &longs;ul<lb/>phure & halinitro incoquitur: inde intectus <lb/>pyrio puluere, &longs;iccatur in &longs;ole: denuò &longs;icca<lb/>to in&longs;pergitur tenui&longs;&longs;imus puluis pyrius, & <lb/>arundine circumueftitur ab A, v&longs;que ad B: <lb/>inde cuneis, lapidibú&longs;que C, o&longs;tium, & <lb/>v&longs;que ad D, clauditur adeò diligenter, vt <lb/>&longs;olius arundinis locus relinquatur. </s>

<cell>&longs;ecundi ad <expan abbr="&longs;ext&utilde;">&longs;extum</expan>, & ter</cell>

<s>Igitur <lb/>accen&longs;o B, funis initio, celerrimè ob pul<lb/>uerem pyrium ignis v&longs;que ad A, permeat, <lb/>accenditque puluerem totum: cúmque cu<lb/>neis & lapidibus ob&longs;tructus locus &longs;it, nec &longs;i <lb/>extrudantur vllus pateat exitus, quia E, noo <lb/>e&longs;t in directo A, nec D, in directo C, nec <lb/>B, in directo ED, nece&longs;&longs;arium e&longs;t vt di&longs;ru<lb/>pto monte, quicquid &longs;uperius e&longs;t euertat, <lb/>totam montis molem concutiens. </s>

</row>

<row>

<s>Ob id <lb/>viam BA, <expan abbr="nõ">non</expan> breuem e&longs;&longs;e oportet: nec locum <lb/>A, aliqua ex tenui montis parte, ne qua <lb/>tenue e&longs;&longs;et ob&longs;taculum ignis erumperet, &longs;u<lb/>periorémque locum illæ&longs;um permittere. <lb/></s>

<cell/>

<cell>tij ad quartum.</cell>

<s>Obliquitas igitur &longs;pecustanti miraculi cau<lb/>&longs;a e&longs;t, vt etiam montes euertantur. </s>

</row>

<row>

<s>Refe<lb/>runt hæc cuniculorum antiquam rationem <lb/>omnibus tunc notam: cùm & pari modo <lb/>obuiam tuti&longs;&longs;imè itur effo&longs;&longs;a è regione ter<lb/>ra, vt cuniculis occurrentes ignem exhala<lb/>re cogamus, & irritum illius impetum red<lb/>damus. </s>

<cell>&longs;ecundi ad quartum, &</cell>

<s>Vt verò rectè cuniculis occurramus, <lb/>docet &longs;onus fodientium, qui va&longs;is æneis cir<lb/>cum circa iuxta aggerem intus di&longs;po&longs;itis, per <lb/>noctis &longs;ilentium excipitur. </s>

</row>

<row>

<s>Et quamvis in<lb/>fatigabili opere illum ob&longs;curare inconditis <lb/>&longs;trepitibus ho&longs;tes nitantur: &longs;i tamen ob&longs;e&longs;&longs;i <lb/>accuratius atque diligentius rei incumbant <lb/>indu&longs;tria atque &longs;olertia, faba in auctorem <lb/>cudetur: ip&longs;i&longs;que doli auctoribus inuentum <lb/>damno&longs;ius erit, quàm his aduer&longs;us quos do<lb/>lus hic excogitatus e&longs;t. </s>

<cell/>

<cell>tertij ad &longs;extum.</cell>

<s>Perilai boui &longs;imilem <lb/>exitum habens. </s>

</row>

<row>

<s>Adde quòd per&longs;æpe, vt in <lb/>Cunnei præ&longs;enti ob&longs;idione parum peritis <lb/>Ducibus ab eli&longs;a murorum, & terræ mole <lb/>acies militum obruuntur, vt quaqua ver<lb/>&longs;um, & quam longè ca&longs;ura &longs;it præ&longs;cire opor<lb/>teat. </s>

<cell/>

<cell>Secundi ad quartum.</cell>

<s>Porrò quomodo hæc docere conue<lb/>niat, in libris de Æternitatis arcanis defini<lb/>tum e&longs;t. </s>

</row>

<row>

<s>Sed cui nondum ratio ex libris illis <lb/>tradendi, vtendique non in bonorum perni<lb/>ciem per&longs;pecta fuerit, nepharij propo&longs;iti e&longs;t <lb/>etiam vulgata, nedum abdita, huius generis <lb/>tradere. </s>

<cell>primi ad tertium, & &longs;ex</cell>

<s><margin.target id="marg101"/>Cuniculo<lb/>rum igneo<lb/>rum quos <lb/>minas vo<lb/>cant, ratio.</s>

</row>

<row>

<s>Sed his relictis, rur&longs;us ad ignis vim re<lb/><arrow.to.target n="marg102"/><lb/>deamus, ex qua non leues dubitationes or<lb/>tum habent. </s>

<cell/>

<cell>ti ad quintum.</cell>

<s>Nam cùm dixerimus motu il<lb/>lum con&longs;eruari, cur, dicet aliquis, melius <lb/>&longs;ub cineribus pruna &longs;eruatur quam detecta, <lb/>cùm cineres omnem prohibeant motum <gap/><lb/>Hæc facilis e&longs;t dubitatio, atque ad hunc li<lb/>brum minimè pertinens, in quo propo&longs;itum <lb/>e&longs;t, &longs;olum magna & difficillima ac pulcher<lb/>rima per&longs;equi. </s>

</row>

<row>

<s>Quamobrem in po&longs;terum <gap/><lb/>talibus ab&longs;tinebo, qualis e&longs;t hæc propo&longs;ita <lb/>dubitatio. </s>

<cell>primi ad quintum, et &longs;ex</cell>

<s>Itaque illi re&longs;pondere &longs;atis e&longs;t, <lb/>ignem &longs;emper motum habere aliquem, &longs;ed <lb/>prunas admodum tenuem, qui etiam &longs;ub ci<lb/>neribus maneat. </s>

</row>

<row>

<s>Cùm igitur prunæ detectæ <lb/>&longs;unt, aër corrumpit ignem illum circum<lb/>&longs;tans: mauult enim corrumpere quam cor<lb/>rumpi: nec tam tenuis motus illum &longs;eruare <lb/>pote&longs;t, verum contectus cinere, ab aëris <lb/>offen&longs;a tutus e&longs;t. </s>

<cell/>

<cell>ti ad tertium.</cell>

<s>Itaque tribus modis ignis <lb/>&longs;eruatur: vel cum motum ex &longs;eip&longs;o excitat, <lb/>vt in cereis, & generaliter vbi flamma mo<lb/>tu &longs;uo &longs;eip&longs;am tuetur: vel cùm aliunde mo<lb/>tu fouetur, vt flante vento, vel follibus, <lb/>vnde magna incendia fermè omnia dum <lb/>venti validi flarent, facta &longs;unt. </s>

</row>

<row>

<s>Tertiò, cùm <lb/>tutus e&longs;t ab aëre, &longs;ic tamen vt re&longs;pirare po&longs;<lb/>&longs;it, velut &longs;ub cineribus. </s>

<cell/>

<cell>Secundi ad &longs;extum.</cell>

<s>Nec refert an cine<lb/>res alieni &longs;int, an vt in quibu&longs;dam lignis <lb/><arrow.to.target n="marg103"/><lb/>contingit, illos &longs;ibi circumcirca paret. </s>

</row>

<row>

<s>Alia <lb/>e&longs;t etiam dubitatio cur ignem magis &longs;olea<lb/>mus dicere &longs;ub&longs;tantiam quam glaciem: nam <lb/>nemo glaciem &longs;ub&longs;tantiam dixit, ignem <pb xlink:href="016/01/030.jpg" pagenum="381"/>autem plerique non &longs;olum dixerunt, &longs;ed <lb/>etiam exi&longs;timauerunt, cùm tamen ambo ac<lb/>cidentia &longs;int. </s>

<cell>primi ad <expan abbr="quint&utilde;">quintum</expan>, & quar</cell>

<s>Cau&longs;a e&longs;t in promptu. </s>

</row>

<row>

<s>Acciden<lb/>tia &longs;olemus appellare, quæ ad&longs;unt non cor<lb/>rupto &longs;ubiecto: talis autem videtur glacies. <lb/></s>

