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(download) - view tree Revision 1.3, Thu Jun 27 17:24:39 2002 UTC (10 years, 10 months ago) by bcfuchs Branch: MAIN Changes since 1.2: +21 -43 lines changed dtd to right one and added xml declaration |
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]>
<archimedes>
<info>
<author>Monantheuil, Henri</author>
<title>Aristotelis Mechanica</title>
<date>1599</date>
<place>Paris</place>
<editor></editor>
<publisher></publisher>
<translator></translator>
<lang>la</lang>
<chunk unit="page*">page</chunk>
<locator>000000071.xml</locator>
</info>
<text>
<front>
</front>
<body>
<chap>
<pb/>
<p type="head">
<s>ARISTOTELIS <lb/>MECHANICA <lb/>Græca, emendata, Latina facta, & <lb/>Commentariis illu&longs;trata. <lb/>A B <lb/><emph type="italics"/>HENRICO MONANTHOLIO <lb/>Medico, & Mathematicarum artium <lb/>Profe&longs;&longs;ore Regio.<emph.end type="italics"/><lb/>A D <lb/>HENRICVM IIII. GALLIÆ & NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;simum.</s>
</p>
<figure></figure>
<p type="head">
<s>PARISIIS, <lb/>Apud <gap/>EMIAM PERIER via Iacobæa, &longs;ub &longs;igno Bellerophontis.</s>
</p>
<p type="head">
<s>M. D. XCIX. <lb/><emph type="italics"/>CUM PRIVILEGIO REGIS.<emph.end type="italics"/></s>
</p>
<pb/>
<figure></figure>
<p type="head">
<s>HENRICO IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D.</s>
</p>
<p type="main">
<s>Ecce maie&longs;tati tuæ, <lb/>Rex Chri&longs;tiani&longs;&longs;ime, <lb/>nouum <expan abbr="fructũ">fructum</expan>, & tan­<lb/>quam primitias tuæàte <lb/>nuper re&longs;titutæ Acade­<lb/>miæ, Mechanica Ari­<lb/>&longs;totelis philo&longs;ophorum principis Gr&ecedil;­<lb/>ca, emendata, Latina facta, & commen­<lb/>tariis illu&longs;trata offero, dico, con&longs;ecro. <lb/>Noli, ob&longs;ecrote, ad Mechanicorum ti­<lb/>tulum munus hoc, qua&longs;i minus inge­<lb/>nuum, nec&longs;atis liberaliingenio, nedum <lb/>imperatorio & regali dignum, &longs;ubhor­<lb/>re&longs;cere, & ex prima i&longs;ta <expan abbr="frõte">fronte</expan> de&longs;picere. <lb/><expan abbr="Ferũt">Ferunt</expan> Platonem, quo philo&longs;ophorum
<pb/>nemo de Deo diuinius, <expan abbr="neq;">neque</expan> &longs;anctius <expan abbr="s&etilde;-&longs;it">sen­<lb/>&longs;it</expan>, <expan abbr="cũinterrogaretur">cuninterrogaretur</expan>, quid ageret Deus, <lb/>re&longs;pondi&longs;&longs;e <foreign lang="greek">a)eigewmebei_n.</foreign> Hoc verbum Lati­<lb/>nè expre&longs;&longs;um &longs;ignificat. A&longs;&longs;iduè terram <lb/>metiri. Quæactio &longs;i&longs;impliciter &longs;pecte­<lb/>tur, &à Geometri&ecedil; nomine ridiculo, vt <lb/>alibi appellat Plato, <expan abbr="exp&etilde;datur">expendatur</expan>, ridicula, <lb/>& Dei maie&longs;tate indigna iudicabitur. <lb/>Sed &longs;i ex ip&longs;ius artis viribus, & magnifi­<lb/>cis promi&longs;&longs;is illud <foreign lang="greek">a)eigewmebei_n</foreign> æ&longs;timetur, <lb/>quode&longs;t vniuer&longs;i <expan abbr="quãtumuis">quantumuis</expan> fusè <expan abbr="latéq;">latéque</expan> <lb/>patentis, <expan abbr="corporũ">corporum</expan> in eo omnium, &longs;uper­<lb/>ficierum, linearum, <expan abbr="omniúmq;">omniúmque</expan> men&longs;u­<lb/>rabilium <expan abbr="m&etilde;&longs;uram">men&longs;uram</expan> ratione, proportio­<lb/>ne, &longs;imilitudine con&longs;tituere, de&longs;ignare, <lb/>permetiri: actio certè erit tantò priore <lb/>nobilior: quantò totum <expan abbr="finitũ">finitum</expan> quidem, <lb/>&longs;ed infinito per&longs;imile exigua, & infima <lb/>&longs;ui parte e&longs;t nobilius, & excellentius: & <lb/>qui <expan abbr="hãc">hanc</expan> actionem accurate ponderibus <lb/>librarit&longs;uis, <expan abbr="nequaquã">nequaquam</expan> indignam, circa <lb/>quam Deus ver&longs;etur, & &longs;e&longs;e occupet, iu­<lb/>dicabit. Verumenimuerò &longs;iad illud <foreign lang="greek">a)eigew­<lb/>mebei_n</foreign> addi&longs;&longs;et Plato, <foreign lang="greek">kai\ a)eimhxana_<gap/>ai,</foreign> luculen-
<pb/>tius multò meo iudicio, & diuinæ maie­<lb/>&longs;tati congruentius, <expan abbr="atq;">atque</expan> magnificentius <lb/>re&longs;pondi&longs;&longs;et. Quid enim e&longs;t Mundum <lb/>huncex nihilo condidi&longs;&longs;e: &longs;uis omnibus <lb/>numeris ab&longs;olui&longs;&longs;e: ponderibus <expan abbr="vndiq;">vndique</expan> <lb/>&longs;uis æquilibra&longs;&longs;e: longitudine, latitudi­<lb/>ne, altitudine, in omni habitudine, & <lb/>re&longs;pectu commen&longs;uraui&longs;&longs;e: eundém­<lb/>que in eodem &longs;tatu & perfectione a&longs;&longs;i­<lb/>duò retinere, &longs;tabilire, con&longs;eruare, quam <lb/><foreign lang="greek">a)eigewmetrei_n kai\ a)eimhxana_<gap/>ai?</foreign> Mundus enim <lb/>hic machina e&longs;t, & quidem machina­<lb/>rum maxima, efficaci&longs;&longs;ima, firmi&longs;&longs;ima, <lb/>formo&longs;i&longs;&longs;ima. An non omnia corpora <lb/>complectitur, quod eius <expan abbr="imm&etilde;&longs;itatem">immen&longs;itatem</expan> <lb/>arguit? An <expan abbr="nõ">non</expan> ad omnium mutabilium <lb/>lationem, alterationem, generationem, <lb/>auctionem, con&longs;eruationem, & <expan abbr="dura-tion&etilde;">dura­<lb/>tionem</expan>, vt Dei &longs;ui auctoris <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> <lb/>concurrit, quod eius vim, & efficaciam <lb/>o&longs;tendit? An non quinquies mille <expan abbr="quin-g&etilde;tos">quin­<lb/>gentos</expan> &longs;exaginta & <expan abbr="vnũ">vnum</expan> annos, quoad &longs;ui <lb/><expan abbr="quinq;">quinque</expan> partes primas, & &longs;implices, per­<lb/>&longs;euerat omnis mutationis expers: quod
<pb/>eius <expan abbr="firmitat&etilde;">firmitatem</expan> plu&longs;quam adamantinam <lb/>te&longs;tatur? An non huius totius ad omnes <lb/>&longs;uas partes, & omnium <expan abbr="&longs;uarũ">&longs;uarum</expan> partium, <lb/>particularum que cum inter&longs;e, tum ad <lb/>ip&longs;um &longs;ummus e&longs;t con&longs;en&longs;us, con&longs;pira­<lb/>tio &longs;umma, omnium hominum oculis <lb/>& menti iucun di&longs;sima &longs;ymmetria, pro­<lb/>portio, æquabilitas, vnà cum totius fi­<lb/>gura pulcherrima, & conuenienti&longs;&longs;ima, <lb/>quæ vnica e&longs;t &longs;uperficie terminata pari­<lb/>bus ab vno puncto vndique di&longs;tante <lb/>interuallis, & cum tot <expan abbr="a&longs;trorũ">a&longs;trorum</expan> tan quam <lb/>gemmarum pretio&longs;i&longs;&longs;imarum hîc illîc <lb/>in eminentiori, & apparentiori &longs;ui par­<lb/>te collocatorum perenniluce, qua qua­<lb/>litate nec formo&longs;ior, nec <expan abbr="hominũ">hominum</expan> ocu­<lb/>lis gratior, nec v&longs;ibus humanis vtilior <lb/>apparere pote&longs;t: quod eius pulchritudi­<lb/>nem vbique o&longs;tentat, & mirabiles &longs;ui <lb/>ip&longs;i^{9} amores excitat? Deus igitur, <expan abbr="pr&ecedil;ter-quã">pr&ecedil;ter­<lb/>quam</expan> quod e&longs;t accurati&longs;&longs;imus, <expan abbr="a&longs;&longs;iduu&longs;q;">a&longs;&longs;iduu&longs;que</expan> <lb/>Geometra, diuini Platonis <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan>, e&longs;t <lb/>etiam no&longs;tra, & operum tot magnifi­<lb/>corum euidentia, &longs;apienti&longs;&longs;imus, opti-
<pb/>mus, potenti&longs;&longs;imus <foreign lang="greek">mhxanao\s,</foreign> & <foreign lang="greek">mhxanepoio\s.</foreign><lb/>Ip&longs;eidem, qui <foreign lang="greek">makro/kosmon</foreign> magnum mun­<lb/>dum fecit, fecit & <foreign lang="greek">mikro/kosmon</foreign> <expan abbr="paruũ">paruum</expan> mun­<lb/>dum, hominem &longs;cilicet: & fecit ad ima­<lb/>ginem &longs;uam, atque vt &longs;e imitaretur beni­<lb/>gni&longs;&longs;ima liberalitate impertitus e&longs;t ei <lb/>mentem, quæ e&longs;&longs;et <foreign lang="greek">te/xnh te/xnwn,</foreign> ars artium, <lb/>& manum, quæ e&longs;&longs;et <foreign lang="greek">o)/rganono)rga/nwn,</foreign> in&longs;tru­<lb/>mentum in&longs;trumentorum, quibus ho­<lb/>mo, quem volebat e&longs;&longs;e &longs;apienti&longs;&longs;imum <lb/>animalium, machinas & in&longs;trumenta <lb/>alia fabricaretur, & iis adiutus &longs;olus, vel <lb/>cum paucis onera quantumuis ingentia <lb/>dimoueret, deduceret, quo vellet collo­<lb/>caret: vrbes, <expan abbr="t&etilde;pla">templa</expan>, palatia, collegia, por­<lb/>ticus, pontes, domos ædificaret, perde­<lb/>ret, re&longs;tauraret, con&longs;eruaret: terram ver­<lb/>teret, in terræ vi&longs;cera de&longs;cenderet, terræ <lb/>campos, valles, montes bigis, quadrigis <lb/>peragraret: maria omnia, fluuios remis, <lb/>velis tranaret: ventis imperaret: anima­<lb/>lium genus omne &longs;ibi &longs;ubiiceret: tantas <lb/><expan abbr="deniq;">denique</expan>, & tam multas resfaceret, vt eas, <lb/>ni&longs;i quotidie fieri, & factas e&longs;&longs;e &longs;æpius
<pb/>alij homines &longs;pectarent, omninò fieri <lb/>non po&longs;&longs;e iurarent. Iidem cum facta­<lb/>rum rationes, virium que in in&longs;trumen­<lb/>tis, & machinis adhibitis cau&longs;as non in­<lb/>telligunt, miracula e&longs;&longs;e pleno ore pro­<lb/>clamant. Vndefortèillud Martialis.</s>
</p>
<p type="main">
<s><emph type="italics"/>Barbara Pyramidum &longs;ileat miracula <lb/>Memphis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Tum &longs;eptem illa, quæ vulgò iactantur <lb/>orbis miracula. Quæ profectò &longs;apien­<lb/>ter Deus homini dedit & po&longs;&longs;e, & fa­<lb/>bricari: ne mundum hunc à&longs;e <expan abbr="cõditum">conditum</expan>, <lb/>con&longs;eruatum, con&longs;eruandum, quandiu <lb/>voluerit, hominibus foret incredibile. <lb/>His enim tantis, & tam multis quæab <lb/>homine <foreign lang="greek">mhxanqpomtikw_|</foreign> manife&longs;tè & in om­<lb/>nium oculis fiunt, & con&longs;eruantur, fa­<lb/>cillimum e&longs;t, qui&longs;quis mentem habet, <lb/>credere, cogno&longs;cere, complecti, etiam &longs;i <lb/>cum fieret, abfuerit, mundum <expan abbr="hũc">hunc</expan>, <expan abbr="ma-ximũ">ma­<lb/>ximum</expan> certè operum opus, factum e&longs;&longs;e, <lb/>& con&longs;eruari: non autem ab vllo homi­<lb/>ne, &longs;ed ab alio <foreign lang="greek">mhxanopoihtikw_|</foreign> tantò homi­<lb/>nem præ&longs;tantia, &longs;apientia, potentia, imò
<pb/>infinitè &longs;uperante: quantò hæc mundi <lb/>machina omnium hominum etiam Ar­<lb/>chimedeorum machinas &longs;uperat, atque <lb/>antecellit. Hic autem quis pote&longs;t e&longs;&longs;e <lb/>alius, præterquam is, quem Deum om­<lb/>nes appellam^{9}. Sed & ex eo fit perquam <lb/>credibile, ad huius magnæ molis archi­<lb/>tecturam <expan abbr="architectũ">architectum</expan> &longs;uum nihil eguï&longs;&longs;e <lb/>ferramentis, vecte, cuneis, trochleis, axe <lb/>in peritrochio, molitione, conatu, quæ <lb/>impius i&longs;te Velleius ex Epicuri &longs;enten­<lb/>tia apud Ciceronem di&longs;putans &longs;tultè re­<lb/>quirebat. In quo enim immen&longs;usille au­<lb/>thor, factorque hominis, in proprij <lb/>operis fabricahomini ip&longs;i præpolleret, <lb/>&longs;i machinis, & in&longs;trumentis, materia, & <lb/>molimine, vt homo, indigeret? quan­<lb/>quam po&longs;t &longs;emel à &longs;e mundum ex nihilo <lb/>creatum, ille liberrimum &longs;emper, & po­<lb/>tenti&longs;&longs;imum agens, cum his adiunctis, <lb/>& &longs;ine his quando, quotie&longs;que vult, ni­<lb/>hilominus operatur. Quæ &longs;i rectè & ve­<lb/>rè Deo, <expan abbr="quantũ">quantum</expan> fas e&longs;t homini, dicta <lb/>&longs;unt: ecquidiam &longs;upere&longs;t, Rex Chri&longs;tia­
<pb/>ni&longs;&longs;ime, quapropter ab hoc munere vt <lb/>vili abhorreas, & ip&longs;e reformidem, licet <lb/>Mechanicorum <expan abbr="titulũ">titulum</expan> in fronti&longs;picio <lb/>gerat, hoc adeò in&longs;igne opus ab Ari­<lb/>&longs;totele profectum, vtile, <expan abbr="iucũdum">iucundum</expan>, &longs;ub­<lb/>tili&longs;&longs;imè tractatum: &longs;ed temporum iniu­<lb/>ria multis mendis fœdum, ob&longs;curum, <lb/>captu difficile, nunc opera no&longs;tra niti­<lb/>dum, clarum, & captu facile &longs;anctæ ma­<lb/>ie&longs;tati tuæ dicare, ac <expan abbr="cõ&longs;ecrare">con&longs;ecrare</expan>? Ad quod <lb/>faciendum in&longs;uper me inuitauit cau&longs;a <lb/>alia, ni&longs;i me fallit animus, iu&longs;ti&longs;&longs;ima. <lb/>Qui&longs;quis enim duas res omnium, quæ <lb/>&longs;untin vita <expan abbr="hominũ">hominum</expan>, maximas perfecit, <lb/>quarúmque temporibus atque fabricis <lb/>&longs;ummus e&longs;t & frequenti&longs;&longs;imus machi­<lb/>narum, & <expan abbr="in&longs;trum&etilde;torum">in&longs;trumentorum</expan> v&longs;us: ille non <lb/>pote&longs;t machinamentorum, & <expan abbr="in&longs;tru-m&etilde;torum">in&longs;tru­<lb/>mentorum</expan> formis, rationibus, adinuen­<lb/>tionibus, & virium <expan abbr="eorũ">eorum</expan> admirabilium, <lb/><expan abbr="incredibiliumq;">incredibiliumque</expan> cau&longs;is, ac principiis per <lb/>ceptis non magno pere delectari, atque <lb/>cos, qui de iis &longs;ubtiliter, & ingeniose tra­<lb/>ctarint, libros oblatos non grati&longs;&longs;imè
<pb/>excipere: tu, Rex potenti&longs;&longs;ime, duas il­<lb/>las res perfeci&longs;ti, bellum &longs;cilicet, & pa­<lb/>cem. In vtriu&longs;que tempore a&longs;&longs;iduus ma­<lb/>chinarum, & in&longs;trumentorum v&longs;us, at­<lb/>que opportunitas. Tunam que bellum <lb/>(hîc me patiare, rex potenti&longs;&longs;ime, in me­<lb/>ritas aliquot tuas laudes paulò amplius, <lb/>non extra rem tamen excurrere, & ex­<lb/>patiari.) Tu inquam bellum (ô onus <lb/><foreign lang="greek">kolo<gap/>ikw/ta<gap/>on,</foreign> graui&longs;&longs;imum certè, & num­<lb/>quam &longs;i fieri po&longs;&longs;et, commouendum: <lb/>vbi, vbitamen nece&longs;&longs;arium e&longs;t, mouen­<lb/>dum, &longs;u&longs;cipiendum, gerendum) ad­<lb/>uer&longs;us dome&longs;ticos in&longs;anientes, rebel­<lb/>le&longs;que: aduer&longs;us extraneos intraneo­<lb/>rum tumultu &longs;uperbientes, ferocien­<lb/>tes, & occa&longs;ionem regni inuadendi <lb/>opportuni&longs;&longs;imam nactoş & nihil non <lb/>inde &longs;ibi pollicitiş animo plu&longs;quam <lb/>Herculeo &longs;u&longs;cepi&longs;ti: hoc ip&longs;um, li­<lb/>cet omnium bellorum, quorum hi­<lb/>&longs;torias, & annales no&longs;tros legens me­<lb/>mini&longs;&longs;e mihi videor, acerbi&longs;&longs;imum,
<pb/>pernitio&longs;i&longs;&longs;imum, exitio&longs;i&longs;&longs;imumque, <lb/>plurium intus & foris contentione, & <lb/><expan abbr="cõiuratione">coniuratione</expan> vi&longs;um in&longs;uperabile, moui­<lb/>&longs;ti, ge&longs;&longs;i&longs;ti, &longs;uperaui&longs;ti. Quomodo <expan abbr="aut&etilde;">autem</expan>? <lb/>dicam pro meo &longs;en&longs;u: tu melius. Omnes <lb/>omnium tuarum prouinciarum &longs;ubie­<lb/>ctos rebelles, partim armis, quæ fuit tua <lb/>in pugnando terribilis &longs;emper inimicis <lb/>& audacia, & fortitudo: partim auro ex <lb/>propriis eorum fodinis effo&longs;&longs;o, recto <lb/>&longs;anè iudicio, quæ tua fuit &longs;umma cum <lb/>prudentia iu&longs;ticia, vtin po&longs;terum &longs;ciant <lb/>&longs;uis à Deo datis obtemperare regibus, <lb/>neque vnquam ab illorum contrariis <lb/>&longs;tare partibus: partim benignitate, & <lb/>man&longs;uetudine, quæ te &longs;uperis pulcher­<lb/>rima æquat virtus.</s>
</p>
<p type="main">
<s><emph type="italics"/>Nam<emph.end type="italics"/> (vt ait grauis vnus è poëtis) <emph type="italics"/>cum <lb/>vincamur in omni<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Munere: &longs;ola Deos æquat clementia nobis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Ad concordiam inter &longs;e, & tecum &longs;er­<lb/>uandam: ad beneuolentiam ergate præ­<lb/>&longs;tandam, obedientiam, fidelitatem rede<gap/><lb/>gi&longs;ti. Extraneos verò longo bello: bre-
<pb/>uioritamen, quam &longs;perare, aut promit­<lb/>tere nobis au&longs;i fuerimus, fractos, &longs;æpe <lb/>Marte aperto, & manibus <expan abbr="vtrinq;">vtrinque</expan> con­<lb/>&longs;ertis victos, fugatos, tandem procul <lb/>ab omnibus Galliæ finibus reieci&longs;ti: & <lb/>quan quam anteà &longs;emperab omni pacis <lb/>conditione alieni&longs;&longs;imos, vt pacem ip&longs;i <lb/>appeterent, & peterent coëgi&longs;ti. Quid <lb/>tuilico? Quandoquidem pax victo &longs;em­<lb/>per &longs;it nece&longs;&longs;aria, & victoriea, quæ nihil <lb/>po&longs;t &longs;e ferat in&longs;idiarum, &longs;emper expe­<lb/>diat: &longs;tatim eius ineundæ, & cum <expan abbr="po-t&etilde;ti&longs;&longs;imo">po­<lb/>tenti&longs;&longs;imo</expan> ho&longs;te Philippo Hi&longs;paniarum <lb/>rege conciliandæ <expan abbr="occa&longs;ion&etilde;">occa&longs;ionem</expan> quæ&longs;itam, <lb/>& oblatam à Clemente VIII. pontifice <lb/>&longs;ummo, verè vtriu&longs;que gentis commu­<lb/>ni <expan abbr="par&etilde;te">parente</expan> clementi&longs;&longs;imo, per &longs;uum lega­<lb/>tum Alexandrum de Medicis Cardina­<lb/>lem, & Archiepi&longs;copum Florentinum, <lb/>qui huic paci tractandæ, conficiendæ, <lb/>& ni&longs;i perfectare <expan abbr="nõ">non</expan> relinquendæ &longs;em­<lb/>per interfuit, & qua&longs;i præfuit, arripui­<lb/>&longs;ti. Duobus etuo &longs;anctiore con&longs;ilio de­<lb/>lectis con&longs;iliariis tibi, id e&longs;t patriæ
<pb/>&longs;aluti addicti&longs;&longs;imis (permittes bona tua <lb/>venia, Rex clementi&longs;&longs;ime, honoris & <lb/>gratæ erga viros tam bene de te, totaque <lb/>Gallia meritos memoriæ no&longs;træ gratia, <lb/>hîc illos nominari) Pomponio Belle­<lb/>ureo & Nicolao Brulartio, toto tantæ <lb/>molis negotio perte commi&longs;&longs;o, pacem <lb/>tibi, tuis, toti Galliæ honorificenti&longs;&longs;i­<lb/>mam conciliaui&longs;ti: pacem inquam ab­<lb/>&longs;entem, & ad multos annos exulem re­<lb/>duxi&longs;ti: iureiurando &longs;olemni&longs;&longs;imo, &longs;i­<lb/>gillis vtriu&longs;que regni confirmatam per <lb/>præcones tuos proclamari iu&longs;&longs;i&longs;ti: arma <lb/>de manibus militum, quæ erant &longs;umpta <lb/>pro te, & contra te &longs;u&longs;tuli&longs;ti: iam tuo­<lb/>rum in ligones, aratrorum dentes, fal­<lb/>ces, vngues ferreos, vectes, trochleas, <lb/>malleos, aliaque in&longs;trumenta vitæ mi­<lb/>tioris, & pacificæ conuerti&longs;ti: iam arua <lb/>feracis Galliæ recoli cœpta, vbique re­<lb/>uire&longs;cunt: lætæ &longs;egetes, agri vberes cul­<lb/>mis ari&longs;ti&longs;que luxuriant: ex ædificijs &longs;e­<lb/>miruta re&longs;taurantur, dirutorum loco <lb/>noua &longs;tatuuntur: leges liberè pronun-
<pb/>ciant: iu&longs;ticia libritenens fide zygo&longs;tati­<lb/>ca omnia iudicat: linguarum & bona­<lb/>rum <expan abbr="artiũ">artium</expan>, te earum re&longs;tauratore, & vin­<lb/>dice & cu&longs;tode, eruditio in <expan abbr="Academiã">Academiam</expan> <lb/>reuer&longs;a frequentatur: ingenia, quæ in ea <lb/>&longs;unt præclara, in variarum artium iam <lb/>redundant elegantiam, fœtu&longs;que &longs;uos <lb/>producere ge&longs;tiunt: mercatura denique <lb/>tutò vagatur, peregrinatur, ru&longs;ticatur. <lb/>Harum duarum rerum belli, & pacis <lb/>magnitudinem, <expan abbr="difficultat&etilde;">difficultatem</expan>, <expan abbr="impedim&etilde;-ta">impedimen­<lb/>ta</expan> &longs;oli <expan abbr="cõplectentur">complectentur</expan>, quitam di&longs;&longs;ociatas <lb/>Gallorum & Hi&longs;panorum <expan abbr="volũtates">voluntates</expan>: <expan abbr="tã">tam</expan> <lb/>multa, & multiplici <expan abbr="&longs;imultatũ">&longs;imultatum</expan> <expan abbr="atq;">atque</expan> odio­<lb/>rum crudelitate &longs;auciatas: tot mordaci­<lb/>bus dictis, &longs;criptis, factis in &longs;e&longs;e mutuis <lb/>exulceratas: tam deiecta, <expan abbr="atq;">atque</expan> perturbata <lb/>omnia ip&longs;i &longs;uis oculis viderunt. <expan abbr="Nã">Nam</expan> qui <lb/><expan abbr="nõ">non</expan> <expan abbr="viderũt">viderunt</expan>, licet ab alijs recitata <expan abbr="audiãt">audiant</expan>, <lb/>aut <expan abbr="monum&etilde;tis">monumentis</expan> <expan abbr="cõm&etilde;data">commendata</expan> <expan abbr="legãt">legant</expan>, non ar­<lb/>bitror <expan abbr="tam&etilde;">tamen</expan> vllius vlla <expan abbr="quantũuis">quantunuis</expan> elegan­<lb/>ti, & probabili narratione adduci po&longs;&longs;e, <lb/>vt <expan abbr="credãt">credant</expan>, quando <expan abbr="quid&etilde;">quidem</expan> nos, qui hæc vi­<lb/>dimus, &longs;i <expan abbr="quãdo">quando</expan> in <expan abbr="memoriãreducimus">memoriarreducimus</expan>,
<pb/>mera &longs;omnia videre nobis videmur: <lb/>Quid igitur ab&longs;urdum? quidve inele­<lb/>gans facimus? &longs;i tibi qui cum tanta glo­<lb/>ria hæc duo perfeceris, de pacis & belli <lb/>in&longs;trumentis, vel potius de horum in­<lb/>&longs;trumentorum viribus, & virium cau­<lb/>&longs;is, &, quod admirabilius, vno <expan abbr="earũ">earum</expan> prin <lb/>cipio, quod e&longs;t circulus, librum offeri­<lb/>mus? qui te præterea videamus magni­<lb/>ficis ædificiorum &longs;ub&longs;tructionibus, ita <lb/>delectari, vt nihil, <expan abbr="nõ">non</expan> dicam nunc, cum <lb/>&longs;int hæc pacis opera: &longs;ed etiam in ip&longs;o <lb/>belli flagranti&longs;&longs;imiardore, ab ijs auocare <lb/>aut retardare potuerit. Porticus diues, <lb/>&longs;uperba, amu&longs;&longs;itata, quæ à tua Lupara <lb/>ad tuas ædes lateritias te, <expan abbr="tuo&longs;q;">tuo&longs;que</expan> delatura <lb/>& illinc ad <expan abbr="vrb&etilde;">vrbem</expan> de&longs;uper ventura, te <expan abbr="in-u&etilde;tore">in­<lb/>uentore</expan>, & excogitatore, tuis &longs;umptibus <lb/>extruitur: Ædium lateritiarum cochlea­<lb/>ri&longs;cal&ecedil;, octauo orbis miraculo <expan abbr="colophõ">colophom</expan> <lb/>impo&longs;itus: Ca&longs;tella Fontisbellaquei, <lb/>Sanctogermani, Moncelli colophoni <lb/>&longs;uo proxima, nuper Reuerendi&longs;&longs;imo <lb/>Legato hinc in Italiam redeunti, nobi
<pb/>li&longs;&longs;imis illis Hi&longs;panis, Flandri&longs;que, qui <lb/>ad pacem iureiurando confirmandam <lb/>aduenerant, cum tua incredibili vo­<lb/>luptate o&longs;tentata, & eorum maiori ad­<lb/>miratione ab illis &longs;pectata luculenter te­<lb/>&longs;tantur, <expan abbr="atq;">atque</expan> <expan abbr="hãc">hanc</expan> animi tui <expan abbr="delectation&etilde;">delectationem</expan> <lb/>rege magnifico <expan abbr="digni&longs;&longs;imã">digni&longs;&longs;imam</expan> declararunt, <lb/>& vi&longs;uris, quotquot venient in po&longs;te­<lb/>rum, declarabunt. Spemque adferunt <lb/><expan abbr="nõmediocrem">nommediocrem</expan>, te, pro tuorum in Aca­<lb/>demia profe&longs;&longs;orum collegio, quale edi­<lb/>ta pro eo oratione à me de&longs;criptum <lb/>e&longs;t: aut ab alio magnificentius de&longs;cribe­<lb/>tur, ædificando, aliquandoe&longs;&longs;e cogitatu­<lb/>rum, & perfecturum. Hæc igitur mihi <lb/><expan abbr="per&longs;ua&longs;erũt">per&longs;ua&longs;erunt</expan>, ne quicquam vererer opus <lb/>hoc, ratione opellæ <expan abbr="quali&longs;cunq;">quali&longs;cunque</expan> no&longs;træ, <lb/>exiguum &longs;cio: &longs;ed ratione authoris &longs;ui, <lb/>Ari&longs;totelis, magnum, &longs;anctæ maie&longs;tati <lb/>tuæ co&longs;ecrare. Quod <expan abbr="nũc">nunc</expan> igitur tam lu­<lb/>benter facio: quam Deum <expan abbr="optimũ">optimum</expan> ma­<lb/>ximum obnixè precor, vt vitam tibi <lb/>impertiat, in duas annorum quadrage­<lb/>narias ita partitam vt &longs;ecundam, quam
<pb/>belli reliquiis, & pace in ea confectis fœ­<lb/>liciter ingre&longs;&longs;us es, tot rebus pacis tam <lb/>magnificis, & glorio&longs;is adhuc aggre­<lb/>diundis, & perficiundis con&longs;umas: quot <lb/>in rebus belli admirabilibus, atque in­<lb/>credibilibus perfectis primam con&longs;um­<lb/>p&longs;i&longs;ti. Hoc, &longs;i tibi, Deo ita volente, eue­<lb/>niat, haud profectò verendum erit di­<lb/>cere, & palam, quod omnium hi&longs;toriæ <lb/>conte&longs;tabuntur, proclamare, te <expan abbr="rerũ">rerum</expan> ad­<lb/>mirabili&longs;&longs;imarum regem, & regum, qui <lb/>hactenus in quacunque orbis regione <lb/>regnauere, fore præ&longs;tanti&longs;&longs;imum, & ad­<lb/>mirabili&longs;&longs;imum. Vale, & duas illas per­<lb/>optatas annorum quadragenarias tibi, <lb/>& nobis &longs;ic viue. Scriptum Lutetiæ eo <lb/>die, quo quinquennio ante à te ciui­<lb/>tas Hi&longs;panis erepta, & &longs;uis ciuibus fœli­<lb/>citer e&longs;t re&longs;tituta.</s>
</p>
<p type="main">
<s>MAIESTATIS</s>
</p>
<p type="main">
<s>Humillimus &longs;eruus</s>
</p>
<p type="main">
<s>HENRICVS MONANTHOLIVS.</s>
</p>
<pb/>
<p type="head">
<s>A D <lb/>HENRICVM IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;&longs;imum.</s>
</p>
<p type="main">
<s><emph type="italics"/>Pacatos fecit tua nos victoria ciues. <lb/>Inde caput Laurus: digitos ornabit Oliua <lb/>Semper, & ingentem per vtrâque volabis Olympum.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>THEODORICVS MONANTHOLII filius.</s>
</p>
<p type="head">
<s>De libro <foreign lang="greek"><gap/> mhxanikw_n,</foreign> Ari&longs;totele, <lb/>& Monantholio.</s>
</p>
<p type="main">
<s><emph type="italics"/>Inter Ari&longs;totelis libros &longs;ubtilior i&longs;to<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Nullus<emph.end type="italics"/> <foreign lang="greek">*mhxanikw_n,</foreign> <emph type="italics"/>vtiliorque fuit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sed mendis fœdus merito &longs;ine honore iacebat,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Non authore &longs;uo dignus Aristotele.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Lectus erat nulli, nulli intellectus agebat<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vitam cum blattis, muribus, & tineis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Liber ab his, captu facilis, bene comptus en exit<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In lucem, vigilis luce Monantholij.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sic dat Ari&longs;toteli vitam, claréque vicißine<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Accipit ex ip&longs;o, quam dedit ille, parem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vna dies ambos &longs;eruabit, & eximet æuo,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Amborúmque &longs;imul fama &longs;uper&longs;tes erit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>RICHARDVS MERCES</s>
</p>
<p type="main">
<s>Doct. Med. Pari&longs;.</s>
</p>
<pb/>
<figure></figure>
<p type="head">
<s>PRAEFATIO IN <lb/>MECHANICA ARISTO­<lb/>TELIS, AD LECTOREM.</s>
</p>
<p type="main">
<s>Philosophari in vno rerum quo­<lb/>libet genere, <expan abbr="cãdide">candide</expan> lector, res e&longs;t per­<lb/>quam dulcis. Philo&longs;ophari appello re­<lb/>rum e&longs;&longs;entiam, cau&longs;as, proprietates, <lb/>facultates inue&longs;tigare, & inuento rum <lb/>quæ vtilia &longs;unt in opus ad vitæ homi­<lb/>num fœlicius <expan abbr="deg&etilde;dæ">degendæ</expan> commoda edu­<lb/>cere. Ita enim demum verè ille erit, vt ait poëta,</s>
</p>
<p type="main">
<s><emph type="italics"/>Fœlix, qui poterit rerum cogno&longs;cere cau&longs;as.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Alio qui inutilia, vel vtilia: &longs;ed inutiliter id e&longs;t &longs;ine actio­<lb/>ne vel opere, qu&ecedil; fines &longs;unt omnis <expan abbr="cõtemplationis">contemplationis</expan> vtilis, <lb/>contemplari, & in his philo&longs;ophando plu&longs;quam paucis <lb/>commorari, parum omnino, aut nihil fœlicitatis in hac <lb/>rerum vniuer&longs;itate habere arbitror. Verumenimuerò re­<lb/>rum quia propemodum e&longs;t infinita multitudo, licet ani­<lb/>mus hominis (quod e&longs;t ab Ari&longs;totele dictum, & ita e&longs;t, <lb/>pote&longs;tate cogno&longs;cendi, & va&longs;is in&longs;tar &longs;pirituales rerum <lb/>formas recipiendi) &longs;it omnia: vix tamen ita qui&longs;quam <lb/>bene animo con&longs;titutus fuit, vt ip&longs;um ad omnia genera <lb/>appellens in &longs;ingulis excelleret, & magnum quid con&longs;e­<lb/>queretur: vt cuique tamen contigit maior: ita quo que <lb/>maiora con&longs;ecutus e&longs;&longs;e legitur. Pythagoram, Hippocra­<lb/>tem medicum, Platonem, Ari&longs;totelem, Theophra&longs;tum, <lb/>Galenum &longs;i non omnia tenui&longs;&longs;e: quamplurima certè & <lb/>aliorum libri, & commentarij ab illis po&longs;teritati relicti <lb/>copiosè loquuntur. Sed quibus non ita magnus vel fuit,
<pb/>vel e&longs;t animus, illi vel propen&longs;ione naturali, vel iudicio, <lb/>vel ca&longs;u aliquo de multis nonnulla &longs;eligunt, in quibus <lb/>tempus & operam non &longs;ine v&longs;ura collocent &longs;uam. Om­<lb/>nium, quæ &longs;unt, genera quatuor e&longs;&longs;e reperio, &longs;ingula cer­<lb/>tè digni&longs;&longs;ima hominis contemplatione. Diuina, cœle­<lb/>&longs;tia, elementaria, artificialia. In quorum &longs;ingulis multos <lb/>excellui&longs;&longs;e clarius e&longs;t: quam vt cuiu&longs;quam nominis com­<lb/>memoratione opus &longs;it. Et certè diuina &longs;unt eiu&longs;modi, vt <lb/>licet ad corum intuitum, &longs;icut ad Solis ve&longs;pertilionis: Ita <lb/>mentis no&longs;træ oculi caligent, &longs;i quis tamen diuinitatis <lb/><expan abbr="etiã">etiam</expan> exiguus repente, & &longs;ubinde radius recipiatur & ocu­<lb/>los &longs;ubintret, plus voluptatis menti adferat: quam alio­<lb/>rum quorumlibet plena cognitio. Quæ vna res adiuncto <lb/>contemplationis diuinorum fine (quem Dei cognitio­<lb/>nem, amorem, & cultum arbitror) fecit, vt philo&longs;ophiæ <lb/>diuinorum quamplurimi homines totos &longs;e&longs;e dediderint, <lb/>dedantque quotidie. Huic philo&longs;ophiæ proxima e&longs;t cœ­<lb/>le&longs;tium & elementariorum id e&longs;t <foreign lang="greek">tou_ maxroxosmou_</foreign> mundi <lb/>&longs;cilicet huius, cuius &longs;ine machinis fabrica in &longs;ub&longs;tantia, <lb/>magnitudine, figura, numero, &longs;itu, connexione, faculta­<lb/>tibus, & v&longs;u partium <expan abbr="omniũ">omnium</expan> &longs;ui fabricatoris bonitatem, <lb/>&longs;apientiam, <expan abbr="pot&etilde;tiam">potentiam</expan>, &longs;umma i&longs;thæc omnia arguit, & de­<lb/>mon&longs;trat. Luculenti&longs;&longs;imè in&longs;uper o&longs;tendit Deum, & eius <lb/>admini&longs;tram naturam &longs;ine actione, &longs;ine opere nu&longs;quam <lb/>e&longs;&longs;e. Multò de his plura: quam de diuinis philo&longs;ophando <lb/>homines con&longs;ecuti &longs;unt, <expan abbr="neq;">neque</expan> &longs;ine incredibili animorum <lb/>&longs;uorum voluptate, & innumerabili ad v&longs;us humanos vti­<lb/>litate. Nam cum hæc ita e&longs;&longs;e homines <expan abbr="depreh&etilde;di&longs;&longs;ent">deprehendi&longs;&longs;ent</expan>, vt <lb/>ad multò plures v&longs;us, quam ad quos <expan abbr="&longs;põtè">&longs;pontè</expan> nata e&longs;&longs;e com­<lb/>perirentur, <expan abbr="trãsferri">transferri</expan> & aptati po&longs;&longs;ent, <expan abbr="perciperentq;">perciperentque</expan> non <lb/>fru&longs;trà &longs;uis animis in&longs;itas non <expan abbr="&longs;olũ">&longs;olum</expan> facultates i&longs;ta transfe­<lb/>rendi & aptandi: &longs;ed etiam congenita corporibus &longs;uis <expan abbr="in-&longs;trum&etilde;ta">in­<lb/>&longs;trumenta</expan>, quibus vel ex&longs;e, vel à &longs;e factis <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> tran&longs;­<lb/>ferrent & aptarent, non &longs;o la cognitione <expan abbr="cõtenti">contenti</expan> ad agen­<lb/>dum &longs;e <expan abbr="contulerũt">contulerunt</expan>. Hinc quartum genus illud <expan abbr="rerũ">rerum</expan>, quas <lb/>diximus, artificialium emanauit, primùm vt credibile e&longs;t
<pb/>nece&longs;&longs;ariarum, deinde <expan abbr="delectabiliũ">delectabilium</expan>, quod eò, imitatione <lb/>cœle&longs;tium & <expan abbr="elem&etilde;tariorũ">elementariorum</expan>, & in <expan abbr="horũ">horum</expan> nonnullis &longs;upera­<lb/>tione proce&longs;&longs;it, vt homo qui manu mentis con&longs;ilio dire­<lb/>cta tot & <expan abbr="tãta">tanta</expan>, quanta <expan abbr="nũc">nunc</expan> po&longs;&longs;idemus, peregerit, ab Ana­<lb/>xagora quia haberet <expan abbr="manũ">manum</expan>, &longs;apienti&longs;&longs;imus fueritiudica­<lb/>tus. Ego <expan abbr="quoq;">quoque</expan> <expan abbr="potenti&longs;&longs;imũ">potenti&longs;&longs;imum</expan> <expan abbr="ead&etilde;">eadem</expan> de cau&longs;a <expan abbr="iudic&etilde;">iudicem</expan>. quid <lb/>enim e&longs;t, quod non &longs;uis v&longs;ibus accommodarit? quibus &longs;i <lb/><expan abbr="bonitat&etilde;">bonitatem</expan> exemplo Dei Opt. Max. &longs;em per <expan abbr="adiũxerit">adiunxerit</expan>, alte­<lb/>rùm <expan abbr="quoq;">quoque</expan> <expan abbr="Deũ">Deum</expan> inter mortales e&longs;&longs;e dicere non recu&longs;em. <lb/>E&longs;t certè animus in homine ars <expan abbr="artiũ">artium</expan>. Inuenitenim om­<lb/>nia, & manus <expan abbr="organũ">organum</expan> organorum. Facit enim omnia. Et &longs;i <lb/><foreign lang="greek">mhxana_<gap/></foreign> &longs;it moliri & excogitare quibus in&longs;trumentis <lb/>opus ad agendum <expan abbr="propo&longs;itũ">propo&longs;itum</expan> efficiatur, <foreign lang="greek">mhxa/nhma</foreign> erit mo­<lb/>litio & <expan abbr="inu&etilde;tio">inuentio</expan> <expan abbr="in&longs;trumentorũ">in&longs;trumentorum</expan> ad opus. quæ cum &longs;ine ra­<lb/>tione non po&longs;&longs;int exi&longs;tere, ratio <expan abbr="aut&etilde;">autem</expan> vnius hominis pro­<lb/>pria &longs;it, <foreign lang="greek">mhxanixo\n</foreign> e&longs;&longs;e &longs;olius erit hominis, <expan abbr="quemadmodũ">quemadmodum</expan> <lb/>loqui, ratiocinari, & omnia quæ à Dei &longs;olo nutu, &longs;ine ve­<lb/>cte, &longs;ine ferramentis, &longs;ine machina vlla confecta & creata <lb/><expan abbr="sũt">sunt</expan>, molitione, machinatione & <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> imitari, om­<lb/>nia denique ad v&longs;us &longs;uos transferre. Archimedes primus <lb/>cœlum, alteram mundi partem ampli&longs;&longs;imam & præ&longs;tan­<lb/>ti&longs;&longs;imam, tanta arte vnius machinæ vitreæ artificio re­<lb/>præ&longs;entauit, vt &longs;i Claudiano credimus, artificij elegantia <lb/>voluptatem & admirationem Ioui pepererit. Sed præ&longs;tat <lb/>eleganti&longs;&longs;imos huius poëtæ ver&longs;us recitare.</s>
</p>
<p type="main">
<s><emph type="italics"/>Iuppiter, in paruo cum cerneret æthera vitro, <lb/>Ri&longs;it, & ad &longs;uperos talia dicta dedit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Hoccine mortalis progre&longs;&longs;a potentia curæ? <lb/>I am meus in fragili luditur orbe labor.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Iura poli, rerumque fidem, lege&longs;que deorum <lb/>Ecce Syracu&longs;ius tran&longs;tulit arte &longs;enex.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Inclu&longs;us varijs famulatur &longs;piritus a&longs;tris, <lb/>Et viuum certis motibus vrget opus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Percurrit proprium mentitus &longs;ignifer annum, <lb/>Et &longs;imulata nouo Cynthia men&longs;e redit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Iamque &longs;uum voluens audax indu&longs;tria mundum<emph.end type="italics"/>
<pb/><emph type="italics"/>Gauder, & humana &longs;idera mente regit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quid &longs;al&longs;o in&longs;ontem tonitru Salmonea miror? <lb/>AE mula naturæ parua reperta manus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sal monci huius fal&longs;um tonitru &longs;tatim in memoriam vo­<lb/>cat, non iam fal&longs;a <expan abbr="hominũ">hominum</expan>, qui nunc viuunt to nitrua, <expan abbr="vi-brataq;">vi­<lb/>brataque</expan> è &longs;uis &longs;clopetis, <expan abbr="bõbardi&longs;que">bombardi&longs;que</expan> fulmina, &longs;oni frago­<lb/>re, ictus conqua&longs;&longs;atione, & <expan abbr="pluriũ">plurium</expan> &longs;trage non modo Iouis <lb/>fulmen imitantia: &longs;ed longe &longs;uperantia. Quoties fulmen <lb/>&longs;uum mittit Iupiter aut <expan abbr="nemin&etilde;">neminem</expan>, aut <expan abbr="vnũ">vnum</expan> atque alterum <lb/>præcipitat: hæc verò certo ictu &longs;emper de&longs;tinata vrbium <lb/>mœnia deua&longs;tant: quot homines attingunt, perdunt, & <lb/><expan abbr="quid&etilde;">quidem</expan> tanta celeritate, tantáque vi, vt qu&ecedil; ab antiquis in­<lb/>geniosè, vel ad oppugnandos ho&longs;tes, vel ab his &longs;e <expan abbr="defen-dendũ">defen­<lb/>dendum</expan> inuenta erant <expan abbr="in&longs;trum&etilde;ta">in&longs;trumenta</expan> bellica, Scorpiones, ca­<lb/>tapultæ, bali&longs;tæ, arietes, turres ambulatoriæ, te&longs;tudines, <lb/>helepoles, fundæ, & reliqua eiu&longs;modi poliorcetica, præ <lb/>illis qua&longs;i in <expan abbr="de&longs;uetudin&etilde;">de&longs;uetudinem</expan>, & <expan abbr="obliuion&etilde;">obliuionem</expan> abierint. Præclara <lb/>&longs;anè illa &longs;unt <foreign lang="greek">mhxa<gap/>hma<gap/>,</foreign> &longs;i his homines vterentur <expan abbr="tantũ">tantum</expan>, <lb/>vt patria ab ho&longs;tili &longs;eruitute liberetur, &longs;ubacto ho&longs;te fines <lb/>amplificentur, <expan abbr="adiũctis">adiunctis</expan> prouincijs <expan abbr="dilat&etilde;tur">dilatentur</expan>, & &longs;ic longè <lb/>laté que optimi regis dominatio <expan abbr="ext&etilde;datur">extendatur</expan>. Vt veteribus <lb/>illis &longs;olis in&longs;tructus cum Alexan der parua hominum ad <lb/>30000 manu tot prouincias, tot regna, tot vrbes &longs;ubegi&longs;­<lb/>&longs;et, dictum &longs;it abillo vtilius fui&longs;&longs;e &longs;ubigi: quam <expan abbr="regũ">regum</expan> <expan abbr="pri-&longs;tinorũ">pri­<lb/>&longs;tinorum</expan> in&longs;ul&longs;a pote&longs;tate diutius detineri. <expan abbr="Igniũ">Ignium</expan> vero cœ­<lb/>le&longs;tium, &longs;eu <expan abbr="a&longs;trorũ">a&longs;trorum</expan> lumina faces no&longs;træ ardentes <expan abbr="quantũ">quantum</expan> <lb/>v&longs;ibus humanis &longs;atis e&longs;t, imitantur. Fontium <expan abbr="per&etilde;nitates">perennitates</expan> <lb/>Heronis inuenta &longs;uppeditant, vt & Cte&longs;ibij hydraulica <lb/>in&longs;trumenta, & merulæ hominum voces <expan abbr="auiumq;">auiumque</expan> cantus <lb/>imitantes, & <foreign lang="greek">e)g<gap/>ei/<gap/>a<gap/></foreign> funiculis, ponderibus, orbiculis, <lb/>&longs;piritu inclu&longs;o humanos motus &longs;ine voce <expan abbr="ed&etilde;tes">edentes</expan> perbellè <lb/>expre&longs;&longs;erunt. <expan abbr="No&longs;troq;">No&longs;troque</expan> <expan abbr="t&etilde;pore">tempore</expan> alij multi in oculis no&longs;tris <lb/>&longs;imilia plurima po&longs;uerunt. quales fuerunt icunculæ illæ <lb/>ad <expan abbr="cantũ">cantum</expan> cytharæ &longs;altitantes, manus manibus iungentes, <lb/>in equos, in currus con&longs;cendentes, modò rur&longs;us <expan abbr="curr&etilde;tes">currentes</expan>, <lb/>modo re&longs;titantes. Tum ca&longs;tellum illud mirabile, in quo <lb/><expan abbr="fabrorũ">fabrorum</expan> genus omne &longs;uum munus affabrè, nec o&longs;citanter
<pb/>exercebat, quod hîc Lutetiæ vidimus. Vt & Noribergæ <lb/>mu&longs;ca ferrea <expan abbr="cõmemoratur">commemoratur</expan> è manu artificis &longs;ui cuola&longs;&longs;e, <lb/>& conuiuas circumuolita&longs;&longs;e, <expan abbr="tandemq;">tandemque</expan> veluti defe&longs;&longs;a in <lb/>&longs;ui domini manum redij&longs;&longs;e: tum aquila illa, quæ in aëre <lb/>&longs;ublimis Carolo imperatori huius nominis quinto ad vr­<lb/>bem aduentanti obuia facta, <expan abbr="v&longs;q;">v&longs;que</expan> ad vrbis <expan abbr="portã">portam</expan> cundem <lb/>comitata e&longs;t, ne fabulam exi&longs;timemus quod de columba <lb/>Architæ <expan abbr="volãte">volante</expan> à veteribus <expan abbr="cõmemoratum">commemoratum</expan> e&longs;t: <expan abbr="neq;">neque</expan> illud <lb/>quod fertur de Dædaleis operibus, & Vulcani tripodi­<lb/>bus, pectinibus, malleis, qui iniu&longs;&longs;i ad opus &longs;ponte &longs;ua ve­<lb/>niebant, & ni&longs;i vinculis coercerentur, aufugiebant. Sed <lb/>hæc ad delectationem tantum &longs;unt comparata, vtilia & <lb/>vitæ human&ecedil; <expan abbr="trã&longs;ig&etilde;dæ">tran&longs;igendæ</expan> nece&longs;&longs;aria omnino &longs;unt Agricul­<lb/>turæ, Militaris, Architecturæ, Medicinæ, Nauticæ, Mer­<lb/>caturæ munera: quibus <expan abbr="alim&etilde;ta">alimenta</expan>, tecta, &longs;anitas, ve&longs;titus, di­<lb/>uitiæ, & ab cœli, <expan abbr="ho&longs;tiumq;">ho&longs;tiumque</expan> iniurijs defen&longs;io quæruntur. <lb/>At quid artes illæ e&longs;&longs;e po&longs;&longs;ent, ni&longs;i machinæ <expan abbr="inu&etilde;tæ">inuentæ</expan> fui&longs;­<lb/>&longs;ent, & in&longs;trumenta, quibus vnâ <expan abbr="cũ">cum</expan> <expan abbr="hominũ">hominum</expan> parua vi, mo­<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="ing&etilde;tes">ingentes</expan> loco <expan abbr="di-mou&etilde;tur">di­<lb/>mouentur</expan>, pelluntur, trahuntur, <expan abbr="cõuehuntur">conuehuntur</expan>, in <expan abbr="gyrũ">gyrum</expan> con­<lb/>torquentur, & <expan abbr="tãdem">tandem</expan> alti&longs;&longs;imis locis & difficilimis repo­<lb/>nuntur? aut <expan abbr="eæd&etilde;">eædem</expan> iu&longs;ta quantitate appen&longs;æ, aut <expan abbr="m&etilde;&longs;uratæ">men&longs;uratæ</expan> <lb/><expan abbr="cuiq;">cuique</expan> &longs;uum quærenti di&longs;tribuuntur? Vnde &longs;ex &longs;unt illa ex <lb/>innumeris à veteribus <expan abbr="inu&etilde;ta">inuenta</expan>, <expan abbr="quorũ">quorum</expan> &longs;ingula &longs;eor&longs;um ma­<lb/>gna vi: <expan abbr="coniũcta">coniuncta</expan> verò, & multiplicata infinitis propemo­<lb/>dum viribus pollere animaduertuntur, libra, vectis, tro­<lb/>chlea, axis in peritrochio, cuncus, & cochlea. Sed qu&ecedil; au­<lb/>dio hîc dicet aliquis? Nunquid <expan abbr="in&longs;trum&etilde;ta">in&longs;trumenta</expan> mercatorum, <lb/><expan abbr="cœm&etilde;tariorum">cœmentariorum</expan>, baiulorum, <expan abbr="phalangariorũ">phalangariorum</expan>, lignatorum, <lb/>lapicidarum, <expan abbr="vinitorũ">vinitorum</expan>, & eiu&longs;modi <expan abbr="viliũ">vilium</expan> &longs;or dido rum que <lb/><expan abbr="hominũ">hominum</expan>? Audis &longs;anè: &longs;ed & A&longs;treæ, & Neptuni, & Mar­<lb/>tis, & Vulcani, & Cereris, & Palladis, qui tanto pere pro­<lb/>pter hæc &longs;ua inuenta anti quis <expan abbr="placuerũt">placuerunt</expan>, vt &longs;int ab illis in <lb/>deorum <expan abbr="numerũ">numerum</expan>, eorumque <expan abbr="maiorũ">maiorum</expan> relati. Trutinarum <lb/>librarumque examinatio reperta, inquit Vitruuius, vin­<lb/>dicat ab iniquitate iu&longs;tis moribus <expan abbr="vitã">vitam</expan>. Vnde &longs;tatera do­<lb/>lo&longs;a abhominatio e&longs;t apud Deum, dixit <expan abbr="&longs;api&etilde;s">&longs;apiens</expan>, & pondus
<pb/>æquum voluntas eius, & alibi abhominatio e&longs;t apud Deum <lb/>pondus & pondus. Itaque libræ inucntrix A &longs;træa pro dea <lb/>lu&longs;tici&ecedil; culta e&longs;t. Libra ip&longs;a iudicum oculis in fori &longs;ui tabu­<lb/>lis, & &longs;ignis propo&longs;ita, ad quam intuerentur, & denique in <lb/>cœle&longs;te &longs;ignum conuer&longs;a, quæ diem naturalem, quem Sol <lb/>æquatorem peragrans circulum conficit, in tempus lucis & <lb/>tenebrarum æqualiter vbique diuideret. Vnde poëta,</s>
</p>
<p type="main">
<s><emph type="italics"/>Libra die, &longs;omnique pares vbi fecerit horas,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Et medium luci atque vmbris iam diuidet orbem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Neptuno verò, cum tridentem antiquitas attribuit, quid <lb/>aliud, quam vectem? Græci appellant <foreign lang="greek">mo/xlon</foreign> vnde ille <foreign lang="greek">mox­<lb/>leuth\s</foreign> vectiarius à poëtis dictus e&longs;t, & terræ mati&longs;que con­<lb/>cu&longs;&longs;or, & hac machina Syrtes &longs;ubleuans, quo plus Troianis <lb/>apparerent à poëta inducitur,</s>
</p>
<p type="main">
<s><emph type="italics"/>Leuat ip&longs;e tridenti,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Et va&longs;tas aperit Syrtes.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Certè vectis palus e&longs;t <expan abbr="oblõgior">oblongior</expan>, materiæ firmæ, cu&longs;pide acu­<lb/>ta, & paulo latiori linguæ in&longs;tar, quam propè, quando e&longs;t <lb/>&longs;ubditum hypomochlium, huic pondus in cumbens, id que <lb/>grauius quam quod à decem hominum &longs;olis manibus di­<lb/>moueri loco po&longs;&longs;et, vnius <expan abbr="tam&etilde;">tamen</expan> viribus caput huius pali de­<lb/>primentibus, vel &longs;i terra &longs;ubdita pro hypomochlio e&longs;t &longs;uble­<lb/>uantibus, dimouetur. Vnde in magnis <expan abbr="ædificiorũ">ædificiorum</expan> &longs;ub&longs;tru­<lb/>ctionibus vnus vectis pro multorum manibus, vnus homo <lb/>bimanus pro Briareo centimano, modò pondera lapidum, <lb/>trabiúm que colo&longs;&longs;icotera fabris & architectis loco dimo­<lb/>uet, & &longs;ubleuat: modò <expan abbr="ei&longs;d&etilde;">ei&longs;dem</expan> collopis figura &longs;ucculas ver&longs;at: <lb/>modo tollenonis &longs;pecie aquas è puteis operis & olitoribus <lb/>exhaurit: modo phalangæ forma baiulis & phalangarijs <lb/>proportionalia tanquam in bilance pondera partitur, mo­<lb/>do iugi nomine in aratro bobus æquum arationis laborem <lb/>di&longs;pen&longs;at &longs;iue æquales &longs;iue inæquales.</s>
</p>
<p type="main">
<s><emph type="italics"/>Veniant ad aratra iuuenci.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sed cum naui tran&longs;mittitur flumen, aut mare tran&longs;meatur, <lb/>quid e&longs;t in ea remus aliud, quam vectis inuer&longs;us, habens in <lb/>&longs;calmo hypomochlium? <expan abbr="aquã">aquam</expan> pro pondere loco dimouens? <lb/>vt in eum cedat nauis, & quidem impul&longs;us ille à remige pro
<pb/>vectiatio tanquam tridens à Neptuno? Quin & guberna­<lb/>calum, quo gubernator in puppi <expan abbr="&longs;ed&etilde;s">&longs;edens</expan> tam facilè obliquat <lb/>nauim etiam ingentem, & cum magna in prora loci muta­<lb/>tione, licet in puppi adeò exigua, vt nihil agere, aut <expan abbr="etiã">etiam</expan> lu­<lb/>dere videatur: aliud <expan abbr="tam&etilde;">tamen</expan> nihil, quam vectis e&longs;&longs;e <expan abbr="cõperietur">comperietur</expan>. <lb/>Neque malus erectus in medio nauis e&longs;t aliud. Calx enim, <lb/>&longs;eu edolium e&longs;t hypomochlium, pars è qua pendet carche­<lb/>&longs;ium cum pa&longs;&longs;is velis, <expan abbr="tanquã">tanquam</expan> alis Dædaleis perflante vento <lb/>propul&longs;a propellit pondus, nauim &longs;cilicet, & quod e&longs;t admi­<lb/>rabilius ibi non aliter venti, quam equi reguntur, <expan abbr="dũ">dum</expan> ex car­<lb/>che&longs;ij vt fræni &longs;itu modò altiore: modò depre&longs;&longs;iore provt <lb/>&longs;unt admi&longs;&longs;i: ita nauis modò vehementius, modò remi&longs;&longs;ius <lb/>impellitur.</s>
</p>
<p type="main">
<s>Sed hæc devecte &longs;atis. <expan abbr="Trochleã">Trochleam</expan> verò, quæ orbiculus e&longs;t <lb/>circa axem immobilem fune conuolutus, quantis viribus <lb/><expan abbr="præditã">præditam</expan> e&longs;&longs;e animaduertimus. Ex hac multiplicata, factum <lb/>e&longs;t tri&longs;pa&longs;ton, pentepa&longs;ton, poly&longs;pa&longs;ton, viribus <expan abbr="quorũ">quorum</expan> <expan abbr="cõfi-&longs;us">confi­<lb/>&longs;us</expan> Archimedes cum audiret <expan abbr="aliqu&etilde;">aliquem</expan> <expan abbr="di&longs;putãtem">di&longs;putantem</expan> plures e&longs;&longs;e <lb/>mundos coram Heronerege Syracu&longs;arum, au&longs;us e&longs;t dicere. <lb/>Da mihi vbi &longs;i&longs;tam pedem, & hanc ego <expan abbr="terrã">terram</expan> loco &longs;uo dimo­<lb/>uebo. cuius admirabilis dicti <expan abbr="cũ">cum</expan> rogatus e&longs;&longs;et à rege, vt &longs;pe­<lb/>cimen aliquod ederet, vna manu læua quinquies millenûm <lb/>modiorum <expan abbr="põdus">pondus</expan> attraxit: nauem in &longs;iccum littus eiectam <lb/>& grauiter <expan abbr="oneratã">oneratam</expan> ad &longs;e perinde pertraxit, ac &longs;i in mari re­<lb/>mis, veli&longs;ve impul&longs;a fui&longs;&longs;et: aliam po&longs;tea recens <expan abbr="cõ&longs;tructam">con&longs;tructam</expan> <lb/>ingentis magnitudinis ab Herone regi Ægyptiorum Ptolo­<lb/>mæo dono mittendam, quam omnes <expan abbr="Syracu&longs;anorũ">Syracu&longs;anorum</expan> ciuium <lb/>vires <expan abbr="cõiunctæ">coniunctæ</expan> dimouere loco non <expan abbr="potuerãt">potuerant</expan>, vt &longs;olus Hiero <lb/>machinis adiutus in mare educerer, perfecit: & <expan abbr="quid&etilde;">quidem</expan> cum <lb/>tanta ip&longs;ius regis admiratione, vt exclamarit, <foreign lang="greek"><gap/>po\ tau/ths <gap/><lb/>k(me/<gap/>as w_<gap/>i\ w_anto\s *arxhmh/<gap/> le/<gap/>n<gap/>i pi<gap/>eute/on.</foreign> Ab hoc die <lb/>quic quid dixerit Archimedes huic <expan abbr="credendũ">credendum</expan>. At ab eo die <lb/>ab Archimede prodijt illud problema inexpertis in credibi­<lb/>le, cruditis tamen demon&longs;tratum. Datum pondus à data <lb/>potentia moueri. quod in vectc, trochlea, & axe in peritro­<lb/>chio nuper à Guidone Vbaldo demon&longs;trationibus geome­<lb/>tricis habemus confirmatum. Vectis &longs;olus pondera de loco
<pb/>propellit &longs;uo, trochlea euellit, & eadem ad alti&longs;&longs;imas ædi­<lb/>ficiorum vbi opus e&longs;t &longs;edes trahit. Sit in polo horizontis qui <lb/>trochleæ appendiculum firmet, & ad eum homo ip&longs;e &longs;e &longs;u­<lb/>bleuabit. Sed longior &longs;um in troch&longs;ea, in reliquis ero bre­<lb/>uior. Axis in peritrochio cylindrus e&longs;t duobus fulcris per <lb/>extrema &longs;u&longs;tentatus, habens propè vnum extremorum tym­<lb/>panum &longs;cytalis aliquot in peripheria in fixis perforatum, ita <lb/>quidem, vt <expan abbr="pot&etilde;tia">potentia</expan>, quæ &longs;emper in &longs;cytalis e&longs;t, dum circum­<lb/>uertit tympanum & axem, &longs;ur&longs;um etiam ex inferis euehat <lb/>pondus quodlibet axi fune circa ip&longs;um axem reuoluto <lb/>appen&longs;um. Huius machinæ beneficio de&longs;cenditur in vi&longs;ce­<lb/>ra terræ, & illinc effo&longs;&longs;æ opes, non vt Ouidius ait, &longs;emper</s>
</p>
<p type="main">
<s><emph type="italics"/>Irritamenta malorum:<emph.end type="italics"/></s>
</p>
<p type="main">
<s>quin potius occa&longs;iones & adiumenta bonorum multorum, <lb/>&longs;i <expan abbr="bonũ">bonum</expan> <expan abbr="po&longs;&longs;e&longs;&longs;or&etilde;">po&longs;&longs;e&longs;&longs;orem</expan> nactæ &longs;int. Nam vt recte dixit Pindarus,</s>
</p>
<p type="main">
<s><emph type="italics"/>Quæ Virtute pecunia<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Exornata nitet, &longs;uppeditat Vias<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Non vnas, bene agas, quibus<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quæ &longs;ors cunque ferens obtulerit tibi:<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et vt Antiphanes,</s>
</p>
<p type="main">
<s><emph type="italics"/>Per deos cur optet quis dite&longs;cere?<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Pecuniæ cur optet habere plurimum:<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quam po&longs;sit auxiliari vt amicis? Gratiæ<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Fructúmque &longs;erere Diuarum &longs;uaui&longs;simæ?<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Illinc in quam effo&longs;&longs;æ opes, &longs;ucci, terræ medicatæ, metalli <lb/>omne genus, lapides, arena, ad ædificiorum &longs;ub&longs;tructiones, <lb/>ad medicamenta prauarum & contumacium affectionum, <lb/>ad ornamenta in altum, lucém que euehuntur.</s>
</p>
<p type="main">
<s>Cuneus vero e&longs;t <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> exiguum in formam pyra­<lb/>midis quadrangul&ecedil;, ad vnam <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan> fa&longs;tigiatæ ad diui­<lb/>dendum ligna factum. Hoc <expan abbr="cũ">cum</expan> malleo lignator in&longs;tructus, <lb/>&longs;yluam breuiori tempore integram diui&longs;erit: quam &longs;ine ijs <lb/>arboris vnius vnum truncum. Milo Crotoniates Athleta <lb/>ille ro bu&longs;ti&longs;&longs;imus fertur cum arborem bifurcatam proprijs <lb/>viribus diuellere contenderet, & diuelli in cœptam retinere <lb/>non po&longs;&longs;et, quin partes diuul&longs;æ &longs;umma celeritate in &longs;e&longs;e re­<lb/>dirent, vnâque raptas manus interciperent, præda vt im­
<pb/>bellis ouis fui&longs;&longs;e lupis. Itaque proprijs,</s>
</p>
<p type="main">
<s><emph type="italics"/>viribus ille<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Confi&longs;us perÿt,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>qui &longs;i cuneo id ip&longs;um facere volui&longs;&longs;et, in eam calamitatem <lb/>non incidi&longs;&longs;et. Quis vero <expan abbr="nõ">non</expan> intelligit Martis, Cereris, Vul­<lb/>canique arma & in&longs;trumenta en&longs;es, gladios, mucrones, &longs;e­<lb/>cures, aratra, ligones, a&longs;cias, falces, vngues ferreos & &longs;imilia, <lb/>quæ percu&longs;&longs;ione, &longs;iue impul&longs;u incidunt, diuidunt, <expan abbr="perforãt">perforant</expan>, <lb/>ad huiu&longs;modi facultatis in&longs;trumentum commode referri <lb/>po&longs;&longs;e? Ligones agricolarum quid &longs;unt aliud, quam cunei <lb/>mallco connexi? Forfex verò ad Palladis & Æ&longs;culapij Ma­<lb/>chaoni&longs;que artes <expan abbr="tã">tam</expan> nece&longs;&longs;arius, quid aliud, <expan abbr="quã">quam</expan> duplex cu­<lb/>neus, & totuplex vectis? &longs;icuti forceps tantum vectis e&longs;t du­<lb/>plicatus. In&longs;trumentum Vulcani perpetuò in manibus, quò <lb/>pruna, ferrum candens, æs, <expan abbr="argentũ">argentum</expan>, aurum apprehenditur.</s>
</p>
<p type="main">
<s><emph type="italics"/>Pren&longs;ant<emph.end type="italics"/> (enim vt poëta ait,) <emph type="italics"/>ver&longs;antque tenaci<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Forcipe ferrum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>At cuneus &longs;implex percu&longs;&longs;ione mallei adigitur. Idem mul­<lb/>tiplicatus &longs;ine percu&longs;&longs;ione rota cum &longs;cytalis in cochlea ita <lb/>penetrare cogitur, vt vuæ, oleæ, nuces, mala, pyra, cætera­<lb/>que humida prœlis &longs;ubiecta quicquid &longs;ucci & liquoris ha­<lb/>bent, Domino per&longs;oluere cogantur. Hoc beneficium ma­<lb/>gni e&longs;t momenti ad vitæ commoda. At vt longæua v&longs;que in <lb/>&longs;ecula &longs;int &longs;empiterni doctorum hominum commentarij, <lb/>& con&longs;criptæ cogitationes, quantum confert prœlum ty­<lb/>pographicum cochleæ vnius beneficio compre&longs;&longs;um? Quid <lb/>dicam ab his fontibus etiam deducta omnia poliorcetica, <lb/>quorum &longs;olorum opè vnus Archimedes Marcelli Syracu­<lb/>&longs;as terra marique <expan abbr="ob&longs;id&etilde;tis">ob&longs;identis</expan> vires diu, <expan abbr="multumq;">multumque</expan> ludificatus <lb/>e&longs;t, pro qua re hûc Titi Liuij lubet conferre admirabile re­<lb/>&longs;timonium. Terra, inquit, marique &longs;imul cœptæ oppugnari <lb/>Syracu&longs;æ, terra ab Hexapylo: mari ab Acradina. Et habui&longs;­<lb/>&longs;et tantò impetu cœpta res fortunam, ni&longs;i vnus homo Syra­<lb/>cu&longs;is ea <expan abbr="t&etilde;pe&longs;tate">tempe&longs;tate</expan> fui&longs;&longs;et Archimedes. Is erat vnicus &longs;pecta­<lb/>tor cœli &longs;iderum que: mirabilior tamen inuentor ac machi­<lb/>nator bellicorum <expan abbr="torm&etilde;torum">tormentorum</expan>, operumque: quibus ea quæ <lb/>ho&longs;tes ingenti mole agerent ip&longs;e perleui momento ludi&longs;i-
<pb/>caretur. Murum per in&ecedil;quales ductum colles, pleraque alta <lb/>& difficilia aditu, &longs;ummi&longs;&longs;a quædam, & quæ planis vallibus <lb/>adiri po&longs;&longs;ent, vt cuique aptum vi&longs;um e&longs;t loco, ita omni ge­<lb/>nere tormento rum in&longs;truxit. A cradinæ murum, qui, vt ante <lb/>dictum e&longs;t, mari alluitur ex quinqueremibus Marcellus <lb/>oppugnabat. ex cæteris nauibus &longs;agittarij, funditore&longs;que, <lb/>& velites etiam quorum telum inhabile ad remittendum <lb/>imperitis e&longs;t: vix quenquam &longs;ine vulnere con&longs;i&longs;tere in muro <lb/>patiebantur. Hi, quia &longs;patio mi&longs;&longs;ilibus opus e&longs;t: procul mu­<lb/>ro <expan abbr="tenebãt">tenebant</expan> naues. Iunctæ aliæ binæ ad quinqueremes dem­<lb/>ptis interioribus remis, vt latus lateri appropinquaretur: <lb/>cum exteriore ordine remorum velut naues agerentur: tur­<lb/>res contabulatas, machinamentá que alia quatiendis muris <lb/>portabant. A duer&longs;us hunc naualem apparatum Archime­<lb/>des variæ magnitudinis tormenta in muris di&longs;po&longs;uit. In eas <lb/>quæ procul erant, naues &longs;axa ingenti pondere emittebat: <lb/>propiores leuioribus, eóque magis crebris petebat telis. Po­<lb/>&longs;tremò vt &longs;ui vulnere intacti tela in ho&longs;tem ingererent: mu­<lb/>rum ab imo &longs;ummum crebris cubitalibus ferè caueis ape­<lb/>ruit. per quæ caua pars &longs;agittis: pars &longs;corpionibus modicis <lb/>ex occulto petebant ho&longs;tem. Quæ propius <expan abbr="quid&etilde;">quidem</expan> &longs;ubibant <lb/>naues, quo interiores ictibus <expan abbr="torm&etilde;torum">tormentorum</expan> e&longs;&longs;ent: in eas tol­<lb/>lendas de&longs;uper murum eminentem ferrea manus firmæ ca­<lb/>thenæ illigata, cum iniecta proræ e&longs;&longs;et, grauique libramen­<lb/>to plumbi recelleret ad &longs;olum: <expan abbr="&longs;u&longs;p&etilde;&longs;a">&longs;u&longs;pen&longs;a</expan> prora, nauim in pup­<lb/>pim &longs;tatuebat. Dein remi&longs;&longs;a &longs;ubitò, velut ex muro caden­<lb/>tem nauim cum ingenti trepidatione nautarum ita vndæ <lb/>affligebant: vt etiam&longs;i recta recideret aliquantum aquæ ac­<lb/>ciperet. Ita maritima oppugnatio e&longs;t elu&longs;a, omni&longs;que vis e&longs;t <lb/>auer&longs;a, vt totis viribus terra aggrederentur. Sed ea quoque <lb/>pars eodem omni apparatu tormentorum in&longs;tructa erat, <lb/>Hieronis impen&longs;is, curaque per multos annos Archimedis <lb/>vnica arte. Ita con&longs;ilio habito, cum omnis conatus ludibrio <lb/>e&longs;&longs;et: ab&longs;i&longs;tere oppugnatione atque ob&longs;idendo tantum ar­<lb/>cere terra marique commeatibus ho&longs;tem placuit. Hæc Ti­<lb/>tus Liuius lib. 4. decad. 3. Vilium igitur, &longs;ordidorum que ho­<lb/>minum ne dixerimus ea e&longs;&longs;e in&longs;trumenta, quæ vel à dijs, vel
<pb/>à nobili&longs;&longs;imis hominibus inuenta, & v&longs;urpata &longs;unt, & nunc <lb/>ad v&longs;us humanos perquam nece&longs;&longs;aria hone&longs;ti&longs;&longs;imum quæ­<lb/>&longs;tum, & qualem agricultura dominis agricolis &longs;uppeditant. <lb/>Quanquam non co animo à nobis hæc dicuntur, vt ad eas <lb/>artes, quarum &longs;unt in&longs;trumenta, ve&longs;tras animi, corpori&longs;que <lb/>vires &longs;uadeam conferatis: vos dico,</s>
</p>
<p type="main">
<s><emph type="italics"/>Queis meliore luto finxit præcordia Titan:<emph.end type="italics"/></s>
</p>
<p type="main">
<s>atque quos ad his altiora præmeditanda iamdudum euexit <lb/>animus, vbi tamen nihil aliud e&longs;&longs;et, quod ageretur, cur non <lb/>aliquod horum relaxamenti gratia etiam quæratis? vel &longs;i rei <lb/>familiaris exiguitas po&longs;tulat, cum ijs agatis, potius, quam <lb/>nihil? Neque enim magis horum aliquod nobis indecorum <lb/>putare debemus: quam &longs;ibi A&longs;cræus ille poëta,</s>
</p>
<p type="main">
<s><emph type="italics"/>Qui alium ditem cernens, cum dee&longs;t quod agatur,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ip&longs;e &longs;olum vertit tauris, & &longs;emina ponit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sed co animo h&ecedil;c pr&ecedil;&longs;ertim <expan abbr="nũc">nunc</expan> à me dicuntur, vt audacter <lb/>& &longs;ine rubore aliquando ingrediamur officinas fabrorum <lb/>generis omnis, vt & in&longs;trumenta, & machinas quibus vtun­<lb/>tur in &longs;uis operibus con&longs;icien dis primum digno&longs;camus, mi­<lb/>rificas ex i&longs;ta dignotione voluptates con&longs;ecuturi, maximè <lb/>cum eas, quæ magna vi pollent, &longs;ummo&longs;que habent v&longs;us <lb/>cognouerimus, ma<gap/>ores adhuc multo po&longs;tea percepturi, &longs;i <lb/>tantæ efficaciæ adiumenti que cau&longs;as inue&longs;tigantes inuene­<lb/><gap/>imus, quod feci&longs;&longs;e Ari&longs;totelem non puduit, qui vno hoc li­<lb/>bello <foreign lang="greek"><gap/>i\ mnxanika_n</foreign> certè iucundo & vtili edito tanta inge­<lb/>nij &longs;ubtilitate atque diligentia per&longs;ecutus e&longs;t, vt omnia ad <lb/>vnum princip<gap/>um, quod e&longs;t circulus, reuocari po&longs;&longs;e inue­<lb/>nerit, & reuocanda e&longs;&longs;e non quidem leuibus probabilium <lb/>argumentorum: &longs;ed graui&longs;&longs;imis demon&longs;trationum geome­<lb/>tricarum momentis o&longs;tenderit. Itaque &longs;i quis audito huius <lb/>libelli titulo, &longs;tatim ab huius lectione volens aufugere, in&longs;u­<lb/>per pue<gap/>iliter irrideat, quod regius mathem aticarum ar­<lb/>tium profe&longs;&longs;or in rebus, vt putabit, vili&longs;&longs;imis philo&longs;ophari, <lb/>& <foreign lang="greek">g<gap/>wmebu_n</foreign> contenderit. Huic re&longs;pondebimus, quod ali­<lb/>quando Hera clitum dixi&longs;&longs;c ferunt ijs, qui cum alioqui evm <lb/>vellent, quod forte in ca&longs;a furnatia caloris gratia &longs;edentem <lb/>vid<gap/>&longs;&longs;ent, accedere temperarunt, & ingredi fidenter cum
<pb/>iu&longs;&longs;i&longs;&longs;et. Ne quidem, inquit ille, huic loco dij de&longs;unt im­<lb/>mortales: &longs;ic nec i&longs;ti rerum generi dulci&longs;&longs;ima & vtili&longs;&longs;ima, <lb/>& <expan abbr="cũ">cum</expan> &longs;umma ingenij humani voluptate coniuncta &longs;ua dee&longs;t <lb/>philo&longs;ophia, vt in qua explicanda, & <expan abbr="exornãda">exornanda</expan> præter Ari­<lb/>&longs;totelem multi viri præclari &longs;tudium &longs;uum collocauerint, <lb/>Cliades, Architas, Archimedes, Cte&longs;ibius, Nymphodorus, <lb/>Philo byzanteus, Diphilas, Charidas, Polyides, Phyrus, <lb/>Age&longs;i&longs;tratus, ex quorum <expan abbr="cõmentarijs">commentarijs</expan> quæ vtilia e&longs;&longs;ent ædi­<lb/>ficationi collecta in vnum Vitruuius corpus coëgit: &longs;ed & <lb/>præter illos quorum ferè nobis <expan abbr="re&longs;tãt">re&longs;tant</expan> &longs;ola nomina Pappus, <lb/>Hero vterque, Tzetzes, Iordanus, & è recentio ribus Leoni­<lb/>cus, Picolominus, Cardanus, Guido Vbaldus, quorum in­<lb/>genia &longs;eruilia nunquam rectè quis dixerit aut putarit. quin <lb/>& Hippocratcs magnus ille medicus à &longs;e nonnulla luxatio­<lb/>nibus, & fracturis reponendis inuenta commoda gloriatur, <lb/>cuiu&longs;modi &longs;unt <foreign lang="greek">o)/noi, o)/<gap/>iskoi\,</foreign> & &longs;camnum, quæ vnà cum alijs <lb/>Galenus quo que paruis eorum exemplaribus vtens &longs;uos &longs;e <lb/>di&longs;cipulos docere te&longs;tatus e&longs;t. In i&longs;tam igitur inqui&longs;itio­<lb/>nem, tractationem, commentationem nobilem, ingenuam <lb/>& philo&longs;ophi non vulgariter vt multi: &longs;ed in Geometria <lb/>magnopere eruditi ingenio digni&longs;&longs;imam, tot magnorum <lb/>virorum exemplo, &longs;i, can dide lector, me hortante atque his <lb/>no&longs;trorum commentariorum vigilijs, vtcunque adiuuante, <lb/>diligenter incubueris, tui te laboris, mihi crede, penitebit <lb/>numquam. Vale.</s>
</p>
<pb/>
<p type="head">
<s><emph type="italics"/>Extraict du Priuilege du Roy.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Par grace & priuilege du Roy, il e&longs;t permis à Ie­<lb/>remie Perier marchant Libraire à Paris, d'impri­<lb/>mer ou faire imprimer vn liure intitulé <emph type="italics"/>Ari&longs;totelis <lb/>Mechanica, Græca emendata, Latina facta, & commen­<lb/>tarÿs illu&longs;trata, ab Henrico Monantholio Medico, & Ma­<lb/>thematicarum artium Profe&longs;&longs;ore Regio.<emph.end type="italics"/> Et deffen&longs;es &longs;ont <lb/>faictes à toutes per&longs;onnes de quelque e&longs;tat qualité & <lb/>condition qu'ils &longs;oyent, en quelques lieux & villes de <lb/>ce Royaume, de ne le faire imprimer ou faire faire im­<lb/>primer à peine des articles po&longs;és à l'original du pre­<lb/>&longs;ent priuilege, iu&longs;ques au temps & terme de dix ans, <lb/>finis & accomplis à conter du iour & datte de la pre­<lb/>&longs;ante impre&longs;&longs;ion, nonob&longs;tant toutes oppo&longs;itions ou <lb/>appellations quelconques, & &longs;ans preiudice d'icelle, <lb/>car tel e&longs;t le plai&longs;ir de &longs;a Mage&longs;té. Donné à Paris le <lb/>23. de Decembre 1598.</s>
</p>
<p type="main">
<s><emph type="italics"/>Signé par le Con&longs;eil<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>D<emph.end type="italics"/>E LAVETS.</s>
</p>
<pb/>
<p type="head">
<s>INDEX MEMOR ABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>& eorum Commentarijs.<lb/>
<arrow.to.target n="table1"></arrow.to.target></s>
</p>
<table>
<table.target id="table1"></table.target>
<row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/><foreign lang="greek">*abuasos vnde.</foreign> pag.<emph.end type="italics"/></cell><cell>209</cell></row>
<row><cell><emph type="italics"/>Ab&longs;is pro circunferen-tia rotæ.<emph.end type="italics"/></cell><cell>100</cell></row>
<row><cell><emph type="italics"/>Acatium ante naues.<emph.end type="italics"/></cell><cell>65</cell></row>
<row><cell><emph type="italics"/>Actiones manuum in opi&longs;ic&ydot;s egent &longs;tatione, vel &longs;ebione tantùm<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Admiratio quid.<emph.end type="italics"/></cell><cell>4.5</cell></row>
<row><cell><emph type="italics"/>Agriculturæ nece&longs;&longs;aria.<emph.end type="italics"/></cell><cell>14</cell></row>
<row><cell><emph type="italics"/>Ædes rotunda mirifica.<emph.end type="italics"/></cell><cell>10</cell></row>
<row><cell><emph type="italics"/>Ædificium durabile rectà in&longs;i&longs;tit.<emph.end type="italics"/></cell><cell>196</cell></row>
<row><cell><emph type="italics"/>Æolus primus v&longs;us velis.<emph.end type="italics"/></cell><cell>92</cell></row>
<row><cell><emph type="italics"/>Æquale e&longs;t cau&longs;a quietis.<emph.end type="italics"/></cell><cell>193.196</cell></row>
<row><cell><emph type="italics"/>Æquilibrium in ponder atione.<emph.end type="italics"/></cell><cell>149</cell></row>
<row><cell><foreign lang="greek">*alou<gap/>gopw/lai</foreign> <emph type="italics"/>qui.<emph.end type="italics"/></cell><cell>47</cell></row>
<row><cell><emph type="italics"/>Ambulare pronum conuenit brutis.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Angulus rectus e&longs;t angubus æqualitatis, ideóque quietis.<emph.end type="italics"/></cell><cell>193.196</cell></row>
<row><cell><emph type="italics"/>Ad angulos rectos omniaæ <expan abbr="quit&longs;cũt">quit&longs;cunt</expan>.<emph.end type="italics"/></cell><cell>196</cell></row>
<row><cell><emph type="italics"/>Antemna quid.<emph.end type="italics"/></cell><cell>92</cell></row>
<row><cell><emph type="italics"/>Antemnæ motio.<emph.end type="italics"/></cell><cell>92</cell></row>
<row><cell><emph type="italics"/>Antiperi&longs;ta&longs;is medÿ confert ad motum proiecti.<emph.end type="italics"/></cell><cell>203</cell></row>
<row><cell><emph type="italics"/>Antiphonis dictum, cum iret ad &longs;uppli-cium.<emph.end type="italics"/></cell><cell>12</cell></row>
<row><cell><emph type="italics"/>Antiphonis ver&longs;us de natura & arte.<emph.end type="italics"/></cell><cell>8. 12</cell></row>
<row><cell><emph type="italics"/>Arbores, & plantæ in&longs;i&longs;lunt plane terræ ad rectos angulos.<emph.end type="italics"/></cell><cell>196</cell></row>
<row><cell><emph type="italics"/>Archelairegis factum in edip&longs;i Solis.<emph.end type="italics"/></cell><cell>5</cell></row>
<row><cell><emph type="italics"/>Archimedeum problema, datum pondus data potentia mouere.<emph.end type="italics"/></cell><cell>60</cell></row>
<row><cell><emph type="italics"/>Archimedis factum Mechanicum.<emph.end type="italics"/></cell><cell>12</cell></row>
<row><cell><emph type="italics"/>Architectureæ tres partes.<emph.end type="italics"/></cell><cell>9</cell></row>
<row><cell><emph type="italics"/>Argo prima nauis.<emph.end type="italics"/></cell><cell>62</cell></row>
<row><cell><emph type="italics"/>Ari&longs;toteles reprehen&longs;us à Nonio.<emph.end type="italics"/></cell><cell>84</cell></row>
<row><cell><emph type="italics"/>Ars &longs;lectit naturam, & ad alium &longs;co-pum vertit.<emph.end type="italics"/></cell><cell>6</cell></row>
<row><cell><emph type="italics"/>Ars e&longs;t admirationis plenæ.<emph.end type="italics"/></cell><cell>6</cell></row>
<row><cell><emph type="italics"/>Artis, & naturæ differentia.<emph.end type="italics"/></cell><cell>6</cell></row>
<row><cell><emph type="italics"/>Artium diui&longs;io in liberales, & &longs;ordi-das.<emph.end type="italics"/></cell><cell>3</cell></row>
<row><cell><emph type="italics"/>Artes liberales.<emph.end type="italics"/></cell><cell>3</cell></row>
<row><cell><emph type="italics"/>Artes pueriles.<emph.end type="italics"/></cell><cell>3</cell></row>
<row><cell><emph type="italics"/>Artes magnæ.<emph.end type="italics"/></cell><cell>3</cell></row>
<row><cell><emph type="italics"/>Artes imperantes.<emph.end type="italics"/></cell><cell>3.4</cell></row>
<row><cell><emph type="italics"/>Artes architectonicæ.<emph.end type="italics"/></cell><cell>3</cell></row>
<row><cell><emph type="italics"/>Ars Typographica nihil e&longs;&longs;et &longs;ine co-chlea.<emph.end type="italics"/></cell><cell>133</cell></row>
<row><cell><emph type="italics"/>A&longs;inus, & aues longo collo vident cœ-lum, vt homo.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/>Axis in peritrochio.<emph.end type="italics"/></cell><cell>120</cell></row>
<row><cell><foreign lang="greek">*au<gap/>/mata.</foreign></cell><cell>10</cell></row>
<row><cell><emph type="italics"/>B<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Baiulus cum &longs;uo onere e&longs;t turbo, vel conus inuer&longs;us.<emph.end type="italics"/></cell><cell>199.200</cell></row>
<row><cell><emph type="italics"/>Baiuli Pari&longs;ien&longs;es facile ferunt ingentia pondera.<emph.end type="italics"/></cell><cell>198.199</cell></row>
<row><cell><emph type="italics"/>Baiuli cum onere tutò a&longs;cendunt, pericu-losè de&longs;cendunt.<emph.end type="italics"/></cell><cell>199</cell></row>
<row><cell><emph type="italics"/>B. Feratinus Amerinus <expan abbr="cãcellariæ">cancellariæ</expan> Apo-&longs;tolicæ regens con&longs;ecrat, & compreca-tur multa &longs;uper crucem apici obeli&longs;ci imponendam.<emph.end type="italics"/></cell><cell>142</cell></row>
<row><cell><emph type="italics"/>Bombi tormentorum multi editi &longs;tatim atque crux impo&longs;ita fuit apici obe-li&longs;ci.<emph.end type="italics"/></cell><cell>142</cell></row>
<pb/>
<row><cell><emph type="italics"/>Bouilli error, qui put abat rectam iuuen-tam equalem peripheriæ ex circuli &longs;uper planum reuolutione.<emph.end type="italics"/></cell><cell>174</cell></row>
<row><cell><emph type="italics"/>Boues ad <expan abbr="aratrũ">aratrum</expan> pariter &longs;ubiugandi.<emph.end type="italics"/></cell><cell>192</cell></row>
<row><cell><emph type="italics"/>Boüm in iugo imbecillior &longs;ubleuari po-te&longs;t.<emph.end type="italics"/></cell><cell>192</cell></row>
<row><cell><emph type="italics"/>Bruta ventrem ad terram conuer&longs;um habent.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/>Bruti&longs;pina pedib^{9} ad rectos imminet.<emph.end type="italics"/></cell><cell>198</cell></row>
<row><cell><emph type="italics"/>Brutum nihil admir atur.<emph.end type="italics"/></cell><cell>5</cell></row>
<row><cell><emph type="italics"/>Bruta nonnulla apta <expan abbr="fer&etilde;dis">ferendis</expan> &longs;arcinis.<emph.end type="italics"/></cell><cell>198</cell></row>
<row><cell><emph type="italics"/>Brutum nullum pote&longs;t &longs;edere.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>C<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><foreign lang="greek">*ka/<gap/>ar</foreign> <emph type="italics"/>in fund a quid &longs;it.<emph.end type="italics"/></cell><cell>117</cell></row>
<row><cell><emph type="italics"/>Calliæ Rhodien&longs;is factum <expan abbr="mechanicũ">mechanicum</expan>.<emph.end type="italics"/></cell><cell>12</cell></row>
<row><cell><emph type="italics"/>Cardanus reprehen&longs;us à Scaligero.<emph.end type="italics"/></cell><cell>145</cell></row>
<row><cell><emph type="italics"/>Cardanus ob&longs;curè & imper&longs;ectè: inge-niosè tamen&longs;crip&longs;it.<emph.end type="italics"/></cell><cell>180</cell></row>
<row><cell><emph type="italics"/>Carche&longs;ium quid.<emph.end type="italics"/></cell><cell>92</cell></row>
<row><cell><emph type="italics"/>Cathelina mu&longs;ca Rhemen&longs;ibus dicta e&longs;t <expan abbr="ex&etilde;plar">exemplar</expan> puncti duabus lationibus eo-dem tempore moti.<emph.end type="italics"/></cell><cell>32.33</cell></row>
<row><cell><emph type="italics"/>Cauda e&longs;t omnipi&longs;ci progubernaculo.<emph.end type="italics"/></cell><cell>77</cell></row>
<row><cell><emph type="italics"/>Celeritas duplex.<emph.end type="italics"/></cell><cell>27</cell></row>
<row><cell><emph type="italics"/>Centrobarica pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row>
<row><cell><emph type="italics"/>Cercopithecus proxime accedit ad figu-ram hominis.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/>Cercopithecus, & &longs;imia e&longs;t ridicula ho-minis imitatio.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/>Cercopitheci manus differt ab hominis manu.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/>Cercopitheci pollex non e&longs;t <foreign lang="greek">a)ntixeir,</foreign> vt in manu hominis.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/>Centrum duorum circulorum connexo-rum non e&longs;t idem.<emph.end type="italics"/></cell><cell>173</cell></row>
<row><cell><emph type="italics"/>Chirurgi togati nolunt dentes cuellere, licet&longs;u operatio chirurgica.<emph.end type="italics"/></cell><cell>153</cell></row>
<row><cell><emph type="italics"/>Circini author Dædalus.<emph.end type="italics"/></cell><cell>17</cell></row>
<row><cell><emph type="italics"/>Circulus e&longs;t <expan abbr="principiũ">principium</expan> omnium virium, quæ&longs;unt in machinis motricibus.<emph.end type="italics"/></cell><cell>15</cell></row>
<row><cell><emph type="italics"/>Circulus admirabilißimus.<emph.end type="italics"/></cell><cell>15</cell></row>
<row><cell><emph type="italics"/>Circulus habet in &longs;e quinque repugnan-tias.<emph.end type="italics"/></cell><cell>16</cell></row>
<row><cell><emph type="italics"/>Circulus &longs;ecit miracula in templis paga-norum.<emph.end type="italics"/></cell><cell>25</cell></row>
<row><cell><emph type="italics"/>Circulus ante, & pone mouetur &longs;imul.<emph.end type="italics"/></cell><cell>20.21</cell></row>
<row><cell><emph type="italics"/>Circulus maior ad minorem &longs;emper nu-tum habet.<emph.end type="italics"/></cell><cell>106</cell></row>
<row><cell><emph type="italics"/>Circuli nutus e&longs;t perpetuus.<emph.end type="italics"/></cell><cell>107</cell></row>
<row><cell><emph type="italics"/>Circuli qua&longs;i motus e&longs;t perpetuus.<emph.end type="italics"/></cell><cell>107</cell></row>
<row><cell><emph type="italics"/>Circuli minores infiniti &longs;unt in maiore circulo.<emph.end type="italics"/></cell><cell>108</cell></row>
<row><cell><emph type="italics"/>Circuli maiores &longs;unt mouentiores.<emph.end type="italics"/></cell><cell>109</cell></row>
<row><cell><emph type="italics"/>Circulus <expan abbr="cõtingit">contingit</expan> <expan abbr="planũ">planum</expan> in vno <expan abbr="pũcto">puncto</expan>.<emph.end type="italics"/></cell><cell>101</cell></row>
<row><cell><emph type="italics"/>Circuli maioris minor e&longs;t angulus conta-ctus quam minoris.<emph.end type="italics"/></cell><cell>115</cell></row>
<row><cell><emph type="italics"/>Circulus maior cum minore per æqualem orbitam reuoluitur & contra.<emph.end type="italics"/></cell><cell>164</cell></row>
<row><cell><emph type="italics"/>Circuli <expan abbr="cõcentrici">concentrici</expan> inæquales iuncti æqua-lem orbitam <expan abbr="percurrũt">percurrunt</expan>.<emph.end type="italics"/></cell><cell>166.167.174</cell></row>
<row><cell><emph type="italics"/>Circuli maioris motus &longs;ecundum natu-ram maior e&longs;t quam minoris.<emph.end type="italics"/></cell><cell>43</cell></row>
<row><cell><emph type="italics"/>in Circulo in&longs;criptas &longs;i &longs;ecet recta ad re-ctos ab&longs;ci&longs;&longs;a exdiametro erit maxima & <gap/>pinquior remotiore maior.<emph.end type="italics"/></cell><cell>68.69</cell></row>
<row><cell><emph type="italics"/>Circulum minorem qui datum maiorem interius tangat de&longs;cribere.<emph.end type="italics"/></cell><cell>41</cell></row>
<row><cell><emph type="italics"/>Cœli motus unde.<emph.end type="italics"/></cell><cell>104</cell></row>
<row><cell><emph type="italics"/>Cœlum videre quid apud <expan abbr="Platon&etilde;">Platonem</expan>.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/><expan abbr="Colũba">Columba</expan> volans Acchitæ <expan abbr="nõ">non</expan> e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row>
<row><cell><emph type="italics"/>Contraria quæ &longs;int verè.<emph.end type="italics"/></cell><cell>18</cell></row>
<row><cell><emph type="italics"/>Commotum facilius mouetur, quam quie&longs;cens.<emph.end type="italics"/></cell><cell>199</cell></row>
<row><cell><emph type="italics"/>Connexum & concauum non &longs;unt con-traria.<emph.end type="italics"/></cell><cell>19</cell></row>
<row><cell><emph type="italics"/>Cochlea quid.<emph.end type="italics"/></cell><cell>131</cell></row>
<row><cell><emph type="italics"/>Cochleæ effecta.<emph.end type="italics"/></cell><cell>133</cell></row>
<row><cell><emph type="italics"/>Cochlea magnes vires habet.<emph.end type="italics"/></cell><cell>133</cell></row>
<row><cell><emph type="italics"/>Cochlea infinita.<emph.end type="italics"/></cell><cell>133</cell></row>
<row><cell><emph type="italics"/>Cochleæ Ari&longs;toteles non meminit.<emph.end type="italics"/></cell><cell>131</cell></row>
<row><cell><emph type="italics"/>Cochlea e&longs;t cuneus multiplicatus, vel vnus cuneus continuatus.<emph.end type="italics"/></cell><cell>131</cell></row>
<row><cell><emph type="italics"/>Cuneus e&longs;t vectu duplicatus.<emph.end type="italics"/></cell><cell>127</cell></row>
<row><cell><emph type="italics"/>Cuneum vicem gerere duorum vectium demon&longs;tratio linearis.<emph.end type="italics"/></cell><cell>130</cell></row>
<row><cell><emph type="italics"/>Cuneus quid.<emph.end type="italics"/></cell><cell>126</cell></row>
<row><cell><emph type="italics"/>Cunci v&longs;us.<emph.end type="italics"/></cell><cell>127</cell></row>
<pb/>
<row><cell><emph type="italics"/>Cuneimagna vis.<emph.end type="italics"/></cell><cell>127.127</cell></row>
<row><cell><emph type="italics"/>Cuneo magnæ moles diuiduntur.<emph.end type="italics"/></cell><cell>125</cell></row>
<row><cell><emph type="italics"/>Crocæ Ari&longs;toteliquid.<emph.end type="italics"/></cell><cell>123</cell></row>
<row><cell><emph type="italics"/>Crocæ rotundæ.<emph.end type="italics"/></cell><cell>122.123</cell></row>
<row><cell><emph type="italics"/>Cubus &longs;tabilißima figurarum.<emph.end type="italics"/></cell><cell>103</cell></row>
<row><cell><emph type="italics"/>Currus iam commotus facilius moue-tur.<emph.end type="italics"/></cell><cell>200</cell></row>
<row><cell><emph type="italics"/>D<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Dædali &longs;tatuæliberæ, & ligatæ.<emph.end type="italics"/></cell><cell>25</cell></row>
<row><cell><emph type="italics"/>Decubitus &longs;anorum in lecto.<emph.end type="italics"/></cell><cell>176</cell></row>
<row><cell><emph type="italics"/>Dens corro&longs;us eximidebet.<emph.end type="italics"/></cell><cell>153</cell></row>
<row><cell><emph type="italics"/>Dens non temere eximi debet.<emph.end type="italics"/></cell><cell>153</cell></row>
<row><cell><emph type="italics"/>Dens forcipe facilius, quam manu euelli-tur.<emph.end type="italics"/></cell><cell>153</cell></row>
<row><cell><emph type="italics"/>Dentiducus quid.<emph.end type="italics"/></cell><cell>132</cell></row>
<row><cell><emph type="italics"/><expan abbr="D&etilde;tes">Dentes</expan> <expan abbr="animaliũ">animalium</expan> inci&longs;orÿ &longs;unt cunei.<emph.end type="italics"/></cell><cell>129</cell></row>
<row><cell><emph type="italics"/>Dens priu&longs;quam eximatur duo fieri po-&longs;tulat.<emph.end type="italics"/></cell><cell>154</cell></row>
<row><cell><emph type="italics"/>Dentis euellendi differentia à clauo in-fixo.<emph.end type="italics"/></cell><cell>154</cell></row>
<row><cell><emph type="italics"/>Deusnon admiratur.<emph.end type="italics"/></cell><cell>5</cell></row>
<row><cell><emph type="italics"/>Diaconus &longs;acris ve&longs;tibus indutus imponit crucem apici obeli&longs;ci.<emph.end type="italics"/></cell><cell>142</cell></row>
<row><cell><emph type="italics"/>Diameter circuli, & Sphæræ in&longs;i&longs;tit plano ad rectos.<emph.end type="italics"/></cell><cell>105</cell></row>
<row><cell><emph type="italics"/>Diametri ad peripheriam quæratio.<emph.end type="italics"/></cell><cell>32</cell></row>
<row><cell><emph type="italics"/>Dies impo&longs;itæ crucis obeli&longs;co.<emph.end type="italics"/></cell><cell>142</cell></row>
<row><cell><emph type="italics"/>Dolabra e&longs;t cuneus.<emph.end type="italics"/></cell><cell>130</cell></row>
<row><cell><emph type="italics"/>Dominicus Fontana machinator in&longs;i-gnis.<emph.end type="italics"/></cell><cell>139</cell></row>
<row><cell><emph type="italics"/>Dominici Fontanæ triumphus.<emph.end type="italics"/></cell><cell>142</cell></row>
<row><cell><emph type="italics"/>Domus integra à &longs;undamentis &longs;ublata, & aliò tran&longs;lata.<emph.end type="italics"/></cell><cell>133</cell></row>
<row><cell><emph type="italics"/>E<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Elementa quie&longs;icunt adrectos angu-los &longs;ita.<emph.end type="italics"/></cell><cell>196</cell></row>
<row><cell><emph type="italics"/>En&longs;is e&longs;t cuneus.<emph.end type="italics"/></cell><cell>130</cell></row>
<row><cell><foreign lang="greek">*epipo/laia</foreign> <emph type="italics"/>vis quæ.<emph.end type="italics"/></cell><cell>201.202</cell></row>
<row><cell><emph type="italics"/>Equus Troianus machina er at.<emph.end type="italics"/></cell><cell>12</cell></row>
<row><cell><emph type="italics"/>Ergat a quid.<emph.end type="italics"/></cell><cell>119</cell></row>
<row><cell><emph type="italics"/>Ergatæ, & &longs;ucculæ di&longs;tinctio.<emph.end type="italics"/></cell><cell>129</cell></row>
<row><cell><emph type="italics"/>Ergatam collopes maiores minoribus fa-cilius mouent.<emph.end type="italics"/></cell><cell>118.119</cell></row>
<row><cell><emph type="italics"/>Exercitium militum in exercitu ferian-tium.<emph.end type="italics"/></cell><cell>125</cell></row>
<row><cell><emph type="italics"/>Exigua quæ.<emph.end type="italics"/></cell><cell>204</cell></row>
<row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Fabrilis ars certitudine vincit cæte-ras.<emph.end type="italics"/></cell><cell>4</cell></row>
<row><cell><emph type="italics"/>Figura hominis <expan abbr="decũbentis">decumbentis</expan> exirema.<emph.end type="italics"/></cell><cell>176</cell></row>
<row><cell><emph type="italics"/>Figura <expan abbr="corporũiuuat">corporuniuuat</expan>, velimpedit mul-tum corum inclinationes, & natura-les impetus.<emph.end type="italics"/></cell><cell>164</cell></row>
<row><cell><emph type="italics"/>Figura decubitus humida, &longs;eu mediæ quæ.<emph.end type="italics"/></cell><cell>176</cell></row>
<row><cell><emph type="italics"/>Forceps, & forfex quid.<emph.end type="italics"/></cell><cell>152</cell></row>
<row><cell><emph type="italics"/>Fortuna in&longs;i&longs;tit Spharæ.<emph.end type="italics"/></cell><cell>103</cell></row>
<row><cell><emph type="italics"/>Funda quid.<emph.end type="italics"/></cell><cell>116</cell></row>
<row><cell><emph type="italics"/>Funda inuentum Phænicuno.<emph.end type="italics"/></cell><cell>116</cell></row>
<row><cell><emph type="italics"/>Fundæ v&longs;us.<emph.end type="italics"/></cell><cell>116.117</cell></row>
<row><cell><emph type="italics"/>Fundæ cur Balearis.<emph.end type="italics"/></cell><cell>116</cell></row>
<row><cell><emph type="italics"/>Funda longius proÿcit, quam manus.<emph.end type="italics"/></cell><cell>115.117</cell></row>
<row><cell><emph type="italics"/>Fundaiacit lapidem & plumbum.<emph.end type="italics"/></cell><cell>117</cell></row>
<row><cell><emph type="italics"/>Fu&longs;tis ad genu fractus non lædit.<emph.end type="italics"/></cell><cell>122</cell></row>
<row><cell><emph type="italics"/>Fu&longs;tis duobus cyphis impo&longs;itus frangitur &longs;ine cyphorum fractione & aquæ effu-&longs;ione.<emph.end type="italics"/></cell><cell>122</cell></row>
<row><cell><emph type="italics"/>G<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Georgij Lhullerÿ machina.<emph.end type="italics"/></cell><cell>137.138</cell></row>
<row><cell><emph type="italics"/>Gubernaculum & eius partes.<emph.end type="italics"/></cell><cell>73</cell></row>
<row><cell><emph type="italics"/>Gubernaculi & remi differentia.<emph.end type="italics"/></cell><cell>76</cell></row>
<row><cell><emph type="italics"/>Gubernaculi magna vis in nauis motio-ne.<emph.end type="italics"/></cell><cell>71.72</cell></row>
<row><cell><emph type="italics"/>Gyraphi &longs;oli crura po&longs;teriora prioribus breuiora habent.<emph.end type="italics"/></cell><cell>112</cell></row>
<row><cell><emph type="italics"/>H<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Ha&longs;tæ ferrum e&longs;t cuneus.<emph.end type="italics"/></cell><cell>190</cell></row>
<row><cell><emph type="italics"/>Hominem quie&longs;cere, &longs;edare, &longs;urge-re, &longs;tare, ambulare, currere e&longs;t ex v&longs;u Geometriæ,<emph.end type="italics"/></cell><cell>198</cell></row>
<row><cell><emph type="italics"/>Hominis quies e&longs;t per rectos angulos.<emph.end type="italics"/></cell><cell>196</cell></row>
<row><cell><emph type="italics"/>Hominis ambulatio, & progre&longs;sio, vs fiat.<emph.end type="italics"/></cell><cell>198</cell></row>
