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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
| children |
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<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info> <author>Monantheuil, Henri de</author> <title>Aristotelis Mechanica</title> <date>1599</date> <place>Paris</place> <translator></translator> <lang>la</lang> <cvs_file>monan_mecha_035_la_1599.xml</cvs_file> <cvs_version></cvs_version> <locator>035.xml</locator> </info> <text> <front> <section> <pb xlink:href="035/01/001.jpg"></pb> <p type="head"> <s id="id.000001">ARISTOTELIS <lb></lb>MECHANICA <lb></lb>Græca, emendata, Latina facta, & <lb></lb>Commentariis illuſtrata. <lb></lb></s> <s id="id.000002">AB <lb></lb><emph type="italics"></emph>HENRICO MONANTHOLIO <lb></lb>Medico, & Mathematicarum artium <lb></lb>Profeſſore Regio. </s> <s><emph.end type="italics"></emph.end><lb></lb>A D <lb></lb>HENRICVM IIII. GALLIÆ & NAVARRÆ <lb></lb>Regem Chriſtianiſsimum. </s> </p> <figure id="id.035.01.001.1.jpg" xlink:href="035/01/001/1.jpg"></figure> <p type="head"> <s id="id.000003">PARISIIS, <lb></lb>Apud IEREMIAM PERIER via Iacobæa, ſub ſigno Bellerophontis. </s> </p> <p type="head"> <s id="id.000004">M. D. XCIX. <lb></lb><emph type="italics"></emph>CUM PRIVILEGIO REGIS. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/002.jpg"></pb> <pb xlink:href="035/01/003.jpg"></pb> <figure id="id.035.01.003.1.jpg" xlink:href="035/01/003/1.jpg"></figure> <p type="head"> <s id="id.000005">HENRICO IIII. <lb></lb>GALLIÆ ET NAVARRÆ <lb></lb>REGI CHRISTIANISSIMO. <lb></lb>S. P. D. </s> </p> <p type="main"> <s id="id.000006">Ecce maieſtati tuæ, <lb></lb>Rex Chriſtianiſſime, <lb></lb>nouum <expan abbr="fructũ">fructum</expan>, & tan<lb></lb>quam primitias tuæ à te <lb></lb>nuper reſtitutæ Acade<lb></lb>miæ, Mechanica Ari<lb></lb>ſtotelis philoſophorum principis Grę<lb></lb>ca, emendata, Latina facta, & commen<lb></lb>tariis illuſtrata offero, dico, conſecro. <lb></lb></s> <s id="id.000007">Noli, obſecro te, ad Mechanicorum ti<lb></lb>tulum munus hoc, quaſi minus inge<lb></lb>nuum, nec ſatis liberali ingenio, nedum <lb></lb>imperatorio & regali dignum, ſubhor<lb></lb>reſcere, & ex prima iſta <expan abbr="frõte">fronte</expan> deſpicere. <lb></lb></s> <s id="id.000008"><expan abbr="Ferũt">Ferunt</expan> Platonem, quo philoſophorum <pb xlink:href="035/01/004.jpg"></pb>nemo de Deo diuinius, <expan abbr="neq;">neque</expan> ſanctius <expan abbr="sẽſit">sen<lb></lb>ſit</expan>, <expan abbr="cũinterrogaretur">cum interrogaretur</expan>, quid ageret Deus, <lb></lb>reſpondiſſe <foreign lang="el">a)ei gewmetrei=n. </foreign></s> <s id="id.000009">Hoc verbum Lati<lb></lb>nè expreſſum ſignificat, Aſſiduè terram <lb></lb>metiri. </s> <s id="id.000010">Quæ actio ſi ſimpliciter ſpecte<lb></lb>tur, & à Geometrię nomine ridiculo, vt <lb></lb>alibi appellat Plato, <expan abbr="expẽdatur">expendatur</expan>, ridicula, <lb></lb>& Dei maieſtate indigna iudicabitur. <lb></lb></s> <s id="id.000011">Sed ſi ex ipſius artis viribus, & magnifi<lb></lb>cis promiſſis illud <foreign lang="el">a)ei gewmetrei=n</foreign> æſtimetur, <lb></lb>quod eſt vniuerſi <expan abbr="quãtumuis">quantumuis</expan> fusè <expan abbr="latéq;">latéque</expan> <lb></lb>patentis, <expan abbr="corporũ">corporum</expan> in eo omnium, ſuper<lb></lb>ficierum, linearum, <expan abbr="omniúmq;">omniúmque</expan> menſu<lb></lb>rabilium <expan abbr="mẽſuram">menſuram</expan> ratione, proportio<lb></lb>ne, ſimilitudine conſtituere, deſignare, <lb></lb>permetiri: actio certè erit tantò priore <lb></lb>nobilior: quantò totum <expan abbr="finitũ">finitum</expan> quidem, <lb></lb>ſed infinito perſimile exigua, & infima <lb></lb>ſui parte eſt nobilius, & excellentius: & <lb></lb>qui <expan abbr="hãc">hanc</expan> actionem accurate ponderibus <lb></lb>librarit ſuis, <expan abbr="nequaquã">nequaquam</expan> indignam, circa <lb></lb>quam Deus verſetur, & ſeſe occupet, iu<lb></lb>dicabit. </s> <s id="id.000012">Verumenimuerò ſi ad illud <foreign lang="el">a)ei gew<lb></lb>metrei=n</foreign> addiſſet Plato, <foreign lang="el">kai\ a)ei mhxana=sqai,</foreign> luculen<pb xlink:href="035/01/005.jpg"></pb>tius multò meo iudicio, & diuinæ maie<lb></lb>ſtati congruentius, <expan abbr="atq;">atque</expan> magnificentius <lb></lb>reſpondiſſet. </s> <s id="id.000013">Quid enim eſt Mundum <lb></lb>hunc ex nihilo condidiſſe: ſuis omnibus <lb></lb>numeris abſoluiſſe: ponderibus <expan abbr="vndiq;">vndique</expan> <lb></lb>ſuis æquilibraſſe: longitudine, latitudi<lb></lb>ne, altitudine, in omni habitudine, & <lb></lb>reſpectu commenſurauiſſe: eundém<lb></lb>que in eodem ſtatu & perfectione aſſi<lb></lb>duò retinere, ſtabilire, conſeruare, quam <lb></lb><foreign lang="el">a)ei gewmetrei=n kai\ a)eimhxana=sqai?</foreign> Mundus enim <lb></lb>hic machina eſt, & quidem machina<lb></lb>rum maxima, efficaciſſima, firmiſſima, <lb></lb>formoſiſſima. </s> <s id="id.000014">An non omnia corpora <lb></lb>complectitur, quod eius <expan abbr="immẽſitatem">immenſitatem</expan> <lb></lb>arguit? </s> <s id="id.000015">An <expan abbr="nõ">non</expan> ad omnium mutabilium <lb></lb>lationem, alterationem, generationem, <lb></lb>auctionem, conſeruationem, & <expan abbr="durationẽ">dura<lb></lb>tionem</expan>, vt Dei ſui auctoris <expan abbr="inſtrumẽtum">inſtrumentum</expan> <lb></lb>concurrit, quod eius vim, & efficaciam <lb></lb>oſtendit? </s> <s id="id.000016">An non quinquies mille <expan abbr="quingẽtos">quin<lb></lb>gentos</expan> ſexaginta & <expan abbr="vnũ">vnum</expan> annos, quoad ſui <lb></lb><expan abbr="quinq;">quinque</expan> partes primas, & ſimplices, per<lb></lb>ſeuerat omnis mutationis expers: quod <pb xlink:href="035/01/006.jpg"></pb>eius <expan abbr="firmitatẽ">firmitatem</expan> pluſquam adamantinam <lb></lb>teſtatur? </s> <s id="id.000017">An non huius totius ad omnes <lb></lb>ſuas partes, & omnium <expan abbr="ſuarũ">ſuarum</expan> partium, <lb></lb>particularum que cum inter ſe, tum ad <lb></lb>ipſum ſummus eſt conſenſus, conſpira<lb></lb>tio ſumma, omnium hominum oculis <lb></lb>& menti iucundiſsima ſymmetria, pro<lb></lb>portio, æquabilitas, vnà cum totius fi<lb></lb>gura pulcherrima, & conuenientiſſima, <lb></lb>quæ vnica eſt ſuperficie terminata pari<lb></lb>bus ab vno puncto vndique diſtante <lb></lb>interuallis, & cum tot <expan abbr="aſtrorũ">aſtrorum</expan> tanquam <lb></lb>gemmarum pretioſiſſimarum hîc illîc <lb></lb>in eminentiori, & apparentiori ſui par<lb></lb>te collocatorum perenni luce, qua qua<lb></lb>litate nec formoſior, nec <expan abbr="hominũ">hominum</expan> ocu<lb></lb>lis gratior, nec vſibus humanis vtilior <lb></lb>apparere poteſt: quod eius pulchritudi<lb></lb>nem vbique oſtentat, & mirabiles ſui <lb></lb>ipſius amores excitat? </s> <s id="id.000018">Deus igitur, <expan abbr="pręterquã">pręter<lb></lb>quam</expan> quod eſt accuratiſſimus, <expan abbr="aſſiduuſq;">aſſiduuſque</expan> <lb></lb>Geometra, diuini Platonis <expan abbr="ſentẽtia">ſententia</expan>, eſt <lb></lb>etiam noſtra, & operum tot magnifi<lb></lb>corum euidentia, ſapientiſſimus, opti<pb xlink:href="035/01/007.jpg"></pb>mus, potentiſſimus <foreign lang="el">mhxaniko\s,</foreign> & <foreign lang="el">mhxanopoio\s. </foreign><lb></lb></s> <s>Ipſe idem, qui <foreign lang="el">makro/kosmon</foreign> magnum mun<lb></lb>dum fecit, fecit & <foreign lang="el">mikro/kosmon</foreign> <expan abbr="paruũ">paruum</expan> mun<lb></lb>dum, hominem ſcilicet: & fecit ad ima<lb></lb>ginem ſuam, atque vt ſe imitaretur beni<lb></lb>gniſſima liberalitate impertitus eſt ei <lb></lb>mentem, quæ eſſet <foreign lang="el">te/xnh te/xnwn,</foreign> ars artium, <lb></lb>& manum, quæ eſſet <foreign lang="el">o)/rganon o)rga/nwn,</foreign> inſtru<lb></lb>mentum inſtrumentorum, quibus ho<lb></lb>mo, quem volebat eſſe ſapientiſſimum <lb></lb>animalium, machinas & inſtrumenta <lb></lb>alia fabricaretur, & iis adiutus ſolus, vel <lb></lb>cum paucis onera quantumuis ingentia <lb></lb>dimoueret, deduceret, quo vellet collo<lb></lb>caret: vrbes, <expan abbr="tẽpla">templa</expan>, palatia, collegia, por<lb></lb>ticus, pontes, domos ædificaret, perde<lb></lb>ret, reſtauraret, conſeruaret: terram ver<lb></lb>teret, in terræ viſcera deſcenderet, terræ <lb></lb>campos, valles, montes bigis, quadrigis <lb></lb>peragraret: maria omnia, fluuios remis, <lb></lb>velis tranaret: ventis imperaret: anima<lb></lb>lium genus omne ſibi ſubiiceret: tantas <lb></lb><expan abbr="deniq;">denique</expan>, & tam multas res faceret, vt eas, <lb></lb>niſi quotidie fieri, & factas eſſe ſæpius <pb xlink:href="035/01/008.jpg"></pb>alij homines ſpectarent, omninò fieri <lb></lb>non poſſe iurarent. </s> <s id="id.000019">Iidem cum facta<lb></lb>rum rationes, virium que in inſtrumen<lb></lb>tis, & machinis adhibitis cauſas non in<lb></lb>telligunt, miracula eſſe pleno ore pro<lb></lb>clamant. </s> <s id="id.000020">Vnde fortè illud Martialis. </s> </p> <p type="main"> <s id="id.000021"><emph type="italics"></emph>Barbara Pyramidum ſileat miracula <lb></lb>Memphis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000022">Tum ſeptem illa, quæ vulgò iactantur <lb></lb>orbis miracula. </s> <s id="id.000023">Quæ profectò ſapien<lb></lb>ter Deus homini dedit & poſſe, & fa<lb></lb>bricari: ne mundum hunc à ſe <expan abbr="cõditum">conditum</expan>, <lb></lb>conſeruatum, conſeruandum, quandiu <lb></lb>voluerit, hominibus foret incredibile. <lb></lb></s> <s id="id.000024">His enim tantis, & tam multis quæ ab <lb></lb>homine <foreign lang="el">mhxanopoihtikw=|</foreign> manifeſtè & in om<lb></lb>nium oculis fiunt, & conſeruantur, fa<lb></lb>cillimum eſt, quiſquis mentem habet, <lb></lb>credere, cognoſcere, complecti, etiam ſi <lb></lb>cum fieret, abfuerit, mundum <expan abbr="hũc">hunc</expan>, <expan abbr="maximũ">ma<lb></lb>ximum</expan> certè operum opus, factum eſſe, <lb></lb>& conſeruari: non autem ab vllo homi<lb></lb>ne, ſed ab alio <foreign lang="el">mhxanopoihtikw=|</foreign> tantò homi<lb></lb>nem præſtantia, ſapientia, potentia, imò <pb xlink:href="035/01/009.jpg"></pb>infinitè ſuperante: quantò hæc mundi <lb></lb>machina omnium hominum etiam Ar<lb></lb>chimedeorum machinas ſuperat, atque <lb></lb>antecellit. </s> <s id="id.000025">Hic autem quis poteſt eſſe <lb></lb>alius, præterquam is, quem Deum om<lb></lb>nes appellamus. </s> <s>Sed & ex eo fit perquam <lb></lb>credibile, ad huius magnæ molis archi<lb></lb>tecturam <expan abbr="architectũ">architectum</expan> ſuum nihil eguïſſe <lb></lb>ferramentis, vecte, cuneis, trochleis, axe <lb></lb>in peritrochio, molitione, conatu, quæ <lb></lb>impius iſte Velleius ex Epicuri ſenten<lb></lb>tia apud Ciceronem diſputans ſtultè re<lb></lb>quirebat. </s> <s id="id.000026">In quo enim immenſus ille au<lb></lb>thor, factorque hominis, in proprij <lb></lb>operis fabrica homini ipſi præpolleret, <lb></lb>ſi machinis, & inſtrumentis, materia, & <lb></lb>molimine, vt homo, indigeret? </s> <s id="id.000027">quan<lb></lb>quam poſt ſemel à ſe mundum ex nihilo <lb></lb>creatum, ille liberrimum ſemper, & po<lb></lb>tentiſſimum agens, cum his adiunctis, <lb></lb>& ſine his quando, quotieſque vult, ni<lb></lb>hilominus operatur. </s> <s id="id.000028">Quæ ſi rectè & ve<lb></lb>rè Deo, <expan abbr="quantũ">quantum</expan> fas eſt homini, dicta <lb></lb>ſunt: ecquid iam ſupereſt, Rex Chriſtia<pb xlink:href="035/01/010.jpg"></pb>niſſime, quapropter ab hoc munere vt <lb></lb>vili abhorreas, & ipſe reformidem, licet <lb></lb>Mechanicorum <expan abbr="titulũ">titulum</expan> in frontiſpicio <lb></lb>gerat, hoc adeò inſigne opus ab Ari<lb></lb>ſtotele profectum, vtile, <expan abbr="iucũdum">iucundum</expan>, ſub<lb></lb>tiliſſimè tractatum: ſed temporum iniu<lb></lb>ria multis mendis fœdum, obſcurum, <lb></lb>captu difficile, nunc opera noſtra niti<lb></lb>dum, clarum, & captu facile ſanctæ ma<lb></lb>ieſtati tuæ dicare, ac <expan abbr="cõſecrare">conſecrare</expan>? </s> <s id="id.000029">Ad quod <lb></lb>faciendum inſuper me inuitauit cauſa <lb></lb>alia, niſi me fallit animus, iuſtiſſima. <lb></lb></s> <s id="id.000030">Quiſquis enim duas res omnium, quæ <lb></lb>ſunt in vita <expan abbr="hominũ">hominum</expan>, maximas perfecit, <lb></lb>quarúmque temporibus atque fabricis <lb></lb>ſummus eſt & frequentiſſimus machi<lb></lb>narum, & <expan abbr="inſtrumẽtorum">inſtrumentorum</expan> vſus: ille non <lb></lb>poteſt machinamentorum, & <expan abbr="inſtrumẽtorum">inſtru<lb></lb>mentorum</expan> formis, rationibus, adinuen<lb></lb>tionibus, & virium <expan abbr="eorũ">eorum</expan> admirabilium, <lb></lb><expan abbr="incredibiliumq;">incredibiliumque</expan> cauſis, ac principiis per<lb></lb>ceptis non magnopere delectari, atque <lb></lb>eos, qui de iis ſubtiliter, & ingeniose tra<lb></lb>ctarint, libros oblatos non gratiſſimè <pb xlink:href="035/01/011.jpg"></pb>excipere: tu, Rex potentiſſime, duas il<lb></lb>las res perfeciſti, bellum ſcilicet, & pa<lb></lb>cem. </s> <s id="id.000031">In vtriuſque tempore aſſiduus ma<lb></lb>chinarum, & inſtrumentorum vſus, at<lb></lb>que opportunitas. </s> <s id="id.000032">Tu namque bellum <lb></lb>( hîc me patiare, rex potentiſſime, in me<lb></lb>ritas aliquot tuas laudes paulò amplius, <lb></lb>non extra rem tamen excurrere, & ex<lb></lb>patiari. ) Tu inquam bellum ( ô onus <lb></lb><foreign lang="el">kolossikw/taton,</foreign> grauiſſimum certè, & num<lb></lb>quam ſi fieri poſſet, commouendum: <lb></lb>vbi, vbi tamen neceſſarium eſt, mouen<lb></lb>dum, ſuſcipiendum, gerendum ) ad<lb></lb>uerſus domeſticos inſanientes, rebel<lb></lb>leſque: aduerſus extraneos intraneo<lb></lb>rum tumultu ſuperbientes, ferocien<lb></lb>tes, & occaſionem regni inuadendi <lb></lb>opportuniſſimam nactoş & nihil non <lb></lb>inde ſibi pollicitiş animo pluſquam <lb></lb>Herculeo ſuſcepiſti: hoc ipſum, li<lb></lb>cet omnium bellorum, quorum hi<lb></lb>ſtorias, & annales noſtros legens me<lb></lb>miniſſe mihi videor, acerbiſſimum, <pb xlink:href="035/01/012.jpg"></pb>pernitioſiſſimum, exitioſiſſimumque, <lb></lb>plurium intus & foris contentione, & <lb></lb><expan abbr="cõiuratione">coniuratione</expan> viſum inſuperabile, moui<lb></lb>ſti, geſſiſti, ſuperauiſti. </s> <s id="id.000033">Quomodo <expan abbr="autẽ">autem</expan>? <lb></lb></s> <s id="id.000034">dicam pro meo ſenſu: tu melius. </s> <s id="id.000035">Omnes <lb></lb>omnium tuarum prouinciarum ſubie<lb></lb>ctos rebelles, partim armis, quæ fuit tua <lb></lb>in pugnando terribilis ſemper inimicis <lb></lb>& audacia, & fortitudo: partim auro ex <lb></lb>propriis eorum fodinis effoſſo, recto <lb></lb>ſanè iudicio, quæ tua fuit ſumma cum <lb></lb>prudentia iuſticia, vt in poſterum ſciant <lb></lb>ſuis à Deo datis obtemperare regibus, <lb></lb>neque vnquam ab illorum contrariis <lb></lb>ſtare partibus: partim benignitate, & <lb></lb>manſuetudine, quæ te ſuperis pulcher<lb></lb>rima æquat virtus. </s> </p> <p type="main"> <s id="id.000036"><emph type="italics"></emph>Nam<emph.end type="italics"></emph.end> ( vt ait grauis vnus è poëtis ) <emph type="italics"></emph>cum <lb></lb>vincamur in omni<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000037"><emph type="italics"></emph>Munere: ſola Deos æquat clementia nobis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000038">Ad concordiam inter ſe, & tecum ſer<lb></lb>uandam: ad beneuolentiam erga te præ<lb></lb>ſtandam, obedientiam, fidelitatem rede<lb></lb>giſti. </s> <s id="id.000039">Extraneos verò longo bello: bre<pb xlink:href="035/01/013.jpg"></pb>uiori tamen, quam ſperare, aut promit<lb></lb>tere nobis auſi fuerimus, fractos, ſæpe <lb></lb>Marte aperto, & manibus <expan abbr="vtrinq;">vtrinque</expan> con<lb></lb>ſertis victos, fugatos, tandem procul <lb></lb>ab omnibus Galliæ finibus reieciſti: & <lb></lb>quanquam anteà ſemper ab omni pacis <lb></lb>conditione alieniſſimos, vt pacem ipſi <lb></lb>appeterent, & peterent coëgiſti. </s> <s id="id.000040">Quid <lb></lb>tu ilico? </s> <s id="id.000041">Quandoquidem pax victo ſem<lb></lb>per ſit neceſſaria, & victori ea, quæ nihil <lb></lb>poſt ſe ferat inſidiarum, ſemper expe<lb></lb>diat: ſtatim eius ineundæ, & cum <expan abbr="potẽtiſſimo">po<lb></lb>tentiſſimo</expan> hoſte Philippo Hiſpaniarum <lb></lb>rege conciliandæ <expan abbr="occaſionẽ">occaſionem</expan> quæſitam, <lb></lb>& oblatam à Clemente VIII. pontifice <lb></lb>ſummo, verè vtriuſque gentis commu<lb></lb>ni <expan abbr="parẽte">parente</expan> clementiſſimo, per ſuum lega<lb></lb>tum Alexandrum de Medicis Cardina<lb></lb>lem, & Archiepiſcopum Florentinum, <lb></lb>qui huic paci tractandæ, conficiendæ, <lb></lb>& niſi perfecta re <expan abbr="nõ">non</expan> relinquendæ ſem<lb></lb>per interfuit, & quaſi præfuit, arripui<lb></lb>ſti. </s> <s id="id.000042">Duobus e tuo ſanctiore conſilio de<lb></lb>lectis conſiliariis tibi, id eſt patriæ <pb xlink:href="035/01/014.jpg"></pb>ſaluti addictiſſimis ( permittes bona tua <lb></lb>venia, Rex clementiſſime, honoris & <lb></lb>gratæ erga viros tam bene de te, totaque <lb></lb>Gallia meritos memoriæ noſtræ gratia, <lb></lb>hîc illos nominari ) Pomponio Belle<lb></lb>ureo & Nicolao Brulartio, toto tantæ <lb></lb>molis negotio per te commiſſo, pacem <lb></lb>tibi, tuis, toti Galliæ honorificentiſſi<lb></lb>mam conciliauiſti: pacem inquam ab<lb></lb>ſentem, & ad multos annos exulem re<lb></lb>duxiſti: iureiurando ſolemniſſimo, ſi<lb></lb>gillis vtriuſque regni confirmatam per <lb></lb>præcones tuos proclamari iuſſiſti: arma <lb></lb>de manibus militum, quæ erant ſumpta <lb></lb>pro te, & contra te ſuſtuliſti: iam tuo<lb></lb>rum in ligones, aratrorum dentes, fal<lb></lb>ces, vngues ferreos, vectes, trochleas, <lb></lb>malleos, aliaque inſtrumenta vitæ mi<lb></lb>tioris, & pacificæ conuertiſti: iam arua <lb></lb>feracis Galliæ recoli cœpta, vbique re<lb></lb>uireſcunt: lætæ ſegetes, agri vberes cul<lb></lb>mis ariſtiſque luxuriant: ex ædificijs ſe<lb></lb>miruta reſtaurantur, dirutorum loco <lb></lb>noua ſtatuuntur: leges liberè pronun<pb xlink:href="035/01/015.jpg"></pb>ciant: iuſticia libritenens fide zygoſtati<lb></lb>ca omnia iudicat: linguarum & bona<lb></lb>rum <expan abbr="artiũ">artium</expan>, te earum reſtauratore, & vin<lb></lb>dice & cuſtode, eruditio in <expan abbr="Academiã">Academiam</expan> <lb></lb>reuerſa frequentatur: ingenia, quæ in ea <lb></lb>ſunt præclara, in variarum artium iam <lb></lb>redundant elegantiam, fœtuſque ſuos <lb></lb>producere geſtiunt: mercatura denique <lb></lb>tutò vagatur, peregrinatur, ruſticatur. <lb></lb></s> <s id="id.000043">Harum duarum rerum belli, & pacis <lb></lb>magnitudinem, <expan abbr="difficultatẽ">difficultatem</expan>, <expan abbr="impedimẽta">impedimen<lb></lb>ta</expan> ſoli <expan abbr="cõplectentur">complectentur</expan>, quitam diſſociatas <lb></lb>Gallorum & Hiſpanorum <expan abbr="volũtates">voluntates</expan>: <expan abbr="tã">tam</expan> <lb></lb>multa, & multiplici <expan abbr="ſimultatũ">ſimultatum</expan> <expan abbr="atq;">atque</expan> odio<lb></lb>rum crudelitate ſauciatas: tot mordaci<lb></lb>bus dictis, ſcriptis, factis in ſeſe mutuis <lb></lb>exulceratas: tam deiecta, <expan abbr="atq;">atque</expan> perturbata <lb></lb>omnia ipſi ſuis oculis viderunt. </s> <s id="id.000044"><expan abbr="Nã">Nam</expan> qui <lb></lb><expan abbr="nõ">non</expan> <expan abbr="viderũt">viderunt</expan>, licet ab alijs recitata <expan abbr="audiãt">audiant</expan>, <lb></lb>aut <expan abbr="monumẽtis">monumentis</expan> <expan abbr="cõmẽdata">commendata</expan> <expan abbr="legãt">legant</expan>, non ar<lb></lb>bitror <expan abbr="tamẽ">tamen</expan> vllius vlla <expan abbr="quantũuis">quantumuis</expan> elegan<lb></lb>ti, & probabili narratione adduci poſſe, <lb></lb>vt <expan abbr="credãt">credant</expan>, quando <expan abbr="quidẽ">quidem</expan> nos, qui hæc vi<lb></lb>dimus, ſi <expan abbr="quãdo">quando</expan> in <expan abbr="memoriãreducimus">memoriam reducimus</expan>, <pb xlink:href="035/01/016.jpg"></pb>mera ſomnia videre nobis videmur: <lb></lb>Quid igitur abſurdum? </s> <s id="id.000045">quidve inele<lb></lb>gans facimus? </s> <s id="id.000046">ſi tibi qui cum tanta glo<lb></lb>ria hæc duo perfeceris, de pacis & belli <lb></lb>inſtrumentis, vel potius de horum in<lb></lb>ſtrumentorum viribus, & virium cau<lb></lb>ſis, &, quod admirabilius, vno <expan abbr="earũ">earum</expan> prin<lb></lb>cipio, quod eſt circulus, librum offeri<lb></lb>mus? </s> <s id="id.000047">qui te præterea videamus magni<lb></lb>ficis ædificiorum ſubſtructionibus, ita <lb></lb>delectari, vt nihil, <expan abbr="nõ">non</expan> dicam nunc, cum <lb></lb>ſint hæc pacis opera: ſed etiam in ipſo <lb></lb>belli flagrantiſſimi ardore, ab ijs auocare <lb></lb>aut retardare potuerit. </s> <s id="id.000048">Porticus diues, <lb></lb>ſuperba, amuſſitata, quæ à tua Lupara <lb></lb>ad tuas ædes lateritias te, <expan abbr="tuoſq;">tuoſque</expan> delatura <lb></lb>& illinc ad <expan abbr="vrbẽ">vrbem</expan> deſuper ventura, te <expan abbr="inuẽtore">in<lb></lb>uentore</expan>, & excogitatore, tuis ſumptibus <lb></lb>extruitur: Ædium lateritiarum cochlea<lb></lb>ri ſcalę, octauo orbis miraculo <expan abbr="colophõ">colophon</expan> <lb></lb>impoſitus: Caſtella Fontisbellaquei, <lb></lb>Sanctogermani, Moncelli colophoni <lb></lb>ſuo proxima, nuper Reuerendiſſimo <lb></lb>Legato hinc in Italiam redeunti, nobi<pb xlink:href="035/01/017.jpg"></pb>liſſimis illis Hiſpanis, Flandriſque, qui <lb></lb>ad pacem iureiurando confirmandam <lb></lb>aduenerant, cum tua incredibili vo<lb></lb>luptate oſtentata, & eorum maiori ad<lb></lb>miratione ab illis ſpectata luculenter te<lb></lb>ſtantur, <expan abbr="atq;">atque</expan> <expan abbr="hãc">hanc</expan> animi tui <expan abbr="delectationẽ">delectationem</expan> <lb></lb>rege magnifico <expan abbr="digniſſimã">digniſſimam</expan> declararunt, <lb></lb>& viſuris, quotquot venient in poſte<lb></lb>rum, declarabunt. </s> <s id="id.000049">Spemque adferunt <lb></lb><expan abbr="nõmediocrem">non mediocrem</expan>, te, pro tuorum in Aca<lb></lb>demia profeſſorum collegio, quale edi<lb></lb>ta pro eo oratione à me deſcriptum <lb></lb>eſt: aut ab alio magnificentius deſcribe<lb></lb>tur, ædificando, aliquando eſſe cogitatu<lb></lb>rum, & perfecturum. </s> <s id="id.000050">Hæc igitur mihi <lb></lb><expan abbr="perſuaſerũt">perſuaſerunt</expan>, ne quicquam vererer opus <lb></lb>hoc, ratione opellæ <expan abbr="qualiſcunq;">qualiſcunque</expan> noſtræ, <lb></lb>exiguum ſcio: ſed ratione authoris ſui, <lb></lb>Ariſtotelis, magnum, ſanctæ maieſtati <lb></lb>tuæ conſecrare. </s> <s id="id.000051">Quod <expan abbr="nũc">nunc</expan> igitur tam lu<lb></lb>benter facio: quam Deum <expan abbr="optimũ">optimum</expan> ma<lb></lb>ximum obnixè precor, vt vitam tibi <lb></lb>impertiat, in duas annorum quadrage<lb></lb>narias ita partitam vt ſecundam, quam <pb xlink:href="035/01/018.jpg"></pb>belli reliquiis, & pace in ea confectis fœ<lb></lb>liciter ingreſſus es, tot rebus pacis tam <lb></lb>magnificis, & glorioſis adhuc aggre<lb></lb>diundis, & perficiundis conſumas: quot <lb></lb>in rebus belli admirabilibus, atque in<lb></lb>credibilibus perfectis primam conſum<lb></lb>pſiſti. </s> <s id="id.000052">Hoc, ſi tibi, Deo ita volente, eue<lb></lb>niat, haud profectò verendum erit di<lb></lb>cere, & palam, quod omnium hiſtoriæ <lb></lb>conteſtabuntur, proclamare, te <expan abbr="rerũ">rerum</expan> ad<lb></lb>mirabiliſſimarum regem, & regum, qui <lb></lb>hactenus in quacunque orbis regione <lb></lb>regnauere, fore præſtantiſſimum, & ad<lb></lb>mirabiliſſimum. </s> <s id="id.000053">Vale, & duas illas per<lb></lb>optatas annorum quadragenarias tibi, <lb></lb>& nobis ſic viue. </s> <s id="id.000054">Scriptum Lutetiæ eo <lb></lb>die, quo quinquennio ante à te ciui<lb></lb>tas Hiſpanis erepta, & ſuis ciuibus fœli<lb></lb>citer eſt reſtituta. </s> </p> <p type="main"> <s id="id.000055">MAIESTATIS</s> </p> <p type="main"> <s id="id.000056">Humillimus ſeruus</s> </p> <p type="main"> <s id="id.000057">HENRICVS MONANTHOLIVS. </s> </p> </section> <pb xlink:href="035/01/019.jpg"></pb> <section> <p type="head"> <s id="id.000058">A D <lb></lb>HENRICVM IIII. <lb></lb>GALLIÆ ET NAVARRÆ <lb></lb>Regem Chriſtianiſſimum. </s> </p> <p type="main"> <s id="id.000059"><emph type="italics"></emph>Pacatos fecit tua nos victoria ciues. <lb></lb></s> <s id="id.000060">Inde caput Laurus: digitos ornabit Oliua <lb></lb>Semper, & ingentem per vtrâque volabis Olympum. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.000061">THEODORICVS MONANTHOLII filius. </s> </p> <p type="head"> <s id="id.000062">De libro <foreign lang="el">tw=n mhxanikw=n,</foreign> Ariſtotele, <lb></lb>& Monantholio. </s> </p> <p type="main"> <s id="id.000063"><emph type="italics"></emph>Inter Ariſtotelis libros ſubtilior iſto<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000064"><emph type="italics"></emph>Nullus<emph.end type="italics"></emph.end> <foreign lang="el">*mhxanikw=n,</foreign> <emph type="italics"></emph>vtiliorque fuit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000065"><emph type="italics"></emph>Sed mendis fœdus merito ſine honore iacebat,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000066"><emph type="italics"></emph>Non authore ſuo dignus Aristotele. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000067"><emph type="italics"></emph>Lectus erat nulli, nulli intellectus agebat<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000068"><emph type="italics"></emph>Vitam cum blattis, muribus, & tineis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000069"><emph type="italics"></emph>Liber ab his, captu facilis, bene comptus en exit<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000070"><emph type="italics"></emph>In lucem, vigilis luce Monantholij. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000071"><emph type="italics"></emph>Sic dat Ariſtoteli vitam, claréque vicißim<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000072"><emph type="italics"></emph>Accipit ex ipſo, quam dedit ille, parem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000073"><emph type="italics"></emph>Vna dies ambos ſeruabit, & eximet æuo,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000074"><emph type="italics"></emph>Amborúmque ſimul fama ſuperſtes erit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000075">RICHARDVS MERCES</s> </p> <p type="main"> <s id="id.000076">Doct. Med. Pariſ. </s> </p> </section> <pb xlink:href="035/01/020.jpg"></pb> <section> <figure id="id.035.01.020.1.jpg" xlink:href="035/01/020/1.jpg"></figure> <p type="head"> <s id="id.000077">PRAEFATIO IN <lb></lb>MECHANICA ARISTO<lb></lb>TELIS, AD LECTOREM. </s> </p> <p type="main"> <s id="id.000078">Philosophari in vno rerum quo<lb></lb>libet genere, <expan abbr="cãdide">candide</expan> lector, res eſt per<lb></lb>quam dulcis. </s> <s id="id.000079">Philoſophari appello re<lb></lb>rum eſſentiam, cauſas, proprietates, <lb></lb>facultates inueſtigare, & inuento rum <lb></lb>quæ vtilia ſunt in opus ad vitæ homi<lb></lb>num fœlicius <expan abbr="degẽdæ">degendæ</expan> commoda edu<lb></lb>cere. </s> <s id="id.000080">Ita enim demum verè ille erit, vt ait poëta,</s> </p> <p type="main"> <s id="id.000081"><emph type="italics"></emph>Fœlix, qui poterit rerum cognoſcere cauſas. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000082">Alio qui inutilia, vel vtilia: ſed inutiliter id eſt ſine actio<lb></lb>ne vel opere, quę fines ſunt omnis <expan abbr="cõtemplationis">contemplationis</expan> vtilis, <lb></lb>contemplari, & in his philoſophando pluſquam paucis <lb></lb>commorari, parum omnino, aut nihil fœlicitatis in hac <lb></lb>rerum vniuerſitate habere arbitror. </s> <s id="id.000083">Verumenimuerò re<lb></lb>rum quia propemodum eſt infinita multitudo, licet ani<lb></lb>mus hominis ( quod eſt ab Ariſtotele dictum, & ita eſt, <lb></lb>poteſtate cognoſcendi, & vaſis inſtar ſpirituales rerum <lb></lb>formas recipiendi ) ſit omnia: vix tamen ita quiſquam <lb></lb>bene animo conſtitutus fuit, vt ipſum ad omnia genera <lb></lb>appellens in ſingulis excelleret, & magnum quid conſe<lb></lb>queretur: vt cuique tamen contigit maior: ita quo que <lb></lb>maiora conſecutus eſſe legitur. </s> <s id="id.000084">Pythagoram, Hippocra<lb></lb>tem medicum, Platonem, Ariſtotelem, Theophraſtum, <lb></lb>Galenum ſi non omnia tenuiſſe: quamplurima certè & <lb></lb>aliorum libri, & commentarij ab illis poſteritati relicti <lb></lb>copiosè loquuntur. </s> <s id="id.000085">Sed quibus non ita magnus vel fuit, <pb xlink:href="035/01/021.jpg"></pb>vel eſt animus, illi vel propenſione naturali, vel iudicio, <lb></lb>vel caſu aliquo de multis nonnulla ſeligunt, in quibus <lb></lb>tempus & operam non ſine vſura collocent ſuam. </s> <s id="id.000086">Om<lb></lb>nium, quæ ſunt, genera quatuor eſſe reperio, ſingula cer<lb></lb>tè digniſſima hominis contemplatione. </s> <s id="id.000087">Diuina, cœle<lb></lb>ſtia, elementaria, artificialia. </s> <s id="id.000088">In quorum ſingulis multos <lb></lb>excelluiſſe clarius eſt: quam vt cuiuſquam nominis com<lb></lb>memoratione opus ſit. </s> <s id="id.000089">Et certè diuina ſunt eiuſmodi, vt <lb></lb>licet ad eorum intuitum, ſicut ad Solis veſpertilionis: Ita <lb></lb>mentis noſtræ oculi caligent, ſi quis tamen diuinitatis <lb></lb><expan abbr="etiã">etiam</expan> exiguus repente, & ſubinde radius recipiatur & ocu<lb></lb>los ſubintret, plus voluptatis menti adferat: quam alio<lb></lb>rum quorumlibet plena cognitio. </s> <s id="id.000090">Quæ vna res adiuncto <lb></lb>contemplationis diuinorum fine ( quem Dei cognitio<lb></lb>nem, amorem, & cultum arbitror ) fecit, vt philoſophiæ <lb></lb>diuinorum quamplurimi homines totos ſeſe dediderint, <lb></lb>dedantque quotidie. </s> <s id="id.000091">Huic philoſophiæ proxima eſt cœ<lb></lb>leſtium & elementariorum id eſt <foreign lang="el">tou= makrokosmou=</foreign> mundi <lb></lb>ſcilicet huius, cuius ſine machinis fabrica in ſubſtantia, <lb></lb>magnitudine, figura, numero, ſitu, connexione, faculta<lb></lb>tibus, & vſu partium <expan abbr="omniũ">omnium</expan> ſui fabricatoris bonitatem, <lb></lb>ſapientiam, <expan abbr="potẽtiam">potentiam</expan>, ſumma iſthæc omnia arguit, & de<lb></lb>monſtrat. </s> <s id="id.000092">Luculentiſſimè inſuper oſtendit Deum, & eius <lb></lb>adminiſtram naturam ſine actione, ſine opere nuſquam <lb></lb>eſſe. </s> <s id="id.000093">Multò de his plura: quam de diuinis philoſophando <lb></lb>homines conſecuti ſunt, <expan abbr="neq;">neque</expan> ſine incredibili animorum <lb></lb>ſuorum voluptate, & innumerabili ad vſus humanos vti<lb></lb>litate. </s> <s id="id.000094">Nam cum hæc ita eſſe homines <expan abbr="deprehẽdiſſent">deprehendiſſent</expan>, vt <lb></lb>ad multò plures vſus, quam ad quos <expan abbr="ſpõtè">ſpontè</expan> nata eſſe com<lb></lb>perirentur, <expan abbr="trãsferri">transferri</expan> & aptati poſſent, <expan abbr="perciperentq;">perciperentque</expan> non <lb></lb>fruſtrà ſuis animis inſitas non <expan abbr="ſolũ">ſolum</expan> facultates iſta transfe<lb></lb>rendi & aptandi: ſed etiam congenita corporibus ſuis <expan abbr="inſtrumẽta">in<lb></lb>ſtrumenta</expan>, quibus vel ex ſe, vel à ſe factis <expan abbr="inſtrumẽtis">inſtrumentis</expan> tranſ<lb></lb>ferrent & aptarent, non ſola cognitione <expan abbr="cõtenti">contenti</expan> ad agen<lb></lb>dum ſe <expan abbr="contulerũt">contulerunt</expan>. </s> <s id="id.000095">Hinc quartum genus illud <expan abbr="rerũ">rerum</expan>, quas <lb></lb>diximus, artificialium emanauit, primùm vt credibile eſt <pb xlink:href="035/01/022.jpg"></pb>neceſſariarum, deinde <expan abbr="delectabiliũ">delectabilium</expan>, quod eò, imitatione <lb></lb>cœleſtium & <expan abbr="elemẽtariorũ">elementariorum</expan>, & in <expan abbr="horũ">horum</expan> nonnullis ſupera<lb></lb>tione proceſſit, vt homo qui manu mentis conſilio dire<lb></lb>cta tot & <expan abbr="tãta">tanta</expan>, quanta <expan abbr="nũc">nunc</expan> poſſidemus, peregerit, ab Ana<lb></lb>xagora quia haberet <expan abbr="manũ">manum</expan>, ſapientiſſimus fuerit iudica<lb></lb>tus. </s> <s id="id.000096">Ego <expan abbr="quoq;">quoque</expan> <expan abbr="potentiſſimũ">potentiſſimum</expan> <expan abbr="eadẽ">eadem</expan> de cauſa <expan abbr="iudicẽ">iudicem</expan>. </s> <s id="id.000097">quid <lb></lb>enim eſt, quod non ſuis vſibus accommodarit? </s> <s id="id.000098">quibus ſi <lb></lb><expan abbr="bonitatẽ">bonitatem</expan> exemplo Dei Opt. Max. ſemper <expan abbr="adiũxerit">adiunxerit</expan>, alte<lb></lb>rùm <expan abbr="quoq;">quoque</expan> <expan abbr="Deũ">Deum</expan> inter mortales eſſe dicere non recuſem. <lb></lb></s> <s id="id.000099">Eſt certè animus in homine ars <expan abbr="artiũ">artium</expan>. </s> <s id="id.000100">Inuenit enim om<lb></lb>nia, & manus <expan abbr="organũ">organum</expan> organorum. </s> <s id="id.000101">Facit enim omnia. </s> <s id="id.000102">Et ſi <lb></lb><foreign lang="el">mhxana=sqai</foreign> ſit moliri & excogitare quibus inſtrumentis <lb></lb>opus ad agendum <expan abbr="propoſitũ">propoſitum</expan> efficiatur, <foreign lang="el">mhxa/nhma</foreign> erit mo<lb></lb>litio & <expan abbr="inuẽtio">inuentio</expan> <expan abbr="inſtrumentorũ">inſtrumentorum</expan> ad opus. </s> <s id="id.000103">quæ cum ſine ra<lb></lb>tione non poſſint exiſtere, ratio <expan abbr="autẽ">autem</expan> vnius hominis pro<lb></lb>pria ſit, <foreign lang="el">mhxaniko\n</foreign> eſſe ſolius erit hominis, <expan abbr="quemadmodũ">quemadmodum</expan> <lb></lb>loqui, ratiocinari, & omnia quæ à Dei ſolo nutu, ſine ve<lb></lb>cte, ſine ferramentis, ſine machina vlla confecta & creata <lb></lb><expan abbr="sũt">sunt</expan>, molitione, machinatione & <expan abbr="inſtrumẽtis">inſtrumentis</expan> imitari, om<lb></lb>nia denique ad vſus ſuos transferre. </s> <s id="id.000104">Archimedes primus <lb></lb>cœlum, alteram mundi partem ampliſſimam & præſtan<lb></lb>tiſſimam, tanta arte vnius machinæ vitreæ artificio re<lb></lb>præſentauit, vt ſi Claudiano credimus, artificij elegantia <lb></lb>voluptatem & admirationem Ioui pepererit. </s> <s id="id.000105">Sed præſtat <lb></lb>elegantiſſimos huius poëtæ verſus recitare. </s> </p> <p type="main"> <s id="id.000106"><emph type="italics"></emph>Iuppiter, in paruo cum cerneret æthera vitro, <lb></lb>Riſit, & ad ſuperos talia dicta dedit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000107"><emph type="italics"></emph>Hoccine mortalis progreſſa potentia curæ? <lb></lb></s> <s id="id.000108">Iam meus in fragili luditur orbe labor. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000109"><emph type="italics"></emph>Iura poli, rerumque fidem, legeſque deorum <lb></lb>Ecce Syracuſius tranſtulit arte ſenex. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000110"><emph type="italics"></emph>Incluſus varijs famulatur ſpiritus aſtris, <lb></lb>Et viuum certis motibus vrget opus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000111"><emph type="italics"></emph>Percurrit proprium mentitus ſignifer annum, <lb></lb>Et ſimulata nouo Cynthia menſe redit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000112"><emph type="italics"></emph>Iamque ſuum voluens audax induſtria mundum<emph.end type="italics"></emph.end><pb xlink:href="035/01/023.jpg"></pb><emph type="italics"></emph>Gaudet, & humana ſidera mente regit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000113"><emph type="italics"></emph>Quid ſalſo inſontem tonitru Salmonea miror? <lb></lb></s> <s id="id.000114">AEmula naturæ parua reperta manus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000115">Sal monei huius falſum tonitru ſtatim in memoriam vo<lb></lb>cat, non iam falſa <expan abbr="hominũ">hominum</expan>, qui nunc viuunt tonitrua, <expan abbr="vibrataq;">vi<lb></lb>brataque</expan> è ſuis ſclopetis, <expan abbr="bõbardiſque">bombardiſque</expan> fulmina, ſoni frago<lb></lb>re, ictus conquaſſatione, & <expan abbr="pluriũ">plurium</expan> ſtrage non modo Iouis <lb></lb>fulmen imitantia: ſed longe ſuperantia. </s> <s id="id.000116">Quoties fulmen <lb></lb>ſuum mittit Iupiter aut <expan abbr="neminẽ">neminem</expan>, aut <expan abbr="vnũ">vnum</expan> atque alterum <lb></lb>præcipitat: hæc verò certo ictu ſemper deſtinata vrbium <lb></lb>mœnia deuaſtant: quot homines attingunt, perdunt, & <lb></lb><expan abbr="quidẽ">quidem</expan> tanta celeritate, tantáque vi, vt quę ab antiquis in<lb></lb>geniosè, vel ad oppugnandos hoſtes, vel ab his ſe <expan abbr="defendendũ">defen<lb></lb>dendum</expan> inuenta erant <expan abbr="inſtrumẽta">inſtrumenta</expan> bellica, Scorpiones, ca<lb></lb>tapultæ, baliſtæ, arietes, turres ambulatoriæ, teſtudines, <lb></lb>helepoles, fundæ, & reliqua eiuſmodi poliorcetica, præ <lb></lb>illis quaſi in <expan abbr="deſuetudinẽ">deſuetudinem</expan>, & <expan abbr="obliuionẽ">obliuionem</expan> abierint. </s> <s id="id.000117">Præclara <lb></lb>ſanè illa ſunt <foreign lang="el">mhxanh/mata,</foreign> ſi his homines vterentur <expan abbr="tantũ">tantum</expan>, <lb></lb>vt patria ab hoſtili ſeruitute liberetur, ſubacto hoſte fines <lb></lb>amplificentur, <expan abbr="adiũctis">adiunctis</expan> prouincijs <expan abbr="dilatẽtur">dilatentur</expan>, & ſic longè <lb></lb>laté que optimi regis dominatio <expan abbr="extẽdatur">extendatur</expan>. </s> <s id="id.000118">Vt veteribus <lb></lb>illis ſolis inſtructus cum Alexander parua hominum ad <lb></lb>30000 manu tot prouincias, tot regna, tot vrbes ſubegiſ<lb></lb>ſet, dictum ſit ab illo vtilius fuiſſe ſubigi: quam <expan abbr="regũ">regum</expan> <expan abbr="priſtinorũ">pri<lb></lb>ſtinorum</expan> inſulſa poteſtate diutius detineri. </s> <s id="id.000119"><expan abbr="Igniũ">Ignium</expan> vero cœ<lb></lb>leſtium, ſeu <expan abbr="aſtrorũ">aſtrorum</expan> lumina faces noſtræ ardentes <expan abbr="quantũ">quantum</expan> <lb></lb>vſibus humanis ſatis eſt, imitantur. </s> <s id="id.000120">Fontium <expan abbr="perẽnitates">perennitates</expan> <lb></lb>Heronis inuenta ſuppeditant, vt & Cteſibij hydraulica <lb></lb>inſtrumenta, & merulæ hominum voces <expan abbr="auiumq;">auiumque</expan> cantus <lb></lb>imitantes, & <foreign lang="el">e)ggei/bata</foreign> funiculis, ponderibus, orbiculis, <lb></lb>ſpiritu incluſo humanos motus ſine voce <expan abbr="edẽtes">edentes</expan> perbellè <lb></lb>expreſſerunt. </s> <s id="id.000121"><expan abbr="Noſtroq;">Noſtroque</expan> <expan abbr="tẽpore">tempore</expan> alij multi in oculis noſtris <lb></lb>ſimilia plurima poſuerunt. </s> <s id="id.000122">quales fuerunt icunculæ illæ <lb></lb>ad <expan abbr="cantũ">cantum</expan> cytharæ ſaltitantes, manus manibus iungentes, <lb></lb>in equos, in currus conſcendentes, modò rurſus <expan abbr="currẽtes">currentes</expan>, <lb></lb>modo reſtitantes. </s> <s id="id.000123">Tum caſtellum illud mirabile, in quo <lb></lb><expan abbr="fabrorũ">fabrorum</expan> genus omne ſuum munus affabrè, nec oſcitanter <pb xlink:href="035/01/024.jpg"></pb>exercebat, quod hîc Lutetiæ vidimus. </s> <s id="id.000124">Vt & Noribergæ <lb></lb>muſca ferrea <expan abbr="cõmemoratur">commemoratur</expan> è manu artificis ſui euolaſſe, <lb></lb>& conuiuas circumuolitaſſe, <expan abbr="tandemq;">tandemque</expan> veluti defeſſa in <lb></lb>ſui domini manum redijſſe: tum aquila illa, quæ in aëre <lb></lb>ſublimis Carolo imperatori huius nominis quinto ad vr<lb></lb>bem aduentanti obuia facta, <expan abbr="vſq;">vſque</expan> ad vrbis <expan abbr="portã">portam</expan> eundem <lb></lb>comitata eſt, ne fabulam exiſtimemus quod de columba <lb></lb>Architæ <expan abbr="volãte">volante</expan> à veteribus <expan abbr="cõmemoratum">commemoratum</expan> eſt: <expan abbr="neq;">neque</expan> illud <lb></lb>quod fertur de Dædaleis operibus, & Vulcani tripodi<lb></lb>bus, pectinibus, malleis, qui iniuſſi ad opus ſponte ſua ve<lb></lb>niebant, & niſi vinculis coercerentur, aufugiebant. </s> <s id="id.000125">Sed <lb></lb>hæc ad delectationem tantum ſunt comparata, vtilia & <lb></lb>vitæ humanę <expan abbr="trãſigẽdæ">tranſigendæ</expan> neceſſaria omnino ſunt Agricul<lb></lb>turæ, Militaris, Architecturæ, Medicinæ, Nauticæ, Mer<lb></lb>caturæ munera: quibus <expan abbr="alimẽta">alimenta</expan>, tecta, ſanitas, veſtitus, di<lb></lb>uitiæ, & ab cœli, <expan abbr="hoſtiumq;">hoſtiumque</expan> iniurijs defenſio quæruntur. <lb></lb></s> <s id="id.000126">At quid artes illæ eſſe poſſent, niſi machinæ <expan abbr="inuẽtæ">inuentæ</expan> fuiſ<lb></lb>ſent, & inſtrumenta, quibus vnâ <expan abbr="cũ">cum</expan> <expan abbr="hominũ">hominum</expan> parua vi, mo<lb></lb>les <expan abbr="lapidũ">lapidum</expan>, <expan abbr="lignorũ">lignorum</expan>, <expan abbr="frugũ">frugum</expan>, <expan abbr="terrarũ">terrarum</expan>, <expan abbr="mariũ">marium</expan> <expan abbr="ingẽtes">ingentes</expan> loco <expan abbr="dimouẽtur">di<lb></lb>mouentur</expan>, pelluntur, trahuntur, <expan abbr="cõuehuntur">conuehuntur</expan>, in <expan abbr="gyrũ">gyrum</expan> con<lb></lb>torquentur, & <expan abbr="tãdem">tandem</expan> altiſſimis locis & difficilimis repo<lb></lb>nuntur? </s> <s id="id.000127">aut <expan abbr="eædẽ">eædem</expan> iuſta quantitate appenſæ, aut <expan abbr="mẽſuratæ">menſuratæ</expan> <lb></lb><expan abbr="cuiq;">cuique</expan> ſuum quærenti diſtribuuntur? </s> <s id="id.000128">Vnde ſex ſunt illa ex <lb></lb>innumeris à veteribus <expan abbr="inuẽta">inuenta</expan>, <expan abbr="quorũ">quorum</expan> ſingula ſeorſum ma<lb></lb>gna vi: <expan abbr="coniũcta">coniuncta</expan> verò, & multiplicata infinitis propemo<lb></lb>dum viribus pollere animaduertuntur, libra, vectis, tro<lb></lb>chlea, axis in peritrochio, cuneus, & cochlea. </s> <s id="id.000129">Sed quę au<lb></lb>dio hîc dicet aliquis? </s> <s id="id.000130">Nunquid <expan abbr="inſtrumẽta">inſtrumenta</expan> mercatorum, <lb></lb><expan abbr="cœmẽtariorum">cœmentariorum</expan>, baiulorum, <expan abbr="phalangariorũ">phalangariorum</expan>, lignatorum, <lb></lb>lapicidarum, <expan abbr="vinitorũ">vinitorum</expan>, & eiuſmodi <expan abbr="viliũ">vilium</expan> ſordidorumque <lb></lb><expan abbr="hominũ">hominum</expan>? </s> <s id="id.000131">Audis ſanè: ſed & Aſtreæ, & Neptuni, & Mar<lb></lb>tis, & Vulcani, & Cereris, & Palladis, qui tantopere pro<lb></lb>pter hæc ſua inuenta antiquis <expan abbr="placuerũt">placuerunt</expan>, vt ſint ab illis in <lb></lb>deorum <expan abbr="numerũ">numerum</expan>, eorumque <expan abbr="maiorũ">maiorum</expan> relati. </s> <s id="id.000132">Trutinarum <lb></lb>librarumque examinatio reperta, inquit Vitruuius, vin<lb></lb>dicat ab iniquitate iuſtis moribus <expan abbr="vitã">vitam</expan>. </s> <s id="id.000133">Vnde ſtatera do<lb></lb>loſa abhominatio eſt apud Deum, dixit <expan abbr="ſapiẽs">ſapiens</expan>, & pondus <pb xlink:href="035/01/025.jpg"></pb>æquum voluntas eius, & alibi abhominatio eſt apud Deum <lb></lb>pondus & pondus. </s> <s id="id.000134">Itaque libræ inuentrix Aſtræa pro dea <lb></lb>luſticię culta eſt. </s> <s id="id.000135">Libra ipſa iudicum oculis in fori ſui tabu<lb></lb>lis, & ſignis propoſita, ad quam intuerentur, & denique in <lb></lb>cœleſte ſignum conuerſa, quæ diem naturalem, quem Sol <lb></lb>æquatorem peragrans circulum conficit, in tempus lucis & <lb></lb>tenebrarum æqualiter vbique diuideret. </s> <s id="id.000136">Vnde poëta,</s> </p> <p type="main"> <s id="id.000137"><emph type="italics"></emph>Libra die, ſomnique pares vbi fecerit horas,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000138"><emph type="italics"></emph>Et medium luci atque vmbris iam diuidet orbem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000139">Neptuno verò, cum tridentem antiquitas attribuit, quid <lb></lb>aliud, quam vectem? </s> <s id="id.000140">Græci appellant <foreign lang="el">mo/xlon</foreign> vnde ille <foreign lang="el">mox<lb></lb>leuth\s</foreign> vectiarius à poëtis dictus eſt, & terræ matiſque con<lb></lb>cuſſor, & hac machina Syrtes ſubleuans, quo plus Troianis <lb></lb>apparerent à poëta inducitur,</s> </p> <p type="main"> <s id="id.000141"><emph type="italics"></emph>Leuat ipſe tridenti,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000142"><emph type="italics"></emph>Et vaſtas aperit Syrtes. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000143">Certè vectis palus eſt <expan abbr="oblõgior">oblongior</expan>, materiæ firmæ, cuſpide acu<lb></lb>ta, & paulo latiori linguæ inſtar, quam propè, quando eſt <lb></lb>ſubditum hypomochlium, huic pondus incumbens, id que <lb></lb>grauius quam quod à decem hominum ſolis manibus di<lb></lb>moueri loco poſſet, vnius <expan abbr="tamẽ">tamen</expan> viribus caput huius pali de<lb></lb>primentibus, vel ſi terra ſubdita pro hypomochlio eſt ſuble<lb></lb>uantibus, dimouetur. </s> <s id="id.000144">Vnde in magnis <expan abbr="ædificiorũ">ædificiorum</expan> ſubſtru<lb></lb>ctionibus vnus vectis pro multorum manibus, vnus homo <lb></lb>bimanus pro Briareo centimano, modò pondera lapidum, <lb></lb>trabiúm que coloſſicotera fabris & architectis loco dimo<lb></lb>uet, & ſubleuat: modò <expan abbr="eiſdẽ">eiſdem</expan> collopis figura ſucculas verſat: <lb></lb>modo tollenonis ſpecie aquas è puteis operis & olitoribus <lb></lb>exhaurit: modo phalangæ forma baiulis & phalangarijs <lb></lb>proportionalia tanquam in bilance pondera partitur, mo<lb></lb>do iugi nomine in aratro bobus æquum arationis laborem <lb></lb>diſpenſat ſiue æquales ſiue inæquales. </s> </p> <p type="main"> <s id="id.000145"><emph type="italics"></emph>Veniant ad aratra iuuenci. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000146">Sed cum naui tranſmittitur flumen, aut mare tranſmeatur, <lb></lb>quid eſt in ea remus aliud, quam vectis inuerſus, habens in <lb></lb>ſcalmo hypomochlium? </s> <s id="id.000147"><expan abbr="aquã">aquam</expan> pro pondere loco dimouens? <lb></lb></s> <s id="id.000148">vt in eum cedat nauis, & quidem impulſus ille à remige pro <pb xlink:href="035/01/026.jpg"></pb>vectiatio tanquam tridens à Neptuno? </s> <s id="id.000149">Quin & guberna<lb></lb>calum, quo gubernator in puppi <expan abbr="ſedẽs">ſedens</expan> tam facilè obliquat <lb></lb>nauim etiam ingentem, & cum magna in prora loci muta<lb></lb>tione, licet in puppi adeò exigua, vt nihil agere, aut <expan abbr="etiã">etiam</expan> lu<lb></lb>dere videatur: aliud <expan abbr="tamẽ">tamen</expan> nihil, quam vectis eſſe <expan abbr="cõperietur">comperietur</expan>. <lb></lb></s> <s id="id.000150">Neque malus erectus in medio nauis eſt aliud. </s> <s id="id.000151">Calx enim, <lb></lb>ſeu edolium eſt hypomochlium, pars è qua pendet carche<lb></lb>ſium cum paſſis velis, <expan abbr="tanquã">tanquam</expan> alis Dædaleis perflante vento <lb></lb>propulſa propellit pondus, nauim ſcilicet, & quod eſt admi<lb></lb>rabilius ibi non aliter venti, quam equi reguntur, <expan abbr="dũ">dum</expan> ex car<lb></lb>cheſij vt fræni ſitu modò altiore: modò depreſſiore provt <lb></lb>ſunt admiſſi: ita nauis modò vehementius, modò remiſſius <lb></lb>impellitur. </s> </p> <p type="main"> <s id="id.000152">Sed hæc devecte ſatis. </s> <s id="id.000153"><expan abbr="Trochleã">Trochleam</expan> verò, quæ orbiculus eſt <lb></lb>circa axem immobilem fune conuolutus, quantis viribus <lb></lb><expan abbr="præditã">præditam</expan> eſſe animaduertimus. </s> <s id="id.000154">Ex hac multiplicata, factum <lb></lb>eſt triſpaſton, pentepaſton, polyſpaſton, viribus <expan abbr="quorũ">quorum</expan> <expan abbr="cõfiſus">confi<lb></lb>ſus</expan> Archimedes cum audiret <expan abbr="aliquẽ">aliquem</expan> <expan abbr="diſputãtem">diſputantem</expan> plures eſſe <lb></lb>mundos coram Herone rege Syracuſarum, auſus eſt dicere. <lb></lb></s> <s id="id.000155">Da mihi vbi ſiſtam pedem, & hanc ego <expan abbr="terrã">terram</expan> loco ſuo dimo<lb></lb>uebo. </s> <s id="id.000156">cuius admirabilis dicti <expan abbr="cũ">cum</expan> rogatus eſſet à rege, vt ſpe<lb></lb>cimen aliquod ederet, vna manu læua quinquies millenûm <lb></lb>modiorum <expan abbr="põdus">pondus</expan> attraxit: nauem in ſiccum littus eiectam <lb></lb>& grauiter <expan abbr="oneratã">oneratam</expan> ad ſe perinde pertraxit, ac ſi in mari re<lb></lb>mis, veliſve impulſa fuiſſet: aliam poſtea recens <expan abbr="cõſtructam">conſtructam</expan> <lb></lb>ingentis magnitudinis ab Herone regi Ægyptiorum Ptolo<lb></lb>mæo dono mittendam, quam omnes <expan abbr="Syracuſanorũ">Syracuſanorum</expan> ciuium <lb></lb>vires <expan abbr="cõiunctæ">coniunctæ</expan> dimouere loco non <expan abbr="potuerãt">potuerant</expan>, vt ſolus Hiero <lb></lb>machinis adiutus in mare educerer, perfecit: & <expan abbr="quidẽ">quidem</expan> cum <lb></lb>tanta ipſius regis admiratione, vt exclamarit, <foreign lang="el">a)po\ tau/ths th=s <lb></lb>h(me/ras peri\ p=anto\s *arxhmh/dei le/gonti pisteute/on. </foreign></s> <s> Ab hoc die <lb></lb>quicquid dixerit Archimedes huic <expan abbr="credendũ">credendum</expan>. </s> <s id="id.000157">At ab eo die <lb></lb>ab Archimede prodijt illud problema inexpertis in credibi<lb></lb>le, eruditis tamen demonſtratum. </s> <s id="id.000158">Datum pondus à data <lb></lb>potentia moueri. </s> <s id="id.000159">quod in vecte, trochlea, & axe in peritro<lb></lb>chio nuper à Guidone Vbaldo demonſtrationibus geome<lb></lb>tricis habemus confirmatum. </s> <s id="id.000160">Vectis ſolus pondera de loco <pb xlink:href="035/01/027.jpg"></pb>propellit ſuo, trochlea euellit, & eadem ad altiſſimas ædi<lb></lb>ficiorum vbi opus eſt ſedes trahit. </s> <s id="id.000161">Sit in polo horizontis qui <lb></lb>trochleæ appendiculum firmet, & ad eum homo ipſe ſe ſu<lb></lb>bleuabit. </s> <s id="id.000162">Sed longior ſum in trochlea, in reliquis ero bre<lb></lb>uior. </s> <s id="id.000163">Axis in peritrochio cylindrus eſt duobus fulcris per <lb></lb>extrema ſuſtentatus, habens propè vnum extremorum tym<lb></lb>panum ſcytalis aliquot in peripheria in fixis perforatum, ita <lb></lb>quidem, vt <expan abbr="potẽtia">potentia</expan>, quæ ſemper in ſcytalis eſt, dum circum<lb></lb>uertit tympanum & axem, ſurſum etiam ex inferis euehat <lb></lb>pondus quodlibet axi fune circa ipſum axem reuoluto <lb></lb>appenſum. </s> <s id="id.000164">Huius machinæ beneficio deſcenditur in viſce<lb></lb>ra terræ, & illinc effoſſæ opes, non vt Ouidius ait, ſemper</s> </p> <p type="main"> <s id="id.000165"><emph type="italics"></emph>Irritamenta malorum:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000166">quin potius occaſiones & adiumenta bonorum multorum, <lb></lb>ſi <expan abbr="bonũ">bonum</expan> <expan abbr="poſſeſſorẽ">poſſeſſorem</expan> nactæ ſint. </s> <s id="id.000167">Nam vt recte dixit Pindarus,</s> </p> <p type="main"> <s id="id.000168"><emph type="italics"></emph>Quæ Virtute pecunia<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000169"><emph type="italics"></emph>Exornata nitet, ſuppeditat Vias<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000170"><emph type="italics"></emph>Non vnas, bene agas, quibus<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000171"><emph type="italics"></emph>Quæ ſors cunque ferens obtulerit tibi:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000172">Et vt Antiphanes,</s> </p> <p type="main"> <s id="id.000173"><emph type="italics"></emph>Per deos cur optet quis diteſcere?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000174"><emph type="italics"></emph>Pecuniæ cur optet habere plurimum:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000175"><emph type="italics"></emph>Quam poſsit auxiliari vt amicis? </s> <s id="id.000176">Gratiæ<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000177"><emph type="italics"></emph>Fructúmque ſerere Diuarum ſuauiſsimæ?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000178">Illinc in quam effoſſæ opes, ſucci, terræ medicatæ, metalli <lb></lb>omne genus, lapides, arena, ad ædificiorum ſubſtructiones, <lb></lb>ad medicamenta prauarum & contumacium affectionum, <lb></lb>ad ornamenta in altum, lucém que euehuntur. </s> </p> <p type="main"> <s id="id.000179">Cuneus vero eſt <expan abbr="inſtrumẽtum">inſtrumentum</expan> exiguum in formam pyra<lb></lb>midis quadrangulę, ad vnam <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan> faſtigiatæ ad diui<lb></lb>dendum ligna factum. </s> <s id="id.000180">Hoc <expan abbr="cũ">cum</expan> malleo lignator inſtructus, <lb></lb>ſyluam breuiori tempore integram diuiſerit: quam ſine ijs <lb></lb>arboris vnius vnum truncum. </s> <s id="id.000181">Milo Crotoniates Athleta <lb></lb>ille robuſtiſſimus fertur cum arborem bifurcatam proprijs <lb></lb>viribus diuellere contenderet, & diuelli in cœptam retinere <lb></lb>non poſſet, quin partes diuulſæ ſumma celeritate in ſeſe re<lb></lb>dirent, vnâque raptas manus interciperent, præda vt im<pb xlink:href="035/01/028.jpg"></pb>bellis ouis fuiſſe lupis. </s> <s id="id.000182">Itaque proprijs,</s> </p> <p type="main"> <s id="id.000183"><emph type="italics"></emph>viribus ille<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000184"><emph type="italics"></emph>Confiſus perijt,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000185">qui ſi cuneo id ipſum facere voluiſſet, in eam calamitatem <lb></lb>non incidiſſet. </s> <s id="id.000186">Quis vero <expan abbr="nõ">non</expan> intelligit Martis, Cereris, Vul<lb></lb>canique arma & inſtrumenta enſes, gladios, mucrones, ſe<lb></lb>cures, aratra, ligones, aſcias, falces, vngues ferreos & ſimilia, <lb></lb>quæ percuſſione, ſiue impulſu incidunt, diuidunt, <expan abbr="perforãt">perforant</expan>, <lb></lb>ad huiuſmodi facultatis inſtrumentum commode referri <lb></lb>poſſe? </s> <s id="id.000187">Ligones agricolarum quid ſunt aliud, quam cunei <lb></lb>malleo connexi? </s> <s id="id.000188">Forfex verò ad Palladis & Æſculapij Ma<lb></lb>chaoniſque artes <expan abbr="tã">tam</expan> neceſſarius, quid aliud, <expan abbr="quã">quam</expan> duplex cu<lb></lb>neus, & totuplex vectis? </s> <s id="id.000189">ſicuti forceps tantum vectis eſt du<lb></lb>plicatus. </s> <s id="id.000190">Inſtrumentum Vulcani perpetuò in manibus, quò <lb></lb>pruna, ferrum candens, æs, <expan abbr="argentũ">argentum</expan>, aurum apprehenditur. </s> </p> <p type="main"> <s id="id.000191"><emph type="italics"></emph>Prenſant<emph.end type="italics"></emph.end> ( enim vt poëta ait, ) <emph type="italics"></emph>verſantque tenaci<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000192"><emph type="italics"></emph>Forcipe ferrum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000193">At cuneus ſimplex percuſſione mallei adigitur. </s> <s id="id.000194">Idem mul<lb></lb>tiplicatus ſine percuſſione rota cum ſcytalis in cochlea ita <lb></lb>penetrare cogitur, vt vuæ, oleæ, nuces, mala, pyra, cætera<lb></lb>que humida prœlis ſubiecta quicquid ſucci & liquoris ha<lb></lb>bent, Domino perſoluere cogantur. </s> <s id="id.000195">Hoc beneficium ma<lb></lb>gni eſt momenti ad vitæ commoda. </s> <s id="id.000196">At vt longæua vſque in <lb></lb>ſecula ſint ſempiterni doctorum hominum commentarij, <lb></lb>& conſcriptæ cogitationes, quantum confert prœlum ty<lb></lb>pographicum cochleæ vnius beneficio compreſſum? </s> <s id="id.000197">Quid <lb></lb>dicam ab his fontibus etiam deducta omnia poliorcetica, <lb></lb>quorum ſolorum opè vnus Archimedes Marcelli Syracu<lb></lb>ſas terra marique <expan abbr="obſidẽtis">obſidentis</expan> vires diu, <expan abbr="multumq;">multumque</expan> ludificatus <lb></lb>eſt, pro qua re hûc Titi Liuij lubet conferre admirabile te<lb></lb>ſtimonium. </s> <s id="id.000198">Terra, inquit, marique ſimul cœptæ oppugnari <lb></lb>Syracuſæ, terra ab Hexapylo: mari ab Acradina. </s> <s id="id.000199">Et habuiſ<lb></lb>ſet tantò impetu cœpta res fortunam, niſi vnus homo Syra<lb></lb>cuſis ea <expan abbr="tẽpeſtate">tempeſtate</expan> fuiſſet Archimedes. </s> <s id="id.000200">Is erat vnicus ſpecta<lb></lb>tor cœli ſiderum que: mirabilior tamen inuentor ac machi<lb></lb>nator bellicorum <expan abbr="tormẽtorum">tormentorum</expan>, operumque: quibus ea quæ <lb></lb>hoſtes ingenti mole agerent ipſe perleui momento ludifi<pb xlink:href="035/01/029.jpg"></pb>caretur. </s> <s id="id.000201">Murum per inęquales ductum colles, pleraque alta <lb></lb>& difficilia aditu, ſummiſſa quædam, & quæ planis vallibus <lb></lb>adiri poſſent, vt cuique aptum viſum eſt loco, ita omni ge<lb></lb>nere tormento rum inſtruxit. </s> <s id="id.000202">Acradinæ murum, qui, vt ante <lb></lb>dictum eſt, mari alluitur ex quinqueremibus Marcellus <lb></lb>oppugnabat. </s> <s id="id.000203">ex cæteris nauibus ſagittarij, funditoreſque, <lb></lb>& velites etiam quorum telum inhabile ad remittendum <lb></lb>imperitis eſt: vix quenquam ſine vulnere conſiſtere in muro <lb></lb>patiebantur. </s> <s id="id.000204">Hi, quia ſpatio miſſilibus opus eſt: procul mu<lb></lb>ro <expan abbr="tenebãt">tenebant</expan> naues. </s> <s id="id.000205">Iunctæ aliæ binæ ad quinqueremes dem<lb></lb>ptis interioribus remis, vt latus lateri appropinquaretur: <lb></lb>cum exteriore ordine remorum velut naues agerentur: tur<lb></lb>res contabulatas, machinamentá que alia quatiendis muris <lb></lb>portabant. </s> <s id="id.000206">Aduerſus hunc naualem apparatum Archime<lb></lb>des variæ magnitudinis tormenta in muris diſpoſuit. </s> <s id="id.000207">In eas <lb></lb>quæ procul erant, naues ſaxa ingenti pondere emittebat: <lb></lb>propiores leuioribus, eóque magis crebris petebat telis. </s> <s id="id.000208">Po<lb></lb>ſtremò vt ſui vulnere intacti tela in hoſtem ingererent: mu<lb></lb>rum ab imo ſummum crebris cubitalibus ferè caueis ape<lb></lb>ruit. </s> <s id="id.000209">per quæ caua pars ſagittis: pars ſcorpionibus modicis <lb></lb>ex occulto petebant hoſtem. </s> <s id="id.000210">Quæ propius <expan abbr="quidẽ">quidem</expan> ſubibant <lb></lb>naues, quo interiores ictibus <expan abbr="tormẽtorum">tormentorum</expan> eſſent: in eas tol<lb></lb>lendas deſuper murum eminentem ferrea manus firmæ ca<lb></lb>thenæ illigata, cum iniecta proræ eſſet, grauique libramen<lb></lb>to plumbi recelleret ad ſolum: <expan abbr="ſuſpẽſa">ſuſpenſa</expan> prora, nauim in pup<lb></lb>pim ſtatuebat. </s> <s id="id.000211">Dein remiſſa ſubitò, velut ex muro caden<lb></lb>tem nauim cum ingenti trepidatione nautarum ita vndæ <lb></lb>affligebant: vt etiamſi recta recideret aliquantum aquæ ac<lb></lb>ciperet. </s> <s id="id.000212">Ita maritima oppugnatio eſt eluſa, omniſque vis eſt <lb></lb>auerſa, vt totis viribus terra aggrederentur. </s> <s id="id.000213">Sed ea quoque <lb></lb>pars eodem omni apparatu tormentorum inſtructa erat, <lb></lb>Hieronis impenſis, curaque per multos annos Archimedis <lb></lb>vnica arte. </s> <s id="id.000214">Ita conſilio habito, cum omnis conatus ludibrio <lb></lb>eſſet: abſiſtere oppugnatione atque obſidendo tantum ar<lb></lb>cere terra marique commeatibus hoſtem placuit. </s> <s id="id.000215">Hæc Ti<lb></lb>tus Liuius lib.4.decad.3. </s> <s id="id.000216">Vilium igitur, ſordidorum que ho<lb></lb>minum ne dixerimus ea eſſe inſtrumenta, quæ vel à dijs, vel <pb xlink:href="035/01/030.jpg"></pb>à nobiliſſimis hominibus inuenta, & vſurpata ſunt, & nunc <lb></lb>ad vſus humanos perquam neceſſaria honeſtiſſimum quæ<lb></lb>ſtum, & qualem agricultura dominis agricolis ſuppeditant. <lb></lb></s> <s id="id.000217">Quanquam non eo animo à nobis hæc dicuntur, vt ad eas <lb></lb>artes, quarum ſunt inſtrumenta, veſtras animi, corporiſque <lb></lb>vires ſuadeam conferatis: vos dico,</s> </p> <p type="main"> <s id="id.000218"><emph type="italics"></emph>Queis meliore luto finxit præcordia Titan:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000219">atque quos ad his altiora præmeditanda iamdudum euexit <lb></lb>animus, vbi tamen nihil aliud eſſet, quod ageretur, cur non <lb></lb>aliquod horum relaxamenti gratia etiam quæratis? </s> <s id="id.000220">vel ſi rei <lb></lb>familiaris exiguitas poſtulat, cum ijs agatis, potius, quam <lb></lb>nihil? </s> <s id="id.000221">Neque enim magis horum aliquod nobis indecorum <lb></lb>putare debemus: quam ſibi Aſcræus ille poëta,</s> </p> <p type="main"> <s id="id.000222"><emph type="italics"></emph>Qui alium ditem cernens, cum deeſt quod agatur,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000223"><emph type="italics"></emph>Ipſe ſolum vertit tauris, & ſemina ponit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000224">Sed eo animo hęc pręſertim <expan abbr="nũc">nunc</expan> à me dicuntur, vt audacter <lb></lb>& ſine rubore aliquando ingrediamur officinas fabrorum <lb></lb>generis omnis, vt & inſtrumenta, & machinas quibus vtun<lb></lb>tur in ſuis operibus conficiendis primum dignoſcamus, mi<lb></lb>rificas ex iſta dignotione voluptates conſecuturi, maximè <lb></lb>cum eas, quæ magna vi pollent, ſummoſque habent vſus <lb></lb>cognouerimus, maiores adhuc multo poſtea percepturi, ſi <lb></lb>tantæ efficaciæ adiumenti que cauſas inueſtigantes inuene<lb></lb>rimus, quod feciſſe Ariſtotelem non puduit, qui vno hoc li<lb></lb>bello <foreign lang="el">peri\ mhxanikw=n</foreign> certè iucundo & vtili edito tanta inge<lb></lb>nij ſubtilitate atque diligentia perſecutus eſt, vt omnia ad <lb></lb>vnum principium, quod eſt circulus, reuocari poſſe inue<lb></lb>nerit, & reuocanda eſſe non quidem leuibus probabilium <lb></lb>argumentorum: ſed grauiſſimis demonſtrationum geome<lb></lb>tricarum momentis oſtenderit. </s> <s id="id.000225">Itaque ſi quis audito huius <lb></lb>libelli titulo, ſtatim ab huius lectione volens aufugere, inſu<lb></lb>per pueriliter irrideat, quod regius mathematicarum ar<lb></lb>tium profeſſor in rebus, vt putabit, viliſſimis philoſophari, <lb></lb>& <foreign lang="el">gewmetrei=n</foreign> contenderit. </s> <s id="id.000226">Huic reſpondebimus, quod ali<lb></lb>quando Heraclitum dixiſſe ferunt ijs, qui cum alioqui evm <lb></lb>vellent, quod forte in caſa furnaria caloris gratia ſedentem <lb></lb>vidiſſent, accedere temperarunt, & ingredi fidenter cum <pb xlink:href="035/01/031.jpg"></pb>iuſſiſſet. </s> <s id="id.000227">Ne quidem, inquit ille, huic loco dij deſunt im<lb></lb>mortales: ſic nec iſti rerum generi dulciſſima & vtiliſſima, <lb></lb>& <expan abbr="cũ">cum</expan> ſumma ingenij humani voluptate coniuncta ſua deeſt <lb></lb>philoſophia, vt in qua explicanda, & <expan abbr="exornãda">exornanda</expan> præter Ari<lb></lb>ſtotelem multi viri præclari ſtudium ſuum collocauerint, <lb></lb>Cliades, Architas, Archimedes, Cteſibius, Nymphodorus, <lb></lb>Philo byzanteus, Diphilas, Charidas, Polyides, Phyrus, <lb></lb>Ageſiſtratus, ex quorum <expan abbr="cõmentarijs">commentarijs</expan> quæ vtilia eſſent ædi<lb></lb>ficationi collecta in vnum Vitruuius corpus coëgit: ſed & <lb></lb>præter illos quorum ferè nobis <expan abbr="reſtãt">reſtant</expan> ſola nomina Pappus, <lb></lb>Hero vterque, Tzetzes, Iordanus, & è recentioribus Leoni<lb></lb>cus, Picolominus, Cardanus, Guido Vbaldus, quorum in<lb></lb>genia ſeruilia nunquam rectè quis dixerit aut putarit. </s> <s id="id.000228">quin <lb></lb>& Hippocratcs magnus ille medicus à ſe nonnulla luxatio<lb></lb>nibus, & fracturis reponendis inuenta commoda gloriatur, <lb></lb>cuiuſmodi ſunt <foreign lang="el">o)/noi, o)/niskoi\,</foreign> & ſcamnum, quæ vnà cum alijs <lb></lb>Galenus quo que paruis eorum exemplaribus vtens ſuos ſe <lb></lb>diſcipulos docere teſtatus eſt. </s> <s id="id.000229">In iſtam igitur inquiſitio<lb></lb>nem, tractationem, commentationem nobilem, ingenuam <lb></lb>& philoſophi non vulgariter vt multi: ſed in Geometria <lb></lb>magnopere eruditi ingenio digniſſimam, tot magnorum <lb></lb>virorum exemplo, ſi, candide lector, me hortante atque his <lb></lb>noſtrorum commentariorum vigilijs, vtcunque adiuuante, <lb></lb>diligenter incubueris, tui te laboris, mihi crede, penitebit <lb></lb>numquam. </s> <s id="id.000230">Vale. </s> </p> </section> <pb xlink:href="035/01/032.jpg"></pb> <section> <p type="head"> <s id="id.000231"><emph type="italics"></emph>Extraict du Priuilege du Roy. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000232"><foreign lang="fr">Par grace & priuilege du Roy, il eſt permis à Ie<lb></lb>remie Perier marchant Libraire à Paris, d'impri<lb></lb>mer ou faire imprimer vn liure intitulé</foreign> <emph type="italics"></emph>Ariſtotelis <lb></lb>Mechanica, Græca emendata, Latina facta, & commen<lb></lb>tarijs illuſtrata, ab Henrico Monantholio Medico, & Ma<lb></lb>thematicarum artium Profeſſore Regio. <emph.end type="italics"></emph.end></s> <s id="id.000233"><foreign lang="fr">Et deffenſes ſont <lb></lb>faictes à toutes perſonnes de quelque eſtat qualité & <lb></lb>condition qu'ils ſoyent, en quelques lieux & villes de <lb></lb>ce Royaume, de ne le faire imprimer ou faire faire im<lb></lb>primer à peine des articles poſés à l'original du pre<lb></lb>ſent priuilege, iuſques au temps & terme de dix ans, <lb></lb>finis & accomplis à conter du iour & datte de la pre<lb></lb>ſante impreſſion, nonobſtant toutes oppoſitions ou <lb></lb>appellations quelconques, & ſans preiudice d'icelle, <lb></lb>car tel eſt le plaiſir de ſa Mageſté. </foreign></s> <s id="id.000234"><foreign lang="fr">Donné à Paris le <lb></lb>23. de Decembre 1598. </foreign></s> </p> <p type="main"> <s id="id.000235"><foreign lang="fr"><emph type="italics"></emph>Signé par le Conſeil<emph.end type="italics"></emph.end></foreign></s> </p> <p type="main"> <s id="id.000236"><foreign lang="fr"><emph type="italics"></emph>D<emph.end type="italics"></emph.end>E LAVETS. </foreign></s> </p> </section> <pb xlink:href="035/01/033.jpg"></pb> <section> <p type="head"> <s id="id.000237">INDEX MEMORABILIVM <lb></lb>IN MECHANICIS ARISTOTELIS <lb></lb>& eorum Commentarijs. <lb></lb><arrow.to.target n="table1"></arrow.to.target></s> </p> <table> <table.target id="table1"></table.target> <row> <cell><emph type="italics"></emph>A<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph><foreign lang="el">*abussos</foreign> unde. pag. <emph.end type="italics"></emph.end></cell> <cell>209</cell> </row> <row> <cell><emph type="italics"></emph>Abſis pro circunferentia rotæ. <emph.end type="italics"></emph.end></cell> <cell>100</cell> </row> <row> <cell><emph type="italics"></emph>Acatium ante naues. <emph.end type="italics"></emph.end></cell> <cell>65</cell> </row> <row> <cell><emph type="italics"></emph>Actiones manuum in opificijs egent ſtatione, vel ſeßione tantùm<emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Admiratio quid. <emph.end type="italics"></emph.end></cell> <cell>4.5</cell> </row> <row> <cell><emph type="italics"></emph>Agriculturæ neceſſaria. <emph.end type="italics"></emph.end></cell> <cell>14</cell> </row> <row> <cell><emph type="italics"></emph>Ædes rotunda mirifica. <emph.end type="italics"></emph.end></cell> <cell>10</cell> </row> <row> <cell><emph type="italics"></emph>Ædificium durabile rectà inſiſtit. <emph.end type="italics"></emph.end></cell> <cell>196</cell> </row> <row> <cell><emph type="italics"></emph>Æolus primus vſus velis. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <row> <cell><emph type="italics"></emph>Æquale eſt cauſa quietis. <emph.end type="italics"></emph.end></cell> <cell>193.196</cell> </row> <row> <cell><emph type="italics"></emph>Æquilibrium in ponderatione. <emph.end type="italics"></emph.end></cell> <cell>149</cell> </row> <row> <cell><foreign lang="el">*alourgopw/lai</foreign> <emph type="italics"></emph>qui. <emph.end type="italics"></emph.end></cell> <cell>47</cell> </row> <row> <cell><emph type="italics"></emph>Ambulare pronum conuenit brutis. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Angulus rectus eſt angulus æqualitatis, ideóque quietis. <emph.end type="italics"></emph.end></cell> <cell>193.196</cell> </row> <row> <cell><emph type="italics"></emph>Ad angulos rectos omnia <expan abbr="quieſcũt">quieſcunt</expan>. <emph.end type="italics"></emph.end></cell> <cell>196</cell> </row> <row> <cell><emph type="italics"></emph>Antemna quid. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <row> <cell><emph type="italics"></emph>Antemnæ motio. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <row> <cell><emph type="italics"></emph>Antiperiſtaſis medij confert ad motum proiecti. <emph.end type="italics"></emph.end></cell> <cell>203</cell> </row> <row> <cell><emph type="italics"></emph>Antiphonis dictum, cum iret ad ſupplicium. <emph.end type="italics"></emph.end></cell> <cell>12</cell> </row> <row> <cell><emph type="italics"></emph>Antiphonis verſus de natura & arte. <emph.end type="italics"></emph.end></cell> <cell>8. 12</cell> </row> <row> <cell><emph type="italics"></emph>Arbores, & plantæ inſiſlunt plane terræ ad rectos angulos. <emph.end type="italics"></emph.end></cell> <cell>196</cell> </row> <row> <cell><emph type="italics"></emph>Archelai regis factum in eclipſi Solis. <emph.end type="italics"></emph.end></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"></emph>Archimedeum problema, datum pondus data potentia mouere. <emph.end type="italics"></emph.end></cell> <cell>60</cell> </row> <row> <cell><emph type="italics"></emph>Archimedis factum Mechanicum. <emph.end type="italics"></emph.end></cell> <cell>12</cell> </row> <row> <cell><emph type="italics"></emph>Architecturæ tres partes. <emph.end type="italics"></emph.end></cell> <cell>9</cell> </row> <row> <cell><emph type="italics"></emph>Argo prima nauis. <emph.end type="italics"></emph.end></cell> <cell>62</cell> </row> <row> <cell><emph type="italics"></emph>Ariſtoteles reprehenſus à Nonio. <emph.end type="italics"></emph.end></cell> <cell>84</cell> </row> <row> <cell><emph type="italics"></emph>Ars ſlectit naturam, & ad alium ſcopum vertit. <emph.end type="italics"></emph.end></cell> <cell>6</cell> </row> <row> <cell><emph type="italics"></emph>Ars eſt admirationis plena. <emph.end type="italics"></emph.end></cell> <cell>6</cell> </row> <row> <cell><emph type="italics"></emph>Artis, & naturæ differentia. <emph.end type="italics"></emph.end></cell> <cell>6</cell> </row> <row> <cell><emph type="italics"></emph>Artium diuiſio in liberales, & ſordidas. <emph.end type="italics"></emph.end></cell> <cell>3</cell> </row> <row> <cell><emph type="italics"></emph>Artes liberales. <emph.end type="italics"></emph.end></cell> <cell>3</cell> </row> <row> <cell><emph type="italics"></emph>Artes pueriles. <emph.end type="italics"></emph.end></cell> <cell>3</cell> </row> <row> <cell><emph type="italics"></emph>Artes magnæ. <emph.end type="italics"></emph.end></cell> <cell>3</cell> </row> <row> <cell><emph type="italics"></emph>Artes imperantes. <emph.end type="italics"></emph.end></cell> <cell>3.4</cell> </row> <row> <cell><emph type="italics"></emph>Artes architectonicæ. <emph.end type="italics"></emph.end></cell> <cell>3</cell> </row> <row> <cell><emph type="italics"></emph>Ars Typographica nihil eſſet ſine cochlea. <emph.end type="italics"></emph.end></cell> <cell>133</cell> </row> <row> <cell><emph type="italics"></emph>Aſinus, & aues longo collo vident cœlum, vt homo. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph>Axis in peritrochio. <emph.end type="italics"></emph.end></cell> <cell>120</cell> </row> <row> <cell><foreign lang="el">*auto/mata. </foreign></cell> <cell>10</cell> </row> <row> <cell><emph type="italics"></emph>B<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Baiulus cum ſuo onere eſt turbo, vel conus inuerſus. <emph.end type="italics"></emph.end></cell> <cell>199.200</cell> </row> <row> <cell><emph type="italics"></emph>Baiuli Pariſienſes facile ferunt ingentia pondera. <emph.end type="italics"></emph.end></cell> <cell>198.199</cell> </row> <row> <cell><emph type="italics"></emph>Baiuli cum onere tutò aſcendunt, periculosè deſcendunt. <emph.end type="italics"></emph.end></cell> <cell>199</cell> </row> <row> <cell><emph type="italics"></emph>B. Feratinus Amerinus <expan abbr="cãcellariæ">cancellariæ</expan> Apoſtolicæ regens conſecrat, & comprecatur multa ſuper crucem apici obeliſci imponendam. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <row> <cell><emph type="italics"></emph>Bombi tormentorum multi editi ſtatim atque crux impoſita fuit apici obeliſci. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <pb xlink:href="035/01/034.jpg"></pb> <row> <cell><emph type="italics"></emph>Bouilli error, qui putabat rectam iuuentam æqualem peripheriæ ex circuli ſuper planum reuolutione. <emph.end type="italics"></emph.end></cell> <cell>174</cell> </row> <row> <cell><emph type="italics"></emph>Boues ad <expan abbr="aratrũ">aratrum</expan> pariter ſubiugandi. <emph.end type="italics"></emph.end></cell> <cell>192</cell> </row> <row> <cell><emph type="italics"></emph>Boüm in iugo imbecillior ſubleuari poteſt. <emph.end type="italics"></emph.end></cell> <cell>192</cell> </row> <row> <cell><emph type="italics"></emph>Bruta ventrem ad terram conuerſum habent. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph>Brutiſpina pedibus ad rectos imminet. <emph.end type="italics"></emph.end></cell> <cell>198</cell> </row> <row> <cell><emph type="italics"></emph>Brutum nihil admiratur. <emph.end type="italics"></emph.end></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"></emph>Bruta nonnulla apta <expan abbr="ferẽdis">ferendis</expan> ſarcinis. <emph.end type="italics"></emph.end></cell> <cell>198</cell> </row> <row> <cell><emph type="italics"></emph>Brutum nullum poteſt ſedere. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>C<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><foreign lang="el">*ka/iar</foreign> <emph type="italics"></emph>in fund a quid ſit. <emph.end type="italics"></emph.end></cell> <cell>117</cell> </row> <row> <cell><emph type="italics"></emph>Calliæ Rhodienſis factum <expan abbr="mechanicũ">mechanicum</expan>. <emph.end type="italics"></emph.end></cell> <cell>12</cell> </row> <row> <cell><emph type="italics"></emph>Cardanus reprehenſus à Scaligero. <emph.end type="italics"></emph.end></cell> <cell>145</cell> </row> <row> <cell><emph type="italics"></emph>Cardanus obſcurè & imperſectè: ingeniosè tamenſcripſit. <emph.end type="italics"></emph.end></cell> <cell>180</cell> </row> <row> <cell><emph type="italics"></emph>Carcheſium quid. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <row> <cell><emph type="italics"></emph>Cathelina muſca Rhemenſibus dicta eſt <expan abbr="exẽplar">exemplar</expan> puncti duabus lationibus eodem tempore moti. <emph.end type="italics"></emph.end></cell> <cell>32.33</cell> </row> <row> <cell><emph type="italics"></emph>Cauda eſt omnipiſci progubernaculo. <emph.end type="italics"></emph.end></cell> <cell>77</cell> </row> <row> <cell><emph type="italics"></emph>Celeritas duplex. <emph.end type="italics"></emph.end></cell> <cell>27</cell> </row> <row> <cell><emph type="italics"></emph>Centrobarica pars Mechanices. <emph.end type="italics"></emph.end></cell> <cell>11</cell> </row> <row> <cell><emph type="italics"></emph>Cercopithecus proxime accedit ad figuram hominis. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph>Cercopithecus, & ſimia eſt ridicula hominis imitatio. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph>Cercopitheci manus differt ab hominis manu. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph>Cercopitheci pollex non eſt <foreign lang="el">a)nti/xeir,</foreign> vt in manu hominis. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph>Centrum duorum circulorum connexorum non eſt idem. <emph.end type="italics"></emph.end></cell> <cell>173</cell> </row> <row> <cell><emph type="italics"></emph>Chirurgi togati nolunt dentes cuellere, licetſu operatio chirurgica. <emph.end type="italics"></emph.end></cell> <cell>153</cell> </row> <row> <cell><emph type="italics"></emph>Circini author Dædalus. <emph.end type="italics"></emph.end></cell> <cell>17</cell> </row> <row> <cell><emph type="italics"></emph>Circulus eſt <expan abbr="principiũ">principium</expan> omnium virium, quæſunt in machinis motricibus. <emph.end type="italics"></emph.end></cell> <cell>15</cell> </row> <row> <cell><emph type="italics"></emph>Circulus admirabilißimus. <emph.end type="italics"></emph.end></cell> <cell>15</cell> </row> <row> <cell><emph type="italics"></emph>Circulus habet in ſe quinque repugnantias. <emph.end type="italics"></emph.end></cell> <cell>16</cell> </row> <row> <cell><emph type="italics"></emph>Circulus ſecit miracula in templis paganorum. <emph.end type="italics"></emph.end></cell> <cell>25</cell> </row> <row> <cell><emph type="italics"></emph>Circulus ante, & pone mouetur ſimul. <emph.end type="italics"></emph.end></cell> <cell>20.21</cell> </row> <row> <cell><emph type="italics"></emph>Circulus maior ad minorem ſemper nutum habet. <emph.end type="italics"></emph.end></cell> <cell>106</cell> </row> <row> <cell><emph type="italics"></emph>Circuli nutus eſt perpetuus. <emph.end type="italics"></emph.end></cell> <cell>107</cell> </row> <row> <cell><emph type="italics"></emph>Circuli quaſi motus eſt perpetuus. <emph.end type="italics"></emph.end></cell> <cell>107</cell> </row> <row> <cell><emph type="italics"></emph>Circuli minores infiniti ſunt in maiore circulo. <emph.end type="italics"></emph.end></cell> <cell>108</cell> </row> <row> <cell><emph type="italics"></emph>Circuli maiores ſunt mouentiores. <emph.end type="italics"></emph.end></cell> <cell>109</cell> </row> <row> <cell><emph type="italics"></emph>Circulus <expan abbr="cõtingit">contingit</expan> <expan abbr="planũ">planum</expan> in vno <expan abbr="pũcto">puncto</expan>. <emph.end type="italics"></emph.end></cell> <cell>101</cell> </row> <row> <cell><emph type="italics"></emph>Circuli maioris minor eſt angulus contactus quam minoris. <emph.end type="italics"></emph.end></cell> <cell>115</cell> </row> <row> <cell><emph type="italics"></emph>Circulus maior cum minore per æqualem orbitam reuoluitur & contra. <emph.end type="italics"></emph.end></cell> <cell>164</cell> </row> <row> <cell><emph type="italics"></emph>Circuli <expan abbr="cõcentrici">concentrici</expan> inæquales iuncti æqualem orbitam <expan abbr="percurrũt">percurrunt</expan>. <emph.end type="italics"></emph.end></cell> <cell>166.167.174</cell> </row> <row> <cell><emph type="italics"></emph>Circuli maioris motus ſecundum naturam maior eſt quam minoris. <emph.end type="italics"></emph.end></cell> <cell>43</cell> </row> <row> <cell><emph type="italics"></emph>in Circulo inſcriptas ſi ſecet recta ad rectos abſciſſa exdiametro erit maxima & <gap></gap>pinquior remotiore maior. <emph.end type="italics"></emph.end></cell> <cell>68.69</cell> </row> <row> <cell><emph type="italics"></emph>Circulum minorem qui datum maiorem interius tangat deſcribere. <emph.end type="italics"></emph.end></cell> <cell>41</cell> </row> <row> <cell><emph type="italics"></emph>Cœli motus unde. <emph.end type="italics"></emph.end></cell> <cell>104</cell> </row> <row> <cell><emph type="italics"></emph>Cœlum videre quid apud <expan abbr="Platonẽ">Platonem</expan>. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph><expan abbr="Colũba">Columba</expan> volans Acchitæ <expan abbr="nõ">non</expan> eſt fabula. <emph.end type="italics"></emph.end></cell> <cell>26</cell> </row> <row> <cell><emph type="italics"></emph>Contraria quæ ſint verè. <emph.end type="italics"></emph.end></cell> <cell>18</cell> </row> <row> <cell><emph type="italics"></emph>Commotum facilius mouetur, quam quieſcens. <emph.end type="italics"></emph.end></cell> <cell>199</cell> </row> <row> <cell><emph type="italics"></emph>Connexum & concauum non ſunt contraria. <emph.end type="italics"></emph.end></cell> <cell>19</cell> </row> <row> <cell><emph type="italics"></emph>Cochlea quid. <emph.end type="italics"></emph.end></cell> <cell>131</cell> </row> <row> <cell><emph type="italics"></emph>Cochleæ effecta. <emph.end type="italics"></emph.end></cell> <cell>133</cell> </row> <row> <cell><emph type="italics"></emph>Cochlea magnes vires habet. <emph.end type="italics"></emph.end></cell> <cell>133</cell> </row> <row> <cell><emph type="italics"></emph>Cochlea infinita. <emph.end type="italics"></emph.end></cell> <cell>133</cell> </row> <row> <cell><emph type="italics"></emph>Cochleæ Ariſtoteles non meminit. <emph.end type="italics"></emph.end></cell> <cell>131</cell> </row> <row> <cell><emph type="italics"></emph>Cochlea eſt cuneus multiplicatus, vel vnus cuneus continuatus. <emph.end type="italics"></emph.end></cell> <cell>131</cell> </row> <row> <cell><emph type="italics"></emph>Cuneus eſt vectu duplicatus. <emph.end type="italics"></emph.end></cell> <cell>127</cell> </row> <row> <cell><emph type="italics"></emph>Cuneum vicem gerere duorum vectium demonſtratio linearis. <emph.end type="italics"></emph.end></cell> <cell>130</cell> </row> <row> <cell><emph type="italics"></emph>Cuneus quid. <emph.end type="italics"></emph.end></cell> <cell>126</cell> </row> <row> <cell><emph type="italics"></emph>Cunci vſus. <emph.end type="italics"></emph.end></cell> <cell>127</cell> </row> <pb xlink:href="035/01/035.jpg"></pb> <row> <cell><emph type="italics"></emph>Cuneimagna vis. <emph.end type="italics"></emph.end></cell> <cell>127.127</cell> </row> <row> <cell><emph type="italics"></emph>Cuneo magnæ moles diuiduntur. <emph.end type="italics"></emph.end></cell> <cell>125</cell> </row> <row> <cell><emph type="italics"></emph>Crocæ Ariſtoteliquid. <emph.end type="italics"></emph.end></cell> <cell>123</cell> </row> <row> <cell><emph type="italics"></emph>Crocæ rotundæ. <emph.end type="italics"></emph.end></cell> <cell>122.123</cell> </row> <row> <cell><emph type="italics"></emph>Cubus ſtabilißima figurarum. <emph.end type="italics"></emph.end></cell> <cell>103</cell> </row> <row> <cell><emph type="italics"></emph>Currus iam commotus facilius mouetur. <emph.end type="italics"></emph.end></cell> <cell>200</cell> </row> <row> <cell><emph type="italics"></emph>D<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Dædali ſtatuæliberæ, & ligatæ. <emph.end type="italics"></emph.end></cell> <cell>25</cell> </row> <row> <cell><emph type="italics"></emph>Decubitus ſanorum in lecto. <emph.end type="italics"></emph.end></cell> <cell>176</cell> </row> <row> <cell><emph type="italics"></emph>Dens corroſus eximidebet. <emph.end type="italics"></emph.end></cell> <cell>153</cell> </row> <row> <cell><emph type="italics"></emph>Dens non temere eximi debet. <emph.end type="italics"></emph.end></cell> <cell>153</cell> </row> <row> <cell><emph type="italics"></emph>Dens forcipe facilius, quam manu euellitur. <emph.end type="italics"></emph.end></cell> <cell>153</cell> </row> <row> <cell><emph type="italics"></emph>Dentiducus quid. <emph.end type="italics"></emph.end></cell> <cell>132</cell> </row> <row> <cell><emph type="italics"></emph><expan abbr="Dẽtes">Dentes</expan> <expan abbr="animaliũ">animalium</expan> inciſij ſunt cunei. <emph.end type="italics"></emph.end></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"></emph>Dens priuſquam eximatur duo fieri poſtulat. <emph.end type="italics"></emph.end></cell> <cell>154</cell> </row> <row> <cell><emph type="italics"></emph>Dentis euellendi differentia à clauo infixo. <emph.end type="italics"></emph.end></cell> <cell>154</cell> </row> <row> <cell><emph type="italics"></emph>Deusnon admiratur. <emph.end type="italics"></emph.end></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"></emph>Diaconus ſacris veſtibus indutus imponit crucem apici obeliſci. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <row> <cell><emph type="italics"></emph>Diameter circuli, & Sphæræ inſiſtit plano ad rectos. <emph.end type="italics"></emph.end></cell> <cell>105</cell> </row> <row> <cell><emph type="italics"></emph>Diametri ad peripheriam quæratio. <emph.end type="italics"></emph.end></cell> <cell>32</cell> </row> <row> <cell><emph type="italics"></emph>Dies impoſitæ crucis obeliſco. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <row> <cell><emph type="italics"></emph>Dolabra eſt cuneus. <emph.end type="italics"></emph.end></cell> <cell>130</cell> </row> <row> <cell><emph type="italics"></emph>Dominicus Fontana machinator inſignis. <emph.end type="italics"></emph.end></cell> <cell>139</cell> </row> <row> <cell><emph type="italics"></emph>Dominici Fontanæ triumphus. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <row> <cell><emph type="italics"></emph>Domus integra à ſundamentis ſublata, & aliò tranſlata. <emph.end type="italics"></emph.end></cell> <cell>133</cell> </row> <row> <cell><emph type="italics"></emph>E<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Elementa quieſicunt adrectos angulos ſita. <emph.end type="italics"></emph.end></cell> <cell>196</cell> </row> <row> <cell><emph type="italics"></emph>Enſis eſt cuneus. <emph.end type="italics"></emph.end></cell> <cell>130</cell> </row> <row> <cell><foreign lang="el">*epipo/laia</foreign> <emph type="italics"></emph>vis quæ. <emph.end type="italics"></emph.end></cell> <cell>201.202</cell> </row> <row> <cell><emph type="italics"></emph>Equus Troianus machina er at. <emph.end type="italics"></emph.end></cell> <cell>12</cell> </row> <row> <cell><emph type="italics"></emph>Ergat a quid. <emph.end type="italics"></emph.end></cell> <cell>119</cell> </row> <row> <cell><emph type="italics"></emph>Ergatæ, & ſucculæ diſtinctio. <emph.end type="italics"></emph.end></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"></emph>Ergatam collopes maiores minoribus facilius mouent. <emph.end type="italics"></emph.end></cell> <cell>118.119</cell> </row> <row> <cell><emph type="italics"></emph>Exercitium militum in exercitu feriantium. <emph.end type="italics"></emph.end></cell> <cell>125</cell> </row> <row> <cell><emph type="italics"></emph>Exigua quæ. <emph.end type="italics"></emph.end></cell> <cell>204</cell> </row> <row> <cell><emph type="italics"></emph>F<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Fabrilis ars certitudine vincit cæteras. <emph.end type="italics"></emph.end></cell> <cell>4</cell> </row> <row> <cell><emph type="italics"></emph>Figura hominis <expan abbr="decũbentis">decumbentis</expan> exirema. <emph.end type="italics"></emph.end></cell> <cell>176</cell> </row> <row> <cell><emph type="italics"></emph>Figura <expan abbr="corporũiuuat">corporuniuuat</expan>, velimpedit multum corum inclinationes, & naturales impetus. <emph.end type="italics"></emph.end></cell> <cell>164</cell> </row> <row> <cell><emph type="italics"></emph>Figura decubitus humida, ſeu mediæ quæ. <emph.end type="italics"></emph.end></cell> <cell>176</cell> </row> <row> <cell><emph type="italics"></emph>Forceps, & forfex quid. <emph.end type="italics"></emph.end></cell> <cell>152</cell> </row> <row> <cell><emph type="italics"></emph>Fortuna inſiſtit Spharæ. <emph.end type="italics"></emph.end></cell> <cell>103</cell> </row> <row> <cell><emph type="italics"></emph>Funda quid. <emph.end type="italics"></emph.end></cell> <cell>116</cell> </row> <row> <cell><emph type="italics"></emph>Funda inuentum Phænicuno. <emph.end type="italics"></emph.end></cell> <cell>116</cell> </row> <row> <cell><emph type="italics"></emph>Fundæ vſus. <emph.end type="italics"></emph.end></cell> <cell>116.117</cell> </row> <row> <cell><emph type="italics"></emph>Fundæ cur Balearis. <emph.end type="italics"></emph.end></cell> <cell>116</cell> </row> <row> <cell><emph type="italics"></emph>Funda longius proijcit, quam manus. <emph.end type="italics"></emph.end></cell> <cell>115.117</cell> </row> <row> <cell><emph type="italics"></emph>Fundaiacit lapidem & plumbum. <emph.end type="italics"></emph.end></cell> <cell>117</cell> </row> <row> <cell><emph type="italics"></emph>Fuſtis ad genu fractus non lædit. <emph.end type="italics"></emph.end></cell> <cell>122</cell> </row> <row> <cell><emph type="italics"></emph>Fuſtis duobus cyphis impoſitus frangitur ſine cyphorum fractione & aquæ effuſione. <emph.end type="italics"></emph.end></cell> <cell>122</cell> </row> <row> <cell><emph type="italics"></emph>G<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Georgij Lhullerij machina. <emph.end type="italics"></emph.end></cell> <cell>137.138</cell> </row> <row> <cell><emph type="italics"></emph>Gubernaculum & eius partes. <emph.end type="italics"></emph.end></cell> <cell>73</cell> </row> <row> <cell><emph type="italics"></emph>Gubernaculi & remi differentia. <emph.end type="italics"></emph.end></cell> <cell>76</cell> </row> <row> <cell><emph type="italics"></emph>Gubernaculi magna vis in nauis motione. <emph.end type="italics"></emph.end></cell> <cell>71.72</cell> </row> <row> <cell><emph type="italics"></emph>Gyraphi ſoli crura poſteriora prioribus breuiora habent. <emph.end type="italics"></emph.end></cell> <cell>112</cell> </row> <row> <cell><emph type="italics"></emph>H<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Haſtæ ferrum eſt cuneus. <emph.end type="italics"></emph.end></cell> <cell>190</cell> </row> <row> <cell><emph type="italics"></emph>Hominem quieſcere, ſedare, ſurgere, ſtare, ambulare, currere eſt ex vſu Geometriæ,<emph.end type="italics"></emph.end></cell> <cell>198</cell> </row> <row> <cell><emph type="italics"></emph>Hominis quies eſt per rectos angulos. <emph.end type="italics"></emph.end></cell> <cell>196</cell> </row> <row> <cell><emph type="italics"></emph>Hominis ambulatio, & progreſsio, vs fiat. <emph.end type="italics"></emph.end></cell> <cell>198</cell> </row> <row> <cell><emph type="italics"></emph>Homo <expan abbr="nõ">non</expan> ſtatrectus, vt <expan abbr="cælũ">cælum</expan> videus. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Homo vnde factus Mechanicus. <emph.end type="italics"></emph.end></cell> <cell>7.8</cell> </row> <row> <cell><emph type="italics"></emph>Homo ſolus admiratur. <emph.end type="italics"></emph.end></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"></emph>Homo ſolus artifex. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <pb xlink:href="035/01/036.jpg"></pb> <row> <cell><emph type="italics"></emph>Homo ſoius ſedere poteſt. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Homo magnus & paruuus quis. <emph.end type="italics"></emph.end></cell> <cell>19</cell> </row> <row> <cell><emph type="italics"></emph>Homines duo ferentes pondus cum pertica, ſi pondus non eſt in eius medio, non æqualiter premuntur. <emph.end type="italics"></emph.end></cell> <cell>190.191</cell> </row> <row> <cell><emph type="italics"></emph>Horologia nostritemporis veterum clepſydras, & gnemones antecellunt. <emph.end type="italics"></emph.end></cell> <cell>26</cell> </row> <row> <cell><emph type="italics"></emph>Plorologium Argentorati <expan abbr="magniſicũ">magnificum</expan>. <emph.end type="italics"></emph.end></cell> <cell>26</cell> </row> <row> <cell><emph type="italics"></emph>Humero dextro onera difficilius feruntur, quam ſiniſtro. <emph.end type="italics"></emph.end></cell> <cell>187</cell> </row> <row> <cell><emph type="italics"></emph>Hypomochlium quid. <emph.end type="italics"></emph.end></cell> <cell>14.55</cell> </row> <row> <cell><emph type="italics"></emph>I<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Iaccre ſupinum quid. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>lacere pronum. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Jacere ſupinum & pronum commune eſt multis anim antibus. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Joannis iucundi problema. <emph.end type="italics"></emph.end></cell> <cell>145</cell> </row> <row> <cell><emph type="italics"></emph>L<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Lancea <expan abbr="perpẽdicularis">perpendicularis</expan> facilius fertur, quam obliquata. <emph.end type="italics"></emph.end></cell> <cell>185</cell> </row> <row> <cell><emph type="italics"></emph>Lecti lateribus cur fiunt dupli. <emph.end type="italics"></emph.end></cell> <cell>175</cell> </row> <row> <cell><emph type="italics"></emph>Libra maior eſt exactior minore. <emph.end type="italics"></emph.end></cell> <cell>27.44. 45</cell> </row> <row> <cell><emph type="italics"></emph>Libræ finis. <emph.end type="italics"></emph.end></cell> <cell>4</cell> </row> <row> <cell><emph type="italics"></emph>Libræpartes. <emph.end type="italics"></emph.end></cell> <cell>45.46</cell> </row> <row> <cell><emph type="italics"></emph>Libræfallaciæ. <emph.end type="italics"></emph.end></cell> <cell>46.47</cell> </row> <row> <cell><emph type="italics"></emph>Libræ valde exigua examinantis fabrica. <emph.end type="italics"></emph.end></cell> <cell>47</cell> </row> <row> <cell><emph type="italics"></emph>Librile <expan abbr="abſq;">abſque</expan> <expan abbr="põdere">pondere</expan> facilius mouetur. <emph.end type="italics"></emph.end></cell> <cell>112</cell> </row> <row> <cell><emph type="italics"></emph>Librilis brachia vt <expan abbr="maneãt">maneant</expan>, aut redeant ad <expan abbr="æquilibriũ">æquilibrium</expan> ſublatis <expan abbr="põderilus">ponderilus</expan>. <emph.end type="italics"></emph.end></cell> <cell>49.50</cell> </row> <row> <cell><emph type="italics"></emph>Librile <expan abbr="ligneũ">ligneum</expan> facilius mouetur ferreo. <emph.end type="italics"></emph.end></cell> <cell>113</cell> </row> <row> <cell><emph type="italics"></emph>Lignalongiora ſunt imbecilliora. <emph.end type="italics"></emph.end></cell> <cell>124</cell> </row> <row> <cell><emph type="italics"></emph>Ligna longa ab extremo difficilius <expan abbr="ferũtur">feruntur</expan> bumere, quam à medio. <emph.end type="italics"></emph.end></cell> <cell>183.184</cell> </row> <row> <cell><emph type="italics"></emph>Lignum vt è genu facilius <expan abbr="frãgatur">frangatur</expan>. <emph.end type="italics"></emph.end></cell> <cell>121</cell> </row> <row> <cell><emph type="italics"></emph>Linea deſcribens circulum <expan abbr="ſecundũ">ſecundum</expan> duas lationes ſertur. <emph.end type="italics"></emph.end></cell> <cell>28.34</cell> </row> <row> <cell><emph type="italics"></emph><expan abbr="Longũ">Longum</expan> pondus difficilius fertur humero, <expan abbr="quã">quam</expan> brcue, vt ſit <expan abbr="põdere">pondere</expan> æquale. <emph.end type="italics"></emph.end></cell> <cell>186.187</cell> </row> <row> <cell><emph type="italics"></emph>Lorain lectis extenduntur non ſecundum diametrum. <emph.end type="italics"></emph.end></cell> <cell>175.177</cell> </row> <row> <cell><emph type="italics"></emph>M<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Machina quid. <emph.end type="italics"></emph.end></cell> <cell>2</cell> </row> <row> <cell><emph type="italics"></emph>Machinarum quædam per ſe, quædamnon perſe mouentur. <emph.end type="italics"></emph.end></cell> <cell>10</cell> </row> <row> <cell><emph type="italics"></emph>Machinæ valentißimæ tres ex ſententia Hippocratis. <emph.end type="italics"></emph.end></cell> <cell>119</cell> </row> <row> <cell><emph type="italics"></emph>Machinarum pluribus, & diuerſarum compoſitio adæquat vnam, quæ tanta, quanta opus eſſet fierinon poteſt, propter defectum materiæ. <emph.end type="italics"></emph.end></cell> <cell>138.139</cell> </row> <row> <cell><emph type="italics"></emph>Machinæ ad ædificia, & ad bellum. <emph.end type="italics"></emph.end></cell> <cell>10</cell> </row> <row> <cell><emph type="italics"></emph>in Machinis faciendis lex obſeruanda. <emph.end type="italics"></emph.end></cell> <cell>10</cell> </row> <row> <cell><emph type="italics"></emph>Magnetis vis. <emph.end type="italics"></emph.end></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"></emph>Magna quæ. <emph.end type="italics"></emph.end></cell> <cell>204</cell> </row> <row> <cell><emph type="italics"></emph>Malus nauis. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <row> <cell><emph type="italics"></emph>Mali pterna. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <row> <cell><emph type="italics"></emph>Mallei <expan abbr="lõgius">longius</expan> <expan abbr="manubriũ">manubrium</expan> grauius ferit. <emph.end type="italics"></emph.end></cell> <cell>128</cell> </row> <row> <cell><emph type="italics"></emph>Manganaria pars Mechanices. <emph.end type="italics"></emph.end></cell> <cell>11</cell> </row> <row> <cell><emph type="italics"></emph>Manus eſt <expan abbr="inſtrumẽtũ">inſtrumentum</expan> <expan abbr="inſtrumẽtorũ">inſtrumentorum</expan>. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Manus tres partes. <emph.end type="italics"></emph.end></cell> <cell>118</cell> </row> <row> <cell><emph type="italics"></emph>Mechanica cur non eſſe Aristotelis viſum ſit Cardano & <expan abbr="Frãciſco">Franciſco</expan> patricio. <emph.end type="italics"></emph.end></cell> <cell>1</cell> </row> <row> <cell><emph type="italics"></emph>Mechanica ſunt Aristotelis. <emph.end type="italics"></emph.end></cell> <cell>2</cell> </row> <row> <cell><emph type="italics"></emph>Mechanicorum diuiſio. <emph.end type="italics"></emph.end></cell> <cell>2</cell> </row> <row> <cell><emph type="italics"></emph>Mechanica vnde dicta. <emph.end type="italics"></emph.end></cell> <cell>2.11</cell> </row> <row> <cell><emph type="italics"></emph>Mechanica quæ dici debeant. <emph.end type="italics"></emph.end></cell> <cell>2</cell> </row> <row> <cell><emph type="italics"></emph>Mechanice quid. <emph.end type="italics"></emph.end></cell> <cell>8.9</cell> </row> <row> <cell><emph type="italics"></emph>Mechanice partim eſt phyſica, partim mathematica. <emph.end type="italics"></emph.end></cell> <cell>4.12.13</cell> </row> <row> <cell><emph type="italics"></emph>Mechanicæ artes vnde dictæ. <emph.end type="italics"></emph.end></cell> <cell>2.3</cell> </row> <row> <cell><emph type="italics"></emph>Mechanice pars eſt philoſophiæ. <emph.end type="italics"></emph.end></cell> <cell>9</cell> </row> <row> <cell><emph type="italics"></emph>Mechanices finis. <emph.end type="italics"></emph.end></cell> <cell>9</cell> </row> <row> <cell><emph type="italics"></emph>Mechanicus ante aggreßionem operis quid conſiderare debeat. <emph.end type="italics"></emph.end></cell> <cell>13</cell> </row> <row> <cell><emph type="italics"></emph>Mechanice dicendi<emph.end type="italics"></emph.end> <foreign lang="el">paradocopoioi\. </foreign></cell> <cell>12</cell> </row> <row> <cell><emph type="italics"></emph>laus Mechanicorum. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <row> <cell><emph type="italics"></emph>Mens eſt ars artium. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Menſura rei cuiuſque debet eſſe determinata. <emph.end type="italics"></emph.end></cell> <cell>44</cell> </row> <row> <cell><emph type="italics"></emph>Mercatura opulenta. <emph.end type="italics"></emph.end></cell> <cell>4</cell> </row> <row> <cell><emph type="italics"></emph>Mercurius inſistit cubo. <emph.end type="italics"></emph.end></cell> <cell>103</cell> </row> <row> <cell><emph type="italics"></emph>Milij grana non ſunt ſimpliciter exigua. <emph.end type="italics"></emph.end></cell> <cell>204</cell> </row> <row> <cell><emph type="italics"></emph>Militaris ars vtilitate vincit cæteras. <emph.end type="italics"></emph.end></cell> <cell>4</cell> </row> <row> <cell><emph type="italics"></emph>Milo cuneum contemnens peryt. <emph.end type="italics"></emph.end></cell> <cell>127</cell> </row> <row> <cell><emph type="italics"></emph>Mobile motum quò vergit facile moue<emph.end type="italics"></emph.end><pb xlink:href="035/01/037.jpg"></pb><emph type="italics"></emph>tur. <emph.end type="italics"></emph.end></cell> <cell>103</cell> </row> <row> <cell><emph type="italics"></emph>Mobilis primi velocitas vt intelligatur. <emph.end type="italics"></emph.end></cell> <cell>104. </cell> </row> <row> <cell><emph type="italics"></emph>Mobilis primi motus eſt menſura aliorum motuum. <emph.end type="italics"></emph.end></cell> <cell>104</cell> </row> <row> <cell><emph type="italics"></emph>Mobile latius mouetur difficilius. <emph.end type="italics"></emph.end></cell> <cell>104</cell> </row> <row> <cell><emph type="italics"></emph>Moles exigua ſæpe magnam vim obtinet. <emph.end type="italics"></emph.end></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"></emph>Motus fit in tempore, & ſucceßiuè. <emph.end type="italics"></emph.end></cell> <cell>205</cell> </row> <row> <cell><emph type="italics"></emph>Motus minimus quis. <emph.end type="italics"></emph.end></cell> <cell>104</cell> </row> <row> <cell><emph type="italics"></emph>Mota duobus motibus ad eundem <expan abbr="terminũ">terminum</expan> <expan abbr="tendẽtibus">tendentibus</expan> celerius <expan abbr="mouẽtur">mouentur</expan>. <emph.end type="italics"></emph.end></cell> <cell>163</cell> </row> <row> <cell><emph type="italics"></emph>Motum duabus lationibus rationem habentibus fertur <expan abbr="ſecundũ">ſecundum</expan> <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan>. <emph.end type="italics"></emph.end></cell> <cell>30</cell> </row> <row> <cell><emph type="italics"></emph>Motum duabus lationibus rationem non habentibus <expan abbr="nõ">non</expan> fertur <expan abbr="ſecundũ">ſecundum</expan> <expan abbr="rectã">rectam</expan>. <emph.end type="italics"></emph.end></cell> <cell>30</cell> </row> <row> <cell><emph type="italics"></emph>Motus circularis omnium machinationum principia continet. <emph.end type="italics"></emph.end></cell> <cell>60</cell> </row> <row> <cell><emph type="italics"></emph>Motus difficultas in mobili à quibus pendeat. <emph.end type="italics"></emph.end></cell> <cell>101</cell> </row> <row> <cell><emph type="italics"></emph>Mulier parua non eſt pulchræ. <emph.end type="italics"></emph.end></cell> <cell>19</cell> </row> <row> <cell><emph type="italics"></emph>Mundus nutans non vere dici de terra à poëta. <emph.end type="italics"></emph.end></cell> <cell>104</cell> </row> <row> <cell><emph type="italics"></emph>Muſculus vecti comparatus à Galeno. <emph.end type="italics"></emph.end></cell> <cell>56</cell> </row> <row> <cell><emph type="italics"></emph>N<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Natura <expan abbr="eodẽ">eodem</expan> modo ſemper operatur, & eundem ſcopum habet. <emph.end type="italics"></emph.end></cell> <cell>6</cell> </row> <row> <cell><emph type="italics"></emph>Natura reſiſtit arti in multis. <emph.end type="italics"></emph.end></cell> <cell>8</cell> </row> <row> <cell><emph type="italics"></emph>Nauigandi ars admirabilis ob ſubtilitatem, & nauigationis pericula. <emph.end type="italics"></emph.end></cell> <cell>62</cell> </row> <row> <cell><emph type="italics"></emph>Nauigij Hieronis deſcriptio incredibilis. <emph.end type="italics"></emph.end></cell> <cell>73</cell> </row> <row> <cell><emph type="italics"></emph>Nauis quid, & partes. <emph.end type="italics"></emph.end></cell> <cell>62</cell> </row> <row> <cell><emph type="italics"></emph>Nauis Ptolemaicæ magnitudo. <emph.end type="italics"></emph.end></cell> <cell>63</cell> </row> <row> <cell><emph type="italics"></emph>Nauis iam mota ſacilius mouetur. <emph.end type="italics"></emph.end></cell> <cell>201</cell> </row> <row> <cell><emph type="italics"></emph>Nauis plus vehitur antrorſum, quam remi palmula retrorſum. <emph.end type="italics"></emph.end></cell> <cell>80</cell> </row> <row> <cell><emph type="italics"></emph>Nauis actuariæ promotio. <emph.end type="italics"></emph.end></cell> <cell>69</cell> </row> <row> <cell><emph type="italics"></emph>Nauis velocit as à quibus. <emph.end type="italics"></emph.end></cell> <cell>93</cell> </row> <row> <cell><emph type="italics"></emph>Nauium ſpecies. <emph.end type="italics"></emph.end></cell> <cell>63</cell> </row> <row> <cell><emph type="italics"></emph>Nauicula è plumbo tenui ſupernatat aquæ. <emph.end type="italics"></emph.end></cell> <cell>164</cell> </row> <row> <cell><emph type="italics"></emph>Nautæ in procellis ſolo vtuntur dolone. <emph.end type="italics"></emph.end></cell> <cell>94</cell> </row> <row> <cell><emph type="italics"></emph>Nautica ars opulenta. <emph.end type="italics"></emph.end></cell> <cell>4</cell> </row> <row> <cell><emph type="italics"></emph>Nuces à nucifrangibulo ſine ictu facilius franguntur, quam cum ictu. <emph.end type="italics"></emph.end></cell> <cell>155.156</cell> </row> <row> <cell><emph type="italics"></emph><expan abbr="Nucifrãgibuli">Nucifrangibuli</expan> & forcipis diſtinctio. <emph.end type="italics"></emph.end></cell> <cell>156</cell> </row> <row> <cell><emph type="italics"></emph>Nucifrangibulum ferreum facilius nucem frangit, quam ligneum. <emph.end type="italics"></emph.end></cell> <cell>167</cell> </row> <row> <cell><emph type="italics"></emph>Nutus quid. <emph.end type="italics"></emph.end></cell> <cell>104.108</cell> </row> <row> <cell><emph type="italics"></emph>Nutus quotuplex. <emph.end type="italics"></emph.end></cell> <cell>108</cell> </row> <row> <cell><emph type="italics"></emph>Nutus maioris peripheriæ maior eſt, quam minoris. <emph.end type="italics"></emph.end></cell> <cell>108</cell> </row> <row> <cell><emph type="italics"></emph>O<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Obeliſcus quid. <emph.end type="italics"></emph.end></cell> <cell>139</cell> </row> <row> <cell><emph type="italics"></emph>Obeliſcus Xyſtiqualis & <expan abbr="quãtus">quantus</expan>. <emph.end type="italics"></emph.end></cell> <cell>139</cell> </row> <row> <cell><emph type="italics"></emph>Obeliſcus Xyſti cuiprimo ſacer. <emph.end type="italics"></emph.end></cell> <cell>140</cell> </row> <row> <cell><emph type="italics"></emph>Obeliſcus vbiſitus erat. <emph.end type="italics"></emph.end></cell> <cell>140</cell> </row> <row> <cell><emph type="italics"></emph>quid Obeliſcus tranſlatus, & Christo ſacer cum cruce ſuper apice ſuo impoſita Christianis ſignificat. <emph.end type="italics"></emph.end></cell> <cell>140</cell> </row> <row> <cell><emph type="italics"></emph>molimina circa Obeliſci tranſlationem quinque, omnia difficillima. <emph.end type="italics"></emph.end></cell> <cell>140</cell> </row> <row> <cell><emph type="italics"></emph>ad Obeliſcum transferendum quæ machinæ, & quot adhibitæ. <emph.end type="italics"></emph.end></cell> <cell>140</cell> </row> <row> <cell><emph type="italics"></emph>circa <expan abbr="Obeliſcũ">Obeliſcum</expan> molitiones quiuque, quomodo, & à quibus perfectæ. <emph.end type="italics"></emph.end></cell> <cell>141</cell> </row> <row> <cell><emph type="italics"></emph>Obeliſci in area V aticani ante portam D. Fetri poſiti Ichnographiæ. <emph.end type="italics"></emph.end></cell> <cell>143</cell> </row> <row> <cell><emph type="italics"></emph>de Obeliſco & Xyſto V. Summ. Pont. & cruce Gulielmi Blanci <expan abbr="epigrãma">epigramma</expan>. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <row> <cell><foreign lang="el">*odonta/gra *h)/ \o)donta/gw=gos</foreign> <emph type="italics"></emph>quid. <emph.end type="italics"></emph.end></cell> <cell>152</cell> </row> <row> <cell><foreign lang="el">*odonta/gw=gos</foreign> <emph type="italics"></emph><expan abbr="plũbeus">plumbeus</expan> in <expan abbr="tẽplo">templo</expan> Apollinis Delphici quid ſignificabat. <emph.end type="italics"></emph.end></cell> <cell>153</cell> </row> <row> <cell><emph type="italics"></emph>Ovos quid. <emph.end type="italics"></emph.end></cell> <cell>119</cell> </row> <row> <cell><emph type="italics"></emph>Os arietinum volæ manus impoſitum frangitur manu illæſa. <emph.end type="italics"></emph.end></cell> <cell>122</cell> </row> <row> <cell><foreign lang="el">*ourano/skopos</foreign> <emph type="italics"></emph>piſcis velit nolio videt cælum. <emph.end type="italics"></emph.end></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"></emph>P<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Palang a quid. <emph.end type="italics"></emph.end></cell> <cell>191</cell> </row> <row> <cell><emph type="italics"></emph>Pedem facere. <emph.end type="italics"></emph.end></cell> <cell>95</cell> </row> <row> <cell><emph type="italics"></emph>Penteſpaston. <emph.end type="italics"></emph.end></cell> <cell>111.134</cell> </row> <row> <cell><emph type="italics"></emph>Percußio quid. <emph.end type="italics"></emph.end></cell> <cell>128</cell> </row> <row> <cell><emph type="italics"></emph>Percuſsionis duo modi. <emph.end type="italics"></emph.end></cell> <cell>128</cell> </row> <row> <cell><emph type="italics"></emph>Percußio à quibus fit maior. <emph.end type="italics"></emph.end></cell> <cell>128</cell> </row> <row> <cell><emph type="italics"></emph>Percußionis validiores cauſæ. <emph.end type="italics"></emph.end></cell> <cell>128.129</cell> </row> <pb xlink:href="035/01/038.jpg"></pb> <row> <cell><emph type="italics"></emph>Percuſsionis magna vis ad mouendum, findendum, frangendum, quatiendum. <emph.end type="italics"></emph.end></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"></emph>Perpendiculares à peripherijs in ſemidiametros circulorum inæqualium æquales auferunt ſegmenta ſemidiametrorum inæqualia, quorum maius eſt quod è minori aufertur. <emph.end type="italics"></emph.end></cell> <cell>40</cell> </row> <row> <cell><emph type="italics"></emph>Peripheriæ maiores à punctis à centro remotioribus deſcribuntur. <emph.end type="italics"></emph.end></cell> <cell>23</cell> </row> <row> <cell><emph type="italics"></emph>Petorita Gallorum petoritis Polonorum difficilius mouentur. <emph.end type="italics"></emph.end></cell> <cell>113</cell> </row> <row> <cell><emph type="italics"></emph>Phalanga quid. <emph.end type="italics"></emph.end></cell> <cell>191</cell> </row> <row> <cell><emph type="italics"></emph>Phalangary qui. <emph.end type="italics"></emph.end></cell> <cell>191</cell> </row> <row> <cell><emph type="italics"></emph>Phalangarij tetraphori, hexaphori. <emph.end type="italics"></emph.end></cell> <cell>191</cell> </row> <row> <cell><emph type="italics"></emph>Phalangij ictus. <emph.end type="italics"></emph.end></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"></emph>Phalanx. <emph.end type="italics"></emph.end></cell> <cell>146</cell> </row> <row> <cell><emph type="italics"></emph>Philoſophia principium duxit ab admiratione. <emph.end type="italics"></emph.end></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"></emph>Philoſophia eſt ars generalis omnibus faciendorum difficultatibus ſuccurrens. <emph.end type="italics"></emph.end></cell> <cell>9</cell> </row> <row> <cell><emph type="italics"></emph>Philoſophandi, vt admirandi ſemper occaſio erit. <emph.end type="italics"></emph.end></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"></emph>Plumbum vtri aëre pleno annexum tardius deſcendit in aquim, quam ſi non eſſet aunexum. <emph.end type="italics"></emph.end></cell> <cell>170</cell> </row> <row> <cell><foreign lang="el">*po/da e)rei=n,</foreign> <emph type="italics"></emph>& canere quid. <emph.end type="italics"></emph.end></cell> <cell>95</cell> </row> <row> <cell><foreign lang="el">*po/des, & pro/podes. </foreign></cell> <cell>96</cell> </row> <row> <cell><foreign lang="el">*poliorkitik*h\</foreign> <emph type="italics"></emph>pars Mechanices. <emph.end type="italics"></emph.end></cell> <cell>11</cell> </row> <row> <cell><foreign lang="el">*polu/spaston. </foreign></cell> <cell>111. 134</cell> </row> <row> <cell><emph type="italics"></emph>Pons Lutetiæ ab Henrico 111. inchoatus ab Henrico 1111. perficietur. <emph.end type="italics"></emph.end></cell> <cell>120</cell> </row> <row> <cell><emph type="italics"></emph>Preßio porrecta. <emph.end type="italics"></emph.end></cell> <cell>14</cell> </row> <row> <cell><emph type="italics"></emph>Problema difficillimum totius libri. <emph.end type="italics"></emph.end></cell> <cell>166</cell> </row> <row> <cell><emph type="italics"></emph>Problematis a theoremate diſtinctio. <emph.end type="italics"></emph.end></cell> <cell>12</cell> </row> <row> <cell><emph type="italics"></emph>Progreßio in animali vt fit. <emph.end type="italics"></emph.end></cell> <cell>187</cell> </row> <row> <cell><emph type="italics"></emph>Proiecta cur moueri deſinunt. <emph.end type="italics"></emph.end></cell> <cell>201</cell> </row> <row> <cell><emph type="italics"></emph>in Proiectis impreſſa vis impellens à motore eſt canſa eorum lationis. <emph.end type="italics"></emph.end></cell> <cell>201</cell> </row> <row> <cell><emph type="italics"></emph>Proiecta nec exigua nec magna ſeruntur procul. <emph.end type="italics"></emph.end></cell> <cell>203.205</cell> </row> <row> <cell><emph type="italics"></emph>Publ. Scipio & C. Lælius colligentes crocas quæ dicerent. <emph.end type="italics"></emph.end></cell> <cell>123</cell> </row> <row> <cell><emph type="italics"></emph>Purpura quid. <emph.end type="italics"></emph.end></cell> <cell>47.48</cell> </row> <row> <cell><emph type="italics"></emph>Q<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Qvieſcens vim motoris diminuit. <emph.end type="italics"></emph.end></cell> <cell>200</cell> </row> <row> <cell><emph type="italics"></emph>R<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Radius minor plus retrahitur ad centrum, quam maior. <emph.end type="italics"></emph.end></cell> <cell>38.39</cell> </row> <row> <cell><emph type="italics"></emph>Rectilineæ figuræ, & cubus difficulter mouentur ſuper planum. <emph.end type="italics"></emph.end></cell> <cell>102</cell> </row> <row> <cell><emph type="italics"></emph>Remus quid. <emph.end type="italics"></emph.end></cell> <cell>63</cell> </row> <row> <cell><emph type="italics"></emph>Remiges qui. <emph.end type="italics"></emph.end></cell> <cell>63</cell> </row> <row> <cell><emph type="italics"></emph>Remigum differentiæ. <emph.end type="italics"></emph.end></cell> <cell>64</cell> </row> <row> <cell><emph type="italics"></emph>Remiges meſonei maximè mouent nauim. <emph.end type="italics"></emph.end></cell> <cell>61</cell> </row> <row> <cell><emph type="italics"></emph>Remi digitis manuum comparati. <emph.end type="italics"></emph.end></cell> <cell>65</cell> </row> <row> <cell><emph type="italics"></emph>Remus vt plurimum maris diuidit. <emph.end type="italics"></emph.end></cell> <cell>71</cell> </row> <row> <cell><emph type="italics"></emph>de Remi motione comparata ad motionem nauis. <emph.end type="italics"></emph.end></cell> <cell>84.85.86.87.88.89</cell> </row> <row> <cell><emph type="italics"></emph>qui <expan abbr="Remigũ">Remigum</expan> plus nauim promoueant. <emph.end type="italics"></emph.end></cell> <cell>68</cell> </row> <row> <cell><emph type="italics"></emph>in Rhombo punctum vnum extremum lateris motum duobus motibus minus ſpaty conficit, quam latus ipſum. <emph.end type="italics"></emph.end></cell> <cell>159</cell> </row> <row> <cell><emph type="italics"></emph>Rhombus conſtituitur cuius angulus acutus eſt dimidio obtuſi minor. <emph.end type="italics"></emph.end></cell> <cell>161</cell> </row> <row> <cell><emph type="italics"></emph>in Rhombo alterum punctorum extremorum non æqualem <expan abbr="rectã">rectam</expan> tranſit. <emph.end type="italics"></emph.end></cell> <cell>157</cell> </row> <row> <cell><emph type="italics"></emph>Rhombus quid. <emph.end type="italics"></emph.end></cell> <cell>159</cell> </row> <row> <cell><emph type="italics"></emph>Rotæ binæ quaternis faciliores. <emph.end type="italics"></emph.end></cell> <cell>111</cell> </row> <row> <cell><emph type="italics"></emph>in Rotis quaternis poſteriores prioribus maioreseſſe debent. <emph.end type="italics"></emph.end></cell> <cell>111</cell> </row> <row> <cell><emph type="italics"></emph>Rotæ curruum maiores commodiores ad facilitatem & celeritatem. <emph.end type="italics"></emph.end></cell> <cell>110</cell> </row> <row> <cell><emph type="italics"></emph>Rotunda figura difficulter patitur. <emph.end type="italics"></emph.end></cell> <cell>124</cell> </row> <row> <cell><emph type="italics"></emph>Rotunda maiora facilius mouentur minoribus. <emph.end type="italics"></emph.end></cell> <cell>99.100</cell> </row> <row> <cell><emph type="italics"></emph><expan abbr="Rotũdorum">Rotundorum</expan> motus accurata diuiſio. <emph.end type="italics"></emph.end></cell> <cell>100</cell> </row> <row> <cell><emph type="italics"></emph>S<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Sarcina maior in anteriore plaustri parte poni debet. <emph.end type="italics"></emph.end></cell> <cell>111</cell> </row> <row> <cell><emph type="italics"></emph>Saxa tritalantaria ſimpliciter non ſunt magna. <emph.end type="italics"></emph.end></cell> <cell>204</cell> </row> <row> <cell><emph type="italics"></emph>Scorpionis ictus. <emph.end type="italics"></emph.end></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"></emph>Scytala quid, & quotuplex. <emph.end type="italics"></emph.end></cell> <cell>111.114</cell> </row> <row> <cell><emph type="italics"></emph>Scytalæ vſus duplex. <emph.end type="italics"></emph.end></cell> <cell>111</cell> </row> <row> <cell><emph type="italics"></emph>Super Scytalis onera facilius geſtantur,<emph.end type="italics"></emph.end><pb xlink:href="035/01/039.jpg"></pb><emph type="italics"></emph>quam ſuper curribus. <emph.end type="italics"></emph.end></cell> <cell>113</cell> </row> <row> <cell><emph type="italics"></emph>Securis magna diuidit. <emph.end type="italics"></emph.end></cell> <cell>145</cell> </row> <row> <cell><emph type="italics"></emph>Securis feriens diuidit, premens non item. <emph.end type="italics"></emph.end></cell> <cell>144</cell> </row> <row> <cell><emph type="italics"></emph>Securis eſt cuneus annexus malleo. <emph.end type="italics"></emph.end></cell> <cell>145</cell> </row> <row> <cell><emph type="italics"></emph>Sedere quid. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Sedens caput habet ad pedes parallelum, & nequaquam in vnarecta. <emph.end type="italics"></emph.end></cell> <cell>193</cell> </row> <row> <cell><emph type="italics"></emph>Sedentariæ artes vtuntur ſeßione ſecura. <emph.end type="italics"></emph.end></cell> <cell>197</cell> </row> <row> <cell><emph type="italics"></emph>Sedile idem non congruit omni homini. <emph.end type="italics"></emph.end></cell> <cell>196</cell> </row> <row> <cell><emph type="italics"></emph>Seßio propriè dista & latè<emph.end type="italics"></emph.end></cell> <cell>197</cell> </row> <row> <cell><emph type="italics"></emph>Seßio cum ſecuritate. <emph.end type="italics"></emph.end></cell> <cell>197</cell> </row> <row> <cell><emph type="italics"></emph>Sedens altius ſurgit facilius. <emph.end type="italics"></emph.end></cell> <cell>197.198</cell> </row> <row> <cell><foreign lang="el">*s*h/kwma</foreign> <emph type="italics"></emph>quid. <emph.end type="italics"></emph.end></cell> <cell>151</cell> </row> <row> <cell><emph type="italics"></emph>Spartion pro anſa. <emph.end type="italics"></emph.end></cell> <cell>148</cell> </row> <row> <cell><emph type="italics"></emph>Sphæra quale corpus. <emph.end type="italics"></emph.end></cell> <cell>16</cell> </row> <row> <cell><emph type="italics"></emph>Sphæra corpus eſt mobilißimum & mouentißimum. <emph.end type="italics"></emph.end></cell> <cell>16</cell> </row> <row> <cell><emph type="italics"></emph>Sphæra contingit planum in puncto. <emph.end type="italics"></emph.end></cell> <cell>101</cell> </row> <row> <cell><emph type="italics"></emph>Sphæra Archimedis per ſe mobilis non eſt fabula. <emph.end type="italics"></emph.end></cell> <cell>26</cell> </row> <row> <cell><emph type="italics"></emph>Sphæratopæia pars eſt mechanices. <emph.end type="italics"></emph.end></cell> <cell>11</cell> </row> <row> <cell><emph type="italics"></emph>Stateræ partes. <emph.end type="italics"></emph.end></cell> <cell>147</cell> </row> <row> <cell><emph type="italics"></emph>Stateræ vſus. <emph.end type="italics"></emph.end></cell> <cell>148</cell> </row> <row> <cell><emph type="italics"></emph>Statera in pretioſis expendendis non vſurpatur, ſed libra. <emph.end type="italics"></emph.end></cell> <cell>147</cell> </row> <row> <cell><emph type="italics"></emph>Statera commodior libra. <emph.end type="italics"></emph.end></cell> <cell>147</cell> </row> <row> <cell><emph type="italics"></emph>Statera vna mult æ ſunt libræ. <emph.end type="italics"></emph.end></cell> <cell>148.149</cell> </row> <row> <cell><emph type="italics"></emph>Statera eſt vectis inuerſus. <emph.end type="italics"></emph.end></cell> <cell>150</cell> </row> <row> <cell><emph type="italics"></emph>Stateræ paruo æquipondio magna pondera expendunt. <emph.end type="italics"></emph.end></cell> <cell>146.147.148</cell> </row> <row> <cell><emph type="italics"></emph>Stateræ dimidium eſt anſa. <emph.end type="italics"></emph.end></cell> <cell>148</cell> </row> <row> <cell><emph type="italics"></emph>Per Stateram ponderationis factæ demonſtratio. <emph.end type="italics"></emph.end></cell> <cell>152</cell> </row> <row> <cell><emph type="italics"></emph>Stare quid. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Stans eſt perpendicularis terræ. <emph.end type="italics"></emph.end></cell> <cell>193</cell> </row> <row> <cell><emph type="italics"></emph>Stantis diſpoſitio eſt in recta linea. <emph.end type="italics"></emph.end></cell> <cell>196</cell> </row> <row> <cell><emph type="italics"></emph>Statio & ſeßio propria <expan abbr="sũt">sunt</expan> homini. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><foreign lang="el">*stata</foreign> <emph type="italics"></emph>quæ. <emph.end type="italics"></emph.end></cell> <cell>10</cell> </row> <row> <cell><emph type="italics"></emph>Succula quid. <emph.end type="italics"></emph.end></cell> <cell>119</cell> </row> <row> <cell><emph type="italics"></emph>Surrectio eſt motio. <emph.end type="italics"></emph.end></cell> <cell>194</cell> </row> <row> <cell><emph type="italics"></emph>Surrectio è iacente indiget acutis angulis. <emph.end type="italics"></emph.end></cell> <cell>197</cell> </row> <row> <cell><emph type="italics"></emph>Surgentes conſtituunt angulum acutum ex femore cum tibia, tum ex thoræce & femore. <emph.end type="italics"></emph.end></cell> <cell>193.195.196</cell> </row> <row> <cell><emph type="italics"></emph>Surrectionis initium fit per acutos angulos. <emph.end type="italics"></emph.end></cell> <cell>198</cell> </row> <row> <cell><emph type="italics"></emph>Surrectionis medium fit per rectum, & obtuſos angulos. <emph.end type="italics"></emph.end></cell> <cell>198</cell> </row> <row> <cell><emph type="italics"></emph>Symmetria quid. <emph.end type="italics"></emph.end></cell> <cell>19</cell> </row> <row> <cell><emph type="italics"></emph>Symmetria pro analogia. <emph.end type="italics"></emph.end></cell> <cell>205</cell> </row> <row> <cell><emph type="italics"></emph>T<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Telum facilius tenſa penetrat, quam laxa. <emph.end type="italics"></emph.end></cell> <cell>202</cell> </row> <row> <cell><emph type="italics"></emph>Terra cur immobilis. <emph.end type="italics"></emph.end></cell> <cell>103.104</cell> </row> <row> <cell><emph type="italics"></emph>Terra comparata cubo à Pythagoreis, & Platone. <emph.end type="italics"></emph.end></cell> <cell>103.196</cell> </row> <row> <cell><emph type="italics"></emph>Textus Ariſtotelis omnium mendoſiſſimus. <emph.end type="italics"></emph.end></cell> <cell>178.179</cell> </row> <row> <cell><emph type="italics"></emph>Thaletis factum in eclipſi Solis. <emph.end type="italics"></emph.end></cell> <cell>5</cell> </row> <row> <cell><foreign lang="el">*qaumatourgik*h\</foreign> <emph type="italics"></emph>pars Mechanices. <emph.end type="italics"></emph.end></cell> <cell>11</cell> </row> <row> <cell><emph type="italics"></emph>Theorematis à problemate diſtinctio. <emph.end type="italics"></emph.end></cell> <cell>12</cell> </row> <row> <cell><emph type="italics"></emph>Tolleno quid. <emph.end type="italics"></emph.end></cell> <cell>188.189</cell> </row> <row> <cell><emph type="italics"></emph>Tollenonis vſus. <emph.end type="italics"></emph.end></cell> <cell>189</cell> </row> <row> <cell><emph type="italics"></emph>Tollenonis tranſuer ſario pondus adiectum. <emph.end type="italics"></emph.end></cell> <cell>188.190</cell> </row> <row> <cell><emph type="italics"></emph>Tormenta bellica deducenda plures equos poſtulant. <emph.end type="italics"></emph.end></cell> <cell>110.111</cell> </row> <row> <cell><emph type="italics"></emph>Traba quid. <emph.end type="italics"></emph.end></cell> <cell>115</cell> </row> <row> <cell><emph type="italics"></emph>Trispaſton. <emph.end type="italics"></emph.end></cell> <cell>111.134</cell> </row> <row> <cell><emph type="italics"></emph>Trochlea quid. <emph.end type="italics"></emph.end></cell> <cell>111.134</cell> </row> <row> <cell><emph type="italics"></emph>Trochlea eſt vectis. <emph.end type="italics"></emph.end></cell> <cell>136</cell> </row> <row> <cell><emph type="italics"></emph>in Trochleis plures orbiculi facilius, ſed lentius trahunt. <emph.end type="italics"></emph.end></cell> <cell>137</cell> </row> <row> <cell><emph type="italics"></emph>Trochleæ duæ legitimè compofitæ magna pondera adducunt. <emph.end type="italics"></emph.end></cell> <cell>133.134.136</cell> </row> <row> <cell><emph type="italics"></emph>V<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Vectis quid. <emph.end type="italics"></emph.end></cell> <cell>14.55</cell> </row> <row> <cell><emph type="italics"></emph>Vectis, cuneus. <emph.end type="italics"></emph.end></cell> <cell>119</cell> </row> <row> <cell><emph type="italics"></emph>Vectis partes. <emph.end type="italics"></emph.end></cell> <cell>14.15</cell> </row> <row> <cell><emph type="italics"></emph>Vectis vſus duplex. <emph.end type="italics"></emph.end></cell> <cell>55</cell> </row> <row> <cell><emph type="italics"></emph>Vectis refert libram. <emph.end type="italics"></emph.end></cell> <cell>57</cell> </row> <row> <cell><emph type="italics"></emph>pro Vecte vnum ſtadium longo machinæ multæ ſimul. <emph.end type="italics"></emph.end></cell> <cell>139</cell> </row> <row> <cell><emph type="italics"></emph>Velum quid. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <pb xlink:href="035/01/040.jpg"></pb> <row> <cell><emph type="italics"></emph>Veliſpecies. <emph.end type="italics"></emph.end></cell> <cell>92</cell> </row> <row> <cell><emph type="italics"></emph>Ventus ſecundui, aduerſus, iranſuerſus, obliquus. <emph.end type="italics"></emph.end></cell> <cell>96</cell> </row> <row> <cell><emph type="italics"></emph>Vento vt codem in contrarias partes nauigatur demonstratio. <emph.end type="italics"></emph.end></cell> <cell>98</cell> </row> <row> <cell><emph type="italics"></emph>in Vortice aquarum lata ad medium deuoluuntur. <emph.end type="italics"></emph.end></cell> <cell>206.207.209.210</cell> </row> <row> <cell><emph type="italics"></emph>Vortex aquarum. <emph.end type="italics"></emph.end></cell> <cell>206</cell> </row> <row> <cell><emph type="italics"></emph>in Vortice aquoſi multi circuli concentrici. <emph.end type="italics"></emph.end></cell> <cell>206</cell> </row> <row> <cell><emph type="italics"></emph>Vortex aquæ eſt linea ſpiralis vnius, aut plurium reuolutionum. <emph.end type="italics"></emph.end></cell> <cell>209</cell> </row> <row> <cell><emph type="italics"></emph>Vortices quomodo à nautis vitentar. <emph.end type="italics"></emph.end></cell> <cell>210</cell> </row> <row> <cell><emph type="italics"></emph>Vortices inter Roeſt & Loffoet. <emph.end type="italics"></emph.end></cell> <cell>210</cell> </row> <row> <cell><emph type="italics"></emph>in Vorticem vt ſentiunt nautæ ſe impe<gap></gap>giſſe. <emph.end type="italics"></emph.end></cell> <cell>210</cell> </row> <row> <cell><emph type="italics"></emph>difficile ſe liberare à Vortice. <emph.end type="italics"></emph.end></cell> <cell>210.211</cell> </row> <row> <cell><emph type="italics"></emph>aquain Vortice <expan abbr="deſcẽdẽs">deſcendens</expan> quò feratur. <emph.end type="italics"></emph.end></cell> <cell>211</cell> </row> <row> <cell><emph type="italics"></emph>Vtilitas hominum postulat in operibus ſuis varietatem. <emph.end type="italics"></emph.end></cell> <cell>6</cell> </row> <row> <cell><emph type="italics"></emph>X<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><emph type="italics"></emph>Xystus V. Pont. Max. obeliſci tranſferendi author. <emph.end type="italics"></emph.end></cell> <cell>139</cell> </row> <row> <cell><emph type="italics"></emph>Xysti V. Pontificis laus. <emph.end type="italics"></emph.end></cell> <cell>142</cell> </row> <row> <cell><emph type="italics"></emph>Z<emph.end type="italics"></emph.end></cell> <cell></cell> </row> <row> <cell><foreign lang="el">*zugo\s & *zugo\n. </foreign></cell> <cell>45.119</cell> </row> <row> <cell><foreign lang="el">*zugosta/ths. </foreign></cell> <cell>45</cell> </row> <row> <cell><emph type="italics"></emph>Zygostatica fides. <emph.end type="italics"></emph.end></cell> <cell>45</cell> </row> </table> <p type="head"> <s id="id.000238">FINIS. </s> <pb xlink:href="035/01/041.jpg" pagenum="1"></pb> <figure id="id.035.01.041.1.jpg" xlink:href="035/01/041/1.jpg"></figure> </p> </section> </front> <body> <chap> <subchap1> <p type="head"> <s id="id.000239"><foreign lang="el">*a*r*i*s*t*o*t*e*l*o*u*s <lb></lb>*m*h*x*a*n*i*k*a</foreign>. <lb></lb>ARISTOTELIS <lb></lb>MECHANICA. </s> </p> <p type="main"> <s id="id.000241"><foreign lang="el">Ti/ e)sti mhxanh\, kai=\ peri\ ku/klou, tw=n e)n toi=s mhxanikoi=s <lb></lb>qaumasi/wn ai)ti/an e)/xontos. <arrow.to.target n="marg1"></arrow.to.target></foreign></s> </p> <p type="head"> <s id="id.000242"><margin.target id="marg1"></margin.target>Pro <foreign lang="el">mhxanh\,</foreign><lb></lb>lege <foreign lang="el">mhxani<lb></lb>kh/. </foreign></s> </p> <p type="head"> <s id="id.000243"><emph type="italics"></emph>Quid eſt Mechanice, & de circulo in quo admirabilium, <lb></lb>quæ ſunt in Mechanicis, cauſa continetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000244"><foreign lang="el">*q*a*u*m*a*z*e*t*a*i tw=n me\n kata\ fu/sin sumbaino/ntwn, o(/swn <lb></lb>a)gnoei=tai to\ ai)/tion, tw=n de\ para\ fu/sin, o(/sa gi/netai dia\ <lb></lb>te/xnhn pro\s to\ sumfe/ron toi=s a)nqrw/pois.</foreign></s> </p> <p type="main"> <s id="id.000245">MIRA ſunt in his, quæ <lb></lb><expan abbr="ſecundũ">ſecundum</expan> <expan abbr="naturã">naturam</expan> <expan abbr="eueniũt">eue<lb></lb>niunt</expan>, ea: <expan abbr="quorũ">quorum</expan> cauſa igno<lb></lb>ratur, & in his quæ præter <lb></lb>naturam, ea, <expan abbr="quęcunq;">quęcunque</expan> arte <lb></lb>facta hominibus <expan abbr="cõferunt">conferunt</expan>. </s> </p> <p type="head"> <s id="id.000246">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000247"><emph type="italics"></emph>Cardanvs librum hunc Ariſtotelis peripate<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg2"></arrow.to.target><lb></lb><emph type="italics"></emph>ticorum principis eſſe non arbitratur, propter man<lb></lb>cam, & paulo negligentiorem motuum rotundo<lb></lb>rum in eo poſitam diuiſionem. </s> <s id="id.000248">Franciſcus Patri<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg3"></arrow.to.target><lb></lb><emph type="italics"></emph>cius vbi in omnes Ariſtotelis libros diligenter in<lb></lb>quirit, ab eorum numero excluſit, cauſam tamen attulit nullam, niſi <lb></lb>quod multi libri magnorum virorum nomine circumferantur, quo<lb></lb>rum ipſi authores non ſunt. </s> <s id="id.000249">quod licet verum eſſe multis rationibus,<emph.end type="italics"></emph.end><pb xlink:href="035/01/042.jpg" pagenum="2"></pb><emph type="italics"></emph>testimoniis, & exemplis confirmarit: ob id tamen hunc Ariſtoteli <lb></lb>detrahendum eſſe, non eſt neceſſe. </s> <s id="id.000250">Quid ita? </s> <s id="id.000251">Ipſemet Patricius fate<lb></lb>tur hunc<emph.end type="italics"></emph.end> <foreign lang="el">tw=n mhxanikw=n</foreign> <emph type="italics"></emph>librum doctum eſſe, & elegantem: addo <lb></lb>& ſubtilem, & ab Ariſtotelis <expan abbr="verũ">verum</expan> in vnaquaque re, ſimplex. </s> <s id="id.000252">ſyn<lb></lb>cerumque exquirentis ingenio minime abhorrentem, vt ipſum, & <lb></lb>noſtros in ipſum commentarios cuique legenti manifeſtum euadet. <lb></lb></s> <s id="id.000253">Phraſis non repugnat, ſi cum ea <expan abbr="cõferatur">conferatur</expan>, quæ fuit familiaris Ari<lb></lb>ſtoteli in mathematicis, vt cum de Iride, aut de lineis inſecabilibus <lb></lb>diſputat. </s> <s id="id.000254">Diogenes Laërtius inter Ariſtotelis monumenta<emph.end type="italics"></emph.end> <foreign lang="el">mhxani<lb></lb>kw=n</foreign> <emph type="italics"></emph>vnum recenſuit. </s> <s id="id.000255">Multi clari viri noſtri temporis vt Daniel <lb></lb>Barbarus & Guidus Vbaldus ſæpe velut ab Ariſtotele citant. </s> <s id="id.000256">No<lb></lb>nius interpretatus eſt ſuis diſcipulis. </s> <s id="id.000257">Cardani ratio parui eſt <expan abbr="momẽti">momenti</expan>. <lb></lb></s> <s id="id.000258">quia Ariſtoteles etiam in his, qui genuini ſunt eius libri ſine contro<lb></lb>uerſia, non ſemper rerum exquiſitas diuiſiones inſtituit. </s> <s id="id.000259">Quare hunc <lb></lb>librum Ariſtotelis eſſe putabimus, quouſque exoriatur aliquis, qui <lb></lb>vel hunc ſibi vendicare, vel alij tribuere, potiori iure poßit. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000260"><margin.target id="marg2"></margin.target>Lib. de pro<lb></lb>port. </s> </p> <p type="margin"> <s id="id.000261"><margin.target id="marg3"></margin.target>Tom.I.li.3. <lb></lb>Diſcuſſio<lb></lb>num peri<lb></lb>patetic. </s> </p> <p type="main"> <s id="id.000262">Mechanica] <emph type="italics"></emph>Huius libri duæ ſunt partes. </s> <s id="id.000263">prior generalis eſt <lb></lb>in explicatione cauſarum & principiorum, quibus machinæ in mo<lb></lb>uendo magnas, & admirabiles vires habent: poſterior ſpecialis eſt <lb></lb>in explicatione 25. quæstionum de quarundam machinarum viribus <lb></lb>& effectis. </s> <s id="id.000264">Hæc autem <emph.end type="italics"></emph.end><foreign lang="el">tw=n mhxanikw=n</foreign> <emph type="italics"></emph>titulo recte exprimuntur. <lb></lb></s> <s id="id.000265">quia Mechanica dicta ſunt<emph.end type="italics"></emph.end> <foreign lang="el">a)po\ th=s mhxanh=s. </foreign>& <foreign lang="el">*mhxanh\ a)po\ tou= <lb></lb>mh/kous kai\ a)/nein,</foreign> <emph type="italics"></emph>id eſt longè vel multùm aſcendere, pertingere, pene<lb></lb>trare, vt eſt apud Platonem in Cratylo, vnde non quælibet artifi<lb></lb>cia protrita & vulgaria Mechanica dicenda ſunt, ſed ea tantum <lb></lb>quæ vtiliter & iucundè ſuccurrunt, & adminiculantur difficul<lb></lb>tatibus quæ in actionibus humanis ſeſe <expan abbr="obtrudũt">obtrudunt</expan>, ipſaſque <expan abbr="impediũt">impediunt</expan>. <emph.end type="italics"></emph.end><lb></lb></s> <s><foreign lang="el">*mhxanh\</foreign> <emph type="italics"></emph>autem id eſt machina definitur à Vitruuio, continens ex <lb></lb>materia coniunctio, quæ maximas habet, ad onerum motus virtu<lb></lb>tes: & à Plinio inſtrumentum, quo moles aliqua facile, quocumque <lb></lb>volueris impelli poteſt. </s> <s id="id.000267">Igitur tum hæc inſtrumenta & machinæ: <lb></lb>tum doctrina, quæ virium, quibus hæc pollent, rationem docet, & <lb></lb>explicat, rectè Mechanica inſcribuntur. </s> <s id="id.000268">Sed vereor, ne hæc libri <lb></lb>inſcriptio, ex vulgari artium diuiſione in liberales & mechanicas, <lb></lb>quid ſordidi ſubolens multis, ipſos ab huius libri lectione deterruerit <lb></lb>& deterreat. </s> <s id="id.000269">At quæcumque, eluenda eſt macula. </s> <s id="id.000270">Manauit enim à<emph.end type="italics"></emph.end><pb xlink:href="035/01/043.jpg" pagenum="3"></pb><emph type="italics"></emph>quibuſdam philoſophis, iiſque otioſis, qui vt maiorem dignitatem <lb></lb>ſibi fingerent, eas artes nobilitatis titulo ornauere, quæ in ſola con<lb></lb>templatione verſarentur, & contemplantis duntaxat ingenium <lb></lb>acuerent, atque perficerent: viles autem eas putauere, quæ ocium fu<lb></lb>gientes, in negotio atque efficientia occuparentur. </s> <s id="id.000271">At ij melius <lb></lb>meo iudicio feciſſent, ſi eas, quæ ita corporis adminiculo exercen<lb></lb>tur, vt animi ſtudium non multum requirant, cum Græcis appel<lb></lb>laſſent, non<emph.end type="italics"></emph.end> <foreign lang="el">mhxanika\s,</foreign> <emph type="italics"></emph>( neque enim hîc id vocabuli vſurpant ) <lb></lb>ſed<emph.end type="italics"></emph.end> <foreign lang="el">fau/las, a)neleuqe/rous banau/sous a)gorai/ous</foreign> <emph type="italics"></emph>viles, illiberales, <lb></lb>ſordidas, circunforaneas. </s> <s id="id.000272">Melius eſt ergo rem iſtam paulo altius re<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg4"></arrow.to.target><lb></lb><emph type="italics"></emph>petitam aliquantum vltra per ſuas ſpecies deducere. </s> <s id="id.000273">Cum omnis ars, <lb></lb>vt eſt apud Ariſtotelem, referatur ad bonum, nulla per ſe vilis cen<lb></lb>ſeri debet, immo omnis poſſeſſorem ſuum vel meliorem vel vtilio<lb></lb>rem ſibi, vel ſuæ ciuitati reddit: at inter ſe comparatæ aliæ aliis præ<lb></lb>ſtantiores existimatæ ſunt. </s> <s id="id.000274">vnde nata eſt hæc vulgaris artium diui<lb></lb>ſio, vt aliæ liberales eſſent: aliæ mechanicæ. </s> <s id="id.000275">quæ his duobus verſibus <lb></lb>exprimuntur. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000276"><margin.target id="marg4"></margin.target>Lib I.cap i. <lb></lb>Ethic. </s> </p> <p type="main"> <s id="id.000277">Lingua, Tropus, Ratio, Numerus, Tonus, Angulus, Aſtra: <lb></lb> Rus, Nemus, Arma, Faber, Vulnera, Lana, Rates. </s> </p> <p type="main"> <s><emph type="italics"></emph>horum priore ſignificantur Grammatica, Rhetorica, Dialectica, <lb></lb>Arithmetica, Muſica, Geometria, Aſtrologia, liberales ob id di<lb></lb>ctæ, ſiue ingenuæ, quod illis excolatur animus, qui libera & ingenua <lb></lb>pars eſt hominis: Sed & pueriles, quia his ingenui pueri primis an<lb></lb>nis, ſtatim imbiberentur tanquam præuiis, & ad capeſſendas ſcien<lb></lb>tias & magnas artes neceſſariis. </s> </p> <p type="main"> <s id="id.000278">Scientiæ autem erant Philoſophia <lb></lb>moralis, Phyſica, Medicina, Iuriſprudentia, Theologia. </s> <s id="id.000279">Poste<lb></lb>riore ſignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb></lb>Chirurgia, Lanificium, Nautica. </s> <s id="id.000280">In quarum ſingulis aliæ ſunt im<lb></lb>perantes, quæ & architectonicæ dicuntur: aliæ miniſtrantes. </s> <s id="id.000281">Impe<lb></lb>rantes, habere debent præuias illas ſeptem liberales ante dictas, vt <lb></lb>videre eſt apud Vitruuium de ſuo architecto, & in noſtro com<lb></lb>mentario Iuriſiurandi Hipp. de Hippocrateo medico: apud <expan abbr="Virgiliũ">Virgilium</expan> <lb></lb>de ſuo agricola: apud Vegetium de ſuo imperatore, & eadem ratione <lb></lb>in reliquis: ita vt, qui imperantibus iſtis artibus præditi fuerint, in<lb></lb>ter homines præſtantißimi habiti ſemper ſint, & ſemper haberi <lb></lb>debeant, quanquam aliarum opera aliis aut neceſſaria magis, aut<emph.end type="italics"></emph.end><pb xlink:href="035/01/044.jpg" pagenum="4"></pb><emph type="italics"></emph>præſtantiora, aut vtiliora, aut certiora exiſtant. </s> <s id="id.000282">Agriculturæ enim <lb></lb>opus, quod alimenta & medicamenta hominibus ſuppeditat, neceßi<lb></lb>tate vincit cætera: victoria, quæ rebelles & hostes ſubijcit, proprios <lb></lb>ciues conſeruat, vtilitate ſupereminet: Medicina nobilitate ſubiecti, <lb></lb>& præstantia boni nempe ſanitatis, quam procurat, eximia eſt: Cer<lb></lb>titudine operis & operationis Fabrilis anteponenda omnibus: vt <lb></lb>Lanificium, quod ad opes honeſte parandas: & Nautica propter <lb></lb>mercaturam faciunt omnium maximè. </s> <s id="id.000283">Imperantes etiam hoc ha<lb></lb>bent, quod eorum, quæ efficiunt, rationes teneant: Iuueniles corporis <lb></lb>vires non requirant: vitæ poſſeſſoris ſui ſint æquales. </s> <s id="id.000284">Miniſtrantes <lb></lb>non item: ſed vſu potius & conſuetudine diſcantur & exerceantur: <lb></lb>Iuueniles vires poſtulent, & poſſeſſorem ſuum in ſenectute deſe<lb></lb>rant. </s> <s id="id.000285">Ex ijs aliis aliæ materias apparant: aliæ inſtrumenta fabrican<lb></lb>tur. </s> <s id="id.000286">Inſtrumentorum omnium ratio conſiſtit in certa quadam figu<lb></lb>ra, qua quæ eam habent, ad vſum commodiora ſunt. </s> <s id="id.000287">Cur autem hæ <lb></lb>figuræ aptißimæ ſint nulla <expan abbr="miniſtrãtium">miniſtrantium</expan> rationem inueſtigat: Satis <lb></lb>habent, ſi modum fabricandi & vtendi tenuerint. </s> <s id="id.000288">harum tamen <lb></lb>aliquot, cum certæ rationes eſſent ſubtiles, & à fontibus Geometriæ <lb></lb>petitæ, ipſas hoc libello verè aureo, & intelligentibus periucundo <lb></lb>Ariſtoteles partim generaliter, & ex ſuis principiis, partim per ali<lb></lb>quot <expan abbr="exẽpla">exempla</expan>, à rebus multis variíſque petita explicuit. </s> <s id="id.000289">Ob quod liber <lb></lb>rectè inſcribitur<emph.end type="italics"></emph.end> <foreign lang="el">mhxa/nika,</foreign> <emph type="italics"></emph>quia hic explicet cauſas virium in<lb></lb>ſtrumentorum ad Mechanicas artes prædictas pertinentium. </s> <s id="id.000290">cur <lb></lb>ſcilicet ea, quam habent, prædita figura vſui, & effectui commodio<lb></lb>ra exiſtant. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000291">Quid eſt Mechan.] <emph type="italics"></emph>Summa eſt eorum, quæ hoc primo capite <lb></lb>explicantur, ſed imperfectior: quia non, quid ſit mechanice, ſed <lb></lb>quod ſit ars admirabilis, & quod circulus omnium, quæ fiunt in <lb></lb>Mechanica, admirabilium eſſe cauſa oſtenditur: præter quæ etiam <lb></lb>docetur problemata mechanica partim eſſe Phyſica, partim eſſe Ma<lb></lb>thematica. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000292">Mira ſunt in his:] <emph type="italics"></emph>Similitudo hîc quædam eſt: ſed ſine notis <lb></lb>ſimilitudinis expreſſa. </s> <s id="id.000293">ſic igitur erit clarior. </s> <s id="id.000294">Quemadmodum in re<lb></lb>bus naturalibus miræ ſunt illæ, quarum cauſa ignoratur: ita & in <lb></lb>his, quæ præter naturam arte factæ hominibus conferunt, ſi & ea<lb></lb>rum cauſa lateat, vbi notandum admirationem eſſe animi in rem<emph.end type="italics"></emph.end><pb xlink:href="035/01/045.jpg" pagenum="5"></pb><emph type="italics"></emph>propoſitam intuitionem cum cupiditate cauſam cognoſcendi: ex quo <lb></lb>intelligitur Deum qui cognoſcit & tenet cauſas <expan abbr="omniũ">omnium</expan>, Bruta quia <lb></lb><expan abbr="neſciũt">neſciunt</expan>, nec ſcire cupiunt, nihil admirari: <expan abbr="ſolũ">ſolum</expan> hominem inter vtroſ<lb></lb>que poſitum, qui neſciat, ſcire autem cupiat, admirationis eſſe capa<lb></lb>cem, vnde non ſunt ſimpliciter intelligendi hi verſus Horatiani,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000295">Nil admirari propè res eſt vna Numici,</s> </p> <p type="main"> <s id="id.000296">Soláque quæ poſſit facere & ſeruare beatum. </s> </p> <p type="main"> <s id="id.000297"><emph type="italics"></emph>Nec enim hæc res facit Bruta, nec homines, qui ignorant, ſed ſcire <lb></lb>ſeputant, aut ſcire non cupiunt, fœlices: ſed eos, qui cognoſcunt, iux<lb></lb>ta illud<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000298">Fœlix, qui potuit rerum cognoſcere cauſas. </s> </p> <p type="main"> <s id="id.000299"><emph type="italics"></emph>Ab hac admirandi facultate Ariſtoteles <expan abbr="principiũ">principium</expan> Philoſophiæ re<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg5"></arrow.to.target><lb></lb><emph type="italics"></emph>petijt. </s> <s id="id.000300">Qui enim, inquit, admiratur, putat ſe ignorare, & <expan abbr="dubitãs">dubitans</expan> co<lb></lb>natur dubitationibus ſuis ſuccurrere. </s> <s id="id.000301">Homo natura fugiens eſt igno<lb></lb>rantiæ. </s> <s id="id.000302"><expan abbr="Itaq;">Itaque</expan> primò è dubitatis faciliora inqui ſiuit, deinde paulatim <lb></lb>vlterius procedens <expan abbr="etiã">etiam</expan> maiora, vt de affectionibus Lunæ, & ijs quæ <lb></lb>circa Solem & ſtellas fiunt, ac de generatione vniuerſi: atque ſic <lb></lb>Philoſophia orta eſt, ſicque Philoſophus non ſolum rara & ingen<lb></lb>tia, vt vulgus, ſed etiam frequentia & exigua, ſi cauſas latentes ha<lb></lb>beant, admiratur, & quidem cum voluptate: in quo etiam diſſentit à <lb></lb>vulgò, qui quæ admiratur, ſæpe horret, vt Eclipſes Solis & Lunæ,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg6"></arrow.to.target><lb></lb><emph type="italics"></emph>quod de Archelao rege Seneca memorat rerum naturæ adeò ignaro, <lb></lb>vt quo die Solis defectio fuit, regiam clauſerit, & filium, quod in <lb></lb>luctu à rebus aduerſis moris eſt, totunderit. </s> <s id="id.000303">quam contra Thales <lb></lb>rerum naturæ gnarus in aperto fixis in peluim oculis magna cum <lb></lb>animi lætitia intuitus eſſet. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000304"><margin.target id="marg5"></margin.target>Cap. 2. lib. 2. <lb></lb>Metaph. </s> <s><margin.target id="marg6"></margin.target>Cap. 6. lib. 5. <lb></lb>De benefic. </s> </p> <p type="main"> <s id="id.000305">Quorum cauſa ign.] <emph type="italics"></emph>In rebus naturalibus cauſarum omne <lb></lb>genus ineſt, materia, efficiens, forma, finis. </s> <s id="id.000306">Et in ſingularium conti<lb></lb>nentium & proximarum inuentione, & earum ad primam redu<lb></lb>ctione Philoſophia conſiſtit. </s> <s id="id.000307">Sunt autem eiuſmodi, vt ex his aliæ <lb></lb>notæ iam ſint, aliæ adhuc ignotæ perſiſtant, vnde numquam ſtudio<lb></lb>ſis deerit admirandi, & propterea philoſophandi occaſio: difficiles <lb></lb>tantum, ſalebroſoſque aditus habens, ſiquidem<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000308">Multa tegit ſacro inuolucro Natura, neque vllis</s> </p> <p type="main"> <s id="id.000309">Fas eſt ſcire quidem mortalibus omnia: multa</s> </p> <p type="main"> <s id="id.000310">Admirare modò, nec non venerare. </s> </p> <pb xlink:href="035/01/046.jpg" pagenum="6"></pb> <p type="main"> <s id="id.000311"><emph type="italics"></emph>abiecti certè ac beſtias imitantis hominis eſt, quæ neſciat, non admi<lb></lb>rari, & ſi curis, negotiíſque neceſſarijs vacuus eſt, non inquirere, <lb></lb>& venerari. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000312"><foreign lang="el">e)n polloi=s ga\r <lb></lb>h( fu/sis u(penanti/on pro\s to\ xrh/simon h(mi=n poiei=. </foreign></s> <s id="g0110103"><foreign lang="el">h( me\n <lb></lb>ga\r fu/sis a)ei\ to\n au)to\n e)/xei tro/pon kai\ a(plw=s, to\ de\ <lb></lb>xrh/simon metaba/llei pollaxw=s.</foreign></s> <s id="g0110201"><foreign lang="el">o(/tan ou)=n de/h| ti para\ <lb></lb>fu/sin pra=cai, dia\ to\ xalepo\n a)pori/an pare/xei kai\ dei=tai <lb></lb>te/xnhs.</foreign></s> </p> <p type="main"> <s id="id.000313">In multis enim natura ab <lb></lb>vtilitate noſtra diſcedit. </s> <s id="id.000314"><expan abbr="Siquidẽ">Si<lb></lb>quidem</expan> natura <expan abbr="eodẽ">eodem</expan> modo <lb></lb><expan abbr="sẽper">semper</expan> operatur & ſimplici<lb></lb>ter: at <expan abbr="aliũ">alium</expan> <expan abbr="atq;">atque</expan> alium ple<lb></lb>rumque poſtulat vtilitas. <lb></lb></s> <s id="id.000315"><expan abbr="Quãdo">Quando</expan> igitur conuenit fa<lb></lb>cere aliquid pręter <expan abbr="naturã">naturam</expan>, <lb></lb><expan abbr="tũ">tum</expan> difficultas hæſitationem <lb></lb>adfert, & arte opus eſt. </s> </p> <p type="head"> <s id="id.000316">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000317">In multis enim.] <emph type="italics"></emph>Secunda ratio eſt ad probandum in arte fa<lb></lb>ctis quibuſdam aliquid mirum eſſe, deprompta eſt ex effectis Na<lb></lb>turæ contrarijs, ſaltem repugnantibus, ſyllogiſmus ſic inſtitutus <lb></lb>rem ipſam illuſtrabit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000318"><emph type="italics"></emph>Naturam aliò flectere & adducere, quam vergat, mirum eſt, <lb></lb>quia difficultas ex renixu naturæ dubitationem parit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000319"><emph type="italics"></emph>In his quæ arte fiunt aliò natura flectitur & adducitur, quam <lb></lb>vergat. </s> <s id="id.000320">Natura enim eodem modo ſemper agit, vſus autem re<lb></lb>rum humanarum varios modos poſtulat. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000321"><emph type="italics"></emph>Igitur in arte factis aliquid mirum eſt. </s> <s id="id.000322">Pro aſſumptione aſſum<lb></lb>ptionis confirmatio est ex effectis, & effectorum modo naturæ & <lb></lb>artis. </s> <s id="id.000323">Natura enim in multis inclinat aliò, quam vtilitas hominum <lb></lb>poſtulat: Natura item vno modo ſemper operatur: contra Ars vti<lb></lb>litatem hominem ſemper ſpectat, & varios operandi modos pro<lb></lb>ſequitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000324">Siquidem Natura.] <emph type="italics"></emph>Naturalia principium in ſe habent ſui <lb></lb>motus, quo ſi ſimplicia ſunt, ad vnum & vno modo ſimpliciter <lb></lb>mouentur: ſi commixta prædominantis vnius motum ſequuntur, <lb></lb>ſicque ad vnum feruntur. </s> <s id="id.000325">Hæc ſunt demonſtrata ab Aristotele<emph.end type="italics"></emph.end><pb xlink:href="035/01/047.jpg" pagenum="7"></pb><emph type="italics"></emph>lib. de Cœlo & de generat. & corrupt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000327">At alium atque alium.] <emph type="italics"></emph>Hominum vtilitas tum ad eſſe tum <lb></lb>ad bene eſſe multa variáque multò aliter quam natura præferat, pe<lb></lb>tit ſibi fieri, vt <expan abbr="alimẽta">alimenta</expan> & copioſiora, & aliter apparata: <expan abbr="quã">quam</expan> terra, <lb></lb>aër, & mare ſponte ſua ſuppeditent: vt veſtitum, quem connexus <lb></lb>ſtaminis cum ſubtegmine faciens corpora tegendo, ipſa probe tuetur <lb></lb>& ornat: vt ædificia, quæ trabium, lapidumque præter naturam ad <lb></lb>ſuperiorem locum euectio & coagmentatio vtilia facit, ad defenſio<lb></lb>nem contra cœli, aëris, externáſque quaſuis iniurias. </s> <s id="id.000328">Quinetiam va<lb></lb>rietas <expan abbr="cõtra">contra</expan> naturæ curſum expetitur in delectabilibus vt hydrauli<lb></lb>cis, engebatis, merulis, & icunculis voces, cantus, geſtus hominum, <lb></lb>auium, aliorumque animalium imitantibus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000329">Quando igitur.] <emph type="italics"></emph>Omnia licet habeat homo ſui gratia nata: non <lb></lb>ita tamet habet, vt qualia naturaliter prodeunt, talibus <expan abbr="cũctis">cunctis</expan> com<lb></lb>mode vti poßit. </s> <s id="id.000330">Neceßitate igitur & commoditate vtendi rebus à <lb></lb>natura oblatis preſſus, conuertit ad ſuos vſus & <expan abbr="accõmodat">accommodat</expan>: ſed con<lb></lb>uerſio iſta, cum ſit deductio ad aliud, quam quò vergit natura, habet <lb></lb>in ijs naturale principium renitens: hic renixus parit difficultatem <lb></lb>conuerſionis: hæc difficultas huc illuc animum hominis cogitando, <lb></lb>quærendóque, quomodo difficultas iſta ſuperetur, diſtrahit, facitque, <lb></lb>vt mente diu verſet, quid & quomodo agendum, exempli gratia. </s> <s id="id.000331">vt <lb></lb>onus ſubleuet, altè ipſe conſcendat, vehementer quatiat, longè iacu<lb></lb>letur, & ea demum faciat, velit nolit natura, quæ vtilitati homi<lb></lb>num ſeruiant. </s> <s id="id.000332">Hæc cura ſolicitudóque vrget imaginationem, vt lu<lb></lb>men à mente mutuantem & à rationibus mathematicis, nec quodam <lb></lb>ſucceßionis ordine defatigari <expan abbr="rationẽ">rationem</expan> & quieſcere ſinit, priuſquam <lb></lb>quod quæritur, inuentum ſit. </s> <s id="id.000333">Illud inuentum, modúſve inueniendi <lb></lb>generalis eſt. </s> <s id="id.000334">hîc particulariter ad <expan abbr="machinã">machinam</expan> <expan abbr="inſtrumentáq;">inſtrumentáque</expan> refertur, <lb></lb>quibus <expan abbr="onerũ">onerum</expan> motiones fiant opportunæ, per motiones intellige, quæ <lb></lb>fiunt à loco ad locum, vt impulſiones, tractiones, volutationes, ve<lb></lb>ctiones, & in locis altis, medijs, imis pro vſu & decoro repoſitiones: <lb></lb>per onera, quicquid aliò quam quò naturaliter vergit, impellitur, vt <lb></lb>aërem, cum deorſum deſcendere cogitur, vt aquam, vt terram cum <lb></lb>ſurſum aſcendere, & eiuſmodi, quæ vulgus cum admiratione ſuſpi<lb></lb>cit, & niſi fierent, nulla res noſtra non eſſet impedita Atque ſic ra<lb></lb>tio hominis neceſsitate vſus, & vtilitatis ſuæ preſſa, efficiens cauſa <emph.end type="italics"></emph.end><pb xlink:href="035/01/048.jpg" pagenum="8"></pb><emph type="italics"></emph>Mechanices hic ſtatuitur: vt eſt etiam ſtatuta à Vitruuio ſed & per<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg7"></arrow.to.target><lb></lb><emph type="italics"></emph>imitationem rerum à natura procreatarum. </s> <s id="id.000335">Homo enim inquit, ani<lb></lb>maduertens Solis, Lunæ, & reliquorum planetarum continentes <lb></lb>motus, & machinationes naturales, ſine quibus non habuiſſet in <lb></lb>terra lucem, & fructuum maturitates hinc exempla ſumpſit, & ea <lb></lb>imitans, inductus rebus diuinis, commodas vitæ perfecit explicatio<lb></lb>nes. </s> <s id="id.000336">Itaque comparauit, vt eſſent expeditiora alia machinis, & ea<lb></lb>rum verſationibus: alia organis, quæque obſeruauit ad vſum vtilia <lb></lb>eſſe ſtudijs, artibus, inſtitutis, doctrinis gradatim augenda curauit: <lb></lb>hinc tandem extat ars quædam generalis quæ difficultati faciendo<lb></lb>rum præter naturam ad vtiltiatem hominum ſuccurrit. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000337"><margin.target id="marg7"></margin.target>Lib. 10. </s> </p> <p type="main"> <s id="id.000338">Tum difficultas.] <emph type="italics"></emph>Naturæ renixus difficultatem facit. </s> <s id="id.000339">Re<lb></lb>nititur autem Natura ſubſtantia, numero, magnitudine, pondere, <lb></lb>figura, quæ omnia ars <expan abbr="immutãdo">immutando</expan>, addendo, detrahendo, <expan abbr="trãſponendo">tranſponendo</expan>, <lb></lb>poliendo, figurando corrigit, & ad vſus humanos accommodat. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000340"><foreign lang="el">dio\ kai\ kalou=men th=s te/xnhs, to\ pro\s ta\s toiau/tas <lb></lb>a)pori/as bohqou=n me/ros, mhxanh/n, <arrow.to.target n="marg8"></arrow.to.target>kaqa/per ga\r e)poi/hsen <lb></lb>*)antifw=n o( poihth/s, ou(/tw kai\ e)/xei: te/xnh| ga\r kratou=men, <lb></lb>w(=n fu/sei nikw/meqa.</foreign></s> <s id="g0110203"><foreign lang="el">toiau=ta de/ e)stin e)n oi(=s ta/ te e)la/ttona <lb></lb>kratei= tw=n meizo/nwn, kai\ ta\ r(oph\n e)/xonta mikra\n kinei= <lb></lb>ba/rh mega/la, kai\ pa/nta sxedo\n o(/sa tw=n problhma/twn <lb></lb>mhxanika\ prosagoreu/omen.</foreign></s> <lb></lb> </p> <p type="margin"> <s id="id.000341"><margin.target id="marg8"></margin.target><foreign lang="el">mhxanikh\n. </foreign></s> </p> <p type="main"> <s id="id.000342">Atque propterea partem <lb></lb>illius artis quæ hæſitationi <lb></lb>iſti ſuccurrit Mechanicem <lb></lb>vocamus. </s> <s id="id.000343"><expan abbr="Quemadmodũ">Quemadmodum</expan> <lb></lb>enim Antipho poëta di<lb></lb>xit, ita ſe res habet. </s> </p> <p type="main"> <s id="id.000344"><emph type="italics"></emph>Natura vincit: hanc arte <lb></lb>vincimus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000345">vt in his, quæ, cum mino<lb></lb>ra ſint, ſuperant maiora: & <lb></lb>paruum momentum, cum <lb></lb>habeant, ingentia dimo<lb></lb>uent pondera, cæteriſ<lb></lb>que fere, quæ problemata <lb></lb>Mechanica nuncupamus. </s> </p> <p type="head"> <s id="id.000346">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000347">Illius artis.] <emph type="italics"></emph>Ars generalis, cuius hic mentionem facit Ari<lb></lb>ſtoteles, nuſquam ab eo eſt definita, aut nominata. </s> <s id="id.000348">Leonicus, qui <lb></lb>in hunc librum commentarium edidit putat eſſe Architecturam. <emph.end type="italics"></emph.end></s> <s><pb xlink:href="035/01/049.jpg"></pb><emph type="italics"></emph>Quod facit ex ſententia Vitruuij, qui eius tres partes conſtituit, ædi<lb></lb>ficationem in explicatione publicorum & priuatorum operum: <lb></lb>Gnomonicam in deſcriptione Horologiorum: & Machinationem <lb></lb>in cognitione principiorum & diſpoſitione machinarum & orga<lb></lb>norum. </s> <s id="id.000349">Hæc quidem comprehendi Architecturæ nomine Galenus<lb></lb><arrow.to.target n="marg9"></arrow.to.target> etiam teſtatus eſt, nomine inquit, artis Architectorum intelligi volo <lb></lb>Horologiorum, Clepſydrarum, Hydrocopiarum, Machinamento<lb></lb>rumque omnium deſcriptiones, quibus etiam, quæ ſpirabilia vocant, <lb></lb>continentur. </s> <s id="id.000351">Sed cum in his quæ Architecturæ ſubiecta ſunt ſolis <lb></lb>naturæ renixus non vincatur: <expan abbr="verũ">verum</expan> etiam in quibuslibet aliis cuiuſ<lb></lb>cunque artis ſubiectis, ſi qua ſit ars, quæ in vniuerſum id doceat, <lb></lb>multo generalior eſt Architectura. </s> <s id="id.000352">Et quid obeſt dicere hanc eſſe <lb></lb>Philoſophiam? </s> <s id="id.000353">cum Philoſophia ſit cognitio omnium artium & re<lb></lb>rum tam diuinarum: quam humanarum cauſas, proprietates, effecta <lb></lb>conſideret. </s> <s id="id.000354">Atque hac diuiſa in ſuas partes, & partium particulas <lb></lb>vna ex his erit Mechanice. </s> <s id="id.000355">Quæ ad explicationem motuum violen<lb></lb>torum, & admirabilium ſe habebit, vt Phyſica ad explicationem <lb></lb>motuum naturalium: & vt ſub hac Medicina, Agricultura, & <lb></lb>aliæ: ſic ſub illa ars fabrilis, Architectura, Sutoria, & omnes quæ <lb></lb>inſtrumentis artificioſis, induſtriiſque opus ſuum peragunt. </s> <s id="id.000356">quorum <lb></lb>omnium rationes & virium gradus in hac Mechanica tanquam <lb></lb>generali explicantur, vt poſtea cuique facile apparebit. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000357"><margin.target id="marg9"></margin.target>Cap. 3. lib. <lb></lb>de cuiuſque <lb></lb>animi pecc. <lb></lb>cognoſc. </s> </p> <p type="main"> <s id="id.000359">Mechanice.] <emph type="italics"></emph>In Græco Vecheli legitur hîc <emph.end type="italics"></emph.end><foreign lang="el">mhxanh\n</foreign>: <emph type="italics"></emph>vt etiam <lb></lb>in titulo huius capitis: ſed vtrobique legendum <emph.end type="italics"></emph.end><foreign lang="el">mhxanikh\n. </foreign><emph type="italics"></emph>quia ha<lb></lb>ctenus in hoc proëmio non machina vna: ſed ars machinarum lau<lb></lb>data eſt. </s> <s id="id.000360">Nec tamen definita, vt titulus pollicebatur. </s> <s id="id.000361">Definitur au<lb></lb>tem ſic à Picolomino. </s> <s id="id.000362">Mechanice eſt ſcientia ex qua cauſæ & prin<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg10"></arrow.to.target><lb></lb><emph type="italics"></emph>cipia ad quamplurimas artes ſellularias exhauriri poſſunt. </s> <s id="id.000363">Nos peni<lb></lb>tius ipſius rei, quæ definitur naturam, & ad ea quæ cum dicta ſunt <lb></lb>ab Aristotele, quæque dicentur intuentes perfectiùs opinor, ſic de<lb></lb>finiemus. </s> <s id="id.000364">Mechanice eſt ars ad ea quæ vires humanas ſuperant, tra<lb></lb>hendum, impellendum, ferendum, machinarum fabricatrix. </s> <s id="id.000365">vel ſic <lb></lb>Mechanice eſt ars cogendi corpora quantum fieri poteſt vt contra <lb></lb>nutum ferantur. </s> <s id="id.000366">Hæc enim tota poſita eſt, vt ad vſum, delectatio<lb></lb>némue hominum grauia ſurſum, leuia deorſum, tum vtraque in la<lb></lb>tus, in orbem ſeorſim, atque per mixtim è loco in locum moueantur. <emph.end type="italics"></emph.end><pb xlink:href="035/01/050.jpg" pagenum="10"></pb><emph type="italics"></emph>Hæc enim vt fiant, ipſa ars machinas inuenit, & inuentarum, cur <lb></lb>hæc præſtent cauſas reddit. </s> <s id="id.000367">Cæterùm ex huius machinis, quædam <lb></lb>mouentur per ſe:quædam non ſponte. </s> <s id="id.000368">Illæ intra ſe principia ſuæ mo<lb></lb>tionis habent, & <emph.end type="italics"></emph.end><foreign lang="el">a)uto/mata</foreign> <emph type="italics"></emph>vocantur: quorum alia Græcis <emph.end type="italics"></emph.end><foreign lang="el">stata\, </foreign><lb></lb><emph type="italics"></emph>Latinis Stataria, fixa, firma dicuntur: alia <emph.end type="italics"></emph.end><foreign lang="el">u(pa/gonta</foreign> <emph type="italics"></emph>ambulantia. <lb></lb></s> <s id="id.000369">De vtriſque Hero pertractauit, inter quæ pulchrum eſt illud, quod <lb></lb>docuit conſtruere, ſcilicet ædem rotundam, in qua Bacchus pateram <lb></lb>altera manu tenet, altera thyrſum, propè verò adeſt panthera, & <lb></lb>ara: circum autem Bacchides tympana tenentes, ſuprà tholum alata <lb></lb>& coronata Victoria collocatur, atque vno & <expan abbr="eodẽ">eodem</expan> tempore in ara <lb></lb>ignis ſuccenditur, Bacchus lac è patera, vinum è thyrſo verſat in <lb></lb>pantheram, Bacchides circumſalientes tympana pulſant, Victoria <lb></lb>ſe circumagens, & alas qaatiens tuba ſonat. </s> <s id="id.000370">In alia verò diſpoſi<lb></lb>tione fecit inambulantia, ſigilla euntia, & redeuntia, motioneſ<lb></lb>que varias reddentia, vt vſus & voluptas poſtulat pro instituto. <lb></lb></s> <s id="id.000371">Hæ verò motionis principium intra ſe non habent: Sed ex his <lb></lb>aliæ mouentur à rebus inanimis, aliæ ab animatis. </s> <s id="id.000372">Res inani<lb></lb>mæ principium motionis exhibentes ſunt aër, ſpiritus, aqua, ignis, <lb></lb>ſumus. </s> <s id="id.000373">Aer & ſpiritus eſt vel incluſus, ex quò pneumatica ratio ab<lb></lb>ſoluitur, de qua etiam Hero inſtrumenta Muſica, quæ per <emph.end type="italics"></emph.end><foreign lang="el">a)ntonoma<lb></lb>si/an</foreign><emph type="italics"></emph> organa vocant: vel liber, vnde ædificia ad molendum. </s> <s id="id.000374">A qua, <lb></lb>vnde fiunt rotæ etiam ad <expan abbr="molendũ">molendum</expan>, <expan abbr="tũ">tum</expan> tympana, tum ſerræ ad trabes <lb></lb>ſecandas, folles ad <expan abbr="ferrũ">ferrum</expan> tundendum & alia <expan abbr="pleraq́">pleraque</expan>;. </s> <s id="id.000375">Ignis ſeu fumus <lb></lb>quo verrucula conuoluuntur: animatæ ſunt, bruta quæ trahunt cur<lb></lb>rus, ciſia, quadrigas: homines qui verſant, trahunt, erigunt, impel<lb></lb>lunt ad varios belli <expan abbr="paciſq;">paciſque</expan> vſus vtentes vectibus, radijs, trochleis, <lb></lb>cochleis, trutinis, lancibus, ergatis, rotis, tympanis, & ad aſcenden<lb></lb>dum in altum multiplicibus ſcalarum formis, tum munitis, tum ſine <lb></lb>munitione, & ad diſrumpendum, excutiendum, proſternendum, <lb></lb>quatiendum frangendum, iaculandum, arietibus, teſtudinibus, tur<lb></lb>ribus ambulatorijs, catapultis, baliſtis, tormentis reliquis. </s> <s id="id.000376">in quibus <lb></lb>faciendis hæc lex poſita eſt, vt omnia fiant ex paratu facilibus quo <lb></lb>ad materiam: varijs quoad figuras: exiguis quoad menſuras: leuibus <lb></lb>quoad pondera. </s> <s id="id.000377">Quippè quæ à quibuſcumque artificibus citò fieri <lb></lb>queant, erectu interim, <expan abbr="trãslatúque">translatúque</expan> facilia: inſidiatu, fractuque dif<lb></lb>ficilia: ſtabilia, ac tandem eiuſmodi ſint, vt quatenus neceßitas <emph.end type="italics"></emph.end><pb xlink:href="035/01/051.jpg" pagenum="11"></pb><emph type="italics"></emph>poſtulauerit, facile componi, faciléque diſſolui poßint. </s> <s id="id.000378">Sed neque hic <lb></lb>prætermittenda diuiſio Methanices, quæ aliter à Politiano ex He<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg11"></arrow.to.target><lb></lb><emph type="italics"></emph>rone inducta eſt. </s> <s id="id.000379">Mechanices, inquit, altera pars rationalis eſt, quæ <lb></lb>numerorum, menſurarum, ſyderum, naturæ que rationibus perfici<lb></lb>tur: altera<emph.end type="italics"></emph.end> <foreign lang="el">xeirourgikh\,</foreign> <emph type="italics"></emph>cui vel maximè artes illæ, æraria, ædifica<lb></lb>toria, materiaria, picturaque, adminiculantur. </s> <s id="id.000380">Huius autem partes, <lb></lb>Manganaria per quam pondera immania minima vi tolluntur in <lb></lb>altum:<emph.end type="italics"></emph.end> <foreign lang="el">mhxanopoihtikh\,</foreign> <emph type="italics"></emph>quæ facile aquas antlijs extrahit:<emph.end type="italics"></emph.end> <foreign lang="el">*or<lb></lb>ganopoihtikh\,</foreign> <emph type="italics"></emph>quæ bellis accommoda inſtrumenta fabricatur, arie<lb></lb>tes, teſtudines, turres ambulatorias, helepoleis, ſambucas, exoſtras, <lb></lb>tollenones & quæcunque Græco vocabulo<emph.end type="italics"></emph.end> <foreign lang="el">poliorkhtika\</foreign> <emph type="italics"></emph>vocan<lb></lb>tur, tormentorumque varia genera, quæ libris Athenæi, Bitonis, <lb></lb>Heronis, Pappi, Philonis, Apollodorique continentur, vt Latinos <lb></lb>omiſerim. </s> <s id="id.000381">Mox & quæ<emph.end type="italics"></emph.end> <foreign lang="el">qaumatourgikh\</foreign> <emph type="italics"></emph>cuius exempla ſunt<emph.end type="italics"></emph.end> <foreign lang="el">u)drau<lb></lb>lika\</foreign> <emph type="italics"></emph>organa, quæque per ſe ventorum flatu reſonant. </s> <s id="id.000382">Et quod vas <lb></lb>dicæometron vocabant, & quod voces variarum auium exprimit, <lb></lb>& quod indidem merum, mox dilutum vinum, mox aquam cali<lb></lb>dam, mox <expan abbr="frigidã">frigidam</expan>, copioſam <expan abbr="tenuémq;">tenuémque</expan> vicißim funditat. </s> <s id="id.000383">Et<emph.end type="italics"></emph.end> <foreign lang="el">si/fwnes</foreign><lb></lb><emph type="italics"></emph>extinguendis incendijs apti, & medicinabiles cacurbitulæ ſine <lb></lb>ignis ministerio cutem prehendentes, & pilæ ſponte ſaltantes, & <lb></lb>lucerna ſuas ipſa producens ſtuppas: & animal quod à ſtructore dum <lb></lb>ſecatur in menſa, bibit interim, crepitùque ſuo quodam, & voce ſi<lb></lb>tientis repræſentat imaginem: milleque alia id genus, quæ breuita<lb></lb>tis ſtudio præterimus. </s> <s id="id.000384">Hæc igitur ( vt in capita quædam conferatur ) <lb></lb>aut ponderibus vtitur & ſpiritu, quorum præponderatio mouet, <lb></lb>æquilibrium ſiſtit, ( ſicuti etiam Timæus definit): aut neruis & <lb></lb>funiculis animatos quaſi tractus, ac motus imitatur, ac circa illa <lb></lb>quæ ſubnatant aquis, aut circa aquarum vertitur horologia, quo<lb></lb>rum quidem generum primum docet in pneumaticis Heron, alte<lb></lb>rum idem in automatis & Zygijs, quartum rurſus in Hydrijs, ter<lb></lb>tium verò in Ochoumenis Archimedes. </s> <s id="id.000385">Eſt in eadem Mechanicæ <lb></lb>ſerie quæ Centrobarica pars dicitur, ex qua reliquæ pendere dicun<lb></lb>tur & Sphærotopœia, qualis illa Archimedea Claudiani laudata <lb></lb>verſibus. </s> <s id="id.000386">Suppeditat eadem Architecturæ quoque ſcanſorias, tra<lb></lb>ctiles, & ſpirituales machinas. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000387"><margin.target id="marg10"></margin.target>In parapha<lb></lb>ſi huius li<lb></lb>bri. </s> </p> <p type="margin"> <s id="id.000388"><margin.target id="marg11"></margin.target>In Pancpi<lb></lb>ſtemone. </s> </p> <p type="main"> <s id="id.000389">Natura vincit.] <emph type="italics"></emph>Senariolus eſt cuiuſdam antiqui poëtæ nomine <emph.end type="italics"></emph.end><pb xlink:href="035/01/052.jpg" pagenum="12"></pb><emph type="italics"></emph>tenus in hominum memoria ſuperſtitis: niſi ſit is, de quo Ariſtoteles <lb></lb>in ſuis Rhetoricis meminit, lepidumque eius dictum ad ſocios, qui<lb></lb>buſcum vna ducebatur in ſupplicium iuſſu Dionyſij tyranni, reci<lb></lb>tat. </s> <s id="id.000390">hos enim videns capite coopertos. </s> <s id="id.000391">Quid occultamini, inquit, <lb></lb>Socij, cum nullius iſtorum qui frequentes ad vrbis portam ſpectandi <lb></lb>gratia confluunt, cras vos ſit conſpecturus? </s> <s id="id.000392">Eſt alius etiam Antipho <lb></lb>de quo meminit Cicero, vt ſomniorum interprete & ſcriptore for<lb></lb>taſſe is eſt quem fuiſſe Athenienſem monſtroſorum ſomniorum in<lb></lb>terpretem, & poëtam refert Suidas. </s> <s id="id.000393">A quo etiam fortaſſe proma<lb></lb>nauit Senariolus, qui hic citatur ab Ariſtotele, ad probandum <lb></lb>homines arte vincere ea, à quibus natura vincuntur. </s> <s id="id.000394">quod cum fa<lb></lb>ciunt in ijs, in quibus iudicio omnium longe à natura ſuperantur<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">paradoxo/poioi,</foreign> <emph type="italics"></emph>cum Galeno vocari poterunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000395">Vt in his, quæ cum] <emph type="italics"></emph>Vt cum magnas marmorum moles, tra<lb></lb>bes, columnas, coloſſos transferimus, & erigimus, naues ſubduci<lb></lb>mus in mare, quod fecit Archimedes conspiciente Hierone rege <lb></lb>Syracuſarum, Helepoles amplas ſupra muros attrahimus, quod <lb></lb>fecit Callias Rhodienſibus conspicientibus, Equum Troianum in <lb></lb>vrbem adducimus ( erat enim aliud nihil <expan abbr="quã">quam</expan> machina, vt ait poëta,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000396">Inſpectura domos venturáque deſuper vrbi. </s> </p> <p type="main"> <s id="id.000397"><emph type="italics"></emph>quales multæ apud Vegetium & Heronem mechanicum. ) bom<lb></lb>bardas ingentes ad locum destinatum conuertimus. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000398"><foreign lang="el">e)/sti de\ tau=ta toi=s fusikoi=s <lb></lb>problh/masin, ou)/te tau)ta\ pa/mpan, ou)/te kexwrisme/na li/an, <lb></lb>a)lla\ koina\ tw=n te maqhmatikw=n qewrhma/twn, kai\ tw=n <lb></lb>fusikw=n: to\ me\n ga\r w(\s dia\ tw=n maqhmatikw=n dh=lon, to\ <lb></lb>de\ peri\ o(\, dia\ tw=n fusikw=n.</foreign></s> </p> <p type="main"> <s id="id.000399">Sunt vero hæc proble<lb></lb>matis Phyſicis, nec omni<lb></lb>no <expan abbr="eadẽ">eadem</expan>, nec valdè diſſimi<lb></lb>lia: ſed conſentanea theo<lb></lb>tematis, tum mathemati<lb></lb>cis, tum Phyſicis. </s> <s id="id.000400">Etenim <lb></lb>quod ipſum quomodo ad <lb></lb>mathematica pertineat: <lb></lb>ipſum vero circa quod, ad <lb></lb>Phyſica, manifeſtum eſt. </s> </p> <p type="head"> <s id="id.000401">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000402"><emph type="italics"></emph>Apud Euclidem problema à theoremate diſtinguitur, quod <lb></lb>hoc iubeat aliquid contemplari: illud fieri: paßim tamen ab <emph.end type="italics"></emph.end><pb xlink:href="035/01/053.jpg" pagenum="13"></pb><emph type="italics"></emph>Ariſtotele, & alijs pro vtroque, vt hic, indifferenter legitur. </s> <s id="id.000403">Qualia <lb></lb>autem problemata in Mechanicis habeat tractanda explicat Ari<lb></lb>ſtoteles, dicitque ea eſſe, quæ ſint conſentanea Phyſicis & Mathe<lb></lb>maticis, vt quæ habeant ſubiectum petitum è Phyſicis. </s> <s id="id.000404">Machina<lb></lb>rum enim materia lignum eſt vel ferrum & eiuſmodi corpora Phy<lb></lb>ſica: attributum verò è figuris & terminis Mathematicis cuiuſmo<lb></lb>di ſunt in Geometria lineæ, diametri, centra, circuli, & eiuſmodi, <lb></lb>è quibus machinæ conſtare & figuratæ eſſe, & vires ſuas accipere, <lb></lb>augere, diminuere, metiri oſtenduntur. </s> <s id="id.000405">Vnde Mechanice pars eſt <lb></lb>mathematicarum non aliter: quam Muſica, Optica, Aſtronomia, <lb></lb>quas Ariſtoteles dixit eſſe<emph.end type="italics"></emph.end> <foreign lang="el">fusikote/ras,</foreign> <emph type="italics"></emph>ob ſubiecti ſcilicet, quod <lb></lb>tractant naturam Phyſicas: ſed ob<emph.end type="italics"></emph.end> <foreign lang="el">gra/mmikas</foreign> <emph type="italics"></emph>id eſt lineares & <lb></lb>numerales demonſtrationes, quibus ipſum explicant, Mathemati<lb></lb>cas. </s> <s id="id.000406">Cæterum exeo quod dicit Ariſtoteles problemata Mechanica <lb></lb>eſſe Phyſicis & Mathematicis conſentanea, ſub indicare videtur, <lb></lb>ne Mechanicus ante existimet machinas, quarum habuerit demon<lb></lb>ſtrationem in vſum venire poſſe, ſuamque efficaciam ſortiri: niſi <lb></lb>materia Phyſica existat, quæ rem patiatur fieri. </s> <s id="id.000407">Quamuis enim <lb></lb>Geometer demonſtratione concludat, datam rectam lineam infinitè <lb></lb>diuiſibilem eſſe, nulla materia lineata apud phyſicos eſt, quæ non <lb></lb>continuata diuiſione tandem reducatur ad eam, quæ ſi amplius in<lb></lb>telligatur diuidi, amittet formam lineæ Phyſicæ & viſibilis: ſic <lb></lb>licet apud Mechanicos multa demonſtrentur de motu in infinitum <lb></lb>augendo, quale eſt illud problema Archimedeum. </s> <s id="id.000408">Datum pondus <lb></lb>data potentia mouere. </s> <s id="id.000409">Ita tamen intelligenda ſunt, ne exiſtimemus <lb></lb>infinita hominis, <expan abbr="quacũque">quacunque</expan> arte iuuetur, poteſtati ſubeſſe. </s> <s id="id.000410">Sunt enim <lb></lb>certi fines, vltra quos natura rerum ipſum progredi non patitur. <lb></lb></s> <s id="id.000411">Sunt præterea vitia materiæ quæ Geometra, aut Mechanicus de<lb></lb>monſtrans non conſiderat: nec etiam obſtant quo minus quæ propo<lb></lb>ſita ſunt, vera ſint in intellectu: Mechanicus igitur operans, priuſ<lb></lb>quam operi ſe accingat, ne fruſtretur, conſiderare debet, an quod <lb></lb>proponitur effici poßit, habita ratione materiæ ex qua, aut per <expan abbr="quã">quam</expan>, <lb></lb>& circunſtantiarum præſertim temporis quod præſcribitur, & ſum<lb></lb>ptuum quos facere oporteret. </s> <s id="id.000412">Hæc enim ſi abunde ſuppetant, nec ma<lb></lb>teria omnino repugnet, nihil non fieri poterit. <emph.end type="italics"></emph.end></s> </p> </subchap1> <pb xlink:href="035/01/054.jpg" pagenum="14"></pb> <subchap1> <p type="main"> <s id="id.000413"><foreign lang="el">perie/xetai de\ tw=n a)poroume/nwn<lb></lb> e)n tw=| ge/nei tou/tw| ta\ peri\ to\n moxlo/n.</foreign></s> <s id="g0120102"><foreign lang="el">a)/topon ga\r <lb></lb>ei)=nai dokei= to\ kinei=sqai me/ga ba/ros u(po\ mikra=s i)sxu/os, <lb></lb>kai\ tau=ta meta\ ba/rous plei/onos: o(\ ga\r a)/neu moxlou= kinei=n <lb></lb>ou) du/natai/ tis, tou=to au)to\ to\ ba/ros proslabw\n e)/ti to\ <lb></lb>tou= moxlou= ba/ros, kinei= qa=tton.</foreign></s> </p> <p type="main"> <s id="id.000414">Dubitantur <expan abbr="autẽ">autem</expan> in hoc <lb></lb>genere ea, quæ de vecte di<lb></lb>cuntur. </s> <s id="id.000415">Abſurdum enim <lb></lb>videtur ab exigua vi ma<lb></lb>gnum pondus moueri, & <lb></lb>quidem ad pondus addito <lb></lb>pondere. </s> <s id="id.000416">quod enim ſine <lb></lb>vecte quiſpiam non poſſet <lb></lb>mouere, hoc ipſum pon<lb></lb>dus, inſuper <expan abbr="adijciẽs">adijciens</expan> vectis <lb></lb>ipſius <expan abbr="põdus">pondus</expan>, facile mouet. </s> </p> <p type="head"> <s id="id.000417">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000418">Qvæ de vecte.] <emph type="italics"></emph>Vectis eſt machina ſeu inſtrumentum inſtar <lb></lb>pali aut baculi recti longioris, cuius alterum extremum in cu<lb></lb>spidem <expan abbr="acutã">acutam</expan> & paulò latiorem deſinit, <expan abbr="vocaturq;">vocaturque</expan> lingua: alterum <lb></lb><expan abbr="extremũ">extremum</expan> caput eſt, aut manubrium. </s> <s id="id.000419">vecti in vſu aliquando ſupponi<lb></lb>tur fulcimentum, quod Græci<emph.end type="italics"></emph.end> <foreign lang="el">u(pomo/xlion,</foreign> <emph type="italics"></emph>Vitruuius porrectam <lb></lb>preßionem appellat. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000420">Abſurdum enim videtur.] <emph type="italics"></emph>Ostenditur hic cur problema <lb></lb>de vecte in Mechanicis, dubitabile, ſiue dignum quæſitu ſit. </s> <s id="id.000421">Du<lb></lb>bitabilia enim ſunt, quæ reuera fiunt: vt magnum pondus addito <lb></lb>pondere vectis ab exigua potentia, & vna hominis manu moue<lb></lb>ri. </s> <s id="id.000422">Fieri tamen ratio repugnat. </s> <s id="id.000423">Nam in omni motu mouens præua<lb></lb>lere debet mobili: hîc exigua potentia eſt mouens: magnum pondus <lb></lb>eſt mobile: illa quatenus exigua eſt, & ante per ſe impotens, atque <lb></lb>infirma, eſt inæquale minus: hoc quatenus magnum, eſt inæquale <lb></lb>maius, & ei addito vectis onere maius adhuc effici videtur: non <lb></lb>igitur exigua potentia magno oneri & adaucto in motu præua<lb></lb>lere debet. </s> <s id="id.000424">Si non præualet, non mouet: mouet tamen: Relinquitur <lb></lb>ergo vt exiſtimemus aliquam cauſam in hoc problemate motus eius <lb></lb>apparentis latentem ſubeſſe, dignam Philoſophi indagatione. <emph.end type="italics"></emph.end></s> </p> </subchap1> <pb xlink:href="035/01/055.jpg" pagenum="15"></pb> <subchap1> <p type="main"> <s id="id.000425"><foreign lang="el">pa/ntwn de\ tw=n toiou/twn <lb></lb>e)/xei th=s ai)ti/as th\n a)rxh\n o( ku/klos, kai\ tou=to eu)lo/gws <lb></lb>sumbe/bhken.</foreign></s> <s id="g0120104"><foreign lang="el">e)k me\n ga\r qaumasiwte/rou sumbai/nein ti <lb></lb>qaumasto\n ou)de\n a)/topon. </foreign></s> </p> <p type="main"> <s id="id.000426"><expan abbr="Omniũ">Omnium</expan> verò talium cir<lb></lb>culus continet cauſæ prin<lb></lb>cipium. </s> <s id="id.000427">quod etiam ratio<lb></lb>ni valde <expan abbr="cõſentaneum">conſentaneum</expan> eſt. <lb></lb></s> <s id="id.000428">Nec enim abſurdum eſt, <lb></lb>ex admirabiliori quid ad<lb></lb>mirabile contingere. </s> </p> <p type="head"> <s id="id.000429">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000430">Omnium verò talium.] <emph type="italics"></emph>Cauſa quæ latebat in problemate <lb></lb>de vecte aßignatur hic eſſe circulus: quæ ad alia multa Me<lb></lb>chanica poſtea transferetur. </s> <s id="id.000431">Probatur autem id ex forma circuli mi<lb></lb>rabilißima. </s> <s id="id.000432">ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000433"><emph type="italics"></emph>Ex admirabiliori admirabile aliquid fieri non eſt alienum, cauſæ <lb></lb>enim ſibi ſimiles effectus edunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000434"><emph type="italics"></emph>Circulus eſt admirabilis, & admirabilior, quam vectis: quamque <lb></lb>ea quæ à vecte fiunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000435"><emph type="italics"></emph>Ergo à circulo prodire id quod eſt admirabile in vecte, mechani<lb></lb>ciſque problematis non eſt alienum. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000436"><foreign lang="el">qaumasiw/taton de\ to\ tou)nanti/a <lb></lb>gi/nesqai met' a)llh/lwn.</foreign></s> <s id="g0120202"><foreign lang="el">o( de\ ku/klos sune/sthken e)k toiou/twn. </foreign></s> <s id="g0120203"><foreign lang="el"><lb></lb>eu)qu\s ga\r e)k kinoume/nou te gege/nhtai kai\ me/nontos, w(=n h( <lb></lb>fu/sis e)sti\n u(penanti/a a)llh/lois. </foreign></s> <s id="g0120203a"><foreign lang="el">w(/st' e)ntau=qa e)/stin e)pible/yasin <lb></lb>h(=tton qauma/zein ta\s sumbainou/sas u(penantiw/seis <lb></lb>peri\ au)to/n.</foreign></s> </p> <p type="main"> <s id="id.000437">Maximè verò mirabile <lb></lb>eſt contraria sibi inuicem <lb></lb>ſimul fieri: Atqui circulus <lb></lb>ex iis conſtitutus eſt. </s> <s id="id.000438">Sta<lb></lb>tim enim factus eſt ex mo<lb></lb>to, & immobili, quorum <lb></lb>natura ſibi inuicem con<lb></lb>traria eſt. </s> <s id="id.000439">Illùc <expan abbr="itaq;">itaque</expan> inſpi<lb></lb>cientibus <expan abbr="cõtraria">contraria</expan> ab ipſo <lb></lb>prouenire minus erit <expan abbr="mirũ">mirum</expan>. </s> </p> <p type="head"> <s id="id.000440">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000441">Maxime verò.] <emph type="italics"></emph>Circuli admiranda natura declaratur è <lb></lb>quintuplici contrariorum, quæ in eo præter contrariorum <emph.end type="italics"></emph.end><pb xlink:href="035/01/056.jpg" pagenum="16"></pb><emph type="italics"></emph>legem ſimul reperiuntur, repugnantia. </s> <s id="id.000442">Ex his triplex deprehenditur <lb></lb>in circulo dum fit: duplex vero dum factus eſt. </s> <s id="id.000443">Primum enim dum fit <lb></lb>habet hoc admirabile, quod fiat ab vna recta, cuius vnum extremo<lb></lb>rum quieſcit & fixum eſt: alterum vnà cum tota linea mouetur: ſe<lb></lb>cundum quod in mota linea puncta, cum infinita ſint, & omnia ſi<lb></lb>mul moueantur, inæqualiter tamen moueantur: Tertium quod extre<lb></lb>mum motum eodem tempore duobus motibus contrarijs, vno natu<lb></lb>rali ad peripheriam ſcilicet, altero violento ad centrum moueatur. </s> <s id="id.000444">In <lb></lb>facto verò hoc admirabile eſt, quod eius terminus vna linea exi<lb></lb>ſtens, ob ídque latitudinis expers, concauum tamen & conuexum, <lb></lb>quæ quodammodo contraria ſunt, admittat: præterea mobilitas, <lb></lb>quæ ineſt, admirabilis eſt, quia eodem tempore ad contrarias loci dif<lb></lb>ferentias, vt ſurſum deorſum: dextrorſum ſinistrorſum, fiat. </s> <s id="id.000445">Hæc <lb></lb>ſingula ſuis locis delineabuntur & explicabuntur. </s> <s id="id.000446">Sed præter hæc, <lb></lb>quæ ab Ariſtotele de circulo dicuntur, valde notabilia ſunt & alia, <lb></lb>quæ in Geometria in eo ineſſe, partim ponuntur, partim demonſtrata <lb></lb>ſunt. </s> <s id="id.000447">Primum quod vna linea terminetur, eâque ſimplici, ſimilari <lb></lb>vniformi, & carente principio, & fine, neque tamen infinita, vt <lb></lb>cuius, cum partes aliquot ſumptæ ſunt, quæ reſtant, minus ſint, quam <lb></lb>ante quam ſumptæ eſſent, quod repugnat infinito in magnitudine: ſed <lb></lb>tota eſt, & perfecta: vnde circulus figura eſt planarum ſimplicißi<lb></lb>ma, regularißima, perfectißima: Deinde quod ea linea non ſit an<lb></lb>gulus, ad angulum tamen proxime accedat, vt oſtendimus in noſtro <lb></lb>libello de angulo contactus, & ob id <expan abbr="quodãmodo">quodammodo</expan> vndequaque angu<lb></lb>lata, cum nuſquam ſit, dici poßit, & figura<emph.end type="italics"></emph.end> <foreign lang="el">pa/ngwnos & o(lo/gwnos,</foreign><lb></lb><emph type="italics"></emph>tum prima figurarum & vltima: poſtea, quod ex infinitis punctis <lb></lb>quæ in ſpatio ab ea comprehenſo ſunt, vnum eſt tantum, à quo omnes <lb></lb>rectæ ad peripheriam ductæ, ſunt æquales: quod Diametro bifariam <lb></lb>ſecetur: quod hinc ſemicirculus circa Diametrum manentem <lb></lb>voluens, quouſque redierit ad eum locum vnde moueri cœpit, ſphæ<lb></lb>ram constituat, corporum ſimplicißimum, capacißimum, mobilißi<lb></lb>mum, mouentißimum: quod circulus omnium figurarum eiuſdem <lb></lb>perimetri ſit capacißima: quod vno puncto lineam rectam attin<lb></lb>gat, ſicque offenſationibus & occurſationibus minimum pateat, <lb></lb>ſicque inſiſtens dimidia ſui totius parte nutet, vnde propenſißimus <lb></lb>eſt ad motum, & dimotus cum moueat annexa, aptißimus quoque <emph.end type="italics"></emph.end><pb xlink:href="035/01/057.jpg" pagenum="17"></pb><emph type="italics"></emph>erit ad mouendum: poſtremò quod inter rectam circulum tangen<lb></lb>tem, & circuli peripheriam altera recta ſine ſectione cadere non <lb></lb>poßit. </s> <s id="id.000448">quod 16. prop. lib. 3. elem. eſt demonſtratum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000450">Imprimis enim] <emph type="italics"></emph>Prima repugnantia eſt in circulo, quod fiat <lb></lb>è moto & quieto, quæ ſunt oppoſita ex genere priuantium, vnde rur<lb></lb>ſus concluditur, minus eſſe mirum, id eſt minus abſurdum à circulo <lb></lb>produci contraria. </s> <s id="id.000451">Circulum autem fieri ex moto & quieto patet his, <lb></lb>qui eius fabricam repetent è 3. poſtulato element.Eucl. </s> <s id="id.000452">Ibi enim po<lb></lb>ſtulatur, vt è dato centro & interuallo circulum deſcribere conce<lb></lb>datur. </s> <s id="id.000453">Deſcribitur autem cum data recta finita, manente eius vno <lb></lb>extremorum, circummoluitur, quouſque redeat ad locum vnde mo<lb></lb>ueri cœpit, id quod, vt ſine errore fiat inuentus eſt circinus à Talo <lb></lb>Dædali ex ſorore nepote, cuius forma & officium ab Ouidio accom<lb></lb>modate huic loco, ſic eſt expreſſum,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000454">Ex vno duo ferrea brachia nodo <lb></lb>Iunxit, vt æquali ſpatio diſtanti<lb></lb><figure id="id.035.01.057.1.jpg" xlink:href="035/01/057/1.jpg"></figure><lb></lb>bus ipſis</s> </p> <p type="main"> <s id="id.000455">Altera pars ſtaret, pars altera du<lb></lb>ceret orbem. </s> </p> <p type="main"> <s id="id.000456"><emph type="italics"></emph>Sit igitur recta A B inter extrema duo<lb></lb>rum brachiorum circini A C B diua<lb></lb>ricati per interuallum lineæ A B, <lb></lb>cuius extremum A maneat: alterum B <lb></lb>lineæ motu feratur per D quouſque redeat <lb></lb>ad B: ſicque circulus B D B erit fa<lb></lb>ctus. </s> <s id="id.000457">Idque beneficio puncti B cum tota <lb></lb>linea A B moti, atque puncti A quieti, vt hic vult Ariſtoteles. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000458"><foreign lang="el">prw=ton me\n ga\r th=| periexou/sh| grammh=| to\n <lb></lb>ku/klon pla/tos ou)qe\n e)xou/sh|, ta)nanti/a pws prosemfai/netai, <lb></lb>to\ koi=lon kai\ to\ kurto/n.</foreign></s> <s id="g0120204"><foreign lang="el">tau=ta de\ die/sthken a)llh/lwn, <lb></lb>o(\n tro/pon to\ me/ga kai\ to\ mikro/n. </foreign></s> <s id="g0120205"><foreign lang="el">e)kei/nwn te ga\r <lb></lb>me/son to\ i)/son kai\ tou/twn to\ eu)qu/. </foreign></s> <s id="g0120205a"><foreign lang="el">dio\ metaba/llonta ei)s <lb></lb>a)/llhla, ta\ me\n a)nagkai=a i)/sa gene/sqai pro/teron h)\ tw=n<lb></lb> a)/krwn o(poteronou=n, th\n de\ grammh\n eu)qei=an, o(/tan e)k kurth=s <lb></lb>ei)s koi=lon h)\ pa/lin e)k tau/ths gi/nhtai kurth\ kai\ periferh/s. <lb></lb></foreign></s> <s id="g0120205b"><foreign lang="el">e(\n kai\ ou)=n tou=to tw=n a)to/pwn u(pa/rxei peri\ to\n ku/klon.</foreign></s> </p> <p type="main"> <s id="id.000459">Primum ſiquidem lineæ <lb></lb>ipſum circulum <expan abbr="comprehendẽti">compre<lb></lb>hendenti</expan>, licet latitudinem <lb></lb>nullam habeat, contraria <lb></lb>quodammodo, cauum & <lb></lb>conuexum ineſſe <expan abbr="apparẽt">apparent</expan>. <lb></lb></s> <s id="id.000460">Hæc autem ita inter ſe di<lb></lb>ſtant, vt <expan abbr="magnũ">magnum</expan> & paruum. <pb xlink:href="035/01/058.jpg" pagenum="18"></pb></s> <s>horum enim medium eſt <lb></lb>æquale: illorum verò re<lb></lb>ctum. </s> <s id="id.000461">Ideò inuicem cum <lb></lb>commutantur, priùs ne<lb></lb>ceſſe eſt æqualia fieri: li<lb></lb>neam ſanè rectam, cum ex <lb></lb>conuexa fit caua: & rurſus <lb></lb>ex ipſa fit conuexa & ro<lb></lb>tunda. </s> <s id="id.000462">Atque vnum hoc <lb></lb>eſt ex abſurdis quę inſunt <lb></lb>circulo. </s> </p> <p type="head"> <s id="id.000463">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000464">Primum ſiquidem.] <emph type="italics"></emph>Vetuſtatis iniuria multas veterum li<lb></lb>bris, & huic ſane irrepſiſſe mendas, non eſt res dubia, vt hoc loco<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">prw/ton</foreign> <emph type="italics"></emph>pro<emph.end type="italics"></emph.end> <foreign lang="el">deu/teron. </foreign><emph type="italics"></emph>Namque hîc non prima, vt iam patuit: ſed ſe<lb></lb>cunda eſt in circulo repugnantia. </s> <s id="id.000465">Eaque ex eo quod cum circuli peri<lb></lb>pheria ſit vna linea def. 15. lib. 1. elem. & idcirco latitudinis expers <lb></lb>def. 2. lib. eiuſdem: habeat tamen in ſe contraria conuexum ſcilicet, <lb></lb>& concauum: illud quidem quà ſpectat foras: hoc vero quà intra. <lb></lb></s> <s id="id.000469">vbi nota Ariſtotelem dixiſſe hæc<emph.end type="italics"></emph.end> <foreign lang="el">e)nanti/a pws</foreign> <emph type="italics"></emph>contraria quodam<lb></lb>modo. </s> <s id="id.000470">Nec enim vere contraria ſunt, quia vere contraria ſunt ea, <lb></lb>quæ ſecundum ſeipſa ſumpta, ex ſeipſis extreme diſtant, & vnde ſe <lb></lb>expellere nata ſint, habent: at hæc conuexum & concauum non ſic <lb></lb>extreme diſtant: ſed ratione ſitus partium in diuerſis locorum diffe<lb></lb>rentijs, quod ſcilicet aliæ alijs ſint al<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.058.1.jpg" xlink:href="035/01/058/1.jpg"></figure><lb></lb><emph type="italics"></emph>tiores, vel depreßiores. </s> <s id="id.000471">Cum enim re<lb></lb>ctum ſit id in lineis quod ex æquo iacet <lb></lb>inter ſua extrema def. 2. lib. 1. & vt <lb></lb>linea A B, curuum erit quod non ex <lb></lb>æquo iacebit, ſed altius aut depreßius: <lb></lb>idque ſi inter extrema vbique attollatur: <lb></lb>conuexum vt C E D: ſi vero vbique <lb></lb>deprimatur concauum, vt C F D quæ eadem eſt linea ex ſe, ſed <lb></lb>ex locis E E & F F partium mutata. </s> <s>Cum igitur ab eadem C D<emph.end type="italics"></emph.end><pb xlink:href="035/01/059.jpg" pagenum="19"></pb><emph type="italics"></emph>non ſe expellant non erunt verè contraria: qualia tamen apparent ex <lb></lb>diſtantia & differentiis locorum ſurſum deorſum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000473">Hæc autem ita.] <emph type="italics"></emph>Similitudine comprobatur conuexum & <lb></lb>concauum contraria eſſe. </s> <s id="id.000474">Quemadmodum magnum & paruum con<lb></lb>traria ſunt, quia diſtant, inter ſe per medium, quod eſt æquale, & <lb></lb>cum commutantur in inuicem neceſſe eſt prius æquale fieri: ſic con<lb></lb>uexum & concauum contraria erunt, quia diſtant inter ſe per me<lb></lb>dium, quod eſt rectum, & cum commutantur in inuicem prius re<lb></lb>ctum etiam fieri neceſſum eſt. </s> <s id="id.000475">ſunt igitur conuexum & concauum <lb></lb>contraria. </s> <s id="id.000476">Sed & hic aſſumemus per eandem definitionem contra<lb></lb>riorum ante poſitam, & ex ſententia Ariſtotelis in categ. Quanti<lb></lb>tatis, magnum & paruum apparenter duntaxat eſſe contraria. </s> <s id="id.000478">Ap<lb></lb>parenter dico vt illa priora, quia habent aliquid de definitione con<lb></lb>trariorum, quod ſibi conueniat, ſcilicet diſtare inter ſe in eodem ge<lb></lb>nere, & habere medium: ſed non vere tamen eſſe. </s> <s id="id.000479">Quia non habent <lb></lb>omnes prædictæ definitionis particulas ſibi conuenientes. </s> <s id="id.000480">Hæc <lb></lb>enim cum ſint in Relatis, vnum idemque non ex ſe dicitur magnum <lb></lb>aut paruum: ſed reſpectu alicuius, vt canis reſpectu elephantis paruus <lb></lb>eſt, at idem reſpectu muſcæ magnus eſt. </s> <s id="id.000481">Cœterum hic notandum eſt <lb></lb>reſpectum iſtum licet fieri poßit ad quodlibet obuium, cum tamen <lb></lb>hæc vocabula, magnum, paruum, ſimpliciter dicuntur, fieri ad ſym<lb></lb>metrum ſui cuiuſque generis. </s> <s id="id.000482">Symmetrum appello, quod iuſtam ma<lb></lb>gnitudinem in ſuo genere adeptum eſt. </s> <s id="id.000483">Et hoc eſt quod hic dicitur <lb></lb>æquale, medium ſcilicet inter <expan abbr="magnũ">magnum</expan> tanquam excedens, & paruum <lb></lb>tanquam deficiens, neutrobique igitur iuſtum. </s> <s id="id.000484">Vt eſto, quod aiunt <lb></lb>multi, iuſta hominis magnitudo ſex pedum. </s> <s id="id.000485">Qui igitur inter homi<lb></lb>nes ſeptempedalis eſt, magnus: qui quintumpedalis, paruus ſimplici<lb></lb>ter dicetur. </s> <s id="id.000486">Hinc intellige, vt id obiter annotem, quod apud Ariſto<lb></lb>telem memini me legiſſe, nullam paruam mulierem pulchram eſſe, <lb></lb>quia, quod prima pars eſt pulchritudinis non habet, ſymmetrum ſui <lb></lb>generis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000487">Atque vnum hoc eſt.] <foreign lang="el">to\ a)/topon. </foreign><emph type="italics"></emph>Hic vt & alibi ſæpius <lb></lb>pro<emph.end type="italics"></emph.end> <foreign lang="el">qauma/sion</foreign> <emph type="italics"></emph>ſumitur, id eſt igitur eſſe conuexum & concauum <lb></lb>in linea vnum eſt ex admirabilibus circuli. <emph.end type="italics"></emph.end></s> </p> </subchap1> <pb xlink:href="035/01/060.jpg" pagenum="20"></pb> <subchap1> <p type="main"> <s id="id.000488"><foreign lang="el">deu/teron de\ o(/ti a(/ma kinei=tai ta\s e)nanti/as kinh/seis: <lb></lb>a(/ma ga\r ei)s to\n e)/mprosqen kinei=tai to/pon kai\ to\n o)/pisqen: <lb></lb>h(/ te gra/fousa grammh\ to\n ku/klon w(sau/tws e)/xei. </foreign></s> <s id="g0120302a"><foreign lang="el">e)c <lb></lb>ou(= ga\r a)/rxetai to/pou to\ pe/ras au)th=s, ei)s to\n au)to\n tou=ton to/pon <lb></lb>e)/rxetai pa/lin: sunexw=s ga\r kinoume/nhs au)th=s to\ e)/sxaton <lb></lb>pa/lin a)ph=lqe prw=ton, w(/ste kai\ fanero\n o(/ti mete/balen <lb></lb>e)nteu=qen.</foreign></s> <s id="g0120303"><foreign lang="el">dio/, kaqa/per ei)/rhtai pro/teron, ou)de\n a)/topon, to\ <lb></lb>pa/ntwn ei)=nai tw=n qauma/twn au)to\n a)rxh/n.</foreign></s> <s id="g0120401"><foreign lang="el">ta\ me\n ou)=n peri\ <lb></lb>to\n zugo\n gino/mena, ei)s to\n ku/klon a)na/getai, ta\ de\ peri\ <lb></lb>to\n moxlo\n ei)s to\n zugo/n. </foreign></s> <s id="g0120401a"><foreign lang="el">ta\ d' a)/lla pa/nta sxedo\n ta\ <lb></lb>peri\ ta\s kinh/seis ta\s mhxanika\s, ei)s to\n moxlo/n.</foreign></s> </p> <p type="main"> <s id="id.000489">Secundum eſt, quod con<lb></lb>trariis motionibus ſimul <lb></lb>moueatur. </s> <s id="id.000490">Simul enim an<lb></lb>trorſum & retrorſum mo<lb></lb>uetur: atque linea circu<lb></lb>lum <expan abbr="deſcribẽs">deſcribens</expan> ſic ſe habet, <lb></lb>vt ex quo loco extremum <lb></lb>illius incipiat, rurſus ad <lb></lb>eundem redeat. </s> <s id="id.000491">Id ipſum <lb></lb>enim quod in ipſa conti<lb></lb>nenter mota eſt vltimum, <lb></lb>rurſus primum euadit. </s> <s id="id.000492">Ita<lb></lb>que manifeſtum, quod in<lb></lb>de <expan abbr="mutatũ">mutatum</expan> eſt. </s> <s id="id.000493">Propterea, <lb></lb>vt eſt prius dictum, non eſt <lb></lb>abſurdum ipſum admira<lb></lb>bilium omnium eſſe prin<lb></lb>cipium. </s> <s id="id.000494">Igitur & quę circa <lb></lb>libram eueniunt ad circu<lb></lb>lum referuntur, & quę cir<lb></lb>ca vectem ad libram, & <lb></lb>fortaſſis alia omnia, quæ <lb></lb>circa motiones mechani<lb></lb>cas, ad vectem. </s> </p> <p type="head"> <s id="id.000495">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000496">Secundum.] <emph type="italics"></emph>Pro<emph.end type="italics"></emph.end> <foreign lang="el">deu/teron</foreign> <emph type="italics"></emph>legamus ſi placet<emph.end type="italics"></emph.end> <foreign lang="el">trh/ton. </foreign><emph type="italics"></emph>Hic enim <lb></lb>tertia eſt repugnantia in circulo ex contrarijs motionibus, quas <lb></lb>ſimul habet, antè ſcilicet cum pars eius vna mouetur: oppoſita in <lb></lb>ipſomet tempore ponè mouetur. </s> <s id="id.000497">Hoc autem eſt contrarias motiones <lb></lb>ſimul habere. </s> <s>Contrariæ enim ſunt motiones apud Ariſtotelem in <lb></lb>categoria vbi & li. 5. de Phyſico auditu ex diametralibus locorum, <lb></lb>ad quæ fiunt, diſtantijs dextrorſum, ſiniſtrorſum: ſurſum, deorſum: <lb></lb>& antrorſum, retrorſum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000500">Atque linea circulum.] <emph type="italics"></emph>Cur circulus antè & ponè mouea<emph.end type="italics"></emph.end><pb xlink:href="035/01/061.jpg" pagenum="21"></pb><emph type="italics"></emph>tur, ratio adducitur ſumpta ab efficiente circuli cauſa. </s> <s id="id.000501">Sic ſyllo<lb></lb>giſmus inſtitui poteſt. </s> <s id="id.000502">Vt fit circulus ita mouetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000503"><emph type="italics"></emph>Fit circulus à linea continenter mota circa fixum extremorum <lb></lb>vnum, quouſque redeat ad eum locum vnde moueri cœpit, quod <lb></lb>fieri non poteſt niſi per loca quæ ſunt circa extremum fixum oppoſi<lb></lb>ta deducatur, & quod eſt vltimum, rurſus fiat primum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000504"><emph type="italics"></emph>Ergo circulus mouetur per loca è diametro oppoſita circa extre<lb></lb>mum lineæ à qua fit fixum. </s> <s id="id.000505">Quia igitur in his ſunt antè & ponè, <lb></lb>mouebitur antè & ponè: quia inſuper ſunt ſurſum & deorſum, <lb></lb>mouebitur etiam ſimul ſurſum & deorſum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000506"><emph type="italics"></emph>Centrum enim in plano circundatur quatuor loci differentijs, <lb></lb>propter duas quæ in ipſo ad rectos ſe ſecant dimenſiones, vt in circu<lb></lb>lo B C D E, eſto linea fabricans ipſum A B, ibique eſto ante <lb></lb>B. </s> <s>igitur cum erit in D, erit ponè: & cum in C, ſurſum: & <lb></lb>in E, deorſum, & perueniens ad A B, eidem loco reſtituetur, <lb></lb>à quo cœperat moueri, quod eſt vltimum <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.061.1.jpg" xlink:href="035/01/061/1.jpg"></figure><lb></lb><emph type="italics"></emph>fieri primum. </s> <s id="id.000507">Vnde cum circulus moue<lb></lb>tur, poteſt dici ire, & reuerti ſimul: ſic <lb></lb>cum ſphæricum corpus mouetur, in fine <lb></lb>ſemper, & principio motus ſui, etiam tum <lb></lb>ire, tum reuerti veriſimiliter dicetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000508"><emph type="italics"></emph>Cæterum notandum quod motiones dictæ <lb></lb>eſſe in circulo, inſunt quidem: ſed non ſi<lb></lb>mul ſecundum eandem partem. </s> <s id="id.000509">Nam cum B, mouetur ſurſum ver<lb></lb>ſus C, idem B, eodem tempore non fertur deorſum verſus E, ſed <lb></lb>tunc quidem D, altera pars in circulo oppoſita ipſi B, fertur ver<lb></lb>ſus E: vt autem verè eſſent motiones contrariæ deberent fieri ſe<lb></lb>cundum eaſdem partes. </s> <s id="id.000510">Eſt hæc igitur vt aliæ in circulo non vera <lb></lb>ſed apparens repugnantia. </s> <s id="id.000511">ex cuius tamen natura magnorum effe<lb></lb>ctuum poſtea cauſæ repetuntur, cum diametri B D, vt inflexilis <lb></lb>circa A, centrum fixum motæ, ſi B, deprimatur, neceſſe eſt alte<lb></lb>rum extremum D, attolli: & contra. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000512">Propterea vt eſt prius.] <emph type="italics"></emph>Concluſio generalis eſt, huc, vt exi<lb></lb>ſtimo, è fine primi huius capitis, vbi melius collocaretur, <expan abbr="trãspoſita">transpoſita</expan>, <lb></lb>quod amplius declarant ea, quæ ſubijciuntur de vecte & libra, ad <lb></lb>quæ cum referat omnia Mechanica, & ipſa vectis & libra referan<emph.end type="italics"></emph.end><pb xlink:href="035/01/062.jpg" pagenum="22"></pb><emph type="italics"></emph>tur ad circulum, ſequenti etiam capite, quod erat proximum, libræ <lb></lb>motiones explicat. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000513"><foreign lang="el">e)/ti de\ <lb></lb>dia\ to\ mia=s ou)/shs th=s e)k tou= ke/ntrou grammh=s mhqe\n e(/teron <lb></lb>e(te/rw| fe/resqai tw=n shmei/wn tw=n e)n au)th=| i)sotaxw=s, a)ll' a)ei\ <lb></lb>to\ tou= me/nontos pe/ratos porrw/teron o)\n qa=tton, polla\ tw=n qaumazome/nwn <lb></lb>sumbai/nei peri\ ta\s kinh/seis tw=n ku/klwn, peri\ <lb></lb>w(=n e)n toi=s e(pome/nois problh/masin e)/stai dh=lon.</foreign></s> </p> <p type="main"> <s id="id.000514">Præterea etiam, quod, <lb></lb>cum vna ſit ea linea, quæ <lb></lb>ex centro, nullum eorum, <lb></lb>quæ in ea ſunt, <expan abbr="pũctorum">punctorum</expan>, <lb></lb>æquè celeriter fertur: ſed <lb></lb>hoc, quod longius eſt ab <lb></lb>extremo eius immobili, <lb></lb>ſemper celerius: miranda <lb></lb>multa circa motiones cir<lb></lb>culi contingunt, vt in <expan abbr="ſequẽtibus">ſe<lb></lb>quentibus</expan> problematis fiet <lb></lb>manifeſtum. </s> </p> <p type="head"> <s id="id.000515">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000516">Præterea etiam.] <emph type="italics"></emph>Quarta repugnantia eſt in circulo ex inæ<lb></lb>qualitate motuum in eiuſdem lineæ circulum deſcribentis diuer<lb></lb>ſis punctis. </s> <s id="id.000517">Inæqualiter enim moueri dicuntur, & quæ eodem tem<lb></lb>pore diuerſa permeant ſpatia, & quæ in æqualibus temporibus idem: <lb></lb>atque hoc celerius, quod eodem tempore maius ſpatium permeat, vel <lb></lb>breuiori tempore idem: Tardius contra. </s> <s id="id.000518">Punctorum autem, quæ in<lb></lb>ſunt in vna eademque linea circulum deſcribente, illud quod remo<lb></lb>tius eſt à centro, maius ſpatium conficit: quam quod propinquius, li<lb></lb>cet vtraque eodem tempore ſuum perficiant. </s> <s id="id.000519">Linea enim circulum <lb></lb>deſcribens, quo tempore punctis centro propinquis redijt ad locum, <lb></lb>vnde ijſdem moueri cœperat, eodem remotis redit. </s> <s id="id.000520">Spatium autem <lb></lb>illud eſt peripheria, quæ ab vnoquoque eorum quæ ſunt in ſemidia<lb></lb>metro punctorum, deſcribitur, ſi quodlibet <expan abbr="pũctorum">punctorum</expan> in motu lineæ <lb></lb>intelligatur ſui, vt puncti, veſtigium relinquere, vt in eo quod circu<lb></lb>lum vndiquaque comprehendit. </s> <s id="id.000521">Peripheriam autem remotioris pun<lb></lb>cti à centro, id eſt ſemidiametri maioris eſſe maiorem peripheria pun<lb></lb>cti centro propinquioris, id eſt ſemidiametri minoris, ſic demonſtra<lb></lb>bimus. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/063.jpg" pagenum="23"></pb> <p type="main"> <s id="id.000522"><emph type="italics"></emph>Eſto A B C, peripheria ſemidiametri maioris A E: item <lb></lb>D F G, peripheria ſemidiametri D H minoris. </s> <s id="id.000523">Dico periphe<lb></lb>riam A B C maiorem peripheria D F G. </s> <s id="id.000524">Producatur enim A E <lb></lb>recta vt ſit A C <lb></lb>diameter poſtul. <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.063.1.jpg" xlink:href="035/01/063/1.jpg"></figure><lb></lb>2. <emph type="italics"></emph><expan abbr="itẽ">item</expan> D H vt ſit <lb></lb>& D G diame<lb></lb>ter. </s> <s id="id.000525">Quia igi<lb></lb>tur vt diameter <lb></lb>A C ad <expan abbr="ſuã">ſuam</expan> <expan abbr="peripheriã">pe<lb></lb>ripheriam</expan> A B C: <lb></lb>ita & D G diameter ad ſuam peripheriam D F G, per ea quæ <lb></lb>demonſtrata ſunt ab Archimede prop. 3. lib. de dimenſ. circuli, & <lb></lb>vicißim proportionales erunt A C diameter ad D G diametrum: <lb></lb>vt peripheria A B C ad peripheriam D F G prop. 16. lib. 5. & <lb></lb>quia A E & D H partes ſunt pariter multiplicium A C, D G <lb></lb>vtpote ſemidiametri ſuarum diametrorum, erit A E ad D H vt <lb></lb>A C ad D G prop. 15. lib. 5. ergo & peripheria A B C ad peri<lb></lb>pheriam D F G: vt A E ad D H prop. 11. lib. eiuſdem. </s> <s id="id.000529">Eſt <lb></lb>autem A E maior: quam D H ex hypotheſi. </s> <s id="id.000530">Erit igitur peri<lb></lb>pheria A B C maior: quam peripheria D F G. </s> <s id="id.000531">Et ſic peripheria <lb></lb>remotioris puncti à centro maior eſt peripheria puncti centro pro<lb></lb>pinquioris, quod fuit demonſtrandum. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000532"><foreign lang="el">dia\ de\ to\ <lb></lb>ta\s e)nanti/as kinh/seis a(/ma kinei=sqai to\n ku/klon, kai\ to\ <lb></lb>me\n e(/teron th=s diame/trou tw=n a)/krwn, e)f' ou(= to\ a, ei)s tou)/mprosqen <lb></lb>kinei=sqai, qa/teron de/, e)f' ou(= to\ *b ei)s tou)/pisqen <lb></lb>kataskeua/zousi/ tines, w(/st' a)po\ mia=s kinh/sews pollou\s u(penanti/ous <lb></lb>a(/ma kinei=sqai ku/klous, w(/sper ou(\s a)natiqe/asin e)n <lb></lb>toi=s i(eroi=s; poih/santes troxi/skous xalkou=s te kai\ sidhrou=s.</foreign></s> <s id="g0120502"><foreign lang="el"><lb></lb>ei) ga\r ei)/h tou= *a*b ku/klou a(pto/menos e(/teros ku/klos e)f' ou(= <lb></lb>*g*d, tou= ku/klou, e)f' ou(= *a*b, kinoume/nhs th=s diame/trou <lb></lb>ei)s tou)/mprosqen, kinhqh/setai h( *g*d ei)s tou)/pisqen tou= ku/klou <lb></lb>tou= e)f' w(=| *a, kinoume/nhs th=s diame/trou peri\ to\ au)to/.</foreign></s> <s id="g0120503"><foreign lang="el">ei)s <lb></lb>tou)nanti/on a)/ra kinhqh/setai o( e)f' ou(= *g*d ku/klos, tw=| e)f' <lb></lb>ou(= to\ *a*b: kai\ pa/lin au)to\s to\n e)fech=s, e)f' ou(= *e*z, ei)s <lb></lb>tou)nanti/on au(tw=| kinh/sei dia\ th\n au)th\n tau/thn ai)ti/an.</foreign></s> <s id="g0120601"><foreign lang="el">to\n au)to\n de\ <lb></lb>tro/pon ka)\n plei/ous w)=si, tou=to poih/sousin e(no\s mo/nou kinhqe/ntos.</foreign></s> <s id="g0120602"><foreign lang="el"><lb></lb>tau/thn ou)=n labo/ntes u(pa/rxousan e)n tw=| ku/klw| th\n <lb></lb>fu/sin oi( dhmiourgoi\ kataskeua/zousin o)/rganon kru/ptontes <lb></lb>th\n a)rxh/n, o(/pws h)=| tou= mhxanh/matos fanero\n mo/non to\ <lb></lb>qaumasto/n, to\ d' ai)/tion a)/dhlon. <lb></lb></foreign></s> </p> <p type="main"> <s id="id.000533">Quod autem circulus <lb></lb><expan abbr="cõtrariis">contrariis</expan> cieatur motibus, <lb></lb>& alterum extremorum <lb></lb>diametri in quo eſt A, dum <lb></lb>mouetur antrorſum, alte<lb></lb>rum in quo eſt B mouea<lb></lb>tur retrorſum, ideo non<lb></lb>nulli <expan abbr="faciũt">faciunt</expan>, vt ab vna mo<lb></lb>tione multi circuli ſimul <lb></lb>in contraria moueantur: <lb></lb>vt quos in deorum templis <lb></lb>ſtatuunt, efficientes circu<pb xlink:href="035/01/064.jpg" pagenum="24"></pb>los æreos & ferreos. </s> <s id="id.000534">Si <lb></lb>enim circulum in quo eſt <lb></lb>A B, alter circulus in quo <lb></lb>eſt G D attigerit, diame<lb></lb>tro circuli A B antror<lb></lb>ſum mota, diameter circu<lb></lb>li G D retrorſum moue<lb></lb>bitur, circuli in quo eſt A <lb></lb>diametro circa idem mo<lb></lb>ta. </s> <s id="id.000535">Circulus igitur in quo <lb></lb>eſt G D, contrà, quam is, <lb></lb>in quo eſt A B mouebi<lb></lb>tur: idemque ſequentem <lb></lb>in quo eſt E Z propter <lb></lb>eandem cauſam contra ſe <lb></lb>mouebit, & eodem modo <lb></lb>ſi plures fuerint vno com<lb></lb>moto itidem <expan abbr="faciẽt">facient</expan>. </s> <s id="id.000536">Hinc <lb></lb>Architecti Fabri, cum <expan abbr="hãc">hanc</expan> <lb></lb>in circulo naturam depre<lb></lb>hendiſſent, <expan abbr="organũ">organum</expan> fabri<lb></lb>cantur principium occu<lb></lb>lentes, vt ſit de machina, <lb></lb>ſolum hoc, quod admira<lb></lb>bile, apertum: quod autem <lb></lb>cauſa, occultum. </s> </p> <p type="head"> <s id="id.000537">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000538">Qvod autem circulus.] <emph type="italics"></emph>Tertia repugnantia in vnius cir<lb></lb>culi contrarijs motionibus ante poſita amplius declaratur, ab <lb></lb>exemplo plurium: ſed contiguorum ab vnica vi primaria ſecundum <lb></lb>motus contrarios motorum. </s> <s id="id.000539">Vt ſunto tres circuli contingentes quod<lb></lb>que ferè fit denticulis pectinis inſtar ſeſe ſubingredientibus in peri<lb></lb>phcria præditi, quorum primus A B, moueatur antrorſum, ſeu ſe<lb></lb>cundum ſuperiorem peripheriam, vt A feratur verſus C: alter <emph.end type="italics"></emph.end><pb xlink:href="035/01/065.jpg" pagenum="25"></pb><emph type="italics"></emph>G D ad illius motum neceſſario mouebitur propter denticulos, ſed <lb></lb><expan abbr="retrorsũ">retrorsum </expan><emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.065.1.jpg" xlink:href="035/01/065/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſeu <expan abbr="ſecũdum">ſecun<lb></lb>dum</expan> <expan abbr="inferiorẽ">in<lb></lb>feriorem</expan> <lb></lb><expan abbr="peripheriã">periphe<lb></lb>riam</expan>, vt <lb></lb>G ad B: <lb></lb>tum ter<lb></lb>tius E Z ad ſecundi motum mouebitur etiam, ſed antrorſum, vt E <lb></lb>ad F, & ſint deinceps alternatim infiniti denticulis ſeſe ſubinui<lb></lb>cem ingredientibus, ſemper mouebuntur. </s> <s id="id.000540">Vnde tunc à Fabro dato <lb></lb>principio motionis, vertebra vertebram continenter mouet, vltimá<lb></lb>que ab illis ſimulacrorum excita fit præteruectio, non aliter quam in <lb></lb>animalium genere à ſenſu, vel intellectione motionum exorto prin<lb></lb>cipio intrinſecis commotis cauſis, ſeque inuicem mouentibus, vt alij <lb></lb>poſtmodum extrinſecus, cum partium ipſarum, tum etiam vniuerſi <lb></lb>corporis viſuntur motus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000541">Hinc architecti.] <emph type="italics"></emph>Sicuti ante ex vnius circuli contrarijs mo<lb></lb>tibus libram, vectem, mechanicáque inſtrumenta magnam habere <lb></lb>vim ad onera mouendum ſubindicauit: ſic nunc ex circulorum con<lb></lb>tiguorum & variè multiplicatorum contrarij;s motionibus machi<lb></lb>nas quamplurimas effici <expan abbr="oſtẽdit">oſtendit</expan>, quibus credibile eſt veteres paganos, <lb></lb>qui veris miraculis <expan abbr="deſtituebãtur">deſtituebantur</expan>, in templis ſuorum <expan abbr="deorũ">deorum</expan> collocatis, <lb></lb>& etiam per vrbium vicos, & plateas geſtatis, <expan abbr="authoritatẽ">authoritatem</expan> dijs ſuis <lb></lb><expan abbr="cõflauiſſe">conflauiſſe</expan>, & ignaro vulgo mirificis modis ita impoſuiſſe. </s> <s id="id.000542">Huius rei <lb></lb>fecit mentionem Galenus, qui miracula inquit moliuntur principio <lb></lb>motionis exhibito diſcedunt, Machinæ vero ipſæ aliquantiſper, non <lb></lb>multo tamen tempore per ſe ipſæ artiſiciosè impelluntur. cap. 6. lib. de <lb></lb>fœt. format. </s> <s id="id.000545">Herodotus hiſtoria ſecunda videtur ex his aliqua<emph.end type="italics"></emph.end> <foreign lang="el">neu<lb></lb>ro/spasta</foreign> <emph type="italics"></emph>appellaſſe: quaſi diceremus, per funiculos tanquam neruos <lb></lb>circa rotulas inuolutos, varijs motibus agitata. </s> <s id="id.000546">Eiuſmodi erant adeò <lb></lb>celebratæ Dædali ſtatuæ, quæ inquit Plato niſi ligatæ aufugiebant,<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg12"></arrow.to.target><lb></lb><emph type="italics"></emph>& vago quodam ſinuoſoque impetu ferebantur in fugam: ligatæ <lb></lb>vero permanebant, vnde illæ non magno pretio emebantur inſtar <lb></lb>ſerui fugitiui: hæ contra magno. </s> <s id="id.000547">Erant enim præclara opera. <emph.end type="italics"></emph.end><pb xlink:href="035/01/066.jpg" pagenum="26"></pb><emph type="italics"></emph>Hodie etiam noſtri artifices ex hac plurium rotularum mira in<lb></lb>ter ſe coniunctione, aliquoque ex ſe mobili vt animali, vento, fu<lb></lb>mo, aqua, lamina chalybea primum motum ſuppeditante commota<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">au)to/mata</foreign> <emph type="italics"></emph>faciunt non ſolum admirabilia: ſed etiam maximè vti<lb></lb>lia, qualia ſunt horologia veterum clepſydras, & gnomones ſine luce <lb></lb>& ſerenitate inutiles, commoditate & perpetuitate longè ſuperan<lb></lb>tia, quibus hodie dies ciuilis in 24. partes, quas horas vocant, di<lb></lb>ſtribuitur. </s> <s id="id.000548">Ex quibus alia ſunt ſtataria, & in ſummis templorum no<lb></lb>ſtrorum partibus collocata: alia in <expan abbr="hominũ">hominum</expan> collis, Zoníſue <expan abbr="appẽſa">appenſa</expan> præ <lb></lb>exiguitate ponderis nullo modo moleſta, <expan abbr="circunferũtur">circunferuntur</expan>. </s> <s id="id.000549">Sed neſcio an <lb></lb>fama, an fide nobilius ſit illud, quod Aŕgentorati in loco ciuitatis <lb></lb>eminentißimo poſitum eſt, in quo vniuerſi mundi cæleſtis com<lb></lb>pago, orbibus ſuis in ſuas partes diſtincta viſitur, In hoc enim <lb></lb>octaui orbis tardißimum motum, Zodiaci duodecim ſigna, Solis per <lb></lb>puncta ecliptica tranſitum, Lunæ varias apparitiones, ſingulorum <lb></lb>planetarum progreſſus, regreſſus, ſtationes, latitudines, altitudines, <lb></lb>innumeraque alia præter temporum momenta, & horas tum æqua<lb></lb>les, tum inæquales intueri licet. </s> <s id="id.000550">Ita tamen, vt quod hic dicitur, quic<lb></lb>quid eſt rotarum, ponderum, molarum, denticulorum, nolarum, vir<lb></lb>garum, <expan abbr="funiũ">funium</expan>, atque aliorum <expan abbr="inſtrumentorũ">inſtrumentorum</expan> magna ex parte intus <lb></lb>deliteſcat, & occultetur, quæ verò in tanta machina tot admirabilia <lb></lb>ſunt, <expan abbr="appareãt">appareant</expan>. </s> <s id="id.000551">Hæc, & quæ imaguncularum inceſſum, ſaltum, cho<lb></lb>reas repræſentant, faciunt, vt quæ de Architæ columba volatili, & <lb></lb>de Archimedis ſphæra verſatili memoriæ reliquit antiquitas, pro <lb></lb>falſis minime habeamus. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000552"><margin.target id="marg12"></margin.target>In Menone</s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.000553">2. <foreign lang="el">*amfi\ zugou= dia\ ti/ e)n tw|= <lb></lb>ku/klw| h( mei/zwn grammh\ <lb></lb>qa=tton fe/retai th=s e)lattonos, <lb></lb>kai\ e)nteu=qen dia\ ti/ ta\ mei/<lb></lb>zw zuga\ a)kribetera/ e)sti tw=n <lb></lb>e)latto/nwn. </foreign></s> </p> <p type="main"> <s id="id.000554">2. De libra propter quid <lb></lb>maior linea in circulo <lb></lb>celerius fertur, minore. <lb></lb></s> <s id="id.000555">Ex quo fit vt libræ ma<lb></lb>iores minoribus ſint <lb></lb>exactiores. </s> </p> <p type="main"> <s><foreign lang="el">*prw=ton me\n ou)=n ta\ sumbai/nonta peri\ to\n zugo\n a)porei=tai, <lb></lb>dia\ ti/na ai)ti/an a)kribe/stera/ e)sti ta\ zuga\ ta\ mei/zw <lb></lb>tw=n e)latto/nwn.</foreign></s> <s id="g0120702"><foreign lang="el">tou/tou de\ a)rxh/, dia\ ti/ pote e)n tw=| ku/klw| <lb></lb>h( plei=on a)festhkui=a grammh\ tou= ke/ntrou th=s e)ggu\s, th=| <lb></lb>au)th=| i)sxu/i kinoume/nh qa=tton fe/retai th=s e)la/ttonos, to\ <lb></lb>ga\r qa=tton le/getai dixw=s.</foreign></s> <s id="g0120704"><foreign lang="el">a)/n te ga\r e)n e)la/ttoni xro/nw| <lb></lb>i)/son to/pon diece/lqh|, qa=tton ei)=nai le/gomen, kai\ e)a\n e)n i)/sw|, <lb></lb>plei/w.</foreign></s> <s id="g0120705"><foreign lang="el">h( de\ mei/zwn e)n i)/sw| xro/nw| gra/fei mei/zona ku/klon: <lb></lb>o( ga\r e)kto\s mei/zwn tou= e)nto/s.</foreign></s> </p> <p type="main"> <s id="id.000557"><expan abbr="Primũ">Primum</expan> igitur quę circa <expan abbr="librã">li<lb></lb>bram</expan> <expan abbr="cõtingunt">contingunt</expan>, <expan abbr="difficultatẽ">difficultatem</expan> <lb></lb><expan abbr="adferũt">adferunt</expan>. </s> <s id="id.000558">Ob quam cauſam <pb xlink:href="035/01/067.jpg" pagenum="27"></pb>libræ maiores minoribus <lb></lb>ſint exactiores. </s> <s id="id.000559">Huius vero <lb></lb><expan abbr="principiũ">principium</expan> eſt quare in cir<lb></lb>culo <expan abbr="diſtãtior">diſtantior</expan> linea à cen<lb></lb>tro, ei propinquiore <expan abbr="eadẽ">eadem</expan> <lb></lb>vi mota celerius fertur. <lb></lb></s> <s id="id.000560">Celerius autem dicitur bi<lb></lb>fariam, ſiue enim in mino<lb></lb>ri tempore ęquale ſpatium <lb></lb>tranſierit, celerius eſſe di<lb></lb>cimus: ſiue in <expan abbr="tẽpore">tempore</expan> ęqua<lb></lb>li, maius. </s> <s id="id.000561">Maior autem li<lb></lb>nea in æquali <expan abbr="tẽpore">tempore</expan> ma<lb></lb>iorem circulum deſcribit. <lb></lb></s> <s id="id.000562">Qui enim extra eſt, maior <lb></lb>eſt eo, qui intus. </s> </p> <p type="head"> <s id="id.000563">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000564">De libra propter.] <emph type="italics"></emph>In hoc capite Ariſtoteles vult oſtendere <lb></lb>cur libræ longiorum brachiorum ſint exactiores: quam libræ <lb></lb>breuiorum. </s> <s id="id.000565">Et huius problematis cauſam refert ad circulum, circu<lb></lb>lique eam proprietatem, qua radij longiores celerius, id eſt eodem <lb></lb>tempore maius ſpatium conficiunt, quam breuiores. </s> <s id="id.000566">Quod quia futu<lb></lb>rum eſt fundamentum multorum aliorum problematum poſtea ex<lb></lb>plicandorum, diligenter imprimis demonſtrat. </s> <s id="id.000567">Et primum quod re<lb></lb>cta deſcribens circulum ( vno nomine relicta periphraſi radium hîc <lb></lb>appellabimus ) duabus lationibus feratur, iiſque in nulla ratione & <lb></lb>nullo tempore. </s> <s id="id.000568">Et ex his alteram eſſe ſecundum naturam, alteram <lb></lb>præter naturam. </s> <s id="id.000569">Poſtremò quod latio ſecundum naturam in maiore <lb></lb>circulo maior ſit: quam in minore. </s> <s id="id.000570">Latio autem præter naturam in <lb></lb>minore circulo maior ſit: quam in maiore. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000571">Primum igitur.] <emph type="italics"></emph>Proponitur problema de librarum inæqua<lb></lb>lium exactiore iudicio, quod pendet à minorum ponderum deprehen<lb></lb>ſione, vt ea ſit exactior per quam minora pondera expendi poſſunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000572">Huius vero.] <emph type="italics"></emph>Cauſa exactiorum librarum refertur ad circuli <emph.end type="italics"></emph.end><pb xlink:href="035/01/068.jpg" pagenum="28"></pb><emph type="italics"></emph>radios longiores, qui celerius feruntur minoribus, id eſt qui æquali <lb></lb>tempore maius ſpatium, & proinde ſenſibilius tranſeunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000573">Celerius enim.] <emph type="italics"></emph>Celeritatis lationum duos modos adfert ſi<lb></lb>miles ijs quos cap. 2. lib. 6. de Phyſ. auditu attulit, vt vtro longioris <lb></lb>radij celeritas accipi debeat, intelligatur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000574">Qui enim extra.] <emph type="italics"></emph>E duobus circulis concentricis, qui extra eſt, <lb></lb>eſt quoddam <expan abbr="totũ">totum</expan>, & internus eſt externi vna pars. </s> <s id="id.000575">Cum <expan abbr="itaq;">itaque</expan> totum <lb></lb>maius ſit ſua parte ex 9. axiom. lib. 1. ele. externus circulus interno <lb></lb>concentrico erit maior. </s> <s id="id.000578">Præterea <expan abbr="cũ">cum</expan> circuli æquales ſint, <expan abbr="quorũ">quorum</expan> ſemi<lb></lb>diametri ſint æquales def. 1. lib. 3. ele. </s> <s id="id.000580">Illi quorum ſemidiametri ſunt <lb></lb>inæquales, erunt & inæquales, & ille maior, cuius ſemidiameter <lb></lb>maior. </s> <s id="id.000581">Quæ licet vera ſint non tamen ſtatim ſequitur figuræ planæ <lb></lb>cuius area maior eſt, eſſe & perimetrum maiorem vt ex 36. 37. <lb></lb>prop. lib. 1. elem. demonſtrari facile poteſt: neque ſi rurſus perimeter <lb></lb>contineat perimetrum, vt continens contento ſit maior, vt patere <lb></lb>poteſt ex eo, quod eſt à Proclo adductum ad prop. 21. lib. 1. elem. </s> <s id="id.000583">De <lb></lb>duabus rectis intra triangulum, rectangulum vel amblygonium <lb></lb>comprehenſis, quæ maiores conſtitui poſſunt ijs à quibus ambiuntur. <lb></lb></s> <s id="id.000584">Ob hæc igitur, cum hic locus non tam debeat intelligi de circulis, <lb></lb>quam circulorum peripherijs, meritò ante, cum huius proprietatis <lb></lb>mentio fieret, capite præcedenti peripheriam maioris circuli periphe<lb></lb>ria minoris maiorem eſſe demonſtrauimus, ſed etiam huius magni<lb></lb>tudinis maioris cauſa, hic ab Ariſtotele ſubiungitur. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000585"><foreign lang="el"> ai)/tion de\ tou/twn, o(/ti fe/retai <lb></lb>du/o fora\s h( gra/fousa to\n ku/klon.</foreign></s> <s id="g0120707"><foreign lang="el">o(/tan me\n ou)=n e)n lo/gw| <lb></lb>tini\ fe/rhtai, e)p' eu)qei/as a)na/gkh fe/resqai to\ fero/menon, <lb></lb>kai\ gi/netai dia/metros au)th\ tou= sxh/matos o(\ poiou=sin ai( <lb></lb>e)n tou/tw| tw=| lo/gw| sunteqei=sai grammai/.</foreign></s> <s id="g0120708"><foreign lang="el">e)/stw ga\r o( lo/gos <lb></lb>o(\n fe/retai to\ fero/menon, o(\n e)/xei h( *a*b, pro\s th\n *a*g, <lb></lb>kai\ to\ me\n *a*g fere/sqw pro\s to\ *b, h( de\ *a*b u(pofere/sqw <lb></lb>pro\s th\n *h*g: e)nhne/xqw de\ to\ me\n *a pro\s to\ *d, h( de\ e)f' <lb></lb>h(=| *a*b pro\s to\ *e. </foreign></s> <s id="g0120708a"><foreign lang="el">ou)kou=n e)pi\ th=s fora=s o( lo/gos h)=n, o(\n h( <lb></lb>*a*b e)/xei pro\s th\n *a*g, a)na/gkh kai\ th\n *a*d, pro\s th\n <lb></lb>*a*e, tou=ton e)/xein to\n lo/gon, o(/moion a)/ra e)sti\ tw=| lo/gw| to\ <lb></lb>mikro\n tetra/pleuron tw=| mei/zoni, w(/ste kai\ h( au)th\ dia/metros <lb></lb>au)tw=n, kai\ to\ *a e)/stai pro\s to\ *z.</foreign></s> <s id="g0120801"><foreign lang="el">to\n au)to\n dh\ tro/pon <lb></lb>deixqh/setai ka)\n o(pouou=n dialhfqh=| h( fora/: ai)ei\ ga\r <lb></lb>e)/stai e)pi\ th=s diame/trou.</foreign></s> <s id="g0120802"><foreign lang="el">fanero\n ou)=n o(/ti to\ kata\ th\n dia/metron <lb></lb>fero/menon e)n du/o forai=s, a)na/gkh to\n tw=n pleurw=n <lb></lb>fe/resqai lo/gon.</foreign></s> </p> <p type="main"> <s id="id.000586">Horum vero cauſa eſt, <lb></lb>quod recta deſcribens <expan abbr="circulũ">cir<lb></lb>culum</expan> <expan abbr="ſecundũ">ſecundum</expan> duas latio<lb></lb>nes fertur. </s> <s id="id.000587"><expan abbr="Cũ">Cum</expan> igitur in ali<lb></lb>qua ratione duę <expan abbr="sũt">sunt</expan> illæ la<lb></lb>tiones, neceſſe eſt id, quod <lb></lb>fertur <expan abbr="ſecundũ">ſecundum</expan> <expan abbr="rectã">rectam</expan> ferri, <lb></lb>quæ fit diameter figuræ, <lb></lb><expan abbr="quã">quam</expan> rectæ in ea ratione <expan abbr="cõſtitutæ">con<lb></lb>ſtitutæ</expan>, <expan abbr="cõprehendunt">comprehendunt</expan>. </s> <s id="id.000588">Sit <lb></lb>enim ratio <expan abbr="ſecundũ">ſecundum</expan> quam <lb></lb>mobile fertur ea: quam ha<pb xlink:href="035/01/069.jpg" pagenum="29"></pb>bet <foreign lang="el">a b</foreign> ad <foreign lang="el">a g,</foreign> & quidem <lb></lb><foreign lang="el">a</foreign> feratur ad <foreign lang="el">b,</foreign> & <foreign lang="el">a b</foreign><lb></lb>etiam feratur ad <foreign lang="el">h g</foreign>: la<lb></lb>tum vero ſit <foreign lang="el">a</foreign> ad <foreign lang="el">d,</foreign> & <lb></lb><foreign lang="el">a b</foreign> ad <foreign lang="el">e. </foreign>Igitur cum latio<lb></lb>nis ratio erat ea quam ha<lb></lb>bet <foreign lang="el">a b</foreign> ad <foreign lang="el">a g</foreign>: neceſſe <lb></lb>eſt & ipſam <foreign lang="el">a d</foreign> ad <foreign lang="el">a e</foreign> ean<lb></lb>dem habere rationem. </s> <s id="id.000589">Si<lb></lb>mile eſt enim ratione par<lb></lb>uum quadrilaterum maio<lb></lb>ri. </s> <s id="id.000590">Itaque & eadem diame<lb></lb>ter vtriuſque, & ipſum <foreign lang="el">a</foreign><lb></lb>erat vbi <foreign lang="el">z. </foreign></s> <s>Eodem modo <lb></lb>demonſtrabitur <expan abbr="vbicũque">vbicunque</expan> <lb></lb>latio deprehenſa fuerit. </s> <s id="id.000591"><expan abbr="Sẽper">Sem<lb></lb>per</expan> enim ſupra diametrum <lb></lb>erit. </s> <s id="id.000592">Manifeſtum igitur <lb></lb>quod latum <expan abbr="ſecũdum">ſecundum</expan> dia<lb></lb>metrum duabus lationi<lb></lb>bus neceſſe habet in ratio<lb></lb>ne laterum ferri. </s> </p> <p type="head"> <s id="id.000593">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000594">Horum vero cauſa.] <emph type="italics"></emph>Inæqualium <expan abbr="circulorũ">circulorum</expan> ab inæqualibus <lb></lb>radiis <expan abbr="deſcriptorũ">deſcriptorum</expan>, & maioris quidem à maiori multo abſtru<lb></lb>ſior aßignatur cauſa ex radij deſcribentis circulum duabus lationi<lb></lb>bus, quæ inter ſe <expan abbr="nullã">nullam</expan> <expan abbr="rationẽ">rationem</expan> ſeruant. </s> <s id="id.000595">Atque hinc elicitur quinta in <lb></lb>circulo repugnantia, ex qua admiratio eius maior: quam ante eſſe <lb></lb>concluditur. </s> <s id="id.000596">E lationibus enim illis vna eſt ſecundum naturam, <lb></lb>altera præter naturam. </s> <s id="id.000597">Et vtriſque vnum idemque ferri in nullo <lb></lb>tempore, id eſt in inſtanti indiuiſibili, quomodo non eſſet valde ad<lb></lb>mirabile? </s> <s id="id.000598">Circuli igitur radius, qui his duabus ita fertur in deſcri<lb></lb>ptione circuli, & circulus, qui à radio tali efficitur, erit admirabilis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000599">Cum igitur in.] <emph type="italics"></emph>Aggreditur demonſtrare radij duas lationes <lb></lb>nullam habere rationem inter ſe. </s> <s id="id.000600">Syllog. ſic eſt. </s> <s id="id.000601">Omne duabus latio<lb></lb>nibus rationem aliquam inter ſe ſeruantibus latum, fertur ſecundum <emph.end type="italics"></emph.end><pb xlink:href="035/01/070.jpg" pagenum="30"></pb><emph type="italics"></emph>rectam. </s> <s id="id.000602">Radius deſcribens circulum duabus ſuis lationibus, non <lb></lb>fertur ſecundum rectam. </s> <s id="id.000603">Radij igitur lationes in nulla ſunt ra<lb></lb>tione. </s> <s id="id.000604">Propoſitio confirmatur cum ſequenti diagrammate. <lb></lb></s> <s id="id.000605">Eſto rectangulum<emph.end type="italics"></emph.end> <foreign lang="el">a b h g</foreign> <emph type="italics"></emph>com<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.070.1.jpg" xlink:href="035/01/070/1.jpg"></figure><lb></lb><emph type="italics"></emph>prehenſum ſub rectis<emph.end type="italics"></emph.end> <foreign lang="el">a b, a g,</foreign><lb></lb><emph type="italics"></emph>quæ ſint inter ſe in ratione, quam <lb></lb>duæ lationes ipſius<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>habent. <lb></lb></s> <s id="id.000606">Et intelligatur a latum verſus<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">b</foreign> <emph type="italics"></emph>perueniſſe ad<emph.end type="italics"></emph.end> <foreign lang="el">d,</foreign> <emph type="italics"></emph>& verſus<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">g</foreign> <emph type="italics"></emph>perueniſſe ad<emph.end type="italics"></emph.end> <foreign lang="el">e</foreign>: <emph type="italics"></emph>ſicque cum <lb></lb>lationum ipſius<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ratio ſit vt<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">a b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">a g,</foreign> <emph type="italics"></emph>ergo erit &<emph.end type="italics"></emph.end> <foreign lang="el">a d</foreign><lb></lb><emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">a e</foreign>: <emph type="italics"></emph>vt<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">a y,</foreign> <emph type="italics"></emph>& rectrangulum minus<emph.end type="italics"></emph.end> <foreign lang="el">a d z e</foreign> <emph type="italics"></emph>com<lb></lb>munem angulum<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>cum maiori<emph.end type="italics"></emph.end> <foreign lang="el">a b h g</foreign> <emph type="italics"></emph>habens & ſimile erit <lb></lb>def. 1. lib. 6. & proinde circa eandem dimentientem conuerſ. prop. <lb></lb>24. lib. 6. </s> <s><emph type="italics"></emph>Et ſic<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>duabus ſuis ſic lationibus latum erit in<emph.end type="italics"></emph.end> <foreign lang="el">z,</foreign> <emph type="italics"></emph>vt vbi<lb></lb>cumque lationes ipſius<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ſiſtentur, ſemper ſint ſupra diametrum<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">a h. </foreign><emph type="italics"></emph>ſiquidem lationes iſtæ ſunt in ratione<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">a g. </foreign><emph type="italics"></emph>proinde <lb></lb>ſupra rectam, quia omnis diameter rectanguli recta eſt. </s> <s id="id.000609">Huic con<lb></lb>ſentit quod à Proclo ex Gemino acceptum ſic expoſitum eſt. </s> <s id="id.000610">Si qua<lb></lb>drangulum duoſque motus qui æquali celeritate fiant, alterum qui<lb></lb>dem per longitudinem: alterum vero per latitudinem intellexeris <lb></lb>dimetiens producetur recta exiſtens linea, lib. 2. comm. in def. rectæ <lb></lb>lineæ. </s> <s id="id.000612">Nunc igitur ponatur<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>extremum radij duabus lationibus <lb></lb>deſcribere circulum non digrediens à recta producere rectam, quod <lb></lb>eſt contra naturam circuli. </s> <s id="id.000613">Non igitur duæ lationes ipſius<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ferun<lb></lb>tur in ratione<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">a g. </foreign><emph type="italics"></emph>Sed hîc obiici poteſt quod Sol motu pri<lb></lb>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, & motu <lb></lb>proprio ab Occidente in Orientem in aliquo tempore quantum eſt <lb></lb>quod reſpondet æquatori coaſcendenti cum 59'. 8". Eclypticæ. </s> <s id="id.000614">Et ſic <lb></lb>eius duæ lationes ſunt in ratione aliqua, nec tamen Sol fertur ſecun<lb></lb>dum rectam ſed <expan abbr="ſecundũ">ſecundum</expan> arcum Eclypticæ. </s> <s id="id.000615">Ita eſt, ob id <expan abbr="dicendũ">dicendum</expan> hic <lb></lb>dictas ab Ariſtotele duæ lationes non ſimpliciter <expan abbr="intelligẽdas">intelligendas</expan>: ſed ta<lb></lb>les, quæ <expan abbr="ferãtur">ferantur</expan> ambæ <expan abbr="ſecundũ">ſecundum</expan> rectam. </s> <s id="id.000616">Et ſit manebit demonſtratio. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000617">Simile eſt enim.] <foreign lang="el">tw= lo/gw,</foreign> <emph type="italics"></emph>id eſt ratione, redundat quia quæ <lb></lb>ſimilia ſunt quadrangula, habent latera, quæ circum æquales angu<lb></lb>los propertionalia, ex def. 1. lib. 6. elem. <emph.end type="italics"></emph.end></s> </p> </subchap1> <pb xlink:href="035/01/071.jpg" pagenum="31"></pb> <subchap1> <p type="main"> <s id="id.000619"><foreign lang="el">ei) ga\r a)/llon tina/, ou)k oi)sqh/setai kata\ <lb></lb>th\n dia/metron.</foreign></s> <s id="g0120804"><foreign lang="el">e)a\n de\ e)n mhdeni\ lo/gw| fe/rhtai du/o fora\s <lb></lb>kata\ mhde/na xro/non, a)du/naton eu)qei=an ei)=nai th\n fora/n.</foreign></s> <s id="g0120805"><foreign lang="el"><lb></lb>e)/stw ga\r eu)qei=a.</foreign></s> <s id="g0120806"><foreign lang="el">teqei/shs ou)=n tau/ths diame/trou, kai\ paraplhrwqeisw=n <lb></lb>tw=n pleurw=n, a)na/gkh to\n tw=n pleurw=n lo/gon <lb></lb>fe/resqai to\ fero/menon: tou=to ga\r de/deiktai pro/teron.</foreign></s> <s id="g0120807"><foreign lang="el">ou)k <lb></lb>a)/ra poih/sei eu)qei=an to\ e)n mhdeni\ lo/gw| fero/menon mhde/na <lb></lb>xro/non.</foreign></s> <s id="g0120808"><foreign lang="el">e)a\n ga/r tina lo/gon e)nexqh=| e)n xro/nw| tini/, tou=ton <lb></lb>a)na/gkh to\n xro/non eu)qei=an ei)=nai fora\n dia\ ta\ proeirhme/na.</foreign></s> <s id="g0120809"><foreign lang="el"><lb></lb>w(/ste perifere\s gi/netai, du/o fero/menon fora\s e)n mhqeni\ <lb></lb>lo/gw| mhqe/na xro/non.</foreign></s> </p> <p type="main"> <s id="id.000620">Si enim in alia aliqua, <lb></lb>non feretur <expan abbr="ſecũdum">ſecundum</expan> dia<lb></lb>metrum. </s> <s id="id.000621">Si vero mobilis <lb></lb>duæ lationes in nulla ſint <lb></lb>ratione, nulloque in tem<lb></lb>pore, impoſſibile eſt latum <lb></lb>eſſe ſecundum rectam. </s> <s id="id.000622">Sit <lb></lb>enim recta, qua poſita pro <lb></lb>diametro, & completis la<lb></lb>teribus neceſſe eſt mobile <lb></lb>in ratione laterum latum <lb></lb>eſſe. </s> <s id="id.000623">Hoc enim prius fuit <lb></lb>demonſtratum. </s> <s id="id.000624">Non igi<lb></lb>tur ſecundum rectam pro<lb></lb>gredietur, id quod fertur <lb></lb>in nulla ratione, nulloque <lb></lb>in tempore. </s> <s>[Si enim <expan abbr="ſecũdum">ſe<lb></lb>cundum</expan> rationem aliquam <lb></lb>latum ſit in aliquo tempo<lb></lb>re, neceſſe eſt illud tempus <lb></lb>rectam eſſe lationem, pro<lb></lb>pter ea quæ ante dicta ſunt.] </s> <s>Itaque circulare eſt quod <lb></lb>ſecundum duas lationes latum eſt in nulla ratione nullo <lb></lb>in tempore. </s> </p> <p type="head"> <s id="id.000625">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000626">Si enim in alia.] <emph type="italics"></emph>Locus hic paulo obſcurior, debet ſic intelligi, <lb></lb>vt ſi exempli gratia, a duabus lationibus latum non feratur in <lb></lb>ratione quidem data<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">a g</foreign>: <emph type="italics"></emph>ſed<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.071.1.jpg" xlink:href="035/01/071/1.jpg"></figure><lb></lb><emph type="italics"></emph>in alia, non feretur ſecundum diame<lb></lb>trum<emph.end type="italics"></emph.end> <foreign lang="el">a h,</foreign> <emph type="italics"></emph>nihilominus tamen feretur <lb></lb>ſecundum rectam, quæ erit diameter <lb></lb>figuræ à lateribus alterius rationis <lb></lb>conſtitutæ, vt eſt in præſenti dia<lb></lb>grammate<emph.end type="italics"></emph.end> <foreign lang="el">a x</foreign> <emph type="italics"></emph>diameter quadrilateri <lb></lb>ſub<emph.end type="italics"></emph.end> <foreign lang="el">a d, a e</foreign> <emph type="italics"></emph>comprehenſi. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/072.jpg" pagenum="32"></pb> <p type="main"> <s id="id.000627">Si vero mobilis.] <emph type="italics"></emph>Concluſio eſt confirmata reiterato propoſi<lb></lb>tionis præcedentis proſyllogiſmo, ſic. </s> <s id="id.000628">Si duæ lationes puncti mobilis <lb></lb>ſunt in nulla ratione, nulloque in tempore, impoßibile eſt mobile hoc <lb></lb>latum eſſe ſecundum rectam: atqui puncti deſcribentis circulum duæ <lb></lb>lationes ſunt in nulla ratione, nullóque in tempore. </s> <s id="id.000629">Ergo impoßibile <lb></lb>eſt punctum, quod deſcribit circulum, ferri ſecundum rectam. </s> <s id="id.000630">Sint <lb></lb>enim lationes illæ in aliqua ratione. </s> <s id="id.000631">Ergo punctum feretur ſecun<lb></lb>dum rectam: at non fertur ſecundum rectam. </s> <s id="id.000632">Peripheria enim non <lb></lb>eſt recta: ſed curua. </s> <s id="id.000633">Non igitur in aliqua ratione ſunt illius lationes. <lb></lb></s> <s id="id.000634">Et ſi non in vlla ratione. </s> <s id="id.000635">nec igitur in tempore, quia tempora moti<lb></lb>bus analoga ſunt. </s> <s id="id.000636">Hîc duo occurrunt valde difficilia. </s> <s id="id.000637">Prius de <lb></lb>tempore. </s> <s id="id.000638">Demonſtrauit enim Ariſtoteles in Phyſicis, omnem mo<lb></lb>tum eſſe in tempore: alterum, cum ambæ lationes ſint in eodem ge<lb></lb>nere motus, ſcilicet localis, quî fiet, vt rationem non habeant. </s> <s id="id.000639">Hoc <lb></lb>enim repugnat def. 3. lib. 5. elem. </s> <s id="id.000641">quantitas enim motus vnius mul<lb></lb>tiplicata, alterius vicißim quantitatem ſuperare poteſt. </s> <s id="id.000642">Dicimus <lb></lb>ergo quod ad hoc poſterius attinet, rationem illas habere: ſed<emph.end type="italics"></emph.end> <foreign lang="el">a)/r)r(hton,</foreign><lb></lb><emph type="italics"></emph>& non ſolum indicibilem, quod numeris exprimi nequeat: ſed & <lb></lb>quod rectis lineis geometricè id eſt exactè, exprimi non poßit, qualis <lb></lb>non eſt inter duas lationes è quibus recta creatur, cum hæc ſi nume<lb></lb>ris non poßit exprimi, at rectis lineis ſaltem geometricè exprimitur. <lb></lb></s> <s id="id.000643">vt cum duarum rectarum, quæ parallelogrammum conſtituunt, vna <lb></lb>eſt latus quadrati alicuius, altera eſt eius diameter. </s> <s id="id.000644">Tunc enim ratio <lb></lb>eſt rectis illis licet incommenſerabilibus prop. 116. lib. 10. expreſſa. <lb></lb></s> <s id="id.000645">At hîc vt inter peripheriam & diametrum ſit aliqua ratio, veluti <lb></lb>inter arcum & ſubtendentem: hæc tamen neque numeris exprimi <lb></lb>poteſt, nec rectis lineis Geometrice vt videre eſt ex Archimede <lb></lb>lib. <emph.end type="italics"></emph.end> <foreign lang="el">peri\ metrh/s. kuk,</foreign><emph type="italics"></emph>& Ptol. lib. 1. <emph.end type="italics"></emph.end> <foreign lang="el">me/gal. sunt. </foreign><emph type="italics"></emph>quod autem ad <lb></lb>prius attinet in lationibus illis tempus admittitur, ſed hoc eſt eiuſmo<lb></lb>di, vt nullum eius detur inſtans, quo vna latio fiat, quo etiam non <lb></lb>& altera itidem fiat: quod prioribus licet commune eſſe poßit: pro<lb></lb>pter tamen laterum inæqualitatem vbi in æqualia dantur, non ita <lb></lb>ſimplex & indiuiſibile eſt. </s> <s id="id.000648">Cæterum duas has motiones facile ani<lb></lb>mo concipiet, qui viderit pueros noſtrates ſub medio vere, quo genus <lb></lb>hoc inſecti in roſarijs noſtris abundat, captam vnam grandiorem <lb></lb>muſcam viridem Cathelinam ipſi vocant, pede adfuniculum alliga<emph.end type="italics"></emph.end><pb xlink:href="035/01/073.jpg" pagenum="33"></pb><emph type="italics"></emph>tam permittere volare: ita tamen vt digitis alterum extremum funi<lb></lb>culi retineant. </s> <s id="id.000649">Hæc enim in altero extremo muſca, tanquam in ex<lb></lb>tremo radij circulum deſcribentis volatu ſuo deſcribit circulum: hic <lb></lb>volatus compoſitus eſt è duobus motibus: vno, quo hæc muſca pro<lb></lb>prio fertur, <expan abbr="ſecũdum">ſecundum</expan> quem ſeſe è vinculo liberare conatur: altero, quo <lb></lb>per vinculum retinetur, ne euagetur longius, quam longitudo <lb></lb>funiculi permittit. </s> <s id="id.000650">Ibi motus muſcæ violentus eſt, & non naturalis <lb></lb>vt à quo etiam cum pes abrumpitur præ ſuo conatu, aut nodus for<lb></lb>tuitò laxatur, ſi liberatur, ſtatim rectà aufugit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000651">Si enim ſecundum.] <emph type="italics"></emph>Hanc particulam parentheſi ſic [ ] in<lb></lb>tercludendam curauimus, quod eam ſuperuacuam eſſe cum Leonico <lb></lb>exiſtimemus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000652">Itaque circulare.] <emph type="italics"></emph>Proinde eſt ac ſi diceret, cum via ſeu linea <lb></lb>per quam fertur radij extremum mobile ſit maxime vniformis, vt <lb></lb>ex definitione circuli conſtat, nec tamen recta: reſtat, vt ſit circula<lb></lb>ris ſeu rotunda, à medio ſcilicet comprehenſi ſpatij æqualiter ex omni <lb></lb>parte diſtans. </s> <s id="id.000653">quod nulli alij obliquarum linearum conuenire poreſt: <lb></lb>non ellipſi quidem, quia licet vna ſit linea, & extremum in ea fiat <lb></lb>primum, vt in peripheria: nullum tamen punctum in eius medio eſt, <lb></lb>à quo omnes rectæ ad ellipſis peripheriam ſint æquales: non parabo<lb></lb>læ, non hyperbolæ, non ſpirali ſeu volutæ. </s> <s id="id.000654">Quia in nulla harum, quod <lb></lb>eſt extremum fit primum, quod peripheriæ conuenit. </s> <s id="id.000655">Præterea nulla <lb></lb>harum ſimplex eſt linea. </s> <s id="id.000656">Agitur hîc autem de ſimplicibus tantum, <lb></lb>quæ vno ſimplici motu, vel ſi duobus, ijs ſimilibus creantur, & ſi<lb></lb>milares ſunt: quales cum duæ tantum ſint recta ſcilicet & circula<lb></lb>ris, inde bene inferetur è poſita ſimplicè ſi recta non eſt, eſſe cir<lb></lb>cularis. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000657"><foreign lang="el">o(/ti me\n toi/nun h( to\n ku/klon gra/fousa <lb></lb>fe/retai du/o fora\s a(/ma, fanero\n e)/k te tou/twn, <lb></lb>kai\ o(/ti to\ fero/menon kat' eu)qei=an e)pi\ th\n ka/qeton a)fi<lb></lb>knei=tai, w(/ste ei)=nai pa/lin au)th\n a)po\ tou= ke/ntrou ka/qeton.</foreign></s> <s id="g0121001"><foreign lang="el"><lb></lb>e)/stw ku/klos o( *a*b*g, to\ d' a)/kron to\ e)f' ou(= *b, fere/sqw <lb></lb>e)pi\ to\ *d: a)fiknei=tai de/ pote e)pi\ to\ *g.</foreign></s> <s id="g0121002"><foreign lang="el">ei) me\n ou)=n e)n tw=| <lb></lb>lo/gw| e)fe/reto o(\n e)/xei h( *b*d, pro\s th\n *d*g, e)fe/reto a)\n <lb></lb>th\n dia/metron th\n e)f' h(=| *b*g.</foreign></s> <s id="g0121003"><foreign lang="el">nu=n de/, e)pei/per e)n ou)deni\ <lb></lb>lo/gw|, e)pi\ th\n perife/reian fe/retai th\n e)f' h(=| *b e *g.</foreign></s> </p> <p type="main"> <s id="id.000658">Quod vero recta <expan abbr="deſcribẽs">deſcri<lb></lb>bens</expan> circulum duabus ſimul <lb></lb>lationibus feratur, <expan abbr="cũ">cum</expan> ex his <lb></lb>eſt <expan abbr="manifeſtũ">manifeſtum</expan>, <expan abbr="tũ">tum</expan> quod lata <lb></lb><expan abbr="ſecundũ">ſecundum</expan> <expan abbr="rectã">rectam</expan> fieret num<lb></lb>quam perpendicularis. </s> <s id="id.000659">Et <lb></lb>fieri à <expan abbr="cẽtro">centro</expan> <expan abbr="perpendicularẽ">perpendicula<lb></lb>rem</expan> [<expan abbr="demõſtrem">demonſtrem</expan>us]. </s> <s>Sit circu<pb xlink:href="035/01/074.jpg" pagenum="34"></pb><foreign lang="el">b</foreign><lb></lb>lus <foreign lang="el">a b g,</foreign> & extremum <foreign lang="el">b</foreign><lb></lb>feratur ad <foreign lang="el">d,</foreign> perueniet ſa<lb></lb>ne aliquando ad <foreign lang="el">g. </foreign></s> <s>[Si igi<lb></lb>tur ferebatur in ratione <lb></lb>quam habet <foreign lang="el">b e</foreign> ad <foreign lang="el">e g,</foreign> fe<lb></lb>rebatur ſecundum diame<lb></lb>trum <foreign lang="el">b g</foreign>: At nunc cum in <lb></lb>nulla ratione feratur, ſe<lb></lb>cundum peripheriam <foreign lang="el">b e g</foreign><lb></lb>feretur.]</s> </p> <p type="head"> <s id="id.000660">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000661">Qvod vero recta.] <emph type="italics"></emph>Quia ſuperioris ſyllogiſmi aſſumptio aſſu<lb></lb>mebat <expan abbr="Radiũ">Radium</expan> duabus ſimul ferri lationibus, id ipſum hîc breui<lb></lb>ter, ideo valde obſcurè confirmatur. </s> <s id="id.000662">Confirmatio apertior ſic erit. <lb></lb></s> <s id="id.000663">Radius deſcribens circulum vna tantum latione fertur, aut pluri<lb></lb>bus: non vna tantum, quia ad vnam tantum loci differentiam, <lb></lb>cum ſit quid ſimplicißimum, ferretur ( probat enim hoc Ariſtoteles <lb></lb>cap. 2. lib. 1. de Cœlo ) Quinetiam ſi ſic. </s> <s id="id.000664">Idem radius à diametro cir<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.074.1.jpg" xlink:href="035/01/074/1.jpg"></figure><lb></lb><emph type="italics"></emph>culi digrediens in tranſitu ab vna ſemidia<lb></lb>metro ad alteram numquam conſequeretur <lb></lb>cum ſitum, per quem ipſi à centro perpen<lb></lb>dicularis eſſet. </s> <s id="id.000665">Conſequitur autem vt cum <lb></lb>eſt in L<emph.end type="italics"></emph.end> <foreign lang="el">g</foreign> <emph type="italics"></emph>diagrammatis hic deſcri<lb></lb>pti. </s> <s id="id.000666">Non igitur vna latione tantum fer<lb></lb>tur: fertur ergo pluribus. </s> <s id="id.000667">Et quidem vna, vt <lb></lb>antrorſum: qua qua ſi diffunditur, & abſce<lb></lb>dit foras, vt<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>verſus E in hoc diagrammate: altera vt retror<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.074.2.jpg" xlink:href="035/01/074/2.jpg"></figure><lb></lb><emph type="italics"></emph>ſum verſus centrum: qua retrahitur, ne euage<lb></lb>tur longius, quam æqualitas diſtantiæ vndi<lb></lb>que à centro ſeruandæ permittit, vt idem<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign><lb></lb><emph type="italics"></emph>verſus L. </s> <s id="id.000668">Vtraque autem hæc latio quanta ſit <lb></lb>menſuratur lineis rectis, quarum altera in poſte<lb></lb>riore diagrammate eſt ſinus rectus<emph.end type="italics"></emph.end> <foreign lang="el">g e,</foreign> <emph type="italics"></emph>altera <lb></lb>verò eſt ſinus verſus<emph.end type="italics"></emph.end> <foreign lang="el">b g. </foreign></s> </p> <pb xlink:href="035/01/075.jpg" pagenum="35"></pb> <p type="main"> <s id="id.000669">Demonſtremus.] <emph type="italics"></emph>Deeſt hoc vocabulum in Græco ſine quo <lb></lb>ſenſus eſt imperfectus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000670">Si igitur ferebatur.] <emph type="italics"></emph>Rurſus totum hunc textum his notis <lb></lb>[ ] intercluſum inaniter repeti arbitramur. </s> <s id="id.000671">hoc enim eſt quod an<lb></lb>tea eſt demonſtratum. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000672"><foreign lang="el">e)a\n <lb></lb>de\ duoi=n ferome/noin a)po\ th=s au)th=s i)sxu/os, to\ me\n e)kkrou/oito <lb></lb>plei=on, to\ de\ e)/latton, eu)/logon bradu/teron kinhqh=nai <lb></lb>to\ plei=on e)kkrouo/menon tou= e)/latton e)kkrouome/nou, o(\ dokei= <lb></lb>sumbai/nein e)pi\ th=s mei/zonos kai\ e)la/ttonos, tw=n e)k tou= <lb></lb>ke/ntrou grafousw=n tou\s ku/klous.</foreign></s> <s id="g0121102"><foreign lang="el">dia\ ga\r to\ e)ggu/teron <lb></lb>ei)=nai tou= me/nontos th=s e)la/ttonos to\ a)/kron, h)\ to\ th=s mei/zonos, <lb></lb>w(/sper a)ntispw/menon ei)s tou)nanti/on, e)pi\ to\ me/son bradu/teron <lb></lb>fe/retai to\ th=s e)la/ttonos a)/kron.</foreign></s> <s id="g0121201"><foreign lang="el">pa/sh| me\n ou)=n <lb></lb>ku/klon grafou/sh| tou=to sumbai/nei.</foreign></s> </p> <p type="main"> <s id="id.000673">Si vero duorum eadem <lb></lb>vi latorum vnum plus re<lb></lb>pellitur, alterum minus: <lb></lb>æquum eſt, plus repulſum, <lb></lb>altero minus repulſo tar<lb></lb>dius ferri. </s> <s id="id.000674">Quod videtur <lb></lb>contingere maiori & mi<lb></lb>nori lineis ab eodem cen<lb></lb>tro circulos <expan abbr="deſcribẽtibus">deſcribentibus</expan>. <lb></lb></s> <s id="id.000675">Quia enim extremum mi<lb></lb>noris propius eſt quieſcen<lb></lb>ti, quam ſit <expan abbr="extremũ">extremum</expan> maio<lb></lb>ris: quaſi in contrarium re<lb></lb>uulſum, in medium tardius <lb></lb>fertur ipſum minoris extre<lb></lb>mum. </s> <s id="id.000676">Omni igitur circu<lb></lb>lum deſcribenti hoc con<lb></lb>tingit. </s> </p> <p type="head"> <s id="id.000677">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000678">Si vero duorum.] <emph type="italics"></emph>Vbi confirmauit in omni radio circulum <lb></lb>deſcribente duas lationes ineſſe, nunc eas comparat in radijs inæ<lb></lb>qualibus, quod ad celeritatem & tarditatem attinet. </s> <s id="id.000679">Et quidem <lb></lb>eam, quæ ſecundum naturam eſt in radio maiore, maiorem: eam ve<lb></lb>ro, quæ præter naturam, minorem eſſe in eodem demonſtrat, vt ra<lb></lb>dium maiorem celerius ferri minore concludat. </s> <s id="id.000680">Syllogiſmus eſt <lb></lb>connexus ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000681"><emph type="italics"></emph>Si duorum eadem vi motorum vnum plus repellitur, alterum <lb></lb>minus: quod plus repellitur, tardius fertur. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/076.jpg" pagenum="36"></pb> <p type="main"> <s id="id.000682"><emph type="italics"></emph>Radiorem inæqualium eadem vi motorum minor plus <lb></lb>repellitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000683"><emph type="italics"></emph>Radius igitur minor tardius feretur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000684">Quia enim minoris.] <emph type="italics"></emph>proſyllogiſmus eſt aſſumptionis ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000685"><emph type="italics"></emph>Quod propius eſt quieſcenti & immoto plus retrahitur, quod <lb></lb>idem eſt ac plus repellitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000686"><emph type="italics"></emph>Extremum radij minoris mobile propius eſt centro, alteri <lb></lb>ſcilicet extremo quieſcenti & immoto: quam extre<lb></lb>mum maioris. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000687"><emph type="italics"></emph>Ergo extremum radij minoris mobile plus retrahetur retror<lb></lb>ſum, & ab anteriori repelletur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000688"><emph type="italics"></emph>Illuſtrari hæc <expan abbr="cõcluſio">concluſio</expan> poſſet ſimilitudine ampli & latè patentis re<lb></lb>gni, in cuius medio tanquam centro, cum rex præſideat, partes me<lb></lb>dio vicinæ regis legibus magis coarctantur & continentur: quam <lb></lb>remotæ. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000689"><foreign lang="el">kai\ fe/retai th\n me\n <lb></lb>kata\ fu/sin, th\n de\ para\ fu/sin kata\ th\n perife/reian <lb></lb>ei)s to\ pla/gion kai\ to\ ke/ntron. mei/zw d' a)ei\ th\n para\ <lb></lb>fu/sin h( e)la/ttwn fe/retai: dia\ ga\r to\ e)ggu/teron ei)=nai tou= <lb></lb>ke/ntrou tou= a)ntispw=ntos, kratei=tai ma=llon.</foreign></s> </p> <p type="main"> <s id="id.000690">Et fertur motu <expan abbr="ſecundũ">ſecundum</expan> <lb></lb>naturam per peripheriam: <lb></lb>præter <expan abbr="naturã">naturam</expan> vero in <expan abbr="trãſuerſum">tranſ<lb></lb>uerſum</expan>, & centrum verſus. <lb></lb></s> <s id="id.000691">Minor vero [linea] ſemper <lb></lb><expan abbr="maiorẽ">maiorem</expan> motum habet eum, <lb></lb>qui præter <expan abbr="naturã">naturam</expan> eſt. </s> <s id="id.000692">quia <lb></lb>enim centro vicinior eſt ad <lb></lb>ſe <expan abbr="reuellẽti">reuellenti</expan>, vincitur magis. </s> </p> <p type="head"> <s id="id.000693">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000694">Et fertur motu.] <emph type="italics"></emph>E duobus motibus in extremo radij mobili <lb></lb>alterum ſecundum naturam eſſe dicit, nempe qui eſt ſecundum <lb></lb>peripheriam, alterum præter naturam, qui eſt in tranſuerſum, & <lb></lb>verſus centrum. </s> <s id="id.000695">Sed rationem huius hic nullam profert. </s> <s id="id.000696">Hæc au<lb></lb>tem alibi ab eo dicta adferri poteſt. </s> <s id="id.000697">quia quicquid ſimplex exiſtens <lb></lb>duabus lationibus ſimul fertur, alteram naturalem, alteram præter<lb></lb>naturam habere ſeu vt ita dicam ſecundariam, & ab alio penden<lb></lb>tem neceſſe eſt: ſicuti videre eſt in motibus inferiorum orbium cæle<emph.end type="italics"></emph.end><pb xlink:href="035/01/077.jpg" pagenum="37"></pb><emph type="italics"></emph>ſtium, qui proprio ab occaſu in Orientem vergunt, & motu primi <lb></lb>mobilis ab Oriente in occaſum mouentur. </s> <s id="id.000698">Ergo cum extremum radij <lb></lb>mobile aut radius ipſe ſit quid ſimplicißimum, & ſimul duabus la<lb></lb>tionibus feratur, altera harum erit ei naturalis, altera ad vim alte<lb></lb>rius conſequetur. </s> <s id="id.000699">Et illa quidem potius naturalis erit quæ à termino à <lb></lb>quo egredi conatur, & quantum in ſe eſt, diſcedit. </s> <s id="id.000700">Talis autem eſt ea <lb></lb>qua extremum mobile veluti diſcedens à centro ſecundum periphe<lb></lb>riam fertur. </s> <s id="id.000701">Tum qua forma rei acquiritur, qualis latio per circum<lb></lb>ferentiam, cum hæc ſit circuli forma ſeu finis. </s> <s id="id.000702">Relinquitur ergo vt ea <lb></lb>ſit contra <expan abbr="naturã">naturam</expan> & per accidens, qua ad ipſum centrum reuellitur. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000703"><foreign lang="el">o(/ti de\ mei=zon <lb></lb>to\ para\ fu/sin kinei=tai h( e)la/ttwn th=s mei/zonos, tw=n e)k tou= <lb></lb>ke/ntrou grafousw=n tou\s ku/klous, e)k tw=nde dh=lon.</foreign></s> <s id="g0121302"><foreign lang="el">e)/stw <lb></lb>ku/klos e)f' *b*g*d*e, kai\ a)/llos e)n tou/tw| e)la/ttwn, <lb></lb>e)f' ou(= *x*n*m*c, peri\ to\ au)to\ ke/ntron to\ *a, kai\ e)kbeblh/sqwsan <lb></lb>ai( dia/metroi, e)n me\n tw=| mega/lw|, e)f' w(=n *g*d <lb></lb>kai\ *b*e, e)n de\ tw=| e)la/ttoni ai( *m*x *n*c: kai\ to\ e(tero/mhkes <lb></lb>parapeplhrw/sqw, to\ *d*y*r*g. </foreign></s> <s id="g0121302a"><foreign lang="el">ei) dh\ h( *a*b gra/fousa <lb></lb>ku/klon h(/cei e)pi\ to\ au)to\ o(/qen w(rmh/qh e)pi\ th\n *a*e, dh<lb></lb>lono/ti fe/retai pro\s au(th/n.</foreign></s> <s id="g0121303"><foreign lang="el">o(moi/ws de\ kai\ h( *a*x, pro\s th\n <lb></lb>*a*x h(/cei.</foreign></s> <s id="g0121304"><foreign lang="el">bradu/teron de\ fe/retai h( *a*x th=s *a*b, w(/sper <lb></lb>ei)/rhtai, dia\ to\ gi/nesqai mei/zona th\n e)/kkrousin, kai\ a)ntispa=sqai <lb></lb>ma=llon th\n *a*x.</foreign></s> <s id="g0121401"><foreign lang="el">h)/xqw de\ h( *a*q*h, kai\ a)po\ <lb></lb>tou= *q ka/qetos e)pi\ th\n *a*b h( *q*z e)n tw=| ku/klw|, kai\ pa/lin <lb></lb>a)po\ tou= *q h)/xqw para\ th\n *a*b h( *q*w, kai\ h( *w*u, <lb></lb>e)pi\ th\n *a*b ka/qeton, kai\ h( *h*k.</foreign></s> <s id="g0121402"><foreign lang="el">ai( dh\ e)f' w(=n *w*u kai\ <lb></lb>*q*z i)/sai. </foreign></s> <s id="g0121402a"><foreign lang="el">h( a)/ra *b*u e)la/ttwn th=s *x*z: ai( ga\r i)/sai <lb></lb>eu)qei=ai e)p' a)ni/sous ku/klous e)mblhqei=sai pro\s o)rqh=| th=| <lb></lb>diame/trw|, e)/latton tmh=ma a)pote/mnousi th=s diame/trou e)n <lb></lb>toi=s mei/zosi ku/klois.</foreign></s> <s id="g0121402b"><foreign lang="el">e)/sti de\ h( *w*u i)/sh th=| *q*z.</foreign></s> <s id="g0121404"><foreign lang="el">e)n o(/sw|<lb></lb> dh\ xro/nw| h( *a*q th\n *x*q e)nhne/xqh, e)n tosou/tw| xro/nw| e)n <lb></lb>tw=| ku/klw| tw=| mei/zoni, mh\ mei/zona th=s *b*w e)nh/nektai to\ a)/kron <lb></lb>th=s *b*a.</foreign></s> <s id="g0121501"><foreign lang="el">h( me\n ga\r kata\ fu/sin fora\, i)/sh: h( de\ para\ <lb></lb>fu/sin e)la/ttwn, h( *b*u, th=s *z*x.</foreign></s> </p> <p type="main"> <s id="id.000704">Quod vero minor plus <lb></lb>præter naturam moueatur: <lb></lb>quam maior earum, quę ex <lb></lb>centro <expan abbr="deſcribũt">deſcribunt</expan> circulos, <lb></lb>ex his erit manifeſtum. </s> <s id="id.000705">Sit <lb></lb>circulus <foreign lang="el">b g d e,</foreign> & alter <lb></lb>minor <foreign lang="el">x n m c,</foreign> eiuſdem <expan abbr="cẽtri">cen<lb></lb>tri</expan> <foreign lang="el">a,</foreign> Et traductæ ſint dia<lb></lb>metri in magno quidem <lb></lb><foreign lang="el">g d, & b e</foreign>: in minori <foreign lang="el">m c & <lb></lb>x n</foreign>: atque alterolongum <lb></lb>compleatur <foreign lang="el">d y r g. </foreign></s> <s>Si igi<lb></lb>tur <foreign lang="el">a b</foreign> deſcribens <expan abbr="circulũ">circulum</expan> <lb></lb>perueniet ad id vnde mo<lb></lb>ueri cœpit, manifeſtum eſt <lb></lb>quod fertur ad ipſam [<foreign lang="el">a b</foreign>] <lb></lb>ſimiliter <foreign lang="el">a x</foreign> perueniet ad <lb></lb>ipſam <foreign lang="el">a x. </foreign></s> <s>Tardius autem <lb></lb>fertur <foreign lang="el">a x</foreign>: quam <foreign lang="el">a b,</foreign> vt <lb></lb><expan abbr="dictũ">dictum</expan> eſt, propter maiorem <lb></lb><expan abbr="repulſionẽ">repulſionem</expan> & reuulſionem <lb></lb>ipſius <foreign lang="el">a x. </foreign></s> <s>Ducatur vero <lb></lb>recta <foreign lang="el">a q h, & a q</foreign> excitetur <lb></lb>perpendicularis ad <foreign lang="el">a b,</foreign> quę <lb></lb>ſit <foreign lang="el">q z</foreign> in circulo [minori]. </s> <pb xlink:href="035/01/078.jpg" pagenum="38"></pb> <s>Et rurſus per <foreign lang="el">q</foreign> ducatur pa<lb></lb>rallela ipſi <foreign lang="el">a b</foreign> quæ ſit <foreign lang="el">q w <lb></lb>& w n</foreign> perpendicularis ipſi <lb></lb><foreign lang="el">a b</foreign> tum & <foreign lang="el">h k. </foreign></s> <s>Sunt vero <lb></lb><foreign lang="el">w n & q z</foreign> æquales. </s> <s id="id.000706">Rurſus <lb></lb><foreign lang="el">b n</foreign> eſt minor: quam <foreign lang="el">x z. </foreign>In <lb></lb>circulis enim inæqualibus <lb></lb>rectę ęquales ad rectos dia<lb></lb>metro excitatæ, de diame<lb></lb>tro circulorum maiorum <lb></lb><expan abbr="ſegmentũ">ſegmentum</expan> minus auferunt. <lb></lb></s> <s id="id.000707">Eſt autem <foreign lang="el">w n</foreign> æqualis ipſi <lb></lb><foreign lang="el">q z. </foreign>In quanto vero tempo<lb></lb>re <foreign lang="el">a x</foreign> peragrauit <foreign lang="el">x q,</foreign> in <lb></lb><expan abbr="tãto">tanto</expan> in maiore circulo ex<lb></lb>tremum <foreign lang="el">a b</foreign> non maiorem <lb></lb><foreign lang="el">b w</foreign> peragrauit ( etenim <lb></lb>motus ſecundum naturam <lb></lb>æqualis eſſet ) præter na<lb></lb>turam vero minor erat, nempe <foreign lang="el">b n</foreign> quam <foreign lang="el">x z. </foreign></s> </p> <p type="head"> <s id="id.000708">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000709">Qvod vero minor.] <emph type="italics"></emph>Altera eſt confirmatio ſed<emph.end type="italics"></emph.end> <foreign lang="el">grammikh\</foreign><lb></lb><emph type="italics"></emph>linearis aſſumptionis ſyllogiſmi præcedentis. </s> <s id="id.000710">Scilicet quod mi<lb></lb>nor radius plus retrahatur ad centrum, quam maior. </s> <s id="id.000711">Vbi ab vtriſque <lb></lb>ſecundum peripheriam æquale ſpatium confectum eſt. </s> <s id="id.000712">perpendiculis <lb></lb>enim æqualibus ipſum menſurantibus partes abſciſſæ de diametris, <lb></lb>quæ retractionem vtriuſque ad centrum menſurant, inæquales ſunt, <lb></lb>& in minore circulo, maior: in maiore vero minor. </s> <s id="id.000713">vt videre lice<lb></lb>bit in diagrammate hic deſcripto & ſuis rationibus neceſſarijs con<lb></lb>firmato. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000714"><emph type="italics"></emph>Sint duo circuli concentrici maior<emph.end type="italics"></emph.end> <foreign lang="el">b d e y,</foreign> <emph type="italics"></emph>minor<emph.end type="italics"></emph.end> <foreign lang="el">x m n c</foreign> <emph type="italics"></emph>è cen<lb></lb>tro a traiecti diametris<emph.end type="italics"></emph.end> <foreign lang="el">x n & b e. </foreign></s> </p> <p type="main"> <s id="id.000715"><emph type="italics"></emph>A puncto<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ad punctum<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign> <emph type="italics"></emph>ducatur recta<emph.end type="italics"></emph.end> <foreign lang="el">a q,</foreign> <emph type="italics"></emph>& producatur in<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">h</foreign> <emph type="italics"></emph>ſitque<emph.end type="italics"></emph.end> <foreign lang="el">a q h. </foreign></s> </p> <p type="main"> <s id="id.000716"><emph type="italics"></emph>Tum à puncto<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign> <emph type="italics"></emph>excitetur perpendicularis lineæ<emph.end type="italics"></emph.end> <foreign lang="el">a x</foreign> <emph type="italics"></emph>prop. 12. <lb></lb>lib. 1. ſitque<emph.end type="italics"></emph.end> <foreign lang="el">q z. </foreign></s> </p> <pb xlink:href="035/01/079.jpg" pagenum="39"></pb> <p type="main"> <s id="id.000717"><emph type="italics"></emph>Et per punctum<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign> <emph type="italics"></emph>ducatur parallela rectæ<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>prop. 31. lib. 1. <lb></lb>quæ ſit<emph.end type="italics"></emph.end> <foreign lang="el">q w. </foreign></s> </p> <figure id="id.035.01.079.1.jpg" xlink:href="035/01/079/1.jpg"></figure> <p type="main"> <s id="id.000718"><emph type="italics"></emph>Rurſus à puncto<emph.end type="italics"></emph.end> <foreign lang="el">w</foreign> <emph type="italics"></emph>excitetur perpendicularis lineæ<emph.end type="italics"></emph.end> <foreign lang="el">a b,</foreign> <emph type="italics"></emph>ſitque<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">w n</foreign>: <emph type="italics"></emph>& ſic parallelogrammum erit<emph.end type="italics"></emph.end> <foreign lang="el">w n z q</foreign> <emph type="italics"></emph>ex def. </s> <s id="id.000719">parallelog. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000720"><emph type="italics"></emph>Sicque<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>motum ad<emph.end type="italics"></emph.end> <foreign lang="el">w</foreign> <emph type="italics"></emph>tantum confecit ſpatij ſecundum natu<lb></lb>ram, quam<emph.end type="italics"></emph.end> <foreign lang="el">x</foreign> <emph type="italics"></emph>motum ad<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign>. </s> <s><emph type="italics"></emph>Spatia enim cum metiatur perpendicu<lb></lb>laris, vtpote optima <expan abbr="mẽſura">menſura</expan>, quia minima, & ſola regularis & nota. <lb></lb></s> <s id="id.000721">Sint autem<emph.end type="italics"></emph.end> <foreign lang="el">w n, q z</foreign> <emph type="italics"></emph>perpendiculares ex fab. & æquales, quia late<lb></lb>ra oppoſita in parallelogrammo<emph.end type="italics"></emph.end> <foreign lang="el">w n z q</foreign> <emph type="italics"></emph>prop. 34. lib. 1. </s> <s>Erant vtro<lb></lb>bique ſpatia<emph.end type="italics"></emph.end> <foreign lang="el">b w & x q</foreign> <emph type="italics"></emph>æqualia. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000723"><foreign lang="el">b n</foreign> <emph type="italics"></emph>vero eadem ratione metitur ſpatium motus præter naturam <lb></lb>ipſius<emph.end type="italics"></emph.end> <foreign lang="el">b, & x z</foreign> <emph type="italics"></emph>ipſius<emph.end type="italics"></emph.end> <foreign lang="el">x. </foreign><emph type="italics"></emph>ſi igitur<emph.end type="italics"></emph.end> <foreign lang="el">x z</foreign> (<emph type="italics"></emph>quod poſtea demonſtra<lb></lb>bitur ) maior ſit quam<emph.end type="italics"></emph.end> <foreign lang="el">b n,</foreign> <emph type="italics"></emph>erit puncti<emph.end type="italics"></emph.end> <foreign lang="el">x</foreign> <emph type="italics"></emph>motus præter naturam <lb></lb>maior in eodem ſpatio motus naturalis: quam puncti<emph.end type="italics"></emph.end> <foreign lang="el">b. </foreign></s> </p> <pb xlink:href="035/01/080.jpg" pagenum="40"></pb> <p type="main"> <s id="id.000724"><emph type="italics"></emph>Sed & ſi perficiantur parallelogramma<emph.end type="italics"></emph.end> <foreign lang="el">d s t f & d y r g</foreign>: <lb></lb><emph type="italics"></emph>illud erit vtile ad oſtendendum<emph.end type="italics"></emph.end> <foreign lang="el">d</foreign> <emph type="italics"></emph>tralatum vno motu vſque ad<emph.end type="italics"></emph.end> <foreign lang="el">s,</foreign><lb></lb><emph type="italics"></emph>altero motu, quo retrahitur ad centrum, reductum eſſe ad<emph.end type="italics"></emph.end> <foreign lang="el">t</foreign>: <emph type="italics"></emph>& <lb></lb>huius retractiones <expan abbr="menſurã">menſuram</expan> eſſe<emph.end type="italics"></emph.end> <foreign lang="el">s t</foreign> <emph type="italics"></emph>vel<emph.end type="italics"></emph.end> <foreign lang="el">d f</foreign>: <emph type="italics"></emph>hoc vero vtile <expan abbr="etiã">etiam</expan> erit <lb></lb>ad terminandos motus illos duos <expan abbr="naturalẽ">naturalem</expan>, ſcilicet & præter <expan abbr="naturã">naturam</expan>. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000725">Atque alterolongum.] <emph type="italics"></emph>Hoc <expan abbr="quadrilaterũ">quadrilaterum</expan> <expan abbr="oblongũ">oblongum</expan>, & rectan<lb></lb>gulum compleri debuiſſe dici poteſt, vt rectus in eo motus appareat, <lb></lb>quem facturus radius fuiſſet, niſi retraheretur in centrum: tum vt <lb></lb>terminet motus eos, qui ſunt ſecundum naturam & præter naturam. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000726"><foreign lang="el">a q h</foreign>] <emph type="italics"></emph><expan abbr="Punctũ">Punctum</expan><emph.end type="italics"></emph.end> <foreign lang="el">q</foreign> <emph type="italics"></emph>vbi libet in peripheria accipitur ad deſignandum <lb></lb>quoduis <expan abbr="ſpatiũ">ſpatium</expan>, quod confecerit<emph.end type="italics"></emph.end> <foreign lang="el">x</foreign> <emph type="italics"></emph><expan abbr="extremũ">extremum</expan> mobile minoris radij<emph.end type="italics"></emph.end> <foreign lang="el">a x. </foreign></s> </p> <p type="main"> <s id="id.000727">Et <foreign lang="el">a q</foreign> excitetur.] <emph type="italics"></emph>A puncto<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign> <emph type="italics"></emph>extra lineam<emph.end type="italics"></emph.end> <foreign lang="el">a x</foreign> <emph type="italics"></emph>dato ex<lb></lb>citatur in ipſam perpendicularis, quæ eſt<emph.end type="italics"></emph.end> <foreign lang="el">q z</foreign> <emph type="italics"></emph>prop. 12. lib. 1. elem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000728">Et rurſus per <foreign lang="el">q</foreign>] <emph type="italics"></emph>Per punctum<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign> <emph type="italics"></emph>datum datæ rectæ<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>duci<lb></lb>tur parallela prop. 31. lib. 1. elem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000729">Et <foreign lang="el">w n</foreign> perpend.] <emph type="italics"></emph>prop. 12. lib. 1. elem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000731">Sunt vero <foreign lang="el">w n</foreign> &] <emph type="italics"></emph>Quia<emph.end type="italics"></emph.end> <foreign lang="el">q w</foreign> <emph type="italics"></emph>parallela eſt ipſi<emph.end type="italics"></emph.end> <foreign lang="el">z n</foreign> <emph type="italics"></emph>ex fabrica: <lb></lb>tùm<emph.end type="italics"></emph.end> <foreign lang="el">w n</foreign> <emph type="italics"></emph>etiam parallela eſt ipſi<emph.end type="italics"></emph.end> <foreign lang="el">q z,</foreign> <emph type="italics"></emph>quia in eas incidens<emph.end type="italics"></emph.end> <foreign lang="el">z n</foreign> <emph type="italics"></emph>facit an<lb></lb>gulos internos ad <expan abbr="eaſdẽ">eaſdem</expan> partes rectos, ex fab. proinde æquales ax. 10. <lb></lb><expan abbr="itaq;">itaque</expan> parallelæ prop. 28. lib. 1. </s> <s><expan abbr="parallelogrãmũ">parallelogramum</expan> erit<emph.end type="italics"></emph.end> <foreign lang="el">w n z q. </foreign><emph type="italics"></emph>per def. pa<lb></lb>rall. </s> <s id="id.000735">quare eius latera oppoſita<emph.end type="italics"></emph.end> <foreign lang="el">w n & q z</foreign> <emph type="italics"></emph><expan abbr="erũt">erunt</expan> æqualia prop. 34. lib. 1. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000736">In circulis.] <emph type="italics"></emph>Ex hoc loco elicitur hoc theorema. </s> <s id="id.000737">Perpendicula<lb></lb>res à peripheriis in ſemidiametros circulorum inæqualium æquales <lb></lb>ſegmenta auferunt de ſemidiametris inæqualia, & quidem maius in <lb></lb>minori comprehenſum inter peripheriam & perpendicularem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000738">Expo<lb></lb><figure id="id.035.01.080.1.jpg" xlink:href="035/01/080/1.jpg"></figure><lb></lb>ſitio. </s> </p> <p type="main"> <s id="id.000739"><emph type="italics"></emph>Sunto <lb></lb>duo cir<lb></lb>culi in<lb></lb>æqua<lb></lb>les A <lb></lb>B C ma<lb></lb>ior & <lb></lb>D E F <lb></lb>minor, perpendiculares ſint B K, E I & ablatæ A K, D I. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/081.jpg" pagenum="41"></pb> <p type="main"> <s id="id.000740">Deter. <emph type="italics"></emph>Dico D I eſſe maiorem ipſa A K quæ eſt ſegmentum in <lb></lb>maiori circulo. </s> <s id="id.000741">Ante huius fabricam hoc problema eſt <expan abbr="aſſumẽdum">aſſumendum</expan>. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000742"><emph type="italics"></emph>Deſcribere circulum minorem qui alterum datum maiorem <lb></lb>interius tangat. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000743"><emph type="italics"></emph>Sit datus circulus A B K C maior, ab A per D centrum reper<lb></lb>tum prop. 1. lib. 3. </s> <s>ducatur A k diameter. </s> <s id="id.000744">Deſcribendus autem ſit eo <lb></lb>minor, cuius accipiatur E <expan abbr="centrũ">centrum</expan> <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.081.1.jpg" xlink:href="035/01/081/1.jpg"></figure><lb></lb><emph type="italics"></emph>inter A & D, & interuallo <lb></lb>E A deſcribatur A F G. </s> <s>hic <lb></lb>tanget interius circulum A B k <lb></lb>C datum in puncto A. </s> <s id="id.000745">Nam ſi <lb></lb>& ſecet, vt in puncto H, ducta <lb></lb>H E. </s> <s>erit æqualis ipſi E A def. <lb></lb>15. lib. 1. non erit igitur E A mi<lb></lb>nima omnium quæ ab E puncto <lb></lb>extra D centrum circuli A B <lb></lb>K C cadunt in eius concauam pe<lb></lb>ripheriam, quod eſt contra prop. <lb></lb>7. lib. 3. </s> <s>non erat igitur H punctum commune vtrique circulo, & <lb></lb>ſic de alijs. </s> <s id="id.000748">Circulus igitur A F G, tangit circulum A B K C <lb></lb>in puncto A prop. 11. lib. 3. </s> <s>quod oportuit facere. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000749"><emph type="italics"></emph>Iam nunc de A G maiori ſemidiametro detrahatur portio A H <lb></lb>æqualis D H minori prop. 3. lib. 1. centro H interuallo A H deſ<lb></lb>cribatur circulus A M L poſtul. 3. qui erit æqualis dato D E F. <lb></lb>def. 1. lib. 3. </s> <s>Et tanget intus circulum A B C in puncto A ex probl. <lb></lb>præſumpto. </s> <s>per punctum B <expan abbr="ducaeur">ducatur</expan> parallela B M prop. 31. lib. 1. <lb></lb>& per eandem parallela M N quæ per 34. lib. eiuſdem cum ſit <lb></lb>æqualis ipſi B K erit & æqualis ipſi. </s> <s id="id.000754">E I ax. 1. connectantur M H, <lb></lb>E H poſt. 1. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000757">Demonſt. </s> <s><emph type="italics"></emph>Poſtquam ax. 3. A N, D I æquales ſunt quia reli<lb></lb>quæ ex æqualibus A H, D H ex fab. demptis æqualibus N H, <lb></lb>I H quæ latera ſunt ſub æqualibus angulis duorum triangulorum <lb></lb>M N H & I E H habentium duos angulos duobus angulis <lb></lb>æquales, & latus lateri æquale vt eſt in 26. prop. lib. 1. </s> <s>nempe angu<lb></lb>lus qui ad N rectus eſt prop. 29. lib. 1. & qui ad I, rectus ex hypoth. <lb></lb>ideo æquales ax. 10. </s> <s>tum angulus M H N ad centrum conſtitutus <emph.end type="italics"></emph.end><pb xlink:href="035/01/082.jpg" pagenum="42"></pb><emph type="italics"></emph>& angulus E H I ad centrum conſtitutus in æqualibus circulis ex <lb></lb>fab. ſunt æquales prop. 27. lib. 3. quia æquales ſunt peripheriæ A M, <lb></lb>D E ablatæ ſcilicet ab æqualibus ſemißibus M N & E I ex <lb></lb>fab. prop. 3. & 29. lib. 3. </s> <s>& ſic reliquum latus N H æquale eſt re<lb></lb>liquo I H. </s> <s id="id.000765">Ergo cum tota A N æqualis D I ſit maior A K <lb></lb>parte ſua ax. 9. erit & D I maior ipſa A K. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000767">Concl. </s> <s><emph type="italics"></emph>Ergo perpendiculares à peripherijs in ſemidiametros & <lb></lb>ct. </s> <s>quod fuit demonſtrandum. </s> <s id="id.000769">Hoc autem theorema videtur <expan abbr="quodãmodo">quo<lb></lb>dammodo</expan><emph.end type="italics"></emph.end> <foreign lang="el">para/docon. </foreign><emph type="italics"></emph>Erat enim veriſimilius in maiore circulo <expan abbr="ſegmentũ">ſeg<lb></lb>mentum</expan> ſemidiametri eſſe maius, & in minore minus: at non ita eſt vt <lb></lb>patuit. </s> <s id="id.000770">Cauſa autem hæc reddi poteſt, quod eadem recta, ſi fiat arcus <lb></lb>minoris circuli plus incuruetur oportet: quam ſi fiat arcus maioris, <lb></lb>atque his omnibus eo tendit Ariſtoteles, vt oſtendat maiorem circu<lb></lb>lum mobiliorem, & ideo etiam mouentiorem eſſe minori: rationem <lb></lb>autem mobilitatum eſſe, vt ſemidiametrorum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000771">In quanto vero.] <emph type="italics"></emph>Concluſio eſt qua concluditur, vbi motus <lb></lb>ſecundum naturam in vtriſque circulis æquales eſſent: ibi motum <lb></lb>præter naturam in maiori circulo minorem, & in minori maiorem <lb></lb>reperiri. </s> <s id="id.000772">Antea dixerat duas lationes illas eſſe in nulla ratione, in<lb></lb>tellige igitur quæ rectis lineis exactè exprimi poßit. </s> <s id="id.000773">Nam ſinus tam <lb></lb>rectus quam verſus, quibus rationis harum lationum termini expri<lb></lb>muntur, vt ſint rectæ lineæ: hæ tamen non ad vnguem arcus ſuos <lb></lb>metiuntur. </s> <s id="id.000774">Et ſic in nulla ſunt ratione ad vnguem expreſſa: ſunt ta<lb></lb>men vt hic quodammodo, & vt aiunt ferè. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000775"><foreign lang="el">dei= de\ a)na/logon ei)=nai, <lb></lb>w(s to\ kata\ fu/sin pro\s to\ kata\ fu/sin, to\ para\ fu/sin <lb></lb>pro\s to\ para\ fu/sin.</foreign></s> <s id="g0121503"><foreign lang="el">mei/zona a)/ra perife/reian dielh/luqe <lb></lb>th\n *h*b th=s *w*b.</foreign></s> <s id="g0121504"><foreign lang="el">a)na/gkh de\ th\n *h*b e)n tou/tw| tw=| xro/nw| <lb></lb>dielhluqe/nai: e)ntau=qa ga\r e)/stai, o(/tan a)na/logon a)mfote/rws <lb></lb>sumbai/nh| to\ para\ fu/sin, pro\s to\ kata\ fu/sin.</foreign></s> <s id="g0121506"><foreign lang="el">ei) dh\ <lb></lb>mei=zo/n e)sti to\ kata\ fu/sin e)n th=| mei/zoni ku/klw|, kai\ to\ para\ fu/sin <lb></lb>mei=zon, a)\n e)ntau=qa sumpi/ptoi monaxw=s, w(/ste to\ *b, e)nhne/xqai <lb></lb>a)\n th\n *b*h e)n tw=| e)f' ou(= *x shmei=on. </foreign></s> <s id="g0121506a"><foreign lang="el">e)ntau=qa ga\r <lb></lb>kata\ fu/sin me\n gi/netai tw=| *b shmei/w| h( *k *b. </foreign></s> <s id="g0121506b"><foreign lang="el">e)/sti ga\r <lb></lb>au)th\ a)po\ tou= *h ka/qetos, para\ fu/sin de\ e)s th\n *k*b.</foreign></s> <s id="g0121508"><foreign lang="el">e)/sti <lb></lb>de\ w(s th\n *h*k pro\s th\n *k*b, h( *q*z pro\s th\n *z*x. </foreign></s> <s id="g0121508a"><foreign lang="el">fanero\n <lb></lb>de\ e)a\n e)pizeuxqw=sin, a)po\ tw=n *b, *x e)pi\ ta\ *h, *q.</foreign></s> <s id="g0121509"><foreign lang="el">ei) de\ <lb></lb>e)la/ttwn h)\ mei/zwn th=s *h*b e)/stai, h)ne/xqh to\ *b, ou)x o(moi/ws <lb></lb>e)/stai ou)de\ a)na/logon e)n a)mfoi=n to\ kata\ fu/sin pro\s to\ <lb></lb>para\ fu/sin.</foreign></s> <s id="g0121510"><foreign lang="el">di' h(\n me\n toi/nun ai)ti/an a)po\ th=s au)th=s <lb></lb>i)sxu/os fe/retai qa=tton to\ ple/on a)pe/xon tou= ke/ntrou shmei=on [1kai\ m gra/fei h( mei/zwn]1 <lb></lb>dh=lon dia\ tw=n ei)rhme/nwn.</foreign></s> </p> <p type="main"> <s id="id.000776">At oportet analoga eſſe, <lb></lb>vt id quod <expan abbr="ſecundũ">ſecundum</expan> <expan abbr="naturã">naturam</expan>, <lb></lb>ad id quod <expan abbr="ſecũdum">ſecundum</expan> natu<lb></lb>ram: ſic quod præter natu<lb></lb>ram, ad id quod præter <expan abbr="naturã">na<lb></lb>turam</expan>. </s> <s id="id.000777">Igitur maiorem quam <lb></lb><foreign lang="el">b w</foreign> <expan abbr="peripheriã">peripheriam</expan>, vt <foreign lang="el">b h</foreign> <expan abbr="pertrãſijt">per<lb></lb>tranſijt</expan>. </s> <s id="id.000778">Neceſſe igitur in eo <lb></lb>tempore <foreign lang="el">b h</foreign> tranſijſſe. </s> <s id="id.000779">Ibi <lb></lb>enim erit, vbi proportiona<lb></lb>les <expan abbr="cõtingẽt">contingent</expan> <expan abbr="vtrinq;">vtrinque</expan> motus <pb xlink:href="035/01/083.jpg" pagenum="43"></pb><lb></lb>præter naturam ad motus <lb></lb>ſecundum naturam. </s> <s id="id.000780">Si igi<lb></lb>tur maius eſt id quod <expan abbr="ſecũdum">ſecun<lb></lb>dum</expan> <expan abbr="naturã">naturam</expan> in maiore cir<lb></lb>culo, & quod eſt pręter na<lb></lb>turam maius, vtique illuc <lb></lb>concidet vno modo, ita vt <lb></lb><foreign lang="el">b</foreign> ſit latum per lineam <foreign lang="el">b h. </foreign><lb></lb>eo in tempore quo <expan abbr="pũctum">punctum</expan> <lb></lb><foreign lang="el">x</foreign> [per <foreign lang="el">x q</foreign>]. </s> <s>Ibi enim pun<lb></lb>cto <foreign lang="el">b</foreign> ſecundum <expan abbr="quidẽ">quidem</expan> na<lb></lb>turam eſt recta <foreign lang="el">k h,</foreign> ab <foreign lang="el">h</foreign><lb></lb>enim eſt ipſa perpendicu<lb></lb>laris, præter naturam vero <lb></lb><foreign lang="el">b k.</foreign> </s> <s>Eſt ſiquidem vt <foreign lang="el">h k</foreign> ad <lb></lb><foreign lang="el">h k</foreign>: ſic <foreign lang="el">q z</foreign> ad <foreign lang="el">x z,</foreign> quod <lb></lb>erit manifeſtum, ſi à pun<lb></lb>ctis <foreign lang="el">b, x</foreign> ad <foreign lang="el">h, q</foreign> rectæ adiun<lb></lb>ctæ ſint. </s> <s id="id.000781">Si vero minor vel <lb></lb>maior: quam <foreign lang="el">h b</foreign> fuerit ea, <lb></lb>perquam <foreign lang="el">b</foreign> motum eſt, non <lb></lb>ſimiliter neque proportio<lb></lb>naliter in <expan abbr="vtriſq;">vtriſque</expan> erit, quod <lb></lb><arrow.to.target n="marg13"></arrow.to.target><lb></lb>ſecundum naturam ad id <lb></lb>quod præter naturam. </s> <s id="id.000782">Ob <lb></lb><expan abbr="hãc">hanc</expan> igitur cauſam ex dictis <lb></lb>manifeſtum, quod punctum à centro diſtantius, vt ea<lb></lb>dem vi ſit motum, celerius fertur. </s> </p> <p type="margin"> <s id="id.000783"><margin.target id="marg13"></margin.target>Verba ſi<lb></lb>gnis incluſa <lb></lb>in <expan abbr="cõtextu">contextu</expan> <lb></lb>Gręco quia <lb></lb>redundant <lb></lb>non verti<lb></lb>mus. </s> </p> <p type="head"> <s id="id.000784">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000785">At oportet.] <emph type="italics"></emph>Nunc oſtendit in maiore circulo motum ſecun<lb></lb>dum naturam maiorem eſſe motu ſecundum naturam in mino<lb></lb>re circulo eodem tempore factum. </s> <s id="id.000786">Ratio eſt, Circuli inæquales eadem <lb></lb>vi moti ſeruant analogiam in motibus ſcilicet: vt quæ ratio ſit mo<lb></lb>tus in maiore circulo ſecundum naturam ad ſuum motum præter na<emph.end type="italics"></emph.end><pb xlink:href="035/01/084.jpg" pagenum="44"></pb><emph type="italics"></emph>turam: eadem ſit motus in minore circulo ſecundum naturam ad <lb></lb>ſuum motum præter naturam: at hæc analogia tantum reperiri po<lb></lb>teſt, ſi cum<emph.end type="italics"></emph.end> <foreign lang="el">x</foreign> <emph type="italics"></emph>delatum eſt in<emph.end type="italics"></emph.end> <foreign lang="el">q,</foreign> <emph type="italics"></emph>intelligatur etiam<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>delatum in<emph.end type="italics"></emph.end> <foreign lang="el">h,</foreign><lb></lb><emph type="italics"></emph>à quo<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign> <emph type="italics"></emph>eſt perpendicularis<emph.end type="italics"></emph.end> <foreign lang="el">h k</foreign> <emph type="italics"></emph>in diametrum<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>metiens motum <lb></lb>ipſius<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>per peripheriam<emph.end type="italics"></emph.end> <foreign lang="el">b h. </foreign><emph type="italics"></emph></s> <s>Ergo quo tempore<emph.end type="italics"></emph.end> <foreign lang="el">x</foreign> <emph type="italics"></emph>delatum eſt ad<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">q,</foreign> <emph type="italics"></emph>eodem<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>delatum erit ad<emph.end type="italics"></emph.end> <foreign lang="el">h. </foreign><emph type="italics"></emph></s> <s>Cæterum eadem vis in vtriſque cir<lb></lb>culis intelligitur ex æqualitate angulorum ad centrum conſtituto<lb></lb>rum. </s> <s id="id.000787">Æqualis enim eſt angulus<emph.end type="italics"></emph.end> <foreign lang="el">b a h</foreign> <emph type="italics"></emph>angulo<emph.end type="italics"></emph.end> <foreign lang="el">x a q</foreign>. </s> </p> <p type="main"> <s id="id.000788">Ab <foreign lang="el">h</foreign> enim eſt.] <emph type="italics"></emph>Curuas lineas perpendicularis ſola vt breuiſ<lb></lb>ſima, quantum fieri poteſt exacte metitur. </s> <s id="id.000789">vt ſcribit autem Ptolo<lb></lb>mæus in lib. de Analemmate, & Simplicius in lib. de Dimenſione, <lb></lb>menſura cuiuſcunque rei debet eſſe ſtata, determinata, & non indefi<lb></lb>nita. </s> <s id="id.000790">Talis autem eſt perpendicularis ad linearum reliquarum dimen<lb></lb>ſionem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000791">Eſt ſiquidem vt <foreign lang="el">h k. </foreign>] <emph type="italics"></emph>Triangula enim<emph.end type="italics"></emph.end> <foreign lang="el">x q z & b h k</foreign> <emph type="italics"></emph>ſunt <lb></lb>æquiangula. </s> <s id="id.000792">Nam, qui anguli ad<emph.end type="italics"></emph.end> <foreign lang="el">z & k,</foreign> <emph type="italics"></emph>ſunt recti ex fab. qui vero <lb></lb>ad<emph.end type="italics"></emph.end> <foreign lang="el">x & b</foreign> <emph type="italics"></emph>ſunt externus & internus ad eaſdem partes facti à re<lb></lb>cta<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>incidente in parallelas<emph.end type="italics"></emph.end> <foreign lang="el">x q, b h</foreign> <emph type="italics"></emph>prop. 3. lib. 6. </s> <s>Nam<emph.end type="italics"></emph.end> <foreign lang="el">x q</foreign><lb></lb><emph type="italics"></emph>proportionaliter ſecat<emph.end type="italics"></emph.end> <foreign lang="el">a b & a h</foreign> <emph type="italics"></emph>latera trianguli<emph.end type="italics"></emph.end> <foreign lang="el">b a h. </foreign><emph type="italics"></emph></s> <s>Sunt enim<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">a x, a q</foreign> <emph type="italics"></emph>æquales radj,<emph.end type="italics"></emph.end> & <foreign lang="el">x b, q h</foreign> <emph type="italics"></emph>item æquales lineæ, quia re<lb></lb>liquæ ex æqualibus radijs<emph.end type="italics"></emph.end> <foreign lang="el">a b, a h</foreign>: <emph type="italics"></emph>habent autem æquales ad <lb></lb>æquales eandem rationem. </s> <s>Eſt igitur<emph.end type="italics"></emph.end> <foreign lang="el">x q</foreign> <emph type="italics"></emph>parallela baſi<emph.end type="italics"></emph.end> <foreign lang="el">b h,</foreign> <emph type="italics"></emph>& ſic <lb></lb>anguli qui ad<emph.end type="italics"></emph.end> <foreign lang="el">x</foreign> <emph type="italics"></emph>externus, & qui ad<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>internus erunt æquales <lb></lb>prop. 29. lib. 1. </s> <s>Ergo & reliqui qui ad<emph.end type="italics"></emph.end> <foreign lang="el">q & h</foreign> <emph type="italics"></emph>prop. 32. lib. 1. </s> <s>Hæc <lb></lb>igitur duo triangula circa æquales angulos habebunt latera propor<lb></lb>tionalia prop. 4. lib. 6. </s> <s>Sicque erit vt<emph.end type="italics"></emph.end> <foreign lang="el">q z</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">x z</foreign>: <emph type="italics"></emph>ſic<emph.end type="italics"></emph.end> <foreign lang="el">h k</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">k b,</foreign><lb></lb><emph type="italics"></emph>& alternatim vt<emph.end type="italics"></emph.end> <foreign lang="el">q z</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">h k</foreign><emph type="italics"></emph>: ſic<emph.end type="italics"></emph.end> <foreign lang="el">x z</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">k b</foreign> <emph type="italics"></emph>prop. 16. lib. 5. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000795">Ob hanc igitur cauſam.] <emph type="italics"></emph>Concluſio qua tandem concludi<lb></lb>tur punctum à centro diſtantius, vt eadem vi ſit motum, celerius <lb></lb>ferri, id eſt eodem tempore maius loci ſpatium conficere. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000796"><foreign lang="el">dio/ti de\ ta\ me\n mei/zw zuga\ <lb></lb>a)kribe/stera/ e)sti tw=n e)latto/nwn, fanero\n e)k tou/twn.</foreign></s> <s id="g0130102"><foreign lang="el">gi/netai <lb></lb>ga\r to\ me\n spa/rton ke/ntron.</foreign></s> <s id="g0130102a"><foreign lang="el">me/nei ga\r tou=to. </foreign></s> <s id="g0130102b"><foreign lang="el">to\ de\ e)pi\ <lb></lb>e(ka/teron me/ros th=s pla/stiggos, ai( e)k tou= ke/ntrou.</foreign></s> <s id="g0130103"><foreign lang="el">a)po\ ou)=n <lb></lb>tou= au)tou= ba/rous a)na/gkh qa=tton kinei=sqai to\ a)/kron th=s <lb></lb>pla/stiggos, o(/sw| a)\n plei=on a)pe/xh| tou= spa/rtou, kai\ e)/nia <lb></lb>me\n mh\ dh=la ei)=nai e)n toi=s mikroi=s zugoi=s pro\s th\n ai)/sqhsin <lb></lb>e)pitiqe/mena ba/rh: e)n de\ toi=s mega/lois, dh=la. </foreign></s> <s id="g0130105"><foreign lang="el">ou)qe\n ga\r <lb></lb>kwlu/ei e)/latton kinhqh=nai me/geqos, h)\ w(/ste ei)=nai th=| o)/yei <lb></lb>fanero/n.</foreign></s> </p> <p type="main"> <s id="id.000797">Quod vero propterea li<lb></lb>brę maiores minoribus ſint <lb></lb>exactiores, <expan abbr="manifeſtũ">manifeſtum</expan> ex his <lb></lb>erit. </s> <s id="id.000798">Agina enim fit <expan abbr="centrũ">centrum</expan>. <lb></lb></s> <s id="id.000799">Hæc enim quieſcit. </s> <s id="id.000800"><expan abbr="vtræq;">vtræque</expan> <pb xlink:href="035/01/085.jpg" pagenum="45"></pb><lb></lb>vero librilis partes lineæ <lb></lb>ſunt ex centro. </s> <s id="id.000801">Ab eodem <lb></lb>igitur pondere neceſſe eſt <lb></lb>eò celerius extremum li<lb></lb>brilis ferri, quò plus ab agi<lb></lb>na diſtiterit, & nonnulla in <lb></lb>paruis libris pondera im<lb></lb>poſita non manifeſta ſen<lb></lb>ſui eſſe, quæ in magnis ma<lb></lb>nifeſta erunt. </s> <s id="id.000802">Nihil enim <lb></lb>prohibet <expan abbr="minorẽ">minorem</expan> permea<lb></lb>ri magnitudinem: quam vt <lb></lb>viſui ſit manifeſta. </s> </p> <p type="head"> <s id="id.000803">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000804">Qvod vero propterea libræ.] <foreign lang="el">zugo\s</foreign> <emph type="italics"></emph>vel<emph.end type="italics"></emph.end> <foreign lang="el">zugo\n</foreign> <emph type="italics"></emph>præter iu<lb></lb>gum, remigum ſedes, & tranſtra curruum & nauium ſignifi<lb></lb>cat etiam libram & ſtateram, hinc illud Pythagoræ<emph.end type="italics"></emph.end> <foreign lang="el">mh\ zugo\n u(per<lb></lb>bai/nein</foreign> <emph type="italics"></emph>ſtateram ne tranſgrediaris & vt annotat Budæus<emph.end type="italics"></emph.end> <foreign lang="el">zugosta/<lb></lb>tai</foreign> <emph type="italics"></emph>ſunt libripendes per vrbes conſtituti, qui <expan abbr="põderibus">ponderibus</expan> præfecti ap<lb></lb>pellantur, vnde Zygoſtatica fides pro plena & examinata æquitate <lb></lb>à Zygo quod eſt libra publice temperata & conſtituta, vt quemad<lb></lb>modum ait Vitruuius, vindicet ab iniquitate iuſtis moribus vitam. <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg14"></arrow.to.target><lb></lb><emph type="italics"></emph>Statera enim doloſa, vt dixit Sapiens, abhominatio eſt apud Deum, <lb></lb>& pondus æquum voluntas eius. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000805"><margin.target id="marg14"></margin.target>Initio <lb></lb>cap. 11. <lb></lb>Prouerb. </s> </p> <p type="main"> <s id="id.000806">Agina fit cen<lb></lb><figure id="id.035.01.085.1.jpg" xlink:href="035/01/085/1.jpg"></figure><lb></lb><expan abbr="trũ">trum</expan>.] <emph type="italics"></emph><expan abbr="Tandẽ">Tandem</expan> Ari<lb></lb>ſtoteles <expan abbr="accõmodat">accommodat</expan> <lb></lb>problema <expan abbr="propoſitũ">propoſitum</expan> <lb></lb>de libra ad circuli <lb></lb><expan abbr="proprietatẽ">proprietatem</expan> vltimò <lb></lb><expan abbr="demonſtratã">demonſtratam</expan>. </s> <s id="id.000807">Quod <lb></lb>vt intelligatur prius <lb></lb>in libra A D B C <lb></lb>H I partes notan<lb></lb>dæ ſunt. </s> <s id="id.000808">Sit igitur <lb></lb>libræ librile, ſeu <emph.end type="italics"></emph.end><pb xlink:href="035/01/086.jpg" pagenum="46"></pb><emph type="italics"></emph>ſcapus ſeu iugum A B, & C D trutina, ſeu anſa, quæ pro com<lb></lb>muni more ſemper eſt perpendicularis ad horizontis planum: pun<lb></lb>ctum vero C eſt agina,<emph.end type="italics"></emph.end> <foreign lang="el">spa/rtion</foreign> <emph type="italics"></emph>vocatur ab Ariſtotele, & eſt cen<lb></lb>trum libræ circa quod brachia C A, C B moueri intelliguntur <lb></lb>pro ponderibus impoſitis in H vel I lancibus, quas<emph.end type="italics"></emph.end> <foreign lang="el">pla/stiggas</foreign> <emph type="italics"></emph>Ari<lb></lb>ſtoteles appellabit, quo etiam nomine appellat librile, ſeu ſcapum, ſeu <lb></lb>iugum A B. </s> <s id="id.000809">Eſt etiam recta E C F ſemper perpendicularis ipſi <lb></lb>A B vtcunque moueatur. </s> <s id="id.000810">proinde perpendiculum appellatur, ab <lb></lb>alijs æquamentum, ab alijs trutina. </s> <s id="id.000811">His ita declaratis, ilico ex præ<lb></lb>cedentibus conſtat, quod C centro fixo, ſi A C vel C B lineæ quæ <lb></lb>ex centro, moueantur, deſcribent circulum pro ſuo interuallo, in <lb></lb>minore librili, minorem: in maiore maiorem: ſicque cum magnitudo <lb></lb>ſpatij motu tranſiti, quò maior, eò viſibilior, & quò etiam librilis <lb></lb>pars maior, eò mobilior, citius ex æquali pondere, & magis mouebitur <lb></lb>librile maius: <expan abbr="quã">quam</expan> minus, proinde etiam erit exactius. </s> <s id="id.000812">id eſt minores <lb></lb>ponderum differentias patefaciet. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000813"><foreign lang="el">e)pi\ de\ th=s mega/lhs pla/stiggos poiei= o(rato\n to\ <lb></lb>au)to\ ba/ros me/geqos.</foreign></s> <s id="g0130107"><foreign lang="el">e)/nia de\ dh=la me\n e)p' a)mfoi=n e)sti/n, <lb></lb>a)lla\ pollw=| ma=llon e)pi\ tw=n meizo/nwn, dia\ to\ pollw=| <lb></lb>mei=zon gi/nesqai to\ me/geqos th=s r(oph=s u(po\ tou= au)tou= ba/rous <lb></lb>e)n toi=s mei/zosi.</foreign></s> <s id="g0130108"><foreign lang="el">kai\ dia\ tou=to texna/zousin oi( a(lourgopw=lai <lb></lb>pro\s to\ parakrou/esqai i(sta/ntes, to/, te spa/rton <lb></lb>ou)k e)n me/sw| tiqe/ntes, kai\ mo/lubdon th=s fa/laggos ei)s <lb></lb>qa/teron me/ros e)gxe/ontes, h)\ tou= cu/lou to\ pro\s th\n r(i/zan <lb></lb>pro\s o(\ bou/lontai r(e/pein poiou=ntes, h)\ e)a\n e)/xh| o)/zon. </foreign></s> <s id="g0130108a"><foreign lang="el">baru/<lb></lb>teron ga\r e)n w(=| me/ros h( r(i/za tou= cu/lou e)sti/n. </foreign></s> <s id="g0130108b"><foreign lang="el">o( de\ o)/zos r(i/za <lb></lb>ti/s e)stin.</foreign></s> </p> <p type="main"> <s id="id.000814">In magno <expan abbr="autẽ">autem</expan> librili <expan abbr="idẽ">idem</expan> <lb></lb><expan abbr="põdus">pondus</expan> <expan abbr="magnitudinẽ">magnitudinem</expan> reddet <lb></lb><expan abbr="aſpectabilẽ">aſpectabilem</expan>. </s> <s id="id.000815">Nonnulla vero <lb></lb>in <expan abbr="vtriſq;">vtriſque</expan> manifeſta <expan abbr="sũt">sunt</expan>: ſed <lb></lb>multo magis in maioribus. <lb></lb></s> <s id="id.000816">quia in maioribus ab <expan abbr="eodẽ">eodem</expan> <lb></lb><expan abbr="põdere">pondere</expan> multo maior fit in<lb></lb>clinationis magnitudo. </s> <s id="id.000817">Ob <lb></lb>id purpuræ venditores, vt <lb></lb><expan abbr="pendẽdo">pendendo</expan> <expan abbr="defraudẽt">defraudent</expan>, aſtutè <lb></lb>faciunt, qui aginam non in <lb></lb>medio collocant, & plum<lb></lb>bum in altera librilis parte <lb></lb>illinunt, vel è ligno quod <lb></lb>ad <expan abbr="radicẽ">radicem</expan> vergebat, <expan abbr="faciũt">faciunt</expan>, <lb></lb>quo inclinare <expan abbr="deſiderãt">deſiderant</expan>, vel <lb></lb>ſi no <expan abbr="dũ">dum</expan> habuerit. </s> <s id="id.000818">Ligni <expan abbr="enĩ">enim</expan> <lb></lb>grauior eſt illa pars, vbi ra<lb></lb>dix, Eſt vero nodus quæ<lb></lb>dam radix. </s> </p> <pb xlink:href="035/01/087.jpg" pagenum="47"></pb> <p type="head"> <s id="id.000819">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000820">In magno autem.] <emph type="italics"></emph>Ex his colligitur fieri poſſe libram, quæ <lb></lb>examinabit granum vnum, immo grani ſecundam, tertiam, <lb></lb>quartam partem. </s> <s id="id.000821">Quod eſt aliquando neceſſarium cum in pretioſis <lb></lb>rebus, vt ambra griſea, moſcho, auro: tum in medicamentis potentiſ<lb></lb>ſimis, vt elleboro, ſcammonio, opio. </s> <s id="id.000822">Huius autem libræ fabrica pen<lb></lb>det è quatuor. </s> <s id="id.000823">Primum eſt longitudo librilis. </s> <s id="id.000824">Secundum eſt illius & <lb></lb>lancium materiæ ſumma leuitas. </s> <s id="id.000825">Nam tanto maior redditur ratio <lb></lb>ponderis exigui. </s> <s id="id.000826">Tertium eſt librilis firmitas, & rectitudo, ideo de<lb></lb>bet fieri ex chalybe purgato, durato, tenuißimo, naturaque leui. <lb></lb></s> <s id="id.000827">Quartum eſt trutinæ poſitio in exquiſitè medio librilis mobilis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000828">Ob id purpuræ.] <emph type="italics"></emph>Alia eſt ratio qua rurſus confirmatur libri<lb></lb>le maius eſſe exactius. </s> <s id="id.000829">Ducitur ex effectu eorum qui fraudare <expan abbr="volũt">volunt</expan>, <lb></lb>emptores. </s> <s id="id.000830">Imponunt enim pondus rei venditæ leuius æquipondio<emph.end type="italics"></emph.end> <lb></lb>(<foreign lang="el">sfai/rwma</foreign> <emph type="italics"></emph>poſtea vocabitur ) in librilis brachio longiore: ſicque, <lb></lb>vel æquiponderat vel etiam præponderat: & ita paucum pro multo <lb></lb>vendunt. </s> <s id="id.000831">Nec tamen vacua libra ponderibus, iniqua videtur. </s> <s id="id.000832">quia <lb></lb>pars librilis altera, vt æquiponderet: plumbum habebit illitum, vel <lb></lb>etiam ex ligno erit duriore & nodoſiore, ſicque denſiore, & ideo <lb></lb>grauiore. </s> <s id="id.000833">Vel pars librilis longior erit tenuior, vel perforata in ali<lb></lb>quot locis exiguis foraminibus. </s> <s id="id.000834">Vnde vnius grauitas <expan abbr="lõgitudinis">longitudinis</expan> al<lb></lb>terius rationem compenſat. </s> <s id="id.000835">Cardanus docuit libræ metallicæ fabri<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg15"></arrow.to.target><lb></lb><emph type="italics"></emph>cam, quæ pro deunce exhibeat aſſem, licet vacua inſta videatur. </s> <s id="id.000836">Hæc <lb></lb>autem à me hîc ita recitantur, non vt quis abutatur. </s> <s id="id.000837">Abhominatio <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg16"></arrow.to.target><lb></lb><emph type="italics"></emph>enim eſt apud Deum, vt iterum ait ſapiens, pondus & pondus, & <lb></lb>ſtatera doloſa non eſt bona: ſed vt à callidis iſtis mercatoribus ſibi <lb></lb>præcaueat emptor. </s> <s id="id.000838">Fraudem autem iſtam deteget, ſi pondus & æqui<lb></lb>pondium tranſmutentur de lance in lancem. </s> <s id="id.000839">Quod enim ante æqui<lb></lb>ponderabat, tranſlatum in alteram lancem non amplius æquiponde<lb></lb>rabit duplici de cauſa, & quod æquipondium grauius ſit, & quod <lb></lb>librilis in parte maiore ſit. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000840"><margin.target id="marg15"></margin.target>Lib. 1. de <lb></lb>ſubt,</s> </p> <p type="margin"> <s id="id.000841"><margin.target id="marg16"></margin.target>Prouerb. c. <lb></lb>10. </s> </p> <p type="main"> <s id="id.000842">Purpuræ venditores.] <foreign lang="el">a(lourgopw/lai</foreign> <emph type="italics"></emph>dicuntur quia<emph.end type="italics"></emph.end> <foreign lang="el">a(/lour<lb></lb>gon</foreign> <emph type="italics"></emph>purpura eſt<emph.end type="italics"></emph.end> <foreign lang="el">a)po\ tou= a(/ls kai\ e)/rgon</foreign> <emph type="italics"></emph>à maris opere. </s> <s id="id.000843">quia purpura è <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg17"></arrow.to.target><lb></lb><emph type="italics"></emph>concha marina colligitur. </s> <s id="id.000844">Eſt <expan abbr="autẽ">autem</expan>, vt author eſt Plinius, ille magni <emph.end type="italics"></emph.end><pb xlink:href="035/01/088.jpg" pagenum="48"></pb><emph type="italics"></emph>pretij flos tingendis regum veſtibus expetitus. </s> <s id="id.000845">Hunc in medijs fau<lb></lb>cibus conchæ gerunt, candida quadam vena concluſum colore ni<lb></lb>gricantis roſæ pellucidum. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000846"><margin.target id="marg17"></margin.target>Lib. 9. cap. <lb></lb>36. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.000847">3. <foreign lang="el">*dia\ ti\ e)a\n me\n a)/nwqen h)=| to\ <lb></lb>spa/rtion, o(/tan a)qerh| to\ ba/<lb></lb>ros, pa/lin a)naqe/retai to\ zu<lb></lb>go/n: de\ ka/twqen, me/nei. </foreign></s> </p> <p type="main"> <s id="id.000848">3. Propter quid, ſi in ſupe<lb></lb>riore librilis parte fuerit <lb></lb>agina, <expan abbr="quãdo">quando</expan> <expan abbr="põdus">pondus</expan>, ali<lb></lb>quod depreſſerit, rurſus <lb></lb>librile referatur: At ſi in <lb></lb>inferiore, non refertur. </s> </p> <p type="main"> <s id="g0130202"><foreign lang="el">*dia\ ti/, e)a\n me\n a)/nwqen h)=| to\ sparti/on, o(/tan ka/twqen <lb></lb>r(e/yantos a)fe/lh| to\ ba/ros pa/lin a)nafe/retai to\ zugo/n: <lb></lb>e)a\n de\ ka/twqen u(posth=|, ou)k a)nafe/retai, a)lla\ me/nei, h)\ <lb></lb>dio/ti a)/nwqen me\n tou= sparti/ou o)/ntos, plei=on tou= zugou= gi/netai <lb></lb>to\ e)pe/keina th=s kaqe/tou, to\ ga\r sparti/on e)sti\ ka/qetos, <lb></lb>w(/ste a)na/gkh e)sti\ ka/tw r(e/pein to\ ple/on, e(/ws a)\n e)/lqh| h( <lb></lb>di/xa diairou=sa to\ zugo\n e)pi\ th\n ka/qeton au)th/n, e)pikeime/nou <lb></lb>tou= ba/rous e)n tw=| a)nespasme/nw| mori/w| tou= zugou=.</foreign></s> <s id="g0130203"><foreign lang="el"><lb></lb>e)/stw zugo\n o)rqo\n, e)f' ou(= *b*g, sparti/on de\ to\ *a*d. </foreign></s> <s id="g0130203a"><foreign lang="el">e)kballo/menou <lb></lb>dh\ tou=tou, ka/tw ka/qetos e)/stai, e)f' h(=s h( *a*d*m.</foreign></s> <s id="g0130204"><foreign lang="el"><lb></lb>e)a\n ou)=n e)pi\ to\ *b h( r(oph\ e)piteqei/setai, to\ me\n *b ou(= to\ *e, <lb></lb>to\ de\ *g ou(= to\ *z e)/stai, w(/ste h( di/xa diairou=sa to\ zugo\n.</foreign></s> <s id="g0130204a"><foreign lang="el"> prw=ton <lb></lb>me\n h)=n h( *a*d*m th=s kaqe/tou au)th=s.</foreign></s> <s id="g0130204b"><foreign lang="el"> e)pikeime/nhs de\ th=s r(oph=s <lb></lb>e)/stai h( *d*q, w(/ste tou= zugou= e)f' w(=| *e*z, to\ e)/cw th=s kaqe/tou <lb></lb>th=s e)f' h(=s *a*m, tou= e)n w(=| *f*p, mei/zw tou= h(mi/seos.</foreign></s> <s id="g0130205"><foreign lang="el"><lb></lb>e)a\n ou)=n a)faireqh=| to\ ba/ros a)po\ tou= *e, a)na/gkh ka/tw fe/resqai <lb></lb>to\ *z.</foreign></s> <s id="g0130205a"><foreign lang="el">e)/latton ga/r e)sti to\ *e.</foreign></s> <s id="g0130206"><foreign lang="el">e)a\n me\n ou)=n a)/nw to\ <lb></lb>sparti/on e)/xh|, pa/lin dia\ tou=to a)nafe/retai to\ zugo/n.</foreign></s> <s id="g0130207"><foreign lang="el">e)a\n <lb></lb>de\ ka/twqen h)=| to\ u(pokei/menon, tou)nanti/on poiei=: plei=on ga\r <lb></lb>gi/netai tou= h(mi/seos tou= zugou= to\ ka/tw me/ros, h)\ w(s h( ka/qetos <lb></lb>diairei=, w(/ste ou)k a)nafe/retai: koufo/teron ga\r to\ e)phrthme/non.</foreign></s> <s id="g0130208"><foreign lang="el"><lb></lb>e)/stw zugo\n to\ e)f' ou(= *n*c to\ o)rqo/n, ka/qetos de\ h( <lb></lb>*k*l*m, di/xa dh\ diairei=tai to\ *n*c.</foreign></s> <s id="g0130209"><foreign lang="el">e)piteqe/ntos de\ ba/rous <lb></lb>e)pi\ to\ *n, e)/stai to\ me\n *n ou(= to\ *o, to\ de\ *c, ou(= to\ *r.</foreign></s> <s id="g0130209a"><foreign lang="el"> h( de\ <lb></lb>*k*l ou(= to\ *l*q, w(/ste mei=zo/n e)sti to\ *l*o tou= *l*r, tw=| *q*k*l.</foreign></s> <s id="g0130210"><foreign lang="el"><lb></lb>kai\ a)faireqe/ntos ou)=n tou= ba/rous, a)na/gkh me/nein: e)pi/keitai <lb></lb>ga\r w(/sper ba/ros h( u(peroxh\ h( tou= h(mi/seos tou= e)n w(=| to\ *l*o.</foreign></s> </p> <p type="main"> <s id="id.000850">Propter quid ſi in ſupe<lb></lb>riore librilis parte fuerit <lb></lb>agina, cum præ <expan abbr="põdere">pondere</expan> <expan abbr="demiſsũ">de<lb></lb>miſsum</expan> eſt, hoc ſublato rur<lb></lb>ſus redit: Sed ſi in inferiore <lb></lb>fuerit, <expan abbr="nõ">non</expan> redit, ſed manet? <lb></lb></s> <s id="id.000851">an quia ſuperne exiſtente <lb></lb>agina, librilis plus erit ex<lb></lb>tra perpendicularem. </s> <s id="id.000852">Eſt <lb></lb>enim trutina perpendicu<lb></lb>laris. </s> <s id="id.000853"><expan abbr="Itaq;">Itaque</expan> neceſſe eſt, quod <lb></lb>plus eſt deorſum vergere, <lb></lb>incumbente <expan abbr="põdere">pondere</expan> in par<lb></lb>te librilis ſurſum rapta, do<lb></lb>nec venerit eò, vbi ad per<lb></lb>pendicularem ipſam librile <lb></lb>bifariam diuiditur. </s> <s id="id.000854">Eſto li<lb></lb>brile rectum <foreign lang="el">b y,</foreign> trutina <foreign lang="el">a <lb></lb>d</foreign>: at hoc deorſum demiſſo <lb></lb>ſit perpendicularis <foreign lang="el">a d m. </foreign><lb></lb></s> <s>Si igitur pondus impona<lb></lb>tur in lance <foreign lang="el">b,</foreign> erit <foreign lang="el">b</foreign> vbi <foreign lang="el">e, <lb></lb>& g</foreign> vbi <foreign lang="el">z. </foreign></s> <s>Itaque recta bi<lb></lb>fariam diuidens librile, pri<lb></lb>mùm quidem erat <foreign lang="el">a d m,</foreign><lb></lb>ipſa <expan abbr="perpẽdicularis">perpendicularis</expan> <expan abbr="exiſtẽs">exiſtens</expan>: <pb xlink:href="035/01/089.jpg" pagenum="49"></pb>At cum pondus impoſitum <lb></lb>eſt, eſt <foreign lang="el">f p. </foreign></s> <s>Itaque librilis <lb></lb><foreign lang="el">e c</foreign> id quod eſt extra per<lb></lb>pendicularem <foreign lang="el">a m</foreign> in ea <lb></lb>quæ eſt <foreign lang="el">f p</foreign> plus eſt: quam <lb></lb>dimidium. </s> <s id="id.000855">Si igitur pon<lb></lb>dus, quod erat in <foreign lang="el">e</foreign> tolla<lb></lb>tur, neceſſe eſt <foreign lang="el">z</foreign> deorſum <lb></lb>ferri. </s> <s id="id.000856">Eſt enim <foreign lang="el">e</foreign> minus: ſi <lb></lb>igitur in ſuperiori parte <lb></lb>fuerit agina, rurſus ob id li<lb></lb>brile refertur: ſi vero in in<lb></lb>feriori parte ſubijciatur a<lb></lb>gina, contra euenit. </s> <s id="id.000857">Pars <lb></lb>enim maior dimidia libri<lb></lb>lis eſt id, quod infra eſt, & <lb></lb>quod à perpendiculari ſe<lb></lb>catur. </s> <s id="id.000858">Ideo non refertur. <lb></lb></s> <s id="id.000859">Leuior enim eſt pars ſur<lb></lb>ſum lata. </s> <s id="id.000860">Eſto librile <foreign lang="el">n c</foreign> re<lb></lb>ctum, perpendicularis vero <lb></lb><foreign lang="el">k l m,</foreign> quæ bifariam diui<lb></lb>dat <foreign lang="el">n c,</foreign> & impoſito pon<lb></lb>dere in <foreign lang="el">n,</foreign> ſit <foreign lang="el">n</foreign> vbi eſt <foreign lang="el">o, & <lb></lb>x</foreign> vbi eſt <foreign lang="el">r, & k l</foreign> vbi <foreign lang="el">l q</foreign>. <lb></lb></s> <s>Itaque maior erit <foreign lang="el">l o</foreign> quam <lb></lb><foreign lang="el">l r</foreign> ipſo <foreign lang="el">x l q. </foreign></s> <s>Igitur ſu<lb></lb>blato pondere neceſſe eſt <lb></lb>manere. </s> <s id="id.000861">Incumbit enim <lb></lb>ceu pondus exceſſus medietatis, qui eſt in <foreign lang="el">l o. </foreign></s> </p> <p type="head"> <s id="id.000862">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000863">Propter quid.] <emph type="italics"></emph>In hoc capite proponitur aliud diſcutiendum <lb></lb>problema de libra. </s> <s id="id.000864">De qua quæruntur duo. </s> <s id="id.000865">Primum cur ſi cen<lb></lb>trum libræ ſit in ſuperiori parte librilis ſitum, cum pondere impoſito <lb></lb>deorſum venerit librilis vna pars, altera ſurſum, eodem ſublato, & <lb></lb>librili libero relicto brachia librilis redeant ad priſtinum locum. <emph.end type="italics"></emph.end></s> <pb xlink:href="035/01/090.jpg" pagenum="50"></pb> <emph type="italics"></emph> <s>Secundum, cur ſi centrum eius ſit in inferiori parte librilis ſitum, <lb></lb>& pondere impoſito, parteque librilis vna deorſum demiſſa, eodem <lb></lb>ſublato librile liberum relictum non redeat: ſed in eo ſitu maneat. <lb></lb></s> <s id="id.000866">Tertium adiungitur à Guido Vbaldo ( è quo quæ hîc dicemus omnia <lb></lb>ferè deprompſimus ) non minus quæſitu dignum. </s> <s id="id.000867">Cur ſi centrum ſit <lb></lb>exquiſite librilis medium, librile retinebit ſitum quemlibet datum. <lb></lb></s> <s id="id.000868">Quæ vt intelligantur ſcire conuenit vel libram hic capi, cuius librile <lb></lb>latitudinem aliquam effatu dignam habet, vel cum quo trutina ita <lb></lb>connexa eſt, vt ad vnius motum moueatur alterum, & contra: quia <lb></lb>totum continuum eſt. </s> <s id="id.000869">In extremo autem trutinæ, non eo quidem, <lb></lb>quod eſt ei cum librili <expan abbr="cõ">con</expan><emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.090.1.jpg" xlink:href="035/01/090/1.jpg"></figure><lb></lb><emph type="italics"></emph>mune: ſed altero, <expan abbr="cẽtrum">centrum</expan> <lb></lb>circa quod <expan abbr="tanquã">tanquam</expan> <expan abbr="fixũ">fixum</expan>, <lb></lb>ipſa moueantur, <expan abbr="ſitũ">ſitum</expan> ſit. <lb></lb></s> <s id="id.000870">Sine horum enim altero <lb></lb>modo intelligi <expan abbr="nõ">non</expan> poteſt, <lb></lb>quomodo librile, quod <lb></lb>ſecundum longitudinem <lb></lb>eſt, vt vna recta li<lb></lb>nea, admittat dif<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.090.2.jpg" xlink:href="035/01/090/2.jpg"></figure><lb></lb><emph type="italics"></emph>ferentias illas loci <lb></lb><expan abbr="ſursũ">ſursum</expan> deorſum. </s> <s id="id.000871">At <lb></lb>ſiue hoc: ſiue illo <lb></lb>modo librile con<lb></lb>ſtituatur problema <lb></lb>hîc ab Ariſtotele <lb></lb><expan abbr="poſitũ">poſitum</expan> habebit non <lb></lb>ſolum <expan abbr="experientiã">experientiam</expan>, <lb></lb>ſed & rationem <lb></lb>ſibi ſuffragantem, <lb></lb>Exemplum igitur <lb></lb>librilis primi mo<lb></lb>di <expan abbr="cũ">cum</expan> latitudine ſit <lb></lb>A B, cuius <expan abbr="centrũ">centrum</expan> <lb></lb>in ſuperiori parte <lb></lb>latitudinis ſit C,<emph.end type="italics"></emph.end><pb xlink:href="035/01/091.jpg" pagenum="51"></pb><emph type="italics"></emph>cum ſuo ſuſpenſorio ſeu trutina C D: vel ſit & in inferiori parte C <lb></lb>centrum cum ſuo fulcro quod pro trutina eſt etiam C D, & <lb></lb>in vtroque in<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.091.1.jpg" xlink:href="035/01/091/1.jpg"></figure><lb></lb><emph type="italics"></emph>telligatur linea <lb></lb>recta per cen<lb></lb>trum tranſire <lb></lb>perpendiculari<lb></lb>ter ad planum <lb></lb><expan abbr="horizõtis">horizontis</expan> D E. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000872"><emph type="italics"></emph>Exemplum li<lb></lb>brilis <expan abbr="cũ">cum</expan> truti<lb></lb>na immobiliter <lb></lb>connexi ſit vbi <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.091.2.jpg" xlink:href="035/01/091/2.jpg"></figure><lb></lb><emph type="italics"></emph>eſt librile GH, <lb></lb>& trutina K <lb></lb>L, & centrum <lb></lb>libræ L. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000873">An quia ſu<lb></lb>perne.] <emph type="italics"></emph>In<lb></lb>tellectis libræ <lb></lb>generibus ad propoſitum problema accommodatis, nunc eius partis <lb></lb>prioris adfertur ſolutio. </s> <s id="id.000874">quia in vtroque genere librilis cum centrum <lb></lb>libræ ſupernam partem occupat, & à perpendiculari intellecta per <lb></lb>admotum pondus librile à paralleliſmo cum horizonte diſceſſerit, <lb></lb>pars quæ ſuperior fit, maior eſt parte inferiore. </s> <s id="id.000875">Maior autem grauior <lb></lb>eſt. </s> <s id="id.000876">Totum enim librile ſupponitur eſſe materiæ vnigeneris. </s> <s id="id.000877">Redit <lb></lb>igitur libera relicta, ſitumque recuperat, vbi paria momenta <expan abbr="æquiponderãt">æqui<lb></lb>ponderant</expan>. </s> <s id="id.000878">Talis <expan abbr="autẽ">autem</expan> eſt is ſitus in quo llbrile <expan abbr="parallelũ">parallelum</expan> fit horizonti. <lb></lb></s> <s id="id.000879">Contra ſi centrum infernam partem occupet, pars inferior librilis <lb></lb>maior eſt. </s> <s id="id.000880">præponderat igitur. </s> <s id="id.000881">Non itaque per ſe redibit: ſed ſitum <lb></lb>detracta decliuem retinebit: alias id graue, quo excedit, ſurſum ſua <lb></lb>ſponte aſcenderet, contra def. grauis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000883">Itaque librilis <foreign lang="el">e z. </foreign>] <emph type="italics"></emph>Quod pars ſuperior librilis in vno ſitu <lb></lb>centri ſit maior, in altero ſit minor, non eſt probatum ab Ariſtotele: <lb></lb>ſed ex fabrica librilis vtriuſque generis res ilico fit euidens, etiam <lb></lb>pro Ariſtotelis characteribus noſtris ad diagrammata adiunctis. <emph.end type="italics"></emph.end></s> <pb xlink:href="035/01/092.jpg" pagenum="52"></pb> <s><emph type="italics"></emph>Nam in librili primi modi cum obliquatur C F perpendiculum li<lb></lb>brilis, quod ipſum perpetuò bifariam ſecat, digreditur à perpendicu<lb></lb>lari intellecta, quam ſecat<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.092.1.jpg" xlink:href="035/01/092/1.jpg"></figure><lb></lb><emph type="italics"></emph>in centro, ſicque triangu<lb></lb>lum conſtituit comprehen<lb></lb>dens aliquam partem al<lb></lb>terutrius brachij nempe F <lb></lb>C E, vel R C F, quæ ſic <lb></lb>detracta vni, & alteri ad<lb></lb>dita, reddit hoc à quo de<lb></lb>trahitur minus, & eius <lb></lb>detractæ partis duplo alte<lb></lb>rum <expan abbr="brachiũ">brachium</expan> maius. </s> <s id="id.000884">At<lb></lb>que hic modus conuenit <lb></lb>ſenſui Ariſtotelis, vt qui <lb></lb>eo vſurus ſit capite ſequen<lb></lb>ti in problemate de vecte. <lb></lb></s> <s id="id.000885">Et etiam pulchrè reſpon<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.092.2.jpg" xlink:href="035/01/092/2.jpg"></figure><lb></lb><emph type="italics"></emph>det cauſæ iam dictæ ex <lb></lb>proprietate circuli, quate<lb></lb>nus eius radij breuiores <lb></lb>ſunt aut longiores, & pro<lb></lb>pter iſtam inæqualitatem <lb></lb>tardiores aut velociores. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000886"><emph type="italics"></emph>In librili vero ſecundi <lb></lb>modi res erit adhuc aper<lb></lb>tior. </s> <s id="id.000887">Centro ſiquidem L, <lb></lb>& interuallo L K circu<lb></lb>lus deſcribatur, & K <lb></lb><expan abbr="motũ">motum</expan> ſit in P propter vim <lb></lb>allatam: tum L K per<lb></lb>pendicularis intellecta pro<lb></lb>ducta ſecabit brachium <lb></lb>P H, id eſt K H, vt in <lb></lb>M: ſicque P M accreſcet pro longitudine ideo & grauitate ad <lb></lb>P G, redibit igitur G P M. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/093.jpg" pagenum="53"></pb> <figure id="id.035.01.093.1.jpg" xlink:href="035/01/093/1.jpg"></figure> <p type="main"> <s id="id.000888"><emph type="italics"></emph>Contra in alte<lb></lb>ro diagrammate <lb></lb>eiuſmodi ſectio <lb></lb>fiet, vt in O, & <lb></lb>ſic pars O P ac<lb></lb>creſcet ad P H: <lb></lb>ſicque tota O P <lb></lb>H vt longior, ita <lb></lb>grauior O G. <lb></lb></s> <s id="id.000889">Manebit igitur <lb></lb>( præſuppoſito hoc <lb></lb>quod ab H <expan abbr="appẽſa">appenſa</expan> <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.093.2.jpg" xlink:href="035/01/093/2.jpg"></figure><lb></lb><emph type="italics"></emph>lanx inſideat ter<lb></lb>ræ vel alicui ful<lb></lb>cro. </s> <s id="id.000890">Sed & in li<lb></lb>brilibus huius ge<lb></lb>neris reditus & <lb></lb>non reditus alia <lb></lb><expan abbr="etiã">etiam</expan> cauſa eſt, ſci<lb></lb>licet quia <expan abbr="nullũ">nullum</expan> <expan abbr="cẽtrũ">cen<lb></lb>trum</expan> grauitatis ma<lb></lb>net niſi ſuſtinea<lb></lb>tur à linea <expan abbr="perpẽdiculari">per<lb></lb>pendiculari</expan> ad pla<lb></lb>num horizontis. </s> <s id="id.000891">quod eſt demonſtratum ab Vbaldo prop. 1. lib. de lib. <lb></lb></s> <s id="id.000892">Atque P eſt centrum grauitatis magnitudinis compoſitæ è duobus <lb></lb>brachijs librilis G H, & lancibus ponderibuſque vtrimque æqui<lb></lb>ponderantibus, ſi intelligantur admota, vt patet ex prop. 4. lib. 1. <lb></lb>Archimed. de æquipond. </s> <s id="id.000893">L K vero linea eſt perpendicularis ad pla<lb></lb>num horizontis. </s> <s id="id.000894">Non igitur P liberum relictum manebit ita vt eſt <lb></lb>G P M H: Sed & redibit ex natura grauium quouſque occupet<lb></lb>punctum k in perpendiculari horizontis, à qua quia per extre<lb></lb>mum L fixa eſt, ſuſtinebitur. </s> <s id="id.000895">At G O P H manebit ſic, nec <lb></lb>redibit ad G k H, quia, quod eſſet contra naturam, aſcenderet. <lb></lb></s> <s id="id.000896">Vbiautem centrum librilis eſt exquiſitè medium, vt C ipſius A B <lb></lb>cum trutina C D mobili, ſeu ſupra, ſeu infra poſita ſit, quocunque <emph.end type="italics"></emph.end><pb xlink:href="035/01/094.jpg" pagenum="54"></pb><figure id="id.035.01.094.1.jpg" xlink:href="035/01/094/1.jpg"></figure><lb></lb><emph type="italics"></emph>in ſitu fuerit A B vt <lb></lb>in G H manebit, tum <lb></lb>quia brachia manent <lb></lb>æqualia, tum quia cen<lb></lb>trum grauitatis C ſem<lb></lb>per erit in perpendicu<lb></lb>lari horizontis, ſecun<lb></lb>dum quam & ad quam <lb></lb>magnitudo compoſita <lb></lb>ex brachijs C A, C B & lancibus & ponderibus æquiponderan<lb></lb>tibus, ſi impoſita ſint, fertur, ſed ſuſtinetur linea C D vel C E <lb></lb>fixa. </s> <s id="id.000897">Et ſic patet ſolutio tertiæ partis huius problematis ab Ariſtotele <lb></lb>prætermiſſæ. </s> <s id="id.000898">Rarò tamen huic demonſtrationi licet veræ, experien<lb></lb>tia reſpondet, propter inſtrumentorum materiam Phyſicam, in qua <lb></lb>exacte medium conſtituere non datur in puncto geometrico, vtcum<lb></lb>que tamen alias reſpondet. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.000899">4. <foreign lang="el">*tou= moxlou= duna/mews ai)/tion. </foreign></s> </p> <p type="main"> <s id="id.000900">4. Potentiæ vectis cauſa. </s> </p> <p type="main"> <s id="id.000901"><foreign lang="el">*dia\ ti/ kinou=si mega/la ba/rh mikrai\ duna/meis tw=| moxlw=|: <lb></lb>w(/sper e)le/xqh kai\ kat' a)rxh/n: proslabo/nti ba/ros <lb></lb>e)/ti to\ tou= moxlou=; r(a=|dion de\ to\ e)/latto/n e)sti kinh=sai ba/ros.</foreign></s> <s id="g0130301"><foreign lang="el"><lb></lb>e)/latton de/ e)stin a)/neu tou= moxlou=.</foreign></s> <s id="g0130302"><foreign lang="el">h)\ o(/ti ai)/tio/n e)stin o( moxlo/s <lb></lb>zugo\n ka/twqen, e)/xon to\ sparti/on, kai\ ei)s a)/nisa dih|rhme/non, <lb></lb>to\ ga\r u(pomo/xlio/n e)sti to\ sparti/on.</foreign></s> <s id="g0130302a"><foreign lang="el">me/nei <lb></lb>ga\r a)/mfw tau=ta, w(/sper to\ ke/ntron, e)pei\ de\ qa=tton u(po\ <lb></lb>tou= i)/sou ba/rous kinei=tai h( mei/zwn tw=n e)k tou= ke/ntrou.</foreign></s> <s id="g0130302b"><foreign lang="el">e)/sti de\ <lb></lb>tri/a ta\ peri\ to\n moxlo/n.</foreign></s> <s id="g0130302c"><foreign lang="el">to\ me\n u(pomo/xlion, spa/rton, <lb></lb>kai\ ke/ntron.</foreign></s> <s id="g0130302d"><foreign lang="el">du/o de\ ba/rh, o(/, te kinw=n, kai\ to\ kinou/menon.</foreign><arrow.to.target n="marg18"></arrow.to.target></s> </p> <p type="margin"> <s id="id.000902"><margin.target id="marg18"></margin.target>Videtur hic <lb></lb>aliquid de<lb></lb>eſſe & fortè. <lb></lb><emph type="italics"></emph>Radius au<lb></lb>tem minor <lb></lb>tardius. