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DESpecs 2.0 Autumn 2009
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Thu, 02 May 2013 11:14:40 +0200 |
| parents | 22d6a63640c6 |
| children |
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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Monantheuil, Henri de</author> <title>Aristotelis Mechanica</title> <date>1599</date> <place>Paris</place> <translator/> <lang>la</lang> <cvs_file>monan_mecha_035_la_1599.xml</cvs_file> <cvs_version/> <locator>035.xml</locator> </info> <text> <front> <section> <pb xlink:href="035/01/001.jpg" /> <p type="head"> <s id="id.000001">ARISTOTELIS <lb/>MECHANICA <lb/>Græca, emendata, Latina facta, & <lb/>Commentariis illu&longs;trata. <lb/></s> <s id="id.000002">AB <lb/><emph type="italics"/>HENRICO MONANTHOLIO <lb/>Medico, & Mathematicarum artium <lb/>Profe&longs;&longs;ore Regio. </s> <s><emph.end type="italics"/><lb/>A D <lb/>HENRICVM IIII. GALLIÆ & NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;simum. </s> </p> <figure id="id.035.01.001.1.jpg" xlink:href="035/01/001/1.jpg"/> <p type="head"> <s id="id.000003">PARISIIS, <lb/>Apud IEREMIAM PERIER via Iacobæa, &longs;ub &longs;igno Bellerophontis. </s> </p> <p type="head"> <s id="id.000004">M. D. XCIX. <lb/><emph type="italics"/>CUM PRIVILEGIO REGIS. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/002.jpg"/> <pb xlink:href="035/01/003.jpg" /> <figure id="id.035.01.003.1.jpg" xlink:href="035/01/003/1.jpg"/> <p type="head"> <s id="id.000005">HENRICO IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D. </s> </p> <p type="main"> <s id="id.000006">Ecce maie&longs;tati tuæ, <lb/>Rex Chri&longs;tiani&longs;&longs;ime, <lb/>nouum <expan abbr="fructũ">fructum</expan>, & tan­<lb/>quam primitias tuæ à te <lb/>nuper re&longs;titutæ Acade­<lb/>miæ, Mechanica Ari­<lb/>&longs;totelis philo&longs;ophorum principis Gr&etail;­<lb/>ca, emendata, Latina facta, & commen­<lb/>tariis illu&longs;trata offero, dico, con&longs;ecro. <lb/></s> <s id="id.000007">Noli, ob&longs;ecro te, ad Mechanicorum ti­<lb/>tulum munus hoc, qua&longs;i minus inge­<lb/>nuum, nec &longs;atis liberali ingenio, 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/></s> <s id="id.000008"><expan abbr="Ferũt">Ferunt</expan> Platonem, quo philo&longs;ophorum <pb xlink:href="035/01/004.jpg" />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">cum interrogaretur</expan>, quid ageret Deus, <lb/>re&longs;pondi&longs;&longs;e <foreign lang="el">a)ei gewmetrei=n. </foreign></s> <s id="id.000009">Hoc verbum Lati­<lb/>nè expre&longs;&longs;um &longs;ignificat, A&longs;&longs;iduè terram <lb/>metiri. </s> <s id="id.000010">Quæ actio &longs;i &longs;impliciter &longs;pecte­<lb/>tur, & à Geometri&etail; nomine ridiculo, vt <lb/>alibi appellat Plato, <expan abbr="exp&etilde;datur">expendatur</expan>, ridicula, <lb/>& Dei maie&longs;tate indigna iudicabitur. <lb/></s> <s id="id.000011">Sed &longs;i ex ip&longs;ius artis viribus, & magnifi­<lb/>cis promi&longs;&longs;is illud <foreign lang="el">a)ei gewmetrei=n</foreign> æ&longs;timetur, <lb/>quod e&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. </s> <s id="id.000012">Verumenimuerò &longs;i ad illud <foreign lang="el">a)ei gew­<lb/>metrei=n</foreign> addi&longs;&longs;et Plato, <foreign lang="el">kai\ a)ei mhxana=sqai,</foreign> luculen­<pb xlink:href="035/01/005.jpg" />tius multò meo iudicio, & diuinæ maie­<lb/>&longs;tati congruentius, <expan abbr="atq;">atque</expan> magnificentius <lb/>re&longs;pondi&longs;&longs;et. </s> <s id="id.000013">Quid enim e&longs;t Mundum <lb/>hunc ex 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="el">a)ei gewmetrei=n kai\ a)eimhxana=sqai?</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. </s> <s id="id.000014">An non omnia corpora <lb/>complectitur, quod eius <expan abbr="imm&etilde;&longs;itatem">immen&longs;itatem</expan> <lb/>arguit? </s> <s id="id.000015">An <expan abbr="nõ">non</expan> ad omnium mutabilium <lb/>lationem, alterationem, generationem, <lb/>auctionem, con&longs;eruationem, & <expan abbr="dura­tion&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? </s> <s id="id.000016">An non quinquies mille <expan abbr="quin­g&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 xlink:href="035/01/006.jpg" />eius <expan abbr="firmitat&etilde;">firmitatem</expan> plu&longs;quam adamantinam <lb/>te&longs;tatur? </s> <s id="id.000017">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 iucundi&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> tanquam <lb/>gemmarum pretio&longs;i&longs;&longs;imarum hîc illîc <lb/>in eminentiori, & apparentiori &longs;ui par­<lb/>te collocatorum perenni luce, 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;ius amores excitat? </s> <s id="id.000018">Deus igitur, <expan abbr="pr&etail;ter­quã">pr&etail;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 xlink:href="035/01/007.jpg" />mus, potenti&longs;&longs;imus <foreign lang="el">mhxaniko\s,</foreign> & <foreign lang="el">mhxanopoio\s. </foreign><lb/></s> <s>Ip&longs;e idem, qui <foreign lang="el">makro/kosmon</foreign> magnum mun­<lb/>dum fecit, fecit & <foreign lang="el">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="el">te/xnh te/xnwn,</foreign> ars artium, <lb/>& manum, quæ e&longs;&longs;et <foreign lang="el">o)/rganon o)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 res faceret, vt eas, <lb/>ni&longs;i quotidie fieri, & factas e&longs;&longs;e &longs;æpius <pb xlink:href="035/01/008.jpg" />alij homines &longs;pectarent, omninò fieri <lb/>non po&longs;&longs;e iurarent. </s> <s id="id.000019">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. </s> <s id="id.000020">Vnde fortè illud Martialis. </s> </p> <p type="main"> <s id="id.000021"><emph type="italics"/>Barbara Pyramidum &longs;ileat miracula <lb/>Memphis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000022">Tum &longs;eptem illa, quæ vulgò iactantur <lb/>orbis miracula. </s> <s id="id.000023">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/></s> <s id="id.000024">His enim tantis, & tam multis quæ ab <lb/>homine <foreign lang="el">mhxanopoihtikw=|</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="ma­ximũ">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="el">mhxanopoihtikw=|</foreign> tantò homi­<lb/>nem præ&longs;tantia, &longs;apientia, potentia, imò <pb xlink:href="035/01/009.jpg" />infinitè &longs;uperante: quantò hæc mundi <lb/>machina omnium hominum etiam Ar­<lb/>chimedeorum machinas &longs;uperat, atque <lb/>antecellit. </s> <s id="id.000025">Hic autem quis pote&longs;t e&longs;&longs;e <lb/>alius, præterquam is, quem Deum om­<lb/>nes appellamus. </s> <s>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. </s> <s id="id.000026">In quo enim immen&longs;us ille au­<lb/>thor, factorque hominis, in proprij <lb/>operis fabrica homini ip&longs;i præpolleret, <lb/>&longs;i machinis, & in&longs;trumentis, materia, & <lb/>molimine, vt homo, indigeret? </s> <s id="id.000027">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. </s> <s id="id.000028">Quæ &longs;i rectè & ve­<lb/>rè Deo, <expan abbr="quantũ">quantum</expan> fas e&longs;t homini, dicta <lb/>&longs;unt: ecquid iam &longs;upere&longs;t, Rex Chri&longs;tia­<pb xlink:href="035/01/010.jpg" />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>? </s> <s id="id.000029">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/></s> <s id="id.000030">Qui&longs;quis enim duas res omnium, quæ <lb/>&longs;unt in 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;tru­m&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 magnopere delectari, atque <lb/>eos, qui de iis &longs;ubtiliter, & ingeniose tra­<lb/>ctarint, libros oblatos non grati&longs;&longs;imè <pb xlink:href="035/01/011.jpg" />excipere: tu, Rex potenti&longs;&longs;ime, duas il­<lb/>las res perfeci&longs;ti, bellum &longs;cilicet, & pa­<lb/>cem. </s> <s id="id.000031">In vtriu&longs;que tempore a&longs;&longs;iduus ma­<lb/>chinarum, & in&longs;trumentorum v&longs;us, at­<lb/>que opportunitas. </s> <s id="id.000032">Tu namque 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="el">kolossikw/taton,</foreign> graui&longs;&longs;imum certè, & num­<lb/>quam &longs;i fieri po&longs;&longs;et, commouendum: <lb/>vbi, vbi tamen 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 xlink:href="035/01/012.jpg" />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. </s> <s id="id.000033">Quomodo <expan abbr="aut&etilde;">autem</expan>? <lb/></s> <s id="id.000034">dicam pro meo &longs;en&longs;u: tu melius. </s> <s id="id.000035">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, vt in 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 id="id.000036"><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 id="id.000037"><emph type="italics"/>Munere: &longs;ola Deos æquat clementia nobis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000038">Ad concordiam inter &longs;e, & tecum &longs;er­<lb/>uandam: ad beneuolentiam erga te præ­<lb/>&longs;tandam, obedientiam, fidelitatem rede­<lb/>gi&longs;ti. </s> <s id="id.000039">Extraneos verò longo bello: bre­<pb xlink:href="035/01/013.jpg" />uiori tamen, 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/>quanquam anteà &longs;emper ab omni pacis <lb/>conditione alieni&longs;&longs;imos, vt pacem ip&longs;i <lb/>appeterent, & peterent coëgi&longs;ti. </s> <s id="id.000040">Quid <lb/>tu ilico? </s> <s id="id.000041">Quandoquidem pax victo &longs;em­<lb/>per &longs;it nece&longs;&longs;aria, & victori ea, quæ nihil <lb/>po&longs;t &longs;e ferat in&longs;idiarum, &longs;emper expe­<lb/>diat: &longs;tatim eius ineundæ, & cum <expan abbr="po­t&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 perfecta re <expan abbr="nõ">non</expan> relinquendæ &longs;em­<lb/>per interfuit, & qua&longs;i præfuit, arripui­<lb/>&longs;ti. </s> <s id="id.000042">Duobus e tuo &longs;anctiore con&longs;ilio de­<lb/>lectis con&longs;iliariis tibi, id e&longs;t patriæ <pb xlink:href="035/01/014.jpg" />&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 per te 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 xlink:href="035/01/015.jpg" />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/></s> <s id="id.000043">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. </s> <s id="id.000044"><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">quantumuis</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">memoriam reducimus</expan>, <pb xlink:href="035/01/016.jpg" />mera &longs;omnia videre nobis videmur: <lb/>Quid igitur ab&longs;urdum? </s> <s id="id.000045">quidve inele­<lb/>gans facimus? </s> <s id="id.000046">&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? </s> <s id="id.000047">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;imi ardore, ab ijs auocare <lb/>aut retardare potuerit. </s> <s id="id.000048">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="in­u&etilde;tore">in­<lb/>uentore</expan>, & excogitatore, tuis &longs;umptibus <lb/>extruitur: Ædium lateritiarum cochlea­<lb/>ri &longs;cal&etail;, octauo orbis miraculo <expan abbr="colophõ">colophon</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 xlink:href="035/01/017.jpg" />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. </s> <s id="id.000049">Spemque adferunt <lb/><expan abbr="nõmediocrem">non mediocrem</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, aliquando e&longs;&longs;e cogitatu­<lb/>rum, & perfecturum. </s> <s id="id.000050">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 con&longs;ecrare. </s> <s id="id.000051">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 xlink:href="035/01/018.jpg" />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. </s> <s id="id.000052">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. </s> <s id="id.000053">Vale, & duas illas per­<lb/>optatas annorum quadragenarias tibi, <lb/>& nobis &longs;ic viue. </s> <s id="id.000054">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 id="id.000055">MAIESTATIS</s> </p> <p type="main"> <s id="id.000056">Humillimus &longs;eruus</s> </p> <p type="main"> <s id="id.000057">HENRICVS MONANTHOLIVS. </s> </p> </section> <pb xlink:href="035/01/019.jpg" /> <section> <p type="head"> <s id="id.000058">A D <lb/>HENRICVM IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;&longs;imum. </s> </p> <p type="main"> <s id="id.000059"><emph type="italics"/>Pacatos fecit tua nos victoria ciues. <lb/></s> <s id="id.000060">Inde caput Laurus: digitos ornabit Oliua <lb/>Semper, & ingentem per vtrâque volabis Olympum. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.000061">THEODORICVS MONANTHOLII filius. </s> </p> <p type="head"> <s id="id.000062">De libro <foreign lang="el">tw=n mhxanikw=n,</foreign> Ari&longs;totele, <lb/>& Monantholio. </s> </p> <p type="main"> <s id="id.000063"><emph type="italics"/>Inter Ari&longs;totelis libros &longs;ubtilior i&longs;to<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000064"><emph type="italics"/>Nullus<emph.end type="italics"/> <foreign lang="el">*mhxanikw=n,</foreign> <emph type="italics"/>vtiliorque fuit. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000065"><emph type="italics"/>Sed mendis fœdus merito &longs;ine honore iacebat,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000066"><emph type="italics"/>Non authore &longs;uo dignus Aristotele. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000067"><emph type="italics"/>Lectus erat nulli, nulli intellectus agebat<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000068"><emph type="italics"/>Vitam cum blattis, muribus, & tineis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000069"><emph type="italics"/>Liber ab his, captu facilis, bene comptus en exit<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000070"><emph type="italics"/>In lucem, vigilis luce Monantholij. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000071"><emph type="italics"/>Sic dat Ari&longs;toteli vitam, claréque vicißim<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000072"><emph type="italics"/>Accipit ex ip&longs;o, quam dedit ille, parem. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000073"><emph type="italics"/>Vna dies ambos &longs;eruabit, & eximet æuo,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000074"><emph type="italics"/>Amborúmque &longs;imul fama &longs;uper&longs;tes erit. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000075">RICHARDVS MERCES</s> </p> <p type="main"> <s id="id.000076">Doct. Med. Pari&longs;. </s> </p> </section> <pb xlink:href="035/01/020.jpg" /> <section> <figure id="id.035.01.020.1.jpg" xlink:href="035/01/020/1.jpg"/> <p type="head"> <s id="id.000077">PRAEFATIO IN <lb/>MECHANICA ARISTO­<lb/>TELIS, AD LECTOREM. </s> </p> <p type="main"> <s id="id.000078">Philosophari in vno rerum quo­<lb/>libet genere, <expan abbr="cãdide">candide</expan> lector, res e&longs;t per­<lb/>quam dulcis. </s> <s id="id.000079">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. </s> <s id="id.000080">Ita enim demum verè ille erit, vt ait poëta,</s> </p> <p type="main"> <s id="id.000081"><emph type="italics"/>Fœlix, qui poterit rerum cogno&longs;cere cau&longs;as. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000082">Alio qui inutilia, vel vtilia: &longs;ed inutiliter id e&longs;t &longs;ine actio­<lb/>ne vel opere, qu&etail; 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. </s> <s id="id.000083">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. </s> <s id="id.000084">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. </s> <s id="id.000085">Sed quibus non ita magnus vel fuit, <pb xlink:href="035/01/021.jpg" />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. </s> <s id="id.000086">Om­<lb/>nium, quæ &longs;unt, genera quatuor e&longs;&longs;e reperio, &longs;ingula cer­<lb/>tè digni&longs;&longs;ima hominis contemplatione. </s> <s id="id.000087">Diuina, cœle­<lb/>&longs;tia, elementaria, artificialia. </s> <s id="id.000088">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. </s> <s id="id.000089">Et certè diuina &longs;unt eiu&longs;modi, vt <lb/>licet ad eorum 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. </s> <s id="id.000090">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. </s> <s id="id.000091">Huic philo&longs;ophiæ proxima e&longs;t cœ­<lb/>le&longs;tium & elementariorum id e&longs;t <foreign lang="el">tou= makrokosmou=</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. </s> <s id="id.000092">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. </s> <s id="id.000093">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. </s> <s id="id.000094">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;ola cognitione <expan abbr="cõtenti">contenti</expan> ad agen­<lb/>dum &longs;e <expan abbr="contulerũt">contulerunt</expan>. </s> <s id="id.000095">Hinc quartum genus illud <expan abbr="rerũ">rerum</expan>, quas <lb/>diximus, artificialium emanauit, primùm vt credibile e&longs;t <pb xlink:href="035/01/022.jpg" />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 fuerit iudica­<lb/>tus. </s> <s id="id.000096">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>. </s> <s id="id.000097">quid <lb/>enim e&longs;t, quod non &longs;uis v&longs;ibus accommodarit? </s> <s id="id.000098">quibus &longs;i <lb/><expan abbr="bonitat&etilde;">bonitatem</expan> exemplo Dei Opt. Max. &longs;emper <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/></s> <s id="id.000099">E&longs;t certè animus in homine ars <expan abbr="artiũ">artium</expan>. </s> <s id="id.000100">Inuenit enim om­<lb/>nia, & manus <expan abbr="organũ">organum</expan> organorum. </s> <s id="id.000101">Facit enim omnia. </s> <s id="id.000102">Et &longs;i <lb/><foreign lang="el">mhxana=sqai</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="el">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. </s> <s id="id.000103">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="el">mhxaniko\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. </s> <s id="id.000104">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. </s> <s id="id.000105">Sed præ&longs;tat <lb/>eleganti&longs;&longs;imos huius poëtæ ver&longs;us recitare. </s> </p> <p type="main"> <s id="id.000106"><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 id="id.000107"><emph type="italics"/>Hoccine mortalis progre&longs;&longs;a potentia curæ? <lb/></s> <s id="id.000108">Iam meus in fragili luditur orbe labor. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000109"><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 id="id.000110"><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 id="id.000111"><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 id="id.000112"><emph type="italics"/>Iamque &longs;uum voluens audax indu&longs;tria mundum<emph.end type="italics"/><pb xlink:href="035/01/023.jpg" /><emph type="italics"/>Gaudet, & humana &longs;idera mente regit. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000113"><emph type="italics"/>Quid &longs;al&longs;o in&longs;ontem tonitru Salmonea miror? <lb/></s> <s id="id.000114">AEmula naturæ parua reperta manus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000115">Sal monei 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 tonitrua, <expan abbr="vi­brataq;">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. </s> <s id="id.000116">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&etail; ab antiquis in­<lb/>geniosè, vel ad oppugnandos ho&longs;tes, vel ab his &longs;e <expan abbr="defen­dendũ">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. </s> <s id="id.000117">Præclara <lb/>&longs;anè illa &longs;unt <foreign lang="el">mhxanh/mata,</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>. </s> <s id="id.000118">Vt veteribus <lb/>illis &longs;olis in&longs;tructus cum Alexander parua hominum ad <lb/>30000 manu tot prouincias, tot regna, tot vrbes &longs;ubegi&longs;­<lb/>&longs;et, dictum &longs;it ab illo 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. </s> <s id="id.000119"><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. </s> <s id="id.000120">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="el">e)ggei/bata</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. </s> <s id="id.000121"><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. </s> <s id="id.000122">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. </s> <s id="id.000123">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 xlink:href="035/01/024.jpg" />exercebat, quod hîc Lutetiæ vidimus. </s> <s id="id.000124">Vt & Noribergæ <lb/>mu&longs;ca ferrea <expan abbr="cõmemoratur">commemoratur</expan> è manu artificis &longs;ui euola&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> eundem <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. </s> <s id="id.000125">Sed <lb/>hæc ad delectationem tantum &longs;unt comparata, vtilia & <lb/>vitæ human&etail; <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/></s> <s id="id.000126">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="di­mou&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? </s> <s id="id.000127">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? </s> <s id="id.000128">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, cuneus, & cochlea. </s> <s id="id.000129">Sed qu&etail; au­<lb/>dio hîc dicet aliquis? </s> <s id="id.000130">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;ordidorumque <lb/><expan abbr="hominũ">hominum</expan>? </s> <s id="id.000131">Audis &longs;anè: &longs;ed & A&longs;treæ, & Neptuni, & Mar­<lb/>tis, & Vulcani, & Cereris, & Palladis, qui tantopere pro­<lb/>pter hæc &longs;ua inuenta antiquis <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. </s> <s id="id.000132">Trutinarum <lb/>librarumque examinatio reperta, inquit Vitruuius, vin­<lb/>dicat ab iniquitate iu&longs;tis moribus <expan abbr="vitã">vitam</expan>. </s> <s id="id.000133">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 xlink:href="035/01/025.jpg" />æquum voluntas eius, & alibi abhominatio e&longs;t apud Deum <lb/>pondus & pondus. </s> <s id="id.000134">Itaque libræ inuentrix A&longs;træa pro dea <lb/>lu&longs;tici&etail; culta e&longs;t. </s> <s id="id.000135">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. </s> <s id="id.000136">Vnde poëta,</s> </p> <p type="main"> <s id="id.000137"><emph type="italics"/>Libra die, &longs;omnique pares vbi fecerit horas,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000138"><emph type="italics"/>Et medium luci atque vmbris iam diuidet orbem. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000139">Neptuno verò, cum tridentem antiquitas attribuit, quid <lb/>aliud, quam vectem? </s> <s id="id.000140">Græci appellant <foreign lang="el">mo/xlon</foreign> vnde ille <foreign lang="el">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 id="id.000141"><emph type="italics"/>Leuat ip&longs;e tridenti,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000142"><emph type="italics"/>Et va&longs;tas aperit Syrtes. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000143">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 incumbens, 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. </s> <s id="id.000144">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 id="id.000145"><emph type="italics"/>Veniant ad aratra iuuenci. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000146">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? </s> <s id="id.000147"><expan abbr="aquã">aquam</expan> pro pondere loco dimouens? <lb/></s> <s id="id.000148">vt in eum cedat nauis, & quidem impul&longs;us ille à remige pro <pb xlink:href="035/01/026.jpg" />vectiatio tanquam tridens à Neptuno? </s> <s id="id.000149">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/></s> <s id="id.000150">Neque malus erectus in medio nauis e&longs;t aliud. </s> <s id="id.000151">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 id="id.000152">Sed hæc devecte &longs;atis. </s> <s id="id.000153"><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. </s> <s id="id.000154">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 Herone rege Syracu&longs;arum, au&longs;us e&longs;t dicere. <lb/></s> <s id="id.000155">Da mihi vbi &longs;i&longs;tam pedem, & hanc ego <expan abbr="terrã">terram</expan> loco &longs;uo dimo­<lb/>uebo. </s> <s id="id.000156">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="el">a)po\ tau/ths th=s <lb/>h(me/ras peri\ p=anto\s *arxhmh/dei le/gonti pisteute/on. </foreign></s> <s> Ab hoc die <lb/>quicquid dixerit Archimedes huic <expan abbr="credendũ">credendum</expan>. </s> <s id="id.000157">At ab eo die <lb/>ab Archimede prodijt illud problema inexpertis in credibi­<lb/>le, eruditis tamen demon&longs;tratum. </s> <s id="id.000158">Datum pondus à data <lb/>potentia moueri. </s> <s id="id.000159">quod in vecte, trochlea, & axe in peritro­<lb/>chio nuper à Guidone Vbaldo demon&longs;trationibus geome­<lb/>tricis habemus confirmatum. </s> <s id="id.000160">Vectis &longs;olus pondera de loco <pb xlink:href="035/01/027.jpg" />propellit &longs;uo, trochlea euellit, & eadem ad alti&longs;&longs;imas ædi­<lb/>ficiorum vbi opus e&longs;t &longs;edes trahit. </s> <s id="id.000161">Sit in polo horizontis qui <lb/>trochleæ appendiculum firmet, & ad eum homo ip&longs;e &longs;e &longs;u­<lb/>bleuabit. </s> <s id="id.000162">Sed longior &longs;um in trochlea, in reliquis ero bre­<lb/>uior. </s> <s id="id.000163">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. </s> <s id="id.000164">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 id="id.000165"><emph type="italics"/>Irritamenta malorum:<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000166">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. </s> <s id="id.000167">Nam vt recte dixit Pindarus,</s> </p> <p type="main"> <s id="id.000168"><emph type="italics"/>Quæ Virtute pecunia<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000169"><emph type="italics"/>Exornata nitet, &longs;uppeditat Vias<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000170"><emph type="italics"/>Non vnas, bene agas, quibus<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000171"><emph type="italics"/>Quæ &longs;ors cunque ferens obtulerit tibi:<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000172">Et vt Antiphanes,</s> </p> <p type="main"> <s id="id.000173"><emph type="italics"/>Per deos cur optet quis dite&longs;cere?<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000174"><emph type="italics"/>Pecuniæ cur optet habere plurimum:<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000175"><emph type="italics"/>Quam po&longs;sit auxiliari vt amicis? </s> <s id="id.000176">Gratiæ<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000177"><emph type="italics"/>Fructúmque &longs;erere Diuarum &longs;uaui&longs;simæ?<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000178">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 id="id.000179">Cuneus vero e&longs;t <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> exiguum in formam pyra­<lb/>midis quadrangul&etail;, ad vnam <expan abbr="rectã">rectam</expan> <expan abbr="lineã">lineam</expan> fa&longs;tigiatæ ad diui­<lb/>dendum ligna factum. </s> <s id="id.000180">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. </s> <s id="id.000181">Milo Crotoniates Athleta <lb/>ille robu&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 xlink:href="035/01/028.jpg" />bellis ouis fui&longs;&longs;e lupis. </s> <s id="id.000182">Itaque proprijs,</s> </p> <p type="main"> <s id="id.000183"><emph type="italics"/>viribus ille<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000184"><emph type="italics"/>Confi&longs;us perijt,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000185">qui &longs;i cuneo id ip&longs;um facere volui&longs;&longs;et, in eam calamitatem <lb/>non incidi&longs;&longs;et. </s> <s id="id.000186">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? </s> <s id="id.000187">Ligones agricolarum quid &longs;unt aliud, quam cunei <lb/>malleo connexi? </s> <s id="id.000188">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? </s> <s id="id.000189">&longs;icuti forceps tantum vectis e&longs;t du­<lb/>plicatus. </s> <s id="id.000190">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 id="id.000191"><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 id="id.000192"><emph type="italics"/>Forcipe ferrum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000193">At cuneus &longs;implex percu&longs;&longs;ione mallei adigitur. </s> <s id="id.000194">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. </s> <s id="id.000195">Hoc beneficium ma­<lb/>gni e&longs;t momenti ad vitæ commoda. </s> <s id="id.000196">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? </s> <s id="id.000197">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 te­<lb/>&longs;timonium. </s> <s id="id.000198">Terra, inquit, marique &longs;imul cœptæ oppugnari <lb/>Syracu&longs;æ, terra ab Hexapylo: mari ab Acradina. </s> <s id="id.000199">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. </s> <s id="id.000200">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 ludifi­<pb xlink:href="035/01/029.jpg" />caretur. </s> <s id="id.000201">Murum per in&etail;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. </s> <s id="id.000202">Acradinæ murum, qui, vt ante <lb/>dictum e&longs;t, mari alluitur ex quinqueremibus Marcellus <lb/>oppugnabat. </s> <s id="id.000203">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. </s> <s id="id.000204">Hi, quia &longs;patio mi&longs;&longs;ilibus opus e&longs;t: procul mu­<lb/>ro <expan abbr="tenebãt">tenebant</expan> naues. </s> <s id="id.000205">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. </s> <s id="id.000206">Aduer&longs;us hunc naualem apparatum Archime­<lb/>des variæ magnitudinis tormenta in muris di&longs;po&longs;uit. </s> <s id="id.000207">In eas <lb/>quæ procul erant, naues &longs;axa ingenti pondere emittebat: <lb/>propiores leuioribus, eóque magis crebris petebat telis. </s> <s id="id.000208">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. </s> <s id="id.000209">per quæ caua pars &longs;agittis: pars &longs;corpionibus modicis <lb/>ex occulto petebant ho&longs;tem. </s> <s id="id.000210">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. </s> <s id="id.000211">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. </s> <s id="id.000212">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. </s> <s id="id.000213">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. </s> <s id="id.000214">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. </s> <s id="id.000215">Hæc Ti­<lb/>tus Liuius lib.4.decad.3. </s> <s id="id.000216">Vilium igitur, &longs;ordidorum que ho­<lb/>minum ne dixerimus ea e&longs;&longs;e in&longs;trumenta, quæ vel à dijs, vel <pb xlink:href="035/01/030.jpg" />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/></s> <s id="id.000217">Quanquam non eo 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 id="id.000218"><emph type="italics"/>Queis meliore luto finxit præcordia Titan:<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000219">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? </s> <s id="id.000220">vel &longs;i rei <lb/>familiaris exiguitas po&longs;tulat, cum ijs agatis, potius, quam <lb/>nihil? </s> <s id="id.000221">Neque enim magis horum aliquod nobis indecorum <lb/>putare debemus: quam &longs;ibi A&longs;cræus ille poëta,</s> </p> <p type="main"> <s id="id.000222"><emph type="italics"/>Qui alium ditem cernens, cum dee&longs;t quod agatur,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000223"><emph type="italics"/>Ip&longs;e &longs;olum vertit tauris, & &longs;emina ponit. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000224">Sed eo animo h&etail;c pr&etail;&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 conficiendis 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, maiores adhuc multo po&longs;tea percepturi, &longs;i <lb/>tantæ efficaciæ adiumenti que cau&longs;as inue&longs;tigantes inuene­<lb/>rimus, quod feci&longs;&longs;e Ari&longs;totelem non puduit, qui vno hoc li­<lb/>bello <foreign lang="el">peri\ mhxanikw=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 principium, 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. </s> <s id="id.000225">Itaque &longs;i quis audito huius <lb/>libelli titulo, &longs;tatim ab huius lectione volens aufugere, in&longs;u­<lb/>per pueriliter irrideat, quod regius mathematicarum ar­<lb/>tium profe&longs;&longs;or in rebus, vt putabit, vili&longs;&longs;imis philo&longs;ophari, <lb/>& <foreign lang="el">gewmetrei=n</foreign> contenderit. </s> <s id="id.000226">Huic re&longs;pondebimus, quod ali­<lb/>quando Heraclitum dixi&longs;&longs;e ferunt ijs, qui cum alioqui evm <lb/>vellent, quod forte in ca&longs;a furnaria caloris gratia &longs;edentem <lb/>vidi&longs;&longs;ent, accedere temperarunt, & ingredi fidenter cum <pb xlink:href="035/01/031.jpg" />iu&longs;&longs;i&longs;&longs;et. </s> <s id="id.000227">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 recentioribus Leoni­<lb/>cus, Picolominus, Cardanus, Guido Vbaldus, quorum in­<lb/>genia &longs;eruilia nunquam rectè quis dixerit aut putarit. </s> <s id="id.000228">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="el">o)/noi, o)/niskoi\,</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. </s> <s id="id.000229">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, candide lector, me hortante atque his <lb/>no&longs;trorum commentariorum vigilijs, vtcunque adiuuante, <lb/>diligenter incubueris, tui te laboris, mihi crede, penitebit <lb/>numquam. </s> <s id="id.000230">Vale. </s> </p> </section> <pb xlink:href="035/01/032.jpg" /> <section> <p type="head"> <s id="id.000231"><emph type="italics"/>Extraict du Priuilege du Roy. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000232"><foreign lang="fr">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</foreign> <emph type="italics"/>Ari&longs;totelis <lb/>Mechanica, Græca emendata, Latina facta, & commen­<lb/>tarijs illu&longs;trata, ab Henrico Monantholio Medico, & Ma­<lb/>thematicarum artium Profe&longs;&longs;ore Regio. <emph.end type="italics"/></s> <s id="id.000233"><foreign lang="fr">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. </foreign></s> <s id="id.000234"><foreign lang="fr">Donné à Paris le <lb/>23. de Decembre 1598. </foreign></s> </p> <p type="main"> <s id="id.000235"><foreign lang="fr"><emph type="italics"/>Signé par le Con&longs;eil<emph.end type="italics"/></foreign></s> </p> <p type="main"> <s id="id.000236"><foreign lang="fr"><emph type="italics"/>D<emph.end type="italics"/>E LAVETS. </foreign></s> </p> </section> <pb xlink:href="035/01/033.jpg" /> <section> <p type="head"> <s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>& eorum Commentarijs. <lb/><arrow.to.target n="table1"/></s> </p> <table> <table.target id="table1"/> <row> <cell><emph type="italics"/>A<emph.end type="italics"/></cell> <cell/> </row> <row> <cell><emph type="italics"/><foreign lang="el">*abussos</foreign> unde. pag. <emph.end type="italics"/></cell> <cell>209</cell> </row> <row> <cell><emph type="italics"/>Ab&longs;is pro circunferen­tia 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 opificijs egent &longs;tatione, vel &longs;eßione 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 ponderatione. <emph.end type="italics"/></cell> <cell>149</cell> </row> <row> <cell><foreign lang="el">*alourgopw/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 angulus æqualitatis, ideóque quietis. <emph.end type="italics"/></cell> <cell>193.196</cell> </row> <row> <cell><emph type="italics"/>Ad angulos rectos omnia <expan abbr="quie&longs;cũt">quie&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 medij confert ad motum proiecti. <emph.end type="italics"/></cell> <cell>203</cell> </row> <row> <cell><emph type="italics"/>Antiphonis dictum, cum iret ad &longs;uppli­cium. <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"/>Archelai regis factum in eclip&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"/>Architecturæ 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;co­pum vertit. <emph.end type="italics"/></cell> <cell>6</cell> </row> <row> <cell><emph type="italics"/>Ars e&longs;t admirationis plena. <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;ordi­das. <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 co­chlea. <emph.end type="italics"/></cell> <cell>133</cell> </row> <row> <cell><emph type="italics"/>A&longs;inus, & aues longo collo vident cœ­lum, 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="el">*auto/mata. </foreign></cell> <cell>10</cell> </row> <row> <cell><emph type="italics"/>B<emph.end type="italics"/></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, pericu­losè 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, & compreca­tur 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 obe­li&longs;ci. <emph.end type="italics"/></cell> <cell>142</cell> </row> <pb xlink:href="035/01/034.jpg" /> <row> <cell><emph type="italics"/>Bouilli error, qui putabat rectam iuuen­tam æqualem 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 po­te&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 pedibus ad rectos imminet. <emph.end type="italics"/></cell> <cell>198</cell> </row> <row> <cell><emph type="italics"/>Brutum nihil admiratur. <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/> </row> <row> <cell><foreign lang="el">*ka/iar</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: inge­niosè 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 eo­dem 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 figu­ram hominis. <emph.end type="italics"/></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"/>Cercopithecus, & &longs;imia e&longs;t ridicula ho­minis 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="el">a)nti/xeir,</foreign> vt in manu hominis. <emph.end type="italics"/></cell> <cell>195</cell> </row> <row> <cell><emph type="italics"/>Centrum duorum circulorum connexo­rum 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 repugnan­tias. <emph.end type="italics"/></cell> <cell>16</cell> </row> <row> <cell><emph type="italics"/>Circulus &longs;ecit miracula in templis paga­norum. <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 nu­tum 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 conta­ctus 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 æqua­lem 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 natu­ram 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 re­ctos 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 con­traria. <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 xlink:href="035/01/035.jpg" /> <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 moue­tur. <emph.end type="italics"/></cell> <cell>200</cell> </row> <row> <cell><emph type="italics"/>D<emph.end type="italics"/></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 euelli­tur. <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;ij &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 in­fixo. <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;i­gnis. <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/> </row> <row> <cell><emph type="italics"/>Elementa quie&longs;icunt adrectos angu­los &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="el">*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 fa­cilius mouent. <emph.end type="italics"/></cell> <cell>118.119</cell> </row> <row> <cell><emph type="italics"/>Exercitium militum in exercitu ferian­tium. <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/> </row> <row> <cell><emph type="italics"/>Fabrilis ars certitudine vincit cæte­ras. <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 mul­tum corum inclinationes, & natura­les 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 proijcit, 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/> </row> <row> <cell><emph type="italics"/>Georgij Lhullerij 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 motio­ne. <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/> </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;urge­re, &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 xlink:href="035/01/036.jpg" /> <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 perti­ca, &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 cle­p&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">magnificum</expan>. <emph.end type="italics"/></cell> <cell>26</cell> </row> <row> <cell><emph type="italics"/>Humero dextro onera difficilius ferun­tur, 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/> </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/> </row> <row> <cell><emph type="italics"/>Lancea <expan abbr="perp&etilde;dicularis">perpendicularis</expan> facilius fer­tur, 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 fabri­ca. <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="põderilus">ponderilus</expan>. <emph.end type="italics"/></cell> <cell>49.50</cell> </row> <row> <cell><emph type="italics"/>Librile <expan abbr="ligneũ">ligneum</expan> facilius 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="ferũ­tur">ferun­tur</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/> </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, quædam­non 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, pro­pter 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> grauius 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="el">paradocopoioi\. </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 deter­minata. <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 xlink:href="035/01/037.jpg" /><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 alio­rum 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 obti­net. <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="ter­minũ">ter­minum</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 ha­bentibus 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 machinatio­num principia continet. <emph.end type="italics"/></cell> <cell>60</cell> </row> <row> <cell><emph type="italics"/>Motus difficultas in mobili à quibus pen­deat. <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/> </row> <row> <cell><emph type="italics"/>Natura <expan abbr="eod&etilde;">eodem</expan> modo &longs;emper opera­tur, & 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;ubtilita­tem, & nauigationis pericula. <emph.end type="italics"/></cell> <cell>62</cell> </row> <row> <cell><emph type="italics"/>Nauigij Hieronis de&longs;criptio incredibi­lis. <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 re­mi 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 nu­cem 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/> </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;cus 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;i­ta 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 ma­chinæ, & 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, quo­modo, & 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="el">*odonta/gra *h)/ \o)donta/gw=gos</foreign> <emph type="italics"/>quid. <emph.end type="italics"/></cell> <cell>152</cell> </row> <row> <cell><foreign lang="el">*odonta/gw=gos</foreign> <emph type="italics"/><expan abbr="plũbeus">plumbeus</expan> in <expan abbr="t&etilde;plo">templo</expan> Apol­linis 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="el">*ourano/skopos</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/> </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 xlink:href="035/01/038.jpg" /> <row> <cell><emph type="italics"/>Percu&longs;sionis magna vis ad mouendum, findendum, frangendum, quatien­dum. <emph.end type="italics"/></cell> <cell>129</cell> </row> <row> <cell><emph type="italics"/>Perpendiculares à peripherijs in &longs;emi­diametros circulorum inæqualium æquales auferunt &longs;egmenta &longs;emidia­metrorum 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"/>Phalangarij tetraphori, hexaphori. <emph.end type="italics"/></cell> <cell>191</cell> </row> <row> <cell><emph type="italics"/>Phalangij 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 admi­ratione. <emph.end type="italics"/></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"/>Philo&longs;ophia e&longs;t ars generalis omnibus fa­ciendorum difficultatibus &longs;uccurrens. <emph.end type="italics"/></cell> <cell>9</cell> </row> <row> <cell><emph type="italics"/>Philo&longs;ophandi, vt admirandi &longs;emper oc­ca&longs;io erit. <emph.end type="italics"/></cell> <cell>5</cell> </row> <row> <cell><emph type="italics"/>Plumbum vtri aëre pleno annexum tar­dius 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="el">*po/da e)rei=n,</foreign> <emph type="italics"/>& canere quid. <emph.end type="italics"/></cell> <cell>95</cell> </row> <row> <cell><foreign lang="el">*po/des, & pro/podes. </foreign></cell> <cell>96</cell> </row> <row> <cell><foreign lang="el">*poliorkitik*h\</foreign> <emph type="italics"/>pars Mechanices. <emph.end type="italics"/></cell> <cell>11</cell> </row> <row> <cell><foreign lang="el">*polu/spaston. </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 mo­tore 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 cro­cas 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/> </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/> </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 na­uim. <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 motio­nem 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 acu­tus 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 extre­morum 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 mi­noribus. <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/> </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 xlink:href="035/01/039.jpg" /><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;ecu­ra. <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="el">*s*h/kwma</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 & mo­uentißimum. <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 ponde­ra 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 de­mon&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="el">*stata</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 angu­lis. <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 angu­los. <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/> </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="el">*qaumatourgik*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 adie­ctum. <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/> </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 xlink:href="035/01/040.jpg" /> <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 na­uigatur demonstratio. <emph.end type="italics"/></cell> <cell>98</cell> </row> <row> <cell><emph type="italics"/>in Vortice aquarum lata ad medium de­uoluuntur. <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 concentri­ci. <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/> </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/> </row> <row> <cell><foreign lang="el">*zugo\s & *zugo\n. </foreign></cell> <cell>45.119</cell> </row> <row> <cell><foreign lang="el">*zugosta/ths. </foreign></cell> <cell>45</cell> </row> <row> <cell><emph type="italics"/>Zygostatica fides. <emph.end type="italics"/></cell> <cell>45</cell> </row> </table> <p type="head"> <s id="id.000238">FINIS. </s> <pb xlink:href="035/01/041.jpg" pagenum="1" /> <figure id="id.035.01.041.1.jpg" xlink:href="035/01/041/1.jpg"/> </p> </section> </front> <body> <chap> <subchap1> <p type="head"> <s id="id.000239"><foreign lang="el">*a*r*i*s*t*o*t*e*l*o*u*s <lb/>*m*h*x*a*n*i*k*a</foreign>. <lb/>ARISTOTELIS <lb/>MECHANICA. </s> </p> <p type="main"> <s id="id.000241"><foreign lang="el">Ti/ e)sti mhxanh\, kai=\ peri\ ku/klou, tw=n e)n toi=s mhxanikoi=s <lb/>qaumasi/wn ai)ti/an e)/xontos. <arrow.to.target n="marg1"/></foreign></s> </p> <p type="head"> <s id="id.000242"><margin.target id="marg1"/>Pro <foreign lang="el">mhxanh\,</foreign><lb/>lege <foreign lang="el">mhxani­<lb/>kh/. </foreign></s> </p> <p type="head"> <s id="id.000243"><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 id="id.000244"><foreign lang="el">*q*a*u*m*a*z*e*t*a*i tw=n me\n kata\ fu/sin sumbaino/ntwn, o(/swn <lb/>a)gnoei=tai to\ ai)/tion, tw=n de\ para\ fu/sin, o(/sa gi/netai dia\ <lb/>te/xnhn pro\s to\ sumfe/ron toi=s a)nqrw/pois.</foreign></s> </p> <p type="main"> <s id="id.000245">MIRA &longs;unt in his, quæ <lb/><expan abbr="&longs;ecundũ">&longs;ecundum</expan> <expan abbr="naturã">naturam</expan> <expan abbr="eue­niũt">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&etail;cunq;">qu&etail;cunque</expan> arte <lb/>facta hominibus <expan abbr="cõferunt">conferunt</expan>. </s> </p> <p type="head"> <s id="id.000246">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000247"><emph type="italics"/>Cardanvs librum hunc Ari&longs;totelis peripate­<emph.end type="italics"/><lb/><arrow.to.target n="marg2"/><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. </s> <s id="id.000248">Franci&longs;cus Patri­<emph.end type="italics"/><lb/><arrow.to.target n="marg3"/><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. </s> <s id="id.000249">quod licet verum e&longs;&longs;e multis rationibus,<emph.end type="italics"/><pb xlink:href="035/01/042.jpg" pagenum="2" /><emph type="italics"/>testimoniis, & exemplis confirmarit: ob id tamen hunc Ari&longs;toteli <lb/>detrahendum e&longs;&longs;e, non e&longs;t nece&longs;&longs;e. </s> <s id="id.000250">Quid ita? </s> <s id="id.000251">Ip&longs;emet Patricius fate­<lb/>tur hunc<emph.end type="italics"/> <foreign lang="el">tw=n 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. </s> <s id="id.000252">&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/></s> <s id="id.000253">Phra&longs;is non repugnat, &longs;i cum ea <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. </s> <s id="id.000254">Diogenes Laërtius inter Ari&longs;totelis monumenta<emph.end type="italics"/> <foreign lang="el">mhxani­<lb/>kw=n</foreign> <emph type="italics"/>vnum recen&longs;uit. </s> <s id="id.000255">Multi clari viri no&longs;tri temporis vt Daniel <lb/>Barbarus & Guidus Vbaldus &longs;æpe velut ab Ari&longs;totele citant. </s> <s id="id.000256">No­<lb/>nius interpretatus e&longs;t &longs;uis di&longs;cipulis. </s> <s id="id.000257">Cardani ratio parui e&longs;t <expan abbr="mom&etilde;ti">momenti</expan>. <lb/></s> <s id="id.000258">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. </s> <s id="id.000259">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 alij tribuere, potiori iure poßit. <emph.end type="italics"/></s> </p> <p type="margin"> <s id="id.000260"><margin.target id="marg2"/>Lib. de pro­<lb/>port. </s> </p> <p type="margin"> <s id="id.000261"><margin.target id="marg3"/>Tom.I.li.3. <lb/>Di&longs;cu&longs;&longs;io­<lb/>num peri­<lb/>patetic. </s> </p> <p type="main"> <s id="id.000262">Mechanica] <emph type="italics"/>Huius libri duæ &longs;unt partes. </s> <s id="id.000263">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. </s> <s id="id.000264">Hæc autem <emph.end type="italics"/><foreign lang="el">tw=n mhxanikw=n</foreign> <emph type="italics"/>titulo recte exprimuntur. <lb/></s> <s id="id.000265">quia Mechanica dicta &longs;unt<emph.end type="italics"/> <foreign lang="el">a)po\ th=s mhxanh=s. </foreign>& <foreign lang="el">*mhxanh\ a)po\ tou= <lb/>mh/kous kai\ a)/nein,</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 & iucundè &longs;uccurrunt, & adminiculantur 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/></s> <s><foreign lang="el">*mhxanh\</foreign> <emph type="italics"/>autem id e&longs;t machina definitur à Vitruuio, continens ex <lb/>materia coniunctio, quæ maximas habet, ad onerum motus virtu­<lb/>tes: & à Plinio in&longs;trumentum, quo moles aliqua facile, quocumque <lb/>volueris impelli pote&longs;t. </s> <s id="id.000267">Igitur tum hæc in&longs;trumenta & machinæ: <lb/>tum doctrina, quæ virium, quibus hæc pollent, rationem docet, & <lb/>explicat, rectè Mechanica in&longs;cribuntur. </s> <s id="id.000268">Sed vereor, ne hæc libri <lb/>in&longs;criptio, ex vulgari artium diui&longs;ione in liberales & mechanicas, <lb/>quid &longs;ordidi &longs;ubolens multis, ip&longs;os ab huius libri lectione deterruerit <lb/>& deterreat. </s> <s id="id.000269">At quæcumque, eluenda e&longs;t macula. </s> <s id="id.000270">Manauit enim à<emph.end type="italics"/><pb xlink:href="035/01/043.jpg" 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 ornauere, quæ in &longs;ola con­<lb/>templatione ver&longs;arentur, & contemplantis duntaxat ingenium <lb/>acuerent, atque perficerent: viles autem eas putauere, quæ ocium fu­<lb/>gientes, in negotio atque efficientia occuparentur. </s> <s id="id.000271">At ij 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="el">mhxanika\s,</foreign> <emph type="italics"/>( neque enim hîc id vocabuli v&longs;urpant ) <lb/>&longs;ed<emph.end type="italics"/> <foreign lang="el">fau/las, a)neleuqe/rous banau/sous a)gorai/ous</foreign> <emph type="italics"/>viles, illiberales, <lb/>&longs;ordidas, circunforaneas. </s> <s id="id.000272">Melius e&longs;t ergo rem i&longs;tam paulo altius re­<emph.end type="italics"/><lb/><arrow.to.target n="marg4"/><lb/><emph type="italics"/>petitam aliquantum vltra per &longs;uas &longs;pecies deducere. </s> <s id="id.000273">Cum omnis ars, <lb/>vt e&longs;t apud Ari&longs;totelem, referatur ad bonum, nulla per &longs;e vilis cen­<lb/>&longs;eri debet, 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 aliis præ­<lb/>&longs;tantiores existimatæ &longs;unt. </s> <s id="id.000274">vnde nata e&longs;t hæc vulgaris artium diui­<lb/>&longs;io, vt aliæ liberales e&longs;&longs;ent: aliæ mechanicæ. </s> <s id="id.000275">quæ his duobus ver&longs;ibus <lb/>exprimuntur. <emph.end type="italics"/></s> </p> <p type="margin"> <s id="id.000276"><margin.target id="marg4"/>Lib I.cap i. <lb/>Ethic. </s> </p> <p type="main"> <s id="id.000277">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. </s> </p> <p type="main"> <s id="id.000278">Scientiæ autem erant Philo&longs;ophia <lb/>moralis, Phy&longs;ica, Medicina, Iuri&longs;prudentia, Theologia. </s> <s id="id.000279">Poste­<lb/>riore &longs;ignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb/>Chirurgia, Lanificium, Nautica. </s> <s id="id.000280">In quarum &longs;ingulis aliæ &longs;unt im­<lb/>perantes, quæ & architectonicæ dicuntur: aliæ mini&longs;trantes. </s> <s id="id.000281">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 xlink:href="035/01/044.jpg" pagenum="4" /><emph type="italics"/>præ&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. </s> <s id="id.000282">Agriculturæ enim <lb/>opus, quod alimenta & medicamenta hominibus &longs;uppeditat, neceßi­<lb/>tate vincit cætera: victoria, quæ rebelles & hostes &longs;ubijcit, 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. </s> <s id="id.000283">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. </s> <s id="id.000284">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. </s> <s id="id.000285">Ex ijs aliis aliæ materias apparant: aliæ in&longs;trumenta fabrican­<lb/>tur. </s> <s id="id.000286">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. </s> <s id="id.000287">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. </s> <s id="id.000288">harum tamen <lb/>aliquot, cum certæ rationes e&longs;&longs;ent &longs;ubtiles, & à fontibus Geometriæ <lb/>petitæ, ip&longs;as hoc libello 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. </s> <s id="id.000289">Ob quod liber <lb/>rectè in&longs;cribitur<emph.end type="italics"/> <foreign lang="el">mhxa/nika,</foreign> <emph type="italics"/>quia hic explicet cau&longs;as virium in­<lb/>&longs;trumentorum ad Mechanicas artes prædictas pertinentium. </s> <s id="id.000290">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 id="id.000291">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 id="id.000292">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. </s> <s id="id.000293">&longs;ic igitur erit clarior. </s> <s id="id.000294">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 xlink:href="035/01/045.jpg" 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 id="id.000295">Nil admirari propè res e&longs;t vna Numici,</s> </p> <p type="main"> <s id="id.000296">Soláque quæ po&longs;&longs;it facere & &longs;eruare beatum. </s> </p> <p type="main"> <s id="id.000297"><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 id="id.000298">Fœlix, qui potuit rerum cogno&longs;cere cau&longs;as. </s> </p> <p type="main"> <s id="id.000299"><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"/><lb/><emph type="italics"/>petijt. </s> <s id="id.000300">Qui enim, inquit, admiratur, putat &longs;e ignorare, & <expan abbr="dubitãs">dubitans</expan> co­<lb/>natur dubitationibus &longs;uis &longs;uccurrere. </s> <s id="id.000301">Homo natura fugiens e&longs;t igno­<lb/>rantiæ. </s> <s id="id.000302"><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, & ijs 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"/><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. </s> <s id="id.000303">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 id="id.000304"><margin.target id="marg5"/>Cap. 2. lib. 2. <lb/>Metaph. </s> <s><margin.target id="marg6"/>Cap. 6. lib. 5. <lb/>De benefic. </s> </p> <p type="main"> <s id="id.000305">Quorum cau&longs;a ign.] <emph type="italics"/>In rebus naturalibus cau&longs;arum omne <lb/>genus ine&longs;t, materia, efficiens, forma, finis. </s> <s id="id.000306">Et in &longs;ingularium conti­<lb/>nentium & proximarum inuentione, & earum ad primam redu­<lb/>ctione Philo&longs;ophia con&longs;i&longs;tit. </s> <s id="id.000307">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 id="id.000308">Multa tegit &longs;acro inuolucro Natura, neque vllis</s> </p> <p type="main"> <s id="id.000309">Fas e&longs;t &longs;cire quidem mortalibus omnia: multa</s> </p> <p type="main"> <s id="id.000310">Admirare modò, nec non venerare. </s> </p> <pb xlink:href="035/01/046.jpg" pagenum="6" /> <p type="main"> <s id="id.000311"><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;arijs vacuus e&longs;t, non inquirere, <lb/>& venerari. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000312"><foreign lang="el">e)n polloi=s ga\r <lb/>h( fu/sis u(penanti/on pro\s to\ xrh/simon h(mi=n poiei=. </foreign></s> <s id="g0110103"><foreign lang="el">h( me\n <lb/>ga\r fu/sis a)ei\ to\n au)to\n e)/xei tro/pon kai\ a(plw=s, to\ de\ <lb/>xrh/simon metaba/llei pollaxw=s.</foreign></s> <s id="g0110201"><foreign lang="el">o(/tan ou)=n de/h| ti para\ <lb/>fu/sin pra=cai, dia\ to\ xalepo\n a)pori/an pare/xei kai\ dei=tai <lb/>te/xnhs.</foreign></s> </p> <p type="main"> <s id="id.000313">In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. </s> <s id="id.000314"><expan abbr="Si­quid&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: at <expan abbr="aliũ">alium</expan> <expan abbr="atq;">atque</expan> alium ple­<lb/>rumque po&longs;tulat vtilitas. <lb/></s> <s id="id.000315"><expan abbr="Quãdo">Quando</expan> igitur conuenit fa­<lb/>cere aliquid pr&etail;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 id="id.000316">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000317">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 contrarijs, &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 id="id.000318"><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 id="id.000319"><emph type="italics"/>In his quæ arte fiunt aliò natura flectitur & adducitur, quam <lb/>vergat. </s> <s id="id.000320">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 id="id.000321"><emph type="italics"/>Igitur in arte factis aliquid mirum e&longs;t. </s> <s id="id.000322">Pro a&longs;&longs;umptione a&longs;&longs;um­<lb/>ptionis confirmatio est ex effectis, & effectorum modo naturæ & <lb/>artis. </s> <s id="id.000323">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 id="id.000324">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. </s> <s id="id.000325">Hæc &longs;unt demon&longs;trata ab Aristotele<emph.end type="italics"/><pb xlink:href="035/01/047.jpg" pagenum="7" /><emph type="italics"/>lib. de Cœlo & de generat. & corrupt. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000327">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. </s> <s id="id.000328">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 id="id.000329">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. </s> <s id="id.000330">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 ijs 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. </s> <s id="id.000331">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. </s> <s id="id.000332">Hæc cura &longs;olicitudóque vrget imaginationem, vt lu­<lb/>men à mente mutuantem & à rationibus mathematicis, nec quodam <lb/>&longs;ucceßionis ordine defatigari <expan abbr="ration&etilde;">rationem</expan> & quie&longs;cere &longs;init, priu&longs;quam <lb/>quod quæritur, inuentum &longs;it. </s> <s id="id.000333">Illud inuentum, modú&longs;ve inueniendi <lb/>generalis e&longs;t. </s> <s id="id.000334">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, medijs, 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 xlink:href="035/01/048.jpg" 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"/><lb/><emph type="italics"/>imitationem rerum à natura procreatarum. </s> <s id="id.000335">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 maturitates hinc exempla &longs;ump&longs;it, & ea <lb/>imitans, inductus rebus diuinis, commodas vitæ perfecit explicatio­<lb/>nes. </s> <s id="id.000336">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;tudijs, 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 id="id.000337"><margin.target id="marg7"/>Lib. 10. </s> </p> <p type="main"> <s id="id.000338">Tum difficultas.] <emph type="italics"/>Naturæ renixus difficultatem facit. </s> <s id="id.000339">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> </subchap1> <subchap1> <p type="main"> <s id="id.000340"><foreign lang="el">dio\ kai\ kalou=men th=s te/xnhs, to\ pro\s ta\s toiau/tas <lb/>a)pori/as bohqou=n me/ros, mhxanh/n, <arrow.to.target n="marg8"/>kaqa/per ga\r e)poi/hsen <lb/>*)antifw=n o( poihth/s, ou(/tw kai\ e)/xei: te/xnh| ga\r kratou=men, <lb/>w(=n fu/sei nikw/meqa.</foreign></s> <s id="g0110203"><foreign lang="el">toiau=ta de/ e)stin e)n oi(=s ta/ te e)la/ttona <lb/>kratei= tw=n meizo/nwn, kai\ ta\ r(oph\n e)/xonta mikra\n kinei= <lb/>ba/rh mega/la, kai\ pa/nta sxedo\n o(/sa tw=n problhma/twn <lb/>mhxanika\ prosagoreu/omen.</foreign></s> <lb/> </p> <p type="margin"> <s id="id.000341"><margin.target id="marg8"/><foreign lang="el">mhxanikh\n. </foreign></s> </p> <p type="main"> <s id="id.000342">Atque propterea partem <lb/>illius artis quæ hæ&longs;itationi <lb/>i&longs;ti &longs;uccurrit Mechanicem <lb/>vocamus. </s> <s id="id.000343"><expan abbr="Quemadmodũ">Quemadmodum</expan> <lb/>enim Antipho poëta di­<lb/>xit, ita &longs;e res habet. </s> </p> <p type="main"> <s id="id.000344"><emph type="italics"/>Natura vincit: hanc arte <lb/>vincimus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000345">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 id="id.000346">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000347">Illius artis.] <emph type="italics"/>Ars generalis, cuius hic mentionem facit Ari­<lb/>&longs;toteles, nu&longs;quam ab eo e&longs;t definita, aut nominata. </s> <s id="id.000348">Leonicus, qui <lb/>in hunc librum commentarium edidit putat e&longs;&longs;e Architecturam. <emph.end type="italics"/></s> <s><pb xlink:href="035/01/049.jpg" /><emph type="italics"/>Quod facit ex &longs;ententia Vitruuij, qui eius tres partes con&longs;tituit, ædi­<lb/>ficationem in explicatione publicorum & priuatorum operum: <lb/>Gnomonicam in de&longs;criptione Horologiorum: & Machinationem <lb/>in cognitione principiorum & di&longs;po&longs;itione machinarum & orga­<lb/>norum. </s> <s id="id.000349">Hæc quidem comprehendi Architecturæ nomine Galenus<lb/><arrow.to.target n="marg9"/> 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. </s> <s id="id.000351">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. </s> <s id="id.000352">Et quid obe&longs;t dicere hanc e&longs;&longs;e <lb/>Philo&longs;ophiam? </s> <s id="id.000353">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. </s> <s id="id.000354">Atque hac diui&longs;a in &longs;uas partes, & partium particulas <lb/>vna ex his erit Mechanice. </s> <s id="id.000355">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. </s> <s id="id.000356">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 id="id.000357"><margin.target id="marg9"/>Cap. 3. lib. <lb/>de cuiu&longs;que <lb/>animi pecc. <lb/>cogno&longs;c. </s> </p> <p type="main"> <s id="id.000359">Mechanice.] <emph type="italics"/>In Græco Vecheli legitur hîc <emph.end type="italics"/><foreign lang="el">mhxanh\n</foreign>: <emph type="italics"/>vt etiam <lb/>in titulo huius capitis: &longs;ed vtrobique legendum <emph.end type="italics"/><foreign lang="el">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. </s> <s id="id.000360">Nec tamen definita, vt titulus pollicebatur. </s> <s id="id.000361">Definitur au­<lb/>tem &longs;ic à Picolomino. </s> <s id="id.000362">Mechanice e&longs;t &longs;cientia ex qua cau&longs;æ & prin­<emph.end type="italics"/><lb/><arrow.to.target n="marg10"/><lb/><emph type="italics"/>cipia ad quamplurimas artes &longs;ellularias exhauriri po&longs;&longs;unt. </s> <s id="id.000363">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. </s> <s id="id.000364">Mechanice e&longs;t ars ad ea quæ vires humanas &longs;uperant, tra­<lb/>hendum, impellendum, ferendum, machinarum fabricatrix. </s> <s id="id.000365">vel &longs;ic <lb/>Mechanice e&longs;t ars cogendi corpora quantum fieri pote&longs;t vt contra <lb/>nutum ferantur. </s> <s id="id.000366">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 xlink:href="035/01/050.jpg" 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. </s> <s id="id.000367">Cæterùm ex huius machinis, quædam <lb/>mouentur per &longs;e:quædam non &longs;ponte. </s> <s id="id.000368">Illæ intra &longs;e principia &longs;uæ mo­<lb/>tionis habent, & <emph.end type="italics"/><foreign lang="el">a)uto/mata</foreign> <emph type="italics"/>vocantur: quorum alia Græcis <emph.end type="italics"/><foreign lang="el">stata\, </foreign><lb/><emph type="italics"/>Latinis Stataria, fixa, firma dicuntur: alia <emph.end type="italics"/><foreign lang="el">u(pa/gonta</foreign> <emph type="italics"/>ambulantia. <lb/></s> <s id="id.000369">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/>altera 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. </s> <s id="id.000370">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/></s> <s id="id.000371">Hæ verò motionis principium intra &longs;e non habent: Sed ex his <lb/>aliæ mouentur à rebus inanimis, aliæ ab animatis. </s> <s id="id.000372">Res inani­<lb/>mæ principium motionis exhibentes &longs;unt aër, &longs;piritus, aqua, ignis, <lb/>&longs;umus. </s> <s id="id.000373">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="el">a)ntonoma­<lb/>si/an</foreign><emph type="italics"/> organa vocant: vel liber, vnde ædificia ad molendum. </s> <s id="id.000374">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>;. </s> <s id="id.000375">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, radijs, 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 ambulatorijs, catapultis, bali&longs;tis, tormentis reliquis. </s> <s id="id.000376">in quibus <lb/>faciendis hæc lex po&longs;ita e&longs;t, vt omnia fiant ex paratu facilibus quo <lb/>ad materiam: varijs quoad figuras: exiguis quoad men&longs;uras: leuibus <lb/>quoad pondera. </s> <s id="id.000377">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/>ficilia: &longs;tabilia, ac tandem eiu&longs;modi &longs;int, vt quatenus neceßitas <emph.end type="italics"/><pb xlink:href="035/01/051.jpg" pagenum="11" /><emph type="italics"/>po&longs;tulauerit, facile componi, faciléque di&longs;&longs;olui poßint. </s> <s id="id.000378">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"/><lb/><emph type="italics"/>rone inducta e&longs;t. </s> <s id="id.000379">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="el">xeirourgikh\,</foreign> <emph type="italics"/>cui vel maximè artes illæ, æraria, ædifica­<lb/>toria, materiaria, picturaque, adminiculantur. </s> <s id="id.000380">Huius autem partes, <lb/>Manganaria per quam pondera immania minima vi tolluntur in <lb/>altum:<emph.end type="italics"/> <foreign lang="el">mhxanopoihtikh\,</foreign> <emph type="italics"/>quæ facile aquas antlijs extrahit:<emph.end type="italics"/> <foreign lang="el">*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="el">poliorkhtika\</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. </s> <s id="id.000381">Mox & quæ<emph.end type="italics"/> <foreign lang="el">qaumatourgikh\</foreign> <emph type="italics"/>cuius exempla &longs;unt<emph.end type="italics"/> <foreign lang="el">u)drau­<lb/>lika\</foreign> <emph type="italics"/>organa, quæque per &longs;e ventorum flatu re&longs;onant. </s> <s id="id.000382">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. </s> <s id="id.000383">Et<emph.end type="italics"/> <foreign lang="el">si/fwnes</foreign><lb/><emph type="italics"/>extinguendis incendijs 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. </s> <s id="id.000384">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 & Zygijs, quartum rur&longs;us in Hydrijs, ter­<lb/>tium verò in Ochoumenis Archimedes. </s> <s id="id.000385">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. </s> <s id="id.000386">Suppeditat eadem Architecturæ quoque &longs;can&longs;orias, tra­<lb/>ctiles, & &longs;pirituales machinas. <emph.end type="italics"/></s> </p> <p type="margin"> <s id="id.000387"><margin.target id="marg10"/>In parapha­<lb/>&longs;i huius li­<lb/>bri. </s> </p> <p type="margin"> <s id="id.000388"><margin.target id="marg11"/>In Pancpi­<lb/>&longs;temone. </s> </p> <p type="main"> <s id="id.000389">Natura vincit.] <emph type="italics"/>Senariolus e&longs;t cuiu&longs;dam antiqui poëtæ nomine <emph.end type="italics"/><pb xlink:href="035/01/052.jpg" 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. </s> <s id="id.000390">hos enim videns capite coopertos. </s> <s id="id.000391">Quid occultamini, inquit, <lb/>Socij, cum nullius i&longs;torum qui frequentes ad vrbis portam &longs;pectandi <lb/>gratia confluunt, cras vos &longs;it con&longs;pecturus? </s> <s id="id.000392">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. </s> <s id="id.000393">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. </s> <s id="id.000394">quod cum fa­<lb/>ciunt in ijs, in quibus iudicio omnium longe à natura &longs;uperantur<emph.end type="italics"/><lb/><foreign lang="el">paradoxo/poioi,</foreign> <emph type="italics"/>cum Galeno vocari poterunt. