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<?xml version="1.0"?>
<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" >
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
        <author>Monantheuil, Henri de</author>
        <title>Aristotelis Mechanica</title>
        <date>1599</date>
        <place>Paris</place>
        <translator/>
        <lang>la</lang>
        <cvs_file>monan_mecha_01_la_1599</cvs_file>
        <cvs_version/>
        <locator>035.xml</locator>
</info><text><front><section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.001.jpg"/><p type="head">

<s id="id.000001">ARISTOTELIS <lb/>MECHANICA <lb/>Gr&aelig;ca, emendata, Latina facta, &amp; <lb/>Commentariis illu&longs;trata. <lb/></s>

<s id="id.000002">AB <lb/><emph type="italics"/>HENRICO MONANTHOLIO <lb/>Medico, &amp; Mathematicarum artium <lb/>Profe&longs;&longs;ore Regio. </s>

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

<s id="id.000003">PARISIIS, <lb/>Apud IEREMIAM PERIER via Iacob&aelig;a, &longs;ub &longs;igno Bellerophontis. </s></p><p type="head">

<s id="id.000004">M. D. XCIX. <lb/><emph type="italics"/>CUM PRIVILEGIO REGIS. <emph.end type="italics"/></s></p><pb/><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"/><p type="head">

<s id="id.000005">HENRICO IIII. <lb/>GALLI&AElig; ET NAVARR&AElig; <lb/>REGI CHRISTIANISSIMO. <lb/>S. P. D. </s></p><p type="main">

<s id="id.000006">Ecce maie&longs;tati tu&aelig;, <lb/>Rex Chri&longs;tiani&longs;&longs;ime, <lb/>nouum <expan abbr="fruct&utilde;">fructum</expan>, &amp; tan&shy;<lb/>quam primitias tu&aelig; &agrave; te <lb/>nuper re&longs;titut&aelig; Acade&shy;<lb/>mi&aelig;, Mechanica Ari&shy;<lb/>&longs;totelis philo&longs;ophorum principis Gr&ecedil;&shy;<lb/>ca, emendata, Latina facta, &amp; commen&shy;<lb/>tariis illu&longs;trata offero, dico, con&longs;ecro. <lb/></s>

<s id="id.000007">Noli, ob&longs;ecro te, ad Mechanicorum ti&shy;<lb/>tulum munus hoc, qua&longs;i minus inge&shy;<lb/>nuum, nec &longs;atis liberali ingenio, nedum <lb/>imperatorio &amp; regali dignum, &longs;ubhor&shy;<lb/>re&longs;cere, &amp; ex prima i&longs;ta <expan abbr="fr&otilde;te">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&shy;<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></s>

<s id="id.000009">Hoc verbum Lati&shy;<lb/>n&egrave; expre&longs;&longs;um &longs;ignificat, A&longs;&longs;idu&egrave; terram <lb/>metiri. </s>

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

<s id="id.000011">Sed &longs;i ex ip&longs;ius artis viribus, &amp; magnifi&shy;<lb/>cis promi&longs;&longs;is illud <foreign lang="greek">a)ei gewmetrei=n</foreign> &aelig;&longs;timetur, <lb/>quod e&longs;t vniuer&longs;i <expan abbr="qu&atilde;tumuis">quantumuis</expan> fus&egrave; <expan abbr="lat&eacute;q;">lat&eacute;que</expan> <lb/>patentis, <expan abbr="corpor&utilde;">corporum</expan> in eo omnium, &longs;uper&shy;<lb/>ficierum, linearum, <expan abbr="omni&uacute;mq;">omni&uacute;mque</expan> men&longs;u&shy;<lb/>rabilium <expan abbr="m&etilde;&longs;uram">men&longs;uram</expan> ratione, proportio&shy;<lb/>ne, &longs;imilitudine con&longs;tituere, de&longs;ignare, <lb/>permetiri: actio cert&egrave; erit tant&ograve; priore <lb/>nobilior: quant&ograve; totum <expan abbr="finit&utilde;">finitum</expan> quidem, <lb/>&longs;ed infinito per&longs;imile exigua, &amp; infima <lb/>&longs;ui parte e&longs;t nobilius, &amp; excellentius: &amp; <lb/>qui <expan abbr="h&atilde;c">hanc</expan> actionem accurate ponderibus <lb/>librarit &longs;uis, <expan abbr="nequaqu&atilde;">nequaquam</expan> indignam, circa <lb/>quam Deus ver&longs;etur, &amp; &longs;e&longs;e occupet, iu&shy;<lb/>dicabit. </s>

<s id="id.000012">Verumenimuer&ograve; &longs;i ad illud <foreign lang="greek">a)ei gew&shy;<lb/>mtrei=n</foreign> addi&longs;&longs;et Plato, <foreign lang="greek">kai\ a)eimhxana=sqai,</foreign> luculen&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.004.jpg"/>tius mult&ograve; meo iudicio, &amp; diuin&aelig; maie&shy;<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 &aelig;quilibra&longs;&longs;e: longitudine, latitudi&shy;<lb/>ne, altitudine, in omni habitudine, &amp; <lb/>re&longs;pectu commen&longs;uraui&longs;&longs;e: eund&eacute;m&shy;<lb/>que in eodem &longs;tatu &amp; perfectione a&longs;&longs;i&shy;<lb/>du&ograve; 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, &amp; quidem machina&shy;<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="n&otilde;">non</expan> ad omnium mutabilium <lb/>lationem, alterationem, generationem, <lb/>auctionem, con&longs;eruationem, &amp; <expan abbr="dura-tion&etilde;">dura&shy;<lb/>tionem</expan>, vt Dei &longs;ui auctoris <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> <lb/>concurrit, quod eius vim, &amp; efficaciam <lb/>o&longs;tendit? </s>

<s id="id.000016">An non quinquies mille <expan abbr="quin-g&etilde;tos">quin&shy;<lb/>gentos</expan> &longs;exaginta &amp; <expan abbr="vn&utilde;">vnum</expan> annos, quoad &longs;ui <lb/><expan abbr="quinq;">quinque</expan> partes primas, &amp; &longs;implices, per&shy;<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, &amp; 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&shy;<lb/>tio &longs;umma, omnium hominum oculis <lb/>&amp; menti iucundi&longs;sima &longs;ymmetria, pro&shy;<lb/>portio, &aelig;quabilitas, vn&agrave; cum totius fi&shy;<lb/>gura pulcherrima, &amp; conuenienti&longs;&longs;ima, <lb/>qu&aelig; vnica e&longs;t &longs;uperficie terminata pari&shy;<lb/>bus ab vno puncto vndique di&longs;tante <lb/>interuallis, &amp; cum tot <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> tanquam <lb/>gemmarum pretio&longs;i&longs;&longs;imarum h&icirc;c ill&icirc;c <lb/>in eminentiori, &amp; apparentiori &longs;ui par&shy;<lb/>te collocatorum perenni luce, qua qua&shy;<lb/>litate nec formo&longs;ior, nec <expan abbr="homin&utilde;">hominum</expan> ocu&shy;<lb/>lis gratior, nec v&longs;ibus humanis vtilior <lb/>apparere pote&longs;t: quod eius pulchritudi&shy;<lb/>nem vbique o&longs;tentat, &amp; mirabiles &longs;ui <lb/>ip&longs;ius amores excitat? </s>

<s id="id.000018">Deus igitur, <expan abbr="pr&ecedil;ter-qu&atilde;">pr&ecedil;ter&shy;<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, &amp; operum tot magnifi&shy;<lb/>corum euidentia, &longs;apienti&longs;&longs;imus, opti&shy;<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> &amp; <foreign lang="greek">mhxanopoio\s. </foreign><lb/></s>
<s>Ip&longs;e idem, qui <foreign lang="greek">makro/kosmon</foreign> magnum mun&shy;<lb/>dum fecit, fecit &amp; <foreign lang="greek">mikro/kosmon</foreign> <expan abbr="paru&utilde;">paruum</expan> mun&shy;<lb/>dum, hominem &longs;cilicet: &amp; fecit ad ima&shy;<lb/>ginem &longs;uam, atque vt &longs;e imitaretur beni&shy;<lb/>gni&longs;&longs;ima liberalitate impertitus e&longs;t ei <lb/>mentem, qu&aelig; e&longs;&longs;et <foreign lang="greek">te/xnh te/xnwn,</foreign> ars artium, <lb/>&amp; manum, qu&aelig; e&longs;&longs;et <foreign lang="greek">o)/rganon o)rga/nwn,</foreign> in&longs;tru&shy;<lb/>mentum in&longs;trumentorum, quibus ho&shy;<lb/>mo, quem volebat e&longs;&longs;e &longs;apienti&longs;&longs;imum <lb/>animalium, machinas &amp; in&longs;trumenta <lb/>alia fabricaretur, &amp; iis adiutus &longs;olus, vel <lb/>cum paucis onera quantumuis ingentia <lb/>dimoueret, deduceret, quo vellet collo&shy;<lb/>caret: vrbes, <expan abbr="t&etilde;pla">templa</expan>, palatia, collegia, por&shy;<lb/>ticus, pontes, domos &aelig;dificaret, perde&shy;<lb/>ret, re&longs;tauraret, con&longs;eruaret: terram ver&shy;<lb/>teret, in terr&aelig; vi&longs;cera de&longs;cenderet, terr&aelig; <lb/>campos, valles, montes bigis, quadrigis <lb/>peragraret: maria omnia, fluuios remis, <lb/>velis tranaret: ventis imperaret: anima&shy;<lb/>lium genus omne &longs;ibi &longs;ubiiceret: tantas <lb/><expan abbr="deniq;">denique</expan>, &amp; tam multas res faceret, vt eas, <lb/>ni&longs;i quotidie fieri, &amp; factas e&longs;&longs;e &longs;&aelig;pius <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.007.jpg"/>alij homines &longs;pectarent, omnin&ograve; fieri <lb/>non po&longs;&longs;e iurarent. </s>

<s id="id.000019">Iidem cum facta&shy;<lb/>rum rationes, virium que in in&longs;trumen&shy;<lb/>tis, &amp; machinis adhibitis cau&longs;as non in&shy;<lb/>telligunt, miracula e&longs;&longs;e pleno ore pro&shy;<lb/>clamant. </s>

<s id="id.000020">Vnde fort&egrave; illud Martialis. </s></p><p type="main">

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

<s id="id.000022">Tum &longs;eptem illa, qu&aelig; vulg&ograve; iactantur <lb/>orbis miracula. </s>

<s id="id.000023">Qu&aelig; profect&ograve; &longs;apien&shy;<lb/>ter Deus homini dedit &amp; po&longs;&longs;e, &amp; fa&shy;<lb/>bricari: ne mundum hunc &agrave; &longs;e <expan abbr="c&otilde;ditum">conditum</expan>, <lb/>con&longs;eruatum, con&longs;eruandum, quandiu <lb/>voluerit, hominibus foret incredibile. <lb/></s>

<s id="id.000024">His enim tantis, &amp; tam multis qu&aelig; ab <lb/>homine <foreign lang="greek">mhxanopoihtikw=|</foreign> manife&longs;t&egrave; &amp; in om&shy;<lb/>nium oculis fiunt, &amp; con&longs;eruantur, fa&shy;<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&shy;<lb/>ximum</expan> cert&egrave; operum opus, factum e&longs;&longs;e, <lb/>&amp; con&longs;eruari: non autem ab vllo homi&shy;<lb/>ne, &longs;ed ab alio <foreign lang="greek">mhxanopoihtikw=|</foreign> tant&ograve; homi&shy;<lb/>nem pr&aelig;&longs;tantia, &longs;apientia, potentia, im&ograve; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.008.jpg"/>infinit&egrave; &longs;uperante: quant&ograve; h&aelig;c mundi <lb/>machina omnium hominum etiam Ar&shy;<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, pr&aelig;terquam is, quem Deum om&shy;<lb/>nes appellamus. </s>

<s>Sed &amp; ex eo fit perquam <lb/>credibile, ad huius magn&aelig; molis archi&shy;<lb/>tecturam <expan abbr="architect&utilde;">architectum</expan> &longs;uum nihil egu&iuml;&longs;&longs;e <lb/>ferramentis, vecte, cuneis, trochleis, axe <lb/>in peritrochio, molitione, conatu, qu&aelig; <lb/>impius i&longs;te Velleius ex Epicuri &longs;enten&shy;<lb/>tia apud Ciceronem di&longs;putans &longs;tult&egrave; re&shy;<lb/>quirebat. </s>

<s id="id.000026">In quo enim immen&longs;us ille au&shy;<lb/>thor, factorque hominis, in proprij <lb/>operis fabrica homini ip&longs;i pr&aelig;polleret, <lb/>&longs;i machinis, &amp; in&longs;trumentis, materia, &amp; <lb/>molimine, vt homo, indigeret? </s>

<s id="id.000027">quan&shy;<lb/>quam po&longs;t &longs;emel &agrave; &longs;e mundum ex nihilo <lb/>creatum, ille liberrimum &longs;emper, &amp; po&shy;<lb/>tenti&longs;&longs;imum agens, cum his adiunctis, <lb/>&amp; &longs;ine his quando, quotie&longs;que vult, ni&shy;<lb/>hilominus operatur. </s>

<s id="id.000028">Qu&aelig; &longs;i rect&egrave; &amp; ve&shy;<lb/>r&egrave; 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&shy;<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, &amp; ip&longs;e reformidem, licet <lb/>Mechanicorum <expan abbr="titul&utilde;">titulum</expan> in fronti&longs;picio <lb/>gerat, hoc ade&ograve; in&longs;igne opus ab Ari&shy;<lb/>&longs;totele profectum, vtile, <expan abbr="iuc&utilde;dum">iucundum</expan>, &longs;ub&shy;<lb/>tili&longs;&longs;im&egrave; tractatum: &longs;ed temporum iniu&shy;<lb/>ria multis mendis f&oelig;dum, ob&longs;curum, <lb/>captu difficile, nunc opera no&longs;tra niti&shy;<lb/>dum, clarum, &amp; captu facile &longs;anct&aelig; ma&shy;<lb/>ie&longs;tati tu&aelig; dicare, ac <expan abbr="c&otilde;&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, qu&aelig; <lb/>&longs;unt in vita <expan abbr="homin&utilde;">hominum</expan>, maximas perfecit, <lb/>quar&uacute;mque temporibus atque fabricis <lb/>&longs;ummus e&longs;t &amp; frequenti&longs;&longs;imus machi&shy;<lb/>narum, &amp; <expan abbr="in&longs;trum&etilde;torum">in&longs;trumentorum</expan> v&longs;us: ille non <lb/>pote&longs;t machinamentorum, &amp; <expan abbr="in&longs;tru-m&etilde;torum">in&longs;tru&shy;<lb/>mentorum</expan> formis, rationibus, adinuen&shy;<lb/>tionibus, &amp; 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, &amp; ingeniose tra&shy;<lb/>ctarint, libros oblatos non grati&longs;&longs;im&egrave; <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&shy;<lb/>las res perfeci&longs;ti, bellum &longs;cilicet, &amp; pa&shy;<lb/>cem. </s>

<s id="id.000031">In vtriu&longs;que tempore a&longs;&longs;iduus ma&shy;<lb/>chinarum, &amp; in&longs;trumentorum v&longs;us, at&shy;<lb/>que opportunitas. </s>

<s id="id.000032">Tu namque bellum <lb/>(h&icirc;c me patiare, rex potenti&longs;&longs;ime, in me&shy;<lb/>ritas aliquot tuas laudes paul&ograve; amplius, <lb/>non extra rem tamen excurrere, &amp; ex&shy;<lb/>patiari.) Tu inquam bellum (&ocirc; onus <lb/><foreign lang="greek">kolossikw/taton,</foreign> graui&longs;&longs;imum cert&egrave;, &amp; num&shy;<lb/>quam &longs;i fieri po&longs;&longs;et, commouendum: <lb/>vbi, vbi tamen nece&longs;&longs;arium e&longs;t, mouen&shy;<lb/>dum, &longs;u&longs;cipiendum, gerendum) ad&shy;<lb/>uer&longs;us dome&longs;ticos in&longs;anientes, rebel&shy;<lb/>le&longs;que: aduer&longs;us extraneos intraneo&shy;<lb/>rum tumultu &longs;uperbientes, ferocien&shy;<lb/>tes, &amp; occa&longs;ionem regni inuadendi <lb/>opportuni&longs;&longs;imam nacto&scedil; &amp; 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&shy;<lb/>cet omnium bellorum, quorum hi&shy;<lb/>&longs;torias, &amp; annales no&longs;tros legens me&shy;<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 &amp; foris contentione, &amp; <lb/><expan abbr="c&otilde;iuratione">coniuratione</expan> vi&longs;um in&longs;uperabile, moui&shy;<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&shy;<lb/>ctos rebelles, partim armis, qu&aelig; fuit tua <lb/>in pugnando terribilis &longs;emper inimicis <lb/>&amp; audacia, &amp; fortitudo: partim auro ex <lb/>propriis eorum fodinis effo&longs;&longs;o, recto <lb/>&longs;an&egrave; iudicio, qu&aelig; tua fuit &longs;umma cum <lb/>prudentia iu&longs;ticia, vt in po&longs;terum &longs;ciant <lb/>&longs;uis &agrave; Deo datis obtemperare regibus, <lb/>neque vnquam ab illorum contrariis <lb/>&longs;tare partibus: partim benignitate, &amp; <lb/>man&longs;uetudine, qu&aelig; te &longs;uperis pulcher&shy;<lb/>rima &aelig;quat virtus. </s></p><p type="main">

<s id="id.000036"><emph type="italics"/>Nam<emph.end type="italics"/> (vt ait grauis vnus &egrave; po&euml;tis) <emph type="italics"/>cum <lb/>vincamur in omni<emph.end type="italics"/></s></p><p type="main">

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

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

<s id="id.000039">Extraneos ver&ograve; longo bello: bre&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.012.jpg"/>uiori tamen, quam &longs;perare, aut promit&shy;<lb/>tere nobis au&longs;i fuerimus, fractos, &longs;&aelig;pe <lb/>Marte aperto, &amp; manibus <expan abbr="vtrinq;">vtrinque</expan> con&shy;<lb/>&longs;ertis victos, fugatos, tandem procul <lb/>ab omnibus Galli&aelig; finibus reieci&longs;ti: &amp; <lb/>quanquam ante&agrave; &longs;emper ab omni pacis <lb/>conditione alieni&longs;&longs;imos, vt pacem ip&longs;i <lb/>appeterent, &amp; peterent co&euml;gi&longs;ti. </s>
 
<s id="id.000040">Quid <lb/>tu ilico? </s>

<s id="id.000041">Quandoquidem pax victo &longs;em&shy;<lb/>per &longs;it nece&longs;&longs;aria, &amp; victori ea, qu&aelig; nihil <lb/>po&longs;t &longs;e ferat in&longs;idiarum, &longs;emper expe&shy;<lb/>diat: &longs;tatim eius ineund&aelig;, &amp; cum <expan abbr="po-t&etilde;ti&longs;&longs;imo">po&shy;<lb/>tenti&longs;&longs;imo</expan> ho&longs;te Philippo Hi&longs;paniarum <lb/>rege conciliand&aelig; <expan abbr="occa&longs;ion&etilde;">occa&longs;ionem</expan> qu&aelig;&longs;itam, <lb/>&amp; oblatam &agrave; Clemente VIII. pontifice <lb/>&longs;ummo, ver&egrave; vtriu&longs;que gentis commu&shy;<lb/>ni <expan abbr="par&etilde;te">parente</expan> clementi&longs;&longs;imo, per &longs;uum lega&shy;<lb/>tum Alexandrum de Medicis Cardina&shy;<lb/>lem, &amp; Archiepi&longs;copum Florentinum, <lb/>qui huic paci tractand&aelig;, conficiend&aelig;, <lb/>&amp; ni&longs;i perfecta re <expan abbr="n&otilde;">non</expan> relinquend&aelig; &longs;em&shy;<lb/>per interfuit, &amp; qua&longs;i pr&aelig;fuit, arripui&shy;<lb/>&longs;ti. </s>

<s id="id.000042">Duobus e tuo &longs;anctiore con&longs;ilio de&shy;<lb/>lectis con&longs;iliariis tibi, id e&longs;t patri&aelig; <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 &amp; <lb/>grat&aelig; erga viros tam bene de te, totaque <lb/>Gallia meritos memori&aelig; no&longs;tr&aelig; gratia, <lb/>h&icirc;c illos nominari) Pomponio Belle&shy;<lb/>ureo &amp; Nicolao Brulartio, toto tant&aelig; <lb/>molis negotio per te commi&longs;&longs;o, pacem <lb/>tibi, tuis, toti Galli&aelig; honorificenti&longs;&longs;i&shy;<lb/>mam conciliaui&longs;ti: pacem inquam ab&shy;<lb/>&longs;entem, &amp; ad multos annos exulem re&shy;<lb/>duxi&longs;ti: iureiurando &longs;olemni&longs;&longs;imo, &longs;i&shy;<lb/>gillis vtriu&longs;que regni confirmatam per <lb/>pr&aelig;cones tuos proclamari iu&longs;&longs;i&longs;ti: arma <lb/>de manibus militum, qu&aelig; erant &longs;umpta <lb/>pro te, &amp; contra te &longs;u&longs;tuli&longs;ti: iam tuo&shy;<lb/>rum in ligones, aratrorum dentes, fal&shy;<lb/>ces, vngues ferreos, vectes, trochleas, <lb/>malleos, aliaque in&longs;trumenta vit&aelig; mi&shy;<lb/>tioris, &amp; pacific&aelig; conuerti&longs;ti: iam arua <lb/>feracis Galli&aelig; recoli c&oelig;pta, vbique re&shy;<lb/>uire&longs;cunt: l&aelig;t&aelig; &longs;egetes, agri vberes cul&shy;<lb/>mis ari&longs;ti&longs;que luxuriant: ex &aelig;dificijs &longs;e&shy;<lb/>miruta re&longs;taurantur, dirutorum loco <lb/>noua &longs;tatuuntur: leges liber&egrave; pronun&shy;<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&shy;<lb/>ca omnia iudicat: linguarum &amp; bona&shy;<lb/>rum <expan abbr="arti&utilde;">artium</expan>, te earum re&longs;tauratore, &amp; vin&shy;<lb/>dice &amp; cu&longs;tode, eruditio in <expan abbr="Academi&atilde;">Academiam</expan> <lb/>reuer&longs;a frequentatur: ingenia, qu&aelig; in ea <lb/>&longs;unt pr&aelig;clara, in variarum artium iam <lb/>redundant elegantiam, f&oelig;tu&longs;que &longs;uos <lb/>producere ge&longs;tiunt: mercatura denique <lb/>tut&ograve; vagatur, peregrinatur, ru&longs;ticatur. <lb/></s>

<s id="id.000043">Harum duarum rerum belli, &amp; pacis <lb/>magnitudinem, <expan abbr="difficultat&etilde;">difficultatem</expan>, <expan abbr="impedim&etilde;-ta">impedimen&shy;<lb/>ta</expan> &longs;oli <expan abbr="c&otilde;plectentur">complectentur</expan>, quitam di&longs;&longs;ociatas <lb/>Gallorum &amp; Hi&longs;panorum <expan abbr="vol&utilde;tates">voluntates</expan>: <expan abbr="t&atilde;">tam</expan> <lb/>multa, &amp; multiplici <expan abbr="&longs;imultat&utilde;">&longs;imultatum</expan> <expan abbr="atq;">atque</expan> odio&shy;<lb/>rum crudelitate &longs;auciatas: tot mordaci&shy;<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="N&atilde;">Nam</expan> qui <lb/><expan abbr="n&otilde;">non</expan> <expan abbr="vider&utilde;t">viderunt</expan>, licet ab alijs recitata <expan abbr="audi&atilde;t">audiant</expan>, <lb/>aut <expan abbr="monum&etilde;tis">monumentis</expan> <expan abbr="c&otilde;m&etilde;data">commendata</expan> <expan abbr="leg&atilde;t">legant</expan>, non ar&shy;<lb/>bitror <expan abbr="tam&etilde;">tamen</expan> vllius vlla <expan abbr="quant&utilde;uis">quantumuis</expan> elegan&shy;<lb/>ti, &amp; probabili narratione adduci po&longs;&longs;e, <lb/>vt <expan abbr="cred&atilde;t">credant</expan>, quando <expan abbr="quid&etilde;">quidem</expan> nos, qui h&aelig;c vi&shy;<lb/>dimus, &longs;i <expan abbr="qu&atilde;do">quando</expan> in <expan abbr="memori&atilde;reducimus">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&shy;<lb/>gans facimus? </s>

<s id="id.000046">&longs;i tibi qui cum tanta glo&shy;<lb/>ria h&aelig;c duo perfeceris, de pacis &amp; belli <lb/>in&longs;trumentis, vel potius de horum in&shy;<lb/>&longs;trumentorum viribus, &amp; virium cau&shy;<lb/>&longs;is, &amp;, quod admirabilius, vno <expan abbr="ear&utilde;">earum</expan> prin<lb/>cipio, quod e&longs;t circulus, librum offeri&shy;<lb/>mus? </s>

<s id="id.000047">qui te pr&aelig;terea videamus magni&shy;<lb/>ficis &aelig;dificiorum &longs;ub&longs;tructionibus, ita <lb/>delectari, vt nihil, <expan abbr="n&otilde;">non</expan> dicam nunc, cum <lb/>&longs;int h&aelig;c 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, qu&aelig; &agrave; tua Lupara <lb/>ad tuas &aelig;des lateritias te, <expan abbr="tuo&longs;q;">tuo&longs;que</expan> delatura <lb/>&amp; illinc ad <expan abbr="vrb&etilde;">vrbem</expan> de&longs;uper ventura, te <expan abbr="in-u&etilde;tore">in&shy;<lb/>uentore</expan>, &amp; excogitatore, tuis &longs;umptibus <lb/>extruitur: &AElig;dium lateritiarum cochlea&shy;<lb/>ri &longs;cal&ecedil;, octauo orbis miraculo <expan abbr="coloph&otilde;">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&shy;<lb/>luptate o&longs;tentata, &amp; eorum maiori ad&shy;<lb/>miratione ab illis &longs;pectata luculenter te&shy;<lb/>&longs;tantur, <expan abbr="atq;">atque</expan> <expan abbr="h&atilde;c">hanc</expan> animi tui <expan abbr="delectation&etilde;">delectationem</expan> <lb/>rege magnifico <expan abbr="digni&longs;&longs;im&atilde;">digni&longs;&longs;imam</expan> declararunt, <lb/>&amp; vi&longs;uris, quotquot venient in po&longs;te&shy;<lb/>rum, declarabunt. </s>

<s id="id.000049">Spemque adferunt <lb/><expan abbr="n&otilde;mediocrem">non mediocrem</expan>, te, pro tuorum in Aca&shy;<lb/>demia profe&longs;&longs;orum collegio, quale edi&shy;<lb/>ta pro eo oratione &agrave; me de&longs;criptum <lb/>e&longs;t: aut ab alio magnificentius de&longs;cribe&shy;<lb/>tur, &aelig;dificando, aliquando e&longs;&longs;e cogitatu&shy;<lb/>rum, &amp; perfecturum. </s>

<s id="id.000050">H&aelig;c 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 opell&aelig; <expan abbr="quali&longs;cunq;">quali&longs;cunque</expan> no&longs;tr&aelig;, <lb/>exiguum &longs;cio: &longs;ed ratione authoris &longs;ui, <lb/>Ari&longs;totelis, magnum, &longs;anct&aelig; maie&longs;tati <lb/>tu&aelig; co&longs;ecrare. </s>

<s id="id.000051">Quod <expan abbr="n&utilde;c">nunc</expan> igitur tam lu&shy;<lb/>benter facio: quam Deum <expan abbr="optim&utilde;">optimum</expan> ma&shy;<lb/>ximum obnix&egrave; precor, vt vitam tibi <lb/>impertiat, in duas annorum quadrage&shy;<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, &amp; pace in ea confectis f&oelig;&shy;<lb/>liciter ingre&longs;&longs;us es, tot rebus pacis tam <lb/>magnificis, &amp; glorio&longs;is adhuc aggre&shy;<lb/>diundis, &amp; perficiundis con&longs;umas: quot <lb/>in rebus belli admirabilibus, atque in&shy;<lb/>credibilibus perfectis primam con&longs;um&shy;<lb/>p&longs;i&longs;ti. </s>

<s id="id.000052">Hoc, &longs;i tibi, Deo ita volente, eue&shy;<lb/>niat, haud profect&ograve; verendum erit di&shy;<lb/>cere, &amp; palam, quod omnium hi&longs;tori&aelig; <lb/>conte&longs;tabuntur, proclamare, te <expan abbr="rer&utilde;">rerum</expan> ad&shy;<lb/>mirabili&longs;&longs;imarum regem, &amp; regum, qui <lb/>hactenus in quacunque orbis regione <lb/>regnauere, fore pr&aelig;&longs;tanti&longs;&longs;imum, &amp; ad&shy;<lb/>mirabili&longs;&longs;imum. </s>

<s id="id.000053">Vale, &amp; duas illas per&shy;<lb/>optatas annorum quadragenarias tibi, <lb/>&amp; nobis &longs;ic viue. </s>

<s id="id.000054">Scriptum Luteti&aelig; eo <lb/>die, quo quinquennio ante &agrave; te ciui&shy;<lb/>tas Hi&longs;panis erepta, &amp; &longs;uis ciuibus f&oelig;li&shy;<lb/>citer e&longs;t re&longs;tituta. </s></p><p type="main">

<s id="id.000055">MAIESTATIS</s></p><p type="main">

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

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

<s id="id.000058">A D <lb/>HENRICVM IIII. <lb/>GALLI&AElig; ET NAVARR&AElig; <lb/>Regem Chri&longs;tiani&longs;&longs;imum. </s></p><p type="main">

<s id="id.000059"><emph type="italics"/>Pacatos fecit tua nos victoria ciues. <lb/></s>

<s id="id.000060">Inde caput Laurus: digitos ornabit Oliua <lb/>Semper, &amp; ingentem per vtr&acirc;que volabis Olympum. <emph.end type="italics"/></s></p><p type="head">

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

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

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

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

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

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

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

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

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

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

<s id="id.000071"><emph type="italics"/>Sic dat Ari&longs;toteli vitam, clar&eacute;que vici&szlig;im<emph.end type="italics"/></s></p><p type="main">

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

<s id="id.000073"><emph type="italics"/>Vna dies ambos &longs;eruabit, &amp; eximet &aelig;uo,<emph.end type="italics"/></s></p><p type="main">

<s id="id.000074"><emph type="italics"/>Ambor&uacute;mque &longs;imul fama &longs;uper&longs;tes erit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000075">RICHARDVS MERCES</s></p><p type="main">

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

<section>
<figure id="id.035.01.019.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.019.1.jpg"/>

<p type="head">

<s id="id.000077">PRAEFATIO IN <lb/>MECHANICA ARISTO&shy;<lb/>TELIS, AD LECTOREM. </s></p><p type="main">

<s id="id.000078">Philosophari in vno rerum quo&shy;<lb/>libet genere, <expan abbr="c&atilde;dide">candide</expan> lector, res e&longs;t per&shy;<lb/>quam dulcis. </s>

<s id="id.000079">Philo&longs;ophari appello re&shy;<lb/>rum e&longs;&longs;entiam, cau&longs;as, proprietates, <lb/>facultates inue&longs;tigare, &amp; inuento rum <lb/>qu&aelig; vtilia &longs;unt in opus ad vit&aelig; homi&shy;<lb/>num f&oelig;licius <expan abbr="deg&etilde;d&aelig;">degend&aelig;</expan> commoda edu&shy;<lb/>cere. </s>

<s id="id.000080">Ita enim demum ver&egrave; ille erit, vt ait po&euml;ta,</s></p><p type="main">

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

<s id="id.000082">Alio qui inutilia, vel vtilia: &longs;ed inutiliter id e&longs;t &longs;ine actio&shy;<lb/>ne vel opere, qu&ecedil; fines &longs;unt omnis <expan abbr="c&otilde;templationis">contemplationis</expan> vtilis, <lb/>contemplari, &amp; 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">Verumenimuer&ograve; re&shy;<lb/>rum quia propemodum e&longs;t infinita multitudo, licet ani&shy;<lb/>mus hominis (quod e&longs;t ab Ari&longs;totele dictum, &amp; ita e&longs;t, <lb/>pote&longs;tate cogno&longs;cendi, &amp; 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, &amp; magnum quid con&longs;e&shy;<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&shy;<lb/>tem medicum, Platonem, Ari&longs;totelem, Theophra&longs;tum, <lb/>Galenum &longs;i non omnia tenui&longs;&longs;e: quamplurima cert&egrave; &amp; <lb/>aliorum libri, &amp; commentarij ab illis po&longs;teritati relicti <lb/>copios&egrave; 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 &amp; operam non &longs;ine v&longs;ura collocent &longs;uam. </s>

<s id="id.000086">Om&shy;<lb/>nium, qu&aelig; &longs;unt, genera quatuor e&longs;&longs;e reperio, &longs;ingula cer&shy;<lb/>t&egrave; digni&longs;&longs;ima hominis contemplatione. </s>

<s id="id.000087">Diuina, c&oelig;le&shy;<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&shy;<lb/>memoratione opus &longs;it. </s>

<s id="id.000089">Et cert&egrave; diuina &longs;unt eiu&longs;modi, vt <lb/>licet ad eorum intuitum, &longs;icut ad Solis ve&longs;pertilionis: Ita <lb/>mentis no&longs;tr&aelig; oculi caligent, &longs;i quis tamen diuinitatis <lb/><expan abbr="eti&atilde;">etiam</expan> exiguus repente, &amp; &longs;ubinde radius recipiatur &amp; ocu&shy;<lb/>los &longs;ubintret, plus voluptatis menti adferat: quam alio&shy;<lb/>rum quorumlibet plena cognitio. </s>

<s id="id.000090">Qu&aelig; vna res adiuncto <lb/>contemplationis diuinorum fine (quem Dei cognitio&shy;<lb/>nem, amorem, &amp; cultum arbitror) fecit, vt philo&longs;ophi&aelig; <lb/>diuinorum quamplurimi homines totos &longs;e&longs;e dediderint, <lb/>dedantque quotidie. </s>

<s id="id.000091">Huic philo&longs;ophi&aelig; proxima e&longs;t c&oelig;&shy;<lb/>le&longs;tium &amp; 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&shy;<lb/>tibus, &amp; 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;th&aelig;c omnia arguit, &amp; de&shy;<lb/>mon&longs;trat. </s>

<s id="id.000092">Luculenti&longs;&longs;im&egrave; in&longs;uper o&longs;tendit Deum, &amp; 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">Mult&ograve; 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, &amp; innumerabili ad v&longs;us humanos vti&shy;<lb/>litate. </s>

<s id="id.000094">Nam cum h&aelig;c ita e&longs;&longs;e homines <expan abbr="depreh&etilde;di&longs;&longs;ent">deprehendi&longs;&longs;ent</expan>, vt <lb/>ad mult&ograve; plures v&longs;us, quam ad quos <expan abbr="&longs;p&otilde;t&egrave;">&longs;pont&egrave;</expan> nata e&longs;&longs;e com&shy;<lb/>perirentur, <expan abbr="tr&atilde;sferri">transferri</expan> &amp; aptati po&longs;&longs;ent, <expan abbr="perciperentq;">perciperentque</expan> non <lb/>fru&longs;tr&agrave; &longs;uis animis in&longs;itas non <expan abbr="&longs;ol&utilde;">&longs;olum</expan> facultates i&longs;ta transfe&shy;<lb/>rendi &amp; aptandi: &longs;ed etiam congenita corporibus &longs;uis <expan abbr="in-&longs;trum&etilde;ta">in&shy;<lb/>&longs;trumenta</expan>, quibus vel ex &longs;e, vel &agrave; &longs;e factis <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> tran&longs;&shy;<lb/>ferrent &amp; aptarent, non &longs;ola cognitione <expan abbr="c&otilde;tenti">contenti</expan> ad agen&shy;<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, prim&ugrave;m 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 e&ograve;, imitatione <lb/>c&oelig;le&longs;tium &amp; <expan abbr="elem&etilde;tarior&utilde;">elementariorum</expan>, &amp; in <expan abbr="hor&utilde;">horum</expan> nonnullis &longs;upera&shy;<lb/>tione proce&longs;&longs;it, vt homo qui manu mentis con&longs;ilio dire&shy;<lb/>cta tot &amp; <expan abbr="t&atilde;ta">tanta</expan>, quanta <expan abbr="n&utilde;c">nunc</expan> po&longs;&longs;idemus, peregerit, ab Ana&shy;<lb/>xagora quia haberet <expan abbr="man&utilde;">manum</expan>, &longs;apienti&longs;&longs;imus fuerit iudica&shy;<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&shy;<lb/>r&ugrave;m <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 cert&egrave; animus in homine ars <expan abbr="arti&utilde;">artium</expan>. </s>

<s id="id.000100">Inuenit enim om&shy;<lb/>nia, &amp; 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 &amp; 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&shy;<lb/>litio &amp; <expan abbr="inu&etilde;tio">inuentio</expan> <expan abbr="in&longs;trumentor&utilde;">in&longs;trumentorum</expan> ad opus. </s>

<s id="id.000103">qu&aelig; cum &longs;ine ra&shy;<lb/>tione non po&longs;&longs;int exi&longs;tere, ratio <expan abbr="aut&etilde;">autem</expan> vnius hominis pro&shy;<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, &amp; omnia qu&aelig; &agrave; Dei &longs;olo nutu, &longs;ine ve&shy;<lb/>cte, &longs;ine ferramentis, &longs;ine machina vlla confecta &amp; creata <lb/><expan abbr="s&utilde;t">sunt</expan>, molitione, machinatione &amp; <expan abbr="in&longs;trum&etilde;tis">in&longs;trumentis</expan> imitari, om&shy;<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 &amp; pr&aelig;&longs;tan&shy;<lb/>ti&longs;&longs;imam, tanta arte vnius machin&aelig; vitre&aelig; artificio re&shy;<lb/>pr&aelig;&longs;entauit, vt &longs;i Claudiano credimus, artificij elegantia <lb/>voluptatem &amp; admirationem Ioui pepererit. </s>

<s id="id.000105">Sed pr&aelig;&longs;tat <lb/>eleganti&longs;&longs;imos huius po&euml;t&aelig; ver&longs;us recitare. </s></p><p type="main">

<s id="id.000106"><emph type="italics"/>Iuppiter, in paruo cum cerneret &aelig;thera vitro, <lb/>Ri&longs;it, &amp; ad &longs;uperos talia dicta dedit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000107"><emph type="italics"/>Hoccine mortalis progre&longs;&longs;a potentia cur&aelig;? <lb/></s>

<s id="id.000108">Iam meus in fragili luditur orbe labor. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000109"><emph type="italics"/>Iura poli, rerumque fidem, lege&longs;que deorum <lb/>Ecce Syracu&longs;ius tran&longs;tulit arte &longs;enex. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000110"><emph type="italics"/>Inclu&longs;us varijs famulatur &longs;piritus a&longs;tris, <lb/>Et viuum certis motibus vrget opus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000111"><emph type="italics"/>Percurrit proprium mentitus &longs;ignifer annum, <lb/>Et &longs;imulata nouo Cynthia men&longs;e redit. <emph.end type="italics"/></s></p><p type="main">

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

<s id="id.000113"><emph type="italics"/>Quid &longs;al&longs;o in&longs;ontem tonitru Salmonea miror? <lb/></s>

<s id="id.000114">AEmula natur&aelig; parua reperta manus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000115">Sal monei huius fal&longs;um tonitru &longs;tatim in memoriam vo&shy;<lb/>cat, non iam fal&longs;a <expan abbr="homin&utilde;">hominum</expan>, qui nunc viuunt tonitrua, <expan abbr="vi-brataq;">vi&shy;<lb/>brataque</expan> &egrave; &longs;uis &longs;clopetis, <expan abbr="b&otilde;bardi&longs;que">bombardi&longs;que</expan> fulmina, &longs;oni frago&shy;<lb/>re, ictus conqua&longs;&longs;atione, &amp; <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/>pr&aelig;cipitat: h&aelig;c ver&ograve; certo ictu &longs;emper de&longs;tinata vrbium <lb/>m&oelig;nia deua&longs;tant: quot homines attingunt, perdunt, &amp; <lb/><expan abbr="quid&etilde;">quidem</expan> tanta celeritate, tant&aacute;que vi, vt qu&ecedil; ab antiquis in&shy;<lb/>genios&egrave;, vel ad oppugnandos ho&longs;tes, vel ab his &longs;e <expan abbr="defen-dend&utilde;">defen&shy;<lb/>dendum</expan> inuenta erant <expan abbr="in&longs;trum&etilde;ta">in&longs;trumenta</expan> bellica, Scorpiones, ca&shy;<lb/>tapult&aelig;, bali&longs;t&aelig;, arietes, turres ambulatori&aelig;, te&longs;tudines, <lb/>helepoles, fund&aelig;, &amp; reliqua eiu&longs;modi poliorcetica, pr&aelig; <lb/>illis qua&longs;i in <expan abbr="de&longs;uetudin&etilde;">de&longs;uetudinem</expan>, &amp; <expan abbr="obliuion&etilde;">obliuionem</expan> abierint. </s>

<s id="id.000117">Pr&aelig;clara <lb/>&longs;an&egrave; 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>, &amp; &longs;ic long&egrave; <lb/>lat&eacute; 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;&shy;<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&shy;<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;&shy;<lb/>le&longs;tium, &longs;eu <expan abbr="a&longs;tror&utilde;">a&longs;trorum</expan> lumina faces no&longs;tr&aelig; 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 &amp; Cte&longs;ibij hydraulica <lb/>in&longs;trumenta, &amp; merul&aelig; hominum voces <expan abbr="auiumq;">auiumque</expan> cantus <lb/>imitantes, &amp; <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> perbell&egrave; <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 icuncul&aelig; ill&aelig; <lb/>ad <expan abbr="cant&utilde;">cantum</expan> cythar&aelig; &longs;altitantes, manus manibus iungentes, <lb/>in equos, in currus con&longs;cendentes, mod&ograve; 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 affabr&egrave;, nec o&longs;citanter <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.023.jpg"/>exercebat, quod h&icirc;c Luteti&aelig; vidimus. </s>

