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version 1.3, 2002/06/27 17:24:39

version 1.39, 2003/03/29 20:18:48

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<?xml version="1.0"?>

<!DOCTYPE archimedes [

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

<author>Monantheuil, Henri de</author>

<title>Aristotelis Mechanica</title>

<place>Paris</place>

<cvs_file>monan_mecha_01_la_1599</cvs_file>

<cvs_version/>

</info> <text> <front> <section> <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.001.jpg"/>

<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.<emph.end type="italics"/><lb/>A D <lb/>HENRICVM IIII. GALLIÆ & NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;simum.</s><figure id="id.035.01.001.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.001.1.jpg"/>

<s id="id.000003">PARISIIS, <lb/>Apud IEREMIAM PERIER via Iacobæa, &longs;ub &longs;igno Bellerophontis.</s>

<s id="id.000004">M. D. XCIX. <lb/><emph type="italics"/>CUM PRIVILEGIO REGIS.<emph.end type="italics"/></s><pb/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.002.jpg"/><figure id="id.035.01.002.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.002.1.jpg"/>

<s id="id.000005">HENRICO IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D.</s>

<s id="id.000006">Ecce maie&longs;tati tuæ, <lb/>Rex Chri&longs;tiani&longs;&longs;ime, <lb/>nouum <expan abbr="fruct&utilde;">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&ecedil;<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="Fer&utilde;t">Ferunt</expan> Platonem, quo philo&longs;ophorum <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.003.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="c&utilde;interrogaretur">cum interrogaretur</expan>, quid ageret Deus, <lb/>re&longs;pondi&longs;&longs;e <foreign lang="greek">a)ei gewmetrei=n.</foreign> Hoc verbum Lati<lb/>nè expre&longs;&longs;um &longs;ignificat. </s>

<s id="id.000009">A&longs;&longs;iduè terram <lb/>metiri. </s>

<s id="id.000010">Quæ actio &longs;i &longs;impliciter &longs;pecte<lb/>tur, &à Geometri&ecedil; nomine ridiculo, vt <lb/>alibi appellat Plato, <expan abbr="exp&etilde;datur">expendatur</expan>, ridicula, <lb/>& Dei maie&longs;tate indigna iudicabitur. <lb/></s>

<s id="id.000011">Sed &longs;i ex ip&longs;ius artis viribus, & magnifi<lb/>cis promi&longs;&longs;is illud <foreign lang="greek">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="corpor&utilde;">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="finit&utilde;">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="greek">a)ei gew<lb/>mtrei=n</foreign> addi&longs;&longs;et Plato, <foreign lang="greek">kai\ a)eimhxana=sqai,</foreign> luculen-<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.004.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="greek">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="dura-tion&etilde;">dura<lb/>tionem</expan>, vt Dei &longs;ui auctoris <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> <lb/>concurrit, quod eius vim, & efficaciam <lb/>o&longs;tendit? </s>

<s id="id.000016">An non quinquies mille <expan abbr="quin-g&etilde;tos">quin<lb/>gentos</expan> &longs;exaginta & <expan abbr="vn&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.005.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;uar&utilde;">&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;tror&utilde;">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="homin&utilde;">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&ecedil;ter-quã">pr&ecedil;ter<lb/>quam</expan> quod e&longs;t accurati&longs;&longs;imus, <expan abbr="a&longs;&longs;iduu&longs;q;">a&longs;&longs;iduu&longs;que</expan> <lb/>Geometra, diuini Platonis <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan>, e&longs;t <lb/>etiam no&longs;tra, & operum tot magnifi<lb/>corum euidentia, &longs;apienti&longs;&longs;imus, opti-<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.006.jpg"/>mus, potenti&longs;&longs;imus <foreign lang="greek">mhxaniko\s,</foreign> & <foreign lang="greek">mhxanopoio\s.</foreign><lb/>Ip&longs;e idem, qui <foreign lang="greek">makro/kosmon</foreign> magnum mun<lb/>dum fecit, fecit & <foreign lang="greek">mikro/kosmon</foreign> <expan abbr="paru&utilde;">paruum</expan> mun<lb/>dum, hominem &longs;cilicet: & fecit ad ima<lb/>ginem &longs;uam, atque vt &longs;e imitaretur beni<lb/>gni&longs;&longs;ima liberalitate impertitus e&longs;t ei <lb/>mentem, quæ e&longs;&longs;et <foreign lang="greek">te/xnh te/xnwn,</foreign> ars artium, <lb/>& manum, quæ e&longs;&longs;et <foreign lang="greek">o)/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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.007.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>

<s id="id.000021"><emph type="italics"/>Barbara Pyramidum &longs;ileat miracula <lb/>Memphis.<emph.end type="italics"/></s>

<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="greek">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="h&utilde;c">hunc</expan>, <expan abbr="ma-xim&utilde;">ma<lb/>ximum</expan> certè operum opus, factum e&longs;&longs;e, <lb/>& con&longs;eruari: non autem ab vllo homi<lb/>ne, &longs;ed ab alio <foreign lang="greek">mhxanopoihtikw=|</foreign> tantò homi<lb/>nem præ&longs;tantia, &longs;apientia, potentia, imò <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.008.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="architect&utilde;">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="quant&utilde;">quantum</expan> fas e&longs;t homini, dicta <lb/>&longs;unt: ecquid iam &longs;upere&longs;t, Rex Chri&longs;tia<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.009.jpg"/>ni&longs;&longs;ime, quapropter ab hoc munere vt <lb/>vili abhorreas, & ip&longs;e reformidem, licet <lb/>Mechanicorum <expan abbr="titul&utilde;">titulum</expan> in fronti&longs;picio <lb/>gerat, hoc adeò in&longs;igne opus ab Ari<lb/>&longs;totele profectum, vtile, <expan abbr="iuc&utilde;dum">iucundum</expan>, &longs;ub<lb/>tili&longs;&longs;imè tractatum: &longs;ed temporum iniu<lb/>ria multis mendis f&oelig;dum, 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="homin&utilde;">hominum</expan>, maximas perfecit, <lb/>quarúmque temporibus atque fabricis <lb/>&longs;ummus e&longs;t & frequenti&longs;&longs;imus machi<lb/>narum, & <expan abbr="in&longs;trum&etilde;torum">in&longs;trumentorum</expan> v&longs;us: ille non <lb/>pote&longs;t machinamentorum, & <expan abbr="in&longs;tru-m&etilde;torum">in&longs;tru<lb/>mentorum</expan> formis, rationibus, adinuen<lb/>tionibus, & virium <expan abbr="eor&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.010.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="greek">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 nacto&scedil; & nihil non <lb/>inde &longs;ibi polliciti&scedil; 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.011.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>

<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>

<s id="id.000037"><emph type="italics"/>Munere: &longs;ola Deos æquat clementia nobis.<emph.end type="italics"/></s>

<s id="id.000038">Ad concordiam inter &longs;e, & tecum &longs;er<lb/>uandam: ad beneuolentiam ergate præ<lb/>&longs;tandam, obedientiam, fidelitatem rede<lb/>gi&longs;ti. </s>

<s id="id.000039">Extraneos verò longo bello: bre-<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.012.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;emperab 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="po-t&etilde;ti&longs;&longs;imo">po<lb/>tenti&longs;&longs;imo</expan> ho&longs;te Philippo Hi&longs;paniarum <lb/>rege conciliandæ <expan abbr="occa&longs;ion&etilde;">occa&longs;ionem</expan> quæ&longs;itam, <lb/>& oblatam à Clemente VIII. pontifice <lb/>&longs;ummo, verè vtriu&longs;que gentis commu<lb/>ni <expan abbr="par&etilde;te">parente</expan> clementi&longs;&longs;imo, per &longs;uum lega<lb/>tum Alexandrum de Medicis Cardina<lb/>lem, & Archiepi&longs;copum Florentinum, <lb/>qui huic paci tractandæ, conficiendæ, <lb/>& ni&longs;i 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.013.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 c&oelig;pta, 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.014.jpg"/>ciant: iu&longs;ticia libritenens fide zygo&longs;tati<lb/>ca omnia iudicat: linguarum & bona<lb/>rum <expan abbr="arti&utilde;">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, f&oelig;tu&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="vol&utilde;tates">voluntates</expan>: <expan abbr="tã">tam</expan> <lb/>multa, & multiplici <expan abbr="&longs;imultat&utilde;">&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="vider&utilde;t">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="quant&utilde;uis">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.015.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="ear&utilde;">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="in-u&etilde;tore">in<lb/>uentore</expan>, & excogitatore, tuis &longs;umptibus <lb/>extruitur: Ædium lateritiarum cochlea<lb/>ri &longs;cal&ecedil;, octauo orbis miraculo <expan abbr="colophõ">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.016.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;er&utilde;t">per&longs;ua&longs;erunt</expan>, ne quicquam vererer opus <lb/>hoc, ratione opellæ <expan abbr="quali&longs;cunq;">quali&longs;cunque</expan> no&longs;træ, <lb/>exiguum &longs;cio: &longs;ed ratione authoris &longs;ui, <lb/>Ari&longs;totelis, magnum, &longs;anctæ maie&longs;tati <lb/>tuæ co&longs;ecrare. </s>

<s id="id.000051">Quod <expan abbr="n&utilde;c">nunc</expan> igitur tam lu<lb/>benter facio: quam Deum <expan abbr="optim&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.017.jpg"/>belli reliquiis, & pace in ea confectis f&oelig;<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="rer&utilde;">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 f&oelig;li<lb/>citer e&longs;t re&longs;tituta.</s>

<s id="id.000055">MAIESTATIS</s>

<s id="id.000056">Humillimus &longs;eruus</s>

<s id="id.000057">HENRICVS MONANTHOLIVS.</s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.018.jpg"/><section>

<s id="id.000058">A D <lb/>HENRICVM IIII. <lb/>GALLIÆ ET NAVARRÆ <lb/>Regem Chri&longs;tiani&longs;&longs;imum.</s>

<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>

<s id="id.000061">THEODORICVS MONANTHOLII filius.</s>

<s id="id.000062">De libro <foreign lang="greek">tw=n mhxanikw=n,</foreign> Ari&longs;totele, <lb/>& Monantholio.</s>

<s id="id.000063"><emph type="italics"/>Inter Ari&longs;totelis libros &longs;ubtilior i&longs;to<emph.end type="italics"/></s>

<s id="id.000064"><emph type="italics"/>Nullus<emph.end type="italics"/> <foreign lang="greek">*mhxanikw=n,</foreign> <emph type="italics"/>vtiliorque fuit.<emph.end type="italics"/></s>

<s id="id.000065"><emph type="italics"/>Sed mendis f&oelig;dus merito &longs;ine honore iacebat,<emph.end type="italics"/></s>

<s id="id.000066"><emph type="italics"/>Non authore &longs;uo dignus Aristotele.<emph.end type="italics"/></s>

<s id="id.000067"><emph type="italics"/>Lectus erat nulli, nulli intellectus agebat<emph.end type="italics"/></s>

<s id="id.000068"><emph type="italics"/>Vitam cum blattis, muribus, & tineis.<emph.end type="italics"/></s>

<s id="id.000069"><emph type="italics"/>Liber ab his, captu facilis, bene comptus en exit<emph.end type="italics"/></s>

<s id="id.000070"><emph type="italics"/>In lucem, vigilis luce Monantholij.<emph.end type="italics"/></s>

<s id="id.000071"><emph type="italics"/>Sic dat Ari&longs;toteli vitam, claréque vicißim<emph.end type="italics"/></s>

<s id="id.000072"><emph type="italics"/>Accipit ex ip&longs;o, quam dedit ille, parem.<emph.end type="italics"/></s>

<s id="id.000073"><emph type="italics"/>Vna dies ambos &longs;eruabit, & eximet æuo,<emph.end type="italics"/></s>

<s id="id.000074"><emph type="italics"/>Amborúmque &longs;imul fama &longs;uper&longs;tes erit.<emph.end type="italics"/></s>

<s id="id.000075">RICHARDVS MERCES</s>

<s id="id.000076">Doct. Med. Pari&longs;.</s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.019.jpg"/><figure id="id.035.01.019.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.019.1.jpg"/><section>

<s id="id.000077">PRAEFATIO IN <lb/>MECHANICA ARISTO<lb/>TELIS, AD LECTOREM.</s>

<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 f&oelig;licius <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>

<s id="id.000081"><emph type="italics"/>F&oelig;lix, qui poterit rerum cogno&longs;cere cau&longs;as.<emph.end type="italics"/></s>

<s id="id.000082">Alio qui inutilia, vel vtilia: &longs;ed inutiliter id e&longs;t &longs;ine actio<lb/>ne vel opere, qu&ecedil; fines &longs;unt omnis <expan abbr="cõtemplationis">contemplationis</expan> vtilis, <lb/>contemplari, & in his philo&longs;ophando plu&longs;quam paucis <lb/>commorari, parum omnino, aut nihil f&oelig;licitatis 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.020.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, c&oelig;le<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 c&oelig;<lb/>le&longs;tium & elementariorum id e&longs;t <foreign lang="greek">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="omni&utilde;">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;ol&utilde;">&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="contuler&utilde;t">contulerunt</expan>. </s>

<s id="id.000095">Hinc quartum genus illud <expan abbr="rer&utilde;">rerum</expan>, quas <lb/>diximus, artificialium emanauit, primùm vt credibile e&longs;t <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.021.jpg"/>nece&longs;&longs;ariarum, deinde <expan abbr="delectabili&utilde;">delectabilium</expan>, quod eò, imitatione <lb/>c&oelig;le&longs;tium & <expan abbr="elem&etilde;tarior&utilde;">elementariorum</expan>, & in <expan abbr="hor&utilde;">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="n&utilde;c">nunc</expan> po&longs;&longs;idemus, peregerit, ab Ana<lb/>xagora quia haberet <expan abbr="man&utilde;">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;im&utilde;">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="adi&utilde;xerit">adiunxerit</expan>, alte<lb/>rùm <expan abbr="quoq;">quoque</expan> <expan abbr="De&utilde;">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="arti&utilde;">artium</expan>. </s>

<s id="id.000100">Inuenit enim om<lb/>nia, & manus <expan abbr="organ&utilde;">organum</expan> organorum. </s>

<s id="id.000101">Facit enim omnia. </s>

<s id="id.000102">Et &longs;i <lb/><foreign lang="greek">mhxana=sqai</foreign> &longs;it moliri & excogitare quibus in&longs;trumentis <lb/>opus ad agendum <expan abbr="propo&longs;it&utilde;">propo&longs;itum</expan> efficiatur, <foreign lang="greek">mhxa/nhma</foreign> erit mo<lb/>litio & <expan abbr="inu&etilde;tio">inuentio</expan> <expan abbr="in&longs;trumentor&utilde;">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="greek">mhxaniko\n</foreign> e&longs;&longs;e &longs;olius erit hominis, <expan abbr="quemadmod&utilde;">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="s&utilde;t">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/>c&oelig;lum, 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>

<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>

<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>

<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>

<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>

<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>

<s id="id.000112"><emph type="italics"/>Iamque &longs;uum voluens audax indu&longs;tria mundum<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.022.jpg"/><emph type="italics"/>Gaudet, & humana &longs;idera mente regit.<emph.end type="italics"/></s>

<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>

<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="homin&utilde;">hominum</expan>, qui nunc viuunt tonitrua, <expan abbr="vi-brataq;">vi<lb/>brataque</expan> è &longs;uis &longs;clopetis, <expan abbr="bõbardi&longs;que">bombardi&longs;que</expan> fulmina, &longs;oni frago<lb/>re, ictus conqua&longs;&longs;atione, & <expan abbr="pluri&utilde;">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="vn&utilde;">vnum</expan> atque alterum <lb/>præcipitat: hæc verò certo ictu &longs;emper de&longs;tinata vrbium <lb/>m&oelig;nia deua&longs;tant: quot homines attingunt, perdunt, & <lb/><expan abbr="quid&etilde;">quidem</expan> tanta celeritate, tantáque vi, vt qu&ecedil; ab antiquis in<lb/>geniosè, vel ad oppugnandos ho&longs;tes, vel ab his &longs;e <expan abbr="defen-dend&utilde;">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="greek">mhxanh/mata,</foreign> &longs;i his homines vterentur <expan abbr="tant&utilde;">tantum</expan>, <lb/>vt patria ab ho&longs;tili &longs;eruitute liberetur, &longs;ubacto ho&longs;te fines <lb/>amplificentur, <expan abbr="adi&utilde;ctis">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="reg&utilde;">regum</expan> <expan abbr="pri-&longs;tinor&utilde;">pri<lb/>&longs;tinorum</expan> in&longs;ul&longs;a pote&longs;tate diutius detineri. </s>