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000395">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 id="id.000396">In&longs;pectura domos venturáque de&longs;uper vrbi. </s> </p> <p type="main"> <s id="id.000397"><emph type="italics"/>quales multæ apud Vegetium & Heronem mechanicum. ) bom­<lb/>bardas ingentes ad locum destinatum conuertimus. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000398"><foreign lang="el">e)/sti de\ tau=ta toi=s fusikoi=s <lb/>problh/masin, ou)/te tau)ta\ pa/mpan, ou)/te kexwrisme/na li/an, <lb/>a)lla\ koina\ tw=n te maqhmatikw=n qewrhma/twn, kai\ tw=n <lb/>fusikw=n: to\ me\n ga\r w(\s dia\ tw=n maqhmatikw=n dh=lon, to\ <lb/>de\ peri\ o(\, dia\ tw=n fusikw=n.</foreign></s> </p> <p type="main"> <s id="id.000399">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. </s> <s id="id.000400">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 id="id.000401">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000402"><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 xlink:href="035/01/053.jpg" pagenum="13" /><emph type="italics"/>Ari&longs;totele, & alijs pro vtroque, vt hic, indifferenter legitur. </s> <s id="id.000403">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. </s> <s id="id.000404">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. </s> <s id="id.000405">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="el">fusikote/ras,</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="el">gra/mmikas</foreign> <emph type="italics"/>id e&longs;t lineares & <lb/>numerales demon&longs;trationes, quibus ip&longs;um explicant, Mathemati­<lb/>cas. </s> <s id="id.000406">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. </s> <s id="id.000407">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. </s> <s id="id.000408">Datum pondus <lb/>data potentia mouere. </s> <s id="id.000409">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. </s> <s id="id.000410">Sunt enim <lb/>certi fines, vltra quos natura rerum ip&longs;um progredi non patitur. <lb/></s> <s id="id.000411">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, ne fru&longs;tretur, con&longs;iderare debet, an quod <lb/>proponitur effici poßit, habita ratione 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. </s> <s id="id.000412">Hæc enim &longs;i abunde &longs;uppetant, nec ma­<lb/>teria omnino repugnet, nihil non fieri poterit. <emph.end type="italics"/></s> </p> </subchap1> <pb xlink:href="035/01/054.jpg" pagenum="14" /> <subchap1> <p type="main"> <s id="id.000413"><foreign lang="el">perie/xetai de\ tw=n a)poroume/nwn<lb/> e)n tw=| ge/nei tou/tw| ta\ peri\ to\n moxlo/n.</foreign></s> <s id="g0120102"><foreign lang="el">a)/topon ga\r <lb/>ei)=nai dokei= to\ kinei=sqai me/ga ba/ros u(po\ mikra=s i)sxu/os, <lb/>kai\ tau=ta meta\ ba/rous plei/onos: o(\ ga\r a)/neu moxlou= kinei=n <lb/>ou) du/natai/ tis, tou=to au)to\ to\ ba/ros proslabw\n e)/ti to\ <lb/>tou= moxlou= ba/ros, kinei= qa=tton.</foreign></s> </p> <p type="main"> <s id="id.000414">Dubitantur <expan abbr="aut&etilde;">autem</expan> in hoc <lb/>genere ea, quæ de vecte di­<lb/>cuntur. </s> <s id="id.000415">Ab&longs;urdum enim <lb/>videtur ab exigua vi ma­<lb/>gnum pondus moueri, & <lb/>quidem ad pondus addito <lb/>pondere. </s> <s id="id.000416">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 id="id.000417">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000418">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. </s> <s id="id.000419">vecti in v&longs;u aliquando &longs;upponi­<lb/>tur fulcimentum, quod Græci<emph.end type="italics"/> <foreign lang="el">u(pomo/xlion,</foreign> <emph type="italics"/>Vitruuius porrectam <lb/>preßionem appellat. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000420">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. </s> <s id="id.000421">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. </s> <s id="id.000422">Fieri tamen ratio repugnat. </s> <s id="id.000423">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 præua­<lb/>lere debet. </s> <s id="id.000424">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> </subchap1> <pb xlink:href="035/01/055.jpg" pagenum="15" /> <subchap1> <p type="main"> <s id="id.000425"><foreign lang="el">pa/ntwn de\ tw=n toiou/twn <lb/>e)/xei th=s ai)ti/as th\n a)rxh\n o( ku/klos, kai\ tou=to eu)lo/gws <lb/>sumbe/bhken.</foreign></s> <s id="g0120104"><foreign lang="el">e)k me\n ga\r qaumasiwte/rou sumbai/nein ti <lb/>qaumasto\n ou)de\n a)/topon. </foreign></s> </p> <p type="main"> <s id="id.000426"><expan abbr="Omniũ">Omnium</expan> verò talium cir­<lb/>culus continet cau&longs;æ prin­<lb/>cipium. </s> <s id="id.000427">quod etiam ratio­<lb/>ni valde <expan abbr="cõ&longs;entaneum">con&longs;entaneum</expan> e&longs;t. <lb/></s> <s id="id.000428">Nec enim ab&longs;urdum e&longs;t, <lb/>ex admirabiliori quid ad­<lb/>mirabile contingere. </s> </p> <p type="head"> <s id="id.000429">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000430">Omnium verò talium.] <emph type="italics"/>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. </s> <s id="id.000431">Probatur autem id ex forma circuli mi­<lb/>rabilißima. </s> <s id="id.000432">&longs;ic. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000433"><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 id="id.000434"><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 id="id.000435"><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> </subchap1> <subchap1> <p type="main"> <s id="id.000436"><foreign lang="el">qaumasiw/taton de\ to\ tou)nanti/a <lb/>gi/nesqai met' a)llh/lwn.</foreign></s> <s id="g0120202"><foreign lang="el">o( de\ ku/klos sune/sthken e)k toiou/twn. </foreign></s> <s id="g0120203"><foreign lang="el"><lb/>eu)qu\s ga\r e)k kinoume/nou te gege/nhtai kai\ me/nontos, w(=n h( <lb/>fu/sis e)sti\n u(penanti/a a)llh/lois. </foreign></s> <s id="g0120203a"><foreign lang="el">w(/st' e)ntau=qa e)/stin e)pible/yasin <lb/>h(=tton qauma/zein ta\s sumbainou/sas u(penantiw/seis <lb/>peri\ au)to/n.</foreign></s> </p> <p type="main"> <s id="id.000437">Maximè verò mirabile <lb/>e&longs;t contraria sibi inuicem <lb/>&longs;imul fieri: Atqui circulus <lb/>ex iis con&longs;titutus e&longs;t. </s> <s id="id.000438">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. </s> <s id="id.000439">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 id="id.000440">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000441">Maxime verò.] <emph type="italics"/>Circuli admiranda natura declaratur è <lb/>quintuplici contrariorum, quæ in eo præter contrariorum <emph.end type="italics"/><pb xlink:href="035/01/056.jpg" pagenum="16" /><emph type="italics"/>legem &longs;imul reperiuntur, repugnantia. </s> <s id="id.000442">Ex his triplex deprehenditur <lb/>in circulo dum fit: duplex vero dum factus e&longs;t. </s> <s id="id.000443">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 contrarijs, vno natu­<lb/>rali ad peripheriam &longs;cilicet, altero violento ad centrum moueatur. </s> <s id="id.000444">In <lb/>facto verò hoc admirabile e&longs;t, quod eius terminus vna linea exi­<lb/>&longs;tens, ob ídque 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. </s> <s id="id.000445">Hæc <lb/>&longs;ingula &longs;uis locis delineabuntur & explicabuntur. </s> <s id="id.000446">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. </s> <s id="id.000447">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 <expan abbr="quodãmodo">quodammodo</expan> vndequaque angu­<lb/>lata, cum nu&longs;quam &longs;it, dici poßit, & figura<emph.end type="italics"/> <foreign lang="el">pa/ngwnos & 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 offen&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 xlink:href="035/01/057.jpg" 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. </s> <s id="id.000448">quod 16. prop. lib. 3. elem. e&longs;t demon&longs;tratum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000450">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. </s> <s id="id.000451">Circulum autem fieri ex moto & quieto patet his, <lb/>qui eius fabricam repetent è 3. po&longs;tulato element.Eucl. </s> <s id="id.000452">Ibi enim po­<lb/>&longs;tulatur, vt è dato centro & interuallo circulum de&longs;cribere conce­<lb/>datur. </s> <s id="id.000453">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 id="id.000454">Ex vno duo ferrea brachia nodo <lb/>Iunxit, vt æquali &longs;patio di&longs;tanti­<lb/><figure id="id.035.01.057.1.jpg" xlink:href="035/01/057/1.jpg"/><lb/>bus ip&longs;is</s> </p> <p type="main"> <s id="id.000455">Altera pars &longs;taret, pars altera du­<lb/>ceret orbem. </s> </p> <p type="main"> <s id="id.000456"><emph type="italics"/>Sit igitur recta A B inter extrema duo­<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. </s> <s id="id.000457">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> </subchap1> <subchap1> <p type="main"> <s id="id.000458"><foreign lang="el">prw=ton me\n ga\r th=| periexou/sh| grammh=| to\n <lb/>ku/klon pla/tos ou)qe\n e)xou/sh|, ta)nanti/a pws prosemfai/netai, <lb/>to\ koi=lon kai\ to\ kurto/n.</foreign></s> <s id="g0120204"><foreign lang="el">tau=ta de\ die/sthken a)llh/lwn, <lb/>o(\n tro/pon to\ me/ga kai\ to\ mikro/n. </foreign></s> <s id="g0120205"><foreign lang="el">e)kei/nwn te ga\r <lb/>me/son to\ i)/son kai\ tou/twn to\ eu)qu/. </foreign></s> <s id="g0120205a"><foreign lang="el">dio\ metaba/llonta ei)s <lb/>a)/llhla, ta\ me\n a)nagkai=a i)/sa gene/sqai pro/teron h)\ tw=n<lb/> a)/krwn o(poteronou=n, th\n de\ grammh\n eu)qei=an, o(/tan e)k kurth=s <lb/>ei)s koi=lon h)\ pa/lin e)k tau/ths gi/nhtai kurth\ kai\ periferh/s. <lb/></foreign></s> <s id="g0120205b"><foreign lang="el">e(\n kai\ ou)=n tou=to tw=n a)to/pwn u(pa/rxei peri\ to\n ku/klon.</foreign></s> </p> <p type="main"> <s id="id.000459">Primum &longs;iquidem lineæ <lb/>ip&longs;um circulum <expan abbr="compre­hend&etilde;ti">compre­<lb/>hendenti</expan>, licet latitudinem <lb/>nullam habeat, contraria <lb/>quodammodo, cauum & <lb/>conuexum ine&longs;&longs;e <expan abbr="appar&etilde;t">apparent</expan>. <lb/></s> <s id="id.000460">Hæc autem ita inter &longs;e di­<lb/>&longs;tant, vt <expan abbr="magnũ">magnum</expan> & paruum. <pb xlink:href="035/01/058.jpg" pagenum="18" /></s> <s>horum enim medium e&longs;t <lb/>æquale: illorum verò re­<lb/>ctum. </s> <s id="id.000461">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. </s> <s id="id.000462">Atque vnum hoc <lb/>e&longs;t ex ab&longs;urdis qu&etail; in&longs;unt <lb/>circulo. </s> </p> <p type="head"> <s id="id.000463">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000464">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="el">prw/ton</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="el">deu/teron. </foreign><emph type="italics"/>Namque hîc non prima, vt iam patuit: &longs;ed &longs;e­<lb/>cunda e&longs;t in circulo repugnantia. </s> <s id="id.000465">Eaque ex eo quod cum circuli peri­<lb/>pheria &longs;it vna linea def. 15. lib. 1. elem. & idcirco latitudinis expers <lb/>def. 2. lib. eiu&longs;dem: habeat tamen in &longs;e contraria conuexum &longs;cilicet, <lb/>& concauum: illud quidem quà &longs;pectat foras: hoc vero quà intra. <lb/></s> <s id="id.000469">vbi nota Ari&longs;totelem dixi&longs;&longs;e hæc<emph.end type="italics"/> <foreign lang="el">e)nanti/a pws</foreign> <emph type="italics"/>contraria quodam­<lb/>modo. </s> <s id="id.000470">Nec enim vere contraria &longs;unt, quia vere contraria &longs;unt ea, <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/>rentijs, quod &longs;cilicet aliæ alijs &longs;int al­<emph.end type="italics"/><lb/><figure id="id.035.01.058.1.jpg" xlink:href="035/01/058/1.jpg"/><lb/><emph type="italics"/>tiores, vel depreßiores. </s> <s id="id.000471">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. </s> <s>Cum igitur ab eadem C D<emph.end type="italics"/><pb xlink:href="035/01/059.jpg" 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 id="id.000473">Hæc autem ita.] <emph type="italics"/>Similitudine comprobatur conuexum & <lb/>concauum contraria e&longs;&longs;e. </s> <s id="id.000474">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 fieri nece&longs;&longs;um e&longs;t. </s> <s id="id.000475">&longs;unt igitur conuexum & concauum <lb/>contraria. </s> <s id="id.000476">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. </s> <s id="id.000478">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. </s> <s id="id.000479">Quia non habent <lb/>omnes prædictæ definitionis particulas &longs;ibi conuenientes. </s> <s id="id.000480">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. </s> <s id="id.000481">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. </s> <s id="id.000482">Symmetrum appello, quod iu&longs;tam ma­<lb/>gnitudinem in &longs;uo genere adeptum e&longs;t. </s> <s id="id.000483">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. </s> <s id="id.000484">Vt e&longs;to, quod aiunt <lb/>multi, iu&longs;ta hominis magnitudo &longs;ex pedum. </s> <s id="id.000485">Qui igitur inter homi­<lb/>nes &longs;eptempedalis e&longs;t, magnus: qui quintumpedalis, paruus &longs;implici­<lb/>ter dicetur. </s> <s id="id.000486">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 id="id.000487">Atque vnum hoc e&longs;t.] <foreign lang="el">to\ a)/topon. </foreign><emph type="italics"/>Hic vt & alibi &longs;æpius <lb/>pro<emph.end type="italics"/> <foreign lang="el">qauma/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> </subchap1> <pb xlink:href="035/01/060.jpg" pagenum="20" /> <subchap1> <p type="main"> <s id="id.000488"><foreign lang="el">deu/teron de\ o(/ti a(/ma kinei=tai ta\s e)nanti/as kinh/seis: <lb/>a(/ma ga\r ei)s to\n e)/mprosqen kinei=tai to/pon kai\ to\n o)/pisqen: <lb/>h(/ te gra/fousa grammh\ to\n ku/klon w(sau/tws e)/xei. </foreign></s> <s id="g0120302a"><foreign lang="el">e)c <lb/>ou(= ga\r a)/rxetai to/pou to\ pe/ras au)th=s, ei)s to\n au)to\n tou=ton to/pon <lb/>e)/rxetai pa/lin: sunexw=s ga\r kinoume/nhs au)th=s to\ e)/sxaton <lb/>pa/lin a)ph=lqe prw=ton, w(/ste kai\ fanero\n o(/ti mete/balen <lb/>e)nteu=qen.</foreign></s> <s id="g0120303"><foreign lang="el">dio/, kaqa/per ei)/rhtai pro/teron, ou)de\n a)/topon, to\ <lb/>pa/ntwn ei)=nai tw=n qauma/twn au)to\n a)rxh/n.</foreign></s> <s id="g0120401"><foreign lang="el">ta\ me\n ou)=n peri\ <lb/>to\n zugo\n gino/mena, ei)s to\n ku/klon a)na/getai, ta\ de\ peri\ <lb/>to\n moxlo\n ei)s to\n zugo/n. </foreign></s> <s id="g0120401a"><foreign lang="el">ta\ d' a)/lla pa/nta sxedo\n ta\ <lb/>peri\ ta\s kinh/seis ta\s mhxanika\s, ei)s to\n moxlo/n.</foreign></s> </p> <p type="main"> <s id="id.000489">Secundum e&longs;t, quod con­<lb/>trariis motionibus &longs;imul <lb/>moueatur. </s> <s id="id.000490">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 habet, <lb/>vt ex quo loco extremum <lb/>illius incipiat, rur&longs;us ad <lb/>eundem redeat. </s> <s id="id.000491">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. </s> <s id="id.000492">Ita­<lb/>que manife&longs;tum, quod in­<lb/>de <expan abbr="mutatũ">mutatum</expan> e&longs;t. </s> <s id="id.000493">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. </s> <s id="id.000494">Igitur & qu&etail; circa <lb/>libram eueniunt ad circu­<lb/>lum referuntur, & qu&etail; 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 id="id.000495">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000496">Secundum.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="el">deu/teron</foreign> <emph type="italics"/>legamus &longs;i placet<emph.end type="italics"/> <foreign lang="el">trh/ton. </foreign><emph type="italics"/>Hic enim <lb/>tertia e&longs;t repugnantia in circulo ex contrarijs 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. </s> <s id="id.000497">Hoc autem e&longs;t contrarias motiones <lb/>&longs;imul habere. </s> <s>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;tantijs 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 id="id.000500">Atque linea circulum.] <emph type="italics"/>Cur circulus antè & ponè mouea­<emph.end type="italics"/><pb xlink:href="035/01/061.jpg" pagenum="21" /><emph type="italics"/>tur, ratio adducitur &longs;umpta ab efficiente circuli cau&longs;a. </s> <s id="id.000501">Sic &longs;yllo­<lb/>gi&longs;mus in&longs;titui pote&longs;t. </s> <s id="id.000502">Vt fit circulus ita mouetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000503"><emph type="italics"/>Fit circulus à linea continenter mota circa fixum extremorum <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 id="id.000504"><emph type="italics"/>Ergo circulus mouetur per loca è diametro oppo&longs;ita circa extre­<lb/>mum lineæ à qua fit fixum. </s> <s id="id.000505">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 id="id.000506"><emph type="italics"/>Centrum enim in plano circundatur quatuor loci differentijs, <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. </s> <s>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="id.035.01.061.1.jpg" xlink:href="035/01/061/1.jpg"/><lb/><emph type="italics"/>fieri primum. </s> <s id="id.000507">Vnde cum circulus moue­<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 id="id.000508"><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. </s> <s id="id.000509">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. </s> <s id="id.000510">E&longs;t hæc igitur vt aliæ in circulo non vera <lb/>&longs;ed apparens repugnantia. </s> <s id="id.000511">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 alte­<lb/>rum extremum D, attolli: & contra. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000512">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, <expan abbr="trãspo&longs;ita">transpo&longs;ita</expan>, <lb/>quod amplius declarant ea, quæ &longs;ubijciuntur de vecte & libra, ad <lb/>quæ cum referat omnia Mechanica, & ip&longs;a vectis & libra referan­<emph.end type="italics"/><pb xlink:href="035/01/062.jpg" 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> </subchap1> <subchap1> <p type="main"> <s id="id.000513"><foreign lang="el">e)/ti de\ <lb/>dia\ to\ mia=s ou)/shs th=s e)k tou= ke/ntrou grammh=s mhqe\n e(/teron <lb/>e(te/rw| fe/resqai tw=n shmei/wn tw=n e)n au)th=| i)sotaxw=s, a)ll' a)ei\ <lb/>to\ tou= me/nontos pe/ratos porrw/teron o)\n qa=tton, polla\ tw=n qaumazome/nwn <lb/>sumbai/nei peri\ ta\s kinh/seis tw=n ku/klwn, peri\ <lb/>w(=n e)n toi=s e(pome/nois problh/masin e)/stai dh=lon.</foreign></s> </p> <p type="main"> <s id="id.000514">Præterea etiam, quod, <lb/>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: &longs;ed <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;e­qu&etilde;tibus">&longs;e­<lb/>quentibus</expan> problematis fiet <lb/>manife&longs;tum. </s> </p> <p type="head"> <s id="id.000515">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000516">Præterea etiam.] <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. </s> <s id="id.000517">Inæqualiter enim moueri dicuntur, & quæ eodem tem­<lb/>pore diuer&longs;a permeant &longs;patia, & quæ in æqualibus temporibus idem: <lb/>atque hoc celerius, quod eodem tempore maius &longs;patium permeat, vel <lb/>breuiori tempore idem: Tardius contra. </s> <s id="id.000518">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. </s> <s id="id.000519">Linea enim circulum <lb/>de&longs;cribens, quo tempore punctis centro propinquis redijt ad locum, <lb/>vnde ij&longs;dem moueri cœperat, eodem remotis redit. </s> <s id="id.000520">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. </s> <s id="id.000521">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 xlink:href="035/01/063.jpg" pagenum="23" /> <p type="main"> <s id="id.000522"><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. </s> <s id="id.000523">Dico periphe­<lb/>riam A B C maiorem peripheria D F G. </s> <s id="id.000524">Producatur enim A E <lb/>recta vt &longs;it A C <lb/>diameter po&longs;tul. <emph.end type="italics"/><lb/><figure id="id.035.01.063.1.jpg" xlink:href="035/01/063/1.jpg"/><lb/>2. <emph type="italics"/><expan abbr="it&etilde;">item</expan> D H vt &longs;it <lb/>& D G diame­<lb/>ter. </s> <s id="id.000525">Quia igi­<lb/>tur vt diameter <lb/>A C ad <expan abbr="&longs;uã">&longs;uam</expan> <expan abbr="pe­ripheriã">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. </s> <s id="id.000529">E&longs;t <lb/>autem A E maior: quam D H ex hypothe&longs;i. </s> <s id="id.000530">Erit igitur peri­<lb/>pheria A B C maior: quam peripheria D F G. </s> <s id="id.000531">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> </subchap1> <subchap1> <p type="main"> <s id="id.000532"><foreign lang="el">dia\ de\ to\ <lb/>ta\s e)nanti/as kinh/seis a(/ma kinei=sqai to\n ku/klon, kai\ to\ <lb/>me\n e(/teron th=s diame/trou tw=n a)/krwn, e)f' ou(= to\ a, ei)s tou)/mprosqen <lb/>kinei=sqai, qa/teron de/, e)f' ou(= to\ *b ei)s tou)/pisqen <lb/>kataskeua/zousi/ tines, w(/st' a)po\ mia=s kinh/sews pollou\s u(penanti/ous <lb/>a(/ma kinei=sqai ku/klous, w(/sper ou(\s a)natiqe/asin e)n <lb/>toi=s i(eroi=s; poih/santes troxi/skous xalkou=s te kai\ sidhrou=s.</foreign></s> <s id="g0120502"><foreign lang="el"><lb/>ei) ga\r ei)/h tou= *a*b ku/klou a(pto/menos e(/teros ku/klos e)f' ou(= <lb/>*g*d, tou= ku/klou, e)f' ou(= *a*b, kinoume/nhs th=s diame/trou <lb/>ei)s tou)/mprosqen, kinhqh/setai h( *g*d ei)s tou)/pisqen tou= ku/klou <lb/>tou= e)f' w(=| *a, kinoume/nhs th=s diame/trou peri\ to\ au)to/.</foreign></s> <s id="g0120503"><foreign lang="el">ei)s <lb/>tou)nanti/on a)/ra kinhqh/setai o( e)f' ou(= *g*d ku/klos, tw=| e)f' <lb/>ou(= to\ *a*b: kai\ pa/lin au)to\s to\n e)fech=s, e)f' ou(= *e*z, ei)s <lb/>tou)nanti/on au(tw=| kinh/sei dia\ th\n au)th\n tau/thn ai)ti/an.</foreign></s> <s id="g0120601"><foreign lang="el">to\n au)to\n de\ <lb/>tro/pon ka)\n plei/ous w)=si, tou=to poih/sousin e(no\s mo/nou kinhqe/ntos.</foreign></s> <s id="g0120602"><foreign lang="el"><lb/>tau/thn ou)=n labo/ntes u(pa/rxousan e)n tw=| ku/klw| th\n <lb/>fu/sin oi( dhmiourgoi\ kataskeua/zousin o)/rganon kru/ptontes <lb/>th\n a)rxh/n, o(/pws h)=| tou= mhxanh/matos fanero\n mo/non to\ <lb/>qaumasto/n, to\ d' ai)/tion a)/dhlon. <lb/></foreign></s> </p> <p type="main"> <s id="id.000533">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 xlink:href="035/01/064.jpg" pagenum="24" />los æreos & ferreos. </s> <s id="id.000534">Si <lb/>enim circulum in quo e&longs;t <lb/>A B, alter circulus in quo <lb/>e&longs;t G D attigerit, diame­<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. </s> <s id="id.000535">Circulus igitur in quo <lb/>e&longs;t G D, contrà, quam is, <lb/>in quo e&longs;t A B mouebi­<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>. </s> <s id="id.000536">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 id="id.000537">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000538">Qvod autem circulus.] <emph type="italics"/>Tertia repugnantia in vnius cir­<lb/>culi contrarijs motionibus ante po&longs;ita amplius declaratur, ab <lb/>exemplo plurium: &longs;ed contiguorum ab vnica vi primaria &longs;ecundum <lb/>motus contrarios motorum. </s> <s id="id.000539">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 xlink:href="035/01/065.jpg" 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="id.035.01.065.1.jpg" xlink:href="035/01/065/1.jpg"/><lb/><emph type="italics"/>&longs;eu <expan abbr="&longs;ecũ­dum">&longs;ecun­<lb/>dum</expan> <expan abbr="in­ferior&etilde;">in­<lb/>feriorem</expan> <lb/><expan abbr="periphe­riã">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. </s> <s id="id.000540">Vnde tunc à Fabro dato <lb/>principio motionis, vertebra vertebram continenter mouet, vltimá­<lb/>que ab illis &longs;imulacrorum excita fit præteruectio, non aliter quam 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 id="id.000541">Hinc architecti.] <emph type="italics"/>Sicuti ante ex vnius circuli contrarijs 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 contrarij;s 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> dijs &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. </s> <s id="id.000542">Huius rei <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. </s> <s id="id.000545">Herodotus hi&longs;toria &longs;ecunda videtur ex his aliqua<emph.end type="italics"/> <foreign lang="el">neu­<lb/>ro/spasta</foreign> <emph type="italics"/>appella&longs;&longs;e: qua&longs;i diceremus, per funiculos tanquam neruos <lb/>circa rotulas inuolutos, varijs motibus agitata. </s> <s id="id.000546">Eiu&longs;modi 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"/><lb/><emph type="italics"/>& vago quodam &longs;inuo&longs;oque impetu ferebantur in fugam: ligatæ <lb/>vero permanebant, vnde illæ non magno pretio emebantur in&longs;tar <lb/>&longs;erui fugitiui: hæ contra magno. </s> <s id="id.000547">Erant enim præclara opera. <emph.end type="italics"/><pb xlink:href="035/01/066.jpg" 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="el">au)to/mata</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. </s> <s id="id.000548">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>. </s> <s id="id.000549">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 duodecim &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, & horas tum æqua­<lb/>les, tum inæquales intueri licet. </s> <s id="id.000550">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>. </s> <s id="id.000551">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, pro <lb/>fal&longs;is minime habeamus. <emph.end type="italics"/></s> </p> <p type="margin"> <s id="id.000552"><margin.target id="marg12"/>In Menone</s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.000553">2. <foreign lang="el">*amfi\ zugou= dia\ ti/ e)n tw|= <lb/>ku/klw| h( mei/zwn grammh\ <lb/>qa=tton fe/retai th=s e)lattonos, <lb/>kai\ e)nteu=qen dia\ ti/ ta\ mei/­<lb/>zw zuga\ a)kribetera/ e)sti tw=n <lb/>e)latto/nwn. </foreign></s> </p> <p type="main"> <s id="id.000554">2. De libra propter quid <lb/>maior linea in circulo <lb/>celerius fertur, minore. <lb/></s> <s id="id.000555">Ex quo fit vt libræ ma­<lb/>iores minoribus &longs;int <lb/>exactiores. </s> </p> <p type="main"> <s><foreign lang="el">*prw=ton me\n ou)=n ta\ sumbai/nonta peri\ to\n zugo\n a)porei=tai, <lb/>dia\ ti/na ai)ti/an a)kribe/stera/ e)sti ta\ zuga\ ta\ mei/zw <lb/>tw=n e)latto/nwn.</foreign></s> <s id="g0120702"><foreign lang="el">tou/tou de\ a)rxh/, dia\ ti/ pote e)n tw=| ku/klw| <lb/>h( plei=on a)festhkui=a grammh\ tou= ke/ntrou th=s e)ggu\s, th=| <lb/>au)th=| i)sxu/i kinoume/nh qa=tton fe/retai th=s e)la/ttonos, to\ <lb/>ga\r qa=tton le/getai dixw=s.</foreign></s> <s id="g0120704"><foreign lang="el">a)/n te ga\r e)n e)la/ttoni xro/nw| <lb/>i)/son to/pon diece/lqh|, qa=tton ei)=nai le/gomen, kai\ e)a\n e)n i)/sw|, <lb/>plei/w.</foreign></s> <s id="g0120705"><foreign lang="el">h( de\ mei/zwn e)n i)/sw| xro/nw| gra/fei mei/zona ku/klon: <lb/>o( ga\r e)kto\s mei/zwn tou= e)nto/s.</foreign></s> </p> <p type="main"> <s id="id.000557"><expan abbr="Primũ">Primum</expan> igitur qu&etail; circa <expan abbr="li­brã">li­<lb/>bram</expan> <expan abbr="cõtingunt">contingunt</expan>, <expan abbr="difficultat&etilde;">difficultatem</expan> <lb/><expan abbr="adferũt">adferunt</expan>. </s> <s id="id.000558">Ob quam cau&longs;am <pb xlink:href="035/01/067.jpg" pagenum="27" />libræ maiores minoribus <lb/>&longs;int exactiores. </s> <s id="id.000559">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/></s> <s id="id.000560">Celerius autem dicitur bi­<lb/>fariam, &longs;iue enim in mino­<lb/>ri tempore &etail;quale &longs;patium <lb/>tran&longs;ierit, celerius e&longs;&longs;e di­<lb/>cimus: &longs;iue in <expan abbr="t&etilde;pore">tempore</expan> &etail;qua­<lb/>li, maius. </s> <s id="id.000561">Maior autem li­<lb/>nea in æquali <expan abbr="t&etilde;pore">tempore</expan> ma­<lb/>iorem circulum de&longs;cribit. <lb/></s> <s id="id.000562">Qui enim extra e&longs;t, maior <lb/>e&longs;t eo, qui intus. </s> </p> <p type="head"> <s id="id.000563">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000564">De libra propter.] <emph type="italics"/>In hoc capite Ari&longs;toteles vult o&longs;tendere <lb/>cur libræ longiorum brachiorum &longs;int exactiores: quam libræ <lb/>breuiorum. </s> <s id="id.000565">Et huius problematis cau&longs;am refert ad circulum, circu­<lb/>lique eam proprietatem, qua radij longiores celerius, id e&longs;t eodem <lb/>tempore maius &longs;patium conficiunt, quam breuiores. </s> <s id="id.000566">Quod quia futu­<lb/>rum e&longs;t fundamentum multorum aliorum problematum po&longs;tea ex­<lb/>plicandorum, diligenter imprimis demon&longs;trat. </s> <s id="id.000567">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. </s> <s id="id.000568">Et ex his alteram e&longs;&longs;e &longs;ecundum naturam, alteram <lb/>præter naturam. </s> <s id="id.000569">Po&longs;tremò quod latio &longs;ecundum naturam in maiore <lb/>circulo maior &longs;it: quam in minore. </s> <s id="id.000570">Latio autem præter naturam in <lb/>minore circulo maior &longs;it: quam in maiore. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000571">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 id="id.000572">Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli <emph.end type="italics"/><pb xlink:href="035/01/068.jpg" 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 id="id.000573">Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i­<lb/>miles ijs quos cap. 2. lib. 6. de Phy&longs;. auditu attulit, vt vtro longioris <lb/>radij celeritas accipi debeat, intelligatur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000574">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. </s> <s id="id.000575">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. </s> <s id="id.000578">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. </s> <s id="id.000580">Illi quorum &longs;emidiametri &longs;unt <lb/>inæquales, erunt & inæquales, & ille maior, cuius &longs;emidiameter <lb/>maior. </s> <s id="id.000581">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. </s> <s id="id.000583">De <lb/>duabus rectis intra triangulum, rectangulum vel amblygonium <lb/>comprehen&longs;is, quæ maiores con&longs;titui po&longs;&longs;unt ijs à quibus ambiuntur. <lb/></s> <s id="id.000584">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> </subchap1> <subchap1> <p type="main"> <s id="id.000585"><foreign lang="el"> ai)/tion de\ tou/twn, o(/ti fe/retai <lb/>du/o fora\s h( gra/fousa to\n ku/klon.</foreign></s> <s id="g0120707"><foreign lang="el">o(/tan me\n ou)=n e)n lo/gw| <lb/>tini\ fe/rhtai, e)p' eu)qei/as a)na/gkh fe/resqai to\ fero/menon, <lb/>kai\ gi/netai dia/metros au)th\ tou= sxh/matos o(\ poiou=sin ai( <lb/>e)n tou/tw| tw=| lo/gw| sunteqei=sai grammai/.</foreign></s> <s id="g0120708"><foreign lang="el">e)/stw ga\r o( lo/gos <lb/>o(\n fe/retai to\ fero/menon, o(\n e)/xei h( *a*b, pro\s th\n *a*g, <lb/>kai\ to\ me\n *a*g fere/sqw pro\s to\ *b, h( de\ *a*b u(pofere/sqw <lb/>pro\s th\n *h*g: e)nhne/xqw de\ to\ me\n *a pro\s to\ *d, h( de\ e)f' <lb/>h(=| *a*b pro\s to\ *e. </foreign></s> <s id="g0120708a"><foreign lang="el">ou)kou=n e)pi\ th=s fora=s o( lo/gos h)=n, o(\n h( <lb/>*a*b e)/xei pro\s th\n *a*g, a)na/gkh kai\ th\n *a*d, pro\s th\n <lb/>*a*e, tou=ton e)/xein to\n lo/gon, o(/moion a)/ra e)sti\ tw=| lo/gw| to\ <lb/>mikro\n tetra/pleuron tw=| mei/zoni, w(/ste kai\ h( au)th\ dia/metros <lb/>au)tw=n, kai\ to\ *a e)/stai pro\s to\ *z.</foreign></s> <s id="g0120801"><foreign lang="el">to\n au)to\n dh\ tro/pon <lb/>deixqh/setai ka)\n o(pouou=n dialhfqh=| h( fora/: ai)ei\ ga\r <lb/>e)/stai e)pi\ th=s diame/trou.</foreign></s> <s id="g0120802"><foreign lang="el">fanero\n ou)=n o(/ti to\ kata\ th\n dia/metron <lb/>fero/menon e)n du/o forai=s, a)na/gkh to\n tw=n pleurw=n <lb/>fe/resqai lo/gon.</foreign></s> </p> <p type="main"> <s id="id.000586">Horum vero cau&longs;a e&longs;t, <lb/>quod recta de&longs;cribens <expan abbr="cir­culũ">cir­<lb/>culum</expan> <expan abbr="&longs;ecundũ">&longs;ecundum</expan> duas latio­<lb/>nes fertur. </s> <s id="id.000587"><expan abbr="Cũ">Cum</expan> igitur in ali­<lb/>qua ratione du&etail; <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>. </s> <s id="id.000588">Sit <lb/>enim ratio <expan abbr="&longs;ecundũ">&longs;ecundum</expan> quam <lb/>mobile fertur ea: quam ha­<pb xlink:href="035/01/069.jpg" pagenum="29" />bet <foreign lang="el">a b</foreign> ad <foreign lang="el">a g,</foreign> & quidem <lb/><foreign lang="el">a</foreign> feratur ad <foreign lang="el">b,</foreign> & <foreign lang="el">a b</foreign><lb/>etiam feratur ad <foreign lang="el">h g</foreign>: la­<lb/>tum vero &longs;it <foreign lang="el">a</foreign> ad <foreign lang="el">d,</foreign> & <lb/><foreign lang="el">a b</foreign> ad <foreign lang="el">e. </foreign>Igitur cum latio­<lb/>nis ratio erat ea quam ha­<lb/>bet <foreign lang="el">a b</foreign> ad <foreign lang="el">a g</foreign>: nece&longs;&longs;e <lb/>e&longs;t & ip&longs;am <foreign lang="el">a d</foreign> ad <foreign lang="el">a e</foreign> ean­<lb/>dem habere rationem. </s> <s id="id.000589">Si­<lb/>mile e&longs;t enim ratione par­<lb/>uum quadrilaterum maio­<lb/>ri. </s> <s id="id.000590">Itaque & eadem diame­<lb/>ter vtriu&longs;que, & ip&longs;um <foreign lang="el">a</foreign><lb/>erat vbi <foreign lang="el">z. </foreign></s> <s>Eodem modo <lb/>demon&longs;trabitur <expan abbr="vbicũque">vbicunque</expan> <lb/>latio deprehen&longs;a fuerit. </s> <s id="id.000591"><expan abbr="S&etilde;­per">Sem­<lb/>per</expan> enim &longs;upra diametrum <lb/>erit. </s> <s id="id.000592">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 id="id.000593">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000594">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. </s> <s id="id.000595">Atque hinc elicitur quinta in <lb/>circulo repugnantia, ex qua admiratio eius maior: quam ante e&longs;&longs;e <lb/>concluditur. </s> <s id="id.000596">E lationibus enim illis vna e&longs;t &longs;ecundum naturam, <lb/>altera præter naturam. </s> <s id="id.000597">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? </s> <s id="id.000598">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 id="id.000599">Cum igitur in.] <emph type="italics"/>Aggreditur demon&longs;trare radij duas lationes <lb/>nullam habere rationem inter &longs;e. </s> <s id="id.000600">Syllog. &longs;ic e&longs;t. </s> <s id="id.000601">Omne duabus latio­<lb/>nibus rationem aliquam inter &longs;e &longs;eruantibus latum, fertur &longs;ecundum <emph.end type="italics"/><pb xlink:href="035/01/070.jpg" pagenum="30" /><emph type="italics"/>rectam. </s> <s id="id.000602">Radius de&longs;cribens circulum duabus &longs;uis lationibus, non <lb/>fertur &longs;ecundum rectam. </s> <s id="id.000603">Radij igitur lationes in nulla &longs;unt ra­<lb/>tione. </s> <s id="id.000604">Propo&longs;itio confirmatur cum &longs;equenti diagrammate. <lb/></s> <s id="id.000605">E&longs;to rectangulum<emph.end type="italics"/> <foreign lang="el">a b h g</foreign> <emph type="italics"/>com­<emph.end type="italics"/><lb/><figure id="id.035.01.070.1.jpg" xlink:href="035/01/070/1.jpg"/><lb/><emph type="italics"/>prehen&longs;um &longs;ub rectis<emph.end type="italics"/> <foreign lang="el">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="el">a</foreign> <emph type="italics"/>habent. <lb/></s> <s id="id.000606">Et intelligatur a latum ver&longs;us<emph.end type="italics"/><lb/><foreign lang="el">b</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="el">d,</foreign> <emph type="italics"/>& ver&longs;us<emph.end type="italics"/><lb/><foreign lang="el">g</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="el">e</foreign>: <emph type="italics"/>&longs;icque cum <lb/>lationum ip&longs;ius<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ratio &longs;it vt<emph.end type="italics"/><lb/><foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a g,</foreign> <emph type="italics"/>ergo erit &<emph.end type="italics"/> <foreign lang="el">a d</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a e</foreign>: <emph type="italics"/>vt<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a y,</foreign> <emph type="italics"/>& rectrangulum minus<emph.end type="italics"/> <foreign lang="el">a d z e</foreign> <emph type="italics"/>com­<lb/>munem angulum<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>cum maiori<emph.end type="italics"/> <foreign lang="el">a b h g</foreign> <emph type="italics"/>habens & &longs;imile erit <lb/>def. 1. lib. 6. & proinde circa eandem dimentientem conuer&longs;. prop. <lb/>24. lib. 6. </s> <s><emph type="italics"/>Et &longs;ic<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="el">z,</foreign> <emph type="italics"/>vt vbi­<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="el">a h. </foreign><emph type="italics"/>&longs;iquidem lationes i&longs;tæ &longs;unt in ratione<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a g. </foreign><emph type="italics"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. </s> <s id="id.000609">Huic con­<lb/>&longs;entit quod à Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. </s> <s id="id.000610">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. </s> <s id="id.000612">Nunc igitur ponatur<emph.end type="italics"/> <foreign lang="el">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. </s> <s id="id.000613">Non igitur duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ferun­<lb/>tur in ratione<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">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. </s> <s id="id.000614">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. </s> <s id="id.000615">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. </s> <s id="id.000616">Et &longs;it manebit demon&longs;tratio. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000617">Simile e&longs;t enim.] <foreign lang="el">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> </subchap1> <pb xlink:href="035/01/071.jpg" pagenum="31" /> <subchap1> <p type="main"> <s id="id.000619"><foreign lang="el">ei) ga\r a)/llon tina/, ou)k oi)sqh/setai kata\ <lb/>th\n dia/metron.</foreign></s> <s id="g0120804"><foreign lang="el">e)a\n de\ e)n mhdeni\ lo/gw| fe/rhtai du/o fora\s <lb/>kata\ mhde/na xro/non, a)du/naton eu)qei=an ei)=nai th\n fora/n.</foreign></s> <s id="g0120805"><foreign lang="el"><lb/>e)/stw ga\r eu)qei=a.</foreign></s> <s id="g0120806"><foreign lang="el">teqei/shs ou)=n tau/ths diame/trou, kai\ paraplhrwqeisw=n <lb/>tw=n pleurw=n, a)na/gkh to\n tw=n pleurw=n lo/gon <lb/>fe/resqai to\ fero/menon: tou=to ga\r de/deiktai pro/teron.</foreign></s> <s id="g0120807"><foreign lang="el">ou)k <lb/>a)/ra poih/sei eu)qei=an to\ e)n mhdeni\ lo/gw| fero/menon mhde/na <lb/>xro/non.</foreign></s> <s id="g0120808"><foreign lang="el">e)a\n ga/r tina lo/gon e)nexqh=| e)n xro/nw| tini/, tou=ton <lb/>a)na/gkh to\n xro/non eu)qei=an ei)=nai fora\n dia\ ta\ proeirhme/na.</foreign></s> <s id="g0120809"><foreign lang="el"><lb/>w(/ste perifere\s gi/netai, du/o fero/menon fora\s e)n mhqeni\ <lb/>lo/gw| mhqe/na xro/non.</foreign></s> </p> <p type="main"> <s id="id.000620">Si enim in alia aliqua, <lb/>non feretur <expan abbr="&longs;ecũdum">&longs;ecundum</expan> dia­<lb/>metrum. </s> <s id="id.000621">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. </s> <s id="id.000622">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. </s> <s id="id.000623">Hoc enim prius fuit <lb/>demon&longs;tratum. </s> <s id="id.000624">Non igi­<lb/>tur &longs;ecundum rectam pro­<lb/>gredietur, id quod fertur <lb/>in nulla ratione, nulloque <lb/>in tempore. </s> <s>[Si enim <expan abbr="&longs;e­cũdum">&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.] </s> <s>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 id="id.000625">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000626">Si enim in alia.] <emph type="italics"/>Locus hic paulo ob&longs;curior, debet &longs;ic intelligi, <lb/>vt &longs;i exempli gratia, a duabus lationibus latum non feratur in <lb/>ratione quidem data<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">a g</foreign>: <emph type="italics"/>&longs;ed<emph.end type="italics"/><lb/><figure id="id.035.01.071.1.jpg" xlink:href="035/01/071/1.jpg"/><lb/><emph type="italics"/>in alia, non feretur &longs;ecundum diame­<lb/>trum<emph.end type="italics"/> <foreign lang="el">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="el">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="el">a d, a e</foreign> <emph type="italics"/>comprehen&longs;i. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/072.jpg" pagenum="32" /> <p type="main"> <s id="id.000627">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. </s> <s id="id.000628">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. </s> <s id="id.000629">Ergo impoßibile <lb/>e&longs;t punctum, quod de&longs;cribit circulum, ferri &longs;ecundum rectam. </s> <s id="id.000630">Sint <lb/>enim lationes illæ in aliqua ratione. </s> <s id="id.000631">Ergo punctum feretur &longs;ecun­<lb/>dum rectam: at non fertur &longs;ecundum rectam. </s> <s id="id.000632">Peripheria enim non <lb/>e&longs;t recta: &longs;ed curua. </s> <s id="id.000633">Non igitur in aliqua ratione &longs;unt illius lationes. <lb/></s> <s id="id.000634">Et &longs;i non in vlla ratione. </s> <s id="id.000635">nec igitur in tempore, quia tempora moti­<lb/>bus analoga &longs;unt. </s> <s id="id.000636">Hîc duo occurrunt valde difficilia. </s> <s id="id.000637">Prius de <lb/>tempore. </s> <s id="id.000638">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. </s> <s id="id.000639">Hoc <lb/>enim repugnat def. 3. lib. 5. elem. </s> <s id="id.000641">quantitas enim motus vnius mul­<lb/>tiplicata, alterius vicißim quantitatem &longs;uperare pote&longs;t. </s> <s id="id.000642">Dicimus <lb/>ergo quod ad hoc po&longs;terius attinet, rationem illas habere: &longs;ed<emph.end type="italics"/> <foreign lang="el">a)/r)r(hton,</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/></s> <s id="id.000643">vt cum duarum rectarum, quæ parallelogrammum con&longs;tituunt, vna <lb/>e&longs;t latus quadrati alicuius, altera e&longs;t eius diameter. </s> <s id="id.000644">Tunc enim ratio <lb/>e&longs;t rectis illis licet incommen&longs;erabilibus prop. 116. lib. 10. expre&longs;&longs;a. <lb/></s> <s id="id.000645">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="el">peri\ metrh/s. kuk,</foreign><emph type="italics"/>& Ptol. lib. 1. <emph.end type="italics"/> <foreign lang="el">me/gal. sunt. </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. </s> <s id="id.000648">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;arijs 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 xlink:href="035/01/073.jpg" pagenum="33" /><emph type="italics"/>tam permittere volare: ita tamen vt digitis alterum extremum funi­<lb/>culi retineant. </s> <s id="id.000649">Hæc enim in altero extremo mu&longs;ca, tanquam in ex­<lb/>tremo radij 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. </s> <s id="id.000650">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 id="id.000651">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 id="id.000652">Itaque circulare.] <emph type="italics"/>Proinde e&longs;t ac &longs;i diceret, cum via &longs;eu linea <lb/>per quam fertur radij 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;patij æqualiter ex omni <lb/>parte di&longs;tans. </s> <s id="id.000653">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. </s> <s id="id.000654">Quia in nulla harum, quod <lb/>e&longs;t extremum fit primum, quod peripheriæ conuenit. </s> <s id="id.000655">Præterea nulla <lb/>harum &longs;implex e&longs;t linea. </s> <s id="id.000656">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> </subchap1> <subchap1> <p type="main"> <s id="id.000657"><foreign lang="el">o(/ti me\n toi/nun h( to\n ku/klon gra/fousa <lb/>fe/retai du/o fora\s a(/ma, fanero\n e)/k te tou/twn, <lb/>kai\ o(/ti to\ fero/menon kat' eu)qei=an e)pi\ th\n ka/qeton a)fi­<lb/>knei=tai, w(/ste ei)=nai pa/lin au)th\n a)po\ tou= ke/ntrou ka/qeton.</foreign></s> <s id="g0121001"><foreign lang="el"><lb/>e)/stw ku/klos o( *a*b*g, to\ d' a)/kron to\ e)f' ou(= *b, fere/sqw <lb/>e)pi\ to\ *d: a)fiknei=tai de/ pote e)pi\ to\ *g.</foreign></s> <s id="g0121002"><foreign lang="el">ei) me\n ou)=n e)n tw=| <lb/>lo/gw| e)fe/reto o(\n e)/xei h( *b*d, pro\s th\n *d*g, e)fe/reto a)\n <lb/>th\n dia/metron th\n e)f' h(=| *b*g.</foreign></s> <s id="g0121003"><foreign lang="el">nu=n de/, e)pei/per e)n ou)deni\ <lb/>lo/gw|, e)pi\ th\n perife/reian fe/retai th\n e)f' h(=| *b e *g.</foreign></s> </p> <p type="main"> <s id="id.000658">Quod vero recta <expan abbr="de&longs;cri­b&etilde;s">de&longs;cri­<lb/>bens</expan> circulum duabus &longs;imul <lb/>lationibus 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. </s> <s id="id.000659">Et <lb/>fieri à <expan abbr="c&etilde;tro">centro</expan> <expan abbr="perpendicula­r&etilde;">perpendicula­<lb/>rem</expan> [<expan abbr="demõ&longs;trem">demon&longs;trem</expan>us]. </s> <s>Sit circu­<pb xlink:href="035/01/074.jpg" pagenum="34" /><foreign lang="el">b</foreign><lb/>lus <foreign lang="el">a b g,</foreign> & extremum <foreign lang="el">b</foreign><lb/>feratur ad <foreign lang="el">d,</foreign> perueniet &longs;a­<lb/>ne aliquando ad <foreign lang="el">g. </foreign></s> <s>[Si igi­<lb/>tur ferebatur in ratione <lb/>quam habet <foreign lang="el">b e</foreign> ad <foreign lang="el">e g,</foreign> fe­<lb/>rebatur &longs;ecundum diame­<lb/>trum <foreign lang="el">b g</foreign>: At nunc cum in <lb/>nulla ratione feratur, &longs;e­<lb/>cundum peripheriam <foreign lang="el">b e g</foreign><lb/>feretur.]</s> </p> <p type="head"> <s id="id.000660">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000661">Qvod vero recta.] <emph type="italics"/>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. </s> <s id="id.000662">Confirmatio apertior &longs;ic erit. <lb/></s> <s id="id.000663">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. </s> <s id="id.000664">Idem radius à diametro cir­<emph.end type="italics"/><lb/><figure id="id.035.01.074.1.jpg" xlink:href="035/01/074/1.jpg"/><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. </s> <s id="id.000665">Con&longs;equitur autem vt cum <lb/>e&longs;t in L<emph.end type="italics"/> <foreign lang="el">g</foreign> <emph type="italics"/>diagrammatis hic de&longs;cri­<lb/>pti. </s> <s id="id.000666">Non igitur vna latione tantum fer­<lb/>tur: fertur ergo pluribus. </s> <s id="id.000667">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="el">b</foreign> <emph type="italics"/>ver&longs;us E in hoc diagrammate: altera vt retror­<emph.end type="italics"/><lb/><figure id="id.035.01.074.2.jpg" xlink:href="035/01/074/2.jpg"/><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="el">b</foreign><lb/><emph type="italics"/>ver&longs;us L. </s> <s id="id.000668">Vtraque autem hæc latio quanta &longs;it <lb/>men&longs;uratur lineis rectis, quarum altera in po&longs;te­<lb/>riore diagrammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="el">g e,</foreign> <emph type="italics"/>altera <lb/>verò e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="el">b g. </foreign></s> </p> <pb xlink:href="035/01/075.jpg" pagenum="35" /> <p type="main"> <s id="id.000669">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 id="id.000670">Si igitur ferebatur.] <emph type="italics"/>Rur&longs;us totum hunc textum his notis <lb/>[ ] interclu&longs;um inaniter repeti arbitramur. </s> <s id="id.000671">hoc enim e&longs;t quod an­<lb/>tea e&longs;t demon&longs;tratum. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000672"><foreign lang="el">e)a\n <lb/>de\ duoi=n ferome/noin a)po\ th=s au)th=s i)sxu/os, to\ me\n e)kkrou/oito <lb/>plei=on, to\ de\ e)/latton, eu)/logon bradu/teron kinhqh=nai <lb/>to\ plei=on e)kkrouo/menon tou= e)/latton e)kkrouome/nou, o(\ dokei= <lb/>sumbai/nein e)pi\ th=s mei/zonos kai\ e)la/ttonos, tw=n e)k tou= <lb/>ke/ntrou grafousw=n tou\s ku/klous.</foreign></s> <s id="g0121102"><foreign lang="el">dia\ ga\r to\ e)ggu/teron <lb/>ei)=nai tou= me/nontos th=s e)la/ttonos to\ a)/kron, h)\ to\ th=s mei/zonos, <lb/>w(/sper a)ntispw/menon ei)s tou)nanti/on, e)pi\ to\ me/son bradu/teron <lb/>fe/retai to\ th=s e)la/ttonos a)/kron.</foreign></s> <s id="g0121201"><foreign lang="el">pa/sh| me\n ou)=n <lb/>ku/klon grafou/sh| tou=to sumbai/nei.</foreign></s> </p> <p type="main"> <s id="id.000673">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. </s> <s id="id.000674">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/></s> <s id="id.000675">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. </s> <s id="id.000676">Omni igitur circu­<lb/>lum de&longs;cribenti hoc con­<lb/>tingit. </s> </p> <p type="head"> <s id="id.000677">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000678">Si vero duorum.] <emph type="italics"/>Vbi confirmauit in omni radio circulum <lb/>de&longs;cribente duas lationes ine&longs;&longs;e, nunc eas comparat in radijs inæ­<lb/>qualibus, quod ad celeritatem & tarditatem attinet. </s> <s id="id.000679">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. </s> <s id="id.000680">Syllogi&longs;mus e&longs;t <lb/>connexus &longs;ic. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000681"><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 xlink:href="035/01/076.jpg" pagenum="36" /> <p type="main"> <s id="id.000682"><emph type="italics"/>Radiorem inæqualium eadem vi motorum minor plus <lb/>repellitur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000683"><emph type="italics"/>Radius igitur minor tardius feretur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000684">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 id="id.000685"><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 id="id.000686"><emph type="italics"/>Extremum radij 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 id="id.000687"><emph type="italics"/>Ergo extremum radij minoris mobile plus retrahetur retror­<lb/>&longs;um, & ab anteriori repelletur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000688"><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> </subchap1> <subchap1> <p type="main"> <s id="id.000689"><foreign lang="el">kai\ fe/retai th\n me\n <lb/>kata\ fu/sin, th\n de\ para\ fu/sin kata\ th\n perife/reian <lb/>ei)s to\ pla/gion kai\ to\ ke/ntron. mei/zw d' a)ei\ th\n para\ <lb/>fu/sin h( e)la/ttwn fe/retai: dia\ ga\r to\ e)ggu/teron ei)=nai tou= <lb/>ke/ntrou tou= a)ntispw=ntos, kratei=tai ma=llon.</foreign></s> </p> <p type="main"> <s id="id.000690">Et fertur motu <expan abbr="&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/></s> <s id="id.000691">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. </s> <s id="id.000692">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 id="id.000693">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000694">Et fertur motu.] <emph type="italics"/>E duobus motibus in extremo radij 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. </s> <s id="id.000695">Sed rationem huius hic nullam profert. </s> <s id="id.000696">Hæc au­<lb/>tem alibi ab eo dicta adferri pote&longs;t. </s> <s id="id.000697">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 xlink:href="035/01/077.jpg" 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. </s> <s id="id.000698">Ergo cum extremum radij <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. </s> <s id="id.000699">Et illa quidem potius naturalis erit quæ à termino à <lb/>quo egredi conatur, & quantum in &longs;e e&longs;t, di&longs;cedit. </s> <s id="id.000700">Talis autem e&longs;t ea <lb/>qua extremum mobile veluti di&longs;cedens à centro &longs;ecundum periphe­<lb/>riam fertur. </s> <s id="id.000701">Tum qua forma rei acquiritur, qualis latio per circum­<lb/>ferentiam, cum hæc &longs;it circuli forma &longs;eu finis. </s> <s id="id.000702">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> </subchap1> <subchap1> <p type="main"> <s id="id.000703"><foreign lang="el">o(/ti de\ mei=zon <lb/>to\ para\ fu/sin kinei=tai h( e)la/ttwn th=s mei/zonos, tw=n e)k tou= <lb/>ke/ntrou grafousw=n tou\s ku/klous, e)k tw=nde dh=lon.</foreign></s> <s id="g0121302"><foreign lang="el">e)/stw <lb/>ku/klos e)f' *b*g*d*e, kai\ a)/llos e)n tou/tw| e)la/ttwn, <lb/>e)f' ou(= *x*n*m*c, peri\ to\ au)to\ ke/ntron to\ *a, kai\ e)kbeblh/sqwsan <lb/>ai( dia/metroi, e)n me\n tw=| mega/lw|, e)f' w(=n *g*d <lb/>kai\ *b*e, e)n de\ tw=| e)la/ttoni ai( *m*x *n*c: kai\ to\ e(tero/mhkes <lb/>parapeplhrw/sqw, to\ *d*y*r*g. </foreign></s> <s id="g0121302a"><foreign lang="el">ei) dh\ h( *a*b gra/fousa <lb/>ku/klon h(/cei e)pi\ to\ au)to\ o(/qen w(rmh/qh e)pi\ th\n *a*e, dh­<lb/>lono/ti fe/retai pro\s au(th/n.</foreign></s> <s id="g0121303"><foreign lang="el">o(moi/ws de\ kai\ h( *a*x, pro\s th\n <lb/>*a*x h(/cei.</foreign></s> <s id="g0121304"><foreign lang="el">bradu/teron de\ fe/retai h( *a*x th=s *a*b, w(/sper <lb/>ei)/rhtai, dia\ to\ gi/nesqai mei/zona th\n e)/kkrousin, kai\ a)ntispa=sqai <lb/>ma=llon th\n *a*x.</foreign></s> <s id="g0121401"><foreign lang="el">h)/xqw de\ h( *a*q*h, kai\ a)po\ <lb/>tou= *q ka/qetos e)pi\ th\n *a*b h( *q*z e)n tw=| ku/klw|, kai\ pa/lin <lb/>a)po\ tou= *q h)/xqw para\ th\n *a*b h( *q*w, kai\ h( *w*u, <lb/>e)pi\ th\n *a*b ka/qeton, kai\ h( *h*k.</foreign></s> <s id="g0121402"><foreign lang="el">ai( dh\ e)f' w(=n *w*u kai\ <lb/>*q*z i)/sai. </foreign></s> <s id="g0121402a"><foreign lang="el">h( a)/ra *b*u e)la/ttwn th=s *x*z: ai( ga\r i)/sai <lb/>eu)qei=ai e)p' a)ni/sous ku/klous e)mblhqei=sai pro\s o)rqh=| th=| <lb/>diame/trw|, e)/latton tmh=ma a)pote/mnousi th=s diame/trou e)n <lb/>toi=s mei/zosi ku/klois.</foreign></s> <s id="g0121402b"><foreign lang="el">e)/sti de\ h( *w*u i)/sh th=| *q*z.</foreign></s> <s id="g0121404"><foreign lang="el">e)n o(/sw|<lb/> dh\ xro/nw| h( *a*q th\n *x*q e)nhne/xqh, e)n tosou/tw| xro/nw| e)n <lb/>tw=| ku/klw| tw=| mei/zoni, mh\ mei/zona th=s *b*w e)nh/nektai to\ a)/kron <lb/>th=s *b*a.</foreign></s> <s id="g0121501"><foreign lang="el">h( me\n ga\r kata\ fu/sin fora\, i)/sh: h( de\ para\ <lb/>fu/sin e)la/ttwn, h( *b*u, th=s *z*x.</foreign></s> </p> <p type="main"> <s id="id.000704">Quod vero minor plus <lb/>præter naturam moueatur: <lb/>quam maior earum, qu&etail; ex <lb/>centro <expan abbr="de&longs;cribũt">de&longs;cribunt</expan> circulos, <lb/>ex his erit manife&longs;tum. </s> <s id="id.000705">Sit <lb/>circulus <foreign lang="el">b g d e,</foreign> & alter <lb/>minor <foreign lang="el">x n m c,</foreign> eiu&longs;dem <expan abbr="c&etilde;­tri">cen­<lb/>tri</expan> <foreign lang="el">a,</foreign> Et traductæ &longs;int dia­<lb/>metri in magno quidem <lb/><foreign lang="el">g d, & b e</foreign>: in minori <foreign lang="el">m c & <lb/>x n</foreign>: atque alterolongum <lb/>compleatur <foreign lang="el">d y r g. </foreign></s> <s>Si igi­<lb/>tur <foreign lang="el">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="el">a b</foreign>] <lb/>&longs;imiliter <foreign lang="el">a x</foreign> perueniet ad <lb/>ip&longs;am <foreign lang="el">a x. </foreign></s> <s>Tardius autem <lb/>fertur <foreign lang="el">a x</foreign>: quam <foreign lang="el">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="el">a x. </foreign></s> <s>Ducatur vero <lb/>recta <foreign lang="el">a q h, & a q</foreign> excitetur <lb/>perpendicularis ad <foreign lang="el">a b,</foreign> qu&etail; <lb/>&longs;it <foreign lang="el">q z</foreign> in circulo [minori]. </s> <pb xlink:href="035/01/078.jpg" pagenum="38" /> <s>Et rur&longs;us per <foreign lang="el">q</foreign> ducatur pa­<lb/>rallela ip&longs;i <foreign lang="el">a b</foreign> quæ &longs;it <foreign lang="el">q w <lb/>& w n</foreign> perpendicularis ip&longs;i <lb/><foreign lang="el">a b</foreign> tum & <foreign lang="el">h k. </foreign></s> <s>Sunt vero <lb/><foreign lang="el">w n & q z</foreign> æquales. </s> <s id="id.000706">Rur&longs;us <lb/><foreign lang="el">b n</foreign> e&longs;t minor: quam <foreign lang="el">x z. </foreign>In <lb/>circulis enim inæqualibus <lb/>rect&etail; &etail;quales ad rectos dia­<lb/>metro excitatæ, de diame­<lb/>tro circulorum maiorum <lb/><expan abbr="&longs;egmentũ">&longs;egmentum</expan> minus auferunt. <lb/></s> <s id="id.000707">E&longs;t autem <foreign lang="el">w n</foreign> æqualis ip&longs;i <lb/><foreign lang="el">q z. </foreign>In quanto vero tempo­<lb/>re <foreign lang="el">a x</foreign> peragrauit <foreign lang="el">x q,</foreign> in <lb/><expan abbr="tãto">tanto</expan> in maiore circulo ex­<lb/>tremum <foreign lang="el">a b</foreign> non maiorem <lb/><foreign lang="el">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="el">b n</foreign> quam <foreign lang="el">x z. </foreign></s> </p> <p type="head"> <s id="id.000708">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000709">Qvod vero minor.] <emph type="italics"/>Altera e&longs;t confirmatio &longs;ed<emph.end type="italics"/> <foreign lang="el">grammikh\</foreign><lb/><emph type="italics"/>linearis a&longs;&longs;umptionis &longs;yllogi&longs;mi præcedentis. </s> <s id="id.000710">Scilicet quod mi­<lb/>nor radius plus retrahatur ad centrum, quam maior. </s> <s id="id.000711">Vbi ab vtri&longs;que <lb/>&longs;ecundum peripheriam æquale &longs;patium confectum e&longs;t. </s> <s id="id.000712">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. </s> <s id="id.000713">vt videre lice­<lb/>bit in diagrammate hic de&longs;cripto & &longs;uis rationibus nece&longs;&longs;arijs con­<lb/>firmato. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000714"><emph type="italics"/>Sint duo circuli concentrici maior<emph.end type="italics"/> <foreign lang="el">b d e y,</foreign> <emph type="italics"/>minor<emph.end type="italics"/> <foreign lang="el">x m n c</foreign> <emph type="italics"/>è cen­<lb/>tro a traiecti diametris<emph.end type="italics"/> <foreign lang="el">x n & b e. </foreign></s> </p> <p type="main"> <s id="id.000715"><emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ad punctum<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>ducatur recta<emph.end type="italics"/> <foreign lang="el">a q,</foreign> <emph type="italics"/>& producatur in<emph.end type="italics"/><lb/><foreign lang="el">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="el">a q h. </foreign></s> </p> <p type="main"> <s id="id.000716"><emph type="italics"/>Tum à puncto<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="el">a x</foreign> <emph type="italics"/>prop. 12. <lb/>lib. 1. &longs;itque<emph.end type="italics"/> <foreign lang="el">q z. </foreign></s> </p> <pb xlink:href="035/01/079.jpg" pagenum="39" /> <p type="main"> <s id="id.000717"><emph type="italics"/>Et per punctum<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>ducatur parallela rectæ<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>prop. 31. lib. 1. <lb/>quæ &longs;it<emph.end type="italics"/> <foreign lang="el">q w. </foreign></s> </p> <figure id="id.035.01.079.1.jpg" xlink:href="035/01/079/1.jpg"/> <p type="main"> <s id="id.000718"><emph type="italics"/>Rur&longs;us à puncto<emph.end type="italics"/> <foreign lang="el">w</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="el">a b,</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/><lb/><foreign lang="el">w n</foreign>: <emph type="italics"/>& &longs;ic parallelogrammum erit<emph.end type="italics"/> <foreign lang="el">w n z q</foreign> <emph type="italics"/>ex def. </s> <s id="id.000719">parallelog. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000720"><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="el">w</foreign> <emph type="italics"/>tantum confecit &longs;patij &longs;ecundum natu­<lb/>ram, quam<emph.end type="italics"/> <foreign lang="el">x</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="el">q</foreign>. </s> <s><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/></s> <s id="id.000721">Sint autem<emph.end type="italics"/> <foreign lang="el">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="el">w n z q</foreign> <emph type="italics"/>prop. 34. lib. 1. </s> <s>Erant vtro­<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="el">b w & x q</foreign> <emph type="italics"/>æqualia. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000723"><foreign lang="el">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="el">b, & x z</foreign> <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> <foreign lang="el">x. </foreign><emph type="italics"/>&longs;i igitur<emph.end type="italics"/> <foreign lang="el">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="el">b n,</foreign> <emph type="italics"/>erit puncti<emph.end type="italics"/> <foreign lang="el">x</foreign> <emph type="italics"/>motus præter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="el">b. </foreign></s> </p> <pb xlink:href="035/01/080.jpg" pagenum="40" /> <p type="main"> <s id="id.000724"><emph type="italics"/>Sed & &longs;i perficiantur parallelogramma<emph.end type="italics"/> <foreign lang="el">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="el">d</foreign> <emph type="italics"/>tralatum vno motu v&longs;que ad<emph.end type="italics"/> <foreign lang="el">s,</foreign><lb/><emph type="italics"/>altero motu, quo retrahitur ad centrum, reductum e&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="el">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="el">s t</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="el">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 id="id.000725">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 id="id.000726"><foreign lang="el">a q h</foreign>] <emph type="italics"/><expan abbr="Punctũ">Punctum</expan><emph.end type="italics"/> <foreign lang="el">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="el">x</foreign> <emph type="italics"/><expan abbr="extremũ">extremum</expan> mobile minoris radij<emph.end type="italics"/> <foreign lang="el">a x. </foreign></s> </p> <p type="main"> <s id="id.000727">Et <foreign lang="el">a q</foreign> excitetur.] <emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>extra lineam<emph.end type="italics"/> <foreign lang="el">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="el">q z</foreign> <emph type="italics"/>prop. 12. lib. 1. elem. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000728">Et rur&longs;us per <foreign lang="el">q</foreign>] <emph type="italics"/>Per punctum<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>datum datæ rectæ<emph.end type="italics"/> <foreign lang="el">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 id="id.000729">Et <foreign lang="el">w n</foreign> perpend.] <emph type="italics"/>prop. 12. lib. 1. elem. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000731">Sunt vero <foreign lang="el">w n</foreign> &] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="el">q w</foreign> <emph type="italics"/>parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="el">z n</foreign> <emph type="italics"/>ex fabrica: <lb/>tùm<emph.end type="italics"/> <foreign lang="el">w n</foreign> <emph type="italics"/>etiam parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="el">q z,</foreign> <emph type="italics"/>quia in eas incidens<emph.end type="italics"/> <foreign lang="el">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. </s> <s><expan abbr="parallelogrãmũ">parallelogramum</expan> erit<emph.end type="italics"/> <foreign lang="el">w n z q. </foreign><emph type="italics"/>per def. pa­<lb/>rall. </s> <s id="id.000735">quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="el">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 id="id.000736">In circulis.] <emph type="italics"/>Ex hoc loco elicitur hoc theorema. </s> <s id="id.000737">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 id="id.000738">Expo­<lb/><figure id="id.035.01.080.1.jpg" xlink:href="035/01/080/1.jpg"/><lb/>&longs;itio. </s> </p> <p type="main"> <s id="id.000739"><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 xlink:href="035/01/081.jpg" pagenum="41" /> <p type="main"> <s id="id.000740">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. </s> <s id="id.000741">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 id="id.000742"><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 id="id.000743"><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper­<lb/>tum prop. 1. lib. 3. </s> <s>ducatur A k diameter. </s> <s id="id.000744">De&longs;cribendus autem &longs;it eo <lb/>minor, cuius accipiatur E <expan abbr="centrũ">centrum</expan> <emph.end type="italics"/><lb/><figure id="id.035.01.081.1.jpg" xlink:href="035/01/081/1.jpg"/><lb/><emph type="italics"/>inter A & D, & interuallo <lb/>E A de&longs;cribatur A F G. </s> <s>hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. </s> <s id="id.000745">Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. </s> <s>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. </s> <s>non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de alijs. </s> <s id="id.000748">Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 3. </s> <s>quod oportuit facere. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000749"><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. </s> <s>Et tanget intus circulum A B C in puncto A ex probl. <lb/>præ&longs;umpto. </s> <s>per punctum B <expan abbr="ducaeur">ducatur</expan> 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. </s> <s id="id.000754">E I ax. 1. connectantur M H, <lb/>E H po&longs;t. 1. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000757">Demon&longs;t. </s> <s><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. </s> <s>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. </s> <s>tum angulus M H N ad centrum con&longs;titutus <emph.end type="italics"/><pb xlink:href="035/01/082.jpg" 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. </s> <s>& &longs;ic reliquum latus N H æquale e&longs;t re­<lb/>liquo I H. </s> <s id="id.000765">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 id="id.000767">Concl. </s> <s><emph type="italics"/>Ergo perpendiculares à peripherijs in &longs;emidiametros & <lb/>ct. </s> <s>quod fuit demon&longs;trandum. </s> <s id="id.000769">Hoc autem theorema videtur <expan abbr="quo­dãmodo">quo­<lb/>dammodo</expan><emph.end type="italics"/> <foreign lang="el">para/docon. </foreign><emph type="italics"/>Erat enim veri&longs;imilius in maiore circulo <expan abbr="&longs;eg­mentũ">&longs;eg­<lb/>mentum</expan> &longs;emidiametri e&longs;&longs;e maius, & in minore minus: at non ita e&longs;t vt <lb/>patuit. </s> <s id="id.000770">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 id="id.000771">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. </s> <s id="id.000772">Antea dixerat duas lationes illas e&longs;&longs;e in nulla ratione, in­<lb/>tellige igitur quæ rectis lineis exactè exprimi poßit. </s> <s id="id.000773">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. </s> <s id="id.000774">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> </subchap1> <subchap1> <p type="main"> <s id="id.000775"><foreign lang="el">dei= de\ a)na/logon ei)=nai, <lb/>w(s to\ kata\ fu/sin pro\s to\ kata\ fu/sin, to\ para\ fu/sin <lb/>pro\s to\ para\ fu/sin.