<cell/>

<cell>ti ad tertium.</cell>

<s>Nam gelu concreta aqua, lac, vinum, &longs;o<lb/>luto gelu eadem con&longs;piciuntur. </s>

</row>

<row>

<s>At igne ple<lb/>raque corrumpuntur, & quæ manent, vt <lb/>lapides & metalla, læ&longs;a vehementer vi<lb/>dentur, præter aurum & argentum, & pau<lb/>culas gemmas: ob id ignem arbitrabantur <lb/>maius aliquid e&longs;&longs;e quàm calorem. </s>

<cell>primi ad <expan abbr="terti&utilde;">tertium</expan>, & quar</cell>

<s>Huius <lb/>tamen differentiæ cau&longs;am &longs;uperius docui<lb/>mus. <lb/><arrow.to.target n="marg104"/></s>

</row>

<row>

<s><margin.target id="marg102"/>Cur ignis <lb/>&longs;ub cineri<lb/>bus &longs;eru<gap/>ur<gap/></s>

<cell/>

<cell>ti ad quintum.</cell>

<s><margin.target id="marg103"/>Cur ignem <lb/>magis &longs;ub<lb/>&longs;tantiam e&longs;&longs;e<gap/><lb/>dicamus <lb/><expan abbr="quã">quam</expan> glaciem.</s>

</row>

<row>

<s><margin.target id="marg104"/>An aliquis <lb/>ignis non <lb/>&longs;plendeat.</s>

<cell/>

<cell>Tertij ad quartum.</cell>

<s>Erat & aliud dubitatione dignum: quo<lb/>niam ignis quiddam à quocunque calore &longs;e<lb/>paratum videbatur, non tamen e&longs;t, licet co<lb/>lorem mutet, & &longs;ibi &longs;imilem facilè gignat. <lb/></s>

</row>

<row>

<s>Sed non omnis ignis &longs;plendet: etenim fer<lb/>rum igneum &longs;ulphur accendit & vrit, ex <lb/>quo patet ip&longs;um ignis iam formam conce</s>

<cell>primi ad &longs;ecundum, &</cell>

<s><arrow.to.target n="marg105"/><lb/>pi&longs;&longs;e, nec tamen &longs;plendere. </s>

</row>

<row>

<s>Ita diuer&longs;a ra<lb/>tione ignis quem ardens aqua emittit, non <lb/>&longs;olùm ob &longs;ub&longs;tantiæ raritatem, &longs;ed quia mi<lb/>nus calidus e&longs;t: ob id et&longs;i con&longs;umatur & <lb/>&longs;plendeat, vix dicam illum ignem, qui lin<lb/>teum cui inhæret, & quod aqua ip&longs;a maduit, <lb/><arrow.to.target n="marg106"/><lb/>non vrat, ignem dici debere. </s>

<cell/>

<cell>&longs;exti ad quintum.</cell>

<s>Eadem ratio<lb/>&longs;ie &longs;i diutiùs di&longs;tilletur, attenuetúrque ma<lb/>gis, magno miraculo manus ardebit, neque <lb/>&longs;entiet. </s>

</row>

<row>

<s>Itaque &longs;i quis rectè in&longs;piciat, po&longs;t<lb/>quàm calor certam metam attigit, ignis di<lb/>ci meretur: hæc autem meta non vna e&longs;t, <lb/>&longs;ed quum aërem vincere pote&longs;t. </s>

<cell>primi ad quintum, & &longs;ex</cell>

<s>Quum verò <lb/>eò iam peruenerit, &longs;plendoris & lucis ac ro<lb/>boris tantùm acquirit, quantum etiam ca<lb/>lor ip&longs;e, ip&longs;éque ignis augetur. </s>

</row>

<row>

<s>Vim verò <lb/>iuxta &longs;ub&longs;tantiæ, cui ine&longs;t, den&longs;itatem: nam <lb/>pruna calidior ob id flamma e&longs;t, adeò vt py<lb/>rius puluis à pruna &longs;tatim à flamma vix ac<lb/>cendatur: atque id qui cau&longs;am ignorant, <lb/>tanquam rem magnam admirantur. </s>

<cell/>

<cell>ti ad &longs;ecundum.</cell>

<s>Ergo <lb/>vt ab initio dixi, ignis nihil aliud e&longs;t, quàm <lb/>calor valde magnus cum &longs;iccitate iunctus: <lb/><arrow.to.target n="marg107"/><lb/>nam ab&longs;que &longs;iccitate ignis e&longs;&longs;e non pote&longs;t, <lb/>aliter aqua feruens ignis e&longs;&longs;e po&longs;&longs;et. </s>

</row>

<row>

<s>Non <lb/>minus igitur ignis e&longs;&longs;entia à &longs;iccitate ip&longs;a <lb/>pendet, quàm à calore. </s>

<cell/>

<cell>Tertij ad &longs;extum.</cell>

<s>Hac igitur de cau<lb/>&longs;a faces è quocunque ligno facere edocti <lb/>&longs;umus: &longs;ed &longs;i ex den&longs;iore ac &longs;olidiore, diu<lb/><arrow.to.target n="marg108"/><lb/>turniores. </s>

</row>

<row>

<s>Stolonem querneum, cubi cra&longs;<lb/>&longs;itudine à vertice ad imum diuides in pluri<lb/>ma fru&longs;ta, velut duodecim, aut &longs;exdecim, <lb/>pluráve, ita vt imum integrum maneat, in<lb/>de &longs;iccetur in furno duobus, tribú&longs;ve die<lb/>bus: exclu&longs;o itaque humido aqueo quum <lb/>remaneat quod pingue e&longs;t, ardet vt t&oelig;da: <lb/>& &longs;i longitudine hominem æquat, durat <lb/>alacris flamma per horæ ac dimidiæ &longs;patium <lb/>lumine &longs;plendidi&longs;&longs;imo. </s>

<cell>primi ad &longs;ecundum, &</cell>

<s>Ergo, vt iam dixi, <lb/><arrow.to.target n="marg109"/><lb/>tam frigidis ignis extinguitur, quàm humi<lb/>dis obruitur: ab humidis quidem duabus cau<lb/>&longs;is, tum vt contrariis, tum quòd re&longs;pirare ac <lb/>moueri illum prohibeant: à frigidis autem, <lb/>&longs;olùm vt contrariis. </s>

</row>

<row>

<s>Ab aqua igitur, triplici <lb/>ratione extinguitur. <lb/><arrow.to.target n="marg110"/></s>

<cell/>

<cell>quarti ad quintum.</cell>

<s><margin.target id="marg105"/>Aqua <expan abbr="ard&etilde;s">ardens</expan> <lb/>vritur illæ&longs;o <lb/>linteo quòd <lb/>ea madet.</s>

</row>

<row>

<s><margin.target id="marg106"/>Manus vt <lb/>ardeat ho<lb/>mine non <lb/>&longs;entiente.</s>

<cell>primi ad quintum, &</cell>

<s><margin.target id="marg107"/>Ignis ratio <lb/>non minus <lb/>con&longs;tat &longs;ic<lb/>citate quam <lb/>calore.</s>

</row>

<row>

<s><margin.target id="marg108"/>Faces quo<lb/>modo è quo<lb/>cunque ligno <lb/>fiant.</s>

<cell/>

<cell>quarti ad &longs;ecundum.</cell>

<s><margin.target id="marg109"/>Ignis ab <lb/>aqua triplici <lb/>ratione ex<lb/>tinguitur.</s>

</row>

<row>

<s><margin.target id="marg110"/>Modi quibus <lb/>ignis genera<lb/>tur.</s>

<cell/>

<cell>Quarti ad quintum.</cell>

<s>Nunc tandem &longs;upere&longs;t, vt cau&longs;as gene<lb/>rationis illius o&longs;tendamus, neque leuem <lb/>habent in &longs;e ob&longs;curitatem. </s>