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000903">Cur vires exiguæ vecte <lb></lb>magna <expan abbr="mouẽt">mouent</expan> onera, vt eſt <lb></lb>in principio <expan abbr="dictũ">dictum</expan> inſuper <lb></lb><expan abbr="adiiciẽdo">adiiciendo</expan> vectis ipſius onus. <lb></lb></s> <s id="id.000904">Facilius enim eſt minus mo<lb></lb>uere onus: minus vero eſt <lb></lb>abſque vecte. </s> <s id="id.000905">An quia ve<lb></lb>ctis cauſa eſt, qui & inſtar <lb></lb>libræ deorſum habet <expan abbr="aginã">agi<lb></lb>nam</expan>, & in inæqualia diuiſus <lb></lb>eſt? </s> <s id="id.000906">Eſt enim preſſio pro <lb></lb>agina. </s> <s id="id.000907">ambæ enim ſtant vt <lb></lb>centrum. </s> <s id="id.000908">Quoniam vero <lb></lb>celerius ab æquali ponde<lb></lb>re mouetur radius maior. </s> </p> </subchap1> <pb xlink:href="035/01/095.jpg" pagenum="55"></pb> <subchap1> <p type="main"> <s>Sunt vero tria circa <expan abbr="vectẽ">vectem</expan> <lb></lb>preſſio quidem eſt agina & <lb></lb><expan abbr="centrũ">centrum</expan>, duo etiam pondera <lb></lb>mouens ſcilicet, & mobile. </s> </p> <p type="head"> <s id="id.000909">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000910">Potentiæ vectis cauſa.] <emph type="italics"></emph>Vectis definitus eſt à Budæo bacu<lb></lb><arrow.to.target n="marg19"></arrow.to.target><lb></lb>lus validus per mediam machinam traiectus, quo manuducto <lb></lb>machina, dum verſatur, funem ductarium aduoluit. </s> <s id="id.000912">Hæc definitio <lb></lb><expan abbr="nimiũ">nimium</expan> anguſta eſt, neque huic loco <expan abbr="cõuenit">conuenit</expan>, neque ſatis rei ipſi. </s> <s id="id.000913">vectis <lb></lb>enim per ſe machina eſt. </s> <s id="id.000914">Eſt igitur vectis palus oblongior vno <expan abbr="ſuorũ">ſuorum</expan> <lb></lb>extremorum acutus, altero obtuſus ex ligno vel ferro inflexibi<lb></lb>lis ad <expan abbr="commouẽ">commouen</expan><emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.095.1.jpg" xlink:href="035/01/095/1.jpg"></figure><lb></lb><emph type="italics"></emph>da onera factus, <lb></lb>vt eſt A B. pars <lb></lb>obtuſa caput: pars acuta lingula vocatur. </s> <s id="id.000915">Hoc vtendi modus duplex <lb></lb>eſt. </s> <s id="id.000916">Primus cum lingula ſubditur oneri commouendo, & vecti ipſi <lb></lb>quam proxime lingulæ ſubditur corpuſculum firmum, quod Græcis<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">u(pomo/xlion,</foreign> <emph type="italics"></emph>Vitruuio preßio dicitur. </s> <s id="id.000917">Huius figura eſt ferè quæ<lb></lb>uis obuia: expeditior tamen eſt, ſi ſit priſmation, cuius aduerſa duo <lb></lb>plana æqualia ſimilia, parallela, ſint trian<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.095.2.jpg" xlink:href="035/01/095/2.jpg"></figure><lb></lb><emph type="italics"></emph>gula, vteſt A D B C E F. </s> <s id="id.000918">Huius enim <lb></lb>priſmatis lateri vni tanquam centro, ſi <lb></lb>vectis innitentis caput deprimatur, neceſſe <lb></lb>erit ilico lingulam, & conſequenter lin<lb></lb>guæ innixum onus attolli, & ideo com<lb></lb>moueri. </s> <s id="id.000919">Atque hic eſt primus modus vtendi vecte frequentißimus: <lb></lb>ſed & eſt alter non multò infrequentior, cum lingula oneri, vt an<lb></lb>tè, ſubdita nullo ſubdito præter ſolum immobile vecti ipſi hypo<lb></lb>mochlio, vectis caput attollitur. </s> <s id="id.000920">Hoc enim ſurſum lato omnes etiam <lb></lb>vectis partes attolli neceſſe eſt præter extremum lingulæ fixum, quod <lb></lb>centri immobilis rationem ſumit, & terræ vel alij corpori immobili <lb></lb>tanquam hypomochlio innititur. </s> <s id="id.000921">Proinde etiam onus ad partis ve<lb></lb>ctis cui impoſitum eſt, motionem mouebitur, & tunc non ſolum ele<lb></lb>uatur: ſed & ſi opus eſt, fiatque vectis perpendicularis ſolo, ſecundum <emph.end type="italics"></emph.end><pb xlink:href="035/01/096.jpg" pagenum="56"></pb><emph type="italics"></emph>latus impellitur. </s> <s id="id.000922">Vtrumque vectis vſum Vitruuius cap. 8. lib. 10. ſic <lb></lb>explicuit. </s> <s id="id.000923">Ferreus vectis cum eſt commotus ad onus, quod manuum <lb></lb>multitudo non poteſt mouere, ſuppoſita vti centro cito porrecta preſ<lb></lb>ſione, quòd Græci<emph.end type="italics"></emph.end> <foreign lang="el">u(pomo/xlion</foreign> <emph type="italics"></emph>appellant, & vectis lingua ſub <lb></lb>onus ſubdita, caput eius vnius hominis viribus preſſum, id onus ex<lb></lb>tollet. </s> <s id="id.000924">Item ſi ſub onus vectis ferrei lingula ſubiecta fuerit, neque <lb></lb>caput eius preßione in imum: ſed aduerſus in altitudinem extolletur, <lb></lb>lingula fulcta in areæ ſolo habebit eam pro onere, oneris <expan abbr="autẽ">autem</expan> ipſius <lb></lb>angulum pro preßione: ita non tam faciliter quam per preßionem, <lb></lb>ſed aduerſus nihilominus in pondus oneris erit <expan abbr="excitatũ">excitatum</expan>. </s> <s id="id.000925">Hæc Vitr. <lb></lb>à quo parum diſſentimus dum in ſecundo vſu vectis ponit ſolum ſeu <lb></lb>aream pro onere, nos pro centro & hypomochlio, quorſum, dicemus<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg20"></arrow.to.target><lb></lb><emph type="italics"></emph>alibi. </s> <s id="id.000926">Galenus comparauit muſculum, qui eſt inſtrumentum motus <lb></lb>voluntarij vecti. </s> <s id="id.000927">vtque pondera, inquit, quæ mouere manibus nequi<lb></lb>mus, vectibus admotis mouere ſolemus. </s> <s id="id.000928">Ita cum membra corporis <lb></lb>mouere neruis non poßimus, ad ea mouenda muſculi nobis ſunt dati. <lb></lb></s> <s id="id.000929">neruus enim in ſingulis muſculis in fibras diſſolutus, ita cum fibris <lb></lb>copulatur atque coniungitur, vt ex vtriſque vnum quoddam neruo<lb></lb>ſum corpus effectum è corpore muſculi prodeat, qui tendo nomina<lb></lb>tur. </s> <s id="id.000930">Atque hic quidem tendo ex inſtrumentis exoriens, habet illius <lb></lb>extremæ partis vectis rationem quæ ponderibus admouetur. </s> <s id="id.000931">Itaque <lb></lb>hic ijs qui anatomen corporis humani reſpexerunt <expan abbr="iucundũ">iucundum</expan> eſt ipſius <lb></lb>membra, tanquam onera ſexcentis muſculis, tanquam vectibus, tam <lb></lb>varie flecti, intendi ſurſum, ferri deorſum, demitti ad latera, contor<lb></lb>queri, circumuolui, & ad omnes motus, quos voluntas humana vti<lb></lb>litate incitata præſcribit, educi, immo vero ijſdem agentibus in quie<lb></lb>te, & quam medici appellant in media figura, retineri. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.000932"><margin.target id="marg19"></margin.target>Annot. in <lb></lb>Pandectas. </s> </p> <p type="margin"> <s id="id.000933"><margin.target id="marg20"></margin.target>Cap. 10 lib. <lb></lb>1 de plac. <lb></lb>Hipp. & <lb></lb>Plat. </s> </p> <p type="main"> <s id="id.000934">Cur vires exiguæ.] <emph type="italics"></emph>Machina libræ duobus problematis expe<lb></lb>dita eſt: vectis deinde duodecim diſſeritur, è quibus primum eſt ge<lb></lb>nerale. </s> <s id="id.000935">Quæritur ergo hîc, cur homo verbi gratia puſillis viribus <lb></lb>amoueat vecte magna onera, coloßica vocat Vitruuius, id eſt ma<lb></lb>gnæ molis, quales ſunt coloßi. </s> <s id="id.000936">Et apud eundem coloßicotera compa<lb></lb>ratiuum eſt Græcum pro grandiora, vaſtiora, coloßi inſtar ha<lb></lb>bentia. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000937">Facilius enim eſt.] <emph type="italics"></emph>Ratio eſt ad augendam problematis propo<lb></lb>ſiti de vecte difficultatem, quæ ſic concludi poteſt. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/097.jpg" pagenum="57"></pb> <p type="main"> <s id="id.000938"><emph type="italics"></emph>Facilius eſt mouere paruum pondus quam magnum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000939"><emph type="italics"></emph>Moles ſine vecte eſt pondus minus: quam cum vecte. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000940"><emph type="italics"></emph>Ergo facilius eſt mouere molem ſine vecte: quam cum vecte. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000941"><emph type="italics"></emph>Propoſitio eſt vera, quia vires cuiuſlibet citius æquabunt, aut etiam <lb></lb>ſuperabunt pondus minus: quam maius. </s> <s id="id.000942">Aſſumptio verò fallaciam <lb></lb>habet ex varia diſpoſitione vectis cum mole. </s> <s id="id.000943">Nam totus, aut dimi<lb></lb>dia, aut pluſquam dimidia ſui parte ſuppoſitus, aut ſuperpoſitus moli, <lb></lb>adijceret pondus ponderi, ſicque moles ponderoſior reuera euaderet. <lb></lb></s> <s id="id.000944">At diſponitur aliter, nempe libræ in morem, ita vt parte exigua ſup<lb></lb>ponatur moli mouendæ, & ab illi ſuppoſito fulcimento radius, ſeu <lb></lb>caput ad vim mouentem maius fit, ſicque diſpoſitus pondus non <lb></lb>adijcit moli. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000945">An quia vectis.] <emph type="italics"></emph>Solutio eſt problematis, quod vectis cum in <lb></lb>vſum venit referat libram, quæ latitudine effatu digna prædita, <lb></lb>& cuius agina deorſum ſita ſit, tum quæ in inæqualia brachia diui<lb></lb>ſa eorum maius habeat ad partes mouentis, & ſic tum ob libræ agi<lb></lb>nam inferius poſitam, tum ob radij mobilis magnitudinem vectis <lb></lb>facile & velociter mouetur, & vna cum vecte pondus alteri parti <lb></lb>incumbens aut annexum. </s> <s id="id.000946">Ratio hæc concluditur hoc ſyllogiſmo. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000947"><emph type="italics"></emph>Libra deorſum habens aginam & brachium vnum longius, per <lb></lb>id facile deprimitur, & depreſſa manet: vt patuit ex præce<lb></lb>dentibus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000948"><emph type="italics"></emph>Vectis eſt libra deorſum habens <expan abbr="aginã">aginam</expan>, & brachium vnum <lb></lb>longius ( agina enim ſeu centrum fit hypomochlium, & <lb></lb>quidem ita vt ipſam diuidat in partes inæquales, è quibus <lb></lb>quæ ad caput longior ſit, alioqui aliter in vſum adhibitus <lb></lb>vis mouens non magis mouere poteſt, quam ſine vecte.)<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000949"><emph type="italics"></emph>Ergo vectis facile deprimetur, depreſſuſque manebit, & ad eius <lb></lb>motum pondus incumbens mouebitur. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000950"><foreign lang="el">o(\<lb></lb> ou)=n to\ kinou/menon ba/ros pro\s to\ kinou=n, to\ mh=kos pro\s to\ mh=kos <lb></lb>a)ntipe/ponqen.</foreign></s> <s id="g0130304"><foreign lang="el">ai)ei\ de\ o(/sw| a)\n mei=zon a)festh/koi, tou= u(pomoxli/ou, <lb></lb>r(a=|on kinh/sei.</foreign></s> <s id="g0130305"><foreign lang="el">ai)ti/a de/ e)stin h( prolexqei=sa, o(/ti h( <lb></lb>plei=on a)pe/xousa e)k tou= ke/ntrou, mei/zona ku/klon gra/fei.</foreign></s> <s id="g0130306"><foreign lang="el">w(/ste <lb></lb>a)po\ th=s au)th=s i)sxu/os ple/on metasth/setai to\ kinou=n to\ <lb></lb>plei=on tou= u(pomoxli/ou a)pe/xon.</foreign></s> <s id="g0130307"><foreign lang="el">e)/stw moxlo\s e)f' ou(= *a*b. <lb></lb>ba/ros de\ e)f' w(=| to\ *g.to\ de\ kinou=n, e)f' w(=| to\ *d. u(pomo/xlion <lb></lb>e)f' w(=| to\ *e. </foreign></s> <s id="g0130308"><foreign lang="el">to\ de\ e)f' w(=| to\ *d kinh=san, e)f' w(=| to\ *h: kekinhme/non <lb></lb>de\ to\ e)f' ou(= *g. ba/ros e)f' ou(= *k.</foreign></s> </p> <p type="main"> <s id="id.000951">Quod autem eſt mobile <lb></lb>ad mouens, id eſt longitu<lb></lb>do ad longitudinem reci<lb></lb>procè. </s> <s id="id.000952">Semper ſane quantò <lb></lb>longitudo magis diſtabit à <lb></lb>preſſione, facilius mouebit. </s> <pb xlink:href="035/01/098.jpg" pagenum="58"></pb> <s>Cauſa vero ante dicta eſt: <lb></lb>quoniam radius maior ma<lb></lb>iorem deſcribit circulum. <lb></lb></s> <s id="id.000953">Itaque ab eadem vi plus <lb></lb>mutabitur mouens illud, <lb></lb>quod plus diſtat à preſſio<lb></lb>ne. </s> <s id="id.000954">Sit vectis <foreign lang="el">a b,</foreign> pondus <lb></lb>vero <foreign lang="el">g,</foreign> mouens autem <foreign lang="el">d,</foreign><lb></lb>preſſio <foreign lang="el">e. </foreign>Ipſum vero quod <lb></lb>mouerit <foreign lang="el">d,</foreign> ſit vbi <foreign lang="el">h,</foreign> & pon<lb></lb>dus <foreign lang="el">g</foreign> motum vbi <foreign lang="el">k. </foreign></s> </p> <p type="head"> <s id="id.000955">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000956"><emph type="italics"></emph>Locus hic breuißimè totam vectis rationem explicat, vt ſciatur <lb></lb>vectis vſus, & quæ vires, ad quod onus mouendum ſufficiant, <lb></lb>vel non ſufficiant. </s> <s id="id.000957">Quæres vt intelligatur proponemus hoc theore<lb></lb>ma. </s> <s id="id.000958">Vteſt potentia ad pondus ſuſtentum: ita eſt pars vectis ab hypo<lb></lb>mochlio verſus linguam, ad partem ab eodem hypomochlio verſus <lb></lb>caput, quod vt demonſtretur. </s> <s id="id.000959">Sit vectis A B, & huius hypo<lb></lb>mochlium C:<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.098.1.jpg" xlink:href="035/01/098/1.jpg"></figure><lb></lb><emph type="italics"></emph><expan abbr="ſicq;">ſicque</expan> vectis duæ <lb></lb>partes C A ver<lb></lb>ſus linguam, C <lb></lb>B verſus caput: <lb></lb>ſit quoque pon<lb></lb>dus D ſuſpenſum ex perpendiculari A D: potentia autem ſuſtinens <lb></lb>ſit in B. </s> <s id="id.000960">Dico potentiam in B eſſe ad pondus D: vt A C ad B <lb></lb>C ( quod hic vocatur reciprocè ) fiat ergo vt B C ad A C: ita <lb></lb>pondus D ad aliud, vt E. </s> <s>hoc igitur pondus E loco potentiæ ap<lb></lb>penſum in B, ipſum D pondere æquabit. </s> <s id="id.000961">Magnitudines enim in gra<lb></lb>uitate commenſurabiles æquiponderant, ſi permutatim ſuſpendantur <lb></lb>in diſtantijs ſecundum grauitatum rationem <expan abbr="cõſtitutæ">conſtitutæ</expan> prop. 6. lib. 1. <lb></lb>Archim. de æquipond. </s> <s id="id.000962">Et ſic potentia æqualis ipſi E ibidem conſti<lb></lb>tuta pondere æquabit ipſum D, id eſt ne D deorſum vergat, quod fa<emph.end type="italics"></emph.end><pb xlink:href="035/01/099.jpg" pagenum="59"></pb><emph type="italics"></emph>cit pondus E, prohibebit. </s> <s id="id.000963">Nam æqualia ad idem eandem rationem <lb></lb>habent prop. 7. lib. 5. el. </s> <s id="id.000964">Sed E habet eam ad D, quam A C ad B C, ex <lb></lb>fab. </s> <s id="id.000965">ergo potentia in B ad pondus D eam rationem habebit, quam <lb></lb>A C ad B C. </s> <s id="id.000966">Itaque vt eſt potentia ad pondus ſuſtentum: ita eſt <lb></lb>pars vectis &c. </s> <s id="id.000967">quod fuit demonſtrandum. </s> <s id="id.000968">Ex quo duo corollaria <lb></lb>ſtatim eliciuntur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000969">Primum. <emph type="italics"></emph>Hypomochlio bifariam diuidente vectem, potentia <lb></lb>æqualis requiritur: inæqualiter vero inæqualis. </s> <s id="id.000970">Et quidem ſi pars ab <lb></lb>hypomochlio ad caput ſit maius ſegmentum, potentia minor: ſi con<lb></lb>tra pars ab eodem ad lingulam, potentia maior. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000971">Secundum. <emph type="italics"></emph>Quò pars ab hypomochlio ad lingulam minor erit: <lb></lb>eò minor potentia ad ſuſtinendum ſufficiet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000972">Reciproce.] <foreign lang="el">*antipepo/nqhsis. </foreign><emph type="italics"></emph>Reciprocatio quid ſit deſumen<lb></lb>dum eſt ex Eucl. def. 2. lib. 6. vbi reciprocæ figuræ definiuntur cum in <lb></lb>vtraque figura antecedentes & conſequentes rationum termini fue<lb></lb>rint, id eſt quando in altera quidem eſt terminus antecedens primæ <lb></lb>rationis, & conſequens ſecundæ: in altera vero eſt conſequens pri<lb></lb>mæ, & antecedens ſecundæ. </s> <s id="id.000974">Quæ vt conuenire huic loco intelligan<lb></lb>tur, ſumendum eſt pondus mouendum ſimul cum parte vectis ab hy<lb></lb>pomochlio ad lingulam cui appenditur pro vna figura: & potentia <lb></lb>mouens cum reliqua parte vectis pro altera figura. </s> <s id="id.000975">Sicque cum duæ <lb></lb>rationes fiant, vna ponderis ad potentiam: altera partis cui potentia <lb></lb>innititur ad partem cui pondus eſt appenſum. </s> <s id="id.000976">Clarum eſt anteceden<lb></lb>tes & conſequentes rationum terminos in vtraque figura eſſe. </s> <s id="id.000977">Et <lb></lb>ideo figuras eſſe reciprocas. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000978">Semper ſane.] <emph type="italics"></emph>Hoc exſecundo corollario clarum eſt. </s> <s id="id.000979">Quo enim <lb></lb>pars vectis ad lingulam erit minor, eo pars ad caput erit maior. </s> <s id="id.000980">Et <lb></lb>ſic ſi minor potentia ad ſuſtinendum vel dimouendum ſufficiet, <lb></lb>etiam alia quæuis paulo maior vis tanto facilius ſuſtinebit, aut mo<lb></lb>uebit pondus: quanto pars ad caput maior erit. </s> <s id="id.000981">Inæqualium enim <lb></lb>maior ad eandem maiorem rationem habet prop. 8. lib. 5. </s> <s>Sed & <lb></lb>huius rei cauſa adfertur ex his quæ ante demonſtrata ſunt, nempe à <lb></lb>radio maiore maiorem deſcribi circulum. </s> <s id="id.000982">Pars enim vectis ab hy<lb></lb>pomochlio ad caput radij inſtar eſt maioris, qui depreſſus & ideo vo<lb></lb>lutus circa hypomochlium fixum tanquam <expan abbr="cẽtrum">centrum</expan>, deſcribit arcum <lb></lb>tanto maiorem: quanto ipſe radius maior erat. </s> <s id="id.000983">Adde igitur & ex<emph.end type="italics"></emph.end><pb xlink:href="035/01/100.jpg" pagenum="60"></pb><emph type="italics"></emph>antecedentibus, velocius quoque moueri, quod hîc eſt<emph.end type="italics"></emph.end> <foreign lang="el">ra=|on kai\ ple/on <lb></lb>ki/neisqai,</foreign> <emph type="italics"></emph>facilius & plus moueri. </s> <s id="id.000984">Ex his autem colligendum eſt il<lb></lb>lud, quod eſt ab Archimede profectum problema admirabile. </s> <s id="id.000985">Da<lb></lb>tum pondus data potentia mouere, locum habiturum in vecte, ſi tam <lb></lb>longum dari rerum natura pateretur, vt in eo maioris ſegmenti ad <lb></lb>minus ratio fieri poſſet paulo maior. </s> <s id="id.000986">ea, quæ dati ponderis eſſet ad da<lb></lb>tam potentiam. </s> <s id="id.000987">Quod in quouis dato pondere cum rèrum natura non <lb></lb>patiatur, problema alioqui geometricè demonſtratum, in vſu ob ma<lb></lb>teriæ ſatis longæ & firmæ <expan abbr="defectũ">defectum</expan> ſuæ rationi reſpondere <expan abbr="nõ">non</expan> poteſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.000988">Sit vectis <foreign lang="el">a b</foreign>] <emph type="italics"></emph>huius diagrammatis expoſitio ſi non imperfe<lb></lb>cta eſt, adfertur tantum ad oſtendendum quod pondus<emph.end type="italics"></emph.end> <foreign lang="el">g</foreign> <emph type="italics"></emph>ab eo cum <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.100.1.jpg" xlink:href="035/01/100/1.jpg"></figure><lb></lb><emph type="italics"></emph>erat in<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>per depreßionem<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign> <emph type="italics"></emph>tranſlatum eſt ad<emph.end type="italics"></emph.end> <foreign lang="el">k. </foreign></s> <s><emph type="italics"></emph>Sed adhuc <lb></lb>paulo obſcurius. </s> <s id="id.000989">Apertius igitur ſic. </s> <s id="id.000990">Sit vectis<emph.end type="italics"></emph.end> <foreign lang="el">a b,</foreign> <emph type="italics"></emph>pondus vero<emph.end type="italics"></emph.end> <foreign lang="el">g,</foreign><lb></lb><emph type="italics"></emph>mouens autem<emph.end type="italics"></emph.end> <foreign lang="el">d,</foreign> <emph type="italics"></emph>preßio<emph.end type="italics"></emph.end> <foreign lang="el">e. </foreign><emph type="italics"></emph></s> <s>Cum ipſum<emph.end type="italics"></emph.end> <foreign lang="el">d,</foreign> <emph type="italics"></emph>quod moueat, ſit vbi<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign><emph type="italics"></emph>: <lb></lb>& pondus<emph.end type="italics"></emph.end> <foreign lang="el">g</foreign> <emph type="italics"></emph>motum erit vbi<emph.end type="italics"></emph.end> <foreign lang="el">k. </foreign></s> <s><emph type="italics"></emph>quod ita ſe habere oſtendit tertia <lb></lb>proprietas circuli, ex qua cap. 1. huius lib. oſtenſum eſt diametri ex<lb></lb>tremo vno deorſum moto, alterum eodem tempore ſurſum moueri. </s> <s id="id.000991">Eſt <lb></lb>autem hic vectis<emph.end type="italics"></emph.end> <foreign lang="el">b a,</foreign> <emph type="italics"></emph>vt diameter circuli cuius extremum<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>deor<lb></lb>ſum cum ad<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign> <emph type="italics"></emph>mouetur, alterum<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ſurſum ſimul moueri vt ad<emph.end type="italics"></emph.end> <foreign lang="el">k,</foreign> <emph type="italics"></emph>ne<lb></lb>ceſſum eſt. </s> <s id="id.000992">Et ex his denique contendit Ariſtoteles oſtendere circula<lb></lb>rem motum omnium machinationum principia in ſe continere, vt <lb></lb>multis poſtea ſpecialibus exemplis declarabit, in quibus & alijs om<lb></lb>nibus, qui ſcitè diſtinguet, quid oneri reſpondeat, pro quo ſit vectis, <lb></lb>quale ſit hypomochlium, vnde vis mouens habeatur, hic habebit <lb></lb>abundè, quid ſentiendum ſit. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <pb xlink:href="035/01/101.jpg" pagenum="61"></pb> <chap> <subchap1> <p type="main"> <s id="id.000993">5. <foreign lang="el">*dia\ ti/ oi( meso/neoi ma/lista <lb></lb> th\n nau=n kinou=si. </foreign></s> </p> <p type="main"> <s id="id.000994">5. Cur nauim mouent ma<lb></lb>xime remiges, qui in <lb></lb>media naui ſedent. </s> </p> <p type="main"> <s id="g0130401a"><foreign lang="el">*dia\ ti/ oi( meso/neoi ma/lista th\n nau=n kinou=sin; </foreign></s> <s id="g0130402"><foreign lang="el">h)\ dio/ti <lb></lb>h( kw/ph moxlo/s e)stin, u(pomo/xlion me\n ga\r o( skalmo\s gi/netai.</foreign></s> <s id="g0130402a"><foreign lang="el"><lb></lb>me/nei ga\r dh\ ou(=tos.</foreign></s> <s id="g0130402b"><foreign lang="el">to\ de\ ba/ros h( qa/latta, h(\n <lb></lb>a)pwqei= h( kw/ph.</foreign></s> <s id="g0130402c"><foreign lang="el">o( de\ kinw=n to\n moxlo\n o( nau/ths e)sti/n.</foreign></s> <s id="g0130403"><foreign lang="el"><lb></lb>a)ei\ de\ ple/on ba/ros kinei=, o(/sw| a)\n ple/on a)festh/kh| tou= u(pomoxli/ou <lb></lb>o( kinw=n to\ ba/ros.</foreign></s> <s id="g0130404"><foreign lang="el">mei/zwn ga\r ou(/tw gi/netai h( e)k <lb></lb>tou= ke/ntrou.</foreign></s> <s id="g0130404a"><foreign lang="el">o( de\ skalmo\s u(pomo/xlion w)\n ke/ntron e)sti/n.</foreign></s> <s id="g0130405"><foreign lang="el">e)n <lb></lb>me/sh| de\ th=| nhi\, plei=ston th=s kw/phs e)nto/s e)sti.</foreign></s> <s id="g0130405a"><foreign lang="el">kai\ ga\r h( <lb></lb>nau=s tau/th| eu)ruta/th e)sti/n.</foreign></s> <s id="g0130405b"><foreign lang="el">w(/ste plei=on e)p' a)mfo/tera e)nde/xesqai <lb></lb>me/ros th=s kw/phs e(kate/rou toi/xou e)nto\s ei)=nai th=s <lb></lb>new/s.</foreign></s> <s id="g0130406"><foreign lang="el">kinei=tai me\n ou)=n h( nau=s, dia\ to\ a)pereidome/nhs th=s kw/phs <lb></lb>ei)s th\n qa/lassan, to\ a)/kron th=s kw/phs to\ e)nto\s proi+e/nai <lb></lb>ei)s to\ pro/sqen: th\n de\ nau=n prosdedeme/nhn tw=| skalmw=| sumproi+e/nai, <lb></lb>h(=| to\ a)/kron th=s kw/phs.</foreign></s> <s id="g0130408"><foreign lang="el">h(=| ga\r plei/sthn qa/lassan <lb></lb>diairei= h( kw/ph, tau/th| a)na/gkh ma/lista prowqei=sqai.</foreign></s> <s id="g0130408a"><foreign lang="el">plei/sthn <lb></lb>de\ diairei=, h(=| plei=ston me/ros a)po\ tou= skalmou= th=s kw/phs <lb></lb>e)sti/.</foreign></s> <s id="g0130409"><foreign lang="el">dia\ tou=to oi( meso/neoi ma/lista kinou=sin: me/giston ga\r <lb></lb>e)n me/sh| nhi\+, to\ a)po\ tou= skalmou= th=s kw/phs to\ e)nto/s e)stin.</foreign></s> </p> <p type="main"> <s id="id.000996">Cur nauim <expan abbr="mouẽt">mouent</expan> maxi<lb></lb>me remiges mediani? </s> <s id="id.000997">An qa <lb></lb>remus eſt vectis, preſſio <expan abbr="ſiquidẽ">ſi<lb></lb>quidem</expan> ſcalmus efficitur. </s> <s id="id.000998">Hic <lb></lb>enim manet. </s> <s id="id.000999"><expan abbr="põdus">pondus</expan> autem <lb></lb>mare, quod remus propellit: <lb></lb><expan abbr="vectẽ">vectem</expan> vero mouens eſt nau<lb></lb>ta. </s> <s id="id.001000">Sed ſemper plus <expan abbr="põderis">ponderis</expan> <lb></lb>mouet, quanto plus motor <lb></lb>diſtiterit à preſſione. </s> <s id="id.001001">Ibi <lb></lb>enim maior fit radius, & <lb></lb>ſcalmus preſſio <expan abbr="exiſtẽs">exiſtens</expan> <expan abbr="centrũ">cen<lb></lb>trum</expan> eſt. </s> <s id="id.001002">In nauis <expan abbr="autẽ">autem</expan> medio <lb></lb><expan abbr="plurimũ">plurimum</expan> remi intus eſt. </s> <s id="id.001003">Ete<lb></lb>nim nauis ea parte latiſſima <lb></lb>exiſtit: ideo vtrinque remi <lb></lb>partem maiorem intus in <lb></lb>vtro que latere nauis <expan abbr="cõtingit">contin<lb></lb>git</expan> eſſe. </s> <s id="id.001004"><expan abbr="Itaq;">Itaque</expan> mouetur na<lb></lb>uis, quia dum remus inni<lb></lb>titur mari, <expan abbr="extremũ">extremum</expan> remi, <lb></lb>quod intus eſt antrorſum <lb></lb>procedit: Tum que nauim <lb></lb>ſcalmo <expan abbr="alligatã">alligatam</expan> procedere <lb></lb>neceſſe eſt eò, vbi eſt <expan abbr="extremũ">extre<lb></lb>mum</expan> remi. </s> <s id="id.001005">Vbi enim remus <lb></lb><expan abbr="plurimũ">plurimum</expan> maris diuidit, eò <lb></lb>maxime neceſſe eſt impel<lb></lb>li. </s> <s id="id.001006">Ibi <expan abbr="autẽ">autem</expan> <expan abbr="plurimũ">plurimum</expan> diuidit, <lb></lb>vbi maxima pars remi à <lb></lb>ſcalmo eſt. </s> <s id="id.001007">Propter id ma<lb></lb>ximè mouent. </s> <s id="id.001008">Maxima <lb></lb>enim remi pars à ſcalmo intus eſt in medio nauis. </s> </p> <pb xlink:href="035/01/102.jpg" pagenum="62"></pb> <p type="head"> <s id="id.001009">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001010">Cvr remiges.] <emph type="italics"></emph>Specialia deinceps ſunt vndecim de vecte pro<lb></lb>blemata, è quibus priora ſex pertinent ad nauigandi artem, quæ <lb></lb>mirabilior ſit propter audaciam, an propter ſubtilitatem inuentorum <lb></lb>ad bene <expan abbr="nauigãdum">nauigandum</expan> vtilium, dubium eſt. </s> <s id="id.001011">Quid enim audacius quam <lb></lb>ventorum furorem, & maris rabiem contemnere, & vt in eo tran<lb></lb>quilla ſint omnia, ſe tantum duorum ſpatio digitorum à certa, eaque <lb></lb>aßidua morte diſtare cernere! </s> <s>Semper enim<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001012">Eſt tua tam propè mors: quam propè cernis aquam. <lb></lb></s> <s><emph type="italics"></emph>Et quod audacius eſt tam longum iter, tam infidum ob ſcopulos, vor<lb></lb>tices, charybdes, Syllas, breuia, Syrtes ſine vllis certis hoſpicijs etiam <lb></lb>per ſummas tenebras, in quibus homines alioqui domibus ſuis vrba<lb></lb>nis concluſi, horrent, peragere? </s> <s id="id.001013">Et denique vbi eſt aquæ ſemper ſum<lb></lb>ma copia, nullius rei tamen magis, quam aquæ penuria laborare? <lb></lb></s> <s id="id.001014">Rectè ſanè dixit Horatius,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001015">Illi robur & æs triplex</s> </p> <p type="main"> <s id="id.001016">Circa pectus erat, qui fragilem truci</s> </p> <p type="main"> <s id="id.001017">Commiſit pelago ratem</s> </p> <p type="main"> <s id="id.001018">Primus. </s> </p> <p type="main"> <s id="id.001019"><emph type="italics"></emph>Quid vero ſubtilius, quam obſcura etiam nocte, cœlo nubilo, nullo <lb></lb>termino vel lapide certæ viæ indice per tam incertos maris patuli <lb></lb>tramites, rectum tamen iter, tanquam Deo aliquo duce tenere? </s> <s id="id.001020">Et <lb></lb>omnes mundi partes inuiſere, importare, aſportare omnia, quæ vbi<lb></lb>que Dædala Tellus profert, omnibus communicare, tot ad id excogi<lb></lb>taſſe commoda, remos, malos, vela, Temonem, anchoram, pyxidem, <lb></lb>& quod ſupra fidem eſt eodem vento contrarium iter agere. </s> <s id="id.001021">Sed & <lb></lb>iſta ſubtilitas maior apparebit, cum quæ ad artem nauigandi perti<lb></lb>nentia problemata hîc proponuntur ab Ariſtotele explicata fuerint. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001022">In medio nauis.] <emph type="italics"></emph>Nauis eſt ingens machina oblonga, intus <lb></lb>caua, foris prominens, ad laterum media latior ad anteriorem par<lb></lb>tem, quæ prora dicitur, acuta, ad poſteriorem, quæ puppis dicitur ob<lb></lb>tuſior, qua homines, & onera magna ſuper aquam vehuntur. </s> <s id="id.001023">An<lb></lb>tiquißima nauium Argô à Fabro nauali, qui eam ædificauit, ſi <lb></lb>Apollonio creditur, nuncupata eſt. </s> <s id="id.001024">Sic enim in<emph.end type="italics"></emph.end> <foreign lang="el">*argonautikw=n. </foreign></s> </p> <pb xlink:href="035/01/103.jpg" pagenum="63"></pb> <p type="main"> <s id="id.001025"><foreign lang="el">*nh=a d' e)pikrate/ws ar)gou= u(poqhmosu/nh|si</foreign></s> </p> <p type="main"> <s id="id.001026"><foreign lang="el">*ezwsan, pa/mprwton e)u+strefei= e)ndoqen o(/plw|. </foreign><lb></lb><emph type="italics"></emph>quæ ſic reddidit Lazarus Bayfius. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001027">Imprimis nauem diuinis artibus Argi, </s> <s>Extructam, intus compingunt habili armamento. </s> </p> <p type="main"> <s id="id.001028"><emph type="italics"></emph>Tullius tamen in 1. Tuſcula. dicit nominatam Argô, quia Argiui in <lb></lb>ea delecti viri vecti petebant Arietis pellem inauratam. </s> <s id="id.001030">Ante Ar<lb></lb>go ratibus, & paruis acatijs homines tantum vehi ſolere, teſtis eſt <lb></lb>Diodorus ſiculus. </s> <s id="id.001031">Sed poſt hanc, vt eſt hominum ingenium ferax, <lb></lb>naues variæ confectæ ſunt: quarum aliæ velis, quæ onerariæ: aliæ <lb></lb>remis, quæ actuariæ: aliæ velis & remis, quæ longæ dictæ ſunt. </s> <s id="id.001032">Om<lb></lb>nium præcipuæ partes ſunt anterior, quæ prora: poſterior quæ puppis: <lb></lb>latus, quicquid dextra & ſiniſtra inter proram & puppim in<lb></lb>teriacens prominet: Ima, quæ in aqua immerſa alueus & carina di<lb></lb>citur. </s> <s id="id.001033">Sunt & in omnium ambitu fori, per quos nautæ curſitant, & <lb></lb>in proiecturis laterum tranſtra, ſedes ſcilicet quibus acturi nauem <lb></lb>actuariam, vel longam inſident. </s> <s id="id.001034">Hi à remo Remiges dicti. </s> <s id="id.001035">Eſt au<lb></lb>tem Remus palus longus & validus parte vna latior, quæ palmula <lb></lb>dicitur, reliqua <expan abbr="rotũdus">rotundus</expan>, cuius extremum, manubrium dicitur. </s> <s id="id.001036">Remi <lb></lb>fuerunt diuerſæ magnitudinis pro proportione nauis agendæ, & in <lb></lb>eadem naui inæqualis, tractabilis tamen vnius validi remigis viri<lb></lb>bus, propter libramentum, quod à plumbatis manubrijs accedebat ni<lb></lb>xus impellentium brachiorum adiuuans. </s> <s id="id.001037">Athenæus recitat inter <lb></lb>remos quoſdam fuiſſe tantæ longitudinis vt duodequadraginta cu<lb></lb>bitos explerent, quod non erit incredibile memoria repetenti quarun<lb></lb>dam nauium à veteribus fabricatarum vaſtitatem, cuiuſmodi idem, <lb></lb>& Plutarchus memorant fuiſſe illam dictam fluuialem Thalame<lb></lb>gon, quam Ptolomæus Philopator in delicijs habuit, non tam ad <lb></lb>vſum: quam ad oſtentationem, vt quæ in longitudinem ducentos ac <lb></lb>octoginta: & ab imo vſque ad tranſtra duodequinquaginta cubitos <lb></lb>pateret. </s> <s id="id.001038">Quæ amplitudo remi & nauis ( quod alioqui eſt nunc nobis <lb></lb>incredibile videntibus tantum naues, quæ à numero remigum in <lb></lb>vnoquoque tranſtro ſedentium ſunt vniremes, triremes, quadrire<lb></lb>mes, quinquiremes ) probabile facit fuiſſe in vſu apud antiquos naues <lb></lb>multo plurium remigum decem, vndecim, viginti, multò plurium, in <lb></lb>vnoquoque tranſtro & tranſtrorum multos, ordines vnde idem <emph.end type="italics"></emph.end><pb xlink:href="035/01/104.jpg" pagenum="64"></pb><emph type="italics"></emph>Athenæus recenſet Philadelphum ad vſum habuiſſe trieconteres, id <lb></lb>eſt tricenûm ordinum duas: I coſerem vnam, quæ vicenûm erat, qua<lb></lb>tuor quæ ternûm denûm, duas quæ duodenûm, quatuordecim quæ <lb></lb>vndenûm, & alias infra multas. </s> <s id="id.001039">Illam autem, quæ Philopatoris fuit, <lb></lb>fuiſſe quinquaginta ordinum, & in ſingulis tranſtris quadraginta <lb></lb>remis, id eſt, remigibus ( nam & horum poſtea numerum aßignat to<lb></lb>tius fuiſſe 4000.) agi. </s> <s id="id.001040">Remigum autem antiquitus, vt & hodie, <lb></lb>alij voluntarij: alij mercede <expan abbr="cõducti">conducti</expan>: alij vt adacti, vt in bello capti, <lb></lb>aut ab Archipyratis in locis maritimis <expan abbr="comprehẽſi">comprehenſi</expan>, aut ob ſcelera ad <lb></lb>remos à iudicibus damnati, <expan abbr="cõpediti">compediti</expan>, & alligati ſine mercede etiam <lb></lb>nudi ſub flagellis remigant. </s> <s id="id.001041">Omnes intres ordines reduxit quidam <lb></lb>Scholiaſtes Ariſtophanis in Ranis locum illum,<emph.end type="italics"></emph.end> <foreign lang="el">*kai\ a)popardei=n e)s <lb></lb>to\ sto/ma tw=| qala/maki,</foreign> <emph type="italics"></emph>interpretans, dum dicit eos, qui in inferiore <lb></lb>parte nauis <expan abbr="eßẽt">eßent</expan><emph.end type="italics"></emph.end> <foreign lang="el">qalami=tas</foreign> <emph type="italics"></emph>ſeu<emph.end type="italics"></emph.end> <foreign lang="el">qala/makas,</foreign> <emph type="italics"></emph>qui in medio<emph.end type="italics"></emph.end> <foreign lang="el">zugi=tas,</foreign><lb></lb><emph type="italics"></emph>qui in ſuperiore<emph.end type="italics"></emph.end> <foreign lang="el">qrani=tas</foreign> <emph type="italics"></emph>appellatos fuiſſe. </s> <s id="id.001042">Vnde nonnulli exiſtima<lb></lb>runt fuiſſe naues, quæ in parte laterali ſupra aquas eminente, tria fo<lb></lb>ramina<emph.end type="italics"></emph.end> <foreign lang="el">kat' i)/cin</foreign> <emph type="italics"></emph>eius partis habuiſſe, <expan abbr="quorũ">quorum</expan> ſingula ſuum remum <lb></lb>haberet alligatum. </s> <s id="id.001043">Vnde cum hi remi ſitu pro differentia loci ſur<lb></lb>ſum & deorſum eſſent diſtincti: ita quoque ſuos remiges haberent <lb></lb>diſtinctos: ſed eam mentem non fuiſſe ſcholiaſtis illius indicat, <lb></lb>quod paulò pòſt ſubiunxit. <emph.end type="italics"></emph.end> <foreign lang="el">qrani/ths )esti,</foreign> <emph type="italics"></emph>inquit<emph.end type="italics"></emph.end> <foreign lang="el">o( pro\s th\n pru/mnan, <lb></lb>zugi/ths o( mesos, qalami/ths o( pro\s th\n prw/ran. </foreign></s> <s><emph type="italics"></emph>Thranites eſt is, <lb></lb>qui ad puppim remigat, Zygites qui in media naui, Thalamites qui <lb></lb>ad proram, vbi manifeſtè ſuperiorem nauis partem explicat ad pup<lb></lb>pim in qua ſedet gubernator, vt quæ altior eſt: inferiorem ad proram, <lb></lb>quæ inferior eſt, ne gubernatoris obſtruat luminibus: ideo inter istos <lb></lb>zygitæ ſunt, quos hic Ariſtoteles vocabulo compoſito<emph.end type="italics"></emph.end> <foreign lang="el">e)k mesh=s kai\ <lb></lb>ne/ws</foreign> <emph type="italics"></emph>vocat meſoneos. </s> <s id="id.001044">Sed hic non leuis obrepit controuerſia, & pro<lb></lb>pter præſentem Ariſtotelis contextum ante diſſoluenda, ſi poteſt, ex <lb></lb>duobus locis, altero Thucydidis, altero Galeni. </s> <s id="id.001045">Ille enim li. 6. hæc ha<lb></lb>bet. <emph.end type="italics"></emph.end></s> <s><foreign lang="el">tw=n prihra/rxwn )epifora\s pro\s tw=| )ek dimwsi/ou misqw=| dido/ntwn <lb></lb>toi=s qrani/tais,</foreign> <emph type="italics"></emph>Thranitæ præter ſtipendium publicum à trierarchis <lb></lb>donatiuum conſequebantur, cuius rei cauſa ſubdita eſt à ſcholiaste, <lb></lb><expan abbr="quoniã">quoniam</expan> remos longiores trahebant, grauioreque labore vexabantur, <lb></lb>& adhuc hodie eò loci remigant ex omnibus delecti robuſtiores, à <lb></lb>largis ſpatulis Gallis dicti Eppaliers. </s> <s id="id.001047">Hic verò cap. 24. lib. I, de vſu <emph.end type="italics"></emph.end><pb xlink:href="035/01/105.jpg" pagenum="65"></pb><emph type="italics"></emph>partium ſic ait, In triremibus <expan abbr="remorũ">remorum</expan> extremitates ad vnam æqua<lb></lb>litatem perueniunt, cum tamen ipſi omnes non ſint æquales, etenim <lb></lb>etiam ibi medios eandem ob cauſam maximos efficiunt, id eſt, vt vi<lb></lb>dere licet ex iſto cap. Galen. citato, vt manus digiti inæ quales ſunt, <lb></lb>& medius longißimus ad firmam rerum apprehenſionem, & ap<lb></lb>prehenſarum retentionem, quod illius munus eſt, quod non aliter fit <lb></lb>quam quum digitorum extremitates ad æqualitatem perueniunt: ſic <lb></lb>ob nauigationis perfectionem in valido & faciliori nauis, quâ prora <lb></lb>ſpectat impulſu poſitam, remi facti ſunt inæquales, & eorum me<lb></lb>dius maximus: & horum quidem iſta inæqualitas ob eandem cau<lb></lb>ſam, vt ſcilicet remorum extremitates ſimul omnes in remigatione <lb></lb>ad æqualitatem peruenirent. </s> <s id="id.001048">Ex his locis <expan abbr="vtriq;">vtrique</expan> conueniunt eiuſdem <lb></lb>lateris remos eſſe inæquales: ſed in hoc in ſigniter diſcrepant, quod <lb></lb>Galenus aſſerat medios, id eſt remos Zygitarum, ſeu<emph.end type="italics"></emph.end> <foreign lang="el">mesone/wn</foreign> <emph type="italics"></emph>eſſe <lb></lb>maximos: Ariſtoteles non hos, ſed <expan abbr="Thranitarũ">Thranitarum</expan>. </s> <s id="id.001049">Et <expan abbr="verũ">verum</expan> dicere Gale<lb></lb>num cognoſcemus ſi prius intellexerimus quomodo remorum extre<lb></lb>mitates in remigationis ictu ad æqualitatem perueniant. </s> <s id="id.001050">Ad hanc <lb></lb>enim peruenire poſſunt duobus tantum modis, priore ſi intelligamus <lb></lb>tranſtrorum ordines <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.105.1.jpg" xlink:href="035/01/105/1.jpg"></figure><lb></lb><emph type="italics"></emph>poſitos eſſe ita, vt de<lb></lb>ſinant ſecundum re<lb></lb>ctam A B parallelam <lb></lb>rectæ, quæ in naui ex<lb></lb>tenderetur à prora ad <lb></lb>puppim cuiuſmodi eſto <lb></lb>C D, cui etiam altera <lb></lb>E F in mari parallela <lb></lb>ad quam extremitates <lb></lb>peruenirent, ita vt <lb></lb>ſponda nauis ad cuius <lb></lb>G H T ſcalmos eſſent <lb></lb>alligati remi K G P, <lb></lb>M H N, O T P. <lb></lb></s> <s id="id.001051">Sed ſi ſic præterquam <lb></lb>quod Thalamitarum <lb></lb>Zygitarum & Thra<emph.end type="italics"></emph.end><pb xlink:href="035/01/106.jpg" pagenum="66"></pb><emph type="italics"></emph>nitarum Remi eſſent æquales prop. 33. & 34. lib. I. elem. Eucl. quod <lb></lb>eſt contra omnium ſententiam, nauigatio eſſet valde impedita, eo <lb></lb>quod cum aqua ante nauim immota, ideoque difficilius cedens: tum <lb></lb>poſt nauim etiam immota, minimeque eo rediens non compelleret. <lb></lb></s> <s id="id.001053">Moueretur enim aqua ſecundum rectam E F remorum extremita<lb></lb>tes excipientem. </s> <s id="id.001054">Poſterior igitur eſt ſi deſinant ſecundum lineam pa<lb></lb>rallelam ſpondæ nauis quæ ſemper eſt<emph.end type="italics"></emph.end> <foreign lang="el">periferikoeidh\s. </foreign><emph type="italics"></emph>Sic enim <lb></lb>Galenus <expan abbr="digitorũ">digitorum</expan> corpus valde <expan abbr="ſphæricũ">ſphæricum</expan> omnium à manu <expan abbr="apprehẽdendorũ">apprehen<lb></lb>dendorum</expan> <expan abbr="difficillimũ">difficillimum</expan>, <expan abbr="apprehendentiũ">apprehendentium</expan> extremitates vult de ſinere in <lb></lb>eandem circuli ipſum ſecantis <expan abbr="peripheriã">peripheriam</expan>. </s> <s id="id.001055">Quomodo ſi pro E F recta <lb></lb>conſtituamus pe<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.106.1.jpg" xlink:href="035/01/106/1.jpg"></figure><lb></lb><emph type="italics"></emph><expan abbr="riphericã">riphericam</expan> Q L N <lb></lb>P R ad quam <expan abbr="deſinãt">de<lb></lb>ſinant</expan> prædicti re<lb></lb>mi, non ſolum re<lb></lb>morum erit inæ<lb></lb>qualitas, & me<lb></lb>dius erit maxi<lb></lb>mus, vt in manu <lb></lb>digitus medius: <lb></lb>ſed & nauigatio <lb></lb>facilius procedet <lb></lb>propter <expan abbr="cõtrarias">contrarias</expan> <lb></lb>cauſas, quippè ve<lb></lb>luti circulationes <lb></lb><expan abbr="vndarũ">vndarum</expan> circa na<lb></lb>uim fient, vnde <lb></lb>quæ ante eſt pro<lb></lb>pulſa aqua viam <lb></lb>aperiet nauigio, <lb></lb>& retro compreſſa, comprimenſ que nauigium propellet. </s> <s id="id.001056">Quod autem <lb></lb>M H N medius remus ſit longior remis O I P & K G L fa<lb></lb>cile demonſtratur ducta recta G I parallela ipſi K. O. </s> <s id="id.001057">Sic enim <lb></lb>æquales ſunt G K, S M, I O prop. 33. & 34. lib. 1. æquales item <lb></lb>propter paralleliſmum G L, H N, & I P. </s> <s>totæ igitur ex his <lb></lb>æquales axiom. 2. lib. 1. & ad earum vnam nempe ex S M, H N <emph.end type="italics"></emph.end><pb xlink:href="035/01/107.jpg" pagenum="67"></pb><emph type="italics"></emph>cum addatur inſuper S H erit ipſa M S H N remus medius <lb></lb>inæqualis, & vtrolibet aliorum maior ax. 4. </s> <s id="id.001059"> Ergo maximus, quod <lb></lb>fuit probandum. </s> <s id="id.001060">Dicemus igitur ſcholiaſtis & Thucydidis locos <lb></lb>debere intelligi, non de totis remis: ſed remorum partibus, quæ ſunt à <lb></lb>ſcalmo ad mare proportione habita ad eas partes, quæ ſunt à ſcalmo <lb></lb>ad manubrium. </s> <s id="id.001061">Thranitæ enim remus à ſcalmo ad <expan abbr="extremũ">extremum</expan> palmu<lb></lb>læ maiorem longè rationem habet ad partem, quæ eſt ab eodem ſcal<lb></lb>mo ad manubrium, id eſt I P ad I O: quam zygitæ pars H N ad <lb></lb>partem H S M vt docebitur poſtea. </s> <s id="id.001062">Et ea eſt cauſa cur zygites fa<lb></lb>cilius & plus promoueat nauim: contra Thranites laborioſius & <lb></lb>minus, vt docebitur etiam. </s> <s id="id.001063">Atque ſic ſint hi duo loci meo iudicio ex<lb></lb>plicati. </s> <s id="id.001064">Cæterum Remiges, vt & hoc notatu pulchrum adijciamus, <lb></lb>Remigando artificiosè ſimul omnes, quamuis quater mille, inter ſe <lb></lb>conſentientes, alioqui illis corium flagris tam fit maculoſum quam <lb></lb>nutricis pallium, vel curſum nauis accelerant, vel inhibent, vel ſuſti<lb></lb>nent, & vt ait Poeta,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001065">Intentaque brachia remís</s> </p> <p type="main"> <s id="id.001066">Intenti expectant ſignum. </s> </p> <p type="main"> <s id="id.001067"><emph type="italics"></emph>Atque hæc ſint de nauigandi arte, nauibus, remis, remigibus, remi<lb></lb>gum ordine, locis, & officio dicta, quibus etiam in his quæ poſteà <lb></lb>dicentur, alia adijcientur ſcitu digna. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001068">Cur remiges.] <emph type="italics"></emph>E ſex problematis quæ de vecte pertinent ad <lb></lb>nauigandi artem, primum per comparationem proponitur. </s> <s id="id.001069">Eſt autem <lb></lb>eiuſmodi cur remigum in medio ſedens plus mouet nauim: quam qui <lb></lb>ad proram, vel ad puppim. </s> <s id="id.001070">Reſpondet id fieri, quia Remi pars à ſcal<lb></lb>mo ad manubrium eius qui medius eſt, maior eſt ea, quæ eſt à ſcalmo <lb></lb>ad manubrium propè proram vel puppim ſedentis. </s> <s id="id.001071">Tum quia pars à <lb></lb>ſcalmo ad palmulam eius qui medius eſt plus maris diuidit, quam <lb></lb>pars à ſcalmo ad palmulam aliorum. </s> <s id="id.001072">Tota igitur hæc quæſtio hoc <lb></lb>primario ſyllogiſmo ſic concludetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001073"><emph type="italics"></emph>Ille remiges inter plus nauim promouet, cuius remi pars à ſcal<lb></lb>mo ad manubrium maior eſt: & cuius etiam pars à ſcalmo <lb></lb>ad palmulam plurimum maris diuidit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001074"><emph type="italics"></emph>Sed remi pars à ſcalmo ad manubrium eius qui in medio eſt <lb></lb>maior: & ad palmulam eiuſdem plus maris diuidit, <lb></lb>quam aliorum. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/108.jpg" pagenum="68"></pb> <p type="main"> <s id="id.001075"><emph type="italics"></emph>Ergo qui in medio eſt inter remiges plus promouet nauim. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001076">An quia remus.] <emph type="italics"></emph>Prior pars propoſitionis præcedentis ſyllogiſ<lb></lb>mi primo loco illuſtratur, ſic<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001077"><emph type="italics"></emph>Quantò maior eſt vectis pars ab hypomochlio ad caput, tantò <lb></lb>vis mouens facilius & plus mouet, quia ibi maior eſt radius. <lb></lb></s> <s id="id.001078">Hoc ita eſſe patuit ex cap. præced. libri huius. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001079"><emph type="italics"></emph>Sed pars remi à Scalmo ad manubrium eſt pars vectis ab <lb></lb>hypomochlio ad caput. </s> <s id="id.001080">Nam remus eſt vectis. per def. & <lb></lb>ſcalmus eſt hypomochlium. </s> <s id="id.001083">hic enim mouet, pondus vero <lb></lb>mobile mare, & vectem mouens, Remex. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001084"><emph type="italics"></emph>Ergo is plus & facilius nauim promouebit, cuius remi pars à <lb></lb>ſcalmo ad manubrium maior erit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001085">In nauis medio.] <emph type="italics"></emph>Aſſumptio eſt primarij ſyllogiſmi confir<lb></lb>mata ex forma nauis quæ in ſui medio latior eſt & depreßior: in <lb></lb>prora autem & puppi arctior, & ſublimior. </s> <s id="id.001086">Ergo ſuppoſito quod re<lb></lb>mi omnium <expan abbr="remigũ">remigum</expan> ſint æquales, ex his, qui ſcalmis proræ & puppis <lb></lb>ſunt alligati, partem extra <expan abbr="nauẽ">nauem</expan> longiorem habent, alias <expan abbr="eorũ">eorum</expan> palmu<lb></lb>la non diuideret aquam, & intra nauem minorem: contra omnia in <lb></lb>his qui ſcalmis mediorum laterum nauis alligantur. </s> <s id="id.001087">vt ex penultimo <lb></lb>diagrammate qualicunque intelligi poteſt. </s> <s id="id.001088">In quo C eſto prora, D <lb></lb>puppis, G ſcalmus ad proram, T ſcalmus ad puppim, H ſcalmus <lb></lb>ad medium: vbi nauis latior & depreßior eſt, ob id magis diſtans à <lb></lb>recta A B, vtpote chorda arcus A G H T B, quæ deſignes <lb></lb>loca tranſtrorum & quæ à remis partes auferat æquales & partes <lb></lb>inæquales relinquat K G, M H, O T & quidem M H ma<lb></lb>iorem. </s> <s>( quod nos ſequenti theoremate demonſtrabimus ) igitur erit <lb></lb>totum ex M H, & adempto maius quam quod ex K G & <lb></lb>adempto, velex O T & adempto per ax. 5. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001090">Theorema. <emph type="italics"></emph>Si chorda rectas in circulo inſcriptas ad rectos ſe<lb></lb>cet: ſectarum pars, quæ de diametro abſcinditur, eſt maxima, reli<lb></lb>quarum quæ diametro propinquior remotiore maior eſt. </s> <s id="id.001091">Eſto circu<lb></lb>lus A D B E, in quo rectam A B diametrum ſecet chorda D <lb></lb>E ad rectos vt & K I, L H: & ſint ſegmenta C B, è dia<lb></lb>metro: F I è propinquiore: G H è remotiore. </s> <s id="id.001092">Dico C B eſſe <lb></lb>maiorem quam F I: & F I quam G H. </s> <s id="id.001093">Per punctum M cen<lb></lb>trum circuli repertum prop. 1. lib. 3. ducatur parallela M N O P <emph.end type="italics"></emph.end><pb xlink:href="035/01/109.jpg" pagenum="69"></pb><emph type="italics"></emph>rectæ C D prop. 31. lib. 1. ſicque parallelogramma ſunt O F & <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.109.1.jpg" xlink:href="035/01/109/1.jpg"></figure><lb></lb><emph type="italics"></emph>N C. </s> <s id="id.001095">Quoniam igitur diame<lb></lb>ter A B maxima eſt inſcripta<lb></lb>rum in circulo, & K I propin<lb></lb>quior centro ipſi L H remotiore <lb></lb>maior eſt prop. 15. lib. 3. harum <lb></lb>quoque dimidiæ M B, N I, O <lb></lb>H prop. 3. lib. eiuſdem erunt in<lb></lb>æquales & M B maior quam <lb></lb>N I, & N I quam O H. </s> <s id="id.001097">Ab <lb></lb>his igitur ſublatis æqualibus M <lb></lb>C, N F, O G parallelogram<lb></lb>morum O F, N C lateribus oppoſitis prop. 34. lib. 1. reliquæ C B, <lb></lb>F I, G H erunt inæquales ax. 5. </s> <s>Et quidem reliqua C B à maiore M <lb></lb>B maior: quam F I: & F I eadem ratione maior quam G H, & <lb></lb>ſic de cæteris. </s> <s id="id.001099">Igitur ſi chorda rectas, &c. </s> <s id="id.001100">quod fuit <expan abbr="demonſtrandũ">demonſtrandum</expan>. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001101">Itaque mouetur nauis.] <emph type="italics"></emph>Cauſa efficiens motum nauis actua<lb></lb>riæ, & modus quo efficitur, hic exprimitur eſſe impulſio remi à re<lb></lb>mige, mouente animato. </s> <s id="id.001102">Modus eſt cum remi palmula aquam ingreſ<lb></lb>ſa, & aquæ ob ſui copiam, tanquam ſolo, firmiter renitenti innixu <lb></lb>manubrium antrorſum propellitur à remige, & proinde totus remus <lb></lb>vnum continuum & validum inflexileque exiſtens, excepto palmu<lb></lb>læ extremo quod ob aquæ renixum vtcumque immobile manet, & <lb></lb>per conſequens alligata remo, eò quò manubrium, promouentur. <lb></lb></s> <s id="id.001103">Nauis autem per ſcalmum alligata eſt remo. </s> <s id="id.001104">Nauis igitur promouebi<lb></lb>tur antrorſum, ſi eò manubrium <expan abbr="promotũ">promotum</expan> ſit. </s> <s id="id.001105">Dixi ſi eò manubrium <lb></lb>promotum ſit, quia concitato nauigio, quum remiges inhibent, contra <lb></lb>fit. </s> <s id="id.001106">Manubrium ſiquidem mouetur retrorſum, proinde vna cum eo <lb></lb>& nauis. </s> <s id="id.001107">Ad huius rei fidem locus eſt apud Tullium luculentus. <lb></lb></s> <s id="id.001108">Nunc vt ad rem redeam, inquit, inhibere illud tuum, quod valde <lb></lb>mihi arriſerat, vehementer diſplicet. </s> <s id="id.001109">Eſt enim verbum totum nauti<lb></lb>cum: quanquam id quidem ſciebam: ſed arbitrabar ſuſtineri remos, <lb></lb>quum inhibere eſſent remiges iußi. </s> <s id="id.001110">Id non eſſe eiuſmodi, didici heri, <lb></lb>quum ad villam noſtram nauis appelleretur: non enim ſuſtinent, ſed <lb></lb>alio modo remigant, id ab<emph.end type="italics"></emph.end> <foreign lang="el">e)poxh=s</foreign> <emph type="italics"></emph>remotißimum eſt. </s> <s id="id.001111">Et poſtea ſubdit. <lb></lb></s> <s id="id.001112">Inhibitio autem remigum motum habet, & <expan abbr="vehemẽtiorem">vehementiorem</expan> quidem <emph.end type="italics"></emph.end><pb xlink:href="035/01/110.jpg" pagenum="70"></pb><emph type="italics"></emph>remigationis nauem conuertentis ad puppim. </s> <s id="id.001113">Hæc Cicero. </s> <s id="id.001114">quæ non <lb></lb>abs re vt arbitror hîc ſunt inſerta, vt quæ plurimum faciant <lb></lb>ad intelligendum e motibus nauis duos rectos concitationem ſci<lb></lb>licet, & inhibitionem, & vtramque fieri à remo tanquam à <lb></lb>vecte. </s> <s id="id.001115">non tamen vt antea vecte, in quo eius altero extre<lb></lb>mo per vim mouentem depreſſo, eleuetur alterum: ſed in quo cum <lb></lb>eius alterum extremum ſurſum tollatur, alteri ſubiecta aqua renita<lb></lb>tur, & hypomochlij vicem præſtet: non ſcalmus. </s> <s id="id.001116">Scalmus enim non <lb></lb>manet: ſed transfertur vna cum naui, quod eſt contra naturam cen<lb></lb>tri, quale repreſentat id, quod pro hypomochlio eſt. </s> <s id="id.001117">Et aquæ pars exci<lb></lb>piens palmulam, qua patet in latum, vt reuera moueatur: motus ta<lb></lb>men hic vel eſt exiguus, & pro nullo ideo cenſendus: vel retrocedit, <lb></lb>ſed minus quam ſcalmus procedat, vt poſtea demonſtrabitur. </s> <s id="id.001118">Erit <lb></lb>igitur pro centro, neque etiam nautis animus eſt mare: ſed nauem <lb></lb>tanquam pondus propellere. </s> <s id="id.001119">Neque minus interea verum erit, quod <lb></lb>qui in medio mari remigant, ipſam plus propellant. </s> <s id="id.001120">Sed quid dice<lb></lb>mus Aristoteli & Vitruuio qui apertè dicunt ſcalmum eſſe hypo<lb></lb>mochlium, & mare pondus mouendum. </s> <s id="id.001121">Certè ſi ſedulo attendamus, <lb></lb>remigatio vna non vnus eſt ſimplex remi motus: ſed ex quatuor di<lb></lb>uerſis compoſitus. </s> <s id="id.001122">In horum primo palmula extra aquam educitur <lb></lb>depreſſo manubrio: in ſecundo ſuper aquam antrorſum palmula pro<lb></lb>mouetur adducto ad remigem manubrio: in tertio palmula in aquam <lb></lb>demergitur eleuato manubrio: in postremo palmula retrorſum adi<lb></lb>gitur impulſo totis viribus antrorſum manubrio. </s> <s id="id.001123">Atque hi motus <lb></lb>quia nulla valde ſenſibili interpoſita mora fiunt, vnus quaſi circula<lb></lb>ris eſſe videntur: diuerſi tamen ſunt terminis ad quos & à quibus <lb></lb>remus mouetur, & cauſis. </s> <s id="id.001124">Quia in tribus prioribus ſcalmus mani<lb></lb>feſtè eſt hypomochlium, pondus mouendum eſt aqua, vel pars extre<lb></lb>ma remi cum eſt extra aquam. </s> <s id="id.001125">De his igitur poteſt intelligi Ariſto<lb></lb>teles tum Vitruuius. </s> <s id="id.001126">At in quarto aqua renitens palmulæ eſt hypo<lb></lb>mochlium, nauis vero pondus mouendum, vt diximus. </s> <s id="id.001127">Si quis tamen <lb></lb>etiam de hoc poſtremò remi motu velit ſenſiſſe Ariſtotelem non re<lb></lb>luctabor, dummodo concipiat mare pondus quidem mouendum: ſed <lb></lb>quod ob renixum quaſi immobile faciat, vt ſcalmus circa quem tan<lb></lb>quam centrum remus voluitur, cedat loco & promoueatur. </s> <s id="id.001128">Sicque <lb></lb>nauta aliquid faciet quod non quærit, vt aliud conſequatur: mare <emph.end type="italics"></emph.end><pb xlink:href="035/01/111.jpg" pagenum="71"></pb><emph type="italics"></emph>ſcilicet mouebit, vt per antiperiſtaſim inſuper recollectum nauim ex <lb></lb>parte, qua recolligitur, propellat. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001129">Eo vbi eſt.] <emph type="italics"></emph>Non quidem ſemper antrorſum iuſtè ad perpendi<lb></lb>culum: ſed paulo vltra aut citra, pro vt mouens validius: aut imbe<lb></lb>cillius mouet manubrium, & aqua plus, minuſve renititur pauca <lb></lb>enim & tenuis minus: multa & craſſa magis renititur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001130">Vbi enim remus.] <emph type="italics"></emph>Illuſtratio eſt ſecundæ partis propoſitionis <lb></lb>primarij ſyllogiſmi vbi<emph.end type="italics"></emph.end> <foreign lang="el">plei/sthn qa/lassan th\n kw/phn diairei=n. </foreign><emph type="italics"></emph>Re<lb></lb>mum diuidere plurimum maris dici poteſt duobus modis, vno cum <lb></lb>palmula profundius ingrediatur mare. </s> <s id="id.001131">Penetrans enim pedes duos <lb></lb>plus diuidit penetrante vnum: altero cum palmulæ pars intrà aquam <lb></lb>in vno remi impulſu maius ſpatium conficit: vtroque autem modo <lb></lb>palmula mediani remigis plus diuidit mare <expan abbr="quã">quam</expan> <expan abbr="aliorũ">aliorum</expan>. </s> <s id="id.001132">Primo enim <lb></lb>quia pars nauis media eò, quod depreſſa, reddit ſuum ſcalmum aquæ <lb></lb>valde propinquum, & huius remi pars à ſcalmo ad palmulam fere <lb></lb>tota eſt in aqua. </s> <s id="id.001133">Non ita eſt de ſcalmis aliorum cum puppis & prora <lb></lb>paulò ſublimiores ſint lateribus. </s> <s id="id.001134">De altero dicetur poſtea amplius <lb></lb>quia radij maioris peripheria maior eſt. </s> <s id="id.001135">Eſt autem palmula eorum <lb></lb>qui ſunt in medio nauis, quæ intra aquam, radius maior: quam pal<lb></lb>mula aliorum, & ſic maius ſpatium peragrat. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001136">Propter id remiges.] <emph type="italics"></emph>Concluſio eſt primarij ſyllogiſmi cum <lb></lb>repetione cauſæ eiuſdem. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001137">6. <foreign lang="el">*tou= phdali/ou duna/mews <lb></lb>ai)/tion, kai\ tou= ma=llon proe/r<lb></lb>xesqai ei)s tou)nantioon to\ <lb></lb>ploi=on, h)\ th\n th=s kw/phs <lb></lb> pla/thn. </foreign></s> </p> <p type="main"> <s id="id.001138">6. Potentiæ gubernaculi <lb></lb>cauſa, & quod <expan abbr="nauigiũ">nauigium</expan> <lb></lb>magis in <expan abbr="contrariũ">contrarium</expan> pro<lb></lb>cedat: quam remi pal<lb></lb>mula. </s> </p> <p type="main"> <s id="id.001139"><foreign lang="el">*dia\ ti/ to\ phda/lion mikro\n o)/n, kai\ e)p' e)sxa/tw| tw=| <lb></lb>ploi/w|, tosau/thn du/namin e)/xei w(/ste u(po\ mikrou= oi)/akos, kai\ <lb></lb>e(no\s a)nqrw/pou duna/mews, kai\ tau/ths h)remai/as, mega/la kinei=sqai <lb></lb>mege/qh ploi/wn, h)\ dio/ti kai\ to\ phda/lion e)sti\ moxlo\s, <lb></lb>to\ de\ ba/ros h( qa/lassa, o( de\ kubernh/ths o( kinw=n.</foreign></s> <s id="g0130503"><foreign lang="el"><lb></lb>ou) kata\ pla/tos de\ lamba/nei th\n qa/lassan, w(/sper h( kw/ph, <lb></lb>to\ phda/lion. ou) ga\r ei)s to\ pro/sqen kinei= to\ ploi=on, a)lla\ <lb></lb>kinou/menon kli/nei, plagi/ws th\n qa/lattan dexo/menon.</foreign></s> <s id="g0130504"><foreign lang="el">e)pei\ <lb></lb>ga\r to\ ba/ros h)=n h( qa/lassa, tou)nanti/on a)pereido/menon kli/nei <lb></lb>to\ ploi=on. to\ ga\r u(pomo/xlion ei)s tou)nanti/on stre/fetai,<lb></lb> h( qa/lassa de\ e)nto/s: e)kei=no de\ ei)s to\ e)kto/s. tou/tw| de\ a)kolouqei= <lb></lb>to\ ploi=on, dia\ to\ sundede/sqai.</foreign></s> <s id="g0130505"><foreign lang="el">h( me\n ou)=n kw/ph kata\ <lb></lb>pla/tos to\ ba/ros w)qou=sa kai\ u(p' e)kei/nou a)ntwqoume/nh, ei)s to\ <lb></lb>eu)qu\ proa/gei.</foreign></s> <s id="g0130505a"><foreign lang="el">to\ de\ phda/lion, w(/sper ka/qhtai pla/gion, <lb></lb>th\n ei)s to\ pla/gion, h)\ deu=ro, h)\ e)kei= poiei= ki/nhsin.</foreign></s> </p> <p type="main"> <s id="id.001140">Cur gubernaculum par<lb></lb>uum quid exiſtens, & in <lb></lb>extrema parte nauigij tan<lb></lb>tam vim habet, vt ab exi<lb></lb>guo temone, & vnius ho<lb></lb>minis etiam propemodum <lb></lb>quieſcentis viribus, magnæ <pb xlink:href="035/01/112.jpg" pagenum="72"></pb><expan abbr="nauigiorũ">nauigiorum</expan> moles mouean<lb></lb>tur? </s> <s id="id.001141">An quia <expan abbr="gubernaculũ">gubernaculum</expan> <lb></lb>eſt vectis: pondus mare, gu<lb></lb>bernator mouens. </s> <s id="id.001142">Non au<lb></lb>tem <expan abbr="ſecũdum">ſecundum</expan> latitudinem <lb></lb><expan abbr="gubernaculũ">gubernaculum</expan> impellit ma<lb></lb>re, vt remus. </s> <s id="id.001143">Neque enim <lb></lb>nauim mouet in anterio<lb></lb>rem partem: ſed mare in <lb></lb>tranſuerſum accipiens <expan abbr="ipsã">ipsam</expan> <lb></lb>commotam obliquat. </s> <s id="id.001144">quia <lb></lb>enim mare pondus erat ad <lb></lb>contrarium incumbens in<lb></lb>clinat nauim. </s> <s id="id.001145">Ipſum enim <lb></lb>hypomochlium in contra<lb></lb>rium vertitur, mare <expan abbr="quidẽ">quidem</expan> <lb></lb>intrò: illud verò foras: & il<lb></lb>lud ſequitur nauis, quia illi <lb></lb>eſt alligata. </s> <s id="id.001146">Igitur remus <lb></lb>ſecundum latitudinem im<lb></lb>pellens pondus, & ab illo <lb></lb>contra repulſus in rectum <lb></lb>agit: at <expan abbr="gubernaculũ">gubernaculum</expan> quaſi <lb></lb><expan abbr="trãſuerſum">tranſuerſum</expan> iaceat, in tranſ<lb></lb>uerſum etiam hinc inde motionem facit. </s> </p> <p type="head"> <s id="id.001147">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001148">Potentiæ guber.] <emph type="italics"></emph>In hoc capite proponuntur tria ſpecialia de <lb></lb>vecte problemata quorum duo ſunt de gubernaculo & tertium <lb></lb>de remo. </s> <s id="id.001149">Primum eſt cur gubernaculum, paruum cum ſit, magnam <lb></lb>nauigij molem moueat. </s> <s id="id.001150">Et huic differentia quæ eſt inter remi & gu<lb></lb>bernaculi motiones ſubijcitur. </s> <s id="id.001151">Secundum cur gubernaculum in puppi <lb></lb>non in medio aut prora nauis collocetur. </s> <s id="id.001152">Tertium cur nauigium an<lb></lb>trorſum plus procedat, quam remi palmula retrorſum. </s> <s id="id.001153">Atque hæc eo <lb></lb>ordine quo propoſita ſunt, diſſoluentur. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/113.jpg" pagenum="73"></pb> <p type="main"> <s id="id.001154">Gubernaculum.] <emph type="italics"></emph>Gubernaculum remus erat apud antiquos, <lb></lb>ſed multo latioris palmulæ: quam remi, quibus ad latera nauis remi<lb></lb>gabant. </s> <s id="id.001155">Ob id pterigion ab alæ extenſæ ſimilitudine vel latitudine <lb></lb>dicta eſt. </s> <s id="id.001156">Reliqua pars inſtar grandioris pali temo dicitur, qui ad ex<lb></lb>tremum in puppi cardinem retentus, conuoluitur ad obliquandum <lb></lb>nauim. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001157">Cur gubernaculum.] <emph type="italics"></emph>Propoſitio eſt problematis in duas par<lb></lb>tes à nobis antea ſubdiuiſi, vt & Ariſtoteles poſtea ſubdiuidendo <lb></lb>diſſoluit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001158">Vt ab exiguo temone.] <emph type="italics"></emph>Propoſiti problematis admiratio au<lb></lb>getur, ex parte mouentis quidem tripliciter, quod motor ſit vnus ho<lb></lb>mo, ſit propemodum nihil agens, Cicero ludentem poſuit, vtatur ad <lb></lb>id quod facere vult, exiguo inſtrumento nempè temone, vt qui ſem<lb></lb>per breuior ſit longißimo remorum: ex parte vero rei motæ, nempè <lb></lb>totius nauigij, & omnium, quæ <expan abbr="vehẽda">vehenda</expan> naui impoſita ſunt. </s> <s id="id.001159">Quæ, vt <lb></lb>ijs qui viderunt omnia, manifeſtißima ſunt: ita ijs qui non viderunt <lb></lb>incredibilia. </s> <s id="id.001160">præſertim ſi ex antiquorum monumentis <expan abbr="repetãt">repetant</expan>, quan<lb></lb>ta à quibuſdam conſtructa ſunt nauigia è quibus vnum ex Athe<lb></lb>næo placet hîc attexere, vt ex eo diſcant omnes <expan abbr="quãtam">quantam</expan> molem vnus <lb></lb>homo temone exiguo dimouere poßit. </s> <s id="id.001161">Longa eſt, ſed vt ſpero, omni<lb></lb>bus lectu <expan abbr="iucũda">iucunda</expan> hiſtoria. </s> <s id="id.001162">Recitat igitur Athenæus <expan abbr="Hieronẽ">Hieronem</expan> Syra<lb></lb>cuſanorum Regem ad naues fabricandum ambitiosà animum inten<lb></lb>diſſe, & vnam imprimis memorabilem perfeciſſe, ad quam ædifi<lb></lb>candam, materiam in AEtna monte cædendam, indeque deuehen<lb></lb>dam curauiſſe, quæ ſexaginta triremibus conficiendis ſatis eſſe potuiſ<lb></lb>ſet. </s> <s id="id.001163">quo dicto nauigij magnitudinem conijciendam nobis reliquit. <lb></lb></s> <s id="id.001164">Ad nauticum autem inſtrumentum cum æs, ferrum, cannabim, reli<lb></lb>quaque, quibus opus erat, partim ex Italia, partim ex Iberia, partim <lb></lb>Rhodano flumine comparaſſet, trecentos operi faciendo fabros, arti<lb></lb>ficeſque adhibuiſſe: ac materiæ dedolandæ præter adminiſtros fabri<lb></lb>cæ ſubſeruientes opificijs, præfecto ſummæ operis architecto Archia <lb></lb>Corinthio. </s> <s id="id.001165">Quos ipſe cum magnopere hortatus eſſet ad opus aggre<lb></lb>diendum, inſuper etiam dies totos operis ſe curatorem, exactoremque <lb></lb>præbuiſſe: hac diligentia, his artificibus, hoc architecto, Regem ta<lb></lb>men illum dimidium tantum nauis intra ſex menſes perfeciſſe. </s> <s id="id.001166">Quo <lb></lb>facto inchoatam eo modo nauem in mare deducendam mandaſſe: vt <emph.end type="italics"></emph.end><pb xlink:href="035/01/114.jpg" pagenum="74"></pb><emph type="italics"></emph>illìc extremæ manus opificium adipiſceretur. </s> <s id="id.001167">Hac deducta alteram <lb></lb>nauigij partem totidem alijs menſibus Hieronem <expan abbr="cõſummaſſe">conſummaſſe</expan>. </s> <s id="id.001168">Cum <lb></lb>interim clauis æreis denarum librarum plurimis materiam compin<lb></lb>geret, aliquibus etiam ſeſquiplis eius ponderis, qui præ craßitudine. <lb></lb></s> <s id="id.001169">non alias adigi poterant: quam materia perterebrata. </s> <s id="id.001170">His clauis coſtæ <lb></lb>nauis arrectariæ cum aſſamentis tranſuerſarijs coagmentatæ, tegulis <lb></lb>inſuper plumbeis adactis validius aſtringebantur, quibus etiam ſub <lb></lb>ipſis linteola concerpta cum pice infarcta erant. </s> <s id="id.001171">Erat rurſus, inquit <lb></lb>ille, ea nauis apparatu quidem viginti ordinum remigij: ædificij vero <lb></lb>contignatione triplici. </s> <s id="id.001172">Harum infimam contignationem oneri & <lb></lb>mercibus delegauerat, ad quam deſcenſus ſcalis multiplicibus erat: <lb></lb>ad mediam contignationem tranſitus alter erat arte Mechanica fa<lb></lb>ctus, in qua ipſa cœnationes erant numero triginta <expan abbr="ſecundũ">ſecundum</expan> vtrum<lb></lb>que latus nauigij extructæ. </s> <s id="id.001173">In ijs lecti quaterni ſtrati viris accom<lb></lb>modati: inter quas nauclericum conclaue quinque lectorum capax <lb></lb>erat. </s> <s id="id.001174">Præterea thalami tres in eadem contignatione erant, culinaque <lb></lb>ſupradictis locis ſubſeruiens ad puppim ædificata. </s> <s id="id.001175">Omnes autem ſu<lb></lb>pradictæ cœnationes pauimento ſtratæ erant teſſellis vermiculato <lb></lb>lapidis omnis generis. </s> <s id="id.001176">In eo pauimento Troiani belli fabulamentum <lb></lb>viſendo artificio concinnatum legebatur, cum alioquin ea omnia <lb></lb>ædificia tectis laqueatis, & poſtibus exornata ſpectabili opere eſſent. <lb></lb></s> <s id="id.001177">Summa pars nauigij gymnaſium habebat ambulationeſque laxas, <lb></lb>proportione magnitudinis ſuæ, quas etiam ipſas ſimul ambientes hor<lb></lb>ti omni genere <expan abbr="ſtirpiũ">ſtirpium</expan> complectebantur, fictilibus in vaſis & plum<lb></lb>beis conſitorum, ſimul hederæ viteſque opacabant pampinis, ac co<lb></lb>rymbis inumbrantes, quarum radices <expan abbr="alebãt">alebant</expan> dolia terræ plena: pari<lb></lb>ter quidem illæ cum hortis machinamento irriguæ. </s> <s id="id.001178">Ab his erat <lb></lb>Aphrodiſium id eſt conclaue Veneri deæ dicatum: inſtrumentum <lb></lb>etiam ipſum triclínari lectiſternio, pauimentoque ſtratum achate la<lb></lb>pide alijſque varijs & nitentibus diſtincto. </s> <s id="id.001179">Cuiuſmodi lapidum co<lb></lb>pia in Sicilia reperitur. </s> <s id="id.001180">Ac parietes quidem habebat cupreßinis ta<lb></lb>bulis aßibuſque contextos, laqueatumque tectum eadem materia. </s> <s id="id.001181">Fo<lb></lb>res etiam ex ebore & odorata materia compactas, atque eo amplius <lb></lb>pictura ſigilliſque exornatas. </s> <s id="id.001182">Deinceps erat exhedra quinque lecto<lb></lb>rum capax, quorum parietes poſteſque buxo compacti <expan abbr="erãt">erant</expan>, inibique <lb></lb>bibliotheca, & in lacunari ſphæra ad <expan abbr="imitationẽ">imitationem</expan> eius ſolarij effecta,<emph.end type="italics"></emph.end><pb xlink:href="035/01/115.jpg" pagenum="75"></pb><emph type="italics"></emph>quod in Achradina ſitum erat, quæ inſula eſt Syracuſarum. </s> <s id="id.001183">Huic <lb></lb>loco balneum iunctum erat, in quo tres lecti cum ſolio metretarum <lb></lb>quinque capaci, quod ex lapide vario ſcalptum erat, & tribus æneis <lb></lb>Caldarijs. </s> <s id="id.001184">Mitto nunc habitationes militibus deſtinatas: iiſque qui <lb></lb>ſuper ſentinam erant. </s> <s id="id.001185">Mitto equorum præſepia ab vtroque latere na<lb></lb>uigij numero dena ſita cum frænis & ſtratis, & omni equitum in<lb></lb>ſtrumento, eorumque miniſterij atque equorum pabulo. </s> <s id="id.001186">Præterea li<lb></lb>gnarium, & clibanos focos, & piſtrina, aliaque miniſteria in proie<lb></lb>cturis nauis prominentia. </s> <s id="id.001187">Quid dicam Athlantes nouenûm pedum <lb></lb>altitudinis certis interſtitiis firmatos, vt ſcalpturas <expan abbr="prominẽtes">prominentes</expan> ſum<lb></lb>mæ contignatiònis mutulorum vice fulcirent? </s> <s id="id.001188">Quid turres octo? <lb></lb></s> <s id="id.001189">binas in prora & puppi per vtrumque latus extructas, in muriſque <lb></lb>propugnacula. </s> <s id="id.001190">Præter hæc machina erat in medio cataſtromate ſuper <lb></lb>tripodes excitata, Archimedis inuentum ſaxa tritalantaria, telaque <lb></lb>mißilia duodeuiginti pedum facile eiaculans ad quadringentos cu<lb></lb>bitos, quod ſpatium eſt ſtadij. </s> <s id="id.001191">Hæc & alia machinamenta propu<lb></lb>gnatoria vt coruos, lupos, & in ſummo malo carcheſia, ænea <expan abbr="lapidũ">lapidum</expan> <lb></lb>conceptacula ad lapidationem faciendam in hoſtium nauigia, lon<lb></lb>gum eſſet enarrare. </s> <s id="id.001192"><expan abbr="Stabãt">Stabant</expan> enim in vno terni: in alijs bini aut ſingu<lb></lb>li homines lapides eiaculantes, quos ſerui in foris nauis ſtantes viti<lb></lb>libus quallis tempore pugnæ ſuggerebant trochleis ſubuehentes. </s> <s id="id.001193">Sed <lb></lb>vt & huius nauigij magnitudo vaſtitas ac onus animo amplius con<lb></lb>cipi poßit, inſuper adijciam tam multis nonnulla, quæ Athenæus <lb></lb>ſcripſit ad hoc maxime pertinentia. </s> <s id="id.001194">Erat, inquit, in eodem nauigio <lb></lb>ſecundum proram aquæ conceptaculum concluſum capax duorum <lb></lb>milium metretarum aſſamentis & pice & linteorum farctura com<lb></lb>pactile, iuxta quod rurſus piſcina coaxatione & implumbatura <lb></lb>conſtans plena aquæ marinæ. </s> <s id="id.001195">Ita vt in ea commode magna copia <lb></lb>piſcium facile aleretur. </s> <s id="id.001196">Idem alibi frumentum negociatorium in <lb></lb>ea naui exportabant ad millia ſexaginta: ſalſamenta Sicula ad ca<lb></lb>dum decem millia: lanarum talenta viginti millia, & alterius mer<lb></lb>cis altera viginti millia, prætereáque commeatus vectorum nauta<lb></lb>rumque ſexaginta millia. </s> <s id="id.001198">Horum omnium onus, cum Budæus exqui<lb></lb>ſitè perſequitur, comperit ſummam librarum ad quinque & ſeptua<lb></lb>ginta millia excreſcere præter aquam dulcem, præter piſcinam, præ<lb></lb>ter tot dietarum inteſtinum inſtrumentum, præter annonam vecto<emph.end type="italics"></emph.end><pb xlink:href="035/01/116.jpg" pagenum="76"></pb><emph type="italics"></emph>rum, & pabulum equorum, præter denique onus tanti nauigij. </s> <s id="id.001199">Quo<lb></lb>modo igitur non erit admirabile tantam molem vnius hominis vi <lb></lb>propemodum quieſcentis exiguo temone dimoueri & obliquari: atque <lb></lb>hæc de propoſitione dicta ſunto. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001200">An quia gubernaculum.] <emph type="italics"></emph>Solutio eſt primi problematis, ſic. <lb></lb></s> <s id="id.001201">Vecte magna mouentur pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001202"><emph type="italics"></emph>Gubernaculum eſt vectis ( in eo enim cardo ad quem alligatur <lb></lb>eſt centrum: pondus <expan abbr="mouendũ">mouendum</expan> eſt mare: <expan abbr="mouẽs">mouens</expan> gubernator. <emph.end type="italics"></emph.end>)</s> </p> <p type="main"> <s id="id.001203"><emph type="italics"></emph>Ergo gubernaculo nauigij moles mouebitur. </s> <s id="id.001204">De hoc na<lb></lb>uis motu pulchre. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001205"><emph type="italics"></emph>Vitruuius ſic mentionem facit. </s> <s id="id.001206">Nauis onerariæ maximæ guber<lb></lb>nator anſam gubernaculi tenens, quod<emph.end type="italics"></emph.end> <foreign lang="el">o)/iac</foreign> <emph type="italics"></emph>à Græcis ap<lb></lb>pellatur, vna manu momento per centri rationem preßioni<lb></lb>bus artis agitans, verſat eam amplißimis & immanibus <lb></lb>mercis & penus ponderibus oneratam. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001207">Pondus mare.] <emph type="italics"></emph>Vt antè in remis dictum eſt. </s> <s id="id.001208">pondus quod mo<lb></lb>uere intendit gubernator non eſt mare: licet parum impellatur, ſed <lb></lb>nauis. </s> <s id="id.001209">It aque mouet gubernaculum, cuius pterigion latißimum intra <lb></lb>aquam, ob eius copiam firmum manet: & ſic temo ad contrariam <lb></lb>partem impulſus ſibi in cardine alligatam nauis puppim impellit, <lb></lb>quod etiam paulo poſt Ariſtoteles dicet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001210">Non autem ſecundum.] <emph type="italics"></emph>Dißimilitudo eſt gubernaculi & <lb></lb>remi ex differenti loco ad quem vtrumque nauim mouet. </s> <s id="id.001211">Vtrumque <lb></lb>enim nauim mouet ad locum, qui contrarius eſt ei, ad quem mare im<lb></lb>pulſum mouetur. </s> <s id="id.001212">Mouetur enim nauis ad centri, cui eſt annexa, mo<lb></lb>tum. </s> <s id="id.001213">Centrum <expan abbr="autẽ">autem</expan> in remo eſt ſcalmus, in gubernaculo cardo. </s> <s id="id.001214">Mo<lb></lb>uetur hoc contra quam depulſum mare. </s> <s id="id.001215">Mare autem retrorſum rectà <lb></lb>à remo depellitur: mouet igitur remus rectà antrorſum nauim. </s> <s id="id.001216">Con<lb></lb>trà mare à gubernaculo obliquè impellitur, vel dextrorſum vel ſini<lb></lb>ſtrorſum. </s> <s id="id.001217">Mouet igitur obliquè nauim ( quod eſt intelligendum de <lb></lb>puppi non de prora quæ in partem ad quam mare mouetur ) ſini<lb></lb>ſtrorſum, ſi illud dextrorſum: vel dextrorſum, ſi illud ſiniſtrorſum <lb></lb>depulſum eſt. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/117.jpg" pagenum="77"></pb> <p type="main"> <s id="id.001218"><foreign lang="el">e)p' a)/krou <lb></lb>de\ kai\ ou)k e)n me/sw| kei=tai, o(/ti r(a=|ston to\ kinou/menon kinh=sai <lb></lb>a)p' a)/krou kinou=n: ta/xista ga\r fe/retai to\ prw=ton me/ros, <lb></lb>dia\ to\ w(/sper e)n toi=s ferome/nois e)pi\ te/lei lh/gein th\n fora/n, <lb></lb>ou(/tw kai\ tou= sunexou=s e)pi\ te/lous a)sqenesta/th e)sti\n h( fora/. <lb></lb></foreign></s> <s id="g0130507a"><foreign lang="el">h( de\ a)sqenesta/th r(a|di/a e)kkrou/ein. </foreign></s> <s id="g0130508"><foreign lang="el">dia/ te dh\ tau=ta e)n th=| <lb></lb>pru/mnh| to\ phda/lio/n e)sti, kai\ o(/ti e)ntau=qa mikra=s kinh/sews <lb></lb>genome/nhs pollw=| mei=zon to\ dia/sthma e)pi\ tw=| e)sxa/tw| gi/netai, <lb></lb>dia\ to\ th\n i)/shn gwni/an e)pi\ mei/zona kaqh=sqai.</foreign></s> <s id="g0130508a"><foreign lang="el">kai\ o(/sw| <lb></lb>a)\n mei/zous w)=sin ai( perie/xoustai.</foreign></s> </p> <p type="main"> <s>In extremo autem, non <lb></lb>in medio poſitum eſt. </s> <s id="id.001220">quia <lb></lb>motor, id quod iam moue<lb></lb>tur, facillime ab extremo <lb></lb><expan abbr="cõmouet">commouet</expan>. </s> <s id="id.001221">Celerrime enim <lb></lb>fertur nauis prior pars, <lb></lb>Quoniam vt in ijs quæ mo<lb></lb>uentur, ad finem latio defi<lb></lb>cit: ſic ipſius continui in ex<lb></lb>tremo latio imbecillima <lb></lb>eſt. </s> <s id="id.001222">Eſt autem imbecillima <lb></lb>facilis repulſu. </s> <s id="id.001223">Propterea <lb></lb>gubernaculum in puppi ſi<lb></lb>tum eſt. </s> <s id="id.001224">Et quoniam exi<lb></lb>gua in ea motione facta, <lb></lb>multo maior in prora fit in<lb></lb>tercapedo. </s> <s id="id.001225">Angulus enim <lb></lb>æqualis à maiori ſubtendi<lb></lb>tur, & quanto maiores quæ <lb></lb>angulum comprehenderunt lineæ. </s> </p> <p type="head"> <s id="id.001226">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001227">In extremo autem.] <emph type="italics"></emph>Solutio eſt ſecundi problematis duplex, <lb></lb>ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001228"><emph type="italics"></emph>Ibi collocandum gubernaculum, vbi per ipſum motor facilius <lb></lb>& plus nauim mouere poteſt: & vbi ex minore puppis, mu<lb></lb>tatione, maior proræ mutatio adfertur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001229"><emph type="italics"></emph>Sed in puppi gubernaculo collocato gubernator facilius nauim <lb></lb>contorquet, & ex parua puppis mutatione magna proræ ad<lb></lb>fertur mutatio. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001230"><emph type="italics"></emph>Ergo in puppi non in medio gubernaculum collocandum eſt. <lb></lb></s> <s id="id.001231">Ob id etiamſi e piſcibus quidam parte anteriori homini & quadra<lb></lb>pedibus ſimiles ſunt, vt <expan abbr="Tritõ">Triton</expan>, Nereis, elephas, & vitulus: poſteriore <lb></lb>tamen omnes in caudam bifidam deſinunt, paucis admodum exce<lb></lb>ptis, atque id non ob aliam cauſam quam quod, velut in nauis puppi <lb></lb>temo nauim dirigit: Ita piſcis iter cauda. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/118.jpg" pagenum="78"></pb> <p type="main"> <s id="id.001232">Quia motor.] <emph type="italics"></emph>Syllogiſmi præcedentis propoſitio nec poſita, <lb></lb>nec illuſtrata eſt. </s> <s id="id.001233">quia ex ſe euidens. </s> <s id="id.001234">Pro aſſumptione vero hîc prioris <lb></lb>eius partis illuſtratio ponitur, ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001235"><emph type="italics"></emph>Non reſiſtentia, aut minus reſiſtentia, mouere facilius eſt. <lb></lb></s> <s id="id.001236">Vbi autem eſt finis rei motæ ( eſt autem in puppi nauis, non in <lb></lb>eius medio, nec in prora ) ibi reſiſtentia vel nulla vel minor. <lb></lb></s> <s id="id.001237">Contra vbi celerrime mouetur, vt in prora, aut celerius, vt in <lb></lb>medio, ibi maior eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001238"><emph type="italics"></emph>Ergo in puppi nauim mouere facilius eſt: quam in medio, aut in <lb></lb>prora. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001239">Quoniam vt in ijs.] <emph type="italics"></emph>Similitudo eſt ad illuſtrandam præce<lb></lb>dentis ſyllogiſmi aſſumptionem, ſic. </s> <s id="id.001240">Quemadmodum eorum quæ vi <lb></lb>feruntur latio ad finem deficit, & imbecillior eſt: ſic continui lati <lb></lb>extremum imbecillius mouetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001241">Et quoniam exigua.] <emph type="italics"></emph>Similis ſententia eſt apud Ariſtotelem <lb></lb>lib. de animalium motu. </s> <s id="id.001242">Nec vero dubium eſt, inquit, quin parua ad<lb></lb>modum initio facta mutatione in corpore multiplices è longinquo <lb></lb>varietates ſuboriantur, vt cum per temonem paululum tralatum <lb></lb>longè diuerſa proræ poſitio viſitur. </s> <s id="id.001243">Atque hæc eſt altera cauſa cur <lb></lb>gubernaculum in puppi ponitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001244">Angulus enim æqualis.] <emph type="italics"></emph>Licet oculata alioquin fide perci<lb></lb>piatur quanta & quam euidens nauigij temone paulùm vixque con<lb></lb>torto ipſius proræ ſtatim tranſpoſitio multo maior conſequatur: ta<lb></lb>men & id geometrica propoſitione confirmatur quæ imperfecta eſt <lb></lb>ſed ſic perfici poteſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001245"><emph type="italics"></emph>Si duo Iſoſcelia æqualia angulis, inæqualium crurum fuerint: <lb></lb>erunt & inæqualia <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.118.1.jpg" xlink:href="035/01/118/1.jpg"></figure><lb></lb><emph type="italics"></emph>baſibus: & huius ba<lb></lb>ſis maior, cuius crura <lb></lb>maiora. </s> <s id="id.001246">Sint A B E <lb></lb>& A D C duo iſoſ<lb></lb>celia æqualia angulis <lb></lb>qui ad A, & A D <lb></lb>crus eſto maius crure <lb></lb>A B ſicut & A C <lb></lb>ipſo A E. </s> <s id="id.001247">Dico baſim D C maiorem eſſe baſi B E. </s> <s id="id.001248">Nam quia <emph.end type="italics"></emph.end><pb xlink:href="035/01/119.jpg" pagenum="79"></pb><emph type="italics"></emph>tres anguli vnius triangulorum ſunt æquales tribus alterius prop. <lb></lb>32. lib. 1. </s> <s>& anguli qui ad A æquales ex hypotheſi, anguli ad ba<lb></lb>ſim duo duobus ſunt æquales ax. 3. </s> <s>& quia A D C & A C D <lb></lb>ſunt ad baſim Iſoſcelis, ij inter ſe erunt æquales prop. 5. lib. 1. & per <lb></lb>eandem anguli A B E & A E B. </s> <s id="id.001251">Sicque A E B dimidius <lb></lb>cum ſit horum <expan abbr="duorũ">duorum</expan>, angulo A C D etiam dimidio <expan abbr="æqualiũ">æqualium</expan> æqua<lb></lb>lis erit ax. 6. & per idem reliquus reliquo. </s> <s id="id.001253">Sunt igitur A B E & <lb></lb>A D C triangula æquiangula, proinde circum æquales angulos la<lb></lb>tera habebunt proportionalia. </s> <s id="id.001254">prop. 4. lib. 6. ideo vt A D ad D C: <lb></lb>ſic A B ad B E: & vicißim vt A D ad A B: ſic D C ba<lb></lb>ſis ad baſim B E prop. 16. lib. 5. </s> <s>Eſt autem maius A D ipſo A B <lb></lb>ex hypotheſi. </s> <s id="id.001256">Ergo Baſis D C maior erit ipſa B E. </s> <s id="id.001257">Igitur ſi duo <lb></lb>Iſoſcelia æqualia angulis, inæqualia cruribus fuerint &c. </s> <s id="id.001258">quod <lb></lb>fuit demonstrandum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001259"><emph type="italics"></emph>Patet igitur ex his quod cum B C ſit vt longitudo nauis, ſi pup<lb></lb>pis B peruenerit ad E manente A cardine. </s> <s id="id.001260">Tunc C erit in D. <lb></lb></s> <s id="id.001261">Sicque fiunt duo triangula Iſoſcelia A B E & A D C æqualia <lb></lb>angulis ad verticem A oppoſitis prop. 15. lib. 1. </s> <s>Et inæqualia cruri<lb></lb>bus. </s> <s id="id.001262">Nam rectæ ab A puncto Cardini reſpondente in ima parte na<lb></lb>uis propè puppis extremum ad extremum proræ id eſt A D, A C <lb></lb>longè maiores ſunt breuißimis ijs, quæ ſunt ab <expan abbr="eodẽ">eodem</expan> puncto A ad ex<lb></lb>tremum puppis A B, A E. </s> <s id="id.001263">Peragrabit igitur prora D lineam C B <lb></lb>longè maiorem, cum B peragrabit B E multo minorem. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.001264"><foreign lang="el">dh=lon de\ e)k tou/tou, kai\ di' h(\n <lb></lb>ai)ti/an ma=llon proe/rxetai ei)s tou)nanti/on to\ ploi=on h)\ h( th=s <lb></lb>kw/phs pla/th: to\ au)to\ ga\r me/geqos th=| au)th=| i)sxu/i+ kinou/menon <lb></lb>e)n a)e/ri, ple/on h)\: e)n tw=| u(/dati pro/eisin.</foreign></s> <s id="g0130510"><foreign lang="el">e)/stw ga\r h( *a <lb></lb>*b kw/ph, to\ de\ *g o( skalmo/s, to\ de\ *a to\ e)n tw=| ploi/w|, h( <lb></lb>a)rxh\ th=s kw/phs, to\ de\ *b to\ e)n th=| qala/tth|.</foreign></s> <s id="g0130511"><foreign lang="el">ei) dh\ to\ *a <lb></lb>ou(= to\ *d metakeki/nhtai, to\ *b ou)k e)/stai ou(= to\ *e: i)/sh ga\r h( *b <lb></lb>*e th=| *a*d.</foreign></s> <s id="g0130511a"><foreign lang="el">i)/son ou)=n metakexwrhko\s e)/stai, a)ll' h)=n e)/latton. <lb></lb></foreign></s> <s id="g0130512"><foreign lang="el">e)/stai dh\ ou(= to\ *z [1h)\ to\ *q. a)/ra toi/nun th\n *a*b, kai\ ou)x h( to\ <lb></lb>*g, kai\ ka/twqen.]1 </foreign></s> <s id="g0130512a"><foreign lang="el">e)la/ttwn ga\r h( *b*z, th=s *a*d, w(/ste kai\ <lb></lb>h( *q*z th=s *d*q: o(/moia ga\r ta\ tri/gwna.</foreign></s> <s id="g0130513"><foreign lang="el">kaqesthko\s de\ <lb></lb>e)/stai kai\ to\ me/son, to\ e)f' ou(= *g: ei)s tou)nanti/on ga\r tw=| e)n th=| <lb></lb>qala/tth| a)/krw| to\ *b metaxwrei=, h(=|per to\ e)n ploi/w| <lb></lb>a)/kron to\ *a.</foreign></s> <s id="g0130514"><foreign lang="el">mh\ e)gxw/rei de\ ou(= to\ *d. </foreign></s> <s id="g0130514a"><foreign lang="el">ei) mh\ metakinhqh/setai to\ <lb></lb>ploi=on, kai\ e)kei= ou(= h( a)rxh\ th=s kw/phs metafe/retai.</foreign></s> </p> <p type="main"> <s id="id.001265">Ex hoc autem <expan abbr="manifeſtũ">manifeſtum</expan> <lb></lb>eſt, ob quam cauſam nauis <lb></lb>in contrarium magis pro<lb></lb>cedat: quam remi palmula. <lb></lb></s> <s id="id.001266">Eadem enim moles eadem <lb></lb>vi mota per aerem plus, <lb></lb>quam per aquam progre<lb></lb>ditur. </s> <s id="id.001267">Sit enim remus <foreign lang="el">a b</foreign><lb></lb>& ſcalmus <foreign lang="el">g,</foreign> & intra nauim <lb></lb>caput remi <foreign lang="el">a</foreign> palmula intra <lb></lb>mare <foreign lang="el">b. </foreign>Si itaque <foreign lang="el">a</foreign> <expan abbr="tranſlatũ">tranſla<lb></lb>tum</expan> ſit eò, vbi eſt <foreign lang="el">d</foreign>: ipſum <foreign lang="el">b</foreign><pb xlink:href="035/01/120.jpg" pagenum="80"></pb><arrow.to.target n="marg21"></arrow.to.target><lb></lb>non erit vbi eſt <foreign lang="el">e. </foreign>Eſt enim <lb></lb><foreign lang="el">b e</foreign> æqualis ipſi <foreign lang="el">a d. </foreign>Ex <lb></lb>æquo igítur tranſlatum eſ<lb></lb>ſet, ſed minus erat. </s> <s id="id.001268">Eſt igi<lb></lb>tur vbi <foreign lang="el">z. </foreign>Minor enim eſt <lb></lb><foreign lang="el">b z</foreign>: <expan abbr="quã">quam</expan> <foreign lang="el">a d. </foreign>Itaque etiam <lb></lb><foreign lang="el">q z</foreign> quam <foreign lang="el">d q. </foreign></s> <s>Similia enim <lb></lb>ſunt triangula. </s> <s id="id.001269">Conſiſtens <lb></lb>vero erit medium vbi eſt <foreign lang="el">g.</foreign><lb></lb></s> <s>In contrarium enim extre<lb></lb>mo <foreign lang="el">b,</foreign> quod in mari eſt <lb></lb>procedit <expan abbr="extremũ">extremum</expan> <foreign lang="el">a,</foreign> quod <lb></lb>in nauigio eſt. </s> <s id="id.001270">Non autem <lb></lb>ad <foreign lang="el">d</foreign> procederet, niſi mo<lb></lb>ueretur nauis, & eo vbi eſt <lb></lb>caput remi, transferretur. </s> </p> <p type="margin"> <s id="id.001271"><margin.target id="marg21"></margin.target>Incluſa his <lb></lb>notis [] ni<lb></lb>hil faciunt <lb></lb>ad rem. </s> </p> <p type="head"> <s id="id.001272">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001273">Ex hoc autem.] <emph type="italics"></emph>Hic continetur tertium è tribus, quæ hoc <lb></lb>capite diximus contineri problemata. </s> <s id="id.001274">Eſt autem eiuſmodi. </s> <s id="id.001275">An <lb></lb>nauis plus antrorſum vehitur: <expan abbr="quã">quam</expan> palmula remi retrorſum. </s> <s id="id.001276">Reſpon<lb></lb>det Ariſtoteles plus vehi nauem antrorſum. </s> <s id="id.001277">Cauſam dicit. </s> <s id="id.001278">quia ea<lb></lb>dem moles eadem vi mota plus per medium rarum fertur: quam per <lb></lb>denſum. </s> <s id="id.001279">Contra quam rationem duo occurrunt aliena. </s> <s id="id.001280">Prius quod <lb></lb>moles non eſt eadem nauis & remi palmulæ: alterum quod vnum <lb></lb>idemque eſt medium vtriuſque nempe aqua. </s> <s id="id.001281">Eſt enim pars nauis im<lb></lb>merſa aquæ, quæ mouetur, vt & palmula. </s> <s id="id.001282">Dicemus igitur vt ratio <lb></lb>Ariſtotelis concludat duo aſſumenda eſſe. </s> <s id="id.001283">Primum eandem molem, <lb></lb>aut æquales moles intelligere Ariſtotelem remi caput, & palmu<lb></lb>lam: vel partem remi à ſcalmo ad caput: & partem eiuſdem à ſcalmo <lb></lb>ad palmulam. </s> <s id="id.001284">Has enim videtur hîc præſupponere æquales longitu<lb></lb>dine, ſcalmo remum bifariam ſecante: ſin minus pondere: ad æquali<lb></lb>brium enim cum pars palmulæ maior eſt, caput implumbatur vt <lb></lb>æquiponderet. </s> <s id="id.001285">Et ſic cum remus vnius vel plurium remigum viri<lb></lb>bus mouetur, caput per aërem, palmula per aquam: ſicque per diuerſa<emph.end type="italics"></emph.end><pb xlink:href="035/01/121.jpg" pagenum="81"></pb><emph type="italics"></emph>media, mouentur. </s> <s id="id.001286">Et ſic ex ratione Ariſtotelis, ſi vera eſt, caput remi <lb></lb>plus antrorſum mouebitur quam palmula retrorſum. </s> <s id="id.001287">Alterum quod <lb></lb>aſſumendum. </s> <s id="id.001288">eſt nauim tantum antrorſum moueri: quantum & re<lb></lb>mi caput. </s> <s id="id.001289">Quod ſi verum eſſet ſtatim concluſio hæc manifeſta <lb></lb>eſſet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001290"><emph type="italics"></emph>Ergo nauis plus antrorſum mouetur: quam remi palmula re<lb></lb>trorſum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001291"><emph type="italics"></emph>Syllogiſmus igitur ſic eſto,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001292"><emph type="italics"></emph>Quantum caput remi antrorſum mouetur: tantum & nauis. <lb></lb></s> <s id="id.001293">Sed caput remi plus antrorſum mouetur: quam palmula re<lb></lb>trorſum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001294"><emph type="italics"></emph>Ergo nauis plus antrorſum mouetur: quam palmula retrorſum. <emph.end type="italics"></emph.end></s> <s id="id.001295"><emph type="italics"></emph>Huius ſyllogiſmi propoſitio ſine confirmatione deſerta eſt ab Ari<lb></lb>ſtotele. </s> <s id="id.001296">Etiamſi <expan abbr="principiũ">principium</expan> non ſit. </s> <s id="id.001297">Ob id quid veritatis habeat poſtea <lb></lb>diſcutiemus. </s> <s id="id.001298">Aſſumptionis confirmatio pendet ab eo quod cum caput <lb></lb>& palmula remi ſint eadem moles eadem vi mota, illud tamen per <lb></lb>aërem: hæc per aquam medium aëre denſius, moueatur. </s> <s id="id.001299">Quæ ratio <lb></lb>verißima eſt in ijs, quæ ſeorſum mouentur, vt ſi remus totus per <lb></lb>aërem, & totus per aquam ferretur eadem vi, dubium non eſt quin <lb></lb>citius, & plus per aërem, quam per aquam, ob maiorem in aqua <expan abbr="reſiſtẽtiam">reſi<lb></lb>ſtentiam</expan> feratur. </s> <s id="id.001300">At remus vnus eſt, ſed ſuperficie aquæ ſectus, quaſi <lb></lb>duo ſint ita capi poteſt. </s> <s id="id.001301">Et certum eſt quod ſi imaginemur vim ean<lb></lb>dem in capite atque in palmula mouenda cum hæc intra aquam, illud <lb></lb>extra ſit, quod plus prouehetur illud: quam hæc. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001302">Sit enim remus.] <emph type="italics"></emph>Confirmatio eſt geometrica aſſumptionis <lb></lb>præcedentis ſyllogiſmi vbi præſupponit Ariſtoteles moueri nauim <lb></lb>antrorſum. </s> <s id="id.001303">vnde infert caput remi ab eo loco, in quo erat ante remi<lb></lb>gationem, ad alium transferri. </s> <s id="id.001304">Ergo<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>caput remi tranſlatum ſit ad<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">d.</foreign> </s> <s><emph type="italics"></emph>Quo autem tempore<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>tranſlatum eſt ad<emph.end type="italics"></emph.end> <foreign lang="el">d,</foreign> <emph type="italics"></emph>palmula<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>non <lb></lb>transfertur ad<emph.end type="italics"></emph.end> <foreign lang="el">e</foreign><emph type="italics"></emph>: alioqui æqualiter moueretur palmula atque caput, <lb></lb>contra ea quæ ante poſita ſunt. </s> <s id="id.001305">Intelligatur enim remus<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>vbi eſt<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">d e,</foreign> <emph type="italics"></emph>ſcalmo<emph.end type="italics"></emph.end> <foreign lang="el">g</foreign> <emph type="italics"></emph>manente. </s> <s id="id.001306">fiunt duo triangula<emph.end type="italics"></emph.end> <foreign lang="el">a g d & b g e,</foreign><lb></lb><emph type="italics"></emph>quorum anguli qui ad<emph.end type="italics"></emph.end> <foreign lang="el">g,</foreign> <emph type="italics"></emph>quia ad <expan abbr="verticẽ">verticem</expan> oppoſiti, ſunt æquales prop. <lb></lb>15. lib. 1. </s> <s>Tum latera, quæ ipſos continent<emph.end type="italics"></emph.end> <foreign lang="el">a g, d g,</foreign> <emph type="italics"></emph>duobus<emph.end type="italics"></emph.end> <foreign lang="el">b g, <lb></lb>e g</foreign> <emph type="italics"></emph>ſunt æqualia, quia partes ſunt dimidiæ eiuſdem remi<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>ax. 6. <lb></lb></s> <s id="id.001308">erunt igitur baſes<emph.end type="italics"></emph.end> <foreign lang="el">a d, b e</foreign> <emph type="italics"></emph>æquales, vt reliqui anguli prop. 4. lib. 1. <emph.end type="italics"></emph.end></s> <pb xlink:href="035/01/122.jpg" pagenum="82"></pb> <s><emph type="italics"></emph>Et ſic palmula perducta ad<emph.end type="italics"></emph.end> <foreign lang="el">e</foreign> <emph type="italics"></emph>cum<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>caput prouectum eſſet ad<emph.end type="italics"></emph.end> <foreign lang="el">d</foreign><lb></lb><emph type="italics"></emph>æqualiter moueretur, ſed in iſto caſu<emph.end type="italics"></emph.end> <foreign lang="el">g</foreign> <emph type="italics"></emph>ſcalmo manente nauis immo<lb></lb>ta eſſet, <expan abbr="cũ">cum</expan> tamen prouecta eſſe ſupponatur. </s> <s id="id.001309">Intelligatur igitur mini<lb></lb>mùm, vt ad<emph.end type="italics"></emph.end> <foreign lang="el">z</foreign> <emph type="italics"></emph>eſſe perducta palmula<emph.end type="italics"></emph.end> <foreign lang="el">b.</foreign> </s> <s><emph type="italics"></emph>Ex hoc rurſus <expan abbr="cõcludit">concludit</expan> Ari<lb></lb>ſtoteles ex figura à Victore Fauſto & ab alijs paßim rectam<emph.end type="italics"></emph.end> <foreign lang="el">d q</foreign><lb></lb><emph type="italics"></emph>maiorem eſſe: quam<emph.end type="italics"></emph.end> <foreign lang="el">q z.</foreign> </s> <s><emph type="italics"></emph>Et ita eſſe oſtendamus, quia duorum trian<lb></lb>gulorum<emph.end type="italics"></emph.end> <foreign lang="el">a q d & b q z</foreign> <emph type="italics"></emph>anguli, qui ad<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign> <emph type="italics"></emph>ad verticem oppoſiti, <lb></lb>ſunt æquales prop. 15. lib. 1. </s> <s>tum<emph.end type="italics"></emph.end> <foreign lang="el">q a d</foreign> <emph type="italics"></emph>æqualis eſt<emph.end type="italics"></emph.end> <foreign lang="el">q b z</foreign> <emph type="italics"></emph>vel quia <lb></lb>ſunt alterni facti à recta<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>incidente in parallelas<emph.end type="italics"></emph.end> <foreign lang="el">a d, b e.</foreign> </s> <s><emph type="italics"></emph>Ex <lb></lb>præcedenti <expan abbr="demõſtratione">demonſtratione</expan>. </s> <s id="id.001310">Ergo reliquus<emph.end type="italics"></emph.end> <foreign lang="el">q d a</foreign> <emph type="italics"></emph>reliquo<emph.end type="italics"></emph.end> <foreign lang="el">b z q</foreign> <emph type="italics"></emph>æqua<lb></lb>lis erit prop. 32. lib. 1. </s> <s>Et ſic triangula<emph.end type="italics"></emph.end> <foreign lang="el">a q d & b q z</foreign> <emph type="italics"></emph>ſunt æquian<lb></lb>gula, proinde & circum æquales angulos latera proportionalia prop. 4. lib. 6. <lb></lb></s> <s id="id.001311">Eſt igitur vt<emph.end type="italics"></emph.end> <foreign lang="el">a q</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">q d</foreign>: <emph type="italics"></emph>ſic<emph.end type="italics"></emph.end> <foreign lang="el">b q</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">q z,</foreign> <emph type="italics"></emph>& vicißim <lb></lb>prop. 16. lib. 5. vt<emph.end type="italics"></emph.end> <foreign lang="el">a q</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">q b</foreign>: <emph type="italics"></emph>ſic<emph.end type="italics"></emph.end> <foreign lang="el">d q</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">q z.</foreign> </s> <s><emph type="italics"></emph>Eſt <expan abbr="autẽ">autem</expan><emph.end type="italics"></emph.end> <foreign lang="el">a q</foreign> <emph type="italics"></emph>maior: <lb></lb>quam<emph.end type="italics"></emph.end> <foreign lang="el">q b,</foreign> <emph type="italics"></emph>quia<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>erat biſſecta in<emph.end type="italics"></emph.end> <foreign lang="el">g,</foreign> <emph type="italics"></emph>& detracta eſt de dimi<lb></lb>dia<emph.end type="italics"></emph.end> <foreign lang="el">g b</foreign> <emph type="italics"></emph>portio<emph.end type="italics"></emph.end> <foreign lang="el">q g,</foreign> <emph type="italics"></emph>quæ additur ipſi dimidiæ<emph.end type="italics"></emph.end> <foreign lang="el">a g.</foreign> </s> <s><emph type="italics"></emph>Eſt igitur<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">d q</foreign> <emph type="italics"></emph>maior quam<emph.end type="italics"></emph.end> <foreign lang="el">q z. </foreign></s> </p> <p type="main"> <s id="id.001312"><emph type="italics"></emph>Hoc autem quanquam verum ſit, quorſum tamen, dubium eſt. <lb></lb></s> <s id="id.001313">Exiſtimauit Nonius ideò hîc poſitum eſſe, vt oſtendatur B per remi<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.122.1.jpg" xlink:href="035/01/122/1.jpg"></figure><lb></lb><emph type="italics"></emph>gationem factam, non eſſe <lb></lb>in E: ſed vltra vt in K, <lb></lb>vnde nouam hanc deſcri<lb></lb>bit figuram. </s> <s id="id.001314">qua demon<lb></lb>ſtrat cum A caput remi <lb></lb>remigatione facta eſt in <lb></lb>D, palmulam B remi A <lb></lb>B eſſe non in <emph.end type="italics"></emph.end><foreign lang="el"> z</foreign><emph type="italics"></emph>: ſed in K <lb></lb>vltra <emph.end type="italics"></emph.end><foreign lang="el"> z</foreign>. </s> <s id="id.001315"><emph type="italics"></emph>Nihilominuſque <lb></lb>B K motum palmulæ B <lb></lb>retrorſum minorem eſſe A <lb></lb>D motu capitis A an<lb></lb>trorſum, ſecundum ſenten<lb></lb>tiam Ariſtotelis. </s> <s id="id.001316">Et ſic <lb></lb>Nonius remigatione facta <lb></lb>& tranſuecta naui ponit <lb></lb>ſcalmum C tranſuectum eſſe in T: vel ex ſuperiori Victoris figura <emph.end type="italics"></emph.end><pb xlink:href="035/01/123.jpg" pagenum="83"></pb><emph type="italics"></emph>ex<emph.end type="italics"></emph.end> <foreign lang="el">g</foreign> <emph type="italics"></emph>in<emph.end type="italics"></emph.end> <foreign lang="el">q.</foreign> </s> <s><emph type="italics"></emph>Sed ſi ſic eſſet, T idem ſcalmus qui C, propior cum ſit <lb></lb>aquæ: quam ipſe C, ſequeretur vt in vnius remigationis principio, <lb></lb>medio, fine nauis plus & minus mergeretur. </s> <s id="id.001317">quod ſi quando fiat, fit <lb></lb>exaccidenti, nec citra naufragij periculum: imo vero ſic non tam <lb></lb>nauis ferretur antrorſum: quam in profundum. </s> <s id="id.001318">At contrà latum <lb></lb>proſperè nauigium ſeruat eundem ſcalmum, ſeu ſpondam ſuam ſem<lb></lb>per æquidiſtantem aquæ, niſi quod verius eſt, arcum peripheriæ, ſed <lb></lb>non ſimplicem, vt poſtea docebimus, deſcribat, cuius extrema ſunt in <lb></lb>ſuperficie aquæ. <emph.end type="italics"></emph.end><lb></lb></s> <figure id="id.035.01.123.1.jpg" xlink:href="035/01/123/1.jpg"></figure> <s><emph type="italics"></emph>vt, ſit ſponda <lb></lb>nauis G H, & <lb></lb>ſcalmus C, cui <lb></lb>alligatus remus <lb></lb>per medium ſit <lb></lb>A B exiſtens in <lb></lb>principio remi<lb></lb>gationis, & in <lb></lb>fine ſit vbi D E, <lb></lb>tranſlato C per <lb></lb>motum nauigij <lb></lb>impulſi in T: <lb></lb>ſicque motionis <lb></lb>intra aquam pal<lb></lb>mulæ B ſpatium erit B E: nauigij vero erit C T: tum capitis <lb></lb>remi A erit A D. </s> <s id="id.001319">Et quidem cum anguli qui ad E ſint ſemper <lb></lb>æquales prop. 15. lib. 1. </s> <s>Baſes erunt æquales, ſi triangula fiant æqui <lb></lb>crura, ſi iniquicrura, illius trianguli baſis erit maior, cuius latera <lb></lb>angulum continentia ſunt maiora, vt antea ostendimus. </s> <s id="id.001320">Hæc igi<lb></lb>tur cum expendo cogor aliud ſentire quam Nonius licet timidè ( quia <lb></lb>viro huic propter ſcientiam præſtantem, & quod in loco natus ſit, <lb></lb>vixeritque ad nauigandum opportunißimo, multò plura quam mihi <lb></lb>tribuere ſoleo ) dicam tamen quod ſentio nempe concluſionem iſtam<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">d q</foreign> <emph type="italics"></emph>maiorem eſſe<emph.end type="italics"></emph.end> <foreign lang="el">q z,</foreign> <emph type="italics"></emph>pertinere eò, vt inferatur caput remi A <lb></lb>tranſuecti non conſiſtere in<emph.end type="italics"></emph.end> <foreign lang="el">d</foreign>: <emph type="italics"></emph>ſed vltra. </s> <s id="id.001321">vt in figuræ noſtræ pun<lb></lb>cto F. </s> <s id="id.001322">Sicque caput A multo anterius latum erit, quam B retrò. <lb></lb></s> <s id="id.001323">Eſt enim A F maior quam A D axiom. 9. quæ demonſtrata eſt <emph.end type="italics"></emph.end><pb xlink:href="035/01/124.jpg" pagenum="84"></pb><figure id="id.035.01.124.1.jpg" xlink:href="035/01/124/1.jpg"></figure><lb></lb><emph type="italics"></emph>eſſe maior ipſa B E: ſic <lb></lb>etiam C ſcalmus erit in O, <lb></lb>æquediſtanter cum C ab <lb></lb>aqua. </s> <s id="id.001325">quod fieri oportet in <lb></lb>artificioſa & proſpera na<lb></lb>uigatione. </s> <s id="id.001326">An ſic rectè <lb></lb>ſentiamus aliorum eſto iu<lb></lb>dicium: ſed in hoc conueni<lb></lb>mus cum Nonio quod remi <lb></lb>motus in vna remigatione <lb></lb>duplex eſt: proprius, & alie<lb></lb>nus: & ille quidem circularis circa ſcalmum tanquam centrum, <lb></lb>cuius motus ſcalmus expers eſt: hic vero contingit & ob motum <lb></lb>ſcalmi delati vna cum nauigio. </s> <s id="id.001327">Et quod totus motus remi ex his duo<lb></lb>bus maior eſt motu nauigij. </s> <s id="id.001328">Sed & cætera quæ in hoc problema <lb></lb>animaduertit & annotauit Nonius. </s> <s id="id.001329">Hîc ſubijciemus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001330"><emph type="italics"></emph>Primum dicit Ariſtotelis ratiocinationem obſcuram eſſe. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001331"><emph type="italics"></emph>Deinde Ariſtotelem aſſumere duo quorum alterum eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001332"><emph type="italics"></emph>Palmulam retrocedere quoties nauis in anteriora progreditur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001333"><emph type="italics"></emph>Alterum eſt ſcalmum biſſecare remum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001334"><emph type="italics"></emph>Inſuper Nonius aſſerit nauim interdum maius ſpatium percurrere:<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.124.2.jpg" xlink:href="035/01/124/2.jpg"></figure><lb></lb><emph type="italics"></emph>quam caput remi: interdum minus, iuxta <lb></lb>remigum vires, & provt mari remi pal<lb></lb>mula immerſa fuerit: Quæ omnia vt con<lb></lb>ſpicua fiant, demonſtrat quinque <expan abbr="ſequẽtes">ſequentes</expan> <lb></lb>propoſitiones. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001335">Propoſitio prima. </s> </p> <p type="main"> <s id="id.001336"><emph type="italics"></emph>Remigibus nauim mouere potentibus <lb></lb>caput remi plus antrorſum mouetur: <expan abbr="quã">quam</expan> <lb></lb>nauis. </s> <s id="id.001337">Sit remus A C, caput A, ſcal<lb></lb>mus B, qui propter nauis motum percur<lb></lb>rat ſpatium, quod eſt à B in D, in quo <lb></lb>loco remus A C ſitum rectitudinis ha<lb></lb>beat E F: & ſic ſpatium quod A con<lb></lb>ficit curua ſit linea A E, cui recta linea <lb></lb>A E reſpondeat in rectam E F perpen<emph.end type="italics"></emph.end><pb xlink:href="035/01/125.jpg" pagenum="85"></pb><emph type="italics"></emph>dicularis. </s> <s id="id.001338">Nauis vero idem interuallum conficiet quod ſcalmus B. <lb></lb></s> <s id="id.001339">Dico igitur rectam A E maiorem eſſe recta B D. </s> <s id="id.001340">Secet enim re<lb></lb>cta A C rectam E F in G. </s> <s id="id.001341">Quia igitur A G E, & B G D <lb></lb>triangula ſunt æquiangula, erit ſicut A G ad B G: ſic A E <lb></lb>ad B D prop. 4. lib. 6. </s> <s>Maior eſt autem A G ipſa B G, ax. 9. <lb></lb></s> <s id="id.001342">Erit igitur A E maior quam B D. </s> <s id="id.001343">Itaque caput remi A maius <lb></lb>percurrit ſpatium: quam nauis. </s> <s id="id.001344">quod erat demonſtrandum. <emph.end type="italics"></emph.end></s> </p> <figure id="id.035.01.125.1.jpg" xlink:href="035/01/125/1.jpg"></figure> <p type="main"> <s id="id.001345"><emph type="italics"></emph>Quod ſi per punctum B rectam duca<lb></lb>mus H K æqualem remo, & ad rectos <lb></lb>cum recta B D, & inſuper ſecantem A<emph.end type="italics"></emph.end><lb></lb>3 <emph type="italics"></emph>in puncto I, manifeſtè intelligemus <lb></lb>ipſam rectam A E ( quæ eſt totus motus <lb></lb>capitis remi in vna remigatione ) conſtare <lb></lb>ex A I, & I E, quarum prior reſpon<lb></lb>det curuæ A H deſcriptæ per capitis remi <lb></lb>motum proprium: poſterior vero æqualis <lb></lb>eſt rectæ B D ( ſunt enim latera parallelo<lb></lb>grammi oppoſita prop. 34. lib. 1.) quæ motu <lb></lb>nauis decurſa eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001346"><emph type="italics"></emph>Et quia Nonius ſine demonſtratione aſ<lb></lb>ſumit nauim tantùm decurrere, quantùm <lb></lb>ſcalmus, id quoque demonstremus. </s> <s id="id.001347">quia ad <lb></lb>ſequentia etiam vtile eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001348"><emph type="italics"></emph>Ante remigationem remi existentis in ſcalmo B ſit nauis prora C <lb></lb>poſt remigationem ſit B<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.125.2.jpg" xlink:href="035/01/125/2.jpg"></figure><lb></lb><emph type="italics"></emph>in E & prora in D ſic<lb></lb>que C D erit nauis pro<lb></lb>motio, & B E ſcalmi. <lb></lb></s> <s id="id.001349">Dico igitur C D & B E æquales, quia reliquæ ſunt ex æqualibus <lb></lb>B C, E D dempto communi E C axio. 3. </s> <s id="id.001350">Ergo nauis tantùm de<lb></lb>currit quantùm ſcalmus. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001351">Propoſitio ſecunda. </s> </p> <p type="main"> <s id="id.001352"><emph type="italics"></emph>Capite remi motu proprio, & naui æqualiter motis, palmula im<lb></lb>mota veluti centrum manet: & palmula immota, caput remi & <lb></lb>nauis æqualiter mota ſunt. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/126.jpg" pagenum="86"></pb> <figure id="id.035.01.126.1.jpg" xlink:href="035/01/126/1.jpg"></figure> <p type="main"> <s id="id.001353"><emph type="italics"></emph>Remus in principio motus habeat <lb></lb>poſitionem A B C, ducaturque per <lb></lb>punctum C, in quo remi palmula <lb></lb>recta C G rectos efficiens angulos <lb></lb>in puncto G cum recta per quam ad <lb></lb>motum nauis ſcalmus B mouetur. </s> <s id="id.001354">Et <lb></lb>eadem recta C G producatur vſque <lb></lb>ad E, ita vt G E ſit æqualis rectæ <lb></lb>B A ( quæ eſt dimidium remi ) rur<lb></lb>ſus per punctum B ducatur recta Q <lb></lb>B F ad rectos cum ipſa B G, & in <lb></lb>Q B F incidant perpendiculares A <lb></lb>Q C F. </s> <s id="id.001355">Quoniam igitur triangu<lb></lb>lorum A B Q & F B C anguli, <lb></lb>qui ad B ad verticem oppoſiti ſunt <lb></lb>æquales, prop. 15. lib. 1. </s> <s>& anguli qui ad Q & F recti ſunt, tum <lb></lb>latus A B lateri B C, ſunt enim dimidia remi, æquale eſt, erit & <lb></lb>latus A Q æquale lateri F C prop. 26. lib. 1. </s> <s>Ipſi autem F C recta <lb></lb>B G, latus parallelogrammi oppoſitum, æqualis eſt prop. 34. lib. 1. <lb></lb></s> <s id="id.001356">A Q igitur erit æqualis ipſi B G ax. 1. </s> <s id="id.001357">Atque tantum ſpatium B <lb></lb>ſcalmus: quantum nauis. </s> <s>ex antec. </s> <s id="id.001359">Et nauis tantum confecit quan<lb></lb>tum A caput remi ex hypotheſi. </s> <s id="id.001360">A autem conficit ſpatium A q. <lb></lb></s> <s>Igitur B ſcalmus conficiet ſpatium B G. </s> <s id="id.001361">Et quia anguli ad G <lb></lb>recti ſunt, ideo cum ſcalmus peruenerit ad G, habebit remus A C <lb></lb>rectitudinis ſitum E C, quo in loco illius remigationis finis erit. </s> <s id="id.001362">Sic <lb></lb>igitur palmula C à loco ſuo dimota non fuit, quod demonſtrandum <lb></lb>erat. </s> <s id="id.001363">Cæterum Nonius hîc aduertit rectam G C minorem eſſe B C <lb></lb>remi dimidio, pro quantitate C T. </s> <s id="id.001364">Vnde concludit quo tempore <lb></lb>ſcalmus B transfertur in G, palmulam quidem C excurrere in <lb></lb>ipſam longitudinem C T. </s> <s id="id.001365">Sed neque antrorſum neque retrorſum, <lb></lb>quod Ariſtoteles puto vocauit antè, palmulam diuidere mare, quod <lb></lb>ſolum demonſtrare intendebat. </s> <s id="id.001366">vbi etiam aduertes lector ex hoc dia<lb></lb>grammate Nonij & cæteris lineam A L E à capite remi in hac <lb></lb>remigatione deſcriptam, non eſſe ſimplicem arcum: ſed duos, vnum <lb></lb>A L ex motu proprio remi circa B centrum: alterum L E ex motu <lb></lb>conſequente ſcalmi B motum. </s> <s id="id.001367">quod pulchrè conſentit cum his quæ<emph.end type="italics"></emph.end><pb xlink:href="035/01/127.jpg" pagenum="87"></pb><emph type="italics"></emph>antè diximus de remi in vna remigatione varijs motibus. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001368">Propoſitionis conuerſio</s> </p> <p type="main"> <s id="id.001369"><emph type="italics"></emph>Manifeſta eſt, quia ſi remi palmula dimota non fuerit à loco ſuo, <lb></lb>ibique tandiu perſiſtat, donec remus ſitum rectitudinis obtineat, tan<lb></lb>tum ſpatium conficiet caput remi motu proprio: quantum nauis. <lb></lb></s> <s id="id.001370">Recta enim C F æqualis eſt A Q prop. 26. lib. 1. </s> <s>æqualis etiam <lb></lb>B G prop. 34. lib. 1. </s> <s>igitur A Q & B G æquales erunt ax. 1. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001373">Propoſitio tertia. </s> </p> <p type="main"> <s id="id.001374"><emph type="italics"></emph>Capite remi proprio motu conficiente ſpatium duplum ſpatij nauis: <lb></lb>tunc nauis tantùm promouebitur, quantùm palmula retrocedet. <emph.end type="italics"></emph.end></s> </p> <figure id="id.035.01.127.1.jpg" xlink:href="035/01/127/1.jpg"></figure> <p type="main"> <s id="id.001375"><emph type="italics"></emph>Remus incipiente motu ſit A C, <lb></lb>deſinente vero habeat rectitudinis <lb></lb>ſitum F G. </s> <s id="id.001376">Et ſic ſcalmus B pro<lb></lb>pter nauis motum conficiet interual<lb></lb>lum B D. </s> <s id="id.001377">Excitetur igitur à puncto <lb></lb>B in vtramque partem perpendicu<lb></lb>laris E E, prop. 11. lib. 1. </s> <s>In quam <lb></lb>perpendiculares incidant à punctis <lb></lb>A & C, quæ ſint A E, C E prop. 12. lib. 1. <lb></lb></s> <s id="id.001378">Et ſit interuallum A E <lb></lb>quod eſt decurſum à capite remi A <lb></lb>proprio motu, duplum interualli B <lb></lb>D, & recta linea C H reſpondeat <lb></lb>curuæ C G à remi palmula deſcri<lb></lb>ptæ. </s> <s id="id.001379">Dico rectas lineas B D, C H <lb></lb>æquales eſſe. </s> <s id="id.001380">Nam triangulorum B <lb></lb>A E & C B E rectæ A E, C E prop. 26. lib. 1. & in parallelo<lb></lb>grammo B H rectæ oppoſitæ B D, E H etiam æquales prop. 34. <lb></lb>lib. 1. </s> <s id="id.001381">Atqui recta A E dupla eſt rectæ B D ex hypotheſi. </s> <s id="id.001382">Dupla <lb></lb>igitur & C E rectæ H E, quapropter C H & E H æquales <lb></lb>erunt ax. 7. </s> <s id="id.001383">Et ſic C H & B D æquales ſunt ax. 1. </s> <s id="id.001384">Et quia nauis <lb></lb>tantum interualli decurrit ſemper: quantum ſcalmus. </s> <s id="id.001385">Ex antec. igi<lb></lb>tur ſi caput remi motu proprio duplum confecerit ipſius nauis inter<lb></lb>ualli, tantùm prouehetur nauis: quantùm palmula retrocedet. </s> <s id="id.001387">quod <lb></lb>demonſtrandum erat. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/128.jpg" pagenum="88"></pb> <p type="head"> <s id="id.001388">Propoſitionis conuerſio. </s> </p> <p type="main"> <s id="id.001389"><emph type="italics"></emph>Naui æqualiter prouecta, atque palmula retroceßit: motus capitis <lb></lb>remi proprius duplus eſt motus nauis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001390"><emph type="italics"></emph>Si enim C H æqualis ponatur B D, quoniam eidem B D æqua<lb></lb>lis eſt H E in parallelogrammo, æquales igitur erunt C H & <lb></lb>H E ax. 1. </s> <s id="id.001391">Et ſic dupla erit C E ipſius H E: & eadem C E <lb></lb>dupla ipſius B D. </s> <s>æquales porro ſunt C E & A E prop 26. lib. 1. <lb></lb></s> <s>Dupla ergo erit A E rectæ B D. </s> <s>ſed recta A E decurſa eſt à ca<lb></lb>pite remi, & B D à ſcalmo, quantùm autem prouehitur ſcalmus, <lb></lb>tantùm & nauis. </s> <s id="id.001392">Igitur ſi nauis tantùm fuerit prouecta, quantùm <lb></lb>remi palmula retroceßit, duplum conficit caput remi motu proprio <lb></lb>eius interualli, quod nauis conficit. </s> <s id="id.001393">quod fuit demonſtrandum. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001394">Propoſitio quarta. </s> </p> <p type="main"> <s id="id.001395"><emph type="italics"></emph>Nauis decurrens minus ſpatium: quam caput remi decurrat: maius <lb></lb>tamen eius dimidio: magis prouehitur: quam palmula retrocedat: <lb></lb>minus autem dimidio: minus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001396"><emph type="italics"></emph>In poſtremo diagrammate ponatur B D minor, quam A E: <lb></lb>ſed eius dimidio maior. </s> <s id="id.001397">Dico quod ipſa B D maior eſt, quam C H. <lb></lb></s> <s id="id.001398">Nam B D & H E æquales ſunt, ad hæc A E & C E æqua<lb></lb>les ſunt. </s> <s id="id.001399">maior igitur erit H E dimidio ipſius A E. </s> <s>quapropter <lb></lb>reliqua C H minor dimidio erit eiuſdem A E. </s> <s id="id.001400">Et minor igitur <lb></lb>erit C H quam B D. </s> <s id="id.001401">Interuallum autem B D, id eſt quod nauis <lb></lb>confecit, interuallum vero C H remi palmula in contrarium de<lb></lb>currit. </s> <s id="id.001402">Ideo prior pars theorematis vera. </s> <s id="id.001403">Poſterior autem ſimiliter <lb></lb>oſtendetur. </s> <s id="id.001404">Si enim B D minor eſt dimidio ipſius A E, minor <lb></lb>igitur erit & H E dimidio eiuſdem A E. </s> <s id="id.001405">Et quoniam A E & <lb></lb>C E æquales ſunt. </s> <s id="id.001406">Reliqua igitur C H dimidio eiuſdem A E <lb></lb>maior erit. </s> <s id="id.001407">Et proinde minor erit B D quam C H. </s> <s id="id.001408">Nauis igitur <lb></lb>minus interuallum decurret in anteriora: quam remi palmula in <lb></lb>contrarium. </s> <s id="id.001409">quod fuit demonſtrandum. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001410">Corollarium. </s> </p> <p type="main"> <s id="id.001411"><emph type="italics"></emph>Hinc & ex præcedenti infertur, quod ſi caput remi motu pro<lb></lb>prio decurrat interuallum maius, quam nauis, ſiue duplum, ſiue du<lb></lb>plo minus, ſiue maius: ſemper interuallum nauis adiuncto ei quod <lb></lb>palmula retroceſſerit, æquale erit ei, quod à capite remi motu proprio <lb></lb>conficitur. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/129.jpg" pagenum="89"></pb> <p type="main"> <s id="id.001412"><emph type="italics"></emph>Semper enim B D æqualis eſt H E: tota vero C E quæ æqua<lb></lb>lis eſt A E exſuis conſtabit partibus C H, H E. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001413">Propoſitionis conuerſio. </s> </p> <p type="main"> <s id="id.001414"><emph type="italics"></emph>Nauis longius progrediens: quam remi palmula retrocedat, inter<lb></lb>uallum conficit maius dimidio eius, quod motu proprio remi caput <lb></lb>decurrit: ſi minus: minus etiam dimidio. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001415"><emph type="italics"></emph>Huius demonſtratio ex prædictis facilis eſt. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.001416">Propoſitio quinta. </s> </p> <p type="main"> <s id="id.001417"><emph type="italics"></emph>Naui celerius mota quam caput remi: palmula antrorſum moue<lb></lb>bitur, nec quicquam retrocedet, idque ſpatij decurret quo nauis motus <lb></lb>motum capitis remi ſuperat. <emph.end type="italics"></emph.end></s> </p> <figure id="id.035.01.129.1.jpg" xlink:href="035/01/129/1.jpg"></figure> <p type="main"> <s id="id.001418"><emph type="italics"></emph>Habeat remus inci<lb></lb>piente motu poſitionem <lb></lb>A C: deſinente vero <lb></lb><expan abbr="ſitũ">ſitum</expan> rectitudinis F G. <lb></lb></s> <s id="id.001419">Scalmus igitur B pro<lb></lb>pter nauis motum tranſ<lb></lb>latus erit in D. </s> <s id="id.001420">Sit ita<lb></lb>que interuallum B D <lb></lb>maius: <expan abbr="quã">quam</expan> A H, quod <lb></lb>eſt à capite remi motu <lb></lb>proprio decurſum. </s> <s id="id.001421">Sic <lb></lb>enim celerius dicetur <lb></lb>ferri nauis quam caput <lb></lb>remi. </s> <s id="id.001422">Dico quod palmu<lb></lb>la C in vlteriora mouebitur. </s> <s id="id.001423">Nam cum ſcalmus B prouectus fue<lb></lb>rit in D, tranſlata erit ipſa palmula A C, vbi G in rectitudinis <lb></lb>ſitu, interuallumque conficiet C G curuilineum, cui reſpondet C K. <lb></lb></s> <s id="id.001424">Mouebitur igitur palmula in anteriora. </s> <s id="id.001425">Nihil autem vnquam re<lb></lb>trocedere oſtendetur in hunc modum. </s> <s id="id.001426">Eadem celeritate mouentur A <lb></lb>in H, & C verſus <emph.end type="italics"></emph.end><foreign lang="el">z</foreign><emph type="italics"></emph> circa ſcalmum. </s> <s id="id.001427">Atqui per hypotheſim cele<lb></lb>rius fertur nauis: quam C verſus <emph.end type="italics"></emph.end><foreign lang="el">z</foreign><emph type="italics"></emph>. </s> <s id="id.001428">Et mouetur idem C ipſa nauis <lb></lb>celeritate verſus K. </s> <s>celerius igitur feretur C ad K: quam ad <emph.end type="italics"></emph.end><foreign lang="el">z</foreign><emph type="italics"></emph>. <lb></lb></s> <s>quapropter nihil vnquam retrocedet ipſum C. </s> <s id="id.001429">Imo vero in vlte<lb></lb>riora progredietur, interuallumque decurret C K, quod quidem re<lb></lb>linquitur, detracto <emph.end type="italics"></emph.end><foreign lang="el">z</foreign><emph type="italics"></emph> C ex <emph.end type="italics"></emph.end><foreign lang="el">z</foreign><emph type="italics"></emph> K. </s> <s id="id.001430">Si enim remi palmula tota ipſa <emph.end type="italics"></emph.end><pb xlink:href="035/01/130.jpg" pagenum="90"></pb><emph type="italics"></emph>nauigij celeritate moueretur, vltra k progrederetur, cum B perue<lb></lb>niret ad D: ſed retrahitur interim, propter eum motum, qui fit cir<lb></lb>ca B. </s> <s id="id.001431">Sic igitur palmulæ celeritate, quæ à motu nauigij prouenit, re<lb></lb>tardata, decurſum interuallum erit C K. </s> <s id="id.001432">Videtur autem ſolo remo<lb></lb>rum impulſu hoc fieri non poſſe: ſed alia inſuper virtute impellente <lb></lb>opus eſſe: vt vento, vel impetu eò fluentis aquæ. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001433"><emph type="italics"></emph>Atque ex his theorematis concludit Nonius Ariſtotelem con<lb></lb>fusè propoſuiſſe hoc problema, cum non diſtinxerit inter motum re<lb></lb>mi proprium, & motum à naui tranſlata ei aduenientem. </s> <s id="id.001434">Concludit <lb></lb>etiam hac diſtinctione poſita Ariſtotelem inſcitè, & falsò proble<lb></lb>mati ſatisfeciſſe. </s> <s id="id.001435">Quandoquidem non continuò ſi nauis in anteriora <lb></lb>moueatur, remi palmula retrocedet: neque ſi retrocedat, minus inter<lb></lb>uallum in contrarium tranſmittet: quam nauis progrediatur, vt ex <lb></lb>ſecunda & tertia propoſitionibus liquet: præterea cum caput remi <lb></lb>motu proprio, qui circa ſcalmum fit, vnâ cum nauis motu, maius in<lb></lb>teruallum conficiat: quam nauis, ſolo autem proprio motu, ſi contin<lb></lb>gat tantum interuallum conficere: quantum nauis, fieri non poßit, vt <lb></lb>palmula moueatur: fruſtrà Ariſtoteles conatus eſt in vniuerſum <lb></lb>oſtendere remi caput maius ſpatium decurrere: quam palmulam in <lb></lb>contrarium. </s> <s id="id.001436">Poſtremo cum nauis longius progreditur: quam palmula <lb></lb>regreditur: minus quo que interuallum decurrit: quam caput remi, & <lb></lb>ſic non æquale. </s> <s id="id.001437">Atque hæc cum ſint ſuis veris demonſtrationibus <lb></lb>ſtabilita Ariſtotelem in hoc problemate dormitaſſe, quod aliquando <lb></lb>bono Homero contingit, conuincunt. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.001438"><foreign lang="el">to\ d' <lb></lb>au)to\ kai\ to\ phda/lion poiei=.</foreign></s> <s id="g0130515a"><foreign lang="el"> plh\n o(/ti ei)s to\ pro/sqen ou)de\n <lb></lb>sumba/lletai tw=| ploi/w|, w(/sper e)le/xqh e)pi\ a)/nw, a)lla\ <lb></lb>mo/non th\n pru/mnan ei)s to\ pla/gion a)pwqei= e)/nqa h)\ e)/nqa.</foreign></s> <s id="g0130515b"><foreign lang="el">ei)s <lb></lb>tou)nanti/on ga\r h( prw=|ra ou(/tw neu/ei.</foreign></s> <s id="g0130516"><foreign lang="el">h(=| me\n dh\ to\ phda/lion <lb></lb>prose/zeuktai, dei= oi(=o/n ti tou= kinoume/nou me/son noei=n, kai\ w(/sper <lb></lb>o( skalmo\s th=| kw/ph|: to\ de\ me/son u(poxwrei=, h(=| o( oi)/as metakinei=tai.</foreign></s> <s id="g0130517"><foreign lang="el"><lb></lb>e)a\n me\n ei)/sw a)/gh|, kai\ h( pru/mna deu=ro meqe/sthken: <lb></lb>h( de\ prw=|ra ei)s tou)nanti/on neu/ei.</foreign></s> <s id="g0130517a"><foreign lang="el">e)n ga\r tw=| au)tw=| <lb></lb>ou)/shs th=s prw/|ras, to\ ploi=on meqe/sthken o(/lon.</foreign></s> </p> <p type="main"> <s id="id.001439">Id etiam ipſum facit gu<lb></lb>bernaculum, niſi quod an<lb></lb>terius non mouet nauim: <lb></lb>vt antea dictum eſt: ſed <lb></lb>hinc vel hinc puppim ſo<lb></lb>lum in tranſuerſum pellit. <lb></lb></s> <s id="id.001440">Sic enim in <expan abbr="cõtrariũ">contrarium</expan> prora <lb></lb>vergit. </s> <s id="id.001441">Vbi igitur <expan abbr="gubernaculũ">guberna<lb></lb>culum</expan> <expan abbr="adiũctũ">adiunctum</expan> eſt, ibi opor<lb></lb>tet aliquod eius, quod mo<lb></lb>uetur <expan abbr="mediũ">medium</expan> intelligere, & <pb xlink:href="035/01/131.jpg" pagenum="91"></pb>qualis eſt ſcalmus remo: <lb></lb>Illud vero medium proce<lb></lb>dit, quo temo transfertur. <lb></lb></s> <s id="id.001442">Si quidem introrſus agat, <lb></lb>etiam puppis eò transfer<lb></lb>tur, prora verò in con<lb></lb>trarium nutat. </s> <s id="id.001443">In eodem <lb></lb>enim exiſtente prora, nauis <lb></lb>tota transfertur. </s> </p> <p type="head"> <s id="id.001444">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001445">Id etiam ipſum.] <emph type="italics"></emph>Ariſtoteles aſſerit gubernaculum idem fa<lb></lb>cere quod remus. </s> <s id="id.001446">Id eſt temonem plus progredi: quam pterigion. <lb></lb></s> <s id="id.001447">Quod ſi eſt, <expan abbr="animaduertendũ">animaduertendum</expan> in gubernaculo duos ineſſe motus, vt in <lb></lb>remo, proprium ſcilicet, & alienum. </s> <s id="id.001448">Et cum ſimili modo quo remus <lb></lb>veniat in vſum, omnia quæ de remo antea ex Nonio obſeruauimus, <lb></lb>in eo etiam habere locum. </s> <s id="id.001449">Proinde ſi in remi problemate minus per<lb></lb>ſpicax fuerit Ariſtoteles, nec in hoc perſpicacior fuiſſe putandus eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001450">Niſi quod anterius.] <emph type="italics"></emph>Repetitio eſt differentiæ motuum remi <lb></lb>& gubernaculi ſumpta ex diuerſitate terminorum ad quos vterque <lb></lb>ducit de qua igitur ante. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001451">Vbi igitur guber.] <emph type="italics"></emph>Antea in gubernaculi ſimilitudine cum <lb></lb>vecte attulerat Ariſtoteles pondus mouendum mare, motorem eum <lb></lb>qui ſedet in puppi, quod erat tertium de centro, circa quod temo mo<lb></lb>uetur, prætermiſerat. </s> <s id="id.001452">Id nunc adiungit. </s> <s id="id.001453">Eſt autem cardo cui puppis <lb></lb>nauis annectitur non aliter quam ſcalmo remus, vt & circa cardi<lb></lb>nem gubernaculum vertitur, ſicut circa ſcalmum remus. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001454">7. <foreign lang="el">*th=s kerai/as duna/menews ai)/tion. </foreign></s> </p> <p type="main"> <s id="id.001455">7. Cauſa poteſtatis <lb></lb>Antemnæ. </s> </p> <p type="main"> <s id="id.001456"><foreign lang="el">*dia\ ti/ o(/sw| a)\n h( kerai/a a)nwte/ra h)=|, qa=tton plei= ta\ <lb></lb>ploi=a tw=| au)tw=| i(sti/w| kai\ tw=| au)tw=| pneu/mati; </foreign></s> <s id="g0130602"><foreign lang="el">h)\ dio/ti gi/netai <lb></lb>o( me\n i(sto\s moxlo/s, u(pomo/xlion de\ to\ e(dw/lion e)n w(=|<lb></lb> e)mpe/phgen;</foreign></s> <s id="g0130602a"><foreign lang="el">o(\ de\ dei= kinei=n ba/ros, to\ ploi=on, to\ de\ kinou=n, <lb></lb>to\ e)n tw=| i(sti/w| pneu=ma.</foreign></s> <s id="g0130603"><foreign lang="el">ei) d' o(/sw| a)\n por)r(w/teron h)=| to\ u(pomo/xlion, <lb></lb>r(a=|on kinei= kai\ qa=tton h( au)th\ du/namis to\ au)to\ <lb></lb>ba/ros.</foreign></s> <s id="g0130603a"><foreign lang="el">h( ou)=n kerai/a a)nw/teron a)gome/nh, kai\ to\ i(sti/on por)r(w/teron <lb></lb>poiei= tou= e(dwli/ou u(pomoxli/ou o)/ntos.</foreign></s> </p> <p type="main"> <s id="id.001457">Cur quantò antemna ſu<lb></lb>perior fuerit, tantò celerius <lb></lb>nauis feratur <expan abbr="eodẽ">eodem</expan> velo, <expan abbr="eodemq;">eo<lb></lb>demque</expan> <expan abbr="vẽto">vento</expan>? </s> <s id="id.001458">An quia malus <pb xlink:href="035/01/132.jpg" pagenum="92"></pb>eſt vectis, & calx in qua in<lb></lb>figitur, preſſio? </s> <s id="id.001459">Quod vero <lb></lb>pondus mouere oportet, <lb></lb>eſt nauis: & ventus in <expan abbr="velũ">velum</expan>, <lb></lb>eſt mouens. </s> <s id="id.001460">Igitur ſi quan<lb></lb>to remotior fuerit preſſio, <lb></lb>facilius & celerius vis <expan abbr="eadẽ">eadem</expan> <lb></lb>pondus ipſum mouet: an<lb></lb>temna ſublimius poſita à <lb></lb>calce mali, quæ preſſio eſt, <lb></lb>magis diſtare velum faciet. </s> </p> <p type="head"> <s id="id.001461">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001462">Antemnæ.] <emph type="italics"></emph>Antemna lignum eſt per tranſuerſum in malo <lb></lb>nauis poſitum, à quo velum dependet. </s> <s id="id.001463">Latini illius ligni extre<lb></lb>mas partes <expan abbr="vocãt">vocant</expan> cornua ob quod Bayfius putat antemnas dici Græ<lb></lb>cis<emph.end type="italics"></emph.end> <foreign lang="el">kerai/an. </foreign><emph type="italics"></emph></s> <s>Malus vero nauis aliud eſt lignum propè in medio nauis <lb></lb>inſtar <expan abbr="trũci">trunci</expan> arboris perpendiculariter infixum,<emph.end type="italics"></emph.end> <foreign lang="el">i(sto\s,</foreign> <emph type="italics"></emph>cuius partes di<lb></lb>uerſis appellationibus diſtinctæ à Macrobio in quinto Saturnalium <lb></lb>in hæc verba ſunt. </s> <s id="id.001464">Aſclepiades autem vir inter Græcos apprimè <lb></lb>doctus ac diligens carcheſia à nauali re dicta exiſtimat. </s> <s id="id.001465">At enim <lb></lb>naualis mali partem inferiorem, pternam vocari, at circa mediam <lb></lb>ferme partem<emph.end type="italics"></emph.end> <foreign lang="el">tra/xhlon</foreign> <emph type="italics"></emph>dici: ſummam vero partem carcheſium <lb></lb>nominari, & inde diffundi in vtrumque veli latus ea quæ cornua <lb></lb>vocantur. </s> <s id="id.001466">Velum etiam eſt linteum quadrangulum vel triangulum <lb></lb>ex antemna dependens, quod expenſum excipit ventum, cuius im<lb></lb>pulſu nauis tranſuehitur non aliter <expan abbr="quã">quam</expan> antea diximus remis. </s> <s id="id.001467">Æolus <lb></lb>primus mortalium velis vſus eſſe dicitur. </s> <s id="id.001468">Et propterea deus vento<lb></lb>rum eſt habitus. </s> <s id="id.001469">Sic enim de eo apud Diodorum legimus. <emph.end type="italics"></emph.end> </s> <s><foreign lang="el">pro\s de\ <lb></lb>tou/tois th\n tw=n i(sti/wn xrei/an toi=s nautikoi=s ei)shgh/sasqai kai\ di<lb></lb>da/cai. </foreign><emph type="italics"></emph> </s> <s>id eſt inſuper & velorum vſum nautis introduxiſſe, ratio<lb></lb>nemque vtendi docuiſſe. </s> <s id="id.001470">velorum autem apud veteres tria fuerunt <lb></lb>genera Artemo & acatium, quod velum maius: dolo, quod minus <lb></lb>erat: &<emph.end type="italics"></emph.end> <foreign lang="el">e)po/dromos,</foreign> <emph type="italics"></emph>quod velum à tergo ponebatur. </s> <s id="id.001471">vnde nauis à <lb></lb>Iulio polluce<emph.end type="italics"></emph.end> <foreign lang="el">triar/menos,</foreign> <emph type="italics"></emph>Antigoni dicta, quæ tria vela haberet <emph.end type="italics"></emph.end><pb xlink:href="035/01/133.jpg" pagenum="93"></pb><emph type="italics"></emph>trinoſque malos, quod antiquis fuit <expan abbr="rarũ">rarum</expan>, noſtris hodie <expan abbr="frequẽtißimũ">frequentißimum</expan>. <lb></lb></s> <s id="id.001472">quia inuenta pyxide nautica, inquit Cardanus, & lapidis Herculis <lb></lb>auxilio pluribus locis vela dispoſita, melius dirigunt iter: antiquis <lb></lb>contrà, quoniam ſyderibus Cynoſura, & Helice, vias dirigebant, & <lb></lb>ob id non ad amußim, nec ex lineis, craſſa quidem Minerua: ſed certa <lb></lb>deformatis malorum multitudo confuſionem in curſu, & impedi<lb></lb>mentum, maiuſque periculum attuliſſet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001473">Cur quanto.] <emph type="italics"></emph>Quintum eſt ſpeciale problema de vecte conſi<lb></lb>derato in malo nauis. </s> <s id="id.001474">Cur ſcilicet antemna ſublimiore mali loco po<lb></lb>ſita, vt ſit idem velum, idemque ventus velo exceptus, nauis cele<lb></lb>rius feratur. </s> <s id="id.001475">Id eſt vt cætera omnia ſint paria. </s> <s id="id.001476">Nam nauis velocitas, <lb></lb>non ſolum pendet à ventorum impetu & rectitudine, & velorum <lb></lb>magnitudine: ſed & ex loco humiliore, vel ſublimiore, ex cæli ab <lb></lb>Oriente in Occidentem conuerſione, nauis leuitate & forma. </s> <s id="id.001477">quæ <lb></lb>enim non merguntur vt<emph.end type="italics"></emph.end> <foreign lang="el">droma/des</foreign> <emph type="italics"></emph>( ſic enim vocat Ariſtophanes <lb></lb>eas, quas nunc vulgus fregatas appellat ) quaſi aquis innitentes curſu <lb></lb>ſunt velocißimæ, & longiores latis, poſt eas, quæ carinam habent te<lb></lb>nuem, vt aquas facile diuidant, vltimo loco quæ quaſi mediæ ante <lb></lb>quidem tenues, poſt latiores ad velocem curſum & ferendum onera <lb></lb>aptæ, & humiles altis, & leui ex ligno: ſed & parte intra aquam <lb></lb>polita læuigata & ſæuo illita. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001478">An quia malus eſt.] <emph type="italics"></emph>Solutio eſt problematis propoſiti per re<lb></lb>ductionem mali ad vectem, & eius calcis ad hypomochlium. </s> <s id="id.001479">Syllo<lb></lb>giſmus hîc eſt ſuis omnibus partibus abſolutus, ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001480"><emph type="italics"></emph>Quantò pars ab hypomochlio ad caput vectis eſt longior: tantò <lb></lb>vis mouens, ea eſt ventus, onus, id eſt nauim, facilius & ce<lb></lb>lerius mouet. </s> <s id="id.001481">Ex anteced. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001482"><emph type="italics"></emph>Quò autem antemna, intellige cum velo expanſo, ſuperior eſt in <lb></lb>malo: eò pars ab hypomochlio ad caput vectis eſt longior. ax. 9. <lb></lb></s> <s id="id.001484">Eſt enim malus vectis, & mali pterna ſeu calx eſt hypo<lb></lb>mochlium. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001485"><emph type="italics"></emph>Ergo antemna cum ſuperior eſt, ventus facilius & celerius <lb></lb>mouet nauim. <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg22"></arrow.to.target></s> </p> <p type="margin"> <s id="id.001486"><margin.target id="marg22"></margin.target>Cap. 8. lib <lb></lb>10. </s> </p> <p type="main"> <s id="id.001487"><emph type="italics"></emph>Eadem de hoc problemate fuit Vitruuij <expan abbr="ſentẽtia">ſententia</expan> his verbis expreſſa. <lb></lb></s> <s id="id.001488">Nauis onerariæ vela cum ſint per altitudinem mediam mali penden<lb></lb>tia, non poteſt habere nauis celerem curſum: cum autem in ſummo<emph.end type="italics"></emph.end><pb xlink:href="035/01/134.jpg" pagenum="94"></pb><emph type="italics"></emph>cacumine antemnæ ſubductæ ſunt, tunc vehementiori progreditur <lb></lb>impetu, quod non proxime calcem mali, quæ eſt loco centri: ſed in <lb></lb>ſummo longius, & ab eo progreſſa recipiunt in ſe vela ventum. </s> <s id="id.001489">Ita<lb></lb>que vti vectis ſub onere ſubiectus, ſi per medium premitur, durior eſt <lb></lb>neque incumbit. </s> <s id="id.001490">Cum autem caput eius ſummum deducitur, faciliter <lb></lb>onus extollit: humiliter vela cum ſunt per medium temperata, mino<lb></lb>rem habent virtutem. </s> <s id="id.001491">Quæ autem in capite mali ſummo collocantur, <lb></lb>diſcedentia longius à centro non acriore, ſed eodem flatu preßione ca<lb></lb>cuminis vehementius cogunt progredi nauem. </s> <s id="id.001492">Ex his etiam intelli<lb></lb>gere licet cur hodierni nautæ ſolo ſæpe in procellis vtuntur dolone, <lb></lb>velo quidem non tam minimo magnitudine quam altitudine Trin<lb></lb>chetum appellant. </s> <s id="id.001493">Solum enim ſuſtinet nauim, quæ à ventis vel vn<lb></lb>dis mergi ſolet. </s> <s id="id.001494">ab vndis quidem vbi humilior eſt: à ventis vero ex <lb></lb>lateribus & anteriore parte. </s> <s id="id.001495">Siquidem velum illud humile & exi<lb></lb>guum efficit, vt nauis anteriore parte leuis, nec mergatur prona à <lb></lb>ventis, nec aquas ea excipiat, nec tamen impelli poteſt nauis in ſcopu<lb></lb>los, nec euerti ob cauſas dictas. </s> <s id="id.001496">Quin ſi nimium adhuc venti ſæuiant, <lb></lb>dolonem demittant adhuc infra magis, quin & ipſum malum etiam <lb></lb>ſublato velo, aut circa antemnam implexo & inuoluto, & ne nauis <lb></lb>obruatur, antrorſum. </s> <s id="id.001497">Hæc enim pars vim <expan abbr="ventorũ">ventorum</expan> omnem excipit: <lb></lb>gubernatores etiam puppim multa arena, lapilliſque onerare, ſi deſit <lb></lb>aliud onus, ſolent. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001498">8. <foreign lang="el">*dia\ ti/ o(/tan e)kkerai/as bou/<lb></lb>lwntai diadramei=n po/da poiou=si. </foreign></s> </p> <p type="main"> <s id="id.001499">8. Cur quando è cornu vo<lb></lb>lunt nauigare pedem fa<lb></lb>ciunt. </s> </p> <p type="main"> <s id="id.001500"><foreign lang="el">*dia\ ti/ o(/tan e)kke)rai/as bou/lwntai diadramei=n, mh\ ou)ri/ou <lb></lb>tou= pneu/matos o)/ntos, to\ me\n pro\s to\n kubernh/thn tou= i(sti/ou <lb></lb>me/ros ste/llontai, to\ de\ pro\s th\n prw=|ran podiai=on poihsa/menoi <lb></lb>e)fia=sin; </foreign></s> <s id="g0130702"><foreign lang="el">h)\ dio/ti a)ntispa=| to\ phda/lion: pollw=| ma=llon <lb></lb>o)/nti tw=| pneu/mati, ou) du/natai, o)li/gw| de/ o(\ u(poste/llontai.</foreign></s> <s id="g0130703"><foreign lang="el"><lb></lb>proa/gei me\n ou)=n to\ pneu=ma, ei)s ou)/rion de\ kaqi/sthsi to\ <lb></lb>phda/lion, a)ntispw=n kai\ moxleu=on th\n qa/lattan.</foreign></s> <s id="g0130704"><foreign lang="el">a(/ma <lb></lb>de\ kai\ oi( nau=tai ma/xontai tw=| pneu/mati: a)nakli/nousi ga\r <lb></lb>e)pi\ to\ e)nanti/on e(autou/s.</foreign></s> </p> <p type="main"> <s id="id.001501">Cur quando è cornu na<lb></lb>uigare voluerint vento ſe<lb></lb>cundo non exiſtente, par<lb></lb>tem quidem veli ad guber<lb></lb>natorem ſpectantem con<lb></lb>trahunt: <expan abbr="partẽ">partem</expan> vero ad pro<lb></lb>ram <expan abbr="relaxãt">relaxant</expan> pedem facien<lb></lb>tes. </s> <s id="id.001502">An quia gubernacu<lb></lb>lum non poteſt auertere, <lb></lb>cum multus exiftit ventus: <pb xlink:href="035/01/135.jpg" pagenum="95"></pb><expan abbr="cũ">cum</expan> paucus verò poteſt. </s> <s id="id.001503"><expan abbr="vẽtus">ventus</expan> <lb></lb>igitur perpellit, quem ſe<lb></lb>cundum facit gubernacu<lb></lb>lum, auertens & compel<lb></lb>lens mare, ſimul & nautæ <lb></lb>pugnant cum vento, & in <lb></lb>contrariam nituntur par<lb></lb>tem. </s> </p> <p type="head"> <s id="id.001504">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001505">E Cornu volunt nauigare.] <emph type="italics"></emph>Diximus antemnarum extrema <lb></lb>appellari cornua. </s> <s id="id.001506">Hinc è cornu nauigare eſt cum vento cornu <lb></lb>antemnarum obijcitur. </s> <s id="id.001507">Quod feciſſe ſignificabat Troianos Virgi<emph.end type="italics"></emph.end><arrow.to.target n="marg23"></arrow.to.target><lb></lb><emph type="italics"></emph>lius hoc verſu,<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.001508"><margin.target id="marg23"></margin.target>Lib. 3. <lb></lb>Æneid. </s> </p> <p type="main"> <s id="id.001509">Cornua velatarum obuertimus antemnarum. </s> </p> <p type="main"> <s id="id.001510">Pedem faciunt.] <emph type="italics"></emph>Ex textu & rei natura quæ in eo explica<lb></lb>tur ratiocinantes hîc pro<emph.end type="italics"></emph.end> <foreign lang="el">ou(/tws poiou=oi</foreign> <emph type="italics"></emph>repoſuimus<emph.end type="italics"></emph.end> <foreign lang="el">po/da poiou=oi. </foreign><emph type="italics"></emph>Eſt <lb></lb>autem<emph.end type="italics"></emph.end> <foreign lang="el">pou/s</foreign> <emph type="italics"></emph>Græcis, & pes Latinis variæ admodum ſignificationis. <lb></lb></s> <s id="id.001511">Præter cæteras hîc huius duas annotare licet. </s> <s id="id.001512">Prior venit in men<lb></lb>tem ob duos locos apud Galenum à perpaucis intellectos. </s> <s id="id.001513">Alter eſt <lb></lb>cap. 9. lib. 2. de muſc. motu: alter com. 4. in lib. 6. <emph.end type="italics"></emph.end> <foreign lang="el">e(pid. </foreign><emph type="italics"></emph>in Aph. 24. <lb></lb>vbi dicit tibicines, præcones, nuncupatum<emph.end type="italics"></emph.end> <foreign lang="el">po/da,</foreign> <emph type="italics"></emph>id eſt, pedem cane<lb></lb>re. </s> <s id="id.001516">vbi dubium non eſt Galenum ſignificare voluiſſe genus quod<lb></lb>dam vocis, quæ vehementi & longa exufflatione opus habeat, vt <lb></lb><expan abbr="etiã">etiam</expan> ſenſit Hieronymus Mercurialis, qui hos Galeni locos obſerua<lb></lb>uit. </s> <s id="id.001517">Nos <expan abbr="etiã">etiam</expan> legimus in <expan abbr="cõment">comment</expan>. </s> <s id="id.001518">Cæſaris cum <expan abbr="pugnandũ">pugnandum</expan> ſibi foret, <lb></lb>iußiſſe ab equis milites <expan abbr="deſcẽdere">deſcendere</expan>, nequis <expan abbr="ſpẽ">ſpem</expan> fugæ in <expan abbr="equorũ">equorum</expan> celerita<lb></lb>te reponeret. </s> <s id="id.001519">Quæ iußio fortaſſe erat,<emph.end type="italics"></emph.end> <foreign lang="el">e)rei=n po/da,</foreign> <emph type="italics"></emph>dicere <expan abbr="pedẽ">pedem</expan>, vbi <expan abbr="Stẽtorea">Sten<lb></lb>torea</expan> voce opus erat, vt ab omnibus audiretur: contra hodie apud <lb></lb>Gallos, inituris pugnam iubetur aſcendere in equos: poſterior eſt qua <lb></lb>ea pars in velo, quæ acutior & inferior ad nauis latus, vel ad mali <lb></lb><expan abbr="pternã">pternam</expan> religatur, modóque <expan abbr="cõtrahitur">contrahitur</expan> modò relaxatur. </s> <s id="id.001520">vnde Poëta:<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg24"></arrow.to.target></s> </p> <p type="margin"> <s id="id.001521"><margin.target id="marg24"></margin.target>Lib. 5. <lb></lb>Æneid. </s> </p> <p type="main"> <s id="id.001522">vna omnes fecere pedem. </s> </p> <p type="main"> <s id="id.001523"><emph type="italics"></emph>Alij tamen dicunt eſſe funem, quo id fit. </s> <s id="id.001524">Interpres Apollonij Rho<lb></lb>dij funes veli id eſt<emph.end type="italics"></emph.end> <foreign lang="el">ka/lw</foreign> <emph type="italics"></emph>rudentes in tria genera diuidit. </s> <s id="id.001525">Aut enim<arrow.to.target n="marg25"></arrow.to.target><pb xlink:href="035/01/136.jpg" pagenum="96"></pb>detrahitur his velum, & vocantur<emph.end type="italics"></emph.end> <foreign lang="el">mesouri/ai</foreign>: <emph type="italics"></emph>aut intenditur vtrin<lb></lb>que ad proram, & ſunt<emph.end type="italics"></emph.end> <foreign lang="el">pro/tonoi</foreign>: <emph type="italics"></emph>aut conuertitur & laxatur, hi <lb></lb>ſunt<emph.end type="italics"></emph.end> <foreign lang="el">kata\ ta\s gwni/as</foreign> <emph type="italics"></emph>ad angulos, & dicuntur<emph.end type="italics"></emph.end> <foreign lang="el">po/des</foreign> <emph type="italics"></emph>& ante hos<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">pro/podes</foreign> <emph type="italics"></emph>quo ſenſu dixiſſe Plinius videtur lib. 2. cap. 47. </s> <s>Iiſdem <lb></lb>autem ventis in contrarium nauigatur prolatis pedibus vt noctu <lb></lb>plerumque vela concurrant. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.001527"><margin.target id="marg25"></margin.target>Lib. 3. </s> </p> <p type="main"> <s id="id.001528">Cur quando.] <emph type="italics"></emph>Sextum eſt problema ſpeciale de vecte in naui<lb></lb>gatione obliqua, quod ſoluitur triplici ope nempe veli obliqui ex par<lb></lb>te contracti, parteque expanſi gubernaculi tanquam vectis, & re<lb></lb>migum renixus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001529">E cornu nauigare.] <emph type="italics"></emph>Pro<emph.end type="italics"></emph.end> <foreign lang="el">e)k ou)ri/as</foreign> <emph type="italics"></emph>hîc legendum putamus vt <lb></lb>in titulo<emph.end type="italics"></emph.end> <foreign lang="el">e)k kerai/as</foreign> <emph type="italics"></emph>nam hæc ſunt<emph.end type="italics"></emph.end> <foreign lang="el">a)si/stata</foreign> <emph type="italics"></emph>velle nauigare<emph.end type="italics"></emph.end> <foreign lang="el">e)k ou)ri/as</foreign><lb></lb><emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">mh\ ou)ri/ou pneu/ma/tos o(/ntos.</foreign> </s> <s><emph type="italics"></emph>Quomodo enim nauigabitur vento <lb></lb>ſecundo, ſi ventus ſecundus non eſt. </s> <s id="id.001530">At cum ventus ſecundus non <lb></lb>eſt, antemnarum ope rectum nihilominus tenere curſum poßibile eſt, <lb></lb>Et id vt fiat & quibus de cauſis, explicatur hîc ab Ariſtorele. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001531">Vento ſecundo.] <emph type="italics"></emph>Ventus ſecundus eſt cum vt ait Poëta,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001532">A tergo comitatur euntes,</s> </p> <p type="main"> <s id="id.001533"><emph type="italics"></emph>Hic eſt quem nautæ ſibi dari optant vnde eſt illud,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001534">Ferte viam facilem, venti & ſpirate ſecundi. </s> </p> <p type="main"> <s id="id.001535"><emph type="italics"></emph>Qui huic eſt contrarius, dicitur aduerſus, cum in proram inuehitur. <lb></lb></s> <s id="id.001536">Nec eo ſic flante nauis niſi remis agi poteſt, idque magnis viribus <lb></lb>& magno conatu. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001537">Non aliter quam qui aduerſo vix flumine lembum</s> </p> <p type="main"> <s id="id.001538">Remigijs ſubigit, ſi brachia forte remiſit,</s> </p> <p type="main"> <s id="id.001539">Atque illum præceps prono rapit alueus amne. </s> </p> <p type="main"> <s id="id.001540"><emph type="italics"></emph>Inter hos duo ſunt medij, vnus tranſuerſus ad latera nauis perpendi<lb></lb>culariter incidens: alter obliquus <lb></lb><figure id="id.035.01.136.1.jpg" xlink:href="035/01/136/1.jpg"></figure><lb></lb>qui medius eſt inter ſecundum & <lb></lb>tranſuerſum, vel inter aduerſum & <lb></lb>tranſuerſum. </s> <s id="id.001541">Vt eſto nauis G H, <lb></lb>& prora ſit G puppis H, ventus <lb></lb>ex B ſecundus erit, ex A aduer<lb></lb>ſus, ex C vel D tranſuerſus, ex E <lb></lb>vel F obliquus. </s> <s id="id.001542">Horum autem mo<lb></lb>tuum Galenus obliquos per pulchrè <emph.end type="italics"></emph.end><pb xlink:href="035/01/137.jpg" pagenum="97"></pb><emph type="italics"></emph>declarauit ſumpta primùm hac propoſitione. </s> <s id="id.001543">In vniuerſum quando <lb></lb>à duobus motibus ex tranſuerſo ſibi inuicem occurrentibus trahitur <lb></lb>corpus, ſi multò quidem ſupereminet alter, neceſſarium eſt obſcurari, <lb></lb>diſpareréue reliquum: pauca verò cum eſt exuperantia alterius: aut <lb></lb>ambo æqualiter poſſunt, mixtum ex vtriſque fieri eum corporis mo<lb></lb>tum oportet. </s> <s id="id.001544">Videntur autem omnia iſta propemodum quotidie in <lb></lb>ſexcentis exemplis, exempli gratia in remigantibus, ſimul & naui<lb></lb>bus ventum tranſuerſum habentibus. </s> <s id="id.001545">Si enim æquipollet venti & <lb></lb>remigantium robur, mixtum fieri motum neceſſe eſt. </s> <s id="id.001546">Cum neque <lb></lb>antrorſum ſolum, neque ad tranſuerſum naues ferantur, ſed ad am<lb></lb>borum medium ( vbi malè legitur Medicum ) ſi vero remigantium <lb></lb>robur maius fuerit, antrorſum magis, quam ad tranſuerſum. </s> <s id="id.001547">Si au<lb></lb>tem venti violentia vincat, ad tranſuerſum magis, quam antror<lb></lb>ſum. </s> <s id="id.001548">Multus autem ſi fuerit exceſſus, adeo vt alterius vires omnino <lb></lb>vincantur, nauigantium quidem obſcuratis viribus, ad tranſuer<lb></lb>ſum: venti vero, antrorſum magis naues ferentur. </s> <s id="id.001549">Quid tandem ſi <lb></lb>tenuis omnino aura fuerit, nauis verò prælonga, & leuis, quamplu<lb></lb>rimos habens nautas, poterit aliquando motus ab aura eſſe manife<lb></lb>ſtus? </s> <s id="id.001550">Sed neque ſi maximus quidem ſuerit ventus, nauis autem & <lb></lb>maxima & grauis, & duo ſolum aut tres remigent, remigum actio<lb></lb>nem apparere poßibile eſt. </s> <s id="id.001551">cap. 19. lib. 1. de vſ. partium. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001553">An quia gubernaculum.] <emph type="italics"></emph>Solutio eſt problematis propoſiti, <lb></lb>quod ſic fiet euidentius. </s> <s id="id.001554">Cur qui è cornu nauigaturi vento ſcilicet <lb></lb>non ſecundo exiſtente: ſed obliquo vel tranſuerſo eam veli partem, <lb></lb>quæ verſus gubernatorem eſt, contrahunt id eſt ſtringunt, & circa <lb></lb>antemnam implicant. </s> <s id="id.001555">Eam vero, quæ ad proram, relaxant, quod ap<lb></lb>pellant pedem facere. </s> <s id="id.001556">Reſponſio. </s> <s id="id.001557">Quia obliquè vel tranſuerſim naui<lb></lb>gari non poteſt, niſi tunc gubernaculum auertat, atque obliquet na<lb></lb>uim. </s> <s id="id.001558">Eò enim fertur nauis, quò prora dirigitur. </s> <s id="id.001559">Obliquare autem <lb></lb>nauim vel tranſuertere tantò facilius gubernaculum poteſt: quantò <lb></lb>ventus paucior eſt. </s> <s id="id.001560">Paucior autem fit contracto velo, quod ſpectat ad <lb></lb>puppim, & relaxato eo quod eſt ad proram. </s> <s id="id.001561">Sufficiens tamen pro<lb></lb>pellere. </s> <s id="id.001562">Obliquus enim veli relaxati ſinubus totis excipitur. </s> <s id="id.001563">Ideo <expan abbr="cũ">cum</expan> <lb></lb>& ſufficiat gubernaculum auertere atque propellere mare, vocatis <lb></lb>ad id in auxilium, ſi opus eſt, nautis in contrariam vento partem ni<lb></lb>tentibus, fit vt ex obliquo vel tranſuerſo vento feratur nauis. </s> <s id="id.001564">Sic <emph.end type="italics"></emph.end><pb xlink:href="035/01/138.jpg" pagenum="98"></pb><emph type="italics"></emph>enim quantum ventus exempli gratia dextrorſum propellit nauim: <lb></lb>tantum vi ſua gubernaculum cum nautis ſiniſtrorſum illam tor<lb></lb>quet, ac rapit. </s> <s id="id.001565">Et ita neutra ex contrarijs viribus præualente, eò fer<lb></lb>tur nauis, quò vult gubernator, etiamſi ventus minime ſecundus ſit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001566">Quem <expan abbr="ſecundũ">ſecundum</expan>.] <emph type="italics"></emph>Ex hoc loco colligi poteſt cauſa, propter quam <lb></lb>quotidie naues obſeruantur non citra admirationem eodem vento in <lb></lb>contrarias partes nauigare, vt & Plinius etiam recitat. </s> <s id="id.001567">Iiſdem <lb></lb>ventis in contrarium nauigatur prolatis pedibus ( hi ſunt funes de <lb></lb>quibus ante ) vt noctu plerumque vela concurrant. </s> <s id="id.001568">Hoc autem vt <lb></lb>fiat geometricè demonſtratur. <emph.end type="italics"></emph.end></s> </p> <figure id="id.035.01.138.1.jpg" xlink:href="035/01/138/1.jpg"></figure> <p type="main"> <s id="id.001569"><emph type="italics"></emph>Sint naues A tendens ad G, & B tendens ad H. </s> <s>ventus ex <lb></lb>C recta feratur ad D, tanquam ad centrum. </s> <s id="id.001570">Itaque vento pro<lb></lb>pulſa nauis A, feretur in E, & B in F. </s> <s id="id.001571">Fiat igitur in naui per <lb></lb>temonem mutatum angulus G A K, qui ſit æqualis angulo G <lb></lb>A E: tum H B L æqualis angulo H B F. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001572"><emph type="italics"></emph>Quia igitur nauis A à vento fertur in E, & per temonis muta<lb></lb>tionem in K, feretur recta in G, & eadem ratione B in H. <lb></lb></s> <s id="id.001573">Neuter enim cum ſuo impulſu præualeat, medium teneat A G ne<lb></lb>ceſſe eſt, quod ſi ventus præualet, adiungitur remigum renixus, qui <lb></lb>ſi non ſatis ſit, vento cedendum, aut anchora iacienda. </s> <s id="id.001574">Tum autem <lb></lb>vix remiges reſiſtunt, <expan abbr="cũ">cum</expan> nauis eſt in centro, vel radio perpendicula<lb></lb>ri venti, quo in loco propter vim venti maiorem, & anguli per te<emph.end type="italics"></emph.end><pb xlink:href="035/01/139.jpg" pagenum="99"></pb><emph type="italics"></emph>monem faciendi magnitudinem, vt qui rectum æquare debeat, dif<lb></lb>ficillimè ad locum deſtinatum dirigitur: at quantò fuerit remotior <lb></lb>à puncto D, velocius & facilius feretur, quia ventus rectius tan<lb></lb>get puppim, minor enim erit ſemper angulus per temonem facien<lb></lb>dus, vt intelligitur ex G P Q minore: quam G A E, & G I <lb></lb>M minore: quam G P q. </s> <s>Sunt enim duo C A G & G A E, <lb></lb>quia facti à recta G A in rectam C E duobus rectis æquales <lb></lb>prop. 13. lib. 1. & per eandem etiam duo C P G & G P Q duobus <lb></lb>rectis æquales. </s> <s id="id.001575">Ergo duo C A G & G A E duobus C P G & <lb></lb>G P Q ſunt æquales axiom. 1. </s> <s id="id.001576">Eſt autem C P G externus oppo<lb></lb>ſito interno C A G maior, prop. 16. lib. 1. </s> <s>Reliquus igitur G P Q <lb></lb>reliquo G A E minor erit, & ita de cæteris. </s> <s id="id.001577">Sicque nauis proceſſu <lb></lb>ſuo mutabit ſenſim temonem, vt & vela. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001578">9. <foreign lang="el">*dia\ ti/ ta\ periferh= tw=n sxhma/twn eu)kinhto/tera. </foreign></s> </p> <p type="main"> <s id="id.001579">9. Cur è figuris rotundæ <lb></lb>ſunt mobiliores. </s> </p> <p type="main"> <s id="id.001580"><foreign lang="el">*dia\ ti/ ta\ stroggu/la kai\ periferh= tw=n sxhma/twn <lb></lb>eu)kinhto/tera; </foreign></s> <s id="g0130802"><foreign lang="el">trixw=s de\ e)nde/xetai to\n ku/klon kulisqh=nai: <lb></lb>h)\ ga\r kata\ th\n a(yi=da, summetaba/llontos tou= ke/ntrou, <lb></lb>w(/sper o( troxo\s o( th=s a(ma/chs kuli/etai: h)\ peri\ to\ ke/ntron <lb></lb>mo/non, w(/sper ai( troxile/ai tou= ke/ntrou me/nontos, h)\ para\ <lb></lb>to\ e)pi/pedon, tou= ke/ntrou me/nontos, w(/sper o( kerameiko\s troxo\s <lb></lb>kuli/ndetai.</foreign></s> <s id="g0130803"><foreign lang="el">h)\ me\n dh\ ta/xista ta\ toiau=ta, dia/ te to\ <lb></lb>mikrw=| a(/ptesqai tou= e)pipe/dou, w(/sper o( ku/klos kata\ stigmh/n, <lb></lb>kai\ dia\ to\ mh\ prosko/ptein: a)fe/sthke ga\r th=s gh=s <lb></lb>h( gwni/a.</foreign></s> <s id="g0130804"><foreign lang="el">kai\ e)/ti w(=| a)\n a)panth/sh| sw/mati, pa/lin tou/tou <lb></lb>kata\ mikro\n a(/ptetai.</foreign></s> <s id="g0130805"><foreign lang="el">ei) de\ eu)qu/grammon h)=n, th=| eu)qei/a| <lb></lb>e)pi\ polu\ h(/pteto a)\n tou= e)pipe/dou.</foreign></s> </p> <p type="main"> <s id="id.001581">Cur quæ figurarum ro<lb></lb>tundæ & circulares exi<lb></lb>ſtunt, facilius mouentur. <lb></lb></s> <s id="id.001582">Tribus vero modis con<lb></lb>tingit circulum volui. </s> <s id="id.001583">vel <lb></lb>enim ſecundum curuatu<lb></lb>ram vnà centro tranſlato, <lb></lb>qualiter rota plauſtri vol<lb></lb>uitur: vel circa centrum <lb></lb>tantum, quod ipſum quieſ<lb></lb>cat, vt trochleæ vel in pla<lb></lb>no, manente centro, vt fi<lb></lb>guli rota vertitur. </s> <s id="id.001584">An igi<lb></lb>tur hæc celerrima fiunt, <lb></lb>quod parua ſui parte <expan abbr="planũ">planum</expan> <lb></lb><expan abbr="attingãt">attingant</expan>, vt circulus in <expan abbr="pũcto">pun<lb></lb>cto</expan>, & quia non offenſant? <lb></lb></s> <s id="id.001585">Diſtat enim angulus à terra. <lb></lb></s> <s id="id.001586">Et hoc <expan abbr="etiã">etiam</expan> cui occurſant, <pb xlink:href="035/01/140.jpg" pagenum="100"></pb>corpus rurſus parum tan<lb></lb>gant. </s> <s id="id.001587">At ſi recti lineum eſ<lb></lb>ſet, rectitudine ſua mul<lb></lb>tum plani attingeret. </s> </p> <p type="head"> <s id="id.001588">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001589">Cvr quæ figurarum.] <emph type="italics"></emph>In hoc capite redit Ariſtoteles ad fi<lb></lb>guras rotundas, & quærit generaliter cauſas facilitatis motus <lb></lb>earum, eaſque quinque aßignat <expan abbr="modicũ">modicum</expan> tactum, offenſationem exi<lb></lb>guam, nutum dimidiæ partis, motum <expan abbr="perpetuũ">perpetuum</expan>, motum naturalem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001590">Tribus modis.] <emph type="italics"></emph>Rotundorum motus ſimplex per ſpecies indu<lb></lb>citur: ſed diminutè. </s> <s id="id.001591">Perfectè autem ſic. </s> <s id="id.001592">Rotundum omne per ſe mo<lb></lb>uetur, vel ab alio. </s> <s id="id.001593">Per ſe quidem vt cælum, cuius nulla pars primò <lb></lb>moueri dici poteſt: omnes tamen ſimul in loco mouentur. </s> <s id="id.001594">Ab alio <lb></lb>verò, in quo etiam eius quod mouetur pars aliqua primò mouetur, <lb></lb>& quidem duobus modis progrediente axe: vel manente. </s> <s id="id.001595">Progre<lb></lb>diente rurſus duobus modis, priore cum motus incipit à circumfe<lb></lb>rentia, vt in rota ſuper planum volutata: poſteriore <expan abbr="cũ">cum</expan> ab axe, vt in <lb></lb>rota per axem currus circumducta. </s> <s id="id.001596">Manente verò, rurſus duobus <lb></lb>modis, nempè axe moto in ſuo loco: vel etiam immoto. </s> <s id="id.001597">Et moto qui<lb></lb>dem rurſus duobus modis, primo cum motus incipit à circumferen<lb></lb>tia, vt in ſuccula per collopes verſa: ſecundo cum motus incipit ab <lb></lb>axe, vt in mola & rota qua acuuntur gladij: immoto vero, vt in <lb></lb>trochlea, cuius <expan abbr="vertẽtis">vertentis</expan> per funes motus incipit à circumferentia: ſed <lb></lb>axe omnino immoto. </s> <s id="id.001598">Sicque legitima diuiſione & experimento ro<lb></lb>tundorum motus ſex ſpecies infimæ reperiuntur, è quibus prima præ<lb></lb>termiſſa eſt ab Ariſtotele, quia nihil ad Mechanicen, ſecunda præ<lb></lb>termitti non debuit, niſi quia notißima. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001599">Vel enim.] <emph type="italics"></emph>Cum rota currui ſubiecta eſt, tracto curru axis vnà <lb></lb>progreditur. </s> <s id="id.001600">Et cum rota quieſcere nequeat, quia axis tractus pre<lb></lb>mit, & pondus adijcit non ad perpendiculum: ſic enim ad centrum <lb></lb>impelleret: ſed ad latus, quo trahitur, & pondere adiecto ad nutan<lb></lb>tem dimidia ſui parte ſemper rotam, eò labitur. </s> <s id="id.001601">Facilius autem cir<lb></lb>cumuertitur: quam trahatur, itaque procedit. </s> <s id="id.001602">Et ſic ibi quidem rota <lb></lb>ex circumferentia, quam abſidem hîc appellat, mouetur: ſed ab axe <emph.end type="italics"></emph.end><pb xlink:href="035/01/141.jpg" pagenum="101"></pb><emph type="italics"></emph>initium eſt motus. </s> <s id="id.001603">Plurimum itaque confert ad motus facilitatem, <lb></lb>vt tum axis, tum rota intus ſint læuißima, vnde aurigæ axungia <lb></lb>( quæ inde nomen traxit ) ipſa inungunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001604">Quod parua ſui.] <emph type="italics"></emph>Prima cauſa eſt facilitatis motus ſuper plano <lb></lb>in rotundis de modico contactu in omni ſui poſitione. </s> <s id="id.001605">Contactus <lb></lb>enim multa parte ſui facit hærere, & ſimul eſſe ea, quæ ſeſe ſic con<lb></lb>tingunt, & quidem tantò magis, quantò maior eſt hic contactus. <lb></lb></s> <s id="id.001606">quò igitur erit minor, eò minus hærere, citiuſque diuelli faciet. </s> <s id="id.001607">Mul<lb></lb>ta autem præter rotunda vt triangulum æquilaterum, & tetraë<lb></lb>dron planum in puncto contingere poſſunt, ſed non in omni ſui poſi<lb></lb>tione, vt cum ſecundum vnam ſui aream ſuperiacent: at rotunda <lb></lb>ſiue ſphæra ſit, ſiue circulus planum in vno puncto quouis modo ſe<lb></lb>cundum curuaturam poſita attingunt. </s> <s id="id.001608">quod demonſtratum eſt de <lb></lb>illo quidem à Theodoſ. prop. 2. lib. 1. de Sphær. de hoc vero ab Eucli<lb></lb>de prop. 16. lib. 3. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001610">Et quia non off.] <emph type="italics"></emph>Secunda cauſa eſt de occurſantibus, quæ <lb></lb>rurſus cum minimam partem rotundorum attingant, & atterant, <lb></lb>minus impediunt, quam quæ plus attingunt, pluribuſque occurſant. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001611">Diſtat enim angulus.] <emph type="italics"></emph>Cum rotundum incumbit plano ad <lb></lb>omnes rectas à quibus tangitur in ipſo plano angulos facit contin<lb></lb>gentiæ, quorum ſinguli quia ſunt minores quouis acuto angulo re<lb></lb>ctilineo, vt eſt demonſtratum prop. 16. lib. 3. </s> <s>procliues ſunt maxime <lb></lb>ad motum. </s> <s id="id.001612">Latus enim curuum anguli vnius contactus ſemotum <lb></lb>quidem eſt à plano: ſed parum propter anguli anguſtiam. </s> <s id="id.001613">Et ſic non <lb></lb>offenſat, & proximum eſt caſui. </s> <s id="id.001614">Hinc etiam vna cauſa colligi po<lb></lb>teſt, cur rotunda maiora facilius moueantur minoribus, quod <lb></lb>angulos ſui contactus tantò acutiores faciunt: quantò ſunt maiora, <lb></lb>vt in libello noſtro de angulo contactus demonſtrauimus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001615">At ſi rectilineum eſſet.] <emph type="italics"></emph>Difficultas motus in mobili pendet <lb></lb>ab eius internis aut externis. </s> <s id="id.001616">Interna eſt naturalis cuiuſque <expan abbr="propẽſio">propenſio</expan>, <lb></lb>qua extra locum exiſtens, ſi liberum ſinatur mobile, ad <expan abbr="eũ">eum</expan> per ſe fe<lb></lb>ratur. </s> <s id="id.001617">Atque vt ibi vi retineatur, eò tamen quodam motu occulto <lb></lb>tendit, vt graue deorſum, leue ſurſum, & ſemper ſecundum rectam <lb></lb>perpendicularem in qua eſt centrum grauitatis mobilis: aliò nun<lb></lb>quam, niſi vi contraria nixus ille vincatur, vt cum graue ſurſum: <lb></lb>aut leue deorſum: aut vtrumque ad latera propellitur. </s> <s id="id.001618">Itaque prima <emph.end type="italics"></emph.end><pb xlink:href="035/01/142.jpg" pagenum="102"></pb><emph type="italics"></emph>difficultas in <expan abbr="violẽtis">violentis</expan> pendet è renixu. </s> <s id="id.001619">Externa vero ſunt <expan abbr="ſubiectũ">ſubiectum</expan>, <lb></lb>& occurſans, & mobilis figura. </s> <s id="id.001620">Subiectum appello, cui mobile ſu<lb></lb>perincumbit, aut primo inſiſtit, & huic tantò magis qua ſi inhæret <lb></lb>& inſiſtit: quantò pluribus punctis ab eo ſimul tangitur. </s> <s id="id.001621">Tot enim <lb></lb>ſunt lineæ in mobili ad rectos angulos inſiſtentes ſubiecto, quæ vt <lb></lb>vires vnitæ ſe mutuo ſtabiliunt, & fulciunt, ne facile deijciantur: <lb></lb>contrà id, quod antè de Sphærico, vbi cum vna eſſet <expan abbr="tãtum">tantum</expan> quæ in<lb></lb>ſiſteret plano ad rectos, facillima ab illo ſtatu erat deiectio. </s> <s id="id.001622">Maior <lb></lb>igitur inhærentia, maius eſt impedimentum. </s> <s id="id.001623">Occurſans autem dico <lb></lb>quodlibet corpus aliud, vel contra motum, vel cum locum ibi habe<lb></lb>at, minimè <expan abbr="cedẽs">cedens</expan>. </s> <s id="id.001624">Talia ſunt fortuita omnia, quæ vt ſubiectum, quò <lb></lb>pluribus mobilis punctis occurrunt propter eandem cauſam, eò plus. <lb></lb></s> <s id="id.001625">ne fiat inuerſio vel volutatio, impediunt. </s> <s id="id.001626">Tale quoque medium eſt <lb></lb>neceſſarium, per quod fit motus, <expan abbr="rarũ">rarum</expan>, denſum, vtrumque impariter. <lb></lb></s> <s id="id.001627">Hoc enim magis, illud minus: reſiſtit partibus obuijs. </s> <s id="id.001628">Reſiſtens in<lb></lb>ſuper ob loci, in quo eſt, <expan abbr="ſeruãdi">ſeruandi</expan> cupiditatem naturalem, & etiam, ne <lb></lb>admittatur vacuum. </s> <s id="id.001629">Mobilis denique figura quæ quò propius ac<lb></lb>cedit ad ſphæricam vt mobilißimam, eò ad motum pronior: contra <lb></lb>quò remotior. </s> <s id="id.001630">Atque ea ſunt impedimenta, quorum duo ſublatis for<lb></lb>tuitis è figurarum ſuperficialibus rectilineæ, è ſolidis cubo inſunt. <lb></lb></s> <s id="id.001631">Sit enim <lb></lb>ABCD <lb></lb><figure id="id.035.01.142.1.jpg" xlink:href="035/01/142/1.jpg"></figure><lb></lb><expan abbr="rectilineũ">rectili<lb></lb>neum</expan> pla<lb></lb>no E F <lb></lb><expan abbr="inſiſtẽs">inſiſtens</expan>, <lb></lb>& <expan abbr="quidẽ">qui<lb></lb>dem</expan> ſi na<lb></lb>turale eſt <lb></lb>inſita grauitate verget verſus G, & ad rectos inſiſtet rectis A C <lb></lb>& B D & omnibus inter illas interiectis vt H I, K L, M N, <lb></lb>ſicque totidem momentis verſus G contendit. </s> <s id="id.001632">Præterea aër vel <lb></lb>aqua medium occurrens lateri A C, quantum in ſe, eſt impedit tot <lb></lb>punctis, quot ſunt in A C. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001633"><emph type="italics"></emph>Sit & cubus A D, planum K L, vna ſuperficierum ſuarum <lb></lb>E D attingens, tum habeat rectas A E, C F, B D, H G, ad<emph.end type="italics"></emph.end><pb xlink:href="035/01/143.jpg" pagenum="103"></pb><emph type="italics"></emph>rectos inſiſten<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.143.1.jpg" xlink:href="035/01/143/1.jpg"></figure><lb></lb><emph type="italics"></emph>tes, vt totidem <lb></lb>alias, quot ſunt <lb></lb>puncta in ſu<lb></lb>perficie E D <lb></lb>nixu naturali <lb></lb>coniunctæ. </s> <s id="id.001634">Tot <lb></lb>vires nullo <expan abbr="tẽporis">tem<lb></lb>poris</expan> momento alio inclinantes ſe à ſuo ſtatu dimoueri ſinent: medio <lb></lb>etiam obuio ſeu aëre, ſeu aqua totidem ad latus punctis propter æqua<lb></lb>litatem ſuperficierum impediente. </s> <s id="id.001635">Ex quo fit vt figurarum planum <lb></lb>pro vertice habentium ſtabilißima dicatur cubus. </s> <s id="id.001636">Et quia talis eſt, <lb></lb>eius figuram Plato affinxit terræ in loco ſuo prorſus immobili. </s> <s id="id.001637">Ob id <lb></lb>etiam pictores <expan abbr="Virtutẽ">Virtutem</expan> quæ ſola conſtans eſt animi ſtatus, vel etiam <lb></lb>Mercurium qui ſuos ſectatores numquam deſerit cubo inſidentem <lb></lb>repræſentant: ſicut ob contrariam cauſam Fortunam. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001638">Quæ tantùm conſtans in leuitate ſua eſt. <lb></lb></s> <s><emph type="italics"></emph>globo mobilißimo. </s> <s id="id.001639">Sed quod ad figuram attinet quia pluribus planis <lb></lb>clauditur quam tetraedrum, vel pentaedrum, vt qui ſit hexaedrum, <lb></lb>& ideo propius accedit ad ſphæram, ad volutationem adhuc procli<lb></lb>uior eſt, quam illa ſint. </s> <s id="id.001640">hinc teſſerarum talorumque in alueo per hanc <lb></lb><expan abbr="figurã">figuram</expan> planum vnum pro vertice, & planum vnum pro baſi ſemper <lb></lb><expan abbr="ſeruantẽ">ſeruantem</expan> ludus. </s> <s id="id.001641">Sed hîc non immeritò <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.143.2.jpg" xlink:href="035/01/143/2.jpg"></figure><lb></lb><emph type="italics"></emph>quæri poteſt. </s> <s id="id.001642">cur terræ ſtare debenti na<lb></lb>tura figuram attribuit ſphæricam, vt <lb></lb><expan abbr="docẽt">docent</expan> aſtronomi. </s> <s id="id.001643">vnum enim eſt ex <expan abbr="argumẽtis">ar<lb></lb>gumentis</expan> Copernici terram moueri pro<lb></lb>bare volentis. </s> <s id="id.001644">Sed id nullum locum ha<lb></lb>bet, quia quæ hactenus dicta ſunt im<lb></lb>pedimenta figurarum, ſunt <expan abbr="figurarũ">figurarum</expan> in <lb></lb>plano <expan abbr="nõ">non</expan> <expan abbr="autẽ">autem</expan> in concauo ſimili & <expan abbr="cõ">con</expan><emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.143.3.jpg" xlink:href="035/01/143/3.jpg"></figure><lb></lb><emph type="italics"></emph>gruenti <expan abbr="exiſtentiũ">exiſtentium</expan>, cuiuſmodi eſt terra, <lb></lb>cuiuſque omnes partes <expan abbr="rotũdæ">rotundæ</expan> exiſten<lb></lb>tis æquabilius coniuncto nixu ad cen<lb></lb>trum contendunt: quam ſi alterius eſſet <lb></lb>cuiuſcunque figuræ. </s> <s id="id.001645">Sit enim cubica <lb></lb>cuius centrum A & B punctum an<emph.end type="italics"></emph.end><pb xlink:href="035/01/144.jpg" pagenum="104"></pb><emph type="italics"></emph>gulare, & ita remotius quam C laterale, non tanto nixu contendet: <lb></lb>quam ipſum C. </s> <s id="id.001646">Quò enim mobile naturale propius eſt, eò obnixius <lb></lb>incumbit. </s> <s id="id.001647">Eadem eſt ratio cuiuſcumque figuræ præterquam ſphæri<lb></lb>cæ, cuius puncta B, C, D, in eadem ſuperficie æqualiter à centro <lb></lb>ſemper diſtant. </s> <s id="id.001648">Itaque terra, vt medium vndiquaque obtineret, & <lb></lb>vt quæ in ea omnia puncta æquali nixu ad eius centrum niteren<lb></lb>tur, debuit eſſe ſphærica: ob idque immobilißima eſt, nullibique <lb></lb>nutat, contrà quam dixit Poëta,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001649">Aſpice nutantem conuexo pondere mundum. <lb></lb></s> </p> <p type="main"> <s><emph type="italics"></emph>Nutus enim hic eſt inclinatio aliò facta: quam id, à quo ſuſpenditur, <lb></lb>vel ſuſtinetur, inclinet. </s> <s id="id.001650">Cuiuſmodi nihil eſt in mundo, aut in terra: <lb></lb>ſed omne punctum eò fertur, quò id à quo ſuſtinetur, rectà ſcilicet ad <lb></lb>centrum, non vt D ad E, hoc enim eſſet contra naturam grauis, <lb></lb>quippe in diuerſum per ambitum. </s> <s id="id.001651">Quærenti verò cur igitur cœlum <lb></lb>exacte ſphæricum moueatur. </s> <s id="id.001652">Reſpondent moueri in loco non na<lb></lb>turaliter: ſed voluntariè. </s> <s id="id.001653">Omnis enim motus naturalis eſt per rectam <lb></lb>de centro ad locum. </s> <s id="id.001654">Voluntas illa eſt intelligentiæ, quæ cœlo vt mens <lb></lb>corpori præeſt. </s> <s id="id.001655">Et per ſe cum motum hunc creet ſine defatigatione eſt <lb></lb>hic motus in regularißimo corpore regularißimus, & facillimo ad <lb></lb>motum velocißimus, vt eſt apud Ptolomæum concl. 1. lib. 1. <emph.end type="italics"></emph.end> <foreign lang="el">meg. <lb></lb>suntac.</foreign> </s> <s><emph type="italics"></emph>Velocitatem autem intelliget, qui intellexerit quot millia<lb></lb>ria, habeat circulus in cœlo extimo maximus, & quot ex his vno<lb></lb>quoque momento conficiat. </s> <s id="id.001656">Intelligetur quoque quomodo illius cœli <lb></lb>motus ſit omnium motuum <expan abbr="mẽſura">menſura</expan>. </s> <s id="id.001657">Nam cum menſura ſit in vno<lb></lb>quoque genere minimum, vt eſt cap. 4. lib. 2. de Cœl. </s> <s>hic autem mo<lb></lb>tus minimus debet dici, qui per minimam lineam earum quæ æqua<lb></lb>les areas includunt fit, cuiuſmodi eſt circularis, ſicque ſecundum eam <lb></lb>motus erit celerrimus, quia minimus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001658">Multum plani.] <emph type="italics"></emph>Ex hoc loco intelligatur, quod mobile, quantò <lb></lb>latius eſt: tantò difficilius moueri per planum. </s> <s id="id.001659">Attritio enim per <lb></lb>contactum plani cum mobili, tanto maior erit. </s> <s id="id.001660">Ideo tangens in pun<lb></lb>cto facillime mouetur, vt dictum eſt. </s> <s id="id.001661">Tangens in linea difficilius: <lb></lb>tangens per ſuperficiem difficillime. </s> <s id="id.001662">Imò vero plana exquiſita iun<lb></lb>cta ſine ferruminatione ſeparari nequeunt, ſi ſuperius leuiter ap<lb></lb>prehenſum ab inferiore diſiungere quis conetur. </s> <s id="id.001663">Rationem ſi vis <lb></lb>aliquam, vide apud Scaligerum exercit. 333. <emph.end type="italics"></emph.end></s> </p> </subchap1> <pb xlink:href="035/01/145.jpg" pagenum="105"></pb> <subchap1> <p type="main"> <s id="id.001665"><foreign lang="el">e)/ti h(=| e)pire/pei e)pi\ to\ ba/ros, <lb></lb>tau/th| kinei= o( kinw=n. </foreign></s> <s id="id.001665a"><foreign lang="el">o(/tan me\n ga\r pro\s o)/rqh\n h( dia/metros <lb></lb>h)=| tou= ku/klou tw=| e)pipe/dw|, a(ptome/nou tou= ku/klou kata\ stigmh\n <lb></lb>tou= e)pipe/dou, i)/son to\ ba/ros e)p' a)mfo/tera dialamba/nei <lb></lb>h( dia/metros. </foreign></s> <s id="id.001665b"><foreign lang="el">o(/tan de\ kinh=tai eu)qu\s ple/on e)f' w(=| <lb></lb>kinei=tai, w(/sper r(e/pon e)nteu=qen, eu)kinhto/teron tw=| w)qou=nti ei)s <lb></lb>tou)/mprosqen: e)f' o(\ ga\r r(e/pei e(/kaston, eu)ki/nhto/n e)stin. </foreign></s> <s id="id.001665c"><foreign lang="el"><lb></lb>ei)/per kai\ to\ e)pi\ to\ e)nanti/on th=s r(oph=s duski/nhton.</foreign></s> </p> <p type="main"> <s id="id.001666">Præterea quò pondus <lb></lb>vergit, eò motor impellit. <lb></lb></s> <s id="id.001667">Quum igitur diameter cir<lb></lb>culi rectà inſiſtit plano, cir<lb></lb>culo in puncto planum at<lb></lb>tingente, æqualiter vtrim<lb></lb>que diameter pondus di<lb></lb>ſterminat. </s> <s id="id.001668">Quando verò <lb></lb>mouetur ſtatim plus ad id <lb></lb>mouetur, veluti eò repens <lb></lb>motu facilius impellente <lb></lb>in anteriorem partem. </s> <s id="id.001669">Eò <lb></lb>enim, quò vergit vnum<lb></lb>quodque, facilius moue<lb></lb>tur. </s> <s id="id.001670">Quandoquidem ſi in <lb></lb>contrarium: quam quò <lb></lb>vergat, moueatur, difficulter mouebitur. </s> </p> <p type="head"> <s id="id.001671">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001672">Præterea quò.] <emph type="italics"></emph>Tertia cauſa facilitatis eſt motus, quando mo<lb></lb>bile in omni poſitu ſuper plano dimidia ſui parte quoquouerſum <lb></lb>ad planum ipſum acclinat, vt fit in rotundo, quod ipſum tangit in <lb></lb>puncto, vt ante docuimus, ſicque quoquouerſum vergit. </s> <s id="id.001673">Hinc dico <lb></lb>ſphæricum ad latus moueri poſſe quacumque vi, quæ aërem impulſu <lb></lb>vel tractu diuidere poßit. </s> <s id="id.001674">Vnus enim aër circunſtans impedit, quo <lb></lb>minus voluatur. </s> <s id="id.001675">Non enim nixus aſcendendi ſurſum, cum ob graui<lb></lb>tatem eò non nitatur: neque rurſus deorſum deſcendendi, ob æqui<lb></lb>librium enim innixus pondus non adfert, quin potius dimidia ſui <lb></lb>parte quoquouerſum nutans nititur moueri, vt in circulo ad cen<lb></lb>trum: à contactu quoque, quia minimo, non impeditur. </s> <s id="id.001676">Relinqui<lb></lb>tur ergò tantum impediri à medio circunstante. </s> <s id="id.001677">Hoc à quacun<lb></lb>que vi vt oris flatu ſi diuidatur, ſphæricum in locum diuiſionis pro<lb></lb>mouebitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001678">Rectà inſiſtit.] <emph type="italics"></emph>Diameter circuli rectà inſiſtere in plano di<lb></lb>citur cum ad omnes rectas lineas à quibus tangitur in ipſo plano<emph.end type="italics"></emph.end><pb xlink:href="035/01/146.jpg" pagenum="106"></pb><emph type="italics"></emph>rectos angulos ef<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.146.1.jpg" xlink:href="035/01/146/1.jpg"></figure><lb></lb><emph type="italics"></emph>ficit ex def. 3. lib. <lb></lb>11. vt A B dia<lb></lb>meter ad B O, B D, <lb></lb>B E, B F. </s> <s id="id.001680">Et A B <lb></lb>quia diameter eſt <lb></lb>circulum ſuum bi<lb></lb>fariam diuidit ex <lb></lb>def. 17. lib. 1. </s> <s id="id.001681">Sic<lb></lb>que tanta pars eſt <lb></lb>ad G, quanta ad H. </s> <s id="id.001682">Similiter maximus in ſphæra circulus recta <lb></lb>inſiſtens ſphæram bifariam diſpeſcit. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="g0130808"><foreign lang="el">e)/ti le/gousi/ <lb></lb>tines o(/ti kai\ h( grammh\ h( tou= ku/klou, e)n fora=| e)sti\n <lb></lb>a)ei/, w(/sper ta\ me/nonta, dia\ to\ a)nterei/dein, oi(=on kai\ toi=s <lb></lb>mei/zosi ku/klois u(pa/rxei pro\s tou\s e)la/ttonas. </foreign></s> <s id="g0130808a"><foreign lang="el">qa=tton ga\r <lb></lb>u(po\ th=s i)/shs i)sxu/os kinou=ntai oi( mei/zous kai\ ta\ ba/rh kinou=si, <lb></lb>dia\ to\ r(oph/n tina e)/xein th\n gwni/an th\n tou= mei/zonos <lb></lb>ku/klou pro\s th\n tou= e)la/ttonos, kai\ ei)=nai o(/per h( dia/metros <lb></lb>pro\s th\n dia/metron. </foreign></s> <s id="g0130808b"><foreign lang="el">a)lla\ mh\n pa=s ku/klos mei/zwn pro\s<lb></lb> e)la/ttona.</foreign></s> <s id="g0130808c"><foreign lang="el"> a)/peiroi ga\r oi( e)la/ttones.</foreign></s> <s id="g0130809"><foreign lang="el">ei) de\ kai\ pro\s e(/teron <lb></lb>e)/xei r(oph\n o( ku/klos, o(moi/ws de\ eu)ki/nhtos, kai\ a)/llhn a)\n <lb></lb>e)/xoi r(oph\n o( ku/klos kai\ ta\ u(po\ ku/klou kinou/mena, ka)\n mh\ <lb></lb>th=| a(yi/di a(/pthtai tou= e)pipe/dou, a)ll' h)\ para\ to\ e)pi/pedon, <lb></lb>h)\ w(s ai( troxile/ai. </foreign></s> <s id="g0130809a"><foreign lang="el">kai\ ga\r ou(/tws e)/xonta, r(a=|sta kinou=ntai <lb></lb>kai\ kinou=si to\ ba/ros, h)\ ou) tw=| kata\ mikro\n a(/ptesqai kai\ <lb></lb>proskrou/ein, a)lla\ di' a)/llhn ai)ti/an.</foreign></s> <s id="g0130812"><foreign lang="el">au(/th de/ e)stin h( ei)rhme/nh <lb></lb>pro/teron, o(/ti e)k du/o forw=n gege/nhtai o( ku/klos, w(/ste <lb></lb>mi/an au)tw=n ai)ei\ e)/xein r(oph/n, kai\ oi(=on fero/menon au)to\n <lb></lb>ai)ei\, kinou=sin oi( kinou=ntes, o(/tan kinw=sin kata\ th\n perife/reian <lb></lb>o(pwsou=n. </foreign></s> <s id="g0130813"><foreign lang="el">ferome/nhn ga\r au)th\n kinou=sin: th\n me\n ga\r ei)s <lb></lb>to\ pla/gion au)tou= ki/nhsin, w)qei= to\ kinou=n, th\n de\ e)pi\ th=s <lb></lb>diame/trou, au)to\s kinei=tai.</foreign></s> </p> <p type="main"> <s id="id.001683"><arrow.to.target n="marg26"></arrow.to.target></s> </p> <p type="margin"> <s id="id.001684"><margin.target id="marg26"></margin.target>*<foreign lang="el">e)/xh</foreign></s> </p> <p type="main"> <s id="id.001685">Præterea nonnulli di<lb></lb>cunt lineam circuli in per<lb></lb>petuo motu eſſe, vt quæ <lb></lb>manent, propter renixum. <lb></lb></s> <s id="id.001686">Vt maioribus circulis eue<lb></lb>nit reſpectu minorum. </s> <s id="id.001687">Ce<lb></lb>lerius enim ab æquali vi <lb></lb>maiores <expan abbr="mouẽtur">mouentur</expan>, & pon<lb></lb>dera mouent. </s> <s id="id.001688">quia maioris <lb></lb>circuli angulus <expan abbr="nutũ">nutum</expan> quen<lb></lb>dam habet ad minoris an<lb></lb>gulum. </s> <s id="id.001689">Et eſt vt diameter <lb></lb>ad <expan abbr="diametrũ">diametrum</expan>: ſic omnis ma<lb></lb>ior circulus ad minorem. <lb></lb></s> <s id="id.001690">Infiniti autem ſunt mino<lb></lb>res. </s> <s id="id.001691">Si verò etiam circulus <lb></lb>nutum habet ad alterum. <lb></lb></s> <s id="id.001692">Similiter verò facile mobi<lb></lb>lis <expan abbr="aliũ">alium</expan> <expan abbr="nutũ">nutum</expan> habet circulus, <lb></lb>& quæ à circulo <expan abbr="mouẽtur">mouentur</expan>, <lb></lb><expan abbr="etiãſi">etiamſi</expan> ſua curuatura <expan abbr="planũ">planum</expan> <lb></lb><expan abbr="nõ">non</expan> <expan abbr="cõtingat">contingat</expan>: ſed vel propè <lb></lb>planitiem, vel vt trochleæ. <pb xlink:href="035/01/147.jpg" pagenum="107"></pb>Etenim quæ ſic ſe habent, <lb></lb>facillimè <expan abbr="mouẽtur">mouentur</expan>, & mo<lb></lb>uent pondus. </s> <s id="id.001693">an non quia <lb></lb>parua ſui parte tangunt & <lb></lb>offenſant. </s> <s id="id.001694">Sed ob <expan abbr="aliã">aliam</expan> cau<lb></lb>ſam. </s> <s id="id.001695">Hæc vero prius eſt di<lb></lb>cta. </s> <s id="id.001696">quod circulus ex dua<lb></lb>bus lationibus effectus eſt. <lb></lb></s> <s id="id.001697">Itaque vnam harum ſem<lb></lb>per habet nutantem. </s> <s id="id.001698">Et <expan abbr="eũ">eum</expan>, <lb></lb>quaſi ſemper moueatur, <lb></lb>mouent motores, quando <lb></lb>quocunque illum ſecun<lb></lb>dum <expan abbr="peripheriã">peripheriam</expan> mouerint. <lb></lb></s> <s id="id.001699">Motam enim ipſam mo<lb></lb>uent. </s> <s id="id.001700">Eam ſiquidem, qua <lb></lb>mouetur in <expan abbr="obliquũ">obliquum</expan>, mo<lb></lb>tor impellit: illa verò, quæ ſuper diametro efficitur, ipſe<lb></lb>met ſe circulus mouet. </s> </p> <p type="head"> <s id="id.001701">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001702">Præterea nonnulli.] <emph type="italics"></emph>Quarta cauſa eſt de perpetuo motu con<lb></lb>firmata nonnullorum, ſed innominatorum authoritate: & ſimi<lb></lb>litudine e contrarijs ſic. </s> <s id="id.001703">quemadmodum quæ perpetuò manent, ma<lb></lb>nent propter contrarium motui renixum: ſic in quibus eſt ad mo<lb></lb>tum perpetua propenſio, perpetuò moueri ea debent. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001704">Vt maioribus circulis.] <emph type="italics"></emph>Nutus ſeu perpetua propenſio con<lb></lb>firmatur eſſe ſemper in circulo. </s> <s id="id.001705">quia quicunque ſit ſemper in ſe habet <lb></lb>concentricos minores infinitos, & maior tum celerius mouetur ab <lb></lb>æquali vi, & cum eo etiam pondera: tum angulus maioris nutum <lb></lb>habet ad angulum æqualem, qui eſt in minori circulo. </s> <s id="id.001706">quia anguli <lb></lb>maioris crura maiora ſunt, ſempérque eſt, vt diameter ad diame<lb></lb>trum. </s> <s id="id.001707">Sunt enim circulorum ſemidiametri. </s> <s id="id.001708">Partes autem cum pari<lb></lb>ter multiplicibus ſunt in eadem ratione prop. 15. lib. 5. </s> <s>Diameter au<lb></lb>tem maior celerius mouetur, hîc autem notandum eſt angulos non <emph.end type="italics"></emph.end><pb xlink:href="035/01/148.jpg" pagenum="108"></pb><emph type="italics"></emph>ſumi pro inclinatione: ſed pro crurum<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.148.1.jpg" xlink:href="035/01/148/1.jpg"></figure><lb></lb><emph type="italics"></emph><expan abbr="lõgitudine">longitudine</expan>. </s> <s id="id.001709">hæc autem figura hac cir<lb></lb>culorum concentricorum & à cen<lb></lb>tris angulorum illuſtrantur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001710">Nutum habet.] <foreign lang="el">ro/ph</foreign> <emph type="italics"></emph>Nutus <lb></lb>vis eſt cuiuſque impreſſa à Deo & <lb></lb>natura, qua in loco ſuo naturali quieſ<lb></lb>cit, & volenti ab eo diſpellere, reſiſtit. <lb></lb></s> <s id="id.001711">vnde<emph.end type="italics"></emph.end> <foreign lang="el">a)nteirisis</foreign> <emph type="italics"></emph>renixus. </s> <s id="id.001712">Extra locum verò ad eum per breuißi<lb></lb>mam viam mouetur. </s> <s id="id.001713">Deus enim ne omnia in omnibus eſſent, vni<lb></lb>cuique ab initio proprium locum tribuit, in quo & circa quem con<lb></lb>globatur, & ibi hæret. </s> <s id="id.001714">Hinc etiam ſingulæ partes ſuis totis natura <lb></lb>inhærent, & in ijs certum quendam ſitum habent, à quo remotæ ad <lb></lb>ipſum redeunt, vt in arcubus & balliſtis videre licet. </s> <s id="id.001715">Nutus autem <lb></lb>naturalis eſt: vel non naturalis: vel mixtus. </s> <s id="id.001716">Naturalis eſt is, quo res <lb></lb>quælibet natura ſua mouetur: aut <expan abbr="mouẽti">mouenti</expan> reſiſtit habita ratione loci <lb></lb>ſui naturalis, & ſitus ſuarum partium. </s> <s id="id.001717">Non naturalis eſt is, quo nec <lb></lb>ratione loci naturalis, nec ſitus partium mouetur, vt fortuitus vel <lb></lb>voluntarius. </s> <s id="id.001718">Ille vt ventorum, hic vt animalium. </s> <s id="id.001719">Mixtus parti<lb></lb>ceps eſt vtriuſque. </s> <s id="id.001720">Nutus voluntarij mille ſunt modi <expan abbr="nõ">non</expan> aliter, quam <lb></lb>voluntatis decreto determinabiles. </s> <s id="id.001721">At naturalis vnius tantum eſt <lb></lb>à loco non naturali ad naturalem. </s> <s id="id.001722">Hinc linea recta, quæ eſt à termi<lb></lb>no à quo incipit moueri ad terminum in quo quieſcit, linea nutus, <lb></lb>& eadem in terminis contrarijs renixus dicitur, vt ſi ab eo in quo <lb></lb>quieſcit aliena vis ad alium moueret: linea verò ipſam ſecans ad an<lb></lb>gulos inæquales eſt linea obliqui nutus, vel renixus: & ſecans ad <lb></lb>rectos nec ad nutum eſt, nec ad renixum. </s> <s id="id.001723">Nunc igitur hoc cum ve<lb></lb>rum eſſe experiamur, & ratio conuincat, quantò quodque remotius <lb></lb>eſt à loco, in quo naturaliter quieſceret, tantò ad eum magis conari, <lb></lb>remotioris maior erit nutus. </s> <s id="id.001724">In peripheria maiori punctum A re<lb></lb>motius puncto D. </s> <s id="id.001725">Magis igitur nutat. </s> <s id="id.001726">Eſt enim linea A C maior <lb></lb>quam D E vt ex ſimilibus triangulis A B C, D B E demonſtrari <lb></lb>facile poteſt. </s> <s id="id.001727">Et ſic angulus ad angulum nutare dicitur, cum in an<lb></lb>gulorum æqualitate crurum eſt inæqualitas. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001728">Et eſt vt diameter.] <emph type="italics"></emph>Hæc analogia antea à nobis demonſtra<lb></lb>ra eſt. </s> <s id="id.001729">Huc autem adducta confirmat in maioribus circulis maiorem <emph.end type="italics"></emph.end><pb xlink:href="035/01/149.jpg" pagenum="109"></pb><emph type="italics"></emph>nutum ad motum ineſſe: quam in minoribus. </s> <s id="id.001730">Sed cum omnis circu<lb></lb>lus habeat intra ſe infinitos concentricos, omnis peripheria nutum <lb></lb>habebit infinitum, & ideò perpetuum ad motum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001731">Infiniti autem.] <emph type="italics"></emph>Quod infiniti circuli minores concentrici in<lb></lb>ſint in quouis dato circulo ſic demonſtrabimus. </s> <s id="id.001732">Sit circulus C B, <lb></lb>cuius ſemidiameter D B bifariam <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.149.1.jpg" xlink:href="035/01/149/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſecetur, vt in puncto E prop. 10. <lb></lb>lib. 1. </s> <s>Et centro D interuallo D E <lb></lb>deſcriptus circulus poſt. 3. </s> <s id="id.001733">Hic <lb></lb>erit concentricus & minor ipſo <lb></lb>C B def. 1. lib. 3. </s> <s id="id.001734">Rurſus recta D <lb></lb>E bifariam ſecetur, vt in puncto <lb></lb>F, & centro D eodem interuallo <lb></lb>D F deſcriptus circulus erit con<lb></lb>centricus & minor. </s> <s id="id.001735">Et eadem ra<lb></lb>tione deinceps ad infinitum, cum rectam lineam ſemper biſſecare li<lb></lb>ceat prop. 10. lib. 1. </s> <s>Et ſic infiniti erunt circuli concentrici minores <lb></lb>in quouis circulo. </s> <s id="id.001736">quod erat demonſtrandum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001737">Etiamſi curuatura.] <emph type="italics"></emph>Repetit cauſam perpetui motus, aut nu<lb></lb>tus ad motum, quæ in circulo eſt, cum ſua abſide id eſt curuatura at<lb></lb>tingit planum, ineſſe, etiamſi non attingat, vt fit in rotis figulorum, <lb></lb>& in trochleis. </s> <s>de quibus poſtea. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001739">Sed ob aliam cauſam.] <emph type="italics"></emph>Quinta cauſa de naturali motu ſe<lb></lb>cundum peripheriam hîc leuiter attingitur, vel potius ex anteceden<lb></lb>tibus breuiter repetitur. </s> <s id="id.001740">Naturalis autem iſte motus intelligi debet, <lb></lb>dum fit circulus à rectæ manente altero extremo, & moto altero, <lb></lb>quod ſuo motu deſcribit peripheriam. </s> <s id="id.001741">In facto enim circulo, vel glo<lb></lb>bo naturali quatenus particeps eſſet grauitatis reuera motus natura<lb></lb>lis eſt is, quò rectà deorſum fertur. </s> <s id="id.001742">Sed eo impedito ob planum cui in<lb></lb>cumbit non cedens, per vim aliquam impulſus globus ad motum cir<lb></lb>cularem ſe recipit. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001743">10. <foreign lang="el">*dia\ ti/ meizo/nes ku/kloi kinhtikw/teroi.</foreign></s> </p> <p type="main"> <s id="id.001744">10. Cur maiores circuli <lb></lb>ſunt mouentiores. </s> </p> <p type="main"> <s id="id.001745"><foreign lang="el">*dia\ ti/ ta\ dia\ tw=n meizo/nwn ku/klwn ai)ro/mena kai\ <lb></lb>e(lko/mena, r(a=|on kai\ qa=tton kinou=men, oi(=on kai\ ai( troxilai=ai <lb></lb>ai( mei/zous tw=n e)latto/nwn, kai\ ai( skuta/lai o(moi/ws;</foreign></s> <s id="g0130902"><foreign lang="el">h)\ <lb></lb>dio/ti o(/sw| a)\n mei/zwn h( e)k tou= ke/ntrou h)=| e)n tw=| i)/sw| xro/nw|, <lb></lb>ple/on kinei=tai xwri/on. </foreign></s> <s id="g0130903"><foreign lang="el">w(/ste kai\ tou= i)/sou ba/rous e)po/ntos, <lb></lb>poih/sei to\ au)to/, w(/sper ei)/pomen, kai\ ta\ mei/zw zuga\ tw=n <lb></lb>e)latto/nwn a)kribe/stera ei)=nai.</foreign></s> <s id="g0130904"><foreign lang="el">to\ me\n ga\r sparti/on e)sti\ <lb></lb>ke/ntron.</foreign></s> <s id="g0130904a"><foreign lang="el">tou= de\ zugou= ai( e)pi\ ta/de tou= sparti/ou ai( e)k tou= <lb></lb>ke/ntrou.</foreign></s> </p> <p type="main"> <s id="id.001746">Cur per maiores circu<pb xlink:href="035/01/150.jpg" pagenum="110"></pb>los ſublata & tracta faci<lb></lb>lius mouemus, vt ſi tro<lb></lb>chleæ ſint maiores minori<lb></lb>bus, & ſcytalæ ſimiliter. </s> <s id="id.001747">An <lb></lb>quia quantò maior fuerit <lb></lb>radius in tempore æquali, <lb></lb>per maius mouetur <expan abbr="ſpatiũ">ſpatium</expan>. <lb></lb></s> <s id="id.001748"><expan abbr="Itaq;">Itaque</expan> æquali inſiſtente one<lb></lb>re, idem faciet, vt diximus <lb></lb>etiam libras maiores mi<lb></lb>noribus eſſe exactiores. </s> <s id="id.001749">Eſt <lb></lb>enim agina <expan abbr="cẽtrũ">centrum</expan>. </s> <s id="id.001750">Et lineæ <lb></lb>in librili, quæ ſunt ab agina <lb></lb>vtrimque, ſunt radij. </s> </p> <p type="head"> <s id="id.001751">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001752">Cvr per maiores.] <emph type="italics"></emph>In hoc capite tractatur problema de ma<lb></lb>ioribus circulis, & ſphæricis. </s> <s id="id.001753">cur ſcilicet facilius & celerius <lb></lb>moueantur & moueant. </s> <s id="id.001754">Cui reſpondetur ex lineæ à centro longitu<lb></lb>dine maiore. </s> <s id="id.001755">Ratio ſic diſponetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001756"><emph type="italics"></emph>Vbi lineæ à centro ſunt maiores: ibi per motum æquali tempore <lb></lb>maius ſpatium conficitur, & facilis etiam motio fit, tum an<lb></lb>nexa onera mouentur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001757"><emph type="italics"></emph>In circularibus & ſphæricis maioribus lineæ à centro <lb></lb>ſunt maiores: quam in minoribus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001758"><emph type="italics"></emph>Ergo circuli & ſphæræ maiores æquali tempore maius ſpatium <lb></lb>conficient, facilius mouebuntur, & annexa onera moue<lb></lb>bunt: quam minores. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001759"><emph type="italics"></emph>Ex hoc colligimus maiores rotas in curribus vna volutatione tan<lb></lb>tam lineam cum conficiant: quanta orbitæ reſpondet, nec maiori tra<lb></lb>ctu egeant: quam minores, tantò commodiores eſſe ad celeritatem, & <lb></lb>motus facilitatem: quantò maiores extiterint. </s> <s id="id.001760">Et cum in facili tractu <lb></lb>biroti onerati ſarcina tendere debeat ad æquilibrium, vt neque tolla<lb></lb>tur de collo iugum præ pondere poſteriore, neque ſic prematur, vt ſi<lb></lb>mul iumentum trahat, & geſtet: ſed potius trahat: quam geſtet: in<emph.end type="italics"></emph.end><pb xlink:href="035/01/151.jpg" pagenum="111"></pb><emph type="italics"></emph>maioribus autem rotis æquilibrium illud facilius ſit, quia ſarcina al<lb></lb>tior, & ſic trahitur tantum: in paruis depreßior, ſicque nonnihil le<lb></lb>uanda. </s> <s id="id.001761">Vbi autem ſuſtinere & trahere opus eſt, vt in bellicis tor<lb></lb>mentis vnus equus iugum ſuſtinere, alij loris trahere debent. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001762">Vt ſi trochleæ.] <emph type="italics"></emph>Problema illuſtratur duobus exemplis Tro<lb></lb>chleæ & Scytalæ. </s> <s id="id.001763">Eſt autem Trochlea inſtrumentum tractorium ex <lb></lb>rotula circa axiculum fixum alicubi appenſum per <expan abbr="funẽ">funem</expan> ductarium, <lb></lb>in eius circumferentia circumuoluta. </s> <s id="id.001764">Geminatur aliquando, tripli<lb></lb>catur, & amplius multiplicatur. </s> <s id="id.001765">Vnde ſunt illa tractoria infinita<lb></lb>rum propemodum virium Triſpaſton, Penteſpaſton, Polyſpaſton, in <lb></lb>quibus rotulæ ſibi inuicem ſubſeruientes, & tanquam onus attra<lb></lb>hendum diuidentes ſumma facilitate ipſum attrahunt, de quo qui <lb></lb>multa admirabilia videre volet, videat apud Guidum Vbaldum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001766">Etſcytalæ.] <emph type="italics"></emph>Scytala lignum eſt cylindricum cuius pro duplici <lb></lb>vſu duo genera ſtatuuntur. </s> <s id="id.001767">Vnus vſuum eſt ad attrahendum, & ſic <lb></lb>in eius altera extremitate ferrum quoddam inflexum eſt pro manu<lb></lb>brio, vbi annectitur potentia mouens: vel loco ferri vectes <expan abbr="emergũt">emergunt</expan> <lb></lb>aliquot, qui vicißim per vim annexam mouentur: vel loco vectis <lb></lb>rota maior, quod idem eſt: ſicque vel manubrio, vel vectibus, vel <lb></lb>rota mota vnà mouetur illud lignum cylindricum cum ſuo fune du<lb></lb>ctario. </s> <s id="id.001768">Et cum eo pondus alligatum eleuatur. </s> <s id="id.001769">Hoc genus ſcytalæ eſt <lb></lb>idem quod axis in peritrochio de quo poſtea. </s> <s id="id.001770">De hoc autem genere lo<lb></lb>cus hic intelligi debet. </s> <s id="id.001771">De altero dicetur cap. 12. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001772">Vt diximus etiam.] <emph type="italics"></emph>Confirmatio eſt propoſitionis præceden<lb></lb>tis ſyllogiſmi per ſpeciem libræ, quæ tantò exactior exiſtit: quantò li<lb></lb>brile habet longius, è ſuperioribus repetitam. </s> <s id="id.001773">Cæterum præter proble<lb></lb>ma huius capitis alia quæri poſſunt ad idem ferè pertinentia ſcitu <lb></lb>digna, nec minus ſubtilia, nempè. </s> <s id="id.001774">Quare binæ rotæ quaternis facilio<lb></lb>res ſint. </s> <s id="id.001775">Quare prioribus poſteriores rotas maiores eſſe oporteat. <lb></lb></s> <s id="id.001776">Quare maior ſarcina in anteriore plauſtri parte poni debeat. </s> <s id="id.001777">Soluitur <lb></lb>primum quia rota quælibet, vt grauis, ad centrum ſpectat, & arceri <lb></lb>deſcenſu eſt contra eius naturam: arcetur & cum tollitur ſurſum, & <lb></lb>cum trahitur adlatus, quippè in diuerſum per <expan abbr="ambitũ">ambitum</expan>. </s> <s id="id.001778">Plures igitur <lb></lb>rotæ augebunt onus, & ideo trahentis laborem. </s> <s id="id.001779">Itaque binæ rotæ <lb></lb>quaternis faciliores erunt, vnde bellicis tormentis, licet immanibus <lb></lb>duæ ſatis ſunt. </s> <s id="id.001780">Quod autem quis obijceret per rotas plures pondus plus<emph.end type="italics"></emph.end><pb xlink:href="035/01/152.jpg" pagenum="112"></pb><emph type="italics"></emph>diſtribui, & tanquam diuidi. </s> <s id="id.001781">Id ſanè verum eſt & vtile ad facili<lb></lb>tatem ſuſtentationis, non item ad tractum. </s> <s id="id.001782">Etſi biroti ſarcina in pe<lb></lb>toritum transferatur, eadem iumento grauior fiet tantò, quantò gra<lb></lb>uior currus. </s> <s id="id.001783">Sed fallaciæ cauſa eſt quod petorita birotis plus ſuſtinent. <lb></lb></s> <s id="id.001784">Secundum quia maiores tanquam altiores prioribus minoribus quaſi <lb></lb>incumbunt, ſicque in proclinatiores iam partes onus recumbens à <lb></lb>facilius motis maioribus, vna quoque mouetur facilius. </s> <s id="id.001785">Tertium ob <lb></lb>eandem cauſam ſoluitur. </s> <s id="id.001786">Sic enim impoſita ſarcina quaſi inferiore <lb></lb>loco pendens adiuuat tractum. </s> <s id="id.001787">Hinc eſt quod quadrupedum omni <lb></lb>generi ſolis Gyraffis exceptis crura poſteriora longiora ſunt. </s> <s id="id.001788">Mouen<lb></lb>tur enim pulſu primum, deinde tractu. </s> <s id="id.001789">Commodius autem pellit, <lb></lb>quod grauius eſt. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001790">11. <foreign lang="el">*dia\ ti/ p(a=|on a)/neu ba/rois kinei=tai to\ zugo/n.</foreign></s> </p> <p type="main"> <s id="id.001791">11. Cur facilius mouetur li<lb></lb>brile abſque pondere. </s> </p> <p type="main"> <s id="id.001792"><foreign lang="el">*dia\ ti/ r(a=|on, o(/tan a)/neu ba/rous h)=|, kinei=tai to\ zugo/n, <lb></lb>h)\ e)/xon ba/ros; </foreign></s> <s id="g0131002"><foreign lang="el">o(moi/ws de\ kai\ troxo\s, h)\ a)/llo toiou=to. </foreign></s> <s id="g0131002a"><foreign lang="el">to\ <lb></lb>baru/teron me\n, mei=zw de\ tou= e)la/ttonos kai\ koufote/rou.</foreign></s> <s id="g0131003"><foreign lang="el">h)\ <lb></lb>o(/ti ou) mo/non ei)s tou)nanti/on to\ baru/, a)lla\ kai\ ei)s to\ pla/gion <lb></lb>duski/nhto/n e)stin.</foreign></s> <s id="g0131004"><foreign lang="el">e)nanti/on ga\r th=| r(oph=| kinh=sai xalepon, <lb></lb>e)f' o(\ de\ r(e/pei, r(a|di/on: ei)s de\ to\ pla/gion ou) r(e/pei.</foreign></s> </p> <p type="main"> <s id="id.001793">Cur librile quum fuerit <lb></lb>ſine <expan abbr="põdere">pondere</expan>, facilius moue<lb></lb>tur: <expan abbr="quã">quam</expan> quum habet pon<lb></lb>dus. </s> <s id="id.001794">Similiter verò & orbi<lb></lb>culus, vel aliud tale, gra<lb></lb>uius quidem, maius verò <lb></lb>minore & leuiore. </s> <s id="id.001795">An quod <lb></lb>non ſolum in contrarium <lb></lb>id, quod graue eſt: ſed <expan abbr="etiã">etiam</expan> <lb></lb>in <expan abbr="obliquũ">obliquum</expan> difficulter mo<lb></lb>uetur. </s> <s id="id.001796">Difficile enim eſt <lb></lb>contrà propenſionem mo<lb></lb>uere. </s> <s id="id.001797">At quò propendet, fa<lb></lb>cile: non propendet autèm in obliquum. </s> </p> <p type="head"> <s id="id.001798">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001799">Cvr librile.] <emph type="italics"></emph>In hoc capite ſpeciale tractatur problema, quod <lb></lb>generale eſſe poſſet. </s> <s id="id.001800">Eſt autem de librili. </s> <s id="id.001801">cur quò leuius, vel ſine <lb></lb>pondere cum ſit, deprimitur facilius & mouetur: quam cum graue <emph.end type="italics"></emph.end><pb xlink:href="035/01/153.jpg" pagenum="113"></pb><emph type="italics"></emph>eſt. </s> <s id="id.001802">Exempli gratia vnum ligneum ſit, alterum ferreum, illud faci<lb></lb>lius moueatur: quam hoc, quod perinde eſt de vecte, de rotis, de glo<lb></lb>bis, & eiuſmodi contra naturam motis, ſuppoſita eadem firmitate. <lb></lb></s> <s id="id.001803">Ratio ergò quæ redditur generalis eſt, & hoc ſyllogiſmo compre<lb></lb>hendetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001804"><emph type="italics"></emph>Motum contra naturam eò difficilius fertur, quò ipſum grauius <lb></lb>eſt. </s> <s id="id.001805">Plus enim reſiſtit non ſolum in contrarium nutus ſui, ſed <lb></lb>& in obliquum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001806"><emph type="italics"></emph>Librile moueri in obliquum ( vt mouetur neceſſariò propter <lb></lb>ſuæ aginæ ſeu centri immobilitatem: ſic enim non rectà ad <lb></lb>centrum mundi quo natura fertur, deſcendit: ſed per ambi<lb></lb>tum circuli ) eſt contra naturam grauitatis ſuæ moueri, vt <lb></lb>rotam & eiuſmodi. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001807"><emph type="italics"></emph>Ergo librile quò grauius, eò difficilius mouebitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001808"><emph type="italics"></emph>Hinc collige ex leuiori materia facta, dummodo firma, agiliora eſſe, <lb></lb>& exactiora. </s> <s id="id.001809">vnde petorita noſtra rotis in orbita ferreis prædita <lb></lb>difficilius trahuntur, quam <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.153.1.jpg" xlink:href="035/01/153/1.jpg"></figure><lb></lb><emph type="italics"></emph>nobilium Polonorum, quæ ex <lb></lb>ligno ſolo compacta ſunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001810">Non propendet.] <emph type="italics"></emph>Linea <lb></lb>nutus grauis alicuius deor<lb></lb>ſum eſt recta perpendicularis <lb></lb><expan abbr="inſiſtẽs">inſiſtens</expan> plano horizontis, <expan abbr="hãc">hanc</expan> <lb></lb>quæ ſecat ad inæquales an<lb></lb>gulos, eſt obliqua, cuiuſmo<lb></lb>di eſt arcus B F ad rectam <lb></lb>B G lineam nutus puncti <lb></lb>B. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001811">12. <foreign lang="el">*dia\ ti/ e)pi e)pi\ tw=n skuta/lwn <lb></lb>r(a=|on ta\ forti/a komi/zetai, <lb></lb>h)\ e)pi\ tw=n a(macw=n.</foreign></s> </p> <p type="main"> <s id="id.001812">12. Cur ſuper ſcytalis onera <lb></lb>facilius geſtantur: quam <lb></lb>ſuper curribus. </s> </p> <p type="main"> <s id="id.001813"><foreign lang="el">*dia\ ti/ e)pi\ tw=n skuta/lwn r(a=|on ta\ forti/a komi/zetai. <lb></lb></foreign></s> <s id="g0131101"><foreign lang="el">h)\ e)pi\ tw=n a(macw=n, e)xousw=n, tw=n me\n mega/lous troxou/s, <lb></lb>tw=n de\ mikrou/s; </foreign></s> <s id="g0131102"><foreign lang="el">h)\ dio/ti e)pi\ tw=n skuta/lwn ou)demi/an e)/xei <lb></lb>pro/skoyin, to\ de\ e)pi\ tw=n a(macw=n to\n a)/cona, kai\ prosko/ptei <lb></lb>au)tw=|. </foreign></s> <s id="g0131102a"><foreign lang="el">e)/k te ga\r tw=n a)/nwqen pie/zei au)to\n, kai\ e)k <lb></lb>tw=n plagi/wn.</foreign></s> <s id="g0131103"><foreign lang="el">to\ de\ e)pi\ tw=n skuta/lwn, e)pi\ du/o tou/twn kinei=tai, <lb></lb>th=| te ka/tw xw/ra| u(pokeime/nh|, kai\ tw=| ba/rei tw=| <lb></lb>e)pikeime/nw|: e)p' a)mfote/rwn ga\r tou/twn kuli/etai tw=n to/pwn <lb></lb>o( ku/klos, kai\ fero/menos w)qei=tai.</foreign></s> </p> <p type="main"> <s id="id.001814">Cur onera facilius ge<lb></lb>ſtantur ſcytalis: quam cur<pb xlink:href="035/01/154.jpg" pagenum="114"></pb>ribus etiam magnas rotas <lb></lb>habentibus, cum ipſæ par<lb></lb>uas habeant. </s> <s id="id.001815">An quia one<lb></lb>ra in ſcytalis ad nihil offen<lb></lb>ſant: in curribus vero ha<lb></lb>bent axem, ad quem offen<lb></lb>ſant. </s> <s id="id.001816">Supernè enim pre<lb></lb>munt ipſum, & in <expan abbr="obliquũ">obliquum</expan>. <lb></lb></s> <s id="id.001817">In ſcytalis vero ad hæc <lb></lb>duo mouentur, & infernè <lb></lb>ſcilicet ſubſtrato ſpatio, <lb></lb>& onere ſuperimpoſito. </s> <s id="id.001818">In <lb></lb>vtriſque enim his locis re<lb></lb>uoluitur circulus, & conci<lb></lb>tatus impellitur. </s> </p> <p type="head"> <s id="id.001819">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001820">Cvr onera.] <emph type="italics"></emph>Secundum genus ſcytalæ eſt lignum ferrumue <lb></lb>cylindricum oblongum in extremis rotulas habens intra annu<lb></lb>los currui <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.154.1.jpg" xlink:href="035/01/154/1.jpg"></figure><lb></lb><emph type="italics"></emph>affixos <lb></lb>verſatile, <lb></lb>vt eſt fi<lb></lb>gura A <lb></lb>B quæ <lb></lb>mota iu<lb></lb>go rotis annexo, contrà, quam in curribus, in quibus non rotis: ſed <lb></lb>currui annectitur, omnibus ſuis partibus mouetur duobus motibus <lb></lb>ſimul, circumcirca, & antrorſum. </s> <s id="id.001821">quod cauſa eſt vt leuius vertatur, <lb></lb>quam rota in curru. </s> <s id="id.001822">vt cuius axis procedendo tantùm antrorſum <lb></lb>moueatur, non autem circum circa vertatur. </s> <s id="id.001823">Vnde fit vt axis etiam <lb></lb>premat magis, & veluti rotam affigat plano, ſicque remoretur: con<lb></lb>tra in ſcytala rotæ dummodo maiores ſint, quam vt terra obruantur <lb></lb>à ſubiecta planicie inferne ipſam circunferentiam atterente impel<lb></lb>luntur. </s> <s id="id.001824">Supernè etiam ab onere cylindricum premente. </s> <s id="id.001825">Ob has itaque <emph.end type="italics"></emph.end><pb xlink:href="035/01/155.jpg" pagenum="115"></pb><emph type="italics"></emph>cauſas ſcytala commodior erit, & expeditior ad onera conuehenda, <lb></lb>licet minores, quam currus habeat rotas, quod non repugnat ijs quæ <lb></lb>ante 10. cap. dicta <expan abbr="sũt">sunt</expan> de rotis maioribus. </s> <s id="id.001826">Aliud enim facilius attol<lb></lb>lere, & trahere quæcunque pondera, aliud conuehere. </s> <s id="id.001827">Scytala tamen <lb></lb>poteſt eſſe illud curriculi genus quod Galli vocant<emph.end type="italics"></emph.end> Traineau, <emph type="italics"></emph>Itali <emph.end type="italics"></emph.end><lb></lb>Straſcino, <emph type="italics"></emph>apud quendam non ineruditum legi dici poſſe traham. <lb></lb></s> <s id="id.001828">Hæc autem annexa ligno cylindrico ſolas rotas habet verſatiles, quæ <lb></lb>quantò minores, tantò minus occurſant ſubiecto pauimento. </s> <s id="id.001829">vt enim <lb></lb>quò circulus rotæ maior eſt, eò eius cum recta à qua tangitur in pla<lb></lb>no minor eſt an<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.155.1.jpg" xlink:href="035/01/155/1.jpg"></figure><lb></lb><emph type="italics"></emph>gulus. </s> <s id="id.001830">Et contrà <lb></lb>quò circulus mi<lb></lb>nor, eò angulus <lb></lb>contactus maior <lb></lb>euadit. </s> <s id="id.001831">vt angu<lb></lb>lus A B C ro<lb></lb>tæ maioris mi<lb></lb>nor eſt angulo <lb></lb>A B D rotæ <lb></lb>minoris: & con<lb></lb>trà vtrolibet <lb></lb>maior eſt angu<lb></lb>lus A B E rotæ minoris. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001832">13. <foreign lang="el">*dia\ ti/ por)r(wte/rw ta\ be/lh fe/retai a)po\ th=s sfendo/nhs <lb></lb>h)\ a)po\ th=s xeiro/s.</foreign></s> </p> <p type="main"> <s id="id.001833">13. Cur miſſilia longius à <lb></lb>funda: quam à manu <lb></lb>proijciuntur. </s> </p> <p type="main"> <s id="id.001834"><foreign lang="el">*dia\ ti/ por)r(wte/rw ta\ be/lh fe/retai a)po\ th=s sfendo/nhs, <lb></lb>h)\ a)po\ th=s xeiro/s, kai/ toi kratei= ge o( ba/llwn th=| xeiri\<lb></lb> ma=llon, h)\ a)parth/sas to\ kai/ar;</foreign></s> <s id="g0131202"><foreign lang="el">kai\ e)/ti ou(/tw me\n du/o ba/rh <lb></lb>kinei=, to/, te th=s sfendo/nhs, kai\ to\ be/los, e)kei/nws de\ to\ <lb></lb>be/los mo/non.</foreign></s> <s id="g0131203"><foreign lang="el">po/teron o(/ti e)n me\n th=| sfendo/nh| kinou/menon to\ <lb></lb>be/los, r(i/ptei o( ba/llwn. </foreign></s> <s id="g0131203a"><foreign lang="el">periagagw\n ga\r ku/klw| polla/kis, <lb></lb>a)fi/hsin. </foreign></s> <s id="g0131204"><foreign lang="el">e)k de\ th=s xeiro\s a)po\ th=s h)remi/as h( a)rxh/. <lb></lb></foreign></s> <s id="g0131205"><foreign lang="el">pa/nta de\ eu)kinhto/tera kinou/mena h)\ h)remou=nta, h)\ dia/ te <lb></lb>tou=to, kai\ dio/ti e)n me\n tw=| sfendonw=n h( me\n xei\r gi/netai <lb></lb>ke/ntron, h( de\ sfendo/nh h( e)k tou= ke/ntrou o(/sw| a)\n h)=| mei/zwn, <lb></lb>h( a)po\ tou= ke/ntrou kinei=tai qa=tton. </foreign></s> <s id="g0131205a"><foreign lang="el">h( de\ a)po\ th=s xeiro\s <lb></lb>bolh\ pro\s th\n sfendo/nhn braxei=a e)sti/.</foreign></s> </p> <p type="main"> <s id="id.001835">Cur miſſilia longius fe<lb></lb>runtur à funda, quam à <lb></lb>manu, etiamſi proijciens <lb></lb>melius manu, comprehen<lb></lb>dat: quam ſuſpendens è <lb></lb>foſſa fundæ? </s> <s id="id.001836">Præterea ſic <lb></lb>duo pondera moueat, fun<lb></lb>dam ſcilicet, & miſſile: illo <pb xlink:href="035/01/156.jpg" pagenum="116"></pb>verò modo miſſile dunta<lb></lb>xat. </s> <s id="id.001837">An quia in funda miſ<lb></lb>ſile commotum proijciens <lb></lb>iacit. </s> <s id="id.001838">In orbem enim volu<lb></lb>tans ſæpius, proijcit. </s> <s id="id.001839">E ma<lb></lb>nu autem initium à quiete <lb></lb>capit. </s> <s id="id.001840">At omnia commota <lb></lb>facilius: quam quieſcentia <lb></lb><expan abbr="mouẽtur">mouentur</expan>. </s> <s id="id.001841">An propter hoc: <lb></lb>ſed & quia in vſu funda<lb></lb>rum manus quidem fit <expan abbr="cẽtrum">cen<lb></lb>trum</expan>: funda vero linea ex <lb></lb>centro. </s> <s id="id.001842">quantò autem fue<lb></lb>rit hæc maior, <expan abbr="tãtò">tantò</expan> celerius <lb></lb>mouetur. </s> <s id="id.001843">At iactus à manu <lb></lb>reſpectu fundæ breuis eſt. </s> </p> <p type="head"> <s id="id.001844">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001845">A Funda.] <emph type="italics"></emph>Funda eſt funiculus duobus capitibus manu captus, <lb></lb>altero cum anſula digito circumuoluta ne exeat, altero ſine an<lb></lb>ſula, vt dimitti poßit. </s> <s id="id.001846">In medio latior, & paululum excauatus, vt <lb></lb>ibi mißile contineatur, quod aliquoties circumacto in orbem funicu<lb></lb>lo, & ab vno capitum dimiſſo vehementer proijcitur. </s> <s id="id.001847">Inuentam à <lb></lb>Phenicibus fuiſſe refert Plinius cap. 56. lib. 7. ne manus iaculi aſpe<lb></lb>rioris attrectatione læderetur, & vt longius atque validius proijce<lb></lb>retur. </s> <s id="id.001848">Quæ cum intelligeret paſtor ille exilis, ſed Deo dilectus Dauid <lb></lb>funda aduerſus Goliathem immanem gigantem non aliter, quam <lb></lb>ſummo impetu proſternendum, prudenter ſeſe armauit. </s> <s id="id.001849">Erat autem <lb></lb>fundæ vſus adeò frequens Balearium inſularum populis, vt matres <lb></lb>filios non alijs auibus veſci paterentur, quam quas funda ſibi com<lb></lb>paraſſent. </s> <s id="id.001850">Vnde & funda balearis appellatur à Poëta,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001851">Stuppea torquentur balearis verbera fundæ. <lb></lb></s> <s><emph type="italics"></emph>Nec ſolum lapides funda proijciſolere: ſed & alia, vt plumbum, pa<lb></lb>tet ex Ouidio. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/157.jpg" pagenum="117"></pb> <p type="main"> <s id="id.001852">Non ſecus exarſit quam cum balearica plumbum</s> </p> <p type="main"> <s id="id.001853">Funda iacit, volat illud, & incandeſcit eundo. </s> </p> <p type="main"> <s id="id.001854"><emph type="italics"></emph>Et aduerſum bellatores caßidibus, cataphractis, loriciſque munitos <lb></lb>teretes lapides de funda deſtinatos ſagittis omnibus eſſe grauiores <lb></lb>ſcripſit Vegetius. </s> <s id="id.001855">Quandoquidem membris integris, lethale tamen <arrow.to.target n="marg27"></arrow.to.target><lb></lb>vulnus importent, & ſine inuidia ſanguinis hoſtis lapidis ictu in<lb></lb>tereat Quæ res ideò, inquit, ab vniuerſis tyronibus frequenti exerci<lb></lb>tio diſcenda eſt, quia <expan abbr="fundã">fundam</expan> portare nullus labor. </s> <s id="id.001857">Et interdum euenit, <lb></lb>vt in lapidoſis locis conflictus habeatur, vt aut mons aliquis ſit de<lb></lb>fendendus, aut collis, & ab oppugnatione caſtellorum ſiue ciuitatum <lb></lb>lapidibus barbari fundiſque ſint propellendi. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.001858"><margin.target id="marg27"></margin.target>Cap. 16. lib <lb></lb>1. de re mili</s> </p> <p type="main"> <s id="id.001859">Cur miſſilia.] <emph type="italics"></emph>Quærit hîc Ariſtoteles cur iaculum miſſum cum <lb></lb>funda longius proijcitur, quam ſi manu tantum. </s> <s id="id.001860">Cui priuſquam re<lb></lb>ſpondeat, duo repugnare dicit, alterum, quia proiectum à manu ſola <lb></lb>melius comprehendatur: quam quod à funda ſuſpenditur, melior au<lb></lb>tem comprehenſio conducit ad <expan abbr="longiorẽ">longiorem</expan> iactum: alterum, quia proij<lb></lb>ciens cum funda duo ſimul proijcit fundam ſcilicet & iaculum: ma<lb></lb>nu autem vnum tantum, nempe iaculum. </s> <s id="id.001861">At difficilius duo mouere: <lb></lb>quam vnum. </s> <s id="id.001862">His incommodis tamen neglectis ſoluit Ariſtoteles <lb></lb>problema dupliciter, priore modo è motu incitato, & contraria quie<lb></lb>te. </s> <s id="id.001863">Syllogiſmus ſic eſt,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001864"><emph type="italics"></emph>Qui initium proiectionis capit à motu longius iacit: quam à <lb></lb>quiete. </s> <s id="id.001865">Quies enim vt contraria motui, ei repugnat, & ipſi re<lb></lb>nitens, ne fiat impedit. </s> <s id="id.001866">Ideóque omnia commota facilius: quam <lb></lb>quieſcentia mouentur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001867"><emph type="italics"></emph>At proijciens cum funda initium capit à motu. </s> <s id="id.001868">Ante vi<lb></lb>brationem enim funditor fundam ſæpius in circulum <lb></lb>circumagit: contrà cum manu, initium capit à quiete: aut <lb></lb>ſi à motu, multò leuiore tamen. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001869"><emph type="italics"></emph>Igitur proiiciens cum funda longius iacit: quam cum manu ſola. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001870">E foſſa fundæ.] <emph type="italics"></emph>In Græco vocabulum eſt,<emph.end type="italics"></emph.end> <foreign lang="el">to\ kai/ar,</foreign> <emph type="italics"></emph>ſine vo<lb></lb>cabulo<emph.end type="italics"></emph.end> <foreign lang="el">sfendo/nhs.</foreign> </s> <s><emph type="italics"></emph>Significat <expan abbr="autẽ">autem</expan><emph.end type="italics"></emph.end> <foreign lang="el">kaiar</foreign> <emph type="italics"></emph>foſſam terræ concuſſu <expan abbr="factã">factam</expan> <lb></lb>quæ ſignificatio quid ad rem pertineat non video, niſi per metapho<lb></lb>ram intelligamus eam fundæ partem, quæ vt latior, ita & in ſinum <lb></lb>leuiter excauatur ad iaculum continendum, & ſic conuenit rei pro<lb></lb>poſitæ: nonnulli tamen putarunt delendum<emph.end type="italics"></emph.end> <foreign lang="el">to\ kai/ar</foreign> <emph type="italics"></emph>& loco eius <emph.end type="italics"></emph.end><pb xlink:href="035/01/158.jpg" pagenum="118"></pb><emph type="italics"></emph>reponendum<emph.end type="italics"></emph.end> <foreign lang="el">o)i+/sto\n</foreign> <emph type="italics"></emph>id eſt omne quod iaculamus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001871">At omnia commotæ.] <emph type="italics"></emph>Hæc cauſa generalis erit triceſimo <lb></lb>primo capiti huius libri. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001872">An propter hoc.] <emph type="italics"></emph>Alter eſt modus ſolutionis problematis <lb></lb>ſumptus è funda tanquam radio longiore. </s> <s id="id.001873">Syllog. ſic eſt. </s> <s id="id.001874">Quantò li<lb></lb>nea à centro eſt maior, tantò celerius mouet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001875"><emph type="italics"></emph>In proiectione cum funda manus eſt centrum, funda verò eſt <lb></lb>linea à centro: & longior manu. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001876"><emph type="italics"></emph>Igitur proiectio cum funda longior fiet. <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg28"></arrow.to.target></s> </p> <p type="margin"> <s id="id.001877"><margin.target id="marg28"></margin.target>Cap 1. lib. 2. <lb></lb>de vſ. part. </s> </p> <p type="main"> <s id="id.001879">Manus quidem.] <emph type="italics"></emph>Manus apud veteres, vt videre eſt apud <lb></lb>Gal. tres ſunt partes vna quidem brachium, alia vero<emph.end type="italics"></emph.end> <foreign lang="el">ph/xus</foreign> <emph type="italics"></emph>id eſt <lb></lb>cubitus, & tertia<emph.end type="italics"></emph.end> <foreign lang="el">a)kro/keiron</foreign> <emph type="italics"></emph>hoc eſt ſumma extremave manus. <lb></lb></s> <s id="id.001881">Hæc etſi commoueatur cum fundam rotat tanquam manens loco, <lb></lb>tamen & centrum habetur, funda autem radius eſt: at cum ſine fun<lb></lb>da proiectio fit, articulus quo brachium cum humero connectitur, <lb></lb>videtur potius habere rationem centri, & brachium cum cubito, & <lb></lb>extrema manu rationem lineæ à centro. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001882">14. <foreign lang="el">*peri\ kollo/pwn kai\ o)/nwn.</foreign></s> </p> <p type="main"> <s id="id.001883">14. De collopibus & ſuc<lb></lb>culis. </s> </p> <p type="main"> <s id="id.001884"><foreign lang="el">*dia\ ti/ r(a=|on kinou=ntai peri\ to\ au)to\ zugo\n oi( mei/zous <lb></lb>tw=n e)latto/nwn ko/llopes, kai\ oi( au)toi\ o)/noi oi( lepto/teroi <lb></lb>u(po\ th=s au)th=s i)sxu/os tw=n paxute/rwn; </foreign></s> <s id="g0131302"><foreign lang="el">h)\ dio/ti o( me\n o)/nos <lb></lb>kai\ to\ zugo\n ke/ntron e)sti/n, ta\ de\ a)pe/xonta mege/qh ai( e)k <lb></lb>tou= ke/ntrou, qa=tton de\ kinou=ntai, kai\ ple/on a)po\ th=s au)th=s <lb></lb>i)sxu/os, ai( tw=n meizo/nwn ku/klwn h)\ ai( tw=n e)latto/nwn. </foreign></s> <s id="g0131302a"><foreign lang="el">u(po\ <lb></lb>th=s au)th=s ga\r i)sxu/os mei=zon meqi/statai to\ a)/kron to\ por)r(w/teron <lb></lb>tou= ke/ntrou.</foreign></s> <s id="g0131303"><foreign lang="el">dio\ pro\s me\n to\ zugo\n tou\s ko/llopas <lb></lb>o)/rgana poiou=ntai, oi(=s r(a=|on stre/fou=sin. </foreign></s> <s id="g0131303a"><foreign lang="el">e)n de\ toi=s leptoi=s <lb></lb>o)/nois, plei=on gi/netai to\ e)/cw tou= cu/lou. </foreign></s> <s id="g0131303b"><foreign lang="el">au(/th de\ gi/netai <lb></lb>h( e)k tou= ke/ntrou.