<row><cell><emph type="italics"/>Homo <expan abbr="nõ">non</expan> &longs;tatrectus, vt <expan abbr="cælũ">cælum</expan> videus.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Homo vnde factus Mechanicus.<emph.end type="italics"/></cell><cell>7.8</cell></row>
<row><cell><emph type="italics"/>Homo &longs;olus admiratur.<emph.end type="italics"/></cell><cell>5</cell></row>
<row><cell><emph type="italics"/>Homo &longs;olus artifex.<emph.end type="italics"/></cell><cell>194</cell></row>
<pb/>
<row><cell><emph type="italics"/>Homo &longs;oius &longs;edere pote&longs;t.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Homo magnus & paruuus quis.<emph.end type="italics"/></cell><cell>19</cell></row>
<row><cell><emph type="italics"/>Homines duo ferentes pondus cum perti-ca, &longs;i pondus non e&longs;t in eius medio, non æqualiter premuntur.<emph.end type="italics"/></cell><cell>190.191</cell></row>
<row><cell><emph type="italics"/>Horologia nostritemporis veterum cle-p&longs;ydras, & gnemones antecellunt.<emph.end type="italics"/></cell><cell>26</cell></row>
<row><cell><emph type="italics"/>Plorologium Argentorati <expan abbr="magni&longs;icũ">magni&longs;icum</expan>.<emph.end type="italics"/></cell><cell>26</cell></row>
<row><cell><emph type="italics"/>Humero dextro onera difficilius ferun-tur, quam &longs;ini&longs;tro.<emph.end type="italics"/></cell><cell>187</cell></row>
<row><cell><emph type="italics"/>Hypomochlium quid.<emph.end type="italics"/></cell><cell>14.55</cell></row>
<row><cell><emph type="italics"/>I<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Iaccre &longs;upinum quid.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>lacere pronum.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Jacere &longs;upinum & pronum commune e&longs;t multis anim antibus.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Joannis iucundi problema.<emph.end type="italics"/></cell><cell>145</cell></row>
<row><cell><emph type="italics"/>L<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Lancea <expan abbr="perp&etilde;dicularis">perpendicularis</expan> facilius fer-tur, quam obliquata.<emph.end type="italics"/></cell><cell>185</cell></row>
<row><cell><emph type="italics"/>Lecti lateribus cur fiunt dupli.<emph.end type="italics"/></cell><cell>175</cell></row>
<row><cell><emph type="italics"/>Libra maior e&longs;t exactior minore.<emph.end type="italics"/></cell><cell>27.44. 45</cell></row>
<row><cell><emph type="italics"/>Libræ finis.<emph.end type="italics"/></cell><cell>4</cell></row>
<row><cell><emph type="italics"/>Libræpartes.<emph.end type="italics"/></cell><cell>45.46</cell></row>
<row><cell><emph type="italics"/>Libræfallaciæ.<emph.end type="italics"/></cell><cell>46.47</cell></row>
<row><cell><emph type="italics"/>Libræ valde exigua examinantis fabri-ca.<emph.end type="italics"/></cell><cell>47</cell></row>
<row><cell><emph type="italics"/>Librile <expan abbr="ab&longs;q;">ab&longs;que</expan> <expan abbr="põdere">pondere</expan> facilius mouetur.<emph.end type="italics"/></cell><cell>112</cell></row>
<row><cell><emph type="italics"/>Librilis brachia vt <expan abbr="maneãt">maneant</expan>, aut redeant ad <expan abbr="æquilibriũ">æquilibrium</expan> &longs;ublatis <expan abbr="põderil^{9}">ponderil^{9}</expan>.<emph.end type="italics"/></cell><cell>49.50</cell></row>
<row><cell><emph type="italics"/>Librile <expan abbr="ligneũ">ligneum</expan> facili^{9} mouetur ferreo.<emph.end type="italics"/></cell><cell>113</cell></row>
<row><cell><emph type="italics"/>Lignalongiora &longs;unt imbecilliora.<emph.end type="italics"/></cell><cell>124</cell></row>
<row><cell><emph type="italics"/>Ligna longa ab extremo difficilius <expan abbr="fcrũ-tur">fcrun-tur</expan> bumere, quam à medio.<emph.end type="italics"/></cell><cell>183.184</cell></row>
<row><cell><emph type="italics"/>Lignum vt è genu facilius <expan abbr="frãgatur">frangatur</expan>.<emph.end type="italics"/></cell><cell>121</cell></row>
<row><cell><emph type="italics"/>Linea de&longs;cribens circulum <expan abbr="&longs;ecundũ">&longs;ecundum</expan> duas lationes &longs;ertur.<emph.end type="italics"/></cell><cell>28.34</cell></row>
<row><cell><emph type="italics"/><expan abbr="Longũ">Longum</expan> pondus difficilius fertur humero, <expan abbr="quã">quam</expan> brcue, vt &longs;it <expan abbr="põdere">pondere</expan> æquale.<emph.end type="italics"/></cell><cell>186.187</cell></row>
<row><cell><emph type="italics"/>Lorain lectis extenduntur non &longs;ecundum diametrum.<emph.end type="italics"/></cell><cell>175.177</cell></row>
<row><cell><emph type="italics"/>M<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Machina quid.<emph.end type="italics"/></cell><cell>2</cell></row>
<row><cell><emph type="italics"/>Machinarum quædam per &longs;e, quædam-non per&longs;e mouentur.<emph.end type="italics"/></cell><cell>10</cell></row>
<row><cell><emph type="italics"/>Machinæ valentißimæ tres ex &longs;ententia Hippocratis.<emph.end type="italics"/></cell><cell>119</cell></row>
<row><cell><emph type="italics"/>Machinarum pluribus, & diuer&longs;arum compo&longs;itio adæquat vnam, quæ tanta, quanta opus e&longs;&longs;et fierinon pote&longs;t, pro-pter defectum materiæ.<emph.end type="italics"/></cell><cell>138.139</cell></row>
<row><cell><emph type="italics"/>Machinæ ad ædificia, & ad bellum.<emph.end type="italics"/></cell><cell>10</cell></row>
<row><cell><emph type="italics"/>in Machinis faciendis lex ob&longs;eruanda.<emph.end type="italics"/></cell><cell>10</cell></row>
<row><cell><emph type="italics"/>Magnetis vis.<emph.end type="italics"/></cell><cell>129</cell></row>
<row><cell><emph type="italics"/>Magna quæ.<emph.end type="italics"/></cell><cell>204</cell></row>
<row><cell><emph type="italics"/>Malus nauis.<emph.end type="italics"/></cell><cell>92</cell></row>
<row><cell><emph type="italics"/>Mali pterna.<emph.end type="italics"/></cell><cell>92</cell></row>
<row><cell><emph type="italics"/>Mallei <expan abbr="lõgius">longius</expan> <expan abbr="manubriũ">manubrium</expan> graui^{9} ferit.<emph.end type="italics"/></cell><cell>128</cell></row>
<row><cell><emph type="italics"/>Manganaria pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row>
<row><cell><emph type="italics"/>Manus e&longs;t <expan abbr="in&longs;trum&etilde;tũ">in&longs;trumentum</expan> <expan abbr="in&longs;trum&etilde;torũ">in&longs;trumentorum</expan>.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Manus tres partes.<emph.end type="italics"/></cell><cell>118</cell></row>
<row><cell><emph type="italics"/>Mechanica cur non e&longs;&longs;e Aristotelis vi-&longs;um &longs;it Cardano & <expan abbr="Frãci&longs;co">Franci&longs;co</expan> patricio.<emph.end type="italics"/></cell><cell>1</cell></row>
<row><cell><emph type="italics"/>Mechanica &longs;unt Aristotelis.<emph.end type="italics"/></cell><cell>2</cell></row>
<row><cell><emph type="italics"/>Mechanicorum diui&longs;io.<emph.end type="italics"/></cell><cell>2</cell></row>
<row><cell><emph type="italics"/>Mechanica vnde dicta.<emph.end type="italics"/></cell><cell>2.11</cell></row>
<row><cell><emph type="italics"/>Mechanica quæ dici debeant.<emph.end type="italics"/></cell><cell>2</cell></row>
<row><cell><emph type="italics"/>Mechanice quid.<emph.end type="italics"/></cell><cell>8.9</cell></row>
<row><cell><emph type="italics"/>Mechanice partim e&longs;t phy&longs;ica, partim mathematica.<emph.end type="italics"/></cell><cell>4.12.13</cell></row>
<row><cell><emph type="italics"/>Mechanicæ artes vnde dictæ.<emph.end type="italics"/></cell><cell>2.3</cell></row>
<row><cell><emph type="italics"/>Mechanice pars e&longs;t philo&longs;ophiæ.<emph.end type="italics"/></cell><cell>9</cell></row>
<row><cell><emph type="italics"/>Mechanices finis.<emph.end type="italics"/></cell><cell>9</cell></row>
<row><cell><emph type="italics"/>Mechanicus ante aggreßionem operis quid con&longs;iderare debeat.<emph.end type="italics"/></cell><cell>13</cell></row>
<row><cell><emph type="italics"/>Mechanice dicendi<emph.end type="italics"/> <foreign lang="greek">pa<gap/>adosopcioi\.</foreign></cell><cell>12</cell></row>
<row><cell><emph type="italics"/>laus Mechanicorum.<emph.end type="italics"/></cell><cell>142</cell></row>
<row><cell><emph type="italics"/>Mens e&longs;t ars artium.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Men&longs;ura rei cuiu&longs;que debet e&longs;&longs;e deter-minata.<emph.end type="italics"/></cell><cell>44</cell></row>
<row><cell><emph type="italics"/>Mercatura opulenta.<emph.end type="italics"/></cell><cell>4</cell></row>
<row><cell><emph type="italics"/>Mercurius in&longs;istit cubo.<emph.end type="italics"/></cell><cell>103</cell></row>
<row><cell><emph type="italics"/>Milij grana non &longs;unt &longs;impliciter exigua.<emph.end type="italics"/></cell><cell>204</cell></row>
<row><cell><emph type="italics"/>Militaris ars vtilitate vincit cæteras.<emph.end type="italics"/></cell><cell>4</cell></row>
<row><cell><emph type="italics"/>Milo cuneum contemnens peryt.<emph.end type="italics"/></cell><cell>127</cell></row>
<row><cell><emph type="italics"/>Mobile motum quò vergit facile moue-<emph.end type="italics"/>
<pb/><emph type="italics"/>tur.<emph.end type="italics"/></cell><cell>103</cell></row>
<row><cell><emph type="italics"/>Mobilis primi velocitas vt intelligatur.<emph.end type="italics"/></cell><cell>104.</cell></row>
<row><cell><emph type="italics"/>Mobilis primi motus e&longs;t men&longs;ura alio-rum motuum.<emph.end type="italics"/></cell><cell>104</cell></row>
<row><cell><emph type="italics"/>Mobile latius mouetur difficilius.<emph.end type="italics"/></cell><cell>104</cell></row>
<row><cell><emph type="italics"/>Moles exigua &longs;æpe magnam vim obti-net.<emph.end type="italics"/></cell><cell>129</cell></row>
<row><cell><emph type="italics"/>Motus fit in tempore, & &longs;ucceßiuè.<emph.end type="italics"/></cell><cell>205</cell></row>
<row><cell><emph type="italics"/>Motus minimus quis.<emph.end type="italics"/></cell><cell>104</cell></row>
<row><cell><emph type="italics"/>Mota duobus motibus ad eundem <expan abbr="ter-minũ">ter-minum</expan> <expan abbr="tend&etilde;tibus">tendentibus</expan> celerius <expan abbr="mou&etilde;tur">mouentur</expan>.<emph.end type="italics"/></cell><cell>163</cell></row>
<row><cell><emph type="italics"/>Motum duabus lationibus rationem ha-bentibus fertur <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan>.<emph.end type="italics"/></cell><cell>30</cell></row>
<row><cell><emph type="italics"/>Motum duabus lationibus rationem non habentibus <expan abbr="nõ">non</expan> fertur <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan>.<emph.end type="italics"/></cell><cell>30</cell></row>
<row><cell><emph type="italics"/>Motus circularis omnium machinatio-num principia continet.<emph.end type="italics"/></cell><cell>60</cell></row>
<row><cell><emph type="italics"/>Motus difficultas in mobili à quibus pen-deat.<emph.end type="italics"/></cell><cell>101</cell></row>
<row><cell><emph type="italics"/>Mulier parua non e&longs;t pulchræ.<emph.end type="italics"/></cell><cell>19</cell></row>
<row><cell><emph type="italics"/>Mundus nutans non vere dici de terra à poëta.<emph.end type="italics"/></cell><cell>104</cell></row>
<row><cell><emph type="italics"/>Mu&longs;culus vecti comparatus à Galeno.<emph.end type="italics"/></cell><cell>56</cell></row>
<row><cell><emph type="italics"/>N<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Natura <expan abbr="eod&etilde;">eodem</expan> modo &longs;emper opera-tur, & eundem &longs;copum habet.<emph.end type="italics"/></cell><cell>6</cell></row>
<row><cell><emph type="italics"/>Natura re&longs;i&longs;tit arti in multis.<emph.end type="italics"/></cell><cell>8</cell></row>
<row><cell><emph type="italics"/>Nauigandi ars admirabilis ob &longs;ubtilita-tem, & nauigationis pericula.<emph.end type="italics"/></cell><cell>62</cell></row>
<row><cell><emph type="italics"/>Nauigÿ Hieronis de&longs;criptio incredibi-lis.<emph.end type="italics"/></cell><cell>73</cell></row>
<row><cell><emph type="italics"/>Nauis quid, & partes.<emph.end type="italics"/></cell><cell>62</cell></row>
<row><cell><emph type="italics"/>Nauis Ptolemaicæ magnitudo.<emph.end type="italics"/></cell><cell>63</cell></row>
<row><cell><emph type="italics"/>Nauis iam mota &longs;acilius mouetur.<emph.end type="italics"/></cell><cell>201</cell></row>
<row><cell><emph type="italics"/>Nauis plus vehitur antror&longs;um, quam re-mi palmula retror&longs;um.<emph.end type="italics"/></cell><cell>80</cell></row>
<row><cell><emph type="italics"/>Nauis actuariæ promotio.<emph.end type="italics"/></cell><cell>69</cell></row>
<row><cell><emph type="italics"/>Nauis velocit as à quibus.<emph.end type="italics"/></cell><cell>93</cell></row>
<row><cell><emph type="italics"/>Nauium &longs;pecies.<emph.end type="italics"/></cell><cell>63</cell></row>
<row><cell><emph type="italics"/>Nauicula è plumbo tenui &longs;upernatat aquæ.<emph.end type="italics"/></cell><cell>164</cell></row>
<row><cell><emph type="italics"/>Nautæ in procellis &longs;olo vtuntur dolone.<emph.end type="italics"/></cell><cell>94</cell></row>
<row><cell><emph type="italics"/>Nautica ars opulenta.<emph.end type="italics"/></cell><cell>4</cell></row>
<row><cell><emph type="italics"/>Nuces à nucifrangibulo &longs;ine ictu facilius franguntur, quam cum ictu.<emph.end type="italics"/></cell><cell>155.156</cell></row>
<row><cell><emph type="italics"/><expan abbr="Nucifrãgibuli">Nucifrangibuli</expan> & forcipis di&longs;tinctio.<emph.end type="italics"/></cell><cell>156</cell></row>
<row><cell><emph type="italics"/>Nucifrangibulum ferreum facilius nu-cem frangit, quam ligneum.<emph.end type="italics"/></cell><cell>167</cell></row>
<row><cell><emph type="italics"/>Nutus quid.<emph.end type="italics"/></cell><cell>104.108</cell></row>
<row><cell><emph type="italics"/>Nutus quotuplex.<emph.end type="italics"/></cell><cell>108</cell></row>
<row><cell><emph type="italics"/>Nutus maioris peripheriæ maior e&longs;t, quam minoris.<emph.end type="italics"/></cell><cell>108</cell></row>
<row><cell><emph type="italics"/>O<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Obeli&longs;cus quid.<emph.end type="italics"/></cell><cell>139</cell></row>
<row><cell><emph type="italics"/>Obeli&longs;c^{9} Xy&longs;tiqualis & <expan abbr="quãtus">quantus</expan>.<emph.end type="italics"/></cell><cell>139</cell></row>
<row><cell><emph type="italics"/>Obeli&longs;cus Xy&longs;ti cuiprimo &longs;acer.<emph.end type="italics"/></cell><cell>140</cell></row>
<row><cell><emph type="italics"/>Obeli&longs;cus vbi&longs;itus erat.<emph.end type="italics"/></cell><cell>140</cell></row>
<row><cell><emph type="italics"/>quid Obeli&longs;cus tran&longs;latus, & Christo &longs;acer cum cruce &longs;uper apice &longs;uo impo&longs;i-ta Christianis &longs;ignificat.<emph.end type="italics"/></cell><cell>140</cell></row>
<row><cell><emph type="italics"/>molimina circa Obeli&longs;ci tran&longs;lationem quinque, omnia difficillima.<emph.end type="italics"/></cell><cell>140</cell></row>
<row><cell><emph type="italics"/>ad Obeli&longs;cum transferendum quæ ma-chinæ, & quot adhibitæ.<emph.end type="italics"/></cell><cell>140</cell></row>
<row><cell><emph type="italics"/>circa <expan abbr="Obeli&longs;cũ">Obeli&longs;cum</expan> molitiones quiuque, quo-modo, & à quibus perfectæ.<emph.end type="italics"/></cell><cell>141</cell></row>
<row><cell><emph type="italics"/>Obeli&longs;ci in area V aticani ante portam D. Fetri po&longs;iti Ichnographiæ.<emph.end type="italics"/></cell><cell>143</cell></row>
<row><cell><emph type="italics"/>de Obeli&longs;co & Xy&longs;to V. Summ. Pont. & cruce Gulielmi Blanci <expan abbr="epigrãma">epigramma</expan>.<emph.end type="italics"/></cell><cell>142</cell></row>
<row><cell><foreign lang="greek">*odonta/g<gap/>a *h)\o)donta/gw_gos</foreign> <emph type="italics"/>quid.<emph.end type="italics"/></cell><cell>152</cell></row>
<row><cell><foreign lang="greek">*odonta/gw_gos</foreign> <emph type="italics"/><expan abbr="plũbeus">plumbeus</expan> in <expan abbr="t&etilde;plo">templo</expan> Apol-linis Delphici quid &longs;ignificabat.<emph.end type="italics"/></cell><cell>153</cell></row>
<row><cell><emph type="italics"/>Ovos quid.<emph.end type="italics"/></cell><cell>119</cell></row>
<row><cell><emph type="italics"/>Os arietinum volæ manus impo&longs;itum frangitur manu illæ&longs;a.<emph.end type="italics"/></cell><cell>122</cell></row>
<row><cell><foreign lang="greek">*ou<gap/>ano/suopcs</foreign> <emph type="italics"/>pi&longs;cis velit nolio videt cælum.<emph.end type="italics"/></cell><cell>195</cell></row>
<row><cell><emph type="italics"/>P<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Palang a quid.<emph.end type="italics"/></cell><cell>191</cell></row>
<row><cell><emph type="italics"/>Pedem facere.<emph.end type="italics"/></cell><cell>95</cell></row>
<row><cell><emph type="italics"/>Pente&longs;paston.<emph.end type="italics"/></cell><cell>111.134</cell></row>
<row><cell><emph type="italics"/>Percußio quid.<emph.end type="italics"/></cell><cell>128</cell></row>
<row><cell><emph type="italics"/>Percu&longs;sionis duo modi.<emph.end type="italics"/></cell><cell>128</cell></row>
<row><cell><emph type="italics"/>Percußio à quibus fit maior.<emph.end type="italics"/></cell><cell>128</cell></row>
<row><cell><emph type="italics"/>Percußionis validiores cau&longs;æ.<emph.end type="italics"/></cell><cell>128.129</cell></row>
<pb/>
<row><cell><emph type="italics"/>Percu&longs;sionis magna vis ad mouendum, findendum, frangendum, quatien-dum.<emph.end type="italics"/></cell><cell>129</cell></row>
<row><cell><emph type="italics"/>Perpendiculares à peripherÿs in &longs;emi-diametros circulorum inæqualium æquales auferunt &longs;egmenta &longs;emidia-metrorum inæqualia, quorum maius e&longs;t quod è minori aufertur.<emph.end type="italics"/></cell><cell>40</cell></row>
<row><cell><emph type="italics"/>Peripheriæ maiores à punctis à centro remotioribus de&longs;cribuntur.<emph.end type="italics"/></cell><cell>23</cell></row>
<row><cell><emph type="italics"/>Petorita Gallorum petoritis Polonorum difficilius mouentur.<emph.end type="italics"/></cell><cell>113</cell></row>
<row><cell><emph type="italics"/>Phalanga quid.<emph.end type="italics"/></cell><cell>191</cell></row>
<row><cell><emph type="italics"/>Phalangary qui.<emph.end type="italics"/></cell><cell>191</cell></row>
<row><cell><emph type="italics"/>Phalangarÿ tetraphori, hexaphori.<emph.end type="italics"/></cell><cell>191</cell></row>
<row><cell><emph type="italics"/>Phalangÿ ictus.<emph.end type="italics"/></cell><cell>129</cell></row>
<row><cell><emph type="italics"/>Phalanx.<emph.end type="italics"/></cell><cell>146</cell></row>
<row><cell><emph type="italics"/>Philo&longs;ophia principium duxit ab admi-ratione.<emph.end type="italics"/></cell><cell>5</cell></row>
<row><cell><emph type="italics"/>Philo&longs;ophia e&longs;t ars generalis omnibus fa-ciendorum difficultatibus &longs;uccurrens.<emph.end type="italics"/></cell><cell>9</cell></row>
<row><cell><emph type="italics"/>Philo&longs;ophandi, vt admirandi &longs;emper oc-ca&longs;io erit.<emph.end type="italics"/></cell><cell>5</cell></row>
<row><cell><emph type="italics"/>Plumbum vtri aëre pleno annexum tar-dius de&longs;cendit in aquim, quam &longs;i non e&longs;&longs;et aunexum.<emph.end type="italics"/></cell><cell>170</cell></row>
<row><cell><foreign lang="greek">*go/da e)<gap/>ei_n,</foreign> <emph type="italics"/>& canere quid.<emph.end type="italics"/></cell><cell>95</cell></row>
<row><cell><foreign lang="greek">*go/des, & p<gap/>o/podes.</foreign></cell><cell>96</cell></row>
<row><cell><foreign lang="greek">*golio<gap/>uitiu*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row>
<row><cell><foreign lang="greek">*golu/w<gap/>ason.</foreign></cell><cell>111. 134</cell></row>
<row><cell><emph type="italics"/>Pons Lutetiæ ab Henrico 111. inchoatus ab Henrico 1111. perficietur.<emph.end type="italics"/></cell><cell>120</cell></row>
<row><cell><emph type="italics"/>Preßio porrecta.<emph.end type="italics"/></cell><cell>14</cell></row>
<row><cell><emph type="italics"/>Problema difficillimum totius libri.<emph.end type="italics"/></cell><cell>166</cell></row>
<row><cell><emph type="italics"/>Problematis a theoremate di&longs;tinctio.<emph.end type="italics"/></cell><cell>12</cell></row>
<row><cell><emph type="italics"/>Progreßio in animali vt fit.<emph.end type="italics"/></cell><cell>187</cell></row>
<row><cell><emph type="italics"/>Proiecta cur moueri de&longs;inunt.<emph.end type="italics"/></cell><cell>201</cell></row>
<row><cell><emph type="italics"/>in Proiectis impre&longs;&longs;a vis impellens à mo-tore e&longs;t can&longs;a eorum lationis.<emph.end type="italics"/></cell><cell>201</cell></row>
<row><cell><emph type="italics"/>Proiecta nec exigua nec magna &longs;eruntur procul.<emph.end type="italics"/></cell><cell>203.205</cell></row>
<row><cell><emph type="italics"/>Publ. Scipio & C. Lælius colligentes cro-cas quæ dicerent.<emph.end type="italics"/></cell><cell>123</cell></row>
<row><cell><emph type="italics"/>Purpura quid.<emph.end type="italics"/></cell><cell>47.48</cell></row>
<row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Qvie&longs;cens vim motoris diminuit.<emph.end type="italics"/></cell><cell>200</cell></row>
<row><cell><emph type="italics"/>R<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Radius minor plus retrahitur ad centrum, quam maior.<emph.end type="italics"/></cell><cell>38.39</cell></row>
<row><cell><emph type="italics"/>Rectilineæ figuræ, & cubus difficulter mouentur &longs;uper planum.<emph.end type="italics"/></cell><cell>102</cell></row>
<row><cell><emph type="italics"/>Remus quid.<emph.end type="italics"/></cell><cell>63</cell></row>
<row><cell><emph type="italics"/>Remiges qui.<emph.end type="italics"/></cell><cell>63</cell></row>
<row><cell><emph type="italics"/>Remigum differentiæ.<emph.end type="italics"/></cell><cell>64</cell></row>
<row><cell><emph type="italics"/>Remiges me&longs;onei maximè mouent na-uim.<emph.end type="italics"/></cell><cell>61</cell></row>
<row><cell><emph type="italics"/>Remi digitis manuum comparati.<emph.end type="italics"/></cell><cell>65</cell></row>
<row><cell><emph type="italics"/>Remus vt plurimum maris diuidit.<emph.end type="italics"/></cell><cell>71</cell></row>
<row><cell><emph type="italics"/>de Remi motione comparata ad motio-nem nauis.<emph.end type="italics"/></cell><cell>84.85.86.87.88.89</cell></row>
<row><cell><emph type="italics"/>qui <expan abbr="Remigũ">Remigum</expan> plus nauim promoueant.<emph.end type="italics"/></cell><cell>68</cell></row>
<row><cell><emph type="italics"/>in Rhombo punctum vnum extremum lateris motum duobus motibus minus &longs;paty conficit, quam latus ip&longs;um.<emph.end type="italics"/></cell><cell>159</cell></row>
<row><cell><emph type="italics"/>Rhombus con&longs;tituitur cuius angulus acu-tus e&longs;t dimidio obtu&longs;i minor.<emph.end type="italics"/></cell><cell>161</cell></row>
<row><cell><emph type="italics"/>in Rhombo alterum punctorum extre-morum non æqualem <expan abbr="rectã">rectam</expan> tran&longs;it.<emph.end type="italics"/></cell><cell>157</cell></row>
<row><cell><emph type="italics"/>Rhombus quid.<emph.end type="italics"/></cell><cell>159</cell></row>
<row><cell><emph type="italics"/>Rotæ binæ quaternis faciliores.<emph.end type="italics"/></cell><cell>111</cell></row>
<row><cell><emph type="italics"/>in Rotis quaternis po&longs;teriores prioribus maiorese&longs;&longs;e debent.<emph.end type="italics"/></cell><cell>111</cell></row>
<row><cell><emph type="italics"/>Rotæ curruum maiores commodiores ad facilitatem & celeritatem.<emph.end type="italics"/></cell><cell>110</cell></row>
<row><cell><emph type="italics"/>Rotunda figura difficulter patitur.<emph.end type="italics"/></cell><cell>124</cell></row>
<row><cell><emph type="italics"/>Rotunda maiora facilius mouentur mi-noribus.<emph.end type="italics"/></cell><cell>99.100</cell></row>
<row><cell><emph type="italics"/><expan abbr="Rotũdorum">Rotundorum</expan> motus accurata diui&longs;io.<emph.end type="italics"/></cell><cell>100</cell></row>
<row><cell><emph type="italics"/>S<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Sarcina maior in anteriore plaustri parte poni debet.<emph.end type="italics"/></cell><cell>111</cell></row>
<row><cell><emph type="italics"/>Saxa tritalantaria &longs;impliciter non &longs;unt magna.<emph.end type="italics"/></cell><cell>204</cell></row>
<row><cell><emph type="italics"/>Scorpionis ictus.<emph.end type="italics"/></cell><cell>129</cell></row>
<row><cell><emph type="italics"/>Scytala quid, & quotuplex.<emph.end type="italics"/></cell><cell>111.114</cell></row>
<row><cell><emph type="italics"/>Scytalæ v&longs;us duplex.<emph.end type="italics"/></cell><cell>111</cell></row>
<row><cell><emph type="italics"/>Super Scytalis onera facilius ge&longs;tantur,<emph.end type="italics"/>
<pb/><emph type="italics"/>quam &longs;uper curribus.<emph.end type="italics"/></cell><cell>113</cell></row>
<row><cell><emph type="italics"/>Securis magna diuidit.<emph.end type="italics"/></cell><cell>145</cell></row>
<row><cell><emph type="italics"/>Securis feriens diuidit, premens non item.<emph.end type="italics"/></cell><cell>144</cell></row>
<row><cell><emph type="italics"/>Securis e&longs;t cuneus annexus malleo.<emph.end type="italics"/></cell><cell>145</cell></row>
<row><cell><emph type="italics"/>Sedere quid.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Sedens caput habet ad pedes parallelum, & nequaquam in vnarecta.<emph.end type="italics"/></cell><cell>193</cell></row>
<row><cell><emph type="italics"/>Sedentariæ artes vtuntur &longs;eßione &longs;ecu-ra.<emph.end type="italics"/></cell><cell>197</cell></row>
<row><cell><emph type="italics"/>Sedile idem non congruit omni homini.<emph.end type="italics"/></cell><cell>196</cell></row>
<row><cell><emph type="italics"/>Seßio propriè dista & latè<emph.end type="italics"/></cell><cell>197</cell></row>
<row><cell><emph type="italics"/>Seßio cum &longs;ecuritate.<emph.end type="italics"/></cell><cell>197</cell></row>
<row><cell><emph type="italics"/>Sedens altius &longs;urgit facilius.<emph.end type="italics"/></cell><cell>197.198</cell></row>
<row><cell><foreign lang="greek">*e*h/mwma</foreign> <emph type="italics"/>quid.<emph.end type="italics"/></cell><cell>151</cell></row>
<row><cell><emph type="italics"/>Spartion pro an&longs;a.<emph.end type="italics"/></cell><cell>148</cell></row>
<row><cell><emph type="italics"/>Sphæra quale corpus.<emph.end type="italics"/></cell><cell>16</cell></row>
<row><cell><emph type="italics"/>Sphæra corpus e&longs;t mobilißimum & mo-uentißimum.<emph.end type="italics"/></cell><cell>16</cell></row>
<row><cell><emph type="italics"/>Sphæra contingit planum in puncto.<emph.end type="italics"/></cell><cell>101</cell></row>
<row><cell><emph type="italics"/>Sphæra Archimedis per &longs;e mobilis non e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row>
<row><cell><emph type="italics"/>Sphæratopæia pars e&longs;t mechanices.<emph.end type="italics"/></cell><cell>11</cell></row>
<row><cell><emph type="italics"/>Stateræ partes.<emph.end type="italics"/></cell><cell>147</cell></row>
<row><cell><emph type="italics"/>Stateræ v&longs;us.<emph.end type="italics"/></cell><cell>148</cell></row>
<row><cell><emph type="italics"/>Statera in pretio&longs;is expendendis non v&longs;urpatur, &longs;ed libra.<emph.end type="italics"/></cell><cell>147</cell></row>
<row><cell><emph type="italics"/>Statera commodior libra.<emph.end type="italics"/></cell><cell>147</cell></row>
<row><cell><emph type="italics"/>Statera vna mult æ &longs;unt libræ.<emph.end type="italics"/></cell><cell>148.149</cell></row>
<row><cell><emph type="italics"/>Statera e&longs;t vectis inuer&longs;us.<emph.end type="italics"/></cell><cell>150</cell></row>
<row><cell><emph type="italics"/>Stateræ paruo æquipondio magna ponde-ra expendunt.<emph.end type="italics"/></cell><cell>146.147.148</cell></row>
<row><cell><emph type="italics"/>Stateræ dimidium e&longs;t an&longs;a.<emph.end type="italics"/></cell><cell>148</cell></row>
<row><cell><emph type="italics"/>Per Stateram ponderationis factæ de-mon&longs;tratio.<emph.end type="italics"/></cell><cell>152</cell></row>
<row><cell><emph type="italics"/>Stare quid.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Stans e&longs;t perpendicularis terræ.<emph.end type="italics"/></cell><cell>193</cell></row>
<row><cell><emph type="italics"/>Stantis di&longs;po&longs;itio e&longs;t in recta linea.<emph.end type="italics"/></cell><cell>196</cell></row>
<row><cell><emph type="italics"/>Statio & &longs;eßio propria <expan abbr="sũt">sunt</expan> homini.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><foreign lang="greek">*etata</foreign> <emph type="italics"/>quæ.<emph.end type="italics"/></cell><cell>10</cell></row>
<row><cell><emph type="italics"/>Succula quid.<emph.end type="italics"/></cell><cell>119</cell></row>
<row><cell><emph type="italics"/>Surrectio e&longs;t motio.<emph.end type="italics"/></cell><cell>194</cell></row>
<row><cell><emph type="italics"/>Surrectio è iacente indiget acutis angu-lis.<emph.end type="italics"/></cell><cell>197</cell></row>
<row><cell><emph type="italics"/>Surgentes con&longs;tituunt angulum acutum ex femore cum tibia, tum ex thoræce & femore.<emph.end type="italics"/></cell><cell>193.195.196</cell></row>
<row><cell><emph type="italics"/>Surrectionis initium fit per acutos angu-los.<emph.end type="italics"/></cell><cell>198</cell></row>
<row><cell><emph type="italics"/>Surrectionis medium fit per rectum, & obtu&longs;os angulos.<emph.end type="italics"/></cell><cell>198</cell></row>
<row><cell><emph type="italics"/>Symmetria quid.<emph.end type="italics"/></cell><cell>19</cell></row>
<row><cell><emph type="italics"/>Symmetria pro analogia.<emph.end type="italics"/></cell><cell>205</cell></row>
<row><cell><emph type="italics"/>T<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Telum facilius ten&longs;a penetrat, quam laxa.<emph.end type="italics"/></cell><cell>202</cell></row>
<row><cell><emph type="italics"/>Terra cur immobilis.<emph.end type="italics"/></cell><cell>103.104</cell></row>
<row><cell><emph type="italics"/>Terra comparata cubo à Pythagoreis, & Platone.<emph.end type="italics"/></cell><cell>103.196</cell></row>
<row><cell><emph type="italics"/>Textus Ari&longs;totelis omnium mendo&longs;i&longs;-&longs;imus.<emph.end type="italics"/></cell><cell>178.179</cell></row>
<row><cell><emph type="italics"/>Thaletis factum in eclip&longs;i Solis.<emph.end type="italics"/></cell><cell>5</cell></row>
<row><cell><foreign lang="greek">*qanmatou<gap/>gim*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row>
<row><cell><emph type="italics"/>Theorematis à problemate di&longs;tinctio.<emph.end type="italics"/></cell><cell>12</cell></row>
<row><cell><emph type="italics"/>Tolleno quid.<emph.end type="italics"/></cell><cell>188.189</cell></row>
<row><cell><emph type="italics"/>Tollenonis v&longs;us.<emph.end type="italics"/></cell><cell>189</cell></row>
<row><cell><emph type="italics"/>Tollenonis tran&longs;uer &longs;ario pondus adie-ctum.<emph.end type="italics"/></cell><cell>188.190</cell></row>
<row><cell><emph type="italics"/>Tormenta bellica deducenda plures equos po&longs;tulant.<emph.end type="italics"/></cell><cell>110.111</cell></row>
<row><cell><emph type="italics"/>Traba quid.<emph.end type="italics"/></cell><cell>115</cell></row>
<row><cell><emph type="italics"/>Trispa&longs;ton.<emph.end type="italics"/></cell><cell>111.134</cell></row>
<row><cell><emph type="italics"/>Trochlea quid.<emph.end type="italics"/></cell><cell>111.134</cell></row>
<row><cell><emph type="italics"/>Trochlea e&longs;t vectis.<emph.end type="italics"/></cell><cell>136</cell></row>
<row><cell><emph type="italics"/>in Trochleis plures orbiculi facilius, &longs;ed lentius trahunt.<emph.end type="italics"/></cell><cell>137</cell></row>
<row><cell><emph type="italics"/>Trochleæ duæ legitimè compofitæ magna pondera adducunt.<emph.end type="italics"/></cell><cell>133.134.136</cell></row>
<row><cell><emph type="italics"/>V<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Vectis quid.<emph.end type="italics"/></cell><cell>14.55</cell></row>
<row><cell><emph type="italics"/>Vectis, cuneus.<emph.end type="italics"/></cell><cell>119</cell></row>
<row><cell><emph type="italics"/>Vectis partes.<emph.end type="italics"/></cell><cell>14.15</cell></row>
<row><cell><emph type="italics"/>Vectis v&longs;us duplex.<emph.end type="italics"/></cell><cell>55</cell></row>
<row><cell><emph type="italics"/>Vectis refert libram.<emph.end type="italics"/></cell><cell>57</cell></row>
<row><cell><emph type="italics"/>pro Vecte vnum &longs;tadium longo machinæ multæ &longs;imul.<emph.end type="italics"/></cell><cell>139</cell></row>
<row><cell><emph type="italics"/>Velum quid.<emph.end type="italics"/></cell><cell>92</cell></row>
<pb/>
<row><cell><emph type="italics"/>Veli&longs;pecies.<emph.end type="italics"/></cell><cell>92</cell></row>
<row><cell><emph type="italics"/>Ventus &longs;ecundui, aduer&longs;us, iran&longs;uer&longs;us, obliquus.<emph.end type="italics"/></cell><cell>96</cell></row>
<row><cell><emph type="italics"/>Vento vt codem in contrarias partes na-uigatur demonstratio.<emph.end type="italics"/></cell><cell>98</cell></row>
<row><cell><emph type="italics"/>in Vortice aquarum lata ad medium de-uoluuntur.<emph.end type="italics"/></cell><cell>206.207.209.210</cell></row>
<row><cell><emph type="italics"/>Vortex aquarum.<emph.end type="italics"/></cell><cell>206</cell></row>
<row><cell><emph type="italics"/>in Vortice aquo&longs;i multi circuli concentri-ci.<emph.end type="italics"/></cell><cell>206</cell></row>
<row><cell><emph type="italics"/>Vortex aquæ e&longs;t linea &longs;piralis vnius, aut plurium reuolutionum.<emph.end type="italics"/></cell><cell>209</cell></row>
<row><cell><emph type="italics"/>Vortices quomodo à nautis vitentar.<emph.end type="italics"/></cell><cell>210</cell></row>
<row><cell><emph type="italics"/>Vortices inter Roe&longs;t & Loffoet.<emph.end type="italics"/></cell><cell>210</cell></row>
<row><cell><emph type="italics"/>in Vorticem vt &longs;entiunt nautæ &longs;e impe-<gap/>gi&longs;&longs;e.<emph.end type="italics"/></cell><cell>210</cell></row>
<row><cell><emph type="italics"/>difficile &longs;e liberare à Vortice.<emph.end type="italics"/></cell><cell>210.211</cell></row>
<row><cell><emph type="italics"/>aquain Vortice <expan abbr="de&longs;c&etilde;d&etilde;s">de&longs;cendens</expan> quò feratur.<emph.end type="italics"/></cell><cell>211</cell></row>
<row><cell><emph type="italics"/>Vtilitas hominum postulat in operibus &longs;uis varietatem.<emph.end type="italics"/></cell><cell>6</cell></row>
<row><cell><emph type="italics"/>X<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><emph type="italics"/>Xystus V. Pont. Max. obeli&longs;ci tran&longs;-ferendi author.<emph.end type="italics"/></cell><cell>139</cell></row>
<row><cell><emph type="italics"/>Xysti V. Pontificis laus.<emph.end type="italics"/></cell><cell>142</cell></row>
<row><cell><emph type="italics"/>Z<emph.end type="italics"/></cell><cell></cell></row>
<row><cell><foreign lang="greek">*zugo(s & *zugo\n.</foreign></cell><cell>45.119</cell></row>
<row><cell><foreign lang="greek">*zugosa/ths.</foreign></cell><cell>45</cell></row>
<row><cell><emph type="italics"/>Zygostatica fides.<emph.end type="italics"/></cell><cell>45</cell></row></table>
<p type="head">
<s>FINIS.</s>
</p>
<pb pagenum="1"/>
<figure></figure>
<p type="head">
<s><foreign lang="greek">*a*r*i*s*t*o*t*e*l*o*u<gap/></foreign><lb/>MHX ANIKA. <lb/>ARISTOTELIS <lb/>MECHANICA.</s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg1"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg1"></margin.target>Pro <foreign lang="greek">mhxanh\,</foreign><lb/>lege <foreign lang="greek">mhxani­<lb/>kh/.</foreign></s>
</p>
<p type="head">
<s><foreign lang="greek">Ti<gap/>st mhxanh\, kai_\ w<gap/>i\ ku/klou, <gap/> c)n toi_s mhxanikoi_s <lb/><gap/>ow masi/wn ai)ti/an e)/xontos.</foreign></s>
</p>
<p type="head">
<s><emph type="italics"/>Quid e&longs;t Mechanice, & de circulo in quo admirabilium, <lb/>quæ &longs;unt in Mechanicis, cau&longs;a continetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>MIRA &longs;unt in his, quæ <lb/><expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="naturã">naturam</expan> <expan abbr="eue-niũt">eue­<lb/>niunt</expan>, ea: <expan abbr="quorũ">quorum</expan> cau&longs;a igno­<lb/>ratur, & in his quæ præter <lb/>naturam, ea, <expan abbr="qu&ecedil;cunq;">qu&ecedil;cunque</expan> arte <lb/>facta hominibus <expan abbr="cõferunt">conferunt</expan>.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s><emph type="italics"/>Cardanvs librum hunc Ari&longs;totelis peripate-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg2"></arrow.to.target><lb/><emph type="italics"/>ticorum principis e&longs;&longs;e non arbitratur, propter man­<lb/>cam, & paulo negligentiorem motuum rotundo­<lb/>rum in eo po&longs;itam diui&longs;ionem. Franci&longs;cus Patri-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg3"></arrow.to.target><lb/><emph type="italics"/>cius vbi in omnes Ari&longs;totelis libros diligenter in­<lb/>quirit, ab eorum numero exclu&longs;it, cau&longs;am tamen attulit nullam, ni&longs;i <lb/>quod multi libri magnorum virorum nomine circumferantur, quo­<lb/>rum ip&longs;i authores non &longs;unt. quod licet verum e&longs;&longs;e multis rationibus,<emph.end type="italics"/>
<pb pagenum="2"/><emph type="italics"/>testimoniis, & exemplis coufirmarit: ob id tamen hunc Ari&longs;toteli <lb/>detrahendum e&longs;&longs;e, non e&longs;t nece&longs;&longs;e. Quid ita? Ip&longs;emet Patricius fate­<lb/>tur hunc<emph.end type="italics"/> <foreign lang="greek"><gap/> mhxanikw_n</foreign> <emph type="italics"/>librum doctum e&longs;&longs;e, & elegantem: addo <lb/>& &longs;ubtilem, & ab Ari&longs;totelis <expan abbr="verũ">verum</expan> in vnaquaque re, &longs;implex. &longs;yn­<lb/>cerumque exquirentis ingenio minime abhorrentem, vt ip&longs;um, & <lb/>no&longs;tros in ip&longs;um commentarios cuique legenti manife&longs;tum euadet. <lb/>Phra&longs;is non repugnat, &longs;i cumea <expan abbr="cõferatur">conferatur</expan>, quæ fuit familiaris Ari­<lb/>&longs;toteli in mathematicis, vt cum de Iride, aut de lineis in&longs;ecabilibus <lb/>di&longs;putat. Diogenes Laërtiusinter Ari&longs;totelis monumenta<emph.end type="italics"/> <foreign lang="greek">mhxani­<lb/>kw_n</foreign> <emph type="italics"/>vnum recen&longs;uit. Multi clari viri no&longs;tri temporis vt Daniel <lb/>Barbarus & Guidus Vbaldus &longs;æpe velut ab Ari&longs;totele citant. No­<lb/>nius interpretatus e&longs;t&longs;uis di&longs;cipulis. Cardaniratio parui e&longs;t <expan abbr="mom&etilde;ti">momenti</expan>. <lb/>quia Ari&longs;toteles etiam in his, qui genuini &longs;unt eius libri &longs;ine contro­<lb/>uer&longs;ia, non &longs;emper rerum exqui&longs;itas diui&longs;iones in&longs;tituit. Quare hunc <lb/>librum Ari&longs;totelis e&longs;&longs;e putabimus, quou&longs;que exoriatur aliquis, qui <lb/>vel hunc &longs;ibi vendicare, vel alÿ tribuere, potiori iure poßit.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg2"></margin.target>Lib. de pro­<lb/>port.</s>
</p>
<p type="margin">
<s><margin.target id="marg3"></margin.target>Tom.I.li.3. <lb/>Di&longs;cu&longs;&longs;io­<lb/>num pori­<lb/>patctic.</s>
</p>
<p type="main">
<s>Mechanica] <emph type="italics"/>Huius libri duæ &longs;unt partes. prior generalis e&longs;t <lb/>in explicatione cau&longs;arum & principiorum, quibus machinæ in mo­<lb/>uendo magnas, & admirabiles vires habent: po&longs;terior &longs;pecialis e&longs;t <lb/>in explicatione 25. quæstionum de quarundam machinarum viribus <lb/>& effectis. Hæcautem<emph.end type="italics"/> <foreign lang="greek"><gap/> mhxanikw_n</foreign> <emph type="italics"/>titulo recte exprimuntur. <lb/>quia Mechanica dicta&longs;unt<emph.end type="italics"/> <foreign lang="greek"><gap/>po\ th_s mhxanh_s. & *mhxanh\ <gap/>po\ tou_ <lb/>mh/kous kai\ a)n/ein,</foreign> <emph type="italics"/>id e&longs;t longè vel multùm a&longs;cendere, pertingere, pene­<lb/>trare, vt e&longs;t apud Platonem in Cratylo, vnde non quælibet artifi­<lb/>cia protrita & vulgaria Mechanica dicenda &longs;unt, &longs;ed ea tantum <lb/>quæ vtiliter & incundè &longs;uccurrunt, & adminioulantur difficul­<lb/>tatibus quæ in actionibus humanis &longs;e&longs;e <expan abbr="obtrudũt">obtrudunt</expan>, ip&longs;a&longs;que <expan abbr="impediũt">impediunt</expan>.<emph.end type="italics"/><lb/><foreign lang="greek">*mhxanh\</foreign> <emph type="italics"/>autem ide&longs;t machina definitur à Vitruuio, continens ex <lb/>materia coniunctio, quæ maximas habet, ad onerum motus virtu­<lb/>tes: & à P<gap/>nio in&longs;trumentum, quo moles aliquafacile, quocumque <lb/>volueris imp<gap/>lli pote&longs;t. Igitur tum hæc in&longs;trumenta & machinæ: <lb/>tum doctrina, quæ virium, quibus hæcpollent, rationem docet, & <lb/>explicat, reclè Mechanica in&longs;cribuntur. Sed vereor, ne hæclibri <lb/>in&longs;criptio, ex vulgari <gap/>tium diui&longs;ione in liberales & mechanicas, <lb/>quid &longs;or<gap/>di &longs;ubolens multis, ip&longs;os ab huius libri lectione deterruerit <lb/>& deterrea<gap/>. At quæ<gap/> umque, cluenda e&longs;t macula. Manauit enim à<emph.end type="italics"/>
<pb pagenum="3"/><emph type="italics"/>quibu&longs;dam philo&longs;ophis, ii&longs;que otio&longs;is, qui vt maiorem dignitatem <lb/>&longs;ibi fingerent, eas artes nobilitatis titulo ornduere, quæ in &longs;ola con­<lb/>templatione ver&longs;arentur, & contemplantis duntaxat ingenium <lb/>acuerent, atque perficerent: viles autem eas putduere, quæ ocium fu­<lb/>gientes, in negotio atque efficientia occuparentur. At ÿ melius <lb/>meo iudicio feci&longs;&longs;ent, &longs;i eas, quæ ita corporis adminiculo exercen­<lb/>tur, vt animi &longs;tudium non multum requirant, cum Græcis appel­<lb/>la&longs;&longs;ent, non<emph.end type="italics"/> <foreign lang="greek">mhxanika\s,</foreign> <emph type="italics"/>(neque enim hîc id vocabuli v&longs;urpant) <lb/>&longs;ed<emph.end type="italics"/> <foreign lang="greek">fau/las, a)neleuqirous <gap/>anow/oous a)<gap/>ai/ous</foreign> <emph type="italics"/>viles, illiberales, <lb/>&longs;ordidas, circunforaneas. Melius e&longs;t ergo rem i&longs;tam paulo altius re-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg4"></arrow.to.target><lb/><emph type="italics"/>petitam aliquantum vltra per &longs;uas &longs;pecies deducere. Cum omnis ars, <lb/>vt e&longs;t apud Ari&longs;totelem, referatur ad bonum, nulla per &longs;e vilis cen­<lb/>&longs;eridebt, immo omnis po&longs;&longs;e&longs;&longs;orem &longs;uum vel meliorem vel vtilio­<lb/>rem &longs;ibi, vel &longs;uæ ciuitati reddit: at inter &longs;e comparatæ aliæ al<gap/>is præ­<lb/>&longs;tantiores existimatæ &longs;unt. vnde nata e&longs;t hæc vulgaris artium diui­<lb/>&longs;io, vt aliæ liberales e&longs;&longs;ent: aliæ mechanicæ. quæ his duobus ver&longs;ibus <lb/>exprimuntur.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg4"></margin.target>Lib I.cap i. <lb/>Ethic.</s>
</p>
<p type="main">
<s>Lingua, Tropus, Ratio, Numerus, Tonus, Angulus, A&longs;tra: <lb/>Rus, Nemus, Arma, Faber, Vulnera, Lana, Rates.</s>
</p>
<p type="main">
<s><emph type="italics"/>horum priore &longs;ignificantur Grammatica, Rhetorica, Dialectica, <lb/>Arithmetica, Mu&longs;ica, Geometria, A&longs;trologia, liberales ob id di­<lb/>ctæ, &longs;iue ingenuæ, quod illis excolatur animus, qui libera & ingenua <lb/>pars e&longs;t hominis: Sed & pueriles, quia his ingenui pueri primis an­<lb/>nis, &longs;tatim imbiberentur tanquam præuiis, & ad cape&longs;&longs;endas &longs;cien­<lb/>tias & magnas artes nece&longs;&longs;ariis. Scientiæ autem erant Philo&longs;ophia <lb/>moralis, Phy&longs;ica, Medicina, Iuri&longs;prudentia, Theologia. Poste­<lb/>riore &longs;ignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb/>Chirurgia, Lanificium, Nautica. In quarum &longs;ingulis aliæ &longs;unt im­<lb/>perantes, quæ & architectonicæ dicuntur: aliæ mini&longs;trantes. Impe­<lb/>rantes, habere debent præuias illas &longs;eptem liberales ante dictas, vt <lb/>videre e&longs;t apud Vitruuium de &longs;uo architecto, & in no&longs;tro com­<lb/>mentario Iuri&longs;iurandi Hipp. de Hippocrateo medico: apud <expan abbr="Virgiliũ">Virgilium</expan> <lb/>de &longs;uo agricola: apud Vegetium de &longs;uo imperatore, & eadem ratione <lb/>in reliquis: ita vt, qui imperantibus i&longs;tis artibus præditi fuerint, in­<lb/>ter homines præ&longs;tantißimi habiti &longs;emper &longs;int, & &longs;emper haberi <lb/>debeant, quanquam aliarum opera aliis aut nece&longs;&longs;aria magis, aut<emph.end type="italics"/>
<pb pagenum="4"/><emph type="italics"/>præ&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. Agriculturæ enim <lb/>opus, quod alimenta & medicamenta hominibus &longs;uppeditat, neceßi­<lb/>tate vincit cætera: victoria, quæ rebelles & hostes &longs;ubÿcit, proprios <lb/>ciues con&longs;eruat, vtilitate &longs;upereminet: Medicina nobilitate &longs;ubiecti, <lb/>& præstantia boni nempe &longs;anitatis, quam procurat, eximia e&longs;t: Cer­<lb/>titudine operis & operationis Fabrilis anteponenda omnibus: vt <lb/>Lanificium, quod ad opes hone&longs;te parandas: & Nautica propter <lb/>mercaturam faciunt omnium maximè. Imperantes etiam hoc ha­<lb/>bent, quod eorum, quæ efficiunt, rationes teneant: Iuueniles corporis <lb/>vires non requirant: vitæ po&longs;&longs;e&longs;&longs;oris &longs;ui &longs;int æquales. Mini&longs;trantes <lb/>non item: &longs;ed v&longs;u potius & con&longs;uetudine di&longs;cantur & exerceantur: <lb/>Iuueniles vires po&longs;tulent, & po&longs;&longs;e&longs;&longs;orem &longs;uum in &longs;enectute de&longs;e­<lb/>rant. Ex ÿs aliis aliæ materias apparant: aliæ in&longs;trumenta fabrican­<lb/>tur. In&longs;trumentorum omnium ratio con&longs;i&longs;tit in certa quadam figu­<lb/>ra, qua quæ eam habent, ad v&longs;um commodiora &longs;unt. Cur autem hæ <lb/>figuræ aptißimæ &longs;int nulla <expan abbr="mini&longs;trãtium">mini&longs;trantium</expan> rationem inue&longs;tigat: Satis <lb/>habent, &longs;i modum fabricandi & vtendi tenuerint. harum tamen <lb/>aliquot, cum certæ rationes e&longs;&longs;ent &longs;ubtiles, & à fontibus Geometriæ <lb/>petitæ, ip&longs;as hoclibello verè aureo, & intelligentibus periucundo <lb/>Ari&longs;toteles partim generaliter, & ex &longs;uis principiis, partim per ali­<lb/>quot <expan abbr="ex&etilde;pla">exempla</expan>, à rebus multis varií&longs;que petita explicuit. Ob quod liber <lb/>rectè in&longs;cribitur<emph.end type="italics"/> <foreign lang="greek">mhxa/nika,</foreign> <emph type="italics"/>quia hic explicet cau&longs;as virium in­<lb/>&longs;trumentorum ad Mechanicas artes prædictas pertinentium. cur <lb/>&longs;cilicet ea, quam habent, prædita figura v&longs;ui, & effectui commodio­<lb/>ra exi&longs;tant.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quid e&longs;t Mechan.] <emph type="italics"/>Summa e&longs;t eorum, quæ hoc primo capite <lb/>explicantur, &longs;ed imperfectior: quia non, quid &longs;it mechanice, &longs;ed <lb/>quod &longs;it ars admirabilis, & quod circulus omnium, quæ fiunt in <lb/>Mechanica, admirabilium e&longs;&longs;e cau&longs;a o&longs;tenditur: præter quæ etiam <lb/>docetur problemata mechanica partim e&longs;&longs;e Phy&longs;ica, partim e&longs;&longs;e Ma­<lb/>thematica.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Mira &longs;unt in his:] <emph type="italics"/>Similitudo hîc quædam e&longs;t: &longs;ed &longs;ine notis <lb/>&longs;imilitudinis expre&longs;&longs;a. &longs;ic igitur erit clarior. Quemadmodum in re­<lb/>bus naturalibus miræ &longs;unt illæ, quarum cau&longs;a ignoratur: ita & in <lb/>his, quæ præter naturam arte factæ hominibus conferunt, &longs;i & ea­<lb/>rum cau&longs;a lateat, vbi notandum admirationem e&longs;&longs;e animi in rem<emph.end type="italics"/>
<pb pagenum="5"/><emph type="italics"/>propo&longs;itam intuitionem cum cupiditate cau&longs;am cogno&longs;cendi: ex quo <lb/>intelligitur Deum qui cogno&longs;cit & tenet cau&longs;as <expan abbr="omniũ">omnium</expan>, Bruta quia <lb/><expan abbr="ne&longs;ciũt">ne&longs;ciunt</expan>, nec &longs;cire cupiunt, nihil admirari: <expan abbr="&longs;olũ">&longs;olum</expan> hominem inter vtro&longs;­<lb/>que po&longs;itum, qui ne&longs;ciat, &longs;cire autem cupiat, admirationis e&longs;&longs;e capa­<lb/>cem, vnde non &longs;unt &longs;impliciter intelligendi hi ver&longs;us Horatiani,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Nil admirari propè res e&longs;t vna Numici,</s>
</p>
<p type="main">
<s>Soláque quæ po&longs;&longs;it facere & &longs;eruare beatum.</s>
</p>
<p type="main">
<s><emph type="italics"/>Nec enim hæc res facit Bruta, nec homines, qui ignorant, &longs;ed &longs;cire <lb/>&longs;eputant, aut &longs;cire non cupiunt, fœlices: &longs;ed eos, qui cogno&longs;cunt, iux­<lb/>ta illud<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Fœlix, qui potuit rerum cogno&longs;cere cau&longs;as.</s>
</p>
<p type="main">
<s><emph type="italics"/>Ab hac admirandi facultate Ari&longs;toteles <expan abbr="principiũ">principium</expan> Philo&longs;ophiæ re-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg5"></arrow.to.target><lb/><emph type="italics"/>petÿt. Qui enim, inquit, admiratur, putat &longs;e ignorare, & <expan abbr="dubitãs">dubitans</expan> co­<lb/>natur dubitationibus &longs;uis &longs;uccurrere. Homo natura fugiens e&longs;t igno­<lb/>rantiæ. <expan abbr="Itaq;">Itaque</expan> primò è dubitatis faciliora inqui &longs;iuit, deinde paulatim <lb/>vlterius procedens <expan abbr="etiã">etiam</expan> maiora, vt de affectionibus Lunæ, & ÿs quæ <lb/>circa Solem & &longs;tellas fiunt, ac de generatione vniuer &longs;i: atque &longs;ic <lb/>Philo&longs;ophia orta e&longs;t, &longs;icque Philo&longs;ophus non &longs;olum rara & ingen­<lb/>tia, vt vulgus, &longs;ed etiam frequentia & exigua, &longs;i cau&longs;as latentes ha­<lb/>beant, admiratur, & quidem cum voluptate: in quo etiam di&longs;&longs;entit à <lb/>vulgò, qui quæ admiratur, &longs;æpe horret, vt Eclip&longs;es Solis & Lunæ,<emph.end type="italics"/><lb/>
<arrow.to.target n="marg6"></arrow.to.target><lb/><emph type="italics"/>quod de Archelao rege Seneca memorat rerum naturæ adeò ignaro, <lb/>vt quo die Solis defectio fuit, regiam clau&longs;erit, & filium, quod in <lb/>luctu à rebus aduer&longs;is moris e&longs;t, totunderit. quam contra Thales <lb/>rerum naturæ gnarus in aperto fixis in peluim oculis magna cum <lb/>animi lætitia intuitus e&longs;&longs;et.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg5"></margin.target>Cap. 2. lib. 2. <lb/>Metaph.</s>
</p>
<p type="margin">
<s><margin.target id="marg6"></margin.target>Cap. 6. lib. 5. <lb/>De benefic.</s>
</p>
<p type="main">
<s>Quorum cau&longs;a ign.] <emph type="italics"/>In rebus naturalibus cau&longs;arum omne <lb/>genus ine&longs;t, materia, efficiens, forma, finis. Et in &longs;ingularium conti­<lb/>nentium & proximarum inuentione, & earum ad primam redu­<lb/>ctione Philo&longs;ophia con&longs;i&longs;tit. Sunt autem eiu&longs;modi, vt ex his aliæ <lb/>notæ iam &longs;int, aliæ adhuc ignotæ per&longs;i&longs;tant, vnde numquam &longs;tudio­<lb/>&longs;is deerit admirandi, & propterea philo&longs;ophandi occa&longs;io: difficiles <lb/>tantum, &longs;alebro&longs;o&longs;que aditus habens, &longs;iquidem<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Multa tegit &longs;acro inuolucro Natura, neque vllis</s>
</p>
<p type="main">
<s>Fas e&longs;t &longs;cire quidem mortalibus omnia: multa</s>
</p>
<p type="main">
<s>Admirare modò, nec non venerarc.</s>
</p>
<pb pagenum="6"/>
<p type="main">
<s><emph type="italics"/>abiecti certè ac be&longs;tias imitantis hominis e&longs;t, quæ ne&longs;ciat, non admi­<lb/>rari, & &longs;i curis, negotií&longs;que nece&longs;&longs;arÿs vacuus e&longs;t, non inquirere, <lb/>& venerari.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. <expan abbr="Si-quid&etilde;">Si­<lb/>quidem</expan> natura <expan abbr="eod&etilde;">eodem</expan> modo <lb/><expan abbr="s&etilde;per">semper</expan> operatur & &longs;implici­<lb/>ter: <expan abbr="Ataliũ">Atalium</expan> <expan abbr="atq;">atque</expan> alium ple­<lb/>rumque po&longs;tulat vtilitas. <lb/><expan abbr="Quãdo">Quando</expan> igitur conuenit fa­<lb/>cere aliquid pr&ecedil;ter <expan abbr="naturã">naturam</expan>, <lb/><expan abbr="tũ">tum</expan> difficultas hæ&longs;itationem <lb/>adfert, & arte opus e&longs;t.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>In multis enim.] <emph type="italics"/>Secunda ratio e&longs;t ad probandum in arte fa­<lb/>ctis quibu&longs;dam aliquid mirum e&longs;&longs;e, deprompta e&longs;t ex effectis Na­<lb/>turæ contrarÿs, &longs;altem repugnantibus, &longs;yllogi&longs;mus &longs;ic in&longs;titutus <lb/>rem ip&longs;am illu&longs;trabit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Naturam aliò flectere & adducere, quam vergat, mirum e&longs;t, <lb/>quia difficultas ex renixu naturæ dubitationem parit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In his quæ arte fiunt aliò natura flectitur & adducitur, quam <lb/>vergat. Natura enim eodem modo &longs;emper agit, v&longs;us autem re­<lb/>rum humanarum varios modos po&longs;tulat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Igitur in arte factis aliquid mirum e&longs;t. Pro a&longs;&longs;umptione a&longs;&longs;um­<lb/>ptionis confirmatio est ex effectis, & effectorum modo naturæ & <lb/>artis. Natura enim in multis inclinat aliò, quam vtilitas hominum <lb/>po&longs;tulat: Natura item vno modo &longs;emper operatur: contra Ars vti­<lb/>litatem hominem &longs;emper &longs;pectat, & varios operandi modos pro­<lb/>&longs;equitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Siquidem Natura.] <emph type="italics"/>Naturalia principium in &longs;e habent &longs;ui <lb/>motus, quo &longs;i &longs;implicia &longs;unt, ad vnum & vno modo &longs;impliciter <lb/>mouentur: &longs;i commixta prædominantis vnius motum &longs;equuntur, <lb/>&longs;icque ad vnum feruntur. Hæc &longs;unt demon&longs;trata ab Aristotele<emph.end type="italics"/>
<pb pagenum="7"/><emph type="italics"/>lib. de Cœlo & de generat. & corrupt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>At alium atque alium.] <emph type="italics"/>Hominum vtilitas tum ad e&longs;&longs;e tum <lb/>ad bene e&longs;&longs;e multa variáque multò aliter quam natura præferat, pe­<lb/>tit &longs;ibi fieri, vt <expan abbr="alim&etilde;ta">alimenta</expan> & copio&longs;iora, & aliter apparata: <expan abbr="quã">quam</expan> terra, <lb/>aër, & mare &longs;ponte &longs;ua &longs;uppeditent: vt ve&longs;titum, quem connexus <lb/>&longs;taminis cum &longs;ubtegmine faciens corpora tegendo, ip&longs;a probe tuetur <lb/>& ornat: vt ædificia, quæ trabium, lapidumque præter naturam ad <lb/>&longs;uperiorem locum euectio & coagmentatio vtilia facit, ad defen&longs;io­<lb/>nem contra cœli, aëris, externá&longs;que qua&longs;uis iniurias. Quinetiam va­<lb/>rietas <expan abbr="cõtra">contra</expan> naturæ cur&longs;um expetitur in delectabilibus vt hydrauli­<lb/>cis, engebatis, merulis, & icunculis voces, cantus, ge&longs;tus hominum, <lb/>auium, aliorumque animalium imitantibus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quando igitur.] <emph type="italics"/>Omnia licet habeat homo &longs;ui gratia nata: non <lb/>ita tamet habet, vt qualia naturaliter prodeunt, talibus <expan abbr="cũctis">cunctis</expan> com­<lb/>mode vti poßit. Neceßitate igitur & commoditate vtendi rebus à <lb/>natura oblatis pre&longs;&longs;us, conuertit ad &longs;uos v&longs;us & <expan abbr="accõmodat">accommodat</expan>: &longs;ed con­<lb/>uer&longs;io i&longs;ta, cum &longs;it deductio ad aliud, quam quò vergit natura, habet <lb/>in ÿs naturale principium renitens: hic renixus parit difficultatem <lb/>conuer&longs;ionis: hæc difficultas huc illuc animum hominis cogitando, <lb/>quærendóque, quomodo difficultas i&longs;ta &longs;uperetur, di&longs;trahit, facitque, <lb/>vt mente diu ver&longs;et, quid & quomodo agendum, exempli gratia. vt <lb/>onus &longs;ubleuet, altè ip&longs;e con&longs;cendat, vehementer quatiat, longè iacu­<lb/>letur, & ea demum faciat, velit nolit natura, quæ vtilitati homi­<lb/>num &longs;eruiant. Hæc cura &longs;olicitudóque vrget imaginationem, vt lu­<lb/>men à mente mutuantem & à rationibus mathematicis, nec quodam <lb/>&longs;ucce&longs;szlig;ionis ordine defatigari <expan abbr="ration&etilde;">rationem</expan> & quie&longs;cere &longs;mit, priu&longs;quam <lb/>quod quæritur, inuentum &longs;it. Illud inuentum, modú&longs;ve inuenicndi <lb/>generalis e&longs;t. hîc particulariter ad <expan abbr="machinã">machinam</expan> <expan abbr="in&longs;trumentáq;">in&longs;trumentáque</expan> refertur, <lb/>quibus <expan abbr="onerũ">onerum</expan> motiones fiant opportunæ, per motiones intellige, quæ <lb/>fiunt à loco ad locum, vt impul&longs;iones, tractiones, volutationes, ve­<lb/>ctiones, & in locis altis, medÿs, imis pro v&longs;u & decoro repo&longs;itiones: <lb/>per onera, quicquid aliò quam quò naturaliter vergit, impellitur, vt <lb/>aërem, cum deor&longs;um de&longs;cendere cogitur, vt aquam, vt terram cum <lb/>&longs;ur&longs;um a&longs;cendere, & eiu&longs;modi, quæ vulgus cum admiratione &longs;u&longs;pi­<lb/>cit, & ni&longs;i fierent, nulla res no&longs;tra non e&longs;&longs;et impedita Atque &longs;ic ra­<lb/>tio hominis nece&longs;sitate v&longs;us, & vtilitatis &longs;uæ pre&longs;&longs;a, efficiens cau&longs;a<emph.end type="italics"/>
<pb pagenum="8"/><emph type="italics"/>Mechanices hic &longs;tatuitur: vt e&longs;t etiam &longs;tatuta à Vitruuio &longs;ed & per<emph.end type="italics"/><lb/>
<arrow.to.target n="marg7"></arrow.to.target><lb/><emph type="italics"/>imitationem rerum à natura procreatarum. Homo enim inquit, ani­<lb/>maduertens Solis, Lunæ, & reliquorum planetarum continentes <lb/>motus, & machinationes naturales, &longs;ine quibus non habui&longs;&longs;et in <lb/>terra lucem, & fructuum maturit ates hinc exempla &longs;ump &longs;it, & ea <lb/>imitans, inductus rebus diuinis, commodas vitæ perfecit explicatio­<lb/>nes. Itaque comparauit, vt e&longs;&longs;ent expeditiora alia machinis, & ea­<lb/>rum ver&longs;ationibus: alia organis, quæque ob&longs;eruauit ad v&longs;um vtilia <lb/>e&longs;&longs;e &longs;tudÿs, artibus, in&longs;titutis, doctrinis gradatim augenda curauit: <lb/>hinc tandem extat ars quædam generalis quæ difficultati faciendo­<lb/>rum præter naturam ad vtiltiatem hominum &longs;uccurrit.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg7"></margin.target>Lib. 10.</s>
</p>
<p type="main">
<s>Tum difficultas.] <emph type="italics"/>Naturæ renixus difficultatem facit. Re­<lb/>nititur autem Natura &longs;ub&longs;tantia, numero, magnitudine, pondere, <lb/>figura, quæ omnia ars <expan abbr="immutãdo">immutando</expan>, addendo, detrahendo, <expan abbr="trã&longs;ponendo">tran&longs;ponendo</expan>, <lb/>poliendo, figurando corrigit, & ad v&longs;us humanos accommodat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/><lb/>
<arrow.to.target n="marg8"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg8"></margin.target><foreign lang="greek"><gap/>xanik<gap/>.</foreign></s>
</p>
<p type="main">
<s>Atque propterea partem <lb/>illius artis quæ hæ&longs;itationi <lb/>i&longs;ti &longs;uccurrit Mechanicem <lb/>vocamus. <expan abbr="Quemadmodũ">Quemadmodum</expan> <lb/>enim Antipho poëta di­<lb/>xit, ita &longs;e res habet.</s>
</p>
<p type="main">
<s><emph type="italics"/>Natura vincit: hanc arte <lb/>vincimus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>vt in his, quæ, cum mino­<lb/>ra &longs;int, &longs;uperant maiora: & <lb/>paruum momentum, cum <lb/>habeant, ingentia dimo­<lb/>uent pondera, cæteri&longs;­<lb/>que fere, quæ problemata <lb/>Mechanica nuncupamus.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Illius artis.] <emph type="italics"/>Ars gencralis, cuius hic mentionem facit Ari­<lb/>&longs;toteles, nu&longs;quam ab eo e&longs;t definita, aut nominata. Leonicus, qui <lb/>in hunc librum commentarium edidit putat e&longs;&longs;e Architecturam.<emph.end type="italics"/>
<pb/><emph type="italics"/>Quod facit ex &longs;ententia Vitruuÿ, qui eius tres partes con&longs;tituit, ædi­<lb/>ficationem in explicatione publicorum & priuatorum operum: <lb/>Gnomonicam in de&longs;criptione Horologiorum: & Machinationent <lb/>in cognitione principiorum & di&longs;po&longs;itione machinarum & orga­<lb/>norum. Hæc quidem comprehendi Architecturæ nomine Galenus<emph.end type="italics"/></s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg9"></arrow.to.target><lb/><emph type="italics"/>etiam te&longs;tatus e&longs;t, nomine inquit, artis Architectorum intelligi volo <lb/>Horologiorum, Clep&longs;ydrarum, Hydrocopiarum, Machinamento­<lb/>rumque omnium de&longs;criptiones, quibus etiam, quæ &longs;pirabilia vocant, <lb/>continentur. Sed cum in his quæ Architecturæ &longs;ubiecta &longs;unt &longs;olis <lb/>naturæ renixus non vincatur: <expan abbr="verũ">verum</expan> etiam in quibuslibet aliis cuiu&longs;­<lb/>cunque artis &longs;ubiectis, &longs;i qua &longs;it ars, quæ in vniuer&longs;um id doceat, <lb/>multo generalior e&longs;t Architectura. Et quid obe&longs;t dicere hanc e&longs;&longs;e <lb/>Philo&longs;ophiam? cum Philo&longs;ophia &longs;it cognitio omnium artium & re­<lb/>rum tam diuinarum: quam humanarum cau&longs;as, proprietates, effecta <lb/>con&longs;ideret. Atque hac diui&longs;a in &longs;uas partes, & partium particulas <lb/>vna ex his erit Mechanice. Quæ ad explicationem motuum violen­<lb/>torum, & admirabilium &longs;e habebit, vt Phy&longs;ica ad explicationem <lb/>motuum naturalium: & vt &longs;ub hac Medicina, Agricultura, & <lb/>aliæ: &longs;ic&longs;ub illa ars fabrilis, Architectura, Sutoria, & omnes quæ <lb/>in&longs;trumentis artificio&longs;is, indu&longs;trii&longs;que opus &longs;uum peragunt. quorum <lb/>omnium rationes & virium gradus in hac Mechanica tanquam <lb/>generali explicantur, vt po&longs;tea cuique facile apparebit.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg9"></margin.target>Cap. 3. lib. <lb/>de cuiu&longs;que <lb/>animi pecc. <lb/>cogno&longs;c.</s>
</p>
<p type="main">
<s>Mechanice.] <emph type="italics"/>In Græco Vecheli legitur hîc<emph.end type="italics"/> <foreign lang="greek">mhxanh\n</foreign>: <emph type="italics"/>vt etiam <lb/>in titulo huius capitis: &longs;ed vtrobique legendum<emph.end type="italics"/> <foreign lang="greek">mhxanikh\n.</foreign> <emph type="italics"/>quia ha­<lb/>ctenus in hoc proëmio non machina vna: &longs;ed ars machinarum lau­<lb/>data e&longs;t. Nec tamen definita, vt titulus pollicebatur. Definitur au­<lb/>tem &longs;ic à Picolomino. Mechanice e&longs;t &longs;cientia ex qua cau&longs;æ & prin-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg10"></arrow.to.target><lb/><emph type="italics"/>cipia ad quamplurimas artes &longs;ellularias exhauriri po&longs;&longs;unt. Nos peni­<lb/>tius ip&longs;ius rei, quæ definitur naturam, & ad ea quæ cum dicta &longs;unt <lb/>ab Aristotele, quæque dicentur intuentes perfectiùs opinor, &longs;ic de­<lb/>finiemus. Mechanice e&longs;t ars ad ea quæ vires humanas &longs;uperant, tra­<lb/>hendum, impellendum, ferendum, machinarum fabricatrix. vel &longs;ic <lb/>Mechanice e&longs;t ars cogendi corpora quantum fieri pote&longs;t vt contra <lb/>nutum ferantur. Hæc enim tota po&longs;ita e&longs;t, vt ad v&longs;um, delectatio­<lb/>némue hominum grauia &longs;ur&longs;um, leuia deor&longs;um, tum vtraque in la­<lb/>tus, in orbem &longs;eor &longs;im, atque per mixtim è loco in locum moueantur.<emph.end type="italics"/>
<pb pagenum="10"/><emph type="italics"/>Hæc enim vt fiant, ip&longs;a ars machinas inuenit, & inuentarum, cur <lb/>hæc præ&longs;tent cau&longs;as reddit. Cæterùm ex huius machinis, quædam <lb/>mouentur per &longs;e:quædam non &longs;ponte. Illæ intra &longs;e principia &longs;uæ mo­<lb/>tionis habent, &<emph.end type="italics"/> <foreign lang="greek">a)uto/ma<gap/>a</foreign> <emph type="italics"/>vocantur: quorum alia Græcis<emph.end type="italics"/> <foreign lang="greek">sa<gap/>a\,</foreign><lb/><emph type="italics"/>Latinis Stataria, fixa, firma dicuntur: alia<emph.end type="italics"/> <foreign lang="greek">u(pa/<gap/>n<gap/>a</foreign> <emph type="italics"/>ambulantia. <lb/>De vtri&longs;que Hero pertractauit, inter quæ pulchrum e&longs;t illud, quod <lb/>docuit con&longs;truere, &longs;cilicet ædem rotundam, in qua Bacchus pateram <lb/>alrera manu tenet, altera thyr&longs;um, propè verò ade&longs;t panthera, & <lb/>ara: circum autem Bacchides tympana tenentes, &longs;uprà tholum alata <lb/>& coronata Victoria collocatur, atque vno & <expan abbr="eod&etilde;">eodem</expan> tempore in ara <lb/>ignis &longs;uccenditur, Bacchus lac è patera, vinum è thyr&longs;o ver&longs;at in <lb/>pantheram, Bacchides circum&longs;alientes tympana pul&longs;ant, Victoria <lb/>&longs;e circumagens, & alas qaatiens tuba &longs;onat. In alia verò di&longs;po&longs;i­<lb/>tione fecit inambulantia, &longs;igilla euntia, & redeuntia, motione&longs;­<lb/>que varias reddentia, vt v&longs;us & voluptas po&longs;tulat pro instituto. <lb/>Hæ verò motionis principium intra &longs;e non habent: Sed ex his <lb/>aliæ mouentur à rebus inanimis, aliæ ab animatis. Res inani­<lb/>mæ principium motionis exhibentes &longs;unt aër, &longs;piritus, aqua, ignis, <lb/>&longs;umus. Aer & &longs;piritus e&longs;t vel inclu&longs;us, ex quò pneumatica ratio ab­<lb/>&longs;oluitur, de qua etiam Hero in&longs;trumenta Mu&longs;ica, quæ per<emph.end type="italics"/> <foreign lang="greek">an)tono ma­<lb/>si/an</foreign> <emph type="italics"/>organa vocant: vel liber, vnde ædificia ad molendum. A qua, <lb/>vnde fiunt rotæ etiam ad <expan abbr="molendũ">molendum</expan>, <expan abbr="tũ">tum</expan> tympana, tum &longs;erræ ad trabes <lb/>&longs;ecandas, folles ad <expan abbr="ferrũ">ferrum</expan> tundendum & alia <expan abbr="plera&qacute;">pleraque</expan>;. Ignis &longs;eu fumus <lb/>quo verrucula conuoluuntur: animatæ &longs;unt, bruta quæ trahunt cur­<lb/>rus, ci&longs;ia, quadrigas: homines qui ver&longs;ant, trahunt, erigunt, impel­<lb/>lunt ad varios belli <expan abbr="paci&longs;q;">paci&longs;que</expan> v&longs;us vtentes vectibus, radÿs, trochleis, <lb/>cochleis, trutinis, lancibus, ergatis, rotis, tympanis, & ad a&longs;cenden­<lb/>dum in altum multiplicibus &longs;calarum formis, tum munitis, tum &longs;ine <lb/>munitione, & ad di&longs;rumpendum, excutiendum, pro&longs;ternendum, <lb/>quatiendum frangendum, iaculandum, arietibus, te&longs;tudinibus, tur­<lb/>ribus ambulatorÿs, catapultis, bali&longs;tis, tormentis reliquis. in quibus <lb/>&longs;aciendis hæc lex po&longs;ita e&longs;t, vt omnia fiant ex paratu facilibus quo <lb/>ad materiam: varÿs quoad figuras: exiguis quoad men&longs;uras: leuibus <lb/>quoad pondera. Quippè quæ à quibu&longs;cumque artificibus citò fieri <lb/>queant, erectu interim, <expan abbr="trãslatúque">translatúque</expan> facilia: in &longs;idiatu, fractuque dif­<lb/>&longs;icilia: &longs;tabilia, ac tandem eiu&longs;modi &longs;int, vt quatenus neceßitas<emph.end type="italics"/>
<pb pagenum="11"/><emph type="italics"/>po&longs;tulauerit, facile componi, faciléque di&longs;&longs;olui poßint. Sed neque hic <lb/>prætermittenda diui&longs;io Methanices, quæ aliter à Politiano ex He-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg11"></arrow.to.target><lb/><emph type="italics"/>rone inducta e&longs;t. Mechanices, inquit, altera pars rationalis e&longs;t, quæ <lb/>numerorum, men&longs;urarum, &longs;yderum, naturæ que rationibus perfici­<lb/>tur: altera<emph.end type="italics"/> <foreign lang="greek">xeipourgikh\,</foreign> <emph type="italics"/>cui vel maximè artes illæ, æraria, ædifica­<lb/>toria, materiaria, picturaque, adminiculantur. Huius autem partes, <lb/>Manganaria per quam pondera immania minima vi tolluntur in <lb/>altum:<emph.end type="italics"/> <foreign lang="greek">mhxanopoihpkh\,</foreign> <emph type="italics"/>quæ facile aquas antlÿs extrahit:<emph.end type="italics"/> <foreign lang="greek">*or­<lb/>ganopoihtikh\,</foreign> <emph type="italics"/>quæ bellis accommoda in&longs;trumenta fabricatur, arie­<lb/>tes, te&longs;tudines, turres ambulatorias, helepoleis, &longs;ambucas, exo&longs;tras, <lb/>tollenones & quæcunque Græco vocabulo<emph.end type="italics"/> <foreign lang="greek">w_oliorkh<gap/>ika\</foreign> <emph type="italics"/>vocan­<lb/>tur, tormentorumque varia genera, quæ libris Athenæi, Bitonis, <lb/>Heronis, Pappi, Philonis, Apollodorique continentur, vt Latinos <lb/>omi&longs;erim. Mox & quæ<emph.end type="italics"/> <foreign lang="greek"><gap/>auma<gap/>ourgikh\</foreign> <emph type="italics"/>cuius exempla &longs;unt<emph.end type="italics"/> <foreign lang="greek">u)drau­<lb/>lika\</foreign> <emph type="italics"/>organa, quæque per &longs;e ventorum &longs;latu re&longs;onant. Et quod vas <lb/>dicæometron vocabant, & quod voces variarum auium exprimit, <lb/>& quod indidem merum, mox dilutum vinum, mox aquam cali­<lb/>dam, mox <expan abbr="frigidã">frigidam</expan>, copio&longs;am <expan abbr="tenuémq;">tenuémque</expan> vicißim funditat. Et<emph.end type="italics"/> <foreign lang="greek">si/fwnes</foreign><lb/><emph type="italics"/>extinguendis ineendÿs apti, & medicinabiles cacurbitulæ &longs;ine <lb/>ignis ministerio cutem prehendentes, & pilæ &longs;ponte &longs;altantes, & <lb/>lucerna &longs;uas ip&longs;a producens &longs;tuppas: & animal quod à &longs;tructore dum <lb/>&longs;ecatur in men&longs;a, bibit interim, crepitùque &longs;uo quodam, & voce &longs;i­<lb/>tientis repræ&longs;entat imaginem: milleque alia id genus, quæ breuita­<lb/>tis &longs;tudio præterimus. Hæc igitur (vt in capita quædam conferatur) <lb/>aut ponderibus vtitur & &longs;piritu, quorum præponderatio mouet, <lb/>æquilibrium &longs;i&longs;tit, (&longs;icuti etiam Timæus definit): aut neruis & <lb/>funiculis animatos qua&longs;i tractus, ac motus imitatur, ac circa illa <lb/>quæ &longs;ubnatant aquis, aut circa aquarum vertitur horologia, quo­<lb/>rum quidem generum primum docet in pneumaticis Heron, alte­<lb/>rum idem in automatis & Zygÿs, quartum rur&longs;us in Hydrÿs, ter­<lb/>tium verò in Ochoumenis Archimedes. E&longs;t in eadem Mechanicæ <lb/>&longs;erie quæ Centrobarica pars dicitur, ex qua reliquæ pendere dicun­<lb/>tur & Sphærotopœia, qualis illa Archimedea Claudiani laudata <lb/>ver&longs;ibus. Suppeditat eadem Architecturæ quoque &longs;can&longs;orias, tra­<lb/>ctiles, & &longs;pirituales machinas.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg10"></margin.target>In parapha­<lb/>&longs;i huius li­<lb/>bri.</s>
</p>
<p type="margin">
<s><margin.target id="marg11"></margin.target>In Pancpi­<lb/>&longs;temone.</s>
</p>
<p type="main">
<s>Natura vincit.] <emph type="italics"/>Senariolus e&longs;t cuiu&longs;dam antiqui poëtæ nomine<emph.end type="italics"/>
<pb pagenum="12"/><emph type="italics"/>tenus in hominum memoria &longs;uper&longs;titis: ni&longs;i &longs;it is, de quo Ari&longs;toteles <lb/>in &longs;uis Rhetoricis meminit, lepidumque eius dictum ad &longs;ocios, qui­<lb/>bu&longs;cum vna ducebatur in &longs;upplicium iu&longs;&longs;u Diony &longs;ij tyranni, reci­<lb/>tat. hos enim videns capite coopertos. Quid occultamini, inquit, <lb/>Socÿ, cum nullius i&longs;torum qui frequentes ad vrbis portam &longs;pectandi <lb/>gratia confluunt, cras vos &longs;it con&longs;pecturus? E&longs;t alius etiam Antipho <lb/>de quo meminit Cicero, vt &longs;omniorum interprete & &longs;criptore for­<lb/>ta&longs;&longs;e is e&longs;t quem fui&longs;&longs;e Athenien&longs;em mon&longs;tro&longs;orum &longs;omniorum in­<lb/>terpretem, & poëtam refert Suidas. A quo etiam forta&longs;&longs;e proma­<lb/>nauit Senariolus, qui hic citatur ab Ari&longs;totele, ad probandum <lb/>homines arte vincere ea, à quibus natura vincuntur. quod cumfa­<lb/>ciunt in ÿs, in quibus iudicio omnium longe à natura &longs;uperantur<emph.end type="italics"/><lb/><foreign lang="greek">w_<gap/>adozo/poioi,</foreign> <emph type="italics"/>cum Galeno vocari poterunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vt in his, quæ cum] <emph type="italics"/>Vt cum magnas marmorum moles, tra­<lb/>bes, columnas, colo&longs;&longs;os transferimus, & erigimus, naues &longs;ubduci­<lb/>mus in mare, quod fecit Archimedes conspiciente Hierone rege <lb/>Syracu&longs;arum, Helepoles amplas &longs;upra muros attrahimus, quod <lb/>fecit Callias Rhodien&longs;ibus conspicientibus, Equum Troianum in <lb/>vrbem adducimus (erat enim aliud nihil <expan abbr="quã">quam</expan> machina, vt ait poëta,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>In&longs;pectura domos venturáque de&longs;uper vrbi.</s>
</p>
<p type="main">
<s><emph type="italics"/>quales multæ apud Vegetium & Heronem mechanicum.) bom­<lb/>bardas ingentes ad locum destinatum conuertimus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Sunt vero hæc proble­<lb/>matis Phy&longs;icis, nec omni­<lb/>no <expan abbr="ead&etilde;">eadem</expan>, nec valdè di&longs;&longs;imi­<lb/>lia: &longs;ed con&longs;entanea theo­<lb/>tematis, tum mathemati­<lb/>cis, tum Phy&longs;icis. Etenim <lb/>quod ip&longs;um quomodo ad <lb/>mathematica pertineat: <lb/>ip&longs;um vero circa quod, ad <lb/>Phy&longs;ica, manife&longs;tum e&longs;t.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s><emph type="italics"/>Apud Euclidem problema à theoremate di&longs;tinguitur, quod <lb/>hoc iubeat aliquid contemplari: illud fieri: paßim tamen ab<emph.end type="italics"/>
<pb pagenum="13"/><emph type="italics"/>Ari&longs;totele, & alÿs pro vtroque, vt hic, indifferenter legitur. Qualia <lb/>autem problemata in Mechanicis habeat tractanda explicat Ari­<lb/>&longs;toteles, dicitque ea e&longs;&longs;e, quæ &longs;int con&longs;entanea Phy&longs;icis & Mathe­<lb/>maticis, vt quæ habeant &longs;ubiectum petitum è Phy&longs;icis. Machina­<lb/>rum enim materia lignum e&longs;t vel ferrum & eiu&longs;modi corpora Phy­<lb/>&longs;ica: attributum verò è figuris & terminis Mathematicis cuiu&longs;mo­<lb/>di &longs;unt in Geometria lineæ, diametri, centra, circuli, & eiu&longs;modi, <lb/>è quibus machinæ con&longs;tare & figuratæ e&longs;&longs;e, & vires &longs;uas accipere, <lb/>augere, diminuere, metiri o&longs;tenduntur. Vnde Mechanice pars e&longs;t <lb/>mathematicarum non aliter: quam Mu&longs;ica, Optica, A&longs;tronomia, <lb/>quas Ari&longs;toteles dixit e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">fusiko<gap/>e/<gap/>s,</foreign> <emph type="italics"/>ob &longs;ubiecti &longs;cilicet, quod <lb/>tractant naturam Phy&longs;icas: &longs;ed ob<emph.end type="italics"/> <foreign lang="greek">gra/mmikas</foreign> <emph type="italics"/>id e&longs;t lineares & <lb/>numerales demon&longs;trationes, quibus ip&longs;um explicant, Mathemati­<lb/>cas. Cæterum exeo quod dicit Ari&longs;toteles problemata Mechanica <lb/>e&longs;&longs;e Phy&longs;icis & Mathematicis con&longs;entanea, &longs;ub indicare videtur, <lb/>ne Mechanicus ante existimet machinas, quarum habuerit demon­<lb/>&longs;trationem in v&longs;um venire po&longs;&longs;e, &longs;uamque efficaciam &longs;ortiri: ni&longs;i <lb/>materia Phy&longs;ica existat, quæ rem patiatur fieri. Quamuis enim <lb/>Geometer demon&longs;tratione concludat, datam rectam lineam infinitè <lb/>diui&longs;ibilem e&longs;&longs;e, nulla materia lineata apud phy&longs;icos e&longs;t, quæ non <lb/>continuata diui&longs;ione tandem reducatur ad eam, quæ &longs;i amplius in­<lb/>telligatur diuidi, amittet formam lineæ Phy&longs;icæ & vi&longs;ibilis: &longs;ic <lb/>licet apud Mechanicos multa demon&longs;trentur de motu in infinitum <lb/>augendo, quale e&longs;t illud problema Archimedeum. Datum pondus <lb/>data potentia mouere. Ita tamen intelligenda &longs;unt, ne exi&longs;timemus <lb/>infinita hominis, <expan abbr="quacũque">quacunque</expan> arte iuuetur, pote&longs;tati &longs;ube&longs;&longs;e. Sunt enim <lb/>certi fines, vltra quos natura rerum ip&longs;um progredi non patitur. <lb/>Sunt præterea vitia materiæ quæ Geometra, aut Mechanicus de­<lb/>mon&longs;trans non con&longs;iderat: nec etiam ob&longs;tant quo minus quæ propo­<lb/>&longs;ita &longs;unt, vera &longs;int in intellectu: Mechanicus igitur operans, priu&longs;­<lb/>quam operi &longs;e accingat, nefru&longs;tretur, con&longs;iderare debet, an quod <lb/>proponitur effici poßit, habitaratione materiæ ex qua, aut per <expan abbr="quã">quam</expan>, <lb/>& circun&longs;tantiarum præ&longs;ertim temporis quod præ&longs;cribitur, & &longs;um­<lb/>ptuum quos facere oporteret. Hæc enim &longs;i abunde &longs;uppetant, nec ma­<lb/>teria omnino repugnet, nihil non fieri poterit.<emph.end type="italics"/></s>
</p>
<pb pagenum="14"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Dubitantur <expan abbr="aut&etilde;">autem</expan> in hoc <lb/>genere ea, quæ de vecte di­<lb/>cuntur. Ab&longs;urdum enim <lb/>videtur ab exigua vi ma­<lb/>gnum pondus moueri, & <lb/>quidem ad pondus addito <lb/>pondere. quod enim &longs;ine <lb/>vecte qui&longs;piam non po&longs;&longs;et <lb/>mouere, hoc ip&longs;um pon­<lb/>dus, in&longs;uper <expan abbr="adijci&etilde;s">adijciens</expan> vectis <lb/>ip&longs;ius <expan abbr="põdus">pondus</expan>, facile mouet.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Qvæ de vecte.] <emph type="italics"/>Vectis e&longs;t machina &longs;eu in&longs;trumentum in&longs;tar <lb/>pali aut baculi recti longioris, cuius alterum extremum in cu­<lb/>spidem <expan abbr="acutã">acutam</expan> & paulò latiorem de&longs;init, <expan abbr="vocaturq;">vocaturque</expan> lingua: alterum <lb/><expan abbr="extremũ">extremum</expan> caput e&longs;t, aut manubrium. vecti in v&longs;u aliquando &longs;upponi­<lb/>tur fulcimentum, quod Græci<emph.end type="italics"/> <foreign lang="greek"><gap/>(w_omo/xlion,</foreign> <emph type="italics"/>Vitruuius porrectam <lb/>preßionem appellat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Ab&longs;urdum enim videtur.] <emph type="italics"/>Ostenditur hic cur problema <lb/>de vecte in Mechanicis, dubitabile, &longs;iue dignum quæ&longs;itu &longs;it. Du­<lb/>bitabilia enim &longs;unt, quæ reuera fiunt: vt magnum pondus addito <lb/>pondere vectis ab exigua potentia, & vna hominis manu moue­<lb/>ri. Fieri tamen ratio repugnat. Nam in omni motu mouens præua­<lb/>lere debet mobili: hîc exigua potentia e&longs;t mouens: magnum pondus <lb/>e&longs;t mobile: illa quatenus exigua e&longs;t, & ante per &longs;e impotens, atque <lb/>infirma, e&longs;t inæquale minus: hoc quatenus magnum, e&longs;t inæquale <lb/>maius, & ei addito vectis onere maius adhuc effici videtur: non <lb/>igitur exigua potentia magno oneri & adaucto in motu præualer­<lb/>debet. Si non præualet, non mouet: mouet tamen: Relinquitur <lb/>ergo vt exi&longs;timemus aliquam cau&longs;am in hoc problemate motus eius <lb/>apparentis latentem &longs;ube&longs;&longs;e, dignam Philo&longs;ophi indagatione.<emph.end type="italics"/></s>
</p>
<pb pagenum="15"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s><expan abbr="Omniũ">Omnium</expan> verò talium cir­<lb/>culus continet cau&longs;æ prin­<lb/>cipium. quod etiam ratio­<lb/>ni valde <expan abbr="cõ&longs;entaneum">con&longs;entaneum</expan> e&longs;t. <lb/>Nec enim ab&longs;urdum e&longs;t, <lb/>ex admirabiliori quid ad­<lb/>mirabile contingere.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Omnium verò talium.] <emph type="italics"/>Cau&longs;a quæ latebat in problemate <lb/>de vecte aßignatur hic e&longs;&longs;e circulus: quæ ad alia multa Me­<lb/>chanica po&longs;tea transferetur. Probatur autem id ex forma circuli mi­<lb/>rabilißima. &longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ex admirabiliori admirabile aliquid fieri non e&longs;t alienum, cau&longs;æ <lb/>enim &longs;ibi &longs;imiles effectus edunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Circulus e&longs;t admirabilis, & admirabilior, quam vectis: quamque <lb/>ea quæ à vecte fiunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo à circulo prodire id quod e&longs;t admirabile in vecte, mechani­<lb/>ci&longs;que problematis non e&longs;t alienum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Maximè verò mirabile <lb/>e&longs;t contraria fibi inuicem <lb/>&longs;imul fieri: Atqui circulus <lb/>ex iis con&longs;titutus e&longs;t. Sta­<lb/>tim enim factus e&longs;t ex mo­<lb/>to, & immobili, quorum <lb/>natura &longs;ibi inuicem con­<lb/>traria e&longs;t. Illùc <expan abbr="itaq;">itaque</expan> in&longs;pi­<lb/>cientibus <expan abbr="cõtraria">contraria</expan> ab ip&longs;o <lb/>prouenire minus erit <expan abbr="mirũ">mirum</expan>.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Maxime verò.] <emph type="italics"/>Circuli admiranda natura declaratur è <lb/>quintuplici contrariorum, quæ in eo præter contrariorum<emph.end type="italics"/>
<pb pagenum="16"/><emph type="italics"/>legem &longs;imul reperiuntur, repugnantia. Ex his triplex deprehenditur <lb/>in circulo dum fit: duplex vero dum factus e&longs;t. Primum enim dum fit <lb/>habet hoc admirabile, quod fiat ab vna recta, cuius vnum extremo­<lb/>rum quie&longs;cit & fixum e&longs;t: alterum vnà cum tota linea mouetur: &longs;e­<lb/>cundum quod in mota linea puncta, cum infinita &longs;int, & omnia &longs;i­<lb/>mul moueantur, inæqualiter tamen moueantur: Tertium quod extre­<lb/>mum motum eodem tempore duobus motibus contrarÿs, vno natu­<lb/>rali ad peripheriam &longs;cilicet, altero violento ad centrum moueatur. In <lb/>facto verò hoc admirabile e&longs;t, quod eius terminus vna linea exi­<lb/>&longs;tens, obídque latitudinis expers, concauum tamen & conuexum, <lb/>quæ quodammodo contraria &longs;unt, admittat: præterea mobilitas, <lb/>quæ ine&longs;t, admirabilis e&longs;t, quia eodem tempore ad contrarias loci dif­<lb/>ferentias, vt &longs;ur&longs;um deor&longs;um: dextror&longs;um &longs;inistror&longs;um, fiat. Hæc <lb/>&longs;ingula &longs;uis locis delineabuntur & explicabuntur. Sed præter hæc, <lb/>quæ ab Ari&longs;totele de circulo dicuntur, valde notabilia &longs;unt & alia, <lb/>quæ in Geometria in eo ine&longs;&longs;e, partim ponuntur, partim demon&longs;trata <lb/>&longs;unt. Primum quod vna linea terminetur, eâque &longs;implici, &longs;imilari <lb/>vniformi, & carente principio, & fine, neque tamen infinita, vt <lb/>cuius, cum partes aliquot &longs;umptæ &longs;unt, quæ re&longs;tant, minus &longs;int, quam <lb/>ante quam &longs;umptæ e&longs;&longs;ent, quod repugnat infinito in magnitudine: &longs;ed <lb/>tota e&longs;t, & perfecta: vnde circulus figura e&longs;t planarum &longs;implicißi­<lb/>ma, regularißima, perfectißima: Deinde quod ea linea non &longs;it an­<lb/>gulus, ad angulum tamen proxime accedat, vt o&longs;tendimus in no&longs;tro <lb/>libello de angulo contactus, & ob id quodămodo vndequaque angu­<lb/>lata, cum nu&longs;quam &longs;it, dici poßit, & figura<emph.end type="italics"/> <foreign lang="greek">w_an/gwnos & o(lo/gwnos,</foreign><lb/><emph type="italics"/>tum prima figurarum & vltima: po&longs;tea, quod ex infinitis punctis <lb/>quæ in &longs;patio ab ea comprehen&longs;o &longs;unt, vnum e&longs;t tantum, à quo omnes <lb/>rectæ ad peripheriam ductæ, &longs;unt æquales: quod Diametro bifariam <lb/>&longs;ecetur: quod hinc &longs;emicirculus circa Diametrum manentem <lb/>voluens, quou&longs;que redierit ad eum locum vnde moueri cœpit, &longs;phæ­<lb/>ram constituat, corporum &longs;implicißimum, capacißimum, mobilißi­<lb/>mum, mouentißimum: quod circulus omnium figurarum eiu&longs;dem <lb/>perimetri &longs;it capacißima: quod vno puncto lineam rectam attin­<lb/>gat, &longs;icque o&longs;&longs;en&longs;ationibus & occur&longs;ationibus minimum pateat, <lb/>&longs;icque in&longs;i&longs;tens dimidia &longs;ui totius parte nutet, vnde propen&longs;ißimus <lb/>e&longs;t ad motum, & dimotus cum moueat annexa, aptißimus quoque<emph.end type="italics"/>
<pb pagenum="17"/><emph type="italics"/>erit ad mouendum: po&longs;tremò quod inter rectam circulum tangen­<lb/>tem, & circuli peripheriam altera recta &longs;ine &longs;ectione cadere non <lb/>poßit. quod 16. prop. lib. 3. elem. e&longs;t demon&longs;tratum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Imprimis enim] <emph type="italics"/>Prima repugnantia e&longs;t in circulo, quod fiat <lb/>è moto & quieto, quæ &longs;unt oppo&longs;ita ex genere priuantium, vnde rur­<lb/>&longs;us concluditur, minus e&longs;&longs;e mirum, id e&longs;t minus ab&longs;urdum à circulo <lb/>produci contraria. Circulum autem fieri ex moto & quieto patet his, <lb/>qui eius fabricam repetent è 3. po&longs;tulato element. Eucl. Ibi enim po­<lb/>&longs;tulatur, vt è dato centro & interuallo circulum de&longs;cribere conce­<lb/>datur. De&longs;cribitur autem cum data recta finita, manente eius vno <lb/>extremorum, circummoluitur, quou&longs;que redeat ad locum vnde mo­<lb/>ueri cœpit, id quod, vt &longs;ine errore fiat inuentus e&longs;t circinus à Talo <lb/>Dædali ex &longs;orore nepote, cuius forma & officium ab Ouidio accom­<lb/>modate huic loco, &longs;ic e&longs;t expre&longs;&longs;um,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Ex vno duo ferrea brachia nodo <lb/>Iunxit, vt æquali &longs;patio di&longs;tanti­<lb/>
<figure id="fig1"></figure><lb/>busip&longs;is</s>
</p>
<p type="main">
<s>Altera pars &longs;taret, pars altera du­<lb/>ceret orbem.</s>
</p>
<p type="main">
<s><emph type="italics"/>Sit igitur recta A B inter extrema due­<lb/>rum brachiorum circini A C B diua­<lb/>ricati per interuallum lineæ A B, <lb/>cuius extremum A maneat: alterum B <lb/>lineæ motu feratur per D quou&longs;que redeat <lb/>ad B: &longs;icque circulus B D B erit fa­<lb/>ctus. Idque beneficio puncti B cum tota <lb/>linea A B moti, atque puncti A quieti, vt hic vult Ari&longs;toteles.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Primum &longs;iquidem lineæ <lb/>ip&longs;um circulum <expan abbr="compre-hend&etilde;ti">compre­<lb/>hendenti</expan>, licet latitudinem <lb/>nullam habeat, contraria <lb/>quodammodo, cauum & <lb/>conuexum ine&longs;le <expan abbr="appar&etilde;t">apparent</expan>. <lb/>Hæc autem ita inter&longs;e di­<lb/>&longs;tant, vt <expan abbr="magnũ">magnum</expan> & paruum.