</row>

<row>

<s>Igitur primò, <lb/>quot modis fiat con&longs;ideremus. </s>

<cell>&longs;ecundi ad primum, &</cell>

<s>Fit autem <lb/>propagatione, anti&longs;pa&longs;i percu&longs;&longs;ione, fri<lb/>ctione, putredine, coïtione. </s>

</row>

<row>

<s>Nam qui vel <lb/>&longs;peculis concauis, vel &longs;phærulis per&longs;picuis <lb/>generantur, ad coïtionem manife&longs;tè perti<lb/>net. </s>

<cell/>

<cell>tertij ad &longs;extum.</cell>

<s>Sed coïtionis o&longs;cura ratio non e&longs;t, nam<lb/>que &longs;i denis viris nummos denos di&longs;tri<lb/>buas, &longs;inguli habebunt nummum: &longs;ed &longs;i in <lb/>quinque, binos. </s>

</row>

<row>

<s>Si igitur calor qui per ma<lb/>gnum &longs;patium di&longs;per&longs;us e&longs;t, in vnum con<lb/>trahatur, quicquid magnæ illi quantitati <lb/>inerat, & modicæ illi ine&longs;t: quamobrem <lb/>magnus calor in paruo &longs;patio contentus, <lb/>magnos effectus producet, magnú&longs;que ob <lb/>id dici merebitur, atque ob id ignis. </s>

<cell>&longs;ecundi ad &longs;extum, & ter</cell>

<s>Hoc <lb/>enim adeò planè expo&longs;itum e&longs;t, vt repetere <lb/>haud &longs;it nece&longs;&longs;arium. </s>

</row>

<row>

<s>Sed qui anti&longs;pa&longs;i fit, <lb/>ad coïtionem reducitur. </s>

<cell/>

<cell>tij ad primum.</cell>

<s>Non enim ob aliud <lb/>anti&longs;pa&longs;is accedit, quàm quòd in vnum co<lb/>git: ergo & huius cau&longs;a cognita e&longs;t. </s>

</row>

<row>

<s>Propa<lb/>gatione autem o&longs;tendimus quomodo gene<lb/>retur &longs;uperius. </s>

<cell/>

<cell>Quinti ad &longs;extum.</cell>

<s>Vnumquódque enim natura <lb/>con&longs;tantium atque mortalium &longs;ibi &longs;imile ge<lb/>nerare aptum e&longs;t, itaque nihil mirum ex ig<lb/>ne ignem accendi: verùm frictio & percu&longs;<lb/>&longs;io à motu initium habent: putredo autem <lb/>non &longs;ufficit ignem accendere, &longs;ed vel alio <lb/>calore confirmatur, aut motu, aut anti&longs;pa<lb/>&longs;i, atque coïtione. </s>

</row>

<row>

<s>Itaque &longs;i quo modo mo</s>

<cell>primi ad &longs;ecundum, &</cell>

<s><arrow.to.target n="marg111"/><lb/>tu ignis accendatur docuerimus, modos om<lb/>nes &longs;imul quibus ignis accendi po&longs;&longs;it de<lb/>mon&longs;trabimus: & quòd tantùm tres verè <lb/>&longs;int, coïtio, propagationem motus, quan<lb/>quam longè plures e&longs;&longs;e videantur. </s>

</row>

<row>

<s>O&longs;tende<lb/>re autem quomodo ignis à motu generetur, <lb/>non aliud e&longs;t, quàm quomodo motus &longs;it <lb/>cau&longs;a caloris demon&longs;trare: nam &longs;i motus e&longs;t <lb/>cau&longs;a caloris, erit & augmenti illius. </s>

<cell/>

<cell>quarti ad tertium.</cell>

<s>Ignis <lb/>autem ( vt diximus ) nihil aliud e&longs;t, quàm <lb/>color in immen&longs;um auctus. </s>

</row>

<row>

<s>Ergo quónam <lb/>pacto motus calefacit, inquirunt Ari&longs;tote<lb/>lici, ac multa nugantur: tandem verò ad id <lb/>redeunt, vt calor &longs;it effectus motus: e&longs;tque <lb/>hoc ac &longs;i dicerent, Ne&longs;cimus. </s>

<cell>primi ad <expan abbr="terti&utilde;">tertium</expan>, & quar</cell>

<s>Idem enim <lb/>per idem o&longs;tendere, certum nugacis atque <lb/>imperiti argumentum e&longs;t. </s>

</row>

<row>

<s>Quid tandem ob&longs;<lb/><arrow.to.target n="marg112"/><lb/>curè & &longs;uo more dixerunt quidam, quòd <lb/>calor hic in aëre iam e&longs;t, &longs;ed per motum ad <lb/>formam illam deducitur, e&longs;&longs;éque hunc ca<lb/>lorem illum qui à de&longs;ideribus prouenerit? <lb/></s>

<cell/>

<cell>ti ad &longs;ecundum.</cell>

<s>O egregium hominem: calida non cen&longs;ent <lb/>a&longs;tra, inde calorem illum a&longs;trorum ignem <lb/>e&longs;&longs;e volunt. </s>

</row>

</table>

<s>Quòd et&longs;i caliditatem efficere <lb/>&longs;idera, quæ calida e&longs;&longs;e negant concedatur, <lb/>rur&longs;us dubitatio emergit, quomodo calo<lb/>rem illum motus augeat. </s>

<table>

<table.target id="table9"/>

<s>Certum enim e&longs;t, <lb/>conceptam caliditatem antè à &longs;yderibus ab&longs;<lb/>que motu nondum e&longs;&longs;e igneam. </s>

<row>

<s>Alexander <lb/><arrow.to.target n="marg113"/><lb/>rectè &longs;entit in hoc, quòd non ex lapidibus <lb/>excutitur ignis, &longs;ed aër qui ibi continetur, <lb/>attritu repentino vertitur in ignem. </s>

<s>Sed &longs;i <lb/>ita e&longs;t, cur non è &longs;olidi&longs;&longs;imis lapidibus, vt <lb/>porphyrite, ac duri&longs;&longs;imis magis excutitur, <lb/>quàm à mollioribus, vt chry&longs;tallo & chal<lb/>cedonio? </s>

</row>

<s>Rur&longs;us, cur non è duobus lapidi<lb/>bus eiu&longs;dem generis magis, vt chry&longs;tallinis, <lb/>quàm è chry&longs;tallo & chalybe ignis proue<lb/>nit? </s>

<row>

<cell/>

<s>Deinde, cur ( quod maximum e&longs;t ) &longs;i <lb/>&longs;olus aër accenditur, &longs;cintillæ illæ magna <lb/>ex parte, ac veluti graues, lento proce&longs;&longs;u <lb/>de&longs;cendunt? </s>

<cell/>

<s>Nam purus ignis, aut non de&longs;-<pb xlink:href="016/01/031.jpg" pagenum="382"/>cendit, aut &longs;i impetu cogatur, celeriter de&longs;<lb/>cendit. </s>

</row>

<s>Cùm igitur lentè de&longs;cendant quæ<lb/>dam, non ex &longs;olo aëre illæ con&longs;tant. </s>

<row>

<cell/>

<s>Ergo <lb/>quòd non &longs;it in lapide ignis conceptus, re<lb/>ctè dixit Alexander: vret enim ignis lapi<lb/>dem, & rur&longs;us lapis tangentis manum, <lb/>& facilè accenderetur, & alimento indige<lb/>ret, & duobus lapidibus concu&longs;&longs;is &longs;imul fa<lb/>cilè elideretur, vt duobus chalcedoniis, at<lb/>tritus enim &longs;ufficeret ad elidendum ignem: <lb/>quorum nullum cum verum &longs;it, liquidò con<lb/>&longs;tat ignem in lapide non contineri. </s>

<cell/>

<s>Sed nec <lb/>rur&longs;us ( vt dixi <emph type="italics"/>)<emph.end type="italics"/> ex aëre generantur: nam <lb/>lapides vt duriores &longs;unt, indigent maiore <lb/>percu&longs;&longs;ione vt ignis generetur. </s>