<s id="id.000119"><expan abbr="Igni&utilde;">Ignium</expan> vero c&oelig;<lb/>le&longs;tium, &longs;eu <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> lumina faces no&longs;træ ardentes <expan abbr="quant&utilde;">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="greek">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="cant&utilde;">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="fabror&utilde;">fabrorum</expan> genus omne &longs;uum munus affabrè, nec o&longs;citanter <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.023.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&ecedil; <expan abbr="trã&longs;ig&etilde;dæ">tran&longs;igendæ</expan> nece&longs;&longs;aria omnino &longs;unt Agricul<lb/>turæ, Militaris, Architecturæ, Medicinæ, Nauticæ, Mer<lb/>caturæ munera: quibus <expan abbr="alim&etilde;ta">alimenta</expan>, tecta, &longs;anitas, ve&longs;titus, di<lb/>uitiæ, & ab c&oelig;li, <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="c&utilde;">cum</expan> <expan abbr="homin&utilde;">hominum</expan> parua vi, mo<lb/>les <expan abbr="lapid&utilde;">lapidum</expan>, <expan abbr="lignor&utilde;">lignorum</expan>, <expan abbr="frug&utilde;">frugum</expan>, <expan abbr="terrar&utilde;">terrarum</expan>, <expan abbr="mari&utilde;">marium</expan> <expan abbr="ing&etilde;tes">ingentes</expan> loco <expan abbr="di-mou&etilde;tur">di<lb/>mouentur</expan>, pelluntur, trahuntur, <expan abbr="cõuehuntur">conuehuntur</expan>, in <expan abbr="gyr&utilde;">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="quor&utilde;">quorum</expan> &longs;ingula &longs;eor&longs;um ma<lb/>gna vi: <expan abbr="coni&utilde;cta">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&ecedil; 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="c&oelig;m&etilde;tariorum">c&oelig;mentariorum</expan>, baiulorum, <expan abbr="phalangarior&utilde;">phalangariorum</expan>, lignatorum, <lb/>lapicidarum, <expan abbr="vinitor&utilde;">vinitorum</expan>, & eiu&longs;modi <expan abbr="vili&utilde;">vilium</expan> &longs;ordidorumque <lb/><expan abbr="homin&utilde;">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="placuer&utilde;t">placuerunt</expan>, vt &longs;int ab illis in <lb/>deorum <expan abbr="numer&utilde;">numerum</expan>, eorumque <expan abbr="maior&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.024.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&ecedil; 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/>c&oelig;le&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>

<s id="id.000137"><emph type="italics"/>Libra die, &longs;omnique pares vbi fecerit horas,<emph.end type="italics"/></s>

<s id="id.000138"><emph type="italics"/>Et medium luci atque vmbris iam diuidet orbem.<emph.end type="italics"/></s>

<s id="id.000139">Neptuno verò, cum tridentem antiquitas attribuit, quid <lb/>aliud, quam vectem? </s>

<s id="id.000140">Græci appellant <foreign lang="greek">mo/xlon</foreign> vnde ille <foreign lang="greek">mox<lb/>leuth\s</foreign> vectiarius à poëtis dictus e&longs;t, & terræ mati&longs;que con<lb/>cu&longs;&longs;or, & hac machina Syrtes &longs;ubleuans, quo plus Troianis <lb/>apparerent à poëta inducitur,</s>

<s id="id.000141"><emph type="italics"/>Leuat ip&longs;e tridenti,<emph.end type="italics"/></s>

<s id="id.000142"><emph type="italics"/>Et va&longs;tas aperit Syrtes.<emph.end type="italics"/></s>

<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="ædificior&utilde;">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>

<s id="id.000145"><emph type="italics"/>Veniant ad aratra iuuenci.<emph.end type="italics"/></s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.025.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="d&utilde;">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>

<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="quor&utilde;">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="c&utilde;">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;anor&utilde;">Syracu&longs;anorum</expan> ciuium <lb/>vires <expan abbr="cõiunctæ">coniunctæ</expan> dimouere loco non <expan abbr="potuerãt">potuerant</expan>, vt &longs;olus Hiero <lb/>machinis adiutus in mare educerer, perfecit: & <expan abbr="quid&etilde;">quidem</expan> cum <lb/>tanta ip&longs;ius regis admiratione, vt exclamarit, <foreign lang="greek">a)po\ tau/ths th=s <lb/>h(me/ras peri\ p=anto\s *arxhmh/dei le/gonti pisteute/on.</foreign> Ab hoc die <lb/>quic quid dixerit Archimedes huic <expan abbr="credend&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.026.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>

<s id="id.000165"><emph type="italics"/>Irritamenta malorum:<emph.end type="italics"/></s>

<s id="id.000166">quin potius occa&longs;iones & adiumenta bonorum multorum, <lb/>&longs;i <expan abbr="bon&utilde;">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>

<s id="id.000168"><emph type="italics"/>Quæ Virtute pecunia<emph.end type="italics"/></s>

<s id="id.000169"><emph type="italics"/>Exornata nitet, &longs;uppeditat Vias<emph.end type="italics"/></s>

<s id="id.000170"><emph type="italics"/>Non vnas, bene agas, quibus<emph.end type="italics"/></s>

<s id="id.000171"><emph type="italics"/>Quæ &longs;ors cunque ferens obtulerit tibi:<emph.end type="italics"/></s>

<s id="id.000172">Et vt Antiphanes,</s>

<s id="id.000173"><emph type="italics"/>Per deos cur optet quis dite&longs;cere?<emph.end type="italics"/></s>

<s id="id.000174"><emph type="italics"/>Pecuniæ cur optet habere plurimum:<emph.end type="italics"/></s>

<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>

<s id="id.000177"><emph type="italics"/>Fructúmque &longs;erere Diuarum &longs;uaui&longs;simæ?<emph.end type="italics"/></s>

<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>

<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&ecedil;, 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="c&utilde;">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 c&oelig;ptam 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.027.jpg"/>bellis ouis fui&longs;&longs;e lupis. </s>

<s id="id.000182">Itaque proprijs,</s>

<s id="id.000183"><emph type="italics"/>viribus ille<emph.end type="italics"/></s>

<s id="id.000184"><emph type="italics"/>Confi&longs;us perijt,<emph.end type="italics"/></s>

<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="argent&utilde;">argentum</expan>, aurum apprehenditur.</s>

<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>

<s id="id.000192"><emph type="italics"/>Forcipe ferrum.<emph.end type="italics"/></s>

<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 pr&oelig;lis &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 pr&oelig;lum 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 c&oelig;ptæ oppugnari <lb/>Syracu&longs;æ, terra ab Hexapylo: mari ab Acradina. </s>

<s id="id.000199">Et habui&longs;<lb/>&longs;et tantò impetu c&oelig;pta 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 c&oelig;li &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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.028.jpg"/>caretur. </s>

<s id="id.000201">Murum per in&ecedil;quales ductum colles, pleraque alta <lb/>& difficilia aditu, &longs;ummi&longs;&longs;a quædam, & quæ planis vallibus <lb/>adiri po&longs;&longs;ent, vt cuique aptum vi&longs;um e&longs;t loco, ita omni ge<lb/>nere tormento rum in&longs;truxit. </s>

<s id="id.000202">A cradinæ 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.029.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>

<s id="id.000218"><emph type="italics"/>Queis meliore luto finxit præcordia Titan:<emph.end type="italics"/></s>

<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>

<s id="id.000222"><emph type="italics"/>Qui alium ditem cernens, cum dee&longs;t quod agatur,<emph.end type="italics"/></s>

<s id="id.000223"><emph type="italics"/>Ip&longs;e &longs;olum vertit tauris, & &longs;emina ponit.<emph.end type="italics"/></s>

<s id="id.000224">Sed eo animo h&ecedil;c pr&ecedil;&longs;ertim <expan abbr="n&utilde;c">nunc</expan> à me dicuntur, vt audacter <lb/>& &longs;ine rubore aliquando ingrediamur officinas fabrorum <lb/>generis omnis, vt & in&longs;trumenta, & machinas quibus vtun<lb/>tur in &longs;uis operibus con&longs;iciendis 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="greek">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="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.030.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="c&utilde;">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="greek">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.000231"><emph type="italics"/>Extraict du Priuilege du Roy.<emph.end type="italics"/></s>

<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>

<s id="id.000235"><foreign lang="fr"><emph type="italics"/>Signé par le Con&longs;eil<emph.end type="italics"/></foreign></s>

<s id="id.000236"><foreign lang="fr"><emph type="italics"/>D<emph.end type="italics"/>E LAVETS.</foreign></s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.032.jpg"/><section>