<s id="id.000124">Vt &amp; Noriberg&aelig; <lb/>mu&longs;ca ferrea <expan abbr="c&otilde;memoratur">commemoratur</expan> &egrave; manu artificis &longs;ui euola&longs;&longs;e, <lb/>&amp; 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, qu&aelig; in a&euml;re <lb/>&longs;ublimis Carolo imperatori huius nominis quinto ad vr&shy;<lb/>bem aduentanti obuia facta, <expan abbr="v&longs;q;">v&longs;que</expan> ad vrbis <expan abbr="port&atilde;">portam</expan> eundem <lb/>comitata e&longs;t, ne fabulam exi&longs;timemus quod de columba <lb/>Archit&aelig; <expan abbr="vol&atilde;te">volante</expan> &agrave; veteribus <expan abbr="c&otilde;memoratum">commemoratum</expan> e&longs;t: <expan abbr="neq;">neque</expan> illud <lb/>quod fertur de D&aelig;daleis operibus, &amp; Vulcani tripodi&shy;<lb/>bus, pectinibus, malleis, qui iniu&longs;&longs;i ad opus &longs;ponte &longs;ua ve&shy;<lb/>niebant, &amp; ni&longs;i vinculis coercerentur, aufugiebant. </s>

<s id="id.000125">Sed <lb/>h&aelig;c ad delectationem tantum &longs;unt comparata, vtilia &amp; <lb/>vit&aelig; human&ecedil; <expan abbr="tr&atilde;&longs;ig&etilde;d&aelig;">tran&longs;igend&aelig;</expan> nece&longs;&longs;aria omnino &longs;unt Agricul&shy;<lb/>tur&aelig;, Militaris, Architectur&aelig;, Medicin&aelig;, Nautic&aelig;, Mer&shy;<lb/>catur&aelig; munera: quibus <expan abbr="alim&etilde;ta">alimenta</expan>, tecta, &longs;anitas, ve&longs;titus, di&shy;<lb/>uiti&aelig;, &amp; ab c&oelig;li, <expan abbr="ho&longs;tiumq;">ho&longs;tiumque</expan> iniurijs defen&longs;io qu&aelig;runtur. <lb/></s>

<s id="id.000126">At quid artes ill&aelig; e&longs;&longs;e po&longs;&longs;ent, ni&longs;i machin&aelig; <expan abbr="inu&etilde;t&aelig;">inuent&aelig;</expan> fui&longs;&shy;<lb/>&longs;ent, &amp; in&longs;trumenta, quibus vn&acirc; <expan abbr="c&utilde;">cum</expan> <expan abbr="homin&utilde;">hominum</expan> parua vi, mo&shy;<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&shy;<lb/>mouentur</expan>, pelluntur, trahuntur, <expan abbr="c&otilde;uehuntur">conuehuntur</expan>, in <expan abbr="gyr&utilde;">gyrum</expan> con&shy;<lb/>torquentur, &amp; <expan abbr="t&atilde;dem">tandem</expan> alti&longs;&longs;imis locis &amp; difficilimis repo&shy;<lb/>nuntur? </s>

<s id="id.000127">aut <expan abbr="e&aelig;d&etilde;">e&aelig;dem</expan> iu&longs;ta quantitate appen&longs;&aelig;, aut <expan abbr="m&etilde;&longs;urat&aelig;">men&longs;urat&aelig;</expan> <lb/><expan abbr="cuiq;">cuique</expan> &longs;uum qu&aelig;renti di&longs;tribuuntur? </s>

<s id="id.000128">Vnde &longs;ex &longs;unt illa ex <lb/>innumeris &agrave; veteribus <expan abbr="inu&etilde;ta">inuenta</expan>, <expan abbr="quor&utilde;">quorum</expan> &longs;ingula &longs;eor&longs;um ma&shy;<lb/>gna vi: <expan abbr="coni&utilde;cta">coniuncta</expan> ver&ograve;, &amp; multiplicata infinitis propemo&shy;<lb/>dum viribus pollere animaduertuntur, libra, vectis, tro&shy;<lb/>chlea, axis in peritrochio, cuneus, &amp; cochlea. </s>

<s id="id.000129">Sed qu&ecedil; au&shy;<lb/>dio h&icirc;c 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>, &amp; 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;an&egrave;: &longs;ed &amp; A&longs;tre&aelig;, &amp; Neptuni, &amp; Mar&shy;<lb/>tis, &amp; Vulcani, &amp; Cereris, &amp; Palladis, qui tantopere pro&shy;<lb/>pter h&aelig;c &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&shy;<lb/>dicat ab iniquitate iu&longs;tis moribus <expan abbr="vit&atilde;">vitam</expan>. </s>

<s id="id.000133">Vnde &longs;tatera do&shy;<lb/>lo&longs;a abhominatio e&longs;t apud Deum, dixit <expan abbr="&longs;api&etilde;s">&longs;apiens</expan>, &amp; pondus <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.024.jpg"/>&aelig;quum voluntas eius, &amp; alibi abhominatio e&longs;t apud Deum <lb/>pondus &amp; pondus. </s>

<s id="id.000134">Itaque libr&aelig; inuentrix A&longs;tr&aelig;a 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&shy;<lb/>lis, &amp; &longs;ignis propo&longs;ita, ad quam intuerentur, &amp; denique in <lb/>c&oelig;le&longs;te &longs;ignum conuer&longs;a, qu&aelig; diem naturalem, quem Sol <lb/>&aelig;quatorem peragrans circulum conficit, in tempus lucis &amp; <lb/>tenebrarum &aelig;qualiter vbique diuideret. </s>

<s id="id.000136">Vnde po&euml;ta,</s></p><p type="main">

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

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

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

<s id="id.000140">Gr&aelig;ci appellant <foreign lang="greek">mo/xlon</foreign> vnde ille <foreign lang="greek">mox&shy;<lb/>leuth\s</foreign> vectiarius &agrave; po&euml;tis dictus e&longs;t, &amp; terr&aelig; mati&longs;que con&shy;<lb/>cu&longs;&longs;or, &amp; hac machina Syrtes &longs;ubleuans, quo plus Troianis <lb/>apparerent &agrave; po&euml;ta inducitur,</s></p><p type="main">

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

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

<s id="id.000143">Cert&egrave; vectis palus e&longs;t <expan abbr="obl&otilde;gior">oblongior</expan>, materi&aelig; firm&aelig;, cu&longs;pide acu&shy;<lb/>ta, &amp; paulo latiori lingu&aelig; in&longs;tar, quam prop&egrave;, quando e&longs;t <lb/>&longs;ubditum hypomochlium, huic pondus incumbens, id que <lb/>grauius quam quod &agrave; decem hominum &longs;olis manibus di&shy;<lb/>moueri loco po&longs;&longs;et, vnius <expan abbr="tam&etilde;">tamen</expan> viribus caput huius pali de&shy;<lb/>primentibus, vel &longs;i terra &longs;ubdita pro hypomochlio e&longs;t &longs;uble&shy;<lb/>uantibus, dimouetur. </s>

<s id="id.000144">Vnde in magnis <expan abbr="&aelig;dificior&utilde;">&aelig;dificiorum</expan> &longs;ub&longs;tru&shy;<lb/>ctionibus vnus vectis pro multorum manibus, vnus homo <lb/>bimanus pro Briareo centimano, mod&ograve; pondera lapidum, <lb/>trabi&uacute;m que colo&longs;&longs;icotera fabris &amp; architectis loco dimo&shy;<lb/>uet, &amp; &longs;ubleuat: mod&ograve; <expan abbr="ei&longs;d&etilde;">ei&longs;dem</expan> collopis figura &longs;ucculas ver&longs;at: <lb/>modo tollenonis &longs;pecie aquas &egrave; puteis operis &amp; olitoribus <lb/>exhaurit: modo phalang&aelig; forma baiulis &amp; phalangarijs <lb/>proportionalia tanquam in bilance pondera partitur, mo&shy;<lb/>do iugi nomine in aratro bobus &aelig;quum arationis laborem <lb/>di&longs;pen&longs;at &longs;iue &aelig;quales &longs;iue in&aelig;quales. </s></p><p type="main">

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

<s id="id.000146">Sed cum naui tran&longs;mittitur flumen, aut mare tran&longs;meatur, <lb/>quid e&longs;t in ea remus aliud, quam vectis inuer&longs;us, habens in <lb/>&longs;calmo hypomochlium? </s>

<s id="id.000147"><expan abbr="aqu&atilde;">aquam</expan> pro pondere loco dimouens? <lb/></s>

<s id="id.000148">vt in eum cedat nauis, &amp; quidem impul&longs;us ille &agrave; remige pro <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.025.jpg"/>vectiatio tanquam tridens &agrave; Neptuno? </s>

<s id="id.000149">Quin &amp; guberna&shy;<lb/>calum, quo gubernator in puppi <expan abbr="&longs;ed&etilde;s">&longs;edens</expan> tam facil&egrave; obliquat <lb/>nauim etiam ingentem, &amp; cum magna in prora loci muta&shy;<lb/>tione, licet in puppi ade&ograve; exigua, vt nihil agere, aut <expan abbr="eti&atilde;">etiam</expan> lu&shy;<lb/>dere videatur: aliud <expan abbr="tam&etilde;">tamen</expan> nihil, quam vectis e&longs;&longs;e <expan abbr="c&otilde;perietur">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 &egrave; qua pendet carche&shy;<lb/>&longs;ium cum pa&longs;&longs;is velis, <expan abbr="tanqu&atilde;">tanquam</expan> alis D&aelig;daleis perflante vento <lb/>propul&longs;a propellit pondus, nauim &longs;cilicet, &amp; quod e&longs;t admi&shy;<lb/>rabilius ibi non aliter venti, quam equi reguntur, <expan abbr="d&utilde;">dum</expan> ex car&shy;<lb/>che&longs;ij vt fr&aelig;ni &longs;itu mod&ograve; altiore: mod&ograve; depre&longs;&longs;iore provt <lb/>&longs;unt admi&longs;&longs;i: ita nauis mod&ograve; vehementius, mod&ograve; remi&longs;&longs;ius <lb/>impellitur. </s></p><p type="main">

<s id="id.000152">Sed h&aelig;c devecte &longs;atis. </s>

<s id="id.000153"><expan abbr="Trochle&atilde;">Trochleam</expan> ver&ograve;, qu&aelig; orbiculus e&longs;t <lb/>circa axem immobilem fune conuolutus, quantis viribus <lb/><expan abbr="pr&aelig;dit&atilde;">pr&aelig;ditam</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="c&otilde;fi-&longs;us">confi&shy;<lb/>&longs;us</expan> Archimedes cum audiret <expan abbr="aliqu&etilde;">aliquem</expan> <expan abbr="di&longs;put&atilde;tem">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, &amp; hanc ego <expan abbr="terr&atilde;">terram</expan> loco &longs;uo dimo&shy;<lb/>uebo. </s>

<s id="id.000156">cuius admirabilis dicti <expan abbr="c&utilde;">cum</expan> rogatus e&longs;&longs;et &agrave; rege, vt &longs;pe&shy;<lb/>cimen aliquod ederet, vna manu l&aelig;ua quinquies millen&ucirc;m <lb/>modiorum <expan abbr="p&otilde;dus">pondus</expan> attraxit: nauem in &longs;iccum littus eiectam <lb/>&amp; grauiter <expan abbr="onerat&atilde;">oneratam</expan> ad &longs;e perinde pertraxit, ac &longs;i in mari re&shy;<lb/>mis, veli&longs;ve impul&longs;a fui&longs;&longs;et: aliam po&longs;tea recens <expan abbr="c&otilde;&longs;tructam">con&longs;tructam</expan> <lb/>ingentis magnitudinis ab Herone regi &AElig;gyptiorum Ptolo&shy;<lb/>m&aelig;o dono mittendam, quam omnes <expan abbr="Syracu&longs;anor&utilde;">Syracu&longs;anorum</expan> ciuium <lb/>vires <expan abbr="c&otilde;iunct&aelig;">coniunct&aelig;</expan> dimouere loco non <expan abbr="potuer&atilde;t">potuerant</expan>, vt &longs;olus Hiero <lb/>machinis adiutus in mare educerer, perfecit: &amp; <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></s>

<s> Ab hoc die <lb/>quicquid 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&shy;<lb/>le, eruditis tamen demon&longs;tratum. </s>

<s id="id.000158">Datum pondus &agrave; data <lb/>potentia moueri. </s>

<s id="id.000159">quod in vecte, trochlea, &amp; axe in peritro&shy;<lb/>chio nuper &agrave; Guidone Vbaldo demon&longs;trationibus geome&shy;<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, &amp; eadem ad alti&longs;&longs;imas &aelig;di&shy;<lb/>ficiorum vbi opus e&longs;t &longs;edes trahit. </s>

<s id="id.000161">Sit in polo horizontis qui <lb/>trochle&aelig; appendiculum firmet, &amp; ad eum homo ip&longs;e &longs;e &longs;u&shy;<lb/>bleuabit. </s>

<s id="id.000162">Sed longior &longs;um in trochlea, in reliquis ero bre&shy;<lb/>uior. </s>

<s id="id.000163">Axis in peritrochio cylindrus e&longs;t duobus fulcris per <lb/>extrema &longs;u&longs;tentatus, habens prop&egrave; vnum extremorum tym&shy;<lb/>panum &longs;cytalis aliquot in peripheria in fixis perforatum, ita <lb/>quidem, vt <expan abbr="pot&etilde;tia">potentia</expan>, qu&aelig; &longs;emper in &longs;cytalis e&longs;t, dum circum&shy;<lb/>uertit tympanum &amp; 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 machin&aelig; beneficio de&longs;cenditur in vi&longs;ce&shy;<lb/>ra terr&aelig;, &amp; illinc effo&longs;&longs;&aelig; opes, non vt Ouidius ait, &longs;emper</s></p><p type="main">

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

<s id="id.000166">quin potius occa&longs;iones &amp; 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> nact&aelig; &longs;int. </s>

<s id="id.000167">Nam vt recte dixit Pindarus,</s></p><p type="main">

<s id="id.000168"><emph type="italics"/>Qu&aelig; Virtute pecunia<emph.end type="italics"/></s></p><p type="main">

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

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

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

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

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

<s id="id.000174"><emph type="italics"/>Pecuni&aelig; cur optet habere plurimum:<emph.end type="italics"/></s></p><p type="main">

<s id="id.000175"><emph type="italics"/>Quam po&longs;sit auxiliari vt amicis? </s>

<s id="id.000176">Grati&aelig;<emph.end type="italics"/></s></p><p type="main">

<s id="id.000177"><emph type="italics"/>Fruct&uacute;mque &longs;erere Diuarum &longs;uaui&longs;sim&aelig;?<emph.end type="italics"/></s></p><p type="main">

<s id="id.000178">Illinc in quam effo&longs;&longs;&aelig; opes, &longs;ucci, terr&aelig; medicat&aelig;, metalli <lb/>omne genus, lapides, arena, ad &aelig;dificiorum &longs;ub&longs;tructiones, <lb/>ad medicamenta prauarum &amp; contumacium affectionum, <lb/>ad ornamenta in altum, luc&eacute;m que euehuntur. </s></p><p type="main">

<s id="id.000179">Cuneus vero e&longs;t <expan abbr="in&longs;trum&etilde;tum">in&longs;trumentum</expan> exiguum in formam pyra&shy;<lb/>midis quadrangul&ecedil;, ad vnam <expan abbr="rect&atilde;">rectam</expan> <expan abbr="line&atilde;">lineam</expan> fa&longs;tigiat&aelig; ad diui&shy;<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, &amp; diuelli in c&oelig;ptam retinere <lb/>non po&longs;&longs;et, quin partes diuul&longs;&aelig; &longs;umma celeritate in &longs;e&longs;e re&shy;<lb/>dirent, vn&acirc;que raptas manus interciperent, pr&aelig;da vt im&shy;<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></p><p type="main">

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

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

<s id="id.000185">qui &longs;i cuneo id ip&longs;um facere volui&longs;&longs;et, in eam calamitatem <lb/>non incidi&longs;&longs;et. </s>

<s id="id.000186">Quis vero <expan abbr="n&otilde;">non</expan> intelligit Martis, Cereris, Vul&shy;<lb/>canique arma &amp; in&longs;trumenta en&longs;es, gladios, mucrones, &longs;e&shy;<lb/>cures, aratra, ligones, a&longs;cias, falces, vngues ferreos &amp; &longs;imilia, <lb/>qu&aelig; percu&longs;&longs;ione, &longs;iue impul&longs;u incidunt, diuidunt, <expan abbr="perfor&atilde;t">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 ver&ograve; ad Palladis &amp; &AElig;&longs;culapij Ma&shy;<lb/>chaoni&longs;que artes <expan abbr="t&atilde;">tam</expan> nece&longs;&longs;arius, quid aliud, <expan abbr="qu&atilde;">quam</expan> duplex cu&shy;<lb/>neus, &amp; totuplex vectis? </s>

<s id="id.000189">&longs;icuti forceps tantum vectis e&longs;t du&shy;<lb/>plicatus. </s>

<s id="id.000190">In&longs;trumentum Vulcani perpetu&ograve; in manibus, qu&ograve; <lb/>pruna, ferrum candens, &aelig;s, <expan abbr="argent&utilde;">argentum</expan>, aurum apprehenditur. </s></p><p type="main">

<s id="id.000191"><emph type="italics"/>Pren&longs;ant<emph.end type="italics"/> (enim vt po&euml;ta ait,) <emph type="italics"/>ver&longs;antque tenaci<emph.end type="italics"/></s></p><p type="main">

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

<s id="id.000193">At cuneus &longs;implex percu&longs;&longs;ione mallei adigitur. </s>

<s id="id.000194">Idem mul&shy;<lb/>tiplicatus &longs;ine percu&longs;&longs;ione rota cum &longs;cytalis in cochlea ita <lb/>penetrare cogitur, vt vu&aelig;, ole&aelig;, nuces, mala, pyra, c&aelig;tera&shy;<lb/>que humida pr&oelig;lis &longs;ubiecta quicquid &longs;ucci &amp; liquoris ha&shy;<lb/>bent, Domino per&longs;oluere cogantur. </s>

<s id="id.000195">Hoc beneficium ma&shy;<lb/>gni e&longs;t momenti ad vit&aelig; commoda. </s>

<s id="id.000196">At vt long&aelig;ua v&longs;que in <lb/>&longs;ecula &longs;int &longs;empiterni doctorum hominum commentarij, <lb/>&amp; con&longs;cript&aelig; cogitationes, quantum confert pr&oelig;lum ty&shy;<lb/>pographicum cochle&aelig; 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 op&egrave; vnus Archimedes Marcelli Syracu&shy;<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 h&ucirc;c Titi Liuij lubet conferre admirabile te&shy;<lb/>&longs;timonium. </s>

<s id="id.000198">Terra, inquit, marique &longs;imul c&oelig;pt&aelig; oppugnari <lb/>Syracu&longs;&aelig;, terra ab Hexapylo: mari ab Acradina. </s>

<s id="id.000199">Et habui&longs;&shy;<lb/>&longs;et tant&ograve; impetu c&oelig;pta res fortunam, ni&longs;i vnus homo Syra&shy;<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&shy;<lb/>tor c&oelig;li &longs;iderum que: mirabilior tamen inuentor ac machi&shy;<lb/>nator bellicorum <expan abbr="torm&etilde;torum">tormentorum</expan>, operumque: quibus ea qu&aelig; <lb/>ho&longs;tes ingenti mole agerent ip&longs;e perleui momento ludifi&shy;<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/>&amp; difficilia aditu, &longs;ummi&longs;&longs;a qu&aelig;dam, &amp; qu&aelig; planis vallibus <lb/>adiri po&longs;&longs;ent, vt cuique aptum vi&longs;um e&longs;t loco, ita omni ge&shy;<lb/>nere tormento rum in&longs;truxit. </s>

<s id="id.000202">Acradin&aelig; murum, qui, vt ante <lb/>dictum e&longs;t, mari alluitur ex quinqueremibus Marcellus <lb/>oppugnabat. </s>

<s id="id.000203">ex c&aelig;teris nauibus &longs;agittarij, funditore&longs;que, <lb/>&amp; 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&shy;<lb/>ro <expan abbr="teneb&atilde;t">tenebant</expan> naues. </s>

<s id="id.000205">Iunct&aelig; ali&aelig; bin&aelig; ad quinqueremes dem&shy;<lb/>ptis interioribus remis, vt latus lateri appropinquaretur: <lb/>cum exteriore ordine remorum velut naues agerentur: tur&shy;<lb/>res contabulatas, machinament&aacute; que alia quatiendis muris <lb/>portabant. </s>

<s id="id.000206">Aduer&longs;us hunc naualem apparatum Archime&shy;<lb/>des vari&aelig; magnitudinis tormenta in muris di&longs;po&longs;uit. </s>

<s id="id.000207">In eas <lb/>qu&aelig; procul erant, naues &longs;axa ingenti pondere emittebat: <lb/>propiores leuioribus, e&oacute;que magis crebris petebat telis. </s>

<s id="id.000208">Po&shy;<lb/>&longs;trem&ograve; vt &longs;ui vulnere intacti tela in ho&longs;tem ingererent: mu&shy;<lb/>rum ab imo &longs;ummum crebris cubitalibus fer&egrave; caueis ape&shy;<lb/>ruit. </s>

<s id="id.000209">per qu&aelig; caua pars &longs;agittis: pars &longs;corpionibus modicis <lb/>ex occulto petebant ho&longs;tem. </s>

<s id="id.000210">Qu&aelig; 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&shy;<lb/>lendas de&longs;uper murum eminentem ferrea manus firm&aelig; ca&shy;<lb/>then&aelig; illigata, cum iniecta pror&aelig; e&longs;&longs;et, grauique libramen&shy;<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&shy;<lb/>pim &longs;tatuebat. </s>

<s id="id.000211">Dein remi&longs;&longs;a &longs;ubit&ograve;, velut ex muro caden&shy;<lb/>tem nauim cum ingenti trepidatione nautarum ita vnd&aelig; <lb/>affligebant: vt etiam&longs;i recta recideret aliquantum aqu&aelig; ac&shy;<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&shy;<lb/>cere terra marique commeatibus ho&longs;tem placuit. </s>

<s id="id.000215">H&aelig;c Ti&shy;<lb/>tus Liuius lib.4.decad.3. </s>

<s id="id.000216">Vilium igitur, &longs;ordidorum que ho&shy;<lb/>minum ne dixerimus ea e&longs;&longs;e in&longs;trumenta, qu&aelig; vel &agrave; dijs, vel <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.029.jpg"/>&agrave; nobili&longs;&longs;imis hominibus inuenta, &amp; v&longs;urpata &longs;unt, &amp; nunc <lb/>ad v&longs;us humanos perquam nece&longs;&longs;aria hone&longs;ti&longs;&longs;imum qu&aelig;&shy;<lb/>&longs;tum, &amp; qualem agricultura dominis agricolis &longs;uppeditant. <lb/></s>

<s id="id.000217">Quanquam non eo animo &agrave; nobis h&aelig;c dicuntur, vt ad eas <lb/>artes, quarum &longs;unt in&longs;trumenta, ve&longs;tras animi, corpori&longs;que <lb/>vires &longs;uadeam conferatis: vos dico,</s></p><p type="main">

<s id="id.000218"><emph type="italics"/>Queis meliore luto finxit pr&aelig;cordia Titan:<emph.end type="italics"/></s></p><p type="main">

<s id="id.000219">atque quos ad his altiora pr&aelig;meditanda iamdudum euexit <lb/>animus, vbi tamen nihil aliud e&longs;&longs;et, quod ageretur, cur non <lb/>aliquod horum relaxamenti gratia etiam qu&aelig;ratis? </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;cr&aelig;us ille po&euml;ta,</s></p><p type="main">

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

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

<s id="id.000224">Sed eo animo h&ecedil;c pr&ecedil;&longs;ertim <expan abbr="n&utilde;c">nunc</expan> &agrave; me dicuntur, vt audacter <lb/>&amp; &longs;ine rubore aliquando ingrediamur officinas fabrorum <lb/>generis omnis, vt &amp; in&longs;trumenta, &amp; machinas quibus vtun&shy;<lb/>tur in &longs;uis operibus conficiendis primum digno&longs;camus, mi&shy;<lb/>rificas ex i&longs;ta dignotione voluptates con&longs;ecuturi, maxim&egrave; <lb/>cum eas, qu&aelig; magna vi pollent, &longs;ummo&longs;que habent v&longs;us <lb/>cognouerimus, maiores adhuc multo po&longs;tea percepturi, &longs;i <lb/>tant&aelig; efficaci&aelig; adiumenti que cau&longs;as inue&longs;tigantes inuene&shy;<lb/>rimus, quod feci&longs;&longs;e Ari&longs;totelem non puduit, qui vno hoc li&shy;<lb/>bello <foreign lang="greek">peri\ mhxanikw=n</foreign> cert&egrave; iucundo &amp; vtili edito tanta inge&shy;<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&shy;<lb/>nerit, &amp; reuocanda e&longs;&longs;e non quidem leuibus probabilium <lb/>argumentorum: &longs;ed graui&longs;&longs;imis demon&longs;trationum geome&shy;<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&shy;<lb/>per pueriliter irrideat, quod regius mathematicarum ar&shy;<lb/>tium profe&longs;&longs;or in rebus, vt putabit, vili&longs;&longs;imis philo&longs;ophari, <lb/>&amp; <foreign lang="greek">gewmetrei=n</foreign> contenderit. </s>

<s id="id.000226">Huic re&longs;pondebimus, quod ali&shy;<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, &amp; 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&shy;<lb/>mortales: &longs;ic nec i&longs;ti rerum generi dulci&longs;&longs;ima &amp; vtili&longs;&longs;ima, <lb/>&amp; <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, &amp; <expan abbr="exorn&atilde;da">exornanda</expan> pr&aelig;ter Ari&shy;<lb/>&longs;totelem multi viri pr&aelig;clari &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="c&otilde;mentarijs">commentarijs</expan> qu&aelig; vtilia e&longs;&longs;ent &aelig;di&shy;<lb/>ficationi collecta in vnum Vitruuius corpus co&euml;git: &longs;ed &amp; <lb/>pr&aelig;ter illos quorum fer&egrave; nobis <expan abbr="re&longs;t&atilde;t">re&longs;tant</expan> &longs;ola nomina Pappus, <lb/>Hero vterque, Tzetzes, Iordanus, &amp; &egrave; recentioribus Leoni&shy;<lb/>cus, Picolominus, Cardanus, Guido Vbaldus, quorum in&shy;<lb/>genia &longs;eruilia nunquam rect&egrave; quis dixerit aut putarit. </s>

<s id="id.000228">quin <lb/>&amp; Hippocratcs magnus ille medicus &agrave; &longs;e nonnulla luxatio&shy;<lb/>nibus, &amp; fracturis reponendis inuenta commoda gloriatur, <lb/>cuiu&longs;modi &longs;unt <foreign lang="greek">o)/noi, o)/niskoi\,</foreign> &amp; &longs;camnum, qu&aelig; vn&agrave; 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&shy;<lb/>nem, tractationem, commentationem nobilem, ingenuam <lb/>&amp; philo&longs;ophi non vulgariter vt multi: &longs;ed in Geometria <lb/>magnopere eruditi ingenio digni&longs;&longs;imam, tot magnorum <lb/>virorum exemplo, &longs;i, candide lector, me hortante atque his <lb/>no&longs;trorum commentariorum vigilijs, vtcunque adiuuante, <lb/>diligenter incubueris, tui te laboris, mihi crede, penitebit <lb/>numquam. </s>

<s id="id.000230">Vale. </s></p></section><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.031.jpg"/><section><p type="head">

<s id="id.000231"><emph type="italics"/>Extraict du Priuilege du Roy. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000232"><foreign lang="fr">Par grace &amp; priuilege du Roy, il e&longs;t permis &agrave; Ie&shy;<lb/>remie Perier marchant Libraire &agrave; Paris, d'impri&shy;<lb/>mer ou faire imprimer vn liure intitul&eacute;</foreign> <emph type="italics"/>Ari&longs;totelis <lb/>Mechanica, Gr&aelig;ca emendata, Latina facta, &amp; commen&shy;<lb/>tarijs illu&longs;trata, ab Henrico Monantholio Medico, &amp; Ma&shy;<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 &agrave; toutes per&longs;onnes de quelque e&longs;tat qualit&eacute; &amp; <lb/>condition qu'ils &longs;oyent, en quelques lieux &amp; villes de <lb/>ce Royaume, de ne le faire imprimer ou faire faire im&shy;<lb/>primer &agrave; peine des articles po&longs;&eacute;s &agrave; l'original du pre&shy;<lb/>&longs;ent priuilege, iu&longs;ques au temps &amp; terme de dix ans, <lb/>finis &amp; accomplis &agrave; conter du iour &amp; datte de la pre&shy;<lb/>&longs;ante impre&longs;&longs;ion, nonob&longs;tant toutes oppo&longs;itions ou <lb/>appellations quelconques, &amp; &longs;ans preiudice d'icelle, <lb/>car tel e&longs;t le plai&longs;ir de &longs;a Mage&longs;t&eacute;. </foreign></s>

<s id="id.000234"><foreign lang="fr">Donn&eacute; &agrave; Paris le <lb/>23. de Decembre 1598. </foreign></s></p><p type="main">

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

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

<s id="id.000237">INDEX MEMORABILIVM <lb/>IN MECHANICIS ARISTOTELIS <lb/>&amp; eorum Commentarijs. <lb/><arrow.to.target n="table1"/></s></p><table><table.target id="table1"/><row><cell><emph type="italics"/>A<emph.end type="italics"/></cell><cell/></row><row><cell><emph type="italics"/><foreign lang="greek">*abussos</foreign> unde. pag. <emph.end type="italics"/></cell><cell>209</cell></row><row><cell><emph type="italics"/>Ab&longs;is pro circunferen&shy;tia rot&aelig;. <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;e&szlig;ione  tant&ugrave;m<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"/>Agricultur&aelig; nece&longs;&longs;aria. <emph.end type="italics"/></cell><cell>14</cell></row><row><cell><emph type="italics"/>&AElig;des rotunda mirifica. <emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>&AElig;dificium durabile rect&agrave; in&longs;i&longs;tit. <emph.end type="italics"/></cell><cell>196</cell></row><row><cell><emph type="italics"/>&AElig;olus primus v&longs;us velis. <emph.end type="italics"/></cell><cell>92</cell></row><row><cell><emph type="italics"/>&AElig;quale e&longs;t cau&longs;a quietis. <emph.end type="italics"/></cell><cell>193.196</cell></row><row><cell><emph type="italics"/>&AElig;quilibrium 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 &aelig;qualitatis,   ide&oacute;que 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"/>Antemn&aelig; 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 &amp; arte. <emph.end type="italics"/></cell><cell>8. 12</cell></row><row><cell><emph type="italics"/>Arbores, &amp; plant&aelig; in&longs;i&longs;lunt plane terr&aelig;   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"/>Architectur&aelig; 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 &agrave; Nonio. <emph.end type="italics"/></cell><cell>84</cell></row><row><cell><emph type="italics"/>Ars &longs;lectit naturam, &amp; 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, &amp; natur&aelig; differentia. <emph.end type="italics"/></cell><cell>6</cell></row><row><cell><emph type="italics"/>Artium diui&longs;io in liberales, &amp; &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 magn&aelig;. <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 architectonic&aelig;. <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, &amp; 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 tut&ograve; a&longs;cendunt, pericu-los&egrave; de&longs;cendunt. <emph.end type="italics"/></cell><cell>199</cell></row><row><cell><emph type="italics"/>B. Feratinus Amerinus <expan abbr="c&atilde;cellari&aelig;">cancellari&aelig;</expan> Apo-&longs;tolic&aelig; regens con&longs;ecrat, &amp; 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 &aelig;qualem peripheri&aelig; 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"/>Bo&uuml;m 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"/>Calli&aelig; 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 &agrave; Scaligero. <emph.end type="italics"/></cell><cell>145</cell></row><row><cell><emph type="italics"/>Cardanus ob&longs;cur&egrave; &amp; imper&longs;ect&egrave;: inge-nios&egrave; 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, &amp; &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 D&aelig;dalus. <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,   qu&aelig;&longs;unt in machinis motricibus. <emph.end type="italics"/></cell><cell>15</cell></row><row><cell><emph type="italics"/>Circulus admirabili&szlig;imus. <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, &amp; 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="c&otilde;tingit">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 &aelig;qualem   orbitam reuoluitur &amp; contra. <emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Circuli <expan abbr="c&otilde;centrici">concentrici</expan> in&aelig;quales iuncti &aelig;qua-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   &amp; <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 Acchit&aelig; <expan abbr="n&otilde;">non</expan> e&longs;t fabula. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Contraria qu&aelig; &longs;int ver&egrave;. <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 &amp; 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"/>Cochle&aelig; 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"/>Cochle&aelig; 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 magn&aelig; moles diuiduntur. <emph.end type="italics"/></cell><cell>125</cell></row><row><cell><emph type="italics"/>Croc&aelig; Ari&longs;toteliquid. <emph.end type="italics"/></cell><cell>123</cell></row><row><cell><emph type="italics"/>Croc&aelig; rotund&aelig;. <emph.end type="italics"/></cell><cell>122.123</cell></row><row><cell><emph type="italics"/>Cubus &longs;tabili&szlig;ima 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"/>D&aelig;dali &longs;tatu&aelig;liber&aelig;, &amp; ligat&aelig;. <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 &agrave; 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, &amp; Sph&aelig;r&aelig; 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 qu&aelig;ratio. <emph.end type="italics"/></cell><cell>32</cell></row><row><cell><emph type="italics"/>Dies impo&longs;it&aelig; 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 Fontan&aelig; triumphus. <emph.end type="italics"/></cell><cell>142</cell></row><row><cell><emph type="italics"/>Domus integra &agrave; &longs;undamentis &longs;ublata,   &amp; ali&ograve; 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 qu&aelig;. <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"/>Ergat&aelig;, &amp; &longs;uccul&aelig; 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 qu&aelig;. <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 c&aelig;te-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, &amp; natura-les impetus. <emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Figura decubitus humida, &longs;eu medi&aelig;   qu&aelig;. <emph.end type="italics"/></cell><cell>176</cell></row><row><cell><emph type="italics"/>Forceps, &amp; forfex quid. <emph.end type="italics"/></cell><cell>152</cell></row><row><cell><emph type="italics"/>Fortuna in&longs;i&longs;tit Sphar&aelig;. <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 Ph&aelig;nicuno. <emph.end type="italics"/></cell><cell>116</cell></row><row><cell><emph type="italics"/>Fund&aelig; v&longs;us. <emph.end type="italics"/></cell><cell>116.117</cell></row><row><cell><emph type="italics"/>Fund&aelig; 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 &amp; plumbum. <emph.end type="italics"/></cell><cell>117</cell></row><row><cell><emph type="italics"/>Fu&longs;tis ad genu fractus non l&aelig;dit. <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 &amp; aqu&aelig; 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 &amp; eius partes. <emph.end type="italics"/></cell><cell>73</cell></row><row><cell><emph type="italics"/>Gubernaculi &amp; 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;t&aelig; 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   Geometri&aelig;,<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, &amp; progre&longs;sio, vs   fiat. <emph.end type="italics"/></cell><cell>198</cell></row><row><cell><emph type="italics"/>Homo <expan abbr="n&otilde;">non</expan> &longs;tatrectus, vt <expan abbr="c&aelig;l&utilde;">c&aelig;lum</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 &amp; 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   &aelig;qualiter premuntur. <emph.end type="italics"/></cell><cell>190.191</cell></row><row><cell><emph type="italics"/>Horologia nostritemporis veterum cle-p&longs;ydras, &amp; gnemones antecellunt. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Plorologium Argentorati <expan abbr="magni&longs;ic&utilde;">magnificum</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 &amp; 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"/>Libr&aelig; finis. <emph.end type="italics"/></cell><cell>4</cell></row><row><cell><emph type="italics"/>Libr&aelig;partes. <emph.end type="italics"/></cell><cell>45.46</cell></row><row><cell><emph type="italics"/>Libr&aelig;fallaci&aelig;. <emph.end type="italics"/></cell><cell>46.47</cell></row><row><cell><emph type="italics"/>Libr&aelig; 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="p&otilde;dere">pondere</expan> facilius mouetur. <emph.end type="italics"/></cell><cell>112</cell></row><row><cell><emph type="italics"/>Librilis brachia vt <expan abbr="mane&atilde;t">maneant</expan>, aut redeant   ad <expan abbr="&aelig;quilibri&utilde;">&aelig;quilibrium</expan> &longs;ublatis <expan abbr="p&otilde;derilus">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="fer&utilde;-tur">ferun-tur</expan> bumere, quam &agrave; medio. <emph.end type="italics"/></cell><cell>183.184</cell></row><row><cell><emph type="italics"/>Lignum vt &egrave; genu facilius <expan abbr="fr&atilde;gatur">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="qu&atilde;">quam</expan> brcue, vt &longs;it <expan abbr="p&otilde;dere">pondere</expan> &aelig;quale. <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 qu&aelig;dam per &longs;e, qu&aelig;dam-non per&longs;e mouentur. <emph.end type="italics"/></cell><cell>10</cell></row><row><cell><emph type="italics"/>Machin&aelig; valenti&szlig;im&aelig; tres ex &longs;ententia   Hippocratis. <emph.end type="italics"/></cell><cell>119</cell></row><row><cell><emph type="italics"/>Machinarum pluribus, &amp; diuer&longs;arum   compo&longs;itio ad&aelig;quat vnam, qu&aelig; tanta,   quanta opus e&longs;&longs;et fierinon pote&longs;t, pro-pter defectum materi&aelig;. <emph.end type="italics"/></cell><cell>138.139</cell></row><row><cell><emph type="italics"/>Machin&aelig; ad &aelig;dificia, &amp; 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 qu&aelig;. <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="l&otilde;gius">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 &amp; <expan abbr="Fr&atilde;ci&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 qu&aelig; 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"/>Mechanic&aelig; artes vnde dict&aelig;. <emph.end type="italics"/></cell><cell>2.3</cell></row><row><cell><emph type="italics"/>Mechanice pars e&longs;t philo&longs;ophi&aelig;. <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 aggre&szlig;ionem 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 c&aelig;teras. <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 qu&ograve; vergit facile moue&shy;<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;&aelig;pe magnam vim obti-net. <emph.end type="italics"/></cell><cell>129</cell></row><row><cell><emph type="italics"/>Motus fit in tempore, &amp; &longs;ucce&szlig;iu&egrave;. <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="rect&atilde;">rectam</expan> <expan abbr="line&atilde;">lineam</expan>. <emph.end type="italics"/></cell><cell>30</cell></row><row><cell><emph type="italics"/>Motum duabus lationibus rationem non   habentibus <expan abbr="n&otilde;">non</expan> fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">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 &agrave; quibus pen-deat. <emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Mulier parua non e&longs;t pulchr&aelig;. <emph.end type="italics"/></cell><cell>19</cell></row><row><cell><emph type="italics"/>Mundus nutans non vere dici de terra &agrave;   po&euml;ta. <emph.end type="italics"/></cell><cell>104</cell></row><row><cell><emph type="italics"/>Mu&longs;culus vecti comparatus &agrave; 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, &amp; 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, &amp; 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, &amp; partes. <emph.end type="italics"/></cell><cell>62</cell></row><row><cell><emph type="italics"/>Nauis Ptolemaic&aelig; 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 actuari&aelig; promotio. <emph.end type="italics"/></cell><cell>69</cell></row><row><cell><emph type="italics"/>Nauis velocit as &agrave; 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 &egrave; plumbo tenui &longs;upernatat   aqu&aelig;. <emph.end type="italics"/></cell><cell>164</cell></row><row><cell><emph type="italics"/>Naut&aelig; 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 &agrave; 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="Nucifr&atilde;gibuli">Nucifrangibuli</expan> &amp; 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 peripheri&aelig; 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 &amp; <expan abbr="qu&atilde;tus">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, &amp; 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 qu&aelig; ma-chin&aelig;, &amp; quot adhibit&aelig;. <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, &amp; &agrave; quibus perfect&aelig;. <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 Ichnographi&aelig;. <emph.end type="italics"/></cell><cell>143</cell></row><row><cell><emph type="italics"/>de Obeli&longs;co &amp; Xy&longs;to V. Summ. Pont. &amp;   cruce Gulielmi Blanci <expan abbr="epigr&atilde;ma">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 vol&aelig; manus impo&longs;itum   frangitur manu ill&aelig;&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   c&aelig;lum. <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"/>Percu&szlig;io 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"/>Percu&szlig;io &agrave; quibus fit maior. <emph.end type="italics"/></cell><cell>128</cell></row><row><cell><emph type="italics"/>Percu&szlig;ionis validiores cau&longs;&aelig;. <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 &agrave; peripherijs in &longs;emi-diametros circulorum in&aelig;qualium   &aelig;quales auferunt &longs;egmenta &longs;emidia-metrorum in&aelig;qualia, quorum maius   e&longs;t quod &egrave; minori aufertur. <emph.end type="italics"/></cell><cell>40</cell></row><row><cell><emph type="italics"/>Peripheri&aelig; maiores &agrave; punctis &agrave; 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 a&euml;re 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"/>&amp; canere quid. <emph.end type="italics"/></cell><cell>95</cell></row><row><cell><foreign lang="greek">*po/des, &amp; 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 Luteti&aelig; ab Henrico 111. inchoatus   ab Henrico 1111. perficietur. <emph.end type="italics"/></cell><cell>120</cell></row><row><cell><emph type="italics"/>Pre&szlig;io 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"/>Progre&szlig;io 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 &agrave; 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 &amp; C. L&aelig;lius colligentes cro-cas qu&aelig; 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"/>Rectiline&aelig; figur&aelig;, &amp; 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 differenti&aelig;. <emph.end type="italics"/></cell><cell>64</cell></row><row><cell><emph type="italics"/>Remiges me&longs;onei maxim&egrave; 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 &aelig;qualem <expan abbr="rect&atilde;">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"/>Rot&aelig; bin&aelig; 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"/>Rot&aelig; curruum maiores commodiores ad   facilitatem &amp; 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, &amp; quotuplex. <emph.end type="italics"/></cell><cell>111.114</cell></row><row><cell><emph type="italics"/>Scytal&aelig; 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,   &amp; nequaquam in vnarecta. <emph.end type="italics"/></cell><cell>193</cell></row><row><cell><emph type="italics"/>Sedentari&aelig; artes vtuntur &longs;e&szlig;ione &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"/>Se&szlig;io propri&egrave; dista &amp; lat&egrave;<emph.end type="italics"/></cell><cell>197</cell></row><row><cell><emph type="italics"/>Se&szlig;io 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"/>Sph&aelig;ra quale corpus. <emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra corpus e&longs;t mobili&szlig;imum &amp; mo-uenti&szlig;imum. <emph.end type="italics"/></cell><cell>16</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra contingit planum in puncto. <emph.end type="italics"/></cell><cell>101</cell></row><row><cell><emph type="italics"/>Sph&aelig;ra Archimedis per &longs;e mobilis non   e&longs;t fabula. <emph.end type="italics"/></cell><cell>26</cell></row><row><cell><emph type="italics"/>Sph&aelig;ratop&aelig;ia pars e&longs;t mechanices. <emph.end type="italics"/></cell><cell>11</cell></row><row><cell><emph type="italics"/>Stater&aelig; partes. <emph.end type="italics"/></cell><cell>147</cell></row><row><cell><emph type="italics"/>Stater&aelig; 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 &aelig; &longs;unt libr&aelig;. <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"/>Stater&aelig; paruo &aelig;quipondio magna ponde-ra expendunt. <emph.end type="italics"/></cell><cell>146.147.148</cell></row><row><cell><emph type="italics"/>Stater&aelig; dimidium e&longs;t an&longs;a. <emph.end type="italics"/></cell><cell>148</cell></row><row><cell><emph type="italics"/>Per Stateram ponderationis fact&aelig; 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 terr&aelig;. <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 &amp; &longs;e&szlig;io 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"/>qu&aelig;. <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 &egrave; 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 thor&aelig;ce   &amp; 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, &amp;   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 &agrave; Pythagoreis, &amp;   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 &agrave; 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"/>Trochle&aelig; du&aelig; legitim&egrave; compofit&aelig; 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 machin&aelig;   mult&aelig; &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 aqu&aelig; 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 &agrave; nautis vitentar. <emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>Vortices inter Roe&longs;t &amp; Loffoet. <emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>in Vorticem vt &longs;entiunt naut&aelig; &longs;e impe&shy;<gap/>gi&longs;&longs;e. <emph.end type="italics"/></cell><cell>210</cell></row><row><cell><emph type="italics"/>difficile &longs;e liberare &agrave; 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> qu&ograve; 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 &amp; *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><p type="head">