<pb pagenum="18"/><gap/><lb/>horum enim medium e&longs;t <lb/>æquale: illorum verò re­<lb/>ctum. Ideò inuicem cum <lb/>commutantur, priùs ne­<lb/>ce&longs;&longs;e e&longs;t æqualia fieri: li­<lb/>neam &longs;anè rectam, cum ex <lb/>conuexa fit caua: & rur&longs;us <lb/>ex ip&longs;a fit conuexa & ro­<lb/>tunda. Atque vnum hoc <lb/>e&longs;t ex ab&longs;urdis qu&ecedil; in&longs;unt <lb/>circulo.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Primum &longs;iquidem.] <emph type="italics"/>Vetu&longs;tatis iniuria multas veterum li­<lb/>bris, & huic &longs;ane irrep&longs;i&longs;&longs;e mendas, non e&longs;t res dubia, vt hoc loco<emph.end type="italics"/><lb/><foreign lang="greek">w_rw/ton</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">deu/teron.</foreign> <emph type="italics"/>Namque hîcnon prima, vtiam patuit: &longs;ed &longs;e­<lb/>cunda e&longs;t in circulo repugnantia. Eaque ex eo quod cum circuli peri­<lb/>pheria &longs;ir vna linea def. 15. lib. 1. elem. & idcirco latitudinis expers <lb/>def. 2. lib. eiu&longs;dem: habeat tamen in &longs;econtraria conuexum &longs;cilicet, <lb/>& concauum: illud quidem quà &longs;pectat foras: hoc vero quà intra. <lb/>vbinota Ari&longs;totelem dixi&longs;&longs;e hæe<emph.end type="italics"/> <foreign lang="greek">en)an<gap/>ia w_<gap/>s</foreign> <emph type="italics"/>contraria quodam­<lb/>modo. Nec enim vere contraria &longs;unt, quia vere contraria &longs;untea, <lb/>quæ &longs;ecundum &longs;eip&longs;a &longs;umpta, ex &longs;eip&longs;is extreme di&longs;tant, & vnde &longs;e <lb/>expellere nata &longs;int, habent: at hæc conuexum & concauum non &longs;ic <lb/>extreme di&longs;tant: &longs;ed ratione &longs;itus partium in diuer&longs;is locorum diffe­<lb/>rentÿs, quod &longs;cilicet aliæ alÿs &longs;int al-<emph.end type="italics"/><lb/>
<figure id="fig2"></figure><lb/><emph type="italics"/>tiores, vel depreßiores. Cum enim re­<lb/>ctum &longs;it id in lineis quod ex æquo iacet <lb/>inter &longs;ua extrema def. 2. lib. 1. & vt <lb/>linea A B, curuum erit quod non ex <lb/>æquo iacebit, &longs;ed altius aut depreßius: <lb/>idque &longs;i inter extrema vbique attollatur: <lb/>conuexum vt C E D: &longs;i vero vbique <lb/>deprimatur concauum, vt C F D quæ eadem e&longs;t linea ex &longs;e, &longs;ed <lb/>ex locis E E & F F partium mutata, Cum igitur ab eadem C D<emph.end type="italics"/>
<pb pagenum="19"/><emph type="italics"/>non &longs;e expellant non erunt verè contraria: qualia tamen apparent ex <lb/>di&longs;tantia & differentiis locorum &longs;ur&longs;um deor&longs;um.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Hæc autem ita.] <emph type="italics"/>Similitudine comprobatur conuexum & <lb/>concauum contraria e&longs;&longs;e. Quemadmodum magnum & paruum con­<lb/>traria &longs;unt, quia di&longs;tant, inter &longs;e per medium, quod e&longs;t æquale, & <lb/>cum commutantur in inuicem nece&longs;&longs;e e&longs;t prius æquale fieri: &longs;ic con­<lb/>uexum & concauum contraria erunt, quia di&longs;tant inter &longs;e per me­<lb/>dium, quod e&longs;t rectum, & cum commutantur in inuicem prius re­<lb/>ctum etiam fierinece&longs;&longs;um e&longs;t. &longs;unt igitur conuexum & concauum <lb/>contraria. Sed & hic a&longs;&longs;umemus per eandem definitionem contra­<lb/>riorum ante po&longs;itam, & ex &longs;ententia Ari&longs;totelis in categ. Quanti­<lb/>tatis, magnum & paruum apparenter duntaxat e&longs;&longs;e contraria. Ap­<lb/>parenter dico vt illa priora, quia habent aliquid de definitione con­<lb/>trariorum, quod &longs;ibi conueniat, &longs;cilicet di&longs;tare inter&longs;e in eodem ge­<lb/>nere, & habere medium: &longs;ed non vere tamen e&longs;&longs;e. Quia non habent <lb/>omnes prædictæ definitionis particulas &longs;ibi conuenientes. Hæc <lb/>enim cum &longs;int in Relatis, vnum idemque non ex&longs;e dicitur magnum <lb/>aut paruum: &longs;ed re&longs;pectu alicuius, vt canis re&longs;pectu elephantis paruus <lb/>e&longs;t, at idem re&longs;pectu mu&longs;cæ magnus e&longs;t. Cœterum hic notandum e&longs;t <lb/>re&longs;pectum i&longs;tum licet fieri poßit ad quodlibet obuium, cum tamen <lb/>hæc vocabula, magnum, paruum, &longs;impliciter dicuntur, fieri ad &longs;ym­<lb/>metrum &longs;ui cuiu&longs;que generis. Symmetrum appello, quod iu&longs;tam ma­<lb/>gnitudinem in &longs;uo genere adeptum e&longs;t. Et hoc e&longs;t quod hic dicitur <lb/>æquale, medium &longs;cilicet inter <expan abbr="magnũ">magnum</expan> tanquam excedens, & paruum <lb/>tanquam deficiens, neutrobique igitur iu&longs;tum. Vt e&longs;to, quod aiunt <lb/>multi, iu&longs;ta hominis magnitudo &longs;ex pedum. Qui igitur inter homi­<lb/>nes &longs;eptempedalis e&longs;t, magnus: qui quintumpedalis, paruus &longs;implici­<lb/>ter dicetur. Hinc intellige, vt id obiter annotem, quod apud Ari&longs;to­<lb/>telem memini me legi&longs;&longs;e, nullam paruam mulierem pulchram e&longs;&longs;e, <lb/>quia, quod prima pars e&longs;t pulchritudinis non habet, &longs;ymmetrum &longs;ui <lb/>generis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Atque vnum hoc e&longs;t.] <foreign lang="greek">to\ a)/topcn.</foreign> <emph type="italics"/>Hic vt & alibi &longs;æpius <lb/>pro<emph.end type="italics"/> <foreign lang="greek"><gap/>auma/ sion</foreign> <emph type="italics"/>&longs;umitur, id e&longs;t igitur e&longs;&longs;e conuexum & concauum <lb/>in linea vnum e&longs;t ex admirabilibus circuli.<emph.end type="italics"/></s>
</p>
<pb pagenum="20"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Secundum e&longs;t, quod con­<lb/>trariis motionibus &longs;imul <lb/>moueatur. Simul enim an­<lb/>tror&longs;um & retror&longs;um mo­<lb/>uetur: atque linea circu­<lb/>lum <expan abbr="de&longs;crib&etilde;s">de&longs;cribens</expan> &longs;ic &longs;e haber, <lb/>vt ex quo loco extremum <lb/>illius incipiat, rur&longs;us ad <lb/>eundem redeat. Id ip&longs;um <lb/>enim quod in ip&longs;a conti­<lb/>nenter mota e&longs;t vltimum, <lb/>rur&longs;us primum euadit. Ita­<lb/>que manife&longs;tum, quod in­<lb/>de <expan abbr="mutatũ">mutatum</expan> e&longs;t. Propterea, <lb/>vt e&longs;t prius dictum, non e&longs;t <lb/>ab&longs;urdum ip&longs;um admira­<lb/>bilium omnium e&longs;&longs;e prin­<lb/>cipium. Igitur & qu&ecedil; circa <lb/>libram eueniunt ad circu­<lb/>lum referuntur, & qu&ecedil; cir­<lb/>ca vectem ad libram, & <lb/>forta&longs;&longs;is alia omnia, quæ <lb/>circa motiones mechani­<lb/>cas, ad vectem.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Secundum.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="greek">d<gap/>/u<gap/>eron</foreign> <emph type="italics"/>legamus &longs;i placet<emph.end type="italics"/> <foreign lang="greek">trh/ton.</foreign> <emph type="italics"/>Hic enim <lb/>tertia e&longs;t repugnantia in circulo ex contrarÿs motionibus, quas <lb/>&longs;imul habet, antè &longs;cilicet cum pars eius vna mouetur: oppo&longs;ita in <lb/>ip&longs;omet tempore ponè mouetur. Hoc autem e&longs;t contrarias motiones <lb/>&longs;imul habere. Contrariæ enim &longs;unt motiones apud Ari&longs;totelem in <lb/>categoria vbi & li. 5. de Phy&longs;ico auditu ex diametralibus locorum, <lb/>ad quæ fiunt, di&longs;tantÿs dextror&longs;um, &longs;ini&longs;tror&longs;um: &longs;ur&longs;um, deor&longs;um: <lb/>& antror&longs;um, retror&longs;um.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Atque linea circulum.] <emph type="italics"/>Cur circulus antè & ponè mouea-<emph.end type="italics"/>
<pb pagenum="21"/><emph type="italics"/>tur, ratio adducitur &longs;umpta ab efficiente circuli cau&longs;a. Sic &longs;yllo­<lb/>gi&longs;mus in&longs;titui pote&longs;t. Vt fit circulus ita mouetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Fit circulus à linea continenter mota circa fixum extremor<gap/>m <lb/>vnum, quou&longs;que redeat ad eum locum vnde moueri cœpit, quod <lb/>fieri non pote&longs;t ni&longs;i per loca quæ &longs;unt circa extremum fixum oppo&longs;i­<lb/>ta deducatur, & quod e&longs;t vltimum, rur&longs;us fiat primum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo circulus mouetur per loca è diametro oppo&longs;ita circa extre­<lb/>mum lineæ à qua fit fixum. Quia igitur in his &longs;unt antè & ponè, <lb/>mouebitur antè & ponè: quia in&longs;uper &longs;unt &longs;ur&longs;um & deor&longs;um, <lb/>mouebitur etiam &longs;imul &longs;ur&longs;um & deor&longs;um.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Centrum enim in plano circundatur quatuor loci differentÿs, <lb/>propter duas quæ in ip&longs;o ad rectos &longs;e &longs;ecant dimen&longs;iones, vt in circu­<lb/>lo B C D E, e&longs;to linea fabricans ip&longs;um A B, ibique e&longs;to ante <lb/>B. igitur cum erit in D, erit ponè: & cum in C, &longs;ur&longs;um: & <lb/>in E, deor&longs;um, & perueniens ad A B, eidem loco re&longs;tituetur, <lb/>à quo cœperat moueri, quod e&longs;t vltimum<emph.end type="italics"/><lb/>
<figure id="fig3"></figure><lb/><emph type="italics"/>fieri primum. Vnde cum circulu<gap/>oue­<lb/>tur, pote&longs;t dici ire, & reuerti &longs;imul: &longs;ic <lb/>cum &longs;phæricum corpus mouetur, in fine <lb/>&longs;emper, & principio motus &longs;ui, etiam tum <lb/>ire, tum reuerti veri&longs;imiliter dicetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cæterum notandum quod motiones dictæ <lb/>e&longs;&longs;e in circulo, in&longs;unt quidem: &longs;ed non &longs;i­<lb/>mul &longs;ecundum eandem partem. Nam cum B, mouetur &longs;ur&longs;um ver­<lb/>&longs;us C, idem B, eodem tempore non fertur deor&longs;um ver&longs;us E, &longs;ed <lb/>tunc quidem D, altera pars in circulo oppo&longs;ita ip&longs;i B, fertur ver­<lb/>&longs;us E: vt autem verè e&longs;&longs;ent motiones contrariæ deberent fieri &longs;e­<lb/>cundum ea&longs;dem partes. E&longs;t hæc igitur vt aliæ in circulo non vera <lb/>&longs;ed apparens repugnantia. ex cuius tamen natura magnorum effe­<lb/>ctuum po&longs;tea cau&longs;æ repetuntur, cum diametri B D, vt inflexilis <lb/>circa A, centrum fixum motæ, &longs;i B, deprimatur, nece&longs;&longs;e e&longs;t a<gap/>e­<lb/>rum extremum D, attolli: & contra.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Propterea vt e&longs;t prius.] <emph type="italics"/>Conclu&longs;io generalis e&longs;t, huc, vt exi­<lb/>&longs;timo, è fine primi huius capitis, vbi melius collocaretur, tràspo&longs;ita, <lb/>quod amplius declarant ea, quæ &longs;ubÿciuntur de vecte & libra, ad <lb/>quæ cum referat omnia Mechanica, & ip&longs;a vectis & libra referan-<emph.end type="italics"/>
<pb pagenum="22"/><emph type="italics"/>tur ad circulum, &longs;equenti etiam capite, quod erat proximum, libræ <lb/>motiones explicat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Præterea etiam, quod, <lb/>cum vna &longs;it ea linea, quæ <lb/>ex centro, nullum eorum, <lb/>quæ in ea &longs;unt, <expan abbr="pũctorum">punctorum</expan>, <lb/>æquè celeriter fertur: fed <lb/>hoc, quod longius e&longs;t ab <lb/>extremo eius immobili, <lb/>&longs;emper celerius: miranda <lb/>multa circa motiones cir­<lb/>culi contingunt, vt in <expan abbr="&longs;e-qu&etilde;tibus">&longs;e­<lb/>quentibus</expan> problematis fiet <lb/>manifc&longs;tum.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Præterea ctiam.] <emph type="italics"/>Quarta repugnantia e&longs;t in circulo ex inæ­<lb/>qualitate motuum in eiu&longs;dem lineæ circulum de&longs;cribentis diuer­<lb/>&longs;is punctis. Inæqualiter enim moueri dicuntur, & quæ eodem tem­<lb/>pore diuer&longs;a permeant &longs;patia, & quæin æqualibus temporibus idem: <lb/>atque hoc celerius, quod eodem tempore maius &longs;patium permeat, vel <lb/>breuiori tempore idem: Tardius contra. Punctorum autem, quæ in­<lb/>&longs;unt in vna eademque linea circulum de&longs;cribente, illud quod remo­<lb/>tius e&longs;t à centro, maius &longs;patium conficit: quam quod propinquius, li­<lb/>cet vtraque eodem tempore &longs;uum perficiant. Linea enim circulum <lb/>de&longs;cribens, quo tempore punctis centro propinquis redÿt ad locum, <lb/>vnde ÿ&longs;dem moueri cœperat, eodem remotis redit. Spatium autem <lb/>illud e&longs;t peripheria, quæ ab vnoquoque eorum quæ &longs;unt in &longs;emidia­<lb/>metro punctorum, de&longs;cribitur, &longs;i quodlibet <expan abbr="pũctorum">punctorum</expan> in motu lineæ <lb/>intelligatur &longs;ui, vt puncti, ve&longs;tigium relinquere, vt in eo quod circu­<lb/>lum vndiquaque comprehendit. Peripheriam autem remotioris pun­<lb/>cti à centro, id e&longs;t &longs;emidiametri maioris e&longs;&longs;e maiorem peripheria pun­<lb/>cti centro propinquioris, id e&longs;t &longs;emidiametri minoris, &longs;ic demon&longs;tra­<lb/>bimus.<emph.end type="italics"/></s>
</p>
<pb pagenum="23"/>
<p type="main">
<s><emph type="italics"/>E&longs;to A B C, peripheria &longs;emidiametri maioris A E: item <lb/>D F G, peripheria &longs;emidiametri D H minoris. Dico periphe­<lb/>riam A B C maiorem peripheria D F G. Producatur enim A E <lb/>recta vt &longs;it A C <lb/>diameter po&longs;tul.<emph.end type="italics"/><lb/>
<figure id="fig4"></figure><lb/>2. <emph type="italics"/><expan abbr="it&etilde;">item</expan> D H vt &longs;it <lb/>& D G diame­<lb/>ter. Quia igi­<lb/>tur vt diameter <lb/>A C ad <expan abbr="&longs;uã">&longs;uam</expan> <expan abbr="pe-ripheriã">pe­<lb/>ripheriam</expan> A B C: <lb/>ita & D G diameter ad &longs;uam peripheriam D F G, per ea quæ <lb/>demon&longs;trata &longs;unt ab Archimede prop. 3. lib. de dimen&longs;. circuli, & <lb/>vicißim proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. 16. lib. 5. & <lb/>quia A E & D H partes &longs;unt pariter multiplicium A C, D G <lb/>vtpote &longs;emidiametri &longs;uarum diametrorum, erit A E ad D H vt <lb/>A C ad D G prop. 15. lib. 5. ergo & peripheria A B C ad peri­<lb/>pheriam D F G: vt A E ad D H prop. 11. lib. eiu&longs;dem. E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. Erit igitur peri­<lb/>pheria A B C maior: quam peripheria D F G. Et &longs;ic peripheria <lb/>remotioris puncti à centro maior e&longs;t peripheria puncti centro pro­<lb/>pinquioris, quod fuit demon&longs;trandum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Quod autem circulus <lb/><expan abbr="cõtrariis">contrariis</expan> cieatur motibus, <lb/>& alterum extremorum <lb/>diametri in quo e&longs;t A, dum <lb/>mouetur antror&longs;um, alte­<lb/>rum in quo e&longs;t B mouea­<lb/>tur retror&longs;um, ideo non­<lb/>nulli <expan abbr="faciũt">faciunt</expan>, vt ab vna mo­<lb/>tione multi circuli &longs;imul <lb/>in contraria moueantur: <lb/>vt quos in deorum templis <lb/>&longs;tatuunt, efficientes circu-
<pb pagenum="24"/><gap/><lb/>los æreos & ferreos. Si <lb/>enim circulum in quo e&longs;t <lb/>A B, alter circulus in quo <lb/>e&longs;t G D attigerit, diamc­<lb/>tro circuli A B antror­<lb/>&longs;um mota, diameter circu­<lb/>li G D retror&longs;um moue­<lb/>bitur, circuli in quo e&longs;t A <lb/>diametro circa idem mo­<lb/>ta. Circulus igitur in quo <lb/>e&longs;t G D, contrà, quam is, <lb/>in quo e&longs;t A B moucbi­<lb/>tur: idemque &longs;equentem <lb/>in quo e&longs;t E Z propter <lb/>eandem cau&longs;am contra &longs;e <lb/>mouebit, & eodem modo <lb/>&longs;i plures fuerint vno com­<lb/>moto itidem <expan abbr="faci&etilde;t">facient</expan>. Hinc <lb/>Architecti Fabri, cum <expan abbr="hãc">hanc</expan> <lb/>in circulo naturam depre­<lb/>hendi&longs;&longs;ent, <expan abbr="organũ">organum</expan> fabri­<lb/>cantur principium occu­<lb/>lentes, vt &longs;it de machina, <lb/>&longs;olum hoc, quod admira­<lb/>bile, apertum: quod autem <lb/>cau&longs;a, occultum.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Qvod autem circulus.] <emph type="italics"/>Tertia repugnantia in vnius cir­<lb/>culi contrarÿs motionibus ante po&longs;ita amplius declaratur, ab <lb/>exemplo plurium: &longs;ed contiguorum ab vnica vi primaria &longs;ecundum <lb/>motus contrarios motorum. Vt &longs;unto tres circuli contingentes quod­<lb/>que ferè fit denticulis pectinis in&longs;tar &longs;e&longs;e &longs;ubingredientibus in peri­<lb/>phcria præditi, quorum primus A B, moueatur antror&longs;um, &longs;eu&longs;e­<lb/>cundum &longs;uperiorem peripheriam, vt A feratur ver&longs;us C: alter<emph.end type="italics"/>
<pb pagenum="25"/><emph type="italics"/>G D ad illius motum nece&longs;&longs;ario mouebitur propter denticulos, &longs;ed <lb/><expan abbr="retrorsũ">retrorsum</expan><emph.end type="italics"/><lb/>
<figure id="fig5"></figure><lb/><emph type="italics"/>&longs;eu <expan abbr="&longs;ecũ-dum">&longs;ecun­<lb/>dum</expan> <expan abbr="in-ferior&etilde;">in­<lb/>feriorem</expan> <lb/><expan abbr="periphe-riã">periphe­<lb/>riam</expan>, vt <lb/>G ad B: <lb/>tum ter­<lb/>tius E Z ad &longs;ecundi motum mouebitur etiam, &longs;ed antror&longs;um, vt E <lb/>ad F, & &longs;int deinceps alternatim infiniti denticulis &longs;e&longs;e &longs;ubinui­<lb/>cem ingredientibus, &longs;emper mouebuntur. Vnde tunc à Fabro dato <lb/>principio motionis, vertebra vertebram continenter mouet, vltimá­<lb/>que ab illis &longs;imulacrorum excita fit præteruectio, non aliter quans in <lb/>animalium genere à &longs;en&longs;u, vel intellectione motionum exorto prin­<lb/>cipio intrin&longs;ecis commotis cau&longs;is, &longs;eque inuicem mouentibus, vt alij <lb/>po&longs;tmodum extrin&longs;ecus, cum partium ip&longs;arum, tum etiam vniuer&longs;i <lb/>corporis vi&longs;untur motus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Hinc architecti.] <emph type="italics"/>Sicuti ante ex vnius circuli contrarÿs mo­<lb/>tibus libram, vectem, mechanicáque in&longs;trumenta magnam habere <lb/>vim ad onera mouendum &longs;ubindicauit: &longs;ic nunc ex circulorum con­<lb/>tiguorum & variè multiplicatorum contrarÿs motionibus machi­<lb/>nas quamplurimas effici <expan abbr="o&longs;t&etilde;dit">o&longs;tendit</expan>, quibus credibile e&longs;t veteres paganos, <lb/>qui veris miraculis <expan abbr="de&longs;tituebãtur">de&longs;tituebantur</expan>, in templis &longs;uorum <expan abbr="deorũ">deorum</expan> collocatis, <lb/>& etiam per vrbium vicos, & plateas ge&longs;tatis, <expan abbr="authoritat&etilde;">authoritatem</expan> dÿs &longs;uis <lb/><expan abbr="cõflaui&longs;&longs;e">conflaui&longs;&longs;e</expan>, & ignaro vulgo mirificis modis ita impo&longs;ui&longs;&longs;e. Huius rci <lb/>fecit mentionem Galenus, qui miracula inquit moliuntur principio <lb/>motionis exhibito di&longs;cedunt, Machinæ vero ip&longs;æ aliquanti&longs;per, non <lb/>multo tamen tempore per &longs;e ip&longs;æ arti&longs;iciosè impelluntur. cap. 6. lib. de <lb/>fœt. format. Herodotus hi&longs;toria &longs;ecunda videtur ex his aliqua<emph.end type="italics"/> <foreign lang="greek">neu­<lb/>ro/dpasa</foreign> <emph type="italics"/>appella&longs;&longs;e: qua&longs;i diceremus, per funiculos tanquam neruos <lb/>circa rotulas inuolutos, varÿs motibus agitata. Eiu&longs;modij erant adeò <lb/>celebratæ Dædali &longs;tatuæ, quæ inquit Plato ni&longs;i ligatæ aufugiebant,<emph.end type="italics"/><lb/>
<arrow.to.target n="marg12"></arrow.to.target><lb/><emph type="italics"/>& vago quodam &longs;inuo&longs;oque impetu ferebantur in fugam: ligaræ <lb/>vero permanebant, vnde illæ non magno pretio emebantur in&longs;tar <lb/>&longs;erui fugitiui: hæ contra magno. Erant enim præclara opera.<emph.end type="italics"/>
<pb pagenum="26"/><emph type="italics"/>Hodie etiam no&longs;tri artifices ex hac plurium rotularum mira in­<lb/>ter &longs;e coniunctione, aliquoque ex &longs;e mobili vt animali, vento, fu­<lb/>mo, aqua, lamina chalybea primum motum &longs;uppeditante commota<emph.end type="italics"/><lb/><foreign lang="greek">ao)to/ma<gap/>a</foreign> <emph type="italics"/>faciunt non &longs;olum admirabilia: &longs;ed etiam maximè vti­<lb/>lia, qualia &longs;unt horologia veterum clep&longs;ydras, & gnomones &longs;ine luce <lb/>& &longs;erenitate inutiles, commoditate & perpetuitate longè &longs;uperan­<lb/>tia, quibus hodie dies ciuilis in 24. partes, quas horas vocant, di­<lb/>&longs;tribuitur. Ex quibus alia &longs;unt &longs;tataria, & in &longs;ummis templorum no­<lb/>&longs;trorum partibus collocata: alia in <expan abbr="hominũ">hominum</expan> collis, Zoní&longs;ue <expan abbr="app&etilde;&longs;a">appen&longs;a</expan> præ <lb/>exiguitate ponderis nullo modo mole&longs;ta, <expan abbr="circunferũtur">circunferuntur</expan>. Sed ne&longs;cio an <lb/>fama, an fide nobilius &longs;it illud, quod Aŕgentorati in loco ciuitatis <lb/>eminentißimo po&longs;itum e&longs;t, in quo vniuer&longs;i mundi cæle&longs;tis com­<lb/>pago, orbibus &longs;uis in &longs;uas partes di&longs;tincta vi&longs;itur, In hoc enim <lb/>octaui orbis tardißimum motum, Zodiaci duodccim &longs;igna, Solis per <lb/>puncta ecliptica tran&longs;itum, Lunæ varias apparitiones, &longs;ingulorum <lb/>planetarum progre&longs;&longs;us, regre&longs;&longs;us, &longs;tationes, latitudines, altitudines, <lb/>innumeraque alia præter temporum momenta, & horastum æqua­<lb/>les, tum inæquales intueri licet. Ita tamen, vt quod hic dicitur, quic­<lb/>quid e&longs;t rotarum, ponderum, molarum, denticulorum, nolarum, vir­<lb/>garum, <expan abbr="funiũ">funium</expan>, atque aliorum <expan abbr="in&longs;trumentorũ">in&longs;trumentorum</expan> magna ex parte intus <lb/>delite&longs;cat, & occultetur, quæ verò in tanta machina tot admirabilia <lb/>&longs;unt, <expan abbr="appareãt">appareant</expan>. Hæc, & quæ imaguncularum ince&longs;&longs;um, &longs;altum, cho­<lb/>reas repræ&longs;entant, faciunt, vt quæ de Architæ columba volatili, & <lb/>de Archimedis &longs;phæra ver&longs;atili memoriæ reliquit antiquitas, pre <lb/>fal&longs;is minime habeamus.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg12"></margin.target>In Menone</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>2. De libra propter quid <lb/>maior linea in circulo <lb/>celerius fertur, minore. <lb/>Ex quo fit vt libræ ma­<lb/>iores minoribus &longs;int <lb/>exactiores.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s><expan abbr="Primũ">Primum</expan> igitur qu&ecedil; circa <expan abbr="li-brã">li­<lb/>bram</expan> <expan abbr="cõtingunt">contingunt</expan>, <expan abbr="difficultat&etilde;">difficultatem</expan> <lb/><expan abbr="adferũt">adferunt</expan>. Ob quam cau&longs;am
<pb pagenum="27"/><gap/><lb/>libræ maiores minoribus <lb/>&longs;int exactiores. Huius vero <lb/><expan abbr="principiũ">principium</expan> e&longs;t quare in cir­<lb/>culo <expan abbr="di&longs;tãtior">di&longs;tantior</expan> linea à cen­<lb/>tro, ei propinquiore <expan abbr="ead&etilde;">eadem</expan> <lb/>vi mota celerius fertur. <lb/>Celerius autem dicitur bi­<lb/>fariam, &longs;iue enim in mino­<lb/>ri tempore &ecedil;quale &longs;patium <lb/>tran&longs;ierit, celerius e&longs;le di­<lb/>cimus: &longs;iue in <expan abbr="t&etilde;pore">tempore</expan> &ecedil;qua­<lb/>li, maius. Maior autem li­<lb/>nea in æquali <expan abbr="t&etilde;pore">tempore</expan> ma­<lb/>iorem circulum de&longs;cribit. <lb/>Qui enim extra e&longs;t, maior <lb/>e&longs;t eo, qui intus.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>De libra propter.] <emph type="italics"/>In hoc capite Ari&longs;toteles vult o&longs;tendere <lb/>cur libræ longiorum brachiorum &longs;int exactiores: quam libræ <lb/>breuiorum. Et huius problematis cau&longs;am refert ad circulum, circu­<lb/>lique eam proprietatem, qua radÿ longiores celerius, id e&longs;t eodem <lb/>tempore maius &longs;patium conficiunt, quam breuiores. Quod quia futu­<lb/>rum e&longs;t fundamentum multorum aliorum problematum po&longs;tea ex­<lb/>plicandorum, diligenter imprimis demon&longs;trat. Et primum quod re­<lb/>cta de&longs;cribens circulum (vno nomine relicta periphra&longs;i radium hîc <lb/>appellabimus) duabus lationibus feratur, ii&longs;que in nulla ratione & <lb/>nullo tempore. Et ex his alteram e&longs;&longs;e &longs;ecundum naturam, alteram <lb/>præter naturam. Po&longs;tremò quod latio &longs;ecundum naturam in maiore <lb/>circulo maior &longs;it: quam in minore. Latio autem præter naturam in <lb/>minore circulo maior &longs;it: quam in maiore.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Primum igitur.] <emph type="italics"/>Proponitur problema de librarum inæqua­<lb/>lium exactiore iudicio, quod pendet à minorum ponderum deprehen­<lb/>&longs;ione, vt ea &longs;it exactior per quam minora pondera expendi po&longs;&longs;unt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli<emph.end type="italics"/>
<pb pagenum="28"/><emph type="italics"/>radios longiores, qui celerius feruntur minoribus, id e&longs;t qui æquali <lb/>tempore maius &longs;patium, & proinde &longs;en &longs;ibilius tran&longs;eunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i­<lb/>miles ÿs quos cap. 2. lib. 6. de Phy&longs;. auditu attulit, vt vtro longioris <lb/>radÿ celeritas accipi debeat, intelligatur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Qui enim extra.] <emph type="italics"/>E duobus circulis concentricis, qui extra e&longs;t, <lb/>e&longs;t quoddam <expan abbr="totũ">totum</expan>, & internus e&longs;t externi vna pars. Cum <expan abbr="itaq;">itaque</expan> totum <lb/>maius &longs;it &longs;ua parte ex 9. axiom. lib. 1. ele. externus circulus interno <lb/>concentrico erit maior. Præterea <expan abbr="cũ">cum</expan> circuli æquales &longs;int, <expan abbr="quorũ">quorum</expan> &longs;emi­<lb/>diametri &longs;int æquales def. 1. lib. 3. ele. Illi quorum &longs;emidiametri &longs;unt <lb/>inæquales, erunt & inæquales, & ille maior, euius &longs;emidiameter <lb/>maior. Quæ licet vera &longs;int non tamen &longs;tatim &longs;equitur figuræ planæ <lb/>cuius area maior e&longs;t, e&longs;&longs;e & perimetrum maiorem vt ex 36. 37. <lb/>prop. lib. 1. elem. demon&longs;trari facile pote&longs;t: neque &longs;i rur&longs;us perimeter <lb/>contineat perimetrum, vt continens contento &longs;it maior, vt patere <lb/>pote&longs;t ex eo, quod e&longs;t à Proclo adductum ad prop. 21. lib. 1. elem. De <lb/>duabus rectis intra triangulum, rectangulum vel amblygonium <lb/>comprehen&longs;is, quæ maiores con&longs;titui po&longs;&longs;unt ÿs à quibus ambiuntur. <lb/>Ob hæc igitur, cum hic locus non tam debeat intelligi de circulis, <lb/>quam circulorum peripherijs, meritò ante, cum huius proprietatis <lb/>mentio fieret, capite præcedenti peripheriam maioris circuli periphe­<lb/>ria minoris maiorem e&longs;&longs;e demon&longs;trauimus, &longs;ed etiam huius magni­<lb/>tudinis maioris cau&longs;a, hic ab Ari&longs;totele &longs;ubiungitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Horum vero cau&longs;a e&longs;t, <lb/>quod recta de&longs;cribens <expan abbr="cir-culũ">cir­<lb/>culum</expan> <expan abbr="&longs;ecundũ">&longs;ecundum</expan> duas latio­<lb/>nes fertur. <expan abbr="Cũ">Cum</expan> igitur in ali­<lb/>qua ratione du&ecedil; <expan abbr="sũt">sunt</expan> illæ la­<lb/>tiones, nece&longs;&longs;e e&longs;t id, quod <lb/>fertur <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan> ferri, <lb/>quæ fit diameter figuræ, <lb/><expan abbr="quã">quam</expan> rectæ in ea ratione <expan abbr="cõ-&longs;titutæ">con­<lb/>&longs;titutæ</expan>, <expan abbr="cõprehendunt">comprehendunt</expan>. Sit <lb/>enim ratio <expan abbr="&longs;ecundũ">&longs;ecundum</expan> quam <lb/>mobile fertur ea: quam ha-
<pb pagenum="29"/><gap/><lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g,</foreign> & quidem <lb/><foreign lang="greek">a</foreign> feratur ad <foreign lang="greek">b,</foreign> & <foreign lang="greek">a b_</foreign><lb/>etiam feratur ad <foreign lang="greek">h g</foreign>: la­<lb/>tum vero &longs;it <foreign lang="greek">a</foreign> ad <foreign lang="greek">d,</foreign> & <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">e.</foreign> Igitur cum latio­<lb/>nis ratio erat ea quam ha­<lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g</foreign>: nece&longs;&longs;e <lb/>e&longs;t & ip&longs;am <foreign lang="greek">a d</foreign> ad <foreign lang="greek">a e</foreign> ean­<lb/>dem habere rationcm. Si­<lb/>mile e&longs;t enim ratione par­<lb/>uum quadrilaterum maio­<lb/>ri. Itaque & eadem diame­<lb/>ter vtriu&longs;que, & ip&longs;um <foreign lang="greek">a</foreign><lb/>erat vbi <foreign lang="greek">z.</foreign> Eodem modo <lb/>demon&longs;trabitur <expan abbr="vbicũque">vbicunque</expan> <lb/>latio deprehen&longs;a fuerit. <expan abbr="S&etilde;-per">Sen­<lb/>per</expan> enim &longs;upra diametrum <lb/>erit. Manife&longs;tum igitur <lb/>quod latum <expan abbr="&longs;ecũdum">&longs;ecundum</expan> dia­<lb/>metrum duabus lationi­<lb/>bus nece&longs;&longs;e habet in ratio­<lb/>ne laterum ferri.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Horum vero cau&longs;a.] <emph type="italics"/>Inæqualium <expan abbr="circulorũ">circulorum</expan> ab inæqualibus <lb/>radiis <expan abbr="de&longs;criptorũ">de&longs;criptorum</expan>, & maioris quidem à maiori multo ab&longs;tru­<lb/>&longs;ior aßignatur cau&longs;a ex radij de&longs;cribentis circulum duabus lationi­<lb/>bus, quæ inter &longs;e <expan abbr="nullã">nullam</expan> <expan abbr="ration&etilde;">rationem</expan> &longs;eruant. Atque hinc elicitur quinta in <lb/>circulo repugnantia, ex qua admiratio eius maior: quam ante e&longs;&longs;e <lb/>concluditur. E lationibus enim illis vna e&longs;t &longs;ecundum naturam, <lb/>altera præter naturam. Et vtri&longs;que vnum idemque ferri in nullo <lb/>tempore, id e&longs;t in in&longs;tanti indiui&longs;ibili, quomodo non e&longs;&longs;et valde ad­<lb/>mirabile? Circuli igitur radius, qui his duabus ita fertur in de&longs;cri­<lb/>ptione circuli, & circulus, qui à radio tali efficitur, erit admirabilis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cum igitur in.] <emph type="italics"/>Aggreditur demon&longs;trare radÿ duas lationes <lb/>nullam habere rationem inter &longs;e. Syllog. &longs;ic e&longs;t. Omne duabus latio­<lb/>nibus rationem aliquam inter &longs;e &longs;eruantibus latum, fertur &longs;ecundum<emph.end type="italics"/>
<pb pagenum="30"/><emph type="italics"/>rectam. Radius de&longs;cribens circulum duabus &longs;uis lationibus, non <lb/>Jertur &longs;ecundum rectam. Radij igitur iationes in nulla &longs;unt ra­<lb/>tione. Propo&longs;itio confirmatur cum| &longs;equenti diagrammate. <lb/>E&longs;to rectangulum<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>com-<emph.end type="italics"/><lb/>
<figure id="fig6"></figure><lb/><emph type="italics"/>prehen&longs;um &longs;ub rectis<emph.end type="italics"/> <foreign lang="greek">a b, a g,</foreign><lb/><emph type="italics"/>quæ &longs;int inter &longs;e in ratione, quam <lb/>duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>habent. <lb/>Et intelligatur a latum ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">b</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>& ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">g</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">e</foreign>: <emph type="italics"/>&longs;icque cum <lb/>lationum ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ratio &longs;it vt<emph.end type="italics"/><lb/><foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g,</foreign> <emph type="italics"/>ergo erit &<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a e</foreign>: <emph type="italics"/>vt<emph.end type="italics"/> <foreign lang="greek">a <gap/></foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a y,</foreign> <emph type="italics"/>& rectrangulum minus<emph.end type="italics"/> <foreign lang="greek">a d z e</foreign> <emph type="italics"/>com­<lb/>munem angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>cum maiori<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>habens & &longs;imile erit <lb/>def. 1. lib. 6. & proinde circa eandem dimentientem conuer&longs;. prop.<emph.end type="italics"/><lb/>24. <emph type="italics"/>lib. 6. Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="greek">z,</foreign> <emph type="italics"/>vt vbi­<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="greek">a h.</foreign> <emph type="italics"/>&longs;iquidem lationes i&longs;tæ &longs;unt in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. Huic con­<lb/>&longs;entit quod à Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. Si qua­<lb/>drangulum duo&longs;que motus qui æquali celeritate fiant, alterum qui­<lb/>dem per longitudinem: alterum vero per latitudinem intellexeris <lb/>dimetiens producetur recta exi&longs;tens linea, lib. 2. comm. in def. rectæ <lb/>lineæ. Nunc igitur ponatur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>extremum radij duabus lationibus <lb/>de&longs;cribere circulum non digrediens à recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. Non igitur duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun­<lb/>tur in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>Sed hîc obiici pote&longs;t quod Sol motu pri­<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, & motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet æquatori coa&longs;cendenti cum 59'. 8". Eclypticæ. Et &longs;ic <lb/>eius duæ lationes &longs;unt in ratione aliqua, nec tamen Sol fertur &longs;ecun­<lb/>dum rectam &longs;ed <expan abbr="&longs;ecundũ">&longs;ecundum</expan> arcum Eclypticæ. Ita e&longs;t, ob id <expan abbr="dicendũ">dicendum</expan> hic <lb/>dictas ab Ari&longs;totele duæ lationes non &longs;impliciter <expan abbr="intellig&etilde;das">intelligendas</expan>: &longs;ed ta­<lb/>les, quæ <expan abbr="ferãtur">ferantur</expan> ambæ <expan abbr="&longs;ecundũ">&longs;ecundum</expan> rectam. Et &longs;it manebit demon&longs;tratio.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Simile e&longs;t enim.] <foreign lang="greek">tw_ lo/gw,</foreign> <emph type="italics"/>id e&longs;t ratione, redundat quia quæ <lb/>&longs;imilia &longs;unt quadrangula, habent latera, quæ circum æquales angu­<lb/>los propertionalia, ex def. 1. lib. 6. elem.<emph.end type="italics"/></s>
</p>
<pb pagenum="31"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Si enim in alia aliqua, <lb/>non feretur <expan abbr="&longs;ecũdum">&longs;ecundum</expan> dia­<lb/>metrum. Si vero mobilis <lb/>duæ lationes in nulla &longs;int <lb/>ratione, nulloque in tem­<lb/>pore, impo&longs;&longs;ibile e&longs;t latum <lb/>e&longs;&longs;e &longs;ecundum rectam. Sit <lb/>enim recta, qua po&longs;ita pro <lb/>diametro, & completis la­<lb/>teribus nece&longs;&longs;e e&longs;t mobile <lb/>in ratione laterum latum <lb/>e&longs;&longs;e. Hoc enim prius fuit <lb/>demon&longs;tratum. Non igi­<lb/>tur &longs;ecundum rectam pro­<lb/>gredietur, id quod fertur <lb/>in nulla ratione, nulloque <lb/>in tempore. [Si enim <expan abbr="&longs;e-cũdum">&longs;e­<lb/>cundum</expan> rationem aliquam <lb/>latum &longs;it in aliquo tempo­<lb/>re, nece&longs;&longs;e e&longs;t illud tempus <lb/>rectam e&longs;&longs;e lationem, pro­<lb/>pter ea quæ ante dicta &longs;unt.] Itaque circulare e&longs;t quod <lb/>&longs;ecundum duas lationes latum e&longs;t in nulla ratione nullo <lb/>in tempore.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Si enim in alia.] <emph type="italics"/>Locus hic paulo ob&longs;curior, debet &longs;ic intelligi, <lb/>vt &longs;i excmpli gratia, a duabus lationibus latum non feratur in <lb/>ratione quidem data<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g</foreign>: <emph type="italics"/>&longs;ed<emph.end type="italics"/><lb/>
<figure id="fig7"></figure><lb/><emph type="italics"/>in alia, non feretur &longs;ecundum diame­<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, quæ erit diameter <lb/>figuræ à lateribus alterius rationis <lb/>con&longs;titutæ, vt e&longs;t in præ&longs;enti dia­<lb/>grammate<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="greek">a d, a e</foreign> <emph type="italics"/>comprehen&longs;i.<emph.end type="italics"/></s>
</p>
<pb pagenum="32"/>
<p type="main">
<s>Si vero mobilis.] <emph type="italics"/>Conclu&longs;io e&longs;t confirmata reiterato propo&longs;i­<lb/>tionis præcedentis pro&longs;yllogi&longs;mo, &longs;ic. Si duæ lationes puncti mobilis <lb/>&longs;unt in nulla ratione, nulloque in tempore, impoßibile e&longs;t mobile hoc <lb/>latum e&longs;&longs;e &longs;ecundum rectam: atqui puncti de&longs;cribentis circulum duæ <lb/>lationes &longs;unt in nulla ratione, nullóque in tempore. Ergo impoßibile <lb/>e&longs;t punctum, quod de&longs;cribit circulum, ferri &longs;ecundum rectam. Sint <lb/>enim lationes illæ in aliqua ratione. Ergo punctum feretur &longs;ecun­<lb/>dum rectam: at non fertur &longs;ecundum rectam. Peripheria enim non <lb/>e&longs;t recta: &longs;ed curua. Non igitur in aliqua ratione &longs;unt illius lationes. <lb/>Et &longs;i non in vlla ratione. nec igitur in tempore, quia tempora moti­<lb/>bus analoga &longs;unt. Hîc duo occurrunt valde difficilia. Prius de <lb/>tempore. Demon&longs;trauit enim Ari&longs;toteles in Phy&longs;icis, omnem mo­<lb/>tum e&longs;&longs;e in tempore: alterum, cum ambæ lationes &longs;int in eodem ge­<lb/>nere motus, &longs;cilicet localis, quî fiet, vt rationem non habeant. Hoc <lb/>enim repugnat def. 3. lib. 5. elem. quantitas enim motus vnius mul­<lb/>tiplicata, alterius vicißim quantitatem &longs;uperare pote&longs;t. Dicimus <lb/>ergo quod ad hoc po&longs;terius attinet, rationem illas habere: &longs;ed<emph.end type="italics"/> <foreign lang="greek">a)/r)r(n<gap/>ov,</foreign><lb/><emph type="italics"/>& non &longs;olum indicibilem, quod numeris exprimi nequeat: &longs;ed & <lb/>quod rectis lineis geometricè id e&longs;t exactè, exprimi non poßit, qualis <lb/>non e&longs;t inter duas lationes è quibus recta creatur, cum hæc &longs;i nume­<lb/>ris non poßit exprimi, at rectis lineis &longs;altem geometricè exprimitur. <lb/>vt cum duarum rectarum, quæ parallelogrammum con&longs;tituunt, vna <lb/>e&longs;t latus quadrati alicuius, altera e&longs;t eius diameter. Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop. 116. lib. 10. expre&longs;&longs;a. <lb/>At hîc vt inter peripheriam & diametrum &longs;it aliqua ratio, veluti <lb/>inter arcum & &longs;ubtendentem: hæc tamen neque numeris exprimi <lb/>pote&longs;t, nec rectis lineis Geometrice vt videre e&longs;t ex Archimede <lb/>lib.<emph.end type="italics"/> <foreign lang="greek">w_<gap/>i\ uetsh/d. kuk,</foreign> <emph type="italics"/>& Ptol. lib. 1.<emph.end type="italics"/> <foreign lang="greek">me/gal. dw<gap/>.</foreign> <emph type="italics"/>quod autem ad <lb/>prius attinet in lationibus illis tempus admittitur, &longs;ed hoc e&longs;t eiu&longs;mo­<lb/>di, vt nullum eius detur in&longs;tans, quo vna latio fiat, quo etiam non <lb/>& altera itidem fiat: quod prioribus licet commune e&longs;&longs;e poßit: pro­<lb/>pter tamen laterum inæqualitatem vbi in æqualia dantur, non ita <lb/>&longs;implex & indiui&longs;ibile e&longs;t. Cæterum duas has motiones facile ani­<lb/>mo concipiet, qui viderit pueros no&longs;trates &longs;ub medio vere, quo genus <lb/>hoc in&longs;ecti in ro&longs;arÿs no&longs;tris abundat, captam vnam grandiorem <lb/>mu&longs;cam viridem Cathelinam ip&longs;i vocant, pede adfuniculum alliga-<emph.end type="italics"/>
<pb pagenum="33"/><emph type="italics"/>tam permittere volare: ita tamen vt digitis alterum extremum funi­<lb/>culi retineant. Hæc enim in altero extremo mu&longs;ca, tanquam in ex­<lb/>tremo radÿ circulum de&longs;cribentis volatu &longs;uo de&longs;cribit circulum: hic <lb/>volatus compo&longs;itus e&longs;t è duobus motibus: vno, quo hæc mu&longs;ca pro­<lb/>prio fertur, <expan abbr="&longs;ecũdum">&longs;ecundum</expan> quem &longs;e&longs;e è vinculo liberare conatur: altero, quo <lb/>per vinculum retinetur, ne euagetur longius, quam longitudo <lb/>funiculi permittit. Ibi motus mu&longs;cæ violentus e&longs;t, & non naturalis <lb/>vt à quo etiam cum pes abrumpitur præ &longs;uo conatu, aut nodus for­<lb/>tuitò laxatur, &longs;i liberatur, &longs;tatim rectà aufugit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Si enim &longs;ecundum.] <emph type="italics"/>Hanc particulam parenthe&longs;i &longs;ic [ ] in­<lb/>tercludendam curauimus, quod eam &longs;uperuacuam e&longs;&longs;e cum Leonico <lb/>exi&longs;timemus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Itaque circulare.] <emph type="italics"/>Proinde e&longs;t ac &longs;i diceret, cum via &longs;eu linea <lb/>per quam fertur radÿ extremum mobile &longs;it maxime vniformis, vt <lb/>ex definitione circuli con&longs;tat, nec tamen recta: re&longs;tat, vt &longs;it circula­<lb/>ris &longs;eu rotunda, à medio &longs;cilicet comprehen&longs;i &longs;patÿ æqualiter ex omni <lb/>parte di&longs;tans. quod nulli alij obliquarum linearum conuenire pore&longs;t: <lb/>non ellip&longs;i quidem, quia licet vna &longs;it linea, & extremum in ea fiat <lb/>primum, vt in peripheria: nullum tamen punctum in eius medio e&longs;t, <lb/>à quo omnes rectæ ad ellip&longs;is peripheriam &longs;int æquales: non parabo­<lb/>læ, non hyperbolæ, non &longs;pirali &longs;eu volutæ. Quia in nulla harum, quod <lb/>e&longs;t extremum fit primum, quod peripheriæ conuenit. Præterea nulla <lb/>harum &longs;implex e&longs;t linea. Agitur hîc autem de &longs;implicibus tantum, <lb/>quæ vno &longs;implici motu, vel &longs;i duobus, ijs &longs;imilibus creantur, & &longs;i­<lb/>milares &longs;unt: quales cum duæ tantum &longs;int recta &longs;cilicet & circula­<lb/>ris, inde bene inferetur è po&longs;ita &longs;implicè &longs;i recta non e&longs;t, e&longs;&longs;e cir­<lb/>cularis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Quod vero recta <expan abbr="de&longs;cri-b&etilde;s">de&longs;cri­<lb/>bens</expan> circulum duabus &longs;imul <lb/>lationib^{9} feratur, <expan abbr="cũ">cum</expan> ex his <lb/>e&longs;t <expan abbr="manife&longs;tũ">manife&longs;tum</expan>, <expan abbr="tũ">tum</expan> quod lata <lb/><expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan> fieret num­<lb/>quam perpendicularis. Et <lb/>fieri à <expan abbr="c&etilde;tro">centro</expan> <expan abbr="perpendicula-r&etilde;">perpendicula­<lb/>rem</expan> [demõ&longs;trem^{9}]. Sit circu­
<pb pagenum="34"/><gap/><lb/>lus <foreign lang="greek">a b g,</foreign> & extremum <foreign lang="greek">b</foreign><lb/>feratur ad <foreign lang="greek">d,</foreign> perueniet &longs;a­<lb/>ne aliquando ad <foreign lang="greek">g.</foreign> [Si igi­<lb/>tur ferebatur in ratione <lb/>quam habet <foreign lang="greek">b e</foreign> ad <foreign lang="greek">e g,</foreign> fe­<lb/>rebatur &longs;ecundum diame­<lb/>trum <foreign lang="greek"><gap/> g</foreign>: Atnunc cum in <lb/>nulla ratione feratur, &longs;e­<lb/>cundum peripheriam <foreign lang="greek">b e g</foreign><lb/>feretur.]</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Qvod vero recta.] <emph type="italics"/>Quia &longs;uperioris &longs;yllogi&longs;mi a&longs;&longs;umptio a&longs;&longs;u­<lb/>mebat <expan abbr="Radiũ">Radium</expan> duabus &longs;imul ferri lationibus, id ip&longs;um hîc breui­<lb/>ter, ideo valde ob&longs;curè confirmatur. Confirmatio apertior &longs;ic erit. <lb/>Radius de&longs;cribens circulum vna tantum latione fertur, aut pluri­<lb/>bus: non vna tantum, quia ad vnam tantum loci differentiam, <lb/>cum &longs;it quid &longs;implicißimum, ferretur (probat enim hoc Ari&longs;toteles <lb/>cap. 2. lib. 1. de Cœlo) Quinetiam &longs;i &longs;ic. Idem radius à diametro cir-<emph.end type="italics"/><lb/>
<figure id="fig8"></figure><lb/><emph type="italics"/>culi digrediens in tran&longs;itu ab vna &longs;emidia­<lb/>metro ad alteram numquam con&longs;equeretur <lb/>cum &longs;itum, per quem ip&longs;i à centro perpen­<lb/>dicularis e&longs;&longs;et. Con&longs;equitur autem vt cum <lb/>e&longs;t in L<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>diagrammatis hic de&longs;cri­<lb/>pti. Non igitur vna latione tantum fer­<lb/>tur: fertur ergo pluribus. Et quidem vna, vt <lb/>antror&longs;um: qua qua &longs;i diffunditur, & ab&longs;ce­<lb/>dit foras, vt<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us E in hoc diagrammate: altera vt retror-<emph.end type="italics"/><lb/>
<figure id="fig9"></figure><lb/><emph type="italics"/>&longs;um ver&longs;us centrum: qua retrahitur, ne euage­<lb/>tur longius, quam æqualitas di&longs;tantiæ vndi­<lb/>que à centro &longs;eruandæ permittit, vt idem<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ver&longs;us L. V traque autem hæc latio quanta &longs;it <lb/>men&longs;uraturlineisrectis, quarum altera in po&longs;te­<lb/>riore diaorammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>verò e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g.</foreign></s>
</p>
<pb pagenum="35"/>
<p type="main">
<s>Demon&longs;tremus.] <emph type="italics"/>Dee&longs;t hoc vocabulum in Græco &longs;ine quo <lb/>&longs;en&longs;us e&longs;t imperfectus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Si igitur ferebatur.] <emph type="italics"/>Rur&longs;us totum hunc textum his notis <lb/>[ ] interclu&longs;um inaniter repeti arbitramur. hoc enim e&longs;t quod an­<lb/>teae&longs;t demon&longs;tratum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Si vero duorum eadem <lb/>vi latorum vnum plus re­<lb/>pellitur, alterum minus: <lb/>æquum e&longs;t, plus repul&longs;um, <lb/>altero minus repul&longs;o tar­<lb/>dius ferri. Quod videtur <lb/>contingere maiori & mi­<lb/>nori lineis ab eodem cen­<lb/>tro circulos <expan abbr="de&longs;crib&etilde;tibus">de&longs;cribentibus</expan>. <lb/>Quia enim extremum mi­<lb/>noris propius e&longs;t quie&longs;cen­<lb/>ti, quam &longs;it <expan abbr="extremũ">extremum</expan> maio­<lb/>ris: qua&longs;i in contrarium re­<lb/>uul&longs;um, in medium tardius <lb/>fertur ip&longs;um minoris extre­<lb/>mum. Omni igitur circu­<lb/>lum de&longs;cribenti hoc con­<lb/>tingit.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Si vero duorum.] <emph type="italics"/>Vbi confirmauit in omni radio circulum <lb/>de&longs;cribente duas lationes ine&longs;&longs;e, nunc eas comparat in radÿs inæ­<lb/>qualibus, quod ad celeritatem & tarditatem attinet. Et quidem <lb/>eam, quæ &longs;ecundum naturam e&longs;t in radio maiore, maiorem: eam ve­<lb/>ro, quæ præter naturam, minorem e&longs;&longs;e in eodem demon&longs;trat, vt ra­<lb/>dium maiorem celerius ferri minore concludat. Syllogi&longs;mus e&longs;t <lb/>connexus &longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Si duorum eadem vi motorum vnum plus repellitur, alterum <lb/>minus: quod plus repellitur, tardius fertur.<emph.end type="italics"/></s>
</p>
<pb pagenum="36"/>
<p type="main">
<s><emph type="italics"/>Radiorem inæqualium eadem vi motorum minor plus <lb/>repellitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Radius igitur minor tardius feretur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quia enim minoris.] <emph type="italics"/>pro&longs;yllogi&longs;mus e&longs;t a&longs;&longs;umptionis &longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quod propius e&longs;t quie&longs;centi & immoto plus retrahitur, quod <lb/>idem e&longs;t ac plus repellitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Extremum radÿ minoris mobile propius e&longs;t centro, alteri <lb/>&longs;cilicet extremo quie&longs;centi & immoto: quam extre­<lb/>mum maioris.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo extremum radÿ minoris mobile plus retrahetur retror­<lb/>&longs;um, & ab anteriori repelletur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Illu&longs;trari hæc <expan abbr="cõclu&longs;io">conclu&longs;io</expan> po&longs;&longs;et &longs;imilitudine ampli & latè patentis re­<lb/>gni, in cuius medio tanquam centro, cum rex præ&longs;ideat, partes me­<lb/>dio vicinæ regis legibus magis coarctantur & continentur: quam <lb/>remotæ.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Et fertur motu <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <lb/>naturam per peripheriam: <lb/>præter <expan abbr="naturã">naturam</expan> vero in <expan abbr="trã&longs;-uer&longs;um">tran&longs;­<lb/>uer&longs;um</expan>, & centrum ver&longs;us. <lb/>Minor vero [linea] &longs;emper <lb/><expan abbr="maior&etilde;">maiorem</expan> motum habet eum, <lb/>qui præter <expan abbr="naturã">naturam</expan> e&longs;t. quia <lb/>enim centro vicinior e&longs;t ad <lb/>&longs;e <expan abbr="reuell&etilde;ti">reuellenti</expan>, vincitur magis.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Et fertur motu.] <emph type="italics"/>E duobus motibus in extremo radÿ mobili <lb/>alterum &longs;ecundum naturam e&longs;&longs;e dicit, nempe qui e&longs;t &longs;ecundum <lb/>peripheriam, alterum præter naturam, qui e&longs;t in tran&longs;uer&longs;um, & <lb/>ver&longs;us centrum. Sed rationem huius hic nullam profert. Hæc au­<lb/>tem alibi ab eo dicta adferri pote&longs;t. quia quicquid &longs;implex exi&longs;tens <lb/>duabus lationibus &longs;imul fertur, alteram naturalem, alteram præter­<lb/>naturam habere &longs;eu vt ita dicam &longs;ecundariam, & ab alio penden­<lb/>tem nece&longs;&longs;e e&longs;t: &longs;icuti videre e&longs;t in motibus inferiorum orbium cæle-<emph.end type="italics"/>
<pb pagenum="37"/><emph type="italics"/>&longs;tium, qui proprio ab occa&longs;u in Orientem vergunt, & motu primi <lb/>mobilis ab Oriente in occa&longs;um mouentur. Ergo cum extremum radÿ <lb/>mobile aut radius ip&longs;e &longs;it quid &longs;implicißimum, & &longs;imul duabus la­<lb/>tionibus feratur, altera harum erit ei naturalis, altera ad vim alte­<lb/>rius con&longs;equetur. Et illa quidem potius naturalis erit quæ à termino à <lb/>quo egredi conatur, & quantum in &longs;e e&longs;t, di&longs;cedit. Talis autem e&longs;t ea <lb/>qua extremum mobile veluti di&longs;cedens à centro &longs;ecundum periphe­<lb/>riam fertur. Tum qua forma rei acquiritur, qualis latio per circum­<lb/>ferentiam, cum hæc &longs;it circuli forma &longs;eu finis. Relinquitur ergo vt ea <lb/>&longs;it contra <expan abbr="naturã">naturam</expan> & per accidens, qua ad ip&longs;um centrum reuellitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Quod vero minor plus <lb/>præter naturam moueatur: <lb/>quam maior earum, qu&ecedil; ex <lb/>centro <expan abbr="de&longs;cribũt">de&longs;cribunt</expan> circulos, <lb/>ex his erit manife&longs;tum. Sit <lb/>circulus <foreign lang="greek">b g d e,</foreign> & alter <lb/>minor <foreign lang="greek">x n m c,</foreign> eiu&longs;dem <expan abbr="c&etilde;-tri">cen­<lb/>tri</expan> <foreign lang="greek">a,</foreign> Et traductæ &longs;int dia­<lb/>metri in magno quidem <lb/><foreign lang="greek">g d, & b e</foreign>: in minori <foreign lang="greek">m c & <lb/>x n</foreign>: atque alterolongum <lb/>compleatur <foreign lang="greek">d y r g.</foreign> Si igi­<lb/>tur <foreign lang="greek">a b</foreign> de&longs;cribens <expan abbr="circulũ">circulum</expan> <lb/>perueniet ad id vnde mo­<lb/>ueri cœpit, manife&longs;tum e&longs;t <lb/>quod fertur ad ip&longs;am [<foreign lang="greek">a b</foreign>] <lb/>&longs;imiliter <foreign lang="greek">a x</foreign> perueniet ad <lb/>ip&longs;am <foreign lang="greek">a x.</foreign> Tardius autem <lb/>fertur <foreign lang="greek">a x</foreign>: quam <foreign lang="greek">a b,</foreign> vt <lb/><expan abbr="dictũ">dictum</expan> e&longs;t, propter maiorem <lb/><expan abbr="repul&longs;ion&etilde;">repul&longs;ionem</expan> & reuul&longs;ionem <lb/>ip&longs;ius <foreign lang="greek">a x.</foreign> Ducatur vero <lb/>recta <foreign lang="greek">a q h, & a q</foreign> excitetur <lb/>perpendicularis ad <foreign lang="greek">a b,</foreign> qu&ecedil; <lb/>&longs;it <foreign lang="greek">q z</foreign> in circulo [minori].
<pb pagenum="38"/><gap/><lb/>Et rur&longs;us per <foreign lang="greek">q</foreign> ducatur pa­<lb/>rallela ip&longs;i <foreign lang="greek">a b</foreign> quæ &longs;it <foreign lang="greek">q w <lb/>& w n</foreign> perpendicularis ip&longs;i <lb/><foreign lang="greek">a b</foreign> tum & <foreign lang="greek">h k.</foreign> Sunt vero <lb/><foreign lang="greek">w n & q z</foreign> æquales. Rur&longs;us <lb/><foreign lang="greek">b n</foreign> e&longs;t minor: quam <foreign lang="greek">x z.</foreign> In <lb/>circulis enim inæqualibus <lb/>rect&ecedil; &ecedil;quales ad rectos dia­<lb/>metro excitatæ, de diame­<lb/>tro circulorum maiorum <lb/><expan abbr="&longs;egmentũ">&longs;egmentum</expan> minus auferunt. <lb/>E&longs;t autem <foreign lang="greek">w n</foreign> æqualis ip&longs;i <lb/><foreign lang="greek">q z.</foreign> In quanto vero tempo­<lb/>re <foreign lang="greek">a x</foreign> peragrauit <foreign lang="greek">x q,</foreign> in <lb/><expan abbr="tãto">tanto</expan> in maiore circulo ex­<lb/>tremum <foreign lang="greek">a b</foreign> non maiorem <lb/><foreign lang="greek">b w</foreign> peragrauit (etenim <lb/>motus &longs;ecundum naturam <lb/>æqualis e&longs;&longs;et) præter na­<lb/>turam vero minor erat, nempe <foreign lang="greek">b n</foreign> quam <foreign lang="greek">x z.</foreign></s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Qvod vero minor.] <emph type="italics"/>Altera e&longs;t confirmatio &longs;ed<emph.end type="italics"/> <foreign lang="greek"><gap/>ammikh\</foreign><lb/><emph type="italics"/>linearis a&longs;&longs;umptionis &longs;yllogi&longs;mi præcedentis. Scilicet quod mi­<lb/>norradius plus retrahatur ad centrum, quam maior. Vbi ab vtri&longs;que <lb/>&longs;ecundum peripheriam æquale &longs;patium confectum e&longs;t. perpendiculis <lb/>enim æqualibus ip&longs;um men&longs;urantibus partes ab&longs;ci&longs;&longs;æ de diametris, <lb/>quæ retractionem vtriu&longs;que ad centrum men&longs;urant, inæquales &longs;unt, <lb/>& in minore circulo, maior: in maiore vero minor. vt videre lice­<lb/>bit in diagrammate hic de&longs;cripto & &longs;uis rationibus nece&longs;&longs;arÿs con­<lb/>firmato.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sint duo circuli concentrici maior<emph.end type="italics"/> <foreign lang="greek">b d e y,</foreign> <emph type="italics"/>minor<emph.end type="italics"/> <foreign lang="greek">x m n c</foreign> <emph type="italics"/>è cen­<lb/>tro a traiecti diametris<emph.end type="italics"/> <foreign lang="greek">x n & b e.</foreign></s>
</p>
<p type="main">
<s><emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ad punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur recta<emph.end type="italics"/> <foreign lang="greek">a q,</foreign> <emph type="italics"/>& producatur in<emph.end type="italics"/><lb/><foreign lang="greek">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="greek">a q h.</foreign></s>
</p>
<p type="main">
<s><emph type="italics"/>Tum à puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>prop. 12. <lb/>lib. 1. &longs;itque<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s>
</p>
<pb pagenum="39"/>
<p type="main">
<s><emph type="italics"/>Et per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur parallela rectæ<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>prop. 31. lib. 1. <lb/>quæ &longs;it<emph.end type="italics"/> <foreign lang="greek">q w.</foreign></s>
</p>
<figure></figure>
<p type="main">
<s><emph type="italics"/>Rur&longs;us à puncto<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/><lb/><foreign lang="greek">w n</foreign>: <emph type="italics"/>& &longs;ic parallelogrammum erit<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>ex def. parallelog.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>tantum confecit &longs;patÿ &longs;ecundum natu­<lb/>ram, quam<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek"><expan abbr="q.">que</expan></foreign> <emph type="italics"/>Spatia enim cum metiatur perpendicu­<lb/>laris, vtpote optima <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>, quia minima, & &longs;ola regularis & nota. <lb/>Sint autem<emph.end type="italics"/> <foreign lang="greek">w n, q z</foreign> <emph type="italics"/>perpendiculares ex fab. & æquales, quia late­<lb/>ra oppo&longs;ita in parallelogrammo<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>prop. 34. lib. 1. Erant vtro­<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w & x q</foreign> <emph type="italics"/>æqualia.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><foreign lang="greek">b n</foreign> <emph type="italics"/>vero eadem ratione metitur &longs;patium motus præter naturam <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b, & x z</foreign> <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">x.</foreign> <emph type="italics"/>&longs;i igitur<emph.end type="italics"/> <foreign lang="greek">x z</foreign> (<emph type="italics"/>quod po&longs;tea demon&longs;tra­<lb/>bitur) maior &longs;it quam<emph.end type="italics"/> <foreign lang="greek">b n,</foreign> <emph type="italics"/>erit puncti<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motus præter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="greek">b.</foreign></s>
</p>
<pb pagenum="40"/>
<p type="main">
<s><emph type="italics"/>Sed & &longs;i perficiantur parallelogramma<emph.end type="italics"/> <foreign lang="greek">d s t f & d y r g</foreign>: <lb/><emph type="italics"/>illud erit vtile ad o&longs;tendendum<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>tralatum vno motu v&longs;que ad<emph.end type="italics"/> <foreign lang="greek">s,</foreign><lb/><emph type="italics"/>altero motu, quo retrahitur ad centrum, reductum e&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">t</foreign>: <emph type="italics"/>& <lb/>huius retractiones <expan abbr="men&longs;urã">men&longs;uram</expan> e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">s t</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">d f</foreign>: <emph type="italics"/>hoc vero vtile <expan abbr="etiã">etiam</expan> erit <lb/>ad terminandos motus illos duos <expan abbr="natural&etilde;">naturalem</expan>, &longs;cilicet & præter <expan abbr="naturã">naturam</expan>.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Atque alterolongum.] <emph type="italics"/>Hoc <expan abbr="quadrilaterũ">quadrilaterum</expan> <expan abbr="oblongũ">oblongum</expan>, & rectan­<lb/>gulum compleri debui&longs;&longs;e dici pote&longs;t, vt rectus in eo motus appareat, <lb/>quem facturus radius fui&longs;&longs;et, ni&longs;i retraheretur in centrum: tum vt <lb/>terminet motus eos, qui &longs;unt &longs;ecundum naturam & præter naturam.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><foreign lang="greek">a q h</foreign>] <emph type="italics"/><expan abbr="Punctũ">Punctum</expan><emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>vbi libet in peripheria accipitur ad de&longs;ignandum <lb/>quoduis <expan abbr="&longs;patiũ">&longs;patium</expan>, quod confecerit<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/><expan abbr="extremũ">extremum</expan> mobile minoris radÿ<emph.end type="italics"/> <foreign lang="greek">a x.</foreign></s>
</p>
<p type="main">
<s>Et <foreign lang="greek">a q</foreign> excitetur.] <emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>extra lineam<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>dato ex­<lb/>citatur in ip&longs;am perpendicularis, quæ e&longs;t<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>prop. 12. lib. 1. elem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et rur&longs;us per <foreign lang="greek">q</foreign>] <emph type="italics"/>Per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>datum datæ rectæ<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>duci­<lb/>tur parallela prop. 31. lib. 1. elem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et <foreign lang="greek">w n</foreign> perpend.] <emph type="italics"/>prop. 12. lib. 1. elem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sunt vero <foreign lang="greek">w n</foreign> &] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="greek">q w</foreign> <emph type="italics"/>parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>ex fabrica: <lb/>tùm<emph.end type="italics"/> <foreign lang="greek">w n</foreign> <emph type="italics"/>etiam parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>quia in eas incidens<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>facit an­<lb/>gulos internos ad <expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> partes rectos, ex fab. proinde æquales ax. 10. <lb/><expan abbr="itaq;">itaque</expan> parallelæ prop. 28. lib. 1. <expan abbr="parallelogrãmũ">parallelogrammum</expan> erit<emph.end type="italics"/> <foreign lang="greek">w n z <expan abbr="q.">que</expan></foreign> <emph type="italics"/>per def. pa­<lb/>rall. quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="greek">w n & q z</foreign> <emph type="italics"/><expan abbr="erũt">erunt</expan> æqualia prop. 34. lib. 1.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>In circulis.] <emph type="italics"/>Ex hoc loco elicitur hoc theorema. Perpendicula­<lb/>res à peripheriis in &longs;emidiametros circulorum inæqualium æquales <lb/>&longs;egmenta auferunt de &longs;emidiametris inæqualia, & quidem maius in <lb/>minori comprehen&longs;um inter peripheriam & perpendicularem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Expo­<lb/>
<figure id="fig10"></figure><lb/>&longs;itio.</s>
</p>
<p type="main">
<s><emph type="italics"/>Sunto <lb/>duo cir <lb/>culi in­<lb/>æqua­<lb/>les A <lb/>B C ma <lb/>ior & <lb/>D E F <lb/>minor, perpendiculares &longs;int B K, E I & ablatæ A K, D I.<emph.end type="italics"/></s>
</p>
<pb pagenum="41"/>
<p type="main">
<s>Deter. <emph type="italics"/>Dico D I e&longs;&longs;e maiorem ip&longs;a A K quæ e&longs;t &longs;egmentum in <lb/>maiori circulo. Ante huius fabricam hoc problema e&longs;t <expan abbr="a&longs;&longs;um&etilde;dum">a&longs;&longs;umendum</expan>.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>De&longs;cribere circulum minorem qui alterum datum maiorem <lb/>interius tangat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper­<lb/>tum prop. 1. lib. 3. ducatur A k diameter. De&longs;cribendus autem &longs;it eo <lb/>minor, cuius accipiatur E <expan abbr="centrũ">centrum</expan><emph.end type="italics"/><lb/>
<figure id="fig11"></figure><lb/><emph type="italics"/>inter A & D, & interuallo <lb/>E A de&longs;cribatur A F G. hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. erit æqualis ip&longs;i E A def. <lb/>15. lib. 1. non erit igitur E A mi­<lb/>nima omnium quæ ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe­<lb/>ripheriam, quod e&longs;t contra prop. <lb/>7. lib. 3. non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alÿs. Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 3. quod oportuit facere.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Iam nunc de A G maiori &longs;emidiametro detrahatur portio A H <lb/>æqualis D H minori prop. 3. lib. 1. centro H interuallo A H de&longs;­<lb/>cribatur circulus A M L po&longs;tul. 3. qui erit æqualis dato D E F. <lb/>def. 1. lib. 3. Et tanget intus circulum A B C in puncto A exprobl. <lb/>præ&longs;umpto. per punctum B ducaeur parallela B M prop. 31. lib. 1. <lb/>& per eandem parallela M N quæ per 34. lib. eiu&longs;dem cum &longs;it <lb/>æqualis ip&longs;i B K erit & æqualis ip&longs;i. E I ax. 1. connectantur M H, <lb/>E H po&longs;t. 1.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Demon&longs;t. <emph type="italics"/>Po&longs;tquam ax. 3. A N, D I æquales &longs;unt quia reli­<lb/>quæ ex æqualibus A H, D H ex fab. demptis æqualibus N H, <lb/>I H quæ latera &longs;unt &longs;ub æqualibus angulis duorum triangulorum <lb/>M N H & I E H habentium duos angulos duobus angulis <lb/>æquales, & latus lateri æquale vt e&longs;t in 26. prop. lib. 1. nempe angu­<lb/>lus qui ad N rectus e&longs;t prop. 29. lib. 1. & qui ad I, rectus ex hypoth. <lb/>ideo æquales ax. 10. tum angulus M H N ad centrum con&longs;titutus<emph.end type="italics"/>
<pb pagenum="42"/><emph type="italics"/>& angulus E H I ad centrum con&longs;titutus in æqualibus circulis ex <lb/>fab. &longs;unt æquales prop. 27. lib. 3. quia æquales &longs;unt peripheriæ A M, <lb/>D E ablatæ &longs;cilicet ab æqualibus &longs;emißibus M N & E I ex <lb/>fab. prop. 3. & 29. lib. 3. & &longs;icreliquum latus N H æquale e&longs;t re­<lb/>liquo I H. Ergo cum tota A N æqualis D I &longs;it maior A K <lb/>parte &longs;ua ax. 9. erit & D I maior ip&longs;a A K.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Concl. <emph type="italics"/>Ergo perpendiculares à peripherÿs in &longs;emidiametros & <lb/>ct. quod fuit demon&longs;trandum. Hoc autem theorema videtur <expan abbr="quo-dãmodo">quo­<lb/>dammodo</expan><emph.end type="italics"/> <foreign lang="greek"><gap/>a/doxon.</foreign> <emph type="italics"/>Erat enim veri&longs;imilius in maiore circulo <expan abbr="&longs;eg-mentũ">&longs;eg­<lb/>mentum</expan> &longs;emidiametri e&longs;&longs;e maius, & in minore minus: at non ita e&longs;t vt <lb/>patuit. Cau&longs;a autem hæc reddi pote&longs;t, quod eadem recta, &longs;i fiat arcus <lb/>minoris circuli plus incuruetur oportet: quam &longs;i fiat arcus maioris, <lb/>atque his omnibus eo tendit Ari&longs;toteles, vt o&longs;tendat maiorem circu­<lb/>lum mobiliorem, & ideo etiam mouentiorem e&longs;&longs;e minori: rationem <lb/>autem mobilitatum e&longs;&longs;e, vt &longs;emidiametrorum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>In quanto vero.] <emph type="italics"/>Conclu&longs;io e&longs;t qua concluditur, vbi motus <lb/>&longs;ecundum naturam in vtri&longs;que circulis æquales e&longs;&longs;ent: ibi motum <lb/>præter naturam in maiori circulo minorem, & in minori maiorem <lb/>reperiri. Antea dixerat duas lationes illas e&longs;&longs;e in nulla ratione, in­<lb/>tellige igitur quæ rectis lineis exactè exprimi poßit. Nam &longs;inus tam <lb/>rectus quam ver&longs;us, quibus rationis harum lationum termini expri­<lb/>muntur, vt &longs;int rectæ lineæ: hæ tamen non ad vnguem arcus &longs;uos <lb/>metiuntur. Et &longs;ic in nulla &longs;unt ratione ad vnguem expre&longs;&longs;a: &longs;unt ta­<lb/>men vt hic quodammodo, & vt aiunt ferè.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>At oportet analoga e&longs;&longs;e, <lb/>vt id quod <expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="naturã">naturam</expan>, <lb/>ad id quod <expan abbr="&longs;ecũdum">&longs;ecundum</expan> natu­<lb/>ram: &longs;ic quod præter natu­<lb/>ram, ad id quod præter <expan abbr="na-turã">na­<lb/>turam</expan>. Igitur maiorem quam <lb/><foreign lang="greek">b w</foreign> <expan abbr="peripheriã">peripheriam</expan>, vt <foreign lang="greek">b h</foreign> <expan abbr="per-trã&longs;ijt">per­<lb/>tran&longs;ijt</expan>. Nece&longs;&longs;e igitur in eo <lb/>tempore <foreign lang="greek">b h</foreign> tran&longs;ij&longs;&longs;e. Ibi <lb/>enim erit, vbi proportiona­<lb/>les <expan abbr="cõting&etilde;t">contingent</expan> <expan abbr="vtrinq;">vtrinque</expan> motus
<pb pagenum="43"/><gap/><lb/>præter naturam ad motus <lb/>&longs;ecundum naturam. Si igi­<lb/>tur maius e&longs;t id quod <expan abbr="&longs;ecũ-dum">&longs;ecun­<lb/>dum</expan> <expan abbr="naturã">naturam</expan> in maiore cir­<lb/>culo, & quod e&longs;t pr&ecedil;ter na­<lb/>turam maius, vtique illuc <lb/>concidet vno modo, ita vt <lb/><foreign lang="greek">b</foreign> &longs;it latum per lineam <foreign lang="greek">b h.</foreign><lb/>eo in tempore quo <expan abbr="pũctum">punctum</expan> <lb/><foreign lang="greek">x</foreign> [per <foreign lang="greek">x q</foreign>]. Ibi enim pun­<lb/>cto <foreign lang="greek">b</foreign> &longs;ecundum <expan abbr="quid&etilde;">quidem</expan> na­<lb/>turam e&longs;t recta <foreign lang="greek">k h,</foreign> ab <foreign lang="greek">h</foreign><lb/>enim e&longs;t ip&longs;a perpendicu­<lb/>laris, præter naturam vero <lb/><foreign lang="greek">b k.</foreign> E&longs;t &longs;iquidem vt <foreign lang="greek">h k</foreign> ad <lb/><foreign lang="greek"><gap/> k</foreign>: &longs;ic <foreign lang="greek">q z</foreign> ad <foreign lang="greek">x z,</foreign> quod <lb/>erit manife&longs;tum, &longs;i à pun­<lb/>ctis <foreign lang="greek">b, x</foreign> ad <foreign lang="greek">h, q</foreign> rectæ adiun­<lb/>ctæ &longs;int. Si vero minor vel <lb/>maior: quam <foreign lang="greek">h b</foreign> fuerit ea, <lb/>perquam <foreign lang="greek">b</foreign> motum e&longs;t, non <lb/>&longs;imiliter neque proportio­<lb/>naliter in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> erit, quod <lb/>
<arrow.to.target n="marg13"></arrow.to.target><lb/>&longs;ecundum naturam ad id <lb/>quod præter naturam. Ob <lb/><expan abbr="hãc">hanc</expan> igitur cau&longs;am ex dictis <lb/>manife&longs;tum, quod punctum à centro di&longs;tantius, vt ea­<lb/>dem vi &longs;it motum, celerius fertur.</s>
</p>
<p type="margin">
<s><margin.target id="marg13"></margin.target>Vetba &longs;i­<lb/>gnis inclu&longs;a <lb/>in <expan abbr="cõtextu">contextu</expan> <lb/>Gr&ecedil;co quia <lb/>redundant <lb/>non verti­<lb/>mus.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>At oportet.] <emph type="italics"/>Nunc o&longs;tendit in maiore circulo motum &longs;ecun­<lb/>dum naturam maiorem e&longs;&longs;e motu &longs;ecundum naturam in mino­<lb/>re circulo eodem tempore factum. Ratio e&longs;t, Circuli inæquales eadem <lb/>vi moti &longs;eruant analogiam in motibus &longs;cilicet: vt quæ ratio &longs;it mo­<lb/>tus in maiore circulo &longs;ecundum naturam ad &longs;uum motum præter na-<emph.end type="italics"/>
<pb pagenum="44"/><emph type="italics"/>turam: eadem &longs;it motus in minore circulo &longs;ecundum naturam ad <lb/>&longs;uum motum præter naturam: at hæc analogia tantum reperiri po­<lb/>te&longs;t, &longs;i cum<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>delatum e&longs;t in<emph.end type="italics"/> <foreign lang="greek">q,</foreign> <emph type="italics"/>intelligatur etiam<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum in<emph.end type="italics"/> <foreign lang="greek">h,</foreign><lb/><emph type="italics"/>à quo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>e&longs;t perpendicularis<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>in diametrum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>metiens motum <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>per peripheriam<emph.end type="italics"/> <foreign lang="greek">b h.</foreign> <emph type="italics"/>Ergo quo tempore<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>delatum e&longs;t ad<emph.end type="italics"/><lb/><foreign lang="greek">q,</foreign> <emph type="italics"/>eodem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum erit ad<emph.end type="italics"/> <foreign lang="greek">h.</foreign> <emph type="italics"/>Cæterum eadem vis in vtri&longs;que cir­<lb/>culis intelligitur ex æqualitate angulorum ad centrum con&longs;tituto­<lb/>rum. Æqualis enim e&longs;t angulus<emph.end type="italics"/> <foreign lang="greek"><gap/> a h</foreign> <emph type="italics"/>angulo<emph.end type="italics"/> <foreign lang="greek">x a <expan abbr="q.">que</expan></foreign></s>
</p>
<p type="main">
<s>Ab <foreign lang="greek">h</foreign> enim e&longs;t.] <emph type="italics"/>Curuas lineas perpendicularis &longs;ola vt breui&longs;­<lb/>&longs;ima, quantum fieri pote&longs;t exacte metitur. vt &longs;cribit autem Ptolo­<lb/>mæus in lib. de Analemmate, & Simplicius in lib. de Dimen&longs;ione, <lb/>men&longs;ura cuiu&longs;cunque rei debet e&longs;&longs;e &longs;tata, determinata, & non indefi­<lb/>nita. Talis autem e&longs;t perpendicularis ad linearum reliquarum dimen­<lb/>&longs;ionem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>E&longs;t &longs;iquidem vt <foreign lang="greek">h k.</foreign>] <emph type="italics"/>Triangula enim<emph.end type="italics"/> <foreign lang="greek">x q z & b h k</foreign> <emph type="italics"/>&longs;unt <lb/>æquiangula. Nam, qui anguli ad<emph.end type="italics"/> <foreign lang="greek"><gap/> & k,</foreign> <emph type="italics"/>&longs;unt recti ex fab. qui vero <lb/>ad<emph.end type="italics"/> <foreign lang="greek">x & b</foreign> <emph type="italics"/>&longs;unt externus & internus ad ea&longs;dem partes facti à re­<lb/>cta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">x q, b h</foreign> <emph type="italics"/>prop. 3. lib. 6. Nam<emph.end type="italics"/> <foreign lang="greek">x q</foreign><lb/><emph type="italics"/>proportionaliter &longs;ecat<emph.end type="italics"/> <foreign lang="greek">a b & a h</foreign> <emph type="italics"/>latera trianguli<emph.end type="italics"/> <foreign lang="greek">b a h.</foreign> <emph type="italics"/>Sunt enim<emph.end type="italics"/><lb/><foreign lang="greek">a x, a q</foreign> <emph type="italics"/>æquales radj,<emph.end type="italics"/> & <foreign lang="greek">x b, q h</foreign> <emph type="italics"/>item æquales lineæ, quia re­<lb/>liquæ ex æqualibus radÿs<emph.end type="italics"/> <foreign lang="greek">a b, a h</foreign>: <emph type="italics"/>habent autem æquales ad <lb/>æquales eandem rationem E&longs;t igitur<emph.end type="italics"/> <foreign lang="greek">x q</foreign> <emph type="italics"/>parallela ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b h,</foreign> <emph type="italics"/>& &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>externus, & qui ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>internus erunt æquales <lb/>prop. 29. lib. 1. Ergo & reliqui qui ad<emph.end type="italics"/> <foreign lang="greek">q & h</foreign> <emph type="italics"/>prop. 32. lib. 1. Hæc <lb/>igitur duo triangula circa æquales angulos habebunt latera propor­<lb/>tionalia prop. 4. lib. 6. Sicque erit vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">x z</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b,</foreign><lb/><emph type="italics"/>& alternatim vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="greek">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b</foreign> <emph type="italics"/>prop. 16. lib. 5.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Ob hanc igitur cau&longs;am.] <emph type="italics"/>Conclu&longs;io qua tandem concludi­<lb/>tur punctum à centro di&longs;tantius, vt eadem vi &longs;it motum, celerius <lb/>ferri, id e&longs;t eodem tempore maius loci &longs;patium conficere.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Quod vero propterea li­<lb/>br&ecedil; maiores minoribus &longs;int <lb/>exactiores, <expan abbr="manife&longs;tũ">manife&longs;tum</expan> ex his <lb/>erit. Agina enim fit <expan abbr="centrũ">centrum</expan>. <lb/>Hæc enim quie&longs;cit. <expan abbr="vtræq;">vtræque</expan>
<pb pagenum="45"/><gap/><lb/>vero librilis partes lineæ <lb/>&longs;unt ex centro. Ab eodem <lb/>igitur pondere nece&longs;&longs;e e&longs;t <lb/>eò celerius extremum li­<lb/>brilis ferri, quò plus ab agi­<lb/>na di&longs;titerit, & nonnulla in <lb/>paruis libris pondera im­<lb/>po&longs;ita non manife&longs;ta &longs;en­<lb/>&longs;ui e&longs;&longs;e, quæ in magnis ma­<lb/>nife&longs;ta erunt. Nihil enim <lb/>prohibet <expan abbr="minor&etilde;">minorem</expan> permea­<lb/>ri magnitudinem: quam vt <lb/>vi&longs;ui &longs;it manife&longs;ta.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Qvod vero propterea libræ.] <foreign lang="greek"><gap/>u<gap/>s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek"><gap/>u<gap/>n</foreign> <emph type="italics"/>præter iu­<lb/>gum, remigum &longs;edes, & tran&longs;tra curruum & nauium &longs;ignifi­<lb/>cat etiam libram & &longs;tateram, hinc illud Pythagoræ<emph.end type="italics"/> <foreign lang="greek">mh\zu<gap/>n u(per­<lb/><gap/>a/inein</foreign> <emph type="italics"/>&longs;tateram ne tran&longs;grediaris & vt annotat Budæus<emph.end type="italics"/> <foreign lang="greek">zu<gap/>a/­<lb/>tai</foreign> <emph type="italics"/>&longs;unt libripendes per vrbes con&longs;tituti, qui <expan abbr="põderibus">ponderibus</expan> præfecti ap­<lb/>pellantur, vnde Zygo&longs;tatica fides pro plena & examinata æquitate <lb/>à Zygo quod e&longs;t libra publice temperata & con&longs;tituta, vt quemad­<lb/>modum ait Vitruuius, vindicet ab iniquitate iu&longs;tis moribus vitam.<emph.end type="italics"/><lb/>
<arrow.to.target n="marg14"></arrow.to.target><lb/><emph type="italics"/>Statera enim dolo&longs;a, vt dixit Sapiens, abhominatio e&longs;t apud Deum, <lb/>& pondus æquum voluntas eius.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg14"></margin.target>Initio <lb/>cap. 11. <lb/>Prouerb.</s>
</p>
<p type="main">
<s>Agina fit cen­<lb/>
<figure id="fig12"></figure><lb/><expan abbr="trũ">trum</expan>.] <emph type="italics"/><expan abbr="Tand&etilde;">Tandem</expan> Ari­<lb/>&longs;toteles <expan abbr="accõmodat">accommodat</expan> <lb/>problema <expan abbr="propo&longs;itũ">propo&longs;itum</expan> <lb/>de libra ad circuli <lb/><expan abbr="proprietat&etilde;">proprietatem</expan> vltimò <lb/><expan abbr="demon&longs;tratã">demon&longs;tratam</expan>. Quod <lb/>vt intelligaturprius <lb/>in libra A D B C <lb/>H I partes notan­<lb/>dæ &longs;unt. Sit igitur <lb/>libræ librile, &longs;eu<emph.end type="italics"/>
<pb pagenum="46"/><emph type="italics"/>&longs;capus &longs;eu iugum A B, & C D trutina, &longs;eu an&longs;a, quæ pro com­<lb/>muni more &longs;emper e&longs;t perpendicularis ad horizontis planum: pun­<lb/>ctum vero C e&longs;t agina,<emph.end type="italics"/> <foreign lang="greek"><gap/>ar/tion</foreign> <emph type="italics"/>vocatur ab Ari&longs;totele, & e&longs;t cen­<lb/>trum libræ circa quod brachia C A, C B moueri intelliguntur <lb/>pro ponderibus impo&longs;itis in H vel I lancibus, quas<emph.end type="italics"/> <foreign lang="greek">pla/<gap/>as</foreign> <emph type="italics"/>Ari­<lb/>&longs;toteles appellabit, quo etiam nomine appellat librile, &longs;eu &longs;capum, &longs;eu <lb/>iugum A B. E&longs;t etiam recta E C F &longs;emper perpendicularis ip&longs;i <lb/>A B vtcunque moueatur. proinde perpendiculum appellatur, ab <lb/>alÿs æquamentum, ab alÿs trutina. His ita declaratis, ilico ex præ­<lb/>cedentibus con&longs;tat, quod C centro fixo, &longs;i A C vel C B lineæ quæ <lb/>ex centro, moueantur, de&longs;cribent circulum pro &longs;uo interuallo, in <lb/>minore librili, minorem: in maiore maiorem: &longs;icque cum magnitudo <lb/>&longs;patÿ motu tran&longs;iti, quò maior, eò vi&longs;ibilior, & quò etiam librilis <lb/>pars maior, eò mobilior, citius ex æquali pondere, & magis mouebitur <lb/>librile maius: <expan abbr="quã">quam</expan> minus, proinde etiam erit exactius. id e&longs;t minores <lb/>ponderum differentias patefaciet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>In magno <expan abbr="aut&etilde;">autem</expan> librili <expan abbr="id&etilde;">idem</expan> <lb/><expan abbr="põdus">pondus</expan> <expan abbr="magnitudin&etilde;">magnitudinem</expan> reddet <lb/><expan abbr="a&longs;pectabil&etilde;">a&longs;pectabilem</expan>. Nonnulla vero <lb/>in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> manife&longs;ta <expan abbr="sũt">sunt</expan>: &longs;ed <lb/>multo magis in maioribus. <lb/>quia in maioribus ab <expan abbr="eod&etilde;">eodem</expan> <lb/><expan abbr="põdere">pondere</expan> multo maior fit in­<lb/>clinationis magnitudo. Ob <lb/>id purpuræ venditores, vt <lb/><expan abbr="pend&etilde;do">pendendo</expan> <expan abbr="defraud&etilde;t">defraudent</expan>, a&longs;tutè <lb/>faciunt, qui aginam non in <lb/>medio collocant, & plum­<lb/>bum in altera librilis parte <lb/>illinunt, vel èligno quod <lb/>ad <expan abbr="radic&etilde;">radicem</expan> vergebat, <expan abbr="faciũt">faciunt</expan>, <lb/>quo inclinare <expan abbr="de&longs;iderãt">de&longs;iderant</expan>, vel <lb/>&longs;i no <expan abbr="dũ">dum</expan> habuerit. Ligni <expan abbr="enĩ">enim</expan> <lb/>grauior e&longs;t illa pars, vbi ra­<lb/>dix, E&longs;t vero nodus quæ­<lb/>dam radix.</s>
</p>
<pb pagenum="47"/>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>In magno autem.] <emph type="italics"/>Ex his colligitur fieri po&longs;&longs;e libram, quæ <lb/>examinabit granum vnum, immo grani &longs;ecundam, tertiam, <lb/>quartam partem. Quod e&longs;t aliquando nece&longs;&longs;arium cum in pretio&longs;is <lb/>rebus, vt ambra gri&longs;ea, mo&longs;cho, auro: tum in medicamentis potenti&longs;­<lb/>&longs;imis, vt elleboro, &longs;cammonio, opio. Huius autem libræ fabrica pen­<lb/>det è quatuor. Primum e&longs;t longitudo librilis. Secundum e&longs;t illius & <lb/>lancium materiæ &longs;umma leuitas. Nam tanto maior redditur ratio <lb/>ponderis exigui. Tertium e&longs;t librilis firmitas, & rectitudo, ideo de­<lb/>bet fieri ex chalybe purgato, durato, tenuißimo, naturaque leui. <lb/>Quartum e&longs;t trutinæ po&longs;itio in exqui&longs;itè medio librilis mobilis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Ob id purpuræ.] <emph type="italics"/>Alia e&longs;t ratio qua rur&longs;us confirmatur libri­<lb/>le maius e&longs;&longs;e exactius. Ducitur ex effectu eorum qui fraudare <expan abbr="volũt">volunt</expan>, <lb/>emptores. Imponunt enim pondus rei venditæ leuius æquipondio<emph.end type="italics"/><lb/>(<foreign lang="greek">sfai/rwma</foreign> <emph type="italics"/>po&longs;tea vocabitur) in librilis brachio longiore: &longs;icque, <lb/>vel æquiponderat vel etiam præponderat: & ita paucum pro multo <lb/>vendunt. Nec tamen vacua libra ponderibus, iniqua videtur. quia <lb/>pars librilis altera, vt æquiponderet: plumbum habebit illitum, vel <lb/>etiam ex ligno erit duriore & nodo&longs;iore, &longs;icque den&longs;iore, & ideo <lb/>grauiore. Vel pars librilis longior erit tenuior, vel perforata in ali­<lb/>quot locis exiguis foraminibus. Vnde vnius grauitas <expan abbr="lõgitudinis">longitudinis</expan> al­<lb/>terius rationem compen&longs;at. Cardanus docuit libræ metallicæ fabri-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg15"></arrow.to.target><lb/><emph type="italics"/>cam, quæ pro deunce exhibeat a&longs;&longs;em, licet vacua in&longs;ta videatur. Hæc <lb/>autem à me hîc ita recitantur, non vt quis abutatur. Abhominatio<emph.end type="italics"/><lb/>
<arrow.to.target n="marg16"></arrow.to.target><lb/><emph type="italics"/>enime&longs;t apud Deum, vt iterum ait &longs;apiens, pondus & pondus, & <lb/>&longs;tatera dolo&longs;a non e&longs;t bona: &longs;ed vt à callidis i&longs;tis mercatoribus &longs;ibi <lb/>præcaueat emptor. Fraudem autem i&longs;tam deteget, &longs;i pondus & æqui­<lb/>pondium tran&longs;mutentur de lance in lancem. Quod enim ante æqui­<lb/>ponderabat, tran&longs;latum in alteram lancem no <gap/>amplius æquiponde­<lb/>rabit duplici de cau&longs;a, & quod æquipondium grauius &longs;it, & quod <lb/>librilis in parte maiore &longs;it.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg15"></margin.target>Lib. 1. de <lb/>&longs;ubt,</s>
</p>
<p type="margin">
<s><margin.target id="marg16"></margin.target>Prouerb. c. <lb/>10.</s>
</p>
<p type="main">
<s>Purpuræ venditores.] <foreign lang="greek">a(lour<gap/>pw/lom</foreign> <emph type="italics"/>dicuntur quia<emph.end type="italics"/> <foreign lang="greek">a(/lour­<lb/>gon</foreign> <emph type="italics"/>purpura e&longs;t<emph.end type="italics"/> <foreign lang="greek"><gap/>po\ tou_ a(/ls kai\ e)/r<gap/>n</foreign> <emph type="italics"/>à maris opere. quia purpura è<emph.end type="italics"/><lb/>
<arrow.to.target n="marg17"></arrow.to.target><lb/><emph type="italics"/>concha marina colligitur. E&longs;t <expan abbr="aut&etilde;">autem</expan>, vt author e&longs;t Plinius, ille magni<emph.end type="italics"/>
<pb pagenum="48"/><emph type="italics"/>pretÿ flos tingendis regum ve&longs;tibus expetitus. Hunc in medÿs fau­<lb/>cibus conchæ gerunt, candida quadam vena conclu&longs;um colore ni­<lb/>gricantis ro&longs;æ pellucidum.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg17"></margin.target>Lib. 9. cap. <lb/>36.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>3. Propter quid, &longs;i in &longs;upe­<lb/>riore librilis parte fuerit <lb/>agina, <expan abbr="quãdo">quando</expan> <expan abbr="põdus">pondus</expan>, ali­<lb/>quod depre&longs;&longs;erit, rur&longs;us <lb/>librile referatur: At &longs;i in <lb/>inferiore, non refertur.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Propter quid &longs;i in &longs;upe­<lb/>riore librilis parte fuerit <lb/>agina, cum præ <expan abbr="põdere">pondere</expan> <expan abbr="de-mi&longs;sũ">de­<lb/>mi&longs;sum</expan> e&longs;t, hoc &longs;ublato rur­<lb/>&longs;us redit: Sed &longs;i in inferiore <lb/>fuorit, <expan abbr="nõ">non</expan> redit, &longs;ed manet? <lb/>an quia &longs;uperne exi&longs;tente <lb/>agina, librilis plus erit ex­<lb/>tra perpendicularem. E&longs;t <lb/>enim trutina perpendicu­<lb/>laris. <expan abbr="Itaq;">Itaque</expan> nece&longs;&longs;e e&longs;t, quod <lb/>plus e&longs;t deor&longs;um vergere, <lb/>incumbente <expan abbr="põdere">pondere</expan> in par­<lb/>te librilis &longs;ur&longs;um rapta, do­<lb/>nec venerit eò, vbi ad per­<lb/>pendicularem ip&longs;am librile <lb/>bifariam diuiditur. E&longs;to li­<lb/>brile rectum <foreign lang="greek">b y,</foreign> trutina <foreign lang="greek">a <lb/>d</foreign>: at hoc deor&longs;um demi&longs;&longs;o <lb/>&longs;it perpendicularis <foreign lang="greek">a d m.</foreign><lb/>Si igitur pondus impona­<lb/>tur in lance <foreign lang="greek">b,</foreign> erit <foreign lang="greek">b</foreign> vbi <foreign lang="greek">e, <lb/>& g</foreign> vbi <foreign lang="greek">z.</foreign> Itaque recta bi­<lb/>fariam diuidens librile, pri. <lb/>mùm quidem erat <foreign lang="greek">a d m,</foreign><lb/>ip&longs;a <expan abbr="perp&etilde;dicularis">perpendicularis</expan> <expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan>:
<pb pagenum="49"/><gap/><lb/>At cum pondus impo&longs;itum <lb/>e&longs;t, e&longs;t <foreign lang="greek">f p.</foreign> Itaque librilis <lb/><foreign lang="greek">e c</foreign> id quod e&longs;t extra per­<lb/>pendicularem <foreign lang="greek">a m</foreign> in ea <lb/>quæ e&longs;t <foreign lang="greek">f p</foreign> plus e&longs;t: quam <lb/>dimidium. Si igitur pon­<lb/>dus, quod erat in <foreign lang="greek">e</foreign> tolla­<lb/>tur, nece&longs;&longs;e e&longs;t <foreign lang="greek">z</foreign> deor&longs;um <lb/>ferri. E&longs;t enim <foreign lang="greek">e</foreign> minus: &longs;i <lb/>igitur in &longs;uperiori parte <lb/>fuerit agina, rur&longs;us ob id li­<lb/>brile refertur: &longs;i vero in in­<lb/>feriori parte &longs;ubijciatur a­<lb/>gina, contra euenit. Pars <lb/>enim maior dimidia libri­<lb/>lis e&longs;t id, quod infra e&longs;t, & <lb/>quod à perpendiculari &longs;e­<lb/>catur. Ideo non refertur. <lb/>Leuior enim e&longs;t pars &longs;ur­<lb/>&longs;um lata. E&longs;to librile <foreign lang="greek">n c</foreign> re­<lb/>ctum, perpendicularis vero <lb/><foreign lang="greek">k l m,</foreign> quæ bifariam diui­<lb/>dat <foreign lang="greek">n c,</foreign> & impo&longs;ito pon­<lb/>dere in <foreign lang="greek">n,</foreign> &longs;it <foreign lang="greek">n</foreign> vbi e&longs;t <foreign lang="greek">o, & <lb/>x</foreign> vbi e&longs;t <foreign lang="greek">r, & k l</foreign> vbi <foreign lang="greek">l <expan abbr="q.">que</expan></foreign><lb/>Itaque maior erit <foreign lang="greek">l o</foreign> quam <lb/><foreign lang="greek">l r</foreign> ip&longs;o <foreign lang="greek">x l <expan abbr="q.">que</expan></foreign> Igitur &longs;u­<lb/>blato pondere nece&longs;&longs;e e&longs;t <lb/>manere. Incumbit enim <lb/>ceu pondus exce&longs;&longs;us medietatis, qui e&longs;t in <foreign lang="greek">l o.</foreign></s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Propter quid.] <emph type="italics"/>In hoc capite proponitur aliud di&longs;cutiendum <lb/>problema de libra. De qua quæruntur duo. Primum cur &longs;i cen­<lb/>trum libræ &longs;it in &longs;uperiori parte librilis &longs;itum, cum pondere impo&longs;ito <lb/>deor&longs;um venerit librilis vna pars, altera &longs;ur&longs;um, eodem &longs;ublato, & <lb/>librili libero relicto brachia librilis redeant ad pri&longs;tinum locum.<emph.end type="italics"/>
<pb pagenum="50"/><emph type="italics"/>Secundum, cur &longs;i centrum eius &longs;it in inferiori parte librilis &longs;itum, <lb/>& pondere impo&longs;ito, parteque librilis vna deor&longs;um demi&longs;&longs;a, eodem <lb/>&longs;ublato librile liberum relictum non redeat: &longs;ed in eo &longs;itu maneat. <lb/>Tertium adiungitur à Guido V baldo (è quo quæ hîc dicemus omnia <lb/>ferè depromp &longs;imus) non minus quæ&longs;itu dignum. Cur &longs;i centrum &longs;it <lb/>exqui&longs;ite librilis medium, librile retinebit &longs;itum quemlibet datum. <lb/>Quæ vt intelligantur &longs;cire conuenit vel libram hic capi, cuius librile <lb/>latitudinem aliquam effatu dignam habet, vel cum quo trutina ita <lb/>connexa e&longs;t, vt ad vnius motum moueatur alterum, & contra: quia <lb/>totum continuum e&longs;t. In extremo autem trutinæ, non eo quidem, <lb/>quod e&longs;t ei cum librili <expan abbr="cõ-">con-</expan><emph.end type="italics"/><lb/>
<figure id="fig13"></figure><lb/><emph type="italics"/>mune: &longs;ed altero, <expan abbr="c&etilde;trum">centrum</expan> <lb/>circa quod <expan abbr="tanquã">tanquam</expan> <expan abbr="fixũ">fixum</expan>, <lb/>ip&longs;a moueantur, <expan abbr="&longs;itũ">&longs;itum</expan> &longs;it. <lb/>Sine horum enim altero <lb/>modo intelligi <expan abbr="nõ">non</expan> pote&longs;t, <lb/>quomodo librile, quod <lb/>&longs;ecundum longitudinem <lb/>e&longs;t, vt vna recta li­<lb/>nea, admittat dif-<emph.end type="italics"/><lb/>
<figure id="fig14"></figure><lb/><emph type="italics"/>ferentias illas loci <lb/><expan abbr="&longs;ursũ">&longs;ursum</expan> deor&longs;um. At <lb/>&longs;iue hoc: &longs;iue illo <lb/>modo librile con­<lb/>&longs;tituaturproblema <lb/>hîc ab Ari&longs;totele <lb/><expan abbr="po&longs;itũ">po&longs;itum</expan> habebit non <lb/>&longs;olum <expan abbr="experientiã">experientiam</expan>, <lb/>&longs;ed & rationem <lb/>&longs;ibi &longs;uffragantem, <lb/>Exemplum igitur <lb/>librilis primi mo­<lb/>di <expan abbr="cũ">cum</expan> latitudine &longs;it <lb/>A B, cuius <expan abbr="centrũ">centrum</expan> <lb/>in &longs;uperiori parte <lb/>latitudinis &longs;it C,<emph.end type="italics"/>
<pb pagenum="51"/><emph type="italics"/>cum &longs;uo &longs;u&longs;pen&longs;orio &longs;eu trutina C D: vel &longs;it & in inferiori parte C <lb/>centrum cum &longs;uo fulcro quod pro trutina e&longs;t etiam C D, & <lb/>in vtroque in-<emph.end type="italics"/><lb/>
<figure id="fig15"></figure><lb/><emph type="italics"/>telligatur linea <lb/>recta per cen­<lb/>trum tran&longs;ire <lb/>perpendiculari­<lb/>ter ad planum <lb/><expan abbr="horizõtis">horizontis</expan> D E.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Exemplum li­<lb/>brilis <expan abbr="cũ">cum</expan> truti­<lb/>na immobiliter <lb/>connexi &longs;it vbi<emph.end type="italics"/><lb/>
<figure id="fig16"></figure><lb/><emph type="italics"/>e&longs;t librile GH, <lb/>& trutina K <lb/>L, & centrum <lb/>libræ L.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia &longs;u­<lb/>perne.] <emph type="italics"/>In­<lb/>tellectis libræ <lb/>generibus ad propo&longs;itum problema accommodatis, nunc eius partis <lb/>prioris adfertur &longs;olutio. quia in vtroque genere librilis cum centrum <lb/>libræ &longs;upernam partem occupat, & à perpendiculari intellecta per <lb/>admotum pondus librile à paralleli&longs;mo cum horizonte di&longs;ce&longs;&longs;erit, <lb/>pars quæ &longs;uperior fit, maior e&longs;t parte inferiore. Maior autem grauior <lb/>e&longs;t. Totum enim librile &longs;upponitur e&longs;&longs;e materiæ vnigeneris. Redit <lb/>igitur libera relicta, &longs;itumquerecuperat, vbi paria momenta <expan abbr="æqui-ponderãt">æqui­<lb/>ponderant</expan>. Talis <expan abbr="aut&etilde;">autem</expan> e&longs;t is &longs;itus in quo llbrile <expan abbr="parallelũ">parallelum</expan> fit horizonti. <lb/>Contra &longs;i centrum infernam partem occupet, pars inferior librilis <lb/>maior e&longs;t. præponderat igitur. Non itaque per &longs;eredibit: &longs;ed &longs;itum <lb/>detracta decliuem retinebit: alias id graue, quo excedit, &longs;ur&longs;um &longs;ua <lb/>&longs;ponte a&longs;cenderet, contra def. grauis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Itaque librilis <foreign lang="greek">e z.</foreign>] <emph type="italics"/>Quod pars &longs;uperior librilis in vno &longs;itu <lb/>centri &longs;it maior, in altero &longs;it minor, non e&longs;t probatum ab Ari&longs;totele: <lb/>&longs;ed ex fabrica librilis vtriu&longs;que generis res ilico fit euidens, etiam <lb/>pro Ari&longs;totelis characteribus no&longs;tris ad diagrammata adiunctis.<emph.end type="italics"/>
<pb pagenum="52"/><emph type="italics"/>Nam in librili primi modi cum obliquatur C F perpendiculum li­<lb/>brilis, quod ip&longs;um perpetuò bifariam &longs;ecat, digreditur à perpendicu­<lb/>lari intellecta, quam &longs;ecat<emph.end type="italics"/><lb/>
<figure id="fig17"></figure><lb/><emph type="italics"/>in centro, &longs;icque triangu­<lb/>lum con&longs;tituit comprehen­<lb/>dens aliquam partem al­<lb/>terutrius brachÿ nempe F <lb/>C E, vel R C F, quæ &longs;ic <lb/>detracta vni, & alteri ad­<lb/>dita, reddit hoc à quo de­<lb/>trahitur minus, & eius <lb/>detractæ partis duplo alte­<lb/>rum <expan abbr="brachiũ">brachium</expan> maius. At­<lb/>que hic modus conuenit <lb/>&longs;en&longs;ui Ari&longs;totelis, vt qui <lb/>eo v&longs;urus &longs;it capite &longs;equen­<lb/>ti in problemate de vecte. <lb/>Et etiam pulchrè re&longs;pon-<emph.end type="italics"/><lb/>
<figure id="fig18"></figure><lb/><emph type="italics"/>det cau&longs;æ iam dictæ ex <lb/>proprietate circuli, quate­<lb/>nus eius radÿ breuiores <lb/>&longs;unt aut longiores, & pro­<lb/>pter i&longs;tam inæqualitatem <lb/>tardiores aut velociores.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In librili vero &longs;ecundi <lb/>modi res erit adhuc aper­<lb/>tior. Centro &longs;iquidem L, <lb/>& interuallo L K circu­<lb/>lus de&longs;cribatur, & K <lb/><expan abbr="motũ">motum</expan> &longs;it in P propter vim <lb/>allatam: tum L K per­<lb/>pendicularis intellecta pro­<lb/>ducta &longs;ecabit brachium <lb/>P H, id e&longs;t K H, vt in <lb/>M: &longs;icque P M accre&longs;cet pro longitudine ideo & grauitate ad <lb/>P G, redibit igitur G P M.<emph.end type="italics"/></s>
</p>
<pb pagenum="53"/>
<figure></figure>
<p type="main">
<s><emph type="italics"/>Contra in alte­<lb/>ro diagrammate <lb/>eiu&longs;modi &longs;ectio <lb/>fiet, vt in O, & <lb/>&longs;ic pars O P ac­<lb/>cre&longs;cet ad P H: <lb/>&longs;icque tota O P <lb/>H vt longior, ita <lb/>grauior O G. <lb/>Manebit igitur <lb/>(præ&longs;uppo&longs;ito hoc <lb/>quod ab H <expan abbr="app&etilde;&longs;a">appen&longs;a</expan><emph.end type="italics"/><lb/>
<figure id="fig19"></figure><lb/><emph type="italics"/>lanx in&longs;ideat ter­<lb/>ræ vel alicui ful­<lb/>cro. Sed & in li­<lb/>brilibus huius ge­<lb/>neris reditus & <lb/>non reditus alia <lb/><expan abbr="etiã">etiam</expan> cau&longs;a e&longs;t, &longs;ci­<lb/>licet quia <expan abbr="nullũ">nullum</expan> <expan abbr="c&etilde;">cem</expan> <lb/><expan abbr="trũ">trum</expan> grauitatis ma­<lb/>net ni&longs;i &longs;u&longs;tinea­<lb/>tur à linea <expan abbr="per-p&etilde;diculari">per­<lb/>pendiculari</expan> ad pla­<lb/>num horizontis. quod e&longs;t demon&longs;tratum ab V baldo prop. 1. lib. de lib. <lb/>Atque P e&longs;t centrum grauitatis magnitudinis compo&longs;itæ è duobus <lb/>brachÿs librilis G H, & lancibus ponderibu&longs;que vtrimque æqui­<lb/>ponderantibus, &longs;i intelligantur admota, vt patet ex prop. 4. lib. 1. <lb/>Archimed. de æquipond. L K vero linea e&longs;t perpendicularis ad pla­<lb/>num horizontis. Non igitur P liberum relictum manebit ita vt e&longs;t <lb/>G P M H: Sed & redibit ex natura grauium quou&longs;que occupe<gap/><lb/>punctum k in perpendiculari horizontis, à qua quia per extre­<lb/>mum L fixa e&longs;t, &longs;u&longs;tinebitur. At G O P H manebit &longs;ic, nec <lb/>redibit ad G k H, quia, quod e&longs;&longs;et contra naturam, a&longs;cenderet. <lb/>Vbiautem centrum librilis e&longs;t exqui&longs;itè medium, vt C ip&longs;ius A B <lb/>cum trutina C D mobili, &longs;eu &longs;upra, &longs;eu infra po&longs;ita &longs;it, quocunqu<gap/><emph.end type="italics"/>
<pb pagenum="54"/>
<figure id="fig20"></figure><lb/><emph type="italics"/>in &longs;itu fuerit A B vt <lb/>in G H manebit, tum <lb/>quia brachia manent <lb/>æqualia, tum quia cen­<lb/>trum grauitatis C &longs;em­<lb/>per erit in perpendicu­<lb/>lari horizontis, &longs;ecun­<lb/>dum quam & ad quam <lb/>magnitudo compo&longs;ita <lb/>exbrachÿs C A, C B & lancibus & ponderibus æquiponderan­<lb/>tibus, &longs;i impo&longs;ita &longs;int, fertur, &longs;ed &longs;u&longs;tinetur linea C D vel C E <lb/>fixa. Et &longs;ic patet &longs;olutio tertiæ partis huius problematis ab Ari&longs;totele <lb/>prætermi&longs;&longs;æ. Rarò tamen huic demon&longs;trationi licet veræ, experien­<lb/>tia re&longs;pondet, propter in&longs;trumentorum materiam Phy&longs;icam, in qua <lb/>exacte medium con&longs;tituere non datur in puncto geometrico, vtcum­<lb/>que tamen alias re&longs;pondet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>4. Potentiæ vectis cau&longs;a.</s>
</p>
<p type="main">
<s><gap/><lb/>
<arrow.to.target n="marg18"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg18"></margin.target>Videtur hic <lb/>aliquid de­<lb/>e&longs;&longs;e & fortè. <lb/><emph type="italics"/>Radius au­<lb/>tem minor <lb/>tardius.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cur vires exiguæ vecte <lb/>magna <expan abbr="mou&etilde;t">mouent</expan> onera, vt e&longs;t <lb/>in principio <expan abbr="dictũ">dictum</expan> in&longs;uper <lb/><expan abbr="adiici&etilde;do">adiiciendo</expan> vectis ip&longs;i^{9} onus. <lb/>Facilius enim e&longs;t min^{9} mo­<lb/>uere onus: minus vero e&longs;t <lb/>ab&longs;que vecte. An quia ve­<lb/>ctis cau&longs;a e&longs;t, qui & in&longs;tar <lb/>libræ deor&longs;um habet <expan abbr="agi-nã">agi­<lb/>nam</expan>, & in inæqualia diui&longs;us <lb/>e&longs;t? E&longs;t enim pre&longs;&longs;io pro <lb/>agina. ambæ enim &longs;tant vt <lb/>centrum. Quoniam vero <lb/>celerius ab æquali ponde­<lb/>re mouetur radius maior.