</foreign></s> </p> <p type="main"> <s id="id.001885">Cur circa eandem erga<lb></lb>tam collopes maiores mi<lb></lb>noribus facilius <expan abbr="mouẽtur">mouentur</expan>, <lb></lb>& ipſæ ſucculæ graciliores <lb></lb>ab <expan abbr="eadẽ">eadem</expan> vi craſſiotibus, An <lb></lb>quia ſuccula & ergata cen<lb></lb>trum eſt. </s> <s id="id.001886">Longitudines au<lb></lb>tem diſtantes ſunt lineæ ex <lb></lb>centro. </s> <s id="id.001887">At & celerius mo<lb></lb>uentur, & plus ab eadem vi <lb></lb>lineæ <expan abbr="maiorũ">maiorum</expan> circulorum: <lb></lb>quam <expan abbr="minorũ">minorum</expan>. </s> <s id="id.001888">Ab eadem <lb></lb>enim vi extremum, quod <lb></lb>longiùs eſt à centro, plus <lb></lb>transfertur, ideo collopas <lb></lb>organa ad ergatas <expan abbr="adijciũt">adijciunt</expan>, <pb xlink:href="035/01/159.jpg" pagenum="119"></pb>quibus facilius vertunt. </s> <s id="id.001889">In <lb></lb>ſucculis vero tenuibus ma<lb></lb>ius fit id quod extra eſt, li<lb></lb>gnum. </s> <s id="id.001890">Et id linea eſt quæ <lb></lb>ex centro. </s> </p> <p type="head"> <s id="id.001891">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001892">Cvr circa eandem.] <emph type="italics"></emph>In hoc capite continentur duo proble<lb></lb>mata vnum de ergatis, alterum de ſucculis. </s> <s id="id.001893">Illud cur ergatæ à <lb></lb>maioribus collopibus facilius mouentur: quam à minoribus. </s> <s id="id.001894">Hoc cur <lb></lb>ſucculæ graciliores etiam facilius <expan abbr="mouẽtur">mouentur</expan>, quam craßiores. </s> <s id="id.001895">Vtrum<lb></lb>que ſoluitur ex lineæ è centro longitudine maiore. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001896"><emph type="italics"></emph>Maiores lineæ ex centro facilius & celerius mouentur ab eadem <lb></lb>vi minoribus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001897"><emph type="italics"></emph>Ergata & ſuccula collopibus verſatæ, ſunt centrum, & col<lb></lb>lopes ſunt lineæ ex centro, & quidem tantò maiores, quan<lb></lb>tò ſuccula gracilior eſt ( pars enim quam craßitudo tegeret <lb></lb>ob gracilitatem detegitur.)<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001898"><emph type="italics"></emph>Ergo ergata & ſuccula gracilior à collopibus maioribus facilius <lb></lb>ab eadem vi mouebuntur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001899"><emph type="italics"></emph>Cæterum quid hîc<emph.end type="italics"></emph.end> <foreign lang="el">zugo\n</foreign> <emph type="italics"></emph>ergata differat à ſuccula,<emph.end type="italics"></emph.end> <foreign lang="el">o)/non</foreign> <emph type="italics"></emph>Græci vo<lb></lb>cant, & ſcytalæ primum genus, parum video, niſi fulcris, aut craßi<lb></lb>tudine. </s> <s id="id.001900">Horum enim vnumquodque axis eſt circum quem voluitur <lb></lb>funis ductarius ad tollenda, vel trahenda onera tranſuerſas habens <lb></lb>collopas, id eſt ligna oblonga in altera extremitate, vel vtraque, quæ <lb></lb>ſunt tanquam vectes à vi adiuncta deprimendi vicißim. </s> <s id="id.001901">Differre <lb></lb>tamen poſſunt quod ergata erectum axem habeat, vel fulciatur dua<lb></lb>bus trabibus perpendiculariter erectis: ſuccula ſupinum habet axem <lb></lb>vel etiam quatuor tignis ex vtraque parte binis ſuſtentetur, vnde<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">o)/nos</foreign> <emph type="italics"></emph>dicitur, tanquam geſtanti cuidam aſino ſimilis ſit. </s> <s id="id.001902">Huius fecit <lb></lb>mentionem Hippocrates ſect. 3. lib. de fract. </s> <s id="id.001904">Ex vniuerſis inquit, <lb></lb>machinationibus, quæ ab hominibus excogitatæ ſunt, hæ tres om<lb></lb>nium valentißimæ,<emph.end type="italics"></emph.end> <foreign lang="el">o)/nou</foreign> <emph type="italics"></emph>id eſt axis verſatio, impulſus per vectem, & <lb></lb>cuneus adactus. </s> <s id="id.001905">Namque homines ſine aliquo vno, vel ſine omnibus <lb></lb>nullum opus, quod maximam vim poſtulet, perficiunt. </s> <s id="id.001906">Hæc Hipp. <emph.end type="italics"></emph.end><pb xlink:href="035/01/160.jpg" pagenum="120"></pb><emph type="italics"></emph>Succularum <expan abbr="tamẽ">tamen</expan> multa ſunt genera vt videre eſt apud Vitruuium. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001907"><emph type="italics"></emph>Et Pappus lib. 8. Mathemat collectionum fabricam inſtrumenti <lb></lb>docet, quod huc referri debet, eſt autem eiuſmodi. </s> <s id="id.001908">vocat axem M B,<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.160.1.jpg" xlink:href="035/01/160/1.jpg"></figure><lb></lb><emph type="italics"></emph><expan abbr="tympanũ">tympanum</expan> C D, circa tympani <expan abbr="peripheriã">peripheriam</expan> ſcytalas vel collopes in fora<lb></lb>minibus tympani F G, H F, &ct: ita, vt potentia quæ ſemper in <lb></lb>ſcytalis eſt, vel in peripheria tympani vt in F, dum circumuertit <lb></lb>tympanum, & axem ſurſum quoque mouet pondus K axi appenſum <lb></lb>fune M circa axem reuoluto. </s> <s id="id.001909">Qui amplius videre volet, cur ab <lb></lb>hoc inſtrumento, quod axis in peritrochio vocatur, magna pondera <lb></lb>ab exigua virtute, quo ve etiam modo moueantur, quæ ratio tempo<lb></lb>ris, ſpatij, potentiæ, ac moti ponderis inter ſe, & vt vſus ipſius ad ve<lb></lb>ctem referatur. </s> <s id="id.001910">Videat apud Guidum Vbaldum in Mechanicis. </s> <s id="id.001911">Ad <lb></lb>hoc genus etiam inſtrumenti referantur ingentes illæ rotæ in vno <lb></lb>axe quarum vna labore vnius atque alterius hominis vertitur: alte<lb></lb>ra ſitulis quibus in ſua circumferentia accommodate dispoſitis con<lb></lb>ferta eſt ſui conuerſione ex vna parte aquam Sequanæ ſeptis contra<lb></lb>ctam exhauſit, ex altera aliò refudit, vt ex lapide quadrato firma <lb></lb><expan abbr="iacerẽtur">iacerentur</expan> fundamenta illius eximij pontis, qui magno ornamento & <lb></lb>commoditate celeberrimæ vrbium Lutetiæ, iuſſu Henrici III. Regis<emph.end type="italics"></emph.end><pb xlink:href="035/01/161.jpg" pagenum="121"></pb><emph type="italics"></emph>noſtri Chriſtianißimi inchoatus, & maiori iam ex parte conſtru<lb></lb>ctus perfectionem ab Henrico IIII. </s> <s id="id.001912">Rege nunc noſtro magnifi<lb></lb>centißimo deſiderat, ea in parte, qua flumen à ſchola S. Germani <lb></lb>ad plateam Auguſtinorum traducitur. </s> <s id="id.001913">Hanc, vt ſpero, exorabit cla<lb></lb>rißimus vir dominus Marlyius rationum regiarum præſes, & mer<lb></lb>catorum præfectus dignißimus. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001914">15. <foreign lang="el">peri\ cu/lon a)gmou=.</foreign></s> </p> <p type="main"> <s id="id.001915">15. De fractura ligni. </s> </p> <p type="main"> <s id="id.001916"><foreign lang="el">*dia\ ti/ to\ au)to\ me/geqos cu/lon r(a=|on katea/ssetai, para\ <lb></lb>to\ go/nu e)a\n i)/son a)posth/sas tw=n a)/krwn, e)xo/menos katagnu/h|, <lb></lb>h)\ para\ to\ go/nu e)ggu\s ou)/sas: kai\ e)a\n pro\s th\n gh=n <lb></lb>e)rei/sas, kai\ tw=| podi\ prosba\s po/r)r(wqen th=| xeiri\ katagnu/h|, <lb></lb>h)\ e)ggu/qen, h)\ dio/ti e)/nqa me\n to\ go/nu ke/ntron, e)/nqa de\ o( <lb></lb>pou/s.</foreign></s> <s id="g0131402"><foreign lang="el">o(/sw| d' a)\n por)r(w/teron h)=| tou= ke/ntrou, r(a=|on kinei=tai <lb></lb>a(/pan. kinhqh=nai de\ a)na/gkh katagnu/menon.</foreign></s> </p> <p type="main"> <s id="id.001917">Cur lignum <expan abbr="eiuſdẽ">eiuſdem</expan> ma<lb></lb>gnitudinis facilius è genu <lb></lb><expan abbr="frãgitur">frangitur</expan>, ſi in extremis ma<lb></lb>nus æqualiter diductas ha<lb></lb>bens fregerit: quam ſi ad <lb></lb>genu propinquas habuerit. <lb></lb></s> <s id="id.001918">Præterea ſi ad terram ap<lb></lb>plicans, & pede impellens, <lb></lb>manu diſtante frangat: <expan abbr="quã">quam</expan> <lb></lb>propinqua. </s> <s id="id.001919">An quia illîc <lb></lb>genu quidem eſt centrum: <lb></lb>hîc verò pes. </s> <s id="id.001920">quantò autem <lb></lb>quodque à centro fuerit <lb></lb>diſtantius, id omne facilius <lb></lb>mouetur. </s> <s id="id.001921">Quod frangitur autem moueri neceſſe eſt. </s> </p> <p type="head"> <s id="id.001922">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001923"><emph type="italics"></emph>Mos eſt ignem excitare in paruo foco volentium, baculos lon<lb></lb>giores bifariam frangere. </s> <s id="id.001924">Itaque arreptos tractoſque vtraque <lb></lb>manu per extrema medios ad genu applicantes, parua vi frangunt. <lb></lb></s> <s id="id.001925">Idem faciunt ſi alterum extremorum ad terram applicent: alterum <lb></lb>eleuatum obliquè manu teneant, & medium pede conculcent. </s> <s id="id.001926">Quæ<lb></lb>rit igitur Ariſtoteles cur fractio hæc facilior fit manibus ad extre<lb></lb>ma diductis: quam ad medium propius accedentibus. </s> <s id="id.001927">Et ſoluit è ra<lb></lb>dijs maioribus, ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001928"><emph type="italics"></emph>Quantò quidque à centro fuerit remotius, tantò facilius moue<lb></lb>tur, & quia fractio eſt motio, frangitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001929"><emph type="italics"></emph>In fractione ligni cum manus ſunt in extremis, remotiores<emph.end type="italics"></emph.end><pb xlink:href="035/01/162.jpg" pagenum="122"></pb><emph type="italics"></emph>ſunt à centro ( quod eſt genu cum ad hoc applicatum eſt li<lb></lb>gnum: vel pes, cum ipſum pede conculcatur ) quam cum <lb></lb>non ſunt in extremis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001930"><emph type="italics"></emph>Ergo fractio ligni manibus in extremis exiſtentibus facilior fiet <lb></lb>quam ſi propius exiſtant. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001931"><emph type="italics"></emph>Quæri autem hic poteſt, an qui ſic fuſtem frangunt, genu non offen<lb></lb>dant. </s> <s id="id.001932">Et non offendere experientia comprobat. </s> <s id="id.001933">Ratio tamen non ita <lb></lb>aperta eſt. </s> <s id="id.001934">Eſt autem vt arbitror, quia genu vt centrum, vel hypo<lb></lb>mochlium quieſcit: partes vero fuſtis, vbi fit ruptio, exterius mouen<lb></lb>tur. </s> <s id="id.001935">Itaque à genu diſcedunt. </s> <s id="id.001936">Ob eandem cauſam cyphi duo vitrei <lb></lb>æquales, & aqua pleni fuſtem oblongum extremis ſuis ſuper impoſi<lb></lb>tum adacto celeriter per medium altero fuſte frangi ipſi infracti & <lb></lb>ſine aquæ effuſione tolerant. </s> <s id="id.001937">In hoc tamen differentia eſt, quod cyphi <lb></lb>hypomochlium ſunt, itá que in extremis, & partes à cyphis ad me<lb></lb>dium ſunt lineæ à centro, ſicque impulſæ mouentur. </s> <s id="id.001938">Vt & cum cru<lb></lb>ris arietini os nudatum perioſtio, & manus eo, qui ad pollicem eſt <lb></lb>monticulo atque hypothenare ſuſtentum dorſi gladij ad medium ce<lb></lb>leriter adacti vno ictu ſine manus offenſione frangitur, contrà, <lb></lb>quam in fuſte è genu fracto. </s> <s id="id.001939">Hæc vulgaria ſunt, ſed cauſa non vti<lb></lb>que vulgaris. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001940">16. <foreign lang="el">*dia\ ti/ ai( kro/kai stroggu/lai.</foreign></s> </p> <p type="main"> <s id="id.001941">16. Cur crocæ rotundæ. </s> </p> <p type="main"> <s id="id.001942"><foreign lang="el">*dia\ ti/ peri\ tou\s ai)gialou\s ai( kalou/menai kro/kai stroggu/lai <lb></lb>ei)si/n, e)k makrw=n tw=n li/qwn kai\ o)stra/kwn to\ e)c <lb></lb>u(parxh=s o)/ntwn; </foreign></s> <s id="g0131502"><foreign lang="el">h)\ dio/ti ta\ plei=on a)pe/xonta tou= me/sou e)n <lb></lb>tai=s kinh/sesi, qa=tton fe/retai.</foreign></s> <s id="g0131503"><foreign lang="el">to\ me\n ga\r me/son gi/netai <lb></lb>ke/ntron, to\ de\ dia/sthma, h( e)k tou= ke/ntrou.</foreign></s> <s id="g0131504"><foreign lang="el">a)ei\ de\ h( mei/zwn <lb></lb>a)po\ th=s i)/shs kinh/sews, mei/zw gra/fei ku/klon. </foreign></s> <s id="g0131504a"><foreign lang="el">to\ d' e)n <lb></lb>i)/sw| xro/nw| mei/zon diecio\n, qa=tton fe/retai. </foreign></s> <s id="g0131504b"><foreign lang="el">ta\ de\ fero/mena <lb></lb>qa=tton e)k tou= i)/sou a)posth/matos, sfodro/teron tu/ptei. </foreign></s> <s id="g0131505"><foreign lang="el">ta\ de\ <lb></lb>tu/ptonta ma=llon kai\ au)ta\ tu/ptetai ma=llon, w(/ste a)na/gkh <lb></lb>qrau/esqai ai)ei\ ta\ ple/on a)pe/xonta tou= me/sou. </foreign></s> <s id="g0131505a"><foreign lang="el">tou=to de\ <lb></lb>pa/sxonta, a)na/gkh gi/nesqai periferh=.</foreign></s> <s id="g0131506"><foreign lang="el">tai=s de\ kro/kais dia\<lb></lb> th\n th=s qala/tths ki/nhsin, dia\ to\ meta\ th=s qala/tths kinei=sqai, <lb></lb>sumbai/nei a)ei\ e)n kinh/sei ei)=nai, kai\ kuliome/nais <lb></lb>prosko/ptein.</foreign></s> <s id="g0131507"><foreign lang="el">tou=to de\ a)na/gkh ma/lista sumbai/nein au)toi=s <lb></lb>toi=s a)/krois.</foreign></s> </p> <p type="main"> <s id="id.001943">Cur circa littora crocæ, <lb></lb>vt vocantur, rotundæ ſunt, <lb></lb>è magnis qui erant à prin<lb></lb>cipio lapidibus, & oſtreis <lb></lb>factæ. </s> <s id="id.001944">An quia in motibus <lb></lb>magis à medio diſtantia ce<lb></lb>lerius <expan abbr="ferũtur">feruntur</expan>. </s> <s id="id.001945">Etenim me<lb></lb>dium quidem fit centrum: <lb></lb><expan abbr="interuallũ">interuallum</expan> vero linea ex <expan abbr="cẽtro">cen<lb></lb>tro</expan>. </s> <s id="id.001946">Semper <expan abbr="autẽ">autem</expan> maior ab <lb></lb><expan abbr="eadẽ">eadem</expan> motione <expan abbr="maiorẽ">maiorem</expan> de<lb></lb>ſcribit <expan abbr="circulũ">circulum</expan>. </s> <s id="id.001947">Et quod eſt <lb></lb>maius <expan abbr="ſpatiũ">ſpatium</expan> æquali <expan abbr="tẽpore">tempore</expan> <pb xlink:href="035/01/163.jpg" pagenum="123"></pb><expan abbr="trãfiens">tranfiens</expan> celerius fertur. </s> <s id="id.001948">La<lb></lb>ta vero celerius in æquali <lb></lb>ſpatio, vehementius pul<lb></lb>ſant. </s> <s id="id.001949">Et magis pulſantia <lb></lb>magis etiam percutiuntur. <lb></lb></s> <s id="id.001950">Ita que neceſſe eſt plus di<lb></lb>ſtantia à medio ſemper at<lb></lb>teri. </s> <s id="id.001951">Et quæ id patiuntur, <lb></lb><expan abbr="rotũda">rotunda</expan> fieri. </s> <s id="id.001952">Crocis autem <lb></lb>propter maris motum, cum <lb></lb>quo etiam mouentur, con<lb></lb>tingit in perpetua motione <lb></lb>eſſe, & in conuolutione of<lb></lb>fenſare, & neceſſe eſt præ<lb></lb>cipuè id contingere earum <lb></lb>extremitatibus. </s> </p> <p type="head"> <s id="id.001953">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001954">Cvr circa.] <emph type="italics"></emph>Credibile eſt duo lumina ſapientiæ, & virtutis, <lb></lb>Pub. Scipionem Africanum minorem, & Caium Lælium cum <lb></lb>propter actuoſam vitam animi remißioni aliquando acquieſcentes, <lb></lb>& ruri feriantes ad Caietam portum Campaniæ, Lucrinumque la<lb></lb>cum conchas id eſt duriores teſtas <expan abbr="piſciũ">piſcium</expan>, vt purpuræ, muricis, oſtreo<lb></lb>rum, & vmbilicos id eſt rotundos calculos in ſpeciem noſtri vmbi<emph.end type="italics"></emph.end><arrow.to.target n="marg29"></arrow.to.target><lb></lb><emph type="italics"></emph>lici puerorum more colligerent ( vt recenſent Cicero & Valerius <lb></lb>maximus ) quæſiſſeidem quod hî Ariſtoteles. </s> <s id="id.001956">Cur ſcilicet vmbilici <lb></lb>illi ( crocas Ariſtoteles appellat ) rotundi ſint, cum antea eſſent lapi<lb></lb>des maiuſculi minime <expan abbr="rotũdi">rotundi</expan>, ſed angulati, vt & partes concharum <lb></lb>oſtreorum inæquales & aſperæ. </s> <s id="id.001957">Quod problema licet ſpeciale ſit de <lb></lb>crocis, generale tamen fieri poteſt de omnibus non rotundis. </s> <s id="id.001958">Et cauſa <lb></lb>generalis eſſet hoc modo: quæcunque non ſunt rotunda frequenti, & <lb></lb>celeri, & maiori conuerſione eminentis vt anguli atteruntur, pul<lb></lb>ſant enim ea parte magis occurrentia quælibet ſiue liquida, ſiue ſoli<lb></lb>da, & vicißim pulſantur ab occurrentibus: ſicque ſublatis per attri<lb></lb>tionem eminentijs & angulis rotundantur. <emph.end type="italics"></emph.end><pb xlink:href="035/01/164.jpg" pagenum="124"></pb><arrow.to.target n="marg30"></arrow.to.target></s> </p> <p type="margin"> <s id="id.001959"><margin.target id="marg29"></margin.target>Lib. 2. de <lb></lb>Orat. cap. 8. <lb></lb>lib. 8. </s> </p> <p type="margin"> <s id="id.001960"><margin.target id="marg30"></margin.target>Cap. 11. lib. <lb></lb>1. de vſu <lb></lb>part. </s> </p> <p type="main"> <s id="id.001961">Itaque neceſſe eſt.] <emph type="italics"></emph>Ex his collige verum eſſe illud quod eſt <lb></lb>apud Galenum, ſolam figurarum rotundam ad vix patiendum ex<lb></lb>quiſitè comparatam eſſe, vt quæ nullum expoſitum angulum frangi <lb></lb>potentem habeat, id eſt, vt ex hoc capite interpretor, nullam partem <lb></lb>exteriorem à medio alteram altera diſtantiorem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001962">Semper atteri.] <emph type="italics"></emph>Vt Gutta ſæpius cadendo lapidem immotum <lb></lb>cauat: ſic aqua in vertiginem commotum atterit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001963">Gutta cauat lapidem, conſumitur annulus vſu. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001964">17. <foreign lang="el">*dia\ ti/ makro/tera cu/la <lb></lb>a)sqene/stera.</foreign></s> </p> <p type="main"> <s id="id.001965">17. Cur ligna longiora ſunt <lb></lb>imbecilliora. </s> </p> <p type="main"> <s id="id.001966"><foreign lang="el">*dia\ ti/, o(/sw| a)\n h)=| makro/tera ta\ cu/la, tosou/tw| a)sqene/stera <lb></lb>gi/netai, kai\ ka/mptetai ai)ro/mena ma=llon, ka)\n h)=| <lb></lb>to\ me\n braxu/ o(/son di/phxu lepto/n, to\ de\ e(kato\n phxw=n, <lb></lb>paxu/, h)\ dio/ti moxlo\s gi/netai kai\ ba/ros, kai\ u(pomo/xlion <lb></lb>e)n tw=| ai)/resqai tou= cu/lou to\ mh=kos; </foreign></s> <s id="g0131603"><foreign lang="el">to\ me\n ga\r prw=ton me/ros <lb></lb>au)tou=, o(\ h( xei\r ai)/rei, oi(=on u(pomo/xlion gi/netai: to\ d' <lb></lb>e)pi\ tw=| a)/krw|, ba/ros.</foreign></s> <s id="g0131604"><foreign lang="el">w(/ste o(/sw| a)\n h)=| makro/teron to\ a)po\ tou= <lb></lb>u(pomoxli/ou, tosou/tw| a)na/gkh ka/mptesqai ma=llon.</foreign></s> <s id="g0131604a"><foreign lang="el">[1o(/sw| <lb></lb>ga\r a)\n ple/on a)pe/xh| tou= u(pomoxli/ou, tosou/tws a)na/gkh <lb></lb>ka/mptesqai mei=zon.]1</foreign></s> <s id="g0131605"><foreign lang="el">a)na/gkh ou)=n ai)/resqai ta\ a)/kra tou= <lb></lb>moxlou=.</foreign></s> <s id="g0131606"><foreign lang="el">e)a\n ou)=n h)=| kampto/menos o( moxlo/s, a)na/gkh au)to\n <lb></lb>ka/mptesqai ma=llon ai)ro/menon, o(/per sumbai/nei e)pi\ tw=n <lb></lb>cu/lwn tw=n makrw=n, e)n de\ toi=s braxe/sin e)ggu\s to\ e)/sxaton <lb></lb>tou= u(pomoxli/ou gi/netai tou= h)remou=ntos.</foreign></s> </p> <p type="main"> <s id="id.001967"><arrow.to.target n="marg31"></arrow.to.target></s> </p> <p type="margin"> <s id="id.001968"><margin.target id="marg31"></margin.target>[bis <expan abbr="dictũ]">dictum]</expan> <lb></lb>fruftra. </s> </p> <p type="main"> <s id="id.001969">Cur quantò ligna fue<lb></lb>rint longiora, tantò fiunt <lb></lb>imbecilliora, & ſublata <lb></lb>magis <expan abbr="curuãtur">curuantur</expan>, licet breue <lb></lb>ſit quod tenue, vt <expan abbr="bicubitũ">bicubi<lb></lb>tum</expan>, & quod centum cubito<lb></lb>rum, craſſum, An quia ligni <lb></lb>longitudo, dum attollitur, <lb></lb>fit vectis, pondus, & <expan abbr="hypomochliũ">hypo<lb></lb>mochlium</expan>? </s> <s id="id.001970">prima enim ipſius <lb></lb>pars, quam manus attollit, <lb></lb>fit vt hypomochlium: quæ <lb></lb>autem in extremo, vt pon<lb></lb>dus. </s> <s id="id.001971">Itaque quantò diſtite<lb></lb>rit magis ab hypomochlio: <lb></lb>tantò magis curuari neceſ<lb></lb>ſe eſt. </s> <s id="id.001972">Neceſſe igitur extre<lb></lb>ma vectis eleuari. </s> <s id="id.001973">Si verò <lb></lb>flexilis vectis fuerit, neceſ<lb></lb>ſe erit ipſum magis inflecti <lb></lb>cum attollitur: quod & li<lb></lb>gnis longis contingit. </s> <s id="id.001974">At in <lb></lb>breuibus <expan abbr="extremũ">extremum</expan> fit vici<pb xlink:href="035/01/165.jpg" pagenum="125"></pb>num hypomochlio quieſ<lb></lb>centi. </s> </p> <p type="head"> <s id="id.001975">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001976">Cvr quantò.] <emph type="italics"></emph>In exercitu ſæpe milites dum feriantur roboris <lb></lb>experiundi, vel exercendi gratia longas haſtas humi iacentes <lb></lb>vna manu, aut vtraque in alterum extremorum iniecta & compre<lb></lb>hendente nituntur attollere, quouſque perpendiculares fiant plano <lb></lb>horizontis: qua in ſublatione videre licet haſtas illas longas vt craſ<lb></lb>ſiores ſint, inflecti tamen magis medio ſublationis tempore: quam <lb></lb>breues, licet tenuiores ſint. </s> <s id="id.001977">Quærit igitur hî Ariſtoteles non ſolum <lb></lb>cur ſic fiat, non in his tantum: ſed & in omnibus flexilibus. </s> <s id="id.001978">Cauſam <lb></lb>repetit ex eo quod flexilia illa ſint vectis, <expan abbr="põdus">pondus</expan>, & hypomochlium, <lb></lb>non eadem parte tamen: ſed diuerſis. </s> <s id="id.001979">In extremo enim manu compre<lb></lb>henſo eſt hypomochlium. </s> <s id="id.001980">In altero eſt pondus. </s> <s id="id.001981">Longitudo vero inter <lb></lb>media eſt vectis. </s> <s id="id.001982">Ratio itaque ſic diſponetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001983"><emph type="italics"></emph>Pondus quò magis diſtiterit ab hypomochlio, eò magis vectem, <lb></lb>ſi flexilis eſt, incuruat, dum attollitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001984"><emph type="italics"></emph>In longis lignis, vt flexilibus, pondus magis diſtat ab hypo<lb></lb>mochlio: extremum ſcilicet ab extremo: quam in breuibus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001985"><emph type="italics"></emph>Ligna igitur longa magis incuruabuntur: quam breuia, dum ſic <lb></lb>attolluntur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.001986"><emph type="italics"></emph>Sed & ligna medio ſui comprehenſa, & ſic eleuata ſemper quo lon<lb></lb>giora, eo magis incuruabuntur. </s> <s id="id.001987">At tunc hypomochlium erit in me<lb></lb>dio. </s> <s id="id.001988">Pondera duo erunt in extremis. </s> <s id="id.001989">Curuari autem magis imbecilli<lb></lb>tatis eſt. </s> <s id="id.001990">Curuatio enim à fractura non differt, niſi ſecundum magis <lb></lb>& minus. </s> <s id="id.001991">Si plus enim curuatur: quam vnitas partium ferat, ſolui<lb></lb>tur continuum, & ſic frangitur. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001992">18. <foreign lang="el">*tou= sfhno\s duna/meos <lb></lb>ai)/tion.</foreign></s> </p> <p type="main"> <s id="id.001993">18. Cauſa poteſtatis <lb></lb>cunei. </s> </p> <p type="main"> <s id="id.001994"><foreign lang="el">*dia\ ti/ tw=| sfhni\ o)/nti mikrw=|, mega/la ba/rh dii/+statai, <lb></lb>kai\ mege/qh swma/twn, kai\ qli=yis i)sxura\ gi/netai; </foreign></s> <s id="g0131702"><foreign lang="el">h)\ dio/ti <lb></lb>o( sfh\n, du/o moxloi/ ei)sin e)nanti/oi a)llh/lois.</foreign></s> <s id="g0131702a"><foreign lang="el">e)/xei de\ e(ka/teros, <lb></lb>to\ me\n ba/ros, to\ de\ u(pomo/xlion, o(\ kai\ a)naspa=| h)\ <lb></lb>pie/zei.</foreign></s> <s id="g0131703"><foreign lang="el">e)/ti de\ h( th=s plhgh=s fora\, to\ ba/ros, o(\ tu/ptei kai\ <lb></lb>kinei=, poiei= me/ga, kai\ dia\ to\ kinou/menon kinei=n th=| taxu/thti <lb></lb>i)sxu/ei e)/ti ple/on. </foreign></s> <s id="g0131703a"><foreign lang="el">mikrw=| de\ o)/nti mega/lai duna/meis <lb></lb>a)kolouqou=si.</foreign></s> <s id="g0131704"><foreign lang="el">dio\ lanqa/nei kinw=n, para\ th\n a)ci/an tou= mege/qous.</foreign></s> <s id="g0131705"><foreign lang="el"><lb></lb>e)/stw sfh\n e)f' w(=| *a*b*g, to\ de\ sfhnou/menon *d*e*h*z. <lb></lb></foreign></s> <s id="g0131705a"><foreign lang="el">moxlo\s dh\ gi/netai h( *a*b.</foreign></s> <s id="g0131705b"><foreign lang="el">ba/ros de\ to\ tou= *b ka/twqen, <lb></lb>u(pomo/xlion de\ to\ *m*n.</foreign></s> <s id="g0131705c"><foreign lang="el">e)nanti/os de\ tou/tw| moxlo\s, to\ *b*g.</foreign></s> <s id="g0131706"><foreign lang="el"><lb></lb>h( de\ *a*g koptome/nh, e(kate/ra| tou/twn xrh=tai moxlw=|: a)naspa=| <lb></lb>ga\r to\ *b.</foreign></s> </p> <p type="main"> <s id="id.001995">Cur à cuneo re parua ma<lb></lb>gnæ moles, & <expan abbr="corporũ">corporum</expan> ma<lb></lb>gnitudines <expan abbr="diuidũtur">diuiduntur</expan>, im<pb xlink:href="035/01/166.jpg" pagenum="126"></pb>preſſioque valida efficitur. <lb></lb></s> <s id="id.001996">An quia cuneus vectes duo <lb></lb>ſunt ſibi inuicem <expan abbr="cõtrarij">contrarij</expan>, <lb></lb>vterque verò habet & pon<lb></lb>dus, & <expan abbr="hypomochliũ">hypomochlium</expan>, quod <lb></lb>diuellit, vel <expan abbr="cõprimit">comprimit</expan>. </s> <s id="id.001997">Præ<lb></lb>terea percuſſio <expan abbr="põdus">pondus</expan> quod <lb></lb>percutit, & mouet <expan abbr="magnũ">magnum</expan> <lb></lb>facit, & quia motum mo<lb></lb>uet celeritate valentius eſt. <lb></lb></s> <s id="id.001998">Paruo vero exiſtente vecte <lb></lb>magnæ vires conſequun<lb></lb>tur, ideò mouens latet præ<lb></lb>ratione magnitudinis. </s> </p> <figure id="id.035.01.166.1.jpg" xlink:href="035/01/166/1.jpg"></figure> <p type="main"> <s id="id.001999">Eſto cuneus vbi eſt <foreign lang="el">a b <lb></lb>g,</foreign> quod vero cuneo fin<lb></lb>ditur <foreign lang="el">d n z.</foreign> </s> <s>Vectis itaque <lb></lb>fiet <foreign lang="el">a b,</foreign> pondus vero ipſius <lb></lb><foreign lang="el">b</foreign> inferior pars: hypo<lb></lb>mochlium autem <foreign lang="el">m & n,</foreign><lb></lb>huic vero contrarius ve<lb></lb>ctis <foreign lang="el">b g,</foreign> tum pars <foreign lang="el">a g</foreign> per<lb></lb>cuſſa. </s> <s id="id.002000"><expan abbr="vtroq;">vtroque</expan> illorum vecte vtitur. </s> <s id="id.002001">diuellit enim ipſum <foreign lang="el">b. </foreign></s> </p> <p type="head"> <s id="id.002002">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002003">Cauſa poteſtatis cunei.] <emph type="italics"></emph>Cuneus eſt inſtrumentum ex ma<lb></lb>teria firma inſtar pyramidis à baſi lata in anguſtum faſtigia<emph.end type="italics"></emph.end><pb xlink:href="035/01/167.jpg" pagenum="127"></pb><figure id="id.035.01.167.1.jpg" xlink:href="035/01/167/1.jpg"></figure><lb></lb><emph type="italics"></emph>tum. </s> <s id="id.002004">Vt A B C D E F. </s> <s id="id.002005">In <lb></lb>hac forma duo conſideranda ſunt, <lb></lb>alterum eſt ex amplitudine baſis, <lb></lb>qua cuneus ad ſuſcipiendam ſuſti<lb></lb>nendamque percußionem aptißi<lb></lb>mus eſt: alterum eſt ex vertice acu<lb></lb>to, qui ob id facile intrà corpora penetrans ſibi viam facit. </s> <s id="id.002006">Vſus <lb></lb>eius eſt ad magnos arborum truncos diuidendum, quod fit magna <lb></lb>cum facilitate <expan abbr="etiã">etiam</expan> à puero, beneficio ipſius cunei per rimulam primò <lb></lb>factam, qua parte acutior eſt, immiſsi & qua parte oppoſita latior <lb></lb>eſt à malleo percuſsi, quod à Milone licet athleta robuſtiſsimo per ſe <lb></lb>fieri non potuit. </s> <s id="id.002007">Hic enim cum aliquando conspiceret adoleſcentem <lb></lb>cuneis immißis findentem arbores, fertur ſubriſiſſe & ſubmouiſſe. <lb></lb></s> <s id="id.002008">Tum non alio vtens inſtrumento, quam ſuis manibus auſus eſt trun<lb></lb>cum diducere. </s> <s id="id.002009">Mox quicquid habebat roboris in primo impetu colli<lb></lb>gens, diduxit hûc atque illûc partes, interim elapſis cuneis, quoniam <lb></lb>reliquam arboris partem diducere non poſſet, diù quidem obnixus eſt, <lb></lb>tandem victus educere non potuit: ſed ab arboris partibus in ſeſe cele<lb></lb>riter coëuntibus comprehenſæ, primum quidem ipſæ contritæ ſunt, <lb></lb>mox & ipſi miſerandi exitij fuere cauſa, vt refert Galenus in lib. de <lb></lb>exhort. ad bonas artes. </s> <s id="id.002011">Hic eſt de quo Iuuenalis,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002012">Viribus ille</s> </p> <p type="main"> <s id="id.002013">Confiſus perijt. </s> </p> <p type="main"> <s id="id.002014">Cur à cuneo.] <emph type="italics"></emph>Antea vectis conſideratus eſt generaliter, dein<lb></lb>de ſpecialiter: ſed ſimplex vt in remo, gubernaculo, malo, collope: <lb></lb>nunc etiam idem ſpecialiter conſideratur, ſed multiplex. </s> <s id="id.002015">Et primum <lb></lb>quidem duplicatus, vt in cuneo. </s> <s id="id.002016">Nam hic quod paruus exiſtens ma<lb></lb>gnos arborum truncos penetrando diuidat, non aliunde habet quam <lb></lb>quia duplex eſt vectis, & à percuſsione motus. </s> <s id="id.002017">Ex hoc enim quod ve<lb></lb>ctis facile mouet. </s> <s id="id.002018">Ex hoc quod eſt duo vectes, cum hi ex aduerſo ſibi <lb></lb>inuicem contrarij ſint, & mutuas operas ſibi tradant, magis & faci<lb></lb>lius mouet. </s> <s id="id.002019">Ex hoc quod à percuſsione, eaque celeri, quæ motus eſt, ma<lb></lb>gis adhuc mouetur: ſicque à tribus ijs coniunctis effectus à cuneo ad<lb></lb>mirandi prodeuntis habetur cauſa. </s> <s id="id.002020">Notandum autem quod inter <lb></lb>cuneos, qui angulum ad verticem <expan abbr="acutiorẽ">acutiorem</expan> habet facilius mouet, ac <lb></lb>ſcindit: quam qui obtuſiorem. </s> <s id="id.002021">Mouetur enim cuneus anguli maioris <emph.end type="italics"></emph.end><pb xlink:href="035/01/168.jpg" pagenum="128"></pb><emph type="italics"></emph>per maius ſpatium, quam minoris, ſiquidem maioris anguli maior eſt <lb></lb>ſubtenſa, cum anguli ſunt æquicruri prop. 26. lib. 1. </s> <s>A potentia verò <lb></lb>facilius eodem tempore mouetur aliquid per minus ſpatium: quam <lb></lb>per maius cum cætera paria ſunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002022">An quia.] <emph type="italics"></emph>Prior cauſa eſt ad ſolutionem problematis, quæ hoc <lb></lb>ſyllogiſmo concludetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002023"><emph type="italics"></emph>Duo vectes ſimul iuncti multum mouent, & magnas moles <lb></lb>diſtrahunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002024"><emph type="italics"></emph>Cuneus eſt duo vectes, ijque ſibi inuicem contrarij: ſed <lb></lb>iuncti. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002025"><emph type="italics"></emph>Cuneus igitur multum mouet, & magnas moles diſtrahet. <lb></lb></s> <s id="id.002026">Syllogiſmi propoſitio confirmationem non habet: ſed hæc repeti po<lb></lb>teſt ex vnius vectis potentia anteà confirmata, quæ in duobus igitur <lb></lb>iunctis maior erit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002027">Vterque verò habet.] <emph type="italics"></emph>Confirmatio eſt aſſumptionis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002028"><emph type="italics"></emph>Vbi eſt longitudo duplex, hypomochlia duo, & pondus, ibi ſunt <lb></lb>duo vectes. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002029"><emph type="italics"></emph>In cuneo eſt vtrinque longitudo, labra rimæ quam ingredi<lb></lb>tur cuneus, ſunt hypomochlia: truncus findendus eſt <lb></lb>pondus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002030"><emph type="italics"></emph>Eſt igitur cuneus duo vectes. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002031">Præterea percuſſio.] <emph type="italics"></emph>Secunda eſt cauſa ad ſolutionem proble<lb></lb>matis, quod cuneus adigatur non ſimplici pulſu: ſed percuſſu, qui ve<lb></lb>hemens & celer eſt motus: iam motum autem mouendum vehemen<lb></lb>tius mouet. </s> <s id="id.002032">Percußio autem duobus fit modis, vel ex eo ipſo ſolo quod <lb></lb>percutit tanquam graui e loco ſuperiori deorſum incidente: at que hoc <lb></lb>quò grauius eſt, eò maior fit percußio: quin & quò longius diſtiterit <lb></lb>primum incidens, magis percutit. </s> <s id="id.002033">Graue enim vnumquodque dum <lb></lb>mouetur grauitatis magis aſſumit motum: quam quieſcens: & adhuc <lb></lb>magis quo longius mouet. </s> <s id="id.002034">quilibet enim aër addit ſuper motum iam <lb></lb>acquiſitum. </s> <s id="id.002035">Inde caſus lapidis aut ictus ab altiore loco grauius per<lb></lb>cutit: vel ex eo quidem quod percutit, ſed recto atque moto, ab aliqua <lb></lb>potentia percutiente, vt ſi per manubrium mallei, quod vna vel duæ <lb></lb>manus moueant. </s> <s id="id.002036">Certum eſt quod quò grauior erit malleus, & quò <lb></lb>longius manubrium, eò maior fiet percuſsio, vt ex præcedentibus ſatis <lb></lb>patere poteſt, cum malleus tanquam pondus à centro, quod eſt in ma<emph.end type="italics"></emph.end><pb xlink:href="035/01/169.jpg" pagenum="129"></pb><emph type="italics"></emph>nubrio, vbi manus ipſum comprehendunt, plus diſtet. </s> <s id="id.002037">Præterea cer<lb></lb>tum eſt quod quantò potentia percutiens validior eſt, validiori tantò <lb></lb>impellet pulſu. </s> <s id="id.002038">his adde quod eſt ab Hippocrate<emph.end type="italics"></emph.end> <foreign lang="el">e)n toi=s trw/masi</foreign><lb></lb><emph type="italics"></emph>annotatum. </s> <s id="id.002039">Quantò impulſus magis fiet<emph.end type="italics"></emph.end> <foreign lang="el">kat' i)/cin</foreign> <emph type="italics"></emph>è directo, id eſt vt <lb></lb>interpretor è perpendiculari. </s> <s id="id.002040">Cæterum percußionem vim habere ad <lb></lb>mouendum validißimam docebit Ariſtoteles prob. 19. huius libri: <lb></lb>ſed ex multis colligere id ita eſſe poſſumus. </s> <s id="id.002042">Primum quod licet cuneo <lb></lb>baſi ſua ſuper plano inſiſtenti, pondus alioqui valde ingens impona<lb></lb>tur, ipſum non diuidet, aut parùm, ſi ad diuiſionem percußione fa<lb></lb>ctam compares. </s> <s id="id.002043">Secundum ſi cuneo vel vectis vel cochlea vel aliud <lb></lb>aliquod inſtrumentum aptetur, vt ipſe intimius propellatur, effectus <lb></lb>inde conſequens parui erit momenti,<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.169.1.jpg" xlink:href="035/01/169/1.jpg"></figure><lb></lb><emph type="italics"></emph>reſpectu eius, qui à percußione pro<lb></lb>ficiſcitur. </s> <s id="id.002044">Guidus Vbaldus commo<lb></lb>de hoc adfert exemplum. </s> <s id="id.002045">Sit A cor<lb></lb>pus lapideum ex quo angulus ſolidus <lb></lb>B ſit auferendus, mallei ferrei per<lb></lb>cuſſu facile id fit, ſine percuſſu, nec <lb></lb>cum hoc, nec cum alio quouis inſtru<lb></lb>mento, niſi cum maxima difficulta<lb></lb>te fieri poterit. </s> <s id="id.002046">Percuſsio igitur cauſa eſt, cur magna ſcindantur <lb></lb>pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002047">Paruo verò.] <emph type="italics"></emph>Occurrit obiectioni, quæ fit propter exiguitatem <lb></lb>cunei, ob idque & vectis, ſed hanc dicit compenſari vehementia & <lb></lb>celeritate percuſsionis, & quanquam ratione motus, motor exiguus <lb></lb>videatur, & ita lateat, magnus eſt tamen viribus. </s> <s id="id.002048">Sic in rebus natu<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg32"></arrow.to.target><lb></lb><emph type="italics"></emph>ralibus, vt eſt apud Galenum, paruæ molis res quædam ſolo tactu, <lb></lb>quædam exiguo morſu maximas corporibus inducunt alterationes. <lb></lb></s> <s id="id.002049">Id quod in heraclio lapide, quem <expan abbr="magnetẽ">magnetem</expan> nominant, videre eſt, fer<lb></lb>rum enim quod tetigerit, ei adhæret vel nullo adhibito vinculo: dein<lb></lb>de ſi aliud id, quod primo tactum fuerit, tetigerit, ſimiliter vt pri<lb></lb>mum, illi inhærebit, poſtea tertium ſecundo. </s> <s id="id.002050">Præterea à Phalangij <lb></lb>ictu totum corpus affici videtur exiguo veneno per foramen iniecto: <lb></lb>ſed longè maiori admiratione dignus eſt Scorpionis ictus, qui breui <lb></lb>admodum tempore grauißima infert accidentia. </s> <s id="id.002051">Hæc Galenus quæ <lb></lb>ideo attuli, vt intelligant morſus ab animalium dentibus inciſorijs <emph.end type="italics"></emph.end><pb xlink:href="035/01/170.jpg" pagenum="130"></pb><emph type="italics"></emph>maxillarum impetu adactis in rem morſam vt pondus diuidendum, <lb></lb>tanquam à cuneis eſſe factos, vt & vulnera ab enſibus, haſtis, dola<lb></lb>bris, ſecuribus & id genus inſtrumentis. </s> <s id="id.002052">Serra quoque & lima ad <lb></lb>hoc genus, quòd ad ſuos denticulos ſpectat reduci poteſt, quot enim <lb></lb>denticuli tot cunei, & ij alligati, aut continui ſuo vecti, id eſt, manu<lb></lb>brio, quod pro vt longius, vel breuius eſt, ita maiorem vim impulſus <lb></lb>aut tractus obtinet. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.002053"><margin.target id="marg32"></margin.target>Lib. 5. de <lb></lb>loc. aff. </s> </p> <p type="main"> <s id="id.002054">Eſto cuneus.] <emph type="italics"></emph>Hîc eſt demonſtratio linearis ad ostenden<lb></lb>dum cuneum diuidendo ponderi duorum vectium vicem prorſus ge<lb></lb>rere, eorumque ſibi inuicem contrariorum. </s> <s id="id.002055">Sed hanc ſic paulò am<lb></lb>plius & apertius repetemus. </s> <s id="id.002056">Sit cuneus A B C cuius vertex B: <lb></lb>& ſit A B æqualis B C, <lb></lb>quod autem diuidendum<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.170.1.jpg" xlink:href="035/01/170/1.jpg"></figure><lb></lb><emph type="italics"></emph>eſt, ſit D E F G, ſitque <lb></lb>pars cunei H B K intra <lb></lb>D E F G, & H B ſit <lb></lb>æqualis ipſi B K. </s> <s>percu<lb></lb>tiatur vt fieri ſolet cuneus <lb></lb>in A C. </s> <s id="id.002057">Dum cuneus in <lb></lb>A C percutitur, A B fit <lb></lb>vectis, cuius hypomoch<lb></lb>lium eſt H, & pondus in <lb></lb>B, eodemque modo C B <lb></lb>fit vectis, cuius hypomo<lb></lb>chlium eſt K, & pondus ſimiliter in B. </s> <s id="id.002058">Sed dum percutitur cuneus <lb></lb>maiori adhuc ipſius portione, intra ipſum D E F G ingreditur, <lb></lb>quam prius eſſet: ſit autem portio hæc M B L, ſitque M B ipſi <lb></lb>B L æqualis. </s> <s id="id.002059">Et cum M B, B L ſint ipſis H B, B K maiores: <lb></lb>erit M L maior H K. </s> <s id="id.002060">Dum igitur M L erit in ſitu H K, opor<lb></lb>tet vt fiat maior diuiſio, & D moueatur verſus O: G autem ver<lb></lb>ſus N, & quò maior pars cunei intra D E F G ingredietur, eò <lb></lb>maior fiet diuiſio: & D, G magis adhuc impellentur verſus O, <lb></lb>N. </s> <s id="id.002061">Pars igitur K G eius quod diuiditur mouebitur à vecte A B, <lb></lb>cuius hypomochlium eſt H, & pondus in B, ita vt punctum B <lb></lb>ipſius vectis A B impellat partem k G: & pars H D mouebi<lb></lb>tur à vecte C B, cuius hypomochlium eſt k, ita vt B vecte C B <emph.end type="italics"></emph.end><pb xlink:href="035/01/171.jpg" pagenum="131"></pb><emph type="italics"></emph>partem H D impellat. </s> <s id="id.002062">Atque hæc eſt ſententia Ariſtotelis de du<lb></lb>plici vecte in cuneo. </s> <s id="id.002063">Aliam habet Guidus Vbaldus, quam exiſtimat <lb></lb>meliorem. </s> <s id="id.002064">Eſt autem eiuſmodi, vt figuræ iam poſitæ vectis A B <lb></lb>habeat hypomochlium B, & pondus mouendum H, ſicut vectis <lb></lb>C B, habeat item hypomochlium B & pondus mouendum ſit K: it a <lb></lb>vt pars H D moueatur à vecte A B, & pars k G à vecte C B. <lb></lb></s> <s id="id.002065">Ratio eſt, quia inſtrumenta mouent per contactum: vectis autem A <lb></lb>B tangit partem H D motam in H, non ſimiliter tangit in B. <lb></lb></s> <s id="id.002066">Id ipſum inſuper comprobat ex cuneo inter duas moles ſeparatas in<lb></lb>terpoſito: ſed quod pace tanti viri dixerim certum eſt, quod niſi B <lb></lb>vertex cunei tangeret molem in B, & ipſam impelleret atque diui<lb></lb>deret, partes H D, K G non vtrinque cederent in O & N. </s> <s id="id.002067">Quod <lb></lb>igitur cedant motus is ſecundarius eſt, & priorem qui eſt in B con<lb></lb>ſequens. </s> <s id="id.002068">Quod autem ad moles ſeparatas attinet, in his aër pondus eſt <lb></lb>mouendum, quem ſi nequaquam cedere fingamus, non vltra ingre<lb></lb>diente cuneo, partes molium inter quas erit cuneus conſiſtent. </s> <s id="id.002069">Cæte<lb></lb>rum vt cuneus vectis eſt multiplicatus: ita cochlea, cuius nullam <lb></lb><expan abbr="mentionẽ">mentionem</expan> feciſſe <expan abbr="Ariſtotelẽ">Ariſtotelem</expan> totis his mechanicis miror, <expan abbr="cū">cum</expan> ſit cuneus <lb></lb>multiplicatus, vel vnus continuatus. </s> <s id="id.002070">Eſt enim cochlea ( vt de hac <lb></lb>pauca quæ ex Pappo, Vbaldo, Munſtero ſelegimus, dicamus ) cuneus <lb></lb>cylindro circumuolutus helicis inſtar, percußionis quidem expers, <lb></lb>ſed per vectem cylindri axi annexum verſus, faciens motionem ma<lb></lb>gnorum ponderum. </s> <s id="id.002071">Quod vt intelligatur. </s> <s id="id.002072">Sit cuneus A B C circa<emph.end type="italics"></emph.end></s> </p> <figure id="id.035.01.171.1.jpg" xlink:href="035/01/171/1.jpg"></figure> <p type="caption"> <s id="id.002073">Cochlea ſine matrice. <lb></lb></s> </p> <p type="main"> <s><emph type="italics"></emph>cylindrum D E, qui ſine <expan abbr="impedimẽto">impedimento</expan> verti poßit per vectem K F <emph.end type="italics"></emph.end><pb xlink:href="035/01/172.jpg" pagenum="132"></pb><emph type="italics"></emph>cylindri axi an<emph.end type="italics"></emph.end></s> </p> <figure id="id.035.01.172.1.jpg" xlink:href="035/01/172/1.jpg"></figure> <p type="caption"> <s id="id.002074">Cochlea cum matrice. <lb></lb></s> </p> <p type="main"> <s><emph type="italics"></emph>nexum: pondus <lb></lb>mouendum ſit <lb></lb>L M N O ex <lb></lb>parte M N im<lb></lb>mobile, vt in <lb></lb>his quæ <expan abbr="ſcindūtur">ſcindun<lb></lb>tur</expan>, fieri ſolet: <lb></lb>cunei vero vertex A ſit intra rimam R S. </s> <s id="id.002075">Itaque facile eſt videre <lb></lb>quod dum K F circumuerſus erit vbi K P, vertex A non erit <lb></lb>amplius intra R S: ſed cunei pars alia vt T V: quæ cum maior <lb></lb>ſit, quam R S. </s> <s id="id.002076">Eſt enim pars quæque cunei remotior à vertice, latior <lb></lb>propinquiore: ergo vt T V ſit intra K S, oportet vt R cedat, mo<lb></lb>ueaturque verſus X, & S verſus E vt faciunt ea quæ ſcindun<lb></lb>tur. </s> <s id="id.002077">Totum ergo L M N O ſcindetur. </s> <s id="id.002078">Nam dum rurſus vectis K <lb></lb>P peruenerit ad K Q, tunc B C erit intra R S, erit R ſiquidem <lb></lb>in X & S in E, vt X E ſit æqualis B C: ſemperque conti<lb></lb>nuato cuneo progredienteque A vertice vltrà, pondus L M N O, <lb></lb>ſcindetur, vel pondus G mobile impelletur, attrahetur, attolletur,<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.172.2.jpg" xlink:href="035/01/172/2.jpg"></figure><lb></lb><emph type="italics"></emph>prout cylindrus cochleæ poſitus erit ad planum horizontis cum ſua, <lb></lb>vel ſine fœmina ſeu matrice. </s> <s id="id.002079">Quod ſi rurſus cochleæ <expan abbr="tympanũ">tympanum</expan> rectè <emph.end type="italics"></emph.end><pb xlink:href="035/01/173.jpg" pagenum="133"></pb><emph type="italics"></emph>vel obliquè denticulatum, ita vt helici facilè congruat, aptetur: ma<lb></lb>nifeſtum eſt, quod ad motum cochleæ etiam tympani C dentes ſuper <lb></lb>helicem cochleæ ad infinitum <expan abbr="circumuertẽtur">circumuertentur</expan>. </s> <s id="id.002080">Vnde hæc cochlea di<lb></lb>citur infinita, id eſt tandiu vertetur, quandiu quis volet. </s> <s id="id.002081">Eodem enim <lb></lb>modo ſemper ſe habebit tympanum ad cochleam. </s> <s id="id.002082">Porrò cochleæ vi <lb></lb>& beneficio admirabile certè quanta pondera moueantur. </s> <s id="id.002083">Refert <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg33"></arrow.to.target><lb></lb><emph type="italics"></emph>Munſterus Baſileæ ſe vidiſſe longißimas ſudes præacutis ferreis ro<lb></lb>ſtris munitas olim in fundum profundiſsimè actas auelli. </s> <s id="id.002084">Quinetiam <lb></lb>aliquando integras domos ex lignis compaginatas in ſublime ſuble<lb></lb>uari & cylindris aliquot ſubmiſsis aliò deferri: ſed & homińum <lb></lb>vſu propemodum immenſo quotidie experimur, quantum valeat <lb></lb>torquendo & premendo, dum vinum, oleum, ſuccos quoſlibet à <lb></lb>ſuis fructibus exprimimus, & honeſtam vſuram dominis ſuis <lb></lb>perſoluere cogimus, ita ad vltimum quadrantem vſque, vt à pu<lb></lb>mice poſtea aquam citius extrahas: quam à fæcibus reliquis ſuc<lb></lb>cum aliquem. </s> <s id="id.002085">Immo verò, quæ laudari nunquam ſatis poteſt, ſine <lb></lb>cochlea ars Typographica quid eſſe poſſet, Duo autem efficiunt vt <lb></lb>cochlea tanta poſsit. </s> <s id="id.002086">Primum quia eſt helix circa cochleam, quæ quò <lb></lb>eſt vertex cunei acutioris, eò facilius: ſed tardius mouet. </s> <s id="id.002087">Alterum <lb></lb>quia eſt vectis, quo cochlea circumuertitur, qui etiam quò longior, eò <lb></lb>facilius: ſed etiam tardius mouet. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.002088"><margin.target id="marg33"></margin.target>Lib 1. Rud. <lb></lb>Math. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002089">19. <foreign lang="el">*peri\ troxilaiw=n.</foreign></s> </p> <p type="main"> <s id="id.002090">19. De trochleis. </s> </p> <p type="main"> <s id="id.002091"><foreign lang="el">*dia\ ti/, e)a/n tis du/o troxilai/as poih/sas e)pi\ dusi\ cu/lois <lb></lb>sumba/llousin e(autoi=s e)nanti/ws, au(tai=s ku/klw| periba/lh| <lb></lb>kalw/dion, e)/xon to\ a)/rthma e)k qate/rou tw=n cu/lwn, <lb></lb>qa/teron de\ h)=| proserhreisme/non h)\ prosteqeime/non kata\ ta\s <lb></lb>troxali/as, e)a\n e(/lkh| tis th=| a)rxh=| tou= kalwdi/ou, mega/la <lb></lb>ba/rh prosa/gei, ka)\n h)=| mikra\ h( e(/lkousa i)sxu/s;</foreign></s> </p> <p type="main"> <s id="id.002092">Quare ſi quis in duobus <lb></lb>tignis inter ſe <expan abbr="iũctisè">iunctisè</expan> <expan abbr="cõtrario">contra<lb></lb>rio</expan> duas trochleas <expan abbr="cõponẽs">componens</expan> <lb></lb>ipſis in circulo circum du<lb></lb>xerit funiculum, qui lorum <lb></lb>quòd ſuſpendatur ex altero <lb></lb>tignorum, & alterum inni<lb></lb>tatur, aut appoſitum ſit ad <lb></lb>trochleas, atque initium <lb></lb>funiculi traxerit, vt parua <lb></lb>vi trahat, magna tamen <lb></lb>pondera adducet. </s> </p> <pb xlink:href="035/01/174.jpg" pagenum="134"></pb> <p type="head"> <s id="id.002093">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002094">De trochleis.] <emph type="italics"></emph>Trochlea eſt inſtrumentum vno aut pluribus <lb></lb>orbiculis circa ſuos axiculos mobilibus & fune ductario con<lb></lb>ſtans ad trahendum, & attollendum onera aptum. </s> <s id="id.002095">Geminatur ali<lb></lb>quando, triplicatur, & amplius multiplicatur. </s> <s id="id.002096">Si duobus orbiculis <lb></lb>conſter<emph.end type="italics"></emph.end> <foreign lang="el">di/spastos,</foreign> <emph type="italics"></emph>ſi tribus<emph.end type="italics"></emph.end> <foreign lang="el">tri/spastos,</foreign> <emph type="italics"></emph>ſi quinque<emph.end type="italics"></emph.end> <foreign lang="el">pente/spastos,</foreign> <emph type="italics"></emph>ſi plu<lb></lb>ribus<emph.end type="italics"></emph.end> <foreign lang="el">polu/spastos</foreign> <emph type="italics"></emph>dicitur, ex quo ſunt illa tractoria inſtrumenta in<lb></lb>finitarum prope modum virium. </s> <s id="id.002097">vt in quibus orbiculi plures ſibi in<lb></lb>uicem ſubſeruientes, & tanquam onus attrahendum diuidentes, ſum<lb></lb>ma facilitate ipſum attrahunt. </s> <s id="id.002098">Notandum etiam ſolum orbiculum <lb></lb>etiam aliquando trochleam appellari, & ad vſum vnam aliquando <lb></lb>trochleam, aliquando duas & plures vſurpari, quod vbi fit, ſi in vna <lb></lb>trochlea ſint plures orbiculi inferioris trochleæ orbiculus ſuperior <lb></lb>debet ſemper eſſe minor inferiore: vt & ſuperioris inferior, ne funes <lb></lb>ductarij inter ſe inuicem complicentur & ſibi obſint. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002099">Quare ſi quis.] <emph type="italics"></emph>Problema de trochleis cur duabus magna one<lb></lb>ra parua vi trahuntur, proponitur, apertè quidem, niſi vbi de alliga<lb></lb>tione ipſarum agitur. </s> <s id="id.002100">Tota enim particula contextus huius<emph.end type="italics"></emph.end> <foreign lang="el">e)/xon to\ <lb></lb>a)/rthma e)k qate/rou tw=n cu/lwn, qa/teron de\ h)= proserhreime/non h)\ pro<lb></lb>steqeime/non kata\ ta\s troxali/as,</foreign> <emph type="italics"></emph>mendoſa meo iudicio eſt. </s> <s id="id.002101">Quid enim <lb></lb>eſt habere lorum quod dependeat, ab altero tignorum: alterum vero <lb></lb>eſſe infixum, & appoſitum ad trochleas, quid eſt illud alterum, quod <lb></lb>dicitur infigi, & apponi <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.174.1.jpg" xlink:href="035/01/174/1.jpg"></figure><lb></lb><emph type="italics"></emph>ad trochleas, intelligi certè <lb></lb>non poteſt. </s> <s id="id.002102">Si igitur quid <lb></lb>rei natura, & vſus oſten<lb></lb>dat, ponamus: illam parti<lb></lb>culam ſic <expan abbr="cõmutabimus">commutabimus</expan>, <lb></lb>vt dicamus vnam è dua<lb></lb>bus trochleis habere <expan abbr="lorũ">lorum</expan>, <lb></lb>quod dependeat ab altero <lb></lb>vel vtroque tignorum: al<lb></lb>teri vero infixum & <expan abbr="appoſitũ">ap<lb></lb>poſitum</expan> eſſe pondus trahen<lb></lb>dum vel attollendum. </s> <s id="id.002103">Vt <lb></lb>ſint duo tigna ſeſe ex ad<emph.end type="italics"></emph.end><pb xlink:href="035/01/175.jpg" pagenum="135"></pb><emph type="italics"></emph>uerſo fulcientia C D & E F <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.175.1.jpg" xlink:href="035/01/175/1.jpg"></figure><lb></lb><emph type="italics"></emph>(plura duobus vt tria, & qua<lb></lb>tuor, vt ſe validius fulciant, vt <lb></lb>plurimum ſtatuuntur ) ſint & <lb></lb>duæ trochleæ A & B, qua<lb></lb>rum altera A ad vtrumque ti<lb></lb>gnum reuinciatur loro H A, <lb></lb>alteri vero B appoſitum ſit pon<lb></lb>dus G, tracto loro ab ini<lb></lb>tio vbi I, pondus G cum tro<lb></lb>chlea B attolletur verſus A. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002104"><emph type="italics"></emph>Vel etiam ſit trochlea in<lb></lb>ferior in qua orbiculi duo cui <lb></lb>pondus A per vncum apponi<lb></lb>tur, ſuperior in qua duo item or<lb></lb>biculi. </s> <s id="id.002105">funis primò alligari de<lb></lb>bet vnco, qui eſt in ea, & cir<lb></lb>cum agi circa ſuperiorem orbicu<lb></lb>lorum inferioris trochleæ, ita vt <lb></lb>aſcendens circum inferiorem ſu<lb></lb>perioris, deuoluatur poſtea circa <lb></lb>inferiorem inferioris, & reuol<lb></lb>uatur adhuc circa ſuperiorem ſu<lb></lb>perioris, habens tandem initium <lb></lb>ſui in G vbi motor intelligitur. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002106"><foreign lang="el">h)\ dio/ti to\ <lb></lb>au)to\ ba/ros a)po\ e)la/ttonos i)sxu/os ei) moxleu/etai, e)gei/retai, <lb></lb>h)\ a)po\ xeiro/s;</foreign></s> <s id="g0131802a"><foreign lang="el">h( de\ troxile/a to\ au)to\ poiei= tw=| mo<lb></lb>xlw=|;</foreign></s> <s id="g0131802b"><foreign lang="el">w(/ste h( mi/a r(a=|on e(/lcei, kai\ a)po\ mia=s o(lkh=s tou= <lb></lb>kata\ xei=ra, polu\ e(/lcei baru/teron.</foreign></s> <s id="g0131802c"><foreign lang="el">tou=to d' ai( du/o troxali/ai <lb></lb>ple/on, h)\ diplasi/w| ta/xei ai)/rousi.</foreign></s> <s id="g0131803"><foreign lang="el">e)/latton ga\r <lb></lb>e)/ti h( e(te/ra e(/lkei, h)\ ei) au)th\ kaq' e(auth\n ei(=lken, o(/tan <lb></lb>para\ th=s e(te/ras e)piblhqh=| to\ sxoini/on.</foreign></s> <s id="g0131804"><foreign lang="el">e)kei/nh ga\r e)/ti <lb></lb>e)/latton e)poi/hse to\ ba/ros, kai\ ou(/tws e)a\n ei)s plei/ous e)piba/llhtai <lb></lb>to\ kalw/dion, e)n o)li/gais troxilai/ais pollh\ gi/netai <lb></lb>diafora/.</foreign></s> <s id="g0131804a"><foreign lang="el">h)\ w(/ste u(po\ th=s prw/ths tou= ba/rous e(/lkontos <lb></lb>te/ttaras mna=s, u(po\ th=s teleutai/as e(/lkesqai pollw=| <lb></lb>e)la/ttw.</foreign></s> </p> <p type="main"> <s id="id.002107">An quia <expan abbr="idẽ">idem</expan> pondus à mi<lb></lb>nore vi, ſi vecte moueatur, <lb></lb><expan abbr="trãsfertur">transfertur</expan> magis: <expan abbr="quã">quam</expan> ſi ma<lb></lb>nu. </s> <s id="id.002108">Trochlea <expan abbr="autẽ">autem</expan> id facit, <lb></lb>quod vectis. </s> <s id="id.002109"><expan abbr="Itaq;">Itaque</expan> ſi vna fa<lb></lb>cilius trahat, & ab vnico tra<lb></lb>ctu: <expan abbr="quã">quam</expan> manu, grauius multò <lb></lb>trahet. </s> <s id="id.002110">Hoc vero duæ tro<pb xlink:href="035/01/176.jpg" pagenum="136"></pb>chleæ plus in dupla veloci<lb></lb>tate attollent. </s> <s id="id.002111">Minus enim <lb></lb>altera trahit quam ſi ipſa <lb></lb>per ſeipſam traheret. </s> <s id="id.002112">quo<lb></lb>niam iuxta <expan abbr="alterã">alteram</expan> iniectus <lb></lb>fuerit funiculus. </s> <s id="id.002113">Hęc enim <lb></lb>inſuper pondus minus effe<lb></lb>cit. </s> <s id="id.002114">Et ſic ſi in plures tro<lb></lb>chleas iniectus fuerit funi<lb></lb>culus, in paucis trochleis <lb></lb>multum intereſt. </s> <s id="id.002115">Itaque à <lb></lb>prima trahente <expan abbr="põdus">pondus</expan> qua<lb></lb>tuor librarum, ab vltima <lb></lb>trahi multo minus. </s> </p> <p type="head"> <s id="id.002116">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002117">An quia idem.] <emph type="italics"></emph>Solutio eſt propoſiti problematis ſumpta è <lb></lb>vecte multiplicato. </s> <s id="id.002118">Syllogiſmus ſic erit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002119"><emph type="italics"></emph>Quod ſolum magna moueret pondera parua vi, hoc etiam gemi<lb></lb>natum trahet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002120"><emph type="italics"></emph>Trochlea parua vi magna trahit pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002121"><emph type="italics"></emph>Trochlea ergo geminata parua vi magna trahet pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002122"><emph type="italics"></emph>Huius ſyllogiſmi propoſitio clara eſt, ex eo quod vires bene compoſi<lb></lb>tæ & multiplicatæ plus poſſunt: quam ſolæ & ſimplices. </s> <s id="id.002123">Aſſumptio <lb></lb>verò ſic confirmatur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002124"><emph type="italics"></emph>Trochlea idem facit, quod vectis. </s> <s id="id.002125">Eſt enim ipſa vectis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002126"><emph type="italics"></emph>Vectis parua vi magna mouet pondera. </s> <s id="id.002127">ex anteced. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002128"><emph type="italics"></emph>Ergo trochlea parua vi magna trahet pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002129"><emph type="italics"></emph>Quod autem trochlea ſit vectis, patet. </s> <s id="id.002130">quia hypomochlium eſt in axi<lb></lb>culo immobili, diameter orbiculi eſt longitudo vectis deorſum vna <lb></lb>parte tracta per funem circumductum: altera ſurſum eleuata. </s> <s id="id.002131"><expan abbr="Mouẽs">Mouens</expan> <lb></lb><expan abbr="cutẽ">cutem</expan> eſt virtus trahentis ad initium funis. </s> <s id="id.002132">Et <expan abbr="põdus">pondus</expan> quod eſt vni tro<lb></lb>chlearum appoſitum eſt mobile. </s> <s id="id.002133">Cum autem virtus trahit per plures <lb></lb>orbiculos, vt pluribus vectibus vtens vna opera, & eodem temporis <lb></lb>momento facilius trahit & minore vi, quandoquidem pondus, vt <emph.end type="italics"></emph.end><pb xlink:href="035/01/177.jpg" pagenum="137"></pb><emph type="italics"></emph>pluribus diuiſum orbiculis, minus id eſt leuius apparet. </s> <s id="id.002134">Itaque quo<lb></lb>niam facilius eſt mouere pondus vecte: quam manu, & trochlea ve<lb></lb>ctis eſt, facilius erit trochlea: quam manu. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002135">Pluſquam in dupla.] <emph type="italics"></emph>Quò plures ſunt orbiculi in trochleis, eò <lb></lb>quidem facilius, & minore vi pondus trahitur, vt eſt demonſtra<lb></lb>tum à Guido Vbaldo prop. 3. & aliquot ſequentibus in tractatu de <lb></lb>trochlea. </s> <s id="id.002136">Sed etiam vbi ſunt plures, ibi lentior eſt tractio, quia po<lb></lb>tentia in æquali tempore, ſpatio ſecundum duplum, triplum, & ſic <lb></lb>deinceps ampliori ſine huiuſmodi trochleis idem pondus moueret: ſi <lb></lb>quidem per ſe ſufficiat. </s> <s id="id.002137">Vnde arbitror hûc irrepſiſſe mendum in vo<lb></lb>cabulo<emph.end type="italics"></emph.end> <foreign lang="el">ta/xei</foreign> <emph type="italics"></emph>pro<emph.end type="italics"></emph.end> <foreign lang="el">logw|</foreign> <emph type="italics"></emph>vel<emph.end type="italics"></emph.end> <foreign lang="el">diplasi/w|. </foreign><emph type="italics"></emph>pro<emph.end type="italics"></emph.end> <foreign lang="el">u(podiplasi/w|</foreign> <emph type="italics"></emph>tollendo<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">ple/on h)\</foreign> <emph type="italics"></emph>vel potius pro<emph.end type="italics"></emph.end> <foreign lang="el">h)\</foreign> <emph type="italics"></emph>reponendo<emph.end type="italics"></emph.end> <foreign lang="el">mh\</foreign> <emph type="italics"></emph>ſic enim ſententia vera erit. <emph.end type="italics"></emph.end> <lb></lb></s> <s>Hoc vero duæ trochleæ plus non in dupla velocitate <expan abbr="attollẽt">at<lb></lb>tollent</expan>. </s> <s><emph type="italics"></emph><expan abbr="Cæterũ">Cæterum</expan> quomodo per trochleas, quanto <expan abbr="tẽpore">tempore</expan>, & ſpatio, pon<lb></lb>dera moueantur, <expan abbr="quodnã">quodnam</expan> ſuperioris & inferioris trochleæ fuerit offi<lb></lb>cium, orbiculorum diametri vt moueantur, vt in omni ratione quæ <lb></lb>in numeris eſt, pondus & potentia ſtatui poſsint, quæ omnia certè <lb></lb>ſcitu digniſsima ſunt Geometricè demonſtrata, qui ſcire volet, vi<lb></lb>deat apud Guidum Vbaldum prædicto tractatu, ne maior pars il<lb></lb>lius præſtantiſsimi operis, quod edidit de mechanicis, mihi ſit hûc <lb></lb>transferenda. </s> <s id="id.002138">Huic verò loco non poſſum non inſerere vnam ma<lb></lb>chinam e ſex trochleis: & funiculis quinque compoſitam ( è pluri<lb></lb>bus componi, ſi vſus poſtulet, nihil obeſt ) mira celeritate, & funis <lb></lb>ductarij paucitate atque compendio pondus attollentem, quam mihi <lb></lb>communicauit Georgius Lhullierius vir ſine honoris titulo <expan abbr="nũquam">nunquam</expan> <lb></lb>mihi nominandus, propter <expan abbr="ſuũ">ſuum</expan> in artes mathematicas & <expan abbr="mathematũ">mathema<lb></lb>tum</expan> ſtudioſos <expan abbr="quãdiu">quandiu</expan> vixit ſingularem <expan abbr="amorẽ">amorem</expan>. </s> <s id="id.002139">Machina eſt eiuſmodi, <lb></lb>ſit tignum A B perpendiculariter inſiſtens, cui etiam ad rectos al<lb></lb>terum in ſiſtat vt C D: ſint ſex trochleæ E, F, G, H, I, K, <lb></lb>funiculi quinque L A, N M, Q P, S R, B T, quorum pri<lb></lb>mus circumuoluitur circa duos orbiculos E & F in extremis ti<lb></lb>gnorum circa ſuos axiculos mobiles reliquorum ſinguli circa ſingu<lb></lb>los à proximè antecedentibus funiculis ſuſpenſos. </s> <s id="id.002140">In X autem ſit <lb></lb>harpago ad apprehendendum pondus E attollendum vel deprimen<lb></lb>dum. </s> <s id="id.002141">Si enim extremum L ab harpagone V liberetur, & ad A <lb></lb>traducatur, deſcendet vno quaſi nictu oculi pondus E, tantum <emph.end type="italics"></emph.end><pb xlink:href="035/01/178.jpg" pagenum="138"></pb><figure id="id.035.01.178.1.jpg" xlink:href="035/01/178/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſpatij, quanti ſunt funiculi N M, Q P, <lb></lb>R S, B T. </s> <s id="id.002142">Tanti erunt autem, <lb></lb>quantos loci, ad quem deſcendere, vel <lb></lb>è quo educere volumus, profunditas, <lb></lb>poſtulat. </s> <s id="id.002143">Si autem attollere oporteat, <lb></lb>extremum L cum erit in A, traduce<lb></lb>tur ad harpagonem V. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002144"><emph type="italics"></emph>In hac machina igitur hæc duo in<lb></lb>ſunt, facilitas motionis ob multitudi<lb></lb>nem trochlearum, & celeritas motio<lb></lb>nis. </s> <s id="id.002145">quia quanto temporis ſpatio extre<lb></lb>mum funiculi L ab A transfertur <lb></lb>ad harpagonem V, eodem pondus E <lb></lb>ex infimo loco ſurſum per decuplam <lb></lb>longitudinem & amplius, ſi quis vo<lb></lb>let, euehitur, aut contra. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002146"><foreign lang="el">kai\ e)n toi=s oi)kodomikoi=s e)/rgois r(a|di/ws kinou=si mega/la <lb></lb>ba/rh: metafe/rousi ga\r a)po\ th=s au)th=s troxilai/as <lb></lb>e)f' e(te/ran, kai\ pa/lin a)p' e)kei/nhs ei)s o)/nous kai\ moxlou/s: <lb></lb>tou=to de\ tau)to/n e)sti, tw=| poiei=n polla\s troxile/as.</foreign></s> </p> <p type="main"> <s id="id.002147">Atque in ar<lb></lb>chitectura faci<lb></lb>le mouent ma<lb></lb>gna pondera, <lb></lb><expan abbr="Trãsferũt">Transferunt</expan> enim <lb></lb>ab ipſa trochlea <lb></lb>ad <expan abbr="alterã">alteram</expan> & rur<lb></lb>ſus ab ipſa ad ſu<lb></lb>culas & vectes, <lb></lb>quod <expan abbr="idẽ">idem</expan> eſt ac <lb></lb>ſi multas <expan abbr="cõponerẽt">compo<lb></lb>nerent</expan> trochleas. </s> </p> <p type="head"> <s id="id.002148">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002149">Atque in architect.] <emph type="italics"></emph>Vt funis <lb></lb>facilius trahatur in magnis ponde<lb></lb>ribus dimouendis ergata, aut ſucula adhibetur ad tigna, vt & rota <lb></lb>& collopes. </s> <s id="id.002150">quæ eò facilius trahunt, quò longiores fuerint. </s> <s id="id.002151">Atque<emph.end type="italics"></emph.end><pb xlink:href="035/01/179.jpg" pagenum="139"></pb><emph type="italics"></emph>huius compoſitionis quæ adæquat multas trochleas, aut etiam lon<lb></lb>gißimum vectem maximus eſt vſus. </s> <s id="id.002152"><expan abbr="Quandoquidẽ">Quandoquidem</expan> cum materia ad <lb></lb>vectem, cuius longitudo vnius ſtadij requireretur, idonea <expan abbr="nuſquã">nuſquam</expan> in<lb></lb>ueniri poßit, plurium tamen trochlearum, ergatarum, ſucularum, <lb></lb>tympanorum, collopum compoſitione apta proportionalium, fiet ma<lb></lb>china tractabilis, cuius vis maior eſſe poteſt: quam vectis, cuius lon<lb></lb>gitudo eſſet ſtadij vnius. </s> <s id="id.002153">Rei huius ſpecimen luculentum Romæ ex<lb></lb>hibitum eſt à Dominico Fontana Mili in <expan abbr="Comẽſi">Comenſi</expan> diocœſi orto, con<lb></lb>ſilio, adhortatione, ſumptibus X iſti V. pontificis maximi, in tran<lb></lb>ſponendo obeliſco, qui Soli primùm à Pherone Rege Ægypti, Helio<lb></lb>poli antè Troiani belli tempora factus, & dicatus: poſtea à Caio Ca<lb></lb>ligula Romam tranſuectus Auguſto & Tiberio Cæſaribus ſacer, <lb></lb>temporibus noſtris pænè obrutus ruderibus ædium, quæ circum eum <lb></lb>corruerant, parietinis & cœmentis, nullam tamen iniuriam à tot <lb></lb>Romani nominis hoſtibus paſſus, nulla ex parte exeſus, aut comminu<lb></lb>tus, magna omnium aduentantium admiratione parte adhuc ſui ali<lb></lb>qua loco valde inepto conſpicuus, viſebatur. </s> <s id="id.002154">Vt totum hoc negotium <lb></lb>geſtum ſit, licet iam à multis doctis viris literarum monumentis <lb></lb>commendatum, ineptißimus tamen ſim, aut eorum, quæ mea ætate <lb></lb>fiunt maxime memorabilium, ignarus, ſi ipſum in huius loci id <lb></lb>exempli maxime poſtulantis illuſtratione, prætermittam, breuiter <lb></lb>ergo commemorabo. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002155"><emph type="italics"></emph>Primum ſcire oportet, quod obeliſcus eſt vnus ingenti magnitu<lb></lb>dine lapis, qui ab imo vſque ad ſummum rectis lineis inſtar acus, aut <lb></lb>potius exigui veru in cuſpidem terminatur. </s> <s id="id.002156">Varia eſt obeliſcorum <lb></lb>materia, forma, & altitudo. </s> <s id="id.002157">Hic de quo agitur ex vno lapide, eoque <lb></lb>durißimo, qui pyrhopæcilos dicitur, quod punctis quibuſdam ignei <lb></lb>coloris diſtinctus ſit, ac varius vndique interluceat, ſine notis hie<lb></lb>roglyphicis ( quod alijs obeliſcis frequens eſt, per has regibus Ægypti <lb></lb>ſuas res geſtas memoriæ commendantibus ) ſemper eadem forma, ea<lb></lb>que quadrangulari ex infima ſui parte minus ampla & ſpatioſa, ob <lb></lb>idque pulcherrima, cuius craßitudo, ſi Serlius antiquitatum Roma<lb></lb>narum ſcriptor rectè metitus eſt, pedibus 9. minutiſque 24. altitu<lb></lb>do pedibus 85. ſummaque demum craßitudo pedibus 6. & minutis<emph.end type="italics"></emph.end><lb></lb>8. <emph type="italics"></emph>comprehenditur, ad imanque ipſius radicem hæ literæ in epitaphij <lb></lb>ordinem digeſtæ ac diſtributæ legebantur. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/180.jpg" pagenum="140"></pb> <p type="main"> <s id="id.002158">Diuo Cæſari Diui Iulij. </s> <s id="id.002159">F. Auguſto: Ti.Cæſari Diui Auguſti. </s> </p> <p type="main"> <s id="id.002160">F. Auguſto ſacrum. </s> </p> <p type="main"> <s id="id.002162"><emph type="italics"></emph>Hic igitur cum ob ſitum ( attingebat enim propemodum ſacrarium <lb></lb>baſilicæ S. Petri, quod ad meridiem vergit ) & eorum quibus ſacra<lb></lb>tus erat execrationem, ſummo pontifici diſplicuiſſet, vt alijs nonnul<lb></lb>lis, qui ante eum in cathedra D. Petri ſederunt: ſed qui rem ob eius, vt <lb></lb>exiſtimabant,<emph.end type="italics"></emph.end> <foreign lang="el">a)dunami/an</foreign>: <emph type="italics"></emph>aut ob ſumptuum magnitudinem ab ag<lb></lb>greßione deterriti, nunquam attentarunt. </s> <s id="id.002164">Sanctitati viſum eſt, vt in <lb></lb>media Vaticani area ante templi, quo nullum eſt magnificentius, ve<lb></lb>ſtibulum, loco Romæ amplißimo & celeberrimo, & pontificalibus <lb></lb>actionibus dedicato, collocaretur, & ſigno crucis eius apici impoſito, <lb></lb>Chriſto Chriſtianorum duci vnico, & ſeruatori, obliterata prorſus <lb></lb>Paganorum conſecratione, conſecraretur, & totus denique Chriſtia<lb></lb>nos præmoneret, vt quemadmodum eius quatuor latera ab infima <lb></lb>parte ſurſum verſus paulatim gracileſcunt, quouſque acutiſsimo <lb></lb>apice, in quo eſt Chriſtus, terminetur: ſic diſcant <expan abbr="mẽtes">mentes</expan> ſuas ab hono<lb></lb>rum, diuitiarum, aliarum que rerum terreſtrium, quibus maxime pa<lb></lb>tent, cogitationibus & cupiditatibus ſubtrahere & ſubducere, nec <lb></lb>ante conſiſtant: quam illæ in altum paulatim erectæ, & acutiores <lb></lb>factæ, Chriſtum, eumque crucifixum inueniant, ſolum ament, hunc <lb></lb>ſomnient, in ſolo quieſcant, & in eo ſeſe noctes dieſque oblectent. <lb></lb></s> <s id="id.002165">Hoc igitur vt fieret, ipſum obeliſcum ſine offenſionis periculo pri<lb></lb>mum oportebat è ſuo ſtylobata auellere: deinde humi vel ſuper curri<lb></lb>culo reclinare: poſtea tranſuehere ad locum deſtinatum, ab hoc mille <lb></lb>pedes diſtantem per tumulum aggeſtum paulatim eminentiorem va<lb></lb>lidiſsimis trabibus per aliquot tignorum ſtatutiones religatis vndi<lb></lb>quaque coercitum, ne immenſa vecturæ mole fatiſceret: poſtea ſenſim <lb></lb>in ſublime ſubrigere: poſtremo perpendiculariter ſubrectum ſuper <lb></lb>ſtylobata ſuo collocare: nunc qui vectes, quæ ferramenta, quæ machi<lb></lb>næ, quot operæ, qui modus tot molitionibus, quarum quælibet factu <lb></lb>propemodum<emph.end type="italics"></emph.end> <foreign lang="el">a)du/natos</foreign> <emph type="italics"></emph>iudicabatur, adhibita ſunt, dicam, vt ex qua<lb></lb>dam epistola familiari Roma in Hiſpaniam ad P.Velleium de hac <lb></lb>re miſſa, & aliorum doctorum <expan abbr="hominũ">hominum</expan> ſcriptis, breuiter collegimus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002166"><emph type="italics"></emph>Primum obeliſcus validiſsimis octo columnis per latera circum<lb></lb>uallatus eſt, hæ concathenatæ, atque alijs ſuccreſcentibus & conne<lb></lb>xis apicem obeliſci ad ſex palmos præcellebant. </s> <s id="id.002167">His totidem faſtigia <emph.end type="italics"></emph.end><pb xlink:href="035/01/181.jpg" pagenum="141"></pb><emph type="italics"></emph>ſuperimpoſita, à quibus perpetuæ intrà extrá que ſuccedentes fulctu<lb></lb>ræ ſtatuta tigna ſuſtentabant, ſic enim caſui & inflexionibus pro<lb></lb>ſpectum. </s> <s id="id.002168">Tota hæc machina validiſsimis laminis, ferreiſque clauis à <lb></lb>vertice ad calcem religata, plurimis & retinaculis, & ductarijs fu<lb></lb>nibus vndequaque ſuffulta. </s> <s id="id.002169">Quadraginta trochleæ à totidem ergatis <lb></lb>mouendæ faſtigijs dictis alligatæ erant. </s> <s id="id.002170">Horum ſingulis homines <lb></lb>quindecim, equi duo deſtinati ſunt, qui ad nutum præfecti ( præerat <lb></lb>autem, cuique ergatæ vnus ) præſto eſſent. </s> <s id="id.002171">Præfecti ad ſignum tubæ <lb></lb>vrgebant molitionem, cymbali ſiſtebant. </s> <s id="id.002172">Vectes adiuncti ſunt quin<lb></lb>que ſeptuaginta palmorum longitudine ex validiſsimis trabibus <lb></lb>compacti, tres ab obeliſci fronte: duo à tergo. </s> <s id="id.002173">Primo impetu ferrea <lb></lb>quædam lamina, quæ machinam obeliſcum ambientem religabat, <lb></lb>diſrupta eſt, ſed hac vnius horæ ſpatio reſtituta, decem demum im<lb></lb>pulſibus duos palmos, ac <expan abbr="dimidiū">dimidium</expan> in altum obeliſcus eleuatur, ne ta<lb></lb>men tanta pendente mole ſiniſtrum quid accideret, cunei ſtatim ac <lb></lb>tignorum cæſuræ, quibus obniteretur, ſuppoſitæ. </s> <s id="id.002174">Tum deinde aſſeri<lb></lb>bus ac cylindris, cubi quidam, quibus inſidebat, dimoti, & quædam <lb></lb>traha ſuppoſita. </s> <s id="id.002175">Hoc facto, quæ prima ad auellendum molitio acer<lb></lb>rima fuit, ſuſtenta tamen magnum ad reliquas aggrediendas adiecit <lb></lb>animum. </s> <s id="id.002176">Itaque ergatæ, trabes, funes ductarij, cæteraque, vt conue<lb></lb>niebat, mutata, atque in diuerſam formam compoſita: & ima pars <lb></lb>obeliſci quatuor ergatarum viribus, quæ à tergo mouebantur, cæteris <lb></lb>quæ à fronte erant, funes remittentibus, trahi paulatim cœpit. </s> <s id="id.002177">Ipſe <lb></lb>vero apex clementiſsimè vergebat, quouſque famoſiſsima moles om<lb></lb>nino integra, ac ſine vlla iactura humi decubuit. </s> <s id="id.002178">Atque hæc ſecun<lb></lb>da molitio fuit. </s> <s id="id.002179">Poſtea per dictum tumulum ſex ergatarum vi trahi <lb></lb>cœpta eſt, & quia huic ſpectaculo intererat ipſe ſummus pontifex, <lb></lb>huius tanti tantæ molitionis curatoris exactoriſque inſtigante <lb></lb>operarum moras præſentia, breuius quidem, quam cogitari poteſt, <lb></lb>pertracta eſt. </s> <s id="id.002180">Atque hæc tertia molitio fuit. </s> <s id="id.002181">poſtquam ad aliquot <lb></lb>dies, ne funes nimio calore conflagrarent, ob motum, & aëris æſtuo<lb></lb>ſam tunc temporis conſtitutionem, ceſſatum eſt, tandem eadem ma<lb></lb>china, qua auulſus: ſed altiore propter loci eminentiam, externo in<lb></lb>ternoque chomate munitiſsima, adhibitis ergatis quadraginta ſex, <lb></lb>equis centum quadraginta, hominibus ſexcentis, ex ergatiſque qua<lb></lb>tuor imam obeliſci partem <expan abbr="trahẽtibus">trahentibus</expan>. </s> <s id="id.002182">Reliquæ à cuſpide ad medium <emph.end type="italics"></emph.end><pb xlink:href="035/01/182.jpg" pagenum="142"></pb><emph type="italics"></emph>religatum erexerunt, atque tandem quadraginta ſeptem niſibus ſte<lb></lb>tit moles. </s> <s id="id.002183">Cubi, quibus antea inſidebat, ſuppoſiti, & in omnis ſeculi <lb></lb>memoriam iam quinquaginta ſex & amplius doctorum hominum <lb></lb>ſcriptis editis celebrata, ad perpendiculum collocata eſt. </s> <s id="id.002184">Hæc quarta <lb></lb>& quinta ſunt molitio. </s> <s id="id.002185">Poſtquam viceſima ſexta menſis dicti glo<lb></lb>rioſißimo huic triumpho à pontifice delecta per B <expan abbr="Feratinū">Feratinum</expan> Epiſco<lb></lb>pum <expan abbr="Amerinū">Amerinum</expan> & cancellariæ Apoſtolicæ <expan abbr="regentẽ">regentem</expan> ſolemni prius ad <lb></lb>Petri altare ſacrificio facto, & circà obeliſcum frequenti ſupplicatio<lb></lb>ne peracta, multaque ſuper ſanctißimæ Crucis <expan abbr="ſtatuã">ſtatuam</expan> æream, ſed affa<lb></lb>brè inauratam, <expan abbr="precatū">precatum</expan>, tradita eſt Crux Diacono ſacris adhuc veſti<lb></lb>bus induto, à quo denique in mucrone obeliſci collocata eſt. </s> <s id="id.002186">quo tem<lb></lb>poris momento cuncta tormentorum genera, quæ in Sancti Angeli <lb></lb>arce erant, aſsiduos edidere bombos. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002187"><emph type="italics"></emph>Itaque quod priſcis illis naturæ miraculis quæ à Leone decimo ad <lb></lb>Paulum III. orbis tulit, desperatum planè opus <expan abbr="iudicatū">iudicatum</expan> erat. </s> <s id="id.002188">Id <expan abbr="nūc">nunc</expan> <lb></lb>Sixti V. Pontificis cura & magnificentia, Dominici Fontanæ ope<lb></lb>ra & induſtria, &<emph.end type="italics"></emph.end> <foreign lang="el">tw=n mhxanikw=n</foreign> <emph type="italics"></emph>auxilia <expan abbr="perfecerūt">perfecerunt</expan>, atque abſol<lb></lb>uerunt tanto ſpectantium applauſu, vt cum Fontana perfecto opere <lb></lb>domum reductus eſt, diceres Camillum vel Fabium magnum in ca<lb></lb>pitolium triumphantem duci. </s> <s id="id.002190">Area vero Vaticani in qua obeliſcus, <lb></lb>qualem in ſequenti pagina tibi cum ſuis titulis repræſentamus, licet <lb></lb>ampliſsima, hominum ad rei miraculum confluentium per multos <lb></lb>poſtea dies concurſum vix capere potuit. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.002191">E MVLTIS EPIGRAMMIS DE <lb></lb>obeliſco, Cruce, & Sixto ſummo Pontifice <lb></lb>hoc ſelectum hîc inſcripſimus. </s> </p> <p type="main"> <s id="id.002192">Ænea ſerpentis Moſes ſimulachra ſacerdos <lb></lb>Extulit, ægrotis vt medicina foret</s> </p> <p type="main"> <s id="id.002193">Nunc alter Moſes obeliſci in vertice Sixtus <lb></lb>Erigit ægrotis ærea ſigna Crucis</s> </p> <p type="main"> <s id="id.002194">Vos ô Romani ſuſtollite ad æthera vultus, <lb></lb>A Cruce nam vobis veſtra petenda ſalus. </s> </p> <p type="main"> <s id="id.002195"><emph type="italics"></emph>Gulielmus Blancus Albienſi. I. C. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/183.jpg" pagenum="143"></pb> <figure id="id.035.01.183.1.jpg" xlink:href="035/01/183/1.jpg"></figure> <p type="caption"> <s id="id.002197">Sanctiſſimæ Cruci ſacra<lb></lb>uit Sixtus V. Pont. Max. <lb></lb>è priore ſede auulſum & <lb></lb>Cæſaribus Aug. & Tib. <lb></lb>11.ablatum. </s> </p> <p type="caption"> <s id="id.002198"><emph type="italics"></emph>Faciata à leuante. <emph.end type="italics"></emph.end></s> </p> <p type="caption"> <s id="id.002199">Ecce Crux Domini <lb></lb>fugite partes aduerſæ <lb></lb>vincit leo de Tribu <lb></lb>Iuda. </s> </p> <p type="caption"> <s id="id.002200"><emph type="italics"></emph>Faciata à Tramontana. <emph.end type="italics"></emph.end></s> </p> <p type="caption"> <s id="id.002201">Sixtus V. Pontif. Max. Cruci <lb></lb>inuictæ obeliſcum vaticanum <lb></lb>ab impura ſuperſtitione expia<lb></lb>tum Iuſtius & Felicius conſe<lb></lb>crauit Ann. M. D. LXXXVI. <lb></lb>Pont. II. </s> </p> <p type="caption"> <s id="id.002202">Diuo Cæſ. Diui <lb></lb>Iulij F. Auguſto Ti. <lb></lb>Cæſ. Diui Auguſt. <lb></lb>F. Auguſt. ſacrum. </s> </p> <p type="caption"> <s id="id.002204"><emph type="italics"></emph>Faciata in verſo pietro. <emph.end type="italics"></emph.end></s> </p> <p type="caption"> <s id="id.002205">Chriſtus vincit, <lb></lb>Chriſtus regnat, <lb></lb>Chriſtus imperat, <lb></lb>Chriſtus ab omni malo <lb></lb>plebem ſuam defendat. </s> </p> <p type="caption"> <s id="id.002209"><emph type="italics"></emph>Della faciata à mezzo giorne. <emph.end type="italics"></emph.end></s> </p> <p type="caption"> <s id="id.002210">Sixtus V. Pont. Max. obeli <lb></lb>vaticanum, <lb></lb>diſ. gentium. <lb></lb></s> <s id="id.002212">Impio cultu dicatum ad Apoſtolo <lb></lb>rum limina operoſo labore <lb></lb></s> <s>Tranſtulit. </s> <s id="id.002213">Ann. M.D. LXXXV. Pont. II. </s> </p> </subchap1> </chap> <pb xlink:href="035/01/184.jpg" pagenum="144"></pb> <chap> <subchap1> <p type="main"> <s id="id.002214">20. <foreign lang="el">*dia\ ti/ tupto/menos pe/le<lb></lb>kus diasxi/zei, pie/zwn de\ <lb></lb>ou)k e)/ti.</foreign></s> </p> <p type="main"> <s id="id.002215">20. Cur ſecuris feriens di<lb></lb>uidit: premens vero non <lb></lb>item. </s> </p> <p type="main"> <s id="id.002216"><foreign lang="el">*dia\ ti/, e)a\n me/n tis e)piqh=| e)pi\ to\ cu/lon pe/lekun me/gan, <lb></lb>kai\ forti/on me/ga e)p' au)tw=|, ou) diairei= to\ cu/lon, o(/ kai\ <lb></lb>lo/gou a)/cion: e)a\n de\ a)/ras to\n pe/leku/n tis pata/ch|, au)to\ <lb></lb>diasxi/zei, e)/latton ba/ros e)/xontos tou= tuptome/nou polu\ ma=llon, <lb></lb>h)\ tou= e)pikeime/nou kai\ piezou=ntos; </foreign></s> <s id="g0131902"><foreign lang="el">h)\ dio/ti pa/nta th=| kinh/sei <lb></lb>e)rga/zetai, kai\ to\ baru\ th\n tou= ba/rous ki/nhsin lamba/nei <lb></lb>ma=llon kinou/menon h)\ h)remou=n; </foreign></s> <s id="g0131903"><foreign lang="el">e)pikei/menon ou)=n ou) kinei=tai th\n <lb></lb>tou= ba/rous ki/nhsin.</foreign></s> <s id="g0131903a"><foreign lang="el">fero/menon de\, tau/thn te kai\ th\n tou= <lb></lb>tu/ptontos.</foreign></s> </p> <p type="main"> <s id="id.002217">Cur ſi quis magnam ſe<lb></lb>curim ſuper lignum impo<lb></lb>ſuerit, & illi inſuper ma<lb></lb>gnum pondus, lignum non <lb></lb>diuidit, quod ſit effatu di<lb></lb>gnum: at ſi quis ſecurim at<lb></lb>tollens percuſſerit, ipſum <lb></lb>diuidit, ipſo percutiente <lb></lb>multò minus pondus ha<lb></lb>bente: quam ſit id, quod <lb></lb>impoſitum erat, & preme<lb></lb>bat. </s> <s id="id.002218">An quia omnia motio<lb></lb>ne fiunt: & graue commo<lb></lb>tum magis: quam <expan abbr="quieſcẽs">quieſcens</expan> <lb></lb>motionem grauitatis acci<lb></lb>pit. </s> <s id="id.002219">Impoſitum igitur non <lb></lb>mouetur, niſi motione gra<lb></lb>uitatis [propriæ]: commotum vero & ipſa & motione <lb></lb>percutientis. </s> </p> <p type="head"> <s id="id.002220">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002221">Cvrſi quis.] <emph type="italics"></emph>Problema de ſecuri, quæ ſecat dum percutit, non <lb></lb>autem dum ſimpliciter incumbit, duobus modis ſoluitur. </s> <s id="id.002222">Prior <lb></lb>ſumptus eſt è communi ſententia phyſicorum aſſerentium, omnia <lb></lb>motione fieri. </s> <s id="id.002223">Syllogiſmus igitur ſic eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002224"><emph type="italics"></emph>Cum omnia motione fiant, proinde & ſectio, quod duplici mo<lb></lb>tione commotum erit, magis mouebit: quam id, quod vna. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002225"><emph type="italics"></emph>Sed graue commotum, vt magna ſecuris feriens, duplici <lb></lb>motione mouetur, vna grauitatis propriæ: altera percu<lb></lb>tientis. </s> <s id="id.002226">Graue autem impoſitum vna tantum mouetur, <lb></lb>nempe grauitatis propriæ. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/185.jpg" pagenum="145"></pb> <p type="main"> <s id="id.002227"><emph type="italics"></emph>Ergo magna ſecuris feriens ſecabit: impoſita vero minimè. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002228">Motione grauitatis.] <foreign lang="el">ki/nhsis tou= ba/rous</foreign> <emph type="italics"></emph>eſt motus cuique <lb></lb>graui occultus inhærens. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002229"><foreign lang="el">e)/ti de\ kai\ gi/netai sfh\n o( pe/lekus: o( de\ sfh\n <lb></lb>mikro\s w)\n, mega/la dii/+sthsi, dia\ to\ ei)=nai e)k du/o moxlw=n <lb></lb>e)nanti/ws sugkeime/nwn.</foreign></s> </p> <p type="main"> <s id="id.002230">Præterea ſecuris fit cu<lb></lb>neus. </s> <s id="id.002231">Cuneus <expan abbr="autẽ">autem</expan> paruus <lb></lb><expan abbr="exiſtẽs">exiſtens</expan> magna diuidit. </s> <s id="id.002232">quia <lb></lb>ex duobus vectibus conſti<lb></lb>tutus eſt contrario modo <lb></lb>collocatis. </s> </p> <p type="head"> <s id="id.002233">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002234">Præterea ſecuris.] <emph type="italics"></emph>Altera eſt problematis propoſiti ſolutio <lb></lb>ſumpta è cunei forma, quæ in ſecuri propter aciem acutam, & ſu<lb></lb>perioris partis latitudinem conſpicua eſt. </s> <s id="id.002235">Comprehendetur hoc ſyl<lb></lb>logiſmo. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002236"><emph type="italics"></emph>Cuneus paruus cum ſit, magna diuidit. ( ex anteced. )<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002237"><emph type="italics"></emph>Securis feriens eſt cuneus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002238"><emph type="italics"></emph>Ergo ſecuris feriens magna diuidet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002239"><emph type="italics"></emph>Sed hic obijci poteſt, quod ſecuris impoſita etiam eſt cuneus. </s> <s id="id.002240">Et ita <lb></lb>eſt, ſed non actu. </s> <s id="id.002241">Quia opus eſt malleo percutiente, tanquam motore <lb></lb>vectium. </s> <s id="id.002242">Securis autem feriens eſt cuneus annexus malleo, & ideo <lb></lb>actu cuneus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002243"><emph type="italics"></emph>Cardanus propoſitum problema aliter ſoluit, cauſamque putat. <lb></lb></s> <s id="id.002244">quia aër non poteſt in ictu effugere. </s> <s id="id.002245">quanquam enim acuta cuſpide ſit <lb></lb>ſecuris, momento tamen tam paruo temporis effugere nequit. </s> <s id="id.002246">Ne igi<lb></lb>tur nimis denſetur, cogitur in poros ingredi ſubiecti ligni, at que cu<lb></lb>nei vice diuidere illud. </s> <s id="id.002247">Indicio eſt, inquit, quod paulo tardior ictus <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg34"></arrow.to.target><lb></lb><emph type="italics"></emph>maximum in diuidendo diſcrimen adfert dilabente aëre. </s> <s id="id.002248">Solutionem <lb></lb>hanc reprehendit Scaliger, conſentitque cum Ariſtotele motum mo<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg35"></arrow.to.target><lb></lb><emph type="italics"></emph>uere, & ſecurim, ſi comprimatur manu, ſecare propter nixum: multo <lb></lb>magis ſi ictu adigatur, & ex Ioanne Iucundo proponit aliud proble<lb></lb>ma dignum quæſitu. </s> <s id="id.002249">Quot pondo proportionem habeat pugnus ho<lb></lb>minis ferientis, cum ſeipſo non feriente comparatus. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/186.jpg" pagenum="146"></pb> <p type="margin"> <s id="id.002250"><margin.target id="marg34"></margin.target>Lib. 17. de <lb></lb>ſubt. </s> </p> <p type="margin"> <s id="id.002251"><margin.target id="marg35"></margin.target>Exerc. 331. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002252">21. <foreign lang="el">*peri\ fala/ggwn.</foreign></s> </p> <p type="main"> <s id="id.002253">21. De ſtateris. </s> </p> <p type="main"> <s id="id.002254"><foreign lang="el">*dia\ ti/ ai( fa/lagges ta\ kre/a i(sta=sin a)po\ mikrou= a)rth/matos <lb></lb>mega/la ba/rh, tou= o(/lou h(mizugi/ou o)/ntos; ou(= me\n ga\r <lb></lb>to\ ba/ros e)nti/qetai, kath/rthtai mo/non h( pla/stigc, e)pi\ qa/teron <lb></lb>de\ h( fa/lagc e)sti\ mo/non.</foreign></s> <s id="g0132002"><foreign lang="el">h)\ o(/ti a(/ma sumbai/nei zugo\n <lb></lb>kai\ moxlo\n ei)=nai th\n fa/lagga; zugo\n me\n ga\r, h(=| <lb></lb>tw=n sparti/wn e(/kaston gi/netai to\ ke/ntron th=s fa/laggos.</foreign></s> <s id="g0132002a"><foreign lang="el">to\ <lb></lb>me\n ou)=n e)pi\ qa/tera e)/xei pla/stigga, to\ de\ e)pi\ qa/tera, a)nti\ <lb></lb>th=s pla/stiggos to\ sfai/rwma, o(\ tw=| zugw=| pro/skeitai, w(/sper <lb></lb>ei)/ tis th\n e(te/ran pla/stigga, kai\ to\n staqmo\n, e)piqei/h e)pi\ to\ <lb></lb>a)/kron th=s pla/stiggos: dh=lon ga\r, o(/ti e(/lkei tosou=ton ba/ros <lb></lb>e)n th=| e(te/ra| kei/menon pla/stiggi.</foreign></s> <s id="g0132004"><foreign lang="el">o(/pws de\ to\ e(\n zugo\n polla\ <lb></lb>h)=| zuga/, toiau=ta ta\ sparti/a polla\ e)/gkeitai e)n tw=| toiou/tw| <lb></lb>zugw=|, w(=n e(ka/ston to\ e)pi\ ta/de e)pi\ to\ sfai/rwma to\ h(/misu <lb></lb>th=s fa/laggo/s e)sti.</foreign></s> </p> <p type="main"> <s id="id.002255">Cur ſtateræ paruo æqui<lb></lb>pondio carnium magna <lb></lb>pondera expendunt, cum <lb></lb>totæ dimidia ſint libra. </s> <s id="id.002256">Vbi <lb></lb>enim pondus apponitur, <lb></lb>appenſa eſt duntaxat lanx. <lb></lb></s> <s id="id.002257">Ex altera vero parte ſolum <lb></lb>eſt ſtateræ ſcapus. </s> <s id="id.002258">An quia <lb></lb>contingit ſtateram ſimul <lb></lb>eſſe libram & vectem. </s> <s id="id.002259">Li<lb></lb>bra <expan abbr="quidẽ">quidem</expan> eſt, vbi vnaquæ<lb></lb>que anſarum fit centrum <lb></lb>ſtateræ. </s> <s id="id.002260">Igitur in alter a par<lb></lb>te habet lancem: in altera <lb></lb>pro lance æquipondium, <lb></lb>quod libræ incumbit. <lb></lb></s> <s id="id.002261">Quemadmodum ſi quis al<lb></lb>teram lancem & pondus <lb></lb>in eius ſummitate impo<lb></lb>neret. </s> <s id="id.002262">Clarum enim eſt, <lb></lb>quod hoc pondus in altera <lb></lb>lance ſitum trahit. </s> <s id="id.002263">Vt au<lb></lb>tem vna libra multæ libræ <lb></lb>ſint in tali libra, multæ anſę <lb></lb>adiectæ ſunt, è quibus vna<lb></lb>quæque ad eas partes, vbi <lb></lb>eſt æquipondium, dimi<lb></lb>dium eſt ſtateræ. </s> </p> <p type="head"> <s id="id.002264">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002265">De ſtateris.] <foreign lang="el">fa/lagc</foreign> <emph type="italics"></emph>apud Græcos multa ſignificat vt in<lb></lb>ternodium in digitis, ordinem & agmem militare longius <lb></lb>quam latius, ligna teretia, quibus naues in mare deuoluuntur: ſed hîc <emph.end type="italics"></emph.end><pb xlink:href="035/01/187.jpg" pagenum="147"></pb><emph type="italics"></emph>ſignificat libræ genus, quod trutina, ab alijs ſtatera appellatur. </s> <s id="id.002266">Huius <lb></lb>partes quatuor ſunt A B ſcapus, C D anſa, A E harpago vel <lb></lb>lanx, F G<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.187.1.jpg" xlink:href="035/01/187/1.jpg"></figure><lb></lb><emph type="italics"></emph><expan abbr="æquipõdium">æquipondium</expan> <lb></lb>Græcis di<lb></lb>ctum<emph.end type="italics"></emph.end> <foreign lang="el">sfai/<lb></lb>rwma</foreign> <emph type="italics"></emph>noſtris <lb></lb>Marcum vel <lb></lb><expan abbr="Romanũ">Romanum</expan>. </s> <s id="id.002267">Vi<lb></lb>truuius dixit inuentam fuiſſe ſtateram, vt ab iniquitate iuſtis mori<lb></lb>bus hominum vita vindicetur. </s> <s id="id.002268">Vnde eſt apud ſapientem ſtatera do<lb></lb>loſa abhominatio eſt apud Deum, & pondus æquum voluntas eius. <lb></lb></s> <s id="id.002269">In rebus autem pretioſis licet libra, non ſtatera vſurpetur, quia tam <lb></lb>exacta eſſe non poteſt: in vilioribus tamen, quia iniquitatis parua ia<lb></lb>ctura eſt, frequentißimè vſurpatur, propter operis commoditatem. <lb></lb></s> <s id="id.002270">Nam libra vti non poſſumus, niſi paria pondera penſionibus ſemper <lb></lb>habeantur, quarum apparatus atque tractatio eſt magis operoſa & <lb></lb>moleſta. </s> <s id="id.002271">In ſtateris autem quicquid appenderis ſeu magnum, ſeu par<lb></lb>uum vnico pondere, hoc eſt æquipondio: distinctione tamen puncto<lb></lb>rum in ſcapo examinatur. </s> <s id="id.002272">Id enim in ſcapo ita impoſitum eſt, vt mo<lb></lb>dò ad anſam, modò ab anſa remoueatur, vt maiora & minora pon<lb></lb>dera libret, & vi mouenti reſpondeat. </s> <s id="id.002273">Nam velut aliqua manus va<lb></lb>lida longiorem ſtateræ ſcapum deprimit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002274">Cur ſtateræ.] <emph type="italics"></emph>Problema eſt de ſtatera, quæ paruo æquipondio <lb></lb>magna appendit pondera. </s> <s id="id.002275">Et problematis difficultas hinc oſtenditur, <lb></lb>quod ſtatera videatur tantum eſſe dimidia libra, vt in cuius vna <lb></lb>parte lanx eſt vna dependens, ex altera vero ſcapus. </s> <s id="id.002276">Rationi igitur <lb></lb>conſentaneum eſtne tanta pendat, quanta libra integra. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002277">An quia contingit.] <emph type="italics"></emph>Solutio problematis petitur ex libra, & <lb></lb>vecte, ex libra dupliciter. </s> <s id="id.002278">Syllogiſmus prior ſic erit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002279"><emph type="italics"></emph>Libra expendit magna pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002280"><emph type="italics"></emph>Statera eſt libra, vt in cuius vna parte vna eſt lanx, in altera <lb></lb>vice alterius lancis, eſt æquipondium, quod pro ſua grauitate <lb></lb>deprimit ſcapum, & facit æquilibrium, & extremum anſæ <lb></lb>eſt centrum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002281"><emph type="italics"></emph>Ergo & ſtatera magna expendet pondera. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/188.jpg" pagenum="148"></pb> <p type="main"> <s id="id.002282">Vt autem vna libra.] <emph type="italics"></emph>Syllogiſmus poſterior ſic eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002283"><emph type="italics"></emph>Multæ ſimul libræ magna expendunt pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002284"><emph type="italics"></emph>Statera, cui plures anſæ adiectæ ſunt, vel vna, ſed per plura <lb></lb>puncta mobilis, eſt multæ libræ ſimul. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002285"><emph type="italics"></emph>Ergo ſtatera magna expendet pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002286"><emph type="italics"></emph>Statera certe multæ ſunt libræ actu & poteſtate. </s> <s id="id.002287">Et primum actu <lb></lb>cum anſæ ( ſic enim<emph.end type="italics"></emph.end> <foreign lang="el">ta\ spa/rtia</foreign> <emph type="italics"></emph>exprimi debere declarant multi <lb></lb>huius contextus loci inter ſe comparati ) plures ſunt in vno ſcapo, vt <lb></lb>duæ, quod frequentißimum, vel tres, quod rarius: cuiuſmodi ſunt in <lb></lb>A B ſcapo<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.188.1.jpg" xlink:href="035/01/188/1.jpg"></figure><lb></lb><emph type="italics"></emph>duæ C D, E F <lb></lb>quarum pro<lb></lb>piore lanci, <lb></lb>qui vtuntur, <lb></lb>pondera ad <lb></lb><expan abbr="craßiorẽ">craßiorem</expan> tru<lb></lb>tinam ſe ex<lb></lb>pendere dicunt. </s> <s id="id.002288">quod huius notæ longius inter ſe diſtent: qui vero re<lb></lb>motiore, ad ſubtiliorem, vt in qua notæ minus diſtent in lateribus <lb></lb>ſcapi ſignatæ. </s> <s id="id.002289">Deinde poteſtate plures ſunt, cum anſa vna eſt, ſed mi<lb></lb>nimè fixa, verum libero modo propius A, modo remotius colloca<lb></lb>tur. </s> <s id="id.002290">Semper autem in aliquo puncto inter A & B intermedio. <lb></lb></s> <s id="id.002291">Vnde eſt quod hîc dicat Ariſtoteles anſam ad partes, vbi eſt æqui<lb></lb>pondium, eſſe dimidium ſtateræ, non ſumendo dimidium exactè, <lb></lb>quandoquidem extremo, à quo lanx <expan abbr="depẽdet">dependet</expan> ſemper propior ſit. </s> <s id="id.002292">Hinc <lb></lb>elicitur pulchra regula è qua poſtea ferè omnia, quæ ad ſtateræ ratio<lb></lb>nem pertinent, deducuntur. </s> <s id="id.002293">quæ eſt eiuſmodi. </s> <s id="id.002294">Cum ſcapus integer ad <lb></lb>pondus appenſum, rationem eam habet: quam duplum partis, quæ eſt <lb></lb>ab anſa verſus lancem ad reliquum: tunc <expan abbr="põdus">pondus</expan> ſcapum vniformem, <lb></lb>& omnibus ſuis partibus æqualem in æquilubrio conſtituit. </s> <s id="id.002295">Vt eſto <lb></lb>ſcapus A B duodecim vnciarum, & pars A F <expan abbr="duarũ">duarum</expan>: huius partis <lb></lb>duplum eſt 4. & reliquum 8. </s> <s>Quemadmodum ergo 4. ad 8. ſic ſca<lb></lb>pus rotus id eſt 12. erit ad pondus, quod per regulam trium inuenie<lb></lb>tur eſſe 4. vnciarum. </s> <s id="id.002296">Rurſus ſit anſa in D & A D ſit vna vn<lb></lb>cia. </s> <s id="id.002297">Huius duplum eſt 2. </s> <s>Reliquum eſt 10. </s> <s>Vt igitur 2. ad 10. ſic 12. <lb></lb>totus ſcapus erit ad pondus: quod per regulam trium inuenietur eſſe<emph.end type="italics"></emph.end><pb xlink:href="035/01/189.jpg" pagenum="149"></pb>60. <emph type="italics"></emph>vnciarum. </s> <s id="id.002298">Vbi notandum lancem in hoc numero pro ſuo pon<lb></lb>dere includi. </s> <s id="id.002299">Notandum etiam pondus impoſitum lanci eſſe perinde <lb></lb>atque ſi in puncto A imponeretur. </s> <s id="id.002300">Sed de his qui multò plura vide<lb></lb>re volet, videat apud Cardanum lib. 1. de ſubtilitate. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002301"><foreign lang="el">kai\ o( staqmo\s di' i)/sou tw=n a)p' a)llh/lwn <lb></lb>tw=n sparti/wn kinoume/nwn, w(/ste summetrei=sqai po/son ba/ros<lb></lb> e(/lkei to\ e)n th=| pla/stiggi kei/menon, w(/ste ginw/skein o(/tan <lb></lb>o)rqh\ h( fa/lagc h)=|, a)po\ poi/ou spa/rtou po/son ba/ros e)/xei h( <lb></lb>pla/stigc, kaqa/per ei)/rhtai.</foreign></s> <s id="g0132005"><foreign lang="el">o(/lws me/n e)sti tou=to zugo/n, e)/xon <lb></lb>mi/an me\n pla/stigga, e)n h(=| i(/statai to\ ba/ros, th\n d' e(te/ran, <lb></lb>e)n h(=| o( staqmo\s e)n th=| fa/laggi.</foreign></s> <s id="g0132006"><foreign lang="el">dio\ sfai/rwma/ e)stin h( <lb></lb>fa/lagc e)pi\ qa/teron.</foreign></s> <s id="g0132006a"><foreign lang="el">toiou=ton de\ o)\n, polla\ zuga/ e)sti, kai\ <lb></lb>tosau=ta, o(/sa pe/r e)sti ta\ sparti/a.</foreign></s> </p> <p type="main"> <s id="id.002302">Et æquipondium ab an<lb></lb>ſulis inuicem commotis, vt <lb></lb>commetiatur quantum ſit <lb></lb>pondus, trahit id, quod eſt <lb></lb>in lance poſitum. </s> <s id="id.002303"><expan abbr="Atq;">Atque</expan> co<lb></lb>gnoſcere licet, <expan abbr="quantũ">quantum</expan> pon<lb></lb>dus lanx habeat, quando <lb></lb>ſtateræ ſcapus ad anſam re<lb></lb>ctus fuerit. </s> <s id="id.002304">Omnino qui<lb></lb>dem hoc eſt libra habens <lb></lb>vnam lancem, in qua pon<lb></lb>dus appenditur, & ex alte<lb></lb>ra parte in ſtatera equipon<lb></lb>dium. </s> <s id="id.002305">Propterea altera pars <lb></lb>ſtateræ eſt æquipondium. <lb></lb></s> <s id="id.002306">Et talis exiſtens multæ ſunt <lb></lb>libræ, & quidem tot, quot <lb></lb>ſunt anſæ. </s> </p> <p type="head"> <s id="id.002307">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002308">Et æquipondium.] <emph type="italics"></emph>Hic textus interiectus quidem eſſe vide<lb></lb>tur, non ita tamen inutilis, vt totus reijciendus ſit, quod aliquis <lb></lb>interpres fecit. </s> <s id="id.002309">Indicat enim modum, quo cognoſcatur <expan abbr="põderationis">ponderationis</expan> <lb></lb>æquilibrium. </s> <s id="id.002310">quod eſt vbi in appendendo ſcapus ſtateræ cum anſa <lb></lb>rectos conſtituit angulos, tuncque eſt parallellus plano horizontis. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002311"><foreign lang="el">ai)ei\ de\ to\ e)ggu/teron <lb></lb>sparti/on th=s pla/stiggos kai\ tou= i(stame/nou ba/rous, mei=zon e(/lkei <lb></lb>ba/ros, dia\ to\ gi/nesqai th\n me\n fa/lagga pa=san moxlo\n <lb></lb>a)nestramme/non.</foreign></s> <s id="g0132007a"><foreign lang="el">u(pomo/xlion me\n ga\r to\ sparti/on <lb></lb>e(/kaston a)/nwqen o)/n, to\ de\ ba/ros to\ e)no\n e)n th=| pla/stiggi.</foreign></s> <s id="g0132008"><foreign lang="el"><lb></lb>o(/sw| d' a)\n makro/teron h)=| to\ mh=kos tou= moxlou= tou= a)po\ tou= <lb></lb>u(pomoxli/ou, tosou/tw| e)kei= me\n r(a=|on kinei=.</foreign></s> <s id="g0132008a"><foreign lang="el">e)ntau=qa de\ sh/kwma <lb></lb>poiei=, kai\ i(/sthsi to\ pro\s to\ sfai/rwma ba/ros th=s <lb></lb>fa/laggos.</foreign></s> </p> <p type="main"> <s id="id.002312">Semper autem anſa pro<lb></lb>pinquior lanci, ponderan<lb></lb>doque oneri, trahit maius <lb></lb>pondus. </s> <s id="id.002313">quia ſtatera effici<pb xlink:href="035/01/190.jpg" pagenum="150"></pb>tur vectis inuerſus. </s> <s id="id.002315">Eſt enim <lb></lb>anſa quælibet ſupernè exi<lb></lb>ſtens hypomochlium. </s> <s id="id.002316">Et <lb></lb>pondus id quod eſt in lan<lb></lb>ce. </s> <s id="id.002317">Quantò autem longi<lb></lb>tudo vectis maior fuerit ab <lb></lb>hypomochlio: tantò ibi fa<lb></lb>cilius mouet. </s> <s id="id.002318">Hîc autem <lb></lb>ſacoma facit & ponderat <lb></lb>ad æquipondium pondus <lb></lb>ſtateræ. </s> </p> <p type="head"> <s id="id.002319">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002320">Omnino quidem.] <emph type="italics"></emph>Repetitio eſt aſſumptionum præceden<lb></lb>tium ſyllogiſmorum ſcilicet,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002321"><emph type="italics"></emph>Statera eſt omnino libra. <lb></lb></s> <s id="id.002322">& <lb></lb>Statera multæ ſunt libræ. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002323">Semper autem.] <emph type="italics"></emph>Poſtquam oſtenſum eſt ſtateram magna pon<lb></lb>derare pondera: nunc quæritur quare tantò maiora ponderet: quantò <lb></lb>anſam lanci habet propinquiorem. </s> <s id="id.002324">Ratio eſt quia vectis eſt, & ſic <lb></lb>concluditur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002325"><emph type="italics"></emph>Quò vectis habet hypomochlium propius ponderi mouendo, eò <lb></lb>maius mouet. </s> <s id="id.002326">Reliquum enim ab hypomochlio longius eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002327"><emph type="italics"></emph>Statera eſt vectis inuerſus. </s> <s id="id.002328">Nam anſa eſt hypomochlium ſu<lb></lb>perne exiſtens, & id quod lanci imponitur eſt pondus <lb></lb>mouendum, vis mouens eſt æquipondium. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002329"><emph type="italics"></emph>Ergo quò anſa erit propior ponderi, eò ſtatera maiora pondera<lb></lb>bit pondera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002330">Hîc autem ſacoma.] <emph type="italics"></emph>Hic locus è Græco in Latinum verbo <lb></lb>ad verbum verſus difficilem, ne dicam nullum ſenſum habet. </s> <s id="id.002331">Vide<lb></lb>tur tamen Ariſtoteles & appoſitè voluiſſe ſignificare æquipondium <lb></lb>eſſe in ſtatera, vim mouentem, & vnum actu cum ſit, quia tamen <lb></lb>per varias notas diſcurrere poteſt in ſtatera, præſtare ad diuerſa pon<lb></lb>dera pendenda, quod in altera libræ lance diuerſa ſacomata. </s> <s id="id.002332">Eſt enim<emph.end type="italics"></emph.end><pb xlink:href="035/01/191.jpg" pagenum="151"></pb><foreign lang="el">sh/kwma,</foreign> <emph type="italics"></emph>vt annotauit Budæus in Pandect. quod apponitur in libra <lb></lb>ad æquilibrium faciendum. </s> <s id="id.002333">Vnde & apud Vitruuium legimus re<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg36"></arrow.to.target><lb></lb><emph type="italics"></emph>demptorem ad tempus opus manufactum ſubtiliter regi approba<lb></lb>uiſſe, & ad ſacoma pondus coronæ viſum eſſe præſtitiſſe. </s> <s id="id.002334">Cæterum <lb></lb>quam rationem habeat æquipondium ad ſeſe pro varijs interſtitüs, <lb></lb>quibus remouetur ab anſa, colligi poteſt ex Vbaldo per corollarium <lb></lb>quod deduxit è prop. 6. tractatus de lib. in Mech. quod tale eſt. </s> <s id="id.002335">Ma<lb></lb>nifeſtum eſt quò pondus à centro libræ magis diſtat, eò grauius eſſe, <lb></lb>& per conſequens velocius moueri. </s> <s id="id.002336">Et æquipondij grauitatem in <lb></lb>vno loco ad grauitatem eiuſdem in altero, eam rationem habere per <lb></lb>experientiam nouiſſe ſe dicit Cardanus, quam habet remotio ad re<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg37"></arrow.to.target><lb></lb><emph type="italics"></emph><expan abbr="motionẽ">motionem</expan>. <lb></lb> </s> <emph.end type="italics"></emph.end> <lb></lb> <figure id="id.035.01.191.1.jpg" xlink:href="035/01/191/1.jpg"></figure> <s><emph type="italics"></emph>vt ſi æqui <lb></lb><expan abbr="pondiũ">pondium</expan> K <lb></lb>in D ele<lb></lb>uet libras <lb></lb>20. & in <lb></lb>E 25. ele<lb></lb>uabit in F <lb></lb>30. In G 35. In H 40. </s> <s>Sic æquali ſpatio æquale <expan abbr="acquirẽs">acquirens</expan> <expan abbr="augmentũ">augmentum</expan>. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.002337"><margin.target id="marg36"></margin.target>Cap. 3. lib. <margin.target id="marg37"></margin.target>65. c. Arich</s> </p> <p type="main"> <s id="id.002338"><emph type="italics"></emph>Et quidem ſtateræ ratio demonſtrari poteſt. </s> <s id="id.002339">Sit ſtateræ ſcapus <lb></lb>H B cu<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.191.2.jpg" xlink:href="035/01/191/2.jpg"></figure><lb></lb><emph type="italics"></emph>ius anſa <lb></lb>ſit A C, <lb></lb>& eius <lb></lb>æquipon<lb></lb>dium E, <lb></lb>appenda<lb></lb>tur vero <lb></lb>ex H <expan abbr="põdus">pon<lb></lb>dus</expan> D, <lb></lb>quod æquiponderet æquipondio E in F appenſo. </s> <s id="id.002340">Aliud quoque pon<lb></lb>dus G appendatur in H, quod etiam æquipondio in B appenſo <lb></lb>æquiponderet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002342"><emph type="italics"></emph>Dico grauitatem ponderis D ad grauitatem ponderis G ita eſſe <lb></lb>vt C F ad C B. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/192.jpg" pagenum="152"></pb> <p type="head"> <s id="id.002343">Demonſt. </s> </p> <p type="main"> <s id="id.002344"><emph type="italics"></emph>Quia grauitas ponderis D eſt æqualis grauitati ponderis E ex F <lb></lb>dependentis, & grauitas ponderis G eſt æqualis grauitati ponderis <lb></lb>E ex B, erit grauitas ponderis D ad grauitatem E ex F: vt gra<lb></lb>uitas ponderis G ad grauitatem ponderis E ex B, & permutatim <lb></lb>prop. 16. lib. 5. </s> <s>vt grauitas ponderis D ad grauitatem ponderis G: <lb></lb>ita grauitas ipſius E ex F ad ipſum E ex B. </s> <s id="id.002345">Grauitas autem pon<lb></lb>deris E ex F dependentis ad grauitatem ponderis E ex B eſt: vt <lb></lb>C F ad C B, vt demonſtrat Vbaldus prop. 6. tract. delib. </s> <s>vt igitur <lb></lb>grauitas ponderis D ad pondus G: ita eſt C F ad C B. </s> <s id="id.002346">Si ergo <lb></lb>pars ſcapi C B diuidatur in partes æquales ſolo pondere E, & pro<lb></lb>pius & longius à puncto C poſito, ponderum grauitates ex puncto <lb></lb>H appenſæ notæ erunt. </s> <s id="id.002347">Exempli gratia ſit diſtantia C B tripla ad <lb></lb>C F, erit pondus G triplum ponderis D. </s> <s>quod demonſtrare oportebat. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002348">22. <foreign lang="el">*peri\ o)donta/gras.</foreign></s> </p> <p type="main"> <s id="id.002349">22. De dentiduco. </s> </p> <p type="main"> <s id="id.002350"><foreign lang="el">*dia\ ti/ oi( i)atroi\ r(a=|on e)cairou=si tou\s o)do/ntas proslamba/nontes <lb></lb>ba/ros th\n o)donta/gran, h)\ th=| xeiri\ mo/nh| yilh=|; </foreign></s> <s id="g0132102"><foreign lang="el"><lb></lb>po/teron dia\ to\ ma=llon e)colisqai/nein dia\ th=s xeiro\s to\n <lb></lb>o)do/nta, h)\ e)k th=s o)donta/gras; </foreign></s> <s id="g0132102a"><foreign lang="el">h)\ ma=llon o)lisqai/nei th=s <lb></lb>xeiro\s o( si/dhros, kai\ ou) perilamba/nei au)to\n ku/klw|: malqakh\ <lb></lb>ga\r ou)=sa h( sa\rc tw=n daktu/lwn, kai\ prosme/nei ma=llon <lb></lb>kai\ periarmo/ttei.</foreign></s> <s id="g0132103"><foreign lang="el">a)ll' o(/ti h( o)donta/gra du/o moxloi/ <lb></lb>ei)sin a)ntikei/menoi, e(\n to\ u(pomo/xlion e)/xontes th\n su/nayin <lb></lb>th=s qermastri/dos.</foreign></s> <s id="g0132104"><foreign lang="el">tou= r(a=|on ou)=n kinh=sai xrw=ntai tw=| o)rga/nw| <lb></lb>pro\s th\n e)cai/resin.</foreign></s> <s id="g0132105"><foreign lang="el">e)/stw ga\r th=s o)donta/gras to\ me\n e(/teron <lb></lb>a)/kron e)f' w(=| to\ *a, to\ de\ e(/teron to\ *b, o(\ e)cairei=.</foreign></s> <s id="g0132105a"><foreign lang="el">o( <lb></lb>de\ moxlo\s e)f' w(=| *a*q*z, o( de\ a)/llos moxlo\s e)f' w(=| *b<lb></lb>*g*e.</foreign></s> <s id="g0132105b"><foreign lang="el">u(pomo/xlion de\ to\ *q, e)f' ou(= h( su/nayis, o( de\ o)dou\s, <lb></lb> to\ ba/ros.</foreign></s> <s id="g0132106"><foreign lang="el">e(kate/rw| ou)=n tw=n *b, *z, kai\ a(/ma labw\n <lb></lb>kinei=: o(/tan de\ kinh/sh|, o)cei=le r(a=|on th=| xeiri\, h)\ tw=| <lb></lb>o)rga/nw|.