</foreign></s> <s id="g0121503"><foreign lang="el">mei/zona a)/ra perife/reian dielh/luqe <lb/>th\n *h*b th=s *w*b.</foreign></s> <s id="g0121504"><foreign lang="el">a)na/gkh de\ th\n *h*b e)n tou/tw| tw=| xro/nw| <lb/>dielhluqe/nai: e)ntau=qa ga\r e)/stai, o(/tan a)na/logon a)mfote/rws <lb/>sumbai/nh| to\ para\ fu/sin, pro\s to\ kata\ fu/sin.</foreign></s> <s id="g0121506"><foreign lang="el">ei) dh\ <lb/>mei=zo/n e)sti to\ kata\ fu/sin e)n th=| mei/zoni ku/klw|, kai\ to\ para\ fu/sin <lb/>mei=zon, a)\n e)ntau=qa sumpi/ptoi monaxw=s, w(/ste to\ *b, e)nhne/xqai <lb/>a)\n th\n *b*h e)n tw=| e)f' ou(= *x shmei=on. </foreign></s> <s id="g0121506a"><foreign lang="el">e)ntau=qa ga\r <lb/>kata\ fu/sin me\n gi/netai tw=| *b shmei/w| h( *k *b. </foreign></s> <s id="g0121506b"><foreign lang="el">e)/sti ga\r <lb/>au)th\ a)po\ tou= *h ka/qetos, para\ fu/sin de\ e)s th\n *k*b.</foreign></s> <s id="g0121508"><foreign lang="el">e)/sti <lb/>de\ w(s th\n *h*k pro\s th\n *k*b, h( *q*z pro\s th\n *z*x. </foreign></s> <s id="g0121508a"><foreign lang="el">fanero\n <lb/>de\ e)a\n e)pizeuxqw=sin, a)po\ tw=n *b, *x e)pi\ ta\ *h, *q.</foreign></s> <s id="g0121509"><foreign lang="el">ei) de\ <lb/>e)la/ttwn h)\ mei/zwn th=s *h*b e)/stai, h)ne/xqh to\ *b, ou)x o(moi/ws <lb/>e)/stai ou)de\ a)na/logon e)n a)mfoi=n to\ kata\ fu/sin pro\s to\ <lb/>para\ fu/sin.</foreign></s> <s id="g0121510"><foreign lang="el">di' h(\n me\n toi/nun ai)ti/an a)po\ th=s au)th=s <lb/>i)sxu/os fe/retai qa=tton to\ ple/on a)pe/xon tou= ke/ntrou shmei=on [1kai\ m gra/fei h( mei/zwn]1 <lb/>dh=lon dia\ tw=n ei)rhme/nwn.</foreign></s> </p> <p type="main"> <s id="id.000776">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="na­turã">na­<lb/>turam</expan>. </s> <s id="id.000777">Igitur maiorem quam <lb/><foreign lang="el">b w</foreign> <expan abbr="peripheriã">peripheriam</expan>, vt <foreign lang="el">b h</foreign> <expan abbr="per­trã&longs;ijt">per­<lb/>tran&longs;ijt</expan>. </s> <s id="id.000778">Nece&longs;&longs;e igitur in eo <lb/>tempore <foreign lang="el">b h</foreign> tran&longs;ij&longs;&longs;e. </s> <s id="id.000779">Ibi <lb/>enim erit, vbi proportiona­<lb/>les <expan abbr="cõting&etilde;t">contingent</expan> <expan abbr="vtrinq;">vtrinque</expan> motus <pb xlink:href="035/01/083.jpg" pagenum="43" /><lb/>præter naturam ad motus <lb/>&longs;ecundum naturam. </s> <s id="id.000780">Si igi­<lb/>tur maius e&longs;t id quod <expan abbr="&longs;ecũ­dum">&longs;ecun­<lb/>dum</expan> <expan abbr="naturã">naturam</expan> in maiore cir­<lb/>culo, & quod e&longs;t pr&etail;ter na­<lb/>turam maius, vtique illuc <lb/>concidet vno modo, ita vt <lb/><foreign lang="el">b</foreign> &longs;it latum per lineam <foreign lang="el">b h. </foreign><lb/>eo in tempore quo <expan abbr="pũctum">punctum</expan> <lb/><foreign lang="el">x</foreign> [per <foreign lang="el">x q</foreign>]. </s> <s>Ibi enim pun­<lb/>cto <foreign lang="el">b</foreign> &longs;ecundum <expan abbr="quid&etilde;">quidem</expan> na­<lb/>turam e&longs;t recta <foreign lang="el">k h,</foreign> ab <foreign lang="el">h</foreign><lb/>enim e&longs;t ip&longs;a perpendicu­<lb/>laris, præter naturam vero <lb/><foreign lang="el">b k.</foreign> </s> <s>E&longs;t &longs;iquidem vt <foreign lang="el">h k</foreign> ad <lb/><foreign lang="el">h k</foreign>: &longs;ic <foreign lang="el">q z</foreign> ad <foreign lang="el">x z,</foreign> quod <lb/>erit manife&longs;tum, &longs;i à pun­<lb/>ctis <foreign lang="el">b, x</foreign> ad <foreign lang="el">h, q</foreign> rectæ adiun­<lb/>ctæ &longs;int. </s> <s id="id.000781">Si vero minor vel <lb/>maior: quam <foreign lang="el">h b</foreign> fuerit ea, <lb/>perquam <foreign lang="el">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"/><lb/>&longs;ecundum naturam ad id <lb/>quod præter naturam. </s> <s id="id.000782">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 id="id.000783"><margin.target id="marg13"/>Verba &longs;i­<lb/>gnis inclu&longs;a <lb/>in <expan abbr="cõtextu">contextu</expan> <lb/>Gr&etail;co quia <lb/>redundant <lb/>non verti­<lb/>mus. </s> </p> <p type="head"> <s id="id.000784">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000785">At oportet.] <emph type="italics"/>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. </s> <s id="id.000786">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 xlink:href="035/01/084.jpg" 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="el">x</foreign> <emph type="italics"/>delatum e&longs;t in<emph.end type="italics"/> <foreign lang="el">q,</foreign> <emph type="italics"/>intelligatur etiam<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>delatum in<emph.end type="italics"/> <foreign lang="el">h,</foreign><lb/><emph type="italics"/>à quo<emph.end type="italics"/> <foreign lang="el">h</foreign> <emph type="italics"/>e&longs;t perpendicularis<emph.end type="italics"/> <foreign lang="el">h k</foreign> <emph type="italics"/>in diametrum<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>metiens motum <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>per peripheriam<emph.end type="italics"/> <foreign lang="el">b h. </foreign><emph type="italics"/></s> <s>Ergo quo tempore<emph.end type="italics"/> <foreign lang="el">x</foreign> <emph type="italics"/>delatum e&longs;t ad<emph.end type="italics"/><lb/><foreign lang="el">q,</foreign> <emph type="italics"/>eodem<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>delatum erit ad<emph.end type="italics"/> <foreign lang="el">h. </foreign><emph type="italics"/></s> <s>Cæterum eadem vis in vtri&longs;que cir­<lb/>culis intelligitur ex æqualitate angulorum ad centrum con&longs;tituto­<lb/>rum. </s> <s id="id.000787">Æqualis enim e&longs;t angulus<emph.end type="italics"/> <foreign lang="el">b a h</foreign> <emph type="italics"/>angulo<emph.end type="italics"/> <foreign lang="el">x a q</foreign>. </s> </p> <p type="main"> <s id="id.000788">Ab <foreign lang="el">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. </s> <s id="id.000789">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. </s> <s id="id.000790">Talis autem e&longs;t perpendicularis ad linearum reliquarum dimen­<lb/>&longs;ionem. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000791">E&longs;t &longs;iquidem vt <foreign lang="el">h k. </foreign>] <emph type="italics"/>Triangula enim<emph.end type="italics"/> <foreign lang="el">x q z & b h k</foreign> <emph type="italics"/>&longs;unt <lb/>æquiangula. </s> <s id="id.000792">Nam, qui anguli ad<emph.end type="italics"/> <foreign lang="el">z & k,</foreign> <emph type="italics"/>&longs;unt recti ex fab. qui vero <lb/>ad<emph.end type="italics"/> <foreign lang="el">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="el">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="el">x q, b h</foreign> <emph type="italics"/>prop. 3. lib. 6. </s> <s>Nam<emph.end type="italics"/> <foreign lang="el">x q</foreign><lb/><emph type="italics"/>proportionaliter &longs;ecat<emph.end type="italics"/> <foreign lang="el">a b & a h</foreign> <emph type="italics"/>latera trianguli<emph.end type="italics"/> <foreign lang="el">b a h. </foreign><emph type="italics"/></s> <s>Sunt enim<emph.end type="italics"/><lb/><foreign lang="el">a x, a q</foreign> <emph type="italics"/>æquales radj,<emph.end type="italics"/> & <foreign lang="el">x b, q h</foreign> <emph type="italics"/>item æquales lineæ, quia re­<lb/>liquæ ex æqualibus radijs<emph.end type="italics"/> <foreign lang="el">a b, a h</foreign>: <emph type="italics"/>habent autem æquales ad <lb/>æquales eandem rationem. </s> <s>E&longs;t igitur<emph.end type="italics"/> <foreign lang="el">x q</foreign> <emph type="italics"/>parallela ba&longs;i<emph.end type="italics"/> <foreign lang="el">b h,</foreign> <emph type="italics"/>& &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="el">x</foreign> <emph type="italics"/>externus, & qui ad<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>internus erunt æquales <lb/>prop. 29. lib. 1. </s> <s>Ergo & reliqui qui ad<emph.end type="italics"/> <foreign lang="el">q & h</foreign> <emph type="italics"/>prop. 32. lib. 1. </s> <s>Hæc <lb/>igitur duo triangula circa æquales angulos habebunt latera propor­<lb/>tionalia prop. 4. lib. 6. </s> <s>Sicque erit vt<emph.end type="italics"/> <foreign lang="el">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">x z</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="el">h k</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">k b,</foreign><lb/><emph type="italics"/>& alternatim vt<emph.end type="italics"/> <foreign lang="el">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="el">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">k b</foreign> <emph type="italics"/>prop. 16. lib. 5. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000795">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> </subchap1> <subchap1> <p type="main"> <s id="id.000796"><foreign lang="el">dio/ti de\ ta\ me\n mei/zw zuga\ <lb/>a)kribe/stera/ e)sti tw=n e)latto/nwn, fanero\n e)k tou/twn.</foreign></s> <s id="g0130102"><foreign lang="el">gi/netai <lb/>ga\r to\ me\n spa/rton ke/ntron.</foreign></s> <s id="g0130102a"><foreign lang="el">me/nei ga\r tou=to. </foreign></s> <s id="g0130102b"><foreign lang="el">to\ de\ e)pi\ <lb/>e(ka/teron me/ros th=s pla/stiggos, ai( e)k tou= ke/ntrou.</foreign></s> <s id="g0130103"><foreign lang="el">a)po\ ou)=n <lb/>tou= au)tou= ba/rous a)na/gkh qa=tton kinei=sqai to\ a)/kron th=s <lb/>pla/stiggos, o(/sw| a)\n plei=on a)pe/xh| tou= spa/rtou, kai\ e)/nia <lb/>me\n mh\ dh=la ei)=nai e)n toi=s mikroi=s zugoi=s pro\s th\n ai)/sqhsin <lb/>e)pitiqe/mena ba/rh: e)n de\ toi=s mega/lois, dh=la. </foreign></s> <s id="g0130105"><foreign lang="el">ou)qe\n ga\r <lb/>kwlu/ei e)/latton kinhqh=nai me/geqos, h)\ w(/ste ei)=nai th=| o)/yei <lb/>fanero/n.</foreign></s> </p> <p type="main"> <s id="id.000797">Quod vero propterea li­<lb/>br&etail; maiores minoribus &longs;int <lb/>exactiores, <expan abbr="manife&longs;tũ">manife&longs;tum</expan> ex his <lb/>erit. </s> <s id="id.000798">Agina enim fit <expan abbr="centrũ">centrum</expan>. <lb/></s> <s id="id.000799">Hæc enim quie&longs;cit. </s> <s id="id.000800"><expan abbr="vtræq;">vtræque</expan> <pb xlink:href="035/01/085.jpg" pagenum="45" /><lb/>vero librilis partes lineæ <lb/>&longs;unt ex centro. </s> <s id="id.000801">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. </s> <s id="id.000802">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 id="id.000803">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000804">Qvod vero propterea libræ.] <foreign lang="el">zugo\s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="el">zugo\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="el">mh\ zugo\n u(per­<lb/>bai/nein</foreign> <emph type="italics"/>&longs;tateram ne tran&longs;grediaris & vt annotat Budæus<emph.end type="italics"/> <foreign lang="el">zugosta/­<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"/><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 id="id.000805"><margin.target id="marg14"/>Initio <lb/>cap. 11. <lb/>Prouerb. </s> </p> <p type="main"> <s id="id.000806">Agina fit cen­<lb/><figure id="id.035.01.085.1.jpg" xlink:href="035/01/085/1.jpg"/><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>. </s> <s id="id.000807">Quod <lb/>vt intelligatur prius <lb/>in libra A D B C <lb/>H I partes notan­<lb/>dæ &longs;unt. </s> <s id="id.000808">Sit igitur <lb/>libræ librile, &longs;eu <emph.end type="italics"/><pb xlink:href="035/01/086.jpg" 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="el">spa/rtion</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="el">pla/stiggas</foreign> <emph type="italics"/>Ari­<lb/>&longs;toteles appellabit, quo etiam nomine appellat librile, &longs;eu &longs;capum, &longs;eu <lb/>iugum A B. </s> <s id="id.000809">E&longs;t etiam recta E C F &longs;emper perpendicularis ip&longs;i <lb/>A B vtcunque moueatur. </s> <s id="id.000810">proinde perpendiculum appellatur, ab <lb/>alijs æquamentum, ab alijs trutina. </s> <s id="id.000811">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;patij 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. </s> <s id="id.000812">id e&longs;t minores <lb/>ponderum differentias patefaciet. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.000813"><foreign lang="el">e)pi\ de\ th=s mega/lhs pla/stiggos poiei= o(rato\n to\ <lb/>au)to\ ba/ros me/geqos.</foreign></s> <s id="g0130107"><foreign lang="el">e)/nia de\ dh=la me\n e)p' a)mfoi=n e)sti/n, <lb/>a)lla\ pollw=| ma=llon e)pi\ tw=n meizo/nwn, dia\ to\ pollw=| <lb/>mei=zon gi/nesqai to\ me/geqos th=s r(oph=s u(po\ tou= au)tou= ba/rous <lb/>e)n toi=s mei/zosi.</foreign></s> <s id="g0130108"><foreign lang="el">kai\ dia\ tou=to texna/zousin oi( a(lourgopw=lai <lb/>pro\s to\ parakrou/esqai i(sta/ntes, to/, te spa/rton <lb/>ou)k e)n me/sw| tiqe/ntes, kai\ mo/lubdon th=s fa/laggos ei)s <lb/>qa/teron me/ros e)gxe/ontes, h)\ tou= cu/lou to\ pro\s th\n r(i/zan <lb/>pro\s o(\ bou/lontai r(e/pein poiou=ntes, h)\ e)a\n e)/xh| o)/zon. </foreign></s> <s id="g0130108a"><foreign lang="el">baru/­<lb/>teron ga\r e)n w(=| me/ros h( r(i/za tou= cu/lou e)sti/n. </foreign></s> <s id="g0130108b"><foreign lang="el">o( de\ o)/zos r(i/za <lb/>ti/s e)stin.</foreign></s> </p> <p type="main"> <s id="id.000814">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>. </s> <s id="id.000815">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/></s> <s id="id.000816">quia in maioribus ab <expan abbr="eod&etilde;">eodem</expan> <lb/><expan abbr="põdere">pondere</expan> multo maior fit in­<lb/>clinationis magnitudo. </s> <s id="id.000817">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 è ligno 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. </s> <s id="id.000818">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 xlink:href="035/01/087.jpg" pagenum="47" /> <p type="head"> <s id="id.000819">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000820">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. </s> <s id="id.000821">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. </s> <s id="id.000822">Huius autem libræ fabrica pen­<lb/>det è quatuor. </s> <s id="id.000823">Primum e&longs;t longitudo librilis. </s> <s id="id.000824">Secundum e&longs;t illius & <lb/>lancium materiæ &longs;umma leuitas. </s> <s id="id.000825">Nam tanto maior redditur ratio <lb/>ponderis exigui. </s> <s id="id.000826">Tertium e&longs;t librilis firmitas, & rectitudo, ideo de­<lb/>bet fieri ex chalybe purgato, durato, tenuißimo, naturaque leui. <lb/></s> <s id="id.000827">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 id="id.000828">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. </s> <s id="id.000829">Ducitur ex effectu eorum qui fraudare <expan abbr="volũt">volunt</expan>, <lb/>emptores. </s> <s id="id.000830">Imponunt enim pondus rei venditæ leuius æquipondio<emph.end type="italics"/> <lb/>(<foreign lang="el">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. </s> <s id="id.000831">Nec tamen vacua libra ponderibus, iniqua videtur. </s> <s id="id.000832">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. </s> <s id="id.000833">Vel pars librilis longior erit tenuior, vel perforata in ali­<lb/>quot locis exiguis foraminibus. </s> <s id="id.000834">Vnde vnius grauitas <expan abbr="lõgitudinis">longitudinis</expan> al­<lb/>terius rationem compen&longs;at. </s> <s id="id.000835">Cardanus docuit libræ metallicæ fabri­<emph.end type="italics"/><lb/><arrow.to.target n="marg15"/><lb/><emph type="italics"/>cam, quæ pro deunce exhibeat a&longs;&longs;em, licet vacua in&longs;ta videatur. </s> <s id="id.000836">Hæc <lb/>autem à me hîc ita recitantur, non vt quis abutatur. </s> <s id="id.000837">Abhominatio <emph.end type="italics"/><lb/><arrow.to.target n="marg16"/><lb/><emph type="italics"/>enim e&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. </s> <s id="id.000838">Fraudem autem i&longs;tam deteget, &longs;i pondus & æqui­<lb/>pondium tran&longs;mutentur de lance in lancem. </s> <s id="id.000839">Quod enim ante æqui­<lb/>ponderabat, tran&longs;latum in alteram lancem non 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 id="id.000840"><margin.target id="marg15"/>Lib. 1. de <lb/>&longs;ubt,</s> </p> <p type="margin"> <s id="id.000841"><margin.target id="marg16"/>Prouerb. c. <lb/>10. </s> </p> <p type="main"> <s id="id.000842">Purpuræ venditores.] <foreign lang="el">a(lourgopw/lai</foreign> <emph type="italics"/>dicuntur quia<emph.end type="italics"/> <foreign lang="el">a(/lour­<lb/>gon</foreign> <emph type="italics"/>purpura e&longs;t<emph.end type="italics"/> <foreign lang="el">a)po\ tou= a(/ls kai\ e)/rgon</foreign> <emph type="italics"/>à maris opere. </s> <s id="id.000843">quia purpura è <emph.end type="italics"/><lb/><arrow.to.target n="marg17"/><lb/><emph type="italics"/>concha marina colligitur. </s> <s id="id.000844">E&longs;t <expan abbr="aut&etilde;">autem</expan>, vt author e&longs;t Plinius, ille magni <emph.end type="italics"/><pb xlink:href="035/01/088.jpg" pagenum="48" /><emph type="italics"/>pretij flos tingendis regum ve&longs;tibus expetitus. </s> <s id="id.000845">Hunc in medijs 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 id="id.000846"><margin.target id="marg17"/>Lib. 9. cap. <lb/>36. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.000847">3. <foreign lang="el">*dia\ ti\ e)a\n me\n a)/nwqen h)=| to\ <lb/>spa/rtion, o(/tan a)qerh| to\ ba/­<lb/>ros, pa/lin a)naqe/retai to\ zu­<lb/>go/n: de\ ka/twqen, me/nei. </foreign></s> </p> <p type="main"> <s id="id.000848">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 id="g0130202"><foreign lang="el">*dia\ ti/, e)a\n me\n a)/nwqen h)=| to\ sparti/on, o(/tan ka/twqen <lb/>r(e/yantos a)fe/lh| to\ ba/ros pa/lin a)nafe/retai to\ zugo/n: <lb/>e)a\n de\ ka/twqen u(posth=|, ou)k a)nafe/retai, a)lla\ me/nei, h)\ <lb/>dio/ti a)/nwqen me\n tou= sparti/ou o)/ntos, plei=on tou= zugou= gi/netai <lb/>to\ e)pe/keina th=s kaqe/tou, to\ ga\r sparti/on e)sti\ ka/qetos, <lb/>w(/ste a)na/gkh e)sti\ ka/tw r(e/pein to\ ple/on, e(/ws a)\n e)/lqh| h( <lb/>di/xa diairou=sa to\ zugo\n e)pi\ th\n ka/qeton au)th/n, e)pikeime/nou <lb/>tou= ba/rous e)n tw=| a)nespasme/nw| mori/w| tou= zugou=.</foreign></s> <s id="g0130203"><foreign lang="el"><lb/>e)/stw zugo\n o)rqo\n, e)f' ou(= *b*g, sparti/on de\ to\ *a*d. </foreign></s> <s id="g0130203a"><foreign lang="el">e)kballo/menou <lb/>dh\ tou=tou, ka/tw ka/qetos e)/stai, e)f' h(=s h( *a*d*m.</foreign></s> <s id="g0130204"><foreign lang="el"><lb/>e)a\n ou)=n e)pi\ to\ *b h( r(oph\ e)piteqei/setai, to\ me\n *b ou(= to\ *e, <lb/>to\ de\ *g ou(= to\ *z e)/stai, w(/ste h( di/xa diairou=sa to\ zugo\n.</foreign></s> <s id="g0130204a"><foreign lang="el"> prw=ton <lb/>me\n h)=n h( *a*d*m th=s kaqe/tou au)th=s.</foreign></s> <s id="g0130204b"><foreign lang="el"> e)pikeime/nhs de\ th=s r(oph=s <lb/>e)/stai h( *d*q, w(/ste tou= zugou= e)f' w(=| *e*z, to\ e)/cw th=s kaqe/tou <lb/>th=s e)f' h(=s *a*m, tou= e)n w(=| *f*p, mei/zw tou= h(mi/seos.</foreign></s> <s id="g0130205"><foreign lang="el"><lb/>e)a\n ou)=n a)faireqh=| to\ ba/ros a)po\ tou= *e, a)na/gkh ka/tw fe/resqai <lb/>to\ *z.</foreign></s> <s id="g0130205a"><foreign lang="el">e)/latton ga/r e)sti to\ *e.</foreign></s> <s id="g0130206"><foreign lang="el">e)a\n me\n ou)=n a)/nw to\ <lb/>sparti/on e)/xh|, pa/lin dia\ tou=to a)nafe/retai to\ zugo/n.</foreign></s> <s id="g0130207"><foreign lang="el">e)a\n <lb/>de\ ka/twqen h)=| to\ u(pokei/menon, tou)nanti/on poiei=: plei=on ga\r <lb/>gi/netai tou= h(mi/seos tou= zugou= to\ ka/tw me/ros, h)\ w(s h( ka/qetos <lb/>diairei=, w(/ste ou)k a)nafe/retai: koufo/teron ga\r to\ e)phrthme/non.</foreign></s> <s id="g0130208"><foreign lang="el"><lb/>e)/stw zugo\n to\ e)f' ou(= *n*c to\ o)rqo/n, ka/qetos de\ h( <lb/>*k*l*m, di/xa dh\ diairei=tai to\ *n*c.</foreign></s> <s id="g0130209"><foreign lang="el">e)piteqe/ntos de\ ba/rous <lb/>e)pi\ to\ *n, e)/stai to\ me\n *n ou(= to\ *o, to\ de\ *c, ou(= to\ *r.</foreign></s> <s id="g0130209a"><foreign lang="el"> h( de\ <lb/>*k*l ou(= to\ *l*q, w(/ste mei=zo/n e)sti to\ *l*o tou= *l*r, tw=| *q*k*l.</foreign></s> <s id="g0130210"><foreign lang="el"><lb/>kai\ a)faireqe/ntos ou)=n tou= ba/rous, a)na/gkh me/nein: e)pi/keitai <lb/>ga\r w(/sper ba/ros h( u(peroxh\ h( tou= h(mi/seos tou= e)n w(=| to\ *l*o.</foreign></s> </p> <p type="main"> <s id="id.000850">Propter quid &longs;i in &longs;upe­<lb/>riore librilis parte fuerit <lb/>agina, cum præ <expan abbr="põdere">pondere</expan> <expan abbr="de­mi&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/>fuerit, <expan abbr="nõ">non</expan> redit, &longs;ed manet? <lb/></s> <s id="id.000851">an quia &longs;uperne exi&longs;tente <lb/>agina, librilis plus erit ex­<lb/>tra perpendicularem. </s> <s id="id.000852">E&longs;t <lb/>enim trutina perpendicu­<lb/>laris. </s> <s id="id.000853"><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. </s> <s id="id.000854">E&longs;to li­<lb/>brile rectum <foreign lang="el">b y,</foreign> trutina <foreign lang="el">a <lb/>d</foreign>: at hoc deor&longs;um demi&longs;&longs;o <lb/>&longs;it perpendicularis <foreign lang="el">a d m. </foreign><lb/></s> <s>Si igitur pondus impona­<lb/>tur in lance <foreign lang="el">b,</foreign> erit <foreign lang="el">b</foreign> vbi <foreign lang="el">e, <lb/>& g</foreign> vbi <foreign lang="el">z. </foreign></s> <s>Itaque recta bi­<lb/>fariam diuidens librile, pri­<lb/>mùm quidem erat <foreign lang="el">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 xlink:href="035/01/089.jpg" pagenum="49" />At cum pondus impo&longs;itum <lb/>e&longs;t, e&longs;t <foreign lang="el">f p. </foreign></s> <s>Itaque librilis <lb/><foreign lang="el">e c</foreign> id quod e&longs;t extra per­<lb/>pendicularem <foreign lang="el">a m</foreign> in ea <lb/>quæ e&longs;t <foreign lang="el">f p</foreign> plus e&longs;t: quam <lb/>dimidium. </s> <s id="id.000855">Si igitur pon­<lb/>dus, quod erat in <foreign lang="el">e</foreign> tolla­<lb/>tur, nece&longs;&longs;e e&longs;t <foreign lang="el">z</foreign> deor&longs;um <lb/>ferri. </s> <s id="id.000856">E&longs;t enim <foreign lang="el">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. </s> <s id="id.000857">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. </s> <s id="id.000858">Ideo non refertur. <lb/></s> <s id="id.000859">Leuior enim e&longs;t pars &longs;ur­<lb/>&longs;um lata. </s> <s id="id.000860">E&longs;to librile <foreign lang="el">n c</foreign> re­<lb/>ctum, perpendicularis vero <lb/><foreign lang="el">k l m,</foreign> quæ bifariam diui­<lb/>dat <foreign lang="el">n c,</foreign> & impo&longs;ito pon­<lb/>dere in <foreign lang="el">n,</foreign> &longs;it <foreign lang="el">n</foreign> vbi e&longs;t <foreign lang="el">o, & <lb/>x</foreign> vbi e&longs;t <foreign lang="el">r, & k l</foreign> vbi <foreign lang="el">l q</foreign>. <lb/></s> <s>Itaque maior erit <foreign lang="el">l o</foreign> quam <lb/><foreign lang="el">l r</foreign> ip&longs;o <foreign lang="el">x l q. </foreign></s> <s>Igitur &longs;u­<lb/>blato pondere nece&longs;&longs;e e&longs;t <lb/>manere. </s> <s id="id.000861">Incumbit enim <lb/>ceu pondus exce&longs;&longs;us medietatis, qui e&longs;t in <foreign lang="el">l o. </foreign></s> </p> <p type="head"> <s id="id.000862">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000863">Propter quid.] <emph type="italics"/>In hoc capite proponitur aliud di&longs;cutiendum <lb/>problema de libra. </s> <s id="id.000864">De qua quæruntur duo. </s> <s id="id.000865">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"/></s> <pb xlink:href="035/01/090.jpg" pagenum="50" /> <emph type="italics"/> <s>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/></s> <s id="id.000866">Tertium adiungitur à Guido Vbaldo ( è quo quæ hîc dicemus omnia <lb/>ferè depromp&longs;imus ) non minus quæ&longs;itu dignum. </s> <s id="id.000867">Cur &longs;i centrum &longs;it <lb/>exqui&longs;ite librilis medium, librile retinebit &longs;itum quemlibet datum. <lb/></s> <s id="id.000868">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. </s> <s id="id.000869">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="id.035.01.090.1.jpg" xlink:href="035/01/090/1.jpg"/><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/></s> <s id="id.000870">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="id.035.01.090.2.jpg" xlink:href="035/01/090/2.jpg"/><lb/><emph type="italics"/>ferentias illas loci <lb/><expan abbr="&longs;ursũ">&longs;ursum</expan> deor&longs;um. </s> <s id="id.000871">At <lb/>&longs;iue hoc: &longs;iue illo <lb/>modo librile con­<lb/>&longs;tituatur problema <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 xlink:href="035/01/091.jpg" 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="id.035.01.091.1.jpg" xlink:href="035/01/091/1.jpg"/><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 id="id.000872"><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="id.035.01.091.2.jpg" xlink:href="035/01/091/2.jpg"/><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 id="id.000873">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. </s> <s id="id.000874">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. </s> <s id="id.000875">Maior autem grauior <lb/>e&longs;t. </s> <s id="id.000876">Totum enim librile &longs;upponitur e&longs;&longs;e materiæ vnigeneris. </s> <s id="id.000877">Redit <lb/>igitur libera relicta, &longs;itumque recuperat, vbi paria momenta <expan abbr="æqui­ponderãt">æqui­<lb/>ponderant</expan>. </s> <s id="id.000878">Talis <expan abbr="aut&etilde;">autem</expan> e&longs;t is &longs;itus in quo llbrile <expan abbr="parallelũ">parallelum</expan> fit horizonti. <lb/></s> <s id="id.000879">Contra &longs;i centrum infernam partem occupet, pars inferior librilis <lb/>maior e&longs;t. </s> <s id="id.000880">præponderat igitur. </s> <s id="id.000881">Non itaque per &longs;e redibit: &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 id="id.000883">Itaque librilis <foreign lang="el">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"/></s> <pb xlink:href="035/01/092.jpg" pagenum="52" /> <s><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="id.035.01.092.1.jpg" xlink:href="035/01/092/1.jpg"/><lb/><emph type="italics"/>in centro, &longs;icque triangu­<lb/>lum con&longs;tituit comprehen­<lb/>dens aliquam partem al­<lb/>terutrius brachij 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. </s> <s id="id.000884">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/></s> <s id="id.000885">Et etiam pulchrè re&longs;pon­<emph.end type="italics"/><lb/><figure id="id.035.01.092.2.jpg" xlink:href="035/01/092/2.jpg"/><lb/><emph type="italics"/>det cau&longs;æ iam dictæ ex <lb/>proprietate circuli, quate­<lb/>nus eius radij 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 id="id.000886"><emph type="italics"/>In librili vero &longs;ecundi <lb/>modi res erit adhuc aper­<lb/>tior. </s> <s id="id.000887">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 xlink:href="035/01/093.jpg" pagenum="53" /> <figure id="id.035.01.093.1.jpg" xlink:href="035/01/093/1.jpg"/> <p type="main"> <s id="id.000888"><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/></s> <s id="id.000889">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="id.035.01.093.2.jpg" xlink:href="035/01/093/2.jpg"/><lb/><emph type="italics"/>lanx in&longs;ideat ter­<lb/>ræ vel alicui ful­<lb/>cro. </s> <s id="id.000890">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;trũ">cen<lb/>trum</expan> grauitatis ma­<lb/>net ni&longs;i &longs;u&longs;tinea­<lb/>tur à linea <expan abbr="per­p&etilde;diculari">per­<lb/>pendiculari</expan> ad pla­<lb/>num horizontis. </s> <s id="id.000891">quod e&longs;t demon&longs;tratum ab Vbaldo prop. 1. lib. de lib. <lb/></s> <s id="id.000892">Atque P e&longs;t centrum grauitatis magnitudinis compo&longs;itæ è duobus <lb/>brachijs 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. </s> <s id="id.000893">L K vero linea e&longs;t perpendicularis ad pla­<lb/>num horizontis. </s> <s id="id.000894">Non igitur P liberum relictum manebit ita vt e&longs;t <lb/>G P M H: Sed & redibit ex natura grauium quou&longs;que occupet<lb/>punctum k in perpendiculari horizontis, à qua quia per extre­<lb/>mum L fixa e&longs;t, &longs;u&longs;tinebitur. </s> <s id="id.000895">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/></s> <s id="id.000896">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, quocunque <emph.end type="italics"/><pb xlink:href="035/01/094.jpg" pagenum="54" /><figure id="id.035.01.094.1.jpg" xlink:href="035/01/094/1.jpg"/><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/>ex brachijs 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. </s> <s id="id.000897">Et &longs;ic patet &longs;olutio tertiæ partis huius problematis ab Ari&longs;totele <lb/>prætermi&longs;&longs;æ. </s> <s id="id.000898">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.000899">4. <foreign lang="el">*tou= moxlou= duna/mews ai)/tion. </foreign></s> </p> <p type="main"> <s id="id.000900">4. Potentiæ vectis cau&longs;a. </s> </p> <p type="main"> <s id="id.000901"><foreign lang="el">*dia\ ti/ kinou=si mega/la ba/rh mikrai\ duna/meis tw=| moxlw=|: <lb/>w(/sper e)le/xqh kai\ kat' a)rxh/n: proslabo/nti ba/ros <lb/>e)/ti to\ tou= moxlou=; r(a=|dion de\ to\ e)/latto/n e)sti kinh=sai ba/ros.</foreign></s> <s id="g0130301"><foreign lang="el"><lb/>e)/latton de/ e)stin a)/neu tou= moxlou=.</foreign></s> <s id="g0130302"><foreign lang="el">h)\ o(/ti ai)/tio/n e)stin o( moxlo/s <lb/>zugo\n ka/twqen, e)/xon to\ sparti/on, kai\ ei)s a)/nisa dih|rhme/non, <lb/>to\ ga\r u(pomo/xlio/n e)sti to\ sparti/on.</foreign></s> <s id="g0130302a"><foreign lang="el">me/nei <lb/>ga\r a)/mfw tau=ta, w(/sper to\ ke/ntron, e)pei\ de\ qa=tton u(po\ <lb/>tou= i)/sou ba/rous kinei=tai h( mei/zwn tw=n e)k tou= ke/ntrou.</foreign></s> <s id="g0130302b"><foreign lang="el">e)/sti de\ <lb/>tri/a ta\ peri\ to\n moxlo/n.</foreign></s> <s id="g0130302c"><foreign lang="el">to\ me\n u(pomo/xlion, spa/rton, <lb/>kai\ ke/ntron.</foreign></s> <s id="g0130302d"><foreign lang="el">du/o de\ ba/rh, o(/, te kinw=n, kai\ to\ kinou/menon.</foreign><arrow.to.target n="marg18"/></s> </p> <p type="margin"> <s id="id.000902"><margin.target id="marg18"/>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 id="id.000903">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;ius onus. <lb/></s> <s id="id.000904">Facilius enim e&longs;t minus mo­<lb/>uere onus: minus vero e&longs;t <lb/>ab&longs;que vecte. </s> <s id="id.000905">An quia ve­<lb/>ctis cau&longs;a e&longs;t, qui & in&longs;tar <lb/>libræ deor&longs;um habet <expan abbr="agi­nã">agi­<lb/>nam</expan>, & in inæqualia diui&longs;us <lb/>e&longs;t? </s> <s id="id.000906">E&longs;t enim pre&longs;&longs;io pro <lb/>agina. </s> <s id="id.000907">ambæ enim &longs;tant vt <lb/>centrum. </s> <s id="id.000908">Quoniam vero <lb/>celerius ab æquali ponde­<lb/>re mouetur radius maior. </s> </p> </subchap1> <pb xlink:href="035/01/095.jpg" pagenum="55" /> <subchap1> <p type="main"> <s>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 id="id.000909">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000910">Potentiæ vectis cau&longs;a.] <emph type="italics"/>Vectis definitus e&longs;t à Budæo bacu­<lb/><arrow.to.target n="marg19"/><lb/>lus validus per mediam machinam traiectus, quo manuducto <lb/>machina, dum ver&longs;atur, funem ductarium aduoluit. </s> <s id="id.000912">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. </s> <s id="id.000913">vectis <lb/>enim per &longs;e machina e&longs;t. </s> <s id="id.000914">E&longs;t igitur 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="id.035.01.095.1.jpg" xlink:href="035/01/095/1.jpg"/><lb/><emph type="italics"/>da onera factus, <lb/>vt e&longs;t A B. pars <lb/>obtu&longs;a caput: pars acuta lingula vocatur. </s> <s id="id.000915">Hoc vtendi modus duplex <lb/>e&longs;t. </s> <s id="id.000916">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="el">u(pomo/xlion,</foreign> <emph type="italics"/>Vitruuio preßio dicitur. </s> <s id="id.000917">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="id.035.01.095.2.jpg" xlink:href="035/01/095/2.jpg"/><lb/><emph type="italics"/>gula, vte&longs;t A D B C E F. </s> <s id="id.000918">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. </s> <s id="id.000919">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. </s> <s id="id.000920">Hoc enim &longs;ur&longs;um lato omnes etiam <lb/>vectis partes attolli nece&longs;&longs;e e&longs;t præter extremum lingulæ fixum, quod <lb/>centri immobilis rationem &longs;umit, & terræ vel alij corpori immobili <lb/>tanquam hypomochlio innititur. </s> <s id="id.000921">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 xlink:href="035/01/096.jpg" pagenum="56" /><emph type="italics"/>latus impellitur. </s> <s id="id.000922">Vtrumque vectis v&longs;um Vitruuius cap. 8. lib. 10. &longs;ic <lb/>explicuit. </s> <s id="id.000923">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="el">u(pomo/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. </s> <s id="id.000924">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>. </s> <s id="id.000925">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"/><lb/><emph type="italics"/>alibi. </s> <s id="id.000926">Galenus comparauit mu&longs;culum, qui e&longs;t in&longs;trumentum motus <lb/>voluntarij vecti. </s> <s id="id.000927">vtque pondera, inquit, quæ mouere manibus nequi­<lb/>mus, vectibus admotis mouere &longs;olemus. </s> <s id="id.000928">Ita cum membra corporis <lb/>mouere neruis non poßimus, ad ea mouenda mu&longs;culi nobis &longs;unt dati. <lb/></s> <s id="id.000929">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. </s> <s id="id.000930">Atque hic quidem tendo ex in&longs;trumentis exoriens, habet illius <lb/>extremæ partis vectis rationem quæ ponderibus admouetur. </s> <s id="id.000931">Itaque <lb/>hic ijs 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 ij&longs;dem agentibus in quie­<lb/>te, & quam medici appellant in media figura, retineri. <emph.end type="italics"/></s> </p> <p type="margin"> <s id="id.000932"><margin.target id="marg19"/>Annot. in <lb/>Pandectas. </s> </p> <p type="margin"> <s id="id.000933"><margin.target id="marg20"/>Cap. 10 lib. <lb/>1 de plac. <lb/>Hipp. & <lb/>Plat. </s> </p> <p type="main"> <s id="id.000934">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. </s> <s id="id.000935">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. </s> <s id="id.000936">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 id="id.000937">Facilius enim e&longs;t.] <emph type="italics"/>Ratio e&longs;t ad augendam problematis propo­<lb/>&longs;iti de vecte difficultatem, quæ &longs;ic concludi pote&longs;t. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/097.jpg" pagenum="57" /> <p type="main"> <s id="id.000938"><emph type="italics"/>Facilius e&longs;t mouere paruum pondus quam magnum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000939"><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 id="id.000940"><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 id="id.000941"><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. </s> <s id="id.000942">A&longs;&longs;umptio verò fallaciam <lb/>habet ex varia di&longs;po&longs;itione vectis cum mole. </s> <s id="id.000943">Nam totus, aut dimi­<lb/>dia, aut plu&longs;quam dimidia &longs;ui parte &longs;uppo&longs;itus, aut &longs;uperpo&longs;itus moli, <lb/>adijceret pondus ponderi, &longs;icque moles pondero&longs;ior reuera euaderet. <lb/></s> <s id="id.000944">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/>adijcit moli. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000945">An quia vectis.] <emph type="italics"/>Solutio e&longs;t problematis, quod vectis cum in <lb/>v&longs;um venit referat 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 radij mobilis magnitudinem vectis <lb/>facile & velociter mouetur, & vna cum vecte pondus alteri parti <lb/>incumbens aut annexum. </s> <s id="id.000946">Ratio hæc concluditur hoc &longs;yllogi&longs;mo. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000947"><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 id="id.000948"><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 id="id.000949"><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> </subchap1> <subchap1> <p type="main"> <s id="id.000950"><foreign lang="el">o(\<lb/> ou)=n to\ kinou/menon ba/ros pro\s to\ kinou=n, to\ mh=kos pro\s to\ mh=kos <lb/>a)ntipe/ponqen.</foreign></s> <s id="g0130304"><foreign lang="el">ai)ei\ de\ o(/sw| a)\n mei=zon a)festh/koi, tou= u(pomoxli/ou, <lb/>r(a=|on kinh/sei.</foreign></s> <s id="g0130305"><foreign lang="el">ai)ti/a de/ e)stin h( prolexqei=sa, o(/ti h( <lb/>plei=on a)pe/xousa e)k tou= ke/ntrou, mei/zona ku/klon gra/fei.</foreign></s> <s id="g0130306"><foreign lang="el">w(/ste <lb/>a)po\ th=s au)th=s i)sxu/os ple/on metasth/setai to\ kinou=n to\ <lb/>plei=on tou= u(pomoxli/ou a)pe/xon.</foreign></s> <s id="g0130307"><foreign lang="el">e)/stw moxlo\s e)f' ou(= *a*b. <lb/>ba/ros de\ e)f' w(=| to\ *g.to\ de\ kinou=n, e)f' w(=| to\ *d. u(pomo/xlion <lb/>e)f' w(=| to\ *e. </foreign></s> <s id="g0130308"><foreign lang="el">to\ de\ e)f' w(=| to\ *d kinh=san, e)f' w(=| to\ *h: kekinhme/non <lb/>de\ to\ e)f' ou(= *g. ba/ros e)f' ou(= *k.</foreign></s> </p> <p type="main"> <s id="id.000951">Quod autem e&longs;t mobile <lb/>ad mouens, id e&longs;t longitu­<lb/>do ad longitudinem reci­<lb/>procè. </s> <s id="id.000952">Semper &longs;ane quantò <lb/>longitudo magis di&longs;tabit à <lb/>pre&longs;&longs;ione, facilius mouebit. </s> <pb xlink:href="035/01/098.jpg" pagenum="58" /> <s>Cau&longs;a vero ante dicta e&longs;t: <lb/>quoniam radius maior ma­<lb/>iorem de&longs;cribit circulum. <lb/></s> <s id="id.000953">Itaque ab eadem vi plus <lb/>mutabitur mouens illud, <lb/>quod plus di&longs;tat à pre&longs;&longs;io­<lb/>ne. </s> <s id="id.000954">Sit vectis <foreign lang="el">a b,</foreign> pondus <lb/>vero <foreign lang="el">g,</foreign> mouens autem <foreign lang="el">d,</foreign><lb/>pre&longs;&longs;io <foreign lang="el">e. </foreign>Ip&longs;um vero quod <lb/>mouerit <foreign lang="el">d,</foreign> &longs;it vbi <foreign lang="el">h,</foreign> & pon­<lb/>dus <foreign lang="el">g</foreign> motum vbi <foreign lang="el">k. </foreign></s> </p> <p type="head"> <s id="id.000955">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.000956"><emph type="italics"/>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. </s> <s id="id.000957">Quæres vt intelligatur proponemus hoc theore­<lb/>ma. </s> <s id="id.000958">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. </s> <s id="id.000959">Sit vectis A B, & huius hypo­<lb/>mochlium C:<emph.end type="italics"/><lb/><figure id="id.035.01.098.1.jpg" xlink:href="035/01/098/1.jpg"/><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. </s> <s id="id.000960">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. </s> <s>hoc igitur pondus E loco potentiæ ap­<lb/>pen&longs;um in B, ip&longs;um D pondere æquabit. </s> <s id="id.000961">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. </s> <s id="id.000962">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 xlink:href="035/01/099.jpg" pagenum="59" /><emph type="italics"/>cit pondus E, prohibebit. </s> <s id="id.000963">Nam æqualia ad idem eandem rationem <lb/>habent prop. 7. lib. 5. el. </s> <s id="id.000964">Sed E habet eam ad D, quam A C ad B C, ex <lb/>fab. </s> <s id="id.000965">ergo potentia in B ad pondus D eam rationem habebit, quam <lb/>A C ad B C. </s> <s id="id.000966">Itaque vt e&longs;t potentia ad pondus &longs;u&longs;tentum: ita e&longs;t <lb/>pars vectis &c. </s> <s id="id.000967">quod fuit demon&longs;trandum. </s> <s id="id.000968">Ex quo duo corollaria <lb/>&longs;tatim eliciuntur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000969">Primum. <emph type="italics"/>Hypomochlio bifariam diuidente vectem, potentia <lb/>æqualis requiritur: inæqualiter vero inæqualis. </s> <s id="id.000970">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 id="id.000971">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 id="id.000972">Reciproce.] <foreign lang="el">*antipepo/nqhsis. </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. </s> <s id="id.000974">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. </s> <s id="id.000975">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. </s> <s id="id.000976">Clarum e&longs;t anteceden­<lb/>tes & con&longs;equentes rationum terminos in vtraque figura e&longs;&longs;e. </s> <s id="id.000977">Et <lb/>ideo figuras e&longs;&longs;e reciprocas. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.000978">Semper &longs;ane.] <emph type="italics"/>Hoc ex&longs;ecundo corollario clarum e&longs;t. </s> <s id="id.000979">Quo enim <lb/>pars vectis ad lingulam erit minor, eo pars ad caput erit maior. </s> <s id="id.000980">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. </s> <s id="id.000981">Inæqualium enim <lb/>maior ad eandem maiorem rationem habet prop. 8. lib. 5. </s> <s>Sed & <lb/>huius rei cau&longs;a adfertur ex his quæ ante demon&longs;trata &longs;unt, nempe à <lb/>radio maiore maiorem de&longs;cribi circulum. </s> <s id="id.000982">Pars enim vectis ab hy­<lb/>pomochlio ad caput radij 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. </s> <s id="id.000983">Adde igitur & ex<emph.end type="italics"/><pb xlink:href="035/01/100.jpg" pagenum="60" /><emph type="italics"/>antecedentibus, velocius quoque moueri, quod hîc e&longs;t<emph.end type="italics"/> <foreign lang="el">ra=|on kai\ ple/on <lb/>ki/neisqai,</foreign> <emph type="italics"/>facilius & plus moueri. </s> <s id="id.000984">Ex his autem colligendum e&longs;t il­<lb/>lud, quod e&longs;t ab Archimede profectum problema admirabile. </s> <s id="id.000985">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. </s> <s id="id.000986">ea, quæ dati ponderis e&longs;&longs;et ad da­<lb/>tam potentiam. </s> <s id="id.000987">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 id="id.000988">Sit vectis <foreign lang="el">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="el">g</foreign> <emph type="italics"/>ab eo cum <emph.end type="italics"/><lb/><figure id="id.035.01.100.1.jpg" xlink:href="035/01/100/1.jpg"/><lb/><emph type="italics"/>erat in<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>per depreßionem<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">h</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="el">k. </foreign></s> <s><emph type="italics"/>Sed adhuc <lb/>paulo ob&longs;curius. </s> <s id="id.000989">Apertius igitur &longs;ic. </s> <s id="id.000990">Sit vectis<emph.end type="italics"/> <foreign lang="el">a b,</foreign> <emph type="italics"/>pondus vero<emph.end type="italics"/> <foreign lang="el">g,</foreign><lb/><emph type="italics"/>mouens autem<emph.end type="italics"/> <foreign lang="el">d,</foreign> <emph type="italics"/>preßio<emph.end type="italics"/> <foreign lang="el">e. </foreign><emph type="italics"/></s> <s>Cum ip&longs;um<emph.end type="italics"/> <foreign lang="el">d,</foreign> <emph type="italics"/>quod moueat, &longs;it vbi<emph.end type="italics"/> <foreign lang="el">h</foreign><emph type="italics"/>: <lb/>& pondus<emph.end type="italics"/> <foreign lang="el">g</foreign> <emph type="italics"/>motum erit vbi<emph.end type="italics"/> <foreign lang="el">k. </foreign></s> <s><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. </s> <s id="id.000991">E&longs;t <lb/>autem hic vectis<emph.end type="italics"/> <foreign lang="el">b a,</foreign> <emph type="italics"/>vt diameter circuli cuius extremum<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>deor­<lb/>&longs;um cum ad<emph.end type="italics"/> <foreign lang="el">h</foreign> <emph type="italics"/>mouetur, alterum<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>&longs;ur&longs;um &longs;imul moueri vt ad<emph.end type="italics"/> <foreign lang="el">k,</foreign> <emph type="italics"/>ne­<lb/>ce&longs;&longs;um e&longs;t. </s> <s id="id.000992">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> </subchap1> </chap> <pb xlink:href="035/01/101.jpg" pagenum="61" /> <chap> <subchap1> <p type="main"> <s id="id.000993">5. <foreign lang="el">*dia\ ti/ oi( meso/neoi ma/lista <lb/> th\n nau=n kinou=si. </foreign></s> </p> <p type="main"> <s id="id.000994">5. Cur nauim mouent ma­<lb/>xime remiges, qui in <lb/>media naui &longs;edent. </s> </p> <p type="main"> <s id="g0130401a"><foreign lang="el">*dia\ ti/ oi( meso/neoi ma/lista th\n nau=n kinou=sin; </foreign></s> <s id="g0130402"><foreign lang="el">h)\ dio/ti <lb/>h( kw/ph moxlo/s e)stin, u(pomo/xlion me\n ga\r o( skalmo\s gi/netai.</foreign></s> <s id="g0130402a"><foreign lang="el"><lb/>me/nei ga\r dh\ ou(=tos.</foreign></s> <s id="g0130402b"><foreign lang="el">to\ de\ ba/ros h( qa/latta, h(\n <lb/>a)pwqei= h( kw/ph.</foreign></s> <s id="g0130402c"><foreign lang="el">o( de\ kinw=n to\n moxlo\n o( nau/ths e)sti/n.</foreign></s> <s id="g0130403"><foreign lang="el"><lb/>a)ei\ de\ ple/on ba/ros kinei=, o(/sw| a)\n ple/on a)festh/kh| tou= u(pomoxli/ou <lb/>o( kinw=n to\ ba/ros.</foreign></s> <s id="g0130404"><foreign lang="el">mei/zwn ga\r ou(/tw gi/netai h( e)k <lb/>tou= ke/ntrou.</foreign></s> <s id="g0130404a"><foreign lang="el">o( de\ skalmo\s u(pomo/xlion w)\n ke/ntron e)sti/n.</foreign></s> <s id="g0130405"><foreign lang="el">e)n <lb/>me/sh| de\ th=| nhi\, plei=ston th=s kw/phs e)nto/s e)sti.</foreign></s> <s id="g0130405a"><foreign lang="el">kai\ ga\r h( <lb/>nau=s tau/th| eu)ruta/th e)sti/n.</foreign></s> <s id="g0130405b"><foreign lang="el">w(/ste plei=on e)p' a)mfo/tera e)nde/xesqai <lb/>me/ros th=s kw/phs e(kate/rou toi/xou e)nto\s ei)=nai th=s <lb/>new/s.</foreign></s> <s id="g0130406"><foreign lang="el">kinei=tai me\n ou)=n h( nau=s, dia\ to\ a)pereidome/nhs th=s kw/phs <lb/>ei)s th\n qa/lassan, to\ a)/kron th=s kw/phs to\ e)nto\s proi+e/nai <lb/>ei)s to\ pro/sqen: th\n de\ nau=n prosdedeme/nhn tw=| skalmw=| sumproi+e/nai, <lb/>h(=| to\ a)/kron th=s kw/phs.</foreign></s> <s id="g0130408"><foreign lang="el">h(=| ga\r plei/sthn qa/lassan <lb/>diairei= h( kw/ph, tau/th| a)na/gkh ma/lista prowqei=sqai.</foreign></s> <s id="g0130408a"><foreign lang="el">plei/sthn <lb/>de\ diairei=, h(=| plei=ston me/ros a)po\ tou= skalmou= th=s kw/phs <lb/>e)sti/.</foreign></s> <s id="g0130409"><foreign lang="el">dia\ tou=to oi( meso/neoi ma/lista kinou=sin: me/giston ga\r <lb/>e)n me/sh| nhi\+, to\ a)po\ tou= skalmou= th=s kw/phs to\ e)nto/s e)stin.</foreign></s> </p> <p type="main"> <s id="id.000996">Cur nauim <expan abbr="mou&etilde;t">mouent</expan> maxi­<lb/>me remiges mediani? </s> <s id="id.000997">An qa <lb/>remus e&longs;t vectis, pre&longs;&longs;io <expan abbr="&longs;i­quid&etilde;">&longs;i­<lb/>quidem</expan> &longs;calmus efficitur. </s> <s id="id.000998">Hic <lb/>enim manet. </s> <s id="id.000999"><expan abbr="põdus">pondus</expan> autem <lb/>mare, quod remus propellit: <lb/><expan abbr="vect&etilde;">vectem</expan> vero mouens e&longs;t nau­<lb/>ta. </s> <s id="id.001000">Sed &longs;emper plus <expan abbr="põderis">ponderis</expan> <lb/>mouet, quanto plus motor <lb/>di&longs;titerit à pre&longs;&longs;ione. </s> <s id="id.001001">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="cen­trũ">cen­<lb/>trum</expan> e&longs;t. </s> <s id="id.001002">In nauis <expan abbr="aut&etilde;">autem</expan> medio <lb/><expan abbr="plurimũ">plurimum</expan> remi intus e&longs;t. </s> <s id="id.001003">Ete­<lb/>nim nauis ea parte lati&longs;&longs;ima <lb/>exi&longs;tit: ideo vtrinque remi <lb/>partem maiorem intus in <lb/>vtro que latere nauis <expan abbr="cõtin­git">contin­<lb/>git</expan> e&longs;&longs;e. </s> <s id="id.001004"><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="extre­mũ">extre­<lb/>mum</expan> remi. </s> <s id="id.001005">Vbi enim remus <lb/><expan abbr="plurimũ">plurimum</expan> maris diuidit, eò <lb/>maxime nece&longs;&longs;e e&longs;t impel­<lb/>li. </s> <s id="id.001006">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. </s> <s id="id.001007">Propter id ma­<lb/>ximè mouent. </s> <s id="id.001008">Maxima <lb/>enim remi pars à &longs;calmo intus e&longs;t in medio nauis. </s> </p> <pb xlink:href="035/01/102.jpg" pagenum="62" /> <p type="head"> <s id="id.001009">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001010">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 inuentorum <lb/>ad bene <expan abbr="nauigãdum">nauigandum</expan> vtilium, dubium e&longs;t. </s> <s id="id.001011">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! </s> <s>Semper enim<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001012">E&longs;t tua tam propè mors: quam propè cernis aquam. <lb/></s> <s><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;picijs etiam <lb/>per &longs;ummas tenebras, in quibus homines alioqui domibus &longs;uis vrba­<lb/>nis conclu&longs;i, horrent, peragere? </s> <s id="id.001013">Et denique vbi e&longs;t aquæ &longs;emper &longs;um­<lb/>ma copia, nullius rei tamen magis, quam aquæ penuria laborare? <lb/></s> <s id="id.001014">Rectè &longs;anè dixit Horatius,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001015">Illi robur & æs triplex</s> </p> <p type="main"> <s id="id.001016">Circa pectus erat, qui fragilem truci</s> </p> <p type="main"> <s id="id.001017">Commi&longs;it pelago ratem</s> </p> <p type="main"> <s id="id.001018">Primus. </s> </p> <p type="main"> <s id="id.001019"><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? </s> <s id="id.001020">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. </s> <s id="id.001021">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 id="id.001022">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. </s> <s id="id.001023">An­<lb/>tiquißima nauium Argô à Fabro nauali, qui eam ædificauit, &longs;i <lb/>Apollonio creditur, nuncupata e&longs;t. </s> <s id="id.001024">Sic enim in<emph.end type="italics"/> <foreign lang="el">*argonautikw=n. </foreign></s> </p> <pb xlink:href="035/01/103.jpg" pagenum="63" /> <p type="main"> <s id="id.001025"><foreign lang="el">*nh=a d' e)pikrate/ws ar)gou= u(poqhmosu/nh|si</foreign></s> </p> <p type="main"> <s id="id.001026"><foreign lang="el">*ezwsan, pa/mprwton e)u+strefei= e)ndoqen o(/plw|. </foreign><lb/><emph type="italics"/>quæ &longs;ic reddidit Lazarus Bayfius. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001027">Imprimis nauem diuinis artibus Argi, </s> <s>Extructam, intus compingunt habili armamento. </s> </p> <p type="main"> <s id="id.001028"><emph type="italics"/>Tullius tamen in 1. Tu&longs;cula. dicit nominatam Argô, quia Argiui in <lb/>ea delecti viri vecti petebant Arietis pellem inauratam. </s> <s id="id.001030">Ante Ar­<lb/>go ratibus, & paruis acatijs homines tantum vehi &longs;olere, te&longs;tis e&longs;t <lb/>Diodorus &longs;iculus. </s> <s id="id.001031">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. </s> <s id="id.001032">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. </s> <s id="id.001033">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. </s> <s id="id.001034">Hi à remo Remiges dicti. </s> <s id="id.001035">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. </s> <s id="id.001036">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 manubrijs accedebat ni­<lb/>xus impellentium brachiorum adiuuans. </s> <s id="id.001037">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 delicijs 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. </s> <s id="id.001038">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 xlink:href="035/01/104.jpg" 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 vnam, quæ vicenûm erat, qua­<lb/>tuor quæ ternûm denûm, duas quæ duodenûm, quatuordecim quæ <lb/>vndenûm, & alias infra multas. </s> <s id="id.001039">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. </s> <s id="id.001040">Remigum autem antiquitus, vt & hodie, <lb/>alij voluntarij: alij mercede <expan abbr="cõducti">conducti</expan>: alij 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. </s> <s id="id.001041">Omnes intres ordines reduxit quidam <lb/>Scholia&longs;tes Ari&longs;tophanis in Ranis locum illum,<emph.end type="italics"/> <foreign lang="el">*kai\ a)popardei=n e)s <lb/>to\ sto/ma tw=| qala/maki,</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="el">qalami=tas</foreign> <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="el">qala/makas,</foreign> <emph type="italics"/>qui in medio<emph.end type="italics"/> <foreign lang="el">zugi=tas,</foreign><lb/><emph type="italics"/>qui in &longs;uperiore<emph.end type="italics"/> <foreign lang="el">qrani=tas</foreign> <emph type="italics"/>appellatos fui&longs;&longs;e. </s> <s id="id.001042">Vnde 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="el">kat' i)/cin</foreign> <emph type="italics"/>eius partis habui&longs;&longs;e, <expan abbr="quorũ">quorum</expan> &longs;ingula &longs;uum remum <lb/>haberet alligatum. </s> <s id="id.001043">Vnde cum hi remi &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 haberent <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="el">qrani/ths )esti,</foreign> <emph type="italics"/>inquit<emph.end type="italics"/> <foreign lang="el">o( pro\s th\n pru/mnan, <lb/>zugi/ths o( mesos, qalami/ths o( pro\s th\n prw/ran. </foreign></s> <s><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/>zygitæ &longs;unt, quos hic Ari&longs;toteles vocabulo compo&longs;ito<emph.end type="italics"/> <foreign lang="el">e)k mesh=s kai\ <lb/>ne/ws</foreign> <emph type="italics"/>vocat me&longs;oneos. </s> <s id="id.001044">Sed hic non leuis obrepit controuer&longs;ia, & pro­<lb/>pter præ&longs;entem Ari&longs;totelis contextum ante di&longs;&longs;oluenda, &longs;i pote&longs;t, ex <lb/>duobus locis, altero Thucydidis, altero Galeni. </s> <s id="id.001045">Ille enim li. 6. hæc ha­<lb/>bet. <emph.end type="italics"/></s> <s><foreign lang="el">tw=n prihra/rxwn )epifora\s pro\s tw=| )ek dimwsi/ou misqw=| dido/ntwn <lb/>toi=s qrani/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="quoniã">quoniam</expan> remos 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. </s> <s id="id.001047">Hic verò cap. 24. lib. I, de v&longs;u <emph.end type="italics"/><pb xlink:href="035/01/105.jpg" 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, & eorum 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. </s> <s id="id.001048">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="el">mesone/wn</foreign> <emph type="italics"/>e&longs;&longs;e <lb/>maximos: Ari&longs;toteles non hos, &longs;ed <expan abbr="Thranitarũ">Thranitarum</expan>. </s> <s id="id.001049">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. </s> <s id="id.001050">Ad hanc <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="id.035.01.105.1.jpg" xlink:href="035/01/105/1.jpg"/><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/></s> <s id="id.001051">Sed &longs;i &longs;ic præterquam <lb/>quod Thalamitarum <lb/>Zygitarum & Thra­<emph.end type="italics"/><pb xlink:href="035/01/106.jpg" 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/></s> <s id="id.001053">Moueretur enim aqua &longs;ecundum rectam E F remorum extremita­<lb/>tes excipientem. </s> <s id="id.001054">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="el">periferikoeidh\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>. </s> <s id="id.001055">Quomodo &longs;i pro E F recta <lb/>con&longs;tituamus pe­<emph.end type="italics"/><lb/><figure id="id.035.01.106.1.jpg" xlink:href="035/01/106/1.jpg"/><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. </s> <s id="id.001056">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. </s> <s id="id.001057">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. </s> <s>totæ igitur ex his <lb/>æquales axiom. 2. lib. 1. & ad earum vnam nempe ex S M, H N <emph.end type="italics"/><pb xlink:href="035/01/107.jpg" 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. </s> <s id="id.001059"> Ergo maximus, quod <lb/>fuit probandum. </s> <s id="id.001060">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. </s> <s id="id.001061">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. </s> <s id="id.001062">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. </s> <s id="id.001063">Atque &longs;ic &longs;int hi duo loci meo iudicio ex­<lb/>plicati. </s> <s id="id.001064">Cæterum Remiges, vt & hoc notatu pulchrum adijciamus, <lb/>Remigando artificiosè &longs;imul omnes, quamuis quater mille, inter &longs;e <lb/>con&longs;entientes, alioqui illis corium flagris 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 id="id.001065">Intentaque brachia remís</s> </p> <p type="main"> <s id="id.001066">Intenti expectant &longs;ignum. </s> </p> <p type="main"> <s id="id.001067"><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 adijcientur &longs;citu digna. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001068">Cur remiges.] <emph type="italics"/>E &longs;ex problematis quæ de vecte pertinent ad <lb/>nauigandi artem, primum per comparationem proponitur. </s> <s id="id.001069">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. </s> <s id="id.001070">Re&longs;pondet id fieri, 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. </s> <s id="id.001071">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. </s> <s id="id.001072">Tota igitur hæc quæ&longs;tio hoc <lb/>primario &longs;yllogi&longs;mo &longs;ic concludetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001073"><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> </p> <p type="main"> <s id="id.001074"><emph type="italics"/>Sed remi pars à &longs;calmo ad manubrium eius qui in medio e&longs;t <lb/>maior: & ad palmulam eiu&longs;dem plus maris diuidit, <lb/>quam aliorum. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/108.jpg" pagenum="68" /> <p type="main"> <s id="id.001075"><emph type="italics"/>Ergo qui in medio e&longs;t inter remiges plus promouet nauim. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001076">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> </p> <p type="main"> <s id="id.001077"><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/></s> <s id="id.001078">Hoc ita e&longs;&longs;e patuit ex cap. præced. libri huius. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001079"><emph type="italics"/>Sed pars remi à Scalmo ad manubrium e&longs;t pars vectis ab <lb/>hypomochlio ad caput. </s> <s id="id.001080">Nam remus e&longs;t vectis. per def. & <lb/>&longs;calmus e&longs;t hypomochlium. </s> <s id="id.001083">hic enim mouet, pondus vero <lb/>mobile mare, & vectem mouens, Remex. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001084"><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> </p> <p type="main"> <s id="id.001085">In nauis medio.] <emph type="italics"/>A&longs;&longs;umptio e&longs;t primarij &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. </s> <s id="id.001086">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. </s> <s id="id.001087">vt ex penultimo <lb/>diagrammate qualicunque intelligi pote&longs;t. </s> <s id="id.001088">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. </s> <s>( quod nos &longs;equenti theoremate demon&longs;trabimus ) igitur 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> </p> <p type="main"> <s id="id.001090">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. </s> <s id="id.001091">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. </s> <s id="id.001092">Dico C B e&longs;&longs;e <lb/>maiorem quam F I: & F I quam G H. </s> <s id="id.001093">Per punctum M cen­<lb/>trum circuli repertum prop. 1. lib. 3. ducatur parallela M N O P <emph.end type="italics"/><pb xlink:href="035/01/109.jpg" 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="id.035.01.109.1.jpg" xlink:href="035/01/109/1.jpg"/><lb/><emph type="italics"/>N C. </s> <s id="id.001095">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. </s> <s id="id.001097">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 inæquales ax. 5. </s> <s>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. </s> <s id="id.001099">Igitur &longs;i chorda rectas, &c. </s> <s id="id.001100">quod fuit <expan abbr="demon&longs;trandũ">demon&longs;trandum</expan>. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001101">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. </s> <s id="id.001102">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/></s> <s id="id.001103">Nauis autem per &longs;calmum alligata e&longs;t remo. </s> <s id="id.001104">Nauis igitur promouebi­<lb/>tur antror&longs;um, &longs;i eò manubrium <expan abbr="promotũ">promotum</expan> &longs;it. </s> <s id="id.001105">Dixi &longs;i eò manubrium <lb/>promotum &longs;it, quia concitato nauigio, quum remiges inhibent, contra <lb/>fit. </s> <s id="id.001106">Manubrium &longs;iquidem mouetur retror&longs;um, proinde vna cum eo <lb/>& nauis. </s> <s id="id.001107">Ad huius rei fidem locus e&longs;t apud Tullium luculentus. <lb/></s> <s id="id.001108">Nunc vt ad rem redeam, inquit, inhibere illud tuum, quod valde <lb/>mihi arri&longs;erat, vehementer di&longs;plicet. </s> <s id="id.001109">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. </s> <s id="id.001110">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="el">e)poxh=s</foreign> <emph type="italics"/>remotißimum e&longs;t. </s> <s id="id.001111">Et po&longs;tea &longs;ubdit. <lb/></s> <s id="id.001112">Inhibitio autem remigum motum habet, & <expan abbr="vehem&etilde;tiorem">vehementiorem</expan> quidem <emph.end type="italics"/><pb xlink:href="035/01/110.jpg" pagenum="70" /><emph type="italics"/>remigationis nauem conuertentis ad puppim. </s> <s id="id.001113">Hæc Cicero. </s> <s id="id.001114">quæ non <lb/>abs re vt arbitror hîc &longs;unt in&longs;erta, vt quæ plurimum faciant <lb/>ad intelligendum e motibus nauis duos rectos concitationem &longs;ci­<lb/>licet, & inhibitionem, & vtramque fieri à remo tanquam à <lb/>vecte. </s> <s id="id.001115">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, & hypomochlij vicem præ&longs;tet: non &longs;calmus. </s> <s id="id.001116">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. </s> <s id="id.001117">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. </s> <s id="id.001118">Erit <lb/>igitur pro centro, neque etiam nautis animus e&longs;t mare: &longs;ed nauem <lb/>tanquam pondus propellere. </s> <s id="id.001119">Neque minus interea verum erit, quod <lb/>qui in medio mari remigant, ip&longs;am plus propellant. </s> <s id="id.001120">Sed quid dice­<lb/>mus Aristoteli & Vitruuio qui apertè dicunt &longs;calmum e&longs;&longs;e hypo­<lb/>mochlium, & mare pondus mouendum. </s> <s id="id.001121">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. </s> <s id="id.001122">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. </s> <s id="id.001123">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. </s> <s id="id.001124">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. </s> <s id="id.001125">De his igitur pote&longs;t intelligi Ari&longs;to­<lb/>teles tum Vitruuius. </s> <s id="id.001126">At in quarto aqua renitens palmulæ e&longs;t hypo­<lb/>mochlium, nauis vero pondus mouendum, vt diximus. </s> <s id="id.001127">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. </s> <s id="id.001128">Sicque <lb/>nauta aliquid faciet quod non quærit, vt aliud con&longs;equatur: mare <emph.end type="italics"/><pb xlink:href="035/01/111.jpg" 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> </p> <p type="main"> <s id="id.001129">Eo vbi e&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> </p> <p type="main"> <s id="id.001130">Vbi enim remus.] <emph type="italics"/>Illu&longs;tratio e&longs;t &longs;ecundæ partis propo&longs;itionis <lb/>primarij &longs;yllogi&longs;mi vbi<emph.end type="italics"/> <foreign lang="el">plei/sthn qa/lassan th\n kw/phn diairei=n. </foreign><emph type="italics"/>Re­<lb/>mum diuidere plurimum maris dici pote&longs;t duobus modis, vno cum <lb/>palmula profundius ingrediatur mare. </s> <s id="id.001131">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>. </s> <s id="id.001132">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. </s> <s id="id.001133">Non ita e&longs;t de &longs;calmis aliorum cum puppis & prora <lb/>paulò &longs;ublimiores &longs;int lateribus. </s> <s id="id.001134">De altero dicetur po&longs;tea amplius <lb/>quia radij maioris peripheria maior e&longs;t. </s> <s id="id.001135">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> </p> <p type="main"> <s id="id.001136">Propter id remiges.] <emph type="italics"/>Conclu&longs;io e&longs;t primarij &longs;yllogi&longs;mi cum <lb/>repetione cau&longs;æ eiu&longs;dem. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001137">6. <foreign lang="el">*tou= phdali/ou duna/mews <lb/>ai)/tion, kai\ tou= ma=llon proe/r­<lb/>xesqai ei)s tou)nantioon to\ <lb/>ploi=on, h)\ th\n th=s kw/phs <lb/> pla/thn. </foreign></s> </p> <p type="main"> <s id="id.001138">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> </p> <p type="main"> <s id="id.001139"><foreign lang="el">*dia\ ti/ to\ phda/lion mikro\n o)/n, kai\ e)p' e)sxa/tw| tw=| <lb/>ploi/w|, tosau/thn du/namin e)/xei w(/ste u(po\ mikrou= oi)/akos, kai\ <lb/>e(no\s a)nqrw/pou duna/mews, kai\ tau/ths h)remai/as, mega/la kinei=sqai <lb/>mege/qh ploi/wn, h)\ dio/ti kai\ to\ phda/lion e)sti\ moxlo\s, <lb/>to\ de\ ba/ros h( qa/lassa, o( de\ kubernh/ths o( kinw=n.</foreign></s> <s id="g0130503"><foreign lang="el"><lb/>ou) kata\ pla/tos de\ lamba/nei th\n qa/lassan, w(/sper h( kw/ph, <lb/>to\ phda/lion. ou) ga\r ei)s to\ pro/sqen kinei= to\ ploi=on, a)lla\ <lb/>kinou/menon kli/nei, plagi/ws th\n qa/lattan dexo/menon.</foreign></s> <s id="g0130504"><foreign lang="el">e)pei\ <lb/>ga\r to\ ba/ros h)=n h( qa/lassa, tou)nanti/on a)pereido/menon kli/nei <lb/>to\ ploi=on. to\ ga\r u(pomo/xlion ei)s tou)nanti/on stre/fetai,<lb/> h( qa/lassa de\ e)nto/s: e)kei=no de\ ei)s to\ e)kto/s. tou/tw| de\ a)kolouqei= <lb/>to\ ploi=on, dia\ to\ sundede/sqai.</foreign></s> <s id="g0130505"><foreign lang="el">h( me\n ou)=n kw/ph kata\ <lb/>pla/tos to\ ba/ros w)qou=sa kai\ u(p' e)kei/nou a)ntwqoume/nh, ei)s to\ <lb/>eu)qu\ proa/gei.</foreign></s> <s id="g0130505a"><foreign lang="el">to\ de\ phda/lion, w(/sper ka/qhtai pla/gion, <lb/>th\n ei)s to\ pla/gion, h)\ deu=ro, h)\ e)kei= poiei= ki/nhsin.</foreign></s> </p> <p type="main"> <s id="id.001140">Cur gubernaculum par­<lb/>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 etiam propemodum <lb/>quie&longs;centis viribus, magnæ <pb xlink:href="035/01/112.jpg" pagenum="72" /><expan abbr="nauigiorũ">nauigiorum</expan> moles mouean­<lb/>tur? </s> <s id="id.001141">An quia <expan abbr="gubernaculũ">gubernaculum</expan> <lb/>e&longs;t vectis: pondus mare, gu­<lb/>bernator mouens. </s> <s id="id.001142">Non au­<lb/>tem <expan abbr="&longs;ecũdum">&longs;ecundum</expan> latitudinem <lb/><expan abbr="gubernaculũ">gubernaculum</expan> impellit ma­<lb/>re, vt remus. </s> <s id="id.001143">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. </s> <s id="id.001144">quia <lb/>enim mare pondus erat ad <lb/>contrarium incumbens in­<lb/>clinat nauim. </s> <s id="id.001145">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. </s> <s id="id.001146">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> </p> <p type="head"> <s id="id.001147">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001148">Potentiæ guber.] <emph type="italics"/>In hoc capite proponuntur tria &longs;pecialia de <lb/>vecte problemata quorum duo &longs;unt de gubernaculo & tertium <lb/>de remo. </s> <s id="id.001149">Primum e&longs;t cur gubernaculum, paruum cum &longs;it, magnam <lb/>nauigij molem moueat. </s> <s id="id.001150">Et huic differentia quæ e&longs;t inter remi & gu­<lb/>bernaculi motiones &longs;ubijcitur. </s> <s id="id.001151">Secundum cur gubernaculum in puppi <lb/>non in medio aut prora nauis collocetur. </s> <s id="id.001152">Tertium cur nauigium an­<lb/>tror&longs;um plus procedat, quam remi palmula retror&longs;um. </s> <s id="id.001153">Atque hæc eo <lb/>ordine quo propo&longs;ita &longs;unt, di&longs;&longs;oluentur. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/113.jpg" pagenum="73" /> <p type="main"> <s id="id.001154">Gubernaculum.] <emph type="italics"/>Gubernaculum remus erat apud antiquos, <lb/>&longs;ed multo latioris palmulæ: quam remi, quibus ad latera nauis remi­<lb/>gabant. </s> <s id="id.001155">Ob id pterigion ab alæ exten&longs;æ &longs;imilitudine vel latitudine <lb/>dicta e&longs;t. </s> <s id="id.001156">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> </p> <p type="main"> <s id="id.001157">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> </p> <p type="main"> <s id="id.001158">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 nauigij, & omnium, quæ <expan abbr="veh&etilde;da">vehenda</expan> naui impo&longs;ita &longs;unt. </s> <s id="id.001159">Quæ, vt <lb/>ijs qui viderunt omnia, manife&longs;tißima &longs;unt: ita ijs qui non viderunt <lb/>incredibilia. </s> <s id="id.001160">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. </s> <s id="id.001161">Longa e&longs;t, &longs;ed vt &longs;pero, omni­<lb/>bus lectu <expan abbr="iucũda">iucunda</expan> hi&longs;toria. </s> <s id="id.001162">Recitat igitur Athenæus <expan abbr="Hieron&etilde;">Hieronem</expan> Syra­<lb/>cu&longs;anorum Regem ad naues fabricandum ambitiosà animum inten­<lb/>di&longs;&longs;e, & vnam imprimis memorabilem perfeci&longs;&longs;e, ad quam ædifi­<lb/>candam, materiam in AEtna 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. </s> <s id="id.001163">quo dicto nauigij magnitudinem conijciendam nobis reliquit. <lb/></s> <s id="id.001164">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 faciendo fabros, arti­<lb/>fice&longs;que adhibui&longs;&longs;e: ac materiæ dedolandæ præter admini&longs;tros fabri­<lb/>cæ &longs;ub&longs;eruientes opificijs, præfecto &longs;ummæ operis architecto Archia <lb/>Corinthio. </s> <s id="id.001165">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. </s> <s id="id.001166">Quo <lb/>facto inchoatam eo modo nauem in mare deducendam manda&longs;&longs;e: vt <emph.end type="italics"/><pb xlink:href="035/01/114.jpg" pagenum="74" /><emph type="italics"/>illìc extremæ manus opificium adipi&longs;ceretur. </s> <s id="id.001167">Hac deducta alteram <lb/>nauigij partem totidem alijs men&longs;ibus Hieronem <expan abbr="cõ&longs;umma&longs;&longs;e">con&longs;umma&longs;&longs;e</expan>. </s> <s id="id.001168">Cum <lb/>interim clauis æreis denarum librarum plurimis materiam compin­<lb/>geret, aliquibus etiam &longs;e&longs;quiplis eius ponderis, qui præ craßitudine. <lb/></s> <s id="id.001169">non alias adigi poterant: quam materia perterebrata. </s> <s id="id.001170">His clauis co&longs;tæ <lb/>nauis arrectariæ cum a&longs;&longs;amentis tran&longs;uer&longs;arijs 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. </s> <s id="id.001171">Erat rur&longs;us, inquit <lb/>ille, ea nauis apparatu quidem viginti ordinum remigij: ædificij vero <lb/>contignatione triplici. </s> <s id="id.001172">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. </s> <s id="id.001173">In ijs lecti quaterni &longs;trati viris accom­<lb/>modati: inter quas nauclericum conclaue quinque lectorum capax <lb/>erat. </s> <s id="id.001174">Præterea thalami tres in eadem contignatione erant, culinaque <lb/>&longs;upradictis locis &longs;ub&longs;eruiens ad puppim ædificata. </s> <s id="id.001175">Omnes autem &longs;u­<lb/>pradictæ cœnationes pauimento &longs;tratæ erant te&longs;&longs;ellis vermiculato <lb/>lapidis omnis generis. </s> <s id="id.001176">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/></s> <s id="id.001177">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. </s> <s id="id.001178">Ab his erat <lb/>Aphrodi&longs;ium id e&longs;t conclaue Veneri deæ dicatum: in&longs;trumentum <lb/>etiam ip&longs;um triclínari lecti&longs;ternio, pauimentoque &longs;tratum achate la­<lb/>pide alij&longs;que varijs & nitentibus di&longs;tincto. </s> <s id="id.001179">Cuiu&longs;modi lapidum co­<lb/>pia in Sicilia reperitur. </s> <s id="id.001180">Ac parietes quidem habebat cupreßinis ta­<lb/>bulis aßibu&longs;que contextos, laqueatumque tectum eadem materia. </s> <s id="id.001181">Fo­<lb/>res etiam ex ebore & odorata materia compactas, atque eo amplius <lb/>pictura &longs;igilli&longs;que exornatas. </s> <s id="id.001182">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 xlink:href="035/01/115.jpg" pagenum="75" /><emph type="italics"/>quod in Achradina &longs;itum erat, quæ in&longs;ula e&longs;t Syracu&longs;arum. </s> <s id="id.001183">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. </s> <s id="id.001184">Mitto nunc habitationes militibus de&longs;tinatas: ii&longs;que qui <lb/>&longs;uper &longs;entinam erant. </s> <s id="id.001185">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. </s> <s id="id.001186">Præterea li­<lb/>gnarium, & clibanos focos, & pi&longs;trina, aliaque mini&longs;teria in proie­<lb/>cturis nauis prominentia. </s> <s id="id.001187">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? </s> <s id="id.001188">Quid turres octo? <lb/></s> <s id="id.001189">binas in prora & puppi per vtrumque latus extructas, in muri&longs;que <lb/>propugnacula. </s> <s id="id.001190">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;tadij. </s> <s id="id.001191">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. </s> <s id="id.001192"><expan abbr="Stabãt">Stabant</expan> enim in vno terni: in alijs 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. </s> <s id="id.001193">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. </s> <s id="id.001194">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/>pactile, iuxta quod rur&longs;us pi&longs;cina coaxatione & implumbatura <lb/>con&longs;tans plena aquæ marinæ. </s> <s id="id.001195">Ita vt in ea commode magna copia <lb/>pi&longs;cium facile aleretur. </s> <s id="id.001196">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. </s> <s id="id.001198">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 xlink:href="035/01/116.jpg" pagenum="76" /><emph type="italics"/>rum, & pabulum equorum, præter denique onus tanti nauigij. </s> <s id="id.001199">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 id="id.001200">An quia gubernaculum.] <emph type="italics"/>Solutio e&longs;t primi problematis, &longs;ic. <lb/></s> <s id="id.001201">Vecte magna mouentur pondera. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001202"><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 id="id.001203"><emph type="italics"/>Ergo gubernaculo nauigij moles mouebitur. </s> <s id="id.001204">De hoc na­<lb/>uis motu pulchre. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001205"><emph type="italics"/>Vitruuius &longs;ic mentionem facit. </s> <s id="id.001206">Nauis onerariæ maximæ guber­<lb/>nator an&longs;am gubernaculi tenens, quod<emph.end type="italics"/> <foreign lang="el">o)/iac</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 id="id.001207">Pondus mare.] <emph type="italics"/>Vt antè in remis dictum e&longs;t. </s> <s id="id.001208">pondus quod mo­<lb/>uere intendit gubernator non e&longs;t mare: licet parum impellatur, &longs;ed <lb/>nauis. </s> <s id="id.001209">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 id="id.001210">Non autem &longs;ecundum.] <emph type="italics"/>Dißimilitudo e&longs;t gubernaculi & <lb/>remi ex differenti loco ad quem vtrumque nauim mouet. </s> <s id="id.001211">Vtrumque <lb/>enim nauim mouet ad locum, qui contrarius e&longs;t ei, ad quem mare im­<lb/>pul&longs;um mouetur. </s> <s id="id.001212">Mouetur enim nauis ad centri, cui e&longs;t annexa, mo­<lb/>tum. </s> <s id="id.001213">Centrum <expan abbr="aut&etilde;">autem</expan> in remo e&longs;t &longs;calmus, in gubernaculo cardo. </s> <s id="id.001214">Mo­<lb/>uetur hoc contra quam depul&longs;um mare. </s> <s id="id.001215">Mare autem retror&longs;um rectà <lb/>à remo depellitur: mouet igitur remus rectà antror&longs;um nauim. </s> <s id="id.001216">Con­<lb/>trà mare à gubernaculo obliquè impellitur, vel dextror&longs;um vel &longs;ini­<lb/>&longs;tror&longs;um. </s> <s id="id.001217">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 xlink:href="035/01/117.jpg" pagenum="77" /> <p type="main"> <s id="id.001218"><foreign lang="el">e)p' a)/krou <lb/>de\ kai\ ou)k e)n me/sw| kei=tai, o(/ti r(a=|ston to\ kinou/menon kinh=sai <lb/>a)p' a)/krou kinou=n: ta/xista ga\r fe/retai to\ prw=ton me/ros, <lb/>dia\ to\ w(/sper e)n toi=s ferome/nois e)pi\ te/lei lh/gein th\n fora/n, <lb/>ou(/tw kai\ tou= sunexou=s e)pi\ te/lous a)sqenesta/th e)sti\n h( fora/. <lb/></foreign></s> <s id="g0130507a"><foreign lang="el">h( de\ a)sqenesta/th r(a|di/a e)kkrou/ein. </foreign></s> <s id="g0130508"><foreign lang="el">dia/ te dh\ tau=ta e)n th=| <lb/>pru/mnh| to\ phda/lio/n e)sti, kai\ o(/ti e)ntau=qa mikra=s kinh/sews <lb/>genome/nhs pollw=| mei=zon to\ dia/sthma e)pi\ tw=| e)sxa/tw| gi/netai, <lb/>dia\ to\ th\n i)/shn gwni/an e)pi\ mei/zona kaqh=sqai.</foreign></s> <s id="g0130508a"><foreign lang="el">kai\ o(/sw| <lb/>a)\n mei/zous w)=sin ai( perie/xoustai.</foreign></s> </p> <p type="main"> <s>In extremo autem, non <lb/>in medio po&longs;itum e&longs;t. </s> <s id="id.001220">quia <lb/>motor, id quod iam moue­<lb/>tur, facillime ab extremo <lb/><expan abbr="cõmouet">commouet</expan>. </s> <s id="id.001221">Celerrime 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. </s> <s id="id.001222">E&longs;t autem imbecillima <lb/>facilis repul&longs;u. </s> <s id="id.001223">Propterea <lb/>gubernaculum in puppi &longs;i­<lb/>tum e&longs;t. </s> <s id="id.001224">Et quoniam exi­<lb/>gua in ea motione facta, <lb/>multo maior in prora fit in­<lb/>tercapedo. </s> <s id="id.001225">Angulus enim <lb/>æqualis à maiori &longs;ubtendi­<lb/>tur, & quanto maiores quæ <lb/>angulum comprehenderunt lineæ. </s> </p> <p type="head"> <s id="id.001226">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001227">In extremo autem.] <emph type="italics"/>Solutio e&longs;t &longs;ecundi problematis duplex, <lb/>&longs;ic. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001228"><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 id="id.001229"><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 id="id.001230"><emph type="italics"/>Ergo in puppi non in medio gubernaculum collocandum e&longs;t. <lb/></s> <s id="id.001231">Ob id etiam&longs;i e pi&longs;cibus quidam parte anteriori homini & quadra­<lb/>pedibus &longs;imiles &longs;unt, vt <expan abbr="Tritõ">Triton</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 xlink:href="035/01/118.jpg" pagenum="78" /> <p type="main"> <s id="id.001232">Quia motor.] <emph type="italics"/>Syllogi&longs;mi præcedentis propo&longs;itio nec po&longs;ita, <lb/>nec illu&longs;trata e&longs;t. </s> <s id="id.001233">quia ex &longs;e euidens. </s> <s id="id.001234">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 id="id.001235"><emph type="italics"/>Non re&longs;i&longs;tentia, aut minus re&longs;i&longs;tentia, mouere facilius e&longs;t. <lb/></s> <s id="id.001236">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/></s> <s id="id.001237">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 id="id.001238"><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 id="id.001239">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. </s> <s id="id.001240">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 id="id.001241">Et quoniam exigua.] <emph type="italics"/>Similis &longs;ententia e&longs;t apud Ari&longs;totelem <lb/>lib. de animalium motu. </s> <s id="id.001242">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. </s> <s id="id.001243">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 id="id.001244">Angulus enim æqualis.] <emph type="italics"/>Licet oculata alioquin fide perci­<lb/>piatur quanta & quam euidens nauigij 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 id="id.001245"><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="id.035.01.118.1.jpg" xlink:href="035/01/118/1.jpg"/><lb/><emph type="italics"/>ba&longs;ibus: & huius ba­<lb/>&longs;is maior, cuius crura <lb/>maiora. </s> <s id="id.001246">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. </s> <s id="id.001247">Dico ba&longs;im D C maiorem e&longs;&longs;e ba&longs;i B E. </s> <s id="id.001248">Nam quia <emph.end type="italics"/><pb xlink:href="035/01/119.jpg" pagenum="79" /><emph type="italics"/>tres anguli vnius triangulorum &longs;unt æquales tribus alterius prop. <lb/>32. lib. 1. </s> <s>& anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba­<lb/>&longs;im duo duobus &longs;unt æquales ax. 3. </s> <s>& quia A D C & A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, ij inter &longs;e erunt æquales prop. 5. lib. 1. & per <lb/>eandem anguli A B E & A E B. </s> <s id="id.001251">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> æqua­<lb/>lis erit ax. 6. & per idem reliquus reliquo. </s> <s id="id.001253">Sunt igitur A B E & <lb/>A D C triangula æquiangula, proinde circum æquales angulos la­<lb/>tera habebunt proportionalia. </s> <s id="id.001254">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. </s> <s>E&longs;t autem maius A D ip&longs;o A B <lb/>ex hypothe&longs;i. </s> <s id="id.001256">Ergo Ba&longs;is D C maior erit ip&longs;a B E. </s> <s id="id.001257">Igitur &longs;i duo <lb/>I&longs;o&longs;celia æqualia angulis, inæqualia cruribus fuerint &c. </s> <s id="id.001258">quod <lb/>fuit demonstrandum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001259"><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. </s> <s id="id.001260">Tunc C erit in D. <lb/></s> <s id="id.001261">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. </s> <s>Et inæqualia cruri­<lb/>bus. </s> <s id="id.001262">Nam rectæ 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 ijs, quæ &longs;unt ab <expan abbr="eod&etilde;">eodem</expan> puncto A ad ex­<lb/>tremum puppis A B, A E. </s> <s id="id.001263">Peragrabit igitur prora D lineam C B <lb/>longè maiorem, cum B peragrabit B E multo minorem. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.001264"><foreign lang="el">dh=lon de\ e)k tou/tou, kai\ di' h(\n <lb/>ai)ti/an ma=llon proe/rxetai ei)s tou)nanti/on to\ ploi=on h)\ h( th=s <lb/>kw/phs pla/th: to\ au)to\ ga\r me/geqos th=| au)th=| i)sxu/i+ kinou/menon <lb/>e)n a)e/ri, ple/on h)\: e)n tw=| u(/dati pro/eisin.</foreign></s> <s id="g0130510"><foreign lang="el">e)/stw ga\r h( *a <lb/>*b kw/ph, to\ de\ *g o( skalmo/s, to\ de\ *a to\ e)n tw=| ploi/w|, h( <lb/>a)rxh\ th=s kw/phs, to\ de\ *b to\ e)n th=| qala/tth|.</foreign></s> <s id="g0130511"><foreign lang="el">ei) dh\ to\ *a <lb/>ou(= to\ *d metakeki/nhtai, to\ *b ou)k e)/stai ou(= to\ *e: i)/sh ga\r h( *b <lb/>*e th=| *a*d.</foreign></s> <s id="g0130511a"><foreign lang="el">i)/son ou)=n metakexwrhko\s e)/stai, a)ll' h)=n e)/latton. <lb/></foreign></s> <s id="g0130512"><foreign lang="el">e)/stai dh\ ou(= to\ *z [1h)\ to\ *q. a)/ra toi/nun th\n *a*b, kai\ ou)x h( to\ <lb/>*g, kai\ ka/twqen.]1 </foreign></s> <s id="g0130512a"><foreign lang="el">e)la/ttwn ga\r h( *b*z, th=s *a*d, w(/ste kai\ <lb/>h( *q*z th=s *d*q: o(/moia ga\r ta\ tri/gwna.</foreign></s> <s id="g0130513"><foreign lang="el">kaqesthko\s de\ <lb/>e)/stai kai\ to\ me/son, to\ e)f' ou(= *g: ei)s tou)nanti/on ga\r tw=| e)n th=| <lb/>qala/tth| a)/krw| to\ *b metaxwrei=, h(=|per to\ e)n ploi/w| <lb/>a)/kron to\ *a.</foreign></s> <s id="g0130514"><foreign lang="el">mh\ e)gxw/rei de\ ou(= to\ *d. </foreign></s> <s id="g0130514a"><foreign lang="el">ei) mh\ metakinhqh/setai to\ <lb/>ploi=on, kai\ e)kei= ou(= h( a)rxh\ th=s kw/phs metafe/retai.</foreign></s> </p> <p type="main"> <s id="id.001265">Ex hoc autem <expan abbr="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/></s> <s id="id.001266">Eadem enim moles eadem <lb/>vi mota per aerem plus, <lb/>quam per aquam progre­<lb/>ditur. </s> <s id="id.001267">Sit enim remus <foreign lang="el">a b</foreign><lb/>& &longs;calmus <foreign lang="el">g,</foreign> & intra nauim <lb/>caput remi <foreign lang="el">a</foreign> palmula intra <lb/>mare <foreign lang="el">b. </foreign>Si itaque <foreign lang="el">a</foreign> <expan abbr="tran&longs;la­tũ">tran&longs;la­<lb/>tum</expan> &longs;it eò, vbi e&longs;t <foreign lang="el">d</foreign>: ip&longs;um <foreign lang="el">b</foreign><pb xlink:href="035/01/120.jpg" pagenum="80" /><arrow.to.target n="marg21"/><lb/>non erit vbi e&longs;t <foreign lang="el">e. </foreign>E&longs;t enim <lb/><foreign lang="el">b e</foreign> æqualis ip&longs;i <foreign lang="el">a d. </foreign>Ex <lb/>æquo igítur tran&longs;latum e&longs;­<lb/>&longs;et, &longs;ed minus erat. </s> <s id="id.001268">E&longs;t igi­<lb/>tur vbi <foreign lang="el">z. </foreign>Minor enim e&longs;t <lb/><foreign lang="el">b z</foreign>: <expan abbr="quã">quam</expan> <foreign lang="el">a d. </foreign>Itaque etiam <lb/><foreign lang="el">q z</foreign> quam <foreign lang="el">d q. </foreign></s> <s>Similia enim <lb/>&longs;unt triangula. </s> <s id="id.001269">Con&longs;i&longs;tens <lb/>vero erit medium vbi e&longs;t <foreign lang="el">g.</foreign><lb/></s> <s>In contrarium enim extre­<lb/>mo <foreign lang="el">b,</foreign> quod in mari e&longs;t <lb/>procedit <expan abbr="extremũ">extremum</expan> <foreign lang="el">a,</foreign> quod <lb/>in nauigio e&longs;t. </s> <s id="id.001270">Non autem <lb/>ad <foreign lang="el">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 id="id.001271"><margin.target id="marg21"/>Inclu&longs;a his <lb/>notis [] ni­<lb/>hil faciunt <lb/>ad rem. </s> </p> <p type="head"> <s id="id.001272">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001273">Ex hoc autem.] <emph type="italics"/>Hic continetur tertium è tribus, quæ hoc <lb/>capite diximus contineri problemata. </s> <s id="id.001274">E&longs;t autem eiu&longs;modi. </s> <s id="id.001275">An <lb/>nauis plus antror&longs;um vehitur: <expan abbr="quã">quam</expan> palmula remi retror&longs;um. </s> <s id="id.001276">Re&longs;pon­<lb/>det Ari&longs;toteles plus vehi nauem antror&longs;um. </s> <s id="id.001277">Cau&longs;am dicit. </s> <s id="id.001278">quia ea­<lb/>dem moles eadem vi mota plus per medium rarum fertur: quam per <lb/>den&longs;um. </s> <s id="id.001279">Contra quam rationem duo occurrunt aliena. </s> <s id="id.001280">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. </s> <s id="id.001281">E&longs;t enim pars nauis im­<lb/>mer&longs;a aquæ, quæ mouetur, vt & palmula. </s> <s id="id.001282">Dicemus igitur vt ratio <lb/>Ari&longs;totelis concludat duo a&longs;&longs;umenda e&longs;&longs;e. </s> <s id="id.001283">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. </s> <s id="id.001284">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. </s> <s id="id.001285">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 xlink:href="035/01/121.jpg" pagenum="81" /><emph type="italics"/>media, mouentur. </s> <s id="id.001286">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. </s> <s id="id.001287">Alterum quod <lb/>a&longs;&longs;umendum. </s> <s id="id.001288">e&longs;t nauim tantum antror&longs;um moueri: quantum & re­<lb/>mi caput. </s> <s id="id.001289">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 id="id.001290"><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 id="id.001291"><emph type="italics"/>Syllogi&longs;mus igitur &longs;ic e&longs;to,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001292"><emph type="italics"/>Quantum caput remi antror&longs;um mouetur: tantum & nauis. <lb/></s> <s id="id.001293">Sed caput remi plus antror&longs;um mouetur: quam palmula re­<lb/>tror&longs;um. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001294"><emph type="italics"/>Ergo nauis plus antror&longs;um mouetur: quam palmula retror&longs;um. <emph.end type="italics"/></s> <s id="id.001295"><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. </s> <s id="id.001296">Etiam&longs;i <expan abbr="principiũ">principium</expan> non &longs;it. </s> <s id="id.001297">Ob id quid veritatis habeat po&longs;tea <lb/>di&longs;cutiemus. </s> <s id="id.001298">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. </s> <s id="id.001299">Quæ ratio <lb/>verißima e&longs;t in ijs, 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. </s> <s id="id.001300">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. </s> <s id="id.001301">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 id="id.001302">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. </s> <s id="id.001303">vnde infert caput remi ab eo loco, in quo erat ante remi­<lb/>gationem, ad alium transferri. </s> <s id="id.001304">Ergo<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>caput remi tran&longs;latum &longs;it ad<emph.end type="italics"/><lb/><foreign lang="el">d.</foreign> </s> <s><emph type="italics"/>Quo autem tempore<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="el">d,</foreign> <emph type="italics"/>palmula<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>non <lb/>transfertur ad<emph.end type="italics"/> <foreign lang="el">e</foreign><emph type="italics"/>: alioqui æqualiter moueretur palmula atque caput, <lb/>contra ea quæ ante po&longs;ita &longs;unt. </s> <s id="id.001305">Intelligatur enim remus<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>vbi e&longs;t<emph.end type="italics"/><lb/><foreign lang="el">d e,</foreign> <emph type="italics"/>&longs;calmo<emph.end type="italics"/> <foreign lang="el">g</foreign> <emph type="italics"/>manente. </s> <s id="id.001306">fiunt duo triangula<emph.end type="italics"/> <foreign lang="el">a g d & b g e,</foreign><lb/><emph type="italics"/>quorum anguli qui ad<emph.end type="italics"/> <foreign lang="el">g,</foreign> <emph type="italics"/>quia ad <expan abbr="vertic&etilde;">verticem</expan> oppo&longs;iti, &longs;unt æquales prop. <lb/>15. lib. 1. </s> <s>Tum latera, quæ ip&longs;os continent<emph.end type="italics"/> <foreign lang="el">a g, d g,</foreign> <emph type="italics"/>duobus<emph.end type="italics"/> <foreign lang="el">b g, <lb/>e g</foreign> <emph type="italics"/>&longs;unt æqualia, quia partes &longs;unt dimidiæ eiu&longs;dem remi<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ax. 6. <lb/></s> <s id="id.001308">erunt igitur ba&longs;es<emph.end type="italics"/> <foreign lang="el">a d, b e</foreign> <emph type="italics"/>æquales, vt reliqui anguli prop. 4. lib. 1. <emph.end type="italics"/></s> <pb xlink:href="035/01/122.jpg" pagenum="82" /> <s><emph type="italics"/>Et &longs;ic palmula perducta ad<emph.end type="italics"/> <foreign lang="el">e</foreign> <emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>caput prouectum e&longs;&longs;et ad<emph.end type="italics"/> <foreign lang="el">d</foreign><lb/><emph type="italics"/>æqualiter moueretur, &longs;ed in i&longs;to ca&longs;u<emph.end type="italics"/> <foreign lang="el">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. </s> <s id="id.001309">Intelligatur igitur mini­<lb/>mùm, vt ad<emph.end type="italics"/> <foreign lang="el">z</foreign> <emph type="italics"/>e&longs;&longs;e perducta palmula<emph.end type="italics"/> <foreign lang="el">b.</foreign> </s> <s><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 alijs paßim rectam<emph.end type="italics"/> <foreign lang="el">d q</foreign><lb/><emph type="italics"/>maiorem e&longs;&longs;e: quam<emph.end type="italics"/> <foreign lang="el">q z.</foreign> </s> <s><emph type="italics"/>Et ita e&longs;&longs;e o&longs;tendamus, quia duorum trian­<lb/>gulorum<emph.end type="italics"/> <foreign lang="el">a q d & b q z</foreign> <emph type="italics"/>anguli, qui ad<emph.end type="italics"/> <foreign lang="el">q</foreign> <emph type="italics"/>ad verticem oppo&longs;iti, <lb/>&longs;unt æquales prop. 15. lib. 1. </s> <s>tum<emph.end type="italics"/> <foreign lang="el">q a d</foreign> <emph type="italics"/>æqualis e&longs;t<emph.end type="italics"/> <foreign lang="el">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti à recta<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="el">a d, b e.</foreign> </s> <s><emph type="italics"/>Ex <lb/>præcedenti <expan abbr="demõ&longs;tratione">demon&longs;tratione</expan>. </s> <s id="id.001310">Ergo reliquus<emph.end type="italics"/> <foreign lang="el">q d a</foreign> <emph type="italics"/>reliquo<emph.end type="italics"/> <foreign lang="el">b z q</foreign> <emph type="italics"/>æqua­<lb/>lis erit prop. 32. lib. 1. </s> <s>Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="el">a q d & b q z</foreign> <emph type="italics"/>&longs;unt æquian­<lb/>gula, proinde & circum æquales angulos latera proportionalia prop. 4. lib. 6. <lb/></s> <s id="id.001311">E&longs;t igitur vt<emph.end type="italics"/> <foreign lang="el">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">q d</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="el">b q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">q z,</foreign> <emph type="italics"/>& vicißim <lb/>prop. 16. lib. 5. vt<emph.end type="italics"/> <foreign lang="el">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">q b</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="el">d q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">q z.</foreign> </s> <s><emph type="italics"/>E&longs;t <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="el">a q</foreign> <emph type="italics"/>maior: <lb/>quam<emph.end type="italics"/> <foreign lang="el">q b,</foreign> <emph type="italics"/>quia<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>erat bi&longs;&longs;ecta in<emph.end type="italics"/> <foreign lang="el">g,</foreign> <emph type="italics"/>& detracta e&longs;t de dimi­<lb/>dia<emph.end type="italics"/> <foreign lang="el">g b</foreign> <emph type="italics"/>portio<emph.end type="italics"/> <foreign lang="el">q g,</foreign> <emph type="italics"/>quæ additur ip&longs;i dimidiæ<emph.end type="italics"/> <foreign lang="el">a g.</foreign> </s> <s><emph type="italics"/>E&longs;t igitur<emph.end type="italics"/><lb/><foreign lang="el">d q</foreign> <emph type="italics"/>maior quam<emph.end type="italics"/> <foreign lang="el">q z. </foreign></s> </p> <p type="main"> <s id="id.001312"><emph type="italics"/>Hoc autem quanquam verum &longs;it, quor&longs;um tamen, dubium e&longs;t. <lb/></s> <s id="id.001313">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="id.035.01.122.1.jpg" xlink:href="035/01/122/1.jpg"/><lb/><emph type="italics"/>gationem factam, non e&longs;&longs;e <lb/>in E: &longs;ed vltra vt in K, <lb/>vnde nouam hanc de&longs;cri­<lb/>bit figuram. </s> <s id="id.001314">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 <emph.end type="italics"/><foreign lang="el"> z</foreign><emph type="italics"/>: &longs;ed in K <lb/>vltra <emph.end type="italics"/><foreign lang="el"> z</foreign>. </s> <s id="id.001315"><emph type="italics"/>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. </s> <s id="id.001316">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 xlink:href="035/01/123.jpg" pagenum="83" /><emph type="italics"/>ex<emph.end type="italics"/> <foreign lang="el">g</foreign> <emph type="italics"/>in<emph.end type="italics"/> <foreign lang="el">q.</foreign> </s> <s><emph type="italics"/>Sed &longs;i &longs;ic e&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. </s> <s id="id.001317">quod &longs;i quando fiat, fit <lb/>exaccidenti, nec citra naufragij periculum: imo vero &longs;ic non tam <lb/>nauis ferretur antror&longs;um: quam in profundum. </s> <s id="id.001318">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/></s> <figure id="id.035.01.123.1.jpg" xlink:href="035/01/123/1.jpg"/> <s><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. </s> <s id="id.001319">Et quidem cum anguli qui ad E &longs;int &longs;emper <lb/>æquales prop. 15. lib. 1. </s> <s>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. </s> <s id="id.001320">Hæc igi­<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="el">d q</foreign> <emph type="italics"/>maiorem e&longs;&longs;e<emph.end type="italics"/> <foreign lang="el">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="el">d</foreign>: <emph type="italics"/>&longs;ed vltra. </s> <s id="id.001321">vt in figuræ no&longs;træ pun­<lb/>cto F. </s> <s id="id.001322">Sicque caput A multo anterius latum erit, quam B retrò. <lb/></s> <s id="id.001323">E&longs;t enim A F maior quam A D axiom. 9. quæ demon&longs;trata e&longs;t <emph.end type="italics"/><pb xlink:href="035/01/124.jpg" pagenum="84" /><figure id="id.035.01.124.1.jpg" xlink:href="035/01/124/1.jpg"/><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. </s> <s id="id.001325">quod fieri oportet in <lb/>artificio&longs;a & pro&longs;pera na­<lb/>uigatione. </s> <s id="id.001326">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. </s> <s id="id.001327">Et quod totus motus remi ex his duo­<lb/>bus maior e&longs;t motu nauigij. </s> <s id="id.001328">Sed & cætera quæ in hoc problema <lb/>animaduertit & annotauit Nonius. </s> <s id="id.001329">Hîc &longs;ubijciemus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001330"><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 id="id.001331"><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 id="id.001332"><emph type="italics"/>Palmulam retrocedere quoties nauis in anteriora progreditur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001333"><emph type="italics"/>Alterum e&longs;t &longs;calmum bi&longs;&longs;ecare remum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001334"><emph type="italics"/>In&longs;uper Nonius a&longs;&longs;erit nauim interdum maius &longs;patium percurrere:<emph.end type="italics"/><lb/><figure id="id.035.01.124.2.jpg" xlink:href="035/01/124/2.jpg"/><lb/><emph type="italics"/>quam caput remi: interdum minus, iuxta <lb/>remigum vires, & provt mari remi 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 id="id.001335">Propo&longs;itio prima. </s> </p> <p type="main"> <s id="id.001336"><emph type="italics"/>Remigibus nauim mouere potentibus <lb/>caput remi plus antror&longs;um mouetur: <expan abbr="quã">quam</expan> <lb/>nauis. </s> <s id="id.001337">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 xlink:href="035/01/125.jpg" pagenum="85" /><emph type="italics"/>dicularis. </s> <s id="id.001338">Nauis vero idem interuallum conficiet quod &longs;calmus B. <lb/></s> <s id="id.001339">Dico igitur rectam A E maiorem e&longs;&longs;e recta B D. </s> <s id="id.001340">Secet enim re­<lb/>cta A C rectam E F in G. </s> <s id="id.001341">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. </s> <s>Maior e&longs;t autem A G ip&longs;a B G, ax. 9. <lb/></s> <s id="id.001342">Erit igitur A E maior quam B D. </s> <s id="id.001343">Itaque caput remi A maius <lb/>percurrit &longs;patium: quam nauis. </s> <s id="id.001344">quod erat demon&longs;trandum. <emph.end type="italics"/></s> </p> <figure id="id.035.01.125.1.jpg" xlink:href="035/01/125/1.jpg"/> <p type="main"> <s id="id.001345"><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;t rectæ 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 id="id.001346"><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. </s> <s id="id.001347">quia ad <lb/>&longs;equentia etiam vtile e&longs;t. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001348"><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="id.035.01.125.2.jpg" xlink:href="035/01/125/2.jpg"/><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/></s> <s id="id.001349">Dico igitur C D & B E æquales, quia reliquæ &longs;unt ex æqualibus <lb/>B C, E D dempto communi E C axio. 3. </s> <s id="id.001350">Ergo nauis tantùm de­<lb/>currit quantùm &longs;calmus. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.001351">Propo&longs;itio &longs;ecunda. </s> </p> <p type="main"> <s id="id.001352"><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 xlink:href="035/01/126.jpg" pagenum="86" /> <figure id="id.035.01.126.1.jpg" xlink:href="035/01/126/1.jpg"/> <p type="main"> <s id="id.001353"><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. </s> <s id="id.001354">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. </s> <s id="id.001355">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. </s> <s>& 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. </s> <s>Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, æqualis e&longs;t prop. 34. lib. 1. <lb/></s> <s id="id.001356">A Q igitur erit æqualis ip&longs;i B G ax. 1. </s> <s id="id.001357">Atque tantum &longs;patium B <lb/>&longs;calmus: quantum nauis. </s> <s>ex antec. </s> <s id="id.001359">Et nauis tantum confecit quan­<lb/>tum A caput remi ex hypothe&longs;i. </s> <s id="id.001360">A autem conficit &longs;patium A q. <lb/></s> <s>Igitur B &longs;calmus conficiet &longs;patium B G. </s> <s id="id.001361">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. </s> <s id="id.001362">Sic <lb/>igitur palmula C à loco &longs;uo dimota non fuit, quod demon&longs;trandum <lb/>erat. </s> <s id="id.001363">Cæterum Nonius hîc aduertit rectam G C minorem e&longs;&longs;e B C <lb/>remi dimidio, pro quantitate C T. </s> <s id="id.001364">Vnde concludit quo tempore <lb/>&longs;calmus B transfertur in G, palmulam quidem C excurrere in <lb/>ip&longs;am longitudinem C T. </s> <s id="id.001365">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. </s> <s id="id.001366">vbi etiam aduertes lector ex hoc dia­<lb/>grammate Nonij & 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. </s> <s id="id.001367">quod pulchrè con&longs;entit cum his quæ<emph.end type="italics"/><pb xlink:href="035/01/127.jpg" pagenum="87" /><emph type="italics"/>antè diximus de remi in vna remigatione varijs motibus. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.001368">Propo&longs;itionis conuer&longs;io</s> </p> <p type="main"> <s id="id.001369"><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/></s> <s id="id.001370">Recta enim C F æqualis e&longs;t A Q prop. 26. lib. 1. </s> <s>æqualis etiam <lb/>B G prop. 34. lib. 1. </s> <s>igitur A Q & B G æquales erunt ax. 1. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.001373">Propo&longs;itio tertia. </s> </p> <p type="main"> <s id="id.001374"><emph type="italics"/>Capite remi proprio motu conficiente &longs;patium duplum &longs;patij nauis: <lb/>tunc nauis tantùm promouebitur, quantùm palmula retrocedet. <emph.end type="italics"/></s> </p> <figure id="id.035.01.127.1.jpg" xlink:href="035/01/127/1.jpg"/> <p type="main"> <s id="id.001375"><emph type="italics"/>Remus incipiente motu &longs;it A C, <lb/>de&longs;inente vero habeat rectitudinis <lb/>&longs;itum F G. </s> <s id="id.001376">Et &longs;ic &longs;calmus B pro­<lb/>pter nauis motum conficiet interual­<lb/>lum B D. </s> <s id="id.001377">Excitetur igitur à puncto <lb/>B in vtramque partem perpendicu­<lb/>laris E E, prop. 11. lib. 1. </s> <s>In quam <lb/>perpendiculares incidant à punctis <lb/>A & C, quæ &longs;int A E, C E prop. 12. lib. 1. <lb/></s> <s id="id.001378">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. </s> <s id="id.001379">Dico rectas lineas B D, C H <lb/>æquales e&longs;&longs;e. </s> <s id="id.001380">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. </s> <s id="id.001381">Atqui recta A E dupla e&longs;t rectæ B D ex hypothe&longs;i. </s> <s id="id.001382">Dupla <lb/>igitur & C E rectæ H E, quapropter C H & E H æquales <lb/>erunt ax. 7. </s> <s id="id.001383">Et &longs;ic C H & B D æquales &longs;unt ax. 1. </s> <s id="id.001384">Et quia nauis <lb/>tantum interualli decurrit &longs;emper: quantum &longs;calmus. </s> <s id="id.001385">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. </s> <s id="id.001387">quod <lb/>demon&longs;trandum erat. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/128.jpg" pagenum="88" /> <p type="head"> <s id="id.001388">Propo&longs;itionis conuer&longs;io. </s> </p> <p type="main"> <s id="id.001389"><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 id="id.001390"><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. </s> <s id="id.001391">Et &longs;ic dupla erit C E ip&longs;ius H E: & eadem C E <lb/>dupla ip&longs;ius B D. </s> <s>æquales porro &longs;unt C E & A E prop 26. lib. 1. <lb/></s> <s>Dupla ergo erit A E rectæ B D. </s> <s>&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. </s> <s id="id.001392">Igitur &longs;i nauis tantùm fuerit prouecta, quantùm <lb/>remi palmula retroceßit, duplum conficit caput remi motu proprio <lb/>eius interualli, quod nauis conficit. </s> <s id="id.001393">quod fuit demon&longs;trandum. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.001394">Propo&longs;itio quarta. </s> </p> <p type="main"> <s id="id.001395"><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 id="id.001396"><emph type="italics"/>In po&longs;tremo diagrammate ponatur B D minor, quam A E: <lb/>&longs;ed eius dimidio maior. </s> <s id="id.001397">Dico quod ip&longs;a B D maior e&longs;t, quam C H. <lb/></s> <s id="id.001398">Nam B D & H E æquales &longs;unt, ad hæc A E & C E æqua­<lb/>les &longs;unt. </s> <s id="id.001399">maior igitur erit H E dimidio ip&longs;ius A E. </s> <s>quapropter <lb/>reliqua C H minor dimidio erit eiu&longs;dem A E. </s> <s id="id.001400">Et minor igitur <lb/>erit C H quam B D. </s> <s id="id.001401">Interuallum autem B D, id e&longs;t quod nauis <lb/>confecit, interuallum vero C H remi palmula in contrarium de­<lb/>currit. </s> <s id="id.001402">Ideo prior pars theorematis vera. </s> <s id="id.001403">Po&longs;terior autem &longs;imiliter <lb/>o&longs;tendetur. </s> <s id="id.001404">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. </s> <s id="id.001405">Et quoniam A E & <lb/>C E æquales &longs;unt. </s> <s id="id.001406">Reliqua igitur C H dimidio eiu&longs;dem A E <lb/>maior erit. </s> <s id="id.001407">Et proinde minor erit B D quam C H. </s> <s id="id.001408">Nauis igitur <lb/>minus interuallum decurret in anteriora: quam remi palmula in <lb/>contrarium. </s> <s id="id.001409">quod fuit demon&longs;trandum. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.001410">Corollarium. </s> </p> <p type="main"> <s id="id.001411"><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 xlink:href="035/01/129.jpg" pagenum="89" /> <p type="main"> <s id="id.001412"><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 id="id.001413">Propo&longs;itionis conuer&longs;io. </s> </p> <p type="main"> <s id="id.001414"><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 id="id.001415"><emph type="italics"/>Huius demon&longs;tratio ex prædictis facilis e&longs;t. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.001416">Propo&longs;itio quinta. </s> </p> <p type="main"> <s id="id.001417"><emph type="italics"/>Naui celerius mota quam caput remi: palmula antror&longs;um moue­<lb/>bitur, nec quicquam retrocedet, idque &longs;patij decurret quo nauis motus <lb/>motum capitis remi &longs;uperat. <emph.end type="italics"/></s> </p> <figure id="id.035.01.129.1.jpg" xlink:href="035/01/129/1.jpg"/> <p type="main"> <s id="id.001418"><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/></s> <s id="id.001419">Scalmus igitur B pro­<lb/>pter nauis motum tran&longs;­<lb/>latus erit in D. </s> <s id="id.001420">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. </s> <s id="id.001421">Sic <lb/>enim celerius dicetur <lb/>ferri nauis quam caput <lb/>remi. </s> <s id="id.001422">Dico quod palmu­<lb/>la C in vlteriora mouebitur. </s> <s id="id.001423">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/></s> <s id="id.001424">Mouebitur igitur palmula in anteriora. </s> <s id="id.001425">Nihil autem vnquam re­<lb/>trocedere o&longs;tendetur in hunc modum. </s> <s id="id.001426">Eadem celeritate mouentur A <lb/>in H, & C ver&longs;us <emph.end type="italics"/><foreign lang="el">z</foreign><emph type="italics"/> circa &longs;calmum. </s> <s id="id.001427">Atqui per hypothe&longs;im cele­<lb/>rius fertur nauis: quam C ver&longs;us <emph.end type="italics"/><foreign lang="el">z</foreign><emph type="italics"/>. </s> <s id="id.001428">Et mouetur idem C ip&longs;a nauis <lb/>celeritate ver&longs;us K. </s> <s>celerius igitur feretur C ad K: quam ad <emph.end type="italics"/><foreign lang="el">z</foreign><emph type="italics"/>. <lb/></s> <s>quapropter nihil vnquam retrocedet ip&longs;um C. </s> <s id="id.001429">Imo vero in vlte­<lb/>riora progredietur, interuallumque decurret C K, quod quidem re­<lb/>linquitur, detracto <emph.end type="italics"/><foreign lang="el">z</foreign><emph type="italics"/> C ex <emph.end type="italics"/><foreign lang="el">z</foreign><emph type="italics"/> K. </s> <s id="id.001430">Si enim remi palmula tota ip&longs;a <emph.end type="italics"/><pb xlink:href="035/01/130.jpg" pagenum="90" /><emph type="italics"/>nauigij 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. </s> <s id="id.001431">Sic igitur palmulæ celeritate, quæ à motu nauigij prouenit, re­<lb/>tardata, decur&longs;um interuallum erit C K. </s> <s id="id.001432">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 id="id.001433"><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. </s> <s id="id.001434">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. </s> <s id="id.001435">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;mittet: quam nauis progrediatur, vt ex <lb/>&longs;ecunda & tertia propo&longs;itionibus liquet: præterea 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. </s> <s id="id.001436">Po&longs;tremo cum nauis longius progreditur: quam palmula <lb/>regreditur: minus quo que interuallum decurrit: quam caput remi, & <lb/>&longs;ic non æquale. </s> <s id="id.001437">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> </subchap1> <subchap1> <p type="main"> <s id="id.001438"><foreign lang="el">to\ d' <lb/>au)to\ kai\ to\ phda/lion poiei=.</foreign></s> <s id="g0130515a"><foreign lang="el"> plh\n o(/ti ei)s to\ pro/sqen ou)de\n <lb/>sumba/lletai tw=| ploi/w|, w(/sper e)le/xqh e)pi\ a)/nw, a)lla\ <lb/>mo/non th\n pru/mnan ei)s to\ pla/gion a)pwqei= e)/nqa h)\ e)/nqa.</foreign></s> <s id="g0130515b"><foreign lang="el">ei)s <lb/>tou)nanti/on ga\r h( prw=|ra ou(/tw neu/ei.</foreign></s> <s id="g0130516"><foreign lang="el">h(=| me\n dh\ to\ phda/lion <lb/>prose/zeuktai, dei= oi(=o/n ti tou= kinoume/nou me/son noei=n, kai\ w(/sper <lb/>o( skalmo\s th=| kw/ph|: to\ de\ me/son u(poxwrei=, h(=| o( oi)/as metakinei=tai.</foreign></s> <s id="g0130517"><foreign lang="el"><lb/>e)a\n me\n ei)/sw a)/gh|, kai\ h( pru/mna deu=ro meqe/sthken: <lb/>h( de\ prw=|ra ei)s tou)nanti/on neu/ei.</foreign></s> <s id="g0130517a"><foreign lang="el">e)n ga\r tw=| au)tw=| <lb/>ou)/shs th=s prw/|ras, to\ ploi=on meqe/sthken o(/lon.</foreign></s> </p> <p type="main"> <s id="id.001439">Id etiam 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/></s> <s id="id.001440">Sic enim in <expan abbr="cõtrariũ">contrarium</expan> prora <lb/>vergit. </s> <s id="id.001441">Vbi igitur <expan abbr="guberna­culũ">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 xlink:href="035/01/131.jpg" pagenum="91" />qualis e&longs;t &longs;calmus remo: <lb/>Illud vero medium proce­<lb/>dit, quo temo transfertur. <lb/></s> <s id="id.001442">Si quidem intror&longs;us agat, <lb/>etiam puppis eò transfer­<lb/>tur, prora verò in con­<lb/>trarium nutat. </s> <s id="id.001443">In eodem <lb/>enim exi&longs;tente prora, nauis <lb/>tota transfertur. </s> </p> <p type="head"> <s id="id.001444">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001445">Id etiam ip&longs;um.] <emph type="italics"/>Ari&longs;toteles a&longs;&longs;erit gubernaculum idem fa­<lb/>cere quod remus. </s> <s id="id.001446">Id e&longs;t temonem plus progredi: quam pterigion. <lb/></s> <s id="id.001447">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. </s> <s id="id.001448">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. </s> <s id="id.001449">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 id="id.001450">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 vterque <lb/>ducit de qua igitur ante. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001451">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. </s> <s id="id.001452">Id nunc adiungit. </s> <s id="id.001453">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001454">7. <foreign lang="el">*th=s kerai/as duna/menews ai)/tion. </foreign></s> </p> <p type="main"> <s id="id.001455">7. Cau&longs;a pote&longs;tatis <lb/>Antemnæ. </s> </p> <p type="main"> <s id="id.001456"><foreign lang="el">*dia\ ti/ o(/sw| a)\n h( kerai/a a)nwte/ra h)=|, qa=tton plei= ta\ <lb/>ploi=a tw=| au)tw=| i(sti/w| kai\ tw=| au)tw=| pneu/mati; </foreign></s> <s id="g0130602"><foreign lang="el">h)\ dio/ti gi/netai <lb/>o( me\n i(sto\s moxlo/s, u(pomo/xlion de\ to\ e(dw/lion e)n w(=|<lb/> e)mpe/phgen;</foreign></s> <s id="g0130602a"><foreign lang="el">o(\ de\ dei= kinei=n ba/ros, to\ ploi=on, to\ de\ kinou=n, <lb/>to\ e)n tw=| i(sti/w| pneu=ma.</foreign></s> <s id="g0130603"><foreign lang="el">ei) d' o(/sw| a)\n por)r(w/teron h)=| to\ u(pomo/xlion, <lb/>r(a=|on kinei= kai\ qa=tton h( au)th\ du/namis to\ au)to\ <lb/>ba/ros.</foreign></s> <s id="g0130603a"><foreign lang="el">h( ou)=n kerai/a a)nw/teron a)gome/nh, kai\ to\ i(sti/on por)r(w/teron <lb/>poiei= tou= e(dwli/ou u(pomoxli/ou o)/ntos.</foreign></s> </p> <p type="main"> <s id="id.001457">Cur quantò antemna &longs;u­<lb/>perior fuerit, tantò celerius <lb/>nauis feratur <expan abbr="eod&etilde;">eodem</expan> velo, <expan abbr="eo­demq;">eo­<lb/>demque</expan> <expan abbr="v&etilde;to">vento</expan>? </s> <s id="id.001458">An quia malus <pb xlink:href="035/01/132.jpg" pagenum="92" />e&longs;t vectis, & calx in qua in­<lb/>figitur, pre&longs;&longs;io? </s> <s id="id.001459">Quod vero <lb/>pondus mouere oportet, <lb/>e&longs;t nauis: & ventus in <expan abbr="velũ">velum</expan>, <lb/>e&longs;t mouens. </s> <s id="id.001460">Igitur &longs;i quan­<lb/>to remotior fuerit pre&longs;&longs;io, <lb/>facilius & celerius vis <expan abbr="ead&etilde;">eadem</expan> <lb/>pondus ip&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 id="id.001461">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001462">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. </s> <s id="id.001463">Latini illius ligni extre­<lb/>mas partes <expan abbr="vocãt">vocant</expan> cornua ob quod Bayfius putat antemnas dici Græ­<lb/>cis<emph.end type="italics"/> <foreign lang="el">kerai/an. </foreign><emph type="italics"/></s> <s>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="el">i(sto\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. </s> <s id="id.001464">A&longs;clepiades autem vir inter Græcos apprimè <lb/>doctus ac diligens carche&longs;ia à nauali re dicta exi&longs;timat. </s> <s id="id.001465">At enim <lb/>naualis mali partem inferiorem, pternam vocari, at circa mediam <lb/>ferme partem<emph.end type="italics"/> <foreign lang="el">tra/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. </s> <s id="id.001466">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. </s> <s id="id.001467">Æolus <lb/>primus mortalium velis v&longs;us e&longs;&longs;e dicitur. </s> <s id="id.001468">Et propterea deus vento­<lb/>rum e&longs;t habitus. </s> <s id="id.001469">Sic enim de eo apud Diodorum legimus. <emph.end type="italics"/> </s> <s><foreign lang="el">pro\s de\ <lb/>tou/tois th\n tw=n i(sti/wn xrei/an toi=s nautikoi=s ei)shgh/sasqai kai\ di­<lb/>da/cai. </foreign><emph type="italics"/> </s> <s>id e&longs;t in&longs;uper & velorum v&longs;um nautis introduxi&longs;&longs;e, ratio­<lb/>nemque vtendi docui&longs;&longs;e. </s> <s id="id.001470">velorum autem apud veteres tria fuerunt <lb/>genera Artemo & acatium, quod velum maius: dolo, quod minus <lb/>erat: &<emph.end type="italics"/> <foreign lang="el">e)po/dromos,</foreign> <emph type="italics"/>quod velum à tergo ponebatur. </s> <s id="id.001471">vnde nauis à <lb/>Iulio polluce<emph.end type="italics"/> <foreign lang="el">triar/menos,</foreign> <emph type="italics"/>Antigoni dicta, quæ tria vela haberet <emph.end type="italics"/><pb xlink:href="035/01/133.jpg" 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/></s> <s id="id.001472">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 id="id.001473">Cur quanto.] <emph type="italics"/>Quintum e&longs;t &longs;peciale problema de vecte con&longs;i­<lb/>derato in malo nauis. </s> <s id="id.001474">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. </s> <s id="id.001475">Id e&longs;t vt cætera omnia &longs;int paria. </s> <s id="id.001476">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. </s> <s id="id.001477">quæ <lb/>enim non merguntur vt<emph.end type="italics"/> <foreign lang="el">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;t eas, 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 id="id.001478">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. </s> <s id="id.001479">Syllo­<lb/>gi&longs;mus hîc e&longs;t &longs;uis omnibus partibus ab&longs;olutus, &longs;ic. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001480"><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. </s> <s id="id.001481">Ex anteced. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001482"><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/></s> <s id="id.001484">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 id="id.001485"><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"/></s> </p> <p type="margin"> <s id="id.001486"><margin.target id="marg22"/>Cap. 8. lib <lb/>10. </s> </p> <p type="main"> <s id="id.001487"><emph type="italics"/>Eadem de hoc problemate fuit Vitruuij <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan> his verbis expre&longs;&longs;a. <lb/></s> <s id="id.001488">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 xlink:href="035/01/134.jpg" 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. </s> <s id="id.001489">Ita­<lb/>que vti vectis &longs;ub onere &longs;ubiectus, &longs;i per medium premitur, durior e&longs;t <lb/>neque incumbit. </s> <s id="id.001490">Cum autem caput eius &longs;ummum deducitur, faciliter <lb/>onus extollit: humiliter vela cum &longs;unt per medium temperata, mino­<lb/>rem habent virtutem. </s> <s id="id.001491">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. </s> <s id="id.001492">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. </s> <s id="id.001493">Solum enim &longs;u&longs;tinet nauim, quæ à ventis vel vn­<lb/>dis mergi &longs;olet. </s> <s id="id.001494">ab vndis quidem vbi humilior e&longs;t: à ventis vero ex <lb/>lateribus & anteriore parte. </s> <s id="id.001495">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. </s> <s id="id.001496">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. </s> <s id="id.001497">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001498">8. <foreign lang="el">*dia\ ti/ o(/tan e)kkerai/as bou/­<lb/>lwntai diadramei=n po/da poiou=si. </foreign></s> </p> <p type="main"> <s id="id.001499">8. Cur quando è cornu vo­<lb/>lunt nauigare pedem fa­<lb/>ciunt. </s> </p> <p type="main"> <s id="id.001500"><foreign lang="el">*dia\ ti/ o(/tan e)kke)rai/as bou/lwntai diadramei=n, mh\ ou)ri/ou <lb/>tou= pneu/matos o)/ntos, to\ me\n pro\s to\n kubernh/thn tou= i(sti/ou <lb/>me/ros ste/llontai, to\ de\ pro\s th\n prw=|ran podiai=on poihsa/menoi <lb/>e)fia=sin; </foreign></s> <s id="g0130702"><foreign lang="el">h)\ dio/ti a)ntispa=| to\ phda/lion: pollw=| ma=llon <lb/>o)/nti tw=| pneu/mati, ou) du/natai, o)li/gw| de/ o(\ u(poste/llontai.</foreign></s> <s id="g0130703"><foreign lang="el"><lb/>proa/gei me\n ou)=n to\ pneu=ma, ei)s ou)/rion de\ kaqi/sthsi to\ <lb/>phda/lion, a)ntispw=n kai\ moxleu=on th\n qa/lattan.</foreign></s> <s id="g0130704"><foreign lang="el">a(/ma <lb/>de\ kai\ oi( nau=tai ma/xontai tw=| pneu/mati: a)nakli/nousi ga\r <lb/>e)pi\ to\ e)nanti/on e(autou/s.</foreign></s> </p> <p type="main"> <s id="id.001501">Cur quando è cornu na­<lb/>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. </s> <s id="id.001502">An quia gubernacu­<lb/>lum non pote&longs;t auertere, <lb/>cum multus exiftit ventus: <pb xlink:href="035/01/135.jpg" pagenum="95" /><expan abbr="cũ">cum</expan> paucus verò pote&longs;t. </s> <s id="id.001503"><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 id="id.001504">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001505">E Cornu volunt nauigare.] <emph type="italics"/>Diximus antemnarum extrema <lb/>appellari cornua. </s> <s id="id.001506">Hinc è cornu nauigare e&longs;t cum vento cornu <lb/>antemnarum obijcitur. </s> <s id="id.001507">Quod feci&longs;&longs;e &longs;ignificabat Troianos Virgi­<emph.end type="italics"/><arrow.to.target n="marg23"/><lb/><emph type="italics"/>lius hoc ver&longs;u,<emph.end type="italics"/></s> </p> <p type="margin"> <s id="id.001508"><margin.target id="marg23"/>Lib. 3. <lb/>Æneid. </s> </p> <p type="main"> <s id="id.001509">Cornua velatarum obuertimus antemnarum. </s> </p> <p type="main"> <s id="id.001510">Pedem faciunt.] <emph type="italics"/>Ex textu & rei natura quæ in eo explica­<lb/>tur ratiocinantes hîc pro<emph.end type="italics"/> <foreign lang="el">ou(/tws poiou=oi</foreign> <emph type="italics"/>repo&longs;uimus<emph.end type="italics"/> <foreign lang="el">po/da poiou=oi. </foreign><emph type="italics"/>E&longs;t <lb/>autem<emph.end type="italics"/> <foreign lang="el">pou/s</foreign> <emph type="italics"/>Græcis, & pes Latinis variæ admodum &longs;ignificationis. <lb/></s> <s id="id.001511">Præter cæteras hîc huius duas annotare licet. </s> <s id="id.001512">Prior venit in men­<lb/>tem ob duos locos apud Galenum à perpaucis intellectos. </s> <s id="id.001513">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="el">e(pid. </foreign><emph type="italics"/>in Aph. 24. <lb/>vbi dicit tibicines, præcones, nuncupatum<emph.end type="italics"/> <foreign lang="el">po/da,</foreign> <emph type="italics"/>id e&longs;t, pedem cane­<lb/>re. </s> <s id="id.001516">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">etiam</expan> &longs;en&longs;it Hieronymus Mercurialis, qui hos Galeni locos ob&longs;erua­<lb/>uit. </s> <s id="id.001517">Nos <expan abbr="etiã">etiam</expan> legimus in <expan abbr="cõment">comment</expan>. </s> <s id="id.001518">Cæ&longs;aris cum <expan abbr="pugnandũ">pugnandum</expan> &longs;ibi foret, <lb/>iußi&longs;&longs;e ab equis milites <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan>, nequis <expan abbr="&longs;p&etilde;">&longs;pem</expan> fugæ in <expan abbr="equorũ">equorum</expan> celerita­<lb/>te reponeret. </s> <s id="id.001519">Quæ iußio forta&longs;&longs;e erat,<emph.end type="italics"/> <foreign lang="el">e)rei=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. </s> <s id="id.001520">vnde Poëta:<emph.end type="italics"/><lb/><arrow.to.target n="marg24"/></s> </p> <p type="margin"> <s id="id.001521"><margin.target id="marg24"/>Lib. 5. <lb/>Æneid. </s> </p> <p type="main"> <s id="id.001522">vna omnes fecere pedem. </s> </p> <p type="main"> <s id="id.001523"><emph type="italics"/>Alij tamen dicunt e&longs;&longs;e funem, quo id fit. </s> <s id="id.001524">Interpres Apollonij Rho­<lb/>dij funes veli id e&longs;t<emph.end type="italics"/> <foreign lang="el">ka/lw</foreign> <emph type="italics"/>rudentes in tria genera diuidit. </s> <s id="id.001525">Aut enim<arrow.to.target n="marg25"/><pb xlink:href="035/01/136.jpg" pagenum="96" />detrahitur his velum, & vocantur<emph.end type="italics"/> <foreign lang="el">mesouri/ai</foreign>: <emph type="italics"/>aut intenditur vtrin­<lb/>que ad proram, & &longs;unt<emph.end type="italics"/> <foreign lang="el">pro/tonoi</foreign>: <emph type="italics"/>aut conuertitur & laxatur, hi <lb/>&longs;unt<emph.end type="italics"/> <foreign lang="el">kata\ ta\s gwni/as</foreign> <emph type="italics"/>ad angulos, & dicuntur<emph.end type="italics"/> <foreign lang="el">po/des</foreign> <emph type="italics"/>& ante hos<emph.end type="italics"/><lb/><foreign lang="el">pro/podes</foreign> <emph type="italics"/>quo &longs;en&longs;u dixi&longs;&longs;e Plinius videtur lib. 2. cap. 47. </s> <s>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 id="id.001527"><margin.target id="marg25"/>Lib. 3. </s> </p> <p type="main"> <s id="id.001528">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 id="id.001529">E cornu nauigare.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="el">e)k ou)ri/as</foreign> <emph type="italics"/>hîc legendum putamus vt <lb/>in titulo<emph.end type="italics"/> <foreign lang="el">e)k kerai/as</foreign> <emph type="italics"/>nam hæc &longs;unt<emph.end type="italics"/> <foreign lang="el">a)si/stata</foreign> <emph type="italics"/>velle nauigare<emph.end type="italics"/> <foreign lang="el">e)k ou)ri/as</foreign><lb/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">mh\ ou)ri/ou pneu/ma/tos o(/ntos.</foreign> </s> <s><emph type="italics"/>Quomodo enim nauigabitur vento <lb/>&longs;ecundo, &longs;i ventus &longs;ecundus non e&longs;t. </s> <s id="id.001530">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 id="id.001531">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 id="id.001532">A tergo comitatur euntes,</s> </p> <p type="main"> <s id="id.001533"><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 id="id.001534">Ferte viam facilem, venti & &longs;pirate &longs;ecundi. </s> </p> <p type="main"> <s id="id.001535"><emph type="italics"/>Qui huic e&longs;t contrarius, dicitur aduer&longs;us, cum in proram inuehitur. <lb/></s> <s id="id.001536">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 id="id.001537">Non aliter quam qui aduer&longs;o vix flumine lembum</s> </p> <p type="main"> <s id="id.001538">Remigijs &longs;ubigit, &longs;i brachia forte remi&longs;it,</s> </p> <p type="main"> <s id="id.001539">Atque illum præceps prono rapit alueus amne. </s> </p> <p type="main"> <s id="id.001540"><emph type="italics"/>Inter hos duo &longs;unt medij, vnus tran&longs;uer&longs;us ad latera nauis perpendi­<lb/>culariter incidens: alter obliquus <lb/><figure id="id.035.01.136.1.jpg" xlink:href="035/01/136/1.jpg"/><lb/>qui medius e&longs;t inter &longs;ecundum & <lb/>tran&longs;uer&longs;um, vel inter aduer&longs;um & <lb/>tran&longs;uer&longs;um. </s> <s id="id.001541">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. </s> <s id="id.001542">Horum autem mo­<lb/>tuum Galenus obliquos per pulchrè <emph.end type="italics"/><pb xlink:href="035/01/137.jpg" pagenum="97" /><emph type="italics"/>declarauit &longs;umpta primùm hac propo&longs;itione. </s> <s id="id.001543">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. </s> <s id="id.001544">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. </s> <s id="id.001545">Si enim æquipollet venti & <lb/>remigantium robur, mixtum fieri motum nece&longs;&longs;e e&longs;t. </s> <s id="id.001546">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. </s> <s id="id.001547">Si au­<lb/>tem venti violentia vincat, ad tran&longs;uer&longs;um magis, quam antror­<lb/>&longs;um. </s> <s id="id.001548">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. </s> <s id="id.001549">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? </s> <s id="id.001550">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. </s> <s id="id.001551">cap. 19. lib. 1. de v&longs;. partium. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001553">An quia gubernaculum.] <emph type="italics"/>Solutio e&longs;t problematis propo&longs;iti, <lb/>quod &longs;ic fiet euidentius. </s> <s id="id.001554">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. </s> <s id="id.001555">Eam vero, quæ ad proram, relaxant, quod ap­<lb/>pellant pedem facere. </s> <s id="id.001556">Re&longs;pon&longs;io. </s> <s id="id.001557">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. </s> <s id="id.001558">Eò enim fertur nauis, quò prora dirigitur. </s> <s id="id.001559">Obliquare autem <lb/>nauim vel tran&longs;uertere tantò facilius gubernaculum pote&longs;t: quantò <lb/>ventus paucior e&longs;t. </s> <s id="id.001560">Paucior autem fit contracto velo, quod &longs;pectat ad <lb/>puppim, & relaxato eo quod e&longs;t ad proram. </s> <s id="id.001561">Sufficiens tamen pro­<lb/>pellere. </s> <s id="id.001562">Obliquus enim veli relaxati &longs;inubus totis excipitur. </s> <s id="id.001563">Ideo <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. </s> <s id="id.001564">Sic <emph.end type="italics"/><pb xlink:href="035/01/138.jpg" 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 rapit. </s> <s id="id.001565">Et ita neutra ex contrarijs 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 id="id.001566">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. </s> <s id="id.001567">Ii&longs;dem <lb/>ventis in contrarium nauigatur prolatis pedibus ( hi &longs;unt funes de <lb/>quibus ante ) vt noctu plerumque vela concurrant. </s> <s id="id.001568">Hoc autem vt <lb/>fiat geometricè demon&longs;tratur. <emph.end type="italics"/></s> </p> <figure id="id.035.01.138.1.jpg" xlink:href="035/01/138/1.jpg"/> <p type="main"> <s id="id.001569"><emph type="italics"/>Sint naues A tendens ad G, & B tendens ad H. </s> <s>ventus ex <lb/>C recta feratur ad D, tanquam ad centrum. </s> <s id="id.001570">Itaque vento pro­<lb/>pul&longs;a nauis A, feretur in E, & B in F. </s> <s id="id.001571">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 id="id.001572"><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/></s> <s id="id.001573">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. </s> <s id="id.001574">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 xlink:href="035/01/139.jpg" 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 q. </s> <s>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. </s> <s id="id.001575">Ergo duo C A G & G A E duobus C P G & <lb/>G P Q &longs;unt æquales axiom. 1. </s> <s id="id.001576">E&longs;t autem C P G externus oppo­<lb/>&longs;ito interno C A G maior, prop. 16. lib. 1. </s> <s>Reliquus igitur G P Q <lb/>reliquo G A E minor erit, & ita de cæteris. </s> <s id="id.001577">Sicque nauis proce&longs;&longs;u <lb/>&longs;uo mutabit &longs;en&longs;im temonem, vt & vela. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001578">9. <foreign lang="el">*dia\ ti/ ta\ periferh= tw=n sxhma/twn eu)kinhto/tera. </foreign></s> </p> <p type="main"> <s id="id.001579">9. Cur è figuris rotundæ <lb/>&longs;unt mobiliores. </s> </p> <p type="main"> <s id="id.001580"><foreign lang="el">*dia\ ti/ ta\ stroggu/la kai\ periferh= tw=n sxhma/twn <lb/>eu)kinhto/tera; </foreign></s> <s id="g0130802"><foreign lang="el">trixw=s de\ e)nde/xetai to\n ku/klon kulisqh=nai: <lb/>h)\ ga\r kata\ th\n a(yi=da, summetaba/llontos tou= ke/ntrou, <lb/>w(/sper o( troxo\s o( th=s a(ma/chs kuli/etai: h)\ peri\ to\ ke/ntron <lb/>mo/non, w(/sper ai( troxile/ai tou= ke/ntrou me/nontos, h)\ para\ <lb/>to\ e)pi/pedon, tou= ke/ntrou me/nontos, w(/sper o( kerameiko\s troxo\s <lb/>kuli/ndetai.</foreign></s> <s id="g0130803"><foreign lang="el">h)\ me\n dh\ ta/xista ta\ toiau=ta, dia/ te to\ <lb/>mikrw=| a(/ptesqai tou= e)pipe/dou, w(/sper o( ku/klos kata\ stigmh/n, <lb/>kai\ dia\ to\ mh\ prosko/ptein: a)fe/sthke ga\r th=s gh=s <lb/>h( gwni/a.</foreign></s> <s id="g0130804"><foreign lang="el">kai\ e)/ti w(=| a)\n a)panth/sh| sw/mati, pa/lin tou/tou <lb/>kata\ mikro\n a(/ptetai.</foreign></s> <s id="g0130805"><foreign lang="el">ei) de\ eu)qu/grammon h)=n, th=| eu)qei/a| <lb/>e)pi\ polu\ h(/pteto a)\n tou= e)pipe/dou.</foreign></s> </p> <p type="main"> <s id="id.001581">Cur quæ figurarum ro­<lb/>tundæ & circulares exi­<lb/>&longs;tunt, facilius mouentur. <lb/></s> <s id="id.001582">Tribus vero modis con­<lb/>tingit circulum volui. </s> <s id="id.001583">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. </s> <s id="id.001584">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="pũ­cto">pun­<lb/>cto</expan>, & quia non offen&longs;ant? <lb/></s> <s id="id.001585">Di&longs;tat enim angulus à terra. <lb/></s> <s id="id.001586">Et hoc <expan abbr="etiã">etiam</expan> cui occur&longs;ant, <pb xlink:href="035/01/140.jpg" pagenum="100" />corpus rur&longs;us parum tan­<lb/>gant. </s> <s id="id.001587">At &longs;i recti lineum e&longs;­<lb/>&longs;et, rectitudine &longs;ua mul­<lb/>tum plani attingeret. </s> </p> <p type="head"> <s id="id.001588">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001589">Cvr quæ figurarum.] <emph type="italics"/>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 id="id.001590">Tribus modis.] <emph type="italics"/>Rotundorum motus &longs;implex per &longs;pecies indu­<lb/>citur: &longs;ed diminutè. </s> <s id="id.001591">Perfectè autem &longs;ic. </s> <s id="id.001592">Rotundum omne per &longs;e mo­<lb/>uetur, vel ab alio. </s> <s id="id.001593">Per &longs;e quidem vt cælum, cuius nulla pars primò <lb/>moueri dici pote&longs;t: omnes tamen &longs;imul in loco mouentur. </s> <s id="id.001594">Ab alio <lb/>verò, in quo etiam eius quod mouetur pars aliqua primò mouetur, <lb/>& quidem duobus modis progrediente axe: vel manente. </s> <s id="id.001595">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. </s> <s id="id.001596">Manente verò, rur&longs;us duobus <lb/>modis, nempè axe moto in &longs;uo loco: vel etiam immoto. </s> <s id="id.001597">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 gladij: 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. </s> <s id="id.001598">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 id="id.001599">Vel enim.] <emph type="italics"/>Cum rota currui &longs;ubiecta e&longs;t, tracto curru axis vnà <lb/>progreditur. </s> <s id="id.001600">Et cum rota quie&longs;cere nequeat, quia axis tractus pre­<lb/>mit, & pondus adijcit 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. </s> <s id="id.001601">Facilius autem cir­<lb/>cumuertitur: quam trahatur, itaque procedit. </s> <s id="id.001602">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 xlink:href="035/01/141.jpg" pagenum="101" /><emph type="italics"/>initium e&longs;t motus. </s> <s id="id.001603">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 id="id.001604">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. </s> <s id="id.001605">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/></s> <s id="id.001606">quò igitur erit minor, eò minus hærere, citiu&longs;que diuelli faciet. </s> <s id="id.001607">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. </s> <s id="id.001608">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 id="id.001610">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 id="id.001611">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. </s> <s>procliues &longs;unt maxime <lb/>ad motum. </s> <s id="id.001612">Latus enim curuum anguli vnius contactus &longs;emotum <lb/>quidem e&longs;t à plano: &longs;ed parum propter anguli angu&longs;tiam. </s> <s id="id.001613">Et &longs;ic non <lb/>offen&longs;at, & proximum e&longs;t ca&longs;ui. </s> <s id="id.001614">Hinc etiam vna cau&longs;a 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> </p> <p type="main"> <s id="id.001615">At &longs;i rectilineum e&longs;&longs;et.] <emph type="italics"/>Difficultas motus in mobili pendet <lb/>ab eius internis aut externis. </s> <s id="id.001616">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. </s> <s id="id.001617">Atque vt ibi vi retineatur, eò tamen quodam motu occulto <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. </s> <s id="id.001618">Itaque prima <emph.end type="italics"/><pb xlink:href="035/01/142.jpg" pagenum="102" /><emph type="italics"/>difficultas in <expan abbr="viol&etilde;tis">violentis</expan> pendet è renixu. </s> <s id="id.001619">Externa vero &longs;unt <expan abbr="&longs;ubiectũ">&longs;ubiectum</expan>, <lb/>& occur&longs;ans, & mobilis figura. </s> <s id="id.001620">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. </s> <s id="id.001621">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 deijciantur: <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. </s> <s id="id.001622">Maior <lb/>igitur inhærentia, maius e&longs;t impedimentum. </s> <s id="id.001623">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>. </s> <s id="id.001624">Talia &longs;unt fortuita omnia, quæ vt &longs;ubiectum, quò <lb/>pluribus mobilis punctis occurrunt propter eandem cau&longs;am, eò plus. <lb/></s> <s id="id.001625">ne fiat inuer&longs;io vel volutatio, impediunt. </s> <s id="id.001626">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/></s> <s id="id.001627">Hoc enim magis, illud minus: re&longs;i&longs;tit partibus obuijs. </s> <s id="id.001628">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. </s> <s id="id.001629">Mobilis denique figura quæ quò propius ac­<lb/>cedit ad &longs;phæricam vt mobilißimam, eò ad motum pronior: contra <lb/>quò remotior. </s> <s id="id.001630">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/></s> <s id="id.001631">Sit enim <lb/>ABCD <lb/><figure id="id.035.01.142.1.jpg" xlink:href="035/01/142/1.jpg"/><lb/><expan abbr="rectili­neũ">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="qui­d&etilde;">qui­<lb/>dem</expan> &longs;i na­<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. </s> <s id="id.001632">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> </p> <p type="main"> <s id="id.001633"><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 xlink:href="035/01/143.jpg" pagenum="103" /><emph type="italics"/>rectos in&longs;i&longs;ten­<emph.end type="italics"/><lb/><figure id="id.035.01.143.1.jpg" xlink:href="035/01/143/1.jpg"/><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. </s> <s id="id.001634">Tot <lb/>vires nullo <expan abbr="t&etilde;­poris">tem­<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. </s> <s id="id.001635">Ex quo fit vt figurarum planum <lb/>pro vertice habentium &longs;tabilißima dicatur cubus. </s> <s id="id.001636">Et quia talis e&longs;t, <lb/>eius figuram Plato affinxit terræ in loco &longs;uo pror&longs;us immobili. </s> <s id="id.001637">Ob id <lb/>etiam pictores <expan abbr="Virtut&etilde;">Virtutem</expan> quæ &longs;ola con&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> </p> <p type="main"> <s id="id.001638">Quæ tantùm con&longs;tans in leuitate &longs;ua e&longs;t. <lb/></s> <s><emph type="italics"/>globo mobilißimo. </s> <s id="id.001639">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. </s> <s id="id.001640">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. </s> <s id="id.001641">Sed hîc non immeritò <emph.end type="italics"/><lb/><figure id="id.035.01.143.2.jpg" xlink:href="035/01/143/2.jpg"/><lb/><emph type="italics"/>quæri pote&longs;t. </s> <s id="id.001642">cur terræ &longs;tare debenti na­<lb/>tura figuram attribuit &longs;phæricam, vt <lb/><expan abbr="doc&etilde;t">docent</expan> a&longs;tronomi. </s> <s id="id.001643">vnum enim e&longs;t ex <expan abbr="ar­gum&etilde;tis">ar­<lb/>gumentis</expan> Copernici terram moueri pro­<lb/>bare volentis. </s> <s id="id.001644">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="id.035.01.143.3.jpg" xlink:href="035/01/143/3.jpg"/><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. </s> <s id="id.001645">Sit enim cubica <lb/>cuius centrum A & B punctum an­<emph.end type="italics"/><pb xlink:href="035/01/144.jpg" pagenum="104" /><emph type="italics"/>gulare, & ita remotius quam C laterale, non tanto nixu contendet: <lb/>quam ip&longs;um C. </s> <s id="id.001646">Quò enim mobile naturale propius e&longs;t, eò obnixius <lb/>incumbit. </s> <s id="id.001647">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. </s> <s id="id.001648">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> </p> <p type="main"> <s id="id.001649">A&longs;pice nutantem conuexo pondere mundum. <lb/></s> </p> <p type="main"> <s><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. </s> <s id="id.001650">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. </s> <s id="id.001651">Quærenti verò cur igitur cœlum <lb/>exacte &longs;phæricum moueatur. </s> <s id="id.001652">Re&longs;pondent moueri in loco non na­<lb/>turaliter: &longs;ed voluntariè. </s> <s id="id.001653">Omnis enim motus naturalis e&longs;t per rectam <lb/>de centro ad locum. </s> <s id="id.001654">Voluntas illa e&longs;t intelligentiæ, quæ cœlo vt mens <lb/>corpori præe&longs;t. </s> <s id="id.001655">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="el">meg. <lb/>suntac.