<s id="id.000238">FINIS. </s><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"/></p></section></front><body><chap><p type="head">

<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></p><p type="main">

<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></p><p type="head">

<s id="id.000242"><margin.target id="marg1"/>Pro <foreign lang="greek">mhxanh\,</foreign><lb/>lege <foreign lang="greek">mhxani&shy;<lb/>kh/. </foreign></s></p><p type="head">

<s id="id.000243"><emph type="italics"/>Quid e&longs;t Mechanice, &amp; de circulo in quo admirabilium, <lb/>qu&aelig; &longs;unt in Mechanicis, cau&longs;a continetur. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000244"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000245">MIRA &longs;unt in his, qu&aelig; <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="natur&atilde;">naturam</expan> <expan abbr="eue-ni&utilde;t">eue&shy;<lb/>niunt</expan>, ea: <expan abbr="quor&utilde;">quorum</expan> cau&longs;a igno&shy;<lb/>ratur, &amp; in his qu&aelig; pr&aelig;ter <lb/>naturam, ea, <expan abbr="qu&ecedil;cunq;">qu&ecedil;cunque</expan> arte <lb/>facta hominibus <expan abbr="c&otilde;ferunt">conferunt</expan>. </s></p><p type="head">

<s id="id.000246">COMMENTARIVS. </s></p><p type="main">

<s id="id.000247"><emph type="italics"/>Cardanvs librum hunc Ari&longs;totelis peripate&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg2"/><lb/><emph type="italics"/>ticorum principis e&longs;&longs;e non arbitratur, propter man&shy;<lb/>cam, &amp; paulo negligentiorem motuum rotundo&shy;<lb/>rum in eo po&longs;itam diui&longs;ionem. </s>

<s id="id.000248">Franci&longs;cus Patri&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg3"/><lb/><emph type="italics"/>cius vbi in omnes Ari&longs;totelis libros diligenter in&shy;<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&shy;<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, &amp; exemplis confirmarit: ob id tamen hunc Ari&longs;toteli <lb/>detrahendum e&longs;&longs;e, non e&longs;t nece&longs;&longs;e. </s>

<s id="id.000250">Quid ita? </s>

<s id="id.000251">Ip&longs;emet Patricius fate&shy;<lb/>tur hunc<emph.end type="italics"/> <foreign lang="greek">tw=n mhxanikw=n</foreign> <emph type="italics"/>librum doctum e&longs;&longs;e, &amp; elegantem: addo <lb/>&amp; &longs;ubtilem, &amp; ab Ari&longs;totelis <expan abbr="ver&utilde;">verum</expan> in vnaquaque re, &longs;implex. </s>

<s id="id.000252">&longs;yn&shy;<lb/>cerumque exquirentis ingenio minime abhorrentem, vt ip&longs;um, &amp; <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="c&otilde;feratur">conferatur</expan>, qu&aelig; fuit familiaris Ari&shy;<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 La&euml;rtius inter Ari&longs;totelis monumenta<emph.end type="italics"/> <foreign lang="greek">mhxani&shy;<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 &amp; Guidus Vbaldus &longs;&aelig;pe velut ab Ari&longs;totele citant. </s>

<s id="id.000256">No&shy;<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&shy;<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 po&szlig;it. <emph.end type="italics"/></s></p><p type="margin">

<s id="id.000260"><margin.target id="marg2"/>Lib. de pro&shy;<lb/>port. </s></p><p type="margin">

<s id="id.000261"><margin.target id="marg3"/>Tom.I.li.3. <lb/>Di&longs;cu&longs;&longs;io&shy;<lb/>num peri&shy;<lb/>patetic. </s></p><p type="main">

<s id="id.000262">Mechanica] <emph type="italics"/>Huius libri du&aelig; &longs;unt partes. </s>

<s id="id.000263">prior generalis e&longs;t <lb/>in explicatione cau&longs;arum &amp; principiorum, quibus machin&aelig; in mo&shy;<lb/>uendo magnas, &amp; admirabiles vires habent: po&longs;terior &longs;pecialis e&longs;t <lb/>in explicatione 25. qu&aelig;stionum de quarundam machinarum viribus <lb/>&amp; effectis. </s>

<s id="id.000264">H&aelig;c 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>&amp; <foreign lang="greek">*mhxanh\ a)po\ tou= <lb/>mh/kous kai\ a)/nein,</foreign> <emph type="italics"/>id e&longs;t long&egrave; vel mult&ugrave;m a&longs;cendere, pertingere, pene&shy;<lb/>trare, vt e&longs;t apud Platonem in Cratylo, vnde non qu&aelig;libet artifi&shy;<lb/>cia protrita &amp; vulgaria Mechanica dicenda &longs;unt, &longs;ed ea tantum <lb/>qu&aelig; vtiliter &amp; iucund&egrave; &longs;uccurrunt, &amp; adminiculantur difficul&shy;<lb/>tatibus qu&aelig; 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 &agrave; Vitruuio, continens ex <lb/>materia coniunctio, qu&aelig; maximas habet, ad onerum motus virtu&shy;<lb/>tes: &amp; &agrave; Plinio in&longs;trumentum, quo moles aliqua facile, quocumque <lb/>volueris impelli pote&longs;t. </s>

<s id="id.000267">Igitur tum h&aelig;c in&longs;trumenta &amp; machin&aelig;: <lb/>tum doctrina, qu&aelig; virium, quibus h&aelig;c pollent, rationem docet, &amp; <lb/>explicat, rect&egrave; Mechanica in&longs;cribuntur. </s>

<s id="id.000268">Sed vereor, ne h&aelig;c libri <lb/>in&longs;criptio, ex vulgari artium diui&longs;ione in liberales &amp; mechanicas, <lb/>quid &longs;ordidi &longs;ubolens multis, ip&longs;os ab huius libri lectione deterruerit <lb/>&amp; deterreat. </s>

<s id="id.000269">At qu&aelig;cumque, eluenda e&longs;t macula. </s>

<s id="id.000270">Manauit enim &agrave;<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, qu&aelig; in &longs;ola con&shy;<lb/>templatione ver&longs;arentur, &amp; contemplantis duntaxat ingenium <lb/>acuerent, atque perficerent: viles autem eas putauere, qu&aelig; ocium fu&shy;<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, qu&aelig; ita corporis adminiculo exercen&shy;<lb/>tur, vt animi &longs;tudium non multum requirant, cum Gr&aelig;cis appel&shy;<lb/>la&longs;&longs;ent, non<emph.end type="italics"/> <foreign lang="greek">mhxanika\s,</foreign> <emph type="italics"/>(neque enim h&icirc;c 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&shy;<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&shy;<lb/>&longs;eri debet, immo omnis po&longs;&longs;e&longs;&longs;orem &longs;uum vel meliorem vel vtilio&shy;<lb/>rem &longs;ibi, vel &longs;u&aelig; ciuitati reddit: at inter &longs;e comparat&aelig; ali&aelig; aliis pr&aelig;&shy;<lb/>&longs;tantiores existimat&aelig; &longs;unt. </s>

<s id="id.000274">vnde nata e&longs;t h&aelig;c vulgaris artium diui&shy;<lb/>&longs;io, vt ali&aelig; liberales e&longs;&longs;ent: ali&aelig; mechanic&aelig;. </s>

<s id="id.000275">qu&aelig; his duobus ver&longs;ibus <lb/>exprimuntur. <emph.end type="italics"/></s></p>

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

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

<p type="main"><s><emph type="italics"/>horum priore &longs;ignificantur Grammatica, Rhetorica, Dialectica, <lb/>Arithmetica, Mu&longs;ica, Geometria, A&longs;trologia, liberales ob id di&shy;<lb/>ct&aelig;, &longs;iue ingenu&aelig;, quod illis excolatur animus, qui libera &amp; ingenua <lb/>pars e&longs;t hominis: Sed &amp; pueriles, quia his ingenui pueri primis an&shy;<lb/>nis, &longs;tatim imbiberentur tanquam pr&aelig;uiis, &amp; ad cape&longs;&longs;endas &longs;cien&shy;<lb/>tias &amp; magnas artes nece&longs;&longs;ariis. </s></p>

<p type="main"><s id="id.000278">Scienti&aelig; autem erant Philo&longs;ophia <lb/>moralis, Phy&longs;ica, Medicina, Iuri&longs;prudentia, Theologia. </s>

<s id="id.000279">Poste&shy;<lb/>riore &longs;ignificatur Agricultura, Venatoria, Militaris, Fabrilis, <lb/>Chirurgia, Lanificium, Nautica. </s>

<s id="id.000280">In quarum &longs;ingulis ali&aelig; &longs;unt im&shy;<lb/>perantes, qu&aelig; &amp; architectonic&aelig; dicuntur: ali&aelig; mini&longs;trantes. </s>

<s id="id.000281">Impe&shy;<lb/>rantes, habere debent pr&aelig;uias illas &longs;eptem liberales ante dictas, vt <lb/>videre e&longs;t apud Vitruuium de &longs;uo architecto, &amp; in no&longs;tro com&shy;<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, &amp; eadem ratione <lb/>in reliquis: ita vt, qui imperantibus i&longs;tis artibus pr&aelig;diti fuerint, in&shy;<lb/>ter homines pr&aelig;&longs;tanti&szlig;imi habiti &longs;emper &longs;int, &amp; &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"/>pr&aelig;&longs;tantiora, aut vtiliora, aut certiora exi&longs;tant. </s>

<s id="id.000282">Agricultur&aelig; enim <lb/>opus, quod alimenta &amp; medicamenta hominibus &longs;uppeditat, nece&szlig;i&shy;<lb/>tate vincit c&aelig;tera: victoria, qu&aelig; rebelles &amp; hostes &longs;ubijcit, proprios <lb/>ciues con&longs;eruat, vtilitate &longs;upereminet: Medicina nobilitate &longs;ubiecti, <lb/>&amp; pr&aelig;stantia boni nempe &longs;anitatis, quam procurat, eximia e&longs;t: Cer&shy;<lb/>titudine operis &amp; operationis Fabrilis anteponenda omnibus: vt <lb/>Lanificium, quod ad opes hone&longs;te parandas: &amp; Nautica propter <lb/>mercaturam faciunt omnium maxim&egrave;. </s>

<s id="id.000283">Imperantes etiam hoc ha&shy;<lb/>bent, quod eorum, qu&aelig; efficiunt, rationes teneant: Iuueniles corporis <lb/>vires non requirant: vit&aelig; po&longs;&longs;e&longs;&longs;oris &longs;ui &longs;int &aelig;quales. </s>

<s id="id.000284">Mini&longs;trantes <lb/>non item: &longs;ed v&longs;u potius &amp; con&longs;uetudine di&longs;cantur &amp; exerceantur: <lb/>Iuueniles vires po&longs;tulent, &amp; po&longs;&longs;e&longs;&longs;orem &longs;uum in &longs;enectute de&longs;e&shy;<lb/>rant. </s>

<s id="id.000285">Ex ijs aliis ali&aelig; materias apparant: ali&aelig; in&longs;trumenta fabrican&shy;<lb/>tur. </s>

<s id="id.000286">In&longs;trumentorum omnium ratio con&longs;i&longs;tit in certa quadam figu&shy;<lb/>ra, qua qu&aelig; eam habent, ad v&longs;um commodiora &longs;unt. </s>

<s id="id.000287">Cur autem h&aelig; <lb/>figur&aelig; apti&szlig;im&aelig; &longs;int nulla <expan abbr="mini&longs;tr&atilde;tium">mini&longs;trantium</expan> rationem inue&longs;tigat: Satis <lb/>habent, &longs;i modum fabricandi &amp; vtendi tenuerint. </s>

<s id="id.000288">harum tamen <lb/>aliquot, cum cert&aelig; rationes e&longs;&longs;ent &longs;ubtiles, &amp; &agrave; fontibus Geometri&aelig; <lb/>petit&aelig;, ip&longs;as hoc libello ver&egrave; aureo, &amp; intelligentibus periucundo <lb/>Ari&longs;toteles partim generaliter, &amp; ex &longs;uis principiis, partim per ali&shy;<lb/>quot <expan abbr="ex&etilde;pla">exempla</expan>, &agrave; rebus multis vari&iacute;&longs;que petita explicuit. </s>

<s id="id.000289">Ob quod liber <lb/>rect&egrave; in&longs;cribitur<emph.end type="italics"/> <foreign lang="greek">mhxa/nika,</foreign> <emph type="italics"/>quia hic explicet cau&longs;as virium in&shy;<lb/>&longs;trumentorum ad Mechanicas artes pr&aelig;dictas pertinentium. </s>

<s id="id.000290">cur <lb/>&longs;cilicet ea, quam habent, pr&aelig;dita figura v&longs;ui, &amp; effectui commodio&shy;<lb/>ra exi&longs;tant. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000291">Quid e&longs;t Mechan.] <emph type="italics"/>Summa e&longs;t eorum, qu&aelig; hoc primo capite <lb/>explicantur, &longs;ed imperfectior: quia non, quid &longs;it mechanice, &longs;ed <lb/>quod &longs;it ars admirabilis, &amp; quod circulus omnium, qu&aelig; fiunt in <lb/>Mechanica, admirabilium e&longs;&longs;e cau&longs;a o&longs;tenditur: pr&aelig;ter qu&aelig; etiam <lb/>docetur problemata mechanica partim e&longs;&longs;e Phy&longs;ica, partim e&longs;&longs;e Ma&shy;<lb/>thematica. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000292">Mira &longs;unt in his:] <emph type="italics"/>Similitudo h&icirc;c qu&aelig;dam 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&shy;<lb/>bus naturalibus mir&aelig; &longs;unt ill&aelig;, quarum cau&longs;a ignoratur: ita &amp; in <lb/>his, qu&aelig; pr&aelig;ter naturam arte fact&aelig; hominibus conferunt, &longs;i &amp; ea&shy;<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 &amp; 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;&shy;<lb/>que po&longs;itum, qui ne&longs;ciat, &longs;cire autem cupiat, admirationis e&longs;&longs;e capa&shy;<lb/>cem, vnde non &longs;unt &longs;impliciter intelligendi hi ver&longs;us Horatiani,<emph.end type="italics"/></s></p><p type="main">

<s id="id.000295">Nil admirari prop&egrave; res e&longs;t vna Numici,</s></p><p type="main">

<s id="id.000296">Sol&aacute;que qu&aelig; po&longs;&longs;it facere &amp; &longs;eruare beatum. </s></p><p type="main">

<s id="id.000297"><emph type="italics"/>Nec enim h&aelig;c 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&shy;<lb/>ta illud<emph.end type="italics"/></s></p><p type="main">

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

<s id="id.000299"><emph type="italics"/>Ab hac admirandi facultate Ari&longs;toteles <expan abbr="principi&utilde;">principium</expan> Philo&longs;ophi&aelig; re&shy;<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, &amp; <expan abbr="dubit&atilde;s">dubitans</expan> co&shy;<lb/>natur dubitationibus &longs;uis &longs;uccurrere. </s>

<s id="id.000301">Homo natura fugiens e&longs;t igno&shy;<lb/>ranti&aelig;. </s>

<s id="id.000302"><expan abbr="Itaq;">Itaque</expan> prim&ograve; &egrave; dubitatis faciliora inqui &longs;iuit, deinde paulatim <lb/>vlterius procedens <expan abbr="eti&atilde;">etiam</expan> maiora, vt de affectionibus Lun&aelig;, &amp; ijs qu&aelig; <lb/>circa Solem &amp; &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 &amp; ingen&shy;<lb/>tia, vt vulgus, &longs;ed etiam frequentia &amp; exigua, &longs;i cau&longs;as latentes ha&shy;<lb/>beant, admiratur, &amp; quidem cum voluptate: in quo etiam di&longs;&longs;entit &agrave; <lb/>vulg&ograve;, qui qu&aelig; admiratur, &longs;&aelig;pe horret, vt Eclip&longs;es Solis &amp; Lun&aelig;,<emph.end type="italics"/><lb/><arrow.to.target n="marg6"/><lb/><emph type="italics"/>quod de Archelao rege Seneca memorat rerum natur&aelig; ade&ograve; ignaro, <lb/>vt quo die Solis defectio fuit, regiam clau&longs;erit, &amp; filium, quod in <lb/>luctu &agrave; rebus aduer&longs;is moris e&longs;t, totunderit. </s>

<s id="id.000303">quam contra Thales <lb/>rerum natur&aelig; gnarus in aperto fixis in peluim oculis magna cum <lb/>animi l&aelig;titia intuitus e&longs;&longs;et. <emph.end type="italics"/></s></p><p type="margin">


<s id="id.000304"><margin.target id="marg5"/>Cap. 2. lib. 2. <lb/>Metaph. </s>

<s><margin.target id="marg6"/>Cap. 6. lib. 5. <lb/>De benefic. </s></p><p type="main">

<s id="id.000305">Quorum cau&longs;a ign.] <emph type="italics"/>In rebus naturalibus cau&longs;arum omne <lb/>genus ine&longs;t, materia, efficiens, forma, finis. </s>

<s id="id.000306">Et in &longs;ingularium conti&shy;<lb/>nentium &amp; proximarum inuentione, &amp; earum ad primam redu&shy;<lb/>ctione Philo&longs;ophia con&longs;i&longs;tit. </s>

<s id="id.000307">Sunt autem eiu&longs;modi, vt ex his ali&aelig; <lb/>not&aelig; iam &longs;int, ali&aelig; adhuc ignot&aelig; per&longs;i&longs;tant, vnde numquam &longs;tudio&shy;<lb/>&longs;is deerit admirandi, &amp; propterea philo&longs;ophandi occa&longs;io: difficiles <lb/>tantum, &longs;alebro&longs;o&longs;que aditus habens, &longs;iquidem<emph.end type="italics"/></s></p><p type="main">

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

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

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

<s id="id.000311"><emph type="italics"/>abiecti cert&egrave; ac be&longs;tias imitantis hominis e&longs;t, qu&aelig; ne&longs;ciat, non admi&shy;<lb/>rari, &amp; &longs;i curis, negoti&iacute;&longs;que nece&longs;&longs;arijs vacuus e&longs;t, non inquirere, <lb/>&amp; venerari. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000312"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

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

<s id="id.000314"><expan abbr="Si-quid&etilde;">Si&shy;<lb/>quidem</expan> natura <expan abbr="eod&etilde;">eodem</expan> modo <lb/><expan abbr="s&etilde;per">semper</expan> operatur &amp; &longs;implici&shy;<lb/>ter: at <expan abbr="ali&utilde;">alium</expan> <expan abbr="atq;">atque</expan> alium ple&shy;<lb/>rumque po&longs;tulat vtilitas. <lb/></s>

<s id="id.000315"><expan abbr="Qu&atilde;do">Quando</expan> igitur conuenit fa&shy;<lb/>cere aliquid pr&ecedil;ter <expan abbr="natur&atilde;">naturam</expan>, <lb/><expan abbr="t&utilde;">tum</expan> difficultas h&aelig;&longs;itationem <lb/>adfert, &amp; arte opus e&longs;t. </s></p><p type="head">

<s id="id.000316">COMMENTARIVS. </s></p><p type="main">

<s id="id.000317">In multis enim.] <emph type="italics"/>Secunda ratio e&longs;t ad probandum in arte fa&shy;<lb/>ctis quibu&longs;dam aliquid mirum e&longs;&longs;e, deprompta e&longs;t ex effectis Na&shy;<lb/>tur&aelig; contrarijs, &longs;altem repugnantibus, &longs;yllogi&longs;mus &longs;ic in&longs;titutus <lb/>rem ip&longs;am illu&longs;trabit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000318"><emph type="italics"/>Naturam ali&ograve; flectere &amp; adducere, quam vergat, mirum e&longs;t, <lb/>quia difficultas ex renixu natur&aelig; dubitationem parit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000319"><emph type="italics"/>In his qu&aelig; arte fiunt ali&ograve; natura flectitur &amp; adducitur, quam <lb/>vergat. </s>

<s id="id.000320">Natura enim eodem modo &longs;emper agit, v&longs;us autem re&shy;<lb/>rum humanarum varios modos po&longs;tulat. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000321"><emph type="italics"/>Igitur in arte factis aliquid mirum e&longs;t. </s>

<s id="id.000322">Pro a&longs;&longs;umptione a&longs;&longs;um&shy;<lb/>ptionis confirmatio est ex effectis, &amp; effectorum modo natur&aelig; &amp; <lb/>artis. </s>

<s id="id.000323">Natura enim in multis inclinat ali&ograve;, quam vtilitas hominum <lb/>po&longs;tulat: Natura item vno modo &longs;emper operatur: contra Ars vti&shy;<lb/>litatem hominem &longs;emper &longs;pectat, &amp; varios operandi modos pro&shy;<lb/>&longs;equitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000324">Siquidem Natura.] <emph type="italics"/>Naturalia principium in &longs;e habent &longs;ui <lb/>motus, quo &longs;i &longs;implicia &longs;unt, ad vnum &amp; vno modo &longs;impliciter <lb/>mouentur: &longs;i commixta pr&aelig;dominantis vnius motum &longs;equuntur, <lb/>&longs;icque ad vnum feruntur. </s>

<s id="id.000325">H&aelig;c &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 &amp; de generat. &amp; corrupt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000327">At alium atque alium.] <emph type="italics"/>Hominum vtilitas tum ad e&longs;&longs;e tum <lb/>ad bene e&longs;&longs;e multa vari&aacute;que mult&ograve; aliter quam natura pr&aelig;ferat, pe&shy;<lb/>tit &longs;ibi fieri, vt <expan abbr="alim&etilde;ta">alimenta</expan> &amp; copio&longs;iora, &amp; aliter apparata: <expan abbr="qu&atilde;">quam</expan> terra, <lb/>a&euml;r, &amp; 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/>&amp; ornat: vt &aelig;dificia, qu&aelig; trabium, lapidumque pr&aelig;ter naturam ad <lb/>&longs;uperiorem locum euectio &amp; coagmentatio vtilia facit, ad defen&longs;io&shy;<lb/>nem contra c&oelig;li, a&euml;ris, extern&aacute;&longs;que qua&longs;uis iniurias. </s>

<s id="id.000328">Quinetiam va&shy;<lb/>rietas <expan abbr="c&otilde;tra">contra</expan> natur&aelig; cur&longs;um expetitur in delectabilibus vt hydrauli&shy;<lb/>cis, engebatis, merulis, &amp; icunculis voces, cantus, ge&longs;tus hominum, <lb/>auium, aliorumque animalium imitantibus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000329">Quando igitur.] <emph type="italics"/>Omnia licet habeat homo &longs;ui gratia nata: non <lb/>ita tamet habet, vt qualia naturaliter prodeunt, talibus <expan abbr="c&utilde;ctis">cunctis</expan> com&shy;<lb/>mode vti po&szlig;it. </s>

<s id="id.000330">Nece&szlig;itate igitur &amp; commoditate vtendi rebus &agrave; <lb/>natura oblatis pre&longs;&longs;us, conuertit ad &longs;uos v&longs;us &amp; <expan abbr="acc&otilde;modat">accommodat</expan>: &longs;ed con&shy;<lb/>uer&longs;io i&longs;ta, cum &longs;it deductio ad aliud, quam qu&ograve; vergit natura, habet <lb/>in ijs naturale principium renitens: hic renixus parit difficultatem <lb/>conuer&longs;ionis: h&aelig;c difficultas huc illuc animum hominis cogitando, <lb/>qu&aelig;rend&oacute;que, quomodo difficultas i&longs;ta &longs;uperetur, di&longs;trahit, facitque, <lb/>vt mente diu ver&longs;et, quid &amp; quomodo agendum, exempli gratia. </s>

<s id="id.000331">vt <lb/>onus &longs;ubleuet, alt&egrave; ip&longs;e con&longs;cendat, vehementer quatiat, long&egrave; iacu&shy;<lb/>letur, &amp; ea demum faciat, velit nolit natura, qu&aelig; vtilitati homi&shy;<lb/>num &longs;eruiant. </s>

<s id="id.000332">H&aelig;c cura &longs;olicitud&oacute;que vrget imaginationem, vt lu&shy;<lb/>men &agrave; mente mutuantem &amp; &agrave; rationibus mathematicis, nec quodam <lb/>&longs;ucce&szlig;ionis ordine defatigari <expan abbr="ration&etilde;">rationem</expan> &amp; quie&longs;cere &longs;init, priu&longs;quam <lb/>quod qu&aelig;ritur, inuentum &longs;it. </s>

<s id="id.000333">Illud inuentum, mod&uacute;&longs;ve inueniendi <lb/>generalis e&longs;t. </s>

<s id="id.000334">h&icirc;c particulariter ad <expan abbr="machin&atilde;">machinam</expan> <expan abbr="in&longs;trument&aacute;q;">in&longs;trument&aacute;que</expan> refertur, <lb/>quibus <expan abbr="oner&utilde;">onerum</expan> motiones fiant opportun&aelig;, per motiones intellige, qu&aelig; <lb/>fiunt &agrave; loco ad locum, vt impul&longs;iones, tractiones, volutationes, ve&shy;<lb/>ctiones, &amp; in locis altis, medijs, imis pro v&longs;u &amp; decoro repo&longs;itiones: <lb/>per onera, quicquid ali&ograve; quam qu&ograve; naturaliter vergit, impellitur, vt <lb/>a&euml;rem, cum deor&longs;um de&longs;cendere cogitur, vt aquam, vt terram cum <lb/>&longs;ur&longs;um a&longs;cendere, &amp; eiu&longs;modi, qu&aelig; vulgus cum admiratione &longs;u&longs;pi&shy;<lb/>cit, &amp; ni&longs;i fierent, nulla res no&longs;tra non e&longs;&longs;et impedita Atque &longs;ic ra&shy;<lb/>tio hominis nece&longs;sitate v&longs;us, &amp; vtilitatis &longs;u&aelig; 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 &agrave; Vitruuio &longs;ed &amp; per<emph.end type="italics"/><lb/><arrow.to.target n="marg7"/><lb/><emph type="italics"/>imitationem rerum &agrave; natura procreatarum. </s>

<s id="id.000335">Homo enim inquit, ani&shy;<lb/>maduertens Solis, Lun&aelig;, &amp; reliquorum planetarum continentes <lb/>motus, &amp; machinationes naturales, &longs;ine quibus non habui&longs;&longs;et in <lb/>terra lucem, &amp; fructuum maturitates hinc exempla &longs;ump&longs;it, &amp; ea <lb/>imitans, inductus rebus diuinis, commodas vit&aelig; perfecit explicatio&shy;<lb/>nes. </s>

<s id="id.000336">Itaque comparauit, vt e&longs;&longs;ent expeditiora alia machinis, &amp; ea&shy;<lb/>rum ver&longs;ationibus: alia organis, qu&aelig;que 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 qu&aelig;dam generalis qu&aelig; difficultati faciendo&shy;<lb/>rum pr&aelig;ter naturam ad vtiltiatem hominum &longs;uccurrit. <emph.end type="italics"/></s></p><p type="margin">

<s id="id.000337"><margin.target id="marg7"/>Lib. 10. </s></p><p type="main">

<s id="id.000338">Tum difficultas.] <emph type="italics"/>Natur&aelig; renixus difficultatem facit. </s>

<s id="id.000339">Re&shy;<lb/>nititur autem Natura &longs;ub&longs;tantia, numero, magnitudine, pondere, <lb/>figura, qu&aelig; omnia ars <expan abbr="immut&atilde;do">immutando</expan>, addendo, detrahendo, <expan abbr="tr&atilde;&longs;ponendo">tran&longs;ponendo</expan>, <lb/>poliendo, figurando corrigit, &amp; ad v&longs;us humanos accommodat. <emph.end type="italics"/></s></p></chap><chap>

<p type="main"><s id="id.000340"><foreign lang="greek"><gap/></foreign><lb/><arrow.to.target n="marg8"/></s></p><p type="margin">

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

<s id="id.000342">Atque propterea partem <lb/>illius artis qu&aelig; h&aelig;&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 po&euml;ta di&shy;<lb/>xit, ita &longs;e res habet. </s></p><p type="main">

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

<s id="id.000345">vt in his, qu&aelig;, cum mino&shy;<lb/>ra &longs;int, &longs;uperant maiora: &amp; <lb/>paruum momentum, cum <lb/>habeant, ingentia dimo&shy;<lb/>uent pondera, c&aelig;teri&longs;&shy;<lb/>que fere, qu&aelig; problemata <lb/>Mechanica nuncupamus. </s></p><p type="head">

<s id="id.000346">COMMENTARIVS. </s></p><p type="main">

<s id="id.000347">Illius artis.] <emph type="italics"/>Ars generalis, cuius hic mentionem facit Ari&shy;<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, &aelig;di&shy;<lb/>ficationem in explicatione publicorum &amp; priuatorum operum: <lb/>Gnomonicam in de&longs;criptione Horologiorum: &amp; Machinationem <lb/>in cognitione principiorum &amp; di&longs;po&longs;itione machinarum &amp; orga&shy;<lb/>norum. </s>

<s id="id.000349">H&aelig;c quidem comprehendi Architectur&aelig; 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&shy;<lb/>rumque omnium de&longs;criptiones, quibus etiam, qu&aelig; &longs;pirabilia vocant, <lb/>continentur. </s>

<s id="id.000351">Sed cum in his qu&aelig; Architectur&aelig; &longs;ubiecta &longs;unt &longs;olis <lb/>natur&aelig; renixus non vincatur: <expan abbr="ver&utilde;">verum</expan> etiam in quibuslibet aliis cuiu&longs;&shy;<lb/>cunque artis &longs;ubiectis, &longs;i qua &longs;it ars, qu&aelig; 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 &amp; re&shy;<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, &amp; partium particulas <lb/>vna ex his erit Mechanice. </s>

<s id="id.000355">Qu&aelig; ad explicationem motuum violen&shy;<lb/>torum, &amp; admirabilium &longs;e habebit, vt Phy&longs;ica ad explicationem <lb/>motuum naturalium: &amp; vt &longs;ub hac Medicina, Agricultura, &amp; <lb/>ali&aelig;: &longs;ic &longs;ub illa ars fabrilis, Architectura, Sutoria, &amp; omnes qu&aelig; <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 &amp; virium gradus in hac Mechanica tanquam <lb/>generali explicantur, vt po&longs;tea cuique facile apparebit. <emph.end type="italics"/></s></p><p type="margin">


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

<s id="id.000359">Mechanice.] <emph type="italics"/>In Gr&aelig;co Vecheli legitur h&icirc;c<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&shy;<lb/>ctenus in hoc pro&euml;mio non machina vna: &longs;ed ars machinarum lau&shy;<lb/>data e&longs;t. </s>

<s id="id.000360">Nec tamen definita, vt titulus pollicebatur. </s>

<s id="id.000361">Definitur au&shy;<lb/>tem &longs;ic &agrave; Picolomino. </s>

<s id="id.000362">Mechanice e&longs;t &longs;cientia ex qua cau&longs;&aelig; &amp; prin&shy;<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&shy;<lb/>tius ip&longs;ius rei, qu&aelig; definitur naturam, &amp; ad ea qu&aelig; cum dicta &longs;unt <lb/>ab Aristotele, qu&aelig;que dicentur intuentes perfecti&ugrave;s opinor, &longs;ic de&shy;<lb/>finiemus. </s>

<s id="id.000364">Mechanice e&longs;t ars ad ea qu&aelig; vires humanas &longs;uperant, tra&shy;<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">H&aelig;c enim tota po&longs;ita e&longs;t, vt ad v&longs;um, delectatio&shy;<lb/>n&eacute;mue hominum grauia &longs;ur&longs;um, leuia deor&longs;um, tum vtraque in la&shy;<lb/>tus, in orbem &longs;eor&longs;im, atque per mixtim &egrave; 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"/>H&aelig;c enim vt fiant, ip&longs;a ars machinas inuenit, &amp; inuentarum, cur <lb/>h&aelig;c pr&aelig;&longs;tent cau&longs;as reddit. </s>

<s id="id.000367">C&aelig;ter&ugrave;m ex huius machinis, qu&aelig;dam <lb/>mouentur per &longs;e:qu&aelig;dam non &longs;ponte. </s>

<s id="id.000368">Ill&aelig; intra &longs;e principia &longs;u&aelig; mo&shy;<lb/>tionis habent, &amp;<emph.end type="italics"/> <foreign lang="greek">a)uto/mata</foreign> <emph type="italics"/>vocantur: quorum alia Gr&aelig;cis<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 qu&aelig; pulchrum e&longs;t illud, quod <lb/>docuit con&longs;truere, &longs;cilicet &aelig;dem rotundam, in qua Bacchus pateram <lb/>altera manu tenet, altera thyr&longs;um, prop&egrave; ver&ograve; ade&longs;t panthera, &amp; <lb/>ara: circum autem Bacchides tympana tenentes, &longs;upr&agrave; tholum alata <lb/>&amp; coronata Victoria collocatur, atque vno &amp; <expan abbr="eod&etilde;">eodem</expan> tempore in ara <lb/>ignis &longs;uccenditur, Bacchus lac &egrave; patera, vinum &egrave; thyr&longs;o ver&longs;at in <lb/>pantheram, Bacchides circum&longs;alientes tympana pul&longs;ant, Victoria <lb/>&longs;e circumagens, &amp; alas qaatiens tuba &longs;onat. </s>

<s id="id.000370">In alia ver&ograve; di&longs;po&longs;i&shy;<lb/>tione fecit inambulantia, &longs;igilla euntia, &amp; redeuntia, motione&longs;&shy;<lb/>que varias reddentia, vt v&longs;us &amp; voluptas po&longs;tulat pro instituto. <lb/></s>

<s id="id.000371">H&aelig; ver&ograve; motionis principium intra &longs;e non habent: Sed ex his <lb/>ali&aelig; mouentur &agrave; rebus inanimis, ali&aelig; ab animatis. </s>

<s id="id.000372">Res inani&shy;<lb/>m&aelig; principium motionis exhibentes &longs;unt a&euml;r, &longs;piritus, aqua, ignis, <lb/>&longs;umus. </s>

<s id="id.000373">Aer &amp; &longs;piritus e&longs;t vel inclu&longs;us, ex qu&ograve; pneumatica ratio ab&shy;<lb/>&longs;oluitur, de qua etiam Hero in&longs;trumenta Mu&longs;ica, qu&aelig; per<emph.end type="italics"/> <foreign lang="greek">a)ntonoma&shy;<lb/>si/an</foreign> <emph type="italics"/>organa vocant: vel liber, vnde &aelig;dificia ad molendum. </s>

<s id="id.000374">A qua, <lb/>vnde fiunt rot&aelig; etiam ad <expan abbr="molend&utilde;">molendum</expan>, <expan abbr="t&utilde;">tum</expan> tympana, tum &longs;err&aelig; ad trabes <lb/>&longs;ecandas, folles ad <expan abbr="ferr&utilde;">ferrum</expan> tundendum &amp; alia <expan abbr="plera&qacute;">pleraque</expan>;. </s>

<s id="id.000375">Ignis &longs;eu fumus <lb/>quo verrucula conuoluuntur: animat&aelig; &longs;unt, bruta qu&aelig; trahunt cur&shy;<lb/>rus, ci&longs;ia, quadrigas: homines qui ver&longs;ant, trahunt, erigunt, impel&shy;<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, &amp; ad a&longs;cenden&shy;<lb/>dum in altum multiplicibus &longs;calarum formis, tum munitis, tum &longs;ine <lb/>munitione, &amp; ad di&longs;rumpendum, excutiendum, pro&longs;ternendum, <lb/>quatiendum frangendum, iaculandum, arietibus, te&longs;tudinibus, tur&shy;<lb/>ribus ambulatorijs, catapultis, bali&longs;tis, tormentis reliquis. </s>

<s id="id.000376">in quibus <lb/>faciendis h&aelig;c 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">Quipp&egrave; qu&aelig; &agrave; quibu&longs;cumque artificibus cit&ograve; fieri <lb/>queant, erectu interim, <expan abbr="tr&atilde;slat&uacute;que">translat&uacute;que</expan> facilia: in&longs;idiatu, fractuque dif&shy;<lb/>ficilia: &longs;tabilia, ac tandem eiu&longs;modi &longs;int, vt quatenus nece&szlig;itas <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, facil&eacute;que di&longs;&longs;olui po&szlig;int. </s>

<s id="id.000378">Sed neque hic <lb/>pr&aelig;termittenda diui&longs;io Methanices, qu&aelig; aliter &agrave; Politiano ex He&shy;<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, qu&aelig; <lb/>numerorum, men&longs;urarum, &longs;yderum, natur&aelig; que rationibus perfici&shy;<lb/>tur: altera<emph.end type="italics"/> <foreign lang="greek">xeirourgikh\,</foreign> <emph type="italics"/>cui vel maxim&egrave; artes ill&aelig;, &aelig;raria, &aelig;difica&shy;<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"/>qu&aelig; facile aquas antlijs extrahit:<emph.end type="italics"/> <foreign lang="greek">*or&shy;<lb/>ganopoihtikh\,</foreign> <emph type="italics"/>qu&aelig; bellis accommoda in&longs;trumenta fabricatur, arie&shy;<lb/>tes, te&longs;tudines, turres ambulatorias, helepoleis, &longs;ambucas, exo&longs;tras, <lb/>tollenones &amp; qu&aelig;cunque Gr&aelig;co vocabulo<emph.end type="italics"/> <foreign lang="greek">poliorkhtika\</foreign> <emph type="italics"/>vocan&shy;<lb/>tur, tormentorumque varia genera, qu&aelig; libris Athen&aelig;i, Bitonis, <lb/>Heronis, Pappi, Philonis, Apollodorique continentur, vt Latinos <lb/>omi&longs;erim. </s>

<s id="id.000381">Mox &amp; qu&aelig;<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&shy;<lb/>lika\</foreign> <emph type="italics"/>organa, qu&aelig;que per &longs;e ventorum flatu re&longs;onant. </s>

<s id="id.000382">Et quod vas <lb/>dic&aelig;ometron vocabant, &amp; quod voces variarum auium exprimit, <lb/>&amp; quod indidem merum, mox dilutum vinum, mox aquam cali&shy;<lb/>dam, mox <expan abbr="frigid&atilde;">frigidam</expan>, copio&longs;am <expan abbr="tenu&eacute;mq;">tenu&eacute;mque</expan> vici&szlig;im funditat. </s>

<s id="id.000383">Et<emph.end type="italics"/> <foreign lang="greek">si/fwnes</foreign><lb/><emph type="italics"/>extinguendis incendijs apti, &amp; medicinabiles cacurbitul&aelig; &longs;ine <lb/>ignis ministerio cutem prehendentes, &amp; pil&aelig; &longs;ponte &longs;altantes, &amp; <lb/>lucerna &longs;uas ip&longs;a producens &longs;tuppas: &amp; animal quod &agrave; &longs;tructore dum <lb/>&longs;ecatur in men&longs;a, bibit interim, crepit&ugrave;que &longs;uo quodam, &amp; voce &longs;i&shy;<lb/>tientis repr&aelig;&longs;entat imaginem: milleque alia id genus, qu&aelig; breuita&shy;<lb/>tis &longs;tudio pr&aelig;terimus. </s>

<s id="id.000384">H&aelig;c igitur (vt in capita qu&aelig;dam conferatur) <lb/>aut ponderibus vtitur &amp; &longs;piritu, quorum pr&aelig;ponderatio mouet, <lb/>&aelig;quilibrium &longs;i&longs;tit, (&longs;icuti etiam Tim&aelig;us definit): aut neruis &amp; <lb/>funiculis animatos qua&longs;i tractus, ac motus imitatur, ac circa illa <lb/>qu&aelig; &longs;ubnatant aquis, aut circa aquarum vertitur horologia, quo&shy;<lb/>rum quidem generum primum docet in pneumaticis Heron, alte&shy;<lb/>rum idem in automatis &amp; Zygijs, quartum rur&longs;us in Hydrijs, ter&shy;<lb/>tium ver&ograve; in Ochoumenis Archimedes. </s>