</row>

<s>Ergo &longs;i &longs;o<lb/>lùm &longs;ufficeret aërem repentè concuti ex tali <lb/>ictu, qualis e&longs;t is quo è chalybe, & chry<lb/>&longs;tallo ignis excutitur, ex duobus chalybis <lb/>fru&longs;tis po&longs;&longs;et ignis generari: at non e&longs;t &longs;ic, <lb/>&longs;ed, ( vt dixi <emph type="italics"/>)<emph.end type="italics"/> duriora vehementiores ictus <lb/>expo&longs;cunt, ignémque creant &longs;olidiorem ac <lb/>viuaciorem, vt cuius quandoque &longs;cintilla <lb/>non paruo maneat tempore. </s>

<row>

<cell/>

<s>Quinetiam qui<lb/>dam &longs;unt lapides vitrei ac molles, qui leui&longs;<lb/>&longs;imis ictibus, vel &longs;olùm tacti, ignem, &longs;ed <lb/>minimè viuacem, edunt. </s>

<cell/>

<s>Indicium verò <lb/>certum e&longs;t ex lapidis &longs;ub&longs;tantia ignem ge<lb/>nerari, quòd &longs;ine illius attritione nunquam <lb/>eliditur: aër etiam <emph type="italics"/>(<emph.end type="italics"/> vt diximus) in flam<lb/>mam, non &longs;cintillas, vertitur. </s>

</row>

<s>Quinetiam <lb/>molæ circumactæ, cùm aqua non aëre ob<lb/>ductæ &longs;int, ignem tamen emittunt: lapides <lb/>etiam ip&longs;i non ni&longs;i ex angulis. </s>

</table>

<s>Itaque non <lb/>in lapidibus abditus latet ignis, nec concu&longs;<lb/>&longs;o aëre ex aëre generantur. </s>

<s id="id000239">Propo&longs;itio &longs;eptima.</s>

<s>Sed nec quòd in <lb/>illis potentia &longs;it ignis, vllum certum e&longs;t in<lb/>dicium: vix enim in ignem proiecti accen<lb/>duntur, nec à frigido vnquam inflamman<lb/>tur, & epoti &longs;trenuè refrigerant. </s>

<s>Quare ma<lb/>nife&longs;tum e&longs;t, ex attritione lapidis ad tenui&longs;<lb/>&longs;imas partes illius &longs;ub&longs;tantia redacta, ignem <lb/>generari, e&longs;&longs;éque huius materiam, vel il<lb/>lius ad hoc aptiorem. </s>

<s id="id000240">In modis qui nece&longs;&longs;ariò produ<lb/>cuntur ex duabus proportionibus, <lb/>cum du&etail; quantitates ex illis, qu&etail; mo <lb/><figure id="id.015.01.029.3.jpg" xlink:href="015/01/029/3.jpg"/>dos conficiunt, æquales fuerint: pro<lb/><arrow.to.target n="table10"/><lb/>portio producta ad quatuor quanti<lb/>tates omiologas reducetur.<lb/><arrow.to.target n="marg25"/></s>

<s>Namque puriores ac <lb/>non parum duri, ac tenui &longs;ub&longs;tantia con<lb/>&longs;tantes, vt chalcedonij, chry&longs;talli, atque <lb/>huiu&longs;cemodi, apti&longs;&longs;imi &longs;unt: contrà fragi<lb/>les, aut præduri, aut cra&longs;&longs;a con&longs;tantes &longs;ub<lb/>&longs;tantia, minimè apti. </s>

<s>Sic etiam ex &longs;agittæ <lb/>motu plumbum lique&longs;cit: quoniam extre<lb/>mæ partes, minimè angulorum, quæ tenui&longs;<lb/>&longs;imæ &longs;unt, atteruntur. </s>

<table>

<s>Idem contingit in <lb/>longo motu, quòd in pluribus exiguis repe<lb/>titis: velut cùm tabulæ gladium affricamus: <lb/>&longs;ed hic eo vehementior attritio, quo id quod <lb/>&longs;uppo&longs;itum e&longs;t, etiam duritie &longs;ua re&longs;i&longs;tit, vt <lb/>aër in medio compre&longs;&longs;us dum attenuatur at<lb/>tenuat. </s>

<table.target id="table10"/>

<row>

<s>Sed ad id vnde digre&longs;&longs;us eram, de <lb/>motu accendente calorem, reuerti opus e&longs;t: <lb/>nam ex hoc omnia fermè pendêre videntur. <lb/></s>

<s>Itaque ex aqua ignem vnquam accendi vi<lb/>demus, ex aëre autem non ni&longs;i propagatio<lb/>ne, non motu: & &longs;i humidorum aliquod <lb/>accenditur, vt oleum ac vinum, ab igne, <lb/>non non motu, inflammatur. </s>

</row>

<row>

<s>Ergo quod <lb/>motu acceenditur, &longs;iccum e&longs;&longs;e oportet, non <lb/>humidum: quod verò ab alio igne, etiam <lb/>humidum e&longs;&longs;e pote&longs;t. </s>

<s>Quòd igitur &longs;iccum <lb/>e&longs;t ac vehementer, iam ex dimidio ignis <lb/>e&longs;t. </s>

</row>

<row>

<s>E&longs;t enim ( vt dixi ) ignis vehemens cali<lb/>ditas ac &longs;iccitas. </s>

<s>Indiget igitur hoc quod <lb/>&longs;iccum e&longs;t, vt tantum incale&longs;cat: verùm <lb/>partis & totius eadem ratio e&longs;t. </s>

</row>

<row>

<s>Si enim in<lb/>cale&longs;cit motu vehementi, etiam vehemen<lb/>ter incale&longs;cet. </s>

<s>Cùm igitur &longs;iccum motu col<lb/>liditur, vt rarum euadat ac tenuè nece&longs;&longs;e <lb/>e&longs;t: at tenuis &longs;ub&longs;tantia & &longs;icca, ignea e&longs;t. <lb/></s>

</row>

<row>

<s>Vnaquæque enim materia &longs;ub certa quan<lb/>titate formam ad &longs;e rapit. </s>

<s>Hoc &longs;olùm e&longs;t igi<lb/>tur bene dictum, quòd calor ille qui è &longs;yde<lb/>bus mi&longs;tis ine&longs;t &longs;iccæ iunctus materiæ, dum <lb/>motu nimis attenuatur non repugnante hu<lb/>mido, quippe cùm &longs;iccam eam iam &longs;uppo<lb/>&longs;uerimus, nec formà priore vt pote lapidis, <lb/>adeò ob tenuitatem debilitatæ, ne &longs;imul <lb/>qualitates lapidis ade&longs;&longs;ent, abe&longs;&longs;et verò &longs;ub<lb/>&longs;tantia, ignis formam &longs;u&longs;cipiunt calore <lb/>agente. </s>

</row>

<row>

<s>Ergo hic modus coïtioni, qua&longs;i con<lb/>trarius e&longs;t: in illo con&longs;tante materia calor <lb/>cogitur, hîc &longs;ub eodem calore materia ip<lb/>&longs;a attenuatur. </s>

<s>Indicio e&longs;t hanc e&longs;&longs;e cau<lb/>&longs;am, quòd aqua motu in aërem verti<lb/>tur, vt qui&longs;que vbi illæ cadunt magno im<lb/>petu pote&longs;t videre. </s>

</row>

</table>

<s>Nam attenuata &longs;ub&longs;tan<lb/>tia cùm humido iuncta &longs;it, aëris formam <lb/>induit. <lb/><arrow.to.target n="marg114"/></s>

<s id="id000242">Sint &longs;ex quantitates a b c d e f, & <lb/>producatur proportio a ad b ex pro<lb/>portione c ad d, & e ad f, tu &longs;cis, quòd <lb/>modi recepti &longs;unt prima cum &longs;ecunda, tertia uel quinta, & &longs;ecunda <lb/>cum quarta, & &longs;exta, & tertia &longs;imiliter cum ei&longs;dem, & quinta eodem <lb/>modo cum ei&longs;dem: &longs;i igitur du&etail; quantitates ex his, qu&etail; faciunt pro

<s><margin.target id="marg111"/>Motus quo<lb/>modo <expan abbr="calor&etilde;">calorem</expan> <lb/>& ignem ge<lb/>neret.</s>