<s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>& eorum Commentarijs.<lb/><arrow.to.target n="table1"/></s><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="greek">*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="greek">*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;c&utilde;t">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;uppli-cium.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Antiphonis ver&longs;us de natura & arte.<emph.end type="italics"/></cell><cell>8. 12</cell></row><row><cell><emph type="italics"/>Arbores, & plantæ in&longs;i&longs;lunt plane terræ ad rectos angulos.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>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;co-pum 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;ordi-das.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes liberales.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes pueriles.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes magnæ.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Artes imperantes.<emph.end type="italics"/></cell><cell>3.4</cell></row><row><cell><emph type="italics"/>Artes architectonicæ.<emph.end type="italics"/></cell><cell>3</cell></row><row><cell><emph type="italics"/>Ars Typographica nihil e&longs;&longs;et &longs;ine co-chlea.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>A&longs;inus, & aues longo collo vident c&oelig;-lum, vt homo.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Axis in peritrochio.<emph.end type="italics"/></cell><cell>120</cell></row><row><cell><foreign lang="greek">*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, pericu-losè de&longs;cendunt.<emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>B. Feratinus Amerinus <expan abbr="cãcellariæ">cancellariæ</expan> Apo-&longs;tolicæ regens con&longs;ecrat, & compreca-tur multa &longs;uper crucem apici obeli&longs;ci imponendam.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Bombi tormentorum multi editi &longs;tatim atque crux impo&longs;ita fuit apici obe-li&longs;ci.<emph.end type="italics"/></cell><cell>142</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.033.jpg"/><row><cell><emph type="italics"/>Bouilli error, qui putabat rectam iuuen-tam 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="aratr&utilde;">aratrum</expan> pariter &longs;ubiugandi.<emph.end type="italics"/></cell><cell>192</cell></row><row><cell><emph type="italics"/>Boüm in iugo imbecillior &longs;ubleuari po-te&longs;t.<emph.end type="italics"/></cell><cell>192</cell></row><row><cell><emph type="italics"/>Bruta ventrem ad terram conuer&longs;um habent.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Bruti&longs;pina 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="greek">*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="mechanic&utilde;">mechanicum</expan>.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Cardanus reprehen&longs;us à Scaligero.<emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Cardanus ob&longs;curè & imper&longs;ectè: inge-niosè tamen&longs;crip&longs;it.<emph.end type="italics"/></cell><cell>180</cell></row><row><cell><emph type="italics"/>Carche&longs;ium quid.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Cathelina mu&longs;ca Rhemen&longs;ibus dicta e&longs;t <expan abbr="ex&etilde;plar">exemplar</expan> puncti duabus lationibus eo-dem tempore moti.<emph.end type="italics"/></cell><cell>32.33</cell></row><row><cell><emph type="italics"/>Cauda e&longs;t omnipi&longs;ci progubernaculo.<emph.end type="italics"/></cell><cell>77</cell></row><row><cell><emph type="italics"/>Celeritas duplex.<emph.end type="italics"/></cell><cell>27</cell></row><row><cell><emph type="italics"/>Centrobarica pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Cercopithecus proxime accedit ad figu-ram hominis.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopithecus, & &longs;imia e&longs;t ridicula ho-minis imitatio.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopitheci manus differt ab hominis manu.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Cercopitheci pollex non e&longs;t <foreign lang="greek">a)nti/xeir,</foreign> vt in manu hominis.<emph.end type="italics"/></cell><cell>195</cell></row><row><cell><emph type="italics"/>Centrum duorum circulorum connexo-rum non e&longs;t idem.<emph.end type="italics"/></cell><cell>173</cell></row><row><cell><emph type="italics"/>Chirurgi togati nolunt dentes cuellere, licet&longs;u operatio chirurgica.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Circini author Dædalus.<emph.end type="italics"/></cell><cell>17</cell></row><row><cell><emph type="italics"/>Circulus e&longs;t <expan abbr="principi&utilde;">principium</expan> omnium virium, quæ&longs;unt in machinis motricibus.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus admirabilißimus.<emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus habet in &longs;e quinque repugnan-tias.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Circulus &longs;ecit miracula in templis paga-norum.<emph.end type="italics"/></cell><cell>25</cell></row><row><cell><emph type="italics"/>Circulus ante, & pone mouetur &longs;imul.<emph.end type="italics"/></cell><cell>20.21</cell></row><row><cell><emph type="italics"/>Circulus maior ad minorem &longs;emper nu-tum habet.<emph.end type="italics"/></cell><cell>106</cell></row><row><cell><emph type="italics"/>Circuli nutus e&longs;t perpetuus.<emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Circuli qua&longs;i motus e&longs;t perpetuus.<emph.end type="italics"/></cell><cell>107</cell></row><row><cell><emph type="italics"/>Circuli minores infiniti &longs;unt in maiore circulo.<emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>Circuli maiores &longs;unt mouentiores.<emph.end type="italics"/></cell><cell>109</cell></row><row><cell><emph type="italics"/>Circulus <expan abbr="cõtingit">contingit</expan> <expan abbr="plan&utilde;">planum</expan> in vno <expan abbr="p&utilde;cto">puncto</expan>.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Circuli maioris minor e&longs;t angulus conta-ctus quam minoris.<emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Circulus maior cum minore per æqualem orbitam reuoluitur & contra.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Circuli <expan abbr="cõcentrici">concentrici</expan> inæquales iuncti æqua-lem orbitam <expan abbr="percurr&utilde;t">percurrunt</expan>.<emph.end type="italics"/></cell><cell>166.167.174</cell></row><row><cell><emph type="italics"/>Circuli maioris motus &longs;ecundum natu-ram maior e&longs;t quam minoris.<emph.end type="italics"/></cell><cell>43</cell></row><row><cell><emph type="italics"/>in Circulo in&longs;criptas &longs;i &longs;ecet recta ad re-ctos ab&longs;ci&longs;&longs;a exdiametro erit maxima & <gap/>pinquior remotiore maior.<emph.end type="italics"/></cell><cell>68.69</cell></row><row><cell><emph type="italics"/>Circulum minorem qui datum maiorem interius tangat de&longs;cribere.<emph.end type="italics"/></cell><cell>41</cell></row><row><cell><emph type="italics"/>C&oelig;li motus unde.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>C&oelig;lum 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="Col&utilde;ba">Columba</expan> volans Acchitæ <expan abbr="nõ">non</expan> e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Contraria quæ &longs;int verè.<emph.end type="italics"/></cell><cell>18</cell></row><row><cell><emph type="italics"/>Commotum facilius mouetur, quam quie&longs;cens.<emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>Connexum & concauum non &longs;unt con-traria.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Cochlea quid.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cochleæ effecta.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochlea magnes vires habet.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochlea infinita.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>Cochleæ Ari&longs;toteles non meminit.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cochlea e&longs;t cuneus multiplicatus, vel vnus cuneus continuatus.<emph.end type="italics"/></cell><cell>131</cell></row><row><cell><emph type="italics"/>Cuneus e&longs;t vectu duplicatus.<emph.end type="italics"/></cell><cell>127</cell></row><row><cell><emph type="italics"/>Cuneum vicem gerere duorum vectium demon&longs;tratio linearis.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Cuneus quid.<emph.end type="italics"/></cell><cell>126</cell></row><row><cell><emph type="italics"/>Cunci v&longs;us.<emph.end type="italics"/></cell><cell>127</cell></row><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.034.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 moue-tur.<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 euelli-tur.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Dentiducus quid.<emph.end type="italics"/></cell><cell>132</cell></row><row><cell><emph type="italics"/><expan abbr="D&etilde;tes">Dentes</expan> <expan abbr="animali&utilde;">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 in-fixo.<emph.end type="italics"/></cell><cell>154</cell></row><row><cell><emph type="italics"/>Deusnon admiratur.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Diaconus &longs;acris ve&longs;tibus indutus imponit crucem apici obeli&longs;ci.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Diameter circuli, & Sphæræ in&longs;i&longs;tit plano ad rectos.<emph.end type="italics"/></cell><cell>105</cell></row><row><cell><emph type="italics"/>Diametri ad peripheriam quæratio.<emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Dies impo&longs;itæ crucis obeli&longs;co.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Dolabra e&longs;t cuneus.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><emph type="italics"/>Dominicus Fontana machinator in&longs;i-gnis.<emph.end type="italics"/></cell><cell>139</cell></row><row><cell><emph type="italics"/>Dominici Fontanæ triumphus.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Domus integra à &longs;undamentis &longs;ublata, & aliò tran&longs;lata.<emph.end type="italics"/></cell><cell>133</cell></row><row><cell><emph type="italics"/>E<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Elementa quie&longs;icunt adrectos angu-los &longs;ita.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>En&longs;is e&longs;t cuneus.<emph.end type="italics"/></cell><cell>130</cell></row><row><cell><foreign lang="greek">*epipo/laia</foreign> <emph type="italics"/>vis quæ.<emph.end type="italics"/></cell><cell>201.202</cell></row><row><cell><emph type="italics"/>Equus Troianus machina er at.<emph.end type="italics"/></cell><cell>12</cell></row><row><cell><emph type="italics"/>Ergat a quid.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Ergatæ, & &longs;ucculæ di&longs;tinctio.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Ergatam collopes maiores minoribus fa-cilius mouent.<emph.end type="italics"/></cell><cell>118.119</cell></row><row><cell><emph type="italics"/>Exercitium militum in exercitu ferian-tium.<emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Exigua quæ.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>F<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Fabrilis ars certitudine vincit cæte-ras.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Figura hominis <expan abbr="dec&utilde;bentis">decumbentis</expan> exirema.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Figura <expan abbr="corpor&utilde;iuuat">corporuniuuat</expan>, velimpedit mul-tum corum inclinationes, & natura-les impetus.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Figura decubitus humida, &longs;eu mediæ quæ.<emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Forceps, & forfex quid.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Fortuna in&longs;i&longs;tit Spharæ.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Funda quid.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Funda inuentum Phænicuno.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Fundæ v&longs;us.<emph.end type="italics"/></cell><cell>116.117</cell></row><row><cell><emph type="italics"/>Fundæ cur Balearis.<emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Funda longius 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 motio-ne.<emph.end type="italics"/></cell><cell>71.72</cell></row><row><cell><emph type="italics"/>Gyraphi &longs;oli crura po&longs;teriora prioribus breuiora habent.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>H<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Ha&longs;tæ ferrum e&longs;t cuneus.<emph.end type="italics"/></cell><cell>190</cell></row><row><cell><emph type="italics"/>Hominem quie&longs;cere, &longs;edare, &longs;urge-re, &longs;tare, ambulare, currere e&longs;t ex v&longs;u Geometriæ,<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Hominis quies e&longs;t per rectos angulos.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Hominis ambulatio, & progre&longs;sio, vs fiat.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Homo <expan abbr="nõ">non</expan> &longs;tatrectus, vt <expan abbr="cæl&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.035.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 perti-ca, &longs;i pondus non e&longs;t in eius medio, non æqualiter premuntur.<emph.end type="italics"/></cell><cell>190.191</cell></row><row><cell><emph type="italics"/>Horologia nostritemporis veterum cle-p&longs;ydras, & gnemones antecellunt.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Plorologium Argentorati <expan abbr="magni&longs;ic&utilde;">magni&longs;icum</expan>.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Humero dextro onera difficilius ferun-tur, quam &longs;ini&longs;tro.<emph.end type="italics"/></cell><cell>187</cell></row><row><cell><emph type="italics"/>Hypomochlium quid.<emph.end type="italics"/></cell><cell>14.55</cell></row><row><cell><emph type="italics"/>I<emph.end type="italics"/></cell><cell/></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 fer-tur, quam obliquata.<emph.end type="italics"/></cell><cell>185</cell></row><row><cell><emph type="italics"/>Lecti lateribus cur fiunt dupli.<emph.end type="italics"/></cell><cell>175</cell></row><row><cell><emph type="italics"/>Libra maior e&longs;t exactior minore.<emph.end type="italics"/></cell><cell>27.44. 45</cell></row><row><cell><emph type="italics"/>Libræ finis.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Libræpartes.<emph.end type="italics"/></cell><cell>45.46</cell></row><row><cell><emph type="italics"/>Libræfallaciæ.<emph.end type="italics"/></cell><cell>46.47</cell></row><row><cell><emph type="italics"/>Libræ valde exigua examinantis fabri-ca.<emph.end type="italics"/></cell><cell>47</cell></row><row><cell><emph type="italics"/>Librile <expan abbr="ab&longs;q;">ab&longs;que</expan> <expan abbr="põdere">pondere</expan> facilius mouetur.<emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Librilis brachia vt <expan abbr="maneãt">maneant</expan>, aut redeant ad <expan abbr="æquilibri&utilde;">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="ligne&utilde;">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="fcr&utilde;-tur">fcrun-tur</expan> bumere, quam à medio.<emph.end type="italics"/></cell><cell>183.184</cell></row><row><cell><emph type="italics"/>Lignum vt è genu facilius <expan abbr="frãgatur">frangatur</expan>.<emph.end type="italics"/></cell><cell>121</cell></row><row><cell><emph type="italics"/>Linea de&longs;cribens circulum <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> duas lationes &longs;ertur.<emph.end type="italics"/></cell><cell>28.34</cell></row><row><cell><emph type="italics"/><expan abbr="Long&utilde;">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, quædam-non per&longs;e mouentur.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Machinæ valentißimæ tres ex &longs;ententia Hippocratis.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Machinarum pluribus, & diuer&longs;arum compo&longs;itio adæquat vnam, quæ tanta, quanta opus e&longs;&longs;et fierinon pote&longs;t, pro-pter defectum materiæ.<emph.end type="italics"/></cell><cell>138.139</cell></row><row><cell><emph type="italics"/>Machinæ ad ædificia, & ad bellum.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>in Machinis faciendis lex ob&longs;eruanda.<emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Magnetis vis.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Magna quæ.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Malus nauis.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Mali pterna.<emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>Mallei <expan abbr="lõgius">longius</expan> <expan abbr="manubri&utilde;">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;t&utilde;">in&longs;trumentum</expan> <expan abbr="in&longs;trum&etilde;tor&utilde;">in&longs;trumentorum</expan>.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Manus tres partes.<emph.end type="italics"/></cell><cell>118</cell></row><row><cell><emph type="italics"/>Mechanica cur non e&longs;&longs;e Aristotelis vi-&longs;um &longs;it Cardano & <expan abbr="Frãci&longs;co">Franci&longs;co</expan> patricio.<emph.end type="italics"/></cell><cell>1</cell></row><row><cell><emph type="italics"/>Mechanica &longs;unt Aristotelis.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanicorum diui&longs;io.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanica vnde dicta.<emph.end type="italics"/></cell><cell>2.11</cell></row><row><cell><emph type="italics"/>Mechanica quæ dici debeant.<emph.end type="italics"/></cell><cell>2</cell></row><row><cell><emph type="italics"/>Mechanice quid.<emph.end type="italics"/></cell><cell>8.9</cell></row><row><cell><emph type="italics"/>Mechanice partim e&longs;t phy&longs;ica, partim mathematica.<emph.end type="italics"/></cell><cell>4.12.13</cell></row><row><cell><emph type="italics"/>Mechanicæ artes vnde dictæ.<emph.end type="italics"/></cell><cell>2.3</cell></row><row><cell><emph type="italics"/>Mechanice pars e&longs;t philo&longs;ophiæ.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Mechanices finis.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Mechanicus ante aggreßionem operis quid con&longs;iderare debeat.<emph.end type="italics"/></cell><cell>13</cell></row><row><cell><emph type="italics"/>Mechanice dicendi<emph.end type="italics"/> <foreign lang="greek">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 deter-minata.<emph.end type="italics"/></cell><cell>44</cell></row><row><cell><emph type="italics"/>Mercatura opulenta.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Mercurius in&longs;istit cubo.<emph.end type="italics"/></cell><cell>103</cell></row><row><cell><emph type="italics"/>Milij grana non &longs;unt &longs;impliciter exigua.<emph.end type="italics"/></cell><cell>204</cell></row><row><cell><emph type="italics"/>Militaris ars vtilitate vincit cæteras.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Milo cuneum contemnens peryt.<emph.end type="italics"/></cell><cell>127</cell></row><row><cell><emph type="italics"/>Mobile motum quò vergit facile moue-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.036.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 alio-rum motuum.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mobile latius mouetur difficilius.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Moles exigua &longs;æpe magnam vim obti-net.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Motus fit in tempore, & &longs;ucceßiuè.<emph.end type="italics"/></cell><cell>205</cell></row><row><cell><emph type="italics"/>Motus minimus quis.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mota duobus motibus ad eundem <expan abbr="ter-min&utilde;">ter-minum</expan> <expan abbr="tend&etilde;tibus">tendentibus</expan> celerius <expan abbr="mou&etilde;tur">mouentur</expan>.<emph.end type="italics"/></cell><cell>163</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem ha-bentibus fertur <expan abbr="&longs;ecund&utilde;">&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;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rectã">rectam</expan>.<emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motus circularis omnium machinatio-num principia continet.<emph.end type="italics"/></cell><cell>60</cell></row><row><cell><emph type="italics"/>Motus difficultas in mobili à quibus pen-deat.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Mulier parua non e&longs;t pulchræ.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Mundus nutans non vere dici de terra à poëta.<emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mu&longs;culus vecti comparatus à Galeno.<emph.end type="italics"/></cell><cell>56</cell></row><row><cell><emph type="italics"/>N<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Natura <expan abbr="eod&etilde;">eodem</expan> modo &longs;emper opera-tur, & eundem &longs;copum habet.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Natura re&longs;i&longs;tit arti in multis.<emph.end type="italics"/></cell><cell>8</cell></row><row><cell><emph type="italics"/>Nauigandi ars admirabilis ob &longs;ubtilita-tem, & nauigationis pericula.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauigij Hieronis de&longs;criptio incredibi-lis.<emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Nauis quid, & partes.<emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauis Ptolemaicæ magnitudo.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Nauis iam mota &longs;acilius mouetur.<emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>Nauis plus vehitur antror&longs;um, quam re-mi palmula retror&longs;um.<emph.end type="italics"/></cell><cell>80</cell></row><row><cell><emph type="italics"/>Nauis actuariæ promotio.<emph.end type="italics"/></cell><cell>69</cell></row><row><cell><emph type="italics"/>Nauis velocit as à quibus.<emph.end type="italics"/></cell><cell>93</cell></row><row><cell><emph type="italics"/>Nauium &longs;pecies.<emph.end type="italics"/></cell><cell>63</cell></row><row><cell><emph type="italics"/>Nauicula è plumbo tenui &longs;upernatat aquæ.<emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Nautæ in procellis &longs;olo vtuntur dolone.<emph.end type="italics"/></cell><cell>94</cell></row><row><cell><emph type="italics"/>Nautica ars opulenta.<emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Nuces à nucifrangibulo &longs;ine ictu facilius franguntur, quam cum ictu.<emph.end type="italics"/></cell><cell>155.156</cell></row><row><cell><emph type="italics"/><expan abbr="Nucifrãgibuli">Nucifrangibuli</expan> & forcipis di&longs;tinctio.<emph.end type="italics"/></cell><cell>156</cell></row><row><cell><emph type="italics"/>Nucifrangibulum ferreum facilius nu-cem frangit, quam ligneum.<emph.end type="italics"/></cell><cell>167</cell></row><row><cell><emph type="italics"/>Nutus quid.<emph.end type="italics"/></cell><cell>104.108</cell></row><row><cell><emph type="italics"/>Nutus quotuplex.<emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>Nutus maioris peripheriæ maior e&longs;t, quam minoris.<emph.end type="italics"/></cell><cell>108</cell></row><row><cell><emph type="italics"/>O<emph.end type="italics"/></cell><cell/></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;i-ta Christianis &longs;ignificat.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>molimina circa Obeli&longs;ci tran&longs;lationem quinque, omnia difficillima.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>ad Obeli&longs;cum transferendum quæ ma-chinæ, & quot adhibitæ.<emph.end type="italics"/></cell><cell>140</cell></row><row><cell><emph type="italics"/>circa <expan abbr="Obeli&longs;c&utilde;">Obeli&longs;cum</expan> molitiones quiuque, quo-modo, & à quibus perfectæ.<emph.end type="italics"/></cell><cell>141</cell></row><row><cell><emph type="italics"/>Obeli&longs;ci in area V aticani ante portam D. Fetri po&longs;iti Ichnographiæ.<emph.end type="italics"/></cell><cell>143</cell></row><row><cell><emph type="italics"/>de Obeli&longs;co & Xy&longs;to V. Summ. Pont. & cruce Gulielmi Blanci <expan abbr="epigrãma">epigramma</expan>.<emph.end type="italics"/></cell><cell>142</cell></row><row><cell><foreign lang="greek">*odonta/gra *h)/ \o)donta/gw=gos</foreign> <emph type="italics"/>quid.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><foreign lang="greek">*odonta/gw=gos</foreign> <emph type="italics"/><expan abbr="pl&utilde;beus">plumbeus</expan> in <expan abbr="t&etilde;plo">templo</expan> Apol-linis Delphici quid &longs;ignificabat.<emph.end type="italics"/></cell><cell>153</cell></row><row><cell><emph type="italics"/>Ovos quid.<emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Os arietinum volæ manus impo&longs;itum frangitur manu illæ&longs;a.<emph.end type="italics"/></cell><cell>122</cell></row><row><cell><foreign lang="greek">*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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.037.jpg"/><row><cell><emph type="italics"/>Percu&longs;sionis magna vis ad mouendum, findendum, frangendum, quatien-dum.<emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Perpendiculares à peripherijs in &longs;emi-diametros circulorum inæqualium æquales auferunt &longs;egmenta &longs;emidia-metrorum inæqualia, quorum maius e&longs;t quod è minori aufertur.<emph.end type="italics"/></cell><cell>40</cell></row><row><cell><emph type="italics"/>Peripheriæ maiores à punctis à centro remotioribus de&longs;cribuntur.<emph.end type="italics"/></cell><cell>23</cell></row><row><cell><emph type="italics"/>Petorita Gallorum petoritis Polonorum difficilius mouentur.<emph.end type="italics"/></cell><cell>113</cell></row><row><cell><emph type="italics"/>Phalanga quid.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>Phalangary qui.<emph.end type="italics"/></cell><cell>191</cell></row><row><cell><emph type="italics"/>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 admi-ratione.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Philo&longs;ophia e&longs;t ars generalis omnibus fa-ciendorum difficultatibus &longs;uccurrens.<emph.end type="italics"/></cell><cell>9</cell></row><row><cell><emph type="italics"/>Philo&longs;ophandi, vt admirandi &longs;emper oc-ca&longs;io erit.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><emph type="italics"/>Plumbum vtri aëre pleno annexum tar-dius de&longs;cendit in aquim, quam &longs;i non e&longs;&longs;et aunexum.<emph.end type="italics"/></cell><cell>170</cell></row><row><cell><foreign lang="greek">*po/da e)rei=n,</foreign> <emph type="italics"/>& canere quid.<emph.end type="italics"/></cell><cell>95</cell></row><row><cell><foreign lang="greek">*po/des, & pro/podes.</foreign></cell><cell>96</cell></row><row><cell><foreign lang="greek">*poliorkitik*h\</foreign> <emph type="italics"/>pars Mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><foreign lang="greek">*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 mo-tore e&longs;t can&longs;a eorum lationis.<emph.end type="italics"/></cell><cell>201</cell></row><row><cell><emph type="italics"/>Proiecta nec exigua nec magna &longs;eruntur procul.<emph.end type="italics"/></cell><cell>203.205</cell></row><row><cell><emph type="italics"/>Publ. Scipio & C. Lælius colligentes cro-cas quæ dicerent.<emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Purpura quid.<emph.end type="italics"/></cell><cell>47.48</cell></row><row><cell><emph type="italics"/>Q<emph.end type="italics"/></cell><cell/></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 na-uim.<emph.end type="italics"/></cell><cell>61</cell></row><row><cell><emph type="italics"/>Remi digitis manuum comparati.<emph.end type="italics"/></cell><cell>65</cell></row><row><cell><emph type="italics"/>Remus vt plurimum maris diuidit.<emph.end type="italics"/></cell><cell>71</cell></row><row><cell><emph type="italics"/>de Remi motione comparata ad motio-nem nauis.<emph.end type="italics"/></cell><cell>84.85.86.87.88.89</cell></row><row><cell><emph type="italics"/>qui <expan abbr="Remig&utilde;">Remigum</expan> plus nauim promoueant.<emph.end type="italics"/></cell><cell>68</cell></row><row><cell><emph type="italics"/>in Rhombo punctum vnum extremum lateris motum duobus motibus minus &longs;paty conficit, quam latus ip&longs;um.<emph.end type="italics"/></cell><cell>159</cell></row><row><cell><emph type="italics"/>Rhombus con&longs;tituitur cuius angulus acu-tus e&longs;t dimidio obtu&longs;i minor.<emph.end type="italics"/></cell><cell>161</cell></row><row><cell><emph type="italics"/>in Rhombo alterum punctorum extre-morum non æqualem <expan abbr="rectã">rectam</expan> tran&longs;it.<emph.end type="italics"/></cell><cell>157</cell></row><row><cell><emph type="italics"/>Rhombus quid.<emph.end type="italics"/></cell><cell>159</cell></row><row><cell><emph type="italics"/>Rotæ binæ quaternis faciliores.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>in Rotis quaternis po&longs;teriores prioribus maiorese&longs;&longs;e debent.<emph.end type="italics"/></cell><cell>111</cell></row><row><cell><emph type="italics"/>Rotæ curruum maiores commodiores ad facilitatem & celeritatem.<emph.end type="italics"/></cell><cell>110</cell></row><row><cell><emph type="italics"/>Rotunda figura difficulter patitur.<emph.end type="italics"/></cell><cell>124</cell></row><row><cell><emph type="italics"/>Rotunda maiora facilius mouentur mi-noribus.<emph.end type="italics"/></cell><cell>99.100</cell></row><row><cell><emph type="italics"/><expan abbr="Rot&utilde;dorum">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.038.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;ecu-ra.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Sedile idem non congruit omni homini.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Seßio propriè dista & latè<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Seßio cum &longs;ecuritate.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Sedens altius &longs;urgit facilius.<emph.end type="italics"/></cell><cell>197.198</cell></row><row><cell><foreign lang="greek">*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 & mo-uentißimum.<emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sphæra contingit planum in puncto.<emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Sphæra Archimedis per &longs;e mobilis non e&longs;t fabula.<emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Sphæratopæia pars e&longs;t mechanices.<emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Stateræ partes.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Stateræ v&longs;us.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Statera in pretio&longs;is expendendis non v&longs;urpatur, &longs;ed libra.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Statera commodior libra.<emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Statera vna mult æ &longs;unt libræ.<emph.end type="italics"/></cell><cell>148.149</cell></row><row><cell><emph type="italics"/>Statera e&longs;t vectis inuer&longs;us.<emph.end type="italics"/></cell><cell>150</cell></row><row><cell><emph type="italics"/>Stateræ paruo æquipondio magna ponde-ra expendunt.<emph.end type="italics"/></cell><cell>146.147.148</cell></row><row><cell><emph type="italics"/>Stateræ dimidium e&longs;t an&longs;a.<emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Per Stateram ponderationis factæ de-mon&longs;tratio.<emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Stare quid.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><emph type="italics"/>Stans e&longs;t perpendicularis terræ.<emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Stantis di&longs;po&longs;itio e&longs;t in recta linea.<emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>Statio & &longs;eßio propria <expan abbr="s&utilde;t">sunt</expan> homini.<emph.end type="italics"/></cell><cell>194</cell></row><row><cell><foreign lang="greek">*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 angu-lis.<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Surgentes con&longs;tituunt angulum acutum ex femore cum tibia, tum ex thoræce & femore.<emph.end type="italics"/></cell><cell>193.195.196</cell></row><row><cell><emph type="italics"/>Surrectionis initium fit per acutos angu-los.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Surrectionis medium fit per rectum, & obtu&longs;os angulos.<emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Symmetria quid.<emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Symmetria pro analogia.<emph.end type="italics"/></cell><cell>205</cell></row><row><cell><emph type="italics"/>T<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/>Telum facilius ten&longs;a penetrat, quam laxa.<emph.end type="italics"/></cell><cell>202</cell></row><row><cell><emph type="italics"/>Terra cur immobilis.<emph.end type="italics"/></cell><cell>103.104</cell></row><row><cell><emph type="italics"/>Terra comparata cubo à Pythagoreis, & Platone.<emph.end type="italics"/></cell><cell>103.196</cell></row><row><cell><emph type="italics"/>Textus Ari&longs;totelis omnium mendo&longs;i&longs;-&longs;imus.<emph.end type="italics"/></cell><cell>178.179</cell></row><row><cell><emph type="italics"/>Thaletis factum in eclip&longs;i Solis.<emph.end type="italics"/></cell><cell>5</cell></row><row><cell><foreign lang="greek">*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 adie-ctum.<emph.end type="italics"/></cell><cell>188.190</cell></row><row><cell><emph type="italics"/>Tormenta bellica deducenda plures equos po&longs;tulant.<emph.end type="italics"/></cell><cell>110.111</cell></row><row><cell><emph type="italics"/>Traba quid.<emph.end type="italics"/></cell><cell>115</cell></row><row><cell><emph type="italics"/>Trispa&longs;ton.<emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Trochlea quid.<emph.end type="italics"/></cell><cell>111.134</cell></row><row><cell><emph type="italics"/>Trochlea e&longs;t vectis.<emph.end type="italics"/></cell><cell>136</cell></row><row><cell><emph type="italics"/>in Trochleis plures orbiculi facilius, &longs;ed lentius trahunt.<emph.end type="italics"/></cell><cell>137</cell></row><row><cell><emph type="italics"/>Trochleæ duæ legitimè compofitæ magna pondera adducunt.<emph.end type="italics"/></cell><cell>133.134.136</cell></row><row><cell><emph type="italics"/>V<emph.end type="italics"/></cell><cell/></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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.039.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 na-uigatur demonstratio.<emph.end type="italics"/></cell><cell>98</cell></row><row><cell><emph type="italics"/>in Vortice aquarum lata ad medium de-uoluuntur.<emph.end type="italics"/></cell><cell>206.207.209.210</cell></row><row><cell><emph type="italics"/>Vortex aquarum.<emph.end type="italics"/></cell><cell>206</cell></row><row><cell><emph type="italics"/>in Vortice aquo&longs;i multi circuli concentri-ci.<emph.end type="italics"/></cell><cell>206</cell></row><row><cell><emph type="italics"/>Vortex aquæ e&longs;t linea &longs;piralis vnius, aut plurium reuolutionum.<emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Vortices quomodo à nautis vitentar.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Vortices inter Roe&longs;t & Loffoet.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>in Vorticem vt &longs;entiunt nautæ &longs;e impe-<gap/>gi&longs;&longs;e.<emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>difficile &longs;e liberare à Vortice.<emph.end type="italics"/></cell><cell>210.211</cell></row><row><cell><emph type="italics"/>aquain Vortice <expan abbr="de&longs;c&etilde;d&etilde;s">de&longs;cendens</expan> quò feratur.<emph.end type="italics"/></cell><cell>211</cell></row><row><cell><emph type="italics"/>Vtilitas hominum postulat in operibus &longs;uis varietatem.<emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>X<emph.end type="italics"/></cell><cell/></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="greek">*zugo\s & *zugo\n.</foreign></cell><cell>45.119</cell></row><row><cell><foreign lang="greek">*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>