<s id="id.000385">E&longs;t in eadem Mechanic&aelig; <lb/>&longs;erie qu&aelig; Centrobarica pars dicitur, ex qua reliqu&aelig; pendere dicun&shy;<lb/>tur &amp; Sph&aelig;rotop&oelig;ia, qualis illa Archimedea Claudiani laudata <lb/>ver&longs;ibus. </s>

<s id="id.000386">Suppeditat eadem Architectur&aelig; quoque &longs;can&longs;orias, tra&shy;<lb/>ctiles, &amp; &longs;pirituales machinas. <emph.end type="italics"/></s></p><p type="margin">

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

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

<s id="id.000389">Natura vincit.] <emph type="italics"/>Senariolus e&longs;t cuiu&longs;dam antiqui po&euml;t&aelig; 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&shy;<lb/>bu&longs;cum vna ducebatur in &longs;upplicium iu&longs;&longs;u Diony&longs;ij tyranni, reci&shy;<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 &amp; &longs;criptore for&shy;<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&shy;<lb/>terpretem, &amp; po&euml;tam refert Suidas. </s>

<s id="id.000393">A quo etiam forta&longs;&longs;e proma&shy;<lb/>nauit Senariolus, qui hic citatur ab Ari&longs;totele, ad probandum <lb/>homines arte vincere ea, &agrave; quibus natura vincuntur. </s>

<s id="id.000394">quod cum fa&shy;<lb/>ciunt in ijs, in quibus iudicio omnium longe &agrave; 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></p><p type="main">

<s id="id.000395">Vt in his, qu&aelig; cum] <emph type="italics"/>Vt cum magnas marmorum moles, tra&shy;<lb/>bes, columnas, colo&longs;&longs;os transferimus, &amp; erigimus, naues &longs;ubduci&shy;<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="qu&atilde;">quam</expan> machina, vt ait po&euml;ta,<emph.end type="italics"/></s></p><p type="main">

<s id="id.000396">In&longs;pectura domos ventur&aacute;que de&longs;uper vrbi. </s></p><p type="main">

<s id="id.000397"><emph type="italics"/>quales mult&aelig; apud Vegetium &amp; Heronem mechanicum.) bom&shy;<lb/>bardas ingentes ad locum destinatum conuertimus. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000398"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000399">Sunt vero h&aelig;c proble&shy;<lb/>matis Phy&longs;icis, nec omni&shy;<lb/>no <expan abbr="ead&etilde;">eadem</expan>, nec vald&egrave; di&longs;&longs;imi&shy;<lb/>lia: &longs;ed con&longs;entanea theo&shy;<lb/>tematis, tum mathemati&shy;<lb/>cis, tum Phy&longs;icis. </s>

<s id="id.000400">Etenim <lb/>quod ip&longs;um quomodo ad <lb/>mathematica pertineat: <lb/>ip&longs;um vero circa quod, ad <lb/>Phy&longs;ica, manife&longs;tum e&longs;t. </s></p><p type="head">

<s id="id.000401">COMMENTARIVS. </s></p><p type="main">

<s id="id.000402"><emph type="italics"/>Apud Euclidem problema &agrave; theoremate di&longs;tinguitur, quod <lb/>hoc iubeat aliquid contemplari: illud fieri: pa&szlig;im 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, &amp; alijs pro vtroque, vt hic, indifferenter legitur. </s>

<s id="id.000403">Qualia <lb/>autem problemata in Mechanicis habeat tractanda explicat Ari&shy;<lb/>&longs;toteles, dicitque ea e&longs;&longs;e, qu&aelig; &longs;int con&longs;entanea Phy&longs;icis &amp; Mathe&shy;<lb/>maticis, vt qu&aelig; habeant &longs;ubiectum petitum &egrave; Phy&longs;icis. </s>

<s id="id.000404">Machina&shy;<lb/>rum enim materia lignum e&longs;t vel ferrum &amp; eiu&longs;modi corpora Phy&shy;<lb/>&longs;ica: attributum ver&ograve; &egrave; figuris &amp; terminis Mathematicis cuiu&longs;mo&shy;<lb/>di &longs;unt in Geometria line&aelig;, diametri, centra, circuli, &amp; eiu&longs;modi, <lb/>&egrave; quibus machin&aelig; con&longs;tare &amp; figurat&aelig; e&longs;&longs;e, &amp; 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 &amp; <lb/>numerales demon&longs;trationes, quibus ip&longs;um explicant, Mathemati&shy;<lb/>cas. </s>

<s id="id.000406">C&aelig;terum exeo quod dicit Ari&longs;toteles problemata Mechanica <lb/>e&longs;&longs;e Phy&longs;icis &amp; Mathematicis con&longs;entanea, &longs;ub indicare videtur, <lb/>ne Mechanicus ante existimet machinas, quarum habuerit demon&shy;<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, qu&aelig; rem patiatur fieri. </s>

<s id="id.000407">Quamuis enim <lb/>Geometer demon&longs;tratione concludat, datam rectam lineam infinit&egrave; <lb/>diui&longs;ibilem e&longs;&longs;e, nulla materia lineata apud phy&longs;icos e&longs;t, qu&aelig; non <lb/>continuata diui&longs;ione tandem reducatur ad eam, qu&aelig; &longs;i amplius in&shy;<lb/>telligatur diuidi, amittet formam line&aelig; Phy&longs;ic&aelig; &amp; 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 pr&aelig;terea vitia materi&aelig; qu&aelig; Geometra, aut Mechanicus de&shy;<lb/>mon&longs;trans non con&longs;iderat: nec etiam ob&longs;tant quo minus qu&aelig; propo&shy;<lb/>&longs;ita &longs;unt, vera &longs;int in intellectu: Mechanicus igitur operans, priu&longs;&shy;<lb/>quam operi &longs;e accingat, ne fru&longs;tretur, con&longs;iderare debet, an quod <lb/>proponitur effici po&szlig;it, habita ratione materi&aelig; ex qua, aut per <expan abbr="qu&atilde;">quam</expan>, <lb/>&amp; circun&longs;tantiarum pr&aelig;&longs;ertim temporis quod pr&aelig;&longs;cribitur, &amp; &longs;um&shy;<lb/>ptuum quos facere oporteret. </s>

<s id="id.000412">H&aelig;c enim &longs;i abunde &longs;uppetant, nec ma&shy;<lb/>teria omnino repugnet, nihil non fieri poterit. <emph.end type="italics"/></s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.053.jpg" pagenum="14"/><chap><p type="main">

<s id="id.000413"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000414">Dubitantur <expan abbr="aut&etilde;">autem</expan> in hoc <lb/>genere ea, qu&aelig; de vecte di&shy;<lb/>cuntur. </s>

<s id="id.000415">Ab&longs;urdum enim <lb/>videtur ab exigua vi ma&shy;<lb/>gnum pondus moueri, &amp; <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&shy;<lb/>dus, in&longs;uper <expan abbr="adijci&etilde;s">adijciens</expan> vectis <lb/>ip&longs;ius <expan abbr="p&otilde;dus">pondus</expan>, facile mouet. </s></p><p type="head">

<s id="id.000417">COMMENTARIVS. </s></p><p type="main">

<s id="id.000418">Qv&aelig; 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&shy;<lb/>spidem <expan abbr="acut&atilde;">acutam</expan> &amp; paul&ograve; 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&shy;<lb/>tur fulcimentum, quod Gr&aelig;ci<emph.end type="italics"/> <foreign lang="greek">u(pomo/xlion,</foreign> <emph type="italics"/>Vitruuius porrectam <lb/>pre&szlig;ionem appellat. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000420">Ab&longs;urdum enim videtur.] <emph type="italics"/>Ostenditur hic cur problema <lb/>de vecte in Mechanicis, dubitabile, &longs;iue dignum qu&aelig;&longs;itu &longs;it. </s>

<s id="id.000421">Du&shy;<lb/>bitabilia enim &longs;unt, qu&aelig; reuera fiunt: vt magnum pondus addito <lb/>pondere vectis ab exigua potentia, &amp; vna hominis manu moue&shy;<lb/>ri. </s>

<s id="id.000422">Fieri tamen ratio repugnat. </s>

<s id="id.000423">Nam in omni motu mouens pr&aelig;ua&shy;<lb/>lere debet mobili: h&icirc;c exigua potentia e&longs;t mouens: magnum pondus <lb/>e&longs;t mobile: illa quatenus exigua e&longs;t, &amp; ante per &longs;e impotens, atque <lb/>infirma, e&longs;t in&aelig;quale minus: hoc quatenus magnum, e&longs;t in&aelig;quale <lb/>maius, &amp; ei addito vectis onere maius adhuc effici videtur: non <lb/>igitur exigua potentia magno oneri &amp; adaucto in motu pr&aelig;ua&shy;<lb/>lere debet. </s>

<s id="id.000424">Si non pr&aelig;ualet, non mouet: mouet tamen: Relinquitur <lb/>ergo vt exi&longs;timemus aliquam cau&longs;am in hoc problemate motus eius <lb/>apparentis latentem &longs;ube&longs;&longs;e, dignam Philo&longs;ophi indagatione. <emph.end type="italics"/></s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.054.jpg" pagenum="15"/><chap><p type="main">

<s id="id.000425"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000426"><expan abbr="Omni&utilde;">Omnium</expan> ver&ograve; talium cir&shy;<lb/>culus continet cau&longs;&aelig; prin&shy;<lb/>cipium. </s>

<s id="id.000427">quod etiam ratio&shy;<lb/>ni valde <expan abbr="c&otilde;&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&shy;<lb/>mirabile contingere. </s></p><p type="head">

<s id="id.000429">COMMENTARIVS. </s></p><p type="main">

<s id="id.000430">Omnium ver&ograve; talium.] <emph type="italics"/>Cau&longs;a qu&aelig; latebat in problemate <lb/>de vecte a&szlig;ignatur hic e&longs;&longs;e circulus: qu&aelig; ad alia multa Me&shy;<lb/>chanica po&longs;tea transferetur. </s>

<s id="id.000431">Probatur autem id ex forma circuli mi&shy;<lb/>rabili&szlig;ima. </s>

<s id="id.000432">&longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000433"><emph type="italics"/>Ex admirabiliori admirabile aliquid fieri non e&longs;t alienum, cau&longs;&aelig; <lb/>enim &longs;ibi &longs;imiles effectus edunt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000434"><emph type="italics"/>Circulus e&longs;t admirabilis, &amp; admirabilior, quam vectis: quamque <lb/>ea qu&aelig; &agrave; vecte fiunt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000435"><emph type="italics"/>Ergo &agrave; circulo prodire id quod e&longs;t admirabile in vecte, mechani&shy;<lb/>ci&longs;que problematis non e&longs;t alienum. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000436"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000437">Maxim&egrave; ver&ograve; 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&shy;<lb/>tim enim factus e&longs;t ex mo&shy;<lb/>to, &amp; immobili, quorum <lb/>natura &longs;ibi inuicem con&shy;<lb/>traria e&longs;t. </s>

<s id="id.000439">Ill&ugrave;c <expan abbr="itaq;">itaque</expan> in&longs;pi&shy;<lb/>cientibus <expan abbr="c&otilde;traria">contraria</expan> ab ip&longs;o <lb/>prouenire minus erit <expan abbr="mir&utilde;">mirum</expan>. </s></p><p type="head">

<s id="id.000440">COMMENTARIVS. </s></p><p type="main">

<s id="id.000441">Maxime ver&ograve;.] <emph type="italics"/>Circuli admiranda natura declaratur &egrave; <lb/>quintuplici contrariorum, qu&aelig; in eo pr&aelig;ter 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&shy;<lb/>rum quie&longs;cit &amp; fixum e&longs;t: alterum vn&agrave; cum tota linea mouetur: &longs;e&shy;<lb/>cundum quod in mota linea puncta, cum infinita &longs;int, &amp; omnia &longs;i&shy;<lb/>mul moueantur, in&aelig;qualiter tamen moueantur: Tertium quod extre&shy;<lb/>mum motum eodem tempore duobus motibus contrarijs, vno natu&shy;<lb/>rali ad peripheriam &longs;cilicet, altero violento ad centrum moueatur. </s>

<s id="id.000444">In <lb/>facto ver&ograve; hoc admirabile e&longs;t, quod eius terminus vna linea exi&shy;<lb/>&longs;tens, ob &iacute;dque latitudinis expers, concauum tamen &amp; conuexum, <lb/>qu&aelig; quodammodo contraria &longs;unt, admittat: pr&aelig;terea mobilitas, <lb/>qu&aelig; ine&longs;t, admirabilis e&longs;t, quia eodem tempore ad contrarias loci dif&shy;<lb/>ferentias, vt &longs;ur&longs;um deor&longs;um: dextror&longs;um &longs;inistror&longs;um, fiat. </s>

<s id="id.000445">H&aelig;c <lb/>&longs;ingula &longs;uis locis delineabuntur &amp; explicabuntur. </s>

<s id="id.000446">Sed pr&aelig;ter h&aelig;c, <lb/>qu&aelig; ab Ari&longs;totele de circulo dicuntur, valde notabilia &longs;unt &amp; alia, <lb/>qu&aelig; 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, e&acirc;que &longs;implici, &longs;imilari <lb/>vniformi, &amp; carente principio, &amp; fine, neque tamen infinita, vt <lb/>cuius, cum partes aliquot &longs;umpt&aelig; &longs;unt, qu&aelig; re&longs;tant, minus &longs;int, quam <lb/>ante quam &longs;umpt&aelig; e&longs;&longs;ent, quod repugnat infinito in magnitudine: &longs;ed <lb/>tota e&longs;t, &amp; perfecta: vnde circulus figura e&longs;t planarum &longs;implici&szlig;i&shy;<lb/>ma, regulari&szlig;ima, perfecti&szlig;ima: Deinde quod ea linea non &longs;it an&shy;<lb/>gulus, ad angulum tamen proxime accedat, vt o&longs;tendimus in no&longs;tro <lb/>libello de angulo contactus, &amp; ob id <expan abbr= "quod&atilde;modo">quodammodo</expan> vndequaque angu&shy;<lb/>lata, cum nu&longs;quam &longs;it, dici po&szlig;it, &amp; figura<emph.end type="italics"/> <foreign lang="greek">pa/ngwnos &amp; o(lo/gwnos,</foreign><lb/><emph type="italics"/>tum prima figurarum &amp; vltima: po&longs;tea, quod ex infinitis punctis <lb/>qu&aelig; in &longs;patio ab ea comprehen&longs;o &longs;unt, vnum e&longs;t tantum, &agrave; quo omnes <lb/>rect&aelig; ad peripheriam duct&aelig;, &longs;unt &aelig;quales: 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;ph&aelig;&shy;<lb/>ram constituat, corporum &longs;implici&szlig;imum, capaci&szlig;imum, mobili&szlig;i&shy;<lb/>mum, mouenti&szlig;imum: quod circulus omnium figurarum eiu&longs;dem <lb/>perimetri &longs;it capaci&szlig;ima: quod vno puncto lineam rectam attin&shy;<lb/>gat, &longs;icque offen&longs;ationibus &amp; occur&longs;ationibus minimum pateat, <lb/>&longs;icque in&longs;i&longs;tens dimidia &longs;ui totius parte nutet, vnde propen&longs;i&szlig;imus <lb/>e&longs;t ad motum, &amp; dimotus cum moueat annexa, apti&szlig;imus 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;trem&ograve; quod inter rectam circulum tangen&shy;<lb/>tem, &amp; circuli peripheriam altera recta &longs;ine &longs;ectione cadere non <lb/>po&szlig;it. </s>

<s id="id.000448">quod 16. prop. lib. 3. elem. e&longs;t demon&longs;tratum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000450">Imprimis enim] <emph type="italics"/>Prima repugnantia e&longs;t in circulo, quod fiat <lb/>&egrave; moto &amp; quieto, qu&aelig; &longs;unt oppo&longs;ita ex genere priuantium, vnde rur&shy;<lb/>&longs;us concluditur, minus e&longs;&longs;e mirum, id e&longs;t minus ab&longs;urdum &agrave; circulo <lb/>produci contraria. </s>

<s id="id.000451">Circulum autem fieri ex moto &amp; quieto patet his, <lb/>qui eius fabricam repetent &egrave; 3. po&longs;tulato element.Eucl. </s>

<s id="id.000452">Ibi enim po&shy;<lb/>&longs;tulatur, vt &egrave; dato centro &amp; interuallo circulum de&longs;cribere conce&shy;<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&shy;<lb/>ueri c&oelig;pit, id quod, vt &longs;ine errore fiat inuentus e&longs;t circinus &agrave; Talo <lb/>D&aelig;dali ex &longs;orore nepote, cuius forma &amp; officium ab Ouidio accom&shy;<lb/>modate huic loco, &longs;ic e&longs;t expre&longs;&longs;um,<emph.end type="italics"/></s></p><p type="main">

<s id="id.000454">Ex vno duo ferrea brachia nodo <lb/>Iunxit, vt &aelig;quali &longs;patio di&longs;tanti&shy;<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></p><p type="main">

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

<s id="id.000456"><emph type="italics"/>Sit igitur recta A B inter extrema duo&shy;<lb/>rum brachiorum circini A C B diua&shy;<lb/>ricati per interuallum line&aelig; A B, <lb/>cuius extremum A maneat: alterum B <lb/>line&aelig; motu feratur per D quou&longs;que redeat <lb/>ad B: &longs;icque circulus B D B erit fa&shy;<lb/>ctus. </s>

<s id="id.000457">Idque beneficio puncti B cum tota <lb/>linea A B moti, atque puncti A quieti, vt hic vult Ari&longs;toteles. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000458"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000459">Primum &longs;iquidem line&aelig; <lb/>ip&longs;um circulum <expan abbr="compre-hend&etilde;ti">compre&shy;<lb/>hendenti</expan>, licet latitudinem <lb/>nullam habeat, contraria <lb/>quodammodo, cauum &amp; <lb/>conuexum ine&longs;&longs;e <expan abbr="appar&etilde;t">apparent</expan>. <lb/></s>

<s id="id.000460">H&aelig;c autem ita inter &longs;e di&shy;<lb/>&longs;tant, vt <expan abbr="magn&utilde;">magnum</expan> &amp; 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/>&aelig;quale: illorum ver&ograve; re&shy;<lb/>ctum. </s>

<s id="id.000461">Ide&ograve; inuicem cum <lb/>commutantur, pri&ugrave;s ne&shy;<lb/>ce&longs;&longs;e e&longs;t &aelig;qualia fieri: li&shy;<lb/>neam &longs;an&egrave; rectam, cum ex <lb/>conuexa fit caua: &amp; rur&longs;us <lb/>ex ip&longs;a fit conuexa &amp; ro&shy;<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></p><p type="head">

<s id="id.000463">COMMENTARIVS. </s></p><p type="main">

<s id="id.000464">Primum &longs;iquidem.] <emph type="italics"/>Vetu&longs;tatis iniuria multas veterum li&shy;<lb/>bris, &amp; 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 h&icirc;c non prima, vt iam patuit: &longs;ed &longs;e&shy;<lb/>cunda e&longs;t in circulo repugnantia. </s>

<s id="id.000465">Eaque ex eo quod cum circuli peri&shy;<lb/>pheria &longs;it vna linea def. 15. lib. 1. elem. &amp; idcirco latitudinis expers <lb/>def. 2. lib. eiu&longs;dem: habeat tamen in &longs;e contraria conuexum &longs;cilicet, <lb/>&amp; concauum: illud quidem qu&agrave; &longs;pectat foras: hoc vero qu&agrave; intra. <lb/></s>

<s id="id.000469">vbi nota Ari&longs;totelem dixi&longs;&longs;e h&aelig;c<emph.end type="italics"/> <foreign lang="greek">e)nanti/a pws</foreign> <emph type="italics"/>contraria quodam&shy;<lb/>modo. </s>

<s id="id.000470">Nec enim vere contraria &longs;unt, quia vere contraria &longs;unt ea, <lb/>qu&aelig; &longs;ecundum &longs;eip&longs;a &longs;umpta, ex &longs;eip&longs;is extreme di&longs;tant, &amp; vnde &longs;e <lb/>expellere nata &longs;int, habent: at h&aelig;c conuexum &amp; concauum non &longs;ic <lb/>extreme di&longs;tant: &longs;ed ratione &longs;itus partium in diuer&longs;is locorum diffe&shy;<lb/>rentijs, quod &longs;cilicet ali&aelig; alijs &longs;int al&shy;<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 depre&szlig;iores. </s>

<s id="id.000471">Cum enim re&shy;<lb/>ctum &longs;it id in lineis quod ex &aelig;quo iacet <lb/>inter &longs;ua extrema def. 2. lib. 1. &amp; vt <lb/>linea A B, curuum erit quod non ex <lb/>&aelig;quo iacebit, &longs;ed altius aut depre&szlig;ius: <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 qu&aelig; eadem e&longs;t linea ex &longs;e, &longs;ed <lb/>ex locis E E &amp; 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 ver&egrave; contraria: qualia tamen apparent ex <lb/>di&longs;tantia &amp; differentiis locorum &longs;ur&longs;um deor&longs;um. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000473">H&aelig;c autem ita.] <emph type="italics"/>Similitudine comprobatur conuexum &amp; <lb/>concauum contraria e&longs;&longs;e. </s>

<s id="id.000474">Quemadmodum magnum &amp; paruum con&shy;<lb/>traria &longs;unt, quia di&longs;tant, inter &longs;e per medium, quod e&longs;t &aelig;quale, &amp; <lb/>cum commutantur in inuicem nece&longs;&longs;e e&longs;t prius &aelig;quale fieri: &longs;ic con&shy;<lb/>uexum &amp; concauum contraria erunt, quia di&longs;tant inter &longs;e per me&shy;<lb/>dium, quod e&longs;t rectum, &amp; cum commutantur in inuicem prius re&shy;<lb/>ctum etiam fieri nece&longs;&longs;um e&longs;t. </s>

<s id="id.000475">&longs;unt igitur conuexum &amp; concauum <lb/>contraria. </s>

<s id="id.000476">Sed &amp; hic a&longs;&longs;umemus per eandem definitionem contra&shy;<lb/>riorum ante po&longs;itam, &amp; ex &longs;ententia Ari&longs;totelis in categ. Quanti&shy;<lb/>tatis, magnum &amp; paruum apparenter duntaxat e&longs;&longs;e contraria. </s>

<s id="id.000478">Ap&shy;<lb/>parenter dico vt illa priora, quia habent aliquid de definitione con&shy;<lb/>trariorum, quod &longs;ibi conueniat, &longs;cilicet di&longs;tare inter &longs;e in eodem ge&shy;<lb/>nere, &amp; habere medium: &longs;ed non vere tamen e&longs;&longs;e. </s>

<s id="id.000479">Quia non habent <lb/>omnes pr&aelig;dict&aelig; definitionis particulas &longs;ibi conuenientes. </s>

<s id="id.000480">H&aelig;c <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;c&aelig; 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 po&szlig;it ad quodlibet obuium, cum tamen <lb/>h&aelig;c vocabula, magnum, paruum, &longs;impliciter dicuntur, fieri ad &longs;ym&shy;<lb/>metrum &longs;ui cuiu&longs;que generis. </s>

<s id="id.000482">Symmetrum appello, quod iu&longs;tam ma&shy;<lb/>gnitudinem in &longs;uo genere adeptum e&longs;t. </s>

<s id="id.000483">Et hoc e&longs;t quod hic dicitur <lb/>&aelig;quale, medium &longs;cilicet inter <expan abbr="magn&utilde;">magnum</expan> tanquam excedens, &amp; 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&shy;<lb/>nes &longs;eptempedalis e&longs;t, magnus: qui quintumpedalis, paruus &longs;implici&shy;<lb/>ter dicetur. </s>

<s id="id.000486">Hinc intellige, vt id obiter annotem, quod apud Ari&longs;to&shy;<lb/>telem memini me legi&longs;&longs;e, nullam paruam mulierem pulchram e&longs;&longs;e, <lb/>quia, quod prima pars e&longs;t pulchritudinis non habet, &longs;ymmetrum &longs;ui <lb/>generis. <emph.end type="italics"/></s></p><p type="main">

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

<s id="id.000488"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000489">Secundum e&longs;t, quod con&shy;<lb/>trariis motionibus &longs;imul <lb/>moueatur. </s>

<s id="id.000490">Simul enim an&shy;<lb/>tror&longs;um &amp; retror&longs;um mo&shy;<lb/>uetur: atque linea circu&shy;<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&shy;<lb/>nenter mota e&longs;t vltimum, <lb/>rur&longs;us primum euadit. </s>

<s id="id.000492">Ita&shy;<lb/>que manife&longs;tum, quod in&shy;<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&shy;<lb/>bilium omnium e&longs;&longs;e prin&shy;<lb/>cipium. </s>

<s id="id.000494">Igitur &amp; qu&ecedil; circa <lb/>libram eueniunt ad circu&shy;<lb/>lum referuntur, &amp; qu&ecedil; cir&shy;<lb/>ca vectem ad libram, &amp; <lb/>forta&longs;&longs;is alia omnia, qu&aelig; <lb/>circa motiones mechani&shy;<lb/>cas, ad vectem. </s></p><p type="head">

<s id="id.000495">COMMENTARIVS. </s></p><p type="main">

<s id="id.000496">Secundum.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="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, ant&egrave; &longs;cilicet cum pars eius vna mouetur: oppo&longs;ita in <lb/>ip&longs;omet tempore pon&egrave; mouetur. </s>

<s id="id.000497">Hoc autem e&longs;t contrarias motiones <lb/>&longs;imul habere. </s>

<s>Contrari&aelig; enim &longs;unt motiones apud Ari&longs;totelem in <lb/>categoria vbi &amp; li. 5. de Phy&longs;ico auditu ex diametralibus locorum, <lb/>ad qu&aelig; fiunt, di&longs;tantijs dextror&longs;um, &longs;ini&longs;tror&longs;um: &longs;ur&longs;um, deor&longs;um: <lb/>&amp; antror&longs;um, retror&longs;um. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000500">Atque linea circulum.] <emph type="italics"/>Cur circulus ant&egrave; &amp; pon&egrave; mouea&shy;<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&shy;<lb/>gi&longs;mus in&longs;titui pote&longs;t. </s>

<s id="id.000502">Vt fit circulus ita mouetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000503"><emph type="italics"/>Fit circulus &agrave; 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 qu&aelig; &longs;unt circa extremum fixum oppo&longs;i&shy;<lb/>ta deducatur, &amp; quod e&longs;t vltimum, rur&longs;us fiat primum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000504"><emph type="italics"/>Ergo circulus mouetur per loca &egrave; diametro oppo&longs;ita circa extre&shy;<lb/>mum line&aelig; &agrave; qua fit fixum. </s>

<s id="id.000505">Quia igitur in his &longs;unt ant&egrave; &amp; pon&egrave;, <lb/>mouebitur ant&egrave; &amp; pon&egrave;: quia in&longs;uper &longs;unt &longs;ur&longs;um &amp; deor&longs;um, <lb/>mouebitur etiam &longs;imul &longs;ur&longs;um &amp; deor&longs;um. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000506"><emph type="italics"/>Centrum enim in plano circundatur quatuor loci differentijs, <lb/>propter duas qu&aelig; in ip&longs;o ad rectos &longs;e &longs;ecant dimen&longs;iones, vt in circu&shy;<lb/>lo B C D E, e&longs;to linea fabricans ip&longs;um A B, ibique e&longs;to ante <lb/>B. </s>

<s>igitur cum erit in D, erit pon&egrave;: &amp; cum in C, &longs;ur&longs;um: &amp; <lb/>in E, deor&longs;um, &amp; perueniens ad A B, eidem loco re&longs;tituetur, <lb/>&agrave; 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&shy;<lb/>tur, pote&longs;t dici ire, &amp; reuerti &longs;imul: &longs;ic <lb/>cum &longs;ph&aelig;ricum corpus mouetur, in fine <lb/>&longs;emper, &amp; principio motus &longs;ui, etiam tum <lb/>ire, tum reuerti veri&longs;imiliter dicetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000508"><emph type="italics"/>C&aelig;terum notandum quod motiones dict&aelig; <lb/>e&longs;&longs;e in circulo, in&longs;unt quidem: &longs;ed non &longs;i&shy;<lb/>mul &longs;ecundum eandem partem. </s>

<s id="id.000509">Nam cum B, mouetur &longs;ur&longs;um ver&shy;<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&shy;<lb/>&longs;us E: vt autem ver&egrave; e&longs;&longs;ent motiones contrari&aelig; deberent fieri &longs;e&shy;<lb/>cundum ea&longs;dem partes. </s>

<s id="id.000510">E&longs;t h&aelig;c igitur vt ali&aelig; in circulo non vera <lb/>&longs;ed apparens repugnantia. </s>

<s id="id.000511">ex cuius tamen natura magnorum effe&shy;<lb/>ctuum po&longs;tea cau&longs;&aelig; repetuntur, cum diametri B D, vt inflexilis <lb/>circa A, centrum fixum mot&aelig;, &longs;i B, deprimatur, nece&longs;&longs;e e&longs;t alte&shy;<lb/>rum extremum D, attolli: &amp; contra. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000512">Propterea vt e&longs;t prius.] <emph type="italics"/>Conclu&longs;io generalis e&longs;t, huc, vt exi&shy;<lb/>&longs;timo, &egrave; fine primi huius capitis, vbi melius collocaretur, <expan abbr="tr&atilde;spo&longs;ita">transpo&longs;ita</expan>, <lb/>quod amplius declarant ea, qu&aelig; &longs;ubijciuntur de vecte &amp; libra, ad <lb/>qu&aelig; cum referat omnia Mechanica, &amp; ip&longs;a vectis &amp; libra referan&shy;<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, libr&aelig; <lb/>motiones explicat. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000513"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000514">Pr&aelig;terea etiam, quod, <lb/>cum vna &longs;it ea linea, qu&aelig; <lb/>ex centro, nullum eorum, <lb/>qu&aelig; in ea &longs;unt, <expan abbr="p&utilde;ctorum">punctorum</expan>, <lb/>&aelig;qu&egrave; 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&shy;<lb/>culi contingunt, vt in <expan abbr="&longs;e-qu&etilde;tibus">&longs;e&shy;<lb/>quentibus</expan> problematis fiet <lb/>manife&longs;tum. </s></p><p type="head">

<s id="id.000515">COMMENTARIVS. </s></p><p type="main">

<s id="id.000516">Pr&aelig;terea etiam.] <emph type="italics"/>Quarta repugnantia e&longs;t in circulo ex in&aelig;&shy;<lb/>qualitate motuum in eiu&longs;dem line&aelig; circulum de&longs;cribentis diuer&shy;<lb/>&longs;is punctis. </s>

<s id="id.000517">In&aelig;qualiter enim moueri dicuntur, &amp; qu&aelig; eodem tem&shy;<lb/>pore diuer&longs;a permeant &longs;patia, &amp; qu&aelig; in &aelig;qualibus 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, qu&aelig; in&shy;<lb/>&longs;unt in vna eademque linea circulum de&longs;cribente, illud quod remo&shy;<lb/>tius e&longs;t &agrave; centro, maius &longs;patium conficit: quam quod propinquius, li&shy;<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, qu&aelig; ab vnoquoque eorum qu&aelig; &longs;unt in &longs;emidia&shy;<lb/>metro punctorum, de&longs;cribitur, &longs;i quodlibet <expan abbr="p&utilde;ctorum">punctorum</expan> in motu line&aelig; <lb/>intelligatur &longs;ui, vt puncti, ve&longs;tigium relinquere, vt in eo quod circu&shy;<lb/>lum vndiquaque comprehendit. </s>

<s id="id.000521">Peripheriam autem remotioris pun&shy;<lb/>cti &agrave; centro, id e&longs;t &longs;emidiametri maioris e&longs;&longs;e maiorem peripheria pun&shy;<lb/>cti centro propinquioris, id e&longs;t &longs;emidiametri minoris, &longs;ic demon&longs;tra&shy;<lb/>bimus. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.062.jpg" pagenum="23"/><p type="main">

<s id="id.000522"><emph type="italics"/>E&longs;to A B C, peripheria &longs;emidiametri maioris A E: item <lb/>D F G, peripheria &longs;emidiametri D H minoris. </s>

<s id="id.000523">Dico periphe&shy;<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/>&amp; D G diame&shy;<lb/>ter. </s>

<s id="id.000525">Quia igi&shy;<lb/>tur vt diameter <lb/>A C ad <expan abbr="&longs;u&atilde;">&longs;uam</expan> <expan abbr="pe-ripheri&atilde;">pe&shy;<lb/>ripheriam</expan> A B C: <lb/>ita &amp; D G diameter ad &longs;uam peripheriam D F G, per ea qu&aelig; <lb/>demon&longs;trata &longs;unt ab Archimede prop. 3. lib. de dimen&longs;. circuli, &amp; <lb/>vici&szlig;im proportionales erunt A C diameter ad D G diametrum: <lb/>vt peripheria A B C ad peripheriam D F G prop. 16. lib. 5. &amp; <lb/>quia A E &amp; 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 &amp; peripheria A B C ad peri&shy;<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&shy;<lb/>pheria A B C maior: quam peripheria D F G. </s>

<s id="id.000531">Et &longs;ic peripheria <lb/>remotioris puncti &agrave; centro maior e&longs;t peripheria puncti centro pro&shy;<lb/>pinquioris, quod fuit demon&longs;trandum. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000532"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000533">Quod autem circulus <lb/><expan abbr="c&otilde;trariis">contrariis</expan> cieatur motibus, <lb/>&amp; alterum extremorum <lb/>diametri in quo e&longs;t A, dum <lb/>mouetur antror&longs;um, alte&shy;<lb/>rum in quo e&longs;t B mouea&shy;<lb/>tur retror&longs;um, ideo non&shy;<lb/>nulli <expan abbr="faci&utilde;t">faciunt</expan>, vt ab vna mo&shy;<lb/>tione multi circuli &longs;imul <lb/>in contraria moueantur: <lb/>vt quos in deorum templis <lb/>&longs;tatuunt, efficientes circu&shy;<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 &aelig;reos &amp; 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&shy;<lb/>tro circuli A B antror&shy;<lb/>&longs;um mota, diameter circu&shy;<lb/>li G D retror&longs;um moue&shy;<lb/>bitur, circuli in quo e&longs;t A <lb/>diametro circa idem mo&shy;<lb/>ta. </s>

<s id="id.000535">Circulus igitur in quo <lb/>e&longs;t G D, contr&agrave;, quam is, <lb/>in quo e&longs;t A B mouebi&shy;<lb/>tur: idemque &longs;equentem <lb/>in quo e&longs;t E Z propter <lb/>eandem cau&longs;am contra &longs;e <lb/>mouebit, &amp; eodem modo <lb/>&longs;i plures fuerint vno com&shy;<lb/>moto itidem <expan abbr="faci&etilde;t">facient</expan>. </s>

<s id="id.000536">Hinc <lb/>Architecti Fabri, cum <expan abbr="h&atilde;c">hanc</expan> <lb/>in circulo naturam depre&shy;<lb/>hendi&longs;&longs;ent, <expan abbr="organ&utilde;">organum</expan> fabri&shy;<lb/>cantur principium occu&shy;<lb/>lentes, vt &longs;it de machina, <lb/>&longs;olum hoc, quod admira&shy;<lb/>bile, apertum: quod autem <lb/>cau&longs;a, occultum. </s></p><p type="head">

<s id="id.000537">COMMENTARIVS. </s></p><p type="main">

<s id="id.000538">Qvod autem circulus.] <emph type="italics"/>Tertia repugnantia in vnius cir&shy;<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&shy;<lb/>que fer&egrave; fit denticulis pectinis in&longs;tar &longs;e&longs;e &longs;ubingredientibus in peri&shy;<lb/>phcria pr&aelig;diti, quorum primus A B, moueatur antror&longs;um, &longs;eu &longs;e&shy;<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&shy;<lb/>dum</expan> <expan abbr="in-ferior&etilde;">in&shy;<lb/>feriorem</expan> <lb/><expan abbr="periphe-ri&atilde;">periphe&shy;<lb/>riam</expan>, vt <lb/>G ad B: <lb/>tum ter&shy;<lb/>tius E Z ad &longs;ecundi motum mouebitur etiam, &longs;ed antror&longs;um, vt E <lb/>ad F, &amp; &longs;int deinceps alternatim infiniti denticulis &longs;e&longs;e &longs;ubinui&shy;<lb/>cem ingredientibus, &longs;emper mouebuntur. </s>

<s id="id.000540">Vnde tunc &agrave; Fabro dato <lb/>principio motionis, vertebra vertebram continenter mouet, vltim&aacute;&shy;<lb/>que ab illis &longs;imulacrorum excita fit pr&aelig;teruectio, non aliter quam in <lb/>animalium genere &agrave; &longs;en&longs;u, vel intellectione motionum exorto prin&shy;<lb/>cipio intrin&longs;ecis commotis cau&longs;is, &longs;eque inuicem mouentibus, vt alij <lb/>po&longs;tmodum extrin&longs;ecus, cum partium ip&longs;arum, tum etiam vniuer&longs;i <lb/>corporis vi&longs;untur motus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000541">Hinc architecti.] <emph type="italics"/>Sicuti ante ex vnius circuli contrarijs mo&shy;<lb/>tibus libram, vectem, mechanic&aacute;que in&longs;trumenta magnam habere <lb/>vim ad onera mouendum &longs;ubindicauit: &longs;ic nunc ex circulorum con&shy;<lb/>tiguorum &amp; vari&egrave; multiplicatorum contrarij;s motionibus machi&shy;<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;titueb&atilde;tur">de&longs;tituebantur</expan>, in templis &longs;uorum <expan abbr="deor&utilde;">deorum</expan> collocatis, <lb/>&amp; etiam per vrbium vicos, &amp; plateas ge&longs;tatis, <expan abbr="authoritat&etilde;">authoritatem</expan> dijs &longs;uis <lb/><expan abbr="c&otilde;flaui&longs;&longs;e">conflaui&longs;&longs;e</expan>, &amp; 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, Machin&aelig; vero ip&longs;&aelig; aliquanti&longs;per, non <lb/>multo tamen tempore per &longs;e ip&longs;&aelig; arti&longs;icios&egrave; 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&shy;<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 ade&ograve; <lb/>celebrat&aelig; D&aelig;dali &longs;tatu&aelig;, qu&aelig; inquit Plato ni&longs;i ligat&aelig; aufugiebant,<emph.end type="italics"/><lb/><arrow.to.target n="marg12"/><lb/><emph type="italics"/>&amp; vago quodam &longs;inuo&longs;oque impetu ferebantur in fugam: ligat&aelig; <lb/>vero permanebant, vnde ill&aelig; non magno pretio emebantur in&longs;tar <lb/>&longs;erui fugitiui: h&aelig; contra magno. </s>

<s id="id.000547">Erant enim pr&aelig;clara 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&shy;<lb/>ter &longs;e coniunctione, aliquoque ex &longs;e mobili vt animali, vento, fu&shy;<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 maxim&egrave; vti&shy;<lb/>lia, qualia &longs;unt horologia veterum clep&longs;ydras, &amp; gnomones &longs;ine luce <lb/>&amp; &longs;erenitate inutiles, commoditate &amp; perpetuitate long&egrave; &longs;uperan&shy;<lb/>tia, quibus hodie dies ciuilis in 24. partes, quas horas vocant, di&shy;<lb/>&longs;tribuitur. </s>

<s id="id.000548">Ex quibus alia &longs;unt &longs;tataria, &amp; in &longs;ummis templorum no&shy;<lb/>&longs;trorum partibus collocata: alia in <expan abbr="homin&utilde;">hominum</expan> collis, Zon&iacute;&longs;ue <expan abbr="app&etilde;&longs;a">appen&longs;a</expan> pr&aelig; <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/>eminenti&szlig;imo po&longs;itum e&longs;t, in quo vniuer&longs;i mundi c&aelig;le&longs;tis com&shy;<lb/>pago, orbibus &longs;uis in &longs;uas partes di&longs;tincta vi&longs;itur, In hoc enim <lb/>octaui orbis tardi&szlig;imum motum, Zodiaci duodecim &longs;igna, Solis per <lb/>puncta ecliptica tran&longs;itum, Lun&aelig; varias apparitiones, &longs;ingulorum <lb/>planetarum progre&longs;&longs;us, regre&longs;&longs;us, &longs;tationes, latitudines, altitudines, <lb/>innumeraque alia pr&aelig;ter temporum momenta, &amp; horas tum &aelig;qua&shy;<lb/>les, tum in&aelig;quales intueri licet. </s>

<s id="id.000550">Ita tamen, vt quod hic dicitur, quic&shy;<lb/>quid e&longs;t rotarum, ponderum, molarum, denticulorum, nolarum, vir&shy;<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, &amp; occultetur, qu&aelig; ver&ograve; in tanta machina tot admirabilia <lb/>&longs;unt, <expan abbr="appare&atilde;t">appareant</expan>. </s>

<s id="id.000551">H&aelig;c, &amp; qu&aelig; imaguncularum ince&longs;&longs;um, &longs;altum, cho&shy;<lb/>reas repr&aelig;&longs;entant, faciunt, vt qu&aelig; de Archit&aelig; columba volatili, &amp; <lb/>de Archimedis &longs;ph&aelig;ra ver&longs;atili memori&aelig; reliquit antiquitas, pro <lb/>fal&longs;is minime habeamus. <emph.end type="italics"/></s></p><p type="margin">

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

<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/&shy;<lb/>zw zuga\ a)kribetera/ e)sti tw=n <lb/>e)latto/nwn. </foreign></s></p><p type="main">

<s id="id.000554">2. De libra propter quid <lb/>maior linea in circulo <lb/>celerius fertur, minore. <lb/></s>

<s id="id.000555">Ex quo fit vt libr&aelig; ma&shy;<lb/>iores minoribus &longs;int <lb/>exactiores. </s></p><p type="main">

<s><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000557"><expan abbr="Prim&utilde;">Primum</expan> igitur qu&ecedil; circa <expan abbr="li-br&atilde;">li&shy;<lb/>bram</expan> <expan abbr="c&otilde;tingunt">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/>libr&aelig; 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&shy;<lb/>culo <expan abbr="di&longs;t&atilde;tior">di&longs;tantior</expan> linea &agrave; cen&shy;<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&shy;<lb/>fariam, &longs;iue enim in mino&shy;<lb/>ri tempore &ecedil;quale &longs;patium <lb/>tran&longs;ierit, celerius e&longs;&longs;e di&shy;<lb/>cimus: &longs;iue in <expan abbr="t&etilde;pore">tempore</expan> &ecedil;qua&shy;<lb/>li, maius. </s>