<s><margin.target id="marg112"/>Auerroës in <lb/>paraphra&longs;i <lb/>Metaphy. <lb/></s>

<pb pagenum="11" xlink:href="015/01/030.jpg"/>portionem productam inter &longs;e fuerint æquales reducetur hæc pro<lb/>portio ad quatuor quantitates omologas, &longs;ciliter abiectis amba<lb/>bus æqualibus. </s>

<s id="id000243">Sit gratia exempli prima æqualis quintæ: & quia <lb/>in octauo modo proportio <expan abbr="&longs;ec&utilde;di">&longs;ecundi</expan> ad quartum producitur ex pro<lb/>portione primi ad quintum, & &longs;exti ad tertium, ergo per expo&longs;ita <lb/>proportio &longs;ecundi ad quartum, ut &longs;exti ad tertium, & ita permutan<lb/>do, & conuertendo &longs;ecundi ad &longs;extum, ut quarti ad tertium, & tertij </s>

<s>tract. 2. <lb/>col. </s>

<s id="id000244"><arrow.to.target n="marg26"/><lb/>ad quartum, ut &longs;exti ad &longs;ecundum.</s>

<s id="id000245"><margin.target id="marg26"/>V<emph type="italics"/>ndecima <lb/>petitione.<emph.end type="italics"/></s>

<s><margin.target id="marg113"/>Quomodo <gap/><lb/>lapidibus ig<lb/>nis excutia<lb/>tur.</s>

<s><margin.target id="marg114"/>Frigus nihil <lb/>e&longs;t actu, &longs;ed <lb/>&longs;ola caloris <lb/>priuatio.</s>

<s id="id000246">Propo&longs;itio octaua.</s>

<s>Verùm dubitabis, in frigido aëre ac ma<lb/>teria, in qua iam frigus &longs;uperat, vt in lapi<lb/>de, cur calor in&longs;urgit, cùm frigus &longs;it poten<lb/>tius? </s>

<s id="id000247">Si duarum <expan abbr="proportion&utilde;">proportionum</expan> &longs;uperiores numeri alternatim cum infe<lb/>rioribus multiplicentur, atque coniungantur: erit proportio aggre<lb/>gati ad productum ex inferioribus inuicem proportio ex primis <lb/>proportionibus compo&longs;ita.</s>

<s>Re&longs;pondeo, frigus &longs;i pro actu intelli<lb/>gatur, nihil e&longs;&longs;e ni&longs;i calorem illum exiguum: <lb/>quod autem non e&longs;t, nullas habet opera<lb/>tiones. </s>

<s>Ob id frigus non in&longs;urgit, cùm &longs;ola <lb/>priuatio quædam &longs;it, &longs;ed calor, qui tamen <lb/>ad paucitatem &longs;ubiectæ materiæ compara<lb/>tus, magnus e&longs;t. </s>

<s id="id000248">Sit proportio una a ad b, alia c ad d, ducatur b in <lb/><arrow.to.target n="marg27"/><lb/>c, fiatque e & a in d, & fiat f, iunganturque e & f & fiat h, <lb/>& ducatur b in d et fiat g: dico <expan abbr="proportion&etilde;">proportionem</expan> h g com<lb/>po&longs;itam e&longs;&longs;e ex proportione a ad b, & c ad d. </s>

<s>Indicio e&longs;t frigus nihil om<lb/>ninò e&longs;&longs;e præter caloris priuationem, ter<lb/>tianarum rigor, in quo cùm nulla &longs;it mate<lb/>ria frigida, &longs;ed &longs;olius caloris fuga, frigus <lb/>tamen non leue &longs;entitur. </s>

<s id="id000249">Quia <lb/><arrow.to.target n="marg28"/><lb/>enim ex b in c fit e, & ex b in d fit g, erit proportio e <lb/>ad g, ut c ad d, & &longs;imiliter, quia ex d in a fit f, & ex d in b fit g, erit f ad <lb/>g ut a ad b. </s>

<s id="id000250">Sed e & f componunt h, igitur proportio h ad g e&longs;t com<lb/>po&longs;ita ex proportionibus e & f ad g, igitur per communem animi <lb/>&longs;ententiam, & diffinitionem compo&longs;itæ proportionis, proportio h <lb/><arrow.to.target n="marg29"/><lb/>ad g compo&longs;ita e&longs;t ex proportionibus a ad b, & c ad d, quod e&longs;t <lb/>propo&longs;itum.</s>

<s>Vbi ergo calor exi<lb/>guus in materia pauca fuerit, &longs;eruatur. </s>

<s>Ea<lb/>dem ratione nec &longs;iccitas aliud e&longs;t, quam hu<lb/>midi priuatio. </s>

<s>Quamobrem &longs;icca humectari </s>

<s id="id000252"><margin.target id="marg28"/>E<emph type="italics"/>x<emph.end type="italics"/> 13 <emph type="italics"/>peti<lb/>tione.<emph.end type="italics"/></s>

<s><arrow.to.target n="marg115"/><lb/>impo&longs;&longs;ibile e&longs;t, cum non &longs;it reditus ad ha<lb/>bitum ex priuatione. </s>

<s>Sed difficilius e&longs;t hu<lb/>mectare, quia humidum principium e&longs;t ex <lb/>elemento, calor ex c&oelig;lo, quod &longs;emper dif<lb/>fundit. </s>

<s id="id000253"><margin.target id="marg29"/>P<emph type="italics"/>er<emph.end type="italics"/> 14 <emph type="italics"/>diffi <lb/>nitionem.<emph.end type="italics"/></s>

<s>Re&longs;taurantur igitur &longs;olis adiectis ma<lb/>teriis. </s>

<s id="id000254">Propo&longs;itio nona.</s>

<s>At infrigidare, aut &longs;iccare, faciliùs <lb/>conceditur, cùm impedimento con&longs;tent hæ <lb/>mutationes. </s>

<s>Iu&longs;tè ætherem, & aquam prin<lb/>cipium naturalium rerum antiqui po&longs;uêre, <lb/>quòd in altero calor dominari exi&longs;timatur <lb/>in reliquo abundet humidum. </s>

<s id="id000255">Si duarum proportionum &longs;uperiores numeri alternatim cum <lb/>inferioribus multiplicentur, minusque productum ex maiore detra<lb/>hatur, erit re&longs;idui ad productum ex inferioribus proportio uelut <lb/>illa, quæ relinquitur detracta minore proportione ex maiore.</s>

<s>Iu&longs;tius aërem, <lb/>&longs;i ille calidus e&longs;&longs;et & humidus. </s>

<s id="id000256">Hæc eodem modo probatur, ut præcedens, ni&longs;i quod h fit de<lb/><arrow.to.target n="marg30"/><lb/>tracto è minore: gratia exempli ex f, & ita ex diffinitione patet pro<lb/>po&longs;itum.</s>

<s>Terram ne<lb/>mo: nam ip&longs;a frigida, &longs;iccáque e&longs;t. </s>

<s>Sed ca<lb/>lida præter naturam difficilè refrigerantur, <lb/>motus enim con&longs;eruat. </s>

<s>Ergo difficilius <lb/>quæ natura talia &longs;unt, motus enim eo<lb/>rum perpetuus. </s>

<s id="id000258">Propo&longs;itio decima.</s>

<s>Verùm in aëre frigido <lb/>&longs;cintilla ignis illicò, ni &longs;uccurratur, extin<lb/>guitur. </s>

<s>Sed aër non pote&longs;t prohibere gene<lb/>rationem quæ intus fit, illo tantùm circum<lb/>ambiente. </s>

<s id="id000259">Si fuerit alicuius quantitatis ad unam partem proportio uelut al<lb/>terius partis ad <expan abbr="&longs;ec&utilde;dam">&longs;ecundam</expan> quantitatem erit proportio cuiu&longs;uis quan<lb/>titatis eiu&longs;dem generis ad &longs;ecundam compo&longs;ita proportio ex pro<lb/>portionibus eiu&longs;dem quantitatis a&longs;&longs;umptæ ad utran que partem pri<lb/>mæ quantitatis &longs;eor&longs;um.<lb/><arrow.to.target n="marg31"/></s>