<s id="id.000238">FINIS.</s></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.040.jpg" pagenum="1"/><figure id="id.035.01.040.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.040.1.jpg"/></front><body><chap>

<s id="id.000239"><foreign lang="greek">*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>

<s id="id.000241"><foreign lang="greek">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>

<s id="id.000242"><margin.target id="marg1"/>Pro <foreign lang="greek">mhxanh\,</foreign><lb/>lege <foreign lang="greek">mhxani<lb/>kh/.</foreign></s>

<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></chap><chap>

<s id="id.000245">MIRA &longs;unt in his, quæ <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="naturã">naturam</expan> <expan abbr="eue-ni&utilde;t">eue<lb/>niunt</expan>, ea: <expan abbr="quor&utilde;">quorum</expan> cau&longs;a igno<lb/>ratur, & in his quæ præter <lb/>naturam, ea, <expan abbr="qu&ecedil;cunq;">qu&ecedil;cunque</expan> arte <lb/>facta hominibus <expan abbr="cõferunt">conferunt</expan>.</s>

<s id="id.000246">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.041.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.000251">Ip&longs;emet Patricius fate<lb/>tur hunc<emph.end type="italics"/> <foreign lang="greek">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="ver&utilde;">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="greek">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>

<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>

<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="greek">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="greek">a)po\ th=s mhxanh=s. </foreign> & <foreign lang="greek">*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="obtrud&utilde;t">obtrudunt</expan>, ip&longs;a&longs;que <expan abbr="impedi&utilde;t">impediunt</expan>.<emph.end type="italics"/><lb/></s>

<s><foreign lang="greek">*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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.042.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="greek">mhxanika\s,</foreign> <emph type="italics"/>(neque enim hîc id vocabuli v&longs;urpant) <lb/>&longs;ed<emph.end type="italics"/> <foreign lang="greek">fau/las, a)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>

<s id="id.000276"><margin.target id="marg4"/>Lib I.cap i. <lb/>Ethic.</s>

<s id="id.000277">Lingua, Tropus, Ratio, Numerus, Tonus, Angulus, A&longs;tra: <lb/> Rus, Nemus, Arma, Faber, Vulnera, Lana, Rates. </s>

<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>

<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="Virgili&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.043.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="greek">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>

<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>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.044.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="omni&utilde;">omnium</expan>, Bruta quia <lb/><expan abbr="ne&longs;ci&utilde;t">ne&longs;ciunt</expan>, nec &longs;cire cupiunt, nihil admirari: <expan abbr="&longs;ol&utilde;">&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>

<s id="id.000295">Nil admirari propè res e&longs;t vna Numici,</s>

<s id="id.000296">Soláque quæ po&longs;&longs;it facere & &longs;eruare beatum.</s>

<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, f&oelig;lices: &longs;ed eos, qui cogno&longs;cunt, iux<lb/>ta illud<emph.end type="italics"/></s>

<s id="id.000298">F&oelig;lix, qui potuit rerum cogno&longs;cere cau&longs;as.</s>

<s id="id.000299"><emph type="italics"/>Ab hac admirandi facultate Ari&longs;toteles <expan abbr="principi&utilde;">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>

<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>

<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>

<s id="id.000308">Multa tegit &longs;acro inuolucro Natura, neque vllis</s>

<s id="id.000309">Fas e&longs;t &longs;cire quidem mortalibus omnia: multa</s>

<s id="id.000310">Admirare modò, nec non venerare.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.045.jpg" pagenum="6"/>

<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></chap><chap>

<s id="id.000313">In multis enim natura ab <lb/>vtilitate no&longs;tra di&longs;cedit. </s>

<s id="id.000314"><expan abbr="Si-quid&etilde;">Si<lb/>quidem</expan> natura <expan abbr="eod&etilde;">eodem</expan> modo <lb/><expan abbr="s&etilde;per">semper</expan> operatur & &longs;implici<lb/>ter: at <expan abbr="ali&utilde;">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&ecedil;ter <expan abbr="naturã">naturam</expan>, <lb/><expan abbr="t&utilde;">tum</expan> difficultas hæ&longs;itationem <lb/>adfert, & arte opus e&longs;t.</s>

<s id="id.000316">COMMENTARIVS.</s>

<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>

<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>

<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>

<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>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.046.jpg" pagenum="7"/><emph type="italics"/>lib. de C&oelig;lo & de generat. & corrupt.<emph.end type="italics"/></s>

<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 c&oelig;li, 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>

<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="c&utilde;ctis">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="oner&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.047.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>

<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></chap><chap>

<s id="id.000341"><margin.target id="marg8"/><foreign lang="greek">mhxanikh\n.</foreign></s>

<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="Quemadmod&utilde;">Quemadmodum</expan> <lb/>enim Antipho poëta di<lb/>xit, ita &longs;e res habet.</s>

<s id="id.000344"><emph type="italics"/>Natura vincit: hanc arte <lb/>vincimus.<emph.end type="italics"/></s>

<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>

<s id="id.000346">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01048.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="ver&utilde;">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>

<s id="id.000357"><margin.target id="marg9"/>Cap. 3. lib. <lb/>de cuiu&longs;que <lb/>animi pecc. <lb/>cogno&longs;c.</s>

<s id="id.000359">Mechanice.] <emph type="italics"/>In Græco Vecheli legitur hîc<emph.end type="italics"/> <foreign lang="greek">mhxanh\n</foreign>: <emph type="italics"/>vt etiam <lb/>in titulo huius capitis: &longs;ed vtrobique legendum<emph.end type="italics"/> <foreign lang="greek">mhxanikh\n.</foreign> <emph type="italics"/>quia ha<lb/>ctenus in hoc proëmio non machina vna: &longs;ed ars machinarum lau<lb/>data e&longs;t. </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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.049.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="greek">a)uto/mata</foreign> <emph type="italics"/>vocantur: quorum alia Græcis<emph.end type="italics"/> <foreign lang="greek">stata\,</foreign><lb/><emph type="italics"/>Latinis Stataria, fixa, firma dicuntur: alia<emph.end type="italics"/> <foreign lang="greek">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="greek">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="molend&utilde;">molendum</expan>, <expan abbr="t&utilde;">tum</expan> tympana, tum &longs;erræ ad trabes <lb/>&longs;ecandas, folles ad <expan abbr="ferr&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.050.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="greek">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="greek">mhxanopoihtikh\,</foreign> <emph type="italics"/>quæ facile aquas antlijs extrahit:<emph.end type="italics"/> <foreign lang="greek">*or<lb/>ganopoihtikh\,</foreign> <emph type="italics"/>quæ bellis accommoda in&longs;trumenta fabricatur, arie<lb/>tes, te&longs;tudines, turres ambulatorias, helepoleis, &longs;ambucas, exo&longs;tras, <lb/>tollenones & quæcunque Græco vocabulo<emph.end type="italics"/> <foreign lang="greek">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="greek">qaumatourgikh\</foreign> <emph type="italics"/>cuius exempla &longs;unt<emph.end type="italics"/> <foreign lang="greek">u)drau<lb/>lika\</foreign> <emph type="italics"/>organa, quæque per &longs;e ventorum 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="greek">si/fwnes</foreign><lb/><emph type="italics"/>extinguendis ineendijs 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 & Sphærotop&oelig;ia, 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>

<s id="id.000387"><margin.target id="marg10"/>In parapha<lb/>&longs;i huius li<lb/>bri.</s>

<s id="id.000388"><margin.target id="marg11"/>In Pancpi<lb/>&longs;temone.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.051.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="greek">paradoxo/poioi,</foreign> <emph type="italics"/>cum Galeno vocari poterunt.<emph.end type="italics"/></s>

<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>

<s id="id.000396">In&longs;pectura domos venturáque de&longs;uper vrbi.</s>

<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></chap><chap>

<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>

<s id="id.000401">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.052.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="greek">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="greek">gra/mmikas</foreign> <emph type="italics"/>id e&longs;t lineares & <lb/>numerales demon&longs;trationes, quibus ip&longs;um explicant, Mathemati<lb/>cas. </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="quac&utilde;que">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></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.053.jpg" pagenum="14"/><chap>

<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>

<s id="id.000417">COMMENTARIVS.</s>

<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="extrem&utilde;">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="greek">u(pomo/xlion,</foreign> <emph type="italics"/>Vitruuius porrectam <lb/>preßionem appellat.<emph.end type="italics"/></s>

<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></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.054.jpg" pagenum="15"/><chap>

<s id="id.000426"><expan abbr="Omni&utilde;">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>

<s id="id.000429">COMMENTARIVS.</s>

<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>

<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>

<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>

<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></chap><chap>

<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="mir&utilde;">mirum</expan>.</s>

<s id="id.000440">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.055.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="greek">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 c&oelig;pit, &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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.056.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>

<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 c&oelig;pit, 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>

<s id="id.000454">Ex vno duo ferrea brachia nodo <lb/>Iunxit, vt æquali &longs;patio di&longs;tanti<lb/><figure id="id.035.01.056.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.056.1.jpg"/><lb/>bus ip&longs;is</s>

<s id="id.000455">Altera pars &longs;taret, pars altera du<lb/>ceret orbem.</s>

<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></chap><chap>

<s id="id.000459">Primum &longs;iquidem lineæ <lb/>ip&longs;um circulum <expan abbr="compre-hend&etilde;ti">compre<lb/>hendenti</expan>, licet latitudinem <lb/>nullam habeat, contraria <lb/>quodammodo, cauum & <lb/>conuexum ine&longs;&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="magn&utilde;">magnum</expan> & paruum. <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.057.jpg" pagenum="18"/></s>

<s><foreign lang="greek"><gap/></foreign>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&ecedil; in&longs;unt <lb/>circulo.</s>

<s id="id.000463">COMMENTARIVS.</s>

<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="greek">prw/ton</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">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="greek">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 alÿs &longs;int al-<emph.end type="italics"/><lb/><figure id="id.035.01.057.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.057.1.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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.058.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>

<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">C&oelig;terum 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="magn&utilde;">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>

<s id="id.000487">Atque vnum hoc e&longs;t.] <foreign lang="greek">to\ a)/topon.</foreign> <emph type="italics"/>Hic vt & alibi &longs;æpius <lb/>pro<emph.end type="italics"/> <foreign lang="greek">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></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.059.jpg" pagenum="20"/><chap>