<s id="id.000561">Maior autem li&shy;<lb/>nea in &aelig;quali <expan abbr="t&etilde;pore">tempore</expan> ma&shy;<lb/>iorem circulum de&longs;cribit. <lb/></s>

<s id="id.000562">Qui enim extra e&longs;t, maior <lb/>e&longs;t eo, qui intus. </s></p><p type="head">

<s id="id.000563">COMMENTARIVS. </s></p><p type="main">

<s id="id.000564">De libra propter.] <emph type="italics"/>In hoc capite Ari&longs;toteles vult o&longs;tendere <lb/>cur libr&aelig; longiorum brachiorum &longs;int exactiores: quam libr&aelig; <lb/>breuiorum. </s>

<s id="id.000565">Et huius problematis cau&longs;am refert ad circulum, circu&shy;<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&shy;<lb/>rum e&longs;t fundamentum multorum aliorum problematum po&longs;tea ex&shy;<lb/>plicandorum, diligenter imprimis demon&longs;trat. </s>

<s id="id.000567">Et primum quod re&shy;<lb/>cta de&longs;cribens circulum (vno nomine relicta periphra&longs;i radium h&icirc;c <lb/>appellabimus) duabus lationibus feratur, ii&longs;que in nulla ratione &amp; <lb/>nullo tempore. </s>

<s id="id.000568">Et ex his alteram e&longs;&longs;e &longs;ecundum naturam, alteram <lb/>pr&aelig;ter naturam. </s>

<s id="id.000569">Po&longs;trem&ograve; quod latio &longs;ecundum naturam in maiore <lb/>circulo maior &longs;it: quam in minore. </s>

<s id="id.000570">Latio autem pr&aelig;ter naturam in <lb/>minore circulo maior &longs;it: quam in maiore. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000571">Primum igitur.] <emph type="italics"/>Proponitur problema de librarum in&aelig;qua&shy;<lb/>lium exactiore iudicio, quod pendet &agrave; minorum ponderum deprehen&shy;<lb/>&longs;ione, vt ea &longs;it exactior per quam minora pondera expendi po&longs;&longs;unt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000572">Huius vero.] <emph type="italics"/>Cau&longs;a exactiorum librarum refertur ad circuli <emph.end type="italics"/><pb xlink:href="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 &aelig;quali <lb/>tempore maius &longs;patium, &amp; proinde &longs;en&longs;ibilius tran&longs;eunt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000573">Celerius enim.] <emph type="italics"/>Celeritatis lationum duos modos adfert &longs;i&shy;<lb/>miles ijs quos cap. 2. lib. 6. de Phy&longs;. auditu attulit, vt vtro longioris <lb/>radij celeritas accipi debeat, intelligatur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000574">Qui enim extra.] <emph type="italics"/>E duobus circulis concentricis, qui extra e&longs;t, <lb/>e&longs;t quoddam <expan abbr="tot&utilde;">totum</expan>, &amp; 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">Pr&aelig;terea <expan abbr="c&utilde;">cum</expan> circuli &aelig;quales &longs;int, <expan abbr="quor&utilde;">quorum</expan> &longs;emi&shy;<lb/>diametri &longs;int &aelig;quales def. 1. lib. 3. ele. </s>

<s id="id.000580">Illi quorum &longs;emidiametri &longs;unt <lb/>in&aelig;quales, erunt &amp; in&aelig;quales, &amp; ille maior, cuius &longs;emidiameter <lb/>maior. </s>

<s id="id.000581">Qu&aelig; licet vera &longs;int non tamen &longs;tatim &longs;equitur figur&aelig; plan&aelig; <lb/>cuius area maior e&longs;t, e&longs;&longs;e &amp; 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 &agrave; 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, qu&aelig; maiores con&longs;titui po&longs;&longs;unt ijs &agrave; quibus ambiuntur. <lb/></s>

<s id="id.000584">Ob h&aelig;c igitur, cum hic locus non tam debeat intelligi de circulis, <lb/>quam circulorum peripherijs, merit&ograve; ante, cum huius proprietatis <lb/>mentio fieret, capite pr&aelig;cedenti peripheriam maioris circuli periphe&shy;<lb/>ria minoris maiorem e&longs;&longs;e demon&longs;trauimus, &longs;ed etiam huius magni&shy;<lb/>tudinis maioris cau&longs;a, hic ab Ari&longs;totele &longs;ubiungitur. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000585"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

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

<s id="id.000587"><expan abbr="C&utilde;">Cum</expan> igitur in ali&shy;<lb/>qua ratione du&ecedil; <expan abbr="s&utilde;t">sunt</expan> ill&aelig; la&shy;<lb/>tiones, nece&longs;&longs;e e&longs;t id, quod <lb/>fertur <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="rect&atilde;">rectam</expan> ferri, <lb/>qu&aelig; fit diameter figur&aelig;, <lb/><expan abbr="qu&atilde;">quam</expan> rect&aelig; in ea ratione <expan abbr="c&otilde;-&longs;titut&aelig;">con&shy;<lb/>&longs;titut&aelig;</expan>, <expan abbr="c&otilde;prehendunt">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&shy;<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> &amp; quidem <lb/><foreign lang="greek">a</foreign> feratur ad <foreign lang="greek">b,</foreign> &amp; <foreign lang="greek">a b</foreign><lb/>etiam feratur ad <foreign lang="greek">h g</foreign>: la&shy;<lb/>tum vero &longs;it <foreign lang="greek">a</foreign> ad <foreign lang="greek">d,</foreign> &amp; <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">e. </foreign>Igitur cum latio&shy;<lb/>nis ratio erat ea quam ha&shy;<lb/>bet <foreign lang="greek">a b</foreign> ad <foreign lang="greek">a g</foreign>: nece&longs;&longs;e <lb/>e&longs;t &amp; ip&longs;am <foreign lang="greek">a d</foreign> ad <foreign lang="greek">a e</foreign> ean&shy;<lb/>dem habere rationem. </s>

<s id="id.000589">Si&shy;<lb/>mile e&longs;t enim ratione par&shy;<lb/>uum quadrilaterum maio&shy;<lb/>ri. </s>

<s id="id.000590">Itaque &amp; eadem diame&shy;<lb/>ter vtriu&longs;que, &amp; 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&shy;<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&shy;<lb/>metrum duabus lationi&shy;<lb/>bus nece&longs;&longs;e habet in ratio&shy;<lb/>ne laterum ferri. </s></p><p type="head">

<s id="id.000593">COMMENTARIVS. </s></p><p type="main">

<s id="id.000594">Horum vero cau&longs;a.] <emph type="italics"/>In&aelig;qualium <expan abbr="circulor&utilde;">circulorum</expan> ab in&aelig;qualibus <lb/>radiis <expan abbr="de&longs;criptor&utilde;">de&longs;criptorum</expan>, &amp; maioris quidem &agrave; maiori multo ab&longs;tru&shy;<lb/>&longs;ior a&szlig;ignatur cau&longs;a ex radij de&longs;cribentis circulum duabus lationi&shy;<lb/>bus, qu&aelig; inter &longs;e <expan abbr="null&atilde;">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 pr&aelig;ter 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&shy;<lb/>mirabile? </s>

<s id="id.000598">Circuli igitur radius, qui his duabus ita fertur in de&longs;cri&shy;<lb/>ptione circuli, &amp; circulus, qui &agrave; radio tali efficitur, erit admirabilis. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000599">Cum igitur in.] <emph type="italics"/>Aggreditur demon&longs;trare radij duas lationes <lb/>nullam habere rationem inter &longs;e. </s>

<s id="id.000600">Syllog. &longs;ic e&longs;t. </s>

<s id="id.000601">Omne duabus latio&shy;<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&shy;<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&shy;<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"/>qu&aelig; &longs;int inter &longs;e in ratione, quam <lb/>du&aelig; 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"/>&amp; 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 &amp;<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"/>&amp; rectrangulum minus<emph.end type="italics"/> <foreign lang="greek">a d z e</foreign> <emph type="italics"/>com&shy;<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 &amp; &longs;imile erit <lb/>def. 1. lib. 6. &amp; 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&shy;<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;t&aelig; &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&shy;<lb/>&longs;entit quod &agrave; Proclo ex Gemino acceptum &longs;ic expo&longs;itum e&longs;t. </s>

<s id="id.000610">Si qua&shy;<lb/>drangulum duo&longs;que motus qui &aelig;quali celeritate fiant, alterum qui&shy;<lb/>dem per longitudinem: alterum vero per latitudinem intellexeris <lb/>dimetiens producetur recta exi&longs;tens linea, lib. 2. comm. in def. rect&aelig; <lb/>line&aelig;. </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 &agrave; recta producere rectam, quod <lb/>e&longs;t contra naturam circuli. </s>

<s id="id.000613">Non igitur du&aelig; lationes ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ferun&shy;<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 h&icirc;c obiici pote&longs;t quod Sol motu pri&shy;<lb/>mi mobilis mouetur ab Oriente in Occidentem in 24. horis, &amp; motu <lb/>proprio ab Occidente in Orientem in aliquo tempore quantum e&longs;t <lb/>quod re&longs;pondet &aelig;quatori coa&longs;cendenti cum 59'. 8&quot;. Eclyptic&aelig;. </s>

<s id="id.000614">Et &longs;ic <lb/>eius du&aelig; lationes &longs;unt in ratione aliqua, nec tamen Sol fertur &longs;ecun&shy;<lb/>dum rectam &longs;ed <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> arcum Eclyptic&aelig;. </s>

<s id="id.000615">Ita e&longs;t, ob id <expan abbr="dicend&utilde;">dicendum</expan> hic <lb/>dictas ab Ari&longs;totele du&aelig; lationes non &longs;impliciter <expan abbr="intellig&etilde;das">intelligendas</expan>: &longs;ed ta&shy;<lb/>les, qu&aelig; <expan abbr="fer&atilde;tur">ferantur</expan> amb&aelig; <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></p><p type="main">

<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 qu&aelig; <lb/>&longs;imilia &longs;unt quadrangula, habent latera, qu&aelig; circum &aelig;quales angu&shy;<lb/>los propertionalia, ex def. 1. lib. 6. elem. <emph.end type="italics"/></s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.070.jpg" pagenum="31"/><chap><p type="main">

<s id="id.000619"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000620">Si enim in alia aliqua, <lb/>non feretur <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> dia&shy;<lb/>metrum. </s>

<s id="id.000621">Si vero mobilis <lb/>du&aelig; lationes in nulla &longs;int <lb/>ratione, nulloque in tem&shy;<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, &amp; completis la&shy;<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&shy;<lb/>tur &longs;ecundum rectam pro&shy;<lb/>gredietur, id quod fertur <lb/>in nulla ratione, nulloque <lb/>in tempore. </s>

<s>[Si enim <expan abbr="&longs;e-c&utilde;dum">&longs;e&shy;<lb/>cundum</expan> rationem aliquam <lb/>latum &longs;it in aliquo tempo&shy;<lb/>re, nece&longs;&longs;e e&longs;t illud tempus <lb/>rectam e&longs;&longs;e lationem, pro&shy;<lb/>pter ea qu&aelig; ante dicta &longs;unt.] </s>

<s>Itaque circulare e&longs;t quod <lb/>&longs;ecundum duas lationes latum e&longs;t in nulla ratione nullo <lb/>in tempore. </s></p><p type="head">

<s id="id.000625">COMMENTARIVS. </s></p><p type="main">

<s id="id.000626">Si enim in alia.] <emph type="italics"/>Locus hic paulo ob&longs;curior, debet &longs;ic intelligi, <lb/>vt &longs;i exempli gratia, a duabus lationibus latum non feratur in <lb/>ratione quidem data<emph.end type="italics"/> <foreign lang="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&shy;<lb/>trum<emph.end type="italics"/> <foreign lang="greek">a h,</foreign> <emph type="italics"/>nihilominus tamen feretur <lb/>&longs;ecundum rectam, qu&aelig; erit diameter <lb/>figur&aelig; &agrave; lateribus alterius rationis <lb/>con&longs;titut&aelig;, vt e&longs;t in pr&aelig;&longs;enti dia&shy;<lb/>grammate<emph.end type="italics"/> <foreign lang="greek">a x</foreign> <emph type="italics"/>diameter quadrilateri <lb/>&longs;ub<emph.end type="italics"/> <foreign lang="greek">a d, a e</foreign> <emph type="italics"/>comprehen&longs;i. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.071.jpg" pagenum="32"/><p type="main">

<s id="id.000627">Si vero mobilis.] <emph type="italics"/>Conclu&longs;io e&longs;t confirmata reiterato propo&longs;i&shy;<lb/>tionis pr&aelig;cedentis pro&longs;yllogi&longs;mo, &longs;ic. </s>

<s id="id.000628">Si du&aelig; lationes puncti mobilis <lb/>&longs;unt in nulla ratione, nulloque in tempore, impo&szlig;ibile e&longs;t mobile hoc <lb/>latum e&longs;&longs;e &longs;ecundum rectam: atqui puncti de&longs;cribentis circulum du&aelig; <lb/>lationes &longs;unt in nulla ratione, null&oacute;que in tempore. </s>

<s id="id.000629">Ergo impo&szlig;ibile <lb/>e&longs;t punctum, quod de&longs;cribit circulum, ferri &longs;ecundum rectam. </s>

<s id="id.000630">Sint <lb/>enim lationes ill&aelig; in aliqua ratione. </s>

<s id="id.000631">Ergo punctum feretur &longs;ecun&shy;<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&shy;<lb/>bus analoga &longs;unt. </s>

<s id="id.000636">H&icirc;c 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&shy;<lb/>tum e&longs;&longs;e in tempore: alterum, cum amb&aelig; lationes &longs;int in eodem ge&shy;<lb/>nere motus, &longs;cilicet localis, qu&icirc; 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&shy;<lb/>tiplicata, alterius vici&szlig;im 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"/>&amp; non &longs;olum indicibilem, quod numeris exprimi nequeat: &longs;ed &amp; <lb/>quod rectis lineis geometric&egrave; id e&longs;t exact&egrave;, exprimi non po&szlig;it, qualis <lb/>non e&longs;t inter duas lationes &egrave; quibus recta creatur, cum h&aelig;c &longs;i nume&shy;<lb/>ris non po&szlig;it exprimi, at rectis lineis &longs;altem geometric&egrave; exprimitur. <lb/></s>

<s id="id.000643">vt cum duarum rectarum, qu&aelig; 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 h&icirc;c vt inter peripheriam &amp; diametrum &longs;it aliqua ratio, veluti <lb/>inter arcum &amp; &longs;ubtendentem: h&aelig;c 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"/>&amp; 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&shy;<lb/>di, vt nullum eius detur in&longs;tans, quo vna latio fiat, quo etiam non <lb/>&amp; altera itidem fiat: quod prioribus licet commune e&longs;&longs;e po&szlig;it: pro&shy;<lb/>pter tamen laterum in&aelig;qualitatem vbi in &aelig;qualia dantur, non ita <lb/>&longs;implex &amp; indiui&longs;ibile e&longs;t. </s>

<s id="id.000648">C&aelig;terum duas has motiones facile ani&shy;<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&shy;<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&shy;<lb/>culi retineant. </s>

<s id="id.000649">H&aelig;c enim in altero extremo mu&longs;ca, tanquam in ex&shy;<lb/>tremo radij circulum de&longs;cribentis volatu &longs;uo de&longs;cribit circulum: hic <lb/>volatus compo&longs;itus e&longs;t &egrave; duobus motibus: vno, quo h&aelig;c mu&longs;ca pro&shy;<lb/>prio fertur, <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> quem &longs;e&longs;e &egrave; 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;c&aelig; violentus e&longs;t, &amp; non naturalis <lb/>vt &agrave; quo etiam cum pes abrumpitur pr&aelig; &longs;uo conatu, aut nodus for&shy;<lb/>tuit&ograve; laxatur, &longs;i liberatur, &longs;tatim rect&agrave; aufugit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000651">Si enim &longs;ecundum.] <emph type="italics"/>Hanc particulam parenthe&longs;i &longs;ic [ ] in&shy;<lb/>tercludendam curauimus, quod eam &longs;uperuacuam e&longs;&longs;e cum Leonico <lb/>exi&longs;timemus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000652">Itaque circulare.] <emph type="italics"/>Proinde e&longs;t ac &longs;i diceret, cum via &longs;eu linea <lb/>per quam fertur radij extremum mobile &longs;it maxime vniformis, vt <lb/>ex definitione circuli con&longs;tat, nec tamen recta: re&longs;tat, vt &longs;it circula&shy;<lb/>ris &longs;eu rotunda, &agrave; medio &longs;cilicet comprehen&longs;i &longs;patij &aelig;qualiter 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, &amp; extremum in ea fiat <lb/>primum, vt in peripheria: nullum tamen punctum in eius medio e&longs;t, <lb/>&agrave; quo omnes rect&aelig; ad ellip&longs;is peripheriam &longs;int &aelig;quales: non parabo&shy;<lb/>l&aelig;, non hyperbol&aelig;, non &longs;pirali &longs;eu volut&aelig;. </s>

<s id="id.000654">Quia in nulla harum, quod <lb/>e&longs;t extremum fit primum, quod peripheri&aelig; conuenit. </s>

<s id="id.000655">Pr&aelig;terea nulla <lb/>harum &longs;implex e&longs;t linea. </s>

<s id="id.000656">Agitur h&icirc;c autem de &longs;implicibus tantum, <lb/>qu&aelig; vno &longs;implici motu, vel &longs;i duobus, ijs &longs;imilibus creantur, &amp; &longs;i&shy;<lb/>milares &longs;unt: quales cum du&aelig; tantum &longs;int recta &longs;cilicet &amp; circula&shy;<lb/>ris, inde bene inferetur &egrave; po&longs;ita &longs;implic&egrave; &longs;i recta non e&longs;t, e&longs;&longs;e cir&shy;<lb/>cularis. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000657"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000658">Quod vero recta <expan abbr="de&longs;cri-b&etilde;s">de&longs;cri&shy;<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="rect&atilde;">rectam</expan> fieret num&shy;<lb/>quam perpendicularis. </s>

<s id="id.000659">Et <lb/>fieri &agrave; <expan abbr="c&etilde;tro">centro</expan> <expan abbr="perpendicula-r&etilde;">perpendicula&shy;<lb/>rem</expan> [<expan abbr="dem&otilde;&longs;trem">demon&longs;trem</expan>us]. </s> 

<s>Sit circu&shy;<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> &amp; extremum <foreign lang="greek">b</foreign><lb/>feratur ad <foreign lang="greek">d,</foreign> perueniet &longs;a&shy;<lb/>ne aliquando ad <foreign lang="greek">g. </foreign></s>

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

<s id="id.000660">COMMENTARIVS. </s></p><p type="main">

<s id="id.000661">Qvod vero recta.] <emph type="italics"/>Quia &longs;uperioris &longs;yllogi&longs;mi a&longs;&longs;umptio a&longs;&longs;u&shy;<lb/>mebat <expan abbr="Radi&utilde;">Radium</expan> duabus &longs;imul ferri lationibus, id ip&longs;um h&icirc;c breui&shy;<lb/>ter, ideo valde ob&longs;cur&egrave; 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&shy;<lb/>bus: non vna tantum, quia ad vnam tantum loci differentiam, <lb/>cum &longs;it quid &longs;implici&szlig;imum, 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 &agrave; diametro cir&shy;<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&shy;<lb/>metro ad alteram numquam con&longs;equeretur <lb/>cum &longs;itum, per quem ip&longs;i &agrave; centro perpen&shy;<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&shy;<lb/>pti. </s>

<s id="id.000666">Non igitur vna latione tantum fer&shy;<lb/>tur: fertur ergo pluribus. </s>

<s id="id.000667">Et quidem vna, vt <lb/>antror&longs;um: qua qua &longs;i diffunditur, &amp; ab&longs;ce&shy;<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&shy;<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&shy;<lb/>tur longius, quam &aelig;qualitas di&longs;tanti&aelig; vndi&shy;<lb/>que &agrave; centro &longs;eruand&aelig; 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 h&aelig;c latio quanta &longs;it <lb/>men&longs;uratur lineis rectis, quarum altera in po&longs;te&shy;<lb/>riore diagrammate e&longs;t &longs;inus rectus<emph.end type="italics"/> <foreign lang="greek">g e,</foreign> <emph type="italics"/>altera <lb/>ver&ograve; e&longs;t &longs;inus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b g. </foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.074.jpg" pagenum="35"/><p type="main">

<s id="id.000669">Demon&longs;tremus.] <emph type="italics"/>Dee&longs;t hoc vocabulum in Gr&aelig;co &longs;ine quo <lb/>&longs;en&longs;us e&longs;t imperfectus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000670">Si igitur ferebatur.] <emph type="italics"/>Rur&longs;us totum hunc textum his notis <lb/>[ ] interclu&longs;um inaniter repeti arbitramur. </s>

<s id="id.000671">hoc enim e&longs;t quod an&shy;<lb/>tea e&longs;t demon&longs;tratum. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000672"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000673">Si vero duorum eadem <lb/>vi latorum vnum plus re&shy;<lb/>pellitur, alterum minus: <lb/>&aelig;quum e&longs;t, plus repul&longs;um, <lb/>altero minus repul&longs;o tar&shy;<lb/>dius ferri. </s>

<s id="id.000674">Quod videtur <lb/>contingere maiori &amp; mi&shy;<lb/>nori lineis ab eodem cen&shy;<lb/>tro circulos <expan abbr="de&longs;crib&etilde;tibus">de&longs;cribentibus</expan>. <lb/></s>

<s id="id.000675">Quia enim extremum mi&shy;<lb/>noris propius e&longs;t quie&longs;cen&shy;<lb/>ti, quam &longs;it <expan abbr="extrem&utilde;">extremum</expan> maio&shy;<lb/>ris: qua&longs;i in contrarium re&shy;<lb/>uul&longs;um, in medium tardius <lb/>fertur ip&longs;um minoris extre&shy;<lb/>mum. </s>

<s id="id.000676">Omni igitur circu&shy;<lb/>lum de&longs;cribenti hoc con&shy;<lb/>tingit. </s></p><p type="head">

<s id="id.000677">COMMENTARIVS. </s></p><p type="main">

<s id="id.000678">Si vero duorum.] <emph type="italics"/>Vbi confirmauit in omni radio circulum <lb/>de&longs;cribente duas lationes ine&longs;&longs;e, nunc eas comparat in radijs in&aelig;&shy;<lb/>qualibus, quod ad celeritatem &amp; tarditatem attinet. </s>

<s id="id.000679">Et quidem <lb/>eam, qu&aelig; &longs;ecundum naturam e&longs;t in radio maiore, maiorem: eam ve&shy;<lb/>ro, qu&aelig; pr&aelig;ter naturam, minorem e&longs;&longs;e in eodem demon&longs;trat, vt ra&shy;<lb/>dium maiorem celerius ferri minore concludat. </s>

<s id="id.000680">Syllogi&longs;mus e&longs;t <lb/>connexus &longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000681"><emph type="italics"/>Si duorum eadem vi motorum vnum plus repellitur, alterum <lb/>minus: quod plus repellitur, tardius fertur. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.075.jpg" pagenum="36"/><p type="main">

<s id="id.000682"><emph type="italics"/>Radiorem in&aelig;qualium eadem vi motorum minor plus <lb/>repellitur. <emph.end type="italics"/></s></p><p type="main">

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

<s id="id.000684">Quia enim minoris.] <emph type="italics"/>pro&longs;yllogi&longs;mus e&longs;t a&longs;&longs;umptionis &longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000685"><emph type="italics"/>Quod propius e&longs;t quie&longs;centi &amp; immoto plus retrahitur, quod <lb/>idem e&longs;t ac plus repellitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000686"><emph type="italics"/>Extremum radij minoris mobile propius e&longs;t centro, alteri <lb/>&longs;cilicet extremo quie&longs;centi &amp; immoto: quam extre&shy;<lb/>mum maioris. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000687"><emph type="italics"/>Ergo extremum radij minoris mobile plus retrahetur retror&shy;<lb/>&longs;um, &amp; ab anteriori repelletur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000688"><emph type="italics"/>Illu&longs;trari h&aelig;c <expan abbr="c&otilde;clu&longs;io">conclu&longs;io</expan> po&longs;&longs;et &longs;imilitudine ampli &amp; lat&egrave; patentis re&shy;<lb/>gni, in cuius medio tanquam centro, cum rex pr&aelig;&longs;ideat, partes me&shy;<lb/>dio vicin&aelig; regis legibus magis coarctantur &amp; continentur: quam <lb/>remot&aelig;. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000689"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000690">Et fertur motu <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <lb/>naturam per peripheriam: <lb/>pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan> vero in <expan abbr="tr&atilde;&longs;-uer&longs;um">tran&longs;&shy;<lb/>uer&longs;um</expan>, &amp; 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 pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan> e&longs;t. </s>

<s id="id.000692">quia <lb/>enim centro vicinior e&longs;t ad <lb/>&longs;e <expan abbr="reuell&etilde;ti">reuellenti</expan>, vincitur magis. </s></p><p type="head">

<s id="id.000693">COMMENTARIVS. </s></p><p type="main">

<s id="id.000694">Et fertur motu.] <emph type="italics"/>E duobus motibus in extremo radij mobili <lb/>alterum &longs;ecundum naturam e&longs;&longs;e dicit, nempe qui e&longs;t &longs;ecundum <lb/>peripheriam, alterum pr&aelig;ter naturam, qui e&longs;t in tran&longs;uer&longs;um, &amp; <lb/>ver&longs;us centrum. </s>

<s id="id.000695">Sed rationem huius hic nullam profert. </s>

<s id="id.000696">H&aelig;c au&shy;<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 pr&aelig;ter&shy;<lb/>naturam habere &longs;eu vt ita dicam &longs;ecundariam, &amp; ab alio penden&shy;<lb/>tem nece&longs;&longs;e e&longs;t: &longs;icuti videre e&longs;t in motibus inferiorum orbium c&aelig;le&shy;<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, &amp; 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;implici&szlig;imum, &amp; &longs;imul duabus la&shy;<lb/>tionibus feratur, altera harum erit ei naturalis, altera ad vim alte&shy;<lb/>rius con&longs;equetur. </s>

<s id="id.000699">Et illa quidem potius naturalis erit qu&aelig; &agrave; termino &agrave; <lb/>quo egredi conatur, &amp; 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 &agrave; centro &longs;ecundum periphe&shy;<lb/>riam fertur. </s>

<s id="id.000701">Tum qua forma rei acquiritur, qualis latio per circum&shy;<lb/>ferentiam, cum h&aelig;c &longs;it circuli forma &longs;eu finis. </s>

<s id="id.000702">Relinquitur ergo vt ea <lb/>&longs;it contra <expan abbr="natur&atilde;">naturam</expan> &amp; per accidens, qua ad ip&longs;um centrum reuellitur. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000703"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000704">Quod vero minor plus <lb/>pr&aelig;ter 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> &amp; alter <lb/>minor <foreign lang="greek">x n m c,</foreign> eiu&longs;dem <expan abbr="c&etilde;-tri">cen&shy;<lb/>tri</expan> <foreign lang="greek">a,</foreign> Et traduct&aelig; &longs;int dia&shy;<lb/>metri in magno quidem <lb/><foreign lang="greek">g d, &amp; b e</foreign>: in minori <foreign lang="greek">m c &amp; <lb/>x n</foreign>: atque alterolongum <lb/>compleatur <foreign lang="greek">d y r g. </foreign></s>

<s>Si igi&shy;<lb/>tur <foreign lang="greek">a b</foreign> de&longs;cribens <expan abbr="circul&utilde;">circulum</expan> <lb/>perueniet ad id vnde mo&shy;<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> &amp; 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, &amp; 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&shy;<lb/>rallela ip&longs;i <foreign lang="greek">a b</foreign> qu&aelig; &longs;it <foreign lang="greek">q w <lb/>&amp; w n</foreign> perpendicularis ip&longs;i <lb/><foreign lang="greek">a b</foreign> tum &amp; <foreign lang="greek">h k. </foreign></s>

<s>Sunt vero <lb/><foreign lang="greek">w n &amp; q z</foreign> &aelig;quales. </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 in&aelig;qualibus <lb/>rect&ecedil; &ecedil;quales ad rectos dia&shy;<lb/>metro excitat&aelig;, de diame&shy;<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> &aelig;qualis ip&longs;i <lb/><foreign lang="greek">q z. </foreign>In quanto vero tempo&shy;<lb/>re <foreign lang="greek">a x</foreign> peragrauit <foreign lang="greek">x q,</foreign> in <lb/><expan abbr="t&atilde;to">tanto</expan> in maiore circulo ex&shy;<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/>&aelig;qualis e&longs;&longs;et) pr&aelig;ter na&shy;<lb/>turam vero minor erat, nempe <foreign lang="greek">b n</foreign> quam <foreign lang="greek">x z. </foreign></s></p><p type="head">

<s id="id.000708">COMMENTARIVS. </s></p><p type="main">

<s id="id.000709">Qvod vero minor.] <emph type="italics"/>Altera e&longs;t confirmatio &longs;ed<emph.end type="italics"/> <foreign lang="greek">grammikh\</foreign><lb/><emph type="italics"/>linearis a&longs;&longs;umptionis &longs;yllogi&longs;mi pr&aelig;cedentis. </s>

<s id="id.000710">Scilicet quod mi&shy;<lb/>nor radius plus retrahatur ad centrum, quam maior. </s>

<s id="id.000711">Vbi ab vtri&longs;que <lb/>&longs;ecundum peripheriam &aelig;quale &longs;patium confectum e&longs;t. </s>

<s id="id.000712">perpendiculis <lb/>enim &aelig;qualibus ip&longs;um men&longs;urantibus partes ab&longs;ci&longs;&longs;&aelig; de diametris, <lb/>qu&aelig; retractionem vtriu&longs;que ad centrum men&longs;urant, in&aelig;quales &longs;unt, <lb/>&amp; in minore circulo, maior: in maiore vero minor. </s>

<s id="id.000713">vt videre lice&shy;<lb/>bit in diagrammate hic de&longs;cripto &amp; &longs;uis rationibus nece&longs;&longs;arijs con&shy;<lb/>firmato. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000714"><emph type="italics"/>Sint duo circuli concentrici maior<emph.end type="italics"/> <foreign lang="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"/>&egrave; cen&shy;<lb/>tro a traiecti diametris<emph.end type="italics"/> <foreign lang="greek">x n &amp; b e. </foreign></s></p><p type="main">

<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"/>&amp; producatur in<emph.end type="italics"/><lb/><foreign lang="greek">h</foreign> <emph type="italics"/>&longs;itque<emph.end type="italics"/> <foreign lang="greek">a q h. </foreign></s></p><p type="main">

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

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

<s id="id.000718"><emph type="italics"/>Rur&longs;us &agrave; puncto<emph.end type="italics"/> <foreign lang="greek">w</foreign> <emph type="italics"/>excitetur perpendicularis line&aelig;<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"/>&amp; &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></p><p type="main">

<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&shy;<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&shy;<lb/>laris, vtpote optima <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>, quia minima, &amp; &longs;ola regularis &amp; 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. &amp; &aelig;quales, quia late&shy;<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. </s>

<s>Erant vtro&shy;<lb/>bique &longs;patia<emph.end type="italics"/> <foreign lang="greek">b w &amp; x q</foreign> <emph type="italics"/>&aelig;qualia. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000723"><foreign lang="greek">b n</foreign> <emph type="italics"/>vero eadem ratione metitur &longs;patium motus pr&aelig;ter naturam <lb/>ip&longs;ius<emph.end type="italics"/> <foreign lang="greek">b, &amp; 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&shy;<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 pr&aelig;ter naturam <lb/>maior in eodem &longs;patio motus naturalis: quam puncti<emph.end type="italics"/> <foreign lang="greek">b. </foreign></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.079.jpg" pagenum="40"/><p type="main">

<s id="id.000724"><emph type="italics"/>Sed &amp; &longs;i perficiantur parallelogramma<emph.end type="italics"/> <foreign lang="greek">d s t f &amp; 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"/>&amp; <lb/>huius retractiones <expan abbr="men&longs;ur&atilde;">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="eti&atilde;">etiam</expan> erit <lb/>ad terminandos motus illos duos <expan abbr="natural&etilde;">naturalem</expan>, &longs;cilicet &amp; pr&aelig;ter <expan abbr="natur&atilde;">naturam</expan>. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000725">Atque alterolongum.] <emph type="italics"/>Hoc <expan abbr="quadrilater&utilde;">quadrilaterum</expan> <expan abbr="oblong&utilde;">oblongum</expan>, &amp; rectan&shy;<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 &amp; pr&aelig;ter naturam. <emph.end type="italics"/></s></p><p type="main">

<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></p><p type="main">

<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&shy;<lb/>citatur in ip&longs;am perpendicularis, qu&aelig; e&longs;t<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>prop. 12. lib. 1. elem. <emph.end type="italics"/></s></p><p type="main">

<s 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 dat&aelig; rect&aelig;<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>duci&shy;<lb/>tur parallela prop. 31. lib. 1. elem. <emph.end type="italics"/></s></p><p type="main">

<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></p><p type="main">

<s id="id.000731">Sunt vero <foreign lang="greek">w n</foreign> &amp;] <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/>t&ugrave;m<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&shy;<lb/>gulos internos ad <expan abbr="ea&longs;d&etilde;">ea&longs;dem</expan> partes rectos, ex fab. proinde &aelig;quales ax. 10. <lb/><expan abbr="itaq;">itaque</expan> parallel&aelig; prop. 28. lib. 1. </s>

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

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

<s id="id.000736">In circulis.] <emph type="italics"/>Ex hoc loco elicitur hoc theorema. </s>

<s id="id.000737">Perpendicula&shy;<lb/>res &agrave; peripheriis in &longs;emidiametros circulorum in&aelig;qualium &aelig;quales <lb/>&longs;egmenta auferunt de &longs;emidiametris in&aelig;qualia, &amp; quidem maius in <lb/>minori comprehen&longs;um inter peripheriam &amp; perpendicularem. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000738">Expo&shy;<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></p><p type="main">

<s id="id.000739"><emph type="italics"/>Sunto <lb/>duo cir<lb/>culi in&shy;<lb/>&aelig;qua&shy;<lb/>les A <lb/>B C ma<lb/>ior &amp; <lb/>D E F <lb/>minor, perpendiculares &longs;int B K, E I &amp; ablat&aelig; A K, D I. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.080.jpg" pagenum="41"/><p type="main">

<s id="id.000740">Deter. <emph type="italics"/>Dico D I e&longs;&longs;e maiorem ip&longs;a A K qu&aelig; e&longs;t &longs;egmentum in <lb/>maiori circulo. </s>

<s id="id.000741">Ante huius fabricam hoc problema e&longs;t <expan abbr="a&longs;&longs;um&etilde;dum">a&longs;&longs;umendum</expan>. <emph.end type="italics"/></s></p><p type="main">

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

<s id="id.000743"><emph type="italics"/>Sit datus circulus A B K C maior, ab A per D centrum reper&shy;<lb/>tum prop. 1. lib. 3. </s>

<s>ducatur A k diameter. </s>

<s id="id.000744">De&longs;cribendus autem &longs;it eo <lb/>minor, cuius accipiatur E <expan abbr="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 &amp; D, &amp; interuallo <lb/>E A de&longs;cribatur A F G. </s>

<s>hic <lb/>tanget interius circulum A B k <lb/>C datum in puncto A. </s>

<s id="id.000745">Nam &longs;i <lb/>&amp; &longs;ecet, vt in puncto H, ducta <lb/>H E. </s>

<s>erit &aelig;qualis ip&longs;i E A def. <lb/>15. lib. 1. non erit igitur E A mi&shy;<lb/>nima omnium qu&aelig; ab E puncto <lb/>extra D centrum circuli A B <lb/>K C cadunt in eius concauam pe&shy;<lb/>ripheriam, quod e&longs;t contra prop. <lb/>7. lib. 3. </s>

<s>non erat igitur H punctum commune vtrique circulo, &amp; <lb/>&longs;ic de alijs. </s>

<s id="id.000748">Circulus igitur A F G, tangit circulum A B K C <lb/>in puncto A prop. 11. lib. 3. </s>

<s>quod oportuit facere. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000749"><emph type="italics"/>Iam nunc de A G maiori &longs;emidiametro detrahatur portio A H <lb/>&aelig;qualis D H minori prop. 3. lib. 1. centro H interuallo A H de&longs;&shy;<lb/>cribatur circulus A M L po&longs;tul. </s>

<s id="id.000750">3. qui erit &aelig;qualis dato D E F. <lb/>def. 1. lib. 3. </s>

<s>Et tanget intus circulum A B C in puncto A ex probl. <lb/>pr&aelig;&longs;umpto. </s>

<s>per punctum B <expan abbr="ducaeur">ducatur</expan> parallela B M prop. 31. lib. 1. <lb/>&amp; per eandem parallela M N qu&aelig; per 34. lib. eiu&longs;dem cum &longs;it <lb/>&aelig;qualis ip&longs;i B K erit &amp; &aelig;qualis ip&longs;i. </s>

<s id="id.000754">E I ax. 1. connectantur M H, <lb/>E H po&longs;t. 1. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000757">Demon&longs;t. </s>

<s><emph type="italics"/>Po&longs;tquam ax. 3. A N, D I &aelig;quales &longs;unt quia reli&shy;<lb/>qu&aelig; ex &aelig;qualibus A H, D H ex fab. demptis &aelig;qualibus N H, <lb/>I H qu&aelig; latera &longs;unt &longs;ub &aelig;qualibus angulis duorum triangulorum <lb/>M N H &amp; I E H habentium duos angulos duobus angulis <lb/>&aelig;quales, &amp; latus lateri &aelig;quale vt e&longs;t in 26. prop. lib. 1. </s>

<s>nempe angu&shy;<lb/>lus qui ad N rectus e&longs;t prop. 29. lib. 1. &amp; qui ad I, rectus ex hypoth. <lb/>ideo &aelig;quales ax. 10. </s>

<s>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"/>&amp; angulus E H I ad centrum con&longs;titutus in &aelig;qualibus circulis ex <lb/>fab. &longs;unt &aelig;quales prop. 27. lib. 3. quia &aelig;quales &longs;unt peripheri&aelig; A M, <lb/>D E ablat&aelig; &longs;cilicet ab &aelig;qualibus &longs;emi&szlig;ibus M N &amp; E I ex <lb/>fab. prop. 3. &amp; 29. lib. 3. </s>

<s>&amp; &longs;ic reliquum latus N H &aelig;quale e&longs;t re&shy;<lb/>liquo I H. </s>

<s id="id.000765">Ergo cum tota A N &aelig;qualis D I &longs;it maior A K <lb/>parte &longs;ua ax. 9. erit &amp; D I maior ip&longs;a A K. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000767">Concl. </s>

<s><emph type="italics"/>Ergo perpendiculares &agrave; peripherijs in &longs;emidiametros &amp; <lb/>ct. </s>

<s>quod fuit demon&longs;trandum. </s>

<s id="id.000769">Hoc autem theorema videtur <expan abbr="quo-d&atilde;modo">quo&shy;<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&shy;<lb/>mentum</expan> &longs;emidiametri e&longs;&longs;e maius, &amp; in minore minus: at non ita e&longs;t vt <lb/>patuit. </s>

<s id="id.000770">Cau&longs;a autem h&aelig;c 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&shy;<lb/>lum mobiliorem, &amp; ideo etiam mouentiorem e&longs;&longs;e minori: rationem <lb/>autem mobilitatum e&longs;&longs;e, vt &longs;emidiametrorum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000771">In quanto vero.] <emph type="italics"/>Conclu&longs;io e&longs;t qua concluditur, vbi motus <lb/>&longs;ecundum naturam in vtri&longs;que circulis &aelig;quales e&longs;&longs;ent: ibi motum <lb/>pr&aelig;ter naturam in maiori circulo minorem, &amp; in minori maiorem <lb/>reperiri. </s>

<s id="id.000772">Antea dixerat duas lationes illas e&longs;&longs;e in nulla ratione, in&shy;<lb/>tellige igitur qu&aelig; rectis lineis exact&egrave; exprimi po&szlig;it. </s>

<s id="id.000773">Nam &longs;inus tam <lb/>rectus quam ver&longs;us, quibus rationis harum lationum termini expri&shy;<lb/>muntur, vt &longs;int rect&aelig; line&aelig;: h&aelig; 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&shy;<lb/>men vt hic quodammodo, &amp; vt aiunt fer&egrave;. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000775"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<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="natur&atilde;">naturam</expan>, <lb/>ad id quod <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> natu&shy;<lb/>ram: &longs;ic quod pr&aelig;ter natu&shy;<lb/>ram, ad id quod pr&aelig;ter <expan abbr="na-tur&atilde;">na&shy;<lb/>turam</expan>. </s>

<s id="id.000777">Igitur maiorem quam <lb/><foreign lang="greek">b w</foreign> <expan abbr="peripheri&atilde;">peripheriam</expan>, vt <foreign lang="greek">b h</foreign> <expan abbr="per-tr&atilde;&longs;ijt">per&shy;<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&shy;<lb/>les <expan abbr="c&otilde;ting&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/>pr&aelig;ter naturam ad motus <lb/>&longs;ecundum naturam. </s>

<s id="id.000780">Si igi&shy;<lb/>tur maius e&longs;t id quod <expan abbr="&longs;ec&utilde;-dum">&longs;ecun&shy;<lb/>dum</expan> <expan abbr="natur&atilde;">naturam</expan> in maiore cir&shy;<lb/>culo, &amp; quod e&longs;t pr&ecedil;ter na&shy;<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&shy;<lb/>cto <foreign lang="greek">b</foreign> &longs;ecundum <expan abbr="quid&etilde;">quidem</expan> na&shy;<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&shy;<lb/>laris, pr&aelig;ter 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 &agrave; pun&shy;<lb/>ctis <foreign lang="greek">b, x</foreign> ad <foreign lang="greek">h, q</foreign> rect&aelig; adiun&shy;<lb/>ct&aelig; &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&shy;<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 pr&aelig;ter naturam. </s>

<s id="id.000782">Ob <lb/><expan abbr="h&atilde;c">hanc</expan> igitur cau&longs;am ex dictis <lb/>manife&longs;tum, quod punctum &agrave; centro di&longs;tantius, vt ea&shy;<lb/>dem vi &longs;it motum, celerius fertur. </s></p><p type="margin">