<s><margin.target id="marg115"/>Siccitas non <lb/>e&longs;t ni&longs;i hu<lb/>midi priua<lb/>tio.</s>

<s>Verùm rur&longs;us dices: &longs;i frigus nihil e&longs;t <lb/>actu, &longs;ed &longs;ola caloris priuatio, quomodo <lb/>frigida refrigerant, vt calida calefaciunt? <lb/></s>

<s>Frigus &longs;emper e&longs;t cùm multa maria, im<lb/>po&longs;&longs;ibile verò tenui&longs;&longs;imum aliquid e&longs;&longs;e fri<lb/>gidum: multa materia impedit, nec ca<lb/>lo penetrare po&longs;&longs;it neque moueri, quare hoc <pb xlink:href="016/01/032.jpg" pagenum="383"/>modo refrigerat. </s>

<s id="id000261">Sit a b quantitas diui&longs;a in c, & &longs;i c ut a b ad a c, <lb/>ita b c ad d: eritque iterum permutando a b ad b c, <lb/>ut a c ad d, & &longs;umatur quædam quantitas e eiu&longs;

<s>Ergo quod calefacit, per <lb/>&longs;e calefacit: quòd refrigerat, &longs;olùm ex ac<lb/>cidenti. </s>

<s>Repugnabis for&longs;an, quoniam re<lb/>frigerari &longs;entimus nos, non aliter à frigidis <lb/>tum repentè, vt à calidis calefieri, vt pro<lb/>ducta frigoris quædam &longs;pecies videatur. <lb/></s>

<pb pagenum="12" xlink:href="015/01/031.jpg"/>dem tamen generis, cum illis dico quòd proportio e ad d e&longs;t com<lb/>po&longs;ita ex proportionibus e ad a c, & e ad b c. </s>

<s id="id000262">Po&longs;ita ergo e tan<08> &longs;u<lb/>periore numero, & a c & c b inferioribus, erit ex octaua propo&longs;itio<lb/>ne huius proportio productorum ex e in a c, & coniunctorum, & <lb/>ex con&longs;equenti per primam &longs;ecundi Elementorum producti ex e in <lb/>a b ad productum ex a c in c b compo&longs;ita ex proportionibus e ad <lb/>a c, & e ad c b: at quod fit ex a c in c b, e&longs;t æquale ei quod fit ex a b in <lb/>d, eo quòd a b, a c, c b & d &longs;unt omiologæ per decimam &longs;extam &longs;exti <lb/><expan abbr="Elem&etilde;torum">Elementorum</expan>: Proportio igitur producti ex e in a b ad productum <lb/>ex d in a b e&longs;t compo&longs;ita ex proportionibus e ad a c, & e ad e b: At <lb/>proportio producti ex e in a b ad productum ex d in a b, e&longs;t uelut e <lb/><arrow.to.target n="marg32"/><lb/>ad d. </s>

<s>Equidem ( vt dixi ) nihil aliud e&longs;t frigidum, <lb/>quàm caloris priuatio: & quæ mouentur <lb/>nec con&longs;i&longs;tunt, refrigerantur, vt aqua, & <lb/>ventorum validorum aër. </s>

<s id="id000263">per &longs;uppo&longs;ita igitur proportio e ad d e&longs;t compo&longs;ita ex propor<lb/>tionibus e ad a c, & e ad b c, quod fuit demon&longs;trandum.</s>

<s>Porrò cùm conta<lb/>ctu re&longs;rigeratur, &longs;olùm &longs;uperficies refrigera<lb/>tur, fugiente intus palàm calore: nec po&longs;&longs;ibi<lb/>le e&longs;t ob hoc &longs;ubitò quippiam refrigerari, <lb/>mora autem ducta refrigerantur etiam pe<lb/>niti&longs;&longs;imæ partes. </s>

<s>Atque hæc vera &longs;unt rerum naturalium <lb/>fundamenta, in quibus nihil e&longs;t repugnans. <lb/></s>

<s>Qui verò eas qualitates &longs;ub&longs;tantiis affixas <lb/>imaginantur, & frigiditatem aliquod e&longs;&longs;e <lb/>naturæ principium, in difficillimas perue<lb/>niunt quæ&longs;tiones, rerúmque quæ videntur <lb/>cau&longs;as dicere non po&longs;&longs;unt, omniáque &longs;ilen<lb/>tio ac verbis ob&longs;curis inuoluere, tum etiam <lb/>ambiguis, nituntur. </s>

<s id="id000265">Propo&longs;itio undecima.</s>

<s>Igitur calor ip&longs;e propria <lb/>qualitas e&longs;t c&oelig;le&longs;tis, hæc agitans corpora, <lb/>quæ motu adiuta ignem creat. </s>

<s id="id000266">Proportio aggregati quarumlibet duarum quantitatum ad ag<lb/>gregatum duarum æqualium quantitatum e&longs;t compo&longs;ita ex pro<lb/>portionibus primis, & diui&longs;a per duplam.<lb/><arrow.to.target n="marg33"/></s>

<s>Si à materia <lb/>obruatur ac impediatur, frigus gignit. </s>

<s>Quæ<lb/>cunque autem motu non eadem manent, <lb/>frigidiora euadunt, vt aqua & aër. </s>

<s>Aëris <lb/>verò temperiem facit radiorum multitu<lb/>do Solis, tum &longs;yderum, quos excipit, <lb/>qui illum calefaciunt. </s>

<s id="id000268">Sit proportio a ad c, & b ad d, & &longs;int c & d <lb/><figure id="id.015.01.031.1.jpg" xlink:href="015/01/031/1.jpg"/><lb/>æquales, dico quòd proportio a b ad c d e&longs;t <lb/>compo&longs;ita ex proportionibus a ad c, & b ad <lb/>d diui&longs;o compo&longs;ito per duplam. </s>

<s>Terra verò non adeò <lb/>e&longs;&longs;e frigida pote&longs;t vt aqua, quoniam non <lb/>mouetur. </s>

<s>His itaque con&longs;titutis, quibus non pauca <lb/>quæ iamdiu latuerunt, o&longs;tendemus naturæ <lb/>&longs;ecreta, ad ignis rur&longs;us hi&longs;toriam reuertan<lb/>tur. </s>

<s id="id000270"><arrow.to.target n="marg34"/><lb/>c & d &longs;unt æquales, erit b ad c, ut b ad d, qua<lb/>re ex diffinitione cùm proportio a b ad c d <lb/><arrow.to.target n="marg35"/><lb/>&longs;it compo&longs;ita ex proportionibus a ad c, & b <lb/>ad c, erit etiam compo&longs;ita ex dictis ex propo&longs;itione a ad c, & b ad d, <lb/><arrow.to.target n="marg36"/><lb/>&longs;tatuatur ergo e æqualis c d media inter a b & c. </s>

<s>Verùm de &longs;ub&longs;tantiarum &longs;ubtilitate ali<lb/><arrow.to.target n="marg116"/><lb/>qua priùs præponere oportet. </s>

<s id="id000271">Et erit per &longs;ecun<lb/>dam propo&longs;itionem proportio aggregati a b ad c producta ex <lb/><arrow.to.target n="marg37"/><lb/>proportione aggregati a b ad c, & e ad c, igitur proportio a b ad e <lb/>erit proportio a b ad c, diui&longs;a per proportionem e ad c, &longs;ed e ad c e&longs;t <lb/><arrow.to.target n="marg38"/><lb/>dupla: igitur proportio a b ad c d e&longs;t proportio a b ad c diui&longs;a per <lb/>duplam.</s>

<s>Quædam igi<lb/>tui dicuntur tenues per &longs;e, vt aër: quædam <lb/>quantitate, vt capilli: quædam quia fluunt, <lb/>vt &longs;anguis: quædam quia in partes tenui&longs;&longs;i<lb/>mas diuidi po&longs;&longs;unt, vt aurum: aliæ quia plu<lb/>ra ex his habent, vt &longs;pititus, qui no&longs;tra<lb/><arrow.to.target n="marg117"/><lb/>rum &longs;unt operationum in&longs;trumenta. </s>