<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="mutat&utilde;">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&ecedil; circa <lb/>libram eueniunt ad circu<lb/>lum referuntur, & qu&ecedil; cir<lb/>ca vectem ad libram, & <lb/>forta&longs;&longs;is alia omnia, quæ <lb/>circa motiones mechani<lb/>cas, ad vectem.</s>

<s id="id.000495">COMMENTARIVS.</s>

<s id="id.000496">Secundum.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="greek">deu/teron</foreign> <emph type="italics"/>legamus &longs;i placet<emph.end type="italics"/> <foreign lang="greek">trh/ton.</foreign> <emph type="italics"/>Hic enim <lb/>tertia e&longs;t repugnantia in circulo ex 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>

<s id="id.000500">Atque linea circulum.] <emph type="italics"/>Cur circulus antè & ponè mouea-<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.060.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>

<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 c&oelig;pit, 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>

<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>

<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. 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 c&oelig;perat moueri, quod e&longs;t vltimum<emph.end type="italics"/><lb/><figure id="id.035.01.060.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.060.1.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>

<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>

<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 abbrev="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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.061.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></chap><chap>

<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="p&utilde;ctorum">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;e-qu&etilde;tibus">&longs;e<lb/>quentibus</expan> problematis fiet <lb/>manife&longs;tum.</s>

<s id="id.000515">COMMENTARIVS.</s>

<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 c&oelig;perat, 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="p&utilde;ctorum">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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.062.jpg" pagenum="23"/>

<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.035.01.062.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.062.1.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="pe-ripheriã">pe<lb/>ripheriam</expan> A B C: <lb/>ita & D G diameter ad &longs;uam peripheriam D F G, per ea quæ <lb/>demon&longs;trata &longs;unt ab Archimede prop. 3. lib. de dimen&longs;. circuli, & <lb/>vicißim proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. 16. lib. 5. & <lb/>quia A E & D H partes &longs;unt pariter multiplicium A C, D G <lb/>vtpote &longs;emidiametri &longs;uarum diametrorum, erit A E ad D H vt <lb/>A C ad D G prop. 15. lib. 5. ergo & peripheria A B C ad peri<lb/>pheriam D F G: vt A E ad D H prop. 11. lib. eiu&longs;dem. </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></chap><chap>

<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="faci&utilde;t">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.063.jpg" pagenum="24"/><foreign lang="greek"><gap/></foreign><lb/>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="organ&utilde;">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>

<s id="id.000537">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.064.jpg" pagenum="25"/><emph type="italics"/>G D ad illius motum nece&longs;&longs;ario mouebitur propter denticulos, &longs;ed <lb/><expan abbr="retrors&utilde;">retrorsum</expan><emph.end type="italics"/><lb/><figure id="id.035.01.064.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.064.1.jpg"/><lb/><emph type="italics"/>&longs;eu <expan abbr="&longs;ec&utilde;-dum">&longs;ecun<lb/>dum</expan> <expan abbr="in-ferior&etilde;">in<lb/>feriorem</expan> <lb/><expan abbr="periphe-riã">periphe<lb/>riam</expan>, vt <lb/>G ad B: <lb/>tum ter<lb/>tius E Z ad &longs;ecundi motum mouebitur etiam, &longs;ed antror&longs;um, vt E <lb/>ad F, & &longs;int deinceps alternatim infiniti denticulis &longs;e&longs;e &longs;ubinui<lb/>cem ingredientibus, &longs;emper mouebuntur. </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>

<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="deor&utilde;">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/>f&oelig;t. format. </s>

<s id="id.000545">Herodotus hi&longs;toria &longs;ecunda videtur ex his aliqua<emph.end type="italics"/> <foreign lang="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.065.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="greek">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="homin&utilde;">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="circunfer&utilde;tur">circunferuntur</expan>. </s>

<s id="id.000549">Sed ne&longs;cio an <lb/>fama, an fide nobilius &longs;it illud, quod A&racute;gentorati 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="funi&utilde;">funium</expan>, atque aliorum <expan abbr="in&longs;trumentor&utilde;">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>

<s id="id.000552"><margin.target id="marg12"/>In Menone</s></chap><chap>

<s id="id.000553">2. <foreign lang="greek">*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>

<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>

<s id="id.000557"><expan abbr="Prim&utilde;">Primum</expan> igitur qu&ecedil; circa <expan abbr="li-brã">li<lb/>bram</expan> <expan abbr="cõtingunt">contingunt</expan>, <expan abbr="difficultat&etilde;">difficultatem</expan> <lb/><expan abbr="adfer&utilde;t">adferunt</expan>. </s>

<s id="id.000558">Ob quam cau&longs;am <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.066.jpg" pagenum="27"/><foreign lang="greek"><gap/></foreign><lb/>libræ maiores minoribus <lb/>&longs;int exactiores. </s>

<s id="id.000559">Huius vero <lb/><expan abbr="principi&utilde;">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 &ecedil;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> &ecedil;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>

<s id="id.000563">COMMENTARIVS.</s>

<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>

<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>

<s id="id.000572">Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.067.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>

<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>

<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="tot&utilde;">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="c&utilde;">cum</expan> circuli æquales &longs;int, <expan abbr="quor&utilde;">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, euius &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></chap><chap>

<s id="id.000586">Horum vero cau&longs;a e&longs;t, <lb/>quod recta de&longs;cribens <expan abbr="cir-cul&utilde;">cir<lb/>culum</expan> <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> duas latio<lb/>nes fertur. </s>

<s id="id.000587"><expan abbr="C&utilde;">Cum</expan> igitur in ali<lb/>qua ratione du&ecedil; <expan abbr="s&utilde;t">sunt</expan> illæ la<lb/>tiones, nece&longs;&longs;e e&longs;t id, quod <lb/>fertur <expan abbr="&longs;ecund&utilde;">&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;ecund&utilde;">&longs;ecundum</expan> quam <lb/>mobile fertur ea: quam ha<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.068.jpg" pagenum="29"/><foreign lang="greek"><gap/></foreign><lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g,</foreign> & quidem <lb/><foreign lang="greek">a</foreign> feratur ad <foreign lang="greek">b,</foreign> & <foreign lang="greek">a b</foreign><lb/>etiam feratur ad <foreign lang="greek">h g</foreign>: la<lb/>tum vero &longs;it <foreign lang="greek">a</foreign> ad <foreign lang="greek">d,</foreign> & <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">e.</foreign> Igitur cum latio<lb/>nis ratio erat ea quam ha<lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g</foreign>: nece&longs;&longs;e <lb/>e&longs;t & ip&longs;am <foreign lang="greek">a d</foreign> ad <foreign lang="greek">a e</foreign> ean<lb/>dem habere rationcm. </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="greek">a</foreign><lb/>erat vbi <foreign lang="greek">z.</foreign></s>

<s>Eodem modo <lb/>demon&longs;trabitur <expan abbr="vbic&utilde;que">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;ec&utilde;dum">&longs;ecundum</expan> dia<lb/>metrum duabus lationi<lb/>bus nece&longs;&longs;e habet in ratio<lb/>ne laterum ferri.</s>

<s id="id.000593">COMMENTARIVS.</s>

<s id="id.000594">Horum vero cau&longs;a.] <emph type="italics"/>Inæqualium <expan abbr="circulor&utilde;">circulorum</expan> ab inæqualibus <lb/>radiis <expan abbr="de&longs;criptor&utilde;">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>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.069.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="greek">a b h g</foreign> <emph type="italics"/>com-<emph.end type="italics"/><lb/><figure id="id.035.01.069.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.069.1.jpg"/><lb/><emph type="italics"/>prehen&longs;um &longs;ub rectis<emph.end type="italics"/> <foreign lang="greek">a b, a g,</foreign><lb/><emph type="italics"/>quæ &longs;int inter &longs;e in ratione, quam <lb/>duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>habent. <lb/></s>

<s id="id.000606">Et intelligatur a latum ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">b</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>& ver&longs;us<emph.end type="italics"/><lb/><foreign lang="greek">g</foreign> <emph type="italics"/>perueni&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">e</foreign>: <emph type="italics"/>&longs;icque cum <lb/>lationum ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ratio &longs;it vt<emph.end type="italics"/><lb/><foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g,</foreign> <emph type="italics"/>ergo erit &<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a e</foreign>: <emph type="italics"/>vt<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a y,</foreign> <emph type="italics"/>& rectrangulum minus<emph.end type="italics"/> <foreign lang="greek">a d z e</foreign> <emph type="italics"/>com<lb/>munem angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>cum maiori<emph.end type="italics"/> <foreign lang="greek">a b h g</foreign> <emph type="italics"/>habens & &longs;imile erit <lb/>def. 1. lib. 6. & proinde circa eandem dimentientem conuer&longs;. prop. <lb/>24. lib. 6. </s>

<s><emph type="italics"/>Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duabus &longs;uis &longs;ic lationibus latum erit in<emph.end type="italics"/> <foreign lang="greek">z,</foreign> <emph type="italics"/>vt vbi<lb/>cumque lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;i&longs;tentur, &longs;emper &longs;int &longs;upra diametrum<emph.end type="italics"/><lb/><foreign lang="greek">a h.</foreign> <emph type="italics"/>&longs;iquidem lationes i&longs;tæ &longs;unt in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>proinde <lb/>&longs;upra rectam, quia omnis diameter rectanguli recta e&longs;t. </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="greek">a</foreign> <emph type="italics"/>extremum radij duabus lationibus <lb/>de&longs;cribere circulum non digrediens à recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. </s>

<s id="id.000613">Non igitur duæ lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun<lb/>tur in ratione<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> <emph type="italics"/>Sed hîc obiici pote&longs;t quod Sol motu pri<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, & motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet æquatori coa&longs;cendenti cum 59'. 8". Eclypticæ. </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;ecund&utilde;">&longs;ecundum</expan> arcum Eclypticæ. </s>

<s id="id.000615">Ita e&longs;t, ob id <expan abbr="dicend&utilde;">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;ecund&utilde;">&longs;ecundum</expan> rectam. </s>

<s id="id.000616">Et &longs;it manebit demon&longs;tratio.<emph.end type="italics"/></s>

<s id="id.000617">Simile e&longs;t enim.] <foreign lang="greek">tw= lo/gw,</foreign> <emph type="italics"/>id e&longs;t ratione, redundat quia quæ <lb/>&longs;imilia &longs;unt quadrangula, habent latera, quæ circum æquales angu<lb/>los propertionalia, ex def. 1. lib. 6. elem.<emph.end type="italics"/></s></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.070.jpg" pagenum="31"/><chap>

<s id="id.000620">Si enim in alia aliqua, <lb/>non feretur <expan abbr="&longs;ec&utilde;dum">&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. [Si enim <expan abbr="&longs;e-c&utilde;dum">&longs;e<lb/>cundum</expan> rationem aliquam <lb/>latum &longs;it in aliquo tempo<lb/>re, nece&longs;&longs;e e&longs;t illud tempus <lb/>rectam e&longs;&longs;e lationem, pro<lb/>pter ea quæ ante dicta &longs;unt.] Itaque circulare e&longs;t quod <lb/>&longs;ecundum duas lationes latum e&longs;t in nulla ratione nullo <lb/>in tempore.</s>

<s id="id.000625">COMMENTARIVS.</s>

<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="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">a g</foreign>: <emph type="italics"/>&longs;ed<emph.end type="italics"/><lb/><figure id="id.035.01.070.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.070.1.jpg"/><lb/><emph type="italics"/>in alia, non feretur &longs;ecundum diame<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, quæ erit diameter <lb/>figuræ à lateribus alterius rationis <lb/>con&longs;titutæ, vt e&longs;t in præ&longs;enti dia<lb/>grammate<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="greek">a d, a e</foreign> <emph type="italics"/>comprehen&longs;i.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.071.jpg" pagenum="32"/>

<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="greek">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="greek">peri\ metrh/s. kuk,</foreign><emph type="italics"/>& Ptol. lib. 1.<emph.end type="italics"/> <foreign lang="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.072.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;ec&utilde;dum">&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>

<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>

<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></chap><chap>

<s id="id.000658">Quod vero recta <expan abbr="de&longs;cri-b&etilde;s">de&longs;cri<lb/>bens</expan> circulum duabus &longs;imul <lb/>lationibus feratur, <expan abbr="c&utilde;">cum</expan> ex his <lb/>e&longs;t <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan>, <expan abbr="t&utilde;">tum</expan> quod lata <lb/><expan abbr="&longs;ecund&utilde;">&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="perpendicula-r&etilde;">perpendicula<lb/>rem</expan> [<expan abbr="demõ&longs;trem">demon&longs;trem</expan>us].</s>

<s>Sit circu<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.073.jpg" pagenum="34"/><foreign lang="greek">b</foreign><lb/>lus <foreign lang="greek">a b g,</foreign> & extremum <foreign lang="greek">b</foreign><lb/>feratur ad <foreign lang="greek">d,</foreign> perueniet &longs;a<lb/>ne aliquando ad <foreign lang="greek">g.</foreign></s>

<s>[Si igi<lb/>tur ferebatur in ratione <lb/>quam habet <foreign lang="greek">b e</foreign> ad <foreign lang="greek">e g,</foreign> fe<lb/>rebatur &longs;ecundum diame<lb/>trum <foreign lang="greek">b g</foreign>: At nunc cum in <lb/>nulla ratione feratur, &longs;e<lb/>cundum peripheriam <foreign lang="greek">b e g</foreign><lb/>feretur.]</s>

<s id="id.000660">COMMENTARIVS.</s>

<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="Radi&utilde;">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 C&oelig;lo) Quinetiam &longs;i &longs;ic. </s>

<s id="id.000664">Idem radius à diametro cir-<emph.end type="italics"/><lb/><figure id="id.035.01.073.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.073.1.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="greek">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="greek">b</foreign> <emph type="italics"/>ver&longs;us E in hoc diagrammate: altera vt retror-<emph.end type="italics"/><lb/><figure id="id.035.01.073.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.073.2.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="greek">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;uraturlineisrectis, quarum altera in po&longs;te<lb/>riore diagrammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>verò e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g.</foreign></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.074.jpg" pagenum="35"/>

<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>

<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></chap><chap>

<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="extrem&utilde;">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>

<s id="id.000677">COMMENTARIVS.</s>

<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>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.075.jpg" pagenum="36"/>

<s id="id.000682"><emph type="italics"/>Radiorem inæqualium eadem vi motorum minor plus <lb/>repellitur.<emph.end type="italics"/></s>

<s id="id.000683"><emph type="italics"/>Radius igitur minor tardius feretur.<emph.end type="italics"/></s>

<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>

<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>

<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>

<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>

<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></chap><chap>

<s id="id.000690">Et fertur motu <expan abbr="&longs;ecund&utilde;">&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>

<s id="id.000693">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.076.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></chap><chap>

<s id="id.000704">Quod vero minor plus <lb/>præter naturam moueatur: <lb/>quam maior earum, qu&ecedil; ex <lb/>centro <expan abbr="de&longs;crib&utilde;t">de&longs;cribunt</expan> circulos, <lb/>ex his erit manife&longs;tum. </s>

<s id="id.000705">Sit <lb/>circulus <foreign lang="greek">b g d e,</foreign> & alter <lb/>minor <foreign lang="greek">x n m c,</foreign> eiu&longs;dem <expan abbr="c&etilde;-tri">cen<lb/>tri</expan> <foreign lang="greek">a,</foreign> Et traductæ &longs;int dia<lb/>metri in magno quidem <lb/><foreign lang="greek">g d, & b e</foreign>: in minori <foreign lang="greek">m c & <lb/>x n</foreign>: atque alterolongum <lb/>compleatur <foreign lang="greek">d y r g.</foreign></s>

<s>Si igi<lb/>tur <foreign lang="greek">a b</foreign> de&longs;cribens <expan abbr="circul&utilde;">circulum</expan> <lb/>perueniet ad id vnde mo<lb/>ueri c&oelig;pit, manife&longs;tum e&longs;t <lb/>quod fertur ad ip&longs;am [<foreign lang="greek">a b</foreign>] <lb/>&longs;imiliter <foreign lang="greek">a x</foreign> perueniet ad <lb/>ip&longs;am <foreign lang="greek">a x.</foreign></s>

<s>Tardius autem <lb/>fertur <foreign lang="greek">a x</foreign>: quam <foreign lang="greek">a b,</foreign> vt <lb/><expan abbr="dict&utilde;">dictum</expan> e&longs;t, propter maiorem <lb/><expan abbr="repul&longs;ion&etilde;">repul&longs;ionem</expan> & reuul&longs;ionem <lb/>ip&longs;ius <foreign lang="greek">a x.</foreign></s>