<s id="id.000783"><margin.target id="marg13"/>Verba &longs;i&shy;<lb/>gnis inclu&longs;a <lb/>in <expan abbr="c&otilde;textu">contextu</expan> <lb/>Gr&ecedil;co quia <lb/>redundant <lb/>non verti&shy;<lb/>mus. </s></p><p type="head">

<s id="id.000784">COMMENTARIVS. </s></p><p type="main">

<s id="id.000785">At oportet.] <emph type="italics"/>Nunc o&longs;tendit in maiore circulo motum &longs;ecun&shy;<lb/>dum naturam maiorem e&longs;&longs;e motu &longs;ecundum naturam in mino&shy;<lb/>re circulo eodem tempore factum. </s>

<s id="id.000786">Ratio e&longs;t, Circuli in&aelig;quales eadem <lb/>vi moti &longs;eruant analogiam in motibus &longs;cilicet: vt qu&aelig; ratio &longs;it mo&shy;<lb/>tus in maiore circulo &longs;ecundum naturam ad &longs;uum motum pr&aelig;ter na&shy;<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 pr&aelig;ter naturam: at h&aelig;c analogia tantum reperiri po&shy;<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"/>&agrave; 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>C&aelig;terum eadem vis in vtri&longs;que cir&shy;<lb/>culis intelligitur ex &aelig;qualitate angulorum ad centrum con&longs;tituto&shy;<lb/>rum. </s>

<s id="id.000787">&AElig;qualis 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></p><p type="main">

<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;&shy;<lb/>&longs;ima, quantum fieri pote&longs;t exacte metitur. </s>

<s id="id.000789">vt &longs;cribit autem Ptolo&shy;<lb/>m&aelig;us in lib. de Analemmate, &amp; Simplicius in lib. de Dimen&longs;ione, <lb/>men&longs;ura cuiu&longs;cunque rei debet e&longs;&longs;e &longs;tata, determinata, &amp; non indefi&shy;<lb/>nita. </s>

<s id="id.000790">Talis autem e&longs;t perpendicularis ad linearum reliquarum dimen&shy;<lb/>&longs;ionem. <emph.end type="italics"/></s></p><p type="main">

<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 &amp; b h k</foreign> <emph type="italics"/>&longs;unt <lb/>&aelig;quiangula. </s>

<s id="id.000792">Nam, qui anguli ad<emph.end type="italics"/> <foreign lang="greek">z &amp; k,</foreign> <emph type="italics"/>&longs;unt recti ex fab. qui vero <lb/>ad<emph.end type="italics"/> <foreign lang="greek">x &amp; b</foreign> <emph type="italics"/>&longs;unt externus &amp; internus ad ea&longs;dem partes facti &agrave; re&shy;<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 &amp; 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"/>&aelig;quales radj,<emph.end type="italics"/> &amp; <foreign lang="greek">x b, q h</foreign> <emph type="italics"/>item &aelig;quales line&aelig;, quia re&shy;<lb/>liqu&aelig; ex &aelig;qualibus radijs<emph.end type="italics"/> <foreign lang="greek">a b, a h</foreign>: <emph type="italics"/>habent autem &aelig;quales ad <lb/>&aelig;quales 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"/>&amp; &longs;ic <lb/>anguli qui ad<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>externus, &amp; qui ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>internus erunt &aelig;quales <lb/>prop. 29. lib. 1. </s>

<s>Ergo &amp; reliqui qui ad<emph.end type="italics"/> <foreign lang="greek">q &amp; h</foreign> <emph type="italics"/>prop. 32. lib. 1. </s>

<s>H&aelig;c <lb/>igitur duo triangula circa &aelig;quales angulos habebunt latera propor&shy;<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"/>&amp; alternatim vt<emph.end type="italics"/> <foreign lang="greek">q z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h k</foreign><emph type="italics"/>: &longs;ic<emph.end type="italics"/> <foreign lang="greek">x z</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">k b</foreign> <emph type="italics"/>prop. 16. lib. 5. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000795">Ob hanc igitur cau&longs;am.] <emph type="italics"/>Conclu&longs;io qua tandem concludi&shy;<lb/>tur punctum &agrave; centro di&longs;tantius, vt eadem vi &longs;it motum, celerius <lb/>ferri, id e&longs;t eodem tempore maius loci &longs;patium conficere. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000796"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000797">Quod vero propterea li&shy;<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">H&aelig;c enim quie&longs;cit. </s>

<s id="id.000800"><expan abbr="vtr&aelig;q;">vtr&aelig;que</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 line&aelig; <lb/>&longs;unt ex centro. </s>

<s id="id.000801">Ab eodem <lb/>igitur pondere nece&longs;&longs;e e&longs;t <lb/>e&ograve; celerius extremum li&shy;<lb/>brilis ferri, qu&ograve; plus ab agi&shy;<lb/>na di&longs;titerit, &amp; nonnulla in <lb/>paruis libris pondera im&shy;<lb/>po&longs;ita non manife&longs;ta &longs;en&shy;<lb/>&longs;ui e&longs;&longs;e, qu&aelig; in magnis ma&shy;<lb/>nife&longs;ta erunt. </s>

<s id="id.000802">Nihil enim <lb/>prohibet <expan abbr="minor&etilde;">minorem</expan> permea&shy;<lb/>ri magnitudinem: quam vt <lb/>vi&longs;ui &longs;it manife&longs;ta. </s></p><p type="head">

<s id="id.000803">COMMENTARIVS. </s></p><p type="main">

<s id="id.000804">Qvod vero propterea libr&aelig;.] <foreign lang="greek">zugo\s</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">zugo\n</foreign> <emph type="italics"/>pr&aelig;ter iu&shy;<lb/>gum, remigum &longs;edes, &amp; tran&longs;tra curruum &amp; nauium &longs;ignifi&shy;<lb/>cat etiam libram &amp; &longs;tateram, hinc illud Pythagor&aelig;<emph.end type="italics"/> <foreign lang="greek">mh\ zugo\n u(per&shy;<lb/>bai/nein</foreign> <emph type="italics"/>&longs;tateram ne tran&longs;grediaris &amp; vt annotat Bud&aelig;us<emph.end type="italics"/> <foreign lang="greek">zugosta/&shy;<lb/>tai</foreign> <emph type="italics"/>&longs;unt libripendes per vrbes con&longs;tituti, qui <expan abbr="p&otilde;deribus">ponderibus</expan> pr&aelig;fecti ap&shy;<lb/>pellantur, vnde Zygo&longs;tatica fides pro plena &amp; examinata &aelig;quitate <lb/>&agrave; Zygo quod e&longs;t libra publice temperata &amp; con&longs;tituta, vt quemad&shy;<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/>&amp; pondus &aelig;quum voluntas eius. <emph.end type="italics"/></s></p><p type="margin">

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

<s id="id.000806">Agina fit cen&shy;<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&shy;<lb/>&longs;toteles <expan abbr="acc&otilde;modat">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> vltim&ograve; <lb/><expan abbr="demon&longs;trat&atilde;">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&shy;<lb/>d&aelig; &longs;unt. </s>

<s id="id.000808">Sit igitur <lb/>libr&aelig; 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, &amp; C D trutina, &longs;eu an&longs;a, qu&aelig; pro com&shy;<lb/>muni more &longs;emper e&longs;t perpendicularis ad horizontis planum: pun&shy;<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, &amp; e&longs;t cen&shy;<lb/>trum libr&aelig; 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&shy;<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 &aelig;quamentum, ab alijs trutina. </s>

<s id="id.000811">His ita declaratis, ilico ex pr&aelig;&shy;<lb/>cedentibus con&longs;tat, quod C centro fixo, &longs;i A C vel C B line&aelig; qu&aelig; <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, qu&ograve; maior, e&ograve; vi&longs;ibilior, &amp; qu&ograve; etiam librilis <lb/>pars maior, e&ograve; mobilior, citius ex &aelig;quali pondere, &amp; magis mouebitur <lb/>librile maius: <expan abbr="qu&atilde;">quam</expan> minus, proinde etiam erit exactius. </s>

<s id="id.000812">id e&longs;t minores <lb/>ponderum differentias patefaciet. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000813"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000814">In magno <expan abbr="aut&etilde;">autem</expan> librili <expan abbr="id&etilde;">idem</expan> <lb/><expan abbr="p&otilde;dus">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="p&otilde;dere">pondere</expan> multo maior fit in&shy;<lb/>clinationis magnitudo. </s>

<s id="id.000817">Ob <lb/>id purpur&aelig; venditores, vt <lb/><expan abbr="pend&etilde;do">pendendo</expan> <expan abbr="defraud&etilde;t">defraudent</expan>, a&longs;tut&egrave; <lb/>faciunt, qui aginam non in <lb/>medio collocant, &amp; plum&shy;<lb/>bum in altera librilis parte <lb/>illinunt, vel &egrave; 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;ider&atilde;t">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&shy;<lb/>dix, E&longs;t vero nodus qu&aelig;&shy;<lb/>dam radix. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.086.jpg" pagenum="47"/><p type="head">

<s id="id.000819">COMMENTARIVS. </s></p><p type="main">

<s id="id.000820">In magno autem.] <emph type="italics"/>Ex his colligitur fieri po&longs;&longs;e libram, qu&aelig; <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;&shy;<lb/>&longs;imis, vt elleboro, &longs;cammonio, opio. </s>

<s id="id.000822">Huius autem libr&aelig; fabrica pen&shy;<lb/>det &egrave; quatuor. </s>

<s id="id.000823">Primum e&longs;t longitudo librilis. </s>

<s id="id.000824">Secundum e&longs;t illius &amp; <lb/>lancium materi&aelig; &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, &amp; rectitudo, ideo de&shy;<lb/>bet fieri ex chalybe purgato, durato, tenui&szlig;imo, naturaque leui. <lb/></s>

<s id="id.000827">Quartum e&longs;t trutin&aelig; po&longs;itio in exqui&longs;it&egrave; medio librilis mobilis. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000828">Ob id purpur&aelig;.] <emph type="italics"/>Alia e&longs;t ratio qua rur&longs;us confirmatur libri&shy;<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 vendit&aelig; leuius &aelig;quipondio<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 &aelig;quiponderat vel etiam pr&aelig;ponderat: &amp; 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 &aelig;quiponderet: plumbum habebit illitum, vel <lb/>etiam ex ligno erit duriore &amp; nodo&longs;iore, &longs;icque den&longs;iore, &amp; ideo <lb/>grauiore. </s>

<s id="id.000833">Vel pars librilis longior erit tenuior, vel perforata in ali&shy;<lb/>quot locis exiguis foraminibus. </s>

<s id="id.000834">Vnde vnius grauitas <expan abbr="l&otilde;gitudinis">longitudinis</expan> al&shy;<lb/>terius rationem compen&longs;at. </s>

<s id="id.000835">Cardanus docuit libr&aelig; metallic&aelig; fabri&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg15"/><lb/><emph type="italics"/>cam, qu&aelig; pro deunce exhibeat a&longs;&longs;em, licet vacua in&longs;ta videatur. </s>

<s id="id.000836">H&aelig;c <lb/>autem &agrave; me h&icirc;c 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 &amp; pondus, &amp; <lb/>&longs;tatera dolo&longs;a non e&longs;t bona: &longs;ed vt &agrave; callidis i&longs;tis mercatoribus &longs;ibi <lb/>pr&aelig;caueat emptor. </s>

<s id="id.000838">Fraudem autem i&longs;tam deteget, &longs;i pondus &amp; &aelig;qui&shy;<lb/>pondium tran&longs;mutentur de lance in lancem. </s>

<s id="id.000839">Quod enim ante &aelig;qui&shy;<lb/>ponderabat, tran&longs;latum in alteram lancem non amplius &aelig;quiponde&shy;<lb/>rabit duplici de cau&longs;a, &amp; quod &aelig;quipondium grauius &longs;it, &amp; quod <lb/>librilis in parte maiore &longs;it. <emph.end type="italics"/></s></p><p type="margin">

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

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



</p><p type="main">

<s id="id.000842">Purpur&aelig; venditores.] <foreign lang="greek">a(lourgopw/lai</foreign> <emph type="italics"/>dicuntur quia<emph.end type="italics"/> <foreign lang="greek">a(/lour&shy;<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"/>&agrave; maris opere. </s>

<s id="id.000843">quia purpura &egrave; <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&shy;<lb/>cibus conch&aelig; gerunt, candida quadam vena conclu&longs;um colore ni&shy;<lb/>gricantis ro&longs;&aelig; pellucidum. <emph.end type="italics"/></s></p><p type="margin">

<s id="id.000846"><margin.target id="marg17"/>Lib. 9. cap. <lb/>36. </s></p></chap><chap><p type="main">

<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/&shy;<lb/>ros, pa/lin a)naqe/retai to\ zu&shy;<lb/>go/n: de\ ka/twqen, me/nei. </foreign></s></p><p type="main">

<s id="id.000848">3. Propter quid, &longs;i in &longs;upe&shy;<lb/>riore librilis parte fuerit <lb/>agina, <expan abbr="qu&atilde;do">quando</expan> <expan abbr="p&otilde;dus">pondus</expan>, ali&shy;<lb/>quod depre&longs;&longs;erit, rur&longs;us <lb/>librile referatur: At &longs;i in <lb/>inferiore, non refertur. </s></p><p type="main">

<s><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000850">Propter quid &longs;i in &longs;upe&shy;<lb/>riore librilis parte fuerit <lb/>agina, cum pr&aelig; <expan abbr="p&otilde;dere">pondere</expan> <expan abbr="de-mi&longs;s&utilde;">de&shy;<lb/>mi&longs;sum</expan> e&longs;t, hoc &longs;ublato rur&shy;<lb/>&longs;us redit: Sed &longs;i in inferiore <lb/>fuerit, <expan abbr="n&otilde;">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&shy;<lb/>tra perpendicularem. </s>

<s id="id.000852">E&longs;t <lb/>enim trutina perpendicu&shy;<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="p&otilde;dere">pondere</expan> in par&shy;<lb/>te librilis &longs;ur&longs;um rapta, do&shy;<lb/>nec venerit e&ograve;, vbi ad per&shy;<lb/>pendicularem ip&longs;am librile <lb/>bifariam diuiditur. </s>

<s id="id.000854">E&longs;to li&shy;<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&shy;<lb/>tur in lance <foreign lang="greek">b,</foreign> erit <foreign lang="greek">b</foreign> vbi <foreign lang="greek">e, <lb/>&amp; g</foreign> vbi <foreign lang="greek">z. </foreign></s>

<s>Itaque recta bi&shy;<lb/>fariam diuidens librile, pri&shy;<lb/>m&ugrave;m 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&shy;<lb/>pendicularem <foreign lang="greek">a m</foreign> in ea <lb/>qu&aelig; e&longs;t <foreign lang="greek">f p</foreign> plus e&longs;t: quam <lb/>dimidium. </s>

<s id="id.000855">Si igitur pon&shy;<lb/>dus, quod erat in <foreign lang="greek">e</foreign> tolla&shy;<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&shy;<lb/>brile refertur: &longs;i vero in in&shy;<lb/>feriori parte &longs;ubijciatur a&shy;<lb/>gina, contra euenit. </s>

<s id="id.000857">Pars <lb/>enim maior dimidia libri&shy;<lb/>lis e&longs;t id, quod infra e&longs;t, &amp; <lb/>quod &agrave; perpendiculari &longs;e&shy;<lb/>catur. </s>

<s id="id.000858">Ideo non refertur. <lb/></s>

<s id="id.000859">Leuior enim e&longs;t pars &longs;ur&shy;<lb/>&longs;um lata. </s>

<s id="id.000860">E&longs;to librile <foreign lang="greek">n c</foreign> re&shy;<lb/>ctum, perpendicularis vero <lb/><foreign lang="greek">k l m,</foreign> qu&aelig; bifariam diui&shy;<lb/>dat <foreign lang="greek">n c,</foreign> &amp; impo&longs;ito pon&shy;<lb/>dere in <foreign lang="greek">n,</foreign> &longs;it <foreign lang="greek">n</foreign> vbi e&longs;t <foreign lang="greek">o, &amp; <lb/>x</foreign> vbi e&longs;t <foreign lang="greek">r, &amp; 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 q. </foreign></s>

<s>Igitur &longs;u&shy;<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></p><p type="head">

<s id="id.000862">COMMENTARIVS. </s></p><p type="main">

<s id="id.000863">Propter quid.] <emph type="italics"/>In hoc capite proponitur aliud di&longs;cutiendum <lb/>problema de libra. </s>

<s id="id.000864">De qua qu&aelig;runtur duo. </s>

<s id="id.000865">Primum cur &longs;i cen&shy;<lb/>trum libr&aelig; &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, &amp; <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/>&amp; 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 &agrave; Guido Vbaldo (&egrave; quo qu&aelig; h&icirc;c dicemus omnia <lb/>fer&egrave; depromp&longs;imus) non minus qu&aelig;&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">Qu&aelig; 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, &amp; contra: quia <lb/>totum continuum e&longs;t. </s>

<s id="id.000869">In extremo autem trutin&aelig;, non eo quidem, <lb/>quod e&longs;t ei cum librili <expan abbr="c&otilde;-">con&shy;</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="tanqu&atilde;">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="n&otilde;">non</expan> pote&longs;t, <lb/>quomodo librile, quod <lb/>&longs;ecundum longitudinem <lb/>e&longs;t, vt vna recta li&shy;<lb/>nea, admittat dif&shy;<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&shy;<lb/>&longs;tituatur problema <lb/>h&icirc;c ab Ari&longs;totele <lb/><expan abbr="po&longs;it&utilde;">po&longs;itum</expan> habebit non <lb/>&longs;olum <expan abbr="experienti&atilde;">experientiam</expan>, <lb/>&longs;ed &amp; rationem <lb/>&longs;ibi &longs;uffragantem, <lb/>Exemplum igitur <lb/>librilis primi mo&shy;<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 &amp; in inferiori parte C <lb/>centrum cum &longs;uo fulcro quod pro trutina e&longs;t etiam C D, &amp; <lb/>in vtroque in&shy;<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&shy;<lb/>trum tran&longs;ire <lb/>perpendiculari&shy;<lb/>ter ad planum <lb/><expan abbr="horiz&otilde;tis">horizontis</expan> D E. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000872"><emph type="italics"/>Exemplum li&shy;<lb/>brilis <expan abbr="c&utilde;">cum</expan> truti&shy;<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/>&amp; trutina K <lb/>L, &amp; centrum <lb/>libr&aelig; L. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000873">An quia &longs;u&shy;<lb/>perne.] <emph type="italics"/>In&shy;<lb/>tellectis libr&aelig; <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/>libr&aelig; &longs;upernam partem occupat, &amp; &agrave; perpendiculari intellecta per <lb/>admotum pondus librile &agrave; paralleli&longs;mo cum horizonte di&longs;ce&longs;&longs;erit, <lb/>pars qu&aelig; &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 materi&aelig; vnigeneris. </s>

<s id="id.000877">Redit <lb/>igitur libera relicta, &longs;itumque recuperat, vbi paria momenta <expan abbr="&aelig;qui-ponder&atilde;t">&aelig;qui&shy;<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">pr&aelig;ponderat igitur. </s>

<s id="id.000881">Non itaque per &longs;e redibit: &longs;ed &longs;itum <lb/>detracta decliuem retinebit: alias id graue, quo excedit, &longs;ur&longs;um &longs;ua <lb/>&longs;ponte a&longs;cenderet, contra def. grauis. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000883">Itaque librilis <foreign lang="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&shy;<lb/>brilis, quod ip&longs;um perpetu&ograve; bifariam &longs;ecat, digreditur &agrave; perpendicu&shy;<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&shy;<lb/>lum con&longs;tituit comprehen&shy;<lb/>dens aliquam partem al&shy;<lb/>terutrius brachij nempe F <lb/>C E, vel R C F, qu&aelig; &longs;ic <lb/>detracta vni, &amp; alteri ad&shy;<lb/>dita, reddit hoc &agrave; quo de&shy;<lb/>trahitur minus, &amp; eius <lb/>detract&aelig; partis duplo alte&shy;<lb/>rum <expan abbr="brachi&utilde;">brachium</expan> maius. </s>

<s id="id.000884">At&shy;<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&shy;<lb/>ti in problemate de vecte. <lb/></s>

<s id="id.000885">Et etiam pulchr&egrave; re&longs;pon&shy;<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;&aelig; iam dict&aelig; ex <lb/>proprietate circuli, quate&shy;<lb/>nus eius radij breuiores <lb/>&longs;unt aut longiores, &amp; pro&shy;<lb/>pter i&longs;tam in&aelig;qualitatem <lb/>tardiores aut velociores. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000886"><emph type="italics"/>In librili vero &longs;ecundi <lb/>modi res erit adhuc aper&shy;<lb/>tior. </s>

<s id="id.000887">Centro &longs;iquidem L, <lb/>&amp; interuallo L K circu&shy;<lb/>lus de&longs;cribatur, &amp; K <lb/><expan abbr="mot&utilde;">motum</expan> &longs;it in P propter vim <lb/>allatam: tum L K per&shy;<lb/>pendicularis intellecta pro&shy;<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 &amp; grauitate ad <lb/>P G, redibit igitur G P M. <emph.end type="italics"/></s></p><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"/><p type="main">

<s id="id.000888"><emph type="italics"/>Contra in alte&shy;<lb/>ro diagrammate <lb/>eiu&longs;modi &longs;ectio <lb/>fiet, vt in O, &amp; <lb/>&longs;ic pars O P ac&shy;<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/>(pr&aelig;&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&shy;<lb/>r&aelig; vel alicui ful&shy;<lb/>cro. </s>

<s id="id.000890">Sed &amp; in li&shy;<lb/>brilibus huius ge&shy;<lb/>neris reditus &amp; <lb/>non reditus alia <lb/><expan abbr="eti&atilde;">etiam</expan> cau&longs;a e&longs;t, &longs;ci&shy;<lb/>licet quia <expan abbr="null&utilde;">nullum</expan> <expan abbr="c&etilde;tr&utilde;">cen<lb/>trum</expan> grauitatis ma&shy;<lb/>net ni&longs;i &longs;u&longs;tinea&shy;<lb/>tur &agrave; linea <expan abbr="per-p&etilde;diculari">per&shy;<lb/>pendiculari</expan> ad pla&shy;<lb/>num horizontis. </s>

<s id="id.000891">quod e&longs;t demon&longs;tratum ab Vbaldo prop. 1. lib. de lib. <lb/></s>

<s id="id.000892">Atque P e&longs;t centrum grauitatis magnitudinis compo&longs;it&aelig; &egrave; duobus <lb/>brachijs librilis G H, &amp; lancibus ponderibu&longs;que vtrimque &aelig;qui&shy;<lb/>ponderantibus, &longs;i intelligantur admota, vt patet ex prop. 4. lib. 1. <lb/>Archimed. de &aelig;quipond. </s>

<s id="id.000893">L K vero linea e&longs;t perpendicularis ad pla&shy;<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 &amp; redibit ex natura grauium quou&longs;que occupet<lb/>punctum k in perpendiculari horizontis, &agrave; qua quia per extre&shy;<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;it&egrave; 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/>&aelig;qualia, tum quia cen&shy;<lb/>trum grauitatis C &longs;em&shy;<lb/>per erit in perpendicu&shy;<lb/>lari horizontis, &longs;ecun&shy;<lb/>dum quam &amp; ad quam <lb/>magnitudo compo&longs;ita <lb/>ex brachijs C A, C B &amp; lancibus &amp; ponderibus &aelig;quiponderan&shy;<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 terti&aelig; partis huius problematis ab Ari&longs;totele <lb/>pr&aelig;termi&longs;&longs;&aelig;. </s>

<s id="id.000898">Rar&ograve; tamen huic demon&longs;trationi licet ver&aelig;, experien&shy;<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&shy;<lb/>que tamen alias re&longs;pondet. <emph.end type="italics"/></s></p></chap><chap><p type="main">

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

<s id="id.000900">4. Potenti&aelig; vectis cau&longs;a. </s></p><p type="main">

<s id="id.000901"><foreign lang="greek"><gap/></foreign><arrow.to.target n="marg18"/></s></p><p type="margin">

<s id="id.000902"><margin.target id="marg18"/>Videtur hic <lb/>aliquid de&shy;<lb/>e&longs;&longs;e &amp; fort&egrave;. <lb/><emph type="italics"/>Radius au&shy;<lb/>tem minor <lb/>tardius. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000903">Cur vires exigu&aelig; 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&shy;<lb/>uere onus: minus vero e&longs;t <lb/>ab&longs;que vecte. </s>

<s id="id.000905">An quia ve&shy;<lb/>ctis cau&longs;a e&longs;t, qui &amp; in&longs;tar <lb/>libr&aelig; deor&longs;um habet <expan abbr="agi-n&atilde;">agi&shy;<lb/>nam</expan>, &amp; in in&aelig;qualia 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">amb&aelig; enim &longs;tant vt <lb/>centrum. </s>

<s id="id.000908">Quoniam vero <lb/>celerius ab &aelig;quali ponde&shy;<lb/>re mouetur radius maior. </s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.094.jpg" pagenum="55"/><chap>

<p type="main"><s><foreign lang="greek"><gap/></foreign></s></p>

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

<s id="id.000909">COMMENTARIVS. </s></p><p type="main">

<s id="id.000910">Potenti&aelig; vectis cau&longs;a.] <emph type="italics"/>Vectis definitus e&longs;t &agrave; Bud&aelig;o bacu&shy;<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">H&aelig;c definitio <lb/><expan abbr="nimi&utilde;">nimium</expan> angu&longs;ta e&longs;t, neque huic loco <expan abbr="c&otilde;uenit">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&shy;<lb/>lis ad <expan abbr="commou&etilde;-">commouen&shy;</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, &amp; vecti ip&longs;i <lb/>quam proxime lingul&aelig; &longs;ubditur corpu&longs;culum firmum, quod Gr&aelig;cis<emph.end type="italics"/><lb/><foreign lang="greek">u(pomo/xlion,</foreign> <emph type="italics"/>Vitruuio pre&szlig;io dicitur. </s>

<s id="id.000917">Huius figura e&longs;t fer&egrave; qu&aelig;&shy;<lb/>uis obuia: expeditior tamen e&longs;t, &longs;i &longs;it pri&longs;mation, cuius aduer&longs;a duo <lb/>plana &aelig;qualia &longs;imilia, parallela, &longs;int trian&shy;<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, &amp; con&longs;equenter lin&shy;<lb/>gu&aelig; innixum onus attolli, &amp; ideo com&shy;<lb/>moueri. </s>

<s id="id.000919">Atque hic e&longs;t primus modus vtendi vecte frequenti&szlig;imus: <lb/>&longs;ed &amp; e&longs;t alter non mult&ograve; infrequentior, cum lingula oneri, vt an&shy;<lb/>t&egrave;, &longs;ubdita nullo &longs;ubdito pr&aelig;ter &longs;olum immobile vecti ip&longs;i hypo&shy;<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 pr&aelig;ter extremum lingul&aelig; fixum, quod <lb/>centri immobilis rationem &longs;umit, &amp; terr&aelig; vel alij corpori immobili <lb/>tanquam hypomochlio innititur. </s>

<s id="id.000921">Proinde etiam onus ad partis ve&shy;<lb/>ctis cui impo&longs;itum e&longs;t, motionem mouebitur, &amp; tunc non &longs;olum ele&shy;<lb/>uatur: &longs;ed &amp; &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;&shy;<lb/>&longs;ione, qu&ograve;d Gr&aelig;ci<emph.end type="italics"/> <foreign lang="greek">u(pomo/xlion</foreign> <emph type="italics"/>appellant, &amp; vectis lingua &longs;ub <lb/>onus &longs;ubdita, caput eius vnius hominis viribus pre&longs;&longs;um, id onus ex&shy;<lb/>tollet. </s>

<s id="id.000924">Item &longs;i &longs;ub onus vectis ferrei lingula &longs;ubiecta fuerit, neque <lb/>caput eius pre&szlig;ione in imum: &longs;ed aduer&longs;us in altitudinem extolletur, <lb/>lingula fulcta in are&aelig; &longs;olo habebit eam pro onere, oneris <expan abbr="aut&etilde;">autem</expan> ip&longs;ius <lb/>angulum pro pre&szlig;ione: ita non tam faciliter quam per pre&szlig;ionem, <lb/>&longs;ed aduer&longs;us nihilominus in pondus oneris erit <expan abbr="excitat&utilde;">excitatum</expan>. </s>

<s id="id.000925">H&aelig;c Vitr. <lb/>&agrave; 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 &amp; 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, qu&aelig; mouere manibus nequi&shy;<lb/>mus, vectibus admotis mouere &longs;olemus. </s>

<s id="id.000928">Ita cum membra corporis <lb/>mouere neruis non po&szlig;imus, 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&shy;<lb/>&longs;um corpus effectum &egrave; corpore mu&longs;culi prodeat, qui tendo nomina&shy;<lb/>tur. </s>

<s id="id.000930">Atque hic quidem tendo ex in&longs;trumentis exoriens, habet illius <lb/>extrem&aelig; partis vectis rationem qu&aelig; 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&shy;<lb/>queri, circumuolui, &amp; ad omnes motus, quos voluntas humana vti&shy;<lb/>litate incitata pr&aelig;&longs;cribit, educi, immo vero ij&longs;dem agentibus in quie&shy;<lb/>te, &amp; quam medici appellant in media figura, retineri. <emph.end type="italics"/></s></p><p type="margin">

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

<p type="margin"><s id="id.000933"><margin.target id="marg20"/>Cap. 10 lib. <lb/>1 de plac. <lb/>Hipp. &amp; <lb/>Plat. </s></p><p type="main">

<s id="id.000934">Cur vires exigu&aelig;.] <emph type="italics"/>Machina libr&aelig; duobus problematis expe&shy;<lb/>dita e&longs;t: vectis deinde duodecim di&longs;&longs;eritur, &egrave; quibus primum e&longs;t ge&shy;<lb/>nerale. </s>

<s id="id.000935">Qu&aelig;ritur ergo h&icirc;c, cur homo verbi gratia pu&longs;illis viribus <lb/>amoueat vecte magna onera, colo&szlig;ica vocat Vitruuius, id e&longs;t ma&shy;<lb/>gn&aelig; molis, quales &longs;unt colo&szlig;i. </s>

<s id="id.000936">Et apud eundem colo&szlig;icotera compa&shy;<lb/>ratiuum e&longs;t Gr&aelig;cum pro grandiora, va&longs;tiora, colo&szlig;i in&longs;tar ha&shy;<lb/>bentia. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000937">Facilius enim e&longs;t.] <emph type="italics"/>Ratio e&longs;t ad augendam problematis propo&shy;<lb/>&longs;iti de vecte difficultatem, qu&aelig; &longs;ic concludi pote&longs;t. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.096.jpg" pagenum="57"/><p type="main">

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

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

<s id="id.000940"><emph type="italics"/>Ergo facilius e&longs;t mouere molem &longs;ine vecte: quam cum vecte. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000941"><emph type="italics"/>Propo&longs;itio e&longs;t vera, quia vires cuiu&longs;libet citius &aelig;quabunt, aut etiam <lb/>&longs;uperabunt pondus minus: quam maius. </s>

<s id="id.000942">A&longs;&longs;umptio ver&ograve; fallaciam <lb/>habet ex varia di&longs;po&longs;itione vectis cum mole. </s>

<s id="id.000943">Nam totus, aut dimi&shy;<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 libr&aelig; in morem, ita vt parte exigua &longs;up&shy;<lb/>ponatur moli mouend&aelig;, &amp; ab illi &longs;uppo&longs;ito fulcimento radius, &longs;eu <lb/>caput ad vim mouentem maius fit, &longs;icque di&longs;po&longs;itus pondus non <lb/>adijcit moli. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000945">An quia vectis.] <emph type="italics"/>Solutio e&longs;t problematis, quod vectis cum in <lb/>v&longs;um venit referat libram, qu&aelig; latitudine effatu digna pr&aelig;dita, <lb/>&amp; cuius agina deor&longs;um &longs;ita &longs;it, tum qu&aelig; in in&aelig;qualia brachia diui&shy;<lb/>&longs;a eorum maius habeat ad partes mouentis, &amp; &longs;ic tum ob libr&aelig; agi&shy;<lb/>nam inferius po&longs;itam, tum ob radij mobilis magnitudinem vectis <lb/>facile &amp; velociter mouetur, &amp; vna cum vecte pondus alteri parti <lb/>incumbens aut annexum. </s>

<s id="id.000946">Ratio h&aelig;c concluditur hoc &longs;yllogi&longs;mo. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000947"><emph type="italics"/>Libra deor&longs;um habens aginam &amp; brachium vnum longius, per <lb/>id facile deprimitur, &amp; depre&longs;&longs;a manet: vt patuit ex pr&aelig;ce&shy;<lb/>dentibus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000948"><emph type="italics"/>Vectis e&longs;t libra deor&longs;um habens <expan abbr="agin&atilde;">aginam</expan>, &amp; brachium vnum <lb/>longius (agina enim &longs;eu centrum fit hypomochlium, &amp; <lb/>quidem ita vt ip&longs;am diuidat in partes in&aelig;quales, &egrave; quibus <lb/>qu&aelig; ad caput longior &longs;it, alioqui aliter in v&longs;um adhibitus <lb/>vis mouens non magis mouere pote&longs;t, quam &longs;ine vecte.)<emph.end type="italics"/></s></p><p type="main">

<s id="id.000949"><emph type="italics"/>Ergo vectis facile deprimetur, depre&longs;&longs;u&longs;que manebit, &amp; ad eius <lb/>motum pondus incumbens mouebitur. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.000950"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000951">Quod autem e&longs;t mobile <lb/>ad mouens, id e&longs;t longitu&shy;<lb/>do ad longitudinem reci&shy;<lb/>proc&egrave;. </s>

<s id="id.000952">Semper &longs;ane quant&ograve; <lb/>longitudo magis di&longs;tabit &agrave; <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&shy;<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 &agrave; pre&longs;&longs;io&shy;<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> &amp; pon&shy;<lb/>dus <foreign lang="greek">g</foreign> motum vbi <foreign lang="greek">k. </foreign></s></p><p type="head">

<s id="id.000955">COMMENTARIVS. </s></p><p type="main">

<s id="id.000956"><emph type="italics"/>Locus hic breui&szlig;im&egrave; totam vectis rationem explicat, vt &longs;ciatur <lb/>vectis v&longs;us, &amp; qu&aelig; vires, ad quod onus mouendum &longs;ufficiant, <lb/>vel non &longs;ufficiant. </s>

<s id="id.000957">Qu&aelig;res vt intelligatur proponemus hoc theore&shy;<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&shy;<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, &amp; huius hypo&shy;<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 du&aelig; <lb/>partes C A ver&shy;<lb/>&longs;us linguam, C <lb/>B ver&longs;us caput: <lb/>&longs;it quoque pon&shy;<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 reciproc&egrave;) fiat ergo vt B C ad A C: ita <lb/>pondus D ad aliud, vt E. </s>

<s>hoc igitur pondus E loco potenti&aelig; ap&shy;<lb/>pen&longs;um in B, ip&longs;um D pondere &aelig;quabit. </s>

<s id="id.000961">Magnitudines enim in gra&shy;<lb/>uitate commen&longs;urabiles &aelig;quiponderant, &longs;i permutatim &longs;u&longs;pendantur <lb/>in di&longs;tantijs &longs;ecundum grauitatum rationem <expan abbr="c&otilde;&longs;titut&aelig;">con&longs;titut&aelig;</expan> prop. 6. lib. 1. <lb/>Archim. de &aelig;quipond. </s>

<s id="id.000962">Et &longs;ic potentia &aelig;qualis ip&longs;i E ibidem con&longs;ti&shy;<lb/>tuta pondere &aelig;quabit ip&longs;um D, id e&longs;t ne D deor&longs;um vergat, quod fa&shy;<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"/>cit pondus E, prohibebit. </s>

<s id="id.000963">Nam &aelig;qualia ad idem eandem rationem <lb/>habent prop. 7. lib. 5. el. </s>

<s id="id.000964">Sed E habet eam ad D, quam A C ad B C, ex <lb/>fab. </s>

<s id="id.000965">ergo potentia in B ad pondus D eam rationem habebit, quam <lb/>A C ad B C. </s>

<s id="id.000966">Itaque vt e&longs;t potentia ad pondus &longs;u&longs;tentum: ita e&longs;t <lb/>pars vectis &amp;c. </s>

<s id="id.000967">quod fuit demon&longs;trandum. </s>

<s id="id.000968">Ex quo duo corollaria <lb/>&longs;tatim eliciuntur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000969">Primum. <emph type="italics"/>Hypomochlio bifariam diuidente vectem, potentia <lb/>&aelig;qualis requiritur: in&aelig;qualiter vero in&aelig;qualis. </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&shy;<lb/>tra pars ab eodem ad lingulam, potentia maior. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000971">Secundum. <emph type="italics"/>Qu&ograve; pars ab hypomochlio ad lingulam minor erit: <lb/>e&ograve; minor potentia ad &longs;u&longs;tinendum &longs;ufficiet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000972">Reciproce.] <foreign lang="greek">*antipepo/nqhsis. </foreign><emph type="italics"/>Reciprocatio quid &longs;it de&longs;umen&shy;<lb/>dum e&longs;t ex Eucl. def. 2. lib. 6. vbi reciproc&aelig; figur&aelig; definiuntur cum in <lb/>vtraque figura antecedentes &amp; con&longs;equentes rationum termini fue&shy;<lb/>rint, id e&longs;t quando in altera quidem e&longs;t terminus antecedens prim&aelig; <lb/>rationis, &amp; con&longs;equens &longs;ecund&aelig;: in altera vero e&longs;t con&longs;equens pri&shy;<lb/>m&aelig;, &amp; antecedens &longs;ecund&aelig;. </s>

<s id="id.000974">Qu&aelig; vt conuenire huic loco intelligan&shy;<lb/>tur, &longs;umendum e&longs;t pondus mouendum &longs;imul cum parte vectis ab hy&shy;<lb/>pomochlio ad lingulam cui appenditur pro vna figura: &amp; potentia <lb/>mouens cum reliqua parte vectis pro altera figura. </s>

<s id="id.000975">Sicque cum du&aelig; <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&shy;<lb/>tes &amp; con&longs;equentes rationum terminos in vtraque figura e&longs;&longs;e. </s>

<s id="id.000977">Et <lb/>ideo figuras e&longs;&longs;e reciprocas. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000978">Semper &longs;ane.] <emph type="italics"/>Hoc ex&longs;ecundo corollario clarum e&longs;t. </s>

<s id="id.000979">Quo enim <lb/>pars vectis ad lingulam erit minor, eo pars ad caput erit maior. </s>

<s id="id.000980">Et <lb/>&longs;ic &longs;i minor potentia ad &longs;u&longs;tinendum vel dimouendum &longs;ufficiet, <lb/>etiam alia qu&aelig;uis paulo maior vis tanto facilius &longs;u&longs;tinebit, aut mo&shy;<lb/>uebit pondus: quanto pars ad caput maior erit. </s>

<s id="id.000981">In&aelig;qualium enim <lb/>maior ad eandem maiorem rationem habet prop. 8. lib. 5. </s>

<s>Sed &amp; <lb/>huius rei cau&longs;a adfertur ex his qu&aelig; ante demon&longs;trata &longs;unt, nempe &agrave; <lb/>radio maiore maiorem de&longs;cribi circulum. </s>

<s id="id.000982">Pars enim vectis ab hy&shy;<lb/>pomochlio ad caput radij in&longs;tar e&longs;t maioris, qui depre&longs;&longs;us &amp; ideo vo&shy;<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 &amp; 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 h&icirc;c e&longs;t<emph.end type="italics"/> <foreign lang="greek">ra=|on kai\ ple/on <lb/>ki/neisqai,</foreign> <emph type="italics"/>facilius &amp; plus moueri. </s>

<s id="id.000984">Ex his autem colligendum e&longs;t il&shy;<lb/>lud, quod e&longs;t ab Archimede profectum problema admirabile. </s>

<s id="id.000985">Da&shy;<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, qu&aelig; dati ponderis e&longs;&longs;et ad da&shy;<lb/>tam potentiam. </s>

<s id="id.000987">Quod in quouis dato pondere cum r&egrave;rum natura non <lb/>patiatur, problema alioqui geometric&egrave; demon&longs;tratum, in v&longs;u ob ma&shy;<lb/>teri&aelig; &longs;atis long&aelig; &amp; firm&aelig; <expan abbr="defect&utilde;">defectum</expan> &longs;u&aelig; rationi re&longs;pondere <expan abbr="n&otilde;">non</expan> pote&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.000988">Sit vectis <foreign lang="greek">a b</foreign>] <emph type="italics"/>huius diagrammatis expo&longs;itio &longs;i non imperfe&shy;<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 depre&szlig;ionem<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"/>pre&szlig;io<emph.end type="italics"/> <foreign lang="greek">e. </foreign><emph type="italics"/></s>

<s>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/>&amp; 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></s>

<s><emph type="italics"/>quod ita &longs;e habere o&longs;tendit tertia <lb/>proprietas circuli, ex qua cap. 1. huius lib. o&longs;ten&longs;um e&longs;t diametri ex&shy;<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&shy;<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&shy;<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&shy;<lb/>rem motum omnium machinationum principia in &longs;e continere, vt <lb/>multis po&longs;tea &longs;pecialibus exemplis declarabit, in quibus &amp; alijs om&shy;<lb/>nibus, qui &longs;cit&egrave; 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/>abund&egrave;, quid &longs;entiendum &longs;it. <emph.end type="italics"/></s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.100.jpg" pagenum="61"/><chap><p type="main">

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

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

<s><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.000996">Cur nauim <expan abbr="mou&etilde;t">mouent</expan> maxi&shy;<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&shy;<lb/>quidem</expan> &longs;calmus efficitur. </s>

<s id="id.000998">Hic <lb/>enim manet. </s>

<s id="id.000999"><expan abbr="p&otilde;dus">pondus</expan> autem <lb/>mare, quod remus propellit: <lb/><expan abbr="vect&etilde;">vectem</expan> vero mouens e&longs;t nau&shy;<lb/>ta. </s>

<s id="id.001000">Sed &longs;emper plus <expan abbr="p&otilde;deris">ponderis</expan> <lb/>mouet, quanto plus motor <lb/>di&longs;titerit &agrave; pre&longs;&longs;ione. </s>