</foreign> </s> <s><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. </s> <s id="id.001656">Intelligetur quoque quomodo illius cœli <lb/>motus &longs;it omnium motuum <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>. </s> <s id="id.001657">Nam cum men&longs;ura &longs;it in vno­<lb/>quoque genere minimum, vt e&longs;t cap. 4. lib. 2. de Cœl. </s> <s>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> </p> <p type="main"> <s id="id.001658">Multum plani.] <emph type="italics"/>Ex hoc loco intelligatur, quod mobile, quantò <lb/>latius e&longs;t: tantò difficilius moueri per planum. </s> <s id="id.001659">Attritio enim per <lb/>contactum plani cum mobili, tanto maior erit. </s> <s id="id.001660">Ideo tangens in pun­<lb/>cto facillime mouetur, vt dictum e&longs;t. </s> <s id="id.001661">Tangens in linea difficilius: <lb/>tangens per &longs;uperficiem difficillime. </s> <s id="id.001662">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. </s> <s id="id.001663">Rationem &longs;i vis <lb/>aliquam, vide apud Scaligerum exercit. 333. <emph.end type="italics"/></s> </p> </subchap1> <pb xlink:href="035/01/145.jpg" pagenum="105" /> <subchap1> <p type="main"> <s id="id.001665"><foreign lang="el">e)/ti h(=| e)pire/pei e)pi\ to\ ba/ros, <lb/>tau/th| kinei= o( kinw=n. </foreign></s> <s id="id.001665a"><foreign lang="el">o(/tan me\n ga\r pro\s o)/rqh\n h( dia/metros <lb/>h)=| tou= ku/klou tw=| e)pipe/dw|, a(ptome/nou tou= ku/klou kata\ stigmh\n <lb/>tou= e)pipe/dou, i)/son to\ ba/ros e)p' a)mfo/tera dialamba/nei <lb/>h( dia/metros. </foreign></s> <s id="id.001665b"><foreign lang="el">o(/tan de\ kinh=tai eu)qu\s ple/on e)f' w(=| <lb/>kinei=tai, w(/sper r(e/pon e)nteu=qen, eu)kinhto/teron tw=| w)qou=nti ei)s <lb/>tou)/mprosqen: e)f' o(\ ga\r r(e/pei e(/kaston, eu)ki/nhto/n e)stin. </foreign></s> <s id="id.001665c"><foreign lang="el"><lb/>ei)/per kai\ to\ e)pi\ to\ e)nanti/on th=s r(oph=s duski/nhton.</foreign></s> </p> <p type="main"> <s id="id.001666">Præterea quò pondus <lb/>vergit, eò motor impellit. <lb/></s> <s id="id.001667">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. </s> <s id="id.001668">Quando verò <lb/>mouetur &longs;tatim plus ad id <lb/>mouetur, veluti eò repens <lb/>motu facilius impellente <lb/>in anteriorem partem. </s> <s id="id.001669">Eò <lb/>enim, quò vergit vnum­<lb/>quodque, facilius moue­<lb/>tur. </s> <s id="id.001670">Quandoquidem &longs;i in <lb/>contrarium: quam quò <lb/>vergat, moueatur, difficulter mouebitur. </s> </p> <p type="head"> <s id="id.001671">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001672">Præterea quò.] <emph type="italics"/>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. </s> <s id="id.001673">Hinc dico <lb/>&longs;phæricum ad latus moueri po&longs;&longs;e quacumque vi, quæ aërem impul&longs;u <lb/>vel tractu diuidere poßit. </s> <s id="id.001674">Vnus enim aër circun&longs;tans impedit, quo <lb/>minus voluatur. </s> <s id="id.001675">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. </s> <s id="id.001676">Relinqui­<lb/>tur ergò tantum impediri à medio circunstante. </s> <s id="id.001677">Hoc à quacun­<lb/>que vi vt oris flatu &longs;i diuidatur, &longs;phæricum in locum diui&longs;ionis pro­<lb/>mouebitur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001678">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 xlink:href="035/01/146.jpg" pagenum="106" /><emph type="italics"/>rectos angulos ef­<emph.end type="italics"/><lb/><figure id="id.035.01.146.1.jpg" xlink:href="035/01/146/1.jpg"/><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. </s> <s id="id.001680">Et A B <lb/>quia diameter e&longs;t <lb/>circulum &longs;uum bi­<lb/>fariam diuidit ex <lb/>def. 17. lib. 1. </s> <s id="id.001681">Sic­<lb/>que tanta pars e&longs;t <lb/>ad G, quanta ad H. </s> <s id="id.001682">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> </p> </subchap1> <subchap1> <p type="main"> <s id="g0130808"><foreign lang="el">e)/ti le/gousi/ <lb/>tines o(/ti kai\ h( grammh\ h( tou= ku/klou, e)n fora=| e)sti\n <lb/>a)ei/, w(/sper ta\ me/nonta, dia\ to\ a)nterei/dein, oi(=on kai\ toi=s <lb/>mei/zosi ku/klois u(pa/rxei pro\s tou\s e)la/ttonas. </foreign></s> <s id="g0130808a"><foreign lang="el">qa=tton ga\r <lb/>u(po\ th=s i)/shs i)sxu/os kinou=ntai oi( mei/zous kai\ ta\ ba/rh kinou=si, <lb/>dia\ to\ r(oph/n tina e)/xein th\n gwni/an th\n tou= mei/zonos <lb/>ku/klou pro\s th\n tou= e)la/ttonos, kai\ ei)=nai o(/per h( dia/metros <lb/>pro\s th\n dia/metron. </foreign></s> <s id="g0130808b"><foreign lang="el">a)lla\ mh\n pa=s ku/klos mei/zwn pro\s<lb/> e)la/ttona.</foreign></s> <s id="g0130808c"><foreign lang="el"> a)/peiroi ga\r oi( e)la/ttones.</foreign></s> <s id="g0130809"><foreign lang="el">ei) de\ kai\ pro\s e(/teron <lb/>e)/xei r(oph\n o( ku/klos, o(moi/ws de\ eu)ki/nhtos, kai\ a)/llhn a)\n <lb/>e)/xoi r(oph\n o( ku/klos kai\ ta\ u(po\ ku/klou kinou/mena, ka)\n mh\ <lb/>th=| a(yi/di a(/pthtai tou= e)pipe/dou, a)ll' h)\ para\ to\ e)pi/pedon, <lb/>h)\ w(s ai( troxile/ai. </foreign></s> <s id="g0130809a"><foreign lang="el">kai\ ga\r ou(/tws e)/xonta, r(a=|sta kinou=ntai <lb/>kai\ kinou=si to\ ba/ros, h)\ ou) tw=| kata\ mikro\n a(/ptesqai kai\ <lb/>proskrou/ein, a)lla\ di' a)/llhn ai)ti/an.</foreign></s> <s id="g0130812"><foreign lang="el">au(/th de/ e)stin h( ei)rhme/nh <lb/>pro/teron, o(/ti e)k du/o forw=n gege/nhtai o( ku/klos, w(/ste <lb/>mi/an au)tw=n ai)ei\ e)/xein r(oph/n, kai\ oi(=on fero/menon au)to\n <lb/>ai)ei\, kinou=sin oi( kinou=ntes, o(/tan kinw=sin kata\ th\n perife/reian <lb/>o(pwsou=n. </foreign></s> <s id="g0130813"><foreign lang="el">ferome/nhn ga\r au)th\n kinou=sin: th\n me\n ga\r ei)s <lb/>to\ pla/gion au)tou= ki/nhsin, w)qei= to\ kinou=n, th\n de\ e)pi\ th=s <lb/>diame/trou, au)to\s kinei=tai.</foreign></s> </p> <p type="main"> <s id="id.001683"><arrow.to.target n="marg26"/></s> </p> <p type="margin"> <s id="id.001684"><margin.target id="marg26"/>*<foreign lang="el">e)/xh</foreign></s> </p> <p type="main"> <s id="id.001685">Præterea nonnulli di­<lb/>cunt lineam circuli in per­<lb/>petuo motu e&longs;&longs;e, vt quæ <lb/>manent, propter renixum. <lb/></s> <s id="id.001686">Vt maioribus circulis eue­<lb/>nit re&longs;pectu minorum. </s> <s id="id.001687">Ce­<lb/>lerius enim ab æquali vi <lb/>maiores <expan abbr="mou&etilde;tur">mouentur</expan>, & pon­<lb/>dera mouent. </s> <s id="id.001688">quia maioris <lb/>circuli angulus <expan abbr="nutũ">nutum</expan> quen­<lb/>dam habet ad minoris an­<lb/>gulum. </s> <s id="id.001689">Et e&longs;t vt diameter <lb/>ad <expan abbr="diametrũ">diametrum</expan>: &longs;ic omnis ma­<lb/>ior circulus ad minorem. <lb/></s> <s id="id.001690">Infiniti autem &longs;unt mino­<lb/>res. </s> <s id="id.001691">Si verò etiam circulus <lb/>nutum habet ad alterum. <lb/></s> <s id="id.001692">Similiter verò facile mobi­<lb/>lis <expan abbr="aliũ">alium</expan> <expan abbr="nutũ">nutum</expan> habet circulus, <lb/>& quæ à circulo <expan abbr="mou&etilde;tur">mouentur</expan>, <lb/><expan abbr="etiã&longs;i">etiam&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 trochleæ. <pb xlink:href="035/01/147.jpg" pagenum="107" />Etenim quæ &longs;ic &longs;e habent, <lb/>facillimè <expan abbr="mou&etilde;tur">mouentur</expan>, & mo­<lb/>uent pondus. </s> <s id="id.001693">an non quia <lb/>parua &longs;ui parte tangunt & <lb/>offen&longs;ant. </s> <s id="id.001694">Sed ob <expan abbr="aliã">aliam</expan> cau­<lb/>&longs;am. </s> <s id="id.001695">Hæc vero prius e&longs;t di­<lb/>cta. </s> <s id="id.001696">quod circulus ex dua­<lb/>bus lationibus effectus e&longs;t. <lb/></s> <s id="id.001697">Itaque vnam harum &longs;em­<lb/>per habet nutantem. </s> <s id="id.001698">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/></s> <s id="id.001699">Motam enim ip&longs;am mo­<lb/>uent. </s> <s id="id.001700">Eam &longs;iquidem, qua <lb/>mouetur in <expan abbr="obliquũ">obliquum</expan>, mo­<lb/>tor impellit: illa verò, quæ &longs;uper diametro efficitur, ip&longs;e­<lb/>met &longs;e circulus mouet. </s> </p> <p type="head"> <s id="id.001701">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001702">Præterea nonnulli.] <emph type="italics"/>Quarta cau&longs;a e&longs;t de perpetuo motu con­<lb/>firmata nonnullorum, &longs;ed innominatorum authoritate: & &longs;imi­<lb/>litudine e contrarijs &longs;ic. </s> <s id="id.001703">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> </p> <p type="main"> <s id="id.001704">Vt maioribus circulis.] <emph type="italics"/>Nutus &longs;eu perpetua propen&longs;io con­<lb/>firmatur e&longs;&longs;e &longs;emper in circulo. </s> <s id="id.001705">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. </s> <s id="id.001706">quia anguli <lb/>maioris crura maiora &longs;unt, &longs;empérque e&longs;t, vt diameter ad diame­<lb/>trum. </s> <s id="id.001707">Sunt enim circulorum &longs;emidiametri. </s> <s id="id.001708">Partes autem cum pari­<lb/>ter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. </s> <s>Diameter au­<lb/>tem maior celerius mouetur, hîc autem notandum e&longs;t angulos non <emph.end type="italics"/><pb xlink:href="035/01/148.jpg" pagenum="108" /><emph type="italics"/>&longs;umi pro inclinatione: &longs;ed pro crurum<emph.end type="italics"/><lb/><figure id="id.035.01.148.1.jpg" xlink:href="035/01/148/1.jpg"/><lb/><emph type="italics"/><expan abbr="lõgitudine">longitudine</expan>. </s> <s id="id.001709">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 id="id.001710">Nutum habet.] <foreign lang="el">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, & volenti ab eo di&longs;pellere, re&longs;i&longs;tit. <lb/></s> <s id="id.001711">vnde<emph.end type="italics"/> <foreign lang="el">a)nteirisis</foreign> <emph type="italics"/>renixus. </s> <s id="id.001712">Extra locum verò ad eum per breuißi­<lb/>mam viam mouetur. </s> <s id="id.001713">Deus enim ne omnia in omnibus e&longs;&longs;ent, vni­<lb/>cuique ab initio proprium locum tribuit, in quo & circa quem con­<lb/>globatur, & ibi hæret. </s> <s id="id.001714">Hinc etiam &longs;ingulæ partes &longs;uis totis natura <lb/>inhærent, & in ijs certum quendam &longs;itum habent, à quo remotæ ad <lb/>ip&longs;um redeunt, vt in arcubus & balli&longs;tis videre licet. </s> <s id="id.001715">Nutus autem <lb/>naturalis e&longs;t: vel non naturalis: vel mixtus. </s> <s id="id.001716">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. </s> <s id="id.001717">Non naturalis e&longs;t is, quo nec <lb/>ratione loci naturalis, nec &longs;itus partium mouetur, vt fortuitus vel <lb/>voluntarius. </s> <s id="id.001718">Ille vt ventorum, hic vt animalium. </s> <s id="id.001719">Mixtus parti­<lb/>ceps e&longs;t vtriu&longs;que. </s> <s id="id.001720">Nutus voluntarij mille &longs;unt modi <expan abbr="nõ">non</expan> aliter, quam <lb/>voluntatis decreto determinabiles. </s> <s id="id.001721">At naturalis vnius tantum e&longs;t <lb/>à loco non naturali ad naturalem. </s> <s id="id.001722">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 contrarijs 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. </s> <s id="id.001723">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. </s> <s id="id.001724">In peripheria maiori punctum A re­<lb/>motius puncto D. </s> <s id="id.001725">Magis igitur nutat. </s> <s id="id.001726">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. </s> <s id="id.001727">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 id="id.001728">Et e&longs;t vt diameter.] <emph type="italics"/>Hæc analogia antea à nobis demon&longs;tra­<lb/>ra e&longs;t. </s> <s id="id.001729">Huc autem adducta confirmat in maioribus circulis maiorem <emph.end type="italics"/><pb xlink:href="035/01/149.jpg" pagenum="109" /><emph type="italics"/>nutum ad motum ine&longs;&longs;e: quam in minoribus. </s> <s id="id.001730">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 id="id.001731">Infiniti autem.] <emph type="italics"/>Quod infiniti circuli minores concentrici in­<lb/>&longs;int in quouis dato circulo &longs;ic demon&longs;trabimus. </s> <s id="id.001732">Sit circulus C B, <lb/>cuius &longs;emidiameter D B bifariam <emph.end type="italics"/><lb/><figure id="id.035.01.149.1.jpg" xlink:href="035/01/149/1.jpg"/><lb/><emph type="italics"/>&longs;ecetur, vt in puncto E prop. 10. <lb/>lib. 1. </s> <s>Et centro D interuallo D E <lb/>de&longs;criptus circulus po&longs;t. 3. </s> <s id="id.001733">Hic <lb/>erit concentricus & minor ip&longs;o <lb/>C B def. 1. lib. 3. </s> <s id="id.001734">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. </s> <s id="id.001735">Et eadem ra­<lb/>tione deinceps ad infinitum, cum rectam lineam &longs;emper bi&longs;&longs;ecare li­<lb/>ceat prop. 10. lib. 1. </s> <s>Et &longs;ic infiniti erunt circuli concentrici minores <lb/>in quouis circulo. </s> <s id="id.001736">quod erat demon&longs;trandum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001737">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, vt fit in rotis figulorum, <lb/>& in trochleis. </s> <s>de quibus po&longs;tea. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001739">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. </s> <s id="id.001740">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. </s> <s id="id.001741">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. </s> <s id="id.001742">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001743">10. <foreign lang="el">*dia\ ti/ meizo/nes ku/kloi kinhtikw/teroi.</foreign></s> </p> <p type="main"> <s id="id.001744">10. Cur maiores circuli <lb/>&longs;unt mouentiores. </s> </p> <p type="main"> <s id="id.001745"><foreign lang="el">*dia\ ti/ ta\ dia\ tw=n meizo/nwn ku/klwn ai)ro/mena kai\ <lb/>e(lko/mena, r(a=|on kai\ qa=tton kinou=men, oi(=on kai\ ai( troxilai=ai <lb/>ai( mei/zous tw=n e)latto/nwn, kai\ ai( skuta/lai o(moi/ws;</foreign></s> <s id="g0130902"><foreign lang="el">h)\ <lb/>dio/ti o(/sw| a)\n mei/zwn h( e)k tou= ke/ntrou h)=| e)n tw=| i)/sw| xro/nw|, <lb/>ple/on kinei=tai xwri/on. </foreign></s> <s id="g0130903"><foreign lang="el">w(/ste kai\ tou= i)/sou ba/rous e)po/ntos, <lb/>poih/sei to\ au)to/, w(/sper ei)/pomen, kai\ ta\ mei/zw zuga\ tw=n <lb/>e)latto/nwn a)kribe/stera ei)=nai.</foreign></s> <s id="g0130904"><foreign lang="el">to\ me\n ga\r sparti/on e)sti\ <lb/>ke/ntron.</foreign></s> <s id="g0130904a"><foreign lang="el">tou= de\ zugou= ai( e)pi\ ta/de tou= sparti/ou ai( e)k tou= <lb/>ke/ntrou.</foreign></s> </p> <p type="main"> <s id="id.001746">Cur per maiores circu­<pb xlink:href="035/01/150.jpg" pagenum="110" />los &longs;ublata & tracta faci­<lb/>lius mouemus, vt &longs;i tro­<lb/>chleæ &longs;int maiores minori­<lb/>bus, & &longs;cytalæ &longs;imiliter. </s> <s id="id.001747">An <lb/>quia quantò maior fuerit <lb/>radius in tempore æquali, <lb/>per maius mouetur <expan abbr="&longs;patiũ">&longs;patium</expan>. <lb/></s> <s id="id.001748"><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. </s> <s id="id.001749">E&longs;t <lb/>enim agina <expan abbr="c&etilde;trũ">centrum</expan>. </s> <s id="id.001750">Et lineæ <lb/>in librili, quæ &longs;unt ab agina <lb/>vtrimque, &longs;unt radij. </s> </p> <p type="head"> <s id="id.001751">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001752">Cvr per maiores.] <emph type="italics"/>In hoc capite tractatur problema de ma­<lb/>ioribus circulis, & &longs;phæricis. </s> <s id="id.001753">cur &longs;cilicet facilius & celerius <lb/>moueantur & moueant. </s> <s id="id.001754">Cui re&longs;pondetur ex lineæ à centro longitu­<lb/>dine maiore. </s> <s id="id.001755">Ratio &longs;ic di&longs;ponetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001756"><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 id="id.001757"><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 id="id.001758"><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 id="id.001759"><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. </s> <s id="id.001760">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 xlink:href="035/01/151.jpg" pagenum="111" /><emph type="italics"/>maioribus autem rotis æquilibrium illud facilius &longs;it, quia &longs;arcina al­<lb/>tior, & &longs;ic trahitur tantum: in paruis depreßior, &longs;icque nonnihil le­<lb/>uanda. </s> <s id="id.001761">Vbi autem &longs;u&longs;tinere & trahere opus e&longs;t, vt in bellicis tor­<lb/>mentis vnus equus iugum &longs;u&longs;tinere, alij loris trahere debent. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001762">Vt &longs;i trochleæ.] <emph type="italics"/>Problema illu&longs;tratur duobus exemplis Tro­<lb/>chleæ & Scytalæ. </s> <s id="id.001763">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. </s> <s id="id.001764">Geminatur aliquando, tripli­<lb/>catur, & amplius multiplicatur. </s> <s id="id.001765">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 id="id.001766">Et&longs;cytalæ.] <emph type="italics"/>Scytala lignum e&longs;t cylindricum cuius pro duplici <lb/>v&longs;u duo genera &longs;tatuuntur. </s> <s id="id.001767">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. </s> <s id="id.001768">Et cum eo pondus alligatum eleuatur. </s> <s id="id.001769">Hoc genus &longs;cytalæ e&longs;t <lb/>idem quod axis in peritrochio de quo po&longs;tea. </s> <s id="id.001770">De hoc autem genere lo­<lb/>cus hic intelligi debet. </s> <s id="id.001771">De altero dicetur cap. 12. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001772">Vt diximus etiam.] <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. </s> <s id="id.001773">Cæterum 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. </s> <s id="id.001774">Quare binæ rotæ quaternis facilio­<lb/>res &longs;int. </s> <s id="id.001775">Quare prioribus po&longs;teriores rotas maiores e&longs;&longs;e oporteat. <lb/></s> <s id="id.001776">Quare maior &longs;arcina in anteriore plau&longs;tri parte poni debeat. </s> <s id="id.001777">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>. </s> <s id="id.001778">Plures igitur <lb/>rotæ augebunt onus, & ideo trahentis laborem. </s> <s id="id.001779">Itaque binæ rotæ <lb/>quaternis faciliores erunt, vnde bellicis tormentis, licet immanibus <lb/>duæ &longs;atis &longs;unt. </s> <s id="id.001780">Quod autem quis obijceret per rotas plures pondus plus<emph.end type="italics"/><pb xlink:href="035/01/152.jpg" pagenum="112" /><emph type="italics"/>di&longs;tribui, & tanquam diuidi. </s> <s id="id.001781">Id &longs;anè verum e&longs;t & vtile ad facili­<lb/>tatem &longs;u&longs;tentationis, non item ad tractum. </s> <s id="id.001782">Et&longs;i biroti &longs;arcina in pe­<lb/>toritum transferatur, eadem iumento grauior fiet tantò, quantò gra­<lb/>uior currus. </s> <s id="id.001783">Sed fallaciæ cau&longs;a e&longs;t quod petorita birotis plus &longs;u&longs;tinent. <lb/></s> <s id="id.001784">Secundum quia maiores tanquam altiores prioribus minoribus qua&longs;i <lb/>incumbunt, &longs;icque in proclinatiores iam partes onus recumbens à <lb/>facilius motis maioribus, vna quoque mouetur facilius. </s> <s id="id.001785">Tertium ob <lb/>eandem cau&longs;am &longs;oluitur. </s> <s id="id.001786">Sic enim impo&longs;ita &longs;arcina qua&longs;i inferiore <lb/>loco pendens adiuuat tractum. </s> <s id="id.001787">Hinc e&longs;t quod quadrupedum omni <lb/>generi &longs;olis Gyraffis exceptis crura po&longs;teriora longiora &longs;unt. </s> <s id="id.001788">Mouen­<lb/>tur enim pul&longs;u primum, deinde tractu. </s> <s id="id.001789">Commodius autem pellit, <lb/>quod grauius e&longs;t. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001790">11. <foreign lang="el">*dia\ ti/ p(a=|on a)/neu ba/rois kinei=tai to\ zugo/n.</foreign></s> </p> <p type="main"> <s id="id.001791">11. Cur facilius mouetur li­<lb/>brile ab&longs;que pondere. </s> </p> <p type="main"> <s id="id.001792"><foreign lang="el">*dia\ ti/ r(a=|on, o(/tan a)/neu ba/rous h)=|, kinei=tai to\ zugo/n, <lb/>h)\ e)/xon ba/ros; </foreign></s> <s id="g0131002"><foreign lang="el">o(moi/ws de\ kai\ troxo\s, h)\ a)/llo toiou=to. </foreign></s> <s id="g0131002a"><foreign lang="el">to\ <lb/>baru/teron me\n, mei=zw de\ tou= e)la/ttonos kai\ koufote/rou.</foreign></s> <s id="g0131003"><foreign lang="el">h)\ <lb/>o(/ti ou) mo/non ei)s tou)nanti/on to\ baru/, a)lla\ kai\ ei)s to\ pla/gion <lb/>duski/nhto/n e)stin.</foreign></s> <s id="g0131004"><foreign lang="el">e)nanti/on ga\r th=| r(oph=| kinh=sai xalepon, <lb/>e)f' o(\ de\ r(e/pei, r(a|di/on: ei)s de\ to\ pla/gion ou) r(e/pei.</foreign></s> </p> <p type="main"> <s id="id.001793">Cur librile quum fuerit <lb/>&longs;ine <expan abbr="põdere">pondere</expan>, facilius moue­<lb/>tur: <expan abbr="quã">quam</expan> quum habet pon­<lb/>dus. </s> <s id="id.001794">Similiter verò & orbi­<lb/>culus, vel aliud tale, gra­<lb/>uius quidem, maius verò <lb/>minore & leuiore. </s> <s id="id.001795">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. </s> <s id="id.001796">Difficile enim e&longs;t <lb/>contrà propen&longs;ionem mo­<lb/>uere. </s> <s id="id.001797">At quò propendet, fa­<lb/>cile: non propendet autèm in obliquum. </s> </p> <p type="head"> <s id="id.001798">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001799">Cvr librile.] <emph type="italics"/>In hoc capite &longs;peciale tractatur problema, quod <lb/>generale e&longs;&longs;e po&longs;&longs;et. </s> <s id="id.001800">E&longs;t autem de librili. </s> <s id="id.001801">cur quò leuius, vel &longs;ine <lb/>pondere cum &longs;it, deprimitur facilius & mouetur: quam cum graue <emph.end type="italics"/><pb xlink:href="035/01/153.jpg" pagenum="113" /><emph type="italics"/>e&longs;t. </s> <s id="id.001802">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/></s> <s id="id.001803">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 id="id.001804"><emph type="italics"/>Motum contra naturam eò difficilius fertur, quò ip&longs;um grauius <lb/>e&longs;t. </s> <s id="id.001805">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 id="id.001806"><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 id="id.001807"><emph type="italics"/>Ergo librile quò grauius, eò difficilius mouebitur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001808"><emph type="italics"/>Hinc collige ex leuiori materia facta, dummodo firma, agiliora e&longs;&longs;e, <lb/>& exactiora. </s> <s id="id.001809">vnde petorita no&longs;tra rotis in orbita ferreis prædita <lb/>difficilius trahuntur, quam <emph.end type="italics"/><lb/><figure id="id.035.01.153.1.jpg" xlink:href="035/01/153/1.jpg"/><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 id="id.001810">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001811">12. <foreign lang="el">*dia\ ti/ e)pi e)pi\ tw=n skuta/lwn <lb/>r(a=|on ta\ forti/a komi/zetai, <lb/>h)\ e)pi\ tw=n a(macw=n.</foreign></s> </p> <p type="main"> <s id="id.001812">12. Cur &longs;uper &longs;cytalis onera <lb/>facilius ge&longs;tantur: quam <lb/>&longs;uper curribus. </s> </p> <p type="main"> <s id="id.001813"><foreign lang="el">*dia\ ti/ e)pi\ tw=n skuta/lwn r(a=|on ta\ forti/a komi/zetai. <lb/></foreign></s> <s id="g0131101"><foreign lang="el">h)\ e)pi\ tw=n a(macw=n, e)xousw=n, tw=n me\n mega/lous troxou/s, <lb/>tw=n de\ mikrou/s; </foreign></s> <s id="g0131102"><foreign lang="el">h)\ dio/ti e)pi\ tw=n skuta/lwn ou)demi/an e)/xei <lb/>pro/skoyin, to\ de\ e)pi\ tw=n a(macw=n to\n a)/cona, kai\ prosko/ptei <lb/>au)tw=|. </foreign></s> <s id="g0131102a"><foreign lang="el">e)/k te ga\r tw=n a)/nwqen pie/zei au)to\n, kai\ e)k <lb/>tw=n plagi/wn.</foreign></s> <s id="g0131103"><foreign lang="el">to\ de\ e)pi\ tw=n skuta/lwn, e)pi\ du/o tou/twn kinei=tai, <lb/>th=| te ka/tw xw/ra| u(pokeime/nh|, kai\ tw=| ba/rei tw=| <lb/>e)pikeime/nw|: e)p' a)mfote/rwn ga\r tou/twn kuli/etai tw=n to/pwn <lb/>o( ku/klos, kai\ fero/menos w)qei=tai.</foreign></s> </p> <p type="main"> <s id="id.001814">Cur onera facilius ge­<lb/>&longs;tantur &longs;cytalis: quam cur­<pb xlink:href="035/01/154.jpg" pagenum="114" />ribus etiam magnas rotas <lb/>habentibus, cum ip&longs;æ par­<lb/>uas habeant. </s> <s id="id.001815">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. </s> <s id="id.001816">Supernè enim pre­<lb/>munt ip&longs;um, & in <expan abbr="obliquũ">obliquum</expan>. <lb/></s> <s id="id.001817">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. </s> <s id="id.001818">In <lb/>vtri&longs;que enim his locis re­<lb/>uoluitur circulus, & conci­<lb/>tatus impellitur. </s> </p> <p type="head"> <s id="id.001819">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001820">Cvr onera.] <emph type="italics"/>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="id.035.01.154.1.jpg" xlink:href="035/01/154/1.jpg"/><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. </s> <s id="id.001821">quod cau&longs;a e&longs;t vt leuius vertatur, <lb/>quam rota in curru. </s> <s id="id.001822">vt cuius axis procedendo tantùm antror&longs;um <lb/>moueatur, non autem circum circa vertatur. </s> <s id="id.001823">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. </s> <s id="id.001824">Supernè etiam ab onere cylindricum premente. </s> <s id="id.001825">Ob has itaque <emph.end type="italics"/><pb xlink:href="035/01/155.jpg" 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 ijs quæ <lb/>ante 10. cap. dicta <expan abbr="sũt">sunt</expan> de rotis maioribus. </s> <s id="id.001826">Aliud enim facilius attol­<lb/>lere, & trahere quæcunque pondera, aliud conuehere. </s> <s id="id.001827">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/></s> <s id="id.001828">Hæc autem annexa ligno cylindrico &longs;olas rotas habet ver&longs;atiles, quæ <lb/>quantò minores, tantò minus occur&longs;ant &longs;ubiecto pauimento. </s> <s id="id.001829">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="id.035.01.155.1.jpg" xlink:href="035/01/155/1.jpg"/><lb/><emph type="italics"/>gulus. </s> <s id="id.001830">Et contrà <lb/>quò circulus mi­<lb/>nor, eò angulus <lb/>contactus maior <lb/>euadit. </s> <s id="id.001831">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001832">13. <foreign lang="el">*dia\ ti/ por)r(wte/rw ta\ be/lh fe/retai a)po\ th=s sfendo/nhs <lb/>h)\ a)po\ th=s xeiro/s.</foreign></s> </p> <p type="main"> <s id="id.001833">13. Cur mi&longs;&longs;ilia longius à <lb/>funda: quam à manu <lb/>proijciuntur. </s> </p> <p type="main"> <s id="id.001834"><foreign lang="el">*dia\ ti/ por)r(wte/rw ta\ be/lh fe/retai a)po\ th=s sfendo/nhs, <lb/>h)\ a)po\ th=s xeiro/s, kai/ toi kratei= ge o( ba/llwn th=| xeiri\<lb/> ma=llon, h)\ a)parth/sas to\ kai/ar;</foreign></s> <s id="g0131202"><foreign lang="el">kai\ e)/ti ou(/tw me\n du/o ba/rh <lb/>kinei=, to/, te th=s sfendo/nhs, kai\ to\ be/los, e)kei/nws de\ to\ <lb/>be/los mo/non.</foreign></s> <s id="g0131203"><foreign lang="el">po/teron o(/ti e)n me\n th=| sfendo/nh| kinou/menon to\ <lb/>be/los, r(i/ptei o( ba/llwn. </foreign></s> <s id="g0131203a"><foreign lang="el">periagagw\n ga\r ku/klw| polla/kis, <lb/>a)fi/hsin. </foreign></s> <s id="g0131204"><foreign lang="el">e)k de\ th=s xeiro\s a)po\ th=s h)remi/as h( a)rxh/. <lb/></foreign></s> <s id="g0131205"><foreign lang="el">pa/nta de\ eu)kinhto/tera kinou/mena h)\ h)remou=nta, h)\ dia/ te <lb/>tou=to, kai\ dio/ti e)n me\n tw=| sfendonw=n h( me\n xei\r gi/netai <lb/>ke/ntron, h( de\ sfendo/nh h( e)k tou= ke/ntrou o(/sw| a)\n h)=| mei/zwn, <lb/>h( a)po\ tou= ke/ntrou kinei=tai qa=tton. </foreign></s> <s id="g0131205a"><foreign lang="el">h( de\ a)po\ th=s xeiro\s <lb/>bolh\ pro\s th\n sfendo/nhn braxei=a e)sti/.</foreign></s> </p> <p type="main"> <s id="id.001835">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? </s> <s id="id.001836">Præterea &longs;ic <lb/>duo pondera moueat, fun­<lb/>dam &longs;cilicet, & mi&longs;&longs;ile: illo <pb xlink:href="035/01/156.jpg" pagenum="116" />verò modo mi&longs;&longs;ile dunta­<lb/>xat. </s> <s id="id.001837">An quia in funda mi&longs;­<lb/>&longs;ile commotum proijciens <lb/>iacit. </s> <s id="id.001838">In orbem enim volu­<lb/>tans &longs;æpius, proijcit. </s> <s id="id.001839">E ma­<lb/>nu autem initium à quiete <lb/>capit. </s> <s id="id.001840">At omnia commota <lb/>facilius: quam quie&longs;centia <lb/><expan abbr="mou&etilde;tur">mouentur</expan>. </s> <s id="id.001841">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. </s> <s id="id.001842">quantò autem fue­<lb/>rit hæc maior, <expan abbr="tãtò">tantò</expan> celerius <lb/>mouetur. </s> <s id="id.001843">At iactus à manu <lb/>re&longs;pectu fundæ breuis e&longs;t. </s> </p> <p type="head"> <s id="id.001844">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001845">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. </s> <s id="id.001846">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 proijcitur. </s> <s id="id.001847">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 proijce­<lb/>retur. </s> <s id="id.001848">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. </s> <s id="id.001849">Erat autem <lb/>fundæ v&longs;us adeò frequens Balearium in&longs;ularum populis, vt matres <lb/>filios non alijs auibus ve&longs;ci paterentur, quam quas funda &longs;ibi com­<lb/>para&longs;&longs;ent. </s> <s id="id.001850">Vnde & funda balearis appellatur à Poëta,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001851">Stuppea torquentur balearis verbera fundæ. <lb/></s> <s><emph type="italics"/>Nec &longs;olum lapides funda proijci&longs;olere: &longs;ed & alia, vt plumbum, pa­<lb/>tet ex Ouidio. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/157.jpg" pagenum="117" /> <p type="main"> <s id="id.001852">Non &longs;ecus exar&longs;it quam cum balearica plumbum</s> </p> <p type="main"> <s id="id.001853">Funda iacit, volat illud, & incande&longs;cit eundo. </s> </p> <p type="main"> <s id="id.001854"><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 grauiores <lb/>&longs;crip&longs;it Vegetius. </s> <s id="id.001855">Quandoquidem membris integris, lethale tamen <arrow.to.target n="marg27"/><lb/>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. </s> <s id="id.001857">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 id="id.001858"><margin.target id="marg27"/>Cap. 16. lib <lb/>1. de re mili</s> </p> <p type="main"> <s id="id.001859">Cur mi&longs;&longs;ilia.] <emph type="italics"/>Quærit hîc Ari&longs;toteles cur iaculum mi&longs;&longs;um cum <lb/>funda longius proijcitur, quam &longs;i manu tantum. </s> <s id="id.001860">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. </s> <s id="id.001861">At difficilius duo mouere: <lb/>quam vnum. </s> <s id="id.001862">His incommodis tamen neglectis &longs;oluit Ari&longs;toteles <lb/>problema dupliciter, priore modo è motu incitato, & contraria quie­<lb/>te. </s> <s id="id.001863">Syllogi&longs;mus &longs;ic e&longs;t,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001864"><emph type="italics"/>Qui initium proiectionis capit à motu longius iacit: quam à <lb/>quiete. </s> <s id="id.001865">Quies enim vt contraria motui, ei repugnat, & ip&longs;i re­<lb/>nitens, ne fiat impedit. </s> <s id="id.001866">Ideóque omnia commota facilius: quam <lb/>quie&longs;centia mouentur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001867"><emph type="italics"/>At proijciens cum funda initium capit à motu. </s> <s id="id.001868">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 id="id.001869"><emph type="italics"/>Igitur proiiciens cum funda longius iacit: quam cum manu &longs;ola. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001870">E fo&longs;&longs;a fundæ.] <emph type="italics"/>In Græco vocabulum e&longs;t,<emph.end type="italics"/> <foreign lang="el">to\ kai/ar,</foreign> <emph type="italics"/>&longs;ine vo­<lb/>cabulo<emph.end type="italics"/> <foreign lang="el">sfendo/nhs.</foreign> </s> <s><emph type="italics"/>Significat <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="el">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="el">to\ kai/ar</foreign> <emph type="italics"/>& loco eius <emph.end type="italics"/><pb xlink:href="035/01/158.jpg" pagenum="118" /><emph type="italics"/>reponendum<emph.end type="italics"/> <foreign lang="el">o)i+/sto\n</foreign> <emph type="italics"/>id e&longs;t omne quod iaculamus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001871">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 id="id.001872">An propter hoc.] <emph type="italics"/>Alter e&longs;t modus &longs;olutionis problematis <lb/>&longs;umptus è funda tanquam radio longiore. </s> <s id="id.001873">Syllog. &longs;ic e&longs;t. </s> <s id="id.001874">Quantò li­<lb/>nea à centro e&longs;t maior, tantò celerius mouet. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001875"><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 id="id.001876"><emph type="italics"/>Igitur proiectio cum funda longior fiet. <emph.end type="italics"/><lb/><arrow.to.target n="marg28"/></s> </p> <p type="margin"> <s id="id.001877"><margin.target id="marg28"/>Cap 1. lib. 2. <lb/>de v&longs;. part. </s> </p> <p type="main"> <s id="id.001879">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="el">ph/xus</foreign> <emph type="italics"/>id e&longs;t <lb/>cubitus, & tertia<emph.end type="italics"/> <foreign lang="el">a)kro/keiron</foreign> <emph type="italics"/>hoc e&longs;t &longs;umma extremave manus. <lb/></s> <s id="id.001881">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001882">14. <foreign lang="el">*peri\ kollo/pwn kai\ o)/nwn.</foreign></s> </p> <p type="main"> <s id="id.001883">14. De collopibus & &longs;uc­<lb/>culis. </s> </p> <p type="main"> <s id="id.001884"><foreign lang="el">*dia\ ti/ r(a=|on kinou=ntai peri\ to\ au)to\ zugo\n oi( mei/zous <lb/>tw=n e)latto/nwn ko/llopes, kai\ oi( au)toi\ o)/noi oi( lepto/teroi <lb/>u(po\ th=s au)th=s i)sxu/os tw=n paxute/rwn; </foreign></s> <s id="g0131302"><foreign lang="el">h)\ dio/ti o( me\n o)/nos <lb/>kai\ to\ zugo\n ke/ntron e)sti/n, ta\ de\ a)pe/xonta mege/qh ai( e)k <lb/>tou= ke/ntrou, qa=tton de\ kinou=ntai, kai\ ple/on a)po\ th=s au)th=s <lb/>i)sxu/os, ai( tw=n meizo/nwn ku/klwn h)\ ai( tw=n e)latto/nwn. </foreign></s> <s id="g0131302a"><foreign lang="el">u(po\ <lb/>th=s au)th=s ga\r i)sxu/os mei=zon meqi/statai to\ a)/kron to\ por)r(w/teron <lb/>tou= ke/ntrou.</foreign></s> <s id="g0131303"><foreign lang="el">dio\ pro\s me\n to\ zugo\n tou\s ko/llopas <lb/>o)/rgana poiou=ntai, oi(=s r(a=|on stre/fou=sin. </foreign></s> <s id="g0131303a"><foreign lang="el">e)n de\ toi=s leptoi=s <lb/>o)/nois, plei=on gi/netai to\ e)/cw tou= cu/lou. </foreign></s> <s id="g0131303b"><foreign lang="el">au(/th de\ gi/netai <lb/>h( e)k tou= ke/ntrou.</foreign></s> </p> <p type="main"> <s id="id.001885">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. </s> <s id="id.001886">Longitudines au­<lb/>tem di&longs;tantes &longs;unt lineæ ex <lb/>centro. </s> <s id="id.001887">At & celerius mo­<lb/>uentur, & plus ab eadem vi <lb/>lineæ <expan abbr="maiorũ">maiorum</expan> circulorum: <lb/>quam <expan abbr="minorũ">minorum</expan>. </s> <s id="id.001888">Ab eadem <lb/>enim 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 xlink:href="035/01/159.jpg" pagenum="119" />quibus facilius vertunt. </s> <s id="id.001889">In <lb/>&longs;ucculis vero tenuibus ma­<lb/>ius fit id quod extra e&longs;t, li­<lb/>gnum. </s> <s id="id.001890">Et id linea e&longs;t quæ <lb/>ex centro. </s> </p> <p type="head"> <s id="id.001891">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001892">Cvr circa eandem.] <emph type="italics"/>In hoc capite continentur duo proble­<lb/>mata vnum de ergatis, alterum de &longs;ucculis. </s> <s id="id.001893">Illud cur ergatæ à <lb/>maioribus collopibus facilius mouentur: quam à minoribus. </s> <s id="id.001894">Hoc cur <lb/>&longs;ucculæ graciliores etiam facilius <expan abbr="mou&etilde;tur">mouentur</expan>, quam craßiores. </s> <s id="id.001895">Vtrum­<lb/>que &longs;oluitur ex lineæ è centro longitudine maiore. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001896"><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 id="id.001897"><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 id="id.001898"><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 id="id.001899"><emph type="italics"/>Cæterum quid hîc<emph.end type="italics"/> <foreign lang="el">zugo\n</foreign> <emph type="italics"/>ergata differat à &longs;uccula,<emph.end type="italics"/> <foreign lang="el">o)/non</foreign> <emph type="italics"/>Græci vo­<lb/>cant, & &longs;cytalæ primum genus, parum video, ni&longs;i fulcris, aut craßi­<lb/>tudine. </s> <s id="id.001900">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. </s> <s id="id.001901">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="el">o)/nos</foreign> <emph type="italics"/>dicitur, tanquam ge&longs;tanti cuidam a&longs;ino &longs;imilis &longs;it. </s> <s id="id.001902">Huius fecit <lb/>mentionem Hippocrates &longs;ect. 3. lib. de fract. </s> <s id="id.001904">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="el">o)/nou</foreign> <emph type="italics"/>id e&longs;t axis ver&longs;atio, impul&longs;us per vectem, & <lb/>cuneus adactus. </s> <s id="id.001905">Namque homines &longs;ine aliquo vno, vel &longs;ine omnibus <lb/>nullum opus, quod maximam vim po&longs;tulet, perficiunt. </s> <s id="id.001906">Hæc Hipp. <emph.end type="italics"/><pb xlink:href="035/01/160.jpg" 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 id="id.001907"><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. </s> <s id="id.001908">vocat axem M B,<emph.end type="italics"/><lb/><figure id="id.035.01.160.1.jpg" xlink:href="035/01/160/1.jpg"/><lb/><emph type="italics"/><expan abbr="tympanũ">tympanum</expan> C D, circa tympani <expan abbr="peripheriã">peripheriam</expan> &longs;cytalas 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. </s> <s id="id.001909">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;patij, potentiæ, ac moti ponderis inter &longs;e, & vt v&longs;us ip&longs;ius ad ve­<lb/>ctem referatur. </s> <s id="id.001910">Videat apud Guidum Vbaldum in Mechanicis. </s> <s id="id.001911">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 xlink:href="035/01/161.jpg" 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. </s> <s id="id.001912">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. </s> <s id="id.001913">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001914">15. <foreign lang="el">peri\ cu/lon a)gmou=.</foreign></s> </p> <p type="main"> <s id="id.001915">15. De fractura ligni. </s> </p> <p type="main"> <s id="id.001916"><foreign lang="el">*dia\ ti/ to\ au)to\ me/geqos cu/lon r(a=|on katea/ssetai, para\ <lb/>to\ go/nu e)a\n i)/son a)posth/sas tw=n a)/krwn, e)xo/menos katagnu/h|, <lb/>h)\ para\ to\ go/nu e)ggu\s ou)/sas: kai\ e)a\n pro\s th\n gh=n <lb/>e)rei/sas, kai\ tw=| podi\ prosba\s po/r)r(wqen th=| xeiri\ katagnu/h|, <lb/>h)\ e)ggu/qen, h)\ dio/ti e)/nqa me\n to\ go/nu ke/ntron, e)/nqa de\ o( <lb/>pou/s.</foreign></s> <s id="g0131402"><foreign lang="el">o(/sw| d' a)\n por)r(w/teron h)=| tou= ke/ntrou, r(a=|on kinei=tai <lb/>a(/pan. kinhqh=nai de\ a)na/gkh katagnu/menon.</foreign></s> </p> <p type="main"> <s id="id.001917">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/></s> <s id="id.001918">Præterea &longs;i ad terram ap­<lb/>plicans, & pede impellens, <lb/>manu di&longs;tante frangat: <expan abbr="quã">quam</expan> <lb/>propinqua. </s> <s id="id.001919">An quia illîc <lb/>genu quidem e&longs;t centrum: <lb/>hîc verò pes. </s> <s id="id.001920">quantò autem <lb/>quodque à centro fuerit <lb/>di&longs;tantius, id omne facilius <lb/>mouetur. </s> <s id="id.001921">Quod frangitur autem moueri nece&longs;&longs;e e&longs;t. </s> </p> <p type="head"> <s id="id.001922">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001923"><emph type="italics"/>Mos e&longs;t ignem excitare in paruo foco volentium, baculos lon­<lb/>giores bifariam frangere. </s> <s id="id.001924">Itaque arreptos tracto&longs;que vtraque <lb/>manu per extrema medios ad genu applicantes, parua vi frangunt. <lb/></s> <s id="id.001925">Idem faciunt &longs;i alterum extremorum ad terram applicent: alterum <lb/>eleuatum obliquè manu teneant, & medium pede conculcent. </s> <s id="id.001926">Quæ­<lb/>rit igitur Ari&longs;toteles cur fractio hæc facilior fit manibus ad extre­<lb/>ma diductis: quam ad medium propius accedentibus. </s> <s id="id.001927">Et &longs;oluit è ra­<lb/>dijs maioribus, &longs;ic. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001928"><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 id="id.001929"><emph type="italics"/>In fractione ligni cum manus &longs;unt in extremis, remotiores<emph.end type="italics"/><pb xlink:href="035/01/162.jpg" pagenum="122" /><emph type="italics"/>&longs;unt à centro ( quod e&longs;t genu cum ad hoc applicatum e&longs;t li­<lb/>gnum: vel pes, cum ip&longs;um pede conculcatur ) quam cum <lb/>non &longs;unt in extremis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001930"><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 id="id.001931"><emph type="italics"/>Quæri autem hic pote&longs;t, an qui &longs;ic fu&longs;tem frangunt, genu non offen­<lb/>dant. </s> <s id="id.001932">Et non offendere experientia comprobat. </s> <s id="id.001933">Ratio tamen non ita <lb/>aperta e&longs;t. </s> <s id="id.001934">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. </s> <s id="id.001935">Itaque à genu di&longs;cedunt. </s> <s id="id.001936">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. </s> <s id="id.001937">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. </s> <s id="id.001938">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 gladij 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. </s> <s id="id.001939">Hæc vulgaria &longs;unt, &longs;ed cau&longs;a non vti­<lb/>que vulgaris. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001940">16. <foreign lang="el">*dia\ ti/ ai( kro/kai stroggu/lai.</foreign></s> </p> <p type="main"> <s id="id.001941">16. Cur crocæ rotundæ. </s> </p> <p type="main"> <s id="id.001942"><foreign lang="el">*dia\ ti/ peri\ tou\s ai)gialou\s ai( kalou/menai kro/kai stroggu/lai <lb/>ei)si/n, e)k makrw=n tw=n li/qwn kai\ o)stra/kwn to\ e)c <lb/>u(parxh=s o)/ntwn; </foreign></s> <s id="g0131502"><foreign lang="el">h)\ dio/ti ta\ plei=on a)pe/xonta tou= me/sou e)n <lb/>tai=s kinh/sesi, qa=tton fe/retai.</foreign></s> <s id="g0131503"><foreign lang="el">to\ me\n ga\r me/son gi/netai <lb/>ke/ntron, to\ de\ dia/sthma, h( e)k tou= ke/ntrou.</foreign></s> <s id="g0131504"><foreign lang="el">a)ei\ de\ h( mei/zwn <lb/>a)po\ th=s i)/shs kinh/sews, mei/zw gra/fei ku/klon. </foreign></s> <s id="g0131504a"><foreign lang="el">to\ d' e)n <lb/>i)/sw| xro/nw| mei/zon diecio\n, qa=tton fe/retai. </foreign></s> <s id="g0131504b"><foreign lang="el">ta\ de\ fero/mena <lb/>qa=tton e)k tou= i)/sou a)posth/matos, sfodro/teron tu/ptei. </foreign></s> <s id="g0131505"><foreign lang="el">ta\ de\ <lb/>tu/ptonta ma=llon kai\ au)ta\ tu/ptetai ma=llon, w(/ste a)na/gkh <lb/>qrau/esqai ai)ei\ ta\ ple/on a)pe/xonta tou= me/sou. </foreign></s> <s id="g0131505a"><foreign lang="el">tou=to de\ <lb/>pa/sxonta, a)na/gkh gi/nesqai periferh=.</foreign></s> <s id="g0131506"><foreign lang="el">tai=s de\ kro/kais dia\<lb/> th\n th=s qala/tths ki/nhsin, dia\ to\ meta\ th=s qala/tths kinei=sqai, <lb/>sumbai/nei a)ei\ e)n kinh/sei ei)=nai, kai\ kuliome/nais <lb/>prosko/ptein.</foreign></s> <s id="g0131507"><foreign lang="el">tou=to de\ a)na/gkh ma/lista sumbai/nein au)toi=s <lb/>toi=s a)/krois.</foreign></s> </p> <p type="main"> <s id="id.001943">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. </s> <s id="id.001944">An quia in motibus <lb/>magis à medio di&longs;tantia ce­<lb/>lerius <expan abbr="ferũtur">feruntur</expan>. </s> <s id="id.001945">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>. </s> <s id="id.001946">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>. </s> <s id="id.001947">Et quod e&longs;t <lb/>maius <expan abbr="&longs;patiũ">&longs;patium</expan> æquali <expan abbr="t&etilde;pore">tempore</expan> <pb xlink:href="035/01/163.jpg" pagenum="123" /><expan abbr="trãfiens">tranfiens</expan> celerius fertur. </s> <s id="id.001948">La­<lb/>ta vero celerius in æquali <lb/>&longs;patio, vehementius pul­<lb/>&longs;ant. </s> <s id="id.001949">Et magis pul&longs;antia <lb/>magis etiam percutiuntur. <lb/></s> <s id="id.001950">Ita que nece&longs;&longs;e e&longs;t plus di­<lb/>&longs;tantia à medio &longs;emper at­<lb/>teri. </s> <s id="id.001951">Et quæ id patiuntur, <lb/><expan abbr="rotũda">rotunda</expan> fieri. </s> <s id="id.001952">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 id="id.001953">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001954">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"/><arrow.to.target n="marg29"/><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. </s> <s id="id.001956">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. </s> <s id="id.001957">Quod problema licet &longs;peciale &longs;it de <lb/>crocis, generale tamen fieri pote&longs;t de omnibus non rotundis. </s> <s id="id.001958">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 eminentijs & angulis rotundantur. <emph.end type="italics"/><pb xlink:href="035/01/164.jpg" pagenum="124" /><arrow.to.target n="marg30"/></s> </p> <p type="margin"> <s id="id.001959"><margin.target id="marg29"/>Lib. 2. de <lb/>Orat. cap. 8. <lb/>lib. 8. </s> </p> <p type="margin"> <s id="id.001960"><margin.target id="marg30"/>Cap. 11. lib. <lb/>1. de v&longs;u <lb/>part. </s> </p> <p type="main"> <s id="id.001961">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 id="id.001962">Semper atteri.] <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 id="id.001963">Gutta cauat lapidem, con&longs;umitur annulus v&longs;u. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001964">17. <foreign lang="el">*dia\ ti/ makro/tera cu/la <lb/>a)sqene/stera.</foreign></s> </p> <p type="main"> <s id="id.001965">17. Cur ligna longiora &longs;unt <lb/>imbecilliora. </s> </p> <p type="main"> <s id="id.001966"><foreign lang="el">*dia\ ti/, o(/sw| a)\n h)=| makro/tera ta\ cu/la, tosou/tw| a)sqene/stera <lb/>gi/netai, kai\ ka/mptetai ai)ro/mena ma=llon, ka)\n h)=| <lb/>to\ me\n braxu/ o(/son di/phxu lepto/n, to\ de\ e(kato\n phxw=n, <lb/>paxu/, h)\ dio/ti moxlo\s gi/netai kai\ ba/ros, kai\ u(pomo/xlion <lb/>e)n tw=| ai)/resqai tou= cu/lou to\ mh=kos; </foreign></s> <s id="g0131603"><foreign lang="el">to\ me\n ga\r prw=ton me/ros <lb/>au)tou=, o(\ h( xei\r ai)/rei, oi(=on u(pomo/xlion gi/netai: to\ d' <lb/>e)pi\ tw=| a)/krw|, ba/ros.</foreign></s> <s id="g0131604"><foreign lang="el">w(/ste o(/sw| a)\n h)=| makro/teron to\ a)po\ tou= <lb/>u(pomoxli/ou, tosou/tw| a)na/gkh ka/mptesqai ma=llon.</foreign></s> <s id="g0131604a"><foreign lang="el">[1o(/sw| <lb/>ga\r a)\n ple/on a)pe/xh| tou= u(pomoxli/ou, tosou/tws a)na/gkh <lb/>ka/mptesqai mei=zon.]1</foreign></s> <s id="g0131605"><foreign lang="el">a)na/gkh ou)=n ai)/resqai ta\ a)/kra tou= <lb/>moxlou=.</foreign></s> <s id="g0131606"><foreign lang="el">e)a\n ou)=n h)=| kampto/menos o( moxlo/s, a)na/gkh au)to\n <lb/>ka/mptesqai ma=llon ai)ro/menon, o(/per sumbai/nei e)pi\ tw=n <lb/>cu/lwn tw=n makrw=n, e)n de\ toi=s braxe/sin e)ggu\s to\ e)/sxaton <lb/>tou= u(pomoxli/ou gi/netai tou= h)remou=ntos.</foreign></s> </p> <p type="main"> <s id="id.001967"><arrow.to.target n="marg31"/></s> </p> <p type="margin"> <s id="id.001968"><margin.target id="marg31"/>[bis <expan abbr="dictũ]">dictum]</expan> <lb/>fruftra. </s> </p> <p type="main"> <s id="id.001969">Cur quantò ligna fue­<lb/>rint longiora, tantò fiunt <lb/>imbecilliora, & &longs;ublata <lb/>magis <expan abbr="curuãtur">curuantur</expan>, licet breue <lb/>&longs;it quod tenue, vt <expan abbr="bicubi­tũ">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="hypo­mochliũ">hypo­<lb/>mochlium</expan>? </s> <s id="id.001970">prima enim ip&longs;ius <lb/>pars, quam manus attollit, <lb/>fit vt hypomochlium: quæ <lb/>autem in extremo, vt pon­<lb/>dus. </s> <s id="id.001971">Itaque quantò di&longs;tite­<lb/>rit magis ab hypomochlio: <lb/>tantò magis curuari nece&longs;­<lb/>&longs;e e&longs;t. </s> <s id="id.001972">Nece&longs;&longs;e igitur extre­<lb/>ma vectis eleuari. </s> <s id="id.001973">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. </s> <s id="id.001974">At in <lb/>breuibus <expan abbr="extremũ">extremum</expan> fit vici­<pb xlink:href="035/01/165.jpg" pagenum="125" />num hypomochlio quie&longs;­<lb/>centi. </s> </p> <p type="head"> <s id="id.001975">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.001976">Cvr quantò.] <emph type="italics"/>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. </s> <s id="id.001977">Quærit igitur hî Ari&longs;toteles non &longs;olum <lb/>cur &longs;ic fiat, non in his tantum: &longs;ed & in omnibus flexilibus. </s> <s id="id.001978">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. </s> <s id="id.001979">In extremo enim manu compre­<lb/>hen&longs;o e&longs;t hypomochlium. </s> <s id="id.001980">In altero e&longs;t pondus. </s> <s id="id.001981">Longitudo vero inter <lb/>media e&longs;t vectis. </s> <s id="id.001982">Ratio itaque &longs;ic di&longs;ponetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.001983"><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 id="id.001984"><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 id="id.001985"><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 id="id.001986"><emph type="italics"/>Sed & ligna medio &longs;ui comprehen&longs;a, & &longs;ic eleuata &longs;emper quo lon­<lb/>giora, eo magis incuruabuntur. </s> <s id="id.001987">At tunc hypomochlium erit in me­<lb/>dio. </s> <s id="id.001988">Pondera duo erunt in extremis. </s> <s id="id.001989">Curuari autem magis imbecilli­<lb/>tatis e&longs;t. </s> <s id="id.001990">Curuatio enim à fractura non differt, ni&longs;i &longs;ecundum magis <lb/>& minus. </s> <s id="id.001991">Si plus enim curuatur: quam vnitas partium ferat, &longs;olui­<lb/>tur continuum, & &longs;ic frangitur. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.001992">18. <foreign lang="el">*tou= sfhno\s duna/meos <lb/>ai)/tion.</foreign></s> </p> <p type="main"> <s id="id.001993">18. Cau&longs;a pote&longs;tatis <lb/>cunei. </s> </p> <p type="main"> <s id="id.001994"><foreign lang="el">*dia\ ti/ tw=| sfhni\ o)/nti mikrw=|, mega/la ba/rh dii/+statai, <lb/>kai\ mege/qh swma/twn, kai\ qli=yis i)sxura\ gi/netai; </foreign></s> <s id="g0131702"><foreign lang="el">h)\ dio/ti <lb/>o( sfh\n, du/o moxloi/ ei)sin e)nanti/oi a)llh/lois.</foreign></s> <s id="g0131702a"><foreign lang="el">e)/xei de\ e(ka/teros, <lb/>to\ me\n ba/ros, to\ de\ u(pomo/xlion, o(\ kai\ a)naspa=| h)\ <lb/>pie/zei.</foreign></s> <s id="g0131703"><foreign lang="el">e)/ti de\ h( th=s plhgh=s fora\, to\ ba/ros, o(\ tu/ptei kai\ <lb/>kinei=, poiei= me/ga, kai\ dia\ to\ kinou/menon kinei=n th=| taxu/thti <lb/>i)sxu/ei e)/ti ple/on. </foreign></s> <s id="g0131703a"><foreign lang="el">mikrw=| de\ o)/nti mega/lai duna/meis <lb/>a)kolouqou=si.</foreign></s> <s id="g0131704"><foreign lang="el">dio\ lanqa/nei kinw=n, para\ th\n a)ci/an tou= mege/qous.</foreign></s> <s id="g0131705"><foreign lang="el"><lb/>e)/stw sfh\n e)f' w(=| *a*b*g, to\ de\ sfhnou/menon *d*e*h*z. <lb/></foreign></s> <s id="g0131705a"><foreign lang="el">moxlo\s dh\ gi/netai h( *a*b.</foreign></s> <s id="g0131705b"><foreign lang="el">ba/ros de\ to\ tou= *b ka/twqen, <lb/>u(pomo/xlion de\ to\ *m*n.</foreign></s> <s id="g0131705c"><foreign lang="el">e)nanti/os de\ tou/tw| moxlo\s, to\ *b*g.</foreign></s> <s id="g0131706"><foreign lang="el"><lb/>h( de\ *a*g koptome/nh, e(kate/ra| tou/twn xrh=tai moxlw=|: a)naspa=| <lb/>ga\r to\ *b.</foreign></s> </p> <p type="main"> <s id="id.001995">Cur à cuneo re parua ma­<lb/>gnæ moles, & <expan abbr="corporũ">corporum</expan> ma­<lb/>gnitudines <expan abbr="diuidũtur">diuiduntur</expan>, im­<pb xlink:href="035/01/166.jpg" pagenum="126" />pre&longs;&longs;ioque valida efficitur. <lb/></s> <s id="id.001996">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>. </s> <s id="id.001997">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/></s> <s id="id.001998">Paruo vero exi&longs;tente vecte <lb/>magnæ vires con&longs;equun­<lb/>tur, ideò mouens latet præ­<lb/>ratione magnitudinis. </s> </p> <figure id="id.035.01.166.1.jpg" xlink:href="035/01/166/1.jpg"/> <p type="main"> <s id="id.001999">E&longs;to cuneus vbi e&longs;t <foreign lang="el">a b <lb/>g,</foreign> quod vero cuneo fin­<lb/>ditur <foreign lang="el">d n z.</foreign> </s> <s>Vectis itaque <lb/>fiet <foreign lang="el">a b,</foreign> pondus vero ip&longs;ius <lb/><foreign lang="el">b</foreign> inferior pars: hypo­<lb/>mochlium autem <foreign lang="el">m & n,</foreign><lb/>huic vero contrarius ve­<lb/>ctis <foreign lang="el">b g,</foreign> tum pars <foreign lang="el">a g</foreign> per­<lb/>cu&longs;&longs;a. </s> <s id="id.002000"><expan abbr="vtroq;">vtroque</expan> illorum vecte vtitur. </s> <s id="id.002001">diuellit enim ip&longs;um <foreign lang="el">b. </foreign></s> </p> <p type="head"> <s id="id.002002">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002003">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 xlink:href="035/01/167.jpg" pagenum="127" /><figure id="id.035.01.167.1.jpg" xlink:href="035/01/167/1.jpg"/><lb/><emph type="italics"/>tum. </s> <s id="id.002004">Vt A B C D E F. </s> <s id="id.002005">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. </s> <s id="id.002006">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. </s> <s id="id.002007">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/></s> <s id="id.002008">Tum non alio vtens in&longs;trumento, quam &longs;uis manibus au&longs;us e&longs;t trun­<lb/>cum diducere. </s> <s id="id.002009">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 coëuntibus comprehen&longs;æ, primum quidem ip&longs;æ contritæ &longs;unt, <lb/>mox & ip&longs;i mi&longs;erandi exitij fuere cau&longs;a, vt refert Galenus in lib. de <lb/>exhort. ad bonas artes. </s> <s id="id.002011">Hic e&longs;t de quo Iuuenalis,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002012">Viribus ille</s> </p> <p type="main"> <s id="id.002013">Confi&longs;us perijt. </s> </p> <p type="main"> <s id="id.002014">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. </s> <s id="id.002015">Et primum <lb/>quidem duplicatus, vt in cuneo. </s> <s id="id.002016">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. </s> <s id="id.002017">Ex hoc enim quod ve­<lb/>ctis facile mouet. </s> <s id="id.002018">Ex hoc quod e&longs;t duo vectes, cum hi ex aduer&longs;o &longs;ibi <lb/>inuicem contrarij &longs;int, & mutuas operas &longs;ibi tradant, magis & faci­<lb/>lius mouet. </s> <s id="id.002019">Ex hoc quod à percu&longs;sione, eaque celeri, quæ motus e&longs;t, ma­<lb/>gis adhuc mouetur: &longs;icque à tribus ijs coniunctis effectus à cuneo ad­<lb/>mirandi prodeuntis habetur cau&longs;a. </s> <s id="id.002020">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. </s> <s id="id.002021">Mouetur enim cuneus anguli maioris <emph.end type="italics"/><pb xlink:href="035/01/168.jpg" 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. </s> <s>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 id="id.002022">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 id="id.002023"><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 id="id.002024"><emph type="italics"/>Cuneus e&longs;t duo vectes, ijque &longs;ibi inuicem contrarij: &longs;ed <lb/>iuncti. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002025"><emph type="italics"/>Cuneus igitur multum mouet, & magnas moles di&longs;trahet. <lb/></s> <s id="id.002026">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 id="id.002027">Vterque verò habet.] <emph type="italics"/>Confirmatio e&longs;t a&longs;&longs;umptionis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002028"><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 id="id.002029"><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 id="id.002030"><emph type="italics"/>E&longs;t igitur cuneus duo vectes. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002031">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. </s> <s id="id.002032">Percußio autem duobus fit modis, vel ex eo ip&longs;o &longs;olo quod <lb/>percutit tanquam graui e 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. </s> <s id="id.002033">Graue enim vnumquodque dum <lb/>mouetur grauitatis magis a&longs;&longs;umit motum: quam quie&longs;cens: & adhuc <lb/>magis quo longius mouet. </s> <s id="id.002034">quilibet enim aër addit &longs;uper motum iam <lb/>acqui&longs;itum. </s> <s id="id.002035">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. </s> <s id="id.002036">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 xlink:href="035/01/169.jpg" pagenum="129" /><emph type="italics"/>nubrio, vbi manus ip&longs;um comprehendunt, plus di&longs;tet. </s> <s id="id.002037">Præterea cer­<lb/>tum e&longs;t quod quantò potentia percutiens validior e&longs;t, validiori tantò <lb/>impellet pul&longs;u. </s> <s id="id.002038">his adde quod e&longs;t ab Hippocrate<emph.end type="italics"/> <foreign lang="el">e)n toi=s trw/masi</foreign><lb/><emph type="italics"/>annotatum. </s> <s id="id.002039">Quantò impul&longs;us magis fiet<emph.end type="italics"/> <foreign lang="el">kat' i)/cin</foreign> <emph type="italics"/>è directo, id e&longs;t vt <lb/>interpretor è perpendiculari. </s> <s id="id.002040">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. </s> <s id="id.002042">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. </s> <s id="id.002043">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="id.035.01.169.1.jpg" xlink:href="035/01/169/1.jpg"/><lb/><emph type="italics"/>re&longs;pectu eius, qui à percußione pro­<lb/>fici&longs;citur. </s> <s id="id.002044">Guidus Vbaldus commo­<lb/>de hoc adfert exemplum. </s> <s id="id.002045">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. </s> <s id="id.002046">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 id="id.002047">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. </s> <s id="id.002048">Sic in rebus natu­<emph.end type="italics"/><lb/><arrow.to.target n="marg32"/><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/></s> <s id="id.002049">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. </s> <s id="id.002050">Præterea à Phalangij <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. </s> <s id="id.002051">Hæc Galenus quæ <lb/>ideo attuli, vt intelligant mor&longs;us ab animalium dentibus inci&longs;orijs <emph.end type="italics"/><pb xlink:href="035/01/170.jpg" 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. </s> <s id="id.002052">Serra quoque & lima ad <lb/>hoc genus, quòd ad &longs;uos denticulos &longs;pectat reduci pote&longs;t, quot enim <lb/>denticuli tot cunei, & ij 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 id="id.002053"><margin.target id="marg32"/>Lib. 5. de <lb/>loc. aff. </s> </p> <p type="main"> <s id="id.002054">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. </s> <s id="id.002055">Sed hanc &longs;ic paulò am­<lb/>plius & apertius repetemus. </s> <s id="id.002056">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="id.035.01.170.1.jpg" xlink:href="035/01/170/1.jpg"/><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. </s> <s>percu­<lb/>tiatur vt fieri &longs;olet cuneus <lb/>in A C. </s> <s id="id.002057">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. </s> <s id="id.002058">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. </s> <s id="id.002059">Et cum M B, B L &longs;int ip&longs;is H B, B K maiores: <lb/>erit M L maior H K. </s> <s id="id.002060">Dum igitur 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. </s> <s id="id.002061">Pars igitur 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 xlink:href="035/01/171.jpg" pagenum="131" /><emph type="italics"/>partem H D impellat. </s> <s id="id.002062">Atque hæc e&longs;t &longs;ententia Ari&longs;totelis de du­<lb/>plici vecte in cuneo. </s> <s id="id.002063">Aliam habet Guidus Vbaldus, quam exi&longs;timat <lb/>meliorem. </s> <s id="id.002064">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, habeat item 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/></s> <s id="id.002065">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/></s> <s id="id.002066">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. </s> <s id="id.002067">Quod <lb/>igitur cedant motus is &longs;ecundarius e&longs;t, & priorem qui e&longs;t in B con­<lb/>&longs;equens. </s> <s id="id.002068">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. </s> <s id="id.002069">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. </s> <s id="id.002070">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. </s> <s id="id.002071">Quod vt intelligatur. </s> <s id="id.002072">Sit cuneus A B C circa<emph.end type="italics"/></s> </p> <figure id="id.035.01.171.1.jpg" xlink:href="035/01/171/1.jpg"/> <p type="caption"> <s id="id.002073">Cochlea &longs;ine matrice. <lb/></s> </p> <p type="main"> <s><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 xlink:href="035/01/172.jpg" pagenum="132" /><emph type="italics"/>cylindri axi an­<emph.end type="italics"/></s> </p> <figure id="id.035.01.172.1.jpg" xlink:href="035/01/172/1.jpg"/> <p type="caption"> <s id="id.002074">Cochlea cum matrice. <lb/></s> </p> <p type="main"> <s><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;cindū­tur">&longs;cindun­<lb/>tur</expan>, fieri &longs;olet: <lb/>cunei vero vertex A &longs;it intra rimam R S. </s> <s id="id.002075">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. </s> <s id="id.002076">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. </s> <s id="id.002077">Totum ergo L M N O &longs;cindetur. </s> <s id="id.002078">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="id.035.01.172.2.jpg" xlink:href="035/01/172/2.jpg"/><lb/><emph type="italics"/>prout cylindrus cochleæ po&longs;itus erit ad planum horizontis cum &longs;ua, <lb/>vel &longs;ine fœmina &longs;eu matrice. </s> <s id="id.002079">Quod &longs;i rur&longs;us cochleæ <expan abbr="tympanũ">tympanum</expan> rectè <emph.end type="italics"/><pb xlink:href="035/01/173.jpg" 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>. </s> <s id="id.002080">Vnde hæc cochlea di­<lb/>citur infinita, id e&longs;t tandiu vertetur, quandiu quis volet. </s> <s id="id.002081">Eodem enim <lb/>modo &longs;emper &longs;e habebit tympanum ad cochleam. </s> <s id="id.002082">Porrò cochleæ vi <lb/>& beneficio admirabile certè quanta pondera moueantur. </s> <s id="id.002083">Refert <emph.end type="italics"/><lb/><arrow.to.target n="marg33"/><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. </s> <s id="id.002084">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. </s> <s id="id.002085">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. </s> <s id="id.002086">Primum quia e&longs;t helix circa cochleam, quæ quò <lb/>e&longs;t vertex cunei acutioris, eò facilius: &longs;ed tardius mouet. </s> <s id="id.002087">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 id="id.002088"><margin.target id="marg33"/>Lib 1. Rud. <lb/>Math. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002089">19. <foreign lang="el">*peri\ troxilaiw=n.</foreign></s> </p> <p type="main"> <s id="id.002090">19. De trochleis. </s> </p> <p type="main"> <s id="id.002091"><foreign lang="el">*dia\ ti/, e)a/n tis du/o troxilai/as poih/sas e)pi\ dusi\ cu/lois <lb/>sumba/llousin e(autoi=s e)nanti/ws, au(tai=s ku/klw| periba/lh| <lb/>kalw/dion, e)/xon to\ a)/rthma e)k qate/rou tw=n cu/lwn, <lb/>qa/teron de\ h)=| proserhreisme/non h)\ prosteqeime/non kata\ ta\s <lb/>troxali/as, e)a\n e(/lkh| tis th=| a)rxh=| tou= kalwdi/ou, mega/la <lb/>ba/rh prosa/gei, ka)\n h)=| mikra\ h( e(/lkousa i)sxu/s;</foreign></s> </p> <p type="main"> <s id="id.002092">Quare &longs;i quis in duobus <lb/>tignis inter &longs;e <expan abbr="iũctisè">iunctisè</expan> <expan abbr="cõtra­rio">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 appo&longs;itum &longs;it ad <lb/>trochleas, atque initium <lb/>funiculi traxerit, vt parua <lb/>vi trahat, magna tamen <lb/>pondera adducet. </s> </p> <pb xlink:href="035/01/174.jpg" pagenum="134" /> <p type="head"> <s id="id.002093">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002094">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. </s> <s id="id.002095">Geminatur ali­<lb/>quando, triplicatur, & amplius multiplicatur. </s> <s id="id.002096">Si duobus orbiculis <lb/>con&longs;ter<emph.end type="italics"/> <foreign lang="el">di/spastos,</foreign> <emph type="italics"/>&longs;i tribus<emph.end type="italics"/> <foreign lang="el">tri/spastos,</foreign> <emph type="italics"/>&longs;i quinque<emph.end type="italics"/> <foreign lang="el">pente/spastos,</foreign> <emph type="italics"/>&longs;i plu­<lb/>ribus<emph.end type="italics"/> <foreign lang="el">polu/spastos</foreign> <emph type="italics"/>dicitur, ex quo &longs;unt illa tractoria in&longs;trumenta in­<lb/>finitarum prope modum virium. </s> <s id="id.002097">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. </s> <s id="id.002098">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 vbi fit, &longs;i in vna <lb/>trochlea &longs;int plures orbiculi inferioris trochleæ orbiculus &longs;uperior <lb/>debet &longs;emper e&longs;&longs;e minor inferiore: vt & &longs;uperioris inferior, ne funes <lb/>ductarij inter &longs;e inuicem complicentur & &longs;ibi ob&longs;int. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002099">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. </s> <s id="id.002100">Tota enim particula contextus huius<emph.end type="italics"/> <foreign lang="el">e)/xon to\ <lb/>a)/rthma e)k qate/rou tw=n cu/lwn, qa/teron de\ h)= proserhreime/non h)\ pro­<lb/>steqeime/non kata\ ta\s troxali/as,</foreign> <emph type="italics"/>mendo&longs;a meo iudicio e&longs;t. </s> <s id="id.002101">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="id.035.01.174.1.jpg" xlink:href="035/01/174/1.jpg"/><lb/><emph type="italics"/>ad trochleas, intelligi certè <lb/>non pote&longs;t. </s> <s id="id.002102">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="ap­po&longs;itũ">ap­<lb/>po&longs;itum</expan> e&longs;&longs;e pondus trahen­<lb/>dum vel attollendum. </s> <s id="id.002103">Vt <lb/>&longs;int duo tigna &longs;e&longs;e ex ad­<emph.end type="italics"/><pb xlink:href="035/01/175.jpg" pagenum="135" /><emph type="italics"/>uer&longs;o fulcientia C D & E F <emph.end type="italics"/><lb/><figure id="id.035.01.175.1.jpg" xlink:href="035/01/175/1.jpg"/><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 id="id.002104"><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. </s> <s id="id.002105">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> </subchap1> <subchap1> <p type="main"> <s id="id.002106"><foreign lang="el">h)\ dio/ti to\ <lb/>au)to\ ba/ros a)po\ e)la/ttonos i)sxu/os ei) moxleu/etai, e)gei/retai, <lb/>h)\ a)po\ xeiro/s;</foreign></s> <s id="g0131802a"><foreign lang="el">h( de\ troxile/a to\ au)to\ poiei= tw=| mo­<lb/>xlw=|;</foreign></s> <s id="g0131802b"><foreign lang="el">w(/ste h( mi/a r(a=|on e(/lcei, kai\ a)po\ mia=s o(lkh=s tou= <lb/>kata\ xei=ra, polu\ e(/lcei baru/teron.</foreign></s> <s id="g0131802c"><foreign lang="el">tou=to d' ai( du/o troxali/ai <lb/>ple/on, h)\ diplasi/w| ta/xei ai)/rousi.</foreign></s> <s id="g0131803"><foreign lang="el">e)/latton ga\r <lb/>e)/ti h( e(te/ra e(/lkei, h)\ ei) au)th\ kaq' e(auth\n ei(=lken, o(/tan <lb/>para\ th=s e(te/ras e)piblhqh=| to\ sxoini/on.</foreign></s> <s id="g0131804"><foreign lang="el">e)kei/nh ga\r e)/ti <lb/>e)/latton e)poi/hse to\ ba/ros, kai\ ou(/tws e)a\n ei)s plei/ous e)piba/llhtai <lb/>to\ kalw/dion, e)n o)li/gais troxilai/ais pollh\ gi/netai <lb/>diafora/.</foreign></s> <s id="g0131804a"><foreign lang="el">h)\ w(/ste u(po\ th=s prw/ths tou= ba/rous e(/lkontos <lb/>te/ttaras mna=s, u(po\ th=s teleutai/as e(/lkesqai pollw=| <lb/>e)la/ttw.</foreign></s> </p> <p type="main"> <s id="id.002107">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. </s> <s id="id.002108">Trochlea <expan abbr="aut&etilde;">autem</expan> id facit, <lb/>quod vectis. </s> <s id="id.002109"><expan abbr="Itaq;">Itaque</expan> &longs;i vna fa­<lb/>cilius trahat, & ab vnico tra­<lb/>ctu: <expan abbr="quã">quam</expan> manu, grauius multò <lb/>trahet. </s> <s id="id.002110">Hoc vero duæ tro­<pb xlink:href="035/01/176.jpg" pagenum="136" />chleæ plus in dupla veloci­<lb/>tate attollent. </s> <s id="id.002111">Minus enim <lb/>altera trahit quam &longs;i ip&longs;a <lb/>per &longs;eip&longs;am traheret. </s> <s id="id.002112">quo­<lb/>niam iuxta <expan abbr="alterã">alteram</expan> iniectus <lb/>fuerit funiculus. </s> <s id="id.002113">H&etail;c enim <lb/>in&longs;uper pondus minus effe­<lb/>cit. </s> <s id="id.002114">Et &longs;ic &longs;i in plures tro­<lb/>chleas iniectus fuerit funi­<lb/>culus, in paucis trochleis <lb/>multum intere&longs;t. </s> <s id="id.002115">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 id="id.002116">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002117">An quia idem.] <emph type="italics"/>Solutio e&longs;t propo&longs;iti problematis &longs;umpta è <lb/>vecte multiplicato. </s> <s id="id.002118">Syllogi&longs;mus &longs;ic erit. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002119"><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 id="id.002120"><emph type="italics"/>Trochlea parua vi magna trahit pondera. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002121"><emph type="italics"/>Trochlea ergo geminata parua vi magna trahet pondera. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002122"><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. </s> <s id="id.002123">A&longs;&longs;umptio <lb/>verò &longs;ic confirmatur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002124"><emph type="italics"/>Trochlea idem facit, quod vectis. </s> <s id="id.002125">E&longs;t enim ip&longs;a vectis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002126"><emph type="italics"/>Vectis parua vi magna mouet pondera. </s> <s id="id.002127">ex anteced. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002128"><emph type="italics"/>Ergo trochlea parua vi magna trahet pondera. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002129"><emph type="italics"/>Quod autem trochlea &longs;it vectis, patet. </s> <s id="id.002130">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. </s> <s id="id.002131"><expan abbr="Mou&etilde;s">Mouens</expan> <lb/><expan abbr="cut&etilde;">cutem</expan> e&longs;t virtus trahentis ad initium funis. </s> <s id="id.002132">Et <expan abbr="põdus">pondus</expan> quod e&longs;t vni tro­<lb/>chlearum appo&longs;itum e&longs;t mobile. </s> <s id="id.002133">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 xlink:href="035/01/177.jpg" pagenum="137" /><emph type="italics"/>pluribus diui&longs;um orbiculis, minus id e&longs;t leuius apparet. </s> <s id="id.002134">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 id="id.002135">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 Vbaldo prop. 3. & aliquot &longs;equentibus in tractatu de <lb/>trochlea. </s> <s id="id.002136">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. </s> <s id="id.002137">Vnde arbitror hûc irrep&longs;i&longs;&longs;e mendum in vo­<lb/>cabulo<emph.end type="italics"/> <foreign lang="el">ta/xei</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="el">logw|</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="el">diplasi/w|. </foreign><emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="el">u(podiplasi/w|</foreign> <emph type="italics"/>tollendo<emph.end type="italics"/><lb/><foreign lang="el">ple/on h)\</foreign> <emph type="italics"/>vel potius pro<emph.end type="italics"/> <foreign lang="el">h)\</foreign> <emph type="italics"/>reponendo<emph.end type="italics"/> <foreign lang="el">mh\</foreign> <emph type="italics"/>&longs;ic enim &longs;ententia vera erit. <emph.end type="italics"/> <lb/></s> <s>Hoc vero duæ trochleæ plus non in dupla velocitate <expan abbr="at­toll&etilde;t">at­<lb/>tollent</expan>. </s> <s><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 Vbaldum prædicto tractatu, ne maior pars il­<lb/>lius præ&longs;tanti&longs;simi operis, quod edidit de mechanicis, mihi &longs;it hûc <lb/>transferenda. </s> <s id="id.002138">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/>ductarij 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="mathema­tũ">mathema­<lb/>tum</expan> &longs;tudio&longs;os <expan abbr="quãdiu">quandiu</expan> vixit &longs;ingularem <expan abbr="amor&etilde;">amorem</expan>. </s> <s id="id.002139">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 ti­<lb/>gnorum circa &longs;uos axiculos mobiles reliquorum &longs;inguli circa &longs;ingu­<lb/>los à proximè antecedentibus funiculis &longs;u&longs;pen&longs;os. </s> <s id="id.002140">In X autem &longs;it <lb/>harpago ad apprehendendum pondus E attollendum vel deprimen­<lb/>dum. </s> <s id="id.002141">Si enim 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 xlink:href="035/01/178.jpg" pagenum="138" /><figure id="id.035.01.178.1.jpg" xlink:href="035/01/178/1.jpg"/><lb/><emph type="italics"/>&longs;patij, quanti &longs;unt funiculi N M, Q P, <lb/>R S, B T. </s> <s id="id.002142">Tanti erunt autem, <lb/>quantos loci, ad quem de&longs;cendere, vel <lb/>è quo educere volumus, profunditas, <lb/>po&longs;tulat. </s> <s id="id.002143">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 id="id.002144"><emph type="italics"/>In hac machina igitur hæc duo in­<lb/>&longs;unt, facilitas motionis ob multitudi­<lb/>nem trochlearum, & celeritas motio­<lb/>nis. </s> <s id="id.002145">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> </subchap1> <subchap1> <p type="main"> <s id="id.002146"><foreign lang="el">kai\ e)n toi=s oi)kodomikoi=s e)/rgois r(a|di/ws kinou=si mega/la <lb/>ba/rh: metafe/rousi ga\r a)po\ th=s au)th=s troxilai/as <lb/>e)f' e(te/ran, kai\ pa/lin a)p' e)kei/nhs ei)s o)/nous kai\ moxlou/s: <lb/>tou=to de\ tau)to/n e)sti, tw=| poiei=n polla\s troxile/as.</foreign></s> </p> <p type="main"> <s id="id.002147">Atque in ar­<lb/>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="cõpo­ner&etilde;t">compo­<lb/>nerent</expan> trochleas. </s> </p> <p type="head"> <s id="id.002148">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002149">Atque in architect.] <emph type="italics"/>Vt funis <lb/>facilius trahatur in magnis ponde­<lb/>ribus dimouendis ergata, aut &longs;ucula adhibetur ad tigna, vt & rota <lb/>& collopes. </s> <s id="id.002150">quæ eò facilius trahunt, quò longiores fuerint. </s> <s id="id.002151">Atque<emph.end type="italics"/><pb xlink:href="035/01/179.jpg" 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. </s> <s id="id.002152"><expan abbr="Quandoquid&etilde;">Quandoquidem</expan> cum materia ad <lb/>vectem, cuius longitudo vnius &longs;tadij 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;tadij vnius. </s> <s id="id.002153">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 X i&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/>Romani nominis 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. </s> <s id="id.002154">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 id="id.002155"><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. </s> <s id="id.002156">Varia e&longs;t obeli&longs;corum <lb/>materia, forma, & altitudo. </s> <s id="id.002157">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 alijs obeli&longs;cis frequens e&longs;t, per has regibus Ægypti <lb/>&longs;uas res ge&longs;tas memoriæ 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 epitaphij <lb/>ordinem dige&longs;tæ ac di&longs;tributæ legebantur. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/180.jpg" pagenum="140" /> <p type="main"> <s id="id.002158">Diuo Cæ&longs;ari Diui Iulij. </s> <s id="id.002159">F. Augu&longs;to: Ti.Cæ&longs;ari Diui Augu&longs;ti. </s> </p> <p type="main"> <s id="id.002160">F. Augu&longs;to &longs;acrum. </s> </p> <p type="main"> <s id="id.002162"><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 alijs 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="el">a)dunami/an</foreign>: <emph type="italics"/>aut ob &longs;umptuum magnitudinem ab ag­<lb/>greßione deterriti, nunquam attentarunt. </s> <s id="id.002164">Sanctitati vi&longs;um e&longs;t, vt in <lb/>media Vaticani 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/></s> <s id="id.002165">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="el">a)du/natos</foreign> <emph type="italics"/>iudicabatur, adhibita &longs;unt, dicam, vt ex qua­<lb/>dam epistola familiari Roma in Hi&longs;paniam ad P.Velleium 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 id="id.002166"><emph type="italics"/>Primum obeli&longs;cus validi&longs;simis octo columnis per latera circum­<lb/>uallatus e&longs;t, hæ concathenatæ, atque alijs &longs;uccre&longs;centibus & conne­<lb/>xis apicem obeli&longs;ci ad &longs;ex palmos præcellebant. </s> <s id="id.002167">His totidem fa&longs;tigia <emph.end type="italics"/><pb xlink:href="035/01/181.jpg" 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 & inflexionibus pro­<lb/>&longs;pectum. </s> <s id="id.002168">Tota hæc machina validi&longs;simis laminis, ferrei&longs;que clauis à <lb/>vertice ad calcem religata, plurimis & retinaculis, & ductarijs fu­<lb/>nibus vndequaque &longs;uffulta. </s> <s id="id.002169">Quadraginta trochleæ à totidem ergatis <lb/>mouendæ fa&longs;tigijs dictis alligatæ erant. </s> <s id="id.002170">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. </s> <s id="id.002171">Præfecti ad &longs;ignum tubæ <lb/>vrgebant molitionem, cymbali &longs;i&longs;tebant. </s> <s id="id.002172">Vectes 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. </s> <s id="id.002173">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. </s> <s id="id.002174">Tum deinde a&longs;&longs;eri­<lb/>bus ac cylindris, cubi quidam, quibus in&longs;idebat, dimoti, & quædam <lb/>traha &longs;uppo&longs;ita. </s> <s id="id.002175">Hoc facto, quæ prima ad auellendum molitio acer­<lb/>rima fuit, &longs;u&longs;tenta tamen magnum ad reliquas aggrediendas adiecit <lb/>animum. </s> <s id="id.002176">Itaque ergatæ, trabes, funes ductarij, 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. </s> <s id="id.002177">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. </s> <s id="id.002178">Atque hæc &longs;ecun­<lb/>da molitio fuit. </s> <s id="id.002179">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, breuius quidem, quam cogitari pote&longs;t, <lb/>pertracta e&longs;t. </s> <s id="id.002180">Atque hæc tertia molitio fuit. </s> <s id="id.002181">po&longs;tquam ad aliquot <lb/>dies, ne funes nimio calore conflagrarent, ob motum, & aëris æ&longs;tuo­<lb/>&longs;am tunc temporis 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>. </s> <s id="id.002182">Reliquæ à cu&longs;pide ad medium <emph.end type="italics"/><pb xlink:href="035/01/182.jpg" pagenum="142" /><emph type="italics"/>religatum erexerunt, atque tandem quadraginta &longs;eptem ni&longs;ibus &longs;te­<lb/>tit moles. </s> <s id="id.002183">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. </s> <s id="id.002184">Hæc quarta <lb/>& quinta &longs;unt molitio. </s> <s id="id.002185">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. </s> <s id="id.002186">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 id="id.002187"><emph type="italics"/>Itaque quod pri&longs;cis illis naturæ miraculis quæ à Leone decimo ad <lb/>Paulum III. orbis tulit, desperatum planè opus <expan abbr="iudicatū">iudicatum</expan> erat. </s> <s id="id.002188">Id <expan abbr="nūc">nunc</expan> <lb/>Sixti V. Pontificis cura & magnificentia, Dominici Fontanæ ope­<lb/>ra & indu&longs;tria, &<emph.end type="italics"/> <foreign lang="el">tw=n 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. </s> <s id="id.002190">Area vero Vaticani 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 id="id.002191">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 id="id.002192">Ænea &longs;erpentis Mo&longs;es &longs;imulachra &longs;acerdos <lb/>Extulit, ægrotis vt medicina foret</s> </p> <p type="main"> <s id="id.002193">Nunc alter Mo&longs;es obeli&longs;ci in vertice Sixtus <lb/>Erigit ægrotis ærea &longs;igna Crucis</s> </p> <p type="main"> <s id="id.002194">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 id="id.002195"><emph type="italics"/>Gulielmus Blancus Albien&longs;i. I. C. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/183.jpg" pagenum="143" /> <figure id="id.035.01.183.1.jpg" xlink:href="035/01/183/1.jpg"/> <p type="caption"> <s id="id.002197">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 id="id.002198"><emph type="italics"/>Faciata à leuante. <emph.end type="italics"/></s> </p> <p type="caption"> <s id="id.002199">Ecce Crux Domini <lb/>fugite partes aduer&longs;æ <lb/>vincit leo de Tribu <lb/>Iuda. </s> </p> <p type="caption"> <s id="id.002200"><emph type="italics"/>Faciata à Tramontana. <emph.end type="italics"/></s> </p> <p type="caption"> <s id="id.002201">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 id="id.002202">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 id="id.002204"><emph type="italics"/>Faciata in ver&longs;o pietro. <emph.end type="italics"/></s> </p> <p type="caption"> <s id="id.002205">Chri&longs;tus vincit, <lb/>Chri&longs;tus regnat, <lb/>Chri&longs;tus imperat, <lb/>Chri&longs;tus ab omni malo <lb/>plebem &longs;uam defendat. </s> </p> <p type="caption"> <s id="id.002209"><emph type="italics"/>Della faciata à mezzo giorne. <emph.end type="italics"/></s> </p> <p type="caption"> <s id="id.002210">Sixtus V. Pont. Max. obeli <lb/>vaticanum, <lb/>di&longs;. gentium. <lb/></s> <s id="id.002212">Impio cultu dicatum ad Apo&longs;tolo­ <lb/>rum limina opero&longs;o labore <lb/></s> <s>Tran&longs;tulit. </s> <s id="id.002213">Ann. M.D. LXXXV. Pont. II. </s> </p> </subchap1> </chap> <pb xlink:href="035/01/184.jpg" pagenum="144" /> <chap> <subchap1> <p type="main"> <s id="id.002214">20. <foreign lang="el">*dia\ ti/ tupto/menos pe/le­<lb/>kus diasxi/zei, pie/zwn de\ <lb/>ou)k e)/ti.</foreign></s> </p> <p type="main"> <s id="id.002215">20. Cur &longs;ecuris feriens di­<lb/>uidit: premens vero non <lb/>item. </s> </p> <p type="main"> <s id="id.002216"><foreign lang="el">*dia\ ti/, e)a\n me/n tis e)piqh=| e)pi\ to\ cu/lon pe/lekun me/gan, <lb/>kai\ forti/on me/ga e)p' au)tw=|, ou) diairei= to\ cu/lon, o(/ kai\ <lb/>lo/gou a)/cion: e)a\n de\ a)/ras to\n pe/leku/n tis pata/ch|, au)to\ <lb/>diasxi/zei, e)/latton ba/ros e)/xontos tou= tuptome/nou polu\ ma=llon, <lb/>h)\ tou= e)pikeime/nou kai\ piezou=ntos; </foreign></s> <s id="g0131902"><foreign lang="el">h)\ dio/ti pa/nta th=| kinh/sei <lb/>e)rga/zetai, kai\ to\ baru\ th\n tou= ba/rous ki/nhsin lamba/nei <lb/>ma=llon kinou/menon h)\ h)remou=n; </foreign></s> <s id="g0131903"><foreign lang="el">e)pikei/menon ou)=n ou) kinei=tai th\n <lb/>tou= ba/rous ki/nhsin.</foreign></s> <s id="g0131903a"><foreign lang="el">fero/menon de\, tau/thn te kai\ th\n tou= <lb/>tu/ptontos.</foreign></s> </p> <p type="main"> <s id="id.002217">Cur &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. </s> <s id="id.002218">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. </s> <s id="id.002219">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 id="id.002220">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002221">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. </s> <s id="id.002222">Prior <lb/>&longs;umptus e&longs;t è communi &longs;ententia phy&longs;icorum a&longs;&longs;erentium, omnia <lb/>motione fieri. </s> <s id="id.002223">Syllogi&longs;mus igitur &longs;ic e&longs;t. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002224"><emph type="italics"/>Cum omnia motione fiant, proinde & &longs;ectio, quod duplici mo­<lb/>tione commotum erit, magis mouebit: quam id, quod vna. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002225"><emph type="italics"/>Sed graue commotum, vt magna &longs;ecuris feriens, duplici <lb/>motione mouetur, vna grauitatis propriæ: altera percu­<lb/>tientis. </s> <s id="id.002226">Graue autem impo&longs;itum vna tantum mouetur, <lb/>nempe grauitatis propriæ. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/185.jpg" pagenum="145" /> <p type="main"> <s id="id.002227"><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 id="id.002228">Motione grauitatis.] <foreign lang="el">ki/nhsis tou= ba/rous</foreign> <emph type="italics"/>e&longs;t motus cuique <lb/>graui occultus inhærens. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002229"><foreign lang="el">e)/ti de\ kai\ gi/netai sfh\n o( pe/lekus: o( de\ sfh\n <lb/>mikro\s w)\n, mega/la dii/+sthsi, dia\ to\ ei)=nai e)k du/o moxlw=n <lb/>e)nanti/ws sugkeime/nwn.</foreign></s> </p> <p type="main"> <s id="id.002230">Præterea &longs;ecuris fit cu­<lb/>neus. </s> <s id="id.002231">Cuneus <expan abbr="aut&etilde;">autem</expan> paruus <lb/><expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan> magna diuidit. </s> <s id="id.002232">quia <lb/>ex duobus vectibus con&longs;ti­<lb/>tutus e&longs;t contrario modo <lb/>collocatis. </s> </p> <p type="head"> <s id="id.002233">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002234">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. </s> <s id="id.002235">Comprehendetur hoc &longs;yl­<lb/>logi&longs;mo. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002236"><emph type="italics"/>Cuneus paruus cum &longs;it, magna diuidit. ( ex anteced. )<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002237"><emph type="italics"/>Securis feriens e&longs;t cuneus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002238"><emph type="italics"/>Ergo &longs;ecuris feriens magna diuidet. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002239"><emph type="italics"/>Sed hic obijci pote&longs;t, quod &longs;ecuris impo&longs;ita etiam e&longs;t cuneus. </s> <s id="id.002240">Et ita <lb/>e&longs;t, &longs;ed non actu. </s> <s id="id.002241">Quia opus e&longs;t malleo percutiente, tanquam motore <lb/>vectium. </s> <s id="id.002242">Securis autem feriens e&longs;t cuneus annexus malleo, & ideo <lb/>actu cuneus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002243"><emph type="italics"/>Cardanus propo&longs;itum problema aliter &longs;oluit, cau&longs;amque putat. <lb/></s> <s id="id.002244">quia aër non pote&longs;t in ictu effugere. </s> <s id="id.002245">quanquam enim acuta cu&longs;pide &longs;it <lb/>&longs;ecuris, momento tamen tam paruo temporis effugere nequit. </s> <s id="id.002246">Ne igi­<lb/>tur nimis den&longs;etur, cogitur in poros ingredi &longs;ubiecti ligni, at que cu­<lb/>nei vice diuidere illud. </s> <s id="id.002247">Indicio e&longs;t, inquit, quod paulo tardior ictus <emph.end type="italics"/><lb/><arrow.to.target n="marg34"/><lb/><emph type="italics"/>maximum in diuidendo di&longs;crimen adfert dilabente aëre. </s> <s id="id.002248">Solutionem <lb/>hanc reprehendit Scaliger, con&longs;entitque cum Ari&longs;totele motum mo­<emph.end type="italics"/><lb/><arrow.to.target n="marg35"/><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. </s> <s id="id.002249">Quot pondo proportionem habeat pugnus ho­<lb/>minis ferientis, cum &longs;eip&longs;o non feriente comparatus. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/186.jpg" pagenum="146" /> <p type="margin"> <s id="id.002250"><margin.target id="marg34"/>Lib. 17. de <lb/>&longs;ubt. </s> </p> <p type="margin"> <s id="id.002251"><margin.target id="marg35"/>Exerc. 331. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002252">21. <foreign lang="el">*peri\ fala/ggwn.</foreign></s> </p> <p type="main"> <s id="id.002253">21. De &longs;tateris. </s> </p> <p type="main"> <s id="id.002254"><foreign lang="el">*dia\ ti/ ai( fa/lagges ta\ kre/a i(sta=sin a)po\ mikrou= a)rth/matos <lb/>mega/la ba/rh, tou= o(/lou h(mizugi/ou o)/ntos; ou(= me\n ga\r <lb/>to\ ba/ros e)nti/qetai, kath/rthtai mo/non h( pla/stigc, e)pi\ qa/teron <lb/>de\ h( fa/lagc e)sti\ mo/non.</foreign></s> <s id="g0132002"><foreign lang="el">h)\ o(/ti a(/ma sumbai/nei zugo\n <lb/>kai\ moxlo\n ei)=nai th\n fa/lagga; zugo\n me\n ga\r, h(=| <lb/>tw=n sparti/wn e(/kaston gi/netai to\ ke/ntron th=s fa/laggos.</foreign></s> <s id="g0132002a"><foreign lang="el">to\ <lb/>me\n ou)=n e)pi\ qa/tera e)/xei pla/stigga, to\ de\ e)pi\ qa/tera, a)nti\ <lb/>th=s pla/stiggos to\ sfai/rwma, o(\ tw=| zugw=| pro/skeitai, w(/sper <lb/>ei)/ tis th\n e(te/ran pla/stigga, kai\ to\n staqmo\n, e)piqei/h e)pi\ to\ <lb/>a)/kron th=s pla/stiggos: dh=lon ga\r, o(/ti e(/lkei tosou=ton ba/ros <lb/>e)n th=| e(te/ra| kei/menon pla/stiggi.</foreign></s> <s id="g0132004"><foreign lang="el">o(/pws de\ to\ e(\n zugo\n polla\ <lb/>h)=| zuga/, toiau=ta ta\ sparti/a polla\ e)/gkeitai e)n tw=| toiou/tw| <lb/>zugw=|, w(=n e(ka/ston to\ e)pi\ ta/de e)pi\ to\ sfai/rwma to\ h(/misu <lb/>th=s fa/laggo/s e)sti.</foreign></s> </p> <p type="main"> <s id="id.002255">Cur &longs;tateræ paruo æqui­<lb/>pondio carnium magna <lb/>pondera expendunt, cum <lb/>totæ dimidia &longs;int libra. </s> <s id="id.002256">Vbi <lb/>enim pondus apponitur, <lb/>appen&longs;a e&longs;t duntaxat lanx. <lb/></s> <s id="id.002257">Ex altera vero parte &longs;olum <lb/>e&longs;t &longs;tateræ &longs;capus. </s> <s id="id.002258">An quia <lb/>contingit &longs;tateram &longs;imul <lb/>e&longs;&longs;e libram & vectem. </s> <s id="id.002259">Li­<lb/>bra <expan abbr="quid&etilde;">quidem</expan> e&longs;t, vbi vnaquæ­<lb/>que an&longs;arum fit centrum <lb/>&longs;tateræ. </s> <s id="id.002260">Igitur in alter a par­<lb/>te habet lancem: in altera <lb/>pro lance æquipondium, <lb/>quod libræ incumbit. <lb/></s> <s id="id.002261">Quemadmodum &longs;i quis al­<lb/>teram lancem & pondus <lb/>in eius &longs;ummitate impo­<lb/>neret. </s> <s id="id.002262">Clarum enim e&longs;t, <lb/>quod hoc pondus in altera <lb/>lance &longs;itum trahit. </s> <s id="id.002263">Vt au­<lb/>tem vna libra multæ libræ <lb/>&longs;int in tali libra, multæ an&longs;&etail; <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 id="id.002264">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002265">De &longs;tateris.] <foreign lang="el">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 xlink:href="035/01/187.jpg" pagenum="147" /><emph type="italics"/>&longs;ignificat libræ genus, quod trutina, ab alijs &longs;tatera appellatur. </s> <s id="id.002266">Huius <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="id.035.01.187.1.jpg" xlink:href="035/01/187/1.jpg"/><lb/><emph type="italics"/><expan abbr="æquipõdium">æquipondium</expan> <lb/>Græcis di­<lb/>ctum<emph.end type="italics"/> <foreign lang="el">sfai/­<lb/>rwma</foreign> <emph type="italics"/>no&longs;tris <lb/>Marcum vel <lb/><expan abbr="Romanũ">Romanum</expan>. </s> <s id="id.002267">Vi<lb/>truuius dixit inuentam fui&longs;&longs;e &longs;tateram, vt ab iniquitate iu&longs;tis mori­<lb/>bus hominum vita vindicetur. </s> <s id="id.002268">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/></s> <s id="id.002269">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/></s> <s id="id.002270">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. </s> <s id="id.002271">In &longs;tateris autem quicquid appenderis &longs;eu magnum, &longs;eu par­<lb/>uum vnico pondere, hoc e&longs;t æquipondio: distinctione tamen puncto­<lb/>rum in &longs;capo examinatur. </s> <s id="id.002272">Id enim 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. </s> <s id="id.002273">Nam velut aliqua manus va­<lb/>lida longiorem &longs;tateræ &longs;capum deprimit. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002274">Cur &longs;tateræ.] <emph type="italics"/>Problema e&longs;t de &longs;tatera, quæ paruo æquipondio <lb/>magna appendit pondera. </s> <s id="id.002275">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. </s> <s id="id.002276">Rationi igitur <lb/>con&longs;entaneum e&longs;tne tanta pendat, quanta libra integra. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002277">An quia contingit.] <emph type="italics"/>Solutio problematis petitur ex libra, & <lb/>vecte, ex libra dupliciter. </s> <s id="id.002278">Syllogi&longs;mus prior &longs;ic erit. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002279"><emph type="italics"/>Libra expendit magna pondera. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002280"><emph type="italics"/>Statera e&longs;t libra, vt in cuius vna parte vna e&longs;t lanx, in altera <lb/>vice alterius lancis, e&longs;t æquipondium, quod pro &longs;ua grauitate <lb/>deprimit &longs;capum, & facit æquilibrium, & extremum an&longs;æ <lb/>e&longs;t centrum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002281"><emph type="italics"/>Ergo & &longs;tatera magna expendet pondera. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/188.jpg" pagenum="148" /> <p type="main"> <s id="id.002282">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 id="id.002283"><emph type="italics"/>Multæ &longs;imul libræ magna expendunt pondera. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002284"><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 id="id.002285"><emph type="italics"/>Ergo &longs;tatera magna expendet pondera. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002286"><emph type="italics"/>Statera certe multæ &longs;unt libræ actu & pote&longs;tate. </s> <s id="id.002287">Et primum actu <lb/>cum an&longs;æ ( &longs;ic enim<emph.end type="italics"/> <foreign lang="el">ta\ spa/rtia</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="id.035.01.188.1.jpg" xlink:href="035/01/188/1.jpg"/><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. </s> <s id="id.002288">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. </s> <s id="id.002289">Deinde pote&longs;tate plures &longs;unt, cum an&longs;a vna e&longs;t, &longs;ed mi­<lb/>nimè fixa, verum libero modo propius A, modo remotius colloca­<lb/>tur. </s> <s id="id.002290">Semper autem in aliquo puncto inter A & B intermedio. <lb/></s> <s id="id.002291">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. </s> <s id="id.002292">Hinc <lb/>elicitur pulchra regula è qua po&longs;tea ferè omnia, quæ ad &longs;tateræ ratio­<lb/>nem pertinent, deducuntur. </s> <s id="id.002293">quæ e&longs;t eiu&longs;modi. </s> <s id="id.002294">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. </s> <s id="id.002295">Vt e&longs;to <lb/>&longs;capus A B duodecim vnciarum, & pars A F <expan abbr="duarũ">duarum</expan>: huius partis <lb/>duplum e&longs;t 4. & reliquum 8. </s> <s>Quemadmodum ergo 4. ad 8. &longs;ic &longs;ca­<lb/>pus rotus id e&longs;t 12. erit ad pondus, quod per regulam trium inuenie­<lb/>tur e&longs;&longs;e 4. vnciarum. </s> <s id="id.002296">Rur&longs;us &longs;it an&longs;a in D & A D &longs;it vna vn­<lb/>cia. </s> <s id="id.002297">Huius duplum e&longs;t 2. </s> <s>Reliquum e&longs;t 10. </s> <s>Vt igitur 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 xlink:href="035/01/189.jpg" pagenum="149" />60. <emph type="italics"/>vnciarum. </s> <s id="id.002298">Vbi notandum lancem in hoc numero pro &longs;uo pon­<lb/>dere includi. </s> <s id="id.002299">Notandum etiam pondus impo&longs;itum lanci e&longs;&longs;e perinde <lb/>atque &longs;i in puncto A imponeretur. </s> <s id="id.002300">Sed de his qui multò plura vide­<lb/>re volet, videat apud Cardanum lib. 1. de &longs;ubtilitate. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002301"><foreign lang="el">kai\ o( staqmo\s di' i)/sou tw=n a)p' a)llh/lwn <lb/>tw=n sparti/wn kinoume/nwn, w(/ste summetrei=sqai po/son ba/ros<lb/> e(/lkei to\ e)n th=| pla/stiggi kei/menon, w(/ste ginw/skein o(/tan <lb/>o)rqh\ h( fa/lagc h)=|, a)po\ poi/ou spa/rtou po/son ba/ros e)/xei h( <lb/>pla/stigc, kaqa/per ei)/rhtai.</foreign></s> <s id="g0132005"><foreign lang="el">o(/lws me/n e)sti tou=to zugo/n, e)/xon <lb/>mi/an me\n pla/stigga, e)n h(=| i(/statai to\ ba/ros, th\n d' e(te/ran, <lb/>e)n h(=| o( staqmo\s e)n th=| fa/laggi.</foreign></s> <s id="g0132006"><foreign lang="el">dio\ sfai/rwma/ e)stin h( <lb/>fa/lagc e)pi\ qa/teron.</foreign></s> <s id="g0132006a"><foreign lang="el">toiou=ton de\ o)\n, polla\ zuga/ e)sti, kai\ <lb/>tosau=ta, o(/sa pe/r e)sti ta\ sparti/a.</foreign></s> </p> <p type="main"> <s id="id.002302">Et æquipondium ab an­<lb/>&longs;ulis inuicem commotis, vt <lb/>commetiatur quantum &longs;it <lb/>pondus, trahit id, quod e&longs;t <lb/>in lance po&longs;itum. </s> <s id="id.002303"><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. </s> <s id="id.002304">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. </s> <s id="id.002305">Propterea altera pars <lb/>&longs;tateræ e&longs;t æquipondium. <lb/></s> <s id="id.002306">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 id="id.002307">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002308">Et æquipondium.] <emph type="italics"/>Hic textus interiectus quidem e&longs;&longs;e vide­<lb/>tur, non ita tamen inutilis, vt totus reijciendus &longs;it, quod aliquis <lb/>interpres fecit. </s> <s id="id.002309">Indicat enim modum, quo cogno&longs;catur <expan abbr="põderationis">ponderationis</expan> <lb/>æquilibrium. </s> <s id="id.002310">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 horizontis. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002311"><foreign lang="el">ai)ei\ de\ to\ e)ggu/teron <lb/>sparti/on th=s pla/stiggos kai\ tou= i(stame/nou ba/rous, mei=zon e(/lkei <lb/>ba/ros, dia\ to\ gi/nesqai th\n me\n fa/lagga pa=san moxlo\n <lb/>a)nestramme/non.</foreign></s> <s id="g0132007a"><foreign lang="el">u(pomo/xlion me\n ga\r to\ sparti/on <lb/>e(/kaston a)/nwqen o)/n, to\ de\ ba/ros to\ e)no\n e)n th=| pla/stiggi.</foreign></s> <s id="g0132008"><foreign lang="el"><lb/>o(/sw| d' a)\n makro/teron h)=| to\ mh=kos tou= moxlou= tou= a)po\ tou= <lb/>u(pomoxli/ou, tosou/tw| e)kei= me\n r(a=|on kinei=.</foreign></s> <s id="g0132008a"><foreign lang="el">e)ntau=qa de\ sh/kwma <lb/>poiei=, kai\ i(/sthsi to\ pro\s to\ sfai/rwma ba/ros th=s <lb/>fa/laggos.</foreign></s> </p> <p type="main"> <s id="id.002312">Semper autem an&longs;a pro­<lb/>pinquior lanci, ponderan­<lb/>doque oneri, trahit maius <lb/>pondus. </s> <s id="id.002313">quia &longs;tatera effici­<pb xlink:href="035/01/190.jpg" pagenum="150" />tur vectis inuer&longs;us. </s> <s id="id.002315">E&longs;t enim <lb/>an&longs;a quælibet &longs;upernè exi­<lb/>&longs;tens hypomochlium. </s> <s id="id.002316">Et <lb/>pondus id quod e&longs;t in lan­<lb/>ce. </s> <s id="id.002317">Quantò autem longi­<lb/>tudo vectis maior fuerit ab <lb/>hypomochlio: tantò ibi fa­<lb/>cilius mouet. </s> <s id="id.002318">Hîc autem <lb/>&longs;acoma facit & ponderat <lb/>ad æquipondium pondus <lb/>&longs;tateræ. </s> </p> <p type="head"> <s id="id.002319">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002320">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 id="id.002321"><emph type="italics"/>Statera e&longs;t omnino libra. <lb/></s> <s id="id.002322">& <lb/>Statera multæ &longs;unt libræ. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002323">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. </s> <s id="id.002324">Ratio e&longs;t quia vectis e&longs;t, & &longs;ic <lb/>concluditur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002325"><emph type="italics"/>Quò vectis habet hypomochlium propius ponderi mouendo, eò <lb/>maius mouet. </s> <s id="id.002326">Reliquum enim ab hypomochlio longius e&longs;t. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002327"><emph type="italics"/>Statera e&longs;t vectis inuer&longs;us. </s> <s id="id.002328">Nam an&longs;a e&longs;t hypomochlium &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 id="id.002329"><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 id="id.002330">Hîc autem &longs;acoma.] <emph type="italics"/>Hic locus è Græco in Latinum verbo <lb/>ad verbum ver&longs;us difficilem, ne dicam nullum &longs;en&longs;um habet. </s> <s id="id.002331">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 notas 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. </s> <s id="id.002332">E&longs;t enim<emph.end type="italics"/><pb xlink:href="035/01/191.jpg" pagenum="151" /><foreign lang="el">sh/kwma,</foreign> <emph type="italics"/>vt annotauit Budæus in Pandect. quod apponitur in libra <lb/>ad æquilibrium faciendum. </s> <s id="id.002333">Vnde & apud Vitruuium legimus re­<emph.end type="italics"/><lb/><arrow.to.target n="marg36"/><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. </s> <s id="id.002334">Cæterum <lb/>quam rationem habeat æquipondium ad &longs;e&longs;e pro varijs inter&longs;titüs, <lb/>quibus remouetur ab an&longs;a, colligi pote&longs;t ex Vbaldo per corollarium <lb/>quod deduxit è prop. 6. tractatus de lib. in Mech. quod tale e&longs;t. </s> <s id="id.002335">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. </s> <s id="id.002336">Et æquipondij 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"/><lb/><emph type="italics"/><expan abbr="motion&etilde;">motionem</expan>. <lb/> </s> <emph.end type="italics"/> <lb/> <figure id="id.035.01.191.1.jpg" xlink:href="035/01/191/1.jpg"/> <s><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. </s> <s>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 id="id.002337"><margin.target id="marg36"/>Cap. 3. lib. <margin.target id="marg37"/>65. c. Arich</s> </p> <p type="main"> <s id="id.002338"><emph type="italics"/>Et quidem &longs;tateræ ratio demon&longs;trari pote&longs;t. </s> <s id="id.002339">Sit &longs;tateræ &longs;capus <lb/>H B cu­<emph.end type="italics"/><lb/><figure id="id.035.01.191.2.jpg" xlink:href="035/01/191/2.jpg"/><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="põ­dus">pon­<lb/>dus</expan> D, <lb/>quod æquiponderet æquipondio E in F appen&longs;o. </s> <s id="id.002340">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 id="id.002342"><emph type="italics"/>Dico grauitatem ponderis D ad grauitatem ponderis G ita e&longs;&longs;e <lb/>vt C F ad C B. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/192.jpg" pagenum="152" /> <p type="head"> <s id="id.002343">Demon&longs;t. </s> </p> <p type="main"> <s id="id.002344"><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. </s> <s>vt grauitas ponderis D ad grauitatem ponderis G: <lb/>ita grauitas ip&longs;ius E ex F ad ip&longs;um E ex B. </s> <s id="id.002345">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 Vbaldus prop. 6. tract. delib. </s> <s>vt igitur <lb/>grauitas ponderis D ad pondus G: ita e&longs;t C F ad C B. </s> <s id="id.002346">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. </s> <s id="id.002347">Exempli gratia &longs;it di&longs;tantia C B tripla ad <lb/>C F, erit pondus G triplum ponderis D. </s> <s>quod demon&longs;trare oportebat. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002348">22. <foreign lang="el">*peri\ o)donta/gras.</foreign></s> </p> <p type="main"> <s id="id.002349">22. De dentiduco. </s> </p> <p type="main"> <s id="id.002350"><foreign lang="el">*dia\ ti/ oi( i)atroi\ r(a=|on e)cairou=si tou\s o)do/ntas proslamba/nontes <lb/>ba/ros th\n o)donta/gran, h)\ th=| xeiri\ mo/nh| yilh=|; </foreign></s> <s id="g0132102"><foreign lang="el"><lb/>po/teron dia\ to\ ma=llon e)colisqai/nein dia\ th=s xeiro\s to\n <lb/>o)do/nta, h)\ e)k th=s o)donta/gras; </foreign></s> <s id="g0132102a"><foreign lang="el">h)\ ma=llon o)lisqai/nei th=s <lb/>xeiro\s o( si/dhros, kai\ ou) perilamba/nei au)to\n ku/klw|: malqakh\ <lb/>ga\r ou)=sa h( sa\rc tw=n daktu/lwn, kai\ prosme/nei ma=llon <lb/>kai\ periarmo/ttei.</foreign></s> <s id="g0132103"><foreign lang="el">a)ll' o(/ti h( o)donta/gra du/o moxloi/ <lb/>ei)sin a)ntikei/menoi, e(\n to\ u(pomo/xlion e)/xontes th\n su/nayin <lb/>th=s qermastri/dos.</foreign></s> <s id="g0132104"><foreign lang="el">tou= r(a=|on ou)=n kinh=sai xrw=ntai tw=| o)rga/nw| <lb/>pro\s th\n e)cai/resin.</foreign></s> <s id="g0132105"><foreign lang="el">e)/stw ga\r th=s o)donta/gras to\ me\n e(/teron <lb/>a)/kron e)f' w(=| to\ *a, to\ de\ e(/teron to\ *b, o(\ e)cairei=.</foreign></s> <s id="g0132105a"><foreign lang="el">o( <lb/>de\ moxlo\s e)f' w(=| *a*q*z, o( de\ a)/llos moxlo\s e)f' w(=| *b<lb/>*g*e.</foreign></s> <s id="g0132105b"><foreign lang="el">u(pomo/xlion de\ to\ *q, e)f' ou(= h( su/nayis, o( de\ o)dou\s, <lb/> to\ ba/ros.</foreign></s> <s id="g0132106"><foreign lang="el">e(kate/rw| ou)=n tw=n *b, *z, kai\ a(/ma labw\n <lb/>kinei=: o(/tan de\ kinh/sh|, o)cei=le r(a=|on th=| xeiri\, h)\ tw=| <lb/>o)rga/nw|.</foreign></s> </p> <p type="main"> <s id="id.002351">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. </s> <s id="id.002352">Vtrum quia <lb/>dens magis manum præ­<lb/>terlabitur, quam dentidu­<lb/>cum? </s> <s id="id.002353">vel ferrum quidem <lb/>magis labitur manu, neque <lb/>ip&longs;um vndique <expan abbr="compreh&etilde;­dit">comprehen­<lb/>dit</expan>. </s> <s id="id.002354">E&longs;t enim digitorum <lb/>caro mollis, & adhæret ma­<lb/>gis, atque vndique con­<lb/>gruit. </s> <s id="id.002355">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. </s> <s id="id.002356">Igitur ad <expan abbr="ex&etilde;ptio­n&etilde;">exemptio­<lb/>nem</expan>, vt facilius <expan abbr="dimoueãt">dimoueant</expan>, hoc <lb/>vtuntur organo. </s> <s id="id.002357">Sit enim <pb xlink:href="035/01/193.jpg" pagenum="153" />dentiduci extremum alte­<lb/><figure id="id.035.01.193.1.jpg" xlink:href="035/01/193/1.jpg"/><lb/>rum <foreign lang="el">a,</foreign> alterum <foreign lang="el">b,</foreign> quod <lb/>eximit, vectis vero <foreign lang="el">a q z,</foreign><lb/>& alter vectis <foreign lang="el">b g e</foreign>: hypo­<lb/>mochlium verò <foreign lang="el">q</foreign> vbi e&longs;t <expan abbr="cõ­mi&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/></s> <s id="id.002358">Vtroque igitur extremo <foreign lang="el">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 id="id.002359">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002360">De dentiduco.] <foreign lang="el">o)donta/gran h)\ o)donta/gwgon</foreign> <emph type="italics"/>vertit Cælius <lb/>Aurelianus cap. 4. lib. 2. <emph.end type="italics"/> <foreign lang="el">xroniw=n</foreign> <emph type="italics"/>paßionum dentiducum: Cel­<lb/>&longs;us forficem, & generaliter forcipem. </s> <s id="id.002361">E&longs;t autem in&longs;trumentum, quo <lb/>dens eximitur. </s> <s id="id.002362">Corro&longs;us enim aut vehementer dolens præ&longs;cripto <lb/>medicorum eximi iubetur. </s> <s id="id.002363">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. </s> <s id="id.002364">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 id="id.002365">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 xlink:href="035/01/194.jpg" pagenum="154" /> <p type="main"> <s id="id.002366"><emph type="italics"/>Pondus adiectum ponderi non facilius mouet. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002367"><emph type="italics"/>Dentiducus e&longs;t pondus, & denti vt ponderi mouendo adij­<lb/>citur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002368"><emph type="italics"/>Non igitur facilius mouet. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002369">Vtrum quia dens.] <emph type="italics"/>Hîc continetur demon&longs;tratio problema­<lb/>tis. </s> <s id="id.002370">Vbi notandum dentem eximendum, vt melius eximatur, duo an­<lb/>te exemptionem po&longs;tulare, prius, vt firmè apprehendatur: alterum <lb/>vt validè dimoueatur. </s> <s id="id.002371">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. </s> <s id="id.002372">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>. </s> <s id="id.002373">quia ip&longs;e &longs;it vectis duplicatus. </s> <s id="id.002374">Ratio igitur &longs;ic concludetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002375"><emph type="italics"/>Pondus facilius vecte: quam manu &longs;ola mouetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002376"><emph type="italics"/>Dentiducus e&longs;t duo vectes &longs;ibi inuicem oppo&longs;iti. </s> <s id="id.002377">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 id="id.002378"><emph type="italics"/>Ergo dens dentiduco facilius: quam manu &longs;ola mouebitur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002379">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 id="id.002380">Quando verò emotus.] <emph type="italics"/>Factis ijs, quæ ante exemptionem <lb/>po&longs;tulabat fieri dens eximendus, vltimum quod e&longs;t exemptio melius <lb/>fieri à digitis: 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. </s> <s id="id.002381">Sed res dißimilis videbitur dili­<lb/>gentius attendenti. </s> <s id="id.002382">Nam in clauo eximendo iam emoto forceps ex <lb/>eminentiori &longs;ui parte vt<emph.end type="italics"/> <foreign lang="el">x</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="el">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. </s> <s id="id.002383">quia motus non fit &longs;ecundum rectam: 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. </s> <s id="id.002384">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 xlink:href="035/01/195.jpg" pagenum="155" /><emph type="italics"/>quaque factæ, vt antea 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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002385">23. <foreign lang="el">*peri\ tw=n o)pga/nwn a(\ poiou=si <lb/>pro\s to\ katagnu=nai ta\ <lb/>ka/rua.</foreign></s> </p> <p type="main"> <s id="id.002386">23. De in&longs;trumentis quæ <lb/>faciunt ad frangendum <lb/>nuces. </s> </p> <p type="main"> <s id="id.002387"><foreign lang="el">*dia\ ti/ ta\ ka/rua r(a|di/ws katagnu/ousin a)/neu plhgh=s e)n <lb/>toi=s o)rga/nois a(\ poiou=si pro\s to\ katagnu/nai au)ta/, pollh\ <lb/>ga\r a)fairei=tai i)sxu\s h( th=s fora=s kai\ bi/as. </foreign></s> <s id="g0132201a"><foreign lang="el">e)/ti de\ sklhrw=| <lb/>kai\ barei= sunqli/bwn, qa=tton a)\n kata/ch| h)\ culi/nw| kai\ kou/fw| <lb/>tw=| o)rga/nw|. </foreign></s> <s id="g0132201b"><foreign lang="el">h)\ dio/ti ou(/tws e)p' a)mfo/tera qli/betai u(po\ du/o <lb/>moxlw=n to\ ka/ruon, tw=| de\ moxlw=| r(a|di/ws diairei=tai ta\ <lb/>ba/rh; </foreign></s> <s id="g0132202"><foreign lang="el">to\ ga\r o)/rganon e)k du/o su/gkeitai moxlw=n, u(pomo/xlion <lb/>e)xo/ntwn to\ au)to\, th\n sunafh\n e)f' h(=s to\ *a.</foreign></s> <s id="g0132203"><foreign lang="el">w(/sper<lb/> ou)=n ei) h)=san e)kbeblhme/nai, au)tw=n kinoume/nwn ei)s ta\ tw=n <lb/>*g*d a)/kra, ai( *e*z sunh/gonto r(a|di/ws a)po\ mikra=s i)sxu/os. </foreign></s> <s id="g0132204"><foreign lang="el"><lb/>h(\n ou)=n e)n th=| plhgh=| to\ ba/ros e)poi/ei, tau/thn h( krei/ttwn tau/ths, <lb/>h( to\ *e*g kai\ *z*d moxloi\ o)/ntes poiou=si. </foreign></s> <s id="g0132204a"><foreign lang="el">th=| a)/rsei ga\r <lb/>ei)s tou)nanti/on ai)/rontai, kai\ qli/bontes katagnu/ousi to\ e)f' w(=| *k.</foreign></s> <s id="g0132205"><foreign lang="el"><lb/>di' au)to\ de\ tou=to kai\ o(/sw| a)\n e)ggu/teron h)=| th=s *a, to\ *a suntri/bhtai <lb/>qa=tton.</foreign></s> <s id="g0132205a"><foreign lang="el">o(/sw| ga\r a)\n plei=on a)pe/xh| tou= u(pomoxli/ou <lb/>o( moxlo/s, r(a=|on kinei= kai\ plei=on a)po\ th=s i)sxu/os th=s au)th=s.</foreign></s> <s id="g0132206"><foreign lang="el"><lb/>e)/stin ou)=n to\ me\n *a u(pomo/xlion, h( de\ *d*a*z moxlo\s, kai\ h( <lb/>*g*a, *e.</foreign></s> <s id="g0132207"><foreign lang="el">o(/sw| a)\n ou)=n to\ *k e)ggute/ron h)=| th=s gwni/as tou= *a, <lb/>tosou/tw| e)ggu/teron gi/netai th=s sunafh=s tou= *a. </foreign></s> <s id="g0132207a"><foreign lang="el">tou=to de/ e)sti <lb/>to\ u(pomo/xlion.</foreign></s> <s id="g0132208"><foreign lang="el">a)na/gkh toi/nun a)po\ th=s au)th=s i)sxu/os sunagou/shs <lb/>to\ *z, *e, ai)/resqai ple/on, w(/ste e)pei/ e)stin e)c e)nanti/as <lb/>h( a)/rsis, a)na/gkh qli/besqai ma=llon: to\ de\ ma=llon qlibo/menon, <lb/>kata/gnutai qa=tton.</foreign></s> </p> <p type="main"> <s id="id.002388">Cur facilius in nucifran­<lb/>gibulis nuces &longs;ine ictu <expan abbr="frã­gunt">fran­<lb/>gunt</expan>. </s> <s id="id.002389">Multa enim vis illa­<lb/>tionis & <expan abbr="viol&etilde;tiæ">violentiæ</expan> demitur. <lb/></s> <s id="id.002390">Præterea duro & graui <expan abbr="cõ­primens">con­<lb/>primens</expan> velocius fregerit: <lb/>quam ligneo & leui in&longs;tru­<lb/>mento. </s> <s id="id.002391">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;trumentum 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. </s> <s id="id.002392">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. </s> <s id="id.002393">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/></s> <s id="id.002394">Elatione enim in <expan abbr="aduersũ">aduersum</expan> <lb/>tollunt, & comprimentes <lb/>frangunt, quod e&longs;t vbi K. <lb/></s> <s id="id.002395">Ob id quantò ip&longs;i K fuerit <lb/>propior commi&longs;&longs;ura A tan­<lb/>tò citius conterit. </s> <s id="id.002396">Quantò <pb xlink:href="035/01/196.jpg" pagenum="156" />enim plus di&longs;titerit vectis <lb/>ab hypomochlio, tantò fa­<lb/>cilius ab eadem vi mouet. <lb/></s> <s id="id.002397">E&longs;t igitur A <expan abbr="hypomochliũ">hypomochlium</expan>, <lb/>& E A D vectis, vt & F A <lb/>C. </s> <s id="id.002398">Quantò igitur ip&longs;um K <lb/>propius fuerit angulo A, <lb/>tantò propius fit commi&longs;&longs;u­<lb/>ræ A. </s> <s id="id.002399">Hæc verò e&longs;t hypo­<lb/>mochlium. </s> <s id="id.002400">Nece&longs;&longs;e igitur <lb/>ab eadem vi coadducente <lb/>E, F plus extolli. </s> <s id="id.002401">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 id="id.002402">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002403">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="id.035.01.196.1.jpg" xlink:href="035/01/196/1.jpg"/><lb/><emph type="italics"/>di e&longs;t F A C E A B. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002404">Cur facilius.] <emph type="italics"/>Quæritur <lb/>cur nucifrangibulum ab&longs;que ictu <lb/>facillimè frangat nucem. </s> <s id="id.002405">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 id="id.002406">Multa enim vis.] <emph type="italics"/>Repugnantia e&longs;t ad augendam problematis <lb/>difficultatem &longs;ic,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002407"><emph type="italics"/>Quod vim adfert motioni, plus valet ad frangendum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002408"><emph type="italics"/>Ictus motioni vim adfert. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002409"><emph type="italics"/>Ictus igitur ad frangendum plus valet. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/197.jpg" pagenum="157" /> <p type="main"> <s id="id.002410">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. </s> <s id="id.002411">Cum tamen contra euenire deberet. </s> <s id="id.002412">Siquidem graue quod e&longs;t, <lb/>difficilius emoueatur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002413">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 id="id.002414"><emph type="italics"/>Valide comprimentia compre&longs;&longs;um frangunt. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002415"><emph type="italics"/>Nucifrangibulum validè nucem comprehen&longs;am comprimit. <lb/></s> <s id="id.002416">quia duplicatus e&longs;t vectis, vnum hypomochlium, vt in A <lb/>commi&longs;&longs;ura habentibus. </s> <s id="id.002417">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. </s> <s id="id.002418">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. </s> <s id="id.002419">Sic enim aliæ partes vectium ab ip&longs;o di&longs;tantes <lb/>maiorem rationem habebunt. </s> <s id="id.002420">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. </s> <s id="id.002421">Sæpè <lb/>enim ictum ob &longs;ui <expan abbr="rotũditatem">rotunditatem</expan> nux eludit. </s> <s id="id.002422">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="el">kat' 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 id="id.002423"><emph type="italics"/>Itaque nucifrangibulum nucem facile &longs;ine ictu franget. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002424">Quantò igitur.] <emph type="italics"/>Repetitio e&longs;t eiu&longs;dem &longs;uperflua. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002425">24. <foreign lang="el">*dia\ ti/ e)n tw=| r(o/mbw| e(ka/­<lb/>teron tw=n a)/krwn shmei/wn ou) <lb/>th\n i)/shn eu)qei=an die/rxetai.</foreign></s> </p> <p type="main"> <s id="id.002426">24. Cur in Rhombo <expan abbr="alterũ">alterum</expan> <lb/><expan abbr="pũctorum">punctorum</expan> extremorum <lb/>non æqualem rectam <lb/>tran&longs;it. </s> </p> <p type="main"> <s id="id.002427"><foreign lang="el">*dia\ ti/ ferome/nwn du/o fora\s e)n tw=| r(o/mbw| tw=n a)/krwn <lb/>shmei/wn a)mfote/rwn, ou) th\n i)/shn e(ka/teron au)tw=n eu)qei=an die/rxetai, <lb/>a)lla\ pollaplasi/an qa/teron; </foreign></s> <s id="g0132302"><foreign lang="el">o( au)to\s de\ lo/gos kai\ <lb/>dia\ ti/ to\ e)pi\ th=s pleura=s fero/menon e)la/ttw die/rxetai th=s <lb/>pleura\s. </foreign></s> <s id="g0132302a"><foreign lang="el">to\ me\n ga\r th\n e)la/ttw dia/metron, h( de\ th\n <lb/>pleura\n mei/zw, kai\ h( me\n mi/an, to\ de\ du/o fe/retai <lb/>fora/s.</foreign></s> <s id="g0132303"><foreign lang="el">fere/sqw ga\r e)pi\ th=s *a*b, to\ me\n *a pro\s to\ *b, to\ <lb/>de\ *b pro\s to\ *d, tw=| au)tw=| ta/xei: fere/sqw de\ kai\ h( *a*b <lb/>e)pi\ th=s *a*g, para\ th\n *g*d tw=| au)tw=| ta/xei tou/tois.</foreign></s> <s id="g0132304"><foreign lang="el">a)na/gkh <lb/>dh\ to\ me\n *a e)pi\ th=s *a*d diame/trou fe/resqai. </foreign></s> <s id="g0132304a"><foreign lang="el">to\ de\ *b e)pi\ <lb/>th=s *b*g, kai\ a(/ma dielhluqe/nai e(kate/ran, kai\ th\n *a*b th\n <lb/>*a*g pleura/n.</foreign></s> <s id="g0132304b"><foreign lang="el">kai\ th\n *b*d th\n *b*a.</foreign></s> <s id="g0132305"><foreign lang="el">e)nhne/xqw ga\r to\ me\n *a, th\n *a*e, h( de\ *a <lb/>*b, th\n *a*z, kai\ e)/stw e)kbeblhme/nh h( *z*h para\ th\n *a*b, <lb/>kai\ a)po\ tou= *e peplhrw/sqw.</foreign></s> <s id="g0132306"><foreign lang="el">o(/moion ou)=n gi/netai to\ paraplhrwqe\n <lb/>tw=| o(/lw|.</foreign></s> <s id="g0132307"><foreign lang="el">i)/sh a)/ra h( *a*z th=| *a*e: h( de\ *a*b th\n *a*z, <lb/>ei)/h a)\n e)nhnegme/nh. </foreign></s> <s id="g0132307a"><foreign lang="el">e)/stai a)/ra e)pi\ th=s diame/trou kata\ to\ *q.</foreign></s> <s id="g0132308"><foreign lang="el"><lb/>kai\ ai)ei\ de\ a)na/gkh au)to\ fe/resqai kata\ th\n dia/metron. <lb/></foreign></s> <s id="g0132308a"><foreign lang="el">kai\ a(/ma h( pleura\ h( *a*b, th\n pleura\n th\n *a*g di/eisi, <lb/>kai\ to\ *a th\n dia/metron di/eisi th\n *a*d.</foreign></s> <s id="g0132309"><foreign lang="el">o(moi/ws de\ deixqh/setai <lb/>kai\ to\ *b e)pi\ th=s *a*g diame/trou fero/menon. </foreign></s> <s id="g0132309a"><foreign lang="el">i)/sh <lb/>ga/r e)stin h( *b*e, th=| *b*h.</foreign></s> <s id="g0132310"><foreign lang="el">paraplhrwqe/ntos ou)=n a)po\ tou= *h, <lb/>o(/moio/n e)sti tw=| o(/lw| to\ e)nto/s: kai\ to\ *b e)pi\ th=s diame/trou <lb/>e)/stai kata\ th\n su/nayin tw=n pleurw=n, kai\ a(/ma di/eisin h(/<lb/> te pleura\ th\n pleura\n, kai\ to\ *b th\n *b*g dia/metron.</foreign></s> <s id="g0132311"><foreign lang="el"><lb/>a(/ma a)/ra kai\ to\ *a th\n pollaplasi/an th=s *b*g di/eisi, <lb/>kai\ h( pleura\ th\n e)la/ttona pleura\n tw=| au)tw=| ta/xei fero/mena, <lb/>kai\ h( pleura\ *b*d mei/zw pleura\n tou= *b*g dielh/luqe mi/an fora\n <lb/>ferome/nh.</foreign></s> <s id="g0132312"><foreign lang="el">o(/sw| ga\r a)\n o)cu/teros ge/nhtai o( r(o/mbos, h( <lb/>me\n dia/metros *a*g, h( e)la/ttwn gi/netai, h( de\ *a*d mei/zwn, h( de\ <lb/>pleura\ th=s *b*g mei/zwn.</foreign></s> </p> <p type="main"> <s id="id.002428">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. </s> <s id="id.002429">&longs;ed alte­<pb xlink:href="035/01/198.jpg" pagenum="158" /><arrow.to.target n="marg38"/><lb/>rum plus. </s> <s id="id.002430">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. </s> <s id="id.002431">Illud enim minorem <lb/>diametrum: hoc verò latus <lb/>maius, licet & hoc vna: illud <lb/>verò duabus feratur latio­<lb/>nibus. </s> <s id="id.002432">Feratur enim &longs;uper <foreign lang="el">a <lb/>b</foreign> <expan abbr="punctũ">punctum</expan> <expan abbr="quid&etilde;">quidem</expan> <foreign lang="el">a</foreign> ver&longs;us <foreign lang="el">b,</foreign><lb/>& <foreign lang="el">b</foreign> ver&longs;us <foreign lang="el">a</foreign> <expan abbr="ead&etilde;">eadem</expan> celerita­<lb/>te: feratur <expan abbr="etiã">etiam</expan> latus <foreign lang="el">a b</foreign> &longs;u­<lb/>per <foreign lang="el">a g</foreign> parallelum ip&longs;i <foreign lang="el">g d</foreign><lb/><expan abbr="ead&etilde;">eadem</expan> celeritate <expan abbr="cũ">cum</expan> his pun­<lb/>ctis. </s> <s id="id.002433">Nece&longs;&longs;e igitur <expan abbr="pũctum">punctum</expan> <lb/><expan abbr="quid&etilde;">quidem</expan> <foreign lang="el">a</foreign> per <expan abbr="diametrũ">diametrum</expan> <foreign lang="el">a d</foreign><lb/>ferri: <foreign lang="el">b</foreign> vero per <foreign lang="el">b g,</foreign> & &longs;i­<lb/>mul vtranque pertran&longs;ii&longs;&longs;e. <lb/></s> <s id="id.002434"><expan abbr="Tũ">Tum</expan> & latus <foreign lang="el">a b</foreign> ip&longs;um <foreign lang="el">a g. </foreign><lb/>Latum <expan abbr="quid&etilde;">quidem</expan> &longs;it <expan abbr="pũctum">punctum</expan> <foreign lang="el">a</foreign><lb/>per <expan abbr="lineã">lineam</expan> <foreign lang="el">a e,</foreign> & <foreign lang="el">a b</foreign> per <foreign lang="el">a z,</foreign><lb/>& &longs;it deducta <foreign lang="el">z h</foreign> parallela <lb/>ip&longs;i <foreign lang="el">a b,</foreign> & per <expan abbr="punctũ">punctum</expan> <foreign lang="el">e</foreign> <expan abbr="cõ­pleatur">com­<lb/>pleatur</expan>. </s> <s id="id.002435">Simile igitur fi<emph type="italics"/>t<emph.end type="italics"/> <expan abbr="cõ­pletum">com­<lb/>pletum</expan> toti parallelogram­<lb/>mo. </s> <s id="id.002436">Igitur æqualis e&longs;t <foreign lang="el">a z</foreign><lb/>ip&longs;i <foreign lang="el">a e: a b</foreign> vero latus <expan abbr="latũ">latum</expan> <lb/>erit per <foreign lang="el">a z. </foreign>Erit itaque in <lb/>diametro iuxta <foreign lang="el">q,</foreign> & &longs;emper <lb/>iuxta <expan abbr="diametrũ">diametrum</expan> ferri nece&longs;­<lb/>&longs;e e&longs;t. </s> <s id="id.002437">Et &longs;imul atque latus <lb/><foreign lang="el">a g</foreign> <expan abbr="etiã">etiam</expan> punctum <foreign lang="el">a</foreign> tran&longs;it <lb/><expan abbr="diametrũ">diametrum</expan> <foreign lang="el">a d. </foreign>Similiter ve­<lb/>rò demon&longs;trabitur etiam <foreign lang="el">b</foreign><lb/><expan abbr="latũ">latum</expan> e&longs;&longs;e per <expan abbr="diametrũ">diametrum</expan> <foreign lang="el">b g. </foreign><lb/>Æqualis enim e&longs;t linea <foreign lang="el">b e</foreign><lb/>ip&longs;i <foreign lang="el">b h. </foreign>Completum igitur <pb xlink:href="035/01/199.jpg" pagenum="159" />per punctum <foreign lang="el">h</foreign> intus <expan abbr="paral­lelogrammũ">paral­<lb/>lelogrammum</expan> &longs;imile e&longs;t toti, <lb/>& <foreign lang="el">b</foreign> erit in diametro iuxta <lb/><expan abbr="contactũ">contactum</expan> laterum. </s> <s id="id.002438">Et &longs;imul <lb/>atque latus pertran&longs;it latus <lb/>etiam ip&longs;um <foreign lang="el">b,</foreign> ip&longs;um <foreign lang="el">b g</foreign><lb/>diametrum. </s> <s id="id.002439">Simile igitur <lb/>ip&longs;um <foreign lang="el">a</foreign> ip&longs;am <foreign lang="el">a d</foreign> multò <lb/><expan abbr="maior&etilde;">maiorem</expan> ip&longs;a <foreign lang="el">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="el">b d</foreign> vna latione <lb/>motum pertran&longs;ijt lineam <lb/>maiorem: quam <foreign lang="el">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="el">b g</foreign> fit mi­<lb/>nor, <foreign lang="el">a d</foreign> vero maior, <expan abbr="tũ">tum</expan> & la­<lb/>tus <foreign lang="el">a b</foreign> maius quam <foreign lang="el">b g. </foreign></s> </p> <p type="margin"> <s id="id.002440"><margin.target id="marg38"/>Quidam le­<lb/>gunt <foreign lang="el">lo/gw</foreign><lb/>pro <foreign lang="el">ta/xei. </foreign></s> </p> <p type="head"> <s id="id.002441">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002442">Cvr amborum.] <emph type="italics"/>In hoc capite duo continentur problemata, <lb/><expan abbr="eorũque">eorumque</expan> &longs;olutiones. </s> <s id="id.002443">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;patij conficit, nempe id <lb/>quod ab acuto angulo di&longs;cedit, alterum minus, nempe. </s> <s id="id.002444">id quod ab <lb/>obtu&longs;o. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002445">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;patij conficiat: <expan abbr="quã">quam</expan> <lb/>latus &longs;uum. </s> <s id="id.002446">Vtrumque problema vt intelligatur &longs;ciendum e&longs;t e def. <lb/>32. lib. 1. Eucl. </s> <s id="id.002448">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. </s> <s id="id.002451"><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="el">a b d g,</foreign> <emph type="italics"/>cuius anguli oppo&longs;iti<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">d</foreign> <emph type="italics"/>&longs;int acuti:<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>vero<emph.end type="italics"/> <pb xlink:href="035/01/200.jpg" pagenum="160" /><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">g</foreign> <emph type="italics"/>obtu&longs;i. </s> <s id="id.002453">Concipiamus ergo<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>tan­<emph.end type="italics"/><lb/><figure id="id.035.01.200.1.jpg" xlink:href="035/01/200/1.jpg"/><lb/><emph type="italics"/>quam formicam ambulantem proprio <lb/>motu ver&longs;us<emph.end type="italics"/> <foreign lang="el">b,</foreign> <emph type="italics"/>vt &<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>proprio iti­<lb/>dem motu ver&longs;us<emph.end type="italics"/> <foreign lang="el">a. </foreign><emph type="italics"/></s> <s>Tum ip&longs;um<emph.end type="italics"/> <foreign lang="el">a b</foreign><lb/><emph type="italics"/>latus ver&longs;us<emph.end type="italics"/> <foreign lang="el">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="el">g d</foreign> <emph type="italics"/>quou&longs;que coniungatur ei. </s> <s id="id.002454">Ad <lb/>huius autem <expan abbr="motũ">motum</expan> moueri etiam<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ver­<lb/>&longs;us<emph.end type="italics"/> <foreign lang="el">g,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>ver&longs;us<emph.end type="italics"/> <foreign lang="el">d. </foreign><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">b</foreign><lb/><emph type="italics"/>mouebuntur duobus motibus, vno per &longs;e: <lb/>altero per accidens. </s> <s id="id.002455">Et po&longs;ito quod mo­<lb/>ueantur in Rhombo. </s> <s id="id.002456">Id e&longs;t quod motus <lb/>illi &longs;int in ratione laterum quibus Rhombus continetur. </s> <s id="id.002457">E&longs;t autem <lb/>i&longs;ta certa, quia e&longs;t ratio æqualitatis vt<emph.end type="italics"/> <foreign lang="el">i</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">i,</foreign> <emph type="italics"/>& in eadem celerita­<lb/>te, id e&longs;t eodem tempore, non immeritò primum problema in medium <lb/>adducitur. </s> <s id="id.002458">quia &longs;i verum &longs;it, cau&longs;am habet minimè vulgarem. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002459">Feratur enim.] <emph type="italics"/>Prioris problematis <expan abbr="veritat&etilde;">veritatem</expan> geometricè o&longs;ten­<lb/>dit. </s> <s id="id.002460">Sit enim vt<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>proce&longs;&longs;erit per &longs;e v&longs;que ad<emph.end type="italics"/> <foreign lang="el">e,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>v&longs;que ad<emph.end type="italics"/><lb/><foreign lang="el">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="el">a e</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">a z</foreign> <emph type="italics"/>erunt æquales. </s> <s id="id.002461">Perficiatur <expan abbr="parallelo­grammũ">parallelo­<lb/>grammum</expan> prop. 31. lib. 1. <expan abbr="n&etilde;pè">nempè</expan><emph.end type="italics"/> <foreign lang="el">a e q z. </foreign><emph type="italics"/></s> <s>Hoc erit &longs;imile toti<emph.end type="italics"/> <foreign lang="el">a b d g. </foreign><lb/><emph type="italics"/>prop. 24. lib. 6. </s> <s>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="el">a q d,</foreign> <emph type="italics"/>& &longs;ic<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>duobus motibus motum prædictis delineauit<emph.end type="italics"/> <foreign lang="el">a q</foreign><lb/><emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="el">z h. </foreign></s> <s><emph type="italics"/>proinde &<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>etiam delineauerit<emph.end type="italics"/> <foreign lang="el">a d</foreign><lb/><emph type="italics"/>cum peruenerit<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">g d. </foreign><emph type="italics"/></s> <s>Simili ratiocinatione conficitur<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>eo­<lb/>dem tempore peragra&longs;&longs;e diametrum<emph.end type="italics"/> <foreign lang="el">b g. </foreign><emph type="italics"/></s> <s>E&longs;t autem<emph.end type="italics"/> <foreign lang="el">b g</foreign> <emph type="italics"/>minor: <lb/>quam<emph.end type="italics"/> <foreign lang="el">a d</foreign> <emph type="italics"/>quia ba&longs;es &longs;unt duorum triangulorum<emph.end type="italics"/> <foreign lang="el">g a b,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">a b d</foreign><lb/><emph type="italics"/>bina latera<emph.end type="italics"/> <foreign lang="el">a g, a b</foreign> <emph type="italics"/>binis<emph.end type="italics"/> <foreign lang="el">a b, b d</foreign> <emph type="italics"/>æqualia habentium. </s> <s id="id.002463">quia &longs;unt <lb/>latera eiu&longs;dem Rhombi, & angulum<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>vtpote acutum minorem <lb/>angulo<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>vtpote obtu&longs;o. </s> <s id="id.002464">Ergo prop. 24. lib. 1. ba&longs;is<emph.end type="italics"/> <foreign lang="el">a d</foreign> <emph type="italics"/>maior e&longs;t <lb/>ba&longs;i<emph.end type="italics"/> <foreign lang="el">b g. </foreign><emph type="italics"/></s> <s>Et &longs;ic<emph.end type="italics"/> <foreign lang="el">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="el">b. </foreign></s> </p> <p type="main"> <s id="id.002465">Licet & hoc.] <emph type="italics"/>Hoc additur ad augendam &longs;ecundi problematis <lb/>difficultatem. </s> <s id="id.002466">Rationi enim con&longs;entaneum videtur, vt motum duo­<lb/>bus motibus &longs;imul plus &longs;patij conficiat: quam quod vno tantum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002467">Nece&longs;&longs;e igitur.] <emph type="italics"/>Nam parallelogramma quæ toti & inter &longs;e<emph.end type="italics"/><pb xlink:href="035/01/201.jpg" pagenum="161" /><emph type="italics"/>&longs;unt &longs;imilia, &longs;unt circa eandem diametrum. </s> <s id="id.002468">conu prop. 24. lib. 6. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002469">Æqualis enim e&longs;t.] <emph type="italics"/>Quia in ratione æqualitatis motum e&longs;t<emph.end type="italics"/> <foreign lang="el">b</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">e</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">h. </foreign></s> </p> <p type="main"> <s id="id.002470">Multò maiorem.] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="el">a d</foreign> <emph type="italics"/>&longs;ubtendit multò maiorem an­<lb/>gulum, vtpote<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>obtu&longs;um, & ideò maiorem recto: quam<emph.end type="italics"/> <foreign lang="el">b g,</foreign> <emph type="italics"/>quæ <lb/>&longs;ubtendit<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>angulum acutum, & ideò etiam minorem recto. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002471">Et latus <foreign lang="el">b d. </foreign>] <emph type="italics"/>Attingit &longs;ecundum problema quod generaliter <lb/>verum non e&longs;t. </s> <s id="id.002472">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="id.035.01.201.1.jpg" xlink:href="035/01/201/1.jpg"/><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/></s> <s>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/></s> <s id="id.002473">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. </s> <s id="id.002474">Po&longs;&longs;e autem <lb/>talem Rhombum con&longs;titui, patet. </s> <s id="id.002475">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. </s> <s>Ergo & tandem dabitur minor dimidio obtu&longs;i. </s> <s id="id.002476">Nam <lb/>& dimidius recti, qui acutus e&longs;t, e&longs;t eo minor prop. 15. lib. 5. </s> <s id="id.002477">Ergo in <lb/>tali Rhombo latus A B per A C vna latione motum, plus &longs;patij <lb/>confecit: quam B, quod peragrans B C duabus lationibus ferebatur. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002478"><foreign lang="el">a)/topon ga/r, w(/sper e)le/xqh, to\ <lb/>du/o fora\s fero/menon e)ni/ote bradu/teron fe/resqai tou= mi/an, <lb/>kai\ a)mfote/rwn i)sotaxw=n shmei/wn doqe/ntwn, mei/zw diecie/nai <lb/>qa/teron.</foreign></s> <s id="g0132314"><foreign lang="el">ai)/tion de\, o(/ti tou= me\n a)po\ th=s a)mblei/as ferome/nou <lb/>sxedo\n e)nanti/ai a)mfo/terai gi/nontai, h(/n te au)th\ <lb/>fe/retai kai\ h(\n u(po\ th=s pleura=s u(pofe/retai. </foreign></s> <s id="g0132315"><foreign lang="el">tou= de\ a)po\ <lb/>th=s o)cei/as, w/(sper sumbai/nei fe/resqai e)pi\ to\ au)to/. </foreign></s> <s id="g0132315a"><foreign lang="el">sunepouri/zei <lb/>ga\r h( th=s pleura=s, th\n e)pi\ th=s diame/trou: kai\ o(/sw| a)\n <lb/>th\n me\n o)cute/ran poih/sh|, th\n de\ a)mblute/ran, h( me\n bradute/ra <lb/>e)/stai, h( de\ qa/ttwn.