<s>Ducatur vero <lb/>recta <foreign lang="greek">a q h, & a q</foreign> excitetur <lb/>perpendicularis ad <foreign lang="greek">a b,</foreign> qu&ecedil; <lb/>&longs;it <foreign lang="greek">q z</foreign> in circulo [minori].</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.077.jpg" pagenum="38"/>

<s><foreign lang="greek"><gap/></foreign>Et rur&longs;us per <foreign lang="greek">q</foreign> ducatur pa<lb/>rallela ip&longs;i <foreign lang="greek">a b</foreign> quæ &longs;it <foreign lang="greek">q w <lb/>& w n</foreign> perpendicularis ip&longs;i <lb/><foreign lang="greek">a b</foreign> tum & <foreign lang="greek">h k.</foreign></s>

<s>Sunt vero <lb/><foreign lang="greek">w n & q z</foreign> æquales. </s>

<s id="id.000706">Rur&longs;us <lb/><foreign lang="greek">b n</foreign> e&longs;t minor: quam <foreign lang="greek">x z.</foreign> In <lb/>circulis enim inæqualibus <lb/>rect&ecedil; &ecedil;quales ad rectos dia<lb/>metro excitatæ, de diame<lb/>tro circulorum maiorum <lb/><expan abbr="&longs;egment&utilde;">&longs;egmentum</expan> minus auferunt. <lb/></s>

<s id="id.000707">E&longs;t autem <foreign lang="greek">w n</foreign> æqualis ip&longs;i <lb/><foreign lang="greek">q z.</foreign> In quanto vero tempo<lb/>re <foreign lang="greek">a x</foreign> peragrauit <foreign lang="greek">x q,</foreign> in <lb/><expan abbr="tãto">tanto</expan> in maiore circulo ex<lb/>tremum <foreign lang="greek">a b</foreign> non maiorem <lb/><foreign lang="greek">b w</foreign> peragrauit (etenim <lb/>motus &longs;ecundum naturam <lb/>æqualis e&longs;&longs;et) præter na<lb/>turam vero minor erat, nempe <foreign lang="greek">b n</foreign> quam <foreign lang="greek">x z.</foreign></s>

<s id="id.000708">COMMENTARIVS.</s>

<s id="id.000709">Qvod vero minor.] <emph type="italics"/>Altera e&longs;t confirmatio &longs;ed<emph.end type="italics"/> <foreign lang="greek">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>

<s id="id.000714"><emph type="italics"/>Sint duo circuli concentrici maior<emph.end type="italics"/> <foreign lang="greek">b d e y,</foreign> <emph type="italics"/>minor<emph.end type="italics"/> <foreign lang="greek">x m n c</foreign> <emph type="italics"/>è cen<lb/>tro a traiecti diametris<emph.end type="italics"/> <foreign lang="greek">x n & b e.</foreign></s>

<s id="id.000715"><emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ad punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur recta<emph.end type="italics"/> <foreign lang="greek">a q,</foreign> <emph type="italics"/>& producatur in<emph.end type="italics"/><lb/><foreign lang="greek">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="greek">a q h.</foreign></s>

<s id="id.000716"><emph type="italics"/>Tum à puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>prop. 12. <lb/>lib. 1. &longs;itque<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.078.jpg" pagenum="39"/>

<s id="id.000717"><emph type="italics"/>Et per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ducatur parallela rectæ<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>prop. 31. lib. 1. <lb/>quæ &longs;it<emph.end type="italics"/> <foreign lang="greek">q w.</foreign></s><figure id="id.035.01.078.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.078.1.jpg"/>

<s id="id.000718"><emph type="italics"/>Rur&longs;us à puncto<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>excitetur perpendicularis lineæ<emph.end type="italics"/> <foreign lang="greek">a b,</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/><lb/><foreign lang="greek">w n</foreign>: <emph type="italics"/>& &longs;ic parallelogrammum erit<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>ex def. </s>

<s id="id.000719">parallelog.<emph.end type="italics"/></s>

<s id="id.000720"><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>tantum confecit &longs;patij &longs;ecundum natu<lb/>ram, quam<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motum ad<emph.end type="italics"/> <foreign lang="greek">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="greek">w n, q z</foreign> <emph type="italics"/>perpendiculares ex fab. & æquales, quia late<lb/>ra oppo&longs;ita in parallelogrammo<emph.end type="italics"/> <foreign lang="greek">w n z q</foreign> <emph type="italics"/>prop. 34. lib. 1. Erant vtro<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w & x q</foreign> <emph type="italics"/>æqualia.<emph.end type="italics"/></s>

<s id="id.000723"><foreign lang="greek">b n</foreign> <emph type="italics"/>vero eadem ratione metitur &longs;patium motus præter naturam <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b, & x z</foreign> <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">x.</foreign> <emph type="italics"/>&longs;i igitur<emph.end type="italics"/> <foreign lang="greek">x z</foreign> (<emph type="italics"/>quod po&longs;tea demon&longs;tra<lb/>bitur) maior &longs;it quam<emph.end type="italics"/> <foreign lang="greek">b n,</foreign> <emph type="italics"/>erit puncti<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>motus præter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="greek">b.</foreign></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.079.jpg" pagenum="40"/>

<s id="id.000724"><emph type="italics"/>Sed & &longs;i perficiantur parallelogramma<emph.end type="italics"/> <foreign lang="greek">d s t f & d y r g</foreign>: <lb/><emph type="italics"/>illud erit vtile ad o&longs;tendendum<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>tralatum vno motu v&longs;que ad<emph.end type="italics"/> <foreign lang="greek">s,</foreign><lb/><emph type="italics"/>altero motu, quo retrahitur ad centrum, reductum e&longs;&longs;e ad<emph.end type="italics"/> <foreign lang="greek">t</foreign>: <emph type="italics"/>& <lb/>huius retractiones <expan abbr="men&longs;urã">men&longs;uram</expan> e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">s t</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">d f</foreign>: <emph type="italics"/>hoc vero vtile <expan abbr="etiã">etiam</expan> erit <lb/>ad terminandos motus illos duos <expan abbr="natural&etilde;">naturalem</expan>, &longs;cilicet & præter <expan abbr="naturã">naturam</expan>.<emph.end type="italics"/></s>

<s id="id.000725">Atque alterolongum.] <emph type="italics"/>Hoc <expan abbr="quadrilater&utilde;">quadrilaterum</expan> <expan abbr="oblong&utilde;">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>

<s id="id.000726"><foreign lang="greek">a q h</foreign>] <emph type="italics"/><expan abbr="Punct&utilde;">Punctum</expan><emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>vbi libet in peripheria accipitur ad de&longs;ignandum <lb/>quoduis <expan abbr="&longs;pati&utilde;">&longs;patium</expan>, quod confecerit<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/><expan abbr="extrem&utilde;">extremum</expan> mobile minoris radij<emph.end type="italics"/> <foreign lang="greek">a x.</foreign></s>

<s id="id.000727">Et <foreign lang="greek">a q</foreign> excitetur.] <emph type="italics"/>A puncto<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>extra lineam<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>dato ex<lb/>citatur in ip&longs;am perpendicularis, quæ e&longs;t<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>prop. 12. lib. 1. elem.<emph.end type="italics"/></s>

<s id="id.000728">Et rur&longs;us per <foreign lang="greek">q</foreign>] <emph type="italics"/>Per punctum<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>datum datæ rectæ<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>duci<lb/>tur parallela prop. 31. lib. 1. elem.<emph.end type="italics"/></s>

<s id="id.000729">Et <foreign lang="greek">w n</foreign> perpend.] <emph type="italics"/>prop. 12. lib. 1. elem.<emph.end type="italics"/></s>

<s id="id.000731">Sunt vero <foreign lang="greek">w n</foreign> &] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="greek">q w</foreign> <emph type="italics"/>parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>ex fabrica: <lb/>tùm<emph.end type="italics"/> <foreign lang="greek">w n</foreign> <emph type="italics"/>etiam parallela e&longs;t ip&longs;i<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>quia in eas incidens<emph.end type="italics"/> <foreign lang="greek">z n</foreign> <emph type="italics"/>facit an<lb/>gulos internos ad <expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> partes rectos, ex fab. proinde æquales ax. 10. <lb/><expan abbr="itaq;">itaque</expan> parallelæ prop. 28. lib. 1. </s>

<s><expan abbr="parallelogrãm&utilde;">parallelogramum</expan> erit<emph.end type="italics"/> <foreign lang="greek">w n z <expan abbr="q.">que</expan></foreign> <emph type="italics"/>per def. pa<lb/>rall.</s>

<s id="id.000735">quare eius latera oppo&longs;ita<emph.end type="italics"/> <foreign lang="greek">w n & q z</foreign> <emph type="italics"/><expan abbr="er&utilde;t">erunt</expan> æqualia prop. 34. lib. 1.<emph.end type="italics"/></s>

<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>

<s id="id.000738">Expo<lb/><figure id="id.035.01.079.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.079.1.jpg"/><lb/>&longs;itio.</s>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.080.jpg" pagenum="41"/>

<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>

<s id="id.000742"><emph type="italics"/>De&longs;cribere circulum minorem qui alterum datum maiorem <lb/>interius tangat.<emph.end type="italics"/></s>

<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. ducatur A k diameter. </s>

<s id="id.000744">De&longs;cribendus autem &longs;it eo <lb/>minor, cuius accipiatur E <expan abbr="centr&utilde;">centrum</expan><emph.end type="italics"/><lb/><figure id="id.035.01.080.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.080.1.jpg"/><lb/><emph type="italics"/>inter A & D, & interuallo <lb/>E A de&longs;cribatur A F G. hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. </s>

<s id="id.000745">Nam &longs;i <lb/>& &longs;ecet, vt in puncto H, ducta <lb/>H E. erit æqualis ip&longs;i E A def. <lb/>15. lib. 1. non erit igitur E A mi<lb/>nima omnium quæ ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe<lb/>ripheriam, quod e&longs;t contra prop. <lb/>7. lib. 3. non erat igitur H punctum commune vtrique circulo, & <lb/>&longs;ic de 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. quod oportuit facere.<emph.end type="italics"/></s>

<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. </s>

<s id="id.000750">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 exprobl. <lb/>præ&longs;umpto. per punctum B ducaeur parallela B M prop. 31. lib. 1. <lb/>& per eandem parallela M N quæ per 34. lib. eiu&longs;dem cum &longs;it <lb/>æqualis ip&longs;i B K erit & æqualis ip&longs;i. </s>

<s id="id.000754">E I ax. 1. connectantur M H, <lb/>E H po&longs;t. </s>

<s id="id.000757">Demon&longs;t. <emph type="italics"/>Po&longs;tquam ax. 3. A N, D I æquales &longs;unt quia reli<lb/>quæ ex æqualibus A H, D H ex fab. demptis æqualibus N H, <lb/>I H quæ latera &longs;unt &longs;ub æqualibus angulis duorum triangulorum <lb/>M N H & I E H habentium duos angulos duobus angulis <lb/>æquales, & latus lateri æquale vt e&longs;t in 26. prop. lib. 1. nempe angu<lb/>lus qui ad N rectus e&longs;t prop. 29. lib. 1. & qui ad I, rectus ex hypoth. <lb/>ideo æquales ax. 10. tum angulus M H N ad centrum con&longs;titutus<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.081.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. & &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>

<s id="id.000767">Concl. <emph type="italics"/>Ergo perpendiculares à peripherijs in &longs;emidiametros & <lb/>ct. quod fuit demon&longs;trandum. </s>

<s id="id.000769">Hoc autem theorema videtur <expan abbr="quo-dãmodo">quo<lb/>dammodo</expan><emph.end type="italics"/> <foreign lang="greek">para/docon.</foreign> <emph type="italics"/>Erat enim veri&longs;imilius in maiore circulo <expan abbr="&longs;eg-ment&utilde;">&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>

<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></chap><chap>

<s id="id.000776">At oportet analoga e&longs;&longs;e, <lb/>vt id quod <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="naturã">naturam</expan>, <lb/>ad id quod <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> natu<lb/>ram: &longs;ic quod præter natu<lb/>ram, ad id quod præter <expan abbr="na-turã">na<lb/>turam</expan>. </s>

<s id="id.000777">Igitur maiorem quam <lb/><foreign lang="greek">b w</foreign> <expan abbr="peripheriã">peripheriam</expan>, vt <foreign lang="greek">b h</foreign> <expan abbr="per-trã&longs;ijt">per<lb/>tran&longs;ijt</expan>. </s>

<s id="id.000778">Nece&longs;&longs;e igitur in eo <lb/>tempore <foreign lang="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.082.jpg" pagenum="43"/><foreign lang="greek"><gap/></foreign><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;ec&utilde;-dum">&longs;ecun<lb/>dum</expan> <expan abbr="naturã">naturam</expan> in maiore cir<lb/>culo, & quod e&longs;t pr&ecedil;ter na<lb/>turam maius, vtique illuc <lb/>concidet vno modo, ita vt <lb/><foreign lang="greek">b</foreign> &longs;it latum per lineam <foreign lang="greek">b h.</foreign><lb/>eo in tempore quo <expan abbr="p&utilde;ctum">punctum</expan> <lb/><foreign lang="greek">x</foreign> [per <foreign lang="greek">x q</foreign>]. </s>

<s>Ibi enim pun<lb/>cto <foreign lang="greek">b</foreign> &longs;ecundum <expan abbr="quid&etilde;">quidem</expan> na<lb/>turam e&longs;t recta <foreign lang="greek">k h,</foreign> ab <foreign lang="greek">h</foreign><lb/>enim e&longs;t ip&longs;a perpendicu<lb/>laris, præter naturam vero <lb/><foreign lang="greek">b k.</foreign> </s>

<s>E&longs;t &longs;iquidem vt <foreign lang="greek">h k</foreign> ad <lb/><foreign lang="greek">h k</foreign>: &longs;ic <foreign lang="greek">q z</foreign> ad <foreign lang="greek">x z,</foreign> quod <lb/>erit manife&longs;tum, &longs;i à pun<lb/>ctis <foreign lang="greek">b, x</foreign> ad <foreign lang="greek">h, q</foreign> rectæ adiun<lb/>ctæ &longs;int. </s>

<s id="id.000781">Si vero minor vel <lb/>maior: quam <foreign lang="greek">h b</foreign> fuerit ea, <lb/>perquam <foreign lang="greek">b</foreign> motum e&longs;t, non <lb/>&longs;imiliter neque proportio<lb/>naliter in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> erit, quod <lb/><arrow.to.target n="marg13"/><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>

<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&ecedil;co quia <lb/>redundant <lb/>non verti<lb/>mus.</s>

<s id="id.000784">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.083.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="greek">x</foreign> <emph type="italics"/>delatum e&longs;t in<emph.end type="italics"/> <foreign lang="greek">q,</foreign> <emph type="italics"/>intelligatur etiam<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum in<emph.end type="italics"/> <foreign lang="greek">h,</foreign><lb/><emph type="italics"/>à quo<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>e&longs;t perpendicularis<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>in diametrum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>metiens motum <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>per peripheriam<emph.end type="italics"/> <foreign lang="greek">b h.</foreign> <emph type="italics"/></s>

<s>Ergo quo tempore<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>delatum e&longs;t ad<emph.end type="italics"/><lb/><foreign lang="greek">q,</foreign> <emph type="italics"/>eodem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>delatum erit ad<emph.end type="italics"/> <foreign lang="greek">h.</foreign> <emph type="italics"/></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="greek">b a h</foreign> <emph type="italics"/>angulo<emph.end type="italics"/> <foreign lang="greek">x a q</foreign>.</s>

<s id="id.000788">Ab <foreign lang="greek">h</foreign> enim e&longs;t.] <emph type="italics"/>Curuas lineas perpendicularis &longs;ola vt breui&longs;<lb/>&longs;ima, quantum fieri pote&longs;t exacte metitur. </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>

<s id="id.000791">E&longs;t &longs;iquidem vt <foreign lang="greek">h k.</foreign>] <emph type="italics"/>Triangula enim<emph.end type="italics"/> <foreign lang="greek">x q z & b h k</foreign> <emph type="italics"/>&longs;unt <lb/>æquiangula. </s>

<s id="id.000792">Nam, qui anguli ad<emph.end type="italics"/> <foreign lang="greek">z & k,</foreign> <emph type="italics"/>&longs;unt recti ex fab. qui vero <lb/>ad<emph.end type="italics"/> <foreign lang="greek">x & b</foreign> <emph type="italics"/>&longs;unt externus & internus ad ea&longs;dem partes facti à re<lb/>cta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">x q, b h</foreign> <emph type="italics"/>prop. 3. lib. 6. </s>