<s id="id.001001">Ibi <lb/>enim maior fit radius, &amp; <lb/>&longs;calmus pre&longs;&longs;io <expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan> <expan abbr="cen-tr&utilde;">cen&shy;<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&shy;<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="c&otilde;tin-git">contin&shy;<lb/>git</expan> e&longs;&longs;e. </s>

<s id="id.001004"><expan abbr="Itaq;">Itaque</expan> mouetur na&shy;<lb/>uis, quia dum remus inni&shy;<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="alligat&atilde;">alligatam</expan> procedere <lb/>nece&longs;&longs;e e&longs;t e&ograve;, vbi e&longs;t <expan abbr="extre-m&utilde;">extre&shy;<lb/>mum</expan> remi. </s>

<s id="id.001005">Vbi enim remus <lb/><expan abbr="plurim&utilde;">plurimum</expan> maris diuidit, e&ograve; <lb/>maxime nece&longs;&longs;e e&longs;t impel&shy;<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 &agrave; <lb/>&longs;calmo e&longs;t. </s>

<s id="id.001007">Propter id ma&shy;<lb/>xim&egrave; mouent. </s>

<s id="id.001008">Maxima <lb/>enim remi pars &agrave; &longs;calmo intus e&longs;t in medio nauis. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.101.jpg" pagenum="62"/><p type="head">

<s id="id.001009">COMMENTARIVS. </s></p><p type="main">

<s id="id.001010">Cvr remiges.] <emph type="italics"/>Specialia deinceps &longs;unt vndecim de vecte pro&shy;<lb/>blemata, &egrave; quibus priora &longs;ex pertinent ad nauigandi artem, qu&aelig; <lb/>mirabilior &longs;it propter audaciam, an propter &longs;ubtilitatem inuentorum <lb/>ad bene <expan abbr="nauig&atilde;dum">nauigandum</expan> vtilium, dubium e&longs;t. </s>

<s id="id.001011">Quid enim audacius quam <lb/>ventorum furorem, &amp; maris rabiem contemnere, &amp; vt in eo tran&shy;<lb/>quilla &longs;int omnia, &longs;e tantum duorum &longs;patio digitorum &agrave; certa, eaque <lb/>a&szlig;idua morte di&longs;tare cernere! </s>

<s>Semper enim<emph.end type="italics"/></s></p><p type="main">

<s id="id.001012">E&longs;t tua tam prop&egrave; mors: quam prop&egrave; cernis aquam. <lb/></s>

<s><emph type="italics"/>Et quod audacius e&longs;t tam longum iter, tam infidum ob &longs;copulos, vor&shy;<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&shy;<lb/>nis conclu&longs;i, horrent, peragere? </s>

<s id="id.001013">Et denique vbi e&longs;t aqu&aelig; &longs;emper &longs;um&shy;<lb/>ma copia, nullius rei tamen magis, quam aqu&aelig; penuria laborare? <lb/></s>

<s id="id.001014">Rect&egrave; &longs;an&egrave; dixit Horatius,<emph.end type="italics"/></s></p><p type="main">

<s id="id.001015">Illi robur &amp; &aelig;s triplex</s></p><p type="main">

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

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

<s id="id.001018">Primus. </s></p><p type="main">

<s id="id.001019"><emph type="italics"/>Quid vero &longs;ubtilius, quam ob&longs;cura etiam nocte, c&oelig;lo nubilo, nullo <lb/>termino vel lapide cert&aelig; vi&aelig; 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, qu&aelig; vbi&shy;<lb/>que D&aelig;dala Tellus profert, omnibus communicare, tot ad id excogi&shy;<lb/>ta&longs;&longs;e commoda, remos, malos, vela, Temonem, anchoram, pyxidem, <lb/>&amp; quod &longs;upra fidem e&longs;t eodem vento contrarium iter agere. </s>

<s id="id.001021">Sed &amp; <lb/>i&longs;ta &longs;ubtilitas maior apparebit, cum qu&aelig; ad artem nauigandi perti&shy;<lb/>nentia problemata h&icirc;c proponuntur ab Ari&longs;totele explicata fuerint. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001022">In medio nauis.] <emph type="italics"/>Nauis e&longs;t ingens machina oblonga, intus <lb/>caua, foris prominens, ad laterum media latior ad anteriorem par&shy;<lb/>tem, qu&aelig; prora dicitur, acuta, ad po&longs;teriorem, qu&aelig; puppis dicitur ob&shy;<lb/>tu&longs;ior, qua homines, &amp; onera magna &longs;uper aquam vehuntur. </s>

<s id="id.001023">An&shy;<lb/>tiqui&szlig;ima nauium Arg&ocirc; &agrave; Fabro nauali, qui eam &aelig;dificauit, &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></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.102.jpg" pagenum="63"/><p type="main">

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

<s id="id.001026"><foreign lang="greek">*ezwsan, pa/mprwton e)u+strefei= e)ndoqen o(/plw|. </foreign><lb/><emph type="italics"/>qu&aelig; &longs;ic reddidit Lazarus Bayfius. <emph.end type="italics"/></s></p><p type="main">

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

<s>Extructam, intus compingunt habili armamento. </s></p><p type="main">

<s id="id.001028"><emph type="italics"/>Tullius tamen in 1. Tu&longs;cula. dicit nominatam Arg&ocirc;, quia Argiui in <lb/>ea delecti viri vecti petebant Arietis pellem inauratam. </s>

<s id="id.001030">Ante Ar&shy;<lb/>go ratibus, &amp; 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 vari&aelig; confect&aelig; &longs;unt: quarum ali&aelig; velis, qu&aelig; onerari&aelig;: ali&aelig; <lb/>remis, qu&aelig; actuari&aelig;: ali&aelig; velis &amp; remis, qu&aelig; long&aelig; dict&aelig; &longs;unt. </s>

<s id="id.001032">Om&shy;<lb/>nium pr&aelig;cipu&aelig; partes &longs;unt anterior, qu&aelig; prora: po&longs;terior qu&aelig; puppis: <lb/>latus, quicquid dextra &amp; &longs;ini&longs;tra inter proram &amp; puppim in&shy;<lb/>teriacens prominet: Ima, qu&aelig; in aqua immer&longs;a alueus &amp; carina di&shy;<lb/>citur. </s>

<s id="id.001033">Sunt &amp; in omnium ambitu fori, per quos naut&aelig; cur&longs;itant, &amp; <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 &agrave; remo Remiges dicti. </s>

<s id="id.001035">E&longs;t au&shy;<lb/>tem Remus palus longus &amp; validus parte vna latior, qu&aelig; 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;&aelig; magnitudinis pro proportione nauis agend&aelig;, &amp; in <lb/>eadem naui in&aelig;qualis, tractabilis tamen vnius validi remigis viri&shy;<lb/>bus, propter libramentum, quod &agrave; plumbatis manubrijs accedebat ni&shy;<lb/>xus impellentium brachiorum adiuuans. </s>

<s id="id.001037">Athen&aelig;us recitat inter <lb/>remos quo&longs;dam fui&longs;&longs;e tant&aelig; longitudinis vt duodequadraginta cu&shy;<lb/>bitos explerent, quod non erit incredibile memoria repetenti quarun&shy;<lb/>dam nauium &agrave; veteribus fabricatarum va&longs;titatem, cuiu&longs;modi idem, <lb/>&amp; Plutarchus memorant fui&longs;&longs;e illam dictam fluuialem Thalame&shy;<lb/>gon, quam Ptolom&aelig;us Philopator in delicijs habuit, non tam ad <lb/>v&longs;um: quam ad o&longs;tentationem, vt qu&aelig; in longitudinem ducentos ac <lb/>octoginta: &amp; ab imo v&longs;que ad tran&longs;tra duodequinquaginta cubitos <lb/>pateret. </s>

<s id="id.001038">Qu&aelig; amplitudo remi &amp; nauis (quod alioqui e&longs;t nunc nobis <lb/>incredibile videntibus tantum naues, qu&aelig; &agrave; numero remigum in <lb/>vnoquoque tran&longs;tro &longs;edentium &longs;unt vniremes, triremes, quadrire&shy;<lb/>mes, quinquiremes) probabile facit fui&longs;&longs;e in v&longs;u apud antiquos naues <lb/>multo plurium remigum decem, vndecim, viginti, mult&ograve; plurium, in <lb/>vnoquoque tran&longs;tro &amp; 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"/>Athen&aelig;us recen&longs;et Philadelphum ad v&longs;um habui&longs;&longs;e trieconteres, id <lb/>e&longs;t tricen&ucirc;m ordinum duas: I co&longs;erem vnam, qu&aelig; vicen&ucirc;m erat, qua&shy;<lb/>tuor qu&aelig; tern&ucirc;m den&ucirc;m, duas qu&aelig; duoden&ucirc;m, quatuordecim qu&aelig; <lb/>vnden&ucirc;m, &amp; alias infra multas. </s>

<s id="id.001039">Illam autem, qu&aelig; Philopatoris fuit, <lb/>fui&longs;&longs;e quinquaginta ordinum, &amp; in &longs;ingulis tran&longs;tris quadraginta <lb/>remis, id e&longs;t, remigibus (nam &amp; horum po&longs;tea numerum a&szlig;ignat to&shy;<lb/>tius fui&longs;&longs;e 4000.) agi. </s>

<s id="id.001040">Remigum autem antiquitus, vt &amp; hodie, <lb/>alij voluntarij: alij mercede <expan abbr="c&otilde;ducti">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 &agrave; iudicibus damnati, <expan abbr="c&otilde;pediti">compediti</expan>, &amp; 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="e&szlig;&etilde;t">e&szlig;ent</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&shy;<lb/>runt fui&longs;&longs;e naues, qu&aelig; in parte laterali &longs;upra aquas eminente, tria fo&shy;<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&shy;<lb/>&longs;um &amp; 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 paul&ograve; p&ograve;&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;t&egrave; &longs;uperiorem nauis partem explicat ad pup&shy;<lb/>pim in qua &longs;edet gubernator, vt qu&aelig; altior e&longs;t: inferiorem ad proram, <lb/>qu&aelig; inferior e&longs;t, ne gubernatoris ob&longs;truat luminibus: ideo inter istos <lb/>zygit&aelig; &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, &amp; pro&shy;<lb/>pter pr&aelig;&longs;entem Ari&longs;totelis contextum ante di&longs;&longs;oluenda, &longs;i pote&longs;t, ex <lb/>duobus locis, altero Thucydidis, altero Galeni. </s>

<s id="id.001045">Ille enim li. 6. h&aelig;c ha&shy;<lb/>bet. <emph.end type="italics"/></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"/>Thranit&aelig; pr&aelig;ter &longs;tipendium publicum &agrave; trierarchis <lb/>donatiuum con&longs;equebantur, cuius rei cau&longs;a &longs;ubdita e&longs;t &agrave; &longs;choliaste, <lb/><expan abbr="quoni&atilde;">quoniam</expan> remos longiores trahebant, grauioreque labore vexabantur, <lb/>&amp; adhuc hodie e&ograve; loci remigant ex omnibus delecti robu&longs;tiores, &agrave; <lb/>largis &longs;patulis Gallis dicti Eppaliers. </s>

<s id="id.001047">Hic ver&ograve; 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 &aelig;qua&shy;<lb/>litatem perueniunt, cum tamen ip&longs;i omnes non &longs;int &aelig;quales, etenim <lb/>etiam ibi medios eandem ob cau&longs;am maximos efficiunt, id e&longs;t, vt vi&shy;<lb/>dere licet ex i&longs;to cap. Galen. citato, vt manus digiti in&aelig; quales &longs;unt, <lb/>&amp; medius longi&szlig;imus ad firmam rerum apprehen&longs;ionem, &amp; ap&shy;<lb/>prehen&longs;arum retentionem, quod illius munus e&longs;t, quod non aliter fit <lb/>quam quum digitorum extremitates ad &aelig;qualitatem perueniunt: &longs;ic <lb/>ob nauigationis perfectionem in valido &amp; faciliori nauis, qu&acirc; prora <lb/>&longs;pectat impul&longs;u po&longs;itam, remi facti &longs;unt in&aelig;quales, &amp; eorum me&shy;<lb/>dius maximus: &amp; horum quidem i&longs;ta in&aelig;qualitas ob eandem cau&shy;<lb/>&longs;am, vt &longs;cilicet remorum extremitates &longs;imul omnes in remigatione <lb/>ad &aelig;qualitatem 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 in&aelig;quales: &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&shy;<lb/>num cogno&longs;cemus &longs;i prius intellexerimus quomodo remorum extre&shy;<lb/>mitates in remigationis ictu ad &aelig;qualitatem 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&shy;<lb/>&longs;inant &longs;ecundum re&shy;<lb/>ctam A B parallelam <lb/>rect&aelig;, qu&aelig; in naui ex&shy;<lb/>tenderetur &agrave; 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 pr&aelig;terquam <lb/>quod Thalamitarum <lb/>Zygitarum &amp; Thra&shy;<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 &aelig;quales prop. 33. &amp; 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&shy;<lb/>tes excipientem. </s>

<s id="id.001054">Po&longs;terior igitur e&longs;t &longs;i de&longs;inant &longs;ecundum lineam pa&shy;<lb/>rallelam &longs;pond&aelig; nauis qu&aelig; &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;ph&aelig;ric&utilde;">&longs;ph&aelig;ricum</expan> omnium &agrave; manu <expan abbr="appreh&etilde;-dendor&utilde;">apprehen&shy;<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="peripheri&atilde;">peripheriam</expan>. </s>

<s id="id.001055">Quomodo &longs;i pro E F recta <lb/>con&longs;tituamus pe&shy;<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="ripheric&atilde;">riphericam</expan> Q L N <lb/>P R ad quam <expan abbr="de-&longs;in&atilde;t">de&shy;<lb/>&longs;inant</expan> pr&aelig;dicti re&shy;<lb/>mi, non &longs;olum re&shy;<lb/>morum erit in&aelig;&shy;<lb/>qualitas, &amp; me&shy;<lb/>dius erit maxi&shy;<lb/>mus, vt in manu <lb/>digitus medius: <lb/>&longs;ed &amp; nauigatio <lb/>facilius procedet <lb/>propter <expan abbr="c&otilde;trarias">contrarias</expan> <lb/>cau&longs;as, quipp&egrave; ve&shy;<lb/>luti circulationes <lb/><expan abbr="vndar&utilde;">vndarum</expan> circa na&shy;<lb/>uim fient, vnde <lb/>qu&aelig; ante e&longs;t pro&shy;<lb/>pul&longs;a aqua viam <lb/>aperiet nauigio, <lb/>&amp; 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 &amp; K G L fa&shy;<lb/>cile demon&longs;tratur ducta recta G I parallela ip&longs;i K. O. </s>

<s id="id.001057">Sic enim <lb/>&aelig;quales &longs;unt G K, S M, I O prop. 33. &amp; 34. lib. 1. &aelig;quales item <lb/>propter paralleli&longs;mum G L, H N, &amp; I P. </s>

<s>tot&aelig; igitur ex his <lb/>&aelig;quales axiom. 2. lib. 1. &amp; 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/>in&aelig;qualis, &amp; 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 &amp; Thucydidis locos <lb/>debere intelligi, non de totis remis: &longs;ed remorum partibus, qu&aelig; &longs;unt &agrave; <lb/>&longs;calmo ad mare proportione habita ad eas partes, qu&aelig; &longs;unt &agrave; &longs;calmo <lb/>ad manubrium. </s>

<s id="id.001061">Thranit&aelig; enim remus &agrave; &longs;calmo ad <expan abbr="extrem&utilde;">extremum</expan> palmu&shy;<lb/>l&aelig; maiorem long&egrave; rationem habet ad partem, qu&aelig; e&longs;t ab eodem &longs;cal&shy;<lb/>mo ad manubrium, id e&longs;t I P ad I O: quam zygit&aelig; 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&shy;<lb/>cilius &amp; plus promoueat nauim: contra Thranites laborio&longs;ius &amp; <lb/>minus, vt docebitur etiam. </s>

<s id="id.001063">Atque &longs;ic &longs;int hi duo loci meo iudicio ex&shy;<lb/>plicati. </s>

<s id="id.001064">C&aelig;terum Remiges, vt &amp; hoc notatu pulchrum adijciamus, <lb/>Remigando artificios&egrave; &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&shy;<lb/>nent, &amp; vt ait Poeta,<emph.end type="italics"/></s></p><p type="main">

<s id="id.001065">Intentaque brachia rem&iacute;s</s></p><p type="main">

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

<s id="id.001067"><emph type="italics"/>Atque h&aelig;c &longs;int de nauigandi arte, nauibus, remis, remigibus, remi&shy;<lb/>gum ordine, locis, &amp; officio dicta, quibus etiam in his qu&aelig; po&longs;te&agrave; <lb/>dicentur, alia adijcientur &longs;citu digna. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001068">Cur remiges.] <emph type="italics"/>E &longs;ex problematis qu&aelig; 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 &agrave; &longs;cal&shy;<lb/>mo ad manubrium eius qui medius e&longs;t, maior e&longs;t ea, qu&aelig; e&longs;t &agrave; &longs;calmo <lb/>ad manubrium prop&egrave; proram vel puppim &longs;edentis. </s>

<s id="id.001071">Tum quia pars &agrave; <lb/>&longs;calmo ad palmulam eius qui medius e&longs;t plus maris diuidit, quam <lb/>pars &agrave; &longs;calmo ad palmulam aliorum. </s>

<s id="id.001072">Tota igitur h&aelig;c qu&aelig;&longs;tio hoc <lb/>primario &longs;yllogi&longs;mo &longs;ic concludetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001073"><emph type="italics"/>Ille remiges inter plus nauim promouet, cuius remi pars &agrave; &longs;cal&shy;<lb/>mo ad manubrium maior e&longs;t: &amp; cuius etiam pars &agrave; &longs;calmo <lb/>ad palmulam plurimum maris diuidit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001074"><emph type="italics"/>Sed remi pars &agrave; &longs;calmo ad manubrium eius qui in medio e&longs;t <lb/>maior: &amp; ad palmulam eiu&longs;dem plus maris diuidit, <lb/>quam aliorum. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.107.jpg" pagenum="68"/><p type="main">

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

<s id="id.001076">An quia remus.] <emph type="italics"/>Prior pars propo&longs;itionis pr&aelig;cedentis &longs;yllogi&longs;&shy;<lb/>mi primo loco illu&longs;tratur, &longs;ic<emph.end type="italics"/></s></p><p type="main">

<s id="id.001077"><emph type="italics"/>Quant&ograve; maior e&longs;t vectis pars ab hypomochlio ad caput, tant&ograve; <lb/>vis mouens facilius &amp; plus mouet, quia ibi maior e&longs;t radius. <lb/></s>

<s id="id.001078">Hoc ita e&longs;&longs;e patuit ex cap. pr&aelig;ced. libri huius. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001079"><emph type="italics"/>Sed pars remi &agrave; 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. &amp; <lb/>&longs;calmus e&longs;t hypomochlium. </s>

<s id="id.001083">hic enim mouet, pondus vero <lb/>mobile mare, &amp; vectem mouens, Remex. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001084"><emph type="italics"/>Ergo is plus &amp; facilius nauim promouebit, cuius remi pars &agrave; <lb/>&longs;calmo ad manubrium maior erit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001085">In nauis medio.] <emph type="italics"/>A&longs;&longs;umptio e&longs;t primarij &longs;yllogi&longs;mi confir&shy;<lb/>mata ex forma nauis qu&aelig; in &longs;ui medio latior e&longs;t &amp; depre&szlig;ior: in <lb/>prora autem &amp; puppi arctior, &amp; &longs;ublimior. </s>

<s id="id.001086">Ergo &longs;uppo&longs;ito quod re&shy;<lb/>mi omnium <expan abbr="remig&utilde;">remigum</expan> &longs;int &aelig;quales, ex his, qui &longs;calmis pror&aelig; &amp; puppis <lb/>&longs;unt alligati, partem extra <expan abbr="nau&etilde;">nauem</expan> longiorem habent, alias <expan abbr="eor&utilde;">eorum</expan> palmu&shy;<lb/>la non diuideret aquam, &amp; 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 &amp; depre&szlig;ior e&longs;t, ob id magis di&longs;tans &agrave; <lb/>recta A B, vtpote chorda arcus A G H T B, qu&aelig; de&longs;ignes <lb/>loca tran&longs;trorum &amp; qu&aelig; &agrave; remis partes auferat &aelig;quales &amp; partes <lb/>in&aelig;quales relinquat K G, M H, O T &amp; quidem M H ma&shy;<lb/>iorem. </s>

<s>(quod nos &longs;equenti theoremate demon&longs;trabimus) igitur erit <lb/>totum ex M H, &amp; adempto maius quam quod ex K G &amp; <lb/>adempto, velex O T &amp; adempto per ax. 5. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001090">Theorema. <emph type="italics"/>Si chorda rectas in circulo in&longs;criptas ad rectos &longs;e&shy;<lb/>cet: &longs;ectarum pars, qu&aelig; de diametro ab&longs;cinditur, e&longs;t maxima, reli&shy;<lb/>quarum qu&aelig; diametro propinquior remotiore maior e&longs;t. </s>

<s id="id.001091">E&longs;to circu&shy;<lb/>lus A D B E, in quo rectam A B diametrum &longs;ecet chorda D <lb/>E ad rectos vt &amp; K I, L H: &amp; &longs;int &longs;egmenta C B, &egrave; dia&shy;<lb/>metro: F I &egrave; propinquiore: G H &egrave; remotiore. </s>

<s id="id.001092">Dico C B e&longs;&longs;e <lb/>maiorem quam F I: &amp; F I quam G H. </s>

<s id="id.001093">Per punctum M cen&shy;<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"/>rect&aelig; C D prop. 31. lib. 1. &longs;icque parallelogramma &longs;unt O F &amp; <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&shy;<lb/>ter A B maxima e&longs;t in&longs;cripta&shy;<lb/>rum in circulo, &amp; K I propin&shy;<lb/>quior centro ip&longs;i L H remotiore <lb/>maior e&longs;t prop. 15. lib. 3. harum <lb/>quoque dimidi&aelig; M B, N I, O <lb/>H prop. 3. lib. eiu&longs;dem erunt in&shy;<lb/>&aelig;quales &amp; M B maior quam <lb/>N I, &amp; N I quam O H. </s>



<s id="id.001097">Ab <lb/>his igitur &longs;ublatis &aelig;qualibus M <lb/>C, N F, O G parallelogram&shy;<lb/>morum O F, N C lateribus oppo&longs;itis prop. 34. lib. 1. reliqu&aelig; C B, <lb/>F I, G H erunt in&aelig;quales ax. 5. </s>

<s>Et quidem reliqua C B &agrave; maiore M <lb/>B maior: quam F I: &amp; F I eadem ratione maior quam G H, &amp; <lb/>&longs;ic de c&aelig;teris. </s>

<s id="id.001099">Igitur &longs;i chorda rectas, &amp;c. </s>

<s id="id.001100">quod fuit <expan abbr="demon&longs;trand&utilde;">demon&longs;trandum</expan>. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001101">Itaque mouetur nauis.] <emph type="italics"/>Cau&longs;a efficiens motum nauis actua&shy;<lb/>ri&aelig;, &amp; modus quo efficitur, hic exprimitur e&longs;&longs;e impul&longs;io remi &agrave; re&shy;<lb/>mige, mouente animato. </s>

<s id="id.001102">Modus e&longs;t cum remi palmula aquam ingre&longs;&shy;<lb/>&longs;a, &amp; aqu&aelig; ob &longs;ui copiam, tanquam &longs;olo, firmiter renitenti innixu <lb/>manubrium antror&longs;um propellitur &agrave; remige, &amp; proinde totus remus <lb/>vnum continuum &amp; validum inflexileque exi&longs;tens, excepto palmu&shy;<lb/>l&aelig; extremo quod ob aqu&aelig; renixum vtcumque immobile manet, &amp; <lb/>per con&longs;equens alligata remo, e&ograve; qu&ograve; 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&shy;<lb/>tur antror&longs;um, &longs;i e&ograve; manubrium <expan abbr="promot&utilde;">promotum</expan> &longs;it. </s>

<s id="id.001105">Dixi &longs;i e&ograve; 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/>&amp; 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&shy;<lb/>cum: quanquam id quidem &longs;ciebam: &longs;ed arbitrabar &longs;u&longs;tineri remos, <lb/>quum inhibere e&longs;&longs;ent remiges iu&szlig;i. </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"/>remoti&szlig;imum 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, &amp; <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">H&aelig;c Cicero. </s>

<s id="id.001114">qu&aelig; non <lb/>abs re vt arbitror h&icirc;c &longs;unt in&longs;erta, vt qu&aelig; plurimum faciant <lb/>ad intelligendum e motibus nauis duos rectos concitationem &longs;ci&shy;<lb/>licet, &amp; inhibitionem, &amp; vtramque fieri &agrave; remo tanquam &agrave; <lb/>vecte. </s>

<s id="id.001115">non tamen vt antea vecte, in quo eius altero extre&shy;<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&shy;<lb/>tur, &amp; hypomochlij vicem pr&aelig;&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&shy;<lb/>tri, quale repre&longs;entat id, quod pro hypomochlio e&longs;t. </s>

<s id="id.001117">Et aqu&aelig; pars exci&shy;<lb/>piens palmulam, qua patet in latum, vt reuera moueatur: motus ta&shy;<lb/>men hic vel e&longs;t exiguus, &amp; 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&shy;<lb/>mus Aristoteli &amp; Vitruuio qui apert&egrave; dicunt &longs;calmum e&longs;&longs;e hypo&shy;<lb/>mochlium, &amp; mare pondus mouendum. </s>

<s id="id.001121">Cert&egrave; &longs;i &longs;edulo attendamus, <lb/>remigatio vna non vnus e&longs;t &longs;implex remi motus: &longs;ed ex quatuor di&shy;<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&shy;<lb/>mouetur adducto ad remigem manubrio: in tertio palmula in aquam <lb/>demergitur eleuato manubrio: in postremo palmula retror&longs;um adi&shy;<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&shy;<lb/>ris e&longs;&longs;e videntur: diuer&longs;i tamen &longs;unt terminis ad quos &amp; &agrave; quibus <lb/>remus mouetur, &amp; cau&longs;is. </s>

<s id="id.001124">Quia in tribus prioribus &longs;calmus mani&shy;<lb/>fe&longs;t&egrave; e&longs;t hypomochlium, pondus mouendum e&longs;t aqua, vel pars extre&shy;<lb/>ma remi cum e&longs;t extra aquam. </s>

<s id="id.001125">De his igitur pote&longs;t intelligi Ari&longs;to&shy;<lb/>teles tum Vitruuius. </s>

<s id="id.001126">At in quarto aqua renitens palmul&aelig; e&longs;t hypo&shy;<lb/>mochlium, nauis vero pondus mouendum, vt diximus. </s>

<s id="id.001127">Si quis tamen <lb/>etiam de hoc po&longs;trem&ograve; remi motu velit &longs;en&longs;i&longs;&longs;e Ari&longs;totelem non re&shy;<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&shy;<lb/>quam centrum remus voluitur, cedat loco &amp; promoueatur. </s>

<s id="id.001128">Sicque <lb/>nauta aliquid faciet quod non qu&aelig;rit, 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></p><p type="main">

<s id="id.001129">Eo vbi e&longs;t.] <emph type="italics"/>Non quidem &longs;emper antror&longs;um iu&longs;t&egrave; ad perpendi&shy;<lb/>culum: &longs;ed paulo vltra aut citra, pro vt mouens validius: aut imbe&shy;<lb/>cillius mouet manubrium, &amp; aqua plus, minu&longs;ve renititur pauca <lb/>enim &amp; tenuis minus: multa &amp; cra&longs;&longs;a magis renititur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001130">Vbi enim remus.] <emph type="italics"/>Illu&longs;tratio e&longs;t &longs;ecund&aelig; 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&shy;<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 palmul&aelig; pars intr&agrave; aquam <lb/>in vno remi impul&longs;u maius &longs;patium conficit: vtroque autem modo <lb/>palmula mediani remigis plus diuidit mare <expan abbr="qu&atilde;">quam</expan> <expan abbr="alior&utilde;">aliorum</expan>. </s>

<s id="id.001132">Primo enim <lb/>quia pars nauis media e&ograve;, quod depre&longs;&longs;a, reddit &longs;uum &longs;calmum aqu&aelig; <lb/>valde propinquum, &amp; huius remi pars &agrave; &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 &amp; prora <lb/>paul&ograve; &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, qu&aelig; intra aquam, radius maior: quam pal&shy;<lb/>mula aliorum, &amp; &longs;ic maius &longs;patium peragrat. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001136">Propter id remiges.] <emph type="italics"/>Conclu&longs;io e&longs;t primarij &longs;yllogi&longs;mi cum <lb/>repetione cau&longs;&aelig; eiu&longs;dem. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001137">6. <foreign lang="greek">*tou= phdali/ou duna/mews <lb/>ai)/tion, kai\ tou= ma=llon proe/r&shy;<lb/>xesqai ei)s tou)nantioon to\ <lb/>ploi=on, h)\ th\n th=s kw/phs <lb/> pla/thn. </foreign></s></p><p type="main">

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

<s id="id.001139"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001140">Cur gubernaculum par&shy;<lb/>uum quid exi&longs;tens, &amp; in <lb/>extrema parte nauigij tan&shy;<lb/>tam vim habet, vt ab exi&shy;<lb/>guo temone, &amp; vnius ho&shy;<lb/>minis etiam propemodum <lb/>quie&longs;centis viribus, magn&aelig; <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&shy;<lb/>tur? </s>

<s id="id.001141">An quia <expan abbr="gubernacul&utilde;">gubernaculum</expan> <lb/>e&longs;t vectis: pondus mare, gu&shy;<lb/>bernator mouens. </s>

<s id="id.001142">Non au&shy;<lb/>tem <expan abbr="&longs;ec&utilde;dum">&longs;ecundum</expan> latitudinem <lb/><expan abbr="gubernacul&utilde;">gubernaculum</expan> impellit ma&shy;<lb/>re, vt remus. </s>

<s id="id.001143">Neque enim <lb/>nauim mouet in anterio&shy;<lb/>rem partem: &longs;ed mare in <lb/>tran&longs;uer&longs;um accipiens <expan abbr="ips&atilde;">ipsam</expan> <lb/>commotam obliquat. </s>

<s id="id.001144">quia <lb/>enim mare pondus erat ad <lb/>contrarium incumbens in&shy;<lb/>clinat nauim. </s>

<s id="id.001145">Ip&longs;um enim <lb/>hypomochlium in contra&shy;<lb/>rium vertitur, mare <expan abbr="quid&etilde;">quidem</expan> <lb/>intr&ograve;: illud ver&ograve; foras: &amp; il&shy;<lb/>lud &longs;equitur nauis, quia illi <lb/>e&longs;t alligata. </s>

<s id="id.001146">Igitur remus <lb/>&longs;ecundum latitudinem im&shy;<lb/>pellens pondus, &amp; ab illo <lb/>contra repul&longs;us in rectum <lb/>agit: at <expan abbr="gubernacul&utilde;">gubernaculum</expan> qua&longs;i <lb/><expan abbr="tr&atilde;&longs;uer&longs;um">tran&longs;uer&longs;um</expan> iaceat, in tran&longs;&shy;<lb/>uer&longs;um etiam hinc inde motionem facit. </s></p><p type="head">

<s id="id.001147">COMMENTARIVS. </s></p><p type="main">

<s id="id.001148">Potenti&aelig; guber.] <emph type="italics"/>In hoc capite proponuntur tria &longs;pecialia de <lb/>vecte problemata quorum duo &longs;unt de gubernaculo &amp; 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 qu&aelig; e&longs;t inter remi &amp; gu&shy;<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&shy;<lb/>tror&longs;um plus procedat, quam remi palmula retror&longs;um. </s>

<s id="id.001153">Atque h&aelig;c eo <lb/>ordine quo propo&longs;ita &longs;unt, di&longs;&longs;oluentur. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.112.jpg" pagenum="73"/><p type="main">

<s id="id.001154">Gubernaculum.] <emph type="italics"/>Gubernaculum remus erat apud antiquos, <lb/>&longs;ed multo latioris palmul&aelig;: quam remi, quibus ad latera nauis remi&shy;<lb/>gabant. </s>

<s id="id.001155">Ob id pterigion ab al&aelig; exten&longs;&aelig; &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&shy;<lb/>tremum in puppi cardinem retentus, conuoluitur ad obliquandum <lb/>nauim. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001157">Cur gubernaculum.] <emph type="italics"/>Propo&longs;itio e&longs;t problematis in duas par&shy;<lb/>tes &agrave; nobis antea &longs;ubdiui&longs;i, vt &amp; Ari&longs;toteles po&longs;tea &longs;ubdiuidendo <lb/>di&longs;&longs;oluit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001158">Vt ab exiguo temone.] <emph type="italics"/>Propo&longs;iti problematis admiratio au&shy;<lb/>getur, ex parte mouentis quidem tripliciter, quod motor &longs;it vnus ho&shy;<lb/>mo, &longs;it propemodum nihil agens, Cicero ludentem po&longs;uit, vtatur ad <lb/>id quod facere vult, exiguo in&longs;trumento nemp&egrave; temone, vt qui &longs;em&shy;<lb/>per breuior &longs;it longi&szlig;imo remorum: ex parte vero rei mot&aelig;, nemp&egrave; <lb/>totius nauigij, &amp; omnium, qu&aelig; <expan abbr="veh&etilde;da">vehenda</expan> naui impo&longs;ita &longs;unt. </s>

<s id="id.001159">Qu&aelig;, vt <lb/>ijs qui viderunt omnia, manife&longs;ti&szlig;ima &longs;unt: ita ijs qui non viderunt <lb/>incredibilia. </s>

<s id="id.001160">pr&aelig;&longs;ertim &longs;i ex antiquorum monumentis <expan abbr="repet&atilde;t">repetant</expan>, quan&shy;<lb/>ta &agrave; quibu&longs;dam con&longs;tructa &longs;unt nauigia &egrave; quibus vnum ex Athe&shy;<lb/>n&aelig;o placet h&icirc;c attexere, vt ex eo di&longs;cant omnes <expan abbr="qu&atilde;tam">quantam</expan> molem vnus <lb/>homo temone exiguo dimouere po&szlig;it. </s>

<s id="id.001161">Longa e&longs;t, &longs;ed vt &longs;pero, omni&shy;<lb/>bus lectu <expan abbr="iuc&utilde;da">iucunda</expan> hi&longs;toria. </s>

<s id="id.001162">Recitat igitur Athen&aelig;us <expan abbr="Hieron&etilde;">Hieronem</expan> Syra&shy;<lb/>cu&longs;anorum Regem ad naues fabricandum ambitios&agrave; animum inten&shy;<lb/>di&longs;&longs;e, &amp; vnam imprimis memorabilem perfeci&longs;&longs;e, ad quam &aelig;difi&shy;<lb/>candam, materiam in AEtna monte c&aelig;dendam, indeque deuehen&shy;<lb/>dam curaui&longs;&longs;e, qu&aelig; &longs;exaginta triremibus conficiendis &longs;atis e&longs;&longs;e potui&longs;&shy;<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 &aelig;s, ferrum, cannabim, reli&shy;<lb/>quaque, quibus opus erat, partim ex Italia, partim ex Iberia, partim <lb/>Rhodano flumine compara&longs;&longs;et, trecentos operi faciendo fabros, arti&shy;<lb/>fice&longs;que adhibui&longs;&longs;e: ac materi&aelig; dedoland&aelig; pr&aelig;ter admini&longs;tros fabri&shy;<lb/>c&aelig; &longs;ub&longs;eruientes opificijs, pr&aelig;fecto &longs;umm&aelig; operis architecto Archia <lb/>Corinthio. </s>

<s id="id.001165">Quos ip&longs;e cum magnopere hortatus e&longs;&longs;et ad opus aggre&shy;<lb/>diendum, in&longs;uper etiam dies totos operis &longs;e curatorem, exactoremque <lb/>pr&aelig;bui&longs;&longs;e: hac diligentia, his artificibus, hoc architecto, Regem ta&shy;<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"/>ill&igrave;c extrem&aelig; manus opificium adipi&longs;ceretur. </s>

<s id="id.001167">Hac deducta alteram <lb/>nauigij partem totidem alijs men&longs;ibus Hieronem <expan abbr="c&otilde;&longs;umma&longs;&longs;e">con&longs;umma&longs;&longs;e</expan>. </s>

<s id="id.001168">Cum <lb/>interim clauis &aelig;reis denarum librarum plurimis materiam compin&shy;<lb/>geret, aliquibus etiam &longs;e&longs;quiplis eius ponderis, qui pr&aelig; cra&szlig;itudine. <lb/></s>

<s id="id.001169">non alias adigi poterant: quam materia perterebrata. </s>

<s id="id.001170">His clauis co&longs;t&aelig; <lb/>nauis arrectari&aelig; cum a&longs;&longs;amentis tran&longs;uer&longs;arijs coagmentat&aelig;, 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: &aelig;dificij vero <lb/>contignatione triplici. </s>

<s id="id.001172">Harum infimam contignationem oneri &amp; <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&shy;<lb/>ctus, in qua ip&longs;a c&oelig;nationes erant numero triginta <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> vtrum&shy;<lb/>que latus nauigij extruct&aelig;. </s>

<s id="id.001173">In ijs lecti quaterni &longs;trati viris accom&shy;<lb/>modati: inter quas nauclericum conclaue quinque lectorum capax <lb/>erat. </s>

<s id="id.001174">Pr&aelig;terea thalami tres in eadem contignatione erant, culinaque <lb/>&longs;upradictis locis &longs;ub&longs;eruiens ad puppim &aelig;dificata. </s>

<s id="id.001175">Omnes autem &longs;u&shy;<lb/>pradict&aelig; c&oelig;nationes pauimento &longs;trat&aelig; 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/>&aelig;dificia tectis laqueatis, &amp; 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;u&aelig;, quas etiam ip&longs;as &longs;imul ambientes hor&shy;<lb/>ti omni genere <expan abbr="&longs;tirpi&utilde;">&longs;tirpium</expan> complectebantur, fictilibus in va&longs;is &amp; plum&shy;<lb/>beis con&longs;itorum, &longs;imul heder&aelig; vite&longs;que opacabant pampinis, ac co&shy;<lb/>rymbis inumbrantes, quarum radices <expan abbr="aleb&atilde;t">alebant</expan> dolia terr&aelig; plena: pari&shy;<lb/>ter quidem ill&aelig; cum hortis machinamento irrigu&aelig;. </s>

<s id="id.001178">Ab his erat <lb/>Aphrodi&longs;ium id e&longs;t conclaue Veneri de&aelig; dicatum: in&longs;trumentum <lb/>etiam ip&longs;um tricl&iacute;nari lecti&longs;ternio, pauimentoque &longs;tratum achate la&shy;<lb/>pide alij&longs;que varijs &amp; nitentibus di&longs;tincto. </s>

<s id="id.001179">Cuiu&longs;modi lapidum co&shy;<lb/>pia in Sicilia reperitur. </s>

<s id="id.001180">Ac parietes quidem habebat cupre&szlig;inis ta&shy;<lb/>bulis a&szlig;ibu&longs;que contextos, laqueatumque tectum eadem materia. </s>

<s id="id.001181">Fo&shy;<lb/>res etiam ex ebore &amp; odorata materia compactas, atque eo amplius <lb/>pictura &longs;igilli&longs;que exornatas. </s>

<s id="id.001182">Deinceps erat exhedra quinque lecto&shy;<lb/>rum capax, quorum parietes po&longs;te&longs;que buxo compacti <expan abbr="er&atilde;t">erant</expan>, inibique <lb/>bibliotheca, &amp; in lacunari &longs;ph&aelig;ra 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, qu&aelig; 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, &amp; tribus &aelig;neis <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 pr&aelig;&longs;epia ab vtroque latere na&shy;<lb/>uigij numero dena &longs;ita cum fr&aelig;nis &amp; &longs;tratis, &amp; omni equitum in&shy;<lb/>&longs;trumento, eorumque mini&longs;terij atque equorum pabulo. </s>

<s id="id.001186">Pr&aelig;terea li&shy;<lb/>gnarium, &amp; clibanos focos, &amp; pi&longs;trina, aliaque mini&longs;teria in proie&shy;<lb/>cturis nauis prominentia. </s>

<s id="id.001187">Quid dicam Athlantes nouen&ucirc;m pedum <lb/>altitudinis certis inter&longs;titiis firmatos, vt &longs;calpturas <expan abbr="promin&etilde;tes">prominentes</expan> &longs;um&shy;<lb/>m&aelig; contignati&ograve;nis mutulorum vice fulcirent? </s>

<s id="id.001188">Quid turres octo? <lb/></s>

<s id="id.001189">binas in prora &amp; puppi per vtrumque latus extructas, in muri&longs;que <lb/>propugnacula. </s>

<s id="id.001190">Pr&aelig;ter h&aelig;c machina erat in medio cata&longs;tromate &longs;uper <lb/>tripodes excitata, Archimedis inuentum &longs;axa tritalantaria, telaque <lb/>mi&szlig;ilia duodeuiginti pedum facile eiaculans ad quadringentos cu&shy;<lb/>bitos, quod &longs;patium e&longs;t &longs;tadij. </s>

<s id="id.001191">H&aelig;c &amp; alia machinamenta propu&shy;<lb/>gnatoria vt coruos, lupos, &amp; in &longs;ummo malo carche&longs;ia, &aelig;nea <expan abbr="lapid&utilde;">lapidum</expan> <lb/>conceptacula ad lapidationem faciendam in ho&longs;tium nauigia, lon&shy;<lb/>gum e&longs;&longs;et enarrare. </s>

<s id="id.001192"><expan abbr="Stab&atilde;t">Stabant</expan> enim in vno terni: in alijs bini aut &longs;ingu&shy;<lb/>li homines lapides eiaculantes, quos &longs;erui in foris nauis &longs;tantes viti&shy;<lb/>libus quallis tempore pugn&aelig; &longs;uggerebant trochleis &longs;ubuehentes. </s>

<s id="id.001193">Sed <lb/>vt &amp; huius nauigij magnitudo va&longs;titas ac onus animo amplius con&shy;<lb/>cipi po&szlig;it, in&longs;uper adijciam tam multis nonnulla, qu&aelig; Athen&aelig;us <lb/>&longs;crip&longs;it ad hoc maxime pertinentia. </s>