<pb pagenum="55"/><gap/><lb/>Sunt vero tria circa|, <expan abbr="vect&etilde;">vectem</expan> <lb/>pre&longs;&longs;io quidem e&longs;t |agina & <lb/><expan abbr="centrũ">centrum</expan>, duo etiam pondera <lb/>mouens &longs;cilicet, & mobile.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Potentiæ vectis cau&longs;a.] <emph type="italics"/>Vectis definitus e&longs;t à Budæo bacu­</s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg19"></arrow.to.target><lb/>lus validus per mediam machinam traiectus, quo manuducto <lb/>machina, dum ver&longs;atur, funem ductarium aduoluit. Hæc definitio <lb/><expan abbr="nimiũ">nimium</expan> angu&longs;ta e&longs;t, neque huic loco <expan abbr="cõuenit">conuenit</expan>, neque &longs;atis rei ip&longs;i. vectis <lb/>enim per &longs;e machina e&longs;t. E&longs;tigitur vectis palus oblongior vno <expan abbr="&longs;uorũ">&longs;uorum</expan> <lb/>extremorum acutus, altero obtu&longs;us ex ligno vel ferro inflexibi­<lb/>lis ad <expan abbr="commou&etilde;-">commouen-</expan><emph.end type="italics"/><lb/>
<figure id="fig21"></figure><lb/><emph type="italics"/>da onera factus, <lb/>vt e&longs;t A B. pars <lb/>obtu&longs;a caput: pars acuta lingula vocatur. Hoc vtendi modus duplex <lb/>e&longs;t. Primus cum lingula &longs;ubditur oneri commouendo, & vecti ip&longs;i <lb/>quam proxime lingulæ &longs;ubditur corpu&longs;culum firmum, quod Græcis<emph.end type="italics"/><lb/><foreign lang="greek">(w_omo/xlion,</foreign> <emph type="italics"/>Vitruuio preßio dicitur. Huius figura e&longs;t ferè quæ­<lb/>uis obuia: expeditior tamen e&longs;t, &longs;i &longs;it pri&longs;mation, cuius aduer&longs;a duo <lb/>plana æqualia &longs;imilia, parallela, &longs;int trian-<emph.end type="italics"/><lb/>
<figure id="fig22"></figure><lb/><emph type="italics"/>gula, vte&longs;t A D B C E F. Huius enim <lb/>pri&longs;matis lateri vni tanquam centro, &longs;i <lb/>vectis innitentis caput deprimatur, nece&longs;&longs;e <lb/>erit ilico lingulam, & con&longs;equenter lin­<lb/>guæ innixum onus attolli, & ideo com­<lb/>moueri. Atque hic e&longs;t primus modus vtendi vecte frequentißimus: <lb/>&longs;ed & e&longs;t alter non multò infrequentior, cum lingula oneri, vt an­<lb/>tè, &longs;ubdita nullo &longs;ubdito præter &longs;olum immobile vecti ip&longs;i hypo­<lb/>mochlio, vectis caput attollitur. Hoc enim &longs;ur&longs;um lato omnes etiam <lb/>vectis partes attolli nece&longs;&longs;e e&longs;t præter extremum lingulæ fixum, quo<gap/><lb/>centri immobilis rationem &longs;umit, & terræ vel alÿ corpori immobili <lb/>tanquam hypomachlio innititur. Proinde etiam onus ad partis ve­<lb/>ctis cui impo&longs;itum e&longs;t, motionem mouebitur, & tunc non &longs;olum ele­<lb/>uatur: &longs;ed & &longs;i opus e&longs;t, fiatque vectis perpendicularis &longs;olo, &longs;ecundum<emph.end type="italics"/>
<pb pagenum="56"/><emph type="italics"/>latus impellitur. Vtrumque vectis v&longs;um Vitruuius cap. 8. lib. 10. &longs;ic <lb/>explicuit. Ferreus vectis cum e&longs;t commotus ad onus, quod manuum <lb/>multitudo non pote&longs;t mouere, &longs;uppo&longs;ita vti centro cito porrecta pre&longs;­<lb/>&longs;ione, quòd Græci<emph.end type="italics"/> <foreign lang="greek">(w_omo/xlion</foreign> <emph type="italics"/>appellant, & vectis lingua &longs;ub <lb/>onus &longs;ubdita, caput eius vnius hominis viribus pre&longs;&longs;um, id onus ex­<lb/>tollet. Item &longs;i &longs;ub onus vectis ferrei lingula &longs;ubiecta fuerit, neque <lb/>caput eius preßione in imum: &longs;ed aduer&longs;us in altitudinem extolletur, <lb/>lingula fulcta in areæ &longs;olo habebit eam pro onere, oneris <expan abbr="aut&etilde;">autem</expan> ip&longs;ius <lb/>angulum pro preßione: ita non tam faciliter quam per preßionem, <lb/>&longs;ed aduer&longs;us nihilominus in pondus oneris erit <expan abbr="excitatũ">excitatum</expan>. Hæc Vitr. <lb/>à quo parum di&longs;&longs;entimus dum in &longs;ecundo v&longs;u vectis ponit &longs;olum &longs;eu <lb/>aream pro onere, nos pro centro & hypomochlio, quor&longs;um, dicemus<emph.end type="italics"/><lb/>
<arrow.to.target n="marg20"></arrow.to.target><lb/><emph type="italics"/>alibi. Galenus comparauit mu&longs;culum, qui e&longs;t in&longs;trumentum motus <lb/>voluntarÿ vecti. vtque pondera, inquit, quæ mouere manibus nequi­<lb/>mus, vectibus admotis mouere &longs;olemus. Ita cum membra corporis <lb/>mouere neruis non poßimus, ad ea mouenda mu&longs;culi nobis &longs;unt dati. <lb/>neruus enim in &longs;ingulis mu&longs;culis in fibras di&longs;&longs;olutus, ita cum fibris <lb/>copulatur atque coniungitur, vt ex vtri&longs;que vnum quoddam neruo­<lb/>&longs;um corpus effectum è corpore mu&longs;culi prodeat, qui tendo nomina­<lb/>tur. Atque hic quidem tendo ex in&longs;trumentis exoriens, habet illius <lb/>extremæ partis vectis rationem quæ ponderibus admouetur. Itaque <lb/>hic ÿs qui anatomen corporis humani re&longs;pexerunt <expan abbr="iucundũ">iucundum</expan> e&longs;t ip&longs;ius <lb/>membra, tanquam onera &longs;excentis mu&longs;culis, tanquam vectibus, tam <lb/>varie flecti, intendi &longs;ur&longs;um, ferri deor&longs;um, demitti ad latera, contor­<lb/>queri, circumuolui, & ad omnes motus, quos voluntas humana vti­<lb/>litate incitata præ&longs;cribit, educi, immo vero ÿ&longs;dem agentibus in quie­<lb/>te, & quam medici appellant in media figura, retineri.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg19"></margin.target>Annot. in <lb/>Pandectas.</s>
</p>
<p type="margin">
<s><margin.target id="marg20"></margin.target>Cap. 10 lib. <lb/>1 de plac. <lb/>H<gap/>pp. & <lb/><gap/></s>
</p>
<p type="main">
<s>Cur vires exiguæ.] <emph type="italics"/>Machina libræ duobus problematis expe­<lb/>dita e&longs;t: vectis deinde duodecim di&longs;&longs;eritur, è quibus primum e&longs;t ge­<lb/>nerale. Quæritur ergo hîc, cur homo verbi gratia pu&longs;illis viribus <lb/>amoueat vecte magna onera, coloßica vocat Vitruuius, id e&longs;t ma­<lb/>gnæ molis, quales &longs;unt coloßi. Et apud eundem coloßicotera compa­<lb/>ratiuum e&longs;t Græcum pro grandiora, va&longs;tiora, coloßi in&longs;tar ha­<lb/>bentia.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Facilius enim e&longs;t.] <emph type="italics"/>Ratio e&longs;t ad augendam problematis propo­<lb/>&longs;itide vecte difficultatem, quæ &longs;ic concludi pote&longs;t.<emph.end type="italics"/></s>
</p>
<pb pagenum="57"/>
<p type="main">
<s><emph type="italics"/>Facilius e&longs;t mouere paruum pondus quam magnum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Moles &longs;ine vecte e&longs;t pondus minus: quam cum vecte.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo facilius e&longs;t mouere molem &longs;ine vecte: quam cum vecte.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Propo&longs;itio e&longs;t vera, quia vires cuiu&longs;libet citius æquabunt, aut etiam <lb/>&longs;uperabunt pondus minus: quam maius. A&longs;&longs;umptio verò fallaciam <lb/>habet ex varia di&longs;po&longs;itione vectis cum mole. Namtotus, aut dimi­<lb/>dia, aut plu&longs;quam dimidia &longs;ui parte &longs;uppo&longs;itus, aut &longs;uperpo&longs;itus moli, <lb/>adÿceret pondus ponderi, &longs;icque moles pondero&longs;ior reuera euaderet. <lb/>At di&longs;ponitur aliter, nempe libræ in morem, ita vt parte exigua &longs;up­<lb/>ponatur moli mouendæ, & ab illi &longs;uppo&longs;ito fulcimento radius, &longs;eu <lb/>caput ad vim mouentem maius fit, &longs;icque di&longs;po&longs;itus pondus non <lb/>adÿcit moli.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia vectis.] <emph type="italics"/>Solutio e&longs;t problematis, quod vectis cum in <lb/>v&longs;um venitreferat libram, quæ latitudine effatu digna prædita, <lb/>& cuius agina deor&longs;um &longs;ita &longs;it, tum quæ in inæqualia brachia diui­<lb/>&longs;a eorum maius habeat ad partes mouentis, & &longs;ic tum ob libræ agi­<lb/>nam inferius po&longs;itam, tum ob radÿ mobilis magnitudinem vectis <lb/>facile & velociter mouetur, & vna cum vecte pondus alteri parti <lb/>incumbens aut annexum. Ratio hæc concluditur hoc &longs;yllogi&longs;mo.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Libra deor&longs;um habens aginam & brachium vnum longius, per <lb/>id facile deprimitur, & depre&longs;&longs;a manet: vt patuit ex præce­<lb/>dentibus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vectis e&longs;t libra deor&longs;um habens <expan abbr="aginã">aginam</expan>, & brachium vnum <lb/>longius (agina enim &longs;eu centrum fit hypomochlium, & <lb/>quidem ita vt ip&longs;am diuidat in partes inæquales, è quibus <lb/>quæ ad caput longior &longs;it, alioqui aliter in v&longs;um adhibitus <lb/>vis mouens non magis mouere pote&longs;t, quam &longs;ine vecte.)<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo vectis facile deprimetur, depre&longs;&longs;u&longs;que manebit, & ad eius <lb/>motum pondus incumbens mouebitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Quod autem e&longs;t mobile <lb/>ad mouens, id e&longs;t longitu­<lb/>do ad longitudinem reci­<lb/>procè. Semper &longs;ane quantò <lb/>longitudo magis di&longs;tabit à <lb/>pre&longs;&longs;ione, facilius mouebit
<pb pagenum="58"/><gap/><lb/>Cau&longs;a vero ante dicta e&longs;t: <lb/>quoniam radius maior ma­<lb/>iorem de&longs;cribit circulum. <lb/>Itaque ab eadem vi plus <lb/>mutabitur mouens illud, <lb/>quod plus di&longs;tat à pre&longs;&longs;io­<lb/>ne. Sit vectis <foreign lang="greek">a b,</foreign> pondus <lb/>vero <foreign lang="greek">g,</foreign> mouens autem <foreign lang="greek">d,</foreign><lb/>pre&longs;&longs;io <foreign lang="greek">e.</foreign> Ip&longs;um vero quod <lb/>mouerit <foreign lang="greek">d,</foreign> &longs;it vbi <foreign lang="greek">h,</foreign> & pon­<lb/>dus <foreign lang="greek">g</foreign> motum vbi <foreign lang="greek">k.</foreign></s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s><emph type="italics"/>Locus hic breuißimè totam vectis rationem explicat, vt &longs;ciatur <lb/>vectis v&longs;us, & quæ vires, ad quod onus mouendum &longs;ufficiant, <lb/>vel non &longs;ufficiant. Quæres vt intelligatur proponemus hoc theore­<lb/>ma. Vte&longs;t potentia ad pondus &longs;u&longs;tentum: ita e&longs;t pars vectis ab hypo­<lb/>mochlio ver&longs;us linguam, ad partem ab eodem hypomochlio ver&longs;us <lb/>caput, quod vt demon&longs;tretur. Sit vectis A B, & huius hypo­<lb/>mochlium C:<emph.end type="italics"/><lb/>
<figure id="fig23"></figure><lb/><emph type="italics"/><expan abbr="&longs;icq;">&longs;icque</expan> vectis duæ <lb/>partes C A ver­<lb/>&longs;us linguam, C <lb/>B ver&longs;us caput: <lb/>&longs;it quoque pon­<lb/>dus D &longs;u&longs;pen&longs;um ex perpendiculari A D: potentia autem &longs;u&longs;tinens <lb/>&longs;it in B. Dico potentiam in B e&longs;&longs;e ad pondus D: vt A C ad B <lb/>C (quod hic vocatur reciprocè) fiat ergo vt B C ad A C: ita <lb/>pondus D ad aliud, vt E. hoc igitur pondus E loco potentiæ ap­<lb/>pen&longs;um in B, ip&longs;um D pondere æquabit. Magnitudines enim in gra­<lb/>uitate commen&longs;urabiles æquiponderant, &longs;i permutatim &longs;u&longs;pendantur <lb/>in di&longs;tantijs &longs;ecundum grauitatum rationem <expan abbr="cõ&longs;titutæ">con&longs;titutæ</expan> prop. 6. lib. 1. <lb/>Archim. de æquipond. Et &longs;ic potentia æqualis ip&longs;i E ibidem con&longs;ti­<lb/>tuta pondere æquabit ip&longs;um D, id e&longs;t ne D deor&longs;um vergat, quod fa-<emph.end type="italics"/>
<pb pagenum="59"/><emph type="italics"/>eit pondus E, prohibebit. Nam æqualia ad idem eandem rationem <lb/>habent prop. 7. lib. 5. el. Sed E habet eam ad D, quam A C and B C, ex <lb/>fab. ergo potentia in B ad pondus D eam rationem habebit, quam <lb/>A C ad B C. Itaque vt e&longs;t potentia ad pondus &longs;u&longs;tentum: ita e&longs;t <lb/>pars vectis &c. quod fuit demon&longs;trandum. Ex quo duo corollaria <lb/>&longs;tatim eliciuntur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Primum. <emph type="italics"/>Hypomochlio bifariam diuidente vectem, potentia <lb/>æqualis requiritur: inæqualiter vero inæqualis. Et quidem &longs;i pars ab <lb/>hypomochlio ad caput &longs;it maius &longs;egmentum, potentia minor: &longs;i con­<lb/>tra pars ab eodem ad lingulam, potentia maior.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Secundum. <emph type="italics"/>Quò pars ab hypomochlio ad lingulam minor erit: <lb/>eò minor potentia ad &longs;u&longs;tinendum &longs;ufficiet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Reciproce.] <foreign lang="greek">*an<gap/>ipepo/n<gap/>hsis.</foreign> <emph type="italics"/>Reciprocatio quid &longs;it de&longs;umen­<lb/>dum e&longs;t ex Eucl. def. 2. lib. 6. vbi reciprocæ figuræ definiuntur cum in <lb/>vtraque figura antecedentes & con&longs;equentes rationum termini fue­<lb/>rint, id e&longs;t quando in altera quidem e&longs;t terminus antecedens primæ <lb/>rationis, & con&longs;equens &longs;ecundæ: in altera vero e&longs;t con&longs;equens pri­<lb/>mæ, & antecedens &longs;ecundæ. Quæ vt conuenire huic loco intelligan­<lb/>tur, &longs;umendum e&longs;t pondus mouendum &longs;imul cum parte vectis ab hy­<lb/>pomochlio ad lingulam cui appenditur pro vna figura: & potentia <lb/>mouens cum reliqua parte vectis pro altera figura. Sicque cum duæ <lb/>rationes fiant, vna ponderis ad potentiam: altera partis cui potentia <lb/>innititur ad partem cui pondus e&longs;t appen&longs;um. Clarum e&longs;t anteceden­<lb/>tes & con&longs;equentes rationum terminos in vtraque figura e&longs;&longs;e. Et <lb/>ideo figuras e&longs;&longs;e reciprocas.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Semper &longs;ane.] <emph type="italics"/>Hoc ex&longs;ecundo corollario clarum e&longs;t. Quo enim <lb/>pars vectis ad lingulam erit minor, eo pars ad caput erit maior. Et <lb/>&longs;ic &longs;i minor potentia ad &longs;u&longs;tinendum vel dimouendum &longs;ufficiet, <lb/>etiam alia quæuis paulo maior vis tanto facilius &longs;u&longs;tinebit, aut mo­<lb/>uebit pondus: quanto pars ad caput maior erit. Inæqualium enim <lb/>maior ad eandem maiorem rationem habet prop. 8. lib. 5. Sed & <lb/>huius rei cau&longs;a adfertur ex his quæ ante demon&longs;trata &longs;unt, nempt à <lb/>radio maiore maiorem de&longs;cribi circulum. Pars enim vectis ab hy­<lb/>pomochlio ad caput radÿ in&longs;tar e&longs;t maioris, qui depre&longs;&longs;us & ideo vo­<lb/>lutus circa hypomochlium fixum tanquam <expan abbr="c&etilde;trum">centrum</expan>, de&longs;cribit arcum <lb/>tanto maiorem: quanto ip&longs;e radius maior erat. Adde igitur & ex<emph.end type="italics"/>
<pb pagenum="60"/><emph type="italics"/>antecedentibus, velocius quoque moueri, quod hîc e&longs;t<emph.end type="italics"/> <foreign lang="greek">ra_|on kai\ ple/on <lb/>ki/nei<gap/>,</foreign> <emph type="italics"/>facilius & plus moueri. Ex his autem colligendum e&longs;t il­<lb/>lud, quod e&longs;t ab Archimede profectum problema admirabile. Da­<lb/>tum pondus data potentia mouere, locum habiturum in vecte, &longs;i tam <lb/>longum dari rerum natura pateretur, vt in eo maioris &longs;egmenti ad <lb/>minus ratio fieri po&longs;&longs;et paulo maior. ea, quæ dati ponderis e&longs;&longs;et ad da­<lb/>tam potentiam. Quod in quouis dato pondere cum rèrum natura non <lb/>patiatur, problema alioqui geometricè demon&longs;tratum, in v&longs;u ob ma­<lb/>teriæ &longs;atis longæ & firmæ <expan abbr="defectũ">defectum</expan> &longs;uæ rationi re&longs;pondere <expan abbr="nõ">non</expan> pote&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sit vectis <foreign lang="greek">a b</foreign>] <emph type="italics"/>huius diagrammatis expo&longs;itio &longs;i non imperfe­<lb/>cta e&longs;t, adfertur tantum ad o&longs;tendendum quod pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>ab eo cum<emph.end type="italics"/><lb/>
<figure id="fig24"></figure><lb/><emph type="italics"/>erat in<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>per depreßionem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>Sed adhuc <lb/>paulo ob&longs;curius. Apertius igitur &longs;ic. Sit vectis<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>pondus vero<emph.end type="italics"/> <foreign lang="greek">g,</foreign><lb/><emph type="italics"/>mouens autem<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>preßio<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Cum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>quod moueat, &longs;it vbi<emph.end type="italics"/> <foreign lang="greek">h</foreign><emph type="italics"/>: <lb/>& pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>motum erit vbi<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>quod ita &longs;e habere o&longs;tendit tertia <lb/>proprietas circuli, ex qua cap. 1. huius lib. o&longs;ten&longs;um e&longs;t diametri ex­<lb/>tremo vno deor&longs;um moto, alterum eodem tempore &longs;ur&longs;um moueri. E&longs;t <lb/>autem hic vectis<emph.end type="italics"/> <foreign lang="greek">b a,</foreign> <emph type="italics"/>vt diameter circuli cuius extremum<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>deor­<lb/>&longs;um cum ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>mouetur, alterum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;ur&longs;um &longs;imul moueri vt ad<emph.end type="italics"/> <foreign lang="greek">k,</foreign> <emph type="italics"/>ne­<lb/>ce&longs;&longs;um e&longs;t. Et ex his denique contendit Ari&longs;toteles o&longs;tendere circula­<lb/>rem motum omnium machinationum principia in &longs;e continere, vt <lb/>multis po&longs;tea &longs;pecialibus exemplis declarabit, in quibus & alijs om­<lb/>nibus, qui &longs;citè di&longs;tinguet, quid oneri re&longs;pondeat, pro quo &longs;it vectis, <lb/>quale &longs;it hypomochlium, vnde vis mouens habeatur, hic habebit <lb/>abundè, quid &longs;entiendum &longs;it.<emph.end type="italics"/></s>
</p>
<pb pagenum="61"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>5. Cur nauim mouent ma­<lb/>xime remiges, qui in <lb/>media naui &longs;edent.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur nauim <expan abbr="mou&etilde;t">mouent</expan> maxi­<lb/>me remiges mediani? An qa <lb/>remus e&longs;t vectis, pre&longs;&longs;io <expan abbr="&longs;i-quid&etilde;">&longs;i­<lb/>quidem</expan> &longs;calm^{9} efficitur. Hic <lb/>enim manet. <expan abbr="põdus">pondus</expan> autem <lb/>mare, quod rem^{9} propellit: <lb/><expan abbr="vect&etilde;">vectem</expan> vero mouens e&longs;t nau­<lb/>ta. Sed &longs;emper plus <expan abbr="põderis">ponderis</expan> <lb/>mouet, quanto plus motor <lb/>di&longs;titerit à pre&longs;&longs;ione. Ibi <lb/>enim maior fit radius, & <lb/>&longs;calmus pre&longs;&longs;io <expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan> <expan abbr="cen-trũ">cen­<lb/>trum</expan> e&longs;t. In nauis <expan abbr="aut&etilde;">autem</expan> medio <lb/><expan abbr="plurimũ">plurimum</expan> remi intus e&longs;t. Ete­<lb/>nim nauis ea parte lati&longs;&longs;ima <lb/>exi&longs;tit: ideo vtrin que remi <lb/>partem maiorem intus in <lb/>vtro que latere nauis <expan abbr="cõtin-git">contin­<lb/>git</expan> e&longs;&longs;e. <expan abbr="Itaq;">Itaque</expan> mouetur na­<lb/>uis, quia dum remus inni­<lb/>titur mari, <expan abbr="extremũ">extremum</expan> remi, <lb/>quod intus e&longs;t antror&longs;um <lb/>procedit: Tum que nauim <lb/>&longs;calmo <expan abbr="alligatã">alligatam</expan> procedere <lb/>nece&longs;&longs;e e&longs;t eò, vbi e&longs;t <expan abbr="extre-mũ">extre­<lb/>mum</expan> remi. Vbi enim remus <lb/><expan abbr="plurimũ">plurimum</expan> maris diuidit, eò <lb/>maxime nece&longs;&longs;e e&longs;t impel­<lb/>li. Ibi <expan abbr="aut&etilde;">autem</expan> <expan abbr="plurimũ">plurimum</expan> diuidit, <lb/>vbi maxima pars remi à <lb/>&longs;calmo e&longs;t. Propter id ma­<lb/>ximè mouent. Maxima <lb/>enim remi pars à &longs;calmo intus e&longs;t in medio nauis.</s>
</p>
<pb pagenum="62"/>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr remiges.] <emph type="italics"/>Specialia deinceps &longs;unt vndecim de vecte pro­<lb/>blemata, è quibus priora &longs;ex pertinent ad nauigandi artem, quæ <lb/>mirabilior &longs;it propter audaciam, an propter &longs;ubtilitatem inuentornm <lb/>ad bene <expan abbr="nauigãdum">nauigandum</expan> vtilium, dubium e&longs;t. Quid enim audacius quam <lb/>ventorum furorem, & maris rabiem contemnere, & vt in eo tran­<lb/>quilla &longs;int omnia, &longs;e tantum duorum &longs;patio digitorum à certa, eaque <lb/>aßidua morte di&longs;tare cernere! Semper enim<emph.end type="italics"/></s>
</p>
<p type="main">
<s>E&longs;t tua tam propè mors: quam propè cernis aquam. <lb/><emph type="italics"/>Et quod audacius e&longs;t tam longum iter, tam infidum ob &longs;copulos, vor­<lb/>tices, charybdes, Syllas, breuia, Syrtes &longs;ine vllis certis ho&longs;picÿs etiam <lb/>per &longs;ummas tenebras, in quibus homines alioqui domibus &longs;uis vrba­<lb/>nis conclu&longs;i, horrent, peragere? Et denique vbie&longs;t aquæ &longs;emper &longs;um­<lb/>ma copia, nullius rei tamen magis, quam aquæ penuria laborare? <lb/>Rectè &longs;anè dixit Horatius,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Illi robur & æs triplex</s>
</p>
<p type="main">
<s>Circa pectus erat, qui fragilem truci</s>
</p>
<p type="main">
<s>Commi&longs;it pelago ratem</s>
</p>
<p type="main">
<s>Primus.</s>
</p>
<p type="main">
<s><emph type="italics"/>Quid vero &longs;ubtilius, quam ob&longs;cura etiam nocte, cœlo nubilo, nullo <lb/>termino vel lapide certæ viæ indice per tam incertos maris patuli <lb/>tramites, rectum tamen iter, tanquam Deo aliquo duce tenere? Et <lb/>omnes mundi partes inui&longs;ere, importare, a&longs;portare omnia, quæ vbi­<lb/>que Dædala Tellus profert, omnibus communicare, tot ad id excogi­<lb/>ta&longs;&longs;e commoda, remos, malos, vela, Temonem, anchoram, pyxidem, <lb/>& quod &longs;upra fidem e&longs;t eodem vento contrarium iter agere. Sed & <lb/>i&longs;ta &longs;ubtilitas maior apparebit, cum quæ ad artem nauigandi perti­<lb/>nentia problemata hîc proponuntur ab Ari&longs;totele explicata fuerint.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>In medio nauis.] <emph type="italics"/>Nauis e&longs;t ingens machina oblonga, intus <lb/>caua, foris prominens, ad laterum media latior ad anteriorem par­<lb/>tem, quæ prora dicitur, acuta, ad po&longs;teriorem, quæ puppis dicitur ob­<lb/>tu&longs;ior, qua homines, & onera magna &longs;uper aquam vehuntur. An­<lb/>tiquißima nauium Argô à Fabro nauali, qui eam ædificauit, &longs;i <lb/>Apollonio creditur, nuncupata e&longs;t. Sic enim in<emph.end type="italics"/> <foreign lang="greek">*argonau<gap/>ikw_n.</foreign></s>
</p>
<pb pagenum="63"/>
<p type="main">
<s><foreign lang="greek">*nh_a d) )<gap/>pikrate/ws ar)gou_ (w_o<gap/>hmosu/nh|si</foreign></s>
</p>
<p type="main">
<s><foreign lang="greek">*ezwsan, pa/mw_rw<gap/>on e)u:<gap/>refei_ en)do<gap/>en o(/pl<gap/>.</foreign><lb/><emph type="italics"/>quæ &longs;ic reddidit Lazarus Bayfius.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Imprimis nauem diuinis artibus Argi,</s>
</p>
<p type="main">
<s>Extructam, intus compingunt habili armamento.</s>
</p>
<p type="main">
<s><emph type="italics"/>Tullius tamen in 1. Tu&longs;cula. dicit nominatam Argô, quia Argiui in <lb/>ea delecti viri vecti petebant Arietis pellem inauratam. Ante Ar­<lb/>goratibus, & paruis acatÿs homines tantum vehi &longs;olere, te&longs;tis e&longs;t <lb/>Diodorus &longs;iculus. Sed po&longs;t hanc, vt e&longs;t hominum ingenium ferax, <lb/>naues variæ confectæ &longs;unt: quarum aliæ velis, quæ onerariæ: aliæ <lb/>remis, quæ actuariæ: aliæ velis & remis, quæ longæ dictæ &longs;unt. Om­<lb/>nium præcipuæ partes &longs;unt anterior, quæ prora: po&longs;terior quæ puppis: <lb/>latus, quicquid dextra & &longs;ini&longs;tra inter proram & puppim in­<lb/>teriacens prominet: Ima, quæ in aqua immer&longs;a alueus & carina di­<lb/>citur. Sunt & in omnium ambitu fori, per quos nautæ cur&longs;itant, & <lb/>in proiecturis laterum tran&longs;tra, &longs;edes &longs;cilicet quibus acturi nauem <lb/>actuariam, vel longam in&longs;ident. Hi à remo Remiges dicti. E&longs;t au­<lb/>tem Remus palus longus & validus parte vna latior, quæ palmula <lb/>dicitur, reliqua <expan abbr="rotũdus">rotundus</expan>, cuius extremum, manubrium dicitur. Remi <lb/>fuerunt diuer&longs;æ magnitudinis pro proportione nauis agendæ, & in <lb/>eadem naui inæqualis, tractabilis tamen vnius validi remigis viri­<lb/>bus, propter libramentum, quod à plumbatis manubrÿs accedebat ni­<lb/>xus impellentium brachiorum adiuuans. Athenæus recitat inter <lb/>remos quo&longs;dam fui&longs;&longs;e tantæ longitudinis vt duodequadraginta cu­<lb/>bitos explerent, quod non erit incredibile memoria repetenti quarun­<lb/>dam nauium à veteribus fabricatarum va&longs;titatem, cuiu&longs;modi idem, <lb/>& Plutarchus memorant fui&longs;&longs;e illam dictam fluuialem Thalame­<lb/>gon, quam Ptolomæus Philopator in delicÿs habuit, non tam ad <lb/>v&longs;um: quam ad o&longs;tentationem, vt quæ in longitudinem ducentos ac <lb/>octoginta: & ab imo v&longs;que ad tran&longs;tra duodequinquaginta cubitos <lb/>pateret. Quæ amplitudo remi & nauis (quod alioqui e&longs;t nunc nobis <lb/>incredibile videntibus tantum naues, quæ à numero remigum in <lb/>vnoquoque tran&longs;tro &longs;edentium &longs;unt vniremes, triremes, quadrire­<lb/>mes, quinquiremes) probabile facit fui&longs;&longs;e in v&longs;u apud antiquos naues <lb/>multo plurium remigum decem, vndecim, viginti, multò plurium, in <lb/>vnoquoque tran&longs;tro & tran&longs;trorum multos, ordines vnde idem<emph.end type="italics"/>
<pb pagenum="64"/><emph type="italics"/>Athenæus recen&longs;et Philadelphum ad v&longs;um habui&longs;&longs;e trieconteres, id <lb/>e&longs;t tricenûm ordinum duas: I co&longs;erem vndm, quæ vicenûm erat, qua­<lb/>tuor quæ ternûm denûm, duas quæ duodenûm, quatuordecim quæ <lb/>vndenûm, & alias infra multas. Illam autem, quæ Philopatoris fuit, <lb/>fui&longs;&longs;e quinquaginta ordinum, & in &longs;ingulis tran&longs;tris quadraginta <lb/>remis, id e&longs;t, remigibus (nam & horum po&longs;tea numerum aßignat to­<lb/>tius fui&longs;&longs;e 4000.) agi. Remigum autem antiquitus, vt & hodie, <lb/>alÿ voluntarÿ: alÿ mercede <expan abbr="cõducti">conducti</expan>: alÿ vt adacti, vt in bello capti, <lb/>aut ab Archipyratis in locis maritimis <expan abbr="compreh&etilde;&longs;i">comprehen&longs;i</expan>, aut ob &longs;celera ad <lb/>remos à iudicibus damnati, <expan abbr="cõpediti">compediti</expan>, & alligati &longs;ine mercede etiam <lb/>nudi &longs;ub flagellis remigant. Omnes intres ordines reduxit quidam <lb/>Scholia&longs;tes Ari&longs;tophanis in Ranis locum illum,<emph.end type="italics"/> <foreign lang="greek">*kai\ <gap/>popa<gap/>d<gap/>_n e)s <lb/>to\ <gap/>o/ma tw_| <gap/>ala/maxi,</foreign> <emph type="italics"/>interpretans, dum dicit eos, qui in inferiore <lb/>parte nauis <expan abbr="eß&etilde;t">eßent</expan><emph.end type="italics"/> <foreign lang="greek"><gap/>alami_tas</foreign> <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="greek"><gap/>ala/maxas,</foreign> <emph type="italics"/>qui in medio<emph.end type="italics"/> <foreign lang="greek"><gap/>ou_tas,</foreign><lb/><emph type="italics"/>qui in &longs;uperiore<emph.end type="italics"/> <foreign lang="greek"><gap/>ani_tas</foreign> <emph type="italics"/>appellatos fui&longs;&longs;e. V nde nonnulli exi&longs;tima­<lb/>runt fui&longs;&longs;e naues, quæ in parte laterali &longs;upra aquas eminente, tria fo­<lb/>ramina<emph.end type="italics"/> <foreign lang="greek">xa<gap/>) i)/sin</foreign> <emph type="italics"/>eius partis habui&longs;&longs;e, <expan abbr="quorũ">quorum</expan> &longs;ingula &longs;uum remum <lb/>haberet alligatum. Vnde cum hiremi &longs;itu pro differentia loci &longs;ur­<lb/>&longs;um & deor&longs;um e&longs;&longs;ent di&longs;tincti: ita quoque &longs;uos remiges haberen<gap/><lb/>di&longs;tinctos: &longs;ed eam mentem non fui&longs;&longs;e &longs;cholia&longs;tis illius indicat, <lb/>quod paulò pò&longs;t &longs;ubiunxit.<emph.end type="italics"/> <foreign lang="greek"><gap/>ani/ths )<gap/>,</foreign> <emph type="italics"/>inquit<emph.end type="italics"/> <foreign lang="greek">o( w_ro\s ti/w\ w_ru/mnan, <lb/><gap/>ugi/ths o( meoos, <gap/>alami/ths o( w_ro\s ti/w\ w_rw/<gap/>an.</foreign> <emph type="italics"/>Thranites e&longs;t is, <lb/>qui ad puppim remigat, Zygites qui in media naui, Thalamites qui <lb/>ad proram, vbi manife&longs;tè &longs;uperiorem nauis partem explicat ad pup­<lb/>pim in qua &longs;edet gubernator, vt quæ altior e&longs;t: inferiorem ad proram, <lb/>quæ inferior e&longs;t, ne gubernatoris ob&longs;truat luminibus: ideo inter istos <lb/><gap/>gitæ &longs;unt, quos hic Ari&longs;toteles vocabulo compo&longs;ito<emph.end type="italics"/> <foreign lang="greek">e)x meoh_s kai\ <lb/>ne/ws</foreign> <emph type="italics"/>vocat me&longs;oneos. Sed hic non leuis obrepit controuer &longs;ia, & pro­<lb/>pter præ&longs;entem Ari&longs;totelis contextumante di&longs;&longs;oluenda, &longs;i pote&longs;t, ex <lb/>duobus locis, altero Thucydidis, altero Galeni. Ille enim li. 6. hæc hæ­<lb/>bet.<emph.end type="italics"/> <foreign lang="greek"><gap/>pihra/fxwn )<gap/>pi<gap/>o<gap/>a\s w_ro\s tw_| )ex dimwoi/ou mi<gap/>w_| dido/ntwn <lb/>pi_s <gap/>ari/tais,</foreign> <emph type="italics"/>Thranitæ præter &longs;tipendium publicum à trierarchis <lb/>donatiuum con&longs;equebantur, cuius rei cau&longs;a &longs;ubdita e&longs;t à &longs;choliaste, <lb/><expan abbr="quoniãremos">quoniarremos</expan> longiores trahebant, grauioreque labore vexabantur, <lb/>& adhuc hodie eò loci remigant ex omnibus delecti robu&longs;tiores, à <lb/>largis &longs;patulis Gallis dicti Eppaliers. Hic verò cap. 24. lib. I, de v&longs;u<emph.end type="italics"/>
<pb pagenum="65"/><emph type="italics"/>partium &longs;ic ait, In triremibus <expan abbr="remorũ">remorum</expan> extremitates ad vnam æqua­<lb/>litatem perueniunt, cum tamen ip&longs;i omnes non &longs;int æquales, etenim <lb/>etiam ibi medios eandem ob cau&longs;am maximos efficiunt, id e&longs;t, vt vi­<lb/>dere licet ex i&longs;to cap. Galen. citato, vt manus digiti inæ quales &longs;unt, <lb/>& medius longißimus ad firmam rerum apprehen &longs;ionem, & ap­<lb/>prehen&longs;arum retentionem, quod illius munus e&longs;t, quod non aliter fit <lb/>quam quum digitorum extremitates ad æqualitatem perueniunt: &longs;ic <lb/>ob nauigationis perfectionem in valido & faciliori nauis, quâ prora <lb/>&longs;pectat impul&longs;u po&longs;itam, remi facti &longs;unt inæquales, & corum me­<lb/>dius maximus: & horum quidem i&longs;ta inæqualitas ob eandem cau­<lb/>&longs;am, vt &longs;cilicet remorum extremitates &longs;imul omnes in remigatione <lb/>ad æqualitatem peruenirent. Ex his locis <expan abbr="vtriq;">vtrique</expan> conueniunt eiu&longs;dem <lb/>lateris remos e&longs;&longs;e inæquales: &longs;ed in hoc in &longs;igniter di&longs;crepant, quod <lb/>Galenus a&longs;&longs;erat medios, id e&longs;t remos Zygitarum, &longs;eu<emph.end type="italics"/> <foreign lang="greek">meoune/wn</foreign> <emph type="italics"/>e&longs;&longs;e <lb/>maximos: Ari&longs;toteles non hos, &longs;ed <expan abbr="Thranitarũ">Thranitarum</expan>. Et <expan abbr="verũ">verum</expan> dicere Gale­<lb/>num cogno&longs;cemus &longs;i prius intellexerimus quomodo remorum extre­<lb/>mitates in remigationis ictu ad æqualitatem perueniant. Ad hane <lb/>enim peruenire po&longs;&longs;unt duobus tantum modis, priore &longs;i intelligamus <lb/>tran&longs;trorum ordines<emph.end type="italics"/><lb/>
<figure id="fig25"></figure><lb/><emph type="italics"/>po&longs;itos e&longs;&longs;e ita, vt de­<lb/>&longs;inant &longs;ecundum re­<lb/>ctam A B parallelam <lb/>rectæ, quæ in naui ex­<lb/>tenderetur à prora ad <lb/>puppim cuiu&longs;modi e&longs;to <lb/>C D, cui etiam altera <lb/>E F in mari parallela <lb/>ad quam extremitates <lb/>peruenirent, ita vt <lb/>&longs;ponda nauis ad cuius <lb/>G H T &longs;calmos e&longs;&longs;ent <lb/>alligati remi K G P, <lb/>M H N, O T P. <lb/>Sed &longs;i &longs;ic præterquam <lb/>quod Thalamitarum <lb/>Zygitarum & Thra-<emph.end type="italics"/>
<pb pagenum="66"/><emph type="italics"/>nitarum Remi e&longs;&longs;ent æquales prop. 33. & 34. lib. I. elem. Eucl. quod <lb/>e&longs;t contra omnium &longs;ententiam, nauigatio e&longs;&longs;et valde impedita, eo <lb/>quod cum aqua ante nauim immota, ideoque difficilius cedens: tum <lb/>po&longs;t nauim etiam immota, minimeque eo rediens non compelleret. <lb/>Moueretur enim aqua &longs;ecundum rectam E F remorum extremita­<lb/>tes excipientem. Po&longs;terior igitur e&longs;t &longs;i de&longs;inant &longs;ecundum lineam pa­<lb/>rallelam &longs;pondæ nauis quæ &longs;emper e&longs;t<emph.end type="italics"/> <foreign lang="greek">w_<gap/>e<gap/>xoeidh\s.</foreign> <emph type="italics"/>Sic enim <lb/>Galenus <expan abbr="digitorũ">digitorum</expan> corpus valde <expan abbr="&longs;phæricũ">&longs;phæricum</expan> omnium à manu <expan abbr="appreh&etilde;-dendorũ">apprehen­<lb/>dendorum</expan> <expan abbr="difficillimũ">difficillimum</expan>, <expan abbr="apprehendentiũ">apprehendentium</expan> extremitates vult de &longs;inere in <lb/>eandem circuli ip&longs;um &longs;ecantis <expan abbr="peripheriã">peripheriam</expan>. Quomodo &longs;i pro E F recta <lb/>con&longs;tituamus pe-<emph.end type="italics"/><lb/>
<figure id="fig26"></figure><lb/><emph type="italics"/><expan abbr="riphericã">riphericam</expan> Q L N <lb/>P R ad quam <expan abbr="de-&longs;inãt">de­<lb/>&longs;inant</expan> prædicti re­<lb/>mi, non &longs;olum re­<lb/>morum erit inæ­<lb/>qualitas, & me­<lb/>dius erit maxi­<lb/>mus, vt in manu <lb/>digitus medius: <lb/>&longs;ed & nauigatio <lb/>facilius procedet <lb/>propter <expan abbr="cõtrarias">contrarias</expan> <lb/>cau&longs;as, quippè ve­<lb/>luti circulationes <lb/><expan abbr="vndarũ">vndarum</expan> circa na­<lb/>uim fient, vnde <lb/>quæ ante e&longs;t pro­<lb/>pul&longs;a aqua viam <lb/>aperiet nauigio, <lb/>& retro compre&longs;&longs;a, comprimen&longs; que nauigium propellet. Quod autem <lb/>M H N medius remus &longs;it longior remis O I P & K G L fa­<lb/>cile demon&longs;tratur ducta recta G I parallela ip&longs;i K. O. Sic enim <lb/>æquales &longs;unt G K, S M, I O prop. 33. & 34. lib. 1. æquales item <lb/>propter paralleli&longs;mum G L, H N, & I P. totæ igitur ex his <lb/>æquales axiom. 2. lib. 1. & ad earum vnam nempe ex S M, H N<emph.end type="italics"/>
<pb pagenum="67"/><emph type="italics"/>cum addatur in&longs;uper S H erit ip&longs;a M S H N remus medius <lb/>inæqualis, & vtrolibet aliorum maior ax. 4. Ergo maximus, quod <lb/>fuit probandum. Dicemus igitur &longs;cholia&longs;tis & Thucydidis locos <lb/>debere intelligi, non de totis remis: &longs;ed remorum partibus, quæ &longs;unt à <lb/>&longs;calmo ad mare proportione habita ad eas partes, quæ &longs;unt à &longs;calmo <lb/>ad manubrium. Thranitæ enim remus à &longs;calmo ad <expan abbr="extremũ">extremum</expan> palmu­<lb/>læ maiorem longè rationem habet ad partem, quæ e&longs;t ab eodem &longs;cal­<lb/>mo ad manubrium, id e&longs;t I P ad I O: quam zygitæ pars H N ad <lb/>partem H S M vt docebitur po&longs;tea. Et ea e&longs;t cau&longs;a cur zygites fa­<lb/>cilius & plus promoueat nauim: contra Thranites laborio&longs;ius & <lb/>minus, vt docebitur etiam. Atque &longs;ic &longs;int hi duo loci meo iudicio ex­<lb/>plicati. Cæterum Remiges, vt & hoc notatu pulchrum adÿciamus, <lb/>Remigando artificiosè &longs;imul omnes, quamuis quater mille, inter &longs;e <lb/>con&longs;entientes, alioqui illis corium fiagris tam fit maculo&longs;um quam <lb/>nutricis pallium, vel cur&longs;um nauis accelerant, vel inhibent, vel &longs;u&longs;ti­<lb/>nent, & vt ait Poeta,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Intentaque brachia remís</s>
</p>
<p type="main">
<s>Intenti expectant &longs;ignum.</s>
</p>
<p type="main">
<s><emph type="italics"/>Atque hæc &longs;int de nauigandi arte, nauibus, remis, remigibus, remi­<lb/>gum ordine, locis, & officio dicta, quibus etiam in his quæ po&longs;teà <lb/>dicentur, alia adÿcientur &longs;citu digna.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cur remiges.] <emph type="italics"/>E &longs;ex problematis quæ de vecte pertinent ad <lb/>nauigandi artem, primum per comparationem proponitur. E&longs;t autem <lb/>eiu&longs;modi cur remigum in medio &longs;edens plus mouet nauim: quam qui <lb/>ad proram, vel ad puppim. Re&longs;pondet idfieri, quia Remi pars à &longs;cal­<lb/>mo ad manubrium eius qui medius e&longs;t, maior e&longs;t ea, quæ e&longs;t à &longs;calmo <lb/>ad manubrium propè proram vel puppim &longs;edentis. Tum quia pars à <lb/>&longs;calmo ad palmulam eius qui medius e&longs;t plus maris diuidit, quam <lb/>pars à &longs;calmo ad palmulam aliorum. Tota igitur hæc quæ&longs;tio hoc <lb/>primario &longs;yllogi&longs;mo &longs;ic concludetur.<emph.end type="italics"/></s>
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<p type="main">
<s><emph type="italics"/>Ille remiges inter plus nauim promouet, cuius remi pars à &longs;cal­<lb/>mo ad manubrium maior e&longs;t: & cuius etiam pars à &longs;calmo <lb/>ad palmulam plurimum maris diuidit.<emph.end type="italics"/></s>
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<p type="main">
<s><emph type="italics"/>Sed remi pars à &longs;calmo ad manubrium cius qui in medio e&longs;t <lb/>maior: & ad palmulam eiu&longs;dem plus maris diuidit, <lb/>quam aliorum.<emph.end type="italics"/></s>
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<pb pagenum="68"/>
<p type="main">
<s><emph type="italics"/>Ergo qui in medio e&longs;t inter remiges plus promouet nauim.<emph.end type="italics"/></s>
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<p type="main">
<s>An quia remus.] <emph type="italics"/>Prior pars propo&longs;itionis præcedentis &longs;yllogi&longs;­<lb/>mi primo loco illu&longs;tratur, &longs;ic<emph.end type="italics"/></s>
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<p type="main">
<s><emph type="italics"/>Quantò maior e&longs;t vectis pars ab hypomochlio ad caput, tantò <lb/>vis mouens facilius & plus mouet, quia ibi maior e&longs;t radius. <lb/>Hoc ita e&longs;&longs;e patuit ex cap. præced. libri huius.<emph.end type="italics"/></s>
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<p type="main">
<s><emph type="italics"/>Sed pars remi à Scalmo ad manubrium e&longs;t pars vectis ab <lb/>hypomochlio ad caput. Nam remus e&longs;t vectis. per def. & <lb/>&longs;calmus e&longs;t hypomochlium. hic enim mouet, pondus vero <lb/>mobile mare, & vectem mouens, Remex.<emph.end type="italics"/></s>
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<p type="main">
<s><emph type="italics"/>Ergo is plus & facilius nauim promouebit, cuius remi pars à <lb/>&longs;calmo ad manubrium maior erit.<emph.end type="italics"/></s>
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<p type="main">
<s>In nauis medio.] <emph type="italics"/>A&longs;&longs;umptio e&longs;t primarÿ &longs;yllogi&longs;mi confir­<lb/>mata ex forma nauis quæ in &longs;ui medio latior e&longs;t & depreßior: in <lb/>prora autem & puppi arctior, & &longs;ublimior. Ergo &longs;uppo&longs;ito quod re­<lb/>mi omnium <expan abbr="remigũ">remigum</expan> &longs;int æquales, ex his, qui &longs;calmis proræ & puppis <lb/>&longs;unt alligati, partem extra <expan abbr="nau&etilde;">nauem</expan> longiorem habent, alias <expan abbr="eorũ">eorum</expan> palmu­<lb/>la non diuideret aquam, & intra nauem minorem: contra omnia in <lb/>his qui &longs;calmis mediorum laterum nauis alligantur. vt ex penultimo <lb/>diagrammate qualicunque intelligi pote&longs;t. In quo C e&longs;to prora, D <lb/>puppis, G &longs;calmus ad proram, T &longs;calmus ad puppim, H &longs;calmus <lb/>ad medium: vbi nauis latior & depreßior e&longs;t, ob id magis di&longs;tans à <lb/>recta A B, vtpote chorda arcus A G H T B, quæ de&longs;ignes <lb/>loca tran&longs;trorum & quæ à remis partes auferat æquales & partes <lb/>inæquales relinquat K G, M H, O T & quidem M H ma­<lb/>iorem. (quod nos &longs;equenti theoremate demon&longs;trabimus) igiur erit <lb/>totum ex M H, & adempto maius quam quod ex K G & <lb/>adempto, velex O T & adempto per ax. 5.<emph.end type="italics"/></s>
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<p type="main">
<s>Theorema. <emph type="italics"/>Si chorda rectas in circulo in&longs;criptas ad rectos &longs;e­<lb/>cet: &longs;ectarum pars, quæ de diametro ab&longs;cinditur, e&longs;t maxima, reli­<lb/>quarum quæ diametro propinquior remotiore maior e&longs;t. E&longs;to circu­<lb/>lus A D B E, in quo rectam A B diametrum &longs;ecet chorda D <lb/>E ad rectos vt & K I, L H: & &longs;int &longs;egmenta C B, è dia­<lb/>metro: F I è propinquiore: G H è remotiore. Dico C B e&longs;&longs;e <lb/>maiorem quam F I: & F I quam G H. Per punctum M cen­<lb/>trum circuli repertum prop. 1. lib. 3. ducatur parallela M N O P<emph.end type="italics"/>
<pb pagenum="69"/><emph type="italics"/>rectæ C D prop. 31. lib. 1. &longs;icque parallelogramma &longs;unt O F &<emph.end type="italics"/><lb/>
<figure id="fig27"></figure><lb/><emph type="italics"/>N C. Quoniam igitur diame­<lb/>ter A B maxima e&longs;t in&longs;cripta­<lb/>rum in circulo, & K I propin­<lb/>quior centro ip&longs;i L H remotiore <lb/>maior e&longs;t prop. 15. lib. 3. harum <lb/>quoque dimidiæ M B, N I, O <lb/>H prop. 3. lib. eiu&longs;dem erunt in­<lb/>æquales & M B maior quam <lb/>N I, & N I quam O H. Ab <lb/>his igitur &longs;ublatis æqualibus M <lb/>C, N F, O G parallelogram­<lb/>morum O F, N C lateribus oppo&longs;itis prop. 34. lib. 1. reliquæ C| B, <lb/>F I, G H erunt iuæquales ax. 5. Et quidem reliqua C B à maiore M <lb/>B maior: quam F I: & F I eadem ratione maior quam G H, & <lb/>&longs;ic de cæteris. Igitur &longs;i chorda rectas, &c. quod fuit <expan abbr="demon&longs;trandũ">demon&longs;trandum</expan>.<emph.end type="italics"/></s>
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<p type="main">
<s>Itaque mouetur nauis.] <emph type="italics"/>Cau&longs;a efficiens motum nauis actua­<lb/>riæ, & modus quo efficitur, hic exprimitur e&longs;&longs;e impul&longs;io remi à re­<lb/>mige, mouente animato. Modus e&longs;t cum remi palmula aquam ingre&longs;­<lb/>&longs;a, & aquæ ob &longs;ui copiam, tanquam &longs;olo, firmiter renitenti innixu <lb/>manubrium antror&longs;um propellitur à remige, & proinde totus remus <lb/>vnum continuum & validum inflexileque exi&longs;tens, excepto palmu­<lb/>læ extremo quod ob aquæ renixum vtcumque immobile manet, & <lb/>per con&longs;equens alligata remo, eò quò manubrium, promouentur. <lb/>Nauis autem per &longs;calmum alligata e&longs;t remo. Nauis igitur promouebi­<lb/>tur antror&longs;um, &longs;i eò manubrium <expan abbr="promotũ">promotum</expan> &longs;it. Dixi &longs;i eò manubrium <lb/>promotum &longs;it, quia concitato nauigio, quum remiges inhibent, contra <lb/>fit. Manubrium &longs;iquidem mouetur retror&longs;um, proinde vna cum eo <lb/>& nauis. Ad huius rei fidem locus e&longs;t apud Tullium luculentus. <lb/>Nunc vt ad rem redeam, inquit, inhibere illud tuum, quod valde <lb/>mihi arri&longs;erat, vehementer di&longs;plicet. E&longs;t enim verbum totum nauti­<lb/>cum: quanquam id quidem &longs;ciebam: &longs;ed arbitrabar &longs;u&longs;tineri remos, <lb/>quum inhibere e&longs;&longs;ent remiges iußi. Id non e&longs;&longs;e eiu&longs;modi, didici heri, <lb/>quum ad villam no&longs;tram nauis appelleretur: non enim &longs;u&longs;tinent, &longs;ed <lb/>alio modo remigant, id ab<emph.end type="italics"/> <foreign lang="greek">e)poxh_s</foreign> <emph type="italics"/>remotißimum e&longs;t. Et po&longs;tea &longs;ubdit. <lb/>Inhibitio autem remigum motum habet, & <expan abbr="vehem&etilde;tiorem">vehementiorem</expan> quidem<emph.end type="italics"/>
<pb pagenum="70"/><emph type="italics"/>remigationis nauem conuertentis ad puppim. Hæc Cicero. quæ non <lb/>abs re vt arbitror hîc &longs;unt in&longs;erta, vt quæ plurimum faciant <lb/>ad intelligendum <gap/>e motibus nauis duos rectos concitationem &longs;ci­<lb/>licet, & inhibitionem, & vtramque fieri à remo tanquam à <lb/>vecte. non tamen vt antea vecte, in quo eius altero extre­<lb/>mo per vim mouentem depre&longs;&longs;o, eleuetur alterum: &longs;ed in quo cum <lb/>eius alterum extremum &longs;ur&longs;um tollatur, alteri &longs;ubiecta aqua renita­<lb/>tur, & hypomochlÿ vicem præ&longs;tet: non &longs;calmus. Scalmus enim non <lb/>manet: &longs;ed transfertur vna cum naui, quod e&longs;t contra naturam cen­<lb/>tri, quale repre&longs;entat id, quod pro hypomochlio e&longs;t. Et aquæ pars exci­<lb/>piens palmulam, qua patet in latum, vt reuera moueatur: motus ta­<lb/>men hic vel e&longs;t exiguus, & pro nullo ideo cen&longs;endus: vel retrocedit, <lb/>&longs;ed minus quam &longs;calmus procedat, vt po&longs;tea demon&longs;trabitur. Erit <lb/>iginur pro centro, neque etiam nautis animus e&longs;t mare: &longs;ed nauem <lb/>tanquam pondus propellere. Neque minus interea verum erit, quod <lb/>qui in medio mari remigant, ip&longs;am plus propellant. Sed quid dice­<lb/>mus Aristoteli & Vitruuio qui apertè dicunt &longs;calmum e&longs;&longs;e hypo­<lb/>mochlium, & mare pondus mouendum. Certè &longs;i &longs;edulo attendamus, <lb/>remigatio vna non vnus e&longs;t &longs;implex remi motus: &longs;ed ex quatuor di­<lb/>uer&longs;is compo&longs;itus. In horum primo palmula extra aquam educitur <lb/>depre&longs;&longs;o manubrio: in &longs;ecundo &longs;uper aquam antror&longs;um palmula pro­<lb/>mouetur adducto ad remigem manubrio: in tertio palmula in aquam <lb/>demergitur eleuato manubrio: in postremo palmula retror&longs;um adi­<lb/>gitur impul&longs;o totis viribus antror&longs;um manubrio. Atque hi motus <lb/>quia nulla valde &longs;en&longs;ibili interpo&longs;ita mora fiunt, vnus qua&longs;i circula­<lb/>ris e&longs;&longs;e videntur: diuer&longs;i tamen &longs;unt terminis ad quos & à quibus <lb/>remus mouetur, & cau&longs;is. Quia in tribus prioribus &longs;calmus mani­<lb/>fe&longs;tè e&longs;t hypomochlium, pondus mouendum e&longs;t aqua, vel pars extre­<lb/>ma remi cum e&longs;t extra aquam. De his igitur pote&longs;t intelligi Ari&longs;to­<lb/>teles tum Vitruuius. At in quarto agua renitens palmulæ e&longs;t hypo­<lb/>mochlium, nauis vero pondus mouendum, vt diximus. Si quis tamen <lb/>etiam de hoc po&longs;tremò remi motu velit &longs;en&longs;i&longs;&longs;e Ari&longs;totelem non re­<lb/>luctabor, dummodo concipiat mare pondus quidem mouendum: &longs;ed <lb/>quod ob renixum qua&longs;i immobile faciat, vt &longs;calmus circa quem tan­<lb/>quam centrum remus voluitur, cedat loco & promoueatur. Sicque <lb/>nauta aliquid faciet quod non quærit, vt aliud con&longs;equatur: mare<emph.end type="italics"/>
<pb pagenum="71"/><emph type="italics"/>&longs;cilicet mouebit, vt per antiperi&longs;ta&longs;im in&longs;uper recollectum nauim ex <lb/>parte, qua recolligitur, propellat.<emph.end type="italics"/></s>
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<p type="main">
<s>Eo vbie&longs;t.] <emph type="italics"/>Non quidem &longs;emper antror&longs;um iu&longs;tè ad perpendi­<lb/>culum: &longs;ed paulo vltra aut citra, pro vt mouens validius: aut imbe­<lb/>cillius mouet manubrium, & aqua plus, minu&longs;ve renititur pauca <lb/>enim & tenuis minus: multa & cra&longs;&longs;a magis renititur.<emph.end type="italics"/></s>
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<s>Vbienim remus.] <emph type="italics"/>Illu&longs;tratio e&longs;t &longs;ecundæ partis propo&longs;itionis <lb/>primarÿ &longs;yllogi&longs;mi vbi<emph.end type="italics"/> <foreign lang="greek">plei/shn <gap/>a/la<gap/>an tlio\ xw/ phn dioa<gap/>ei_n.</foreign> <emph type="italics"/>Re­<lb/>mum diuidere plurimum maris dici pote&longs;t duobus modis, vno cum <lb/>palmula profundius ingrediatur mare. Penetrans enim pedes duos <lb/>plus diuidit penetrante vnum: altero cum palmulæ pars intrà aquam <lb/>in vno remi impul&longs;u maius &longs;patium conficit: vtroque autem modo <lb/>palmula mediani remigis plus diuidit mare <expan abbr="quã">quam</expan> <expan abbr="aliorũ">aliorum</expan>. Primo enim <lb/>quia pars nauis media eò, quod depre&longs;&longs;a, reddit &longs;uum &longs;calmum aquæ <lb/>valde propinquum, & huius remi pars à &longs;calmo ad palmulam fere <lb/>tota e&longs;t in aqua. Non ita e&longs;t de &longs;calmis aliorum cum puppis & prora <lb/>paulò &longs;ublimiores &longs;int lateribus. De altero dicetur po&longs;tea amplius <lb/>quia radÿ maioris peripheria maior e&longs;t. E&longs;t autem palmula eorum <lb/>qui &longs;unt in medio nauis, quæ intra aquam, radius maior: quam pal­<lb/>mula aliorum, & &longs;ic maius &longs;patium peragrat.<emph.end type="italics"/></s>
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<s>Propter id remiges.] <emph type="italics"/>Conclu&longs;io e&longs;t primarÿ &longs;yllogi&longs;mi cuns <lb/>repetione cau&longs;æ eiu&longs;dem.<emph.end type="italics"/></s>
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<p type="main">
<s><gap/></s>
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<p type="main">
<s>6. Potentiæ gubernaculi <lb/>cau&longs;a, & quod <expan abbr="nauigiũ">nauigium</expan> <lb/>magis in <expan abbr="contrariũ">contrarium</expan> pro­<lb/>cedat: quam remi pal­<lb/>mula.</s>
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<p type="main">
<s><gap/></s>
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<p type="main">
<s>Cur gubernaculum par­<lb/>uum quid exi&longs;tens, & in <lb/>extrema parte nauigij tan­<lb/>tam vim habet, vt ab exi­<lb/>guo temone, & vnius ho­<lb/>minis ctiam propemodum <lb/>quie&longs;centis viribus, magnæ
<pb pagenum="72"/><gap/><lb/><expan abbr="nauigiorũ">nauigiorum</expan> moles mouean­<lb/>tur? An quia <expan abbr="gubernaculũ">gubernaculum</expan> <lb/>e&longs;t vect is: pondus mare, gu­<lb/>bernator mouens. Non au­<lb/>tem <expan abbr="&longs;ecũdum">&longs;ecundum</expan> latitudinem <lb/><expan abbr="gubernaculũ">gubernaculum</expan> impellit ma­<lb/>re, vt remus. Neque enim <lb/>nauim mouet in anterio­<lb/>rem partem: &longs;ed mare in <lb/>tran&longs;uer&longs;um accipiens <expan abbr="ipsã">ipsam</expan> <lb/>commotam obliquat. quia <lb/>enim mare pondus erat ad <lb/>contrarium incumbens in­<lb/>clinat nauim. Ip&longs;um enim <lb/>hypomochlium in contra­<lb/>rium vertitur, mare <expan abbr="quid&etilde;">quidem</expan> <lb/>intrò: illud verò foras: & il­<lb/>lud &longs;equitur nauis, quia illi <lb/>e&longs;t alligata. Igitur remus <lb/>&longs;ecundum latitudinem im­<lb/>pellens pondus, & ab illo <lb/>contra repul&longs;us in rectum <lb/>agit: at <expan abbr="gubernaculũ">gubernaculum</expan> qua&longs;i <lb/><expan abbr="trã&longs;uer&longs;um">tran&longs;uer&longs;um</expan> iaceat, in tran&longs;­<lb/>uer&longs;um etiam hinc inde motionem facit.</s>
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<p type="head">
<s>COMMENTARIVS.</s>
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<p type="main">
<s>Po tentiæ guber.] <emph type="italics"/>In hoc capite<gap/> proponuntur tria &longs;pecialia de <lb/>vecte problemata quorum duo &longs;unt de gubernaculo & tertium <lb/>de remo. Primum e&longs;t cur gubernaculum, paruum cum &longs;it, magnam <lb/>nauigÿ molem moueat. Et huic differentia quæ e&longs;t inter remi & gu­<lb/>bernaculi motiones &longs;ubÿcitur. Secundum cur gubernaculum in puppi <lb/>non in medio aut prora nauis collocetur. Tertium cur nauigium an­<lb/>tror&longs;um plus procedat, quam remi palmula retror&longs;um. Atque hæceo <lb/>ordine quo propo&longs;ita &longs;unt, di&longs;&longs;oluentur.<emph.end type="italics"/></s>
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<pb pagenum="73"/>
<p type="main">
<s>Gubernaculum.] <emph type="italics"/>Gubernaculum remus erat apud antiquos, <lb/>&longs;ed multo latioris palmulæ: quamremi, quibus ad latera nauis remi­<lb/>gabant. Ob id pterigion ab alæ exten&longs;æ &longs;imilitudine vel latitudine <lb/>dicta e&longs;t. Reliqua pars in&longs;tar grandioris pali temo dicitur, qui ad ex­<lb/>tremum in puppi cardinem retentus, conuoluitur ad obliquandum <lb/>nauim.<emph.end type="italics"/></s>
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<p type="main">
<s>Cur gubernaculum.] <emph type="italics"/>Propo&longs;itio e&longs;t problematis in duas par­<lb/>tes à nobis antea &longs;ubdiui&longs;i, vt & Ari&longs;toteles po&longs;tea &longs;ubdiuidendo <lb/>di&longs;&longs;oluit.<emph.end type="italics"/></s>
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<p type="main">
<s>Vt ab exiguo temone.] <emph type="italics"/>Propo&longs;iti problematis admiratio au­<lb/>getur, ex parte mouentis quidem tripliciter, quod motor &longs;it vnus ho­<lb/>mo, &longs;it propemodum nihil agens, Cicero ludentem po&longs;uit, vtatur ad <lb/>id quod facere vult, exiguo in&longs;trumento nempè temone, vt qui &longs;em­<lb/>per breuior &longs;it longißimo remorum: ex parte vero rei motæ, nempè <lb/>totius nauigÿ, & omnium, quæ <expan abbr="veh&etilde;da">vehenda</expan> naui impo&longs;ita &longs;unt. Quæ, vt <lb/>ÿs qui viderunt omnia, manife&longs;tißima &longs;unt: ita ÿs qui non viderunt <lb/>incredibilia. præ&longs;ertim &longs;i ex antiquorum monumentis <expan abbr="repetãt">repetant</expan>, quan­<lb/>ta à quibu&longs;dam con&longs;tructa &longs;unt nauigia è quibus vnum ex Athe­<lb/>næo placet hîc attexere, vt ex eo di&longs;cant omnes <expan abbr="quãtam">quantam</expan> molem vnus <lb/>homo temone exiguo dimouere poßit. Longa e&longs;t, &longs;ed vt &longs;pero, omni­<lb/>bus lectu <expan abbr="iucũda">iucunda</expan> hi&longs;toria. Recitat igitur Athenæus <expan abbr="Hieron&etilde;">Hieronem</expan> Syra­<lb/>cu&longs;anorum Regem ad naues fabricandum ambitiose<gap/> animum inten­<lb/>di&longs;&longs;e, & vnam imprimis memorabilem perfeci&longs;&longs;e, ad quam ædifi­<lb/>candam, materiam in A Etna monte cædendam, indeque deuehen­<lb/>dam curaui&longs;&longs;e, quæ &longs;exaginta triremibus conficiendis &longs;atis e&longs;&longs;e potui&longs;­<lb/>&longs;et. quo dicto nauigÿ magnitudinem conÿciendam nobis reliquit. <lb/>Ad nauticum autem in&longs;trumentum cum æs, ferrum, cannabim, reli­<lb/>quaque, quibus opus erat, partim ex Italia, partim ex Iberia, partim <lb/>Rhodano flumine compara&longs;&longs;et, trecentos operi f<gap/> do fabros, arti­<lb/>fice&longs;que adhibui&longs;&longs;e: ac materiæ dedolandæ præter admini&longs;tros fabri­<lb/>cæ &longs;ub&longs;eruientes opificÿs, præfecto &longs;ummæ operis architecto Archia <lb/>Corinthio. Quos ip&longs;e cum magnopere hortatus e&longs;&longs;et ad opus aggre­<lb/>diendum, in&longs;uper etiam dies totos operis &longs;e curatorem, exactoremque <lb/>præbui&longs;&longs;e: hac diligentia, his artificibus, hoc architecto, Regem ta­<lb/>men illum dimidium tantum nauis intra &longs;ex men&longs;es perfeci&longs;&longs;e. Quo <lb/>facto inchoatam eo modo nauem in mare deducendam manda&longs;&longs;e: vt<emph.end type="italics"/>
<pb pagenum="74"/><emph type="italics"/>illìc extremæ manus opificium adipi&longs;ceretur. Hac deducta alteram <lb/>nauigÿ partem totidem alijs men&longs;ibus Hieronem <expan abbr="cõ&longs;umma&longs;&longs;e">con&longs;umma&longs;&longs;e</expan>. Cum <lb/>interim clauis æreis denarum librarum plurimis materiam compin­<lb/>geret, aliquibus etiam &longs;e&longs;quiplis eius ponderis, qui præ craßitudine. <lb/>non alias adigi poterant: quam materia perterebrata. His clauis co&longs;tæ <lb/>nauis arrectariæ cum a&longs;&longs;amentis tran&longs;uer &longs;arÿs coagmentatæ, tegulis <lb/>in&longs;uper plumbeis adactis validius a&longs;tringebantur, quibus etiam &longs;ub <lb/>ip&longs;is linteola concerpta cum pice infarcta erant. Erat rur&longs;us, inquit <lb/>ille, ea nauis apparatu quidem viginti ordinum remigij: ædificij vero <lb/>contignatione triplici. Harum infimam contignationem oneri & <lb/>mercibus delegauerat, ad quam de&longs;cen&longs;us &longs;calis multiplicibus erat: <lb/>ad mediam contignationem tran&longs;itus alter erat arte Mechanica fa­<lb/>ctus, in qua ip&longs;a cœnationes erant numero triginta <expan abbr="&longs;ecundũ">&longs;ecundum</expan> vtrum­<lb/>que latus nauigij extructæ. In ijs lecti quaterni &longs;trati viris accom­<lb/>modati: inter quas nauclericum conclaue quinque lectorum capax <lb/>erat. Præterea thalami tres in eadem contignatione erant, culinaque <lb/>&longs;upradictis locis &longs;ub&longs;eruiens ad puppim ædificata. Omnes autem &longs;u­<lb/>pradictæ cœnationes pauimento &longs;tratæ erant te&longs;&longs;ellis vermiculato <lb/>lapidis omnis generis. In eo pauimento Troiani belli fabulamentum <lb/>vi&longs;endo artificio concinnatum legebatur, cum alioquin ea omnia <lb/>ædificia tectis laqueatis, & po&longs;tibus exornata &longs;pectabili opere e&longs;&longs;ent. <lb/>Summa pars nauigij gymna&longs;ium habebat ambulatione&longs;que laxas, <lb/>proportione magnitudinis &longs;uæ, quas etiam ip&longs;as &longs;imul ambientes hor­<lb/>ti omni genere <expan abbr="&longs;tirpiũ">&longs;tirpium</expan> complectebantur, fictilibus in va&longs;is & plum­<lb/>beis con&longs;itorum, &longs;imul hederæ vite&longs;que opacabant pampinis, ac co­<lb/>rymbis inumbrantes, quarum radices <expan abbr="alebãt">alebant</expan> dolia terræ plena: pari­<lb/>ter quidem illæ cum hortis machinamento irriguæ. Ab his erat <lb/>Aphrodi&longs;ium id e&longs;t conclaue Veneri deæ dicatum: in&longs;trumentum <lb/>etiam ip&longs;um triclí<gap/>ari lecti&longs;ternio, pauimentoque &longs;tratum achate la­<lb/>pide aly&longs;que varÿs & nitentibus di&longs;tincto. Cuiu&longs;modi lapidum co­<lb/>pia in Sicilia reperitur. Ac parietes quidem habebat cupreßinis ta­<lb/>bulis aßibu&longs;que contextos, laqueatumque tectum eadem materia. Fo­<lb/>res etiam ex ebore & odorata materia compactas, atque eo amplius <lb/>pictura &longs;igilli&longs;que exornatas. Deinceps erat exhedra quinque lecto­<lb/>rum capax, quorum parietes po&longs;te&longs;que buxo compacti <expan abbr="erãt">erant</expan>, inibique <lb/>bibliotheca, & in lacunari &longs;phæra ad <expan abbr="imitation&etilde;">imitationem</expan> eius &longs;olarij effecta,<emph.end type="italics"/>
<pb pagenum="75"/><emph type="italics"/>quod in Achradina &longs;itum erat, quæ in&longs;ula e&longs;t Syracu&longs;arum. Huic <lb/>loco balneum iunctum erat, in quo tres lecti cum &longs;olio metretarum <lb/>quinque capaci, quod ex lapide vario &longs;calptum erat, & tribus æneis <lb/>Caldarijs. Mitto nunc habitationes militibus de&longs;tinatas: ii&longs;que qui <lb/>&longs;uper &longs;entinam erant. Mitto equorum præ&longs;epia ab vtroque latere na­<lb/>uigij numero dena &longs;ita cum frænis & &longs;tratis, & omni equitum in­<lb/>&longs;trumento, eorumque mini&longs;terij atque equorum pabulo. Præterea li­<lb/>gnarium, & clibanos focos, & pi&longs;trina, aliaque mini&longs;teria in proie­<lb/>cturis nauis prominentia. Quid dicam Athlantes nouenûm pedum <lb/>altitudinis certis inter&longs;titiis firmatos, vt &longs;calpturas <expan abbr="promin&etilde;tes">prominentes</expan> &longs;um­<lb/>mæ contignatiònis mutulorum vice fulcirent? Quid turres octo? <lb/>binas in prora & puppi per vtrumque latus extructas, in muri&longs;que <lb/>propugnacula. Præter hæc machina erat in medio cata&longs;tromate &longs;uper <lb/>tripodes excitata, Archimedis inuentum &longs;axa tritalantaria, telaque <lb/>mißilia duodeuiginti pedum facile eiaculans ad quadringentos cu­<lb/>bitos, quod &longs;patium e&longs;t &longs;tadÿ. Hæc & alia machinamenta propu­<lb/>gnatoria vt coruos, lupos, & in &longs;ummo malo carche&longs;ia, ænea <expan abbr="lapidũ">lapidum</expan> <lb/>conceptacula ad lapidationem faciendam in ho&longs;tium nauigia, lon­<lb/>gum e&longs;&longs;et enarrare. <expan abbr="Stabãt">Stabant</expan> enim in vno terni: in alÿs bini aut &longs;ingu­<lb/>li homines lapides eiaculantes, quos &longs;erui in foris nauis &longs;tantes viti­<lb/>libus quallis tempore pugnæ &longs;uggerebant trochleis &longs;ubuehentes. Sed <lb/>vt & huius nauigij magnitudo va&longs;titas ac onus animo amplius con­<lb/>cipi poßit, in&longs;uper adijciam tam multis nonnulla, quæ Athenæus <lb/>&longs;crip&longs;it ad hoc maxime pertinentia. Erat, inquit, in eodem nauigio <lb/>&longs;ecundum proram aquæ conceptaculum conclu&longs;um capax duorum <lb/>milium metretarum a&longs;&longs;amentis & pice & linteorum farctura com­<lb/>pictile, iuxta quod rur&longs;us pi&longs;cina coaxatione & implumbatura <lb/>con&longs;tans plena aquæ marinæ. Ita vt in ea commode magna copia <lb/>pi&longs;cium facile aleretur. Idem alibi. frumentum negociatorium in <lb/>ea naui exportabant ad millia &longs;exaginta: &longs;al&longs;amenta Sicula ad ca­<lb/>dum decem millia: lanarum talenta viginti millia, & alterius mer­<lb/>cis altera viginti millia, prætereáque commeatus vectorum nauta­<lb/>rumque &longs;exaginta millia. Horum omnium onus, cum Budæus exqui­<lb/>&longs;itè per&longs;equitur, comperit &longs;ummam librarum ad quinque & &longs;eptua­<lb/>ginta millia excre&longs;cere præter aquam dulcem, præter pi&longs;cinam, præ­<lb/>ter tot dietarum inte&longs;tinum in&longs;trumentum, præter annonam vecto-<emph.end type="italics"/>
<pb pagenum="76"/><emph type="italics"/>rum, & pabulum equorum, præter denique onus tanti nauigij. Quo­<lb/>modo igitur non erit admirabile tantam molem vnius hominis vi <lb/>propemodum quie&longs;centis exiguo temone dimoueri & obliquari: atque <lb/>hæc de propo&longs;itione dicta &longs;unto.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia gubernaculum.] <emph type="italics"/>Solutio e&longs;t primi problematis, &longs;ic. <lb/>Vecte magna mouentur pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Gubernaculum e&longs;t vectis (in eo enim cardo ad quem alligatur <lb/>e&longs;t centrum: pondus <expan abbr="mouendũ">mouendum</expan> e&longs;t mare: <expan abbr="mou&etilde;s">mouens</expan> gubernator.<emph.end type="italics"/>)</s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo gubernaculo nauigij moles mouebitur. De hoc na­<lb/>uis motu pulchre.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vitruuius &longs;ic mentionem facit. Nauis onerariæ maximæ guber­<lb/>nator an&longs;am gubernaculi tenens, quod<emph.end type="italics"/> <foreign lang="greek">o)/iae</foreign> <emph type="italics"/>à Græcis ap­<lb/>pellatur, vna manu momento per centri rationem preßioni­<lb/>bus artis agitans, ver&longs;at eam amplißimis & immanibus <lb/>mercis & penus ponderibus oneratam.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Pondus mare.] <emph type="italics"/>Vtantè in remis dictum e&longs;t. pondus quod mo­<lb/>uere intendit gubernator non e&longs;t mare: licet parum impellatur, &longs;ed <lb/>nauis. It aque mouet gubernaculum, cuius pterigion latißimum intra <lb/>aquam, ob eius copiam firmum manet: & &longs;ic temo ad contrariam <lb/>partem impul&longs;us &longs;ibi in cardine alligatam nauis puppim impellit, <lb/>quod etiam paulo po&longs;t Ari&longs;toteles dicet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Non autem &longs;ecundum.] <emph type="italics"/>Dißimilitudo e&longs;t gubernaculi & <lb/>remi ex differenti loco ad quem vtrumque nauim mouet. Vtrumque <lb/>enim nauim mouet ad locum, qui contrarius e&longs;t ei, ad quem mare im­<lb/>pul&longs;um mouetur. Mouetur enim nauis ad centri, cui e&longs;t annexa, mo­<lb/>tum. Centrum <expan abbr="aut&etilde;">autem</expan> in remo e&longs;t &longs;calmus, in gubernaculo cardo. Mo­<lb/>uetur hoc contra quam depul&longs;um mare. Mare autem retror&longs;um rectà <lb/>à remo depellitur: mouet igitur remus rectà antror&longs;um nauim. Con­<lb/>trà mare à gubernaculo obliquè impellitur, vel dextror&longs;um vel &longs;ini­<lb/>&longs;tror&longs;um. Mouet igitur obliquè nauim (quod e&longs;t intelligendum de <lb/>puppi non de prora quæ in partem ad quam mare mouetur) &longs;ini­<lb/>&longs;tror&longs;um, &longs;i illud dextror&longs;um: vel dextror&longs;um, &longs;i illud &longs;ini&longs;tror&longs;um <lb/>depul&longs;um e&longs;t.<emph.end type="italics"/></s>
</p>
<pb pagenum="77"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>In extremo autem, non <lb/>in medio po&longs;itum e&longs;t. quia <lb/>motor, id quodiam moue­<lb/>tur, facillime ab extremo <lb/><expan abbr="cõmouet">commouet</expan>. Celetrime enim <lb/>fertur nauis prior pars, <lb/>Quoniam vt in ijs quæ mo­<lb/>uentur, ad finem latio defi­<lb/>cit: &longs;ic ip&longs;ius continui in ex­<lb/>tremo latio imbecillima <lb/>e&longs;t. E&longs;t autem imbecillima <lb/>facilis repul&longs;u. Propterea <lb/>gubernaculum in puppi &longs;i­<lb/>tum e&longs;t. Et quoniam exi­<lb/>gua in ea motione facta, <lb/>multo maior in prora fit in­<lb/>tercapedo. Angulus enim <lb/>æqualis à maiori &longs;ubtendi­<lb/>tur, & quanto maiores quæ <lb/>angulum comprehenderunt lineæ.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>In extremo autem.] <emph type="italics"/>Solutio e&longs;t &longs;ecundi problematis duplex, <lb/>&longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ibi collocandum gubernaculum, vbi per ip&longs;um motor facilius <lb/>& plus nauim mouere pote&longs;t: & vbi ex minore puppis, mu­<lb/>tatione, maior proræ mutatio adfertur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sed in puppi gubernaculo collocato gubernator facilius nauim <lb/>contorquet, & ex parua puppis mutatione magna proræ ad­<lb/>fertur mutatio.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo in puppi non in medio gubernaculum collocandum e&longs;t. <lb/>Obid etiam&longs;i e pi&longs;cibus quidam parte anteriori homini & quadra­<lb/>pedibus &longs;imiles &longs;unt, vt <expan abbr="Tritõ">Tritom</expan>, Nereis, elephas, & vitulus: po&longs;teriore <lb/>tamen omnes in caudam bifidam de&longs;inunt, paucis admodum exce­<lb/>ptis, atque id non ob aliam cau&longs;am quam quod, velut in nauis puppi <lb/>temo nauim dirigit: Ita pi&longs;cis iter cauda.<emph.end type="italics"/></s>
</p>
<pb pagenum="78"/>
<p type="main">
<s>Quia motor.] <emph type="italics"/>Syllogi&longs;mi præcedentis propo&longs;itio nec po&longs;ita, <lb/>nec illu&longs;trata e&longs;t. quia ex &longs;e euidens. Pro a&longs;&longs;umptione vero hîc prioris <lb/>eius partis illu&longs;tratio ponitur, &longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Non re&longs;i&longs;tentia, aut minus re&longs;i&longs;tentia, mouere facilius e&longs;t. <lb/>Vbi autem e&longs;t finis rei motæ (e&longs;t autem in puppi nauis, non in <lb/>eius medio, nec in prora) ibi re&longs;i&longs;tentia vel nulla vel minor. <lb/>Contra vbi celerrime mouetur, vt in prora, aut celerius, vt in <lb/>medio, ibi maior e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo in puppi nauim mouere facilius e&longs;t: quam in medio, aut in <lb/>prora.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quoniam vt in ijs.] <emph type="italics"/>Similitudo e&longs;t ad illu&longs;trandam præce­<lb/>dentis &longs;yllogi&longs;mi a&longs;&longs;umptionem, &longs;ic. Quemadmodum eorum quæ vi <lb/>feruntur latio ad finem deficit, & imbecillior e&longs;t: &longs;ic continui lati <lb/>extremum imbecillius mouetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et quoniam exigua.] <emph type="italics"/>Similis &longs;ententia e&longs;t apud Ari&longs;totelem <lb/>lib. de animalium motu. Nec vero dubium e&longs;t, inquit, quin parua ad­<lb/>modum initio facta mutatione in corpore multiplices è longinquo <lb/>varietates &longs;uboriantur, vt cum per temonem paululum tralatum <lb/>longè diuer&longs;a proræ po&longs;itio vi&longs;itur. Atque hæc e&longs;t altera cau&longs;a cur <lb/>gubernaculum in puppi ponitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Angulus enim æqualis.] <emph type="italics"/>Licet oculata alioquin fide perci­<lb/>piatur quanta & quam euidens nauigÿ temone paulùm vixque con­<lb/>torto ip&longs;ius proræ &longs;tatim tran&longs;po&longs;itio multo maior con&longs;equatur: ta­<lb/>men & id geometrica propo&longs;itione confirmatur quæ imperfecta e&longs;t <lb/>&longs;ed &longs;ic perfici pote&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Si duo I&longs;o&longs;celia æqualia angulis, inæqualium crurum fuerint: <lb/>erunt & inæqualia<emph.end type="italics"/><lb/>
<figure id="fig28"></figure><lb/><emph type="italics"/>ba&longs;ibus: & huius ba­<lb/>&longs;is maior, cuius crura <lb/>maiora. Sint A B E <lb/>& A D C duo i&longs;o&longs;­<lb/>celia æqualia angulis <lb/>qui ad A, & A D <lb/>crus e&longs;to maius crure <lb/>A B &longs;icut & A C <lb/>ip&longs;o A E. Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. Nam quia<emph.end type="italics"/>
<pb pagenum="79"/><emph type="italics"/>tres anguli vnius triangulorum &longs;unt æquales tribus alterius prop. <lb/>32. lib. 1. & anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba­<lb/>&longs;im duo duobus &longs;unt æquales ax. 3. & quia A D C & A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, ÿ inter &longs;e erunt æquales prop. 5. lib. 1. & per <lb/>eandem anguli A B E & A E B. Sicque A E B dimidius <lb/>cum &longs;it horum <expan abbr="duorũ">duorum</expan>, angulo A C D etiam dimidio <expan abbr="æqualiũ">æqualium</expan> æ qua­<lb/>lis erit ax. 6. & per idem reliquus reliquo. Sunt igitur A B E & <lb/>A D C triangula æquiangula, proinde circum æquales angulos la­<lb/>tera habebunt proportionalia. prop. 4. lib. 6. ideo vt A D ad D C: <lb/>&longs;ic A B ad B E: & vicißim vt A D ad A B: &longs;ic D C ba­<lb/>&longs;is ad ba&longs;im B E prop. 16. lib. 5. E&longs;t autem maius A D ip&longs;o A B <lb/>ex hypothe&longs;i. Ergo Ba&longs;is D C maior erit ip&longs;a B E. Igitur &longs;i duo <lb/>I&longs;o&longs;celia æqualia angulis, inæqualia cruribus fuerint &c. quod <lb/>fuit demonstrandum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Patet igitur ex his quod cum B C &longs;it vt longitudo nauis, &longs;i pup­<lb/>pis B peruenerit ad E manente A cardine. Tunc C erit in D. <lb/>Sicque fiunt duo triangula I&longs;o&longs;celia A B E & A D C æqualia <lb/>angulis ad verticem A oppo&longs;itis prop. 15. lib. 1. Et inæqualia cruri­<lb/>bus. Namrectæ ab A puncto Cardini re&longs;pondente in ima parte na­<lb/>uis propè puppis extremum ad extremum proræ id e&longs;t A D, A C <lb/>longè maiores &longs;unt breuißimis ÿs, quæ &longs;unt ab <expan abbr="eod&etilde;">eodem</expan> puncto A ad ex­<lb/>tremum puppis A B, A E. Peragrabit igitur prora D lineam C B <lb/>longè maiorem, cum B peragrabit B E multo minorem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Ex hoc autem <expan abbr="manife&longs;tũ">manife&longs;tum</expan> <lb/>e&longs;t, ob quam cau&longs;am nauis <lb/>in contrarium magis pro­<lb/>cedat: quam remi palmula. <lb/>Eadem enim moles eadem <lb/>vi mota per aerem plus, <lb/>quam per aquam progre­<lb/>ditur. Sit enim remus <foreign lang="greek">a b</foreign><lb/>& &longs;calm^{9} <foreign lang="greek">g,</foreign> & intra nauim <lb/>caput remi <foreign lang="greek">a</foreign> palmula intra <lb/>mare <foreign lang="greek">b.</foreign> Si ita que <foreign lang="greek">a</foreign> <expan abbr="tran&longs;la-tũ">tran&longs;la­<lb/>tum</expan> &longs;it eò, vbi e&longs;t <foreign lang="greek">d</foreign>: ip&longs;um <foreign lang="greek">b</foreign>
<pb pagenum="80"/><gap/><lb/>
<arrow.to.target n="marg21"></arrow.to.target><lb/>non erit vbi e&longs;t <foreign lang="greek">e.</foreign> E&longs;t enim <lb/><foreign lang="greek">b e</foreign> æqualis ip&longs;i <foreign lang="greek">a d.</foreign> Ex <lb/>æquo igítur tran&longs;latum e&longs;­<lb/>&longs;et, &longs;ed minus erat. E&longs;t igi­<lb/>tur vbi <foreign lang="greek">z.</foreign> Minor enim e&longs;t <lb/><foreign lang="greek">b z</foreign>: <expan abbr="quã">quam</expan> <foreign lang="greek">a d.</foreign> Itaque etiam <lb/><foreign lang="greek">q z</foreign> quam <foreign lang="greek">d <expan abbr="q.">que</expan></foreign> Similia enim <lb/>&longs;unt triangula. Con&longs;i&longs;tens <lb/>vero erit medium vbi e&longs;t <foreign lang="greek">g.</foreign><lb/>In contrarium enim extre­<lb/>mo <foreign lang="greek">b,</foreign> quod in mari e&longs;t <lb/>procedit <expan abbr="extremũ">extremum</expan> <foreign lang="greek">a,</foreign> quod <lb/>in nauigio e&longs;t. Non autem <lb/>ad <foreign lang="greek">d</foreign> procederet, ni&longs;i mo­<lb/>ueretur nauis, & eo vbi e&longs;t <lb/>caput remi, transferretur.</s>
</p>
<p type="margin">