<s>Nam<emph.end type="italics"/> <foreign lang="greek">x q</foreign><lb/><emph type="italics"/>proportionaliter &longs;ecat<emph.end type="italics"/> <foreign lang="greek">a b & a h</foreign> <emph type="italics"/>latera trianguli<emph.end type="italics"/> <foreign lang="greek">b a h.</foreign> <emph type="italics"/></s>

<s>Sunt enim<emph.end type="italics"/><lb/><foreign lang="greek">a x, a q</foreign> <emph type="italics"/>æquales radj,<emph.end type="italics"/> & <foreign lang="greek">x b, q h</foreign> <emph type="italics"/>item æquales lineæ, quia re<lb/>liquæ ex æqualibus radijs<emph.end type="italics"/> <foreign lang="greek">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="greek">x q</foreign> <emph type="italics"/>parallela ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b h,</foreign> <emph type="italics"/>& &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>externus, & qui ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>internus erunt æquales <lb/>prop. 29. lib. 1. </s>

<s>Ergo & reliqui qui ad<emph.end type="italics"/> <foreign lang="greek">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="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">x z</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b,</foreign><lb/><emph type="italics"/>& alternatim vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="greek">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b</foreign> <emph type="italics"/>prop. 16. lib. 5.<emph.end type="italics"/></s>

<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></chap><chap>

<s id="id.000797">Quod vero propterea li<lb/>br&ecedil; maiores minoribus &longs;int <lb/>exactiores, <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> ex his <lb/>erit. </s>

<s id="id.000798">Agina enim fit <expan abbr="centr&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.084.jpg" pagenum="45"/><foreign lang="greek"><gap/></foreign><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>

<s id="id.000803">COMMENTARIVS.</s>

<s id="id.000804">Qvod vero propterea libræ.] <foreign lang="greek">zugo\s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">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="greek">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="greek">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>

<s id="id.000805"><margin.target id="marg14"/>Initio <lb/>cap. 11. <lb/>Prouerb.</s>

<s id="id.000806">Agina fit cen<lb/><figure id="id.035.01.084.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.084.1.jpg"/><lb/><expan abbr="tr&utilde;">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;it&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.085.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="greek">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="greek">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></chap><chap>

<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="s&utilde;t">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="faci&utilde;t">faciunt</expan>, <lb/>quo inclinare <expan abbr="de&longs;iderãt">de&longs;iderant</expan>, vel <lb/>&longs;i no <expan abbr="d&utilde;">dum</expan> habuerit. </s>

<s id="id.000818">Ligni <expan abbr="en&itilde;">enim</expan> <lb/>grauior e&longs;t illa pars, vbi ra<lb/>dix, E&longs;t vero nodus quæ<lb/>dam radix.</s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.086.jpg" pagenum="47"/>

<s id="id.000819">COMMENTARIVS.</s>

<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>

<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="vol&utilde;t">volunt</expan>, <lb/>emptores. </s>

<s id="id.000830">Imponunt enim pondus rei venditæ leuius æquipondio<emph.end type="italics"/><lb/>(<foreign lang="greek">sfai/rwma</foreign> <emph type="italics"/>po&longs;tea vocabitur) in librilis brachio longiore: &longs;icque, <lb/>vel æquiponderat vel etiam præponderat: & ita paucum pro multo <lb/>vendunt. </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>

<s id="id.000840"><margin.target id="marg15"/>Lib. 1. de <lb/>&longs;ubt,</s>

<s id="id.000841"><margin.target id="marg16"/>Prouerb. c. <lb/>10.</s>

<s id="id.000842">Purpuræ venditores.] <foreign lang="greek">a(lourgopw/lai</foreign> <emph type="italics"/>dicuntur quia<emph.end type="italics"/> <foreign lang="greek">a(/lour<lb/>gon</foreign> <emph type="italics"/>purpura e&longs;t<emph.end type="italics"/> <foreign lang="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.087.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>

<s id="id.000847">3. <foreign lang="greek">*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>

<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>

<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="de-mi&longs;s&utilde;">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="greek">b y,</foreign> trutina <foreign lang="greek">a <lb/>d</foreign>: at hoc deor&longs;um demi&longs;&longs;o <lb/>&longs;it perpendicularis <foreign lang="greek">a d m.</foreign><lb/></s>

<s>Si igitur pondus impona<lb/>tur in lance <foreign lang="greek">b,</foreign> erit <foreign lang="greek">b</foreign> vbi <foreign lang="greek">e, <lb/>& g</foreign> vbi <foreign lang="greek">z.</foreign></s>

<s>Itaque recta bi<lb/>fariam diuidens librile, pri<lb/>mùm quidem erat <foreign lang="greek">a d m,</foreign><lb/>ip&longs;a <expan abbr="perp&etilde;dicularis">perpendicularis</expan> <expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan>: <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.088.jpg" pagenum="49"/><foreign lang="greek"><gap/></foreign><lb/>At cum pondus impo&longs;itum <lb/>e&longs;t, e&longs;t <foreign lang="greek">f p.</foreign></s>

<s>Itaque librilis <lb/><foreign lang="greek">e c</foreign> id quod e&longs;t extra per<lb/>pendicularem <foreign lang="greek">a m</foreign> in ea <lb/>quæ e&longs;t <foreign lang="greek">f p</foreign> plus e&longs;t: quam <lb/>dimidium. </s>

<s id="id.000855">Si igitur pon<lb/>dus, quod erat in <foreign lang="greek">e</foreign> tolla<lb/>tur, nece&longs;&longs;e e&longs;t <foreign lang="greek">z</foreign> deor&longs;um <lb/>ferri. </s>

<s id="id.000856">E&longs;t enim <foreign lang="greek">e</foreign> minus: &longs;i <lb/>igitur in &longs;uperiori parte <lb/>fuerit agina, rur&longs;us ob id li<lb/>brile refertur: &longs;i vero in in<lb/>feriori parte &longs;ubijciatur a<lb/>gina, contra euenit. </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="greek">n c</foreign> re<lb/>ctum, perpendicularis vero <lb/><foreign lang="greek">k l m,</foreign> quæ bifariam diui<lb/>dat <foreign lang="greek">n c,</foreign> & impo&longs;ito pon<lb/>dere in <foreign lang="greek">n,</foreign> &longs;it <foreign lang="greek">n</foreign> vbi e&longs;t <foreign lang="greek">o, & <lb/>x</foreign> vbi e&longs;t <foreign lang="greek">r, & k l</foreign> vbi <foreign lang="greek">l q</foreign>.<lb/></s>

<s>Itaque maior erit <foreign lang="greek">l o</foreign> quam <lb/><foreign lang="greek">l r</foreign> ip&longs;o <foreign lang="greek">x l <expan abbr="q.">que</expan></foreign> Igitur &longs;u<lb/>blato pondere nece&longs;&longs;e e&longs;t <lb/>manere. </s>

<s id="id.000861">Incumbit enim <lb/>ceu pondus exce&longs;&longs;us medietatis, qui e&longs;t in <foreign lang="greek">l o.</foreign></s>

<s id="id.000862">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.089.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.035.01.089.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.089.1.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="fix&utilde;">fixum</expan>, <lb/>ip&longs;a moueantur, <expan abbr="&longs;it&utilde;">&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.035.01.089.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.089.2.jpg"/><lb/><emph type="italics"/>ferentias illas loci <lb/><expan abbr="&longs;urs&utilde;">&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;it&utilde;">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="c&utilde;">cum</expan> latitudine &longs;it <lb/>A B, cuius <expan abbr="centr&utilde;">centrum</expan> <lb/>in &longs;uperiori parte <lb/>latitudinis &longs;it C,<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.090.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.035.01.090.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.090.1.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>

<s id="id.000872"><emph type="italics"/>Exemplum li<lb/>brilis <expan abbr="c&utilde;">cum</expan> truti<lb/>na immobiliter <lb/>connexi &longs;it vbi<emph.end type="italics"/><lb/><figure id="id.035.01.090.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.090.2.jpg"/><lb/><emph type="italics"/>e&longs;t librile GH, <lb/>& trutina K <lb/>L, & centrum <lb/>libræ L.<emph.end type="italics"/></s>

<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="æqui-ponderãt">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="parallel&utilde;">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>

<s id="id.000883">Itaque librilis <foreign lang="greek">e z.</foreign>] <emph type="italics"/>Quod pars &longs;uperior librilis in vno &longs;itu <lb/>centri &longs;it maior, in altero &longs;it minor, non e&longs;t probatum ab Ari&longs;totele: <lb/>&longs;ed ex fabrica librilis vtriu&longs;que generis res ilico fit euidens, etiam <lb/>pro Ari&longs;totelis characteribus no&longs;tris ad diagrammata adiunctis.<emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.091.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.035.01.091.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.091.1.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="brachi&utilde;">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.035.01.091.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.091.2.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>

<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="mot&utilde;">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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.092.jpg" pagenum="53"/><figure id="id.035.01.092.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.092.1.jpg"/>

<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.035.01.092.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.092.2.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="null&utilde;">nullum</expan> <expan abbr="c&etilde;">cen</expan> <lb/><expan abbr="tr&utilde;">trum</expan> grauitatis ma<lb/>net ni&longs;i &longs;u&longs;tinea<lb/>tur à linea <expan abbr="per-p&etilde;diculari">per<lb/>pendiculari</expan> ad pla<lb/>num horizontis. </s>

<s id="id.000891">quod e&longs;t demon&longs;tratum ab V baldo 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.093.jpg" pagenum="54"/><figure id="id.035.01.093.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.093.1.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/>exbrachijs 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></chap><chap>

<s id="id.000899">4. <foreign lang="greek">*tou= moxlou= duna/mews ai)/tion.</foreign></s>

<s id="id.000900">4. Potentiæ vectis cau&longs;a.</s>

<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>

<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="dict&utilde;">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="agi-nã">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></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.094.jpg" pagenum="55"/><chap>

<s>Sunt vero tria circa|, <expan abbr="vect&etilde;">vectem</expan> <lb/>pre&longs;&longs;io quidem e&longs;t |agina & <lb/><expan abbr="centr&utilde;">centrum</expan>, duo etiam pondera <lb/>mouens &longs;cilicet, & mobile.</s>

<s id="id.000909">COMMENTARIVS.</s>

<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="nimi&utilde;">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;uor&utilde;">&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.035.01.094.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.094.1.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="greek">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.035.01.094.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.094.2.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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.095.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="greek">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="excitat&utilde;">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="iucund&utilde;">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>

<s id="id.000932"><margin.target id="marg19"/>Annot. in <lb/>Pandectas.</s>

<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>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.096.jpg" pagenum="57"/>

<s id="id.000938"><emph type="italics"/>Facilius e&longs;t mouere paruum pondus quam magnum.<emph.end type="italics"/></s>

<s id="id.000939"><emph type="italics"/>Moles &longs;ine vecte e&longs;t pondus minus: quam cum vecte.<emph.end type="italics"/></s>

<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>

<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>

<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>

<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>

<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>

<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></chap><chap>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.097.jpg" pagenum="58"/>

<s><foreign lang="greek"><gap/></foreign>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="greek">a b,</foreign> pondus <lb/>vero <foreign lang="greek">g,</foreign> mouens autem <foreign lang="greek">d,</foreign><lb/>pre&longs;&longs;io <foreign lang="greek">e.</foreign> Ip&longs;um vero quod <lb/>mouerit <foreign lang="greek">d,</foreign> &longs;it vbi <foreign lang="greek">h,</foreign> & pon<lb/>dus <foreign lang="greek">g</foreign> motum vbi <foreign lang="greek">k.</foreign></s>

<s id="id.000955">COMMENTARIVS.</s>

<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.035.01.097.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.097.1.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. 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.098.jpg" pagenum="59"/><emph type="italics"/>eit 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 and 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>

<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>

<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>

<s id="id.000972">Reciproce.] <foreign lang="greek">*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>

<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. 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.099.jpg" pagenum="60"/><emph type="italics"/>antecedentibus, velocius quoque moueri, quod hîc e&longs;t<emph.end type="italics"/> <foreign lang="greek">ra=|on kai\ ple/on <lb/>ki/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="defect&utilde;">defectum</expan> &longs;uæ rationi re&longs;pondere <expan abbr="nõ">non</expan> pote&longs;t.<emph.end type="italics"/></s>

<s id="id.000988">Sit vectis <foreign lang="greek">a b</foreign>] <emph type="italics"/>huius diagrammatis expo&longs;itio &longs;i non imperfe<lb/>cta e&longs;t, adfertur tantum ad o&longs;tendendum quod pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>ab eo cum<emph.end type="italics"/><lb/><figure id="id.035.01.099.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.099.1.jpg"/><lb/><emph type="italics"/>erat in<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>per depreßionem<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">k.</foreign></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="greek">a b,</foreign> <emph type="italics"/>pondus vero<emph.end type="italics"/> <foreign lang="greek">g,</foreign><lb/><emph type="italics"/>mouens autem<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>preßio<emph.end type="italics"/> <foreign lang="greek">e.</foreign> <emph type="italics"/>Cum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>quod moueat, &longs;it vbi<emph.end type="italics"/> <foreign lang="greek">h</foreign><emph type="italics"/>: <lb/>& pondus<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>motum erit vbi<emph.end type="italics"/> <foreign lang="greek">k.</foreign> <emph type="italics"/>quod ita &longs;e habere o&longs;tendit tertia <lb/>proprietas circuli, ex qua cap. 1. huius lib. o&longs;ten&longs;um e&longs;t diametri ex<lb/>tremo vno deor&longs;um moto, alterum eodem tempore &longs;ur&longs;um moueri. </s>

<s id="id.000991">E&longs;t <lb/>autem hic vectis<emph.end type="italics"/> <foreign lang="greek">b a,</foreign> <emph type="italics"/>vt diameter circuli cuius extremum<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>deor<lb/>&longs;um cum ad<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>mouetur, alterum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&longs;ur&longs;um &longs;imul moueri vt ad<emph.end type="italics"/> <foreign lang="greek">k,</foreign> <emph type="italics"/>ne<lb/>ce&longs;&longs;um e&longs;t. </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></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.100.jpg" pagenum="61"/><chap>

<s id="id.000993">5. <foreign lang="greek">*dia\ ti/ oi( meso/neoi ma/lista <lb/> th\n nau=n kinou=si.</foreign></s>

<s id="id.000994">5. Cur nauim mouent ma<lb/>xime remiges, qui in <lb/>media naui &longs;edent.</s>

<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;i-quid&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="cen-tr&utilde;">cen<lb/>trum</expan> e&longs;t. </s>

<s id="id.001002">In nauis <expan abbr="aut&etilde;">autem</expan> medio <lb/><expan abbr="plurim&utilde;">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="cõtin-git">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="extrem&utilde;">extremum</expan> remi, <lb/>quod intus e&longs;t antror&longs;um <lb/>procedit: Tum que nauim <lb/>&longs;calmo <expan abbr="alligatã">alligatam</expan> procedere <lb/>nece&longs;&longs;e e&longs;t eò, vbi e&longs;t <expan abbr="extre-m&utilde;">extre<lb/>mum</expan> remi. </s>

<s id="id.001005">Vbi enim remus <lb/><expan abbr="plurim&utilde;">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="plurim&utilde;">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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.101.jpg" pagenum="62"/>

<s id="id.001009">COMMENTARIVS.</s>

<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>

<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>

<s id="id.001015">Illi robur & æs triplex</s>

<s id="id.001016">Circa pectus erat, qui fragilem truci</s>

<s id="id.001017">Commi&longs;it pelago ratem</s>

<s id="id.001018">Primus.</s>

<s id="id.001019"><emph type="italics"/>Quid vero &longs;ubtilius, quam ob&longs;cura etiam nocte, c&oelig;lo 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>

<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="greek">*argonautikw=n.</foreign></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.102.jpg" pagenum="63"/>

<s id="id.001025"><foreign lang="greek">*nh=a d' e)pikrate/ws ar)gou= u(poqhmosu/nh|si</foreign></s>

<s id="id.001026"><foreign lang="greek">*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>

<s id="id.001027">Imprimis nauem diuinis artibus Argi, </s>

<s>Extructam, intus compingunt habili armamento.</s>

<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="rot&utilde;dus">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.103.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="greek">*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="greek">qalami=tas</foreign> <emph type="italics"/>&longs;eu<emph.end type="italics"/> <foreign lang="greek">qala/makas,</foreign> <emph type="italics"/>qui in medio<emph.end type="italics"/> <foreign lang="greek">zugi=tas,</foreign><lb/><emph type="italics"/>qui in &longs;uperiore<emph.end type="italics"/> <foreign lang="greek">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="greek">kat' i)/cin</foreign> <emph type="italics"/>eius partis habui&longs;&longs;e, <expan abbr="quor&utilde;">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="greek">qrani/ths )esti,</foreign> <emph type="italics"/>inquit<emph.end type="italics"/> <foreign lang="greek">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="greek">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><foreign lang="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.104.jpg" pagenum="65"/><emph type="italics"/>partium &longs;ic ait, In triremibus <expan abbr="remor&utilde;">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="greek">mesone/wn</foreign> <emph type="italics"/>e&longs;&longs;e <lb/>maximos: Ari&longs;toteles non hos, &longs;ed <expan abbr="Thranitar&utilde;">Thranitarum</expan>. </s>