<s id="id000272"><margin.target id="marg34"/>E<emph type="italics"/>x &longs;exta<emph.end type="italics"/> A<emph type="italics"/>nim. <lb/>com. </s>

<s>Fiunt <lb/>autem ab arte pleraque tenuia, velut plum<lb/>bum, quòd adeò attenuatur arte, vt in pul<lb/>uerem redigatur, ex quo horologia fieri &longs;o<lb/>lent. </s>

<s id="id000273">&longs;ententia.<emph.end type="italics"/></s>

<s>Liquefactum enim agitatur celerrimè <lb/>in mortario: ideò cum cogi non po&longs;&longs;it, tran<lb/>&longs;it in puluerem. </s>

<s id="id000274"><margin.target id="marg35"/>D<emph type="italics"/>ecimaquarta<emph.end type="italics"/></s>

<s>Et quamvis ars in tenui&longs;&longs;i<lb/>ma redigat ligna, aut lapides, aut metalla, <lb/>non tamen ip&longs;a mi&longs;cet, nec attenuat &longs;ub<lb/>&longs;tantiam, &longs;ed &longs;olùm quantitatem. </s>

<s>Ignis ve<lb/>rò &longs;i attenuat, &longs;eparat: aut &longs;i mi&longs;cet, non <lb/>attenuat. </s>

<s>Separando enim quæ cra&longs;&longs;a &longs;unt, <lb/>attenuantis &longs;peciem præbet. </s>

<s>Sola natura &longs;i<lb/>mul mi&longs;cere atque attenuare &longs;ub&longs;tantiam <lb/>pote&longs;t. </s>

<s>Cùm enim ( vt dixi <emph type="italics"/>)<emph.end type="italics"/> nunc vocem <lb/>&longs;ubtilia quæ duci po&longs;&longs;unt, atque ea ductilia, <lb/>vel humida e&longs;&longs;e nece&longs;&longs;e &longs;it, ignis verò &longs;ic<lb/>cet, attenuare non pote&longs;t, ni&longs;i &longs;eparet. </s>

<s id="id000277"><margin.target id="marg38"/>P<emph type="italics"/>er quintam <emph.end type="italics"/><lb/>A<emph type="italics"/>nim. </s>

<s>At<lb/>tenuat ergo vel comminuendo &longs;icca, vt <lb/>cùm arenam in puluerem redigit, aut col<lb/>liquando, vt metallica: tenues partes &longs;e<lb/>parando, vt in di&longs;tillationibus. </s>

<s id="id000279">&longs;en <lb/>tentiam.<emph.end type="italics"/></s>

<s>Verùm dum <lb/>&longs;icca comminuat, colliquet humida, etiam <lb/><arrow.to.target n="marg118"/><lb/>attenuat. </s>

<s id="id000280">Propo&longs;itio duodecima.</s>

<s>Contigit tamen in di&longs;tillationibus <lb/>aliquid attenuari ac alteri mi&longs;ceri, cùm à <lb/>calido humido, non ab igne fiunt. </s>

<s>Calor <lb/>enim mi&longs;cet, & cum humido attenuat. </s>

<s id="id000281">Propo&longs;itis duabus proportionibus unam alteri iungere ab&longs;que <lb/>multiplicatione.<lb/><arrow.to.target n="marg39"/></s>

<s>Fit <lb/>autem hoc va&longs;es in aquam feruentem im<lb/>mi&longs;&longs;is, vocátque Mariæ balneum. </s>

<s>Proximum <lb/>bonitate di&longs;tillationis genus huic in equino <lb/>fimo: inde quod per cineres præ&longs;tanti&longs;&longs;imum <lb/>in oleum detractum e&longs;t. </s>

<s>Nam cùm calida <lb/>&longs;it ac humida &longs;ub&longs;tantia, per multos men<lb/>&longs;es calorem &longs;eruare pote&longs;t, atque eò longio<lb/>re temporis &longs;patio quàm vuarum acini, quo <lb/>oliuarum &longs;ub&longs;tantia den&longs;ior e&longs;t, ac pinguior. <lb/></s>

<s id="id000283">Sint propo&longs;itæ proportiones a ad c & <lb/><figure id="id.015.01.031.2.jpg" xlink:href="015/01/031/2.jpg"/><lb/>b ad d, & a&longs;&longs;umo e ad c, iuxta ea quæ Eu<lb/>clides demon&longs;trauit, ut b ad d, erit igitur </s>

<s>At nullum horum metalla liquare pote&longs;t, <lb/>&longs;ed illa igne indigent. </s>

<s id="id000284"><arrow.to.target n="marg40"/><lb/>proportio a e ad c, compo&longs;ita ex proportionibus a ad c, & e ad c, <lb/>&longs;ed proportio e ad c e&longs;t, ut b ad d, igitur proportio a e ad c compo<lb/>&longs;ita e&longs;t ex proportionibus a ad c, & b ad d.</s>

<s>Sed vt ardenti&longs;&longs;ima <lb/>di&longs;tillatio fit per ignes, ita mi&longs;tioni ac veræ <lb/>attenuationi inepta: cui fermè &longs;imilis e&longs;t, <lb/>quæ fit per cineres. </s>

<s>Nam &longs;i igne di&longs;tillata <lb/>fæcibus &longs;uis mi&longs;cueris, fiet totum pro mo<lb/>lis ratione grauiùs quàm antea, tum etiam <lb/><arrow.to.target n="marg119"/><lb/>&longs;iccius. </s>

<s id="id000285"><margin.target id="marg40"/>E<emph type="italics"/>x generali <lb/>com.<emph.end type="italics"/> A<emph type="italics"/>nim. &longs;en <lb/>tentia.<emph.end type="italics"/></s>

<s>Non igitur verè attenuat ignis, &longs;ed <lb/>natura ip&longs;a, quæ totam &longs;ub&longs;tantiam conco<lb/>quit ac mi&longs;cet. </s>

<s id="id000286">Aliter ex b in c fiat f ex a in d, g ex c in d h coniunctum ex f g, k.</s>

<s>Vnde ob &longs;ubtilitatem omnia <lb/>in vnum conueniunt, mi&longs;túmque den&longs;ius, <lb/>fit, & tamen ex &longs;ubtili&longs;&longs;imis compo&longs;itum <lb/>partibus. </s>

<s>Ergo in naturali coctione, vt quæ <lb/>in liquido duri&longs;&longs;ima, etiam vim ignis obti<lb/>neat, & mollis balnei in attenuando, partes <lb/>cra&longs;&longs;iores comminuuntur, quod ab igne im<lb/>petrari non pote&longs;t. <lb/><arrow.to.target n="marg120"/></s>

<s><margin.target id="marg116"/>Subtilitatis <lb/>in &longs;ub&longs;tantia <lb/>genera.</s>

<s id="id000287">Quia ergo ex c in b fit f, ex c in d h, erit f ad h, <lb/>ut b ad d, igitur ut e ad c, &longs;ed a ad c, ut g ad h igi<lb/><arrow.to.target n="marg41"/><lb/>tur a e ad c, ut k ad h, &longs;ed k ad h cómponitur ex <lb/>proportionibus a ad c, & b ad d. </s>

<s id="id000288">Ex octaua ha <lb/>rum igitur proportio a c ad c compo&longs;ita e&longs;t ex <lb/>ei&longs;dem. </s>

<s><margin.target id="marg117"/>Subtilitates <lb/>ab arte, na<lb/>tura, & igne <lb/>in quibus <lb/>differant. <lb/></s>

<s id="id000289">For&longs;an quis dicat hanc eandem e&longs;&longs;e <lb/>octauæ &longs;ed <expan abbr="nõ">non</expan> e&longs;t, in illa enim proportio com<lb/>paratur ad productum, in hac ad unam ex <lb/>quantitatibus.</s>

<s>Plumbum <lb/>quomodo in <lb/>puluerem <lb/>tran&longs;eat. <lb/></s>

<s>Ignis quo<lb/>modo atte<lb/>nuet.</s>

<s><margin.target id="marg118"/>Di&longs;tillatio<lb/>nis v&longs;us & <lb/>genera.</s>