</foreign></s> <s id="g0132316"><foreign lang="el">ai( me\n ga\r e)nantiw/terai gi/nontai, <lb/>dia\ to\ a)mblute/ran gi/nesqai th\n gwni/an. </foreign></s> <s id="g0132316a"><foreign lang="el">ai( de\ <lb/>ma=llon e)pi\ ta\ au)ta\, dia\ to\ suna/gesqai ta\s gramma/s. <lb/></foreign></s> <s id="g0132316b"><foreign lang="el">to\ me\n ga\r *a sxedo\n e)pi\ to\ au)to\ fe/retai kat' a)mfote/ras <lb/>ta\s fora/s: sunepouri/zetai ou)=n h( e(te/ra, kai\ o(/sw| a)\n <lb/>o)cute/ra gi/nhtai h( gwni/a, tosou/tw| ma=llon: to\ de\ *a de\ e)pi\ <lb/>tou)nanti/on: au)to\ me\n ga\r pro\s to\ *a fe/retai, h( de\ pleura\ <lb/>u(pofe/rei au)to\ pro\s to\ *g.</foreign></s> <s id="g0132318"><foreign lang="el">kai\ o(/sw| a)\n a)mblute/ra h( gwni/a <lb/>h)=|, e)nantiw/terai ai( forai\ gi/nontai: eu)qute/ra ga\r h( <lb/>grammh\ gi/netai.</foreign></s> <s id="g0132319"><foreign lang="el">ei) d' o(/lws eu)qei=a ge/noito, pantelw=s a)\n <lb/>ei)/hsan e)nanti/ai. h( de\ pleura\ u(p' ou)qeno\s kwlu/etai mi/an <lb/>ferome/nh fora/n. eu)lo/gws ou)=n th\n mei/zw die/rxetai.</foreign></s> </p> <p type="main"> <s id="id.002479">Ab&longs;urdum enim, vt <expan abbr="dictũ">dictum</expan> <lb/>e&longs;t, quod duabus lationibus <lb/>fertur, tardius <expan abbr="nonnunquã">nonnunquam</expan> <lb/>ferri eo, quod vna: & <expan abbr="dato­rũ">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>. </s> <s id="id.002480">Cau&longs;a verò <pb xlink:href="035/01/202.jpg" pagenum="162" />e&longs;t, quod ambæ lationes <lb/>eius, quod ab obtu&longs;o angu<lb/>lo fertur fiunt ferè contra­<lb/>riæ. </s> <s id="id.002481">H&etail;c &longs;cilicet qua per &longs;e <lb/>fertur, & hæc qua per latus <lb/>effertur. </s> <s id="id.002482">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;ecũ­dum">&longs;ecun­<lb/>dum</expan> diametrum. </s> <s id="id.002483">Et quan­<lb/>tò hic angulus fuerit acu­<lb/>tior, ille obtu&longs;ior vna latio <lb/>erit tardior: altera velo­<lb/>cior. </s> <s id="id.002484">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. </s> <s id="id.002485">Ip&longs;um enim <foreign lang="el">a</foreign> fere ad <lb/>idem fertur ex vtri&longs;que la­<lb/>tionibus. </s> <s id="id.002486"><expan abbr="Itaq;">Itaque</expan> altera coad­<lb/>iuuatur. </s> <s id="id.002487">Et <expan abbr="quãtò">quantò</expan> acutior <lb/>fuerit angulus: tantò ma­<lb/>gis: ip&longs;um verò <foreign lang="el">b</foreign> ad con­<lb/>trarium. </s> <s id="id.002488">Ip&longs;um enim ad <foreign lang="el">a</foreign><lb/>fertur. </s> <s id="id.002489">Latus verò effertur <lb/>ver&longs;us ip&longs;um <foreign lang="el">g. </foreign>Et quantò <lb/>fuerit angulus obtu&longs;ior <lb/>magis contrariæ lationes <lb/>fiunt. </s> <s id="id.002490">Rectior enim linea <lb/>fit, quod &longs;i omninò recta <lb/>e&longs;&longs;et, e&longs;&longs;ent lationes omni­<lb/>nò contrariæ. </s> <s id="id.002491">Latus vero <lb/>vno motu motum à nullo <lb/>impeditur. </s> <s id="id.002492">Æquum e&longs;t igitur, vt lineam maiorem tran­<lb/>&longs;eat. </s> </p> <pb xlink:href="035/01/203.jpg" pagenum="163" /> <p type="head"> <s id="id.002493">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002494">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 id="id.002495">Nonnunquam ferri.] <emph type="italics"/>Particula<emph.end type="italics"/> <foreign lang="el">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 id="id.002496">Et datorum amborum.] <emph type="italics"/>Auget difficultatem problematis <lb/>primi. </s> <s id="id.002497">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 id="id.002498">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. </s> <s id="id.002499">quod &longs;cilicet mota duobus motibus, &longs;i ad eundem <lb/>terminum, ad quem tendent, celerius mouentur: &longs;i ad contrarios, tar­<lb/>dius. </s> <s id="id.002500">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/></s> <s id="id.002501">Atqui<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>ab angulo obtu&longs;o motum duorum motuum vno ad<emph.end type="italics"/> <foreign lang="el">a,</foreign> <emph type="italics"/>alte­<lb/>ro ad<emph.end type="italics"/> <foreign lang="el">d</foreign> <emph type="italics"/>tendens ad magis contrarios terminos tendit: quam<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>ten­<lb/>dens dictis motibus ad<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">g. </foreign><emph type="italics"/>E&longs;t enim, vt antea demon&longs;tratum <lb/>e&longs;t,<emph.end type="italics"/> <foreign lang="el">a d</foreign> <emph type="italics"/>diameter & recta maior: quam<emph.end type="italics"/> <foreign lang="el">g d. </foreign><emph type="italics"/>Et quò<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>acutior <lb/>erit angulus, eò<emph.end type="italics"/> <foreign lang="el">a d</foreign> <emph type="italics"/>maior erit ergo æquum e&longs;t, vt<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>tardius fera­<lb/>tur: quam<emph.end type="italics"/> <foreign lang="el">a. </foreign><emph type="italics"/>Et quidem tantò tardius: quantò<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>erit obtu&longs;ior angu­<lb/>lus, &<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>acutior ob cau&longs;am prædictam. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002502">Fere ad idem.] <emph type="italics"/>Particula<emph.end type="italics"/> <foreign lang="el">sxedo\n</foreign> <emph type="italics"/>ferè ad­<emph.end type="italics"/><lb/><figure id="id.035.01.203.1.jpg" xlink:href="035/01/203/1.jpg"/><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="el">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="el">b</foreign><lb/><emph type="italics"/>fertur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002503">Rectior enim linea.] <emph type="italics"/>Id e&longs;t duo latera<emph.end type="italics"/> <foreign lang="el">b a</foreign><lb/><emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">b 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 xlink:href="035/01/204.jpg" pagenum="164" /><emph type="italics"/>erunt vna omnino recta, quod vbi e&longs;&longs;et, vt cum<emph.end type="italics"/> <foreign lang="el">b a</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="el">b <lb/>l,</foreign> <emph type="italics"/>tunc lationes<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">l,</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">d</foreign> <emph type="italics"/>e&longs;&longs;ent ad contrarios omnino <lb/>terminos. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002504">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. </s> <s id="id.002505">Latus autem in dicto Rhombo à nullo impeditur: <lb/>contra<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>impeditur. </s> <s id="id.002506">Ergo<emph.end type="italics"/> <foreign lang="el">l b</foreign> <emph type="italics"/>latus celerius feretur ip&longs;o<emph.end type="italics"/> <foreign lang="el">b. </foreign></s> </p> <p type="main"> <s id="id.002507">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. </s> <s id="id.002508">Cæterum 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. </s> <s id="id.002509">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. </s> <s id="id.002510">In rebus etiam artificialibus <lb/>gladius acuta &longs;ui acie facile &longs;ecat: obtu&longs;a non item. </s> <s id="id.002511">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> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002512">25. <foreign lang="el">*dia\ ti/ o( mei/zwn ku/klos <lb/>tw=| e)la/ttoni i)/shn e)celi/tte­<lb/>tai.</foreign></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002513">25. Cur maior circulus cum <lb/>minore per æqualem re­<lb/>uoluitur. </s> </p> <p type="main"> <s id="id.002514"><foreign lang="el">*)aporei=tai dia\ ti/ pote o( mei/zwn ku/klos tw=| e)la/ttoni <lb/>ku/klw| i)/shn e)celi/ttetai grammh/n, o(/tan peri\ to\ au)to\ ke/ntron <lb/>teqw=si. </foreign></s> <s id="g0132401a"><foreign lang="el">xwri\s de\ e)kkulio/menoi, w(/sper to\ me/geqos au)tw=n <lb/>pro\s to\ me/geqos e)/xei, ou(/tws kai\ ai( grammai\ au)tw=n <lb/>gi/nontai pro\s a)llh/las.</foreign></s> <s id="g0132402"><foreign lang="el">e)/ti de\ e(no\s kai\ tou= au)tou= ke/ntrou <lb/>o)/ntos a)mfoi=n, o(te\ me\n thlikau/th gi/netai h( grammh\, h(\n <lb/>e)kkuli/ontai, h(li/khn o( e)la/ttwn ku/klos kaq' au(to\n e)kkuli/etai, <lb/>o(te\ de\ o(/shn o( mei/zwn.</foreign></s> <s id="g0132403"><foreign lang="el">o(/ti me\n ou)=n mei/zw e)kkuli/etai <lb/>o( mei/zwn, fanero/n. </foreign></s> <s id="g0132403a"><foreign lang="el">gwni/a me\n ga\r dokei= kata\ th\n <lb/>ai)/sqhsin ei)=nai h( perife/reia e(ka/stou th=s oi)kei/as diame/trou, <lb/>h( tou= mei/zonos ku/klou mei/zwn, h( de\ tou= e)la/ttonos, e)la/ttwn <lb/>w(/ste to\n au)to\n tou=ton e(/cousi lo/gon, kaq' a(\s e)cekuli/sqhsan<lb/> ai( grammai\ pro\s a)llh/las kata\ th\n ai)/sqhsin.</foreign></s> <s id="g0132404"><foreign lang="el">a)lla\ mh\n <lb/>kai\ o(/ti th\n i)/shn e)kkuli/ontai, o(/tan peri\ to\ au)to\ ke/ntron <lb/>kei/menoi w)=si, dh=lon, kai\ ou(/tws gi/netai, o(te\ me\n i)/sh th=| <lb/>grammh=|, h(\n o( mei/zwn ku/klos e)kkuli/etai, o(te\ de\ e)la/ttwn.</foreign></s> <s id="g0132405"><foreign lang="el"><lb/>e)/stw ga\r ku/klos o( mei/zwn me\n, e)f' ou(= ta\ *d*z*g, o( de\ <lb/>e)la/ttwn e)f' ou(= ta\ *e*h*b: ke/ntron de\ a)mfoi=n to\ *a, kai\ <lb/>h(\n me\n e)celi/ttetai kaq' au(to\n o( me/gas, h( e)f' h(=s *z*l e)/stw. <lb/></foreign></s> <s id="g0132405a"><foreign lang="el">h(\n de\ o( e)la/ttwn kaq' au(to/n, h( e)f' h(=s *h*k, i)/sh th=| *a*z.</foreign></s> <s id="g0132406"><foreign lang="el"><lb/>e)a\n dh\ kinw= to\n e)la/ttona, to\ au)to\ ke/ntron kinw=, e)f' ou(= <lb/>to\ *a. </foreign></s> <s id="g0132406a"><foreign lang="el">o( de\ me/gas proshrmo/sqw. </foreign></s> <s id="g0132406b"><foreign lang="el">o(/tan ou)=n h( *a*b o)rqh\ ge/nhtai <lb/>pro\s th\n *h*k, a(/ma kai\ h( *a*g gi/netai o)rqh\ pro\s th\n <lb/>*z*l: w(/ste e)/stai i)/shn a)ei\ dielhluqui=a: th\n me\n *h*k, e)f' <lb/>w(=| *h*b perife/reia, th\n de\ *z*l, h( e)f' h(=s *z*g.</foreign></s> <s id="g0132407"><foreign lang="el">ei) de\ to\ <lb/>te/tarton me/ros i)/shn e)celi/ttetai, dh=lon o(/ti kai\ o( o(/los ku/klos <lb/>tw=| o(/lw| ku/klw| i)/shn e)celittetai, w(/ste o(/tan h( *b*h <lb/>grammh\ e)/lqh| e)pi\ to\ *k, kai\ h( *z*g e)/stai perife/reia e)pi\ <lb/>th=s *z*l, kai\ o( ku/klos o(/los e)ceiligme/nos.</foreign></s> <s id="g0132408"><foreign lang="el">o(moi/ws de\ kai\ <lb/>e)a\n to\n me/gan kinw=, e)narmo/sas to\n mikro/n, tou= au)tou= ke/ntrou <lb/>o)/ntos, a(/ma th=| *a*g, h( *a*b ka/qetos kai\ o)rqh\ e)/stai, h( <lb/>me\n pro\s th\n *z*i, h( de\ pro\s th\n *h*q.</foreign></s> <s id="g0132409"><foreign lang="el">w(/ste o(/tan kat' i)/shn, h( <lb/>me\n th=| *h*q e)/stai dielhluqui=a, h( de\ th=| *z*i, kai\ ge/nhtai <lb/>o)rqh\ pa/lin h( *a*g pro\s th\n *z*i, kai\ h( *a*b o)rqh\ pa/lin, pro\s th\n <lb/>*h*q w(s to\ e)c a)rxh=s e)/sontai e)pi\ tw=n *q*i.</foreign></s> <s id="g0132410"><foreign lang="el">to\ de\ mh/te sta/sews <lb/>ginome/nhs tou= mei=zonos tw=| e)la/ttoni, w(/ste me/nein tina\ xro/non <lb/>e)pi\ tou= au)tou= shmei/ou: kinou=ntai ga\r sunexw=s a)/mfw a)mfotera/kis. <lb/></foreign></s> <s id="g0132410a"><foreign lang="el">mh/ te u(perphdw=ntos tou= e)la/ttonos mhqe\n shmei=on, <lb/>to\n me\n mei/zw tw=| e)la/ttoni i)/shn diecie/nai, to\n de\ tw=| mei/zoni, <lb/>a)/topon.</foreign></s> </p> <p type="main"> <s id="id.002515"><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. </s> <s id="id.002516">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 xlink:href="035/01/205.jpg" pagenum="165" />ta fit orbita: quanta e&longs;t ea: <lb/>quam minor circulus pera­<lb/>grat: aliquando verò quam <lb/>maior. </s> <s id="id.002517">Quod igitur maio­<lb/>rem peragret maior mani­<lb/>fe&longs;tum e&longs;t. </s> <s id="id.002518">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&etail; <expan abbr="eand&etilde;">eandem</expan> rationem <lb/>euidenter habebunt inter <lb/>&longs;e. </s> <s id="id.002519">Attamen quod circa <expan abbr="id&etilde;">idem</expan> <lb/><expan abbr="centrũ">centrum</expan> po&longs;iti æqualem <expan abbr="or­bitã">or­<lb/>bitam</expan> <expan abbr="cõficiant">conficiant</expan> etiam <expan abbr="mani­fe&longs;tũ">mani­<lb/>fe&longs;tum</expan>. </s> <s id="id.002520">At que ita vt aliquan­<lb/>do orbita maioris circuli <lb/>&longs;it æqualis linea, aliquando <lb/>orbita minoris. </s> <s id="id.002521">Sit enim <lb/>circulus maior <expan abbr="quid&etilde;">quidem</expan> <foreign lang="el">d z g,</foreign><lb/>minor vero <foreign lang="el">e h b,</foreign> & <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/><expan abbr="centrũ">centrum</expan> <foreign lang="el">a.</foreign> </s> <s>Atque ea quidem <lb/>per quam magnus circulus <lb/>per &longs;e voluitur <foreign lang="el">z l,</foreign> &longs;it & ea <lb/>per quam per &longs;e minor <foreign lang="el">h k</foreign><lb/>æqualis <foreign lang="el">z l.</foreign> </s> <s>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="el">a.</foreign> </s> <s>Magnus au­<lb/>tem connexus e&longs;to. </s> <s id="id.002522">Quum <lb/>igitur <foreign lang="el">a b</foreign> ad rectos fiet li­<lb/>neæ <foreign lang="el">h k,</foreign> &longs;imul etiam <foreign lang="el">a g</foreign><lb/>ad rectos fiet lineæ <foreign lang="el">z l. </foreign></s> </p> <p type="main"> <s id="id.002523">Quare per æqualem erit <lb/>tran&longs;latio, nempè <foreign lang="el">h k</foreign> in <lb/>qua e&longs;t <foreign lang="el">z g. </foreign>Quod &longs;i quarta <lb/>pars per &etail;qualem voluitur, <pb xlink:href="035/01/206.jpg" pagenum="166" />quod totus circulus æqua­<lb/>lem toti circulo reuolua­<lb/>tur, manife&longs;tum e&longs;t. </s> <s id="id.002524">Itaque <lb/>quando linea <foreign lang="el">b h</foreign> peruene­<lb/>rit ad <foreign lang="el">k</foreign> etiam <foreign lang="el">z g</foreign> peri­<lb/>pheria erit in <foreign lang="el">z l</foreign> & circu­<lb/>lus totus conuolutus. </s> <s id="id.002525">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="el">a g</foreign> etiam <foreign lang="el">a b</foreign> perpen­<lb/>dicularis erit. </s> <s id="id.002526">Illa quidem <lb/>ad <foreign lang="el">z i</foreign> hæc verò ad <foreign lang="el">h q</foreign>. </s> <s>Ita­<lb/>que quando per æqualem <lb/>ip&longs;i <foreign lang="el">h q</foreign> vel <foreign lang="el">z i</foreign> rur&longs;um erit <lb/>tran&longs;latio etiam <foreign lang="el">a g</foreign> per­<lb/>pendicularis erit ad <foreign lang="el">z i,</foreign> & <lb/><foreign lang="el">a b</foreign> ad <foreign lang="el">h q,</foreign> vt ab initio <lb/>erunt in <foreign lang="el">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. </s> <s id="id.002527">vter­<lb/>que enim vtroque modo <lb/>continuè mouetur. </s> <s id="id.002528">Neque <lb/>minore vllum punctum <lb/>tran&longs;iliente, & maiorem <lb/>minori æqualem tran&longs;ire, & minorem maiori ab&longs;urdum. </s> </p> <p type="head"> <s id="id.002529">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002530">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. </s> <s id="id.002531">E&longs;t autem eiu&longs;modi, cur circuli concentrici, & inæquales <lb/>iuncti, æqualem tamen orbitam circumuolutione peragrent. </s> <s id="id.002532">Et <expan abbr="qui­d&etilde;">qui­<lb/>dem</expan> hoc euenire duobus modis ponitur. </s> <s id="id.002533">Vno, vt orbita minoris adæque­<emph.end type="italics"/><pb xlink:href="035/01/207.jpg" 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> </p> <p type="main"> <s id="id.002534">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. </s> <s id="id.002535">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> </p> <p type="main"> <s id="id.002536">Præterea vno.] <emph type="italics"/>Duo modi æquationis prædicti explicantur in <lb/>habentibus idem centrum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002537">Quod igitur maiorem.] <emph type="italics"/>Confirmatio e&longs;t difficultatis allatæ <lb/>ex euidentia per &longs;en&longs;um. </s> <s id="id.002538">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. </s> <s id="id.002539">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/></s> <s id="id.002540">In maiore circulo maior: in minore minor ( Sed & hanc euidentiam, <lb/>ne qua e&longs;&longs;et dubitatio, demon&longs;tratione primo capite huius libri de­<lb/>mon&longs;trauimus. ) </s> <s>Erunt igitur & orbitæ inæquales & proportione <lb/>re&longs;pondentes ba&longs;ibus angulorum è &longs;emidiametris con&longs;titutorum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002541">Attamen quod circa.] <emph type="italics"/>Problematis propo&longs;iti veritas demon­<lb/>&longs;tratur figura geometrica in vtroque modo. </s> <s id="id.002542">Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="el">a h z</foreign><lb/><emph type="italics"/>perpendiculariter in&longs;i&longs;tat pla­<emph.end type="italics"/><lb/><figure id="id.035.01.207.1.jpg" xlink:href="035/01/207/1.jpg"/><lb/><emph type="italics"/>no, & ad rectam<emph.end type="italics"/> <foreign lang="el">z i. </foreign><emph type="italics"/>Tum<emph.end type="italics"/> <foreign lang="el">h q</foreign><lb/><emph type="italics"/>rectos angulos faciat, &longs;icque il­<lb/>las tangat in punctis<emph.end type="italics"/> <foreign lang="el">h</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">z,</foreign><lb/><emph type="italics"/>cum quarta pars peripheriæ<emph.end type="italics"/> <foreign lang="el">h b</foreign><lb/><emph type="italics"/>erit reuoluta: ita vt<emph.end type="italics"/> <foreign lang="el">a b</foreign> <emph type="italics"/>rur­<lb/>&longs;us ad rectos &longs;it ad rectam<emph.end type="italics"/> <foreign lang="el">h q,</foreign><lb/><emph type="italics"/>ip&longs;amque tangat, vt in puncto<emph.end type="italics"/><lb/><foreign lang="el">k</foreign>: <emph type="italics"/>tunc &<emph.end type="italics"/> <foreign lang="el">a g</foreign> <emph type="italics"/>etiam ad re­<lb/>ctos erit &longs;uper<emph.end type="italics"/> <foreign lang="el">z i,</foreign> <emph type="italics"/>& &longs;it vt <lb/>tangat in puncto<emph.end type="italics"/> <foreign lang="el">l. </foreign><emph type="italics"/></s> <s>Erunt pro <lb/>29. prop. lib. 1. </s> <s>Duæ<emph.end type="italics"/> <foreign lang="el">z h</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">k l</foreign> <emph type="italics"/>parallelæ & æquales, ex hypoth. <lb/></s> <s id="id.002543">Ergo quæ eas ad ea&longs;dem partes iungunt rectæ<emph.end type="italics"/> <foreign lang="el">z l</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">h k</foreign> <emph type="italics"/>erunt <lb/>æquales, prop 34. eiu&longs;dem. </s> <s id="id.002544">Sunt autem orbitæ ab vtri&longs;que confectæ <lb/>eadem celeritate motis. </s> <s id="id.002545">Eadem ratiocinatione cum<emph.end type="italics"/> <foreign lang="el">a g</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/><pb xlink:href="035/01/208.jpg" pagenum="168" /><emph type="italics"/>puncto<emph.end type="italics"/> <foreign lang="el">i</foreign> <emph type="italics"/>ex reuolutione maioris, &<emph.end type="italics"/> <foreign lang="el">b</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/> <foreign lang="el">q</foreign>: <emph type="italics"/>&longs;icque<emph.end type="italics"/> <foreign lang="el">q i</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">h <lb/>z</foreign> <emph type="italics"/>cum &longs;int æquales & parallelæ, duæ rur&longs;us<emph.end type="italics"/> <foreign lang="el">h q</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">z i</foreign> <emph type="italics"/>erunt pa­<lb/>rallelæ. </s> <s id="id.002546">Quæ autem ratio e&longs;t quartarum circulorum inter &longs;e, eadem <lb/>e&longs;t totorum. </s> <s id="id.002547">Partes enim cum pariter multiplicibus eandem ratio­<lb/>nem habent prop. 15. lib. 5. </s> <s>Igitur in vtroque modo orbitæ concen­<lb/>tricorum inæqualium &longs;unt æquales. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002548">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, reijcit, 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> </subchap1> <subchap1> <p type="main"> <s id="id.002549"><foreign lang="el">e)/ti de\ mia=s kinh/sews ou)/shs a)ei\ to\ ke/ntron <lb/>to\ kinou/menon o(te\ me\n th\n mega/lhn o(te\ de\ th\n e)la/ttona <lb/>e)kkuli/esqai qaumasto/n.</foreign></s> <s id="g0132412"><foreign lang="el">to\ ga\r au)to\ tw=| au)tw=| ta/xei fero/menon <lb/>i)/shn pe/fuke diecie/nai: tw=| au)tw=| de\ ta/xei i)/shn e)sti\ <lb/>kinei=n a)mfotera/kis.</foreign></s> <s id="g0132413"><foreign lang="el">a)rxh\ de\ lhpte/a h(/de peri\ th=s ai)ti/as <lb/>au)tw=n, o(/ti h( au)th\ du/namis kai\ i)/sh to\ me\n bradu/teron <lb/>kinei= me/geqos, to\ de\ taxu/teron.</foreign></s> <s id="g0132414"><foreign lang="el">ei) dh/ ti ei)/h o(\ mh\ pe/fuken <lb/>u(f' e(autou= kinei=sqai, e)a\n tou=to a(/ma kai\ au)to\ kinh=| to\ pefuko\s <lb/>kinei=sqai, bradu/teron kinhqh/setai h)\ ei) au)th\ kaq' <lb/>au(th\n e)kinei=to.</foreign></s> <s id="g0132415"><foreign lang="el">kai\ e)a\n me\n pefuko\s h)=| kinei=sqai, mh\ sugkinh=tai <lb/>de\ mhqe/n, w(sau/tws e(/cei.</foreign></s> <s id="g0132416"><foreign lang="el">kai\ a)du/naton dh\ kinei=sqai <lb/>ple/on h)\ to\ kinou=n: ou) ga\r th\n au(tou= kinei=tai ki/nhsin, a)lla\<lb/> th\n tou= kinou=ntos.</foreign></s> <s id="g0132417"><foreign lang="el">ei)/h dh\ ku/klos o( me\n mei/zwn to\ *a, o( de\ <lb/>e)la/ttwn e)f' w(=| *b. ei) w)qoi/h d' o( e)la/ttwn to\n mei/zw, mh\ <lb/>kuliome/nou au)tou=, fanero\n o(/ti tosou=ton di/eisi th=s eu)qei/as <lb/>o( mei/zwn, o(/son e)w/sqh u(po\ tou= e)la/ttonos. tosou=ton de/ ge <lb/>e)w/sqh o(/son o( mikro\s e)kinh/qh. i)/shn a)/ra th=s eu)qei/as dielhlu/qasin.</foreign></s> <s id="g0132418"><foreign lang="el"><lb/>a)na/gkh toi/nun kai\ ei) kulio/menos o( e)la/ttwn to\n <lb/>mei/zw w)qoi/h, kulisqh=nai me\n a(/ma th=| w)/sei, tosou=ton d' o(/son <lb/>o( e)la/ttwn e)kuli/sqh, ei) mhqe\n au)to\s th=| au)th=| kinh/sei kinei=tai.</foreign></s> <s id="g0132419"><foreign lang="el"><lb/>w(s ga\r kai\ o(/son e)ki/nei, tosou=ton kekinh=sqai a)na/gkh <lb/>to\ kinou/menon u(p' e)kei/nou. a)lla\ mh\n o(/ te ku/klos tosou=ton <lb/>e)ki/nhse to\ au)to/, ku/klw| te kai\ podiai/an [1e)/stw ga\r tosou=ton <lb/>o(\ e)kinh/qh]1, kai\ o( me/gas a)/ra tosou=ton e)kinh/qh.</foreign></s> <s id="g0132420"><foreign lang="el">o(moi/ws <lb/>de\ ka)\n o( me/gas to\n mikro\n kinh/sh|, e)/stai kekinhme/nos o( mikro\s <lb/>w(s kai\ o( mei/zwn.</foreign></s> <s id="g0132421"><foreign lang="el">kaq' au(to\n me\n dh\ kinhqei\s o(poterosou=n, <lb/>e)a/n te taxu\ e)a/n te brade/ws: tw=| au)tw=| de\ ta/xei <lb/>eu)qu\s o(/shn o( mei/zwn pe/fuken e)celixqh=nai grammh/n.</foreign></s> </p> <p type="main"> <s id="id.002550">Præterea vnica latione <lb/><expan abbr="exi&longs;t&etilde;te">exi&longs;tente</expan> <expan abbr="centrũ">centrum</expan> &longs;emper <expan abbr="cõ­tinuè">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. </s> <s id="id.002551">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/></s> <s id="id.002552">Eadem <expan abbr="aut&etilde;">autem</expan> celeritate per <lb/><expan abbr="æqual&etilde;">æqualem</expan> vtro que modo mo­<lb/>uere licet. </s> <s id="id.002553">Cæterum princi­<lb/>pium &longs;umatur ex vtriu&longs;que <lb/>cau&longs;a, quod eadem vis, & <lb/>æqualis vnam quidem <expan abbr="ma­gnitudinũ">ma­<lb/>gnitudinum</expan> tardius: alteram <lb/>celerius moueat. </s> <s id="id.002554">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> per &longs;e moueretur. </s> <pb xlink:href="035/01/209.jpg" pagenum="169" /> <s>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/></s> <s id="id.002555">Et vt plus moueatur: quam <lb/>quod mouet, fieri non po­<lb/>te&longs;t. </s> <s id="id.002556">Non enim &longs;uo ip&longs;ius <lb/>mouetur motu: &longs;ed <expan abbr="mou&etilde;­">mouen­<lb/></expan><arrow.to.target n="marg39"/><lb/>tis. </s> <s>[Sit igitur circulus maior <lb/><expan abbr="quid&etilde;">quidem</expan> vbi <foreign lang="el">g,</foreign> at minor vbi <lb/>b.] </s> <s>Si impellat minor <expan abbr="maio­r&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="quã­tam">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. </s> <s id="id.002557"><expan abbr="Rectã">Rectam</expan> igitur æqua­<lb/>lem pertran&longs;ierunt. </s> <s id="id.002558">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. </s> <s id="id.002559">&longs;i <lb/><expan abbr="neutiquã">neutiquam</expan> ip&longs;e proprio mo­<lb/>tu moueatur. </s> <s id="id.002560">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. </s> <s id="id.002561">Sed circulus &longs;olum <lb/>&longs;e mouerit circulariter pe­<lb/>dem vnum. </s> <s id="id.002562">Sit enim tan­<lb/>tum quod <expan abbr="motũ">motum</expan> e&longs;t. </s> <s id="id.002563">Etiam <lb/>magnus tantundem motus <lb/>erit. </s> <s id="id.002564">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/></s> <s id="id.002565">per &longs;e <expan abbr="quid&etilde;">quidem</expan> motus vtrouis modo &longs;eu celeriter: &longs;eu tardè. </s> </p> </subchap1> <pb xlink:href="035/01/210.jpg" pagenum="170" /> <subchap1> <p type="main"> <s><lb/>Eadem verò celeritate &longs;ta­<lb/>tim per quantam lineam <lb/>natus e&longs;t conuolui maior. </s> </p> <p type="margin"> <s id="id.002566"><margin.target id="marg39"/>Hæc inter­<lb/>po&longs;ita <expan abbr="vid&etilde;­tur">viden­<lb/>tur</expan>. </s> </p> <p type="head"> <s id="id.002567">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002568">Præterea vnica.] <emph type="italics"/>Cum &longs;it o&longs;ten&longs;a problematis veritas rur&longs;us <lb/>o&longs;tendit aliquid admirabile contineri. </s> <s id="id.002569">Ratio admirationis &longs;ic erit <lb/>apertior. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002570"><emph type="italics"/>Idem eadem celeritate latum æqualem <expan abbr="lineã">lineam</expan> tran&longs;ire natum e&longs;t. <lb/></s> <s id="id.002571">Centrum circulorum concentricorum vnum idemque e&longs;t. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002572"><emph type="italics"/>Ergo æqualem tran&longs;ire natum e&longs;t. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002573"><emph type="italics"/>Attamen aliter fit. </s> <s id="id.002574">Nam eadem celeritate latum modò <expan abbr="maior&etilde;">maiorem</expan>, <lb/>modò minorem tran&longs;it. </s> <s id="id.002575">Ergo problema admirationis plenum e&longs;t. </s> <s id="id.002576">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 id="id.002577">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. </s> <s id="id.002578">Primum e&longs;t. </s> <s id="id.002579">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. </s> <s id="id.002580">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. </s> <s id="id.002581">Secundum e&longs;t. </s> <s id="id.002582">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. </s> <s id="id.002583">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. </s> <s id="id.002584">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. </s> <s id="id.002585">Et &longs;ic celerius per maiu&longs;que &longs;patium, quam <emph.end type="italics"/><pb xlink:href="035/01/211.jpg" pagenum="171" /><emph type="italics"/>quòd ferretur per &longs;e. </s> <s id="id.002586">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 id="id.002587">Nece&longs;&longs;e igitur &longs;i.] <emph type="italics"/>Quod maiore<emph.end type="italics"/> <foreign lang="el">z d</foreign> <emph type="italics"/>moto minor<emph.end type="italics"/> <foreign lang="el">h e</foreign> <emph type="italics"/>rapiatur <lb/>in eodem plano duobus concentricis exi&longs;tentibus captu facile e&longs;t. <lb/></s> <s id="id.002588">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. </s> <s id="id.002589">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="el">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> </subchap1> <subchap1> <p type="main"> <s id="id.002590"><foreign lang="el">o(/per <lb/>kai\ poiei= th\n a)pori/an, o(/ti ou)ke/ti o(moi/ws poiou=sin o(/tan sunarmosqw=sin. <lb/>to\ d' e)/stin, ei) o( e(/teros u(po\ tou= e(te/rou kinei=tai <lb/>ou)x h(\n pe/fuken, ou)de\ th\n au(tou= ki/nhsin.</foreign></s> <s id="g0132422"><foreign lang="el">ou)qe\n ga\r <lb/>diafe/rei periqei=nai kai\ e)narmo/sai h)\ prosqei=nai o(poteronou=n <lb/>o(pote/rw|: o(moi/ws ga/r, o(/tan o( me\n kinh=| o( de\ kinh=tai u(po\ <lb/>tou/tou, o(/son a)\n kinh=| a(/teros, tosou=ton kinhqh/setai a(/teros.</foreign></s> <s id="g0132423"><foreign lang="el"><lb/>o(/tan me\n ou)=n proskei/menon kinh=| h)\ proskrema/menon, ou)k a)ei\ <lb/>kuli/ei tis: o(/tan de\ peri\ to\ au)to\ ke/ntron teqw=sin, a)na/gkh <lb/>kuli/esqai a)ei\ to\n e(/teron u(po\ tou= e(te/rou.</foreign></s> <s id="g0132424"><foreign lang="el">a)ll' ou)qe\n h(=tton <lb/>ou) th\n au(tou= ki/nhsin a(/teros kinei=tai, a)ll' w(/sper a)\n ei) mhdemi/an <lb/>ei)=xe ki/nhsin. ka)\n e)/xh|, mh\ xrh=tai d' au)th=|, tau)to\ <lb/>sumbai/nei.</foreign></s> <s id="g0132425"><foreign lang="el">o(/tan me\n ou)=n o( me/gas kinh=| e)ndedeme/non to\n mikro/n, <lb/>o( mikro\s kinei=tai o(/shnper ou(=tos: o(/tan de\ o( mikro/s, <lb/>pa/lin o( me/gas o(/shn ou(=tos. xwrizo/menos de\ e(ka/teros au(to\n <lb/>kinei= au)to/s.</foreign></s> <s id="g0132426"><foreign lang="el">o(/ti de\ tou= au)tou= ke/ntrou o)/ntos kai\ kinou=ntos <lb/>tw=| au)tw=| ta/xei sumbai/nei a)/nison diecie/nai au)tou\s grammh/n, <lb/>paralogi/zetai o( a)porw=n sofistikw=s.</foreign></s> <s id="g0132427"><foreign lang="el">to\ au)to\ me\n <lb/>ga/r e)sti ke/ntron a)mfoi=n, a)lla\ kata\ sumbebhko/s, w(s <lb/>mousiko\n kai\ leuko/n: to\ ga\r ei)=nai e(kate/rou ke/ntrou tw=n <lb/>ku/klwn ou) tw=| au)tw=| xrh=tai.</foreign></s> <s id="g0132428"><foreign lang="el">o(/tan me\n ou)=n o( kinw=n h)=| o( <lb/>mikro/s, w(s e)kei/nou ke/ntron kai\ a)rxh/, o(/tan de\ o( me/gas, w(s <lb/>e)kei/nou.</foreign></s> <s id="g0132429"><foreign lang="el">ou)/koun to\ au)to\ kinei= a(plw=s, a)ll' e)/stin w(/s.</foreign></s> </p> <p type="main"> <s id="id.002591">Quod etiam dubitatio­<lb/>nem adfert, quia &longs;imiliter <lb/>præterea faciunt, quando <lb/>connexi &longs;unt. </s> <s id="id.002592">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. </s> <s id="id.002593">Nihil enim intere&longs;t cir­<lb/>cumponere, & annectere <lb/>vel adiungere <expan abbr="vtrũlibet">vtrumlibet</expan> al­<lb/>teri. </s> <s id="id.002594">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. </s> <s id="id.002595">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;t­alterũ">e&longs;t <lb/>alterum</expan> ab altero conuolui. <pb xlink:href="035/01/212.jpg" pagenum="172" />Sed perinde ac &longs;i &longs;uo motu <lb/>alter non moueatur, nul­<lb/>lum que motum habeat. </s> <s id="id.002596">Et <lb/>&longs;i habeat eo <expan abbr="nõ">non</expan> vtatur, hoc <lb/>accidit. </s> <s id="id.002597">Quando igitur ma­<lb/>gnus paruum <expan abbr="alligatũ">alligatum</expan> mo­<lb/>uerit, hic paruus <expan abbr="tãtundem">tantundem</expan> <lb/>mouetur. </s> <s id="id.002598">Quando verò <lb/>paruus rur&longs;us: tantundem <lb/>magnus. </s> <s id="id.002599">Separatim verò <lb/>vterque &longs;eip&longs;um mouet. <lb/></s> <s id="id.002600">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. </s> <s id="id.002601">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. </s> <s id="id.002602">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/></s> <s id="id.002603">Non igitur idem mouet &longs;impliciter: &longs;ed quodammodo. </s> </p> <p type="head"> <s id="id.002604">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002605">Qvod etiam dubit.] <emph type="italics"/>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/>uer&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="el">ou)k</foreign> <emph type="italics"/>expunximus. </s> <s id="id.002606">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 xlink:href="035/01/213.jpg" pagenum="173" /><figure id="id.035.01.213.1.jpg" xlink:href="035/01/213/1.jpg"/><lb/><emph type="italics"/>vt in A, B, <lb/>C, vbi lineæ <lb/>pro orbitis <lb/>inæqualium <lb/><expan abbr="circulorũ">circulorum</expan>, &longs;ed <lb/><expan abbr="annexorũ">annexorum</expan> D <lb/>E, F G, 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 id="id.002607">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. </s> <s id="id.002608">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. </s> <s id="id.002609">Huius enim <expan abbr="centrũ">centrum</expan>, e&longs;t quod primum <lb/>mouetur, non huius quod &longs;ecundario. </s> <s id="id.002610">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. </s> <s id="id.002611">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/></s> <s id="id.002612">Hæc tamen &longs;olutio quæ &longs;it, relinquo cogitandum. </s> <s id="id.002613">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/>motus habebit. </s> <s id="id.002614">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. </s> <s id="id.002615">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. </s> <s id="id.002616">Motus verò per <expan abbr="circulũ">circulum</expan> fit progrediente centro, <lb/>& huic accedit vt <expan abbr="circũuertatur">circumuertatur</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="el">a</foreign> <emph type="italics"/><expan abbr="centrũ">centrum</expan> perpetuò per<emph.end type="italics"/><lb/><arrow.to.target n="marg40"/><lb/><emph type="italics"/>æquidi&longs;tantem <expan abbr="lineã">lineam</expan> fertur in<emph.end type="italics"/> <foreign lang="el">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. </s> <s id="id.002617">Cæterum cum <expan abbr="tã">tam</expan><emph.end type="italics"/> <foreign lang="el">z g d,</foreign> <emph type="italics"/><expan abbr="quã">quam</expan><emph.end type="italics"/> <foreign lang="el">h b e</foreign> <emph type="italics"/>moueantur &longs;u­<lb/>per rectas<emph.end type="italics"/> <foreign lang="el">z l, h q</foreign> <emph type="italics"/>& quidem ita vt &longs;ingula puncta<emph.end type="italics"/> <foreign lang="el">z g d</foreign> <emph type="italics"/>tangant <lb/>&longs;ingula puncta<emph.end type="italics"/> <foreign lang="el">z l</foreign><emph type="italics"/>: <expan abbr="tũ">tum</expan><emph.end type="italics"/> <foreign lang="el">h b e</foreign> <emph type="italics"/>&longs;ingula puncta ip&longs;ius<emph.end type="italics"/> <foreign lang="el">h q.</foreign> </s> <s><emph type="italics"/>Tamen peri­<lb/>pheria<emph.end type="italics"/> <foreign lang="el">z g d,</foreign> <emph type="italics"/>aut <expan abbr="nõ">non</expan> e&longs;t æqualis rectæ<emph.end type="italics"/> <foreign lang="el">z l</foreign><emph type="italics"/>: aut peripheria<emph.end type="italics"/> <foreign lang="el">z b e</foreign> <emph type="italics"/><expan abbr="nõ">non</expan> e&longs;t <emph.end type="italics"/><pb xlink:href="035/01/214.jpg" pagenum="174" /><emph type="italics"/>æqualis rectæ<emph.end type="italics"/> <foreign lang="el">h q</foreign>: <emph type="italics"/>alioqui &longs;i <emph.end type="italics"/><lb/><figure id="id.035.01.214.1.jpg" xlink:href="035/01/214/1.jpg"/><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;tratum e&longs;t, e&longs;&longs;ent & periphe­<lb/>riæ æquales, maior minori, quod <lb/>ab&longs;urdum. </s> <s id="id.002618">Ex quo exploditur <lb/>ratio Bouilli, qui ex <expan abbr="circũuolu­tione">circumuolu­<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. </s> <s id="id.002619">Quæritur ergo quod e&longs;t &longs;uperiori problemate diffici­<lb/>lius, vt fieri poßit rectarum æqualium peragratio à circulis inæqua­<lb/>libus. </s> <s id="id.002620">Sit igitur vt rotæ axis<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>tran&longs;eat in F. </s> <s id="id.002622">Et quia<emph.end type="italics"/> <foreign lang="el">a h</foreign> <emph type="italics"/>& F G<emph.end type="italics"/><lb/><figure id="id.035.01.214.2.jpg" xlink:href="035/01/214/2.jpg"/><lb/><emph type="italics"/>æquales &longs;unt. </s> <s id="id.002623">Radij enim &longs;unt eiu&longs;dem circuli minoris &<emph.end type="italics"/> <foreign lang="el">h</foreign> <emph type="italics"/>G e&longs;t <lb/>æquidi&longs;tans<emph.end type="italics"/> <foreign lang="el">a</foreign> <emph type="italics"/>F. </s> <s id="id.002624">Erit per demon&longs;trata punctum G in linea F H. <lb/></s> <s id="id.002625">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="el">a</foreign> <emph type="italics"/>M &longs;ecet circulum <lb/>minorem<emph.end type="italics"/> <foreign lang="el">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="el">e,</foreign> <emph type="italics"/>vt in puncto I. </s> <s id="id.002626">Dico quod I e&longs;t punctum G. </s> <s id="id.002627">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="el">a</foreign> <emph type="italics"/>M, <lb/>erit etiam in linea F H. </s> <s id="id.002628">E&longs;t etiam in circulo<emph.end type="italics"/> <foreign lang="el">h</foreign> <emph type="italics"/>F<emph.end type="italics"/> <foreign lang="el">e. </foreign><emph type="italics"/>Ergo in puncto <lb/>communi vtrique. </s> <s id="id.002629">Nullum autem e&longs;t præter G. </s> <s id="id.002630">Igitur I peruenit<emph.end type="italics"/><pb xlink:href="035/01/215.jpg" pagenum="175" /><emph type="italics"/>in G. </s> <s id="id.002631">Sicque M retroceßit per angulum M G H. </s> <s id="id.002632">Contrà I an­<lb/>teceßit per angulum I G F, qui &longs;unt anguli æquales prop. 15. lib. 1. <lb/></s> <s>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. </s> <s id="id.002633">Hæc ex <lb/>Cardan. prop. 196. lib. 5. de proport. <emph.end type="italics"/></s> </p> <p type="margin"> <s id="id.002634"><margin.target id="marg40"/>Vide penul­<lb/>timum dia <lb/>gramma. </s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002635">26. <foreign lang="el">*peri\ tw=n klinw=n.</foreign></s> </p> <p type="main"> <s id="id.002636">26. De lectis. </s> </p> <p type="main"> <s id="id.002637"><foreign lang="el">*dia\ ti/ ta\s kli/nas poiou=si diplasiopleu/rous, th\n me\n<lb/> e(\c podw=n kai\ mikrw=| mei/zw pleura/n, th\n de\ triw=n; kai\ <lb/>dia\ ti/ e)ntei/nousin ou) kata\ dia/metron; </foreign></s> <s id="g0132502"><foreign lang="el">h)\ to\ me\n me/geqos thlikau/tas, <lb/>o(/pws toi=s sw/masin w)=si su/mmetroi; gi/nontai <lb/>ga\r ou(/tw diplasio/pleuroi, tetraph/xeis me\n to\ mh=kos, diph/xeis <lb/>de\ to\ pla/tos.</foreign></s> </p> <p type="main"> <s id="id.002638">Cur lectos lateribus du­<lb/>plos faciunt, vno quidem <lb/>&longs;ex pedum, vel paulò plus: <lb/>altero verò trium. </s> <s id="id.002639">Et cur <lb/>extendunt non &longs;ecundum <lb/>diametrum. </s> <s id="id.002640">An magnitu­<lb/>dine tantos faciunt, vt cor­<lb/>poribus corre&longs;pondeant. <lb/></s> <s id="id.002641">Sic enim lateribus dupli <lb/>efficiuntur, vt longitudine <lb/>quatuor cubitorum, latitu­<lb/>dine verò duorum &longs;int. </s> </p> <p type="head"> <s id="id.002642">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002643">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/></s> <s id="id.002644">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. </s> <s id="id.002645">vbi notandum <lb/>lectos habere formam parallelogrammi rectanguli. </s> <s id="id.002646">Itaque ex def. 1. <lb/>lib. 2. contineri &longs;ub duobus lateribus, quæ rectum angulum compre­<lb/>hendunt. </s> <s id="id.002648">Et hæc &longs;unt quæ hîc <expan abbr="con&longs;iderãtur">con&longs;iderantur</expan> in ratione dupla. </s> <s id="id.002649">Re&longs;pon­<lb/>det igitur &longs;ic fieri, vt corpori decubituro corre&longs;pondeat, & rationem <lb/>habeat vel æqualitatis, vel paulo maioris. </s> <s id="id.002650">Sic enim melius excipit in <lb/>eo <expan abbr="decumb&etilde;s">decumbens</expan> corpus. </s> <s id="id.002651">E&longs;t autem iu&longs;ta hominis magnitudo &longs;ex pedum: <lb/>quam vt pauci excedunt: ita quamplurimi non attingunt. </s> <s id="id.002652">Acce­<lb/>dunt tamen ad eam multi. </s> <s id="id.002653">Sicque plurimis opportuna quæ&longs;ita e&longs;t <emph.end type="italics"/><pb xlink:href="035/01/216.jpg" pagenum="176" /><emph type="italics"/>lecti magnitudo, quod ad <expan abbr="longitudin&etilde;">longitudinem</expan> attinet: &longs;ed nec minus quod ad <lb/>latitudinem. </s> <s id="id.002654">Seu enim &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"/><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. </s> <s id="id.002655">Extremæ autem figuræ &longs;unt, quæ &longs;um­<lb/>mam exten&longs;ionem, aut flexum 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. </s> <s id="id.002656">Ideo humida appel­<lb/>lata e&longs;t ab Hippocrate, cum humida corpora tendi non &longs;oleant. </s> <s id="id.002657">Sic <lb/>autem iacens tantum hinc quantum illinc ad reuolutionem corporis <lb/>&longs;emicubitum, quod &longs;atis e&longs;t, habebit. </s> <s id="id.002658">Nec enim de his agimus, quibus<emph.end type="italics"/> </s> </p> <p type="margin"> <s id="id.002659"><margin.target id="marg41"/>Inprogno&longs;t. </s> </p> <p type="main"> <s>Pinguis aqualiculus extento &longs;e&longs;quipede extat. </s> </p> <p type="main"> <s id="id.002660"><emph type="italics"/>Sed de moderatis hominibus, quibus hæc lecti latitudo conueniens <lb/>erit. </s> <s id="id.002661">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> </subchap1> <subchap1> <p type="main"> <s id="id.002662"><foreign lang="el">e)ntei/nousi de\ ou) kata\ dia/metron a)ll' <lb/>a)p' e)nanti/as, o(/pws ta/ te cu/la h(=tton diaspa=tai: ta/xista <lb/>ga\r sxi/zetai kata\ fu/sin diairou/mena tau/th|, kai\ e(lko/mena <lb/>ponei= ma/lista.</foreign></s> <s id="g0132504"><foreign lang="el">e)/ti e)peidh\ dei= ba/ros du/nasqai ta\ <lb/>sparti/a fe/rein, ou(/tws h(=tton pone/sei locoi=s toi=s sparti/ois <lb/>e)pitiqeme/nou tou= ba/rous h)\ plagi/ois.</foreign></s> <s id="g0132505"><foreign lang="el">e)/ti de\ e)/latton ou(/tw <lb/>sparti/on a)nali/sketai.</foreign></s> </p> <p type="main"> <s id="id.002663">Non extendunt <expan abbr="aut&etilde;">autem</expan> &longs;e­<lb/>cundum diamerrum: &longs;ed <lb/>contrà, vt ligna minus di­<lb/>uellantur. </s> <s id="id.002664">celerrimè enim <lb/>finduntur &longs;ecundum natu­<lb/>ram diui&longs;a, & eadem parte <lb/>di&longs;tracta laborant maximè. <lb/></s> <s id="id.002665">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/></s> <s id="id.002666">Præterea <expan abbr="etiã">etiam</expan> funium <expan abbr="quã­titas">quan­<lb/>titas</expan>: &longs;ic minor erit. </s> </p> <p type="head"> <s id="id.002667">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002668">Non extendunt.] <emph type="italics"/>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 xlink:href="035/01/217.jpg" pagenum="177" /><emph type="italics"/>metrum: &longs;ed in obliquum proten&longs;is, ad quam tripliciter re&longs;pondet. <lb/></s> <s id="id.002669">Primo quia &longs;tudendum e&longs;t durationi, ideo cauendum, ne &longs;pondæ lecti <lb/>findantur: aut rumpantur. </s> <s id="id.002670">Itaque eo modo lora &longs;unt extendenda, <lb/>quo ruptioni fißioniue minus ip&longs;æ obnoxiæ fiunt. </s> <s id="id.002671">At &longs;i obliquè ex­<lb/>tendantur, minus erunt: quam &longs;i &longs;ecundum diametrum. </s> <s id="id.002672">Iuxta ea quæ <lb/>demon&longs;trata &longs;unt cap. 15. lib. huius. </s> <s id="id.002673">Namque vt recta percußio ad <lb/>medium ligni oblongi facta facile ip&longs;um frangit: &longs;ic tractio firma <lb/>è directo à medio. </s> <s id="id.002674">E&longs;t enim tractio percu&longs;sionis &longs;pecies, vel princi­<lb/>pium. </s> <s id="id.002675">Et celerrimè rumpuntur, &longs;i &longs;ecundum naturam, id e&longs;t eam op­<lb/>portunitatem rumpantur. </s> <s id="id.002676">Non ergo lora &longs;ecundum diametrum ex­<lb/>tendi debent: verum obliquitus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002677">Præterea quoniam.] <emph type="italics"/>Secunda e&longs;t ratio. </s> <s id="id.002678">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 id="id.002679"><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. </s> <s id="id.002680">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. </s> <s id="id.002681">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 id="id.002682">Præterea etiam.] <emph type="italics"/>Tertia ratio. </s> <s id="id.002683">Lororum quantitas obliquitus <lb/>extentorum minor e&longs;t: quam &longs;ecundum diametrum. </s> <s id="id.002684">Vt autem &longs;int <lb/>parui pretij, ab&longs;tinendum tamen à &longs;uperfluis. </s> <s id="id.002685">fru&longs;trà enim fit per plu­<lb/>ra, quod fieri pote&longs;t per pauciora. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002686"><foreign lang="el">e)/stw ga\r kli/nh h( *a*z*h*i, kai\ di/xa <lb/>dih|rh/sqw h( *z*h kata\ to\ *b. i)/sa dh\ truph/mata/ e)stin <lb/>e)n th=| *z*b kai\ e)n th=| *z*a. kai\ ga\r ai( pleurai\ i)/sai ei)si/n: <lb/>h( ga\r o(/lh *z*h diplasi/a e)sti/n.</foreign></s> <s id="g0132507"><foreign lang="el">e)ntei/nousi d' w(s ge/graptai, <lb/>a)po\ tou= *a e)pi\ to\ *b, ei)=ta ou(= to\ *g, ei)=ta ou(= to\ *d, ei)=ta ou(= <lb/>to\ *q, ei)=ta ou(= to\ *e. kai\ ou(/tws a)ei/, e(/ws a)\n ei)s gwni/an <lb/>katastre/ywsin a)/llhn: </foreign></s> <s id="g0132508"><foreign lang="el">du/o ga\r e)/xousi gwni/ai ta\s a)rxa\s <lb/>tou= sparti/ou.</foreign></s> <s id="g0132509"><foreign lang="el">i)/sa de/ e)sti ta\ sparti/a kata\ ta\s ka/myeis, <lb/>to/ te *a*b kai\ *b*g tw=| *g*d kai\ *d*q. kai\ ta\ a)/lla de\ <lb/>ta\ toiau=ta/ e)stin, o(/ti ou(/tws e)/xei h( au)th\ a)po/deicis.</foreign></s> <s id="g0132510"><foreign lang="el">h( me\n <lb/>ga\r *a*b th=| *e*q i)/sh: i)/sai ga/r ei)sin ai( pleurai\ tou= *b*h*k <lb/>*a xwri/ou, kai\ ta\ truph/mata i)/sa die/sthken.</foreign></s> <s id="g0132511"><foreign lang="el">h( de\ *b*h i)/sh <lb/>th=| *k*a: h( ga\r *b gwni/a i)/sh th=| *h. e)n i)/sois ga\r h( me\n <lb/>e)kto/s, h( de\ e)nto/s: kai\ h( me\n *b e)sti\n h(mi/seia o)rqh=s: h( <lb/>ga\r *z*b i)/sh th=| *z*a: kai\ gwni/a de\ h( kata\ to\ *z o)rqh/.</foreign></s> <s id="g0132512"><foreign lang="el">h( <lb/>de\ *b gwni/a i)/sh th=| kata\ to\ *h: h( ga\r kata\ to\ *z o)rqh/, <lb/>e)peidh\ diplasio/pleuron to\ e(tero/mhkes kai\ pro\s me/son ke/klastai. <lb/>w(/ste h( *a*g th=| *e*h i)/sh. tau/th| de\ h( *k*q: para/llhlos <lb/>ga/r. w(/ste h( *b*g i)/sh th=| *k*q. h( de\ *g*e th=| *d*q.</foreign></s> <s id="g0132513"><foreign lang="el"><lb/>o(moi/ws de\ kai\ ai( a)/llai dei/knuntai o(/ti i)/sai ei)si\n ai( kata\ <lb/>ta\s ka/myeis du/o tai=s dusi/n.</foreign></s> <s id="g0132514"><foreign lang="el">w(/ste dh=lon o(/ti ta\ thlikau=ta <lb/>sparti/a o(/son to\ *a*b, te/ssara tosau=t' e)/nestin e)n th=| kli/nh|: </foreign></s> <s id="g0132515"><foreign lang="el"><lb/>o(/son d' e)sti\ to\ plh=qos tw=n e)n th=| *z*h pleura=| truphma/twn, <lb/>kai\ e)n tw=| h(mi/sei tw=| *z*b ta\ h(mi/sh.</foreign></s> <s id="g0132516"><foreign lang="el">w(/ste e)n th=| h(misei/a| <lb/>kli/nh| thlikau=ta mege/qh sparti/wn e)sti\n o(/son tw=| *b*a e)/nesti, <lb/>tosau=ta de\ to\ plh=qos o(/saper e)n tw=| *b*h truph/mata.</foreign></s> <s id="g0132517"><foreign lang="el"><lb/>tau=ta de\ ou)de\n diafe/rei le/gein h)\ o(/sa e)n th=| *a*z kai\ *b*z <lb/>ta\ suna/mfw.</foreign></s> <s id="g0132518"><foreign lang="el">ei) de\ kata\ dia/metron e)ntaqh=| ta\ sparti/a, <lb/>w(s e)n th=| *a*b*g*d kli/nh| e)/xei, ta\ h(mi/sea/ ei)sin ou) tosau=ta<lb/> o(/sa ai( pleurai\ a)mfoi=n, ai( *a*z *z*h: ta\ i)/sa de/, o(/sa <lb/>e)n tw=| *z*b*z*a truph/mata e)/nestin.</foreign></s> <s id="g0132519"><foreign lang="el">mei/zones de/ ei)sin ai( *a*z <lb/>*b*z du/o ou)=sai th=s *a*b. w(/ste kai\ to\ sparti/on mei=zon tosou/tw| <lb/>o(/son ai( pleurai\ a)/mfw mei/zous ei)si\ th=s diame/trou.</foreign></s> </p> <p type="main"> <s id="id.002687">Sit lectus <foreign lang="el">a z h i,</foreign> & <foreign lang="el">z h</foreign><lb/>bifariam diuidatur, vt in <foreign lang="el">b. </foreign><lb/></s> <s>Æqualia itaque &longs;unt fora­<lb/>mina, tum in <foreign lang="el">z b,</foreign> tum in <foreign lang="el">z <lb/>a.</foreign> </s> <s>Æqualia enim &longs;unt la­<lb/>tera. </s> <s id="id.002688">Nam totum <foreign lang="el">z h</foreign> du­<lb/>plum e&longs;t [<foreign lang="el">z a. </foreign>] </s> <s>Extendunt <lb/>verò vt &longs;criptum e&longs;t ab <pb xlink:href="035/01/218.jpg" pagenum="178" /><foreign lang="el">a</foreign> ad <foreign lang="el">b</foreign>: deinde vbi e&longs;t <foreign lang="el">g</foreign>: <lb/>po&longs;tea vbi <foreign lang="el">d,</foreign> po&longs;tea vbi <foreign lang="el">q,</foreign><lb/>deinceps vbi <foreign lang="el">e,</foreign> & &longs;ic &longs;em­<lb/>per quou&longs;que ad alium <expan abbr="cõ­uerterint">con­<lb/>uerterint</expan> angulum. </s> <s id="id.002689">Duo <lb/>etenim anguli habent fu­<lb/>nis principia. </s> <s id="id.002690">Sunt verò fu­<lb/>nes iuxta curuaturas æqua­<lb/>les, nempe <foreign lang="el">a b</foreign> & <foreign lang="el">b g</foreign> ip&longs;i <lb/><foreign lang="el">g d</foreign> & <foreign lang="el">d q</foreign>. </s> <s>Et alij &longs;unt eiu&longs;­<lb/>modi, quod eadem &longs;it de­<lb/>mon&longs;tratio. </s> <s id="id.002691">Etenim <foreign lang="el">a b</foreign> æ­<lb/>qualis e&longs;t ip&longs;i <foreign lang="el">e q.</foreign> </s> <s><expan abbr="Sũt">Sunt</expan> enim <lb/>æqualia latera parallelo­<lb/>grammi <foreign lang="el">b h k a,</foreign> & forami­<lb/>na æquedi&longs;tant: Æqualis <lb/>vero e&longs;t <foreign lang="el">b h</foreign> ip&longs;i <foreign lang="el">k a.</foreign> </s> <s>Nam <lb/>angulus <foreign lang="el">b</foreign> æqualis ip&longs;i <foreign lang="el">h.</foreign> </s> <s>In <lb/>parallelis enim hic <expan abbr="quid&etilde;">quidem</expan> <lb/>interior e&longs;t, ille externus, & <lb/><foreign lang="el">b</foreign> e&longs;t &longs;emirectus. </s> <s id="id.002692">E&longs;t enim <foreign lang="el">z <lb/>b</foreign> æqualis ip&longs;i <foreign lang="el">z a,</foreign> & angu­<lb/>lus qui ad <foreign lang="el">z</foreign> rectus, & angu­<lb/>lus <foreign lang="el">b</foreign> æqualis ei qui ad <foreign lang="el">h.</foreign> <lb/></s> <s>Nam qui ad <foreign lang="el">z</foreign> rectus. </s> <s id="id.002693">quo­<lb/>niam lateribus duplum al­<lb/>terolongum, & ad medium <lb/>curuatum e&longs;t. </s> <s id="id.002694">Itaque <foreign lang="el">a d</foreign><lb/>æqualis ip&longs;i <foreign lang="el">e h,</foreign> huic verò <lb/>ip&longs;a <foreign lang="el">k q</foreign> parallela. </s> <s id="id.002695">itaque <foreign lang="el">b <lb/>g</foreign> æqualis e&longs;t ip&longs;i <foreign lang="el">k q,</foreign> & <foreign lang="el">g e</foreign><lb/>ip&longs;i <foreign lang="el">d q.</foreign> </s> <s>Similiter & ali&etail; <expan abbr="de­mõ&longs;trãtur">de­<lb/>mon&longs;trantur</expan>, quod &longs;int æqua­<lb/>les in curuaturis duæ dua­<lb/>bus. </s> <s id="id.002696">Itaque clarum e&longs;t quod tanti &longs;unt in lecto funes: <lb/>quanta e&longs;t <foreign lang="el">a b</foreign> quater. </s> <s id="id.002697">Quanta e&longs;t autem multltudo <pb xlink:href="035/01/219.jpg" pagenum="179" />foraminum in latere <foreign lang="el">z h,</foreign><lb/>etiam in dimidio quod e&longs;t <lb/><foreign lang="el">z b</foreign> <expan abbr="dimidiũ">dimidium</expan> e&longs;t. </s> <s id="id.002698">Quare in <lb/>dimidio lecti, <expan abbr="tãta">tanta</expan> erit ma­<lb/>gnitudo funium: quantum <lb/>e&longs;t <foreign lang="el">a b.</foreign> </s> <s>Multitudine vero <lb/>tot: quot &longs;unt in <foreign lang="el">b h</foreign> fora­<lb/>mina. </s> <s id="id.002699">Quod perinde e&longs;t ac <lb/>dicere quot &longs;unt in <foreign lang="el">a z</foreign> & <lb/><foreign lang="el">b z</foreign> &longs;imul &longs;umptis. </s> <s id="id.002700">Si vero <lb/>&longs;ecundum diametrum <expan abbr="ex­tendãtur">ex­<lb/>tendantur</expan> funes, vt in lecto <lb/><foreign lang="el">a b g d</foreign> &longs;ehabent, dimidia <lb/>&longs;unt, non tot: quot latera <lb/>vtrorum que <foreign lang="el">a z, z h.</foreign> </s> <s>æqua­<lb/>lia vero foramina in&longs;unt <lb/>quot in <foreign lang="el">z b, z a,</foreign> duæ vero <lb/>cum &longs;int <foreign lang="el">a z, b z,</foreign> maiores <lb/>&longs;unt ip&longs;a <foreign lang="el">a b.</foreign> </s> <s>Itaque funis <lb/>tanto maior: quanto ambo <lb/>latera maiora &longs;unt diame­<lb/>tro. </s> </p> <p type="head"> <s id="id.002701">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002702">Sit lectus <foreign lang="el">a z h i. </foreign>] <emph type="italics"/>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. </s> <s id="id.002703">Ob&longs;curitas ex tam corru­<lb/>pto contextu manans 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. </s> <s id="id.002704">Sed in vna octo, in altera decem, non debuerit <emph.end type="italics"/><pb xlink:href="035/01/220.jpg" 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 alijs obliquiores: & tamen duæ antehac rationes videntur in <lb/>vna figura po&longs;tulare obliquas, in altera rectas. </s> <s id="id.002705">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. </s> <s id="id.002706">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. </s> <s id="id.002707">Sic enim diameter non<emph.end type="italics"/> <foreign lang="el">diagw/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. </s> <s id="id.002708">Atque hoc modo &longs;i non intelliga­<lb/>tur diameter: &longs;ed<emph.end type="italics"/> <foreign lang="el">diagw/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. </s> <s id="id.002709">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. </s> <s id="id.002710">Sit igitur prima A B C D, cuius la­<emph.end type="italics"/><lb/><figure id="id.035.01.220.1.jpg" xlink:href="035/01/220/1.jpg"/><lb/><emph type="italics"/>tus A B duplum &longs;it lateris A C, & quidem illud 4. pe­<lb/>dum, hoc duorum. </s> <s id="id.002711">In hac lora &longs;ecundum diametrum &longs;int quidem <lb/>&longs;ecundum longitudinem tria K N. </s> <s id="id.002712">L O, M P, & &longs;ic inter &longs;e <emph.end type="italics"/><pb xlink:href="035/01/221.jpg" pagenum="181" /><emph type="italics"/>& lateri A B æqualia prop. 34. lib. 1. </s> <s>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 id="id.002713"><emph type="italics"/>Sit &longs;ecunda forma<emph.end type="italics"/> <foreign lang="el">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="el">a c, h k, e d</foreign> <emph type="italics"/>tum <emph.end type="italics"/> <foreign lang="el">b c, q i, e g,</foreign> <emph type="italics"/>quæ quia pa­<emph.end type="italics"/><lb/><figure id="id.035.01.221.1.jpg" xlink:href="035/01/221/1.jpg"/><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. </s> <s>Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="el">a c</foreign> <emph type="italics"/>&longs;it ab angulo<emph.end type="italics"/> <foreign lang="el">a</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="el">c</foreign> <emph type="italics"/>medium lateris<emph.end type="italics"/> <foreign lang="el">g d</foreign><emph type="italics"/>: erit hæc æqualis ip&longs;i<emph.end type="italics"/> <foreign lang="el">b c,</foreign> <emph type="italics"/>quia latera <lb/>æqualium quadratorum. </s> <s id="id.002714">Vtrumque enim æquale e&longs;t duobus ex<emph.end type="italics"/> <foreign lang="el">a g, <lb/>g c,</foreign> <emph type="italics"/>vel quod idem e&longs;t ex<emph.end type="italics"/> <foreign lang="el">c d, d b</foreign> <emph type="italics"/>prop. 47. lib. 1. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002715"><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="el">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="el">a b g d. </foreign></s> </p> <p type="main"> <s id="id.002716"><emph type="italics"/>Demon&longs;tratio. </s> <s id="id.002717">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="el">a c, c b</foreign> <emph type="italics"/>duplum <expan abbr="it&etilde;">item</expan> e&longs;t quadrati ex A C. </s> <s id="id.002718">Ip&longs;um enim <expan abbr="cũ">cum</expan> quadratum <lb/>&longs;it. </s> <s id="id.002719"><expan abbr="Nã">Nam</expan><emph.end type="italics"/> <foreign lang="el">a c</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">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="el">a g</foreign> <emph type="italics"/>&<emph.end type="italics"/> <foreign lang="el">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="el">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="el">a c, c b</foreign><pb xlink:href="035/01/222.jpg" 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="el">a z, z b</foreign> <emph type="italics"/>prop. 47. lib. 1. </s> <s>E&longs;t enim angulus<emph.end type="italics"/> <foreign lang="el">a z b</foreign> <emph type="italics"/>rectus, cum &longs;it <lb/>reliquus trium<emph.end type="italics"/> <foreign lang="el">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="el">a z g, b z d</foreign> <emph type="italics"/>per coroll. prop. 32. lib. 1. <lb/></s> <s id="id.002723">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="el">a z, z b</foreign> <emph type="italics"/>cum rectangulo <lb/>bis &longs;ub<emph.end type="italics"/> <foreign lang="el">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="el">a z, z b</foreign> <emph type="italics"/>cum rectangulo bis comprehen&longs;o &longs;ub<emph.end type="italics"/> <foreign lang="el">a z, z b</foreign> <emph type="italics"/>&longs;unt <lb/>potentia lineæ<emph.end type="italics"/> <foreign lang="el">a z b</foreign> <emph type="italics"/>vtcunque &longs;ectæ in<emph.end type="italics"/> <foreign lang="el">z.</foreign> </s> <s><emph type="italics"/>E&longs;t ergo C A B maior <lb/>potentia quam<emph.end type="italics"/> <foreign lang="el">a z b,</foreign> <emph type="italics"/>proinde erit & longitudine maior per coroll. <lb/>è prop. 47. lib. 1. </s> <s>Similiter demon&longs;trabitur de reliquis. </s> <s id="id.002725">E&longs;t ergo maior <lb/>lororum quantitas in lecto A B C D: quam in lecto<emph.end type="italics"/> <foreign lang="el">a b d g,</foreign> <emph type="italics"/>quod <lb/>erat demon&longs;trandum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002726"><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. </s> <s id="id.002727">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. </s> <s id="id.002728">In lecto vero<emph.end type="italics"/><lb/><foreign lang="el">a b g d</foreign> <emph type="italics"/>cum omnes æquales lineæ &longs;int ip&longs;i<emph.end type="italics"/> <foreign lang="el">a z,</foreign> <emph type="italics"/>& &longs;it ex<emph.end type="italics"/> <foreign lang="el">a z</foreign> <emph type="italics"/>qua­<lb/>dratum æquale quadratis ex<emph.end type="italics"/> <foreign lang="el">a g, & g z</foreign> <emph type="italics"/>id e&longs;t 9. & 9. </s> <s>Erit igitur <lb/>18. quadratum ex<emph.end type="italics"/> <foreign lang="el">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. </s> <s>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 id="id.002729">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 id="id.002730">Iuxta curuaturas.] <foreign lang="el">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 id="id.002731">Sunt enim æqualia latera.] <emph type="italics"/>Deinceps ad finem corruptißi­<emph.end type="italics"/><pb xlink:href="035/01/223.jpg" pagenum="183" /><emph type="italics"/>ma ferè &longs;unt omnia. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002732">Angulus qui ad <foreign lang="el">z</foreign> rectus.] <emph type="italics"/>Angulus qui ad<emph.end type="italics"/> <foreign lang="el">z</foreign> <emph type="italics"/>continetur à <lb/>lateribus<emph.end type="italics"/> <foreign lang="el">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 id="id.002733">Angulus <foreign lang="el">b</foreign>] <emph type="italics"/>Id e&longs;t angulus<emph.end type="italics"/> <foreign lang="el">z b a</foreign> <emph type="italics"/>æqualis e&longs;t angulo<emph.end type="italics"/> <foreign lang="el">b h k</foreign><lb/><emph type="italics"/>quod verum e&longs;t. </s> <s id="id.002734">quia &longs;unt anguli externus & internus ad ea&longs;dem <lb/>partes duarum parallelarum<emph.end type="italics"/> <foreign lang="el">a b, k h</foreign> <emph type="italics"/>incidente in ip&longs;as recta<emph.end type="italics"/> <foreign lang="el">z h. </foreign></s> </p> <p type="main"> <s id="id.002735">In parallelis enim.] <emph type="italics"/>Quod hic dicit Ari&longs;toteles<emph.end type="italics"/> <foreign lang="el">i)/sas gra/mmas</foreign><lb/><emph type="italics"/>vertimus parallelas. </s> <s id="id.002736">Sic enim etiam locutus e&longs;t cap. 5. lib. 1. po&longs;teriore <lb/>analytic. </s> <s id="id.002737">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>. </s> <s id="id.002738">quia in omnibus &longs;it rectis. <lb/></s> <s id="id.002739">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 id="id.002740">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. </s> <s id="id.002741">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002742">27. <foreign lang="el">*dia\ ti/ xalepw/teron ta\ <lb/>makra\ cu/la a)p' a)/krou <lb/>fe/rein e)pi\ tw=| w)/mw| h)\ kata\ to\ me/son.</foreign></s> </p> <p type="main"> <s id="id.002743">27. Cur difficilius longa li­<lb/>gna humero feruntur ab <lb/>extremo: quam à medio <lb/>&longs;ui. </s> </p> <p type="main"> <s id="id.002744"><foreign lang="el">*dia\ ti/ xalepw/teron ta\ makra\ cu/la a)p' a)/krou <lb/>fe/rein e)pi\ tw=| w)/mw| h)\ kata\ to\ me/son, i)/sou tou= ba/rous o)/ntos; </foreign></s> <s id="g0132602"><foreign lang="el"><lb/>po/teron o(/ti saleuome/nou tou= cu/lou to\ a)/kron kwlu/ei fe/rein, <lb/>ma=llon a)ntispw=n th=| saleu/sei th\n fora/n; h)\ ka)\n <lb/>mhqe\n ka/mpthtai mhd' e)/xh| polu\ mh=kos, o(/mws xalepw/teron <lb/>fe/rein a)p' a)/krou; a)ll' o(/ti kai\ r(a=|on ai)/retai a)p' <lb/>a)/krou h)\ e)k me/sou, dia\ to\ au)to\ kai\ fe/rein ou(/tw r(a/|dion.</foreign></s> </p> <p type="main"> <s id="id.002745">Cur difficilius feruntur <lb/>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>. </s> <s id="id.002746">An quod <lb/><expan abbr="extremũ">extremum</expan> ligni agitati ferri <lb/>prohibet, vt quod <expan abbr="ge&longs;tatio­n&etilde;">ge&longs;tatio­<lb/>nem</expan> agitatione magis reuel­<lb/>lat? </s> <s id="id.002747">An quoniam, licet nihil <lb/>incuruetur, <expan abbr="neq;">neque</expan> valdè <expan abbr="ma­ior&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. </s> <s id="id.002748">Ob id ip&longs;um etiam facilius fertur. </s> </p> <pb xlink:href="035/01/224.jpg" pagenum="184" /> <p type="head"> <s id="id.002749">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002750">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. </s> <s id="id.002751">Huic dupliciter re&longs;pondetur. </s> <s id="id.002752">Prima re&longs;pon&longs;io e&longs;t &longs;pecialis ad <lb/>lignum quod flexile &longs;i &longs;it incuruatur, & nutat. </s> <s id="id.002753">Nutatio autem cum <lb/>&longs;it motus ad alium terminum: quam ad quem fertur, impedit. </s> <s id="id.002754">quin <lb/>& aggrauans premit magis ferentem. </s> <s id="id.002755">Secunda e&longs;t generalis ex ele­<lb/>uatione faciliori, quæ &longs;ic concludetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002756"><emph type="italics"/>Quo modo lignum vel pondus facilius eleuatur, eodem & fer­<lb/>tur. </s> <s id="id.002757">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 id="id.002758"><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 id="id.002759"><emph type="italics"/>Ergo lignum longum facilius ex humero fertur per medium: <lb/>quam per extremum. <emph.end type="italics"/></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.002760"><foreign lang="el">ai)/tion de\ o(/ti e)k me/sou me\n ai)ro/menon a)ei\ e)pikoufi/zei a)/llhla <lb/>ta\ a)/kra, kai\ qa/teron me/ros to\ e)pi\ qa/teron eu)= ai)/rei. <lb/>w(/sper ga\r ke/ntron gi/netai to\ me/son, h(=| e)/xei to\ ai)=ron h)\ <lb/>fe/ron.</foreign></s> <s id="g0132604"><foreign lang="el">ei)s to\ a)/nw ou)=n koufi/zetai e(ka/teron tw=n a)/krwn ei)s <lb/>to\ ka/tw r(e/pon. a)po\ de\ tou= a)/krou ai)ro/menon h)\ fero/menon ou) <lb/>poiei= tou=to, a)ll' a(/pan to\ ba/ros r(e/pei e)f' e(\n me/son, ei)s <lb/>o(/per ai)/retai h)\ fe/retai.</foreign></s> <s id="g0132605"><foreign lang="el">e)/stw me/son e)f' ou(= *a, a)/kra *b*g.</foreign></s> <s id="g0132606"><foreign lang="el"><lb/>ai)rome/nou ou)=n h)\ ferome/nou kata\ to\ *a, to\ me\n *b ka/tw <lb/>r(e/pon a)/nw ai)/rei to\ *g, to\ de\ *g ka/tw r(e/pon to\ *b a)/nw ai)/rei: <lb/>a(/ma de\ ai)ro/mena a)/nw poiei= tau=ta.</foreign></s> </p> <p type="main"> <s id="id.002761">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. </s> <s id="id.002762">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. </s> <s id="id.002763">Itaque <expan abbr="vtrumq;">vtrumque</expan> <lb/>extremorum deor&longs;um ver­<lb/>gens &longs;ur&longs;um &longs;u&longs;penditur. <lb/></s> <s id="id.002764">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. </s> <s id="id.002765">Hoc &longs;it <foreign lang="el">a,</foreign><lb/>extrema <foreign lang="el">b, g.</foreign> </s> <s>Igitur eleuato <lb/>vel ge&longs;tato qua parte e&longs;t <foreign lang="el">a</foreign>: <pb xlink:href="035/01/225.jpg" pagenum="185" /><figure id="id.035.01.225.1.jpg" xlink:href="035/01/225/1.jpg"/><lb/><foreign lang="el">b</foreign> quidem deor&longs;um ver­<lb/>gens attollit <foreign lang="el">g</foreign>:<foreign lang="el">g</foreign> vero deor­<lb/>&longs;um repens attollit <foreign lang="el">b.</foreign> </s> <s>Si­<lb/>mul autem eleuata idem præ&longs;tant. </s> </p> <p type="head"> <s id="id.002766">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002767">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. </s> <s id="id.002768">Et &longs;ic &longs;e&longs;e mutuò librantia pondera, mutuò etiam &longs;e &longs;ubleuant. <lb/></s> <s id="id.002769">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. </s> <s id="id.002770">Non ita e&longs;t vbi lignum per <lb/>extremum fertur: &longs;ed totum ad partem vnam vergit ab eo per quod <emph.end type="italics"/><lb/><figure id="id.035.01.225.2.jpg" xlink:href="035/01/225/2.jpg"/><lb/><emph type="italics"/>ge&longs;tatur deflectens. </s> <s id="id.002771">Ex deflexione autem <lb/>&longs;eu depreßione extremi, tanquam ponderis <lb/>prementis, labor augetur in ferente. </s> <s id="id.002772">Ergo <lb/>vbi depreßio nulla e&longs;t, vt in priori modo, <lb/>ibi labor minor erit. </s> <s id="id.002773">Et &longs;ic lignum lon­<lb/>gum ab extremo difficilius fertur quam <lb/>à medio. </s> <s id="id.002774">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. </s> <s id="id.002775">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/></s> <s id="id.002776">Præterea in perpendiculari ip&longs;a lancea to­<lb/>ta pondus e&longs;t. </s> <s id="id.002777">Huic &longs;u&longs;tinendæ quæ vis <emph.end type="italics"/><pb xlink:href="035/01/226.jpg" pagenum="186" /><emph type="italics"/>&longs;ufficiet, &longs;ufficiet & <emph.end type="italics"/><lb/><figure id="id.035.01.226.1.jpg" xlink:href="035/01/226/1.jpg"/><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> </subchap1> <subchap1> <p type="main"> <s id="id.002778"><foreign lang="el">*dia\ ti/ li/an makro\n ba/ros<lb/> xalepw/teron fe/rein e)pi\ tou= <lb/>w)/mou, h)\ e)/latton.</foreign></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002779">28. Cur humero difficilius <lb/>fertur valdè <expan abbr="lõgum">longum</expan> pon­<lb/>dus: quam breue. </s> </p> <p type="main"> <s id="id.002780"><foreign lang="el">*dia\ ti/, e)a\n h)=| li/an makro\n to\ au)to\ ba/ros, xalepw/teron <lb/>fe/rein e)pi\ tou= w)/mou, ka)\n me/son fe/rh| tis, h)\ e)a\n <lb/>e)/latton h)=|; </foreign></s> <s id="g0132702"><foreign lang="el">pa/lai e)le/xqh w(s ou)k e)/stin ai)/tion h( sa/leusis: <lb/>a)ll' h( sa/leusis nu=n ai)/tio/n e)stin.</foreign></s> <s id="g0132703"><foreign lang="el">o(/tan ga\r h)=| makro/teron, <lb/>ta\ a)/kra saleu/etai, w(/ste ei)/h a)\n kai\ to\n fe/ronta xalepw/teron <lb/>fe/rein ma=llon.</foreign></s> <s id="g0132704"><foreign lang="el">ai)/tion de\ tou= saleu/esqai ma=llon, <lb/>o(/ti th=s au)th=s kinh/sews ou)/shs meqi/statai ta\ a)/kra, o(/sw|per <lb/>a)\n h)=| makro/teron to\ cu/lon.</foreign></s> <s id="g0132705"><foreign lang="el">o( me\n ga\r w)=mos ke/ntron, e)f' <lb/>ou(= to\ *a [1me/nei ga\r tou=to]1, ai( de\ *a*b kai\ *a*g ai( e)k tou= <lb/>ke/ntrou. o(/sw| d' a)\n h)=| mei=zon to\ e)k tou= ke/ntrou h)\ to\ *a*b <lb/>h)\ kai\ to\ *a*g, ple/on meqi/statai me/geqos. de/deiktai de\ <lb/>tou=to pro/teron.