<s id="id.001049">Et <expan abbr="ver&utilde;">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.035.01.104.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.104.1.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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.105.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="greek">periferikoeidh\s.</foreign> <emph type="italics"/>Sic enim <lb/>Galenus <expan abbr="digitor&utilde;">digitorum</expan> corpus valde <expan abbr="&longs;phæric&utilde;">&longs;phæricum</expan> omnium à manu <expan abbr="appreh&etilde;-dendor&utilde;">apprehen<lb/>dendorum</expan> <expan abbr="difficillim&utilde;">difficillimum</expan>, <expan abbr="apprehendenti&utilde;">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.035.01.105.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.105.1.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="vndar&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.106.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="extrem&utilde;">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>

<s id="id.001065">Intentaque brachia remís</s>

<s id="id.001066">Intenti expectant &longs;ignum.</s>

<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>

<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>

<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>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.107.jpg" pagenum="68"/>

<s id="id.001075"><emph type="italics"/>Ergo qui in medio e&longs;t inter remiges plus promouet nauim.<emph.end type="italics"/></s>

<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>

<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>

<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>

<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>

<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="remig&utilde;">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="eor&utilde;">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) igiur erit <lb/>totum ex M H, & adempto maius quam quod ex K G & <lb/>adempto, velex O T & adempto per ax. 5.<emph.end type="italics"/></s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.108.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.035.01.108.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.108.1.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 iuæquales 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;trand&utilde;">demon&longs;trandum</expan>.<emph.end type="italics"/></s>

<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="promot&utilde;">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="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.109.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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.110.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>

<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>

<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="greek">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="alior&utilde;">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>

<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></chap><chap>

<s id="id.001137">6. <foreign lang="greek">*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>

<s id="id.001138">6. Potentiæ gubernaculi <lb/>cau&longs;a, & quod <expan abbr="nauigi&utilde;">nauigium</expan> <lb/>magis in <expan abbr="contrari&utilde;">contrarium</expan> pro<lb/>cedat: quam remi pal<lb/>mula.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.111.jpg" pagenum="72"/><foreign lang="greek"><gap/></foreign><lb/><expan abbr="nauigior&utilde;">nauigiorum</expan> moles mouean<lb/>tur? </s>

<s id="id.001141">An quia <expan abbr="gubernacul&utilde;">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;ec&utilde;dum">&longs;ecundum</expan> latitudinem <lb/><expan abbr="gubernacul&utilde;">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="gubernacul&utilde;">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>

<s id="id.001147">COMMENTARIVS.</s>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.112.jpg" pagenum="73"/>

<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>

<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>

<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="iuc&utilde;da">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.113.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 c&oelig;nationes erant numero triginta <expan abbr="&longs;ecund&utilde;">&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 c&oelig;nationes 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;tirpi&utilde;">&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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.114.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="lapid&utilde;">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.115.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>

<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>

<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="mouend&utilde;">mouendum</expan> e&longs;t mare: <expan abbr="mou&etilde;s">mouens</expan> gubernator.<emph.end type="italics"/>)</s>

<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>

<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="greek">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>

<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>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.116.jpg" pagenum="77"/>

<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>

<s id="id.001226">COMMENTARIVS.</s>

<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>

<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>

<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>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.117.jpg" pagenum="78"/>

<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>

<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>

<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>

<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>

<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>

<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>

<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.035.01.117.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.117.1.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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.118.jpg" pagenum="79"/><emph type="italics"/>tres anguli vnius triangulorum &longs;unt æquales tribus alterius prop. <lb/>32. lib. 1. & anguli qui ad A æquales ex hypothe&longs;i, anguli ad ba<lb/>&longs;im duo duobus &longs;unt æquales ax. 3. & quia A D C & A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, 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="duor&utilde;">duorum</expan>, angulo A C D etiam dimidio <expan abbr="æquali&utilde;">æqualium</expan> æ qua<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>

<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.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></chap><chap>

<s id="id.001265">Ex hoc autem <expan abbr="manife&longs;t&utilde;">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="greek">a b</foreign><lb/>& &longs;calmus <foreign lang="greek">g,</foreign> & intra nauim <lb/>caput remi <foreign lang="greek">a</foreign> palmula intra <lb/>mare <foreign lang="greek">b.</foreign> Si itaque <foreign lang="greek">a</foreign> <expan abbr="tran&longs;la-t&utilde;">tran&longs;la<lb/>tum</expan> &longs;it eò, vbi e&longs;t <foreign lang="greek">d</foreign>: ip&longs;um <foreign lang="greek">b</foreign><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.119.jpg" pagenum="80"/><foreign lang="greek"><gap/></foreign><lb/><arrow.to.target n="marg21"/><lb/>non erit vbi e&longs;t <foreign lang="greek">e.</foreign> E&longs;t enim <lb/><foreign lang="greek">b e</foreign> æqualis ip&longs;i <foreign lang="greek">a d.</foreign> Ex <lb/>æquo igítur tran&longs;latum e&longs;<lb/>&longs;et, &longs;ed minus erat. </s>

<s id="id.001268">E&longs;t igi<lb/>tur vbi <foreign lang="greek">z.</foreign> Minor enim e&longs;t <lb/><foreign lang="greek">b z</foreign>: <expan abbr="quã">quam</expan> <foreign lang="greek">a d.</foreign> Itaque etiam <lb/><foreign lang="greek">q z</foreign> quam <foreign lang="greek">d <expan abbr="q.">que</expan></foreign> Similia enim <lb/>&longs;unt triangula. </s>

<s id="id.001269">Con&longs;i&longs;tens <lb/>vero erit medium vbi e&longs;t <foreign lang="greek">g.</foreign><lb/>In contrarium enim extre<lb/>mo <foreign lang="greek">b,</foreign> quod in mari e&longs;t <lb/>procedit <expan abbr="extrem&utilde;">extremum</expan> <foreign lang="greek">a,</foreign> quod <lb/>in nauigio e&longs;t. </s>

<s id="id.001270">Non autem <lb/>ad <foreign lang="greek">d</foreign> procederet, ni&longs;i mo<lb/>ueretur nauis, & eo vbi e&longs;t <lb/>caput remi, transferretur.</s>

<s id="id.001271"><margin.target id="marg21"/>Inclu&longs;a his <lb/>notis [] ni<lb/>hil faciunt <lb/>ad rem.</s>

<s id="id.001272">COMMENTARIVS.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.120.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>

<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>

<s id="id.001291"><emph type="italics"/>Syllogi&longs;mus igitur &longs;ic e&longs;to,<emph.end type="italics"/></s>

<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>

<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="principi&utilde;">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>

<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="greek">a</foreign> <emph type="italics"/>caput remi tran&longs;latum &longs;it ad<emph.end type="italics"/><lb/><foreign lang="greek">d.</foreign> </s>

<s><emph type="italics"/>Quo autem tempore<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tran&longs;latum e&longs;t ad<emph.end type="italics"/> <foreign lang="greek">d,</foreign> <emph type="italics"/>palmula<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>non <lb/>transfertur ad<emph.end type="italics"/> <foreign lang="greek">e</foreign><emph type="italics"/>: alioqui æqualiter moueretur palmula atque caput, <lb/>contra ea quæ ante po&longs;ita &longs;unt. </s>

<s id="id.001305">Intelligatur enim remus<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>vbi e&longs;t<emph.end type="italics"/><lb/><foreign lang="greek">d e,</foreign> <emph type="italics"/>&longs;calmo<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>manente. </s>

<s id="id.001306">fiunt duo triangula<emph.end type="italics"/> <foreign lang="greek">a g d & b g e,</foreign><lb/><emph type="italics"/>quorum anguli qui ad<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>quia ad <expan abbr="vertic&etilde;">verticem</expan> oppo&longs;iti, &longs;unt æquales prop. <lb/>15. lib. 1. </s>

<s>Tum latera, quæ ip&longs;os continent<emph.end type="italics"/> <foreign lang="greek">a g, d g,</foreign> <emph type="italics"/>duobus<emph.end type="italics"/> <foreign lang="greek">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="greek">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="greek">a d, b e</foreign> <emph type="italics"/>æquales, vt reliqui anguli prop. 4. lib. 1. <emph.end type="italics"/></s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.121.jpg" pagenum="82"/>

<s><emph type="italics"/>Et &longs;ic palmula perducta ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>caput prouectum e&longs;&longs;et ad<emph.end type="italics"/> <foreign lang="greek">d</foreign><lb/><emph type="italics"/>æqualiter moueretur, &longs;ed in i&longs;to ca&longs;u<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>&longs;calmo manente nauis immo<lb/>ta e&longs;&longs;et, <expan abbr="c&utilde;">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="greek">z</foreign> <emph type="italics"/>e&longs;&longs;e perducta palmula<emph.end type="italics"/> <foreign lang="greek">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="greek">d q</foreign><lb/><emph type="italics"/>maiorem e&longs;&longs;e: quam<emph.end type="italics"/> <foreign lang="greek">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="greek">a q d & b q z</foreign> <emph type="italics"/>anguli, qui ad<emph.end type="italics"/> <foreign lang="greek">q</foreign> <emph type="italics"/>ad verticem oppo&longs;iti, <lb/>&longs;unt æquales prop. 15. lib. 1. tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>æqualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti à recta<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>incidente in parallelas<emph.end type="italics"/> <foreign lang="greek">a d, 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="greek">q d a</foreign> <emph type="italics"/>reliquo<emph.end type="italics"/> <foreign lang="greek">b z q</foreign> <emph type="italics"/>æqua<lb/>lis erit prop. 32. lib. 1. </s>

<s>Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="greek">a q d & b q z</foreign> <emph type="italics"/>&longs;unt æquian<lb/>gula, proinde & circum æquales angulos latera proportionalia prop. 4. lib. 6. <lb/></s>

<s id="id.001311">E&longs;t igitur vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q d</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">b q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>& vicißim <lb/>prop. 16. lib. 5. vt<emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q b</foreign>: <emph type="italics"/>&longs;ic<emph.end type="italics"/> <foreign lang="greek">d q</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">q z.</foreign> </s>

<s><emph type="italics"/>E&longs;t <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">a q</foreign> <emph type="italics"/>maior: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">q b,</foreign> <emph type="italics"/>quia<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>erat bi&longs;&longs;ecta in<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>& detracta e&longs;t de dimi<lb/>dia<emph.end type="italics"/> <foreign lang="greek">g b</foreign> <emph type="italics"/>portio<emph.end type="italics"/> <foreign lang="greek">q g,</foreign> <emph type="italics"/>quæ additur ip&longs;i dimidiæ<emph.end type="italics"/> <foreign lang="greek">a g.</foreign> </s>

<s><emph type="italics"/>E&longs;t igitur<emph.end type="italics"/><lb/><foreign lang="greek">d q</foreign> <emph type="italics"/>maior quam<emph.end type="italics"/> <foreign lang="greek">q z.</foreign></s>

<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.035.01.121.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.121.1.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="greek"> z</foreign><emph type="italics"/>: &longs;ed in K <lb/>vltra <emph.end type="italics"/><foreign lang="greek"> 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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.122.jpg" pagenum="83"/><emph type="italics"/>ex<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>in<emph.end type="italics"/> <foreign lang="greek">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.035.01.122.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.122.1.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="greek">d q</foreign> <emph type="italics"/>maiorem e&longs;&longs;e<emph.end type="italics"/> <foreign lang="greek">q z,</foreign> <emph type="italics"/>pertinere eò, vt inferatur caput remi A <lb/>tran&longs;uecti non con&longs;i&longs;tere in<emph.end type="italics"/> <foreign lang="greek">d</foreign>: <emph type="italics"/>&longs;ed vltra. </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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.123.jpg" pagenum="84"/><figure id="id.035.01.123.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.123.1.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>

<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>

<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>

<s id="id.001332"><emph type="italics"/>Palmulam retrocedere quoties nauis in anteriora progreditur.<emph.end type="italics"/></s>

<s id="id.001333"><emph type="italics"/>Alterum e&longs;t &longs;calmum bi&longs;&longs;ecare remum.<emph.end type="italics"/></s>

<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.035.01.123.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.123.2.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>

<s id="id.001335">Propo&longs;itio prima.</s>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.124.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><figure id="id.035.01.124.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.1.jpg"/>

<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;trectæ B D (&longs;unt enim latera parallelo<lb/>grammi oppo&longs;ita prop. 34. lib. 1.) quæ motu <lb/>nauis decur&longs;a e&longs;t.<emph.end type="italics"/></s>

<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>

<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.035.01.124.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.2.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>

<s id="id.001351">Propo&longs;itio &longs;ecunda.</s>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.125.jpg" pagenum="86"/><figure id="id.035.01.125.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.125.1.jpg"/>

<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. & 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 <expan abbr="q.">que</expan> <lb/>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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.126.jpg" pagenum="87"/><emph type="italics"/>antè diximus de remi in vna remigatione varijs motibus.<emph.end type="italics"/></s>

<s id="id.001368">Propo&longs;itionis conuer&longs;io</s>

<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. æqualis etiam <lb/>B G prop. 34. lib. 1. igitur A Q & B G æquales erunt ax. 1.<emph.end type="italics"/></s>

<s id="id.001373">Propo&longs;itio tertia.</s>

<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><figure id="id.035.01.126.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.126.1.jpg"/>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.127.jpg" pagenum="88"/>

<s id="id.001388">Propo&longs;itionis conuer&longs;io.</s>

<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>

<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. 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>

<s id="id.001394">Propo&longs;itio quarta.</s>

<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>

<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>

<s id="id.001410">Corollarium.</s>

<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><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.128.jpg" pagenum="89"/>

<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>

<s id="id.001413">Propo&longs;itionis conuer&longs;io.</s>

<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>

<s id="id.001415"><emph type="italics"/>Huius demon&longs;tratio ex prædictis facilis e&longs;t.<emph.end type="italics"/></s>

<s id="id.001416">Propo&longs;itio quinta.</s>

<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><figure id="id.035.01.128.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.128.1.jpg"/>

<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;it&utilde;">&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="greek">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="greek">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="greek">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="greek">z</foreign><emph type="italics"/> C ex <emph.end type="italics"/><foreign lang="greek">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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.129.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>

<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></chap><chap>

<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="cõtrari&utilde;">contrarium</expan> prora <lb/>vergit. </s>

<s id="id.001441">Vbi igitur <expan abbr="guberna-cul&utilde;">guberna<lb/>culum</expan> <expan abbr="adi&utilde;ct&utilde;">adiunctum</expan> e&longs;t, ibi opor<lb/>tet aliquod eius, quod mo<lb/>uetur <expan abbr="medi&utilde;">medium</expan> intelligere, & <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.130.jpg" pagenum="91"/><foreign lang="greek"><gap/></foreign><lb/>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>

<s id="id.001444">COMMENTARIVS.</s>

<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="animaduertend&utilde;">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>

<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>

<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></chap><chap>

<s id="id.001454"><foreign lang="greek">*th=s kerai/as duna/menews ai)/tion.</foreign></s>

<s id="id.001455">7. Cau&longs;a pote&longs;tatis <lb/>Antemnæ.</s>

<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="eo-demq;">eo<lb/>demque</expan> <expan abbr="v&etilde;to">vento</expan>? </s>

<s id="id.001458">An quia malus <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.131.jpg" pagenum="92"/><foreign lang="greek"><gap/></foreign><lb/>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="vel&utilde;">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>

<s id="id.001461">COMMENTARIVS.</s>

<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="greek">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="tr&utilde;ci">trunci</expan> arboris perpendiculariter infixum,<emph.end type="italics"/> <foreign lang="greek">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="greek">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="greek">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="greek">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="greek">triar/menos,</foreign> <emph type="italics"/>Antigoni dicta, quæ tria vela haberet<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.132.jpg" pagenum="93"/><emph type="italics"/>trino&longs;que malos, quod antiquis fuit <expan abbr="rar&utilde;">rarum</expan>, no&longs;tris hodie <expan abbr="frequ&etilde;tißim&utilde;">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>

<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="greek">droma/des</foreign> <emph type="italics"/>(&longs;ic enim vocat Ari&longs;tophanes <lb/>eas, quas nunc vulgus fregatas appellat) qua&longs;i aquis innitentes cur&longs;u <lb/>&longs;unt velocißimæ, & longiores latis, po&longs;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>

<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>

<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>

<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. </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>

<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>

<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="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.133.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;æuian