<s id="id000291">Ex hoc &longs;equitur quòd: Quælibet duæ quantitates quarum ag<lb/><arrow.to.target n="marg42"/><lb/>gregatum e&longs;t idem ad eam quantitatem, componunt eandem pro<lb/>portionem.</s>

<s><margin.target id="marg119"/>Ignis <expan abbr="nõ">non</expan> ve<lb/>rè attenuat.</s>

<s><margin.target id="marg120"/>Aquæ diflil<lb/>latæ an vires <lb/>habeant.</s>

<s>Sed ex his non leuis emergit dubitatio. <lb/></s>

<s id="id000293">Propo&longs;itio tertia decima.</s>

<s>Nam &longs;i ignis cuncta calefacit, &longs;iccátque, <lb/>omnes aquæ, quæ di&longs;tillatione habentur, <lb/>calidæ ac &longs;iccæ e&longs;&longs;e deberent. </s>

<s id="id000294">Proportio confu&longs;a aggregati primæ & tertiæ quatuor quantita<lb/>tum omiologarum ad <expan abbr="aggregat&utilde;">aggregatum</expan> &longs;ecundæ & quartæ, e&longs;t uelut com<lb/>po&longs;ita ex ei&longs;dem diui&longs;a per duplam.<lb/><arrow.to.target n="marg43"/></s>

<s>Nec repugnat <lb/>&longs;ub&longs;tantia, quòd aquea &longs;it: talis enim cùm <lb/>fit ardens, & vritur, & corpora humana <lb/>egregiè excalefacit, ac &longs;iccat. </s>

<s>Rur&longs;us aquæ <lb/>omnes frigidæ &longs;unt ac humidæ, vincente <lb/>&longs;ub&longs;tantia. </s>

<s>At neutrum &longs;emper verum e&longs;t, <lb/>imò aliquæ ex his &longs;imiliores &longs;unt his, à <lb/>quibus excipiuntur: vt ro&longs;àcea, odore, &longs;a<lb/>pore, viribus. </s>

<s id="id000296">Sint a ad b, ut c ad d, dico, quòd erit confu&longs;a <lb/><figure id="id.015.01.032.2.jpg" xlink:href="015/01/032/2.jpg"/><arrow.to.target n="table11"/><lb/>proportio a c aggregati ad <expan abbr="aggregat&utilde;">aggregatum</expan> b d, com<lb/>po&longs;itæ ex his proportionibus diui&longs;æ per du<lb/>plam æqualis. </s>

<s>Vrceus aquæ plantaginis <lb/>fluentem vndequaque &longs;anguinem &longs;i&longs;tere po<lb/>te&longs;t. </s>

<s id="id000297">Erit enim aggregati ex a c ad aggregatum ex b d, ue<lb/>lut a ad b per 18 quinti Elementorum. </s>

<s id="id000298">Sed proportiones a ad b, <lb/>& c ad d componunt proportionem producti a in d, & c in b per <lb/>octauam harum, ad <expan abbr="product&utilde;">productum</expan> ex b in d, productum uerò ex a in d <lb/>e&longs;t æquale producto ex b in c per decimam &longs;extam &longs;exti Elemento<lb/>rum, & proportio producti ex b in c ad productum ex b in d e&longs;t ue <lb/>lut c ad d, quare ut aggregati a c ad aggregatum b d, igitur propor<lb/>tio compo&longs;ita ex a ad b, & c ad d, e&longs;t uelut confu&longs;a bis &longs;umpta. </s>

<s>Non idem facit lactucæ aqua, et&longs;i &longs;it <lb/>frigidior. </s>

<s id="id000299">Igi<lb/>tur confu&longs;a e&longs;t uelut compo&longs;ita diui&longs;a per duplam per modum un<lb/>decimæ huius.</s>

<s>Quidam nuper dum memoriam <lb/>augere niteretur, meli&longs;&longs;am triduo albo vino <lb/>infundit, inde leuiter expre&longs;&longs;o vino, aquam <lb/>di&longs;tillando collegit, cuius potu memoriam <lb/>recuperare vi&longs;us e&longs;t. </s>

<table>

<table.target id="table11"/>

<s>Sed cùm calidi e&longs;&longs;et ie<lb/>coris, bonam valetudinem penè funditus <lb/>euertit. </s>

<row>

<s>Atque hunc modum Chymi&longs;tæ vo<lb/>cant, &longs;tellas c&oelig;lo infigere. </s>

</row>

<s>Quæri igitur &longs;olet, an aquæ hæ proprias <lb/>vires retineant? </s>

<row>

<s>Diximus olim, dum de malo <lb/>medendi v&longs;u loqueremur, nullas e&longs;&longs;e vires, <lb/>quòd odore, & &longs;apore <expan abbr="de&longs;tituãtur">de&longs;tituantur</expan>. </s>

</row>

<s>Ab&longs;ynthij <lb/>enim aqua, nec <expan abbr="ab&longs;ynthi&utilde;">ab&longs;ynthium</expan> redolet nec amara <lb/>e&longs;t: imò quod mirum e&longs;t, &longs;ubdulcis. </s>

<row>

<s><expan abbr="Ard&etilde;s">Ardens</expan> ta<lb/>men, vt ro&longs;aceam præteream, <expan abbr="fid&etilde;">fidem</expan> facit ine&longs;&longs;e <lb/>vim aquis. </s>

</row>

<s>Nam &longs;i talem ob ignem e&longs;&longs;e di<lb/>cas, qui e&longs;t quòd nulla aliarum talis &longs;it? <lb/></s>

<row>

<s>Nam hæc egregiè calefacit, &longs;iccat, pene<lb/>trat, acutum olet, ardet. </s>

</row>

<s>Itaque vires aquis <lb/>iam ine&longs;&longs;e certum e&longs;t, &longs;ed nec omnibus, nec <lb/>æquas. </s>

</table>

<s>Quæcunque enim res tenuem &longs;ub<lb/>&longs;tantiam habent frigidæque iunctam, aquam <lb/>emittunt &longs;ibi non ab&longs;imilem, vt ro&longs;a. </s>

<s id="id000300">Propo&longs;itio quarta decima.</s>

<s>Quæ <lb/>verò tenuem & calidam &longs;imilem &longs;ed vren<lb/>tem emittunt, vt vinum, & metallicorum <lb/>quædam. </s>

<s id="id000301">Proportiones confu&longs;æ, & coniunctæ in tribus quantitatibus in<lb/>uicem commutantur.</s>

<s>Quæ cra&longs;&longs;am & calidam, di&longs;&longs;imilem <lb/>& prauam, vt ab&longs;ynthium. </s>

<s>quæ cra&longs;&longs;am ac <lb/>frigidam, di&longs;&longs;imilem, &longs;ed non prauam, vt cu<lb/>curbitæ. </s>

<s id="id000302">Sint tres quantitates, dico, quod proportio c </s>

<s>Iuxta hanc rationem vires aqua-<pb xlink:href="016/01/033.jpg" pagenum="384"/>rum, quæ leui excipiuntur igne facilè perdi&longs;<lb/>ces. </s>

<s>Nam quæ vehementi igne indigent, om<lb/>nes &longs;iccant vehementer, plerunque etiam <lb/>excalefaciunt. </s>

<s id="id000303"><arrow.to.target n="marg44"/><lb/>ad a b confu&longs;a e&longs;t, conuer&longs;a coniunctæ a & b ad <lb/><arrow.to.target n="marg45"/><lb/>c. </s>

<s id="id000304">Nam per dicta proportio a b ad c efficit con<lb/>iunctam ex a b ad c: &longs;ed c ad a b conuer&longs;a e&longs;t eius, quæ e&longs;t a b ad c, & <lb/>proportio c ad a b e&longs;t confu&longs;a eius, quæ e&longs;t c ad a & b. </s>

<s id="id000305">Igitur pro<lb/>portio confu&longs;a in tribus quantitatibus e&longs;t contraria coniunctæ in <lb/>ei&longs;dem.</s>

<s><margin.target id="marg121"/>An &longs;it po&longs;&longs;i<lb/>bile facere <lb/>aquam quæ <lb/>in multa &longs;e<lb/>cula vitam <lb/>pror<gap/>et.</s>