<s><margin.target id="marg21"></margin.target>Inclu&longs;a his <lb/>notis [] ni <lb/>hil faciunt <lb/>ad rem.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Ex hoc autem.] <emph type="italics"/>Hic continetur tertium è tribus, quæ hoc <lb/>capite diximus contineri problemata. E&longs;t autem eiu&longs;modi. An <lb/>nauis plus antror&longs;um vehitur: <expan abbr="quã">quam</expan> palmula remi retror&longs;um. Re&longs;pon­<lb/>det Ari&longs;toteles plus vehi nauem antror&longs;um. Cau&longs;am dicit. quia ea­<lb/>dem moles eadem vi mota plus per medium rarum fertur: quam per <lb/>den&longs;um. Contra quam rationem duo occurrunt aliena. Prius quod <lb/>moles non e&longs;t eadem nauis & remi palmulæ: alterum quod vnum <lb/>idemque e&longs;t medium vtriu&longs;que nempe aqua. E&longs;t enim pars nauis im­<lb/>mer&longs;a aquæ, quæ mouetur, vt & palmula. Dicemus igitur vt ratio <lb/>Ari&longs;totelis concludat duo a&longs;&longs;umenda e&longs;&longs;e. Primum eandem molem, <lb/>aut æquales moles intelligere Ari&longs;totelem remi caput, & palmu­<lb/>lam: vel partem remi à &longs;calmo ad caput: & partem eiu&longs;dem à &longs;calmo <lb/>ad palmulam. Has enim videtur hîc præ&longs;upponere æquales longitu­<lb/>dine, &longs;calmo remum bifariam &longs;ecante: &longs;in minus pondere: ad æquali­<lb/>brium enim cum pars palmulæ maior e&longs;t, caput implumbatur vt <lb/>æquiponderet. Et &longs;ic cum remus vnius vel plurium remigum viri­<lb/>bus mouetur, caput per aërem, palmula per aquam: &longs;icque per diuer&longs;a<emph.end type="italics"/>
<pb pagenum="81"/><emph type="italics"/>media, mouentur. Et &longs;ic ex ratione Ari&longs;totelis, &longs;i vera e&longs;t, caput remi <lb/>plus antror&longs;um mouebitur quam palmula retror&longs;um. Alterum quod <lb/>a&longs;&longs;umendum. e&longs;t nauim tantum antror&longs;um moueri: quantum & re­<lb/>mi caput. Quod &longs;i verum e&longs;&longs;et &longs;tatim conclu&longs;io hæc manife&longs;ta <lb/>e&longs;&longs;et.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo nauis plus antror&longs;um mouetur: quam remi palmula re­<lb/>tror&longs;um.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Syllogi&longs;mus igitur &longs;ic e&longs;to,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quantum caput remi antror&longs;um mouetur: tantum & nauis. <lb/>Sed caputremi plus antror&longs;um mouetur: quam palmulare­<lb/>tror&longs;um.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo nauis plus antror&longs;um mouetur: quam palmula retror&longs;um.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Huius &longs;yllogi&longs;mi propo&longs;itio &longs;ine confirmatione de&longs;erta e&longs;t ab Ari­<lb/>&longs;totele. Etiam&longs;i <expan abbr="principiũ">principium</expan> non &longs;it. Ob id quid veritatis habeat po&longs;tea <lb/>di&longs;cutiemus. A&longs;&longs;umptionis confirmatio pendet ab eo quod cum caput <lb/>& palmula remi &longs;int eadem moles eadem vi mota, illud tamen per <lb/>aërem: hæc per aquam medium aëre den&longs;ius, moueatur. Quæ ratio <lb/>verißima e&longs;t in ÿs, quæ &longs;eor&longs;um mouentur, vt &longs;i remus totus per <lb/>aërem, & totus per aquam ferretur eadem vi, dubium non e&longs;t quin <lb/>citius, & plus per aërem, quam per aquam, ob maiorem in aqua <expan abbr="re&longs;i-&longs;t&etilde;tiam">re&longs;i­<lb/>&longs;tentiam</expan> feratur. At remus vnus e&longs;t, &longs;ed &longs;uperficie aquæ &longs;ectus, qua&longs;i <lb/>duo &longs;int ita capi pote&longs;t. Et certum e&longs;t quod &longs;i imaginemur vim ean­<lb/>dem in capite atque in palmula mouenda cum hæc intra aquam, illud <lb/>extra &longs;it, quod plus prouehetur illud: quam hæc.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sit enim remus.] <emph type="italics"/>Confirmatio e&longs;t geometrica a&longs;&longs;umptionis <lb/>præcedentis &longs;yllogi&longs;mi vbi præ&longs;upponit Ari&longs;toteles moueri nauim <lb/>antror&longs;um. vnde infert caput remi ab eo loco, in quo erat ante remi­<lb/>gationem, ad alium transferri. Ergo<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput remi tran&longs;latum &longs;it ad<emph.end type="italics"/><lb/><foreign lang="greek">d.</foreign> <emph type="italics"/>Quo autem tempore<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>palmula<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>non <lb/>transfertur ad<emph.end type="italics"/> <foreign lang="greek">e</foreign><emph type="italics"/>: alioqui æqualiter moueretur palmula atque caput, <lb/>contra ea quæ ante po&longs;ita &longs;unt. Intelligatur enim remus<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>vbi e&longs;t<emph.end type="italics"/><lb/><foreign lang="greek">d e,</foreign> <emph type="italics"/>&longs;calmo<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>manente. fiunt duo triangula<emph.end type="italics"/> <foreign lang="greek">a g d & b g e,</foreign><lb/><emph type="italics"/>quorum anguli quiad<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>quia ad <expan abbr="vertic&etilde;">verticem</expan> oppo&longs;iti, &longs;unt æquales prop. <lb/>15. lib. 1. Tum latera, quæ ip&longs;os continent<emph.end type="italics"/> <foreign lang="greek">a g, d g,</foreign> <emph type="italics"/>duobus<emph.end type="italics"/> <foreign lang="greek"><gap/> g, <lb/><gap/> g</foreign> <emph type="italics"/>&longs;unt æqualia, quia partes &longs;unt dimidiæ eiu&longs;dem remi<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ax. 6. <lb/>eruntigitur ba&longs;es<emph.end type="italics"/> <foreign lang="greek">a d, b e</foreign> <emph type="italics"/>æquales, vt reliqui anguli prop. 4. lib. 1.<emph.end type="italics"/>
<pb pagenum="82"/><emph type="italics"/>Et &longs;ic palmula perducta ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput prouectum e&longs;&longs;et ad<emph.end type="italics"/> <foreign lang="greek">d</foreign><lb/><emph type="italics"/>æqualiter moueretur, &longs;ed in i&longs;to ca&longs;u<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>&longs;calmo manente nauis immo­<lb/>ta e&longs;&longs;et, <expan abbr="cũ">cum</expan> tamen prouecta e&longs;&longs;e &longs;upponatur. Intelligatur igitur mini­<lb/>mùm, vt ad<emph.end type="italics"/> <foreign lang="greek">z</foreign> <emph type="italics"/>e&longs;&longs;e perducta palmula<emph.end type="italics"/> <foreign lang="greek">b.</foreign> <emph type="italics"/>Ex hoc rur&longs;us <expan abbr="cõcludit">concludit</expan> Ari­<lb/>&longs;toteles ex figura à Victore Fau&longs;to & ab alÿs paßim rectam<emph.end type="italics"/> <foreign lang="greek">d q</foreign><lb/><emph type="italics"/>maiorem e&longs;&longs;e: quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> <emph type="italics"/>Et ita e&longs;&longs;e o&longs;tendamus, quia duorum trian­<lb/>gulorum<emph.end type="italics"/> <foreign lang="greek">a q d & b q z</foreign> <emph type="italics"/>anguli, qui ad<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ad verticem oppo&longs;iti, <lb/>&longs;unt æquales prop. 15. lib. 1. tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>æqualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti à recta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">a d, <gap/> e.</foreign> <emph type="italics"/>Ex <lb/>præcedenti <expan abbr="demõ&longs;tratione">demon&longs;tratione</expan>. Ergo reliquus<emph.end type="italics"/> <foreign lang="greek">q d a</foreign> <emph type="italics"/>reliquo<emph.end type="italics"/> <foreign lang="greek">b z q</foreign> <emph type="italics"/>æqua­<lb/>lis erit prop. 32. lib. 1. Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="greek">a q d & b q z</foreign> <emph type="italics"/>&longs;unt æquian­<lb/>gula, proinde & circum æquales angulos latera proportionalia prop. <lb/>4. lib. 6. E&longs;t igitur vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q d</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">b q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>& vicißim <lb/>prop. 16. lib. 5. vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q b</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">d q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> <emph type="italics"/>E&longs;t <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>maior: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">q b,</foreign> <emph type="italics"/>quia<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>erat bi&longs;&longs;ecta in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>& detracta e&longs;t de dimi­<lb/>dia<emph.end type="italics"/> <foreign lang="greek">g b</foreign> <emph type="italics"/>portio<emph.end type="italics"/> <foreign lang="greek">q g,</foreign> <emph type="italics"/>quæ additur ip&longs;i dimidiæ<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>E&longs;t igitur<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maior quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s>
</p>
<p type="main">
<s><emph type="italics"/>Hoc autem quanquam verum &longs;it, quor&longs;um tamen, dubium e&longs;t. <lb/>Exi&longs;timauit Nonius ideò hîc po&longs;itum e&longs;&longs;e, vt o&longs;tendatur B per remi-<emph.end type="italics"/><lb/>
<figure id="fig29"></figure><lb/><emph type="italics"/>gationem factam, non e&longs;&longs;e <lb/>in E: &longs;ed vltra vt in K, <lb/>vnde nouam hane de&longs;cri­<lb/>bit figuram. qua demon­<lb/>&longs;trat cum A caput remi <lb/>remigatione facta e&longs;t in <lb/>D, palmulam B remi A <lb/>B e&longs;&longs;e non in E: &longs;ed in K <lb/>vltra E. Nihilominu&longs;que <lb/>B K motum palmulæ B <lb/>retror&longs;um minorem e&longs;&longs;e A <lb/>D motu capitis A an­<lb/>tror&longs;um, &longs;ecundum &longs;enten­<lb/>tiam Ari&longs;totelis. Et &longs;ic <lb/>Nonius remigatione facta <lb/>& tran&longs;uecta naui ponit <lb/>&longs;calmum C tran&longs;uectum e&longs;&longs;e in T: vel ex &longs;uperiori Victoris figura<emph.end type="italics"/>
<pb pagenum="83"/><emph type="italics"/>ex<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>in<emph.end type="italics"/> <foreign lang="greek"><expan abbr="q.">que</expan></foreign> <emph type="italics"/>Sed &longs;i &longs;ice&longs;&longs;et, T idem &longs;calmus qui C, propior cum &longs;it <lb/>aquæ: quam ip&longs;e C, &longs;equeretur vt in vnius remigationis principio, <lb/>medio, fine nauis plus & minus mergeretur. quod &longs;i quando fiat, fit <lb/>exaccidenti, nec citra naufragÿ periculum: imo vero &longs;ic non tam <lb/>nauis ferretur antror&longs;um: quam in profundum. At contrà latum <lb/>pro&longs;perè nauigium &longs;eruat eundem &longs;calmum, &longs;eu &longs;pondam &longs;uam &longs;em­<lb/>per æquidi&longs;tantem aquæ, ni&longs;i quod verius e&longs;t, arcum peripheriæ, &longs;ed <lb/>non &longs;implicem, vt po&longs;tea docebimus, de&longs;cribat, cuius extrema &longs;unt in <lb/>&longs;uperficie aquæ.<emph.end type="italics"/><lb/>
<figure id="fig30"></figure><lb/><emph type="italics"/>vt, &longs;it &longs;ponda <lb/>nauis G H, & <lb/>&longs;calmus C, cui <lb/>alligatus remus <lb/>per medium &longs;it <lb/>A B exi&longs;tens in <lb/>principio remi­<lb/>gationis, & in <lb/>fine &longs;it vbi D E, <lb/>tran&longs;lato C per <lb/>motum nauigij <lb/>impul&longs;i in T: <lb/>&longs;icque motionis <lb/>intra aquam pal­<lb/>mulæ B &longs;patium erit B E: nauigij vero erit C T: tum capitis <lb/>remi A erit A D. Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>æquales prop. 15. lib. 1. Ba&longs;es erunt æquales, &longs;i triangula fiant æqui <lb/>crura, &longs;i iniquicrura, illius trianguli ba&longs;is erit maior, cuius latera <lb/>angulum continentia &longs;unt maiora, vt antea ostendimus. Hæcigi­<lb/>tur cum expendo cogor aliud &longs;entire quam Nonius licet timidè (quia <lb/>viro huic propter &longs;cientiam præ&longs;tantem, & quod in loco natus &longs;it, <lb/>vixeritque ad nauigandum opportunißimo, multò plura quam mihi <lb/>tribuere &longs;oleo) dicam tamen quod &longs;entio nempe conclu&longs;ionem i&longs;tam<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maiorem e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>pertinere eò, vt inferatur caput remi A <lb/>tran&longs;uecti non con&longs;i&longs;tere in<emph.end type="italics"/> <foreign lang="greek">d</foreign>: <emph type="italics"/>&longs;ed vltra. vt in figuræ no&longs;træ pun­<lb/>cto F. Sicque caput A multo anterius latum erit, quam B retrò. <lb/>E&longs;t enim A F maior quam A D axiom. 9. quæ demon&longs;trata e&longs;t<emph.end type="italics"/>
<pb pagenum="84"/>
<figure id="fig31"></figure><lb/><emph type="italics"/>e&longs;&longs;e maior ip&longs;a B E: &longs;ic <lb/>etiam C &longs;calmus erit in O, <lb/>æquedi&longs;tanter cum C ab <lb/>aqua. quod fieri oportet in <lb/>artificio&longs;a & pro&longs;pera na­<lb/>uigatione. An &longs;ic rectè <lb/>&longs;entiamus aliorum e&longs;to iu­<lb/>dicium: &longs;ed in hoc conueni­<lb/>mus cum Nonio quod remi <lb/>motus in vna remigatione <lb/>duplex e&longs;t: proprius, & alie­<lb/>nus: & ille quidem circularis circa &longs;calmum tanquam centrum, <lb/>cuius motus &longs;calmus expers e&longs;t: hic vero contingit & ob motum <lb/>&longs;calmi delati vna cum nauigio. Et quod totus motus remi ex his duo­<lb/>bus maior e&longs;t motu nauigÿ. Sed & cætera quæ in hoc problema <lb/>animaduertit & annotauit Nonius. Hîc &longs;ubÿciemus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Primum dicit Ari&longs;totelis ratiocinationem ob&longs;curam e&longs;&longs;e.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Deinde Ari&longs;totelem a&longs;&longs;umere duo quorum alterum e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Palmulam retrocedere quoties nauis in anteriora progreditur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Alterum e&longs;t &longs;calmum bi&longs;&longs;ecare remum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In&longs;uper Nonius a&longs;&longs;erit nauim interdum maius &longs;patium percurrere:<emph.end type="italics"/><lb/>
<figure id="fig32"></figure><lb/><emph type="italics"/>quam caput remi: interdum minus, iuxta <lb/>remigum vires, & provt mariremi pal­<lb/>mula immer&longs;a fuerit: Quæ omnia vt con­<lb/>&longs;picua fiant, demon&longs;trat quinque <expan abbr="&longs;equ&etilde;tes">&longs;equentes</expan> <lb/>propo&longs;itiones.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Propo&longs;itio prima.</s>
</p>
<p type="main">
<s><emph type="italics"/>Remigibus nauim mouere potentibus <lb/>caput remi plus antror&longs;um mouetur: <expan abbr="quã">quam</expan> <lb/>nauis. Sit remus A C, caput A, &longs;cal­<lb/>mus B, qui propter nauis motum percur­<lb/>rat &longs;patium, quod e&longs;t à B in D, in quo <lb/>loco remus A C &longs;itum rectitudinis ha­<lb/>beat E F: & &longs;ic &longs;patium quod A con­<lb/>ficit curua &longs;it linea A E, cui recta linea <lb/>A E re&longs;pondeat in rectam E F perpen-<emph.end type="italics"/>
<pb pagenum="85"/><emph type="italics"/>dicularis. Nauis vero idem interuallum conficiet quod &longs;calmus B. <lb/>Dico igitur rectam A E maiorem e&longs;&longs;erecta B D. Secet enim re­<lb/>cta A C rectam E F in G. Quia igitur A G E, & B G D <lb/>triangula &longs;unt æquiangula, erit &longs;icut A G ad B G: &longs;ic A E <lb/>ad B D prop. 4. lib. 6. Maior e&longs;t autem A G ip&longs;a B G, ax. 9. <lb/>Erit igitur A E maior quam B D. Itaque caput remi A maius <lb/>percurrit &longs;patium: quam nauis. quod erat demon&longs;trandum.<emph.end type="italics"/></s>
</p>
<figure></figure>
<p type="main">
<s><emph type="italics"/>Quod &longs;i per punctum B rectam duca­<lb/>mus H K æqualem remo, & ad rectos <lb/>cum recta B D, & in&longs;uper &longs;ecantem A<emph.end type="italics"/><lb/>3 <emph type="italics"/>in puncto I, manife&longs;tè intelligemus <lb/>ip&longs;am rectam A E (quæ e&longs;t totus motus <lb/>capitis remi in vna remigatione) con&longs;tare <lb/>ex A I, & I E, quarum prior re&longs;pon­<lb/>det curuæ A H de&longs;criptæ per capitis remi <lb/>motum proprium: po&longs;terior vero æqualis <lb/>e&longs;trectæ B D (&longs;unt enim latera parallelo­<lb/>grammi oppo&longs;ita prop. 34. lib. 1.) quæ motu <lb/>nauis decur&longs;a e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Et quia Nonius &longs;ine demon&longs;tratione a&longs;­<lb/>&longs;umit nauim tantùm decurrere, quantùm <lb/>&longs;calmus, id quoque demonstremus. quia ad <lb/>&longs;equentia etiam vtile e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ante remigationem remi existentis in &longs;calmo B &longs;it nauis prora C <lb/>po&longs;t remigationem &longs;it B<emph.end type="italics"/><lb/>
<figure id="fig33"></figure><lb/><emph type="italics"/>in E & prora in D &longs;ic­<lb/>que C D erit nauis pro­<lb/>motio, & B E &longs;calmi. <lb/>Dico igitur C D & B E æquales, quia reliquæ &longs;unt ex æqualibus <lb/>B C, E D dempto communi E C axio. 3. Ergo nauis tantùm de­<lb/>currit quantùm &longs;calmus.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Propo&longs;itio &longs;ecunda.</s>
</p>
<p type="main">
<s><emph type="italics"/>Capite remi motu proprio, & naui æqualiter motis, palmula im­<lb/>mota veluti centrum manet: & palmula immota, caput remi & <lb/>nauis æqualiter mota &longs;unt.<emph.end type="italics"/></s>
</p>
<pb pagenum="86"/>
<figure></figure>
<p type="main">
<s><emph type="italics"/>Remus in principio motus habeat <lb/>po&longs;itionem A B C, ducaturque per <lb/>punctum C, in quo remi palmula <lb/>recta C G rectos efficiens angulos <lb/>in puncto G cum recta per quam ad <lb/>motum nauis &longs;calmus B mouetur. Et <lb/>eadem recta C G producatur v&longs;que <lb/>ad E, ita vt G E &longs;it æqualis rectæ <lb/>B A (quæ e&longs;t dimidium remi) rur­<lb/>&longs;us per punctum B ducatur recta Q <lb/>B F ad rectos cum ip&longs;a B G, & in <lb/>Q B F incidant perpendiculares A <lb/>Q C F. Quoniam igitur triangu­<lb/>lorum A B Q & F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>æquales, prop. 15. lib. 1. & anguli qui ad Q & F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, æquale e&longs;t, erit & <lb/>latus A Q æquale lateri F C prop. 26. lib. 1. Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, æqualis e&longs;t prop. 34. lib. 1. <lb/>A Qigitur erit æqualis ip&longs;i B G ax. 1. Atque tantum &longs;patium B <lb/>&longs;calmus: quantum nauis. ex antec. Et nauis tantum confecit quan­<lb/>tum A caput remi ex hypothe&longs;i. A autem conficit &longs;patium A <expan abbr="q.">que</expan> <lb/>Igitur B &longs;calmus conficiet &longs;patium B G. Et quia anguli ad G <lb/>recti &longs;unt, ideo cum &longs;calmus peruenerit ad G, habebit remus A C <lb/>rectitudinis &longs;itum E C, quo in loco illius remigationis finis erit. Sic <lb/>igitur palmula C à loco &longs;uo dimota non fuit, quod demon&longs;trandum <lb/>erat. Cæterum Nonius hîc aduertitrectam G C minorem e&longs;&longs;e B C <lb/>remi dimidio, pro quantitate C T. Vnde concludit quo tempore <lb/>&longs;calmus B transfertur in G, palmulam quidem C excurrere in <lb/>ip&longs;am longitudinem C T. Sed neque antror&longs;um neque retror&longs;um, <lb/>quod Ari&longs;toteles puto vocauit antè, palmulam diuidere mare, quod <lb/>&longs;olum demon&longs;trare intendebat. vbi etiam aduertes lector ex hoc dia­<lb/>grammate Nonÿ & cæteris lineam A L E à capite remi in hac <lb/>remigatione de&longs;criptam, non e&longs;&longs;e &longs;implicem arcum: &longs;ed duos, vnum <lb/>A L ex motu proprio remi circa B centrum: alterum L E ex motu <lb/>con&longs;equente &longs;calmi B motum. quod pulchrè con&longs;entit cum his quæ<emph.end type="italics"/>
<pb pagenum="87"/><emph type="italics"/>untè diximus de remi in vna remigatione varijs motibus.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Propo&longs;itionis conuer&longs;io</s>
</p>
<p type="main">
<s><emph type="italics"/>Manife&longs;ta e&longs;t, quia &longs;i remi palmula dimota non fuerit à loco &longs;uo, <lb/>ibique tandiu per&longs;i&longs;tat, donec remus &longs;itum rectitudinis obtineat, tan­<lb/>tum &longs;patium conficiet caput remi motu proprio: quantum nauis. <lb/>Recta enim C F æqualis e&longs;t A Q prop. 26. lib. 1. æqualis etiam <lb/>B G prop. 34. lib. 1. igitur A Q & B G æquales erunt ax. 1.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Propo&longs;itio tertia.</s>
</p>
<p type="main">
<s><emph type="italics"/>Capite remi proprio motu conficiente &longs;patium duplum &longs;patÿ nauis: <lb/>tunc nauis tantùm promouebitur, quantùm palmula retrocedet.<emph.end type="italics"/></s>
</p>
<figure></figure>
<p type="main">
<s><emph type="italics"/>Remus incipiente motu &longs;it A C, <lb/>de&longs;inente vero habeat rectitudinis <lb/>&longs;itum F G. Et &longs;ic &longs;calmus B pro­<lb/>pter nauis motum conficiet interual­<lb/>lum B D. Excitetur igitur à puncto <lb/>B in vtramque partem perpendicu­<lb/>laris E E, prop. 11. lib. 1. In quam <lb/>perpendiculares incidant à punctis <lb/>A & C, quæ &longs;int A E, C E prop. <lb/>12. lib. 1. Et &longs;it interuallum A E <lb/>quod e&longs;t decur&longs;um à capite remi A <lb/>proprio motu, duplum interualli B <lb/>D, & recta linea C H re&longs;pondeat <lb/>curuæ C G à remi palmula de&longs;cri­<lb/>ptæ. Dico rectas lineas B D, C H <lb/>æquales e&longs;&longs;e. Nam triangulorum B <lb/>A E & C B E rectæ A E, C E prop. 26. lib. 1. & in parallelo­<lb/>grammo B H rectæ oppo&longs;itæ B D, E H etiam æquales prop. 34. <lb/>lib. 1. Atqui recta A E dupla e&longs;t rectæ B D ex hypothe&longs;i. Dupla <lb/>igitur & C E rectæ H E, quapropter C H & E H æqual<gap/>s <lb/>erunt ax. 7. Et &longs;ic C H & B D æquales &longs;unt ax. 1. Et quia nauis <lb/>tantum interualli decurrit &longs;emper: quantum &longs;calmus. Ex antec. igi­<lb/>tur &longs;i caput remi motu proprio duplum confecerit ip&longs;ius nauis inter­<lb/>ualli, tantùm prouehetur nauis: quantùm palmula retrocedet. quod <lb/>demon&longs;trandum erat.<emph.end type="italics"/></s>
</p>
<pb pagenum="88"/>
<p type="head">
<s>Propo&longs;itionis conuer&longs;io.</s>
</p>
<p type="main">
<s><emph type="italics"/>Naui æqualiter prouecta, atque palmula retroceßit: motus capitis <lb/>remi proprius duplus e&longs;t motus nauis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Si enim C H æqualis ponatur B D, quoniam eidem B D æqua­<lb/>lis e&longs;t H E in parallelogrammo, æquales igitur erunt C H & <lb/>H E ax. 1. Et &longs;ic dupla erit C E ip&longs;ius H E: & eadem C E <lb/>dupla ip&longs;ius B D. æquales porro &longs;unt C E & A E prop 26. lib. 1. <lb/>Dupla ergo erit A E rectæ B D. &longs;ed recta A E decur&longs;a e&longs;t à ca­<lb/>pite remi, & B D à &longs;calmo, quantùm autem prouehitur &longs;calmus, <lb/>tantùm & nauis. Igitur &longs;i nauis tantùm fuerit prouecta, quantùm <lb/>remi palmula retroceßit, duplum conficit caput remi motu proprio <lb/>eius interualli, quod nauis conficit. quod fuit demon &longs;trandum.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Propo&longs;itio quarta.</s>
</p>
<p type="main">
<s><emph type="italics"/>Nauis decurrens minus &longs;patium: quam caput remi decurrat: maius <lb/>tamen eius dimidio: magis prouehitur: quam palmula retrocedat: <lb/>minus autem dimidio: minus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In po&longs;tremo diagrammate ponatur B D minor, quam A E: <lb/>&longs;ed eius dimidio maior. Dico quod ip&longs;a B D maior e&longs;t, quam C H. <lb/>Nam B D & H E æquales &longs;unt, adhæc A E & C E æqua­<lb/>les &longs;unt. maior igitur erit H E dimidio ip&longs;ius A E. quapropter <lb/>reliqua C H minor dimidio erit eiu&longs;dem A E. Et minor igitur <lb/>erit C H quam B D. Interuallum autem B D, id e&longs;t quod nauis <lb/>confecit, interuallum vero C H remi palmula in contrarium de­<lb/>currit. Ideo prior pars theorematis vera. Po&longs;terior autem &longs;imiliter <lb/>o&longs;tendetur. Si enim B D minor e&longs;t dimidio ip&longs;ius A E, minor <lb/>igitur erit & H E dimidio eiu&longs;dem A E. Et quoniam A E & <lb/>C E æquales &longs;unt. Reliqua igitur C H dimidio eiu&longs;dem A E <lb/>maior erit. Et proinde minor erit B D quam C H. Nauis igitur <lb/>minus interuallum decurret in anteriora: quam remi palmula in <lb/>contrarium. quod fuit demon&longs;trandum.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Corollarium.</s>
</p>
<p type="main">
<s><emph type="italics"/>Hinc & ex præcedenti infertur, quod &longs;i caput remi motu pro­<lb/>prio decurrat interuallum maius, quam nauis, &longs;iue duplum, &longs;iue du­<lb/>plo minus, &longs;iue maius: &longs;emper interuallum nauis adiuncto ei quod <lb/>palmula retroce&longs;&longs;erit, æquale erit ei, quod à capite remi motu proprio <lb/>conficitur.<emph.end type="italics"/></s>
</p>
<pb pagenum="89"/>
<p type="main">
<s><emph type="italics"/>Semper enim B D æqualis e&longs;t H E: tota vero C E quæ æqua­<lb/>lis e&longs;t A E ex&longs;uis con&longs;tabit partibus C H, H E.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Propo&longs;itionis conuer&longs;io.</s>
</p>
<p type="main">
<s><emph type="italics"/>Nauis longius progrediens: quam remi palmula retrocedat, inter­<lb/>uallum conficit maius dimidio eius, quod motu proprio remi caput <lb/>decurrit: &longs;i minus: minus etiam dimidio.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Huius demon&longs;tratio ex prædictis facilis e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>Propo&longs;itio quinta.</s>
</p>
<p type="main">
<s><emph type="italics"/>Naui celerius mota quam caput remi: palmula antror&longs;um moue­<lb/>bitur, nec quicquam retrocedet, idque &longs;patÿ decurret quo nauis motus <lb/>motum capitis remi &longs;uperat.<emph.end type="italics"/></s>
</p>
<figure></figure>
<p type="main">
<s><emph type="italics"/>Habeat remus inci­<lb/>piente motu po&longs;itionem <lb/>A C: de&longs;inente vero <lb/><expan abbr="&longs;itũ">&longs;itum</expan> rectitudinis F G. <lb/>Scalmus igitur B pro­<lb/>pter nauis motum tran&longs;­<lb/>latus erit in D. Sit ita­<lb/>que interuallum B D <lb/>maius: <expan abbr="quã">quam</expan> A H, quod <lb/>e&longs;t à capite remi motu <lb/>proprio decur&longs;um. Sic <lb/>enim celerius dicetur <lb/>ferri nauis quam caput <lb/>remi. Dico quod palmu­<lb/>la C in vlteriora mouebitur. Nam cum &longs;calmus B prouectus fue­<lb/>rit in D, tran&longs;lata erit ip&longs;a palmula A C, vbi G in rectitudinis <lb/>&longs;itu, interuallumque conficiet C G curuilineum, cui re&longs;pondet C K. <lb/>Mouebitur igitur palmula in anteriora. Nihil autem vnquam re­<lb/>trocedere o&longs;tendetur in hunc modum. Eadem celeritate mouentur A <lb/>in H, & C ver&longs;us E circa &longs;calmum. Atqui per hypothe&longs;im cele­<lb/>rius fertur nauis: quam C ver&longs;us E. Et mouetur idem C ip&longs;a nauis <lb/>celeritate ver&longs;us K. celerius igitur feretur C ad K: quam ad E. <lb/>quapropter nihil vnquam retrocedet ip&longs;um C. Imo vero in vlte­<lb/>riora progredietur, interuallumque decurret C K, quod quidem re­<lb/>linquitur, detracto E C ex E K. Si enim remi palmula tota ip&longs;a<emph.end type="italics"/>
<pb pagenum="90"/><emph type="italics"/>nauigÿ celeritate moueretur, vltra k progrederetur, cum B perue­<lb/>niret ad D: &longs;ed retrahitur interim, propter eum motum, qui fit cir­<lb/>ca B. Sic igitur palmulæ celeritate, quæ à motu nauigÿ prouenit, re­<lb/>tardata, decur&longs;um interuallum erit C K. Videtur autem &longs;olo remo­<lb/>rum impul&longs;u hoc fieri non po&longs;&longs;e: &longs;ed alia in&longs;uper virtute impellente <lb/>opus e&longs;&longs;e: vt vento, vel impetu eò fluentis aquæ.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Atque ex his theorematis concludit Nonius Ari&longs;totelem con­<lb/>fusè propo&longs;ui&longs;&longs;e hoc problema, cum non di&longs;tinxerit inter motum re­<lb/>mi proprium, & motum à naui tran&longs;lata ei aduenientem. Concludit <lb/>etiam hac di&longs;tinctione po&longs;ita Ari&longs;totelem in&longs;citè, & falsò proble­<lb/>mati &longs;atisfeci&longs;&longs;e. Quandoquidem non continuò &longs;i nauis in anteriora <lb/>moueatur, remi palmula retrocedet: neque &longs;i retrocedat, minus inter­<lb/>uallum in contrarium tran&longs;naittet: quam nauis progrediatur, vt ex <lb/>&longs;ecunda & tertia propo&longs;itionibus liquet: prætered cum caput remi <lb/>motu proprio, qui circa &longs;calmum fit, vnâ cum nauis motu, maius in­<lb/>teruallum conficiat: quam nauis, &longs;olo autem proprio motu, &longs;i contin­<lb/>gat tantum interuallum conficere: quantum nauis, fieri non poßit, vt <lb/>palmula moueatur: fru&longs;trà Ari&longs;toteles conatus e&longs;t in vniuer&longs;um <lb/>o&longs;tendere remi caput maius &longs;patium decurrere: quam palmulam in <lb/>contrarium. Po&longs;tremo cum nauis longius progreditur: quam palmula <lb/>regreditur: minus quo que interuallum decurrit: quam caputremi, & <lb/>&longs;ic non æquale. Atque hæc cum &longs;int &longs;uis veris demon&longs;trationibus <lb/>&longs;tabilita Ari&longs;totelem in hoc problemate dormita&longs;&longs;e, quod aliquando <lb/>bono Homero contingit, conuincunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Id etiam ip&longs;um facit gu­<lb/>bernaculum, ni&longs;i quod an­<lb/>terius non mouet nauim: <lb/>vt antea dictum e&longs;t: &longs;ed <lb/>hinc vel hinc puppim &longs;o­<lb/>lum in tran&longs;uer&longs;um pellit. <lb/>Sic enim in <expan abbr="cõtrariũ">contrarium</expan> prora <lb/>vergit. Vbi igitur <expan abbr="guberna-culũ">guberna­<lb/>culum</expan> <expan abbr="adiũctũ">adiunctum</expan> e&longs;t, ibi opor­<lb/>tet aliquod eius, quod mo­<lb/>uetur <expan abbr="mediũ">medium</expan> intelligere, &
<pb pagenum="91"/><gap/><lb/>qualis e&longs;t &longs;calmus remo: <lb/>Illud vero medium proce­<lb/>dit, quo temo transfertur. <lb/>Si quidem intror&longs;us agat, <lb/>etiam puppis eò transfer­<lb/>tur, prora verò in con­<lb/>trarium nutat. In eodem <lb/>enim exi&longs;tente prora, nauis <lb/>tota transfertur.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Id etiam im&longs;um.] <emph type="italics"/>Ari&longs;toteles a&longs;&longs;erit gubernaculum idem fa­<lb/>cere quod remus. Id e&longs;t temonem plus progredi: quam pterigion. <lb/>Quod &longs;i e&longs;t, <expan abbr="animaduertendũ">animaduertendum</expan> in gubernaculo duos ine&longs;&longs;e motus, vt in <lb/>remo, proprium &longs;cilicet, & alienum. Et cum &longs;imili modo quo remus <lb/>veniat in v&longs;um, omnia quæ de remo antea ex Nonio ob&longs;eruauimus, <lb/>in eo etiam habere locum. Proinde &longs;i in remi problemate minus per­<lb/>&longs;picax fuerit Ari&longs;toteles, nec in hoc per &longs;picacior fui&longs;&longs;e putandus e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Ni&longs;i quod anterius.] <emph type="italics"/>Repetitio e&longs;t differentiæ motuum remi <lb/>& gubernaculi &longs;umpta ex diuer&longs;itate terminorum ad quos vterqne <lb/>ducit de qua igitur ante.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vbi igitur guber.] <emph type="italics"/>Antea in gubernaculi &longs;imilitudine cum <lb/>vecte attulerat Ari&longs;toteles pondus mouendum mare, motorem eum <lb/>qui &longs;edet in puppi, quod erat tertium de centro, circa quod temo mo­<lb/>uetur, prætermi&longs;erat. Id nunc adiungit. E&longs;t autem cardo cui puppis <lb/>nauis annectitur non aliter quam &longs;calmo remus, vt & circa cardi­<lb/>nem gubernaculum vertitur, &longs;icut circa &longs;calmum remus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>7. Cau&longs;a pote&longs;tatis <lb/>Antemnæ.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur quantò antemna &longs;u­<lb/>perior fuerit, tantò celerius <lb/>nauis feratur <expan abbr="eod&etilde;">eodem</expan> velo, <expan abbr="eo-demq;">eo­<lb/>demque</expan> <expan abbr="v&etilde;to">vento</expan>? An quia malus
<pb pagenum="92"/><gap/><lb/>e&longs;t vectis, & calx in qua in­<lb/>figitur, pre&longs;&longs;io? Quod vero <lb/>pondus mouere oportet, <lb/>e&longs;t nauis: & ventus in <expan abbr="velũ">velum</expan>, <lb/>e&longs;t mouens. Igitur &longs;i quan­<lb/>to remotior fuerit pre&longs;&longs;io, <lb/>facilius & celerius vis <expan abbr="ead&etilde;">eadem</expan> <lb/>pondus im&longs;um mouet: an­<lb/>temna &longs;ublimius po&longs;ita à <lb/>calce mali, quæ pre&longs;&longs;io e&longs;t, <lb/>magis di&longs;tare velum faciet.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Antemnæ.] <emph type="italics"/>Antemna lignum e&longs;t per tran&longs;uer&longs;um in malo <lb/>nauis po&longs;itum, à quo velum dependet. Latini illius ligni extre­<lb/>mas partes <expan abbr="vocãt">vocant</expan> cornua ob quod Bayfius<gap/>putat antemnas dici Græ­<lb/>cis<emph.end type="italics"/> <foreign lang="greek">xerai/an.</foreign> <emph type="italics"/>Malus vero nauis aliud e&longs;t lignum propè in medio nauis <lb/>in&longs;tar <expan abbr="trũci">trunci</expan> arboris perpendiculariter infixum,<emph.end type="italics"/> <foreign lang="greek">i(so\s,</foreign> <emph type="italics"/>cuius partes di­<lb/>uer&longs;is appellationibus di&longs;tinctæ à Macrobio in quinto Saturnalium <lb/>in hæc verba &longs;unt. A&longs;clepiades autem vir inter Græcos apprimè <lb/>doctus ac diligens carche&longs;ia à nauali re dicta exi&longs;timat. At enim <lb/>naualis mali partem inferiorem, pternam vocari, at circa mediam <lb/>ferme partem<emph.end type="italics"/> <foreign lang="greek">tea/xhlon</foreign> <emph type="italics"/>dici: &longs;ummam vero partem carche&longs;ium <lb/>nominari, & inde diffundi in vtrumque veli latus ea quæ cornua <lb/>vocantur. Velum etiam e&longs;t linteum quadrangulum vel triangulum <lb/>ex antemna dependens, quod expen&longs;um excipit ventum, cuius im­<lb/>pul&longs;u nauis tran&longs;uehitur non aliter <expan abbr="quã">quam</expan> antea diximus remis. Æolus <lb/>primus mortalium velis v&longs;us e&longs;&longs;e dicitur. Et propterea deus vento­<lb/>rum e&longs;t habitus. Sic enim de eo apud Diodorum legimus.<emph.end type="italics"/> <foreign lang="greek">w_<gap/>\s de\ <lb/>tou/tois ti/w\ <gap/> i(ci/wn xrei/an toi_s nanlikoi_s ei)ongh/oa<gap/> kai\ di­<lb/>da/cai.</foreign> <emph type="italics"/>id e&longs;t in&longs;uper & velorum v&longs;um nautis introduxi&longs;&longs;e, ratio­<lb/>nemque vtendi docui&longs;&longs;e. velorum autem apud veteres tria fuerunt <lb/>genera Artemo & acatium, quod velum maius: dolo, quod minus <lb/>erat: &<emph.end type="italics"/> <foreign lang="greek">e)po/s<gap/>omos,</foreign> <emph type="italics"/>quod velum à tergo ponebatur. vnde nauis à <lb/>Iulio polluce<emph.end type="italics"/> <foreign lang="greek"><gap/>iar/mduos,</foreign> <emph type="italics"/>Antigoni dicta, quæ tria vela haberet<emph.end type="italics"/>
<pb pagenum="93"/><emph type="italics"/>trino&longs;que malos, quod antiquis fuit <expan abbr="rarũ">rarum</expan>, no&longs;tris hodie <expan abbr="frequ&etilde;tißimũ">frequentißimum</expan>. <lb/>quia inuenta pyxide nautica, inquit Cardanus, & lapidis Herculis <lb/>auxilio pluribus locis vela dispo&longs;ita, melius dirigunt iter: antiquis <lb/>contrà, quoniam &longs;yderibus Cyno&longs;ura, & Helice, vias dirigebant, & <lb/>ob id non ad amußim, nec ex lineis, cra&longs;&longs;a quidem Minerua: &longs;ed certa <lb/>deformatis malorum multitudo confu&longs;ionem in cur&longs;u, & impedi­<lb/>mentum, maiu&longs;que periculum attuli&longs;&longs;et.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cur quanto.] <emph type="italics"/>Quintum e&longs;t &longs;peciale problema de vecte con&longs;i­<lb/>derato in malo nauis. Cur &longs;cilicet antemna &longs;ublimiore mali loco po­<lb/>&longs;ita, vt &longs;it idem velum, idemque ventus velo exceptus, nauis cele­<lb/>rius feratur. Id e&longs;t vt cætera omnia &longs;int paria. Nam nauis velocitas, <lb/>non &longs;olum pendet à ventorum impetu & rectitudine, & velorum <lb/>magnitudine: &longs;ed & ex loco humiliore, vel &longs;ublimiore, ex cæli ab <lb/>Oriente in Occidentem conuer&longs;ione, nauis leuitate & forma. quæ <lb/>enim non merguntur vt<emph.end type="italics"/> <foreign lang="greek">droma/des</foreign> <emph type="italics"/>(&longs;ic enim vocat Ari&longs;tophanes <lb/>eas, quas nunc vulgus fregatas appellat) qua&longs;i aquis innitentes cur&longs;u <lb/>&longs;unt velocißimæ, & longiores latis, po&longs;teas, quæ carinam habent te­<lb/>nuem, vt aquas facile diuidant, vltimo loco quæ qua&longs;i mediæ ante <lb/>quidem tenues, po&longs;t latiores ad velocem cur&longs;um & ferendum onera <lb/>aptæ, & humiles altis, & leui ex ligno: &longs;ed & parte intra aquam <lb/>polita læuigata & &longs;æuo illita.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia malus e&longs;t.] <emph type="italics"/>Solutio e&longs;t problematis propo&longs;iti per re­<lb/>ductionem mali ad vectem, & eius calcis ad hypomochlium. Syllo­<lb/>gi&longs;mus hîce&longs;t &longs;uis omnibus partibus ab&longs;olutus, &longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quantò pars ab hypomochlio ad caput vectis e&longs;t longior: tantò <lb/>vis mouens, ea e&longs;t ventus, onus, id e&longs;t nauim, facilius & ce­<lb/>lerius mouet. Ex anteced.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quò autem antemna, intellige cum velo expan&longs;o, &longs;uperior e&longs;t in <lb/>malo: eò pars ab hypomochlio ad caput vectis e&longs;t longior. ax. 9. <lb/>E&longs;t enim malus vectis, & mali pterna &longs;eu calx e&longs;t hypo­<lb/>mochlium.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo antemna cum &longs;uperior e&longs;t, ventus facilius & celerius <lb/>mouet nauim.<emph.end type="italics"/><lb/>
<arrow.to.target n="marg22"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg22"></margin.target>Cap. 8. lib <lb/>10.</s>
</p>
<p type="main">
<s><emph type="italics"/>Eadem de hoc problemate fuit Vitruuÿ <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan> his verbis expre&longs;&longs;a. <lb/>Nauis onerariæ vela cum &longs;int per altitudinem mediam mali penden­<lb/>tia, non pote&longs;t habere nauis celerem cur&longs;um: cum autem in &longs;ummo<emph.end type="italics"/>
<pb pagenum="94"/><emph type="italics"/>cacumine antemnæ &longs;ubductæ &longs;unt, tunc vehementiori progreditur <lb/>impetu, quod non proxime calcem mali, quæ e&longs;t loco centri: &longs;ed in <lb/>&longs;ummo longius, & ab eo progre&longs;&longs;a recipiunt in &longs;e vela ventum. Ita­<lb/>que vti vectis &longs;ub onere &longs;ubiectus, &longs;i per medium premitur, durior e&longs;t <lb/>neque incumbit. Cum autem caput eius &longs;ummum deducitur, faciliter <lb/>onus extollit: humiliter vela cum &longs;unt per medium temperata, mino­<lb/>rem habent virtutem. Quæ autem in capite mali &longs;ummo collocantur, <lb/>di&longs;cedentia longius à centro non acriore, &longs;ed eodem flatu preßione ca­<lb/>cuminis vehementius cogunt progredi nauem. Ex his etiam intelli­<lb/>gere licet cur hodierni nautæ &longs;olo &longs;æpe in procellis vtuntur dolone, <lb/>velo quidem non tam minimo magnitudine quam altitudine Trin­<lb/>chetum appellant. Solum enim &longs;u&longs;tinet nauim, quæ à ventis vel vn­<lb/>dis mergi&longs;olet. ab vndis quidem vbi humilior e&longs;t: à ventis vero ex <lb/>lateribus & anteriore parte. Siquidem velum illud humile & exi­<lb/>guum efficit, vt nauis anteriore parte leuis, nec mergatur prona à <lb/>ventis, nec aquas ea excipiat, nec tamen impelli pote&longs;t nauis in &longs;copu­<lb/>los, nec euerti ob cau&longs;as dictas. Quin &longs;i nimium adhuc venti &longs;æuiant, <lb/>dolonem demittant adhuc infra magis, quin & ip&longs;um malum etiam <lb/>&longs;ublato velo, aut circa antemnam implexo & inuoluto, & ne nauis <lb/>obruatur, antror&longs;um. Hæc enim pars vim <expan abbr="ventorũ">ventorum</expan> omnem excipit: <lb/>gubernatores etiam puppim multa arena, lapilli&longs;que onerare, &longs;i de&longs;it <lb/>aliud onus, &longs;olent.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>8. Cur quando è cornu vo­<lb/>lunt nauigare pedem fa­<lb/>ciunt.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur quando è cornu na­<lb/>uigare voluerint vento &longs;e­<lb/>cundo non exi&longs;tente, par­<lb/>tem quidem veli ad guber­<lb/>natorem &longs;pectantem con­<lb/>trahunt: <expan abbr="part&etilde;">partem</expan> vero ad pro­<lb/>ram <expan abbr="relaxãt">relaxant</expan> pedem facien­<lb/>tes. An quia gubernacu­<lb/>lum non pote&longs;t auertere, <lb/>cum multus exiftit ventus:
<pb pagenum="95"/><gap/><lb/><expan abbr="cũ">cum</expan> pauc^{9} verò pote&longs;t. <expan abbr="v&etilde;tus">ventus</expan> <lb/>igitur perpellit, quem &longs;e­<lb/>cundum facit gubernacu­<lb/>lum, auertens & compel­<lb/>lens mare, &longs;imul & nautæ <lb/>pugnant cum vento, & in <lb/>contrariam nituntur par­<lb/>tem.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Ecornu volunt nauigare.] <emph type="italics"/>Diximus antemnarum extrema <lb/>appellari cornua. Hinc è cornu nauigare e&longs;t cum vento cornu <lb/>antemnarum obijcitur. Quod feci&longs;&longs;e &longs;ignificabat Troianos Virgi-<emph.end type="italics"/></s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg23"></arrow.to.target><lb/><emph type="italics"/>lius hoc ver&longs;u,<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg23"></margin.target>Lib. 3. <lb/>Æneid.</s>
</p>
<p type="main">
<s>Cornua velatarum obuertimus antemnarum.</s>
</p>
<p type="main">
<s>Pedem faciunt.] <emph type="italics"/>Extextu & rei natura quæ in eo explica­<lb/>tur ratiocinantes hîc pro<emph.end type="italics"/> <foreign lang="greek">ou(/tws poiou_oi</foreign> <emph type="italics"/>repo&longs;uimus<emph.end type="italics"/> <foreign lang="greek">po/da poiou_oi.</foreign> <emph type="italics"/>E&longs;t <lb/>autem<emph.end type="italics"/> <foreign lang="greek">w_ou/s</foreign> <emph type="italics"/>Græcis, & pes Latinis variæ admodum &longs;ignificationis. <lb/>Præter cæteras hîc huius duas annotare licet. Prior venit in men­<lb/>tem ob duos locos apud Galenum à perpaucis intellectos. Alter e&longs;t <lb/>cap. 9. lib. 2. de mu&longs;c. motu: alter com. 4. in lib. 6.<emph.end type="italics"/> <foreign lang="greek">e(pid.</foreign> <emph type="italics"/>in Aph. 24. <lb/>vbi dicit tibicines, præcones, nuncupatum<emph.end type="italics"/> <foreign lang="greek">po/da,</foreign> <emph type="italics"/>id e&longs;t, pedem cane­<lb/>re. vbi dubium non e&longs;t Galenum &longs;ignificare volui&longs;&longs;e genus quod­<lb/>dam vocis, quæ vehementi & longa exufflatione opus habeat, vt <lb/><expan abbr="etiã&longs;en&longs;it">etian&longs;en&longs;it</expan> Hieronymus Mercurialis, qui hos Galeni locos ob&longs;erua­<lb/>uit. Nos <expan abbr="etiãlegimus">etiallegimus</expan> in <expan abbr="cõment">comment</expan>. Cæ&longs;aris cum <expan abbr="pugnandũ">pugnandum</expan> &longs;ibi foret, <lb/>iuß&longs;&longs;e ab equis milites <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan>, nequis <expan abbr="&longs;p&etilde;fugæ">&longs;penfugæ</expan> in <expan abbr="equorũ">equorum</expan> celerita­<lb/>te reponeret. Quæ iußio forta&longs;&longs;e erat,<emph.end type="italics"/> <foreign lang="greek">e)ru_n po/da,</foreign> <emph type="italics"/>dicere <expan abbr="ped&etilde;">pedem</expan>, vbi <expan abbr="St&etilde;-torea">Sten­<lb/>torea</expan> voce opus erat, vt ab omnibus audiretur: contra hodie apud <lb/>Gallos, inituris pugnam iubetur a&longs;cendere in equos: po&longs;terior e&longs;t qua <lb/>ea pars in velo, quæ acutior & inferior ad nauis latus, vel ad mali <lb/><expan abbr="pternã">pternam</expan> religatur, modóque <expan abbr="cõtrahitur">contrahitur</expan> modò relaxatur. vnde Poëta:<emph.end type="italics"/><lb/>
<arrow.to.target n="marg24"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg24"></margin.target>Lib. 5. <lb/>Æneid.</s>
</p>
<p type="main">
<s>vna omnes fecere pedem.</s>
</p>
<p type="main">
<s><emph type="italics"/>Alij tamen dicunt e&longs;&longs;e funem, quo id fit. Interpres Apollonij Rho­<lb/>dij funes veli id e&longs;t<emph.end type="italics"/> <foreign lang="greek">xa/lw</foreign> <emph type="italics"/>rudentes in tria genera diuidit. Aut enim<emph.end type="italics"/></s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg25"></arrow.to.target>
<pb pagenum="96"/><emph type="italics"/>detrahitur his velum, & vocantur<emph.end type="italics"/> <foreign lang="greek">mesouri/ai</foreign>: <emph type="italics"/>aut intenditur vtrin­<lb/>que ad proram, & &longs;unt<emph.end type="italics"/> <foreign lang="greek">w_<gap/>/tonoi</foreign>: <emph type="italics"/>aut conuertitur & laxatur, hi <lb/>&longs;unt<emph.end type="italics"/> <foreign lang="greek"><gap/>\ ta\s gwni/as</foreign> <emph type="italics"/>ad angulos, & dicuntur<emph.end type="italics"/> <foreign lang="greek">po/des</foreign> <emph type="italics"/>& ante hos<emph.end type="italics"/><lb/><foreign lang="greek">w_<gap/>/podes</foreign> <emph type="italics"/>quo &longs;en&longs;u dixi&longs;&longs;e Plinius videtur lib. 2. cap. 47. Ii&longs;dem <lb/>autem ventis in contrarium nauigatur prolatis pedibus vt noctu <lb/>plerumque vela concurrant.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg25"></margin.target>Lib. 3.</s>
</p>
<p type="main">
<s>Cur quando.] <emph type="italics"/>Sextum e&longs;t problema &longs;peciale de vecte in naui­<lb/>gatione obliqua, quod &longs;oluitur triplici ope nempe veli obliqui ex par­<lb/>te contracti, parteque expan&longs;i gubernaculi tanquam vectis, & re­<lb/>migum renixus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>E cornu nauigare.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="greek">e)x ou)<gap/>/as</foreign> <emph type="italics"/>hî legendum putamus vt <lb/>in titulo<emph.end type="italics"/> <foreign lang="greek">e)x xerai/as</foreign> <emph type="italics"/>nam hæc &longs;unt<emph.end type="italics"/> <foreign lang="greek">a)s/i<gap/>ata</foreign> <emph type="italics"/>velle nauigare<emph.end type="italics"/> <foreign lang="greek">e)x ou)<gap/>i/as</foreign><lb/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">mh\ ou)<gap/>i/ou w_neu/ ma/los o(/n(los.</foreign> <emph type="italics"/>Quomodo enim nauigabitur vento <lb/>&longs;ecundo, &longs;i ventus &longs;ecundus non e&longs;t. At cum ventus &longs;ecundus non <lb/>e&longs;t, antemnarum ope rectum nihilominus tenere cur&longs;um poßibile e&longs;t, <lb/>Et id vt fiat & quibus de cau&longs;is, explicatur hîc ab Ari&longs;torele.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vento &longs;ecundo.] <emph type="italics"/>Ventus &longs;ecundus e&longs;t cum vt ait Poëta,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>A tergo comitatur euntes,</s>
</p>
<p type="main">
<s><emph type="italics"/>Hic e&longs;t quem nautæ &longs;ibi dari optant vnde e&longs;t illud,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Ferte viam facilem, venti & &longs;pirate &longs;ccundi.</s>
</p>
<p type="main">
<s><emph type="italics"/>Qui huic e&longs;t contrarius, dicitur aduer&longs;us, cum in proram inuehitur. <lb/>Nec eo &longs;ic flante nauis ni&longs;i remis agi pote&longs;t, idque magnis viribus <lb/>& magno conatu.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Non aliter quam qui aduer&longs;o vix flumine lembum</s>
</p>
<p type="main">
<s>Remigijs &longs;ubigit, &longs;i brachia forte remi&longs;it,</s>
</p>
<p type="main">
<s>Atque illum præceps prono rapit alueus amne.</s>
</p>
<p type="main">
<s><emph type="italics"/>Inter hos duo &longs;unt medÿ, vnus tran&longs;uer&longs;us ad latera nauis perpendi­<lb/>culariter incidens: alter obliquus <lb/>
<figure id="fig34"></figure><lb/>qui medius e&longs;t inter &longs;ecundum & <lb/>tran&longs;uer&longs;um, velinter aduer&longs;um & <lb/>tran&longs;uer&longs;um. Vt e&longs;to nauis G H, <lb/>& prora &longs;it G puppis H, ventus <lb/>ex B &longs;ecundus erit, ex A aduer­<lb/>&longs;us, ex C vel D tran&longs;uer&longs;us, ex E <lb/>vel F obliquus. Horum autem mo­<lb/>tuum Galenus obliquos per pulchrè<emph.end type="italics"/>
<pb pagenum="97"/><emph type="italics"/>declarauit &longs;umpta primùm hac propo&longs;itione. In vniuer&longs;um quando <lb/>à duobus motibus ex tran&longs;uer&longs;o &longs;ibi inuicem occurrentibus trahitur <lb/>corpus, &longs;i multò quidem &longs;upereminet alter, nece&longs;&longs;arium e&longs;t ob&longs;curari, <lb/>di&longs;pareréue reliquum: pauca verò cum e&longs;t exuperantia alterius: aut <lb/>ambo æqualiter po&longs;&longs;unt, mixtum ex vtri&longs;que fieri eum corporis mo­<lb/>tum oportet. Videntur autem omnia i&longs;ta propemodum quotidie in <lb/>&longs;excentis exemplis, exempli gratia in remigantibus, &longs;imul & naui­<lb/>bus ventum tran&longs;uer&longs;um habentibus. Si enim æquipollet venti & <lb/>remigantium robur, mixtum fieri motum nece&longs;&longs;e e&longs;t. Cum neque <lb/>antror&longs;um &longs;olum, neque ad tran&longs;uer&longs;um naues ferantur, &longs;ed ad am­<lb/>borum medium (vbi malè legitur Medicum) &longs;i vero remigantium <lb/>robur maius fuerit, antror&longs;um magis, quam ad tran&longs;uer&longs;um. Si au­<lb/>tem venti violentia vincat, ad tran&longs;uer&longs;um magis, quam antror­<lb/>&longs;um. Multus autem &longs;i fuerit exce&longs;&longs;us, adeo vt alterius vires omnino <lb/>vincantur, nauigantium quidem ob&longs;curatis viribus, ad tran&longs;uer­<lb/>&longs;um: venti vero, antror&longs;um magis naues ferentur. Quid tandem &longs;i <lb/>tenuis omnino aura fuerit, nauis verò prælonga, & leuis, quamplu­<lb/>rimos habens nautas, poterit aliquando motus ab aura e&longs;&longs;e manife­<lb/>&longs;tus? Sed neque &longs;i maximus quidem &longs;uerit ventus, nauis autem & <lb/>maxima & grauis, & duo &longs;olum aut tres remigent, remigum actio­<lb/>nem apparere poßibile e&longs;t. cap. 19. lib. 1. de v&longs;. partium.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia gubernaculum.] <emph type="italics"/>Solutio e&longs;t problematis propo&longs;iti, <lb/>quod &longs;ic fiet euidentius. Cur qui è cornu nauigaturi vento &longs;cilicet <lb/>non &longs;ecundo exi&longs;tente: &longs;ed obliquo vel tran&longs;uer&longs;o eam veli partem, <lb/>quæ ver&longs;us gubernatorem e&longs;t, contrahunt id e&longs;t &longs;tringunt, & circa <lb/>antemnam implicant. Eam vero, quæ ad proram, relaxant, quod ap­<lb/>pellant pedem facere. Re&longs;pon&longs;io. Quia obliquè vel tran&longs;uer&longs;im naui­<lb/>gari non pote&longs;t, ni&longs;i tunc gubernaculum auertat, atque obliquet na­<lb/>uim. Eò enim fertur nauis, quò prora dirigitur. Obliquare autem <lb/>nauim vel tran&longs;uertere tantò facilius gubernaculum pote&longs;t: quantò <lb/>ventus paucior e&longs;t. Paucior autem fit contracto velo, quod &longs;pectat ad <lb/>puppim, & relaxato eo quod e&longs;t ad proram. Sufficiens tamen pro­<lb/>pellere. Obliquus enim veli relaxati &longs;inubus totis excipitur. I deo <expan abbr="cũ">cum</expan> <lb/>& &longs;ufficiat gubernaculum auertere atque propellere mare, vocatis <lb/>ad id in auxilium, &longs;i opus e&longs;t, nautis in contrariam vento partem ni­<lb/>tentibus, fit vt ex obliquo vel tran&longs;uer&longs;o vento feratur nauis. Sic<emph.end type="italics"/>
<pb pagenum="98"/><emph type="italics"/>enim quantum ventus exempli gratia dextror&longs;um propellit nauim: <lb/>tantum vi &longs;ua gubernaculum cum nautis &longs;ini&longs;tror&longs;um illam tor­<lb/>quet, ac tapit. Et ita neutra ex contrarÿs viribus præualente, eò fer­<lb/>tur nauis, quò vult gubernator, etiam&longs;i ventus minime &longs;ecundus &longs;it.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quem <expan abbr="&longs;ecundũ">&longs;ecundum</expan>.] <emph type="italics"/>Ex hoc loco colligi pote&longs;t cau&longs;a, propter quam <lb/>quotidie naues ob&longs;eruantur non citra admirationem eodem vento in <lb/>contrarias partes nauigare, vt & Plinius etiam recitat. Ii&longs;dem <lb/>ventis in contrarium nauigatur prolatis pedibus (hi &longs;unt funes de <lb/>quibus ante) vt noctu plerumque vela concurrant. Hoc autem vt <lb/>fiat geometricè demon&longs;tratur.<emph.end type="italics"/></s>
</p>
<figure></figure>
<p type="main">
<s><emph type="italics"/>Sint naues A tendens ad G, & B tendens ad H. ventus ex <lb/>C recta feratur ad D, tanquam ad centrum. Itaque vento pro­<lb/>pul&longs;a nauis A, feretur in E, & B in F. Fiat igitur in naui per <lb/>temonem mutatum angulus G A K, qui &longs;it æqualis angulo G <lb/>A E: tum H B L æqualis angulo H B F.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quia igitur nauis A à vento fertur in E, & per temonis muta­<lb/>tionem in K, feretur recta in G, & eadem ratione B in H. <lb/>Neuter enim cum &longs;uo impul&longs;u præualeat, medium teneat A G ne­<lb/>ce&longs;&longs;e e&longs;t, quod &longs;i ventus præualet, adiungitur remigum renixus, qui <lb/>&longs;i non &longs;atis &longs;it, vento cedendum, aut anchora iacienda. Tum autem <lb/>vix remiges re&longs;i&longs;tunt, <expan abbr="cũ">cum</expan> nauis e&longs;t in centro, vel radio perpendicula­<lb/>ri venti, quo in loco propter vim venti maiorem, & anguli per te-<emph.end type="italics"/>
<pb pagenum="99"/><emph type="italics"/>monem faciendi magnitudinem, vt qui rectum æquare debeat, dif­<lb/>ficillimè ad locum de&longs;tinatum dirigitur: at quantò fuerit remotior <lb/>à puncto D, velocius & facilius feretur, quia ventus rectius tan­<lb/>get puppim, minor enim erit &longs;emper angulus per temonem facien­<lb/>dus, vt intelligitur ex G P Q minore: quam G A E, & G I <lb/>M minore: quam G P <expan abbr="q.">que</expan> Sunt enim duo C A G & G A E, <lb/>quia facti à recta G A in rectam C E duobus rectis æquales <lb/>prop. 13. lib. 1. & per eandem etiam duo C P G & G P Q duobus <lb/>rectis æquales. Ergo duo C A G & G A E duobus C P G & <lb/>G P Q &longs;unt æquales axiom. 1. E&longs;t autem C P G externus oppo­<lb/>&longs;ito interno C A G maior, prop. 16. lib. 1. Reliquus igitur G P Q <lb/>reliquo G A E minor erit, & ita de cæteris. Sicque nauis proce&longs;&longs;u <lb/>&longs;uo mutabit &longs;en&longs;im temonem, vt & vela.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>9. Cur è figuris rotundæ <lb/>&longs;unt mobiliores.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur quæ figurarum ro­<lb/>tundæ & circulares exi­<lb/>&longs;tunt, facilius mouentur. <lb/>Tribus vero modis con­<lb/>tingit circulum volui. vel <lb/>enim &longs;ecundum curuatu­<lb/>ram vnà centro tran&longs;lato, <lb/>qualiter rota plau&longs;tri vol­<lb/>uitur: vel circa centrum <lb/>tantum, quod ip&longs;um quie&longs;­<lb/>cat, vt trochleæ vel in pla­<lb/>no, manente centro, vt fi­<lb/>guli rota vertitur. An igi­<lb/>tur hæc celerrima fiunt, <lb/>quod parua &longs;ui parte <expan abbr="planũ">planum</expan> <lb/><expan abbr="attingãt">attingant</expan>, vt circulus in <expan abbr="pũ-cto">pun­<lb/>cto</expan>, & quia non offen&longs;ant? <lb/>Di&longs;tat enim angul^{9} à terra. <lb/>Et hoc <expan abbr="etiã">etiam</expan> cui occur&longs;ant,
<pb pagenum="100"/><gap/><lb/>corpus rur&longs;us parum tan­<lb/>gant. At &longs;i recti lineum e&longs;­<lb/>&longs;et, rectitudine &longs;ua mul­<lb/>tum plani attingeret.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr quæ figurarum.] <emph type="italics"/>In hoc capite redit Ari&longs;toteles ad fi­<lb/>guras rotundas, & quærit generaliter cau&longs;as facilitatis motus <lb/>earum, ea&longs;que quinque aßignat <expan abbr="modicũ">modicum</expan> tactum, offen&longs;ationem exi­<lb/>guam, nutum dimidiæ partis, motum <expan abbr="perpetuũ">perpetuum</expan>, motum naturalem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Tribus modis.] <emph type="italics"/>Rotundorum motus &longs;implex per &longs;pecies indu­<lb/>citur: &longs;ed diminutè. Perfectè autem &longs;ic. Rotundum omne per &longs;e mo­<lb/>uetur, vel ab alio. Per &longs;e quidem vt cælum, cuius nulla pars primò <lb/>moueri dict pote&longs;t: omnes tamen &longs;imul in loco mouentur. Ab alio <lb/>verò, in quo etiam eius quod mouetur pars aliqua primò mouetur, <lb/>& quidem duobus modis progrediente axe: vel manente. Progre­<lb/>diente rur&longs;us duobus modis, priore cum motus incipit à circumfe­<lb/>rentia, vt in rota &longs;uper planum volutata: po&longs;teriore <expan abbr="cũ">cum</expan> ab axe, vt in <lb/>rota per axem currus circumducta. Manente verò, rur&longs;us duobus <lb/>modis, nempè axe moto in &longs;uo loco: vel etiam immoto. Et moto qui­<lb/>dem rur&longs;us duobus modis, primo cum motus incipit à circumferen­<lb/>tia, vt in &longs;uccula per collopes ver&longs;a: &longs;ecundo cum motus incipit ab <lb/>axe, vt in mola & rota qua acuuntur gladÿ: immoto vero, vt in <lb/>trochlea, cuius <expan abbr="vert&etilde;tis">vertentis</expan> per funes motus incipit à circumferentia: &longs;ed <lb/>axe omnino immoto. Sicque legitima diui&longs;ione & experimento ro­<lb/>tundorum motus &longs;ex &longs;pecies infimæ reperiuntur, è quibus prima præ­<lb/>termi&longs;&longs;a e&longs;t ab Ari&longs;totele, quia nihil ad Mechanicen, &longs;ecunda præ­<lb/>termitti non debuit, ni&longs;i quia notißima.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vel enim.] <emph type="italics"/>Cum rota currui &longs;ubiecta e&longs;t, tracto curru axis vnà <lb/>progreditur. Et cum rota quie&longs;cere nequeat, quia axis tractus pre­<lb/>mit, & pondus adÿcit non ad perpendiculum: &longs;ic enim ad centrum <lb/>impelleret: &longs;ed ad latus, quo trahitur, & pondere adiecto ad nutan­<lb/>tem dimidia &longs;ui parte &longs;emper rotam, eò labitur. Facilius autem cir­<lb/>cumuerti ur: quam trahatur, itaque procedit. Et &longs;ic ibi quidem rota <lb/>ex circumferentia, quam ab&longs;idem hîc appellat, mouetur: &longs;ed ab axe<emph.end type="italics"/>
<pb pagenum="101"/><emph type="italics"/>initium e&longs;t motus. Plurimum itaque confert ad motus facilitatem, <lb/>vt tum axis, tum rota intus &longs;int læuißima, vnde aurigæ axungia <lb/>(quæ inde nomen traxit) ip&longs;a inungunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quod parua &longs;ui.] <emph type="italics"/>Prima cau&longs;a e&longs;t facilitatis motus &longs;uper plano <lb/>in rotundis de modico contactu in omni &longs;ui po&longs;itione. Contactus <lb/>enim multa parte &longs;ui facit hærere, & &longs;imul e&longs;&longs;e ea, quæ &longs;e&longs;e &longs;ic con­<lb/>tingunt, & quidem tantò magis, quantò maior e&longs;t hic contactus. <lb/>quò igitur erit minor, eò minus hærere, citiu&longs;que diuelli faciet. Mul­<lb/>ta autem præter rotunda vt triangulum æquilaterum, & tetraë­<lb/>dron planum in puncto contingere po&longs;&longs;unt, &longs;ed non in omni &longs;ui po&longs;i­<lb/>tione, vt cum &longs;ecundum vnam &longs;ui aream &longs;uperiacent: at rotunda <lb/>&longs;iue &longs;phæra &longs;it, &longs;iue circulus planum in vno puncto quouis modo &longs;e­<lb/>cundum curuaturam po&longs;ita attingunt. quod demon&longs;tratum e&longs;t de <lb/>illo quidem à Theodo&longs;. prop. 2. lib. 1. de Sphær. de hoc vero ab Eucli­<lb/>de prop. 16. lib. 3.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et quia non off.] <emph type="italics"/>Secunda cau&longs;a e&longs;t de occur&longs;antibus, quæ <lb/>rur&longs;us cum minimam partem rotundorum attingant, & atterant, <lb/>minus impediunt, quam quæ plus attingunt, pluribu&longs;que occur&longs;ant.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Di&longs;tat enim angulus.] <emph type="italics"/>Cum rotundum incumbit plano ad <lb/>omnes rectas à quibus tangitur in ip&longs;o plano angulos facit contin­<lb/>gentiæ, quorum &longs;inguli quia &longs;unt minores quouis acuto angulo re­<lb/>ctilineo, vt e&longs;t demon&longs;tratum prop. 16. lib. 3. procliues &longs;unt maxime <lb/>ad motum. Latus enim curuum anguli vnius contactus &longs;emotum <lb/>quidem e&longs;t à plano: &longs;ed parum propter anguli angu&longs;tiam. Et &longs;ic non <lb/>offen&longs;at, & proximum e&longs;t ca&longs;ui. Hinc etiam vna caufa colligi po­<lb/>te&longs;t, cur rotunda maiora facilius moueantur minoribus, quod <lb/>angulos &longs;ui contactus tantò acutiores faciunt: quantò &longs;unt maiora, <lb/>vt in libello no&longs;tro de angulo contactus demon&longs;trauimus.<emph.end type="italics"/></s>
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<p type="main">
<s>At &longs;i rectilineum e&longs;&longs;et.] <emph type="italics"/>Difficultas motus in mobili pendet <lb/>ab eius internis aut externis. Interna e&longs;t naturalis cuiu&longs;que <expan abbr="prop&etilde;&longs;io">propen&longs;io</expan>, <lb/>qua extra locum exi&longs;tens, &longs;i liberum &longs;inatur mobile, ad <expan abbr="eũ">eum</expan> per &longs;e fe­<lb/>ratur. Atque vt ibi vi retineatur, eò tamen quodam motu occulro <lb/>tendit, vt graue deor&longs;um, leue &longs;ur&longs;um, & &longs;emper &longs;ecundum rectam <lb/>perpendicularem in qua e&longs;t centrum grauitatis mobilis: aliò nun­<lb/>quam, ni&longs;i vi contraria nixus ille vincatur, vt cum graue &longs;ur&longs;um: <lb/>aut leue deor&longs;um: aut vtrumque ad latera propellitur. Itaque prima<emph.end type="italics"/>
<pb pagenum="102"/><emph type="italics"/>difficultas in <expan abbr="viol&etilde;tis">violentis</expan> pendet è renixu. Externa vero &longs;unt <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan>, <lb/>& occur&longs;ans, & mobilis figura. Subiectum appello, cui mobile &longs;u­<lb/>perincumbit, aut primo in&longs;i&longs;tit, & huic tantò magis qua &longs;i inhæret <lb/>& in&longs;i&longs;tit: quantò pluribus punctis ab eo &longs;imul tangitur. Tot enim <lb/>&longs;unt lineæ in mobili ad rectos angulos in&longs;i&longs;tentes &longs;ubiecto, quæ vt <lb/>vires vnitæ &longs;e mutuo &longs;tabiliunt, & fulciunt, ne facile deÿciantur: <lb/>contrà id, quod antè de Sphærico, vbi cum vna e&longs;&longs;et <expan abbr="tãtum">tantum</expan> quæ in­<lb/>&longs;i&longs;teret plano ad rectos, facillima ab illo &longs;tatu erat deiectio. Maior <lb/>igitur inhærentia, maius e&longs;t impedimentum. Occur&longs;ans autem dico <lb/>quodlibet corpus aliud, vel contra motum, vel cum locum ibi habe­<lb/>at, minimè <expan abbr="ced&etilde;s">cedens</expan>. Talia &longs;unt fortuita omnia, quæ vt &longs;ubiectum, quò <lb/>pluribus mobilis punctis occurrunt propter eandem cau&longs;am, eò plus. <lb/>ne fiat inuer&longs;io vel volutatio, impediunt. Tale quoque medium e&longs;t <lb/>nece&longs;&longs;arium, per quod fit motus, <expan abbr="rarũ">rarum</expan>, den&longs;um, vtrumque impariter. <lb/>Hoc enim magis, illud minus: re&longs;i&longs;tit partibus obuijs. Re&longs;i&longs;tens in­<lb/>&longs;uper ob loci, in quo e&longs;t, <expan abbr="&longs;eruãdi">&longs;eruandi</expan> cupiditatem naturalem, & etiam, ne <lb/>admittatur vacuum. Mobilis denique figura quæ quò propius ac­<lb/>cedit ad &longs;phæricam vt mobilißimam, eò ad motum pronior: contra <lb/>quò remotior. Atque ea &longs;unt impedimenta, quorum duo &longs;ublatis for­<lb/>tuitis è figurarum &longs;uperficialibus rectilineæ, è &longs;olidis cubo in&longs;unt. <lb/>Sit enim <lb/>ABCD <lb/>
<figure id="fig35"></figure><lb/><expan abbr="rectili-neũ">rectili­<lb/>neum</expan> pla­<lb/>no E F <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan>, <lb/>& <expan abbr="qui-d&etilde;">qui­<lb/>dem</expan> &longs;ina­<lb/>turale e&longs;t <lb/>in&longs;ita grauitate verget ver&longs;us G, & ad rectos in&longs;i&longs;tet rectis A C <lb/>& B D & omnibus inter illas interiectis vt H I, K L, M N, <lb/>&longs;icque totidem momentis ver&longs;us G contendit. Præterea aër vel <lb/>aqua medium occurrens lateri A C, quantum in &longs;e, e&longs;t impedit tot <lb/>punctis, quot &longs;unt in A C.<emph.end type="italics"/></s>
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<p type="main">
<s><emph type="italics"/>Sit & cubus A D, planum K L, vna &longs;uperficierum &longs;uarum <lb/>E D attingens, tum habeat rectas A E, C F, B D, H G, ad<emph.end type="italics"/>
<pb pagenum="103"/><emph type="italics"/>rectos in&longs;i&longs;ten-<emph.end type="italics"/><lb/>
<figure id="fig36"></figure><lb/><emph type="italics"/>tes, vt totidem <lb/>alias, quot &longs;unt <lb/>puncta in &longs;u­<lb/>perficie E D <lb/>nixu naturali <lb/>coniunctæ. Tot <lb/>vires nullo <expan abbr="t&etilde;-poris">ten­<lb/>poris</expan> momento alio inclinantes &longs;e à &longs;uo &longs;tatu dimoueri &longs;inent: medio <lb/>etiam obuio &longs;eu aëre, &longs;eu aqua totidem ad latus punctis propter æqua­<lb/>litatem &longs;uperficierum impediente. Ex quo fit vt figurarum planum <lb/>pro vertice habentium &longs;tabilißima dicatur cubus. Et quia talis e&longs;t, <lb/>eius figuram Plato affinxit terræ in loco &longs;uo pror&longs;us immobili. Ob id <lb/>etiam pictores <expan abbr="Virtut&etilde;">Virtutem</expan> quæ &longs;olacon&longs;tans e&longs;t animi &longs;tatus, vel etiam <lb/>Mercurium qui &longs;uos &longs;ectatores numquam de&longs;erit cubo in&longs;identem <lb/>repræ&longs;entant: &longs;icut ob contrariam cau&longs;am Fortunam.<emph.end type="italics"/></s>
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<p type="main">
<s>Quæ tantùm con&longs;tans in leuitate &longs;ua e&longs;t. <lb/><emph type="italics"/>globo mobilißimo. Sed quod ad figuram attinet quia pluribus planis <lb/>clauditur quam tetraedrum, vel pentaedrum, vt qui &longs;it hexaedrum, <lb/>& ideo propius accedit ad &longs;phæram, ad volutationem adhuc procli­<lb/>uior e&longs;t, quam illa &longs;int. hinc te&longs;&longs;erarum talorumque in alueo per hanc <lb/><expan abbr="figurã">figuram</expan> planum vnum pro vertice, & planum vnum pro ba&longs;i &longs;emper <lb/><expan abbr="&longs;eruant&etilde;">&longs;eruantem</expan> ludus. Sed hîc non immeritò<emph.end type="italics"/><lb/>
<figure id="fig37"></figure><lb/><emph type="italics"/>quæri pote&longs;t. cur terræ &longs;tare debenti na­<lb/>tura figuram attribuit &longs;phæricam, vt <lb/><expan abbr="doc&etilde;t">docent</expan> a&longs;tronomi. vnum enim e&longs;t ex <expan abbr="ar-gum&etilde;tis">ar­<lb/>gumentis</expan> Copernici terram moueri pro­<lb/>bare volentis. Sed id nullum locum ha­<lb/>bet, quia quæ hactenus dicta &longs;unt im­<lb/>pedimenta figurarum, &longs;unt <expan abbr="figurarũ">figurarum</expan> in <lb/>plano <expan abbr="nõ">non</expan> <expan abbr="aut&etilde;">autem</expan> in concauo &longs;imili & <expan abbr="cõ-">con-</expan><emph.end type="italics"/><lb/>
<figure id="fig38"></figure><lb/><emph type="italics"/>gruenti <expan abbr="exi&longs;tentiũ">exi&longs;tentium</expan>, cuiu&longs;modi e&longs;t terra, <lb/>cuiu&longs;que omnes partes <expan abbr="rotũdæ">rotundæ</expan> exi&longs;ten­<lb/>tis æquabilius coniuncto nixu ad cen­<lb/>trum contendunt: quam &longs;i alterius e&longs;&longs;et <lb/>cuiu&longs;cunque figuræ. Sit enim cubica <lb/>cuius centrum A & B punctum an-<emph.end type="italics"/>
<pb pagenum="104"/><emph type="italics"/>gulare, & ita remotius quam C laterale, non tanto nixu contendet: <lb/>quam ip&longs;um C. Quò enim mobile naturale propius e&longs;t, eò obnixius <lb/>incumbit. Eadem e&longs;t ratio cuiu&longs;cumque figuræ præterquam &longs;phæri­<lb/>cæ, cuius puncta B, C, D, in eadem &longs;uperficie æqualiter à centro <lb/>&longs;emper di&longs;tant. Itaque terra, vt medium vndiquaque obtineret, & <lb/>vt quæ in ea omnia puncta æquali nixu ad eius centrum niteren­<lb/>tur, debuit e&longs;&longs;e &longs;phærica: ob idque immobilißima e&longs;t, nullibique <lb/>nutat, contrà quam dixit Poëta,<emph.end type="italics"/></s>
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<p type="main">
<s>A&longs;pice nutantem conuexo pondere mundum. <lb/><emph type="italics"/>Nutus enim hic e&longs;t inclinatio aliò facta: quam id, à quo &longs;u&longs;penditur, <lb/>vel &longs;u&longs;tinetur, inclinet. Cuiu&longs;modi nihil e&longs;t in mundo, aut in terra: <lb/>&longs;ed omne punctum eò fertur, quò id à quo &longs;u&longs;tinetur, rectà &longs;cilicet ad <lb/>centrum, non vt D ad E, hoc enim e&longs;&longs;et contra naturam grauis, <lb/>quippe in diuer&longs;um per ambitum. Quærenti verò cur igitur cœlum <lb/>exacte &longs;phæricum moueatur. Re&longs;pondent moueri in loco non na­<lb/>turaliter: &longs;ed voluntariè. Omnis enim motus naturalis e&longs;t per rectam <lb/>de centro ad locum. V oluntas illa e&longs;t intelligentiæ, quæ cœlo vt mens <lb/>corpori præe&longs;t. Et per &longs;e cum motum hunc creet &longs;ine defatigatione e&longs;t <lb/>hic motus in regularißimo corpore regularißimus, & facillimo ad <lb/>motum velocißimus, vt e&longs;t apud Ptolomæum concl. 1. lib. 1.<emph.end type="italics"/> <foreign lang="greek">meg. <lb/>sun<gap/>.</foreign> <emph type="italics"/>Velocitatem autem intelliget, qui intellexerit quot millia­<lb/>ria, habeat circulus in cœlo extimo maximus, & quot ex his vno­<lb/>quoque momento conficiat. Intelligetur quoque quomodo illius cœli <lb/>motus &longs;it omnium motuum <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>. Nam cum men&longs;ura &longs;it in vno­<lb/>quoque genere minimum, vt e&longs;t cap. 4. lib. 2. de Cœl. hic autem mo­<lb/>tus minimus debet dici, qui per minimam lineam earum quæ æqua­<lb/>les areas includunt fit, cuiu&longs;modi e&longs;t circularis, &longs;icque &longs;ecundum eam <lb/>motus erit celerrimus, quia minimus.<emph.end type="italics"/></s>
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<p type="main">
<s>Multum plani.] <emph type="italics"/>Ex hoc loco intelligatur, quod mobile, quantò <lb/>latius e&longs;t: tantò difficilius moueri per planum. Attritio enim per <lb/>contactum plani cum mobili, tanto maior erit. Ideo tangens in pun­<lb/>cto facillime mouetur, vt dictum e&longs;t. Tangens in linea difficilius: <lb/>tangens per &longs;uperficiem difficillime. Imò vero plana exqui&longs;ita iun­<lb/>cta &longs;ine ferruminatione &longs;eparari nequeunt, &longs;i &longs;uperius leuiter ap­<lb/>prehen&longs;um ab inferiore di&longs;iungere quis conetur. Rationem &longs;i vis <lb/>aliquam, vide apud Scaligerum exercit. 333.<emph.end type="italics"/></s>
</p>
<pb pagenum="105"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Præterca quò pondus <lb/>vergit, eò motor impellit. <lb/>Quum igitur diameter cir <lb/>culi rectà in&longs;i&longs;tit plano, cir­<lb/>culo in puncto planum at­<lb/>tingente, æqualiter vtrim­<lb/>que diameter pondus di­<lb/>&longs;terminat. Quando verò <lb/>mouetur &longs;tatim plus adid <lb/>mouetur, veluti eò repens <lb/>motu facilius impellente <lb/>in anteriorem partem. Eò <lb/>enim, quò vergit vnum­<lb/>quodque, facilius mouc­<lb/>tur. Quandoquidem &longs;i in <lb/>contrarium: quam quò <lb/>vergat, moueatur, difficulter mouebitur.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Præterea quò.] <emph type="italics"/>Tertia cau&longs;a facilitatis e&longs;t motus, quando mo­<lb/>bile in omni po&longs;itu &longs;uper plano dimidia &longs;ui parte quoquouer&longs;um <lb/>ad planum ip&longs;um acclinat, vt fit in rotundo, quod ip&longs;um tangit in <lb/>puncto, vt ante docuimus, &longs;icque quoquouer&longs;um vergit. Hinc dico <lb/>&longs;phæricum ad latus moueri po&longs;&longs;e quacumque vi, quæ aërem impul&longs;u <lb/>vel tractu diuidere poßit. Vnus enim aër circun&longs;tans impedit, quo <lb/>minus voluatur. Non enim nixus a&longs;cendendi &longs;ur&longs;um, cum ob graui­<lb/>tatem eò non nitatur: neque rur&longs;us deor&longs;um de&longs;cendendi, ob æqui­<lb/>librium enim innixus pondus non adfert, quin potius dimidia &longs;ui <lb/>parte quoquouer&longs;um nutans nititur moueri, vt in circulo ad cen­<lb/>trum: à contactu quoque, quia minimo, non impeditur. Relinqui­<lb/>tur ergò tantum impediri à medio circunstante. Hoc à quacun­<lb/>que vi vt or is flatu &longs;i diuidatur, &longs;phæricum in locum diui&longs;ionis pro­<lb/>mouebitur.<emph.end type="italics"/></s>
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<p type="main">
<s>Rectà in&longs;i&longs;tit.] <emph type="italics"/>Diameter circuli rectà in&longs;i&longs;tere in plano di­<lb/>citur cum ad omnes rectas lineas à quibus tangitur in ip&longs;o plano<emph.end type="italics"/>
<pb pagenum="106"/><emph type="italics"/>rectos angulos ef-<emph.end type="italics"/><lb/>
<figure id="fig39"></figure><lb/><emph type="italics"/>ficit ex def. 3. lib. <lb/>11. vt A B dia­<lb/>meter ad B O, B D, <lb/>B E, B F. Et A B <lb/>quia diameter e&longs;t <lb/>circulum &longs;uum bi­<lb/>fariam diuidit ex <lb/>def. 17. lib. 1. Sic­<lb/>que tanta pars e&longs;t <lb/>ad G, quanta ad H. Similiter maximus in &longs;phæra circulus recta <lb/>in&longs;i&longs;tens &longs;phæram bifariam di&longs;pe&longs;cit.<emph.end type="italics"/></s>
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<p type="main">
<s><gap/><lb/>
<arrow.to.target n="marg26"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg26"></margin.target><gap/>i)/x<gap/></s>
</p>
<p type="main">
<s>Præterea nonnulli di­<lb/>cunt lineam circuli in per­<lb/>petuo motu e&longs;&longs;e, vt quæ <lb/>manent, propter renixum. <lb/>Vt maioribus circulis eue­<lb/>nit re&longs;pectu minorum. Ce­<lb/>lerius enim ab æquali vi <lb/>maiores <expan abbr="mou&etilde;tur">mouentur</expan>, & pon­<lb/>dera mouent. quia maioris <lb/>circuli angulus <expan abbr="nutũ">nutum</expan> quen­<lb/>dam habetad minoris an­<lb/>gulum. Et e&longs;t vt diameter <lb/>ad <expan abbr="diametrũ">diametrum</expan>: &longs;ic omnis ma­<lb/>ior circulus ad minorem. <lb/>Infiniti autem &longs;unt mino­<lb/>res. Si verò etiam circulus <lb/>nutum habet ad alterum. <lb/>Similiter verò facile mobi­<lb/>lis <expan abbr="aliũ">alium</expan> <expan abbr="nutũ">nutum</expan> habet circul', <lb/>& quæ à circulo <expan abbr="mou&etilde;tur">mouentur</expan>, <lb/><expan abbr="etiã&longs;i">etian&longs;i</expan> &longs;ua curuatura <expan abbr="planũ">planum</expan> <lb/><expan abbr="nõ">non</expan> <expan abbr="cõtingat">contingat</expan>: &longs;ed vel propè <lb/>planitiem, vel vt tro chleæ.