</foreign></s> </p> <p type="main"> <s id="id.002351">Cur medici facilius den<lb></lb>tes <expan abbr="eximũt">eximunt</expan> <expan abbr="accipiẽtes">accipientes</expan> pon<lb></lb>dus, <expan abbr="dẽtiducum">dentiducum</expan>: <expan abbr="quã">quam</expan> ſi ſola <lb></lb>vtantur manu. </s> <s id="id.002352">Vtrum quia <lb></lb>dens magis manum præ<lb></lb>terlabitur, quam dentidu<lb></lb>cum? </s> <s id="id.002353">vel ferrum quidem <lb></lb>magis labitur manu, neque <lb></lb>ipſum vndique <expan abbr="comprehẽdit">comprehen<lb></lb>dit</expan>. </s> <s id="id.002354">Eſt enim digitorum <lb></lb>caro mollis, & adhæret ma<lb></lb>gis, atque vndique con<lb></lb>gruit. </s> <s id="id.002355">Verum quia denti<lb></lb>ducus eſt duo vectes aduer<lb></lb>ſi, vnum <expan abbr="hypomochliũ">hypomochlium</expan> ha<lb></lb>bentes in concurſu com<lb></lb>miſſuræ. </s> <s id="id.002356">Igitur ad <expan abbr="exẽptionẽ">exemptio<lb></lb>nem</expan>, vt facilius <expan abbr="dimoueãt">dimoueant</expan>, hoc <lb></lb>vtuntur organo. </s> <s id="id.002357">Sit enim <pb xlink:href="035/01/193.jpg" pagenum="153"></pb>dentiduci extremum alte<lb></lb><figure id="id.035.01.193.1.jpg" xlink:href="035/01/193/1.jpg"></figure><lb></lb>rum <foreign lang="el">a,</foreign> alterum <foreign lang="el">b,</foreign> quod <lb></lb>eximit, vectis vero <foreign lang="el">a q z,</foreign><lb></lb>& alter vectis <foreign lang="el">b g e</foreign>: hypo<lb></lb>mochlium verò <foreign lang="el">q</foreign> vbi eſt <expan abbr="cõmiſſura">con<lb></lb>miſſura</expan>: <expan abbr="dẽs">dens</expan> verò <expan abbr="põdus">pondus</expan> eſt. <lb></lb></s> <s id="id.002358">Vtroque igitur extremo <foreign lang="el">b <lb></lb>& z</foreign> ſimul capiens dimouet: <lb></lb>quando vero emotus fuerit, manu facilius: quam inſtru<lb></lb>mento eximetur. </s> </p> <p type="head"> <s id="id.002359">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002360">De dentiduco.] <foreign lang="el">o)donta/gran h)\ o)donta/gwgon</foreign> <emph type="italics"></emph>vertit Cælius <lb></lb>Aurelianus cap. 4. lib. 2. <emph.end type="italics"></emph.end> <foreign lang="el">xroniw=n</foreign> <emph type="italics"></emph>paßionum dentiducum: Cel<lb></lb>ſus forficem, & generaliter forcipem. </s> <s id="id.002361">Eſt autem inſtrumentum, quo <lb></lb>dens eximitur. </s> <s id="id.002362">Corroſus enim aut vehementer dolens præſcripto <lb></lb>medicorum eximi iubetur. </s> <s id="id.002363">Refert tamen Eraſiſtratus, vt eſt apud <lb></lb>Cælium Aurelianum, plumbeum odontagogum apud Delphum in <lb></lb>templo Apollinis, oſtentationis cauſa propoſitum, quo demonſtraba<lb></lb>tur oportere ſolos eos dentes auferri, qui ſint faciles, vel mobilitate <lb></lb>laxati, vel quibus ſufficeret plumbei inſtrumenti conamen ad ſum<lb></lb>mum. </s> <s id="id.002364">Et profectò dens integer, & firmus, quid vtilis eſt ad bene eſſe, <lb></lb>temerè eximi non debet, vt paßim fit, ſine iuſſu medicorum à vulga<lb></lb>ribus & circumforaneis illis, qui ab hac ſola chirurgica actione den<lb></lb>tiduci appellantur, propter quorum inpudentiam multi nobiles chi<lb></lb>rurgi operationem hanc, alioqui neceſſariam aliquando, nec omnibus <lb></lb>facilem, dedignantur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002365">Cur medici.] <emph type="italics"></emph>Propoſitio eſt problematis de dente, cur facilius <lb></lb>dentiduco, quam ſola manu eximatur, cui repugnantia ad augendam <lb></lb>difficultatem ſed vnico ponderis vocabulo in ſinuata, opponitur, qua<lb></lb>ſi diceretur. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/194.jpg" pagenum="154"></pb> <p type="main"> <s id="id.002366"><emph type="italics"></emph>Pondus adiectum ponderi non facilius mouet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002367"><emph type="italics"></emph>Dentiducus eſt pondus, & denti vt ponderi mouendo adij<lb></lb>citur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002368"><emph type="italics"></emph>Non igitur facilius mouet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002369">Vtrum quia dens.] <emph type="italics"></emph>Hîc continetur demonſtratio problema<lb></lb>tis. </s> <s id="id.002370">Vbi notandum dentem eximendum, vt melius eximatur, duo an<lb></lb>te exemptionem poſtulare, prius, vt firmè apprehendatur: alterum <lb></lb>vt validè dimoueatur. </s> <s id="id.002371">In quo conſiſtit præcipuè pars exemptionis, <lb></lb>quandoquidem dens in gingiuæ ſuæ gynglimo eſt, vt clauus ligno <lb></lb>infixus. </s> <s id="id.002372">Horum autem prius primum quidem dentiduco attribuit, <lb></lb>vt minoris tamen momenti etiam relinquit digitis manus, vt quo<lb></lb>rum caro mollis vndiquaque dentem melius apprehendat, atque huic <lb></lb>congruat: ſed alterum quod vim poſtulat maiorem ſoli dentiduco <lb></lb><expan abbr="cõmittit">committit</expan>. </s> <s id="id.002373">quia ipſe ſit vectis duplicatus. </s> <s id="id.002374">Ratio igitur ſic concludetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002375"><emph type="italics"></emph>Pondus facilius vecte: quam manu ſola mouetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002376"><emph type="italics"></emph>Dentiducus eſt duo vectes ſibi inuicem oppoſiti. </s> <s id="id.002377">Habent <lb></lb>enim in commiſſura hypomochlium, & dens eſt pondus <lb></lb>mouendum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002378"><emph type="italics"></emph>Ergo dens dentiduco facilius: quam manu ſola mouebitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002379">Sit enim dentiduci.] <emph type="italics"></emph>Lineari demonſtratione oſtenditur præ<lb></lb>cedentis ſyllogiſmi aſſumptio. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002380">Quando verò emotus.] <emph type="italics"></emph>Factis ijs, quæ ante exemptionem <lb></lb>poſtulabat fieri dens eximendus, vltimum quod eſt exemptio melius <lb></lb>fieri à digitis: quam à dentiduco aſſerit Ariſtoteles, nulla tamen ra<lb></lb>tione adhibita, licet in clauis ferreis è ligno eximendis, totum per for<lb></lb>cipem melius abſoluatur negotium. </s> <s id="id.002381">Sed res dißimilis videbitur dili<lb></lb>gentius attendenti. </s> <s id="id.002382">Nam in clauo eximendo iam emoto forceps ex <lb></lb>eminentiori ſui parte vt<emph.end type="italics"></emph.end> <foreign lang="el">x</foreign> <emph type="italics"></emph>vel<emph.end type="italics"></emph.end> <foreign lang="el">l</foreign> <emph type="italics"></emph>parietem, aut lignum attingit, & <lb></lb>punctum contactus fit fulcimentum, & huic totus vt vectis vnus <lb></lb>effectus innititur, vnde etiam clauus flectitur, & contorquetur in <lb></lb>euulſione. </s> <s id="id.002383">quia motus non fit ſecundum rectam: at in dente eximen<lb></lb>do, non datur locus tali coaptationi propter gingiuæ ſubiectæ molli<lb></lb>ciem, & eiuſdem læſionis periculum, & vt daretur dens potius ſic <lb></lb>frangeretur: quam contorqueretur, ſicque è parte tantum eximeretur <lb></lb>magno dolor is augmento, & reliquæ partis incommodo. </s> <s id="id.002384">Itaque rectà <lb></lb>ſurſum educi poſtulat, quod melius fit manu ob apprehenſionis vndi<emph.end type="italics"></emph.end><pb xlink:href="035/01/195.jpg" pagenum="155"></pb><emph type="italics"></emph>quaque factæ, vt antea dictum eſt, commoditatem <expan abbr="maiorẽ">maiorem</expan>, & rectæ <lb></lb>eleuationis nullis propemodum viribus indigæ opportunitatem. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002385">23. <foreign lang="el">*peri\ tw=n o)pga/nwn a(\ poiou=si <lb></lb>pro\s to\ katagnu=nai ta\ <lb></lb>ka/rua.</foreign></s> </p> <p type="main"> <s id="id.002386">23. De inſtrumentis quæ <lb></lb>faciunt ad frangendum <lb></lb>nuces. </s> </p> <p type="main"> <s id="id.002387"><foreign lang="el">*dia\ ti/ ta\ ka/rua r(a|di/ws katagnu/ousin a)/neu plhgh=s e)n <lb></lb>toi=s o)rga/nois a(\ poiou=si pro\s to\ katagnu/nai au)ta/, pollh\ <lb></lb>ga\r a)fairei=tai i)sxu\s h( th=s fora=s kai\ bi/as. </foreign></s> <s id="g0132201a"><foreign lang="el">e)/ti de\ sklhrw=| <lb></lb>kai\ barei= sunqli/bwn, qa=tton a)\n kata/ch| h)\ culi/nw| kai\ kou/fw| <lb></lb>tw=| o)rga/nw|. </foreign></s> <s id="g0132201b"><foreign lang="el">h)\ dio/ti ou(/tws e)p' a)mfo/tera qli/betai u(po\ du/o <lb></lb>moxlw=n to\ ka/ruon, tw=| de\ moxlw=| r(a|di/ws diairei=tai ta\ <lb></lb>ba/rh; </foreign></s> <s id="g0132202"><foreign lang="el">to\ ga\r o)/rganon e)k du/o su/gkeitai moxlw=n, u(pomo/xlion <lb></lb>e)xo/ntwn to\ au)to\, th\n sunafh\n e)f' h(=s to\ *a.</foreign></s> <s id="g0132203"><foreign lang="el">w(/sper<lb></lb> ou)=n ei) h)=san e)kbeblhme/nai, au)tw=n kinoume/nwn ei)s ta\ tw=n <lb></lb>*g*d a)/kra, ai( *e*z sunh/gonto r(a|di/ws a)po\ mikra=s i)sxu/os. </foreign></s> <s id="g0132204"><foreign lang="el"><lb></lb>h(\n ou)=n e)n th=| plhgh=| to\ ba/ros e)poi/ei, tau/thn h( krei/ttwn tau/ths, <lb></lb>h( to\ *e*g kai\ *z*d moxloi\ o)/ntes poiou=si. </foreign></s> <s id="g0132204a"><foreign lang="el">th=| a)/rsei ga\r <lb></lb>ei)s tou)nanti/on ai)/rontai, kai\ qli/bontes katagnu/ousi to\ e)f' w(=| *k.</foreign></s> <s id="g0132205"><foreign lang="el"><lb></lb>di' au)to\ de\ tou=to kai\ o(/sw| a)\n e)ggu/teron h)=| th=s *a, to\ *a suntri/bhtai <lb></lb>qa=tton.</foreign></s> <s id="g0132205a"><foreign lang="el">o(/sw| ga\r a)\n plei=on a)pe/xh| tou= u(pomoxli/ou <lb></lb>o( moxlo/s, r(a=|on kinei= kai\ plei=on a)po\ th=s i)sxu/os th=s au)th=s.</foreign></s> <s id="g0132206"><foreign lang="el"><lb></lb>e)/stin ou)=n to\ me\n *a u(pomo/xlion, h( de\ *d*a*z moxlo\s, kai\ h( <lb></lb>*g*a, *e.</foreign></s> <s id="g0132207"><foreign lang="el">o(/sw| a)\n ou)=n to\ *k e)ggute/ron h)=| th=s gwni/as tou= *a, <lb></lb>tosou/tw| e)ggu/teron gi/netai th=s sunafh=s tou= *a. </foreign></s> <s id="g0132207a"><foreign lang="el">tou=to de/ e)sti <lb></lb>to\ u(pomo/xlion.</foreign></s> <s id="g0132208"><foreign lang="el">a)na/gkh toi/nun a)po\ th=s au)th=s i)sxu/os sunagou/shs <lb></lb>to\ *z, *e, ai)/resqai ple/on, w(/ste e)pei/ e)stin e)c e)nanti/as <lb></lb>h( a)/rsis, a)na/gkh qli/besqai ma=llon: to\ de\ ma=llon qlibo/menon, <lb></lb>kata/gnutai qa=tton.</foreign></s> </p> <p type="main"> <s id="id.002388">Cur facilius in nucifran<lb></lb>gibulis nuces ſine ictu <expan abbr="frãgunt">fran<lb></lb>gunt</expan>. </s> <s id="id.002389">Multa enim vis illa<lb></lb>tionis & <expan abbr="violẽtiæ">violentiæ</expan> demitur. <lb></lb></s> <s id="id.002390">Præterea duro & graui <expan abbr="cõprimens">con<lb></lb>primens</expan> velocius fregerit: <lb></lb>quam ligneo & leui inſtru<lb></lb>mento. </s> <s id="id.002391">An quia ſic vtrin<lb></lb>que à duobus vectibus nux <lb></lb><expan abbr="cõprimitur">comprimitur</expan>, vecte vero fa<lb></lb>cile pondera diuelluntur, <lb></lb>inſtrumentum enim duo<lb></lb>bus conſtat vectibus, Idem <lb></lb>hypomochlium <expan abbr="habẽtibus">habentibus</expan> <lb></lb>contactum vbi eſt A. </s> <s id="id.002392">Vt <lb></lb>igitur ſi lineæ E D, F C <lb></lb>diductæ eſſent extremis C, <lb></lb>D motis, facile ab exigua <lb></lb>vi coadducerentur. </s> <s id="id.002393">Quod <lb></lb>igitur ex ictu pondus feciſ<lb></lb>ſet, hoc valentius E D & <lb></lb>F C vectes <expan abbr="cũ">cum</expan> ſint, efficiunt. <lb></lb></s> <s id="id.002394">Elatione enim in <expan abbr="aduersũ">aduersum</expan> <lb></lb>tollunt, & comprimentes <lb></lb>frangunt, quod eſt vbi K. <lb></lb></s> <s id="id.002395">Ob id quantò ipſi K fuerit <lb></lb>propior commiſſura A tan<lb></lb>tò citius conterit. </s> <s id="id.002396">Quantò <pb xlink:href="035/01/196.jpg" pagenum="156"></pb>enim plus diſtiterit vectis <lb></lb>ab hypomochlio, tantò fa<lb></lb>cilius ab eadem vi mouet. <lb></lb></s> <s id="id.002397">Eſt igitur A <expan abbr="hypomochliũ">hypomochlium</expan>, <lb></lb>& E A D vectis, vt & F A <lb></lb>C. </s> <s id="id.002398">Quantò igitur ipſum K <lb></lb>propius fuerit angulo A, <lb></lb>tantò propius fit commiſſu<lb></lb>ræ A. </s> <s id="id.002399">Hæc verò eſt hypo<lb></lb>mochlium. </s> <s id="id.002400">Neceſſe igitur <lb></lb>ab eadem vi coadducente <lb></lb>E, F plus extolli. </s> <s id="id.002401">Et quia <lb></lb>eleuatio ex aduerſo eſt, ma<lb></lb>gis conteri neceſſe eſt, ma<lb></lb>gis verò contritum celerius <lb></lb>frangitur. </s> </p> <p type="head"> <s id="id.002402">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002403">De inſtrumentis.] <emph type="italics"></emph>Inſtrumentum ad frangendum nuces <lb></lb>poteſt appellari nucifrangibulum, & hoc non differt à forcipe <lb></lb>niſi quia leuiter in extremis excauatur ad excipiendum nucem fran<lb></lb>gendam commodius, Huiuſmo<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.196.1.jpg" xlink:href="035/01/196/1.jpg"></figure><lb></lb><emph type="italics"></emph>di eſt F A C E A B. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002404">Cur facilius.] <emph type="italics"></emph>Quæritur <lb></lb>cur nucifrangibulum abſque ictu <lb></lb>facillimè frangat nucem. </s> <s id="id.002405">Quod <lb></lb>problema, vt <expan abbr="antecedẽs">antecedens</expan>, generale <lb></lb>eſſe poteſt de quouis forcipe & forfice, ad capiendum ſcindendum <lb></lb>frangendum qualibus multis chirurgi, & quiuis manuales artifices <lb></lb>opera ſua exercent & perficiunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002406">Multa enim vis.] <emph type="italics"></emph>Repugnantia eſt ad augendam problematis <lb></lb>difficultatem ſic,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002407"><emph type="italics"></emph>Quod vim adfert motioni, plus valet ad frangendum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002408"><emph type="italics"></emph>Ictus motioni vim adfert. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002409"><emph type="italics"></emph>Ictus igitur ad frangendum plus valet. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/197.jpg" pagenum="157"></pb> <p type="main"> <s id="id.002410">Præterea duro.] <emph type="italics"></emph>Alterum eſt quaſi problema quod nuci<lb></lb>frangibulum durum & graue facilius frangat: quam ligneum & <lb></lb>leue. </s> <s id="id.002411">Cum tamen contra euenire deberet. </s> <s id="id.002412">Siquidem graue quod eſt, <lb></lb>difficilius emoueatur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002413">An quia ſic vtrinque.] <emph type="italics"></emph>Demonſtratio eſt problematis ſic. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002414"><emph type="italics"></emph>Valide comprimentia compreſſum frangunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002415"><emph type="italics"></emph>Nucifrangibulum validè nucem comprehenſam comprimit. <lb></lb></s> <s id="id.002416">quia duplicatus eſt vectis, vnum hypomochlium, vt in A <lb></lb>commiſſura habentibus. </s> <s id="id.002417">Diductis enim B C extremis <lb></lb>vectium E A B & F A C à viribus in E & F. <lb></lb>alteris vectium extremis exiſtentibus, ſi ipſa compriman<lb></lb>tur etiam B & C comprimentur. </s> <s id="id.002418">Quare & nux D in<lb></lb>terpoſita, & valide compreſſa frangitur, tantò celerius: <lb></lb>quantò extrema B & C minus diſtabunt ab hypomoch<lb></lb>lio A. </s> <s id="id.002419">Sic enim aliæ partes vectium ab ipſo diſtantes <lb></lb>maiorem rationem habebunt. </s> <s id="id.002420">Et proinde facilius moue<lb></lb>bunt pondus mouendum, vt ante ſæpius eſt declaratum, <lb></lb>Quare quod percuſsione, vel ictu pondus aliquod irruens <lb></lb>in nucem feciſſet, id vectes compreßi certius faciunt. </s> <s id="id.002421">Sæpè <lb></lb>enim ictum ob ſui <expan abbr="rotũditatem">rotunditatem</expan> nux eludit. </s> <s id="id.002422">Nam cum nux <lb></lb>ſit rotunda, inſiſtat autem plano attingens ipſam puncto, <lb></lb>& à plano mallei in puncto attingatur, facile elabitur, niſi <lb></lb>ictus<emph.end type="italics"></emph.end> <foreign lang="el">kat' i)/cin</foreign> <emph type="italics"></emph>incidat in rectam, quæ coniungit hæc duo <lb></lb>puncta. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002423"><emph type="italics"></emph>Itaque nucifrangibulum nucem facile ſine ictu franget. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002424">Quantò igitur.] <emph type="italics"></emph>Repetitio eſt eiuſdem ſuperflua. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002425">24. <foreign lang="el">*dia\ ti/ e)n tw=| r(o/mbw| e(ka/<lb></lb>teron tw=n a)/krwn shmei/wn ou) <lb></lb>th\n i)/shn eu)qei=an die/rxetai.</foreign></s> </p> <p type="main"> <s id="id.002426">24. Cur in Rhombo <expan abbr="alterũ">alterum</expan> <lb></lb><expan abbr="pũctorum">punctorum</expan> extremorum <lb></lb>non æqualem rectam <lb></lb>tranſit. </s> </p> <p type="main"> <s id="id.002427"><foreign lang="el">*dia\ ti/ ferome/nwn du/o fora\s e)n tw=| r(o/mbw| tw=n a)/krwn <lb></lb>shmei/wn a)mfote/rwn, ou) th\n i)/shn e(ka/teron au)tw=n eu)qei=an die/rxetai, <lb></lb>a)lla\ pollaplasi/an qa/teron; </foreign></s> <s id="g0132302"><foreign lang="el">o( au)to\s de\ lo/gos kai\ <lb></lb>dia\ ti/ to\ e)pi\ th=s pleura=s fero/menon e)la/ttw die/rxetai th=s <lb></lb>pleura\s. </foreign></s> <s id="g0132302a"><foreign lang="el">to\ me\n ga\r th\n e)la/ttw dia/metron, h( de\ th\n <lb></lb>pleura\n mei/zw, kai\ h( me\n mi/an, to\ de\ du/o fe/retai <lb></lb>fora/s.</foreign></s> <s id="g0132303"><foreign lang="el">fere/sqw ga\r e)pi\ th=s *a*b, to\ me\n *a pro\s to\ *b, to\ <lb></lb>de\ *b pro\s to\ *d, tw=| au)tw=| ta/xei: fere/sqw de\ kai\ h( *a*b <lb></lb>e)pi\ th=s *a*g, para\ th\n *g*d tw=| au)tw=| ta/xei tou/tois.</foreign></s> <s id="g0132304"><foreign lang="el">a)na/gkh <lb></lb>dh\ to\ me\n *a e)pi\ th=s *a*d diame/trou fe/resqai. </foreign></s> <s id="g0132304a"><foreign lang="el">to\ de\ *b e)pi\ <lb></lb>th=s *b*g, kai\ a(/ma dielhluqe/nai e(kate/ran, kai\ th\n *a*b th\n <lb></lb>*a*g pleura/n.</foreign></s> <s id="g0132304b"><foreign lang="el">kai\ th\n *b*d th\n *b*a.</foreign></s> <s id="g0132305"><foreign lang="el">e)nhne/xqw ga\r to\ me\n *a, th\n *a*e, h( de\ *a <lb></lb>*b, th\n *a*z, kai\ e)/stw e)kbeblhme/nh h( *z*h para\ th\n *a*b, <lb></lb>kai\ a)po\ tou= *e peplhrw/sqw.</foreign></s> <s id="g0132306"><foreign lang="el">o(/moion ou)=n gi/netai to\ paraplhrwqe\n <lb></lb>tw=| o(/lw|.</foreign></s> <s id="g0132307"><foreign lang="el">i)/sh a)/ra h( *a*z th=| *a*e: h( de\ *a*b th\n *a*z, <lb></lb>ei)/h a)\n e)nhnegme/nh. </foreign></s> <s id="g0132307a"><foreign lang="el">e)/stai a)/ra e)pi\ th=s diame/trou kata\ to\ *q.</foreign></s> <s id="g0132308"><foreign lang="el"><lb></lb>kai\ ai)ei\ de\ a)na/gkh au)to\ fe/resqai kata\ th\n dia/metron. <lb></lb></foreign></s> <s id="g0132308a"><foreign lang="el">kai\ a(/ma h( pleura\ h( *a*b, th\n pleura\n th\n *a*g di/eisi, <lb></lb>kai\ to\ *a th\n dia/metron di/eisi th\n *a*d.</foreign></s> <s id="g0132309"><foreign lang="el">o(moi/ws de\ deixqh/setai <lb></lb>kai\ to\ *b e)pi\ th=s *a*g diame/trou fero/menon. </foreign></s> <s id="g0132309a"><foreign lang="el">i)/sh <lb></lb>ga/r e)stin h( *b*e, th=| *b*h.</foreign></s> <s id="g0132310"><foreign lang="el">paraplhrwqe/ntos ou)=n a)po\ tou= *h, <lb></lb>o(/moio/n e)sti tw=| o(/lw| to\ e)nto/s: kai\ to\ *b e)pi\ th=s diame/trou <lb></lb>e)/stai kata\ th\n su/nayin tw=n pleurw=n, kai\ a(/ma di/eisin h(/<lb></lb> te pleura\ th\n pleura\n, kai\ to\ *b th\n *b*g dia/metron.</foreign></s> <s id="g0132311"><foreign lang="el"><lb></lb>a(/ma a)/ra kai\ to\ *a th\n pollaplasi/an th=s *b*g di/eisi, <lb></lb>kai\ h( pleura\ th\n e)la/ttona pleura\n tw=| au)tw=| ta/xei fero/mena, <lb></lb>kai\ h( pleura\ *b*d mei/zw pleura\n tou= *b*g dielh/luqe mi/an fora\n <lb></lb>ferome/nh.</foreign></s> <s id="g0132312"><foreign lang="el">o(/sw| ga\r a)\n o)cu/teros ge/nhtai o( r(o/mbos, h( <lb></lb>me\n dia/metros *a*g, h( e)la/ttwn gi/netai, h( de\ *a*d mei/zwn, h( de\ <lb></lb>pleura\ th=s *b*g mei/zwn.</foreign></s> </p> <p type="main"> <s id="id.002428">Cur amborum extremo<lb></lb>rum <expan abbr="pũctorum">punctorum</expan> duabus la<lb></lb>tionibus in rhombo lato<lb></lb>rum, alterum non tranſit <lb></lb>æqualem rectam. </s> <s id="id.002429">ſed alte<pb xlink:href="035/01/198.jpg" pagenum="158"></pb><arrow.to.target n="marg38"></arrow.to.target><lb></lb>rum plus. </s> <s id="id.002430">Idem eſt ſermo <lb></lb>quare motum ſuper latere <lb></lb>minorem tranſit <expan abbr="rectã">rectam</expan>: <expan abbr="quã">quam</expan> <lb></lb>latus. </s> <s id="id.002431">Illud enim minorem <lb></lb>diametrum: hoc verò latus <lb></lb>maius, licet & hoc vna: illud <lb></lb>verò duabus feratur latio<lb></lb>nibus. </s> <s id="id.002432">Feratur enim ſuper <foreign lang="el">a <lb></lb>b</foreign> <expan abbr="punctũ">punctum</expan> <expan abbr="quidẽ">quidem</expan> <foreign lang="el">a</foreign> verſus <foreign lang="el">b,</foreign><lb></lb>& <foreign lang="el">b</foreign> verſus <foreign lang="el">a</foreign> <expan abbr="eadẽ">eadem</expan> celerita<lb></lb>te: feratur <expan abbr="etiã">etiam</expan> latus <foreign lang="el">a b</foreign> ſu<lb></lb>per <foreign lang="el">a g</foreign> parallelum ipſi <foreign lang="el">g d</foreign><lb></lb><expan abbr="eadẽ">eadem</expan> celeritate <expan abbr="cũ">cum</expan> his pun<lb></lb>ctis. </s> <s id="id.002433">Neceſſe igitur <expan abbr="pũctum">punctum</expan> <lb></lb><expan abbr="quidẽ">quidem</expan> <foreign lang="el">a</foreign> per <expan abbr="diametrũ">diametrum</expan> <foreign lang="el">a d</foreign><lb></lb>ferri: <foreign lang="el">b</foreign> vero per <foreign lang="el">b g,</foreign> & ſi<lb></lb>mul vtranque pertranſiiſſe. <lb></lb></s> <s id="id.002434"><expan abbr="Tũ">Tum</expan> & latus <foreign lang="el">a b</foreign> ipſum <foreign lang="el">a g. </foreign><lb></lb>Latum <expan abbr="quidẽ">quidem</expan> ſit <expan abbr="pũctum">punctum</expan> <foreign lang="el">a</foreign><lb></lb>per <expan abbr="lineã">lineam</expan> <foreign lang="el">a e,</foreign> & <foreign lang="el">a b</foreign> per <foreign lang="el">a z,</foreign><lb></lb>& ſit deducta <foreign lang="el">z h</foreign> parallela <lb></lb>ipſi <foreign lang="el">a b,</foreign> & per <expan abbr="punctũ">punctum</expan> <foreign lang="el">e</foreign> <expan abbr="cõpleatur">com<lb></lb>pleatur</expan>. </s> <s id="id.002435">Simile igitur fi<emph type="italics"></emph>t<emph.end type="italics"></emph.end> <expan abbr="cõpletum">com<lb></lb>pletum</expan> toti parallelogram<lb></lb>mo. </s> <s id="id.002436">Igitur æqualis eſt <foreign lang="el">a z</foreign><lb></lb>ipſi <foreign lang="el">a e: a b</foreign> vero latus <expan abbr="latũ">latum</expan> <lb></lb>erit per <foreign lang="el">a z. </foreign>Erit itaque in <lb></lb>diametro iuxta <foreign lang="el">q,</foreign> & ſemper <lb></lb>iuxta <expan abbr="diametrũ">diametrum</expan> ferri neceſ<lb></lb>ſe eſt. </s> <s id="id.002437">Et ſimul atque latus <lb></lb><foreign lang="el">a g</foreign> <expan abbr="etiã">etiam</expan> punctum <foreign lang="el">a</foreign> tranſit <lb></lb><expan abbr="diametrũ">diametrum</expan> <foreign lang="el">a d. </foreign>Similiter ve<lb></lb>rò demonſtrabitur etiam <foreign lang="el">b</foreign><lb></lb><expan abbr="latũ">latum</expan> eſſe per <expan abbr="diametrũ">diametrum</expan> <foreign lang="el">b g. </foreign><lb></lb>Æqualis enim eſt linea <foreign lang="el">b e</foreign><lb></lb>ipſi <foreign lang="el">b h. </foreign>Completum igitur <pb xlink:href="035/01/199.jpg" pagenum="159"></pb>per punctum <foreign lang="el">h</foreign> intus <expan abbr="parallelogrammũ">paral<lb></lb>lelogrammum</expan> ſimile eſt toti, <lb></lb>& <foreign lang="el">b</foreign> erit in diametro iuxta <lb></lb><expan abbr="contactũ">contactum</expan> laterum. </s> <s id="id.002438">Et ſimul <lb></lb>atque latus pertranſit latus <lb></lb>etiam ipſum <foreign lang="el">b,</foreign> ipſum <foreign lang="el">b g</foreign><lb></lb>diametrum. </s> <s id="id.002439">Simile igitur <lb></lb>ipſum <foreign lang="el">a</foreign> ipſam <foreign lang="el">a d</foreign> multò <lb></lb><expan abbr="maiorẽ">maiorem</expan> ipſa <foreign lang="el">b g</foreign> pertranſit, <lb></lb>& latus <expan abbr="motũ">motum</expan> eadem celeri<lb></lb>tate <expan abbr="minorẽ">minorem</expan> <expan abbr="lineã">lineam</expan> [tranſit.] <lb></lb>Et latus <foreign lang="el">b d</foreign> vna latione <lb></lb>motum pertranſijt lineam <lb></lb>maiorem: quam <foreign lang="el">b g. </foreign><expan abbr="quãtò">quantò</expan> <lb></lb>enim acutior eſt Rhombus, <lb></lb>diameter <expan abbr="quidẽ">quidem</expan> <foreign lang="el">b g</foreign> fit mi<lb></lb>nor, <foreign lang="el">a d</foreign> vero maior, <expan abbr="tũ">tum</expan> & la<lb></lb>tus <foreign lang="el">a b</foreign> maius quam <foreign lang="el">b g. </foreign></s> </p> <p type="margin"> <s id="id.002440"><margin.target id="marg38"></margin.target>Quidam le<lb></lb>gunt <foreign lang="el">lo/gw</foreign><lb></lb>pro <foreign lang="el">ta/xei. </foreign></s> </p> <p type="head"> <s id="id.002441">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002442">Cvr amborum.] <emph type="italics"></emph>In hoc capite duo continentur problemata, <lb></lb><expan abbr="eorũque">eorumque</expan> ſolutiones. </s> <s id="id.002443">Prius eſt cur è duobus <expan abbr="pũctis">punctis</expan> in vno Rhom<lb></lb>bi latere extremis eadem motis celeritate duobus ſimul motibus, vno <lb></lb>per ſe; altero ad motum lateris ſui vnum plus ſpatij conficit, nempe id <lb></lb>quod ab acuto angulo diſcedit, alterum minus, nempe. </s> <s id="id.002444">id quod ab <lb></lb>obtuſo. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002445">Idem eſt ſermo.] <emph type="italics"></emph>Poſterius eſt cur vnum ê dictis punctis mo<lb></lb>tum prædictis duobus motibus minus aliquando ſpatij conficiat: <expan abbr="quã">quam</expan> <lb></lb>latus ſuum. </s> <s id="id.002446">Vtrumque problema vt intelligatur ſciendum eſt e def. <lb></lb>32. lib. 1. Eucl. </s> <s id="id.002448">Rhombum eſſe quadrilaterum æquilaterum, & mini<lb></lb>mè rectangulum: Et tamen omnes eius angulos æquales eſſe quatuor <lb></lb>rectis per coroll. prop. 32. li. 1. Eucl. </s> <s id="id.002451"><expan abbr="Cumq;">Cumque</expan> oppoſiti in <expan abbr="parallelogrãmo">parallelogrammo</expan> <lb></lb>ſint æquales prop. 34. lib. <expan abbr="eiuſdẽ">eiuſdem</expan> duo ſunt acuti, reliqui obtuſi, vt ſit <lb></lb><expan abbr="Rhõbus">Rhombus</expan><emph.end type="italics"></emph.end> <foreign lang="el">a b d g,</foreign> <emph type="italics"></emph>cuius anguli oppoſiti<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">d</foreign> <emph type="italics"></emph>ſint acuti:<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>vero<emph.end type="italics"></emph.end> <pb xlink:href="035/01/200.jpg" pagenum="160"></pb><emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">g</foreign> <emph type="italics"></emph>obtuſi. </s> <s id="id.002453">Concipiamus ergo<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>tan<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.200.1.jpg" xlink:href="035/01/200/1.jpg"></figure><lb></lb><emph type="italics"></emph>quam formicam ambulantem proprio <lb></lb>motu verſus<emph.end type="italics"></emph.end> <foreign lang="el">b,</foreign> <emph type="italics"></emph>vt &<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>proprio iti<lb></lb>dem motu verſus<emph.end type="italics"></emph.end> <foreign lang="el">a. </foreign><emph type="italics"></emph></s> <s>Tum ipſum<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign><lb></lb><emph type="italics"></emph>latus verſus<emph.end type="italics"></emph.end> <foreign lang="el">g d,</foreign> <emph type="italics"></emph>eadem etiam celerita<lb></lb>te moueri ſeruando paralleliſmum, cum <lb></lb>ipſo<emph.end type="italics"></emph.end> <foreign lang="el">g d</foreign> <emph type="italics"></emph>quouſque coniungatur ei. </s> <s id="id.002454">Ad <lb></lb>huius autem <expan abbr="motũ">motum</expan> moueri etiam<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ver<lb></lb>ſus<emph.end type="italics"></emph.end> <foreign lang="el">g,</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>verſus<emph.end type="italics"></emph.end> <foreign lang="el">d. </foreign><emph type="italics"></emph>Sicque<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign><lb></lb><emph type="italics"></emph>mouebuntur duobus motibus, vno per ſe: <lb></lb>altero per accidens. </s> <s id="id.002455">Et poſito quod mo<lb></lb>ueantur in Rhombo. </s> <s id="id.002456">Id eſt quod motus <lb></lb>illi ſint in ratione laterum quibus Rhombus continetur. </s> <s id="id.002457">Eſt autem <lb></lb>iſta certa, quia eſt ratio æqualitatis vt<emph.end type="italics"></emph.end> <foreign lang="el">i</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">i,</foreign> <emph type="italics"></emph>& in eadem celerita<lb></lb>te, id eſt eodem tempore, non immeritò primum problema in medium <lb></lb>adducitur. </s> <s id="id.002458">quia ſi verum ſit, cauſam habet minimè vulgarem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002459">Feratur enim.] <emph type="italics"></emph>Prioris problematis <expan abbr="veritatẽ">veritatem</expan> geometricè oſten<lb></lb>dit. </s> <s id="id.002460">Sit enim vt<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>proceſſerit per ſe vſque ad<emph.end type="italics"></emph.end> <foreign lang="el">e,</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>vſque ad<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">z</foreign>: <emph type="italics"></emph>tunc quia motus illi ſunt in ratione laterum Rhombi id eſt in ra<lb></lb>tione æqualitatis<emph.end type="italics"></emph.end> <foreign lang="el">a e</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">a z</foreign> <emph type="italics"></emph>erunt æquales. </s> <s id="id.002461">Perficiatur <expan abbr="parallelogrammũ">parallelo<lb></lb>grammum</expan> prop. 31. lib. 1. <expan abbr="nẽpè">nempè</expan><emph.end type="italics"></emph.end> <foreign lang="el">a e q z. </foreign><emph type="italics"></emph></s> <s>Hoc erit ſimile toti<emph.end type="italics"></emph.end> <foreign lang="el">a b d g. </foreign><lb></lb><emph type="italics"></emph>prop. 24. lib. 6. </s> <s>Ergo per conu <expan abbr="eiuſdẽ">eiuſdem</expan> prop. ſunt circa <expan abbr="eandẽ">eandem</expan> <expan abbr="diametrũ">diametrum</expan><emph.end type="italics"></emph.end><lb></lb><foreign lang="el">a q d,</foreign> <emph type="italics"></emph>& ſic<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>duobus motibus motum prædictis delineauit<emph.end type="italics"></emph.end> <foreign lang="el">a q</foreign><lb></lb><emph type="italics"></emph>cum<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>peruenit ad<emph.end type="italics"></emph.end> <foreign lang="el">z h. </foreign></s> <s><emph type="italics"></emph>proinde &<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>etiam delineauerit<emph.end type="italics"></emph.end> <foreign lang="el">a d</foreign><lb></lb><emph type="italics"></emph>cum peruenerit<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">g d. </foreign><emph type="italics"></emph></s> <s>Simili ratiocinatione conficitur<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>eo<lb></lb>dem tempore peragraſſe diametrum<emph.end type="italics"></emph.end> <foreign lang="el">b g. </foreign><emph type="italics"></emph></s> <s>Eſt autem<emph.end type="italics"></emph.end> <foreign lang="el">b g</foreign> <emph type="italics"></emph>minor: <lb></lb>quam<emph.end type="italics"></emph.end> <foreign lang="el">a d</foreign> <emph type="italics"></emph>quia baſes ſunt duorum triangulorum<emph.end type="italics"></emph.end> <foreign lang="el">g a b,</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">a b d</foreign><lb></lb><emph type="italics"></emph>bina latera<emph.end type="italics"></emph.end> <foreign lang="el">a g, a b</foreign> <emph type="italics"></emph>binis<emph.end type="italics"></emph.end> <foreign lang="el">a b, b d</foreign> <emph type="italics"></emph>æqualia habentium. </s> <s id="id.002463">quia ſunt <lb></lb>latera eiuſdem Rhombi, & angulum<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>vtpote acutum minorem <lb></lb>angulo<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>vtpote obtuſo. </s> <s id="id.002464">Ergo prop. 24. lib. 1. baſis<emph.end type="italics"></emph.end> <foreign lang="el">a d</foreign> <emph type="italics"></emph>maior eſt <lb></lb>baſi<emph.end type="italics"></emph.end> <foreign lang="el">b g. </foreign><emph type="italics"></emph></s> <s>Et ſic<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ab angulo acuto diſcedens ſuis motibus maiorem <lb></lb>in Rhombo lineam tranſit, quam<emph.end type="italics"></emph.end> <foreign lang="el">b. </foreign></s> </p> <p type="main"> <s id="id.002465">Licet & hoc.] <emph type="italics"></emph>Hoc additur ad augendam ſecundi problematis <lb></lb>difficultatem. </s> <s id="id.002466">Rationi enim conſentaneum videtur, vt motum duo<lb></lb>bus motibus ſimul plus ſpatij conficiat: quam quod vno tantum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002467">Neceſſe igitur.] <emph type="italics"></emph>Nam parallelogramma quæ toti & inter ſe<emph.end type="italics"></emph.end><pb xlink:href="035/01/201.jpg" pagenum="161"></pb><emph type="italics"></emph>ſunt ſimilia, ſunt circa eandem diametrum. </s> <s id="id.002468">conu prop. 24. lib. 6. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002469">Æqualis enim eſt.] <emph type="italics"></emph>Quia in ratione æqualitatis motum eſt<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign><lb></lb><emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">e</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">h. </foreign></s> </p> <p type="main"> <s id="id.002470">Multò maiorem.] <emph type="italics"></emph>Quia<emph.end type="italics"></emph.end> <foreign lang="el">a d</foreign> <emph type="italics"></emph>ſubtendit multò maiorem an<lb></lb>gulum, vtpote<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>obtuſum, & ideò maiorem recto: quam<emph.end type="italics"></emph.end> <foreign lang="el">b g,</foreign> <emph type="italics"></emph>quæ <lb></lb>ſubtendit<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>angulum acutum, & ideò etiam minorem recto. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002471">Et latus <foreign lang="el">b d. </foreign>] <emph type="italics"></emph>Attingit ſecundum problema quod generaliter <lb></lb>verum non eſt. </s> <s id="id.002472">In Rhombo enim cuius, qui acutus eſt angulus, maior <lb></lb>eſt dimidio obtuſi, vt in E<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.201.1.jpg" xlink:href="035/01/201/1.jpg"></figure><lb></lb><emph type="italics"></emph>F G H: quia F H an<lb></lb>gulum E maiorem ſubten<lb></lb>dit: quam E H, erit F H <lb></lb>maior E H prop. 18. lib. 1. <lb></lb></s> <s>Sed verum eſt in certo ca<lb></lb>ſu, eo nimirum (licet hîc <lb></lb>non ſit expreſſus ) in quo <lb></lb>Rhombi acutus eſſet mi<lb></lb>nor: quam dimidius obtu<lb></lb>ſi, vt angulus A Rhombi <lb></lb>A B C D ſit minor: quam dimidius obtuſi B, id eſt quam A B C. <lb></lb></s> <s id="id.002473">Dico latus A C maius eſſe diametro B C per eandem prop. 18. <lb></lb>ſubtendit enim trianguli A B C maiorem angulum. </s> <s id="id.002474">Poſſe autem <lb></lb>talem Rhombum conſtitui, patet. </s> <s id="id.002475">quia angulus acutus ſeruata late<lb></lb>rum quorumuis aſſumptorum longitudine, infinitè minor fieri poteſt, <lb></lb>prop. 9. lib. 1. </s> <s>Ergo & tandem dabitur minor dimidio obtuſi. </s> <s id="id.002476">Nam <lb></lb>& dimidius recti, qui acutus eſt, eſt eo minor prop. 15. lib. 5. </s> <s id="id.002477">Ergo in <lb></lb>tali Rhombo latus A B per A C vna latione motum, plus ſpatij <lb></lb>confecit: quam B, quod peragrans B C duabus lationibus ferebatur. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002478"><foreign lang="el">a)/topon ga/r, w(/sper e)le/xqh, to\ <lb></lb>du/o fora\s fero/menon e)ni/ote bradu/teron fe/resqai tou= mi/an, <lb></lb>kai\ a)mfote/rwn i)sotaxw=n shmei/wn doqe/ntwn, mei/zw diecie/nai <lb></lb>qa/teron.</foreign></s> <s id="g0132314"><foreign lang="el">ai)/tion de\, o(/ti tou= me\n a)po\ th=s a)mblei/as ferome/nou <lb></lb>sxedo\n e)nanti/ai a)mfo/terai gi/nontai, h(/n te au)th\ <lb></lb>fe/retai kai\ h(\n u(po\ th=s pleura=s u(pofe/retai. </foreign></s> <s id="g0132315"><foreign lang="el">tou= de\ a)po\ <lb></lb>th=s o)cei/as, w/(sper sumbai/nei fe/resqai e)pi\ to\ au)to/. </foreign></s> <s id="g0132315a"><foreign lang="el">sunepouri/zei <lb></lb>ga\r h( th=s pleura=s, th\n e)pi\ th=s diame/trou: kai\ o(/sw| a)\n <lb></lb>th\n me\n o)cute/ran poih/sh|, th\n de\ a)mblute/ran, h( me\n bradute/ra <lb></lb>e)/stai, h( de\ qa/ttwn.</foreign></s> <s id="g0132316"><foreign lang="el">ai( me\n ga\r e)nantiw/terai gi/nontai, <lb></lb>dia\ to\ a)mblute/ran gi/nesqai th\n gwni/an. </foreign></s> <s id="g0132316a"><foreign lang="el">ai( de\ <lb></lb>ma=llon e)pi\ ta\ au)ta\, dia\ to\ suna/gesqai ta\s gramma/s. <lb></lb></foreign></s> <s id="g0132316b"><foreign lang="el">to\ me\n ga\r *a sxedo\n e)pi\ to\ au)to\ fe/retai kat' a)mfote/ras <lb></lb>ta\s fora/s: sunepouri/zetai ou)=n h( e(te/ra, kai\ o(/sw| a)\n <lb></lb>o)cute/ra gi/nhtai h( gwni/a, tosou/tw| ma=llon: to\ de\ *a de\ e)pi\ <lb></lb>tou)nanti/on: au)to\ me\n ga\r pro\s to\ *a fe/retai, h( de\ pleura\ <lb></lb>u(pofe/rei au)to\ pro\s to\ *g.</foreign></s> <s id="g0132318"><foreign lang="el">kai\ o(/sw| a)\n a)mblute/ra h( gwni/a <lb></lb>h)=|, e)nantiw/terai ai( forai\ gi/nontai: eu)qute/ra ga\r h( <lb></lb>grammh\ gi/netai.</foreign></s> <s id="g0132319"><foreign lang="el">ei) d' o(/lws eu)qei=a ge/noito, pantelw=s a)\n <lb></lb>ei)/hsan e)nanti/ai. h( de\ pleura\ u(p' ou)qeno\s kwlu/etai mi/an <lb></lb>ferome/nh fora/n. eu)lo/gws ou)=n th\n mei/zw die/rxetai.</foreign></s> </p> <p type="main"> <s id="id.002479">Abſurdum enim, vt <expan abbr="dictũ">dictum</expan> <lb></lb>eſt, quod duabus lationibus <lb></lb>fertur, tardius <expan abbr="nonnunquã">nonnunquam</expan> <lb></lb>ferri eo, quod vna: & <expan abbr="datorũ">dato<lb></lb>rum</expan> <expan abbr="amborũ">amborum</expan> <expan abbr="punctorũ">punctorum</expan> æqua<lb></lb>li celeritate <expan abbr="motorũ">motorum</expan> <expan abbr="alterũ">alterum</expan> <lb></lb><expan abbr="maiorẽ">maiorem</expan> <expan abbr="trãſire">tranſire</expan>. </s> <s id="id.002480">Cauſa verò <pb xlink:href="035/01/202.jpg" pagenum="162"></pb>eſt, quod ambæ lationes <lb></lb>eius, quod ab obtuſo angu<lb></lb>lo fertur fiunt ferè contra<lb></lb>riæ. </s> <s id="id.002481">Hęc ſcilicet qua per ſe <lb></lb>fertur, & hæc qua per latus <lb></lb>effertur. </s> <s id="id.002482">Ei verò quod ab <lb></lb>acuto, contingit ad idem <lb></lb>ferri, obſecundat enim la<lb></lb>teris latio ei, quæ eſt <expan abbr="ſecũdum">ſecun<lb></lb>dum</expan> diametrum. </s> <s id="id.002483">Et quan<lb></lb>tò hic angulus fuerit acu<lb></lb>tior, ille obtuſior vna latio <lb></lb>erit tardior: altera velo<lb></lb>cior. </s> <s id="id.002484">Lationes enim magis <lb></lb><expan abbr="cõtrariæ">contrariæ</expan> fiunt propter ob<lb></lb>tuſiorem angulum: contra <lb></lb>verò hæ magis ad <expan abbr="idẽ">idem</expan> pro<lb></lb>pter <expan abbr="propinquitatẽ">propinquitatem</expan> linea<lb></lb>rum. </s> <s id="id.002485">Ipſum enim <foreign lang="el">a</foreign> fere ad <lb></lb>idem fertur ex vtriſque la<lb></lb>tionibus. </s> <s id="id.002486"><expan abbr="Itaq;">Itaque</expan> altera coad<lb></lb>iuuatur. </s> <s id="id.002487">Et <expan abbr="quãtò">quantò</expan> acutior <lb></lb>fuerit angulus: tantò ma<lb></lb>gis: ipſum verò <foreign lang="el">b</foreign> ad con<lb></lb>trarium. </s> <s id="id.002488">Ipſum enim ad <foreign lang="el">a</foreign><lb></lb>fertur. </s> <s id="id.002489">Latus verò effertur <lb></lb>verſus ipſum <foreign lang="el">g. </foreign>Et quantò <lb></lb>fuerit angulus obtuſior <lb></lb>magis contrariæ lationes <lb></lb>fiunt. </s> <s id="id.002490">Rectior enim linea <lb></lb>fit, quod ſi omninò recta <lb></lb>eſſet, eſſent lationes omni<lb></lb>nò contrariæ. </s> <s id="id.002491">Latus vero <lb></lb>vno motu motum à nullo <lb></lb>impeditur. </s> <s id="id.002492">Æquum eſt igitur, vt lineam maiorem tran<lb></lb>ſeat. </s> </p> <pb xlink:href="035/01/203.jpg" pagenum="163"></pb> <p type="head"> <s id="id.002493">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002494">Abſurdum enim.] <emph type="italics"></emph>Repetitio eſt eius, quod problematis ſecun<lb></lb>di antea iam auxit difficultatem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002495">Nonnunquam ferri.] <emph type="italics"></emph>Particula<emph.end type="italics"></emph.end> <foreign lang="el">en)i/ote</foreign> <emph type="italics"></emph>nonnunquam indi<lb></lb>cat ſecundum problema tantum verum eſſe ſpecialiter non in genere, <lb></lb>quod antea eſt demonſtratum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002496">Et datorum amborum.] <emph type="italics"></emph>Auget difficultatem problematis <lb></lb>primi. </s> <s id="id.002497">Videbatur enim rationi conſentaneum, vt duo totidem moti<lb></lb>bus mota, & eadem celeritate id eſt æquali tempore idem ſpatium <lb></lb>conficerent. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002498">Cauſa vero eſt.] <emph type="italics"></emph>Poſtquam problema primum verum eſſe geo<lb></lb>metrice demonſtratum eſt: nunc huius vtpote admirabilis cauſam <lb></lb>adfert Phyſicam. </s> <s id="id.002499">quod ſcilicet mota duobus motibus, ſi ad eundem <lb></lb>terminum, ad quem tendent, celerius mouentur: ſi ad contrarios, tar<lb></lb>dius. </s> <s id="id.002500">Illa enim ſibi inuicem obſequuntur, & vt clauus clauo pellitur: <lb></lb>ita motus motum adiuuat: hæc verò ſibi obſiſtunt, ſeſe impediunt, & <lb></lb>remorantur, & vt magis minuſve contrarij ſunt termini ad quos: <lb></lb>ita quæ ſic mouentur, magis minuſve ſe accelerant, aut retardant. <lb></lb></s> <s id="id.002501">Atqui<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>ab angulo obtuſo motum duorum motuum vno ad<emph.end type="italics"></emph.end> <foreign lang="el">a,</foreign> <emph type="italics"></emph>alte<lb></lb>ro ad<emph.end type="italics"></emph.end> <foreign lang="el">d</foreign> <emph type="italics"></emph>tendens ad magis contrarios terminos tendit: quam<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>ten<lb></lb>dens dictis motibus ad<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">g. </foreign><emph type="italics"></emph>Eſt enim, vt antea demonſtratum <lb></lb>eſt,<emph.end type="italics"></emph.end> <foreign lang="el">a d</foreign> <emph type="italics"></emph>diameter & recta maior: quam<emph.end type="italics"></emph.end> <foreign lang="el">g d. </foreign><emph type="italics"></emph>Et quò<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>acutior <lb></lb>erit angulus, eò<emph.end type="italics"></emph.end> <foreign lang="el">a d</foreign> <emph type="italics"></emph>maior erit ergo æquum eſt, vt<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>tardius fera<lb></lb>tur: quam<emph.end type="italics"></emph.end> <foreign lang="el">a. </foreign><emph type="italics"></emph>Et quidem tantò tardius: quantò<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>erit obtuſior angu<lb></lb>lus, &<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>acutior ob cauſam prædictam. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002502">Fere ad idem.] <emph type="italics"></emph>Particula<emph.end type="italics"></emph.end> <foreign lang="el">sxedo\n</foreign> <emph type="italics"></emph>ferè ad<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.203.1.jpg" xlink:href="035/01/203/1.jpg"></figure><lb></lb><emph type="italics"></emph>iecta indicat non eundem eſſe terminum vtriuſ<lb></lb>que motionis, qua fertur<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>: ſed duos diuerſos, ve<lb></lb>rum propiores, quam ſint termini ad quos<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign><lb></lb><emph type="italics"></emph>fertur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002503">Rectior enim linea.] <emph type="italics"></emph>Id eſt duo latera<emph.end type="italics"></emph.end> <foreign lang="el">b a</foreign><lb></lb><emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">b d</foreign> <emph type="italics"></emph>magis accedunt ad rectam vnam, vtpo<lb></lb>te quia angulus obtuſus ſi augeatur pluſculum, <lb></lb>latera ipſum continentia fient è directo: & tunc <emph.end type="italics"></emph.end><pb xlink:href="035/01/204.jpg" pagenum="164"></pb><emph type="italics"></emph>erunt vna omnino recta, quod vbi eſſet, vt cum<emph.end type="italics"></emph.end> <foreign lang="el">b a</foreign> <emph type="italics"></emph>peruenit ad<emph.end type="italics"></emph.end> <foreign lang="el">b <lb></lb>l,</foreign> <emph type="italics"></emph>tunc lationes<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">l,</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">d</foreign> <emph type="italics"></emph>eſſent ad contrarios omnino <lb></lb>terminos. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002504">Latus verò vno.] <emph type="italics"></emph>Breuiter cauſam attingit ſecundi problema<lb></lb>tis, quod in motu à nullo impeditum æquum eſt celerius moueri: quam <lb></lb>quod impeditur. </s> <s id="id.002505">Latus autem in dicto Rhombo à nullo impeditur: <lb></lb>contra<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>impeditur. </s> <s id="id.002506">Ergo<emph.end type="italics"></emph.end> <foreign lang="el">l b</foreign> <emph type="italics"></emph>latus celerius feretur ipſo<emph.end type="italics"></emph.end> <foreign lang="el">b. </foreign></s> </p> <p type="main"> <s id="id.002507">Æquum eſt igitur.] <emph type="italics"></emph>Id nuſquam in hoc problemate demon<lb></lb>ſtratum eſt, poteſt etiam falſum eſſe. </s> <s id="id.002508">Cæterum ex hoc problemate <lb></lb>collige, quod etiam Leonicus annotauit, quantum corporum confor<lb></lb>mationes & figurarum in illis varietas peculiares illorum inclina<lb></lb>tiones, naturaleſque motus aut adiuuent, aut contra inſigniter impe<lb></lb>diant. </s> <s id="id.002509">Conglobata etenim exempli gratia plumbi maſſa, ſi naturæ <lb></lb>relinquatur ſuæ, rectà citius deorſum fertur: quam ſi eadem pondere <lb></lb>ſeruato extenſa fuerit in laminam: immò rurſus inflexa & inſtar <lb></lb>carinæ conformata fluitabit in aquis. </s> <s id="id.002510">In rebus etiam artificialibus <lb></lb>gladius acuta ſui acie facile ſecat: obtuſa non item. </s> <s id="id.002511">Hæc cum ita <lb></lb>ſint nemini abſurdum videri debet, duo puncta duabus motionibus <lb></lb>æquali celeritate mota non æquale pertranſire ſpatium: ſed muſtò <lb></lb>plus maiuſque illorum alterum, vt ex Rhombi natura certò demon<lb></lb>ſtratum eſt. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002512">25. <foreign lang="el">*dia\ ti/ o( mei/zwn ku/klos <lb></lb>tw=| e)la/ttoni i)/shn e)celi/tte<lb></lb>tai.</foreign></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002513">25. Cur maior circulus cum <lb></lb>minore per æqualem re<lb></lb>uoluitur. </s> </p> <p type="main"> <s id="id.002514"><foreign lang="el">*)aporei=tai dia\ ti/ pote o( mei/zwn ku/klos tw=| e)la/ttoni <lb></lb>ku/klw| i)/shn e)celi/ttetai grammh/n, o(/tan peri\ to\ au)to\ ke/ntron <lb></lb>teqw=si. </foreign></s> <s id="g0132401a"><foreign lang="el">xwri\s de\ e)kkulio/menoi, w(/sper to\ me/geqos au)tw=n <lb></lb>pro\s to\ me/geqos e)/xei, ou(/tws kai\ ai( grammai\ au)tw=n <lb></lb>gi/nontai pro\s a)llh/las.</foreign></s> <s id="g0132402"><foreign lang="el">e)/ti de\ e(no\s kai\ tou= au)tou= ke/ntrou <lb></lb>o)/ntos a)mfoi=n, o(te\ me\n thlikau/th gi/netai h( grammh\, h(\n <lb></lb>e)kkuli/ontai, h(li/khn o( e)la/ttwn ku/klos kaq' au(to\n e)kkuli/etai, <lb></lb>o(te\ de\ o(/shn o( mei/zwn.</foreign></s> <s id="g0132403"><foreign lang="el">o(/ti me\n ou)=n mei/zw e)kkuli/etai <lb></lb>o( mei/zwn, fanero/n. </foreign></s> <s id="g0132403a"><foreign lang="el">gwni/a me\n ga\r dokei= kata\ th\n <lb></lb>ai)/sqhsin ei)=nai h( perife/reia e(ka/stou th=s oi)kei/as diame/trou, <lb></lb>h( tou= mei/zonos ku/klou mei/zwn, h( de\ tou= e)la/ttonos, e)la/ttwn <lb></lb>w(/ste to\n au)to\n tou=ton e(/cousi lo/gon, kaq' a(\s e)cekuli/sqhsan<lb></lb> ai( grammai\ pro\s a)llh/las kata\ th\n ai)/sqhsin.</foreign></s> <s id="g0132404"><foreign lang="el">a)lla\ mh\n <lb></lb>kai\ o(/ti th\n i)/shn e)kkuli/ontai, o(/tan peri\ to\ au)to\ ke/ntron <lb></lb>kei/menoi w)=si, dh=lon, kai\ ou(/tws gi/netai, o(te\ me\n i)/sh th=| <lb></lb>grammh=|, h(\n o( mei/zwn ku/klos e)kkuli/etai, o(te\ de\ e)la/ttwn.</foreign></s> <s id="g0132405"><foreign lang="el"><lb></lb>e)/stw ga\r ku/klos o( mei/zwn me\n, e)f' ou(= ta\ *d*z*g, o( de\ <lb></lb>e)la/ttwn e)f' ou(= ta\ *e*h*b: ke/ntron de\ a)mfoi=n to\ *a, kai\ <lb></lb>h(\n me\n e)celi/ttetai kaq' au(to\n o( me/gas, h( e)f' h(=s *z*l e)/stw. <lb></lb></foreign></s> <s id="g0132405a"><foreign lang="el">h(\n de\ o( e)la/ttwn kaq' au(to/n, h( e)f' h(=s *h*k, i)/sh th=| *a*z.</foreign></s> <s id="g0132406"><foreign lang="el"><lb></lb>e)a\n dh\ kinw= to\n e)la/ttona, to\ au)to\ ke/ntron kinw=, e)f' ou(= <lb></lb>to\ *a. </foreign></s> <s id="g0132406a"><foreign lang="el">o( de\ me/gas proshrmo/sqw. </foreign></s> <s id="g0132406b"><foreign lang="el">o(/tan ou)=n h( *a*b o)rqh\ ge/nhtai <lb></lb>pro\s th\n *h*k, a(/ma kai\ h( *a*g gi/netai o)rqh\ pro\s th\n <lb></lb>*z*l: w(/ste e)/stai i)/shn a)ei\ dielhluqui=a: th\n me\n *h*k, e)f' <lb></lb>w(=| *h*b perife/reia, th\n de\ *z*l, h( e)f' h(=s *z*g.</foreign></s> <s id="g0132407"><foreign lang="el">ei) de\ to\ <lb></lb>te/tarton me/ros i)/shn e)celi/ttetai, dh=lon o(/ti kai\ o( o(/los ku/klos <lb></lb>tw=| o(/lw| ku/klw| i)/shn e)celittetai, w(/ste o(/tan h( *b*h <lb></lb>grammh\ e)/lqh| e)pi\ to\ *k, kai\ h( *z*g e)/stai perife/reia e)pi\ <lb></lb>th=s *z*l, kai\ o( ku/klos o(/los e)ceiligme/nos.</foreign></s> <s id="g0132408"><foreign lang="el">o(moi/ws de\ kai\ <lb></lb>e)a\n to\n me/gan kinw=, e)narmo/sas to\n mikro/n, tou= au)tou= ke/ntrou <lb></lb>o)/ntos, a(/ma th=| *a*g, h( *a*b ka/qetos kai\ o)rqh\ e)/stai, h( <lb></lb>me\n pro\s th\n *z*i, h( de\ pro\s th\n *h*q.</foreign></s> <s id="g0132409"><foreign lang="el">w(/ste o(/tan kat' i)/shn, h( <lb></lb>me\n th=| *h*q e)/stai dielhluqui=a, h( de\ th=| *z*i, kai\ ge/nhtai <lb></lb>o)rqh\ pa/lin h( *a*g pro\s th\n *z*i, kai\ h( *a*b o)rqh\ pa/lin, pro\s th\n <lb></lb>*h*q w(s to\ e)c a)rxh=s e)/sontai e)pi\ tw=n *q*i.</foreign></s> <s id="g0132410"><foreign lang="el">to\ de\ mh/te sta/sews <lb></lb>ginome/nhs tou= mei=zonos tw=| e)la/ttoni, w(/ste me/nein tina\ xro/non <lb></lb>e)pi\ tou= au)tou= shmei/ou: kinou=ntai ga\r sunexw=s a)/mfw a)mfotera/kis. <lb></lb></foreign></s> <s id="g0132410a"><foreign lang="el">mh/ te u(perphdw=ntos tou= e)la/ttonos mhqe\n shmei=on, <lb></lb>to\n me\n mei/zw tw=| e)la/ttoni i)/shn diecie/nai, to\n de\ tw=| mei/zoni, <lb></lb>a)/topon.</foreign></s> </p> <p type="main"> <s id="id.002515"><expan abbr="Dubiũ">Dubium</expan> eſt cur maior cir<lb></lb>culus <expan abbr="æqualẽ">æqualem</expan> minori circu<lb></lb>lo orbitam volutione pera<lb></lb>gret, <expan abbr="quãdo">quando</expan> circa <expan abbr="idẽ">idem</expan> <expan abbr="cẽtrũ">centrum</expan> <lb></lb>poſitus eſt: At <expan abbr="cũ">cum</expan> ſeorſum <lb></lb>voluuntur, vt <expan abbr="horũ">horum</expan> magni<lb></lb>tudines ſe <expan abbr="habẽt">habent</expan> inter ſe, ita <lb></lb><expan abbr="etiã">etiam</expan> <expan abbr="eorũ">eorum</expan> orbitæ. </s> <s id="id.002516">Præterea <lb></lb>vno & eodem <expan abbr="exiſtẽte">exiſtente</expan> cen<lb></lb>tro, <expan abbr="aliquãdo">aliquando</expan> quidem tan<pb xlink:href="035/01/205.jpg" pagenum="165"></pb>ta fit orbita: quanta eſt ea: <lb></lb>quam minor circulus pera<lb></lb>grat: aliquando verò quam <lb></lb>maior. </s> <s id="id.002517">Quod igitur maio<lb></lb>rem peragret maior mani<lb></lb>feſtum eſt. </s> <s id="id.002518">Angulus enim <lb></lb>videtur <expan abbr="euidẽter">euidenter</expan> eſſe peri<lb></lb>pheria cuiuſque <expan abbr="cũ">cum</expan> propria <lb></lb>diametro maioris circuli <lb></lb>maior [minoris minor.] Ita<lb></lb>que orbitę <expan abbr="eandẽ">eandem</expan> rationem <lb></lb>euidenter habebunt inter <lb></lb>ſe. </s> <s id="id.002519">Attamen quod circa <expan abbr="idẽ">idem</expan> <lb></lb><expan abbr="centrũ">centrum</expan> poſiti æqualem <expan abbr="orbitã">or<lb></lb>bitam</expan> <expan abbr="cõficiant">conficiant</expan> etiam <expan abbr="manifeſtũ">mani<lb></lb>feſtum</expan>. </s> <s id="id.002520">At que ita vt aliquan<lb></lb>do orbita maioris circuli <lb></lb>ſit æqualis linea, aliquando <lb></lb>orbita minoris. </s> <s id="id.002521">Sit enim <lb></lb>circulus maior <expan abbr="quidẽ">quidem</expan> <foreign lang="el">d z g,</foreign><lb></lb>minor vero <foreign lang="el">e h b,</foreign> & <expan abbr="vtriuſq;">vtriuſque</expan> <lb></lb><expan abbr="centrũ">centrum</expan> <foreign lang="el">a.</foreign> </s> <s>Atque ea quidem <lb></lb>per quam magnus circulus <lb></lb>per ſe voluitur <foreign lang="el">z l,</foreign> ſit & ea <lb></lb>per quam per ſe minor <foreign lang="el">h k</foreign><lb></lb>æqualis <foreign lang="el">z l.</foreign> </s> <s>Si vero moueo <lb></lb><expan abbr="minorẽ">minorem</expan>, ipſum <expan abbr="cẽtrum">centrum</expan> mo<lb></lb>ueo vbi eſt <foreign lang="el">a.</foreign> </s> <s>Magnus au<lb></lb>tem connexus eſto. </s> <s id="id.002522">Quum <lb></lb>igitur <foreign lang="el">a b</foreign> ad rectos fiet li<lb></lb>neæ <foreign lang="el">h k,</foreign> ſimul etiam <foreign lang="el">a g</foreign><lb></lb>ad rectos fiet lineæ <foreign lang="el">z l. </foreign></s> </p> <p type="main"> <s id="id.002523">Quare per æqualem erit <lb></lb>tranſlatio, nempè <foreign lang="el">h k</foreign> in <lb></lb>qua eſt <foreign lang="el">z g. </foreign>Quod ſi quarta <lb></lb>pars per ęqualem voluitur, <pb xlink:href="035/01/206.jpg" pagenum="166"></pb>quod totus circulus æqua<lb></lb>lem toti circulo reuolua<lb></lb>tur, manifeſtum eſt. </s> <s id="id.002524">Itaque <lb></lb>quando linea <foreign lang="el">b h</foreign> peruene<lb></lb>rit ad <foreign lang="el">k</foreign> etiam <foreign lang="el">z g</foreign> peri<lb></lb>pheria erit in <foreign lang="el">z l</foreign> & circu<lb></lb>lus totus conuolutus. </s> <s id="id.002525">Si<lb></lb>militer ſi maiorem moue<lb></lb>ro, cui ſit annexus minor <lb></lb><expan abbr="eodẽ">eodem</expan> centro exiſtente, vna <lb></lb>cum <foreign lang="el">a g</foreign> etiam <foreign lang="el">a b</foreign> perpen<lb></lb>dicularis erit. </s> <s id="id.002526">Illa quidem <lb></lb>ad <foreign lang="el">z i</foreign> hæc verò ad <foreign lang="el">h q</foreign>. </s> <s>Ita<lb></lb>que quando per æqualem <lb></lb>ipſi <foreign lang="el">h q</foreign> vel <foreign lang="el">z i</foreign> rurſum erit <lb></lb>tranſlatio etiam <foreign lang="el">a g</foreign> per<lb></lb>pendicularis erit ad <foreign lang="el">z i,</foreign> & <lb></lb><foreign lang="el">a b</foreign> ad <foreign lang="el">h q,</foreign> vt ab initio <lb></lb>erunt in <foreign lang="el">q, i</foreign>: atque id nul<lb></lb>la intercedente mora ma<lb></lb>ioris ad minorem, quaſi ad <lb></lb>aliquod tempus in eodem <lb></lb>ipſo puncto moueret. </s> <s id="id.002527">vter<lb></lb>que enim vtroque modo <lb></lb>continuè mouetur. </s> <s id="id.002528">Neque <lb></lb>minore vllum punctum <lb></lb>tranſiliente, & maiorem <lb></lb>minori æqualem tranſire, & minorem maiori abſurdum. </s> </p> <p type="head"> <s id="id.002529">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002530">Dvbium eſt.] <emph type="italics"></emph>Problema quod hoc capite proponitur, omnium <lb></lb>quæ ante propoſita ſunt, & poſtea proponentur fortaßè eſt ſub<lb></lb>tilißimum. </s> <s id="id.002531">Eſt autem eiuſmodi, cur circuli concentrici, & inæquales <lb></lb>iuncti, æqualem tamen orbitam circumuolutione peragrent. </s> <s id="id.002532">Et <expan abbr="quidẽ">qui<lb></lb>dem</expan> hoc euenire duobus modis ponitur. </s> <s id="id.002533">Vno, vt orbita minoris adæque<emph.end type="italics"></emph.end><pb xlink:href="035/01/207.jpg" pagenum="167"></pb><emph type="italics"></emph>tur orbitæ, quam ſeorſum maior conficeret: altero, vt orbita maioris <lb></lb>adæquetur orbitæ, quam ſeorſum minor conficeret. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002534">At cum ſeorſim.] <emph type="italics"></emph>Problematis propoſiti difficultas declara<lb></lb>tur ex orbita, quam ſinguli ſeorſim voluti faciunt. </s> <s id="id.002535">Hæc enim ſem<lb></lb>per è maiore maior eſt, è minore minor, & quidem proportione re<lb></lb>ſpondens magnitudini peripheriarum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002536">Præterea vno.] <emph type="italics"></emph>Duo modi æquationis prædicti explicantur in <lb></lb>habentibus idem centrum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002537">Quod igitur maiorem.] <emph type="italics"></emph>Confirmatio eſt difficultatis allatæ <lb></lb>ex euidentia per ſenſum. </s> <s id="id.002538">Si quis enim notato puncto vt A circumuo<lb></lb>lutionis primo, & quidem circulum maiorem & minorem ſuper re<lb></lb>ctam plani circumuoluat, quouſque redierit contactus in eodem pun<lb></lb>cto maioris circuli maior recta: minoris minor erit per agrata. </s> <s id="id.002539">Sed <lb></lb>& anguli è ſemidiametris conſtituti ( quos angulos circuli vocat <lb></lb>hic Ariſtoteles ) baſes quæ ſunt peripheriæ, euidenter inæquales ſunt. <lb></lb></s> <s id="id.002540">In maiore circulo maior: in minore minor ( Sed & hanc euidentiam, <lb></lb>ne qua eſſet dubitatio, demonſtratione primo capite huius libri de<lb></lb>monſtrauimus. ) </s> <s>Erunt igitur & orbitæ inæquales & proportione <lb></lb>reſpondentes baſibus angulorum è ſemidiametris conſtitutorum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002541">Attamen quod circa.] <emph type="italics"></emph>Problematis propoſiti veritas demon<lb></lb>ſtratur figura geometrica in vtroque modo. </s> <s id="id.002542">Nam poſito quod<emph.end type="italics"></emph.end> <foreign lang="el">a h z</foreign><lb></lb><emph type="italics"></emph>perpendiculariter inſiſtat pla<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.207.1.jpg" xlink:href="035/01/207/1.jpg"></figure><lb></lb><emph type="italics"></emph>no, & ad rectam<emph.end type="italics"></emph.end> <foreign lang="el">z i. </foreign><emph type="italics"></emph>Tum<emph.end type="italics"></emph.end> <foreign lang="el">h q</foreign><lb></lb><emph type="italics"></emph>rectos angulos faciat, ſicque il<lb></lb>las tangat in punctis<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">z,</foreign><lb></lb><emph type="italics"></emph>cum quarta pars peripheriæ<emph.end type="italics"></emph.end> <foreign lang="el">h b</foreign><lb></lb><emph type="italics"></emph>erit reuoluta: ita vt<emph.end type="italics"></emph.end> <foreign lang="el">a b</foreign> <emph type="italics"></emph>rur<lb></lb>ſus ad rectos ſit ad rectam<emph.end type="italics"></emph.end> <foreign lang="el">h q,</foreign><lb></lb><emph type="italics"></emph>ipſamque tangat, vt in puncto<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">k</foreign>: <emph type="italics"></emph>tunc &<emph.end type="italics"></emph.end> <foreign lang="el">a g</foreign> <emph type="italics"></emph>etiam ad re<lb></lb>ctos erit ſuper<emph.end type="italics"></emph.end> <foreign lang="el">z i,</foreign> <emph type="italics"></emph>& ſit vt <lb></lb>tangat in puncto<emph.end type="italics"></emph.end> <foreign lang="el">l. </foreign><emph type="italics"></emph></s> <s>Erunt pro <lb></lb>29. prop. lib. 1. </s> <s>Duæ<emph.end type="italics"></emph.end> <foreign lang="el">z h</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">k l</foreign> <emph type="italics"></emph>parallelæ & æquales, ex hypoth. <lb></lb></s> <s id="id.002543">Ergo quæ eas ad eaſdem partes iungunt rectæ<emph.end type="italics"></emph.end> <foreign lang="el">z l</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">h k</foreign> <emph type="italics"></emph>erunt <lb></lb>æquales, prop 34. eiuſdem. </s> <s id="id.002544">Sunt autem orbitæ ab vtriſque confectæ <lb></lb>eadem celeritate motis. </s> <s id="id.002545">Eadem ratiocinatione cum<emph.end type="italics"></emph.end> <foreign lang="el">a g</foreign> <emph type="italics"></emph>tanget in<emph.end type="italics"></emph.end><pb xlink:href="035/01/208.jpg" pagenum="168"></pb><emph type="italics"></emph>puncto<emph.end type="italics"></emph.end> <foreign lang="el">i</foreign> <emph type="italics"></emph>ex reuolutione maioris, &<emph.end type="italics"></emph.end> <foreign lang="el">b</foreign> <emph type="italics"></emph>tanget in<emph.end type="italics"></emph.end> <foreign lang="el">q</foreign>: <emph type="italics"></emph>ſicque<emph.end type="italics"></emph.end> <foreign lang="el">q i</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">h <lb></lb>z</foreign> <emph type="italics"></emph>cum ſint æquales & parallelæ, duæ rurſus<emph.end type="italics"></emph.end> <foreign lang="el">h q</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">z i</foreign> <emph type="italics"></emph>erunt pa<lb></lb>rallelæ. </s> <s id="id.002546">Quæ autem ratio eſt quartarum circulorum inter ſe, eadem <lb></lb>eſt totorum. </s> <s id="id.002547">Partes enim cum pariter multiplicibus eandem ratio<lb></lb>nem habent prop. 15. lib. 5. </s> <s>Igitur in vtroque modo orbitæ concen<lb></lb>tricorum inæqualium ſunt æquales. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002548">Atque id nulla.] <emph type="italics"></emph>Cauſam admirabilis huius aduentus, quæ <lb></lb>adferri potuiſſet, In primò quidem modo ex tarditate & mora <lb></lb>maioris circuli in quibuſdam rectæ lineæ punctis, dum minor <lb></lb>circulus ipſam peragrat: In ſecundo verò modo ex tranſultu minoris <lb></lb>quaſi exiliat, nec ſimul omnia puncta rectæ attingat: ſed tranſiliat <lb></lb>minor, dum maior contra omnia attingat peragrando, reijcit, mo<lb></lb>ramque nullam in hoc intercedere, neque tranſultum in iſto: ſed <lb></lb>vtriuſque continuas motiones eſſe dicit, quia vnica latio eſt. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002549"><foreign lang="el">e)/ti de\ mia=s kinh/sews ou)/shs a)ei\ to\ ke/ntron <lb></lb>to\ kinou/menon o(te\ me\n th\n mega/lhn o(te\ de\ th\n e)la/ttona <lb></lb>e)kkuli/esqai qaumasto/n.</foreign></s> <s id="g0132412"><foreign lang="el">to\ ga\r au)to\ tw=| au)tw=| ta/xei fero/menon <lb></lb>i)/shn pe/fuke diecie/nai: tw=| au)tw=| de\ ta/xei i)/shn e)sti\ <lb></lb>kinei=n a)mfotera/kis.</foreign></s> <s id="g0132413"><foreign lang="el">a)rxh\ de\ lhpte/a h(/de peri\ th=s ai)ti/as <lb></lb>au)tw=n, o(/ti h( au)th\ du/namis kai\ i)/sh to\ me\n bradu/teron <lb></lb>kinei= me/geqos, to\ de\ taxu/teron.</foreign></s> <s id="g0132414"><foreign lang="el">ei) dh/ ti ei)/h o(\ mh\ pe/fuken <lb></lb>u(f' e(autou= kinei=sqai, e)a\n tou=to a(/ma kai\ au)to\ kinh=| to\ pefuko\s <lb></lb>kinei=sqai, bradu/teron kinhqh/setai h)\ ei) au)th\ kaq' <lb></lb>au(th\n e)kinei=to.</foreign></s> <s id="g0132415"><foreign lang="el">kai\ e)a\n me\n pefuko\s h)=| kinei=sqai, mh\ sugkinh=tai <lb></lb>de\ mhqe/n, w(sau/tws e(/cei.</foreign></s> <s id="g0132416"><foreign lang="el">kai\ a)du/naton dh\ kinei=sqai <lb></lb>ple/on h)\ to\ kinou=n: ou) ga\r th\n au(tou= kinei=tai ki/nhsin, a)lla\<lb></lb> th\n tou= kinou=ntos.</foreign></s> <s id="g0132417"><foreign lang="el">ei)/h dh\ ku/klos o( me\n mei/zwn to\ *a, o( de\ <lb></lb>e)la/ttwn e)f' w(=| *b. ei) w)qoi/h d' o( e)la/ttwn to\n mei/zw, mh\ <lb></lb>kuliome/nou au)tou=, fanero\n o(/ti tosou=ton di/eisi th=s eu)qei/as <lb></lb>o( mei/zwn, o(/son e)w/sqh u(po\ tou= e)la/ttonos. tosou=ton de/ ge <lb></lb>e)w/sqh o(/son o( mikro\s e)kinh/qh. i)/shn a)/ra th=s eu)qei/as dielhlu/qasin.</foreign></s> <s id="g0132418"><foreign lang="el"><lb></lb>a)na/gkh toi/nun kai\ ei) kulio/menos o( e)la/ttwn to\n <lb></lb>mei/zw w)qoi/h, kulisqh=nai me\n a(/ma th=| w)/sei, tosou=ton d' o(/son <lb></lb>o( e)la/ttwn e)kuli/sqh, ei) mhqe\n au)to\s th=| au)th=| kinh/sei kinei=tai.</foreign></s> <s id="g0132419"><foreign lang="el"><lb></lb>w(s ga\r kai\ o(/son e)ki/nei, tosou=ton kekinh=sqai a)na/gkh <lb></lb>to\ kinou/menon u(p' e)kei/nou. a)lla\ mh\n o(/ te ku/klos tosou=ton <lb></lb>e)ki/nhse to\ au)to/, ku/klw| te kai\ podiai/an [1e)/stw ga\r tosou=ton <lb></lb>o(\ e)kinh/qh]1, kai\ o( me/gas a)/ra tosou=ton e)kinh/qh.</foreign></s> <s id="g0132420"><foreign lang="el">o(moi/ws <lb></lb>de\ ka)\n o( me/gas to\n mikro\n kinh/sh|, e)/stai kekinhme/nos o( mikro\s <lb></lb>w(s kai\ o( mei/zwn.</foreign></s> <s id="g0132421"><foreign lang="el">kaq' au(to\n me\n dh\ kinhqei\s o(poterosou=n, <lb></lb>e)a/n te taxu\ e)a/n te brade/ws: tw=| au)tw=| de\ ta/xei <lb></lb>eu)qu\s o(/shn o( mei/zwn pe/fuken e)celixqh=nai grammh/n.</foreign></s> </p> <p type="main"> <s id="id.002550">Præterea vnica latione <lb></lb><expan abbr="exiſtẽte">exiſtente</expan> <expan abbr="centrũ">centrum</expan> ſemper <expan abbr="cõtinuè">con<lb></lb>tinuè</expan> motum, aliquando <lb></lb><expan abbr="quidẽ">quidem</expan> per <expan abbr="maiorẽ">maiorem</expan>, aliquan<lb></lb>do verò per minorem con<lb></lb>uolui eſt admirabile. </s> <s id="id.002551">I dem <lb></lb>enim eadem celeritate <expan abbr="latũ">latum</expan> <lb></lb>æqualem <expan abbr="trãſire">tranſire</expan> natum eſt. <lb></lb></s> <s id="id.002552">Eadem <expan abbr="autẽ">autem</expan> celeritate per <lb></lb><expan abbr="æqualẽ">æqualem</expan> vtro que modo mo<lb></lb>uere licet. </s> <s id="id.002553">Cæterum princi<lb></lb>pium ſumatur ex vtriuſque <lb></lb>cauſa, quod eadem vis, & <lb></lb>æqualis vnam quidem <expan abbr="magnitudinũ">ma<lb></lb>gnitudinum</expan> tardius: alteram <lb></lb>celerius moueat. </s> <s id="id.002554">Si quid <lb></lb>enim fuerit non à ſeipſo <lb></lb>moueri <expan abbr="natũ">natum</expan>, & <expan abbr="ipsũ">ipsum</expan> aliud <lb></lb>quod moueri <expan abbr="natũ">natum</expan> ſit mo<lb></lb>uerit, tardius mouebitur: <lb></lb><expan abbr="quã">quam</expan> ſi <expan abbr="ipsũ">ipsum</expan> per ſe moueretur. </s> <pb xlink:href="035/01/209.jpg" pagenum="169"></pb> <s>Et ſi quidem <expan abbr="natũ">natum</expan> ſit mo<lb></lb>ueri, neque <expan abbr="autẽ">autem</expan> ſimul mo<lb></lb>ueatur, ſimiliter ſe habebit. <lb></lb></s> <s id="id.002555">Et vt plus moueatur: quam <lb></lb>quod mouet, fieri non po<lb></lb>teſt. </s> <s id="id.002556">Non enim ſuo ipſius <lb></lb>mouetur motu: ſed <expan abbr="mouẽ">mouen<lb></lb></expan><arrow.to.target n="marg39"></arrow.to.target><lb></lb>tis. </s> <s>[Sit igitur circulus maior <lb></lb><expan abbr="quidẽ">quidem</expan> vbi <foreign lang="el">g,</foreign> at minor vbi <lb></lb>b.] </s> <s>Si impellat minor <expan abbr="maiorẽ">maio<lb></lb>rem</expan> ipſo ſe minime <expan abbr="voluẽte">voluente</expan>, <lb></lb>manifeſtum quod tantam <lb></lb><expan abbr="rectã">rectam</expan> maior tranſit, ad <expan abbr="quãtam">quan<lb></lb>tam</expan> à minore impulſus eſt: <lb></lb>ad tantam verò impulſus <lb></lb>eſt, ad quantam minor ſe <lb></lb>mouit. </s> <s id="id.002557"><expan abbr="Rectã">Rectam</expan> igitur æqua<lb></lb>lem pertranſierunt. </s> <s id="id.002558">Neceſ<lb></lb>ſe igitur ſi minor conuolu<lb></lb>tus impulerit, <expan abbr="maiorẽ">maiorem</expan> con<lb></lb>uolui quidem cum impul<lb></lb>ſione tantum: <expan abbr="quãtum">quantum</expan> mi<lb></lb>nor conuolutus fuerit. </s> <s id="id.002559">ſi <lb></lb><expan abbr="neutiquã">neutiquam</expan> ipſe proprio mo<lb></lb>tu moueatur. </s> <s id="id.002560">quomodo <lb></lb>enim & quantum mouit, <lb></lb><expan abbr="tãtundem">tantundem</expan> <expan abbr="motũ">motum</expan> eſſe, quod <lb></lb>ab illo mouebatur, neceſ<lb></lb>ſum eſt. </s> <s id="id.002561">Sed circulus ſolum <lb></lb>ſe mouerit circulariter pe<lb></lb>dem vnum. </s> <s id="id.002562">Sit enim tan<lb></lb>tum quod <expan abbr="motũ">motum</expan> eſt. </s> <s id="id.002563">Etiam <lb></lb>magnus tantundem motus <lb></lb>erit. </s> <s id="id.002564">Similiter ſi magnus <lb></lb><expan abbr="paruũ">paruum</expan> mouerit: <expan abbr="tantũ">tantum</expan> paruus, <expan abbr="quantũ">quantum</expan> magnus motus erit. <lb></lb></s> <s id="id.002565">per ſe <expan abbr="quidẽ">quidem</expan> motus vtrouis modo ſeu celeriter: ſeu tardè. </s> </p> </subchap1> <pb xlink:href="035/01/210.jpg" pagenum="170"></pb> <subchap1> <p type="main"> <s><lb></lb>Eadem verò celeritate ſta<lb></lb>tim per quantam lineam <lb></lb>natus eſt conuolui maior. </s> </p> <p type="margin"> <s id="id.002566"><margin.target id="marg39"></margin.target>Hæc inter<lb></lb>poſita <expan abbr="vidẽtur">viden<lb></lb>tur</expan>. </s> </p> <p type="head"> <s id="id.002567">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002568">Præterea vnica.] <emph type="italics"></emph>Cum ſit oſtenſa problematis veritas rurſus <lb></lb>oſtendit aliquid admirabile contineri. </s> <s id="id.002569">Ratio admirationis ſic erit <lb></lb>apertior. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002570"><emph type="italics"></emph>Idem eadem celeritate latum æqualem <expan abbr="lineã">lineam</expan> tranſire natum eſt. <lb></lb></s> <s id="id.002571">Centrum circulorum concentricorum vnum idemque eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002572"><emph type="italics"></emph>Ergo æqualem tranſire natum eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002573"><emph type="italics"></emph>Attamen aliter fit. </s> <s id="id.002574">Nam eadem celeritate latum modò <expan abbr="maiorẽ">maiorem</expan>, <lb></lb>modò minorem tranſit. </s> <s id="id.002575">Ergo problema admirationis plenum eſt. </s> <s id="id.002576">Syllogiſ<lb></lb>mi huius propoſitio eſt euidens: aſſumptio poſtea diſtinguetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002577">Cæterum principium.] <emph type="italics"></emph>Vt admiratio tollatur, duo aſſumun<lb></lb>tur è Phyſicis, quæ ſi diligenter expendantur, ſunt vtraque euiden<lb></lb>ter vera. </s> <s id="id.002578">Primum eſt. </s> <s id="id.002579">Si ab vna & eadem vi duo moueantur, quo<lb></lb>rum alterum quidem à ſe moueri natum eſt ſecundum motum illum, <lb></lb>ſecundum quem à vi <expan abbr="mouẽtis">mouentis</expan> mouetur: alterum verò non eſt natum <lb></lb>eo moueri motu, vel natum quidem ſit, ſed tum motu non vtatur ſuo: <lb></lb>moueantur autem iſta coniunctim, illud quod ex ſe illo motu moueri <lb></lb>natum erat, tardius mouebitur: quam ſi per ſe moueretur. </s> <s id="id.002580">Exemplum <lb></lb>ſit plumbum cum vtre aëre pleno annexum, quod euidenter tardius <lb></lb>deſcendit per aquam: quam ſi liberum fuiſſet ab vtre, vt ſit in con<lb></lb>iuncto eadem, atque in libero erat grauitas. </s> <s id="id.002581">Secundum eſt. </s> <s id="id.002582">Motum <lb></lb>ab alio non plus moueri poteſt: quam quod ipſum mouet, vt quod non <lb></lb>ſuo: ſed motu mouentis moueatur, tum mouens & motum ſunt ſi<lb></lb>mul, vt demonſtratum eſt ab Ariſtotele in lib. de Phyſ. auditu. </s> <s id="id.002583">Cauſa <lb></lb>itaque problematis in hoc continetur, quod è duobus circulis eadem <lb></lb>celeritate motis alter primo mouetur, & alter prior is moti raptum <lb></lb>ſequitur. </s> <s id="id.002584">Itaque ſi minoris raptum ſequatur maior, orbita maioris fiet <lb></lb>æqualis orbitæ minoris, cum maior in motu non vi vtatur ſua, ſed ad <lb></lb>motum minoris moueatur: ſi vero maioris raptum minor ſequatur, <lb></lb>orbita minoris fiet æqualis orbitæ maioris, cum minor eò feratur quò <lb></lb>etiam maior ipſum rapit. </s> <s id="id.002585">Et ſic celerius per maiuſque ſpatium, quam <emph.end type="italics"></emph.end><pb xlink:href="035/01/211.jpg" pagenum="171"></pb><emph type="italics"></emph>quòd ferretur per ſe. </s> <s id="id.002586">Tamen propter annexionem duo illi tardius vel <lb></lb>celerius mouentur: quam per ſe mouerentur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002587">Neceſſe igitur ſi.] <emph type="italics"></emph>Quod maiore<emph.end type="italics"></emph.end> <foreign lang="el">z d</foreign> <emph type="italics"></emph>moto minor<emph.end type="italics"></emph.end> <foreign lang="el">h e</foreign> <emph type="italics"></emph>rapiatur <lb></lb>in eodem plano duobus concentricis exiſtentibus captu facile eſt. <lb></lb></s> <s id="id.002588">Nam maioris peripheria impulſa, vel per axem tracta, ob nutum di<lb></lb>midiæ partis perpetuum, de quo ante, conuoluitur potius: quam vno <lb></lb>puncto eodemque ſemper tangente planum gliſcat. </s> <s id="id.002589">Cauſa enim motus <lb></lb>rotæ ſemper eſt in circulo eius maximo: at quod minor vt<emph.end type="italics"></emph.end> <foreign lang="el">h e</foreign> <emph type="italics"></emph>primo <lb></lb>moueatur, & ad eius motum maior, capi mente difficilius paulò, ta<lb></lb>men & capi poteſt, ſi imaginemur volutationibus inæqualium dua<lb></lb>rum rotarum ſic annexarum, vt ſupponitur, ſupponi duo plana inæ<lb></lb>qualiter alta, & ita vt vnum vnam è rotis, alterum alteram ſuſti<lb></lb>neat, & tunc imaginemur ad minoris motum rotæ maiorem moueri <lb></lb>& rapi. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002590"><foreign lang="el">o(/per <lb></lb>kai\ poiei= th\n a)pori/an, o(/ti ou)ke/ti o(moi/ws poiou=sin o(/tan sunarmosqw=sin. <lb></lb>to\ d' e)/stin, ei) o( e(/teros u(po\ tou= e(te/rou kinei=tai <lb></lb>ou)x h(\n pe/fuken, ou)de\ th\n au(tou= ki/nhsin.</foreign></s> <s id="g0132422"><foreign lang="el">ou)qe\n ga\r <lb></lb>diafe/rei periqei=nai kai\ e)narmo/sai h)\ prosqei=nai o(poteronou=n <lb></lb>o(pote/rw|: o(moi/ws ga/r, o(/tan o( me\n kinh=| o( de\ kinh=tai u(po\ <lb></lb>tou/tou, o(/son a)\n kinh=| a(/teros, tosou=ton kinhqh/setai a(/teros.</foreign></s> <s id="g0132423"><foreign lang="el"><lb></lb>o(/tan me\n ou)=n proskei/menon kinh=| h)\ proskrema/menon, ou)k a)ei\ <lb></lb>kuli/ei tis: o(/tan de\ peri\ to\ au)to\ ke/ntron teqw=sin, a)na/gkh <lb></lb>kuli/esqai a)ei\ to\n e(/teron u(po\ tou= e(te/rou.</foreign></s> <s id="g0132424"><foreign lang="el">a)ll' ou)qe\n h(=tton <lb></lb>ou) th\n au(tou= ki/nhsin a(/teros kinei=tai, a)ll' w(/sper a)\n ei) mhdemi/an <lb></lb>ei)=xe ki/nhsin. ka)\n e)/xh|, mh\ xrh=tai d' au)th=|, tau)to\ <lb></lb>sumbai/nei.</foreign></s> <s id="g0132425"><foreign lang="el">o(/tan me\n ou)=n o( me/gas kinh=| e)ndedeme/non to\n mikro/n, <lb></lb>o( mikro\s kinei=tai o(/shnper ou(=tos: o(/tan de\ o( mikro/s, <lb></lb>pa/lin o( me/gas o(/shn ou(=tos. xwrizo/menos de\ e(ka/teros au(to\n <lb></lb>kinei= au)to/s.</foreign></s> <s id="g0132426"><foreign lang="el">o(/ti de\ tou= au)tou= ke/ntrou o)/ntos kai\ kinou=ntos <lb></lb>tw=| au)tw=| ta/xei sumbai/nei a)/nison diecie/nai au)tou\s grammh/n, <lb></lb>paralogi/zetai o( a)porw=n sofistikw=s.</foreign></s> <s id="g0132427"><foreign lang="el">to\ au)to\ me\n <lb></lb>ga/r e)sti ke/ntron a)mfoi=n, a)lla\ kata\ sumbebhko/s, w(s <lb></lb>mousiko\n kai\ leuko/n: to\ ga\r ei)=nai e(kate/rou ke/ntrou tw=n <lb></lb>ku/klwn ou) tw=| au)tw=| xrh=tai.</foreign></s> <s id="g0132428"><foreign lang="el">o(/tan me\n ou)=n o( kinw=n h)=| o( <lb></lb>mikro/s, w(s e)kei/nou ke/ntron kai\ a)rxh/, o(/tan de\ o( me/gas, w(s <lb></lb>e)kei/nou.</foreign></s> <s id="g0132429"><foreign lang="el">ou)/koun to\ au)to\ kinei= a(plw=s, a)ll' e)/stin w(/s.</foreign></s> </p> <p type="main"> <s id="id.002591">Quod etiam dubitatio<lb></lb>nem adfert, quia ſimiliter <lb></lb>præterea faciunt, quando <lb></lb>connexi ſunt. </s> <s id="id.002592">Hoc autem <lb></lb>eſt, ſi alter ab altero mouea<lb></lb>tur, non ea qua natus eſt, <lb></lb>neque ſua propria motio<lb></lb>ne. </s> <s id="id.002593">Nihil enim intereſt cir<lb></lb>cumponere, & annectere <lb></lb>vel adiungere <expan abbr="vtrũlibet">vtrumlibet</expan> al<lb></lb>teri. </s> <s id="id.002594">Similiter enim <expan abbr="quãdo">quando</expan> <lb></lb>hic <expan abbr="quidẽ">quidem</expan> mouet: ille verò <lb></lb>ab altero mouetur, <expan abbr="quantũ">quantum</expan> <lb></lb>vnus mouerit, tantum alter <lb></lb>mouebitur. </s> <s id="id.002595">quando <expan abbr="quidẽ">quidem</expan> <lb></lb>igitur <expan abbr="adiectũ">adiectum</expan>, vel ſuſpen<lb></lb>ſum mouerit quis, <expan abbr="nõ">non</expan> ſem<lb></lb>per conuoluitur: at <expan abbr="quãdo">quando</expan> <lb></lb>circa idem centrum poſiti <lb></lb>fuerint, ſemper neceſſe <expan abbr="eſtalterũ">eſt <lb></lb>alterum</expan> ab altero conuolui. <pb xlink:href="035/01/212.jpg" pagenum="172"></pb>Sed perinde ac ſi ſuo motu <lb></lb>alter non moueatur, nul<lb></lb>lum que motum habeat. </s> <s id="id.002596">Et <lb></lb>ſi habeat eo <expan abbr="nõ">non</expan> vtatur, hoc <lb></lb>accidit. </s> <s id="id.002597">Quando igitur ma<lb></lb>gnus paruum <expan abbr="alligatũ">alligatum</expan> mo<lb></lb>uerit, hic paruus <expan abbr="tãtundem">tantundem</expan> <lb></lb>mouetur. </s> <s id="id.002598">Quando verò <lb></lb>paruus rurſus: tantundem <lb></lb>magnus. </s> <s id="id.002599">Separatim verò <lb></lb>vterque ſeipſum mouet. <lb></lb></s> <s id="id.002600">Quod verò <expan abbr="eodẽ">eodem</expan> exiſtente <lb></lb>centro, & moto eadem ce<lb></lb>leritate <expan abbr="cõtingit">contingit</expan> ipſos ma<lb></lb>iorem <expan abbr="trãſilire">tranſilire</expan> lineam, pa<lb></lb>ralogiſmus eſt à dubitante <lb></lb>dolosè prolatus. </s> <s id="id.002601">Idem qui<lb></lb>dem eſt centrum vtriſque: <lb></lb>ſed per accidens vt <expan abbr="muſicũ">muſicum</expan> <lb></lb>& album eſſe. </s> <s id="id.002602">Quod enim <lb></lb>eſſet de eſſentia vtriuſque <lb></lb>centri circulorum, non eo<lb></lb>dem vtitur: ſed <expan abbr="quãdo">quando</expan> par<lb></lb>uus mouebit illius eſt, vt <lb></lb><expan abbr="centrũ">centrum</expan> & <expan abbr="principiũ">principium</expan>: quan<lb></lb>do verò magnus, vt ipſius. <lb></lb></s> <s id="id.002603">Non igitur idem mouet ſimpliciter: ſed quodammodo. </s> </p> <p type="head"> <s id="id.002604">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002605">Qvod etiam dubit.] <emph type="italics"></emph>Antea de circulis ad vnum centrum <lb></lb>connexis <expan abbr="demõſtratum">demonſtratum</expan> eſt: perinde etiam in inæqualibus ad di<lb></lb>uerſa puncta connexis ſe habere oſtenditur, niſi <expan abbr="mendũ">mendum</expan> ſubſit aliquod <lb></lb>in contextu è quo particulam<emph.end type="italics"></emph.end> <foreign lang="el">ou)k</foreign> <emph type="italics"></emph>expunximus. </s> <s id="id.002606">Nam & eccentrici <lb></lb>connexi raptum motoris primi ſequuntur, & ſemper orbitarum <lb></lb>æqualitas reperietur ſeu centra ſint in eadem linea: ſiue in diuerſis,<emph.end type="italics"></emph.end><pb xlink:href="035/01/213.jpg" pagenum="173"></pb><figure id="id.035.01.213.1.jpg" xlink:href="035/01/213/1.jpg"></figure><lb></lb><emph type="italics"></emph>vt in A, B, <lb></lb>C, vbi lineæ <lb></lb>pro orbitis <lb></lb>inæqualium <lb></lb><expan abbr="circulorũ">circulorum</expan>, ſed <lb></lb><expan abbr="annexorũ">annexorum</expan> D <lb></lb>E, F G, HI <lb></lb>ſunt æquales <lb></lb>vt facile eſt <lb></lb>demonſtrare <lb></lb>ex adſcripto <lb></lb>diagrammate. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002607">Quod vero eodem.] <emph type="italics"></emph>Reſpondet aſſumptioni præcedentis ſyllo<lb></lb>giſmi, in quo concludebatur ratio admirationis problematis. </s> <s id="id.002608">Negat<lb></lb>que idem etiam concentricorum circulorum ita vt dictum eſt moto<lb></lb>rum, <expan abbr="cẽtrum">centrum</expan> eſſe, niſi captiose. </s> <s id="id.002609">Huius enim <expan abbr="centrũ">centrum</expan>, eſt quod primum <lb></lb>mouetur, non huius quod ſecundario. </s> <s id="id.002610">Huius enim centrum feriatur: <lb></lb>illius verò <expan abbr="cũ">cum</expan> ſit <expan abbr="principiũ">principium</expan> motus, agit, ſeu in actu eſt. </s> <s id="id.002611">Et ſic non <expan abbr="vnũ">vnum</expan> <lb></lb><expan abbr="idemq;">idemque</expan> centrum <expan abbr="vtriuſq;">vtriuſque</expan> eſt, cum <expan abbr="alterũ">alterum</expan> moueat, alterum moueatur. <lb></lb></s> <s id="id.002612">Hæc tamen ſolutio quæ ſit, relinquo cogitandum. </s> <s id="id.002613">quomodo enim ſi <lb></lb><expan abbr="principiũ">principium</expan> motus <expan abbr="concentricorũ">concentricorum</expan> <expan abbr="circulorũ">circulorum</expan> ſit ab axe, vt in mola mole<lb></lb>trinæ, & <expan abbr="vnũ">vnum</expan> <expan abbr="idemq;">idemque</expan> <expan abbr="centrũ">centrum</expan> cum ſit, puta, molæ minoris in maiore <lb></lb>deſcriptæ, non <expan abbr="idẽ">idem</expan> eodem <expan abbr="tẽpore">tempore</expan> ab <expan abbr="eodẽ">eodem</expan> erit in actu & <expan abbr="principiũ">principium</expan>, ſui <lb></lb>motus habebit. </s> <s id="id.002614">Aliter igitur verè ſolueretur, ſi intelligamus aliud eſſe <lb></lb><expan abbr="motũ">motum</expan> <expan abbr="circularẽ">circularem</expan>: aliud <expan abbr="motũ">motum</expan> in circulo vel per circulum. </s> <s id="id.002615">Motus enim <lb></lb>circularis fit <expan abbr="cẽtro">centro</expan> quieſcente, & reliquis omnibus motis, talis eſt mo<lb></lb>tus æquatoris in cælo. </s> <s id="id.002616">Motus verò per <expan abbr="circulũ">circulum</expan> fit progrediente centro, <lb></lb>& huic accedit vt <expan abbr="circũuertatur">circumuertatur</expan>, alioqui nihil aliud eſſet <expan abbr="quã">quam</expan> circu<lb></lb>lus progrediens, & vectio <expan abbr="quædã">quædam</expan>, vt hæc qua<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph><expan abbr="centrũ">centrum</expan> perpetuò per<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg40"></arrow.to.target><lb></lb><emph type="italics"></emph>æquidiſtantem <expan abbr="lineã">lineam</expan> fertur in<emph.end type="italics"></emph.end> <foreign lang="el">g,</foreign> <emph type="italics"></emph>ſeu trahatur ſeu impellatur, & ideo <lb></lb>omnia puncta æqualiter <expan abbr="mouẽtur">mouentur</expan>, & per æquale <expan abbr="ſpatiũ">ſpatium</expan> perinde ac ſi <lb></lb>motus hic merè rectus eſſet, & ſine vlla circumuerſione quaſi fune <lb></lb>circulus traheretur. </s> <s id="id.002617">Cæterum cum <expan abbr="tã">tam</expan><emph.end type="italics"></emph.end> <foreign lang="el">z g d,</foreign> <emph type="italics"></emph><expan abbr="quã">quam</expan><emph.end type="italics"></emph.end> <foreign lang="el">h b e</foreign> <emph type="italics"></emph>moueantur ſu<lb></lb>per rectas<emph.end type="italics"></emph.end> <foreign lang="el">z l, h q</foreign> <emph type="italics"></emph>& quidem ita vt ſingula puncta<emph.end type="italics"></emph.end> <foreign lang="el">z g d</foreign> <emph type="italics"></emph>tangant <lb></lb>ſingula puncta<emph.end type="italics"></emph.end> <foreign lang="el">z l</foreign><emph type="italics"></emph>: <expan abbr="tũ">tum</expan><emph.end type="italics"></emph.end> <foreign lang="el">h b e</foreign> <emph type="italics"></emph>ſingula puncta ipſius<emph.end type="italics"></emph.end> <foreign lang="el">h q.</foreign> </s> <s><emph type="italics"></emph>Tamen peri<lb></lb>pheria<emph.end type="italics"></emph.end> <foreign lang="el">z g d,</foreign> <emph type="italics"></emph>aut <expan abbr="nõ">non</expan> eſt æqualis rectæ<emph.end type="italics"></emph.end> <foreign lang="el">z l</foreign><emph type="italics"></emph>: aut peripheria<emph.end type="italics"></emph.end> <foreign lang="el">z b e</foreign> <emph type="italics"></emph><expan abbr="nõ">non</expan> eſt <emph.end type="italics"></emph.end><pb xlink:href="035/01/214.jpg" pagenum="174"></pb><emph type="italics"></emph>æqualis rectæ<emph.end type="italics"></emph.end> <foreign lang="el">h q</foreign>: <emph type="italics"></emph>alioqui ſi <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.214.1.jpg" xlink:href="035/01/214/1.jpg"></figure><lb></lb><emph type="italics"></emph>ambæ peripheriæ ambabus re<lb></lb>ctis eſſent æquales, cum ipſæ <lb></lb>ſint æquales rectæ, vt demon<lb></lb>ſtratum eſt, eſſent & periphe<lb></lb>riæ æquales, maior minori, quod <lb></lb>abſurdum. </s> <s id="id.002618">Ex quo exploditur <lb></lb>ratio Bouilli, qui ex <expan abbr="circũuolutione">circumuolu<lb></lb>tione</expan> circuli exactè rotundi ſu<lb></lb>per plano ad libellam facto pu<lb></lb>tabat inueniſſe rectam periphe<lb></lb>riæ æqualem. </s> <s id="id.002619">Quæritur ergo quod eſt ſuperiori problemate diffici<lb></lb>lius, vt fieri poßit rectarum æqualium peragratio à circulis inæqua<lb></lb>libus. </s> <s id="id.002620">Sit igitur vt rotæ axis<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>tranſeat in F. </s> <s id="id.002622">Et quia<emph.end type="italics"></emph.end> <foreign lang="el">a h</foreign> <emph type="italics"></emph>& F G<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.214.2.jpg" xlink:href="035/01/214/2.jpg"></figure><lb></lb><emph type="italics"></emph>æquales ſunt. </s> <s id="id.002623">Radij enim ſunt eiuſdem circuli minoris &<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign> <emph type="italics"></emph>G eſt <lb></lb>æquidiſtans<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>F. </s> <s id="id.002624">Erit per demonſtrata punctum G in linea F H. <lb></lb></s> <s id="id.002625">Et ponatur quod punctum fuerit M in maiori circulo, quod tranſla<lb></lb>tum & retrò reuolutum peruenerit ad H, atque<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>M ſecet circulum <lb></lb>minorem<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign> <emph type="italics"></emph>F<emph.end type="italics"></emph.end> <foreign lang="el">e,</foreign> <emph type="italics"></emph>vt in puncto I. </s> <s id="id.002626">Dico quod I eſt punctum G. </s> <s id="id.002627">Nam <lb></lb>quia M eſt H, & in linea F H: præterea I eſt in linea<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign> <emph type="italics"></emph>M, <lb></lb>erit etiam in linea F H. </s> <s id="id.002628">Eſt etiam in circulo<emph.end type="italics"></emph.end> <foreign lang="el">h</foreign> <emph type="italics"></emph>F<emph.end type="italics"></emph.end> <foreign lang="el">e. </foreign><emph type="italics"></emph>Ergo in puncto <lb></lb>communi vtrique. </s> <s id="id.002629">Nullum autem eſt præter G. </s> <s id="id.002630">Igitur I peruenit<emph.end type="italics"></emph.end><pb xlink:href="035/01/215.jpg" pagenum="175"></pb><emph type="italics"></emph>in G. </s> <s id="id.002631">Sicque M retroceßit per angulum M G H. </s> <s id="id.002632">Contrà I an<lb></lb>teceßit per angulum I G F, qui ſunt anguli æquales prop. 15. lib. 1. <lb></lb></s> <s>Et ſic patet cur retrocedente vno tantum: quantum procedit alter, <lb></lb>moueantur æqualiter, id eſt per æquale ſpatium puncta peripheria<lb></lb>rum inæqualium ob centri communis æqualem motum. </s> <s id="id.002633">Hæc ex <lb></lb>Cardan. prop. 196. lib. 5. de proport. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.002634"><margin.target id="marg40"></margin.target>Vide penul<lb></lb>timum dia <lb></lb>gramma. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002635">26. <foreign lang="el">*peri\ tw=n klinw=n.</foreign></s> </p> <p type="main"> <s id="id.002636">26. De lectis. </s> </p> <p type="main"> <s id="id.002637"><foreign lang="el">*dia\ ti/ ta\s kli/nas poiou=si diplasiopleu/rous, th\n me\n<lb></lb> e(\c podw=n kai\ mikrw=| mei/zw pleura/n, th\n de\ triw=n; kai\ <lb></lb>dia\ ti/ e)ntei/nousin ou) kata\ dia/metron; </foreign></s> <s id="g0132502"><foreign lang="el">h)\ to\ me\n me/geqos thlikau/tas, <lb></lb>o(/pws toi=s sw/masin w)=si su/mmetroi; gi/nontai <lb></lb>ga\r ou(/tw diplasio/pleuroi, tetraph/xeis me\n to\ mh=kos, diph/xeis <lb></lb>de\ to\ pla/tos.</foreign></s> </p> <p type="main"> <s id="id.002638">Cur lectos lateribus du<lb></lb>plos faciunt, vno quidem <lb></lb>ſex pedum, vel paulò plus: <lb></lb>altero verò trium. </s> <s id="id.002639">Et cur <lb></lb>extendunt non ſecundum <lb></lb>diametrum. </s> <s id="id.002640">An magnitu<lb></lb>dine tantos faciunt, vt cor<lb></lb>poribus correſpondeant. <lb></lb></s> <s id="id.002641">Sic enim lateribus dupli <lb></lb>efficiuntur, vt longitudine <lb></lb>quatuor cubitorum, latitu<lb></lb>dine verò duorum ſint. </s> </p> <p type="head"> <s id="id.002642">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002643">Cvr lectos.] <emph type="italics"></emph>In hoc capite quæruntur duo, quibus apertè ſatis<lb></lb>facit philoſophus, quod ad primas quæſtionum rationes attinet. <lb></lb></s> <s id="id.002644">Ex his prior eſt, cur lectus fiat è lateribus in ratione dupla, cuiuſmo<lb></lb>di ſunt ſex pedes ad tres, vel quatuor cubiti ad duos. </s> <s id="id.002645">vbi notandum <lb></lb>lectos habere formam parallelogrammi rectanguli. </s> <s id="id.002646">Itaque ex def. 1. <lb></lb>lib. 2. contineri ſub duobus lateribus, quæ rectum angulum compre<lb></lb>hendunt. </s> <s id="id.002648">Et hæc ſunt quæ hîc <expan abbr="conſiderãtur">conſiderantur</expan> in ratione dupla. </s> <s id="id.002649">Reſpon<lb></lb>det igitur ſic fieri, vt corpori decubituro correſpondeat, & rationem <lb></lb>habeat vel æqualitatis, vel paulo maioris. </s> <s id="id.002650">Sic enim melius excipit in <lb></lb>eo <expan abbr="decumbẽs">decumbens</expan> corpus. </s> <s id="id.002651">Eſt autem iuſta hominis magnitudo ſex pedum: <lb></lb>quam vt pauci excedunt: ita quamplurimi non attingunt. </s> <s id="id.002652">Acce<lb></lb>dunt tamen ad eam multi. </s> <s id="id.002653">Sicque plurimis opportuna quæſita eſt <emph.end type="italics"></emph.end><pb xlink:href="035/01/216.jpg" pagenum="176"></pb><emph type="italics"></emph>lecti magnitudo, quod ad <expan abbr="longitudinẽ">longitudinem</expan> attinet: ſed nec minus quod ad <lb></lb>latitudinem. </s> <s id="id.002654">Seu enim ſupinus, aut pronus, quod eſt inſalubre, <expan abbr="nõ">non</expan> plus <lb></lb>loci quam cubitus vnus occupabit: & adhuc paulò minus, ſeu in <lb></lb>dextrum aut ſiniſtrum latus decumbat homo, cuiuſmodi plurimos<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg41"></arrow.to.target><lb></lb><emph type="italics"></emph>ſanos cubare dixit Hippocrates, collo etiam manibus cruribuſque pa<lb></lb>rum reductis, & totis corporibus humentes, id eſt, vt explicat Gale<lb></lb>nus vitatis extremis figuris. </s> <s id="id.002655">Extremæ autem figuræ ſunt, quæ ſum<lb></lb>mam extenſionem, aut flexum habent ſiuè artuum ſint, ſiuè ſpinæ, <lb></lb>& fiunt neruis ſupra modum extentis: non item quæ inter ex<lb></lb>tremas media eſt, hæc enim tenſionem <expan abbr="nõ">non</expan> habet. </s> <s id="id.002656">Ideo humida appel<lb></lb>lata eſt ab Hippocrate, cum humida corpora tendi non ſoleant. </s> <s id="id.002657">Sic <lb></lb>autem iacens tantum hinc quantum illinc ad reuolutionem corporis <lb></lb>ſemicubitum, quod ſatis eſt, habebit. </s> <s id="id.002658">Nec enim de his agimus, quibus<emph.end type="italics"></emph.end> </s> </p> <p type="margin"> <s id="id.002659"><margin.target id="marg41"></margin.target>Inprognoſt. </s> </p> <p type="main"> <s>Pinguis aqualiculus extento ſeſquipede extat. </s> </p> <p type="main"> <s id="id.002660"><emph type="italics"></emph>Sed de moderatis hominibus, quibus hæc lecti latitudo conueniens <lb></lb>erit. </s> <s id="id.002661">Hinc ſi duo in eodem lecto iacere debeant, latitudinem pro ra<lb></lb>tione tantum augendam, non longitudinem lecti conſtat. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002662"><foreign lang="el">e)ntei/nousi de\ ou) kata\ dia/metron a)ll' <lb></lb>a)p' e)nanti/as, o(/pws ta/ te cu/la h(=tton diaspa=tai: ta/xista <lb></lb>ga\r sxi/zetai kata\ fu/sin diairou/mena tau/th|, kai\ e(lko/mena <lb></lb>ponei= ma/lista.</foreign></s> <s id="g0132504"><foreign lang="el">e)/ti e)peidh\ dei= ba/ros du/nasqai ta\ <lb></lb>sparti/a fe/rein, ou(/tws h(=tton pone/sei locoi=s toi=s sparti/ois <lb></lb>e)pitiqeme/nou tou= ba/rous h)\ plagi/ois.</foreign></s> <s id="g0132505"><foreign lang="el">e)/ti de\ e)/latton ou(/tw <lb></lb>sparti/on a)nali/sketai.</foreign></s> </p> <p type="main"> <s id="id.002663">Non extendunt <expan abbr="autẽ">autem</expan> ſe<lb></lb>cundum diamerrum: ſed <lb></lb>contrà, vt ligna minus di<lb></lb>uellantur. </s> <s id="id.002664">celerrimè enim <lb></lb>finduntur ſecundum natu<lb></lb>ram diuiſa, & eadem parte <lb></lb>diſtracta laborant maximè. <lb></lb></s> <s id="id.002665">Præterea quoniam conue<lb></lb>nit funes ſatis eſſe ad pon<lb></lb>dus: ſi tranſuerſi ſint ex im<lb></lb>poſito pondere minus la<lb></lb>borabunt: quam ſi obliqui. <lb></lb></s> <s id="id.002666">Præterea <expan abbr="etiã">etiam</expan> funium <expan abbr="quãtitas">quan<lb></lb>titas</expan>: ſic minor erit. </s> </p> <p type="head"> <s id="id.002667">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002668">Non extendunt.] <emph type="italics"></emph>Poſterior quæſtio eſt, cur lectus cuius late<lb></lb>ra ſunt in ratione dupla pertendatur loris non ſecundum dia<emph.end type="italics"></emph.end><pb xlink:href="035/01/217.jpg" pagenum="177"></pb><emph type="italics"></emph>metrum: ſed in obliquum protenſis, ad quam tripliciter reſpondet. <lb></lb></s> <s id="id.002669">Primo quia ſtudendum eſt durationi, ideo cauendum, ne ſpondæ lecti <lb></lb>findantur: aut rumpantur. </s> <s id="id.002670">Itaque eo modo lora ſunt extendenda, <lb></lb>quo ruptioni fißioniue minus ipſæ obnoxiæ fiunt. </s> <s id="id.002671">At ſi obliquè ex<lb></lb>tendantur, minus erunt: quam ſi ſecundum diametrum. </s> <s id="id.002672">Iuxta ea quæ <lb></lb>demonſtrata ſunt cap. 15. lib. huius. </s> <s id="id.002673">Namque vt recta percußio ad <lb></lb>medium ligni oblongi facta facile ipſum frangit: ſic tractio firma <lb></lb>è directo à medio. </s> <s id="id.002674">Eſt enim tractio percuſsionis ſpecies, vel princi<lb></lb>pium. </s> <s id="id.002675">Et celerrimè rumpuntur, ſi ſecundum naturam, id eſt eam op<lb></lb>portunitatem rumpantur. </s> <s id="id.002676">Non ergo lora ſecundum diametrum ex<lb></lb>tendi debent: verum obliquitus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002677">Præterea quoniam.] <emph type="italics"></emph>Secunda eſt ratio. </s> <s id="id.002678">Lora eo potius exten<lb></lb>denda modo, quo commodius onus decumbentis hominis etiam ſeſe <lb></lb>reuoluentis ferre & ſuſtinere valent, & quam minimùm à ſua ex<lb></lb>tenſione relaxari. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002679"><emph type="italics"></emph>Extenſa obliquitus hæc præſtant propter æqualitatem, per quam <lb></lb>non eſt, cur vnum plus, vel citius relaxetur: quam aliud. </s> <s id="id.002680">Et quod <lb></lb>in ea parte lecti ſeſe implicent vires ſuas iungentia, in medio ſcili<lb></lb>cet, vbi etiam onus corporis grauius eſt, nempe truncus corporis <lb></lb>vna cum natibus: non autem ita in extremis, vbi caput & pedes <lb></lb>leuiora accubant. </s> <s id="id.002681">Hæc vero non perinde præſtant extenſa ſecun<lb></lb>dum diametrum, hoc enim quod <expan abbr="lõgius">longius</expan> eſt breuiori citius relaxa<lb></lb>tur, & ſic ferendo, ſuſtinendo ve oneri relinquit imbecillius. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002682">Præterea etiam.] <emph type="italics"></emph>Tertia ratio. </s> <s id="id.002683">Lororum quantitas obliquitus <lb></lb>extentorum minor eſt: quam ſecundum diametrum. </s> <s id="id.002684">Vt autem ſint <lb></lb>parui pretij, abſtinendum tamen à ſuperfluis. </s> <s id="id.002685">fruſtrà enim fit per plu<lb></lb>ra, quod fieri poteſt per pauciora. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002686"><foreign lang="el">e)/stw ga\r kli/nh h( *a*z*h*i, kai\ di/xa <lb></lb>dih|rh/sqw h( *z*h kata\ to\ *b. i)/sa dh\ truph/mata/ e)stin <lb></lb>e)n th=| *z*b kai\ e)n th=| *z*a. kai\ ga\r ai( pleurai\ i)/sai ei)si/n: <lb></lb>h( ga\r o(/lh *z*h diplasi/a e)sti/n.</foreign></s> <s id="g0132507"><foreign lang="el">e)ntei/nousi d' w(s ge/graptai, <lb></lb>a)po\ tou= *a e)pi\ to\ *b, ei)=ta ou(= to\ *g, ei)=ta ou(= to\ *d, ei)=ta ou(= <lb></lb>to\ *q, ei)=ta ou(= to\ *e. kai\ ou(/tws a)ei/, e(/ws a)\n ei)s gwni/an <lb></lb>katastre/ywsin a)/llhn: </foreign></s> <s id="g0132508"><foreign lang="el">du/o ga\r e)/xousi gwni/ai ta\s a)rxa\s <lb></lb>tou= sparti/ou.</foreign></s> <s id="g0132509"><foreign lang="el">i)/sa de/ e)sti ta\ sparti/a kata\ ta\s ka/myeis, <lb></lb>to/ te *a*b kai\ *b*g tw=| *g*d kai\ *d*q. kai\ ta\ a)/lla de\ <lb></lb>ta\ toiau=ta/ e)stin, o(/ti ou(/tws e)/xei h( au)th\ a)po/deicis.</foreign></s> <s id="g0132510"><foreign lang="el">h( me\n <lb></lb>ga\r *a*b th=| *e*q i)/sh: i)/sai ga/r ei)sin ai( pleurai\ tou= *b*h*k <lb></lb>*a xwri/ou, kai\ ta\ truph/mata i)/sa die/sthken.</foreign></s> <s id="g0132511"><foreign lang="el">h( de\ *b*h i)/sh <lb></lb>th=| *k*a: h( ga\r *b gwni/a i)/sh th=| *h. e)n i)/sois ga\r h( me\n <lb></lb>e)kto/s, h( de\ e)nto/s: kai\ h( me\n *b e)sti\n h(mi/seia o)rqh=s: h( <lb></lb>ga\r *z*b i)/sh th=| *z*a: kai\ gwni/a de\ h( kata\ to\ *z o)rqh/.</foreign></s> <s id="g0132512"><foreign lang="el">h( <lb></lb>de\ *b gwni/a i)/sh th=| kata\ to\ *h: h( ga\r kata\ to\ *z o)rqh/, <lb></lb>e)peidh\ diplasio/pleuron to\ e(tero/mhkes kai\ pro\s me/son ke/klastai. <lb></lb>w(/ste h( *a*g th=| *e*h i)/sh. tau/th| de\ h( *k*q: para/llhlos <lb></lb>ga/r. w(/ste h( *b*g i)/sh th=| *k*q. h( de\ *g*e th=| *d*q.</foreign></s> <s id="g0132513"><foreign lang="el"><lb></lb>o(moi/ws de\ kai\ ai( a)/llai dei/knuntai o(/ti i)/sai ei)si\n ai( kata\ <lb></lb>ta\s ka/myeis du/o tai=s dusi/n.</foreign></s> <s id="g0132514"><foreign lang="el">w(/ste dh=lon o(/ti ta\ thlikau=ta <lb></lb>sparti/a o(/son to\ *a*b, te/ssara tosau=t' e)/nestin e)n th=| kli/nh|: </foreign></s> <s id="g0132515"><foreign lang="el"><lb></lb>o(/son d' e)sti\ to\ plh=qos tw=n e)n th=| *z*h pleura=| truphma/twn, <lb></lb>kai\ e)n tw=| h(mi/sei tw=| *z*b ta\ h(mi/sh.</foreign></s> <s id="g0132516"><foreign lang="el">w(/ste e)n th=| h(misei/a| <lb></lb>kli/nh| thlikau=ta mege/qh sparti/wn e)sti\n o(/son tw=| *b*a e)/nesti, <lb></lb>tosau=ta de\ to\ plh=qos o(/saper e)n tw=| *b*h truph/mata.</foreign></s> <s id="g0132517"><foreign lang="el"><lb></lb>tau=ta de\ ou)de\n diafe/rei le/gein h)\ o(/sa e)n th=| *a*z kai\ *b*z <lb></lb>ta\ suna/mfw.</foreign></s> <s id="g0132518"><foreign lang="el">ei) de\ kata\ dia/metron e)ntaqh=| ta\ sparti/a, <lb></lb>w(s e)n th=| *a*b*g*d kli/nh| e)/xei, ta\ h(mi/sea/ ei)sin ou) tosau=ta<lb></lb> o(/sa ai( pleurai\ a)mfoi=n, ai( *a*z *z*h: ta\ i)/sa de/, o(/sa <lb></lb>e)n tw=| *z*b*z*a truph/mata e)/nestin.</foreign></s> <s id="g0132519"><foreign lang="el">mei/zones de/ ei)sin ai( *a*z <lb></lb>*b*z du/o ou)=sai th=s *a*b. w(/ste kai\ to\ sparti/on mei=zon tosou/tw| <lb></lb>o(/son ai( pleurai\ a)/mfw mei/zous ei)si\ th=s diame/trou.</foreign></s> </p> <p type="main"> <s id="id.002687">Sit lectus <foreign lang="el">a z h i,</foreign> & <foreign lang="el">z h</foreign><lb></lb>bifariam diuidatur, vt in <foreign lang="el">b. </foreign><lb></lb></s> <s>Æqualia itaque ſunt fora<lb></lb>mina, tum in <foreign lang="el">z b,</foreign> tum in <foreign lang="el">z <lb></lb>a.</foreign> </s> <s>Æqualia enim ſunt la<lb></lb>tera. </s> <s id="id.002688">Nam totum <foreign lang="el">z h</foreign> du<lb></lb>plum eſt [<foreign lang="el">z a. </foreign>] </s> <s>Extendunt <lb></lb>verò vt ſcriptum eſt ab <pb xlink:href="035/01/218.jpg" pagenum="178"></pb><foreign lang="el">a</foreign> ad <foreign lang="el">b</foreign>: deinde vbi eſt <foreign lang="el">g</foreign>: <lb></lb>poſtea vbi <foreign lang="el">d,</foreign> poſtea vbi <foreign lang="el">q,</foreign><lb></lb>deinceps vbi <foreign lang="el">e,</foreign> & ſic ſem<lb></lb>per quouſque ad alium <expan abbr="cõuerterint">con<lb></lb>uerterint</expan> angulum. </s> <s id="id.002689">Duo <lb></lb>etenim anguli habent fu<lb></lb>nis principia. </s> <s id="id.002690">Sunt verò fu<lb></lb>nes iuxta curuaturas æqua<lb></lb>les, nempe <foreign lang="el">a b</foreign> & <foreign lang="el">b g</foreign> ipſi <lb></lb><foreign lang="el">g d</foreign> & <foreign lang="el">d q</foreign>. </s> <s>Et alij ſunt eiuſ<lb></lb>modi, quod eadem ſit de<lb></lb>monſtratio. </s> <s id="id.002691">Etenim <foreign lang="el">a b</foreign> æ<lb></lb>qualis eſt ipſi <foreign lang="el">e q.</foreign> </s> <s><expan abbr="Sũt">Sunt</expan> enim <lb></lb>æqualia latera parallelo<lb></lb>grammi <foreign lang="el">b h k a,</foreign> & forami<lb></lb>na æquediſtant: Æqualis <lb></lb>vero eſt <foreign lang="el">b h</foreign> ipſi <foreign lang="el">k a.</foreign> </s> <s>Nam <lb></lb>angulus <foreign lang="el">b</foreign> æqualis ipſi <foreign lang="el">h.</foreign> </s> <s>In <lb></lb>parallelis enim hic <expan abbr="quidẽ">quidem</expan> <lb></lb>interior eſt, ille externus, & <lb></lb><foreign lang="el">b</foreign> eſt ſemirectus. </s> <s id="id.002692">Eſt enim <foreign lang="el">z <lb></lb>b</foreign> æqualis ipſi <foreign lang="el">z a,</foreign> & angu<lb></lb>lus qui ad <foreign lang="el">z</foreign> rectus, & angu<lb></lb>lus <foreign lang="el">b</foreign> æqualis ei qui ad <foreign lang="el">h.</foreign> <lb></lb></s> <s>Nam qui ad <foreign lang="el">z</foreign> rectus. </s> <s id="id.002693">quo<lb></lb>niam lateribus duplum al<lb></lb>terolongum, & ad medium <lb></lb>curuatum eſt. </s> <s id="id.002694">Itaque <foreign lang="el">a d</foreign><lb></lb>æqualis ipſi <foreign lang="el">e h,</foreign> huic verò <lb></lb>ipſa <foreign lang="el">k q</foreign> parallela. </s> <s id="id.002695">itaque <foreign lang="el">b <lb></lb>g</foreign> æqualis eſt ipſi <foreign lang="el">k q,</foreign> & <foreign lang="el">g e</foreign><lb></lb>ipſi <foreign lang="el">d q.</foreign> </s> <s>Similiter & alię <expan abbr="demõſtrãtur">de<lb></lb>monſtrantur</expan>, quod ſint æqua<lb></lb>les in curuaturis duæ dua<lb></lb>bus. </s> <s id="id.002696">Itaque clarum eſt quod tanti ſunt in lecto funes: <lb></lb>quanta eſt <foreign lang="el">a b</foreign> quater. </s> <s id="id.002697">Quanta eſt autem multltudo <pb xlink:href="035/01/219.jpg" pagenum="179"></pb>foraminum in latere <foreign lang="el">z h,</foreign><lb></lb>etiam in dimidio quod eſt <lb></lb><foreign lang="el">z b</foreign> <expan abbr="dimidiũ">dimidium</expan> eſt. </s> <s id="id.002698">Quare in <lb></lb>dimidio lecti, <expan abbr="tãta">tanta</expan> erit ma<lb></lb>gnitudo funium: quantum <lb></lb>eſt <foreign lang="el">a b.</foreign> </s> <s>Multitudine vero <lb></lb>tot: quot ſunt in <foreign lang="el">b h</foreign> fora<lb></lb>mina. </s> <s id="id.002699">Quod perinde eſt ac <lb></lb>dicere quot ſunt in <foreign lang="el">a z</foreign> & <lb></lb><foreign lang="el">b z</foreign> ſimul ſumptis. </s> <s id="id.002700">Si vero <lb></lb>ſecundum diametrum <expan abbr="extendãtur">ex<lb></lb>tendantur</expan> funes, vt in lecto <lb></lb><foreign lang="el">a b g d</foreign> ſehabent, dimidia <lb></lb>ſunt, non tot: quot latera <lb></lb>vtrorum que <foreign lang="el">a z, z h.</foreign> </s> <s>æqua<lb></lb>lia vero foramina inſunt <lb></lb>quot in <foreign lang="el">z b, z a,</foreign> duæ vero <lb></lb>cum ſint <foreign lang="el">a z, b z,</foreign> maiores <lb></lb>ſunt ipſa <foreign lang="el">a b.</foreign> </s> <s>Itaque funis <lb></lb>tanto maior: quanto ambo <lb></lb>latera maiora ſunt diame<lb></lb>tro. </s> </p> <p type="head"> <s id="id.002701">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002702">Sit lectus <foreign lang="el">a z h i. </foreign>] <emph type="italics"></emph>In tertia ratione ſecundæ quæſtionis expli<lb></lb>canda reliquus Ariſtotelis contextus totus eſt: ſed adeo mendoſus <lb></lb>& in verbis, & in diagrammatis, & in diagrammatum characte<lb></lb>ribus, vt ſi Iuppiter cum Æſculapio mederi, & mendas eluere ve<lb></lb>lit, non poßit tamen: ideò ſatius eſt cum ſit nota philoſophi ſenten<lb></lb>tia, totum adimere, & alium ſupplere. </s> <s id="id.002703">Obſcuritas ex tam corru<lb></lb>pto contextu manans fecit, vt nonnulli interpretes Cardano non ſa<lb></lb>tisfecerint, qui negotium numeris abſoluunt, cum tamen demonſtra<lb></lb>tionem geometricam inſtituerint, neque in figuris lectorum aſſum<lb></lb>ptis, & in contextu neſcio à quibus poſitis, eundem numerum linea<lb></lb>rum retineant. </s> <s id="id.002704">Sed in vna octo, in altera decem, non debuerit <emph.end type="italics"></emph.end><pb xlink:href="035/01/220.jpg" pagenum="180"></pb><emph type="italics"></emph>idem numerus vbique eſſe: ſi quidem magnum quid ſit & demon<lb></lb>ſtratu dignum, minus lororum in vna extenſione expendi: quam in <lb></lb>altera: qui <expan abbr="deniq;">denique</expan> in vtraque figura obliquas <expan abbr="habẽt">habent</expan> lineas, quanquam <lb></lb>alias alijs obliquiores: & tamen duæ antehac rationes videntur in <lb></lb>vna figura poſtulare obliquas, in altera rectas. </s> <s id="id.002705">Nos igitur aliter Car<lb></lb>dani veſtigia obſcura, & ni fallor imperfecta, vt ſunt <expan abbr="pleraq;">pleraque</expan> huius <lb></lb>hominis ferè omnia vt arbitror, <expan abbr="quanquã">quanquam</expan> ſemper ingeniosè ſcriben<lb></lb>tis, ſecuti, apertius & perfectius totum hoc <expan abbr="negotiũ">negotium</expan> euoluemus. </s> <s id="id.002706">At<lb></lb>que in primis dicimus extendi lora ſecundum diametrum, non eſſe <lb></lb>ab angulo ad angulum oppoſitum: ſed ſecundum rectas, quæ à latere <lb></lb>ad latus oppoſitum extenduntur, vt ſint aliæ ſecundum longitudi<lb></lb>nem, aliæ ſecundum latitudinem. </s> <s id="id.002707">Sic enim diameter non<emph.end type="italics"></emph.end> <foreign lang="el">diagw/nios</foreign><lb></lb><emph type="italics"></emph>ſumi videtur: quaſi dimetiens, vt quæ dimetiatur longitudinem vel <lb></lb>latitudinem, æqualis videlicet facta, quo modo licet hîc ab Ariſto<lb></lb>tele reiecto, hodie adhuc vtuntur. </s> <s id="id.002708">Atque hoc modo ſi non intelliga<lb></lb>tur diameter: ſed<emph.end type="italics"></emph.end> <foreign lang="el">diagw/nios,</foreign> <emph type="italics"></emph>tam obliquæ erunt in vna forma li<lb></lb>neæ: quam in altera: ſicque quæ de ruptione vel fißione & opportu<lb></lb>nitate dicta ſunt, hîc non conuenient, quod eſſet abſurdum. </s> <s id="id.002709">His igi<lb></lb>tur ita poſitis deſcribantur duæ formæ lecti, in quibus ſint lineæ nu<lb></lb>mero pares, ſitu diuerſæ. </s> <s id="id.002710">Sit igitur prima A B C D, cuius la<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.220.1.jpg" xlink:href="035/01/220/1.jpg"></figure><lb></lb><emph type="italics"></emph>tus A B duplum ſit lateris A C, & quidem illud 4. pe<lb></lb>dum, hoc duorum. </s> <s id="id.002711">In hac lora ſecundum diametrum ſint quidem <lb></lb>ſecundum longitudinem tria K N. </s> <s id="id.002712">L O, M P, & ſic inter ſe <emph.end type="italics"></emph.end><pb xlink:href="035/01/221.jpg" pagenum="181"></pb><emph type="italics"></emph>& lateri A B æqualia prop. 34. lib. 1. </s> <s>Sint & totidem G Q, <lb></lb>E F, H R ſecundum latitudinem extenſa, interſe quoque, & la<lb></lb>teri A C æqualia per eandem. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002713"><emph type="italics"></emph>Sit ſecunda forma<emph.end type="italics"></emph.end> <foreign lang="el">a b g d</foreign> <emph type="italics"></emph>in eadem ratione laterum, & ea<lb></lb>dem magnitudine ſeruata, & linearum ſed obliquarum æquali nu<lb></lb>mero, quæ ſint<emph.end type="italics"></emph.end> <foreign lang="el">a c, h k, e d</foreign> <emph type="italics"></emph>tum <emph.end type="italics"></emph.end> <foreign lang="el">b c, q i, e g,</foreign> <emph type="italics"></emph>quæ quia pa<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.221.1.jpg" xlink:href="035/01/221/1.jpg"></figure><lb></lb><emph type="italics"></emph>rallelæ ſunt, & aduerſæ in ſuis parallelogrammis, omnes inter ſe <lb></lb>æquales ſunt prop. 34. lib. 1. </s> <s>Nam poſito quod<emph.end type="italics"></emph.end> <foreign lang="el">a c</foreign> <emph type="italics"></emph>ſit ab angulo<emph.end type="italics"></emph.end> <foreign lang="el">a</foreign><lb></lb><emph type="italics"></emph>ad<emph.end type="italics"></emph.end> <foreign lang="el">c</foreign> <emph type="italics"></emph>medium lateris<emph.end type="italics"></emph.end> <foreign lang="el">g d</foreign><emph type="italics"></emph>: erit hæc æqualis ipſi<emph.end type="italics"></emph.end> <foreign lang="el">b c,</foreign> <emph type="italics"></emph>quia latera <lb></lb>æqualium quadratorum. </s> <s id="id.002714">Vtrumque enim æquale eſt duobus ex<emph.end type="italics"></emph.end> <foreign lang="el">a g, <lb></lb>g c,</foreign> <emph type="italics"></emph>vel quod idem eſt ex<emph.end type="italics"></emph.end> <foreign lang="el">c d, d b</foreign> <emph type="italics"></emph>prop. 47. lib. 1. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002715"><emph type="italics"></emph>Dico ergo quod lorum K N cum G Q, id eſt A C, A B ma<lb></lb>ius eſt<emph.end type="italics"></emph.end> <foreign lang="el">a c, c b,</foreign> <emph type="italics"></emph>& duo pariter accepta duobus pariter acceptis eſſe <lb></lb>maiora: ſicque totum lorum in lecto A B C D maius eſſe toto, <lb></lb>quod eſt in lecto<emph.end type="italics"></emph.end> <foreign lang="el">a b g d. </foreign></s> </p> <p type="main"> <s id="id.002716"><emph type="italics"></emph>Demonſtratio. </s> <s id="id.002717">Quia rectangulum ſub A C, A B comprehen<lb></lb>ſum duplum eſt quadrati ex A C prop. 1. lib. 6. & rectangulum ſub<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">a c, c b</foreign> <emph type="italics"></emph>duplum <expan abbr="itẽ">item</expan> eſt quadrati ex A C. </s> <s id="id.002718">Ipſum enim <expan abbr="cũ">cum</expan> quadratum <lb></lb>ſit. </s> <s id="id.002719"><expan abbr="Nã">Nam</expan><emph.end type="italics"></emph.end> <foreign lang="el">a c</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">c b</foreign> <emph type="italics"></emph>ſunt æquales ex fabrica, æquale eſt prop. 47. lib. 1. <lb></lb>duobus quadratis ex A C & C F: ſed quod idem eſt ex<emph.end type="italics"></emph.end> <foreign lang="el">a g</foreign> <emph type="italics"></emph>&<emph.end type="italics"></emph.end> <foreign lang="el">g c,</foreign><lb></lb><emph type="italics"></emph>æqualibus ex hypoth. erit <expan abbr="rectangulũ">rectangulum</expan> ſub A C, A B comprehenſum <lb></lb>rectangulo ſub<emph.end type="italics"></emph.end> <foreign lang="el">a c, c b</foreign> <emph type="italics"></emph>comprehenſo. axiom. 6. & per idem rectan<lb></lb>gulum bis ſub A C, A B comprehenſum, rectangulo bis ſub<emph.end type="italics"></emph.end> <foreign lang="el">a c, c b</foreign><pb xlink:href="035/01/222.jpg" pagenum="182"></pb><emph type="italics"></emph>comprehenſo æquale: ſed & quadratum ex A B æquale eſt quadratis <lb></lb>ex<emph.end type="italics"></emph.end> <foreign lang="el">a z, z b</foreign> <emph type="italics"></emph>prop. 47. lib. 1. </s> <s>Eſt enim angulus<emph.end type="italics"></emph.end> <foreign lang="el">a z b</foreign> <emph type="italics"></emph>rectus, cum ſit <lb></lb>reliquus trium<emph.end type="italics"></emph.end> <foreign lang="el">a z g, a z b, b z d</foreign> <emph type="italics"></emph>duobus rectis æqualium prop. 13. <lb></lb>lib. 1. ſublatis duobus ſemirectis<emph.end type="italics"></emph.end> <foreign lang="el">a z g, b z d</foreign> <emph type="italics"></emph>per coroll. prop. 32. lib. 1. <lb></lb></s> <s id="id.002723">Erunt igitur quadrata ex A B, A C cum rectangulo bis ſub A C, <lb></lb>A B comprehenſo maiora quadratis ex<emph.end type="italics"></emph.end> <foreign lang="el">a z, z b</foreign> <emph type="italics"></emph>cum rectangulo <lb></lb>bis ſub<emph.end type="italics"></emph.end> <foreign lang="el">a z, z b</foreign> <emph type="italics"></emph>comprehenſo per quantitatem quadrati ex A C: <lb></lb>ſed quadrata ex A B, A C cum rectangulo bis comprehenſo ſub <lb></lb>A B, A C ſunt potentia lineæ C A B vtcunque ſectæ in A, id eſt <lb></lb>æqualia ſunt quadrato ex C A B prop. 4. lib. 2. & per eandem qua<lb></lb>drata ex<emph.end type="italics"></emph.end> <foreign lang="el">a z, z b</foreign> <emph type="italics"></emph>cum rectangulo bis comprehenſo ſub<emph.end type="italics"></emph.end> <foreign lang="el">a z, z b</foreign> <emph type="italics"></emph>ſunt <lb></lb>potentia lineæ<emph.end type="italics"></emph.end> <foreign lang="el">a z b</foreign> <emph type="italics"></emph>vtcunque ſectæ in<emph.end type="italics"></emph.end> <foreign lang="el">z.</foreign> </s> <s><emph type="italics"></emph>Eſt ergo C A B maior <lb></lb>potentia quam<emph.end type="italics"></emph.end> <foreign lang="el">a z b,</foreign> <emph type="italics"></emph>proinde erit & longitudine maior per coroll. <lb></lb>è prop. 47. lib. 1. </s> <s>Similiter demonſtrabitur de reliquis. </s> <s id="id.002725">Eſt ergo maior <lb></lb>lororum quantitas in lecto A B C D: quam in lecto<emph.end type="italics"></emph.end> <foreign lang="el">a b d g,</foreign> <emph type="italics"></emph>quod <lb></lb>erat demonſtrandum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002726"><emph type="italics"></emph>His ita geometricè demonſtratis, nihil nunc obeſt exquirere, quæ <lb></lb>ſit ex hac forma ſecunda in loris parſimonia. </s> <s id="id.002727">Cum igitur in lecto A <lb></lb>B C D quæ tres ſunt ſecundum longitudinem extenſæ, æquales ſint <lb></lb>ſingulæ lateri A C quod eſt ſex pedum: ſimul ſumptæ erunt 18. pe<lb></lb>dum: & reliquæ ſecundum latitudinem ſingulæ ipſi A C æquales, <lb></lb>faciunt 9. pedes, ideo omnes ſunt 27. pedes lororum. </s> <s id="id.002728">In lecto vero<emph.end type="italics"></emph.end><lb></lb><foreign lang="el">a b g d</foreign> <emph type="italics"></emph>cum omnes æquales lineæ ſint ipſi<emph.end type="italics"></emph.end> <foreign lang="el">a z,</foreign> <emph type="italics"></emph>& ſit ex<emph.end type="italics"></emph.end> <foreign lang="el">a z</foreign> <emph type="italics"></emph>qua<lb></lb>dratum æquale quadratis ex<emph.end type="italics"></emph.end> <foreign lang="el">a g, & g z</foreign> <emph type="italics"></emph>id eſt 9. & 9. </s> <s>Erit igitur <lb></lb>18. quadratum ex<emph.end type="italics"></emph.end> <foreign lang="el">a z,</foreign> <emph type="italics"></emph>cuius radix quadrata ferè eſt 4 2/9, quæ per 6. <lb></lb>multiplicata facit 25 1/3 qui numerus ſuperatur à 27. per 1 2/3. </s> <s>Atque <lb></lb>hoc in loris compendium eſt, quod licet exiguum, non contemnen<lb></lb>dum tamen. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002729">Et ſic ſemper.] <emph type="italics"></emph>Videtur Ariſtoteles voluiſſe in vno lecto fu<lb></lb>nem vnum eſſe continuum, & per parallelogramma diſpergi atque <lb></lb>extendi. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002730">Iuxta curuaturas.] <foreign lang="el">ka/myis</foreign> <emph type="italics"></emph>curuatura reſtium vocatur ea <lb></lb>pars quæ à foramine ad foramen ipſis extrinſecus applicatur ſpon<lb></lb>dis, parallelogrammorumque à reſtibus ſeu loris effectorum minora <lb></lb>efficiunt latera. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002731">Sunt enim æqualia latera.] <emph type="italics"></emph>Deinceps ad finem corruptißi<emph.end type="italics"></emph.end><pb xlink:href="035/01/223.jpg" pagenum="183"></pb><emph type="italics"></emph>ma ferè ſunt omnia. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002732">Angulus qui ad <foreign lang="el">z</foreign> rectus.] <emph type="italics"></emph>Angulus qui ad<emph.end type="italics"></emph.end> <foreign lang="el">z</foreign> <emph type="italics"></emph>continetur à <lb></lb>lateribus<emph.end type="italics"></emph.end> <foreign lang="el">z h, z a</foreign> <emph type="italics"></emph>rectanguli lecti, itaque rectus eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002733">Angulus <foreign lang="el">b</foreign>] <emph type="italics"></emph>Id eſt angulus<emph.end type="italics"></emph.end> <foreign lang="el">z b a</foreign> <emph type="italics"></emph>æqualis eſt angulo<emph.end type="italics"></emph.end> <foreign lang="el">b h k</foreign><lb></lb><emph type="italics"></emph>quod verum eſt. </s> <s id="id.002734">quia ſunt anguli externus & internus ad eaſdem <lb></lb>partes duarum parallelarum<emph.end type="italics"></emph.end> <foreign lang="el">a b, k h</foreign> <emph type="italics"></emph>incidente in ipſas recta<emph.end type="italics"></emph.end> <foreign lang="el">z h. </foreign></s> </p> <p type="main"> <s id="id.002735">In parallelis enim.] <emph type="italics"></emph>Quod hic dicit Ariſtoteles<emph.end type="italics"></emph.end> <foreign lang="el">i)/sas gra/mmas</foreign><lb></lb><emph type="italics"></emph>vertimus parallelas. </s> <s id="id.002736">Sic enim etiam locutus eſt cap. 5. lib. 1. poſteriore <lb></lb>analytic. </s> <s id="id.002737">Si quis igitur inquit demonſtrauerit, quod rectæ non con<lb></lb>currant, videatur huius eſſe <expan abbr="demõſtratio">demonſtratio</expan>. </s> <s id="id.002738">quia in omnibus ſit rectis. <lb></lb></s> <s id="id.002739">Non eſt autem, ſiquidem non, quod ſic æquales ſint, id fit: ſed quate<lb></lb>nus quomodolibet æquales. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002740">Similiter & aliæ.] <emph type="italics"></emph>Ex tribus diagrammatis in contextu deſcri<lb></lb>ptis quod ſecundum eſt oſtendit, extenſionem funium breuiorem ea, <lb></lb>quæ in primo, & tertio eſt, vt argumento problematis conuenire vi<lb></lb>deatur. </s> <s id="id.002741">Eſt enim <expan abbr="lõgitudo">longitudo</expan> funium in eo duntaxat 28. pedum cum 4/5 <lb></lb>vnius pedis: cum in primò ſit 34. pedum ferè, & in tertio 40 1/2 fere. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002742">27. <foreign lang="el">*dia\ ti/ xalepw/teron ta\ <lb></lb>makra\ cu/la a)p' a)/krou <lb></lb>fe/rein e)pi\ tw=| w)/mw| h)\ kata\ to\ me/son.</foreign></s> </p> <p type="main"> <s id="id.002743">27. Cur difficilius longa li<lb></lb>gna humero feruntur ab <lb></lb>extremo: quam à medio <lb></lb>ſui. </s> </p> <p type="main"> <s id="id.002744"><foreign lang="el">*dia\ ti/ xalepw/teron ta\ makra\ cu/la a)p' a)/krou <lb></lb>fe/rein e)pi\ tw=| w)/mw| h)\ kata\ to\ me/son, i)/sou tou= ba/rous o)/ntos; </foreign></s> <s id="g0132602"><foreign lang="el"><lb></lb>po/teron o(/ti saleuome/nou tou= cu/lou to\ a)/kron kwlu/ei fe/rein, <lb></lb>ma=llon a)ntispw=n th=| saleu/sei th\n fora/n; h)\ ka)\n <lb></lb>mhqe\n ka/mpthtai mhd' e)/xh| polu\ mh=kos, o(/mws xalepw/teron <lb></lb>fe/rein a)p' a)/krou; a)ll' o(/ti kai\ r(a=|on ai)/retai a)p' <lb></lb>a)/krou h)\ e)k me/sou, dia\ to\ au)to\ kai\ fe/rein ou(/tw r(a/|dion.</foreign></s> </p> <p type="main"> <s id="id.002745">Cur difficilius feruntur <lb></lb>humero longa ligna ab ex<lb></lb>tremo: <expan abbr="quã">quam</expan> à medio ſui, vt <lb></lb>æquale ſit <expan abbr="põdus">pondus</expan>. </s> <s id="id.002746">An quod <lb></lb><expan abbr="extremũ">extremum</expan> ligni agitati ferri <lb></lb>prohibet, vt quod <expan abbr="geſtationẽ">geſtatio<lb></lb>nem</expan> agitatione magis reuel<lb></lb>lat? </s> <s id="id.002747">An quoniam, licet nihil <lb></lb>incuruetur, <expan abbr="neq;">neque</expan> valdè <expan abbr="maiorẽ">ma<lb></lb>iorem</expan> <expan abbr="lõgitudinem">longitudinem</expan> habeat, <lb></lb><expan abbr="tamẽ">tamen</expan> ab extremo ferre dif<lb></lb>ficilius eſt: ſed quod faci<lb></lb>lius à medio ſubleuetur: <lb></lb>quam ab extremo. </s> <s id="id.002748">Ob id ipſum etiam facilius fertur. </s> </p> <pb xlink:href="035/01/224.jpg" pagenum="184"></pb> <p type="head"> <s id="id.002749">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002750">Cvr difficilius.] <emph type="italics"></emph>Huius capitis problema eſt cur lignum lon<lb></lb>gum difficilius ex humero fertur per extremum: quam per me<lb></lb>dium. </s> <s id="id.002751">Huic dupliciter reſpondetur. </s> <s id="id.002752">Prima reſponſio eſt ſpecialis ad <lb></lb>lignum quod flexile ſi ſit incuruatur, & nutat. </s> <s id="id.002753">Nutatio autem cum <lb></lb>ſit motus ad alium terminum: quam ad quem fertur, impedit. </s> <s id="id.002754">quin <lb></lb>& aggrauans premit magis ferentem. </s> <s id="id.002755">Secunda eſt generalis ex ele<lb></lb>uatione faciliori, quæ ſic concludetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002756"><emph type="italics"></emph>Quo modo lignum vel pondus facilius eleuatur, eodem & fer<lb></lb>tur. </s> <s id="id.002757">Eleuatio enim geſtatio quædam eſt, & etiam geſtationis <lb></lb>pars difficilior, cum ſit ad contrarium omnino terminum, vt <lb></lb>ſurſum: geſtatio verò lateraliter reliqua fiat. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002758"><emph type="italics"></emph>At lignum longum facilius per medium: quam per extre<lb></lb>mum eleuatur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002759"><emph type="italics"></emph>Ergo lignum longum facilius ex humero fertur per medium: <lb></lb>quam per extremum. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002760"><foreign lang="el">ai)/tion de\ o(/ti e)k me/sou me\n ai)ro/menon a)ei\ e)pikoufi/zei a)/llhla <lb></lb>ta\ a)/kra, kai\ qa/teron me/ros to\ e)pi\ qa/teron eu)= ai)/rei. <lb></lb>w(/sper ga\r ke/ntron gi/netai to\ me/son, h(=| e)/xei to\ ai)=ron h)\ <lb></lb>fe/ron.</foreign></s> <s id="g0132604"><foreign lang="el">ei)s to\ a)/nw ou)=n koufi/zetai e(ka/teron tw=n a)/krwn ei)s <lb></lb>to\ ka/tw r(e/pon. a)po\ de\ tou= a)/krou ai)ro/menon h)\ fero/menon ou) <lb></lb>poiei= tou=to, a)ll' a(/pan to\ ba/ros r(e/pei e)f' e(\n me/son, ei)s <lb></lb>o(/per ai)/retai h)\ fe/retai.</foreign></s> <s id="g0132605"><foreign lang="el">e)/stw me/son e)f' ou(= *a, a)/kra *b*g.</foreign></s> <s id="g0132606"><foreign lang="el"><lb></lb>ai)rome/nou ou)=n h)\ ferome/nou kata\ to\ *a, to\ me\n *b ka/tw <lb></lb>r(e/pon a)/nw ai)/rei to\ *g, to\ de\ *g ka/tw r(e/pon to\ *b a)/nw ai)/rei: <lb></lb>a(/ma de\ ai)ro/mena a)/nw poiei= tau=ta.</foreign></s> </p> <p type="main"> <s id="id.002761">Cauſa vero eſt, quod ex <lb></lb>medio ſubleuato ſemper <lb></lb>extrema ſe inuicem ſuble<lb></lb>uant: & altera pars alteram <lb></lb>promptè attollit. </s> <s id="id.002762">Medium <lb></lb>enim quod habet <expan abbr="ſubleuãs">ſubleuans</expan> <lb></lb>vel <expan abbr="ferẽs">ferens</expan> efficitur tanquam <lb></lb>centrum. </s> <s id="id.002763">Itaque <expan abbr="vtrumq;">vtrumque</expan> <lb></lb>extremorum deorſum ver<lb></lb>gens ſurſum ſuſpenditur. <lb></lb></s> <s id="id.002764">At ab extremo <expan abbr="eleuatũ">eleuatum</expan> vel <lb></lb>geſtatum non idem facit: <lb></lb>quin totum onus vergit ad <lb></lb>medium vnum quò eleua<lb></lb>tur vel fertur. </s> <s id="id.002765">Hoc ſit <foreign lang="el">a,</foreign><lb></lb>extrema <foreign lang="el">b, g.</foreign> </s> <s>Igitur eleuato <lb></lb>vel geſtato qua parte eſt <foreign lang="el">a</foreign>: <pb xlink:href="035/01/225.jpg" pagenum="185"></pb><figure id="id.035.01.225.1.jpg" xlink:href="035/01/225/1.jpg"></figure><lb></lb><foreign lang="el">b</foreign> quidem deorſum ver<lb></lb>gens attollit <foreign lang="el">g</foreign>:<foreign lang="el">g</foreign> vero deor<lb></lb>ſum repens attollit <foreign lang="el">b.</foreign> </s> <s>Si<lb></lb>mul autem eleuata idem præſtant. </s> </p> <p type="head"> <s id="id.002766">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002767">Cauſa vero.] <emph type="italics"></emph>Confirmatio eſt aſſumptionis ex æquis extremo<lb></lb>rum ponderibus vicißim ob id ſe ſubleuantibus: ſi enim vnius <lb></lb>propenſio vergit deorſum: alterius reſiſtentia ad motum ſurſum im<lb></lb>pediet. </s> <s id="id.002768">Et ſic ſeſe mutuò librantia pondera, mutuò etiam ſe ſubleuant. <lb></lb></s> <s id="id.002769">Eſt enim medium quod fertur, tanquam centrum, à quo extrema vt <lb></lb>æquæ lances in iuſta libra, ſuſpenduntur. </s> <s id="id.002770">Non ita eſt vbi lignum per <lb></lb>extremum fertur: ſed totum ad partem vnam vergit ab eo per quod <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.225.2.jpg" xlink:href="035/01/225/2.jpg"></figure><lb></lb><emph type="italics"></emph>geſtatur deflectens. </s> <s id="id.002771">Ex deflexione autem <lb></lb>ſeu depreßione extremi, tanquam ponderis <lb></lb>prementis, labor augetur in ferente. </s> <s id="id.002772">Ergo <lb></lb>vbi depreßio nulla eſt, vt in priori modo, <lb></lb>ibi labor minor erit. </s> <s id="id.002773">Et ſic lignum lon<lb></lb>gum ab extremo difficilius fertur quam <lb></lb>à medio. </s> <s id="id.002774">Sed hîc etiam quæri poteſt cur <lb></lb>lignum longum puta lancea ab extremo <lb></lb>vno geſtata facilius feratur, ſi perpendi<lb></lb>cularis ſit plano horizontis: <expan abbr="quã">quam</expan> ad ipſum <lb></lb>inclinata. </s> <s id="id.002775">Hoc fit quia in perpendiculari <lb></lb>partes inferiores ſuſtinent ſuperiores: in <lb></lb>inclinata non item, omnes enim ſine ful<lb></lb>cimento tendunt pro natura ſua deorſum. <lb></lb></s> <s id="id.002776">Præterea in perpendiculari ipſa lancea to<lb></lb>ta pondus eſt. </s> <s id="id.002777">Huic ſuſtinendæ quæ vis <emph.end type="italics"></emph.end><pb xlink:href="035/01/226.jpg" pagenum="186"></pb><emph type="italics"></emph>ſufficiet, ſufficiet & <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.226.1.jpg" xlink:href="035/01/226/1.jpg"></figure><lb></lb><emph type="italics"></emph>ferendæ, inque ſuſti<lb></lb>nenda tantum labo<lb></lb>rat: in inclinata ex<lb></lb>tremum eſt hypomoch<lb></lb>lium, à quo non longè <lb></lb>abeſt vis mouens: pon<lb></lb>dus verò quod eſt reli<lb></lb>qua pars, ab hoc extre<lb></lb>mo alterum extremum <lb></lb>quantò longius: tantò <lb></lb>maiorem rationem ad <lb></lb>vim mouentem habe<lb></lb>bit, & ſic difficilius <lb></lb>feretur. <emph.end type="italics"></emph.end></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002778"><foreign lang="el">*dia\ ti/ li/an makro\n ba/ros<lb></lb> xalepw/teron fe/rein e)pi\ tou= <lb></lb>w)/mou, h)\ e)/latton.</foreign></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002779">28. Cur humero difficilius <lb></lb>fertur valdè <expan abbr="lõgum">longum</expan> pon<lb></lb>dus: quam breue. </s> </p> <p type="main"> <s id="id.002780"><foreign lang="el">*dia\ ti/, e)a\n h)=| li/an makro\n to\ au)to\ ba/ros, xalepw/teron <lb></lb>fe/rein e)pi\ tou= w)/mou, ka)\n me/son fe/rh| tis, h)\ e)a\n <lb></lb>e)/latton h)=|; </foreign></s> <s id="g0132702"><foreign lang="el">pa/lai e)le/xqh w(s ou)k e)/stin ai)/tion h( sa/leusis: <lb></lb>a)ll' h( sa/leusis nu=n ai)/tio/n e)stin.</foreign></s> <s id="g0132703"><foreign lang="el">o(/tan ga\r h)=| makro/teron, <lb></lb>ta\ a)/kra saleu/etai, w(/ste ei)/h a)\n kai\ to\n fe/ronta xalepw/teron <lb></lb>fe/rein ma=llon.</foreign></s> <s id="g0132704"><foreign lang="el">ai)/tion de\ tou= saleu/esqai ma=llon, <lb></lb>o(/ti th=s au)th=s kinh/sews ou)/shs meqi/statai ta\ a)/kra, o(/sw|per <lb></lb>a)\n h)=| makro/teron to\ cu/lon.</foreign></s> <s id="g0132705"><foreign lang="el">o( me\n ga\r w)=mos ke/ntron, e)f' <lb></lb>ou(= to\ *a [1me/nei ga\r tou=to]1, ai( de\ *a*b kai\ *a*g ai( e)k tou= <lb></lb>ke/ntrou. o(/sw| d' a)\n h)=| mei=zon to\ e)k tou= ke/ntrou h)\ to\ *a*b <lb></lb>h)\ kai\ to\ *a*g, ple/on meqi/statai me/geqos. de/deiktai de\ <lb></lb>tou=to pro/teron.</foreign></s> </p> <p type="main"> <s id="id.002781">Cur ſi fuerit pondus <expan abbr="idẽ">idem</expan> <lb></lb>valdè longum humero dif<lb></lb>ficilius fertur, <expan abbr="etiã">etiam</expan> vt quis è <lb></lb>medio ferat, quam ſi fuerit <lb></lb>breue. </s> <s id="id.002782">Huius quod antea <lb></lb>dictum eſt, cauſa <expan abbr="nõ">non</expan> eſt: ſed <lb></lb>agitatio cauſa eſt. </s> <s id="id.002783">Quum <lb></lb>enim longius fuerit extre<lb></lb>ma agitantur. </s> <s id="id.002784">Ideo contin<lb></lb>git ferentem multò diffici<lb></lb>lius ferre. </s> <s id="id.002785">Maioris vero agi<lb></lb>tationis cauſa eſt, quod in <lb></lb><expan abbr="eadẽ">eadem</expan> motione extrema <expan abbr="trãſ">tranſ</expan> <lb></lb><expan abbr="ferũtur">feruntur</expan> magis, <expan abbr="quãtò">quantò</expan> <expan abbr="lignũ">lignum</expan> <lb></lb>fuerit longius. </s> <s id="id.002786">Etenim hu<pb xlink:href="035/01/227.jpg" pagenum="187"></pb>merus ſit <expan abbr="cẽtrum">centrum</expan> vbi eſt <foreign lang="el">a. </foreign><lb></lb></s> <s>hoc enim manet. </s> <s id="id.002787">Sint verò <lb></lb><foreign lang="el">a b</foreign> & <foreign lang="el">a g</foreign> lineæ ex centro. <lb></lb></s> <s id="id.002788"><expan abbr="Quãtò">Quantò</expan> igitur fuerit maius <lb></lb>id, quod ex <expan abbr="cẽtro">centro</expan>, vel ipſum <lb></lb><foreign lang="el">a g,</foreign> tantò plus magnitudo <lb></lb>illa transfertur, quod eſt <lb></lb>prius demonſtratum. </s> </p> <p type="head"> <s id="id.002789">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002790">Cvr ſi fuerint.] <emph type="italics"></emph>Huius capitis problema eſt. </s> <s id="id.002791">cur lignum lon<lb></lb>gius è medio geſtatum breuiori eiuſdem ponderis difficilius ex <lb></lb>humero fertur. </s> <s id="id.002792">Cui vt reſpondeat generalem præcedentis ſolutionem <lb></lb>reijcit, & eam quæ ſpecialis fuit de agitatione vtriuſque extremi ad<lb></lb>fert, vt quæ reuellat in alium terminum, contorqueat, & premat fe<lb></lb>rentem. </s> <s id="id.002793">Hæc autem pendet à maiore diſtantia à medio tanquam cen<lb></lb>tro humeris geſtato. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002794"><emph type="italics"></emph>Sit igitur lignum <lb></lb>longius A B è me<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.227.1.jpg" xlink:href="035/01/227/1.jpg"></figure><lb></lb><emph type="italics"></emph>dio C geſtatum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002795"><emph type="italics"></emph>Sit & breuius <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.227.2.jpg" xlink:href="035/01/227/2.jpg"></figure><lb></lb><emph type="italics"></emph>D E eiuſdem pon<lb></lb>deris puta decem librarum è medio F geſtatum etiam. </s> <s id="id.002796">Quia partes <lb></lb>cum pariter multiplicibus ſunt in eadem ratione prop. 15. lib. 5. & <lb></lb>eſt A B maior ipſo D E, erit dimidium A C maius dimidio D F. <lb></lb></s> <s id="id.002797">Et ſic extremum A magis diſtans à centro C immoto plus mouet, <lb></lb>vel mouetur pro natura ſua deorſum. </s> <s id="id.002798">Item B. </s> <s id="id.002799">Ergo tum A tum B <lb></lb>plus impediunt ferentem ex C: quam D & E ex F. </s> <s id="id.002800">Quæri hic <lb></lb>poſſet cur pondera ſiniſtro humero facilius ferantur, quam dextro. <lb></lb></s> <s id="id.002801">Hoc fit, quia dextrum cum <expan abbr="natũ">natum</expan> ſit ad mouere: ſiniſtrum ad moueri: <lb></lb>illud ſi liberum ſit ab onere impoſito ( quod premit ideoque impedit ) <lb></lb>facilius & maiori vi mouebit. </s> <s id="id.002802">Impeditum enim omne minus probe <lb></lb>fungitur officio. </s> <s id="id.002803">Præterea cum progreßio fiat impulſione vnius cru<lb></lb>ris, & tractione, tum impulſione alterius, melius eſt aliud, quod plus <lb></lb>impulſione & tractione valet ab onere liberari. </s> <s id="id.002804">Eſt <expan abbr="autẽ">autem</expan> <expan abbr="dextrũ">dextrum</expan> crus. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <pb xlink:href="035/01/228.jpg" pagenum="188"></pb> <chap> <subchap1> <p type="main"> <s id="id.002805">29. <foreign lang="el">*dia\ ti/ e)pi\ toi=s fre/asi ta\ <lb></lb>khlw/neia poiou=si tou=ton to\n <lb></lb>tro/pon.</foreign></s> </p> <p type="main"> <s id="id.002806">29. Cur in puteis tolleno<lb></lb>nem faciunt hoc mo<lb></lb>do. </s> </p> <p type="main"> <s id="id.002807"><foreign lang="el">*dia\ ti/ e)pi\ toi=s fre/asi ta\ khlw/neia poiou=si tou=ton to\n <lb></lb>tro/pon; prostiqe/asi ga\r ba/ros e)n tw=| cu/lw| to\n mo/libdon, <lb></lb>o)/ntos ba/rous tou= ka/dou au)tou=, kai\ kenou= kai\ plh/rous o)/ntos.</foreign></s> <s id="g0132802"><foreign lang="el"><lb></lb>h)\ o(/ti e)n dusi\ xro/nois dih|rhme/nou tou= e)/rgou [1ba/yai ga\r dei=, <lb></lb>kai\ tou=t' a)/nw e(lku/sai]1 sumbai/nei kaqie/nai me\n keno\n r(a|<lb></lb>di/ws, ai)/rein de\ plh/rh xalepw=s; </foreign></s> <s id="g0132803"><foreign lang="el">lusitelei= ou)=n mikrw=| bradu/teron <lb></lb>ei)=nai to\ katagagei=n pro\s to\ polu\ koufi/sai to\ <lb></lb>ba/ros a)na/gonti. tou=to ou)=n poiei= e)p' a)/krw| tw=| khlwnei/w| o( <lb></lb>mo/libdos proskei/menos h)\ o( li/qos.</foreign></s> <s id="g0132804"><foreign lang="el">kaqimw=nti me\n ga\r gi/netai <lb></lb>ba/ros mei=zon h)\ ei) mo/non keno\n dei= kata/gein to\n ka/don: <lb></lb>o(/tan de\ plh/rhs h)=|, a)na/gei o( mo/libdos, h)\ o(/ ti a)\n h)=| <lb></lb>to\ proskei/menon ba/ros.</foreign></s> <s id="g0132805"><foreign lang="el">w(/st' e)sti\ r(a=|on au)tw=| ta\ a)/mfw <lb></lb>h)\ e)kei=no.</foreign></s> </p> <p type="main"> <s id="id.002808">Cur in puteis tollenonem <lb></lb><expan abbr="faciũt">faciunt</expan> ſic, vt ligno pondus <lb></lb>plumbum ſcilicet <expan abbr="adijciãt">adijciant</expan>. <lb></lb></s> <s id="id.002809">An quod in duo tempora <lb></lb>diuiſum ſit hauriendi opus <lb></lb>Immergere enim opor<lb></lb>tet ſitulam, & hanc rurſus <lb></lb>ſurſum trahere. </s> <s id="id.002810">Contingit <lb></lb>quidem vacuam facile de<lb></lb>mittere. </s> <s id="id.002811">At plenam attolle<lb></lb>re difficile. </s> <s id="id.002812">Confert igitur <lb></lb>paulo tardius demittere, vt <lb></lb>qui attollit, attollat multò <lb></lb>facilius. </s> <s id="id.002813">Hoc autem pręſtat <lb></lb>plumbum, vel lapis extre<lb></lb>mo tollenonis adiectus. <lb></lb></s> <s id="id.002814">Demittenti enim pondus <lb></lb>redditur maius: quam ſi ſo<lb></lb>lam vacuam ſitulam opor<lb></lb>teret demittere. </s> <s id="id.002815">At quan<lb></lb>do plena fuerit, hanc edu<lb></lb>cit plumbum, vel ſi quod <lb></lb>aliud pondus adiectum ſit. <lb></lb></s> <s id="id.002816"><expan abbr="Itaq;">Itaque</expan> hoc modo vtrumque <lb></lb>factu facilius eſt: quam alterum. </s> </p> <p type="head"> <s id="id.002817">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002818">Cvr in puteis tollenonem.] <foreign lang="el">Khlo/neion</foreign> <emph type="italics"></emph>quid ſit etiamſi hîc <lb></lb>Ariſtoteles non explicet, non eſt tamen difficile coniectura aſ<lb></lb>ſequi, eſſe eam machinam ligneam, qua & antiqui vſi ſunt, & qui <lb></lb>adhuc viuunt vtuntur in hauriendis aquis è puteo ad irrigandos <emph.end type="italics"></emph.end><pb xlink:href="035/01/229.jpg" pagenum="189"></pb><emph type="italics"></emph>hortos, vel ad aliud quod volunt. </s> <s id="id.002819">Vſum hunc pulchre expreßit Colu<lb></lb>mella, ſi rectè Leonicus pro tendentibus corrigens reponit celonius, <lb></lb>ſic igitur de irrigandis hortis loquens dixit Columella:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002820">Vicini quo que ſint amnes, quos incola durus</s> </p> <p type="main"> <s id="id.002821">Attrahat auxilio ſemper ſitientibus hortis:</s> </p> <p type="main"> <s id="id.002822">Aut fons illa chrymet putei non ſede profunda</s> </p> <p type="main"> <s id="id.002823">Ne grauis hauſturis celonius ilia vellat. </s> </p> <p type="main"> <s id="id.002824"><emph type="italics"></emph>Machina hæc quæ ab officio tollendi tolleno dicitur, conſtat trabe <lb></lb>erecta, vt D C, & tigno tranſuerſo circa axiculum in alto trabis <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.229.1.jpg" xlink:href="035/01/229/1.jpg"></figure><lb></lb><emph type="italics"></emph>verſatili, vt A B, à cuius extremo B cum cathena B E pendet <lb></lb>vas E, in altero A pondus plumbeum, vel lapideum G adijcitur ad <lb></lb>commodiorem, vt vult hîc Ariſtottles, à puteo F exhauſtum. </s> <s id="id.002825">Quæ<lb></lb>rit igitur cur in altero tollenonis extremo pondus adijciatur. </s> <s id="id.002826">Huius <lb></lb>quæſtionis difficultas arguitur, quod ſitula ſeu vacua, ſeu plena, ſit <lb></lb>pondus. </s> <s id="id.002827">Pondus autem ponderi adiectum difficilius moueri deberet. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/230.jpg" pagenum="190"></pb> <p type="main"> <s id="id.002828">An quod in duo.] <emph type="italics"></emph>Reſponſio eſt ex diſtinctione duplicis mo<lb></lb>tus exhauſtioni per tollenonem neceſſarij. </s> <s id="id.002829">Alter eſt immerſionis: al<lb></lb>ter eleuationis. </s> <s id="id.002830">Et illum quidem fatetur Ariſtoteles ex adiecto pon<lb></lb>dere reddi difficiliorem: at hunc contra multo effici faciliorem. </s> <s id="id.002831">Ad<lb></lb>mittendum autem in vna totius operis parte leue incommodum, pro<lb></lb>pter ſubſecuturam in altera operoſiori parte longè maiorem commo<lb></lb>ditatem. </s> <s id="id.002832">Vnde autem tum hæc, tum illud pendeat non dicit Ariſtote<lb></lb>les, quia ex antecedentibus facile intellectum. </s> <s id="id.002833">Tignus enim tranſ<lb></lb>uerſus eſt vectis, cuius <expan abbr="fulcimentũ">fulcimentum</expan> eſt in axiculo trabis, <expan abbr="atq;">atque</expan> in motu <lb></lb>immerſionis pondus <expan abbr="mouendũ">mouendum</expan> eſt in A: mouens vero eſt in B, vel in <lb></lb>ſitula E. </s> <s id="id.002834">Quò igitur pondus in A erit grauius, eò difficilius attol<lb></lb>letur, ſic natura grauitatis ferente: & ſic maiore vi opus erit: contrà <lb></lb>in motu eleuationis, pondus mouendum eſt ſitula, mouens eſt in A, <lb></lb>hic adiutus pondere adiecto natura ſua deorſum vergente, facilius <lb></lb>tantò deprimet ipſum A: quantò grauius erit G. </s> <s id="id.002835">Et ſic facilius B <lb></lb>attolletur cum annexa ſitula. </s> <s id="id.002836">Poſſet etiam hæc quæſtio ad libram <lb></lb>commodißimè referri. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002837">30. <foreign lang="el">*dia\ ti/ o(/tan fe/rwsin e)pi\ <lb></lb>cu/lou du/o a)/nqrwpoi i)=son ba/<lb></lb>ros, ou)x o(moi/ws qli/bontai.</foreign></s> </p> <p type="main"> <s id="id.002838">30. Cur cum duo homines <lb></lb><expan abbr="cũ">cum</expan> pertica pondus æqua<lb></lb>le ferunt, non æqualiter <lb></lb>premuntur. </s> </p> <p type="main"> <s id="id.002839"><foreign lang="el">*dia\ ti/, o(/tan fe/rwsin e)pi\ cu/lou h)/ tinos toiou/tou du/o <lb></lb>a)/nqrwpoi i)/son ba/ros, ou)x o(moi/ws qli/bontai, e)a\n mh\ e)pi\ <lb></lb>tw=| me/sw| h)=| to\ ba/ros, a)lla\ ma=llon o(/sw| a)\n e)ggu/teron h)=| <lb></lb>tw=n fero/ntwn; </foreign></s> <s id="g0132902"><foreign lang="el">h)\ dio/ti moxlo\s me\n gi/netai ou(/tws e)xo/ntwn <lb></lb>to\ cu/lon, to\ de\ ba/ros u(pomo/xlion, </foreign></s> <s id="g0132903"><foreign lang="el">o( de\ e)ggu/teros tou= <lb></lb>ba/rous tw=n fero/ntwn to\ ba/ros to\ kinou/menon, a(/teros de\ <lb></lb>tw=n fero/ntwn to\ ba/ros o( kinw=n.</foreign></s> <s id="g0132904"><foreign lang="el">o(/sw| ga\r ple/on a)pe/xei tou= <lb></lb>ba/rous, tosou/tw| r(a=|on kinei=, kai\ qli/bei ma=llon to\n e(/teron <lb></lb>ei)s to\ ka/tw, w(/sper a)nterei/dontos tou= ba/rous tou= e)pikeime/nou <lb></lb>kai\ ginome/nou u(pomoxli/ou.</foreign></s> <s id="g0132905"><foreign lang="el">e)n me/sw| de\ u(pokeime/nou tou= <lb></lb>ba/rous, ou)de\n ma=llon a(/teros qate/rw| gi/netai ba/ros, ou)de\ <lb></lb>kinei=, a)ll' o(moi/ws e(ka/teros e(kate/rw| gi/netai ba/ros.</foreign></s> </p> <p type="main"> <s id="id.002840">Cur cum duo homines <lb></lb>cum pertica, vel aliquo ſi<lb></lb>mili pondus æquale <expan abbr="ferũt">ferunt</expan>, <lb></lb>non ſimiliter premuntur, ſi <lb></lb>ipſum non è medio ſuſpen<lb></lb>datur: ſed <expan abbr="quãtò">quantò</expan> magis pro<lb></lb>pius fuerit ferentibus. </s> <s id="id.002841">An <lb></lb>quia pertica quidem ſic fe<lb></lb>rentium eſt vectis, pondus <lb></lb>verò hypomochlium: Etè <lb></lb>baiulis qui ponderi pro<lb></lb>pior eſt, eſt mobile: alter <lb></lb>verò eſt mouens, qui quò <lb></lb>plus diſtiterit à <expan abbr="põdere">pondere</expan>, eò <pb xlink:href="035/01/231.jpg" pagenum="191"></pb>facilius mouet, & alterum <lb></lb>deorſum premit magis <expan abbr="tãquam">tan<lb></lb>quam</expan> pondus adiectum, <lb></lb>quod eſt hypomochlium <lb></lb>renitatur. </s> <s id="id.002842">At poſito ponde<lb></lb>re in medio, non alter alteri <lb></lb>maiori eſt ponderi, nec ma<lb></lb>gis mouet: ſed <expan abbr="vterq;">vterque</expan> vtri<lb></lb>que ſimile pondus adfert. </s> </p> <p type="head"> <s id="id.002843">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002844">Cvr cum duo.] <emph type="italics"></emph>Fuſtes teretes nodis carentes ad onera goſtan<lb></lb>da apti palangæ à Nonio & Varrone dicuntur, vel phalangæ <lb></lb>à Plinio vnde phalangarij Baiuli ijs <expan abbr="vtẽtes">vtentes</expan>, qui ex numero tetrapho<lb></lb>ri, & hexaphori dicti ſunt. </s> <s id="id.002845">Quærit igitur hîc Ariſtoteles. </s> <s id="id.002846">cur è duo<lb></lb>bus pondus aliquod phalanga ferentibus, quò ponderi propinquior eſt <lb></lb>alter, eò magis remotiori prematur. </s> <s id="id.002847">Cuius quæſtionis <expan abbr="causã">causam</expan> refert ad <lb></lb><expan abbr="vectẽ">vectem</expan>, cuius <expan abbr="hypomochliũ">hypomochlium</expan> ſit in <expan abbr="põdere">pondere</expan> geſtato, vel <expan abbr="ſuſtẽto">ſuſtento</expan>. </s> <s id="id.002848">Siue enim <lb></lb>homines <expan abbr="ambulẽt">ambulent</expan>: ſiue ſtent, nihil intereſt, vtpotè quod grauitate ſua <lb></lb>ne attollatur, ob ſiſtat. </s> <s id="id.002849"><expan abbr="Mouendũ">Mouendum</expan> eſt in ſuſtinente propinquiore: <expan abbr="mouẽs">mouens</expan> <lb></lb>eſt in remotiore. </s> <s id="id.002850">Et cur ita potius, cauſam adfert, quia vectis pars ma<lb></lb>ior facilius mouetur, id eſt vt interpretor ſuſtinetur, vel eleuatur: ſic<lb></lb>que pars minor magis deprimetur, depreſſa <expan abbr="ferentẽ">ferentem</expan> vel <expan abbr="ſuſtinentẽ">ſuſtinentem</expan> ma<lb></lb>gis premet, vt hîc moueri <expan abbr="nõ">non</expan> ſit aliud: <expan abbr="quã">quam</expan> deorſum premi: & mouere <lb></lb>ſuſtinere, vel attollere. </s> <s id="id.002851">Alioqui ſi mouere aliter ſumatur, ratio qua <lb></lb>vectis longior facilius mouet, eſt in motione circa <expan abbr="hypomochliũ">hypomochlium</expan> am<lb></lb>bitus magnitudo, ob <expan abbr="quã">quam</expan> quia motio redditur tardior, & ideò leuior <lb></lb><expan abbr="etiã">etiam</expan> eſt, hîc conuenire <expan abbr="nõ">non</expan> poteſt. </s> <s id="id.002852">Neque enim in hac vectis <expan abbr="circũducitur">circumduci<lb></lb>tur</expan>: ſed premit <expan abbr="tantũ">tantum</expan> ſuſtinentes, vt quid graue. </s> <s id="id.002853">Sed & aliter quam <lb></lb>Ariſtoteles reſponderi poteſt, ita accepto motu, ſi dicamus <expan abbr="alterutrũ">alterutrum</expan> <lb></lb>e ſuſtinentibus eſſe <expan abbr="fulcimentũ">fulcimentum</expan>, & alterum eſſe <expan abbr="potentiã">potentiam</expan>: mobile <expan abbr="autẽ">autem</expan> <lb></lb>eſſe id, quod inter <expan abbr="vtrumq;">vtrumque</expan> appendet. </s> <s id="id.002854">Nam <expan abbr="verũ">verum</expan> eſt quod è tertio co<lb></lb>roll. prop. 2. tractatus de vecte apud <expan abbr="Gvidũ">Gvidum</expan> Vbaldum demonſtrate <lb></lb>deducitur. </s> <s id="id.002856">Nempe ſi in extremis vectis duæ ſint potentiæ, inter quas <lb></lb>pondus ſit ſuſpenſum. </s> <s id="id.002857">Erit vna ad alteram vt interualla inter po<lb></lb>tentias, & pondus reciprocè. </s> <s id="id.002858">Vt ſi ſit vectis A B, poten<lb></lb>tiæ A & B, pondus ſuſtentum C E, erit A ad B. vt B C <lb></lb>ad A C. </s> <s id="id.002859">Sit igitur vt B C ſit minor: quam A C. </s> <s id="id.002860">Ergo A <emph.end type="italics"></emph.end><pb xlink:href="035/01/232.jpg" pagenum="192"></pb><emph type="italics"></emph>potentia <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.232.1.jpg" xlink:href="035/01/232/1.jpg"></figure><lb></lb><emph type="italics"></emph>erit mi<lb></lb>nor: <expan abbr="quã">quam</expan> <lb></lb>B, id eſt <lb></lb>potentia <lb></lb>minor in <lb></lb>A ſic di <lb></lb>ſtante à <lb></lb>C ſufficiet ſuſtinendo ponderi. </s> <s id="id.002861">Poſitis igitur A & B potentijs <lb></lb>æqualibus, A facilius ſuſtinebit, & quidem tantò: quantò A di<lb></lb>ſtabit magis ab C. </s> <s id="id.002862">Sit præterea vt C ſit in medio vectis A B. <lb></lb>quia B C erit æqualis ipſi A C potentiæ æquales A & B eſſe <lb></lb>debent, vt æquè pondus idem ſuſtineant. </s> <s id="id.002863">Ob id rectè dictum eſt illud <lb></lb>ab Ouidio,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002864">Non benè inæquales veniunt ad aratra Iuuenci:</s> </p> <p type="main"> <s id="id.002865">Si qua velis aptè nubere, nube pari. </s> </p> <p type="main"> <s id="id.002866"><emph type="italics"></emph>Si enim inæquales tunc grandior minorem premit magis: ob id periti <lb></lb>agricolæ, ſi quando alterius iugatorum laborem leuare velint, lorum <lb></lb>longius efficientes ad ipſum religant. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002867"><emph type="italics"></emph>Hanc rurſus quæſtionem aliter ſoluere videtur Cardanus, nimi<lb></lb>rum quod E pondus alteri ferentium propius exiſtens ipſum premit <lb></lb>magis, quia deſcendat magis reſpectu B: quam A alterius feren<lb></lb>tium. </s> <s id="id.002868">Nam cum deſcendat ſecundum rectam C E, ſi intelligamus à <lb></lb>puncto B ad Erectam ductam, <lb></lb>& ab A ad E item rectam,<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.232.2.jpg" xlink:href="035/01/232/2.jpg"></figure><lb></lb><emph type="italics"></emph>conſtitutum erit triangulum A <lb></lb>B E, cuius quia A E maior <lb></lb>eſt: quam E B, per prop. 46. <lb></lb>& 47. lib. 1. </s> <s>Eſt enim A diſtans <lb></lb>magis ab C quam B ex hypo<lb></lb>theſi: erit angulus B maior: quam A prop. 18. lib. 1. </s> <s id="id.002869">Et ſic E plus <lb></lb>deſcendit reſpectu B: quam reſpectu A. </s> <s id="id.002870">Igitur E plus grauat B: <lb></lb>quam A ſeu ex cauſa, quod magis premat: ſeu ex effectu, quod ma<lb></lb>gis deſcenderit. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <pb xlink:href="035/01/233.jpg" pagenum="193"></pb> <chap> <subchap1> <p type="main"> <s id="id.002871">31. <foreign lang="el">*dia\ ti/ oi( a)nista/menoi, ou(/tws <lb></lb>a)ni/stantai.</foreign></s> </p> <p type="main"> <s id="id.002872">31. Cur qui ſurgunt, ſic ſur<lb></lb>gant. </s> </p> <p type="main"> <s id="id.002873"><foreign lang="el">*dia\ ti/ oi( a)nista/menoi pa/ntes pro\s o)cei=an gwni/an tw=| <lb></lb>mhrw=| poih/santes th\n knh/mhn a)ni/stantai, kai\ tw=| qw/raki <lb></lb>pro\s to\n mhro/n; ei) de\ mh/, ou)k a)\n du/nainto a)nasth=nai.</foreign></s> <s id="g0133002"><foreign lang="el">po/teron <lb></lb>o(/ti to\ i)/son h)remi/as pantaxou= ai)/tion, h( de\ o)rqh\ gwni/a <lb></lb>tou= i)/sou, kai\ poiei= sta/sin: dio\ kai\ fe/retai pro\s o(moi/as <lb></lb>gwni/as th=| periferei/a| th=s gh=s. ou) ga\r o(/ti kai\ pro\s o)rqh\n <lb></lb>e)/stai tw=| e)pipe/dw|.</foreign></s> <s id="g0133003"><foreign lang="el">h)\ o(/ti a)nista/menos gi/netai o)rqo/s, a)na/gkh <lb></lb>de\ to\n e(stw=ta ka/qeton ei)=nai pro\s th\n gh=n.</foreign></s> <s id="g0133004"><foreign lang="el">ei) ou)=n me/llei <lb></lb>e)/sesqai pro\s o)rqh/n, tou=to de/ e)sti to\ th\n kefalh\n e)/xein <lb></lb>kata\ tou\s po/das, kai\ gi/nesqai dh\ o(/te a)ni/statai.</foreign></s> <s id="g0133005"><foreign lang="el">o(/tan me\n <lb></lb>ou)=n kaqh/menos h)=|, para/llhlon e)/xei th\n kefalh\n kai\ tou\s <lb></lb>po/das, kai\ ou)k e)pi\ mia=s eu)qei/as.</foreign></s> <s id="g0133006"><foreign lang="el">h( kefalh\ *a e)/stw, qw/rac <lb></lb>*a*b, mhro\s *b*g, knh/mh *g*d.</foreign></s> <s id="g0133007"><foreign lang="el">pro\s o)rqh\n de\ gi/netai <lb></lb>o(/ te qw/rac [e)f' w(=n *a*b] tw=| mhrw=| kai\ o( mhro\s th=| knh/mh| <lb></lb>ou(/tws kaqhme/nw|. w(/ste ou(/tws e)/xonta a)du/naton a)nasth=nai.</foreign></s> <s id="g0133008"><foreign lang="el"><lb></lb>a)na/gkh de\ e)gkli=nai th\n knh/mhn kai\ poiei=n tou\s po/das u(po\ <lb></lb>th\n kefalh/n.</foreign></s> <s id="g0133009"><foreign lang="el">tou=to de\ e)/stai, e)a\n h( *g*d e)f' h(=s ta\ *g*z <lb></lb>ge/nhtai, kai\ a(/ma a)nasth=nai sumbh/setai, kai\ e)/xein e)pi\<lb></lb> th=s au)th=s i)/shs th\n kefalh/n te kai\ tou\s po/das. h( de\ *g*z <lb></lb>o)cei=an poiei= gwni/an pro\s th\n *b*g.</foreign></s> </p> <p type="main"> <s id="id.002874">Cur omnes qui ſurgunt <lb></lb><expan abbr="conſtituẽtes">conſtituentes</expan> angulum acu<lb></lb>tum ex femore & tibia, <expan abbr="tũ">tum</expan> <lb></lb>ex thorace & femore ſur<lb></lb>gant: ſin minus, ſurgere <expan abbr="nequeũt">ne<lb></lb>queunt</expan>. </s> <s id="id.002875">An quia, quod ęqua <lb></lb>le eſt, quietis vbique cauſa <lb></lb>eſt. </s> <s id="id.002876">Angulus autem rectus <lb></lb>eſt æqualitatis, & ſtatum <lb></lb>facit. </s> <s id="id.002877">Ideò etiam fertur ad <lb></lb>angulos ſimiles, <expan abbr="cũ">cum</expan> ſuperfi<lb></lb>cie terræ. </s> <s id="id.002878">Sic enim erit ipſi <lb></lb>plano ad rectos: vel quod <lb></lb>ſurgens fit rectus. </s> <s id="id.002879">Neceſſe <lb></lb>eſt autem ſtantem eſſe per<lb></lb>pendicularem terræ. </s> <s id="id.002880">Si igi<lb></lb>tur debet eſſe ad rectos. <lb></lb></s> <s id="id.002881">hoc eſt caput habere è di<lb></lb>recto pedum. </s> <s id="id.002882">Etiam quum <lb></lb>ſurgit fieri oportet. </s> <s id="id.002883">Quan<lb></lb>do igitur ſedet caput habet <lb></lb>ad pedes parallelum, & ne<lb></lb>quaquam in vna recta. </s> <s id="id.002884">Sit <lb></lb>caput <foreign lang="el">a,</foreign> thorax <foreign lang="el">a b,</foreign> fe<lb></lb>mur <foreign lang="el">b g,</foreign> tibiæ <foreign lang="el">g d,</foreign> fiat <lb></lb>verò thorax <foreign lang="el">a b</foreign> ad rectos <lb></lb>femori, & femur tibiæ ſic <lb></lb>ſedenti. </s> <s id="id.002885">Itaque ſic ſe ha<lb></lb>bentem impoſſibile eſt ſur<lb></lb>gere. </s> <s id="id.002886">At neceſſe eſt incli<lb></lb>nare tibiam, & conſtitue<lb></lb>re pedes ſub capite: hoc <lb></lb>autem erit ſi <foreign lang="el">g d</foreign> fiat <foreign lang="el">g</foreign><pb xlink:href="035/01/234.jpg" pagenum="194"></pb><foreign lang="el">z,</foreign> tunc ſimul ſurgere con<lb></lb>tinget. </s> <s id="id.002887">Atque habere tum <lb></lb>caput, tum pedes in eadem <lb></lb>recta: <foreign lang="el">g z</foreign> vero cum <foreign lang="el">b g</foreign><lb></lb>angulum <expan abbr="acutũ">acutum</expan> conſtituet</s> </p> <p type="head"> <s id="id.002888">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002889">Cvr qui ſurgunt.] <emph type="italics"></emph>Surrectio eſt motio, quia homo è iacente <lb></lb>vel ſedente fit ſtans. </s> <s id="id.002890">Quod vt intelligatur ſcire oportet attingi <lb></lb>hîc quatuor figuras, quibus hominis corpus ex certa ſui poſitione fi<lb></lb>gurari poteſt. </s> <s id="id.002891">hæ ſunt iacere ſupinum, iacere pronum, ſedere, ſtare. <lb></lb></s> <s id="id.002892">Iacere ſupinum eſt cum ſpina animalis terram contingit. </s> <s id="id.002893">Iacere <expan abbr="pronũ">pro<lb></lb>num</expan> eſt cum humi venter reclinatus eſt. </s> <s id="id.002894">Hæ duæ figuræ quia ad quie<lb></lb>tem ſomnumque communem comparatæ ſunt, pluribus animalibus <lb></lb>communes eſſe potuerant, ſed pronum ambulare conuenit brutis, qua<lb></lb>ſi ſolùm ad paſtum à natura inſtitutis. </s> <s id="id.002895">Seßio eſt ſitus in quo ſpina <lb></lb>cum femore, & femur cum tibia angulum rectum facit. </s> <s id="id.002896">Statio eſt <lb></lb>ſitus in quo ſpina femur & tibia in vna recta exiſtentes perpendi<lb></lb>culares ſunt horizonti. </s> <s id="id.002897">Hæ duæ ſoli homini propriæ ſunt. </s> <s id="id.002898">quia ſolus <lb></lb>articulos ita à natura ſapiente & architectatrice conformatos ha<lb></lb>bet, vt ſic eius oſſa diſponi valeant. </s> <s id="id.002899">Solus enim articulum femoris <lb></lb>& iſchij ad anteriora flectit, ipſius verò genu retrorſum reflectit,<emph.end type="italics"></emph.end><arrow.to.target n="marg42"></arrow.to.target><lb></lb><emph type="italics"></emph>ſine quibus neque tibia & femur cum ſpina in <expan abbr="vnã">vnam</expan> rectam adduci <lb></lb>poteſt, at in belluis vbi femur <expan abbr="cũ">cum</expan> ſpina <expan abbr="rectũ">rectum</expan> fecit, tibia <expan abbr="nunquã">nunquam</expan> cum <lb></lb>femore rectum faciet: nec etiam ipſa ad terram recta erit. </s> <s id="id.002900">quod ta<lb></lb>men, vt ſeßio ſecura fiat, neceſſum eſt. </s> <s id="id.002901">cum igitur omnia bruta an<lb></lb>trorſum poſteriorum crurum flexiones habeant, ſolus homo ſedet, <lb></lb>& ſtat: & ſapienter ita hunc natura fecit, cum hic ſolus mentem <emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="marg43"></arrow.to.target><emph type="italics"></emph>quæ eſt ars artium habiturus erat, id eſt ſolus artifex futurus erat. <lb></lb></s> <s id="id.002902">Manuum enim, quæ ſint <foreign lang="el">o)/rganon o)rganwn,</foreign> vt vocat noſter Gale<lb></lb>nus actiones in opificijs, duabus his <expan abbr="tãtum">tantum</expan> egent figuris. </s> <s id="id.002903">Nemo enim <lb></lb>ſupinus aut pronus quicquam agit. </s> <s id="id.002904">Ideo etiam, vt id obiter dicam, <lb></lb>qui opinantur ob id rectum ſtare hominem, vt cælum promptè ſuſpi<lb></lb>ciat, dicereque poßit. <emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s id="id.002905"><margin.target id="marg42"></margin.target>Cap. 1. & 3. <lb></lb>lib. 3. de vſu <lb></lb>part. </s> </p> <p type="margin"> <s id="id.002906"><margin.target id="marg43"></margin.target>Cap. 2. lib. 1. <lb></lb>de vſu part. </s> </p> <p type="main"> <s id="id.002907">Reſpicio aduerſus Olympum fronte intrepida. </s> </p> <pb xlink:href="035/01/235.jpg" pagenum="195"></pb> <p type="main"> <s id="id.002908"><emph type="italics"></emph>Illi numquam viderunt piſcem <expan abbr="dictũ">dictum</expan><emph.end type="italics"></emph.end> <foreign lang="el">*ourano/skopon,</foreign> <emph type="italics"></emph>id eſt cæli ſpe<lb></lb>culatorem. </s> <s id="id.002909">Hic namque vel inuitus cælum ſemper intuetur: homo <lb></lb>autem niſi collum reflectat retrorſum, cælum non videt. </s> <s id="id.002910">Atqui hæc <lb></lb>reflexio communis eſt etiam aſinis, vt omittam aues, quæ longo collo <lb></lb>ſunt præditæ, quibus non ſolum facilè eſt ſurſum: ſed & quoquouer<lb></lb>ſum, ſi voluerint aſpicere. </s> <s id="id.002911">Et <expan abbr="quãdo">quando</expan> poſt <expan abbr="Platonẽ">Platonem</expan>, Ouidius dixit illud,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002912">Pronaque cum ſpectant animalia cætera terram,</s> </p> <p type="main"> <s id="id.002913">Os homini ſublime dedit, cælum que videre</s> </p> <p type="main"> <s id="id.002914">Iuſſit, & erectos ad ſidera tollere vultus. </s> </p> <p type="main"> <s id="id.002915"><emph type="italics"></emph>Non ſentit cum Platone & fallitur: ſi cœlum videre intelligit, cum <lb></lb>quis ſupinus ſeipſum reclinarit oſcitans: non autem potius cum quis <lb></lb>naturam cœleſtium mente conſiderat, quod eſt homini, vt erectum <lb></lb>eſſe poſſe, proprium: pronum vero eſſe poſſe, commune eſt illi, cum <lb></lb>belluis, quæ non ſolum iacentes: ſed & ambulantes ſic ſunt. </s> <s id="id.002916">Verſus <lb></lb>enim humum omnes ventrem conuerſum habent, aliæ magis, aliæ <lb></lb>minus modo ſimillimo infantium, qui manibus pedibuſque innixi, ſe <lb></lb>mouent. </s> <s id="id.002917">Vnus cereopithecus proxime accedit ad hominis erectum <lb></lb>ſtatum, diutiuſque ſtare vtcunque poteſt, & manum habet: ſed dißi<lb></lb>milem, vt in qua pollex non eſt reliquis digitis oppoſitus, nec <foreign lang="el">a)nti/<lb></lb>xeir,</foreign> proptereà dicitur à Galeno eſſe ridicula hominis imitatio. </s> <s id="id.002918">ab hoc <lb></lb>enim ſitu pollex<emph.end type="italics"></emph.end> <foreign lang="el">i)/son du/natai tn=| o(/lh| xeiri/. </foreign></s> </p> <p type="main"> <s id="id.002919">Cur omnes qui ſurgunt.] <emph type="italics"></emph>Quærit hîc Ariſtoteles, cur ſur<lb></lb>gens de ſeßione neceſſario conſtituat angu<lb></lb>lum acutum ex tibia cum femore, vel ex <lb></lb>thorace, ſeu ſpina cum femore, vt in ſeſ<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.235.1.jpg" xlink:href="035/01/235/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſione ſit thorax A B, femur B C, tibia C <lb></lb>D, anguli A B C & B C D recti. </s> <s id="id.002920">Ex hoc <lb></lb>ſitu ad ſurgendum innitens neceſſe habet addu<lb></lb>cere C D ad C E, vel A B ad B F, vt è <lb></lb>rectis A B C, B C D angulis, fiant acuti <lb></lb>F B C, B C E. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002921">An quia quod æquale.] <emph type="italics"></emph>Quæſtionem propoſitam ſoluit du<lb></lb>pliciter. </s> <s id="id.002922">Primo modo è cauſa quietis in ſeſsione <expan abbr="perſeuerãte">perſeuerante</expan>, quandiu <lb></lb>recti anguli conſeruantur. </s> <s id="id.002923">hic erit ſyllogiſmus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002924"><emph type="italics"></emph>Cauſa quietis perſeuerante fieri non poteſt ſurrectio, vt quæ mo<lb></lb>tio ſit. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/236.jpg" pagenum="196"></pb> <p type="main"> <s id="id.002925"><emph type="italics"></emph>Angulorum rectitudo eſt cauſa quietis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002926"><emph type="italics"></emph>Ergò quandiu perſeuerauerit, ſurrectio non fiet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002927"><emph type="italics"></emph>Aſſumptionis loco poſita eſt eius confirmatio ab axiomate, & ſic <lb></lb>concludetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002928"><emph type="italics"></emph>Æqualitas eſt vbique cauſa quietis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002929"><emph type="italics"></emph>Angulus rectus eſt æqualitas, quia ſibi & alijs omnibus re<lb></lb>ctis rectilineis eſt æqualis. </s> <s id="id.002930">quod eſt axioma 10. lib. 1. </s> <s>In eo <lb></lb>ſcilicet rectæ ipſum conſtituentes ſibi pariter incumbunt, <lb></lb>ſibique inuicem perpendiculares ſunt. ex def. 10. lib. 1. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002933"><emph type="italics"></emph>Ergò angulus rectus eſt cauſa quietis. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002934"><emph type="italics"></emph>Cæterum axioma hoc de æqualitate cauſa quietis diligenter animad<lb></lb>uertendum eſt in tota <expan abbr="rerũ">rerum</expan> natura. </s> <s id="id.002935">Et vt particulatim expendamus. <lb></lb></s> <s id="id.002936">videamus, vt omnia quieſcant ad rectos angulos. </s> <s id="id.002937">Primum elementa <lb></lb>omnia in planum ſui loci rectà ſurſum vel deorſam feruntur, & in <lb></lb>medio collocata, niſi aliena vi dimoueantur quieſcunt. </s> <s id="id.002938">Itaque in<lb></lb>ſiſtunt medio ad angulos rectos. </s> <s id="id.002939">Ob id terra cubico octonûm recto<lb></lb>rum ſolido à Pythagoreis & à Platone eſt comparata. </s> <s id="id.002940">Deinde arbo<lb></lb>res & plantarum omne genus rectà <expan abbr="inſiſtũt">inſiſtunt</expan> plano. </s> <s id="id.002941">Durabile in ædi<lb></lb>ficijs nihil eſt, niſi rectà inſiſtat. </s> <s id="id.002942">Poſtremò hominis quies, ſeu iaceat <lb></lb>humi, ſeu ſedeat, ſeu ſtet, fit per rectos angulos. </s> <s id="id.002943">Iacet enim humi, <lb></lb>aut in lecto decumbit cum totum quidem corpus plano horizontis <lb></lb>parallelum eſt, aut eidem congruit: ſed tunc omnes craßitudinis di<lb></lb>menſiones plano inſiſtunt ad rectos, vt de pedibus erectis videre eſt. <lb></lb></s> <s id="id.002944">Sedet quis in Hemicyclo? </s> <s id="id.002945">tibijs cum femoribus & femoribus rurſus <lb></lb>cum ſpina dorſi rectos angulos facit. </s> <s id="id.002946">Hinc collige vt vnus calceus <lb></lb>non omni pedi conuenit: ſic nec vnum ſedile omni homini ad ſeßio<lb></lb>nem commodum eſt, maiori maius requiritur minori minus. </s> <s id="id.002947">Stat au<lb></lb>tem? </s> <s id="id.002948">cum omnibus rectis à quibus tangitur in ipſo plano rectos etiam <lb></lb>angulos facit. </s> <s id="id.002949">Ergo quies & ſtatus per angulos rectos fiunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002950">Vel quod ſurgens.] <emph type="italics"></emph>Secundus modus eſt ſolutionis quæſtionis <lb></lb>propoſitæ per modum mutationis, quæ fit dum quis è <expan abbr="ſedẽte">ſedente</expan> fit ſtans, <lb></lb>quæ ſurrectio dicitur. </s> <s id="id.002951">Hæc igitur, ſi quis ſtare debeat facere debet, <lb></lb>vt ſit particeps diſpoſitionis, quæ in ſtante eſt. </s> <s id="id.002952">At diſpoſitio quæ in <lb></lb>ſtante eſt, eſt ſitus pedum & capitis, ſpinæque in eadem recta. </s> <s id="id.002953">Huius <lb></lb>ſeßio non eſt particeps. </s> <s id="id.002954">quia pedes & ſpina ſunt in Lineis parallelis: <lb></lb>contra adductio tibiæ, ita vt angulum acutum cum femore conſti<emph.end type="italics"></emph.end><pb xlink:href="035/01/237.jpg" pagenum="197"></pb><emph type="italics"></emph>tuat: vel thoracis vt cum <lb></lb>femore, quia pedes rectà <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.237.1.jpg" xlink:href="035/01/237/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſub capite, aut ſaltem re<lb></lb>ctius: quam ante collocat, <lb></lb>ſtationis magis eſt parti<lb></lb>ceps. </s> <s id="id.002955">Ad ſurrectionem igi<lb></lb>tur neceſſarij ſunt anguli <lb></lb>acuti facti vel à thorace <lb></lb>cum femoribus, vel à fe<lb></lb>moribus cum tibijs, vt diagrammate<emph.end type="italics"></emph.end> <foreign lang="el">a b g d</foreign> <emph type="italics"></emph>pro ſedente, &<emph.end type="italics"></emph.end> <foreign lang="el">e b <lb></lb>g z</foreign> <emph type="italics"></emph>pro ſurgente declaratur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002956"><emph type="italics"></emph>Et hinc patet quod ſi thorace cum femore, & femore cum tibia <lb></lb>ſimul anguli acuti fiant, facilius ſurgetur: & rurſus quantò an<lb></lb>guli illi erunt acutiores: tantò facilius ſurgetur: ſicque ſurgunt <lb></lb>imbecilli, & conualeſcentes. </s> <s id="id.002957">Porrò ſurrectio è ſedente ad ſtandum <lb></lb>declarata eſt angulis acutis indigere: ſurrectionem è iacente etiam <lb></lb>indigere clarum eſt. </s> <s id="id.002958">Is enim qui iacet, vt ſurgat, & ſtet, quatuor <lb></lb>acutos efficit, utroque brachio & latere: thorace & cruribus: fe<lb></lb>moribus & tibiis, vt ia<lb></lb>ceat A B G D. </s> <s>vt ſur<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.237.2.jpg" xlink:href="035/01/237/2.jpg"></figure><lb></lb><emph type="italics"></emph>gat A B thorax bra<lb></lb>chiorum in acutos con<lb></lb>formatorum adminiculo <lb></lb>adducetur ad E B: ſic<lb></lb>que E B G erit acutus <lb></lb>ex thorace & femoribus, <lb></lb>& G D tibia adducetur in G F: ſicque erit acutus B G F. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002959"><emph type="italics"></emph>Cæterum ſeßio, de qua hîc Aristoteles, eſt propriè dicta, & hanc <lb></lb>Galenus cum ſecuritate eſſe dixit. </s> <s id="id.002960">Et ea maximè vtuntur, qui ſe<lb></lb>dentarias artes exercent. </s> <s id="id.002961">At tamen ſeßio latè ſumpta, fit ad angu<lb></lb>los acutos, vt cum ſella humilior eſt tibijs ſedentis, & ad obtuſos <lb></lb>cum altior eſt. </s> <s id="id.002962">Vnde experientia notum eſt hominem quantò altius <lb></lb>ſedet, tantò facilius ſurgere, quod tamen videtur repugnare prædi<lb></lb>ctis, cum obtuſi anguli longius ab ſint, etiam quam recti, ab acutis. </s> <pb xlink:href="035/01/238.jpg" pagenum="198"></pb> <s>ut ſit thorax A B ſedens ſuper ſella <lb></lb>tibijs. <arrow.to.target n="table2"></arrow.to.target></s> </p> <table> <table.target id="table2"></table.target> <row> <cell></cell> <cell><emph type="italics"></emph>Altiore K<emph.end type="italics"></emph.end></cell> </row> <row> <cell><emph type="italics"></emph>Æquali L<emph.end type="italics"></emph.end></cell> </row> <row> <cell><emph type="italics"></emph>Humiliore M<emph.end type="italics"></emph.end></cell> </row> </table> <p type="main"> <s id="id.002963"><emph type="italics"></emph>Dico quod ex <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.238.1.jpg" xlink:href="035/01/238/1.jpg"></figure><lb></lb><emph type="italics"></emph>K facilius ſur<lb></lb>get: quam ex L: <lb></lb>quamque ex M. <lb></lb></s> <s id="id.002964">Ratio eſt, quia <lb></lb>A B ſuper K <lb></lb>magis eſt parti<lb></lb>ceps ſtationis: <lb></lb>quam ſuper L. <lb></lb></s> <s id="id.002965">Et ſuper L quam <lb></lb>quam ſuper M. <lb></lb></s> <s id="id.002966">Vt enim ſurrectionis initium fiat per angulos acutos: Me<lb></lb>dium tamen perducens ad terminum ad quem, qui eſt ſitum <lb></lb>eſſe in vna recta vt A B G D, tranſit per minus acutos <lb></lb>ad rectum, & tandem ad obtuſos, & obtuſis obtuſiores: quouſque <lb></lb>ad vnam rectam peruentum ſit, in qua eſt ſtatio vt eſt A B G D <lb></lb>relicta ſella K, vel L, vel M. </s> <s id="id.002967">Sed præter hæc obſeruatione di<lb></lb>gnum eſt, quod in ambulatione progreſſuque noſtro femora cum ti<lb></lb>bijs, & thoracem cum femoribus non omnino in rectam: ſed in an<lb></lb>gulos obtuſißimos: tum crura inter ſe in acutum angulum, qui eſt <lb></lb>vertex trianguli Iſoſcelis conformamus. </s> <s id="id.002968">Altero ſcilicet pedum fir<lb></lb>mato in ſolum, altero celeriter circumlato. </s> <s id="id.002969">vt cum P Ramo aduer<lb></lb>ſus philoſophos illos, ſi diis placet, qui Platonicis alis deſtituti, philo<lb></lb>ſophari aggrediuntur, concludamus, quod quieſcimus, quod ſedemus, <lb></lb>quod ſurgimus, quod ſtamus, quod ambulamus, quod currimus, geo<lb></lb>metriæ vſum eſſe. </s> <s id="id.002970">Sed & addemus ex nostro Galeno, id quoque ve<lb></lb>rum eſſe de brutis omnibus, quorum pedes inſiſtunt terræ ad rectos <lb></lb>angulos, <expan abbr="ſpinã">ſpinam</expan> pedibus tanquam columnis ad rectos etiam ſuperemi<lb></lb>nere. </s> <s id="id.002971">Hinc cauſam collige, cur ſint nonnulla ex his tam apta ferendis <lb></lb>ſarcinis & oneribus. </s> <s id="id.002972">Hinc quoque, ſi vis, collige cauſam, cur baiuli <lb></lb>Pariſienſes onera tanta ſuis harpagonibus: alij ſportulis ferant, nimi<lb></lb>rum cum ita componant ſpinam, vt antrorſum reclinata moles ſu<emph.end type="italics"></emph.end><pb xlink:href="035/01/239.jpg" pagenum="199"></pb><emph type="italics"></emph>perna corporis æquiponderet onere & viribus oneri impoſito hu<lb></lb>meris, & ita tamen vt ambo cum femoribus & tibiis, taliſque recta <lb></lb>inſistant ad terram ad angulos rectos, adiectis ad ea firmitatis ſta<lb></lb>tionis gratia, tanquam baſis & fundamenti, tarſo, pedio, & digitis <lb></lb>pedum. </s> <s id="id.002973">Sic enim moles ſuperni corporis, & onus habent aliquid ad <lb></lb>perpendiculum inferiorum partium, quod ſe ſuffulciat. </s> <s id="id.002974">Totuſque ba<lb></lb>iulus cum onere, quod gestat instar turbinis, aut coni vertice terræ <lb></lb>incumbit, baſi ſupereminente. </s> <s id="id.002975">Hinc etiam collige cur baiulis cum <lb></lb>onere aſcenſus graduum facilior eſt: quam deſcenſus. </s> <s id="id.002976">In aſcenſu enim <lb></lb>quantum antrorſum ſe incuruent, nullum inde illis caſus periculum: <lb></lb>at in deſcenſiu vel exigua illis curuatura periculum adfert, ex quo <lb></lb><expan abbr="etiã">etiam</expan> rarò videas, niſi ebiberint plus paulò, baiulos <expan abbr="cũ">cum</expan> onere deſcendere, <lb></lb>aſcendere autem, quoties opus eſt. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002977">32. <foreign lang="el">*dia\ ti/ r(a=|on kinei=tai to\ ki<lb></lb>nou/menon h)\ to\ me/non.</foreign></s> </p> <p type="main"> <s id="id.002978">32. Cur commotum faci<lb></lb>lius moueatur, <expan abbr="quã">quam</expan> quieſ<lb></lb>cens. </s> </p> <p type="main"> <s id="id.002979"><foreign lang="el">*dia\ ti/ r(a=|on kinei=tai to\ kinou/menon h)\ to\ me/non, oi(=on <lb></lb>ta\s a(ma/cas qa=tton kinoume/nas u(pa/gousin h)\ a)rxome/nas; </foreign></s> <s id="g0133102"><foreign lang="el"><lb></lb>h)\ o(/ti xalepw/taton me\n to\ ei)s tou)nanti/on kinou/menon kinh=sai <lb></lb>ba/ros; a)fairei=tai ga/r ti th=s tou= kinou=ntos duna/mews, ka)\n <lb></lb>polu\ qa=tton h)=|: a)na/gkh ga\r bradute/ran gi/nesqai th\n w)=sin <lb></lb>tou= a)ntwqoume/nou.</foreign></s> <s id="g0133103"><foreign lang="el">deu/teron de/, e)a\n h)remh=|: a)ntitei/nei ga\r kai\ <lb></lb>to\ h)remou=n.</foreign></s> <s id="g0133104"><foreign lang="el">to\ de\ kinou/menon e)pi\ to\ au)to\ tw=| w)qou=nti o(/moion <lb></lb>poiei= w(/sper a)\n ei) au)ch/seie/ tis th\n tou= kinou=ntos du/namin <lb></lb>kai\ taxuth=ta: o(\ ga\r u(p' e)kei/nou a)\n e)/pasxe, tou=to au)to\ <lb></lb>poiei= ei)s to\ pro\ o(dou= kinou/menon.</foreign></s> </p> <p type="main"> <s id="id.002980">Cur commotum facilius <lb></lb>moueatur: quam <expan abbr="quieſcẽs">quieſcens</expan>, <lb></lb>velut plauſtra commota ci<lb></lb>tius agitant: quam <expan abbr="incipiẽtia">incipien<lb></lb>tia</expan> moueri. </s> <s id="id.002981">An quia quod <lb></lb>mouetur <expan abbr="põdus">pondus</expan> in contra<lb></lb>rium mouere <expan abbr="difficillimũ">difficillimum</expan>. <lb></lb></s> <s id="id.002982">Aufertur enim aliquid de <lb></lb>potentia motoris, licet ipſe <lb></lb>multò fuerit velocior. </s> <s id="id.002983">Ne<lb></lb>ceſſe eſt enim <expan abbr="impulſionẽ">impulſionem</expan> <lb></lb>eius, quod repellitur, fieri <lb></lb>tardiorem. </s> <s id="id.002984">Deinde verò ſi <lb></lb>quieuerit. </s> <s id="id.002985">Quieſcens enim <lb></lb>reſiſtit. </s> <s id="id.002986">Quod verò motum <lb></lb>eſt, eò quò impellitur, ſimi<lb></lb>le quid impellenti facit, ac <lb></lb>ſi quis vim & celeritatem <lb></lb>motoris augeret, quod etiam ab illo pateretur. </s> <s id="id.002987">hoc ipſum <lb></lb>facit id, quod in via commotum eſt. </s> </p> <pb xlink:href="035/01/240.jpg" pagenum="200"></pb> <p type="head"> <s id="id.002988">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002989">Cvr commotum.] <emph type="italics"></emph>Commotum hîc ita capi debet, vt eò, quò <lb></lb>moueatur, impellatur: non contra, quod ex reſponſione colligere <lb></lb>facilè erit. </s> <s id="id.002990">Quæſtio igitur eſt, cur commotum facilius moueatur: <lb></lb>quam quieſcens. </s> <s id="id.002991">quæ illuſtratur exemplo curruum, quos iam commo<lb></lb>tos facilius eſt continuare in motu, quam quieſcentibus motionis ini<lb></lb>tium dare. </s> <s id="id.002992">Illuſtrari etiam poſſet exemplo nauium. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002993">An quia quod mouetur.] <emph type="italics"></emph>Reſponſio ad quæſtionem ſic con<lb></lb>cludi poteſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002994"><emph type="italics"></emph>Motoris vim & celeritatem augens pondus, facilius impellitur: <lb></lb>contrà diminuens tardius. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002995"><emph type="italics"></emph>Pondus motum eò, quò impellitur, motoris vim & celerita<lb></lb>tem auget, & ſimile quid ſuo impulſori iam facit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002996"><emph type="italics"></emph>Contrà quieſcens, quia aliò nititur, & motu occulto in contra<lb></lb>rium: quam quò impellitur tendit, diminuit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002997"><emph type="italics"></emph>Commotum igitur facilius mouetur: quam quieſcens. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.002998"><emph type="italics"></emph>Quod autem quieſcens vim motoris diminuat, patet. </s> <s id="id.002999">quia ſi ſineretur <lb></lb>nec impelleretur, exempli gratia, ſurſum, vel lateraliter, natura ſua <lb></lb>ſublato impedimento rectà deorſum ferretur. </s> <s id="id.003000">Ergò qua vi eò moue<lb></lb>retur, eadem reſiſtit, ne ſurſum vel lateraliter impellatur. </s> <s id="id.003001">Reſistere <lb></lb>autem motori, diminuere eſt eius vim in mouendo. </s> <s id="id.003002">Imò vera eſt illa <lb></lb>propoſitio. </s> <s id="id.003003">Ab æquali aut minore vi quam ſit impedimentum non <lb></lb>fit motus. </s> <s id="id.003004">Sit enim A B C D <lb></lb>quod reſistat per decem ne ſurſum <emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.240.1.jpg" xlink:href="035/01/240/1.jpg"></figure><lb></lb><emph type="italics"></emph>trahatur. </s> <s id="id.003005">Dico quod ſurſum non <lb></lb>trahetur, neque per 10. neque per 9. <lb></lb>&c. </s> <s id="id.003006">Nam ſubſtracto impedimento, <lb></lb>quod impedit ne A deorſum fera<lb></lb>tur, eo ferretur vt 10. Quod ſi eo<lb></lb>dem tempore ſurſum trahatur à vi <lb></lb>quæ ſit etiam vt 10. tunc tantum <lb></lb>mouebitur deorſum: quantum ſur<lb></lb>ſum, quieſcet igitur. </s> <s id="id.003007">Si verò ſurſum trahatur à vi minore, vt nouem, <lb></lb>quia à maiore vi deorſum fertur, non ſurſum: ſed deorſum ſimpliciter<emph.end type="italics"></emph.end><pb xlink:href="035/01/241.jpg" pagenum="201"></pb><emph type="italics"></emph>feretur. </s> <s id="id.003008">Præterea alia etiam demonſtratione quæſtio ab Aristotele <lb></lb>propoſita concludi poteſt. </s> <s id="id.003009">ſic,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003010"><emph type="italics"></emph>Omne duobus motibus ad diuerſa tendentibus commotum, tan<lb></lb>tò minus vno mouetur: quantò magis altero. </s> <s id="id.003011">quia vis quæ <lb></lb>aliquò mouet plus: plus etiam obſiſtit, & ſic retardat & in<lb></lb>fringit vim, quæ aliò mouet. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003012"><emph type="italics"></emph>Sed currus exempli gratia iam commotus, vel incipiens <lb></lb>moueri, mouetur tum motu naturali deorſum, tum vio<lb></lb>lento ad latus. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003013"><emph type="italics"></emph>Ergo quantò magis hoc mouebitur, minus mouebitur illo: & <lb></lb>contra. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003014"><emph type="italics"></emph>Atqui iam commotus plus mouetur violento. </s> <s id="id.003015">Tunc igitur minus <lb></lb>naturali: contra incipiens moueri, plus naturali. </s> <s id="id.003016">Tunc igitur minus <lb></lb>violento. </s> <s id="id.003017">Ergo commotus facilius mouebitur: quam quieſcens vel <lb></lb>incipiens moueri. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003018">33. <foreign lang="el">*dia\ ti/ pau/etai fero/mena <lb></lb>ta\ r(ife/nta.</foreign></s> </p> <p type="main"> <s id="id.003019">33. Cur proiecta lata ceſ<lb></lb>ſant. </s> </p> <p type="main"> <s id="id.003020"><foreign lang="el">*dia\ ti/ pau/etai fero/mena ta\ r(ife/nta, po/teron o(/tan <lb></lb>lh/gh| h( i)sxu\s h( a)fei=sa, h)\ dia\ to\ a)ntispa=sqai, h)\ dia\ <lb></lb>th\n r(oph/n, e)a\n krei/ttwn h)=| th=s i)sxu/os th=s r(iya/shs; </foreign></s> <s id="g0133203"><foreign lang="el">h)\ a)/topon <lb></lb>to\ tau=t' a)porei=n, a)fe/nta th\n a)rxh/n.</foreign></s> </p> <p type="main"> <s id="id.003021">Cur proiecta lata ceſſant. <lb></lb></s> <s id="id.003022">An vis impellens deſinit, <lb></lb>vel propter <expan abbr="reuulſionẽ">reuulſionem</expan>, vel <lb></lb>propter inclinationem rei <lb></lb>proiectę, ſi vim proiicientis <lb></lb>ſuperauerit. </s> <s id="id.003023">An abſurdum <lb></lb>de eo dubitare eſt eum, qui <lb></lb>principium relinquit. </s> </p> <p type="head"> <s id="id.003024">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003025">Cvr proiecta.] <emph type="italics"></emph>Proiecta dicuntur, quæ manu, funda, arcu, vel <lb></lb>aliò inſtrumento ſurſum, vel ad latus, vel etiam deorſum vio<lb></lb>lenter feruntur. </s> <s id="id.003026">Quæritur igitur cur proiecta tandem moueri deſi<lb></lb>nant. </s> <s id="id.003027">Hîc reſpondet, quia ſublata cauſa ceſſat effectus. </s> <s id="id.003028">Cauſa autem <lb></lb>lationis in proiectis eſt vis impellens à primo motore impreſſa. </s> <s id="id.003029">Hanc <lb></lb>Simplicius Ariſtotelis interpres<emph.end type="italics"></emph.end> <foreign lang="el">)e)pipo/laian</foreign> <emph type="italics"></emph>quaſi diceres ſuperfi<emph.end type="italics"></emph.end><pb xlink:href="035/01/242.jpg" pagenum="202"></pb><emph type="italics"></emph>ciariam appellat comment. in lib. 7. Phyſ. </s> <s id="id.003031">Hæc autem tollitur autà <lb></lb>reſiſtentia medij per quod fertur. </s> <s id="id.003032">Corpus enim eſt quod in ſuo ſeloco <lb></lb>conſeruare nititur: aut à naturali grauitate aliò, quàm quò proijciun<lb></lb>tur tendente. </s> <s id="id.003033">Vt enim calor & frigus in ſubiectis non proprijs ali<lb></lb>quandiu manent: ita & violenti motus impreßio illa. </s> <s id="id.003034">Et vt ferrum <lb></lb>quod diutius fuit in igne, diutius etiam calorem retinet: ſic ma<lb></lb>chinis longioribus emiſſa, quia vim illam magis impreſſam ha<lb></lb>bent, longius feruntur. </s> <s id="id.003035">quod certo indicio eſt vim à motore primo ali<lb></lb>quam in proiectis relinqui, quæ ad aliquod tempus manet. </s> <s id="id.003036">At tan<lb></lb>dem ob cauſas prædictas, perit. </s> <s id="id.003037">Et ſic quæque ad naturam redeunt <lb></lb>ſuam. </s> <s id="id.003038">Nec ſi millies lapidem ſurſum proieceris: tamen vnquam ſur<lb></lb>ſum ferri aſſueſcet. </s> <s id="id.003039">Hæc enim quæ ineſt à natura grauitas, ne vis ſur<lb></lb>ſum mouens perfectè imprimatur, impedit. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003040">An abſurdum.] <emph type="italics"></emph>Altera cauſa videtur huc adferri ceſſationis <lb></lb>in proiectis, aut ſublationis virtutis impellentis impreſſæ. </s> <s id="id.003041">Si per prin<lb></lb>cipium intelligamus motorem, qui motus principium dedit, id eſt pri<lb></lb>mum motorem. </s> <s id="id.003042">Hic enim vbi emiſit, exempli gratia, telum, ſepara<lb></lb>tur ab eo, nec amplius mouet: nihilominus tamen. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003043">Hoc volat emiſſum ſemel irreuocabile telum: <lb></lb><emph type="italics"></emph>Sed ob id tandem deſinit à motione, quia licet vis aliqua impreſſa ſu<lb></lb>per ſit, quæ moueat adhuc, à primo motore non continuatur, ideóque <lb></lb>perit. </s> <s id="id.003044">Abſurdum eſt igitur dubitare de cauſa ceſſationis proiecti cum <lb></lb>ipſum ſuus motor deſerat. </s> <s id="id.003045">Cæterum ſagitta & haſta & quicquid <lb></lb>aliud tale eſt tenſa coria facilius, quam laxa penetrat quod illa qui<lb></lb>dem reſiſtunt: hæc autem cedentia paulatim eorum quæ incidunt, <lb></lb>violentiam exoluunt, Gal. cap. 8. lib. 2. de vſ. part. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003047">34. <foreign lang="el">*dia\ ti/ fe/retai/ ti ou) th\n <lb></lb>au(tou= fora\n, mh\ a)kolouqou=n<lb></lb>tos <lb></lb>w)qou=ntos a)lla\ tou= a)fe/n<lb></lb>tos.</foreign></s> </p> <p type="main"> <s id="id.003048">34. Cur quidpiam non ſua <lb></lb>latione fertur non con<lb></lb>ſequente impulſore: ſed <lb></lb>dimittente. </s> </p> <p type="main"> <s id="id.003049"><foreign lang="el">*dia\ ti/ fe/retai/ ti ou) th\n au(tou= fora\n mh\ a)kolouqou=ntos <lb></lb>tou= w)qou=ntos a)lla\ tou= a)fe/ntos; </foreign></s> <s id="g0133302"><foreign lang="el">h)\ dh=lon o(/ti e)poi/hse toiou=ton <lb></lb>to\ prw=ton w(s qa/teron w)qei=n, kai\ tou=q' e(/teron: </foreign></s> <s id="g0133303"><foreign lang="el">pau/etai de/, <lb></lb>o(/tan mhke/ti du/nhtai poiei=n to\ prowqou=n to\ fero/menon w(/ste <lb></lb>w)qei=n, kai\ o(/tan to\ tou= ferome/nou ba/ros r(e/ph| ma=llon th=s <lb></lb>ei)s to\ pro/sqen duna/mews tou= w)qou=ntos.</foreign></s> </p> <p type="main"> <s id="id.003050">Quare quidpiam non <lb></lb>propria latione fertur, cum <lb></lb>impulſor non conſequa<lb></lb>tur: ſed dimittat. </s> <s id="id.003051">An quia <pb xlink:href="035/01/243.jpg" pagenum="203"></pb>quid tale facit, vt alterum <lb></lb>impellat, & hoc alterum: <lb></lb>ceſſat verò <expan abbr="quãdo">quando</expan> non am<lb></lb>plius poteſt facere primum <lb></lb>impellens, vt id quod fer<lb></lb>tur, impellat. </s> <s id="id.003052">Et quando <lb></lb>grauitas eius quod fertur <lb></lb>deorſum ruit magis: quam <lb></lb>antrorſum impulſoris vis <lb></lb>poſſit impellere. </s> </p> <p type="head"> <s id="id.003053">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003054">Qvare quidpiam.] <emph type="italics"></emph>Cum omne proiectum graue quid ſit, ideó<lb></lb>que natura tendens rectà deorſum. </s> <s id="id.003055">Quærit rurſus Ariſtoteles: <lb></lb>ſed expreßius quam antè. </s> <s id="id.003056">Cur cum proiector non conſequatur proie<lb></lb>ctum, ipſum non feratur potius ſuo motu naturali: quam violento. <lb></lb></s> <s id="id.003057">Cui vt reſpondeat ad cauſam præcedentem, vim ſcilicet impreſſam <lb></lb>à primo motore adijcit medij, per quod proijcitur antiperiſtaſim. </s> <s id="id.003058">Cum <lb></lb>enim proiectum primo antrorſum dimouerit medium vt aërem, hic <lb></lb>ſumma celeritate retrò proiectus, ne vacuum quid (quod abhorret <lb></lb>natura ) relinquatur, conuolat: & ſic deinceps, ita vt quantum aër <lb></lb>anterior ob reſiſtentiam impediuit, factus poſterior cum concurſu <lb></lb>violento motum iuuet, vt ceſſare non deberet motus niſi anterioris <lb></lb>aëris obſiſtentiam iuuaret, & augeret maximè grauitas naturalis, <lb></lb>quibus iunctis: vis tandem impellentis antrorſum ſuperatur, & eua<lb></lb>neſcit: ſicque ceſſat motus violentus, & niſi aliquod adſit impedi<lb></lb>mentum, incipit naturalis, quo deorſum rectà ruit. <emph.end type="italics"></emph.end></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003059">35. <foreign lang="el">*dia\ ti/ ou)/te ta\ e)la/ttona, <lb></lb>ou)/te ta\ mega/la po/r)r(w fe/re<lb></lb>tai r(ipto/mena</foreign></s> </p> <p type="main"> <s id="id.003060">35. Cur <expan abbr="neq;">neque</expan> exigua, neque <lb></lb>magna proiecta feruntur <lb></lb>procul. </s> </p> <p type="main"> <s id="id.003061"><foreign lang="el">*dia\ ti/ ou)/te ta\ e)la/ttona ou)/te ta\ mega/la po/r)r(w fe/retai <lb></lb>r(ipto/mena, a)lla\ dei= summetri/an tina\ e)/xein pro\s <lb></lb>to\n r(iptou=nta; </foreign></s> <s id="g0133402"><foreign lang="el">po/teron o(/ti a)na/gkh to\ r(iptou/menon kai\ <lb></lb>w)qou/menon a)nterei/dein o(/qen w)qei=tai; </foreign></s> <s id="g0133403"><foreign lang="el">to\ de\ mhqe\n u(pei=kon dia\ <lb></lb>me/geqos h)\ mhde\n a)nterei=san di' a)sqe/neian ou) poiei= r(i=yin <lb></lb>ou)de\ w)=sin.</foreign></s> <s id="g0133404"><foreign lang="el">to\ me\n ou)=n polu\ u(perba/llon th=s i)sxu/os th=s <lb></lb>w)qou/shs ou)qe\n u(pei/kei, to\ de\ polu\ a)sqene/steron ou)de\n a)nerei/dei.</foreign></s> <s id="g0133405"><foreign lang="el"><lb></lb>h)\ o(/ti tosou=ton fe/retai to\ fero/menon, o(/son a)\n <lb></lb>a)e/ra kinh/sh| ei)s ba/qos; to\ de\ mhde\n kinou/menon ou)d' a)\n <lb></lb>kinh/seien ou)de/n. sumbai/nei dh\ a)mfo/tera tou/tois e)/xein.</foreign></s> <s id="g0133406"><foreign lang="el"><lb></lb>to/ te ga\r sfo/dra me/ga kai\ to\ sfo/dra mikro\n w(/sper ou)qe\n <lb></lb>kinou/mena/ e)sti: to\ me\n ga\r au)to\ kaq' e(\n kinei=, to\ d' <lb></lb>ou)qe\n kinei=tai.</foreign></s> </p> <p type="main"> <s id="id.003062">Cur <expan abbr="neq;">neque</expan> exigua, neque <lb></lb>magna proiecta procul fe<lb></lb>runtur: ſed oportet corre<pb xlink:href="035/01/244.jpg" pagenum="204"></pb>ſpondere <expan abbr="quodãmodo">quodammodo</expan> pro<lb></lb>ijcienti. </s> <s id="id.003063">An quia neceſſe <lb></lb>eſt, id, quod proijcitur & <lb></lb>impellitur reſiſtere ei, vnde <lb></lb>impellitur. </s> <s id="id.003064">Nihil verò ce<lb></lb>dens propter magnitudi<lb></lb>nem, vel nihil reſiſtens pro<lb></lb>pter imbecillitatem, nec <lb></lb><expan abbr="iactũ">iactum</expan> facit, nec impulſum. <lb></lb></s> <s id="id.003065">Illud <expan abbr="quidẽ">quidem</expan>, quia magno<lb></lb>pere excedit vires impulſo<lb></lb>ris, nequaquam cedit. </s> <s id="id.003066">Hoc <lb></lb>verò quia valdè <expan abbr="imbecillũ">imbecillum</expan>, <lb></lb>nihil reſiſtit. </s> <s id="id.003067">An quia quod <lb></lb>fertur <expan abbr="tãtum">tantum</expan> feratur: quan<lb></lb>tum aëris in profundum <lb></lb>mouerit. </s> <s id="id.003068">Non motum au<lb></lb>tem nec <expan abbr="contingẽs">contingens</expan> eſt mo<lb></lb>uere quicquam. </s> <s id="id.003069">Sic igitur <lb></lb>vtraque ſe habent, quod <lb></lb>enim valde <expan abbr="magnũ">magnum</expan>, quod<lb></lb>que valde paruum, ſeu nequaquam mota exiſtunt. </s> <s id="id.003070">Alte<lb></lb>rum enim nihil mouet: alterum nequaquam mouetur. </s> </p> <p type="head"> <s id="id.003071">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003072">Cvr neque exigua.] <emph type="italics"></emph>Exigua & magna vocabula ſunt in re<lb></lb>latis, & quæ intelligi, vt ante dictum eſt, non poſſunt niſi rela<lb></lb>tione facta ad aliud, ad quod referuntur. </s> <s id="id.003073">Magna igitur ſunt, quæ vi<lb></lb>res proijcientis valde excedunt: exigua vero, quæ viribus nullo modo <lb></lb>reſiſtunt, vel quæ adeò imbecilla ſunt, vt nullam vim mouendi, ne <lb></lb>aërem quidem habeant. </s> <s id="id.003074">Et ſic grana milij quamuis ſint exigua mole: <lb></lb>exigua tamen viribus dici non debent, cum è certo interuallo à quo<lb></lb>dam per foramen acus proiicerentur, nec rurſus magna licet mole eſ<lb></lb>ſent, magna erant ad vires ſaxa illa tritalantaria, telaque mißilia <lb></lb>duodeuiginti pedum, quæ recitat Athenæus facile eiaculata fuiſſe ad<emph.end type="italics"></emph.end><pb xlink:href="035/01/245.jpg" pagenum="205"></pb><emph type="italics"></emph>quadringentos cubitos, quod ſpatium eſt ſtadij, per machinam, quæ <lb></lb>erat in medio cataſtromate ſuper tripodes excitata, illius immenſæ <lb></lb>nauis, de qua antea diximus. </s> <s id="id.003075">Quæritur igitur, cur exigua vt pluma, <lb></lb>& magna vt mola, vel lapis ingens proiecta non procul ferantur: <lb></lb>ſed quæ ſic ferri debent, debeant correſpondere proiicienti, id eſt ha<lb></lb>bere rationem quandam, ita vt motor vel perſe, vel cum alio præ<lb></lb>polleat mouendo. </s> <s id="id.003076">In textu notabis<emph.end type="italics"></emph.end> <foreign lang="el">summebi/an</foreign> <emph type="italics"></emph>poni pro<emph.end type="italics"></emph.end> <foreign lang="el">a)nalogi/a|. </foreign></s> </p> <p type="main"> <s id="id.003077">An quia neceſſe eſt.] <emph type="italics"></emph>Prima reſponſio breuiter ſic concludi <lb></lb>poteſt. </s> <s id="id.003078">Oportet proiiciendum cedere proiectori, & etiam reſiſtere. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003079"><emph type="italics"></emph>Magnum non cedit, quia excedit vires proiectoris. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003080"><emph type="italics"></emph>Exiguum non reſiſtit, quia imbecillum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003081"><emph type="italics"></emph>Neutrum igitur proiectum fertur, nedum procul. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003082"><emph type="italics"></emph>Propoſitionis huius ſyllogiſmi prior pars perſe clara eſt, & illuſtrata <lb></lb>etiam ijs quæ à nobis cap. 32. dicta ſunt. </s> <s id="id.003083">Poſterior de reſiſtentia etiam <lb></lb>vera eſt, quia ſi mobile motori non reſiſtat, motus non fiet in tempo<lb></lb>re, & ſucceßione.: ſed in inſtanti quod eſt contra demonſtrata ab <lb></lb>Ariſtotele lib. 4. de Phiſico audit. </s> <s id="id.003084">Vim enim motoris, ſi nihil retar<lb></lb>dat, quare non ageret ilico? </s> <s id="id.003085">vnde ne tranſlatio ſubita latorum fiat, <lb></lb>non ſolum forma tranſlati obeſt: ſed & medium per quod fertur, <lb></lb>quod quanquam tenue & diaphanum ſit, vt aër, eſt tamen corpus. <lb></lb></s> <s id="id.003086">Eſt itaque hæc propoſitio vera. </s> <s id="id.003087">Præterea vt & hoc demonſtretur ad <lb></lb>ſenſum, ſi ſcorpioni vel arcuballiſtæ palea loco ſagittæ ſuperpona<lb></lb>tur, præter id quod ictum nullum faciet, etiam parum longè <lb></lb>emiſſa procedet. </s> <s id="id.003088">Quod ſi grauiſsimum ſpiculum, etiam lentius & <lb></lb>minus longè emittetur. </s> <s id="id.003089">Eſt igitur aliquod medium optimum, <lb></lb>vbi extrema ambo vitio non carent. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003090">An quia quod fertur.] <emph type="italics"></emph>Altera reſponſio ſic concludi poteſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003091"><emph type="italics"></emph>Quantum quidque aëris mouerit, tantum feretur: & ſi igitur <lb></lb>non mouerit, non feretur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003092"><emph type="italics"></emph>Magnum quia immotum non mouet aerem: imbecillum <lb></lb>quia etiam immotum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003093"><emph type="italics"></emph>Neutrum igitur feretur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003094"><emph type="italics"></emph>Propoſitio rurſus hæc vera eſt, quia cum alioqui penetratio dimen<lb></lb>ſionum fieret, ferri nihil poteſt, niſi medium per quod fertur, cedat <lb></lb>locum: alioqui medium puta aer, & id quod fertur, eſſent in vno. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/246.jpg" pagenum="206"></pb> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003095"><foreign lang="el">*dia\ ti/ ta\ fero/mena e)n tw=| <lb></lb>dinoume/nw| u(/dati ei)s to\ me/son <lb></lb>fe/retai.</foreign></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.003096">36. Cur lata in vortice <lb></lb>aquarum ad medium de<lb></lb>uoluuntur. </s> </p> <p type="main"> <s id="id.003097"><foreign lang="el">*dia\ ti/ ta\ fero/mena e)n tw=| dinoume/nw| u(/dati ei)s to\ <lb></lb>me/son teleutw=nta fe/rontai a(/panta; </foreign></s> <s id="g0133502"><foreign lang="el">po/teron o(/ti me/geqos <lb></lb>e)/xei to\ fero/menon, w(/ste e)n dusi\ ku/klois ei)=nai, tw=| me\n <lb></lb>e)la/ttoni tw=| de\ mei/zoni, e(ka/teron au)tou= tw=n a)/krwn. w(/ste <lb></lb>perispa=| o( mei/zwn dia\ to\ fe/resqai qa=tton, kai\ pla/gion <lb></lb>a)pwqei= au)to\ ei)s to\n e)la/ttw. e)pei\ de\ pla/tos e)/xei to\ <lb></lb>fero/menon, kai\ ou(=tos pa/lin to\ au)to\ poiei=, kai\ a)pwqei= ei)s <lb></lb>to\n e)nto/s, e(/ws a)\n ei)s to\ me/son e)/lqh|.</foreign></s> <s id="g0133503"><foreign lang="el">kai\ to/te me/nei dia\ <lb></lb>to\ o(moi/ws e)/xein pro\s a(/pantas tou\s ku/klous to\ fero/menon, <lb></lb>dia\ to\ me/son: kai\ ga\r to\ me/son i)/son a)pe/xei e)n e(ka/stw| <lb></lb>tw=n ku/klwn.</foreign></s> </p> <p type="main"> <s id="id.003098">Cur lata in vortice aqua<lb></lb>rum omnia tandem ad me<lb></lb>dium <expan abbr="deuoluũtur">deuoluuntur</expan>. </s> <s id="id.003099">An quia <lb></lb>quod fertur <expan abbr="magnitudinẽ">magnitudinem</expan> <lb></lb>habet: vt ſit in duobus cir<lb></lb>culis partim quidem in mi<lb></lb>nore: partim verò in maio<lb></lb>re. </s> <s id="id.003100">Vtrumque ipſius <expan abbr="extremũ">extre<lb></lb>mum</expan>. </s> <s id="id.003101">Itaque maior circum<lb></lb>uellit, quia celerius fertur, <lb></lb>& per tranſuerſum impel<lb></lb>lit ipſum ad <expan abbr="minorẽ">minorem</expan>. </s> <s id="id.003102">Quo<lb></lb>niam vero id quod fertur <lb></lb>latitudinem habet: illéque <lb></lb>rurſus idem facit, & pro<lb></lb>pellit ad <expan abbr="interiorẽ">interiorem</expan>, quouſ<lb></lb>que ad medium peruene<lb></lb>rit. </s> <s id="id.003103">quia quod fertur, ſimi<lb></lb>liter ſe habet ad omnes cir<lb></lb>culos ob medium. </s> <s id="id.003104">Etenim <lb></lb>ipſum in vnoquoque circulorum æqualiter diſtat. </s> </p> <p type="head"> <s id="id.003105">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003106">Cvr lata in vortice.] <foreign lang="el">*dino/menon u(/dwr</foreign> <emph type="italics"></emph>ſeu<emph.end type="italics"></emph.end> <foreign lang="el">di/nh</foreign> <emph type="italics"></emph>Latinis vor<lb></lb>tex aquæ, & gurges. </s> <s id="id.003107">Locus eſt profundus in flumine in quo <lb></lb>aqua vertitur, ſic dictus quod gulæ inſtar ad ſe trahat, & deuoret. <lb></lb></s> <s id="id.003108">Innatantia enim ſeu grauia vt nauim: ſeu leuia vt plumam, ſtatim <lb></lb>atque ad medium ſui adduxit, tam rapidè ſummergit, vt in momen<lb></lb>to nuſquam videas. </s> <s id="id.003109">Ariſtoteles in hoc loco præſupponit<emph.end type="italics"></emph.end> <foreign lang="el">o)n di/nh| su/<lb></lb>strofas tw=n u(da/twn</foreign> <emph type="italics"></emph>vortices aquoſos eſſe multos circulos concen<lb></lb>tricos, quorum vt continens maior eſt contento: ita ſemper celerius <emph.end type="italics"></emph.end><pb xlink:href="035/01/247.jpg" pagenum="207"></pb><emph type="italics"></emph>ferri. </s> <s id="id.003110">quod quam verum ſit, postea docebimus, vbi problema cum <lb></lb>ſuis cauſis ex mente Ariſtote<lb></lb>lis explicuerimus. </s> <s id="id.003111">Quærit igi<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.247.1.jpg" xlink:href="035/01/247/1.jpg"></figure><lb></lb><emph type="italics"></emph>tur Aristoteles cur quæ fe<lb></lb>runtur in vorticoſa aqua, om<lb></lb>nia tandem ad medium deuol<lb></lb>uantur. </s> <s id="id.003112">Sit igitur A medium <lb></lb>aquæ per circulos B C D, <lb></lb>E F G, H I K, L M N, <lb></lb>O P Q volutæ: ſit & vt <lb></lb>nauis R feratur per vorticem <lb></lb>B C D. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003113"><emph type="italics"></emph>Dico quod ad A medium <lb></lb>deuoluetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003114">An quia quod fertur.] <emph type="italics"></emph>Prima eſt<emph.end type="italics"></emph.end> <foreign lang="el">tou= diori/smou=</foreign> <emph type="italics"></emph>problematis <lb></lb>propoſiti demonstratio. </s> <s id="id.003115">quæ ſic concludetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003116"><emph type="italics"></emph>Habentis latitudinem ſi <expan abbr="extremũ">extremum</expan> vnum celerius feratur: quam <lb></lb>alterum, quod celerius fertur, truditur ad locum tardioris. <lb></lb></s> <s id="id.003117">per tranſuerſum enim à celerius moto impellitur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003118"><emph type="italics"></emph>Innatans omne in aqua vorticoſa, vt nauis, latitudinem <lb></lb>habet, & eius extremum quod in exteriori circulo eſt, <lb></lb>celerius fertur: quam quod in interiori. </s> <s id="id.003119">Circulus enim <lb></lb>maior celerius fertur. </s> <s id="id.003120">Exterior autem maior eſt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003121"><emph type="italics"></emph>Ergo innatans trudetur ad locum tardioris id eſt in interiorem <lb></lb>circulum, vt à B ad E & ab E ad H, & ab H ad L, & <lb></lb>ab L ad O, à quo tandem ad A medium. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003122"><emph type="italics"></emph>Similiter enim ſe habet innatans ad omnes circulos vorticis ob me<lb></lb>dium, quod à ſingulis æqualiter distat. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003123">Quia quod fertur.] <emph type="italics"></emph>Ex hoc loco expunximus vocabula hæc <lb></lb>ſine vſu & magna <expan abbr="cõfuſione">confuſione</expan> interiecta<emph.end type="italics"></emph.end> <foreign lang="el">kai\ to\ te me\n ei)</foreign> <emph type="italics"></emph>nec pro<emph.end type="italics"></emph.end> <foreign lang="el">ei)</foreign> <emph type="italics"></emph>re<lb></lb>ponimus<emph.end type="italics"></emph.end> <foreign lang="el">h)\</foreign> <emph type="italics"></emph>quod faciunt aliqui huius loci interpretes, ex hoc attin<lb></lb>gentes ſecundam cauſam problematis, quod ſcilicet omnia finem mo<lb></lb>tus, id eſt quietem appetant, ideo ferri ad locum quietis, qui medius <lb></lb>eſt in vortice. </s> <s id="id.003124">quæ vt vera eſſent, non video tamen exprimi poſſe <lb></lb>ex hoc Ariſtotelis contextu, qui ſuperioris demonstrationis comple<lb></lb>mentum eſt, vt patuit. <emph.end type="italics"></emph.end></s> </p> </subchap1> <pb xlink:href="035/01/248.jpg" pagenum="208"></pb> <subchap1> <p type="main"> <s id="id.003125"><foreign lang="el">h)\ o(/ti o(/swn me\n mh\ kratei= h( fora\ tou= dinoume/nou <lb></lb>u(/datos dia\ to\ me/geqos, a)ll' u(pere/xei th=| baru/thti <lb></lb>th=s tou= ku/klou taxuth=tos, a)na/gkh u(polei/pesqai kai\ bradu/teron <lb></lb>fe/resqai.</foreign></s> <s id="g0133505"><foreign lang="el">bradu/teron de\ o( e)la/ttwn ku/klos fe/retai: <lb></lb>to\ au)to\ ga\r e)n i)/sw| xro/nw| o( me/gas tw=| mikrw=| stre/fetai <lb></lb>ku/klw|, o(/tan w)=si peri\ to\ au)to\ me/son.</foreign></s> <s id="g0133506"><foreign lang="el">w(/ste ei)s to\n <lb></lb>e)la/ttona ku/klon a)nagkai=on a)polei/pesqai, e(/ws a)\n e)pi\ to\ <lb></lb>me/son e)/lqh|.</foreign></s> <s id="g0133507"><foreign lang="el">o(/swn de\ pro/teron kratei= h( fora/, lh/gousa <lb></lb>tau)to\ poih/sei. dei= ga\r to\n me\n eu)qu/, to\n de\ e(/teron kratei=n <lb></lb>th=| taxuth=ti tou= ba/rous, w(/ste ei)s to\n e)nto\s a)ei\ ku/klon <lb></lb>u(polei/pesqai pa=n.</foreign></s> <s id="g0133508"><foreign lang="el">a)na/gkh ga\r au)to\ e)nto\s h)\ e)kto\s kinei=sqai <lb></lb>to\ mh\ kratou/menon.</foreign></s> <s id="g0133509"><foreign lang="el">e)n au)tw=| dh\ toi/nun e)n w(=| e)sti/n, <lb></lb>a)du/naton fe/resqai to\ mh\ kratou/menon. e)/ti de\ h(=tton e)n tw=| <lb></lb>e)kto/s: qa/ttwn ga\r h( fora\ tou= e)kto\s ku/klou.</foreign></s> <s id="g0133510"><foreign lang="el">lei/petai de\ <lb></lb>ei)s to\n e)nto\s to\ mh\ kratou/menon meqi/stasqai. a)ei\ de\ e(/kaston <lb></lb>e)pidi/dwsin ei)s to\ mh\ kratei=sqai.</foreign></s> <s id="g0133511"><foreign lang="el">e)pei\ de\ pe/ras tou= mh\ kinei=sqai <lb></lb>poiei= to\ ei)s me/son e)lqei=n, me/nei de\ to\ ke/ntron mo/non, <lb></lb>a(/panta a)na/gkh ei)s tou=to dh\ a)qroi/zesqai.<lb></lb> *te/los.</foreign></s> </p> <p type="main"> <s id="id.003126">An quia quæ quidem la<lb></lb>tio vorricis aquæ <expan abbr="nõ">non</expan> vincit <lb></lb>ob magnitudinem: ſed ex<lb></lb>cellunt grauitate <expan abbr="celeritatẽ">celeritatem</expan> <lb></lb>circuli, illa neceſſe eſt & <lb></lb>tardius ferri. </s> <s id="id.003127">Minor autem <lb></lb>circulus tardius fertur. </s> <s id="id.003128"><expan abbr="Nõ">non</expan> <lb></lb>enim idem <expan abbr="ſpatiũ">ſpatium</expan> in ęquali <lb></lb>tempore magnus & paruus <lb></lb>circulus voluitur, quan<lb></lb>do fuerint circa idem me<lb></lb>dium. </s> <s id="id.003129">Itaque ad mino<lb></lb>rem <expan abbr="circulũ">circulum</expan> vt deſinat ne<lb></lb>ceſſe eſt, quouſque ad me<lb></lb>dium venerit. </s> <s id="id.003130">Quęcunque <lb></lb>verò latio prius vincit, fi<lb></lb>niens idem faciet. </s> <s id="id.003131">Oportet <lb></lb>enim vt <expan abbr="alterũ">alterum</expan> quidem ſta<lb></lb>tim celeritate grauitatem: <lb></lb>alterum verò grauitate ce<lb></lb>leritatem vincat, vt omnis <lb></lb>ad interiorem <expan abbr="circulũ">circulum</expan> ſem<lb></lb>per relinquatur. </s> <s id="id.003132">Neceſſe <lb></lb>enim ipſum quod non vin<lb></lb>citur intrò vel foras moue<lb></lb>ri. </s> <s id="id.003133">In ipſo verò in quo eſt, <lb></lb>non poteſt ferri, cum non <lb></lb>vincatur: multò minus in <lb></lb>exteriori. </s> <s id="id.003134">Latio enim exte<lb></lb>rioris circuli celerior eſt. <lb></lb></s> <s id="id.003135">Reſtat vt id quod non vin<lb></lb>cit, ad interiorem transfe<lb></lb>ratur. </s> <s id="id.003136">Semper enim nititur <lb></lb>quodlibet, ne vincatur. </s> <s id="id.003137">quoniam terminus, qui eſt non <lb></lb>moueri, facit ad medium venire. </s> <s id="id.003138">Quieſcit enim ſolum <lb></lb>centrum, ad quod omnia neceſſe eſt congregari. </s> </p> <pb xlink:href="035/01/249.jpg" pagenum="209"></pb> <p type="head"> <s id="id.003139">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003140">An quia quæ quidem.] <emph type="italics"></emph>Altera eſt eiuſdem<emph.end type="italics"></emph.end> <foreign lang="el">diorismou=</foreign> <emph type="italics"></emph>pro<lb></lb>blematis demonſtratio. </s> <s id="id.003141">quæ ſic concludetur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003142"><emph type="italics"></emph>Innatantia in vortice latio vorticoſa aquæ vincit, vel non <lb></lb>vincit. </s> <s id="id.003143">Si non vincat ob grauitatem, quæ excedit celeritatem <lb></lb>circuli, non ferentur in eo, in quo ſunt circulo. </s> <s id="id.003144">quia latio vor<lb></lb>ticoſæ aquæ vinceret. </s> <s id="id.003145">Multò minus in maiori. </s> <s id="id.003146">Relinquitur er<lb></lb>gò, vt in minori id eſt interiori, vt qui tardior ſit, ferantur, <lb></lb>& ſimili ratione ab hoc quouſque ad medium veniant. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003147"><emph type="italics"></emph>Si verò vincat, vt primum quidem vincat, tandem tamen <lb></lb>non vincit. </s> <s id="id.003148">Oportet enim vt modò hæc latio grauitatem <lb></lb>innatantium celeritate ſua vincat: modò ipſa innatantia <lb></lb>ſua grauitate celeritatem lationis vorticoſæ aquæ vin<lb></lb>cant. </s> <s id="id.003149">Vnumquodque enim nititur ſemper, ne vincatur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003150"><emph type="italics"></emph>Et ſic idem fiet, quod ante: vt innatantia ad interiorem feran<lb></lb>tur, & ad eum denique terminum, in quo violentia vorticis <lb></lb>non amplius voluantur. </s> <s id="id.003151">Hic autem terminus medium eſt vor<lb></lb>ticis ad quod omnia congregantur. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003152"><emph type="italics"></emph>Innatantia igitur in aqua vorticoſa ad medium deuoluuntur. </s> <s id="id.003153">quod <lb></lb>fuit demonſtrandum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003154"><emph type="italics"></emph>Hactenus fuerunt duæ demonſtrationes Ariſtotelis, quæ vt dixi <lb></lb>præſupponunt gurgitis vortices eſſe circulos concentricos, quod fal<lb></lb>ſum eſt, quia ſunt linea ſpiralis vnius aut plurium reuolutionum. <lb></lb></s> <s id="id.003155">Præterea nullam mentionem facit decliuitatis ſuperficiei aquæ vor<lb></lb>ticoſæ verſus medium, quæ res maximè confert ad deſcenſum rei in<lb></lb>natantis, & eiuſdem deuolutionis ad medium. </s> <s id="id.003156">Ibi enim ſpecus quæ<lb></lb>dam ſub aquis in terra latet, quæ<emph.end type="italics"></emph.end> <foreign lang="el">a)/bussos</foreign> <emph type="italics"></emph>quaſi<emph.end type="italics"></emph.end> <foreign lang="el">a)neu bu/ssou</foreign> <emph type="italics"></emph>ſine <lb></lb>fundo dicta eſt. </s> <s>Et in quam tanquam ex alto confluunt magna ce<lb></lb>leritate aquæ. </s> <s id="id.003157">Indicium huius eſt, quod pluma innatans ad hoc exa<lb></lb>ctè medium cum delata eſt, ſtatim abſorbetur, tracta ſcilicet deſcen<lb></lb>ſu aquæ: alioqui natura leuior infra aquam non deſcendet, tan<lb></lb>tum abeſt, vt quæ grauia ſunt non ibi ſubitò ſummergantur. </s> <s id="id.003158">His <lb></lb>ita poſitis demonſtratio problematis Aristotelici eſt facilis & <lb></lb>breuis. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/250.jpg" pagenum="210"></pb> <p type="main"> <s id="id.003159"><emph type="italics"></emph>Sit A inte<lb></lb>rius extremum, <lb></lb><figure id="id.035.01.250.1.jpg" xlink:href="035/01/250/1.jpg"></figure><lb></lb>& B exterius <lb></lb>lineæ ſpiralis A <lb></lb>B plurium reuo<lb></lb>lutionum, in ex<lb></lb>tremo B ſit na<lb></lb>uis C. </s> <s id="id.003160">Dico quod <lb></lb>C feretur ad A, <lb></lb>& inſuper quod <lb></lb>cum erit in A <lb></lb>ſummergetur in<lb></lb>tra abyſſum A <lb></lb>E. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003161">Demonſt. <lb></lb></s> <s><emph type="italics"></emph><expan abbr="Innatãs">Innatans</expan> in vor<lb></lb>ticoſa aqua fer<lb></lb>tur ad motum <lb></lb>vndæ impulſæ, <lb></lb>vel tractæ. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003162"><emph type="italics"></emph>At aqua vorticoſa fertur ſecundum lineam ſpiralem ad eius interius <lb></lb>medium. </s> <s id="id.003163">Eò enim & decliuitas, & abyſſus trahunt. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003164"><emph type="italics"></emph>Ergò innatans vt C in B principio vorticoſæ aquæ ad medium <lb></lb>interius A deuoluetur, & ibi propter tractum conſecutio<lb></lb>nemque aquæ, tum & naturalem rei innatantis grauitatem <lb></lb>rectà deorſum ruet per abyſſum A E. </s> <s>quod erat demon<lb></lb>ſtrandum. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003165"><emph type="italics"></emph>Ex hac concluſione elici debet monitum, quod nauigantibus vti<lb></lb>lißimum eſt, vitandos ſcilicet illis vortices aquarum tanquam ſcopu<lb></lb>los, qualem referunt in Noruergiæ Oceani inter Roeſt & Loffoet <lb></lb>maximum eſſe, qui naues ſecum in profundum trahat: & ad hos, ſi <lb></lb>forte impegerint ( quod ſentient ſi deprehenderint nauim ſuam ſine <lb></lb>cauſa alia, vt eius venti, qui <expan abbr="Typhõ">Typhon</expan>, vel Ecnephias dicitur, ) circum<lb></lb>agi, primo quoque tempore adhibitis omnibus remis veliſque eniten<lb></lb>dum ab his ſpiris ſeſe excludere. </s> <s id="id.003166">paulò enim pluribus implicati nullis <lb></lb>viribus ſeſe liberabunt. </s> <s id="id.003167">Hîc enim illud poetæ verißimum. <emph.end type="italics"></emph.end></s> </p> <pb xlink:href="035/01/251.jpg" pagenum="211"></pb> <p type="head"> <s id="id.003168">Facilis deſcenſus Auerni:</s> </p> <p type="main"> <s id="id.003169">Sed reuocare gradum, ſuperaſque euadere ad auras, <lb></lb>Hoc opus hic labor eſt. </s> </p> <p type="main"> <s id="id.003170"><emph type="italics"></emph>Sed rurſus de vorticibus hæc quæ ſunt apud Cardanum cap. 6. lib. 1. <lb></lb>de variet. rerum ſcitu digna ſunt. </s> <s id="id.003172">Trahi <expan abbr="quidẽ">quidem</expan> naues, inquit, ac cæ<lb></lb>tera velut Typhone vento haud abſurdum in vorticibus: vortices <lb></lb>quoque eſſe haud dubium eſt: at quomodo deſicendens aqua diſtribua<lb></lb>tur, non adeò perſpicuum eſt, cum ſemper in humiliora feratur. </s> <s id="id.003173">Imo <lb></lb>autem vortice quo modo quicquam humilius eſſe poßit, non facile <lb></lb>oſtendere. </s> <s id="id.003174">videtur autem mihi vortex non ad infima deſcendere: <lb></lb>ſed potius ad ea loca, ex quibus pateat exitus: Nam & vi vento<lb></lb>rum aliquando propellitur loco cedens. </s> <s id="id.003175">Quamuis etiam ad infima deſ<lb></lb>cendat, perſæpe tamen non attingit fundi libramentum: aut ſi infe<lb></lb>rius etiam deſcendit, aliquò exitus patet. </s> <s id="id.003176">Terra ſcilicet, vt hoc ad<lb></lb>dam, exiſtente hoc in loco cuniculoſa & per longißimum canalem <lb></lb>aliquam in ſpecum ſeſe exonerante. <emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="id.003177"><emph type="italics"></emph>Habes nunc, candide lector, opus Ariſtotelis magna ſubtilitate, <lb></lb>& iucunda ſubtilitatum in rebus Mechanicis contemplatione, re<lb></lb>fertum, & multis ob rerum principiorumque tractatorum obſcu<lb></lb>ritatem & ob contextus Græci corruptionem difficultatibus ob<lb></lb>ſtructum, noſtra opera & iudicio, vt ſpero, ita reſeratum, & à men<lb></lb>dis quibus propemodum infinitis ſcatebat, liberatum: vt poſthæc vel <lb></lb>mediocriter geometricis imbutus vel ne imbutus quidem hunc <lb></lb>legere & intelligere & voluptatem ac vtilitatem ex eo capere <lb></lb>poſsis. </s> <s id="id.003178">quinetiam in ſcholis <expan abbr="vulgariũ">vulgarium</expan> illorum philoſophorum, qui pa<lb></lb>rum abſunt, vt omninò<emph.end type="italics"></emph.end> <foreign lang="el">a)gewme/trhtoi</foreign> <emph type="italics"></emph>non ſint, locum eum obtine<lb></lb>re poſsit, quem cæteri qui ab hoc naturæ & artis etiam omnis atque <lb></lb>induſtriæ genio libri prodierunt, quémque ij, qui ab illis publicè le<lb></lb>guntur & explicantur. </s> <s id="id.003179">Quod in numinis diuini bonorum omnium <lb></lb>largitoris gloriam: Henrici IIII. </s> <s id="id.003180">Regis nostri auguſtiſsimi perpe<lb></lb>tuum decus: Ariſtotelis libri huius authoris famam atque authori<lb></lb>tatem maiorem: Reipub. denique noſtræ literariæ vtilitatem cedat, <lb></lb>deſidero. <emph.end type="italics"></emph.end></s> </p> <p type="head"> <s id="id.003181">FINIS. </s> </p> <p type="main"> <s id="id.003182">Cœlo reſtat iter: Cœlo tentabimus ire. </s> </p> </subchap1> </chap> </body> <pb xlink:href="035/01/252.jpg"></pb> <back> <section> <p type="head"> <s id="id.003183">ERRATA. </s> </p> <p type="main"> <s id="id.003184">In corrigendis primus numerus paginam, <lb></lb>Secundus lineam indicat. </s> <s id="id.003185">In his leges. </s> </p> <p type="main"> <s id="id.003186"><emph type="italics"></emph>6.28. hominum 7.11. engibatis 8.11. vtilitatem 8.22. <emph.end type="italics"></emph.end> Hanc ſed <lb></lb>10.4. <emph type="italics"></emph><foreign lang="el">au)to/mata</foreign> 11.17. vinum. 11.19. cucurbitulæ 12.5. nullus <lb></lb>18.19. intrò 19.27. quintupedalis 30.15. dimetientem 30.33. duas <lb></lb>36.1. radiorum 37.5. <emph.end type="italics"></emph.end> <foreign lang="el">e)f' ou=</foreign> <emph type="italics"></emph>39. littera<emph.end type="italics"></emph.end> <foreign lang="el">w</foreign> <emph type="italics"></emph>debet intelligi in angu<lb></lb>lo non ſignato parallelogrammi<emph.end type="italics"></emph.end><lb></lb><figure id="id.035.01.252.1.jpg" xlink:href="035/01/252/1.jpg"></figure><lb></lb><foreign lang="el">u z q</foreign> 48.9. <foreign lang="el">sparti/on</foreign> 77.10. <lb></lb><emph type="italics"></emph>quadrupedibus 81. deeſt figura <lb></lb>96.12. <emph.end type="italics"></emph.end> <foreign lang="el">a)su/stata</foreign> <emph type="italics"></emph>142.24. Epi<lb></lb>grammatis 167.32. per 182. <lb></lb>tota pagina vbi eſt litera<emph.end type="italics"></emph.end> <foreign lang="el">z</foreign> <emph type="italics"></emph>re<lb></lb>ponenda littera<emph.end type="italics"></emph.end> <foreign lang="el">c</foreign> 190.13. <foreign lang="el">tou= <lb></lb>ba/rous. </foreign></s> </p> <p type="main"> <s id="id.003189"><emph type="italics"></emph>In contextu Græco omiſimus de induſtria diagrammata Vve<lb></lb>cheli, partim parſimonia ſumptuum, partim quod poſata in commen<lb></lb>tarijs eorum vtcumque vicem ſupplerent. </s> <s id="id.003190">Si indigeas, ab eo re<lb></lb>petere licet. <emph.end type="italics"></emph.end></s> </p> </section> </back> </text> </archimedes>