</foreign></s> </p> <p type="main"> <s id="id.002781">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. </s> <s id="id.002782">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. </s> <s id="id.002783">Quum <lb/>enim longius fuerit extre­<lb/>ma agitantur. </s> <s id="id.002784">Ideo contin­<lb/>git ferentem multò diffici­<lb/>lius ferre. </s> <s id="id.002785">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. </s> <s id="id.002786">Etenim hu­<pb xlink:href="035/01/227.jpg" pagenum="187" />merus &longs;it <expan abbr="c&etilde;trum">centrum</expan> vbi e&longs;t <foreign lang="el">a. </foreign><lb/></s> <s>hoc enim manet. </s> <s id="id.002787">Sint verò <lb/><foreign lang="el">a b</foreign> & <foreign lang="el">a g</foreign> lineæ ex centro. <lb/></s> <s id="id.002788"><expan abbr="Quãtò">Quantò</expan> igitur fuerit maius <lb/>id, quod ex <expan abbr="c&etilde;tro">centro</expan>, vel ip&longs;um <lb/><foreign lang="el">a g,</foreign> tantò plus magnitudo <lb/>illa transfertur, quod e&longs;t <lb/>prius demon&longs;tratum. </s> </p> <p type="head"> <s id="id.002789">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002790">Cvr &longs;i fuerint.] <emph type="italics"/>Huius capitis problema e&longs;t. </s> <s id="id.002791">cur lignum lon­<lb/>gius è medio ge&longs;tatum breuiori eiu&longs;dem ponderis difficilius ex <lb/>humero fertur. </s> <s id="id.002792">Cui vt re&longs;pondeat generalem præcedentis &longs;olutionem <lb/>reijcit, & 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. </s> <s id="id.002793">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 id="id.002794"><emph type="italics"/>Sit igitur lignum <lb/>longius A B è me­<emph.end type="italics"/><lb/><figure id="id.035.01.227.1.jpg" xlink:href="035/01/227/1.jpg"/><lb/><emph type="italics"/>dio C ge&longs;tatum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002795"><emph type="italics"/>Sit & breuius <emph.end type="italics"/><lb/><figure id="id.035.01.227.2.jpg" xlink:href="035/01/227/2.jpg"/><lb/><emph type="italics"/>D E eiu&longs;dem pon­<lb/>deris puta decem librarum è medio F ge&longs;tatum etiam. </s> <s id="id.002796">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/></s> <s id="id.002797">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. </s> <s id="id.002798">Item B. </s> <s id="id.002799">Ergo tum A tum B <lb/>plus impediunt ferentem ex C: quam D & E ex F. </s> <s id="id.002800">Quæri hic <lb/>po&longs;&longs;et cur pondera &longs;ini&longs;tro humero facilius ferantur, quam dextro. <lb/></s> <s id="id.002801">Hoc fit, quia dextrum cum <expan abbr="natũ">natum</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. </s> <s id="id.002802">Impeditum enim omne minus probe <lb/>fungitur officio. </s> <s id="id.002803">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 & tractione valet ab onere liberari. </s> <s id="id.002804">E&longs;t <expan abbr="aut&etilde;">autem</expan> <expan abbr="dextrũ">dextrum</expan> crus. <emph.end type="italics"/></s> </p> </subchap1> </chap> <pb xlink:href="035/01/228.jpg" pagenum="188" /> <chap> <subchap1> <p type="main"> <s id="id.002805">29. <foreign lang="el">*dia\ ti/ e)pi\ toi=s fre/asi ta\ <lb/>khlw/neia poiou=si tou=ton to\n <lb/>tro/pon.</foreign></s> </p> <p type="main"> <s id="id.002806">29. Cur in puteis tolleno­<lb/>nem faciunt hoc mo­<lb/>do. </s> </p> <p type="main"> <s id="id.002807"><foreign lang="el">*dia\ ti/ e)pi\ toi=s fre/asi ta\ khlw/neia poiou=si tou=ton to\n <lb/>tro/pon; prostiqe/asi ga\r ba/ros e)n tw=| cu/lw| to\n mo/libdon, <lb/>o)/ntos ba/rous tou= ka/dou au)tou=, kai\ kenou= kai\ plh/rous o)/ntos.</foreign></s> <s id="g0132802"><foreign lang="el"><lb/>h)\ o(/ti e)n dusi\ xro/nois dih|rhme/nou tou= e)/rgou [1ba/yai ga\r dei=, <lb/>kai\ tou=t' a)/nw e(lku/sai]1 sumbai/nei kaqie/nai me\n keno\n r(a|­<lb/>di/ws, ai)/rein de\ plh/rh xalepw=s; </foreign></s> <s id="g0132803"><foreign lang="el">lusitelei= ou)=n mikrw=| bradu/teron <lb/>ei)=nai to\ katagagei=n pro\s to\ polu\ koufi/sai to\ <lb/>ba/ros a)na/gonti. tou=to ou)=n poiei= e)p' a)/krw| tw=| khlwnei/w| o( <lb/>mo/libdos proskei/menos h)\ o( li/qos.</foreign></s> <s id="g0132804"><foreign lang="el">kaqimw=nti me\n ga\r gi/netai <lb/>ba/ros mei=zon h)\ ei) mo/non keno\n dei= kata/gein to\n ka/don: <lb/>o(/tan de\ plh/rhs h)=|, a)na/gei o( mo/libdos, h)\ o(/ ti a)\n h)=| <lb/>to\ proskei/menon ba/ros.</foreign></s> <s id="g0132805"><foreign lang="el">w(/st' e)sti\ r(a=|on au)tw=| ta\ a)/mfw <lb/>h)\ e)kei=no.</foreign></s> </p> <p type="main"> <s id="id.002808">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/></s> <s id="id.002809">An quod in duo tempora <lb/>diui&longs;um &longs;it hauriendi opus <lb/>Immergere enim opor­<lb/>tet &longs;itulam, & hanc rur&longs;us <lb/>&longs;ur&longs;um trahere. </s> <s id="id.002810">Contingit <lb/>quidem vacuam facile de­<lb/>mittere. </s> <s id="id.002811">At plenam attolle­<lb/>re difficile. </s> <s id="id.002812">Confert igitur <lb/>paulo tardius demittere, vt <lb/>qui attollit, attollat multò <lb/>facilius. </s> <s id="id.002813">Hoc autem pr&etail;&longs;tat <lb/>plumbum, vel lapis extre­<lb/>mo tollenonis adiectus. <lb/></s> <s id="id.002814">Demittenti enim pondus <lb/>redditur maius: quam &longs;i &longs;o­<lb/>lam vacuam &longs;itulam opor­<lb/>teret demittere. </s> <s id="id.002815">At quan­<lb/>do plena fuerit, hanc edu­<lb/>cit plumbum, vel &longs;i quod <lb/>aliud pondus adiectum &longs;it. <lb/></s> <s id="id.002816"><expan abbr="Itaq;">Itaque</expan> hoc modo vtrumque <lb/>factu facilius e&longs;t: quam alterum. </s> </p> <p type="head"> <s id="id.002817">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002818">Cvr in puteis tollenonem.] <foreign lang="el">Khlo/neion</foreign> <emph type="italics"/>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 xlink:href="035/01/229.jpg" pagenum="189" /><emph type="italics"/>hortos, vel ad aliud quod volunt. </s> <s id="id.002819">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 id="id.002820">Vicini quo que &longs;int amnes, quos incola durus</s> </p> <p type="main"> <s id="id.002821">Attrahat auxilio &longs;emper &longs;itientibus hortis:</s> </p> <p type="main"> <s id="id.002822">Aut fons illa chrymet putei non &longs;ede profunda</s> </p> <p type="main"> <s id="id.002823">Ne grauis hau&longs;turis celonius ilia vellat. </s> </p> <p type="main"> <s id="id.002824"><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="id.035.01.229.1.jpg" xlink:href="035/01/229/1.jpg"/><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 adijcitur ad <lb/>commodiorem, vt vult hîc Ari&longs;tottles, à puteo F exhau&longs;tum. </s> <s id="id.002825">Quæ­<lb/>rit igitur cur in altero tollenonis extremo pondus adijciatur. </s> <s id="id.002826">Huius <lb/>quæ&longs;tionis difficultas arguitur, quod &longs;itula &longs;eu vacua, &longs;eu plena, &longs;it <lb/>pondus. </s> <s id="id.002827">Pondus autem ponderi adiectum difficilius moueri deberet. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/230.jpg" pagenum="190" /> <p type="main"> <s id="id.002828">An quod in duo.] <emph type="italics"/>Re&longs;pon&longs;io e&longs;t ex di&longs;tinctione duplicis mo­<lb/>tus exhau&longs;tioni per tollenonem nece&longs;&longs;arij. </s> <s id="id.002829">Alter e&longs;t immer&longs;ionis: al­<lb/>ter eleuationis. </s> <s id="id.002830">Et illum quidem fatetur Ari&longs;toteles ex adiecto pon­<lb/>dere reddi difficiliorem: at hunc contra multo effici faciliorem. </s> <s id="id.002831">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. </s> <s id="id.002832">Vnde autem tum hæc, tum illud pendeat non dicit Ari&longs;tote­<lb/>les, quia ex antecedentibus facile intellectum. </s> <s id="id.002833">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. </s> <s id="id.002834">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. </s> <s id="id.002835">Et &longs;ic facilius B <lb/>attolletur cum annexa &longs;itula. </s> <s id="id.002836">Po&longs;&longs;et etiam hæc quæ&longs;tio ad libram <lb/>commodißimè referri. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002837">30. <foreign lang="el">*dia\ ti/ o(/tan fe/rwsin e)pi\ <lb/>cu/lou du/o a)/nqrwpoi i)=son ba/­<lb/>ros, ou)x o(moi/ws qli/bontai.</foreign></s> </p> <p type="main"> <s id="id.002838">30. Cur cum duo homines <lb/><expan abbr="cũ">cum</expan> pertica pondus æqua­<lb/>le ferunt, non æqualiter <lb/>premuntur. </s> </p> <p type="main"> <s id="id.002839"><foreign lang="el">*dia\ ti/, o(/tan fe/rwsin e)pi\ cu/lou h)/ tinos toiou/tou du/o <lb/>a)/nqrwpoi i)/son ba/ros, ou)x o(moi/ws qli/bontai, e)a\n mh\ e)pi\ <lb/>tw=| me/sw| h)=| to\ ba/ros, a)lla\ ma=llon o(/sw| a)\n e)ggu/teron h)=| <lb/>tw=n fero/ntwn; </foreign></s> <s id="g0132902"><foreign lang="el">h)\ dio/ti moxlo\s me\n gi/netai ou(/tws e)xo/ntwn <lb/>to\ cu/lon, to\ de\ ba/ros u(pomo/xlion, </foreign></s> <s id="g0132903"><foreign lang="el">o( de\ e)ggu/teros tou= <lb/>ba/rous tw=n fero/ntwn to\ ba/ros to\ kinou/menon, a(/teros de\ <lb/>tw=n fero/ntwn to\ ba/ros o( kinw=n.</foreign></s> <s id="g0132904"><foreign lang="el">o(/sw| ga\r ple/on a)pe/xei tou= <lb/>ba/rous, tosou/tw| r(a=|on kinei=, kai\ qli/bei ma=llon to\n e(/teron <lb/>ei)s to\ ka/tw, w(/sper a)nterei/dontos tou= ba/rous tou= e)pikeime/nou <lb/>kai\ ginome/nou u(pomoxli/ou.</foreign></s> <s id="g0132905"><foreign lang="el">e)n me/sw| de\ u(pokeime/nou tou= <lb/>ba/rous, ou)de\n ma=llon a(/teros qate/rw| gi/netai ba/ros, ou)de\ <lb/>kinei=, a)ll' o(moi/ws e(ka/teros e(kate/rw| gi/netai ba/ros.</foreign></s> </p> <p type="main"> <s id="id.002840">Cur cum duo homines <lb/>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. </s> <s id="id.002841">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 xlink:href="035/01/231.jpg" pagenum="191" />facilius mouet, & alterum <lb/>deor&longs;um premit magis <expan abbr="tã­quam">tan­<lb/>quam</expan> pondus adiectum, <lb/>quod e&longs;t hypomochlium <lb/>renitatur. </s> <s id="id.002842">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 id="id.002843">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002844">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 phalangarij Baiuli ijs <expan abbr="vt&etilde;tes">vtentes</expan>, qui ex numero tetrapho­<lb/>ri, & hexaphori dicti &longs;unt. </s> <s id="id.002845">Quærit igitur hîc Ari&longs;toteles. </s> <s id="id.002846">cur è duo­<lb/>bus pondus aliquod phalanga ferentibus, quò ponderi propinquior e&longs;t <lb/>alter, eò magis remotiori prematur. </s> <s id="id.002847">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>. </s> <s id="id.002848">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. </s> <s id="id.002849"><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. </s> <s id="id.002850">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. </s> <s id="id.002851">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. </s> <s id="id.002852">Neque enim in hac vectis <expan abbr="circũduci­tur">circumduci­<lb/>tur</expan>: &longs;ed premit <expan abbr="tantũ">tantum</expan> &longs;u&longs;tinentes, vt quid graue. </s> <s id="id.002853">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. </s> <s id="id.002854">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. </s> <s id="id.002856">Nempe &longs;i in extremis vectis duæ &longs;int potentiæ, inter quas <lb/>pondus &longs;it &longs;u&longs;pen&longs;um. </s> <s id="id.002857">Erit vna ad alteram vt interualla inter po­<lb/>tentias, & pondus reciprocè. </s> <s id="id.002858">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. </s> <s id="id.002859">Sit igitur vt B C &longs;it minor: quam A C. </s> <s id="id.002860">Ergo A <emph.end type="italics"/><pb xlink:href="035/01/232.jpg" pagenum="192" /><emph type="italics"/>potentia <emph.end type="italics"/><lb/><figure id="id.035.01.232.1.jpg" xlink:href="035/01/232/1.jpg"/><lb/><emph type="italics"/>erit mi­<lb/>nor: <expan abbr="quã">quam</expan> <lb/>B, id e&longs;t <lb/>potentia <lb/>minor in <lb/>A &longs;ic di <lb/>&longs;tante à <lb/>C &longs;ufficiet &longs;u&longs;tinendo ponderi. </s> <s id="id.002861">Po&longs;itis igitur A & B potentijs <lb/>æqualibus, A facilius &longs;u&longs;tinebit, & quidem tantò: quantò A di­<lb/>&longs;tabit magis ab C. </s> <s id="id.002862">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. </s> <s id="id.002863">Ob id rectè dictum e&longs;t illud <lb/>ab Ouidio,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002864">Non benè inæquales veniunt ad aratra Iuuenci:</s> </p> <p type="main"> <s id="id.002865">Si qua velis aptè nubere, nube pari. </s> </p> <p type="main"> <s id="id.002866"><emph type="italics"/>Si enim inæquales tunc grandior minorem premit magis: ob id periti <lb/>agricolæ, &longs;i quando alterius iugatorum laborem leuare velint, lorum <lb/>longius efficientes ad ip&longs;um religant. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002867"><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. </s> <s id="id.002868">Nam cum de&longs;cendat &longs;ecundum rectam 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="id.035.01.232.2.jpg" xlink:href="035/01/232/2.jpg"/><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. </s> <s>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. </s> <s id="id.002869">Et &longs;ic E plus <lb/>de&longs;cendit re&longs;pectu B: quam re&longs;pectu A. </s> <s id="id.002870">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> </subchap1> </chap> <pb xlink:href="035/01/233.jpg" pagenum="193" /> <chap> <subchap1> <p type="main"> <s id="id.002871">31. <foreign lang="el">*dia\ ti/ oi( a)nista/menoi, ou(/tws <lb/>a)ni/stantai.</foreign></s> </p> <p type="main"> <s id="id.002872">31. Cur qui &longs;urgunt, &longs;ic &longs;ur­<lb/>gant. </s> </p> <p type="main"> <s id="id.002873"><foreign lang="el">*dia\ ti/ oi( a)nista/menoi pa/ntes pro\s o)cei=an gwni/an tw=| <lb/>mhrw=| poih/santes th\n knh/mhn a)ni/stantai, kai\ tw=| qw/raki <lb/>pro\s to\n mhro/n; ei) de\ mh/, ou)k a)\n du/nainto a)nasth=nai.</foreign></s> <s id="g0133002"><foreign lang="el">po/teron <lb/>o(/ti to\ i)/son h)remi/as pantaxou= ai)/tion, h( de\ o)rqh\ gwni/a <lb/>tou= i)/sou, kai\ poiei= sta/sin: dio\ kai\ fe/retai pro\s o(moi/as <lb/>gwni/as th=| periferei/a| th=s gh=s. ou) ga\r o(/ti kai\ pro\s o)rqh\n <lb/>e)/stai tw=| e)pipe/dw|.</foreign></s> <s id="g0133003"><foreign lang="el">h)\ o(/ti a)nista/menos gi/netai o)rqo/s, a)na/gkh <lb/>de\ to\n e(stw=ta ka/qeton ei)=nai pro\s th\n gh=n.</foreign></s> <s id="g0133004"><foreign lang="el">ei) ou)=n me/llei <lb/>e)/sesqai pro\s o)rqh/n, tou=to de/ e)sti to\ th\n kefalh\n e)/xein <lb/>kata\ tou\s po/das, kai\ gi/nesqai dh\ o(/te a)ni/statai.</foreign></s> <s id="g0133005"><foreign lang="el">o(/tan me\n <lb/>ou)=n kaqh/menos h)=|, para/llhlon e)/xei th\n kefalh\n kai\ tou\s <lb/>po/das, kai\ ou)k e)pi\ mia=s eu)qei/as.</foreign></s> <s id="g0133006"><foreign lang="el">h( kefalh\ *a e)/stw, qw/rac <lb/>*a*b, mhro\s *b*g, knh/mh *g*d.</foreign></s> <s id="g0133007"><foreign lang="el">pro\s o)rqh\n de\ gi/netai <lb/>o(/ te qw/rac [e)f' w(=n *a*b] tw=| mhrw=| kai\ o( mhro\s th=| knh/mh| <lb/>ou(/tws kaqhme/nw|. w(/ste ou(/tws e)/xonta a)du/naton a)nasth=nai.</foreign></s> <s id="g0133008"><foreign lang="el"><lb/>a)na/gkh de\ e)gkli=nai th\n knh/mhn kai\ poiei=n tou\s po/das u(po\ <lb/>th\n kefalh/n.</foreign></s> <s id="g0133009"><foreign lang="el">tou=to de\ e)/stai, e)a\n h( *g*d e)f' h(=s ta\ *g*z <lb/>ge/nhtai, kai\ a(/ma a)nasth=nai sumbh/setai, kai\ e)/xein e)pi\<lb/> th=s au)th=s i)/shs th\n kefalh/n te kai\ tou\s po/das. h( de\ *g*z <lb/>o)cei=an poiei= gwni/an pro\s th\n *b*g.</foreign></s> </p> <p type="main"> <s id="id.002874">Cur omnes qui &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="ne­queũt">ne­<lb/>queunt</expan>. </s> <s id="id.002875">An quia, quod &etail;qua <lb/>le e&longs;t, quietis vbique cau&longs;a <lb/>e&longs;t. </s> <s id="id.002876">Angulus autem rectus <lb/>e&longs;t æqualitatis, & &longs;tatum <lb/>facit. </s> <s id="id.002877">Ideò etiam fertur ad <lb/>angulos &longs;imiles, <expan abbr="cũ">cum</expan> &longs;uperfi­<lb/>cie terræ. </s> <s id="id.002878">Sic enim erit ip&longs;i <lb/>plano ad rectos: vel quod <lb/>&longs;urgens fit rectus. </s> <s id="id.002879">Nece&longs;&longs;e <lb/>e&longs;t autem &longs;tantem e&longs;&longs;e per­<lb/>pendicularem terræ. </s> <s id="id.002880">Si igi­<lb/>tur debet e&longs;&longs;e ad rectos. <lb/></s> <s id="id.002881">hoc e&longs;t caput habere è di­<lb/>recto pedum. </s> <s id="id.002882">Etiam quum <lb/>&longs;urgit fieri oportet. </s> <s id="id.002883">Quan­<lb/>do igitur &longs;edet caput habet <lb/>ad pedes parallelum, & ne­<lb/>quaquam in vna recta. </s> <s id="id.002884">Sit <lb/>caput <foreign lang="el">a,</foreign> thorax <foreign lang="el">a b,</foreign> fe­<lb/>mur <foreign lang="el">b g,</foreign> tibiæ <foreign lang="el">g d,</foreign> fiat <lb/>verò thorax <foreign lang="el">a b</foreign> ad rectos <lb/>femori, & femur tibiæ &longs;ic <lb/>&longs;edenti. </s> <s id="id.002885">Itaque &longs;ic &longs;e ha­<lb/>bentem impo&longs;&longs;ibile e&longs;t &longs;ur­<lb/>gere. </s> <s id="id.002886">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="el">g d</foreign> fiat <foreign lang="el">g</foreign><pb xlink:href="035/01/234.jpg" pagenum="194" /><foreign lang="el">z,</foreign> tunc &longs;imul &longs;urgere con­<lb/>tinget. </s> <s id="id.002887">Atque habere tum <lb/>caput, tum pedes in eadem <lb/>recta: <foreign lang="el">g z</foreign> vero cum <foreign lang="el">b g</foreign><lb/>angulum <expan abbr="acutũ">acutum</expan> con&longs;tituet</s> </p> <p type="head"> <s id="id.002888">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002889">Cvr qui &longs;urgunt.] <emph type="italics"/>Surrectio e&longs;t motio, quia homo è iacente <lb/>vel &longs;edente fit &longs;tans. </s> <s id="id.002890">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. </s> <s id="id.002891">hæ &longs;unt iacere &longs;upinum, iacere pronum, &longs;edere, &longs;tare. <lb/></s> <s id="id.002892">Iacere &longs;upinum e&longs;t cum &longs;pina animalis terram contingit. </s> <s id="id.002893">Iacere <expan abbr="pro­nũ">pro­<lb/>num</expan> e&longs;t cum humi venter reclinatus e&longs;t. </s> <s id="id.002894">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. </s> <s id="id.002895">Seßio e&longs;t &longs;itus in quo &longs;pina <lb/>cum femore, & femur cum tibia angulum rectum facit. </s> <s id="id.002896">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. </s> <s id="id.002897">Hæ duæ &longs;oli homini propriæ &longs;unt. </s> <s id="id.002898">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. </s> <s id="id.002899">Solus enim articulum femoris <lb/>& i&longs;chij ad anteriora flectit, ip&longs;ius verò genu retror&longs;um reflectit,<emph.end type="italics"/><arrow.to.target n="marg42"/><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> &longs;pina <expan abbr="rectũ">rectum</expan> fecit, tibia <expan abbr="nunquã">nunquam</expan> cum <lb/>femore rectum faciet: nec etiam ip&longs;a ad terram recta erit. </s> <s id="id.002900">quod ta­<lb/>men, vt &longs;eßio &longs;ecura fiat, nece&longs;&longs;um e&longs;t. </s> <s id="id.002901">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"/><emph type="italics"/>quæ e&longs;t ars artium habiturus erat, id e&longs;t &longs;olus artifex futurus erat. <lb/></s> <s id="id.002902">Manuum enim, quæ &longs;int <foreign lang="el">o)/rganon o)rganwn,</foreign> vt vocat no&longs;ter Gale­<lb/>nus actiones in opificijs, duabus his <expan abbr="tãtum">tantum</expan> egent figuris. </s> <s id="id.002903">Nemo enim <lb/>&longs;upinus aut pronus quicquam agit. </s> <s id="id.002904">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 id="id.002905"><margin.target id="marg42"/>Cap. 1. & 3. <lb/>lib. 3. de v&longs;u <lb/>part. </s> </p> <p type="margin"> <s id="id.002906"><margin.target id="marg43"/>Cap. 2. lib. 1. <lb/>de v&longs;u part. </s> </p> <p type="main"> <s id="id.002907">Re&longs;picio aduer&longs;us Olympum fronte intrepida. </s> </p> <pb xlink:href="035/01/235.jpg" pagenum="195" /> <p type="main"> <s id="id.002908"><emph type="italics"/>Illi numquam viderunt pi&longs;cem <expan abbr="dictũ">dictum</expan><emph.end type="italics"/> <foreign lang="el">*ourano/skopon,</foreign> <emph type="italics"/>id e&longs;t cæli &longs;pe­<lb/>culatorem. </s> <s id="id.002909">Hic namque vel inuitus cælum &longs;emper intuetur: homo <lb/>autem ni&longs;i collum reflectat retror&longs;um, cælum non videt. </s> <s id="id.002910">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. </s> <s id="id.002911">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 id="id.002912">Pronaque cum &longs;pectant animalia cætera terram,</s> </p> <p type="main"> <s id="id.002913">Os homini &longs;ublime dedit, cælum que videre</s> </p> <p type="main"> <s id="id.002914">Iu&longs;&longs;it, & erectos ad &longs;idera tollere vultus. </s> </p> <p type="main"> <s id="id.002915"><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;olum iacentes: &longs;ed & ambulantes &longs;ic &longs;unt. </s> <s id="id.002916">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. </s> <s id="id.002917">Vnus cereopithecus 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="el">a)nti/­<lb/>xeir,</foreign> proptereà dicitur à Galeno e&longs;&longs;e ridicula hominis imitatio. </s> <s id="id.002918">ab hoc <lb/>enim &longs;itu pollex<emph.end type="italics"/> <foreign lang="el">i)/son du/natai tn=| o(/lh| xeiri/. </foreign></s> </p> <p type="main"> <s id="id.002919">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="id.035.01.235.1.jpg" xlink:href="035/01/235/1.jpg"/><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. </s> <s id="id.002920">Ex hoc <lb/>&longs;itu ad &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 id="id.002921">An quia quod æquale.] <emph type="italics"/>Quæ&longs;tionem propo&longs;itam &longs;oluit du­<lb/>pliciter. </s> <s id="id.002922">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. </s> <s id="id.002923">hic erit &longs;yllogi&longs;mus. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002924"><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 xlink:href="035/01/236.jpg" pagenum="196" /> <p type="main"> <s id="id.002925"><emph type="italics"/>Angulorum rectitudo e&longs;t cau&longs;a quietis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002926"><emph type="italics"/>Ergò quandiu per&longs;euerauerit, &longs;urrectio non fiet. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002927"><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 id="id.002928"><emph type="italics"/>Æqualitas e&longs;t vbique cau&longs;a quietis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002929"><emph type="italics"/>Angulus rectus e&longs;t æqualitas, quia &longs;ibi & alijs omnibus re­<lb/>ctis rectilineis e&longs;t æqualis. </s> <s id="id.002930">quod e&longs;t axioma 10. lib. 1. </s> <s>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 id="id.002933"><emph type="italics"/>Ergò angulus rectus e&longs;t cau&longs;a quietis. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002934"><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. </s> <s id="id.002935">Et vt particulatim expendamus. <lb/></s> <s id="id.002936">videamus, vt omnia quie&longs;cant ad rectos angulos. </s> <s id="id.002937">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. </s> <s id="id.002938">Itaque in­<lb/>&longs;i&longs;tunt medio ad angulos rectos. </s> <s id="id.002939">Ob id terra cubico octonûm recto­<lb/>rum &longs;olido à Pythagoreis & à Platone e&longs;t comparata. </s> <s id="id.002940">Deinde arbo­<lb/>res & plantarum omne genus rectà <expan abbr="in&longs;i&longs;tũt">in&longs;i&longs;tunt</expan> plano. </s> <s id="id.002941">Durabile in ædi­<lb/>ficijs nihil e&longs;t, ni&longs;i rectà in&longs;i&longs;tat. </s> <s id="id.002942">Po&longs;tremò hominis quies, &longs;eu iaceat <lb/>humi, &longs;eu &longs;edeat, &longs;eu &longs;tet, fit per rectos angulos. </s> <s id="id.002943">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/></s> <s id="id.002944">Sedet quis in Hemicyclo? </s> <s id="id.002945">tibijs cum femoribus & femoribus rur&longs;us <lb/>cum &longs;pina dor&longs;i rectos angulos facit. </s> <s id="id.002946">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. </s> <s id="id.002947">Stat au­<lb/>tem? </s> <s id="id.002948">cum omnibus rectis à quibus tangitur in ip&longs;o plano rectos etiam <lb/>angulos facit. </s> <s id="id.002949">Ergo quies & &longs;tatus per angulos rectos fiunt. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002950">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. </s> <s id="id.002951">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. </s> <s id="id.002952">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. </s> <s id="id.002953">Huius <lb/>&longs;eßio non e&longs;t particeps. </s> <s id="id.002954">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 xlink:href="035/01/237.jpg" pagenum="197" /><emph type="italics"/>tuat: vel thoracis vt cum <lb/>femore, quia pedes rectà <emph.end type="italics"/><lb/><figure id="id.035.01.237.1.jpg" xlink:href="035/01/237/1.jpg"/><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. </s> <s id="id.002955">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="el">a b g d</foreign> <emph type="italics"/>pro &longs;edente, &<emph.end type="italics"/> <foreign lang="el">e b <lb/>g z</foreign> <emph type="italics"/>pro &longs;urgente declaratur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002956"><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. </s> <s id="id.002957">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. </s> <s id="id.002958">Is enim qui iacet, 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. </s> <s>vt &longs;ur­<emph.end type="italics"/><lb/><figure id="id.035.01.237.2.jpg" xlink:href="035/01/237/2.jpg"/><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 id="id.002959"><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. </s> <s id="id.002960">Et ea maximè vtuntur, qui &longs;e­<lb/>dentarias artes exercent. </s> <s id="id.002961">At tamen &longs;eßio latè &longs;umpta, fit ad angu­<lb/>los acutos, vt cum &longs;ella humilior e&longs;t tibijs &longs;edentis, & ad obtu&longs;os <lb/>cum altior e&longs;t. </s> <s id="id.002962">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. </s> <pb xlink:href="035/01/238.jpg" pagenum="198" /> <s>ut &longs;it thorax A B &longs;edens &longs;uper &longs;ella <lb/>tibijs. <arrow.to.target n="table2"/></s> </p> <table> <table.target id="table2"/> <row> <cell/> <cell><emph type="italics"/>Altiore K<emph.end type="italics"/></cell> </row> <row> <cell><emph type="italics"/>Æquali L<emph.end type="italics"/></cell> </row> <row> <cell><emph type="italics"/>Humiliore M<emph.end type="italics"/></cell> </row> </table> <p type="main"> <s id="id.002963"><emph type="italics"/>Dico quod ex <emph.end type="italics"/><lb/><figure id="id.035.01.238.1.jpg" xlink:href="035/01/238/1.jpg"/><lb/><emph type="italics"/>K facilius &longs;ur­<lb/>get: quam ex L: <lb/>quamque ex M. <lb/></s> <s id="id.002964">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/></s> <s id="id.002965">Et &longs;uper L quam <lb/>quam &longs;uper M. <lb/></s> <s id="id.002966">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. </s> <s id="id.002967">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. </s> <s id="id.002968">Altero &longs;cilicet pedum fir­<lb/>mato in &longs;olum, altero celeriter circumlato. </s> <s id="id.002969">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. </s> <s id="id.002970">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. </s> <s id="id.002971">Hinc cau&longs;am collige, cur &longs;int nonnulla ex his tam apta ferendis <lb/>&longs;arcinis & oneribus. </s> <s id="id.002972">Hinc quoque, &longs;i vis, collige cau&longs;am, cur baiuli <lb/>Pari&longs;ien&longs;es onera tanta &longs;uis harpagonibus: alij &longs;portulis ferant, nimi­<lb/>rum cum ita componant &longs;pinam, vt antror&longs;um reclinata moles &longs;u­<emph.end type="italics"/><pb xlink:href="035/01/239.jpg" 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. </s> <s id="id.002973">Sic enim moles &longs;uperni corporis, & onus habent aliquid ad <lb/>perpendiculum inferiorum partium, quod &longs;e &longs;uffulciat. </s> <s id="id.002974">Totu&longs;que ba­<lb/>iulus cum onere, quod gestat instar turbinis, aut coni vertice terræ <lb/>incumbit, ba&longs;i &longs;upereminente. </s> <s id="id.002975">Hinc etiam collige cur baiulis cum <lb/>onere a&longs;cen&longs;us graduum facilior e&longs;t: quam de&longs;cen&longs;us. </s> <s id="id.002976">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="etiã">etiam</expan> rarò 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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.002977">32. <foreign lang="el">*dia\ ti/ r(a=|on kinei=tai to\ ki­<lb/>nou/menon h)\ to\ me/non.</foreign></s> </p> <p type="main"> <s id="id.002978">32. Cur commotum faci­<lb/>lius moueatur, <expan abbr="quã">quam</expan> quie&longs;­<lb/>cens. </s> </p> <p type="main"> <s id="id.002979"><foreign lang="el">*dia\ ti/ r(a=|on kinei=tai to\ kinou/menon h)\ to\ me/non, oi(=on <lb/>ta\s a(ma/cas qa=tton kinoume/nas u(pa/gousin h)\ a)rxome/nas; </foreign></s> <s id="g0133102"><foreign lang="el"><lb/>h)\ o(/ti xalepw/taton me\n to\ ei)s tou)nanti/on kinou/menon kinh=sai <lb/>ba/ros; a)fairei=tai ga/r ti th=s tou= kinou=ntos duna/mews, ka)\n <lb/>polu\ qa=tton h)=|: a)na/gkh ga\r bradute/ran gi/nesqai th\n w)=sin <lb/>tou= a)ntwqoume/nou.</foreign></s> <s id="g0133103"><foreign lang="el">deu/teron de/, e)a\n h)remh=|: a)ntitei/nei ga\r kai\ <lb/>to\ h)remou=n.</foreign></s> <s id="g0133104"><foreign lang="el">to\ de\ kinou/menon e)pi\ to\ au)to\ tw=| w)qou=nti o(/moion <lb/>poiei= w(/sper a)\n ei) au)ch/seie/ tis th\n tou= kinou=ntos du/namin <lb/>kai\ taxuth=ta: o(\ ga\r u(p' e)kei/nou a)\n e)/pasxe, tou=to au)to\ <lb/>poiei= ei)s to\ pro\ o(dou= kinou/menon.</foreign></s> </p> <p type="main"> <s id="id.002980">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. </s> <s id="id.002981">An quia quod <lb/>mouetur <expan abbr="põdus">pondus</expan> in contra­<lb/>rium mouere <expan abbr="difficillimũ">difficillimum</expan>. <lb/></s> <s id="id.002982">Aufertur enim aliquid de <lb/>potentia motoris, licet ip&longs;e <lb/>multò fuerit velocior. </s> <s id="id.002983">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. </s> <s id="id.002984">Deinde verò &longs;i <lb/>quieuerit. </s> <s id="id.002985">Quie&longs;cens enim <lb/>re&longs;i&longs;tit. </s> <s id="id.002986">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. </s> <s id="id.002987">hoc ip&longs;um <lb/>facit id, quod in via commotum e&longs;t. </s> </p> <pb xlink:href="035/01/240.jpg" pagenum="200" /> <p type="head"> <s id="id.002988">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.002989">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. </s> <s id="id.002990">Quæ&longs;tio igitur e&longs;t, cur commotum facilius moueatur: <lb/>quam quie&longs;cens. </s> <s id="id.002991">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. </s> <s id="id.002992">Illu&longs;trari etiam po&longs;&longs;et exemplo nauium. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002993">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 id="id.002994"><emph type="italics"/>Motoris vim & celeritatem augens pondus, facilius impellitur: <lb/>contrà diminuens tardius. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002995"><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 id="id.002996"><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 id="id.002997"><emph type="italics"/>Commotum igitur facilius mouetur: quam quie&longs;cens. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.002998"><emph type="italics"/>Quod autem quie&longs;cens vim motoris diminuat, patet. </s> <s id="id.002999">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. </s> <s id="id.003000">Ergò qua vi eò moue­<lb/>retur, eadem re&longs;i&longs;tit, ne &longs;ur&longs;um vel lateraliter impellatur. </s> <s id="id.003001">Re&longs;istere <lb/>autem motori, diminuere e&longs;t eius vim in mouendo. </s> <s id="id.003002">Imò vera e&longs;t illa <lb/>propo&longs;itio. </s> <s id="id.003003">Ab æquali aut minore vi quam &longs;it impedimentum non <lb/>fit motus. </s> <s id="id.003004">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="id.035.01.240.1.jpg" xlink:href="035/01/240/1.jpg"/><lb/><emph type="italics"/>trahatur. </s> <s id="id.003005">Dico quod &longs;ur&longs;um non <lb/>trahetur, neque per 10. neque per 9. <lb/>&c. </s> <s id="id.003006">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. </s> <s id="id.003007">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 xlink:href="035/01/241.jpg" pagenum="201" /><emph type="italics"/>feretur. </s> <s id="id.003008">Præterea alia etiam demon&longs;tratione quæ&longs;tio ab Aristotele <lb/>propo&longs;ita concludi pote&longs;t. </s> <s id="id.003009">&longs;ic,<emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003010"><emph type="italics"/>Omne duobus motibus ad diuer&longs;a tendentibus commotum, tan­<lb/>tò minus vno mouetur: quantò magis altero. </s> <s id="id.003011">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 id="id.003012"><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 id="id.003013"><emph type="italics"/>Ergo quantò magis hoc mouebitur, minus mouebitur illo: & <lb/>contra. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003014"><emph type="italics"/>Atqui iam commotus plus mouetur violento. </s> <s id="id.003015">Tunc igitur minus <lb/>naturali: contra incipiens moueri, plus naturali. </s> <s id="id.003016">Tunc igitur minus <lb/>violento. </s> <s id="id.003017">Ergo commotus facilius mouebitur: quam quie&longs;cens vel <lb/>incipiens moueri. <emph.end type="italics"/></s> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003018">33. <foreign lang="el">*dia\ ti/ pau/etai fero/mena <lb/>ta\ r(ife/nta.</foreign></s> </p> <p type="main"> <s id="id.003019">33. Cur proiecta lata ce&longs;­<lb/>&longs;ant. </s> </p> <p type="main"> <s id="id.003020"><foreign lang="el">*dia\ ti/ pau/etai fero/mena ta\ r(ife/nta, po/teron o(/tan <lb/>lh/gh| h( i)sxu\s h( a)fei=sa, h)\ dia\ to\ a)ntispa=sqai, h)\ dia\ <lb/>th\n r(oph/n, e)a\n krei/ttwn h)=| th=s i)sxu/os th=s r(iya/shs; </foreign></s> <s id="g0133203"><foreign lang="el">h)\ a)/topon <lb/>to\ tau=t' a)porei=n, a)fe/nta th\n a)rxh/n.</foreign></s> </p> <p type="main"> <s id="id.003021">Cur proiecta lata ce&longs;&longs;ant. <lb/></s> <s id="id.003022">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&etail;, &longs;i vim proiicientis <lb/>&longs;uperauerit. </s> <s id="id.003023">An ab&longs;urdum <lb/>de eo dubitare e&longs;t eum, qui <lb/>principium relinquit. </s> </p> <p type="head"> <s id="id.003024">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003025">Cvr proiecta.] <emph type="italics"/>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. </s> <s id="id.003026">Quæritur igitur cur proiecta tandem moueri de&longs;i­<lb/>nant. </s> <s id="id.003027">Hîc re&longs;pondet, quia &longs;ublata cau&longs;a ce&longs;&longs;at effectus. </s> <s id="id.003028">Cau&longs;a autem <lb/>lationis in proiectis e&longs;t vis impellens à primo motore impre&longs;&longs;a. </s> <s id="id.003029">Hanc <lb/>Simplicius Ari&longs;totelis interpres<emph.end type="italics"/> <foreign lang="el">)e)pipo/laian</foreign> <emph type="italics"/>qua&longs;i diceres &longs;uperfi­<emph.end type="italics"/><pb xlink:href="035/01/242.jpg" pagenum="202" /><emph type="italics"/>ciariam appellat comment. in lib. 7. Phy&longs;. </s> <s id="id.003031">Hæc autem tollitur autà <lb/>re&longs;i&longs;tentia medij per quod fertur. </s> <s id="id.003032">Corpus enim e&longs;t quod in &longs;uo &longs;eloco <lb/>con&longs;eruare nititur: aut à naturali grauitate aliò, quàm quò proijciun­<lb/>tur tendente. </s> <s id="id.003033">Vt enim calor & frigus in &longs;ubiectis non proprijs ali­<lb/>quandiu manent: ita & violenti motus impreßio illa. </s> <s id="id.003034">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. </s> <s id="id.003035">quod certo indicio e&longs;t vim à motore primo ali­<lb/>quam in proiectis relinqui, quæ ad aliquod tempus manet. </s> <s id="id.003036">At tan­<lb/>dem ob cau&longs;as prædictas, perit. </s> <s id="id.003037">Et &longs;ic quæque ad naturam redeunt <lb/>&longs;uam. </s> <s id="id.003038">Nec &longs;i millies lapidem &longs;ur&longs;um proieceris: tamen vnquam &longs;ur­<lb/>&longs;um ferri a&longs;&longs;ue&longs;cet. </s> <s id="id.003039">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 id="id.003040">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. </s> <s id="id.003041">Si per prin­<lb/>cipium intelligamus motorem, qui motus principium dedit, id e&longs;t pri­<lb/>mum motorem. </s> <s id="id.003042">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 id="id.003043">Hoc volat emi&longs;&longs;um &longs;emel irreuocabile telum: <lb/><emph type="italics"/>Sed ob id 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. </s> <s id="id.003044">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. </s> <s id="id.003045">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> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003047">34. <foreign lang="el">*dia\ ti/ fe/retai/ ti ou) th\n <lb/>au(tou= fora\n, mh\ a)kolouqou=n­<lb/>tos <lb/>w)qou=ntos a)lla\ tou= a)fe/n­<lb/>tos.</foreign></s> </p> <p type="main"> <s id="id.003048">34. Cur quidpiam non &longs;ua <lb/>latione fertur non con­<lb/>&longs;equente impul&longs;ore: &longs;ed <lb/>dimittente. </s> </p> <p type="main"> <s id="id.003049"><foreign lang="el">*dia\ ti/ fe/retai/ ti ou) th\n au(tou= fora\n mh\ a)kolouqou=ntos <lb/>tou= w)qou=ntos a)lla\ tou= a)fe/ntos; </foreign></s> <s id="g0133302"><foreign lang="el">h)\ dh=lon o(/ti e)poi/hse toiou=ton <lb/>to\ prw=ton w(s qa/teron w)qei=n, kai\ tou=q' e(/teron: </foreign></s> <s id="g0133303"><foreign lang="el">pau/etai de/, <lb/>o(/tan mhke/ti du/nhtai poiei=n to\ prowqou=n to\ fero/menon w(/ste <lb/>w)qei=n, kai\ o(/tan to\ tou= ferome/nou ba/ros r(e/ph| ma=llon th=s <lb/>ei)s to\ pro/sqen duna/mews tou= w)qou=ntos.</foreign></s> </p> <p type="main"> <s id="id.003050">Quare quidpiam non <lb/>propria latione fertur, cum <lb/>impul&longs;or non con&longs;equa­<lb/>tur: &longs;ed dimittat. </s> <s id="id.003051">An quia <pb xlink:href="035/01/243.jpg" pagenum="203" />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. </s> <s id="id.003052">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> </p> <p type="head"> <s id="id.003053">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003054">Qvare quidpiam.] <emph type="italics"/>Cum omne proiectum graue quid &longs;it, ideó­<lb/>que natura tendens rectà deor&longs;um. </s> <s id="id.003055">Quærit rur&longs;us Ari&longs;toteles: <lb/>&longs;ed expreßius quam antè. </s> <s id="id.003056">Cur cum proiector non con&longs;equatur proie­<lb/>ctum, ip&longs;um non feratur potius &longs;uo motu naturali: quam violento. <lb/></s> <s id="id.003057">Cui vt re&longs;pondeat ad cau&longs;am præcedentem, vim &longs;cilicet impre&longs;&longs;am <lb/>à primo motore adijcit medij, per quod proijcitur antiperi&longs;ta&longs;im. </s> <s id="id.003058">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> </p> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003059">35. <foreign lang="el">*dia\ ti/ ou)/te ta\ e)la/ttona, <lb/>ou)/te ta\ mega/la po/r)r(w fe/re<lb/>tai r(ipto/mena</foreign></s> </p> <p type="main"> <s id="id.003060">35. Cur <expan abbr="neq;">neque</expan> exigua, neque <lb/>magna proiecta feruntur <lb/>procul. </s> </p> <p type="main"> <s id="id.003061"><foreign lang="el">*dia\ ti/ ou)/te ta\ e)la/ttona ou)/te ta\ mega/la po/r)r(w fe/retai <lb/>r(ipto/mena, a)lla\ dei= summetri/an tina\ e)/xein pro\s <lb/>to\n r(iptou=nta; </foreign></s> <s id="g0133402"><foreign lang="el">po/teron o(/ti a)na/gkh to\ r(iptou/menon kai\ <lb/>w)qou/menon a)nterei/dein o(/qen w)qei=tai; </foreign></s> <s id="g0133403"><foreign lang="el">to\ de\ mhqe\n u(pei=kon dia\ <lb/>me/geqos h)\ mhde\n a)nterei=san di' a)sqe/neian ou) poiei= r(i=yin <lb/>ou)de\ w)=sin.</foreign></s> <s id="g0133404"><foreign lang="el">to\ me\n ou)=n polu\ u(perba/llon th=s i)sxu/os th=s <lb/>w)qou/shs ou)qe\n u(pei/kei, to\ de\ polu\ a)sqene/steron ou)de\n a)nerei/dei.</foreign></s> <s id="g0133405"><foreign lang="el"><lb/>h)\ o(/ti tosou=ton fe/retai to\ fero/menon, o(/son a)\n <lb/>a)e/ra kinh/sh| ei)s ba/qos; to\ de\ mhde\n kinou/menon ou)d' a)\n <lb/>kinh/seien ou)de/n. sumbai/nei dh\ a)mfo/tera tou/tois e)/xein.</foreign></s> <s id="g0133406"><foreign lang="el"><lb/>to/ te ga\r sfo/dra me/ga kai\ to\ sfo/dra mikro\n w(/sper ou)qe\n <lb/>kinou/mena/ e)sti: to\ me\n ga\r au)to\ kaq' e(\n kinei=, to\ d' <lb/>ou)qe\n kinei=tai.</foreign></s> </p> <p type="main"> <s id="id.003062">Cur <expan abbr="neq;">neque</expan> exigua, neque <lb/>magna proiecta procul fe­<lb/>runtur: &longs;ed oportet corre­<pb xlink:href="035/01/244.jpg" pagenum="204" />&longs;pondere <expan abbr="quodãmodo">quodammodo</expan> pro­<lb/>ijcienti. </s> <s id="id.003063">An quia nece&longs;&longs;e <lb/>e&longs;t, id, quod proijcitur & <lb/>impellitur re&longs;i&longs;tere ei, vnde <lb/>impellitur. </s> <s id="id.003064">Nihil verò ce­<lb/>dens propter magnitudi­<lb/>nem, vel nihil re&longs;i&longs;tens pro­<lb/>pter imbecillitatem, nec <lb/><expan abbr="iactũ">iactum</expan> facit, nec impul&longs;um. <lb/></s> <s id="id.003065">Illud <expan abbr="quid&etilde;">quidem</expan>, quia magno­<lb/>pere excedit vires impul&longs;o­<lb/>ris, nequaquam cedit. </s> <s id="id.003066">Hoc <lb/>verò quia valdè <expan abbr="imbecillũ">imbecillum</expan>, <lb/>nihil re&longs;i&longs;tit. </s> <s id="id.003067">An quia quod <lb/>fertur <expan abbr="tãtum">tantum</expan> feratur: quan­<lb/>tum aëris in profundum <lb/>mouerit. </s> <s id="id.003068">Non motum au­<lb/>tem nec <expan abbr="conting&etilde;s">contingens</expan> e&longs;t mo­<lb/>uere quicquam. </s> <s id="id.003069">Sic igitur <lb/>vtraque &longs;e habent, quod <lb/>enim valde <expan abbr="magnũ">magnum</expan>, quod­<lb/>que valde paruum, &longs;eu nequaquam mota exi&longs;tunt. </s> <s id="id.003070">Alte­<lb/>rum enim nihil mouet: alterum nequaquam mouetur. </s> </p> <p type="head"> <s id="id.003071">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003072">Cvr neque exigua.] <emph type="italics"/>Exigua & magna vocabula &longs;unt in re­<lb/>latis, & quæ intelligi, vt ante dictum e&longs;t, non po&longs;&longs;unt ni&longs;i rela­<lb/>tione facta ad aliud, ad quod referuntur. </s> <s id="id.003073">Magna igitur &longs;unt, quæ vi­<lb/>res proijcientis valde excedunt: exigua vero, quæ viribus nullo modo <lb/>re&longs;i&longs;tunt, vel quæ adeò imbecilla &longs;unt, vt nullam vim mouendi, ne <lb/>aërem quidem habeant. </s> <s id="id.003074">Et &longs;ic grana milij quamuis &longs;int exigua mole: <lb/>exigua tamen viribus dici non debent, cum è certo interuallo à quo­<lb/>dam per foramen acus proiicerentur, nec rur&longs;us magna licet mole e&longs;­<lb/>&longs;ent, magna erant ad vires &longs;axa illa tritalantaria, telaque mißilia <lb/>duodeuiginti pedum, quæ recitat Athenæus facile eiaculata fui&longs;&longs;e ad<emph.end type="italics"/><pb xlink:href="035/01/245.jpg" pagenum="205" /><emph type="italics"/>quadringentos cubitos, quod &longs;patium e&longs;t &longs;tadij, per machinam, quæ <lb/>erat in medio cata&longs;tromate &longs;uper tripodes excitata, illius immen&longs;æ <lb/>nauis, de qua antea diximus. </s> <s id="id.003075">Quæritur igitur, cur exigua vt pluma, <lb/>& magna vt mola, vel lapis ingens proiecta non procul ferantur: <lb/>&longs;ed quæ &longs;ic ferri debent, debeant corre&longs;pondere proiicienti, id e&longs;t ha­<lb/>bere rationem quandam, ita vt motor vel per&longs;e, vel cum alio præ­<lb/>polleat mouendo. </s> <s id="id.003076">In textu notabis<emph.end type="italics"/> <foreign lang="el">summebi/an</foreign> <emph type="italics"/>poni pro<emph.end type="italics"/> <foreign lang="el">a)nalogi/a|. </foreign></s> </p> <p type="main"> <s id="id.003077">An quia nece&longs;&longs;e e&longs;t.] <emph type="italics"/>Prima re&longs;pon&longs;io breuiter &longs;ic concludi <lb/>pote&longs;t. </s> <s id="id.003078">Oportet proiiciendum cedere proiectori, & etiam re&longs;i&longs;tere. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003079"><emph type="italics"/>Magnum non cedit, quia excedit vires proiectoris. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003080"><emph type="italics"/>Exiguum non re&longs;i&longs;tit, quia imbecillum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003081"><emph type="italics"/>Neutrum igitur proiectum fertur, nedum procul. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003082"><emph type="italics"/>Propo&longs;itionis huius &longs;yllogi&longs;mi prior pars per&longs;e clara e&longs;t, & illu&longs;trata <lb/>etiam ijs quæ à nobis cap. 32. dicta &longs;unt. </s> <s id="id.003083">Po&longs;terior de re&longs;i&longs;tentia etiam <lb/>vera e&longs;t, quia &longs;i mobile motori non re&longs;i&longs;tat, motus non fiet in tempo­<lb/>re, & &longs;ucceßione.: &longs;ed in in&longs;tanti quod e&longs;t contra demon&longs;trata ab <lb/>Ari&longs;totele lib. 4. de Phi&longs;ico audit. </s> <s id="id.003084">Vim enim motoris, &longs;i nihil retar­<lb/>dat, quare non ageret ilico? </s> <s id="id.003085">vnde ne tran&longs;latio &longs;ubita latorum fiat, <lb/>non &longs;olum forma tran&longs;lati obe&longs;t: &longs;ed & medium per quod fertur, <lb/>quod quanquam tenue & diaphanum &longs;it, vt aër, e&longs;t tamen corpus. <lb/></s> <s id="id.003086">E&longs;t itaque hæc propo&longs;itio vera. </s> <s id="id.003087">Præterea vt & hoc demon&longs;tretur ad <lb/>&longs;en&longs;um, &longs;i &longs;corpioni vel arcuballi&longs;tæ palea loco &longs;agittæ &longs;uperpona­<lb/>tur, præter id quod ictum nullum faciet, etiam parum longè <lb/>emi&longs;&longs;a procedet. </s> <s id="id.003088">Quod &longs;i graui&longs;simum &longs;piculum, etiam lentius & <lb/>minus longè emittetur. </s> <s id="id.003089">E&longs;t igitur aliquod medium optimum, <lb/>vbi extrema ambo vitio non carent. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003090">An quia quod fertur.] <emph type="italics"/>Altera re&longs;pon&longs;io &longs;ic concludi pote&longs;t. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003091"><emph type="italics"/>Quantum quidque aëris mouerit, tantum feretur: & &longs;i igitur <lb/>non mouerit, non feretur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003092"><emph type="italics"/>Magnum quia immotum non mouet aerem: imbecillum <lb/>quia etiam immotum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003093"><emph type="italics"/>Neutrum igitur feretur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003094"><emph type="italics"/>Propo&longs;itio rur&longs;us hæc vera e&longs;t, quia cum alioqui penetratio dimen­<lb/>&longs;ionum fieret, ferri nihil pote&longs;t, ni&longs;i medium per quod fertur, cedat <lb/>locum: alioqui medium puta aer, & id quod fertur, e&longs;&longs;ent in vno. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/246.jpg" pagenum="206" /> </subchap1> </chap> <chap> <subchap1> <p type="main"> <s id="id.003095"><foreign lang="el">*dia\ ti/ ta\ fero/mena e)n tw=| <lb/>dinoume/nw| u(/dati ei)s to\ me/son <lb/>fe/retai.</foreign></s> </p> </subchap1> <subchap1> <p type="main"> <s id="id.003096">36. Cur lata in vortice <lb/>aquarum ad medium de­<lb/>uoluuntur. </s> </p> <p type="main"> <s id="id.003097"><foreign lang="el">*dia\ ti/ ta\ fero/mena e)n tw=| dinoume/nw| u(/dati ei)s to\ <lb/>me/son teleutw=nta fe/rontai a(/panta; </foreign></s> <s id="g0133502"><foreign lang="el">po/teron o(/ti me/geqos <lb/>e)/xei to\ fero/menon, w(/ste e)n dusi\ ku/klois ei)=nai, tw=| me\n <lb/>e)la/ttoni tw=| de\ mei/zoni, e(ka/teron au)tou= tw=n a)/krwn. w(/ste <lb/>perispa=| o( mei/zwn dia\ to\ fe/resqai qa=tton, kai\ pla/gion <lb/>a)pwqei= au)to\ ei)s to\n e)la/ttw. e)pei\ de\ pla/tos e)/xei to\ <lb/>fero/menon, kai\ ou(=tos pa/lin to\ au)to\ poiei=, kai\ a)pwqei= ei)s <lb/>to\n e)nto/s, e(/ws a)\n ei)s to\ me/son e)/lqh|.</foreign></s> <s id="g0133503"><foreign lang="el">kai\ to/te me/nei dia\ <lb/>to\ o(moi/ws e)/xein pro\s a(/pantas tou\s ku/klous to\ fero/menon, <lb/>dia\ to\ me/son: kai\ ga\r to\ me/son i)/son a)pe/xei e)n e(ka/stw| <lb/>tw=n ku/klwn.</foreign></s> </p> <p type="main"> <s id="id.003098">Cur lata in vortice aqua­<lb/>rum omnia tandem ad me­<lb/>dium <expan abbr="deuoluũtur">deuoluuntur</expan>. </s> <s id="id.003099">An quia <lb/>quod fertur <expan abbr="magnitudin&etilde;">magnitudinem</expan> <lb/>habet: vt &longs;it in duobus cir­<lb/>culis partim quidem in mi­<lb/>nore: partim verò in maio­<lb/>re. </s> <s id="id.003100">Vtrumque ip&longs;ius <expan abbr="extre­mũ">extre­<lb/>mum</expan>. </s> <s id="id.003101">Itaque maior circum­<lb/>uellit, quia celerius fertur, <lb/>& per tran&longs;uer&longs;um impel­<lb/>lit ip&longs;um ad <expan abbr="minor&etilde;">minorem</expan>. </s> <s id="id.003102">Quo­<lb/>niam vero id quod fertur <lb/>latitudinem habet: illéque <lb/>rur&longs;us idem facit, & pro­<lb/>pellit ad <expan abbr="interior&etilde;">interiorem</expan>, quou&longs;­<lb/>que ad medium peruene­<lb/>rit. </s> <s id="id.003103">quia quod fertur, &longs;imi­<lb/>liter &longs;e habet ad omnes cir­<lb/>culos ob medium. </s> <s id="id.003104">Etenim <lb/>ip&longs;um in vnoquoque circulorum æqualiter di&longs;tat. </s> </p> <p type="head"> <s id="id.003105">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003106">Cvr lata in vortice.] <foreign lang="el">*dino/menon u(/dwr</foreign> <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="el">di/nh</foreign> <emph type="italics"/>Latinis vor­<lb/>tex aquæ, & gurges. </s> <s id="id.003107">Locus e&longs;t profundus in flumine in quo <lb/>aqua vertitur, &longs;ic dictus quod gulæ in&longs;tar ad &longs;e trahat, & deuoret. <lb/></s> <s id="id.003108">Innatantia enim &longs;eu grauia vt nauim: &longs;eu leuia vt plumam, &longs;tatim <lb/>atque ad medium &longs;ui adduxit, tam rapidè &longs;ummergit, vt in momen­<lb/>to nu&longs;quam videas. </s> <s id="id.003109">Ari&longs;toteles in hoc loco præ&longs;upponit<emph.end type="italics"/> <foreign lang="el">o)n di/nh| su/­<lb/>strofas tw=n u(da/twn</foreign> <emph type="italics"/>vortices aquo&longs;os e&longs;&longs;e multos circulos concen­<lb/>tricos, quorum vt continens maior e&longs;t contento: ita &longs;emper celerius <emph.end type="italics"/><pb xlink:href="035/01/247.jpg" pagenum="207" /><emph type="italics"/>ferri. </s> <s id="id.003110">quod quam verum &longs;it, postea docebimus, vbi problema cum <lb/>&longs;uis cau&longs;is ex mente Ari&longs;tote­<lb/>lis explicuerimus. </s> <s id="id.003111">Quærit igi­<emph.end type="italics"/><lb/><figure id="id.035.01.247.1.jpg" xlink:href="035/01/247/1.jpg"/><lb/><emph type="italics"/>tur Aristoteles cur quæ fe­<lb/>runtur in vortico&longs;a aqua, om­<lb/>nia tandem ad medium deuol­<lb/>uantur. </s> <s id="id.003112">Sit igitur A medium <lb/>aquæ per circulos B C D, <lb/>E F G, H I K, L M N, <lb/>O P Q volutæ: &longs;it & vt <lb/>nauis R feratur per vorticem <lb/>B C D. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003113"><emph type="italics"/>Dico quod ad A medium <lb/>deuoluetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003114">An quia quod fertur.] <emph type="italics"/>Prima e&longs;t<emph.end type="italics"/> <foreign lang="el">tou= diori/smou=</foreign> <emph type="italics"/>problematis <lb/>propo&longs;iti demonstratio. </s> <s id="id.003115">quæ &longs;ic concludetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003116"><emph type="italics"/>Habentis latitudinem &longs;i <expan abbr="extremũ">extremum</expan> vnum celerius feratur: quam <lb/>alterum, quod celerius fertur, truditur ad locum tardioris. <lb/></s> <s id="id.003117">per tran&longs;uer&longs;um enim à celerius moto impellitur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003118"><emph type="italics"/>Innatans omne in aqua vortico&longs;a, vt nauis, latitudinem <lb/>habet, & eius extremum quod in exteriori circulo e&longs;t, <lb/>celerius fertur: quam quod in interiori. </s> <s id="id.003119">Circulus enim <lb/>maior celerius fertur. </s> <s id="id.003120">Exterior autem maior e&longs;t. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003121"><emph type="italics"/>Ergo innatans trudetur ad locum tardioris id e&longs;t in interiorem <lb/>circulum, vt à B ad E & ab E ad H, & ab H ad L, & <lb/>ab L ad O, à quo tandem ad A medium. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003122"><emph type="italics"/>Similiter enim &longs;e habet innatans ad omnes circulos vorticis ob me­<lb/>dium, quod à &longs;ingulis æqualiter distat. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003123">Quia quod fertur.] <emph type="italics"/>Ex hoc loco expunximus vocabula hæc <lb/>&longs;ine v&longs;u & magna <expan abbr="cõfu&longs;ione">confu&longs;ione</expan> interiecta<emph.end type="italics"/> <foreign lang="el">kai\ to\ te me\n ei)</foreign> <emph type="italics"/>nec pro<emph.end type="italics"/> <foreign lang="el">ei)</foreign> <emph type="italics"/>re­<lb/>ponimus<emph.end type="italics"/> <foreign lang="el">h)\</foreign> <emph type="italics"/>quod faciunt aliqui huius loci interpretes, ex hoc attin­<lb/>gentes &longs;ecundam cau&longs;am problematis, quod &longs;cilicet omnia finem mo­<lb/>tus, id e&longs;t quietem appetant, ideo ferri ad locum quietis, qui medius <lb/>e&longs;t in vortice. </s> <s id="id.003124">quæ vt vera e&longs;&longs;ent, non video tamen exprimi po&longs;&longs;e <lb/>ex hoc Ari&longs;totelis contextu, qui &longs;uperioris demonstrationis comple­<lb/>mentum e&longs;t, vt patuit. <emph.end type="italics"/></s> </p> </subchap1> <pb xlink:href="035/01/248.jpg" pagenum="208" /> <subchap1> <p type="main"> <s id="id.003125"><foreign lang="el">h)\ o(/ti o(/swn me\n mh\ kratei= h( fora\ tou= dinoume/nou <lb/>u(/datos dia\ to\ me/geqos, a)ll' u(pere/xei th=| baru/thti <lb/>th=s tou= ku/klou taxuth=tos, a)na/gkh u(polei/pesqai kai\ bradu/teron <lb/>fe/resqai.</foreign></s> <s id="g0133505"><foreign lang="el">bradu/teron de\ o( e)la/ttwn ku/klos fe/retai: <lb/>to\ au)to\ ga\r e)n i)/sw| xro/nw| o( me/gas tw=| mikrw=| stre/fetai <lb/>ku/klw|, o(/tan w)=si peri\ to\ au)to\ me/son.</foreign></s> <s id="g0133506"><foreign lang="el">w(/ste ei)s to\n <lb/>e)la/ttona ku/klon a)nagkai=on a)polei/pesqai, e(/ws a)\n e)pi\ to\ <lb/>me/son e)/lqh|.</foreign></s> <s id="g0133507"><foreign lang="el">o(/swn de\ pro/teron kratei= h( fora/, lh/gousa <lb/>tau)to\ poih/sei. dei= ga\r to\n me\n eu)qu/, to\n de\ e(/teron kratei=n <lb/>th=| taxuth=ti tou= ba/rous, w(/ste ei)s to\n e)nto\s a)ei\ ku/klon <lb/>u(polei/pesqai pa=n.</foreign></s> <s id="g0133508"><foreign lang="el">a)na/gkh ga\r au)to\ e)nto\s h)\ e)kto\s kinei=sqai <lb/>to\ mh\ kratou/menon.</foreign></s> <s id="g0133509"><foreign lang="el">e)n au)tw=| dh\ toi/nun e)n w(=| e)sti/n, <lb/>a)du/naton fe/resqai to\ mh\ kratou/menon. e)/ti de\ h(=tton e)n tw=| <lb/>e)kto/s: qa/ttwn ga\r h( fora\ tou= e)kto\s ku/klou.</foreign></s> <s id="g0133510"><foreign lang="el">lei/petai de\ <lb/>ei)s to\n e)nto\s to\ mh\ kratou/menon meqi/stasqai. a)ei\ de\ e(/kaston <lb/>e)pidi/dwsin ei)s to\ mh\ kratei=sqai.</foreign></s> <s id="g0133511"><foreign lang="el">e)pei\ de\ pe/ras tou= mh\ kinei=sqai <lb/>poiei= to\ ei)s me/son e)lqei=n, me/nei de\ to\ ke/ntron mo/non, <lb/>a(/panta a)na/gkh ei)s tou=to dh\ a)qroi/zesqai.<lb/> *te/los.</foreign></s> </p> <p type="main"> <s id="id.003126">An quia quæ quidem la­<lb/>tio vorricis aquæ <expan abbr="nõ">non</expan> vincit <lb/>ob magnitudinem: &longs;ed ex­<lb/>cellunt grauitate <expan abbr="celeritat&etilde;">celeritatem</expan> <lb/>circuli, illa nece&longs;&longs;e e&longs;t & <lb/>tardius ferri. </s> <s id="id.003127">Minor autem <lb/>circulus tardius fertur. </s> <s id="id.003128"><expan abbr="Nõ">non</expan> <lb/>enim idem <expan abbr="&longs;patiũ">&longs;patium</expan> in &etail;quali <lb/>tempore magnus & paruus <lb/>circulus voluitur, quan­<lb/>do fuerint circa idem me­<lb/>dium. </s> <s id="id.003129">Itaque ad mino­<lb/>rem <expan abbr="circulũ">circulum</expan> vt de&longs;inat ne­<lb/>ce&longs;&longs;e e&longs;t, quou&longs;que ad me­<lb/>dium venerit. </s> <s id="id.003130">Qu&etail;cunque <lb/>verò latio prius vincit, fi­<lb/>niens idem faciet. </s> <s id="id.003131">Oportet <lb/>enim vt <expan abbr="alterũ">alterum</expan> quidem &longs;ta­<lb/>tim celeritate grauitatem: <lb/>alterum verò grauitate ce­<lb/>leritatem vincat, vt omnis <lb/>ad interiorem <expan abbr="circulũ">circulum</expan> &longs;em­<lb/>per relinquatur. </s> <s id="id.003132">Nece&longs;&longs;e <lb/>enim ip&longs;um quod non vin­<lb/>citur intrò vel foras moue­<lb/>ri. </s> <s id="id.003133">In ip&longs;o verò in quo e&longs;t, <lb/>non pote&longs;t ferri, cum non <lb/>vincatur: multò minus in <lb/>exteriori. </s> <s id="id.003134">Latio enim exte­<lb/>rioris circuli celerior e&longs;t. <lb/></s> <s id="id.003135">Re&longs;tat vt id quod non vin­<lb/>cit, ad interiorem transfe­<lb/>ratur. </s> <s id="id.003136">Semper enim nititur <lb/>quodlibet, ne vincatur. </s> <s id="id.003137">quoniam terminus, qui e&longs;t non <lb/>moueri, facit ad medium venire. </s> <s id="id.003138">Quie&longs;cit enim &longs;olum <lb/>centrum, ad quod omnia nece&longs;&longs;e e&longs;t congregari. </s> </p> <pb xlink:href="035/01/249.jpg" pagenum="209" /> <p type="head"> <s id="id.003139">COMMENTARIVS. </s> </p> <p type="main"> <s id="id.003140">An quia quæ quidem.] <emph type="italics"/>Altera e&longs;t eiu&longs;dem<emph.end type="italics"/> <foreign lang="el">diorismou=</foreign> <emph type="italics"/>pro­<lb/>blematis demon&longs;tratio. </s> <s id="id.003141">quæ &longs;ic concludetur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003142"><emph type="italics"/>Innatantia in vortice latio vortico&longs;a aquæ vincit, vel non <lb/>vincit. </s> <s id="id.003143">Si non vincat ob grauitatem, quæ excedit celeritatem <lb/>circuli, non ferentur in eo, in quo &longs;unt circulo. </s> <s id="id.003144">quia latio vor­<lb/>tico&longs;æ aquæ vinceret. </s> <s id="id.003145">Multò minus in maiori. </s> <s id="id.003146">Relinquitur er­<lb/>gò, vt in minori id e&longs;t interiori, vt qui tardior &longs;it, ferantur, <lb/>& &longs;imili ratione ab hoc quou&longs;que ad medium veniant. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003147"><emph type="italics"/>Si verò vincat, vt primum quidem vincat, tandem tamen <lb/>non vincit. </s> <s id="id.003148">Oportet enim vt modò hæc latio grauitatem <lb/>innatantium celeritate &longs;ua vincat: modò ip&longs;a innatantia <lb/>&longs;ua grauitate celeritatem lationis vortico&longs;æ aquæ vin­<lb/>cant. </s> <s id="id.003149">Vnumquodque enim nititur &longs;emper, ne vincatur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003150"><emph type="italics"/>Et &longs;ic idem fiet, quod ante: vt innatantia ad interiorem feran­<lb/>tur, & ad eum denique terminum, in quo violentia vorticis <lb/>non amplius voluantur. </s> <s id="id.003151">Hic autem terminus medium e&longs;t vor­<lb/>ticis ad quod omnia congregantur. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003152"><emph type="italics"/>Innatantia igitur in aqua vortico&longs;a ad medium deuoluuntur. </s> <s id="id.003153">quod <lb/>fuit demon&longs;trandum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003154"><emph type="italics"/>Hactenus fuerunt duæ demon&longs;trationes Ari&longs;totelis, quæ vt dixi <lb/>præ&longs;upponunt gurgitis vortices e&longs;&longs;e circulos concentricos, quod fal­<lb/>&longs;um e&longs;t, quia &longs;unt linea &longs;piralis vnius aut plurium reuolutionum. <lb/></s> <s id="id.003155">Præterea nullam mentionem facit decliuitatis &longs;uperficiei aquæ vor­<lb/>tico&longs;æ ver&longs;us medium, quæ res maximè confert ad de&longs;cen&longs;um rei in­<lb/>natantis, & eiu&longs;dem deuolutionis ad medium. </s> <s id="id.003156">Ibi enim &longs;pecus quæ­<lb/>dam &longs;ub aquis in terra latet, quæ<emph.end type="italics"/> <foreign lang="el">a)/bussos</foreign> <emph type="italics"/>qua&longs;i<emph.end type="italics"/> <foreign lang="el">a)neu bu/ssou</foreign> <emph type="italics"/>&longs;ine <lb/>fundo dicta e&longs;t. </s> <s>Et in quam tanquam ex alto confluunt magna ce­<lb/>leritate aquæ. </s> <s id="id.003157">Indicium huius e&longs;t, quod pluma innatans ad hoc exa­<lb/>ctè medium cum delata e&longs;t, &longs;tatim ab&longs;orbetur, tracta &longs;cilicet de&longs;cen­<lb/>&longs;u aquæ: alioqui natura leuior infra aquam non de&longs;cendet, tan­<lb/>tum abe&longs;t, vt quæ grauia &longs;unt non ibi &longs;ubitò &longs;ummergantur. </s> <s id="id.003158">His <lb/>ita po&longs;itis demon&longs;tratio problematis Aristotelici e&longs;t facilis & <lb/>breuis. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/250.jpg" pagenum="210" /> <p type="main"> <s id="id.003159"><emph type="italics"/>Sit A inte­<lb/>rius extremum, <lb/><figure id="id.035.01.250.1.jpg" xlink:href="035/01/250/1.jpg"/><lb/>& B exterius <lb/>lineæ &longs;piralis A <lb/>B plurium reuo­<lb/>lutionum, in ex­<lb/>tremo B &longs;it na­<lb/>uis C. </s> <s id="id.003160">Dico quod <lb/>C feretur ad A, <lb/>& in&longs;uper quod <lb/>cum erit in A <lb/>&longs;ummergetur in­<lb/>tra aby&longs;&longs;um A <lb/>E. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003161">Demon&longs;t. <lb/></s> <s><emph type="italics"/><expan abbr="Innatãs">Innatans</expan> in vor­<lb/>tico&longs;a aqua fer­<lb/>tur ad motum <lb/>vndæ impul&longs;æ, <lb/>vel tractæ. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003162"><emph type="italics"/>At aqua vortico&longs;a fertur &longs;ecundum lineam &longs;piralem ad eius interius <lb/>medium. </s> <s id="id.003163">Eò enim & decliuitas, & aby&longs;&longs;us trahunt. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003164"><emph type="italics"/>Ergò innatans vt C in B principio vortico&longs;æ aquæ ad medium <lb/>interius A deuoluetur, & ibi propter tractum con&longs;ecutio­<lb/>nemque aquæ, tum & naturalem rei innatantis grauitatem <lb/>rectà deor&longs;um ruet per aby&longs;&longs;um A E. </s> <s>quod erat demon­<lb/>&longs;trandum. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003165"><emph type="italics"/>Ex hac conclu&longs;ione elici debet monitum, quod nauigantibus vti­<lb/>lißimum e&longs;t, vitandos &longs;cilicet illis vortices aquarum tanquam &longs;copu­<lb/>los, qualem referunt in Noruergiæ Oceani inter Roe&longs;t & Loffoet <lb/>maximum e&longs;&longs;e, qui naues &longs;ecum in profundum trahat: & ad hos, &longs;i <lb/>forte impegerint ( quod &longs;entient &longs;i deprehenderint nauim &longs;uam &longs;ine <lb/>cau&longs;a alia, vt eius venti, qui <expan abbr="Typhõ">Typhon</expan>, vel Ecnephias dicitur, ) circum­<lb/>agi, primo quoque tempore adhibitis omnibus remis veli&longs;que eniten­<lb/>dum ab his &longs;piris &longs;e&longs;e excludere. </s> <s id="id.003166">paulò enim pluribus implicati nullis <lb/>viribus &longs;e&longs;e liberabunt. </s> <s id="id.003167">Hîc enim illud poetæ verißimum. <emph.end type="italics"/></s> </p> <pb xlink:href="035/01/251.jpg" pagenum="211" /> <p type="head"> <s id="id.003168">Facilis de&longs;cen&longs;us Auerni:</s> </p> <p type="main"> <s id="id.003169">Sed reuocare gradum, &longs;upera&longs;que euadere ad auras, <lb/>Hoc opus hic labor e&longs;t. </s> </p> <p type="main"> <s id="id.003170"><emph type="italics"/>Sed rur&longs;us de vorticibus hæc quæ &longs;unt apud Cardanum cap. 6. lib. 1. <lb/>de variet. rerum &longs;citu digna &longs;unt. </s> <s id="id.003172">Trahi <expan abbr="quid&etilde;">quidem</expan> naues, inquit, ac cæ­<lb/>tera velut Typhone vento haud ab&longs;urdum in vorticibus: vortices <lb/>quoque e&longs;&longs;e haud dubium e&longs;t: at quomodo de&longs;icendens aqua di&longs;tribua­<lb/>tur, non adeò per&longs;picuum e&longs;t, cum &longs;emper in humiliora feratur. </s> <s id="id.003173">Imo <lb/>autem vortice quo modo quicquam humilius e&longs;&longs;e poßit, non facile <lb/>o&longs;tendere. </s> <s id="id.003174">videtur autem mihi vortex non ad infima de&longs;cendere: <lb/>&longs;ed potius ad ea loca, ex quibus pateat exitus: Nam & vi vento­<lb/>rum aliquando propellitur loco cedens. </s> <s id="id.003175">Quamuis etiam ad infima de&longs;­<lb/>cendat, per&longs;æpe tamen non attingit fundi libramentum: aut &longs;i infe­<lb/>rius etiam de&longs;cendit, aliquò exitus patet. </s> <s id="id.003176">Terra &longs;cilicet, vt hoc ad­<lb/>dam, exi&longs;tente hoc in loco cuniculo&longs;a & per longißimum canalem <lb/>aliquam in &longs;pecum &longs;e&longs;e exonerante. <emph.end type="italics"/></s> </p> <p type="main"> <s id="id.003177"><emph type="italics"/>Habes nunc, candide lector, opus Ari&longs;totelis magna &longs;ubtilitate, <lb/>& iucunda &longs;ubtilitatum in rebus Mechanicis contemplatione, re­<lb/>fertum, & multis ob rerum principiorumque tractatorum ob&longs;cu­<lb/>ritatem & ob contextus Græci corruptionem difficultatibus ob­<lb/>&longs;tructum, no&longs;tra opera & iudicio, vt &longs;pero, ita re&longs;eratum, & à men­<lb/>dis quibus propemodum infinitis &longs;catebat, liberatum: vt po&longs;thæc vel <lb/>mediocriter geometricis imbutus vel ne imbutus quidem hunc <lb/>legere & intelligere & voluptatem ac vtilitatem ex eo capere <lb/>po&longs;sis. </s> <s id="id.003178">quinetiam in &longs;cholis <expan abbr="vulgariũ">vulgarium</expan> illorum philo&longs;ophorum, qui pa­<lb/>rum ab&longs;unt, vt omninò<emph.end type="italics"/> <foreign lang="el">a)gewme/trhtoi</foreign> <emph type="italics"/>non &longs;int, locum eum obtine­<lb/>re po&longs;sit, quem cæteri qui ab hoc naturæ & artis etiam omnis atque <lb/>indu&longs;triæ genio libri prodierunt, quémque ij, qui ab illis publicè le­<lb/>guntur & explicantur. </s> <s id="id.003179">Quod in numinis diuini bonorum omnium <lb/>largitoris gloriam: Henrici IIII. </s> <s id="id.003180">Regis nostri augu&longs;ti&longs;simi perpe­<lb/>tuum decus: Ari&longs;totelis libri huius authoris famam atque authori­<lb/>tatem maiorem: Reipub. denique no&longs;træ literariæ vtilitatem cedat, <lb/>de&longs;idero. <emph.end type="italics"/></s> </p> <p type="head"> <s id="id.003181">FINIS. </s> </p> <p type="main"> <s id="id.003182">Cœlo re&longs;tat iter: Cœlo tentabimus ire. </s> </p> </subchap1> </chap> </body> <pb xlink:href="035/01/252.jpg" /> <back> <section> <p type="head"> <s id="id.003183">ERRATA. </s> </p> <p type="main"> <s id="id.003184">In corrigendis primus numerus paginam, <lb/>Secundus lineam indicat. </s> <s id="id.003185">In his leges. </s> </p> <p type="main"> <s id="id.003186"><emph type="italics"/>6.28. hominum 7.11. engibatis 8.11. vtilitatem 8.22. <emph.end type="italics"/> Hanc &longs;ed <lb/>10.4. <emph type="italics"/><foreign lang="el">au)to/mata</foreign> 11.17. vinum. 11.19. cucurbitulæ 12.5. nullus <lb/>18.19. intrò 19.27. quintupedalis 30.15. dimetientem 30.33. duas <lb/>36.1. radiorum 37.5. <emph.end type="italics"/> <foreign lang="el">e)f' ou=</foreign> <emph type="italics"/>39. littera<emph.end type="italics"/> <foreign lang="el">w</foreign> <emph type="italics"/>debet intelligi in angu­<lb/>lo non &longs;ignato parallelogrammi<emph.end type="italics"/><lb/><figure id="id.035.01.252.1.jpg" xlink:href="035/01/252/1.jpg"/><lb/><foreign lang="el">u z q</foreign> 48.9. <foreign lang="el">sparti/on</foreign> 77.10. <lb/><emph type="italics"/>quadrupedibus 81. dee&longs;t figura <lb/>96.12. <emph.end type="italics"/> <foreign lang="el">a)su/stata</foreign> <emph type="italics"/>142.24. Epi­<lb/>grammatis 167.32. per 182. <lb/>tota pagina vbi e&longs;t litera<emph.end type="italics"/> <foreign lang="el">z</foreign> <emph type="italics"/>re­<lb/>ponenda littera<emph.end type="italics"/> <foreign lang="el">c</foreign> 190.13. <foreign lang="el">tou= <lb/>ba/rous. </foreign></s> </p> <p type="main"> <s id="id.003189"><emph type="italics"/>In contextu Græco omi&longs;imus de indu&longs;tria diagrammata Vve­<lb/>cheli, partim par&longs;imonia &longs;umptuum, partim quod po&longs;ata in commen­<lb/>tarijs eorum vtcumque vicem &longs;upplerent. </s> <s id="id.003190">Si indigeas, ab eo re­<lb/>petere licet. <emph.end type="italics"/></s> </p> </section> </back> </text> </archimedes>