<pb pagenum="107"/><gap/><lb/>Etenim quæ &longs;ic &longs;e habent, <lb/>facillimè <expan abbr="mou&etilde;tur">mouentur</expan>, & mo­<lb/>uent pondus. an non quia <lb/>parua &longs;ui parte tangunt & <lb/>offen&longs;ant. Sed ob <expan abbr="aliã">aliam</expan> cau­<lb/>&longs;am. Hæc vero prius e&longs;t di­<lb/>cta. quod circulus ex dua­<lb/>bus lationibus effectus e&longs;t. <lb/>Itaque vnam harum &longs;em­<lb/>per habet nutantem. Et <expan abbr="eũ">eum</expan>, <lb/>qua&longs;i &longs;emper moueatur, <lb/>mouent motores, quando <lb/>quocunque illum &longs;ecun­<lb/>dum <expan abbr="peripheriã">peripheriam</expan> mouerint. <lb/>Motam enim ip&longs;am mo­<lb/>uent. Eam &longs;iquidem, qua <lb/>mouetur in <expan abbr="obliquũ">obliquum</expan>, mo­<lb/>to rimpellit: illa verò, quæ &longs;uper diametro efficitur, ip&longs;e­<lb/>met &longs;e circulus mouet.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Præterea nonnulli.] <emph type="italics"/>Quarta cau&longs;a e&longs;t de perpetuo motu con­<lb/>firmata nonnullorum, &longs;ed innominatorum authoritate: & &longs;imi­<lb/>litudine <gap/> contrarÿs &longs;ic. quemadmodum quæ perpetuò manent, ma­<lb/>nent propter contrarium motui renixum: &longs;ic in quibus e&longs;t ad mo­<lb/>tum perpetua propen&longs;io, perpetuò moueri ea debent.<emph.end type="italics"/></s>
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<p type="main">
<s>Vt maioribus circulis.] <emph type="italics"/>Nutus &longs;eu perpetua propen &longs;io con­<lb/>firmatur e&longs;&longs;e &longs;emper in circulo. quia quicunque &longs;it &longs;emper in &longs;e habet <lb/>concentricos minores infinitos, & maior tum celerius mouetur ab <lb/>æquali vi, & cum eo etiam pondera: tum angulus maioris nutum <lb/>habet ad angulum æqualem, qui e&longs;t in minori circulo. quia angull <lb/>maioris crura maiora &longs;unt, &longs;empérque e&longs;t, vt diameter ad diame­<lb/>trum. Sunt enim circulorum &longs;emidiametri. Partes autem cum pari­<lb/>ter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. Diameter au­<lb/>tem maior celerius mouetur, hîc autem notandum e&longs;t angulos non<emph.end type="italics"/>
<pb pagenum="108"/><emph type="italics"/>&longs;umi pro inclinatione: &longs;ed pro crurum<emph.end type="italics"/><lb/>
<figure id="fig40"></figure><lb/><emph type="italics"/><expan abbr="lõgitudine">longitudine</expan>. hæc autem figura hac cir­<lb/>culorum concentricorum & à cen­<lb/>tris angulorum illu&longs;trantur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Nutum habet.] <foreign lang="greek">ro/ph</foreign> <emph type="italics"/>Nutus <lb/>vis e&longs;t cuiu&longs;que impre&longs;&longs;a à Deo & <lb/>natura, qua in loco &longs;uo naturali quie&longs;­<lb/>cit, & volentiab eo di&longs;pellere, re&longs;i&longs;tit. <lb/>vnde<emph.end type="italics"/> <foreign lang="greek">an)t<gap/><gap/>sis</foreign> <emph type="italics"/>renixus. Extra locum verò ad eum per breuißi­<lb/>mam viam mouetur. Deus enim ne omnia in omnibus e&longs;&longs;ent, vni­<lb/>cuique a<gap/> initio proprium locum tribuit, in quo & circa quem con­<lb/>globatur, & ibi hæret. Hinc etiam &longs;ingulæ partes &longs;uis totis natura <lb/>inhærent, & in ÿs certum quendam &longs;itum habent, àquo remotæ ad <lb/>ip&longs;um redeunt, vt in arcubus & balli&longs;tis videre licet. Nutus autem <lb/>naturalis e&longs;t: vel non naturalis: vel mixtus. Naturalis e&longs;t is, quo res <lb/>quælibet natura &longs;ua mouetur: aut <expan abbr="mou&etilde;ti">mouenti</expan> re&longs;i&longs;tit habita ratione loci <lb/>&longs;ui naturalis, & &longs;itus &longs;uarum partium. Non naturalis e&longs;t is, quo nec <lb/>ratione loci naturalis, nec &longs;itus partium mouetur, vt fortuitus vel <lb/>voluntarius. Ille vt ventorum, hic vt animalium. Mixtus parti­<lb/>ceps e&longs;t vtriu&longs;que. Nutus voluntarÿ mille &longs;unt modi <expan abbr="nõ">non</expan> aliter, quam <lb/>voluntatis decreto determinabiles. At naturalis vnius tantum e&longs;t <lb/>à loco non naturali ad naturalem. Hinc linea recta, quæ e&longs;t à termi­<lb/>no à quo incipit moueri ad terminum in quo quie&longs;cit, linea nutus, <lb/>& eadem in terminis contrarÿs renixus dicitur, vt &longs;i ab eo in quo <lb/>quie&longs;cit aliena vis ad alium moueret: linea verò ip&longs;am &longs;ecans ad an­<lb/>gulos inæquales e&longs;t linea obliqui nutus, vel renixus: & &longs;ecans ad <lb/>rectos nec ad nutum e&longs;t, nec ad renixum. Nunc igitur hoc cum ve­<lb/>rum e&longs;&longs;e experiamur, & ratio conuincat, quantò quodque remotius <lb/>e&longs;t à loco, in quo naturaliter quie&longs;ceret, tantò ad eum magis conari, <lb/>remotioris maior erit nutus. In peripheria maiori punctum A re­<lb/>motius puncto D. Magis igitur nutat. E&longs;t enim linea A C maior <lb/>quam D E vt ex &longs;imilibus triangulis A B C, D B E demon&longs;trari <lb/>facile pote&longs;t. Et &longs;ic angulus ad angulum nutare dicitur, cum in an­<lb/>gulorum æqualitate crurum e&longs;t inæqualitas.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et e&longs;t vt diameter.] <emph type="italics"/>Hæc analogia antea à nobis demon&longs;tra­<lb/>ra e&longs;t. Huc autem adducta confirmat in maioribus circulis maiorem<emph.end type="italics"/>
<pb pagenum="109"/><emph type="italics"/>nutum ad motum ine&longs;&longs;e: quam in minoribus. Sed cum omnis circu­<lb/>lus habeat intra &longs;e infinitos concentricos, omnis peripheria nutum <lb/>habebit infinitum, & ideò perpetuum ad motum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Infiniti autem.] <emph type="italics"/>Quod infiniti circuli minores concentrici in­<lb/>&longs;int in quouis dato circulo &longs;ic demon&longs;trabimus. Sit circulus C B, <lb/>cuius &longs;emidiameter D B bifariam<emph.end type="italics"/><lb/>
<figure id="fig41"></figure><lb/><emph type="italics"/>&longs;ecetur, vt in puncto E prop. 10. <lb/>lib. 1. Et centro D interuallo D E <lb/>de&longs;criptus circulus po&longs;t. 3. Hic <lb/>erit concentricus & minor ip&longs;o <lb/>C B def. 1. lib. 3. Rur&longs;us recta D <lb/>E bifariam &longs;ecetur, vt in puncto <lb/>F, & centro D eodem interuallo <lb/>D F de&longs;criptus circulus erit con­<lb/>centricus & minor. Et eadem ra­<lb/>tione deinceps ad infinitum, cum rectam lineam &longs;emper bi&longs;&longs;ecare li­<lb/>ceat prop. 10. lib. 1. Et &longs;ic infiniti erunt circuli concentrici minores <lb/>in quouis circulo. quod erat demon&longs;trandum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Etiam&longs;i curuatura.] <emph type="italics"/>Repetit cau&longs;am perpetui motus, aut nu­<lb/>tus ad motum, quæ in circulo e&longs;t, cum &longs;ua ab&longs;ide id e&longs;t curuatura at­<lb/>tingit planum, ine&longs;&longs;e, etiam&longs;i non attingat, vtfit in rotis figulorum, <lb/>& in trochleis. de quibus po&longs;tea.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sed ob aliam cau&longs;am.] <emph type="italics"/>Quinta cau&longs;a de naturali motu &longs;e­<lb/>cundum peripheriam hîc leuiter attingitur, vel potius ex anteceden­<lb/>tibus breuiter repetitur. Naturalis autem i&longs;te motus intelligi debet, <lb/>dum fit circulus à rectæ manente altero extremo, & moto altero, <lb/>quod &longs;uo motu de&longs;cribit peripheriam. In facto enim circulo, vel glo­<lb/>bo naturali quatenus particeps e&longs;&longs;et grauitatis reuera motus natura­<lb/>lis e&longs;t is, quò rectà deor&longs;um fertur. Sed eo impedito ob planum cui in­<lb/>cumbit non cedens, per vim aliquam impul&longs;us globus ad motum cir­<lb/>cularem &longs;e recipit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>10. Cur maiores circuli <lb/>&longs;unt mouentiores.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur per maiores circu­
<pb pagenum="110"/><gap/><lb/>los &longs;ublata & tracta faci­<lb/>lius mouemus, vt &longs;i tro­<lb/>chleæ &longs;int maiores minori­<lb/>bus, & &longs;cytalæ &longs;imiliter. An <lb/>quia quantò maior fuerit <lb/>radius in tempore æquali, <lb/>per maius mouetur <expan abbr="&longs;patiũ">&longs;patium</expan>. <lb/><expan abbr="Itaq;">Itaque</expan> æquali in&longs;i&longs;tente one­<lb/>re, idem faciet, vt diximus <lb/>etiam libras maiores mi­<lb/>noribus e&longs;&longs;e exactiores. E&longs;t <lb/>enim agina <expan abbr="c&etilde;trũ">centrum</expan>. Et lineæ <lb/>in librili, quæ &longs;untab agina <lb/>vtrimque, &longs;unt radij.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvrper maiores.] <emph type="italics"/>In hoc capite tractatur problema de ma­<lb/>ioribus circulis, & &longs;phæricis. cur &longs;cilicet facilius & celerius <lb/>moueantur & moueant. Cui re&longs;pondetur ex lineæ à centro longitu­<lb/>dine maiore. Ratio &longs;ic di&longs;ponetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vbi lineæ à centro &longs;unt maiores: ibi per motum æquali tempore <lb/>maius &longs;patium conficitur, & facilis etiam motio fit, tum an­<lb/>nexa onera mouentur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In circularibus & &longs;phæricis maioribus lineæ à centro <lb/>&longs;unt maiores: quam in minoribus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo circuli & &longs;phæræ maiores æquali tempore maius &longs;patium <lb/>conficient, facilius mouebuntur, & annexa onera moue­<lb/>bunt: quam minores.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ex hoc colligimus maiores rotas in curribus vna volutatione tan­<lb/>tam lineam cum conficiant: quanta orbitæ re&longs;pondet, nec maiori tra­<lb/>ctu egeant: quam minores, tantò commodiores e&longs;&longs;e ad celeritatem, & <lb/>motus facilitatem: quantò maiores extiterint. Et cum in facili tractu <lb/>biroti onerati &longs;arcina tendere debeat ad æquilibrium, vt neque tolla­<lb/>tur de collo iugum præ pondere po&longs;teriore, neque &longs;ic prematur, vt &longs;i­<lb/>mul iumentum trahat, & ge&longs;tet: &longs;ed potius trahat: quam ge&longs;tet: in<emph.end type="italics"/>
<pb pagenum="111"/><emph type="italics"/>maioribus autem rotis æquilibrium illud facilius &longs;it, quia &longs;arcina al­<lb/>tior, & &longs;ictrahitur tantum: in paruis depreßior, &longs;icque nonnihil le­<lb/>uanda. Vbi autem &longs;u&longs;tinere & trahere opus e&longs;t, vt in bellicis tor­<lb/>mentis vnus equus iugum &longs;u&longs;tinere, alÿ loris trahere debent.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vt &longs;i tro chleæ.] <emph type="italics"/>Problema illu&longs;tratur duobus exemplis Tro­<lb/>chleæ & Scytalæ. E&longs;t autem Trochlea in&longs;trumentum tractorium ex <lb/>rotula circa axiculum fixum alicubi appen&longs;um per <expan abbr="fun&etilde;">funem</expan> ductarium, <lb/>in eius circumferentia circumuoluta. Geminatur aliquando, tripli­<lb/>catur, & amplius multiplicatur. Vnde &longs;unt illa tractoria infinita­<lb/>rum propemodum virium Tri&longs;pa&longs;ton, Pente&longs;pa&longs;ton, Poly&longs;pa&longs;ton, in <lb/>quibus rotulæ &longs;ibi inuicem &longs;ub&longs;eruientes, & tanquam onus attra­<lb/>hendum diuidentes &longs;umma facilitate ip&longs;um attrahunt, de quo qui <lb/>multa admirabilia videre volet, videat apud Guidum Vbaldum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et&longs;cytalæ.] <emph type="italics"/>Scytala lignum e&longs;t cylindricum cuius pro duplici <lb/>v&longs;u duo genera &longs;tatuuntur. Vnus v&longs;uum e&longs;t ad attrahendum, & &longs;ic <lb/>in eius altera extremitate ferrum quoddam inflexum e&longs;t pro manu­<lb/>brio, vbi annectitur potentia mouens: vel loco ferri vectes <expan abbr="emergũt">emergunt</expan> <lb/>aliquot, qui vicißim per vim annexam mouentur: vel loco vectis <lb/>rota maior, quod idem e&longs;t: &longs;icque vel manubrio, vel vectibus, vel <lb/>rota mota vnà mouetur illud lignum cylindricum cum &longs;uo fune du­<lb/>ctario. Et cum eo pondus alligatum eleuatur. Hoc genus &longs;cytalæ e&longs;t <lb/>idem quod axis in peritrochio de quo po&longs;tea. De hoc autem genere lo­<lb/>cus hic intelligi debet. De altero dicetur cap. 12.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vt diximus ctiam.] <emph type="italics"/>Confirmatio e&longs;t propo&longs;itionis præceden­<lb/>tis &longs;yllogi&longs;mi per &longs;peciem libræ, quæ tantò exactior exi&longs;tit: quantò li­<lb/>brile habet longius, è &longs;uperioribus repetitam. C æterum præter proble­<lb/>ma huius capitis alia quæri po&longs;&longs;unt ad idem ferè pertinentia &longs;citu <lb/>digna, nec minus &longs;ubtilia, nempè. Quare binæ rotæ quaternis facilio­<lb/>res &longs;int. Quare prioribus po&longs;teriores rotas maiores e&longs;&longs;e oporteat. <lb/>Quare maior &longs;arcina in anteriore plau&longs;tri parte poni debeat. Soluitur <lb/>primum quia rota quælibet, vt grauis, ad centrum &longs;pectat, & arceri <lb/>de&longs;cen&longs;u e&longs;t contra eius naturam: arcetur & cum tollitur &longs;ur&longs;um, & <lb/>cum trahitur adlatus, quippè in diuer&longs;um per <expan abbr="ambitũ">ambitum</expan>. Plures igitur <lb/>rotæ augebunt onus, & ideo trahentis laborem. Itaque binæ rotæ <lb/>quaternis faciliores erunt, vnde bellicis tormentis, licet immanibus <lb/>duæ &longs;atis &longs;unt. Quod autem quis obijceret per rotas plures pondus plus<emph.end type="italics"/>
<pb pagenum="112"/><emph type="italics"/>di&longs;tribui, & tanquam diuidi. Id &longs;anè verum e&longs;t & vtile ad facili­<lb/>tatem &longs;u&longs;tentationis, non item ad tractum. Et&longs;i biroti &longs;arcina in pe­<lb/>toritum transferatur, eadem iumento grauior fiet tantò, quantò gra­<lb/>uior currus. Sed fallaciæ cau&longs;a e&longs;t quod petorita birotis plus &longs;u&longs;tinent. <lb/>Secundum quia maiores tanquam altiores prioribus minoribus qua&longs;i <lb/>incumbunt, &longs;icque in proclinatiores iam partes onus recumbensà <lb/>facilius motis maioribus, vna quoque mouetur facilius. Tertium ob <lb/>candem cau&longs;am &longs;oluitur. Sic enim impo&longs;ita &longs;arcina qua&longs;i inferiore <lb/>loco pendens adiuuat tractum. Hinc e&longs;t quod quadrupedum omni <lb/>generi &longs;olis Gyraffis exceptis crura po&longs;teriora longiora &longs;unt. Mouen­<lb/>tur enim pul&longs;u primum, deinde tractu. Commodius autem pellit, <lb/>quod grauius e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>11. Cur facilius mouetur li­<lb/>brile ab&longs;que pondere.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur librile quum fuerit <lb/>&longs;ine <expan abbr="põdere">pondere</expan>, facilius moue­<lb/>tur: <expan abbr="quã">quam</expan> quum habet pon­<lb/>dus. Similiter verò & orbi­<lb/>culus, vel aliud tale, gra­<lb/>uius quidem, maius verò <lb/>minore & leuiore. An quod <lb/>non &longs;olum in contrarium <lb/>id, quod graue e&longs;t: &longs;ed <expan abbr="etiã">etiam</expan> <lb/>in <expan abbr="obliquũ">obliquum</expan> difficulter mo­<lb/>uetur. Difficile enim e&longs;t <lb/>contrà propen&longs;ionem mo­<lb/>uere. At quò propendet, fa­<lb/>cile: non propendet autèm in obliquum.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvrlibrile.] <emph type="italics"/>In hoc capite &longs;peciale tractatur problema, quod <lb/>generale e&longs;&longs;e po&longs;&longs;et. E&longs;t autem de librili. cur quò leuius, vel &longs;ine <lb/>pondere cum &longs;it, deprimitur facilius & mouetur: quam cum graue<emph.end type="italics"/>
<pb pagenum="113"/><emph type="italics"/>e&longs;t. Exempli gratia vnum ligneum &longs;it, alterum ferreum, illud faci­<lb/>lius moueatur: quam hoc, quod perinde e&longs;t de vecte, de rotis, de glo­<lb/>bis, & eiu&longs;modi contra naturam motis, &longs;uppo&longs;ita eadem firmitate. <lb/>Ratio ergò quæ redditur generalis e&longs;t, & hoc &longs;yllogi&longs;mo compre­<lb/>hendetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Motum contra naturam eò difficilius fertur, quò ip&longs;um grauius <lb/>e&longs;t. Plus enim re&longs;i&longs;tit non &longs;olum in contrarium nutus &longs;ui, &longs;ed <lb/>& in obliquum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Librile moueri in obliquum (vt mouetur nece&longs;&longs;ariò propter <lb/>&longs;uæ aginæ &longs;eu centri immobilitatem: &longs;ic enim non rectà ad <lb/>centrum mundi quo natura fertur, de&longs;cendit: &longs;ed per ambi­<lb/>tum circuli) e&longs;t contra naturam grauitatis &longs;uæ moueri, vt <lb/>rotam & eiu&longs;modi.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo librile quò grauius, eò difficilius mouebitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Hinc collige ex leuiori materia facta, dummodo firma, agiliora e&longs;&longs;e, <lb/>& exactiora. vnde petorita no&longs;tra rotis in orbita ferreis prædita <lb/>difficilius trahuntur, quam<emph.end type="italics"/><lb/>
<figure id="fig42"></figure><lb/><emph type="italics"/>nobilium Polonorum, quæ ex <lb/>ligno &longs;olo compacta &longs;unt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Non propendet.] <emph type="italics"/>Linea <lb/>nutus grauis alicuius deor­<lb/>&longs;um e&longs;t recta perpendicularis <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan> plano horizontis, <expan abbr="hãc">hanc</expan> <lb/>quæ &longs;ecat ad inæquales an­<lb/>gulos, e&longs;t obliqua, cuiu&longs;mo­<lb/>di e&longs;t arcus B F ad rectam <lb/>B G lineam nutus puncti <lb/>B.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>12. Cur &longs;uper &longs;cytalis onera <lb/>facilius ge&longs;tantur: quam <lb/>&longs;uper curribus.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur onera facilius ge­<lb/>&longs;tantur &longs;cytalis: quam cur­
<pb pagenum="114"/><gap/><lb/>ribus etiam magnas rotas <lb/>habentibus, cum ip&longs;æ par­<lb/>uas habeant. An quia one­<lb/>ra in &longs;cytalis ad nihil offen­<lb/>&longs;ant: in curribus vero ha­<lb/>bent axem, ad quem offen­<lb/>&longs;ant. Supernè enim pre­<lb/>muntip&longs;um, & in <expan abbr="obliquũ">obliquum</expan>. <lb/>In &longs;cytalis vero ad hæc <lb/>duo mouentur, & infernè <lb/>&longs;cilicet &longs;ub&longs;trato &longs;patio, <lb/>& onere &longs;uperimpo&longs;ito. In <lb/>vtri&longs;que enim his locis re­<lb/>uoluitur circulus, & conci­<lb/>tatus impellitur.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr onera.] <emph type="italics"/>Secundum genus &longs;cytalæ e&longs;t lignum ferrumue <lb/>cylindricum oblongum in extremis rotulas habens intra annu­<lb/>los currui<emph.end type="italics"/><lb/>
<figure id="fig43"></figure><lb/><emph type="italics"/>affixos <lb/>ver&longs;atile, <lb/>vt e&longs;t fi­<lb/>gura A <lb/>B quæ <lb/>mota iu­<lb/>go rotis annexo, contrà, quam in curribus, in quibus non rotis: &longs;ed <lb/>currui annectitur, omnibus &longs;uis partibus mouetur duobus motibus <lb/>&longs;imul, circumcirca, & antror&longs;um. quod cau&longs;a e&longs;t vt leuius vertatur, <lb/>quam rota in curru. vt cuius axis procedendo tantùm antror&longs;um <lb/>moueatur, non autem circum circa vertatur. Vnde fit vt axis etiam <lb/>premat magis, & veluti rotam affigat plano, &longs;icque remoretur: con­<lb/>tra in &longs;cytala rotæ dummodo maiores &longs;int, quam vt terra obruantur <lb/>à &longs;ubiecta planicie inferne ip&longs;am circunferentiam atterente impel­<lb/>luntur. Supernè etiam ab onere cylindricum premente. Ob has itaque<emph.end type="italics"/>
<pb pagenum="115"/><emph type="italics"/>cau&longs;as &longs;cytala commodior erit, & expeditior ad onera conuehenda, <lb/>licet minores, quam currus habeat rotas, quod non repugnat ÿs quæ <lb/>ante 10. cap. dicta <expan abbr="sũt">sunt</expan> derotis maioribus. Aliud enim facilius attol­<lb/>lere, & trahere quæcunque pondera, aliud conuehere. Scytala tamen <lb/>pote&longs;t e&longs;&longs;e illud curriculi genus quod Galli vocant<emph.end type="italics"/> Traineau, <emph type="italics"/>Itali<emph.end type="italics"/><lb/>Stra&longs;cino, <emph type="italics"/>apud quendam non ineruditum legi dici po&longs;&longs;e traham. <lb/>Hæc autem annexa ligno cylindrico &longs;olas rotas habet ver&longs;atiles, quæ <lb/>quantò minores, tantò minus occur&longs;ant &longs;ubiecto pauimento. vt enim <lb/>quò circulus rotæ maior e&longs;t, eò eius cum recta à qua tangitur in pla­<lb/>no minor e&longs;t an-<emph.end type="italics"/><lb/>
<figure id="fig44"></figure><lb/><emph type="italics"/>gulus. Et contrà <lb/>quò circulus mi­<lb/>nor, eò angulus <lb/>contactus maior <lb/>euadit. vt angu­<lb/>lus A B C ro­<lb/>tæ maioris mi­<lb/>nor e&longs;t angulo <lb/>A B D rotæ <lb/>minoris: & con­<lb/>trà vtrolibet <lb/>maior e&longs;t angu­<lb/>lus A B E rotæ minoris.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>13. Cur mi&longs;&longs;ilia longius à <lb/>funda: quam à manu <lb/>proijciuntur.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur mi&longs;&longs;ilia longius fe­<lb/>runtur à funda, quam à <lb/>manu, etiam&longs;i proijciens <lb/>melius manu, comprehen­<lb/>dat: quam &longs;u&longs;pendens è <lb/>fo&longs;&longs;a fundæ? Præterea &longs;ic <lb/>duo pondera moueat, fun­<lb/>dam &longs;cilicet, & mi&longs;&longs;ile: illo
<pb pagenum="116"/><gap/><lb/>verò modo mi&longs;&longs;ile dunta­<lb/>xat. An quia in funda mi&longs;­<lb/>&longs;ile commotum proijciens <lb/>iacit. In orbem enim volu­<lb/>tans &longs;æpius, proijcit. E ma­<lb/>nu autem initium à quiete <lb/>capit. At omnia commota <lb/>facilius: quam quie&longs;centia <lb/><expan abbr="mou&etilde;tur">mouentur</expan>. An propter hoc: <lb/>&longs;ed & quia in v&longs;u funda­<lb/>rum manus quidem fit <expan abbr="c&etilde;-trum">cen­<lb/>trum</expan>: funda vero linea ex <lb/>centro. quantò autem fue­<lb/>rit hæc maior, <expan abbr="tãtò">tantò</expan> celerius <lb/>mouetur. At iactus à manu­<lb/>re&longs;pectu fundæ breuis e&longs;t.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>A Funda.] <emph type="italics"/>Funda e&longs;t funiculus duobus capitibus manu captus, <lb/>altero cum an&longs;ula digito circumuoluta ne exeat, altero &longs;ine an­<lb/>&longs;ula, vt dimitti poßit. In medio latior, & paululum excauatus, vt <lb/>ibi mißile contineatur, quod aliquoties circumacto in orbem funicu­<lb/>lo, & ab vno capitum dimi&longs;&longs;o vehementer proÿcitur. Inuentam à <lb/>Phenicibus fui&longs;&longs;e refert Plinius cap. 56. lib. 7. ne manus iaculi a&longs;pe­<lb/>rioris attrectatione læderetur, & vt longius atque validius proÿce­<lb/>retur. Quæ cum intelligeret pa&longs;tor ille exilis, &longs;ed Deo dilectus Dauid <lb/>funda aduer&longs;us Goliathem immanem gigantem non aliter, quam <lb/>&longs;ummo impetu pro&longs;ternendum, prudenter &longs;e&longs;e armauit. Erat autem <lb/>fundæ v&longs;us adeò frequens Balearium in&longs;ularum populis, vt matres <lb/>filios non alÿs auibus ve&longs;ci paterentur, quam quas funda &longs;ibi com­<lb/>para&longs;&longs;ent. Vnde & funda balearis appellatur à Poëta,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Stuppea torquentur balearis verbera fundæ. <lb/><emph type="italics"/>Nec&longs;olum lapides funda proÿci&longs;olere: &longs;ed & alia, vt plumbum, pa­<lb/>tet ex Ouidio.<emph.end type="italics"/></s>
</p>
<pb pagenum="117"/>
<p type="main">
<s>Non &longs;ecus exar&longs;it quam cum balearica plumbum</s>
</p>
<p type="main">
<s>Funda iacit, volat illud, & in cande&longs;cit eundo.</s>
</p>
<p type="main">
<s><emph type="italics"/>Et aduer&longs;um bellatores caßidibus, cataphractis, lorici&longs;que munitos <lb/>teretes lapides de funda de&longs;tinatos &longs;agittis omnibus e&longs;&longs;e grauiones <lb/>&longs;crip&longs;it Vegetius. Quandoquidem membris integris, lethale tamen<emph.end type="italics"/></s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg27"></arrow.to.target><lb/><emph type="italics"/>vulnus importent, & &longs;ine inuidia &longs;anguinis ho&longs;tis lapidis ictu in­<lb/>tereat Quæ res ideò, inquit, ab vniuer&longs;is tyronibus frequenti exerci­<lb/>tio di&longs;cenda e&longs;t, quia <expan abbr="fundã">fundam</expan> portare nullus labor. Et interdum euenit, <lb/>vt in lapido &longs;is locis conflictus habeatur, vt aut mons aliquis &longs;it de­<lb/>fendendus, aut collis, & ab oppugnatione ca&longs;tellorum &longs;iue ciuitatum <lb/>lapidibus barbari fundi&longs;que &longs;int propellendi.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg27"></margin.target>Cap. 16. lib <lb/>1. de re mili</s>
</p>
<p type="main">
<s>Cur mi&longs;&longs;ilia.] <emph type="italics"/>Quærit hîc Ari&longs;toteles cur iaculum mi&longs;&longs;um cum <lb/>funda longius proÿcitur, quam &longs;i manu tantum. Cui priu&longs;quam re­<lb/>&longs;pondeat, duo repugnare dicit, alterum, quia proiectum à manu &longs;ola <lb/>melius comprehendatur: quam quod à funda &longs;u&longs;penditur, melior au­<lb/>tem comprehen&longs;io conducit ad <expan abbr="longior&etilde;">longiorem</expan> iactum: alterum, quia proij­<lb/>ciens cum funda duo &longs;imul proijcit fundam &longs;cilicet & iaculum: ma­<lb/>nu autem vnum tantum, nempe iaculum. At difficilius duo mouere: <lb/>quam vnum. His incommodis tamen neglectis &longs;oluit Ari&longs;toteles <lb/>problema dupliciter, priore modo è motu incitato, & contraria quie­<lb/>te. Syllogi&longs;mus &longs;ic e&longs;t,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Qui initium proiectionis capit à motu longius iacit: quam à <lb/>quiete. Quies enim vt contraria motui, ei repugnat, & ip&longs;i re­<lb/>nitens, ne fiat impedit. Ideóque omnia commota facilius: quam <lb/>quie&longs;centia mouentur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>At proijciens cum funda initium capit à motu. Ante vi­<lb/>brationem enim funditor fundam &longs;æpius in circulum <lb/>circumagit: contrà cum manu, initium capit à quiete: aut <lb/>&longs;i à motu, multò leuiore tamen.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Igitur proiiciens cum funda longius iacit: quam cum manu &longs;ola.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>E fo&longs;&longs;a fundæ.] <emph type="italics"/>In Græco vocabulum e&longs;t,<emph.end type="italics"/> <foreign lang="greek">to\kai/ar,</foreign> <emph type="italics"/>&longs;ine vo­<lb/>cabulo<emph.end type="italics"/> <foreign lang="greek">sfendo/nhs.</foreign> <emph type="italics"/>Significat <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">kaiar</foreign> <emph type="italics"/>fo&longs;&longs;am terræ concu&longs;&longs;u <expan abbr="factã">factam</expan> <lb/>quæ &longs;ignificatio quid ad rem pertineat non video, ni&longs;i per metapho­<lb/>ram intelligamus eam fundæ partem, quæ vt latior, ita & in &longs;inum <lb/>leuiter excauatur ad iaculum continendum, & &longs;ic conuenit rei pro­<lb/>po&longs;itæ: nonnulli tamen putarunt delendum<emph.end type="italics"/> <foreign lang="greek">to\ kai/ar</foreign> <emph type="italics"/>& loco cius<emph.end type="italics"/>
<pb pagenum="118"/><emph type="italics"/>reponendum<emph.end type="italics"/> <foreign lang="greek">o)i+/zo\n</foreign> <emph type="italics"/>id e&longs;t omne quod iaculamus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>At omnia commotæ.] <emph type="italics"/>Hæc cau&longs;a generalis erit trice&longs;imo <lb/>primo capiti huius libri.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An propter hoc.] <emph type="italics"/>Alter e&longs;t modus &longs;olutionis problematis <lb/>&longs;umptus è funda tanquam radio longiore. Syllog. &longs;ic e&longs;t. Quantò li­<lb/>nea à centro e&longs;t maior, tantò celerius mouet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In proiectione cum funda manus e&longs;t centrum, funda verò e&longs;t <lb/>linea à centro: & longior manu.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Igitur proiectio cum funda longior fiet.<emph.end type="italics"/><lb/>
<arrow.to.target n="marg28"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg28"></margin.target>Cap 1. lib. 2. <lb/>de v&longs;. part.</s>
</p>
<p type="main">
<s>Manus quidem.] <emph type="italics"/>Manus apud veteres, vt videre e&longs;t apud <lb/>Gal. tres &longs;unt partes vna quidem brachium, alia vero<emph.end type="italics"/> <foreign lang="greek">ph/xus</foreign> <emph type="italics"/>id e&longs;t <lb/>cubitus, & tertia<emph.end type="italics"/> <foreign lang="greek">a)kro/keiron</foreign> <emph type="italics"/>hoc e&longs;t &longs;umma extremave manus. <lb/>Hæc et&longs;i commoueatur cum fundam rotat tanquam manens loco, <lb/>tamen & centrum habetur, funda autem radius e&longs;t: at cum &longs;ine fun­<lb/>da proiectio fit, articulus quo brachium cum humero connectitur, <lb/>videtur potius habere rationem centri, & brachium cum cubito, & <lb/>extrema manu rationem lineæ à centro.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>14. De collopibus & &longs;uc­<lb/>culis.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur circa eandem erga­<lb/>tam collopes maiores mi­<lb/>noribus facilius <expan abbr="mou&etilde;tur">mouentur</expan>, <lb/>& ip&longs;æ &longs;ucculæ graciliores <lb/>ab <expan abbr="ead&etilde;">eadem</expan> vi cra&longs;&longs;iotibus, An <lb/>quia &longs;uccula & ergata cen­<lb/>trum e&longs;t. Longitudines au­<lb/>tem di&longs;tantes &longs;unt lineæ ex <lb/>centro. At & celerius mo­<lb/>uentur, & plus ab eadem vi <lb/>lineæ <expan abbr="maiorũ">maiorum</expan> circulorum: <lb/>quam <expan abbr="minorũ">minorum</expan>. Ab eadem <lb/>cnim vi extremum, quod <lb/>longiùs e&longs;t à centro, plus <lb/>transfertur, ideo collopas <lb/>organa ad ergatas <expan abbr="adijciũt">adijciunt</expan>,
<pb pagenum="119"/><gap/><lb/>quibus facilius vertunt. In <lb/>&longs;ucculis vero tenuibus ma­<lb/>ius fit id quod extra e&longs;t, li­<lb/>gnum. Et id linea e&longs;t quæ <lb/>ex centro.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr circa eandem.] <emph type="italics"/>In hoc capite continentur duo proble­<lb/>mata vnum de ergatis, alterum de &longs;ucculis. Illud cur ergatæ à <lb/>maioribus collopibus facilius mouentur: quam à minoribus. Hoc cur <lb/>&longs;ucculæ graciliores etiam facilius <expan abbr="mou&etilde;tur">mouentur</expan>, quam craßiores. Vtrum­<lb/>que &longs;oluitur ex lineæ è centro longitudine maiore.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Maiores lineæ ex centro facilius & celerius mouentur ab eadem <lb/>vi minoribus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergata & &longs;uccula collopibus ver&longs;atæ, &longs;unt centrum, & col­<lb/>lopes &longs;unt lineæ ex centro, & quidem tantò maiores, quan­<lb/>tò &longs;uccula gracilior e&longs;t (pars enim quam craßitudo tegeret <lb/>ob gracilitatem detegitur.)<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo ergata & &longs;uccula gracilior à collopibus maioribus facilius <lb/>ab eadem vi mouebuntur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cæterum quid hî<emph.end type="italics"/> <foreign lang="greek">zugo\n</foreign> <emph type="italics"/>ergata differat à &longs;uccula,<emph.end type="italics"/> <foreign lang="greek">o)/non</foreign> <emph type="italics"/>Græci vo­<lb/>cant, & &longs;cytalæ primum genus, parum video, ni&longs;i fulcris, aut craßi­<lb/>tudine. Horum enim vnumquodque axis e&longs;t circum quem voluitur <lb/>funis ductarius ad tollenda, vel trahenda onera tran&longs;uer&longs;as habens <lb/>collopas, id e&longs;t ligna oblonga in altera extremitate, vel vtraque, quæ <lb/>&longs;unt tanquam vectes à vi adiuncta deprimendi vicißim. Differre <lb/>tamen po&longs;&longs;unt quod ergata erectum axem habeat, vel fulciatur dua­<lb/>bus trabibus perpendiculariter erectis: &longs;uccula &longs;upinum habet axem <lb/>vel etiam quatuor tignis ex vtraque parte binis &longs;u&longs;tentetur, vnde<emph.end type="italics"/><lb/><foreign lang="greek">o)/nos</foreign> <emph type="italics"/>dicitur, tanquam ge&longs;tanti cuidam a&longs;ino &longs;imilis &longs;it. Huius fecit <lb/>mentionem Hippocrates &longs;ect. 3. lib. de fract. Ex vniuer&longs;is inquit, <lb/>machinationibus, quæ ab hominibus excogitatæ &longs;unt, hæ tres om­<lb/>nium valentißimæ,<emph.end type="italics"/> <foreign lang="greek">o)/nou</foreign> <emph type="italics"/>id e&longs;t axis ver&longs;atio, impul&longs;us per vectem, & <lb/>cuneus adactus. Namque homines &longs;ine aliquo vno, vel &longs;ine omnibus <lb/>nullum opus, quod maximam vim po&longs;tulet, perficiunt. Hæc Hipp.<emph.end type="italics"/>
<pb pagenum="120"/><emph type="italics"/>Succularum <expan abbr="tam&etilde;">tamen</expan> multa &longs;unt genera vt videre e&longs;t apud Vitruuium.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Et Pappus lib. 8. Mathemat collectionum fabricam in&longs;trumenti <lb/>docet, quod huc referri debet, e&longs;t autem eiu&longs;modi. vocat axem M B,<emph.end type="italics"/><lb/>
<figure id="fig45"></figure><lb/><emph type="italics"/><expan abbr="tympanũ">tympanum</expan> C D, circa tympani <expan abbr="peripheriã&longs;cytalas">peripherian&longs;cytalas</expan> vel collopes in fora­<lb/>minibus tympani F G, H F, & ct:ita, vt potentia quæ &longs;emper in <lb/>&longs;cytalis e&longs;t, vel in peripheria tympani vt in F, dum circumuertit <lb/>tympanum, & axem &longs;ur&longs;um quoque mouet pondus K axi appen&longs;um <lb/>fune M circa axem reuoluto. Qui amplius videre volet, cur ab <lb/>hoc in&longs;trumento, quod axis in peritrochio vocatur, magna pondera <lb/>ab exigua virtute, quo ve etiam modo moueantur, quæ ratio tempo­<lb/>ris, &longs;patÿ, potentiæ, ac moti ponderis inter &longs;e, & vt v&longs;us ip&longs;ius ad ve­<lb/>ctem referatur. Videat apud Guidum V baldum in Mechanicis. Ad <lb/>hoc genus etiam in&longs;trumenti referantur ingentes illæ rotæ in vno <lb/>axe quarum vna labore vnius atque alterius hominis vertitur: alte­<lb/>ra &longs;itulis quibus in &longs;ua circumferentia accommodate dispo&longs;itis con­<lb/>ferta e&longs;t &longs;ui conuer&longs;ione ex vna parte aquam Sequanæ &longs;eptis contra­<lb/>ctam exhau&longs;it, ex altera aliò refudit, vt ex lapide quadrato firma <lb/><expan abbr="iacer&etilde;tur">iacerentur</expan> fundamenta illius eximij pontis, qui magno ornamento & <lb/>commoditate celeberrimæ vrbium Lutetiæ, iu&longs;&longs;u Henrici III. Regis<emph.end type="italics"/>
<pb pagenum="121"/><emph type="italics"/>no&longs;tri Chri&longs;tianißimi inchoatus, & maiori iam ex parte con&longs;tru­<lb/>ctus perfectionem ab Henrico IIII. Rege nunc no&longs;tro magnifi­<lb/>centißimo de&longs;iderat, ea in parte, qua flumen à &longs;chola S. Germani <lb/>ad plateam Augu&longs;tinorum traducitur. Hanc, vt &longs;pero, exorabit cla­<lb/>rißimus vir dominus Marlyius rationum regiarum præ&longs;es, & mer­<lb/>catorum præfectus dignißimus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>15. De fractura ligni.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur lignum <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> ma­<lb/>gnitudinis facilius è genu <lb/><expan abbr="frãgitur">frangitur</expan>, &longs;i in extremis ma­<lb/>nus æqualiter diductas ha­<lb/>bens fregerit: quam &longs;i ad <lb/>genu propinquas habuerit. <lb/>Præterea &longs;i ad terram ap­<lb/>plicans, & pede impellens, <lb/>manu di&longs;tante frangat: <expan abbr="quã">quam</expan> <lb/>propinqua. An quia illîc <lb/>genu quidem e&longs;t centrum: <lb/>hîc verò pes. quantò autem <lb/>quodque à centro fuerit <lb/>di&longs;tantius, id omne facilius <lb/>mouetur. Quod frangitur autem moueri nece&longs;&longs;e e&longs;t.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s><emph type="italics"/>Mos e&longs;t ignem excitare in paruo foco volentium, baculos lon­<lb/>giores bifariam frangere. Itaque arreptos tracto&longs;que vtraque <lb/>manu per extrema medios ad genu applicantes, parua vi frangunt. <lb/>Idem faciunt &longs;i alterum extremorum ad terram applicent: alterum <lb/>eleuatum obliquè manu teneant, & medium pede conculcent. Quæ­<lb/>rit igitur Ari&longs;toteles cur fractio hæc facilior fit manibus ad extre­<lb/>ma diductis: quam ad medium propius accedentibus. Et &longs;oluit è ra­<lb/>dijs maioribus, &longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quantò quidque à centro fuerit remotius, tantò facilius moue­<lb/>tur, & quia fractio e&longs;t motio, frangitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In fractione ligni cum manus &longs;unt in extremis, remotiores<emph.end type="italics"/>
<pb pagenum="122"/><emph type="italics"/>&longs;unt à centro (quod e&longs;t genu cum ad hoc applicatum e&longs;t li­<lb/>gnum: velpes, cum ip&longs;um pede conculcatur) quam cum <lb/>non &longs;unt in extremis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo fractio ligni manibus in extremis exi&longs;tentibus facilior fiet <lb/>quam &longs;i propius exi&longs;tant.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quæri autem hic pote&longs;t, an qui &longs;ic fu&longs;tem frangunt, genu non offen­<lb/>dant. Et non offendere experientia comprobat. Ratio tamen non ita <lb/>aperta e&longs;t. E&longs;t autem vt arbitror, quia genu vt centrum, vel hypo­<lb/>mochlium quie&longs;cit: partes vero fu&longs;tis, vbi fit ruptio, exterius mouen­<lb/>tur. Itaque à genu di&longs;cedunt. Ob eandem cau&longs;am cyphi duo vitrei <lb/>æquales, & aqua pleni fu&longs;tem oblongum extremis &longs;uis &longs;uper impo&longs;i­<lb/>tum adacto celeriter per medium altero fu&longs;te frangi ip&longs;i infracti & <lb/>&longs;ine aquæ effu&longs;ione tolerant. In hoc tamen differentia e&longs;t, quod cyphi <lb/>hypomochlium &longs;unt, itá que in extremis, & partes à cyphis ad me­<lb/>dium &longs;unt lineæ à centro, &longs;icque impul&longs;æ mouentur. Vt & cum cru­<lb/>ris arietini os nudatum perio&longs;tio, & manus eo, qui ad pollicem e&longs;t <lb/>monticulo atque hypothenare &longs;u&longs;tentum dor&longs;i gladÿ ad medium ce­<lb/>leriter adacti vno ictu &longs;ine manus offen&longs;ione frangitur, contrà, <lb/>quam in fu&longs;te è genu fracto. Hæc vulgaria &longs;unt, &longs;ed cau&longs;a non vti­<lb/>que vulgaris.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>16. Cur crocæ rotundæ.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur circa littora crocæ, <lb/>vt vocantur, rotundæ &longs;unt, <lb/>è magnis qui erant à prin­<lb/>cipio lapidibus, & o&longs;treis <lb/>factæ. An quia in motibus <lb/>magis à medio di&longs;tantia ce­<lb/>lerius <expan abbr="ferũtur">feruntur</expan>. Etenim me­<lb/>dium quidem fit centrum: <lb/><expan abbr="interuallũ">interuallum</expan> vero linea ex <expan abbr="c&etilde;-tro">cen­<lb/>tro</expan>. Semper <expan abbr="aut&etilde;">autem</expan> maior ab <lb/><expan abbr="ead&etilde;">eadem</expan> motione <expan abbr="maior&etilde;">maiorem</expan> de­<lb/>&longs;cribit <expan abbr="circulũ">circulum</expan>. Et quod e&longs;t <lb/>maius <expan abbr="&longs;patiũ">&longs;patium</expan> æquali <expan abbr="t&etilde;pore">tempore</expan>
<pb pagenum="123"/><gap/><lb/><expan abbr="trãfiens">tranfiens</expan> celerius fertur. La­<lb/>ta vero celerius in æquali <lb/>&longs;patio, vehementius pul­<lb/>&longs;ant. Et magis pul&longs;antia <lb/>magis etiam percutiuntur. <lb/>Ita que nece&longs;&longs;e e&longs;t plus di­<lb/>&longs;tantia à medio &longs;emper at­<lb/>teri. Et quæ id patiuntur, <lb/><expan abbr="rotũda">rotunda</expan> fieri. Crocis autem <lb/>propter maris motum, cum <lb/>quo etiam mouentur, con­<lb/>tingit in perpetua motione <lb/>e&longs;&longs;e, & in conuolutione of­<lb/>fen&longs;are, & nece&longs;&longs;e e&longs;t præ­<lb/>cipuè id contingere earum <lb/>extremitatibus.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr circa.] <emph type="italics"/>Credibile e&longs;t duo lumina &longs;apientiæ, & virtutis, <lb/>Pub. Scipionem Africanum minorem, & Caium Lælium cum <lb/>propter actuo&longs;am vitam animi remißioni aliquando acquie&longs;centes, <lb/>& ruri feriantes ad Caietam portum Campaniæ, Lucrinumque la­<lb/>cum conchas id e&longs;t duriores te&longs;tas <expan abbr="pi&longs;ciũ">pi&longs;cium</expan>, vt purpuræ, muricis, o&longs;treo­<lb/>rum, & vmbilicos id e&longs;t rotundos calculos in &longs;peciem no&longs;tri vmbi-<emph.end type="italics"/></s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg29"></arrow.to.target><lb/><emph type="italics"/>lici puerorum more colligerent (vt recen&longs;ent Cicero & Valerius <lb/>maximus) quæ&longs;i&longs;&longs;eidem quod hî Ari&longs;toteles. Cur &longs;cilicet vmbilici <lb/>illi (crocas Ari&longs;toteles appellat) rotundi &longs;int, cum antea e&longs;&longs;ent lapi­<lb/>des maiu&longs;culi minime <expan abbr="rotũdi">rotundi</expan>, &longs;ed angulati, vt & partes concharum <lb/>o&longs;treorum inæquales & a&longs;peræ. Quod problema licet &longs;peciale &longs;it de <lb/>crocis, generale tamen fieri pote&longs;t de omnibus non rotundis. Et cau&longs;a <lb/>generalis e&longs;&longs;et hoc modo: quæcunque non &longs;unt rotunda frequenti, & <lb/>celeri, & maiori conuer &longs;ione eminentis vt anguli atteruntur, pul­<lb/>&longs;ant enim ea parte magis occurrentia quælibet &longs;iue liquida, &longs;iue &longs;oli­<lb/>da, & vicißim pul&longs;antur ab occurrentibus: &longs;icque &longs;ublatis per attri­<lb/>tionem eminentÿs & angulis rotundantur.<emph.end type="italics"/>
<pb pagenum="124"/>
<arrow.to.target n="marg30"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg29"></margin.target>Lib. 2. de <lb/>Orat. cap. 8. <lb/>lib. 8.</s>
</p>
<p type="margin">
<s><margin.target id="marg30"></margin.target>Cap. 11. lib. <lb/>1. de v&longs;u <lb/>part.</s>
</p>
<p type="main">
<s>Itaque nece&longs;&longs;e e&longs;t.] <emph type="italics"/>Ex his collige verum e&longs;&longs;e illud quod e&longs;t <lb/>apud Galenum, &longs;olam figurarum rotundam ad vix patiendum ex­<lb/>qui&longs;itè comparatam e&longs;&longs;e, vt quæ nullum expo&longs;itum angulum frangi <lb/>potentem habeat, id e&longs;t, vt ex hoc capite interpretor, nullam partem <lb/>exteriorem à medio alteram altera di&longs;tantiorem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Semperatteri.] <emph type="italics"/>Vt Gutta &longs;æpius cadendo lapidem immotum <lb/>cauat: &longs;ic aqua in vertiginem commotum atterit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Gutta cauat lapidem, con&longs;umitur annulus v&longs;u.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>17. Cur ligna longiora &longs;unt <lb/>imbecilliora.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>
<arrow.to.target n="marg31"></arrow.to.target></s>
</p>
<p type="margin">
<s><margin.target id="marg31"></margin.target>[bis <expan abbr="dictũ]">dictun]</expan> <lb/>fruftra.</s>
</p>
<p type="main">
<s>Cur quantò ligna fue­<lb/>rin<gap/> longiora, tantò fiunt <lb/>imbecilliora, & &longs;ublata <lb/>magis <expan abbr="curuãtur">curuantur</expan>, licet breue <lb/>&longs;it quod tenue, vt <expan abbr="bicubi-tũ">bicubi­<lb/>tum</expan>, & quod centum cubito­<lb/>rum, cra&longs;&longs;um, An quia ligni <lb/>longitudo, dum attollitur, <lb/>fit vectis, pondus, & <expan abbr="hypo-mochliũ">hypo­<lb/>mochlium</expan>? prima enim ip&longs;ius <lb/>pars, quam manus attollit, <lb/>fit vt hypomochlium: quæ <lb/>autem in extremo, vt pon­<lb/>dus. Itaque quantò di&longs;tite­<lb/>rit magis ab hypomochlio: <lb/>tantò magis curuari nece&longs;­<lb/>&longs;e e&longs;t. Nece&longs;&longs;e igitur extre­<lb/>ma vectis eleuari. Si verò <lb/>flexilis vectis fuerit, nece&longs;­<lb/>&longs;e erit ip&longs;um magis inflecti <lb/>cum attollitur: quod & li­<lb/>gnis longis contingit. At in <lb/>breuibus <expan abbr="extremũ">extremum</expan> fit vici-
<pb pagenum="125"/><gap/><lb/>num hypomochlio quie&longs;­<lb/>centi.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr quantò.] <emph type="italics"/>In exercitu &longs;æpe milites dum feriantur roboris <lb/>experiundi, vel exercendi gratia longas ha&longs;tas humi iacentes <lb/>vna manu, aut vtraque in alterum extremorum iniecta & compre­<lb/>hendente nituntur attollere, quou&longs;que perpendiculares fiant plano <lb/>horizontis: qua in &longs;ublatione videre licet ha&longs;tas illas longas vt cra&longs;­<lb/>&longs;iores &longs;int, inflecti tamen magis medio &longs;ublationis tempore: quam <lb/>breues, licet tenuiores &longs;int. Quærit igitur hî Ari&longs;toteles non &longs;olum <lb/>cur &longs;ic fiat, non in his tantum: &longs;ed & in omnibus flexilibus. Cau&longs;am <lb/>repetit ex eo quod flexilia illa &longs;int vectis, <expan abbr="põdus">pondus</expan>, & hypomochlium, <lb/>non eadem parte tamen: &longs;ed diuer&longs;is. In extremo enim manu compre­<lb/>hen&longs;o e&longs;t hypomochlium. In altero e&longs;t pondus. Longitudo vero inter <lb/>media e&longs;t vectis. Ratio itaque &longs;ic di&longs;ponetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Pondus quò magis di&longs;titerit ab hypomochlio, eò magis vectem, <lb/>&longs;i flexilis e&longs;t, incuruat, dum attollitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In longis lignis, vt flexilibus, pondus magis di&longs;tat ab hypo­<lb/>mochlio: extremum &longs;cilicet ab extremo: quam in breuibus,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ligna igitur longa magis incuruabuntur: quam breuia, dum &longs;ic <lb/>attolluntur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sed & ligna medio &longs;ui comprehen&longs;a, & &longs;ic eleuata &longs;emper quo lon­<lb/>giora, eo magis incuruabuntur. At tunc hypomochlium erit in me­<lb/>dio. Pondera duo erunt in extremis. Curuari autem magis imbecilli­<lb/>tatis e&longs;t. Curuatio enim à fractura non differt, ni&longs;i &longs;ecundum magis <lb/>& minus. Si plus enim curuatur: quam vnitas partium ferat, &longs;olui­<lb/>tur continuum, & &longs;ic frangitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>18. Cau&longs;a pote&longs;tatis <lb/>cunei.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur à cuneo re parua ma­<lb/>gnæ moles, & <expan abbr="corporũ">corporum</expan> ma­<lb/>gnitudines <expan abbr="diuidũtur">diuiduntur</expan>, im­
<pb pagenum="126"/><gap/><lb/>pre&longs;&longs;ioque valida efficitur. <lb/>An quia cuneus vectes duo <lb/>&longs;unt &longs;ibi inuicem <expan abbr="cõtrarij">contrarij</expan>, <lb/>vterque verò habet & pon­<lb/>dus, & <expan abbr="hypomochliũ">hypomochlium</expan>, quod <lb/>diuellit, vel <expan abbr="cõprimit">comprimit</expan>. Præ­<lb/>terea percu&longs;&longs;io <expan abbr="põdus">pondus</expan> quod <lb/>percutit, & mouet <expan abbr="magnũ">magnum</expan> <lb/>facit, & quia motum mo­<lb/>uet celeritate valentius e&longs;t. <lb/>Paruo vero exi&longs;tente vecte <lb/>magnæ vires con&longs;equun­<lb/>tur, ideò mouens latet præ­<lb/>ratione magnitudinis.</s>
</p>
<figure></figure>
<p type="main">
<s>E&longs;to cuneus vbi e&longs;t <foreign lang="greek">a b <lb/>g,</foreign> quod vero cuneo fin­<lb/>ditur <foreign lang="greek">d n z.</foreign> Vectis itaque <lb/>fiet <foreign lang="greek">a b,</foreign> pondus vero ip&longs;ius <lb/><foreign lang="greek">b</foreign> inferior pars: hypo­<lb/>mochlium autem <foreign lang="greek">ms&sn,</foreign><lb/>huic vero contrarius ve­<lb/>ctis <foreign lang="greek">b g,</foreign> tum pars <foreign lang="greek">a g</foreign> per­<lb/>cu&longs;&longs;a. <expan abbr="vtroq;">vtroque</expan> illorum vecte vtitur. diuellit enim ip&longs;um <foreign lang="greek">b.</foreign></s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cau&longs;a pote&longs;tatis cunei.] <emph type="italics"/>Cuneus e&longs;t in&longs;trumentum ex ma­<lb/>teria firma in&longs;tar pyramidis à ba&longs;i lata in angu&longs;tum fa&longs;tigia-<emph.end type="italics"/>
<pb pagenum="127"/>
<figure id="fig46"></figure><lb/><emph type="italics"/>tum. Vt A B C D E F. In <lb/>hac forma duo con&longs;ideranda &longs;unt, <lb/>alterum e&longs;t ex amplitudine ba&longs;is, <lb/>qua cuneus ad &longs;u&longs;cipiendam &longs;u&longs;ti­<lb/>nendamque percußionem aptißi­<lb/>mus e&longs;t: alterum e&longs;t ex vertice acu­<lb/>to, qui ob id facile intrà corpora penetrans &longs;ibi viam facit. V&longs;us <lb/>eius e&longs;t ad magnos arborum truncos diuidendum, quod fit magna <lb/>cum facilitate <expan abbr="etiã">etiam</expan> à puero, beneficio ip&longs;ius cunei per rimulam primò <lb/>factam, qua parte acutior e&longs;t, immi&longs;si & qua parte oppo&longs;ita latior <lb/>e&longs;t à malleo percu&longs;si, quod à Milone licet athleta robu&longs;ti&longs;simo per &longs;e <lb/>fieri non potuit. Hic enim cum aliquando conspiceret adole&longs;centem <lb/>cuneis immißis findentem arbores, fertur &longs;ubri&longs;i&longs;&longs;e & &longs;ubmoui&longs;&longs;e. <lb/>Tum non alio vtens in&longs;trumento, quam &longs;uis manibus au&longs;us e&longs;t trun­<lb/>cum diducere. Mox quicquid habebat roboris in primo impetu colli­<lb/>gens, diduxit hûc atque illûc partes, interim elap&longs;is cuneis, quoniam <lb/>reliquam arboris partem diducere non po&longs;&longs;et, diù quidem obnixus e&longs;t, <lb/>tandem victus educere non potuit: &longs;ed ab arboris partibus in &longs;e&longs;e cele­<lb/>riter <expan abbr="co&etilde;untibus">coenuntibus</expan> comprehen&longs;æ, primum quidem ip&longs;æ contritæ &longs;unt, <lb/>mox & ip&longs;i mi&longs;erandi exitÿ fuere cau&longs;a, vt refert Galenus in lib. de <lb/>exhort. ad bonas artes. Hic e&longs;t de quo Iuuenalis,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Viribus ille</s>
</p>
<p type="main">
<s>Confi&longs;us perijt.</s>
</p>
<p type="main">
<s>Cur à cuneo.] <emph type="italics"/>Antea vectis con&longs;ideratus e&longs;t generaliter, dein­<lb/>de &longs;pecialiter: &longs;ed &longs;implex vt in remo, gubernaculo, malo, collope: <lb/>nunc etiam idem &longs;pecialiter con&longs;ideratur, &longs;ed multiplex. Et primum <lb/>quidem duplicatus, vt in cuneo. Nam hic quod paruus exi&longs;tens ma­<lb/>gnos arborum truncos penetrando diuidat, non aliunde habet quam <lb/>quia duplex e&longs;t vectis, & à percu&longs;sione motus. Ex hoc enim quod ve­<lb/>ctis facile mouet. Ex hoc quod e&longs;t duo vectes, cum hi ex aduer&longs;o &longs;ibi <lb/>inuicem contrarÿ &longs;int, & mutuas operas &longs;ibi tradant, magis & faci­<lb/>lius mouet. Ex hoc quod à percu&longs;sione, eaque celeri, quæ motus e&longs;t, ma­<lb/>gis adhuc mouetur: &longs;icque à tribus ÿs coniunctis effectus à cuneo ad­<lb/>mirandi prodeuntis habetur cau&longs;a. Notandum autem quod inter <lb/>cuneos, qui angulum ad verticem <expan abbr="acutior&etilde;">acutiorem</expan> habet facilius mouet, ac <lb/>&longs;cindit: quam qui obtu&longs;iorem. Mouetur enim cuneus anguli maioris<emph.end type="italics"/>
<pb pagenum="128"/><emph type="italics"/>per maius &longs;patium, quam minoris, &longs;iquidem maioris anguli maior e&longs;t <lb/>&longs;ubten&longs;a, cum anguli &longs;unt æquicruri prop. 26. lib. 1. A potentia verò <lb/>facilius eodem tempore mouetur aliquid per minus &longs;patium: quam <lb/>per maius cum cætera paria &longs;unt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia.] <emph type="italics"/>Prior cau&longs;a e&longs;t ad &longs;olutionem problematis, quæ hoc <lb/>&longs;yllogi&longs;mo concludetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Duo vectes &longs;imul iuncti multum mouent, & magnas moles <lb/>di&longs;trahunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cuneus e&longs;t duo vectes, ÿque &longs;ibi inuicem contrarÿ: &longs;ed <lb/>iuncti.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cuneus igitur multum mouet, & magnas moles di&longs;trahet. <lb/>Syllogi&longs;mi propo&longs;itio confirmationem non habet: &longs;ed hæc repeti po­<lb/>te&longs;t ex vnius vectis potentia anteà confirmata, quæ in duobus igitur <lb/>iunctis maior erit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vterque verò habet.] <emph type="italics"/>Confirmatio e&longs;t a&longs;&longs;umptionis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vbi e&longs;t longitudo duplex, hypomochlia duo, & pondus, ibi &longs;unt <lb/>duo vectes.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In cuneo e&longs;t vtrinque longitudo, labra rimæ quam ingredi­<lb/>tur cuneus, &longs;unt hypomochlia: truncus findendus e&longs;t <lb/>pondus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>E&longs;t igitur cuneus duo vectes.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Præterea percu&longs;&longs;io.] <emph type="italics"/>Secunda e&longs;t cau&longs;a ad &longs;olutionem proble­<lb/>matis, quod cuneus adigatur non &longs;implici pul&longs;u: &longs;ed percu&longs;&longs;u, qui ve­<lb/>hemens & celer e&longs;t motus: iam motum autem mouendum vehemen­<lb/>tius mouet. Percußio autem duobus fit modis, vel ex eo ip&longs;o &longs;olo quod <lb/>percutit tanquam graui<gap/> loco &longs;uperiori deor&longs;um incidente: at que hoc <lb/>quò grauius e&longs;t, eò maior fit percußio: quin & quò longius di&longs;titerit <lb/>primum incidens, magis percutit. Graue enim vnumquodque dum <lb/>mouetur grauitatis magis a&longs;&longs;umit motum: quam quie&longs;cens: & adhuc <lb/>magis quo longius mouet. quilibet enim aër addit &longs;uper motum iam <lb/>acqui&longs;itum. Inde ca&longs;us lapidis aut ictus ab altiore loco grauius per­<lb/>cutit: vel ex eo quidem quod percutit, &longs;ed recto atque moto, ab aliqua <lb/>potentia percutiente, vt &longs;i per manubrium mallei, quod vna vel duæ <lb/>manus moueant. Certum e&longs;t quod quò grauior erit malleus, & quò <lb/>longius manubrium, eò maior fiet percu&longs;sio, vt ex præcedentibus &longs;atis <lb/>patere pote&longs;t, cum malleus tanquam pondus à centro, quod e&longs;t in ma-<emph.end type="italics"/>
<pb pagenum="129"/><emph type="italics"/>nubrio, vbi manus ip&longs;um comprehendunt, plus di&longs;tet. Præterea cer­<lb/>tum e&longs;t quod quantò potentia percutiens validior e&longs;t, validiori tantò <lb/>impellet pul&longs;u. his adde quod e&longs;t ab Hippocrate<emph.end type="italics"/> <foreign lang="greek"><gap/>)n toi_s tsw/masi</foreign><lb/><emph type="italics"/>annotatum. Quantò impul&longs;us magis fiet<emph.end type="italics"/> <foreign lang="greek">ka(<gap/>) i)/cin</foreign> <emph type="italics"/>è directo, id e&longs;t vt <lb/>interpretor è perpendiculari. Cæterum percußionem vim habere ad <lb/>mouendum validißimam docebit Ari&longs;toteles prob. 19. huius libri: <lb/>&longs;ed ex multis colligere id ita e&longs;&longs;e po&longs;&longs;umus. Primum quod licet cuneo <lb/>ba&longs;i &longs;ua &longs;uper plano in&longs;i&longs;tenti, pondus alioqui valde ingens impona­<lb/>tur, ip&longs;um non diuidet, aut parùm, &longs;i ad diui&longs;ionem percußione fa­<lb/>ctam compares. Secundum &longs;i cuneo vel vectis vel cochlea vel aliud <lb/>aliquod in&longs;trumentum aptetur, vt ip&longs;e intimius propellatur, effectus <lb/>inde con&longs;equens parui erit momenti,<emph.end type="italics"/><lb/>
<figure id="fig47"></figure><lb/><emph type="italics"/>re&longs;pectu eius, qui à percußione pro­<lb/>fici&longs;citur. Guidus V baldus commo­<lb/>de hoc adfert exemplum. Sit A cor­<lb/>pus lapideum ex quo angulus &longs;olidus <lb/>B &longs;it auferendus, mallei ferrei per­<lb/>cu&longs;&longs;u facile id fit, &longs;ine percu&longs;&longs;u, nec <lb/>cum hoc, nec cum alio quouis in&longs;tru­<lb/>mento, ni&longs;i cum maxima difficulta­<lb/>te fieri poterit. Percu&longs;sio igitur cau&longs;a e&longs;t, cur magna &longs;cindantur <lb/>pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Paruo verò.] <emph type="italics"/>Occurrit obiectioni, quæ fit propter exiguitatem <lb/>cunei, ob idque & vectis, &longs;ed hanc dicit compen&longs;ari vehementia & <lb/>celeritate percu&longs;sionis, & quanquam ratione motus, motor exiguus <lb/>videatur, & ita lateat, magnus e&longs;t tamen viribus. Sic in rebus natu-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg32"></arrow.to.target><lb/><emph type="italics"/>ralibus, vt e&longs;t apud Galenum, paruæ molis res quædam &longs;olo tactu, <lb/>quædam exiguo mor&longs;u maximas corporibus inducunt alterationes. <lb/>Id quod in heraclio lapide, quem <expan abbr="magnet&etilde;">magnetem</expan> nominant, videre e&longs;t, fer­<lb/>rum enim quod tetigerit, ei adhæret vel nullo adhibito vinculo: dein­<lb/>de &longs;i aliud id, quod primo tactum fuerit, tetigerit, &longs;imiliter vt pri­<lb/>mum, illi inhærebit, po&longs;tea tertium &longs;ecundo. Præterea à Phalangÿ <lb/>ictu totum corpus affici videtur exiguo veneno per foramen iniecto: <lb/>&longs;ed longè maiori admiratione dignus e&longs;t Scorpionis ictus, qui breui <lb/>admodum tempore grauißima infert accidentia. Hæc Galenus quæ <lb/>ideo attuli, vt intelligant mor&longs;us ab animalium dentibus inci&longs;orÿs<emph.end type="italics"/>
<pb pagenum="130"/><emph type="italics"/>maxillarum impetu adactis in rem mor&longs;am vt pondus diuidendum, <lb/>tanquam à cuneis e&longs;&longs;e factos, vt & vulnera ab en&longs;ibus, ha&longs;tis, dola­<lb/>bris, &longs;ecuribus & id genus in&longs;trumentis. Serra quoque & lima ad <lb/>hoc genus, quòd ad &longs;uos denticulos &longs;pectatreduci pote&longs;t, quot enim <lb/>denticuli totcunei, & ÿ alligati, aut continui &longs;uo vecti, id e&longs;t, manu­<lb/>brio, quod pro vt longius, vel breuius e&longs;t, ita maiorem vim impul&longs;us <lb/>aut tractus obtinet.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg32"></margin.target>Lib. 5. de <lb/>loc aff.</s>
</p>
<p type="main">
<s>E&longs;to cuneus.] <emph type="italics"/>Hîc e&longs;t demon&longs;tratio linearis ad ostenden­<lb/>dum cuneum diuidendo ponderi duorum vectium vicem pror&longs;us ge­<lb/>rere, eorumque &longs;ibi inuicem contrariorum. Sed hanc &longs;ic paulò am­<lb/>plius & apertius repetemus. Sit cuneus A B C cuius vertex B: <lb/>& &longs;it A B æqualis B C, <lb/>quod autem diuidendum<emph.end type="italics"/><lb/>
<figure id="fig48"></figure><lb/><emph type="italics"/>e&longs;t, &longs;it D E F G, &longs;itque <lb/>pars cunei H B K intra <lb/>D E F G, & H B &longs;it <lb/>æqualis ip&longs;i B K. percu­<lb/>tiatur vt fieri &longs;olet cuneus <lb/>in A C. Dum cuneus in <lb/>A C percutitur, A B fit <lb/>vectis, cuius hypomoch­<lb/>lium e&longs;t H, & pondus in <lb/>B, eodemque modo C B <lb/>fit vectis, cuius hypomo­<lb/>chlium e&longs;t K, & pondus &longs;imiliter in B. Sed dum percutitur cuneus <lb/>maiori adhuc ip&longs;ius portione, intra ip&longs;um D E F G ingreditur, <lb/>quam prius e&longs;&longs;et: &longs;it autem portio hæc M B L, &longs;itque M B ip&longs;i <lb/>B L æqualis. Et cum M B, B L &longs;int ip&longs;is H B, B K maiores: <lb/>erit M L maior H K. Dumigitur M L erit in &longs;itu H K, opor­<lb/>tet vt fiat maior diui&longs;io, & D moueatur ver&longs;us O: G autem ver­<lb/>&longs;us N, & quò maior pars cunei intra D E F G ingredietur, eò <lb/>maior fiet diui&longs;io: & D, G magis adhuc impellentur ver&longs;us O, <lb/>N. Parsigitur K G eius quod diuiditur mouebitur à vecte A B, <lb/>cuius hypomochlium e&longs;t H, & pondus in B, ita vt punctum B <lb/>ip&longs;ius vectis A B impellat partem k G: & pars H D mouebi­<lb/>tur à vecte C B, cuius hypomochlium e&longs;t k, ita vt B vecte C B<emph.end type="italics"/>
<pb pagenum="131"/><emph type="italics"/>partem H D impellat. Atque hæc e&longs;t &longs;ententia Ari&longs;totelis de du­<lb/>plici vecte in cuneo. Aliam habet Guidus Vbaldus, quam exi&longs;timat <lb/>meliorem. E&longs;t autem eiu&longs;modi, vt figuræ iam po&longs;itæ vectis A B <lb/>habeat hypomochlium B, & pondus mouendum H, &longs;icut vectis <lb/>C B, habeatitem hypomochlium B & pondus mouendum &longs;it K: it a <lb/>vt pars H D moueatur à vecte A B, & pars k G à vecte C B. <lb/>Ratio e&longs;t, quia in&longs;trumenta mouent per contactum: vectis autem A <lb/>B tangit partem H D motam in H, non &longs;imiliter tangit in B. <lb/>Id ip&longs;um in&longs;uper comprobat ex cuneo inter duas moles &longs;eparatas in­<lb/>terpo&longs;ito: &longs;ed quod pace tanti viri dixerim certum e&longs;t, quod ni&longs;i B <lb/>vertex cunei tangeret molem in B, & ip&longs;am impelleret atque diui­<lb/>deret, partes H D, K G non vtrinque cederent in O & N. Quod <lb/>igitur cedant motus is &longs;ecundarius e&longs;t, & priorem qui e&longs;t in B con­<lb/>&longs;equens. Quod autem ad moles &longs;eparatas attinet, in his aër pondus e&longs;t <lb/>mouendum, quem &longs;i nequaquam cedere fingamus, non vltra ingre­<lb/>diente cuneo, partes molium inter quas erit cuneus con&longs;i&longs;tent. Cæte­<lb/>rum vt cuneus vectis e&longs;t multiplicatus: ita cochlea, cuius nullam <lb/><expan abbr="mention&etilde;">mentionem</expan> feci&longs;&longs;e <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan> totis his mechanicis miror, <expan abbr="cū">cum</expan> &longs;it cuneus <lb/>multiplicatus, vel vnus continuatus. E&longs;t enim cochlea (vt de hac <lb/>pauca quæ ex Pappo, Vbaldo, Mun&longs;tero &longs;elegimus, dicamus) cuneus <lb/>cylindro circumuolutus helicis in&longs;tar, percußionis quidem expers, <lb/>&longs;ed per vectem cylindri axi annexum ver&longs;us, faciens motionem ma­<lb/>gnorum ponderum. Quod vt intelligatur. Sit cuneus A B C circa<emph.end type="italics"/></s>
</p>
<figure></figure>
<p type="caption">
<s>Cochlea &longs;ine matrice.<lb/><emph type="italics"/>cylindrum D E, qui &longs;ine <expan abbr="impedim&etilde;to">impedimento</expan> verti poßit per vectem K F<emph.end type="italics"/>
<pb pagenum="132"/><emph type="italics"/>cylindri axi an-<emph.end type="italics"/></s>
</p>
<figure></figure>
<p type="caption">
<s>Cochlea cum matrice.<lb/><emph type="italics"/>nexum: pondus <lb/>mouendum &longs;it <lb/>L M N O ex <lb/>parte M N im­<lb/>mobile, vt in <lb/>his quæ <expan abbr="&longs;cindū-tur">&longs;cindun­<lb/>tur</expan>, fieri &longs;olet: <lb/>cunei vero vertex A &longs;it intra rimam R S. Itaque facile e&longs;t videre <lb/>quod dum K F circumuer&longs;us erit vbi K P, vertex A non erit <lb/>amplius intra R S: &longs;ed cunei pars alia vt T V: quæ cum maior <lb/>&longs;it, quam R S. E&longs;t enim pars quæque cunei remotior à vertice, latior <lb/>propinquiore: ergo vt T V &longs;it intra K S, oportet vt R cedat, mo­<lb/>ueaturque ver&longs;us X, & S ver&longs;us E vt faciunt ea quæ &longs;cindun­<lb/>tur. Totum ergo L M N O &longs;cindetur. Nam dum rur&longs;us vectis K <lb/>P peruenerit ad K Q, tunc B C erit intra R S, erit R &longs;iquidem <lb/>in X & S in E, vt X E &longs;it æqualis B C: &longs;emperque conti­<lb/>nuato cuneo progredienteque A vertice vltrà, pondus L M N O, <lb/>&longs;cindetur, vel pondus G mobile impelletur, attrahetur, attolletur,<emph.end type="italics"/><lb/>
<figure id="fig49"></figure><lb/><emph type="italics"/>prout cylindrus cochleæ po&longs;itus erit ad planum horizontis cum &longs;ua, <lb/>vel &longs;inefcemina &longs;eu matrice. Quod &longs;irur&longs;us cochleæ <expan abbr="tympanūrectè">tympanurrectè</expan><emph.end type="italics"/>
<pb pagenum="133"/><emph type="italics"/>vel obliquè denticulatum, ita vt helici facilè congruat, aptetur: ma­<lb/>nife&longs;tum e&longs;t, quod ad motum cochleæ etiam tympani C dentes &longs;uper <lb/>helicem cochleæ ad infinitum <expan abbr="circumuert&etilde;tur">circumuertentur</expan>. Vnde hæc cochlea di­<lb/>citur infinita, id e&longs;t tandiu vertetur, quandiu quis volet. Eodem enim <lb/>modo &longs;emper &longs;e habebit tympanum ad cochleam. Porrò cochleæ vi <lb/>& beneficio admirabile certè quanta pondera moueantur. Refert<emph.end type="italics"/><lb/>
<arrow.to.target n="marg33"></arrow.to.target><lb/><emph type="italics"/>Mun&longs;terus Ba&longs;ileæ &longs;e vidi&longs;&longs;e longißimas &longs;udes præacutis ferreis ro­<lb/>&longs;tris munitas olim in fundum profundi&longs;simè actas auelli. Quinetiam <lb/>aliquando integras domos ex lignis compaginatas in &longs;ublime &longs;uble­<lb/>uari & cylindris aliquot &longs;ubmi&longs;sis aliò deferri: &longs;ed & homińum <lb/>v&longs;u propemodum immen&longs;o quotidie experimur, quantum valeat <lb/>torquendo & premendo, dum vinum, oleum, &longs;uccos quo&longs;libet à <lb/>&longs;uis fructibus exprimimus, & hone&longs;tam v&longs;uram dominis &longs;uis <lb/>per&longs;oluere cogimus, ita ad vltimum quadrantem v&longs;que, vt à pu­<lb/>mice po&longs;tea aquam citius extrahas: quam à fæcibus reliquis &longs;uc­<lb/>cum aliquem. Immo verò, quæ laudari nunquam &longs;atis pote&longs;t, &longs;ine <lb/>cochlea ars Typographica quid e&longs;&longs;e po&longs;&longs;et, Duo autem efficiunt vt <lb/>cochlea tanta po&longs;sit. Primum quia e&longs;t helix circa cochleam, quæ quò <lb/>e&longs;t vertex cunei acutioris, eò facilius: &longs;ed tardius mouet. Alterum <lb/>quia e&longs;t vectis, quo cochlea circumuertitur, qui etiam quò longior, eò <lb/>facilius: &longs;ed etiam tardius mouet.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg33"></margin.target>Lib 1. R <lb/>Math.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>19. Detrochleis.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Quare &longs;i quis in duobus <lb/>tignis inter &longs;e <expan abbr="iũctisè">iunctisè</expan> <expan abbr="cõtra-rio">contra­<lb/>rio</expan> duas trochleas <expan abbr="cõpon&etilde;s">componens</expan> <lb/>ip&longs;is in circulo circum du­<lb/>xerit funiculum, qui lorum <lb/>quòd &longs;u&longs;pendatur ex altero <lb/>tignorum, & alterum inni­<lb/>tatur, aut appofitum &longs;it ad <lb/>trochleas, atque initium <lb/>funiculi traxerit, vt parua <lb/>vi trahat, magna tamen <lb/>pondera adducet.</s>
</p>
<pb pagenum="134"/>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>De trochleis.] <emph type="italics"/>Trochlea e&longs;t in&longs;trumentum vno aut pluribus <lb/>orbiculis circa &longs;uos axiculos mobilibus & fune ductario con­<lb/>&longs;tans ad trahendum, & attollendum onera aptum. Geminatur ali­<lb/>quando, triplicatur, & amplius multiplicatur. Si duobus orbiculis <lb/>con&longs;ter<emph.end type="italics"/> <foreign lang="greek">di/swas|os,</foreign> <emph type="italics"/>&longs;i tribus<emph.end type="italics"/> <foreign lang="greek">tr|i/swasos,</foreign> <emph type="italics"/>&longs;i quinque<emph.end type="italics"/> <foreign lang="greek">pen<gap/>e/swasos,</foreign> <emph type="italics"/>&longs;i plu­<lb/>ribus<emph.end type="italics"/> <foreign lang="greek">polu/swasos</foreign> <emph type="italics"/>dicitur, ex quo &longs;unt illa tractoria in&longs;trumenta in­<lb/>finitarum prope modum virium. vt in quibus orbiculi plures &longs;ibi in­<lb/>uicem &longs;ub&longs;eruientes, & tanquam onus attrahendum diuidentes, &longs;um­<lb/>ma facilitate ip&longs;um attrahunt. Notandum etiam &longs;olum orbiculum <lb/>etiam aliquando trochleam appellari, & ad v&longs;um vnam aliquando <lb/>trochleam, aliquando duas & plures v&longs;urpari, quod vbifit, &longs;i in vna <lb/>trochlca &longs;int plures orbiculi inferioris trochleæ orbiculus &longs;uperior <lb/>debet &longs;emper e&longs;&longs;eminor inferiore: vt & &longs;uperioris inferior, ne funes <lb/>ductarÿ inter &longs;e inuicem complicentur & &longs;ibi ob&longs;int.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quare &longs;i quis.] <emph type="italics"/>Problema de trochleis cur duabus magna one­<lb/>ra parua vi trahuntur, proponitur, apertè quidem, ni&longs;i vbi de alliga­<lb/>tione ip&longs;arum agitur. Tota enim particula contextus huius<emph.end type="italics"/> <foreign lang="greek">e)/xon to\ <lb/>ar)/thma e)k <gap/>ate/rou t<gap/> cu/lwn, <gap/>a/teron de\ h)_ w_<gap/>serhreimu/on h)\ w_<gap/>­<lb/>se<gap/>u/on <gap/> ta\s t<gap/>oxali/as,</foreign> <emph type="italics"/>mendo&longs;a meo iudicio e&longs;t. Quid enim <lb/>e&longs;t habere lorum quod dependeat, ab altero tignorum: alterum vero <lb/>e&longs;&longs;e infixum, & appo&longs;itum ad trochleas, quid e&longs;t illud alterum, quod <lb/>dicitur infigi, & apponi<emph.end type="italics"/><lb/>
<figure id="fig50"></figure><lb/><emph type="italics"/>ad trochleas, intelligi certè <lb/>non pote&longs;t. Si igitur quid <lb/>rei natura, & v&longs;us o&longs;ten­<lb/>dat, ponamus: illam parti­<lb/>culam &longs;ic <expan abbr="cõmutabimus">commutabimus</expan>, <lb/>vt dicamus vnam è dua­<lb/>bus trochleis habere <expan abbr="lorũ">lorum</expan>, <lb/>quod dependeat ab altero <lb/>vel vtroque tignorum: al­<lb/>teri vero infixum & <expan abbr="ap-po&longs;itũ">ap­<lb/>po&longs;itum</expan> e&longs;&longs;e pondus trahen­<lb/>dum vel attollendum. Vt <lb/>&longs;int duo tigna &longs;e&longs;e ex ad-<emph.end type="italics"/>
<pb pagenum="135"/><emph type="italics"/>uer&longs;o fulcientia C D & E F<emph.end type="italics"/><lb/>
<figure id="fig51"></figure><lb/><emph type="italics"/>(plura duobus vt tria, & qua­<lb/>tuor, vt &longs;e validius fulciant, vt <lb/>plurimum &longs;tatuuntur) &longs;int & <lb/>duæ trochleæ A & B, qua­<lb/>rum altera A ad vtrumque ti­<lb/>gnum reuinciatur loro H A, <lb/>alteri vero B appo&longs;itum &longs;it pon­<lb/>dus G, tracto loro ab ini­<lb/>tio vbi I, pondus G cum tro­<lb/>chlea B attolletur ver&longs;us A.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vel etiam &longs;it trochlea in­<lb/>ferior in qua orbiculi duo cui <lb/>pondus A per vncum apponi­<lb/>tur, &longs;uperior in qua duo item or­<lb/>biculi. funis primò alligari de­<lb/>bet vnco, qui e&longs;t in ea, & cir­<lb/>cum agi circa &longs;uperiorem orbicu­<lb/>lorum inferioris trochleæ, ita vt <lb/>a&longs;cendens circum inferiorem &longs;u­<lb/>perioris, deuoluatur po&longs;tea circa <lb/>inferiorem inferioris, & reuol­<lb/>uatur adhuc circa &longs;uperiorem &longs;u­<lb/>perioris, habens tandem initium <lb/>&longs;ui in G vbi motor intelligitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>An quia <expan abbr="id&etilde;">idem</expan> pondus à mi­<lb/>nore vi, &longs;i vecte moueatur, <lb/><expan abbr="trãsfertur">transfertur</expan> magis: <expan abbr="quã">quam</expan> &longs;i ma­<lb/>nu. Trochlea <expan abbr="aut&etilde;">autem</expan> id facit, <lb/>quod vectis. <expan abbr="Itaq;">Itaque</expan> &longs;i vna fa­<lb/>cili^{9} trahat, & ab vnico tra­<lb/>ctu: <expan abbr="quã">quam</expan> manu, graui^{9} multò <lb/>trahet. Hoc vero duæ tro­
<pb pagenum="136"/><gap/><lb/>chleæ plus in dupla veloci­<lb/>tate attollent. Minus enim <lb/>altera trahit quam &longs;i ip&longs;a <lb/>per &longs;eip&longs;am traheret. quo­<lb/>niam iuxta <expan abbr="alterã">alteram</expan> iniectus <lb/>fuerit funiculus. H&ecedil;c enim <lb/>in&longs;uper pondus minus effe­<lb/>cit. Et &longs;ic &longs;i in plures tro­<lb/>chleas iniectus fuerit funi­<lb/>culus, in paucis trochleis <lb/>multum intere&longs;t. Itaque à <lb/>prima trahente <expan abbr="põdus">pondus</expan> qua­<lb/>tuor librarum, ab vltima <lb/>trahi multo minus.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>An quiaidem.] <emph type="italics"/>Solutio e&longs;t propo&longs;iti problematis &longs;umpta è <lb/>vecte multiplicato. Syllogi&longs;mus &longs;ic erit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quod &longs;olum magna moueret pondera parua vi, hoc etiam gemi­<lb/>natum trahet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Trochlea parua vi magna trahit pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Trochlea ergo geminata parua vi magna trahet pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Huius &longs;yllogi&longs;mi propo&longs;itio clara e&longs;t, ex eo quod vires bene compo &longs;i­<lb/>tæ & multiplicatæ plus po&longs;&longs;unt: quam &longs;olæ & &longs;implices. A&longs;&longs;umptio <lb/>verò &longs;ic confirmatur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Trochlea idem facit, quod vectis. E&longs;t enim ip&longs;a vectis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Vectis parua vi magna mouet pondera. ex anteced.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo trochlea parua vi magna trahet pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quod autem trochlea &longs;it vectis, patet. quia hypomochlium e&longs;t in axi­<lb/>culo immobili, diameter orbiculi e&longs;t longitudo vectis deor&longs;um vna <lb/>parte tracta per funem circumductum: altera &longs;ur&longs;um eleuata. <expan abbr="Mou&etilde;s">Mouens</expan> <lb/><expan abbr="cut&etilde;">cutem</expan> e&longs;t virtus trahentis ad initium funis. Et <expan abbr="põdus">pondus</expan> quod e&longs;t vni tro­<lb/>chlearum appo&longs;itum e&longs;t mobile. Cum autem virtus trahit per plures <lb/>orbiculos, vt pluribus vectibus vtens vna opera, & eodem temporis <lb/>momento facilius trahit & minore vi, quandoquidem pondus, vt<emph.end type="italics"/>
<pb pagenum="137"/><emph type="italics"/>pluribus diui&longs;um orbiculis, minus id e&longs;t leuius apparet. Itaque quo­<lb/>niam facilius e&longs;t mouere pondus vecte: quam manu, & trochlea ve­<lb/>ctis e&longs;t, facilius erit trochlea: quam manu.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Plu&longs;quam in dupla.] <emph type="italics"/>Quò plures &longs;unt orbiculi in trochleis, eò <lb/>quidem facilius, & minore vi pondus trahitur, vt e&longs;t demon&longs;tra­<lb/>tum à Guido V baldo prop. 3. & aliquot &longs;equentibus in tractatu de <lb/>trochlea. Sed etiam vbi &longs;unt plures, ibi lentior e&longs;t tractio, quia po­<lb/>tentia in æquali tempore, &longs;patio &longs;ecundum duplum, triplum, & &longs;ic <lb/>deinceps ampliori &longs;ine huiu&longs;modi trochleis idem pondus moueret: &longs;i <lb/>quidem per &longs;e &longs;ufficiat. Vnde arbitror hûc irrep&longs;i&longs;&longs;e mendum in vo­<lb/>cabulo<emph.end type="italics"/> <foreign lang="greek">ta/xei</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">logw|</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">diplasi/w|.</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">(wodiplasi/w|</foreign> <emph type="italics"/>tollendo<emph.end type="italics"/><lb/><foreign lang="greek">ple/on h)\</foreign> <emph type="italics"/>vel potius pro<emph.end type="italics"/> <foreign lang="greek">h)\</foreign> <emph type="italics"/>reponendo<emph.end type="italics"/> <foreign lang="greek">mh\</foreign> <emph type="italics"/>&longs;ic enim &longs;ententia vera erit.<emph.end type="italics"/><lb/>Hoc vero duæ trochleæ plus non in dupla velocitate <expan abbr="at-toll&etilde;t">at­<lb/>tollent</expan>. <emph type="italics"/><expan abbr="Cæterũ">Cæterum</expan> quomodo per trochleas, quanto <expan abbr="t&etilde;pore">tempore</expan>, & &longs;patio, pon­<lb/>dera moueantur, <expan abbr="quodnã">quodnam</expan> &longs;uperioris & inferioris trochleæ fuerit offi­<lb/>cium, orbiculorum diametri vt moueantur, vt in omni ratione quæ <lb/>in numeris e&longs;t, pondus & potentia &longs;tatui po&longs;sint, quæ omnia certè <lb/>&longs;citu digni&longs;sima &longs;unt Geometricè demon&longs;trata, qui &longs;cire volet, vi­<lb/>deat apud Guidum V baldum prædicto tractatu, ne maior pars il­<lb/>lius præ&longs;tanti&longs;simi operis, quod edidit de mechanicis, mihi &longs;it hûc <lb/>transferenda. Huic verò loco non po&longs;&longs;um non in&longs;erere vnam ma­<lb/>chinam e &longs;ex trochleis: & funiculis quinque compo&longs;itam (è pluri­<lb/>bus componi, &longs;i v&longs;us po&longs;tulet, nihil obe&longs;t) mira celeritate, & funis <lb/>ductarÿ paucitate atque compendio pondus attollentem, quam mihi <lb/>communicauit Georgius Lhullierius vir &longs;ine honoris titulo <expan abbr="nũquam">nunquam</expan> <lb/>mihi nominandus, propter <expan abbr="&longs;uũ">&longs;uum</expan> in artes mathematicas & <expan abbr="mathema-tũ">mathema­<lb/>tum</expan> <expan abbr="&longs;tudio&longs;osquãdiu">&longs;tudio&longs;osquandiu</expan> vixit &longs;ingularem <expan abbr="amor&etilde;">amorem</expan>. Machina e&longs;t eiu&longs;modi, <lb/>&longs;it tignum A B perpendiculariter in&longs;i&longs;tens, cui etiam ad rectos al­<lb/>terum in &longs;i&longs;tat vt C D: &longs;int &longs;ex trochleæ E, F, G, H, I, K, <lb/>funiculi quinque L A, N M, Q P, S R, B T, quorum pri­<lb/>mus circumuoluitur circa duos orbiculos E & F in extremis <gap/>i­<lb/>gnorum circa &longs;uos axiculos mobiles reliquorum &longs;inguli circa &longs;inga­<lb/>los à proximè antecedentibus funiculis &longs;u&longs;pen&longs;os. In X autem &longs;it <lb/>harpago ad apprehendendum pondus E attollendum vel deprimen­<lb/>dum. Si eni<gap/> extremum L ab harpagone V liberetur, & ad A <lb/>traducatur, de&longs;cendet vno qua&longs;i nictu oculi pondus E, tantum<emph.end type="italics"/>
<pb pagenum="138"/>
<figure id="fig52"></figure><lb/><emph type="italics"/>&longs;patÿ, quanti &longs;unt funiculi N M, Q P, <lb/>R S, B T. Tanti erunt autem, <lb/>quantos loci, ad quem de&longs;cendere, vel <lb/>è quo educere volumus, profunditas, <lb/>po&longs;tulat. Si autem attollere oporteat, <lb/>extremum L cum erit in A, traduce­<lb/>tur ad harpagonem V.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>In hac machina igitur hæc duo in­<lb/>&longs;unt, facilitas motionis ob multitudi­<lb/>nem trochlearum, & celeritas motio­<lb/>nis. quia quanto temporis &longs;patio extre­<lb/>mum funiculi L ab A transfertur <lb/>ad harpagonem V, eodem pondus E <lb/>ex infimo loco &longs;ur&longs;um per decuplam <lb/>longitudinem & amplius, &longs;i quis vo­<lb/>let, euehitur, aut contra.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Atque in ar­<lb/>chitectura faci­<lb/>le mouent ma­<lb/>gna pondera, <lb/><expan abbr="Trãsferũt">Transferunt</expan> enim <lb/>ab ip&longs;a trochlea <lb/>ad <expan abbr="alterã">alteram</expan> & rur­<lb/>&longs;us ab ip&longs;a ad &longs;u­<lb/>culas & vectes, <lb/>quod <expan abbr="id&etilde;">idem</expan> e&longs;t ac <lb/>&longs;i multas <expan abbr="cõpo-ner&etilde;t">compo­<lb/>nerent</expan> trochleas.</s>
</p>
<p type="head">
<s>COMMINTARIVS.</s>
</p>
<p type="main">
<s>At que in architect.] <emph type="italics"/>Vt funis <lb/>facilius trahatur in magnis ponde­<lb/>ribus dimouendis ergata, aut &longs;ucula adhibetur ad tigna, vt & rota <lb/>& collopes. quæ eò facilius trahunt, quò longiores fuerint. Atque<emph.end type="italics"/>
<pb pagenum="139"/><emph type="italics"/>huius compo&longs;itionis quæ adæquat multas trochleas, aut etiam lon­<lb/>gißimum vectem maximus e&longs;t v&longs;us. <expan abbr="Quandoquid&etilde;">Quandoquidem</expan> cum materia ad <lb/>vectem, cuius longitudo vnius &longs;tadÿ requireretur, idonea <expan abbr="nu&longs;quã">nu&longs;quam</expan> in­<lb/>ueniri poßit, plurium tamen trochlearum, ergatarum, &longs;ucularum, <lb/>tympanorum, collopum compo&longs;itione apta proportionalium, fiet ma­<lb/>china tractabilis, cuius vis maior e&longs;&longs;e pote&longs;t: quam vectis, cuius lon­<lb/>gitudo e&longs;&longs;et &longs;tadÿ vnius. Rei huius &longs;pecimen luculentum Romæ ex­<lb/>hibitum e&longs;t à Dominico Fontana Mili in <expan abbr="Com&etilde;&longs;i">Comen&longs;i</expan> diocœ&longs;i orto, con­<lb/>&longs;ilio, adhortatione, &longs;umptibus Xi&longs;ti V. pontificis maximi, in tran­<lb/>&longs;ponendo obeli&longs;co, qui Soli primùm à Pherone Rege Ægypti, Helio­<lb/>poli antè Troiani belli tempora factus, & dicatus: po&longs;tea à Caio Ca­<lb/>ligula Romam tran&longs;uectus Augu&longs;to & Tiberio Cæ&longs;aribus &longs;acer, <lb/>temporibus no&longs;tris pænè obrutus ruderibus ædium, quæ circum eum <lb/>corruerant, parietinis & cœmentis, nullam tamen iniuriam à tot <lb/>Romaninominis ho&longs;tibus pa&longs;&longs;us, nulla ex parte exe&longs;us, aut comminu­<lb/>tus, magna omnium aduentantium admiratione parte adhuc &longs;ui ali­<lb/>qua loco valde inepto con&longs;picuus, vi&longs;ebatur. Vt totum hoc negotium <lb/>ge&longs;tum &longs;it, licet iam à multis doctis viris literarum monumentis <lb/>commendatum, ineptißimus tamen &longs;im, aut eorum, quæ mea ætate <lb/>fiunt maxime memorabilium, ignarus, &longs;i ip&longs;um in huius loci id <lb/>exempli maxime po&longs;tulantis illu&longs;tratione, prætermittam, breuiter <lb/>ergo commemorabo.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Primum &longs;cire oportet, quod obeli&longs;cus e&longs;t vnus ingenti magnitu­<lb/>dine lapis, qui ab imo v&longs;que ad &longs;ummum rectis lineis in&longs;tar acus, aut <lb/>potius exigui veru in cu&longs;pidem terminatur. V aria e&longs;t obeli&longs;corum <lb/>materia, forma, & altitudo. Hic de quo agitur ex vno lapide, eoque <lb/>durißimo, qui pyrhopæcilos dicitur, quod punctis quibu&longs;dam ignei <lb/>coloris di&longs;tinctus &longs;it, ac varius vndique interluceat, &longs;ine notis hie­<lb/>roglyphicis (quod alÿs obeli&longs;cis frequens e&longs;t, per has regibus Ægypti <lb/>&longs;uas res ge&longs;tas memori<gap/> commendantibus) &longs;emper eadem forma, ea­<lb/>que quadrangulari ex infima &longs;ui parte minus ampla & &longs;patio&longs;a, ob <lb/>idque pulcherrima, cuius craßitudo, &longs;i Serlius antiquitatum Roma­<lb/>narum &longs;criptor rectè metitus e&longs;t, pedibus 9. minuti&longs;que 24. altitu­<lb/>do pedibus 85. &longs;ummaque demum craßitudo pedibus 6. & minutis<emph.end type="italics"/><lb/>8. <emph type="italics"/>comprehenditur, ad imanque ip&longs;ius radicem hæ literæ in epitaphÿ <lb/>ordinem dige&longs;tæ ac di&longs;tributæ legebantur.<emph.end type="italics"/></s>
</p>
<pb pagenum="140"/>
<p type="main">
<s>Diuo Cæ&longs;ari Diui Iulij. F. Augu&longs;to: Ti.</s>
</p>
<p type="main">
<s>Cæ&longs;ari Diui Augu&longs;ti. F. Augu&longs;to &longs;acrum.</s>
</p>
<p type="main">
<s><emph type="italics"/>Hic igitur cum ob &longs;itum (attingebat enim propemodum &longs;acrarium <lb/>ba&longs;ilicæ S. Petri, quod ad meridiem vergit) & eorum quibus &longs;acra­<lb/>tus erat execrationem, &longs;ummo pontifici di&longs;plicui&longs;&longs;et, vt alÿs nonnul­<lb/>lis, qui ante eum in cathedra D. Petri &longs;ederunt: &longs;ed qui rem ob eius, vt <lb/>exi&longs;timabant,<emph.end type="italics"/> <foreign lang="greek">a)dunami/an</foreign>: <emph type="italics"/>aut ob &longs;umptuum magnitudinem ab ag­<lb/>greßione deterriti, nunquam attentarunt. Sanctitati vi&longs;um e&longs;t, vt in <lb/>media V aticani area ante templi, quo nullum e&longs;t magnificentius, ve­<lb/>&longs;tibulum, loco Romæ amplißimo & celeberrimo, & pontificalibus <lb/>actionibus dedicato, collocaretur, & &longs;igno crucis eius apici impo&longs;ito, <lb/>Chri&longs;to Chri&longs;tianorum duci vnico, & &longs;eruatori, obliterata pror&longs;us <lb/>Paganorum con&longs;ecratione, con&longs;ecraretur, & totus denique Chri&longs;tia­<lb/>nos præmoneret, vt quemadmodum eius quatuor latera ab infima <lb/>parte &longs;ur&longs;um ver&longs;us paulatim gracile&longs;cunt, quou&longs;que acuti&longs;simo <lb/>apice, in quo e&longs;t Chri&longs;tus, terminetur: &longs;ic di&longs;cant <expan abbr="m&etilde;tes">mentes</expan> &longs;uas ab hono­<lb/>rum, diuitiarum, aliarum que rerum terre&longs;trium, quibus maxime pa­<lb/>tent, cogitationibus & cupiditatibus &longs;ubtrahere & &longs;ubducere, nec <lb/>ante con&longs;i&longs;tant: quam illæ in altum paulatim erectæ, & acutiores <lb/>factæ, Chri&longs;tum, eumque crucifixum inueniant, &longs;olum ament, hunc <lb/>&longs;omnient, in &longs;olo quie&longs;cant, & in eo &longs;e&longs;e noctes die&longs;que oblectent. <lb/>Hoc igitur vt fieret, ip&longs;um obeli&longs;cum &longs;ine offen&longs;ionis periculo pri­<lb/>mum oportebat è &longs;uo &longs;tylobata auellere: deinde humi vel &longs;uper curri­<lb/>culo reclinare: po&longs;tea tran&longs;uehere ad locum de&longs;tinatum, ab hoc mille <lb/>pedes di&longs;tantem per tumulum agge&longs;tum paulatim eminentiorem va­<lb/>lidi&longs;simis trabibus per aliquot tignorum &longs;tatutiones religatis vndi­<lb/>quaque coercitum, ne immen&longs;a vecturæ mole fati&longs;ceret: po&longs;tea &longs;en &longs;im <lb/>in &longs;ublime &longs;ubrigere: po&longs;tremo perpendiculariter &longs;ubrectum &longs;uper <lb/>&longs;tylobata &longs;uo collocare: nunc qui vectes, quæ ferramenta, quæ machi­<lb/>næ, quot operæ, qui modus tot molitionibus, quarum quælibet factu <lb/>propemodum<emph.end type="italics"/> <foreign lang="greek">a)du/na<gap/>os</foreign> <emph type="italics"/>iudicabatur, adhibita &longs;unt, dicam, vt ex qua­<lb/>dam epistola familiari Roma in Hi&longs;paniam ad P.V elleium de hac <lb/>re mi&longs;&longs;a, & aliorum doctorum <expan abbr="hominũ">hominum</expan> &longs;criptis, breuiter collegimus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Primum obeli&longs;cus validi&longs;simis octo columnis per latera circum­<lb/>uallatus e&longs;t, hæ concathenatæ, atque alÿs &longs;uccre&longs;centibus & conne­<lb/>xis apicem obeli&longs;ci ad &longs;ix palmos præcellebant. His totidem fa&longs;tigia<emph.end type="italics"/>
<pb pagenum="141"/><emph type="italics"/>&longs;uperimpo&longs;ita, à quibus perpetuæ intrà extrá que &longs;uccedentes fulctu­<lb/>ræ &longs;tatuta tigna &longs;u&longs;tentabant, &longs;ic enim ca&longs;ui & in&longs;lexionibus pro­<lb/>&longs;pectum. Tota hæc machina validi&longs;simis laminis, ferrei&longs;que clauis à <lb/>vertice ad calcem religata, plurimis & retinaculis, & ductarÿs fu­<lb/>nibus vndequaque &longs;uffulta. Quadraginta trochleæ à totidem ergatis <lb/>mouendæ fa&longs;tigijs dictis alligatæ erant. Horum &longs;ingulis homines <lb/>quindecim, equi duo de&longs;tinati &longs;unt, qui ad nutum præfecti (præerat <lb/>autem, cuique ergatæ vnus) præ&longs;to e&longs;&longs;ent. Præfecti ad &longs;ignum tubæ <lb/>vrgebant molitionem, cymbali &longs;i&longs;tebant. V ectes adiuncti &longs;unt quin­<lb/>que &longs;eptuaginta palmorum longitudine ex validi&longs;simis trabibus <lb/>compacti, tres ab obeli&longs;ci fronte: duo à tergo. Primo impetu ferrea <lb/>quædam lamina, quæ machinam obeli&longs;cum ambientem religabat, <lb/>di&longs;rupta e&longs;t, &longs;ed hac vnius horæ &longs;patio re&longs;tituta, decem demum im­<lb/>pul&longs;ibus duos palmos, ac <expan abbr="dimidiū">dimidium</expan> in altum obeli&longs;cus eleuatur, ne ta­<lb/>men tanta pendente mole &longs;ini&longs;trum quid accideret, cunei &longs;tatim ac <lb/>tignorum cæ&longs;uræ, quibus obniteretur, &longs;uppo&longs;itæ. Tum deinde a&longs;&longs;eri­<lb/>bus ac cylindris, cubi quidam, quibus in&longs;idebat, dimoti, & quædam <lb/>traha &longs;uppo&longs;ita. Hoc facto, quæ prima ad auellendum molitio acer­<lb/>rima fuit, &longs;u&longs;tenta tamen magnum ad reliquas aggrediendas adiecit <lb/>animum. Itaque ergatæ, trabes, funes ductarÿ, cæteraque, vt conue­<lb/>niebat, mutata, atque in diuer&longs;am formam compo&longs;ita: & ima pars <lb/>obeli&longs;ci quatuor ergatarum viribus, quæ à tergo mouebantur, cæteris <lb/>quæ à fronte erant, funes remittentibus, trahi paulatim cœpit. Ip&longs;e <lb/>vero apex clementi&longs;simè vergebat, quou&longs;que famo &longs;i&longs;sima moles om­<lb/>nino integra, ac &longs;ine vlla iactura humi decubuit. Atque hæc &longs;ecun­<lb/>da molitio fuit. Po&longs;tea per dictum tumulum &longs;ex ergatarum vi trahi <lb/>cœpta e&longs;t, & quia huic &longs;pectaculo intererat ip&longs;e &longs;ummus pontifex, <lb/>huius tanti tantæ molitionis curatoris exactori&longs;que in&longs;tigante <lb/>operarum moras præ&longs;entia, brcuius quidem, quam cogitari pote&longs;t, <lb/>pertracta e&longs;t. Atque hæc tertia molitio fuit. po&longs;tquam ad aliquot <lb/>dies, ne funes nimio calore conflagrarent, ob motum, & aëris æ&longs;t<gap/>o­<lb/>&longs;am tunctemporis con&longs;titutionem, ce&longs;&longs;atum e&longs;t, tandem eadem ma­<lb/>china, qua auul&longs;us: &longs;ed altiore propter loci eminentiam, externo in­<lb/>ternoque chomate muniti&longs;sima, adhibitis ergatis quadraginta &longs;ex, <lb/>equis centum quadraginta, hominibus &longs;excentis, ex ergati&longs;que qua­<lb/>tuor imam obeli&longs;ci partem <expan abbr="trah&etilde;tibus">trahentibus</expan>. Reliquæ à cu&longs;pide ad medium<emph.end type="italics"/>
<pb pagenum="142"/><emph type="italics"/>religatum erexerunt, atque tandem quadraginta &longs;eptem ni&longs;ibus &longs;te­<lb/>tit moles. Cubi, quibus antea in&longs;idebat, &longs;uppo&longs;iti, & in omnis &longs;eculi <lb/>memoriam iam quinquaginta &longs;ex & amplius doctorum hominum <lb/>&longs;criptis editis celebrata, ad perpendiculum collocata e&longs;t. Hæc quarta <lb/>& quinta &longs;unt molitio. Po&longs;tquam vice&longs;ima &longs;exta men&longs;is dicti glo­<lb/>rio&longs;ißimo huic triumpho à pontifice delecta per B <expan abbr="Feratinū">Feratinum</expan> Epi&longs;co­<lb/>pum <expan abbr="Amerinū">Amerinum</expan> & cancellariæ Apo&longs;tolicæ <expan abbr="regent&etilde;">regentem</expan> &longs;olemni prius ad <lb/>Petri altare &longs;acrificio facto, & circà obeli&longs;cum frequenti &longs;upplicatio­<lb/>ne peracta, multaque &longs;uper &longs;anctißimæ Crucis <expan abbr="&longs;tatuã">&longs;tatuam</expan> æream, &longs;ed affa­<lb/>brè inauratam, <expan abbr="precatū">precatum</expan>, tradita e&longs;t Crux Diacono &longs;acris adhuc ve&longs;ti­<lb/>bus induto, à quo denique in mucrone obeli&longs;ci collocata e&longs;t. quo tem­<lb/>poris momento cuncta tormentorum genera, quæ in Sancti Angeli <lb/>arce erant, a&longs;siduos edidere bombos.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Itaque quod pri&longs;cis illis naturæ miraculis quæ à Leone decimo ad <lb/>Paulum III. or bis tulit, desperatum planè opus <expan abbr="iudicatū">iudicatum</expan> erat. Id <expan abbr="nūc">nunc</expan> <lb/>Sixti V. Pontificis cura & magnificentia, Dominici Fontanæ ope­<lb/>ra & indu&longs;tria, &<emph.end type="italics"/> <foreign lang="greek"><gap/> mhxanikw_n</foreign> <emph type="italics"/>auxilia <expan abbr="perfecerūt">perfecerunt</expan>, atque ab&longs;ol­<lb/>uerunt tanto &longs;pectantium applau&longs;u, vt cum Fontana perfecto opere <lb/>domum reductus e&longs;t, diceres Camillum vel Fabium magnum in ca­<lb/>pitolium triumphantem duci. Area vero V aticani in qua obeli&longs;cus, <lb/>qualem in &longs;equenti pagina tibi cum &longs;uis titulis repræ&longs;entamus, licet <lb/>ampli&longs;sima, hominum ad rei miraculum confluentium per multos <lb/>po&longs;tea dies concur&longs;um vix capere potuit.<emph.end type="italics"/></s>
</p>
<p type="head">
<s>E MVLTIS EPIGRAMMIS DE <lb/>obeli&longs;co, Cruce, & Sixto &longs;ummo Pontifice <lb/>hoc &longs;electum hîc in&longs;crip&longs;imus.</s>
</p>
<p type="main">
<s>Ænea &longs;erpentis Mo&longs;es &longs;imulachra &longs;acerdos <lb/>Extulit, ægrotis vt medicina foret</s>
</p>
<p type="main">
<s>Nunc alter Mo&longs;es obeli&longs;ci in vertice Sixtus <lb/>Erigit ægrotis ærea &longs;igna Crucis</s>
</p>
<p type="main">
<s>Vos ô Romani &longs;u&longs;tollite ad æthera vultus, <lb/>A Cruce nam vobis ve&longs;tra petenda &longs;alus.</s>
</p>
<p type="main">
<s><emph type="italics"/>Gulielmus Blancus Albien&longs;i. I. C.<emph.end type="italics"/></s>
</p>
<pb pagenum="143"/>
<figure></figure>
<p type="caption">
<s>Sancti&longs;&longs;imæ Cruci &longs;acra­<lb/>uit Sixtus V. Pont. Max. <lb/>è priore &longs;ede auul&longs;um & <lb/>Cæ&longs;aribus Aug. & Tib. <lb/>11.ablatum.</s>
</p>
<p type="caption">
<s><emph type="italics"/>Faciata à leuante.<emph.end type="italics"/></s>
</p>
<p type="caption">
<s>Ecce Crux Domini <lb/>fugite partes aduer&longs;æ <lb/>vincit leo de Tribu <lb/>Iuda.</s>
</p>
<p type="caption">
<s><emph type="italics"/>Faciata à Tramontana.<emph.end type="italics"/></s>
</p>
<p type="caption">
<s>Sixtus V. Pontif. Max. Cruci <lb/>inuictæ obeli&longs;cum vaticanum <lb/>ab impura &longs;uper&longs;titione expia­<lb/>tum Iu&longs;tius & Felicius con&longs;e­<lb/>crauit Ann. M. D. LXXXVI. <lb/>Pont. II.</s>
</p>
<p type="caption">
<s>Diuo Cæ&longs;. Diui <lb/>Iulij F. Augu&longs;to Ti. <lb/>Cæ&longs;. Diui Augu&longs;t. <lb/>F. Augu&longs;t. &longs;acrum.</s>
</p>
<p type="caption">
<s><emph type="italics"/>Faciata in ver&longs;o pietro.<emph.end type="italics"/></s>
</p>
<p type="caption">
<s>Chri&longs;tus vincit,</s>
</p>
<p type="caption">
<s>Chri&longs;tus regnat,</s>
</p>
<p type="caption">
<s>Chri&longs;tus imperat,</s>
</p>
<p type="caption">
<s>Chri&longs;tus ab omni malo <lb/>plebem &longs;uam defendat.</s>
</p>
<p type="caption">
<s><emph type="italics"/>Della faciata à mez zo giorne.<emph.end type="italics"/></s>
</p>
<p type="caption">
<s>Sixtus V. Pont. Max. obeli <lb/>vaticanum, <lb/>di&longs;. gentium.</s>
</p>
<p type="caption">
<s>Impio cultu dicatum ad Apo&longs;t <lb/>rum limina opero&longs;o labore <lb/>Tran&longs;tulit.</s>
</p>
<p type="caption">
<s>Ann. M.D. LXXXV. Pont</s>
</p>
<pb pagenum="144"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>20. Cur &longs;ecuris feriens di­<lb/>uidit: premens vero non <lb/>item.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Our &longs;i quis magnam &longs;e­<lb/>curim &longs;uper lignum impo­<lb/>&longs;uerit, & illi in&longs;uper ma­<lb/>gnum pondus, lignum non <lb/>diuidit, quod &longs;it effatu di­<lb/>gnum: at &longs;i quis &longs;ecurim at­<lb/>tollens percu&longs;&longs;erit, ip&longs;um <lb/>diuidit, ip&longs;o percutiente <lb/>multò minus pondus ha­<lb/>bente: quam &longs;it id, quod <lb/>impo&longs;itum erat, & preme­<lb/>bat. An quia omnia motio­<lb/>ne fiunt: & graue commo­<lb/>tum magis: quam <expan abbr="quie&longs;c&etilde;s">quie&longs;cens</expan> <lb/>motionem grauitatis acci­<lb/>pit. Impo&longs;itum igitur non <lb/>mouetur, ni&longs;i motione gra­<lb/>uitatis [propriæ]: commotum vero & ip&longs;a & motione <lb/>percutientis.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr&longs;i quis.] <emph type="italics"/>Problema de &longs;ecuri, quæ&longs;ecat dum percutit, non <lb/>autem dum &longs;impliciter incumbit, duobus modis &longs;oluitur. Prior <lb/>&longs;umptus e&longs;t è communi &longs;ententia phy&longs;icorum a&longs;&longs;erentium, omnia <lb/>motione fieri. Syllogi&longs;mus igitur &longs;ic e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cum omnia motione fiant, proinde & &longs;ectio, quod duplici mo­<lb/>tione commotum crit, magis mouebit: quam id, quod vna.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sed graue commotum, vt magna &longs;ecuris feriens, duplici <lb/>motione mouetur, vna grauitatis propriæ: altera percu­<lb/>tientis. Graue autem impo&longs;itum vna tantum mouetur, <lb/>nempe grauitatis propriæ.<emph.end type="italics"/></s>
</p>
<pb pagenum="145"/>
<p type="main">
<s><emph type="italics"/>Ergo magna &longs;ecuris feriens &longs;ecabit: impo&longs;ita vero minimè.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Motione grauitatis.] <foreign lang="greek">xi/nhsis tou_ bar/ous</foreign> <emph type="italics"/>e&longs;t motus cuique <lb/>graui occultus inhærens.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Præterea &longs;ecuris fit cu­<lb/>neus. Cuneus <expan abbr="aut&etilde;">autem</expan> paruus <lb/><expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan> magna diuidit. quia <lb/>ex duobus vectibus con&longs;ti­<lb/>tutus e&longs;t contrario modo <lb/>collocatis.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Præterea &longs;ecuris.] <emph type="italics"/>Altera e&longs;t problematis propo&longs;iti &longs;olutio <lb/>&longs;umpta è cunei forma, quæ in &longs;ecuri propter aciem acutam, & &longs;u­<lb/>perioris partis latitudinem con&longs;picua e&longs;t. Comprehendetur hoc &longs;yl­<lb/>logi&longs;mo.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cuneus paruus cum &longs;it, magna diuidit. (ex anteced.)<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Securis feriens e&longs;t cuneus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo &longs;ecuris feriens magna diuidet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sed hic obÿci pote&longs;t, quod &longs;ecuris impo&longs;ita etiam e&longs;t cuneus. Et ita <lb/>e&longs;t, &longs;ed nonactu. Quia opus e&longs;t malleo percutiente, tanquam motore <lb/>vectium. Securis autem feriens e&longs;t cuneus annexus malleo, & ideo <lb/>actu cuneus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cardanus propo&longs;itum problema aliter &longs;oluit, cau&longs;amque putat. <lb/>quia aër non pote&longs;t in ictu effugere. quanquam enim acuta cu&longs;pide &longs;it <lb/>&longs;ecuris, momento tamen tam paruo temporis effugere nequit. Ne igi­<lb/>tur nimis den&longs;etur, cogitur in poros ingredi &longs;ubiecti ligni, at que cu­<lb/>nei vice diuidere illud. Indicio e&longs;t, inquit, quod paulo tardior ictus<emph.end type="italics"/><lb/>
<arrow.to.target n="marg34"></arrow.to.target><lb/><emph type="italics"/>maximum in diuidendo di&longs;crimen adfert dilabente aëre. Solutionem <lb/>hanc reprehendit Scaliger, con&longs;entitque cum Ari&longs;totele motum mo-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg35"></arrow.to.target><lb/><emph type="italics"/>uere, & &longs;ecurim, &longs;i comprimatur manu, &longs;ecare propter nixum: multo <lb/>magis &longs;i ictu adigatur, & ex Ioanne Iucundo proponit aliud proble­<lb/>ma dignum quæ&longs;itu. Quot pondo proportionem habeat pugnus ho­<lb/>minis ferientis, cum &longs;eip&longs;o non feriente comparatus.<emph.end type="italics"/></s>
</p>
<pb pagenum="146"/>
<p type="margin">
<s><margin.target id="marg34"></margin.target>Lib. 17. de <lb/>&longs;ubt.</s>
</p>
<p type="margin">
<s><margin.target id="marg35"></margin.target>Exerc. 331.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>21. De &longs;tateris.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur &longs;tateræ paruo æqui­<lb/>pondio carnium magna <lb/>pondera expendunt, cum <lb/>totæ dimidia &longs;int libra. Vbi <lb/>enim pondus apponitur, <lb/>appen&longs;a e&longs;t duntaxat lanx. <lb/>Ex altera vero parte &longs;olum <lb/>e&longs;t &longs;tateræ &longs;capus. An quia <lb/>contingit &longs;tateram &longs;imul <lb/>e&longs;&longs;e libram & vectem. Li­<lb/>bra <expan abbr="quid&etilde;">quidem</expan> e&longs;t, vbi vnaquæ­<lb/>que an&longs;arum fit centrum <lb/>&longs;tateræ. I gitur in alter a par­<lb/>te habet lancem: in altera <lb/>pro lance æquipondium, <lb/>quod libræ incumbit. <lb/>Quemadmodum &longs;i quis al­<lb/>teram lancem & pondus <lb/>in eius &longs;ummitate impo­<lb/>neret. Clarum enim e&longs;t, <lb/>quod hoc pondus in altera <lb/>lance &longs;itum trahit. Vt au­<lb/>tem vna libra multæ libræ <lb/>&longs;int in tali libra, multæ an&longs;&ecedil; <lb/>adiectæ &longs;unt, è quibus vna­<lb/>quæque ad eas partes, vbi <lb/>e&longs;t æquipondium, dimi­<lb/>dium e&longs;t &longs;tateræ.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>De &longs;tateris.] <foreign lang="greek">fa/lagc</foreign> <emph type="italics"/>apud Græcos multa &longs;ignificat vt in­<lb/>ternodium in digitis, ordinem & agmem militare longius <lb/>quam latius, ligna teretia, quibus naues in mare deuoluuntur: &longs;ed hîc<emph.end type="italics"/>
<pb pagenum="147"/><emph type="italics"/>&longs;ignificat libræ genus, quod trutina, ab alÿs &longs;tatera appellatur. Huitis <lb/>partes quatuor &longs;unt A B &longs;capus, C D an&longs;a, A E harpago vel <lb/>lanx, F G<emph.end type="italics"/><lb/>
<figure id="fig53"></figure><lb/><emph type="italics"/><expan abbr="æquipõdium">æquipondium</expan> <lb/>Græcis di­<lb/>ctum<emph.end type="italics"/> <foreign lang="greek">sfai/­<lb/>rwma</foreign> <emph type="italics"/>no&longs;tris <lb/>Marcum vel <lb/><expan abbr="Romanũ">Romanum</expan>. Vi <lb/>truuius dixit inuentam fui&longs;&longs;e &longs;tateram, vt ab iniquitate iu&longs;tis mori­<lb/>bus hominum vita vindicetur. Vnde e&longs;t apud &longs;apientem &longs;tatera do­<lb/>lo&longs;a abhominatio e&longs;t apud Deum, & pondus æquum voluntas eius. <lb/>In rebus autem pretio&longs;is licet libra, non &longs;tatera v&longs;urpetur, quia tam <lb/>exacta e&longs;&longs;e non pote&longs;t: in vilioribus tamen, quia iniquitatis parua ia­<lb/>ctura e&longs;t, frequentißimè v&longs;urpatur, propter operis commoditatem. <lb/>Nam libra vti non po&longs;&longs;umus, ni&longs;i paria pondera pen&longs;ionibus &longs;emper <lb/>habeantur, quarum apparatus atque tractatio e&longs;t magis opero&longs;a & <lb/>mole&longs;ta. In &longs;tater is autem quicquid appender is &longs;eu magnum, &longs;eu par­<lb/>uum vnico pondere, hoc e&longs;t æquipondio: distinctione tamen puncto­<lb/>rum in &longs;capo examinatur. Id cnim in &longs;capo ita impo&longs;itum e&longs;t, vt mo­<lb/>dò ad an&longs;am, modò ab an&longs;a remoueatur, vt maiora & minora pon­<lb/>dera libret, & vi mouenti re&longs;pondeat. Nam velut aliqua manus va­<lb/>lida longiorem &longs;tateræ &longs;capum deprimit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cur &longs;tateræ.] <emph type="italics"/>Problema e&longs;t de &longs;tatera, quæ paruo æquipondio <lb/>magna appendit pondera. Et problematis difficultas hinc o&longs;tenditur, <lb/>quod &longs;tatera videatur tantum e&longs;&longs;e dimidia libra, vt in cuius vna <lb/>parte lanx e&longs;t vna dependens, ex altera vero &longs;capus. Rationi igitur <lb/>con&longs;entaneum e&longs;tne tanta pendat, quanta libra integra.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia contingit.] <emph type="italics"/>Solutio problematis petitur ex libra, & <lb/>vecte, ex libra dupliciter. Syllogi&longs;mus prior &longs;ic erit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Libra expendit magna pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Statera e&longs;t libra, vt in cuius vna parte vna e&longs;t lanx, in alter<gap/><lb/>vice alterius lancis, e&longs;t æquipondium, quod pro &longs;ua gra<gap/>itate <lb/>deprimit &longs;capum, & facit æquilibrium, & extremum an&longs;<gap/><lb/>e&longs;t centrum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo & &longs;tatera magna expendet pondera.<emph.end type="italics"/></s>
</p>
<pb pagenum="148"/>
<p type="main">
<s>Vt autem vna libra.] <emph type="italics"/>Syllogi&longs;mus po&longs;terior &longs;ic e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Multæ &longs;imul libræ magna expendunt pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Statera, cui plures an&longs;æ adiectæ &longs;unt, vel vna, &longs;ed per plura <lb/>puncta mobilis, e&longs;t multæ libræ &longs;imul.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo &longs;tatera magna expendet pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Statera certe multæ &longs;unt libræ actu & pote&longs;tate. Et primum actu <lb/>cum an&longs;æ (&longs;ic enim<emph.end type="italics"/> <foreign lang="greek">ta\ <gap/>ar/tia</foreign> <emph type="italics"/>exprimi debere declarant multi <lb/>huius contextus loci inter &longs;e comparati) plures &longs;unt in vno &longs;capo, vt <lb/>duæ, quod frequentißimum, vel tres, quod rarius: cuiu&longs;modi &longs;unt in <lb/>A B &longs;capo<emph.end type="italics"/><lb/>
<figure id="fig54"></figure><lb/><emph type="italics"/>duæ C D, E F <lb/>quarum pro­<lb/>piore lanci, <lb/>qui vtuntur, <lb/>pondera ad <lb/><expan abbr="craßior&etilde;">craßiorem</expan> tru­<lb/>tinam &longs;e ex­<lb/>pendere dicunt. quod huius notæ longius inter&longs;e di&longs;tent: qui vero re­<lb/>motiore, ad &longs;ubtiliorem, vt in qua notæ minus di&longs;tent in lateribus <lb/>&longs;capi &longs;ignatæ. Deinde pote&longs;tate plures &longs;unt, cuman&longs;a vna e&longs;t, &longs;ed mi­<lb/>nimè fixa, verum libero modo propius A, modo remotius colloca­<lb/>tur. Semper autem in aliquo puncto inter A & B intermedio. <lb/>Vnde e&longs;t quod hîc dicat Ari&longs;toteles an&longs;am ad partes, vbi e&longs;t æqui­<lb/>pondium, e&longs;&longs;e dimidium &longs;tateræ, non &longs;umendo dimidium exactè, <lb/>quandoquidem extremo, à quo lanx <expan abbr="dep&etilde;det">dependet</expan> &longs;emper propior &longs;it. Hinc <lb/>elicitur pulchra regula è qua po&longs;tea ferè omnia, quæ ad &longs;tateræ ratio­<lb/>nem pertinent, dedueuntur. quæ e&longs;t eiu&longs;modi. Cum &longs;capus integer ad <lb/>pondus appen&longs;um, rationem eam habet: quam duplum partis, quæ e&longs;t <lb/>ab an&longs;a ver&longs;us lancem ad reliquum: tunc <expan abbr="põdus">pondus</expan> &longs;capum vniformem, <lb/>& omnibus &longs;uis partibus æqualem in æquilubrio con&longs;tituit. Vt e&longs;to <lb/>&longs;capus A B duodecim vnciarum, & pars A F <expan abbr="dudrũ">dudrum</expan>: huius partis <lb/>duplum e&longs;t 4. & reliquum 8. Quemadmodum ergo 4. ad 8. &longs;ic &longs;ca­<lb/>pus <gap/>otus id e&longs;t 12. erit ad pondus, quod per regulam trium inuenie­<lb/>tur e&longs;&longs;e 4. vnciarum. Rur&longs;us &longs;it an&longs;a in D & A D &longs;it vna vn­<lb/>cia. Huius duplum e&longs;t 2. Reliquum e&longs;t 10. Vtigitur 2. ad 10. &longs;ic 12. <lb/>totus &longs;capus erit ad pondus: quod per regulam trium inuenietur e&longs;&longs;e<emph.end type="italics"/>
<pb pagenum="149"/>60. <emph type="italics"/>vnciarum. Vbi notandum lancem in hoc numero pro &longs;uo pon­<lb/>dere includi. Notandum etiam pondus impo&longs;itum lanci e&longs;&longs;e perinde <lb/>atque &longs;i in puncto A imponeretur. Sed de his qui multò plura vide­<lb/>re volet, videat apud Cardanum lib. 1. de &longs;ubtilitate.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Et æquipondium ab an­<lb/>&longs;ulis inuicem commotis, vt <lb/>commetiatur quantum &longs;it <lb/>pondus, trahit id, quod e&longs;t <lb/>in lance po&longs;itum. <expan abbr="Atq;">Atque</expan> co­<lb/>gno&longs;cere licet, <expan abbr="quantũ">quantum</expan> pon­<lb/>dus lanx habeat, quando <lb/>&longs;tateræ &longs;capus ad an&longs;am re­<lb/>ctus fuerit. Omnino qui­<lb/>dem hoc e&longs;t libra habens <lb/>vnam lancem, in qua pon­<lb/>dus appenditur, & ex alte­<lb/>ra parte in &longs;tatera equipon­<lb/>dium. Propterea altera pars <lb/>&longs;tateræ e&longs;t æquipondium. <lb/>Et talis exi&longs;tens multæ &longs;unt <lb/>libræ, & quidem tot, quot <lb/>&longs;unt an&longs;æ.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Et æquipondium.] <emph type="italics"/>Hic textus interiectus quidem e&longs;&longs;e vide­<lb/>tur, non ita tamen inutilis, vt totus reÿciendus &longs;it, quod aliquis <lb/>interpres fecit. Indicat enim modum, quo cogno&longs;catur <expan abbr="põderation">ponderation</expan> is <lb/>æquilibrium. quod e&longs;t vbi in appendendo &longs;capus &longs;tateræ cum an&longs;a <lb/>rectos con&longs;tituit angulos, tuncque e&longs;t parallellus plano horizon<gap/>is.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Semper autem an&longs;a pro­<lb/>pinquior lanci, ponderan­<lb/>doque oneri, trahit maius <lb/>pondus. quia &longs;tatera cffici-
<pb pagenum="150"/><gap/></s>
</p>
<p type="main">
<s>tur vectisinuer&longs;us. E&longs;t enim <lb/>an&longs;a quælibet &longs;upernè exi­<lb/>&longs;tens hypomochlium. Et <lb/>pondus id quod e&longs;t in lan­<lb/>ce. Quantò autem longi­<lb/>tudo vectis maior fuerit ab <lb/>hypomochlio: tantò ibi fa­<lb/>cilius mouet. Hîc autem <lb/>&longs;acoma facit & ponderat <lb/>ad æquipondium pondus <lb/>&longs;tateræ.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Omnino quidem.] <emph type="italics"/>Repetitio e&longs;t a&longs;&longs;umptionum præceden­<lb/>tium &longs;yllogi&longs;morum &longs;cilicet,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Statera e&longs;t omnino libra. <lb/>& <lb/>Statera multæ &longs;unt libræ.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Semper autem.] <emph type="italics"/>Po&longs;tquam o&longs;ten&longs;um e&longs;t &longs;tateram magna pon­<lb/>derare pondera: nunc quæritur quare tantò maiora ponderet: quantò <lb/>an&longs;am lanci habet propinquiorem. Ratio e&longs;t quia vectis e&longs;t, & &longs;ic <lb/>concluditur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quò vectis habet hypomochlium propius ponderi mouendo, eò <lb/>maius mouet. Reliquum enim ab hypomochlio longius e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Statera e&longs;t vectis inuer&longs;us. Nam an&longs;a e&longs;t by pomochlium &longs;u­<lb/>perne exi&longs;tens, & id quod lanci imponitur e&longs;t pondus <lb/>mouendum, vis mouens e&longs;t æquipondium.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo quò an&longs;a erit propior ponderi, eò &longs;tatera maiora pondera­<lb/>bit pondera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Hîc autem &longs;acoma.] <emph type="italics"/>Hic locus è Græco in Latinuna verbo <lb/>ad verbum ver&longs;us difficilem, ne dicam nullum &longs;en&longs;um habet. Vide­<lb/>tur tamen Ari&longs;toteles & appo&longs;itè volui&longs;&longs;e &longs;ignificare æquipondium <lb/>e&longs;&longs;e in &longs;tatera, vim mouentem, & vnum actu cum &longs;it, quia tamen <lb/>per varias not as di&longs;currere pote&longs;t in &longs;tatera, præ&longs;tare ad diuer&longs;a pon­<lb/>dera pendenda, quod in altera libræ lance diuer&longs;a &longs;acomata. E&longs;t enim<emph.end type="italics"/>
<pb pagenum="151"/><foreign lang="greek">sh/xw ma,</foreign> <emph type="italics"/>vt annotauit Budæus in Pandect. quod apponitur in libra <lb/>ad æquilibrium faciendum. Vnde & apud Vitruuium legimus re-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg36"></arrow.to.target><lb/><emph type="italics"/>demptorem ad tempus opus manufactum &longs;ubtiliter regi approba­<lb/>ui&longs;&longs;e, & ad &longs;acoma pondus coronæ vi&longs;um e&longs;&longs;e præ&longs;titi&longs;&longs;e. Cæterum <lb/>quam rationem habeat æquipondium ad &longs;e&longs;e pro varÿs inter&longs;titüs, <lb/>quibus remouetur ab an&longs;a, colligi pote&longs;t ex V baldo per corollarium <lb/>quod deduxit è prop. 6. tractatus de lib. in Mech. quod tale e&longs;t. Ma­<lb/>nife&longs;tum e&longs;t quò pondus à centro libræ magis di&longs;tat, eò grauius e&longs;&longs;e, <lb/>& per con&longs;equens velocius moueri. Et æquipondÿ grauitatem in <lb/>vno loco ad grauitatem eiu&longs;dem in altero, eam rationem habere per <lb/>experientiam noui&longs;&longs;e &longs;e dicit Cardanus, quam habet remotio ad re-<emph.end type="italics"/><lb/>
<arrow.to.target n="marg37"></arrow.to.target><lb/><emph type="italics"/><expan abbr="motion&etilde;">motionem</expan>.<emph.end type="italics"/><lb/>
<figure id="fig55"></figure><lb/><emph type="italics"/>vt &longs;i æqui <lb/><expan abbr="pondiũ">pondium</expan> K <lb/>in D ele­<lb/>uet libras <lb/>20. & in <lb/>E 25. ele­<lb/>uabit in F <lb/>30. In G 35. In H 40. Sic æquali &longs;patio æquale <expan abbr="acquir&etilde;s">acquirens</expan> <expan abbr="augmentũ">augmentum</expan>.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg36"></margin.target>Cap. 3. lib.</s>
</p>
<p type="margin">
<s><margin.target id="marg37"></margin.target>65. c. Arich</s>
</p>
<p type="main">
<s><emph type="italics"/>Et quidem &longs;tateræ ratio demon&longs;trari pote&longs;t. Sit &longs;tateræ &longs;capus <lb/>H B cu-<emph.end type="italics"/><lb/>
<figure id="fig56"></figure><lb/><emph type="italics"/>ius an&longs;a <lb/>&longs;it A C, <lb/>& eius <lb/>æquipon­<lb/>dium E, <lb/>appenda­<lb/>tur vero <lb/>ex H <expan abbr="põ-dus">pon­<lb/>dus</expan> D, <lb/>quod æquiponderet æquipondio E in F appen&longs;o. Aliud quoque pon­<lb/>dus G appendatur in H, quod etiam æquipondio in B appen&longs;o. <lb/>æquiponderet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Dico grauitatem ponderis D ad grauitatem ponderis G i<gap/><lb/>vt C F ad C B.<emph.end type="italics"/></s>
</p>
<pb pagenum="152"/>
<p type="head">
<s>Demon&longs;t.</s>
</p>
<p type="main">
<s><emph type="italics"/>Quia grauitas ponderis D e&longs;t æqualis grauitati ponderis E ex F <lb/>dependentis, & grauitas ponderis G e&longs;t æqualis grauitati ponderis <lb/>E ex B, erit grauitas ponderis D ad grauitatem E ex F: vt gra­<lb/>uitas ponderis G ad grauitatem ponderis E ex B, & permutatim <lb/>prop. 16. lib. 5. vt grauitas ponderis D ad grauitatem ponderis G: <lb/>ita grauitas ip&longs;ius E ex F ad ip&longs;um E ex B. Grauitas autem pon­<lb/>deris E ex F dependentis ad grauitatem ponderis E ex B e&longs;t: vt <lb/>C F ad C B, vt demon&longs;trat V baldus prop. 6. tract. delib. vt igitur <lb/>grauitas ponderis D ad pondus G: ita e&longs;t C F ad C B. Si ergo <lb/>pars &longs;capi C B diuidatur in partes æquales &longs;olo pondere E, & pro­<lb/>pius & longius à puncto C po&longs;ito, ponderum grauitates ex puncto <lb/>H appen&longs;æ notæ erunt. Exempli gratia &longs;it di&longs;tantia C B tripla ad <lb/>C F, erit pondus G triplum ponder is D. quod demon&longs;trare oportebat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>22. De dentiduco.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur medici facilius den­<lb/>tes <expan abbr="eximũt">eximunt</expan> <expan abbr="accipi&etilde;tes">accipientes</expan> pon­<lb/>dus, <expan abbr="d&etilde;tiducum">dentiducum</expan>: <expan abbr="quã">quam</expan> &longs;i &longs;ola <lb/>vtantur manu. Vtrum quia <lb/>dens magis manum præ­<lb/>terlabitur, quam dentidu­<lb/>cum? vel ferrum quidem <lb/>magis labitur manu, neque <lb/>ip&longs;um vndique <expan abbr="compreh&etilde;-dit">comprehen­<lb/>dit</expan>. E&longs;t enim digitorum <lb/>caro mollis, & adhæret ma­<lb/>gis, atque vndique con­<lb/>gruit. Verum quia denti­<lb/>ducus e&longs;t duo vectes aduer­<lb/>&longs;i, vnum <expan abbr="hypomochliũ">hypomochlium</expan> ha­<lb/>bentes in concur&longs;u com­<lb/>mi&longs;&longs;uræ. I gitur ad <expan abbr="ex&etilde;ptio-n&etilde;">exemptio­<lb/>nem</expan>, vt facili^{9} <expan abbr="dimoueãt">dimoueant</expan>, hoc <lb/>vtuntur organo. Sit enim
<pb pagenum="153"/><gap/><lb/>dentiduci extremum alte­<lb/>
<figure id="fig57"></figure><lb/>rum <foreign lang="greek">a,</foreign> alterum <foreign lang="greek">b,</foreign> quod <lb/>eximit, vectis vero <foreign lang="greek">a q z,</foreign><lb/>& alter vectis <foreign lang="greek">b g e</foreign>: hypo­<lb/>mochlium verò <foreign lang="greek">q</foreign> vbi e&longs;t <expan abbr="cõ-mi&longs;&longs;ura">con­<lb/>mi&longs;&longs;ura</expan>: <expan abbr="d&etilde;s">dens</expan> verò <expan abbr="põdus">pondus</expan> e&longs;t. <lb/>Vtroque igitur extremo <foreign lang="greek">b <lb/>& z</foreign> &longs;imul capiens dimouet: <lb/>quando vero emotus fuerit, manu facilius: quam in&longs;tru­<lb/>mento eximetur.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>De dentiduco.] <foreign lang="greek">o)donta/<gap/>an h)\ o)donta/gw<gap/>n</foreign> <emph type="italics"/>vertit Cælius <lb/>Aurelianus cap. 4. lib. 2.<emph.end type="italics"/> <foreign lang="greek"><gap/>oniw_n</foreign> <emph type="italics"/>paßionum dentiducum: Cel­<lb/>&longs;us forficem, & generaliter forcipem. E&longs;t autem in&longs;trumentum, quo <lb/>dens eximitur. Corro&longs;us enim aut vehementer dolens præ&longs;cripto <lb/>medicorum eximi iubetur. Refert tamen Era&longs;i&longs;tratus, vt e&longs;t apud <lb/>Cælium Aurelianum, plumbeum odontagogum apud Delphum in <lb/>templo Apollinis, o&longs;tentationis cau&longs;a propo&longs;itum, quo demon&longs;traba­<lb/>tur oportere &longs;olos eos dentes auferri, qui &longs;int faciles, vel mobilitate <lb/>laxati, vel quibus &longs;ufficeret plumbei in&longs;trumenti conamen ad &longs;um­<lb/>mum. Et profectò dens integer, & firmus, quid vtilis e&longs;t ad bene e&longs;&longs;e, <lb/>temerè eximi non debet, vt paßim fit, &longs;ine iu&longs;&longs;u medicorum à vulga­<lb/>ribus & circumforaneis illis, qui ab hac &longs;ola chirurgica actione den­<lb/>tiduci appellantur, propter quorum inpudentiam multi nobiles chi­<lb/>rurgi operationem hanc, alioqui nece&longs;&longs;ariam aliquando, nec omnibus <lb/>facilem, dedignantur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cur medici.] <emph type="italics"/>Propo&longs;itio e&longs;t problematis de dente, cur facilius <lb/>dentiduco, quam &longs;ola manu eximatur, cui repugnantia ad augendam <lb/>difficultatem &longs;ed vnico ponderis vocabulo in &longs;inuata, opponitur, qua­<lb/>&longs;i diceretur.<emph.end type="italics"/></s>
</p>
<pb pagenum="154"/>
<p type="main">
<s><emph type="italics"/>Pondus adiectum ponderi non facilius mouet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Dentiducus e&longs;t pondus, & denti vt ponderi mouendo adÿ­<lb/>citur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Non igitur facilius mouet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vtrum quia dens.] <emph type="italics"/>Hîc continetur demon&longs;tratio problema­<lb/>tis. V bi notandum dentem eximendum, vt melius eximatur, duo an­<lb/>te exemptionem po&longs;tulare, prius, vt firmè apprehendatur: alterum <lb/>vt validè dimoueatur. In quo con&longs;i&longs;tit præcipuè pars exemptionis, <lb/>quandoquidem dens in gingiuæ &longs;uæ gynglimo e&longs;t, vt clauus ligno <lb/>infixus. Horum autem prius primum quidem dentiduco attribuit, <lb/>vt minoris tamen momenti etiam relinquit digitis manus, vt quo­<lb/>rum caro mollis vndiquaque dentem melius apprehendat, atque huic <lb/>congruat: &longs;ed alterum quod vim po&longs;tulat maiorem &longs;oli dentiduco <lb/><expan abbr="cõmittit">committit</expan>. quia ip&longs;e &longs;it vectis duplicatus. Ratio igitur &longs;ic concludetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Pondus facilius vecte: quam manu &longs;ola mouetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Dentiducus e&longs;t duo vectes &longs;ibi inuicem oppo&longs;iti. Habent <lb/>enim in commi&longs;&longs;ura hypomochlium, & dens e&longs;t pondus <lb/>mouendum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo dens dentiduco facilius: quam manu &longs;ola mouebitur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sit enim dentiduci.] <emph type="italics"/>Lineari demon&longs;tratione o&longs;tenditur præ­<lb/>cedentis &longs;yllogi&longs;mi a&longs;&longs;umptio.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quando verò emotus.] <emph type="italics"/>Factis ÿs, quæ ante exemptionem <lb/>po&longs;tulabat fieri dens eximendus, vltimum quod e&longs;t exemptio melius <lb/>fieri à digit is: quam à dentiduco a&longs;&longs;erit Ari&longs;toteles, nulla tamen ra­<lb/>tione adhibita, licet in clauis ferreis è ligno eximendis, totum per for­<lb/>cipem melius ab&longs;oluatur negotium. Sed res dißimilis videbitur dili­<lb/>gentius attendenti. Nam in clauo eximendo iam emoto forceps ex <lb/>eminentiori &longs;ui parte vt<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">l</foreign> <emph type="italics"/>parietem, aut lignum attingit, & <lb/>punctum contactus fit fulcimentum, & huic totus vt vectis vnus <lb/>effectus innititur, vnde etiam clauus flectitur, & contorquetur in <lb/>euul&longs;ione. quia motus non fit &longs;ecundumrectam: at in dente eximen­<lb/>do, non datur locus tali coaptationi propter gingiuæ &longs;ubiectæ molli­<lb/>ciem, & eiu&longs;dem læ&longs;ionis periculum, & vt daretur dens potius &longs;ic <lb/>frangeretur: quam contorqueretur, &longs;icque è parte tantum eximeretur <lb/>magno dolor is augmento, & reliquæ partis incommodo. Itaque rectà <lb/>&longs;ur&longs;um educi po&longs;tulat, quod melius fit manu ob apprehen&longs;ionis vndi-<emph.end type="italics"/>
<pb pagenum="155"/><emph type="italics"/>quaque factæ, vt anted dictum e&longs;t, commoditatem <expan abbr="maior&etilde;">maiorem</expan>, & rectæ <lb/>eleuationis nullis propemodum viribus indigæ opportunitatem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>23. De in&longs;trumentis quæ <lb/>faciunt ad frangendum <lb/>nuces.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur facilius in nucifran­<lb/>gibulis nuces &longs;ine ictu <expan abbr="frã-gunt">fran­<lb/>gunt</expan>. Multa enim vis illa­<lb/>tionis & <expan abbr="viol&etilde;tiæ">violentiæ</expan> demitur. <lb/>Præterea duro & graui <expan abbr="cõ-primens">con­<lb/>primens</expan> velocius fregetit: <lb/>quam ligneo & leui in&longs;tru­<lb/>mento. An quia &longs;ic vtrin­<lb/>que à duobus vectibus nux <lb/><expan abbr="cõprimitur">comprimitur</expan>, vecte vero fa­<lb/>cile pondera diuelluntur, <lb/>in&longs;trumencum enim duo­<lb/>bus con&longs;tat vectibus, Idem <lb/>hypomochlium <expan abbr="hab&etilde;tibus">habentibus</expan> <lb/>contactum vbi e&longs;t A. Vt <lb/>igitur &longs;i lineæ E D, F C <lb/>diductæ e&longs;&longs;ent extremis C, <lb/>D motis, facile ab exigua <lb/>vi coadducerentur. Quod <lb/>igitur ex ictu pondus feci&longs;­<lb/>&longs;et, hoc valentius E D & <lb/>F C vectes <expan abbr="cũ">cum</expan> &longs;int, efficiunt. <lb/>Elatione enim in <expan abbr="aduersũ">aduersum</expan> <lb/>tollunt, & comprimentes <lb/>frangunt, quod e&longs;t vbi K. <lb/>Ob id quantò ip&longs;i K fuerit <lb/>propior commi&longs;&longs;ura A tan­<lb/>tò citius conterit. Quantò
<pb pagenum="156"/><gap/><lb/>enim plus di&longs;titerit vectis <lb/>ab hypomochlio, tantò fa­<lb/>cilius ab eadem vi mouet. <lb/>E&longs;t igitur A <expan abbr="hypomochliũ">hypomochlium</expan>, <lb/>& E A D vectis, vt & F A <lb/>C. Quantò igitur ip&longs;um K <lb/>propius fuerit angulo A, <lb/>tantò propius fit commi&longs;&longs;u­<lb/>ræ A. Hæc verò e&longs;t hy po­<lb/>mochlium. Nece&longs;&longs;e igitur <lb/>ab eadem vi coadducente <lb/>E, F plus extolli. Et quia <lb/>eleuatio ex aduer&longs;o e&longs;t, ma­<lb/>gis conteri nece&longs;&longs;e e&longs;t, ma­<lb/>gis verò contritum celerius <lb/>frangitur.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>De in&longs;trumentis.] <emph type="italics"/>In&longs;trumentum ad frangendum nuces <lb/>pote&longs;t appellari nucifrangibulum, & hoc non differt à forcipe <lb/>ni&longs;i quia leuiter in extremis excauatur ad excipiendum nucem fran­<lb/>gendam commodius, Huiu&longs;mo-<emph.end type="italics"/><lb/>
<figure id="fig58"></figure><lb/><emph type="italics"/>di e&longs;t F A C E A B.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cur facilius.] <emph type="italics"/>Quæritur <lb/>cur nucifrangibulum ab&longs;que ictu <lb/>facillimè frangat nucem. Quod <lb/>problema, vt <expan abbr="anteced&etilde;s">antecedens</expan>, generale <lb/>e&longs;&longs;e pote&longs;t de quouis forcipe & forfice, ad capiendum &longs;cindendum <lb/>frangendum qualibus multis chirurgi, & quiuis manuales artifices <lb/>opera &longs;ua exercent & perficiunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Multa enim vis.] <emph type="italics"/>Repugnantia e&longs;tad augendam problematis <lb/>difficultatem &longs;ic,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quod vim adfert motioni, plus valet ad frangendum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ictus motioni vim adfert.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ictus igitur ad frangendum plus valet.<emph.end type="italics"/></s>
</p>
<pb pagenum="157"/>
<p type="main">
<s>Præterea duro.] <emph type="italics"/>Alterum e&longs;t qua&longs;i problema quod nuci­<lb/>frangibulum durum & graue facilius frangat: quam ligneum & <lb/>leue. Cum tamen contra euenire deberet. Siquidem graue quod e&longs;t, <lb/>difficilius emoueatur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia &longs;ic vtrinque.] <emph type="italics"/>Demon&longs;tratio e&longs;t problematis &longs;ic.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Valide comprimentia compre&longs;&longs;um frangunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Nucifrangibulum validè nucem comprehen&longs;am comprimit. <lb/>quia duplicatus e&longs;t vectis, vnum hypomochlium, vt in A <lb/>commi&longs;&longs;ura habentibus. Diductis enim B C extremis <lb/>vectium E A B & F A C à viribus in E & F. <lb/>alteris vectium extremis exi&longs;tentibus, &longs;i ip&longs;a compriman­<lb/>tur etiam B & C comprimentur. Quare & nux D in­<lb/>terpo&longs;ita, & valide compre&longs;&longs;a frangitur, tantò celerius: <lb/>quantò extrema B & C minus di&longs;tabunt ab hypomoch­<lb/>lio A. Sic enim aliæ partes vectium ab ip&longs;o di&longs;tantes <lb/>maiorem rationem habebunt. Et proinde facilius moue­<lb/>bunt pondus mouendum, vt ante &longs;æpius e&longs;t declaratum, <lb/>Quare quod percu&longs;sione, vel ictu pondus aliquod irruens <lb/>in nucem feci&longs;&longs;et, id vectes compreßi certius faciunt. Sæpè <lb/>enim ictum ob &longs;ui <expan abbr="rotũditatem">rotunditatem</expan> nux eludit. Nam cum nux <lb/>&longs;it rotunda, in&longs;i&longs;tat autem plano attingens ip&longs;am puncto, <lb/>& à plano mallei in puncto attingatur, facile elabitur, ni&longs;i <lb/>ictus<emph.end type="italics"/> <foreign lang="greek">xa<gap/>) i)/cin</foreign> <emph type="italics"/>incidat in rectam, quæ coniungit hæc duo <lb/>puncta.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Itaque nucifrangibulum nucem facile &longs;ine ictu franget.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quantò igitur.] <emph type="italics"/>Repetitio e&longs;t eiu&longs;dem &longs;uperflua.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>24. Cur in Rhombo <expan abbr="alterũ">alterum</expan> <lb/><expan abbr="pũctorum">punctorum</expan> extremorum <lb/>non æqualem rectam <lb/>tran&longs;it.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur amborum extremo­<lb/>rum <expan abbr="pũctorum">punctorum</expan> duabus la­<lb/>tionibus in rhombo lato­<lb/>rum, alterum non tran&longs;it <lb/>æqualem rectam. &longs;ed alte­
<pb pagenum="158"/><gap/><lb/>
<arrow.to.target n="marg38"></arrow.to.target><lb/>rum plus. Idem e&longs;t &longs;ermo <lb/>quare motum &longs;uper latere <lb/>minorem tran&longs;it <expan abbr="rectã">rectam</expan>: <expan abbr="quã">quam</expan> <lb/>latus. Illud enim minorem <lb/>diametrum: hoc verò latus <lb/>mai', licet & hoc vna: illud <lb/>verò duabus feratur latio­<lb/>nibus. Feratur enim &longs;uper <foreign lang="greek">a <lb/>b</foreign> <expan abbr="punctũ">punctum</expan> <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">a</foreign> ver&longs;us <foreign lang="greek">b,</foreign><lb/>& <foreign lang="greek">b</foreign> ver&longs;us <foreign lang="greek">a</foreign> <expan abbr="ead&etilde;">eadem</expan> celerita­<lb/>te: feratur <expan abbr="etiã">etiam</expan> latus <foreign lang="greek">a b</foreign> &longs;u­<lb/>per <foreign lang="greek">a g</foreign> parallelum ip&longs;i <foreign lang="greek">g d</foreign><lb/><expan abbr="ead&etilde;">eadem</expan> celeritate <expan abbr="cũ">cum</expan> his pun­<lb/>ctis. Nece&longs;&longs;e igitur <expan abbr="pũctum">punctum</expan> <lb/><expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">a</foreign> per <expan abbr="diametrũ">diametrum</expan> <foreign lang="greek">a d</foreign><lb/>ferri: <foreign lang="greek">b</foreign> vero per <foreign lang="greek"><gap/> g,</foreign> & &longs;i­<lb/>mul vtranque pertran&longs;ii&longs;&longs;e. <lb/><expan abbr="Tũ">Tum</expan> & latus <foreign lang="greek">a b</foreign> ip&longs;um <foreign lang="greek">a g.</foreign><lb/>Latum <expan abbr="quid&etilde;">quidem</expan> &longs;it <expan abbr="pũctum">punctum</expan> <foreign lang="greek">a</foreign><lb/>per <expan abbr="lineã">lineam</expan> <foreign lang="greek">a e,</foreign> & <foreign lang="greek">a b</foreign> per <foreign lang="greek">a z,</foreign><lb/>& &longs;it deducta <foreign lang="greek">z h</foreign> parallela <lb/>ip&longs;i <foreign lang="greek">a b,</foreign> & per <expan abbr="punctũ">punctum</expan> <foreign lang="greek">e</foreign> <expan abbr="cõ-pleatur">con­<lb/>pleatur</expan>. Simile igitur fi<emph type="italics"/>t<emph.end type="italics"/> <expan abbr="cõ-pletum">con­<lb/>pletum</expan> toti parallelogram­<lb/>mo. Igitur æqualis e&longs;t <foreign lang="greek">a z</foreign><lb/>ip&longs;i <foreign lang="greek">a e: a b</foreign> vero latus <expan abbr="latũ">latum</expan> <lb/>erit per <foreign lang="greek">a z.</foreign> Erit itaque in <lb/>diametro iuxta <foreign lang="greek">q,</foreign> & &longs;emper <lb/>iuxta <expan abbr="diametrũ">diametrum</expan> ferri nece&longs;­<lb/>&longs;e e&longs;t. Et &longs;imul atque latus <lb/><foreign lang="greek">a g</foreign> <expan abbr="etiã">etiam</expan> punctum <foreign lang="greek">a</foreign> tran&longs;it <lb/><expan abbr="diametrũ">diametrum</expan> <foreign lang="greek">a d.</foreign> Similiter ve­<lb/>rò demon&longs;trabitur etiam <foreign lang="greek">b</foreign><lb/><expan abbr="latũ">latum</expan> e&longs;&longs;e per <expan abbr="diametrũ">diametrum</expan> <foreign lang="greek">b g.</foreign><lb/>Æqualis enim e&longs;t linea <foreign lang="greek">b e</foreign><lb/>ip&longs;i <foreign lang="greek">b h.</foreign> Completum igitur
<pb pagenum="159"/><gap/><lb/>per punctum <foreign lang="greek">h</foreign> intus <expan abbr="paral-lelogrammũ">paral­<lb/>lelogrammum</expan> &longs;imile e&longs;t toti, <lb/>& <foreign lang="greek">b</foreign> erit in diametro iuxta <lb/><expan abbr="contactũ">contactum</expan> laterum. Et &longs;imul <lb/>atque latus pertran&longs;it latus <lb/>etiam ip&longs;um <foreign lang="greek">b,</foreign> ip&longs;um <foreign lang="greek">b g</foreign><lb/>diametrum. Simile igitur <lb/>ip&longs;um <foreign lang="greek">a</foreign> ip&longs;am <foreign lang="greek">a d</foreign> multò <lb/><expan abbr="maior&etilde;">maiorem</expan> ip&longs;a <foreign lang="greek">b g</foreign> pertran&longs;it, <lb/>& latus <expan abbr="motũ">motum</expan> eadem celeri­<lb/>tate <expan abbr="minor&etilde;">minorem</expan> <expan abbr="lineã">lineam</expan> [tran&longs;it.] <lb/>Et latus <foreign lang="greek">b d</foreign> vna lationc <lb/>motum pertran&longs;ijt lineam <lb/>maiorem: quam <foreign lang="greek">b g.</foreign> <expan abbr="quãtò">quantò</expan> <lb/>enim acutior e&longs;t Rhombus, <lb/>diameter <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">b g</foreign> fit mi­<lb/>nor, <foreign lang="greek">a d</foreign> vero maior, <expan abbr="tũ">tum</expan> & la­<lb/>tus <foreign lang="greek">a b</foreign> maius quam <foreign lang="greek">b g.</foreign></s>
</p>
<p type="margin">
<s><margin.target id="marg38"></margin.target>Quidam le­<lb/>gunt <foreign lang="greek">lo/gw</foreign><lb/>pro <foreign lang="greek">ta/xei.</foreign></s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvramborum.] <emph type="italics"/>In hoc capite duo continentur problemata, <lb/><expan abbr="eorũque">eorunque</expan> &longs;olutiones. Prius e&longs;t cur è duobus <expan abbr="pũctis">punctis</expan> in vno Rhom­<lb/>bi latere extremis eadem motis celeritate duobus &longs;imul motibus, vno <lb/>per &longs;e; altero ad motum lateris &longs;ui vnum plus &longs;patÿ conficit, nempe id <lb/>quod ab acuto angulo di&longs;cedit, alterum minus, nempe. id quod ab <lb/>obtu&longs;o.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Idem e&longs;t &longs;ermo.] <emph type="italics"/>Po&longs;terius e&longs;t cur vnum ê dictis punctis mo­<lb/>tum prædictis duobus motibus minus aliquando &longs;patÿ conficiat: <expan abbr="quã">quam</expan> <lb/>latus &longs;uum. Vtrumque problema vt intelligatur &longs;ciendum e&longs;t e def. <lb/>32. lib. 1. Eucl. Rhombum e&longs;&longs;e quadrilaterum æquilaterum, & mini­<lb/>mè rectangulum: Et tamen omnes eius angulos æquales e&longs;&longs;e quatuor <lb/>rectis per coroll. prop. 32. li. 1. Eucl. <expan abbr="Cumq;">Cumque</expan> oppo&longs;iti in <expan abbr="parallelogrãmo">parallelogrammo</expan> <lb/>&longs;int æquales prop. 34. lib. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> duo &longs;unt acuti, reliqui obtu&longs;i, vt &longs;it <lb/><expan abbr="Rhõbus">Rhombus</expan><emph.end type="italics"/> <foreign lang="greek">a b d g,</foreign> <emph type="italics"/>cuius anguli oppo&longs;iti<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>&longs;int acuti:<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>vero<emph.end type="italics"/>
<pb pagenum="160"/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>obtu&longs;i. Coneipiamus ergo<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tan-<emph.end type="italics"/><lb/>
<figure id="fig59"></figure><lb/><emph type="italics"/>quam formicam ambulantem proprio <lb/>motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b,</foreign> <emph type="italics"/>vt &<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>proprio iti­<lb/>dem motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">a.</foreign> <emph type="italics"/>Tum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">a b</foreign><lb/><emph type="italics"/>latus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">g d,</foreign> <emph type="italics"/>eadem etiam celerita­<lb/>te moueri &longs;eruando paralleli&longs;mum, cum <lb/>ip&longs;o<emph.end type="italics"/> <foreign lang="greek">g d</foreign> <emph type="italics"/>quou&longs;que coniungatur ei. Ad <lb/>huius autem <expan abbr="motũ">motum</expan> moueri etiam<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ver­<lb/>&longs;us<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us<emph.end type="italics"/> <foreign lang="greek">d.</foreign> <emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>mouebuntur duobus motibus, vno per &longs;e: <lb/>altero per accidens. Et po&longs;ito quod mo­<lb/>ueantur in Rhombo. Id e&longs;t quod motus <lb/>illi &longs;int in ratione laterum quibus Rhombus continetur. E&longs;t autem <lb/>i&longs;ta certa, quia e&longs;t ratio æqualitatis vt<emph.end type="italics"/> <foreign lang="greek">i</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">i,</foreign> <emph type="italics"/>& in eadem celerita­<lb/>te, id e&longs;t eodem tempore, non immeritò primum problema in medium <lb/>adducitur. quia &longs;i verum &longs;it, cau&longs;am habet minimè vulgarem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Feratur enim.] <emph type="italics"/>Prioris problematis <expan abbr="veritat&etilde;">veritatem</expan> geometricè o&longs;ten­<lb/>dit. Sit enim vt<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>proce&longs;&longs;erit per &longs;e v&longs;que ad<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>v&longs;que ad<emph.end type="italics"/><lb/><foreign lang="greek">z</foreign>: <emph type="italics"/>tunc quia motus illi &longs;unt in ratione laterum Rhombi id e&longs;t in ra­<lb/>tione æqualitatis<emph.end type="italics"/> <foreign lang="greek">a e</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a z</foreign> <emph type="italics"/>erunt æquales. Perficiatur <expan abbr="parallelo-grammũ">parallelo­<lb/>grammum</expan> prop. 31. lib. 1. <expan abbr="n&etilde;pè">nempè</expan><emph.end type="italics"/> <foreign lang="greek">a e q z.</foreign> <emph type="italics"/>Hoc erit &longs;imile toti<emph.end type="italics"/> <foreign lang="greek">a b d g.</foreign><lb/><emph type="italics"/>prop. 24. lib. 6. Ergo per conu <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> prop. &longs;unt circa <expan abbr="eand&etilde;">eandem</expan> <expan abbr="diametrũ">diametrum</expan><emph.end type="italics"/><lb/><foreign lang="greek">a q d,</foreign> <emph type="italics"/>& &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duobus motibus motum prædictis delineauit<emph.end type="italics"/> <foreign lang="greek">a q</foreign><lb/><emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="greek">z h.</foreign> <emph type="italics"/>proinde &<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>etiam delineauerit<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>cum peruenerit<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">g d.</foreign> <emph type="italics"/>Simili ratiocinatione conficitur<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>eo­<lb/>dem tempore peragra&longs;&longs;e diametrum<emph.end type="italics"/> <foreign lang="greek">b g.</foreign> <emph type="italics"/>E&longs;t autem<emph.end type="italics"/> <foreign lang="greek">b g</foreign> <emph type="italics"/>minor: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>quia ba&longs;es &longs;unt duorum triangulorum<emph.end type="italics"/> <foreign lang="greek">g a b,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a b d</foreign><lb/><emph type="italics"/>bina latera<emph.end type="italics"/> <foreign lang="greek">a g, a b</foreign> <emph type="italics"/>binis<emph.end type="italics"/> <foreign lang="greek">a b, b d</foreign> <emph type="italics"/>æqualia habentium. quia &longs;unt <lb/>latera eiu&longs;dem Rhombi, & angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>vtpote acutum minorem <lb/>angulo<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>vtpote obtu&longs;o. Ergo prop. 24. lib. 1. ba&longs;is<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>maior e&longs;t <lb/>ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b g.</foreign> <emph type="italics"/>Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ab angulo acuto di&longs;cedens &longs;uis motibus maiorem <lb/>in Rhombo lineam tran&longs;it, quam<emph.end type="italics"/> <foreign lang="greek"><gap/>.</foreign></s>
</p>
<p type="main">
<s>Licet & hoc.] <emph type="italics"/>Hoc additur ad augendam &longs;ecundi problematis <lb/>difficultatem. Rationi enim con&longs;entaneum videtur, vt motum duo­<lb/>bus motibus &longs;imul plus &longs;patÿ conficiat: quam quod vno tantum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Nece&longs;&longs;e igitur.] <emph type="italics"/>Nam parallelogramma quæ toti & inter &longs;e<emph.end type="italics"/>
<pb pagenum="161"/><emph type="italics"/>&longs;unt &longs;imilia, &longs;unt circa eandem diametrum. conu prop. 24. lib. 6.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Æqualis enim e&longs;t.] <emph type="italics"/>Quia in ratione æqualitatis motum e&longs;t<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h.</foreign></s>
</p>
<p type="main">
<s>Multò maiorem.] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>&longs;ubtendit multò maiorcm an­<lb/>gulum, vtpote<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>obtu&longs;um, & ideò maiorem recto: quam<emph.end type="italics"/> <foreign lang="greek">b g,</foreign> <emph type="italics"/>quæ <lb/>&longs;ubtendit<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>angulum acutum, & ideò etiam minorem recto.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Etlatus <foreign lang="greek">b d.</foreign>] <emph type="italics"/>Attingit &longs;ecundum problema quod generaliter <lb/>verum non e&longs;t. In Rhombo enim cuius, qui acutus e&longs;t angulus, maior <lb/>e&longs;t dimidio obtu&longs;i, vt in E<emph.end type="italics"/><lb/>
<figure id="fig60"></figure><lb/><emph type="italics"/>F G H: quia F H an­<lb/>gulum E maiorem &longs;ubten­<lb/>dit: quam E H, erit F H <lb/>maior E H prop. 18. lib. 1. <lb/>Sed verum e&longs;t in certo ca­<lb/>&longs;u, eo nimirum (licet hîc <lb/>non &longs;it expre&longs;&longs;us) in quo <lb/>Rhombi acutus e&longs;&longs;et mi­<lb/>nor: quam dimidius obtu­<lb/>&longs;i, vt angulus A Rhombi <lb/>A B C D &longs;it minor: quam dimidius obtu&longs;i B, id e&longs;t quam A B C. <lb/>Dico latus A C maius e&longs;&longs;e diametro B C per eandem prop. 18. <lb/>&longs;ubtendit enim trianguli A B C maiorem angulum. Po&longs;&longs;e autem <lb/>talem Rhombum con&longs;titui, patet. quia angulus acutus &longs;eruata late­<lb/>rum quorumuis a&longs;&longs;umptorum longitudine, infinitè minor fieri pote&longs;t, <lb/>prop. 9. lib. 1. Ergo & tandem dabitur minor dimidio obtu&longs;i. Nam <lb/>& dimidius recti, qui acutus e&longs;t, e&longs;t eo minor prop. 15. lib. 5. Ergo in <lb/>tali Rhombo latus A B per A C vna latione motum, plus &longs;patÿ <lb/>confecit: quam B, quod peragrans B C duabus lationibus ferebatur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Ab&longs;urdum enim, vt <expan abbr="dictũ">dictum</expan> <lb/>e&longs;t, quod duab^{9} lationibus <lb/>fertur, tardius <expan abbr="nonnunquã">nonnunquam</expan> <lb/>ferri eo, quod vna: & <expan abbr="dato-rũ">dato­<lb/>rum</expan> <expan abbr="amborũ">amborum</expan> <expan abbr="punctorũ">punctorum</expan> æqua­<lb/>li celeritate <expan abbr="motorũ">motorum</expan> <expan abbr="alterũ">alterum</expan> <lb/><expan abbr="maior&etilde;">maiorem</expan> <expan abbr="trã&longs;ire">tran&longs;ire</expan>. Cau&longs;a verò
<pb pagenum="162"/><gap/><lb/>e&longs;t, quod ambæ lationes <lb/>eius, quod ab obtu&longs;o angu <lb/>lo fertur fiunt ferè contra­<lb/>riæ. H&ecedil;c &longs;cilicet qua per &longs;e <lb/>fertur, & hæc qua per latus <lb/>effertur. Ei verò quod ab <lb/>acuto, contingit ad idem <lb/>ferri, ob&longs;ecundat enim la­<lb/>teris latio ei, quæ e&longs;t <expan abbr="&longs;ecũ-dum">&longs;ecun­<lb/>dum</expan> diametrum. Et quan­<lb/>tò hic angulus fuerit acu­<lb/>tior, ille obtu&longs;ior vna latio <lb/>erit tardior: altera velo­<lb/>cior. Lationes enim magis <lb/><expan abbr="cõtrariæ">contrariæ</expan> fiunt propter ob­<lb/>tu&longs;iorem angulum: contra <lb/>verò hæ magis ad <expan abbr="id&etilde;">idem</expan> pro­<lb/>pter <expan abbr="propinquitat&etilde;">propinquitatem</expan> linea­<lb/>rum. I p&longs;um enim <foreign lang="greek">a</foreign> ferc ad <lb/>idem fertur ex vtri&longs;que la­<lb/>tionibus. <expan abbr="Itaq;">Itaque</expan> altera coad­<lb/>iuuatur. Et <expan abbr="quãtò">quantò</expan> acutior <lb/>fuerit angulus: tantò ma­<lb/>gis: ip&longs;um verò <foreign lang="greek"><gap/></foreign> ad con­<lb/>trarium. Ip&longs;um enim ad <foreign lang="greek">a</foreign><lb/>fertur. Latus verò effertur <lb/>ver&longs;us ip&longs;um <foreign lang="greek">g.</foreign> Et quantò <lb/>fuerit angulus obtu&longs;ior <lb/>magis contrariæ lationes <lb/>fiunt. Rectior enim linea <lb/>fit, quod &longs;i omninò recta <lb/>e&longs;&longs;et, e&longs;&longs;ent lationes omni­<lb/>nò contrariæ. Latus vero <lb/>vno motu motum à nullo <lb/>impeditur. Æquum e&longs;t igitur, vt lineam maiorem tran­<lb/>&longs;eat.</s>
</p>
<pb pagenum="163"/>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Ab&longs;urdum enim.] <emph type="italics"/>Repetitio e&longs;t eius, quod problematis &longs;ecun­<lb/>di antea iam auxit difficultatem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Nonnunquam ferri.] <emph type="italics"/>Particula<emph.end type="italics"/> <foreign lang="greek">en)i/ote</foreign> <emph type="italics"/>nonnunquam indi­<lb/>cat &longs;ecundum problema tantum verum e&longs;&longs;e &longs;pecialiter non in genere, <lb/>quod antea e&longs;t demon&longs;tratum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et datorum amborum.] <emph type="italics"/>Auget difficultatem problematis <lb/>primi. Videbatur enim rationi con&longs;entaneum, vt duo totidem moti­<lb/>bus mota, & eadem celeritate id e&longs;t æquali tempore idem &longs;patium <lb/>conficerent.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cau&longs;a vero e&longs;t.] <emph type="italics"/>Po&longs;tquam problema primum verum e&longs;&longs;e geo­<lb/>metrice demon&longs;tratum e&longs;t: nunc huius vtpote admirabilis cau&longs;am <lb/>adfert Phy&longs;icam. quod &longs;cilicet mota duobus motibus, &longs;i ad eundens <lb/>terminum, ad quem tendent, celerius mouentur: &longs;i ad contrarios, tar­<lb/>dius. Illa enim &longs;ibi inuicem ob&longs;equuntur, & vt clauus clauo pellitur: <lb/>ita motus motum adiuuat: hæc verò &longs;ibi ob&longs;i&longs;tunt, &longs;e&longs;e impediunt, & <lb/>remorantur, & vt magis minu&longs;ve contrarij &longs;unt termini ad quos: <lb/>ita quæ &longs;ic mouentur, magis minu&longs;ve &longs;e accelerant, aut retardant. <lb/>Atqui<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> <emph type="italics"/>ab angulo obtu&longs;o motum duorum motuum vno ad<emph.end type="italics"/> <foreign lang="greek">a,</foreign> <emph type="italics"/>alte­<lb/>ro ad<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>tendens ad magis contrarios terminos tendit: quam<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ten­<lb/>dens dictis motibus ad<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">g.</foreign> <emph type="italics"/>E&longs;t enim, vt antea demon&longs;tratum <lb/>e&longs;t,<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>diameter & recta maior: quam<emph.end type="italics"/> <foreign lang="greek">g d.</foreign> <emph type="italics"/>Et quò<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>acutior <lb/>erit angulus, eò<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>maior erit ergo æquum e&longs;t, vt<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> <emph type="italics"/>tardius fera­<lb/>tur: quam<emph.end type="italics"/> <foreign lang="greek">a.</foreign> <emph type="italics"/>Et quidem tantò tardius: quantò<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> <emph type="italics"/>erit obtu&longs;ior angu­<lb/>lus, &<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>acutior ob cau&longs;am prædictam.<emph.end type="italics"/></s>
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<p type="main">
<s>Fere ad idem.] <emph type="italics"/>Particula<emph.end type="italics"/> <foreign lang="greek">sxedo\n</foreign> <emph type="italics"/>ferè ad-<emph.end type="italics"/><lb/>
<figure id="fig61"></figure><lb/><emph type="italics"/>iecta indicat non eundem e&longs;&longs;e terminum vtriu&longs;­<lb/>que motionis, qua fertur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>: &longs;ed duos diuer&longs;os, ve­<lb/>rum propiores, quam &longs;int termini ad quos<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign><lb/><emph type="italics"/>fertur.<emph.end type="italics"/></s>
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<p type="main">
<s>Rectior enim linea.] <emph type="italics"/>Id e&longs;t duo latera<emph.end type="italics"/> <foreign lang="greek"><gap/> a</foreign><lb/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek"><gap/> d</foreign> <emph type="italics"/>magis accedunt ad rectam vnam, vtpo­<lb/>te quia angulus obtu&longs;us &longs;i augeatur plu&longs;culum, <lb/>latera ip&longs;um continentia fient è directo: & tunc<emph.end type="italics"/>
<pb pagenum="164"/><emph type="italics"/>erunt vna omnino recta, quod vbi e&longs;&longs;et, vt cum<emph.end type="italics"/> <foreign lang="greek">b a</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="greek">b <lb/>l,</foreign> <emph type="italics"/>tunc lationes<emph.end type="italics"/> <foreign lang="greek"><gap/></foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">l,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>e&longs;&longs;ent ad contrarios omnino <lb/>terminos.<emph.end type="italics"/></s>
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<p type="main">
<s>Latus verò vno.] <emph type="italics"/>Breuiter cau&longs;am attingit &longs;ecundi problema­<lb/>tis, quod in motu à nullo impeditum æquum e&longs;t celerius moueri: quam <lb/>quod impeditur. Latus autem in dicto Rhombo à nullo impeditur: <lb/>contra<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>impeditur. Ergo<emph.end type="italics"/> <foreign lang="greek">l b</foreign> <emph type="italics"/>latus celerius feretur ip&longs;o<emph.end type="italics"/> <foreign lang="greek">b.</foreign></s>
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<p type="main">
<s>Æquum e&longs;t igitur.] <emph type="italics"/>Id nu&longs;quam in hoc problemate demon­<lb/>&longs;tratum e&longs;t, pote&longs;t etiam fal&longs;um e&longs;&longs;e. C æterum ex hoc problemate <lb/>collige, quod etiam Leonicus annotauit, quantum corporum confor­<lb/>mationes & figurarum in illis varietas peculiares illorum inclina­<lb/>tiones, naturale&longs;que motus aut adiuuent, aut contra in &longs;igniter impe­<lb/>diant. Conglobata etenim exempli gratia plumbi ma&longs;&longs;a, &longs;i naturæ <lb/>relinquatur &longs;uæ, rectà citius deor&longs;um fertur: quam &longs;i eadem pondere <lb/>&longs;eruato exten&longs;a fuerit in laminam: immò rur&longs;us inflexa & in&longs;tar <lb/>carinæ conformata fluitabit in aquis. In rebus etiam artificialibus <lb/>gladius acuta &longs;ui acie facile &longs;ecat: obtu&longs;a non item. Hæc cum ita <lb/>&longs;int nemini ab&longs;urdum videri debet, duo puncta duabus motionibus <lb/>æquali celeritate mota non æquale pertran&longs;ire &longs;patium: &longs;ed mu&longs;tò <lb/>plus maiu&longs;que illorum alterum, vt ex Rhombi natura certò demon­<lb/>&longs;tratum e&longs;t.<emph.end type="italics"/></s>
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<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>25. Cur maior circulus cum <lb/>minore per æqualem re­<lb/>uoluitur.</s>
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<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s><expan abbr="Dubiũ">Dubium</expan> e&longs;t cur maior cir­<lb/>culus <expan abbr="æqual&etilde;">æqualem</expan> minori circu­<lb/>lo orbitam volutione pera­<lb/>gret, <expan abbr="quãdo">quando</expan> circa <expan abbr="id&etilde;">idem</expan> <expan abbr="c&etilde;trũ">centrum</expan> <lb/>po&longs;itus e&longs;t: At <expan abbr="cũ">cum</expan> &longs;eor&longs;um <lb/>voluuntur, vt <expan abbr="horũ">horum</expan> magni­<lb/>tudines &longs;e <expan abbr="hab&etilde;t">habent</expan> inter &longs;e, ita <lb/><expan abbr="etiã">etiam</expan> <expan abbr="eorũ">eorum</expan> orbitæ. Præterea <lb/>vno & eodem <expan abbr="exi&longs;t&etilde;te">exi&longs;tente</expan> cen­<lb/>tro, <expan abbr="aliquãdo">aliquando</expan> quidem tan-
<pb pagenum="165"/><gap/><lb/>ta fit orbita: quanta e&longs;t ea: <lb/>quam minor circulus pera­<lb/>grat: aliquando verò quam <lb/>maior. Quod igitur maio­<lb/>rem peragret maior mani­<lb/>fe&longs;tum e&longs;t. Angulus enim <lb/>videtur <expan abbr="euid&etilde;ter">euidenter</expan> e&longs;&longs;e peri­<lb/>pheria cuiu&longs;que <expan abbr="cũ">cum</expan> propria <lb/>diametro maioris circuli <lb/>maior [minoris minor.] Ita­<lb/>que orbit&ecedil; <expan abbr="eand&etilde;">eandem</expan> rationem <lb/>euidenter habebunt inter <lb/>&longs;e. Attamen quod circa <expan abbr="id&etilde;">idem</expan> <lb/><expan abbr="centrũ">centrum</expan> po&longs;iti æqualem <expan abbr="or-bitã">or­<lb/>bitam</expan> <expan abbr="cõficiant">conficiant</expan> etiam <expan abbr="mani-fe&longs;tũ">mani­<lb/>fe&longs;tum</expan>. At que ita vt aliquan­<lb/>do orbita maioris circuli <lb/>&longs;it æqualis linea, aliquando <lb/>orbita minoris. Sit enim <lb/>circulus maior <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">d z g,</foreign><lb/>minor vero <foreign lang="greek">e h b,</foreign> & <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/><expan abbr="centrũ">centrum</expan> <foreign lang="greek">a.</foreign> Atque ca quidem <lb/>per quam magnus circulus <lb/>per &longs;e voluitur <foreign lang="greek">z l,</foreign> &longs;it & ea <lb/>per quam per &longs;e minor <foreign lang="greek">h k</foreign><lb/>æqualis <foreign lang="greek">z l.</foreign> Si vero moueo <lb/><expan abbr="minor&etilde;">minorem</expan>, ip&longs;um <expan abbr="c&etilde;trum">centrum</expan> mo­<lb/>ueo vbi e&longs;t <foreign lang="greek">a.</foreign> Magnus au­<lb/>tem connexus e&longs;to. Quum <lb/>igitur <foreign lang="greek">a b</foreign> ad rectos fiet li­<lb/>neæ <foreign lang="greek">h k,</foreign> &longs;imul etiam <foreign lang="greek">a g</foreign><lb/>ad rectos fiet lineæ <foreign lang="greek">z l.</foreign></s>
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<p type="main">
<s>Quare per æqualem erit <lb/>tran&longs;latio, nempè <foreign lang="greek">h k</foreign> in <lb/>qua e&longs;t <foreign lang="greek">z g.</foreign> Quod &longs;i quarta <lb/>pars per e/qualem voluitur,
<pb pagenum="166"/><gap/><lb/>quod totus circulus æqua­<lb/>lem toti circulo reuolua­<lb/>tur, manife&longs;tum e&longs;t. Itaque <lb/>quando linea <foreign lang="greek">b h</foreign> peruene­<lb/>rit ad <foreign lang="greek">k</foreign> etiam <foreign lang="greek">z g</foreign> peri­<lb/>pheria erit in <foreign lang="greek">z l</foreign> & circu­<lb/>lus totus conuolutus. Si­<lb/>militer &longs;i maiorem moue­<lb/>ro, cui &longs;it annexus minor <lb/><expan abbr="eod&etilde;">eodem</expan> centro exi&longs;tente, vna <lb/>cum <foreign lang="greek">a g</foreign> etiam <foreign lang="greek">a b</foreign> perpen­<lb/>dicularis erit. Illa quidem <lb/>ad <foreign lang="greek">z i</foreign> hæc verò ad <foreign lang="greek">h <expan abbr="q.">que</expan></foreign> Ita­<lb/>que quando per æqualem <lb/>ip&longs;i <foreign lang="greek">h q</foreign> vol <foreign lang="greek">z i</foreign> rur&longs;um erit <lb/>tran&longs;latio etiam <foreign lang="greek">a g</foreign> per­<lb/>pendicularis erit ad <foreign lang="greek">z i,</foreign> & <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">h q,</foreign> vt ab initio <lb/>erunt in <foreign lang="greek">q, i</foreign>: atque id nul­<lb/>la intercedente mora ma­<lb/>ioris ad minorem, qua&longs;i ad <lb/>aliquod tempus in eodem <lb/>ip&longs;o puncto moueret. vter­<lb/>que enim vtroque modo <lb/>continuè mouetur. Neque <lb/>minore vllum punctum <lb/>tran&longs;iliente, & maiorem <lb/>minori æqualem tran&longs;ire, & minorem maiori ab&longs;urdum.</s>
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<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Dvbium e&longs;t.] <emph type="italics"/>Problema quod hoc capite proponitur, omnium <lb/>quæ ante propo &longs;ita &longs;unt, & po&longs;tea proponentur fortaßè e&longs;t &longs;ub­<lb/>tilißimum. E&longs;t autem eiu&longs;modi, cur circuli concentrici, & inæquales <lb/>iuncti, æqualem tamen orbitam circumuolutione peragrent. Et <expan abbr="qui-d&etilde;">qui­<lb/>dem</expan> hoc euenire duobus modis ponitur. Vno, vt orbita minoris adæque-<emph.end type="italics"/>
<pb pagenum="167"/><emph type="italics"/>tur orbitæ, quam &longs;eor&longs;um maior conficeret: altero, vt orbita maioris <lb/>adæquetur orbitæ, quam &longs;eor&longs;um minor conficeret.<emph.end type="italics"/></s>
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<p type="main">
<s>At cum &longs;eor&longs;im.] <emph type="italics"/>Problematis propo&longs;iti difficultas declara­<lb/>tur ex orbita, quam &longs;inguli &longs;eor&longs;im voluti faciunt. Hæc enim &longs;em­<lb/>per è maiore maior e&longs;t, è minore minor, & quidem proportione re­<lb/>&longs;pondens magnitudini peripheriarum.<emph.end type="italics"/></s>
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<p type="main">
<s>Præterea vno.] <emph type="italics"/>Duo modi æquationis prædicti explicantur in <lb/>habentibus idem centrum.<emph.end type="italics"/></s>
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<p type="main">
<s>Quod igitur maiorem.] <emph type="italics"/>Confirmatio e&longs;t difficultatis allat æ <lb/>ex euidentia per &longs;en&longs;um. Si quis enim notato puncto vt A circumuo­<lb/>lutionis primo, & quidem circulum maiorem & minorem &longs;uper re­<lb/>ctam plani circumuoluat, quou&longs;que redierit contactus in eodem pun­<lb/>cto maioris circuli maior recta: minoris minor erit per agrata. Sed <lb/>& anguli è &longs;emidiametris con&longs;tituti (quos angulos circuli vocat <lb/>hic Ari&longs;toteles) ba&longs;es quæ &longs;unt peripheriæ, euidenter inæquales &longs;unt. <lb/>In maiore circulo maior: in minore minor (Sed & hanc euidentiam, <lb/>ne qua e&longs;&longs;et dubitatio, demon&longs;tratione primo eapite huius libri de­<lb/>mon&longs;trauimus.) Erunt igitur & orbitæ inæquales & proportione <lb/>re&longs;pondentes ba&longs;ibus angulorum è &longs;emidiametris con&longs;titutorum.<emph.end type="italics"/></s>
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<p type="main">
<s>Attamen quod circa.] <emph type="italics"/>Problematis propo &longs;iti veritas demon­<lb/>&longs;tratur figura geometrica in vtroque modo. Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="greek">a h z</foreign><lb/><emph type="italics"/>perpendiculariter in&longs;i&longs;tat pla-<emph.end type="italics"/><lb/>
<figure id="fig62"></figure><lb/><emph type="italics"/>no, & ad rectam<emph.end type="italics"/> <foreign lang="greek">z i.</foreign> <emph type="italics"/>Tum<emph.end type="italics"/> <foreign lang="greek">h q</foreign><lb/><emph type="italics"/>rectos angulos faciat, &longs;icque il­<lb/>las tangat in punctis<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">z,</foreign><lb/><emph type="italics"/>cum quarta pars peripheriæ<emph.end type="italics"/> <foreign lang="greek">h b</foreign><lb/><emph type="italics"/>orit reuoluta: ita vt<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>rur­<lb/>&longs;us ad rectos &longs;it ad rectam<emph.end type="italics"/> <foreign lang="greek">h q,</foreign><lb/><emph type="italics"/>ip&longs;amque tangat, vt in puncto<emph.end type="italics"/><lb/><foreign lang="greek">k</foreign>: <emph type="italics"/>tunc &<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>etiam ad re­<lb/>ctos erit &longs;uper<emph.end type="italics"/> <foreign lang="greek">z i,</foreign> <emph type="italics"/>& &longs;it vt <lb/>tangat in puncto<emph.end type="italics"/> <foreign lang="greek">l.</foreign> <emph type="italics"/>Erunt pro <lb/>29. prop. lib. 1. Duæ<emph.end type="italics"/> <foreign lang="greek">z h</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">k l</foreign> <emph type="italics"/>parallelæ & æquales, ex hypoth. <lb/>Ergo quæ eas ad ea&longs;dem partes iungunt rectæ<emph.end type="italics"/> <foreign lang="greek">z l</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>erunt <lb/>æquales, prop 34. eiu&longs;dem. Sunt autem orbitæ ab vtri&longs;que confectæ <lb/>eadem celeritate motis. Eadem ratiocinatione cum<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/>
<pb pagenum="168"/><emph type="italics"/>puncto<emph.end type="italics"/> <foreign lang="greek">i</foreign> <emph type="italics"/>ex reuolutione maioris, &<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/> <foreign lang="greek">q</foreign>: <emph type="italics"/>&longs;icque<emph.end type="italics"/> <foreign lang="greek">q i</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">h <lb/>z</foreign> <emph type="italics"/>cum &longs;int æquales & parallelæ, duæ rur&longs;us<emph.end type="italics"/> <foreign lang="greek">h q</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">z i</foreign> <emph type="italics"/>erunt pa­<lb/>rallelæ. Quæ autem ratio e&longs;t quartarum circulorum inter &longs;e, eadem <lb/>e&longs;t totorum. Partes enim cum pariter multiplicibus eandem ratio­<lb/>nem habent prop. 15. lib. 5. Igitur in vtroque modo orbitæ coneen­<lb/>tricorum inæqualium &longs;unt æquales.<emph.end type="italics"/></s>
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<p type="main">
<s>Atque id nulla.] <emph type="italics"/>Cau&longs;am admirabilis huius aduentus, quæ <lb/>adferri potui&longs;&longs;et, In primò quidem modo ex tarditate & mora <lb/>maioris circuli in quibu&longs;dam rectæ lineæ punctis, dum minor <lb/>circulus ip&longs;am peragrat: In &longs;ecundo verò modo ex tran&longs;ultu minoris <lb/>qua&longs;i exiliat, nec &longs;imul omnia puncta rectæ attingat: &longs;ed tran&longs;iliat <lb/>minor, dum maior contra omnia attingat peragrando, reÿcit, mo­<lb/>ramque nullam in hoc intercedere, neque tran&longs;ultum in i&longs;to: &longs;ed <lb/>vtriu&longs;que continuas motiones e&longs;&longs;e dicit, quia vnica latio e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Præterea vnica latione <lb/><expan abbr="exi&longs;t&etilde;te">exi&longs;tente</expan> <expan abbr="centrũ">centrum</expan> &longs;emper <expan abbr="cõ-tinuè">con­<lb/>tinuè</expan> motum, aliquando <lb/><expan abbr="quid&etilde;">quidem</expan> per <expan abbr="maior&etilde;">maiorem</expan>, aliquan­<lb/>do verò per minorem con­<lb/>uolui e&longs;t admirabile. I dem <lb/>enim eadem celeritate <expan abbr="latũ">latum</expan> <lb/>æqualem <expan abbr="trã&longs;ire">tran&longs;ire</expan> natum e&longs;t. <lb/>Eadem <expan abbr="aut&etilde;">autem</expan> celeritate per <lb/><expan abbr="æqual&etilde;">æqualem</expan> vtro que modo mo­<lb/>uere licet. Cæterum princi­<lb/>pium &longs;umatur ex vtriu&longs;que <lb/>cau&longs;a, quod eadem vis, & <lb/>æqualis vnam quidem <expan abbr="ma-gnitudinũ">ma­<lb/>gnitudinum</expan> tardius: alteram <lb/>celerius moueat. Si quid <lb/>enim fuerit non à &longs;eip&longs;o <lb/>moueri <expan abbr="natũ">natum</expan>, & <expan abbr="ipsũ">ipsum</expan> aliud <lb/>quod moueri <expan abbr="natũ">natum</expan> &longs;it mo­<lb/>uerit, tardius mouebitur: <lb/><expan abbr="quã">quam</expan> &longs;i <expan abbr="ipsũ">ipsum</expan> p &longs;e moueretur.
<pb pagenum="169"/><gap/><lb/>Et &longs;i quidem <expan abbr="natũ">natum</expan> &longs;it mo­<lb/>ueri, neque <expan abbr="aut&etilde;">autem</expan> &longs;imul mo­<lb/>ueatur, &longs;imiliter &longs;e habebit. <lb/>Et vt plus moueatur: quam <lb/>quod mouet, fieri non po­<lb/>te&longs;t. Non enim &longs;uo ip&longs;ius <lb/>mouetur motu: &longs;ed <expan abbr="mou&etilde;-">mouen­<lb/></expan>
<arrow.to.target n="marg39"></arrow.to.target><lb/>tis. [Sit igitur circul^{9} maior <lb/><expan abbr="quid&etilde;">quidem</expan> vbi <foreign lang="greek">g,</foreign> at minor vbi <lb/><gap/>.] Si impeliat minor <expan abbr="maio-r&etilde;">maio­<lb/>rem</expan> ip&longs;o &longs;e minime <expan abbr="volu&etilde;te">voluente</expan>, <lb/>manife&longs;tum quod tantam <lb/><expan abbr="rectã">rectam</expan> maior tran&longs;it, ad <expan abbr="quã-tam">quan­<lb/>tam</expan> à minore impul&longs;us e&longs;t: <lb/>ad tantam verò impul&longs;us <lb/>e&longs;t, ad quantam minor &longs;e <lb/>mouit. <expan abbr="Rectã">Rectam</expan> igitur æqua­<lb/>lem pertran&longs;ierunt. Nece&longs;­<lb/>&longs;e igitur &longs;i minor conuolu­<lb/>tus impulerit, <expan abbr="maior&etilde;">maiorem</expan> con­<lb/>uolui quidem cum impul­<lb/>&longs;ione tantum: <expan abbr="quãtum">quantum</expan> mi­<lb/>nor conuolutus fuerit. &longs;i <lb/>neuti <expan abbr="quã">quam</expan> ip&longs;e proprio mo­<lb/>tu moueatur. quomodo <lb/>enim & quantum mouit, <lb/><expan abbr="tãtundem">tantundem</expan> <expan abbr="motũ">motum</expan> e&longs;&longs;e, quod <lb/>ab illo mouebatur, nece&longs;­<lb/>&longs;um e&longs;t. Sed circulus &longs;olum <lb/>&longs;e mouerit circulariter pe­<lb/>dem vnum. Sit enim tan­<lb/>tum quod <expan abbr="motũ">motum</expan> e&longs;t. Etiam <lb/>magnus tantundem motus <lb/>erit. Similiter &longs;i magnus <lb/><expan abbr="paruũ">paruum</expan> mouerit: <expan abbr="tantũ">tantum</expan> paruus, <expan abbr="quantũ">quantum</expan> magnus motus erit. <lb/>per &longs;e <expan abbr="quid&etilde;">quidem</expan> motus vtrouis modo &longs;eu celeriter: &longs;eu tacdè.
<pb pagenum="170"/><gap/><lb/>Eadem verò celeritate &longs;ta­<lb/>tim per quantam lineam <lb/>natus e&longs;t conuolui maior.</s>
</p>
<p type="margin">
<s><margin.target id="marg39"></margin.target>Hæc inter­<lb/>po&longs;ita <expan abbr="vid&etilde;-tur">viden­<lb/>tur</expan>.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Præterea vnica.] <emph type="italics"/>Cum &longs;it o&longs;ten&longs;a problematis veritas rur&longs;us <lb/>o&longs;tendit aliquid admir abile contineri. Ratio admirationis &longs;ic erit <lb/>apertior.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Idem eadem celeritate latum æqualem <expan abbr="lineã">lineam</expan> tran&longs;ire natum e&longs;t. <lb/>Centrum circulorum concentricorum vnum idemque e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo æqualem tran&longs;ire natum e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Attamen aliter fit. Nam eadem celeritate latum modò <expan abbr="maior&etilde;">maiorem</expan>, <lb/>modò minorem tran&longs;it. Ergo problema admirationis plenum e&longs;t. Syllogi&longs;­<lb/>mi huius propo &longs;itio e&longs;t euidens: a&longs;&longs;umptio po&longs;tea di&longs;tinguetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Cæterum principium.] <emph type="italics"/>Vt admiratio tollatur, duo a&longs;&longs;umun­<lb/>tur è Phy&longs;icis, quæ &longs;i diligenter expendantur, &longs;unt vtraque euiden­<lb/>ter vera. Primum e&longs;t. Si ab vna & eadem vi duo moueantur, quo­<lb/>rum alterum quidem à &longs;e moueri natum e&longs;t &longs;ecundum motum illum, <lb/>&longs;ecundum quem à vi <expan abbr="mou&etilde;tis">mouentis</expan> mouetur: alterum verò non e&longs;t natum <lb/>eo moueri motu, vel natum quidem &longs;it, &longs;ed tum motu non vtatur &longs;uo: <lb/>moueantur autem i&longs;ta coniunctim, illud quod ex &longs;e illo motu moueri <lb/>natum erat, tardius mouebitur: quam &longs;i per &longs;e moueretur. Exemplum <lb/>&longs;it plumbum cum vtre aëre pleno annexum, quod euidenter tardius <lb/>de&longs;cendit per aquam: quam &longs;i liberum fui&longs;&longs;et ab vtre, vt &longs;it in con­<lb/>iuncto eadem, atque in libero erat grauitas. Secundum e&longs;t. Motum <lb/>ab alio non plus moueri pote&longs;t: quam quod ip&longs;um mouet, vt quod non <lb/>&longs;uo: &longs;ed motu mouentis moueatur, tum mouens & motum &longs;unt &longs;i­<lb/>mul, vt demon&longs;tratum e&longs;t ab Ari&longs;totele in lib. de Phy&longs;. auditu. Cau&longs;a <lb/>itaque problematis in hoc continetur, quod è duobus circulis eadem <lb/>celeritate motis alter primo mouetur, & alter prior is moti raptum <lb/>&longs;equitur. Itaque &longs;i minoris raptum &longs;equatur maior, orbita maioris fiet <lb/>æqualis orbitæ minoris, cum maior in motu non vi vtatur &longs;ua, &longs;ed ad <lb/>motum minoris moueatur: &longs;i vero maioris raptum minor &longs;equatur, <lb/>orbita minoris fiet æqualis orbitæ maioris, cum minor eò feratur quò <lb/>etiam maior ip&longs;um rapit. Et &longs;ic celerius per maiu&longs;que &longs;parium, quam<emph.end type="italics"/>
<pb pagenum="171"/><emph type="italics"/>quòd ferretur per &longs;e. Tamen propter annexionem duo illi tardius vel <lb/>celerius mouentur: quam per &longs;e mouerentur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Nece&longs;&longs;e igitur &longs;i.] <emph type="italics"/>Quod maiore<emph.end type="italics"/> <foreign lang="greek">z d</foreign> <emph type="italics"/>moto minor<emph.end type="italics"/> <foreign lang="greek">h e</foreign> <emph type="italics"/>rapiatur <lb/>in eodem plano duobus concentricis exi&longs;tentibus captu facile e&longs;t. <lb/>Nam maioris peripheria impul&longs;a, vel per axem tracta, ob nutum di­<lb/>midiæ partis perpetuum, de quo ante, conuoluitur potius: quam vno <lb/>puncto eodemque &longs;emper tangente planum gli&longs;cat. Cau&longs;a enim motus <lb/>rotæ &longs;emper e&longs;t in circulo eius maximo: at quod minor vt<emph.end type="italics"/> <foreign lang="greek">h e</foreign> <emph type="italics"/>primo <lb/>moueatur, & ad eius motum maior, capi mente difficilius paulò, ta­<lb/>men & capi pote&longs;t, &longs;i imaginemur volutationibus inæqualium dua­<lb/>rum rotarum &longs;ic annexarum, vt &longs;upponitur, &longs;upponi duo plana inæ­<lb/>qualiter alta, & ita vt vnum vnam è rotis, alterum alteram &longs;u&longs;ti­<lb/>neat, & tunc imaginemur ad minoris motum rotæ maiorem moueri <lb/>& rapi.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Quod etiam dubitatio­<lb/>nem adfert, quia &longs;imiliter <lb/>præterea faciunt, quando <lb/>connexi &longs;unt. Hoc autem <lb/>e&longs;t, &longs;i alter ab altero mouea <lb/>tur, non ea qua natus e&longs;t, <lb/>neque &longs;ua propria motio­<lb/>ne. Nihil enim intere&longs;t cir­<lb/>cumponere, & annectere <lb/>vel adiungere <expan abbr="vtrũlibet">vtrullibet</expan> al­<lb/>teri. Similiter enim <expan abbr="quãdo">quando</expan> <lb/>hic <expan abbr="quid&etilde;">quidem</expan> mouet: ille verò <lb/>ab altero mouetur, <expan abbr="quantũ">quantum</expan> <lb/>vnus mouerit, tantum alter <lb/>mouebitur. quando <expan abbr="quid&etilde;">quidem</expan> <lb/>igitur <expan abbr="adiectũ">adiectum</expan>, vel &longs;u&longs;pen­<lb/>&longs;um mouerit quis, <expan abbr="nõ">non</expan> &longs;em­<lb/>per conuoluitur: at <expan abbr="quãdo">quando</expan> <lb/>circa idem centrum po&longs;iti <lb/>fuerint, &longs;emper nece&longs;&longs;e <expan abbr="e&longs;t-alterũ">e&longs;t­<lb/>alterum</expan> ab altero conuolui.
<pb pagenum="172"/><gap/><lb/>Sed perinde ac &longs;i &longs;uo motu <lb/>alter non moueatur, nul­<lb/>lum que motum habeat. Et <lb/>&longs;i habeat eo <expan abbr="nõ">non</expan> vtatur, hoc <lb/>accidit. Quando igitur ma­<lb/>gnus paruum <expan abbr="alligatũ">alligatum</expan> mo­<lb/>uerit, hic paruus <expan abbr="tãtundem">tantundem</expan> <lb/>mouetur. Quando verò <lb/>paruus rur&longs;us: tantundem <lb/>magnus. Separatim verò <lb/>vterque &longs;eip&longs;um mouet. <lb/>Quod verò <expan abbr="eod&etilde;">eodem</expan> exi&longs;tente <lb/>centro, & moto eadem ce­<lb/>leritate <expan abbr="cõtingit">contingit</expan> ip&longs;os ma­<lb/>iorem <expan abbr="trã&longs;ilire">tran&longs;ilire</expan> lineam, pa­<lb/>ralogi&longs;mus e&longs;t à dubitante <lb/>dolosè prolatus. Idem qui­<lb/>dem e&longs;t centrum vtri&longs;que: <lb/>&longs;ed per accidens vt <expan abbr="mu&longs;icũ">mu&longs;icum</expan> <lb/>& album e&longs;&longs;e. Quod enim <lb/>e&longs;&longs;et de e&longs;&longs;entia vtriu&longs;que <lb/>centri circulorum, non eo­<lb/>dem vtitur: &longs;ed <expan abbr="quãdo">quando</expan> par­<lb/>uus mouebit illius e&longs;t, vt <lb/><expan abbr="centrũ">centrum</expan> & <expan abbr="principiũ">principium</expan>: quan­<lb/>do verò magnus, vt ip&longs;ius. <lb/>Non igitur idem mouet &longs;impliciter: &longs;ed quodammodo.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Qvod etiam dubit.] <emph type="italics"/>Antea de circulis ad vnum centrum <lb/>connexis <expan abbr="demõ&longs;tratum">demon&longs;tratum</expan> e&longs;t: perinde etiam in inæqualibus ad di­<lb/>wer&longs;a puncta connexis &longs;e habere o&longs;tenditur, ni&longs;i <expan abbr="mendũ">mendum</expan> &longs;ub&longs;it aliquod <lb/>in contextu è quo particulam<emph.end type="italics"/> <foreign lang="greek">ou)k</foreign> <emph type="italics"/>expunximus. Nam & eccentrici <lb/>connexi raptum motoris primi &longs;equuntur, & &longs;emper orbitarum <lb/>æqualitas reperietur &longs;eu centra &longs;int in eadem linea: &longs;iue in diuer&longs;is,<emph.end type="italics"/>
<pb pagenum="173"/>
<figure id="fig63"></figure><lb/><emph type="italics"/>vtin A, B, <lb/>C, vbi lineæ <lb/>pro <gap/>rbitis <lb/>inæqualium <lb/><expan abbr="circulorũ">circulorum</expan>, &longs;ed <lb/><expan abbr="annexorũ">annexorum</expan> D <lb/>E, FG, HI <lb/>&longs;unt æquales <lb/>vt facile e&longs;t <lb/>demon&longs;trare <lb/>ex ad&longs;cripto <lb/>diagrammate.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Quod vero eodem.] <emph type="italics"/>Re&longs;pondet a&longs;&longs;umptioni præcedentis &longs;yllo­<lb/>gi&longs;mi, in quo concludebatur ratio admirationis problematis. Negat­<lb/>que idem etiam concentricorum circulorum ita vt dictum e&longs;t moto­<lb/>rum, <expan abbr="c&etilde;trum">centrum</expan> e&longs;&longs;e, ni&longs;i captiose. Huius enim <expan abbr="centrũ">centrum</expan>, e&longs;t quod primum <lb/>mouetur, non huius quod &longs;ecundario. Huius enim centrum feriatur: <lb/>illius verò <expan abbr="cũ">cum</expan> &longs;it <expan abbr="principiũ">principium</expan> motus, agit, &longs;eu in actu e&longs;t. Et &longs;ic non <expan abbr="vnũ">vnum</expan> <lb/><expan abbr="idemq;">idemque</expan> centrum <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> e&longs;t, cum <expan abbr="alterũ">alterum</expan> moueat, alterum moueatur. <lb/>Hæc tamen &longs;olutio quæ &longs;it, relinquo cogitandum. quomodo enim &longs;i <lb/><expan abbr="principiũ">principium</expan> motus <expan abbr="concentricorũ">concentricorum</expan> <expan abbr="circulorũ">circulorum</expan> &longs;it ab axe, vt in mola mole­<lb/>trinæ, & <expan abbr="vnũ">vnum</expan> <expan abbr="idemq;">idemque</expan> <expan abbr="centrũ">centrum</expan> cum &longs;it, puta, molæ minoris in maiore <lb/>de&longs;criptæ, non <expan abbr="id&etilde;">idem</expan> eodem <expan abbr="t&etilde;pore">tempore</expan> ab <expan abbr="eod&etilde;">eodem</expan> erit in actu & <expan abbr="principiũ">principium</expan>, &longs;ui <lb/>mot^{9} habebit. Aliter igitur verè &longs;olueretur, &longs;i intelligamus aliud e&longs;&longs;e <lb/><expan abbr="motũ">motum</expan> <expan abbr="circular&etilde;">circularem</expan>: aliud <expan abbr="motũ">motum</expan> in circulo vel per circulum. Motus enim <lb/>circularis fit <expan abbr="c&etilde;tro">centro</expan> quie&longs;cente, & reliquis omnibus motis, talis e&longs;t mo­<lb/>tus æquatoris in cælo. Motus verò per <expan abbr="circulũ">circulum</expan> fit progrediente centro, <lb/>& huic accedit vt <expan abbr="circũuertatur">circunuertatur</expan>, alioqui nihil aliud e&longs;&longs;et <expan abbr="quã">quam</expan> circu­<lb/>lus progrediens, & vectio <expan abbr="quædã">quædam</expan>, vt hæc qua<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/><expan abbr="centrũ">centrum</expan> perpetuò per<emph.end type="italics"/><lb/>
<arrow.to.target n="marg40"></arrow.to.target><lb/><emph type="italics"/>æquidi&longs;tantem <expan abbr="lineã">lineam</expan> fertur in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&longs;eu trahatur &longs;eu impellatur, & ideo <lb/>omnia puncta æqualiter <expan abbr="mou&etilde;tur">mouentur</expan>, & per æquale <expan abbr="&longs;patiũ">&longs;patium</expan> perinde ac &longs;i <lb/>motus hic merè rectus e&longs;&longs;et, & &longs;ine vlla circumuer&longs;ione qua&longs;i fune <lb/>circulus traheretur. Cæterum cum <expan abbr="tã">tam</expan><emph.end type="italics"/> <foreign lang="greek">z g d,</foreign> <emph type="italics"/><expan abbr="quã">quam</expan><emph.end type="italics"/> <foreign lang="greek">h b e</foreign> <emph type="italics"/>moueantur &longs;u­<lb/>per rectas<emph.end type="italics"/> <foreign lang="greek">zl, h q</foreign> <emph type="italics"/>& quidem ita vt &longs;ingula puncta<emph.end type="italics"/> <foreign lang="greek">z g d</foreign> <emph type="italics"/>tangant <lb/>&longs;ingula puncta<emph.end type="italics"/> <foreign lang="greek">z l</foreign><emph type="italics"/>: <expan abbr="tũ">tum</expan><emph.end type="italics"/> <foreign lang="greek">h b e</foreign> <emph type="italics"/>&longs;ingula puncta ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">h <expan abbr="q.">que</expan></foreign> <emph type="italics"/>Tamen peri­<lb/>pheria<emph.end type="italics"/> <foreign lang="greek">z g d,</foreign> <emph type="italics"/>aut <expan abbr="nõ">non</expan> e&longs;t æqualis rectæ<emph.end type="italics"/> <foreign lang="greek">z l</foreign><emph type="italics"/>: aut peripheria<emph.end type="italics"/> <foreign lang="greek">z b e</foreign> <emph type="italics"/><expan abbr="nõ">non</expan> e&longs;t<emph.end type="italics"/>
<pb pagenum="174"/><emph type="italics"/>æqualis rectæ<emph.end type="italics"/> <foreign lang="greek">h q</foreign>: <emph type="italics"/>alioqui &longs;i<emph.end type="italics"/><lb/>
<figure id="fig64"></figure><lb/><emph type="italics"/>ambæ peripheriæ ambabus re­<lb/>ctis e&longs;&longs;ent æquales, cum ip&longs;æ <lb/>&longs;int æquales rectæ, vt demon­<lb/>&longs;tratume&longs;t, e&longs;&longs;ent & periphe­<lb/>riæ æquales, maior minori, quod <lb/>ab&longs;urdum. Ex quo exploditur <lb/>ratio Bouilli, qui ex <expan abbr="circũuolu-tione">circunuolu­<lb/>tione</expan> circuli exactè rotundi &longs;u­<lb/>per plano ad libellam facto pu­<lb/>tabat inueni&longs;&longs;e rectam periphe­<lb/>riæ æqualem. Quæritur ergo quod e&longs;t &longs;uperiori problemate diffici­<lb/>lius, vt fieri poßit rectarum æqualium peragratio à circulis inæqua­<lb/>libus. Sit igitur. vt rotæ axis<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;eat in F. Et quia<emph.end type="italics"/> <foreign lang="greek">a h</foreign> <emph type="italics"/>& F G<emph.end type="italics"/><lb/>
<figure id="fig65"></figure><lb/><emph type="italics"/>æquales &longs;unt. Radij enim &longs;unt eiu&longs;dem circuli minoris &<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>G e&longs;t <lb/>æquidi&longs;tans<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>F. Erit per demon&longs;trata punctum G in linea F H. <lb/>Et ponatur quod punctum fuerit M in maiori circulo, quod tran&longs;la­<lb/>tum & retrò reuolutum peruenerit ad H, atque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M &longs;ecet circulum <lb/>minorem<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>vt in puncto I. Dico quod I e&longs;t punctum G. Nam <lb/>quia M e&longs;t H, & in linea F H: præterea I e&longs;t in linea<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>M, <lb/>erit etiam in linea F H. E&longs;t etiam in circulo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Ergo in puncto <lb/>communi vtrique. Nullum autem e&longs;t præter G. Igitur I peruenit<emph.end type="italics"/>
<pb pagenum="175"/><emph type="italics"/>in G. Sicque M retroceßit per angulum M G H. Contrà I an­<lb/>teceßit per angulum I G F, qui &longs;unt anguli æquales prop. 15. lib. 1. <lb/>Et &longs;ic patet cur retrocedente vno tantum: quantum procedit alter, <lb/>moueantur æqualiter, id e&longs;t per æquale &longs;patium puncta peripheria­<lb/>rum inæqualium ob centri communis æqualem motum. Hæc ex <lb/>Cardan. prop. 196. lib. 5. de proport.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg40"></margin.target>Vide penul <lb/>timum dia <lb/>gramma.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>26. De lectis.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur lectos lateribus du­<lb/>plos faciunt, vno quidem <lb/>&longs;ex pedum, vel paulò plus: <lb/>altero verò trium. Et cur <lb/>extendunt non &longs;ecundum <lb/>diametrum. An magnitu­<lb/>dine tantos faciunt, vt cor­<lb/>poribus corre&longs;pondeant. <lb/>Sic enim lateribus dupli <lb/>efficiuntur, vt longitudine <lb/>quatuor cubitorum, latitu­<lb/>dine verò duorum &longs;int.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr lectos.] <emph type="italics"/>In hoc capite quæruntur duo, quibus apertè &longs;atis­<lb/>facit philo&longs;ophus, quod ad primas quæ&longs;tionum rationes attinet. <lb/>Ex his prior e&longs;t, cur lectus fiat è lateribus in ratione dupla, cuiu&longs;mo­<lb/>di &longs;unt &longs;ex pedes ad tres, vel quatuor cubiti ad duos. vbi notandum <lb/>lectos habere formam parallelogrammi rectanguli. Itaque ex def. 1. <lb/>lib. 2. contineri &longs;ub duobus lateribus, quæ rectum angulum compre­<lb/>hendunt. Et hæc &longs;unt quæ hîc <expan abbr="con&longs;iderãtur">con&longs;iderantur</expan> in ratione dupla. Re&longs;pon­<lb/>det igitur &longs;ic fieri, vt corpori decubituro corre&longs;pondeat, & rationem <lb/>habeat vel æqualitatis, vel paulo maioris. Sic enim melius excipit in <lb/>eo <expan abbr="decumb&etilde;s">decumbens</expan> corpus. E&longs;t autem iu&longs;ta hominis magnitudo &longs;ex pedum: <lb/>quam vt pauci excedunt: ita quamplurimi non attingunt. Acce­<lb/>dunt tamen ad eam multi. Sicque plurimis opportuna quæ &longs;ita e&longs;t<emph.end type="italics"/>
<pb pagenum="176"/><emph type="italics"/>lecti magnitudo, quod ad <expan abbr="longitudin&etilde;">longitudinem</expan> attinet: &longs;ed nec minus quod ad <lb/>latitudinem. Seuenim &longs;upinus, aut pronus, quod e&longs;t in&longs;alubre, <expan abbr="nõ">non</expan> plus <lb/>loci quam cubitus vnus occupabit: & adhuc paulò minus, &longs;eu in <lb/>dextrum aut &longs;ini&longs;trum latus decumbat homo, cuiu&longs;modi plurimos<emph.end type="italics"/><lb/>
<arrow.to.target n="marg41"></arrow.to.target><lb/><emph type="italics"/>&longs;anos cubare dixit Hippocrates, collo etiam manibus cruribu&longs;que pa­<lb/>rum reductis, & totis corporibus humentes, id e&longs;t, vt explicat Gale­<lb/>nus vitatis extremis figuris. Extremæ autem figuræ &longs;unt, quæ &longs;um­<lb/>mam exten&longs;ionem, aut &longs;lexum habent &longs;iuè artuum &longs;int, &longs;iuè &longs;pinæ, <lb/>& fiunt neruis &longs;upra modum extentis: non item quæ inter ex­<lb/>tremas media e&longs;t, hæc enim ten&longs;ionem <expan abbr="nõ">non</expan> habet. Ideo humida appel­<lb/>lata e&longs;t ab Hippocrate, cum humida corpora tendi non &longs;oleant. Sic <lb/>autem iacens tantum hinc quantum illinc ad reuolutionem corporis <lb/>&longs;emicubitum, quod &longs;atis e&longs;t, habebit. Nec enim de his agimus, quibus<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg41"></margin.target>Inprogno&longs;t.</s>
</p>
<p type="main">
<s>Pinguis aqualiculus extento &longs;e&longs;quipede extat.</s>
</p>
<p type="main">
<s><emph type="italics"/>Sed de moderatis hominibus, quibus hæc lecti latitudo conueniens <lb/>erit. Hinc &longs;i duo in eodem lecto iacere debeant, latitudinem pro ra­<lb/>tione tantum augendam, non longitudinem lecti con&longs;tat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Non extendunt <expan abbr="aut&etilde;">autem</expan> &longs;e­<lb/>cundum diamerrum: &longs;ed <lb/>contrà, vt ligna minus di­<lb/>uellantur. celerrimè enim <lb/>finduntur &longs;ecundum natu­<lb/>ram diui&longs;a, & eadem parte <lb/>di&longs;tracta laborant maximè. <lb/>Præterea quoniam conue­<lb/>nit funes &longs;atis e&longs;&longs;e ad pon­<lb/>dus: &longs;i tran&longs;uer&longs;i &longs;int ex im­<lb/>po&longs;ito pondere minus la­<lb/>borabunt: quam &longs;i obliqui. <lb/>Præterea <expan abbr="etiã">etiam</expan> funium <expan abbr="quã-titas">quan­<lb/>titas</expan>: &longs;ic minor erit.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Non extendunt.] <emph type="italics"/>Po&longs;terior quæ&longs;tio e&longs;t, cur lectus cuius late­<lb/>ra &longs;unt in ratione dupla pertendatur loris non &longs;ecundum dia-<emph.end type="italics"/>
<pb pagenum="177"/><emph type="italics"/>metrum: &longs;ed in obliquum proten&longs;is, ad quam tripliciter re&longs;pondet. <lb/>Primo quia &longs;tudendum e&longs;t durationi, ideo cauendum, ne &longs;pondæ lecti <lb/>findantur: aut rumpantur. Itaque eo modo lora &longs;unt extendenda, <lb/>quo ruptioni fißioniue minus ip&longs;æ obnoxiæ fiunt. At &longs;i obliquè ex­<lb/>tendantur, minus erunt: quam &longs;i &longs;ecundum diametrum. I uxta ed quæ <lb/>demon&longs;trata &longs;unt cap. 15. lib. huius. Namque vt recta percußio ad <lb/>medium ligni oblongi facta facile ip&longs;um frangit: &longs;ic tractio firma <lb/>è directo à medio. E&longs;t enim tractio percu&longs;sionis &longs;pecies, vel princi­<lb/>pium. Et celerrimè rumpuntur, &longs;i &longs;ecundum naturam, id e&longs;t eam op­<lb/>portunitatem rumpantur. Non ergo lora &longs;ecundum diametrum ex­<lb/>tendi debent: verum obliquitus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Præterea quoniam.] <emph type="italics"/>Secunda e&longs;tratio. Lora eo potius exten­<lb/>denda modo, quo commodius onus decumbentis hominis etiam &longs;e&longs;e <lb/>reuoluentis ferre & &longs;u&longs;tinere valent, & quam minimùm à &longs;ua ex­<lb/>ten&longs;ione relaxari.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Exten&longs;a obliquitus hæc præ&longs;tant propter æqualitatem, per quam <lb/>non e&longs;t, cur vnum plus, vel citius relaxetur: quam aliud. Et quod <lb/>in ea parte lecti &longs;e&longs;e implicent vires &longs;uas iungentia, in medio &longs;cili­<lb/>cet, vbi etiam onus corporis grauius e&longs;t, nempe truncus corporis <lb/>vna cum natibus: non autem ita in extremis, vbi caput & pedes <lb/>leuiora accubant. Hæc vero non perinde præ&longs;tant exten&longs;a &longs;ecun­<lb/>dum diametrum, hoc enim quod <expan abbr="lõgius">longius</expan> e&longs;t breuiori citius relaxa­<lb/>tur, & &longs;ic ferendo, &longs;u&longs;tinendo ve oneri relinquit imbecillius.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Præterea etiam.] <emph type="italics"/>Tertia ratio. Lororum quantitas obliquitus <lb/>extentorum minor e&longs;t: quam &longs;ecundum diametrum. Vt autem &longs;int <lb/>parui pretij, ab&longs;tinendum tamen à &longs;uperfluis. fru&longs;trà enim fit per plu­<lb/>ra, quod fieri pote&longs;t per pauciora.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Sit lectus <foreign lang="greek">a z h i,</foreign> & <foreign lang="greek">z h</foreign><lb/>bifariam diuidatur, vt in <foreign lang="greek"><gap/>.</foreign><lb/>Æqualia itaque &longs;unt fora­<lb/>mina, tum in <foreign lang="greek">z <gap/>,</foreign> tum in <foreign lang="greek">z <lb/>a.</foreign> Æqualia enim &longs;unt la­<lb/>tera. Nam totum <foreign lang="greek">z h</foreign> du­<lb/>plum e&longs;t [<foreign lang="greek">za.</foreign>] Extendunt <lb/>verò vt &longs;criptum e&longs;t ab
<pb pagenum="178"/><gap/><lb/><foreign lang="greek">a</foreign> ad <foreign lang="greek">b</foreign>: deinde vbi e&longs;t <foreign lang="greek">g</foreign>: <lb/>po&longs;tea vbi <foreign lang="greek">d,</foreign> po&longs;tea vbi <foreign lang="greek">q,</foreign><lb/>deinceps vbi <foreign lang="greek">e,</foreign> & &longs;ic &longs;em­<lb/>per quou&longs;que ad alium <expan abbr="cõ-uerterint">con­<lb/>uerterint</expan> angulum. Duo <lb/>etenim anguli habent fu­<lb/>nis principia. Sunt verò fu­<lb/>nes iuxta curuaturas æqua­<lb/>les, nempe <foreign lang="greek">a b</foreign> & <foreign lang="greek"><gap/> g</foreign> ip&longs;i <lb/><foreign lang="greek">g d</foreign> & <foreign lang="greek">d <expan abbr="q.">que</expan></foreign> Et alij &longs;unt eiu&longs;­<lb/>modi, quod eadem &longs;it de­<lb/>mon&longs;tratio. Etenim <foreign lang="greek">a b</foreign> æ­<lb/>qualis e&longs;t ip&longs;i <foreign lang="greek">e <expan abbr="q.">que</expan></foreign> <expan abbr="Sũt">Sunt</expan> enim <lb/>æqualia latera parallelo­<lb/>grammi <foreign lang="greek"><gap/> h k a,</foreign> & forami­<lb/>na æquedi&longs;tant: Æqualis <lb/>vero e&longs;t <foreign lang="greek">b h</foreign> ip&longs;i <foreign lang="greek">k a.</foreign> Nam <lb/>angulus <foreign lang="greek">b</foreign> æqualis ip&longs;i <foreign lang="greek">h.</foreign> In <lb/>parallelis enim hic <expan abbr="quid&etilde;">quidem</expan> <lb/>interior e&longs;t, ille externus, & <lb/><foreign lang="greek">b</foreign> e&longs;t &longs;emirectus. E&longs;t enim <foreign lang="greek">z <lb/>b</foreign> æqualis ip&longs;i <foreign lang="greek">z a,</foreign> & angu­<lb/>lus qui ad <foreign lang="greek">z</foreign> rectus, & angu­<lb/>lus <foreign lang="greek">b</foreign> æqualis ei qui ad <foreign lang="greek">h.</foreign><lb/>Nam qui ad <foreign lang="greek">z</foreign> rectus. quo­<lb/>niam lateribus duplum al­<lb/>terolongum, & ad medium <lb/>curuatum e&longs;t. Itaque <foreign lang="greek">a d</foreign><lb/>æqualis ip&longs;i <foreign lang="greek">e h,</foreign> huic verò <lb/>ip&longs;a <foreign lang="greek">k q</foreign> parallela. itaque <foreign lang="greek"><gap/><lb/>g</foreign> æqualis e&longs;t ip&longs;i <foreign lang="greek">k q,</foreign> & <foreign lang="greek">g e</foreign><lb/>ip&longs;i <foreign lang="greek">d <expan abbr="q.">que</expan></foreign> Similiter & ali&ecedil; <expan abbr="de-mõ&longs;trãtur">de­<lb/>mon&longs;trantur</expan>, quod &longs;int æqua­<lb/>les in curuaturis duæ dua­<lb/>bus. Itaque clarum e&longs;t quod tanti &longs;unt in lecto funes: <lb/>quanta e&longs;t <foreign lang="greek">a b</foreign> quater. Quanta e&longs;t autem multltudo
<pb pagenum="179"/><gap/><lb/>foraminum in latere <foreign lang="greek">zh,</foreign><lb/>etiam in dimidio quod e&longs;t <lb/><foreign lang="greek">z b</foreign> <expan abbr="dimidiũ">dimidium</expan> e&longs;t. Quare in <lb/>dimidio lecti, <expan abbr="tãta">tanta</expan> erit ma­<lb/>gnitudo funium: quantum <lb/>e&longs;t <foreign lang="greek">a b.</foreign> Multitudine vero <lb/>tot: quot &longs;unt in <foreign lang="greek">b h</foreign> fora­<lb/>mina. Quod perinde e&longs;t ac <lb/>dicere quot &longs;unt in <foreign lang="greek">a z</foreign> & <lb/><foreign lang="greek">b z</foreign> &longs;imul &longs;umptis. Si vero <lb/>&longs;ecundum diametrum <expan abbr="ex-tendãtur">ex­<lb/>tendantur</expan> funes, vt in lecto <lb/><foreign lang="greek">a b g d</foreign> &longs;ehabent, dimidia <lb/>&longs;unt, non tot: quot latera <lb/>vtrorum que <foreign lang="greek">a z, z h.</foreign> æqua­<lb/>lia vero foramina in&longs;unt <lb/>quot in <foreign lang="greek">z b, z a,</foreign> duæ vero <lb/>cum &longs;int <foreign lang="greek">a z, b z,</foreign> maiores <lb/>&longs;unt ip&longs;a <foreign lang="greek">a b.</foreign> Itaque funis <lb/>tanto maior: quanto ambo <lb/>latera maiora &longs;unt diame­<lb/>tro.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Sit lectus <foreign lang="greek">a z h i.</foreign>] <emph type="italics"/>In tertia ratione &longs;ecundæ quæ&longs;tionis expli­<lb/>canda reliquus Ari&longs;totelis contextus totus e&longs;t: &longs;ed adeo mendo&longs;us <lb/>& in verbis, & in diagrammatis, & in diagrammatum characte­<lb/>ribus, vt &longs;i Iuppiter cum Æ&longs;culapio mederi, & mendas eluere ve­<lb/>lit, non poßit tamen: ideò &longs;atius e&longs;t cum &longs;it nota philo&longs;ophi &longs;enten­<lb/>tia, totum adimere, & alium &longs;upplere. Ob&longs;curitas ex tam corru­<lb/>pto contextumanans fecit, vt nonnulli interpretes Cardano non &longs;a­<lb/>tisfecerint, qui negotium numeris ab&longs;oluunt, cum tamen demon&longs;tra­<lb/>tionem geometricam in&longs;tituerint, neque in figuris lectorum a&longs;&longs;um­<lb/>ptis, & in contextu ne&longs;cio à quibus po&longs;itis, eundem numerum linea­<lb/>rum retineant. Sed in vna octo, in altera decem, non debuerit<emph.end type="italics"/>
<pb pagenum="180"/><emph type="italics"/>idem numerus vbique e&longs;&longs;e: &longs;i quidem magnum quid &longs;it & demon­<lb/>&longs;tratu dignum, minus lororum in vna exten&longs;ione expendi: quam in <lb/>altera: qui <expan abbr="deniq;">denique</expan> in vtraque figura obliquas <expan abbr="hab&etilde;t">habent</expan> lineas, quanquam <lb/>alias alÿs obliquiores: & tamen duæ antehac rationes videntur in <lb/>vna figura po&longs;tulare obliquas, in altera rectas. Nos igitur aliter Car­<lb/>dani ve&longs;tigia ob&longs;cura, & ni fallor imperfecta, vt &longs;unt <expan abbr="pleraq;">pleraque</expan> huius <lb/>hominis ferè omnia vt arbitror, <expan abbr="quanquã">quanquam</expan> &longs;emper ingeniosè &longs;criben­<lb/>tis, &longs;ecuti, apertius & perfectius totum hoc <expan abbr="negotiũ">negotium</expan> euoluemus. At­<lb/>que in primis dicimus extendi lora &longs;ecundum diametrum, non e&longs;&longs;e <lb/>ab angulo ad angulum oppo&longs;itum: &longs;ed &longs;ecundum rectas, quæ à latere <lb/>ad latus oppo&longs;itum extenduntur, vt &longs;int aliæ &longs;ecundum longitudi­<lb/>nem, aliæ &longs;ecundum latitudinem. Sic enim diameter non<emph.end type="italics"/> <foreign lang="greek"><gap/> gw/nios</foreign><lb/><emph type="italics"/>&longs;umi videtur: qua&longs;i dimetiens, vt quæ dimetiatur longitudinem vel <lb/>latitudinem, æqualis videlicet facta, quo modo licet hîc ab Ari&longs;to­<lb/>tele reiecto, hodie adhuc vtuntur. Atque hoc modo &longs;i non intelliga­<lb/>tur diameter: &longs;ed<emph.end type="italics"/> <foreign lang="greek"><gap/>a gw/nios,</foreign> <emph type="italics"/>tam obliquæ erunt in vna forma li­<lb/>neæ: quam in altera: &longs;icque quæ de ruptione vel fißione & opportu­<lb/>nitate dicta &longs;unt, hîc non conuenient, quod e&longs;&longs;et ab&longs;urdum. His igi­<lb/>tur ita po&longs;itis de&longs;cribantur duæ formæ lecti, in quibus &longs;int lineæ nu­<lb/>mero pares, &longs;itu diuer&longs;æ. Sit igitur prima A B C D, cuius la-<emph.end type="italics"/><lb/>
<figure id="fig66"></figure><lb/><emph type="italics"/>tus A B duplum &longs;it lateris A C, & quidem illud 4. pe­<lb/>dum, hoc duorum. In hac lora &longs;ecundum diametrum &longs;int quidem <lb/>&longs;ecundum longitudinem tria K N. L O, M P, & &longs;ic inter &longs;e<emph.end type="italics"/>
<pb pagenum="181"/><emph type="italics"/>& lateri A B æqualia prop. 34. lib. 1. Sint & totidem G Q, <lb/>E F, H R &longs;ecundum latitudinem exten&longs;a, inter&longs;e quoque, & la­<lb/>teri A C æqualia per eandem.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sit &longs;ecunda forma<emph.end type="italics"/> <foreign lang="greek">a b g d</foreign> <emph type="italics"/>in eadem ratione laterum, & ea­<lb/>dem magnitudine &longs;eruata, & linearum &longs;ed obliquarum æquali nu­<lb/>mero, quæ &longs;int<emph.end type="italics"/> <foreign lang="greek">a c, h k, e d</foreign> <emph type="italics"/>tum.<emph.end type="italics"/> <foreign lang="greek">b c, q i, e g,</foreign> <emph type="italics"/>quæ quia pa-<emph.end type="italics"/><lb/>
<figure id="fig67"></figure><lb/><emph type="italics"/>rallelæ &longs;unt, & aduer&longs;æ in &longs;uis parallelogrammis, omnes inter &longs;e <lb/>æquales &longs;unt prop. 34. lib. 1. Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="greek">a c</foreign> <emph type="italics"/>&longs;it ab angulo<emph.end type="italics"/> <foreign lang="greek">a</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">c</foreign> <emph type="italics"/>medium lateris<emph.end type="italics"/> <foreign lang="greek">g d</foreign><emph type="italics"/>: erit hæc æqualis ip&longs;i<emph.end type="italics"/> <foreign lang="greek">b c,</foreign> <emph type="italics"/>quia latera <lb/>æqualium quadratorum. V trumque enim æquale e&longs;t duobus ex<emph.end type="italics"/> <foreign lang="greek">a g, <lb/>g c,</foreign> <emph type="italics"/>vel quod idem e&longs;tex<emph.end type="italics"/> <foreign lang="greek">c d, d <gap/></foreign> <emph type="italics"/>prop. 47. lib. 1.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Dico ergo quod lorum K N cum G Q, id e&longs;t A C, A B ma­<lb/>ius e&longs;t<emph.end type="italics"/> <foreign lang="greek">a c, c b,</foreign> <emph type="italics"/>& duo pariter accepta duobus pariter acceptis e&longs;&longs;e <lb/>maiora: &longs;icque totum lorum in lecto A B C D maius e&longs;&longs;e toto, <lb/>quod e&longs;t in lecto<emph.end type="italics"/> <foreign lang="greek">a b g d.</foreign></s>
</p>
<p type="main">
<s><emph type="italics"/>Demon&longs;tratio. Quia rectangulum &longs;ub A C, A B comprehen­<lb/>&longs;um duplum e&longs;t quadrati ex A C prop. 1. lib. 6. & rectangulum &longs;ub<emph.end type="italics"/><lb/><foreign lang="greek">a c, c b</foreign> <emph type="italics"/>duplum <expan abbr="it&etilde;">item</expan> e&longs;t quadrati ex A C. Ip&longs;um enim <expan abbr="cũ">cum</expan> quadratum <lb/>&longs;it. <expan abbr="Nã">Nam</expan><emph.end type="italics"/> <foreign lang="greek">a c</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">c b</foreign> <emph type="italics"/>&longs;unt æquales ex fabrica, æquale e&longs;t prop. 47. lib. 1. <lb/>duobus quadratis ex A C & C F: &longs;ed quod idem e&longs;t ex<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="greek">g c,</foreign><lb/><emph type="italics"/>æqualibus ex hypoth, erit <expan abbr="rectangulũ">rectangulum</expan> &longs;ub A C, A B comprehen&longs;um <lb/>rectangulo &longs;ub<emph.end type="italics"/> <foreign lang="greek">a c, c b</foreign> <emph type="italics"/>comprehen&longs;o. axiom. 6. & per idem rectan­<lb/>gulum bis &longs;ub A C, A B comprehen&longs;um, rectangulo bis &longs;ub<emph.end type="italics"/> <foreign lang="greek">a c, c b</foreign>
<pb pagenum="182"/><emph type="italics"/>comprehen&longs;o æquale: &longs;ed & quadratum ex A B æquale e&longs;t quadratis <lb/>ex<emph.end type="italics"/> <foreign lang="greek">a z, zb</foreign> <emph type="italics"/>prop. 47. lib. 1. E&longs;t enim angulus<emph.end type="italics"/> <foreign lang="greek">a z b</foreign> <emph type="italics"/>rectus, cum &longs;it <lb/>reliquus trium<emph.end type="italics"/> <foreign lang="greek">a z g, a z b, b z d</foreign> <emph type="italics"/>duobus rectis æqualium prop. 13. <lb/>lib. 1. &longs;ublatis duobus &longs;emirectis<emph.end type="italics"/> <foreign lang="greek">a z g, <gap/> z d</foreign> <emph type="italics"/>per coroll. prop. 32. lib. 1. <lb/>Erunt igitur quadrata ex A B, A C cum rectangulo bis &longs;ub A C, <lb/>A B comprehen&longs;o maiora quadratis ex<emph.end type="italics"/> <foreign lang="greek">a z, z <gap/></foreign> <emph type="italics"/>cum rectangulo <lb/>bis &longs;ub<emph.end type="italics"/> <foreign lang="greek">a z, z b</foreign> <emph type="italics"/>comprehen&longs;o per quantitatem quadrati ex A C: <lb/>&longs;ed quadrata ex A B, A C cum rectangulo bis comprehen&longs;o &longs;ub <lb/>A B, A C &longs;unt potentia lineæ C A B vtcunque &longs;ectæ in A, id e&longs;t <lb/>æqualia &longs;unt quadrato ex C A B prop. 4. lib. 2. & per eandem qua­<lb/>drata ex<emph.end type="italics"/> <foreign lang="greek">a z, z <gap/></foreign> <emph type="italics"/>cum rectangulo bis comprehen&longs;o &longs;ub<emph.end type="italics"/> <foreign lang="greek">a z, z b</foreign> <emph type="italics"/>&longs;unt <lb/>potentia lineæ<emph.end type="italics"/> <foreign lang="greek">a z b</foreign> <emph type="italics"/>vtcunque &longs;ectæ in<emph.end type="italics"/> <foreign lang="greek">z.</foreign> <emph type="italics"/>E&longs;t ergo C A B maior <lb/>potentia quam<emph.end type="italics"/> <foreign lang="greek">a z b,</foreign> <emph type="italics"/>proinde erit & longitudine maior per coroll. <lb/>è prop. 47. lib. 1. Similiter demon&longs;trabitur de reliquis. E&longs;t ergo maior <lb/>lororum quantitas in lecto A B C D: quam in lecto<emph.end type="italics"/> <foreign lang="greek">a b d g,</foreign> <emph type="italics"/>quod <lb/>erat demon&longs;trandum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>His ita geometricè demon&longs;tratis, nihil nunc obe&longs;t exquirere, quæ <lb/>&longs;it ex hac forma &longs;ecunda in loris par&longs;imonia. Cum igitur in lecto A <lb/>B C D quæ tres &longs;unt &longs;ecundum longitudinem exten&longs;æ, æquales &longs;int <lb/>&longs;ingulæ lateri A C quod e&longs;t &longs;ex pedum: &longs;imul &longs;umptæ erunt 18. pe­<lb/>dum: & reliquæ &longs;ecundum latitudinem &longs;ingulæ ip&longs;i A C æquales, <lb/>faciunt 9. pedes, ideo omnes &longs;unt 27. pedes lororum. In lecto vero<emph.end type="italics"/><lb/><foreign lang="greek">a <gap/> g d</foreign> <emph type="italics"/>cum omnes æquales lineæ &longs;int ip&longs;i<emph.end type="italics"/> <foreign lang="greek">a z,</foreign> <emph type="italics"/>& &longs;it ex<emph.end type="italics"/> <foreign lang="greek">a z</foreign> <emph type="italics"/>qua­<lb/>dratum æquale quadratis ex<emph.end type="italics"/> <foreign lang="greek">a g, & g z</foreign> <emph type="italics"/>id e&longs;t 9. & 9. Erit igitur <lb/>18. quadratum ex<emph.end type="italics"/> <foreign lang="greek">a z,</foreign> <emph type="italics"/>cuius radix quadrata ferè e&longs;t 4 2/9, quæ per 6. <lb/>multiplicata facit 25 1/3 qui numerus &longs;uperatur à 27. per 1 2/3. Atque <lb/>hoc in loris compendium e&longs;t, quod licet exiguum, non contemnen­<lb/>dum tamen.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Et &longs;ic &longs;emper.] <emph type="italics"/>Videtur Ari&longs;toteles volui&longs;&longs;e in vno lecto fu­<lb/>nem vnum e&longs;&longs;e continuum, & per parallelogramma di&longs;pergi atque <lb/>extendi.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Iuxta curuaturas.] <foreign lang="greek">ka/myis</foreign> <emph type="italics"/>curuatura re&longs;tium vocatur ea <lb/>pars quæ à foramine ad foramen ip&longs;is extrin&longs;ecus applicatur &longs;pon­<lb/>dis, parallelogrammorumque à re&longs;tibus &longs;eu loris effectorum minora <lb/>efficiunt latera.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Sunt enim æqualia latera.] <emph type="italics"/>Deinceps ad finem corruptißi-<emph.end type="italics"/>
<pb pagenum="183"/><emph type="italics"/>ma ferè &longs;unt omnia.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Angulus qui ad <foreign lang="greek">z</foreign> rectus.] <emph type="italics"/>Angulus qui ad<emph.end type="italics"/> <foreign lang="greek">z</foreign> <emph type="italics"/>continetur à <lb/>lateribus<emph.end type="italics"/> <foreign lang="greek">z h, z a</foreign> <emph type="italics"/>rectanguli lecti, itaque rectus e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Angulus <foreign lang="greek">b</foreign>] <emph type="italics"/>Id e&longs;t angulus<emph.end type="italics"/> <foreign lang="greek">z b a</foreign> <emph type="italics"/>æqualis e&longs;t angulo<emph.end type="italics"/> <foreign lang="greek">b h k</foreign><lb/><emph type="italics"/>quod verum e&longs;t. quia &longs;unt anguli externus & internus ad ea&longs;dem <lb/>partes duarum parallelarum<emph.end type="italics"/> <foreign lang="greek">a b, k h</foreign> <emph type="italics"/>incidente in ip&longs;as recta<emph.end type="italics"/> <foreign lang="greek">z h.</foreign></s>
</p>
<p type="main">
<s>In parallelis enim.] <emph type="italics"/>Quod hic dicit Ari&longs;toteles<emph.end type="italics"/> <foreign lang="greek">i)/sas <gap/>a/mmas</foreign><lb/><emph type="italics"/>vertimus parallelas. Sic enim etiam locutus e&longs;t cap. 5. lib. 1. po&longs;teriore <lb/>analytic. Si quis igitur inquit demon&longs;trauerit, quod rectæ non con­<lb/>currant, videatur huius e&longs;&longs;e <expan abbr="demõ&longs;tratio">demon&longs;tratio</expan>. quia in omnibus &longs;it rectis. <lb/>Non e&longs;t autem, &longs;iquidem non, quod &longs;ic æquales &longs;int, id fit: &longs;ed quate­<lb/>nus quomodolibet æquales.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Similiter & aliæ.] <emph type="italics"/>Ex tribus diagrammatis in contextu de&longs;cri­<lb/>ptis quod &longs;ecundum e&longs;t o&longs;tendit, exten&longs;ionem funium breuiorem ea, <lb/>quæ in primo, & tertio e&longs;t, vt argumento problematis conuenire vi­<lb/>deatur. E&longs;t enim <expan abbr="lõgitudo">longitudo</expan> funium in eo duntaxat 28. pedum cum 4/5 <lb/>vnius pedis: cum in primò &longs;it 34. pedum ferè, & in tertio 40 1/2 fere.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>27. Cur difficilius longali­<lb/>gna humero feruntur ab <lb/>extremo: quam à medio <lb/>&longs;ui.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur difficilius feruntur <lb/>humero longa ligna ab ex­<lb/>tremo: <expan abbr="quã">quam</expan> à medio &longs;ui, vt <lb/>æquale &longs;it <expan abbr="põdus">pondus</expan>. An quod <lb/><expan abbr="extremũ">extremum</expan> ligni agitati ferri <lb/>prohibet, vt quod <expan abbr="ge&longs;tatio-n&etilde;">ge&longs;tatio­<lb/>nem</expan> agitatione magis reuel­<lb/>lat? An quoniam, licet nihil <lb/>incuruetur, <expan abbr="neq;">neque</expan> valdè <expan abbr="ma-ior&etilde;">ma­<lb/>iorem</expan> <expan abbr="lõgitudinem">longitudinem</expan> habeat, <lb/><expan abbr="tam&etilde;">tamen</expan> ab extremo ferre dif­<lb/>ficilius e&longs;t: &longs;ed quod faci­<lb/>lius à medio &longs;ubleuetur: <lb/>quam ab extremo. Ob id ip&longs;um etiam facilius fertur.</s>
</p>
<pb pagenum="184"/>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr difficilius.] <emph type="italics"/>Huius capitis problema e&longs;t cur lignum lon­<lb/>gum difficilius ex humero fertur per extremum: quam per me­<lb/>dium. Huic dupliciter re&longs;pondetur. Prima re&longs;pon&longs;io e&longs;t &longs;pecialis ad <lb/>lignum quod flexile &longs;i &longs;it incuruatur, & nutat. Nutatio autem cum <lb/>&longs;it motus ad alium terminum: quam ad quem fertur, impedit. quin <lb/>& aggrauans premit magis ferentem. Secunda e&longs;t generalis ex ele­<lb/>uatione faciliori, quæ &longs;ic concludetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quo modo lignum vel pondus facilius eleuatur, eodem & fer­<lb/>tur. Eleuatio enim ge&longs;tatio quædam e&longs;t, & etiam ge&longs;tationis <lb/>pars difficilior, cum &longs;it ad contrarium omnino terminum, vt <lb/>&longs;ur&longs;um: ge&longs;tatio verò lateraliter reliqua fiat.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>At lignum longum facilius per medium: quam per extre­<lb/>mum eleuatur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo lignum longum facilius ex humero fertur per medium: <lb/>quam per extremum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cau&longs;a vero e&longs;t, quod ex <lb/>medio &longs;ubleuato &longs;emper <lb/>extrema &longs;e inuicem &longs;uble­<lb/>uant: & altera pars alteram <lb/>promptè attollit. Medium <lb/>enim quod habet <expan abbr="&longs;ubleuãs">&longs;ubleuans</expan> <lb/>vel <expan abbr="fer&etilde;s">ferens</expan> efficitur tanquam <lb/>centrum. Itaque <expan abbr="vtrumq;">vtrumque</expan> <lb/>extremorum deor&longs;um ver­<lb/>gens &longs;ur&longs;um &longs;u&longs;penditur. <lb/>At ab extremo <expan abbr="eleuatũ">eleuatum</expan> vel <lb/>ge&longs;tatum non idem facit: <lb/>quin totum onus vergit ad <lb/>medium vnum quò eleua­<lb/>tur vel fertur. Hoc &longs;it <foreign lang="greek">a,</foreign><lb/>extrema <foreign lang="greek">b, g.</foreign> Igitur eleuato <lb/>vel ge&longs;tato qua parte e&longs;t <foreign lang="greek">a</foreign>:
<pb pagenum="185"/><gap/><lb/>
<figure id="fig68"></figure><lb/><foreign lang="greek">b</foreign> quidem deor&longs;um ver­<lb/>gens attollit <foreign lang="greek">g:g</foreign> vero deor­<lb/>&longs;um repens attollit <foreign lang="greek">b.</foreign> Si­<lb/>mul autem eleuata idem præ&longs;tant.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cau&longs;a vero.] <emph type="italics"/>Confirmatio e&longs;t a&longs;&longs;umptionis ex æquis extremo­<lb/>rum ponderibus vicißim ob id &longs;e &longs;ubleuantibus: &longs;i enim vnius <lb/>propen &longs;io vergit deor&longs;um: alterius re&longs;i&longs;tentia ad motum &longs;ur&longs;um im­<lb/>pediet. Et &longs;ic &longs;e&longs;e mutuò librantia pondera, mutuò etiam &longs;e &longs;ubleuant. <lb/>E&longs;t enim medium quod fertur, tanquam centrum, à quo extrema vt <lb/>æquæ lances in iu&longs;ta libra, &longs;u&longs;penduntur. Non ita e&longs;t vbi lignum per <lb/>extremum fertur: &longs;ed totum ad partem vnam vergit ab co per quod<emph.end type="italics"/><lb/>
<figure id="fig69"></figure><lb/><emph type="italics"/>ge&longs;tatur deflectens. Ex deflexione autem <lb/>&longs;eu depreßione extremi, tanquam ponderis <lb/>prementis, labor augetur in ferente. Ergo <lb/>vbi depreßio nulla e&longs;t, vt in priori modo, <lb/>ibi labor minor erit. Et &longs;ic lignum lon­<lb/>gum ab extremo difficilius fertur quam <lb/>à medio. Sed hîc etiam quæri pote&longs;t cur <lb/>lignum longum puta lancea ab extremo <lb/>vno ge&longs;tata facilius feratur, &longs;i perpendi­<lb/>cularis &longs;it plano horizontis: <expan abbr="quã">quam</expan> ad ip&longs;um <lb/>inclinata. Hoc fit quia in perpendiculari <lb/>partes inferiores &longs;u&longs;tinent &longs;uperiores: in <lb/>inclinata non item, omnes enim &longs;ine ful­<lb/>cimento tendunt pro natura &longs;ua deor&longs;um. <lb/>Præterea in perpendiculari ip&longs;a lancea to­<lb/>ta pondus e&longs;t. Huic &longs;u&longs;tinendæ quæ vis<emph.end type="italics"/>
<pb pagenum="186"/><emph type="italics"/>&longs;ufficiet, &longs;ufficiet &<emph.end type="italics"/><lb/>
<figure id="fig70"></figure><lb/><emph type="italics"/>ferendæ, inque &longs;u&longs;ti­<lb/>nenda tantum labo­<lb/>rat: in inclinata ex­<lb/>tremum e&longs;t hypomoch­<lb/>lium, à quo non longè <lb/>abe&longs;t vis mouens: pon­<lb/>dus verò quod e&longs;t reli­<lb/>qua pars, ab hoc extre­<lb/>mo alterum extremum <lb/>quantò longius: tantò <lb/>maiorem rationem ad <lb/>vim mouentem habe­<lb/>bit, & &longs;ic difficilius <lb/>feretur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>28. Cur humero difficilius <lb/>fertur valdè <expan abbr="lõgum">longum</expan> pon­<lb/>dus: quam breue.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur &longs;i fuerit pondus <expan abbr="id&etilde;">idem</expan> <lb/>valdè longum humero dif­<lb/>ficilius fertur, <expan abbr="etiã">etiam</expan> vt quis è <lb/>medio ferat, quam &longs;i fuerit <lb/>breue. Huius quod antea <lb/>dictum e&longs;t, cau&longs;a <expan abbr="nõ">non</expan> e&longs;t: &longs;ed <lb/>agitatio cau&longs;a e&longs;t. Quum <lb/>enim longius fuerit extre­<lb/>ma agitantur. Ideo contin­<lb/>git ferentem multò diffici­<lb/>lius ferre. Maioris vero agi­<lb/>tationis cau&longs;a e&longs;t, quod in <lb/><expan abbr="ead&etilde;">eadem</expan> motione extrema <expan abbr="trã&longs;">tran&longs;</expan> <lb/><expan abbr="ferũtur">feruntur</expan> magis, <expan abbr="quãtò">quantò</expan> <expan abbr="lignũ">lignum</expan> <lb/>fuerit longius. Etenim hu-
<pb pagenum="187"/><gap/><lb/>merus &longs;it <expan abbr="c&etilde;trum">centrum</expan> vbi e&longs;t <foreign lang="greek">a.</foreign><lb/>hoc enim manet. Sint verò <lb/><foreign lang="greek">a b</foreign> & <foreign lang="greek">a g</foreign> lineæ ex centro. <lb/><expan abbr="Quãtò">Quantò</expan> igitur fuerit maius <lb/>id, quod ex <expan abbr="c&etilde;tro">centro</expan>, velip &longs;um <lb/><foreign lang="greek">a g,</foreign> tantò plus magnitudo <lb/>illa transfertur, quod e&longs;t <lb/>prius demon&longs;tratum.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr &longs;i fuerint.] <emph type="italics"/>Huius capitis problema e&longs;t. cur lignum lon­<lb/>gius è medio ge&longs;tatum breuiori eiu&longs;dem ponderis difficilius ex <lb/>humero fertur. Cui vt re&longs;pondeat generalem præcedentis &longs;olutionem <lb/>reÿcit, & eam quæ &longs;pecialis fuit de agitatione vtriu&longs;que extremi ad­<lb/>fert, vt quæ reuellat in alium terminum, contorqueat, & premat fe­<lb/>rentem. Hæc autem pendet à maiore di&longs;tantia à medio tanquam cen­<lb/>tro humeris ge&longs;tato.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sit igitur lignum <lb/>longius A B è me-<emph.end type="italics"/><lb/>
<figure id="fig71"></figure><lb/><emph type="italics"/>dio C ge&longs;tatum.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sit & breuius<emph.end type="italics"/><lb/>
<figure id="fig72"></figure><lb/><emph type="italics"/>D E eiu&longs;dem pon­<lb/>deris puta decem librarum è medio F ge&longs;tatum etiam. Quia partes <lb/>cum pariter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. & <lb/>e&longs;t A B maior ip&longs;o D E, erit dimidium A C maius dimidio D F. <lb/>Et &longs;ic extremum A magis di&longs;tans à centro C immoto plus mouet, <lb/>vel mouetur pro natura &longs;ua deor&longs;um. Item B. Ergotum A tum B <lb/>plus impediunt ferentem ex C: quam D & E ex F. Quæri hic <lb/>po&longs;&longs;et cur pondera &longs;ini&longs;tro humero facilius ferantur, quam dextro. <lb/>Hoc fit, quia dextrum <expan abbr="cumnatũ">cumnatum</expan> &longs;it ad mouere: &longs;ini&longs;trum ad moueri: <lb/>illud &longs;i liberum &longs;it ab onere impo&longs;ito (quod premit ideoque impedit) <lb/>facilius & maiori vi mouebit. Impeditum enim omne minus probe <lb/>fungitur officio. Præterea cum progreßio fiat impul&longs;ione vnius cru­<lb/>ris, & tractione, tum impul&longs;ione alterius, melius e&longs;t aliud, quod plus <lb/>impul&longs;ione & tractionevalet ab onere liberari. E&longs;t <expan abbr="aut&etilde;">autem</expan> <expan abbr="dextrũ">dextrum</expan> crus.<emph.end type="italics"/></s>
</p>
<pb pagenum="188"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>29. Cur in puteis tolleno­<lb/>nem faciunt hoc mo­<lb/>do.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur in puteis tollenonem <lb/><expan abbr="faciũt">faciunt</expan> &longs;ic, vt ligno pondus <lb/>plumbum &longs;cilicet <expan abbr="adijciãt">adijciant</expan>. <lb/>An quod in duo tempora <lb/>diui&longs;um &longs;it hauriendi opus <lb/>Immergere enim opor­<lb/>tet &longs;itulam, & hancrur&longs;us <lb/>&longs;ur&longs;um trahere. Contingit <lb/>quidem vacuam facile de­<lb/>mittere. At plenam attolle­<lb/>re difficile. Confert igitur <lb/>paulo tardius demittere, vt <lb/>qui attollit, attollat multò <lb/>facilius. Hoc autem pr&ecedil;&longs;tat <lb/>plumbum, vel lapis extre­<lb/>mo tollenonis adiectus. <lb/>Demittenti enim pondus <lb/>redditur maius: quam &longs;i &longs;o­<lb/>lam vacuam &longs;itulam opor­<lb/>teret demittere. At quan­<lb/>do plena fuerit, hanc edu­<lb/>cit plumbum, vel &longs;i quod <lb/>aliud pondus adiectum &longs;it. <lb/><expan abbr="Itaq;">Itaque</expan> hoc modo vtrumque <lb/>factu facilius e&longs;t: quam alterum.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr in puteis tollenonem.] <foreign lang="greek">Khlo/neion</foreign> <emph type="italics"/>quid &longs;it etiam&longs;i hîc <lb/>Ari&longs;toteles non explicet, non e&longs;t tamen difficile coniectura a&longs;­<lb/>&longs;equi, e&longs;&longs;e eam machinam ligneam, qua & antiqui v&longs;i&longs;unt, & qui <lb/>adhuc viuunt vtuntur in hauriendis aquis è puteo ad irrigandos<emph.end type="italics"/>
<pb pagenum="189"/><emph type="italics"/>hortos, vel ad aliud quod volunt. V&longs;um hunc pulchre expreßit Colu­<lb/>mella, &longs;i rectè Leonicus pro tendentibus corrigens reponit celonius, <lb/>&longs;ic igitur de irrigandis hortis loquens dixit Columella:<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vicini quo que &longs;int amnes, quos incola durus</s>
</p>
<p type="main">
<s>Attrahat auxilio &longs;emper &longs;itientibus hortis:</s>
</p>
<p type="main">
<s>Aut fons illachrymet putei non &longs;ede pro funda</s>
</p>
<p type="main">
<s>Ne grauis hau&longs;turis celonius ilia vellat.</s>
</p>
<p type="main">
<s><emph type="italics"/>Machina hæc quæ ab officio tollendi tolleno dicitur, con&longs;tat trabe <lb/>erecta, vt D C, & tigno tran&longs;uer&longs;o circa axiculum in alto trabis<emph.end type="italics"/><lb/>
<figure id="fig73"></figure><lb/><emph type="italics"/>ver&longs;atili, vt A B, à cuius extremo B cum cathena B E pendet <lb/>vas E, in altero A pondus plumbeum, vel lapideum G adÿcitur ad <lb/>commodiorem, vt vult hîc Ari&longs;tottles, à puteo F exhau&longs;tum. Quæ­<lb/>rit igitur cur in altero tollenonis extremo pondus adÿciatur. Huius <lb/>quæ&longs;tionis difficultas arguitur, quod &longs;itula &longs;eu vacua, &longs;eu plena, &longs;it <lb/>pondus. Pondus autem ponderi adiectum difficilius moueri deberet.<emph.end type="italics"/></s>
</p>
<pb pagenum="190"/>
<p type="main">
<s>An quod in duo.] <emph type="italics"/>Re&longs;pon&longs;io e&longs;tex di&longs;tinctione duplicis mo­<lb/>tus exhau&longs;tioni per tollenonem nece&longs;&longs;arÿ. Alter e&longs;t immer&longs;ionis: al­<lb/>ter eleuationis. Et illum quidem fatetur Ari&longs;toteles ex adiecto pon­<lb/>dere reddi difficiliorem: at hunc contra multo effici faciliorem. Ad­<lb/>mittendum autem in vna totius operis parte leue incommodum, pro­<lb/>pter &longs;ub&longs;ecuturam in altera opero&longs;iori parte longè maiorem commo­<lb/>ditatem. Vnde autem tum hæc, tum illud pendeat non dicit Ari&longs;tote­<lb/>les, quia ex antecedentibus facile intellectum. Tignus enim tran&longs;­<lb/>uer&longs;us e&longs;t vectis, cuius <expan abbr="fulcimentũ">fulcimentum</expan> e&longs;t in axiculo trabis, <expan abbr="atq;">atque</expan> in motu <lb/>immer&longs;ionis pondus <expan abbr="mouendũ">mouendum</expan> e&longs;t in A: mouens vero e&longs;t in B, vel in <lb/>&longs;itula E. Quò igitur pondus in A erit grauius, eò difficilius attol­<lb/>letur, &longs;ic natura grauitatis ferente: & &longs;ic maiore vi opus erit: contrà <lb/>in motu eleuationis, pondus mouendum e&longs;t &longs;itula, mouens e&longs;t in A, <lb/>hic adiutus pondere adiecto natura &longs;ua deor&longs;um vergente, facilius <lb/>tantò deprimet ip&longs;um A: quantò grauius erit G. Et &longs;ic facilius B <lb/>attolletur cum annexa &longs;itula. Po&longs;&longs;et etiam hæc quæ&longs;tio ad libram <lb/>commodißimè referri.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>30. Cur cum duo homines <lb/><expan abbr="cũ">cum</expan> pertica pondus æqua­<lb/>le ferunt, non æqualiter <lb/>premuntur.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur cum duo homines <lb/>cum pertica, vel aliquo &longs;i­<lb/>mili pondus æquale <expan abbr="ferũt">ferunt</expan>, <lb/>non &longs;imiliter premuntur, &longs;i <lb/>ip&longs;um non è medio &longs;u&longs;pen­<lb/>datur: &longs;ed <expan abbr="quãtò">quantò</expan> magis pro­<lb/>pius fuerit ferentibus. An <lb/>quia pertica quidem &longs;ic fe­<lb/>rentium e&longs;t vectis, pondus <lb/>verò hypomochlium: Etè <lb/>baiulis qui ponderi pro­<lb/>pior e&longs;t, e&longs;t mobile: alter <lb/>verò e&longs;t mouens, qui quò <lb/>plus di&longs;titerit à <expan abbr="põdere">pondere</expan>, eò
<pb pagenum="191"/><gap/><lb/>facilius mouet, & alterum <lb/>deor&longs;um premit magis <expan abbr="tã-quam">tan­<lb/>quam</expan> pondus adiectum, <lb/>quod e&longs;t hypomochlium <lb/>renitatur. At po&longs;ito ponde­<lb/>re in medio, non alter alteri <lb/>maiori e&longs;t ponderi, nec ma­<lb/>gis mouet: &longs;ed <expan abbr="vterq;">vterque</expan> vtri­<lb/>que &longs;imile pondus adfert.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr cum duo.] <emph type="italics"/>Fu&longs;tes teretes nodis carentes ad onera go&longs;tan­<lb/>da apti palangæ à Nonio & Varrone dicuntur, vel phalangæ <lb/>à Plinio vnde phalangarÿ Baiuli ÿs <expan abbr="vt&etilde;tes">vtentes</expan>, qui ex numero tetrapho­<lb/>ri, & hexaphori dicti &longs;unt. Quærit igitur hîc Ari&longs;toteles. cur è duo­<lb/>bus pondus aliquod phalanga ferentibus, quò ponderi propinquior e&longs;t <lb/>alter, eò magis remotiori prematur. Cuius quæ&longs;tionis <expan abbr="causã">causam</expan> refert ad <lb/><expan abbr="vect&etilde;">vectem</expan>, cuius <expan abbr="hypomochliũ">hypomochlium</expan> &longs;it in <expan abbr="põdere">pondere</expan> ge&longs;tato, vel <expan abbr="&longs;u&longs;t&etilde;to">&longs;u&longs;tento</expan>. Siue enim <lb/>homines <expan abbr="ambul&etilde;t">ambulent</expan>: &longs;iue &longs;tent, nihil intere&longs;t, vtpotè quod grauitate &longs;ua <lb/>ne attollatur, ob &longs;i&longs;tat. <expan abbr="Mouendũ">Mouendum</expan> e&longs;t in &longs;u&longs;tinente propinquiore: <expan abbr="mou&etilde;s">mouens</expan> <lb/>e&longs;t in remotiore. Et cur ita potius, cau&longs;am adfert, quia vectis pars ma­<lb/>ior facilius mouetur, id e&longs;t vt interpretor &longs;u&longs;tinetur, vel eleuatur: &longs;ic­<lb/>que pars minor magis deprimetur, depre&longs;&longs;a <expan abbr="ferent&etilde;">ferentem</expan> vel <expan abbr="&longs;u&longs;tinent&etilde;">&longs;u&longs;tinentem</expan> ma­<lb/>gis premet, vt hîc moueri <expan abbr="nõ">non</expan> &longs;it aliud: <expan abbr="quã">quam</expan> deor&longs;um premi: & mouere <lb/>&longs;u&longs;tinere, vel attollere. Alioqui &longs;i mouere aliter &longs;umatur, ratio qua <lb/>vectis longior facilius mouet, e&longs;t in motione circa <expan abbr="hypomochliũ">hypomochlium</expan> am­<lb/>bitus magnitudo, ob <expan abbr="quã">quam</expan> quia motio redditur tardior, & ideò leuior <lb/><expan abbr="etiã">etiam</expan> e&longs;t, hîc conuenire <expan abbr="nõ">non</expan> pote&longs;t. Neque enim in hac vectis <expan abbr="circũduci-tur">circunduci­<lb/>tur</expan>: &longs;ed premit <expan abbr="tantũ">tantum</expan> &longs;u&longs;tinentes, vt quid graue. Sed & aliter quam <lb/>Ari&longs;toteles re&longs;ponderi pote&longs;t, ita accepto motu, &longs;i dicamus <expan abbr="alterutrũ">alterutrum</expan> <lb/>e &longs;u&longs;tinentibus e&longs;&longs;e <expan abbr="fulcimentũ">fulcimentum</expan>, & alterum e&longs;&longs;e <expan abbr="potentiã">potentiam</expan>: mobile <expan abbr="aut&etilde;">autem</expan> <lb/>e&longs;&longs;e id, quod inter <expan abbr="vtrumq;">vtrumque</expan> appendet. Nam <expan abbr="verũ">verum</expan> e&longs;t quod è tertio co­<lb/>roll. prop. 2. tractatus de vecte apud <expan abbr="Gvidũ">Gvidum</expan> Vbaldum demon&longs;trate <lb/>deducitur. Nempe &longs;i in extremis vectis duæ &longs;int potentiæ, inter quas <lb/>pondus &longs;it &longs;u&longs;pen&longs;um. Erit vna ad alteram vt interualla inter po­<lb/>tentias, & pondus reciprocè. Vt &longs;i &longs;it vectis A B, poten­<lb/>tiæ A & B, pondus &longs;u&longs;tentum C E, erit A ad B. vt B C <lb/>ad A C. Sit igitur vt B C &longs;it minor: quam A C. Ergo A.<emph.end type="italics"/>
<pb pagenum="192"/><emph type="italics"/>potentia<emph.end type="italics"/><lb/>
<figure id="fig74"></figure><lb/><emph type="italics"/>erit mi­<lb/>nor: <expan abbr="quã">quam</expan> <lb/>B, id e&longs;t <lb/>potentia <lb/>minorin <lb/>A &longs;ic di <lb/>&longs;tante à <lb/>C &longs;ufficiet &longs;u&longs;tinendo ponderi. Po&longs;itis igitur A & B potentÿs <lb/>æqualibus, A facilius &longs;u&longs;tinebit, & quidem tantò: quantò A <gap/>­<lb/>&longs;tabit magis ab C. Sit præterea vt C &longs;it in medio vectis A B. <lb/>quia B C erit æqualis ip&longs;i A C potentiæ æquales A & B e&longs;&longs;e <lb/>debent, vt æquè pondus idem &longs;u&longs;tineant. Ob id rectè dictum e&longs;t illud <lb/>ab Ouidio,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Non benè inæquales veniunt ad aratra Iuuenci:</s>
</p>
<p type="main">
<s>Si qua velis aptè nubere, nube pari.</s>
</p>
<p type="main">
<s><emph type="italics"/>Si enim inæquales tunc grandior minorem premit magis: ob id periti <lb/>agricolæ, &longs;i quando alterius iugatornm laborem leuare velint, lorum <lb/>longius efficientes ad ip&longs;um religant.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Hanc rur&longs;us quæ&longs;tionem aliter &longs;oluere videtur Cardanus, nimi­<lb/>rum quod E pondus alteri ferentium propius exi&longs;tens ip&longs;um premit <lb/>magis, quia de&longs;cendat magis re&longs;pectu B: quam A alterius feren­<lb/>tium. Nam cum de&longs;cendat &longs;ecundumrectam C E, &longs;i intelligamus à <lb/>puncto B ad Erectam ductam, <lb/>& ab A ad E item rectam,<emph.end type="italics"/><lb/>
<figure id="fig75"></figure><lb/><emph type="italics"/>con&longs;titutum erit triangulum A <lb/>B E, cuius quia A E maior <lb/>e&longs;t: quam E B, per prop. 46. <lb/>& 47. lib. 1. E&longs;t enim A di&longs;tans <lb/>magis ab C quam B ex hypo­<lb/>the&longs;i: erit angulus B maior: quam A prop. 18. lib. 1. Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. Igitur E plus grauat B: <lb/>quam A &longs;eu ex cau&longs;a, quod magis premat: &longs;eu ex effectu, quod ma­<lb/>gis de&longs;cenderit.<emph.end type="italics"/></s>
</p>
<pb pagenum="193"/>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>31. Cur qui &longs;urgunt, &longs;ic &longs;ur­<lb/>gant.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur omnes qui &longs;urgunt <lb/><expan abbr="con&longs;titu&etilde;tes">con&longs;tituentes</expan> angulum acu­<lb/>tum ex femore & tibia, <expan abbr="tũ">tum</expan> <lb/>ex thorace & femore &longs;ur­<lb/>gant: &longs;in minus, &longs;urgere <expan abbr="ne-queũt">ne­<lb/>queunt</expan>. An quia, quod &ecedil;qua <lb/>le e&longs;t, quietis vbique cau&longs;a <lb/>e&longs;t. Angulus autem rectus <lb/>e&longs;t æqualitatis, & &longs;tatum <lb/>facit. Ideò etiam fertur ad <lb/>angulos &longs;imiles, <expan abbr="cũ">cum</expan> &longs;uperfi­<lb/>cie terræ. Sic enim erit ip&longs;i <lb/>plano ad rectos: vel quod <lb/>&longs;urgens fit rectus. Nece&longs;&longs;e <lb/>e&longs;t autem &longs;tantem e&longs;&longs;e per­<lb/>pendicularem terræ. Si igi­<lb/>tur debet e&longs;&longs;e ad rectos. <lb/>hoc e&longs;t capur habere è di­<lb/>recto pedum. Etiam quum <lb/>&longs;urgit fieri oportet. Quan­<lb/>do igitur &longs;edet caput habet <lb/>ad pedes parallelum, & ne­<lb/>quaquam in vna recta. Sit <lb/>caput <foreign lang="greek">a,</foreign> thorax <foreign lang="greek">a b,</foreign> fe­<lb/>mut <foreign lang="greek"><gap/> g,</foreign> tibiæ <foreign lang="greek">g d,</foreign> fiat <lb/>verò thorax <foreign lang="greek">a <gap/></foreign> ad rectos <lb/>femori, & femur tibiæ &longs;ic <lb/>&longs;edenti. Itaque &longs;ic &longs;e ha­<lb/>bentem impo&longs;&longs;ibile e&longs;t &longs;ur­<lb/>gere. At nece&longs;&longs;e e&longs;t incli­<lb/>nare tibiam, & con&longs;titue­<lb/>re pedes &longs;ub capite: hoc <lb/>autem erit &longs;i <foreign lang="greek">g d</foreign> fiat <foreign lang="greek">g</foreign>
<pb pagenum="194"/><gap/><lb/><foreign lang="greek">z,</foreign> tunc &longs;imul &longs;urgere con­<lb/>tinget. Atque habere tum <lb/>caput, tum pedes in eadem <lb/>recta: <foreign lang="greek">g z</foreign> vero cum <foreign lang="greek"><gap/> g</foreign><lb/>angulum <expan abbr="acutũ">acutum</expan> con&longs;tituet</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr qui &longs;urgunt.] <emph type="italics"/>Surrectio e&longs;t motio, quia homo è iacente <lb/>vel &longs;edente fit &longs;tans. Quod vt intelligatur &longs;cire oportet attingi <lb/>hîc quatuor figuras, quibus hominis corpus ex certa &longs;ui po&longs;itione fi­<lb/>gurari pote&longs;t. hæ &longs;unt iacere &longs;upinum, iacere pronum, &longs;edere, &longs;tare. <lb/>Iacere &longs;upinum e&longs;t cum &longs;pina animalis terram contingit. Iacere <expan abbr="pro-nũ">pro­<lb/>num</expan> e&longs;t cum humi venter reclinatus e&longs;t. Hæ duæ figuræ quia ad quie­<lb/>tem &longs;omnumque communem comparatæ &longs;unt, pluribus animalibus <lb/>communes e&longs;&longs;e potuerant, &longs;ed pronum ambulare conuenit brutis, qua­<lb/>&longs;i &longs;olùm ad pa&longs;tum à natura in&longs;titutis. Seßio e&longs;t &longs;itus in quo &longs;pina <lb/>cum femore, & femur cum tibia angulum rectum facit. Statio e&longs;t <lb/>&longs;itus in quo &longs;pina femur & tibia in vna recta exi&longs;tentes perpendi­<lb/>culares &longs;unt horizonti. Hæ duæ &longs;oli homini propriæ &longs;unt. quia &longs;olus <lb/>articulos ita à natura &longs;apiente & architectatrice conformatos ha­<lb/>bet, vt &longs;ic eius o&longs;&longs;a di&longs;poni valeant. Solus enim articulum femoris <lb/>& i&longs;chÿ ad anteriora flectit, ip&longs;ius verò genu retror&longs;um reflectit,<emph.end type="italics"/><lb/>
<arrow.to.target n="marg42"></arrow.to.target><lb/><emph type="italics"/>&longs;ine quibus neque tibia & femur cum &longs;pina in <expan abbr="vnã">vnam</expan> rectam adduci <lb/>pote&longs;t, at in belluis vbi femur <expan abbr="cũ">cum</expan> <expan abbr="&longs;pinarectũ">&longs;pinarectum</expan> fecit, tibia <expan abbr="nunquã">nunquam</expan> cum <lb/>femore rectum faciet: nec etiam ip&longs;a ad terram recta erit. quod ta­<lb/>men, vt &longs;eßio &longs;ecura fiat, nece&longs;&longs;um e&longs;t. cum igitur omnia bruta an­<lb/>tror&longs;um po&longs;teriorum crurum flexiones habeant, &longs;olus homo &longs;edet, <lb/>& &longs;tat: & &longs;apienter ita hunc natura fecit, cum hic &longs;olus mentem<emph.end type="italics"/><lb/>
<arrow.to.target n="marg43"></arrow.to.target><lb/><emph type="italics"/>quæ e&longs;t ars artium habiturus erat, id e&longs;t &longs;olus artifex futurus erat. <lb/>Manuum enim, quæ &longs;int <foreign lang="greek">o)/rganon o)rganwn,</foreign> vt vocat no&longs;ter Gale­<lb/>nus actiones in opificÿs, duabus his <expan abbr="tãtum">tantum</expan> egent figuris. Nemo enim <lb/>&longs;upinus aut pronus quicquamagit. Ideo etiam, vt id obiter dicam, <lb/>qui opinantur ob id rectum &longs;tare hominem, vt cælum promptè &longs;u&longs;pi­<lb/>ciat, dicereque poßit.<emph.end type="italics"/></s>
</p>
<p type="margin">
<s><margin.target id="marg42"></margin.target>Cap. 1. & 3. <lb/>lib. 3. de v&longs;u <lb/>part.</s>
</p>
<p type="margin">
<s><margin.target id="marg43"></margin.target>Cap. 2. lib. 1. <lb/>de v&longs;u part.</s>
</p>
<p type="main">
<s>Re&longs;picio aduer&longs;us Olympum fronte intrepida.</s>
</p>
<pb pagenum="195"/>
<p type="main">
<s><emph type="italics"/>Illi numquam viderunt pi&longs;cem <expan abbr="dictũ">dictum</expan><emph.end type="italics"/> <foreign lang="greek">*ou<gap/>ano/skopon,</foreign> <emph type="italics"/>id e&longs;t cæli &longs;pe­<lb/>culatorem. Hic namque vel inuitus cælum &longs;emper intuetur: homo <lb/>autem ni&longs;i collum reflectat retror&longs;um, cælum non videt. Atqui hæc <lb/>reflexio communis e&longs;t etiam a&longs;inis, vt omittam aues, quæ longo collo <lb/>&longs;unt præditæ, quibus non &longs;olum facilè e&longs;t &longs;ur&longs;um: &longs;ed & quoquouer­<lb/>&longs;um, &longs;i voluerint a&longs;picere. Et <expan abbr="quãdo">quando</expan> po&longs;t <expan abbr="Platon&etilde;">Platonem</expan>, Ouidius dixit illud,<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Pronaque cum &longs;pectant animalia cætera terram,</s>
</p>
<p type="main">
<s>Os homini &longs;ublime dedit, cælum que videre</s>
</p>
<p type="main">
<s>Iu&longs;&longs;it, & erectos ad &longs;idera tollere vultus.</s>
</p>
<p type="main">
<s><emph type="italics"/>Non &longs;entit cum Platone & fallitur: &longs;i cœlum videre intelligit, cum <lb/>quis &longs;upinus &longs;eip&longs;um reclinarit o&longs;citans: non autem potius cum quis <lb/>naturam cœle&longs;tium mente con&longs;iderat, quod e&longs;t homini, vt erectum <lb/>e&longs;&longs;e po&longs;&longs;e, proprium: pronum vero e&longs;&longs;e po&longs;&longs;e, commune e&longs;t illi, cum <lb/>belluis, quæ non &longs;olumiacentes: &longs;ed & ambulantes &longs;ic &longs;unt. Ver&longs;us <lb/>enim humum omnes ventrem conuer&longs;um habent, aliæ magis, aliæ <lb/>minus modo &longs;imillimo infantium, qui manibus pedibu&longs;que innixi, &longs;e <lb/>mouent. Vnus cercopithecus proxime accedit ad hominis erectum <lb/>&longs;tatum, diutiu&longs;que &longs;tare vtcunque pote&longs;t, & manum habet: &longs;ed dißi­<lb/>milem, vt in qua pollex non e&longs;t reliquis digitis oppo&longs;itus, nec <foreign lang="greek">an)ti/­<lb/>xeir,</foreign> proptereà dicitur à Galeno e&longs;&longs;e ridicula hominis imitatio. ab hoc <lb/>enim &longs;itu pollex<emph.end type="italics"/> <foreign lang="greek">i)/son dun/atai tn_| o(/lh xeiei/.</foreign></s>
</p>
<p type="main">
<s>Cur omnes qui &longs;urgunt.] <emph type="italics"/>Quærit hîc Ari&longs;toteles, cur &longs;ur­<lb/>gens de &longs;eßione nece&longs;&longs;ario con&longs;tituat angu­<lb/>lum acutum ex tibia cum femore, vel ex <lb/>thorace, &longs;eu &longs;pina cum femore, vt in &longs;e&longs;-<emph.end type="italics"/><lb/>
<figure id="fig76"></figure><lb/><emph type="italics"/>&longs;ione &longs;it thorax A B, femur B C, tibia C <lb/>D, anguli A B C & B C D recti. Ex hoc <lb/>&longs;ituad &longs;urgendum innitens nece&longs;&longs;e habet addu­<lb/>cere C D ad C E, vel A B ad B F, vt è <lb/>rectis A B C, B C D angulis, fiant acuti <lb/>F B C, B C E.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia quod æquale.] <emph type="italics"/>Quæ&longs;tionem propo&longs;itam &longs;oluit du­<lb/>pliciter. Primo modo è cau&longs;a quietis in &longs;e&longs;sione <expan abbr="per&longs;euerãte">per&longs;euerante</expan>, quandiu <lb/>recti anguli con&longs;eruantur. hic erit &longs;yllogi&longs;mus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cau&longs;a quietis per&longs;euerante fieri non pote&longs;t &longs;urrectio, vt quæ mo­<lb/>tio &longs;it.<emph.end type="italics"/></s>
</p>
<pb pagenum="196"/>
<p type="main">
<s><emph type="italics"/>Angulorum rectitudo e&longs;t cau&longs;a quietis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergò quandiu per&longs;euerauerit, &longs;urrectio non fiet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>A&longs;&longs;umptionis loco po&longs;ita e&longs;t eius confirmatio ab axiomate, & &longs;ic <lb/>concludetur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Æqualitas e&longs;t vbique cau&longs;a quietis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Angulus rectus e&longs;t æqualitas, quia &longs;ibi & alÿs omnibus re­<lb/>ctis rectilineis e&longs;t æqualis. quod e&longs;t axioma 10. lib. 1. In eo <lb/>&longs;cilicet rectæ ip&longs;um con&longs;tituentes &longs;ibi pariter incumbunt, <lb/>&longs;ibique inuicem perpendiculares &longs;unt. ex def. 10. lib. 1.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergò angulus rectus e&longs;t cau&longs;a quietis.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cæterum axioma hoc de æqualitate cau&longs;a quietis diligenter animad­<lb/>uertendum e&longs;t in tota <expan abbr="rerũ">rerum</expan> natura. Et vt particulatim expendamus. <lb/>videamus, vt omnia quie&longs;cant ad rectos angulos. Primum elementa <lb/>omnia in planum &longs;ui loci rectà &longs;ur&longs;um vel deor&longs;am feruntur, & in <lb/>medio collocata, ni&longs;i aliena vi dimoueantur quie&longs;cunt. Itaque in­<lb/>&longs;i&longs;tunt medio ad angulos rectos. Ob id terra cubico octonûm recto­<lb/>rum &longs;olido à Pythagoreis & à Platone e&longs;t comparata. Deinde arbo­<lb/>res & plantarum omne genus rectà <expan abbr="in&longs;i&longs;tũt">in&longs;i&longs;tunt</expan> plano. Durabile in ædi­<lb/>ficÿs nihil e&longs;t, ni&longs;i rectà in&longs;i&longs;tat. Po&longs;tremò hominis quies, &longs;eu iaceat <lb/>humi, &longs;eu &longs;edeat, &longs;eu &longs;tet, fit per rectos angulos. Iacet enim humi, <lb/>aut in lecto decumbit cum totum quidem corpus plano horizontis <lb/>parallelum e&longs;t, aut eidem congruit: &longs;ed tunc omnes craßitudinis di­<lb/>men&longs;iones plano in&longs;i&longs;tunt ad rectos, vt de pedibus erectis videre e&longs;t. <lb/>Sedet quis in Hemicyclo? tibÿs cum femoribus & femoribus rur&longs;us <lb/>cum &longs;pina dor&longs;i rectos angulos facit. Hinc collige vt vnus calceus <lb/>non omni pedi conuenit: &longs;ic nec vnum &longs;edile omni homini ad &longs;eßio­<lb/>nem commodum e&longs;t, maiori maius requiritur minori minus. Stat au­<lb/>tem? cum omnibus rectis à quibus tangitur in ip&longs;o plano rectos etiam <lb/>angulos facit. Ergo quies & &longs;tatus per angulos rectos fiunt.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Vel quod &longs;urgens.] <emph type="italics"/>Secundus modus e&longs;t &longs;olutionis quæ&longs;tionis <lb/>propo&longs;itæ per modum mutationis, quæ fit dum quis è <expan abbr="&longs;ed&etilde;te">&longs;edente</expan> fit &longs;tans, <lb/>quæ &longs;urrectio dicitur. Hæc igitur, &longs;i quis &longs;tare debeat facere debet, <lb/>vt &longs;it particeps di&longs;po&longs;itionis, quæ in &longs;tante e&longs;t. At di&longs;po&longs;itio quæ in <lb/>&longs;tante e&longs;t, e&longs;t &longs;itus pedum & capitis, &longs;pinæque in eadem recta. Huius <lb/>&longs;eßio non e&longs;t particeps. quia pedes & &longs;pina &longs;unt in Lineis parallelis: <lb/>contra adductio tibiæ, ita vt angulum acutum cum femore con&longs;ti-<emph.end type="italics"/>
<pb pagenum="197"/><emph type="italics"/>tuat: vel thoracis vt cum <lb/>femore, quia pedes rectà<emph.end type="italics"/><lb/>
<figure id="fig77"></figure><lb/><emph type="italics"/>&longs;ub capite, aut &longs;altem re­<lb/>ctius: quam ante collocat, <lb/>&longs;tationis magis e&longs;t parti­<lb/>ceps. Ad &longs;urrectionem igi­<lb/>tur nece&longs;&longs;arij &longs;unt anguli <lb/>acuti facti vel à thorace <lb/>cum femoribus, vel à fe­<lb/>moribus cum tibijs, vt diagrammate<emph.end type="italics"/> <foreign lang="greek">a b g d</foreign> <emph type="italics"/>pro &longs;edente, &<emph.end type="italics"/> <foreign lang="greek">e b <lb/>g z</foreign> <emph type="italics"/>pro &longs;urgente declaratur.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Et hinc patet quod &longs;i thorace cum femore, & femore cum tibia <lb/>&longs;imul anguli acuti fiant, facilius &longs;urgetur: & rur&longs;us quantò an­<lb/>guli illi erunt acutiores: tantò facilius &longs;urgetur: &longs;icque &longs;urgunt <lb/>imbecilli, & conuale&longs;centes. Porrò &longs;urrectio è &longs;edente ad &longs;tandum <lb/>declarata e&longs;t angulis acutis indigere: &longs;urrectionem è iacente etiam <lb/>indigere clarum e&longs;t. Is enim qui iace<gap/>, vt &longs;urgat, & &longs;tet, quatuor <lb/>acutos efficit, utroque brachio & latere: thorace & cruribus: fe­<lb/>moribus & tibiis, vt ia­<lb/>ceat A B G D. vt &longs;ur-<emph.end type="italics"/><lb/>
<figure id="fig78"></figure><lb/><emph type="italics"/>gat A B thorax bra­<lb/>chiorum in acutos con­<lb/>formatorum adminiculo <lb/>adducetur ad E B: &longs;ic­<lb/>que E B G erit acutus <lb/>ex thorace & femoribus, <lb/>& G D tibia adducetur in G F: &longs;icque erit acutus B G F.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Cæterum &longs;eßio, de qua hîc Aristoteles, e&longs;t propriè dicta, & hanc <lb/>Galenus cum &longs;ecuritate e&longs;&longs;e dixit. Et ea maximè vtuntur, qui &longs;e­<lb/>dentarias artes exercent. At tamen &longs;eßio latè &longs;umpta, fit ad angu­<lb/>los acutos, vt cum &longs;ella humilior e&longs;t tibÿs &longs;edentis, & ad obtu&longs;os <lb/>cum altior e&longs;t. Vnde experientia notum e&longs;t hominem quantò altius <lb/>&longs;edet, tantò facilius &longs;urgere, quod tamen videtur repugnare prædi­<lb/>ctis, cum obtu&longs;i anguli longius ab &longs;int, etiam quam recti, ab acutis.<emph.end type="italics"/>
<pb pagenum="198"/>
<arrow.to.target n="table2"></arrow.to.target></s>
</p>
<table>
<table.target id="table2"></table.target>
<row><cell></cell><cell><emph type="italics"/>Altiore K<emph.end type="italics"/></cell></row>
<row><cell><emph type="italics"/>vt &longs;it thorax A B &longs;edens &longs;uper &longs;ella<emph.end type="italics"/></cell><cell><emph type="italics"/>Æquali L<emph.end type="italics"/></cell></row>
<row><cell><emph type="italics"/>tibÿs.<emph.end type="italics"/></cell><cell><emph type="italics"/>Humiliore M<emph.end type="italics"/></cell></row></table>
<p type="main">
<s><emph type="italics"/>Dico quod ex<emph.end type="italics"/><lb/>
<figure id="fig79"></figure><lb/><emph type="italics"/>K facilius &longs;ur­<lb/>get: quam ex L: <lb/>quamque ex M. <lb/>Ratio e&longs;t, quia <lb/>A B &longs;uper K <lb/>magis e&longs;t parti­<lb/>ceps &longs;tationis: <lb/>quam &longs;uper L. <lb/>Et &longs;uper L quam <lb/>quam &longs;uper M. <lb/>Vt enim &longs;urrectionis initium fiat per angulos acutos: Me­<lb/>dium tamen perducens ad terminum ad quem, qui e&longs;t &longs;itum <lb/>e&longs;&longs;e in vna recta vt A B G D, tran&longs;it per minus acutos <lb/>ad rectum, & tandem ad obtu&longs;os, & obtu&longs;is obtu&longs;iores: quou&longs;que <lb/>ad vnam rectam peruentum &longs;it, in qua e&longs;t &longs;tatio vt e&longs;t A B G D <lb/>relicta &longs;ella K, vel L, vel M. Sed præter hæc ob&longs;eruatione di­<lb/>gnum e&longs;t, quod in ambulatione progre&longs;&longs;uque no&longs;tro femora cum ti­<lb/>bijs, & thoracem cum femoribus non omnino in rectam: &longs;ed in an­<lb/>gulos obtu&longs;ißimos: tum crura inter &longs;e in acutum angulum, qui e&longs;t <lb/>vertex trianguli I&longs;o&longs;celis conformamus. Altero &longs;cilicet pedum fir­<lb/>mato in &longs;olum, altero celeriter circumlato. vt cum P Ramo aduer­<lb/>&longs;us philo&longs;ophos illos, &longs;i diis placet, qui Platonicis alis de&longs;tituti, philo­<lb/>&longs;ophari aggrediuntur, concludamus, quod quie&longs;cimus, quod &longs;edemus, <lb/>quod &longs;urgimus, quod &longs;tamus, quod ambulamus, quod currimus, geo­<lb/>metriæ v&longs;um e&longs;&longs;e. Sed & addemus ex nostro Galeno, id quoque ve­<lb/>rum e&longs;&longs;e de brutis omnibus, quorum pedes in&longs;i&longs;tunt terræ ad rectos <lb/>angulos, <expan abbr="&longs;pinã">&longs;pinam</expan> pedibus tanquam columnis ad rectos etiam &longs;uperemi­<lb/>nere. Hinc cau&longs;am collige, cur &longs;int nonnulla ex his tam apta ferendis <lb/>&longs;arcinis & oneribus. Hinc quoque, &longs;i vis, collige cau&longs;am, cur baiuli <lb/>Pari&longs;ien&longs;es onera tanta &longs;uis harpagonibus: alÿ &longs;portulis ferant, nimi­<lb/>rum cum ita componant &longs;pinam, vt antror&longs;um reclinata moles &longs;u-<emph.end type="italics"/>
<pb pagenum="199"/><emph type="italics"/>perna corporis æquiponderet onere & viribus oneri impo&longs;ito hu­<lb/>meris, & ita tamen vt ambo cum femoribus & tibiis, tali&longs;que recta <lb/>in&longs;istant ad terram ad angulos rectos, adiectis ad ea firmitatis &longs;ta­<lb/>tionis gratia, tanquam ba&longs;is & fundamenti, tar&longs;o, pedio, & digitis <lb/>pedum. Sic enim moles &longs;uperni corporis, & onus habent aliquid ad <lb/>perpendiculum inferiorum partium, quod &longs;e &longs;uffulciat. Totu&longs;que ba­<lb/>iulus cum onere, quod gestat instar turbinis, aut coni vertice terræ <lb/>incumbit, ba&longs;i &longs;upereminente. Hinc etiam collige cur baiulis cum <lb/>onere a&longs;cen&longs;us graduum facilior e&longs;t: quam de&longs;cen&longs;us. In a&longs;cen&longs;u enim <lb/>quantum antror&longs;um &longs;e incuruent, nullum inde illis ca&longs;us periculum: <lb/>at in de&longs;cen&longs;iu vel exigua illis curuatura periculum adfert, ex quo <lb/><expan abbr="etiãrarò">etiarrarò</expan> videas, ni&longs;i ebiberint plus paulò, baiulos <expan abbr="cũ">cum</expan> onere de&longs;cendere, <lb/>a&longs;cendere autem, quoties opus e&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>32. Cur commotum faci­<lb/>lius moueatur, <expan abbr="quã">quam</expan> quie&longs;­<lb/>cens.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur commotum facilius <lb/>moueatur: quam <expan abbr="quie&longs;c&etilde;s">quie&longs;cens</expan>, <lb/>velut plau&longs;tra commota ci­<lb/>tius agitant: quam <expan abbr="incipi&etilde;-tia">incipien­<lb/>tia</expan> moueri. An quia quod <lb/>mouetur <expan abbr="põdus">pondus</expan> in contra­<lb/>rium mouere <expan abbr="difficillimũ">difficillimum</expan>. <lb/>Aufertur enim aliquid de <lb/>potentia motoris, licet ip&longs;e <lb/>multò fuerit velocior. Ne­<lb/>ce&longs;&longs;e e&longs;t enim <expan abbr="impul&longs;ion&etilde;">impul&longs;ionem</expan> <lb/>eius, quod repellitur, fieri <lb/>tardiorem. Deinde verò &longs;i <lb/>quieuerit. Quie&longs;cens enim <lb/>re&longs;i&longs;tit. Quod verò motum <lb/>e&longs;t, eò quò impellitur, &longs;imi­<lb/>le quid impellenti facit, ac <lb/>&longs;i quis vim & celeritatem <lb/>motoris augeret, quod etiam ab illo pateretur. hoc ip&longs;um <lb/>facitid, quod in via commotum e&longs;t.</s>
</p>
<pb pagenum="200"/>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr commotum.] <emph type="italics"/>Commotum hîc ita capi debet, vt eò, quò <lb/>moueatur, impellatur: non contra, quod ex re&longs;pon&longs;ione colligere <lb/>facilè erit. Quæ&longs;tio igitur e&longs;t, cur commotum facilius moueatur: <lb/>quam quie&longs;cens. quæ illu&longs;tratur exemplo curruum, quos iam commo­<lb/>tos facilius e&longs;t continuare in motu, quam quie&longs;centibus motionis ini­<lb/>tium dare. Illu&longs;trari etiam po&longs;&longs;et exemplo nauium.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An quia quod mouetur.] <emph type="italics"/>Re&longs;pon&longs;io ad quæ&longs;tionem &longs;ic con­<lb/>cludi pote&longs;t.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Motoris vim & celeritatem augens pondus, facilius impellitur: <lb/>contrà diminuens tardius.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Pondus motum eò, quò impellitur, motoris vim & celerita­<lb/>tem auget, & &longs;imile quid &longs;uo impul&longs;ori iam facit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Contrà quie&longs;cens, quia aliò nititur, & motu occulto in contra­<lb/>rium: quam quò impellitur tendit, diminuit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Commotum igitur facilius mouetur: quam quie&longs;cens.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Quod autem quie&longs;cens vim motoris diminuat, patet. quia &longs;i &longs;ineretur <lb/>nec impelleretur, exempli gratia, &longs;ur&longs;um, vel lateraliter, natura &longs;ua <lb/>&longs;ublato impedimento rectà deor&longs;um ferretur. Ergò qua vieò moue­<lb/>retur, eadem re&longs;i&longs;tit, ne &longs;ur&longs;um vellateraliter impellatur. Re&longs;istere <lb/>autem motori, diminuere e&longs;t eius vim in mouendo. Imò vera e&longs;t illa <lb/>propo&longs;itio. Ab æquali aut minore vi quam &longs;it impedimentum non <lb/>fit motus. Sit enim A B C D <lb/>quod re&longs;istat per decem ne &longs;ur&longs;um<emph.end type="italics"/><lb/>
<figure id="fig80"></figure><lb/><emph type="italics"/>trahatur. Dico quod &longs;ur&longs;um non <lb/>trahetur, neque per 10. neque per 9. <lb/>&c. Nam &longs;ub&longs;tracto impedimento, <lb/>quod impedit ne A deor&longs;um fera­<lb/>tur, eo ferretur vt 10. Quod &longs;i eo­<lb/>dem tempore &longs;ur&longs;um trahatur à vi <lb/>quæ &longs;it etiam vt 10. tunc tantum <lb/>mouebitur deor&longs;um: quantum &longs;ur­<lb/>&longs;um, quie&longs;cet igitur. Si verò &longs;ur&longs;um trahatur à vi minore, vt nouem, <lb/>quia à maiore vi deor&longs;um fertur, non &longs;ur&longs;um: &longs;ed deor&longs;um &longs;impliciter<emph.end type="italics"/>
<pb pagenum="201"/><emph type="italics"/>feretur. Præterea alia etiam demon&longs;tratione quæ&longs;tio ab Aristotele <lb/>propo&longs;ita concludi pote&longs;t. &longs;ic,<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Omne duobus motibus ad diuer&longs;a tendentibus commotum, tan­<lb/>tò minus vno mouetur: quantò magis altero. quia vis quæ <lb/>aliquò mouet plus: plus etiam ob&longs;i&longs;tit, & &longs;ic retardat & in­<lb/>fringit vim, quæ aliò mouet.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Sed currus exempli gratia iam commotus, vel incipiens <lb/>moueri, mouetur tum motu naturali deor&longs;um, tum vio­<lb/>lento ad latus.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Ergo quantò magis hoc mouebitur, minus mouebitur illo: & <lb/>contra.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><emph type="italics"/>Atqui iam commotus plus mouetur violento. Tunc igitur minus <lb/>naturali: contra incipiens moueri, plus naturali. Tunc igitur minus <lb/>violento. Ergo commotus facilius mouebitur: quam quie&longs;cens vel <lb/>incipiens moueri.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>33. Cur proiecta lata ce&longs;­<lb/>&longs;ant.</s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>Cur proiecta lata ce&longs;&longs;ant. <lb/>An vis impellens de&longs;init, <lb/>vel propter <expan abbr="reuul&longs;ion&etilde;">reuul&longs;ionem</expan>, vel <lb/>propter inclinationem rei <lb/>proiect&ecedil;, &longs;i vim proiicientis <lb/>&longs;uperauerit. An ab&longs;urdum <lb/>de eo dubitare e&longs;t eum, qui <lb/>principium relinquit.</s>
</p>
<p type="head">
<s>COMMENTARIVS.</s>
</p>
<p type="main">
<s>Cvr proiecta.] <emph type="italics"/>Proiecta dicuntur, quæ manu, funda, arcu, vel <lb/>aliò in&longs;trumento &longs;ur&longs;um, vel ad latus, vel etiam deor&longs;um vio­<lb/>lenter feruntur. Quæritur igitur cur proiecta tandem moueri de&longs;i­<lb/>nant. Hîc re&longs;pondet, quia &longs;ublata cau&longs;a ce&longs;&longs;at effectus. Cau&longs;a autem <lb/>lationis in proiectis e&longs;t vis impellens à primo motore impre&longs;&longs;a. Hanc <lb/>Simplicius Ari&longs;totelis interpres<emph.end type="italics"/> <foreign lang="greek">)<gap/>pipo/laian</foreign> <emph type="italics"/>qua&longs;i diceres &longs;uperfi-<emph.end type="italics"/>
<pb pagenum="202"/><emph type="italics"/>ciariam appellat comment. in lib. 7. Phy&longs;. Hæc autem tollitur autà <lb/>re&longs;i&longs;tentia medÿ per quod fertur. Corpus enim e&longs;t quod in &longs;uo &longs;eloco <lb/>con&longs;eruare nititur: aut à naturali grauitate aliò, quàm quò proÿciun­<lb/>tur tendente. Vt enim calor & frigus in &longs;ubiectis non proprÿs ali­<lb/>quandiu manent: ita & violenti motus impreßio illa. Et vt ferrum <lb/>quod diutius fuit in igne, diutius etiam calorem retinet: &longs;ic ma­<lb/>chinis longioribus emi&longs;&longs;a, quia vim illam magis impre&longs;&longs;am ha­<lb/>bent, longius feruntur. quod certo indicio e&longs;t vim à motore primo ali­<lb/>quam in proiectis relinqui, quæ ad aliquod tempus manet. At tan­<lb/>dem ob cau&longs;as prædictas, perit. Et &longs;ic quæque ad naturam redeunt <lb/>&longs;uam. Nec &longs;i millies lapidem &longs;ur&longs;um proieceris: tamen vnquam &longs;ur­<lb/>&longs;um ferri a&longs;&longs;ue&longs;cet. Hæc enim quæ ine&longs;t à natura grauitas, ne vis &longs;ur­<lb/>&longs;um mouens perfectè imprimatur, impedit.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>An ab&longs;urdum.] <emph type="italics"/>Altera cau&longs;a videtur huc adferri ce&longs;&longs;ationis <lb/>in proiectis, aut &longs;ublationis virtutis impellentis impre&longs;&longs;æ. Si per prin­<lb/>cipium intelligamus motorem, qui motus principium dedit, id e&longs;t pri­<lb/>mum motorem. Hic enim vbi emi&longs;it, exempli gratia, telum, &longs;epara­<lb/>tur ab eo, nec amplius mouet: nihilominus tamen.<emph.end type="italics"/></s>
</p>
<p type="main">
<s>Hoc volat emi&longs;&longs;um &longs;emel irreuo cabile telum: <lb/><emph type="italics"/>Sed obid tandem de&longs;init à motione, quia licet vis aliqua impre&longs;&longs;a &longs;u­<lb/>per &longs;it, quæ moueat adhuc, à primo motore non continuatur, ideóque <lb/>perit. Ab&longs;urdum e&longs;t igitur dubitare de cau&longs;a ce&longs;&longs;ationis proiecti cum <lb/>ip&longs;um &longs;uus motor de&longs;erat. Cæterum &longs;agitta & ha&longs;ta & quicquid <lb/>aliud tale e&longs;t ten&longs;a coria facilius, quam laxa penetrat quod illa qui­<lb/>dem re&longs;i&longs;tunt: hæc autem cedentia paulatim eorum quæ incidunt, <lb/>violentiam exoluunt, Gal. cap. 8. lib. 2. de v&longs;. part.<emph.end type="italics"/></s>
</p>
<p type="main">
<s><gap/></s>
</p>
<p type="main">
<s>34. Cur quidpiam non &longs;ua <lb/>latione fertur non con­<lb/>&longs;equente impul&longs;ore: &longs;ed <lb/>dimittente.</s>
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<s><gap/></s>
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<s>Quare quidpiam non <lb/>propria latione fertur, cum <lb/>impul&longs;or non con&longs;equa­<lb/>tur: &longs;ed dimittat. An quia
<pb pagenum="203"/><gap/><lb/>quid tale facit, vt alterum <lb/>impellat, & hoc alterum: <lb/>ce&longs;&longs;at verò <expan abbr="quãdo">quando</expan> non am­<lb/>plius pote&longs;t facere primum <lb/>impellens, vt id quod fer­<lb/>tur, impellat. Et quando <lb/>grauitas eius quod fertur <lb/>deor&longs;um ruit magis: quam <lb/>antror&longs;um impul&longs;oris vis <lb/>po&longs;&longs;it impellere.</s>
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<s>COMMENTARIVS.</s>
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<s>Qvare quidpiam.] <emph type="italics"/>Cum omne proiectum graue quid &longs;it, ideó­<lb/>que natura tendens rectà deor&longs;um. Quærit rur&longs;us Ari&longs;toteles: <lb/>&longs;ed expreßius quam antè. Cur cum proiector non con&longs;equatur proie­<lb/>ctum, ip&longs;um non feratur potius &longs;uo motu naturali: quam violento. <lb/>Cui vt re&longs;pondeat ad cau&longs;am præcedentem, vim &longs;cilicet impre&longs;&longs;am <lb/>à primo motore adÿcit medÿ, per quod proÿcitur antiperi&longs;ta&longs;im. Cum <lb/>enim proiectum primo antror&longs;um dimouerit medium vt aërem, hic <lb/>&longs;umma celeritate retrò proiectus, ne vacuum quid (quod abhorret <lb/>natura) relinquatur, conuolat: & &longs;ic deinceps, ita vt quantum aër <lb/>anterior ob re&longs;i&longs;tentiam impediuit, factus po&longs;terior cum concur&longs;u <lb/>violento motum iuuet, vt ce&longs;&longs;are non deberet motus ni&longs;i anterioris <lb/>aëris ob&longs;i&longs;tentiam iuuaret, & augeret maximè grauitas naturalis, <lb/>quibus iunctis: vis tandem impellentis antror&longs;um &longs;uperatur, & eua­<lb/>ne&longs;cit: &longs;icque ce&longs;&longs;at motus violentus, & ni&longs;i aliquod ad&longs;it impedi­<lb/>mentum, incipit naturalis, quo deor&longs;um rectà ruit.<emph.end type="italics"/></s>
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<s><gap/></s>
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<s>35. Cur <expan abbr="neq;">neque</