<s id="id.001194">Erat, inquit, in eodem nauigio <lb/>&longs;ecundum proram aqu&aelig; conceptaculum conclu&longs;um capax duorum <lb/>milium metretarum a&longs;&longs;amentis &amp; pice &amp; linteorum farctura com&shy;<lb/>pactile, iuxta quod rur&longs;us pi&longs;cina coaxatione &amp; implumbatura <lb/>con&longs;tans plena aqu&aelig; marin&aelig;. </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&shy;<lb/>dum decem millia: lanarum talenta viginti millia, &amp; alterius mer&shy;<lb/>cis altera viginti millia, pr&aelig;tere&aacute;que commeatus vectorum nauta&shy;<lb/>rumque &longs;exaginta millia. </s>

<s id="id.001198">Horum omnium onus, cum Bud&aelig;us exqui&shy;<lb/>&longs;it&egrave; per&longs;equitur, comperit &longs;ummam librarum ad quinque &amp; &longs;eptua&shy;<lb/>ginta millia excre&longs;cere pr&aelig;ter aquam dulcem, pr&aelig;ter pi&longs;cinam, pr&aelig;&shy;<lb/>ter tot dietarum inte&longs;tinum in&longs;trumentum, pr&aelig;ter annonam vecto&shy;<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, &amp; pabulum equorum, pr&aelig;ter denique onus tanti nauigij. </s>

<s id="id.001199">Quo&shy;<lb/>modo igitur non erit admirabile tantam molem vnius hominis vi <lb/>propemodum quie&longs;centis exiguo temone dimoueri &amp; obliquari: atque <lb/>h&aelig;c de propo&longs;itione dicta &longs;unto. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001200">An quia gubernaculum.] <emph type="italics"/>Solutio e&longs;t primi problematis, &longs;ic. <lb/></s>

<s id="id.001201">Vecte magna mouentur pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001202"><emph type="italics"/>Gubernaculum e&longs;t vectis (in eo enim cardo ad quem alligatur <lb/>e&longs;t centrum: pondus <expan abbr="mouend&utilde;">mouendum</expan> e&longs;t mare: <expan abbr="mou&etilde;s">mouens</expan> gubernator. <emph.end type="italics"/>)</s></p><p type="main">

<s id="id.001203"><emph type="italics"/>Ergo gubernaculo nauigij moles mouebitur. </s>

<s id="id.001204">De hoc na&shy;<lb/>uis motu pulchre. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001205"><emph type="italics"/>Vitruuius &longs;ic mentionem facit. </s>

<s id="id.001206">Nauis onerari&aelig; maxim&aelig; guber&shy;<lb/>nator an&longs;am gubernaculi tenens, quod<emph.end type="italics"/> <foreign lang="greek">o)/iac</foreign> <emph type="italics"/>&agrave; Gr&aelig;cis ap&shy;<lb/>pellatur, vna manu momento per centri rationem pre&szlig;ioni&shy;<lb/>bus artis agitans, ver&longs;at eam ampli&szlig;imis &amp; immanibus <lb/>mercis &amp; penus ponderibus oneratam. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001207">Pondus mare.] <emph type="italics"/>Vt ant&egrave; in remis dictum e&longs;t. </s>

<s id="id.001208">pondus quod mo&shy;<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 lati&szlig;imum intra <lb/>aquam, ob eius copiam firmum manet: &amp; &longs;ic temo ad contrariam <lb/>partem impul&longs;us &longs;ibi in cardine alligatam nauis puppim impellit, <lb/>quod etiam paulo po&longs;t Ari&longs;toteles dicet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001210">Non autem &longs;ecundum.] <emph type="italics"/>Di&szlig;imilitudo e&longs;t gubernaculi &amp; <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&shy;<lb/>pul&longs;um mouetur. </s>

<s id="id.001212">Mouetur enim nauis ad centri, cui e&longs;t annexa, mo&shy;<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&shy;<lb/>uetur hoc contra quam depul&longs;um mare. </s>

<s id="id.001215">Mare autem retror&longs;um rect&agrave; <lb/>&agrave; remo depellitur: mouet igitur remus rect&agrave; antror&longs;um nauim. </s>

<s id="id.001216">Con&shy;<lb/>tr&agrave; mare &agrave; gubernaculo obliqu&egrave; impellitur, vel dextror&longs;um vel &longs;ini&shy;<lb/>&longs;tror&longs;um. </s>

<s id="id.001217">Mouet igitur obliqu&egrave; nauim (quod e&longs;t intelligendum de <lb/>puppi non de prora qu&aelig; in partem ad quam mare mouetur) &longs;ini&shy;<lb/>&longs;tror&longs;um, &longs;i illud dextror&longs;um: vel dextror&longs;um, &longs;i illud &longs;ini&longs;tror&longs;um <lb/>depul&longs;um e&longs;t. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.116.jpg" pagenum="77"/><p type="main">

<s id="id.001218"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s>In extremo autem, non <lb/>in medio po&longs;itum e&longs;t. </s>

<s id="id.001220">quia <lb/>motor, id quod iam moue&shy;<lb/>tur, facillime ab extremo <lb/><expan abbr="c&otilde;mouet">commouet</expan>. </s>

<s id="id.001221">Celerrime enim <lb/>fertur nauis prior pars, <lb/>Quoniam vt in ijs qu&aelig; mo&shy;<lb/>uentur, ad finem latio defi&shy;<lb/>cit: &longs;ic ip&longs;ius continui in ex&shy;<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&shy;<lb/>tum e&longs;t. </s>

<s id="id.001224">Et quoniam exi&shy;<lb/>gua in ea motione facta, <lb/>multo maior in prora fit in&shy;<lb/>tercapedo. </s>

<s id="id.001225">Angulus enim <lb/>&aelig;qualis &agrave; maiori &longs;ubtendi&shy;<lb/>tur, &amp; quanto maiores qu&aelig; <lb/>angulum comprehenderunt line&aelig;. </s></p><p type="head">

<s id="id.001226">COMMENTARIVS. </s></p><p type="main">

<s id="id.001227">In extremo autem.] <emph type="italics"/>Solutio e&longs;t &longs;ecundi problematis duplex, <lb/>&longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001228"><emph type="italics"/>Ibi collocandum gubernaculum, vbi per ip&longs;um motor facilius <lb/>&amp; plus nauim mouere pote&longs;t: &amp; vbi ex minore puppis, mu&shy;<lb/>tatione, maior pror&aelig; mutatio adfertur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001229"><emph type="italics"/>Sed in puppi gubernaculo collocato gubernator facilius nauim <lb/>contorquet, &amp; ex parua puppis mutatione magna pror&aelig; ad&shy;<lb/>fertur mutatio. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001230"><emph type="italics"/>Ergo in puppi non in medio gubernaculum collocandum e&longs;t. <lb/></s>

<s id="id.001231">Ob id etiam&longs;i e pi&longs;cibus quidam parte anteriori homini &amp; quadra&shy;<lb/>pedibus &longs;imiles &longs;unt, vt <expan abbr="Trit&otilde;">Triton</expan>, Nereis, elephas, &amp; vitulus: po&longs;teriore <lb/>tamen omnes in caudam bifidam de&longs;inunt, paucis admodum exce&shy;<lb/>ptis, atque id non ob aliam cau&longs;am quam quod, velut in nauis puppi <lb/>temo nauim dirigit: Ita pi&longs;cis iter cauda. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.117.jpg" pagenum="78"/><p type="main">

<s id="id.001232">Quia motor.] <emph type="italics"/>Syllogi&longs;mi pr&aelig;cedentis 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 h&icirc;c prioris <lb/>eius partis illu&longs;tratio ponitur, &longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001235"><emph type="italics"/>Non re&longs;i&longs;tentia, aut minus re&longs;i&longs;tentia, mouere facilius e&longs;t. <lb/></s>

<s id="id.001236">Vbi autem e&longs;t finis rei mot&aelig; (e&longs;t autem in puppi nauis, non in <lb/>eius medio, nec in prora) ibi re&longs;i&longs;tentia vel nulla vel minor. <lb/></s>

<s id="id.001237">Contra vbi celerrime mouetur, vt in prora, aut celerius, vt in <lb/>medio, ibi maior e&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001238"><emph type="italics"/>Ergo in puppi nauim mouere facilius e&longs;t: quam in medio, aut in <lb/>prora. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001239">Quoniam vt in ijs.] <emph type="italics"/>Similitudo e&longs;t ad illu&longs;trandam pr&aelig;ce&shy;<lb/>dentis &longs;yllogi&longs;mi a&longs;&longs;umptionem, &longs;ic. </s>

<s id="id.001240">Quemadmodum eorum qu&aelig; vi <lb/>feruntur latio ad finem deficit, &amp; imbecillior e&longs;t: &longs;ic continui lati <lb/>extremum imbecillius mouetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001241">Et quoniam exigua.] <emph type="italics"/>Similis &longs;ententia e&longs;t apud Ari&longs;totelem <lb/>lib. de animalium motu. </s>

<s id="id.001242">Nec vero dubium e&longs;t, inquit, quin parua ad&shy;<lb/>modum initio facta mutatione in corpore multiplices &egrave; longinquo <lb/>varietates &longs;uboriantur, vt cum per temonem paululum tralatum <lb/>long&egrave; diuer&longs;a pror&aelig; po&longs;itio vi&longs;itur. </s>

<s id="id.001243">Atque h&aelig;c e&longs;t altera cau&longs;a cur <lb/>gubernaculum in puppi ponitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001244">Angulus enim &aelig;qualis.] <emph type="italics"/>Licet oculata alioquin fide perci&shy;<lb/>piatur quanta &amp; quam euidens nauigij temone paul&ugrave;m vixque con&shy;<lb/>torto ip&longs;ius pror&aelig; &longs;tatim tran&longs;po&longs;itio multo maior con&longs;equatur: ta&shy;<lb/>men &amp; id geometrica propo&longs;itione confirmatur qu&aelig; imperfecta e&longs;t <lb/>&longs;ed &longs;ic perfici pote&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001245"><emph type="italics"/>Si duo I&longs;o&longs;celia &aelig;qualia angulis, in&aelig;qualium crurum fuerint: <lb/>erunt &amp; in&aelig;qualia <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: &amp; huius ba&shy;<lb/>&longs;is maior, cuius crura <lb/>maiora. </s>

<s id="id.001246">Sint A B E <lb/>&amp; A D C duo i&longs;o&longs;&shy;<lb/>celia &aelig;qualia angulis <lb/>qui ad A, &amp; A D <lb/>crus e&longs;to maius crure <lb/>A B &longs;icut &amp; 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 &aelig;quales tribus alterius prop. <lb/>32. lib. 1. </s>

<s>&amp; anguli qui ad A &aelig;quales ex hypothe&longs;i, anguli ad ba&shy;<lb/>&longs;im duo duobus &longs;unt &aelig;quales ax. 3. </s>

<s>&amp; quia A D C &amp; A C D <lb/>&longs;unt ad ba&longs;im I&longs;o&longs;celis, ij inter &longs;e erunt &aelig;quales prop. 5. lib. 1. &amp; per <lb/>eandem anguli A B E &amp; 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="&aelig;quali&utilde;">&aelig;qualium</expan> &aelig;qua&shy;<lb/>lis erit ax. 6. &amp; per idem reliquus reliquo. </s>

<s id="id.001253">Sunt igitur A B E &amp; <lb/>A D C triangula &aelig;quiangula, proinde circum &aelig;quales angulos la&shy;<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: &amp; vici&szlig;im vt A D ad A B: &longs;ic D C ba&shy;<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 &aelig;qualia angulis, in&aelig;qualia cruribus fuerint &amp;c. </s>

<s id="id.001258">quod <lb/>fuit demonstrandum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001259"><emph type="italics"/>Patet igitur ex his quod cum B C &longs;it vt longitudo nauis, &longs;i pup&shy;<lb/>pis B peruenerit ad E manente A cardine. </s>

<s id="id.001260">Tunc C erit in D. <lb/></s>

<s id="id.001261">Sicque fiunt duo triangula I&longs;o&longs;celia A B E &amp; A D C &aelig;qualia <lb/>angulis ad verticem A oppo&longs;itis prop. 15. lib. 1. </s>

<s>Et in&aelig;qualia cruri&shy;<lb/>bus. </s>

<s id="id.001262">Nam rect&aelig; ab A puncto Cardini re&longs;pondente in ima parte na&shy;<lb/>uis prop&egrave; puppis extremum ad extremum pror&aelig; id e&longs;t A D, A C <lb/>long&egrave; maiores &longs;unt breui&szlig;imis ijs, qu&aelig; &longs;unt ab <expan abbr="eod&etilde;">eodem</expan> puncto A ad ex&shy;<lb/>tremum puppis A B, A E. </s>

<s id="id.001263">Peragrabit igitur prora D lineam C B <lb/>long&egrave; maiorem, cum B peragrabit B E multo minorem. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001264"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<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&shy;<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&shy;<lb/>ditur. </s>

<s id="id.001267">Sit enim remus <foreign lang="greek">a b</foreign><lb/>&amp; &longs;calmus <foreign lang="greek">g,</foreign> &amp; 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&shy;<lb/>tum</expan> &longs;it e&ograve;, 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> &aelig;qualis ip&longs;i <foreign lang="greek">a d. </foreign>Ex <lb/>&aelig;quo ig&iacute;tur tran&longs;latum e&longs;&shy;<lb/>&longs;et, &longs;ed minus erat. </s>

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

<s>Similia enim <lb/>&longs;unt triangula. </s>

<s id="id.001269">Con&longs;i&longs;tens <lb/>vero erit medium vbi e&longs;t <foreign lang="greek">g. </foreign><lb/>In contrarium enim extre&shy;<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&shy;<lb/>ueretur nauis, &amp; eo vbi e&longs;t <lb/>caput remi, transferretur. </s></p><p type="margin">

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

<s id="id.001272">COMMENTARIVS. </s></p><p type="main">

<s id="id.001273">Ex hoc autem.] <emph type="italics"/>Hic continetur tertium &egrave; tribus, qu&aelig; 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="qu&atilde;">quam</expan> palmula remi retror&longs;um. </s>

<s id="id.001276">Re&longs;pon&shy;<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&shy;<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 &amp; remi palmul&aelig;: 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&shy;<lb/>mer&longs;a aqu&aelig;, qu&aelig; mouetur, vt &amp; 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 &aelig;quales moles intelligere Ari&longs;totelem remi caput, &amp; palmu&shy;<lb/>lam: vel partem remi &agrave; &longs;calmo ad caput: &amp; partem eiu&longs;dem &agrave; &longs;calmo <lb/>ad palmulam. </s>

<s id="id.001284">Has enim videtur h&icirc;c pr&aelig;&longs;upponere &aelig;quales longitu&shy;<lb/>dine, &longs;calmo remum bifariam &longs;ecante: &longs;in minus pondere: ad &aelig;quali&shy;<lb/>brium enim cum pars palmul&aelig; maior e&longs;t, caput implumbatur vt <lb/>&aelig;quiponderet. </s>

<s id="id.001285">Et &longs;ic cum remus vnius vel plurium remigum viri&shy;<lb/>bus mouetur, caput per a&euml;rem, 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 &amp; re&shy;<lb/>mi caput. </s>

<s id="id.001289">Quod &longs;i verum e&longs;&longs;et &longs;tatim conclu&longs;io h&aelig;c manife&longs;ta <lb/>e&longs;&longs;et. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001290"><emph type="italics"/>Ergo nauis plus antror&longs;um mouetur: quam remi palmula re&shy;<lb/>tror&longs;um. <emph.end type="italics"/></s></p><p type="main">

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

<s id="id.001292"><emph type="italics"/>Quantum caput remi antror&longs;um mouetur: tantum &amp; nauis. <lb/></s>

<s id="id.001293">Sed caput remi plus antror&longs;um mouetur: quam palmula re&shy;<lb/>tror&longs;um. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001294"><emph type="italics"/>Ergo nauis plus antror&longs;um mouetur: quam palmula retror&longs;um. <emph.end type="italics"/></s>

<s id="id.001295"><emph type="italics"/>Huius &longs;yllogi&longs;mi propo&longs;itio &longs;ine confirmatione de&longs;erta e&longs;t ab Ari&shy;<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/>&amp; palmula remi &longs;int eadem moles eadem vi mota, illud tamen per <lb/>a&euml;rem: h&aelig;c per aquam medium a&euml;re den&longs;ius, moueatur. </s>

<s id="id.001299">Qu&aelig; ratio <lb/>veri&szlig;ima e&longs;t in ijs, qu&aelig; &longs;eor&longs;um mouentur, vt &longs;i remus totus per <lb/>a&euml;rem, &amp; totus per aquam ferretur eadem vi, dubium non e&longs;t quin <lb/>citius, &amp; plus per a&euml;rem, quam per aquam, ob maiorem in aqua <expan abbr="re&longs;i-&longs;t&etilde;tiam">re&longs;i&shy;<lb/>&longs;tentiam</expan> feratur. </s>

<s id="id.001300">At remus vnus e&longs;t, &longs;ed &longs;uperficie aqu&aelig; &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&shy;<lb/>dem in capite atque in palmula mouenda cum h&aelig;c intra aquam, illud <lb/>extra &longs;it, quod plus prouehetur illud: quam h&aelig;c. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001302">Sit enim remus.] <emph type="italics"/>Confirmatio e&longs;t geometrica a&longs;&longs;umptionis <lb/>pr&aelig;cedentis &longs;yllogi&longs;mi vbi pr&aelig;&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&shy;<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 &aelig;qualiter moueretur palmula atque caput, <lb/>contra ea qu&aelig; 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 &amp; 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 &aelig;quales prop. <lb/>15. lib. 1. </s>

<s>Tum latera, qu&aelig; 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 &aelig;qualia, quia partes &longs;unt dimidi&aelig; 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"/>&aelig;quales, 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"/>&aelig;qualiter 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&shy;<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&shy;<lb/>m&ugrave;m, 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="c&otilde;cludit">concludit</expan> Ari&shy;<lb/>&longs;toteles ex figura &agrave; Victore Fau&longs;to &amp; ab alijs pa&szlig;im 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&shy;<lb/>gulorum<emph.end type="italics"/> <foreign lang="greek">a q d &amp; 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 &aelig;quales prop. 15. lib. 1. </s>

<s>tum<emph.end type="italics"/> <foreign lang="greek">q a d</foreign> <emph type="italics"/>&aelig;qualis e&longs;t<emph.end type="italics"/> <foreign lang="greek">q b z</foreign> <emph type="italics"/>vel quia <lb/>&longs;unt alterni facti &agrave; 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/>pr&aelig;cedenti <expan abbr="dem&otilde;&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"/>&aelig;qua&shy;<lb/>lis erit prop. 32. lib. 1. </s>

<s>Et &longs;ic triangula<emph.end type="italics"/> <foreign lang="greek">a q d &amp; b q z</foreign> <emph type="italics"/>&longs;unt &aelig;quian&shy;<lb/>gula, proinde &amp; circum &aelig;quales 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"/>&amp; vici&szlig;im <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"/>&amp; detracta e&longs;t de dimi&shy;<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"/>qu&aelig; additur ip&longs;i dimidi&aelig;<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></p><p type="main">

<s id="id.001312"><emph type="italics"/>Hoc autem quanquam verum &longs;it, quor&longs;um tamen, dubium e&longs;t. <lb/></s>

<s id="id.001313">Exi&longs;timauit Nonius ide&ograve; h&icirc;c po&longs;itum e&longs;&longs;e, vt o&longs;tendatur B per remi&shy;<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&shy;<lb/>bit figuram. </s>

<s id="id.001314">qua demon&shy;<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 palmul&aelig; B <lb/>retror&longs;um minorem e&longs;&longs;e A <lb/>D motu capitis A an&shy;<lb/>tror&longs;um, &longs;ecundum &longs;enten&shy;<lb/>tiam Ari&longs;totelis. </s>

<s id="id.001316">Et &longs;ic <lb/>Nonius remigatione facta <lb/>&amp; 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/>aqu&aelig;: quam ip&longs;e C, &longs;equeretur vt in vnius remigationis principio, <lb/>medio, fine nauis plus &amp; 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 contr&agrave; latum <lb/>pro&longs;per&egrave; nauigium &longs;eruat eundem &longs;calmum, &longs;eu &longs;pondam &longs;uam &longs;em&shy;<lb/>per &aelig;quidi&longs;tantem aqu&aelig;, ni&longs;i quod verius e&longs;t, arcum peripheri&aelig;, &longs;ed <lb/>non &longs;implicem, vt po&longs;tea docebimus, de&longs;cribat, cuius extrema &longs;unt in <lb/>&longs;uperficie aqu&aelig;. <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, &amp; <lb/>&longs;calmus C, cui <lb/>alligatus remus <lb/>per medium &longs;it <lb/>A B exi&longs;tens in <lb/>principio remi&shy;<lb/>gationis, &amp; 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&shy;<lb/>mul&aelig; 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/>&aelig;quales prop. 15. lib. 1. </s>

<s>Ba&longs;es erunt &aelig;quales, &longs;i triangula fiant &aelig;qui <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">H&aelig;c igi&shy;<lb/>tur cum expendo cogor aliud &longs;entire quam Nonius licet timid&egrave; (quia <lb/>viro huic propter &longs;cientiam pr&aelig;&longs;tantem, &amp; quod in loco natus &longs;it, <lb/>vixeritque ad nauigandum opportuni&szlig;imo, mult&ograve; 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 e&ograve;, 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 figur&aelig; no&longs;tr&aelig; pun&shy;<lb/>cto F. </s>

<s id="id.001322">Sicque caput A multo anterius latum erit, quam B retr&ograve;. <lb/></s>

<s id="id.001323">E&longs;t enim A F maior quam A D axiom. 9. qu&aelig; 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/>&aelig;quedi&longs;tanter cum C ab <lb/>aqua. </s>

<s id="id.001325">quod fieri oportet in <lb/>artificio&longs;a &amp; pro&longs;pera na&shy;<lb/>uigatione. </s>

<s id="id.001326">An &longs;ic rect&egrave; <lb/>&longs;entiamus aliorum e&longs;to iu&shy;<lb/>dicium: &longs;ed in hoc conueni&shy;<lb/>mus cum Nonio quod remi <lb/>motus in vna remigatione <lb/>duplex e&longs;t: proprius, &amp; alie&shy;<lb/>nus: &amp; ille quidem circularis circa &longs;calmum tanquam centrum, <lb/>cuius motus &longs;calmus expers e&longs;t: hic vero contingit &amp; ob motum <lb/>&longs;calmi delati vna cum nauigio. </s>

<s id="id.001327">Et quod totus motus remi ex his duo&shy;<lb/>bus maior e&longs;t motu nauigij. </s>

<s id="id.001328">Sed &amp; c&aelig;tera qu&aelig; in hoc problema <lb/>animaduertit &amp; annotauit Nonius. </s>

<s id="id.001329">H&icirc;c &longs;ubijciemus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001330"><emph type="italics"/>Primum dicit Ari&longs;totelis ratiocinationem ob&longs;curam e&longs;&longs;e. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001331"><emph type="italics"/>Deinde Ari&longs;totelem a&longs;&longs;umere duo quorum alterum e&longs;t. <emph.end type="italics"/></s></p><p type="main">

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

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

<s id="id.001334"><emph type="italics"/>In&longs;uper Nonius a&longs;&longs;erit nauim interdum maius &longs;patium percurrere:<emph.end type="italics"/><lb/><figure id="id.035.01.123.2.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, &amp; provt mari remi pal&shy;<lb/>mula immer&longs;a fuerit: Qu&aelig; omnia vt con&shy;<lb/>&longs;picua fiant, demon&longs;trat quinque <expan abbr="&longs;equ&etilde;tes">&longs;equentes</expan> <lb/>propo&longs;itiones. <emph.end type="italics"/></s></p><p type="head">

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

<s id="id.001336"><emph type="italics"/>Remigibus nauim mouere potentibus <lb/>caput remi plus antror&longs;um mouetur: <expan abbr="qu&atilde;">quam</expan> <lb/>nauis. </s>

<s id="id.001337">Sit remus A C, caput A, &longs;cal&shy;<lb/>mus B, qui propter nauis motum percur&shy;<lb/>rat &longs;patium, quod e&longs;t &agrave; B in D, in quo <lb/>loco remus A C &longs;itum rectitudinis ha&shy;<lb/>beat E F: &amp; &longs;ic &longs;patium quod A con&shy;<lb/>ficit curua &longs;it linea A E, cui recta linea <lb/>A E re&longs;pondeat in rectam E F perpen&shy;<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&shy;<lb/>cta A C rectam E F in G. </s>

<s id="id.001341">Quia igitur A G E, &amp; B G D <lb/>triangula &longs;unt &aelig;quiangula, erit &longs;icut A G ad B G: &longs;ic A E <lb/>ad B D prop. 4. lib. 6. </s>

<s>Maior e&longs;t autem A G ip&longs;a B G, ax. 9. <lb/></s>

<s id="id.001342">Erit igitur A E maior quam B D. </s>

<s id="id.001343">Itaque caput remi A maius <lb/>percurrit &longs;patium: quam nauis. </s>

<s id="id.001344">quod erat demon&longs;trandum. <emph.end type="italics"/></s></p><figure id="id.035.01.124.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.1.jpg"/><p type="main">

<s id="id.001345"><emph type="italics"/>Quod &longs;i per punctum B rectam duca&shy;<lb/>mus H K &aelig;qualem remo, &amp; ad rectos <lb/>cum recta B D, &amp; in&longs;uper &longs;ecantem A<emph.end type="italics"/><lb/>3 <emph type="italics"/>in puncto I, manife&longs;t&egrave; intelligemus <lb/>ip&longs;am rectam A E (qu&aelig; e&longs;t totus motus <lb/>capitis remi in vna remigatione) con&longs;tare <lb/>ex A I, &amp; I E, quarum prior re&longs;pon&shy;<lb/>det curu&aelig; A H de&longs;cript&aelig; per capitis remi <lb/>motum proprium: po&longs;terior vero &aelig;qualis <lb/>e&longs;t rect&aelig; B D (&longs;unt enim latera parallelo&shy;<lb/>grammi oppo&longs;ita prop. 34. lib. 1.) qu&aelig; motu <lb/>nauis decur&longs;a e&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001346"><emph type="italics"/>Et quia Nonius &longs;ine demon&longs;tratione a&longs;&shy;<lb/>&longs;umit nauim tant&ugrave;m decurrere, quant&ugrave;m <lb/>&longs;calmus, id quoque demonstremus. </s>

<s id="id.001347">quia ad <lb/>&longs;equentia etiam vtile e&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001348"><emph type="italics"/>Ante remigationem remi existentis in &longs;calmo B &longs;it nauis prora C <lb/>po&longs;t remigationem &longs;it B<emph.end type="italics"/><lb/><figure id="id.035.01.124.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.124.2.jpg"/><lb/><emph type="italics"/>in E &amp; prora in D &longs;ic&shy;<lb/>que C D erit nauis pro&shy;<lb/>motio, &amp; B E &longs;calmi. <lb/></s>

<s id="id.001349">Dico igitur C D &amp; B E &aelig;quales, quia reliqu&aelig; &longs;unt ex &aelig;qualibus <lb/>B C, E D dempto communi E C axio. 3. </s>

<s id="id.001350">Ergo nauis tant&ugrave;m de&shy;<lb/>currit quant&ugrave;m &longs;calmus. <emph.end type="italics"/></s></p><p type="head">

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

<s id="id.001352"><emph type="italics"/>Capite remi motu proprio, &amp; naui &aelig;qualiter motis, palmula im&shy;<lb/>mota veluti centrum manet: &amp; palmula immota, caput remi &amp; <lb/>nauis &aelig;qualiter mota &longs;unt. <emph.end type="italics"/></s></p><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"/><p type="main">

<s id="id.001353"><emph type="italics"/>Remus in principio motus habeat <lb/>po&longs;itionem A B C, ducaturque per <lb/>punctum C, in quo remi palmula <lb/>recta C G rectos efficiens angulos <lb/>in puncto G cum recta per quam ad <lb/>motum nauis &longs;calmus B mouetur. </s>

<s id="id.001354">Et <lb/>eadem recta C G producatur v&longs;que <lb/>ad E, ita vt G E &longs;it &aelig;qualis rect&aelig; <lb/>B A (qu&aelig; e&longs;t dimidium remi) rur&shy;<lb/>&longs;us per punctum B ducatur recta Q <lb/>B F ad rectos cum ip&longs;a B G, &amp; in <lb/>Q B F incidant perpendiculares A <lb/>Q C F. </s>

<s id="id.001355">Quoniam igitur triangu&shy;<lb/>lorum A B Q &amp; F B C anguli, <lb/>qui ad B ad verticem oppo&longs;iti &longs;unt <lb/>&aelig;quales, prop. 15. lib. 1. </s>

<s>&amp; anguli qui ad Q &amp; F recti &longs;unt, tum <lb/>latus A B lateri B C, &longs;unt enim dimidia remi, &aelig;quale e&longs;t, erit &amp; <lb/>latus A Q &aelig;quale lateri F C prop. 26. lib. 1. </s>

<s>Ip&longs;i autem F C recta <lb/>B G, latus parallelogrammi oppo&longs;itum, &aelig;qualis e&longs;t prop. 34. lib. 1. <lb/></s>

<s id="id.001356">A Q igitur erit &aelig;qualis 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&shy;<lb/>tum A caput remi ex hypothe&longs;i. </s>

<s id="id.001360">A autem conficit &longs;patium A q. <lb/></s>

<s>Igitur B &longs;calmus conficiet &longs;patium B G. </s>

<s id="id.001361">Et quia anguli ad G <lb/>recti &longs;unt, ideo cum &longs;calmus peruenerit ad G, habebit remus A C <lb/>rectitudinis &longs;itum E C, quo in loco illius remigationis finis erit. </s>

<s id="id.001362">Sic <lb/>igitur palmula C &agrave; loco &longs;uo dimota non fuit, quod demon&longs;trandum <lb/>erat. </s>

<s id="id.001363">C&aelig;terum Nonius h&icirc;c 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 ant&egrave;, palmulam diuidere mare, quod <lb/>&longs;olum demon&longs;trare intendebat. </s>

<s id="id.001366">vbi etiam aduertes lector ex hoc dia&shy;<lb/>grammate Nonij &amp; c&aelig;teris lineam A L E &agrave; 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 pulchr&egrave; con&longs;entit cum his qu&aelig;<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"/>ant&egrave; diximus de remi in vna remigatione varijs motibus. <emph.end type="italics"/></s></p><p type="head">

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

<s id="id.001369"><emph type="italics"/>Manife&longs;ta e&longs;t, quia &longs;i remi palmula dimota non fuerit &agrave; loco &longs;uo, <lb/>ibique tandiu per&longs;i&longs;tat, donec remus &longs;itum rectitudinis obtineat, tan&shy;<lb/>tum &longs;patium conficiet caput remi motu proprio: quantum nauis. <lb/></s>

<s id="id.001370">Recta enim C F &aelig;qualis e&longs;t A Q prop. 26. lib. 1. </s>

<s>&aelig;qualis etiam <lb/>B G prop. 34. lib. 1. </s>

<s>igitur A Q &amp; B G &aelig;quales erunt ax. 1. <emph.end type="italics"/></s></p><p type="head">

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

<s id="id.001374"><emph type="italics"/>Capite remi proprio motu conficiente &longs;patium duplum &longs;patij nauis: <lb/>tunc nauis tant&ugrave;m promouebitur, quant&ugrave;m palmula retrocedet. <emph.end type="italics"/></s></p><figure id="id.035.01.126.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.126.1.jpg"/><p type="main">

<s id="id.001375"><emph type="italics"/>Remus incipiente motu &longs;it A C, <lb/>de&longs;inente vero habeat rectitudinis <lb/>&longs;itum F G. </s>

<s id="id.001376">Et &longs;ic &longs;calmus B pro&shy;<lb/>pter nauis motum conficiet interual&shy;<lb/>lum B D. </s>

<s id="id.001377">Excitetur igitur &agrave; puncto <lb/>B in vtramque partem perpendicu&shy;<lb/>laris E E, prop. 11. lib. 1. </s>

<s>In quam <lb/>perpendiculares incidant &agrave; punctis <lb/>A &amp; C, qu&aelig; &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 &agrave; capite remi A <lb/>proprio motu, duplum interualli B <lb/>D, &amp; recta linea C H re&longs;pondeat <lb/>curu&aelig; C G &agrave; remi palmula de&longs;cri&shy;<lb/>pt&aelig;. </s>

<s id="id.001379">Dico rectas lineas B D, C H <lb/>&aelig;quales e&longs;&longs;e. </s>

<s id="id.001380">Nam triangulorum B <lb/>A E &amp; C B E rect&aelig; A E, C E prop. 26. lib. 1. &amp; in parallelo&shy;<lb/>grammo B H rect&aelig; oppo&longs;it&aelig; B D, E H etiam &aelig;quales prop. 34. <lb/>lib. 1. </s>

<s id="id.001381">Atqui recta A E dupla e&longs;t rect&aelig; B D ex hypothe&longs;i. </s>

<s id="id.001382">Dupla <lb/>igitur &amp; C E rect&aelig; H E, quapropter C H &amp; E H &aelig;quales <lb/>erunt ax. 7. </s>

<s id="id.001383">Et &longs;ic C H &amp; B D &aelig;quales &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&shy;<lb/>tur &longs;i caput remi motu proprio duplum confecerit ip&longs;ius nauis inter&shy;<lb/>ualli, tant&ugrave;m prouehetur nauis: quant&ugrave;m palmula retrocedet. </s>

<s id="id.001387">quod <lb/>demon&longs;trandum erat. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.127.jpg" pagenum="88"/><p type="head">

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

<s id="id.001389"><emph type="italics"/>Naui &aelig;qualiter prouecta, atque palmula retroce&szlig;it: motus capitis <lb/>remi proprius duplus e&longs;t motus nauis. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001390"><emph type="italics"/>Si enim C H &aelig;qualis ponatur B D, quoniam eidem B D &aelig;qua&shy;<lb/>lis e&longs;t H E in parallelogrammo, &aelig;quales igitur erunt C H &amp; <lb/>H E ax. 1. </s>

<s id="id.001391">Et &longs;ic dupla erit C E ip&longs;ius H E: &amp; eadem C E <lb/>dupla ip&longs;ius B D. </s>

<s>&aelig;quales porro &longs;unt C E &amp; A E prop 26. lib. 1. <lb/></s>

<s>Dupla ergo erit A E rect&aelig; B D. </s>

<s>&longs;ed recta A E decur&longs;a e&longs;t &agrave; ca&shy;<lb/>pite remi, &amp; B D &agrave; &longs;calmo, quant&ugrave;m autem prouehitur &longs;calmus, <lb/>tant&ugrave;m &amp; nauis. </s>

<s id="id.001392">Igitur &longs;i nauis tant&ugrave;m fuerit prouecta, quant&ugrave;m <lb/>remi palmula retroce&szlig;it, duplum conficit caput remi motu proprio <lb/>eius interualli, quod nauis conficit. </s>

<s id="id.001393">quod fuit demon&longs;trandum. <emph.end type="italics"/></s></p><p type="head">

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

<s id="id.001395"><emph type="italics"/>Nauis decurrens minus &longs;patium: quam caput remi decurrat: maius <lb/>tamen eius dimidio: magis prouehitur: quam palmula retrocedat: <lb/>minus autem dimidio: minus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001396"><emph type="italics"/>In po&longs;tremo diagrammate ponatur B D minor, quam A E: <lb/>&longs;ed eius dimidio maior. </s>

<s id="id.001397">Dico quod ip&longs;a B D maior e&longs;t, quam C H. <lb/></s>

<s id="id.001398">Nam B D &amp; H E &aelig;quales &longs;unt, ad h&aelig;c A E &amp; C E &aelig;qua&shy;<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&shy;<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 &amp; H E dimidio eiu&longs;dem A E. </s>

<s id="id.001405">Et quoniam A E &amp; <lb/>C E &aelig;quales &longs;unt. </s>

<s id="id.001406">Reliqua igitur C H dimidio eiu&longs;dem A E <lb/>maior erit. </s>

<s id="id.001407">Et proinde minor erit B D quam C H. </s>

<s id="id.001408">Nauis igitur <lb/>minus interuallum decurret in anteriora: quam remi palmula in <lb/>contrarium. </s>

<s id="id.001409">quod fuit demon&longs;trandum. <emph.end type="italics"/></s></p><p type="head">

<s id="id.001410">Corollarium. </s></p><p type="main">

<s id="id.001411"><emph type="italics"/>Hinc &amp; ex pr&aelig;cedenti infertur, quod &longs;i caput remi motu pro&shy;<lb/>prio decurrat interuallum maius, quam nauis, &longs;iue duplum, &longs;iue du&shy;<lb/>plo minus, &longs;iue maius: &longs;emper interuallum nauis adiuncto ei quod <lb/>palmula retroce&longs;&longs;erit, &aelig;quale erit ei, quod &agrave; capite remi motu proprio <lb/>conficitur. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.128.jpg" pagenum="89"/><p type="main">

<s id="id.001412"><emph type="italics"/>Semper enim B D &aelig;qualis e&longs;t H E: tota vero C E qu&aelig; &aelig;qua&shy;<lb/>lis e&longs;t A E ex&longs;uis con&longs;tabit partibus C H, H E. <emph.end type="italics"/></s></p><p type="head">

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

<s id="id.001414"><emph type="italics"/>Nauis longius progrediens: quam remi palmula retrocedat, inter&shy;<lb/>uallum conficit maius dimidio eius, quod motu proprio remi caput <lb/>decurrit: &longs;i minus: minus etiam dimidio. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001415"><emph type="italics"/>Huius demon&longs;tratio ex pr&aelig;dictis facilis e&longs;t. <emph.end type="italics"/></s></p><p type="head">

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

<s id="id.001417"><emph type="italics"/>Naui celerius mota quam caput remi: palmula antror&longs;um moue&shy;<lb/>bitur, nec quicquam retrocedet, idque &longs;patij decurret quo nauis motus <lb/>motum capitis remi &longs;uperat. <emph.end type="italics"/></s></p><figure id="id.035.01.128.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.128.1.jpg"/><p type="main">

<s id="id.001418"><emph type="italics"/>Habeat remus inci&shy;<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&shy;<lb/>pter nauis motum tran&longs;&shy;<lb/>latus erit in D. </s>

<s id="id.001420">Sit ita&shy;<lb/>que interuallum B D <lb/>maius: <expan abbr="qu&atilde;">quam</expan> A H, quod <lb/>e&longs;t &agrave; 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&shy;<lb/>la C in vlteriora mouebitur. </s>

<s id="id.001423">Nam cum &longs;calmus B prouectus fue&shy;<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&shy;<lb/>trocedere o&longs;tendetur in hunc modum. </s>

<s id="id.001426">Eadem celeritate mouentur A <lb/>in H, &amp; 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&shy;<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&shy;<lb/>riora progredietur, interuallumque decurret C K, quod quidem re&shy;<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&shy;<lb/>niret ad D: &longs;ed retrahitur interim, propter eum motum, qui fit cir&shy;<lb/>ca B. </s>

<s id="id.001431">Sic igitur palmul&aelig; celeritate, qu&aelig; &agrave; motu nauigij prouenit, re&shy;<lb/>tardata, decur&longs;um interuallum erit C K. </s>

<s id="id.001432">Videtur autem &longs;olo remo&shy;<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 e&ograve; fluentis aqu&aelig;. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001433"><emph type="italics"/>Atque ex his theorematis concludit Nonius Ari&longs;totelem con&shy;<lb/>fus&egrave; propo&longs;ui&longs;&longs;e hoc problema, cum non di&longs;tinxerit inter motum re&shy;<lb/>mi proprium, &amp; motum &agrave; 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;cit&egrave;, &amp; fals&ograve; proble&shy;<lb/>mati &longs;atisfeci&longs;&longs;e. </s>

<s id="id.001435">Quandoquidem non continu&ograve; &longs;i nauis in anteriora <lb/>moueatur, remi palmula retrocedet: neque &longs;i retrocedat, minus inter&shy;<lb/>uallum in contrarium tran&longs;mittet: quam nauis progrediatur, vt ex <lb/>&longs;ecunda &amp; tertia propo&longs;itionibus liquet: pr&aelig;terea cum caput remi <lb/>motu proprio, qui circa &longs;calmum fit, vn&acirc; cum nauis motu, maius in&shy;<lb/>teruallum conficiat: quam nauis, &longs;olo autem proprio motu, &longs;i contin&shy;<lb/>gat tantum interuallum conficere: quantum nauis, fieri non po&szlig;it, vt <lb/>palmula moueatur: fru&longs;tr&agrave; 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, &amp; <lb/>&longs;ic non &aelig;quale. </s>

<s id="id.001437">Atque h&aelig;c cum &longs;int &longs;uis veris demon&longs;trationibus <lb/>&longs;tabilita Ari&longs;totelem in hoc problemate dormita&longs;&longs;e, quod aliquando <lb/>bono Homero contingit, conuincunt. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001438"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001439">Id etiam ip&longs;um facit gu&shy;<lb/>bernaculum, ni&longs;i quod an&shy;<lb/>terius non mouet nauim: <lb/>vt antea dictum e&longs;t: &longs;ed <lb/>hinc vel hinc puppim &longs;o&shy;<lb/>lum in tran&longs;uer&longs;um pellit. <lb/></s>

<s id="id.001440">Sic enim in <expan abbr="c&otilde;trari&utilde;">contrarium</expan> prora <lb/>vergit. </s>

<s id="id.001441">Vbi igitur <expan abbr="guberna-cul&utilde;">guberna&shy;<lb/>culum</expan> <expan abbr="adi&utilde;ct&utilde;">adiunctum</expan> e&longs;t, ibi opor&shy;<lb/>tet aliquod eius, quod mo&shy;<lb/>uetur <expan abbr="medi&utilde;">medium</expan> intelligere, &amp; <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&shy;<lb/>dit, quo temo transfertur. <lb/></s>

<s id="id.001442">Si quidem intror&longs;us agat, <lb/>etiam puppis e&ograve; transfer&shy;<lb/>tur, prora ver&ograve; in con&shy;<lb/>trarium nutat. </s>

<s id="id.001443">In eodem <lb/>enim exi&longs;tente prora, nauis <lb/>tota transfertur. </s></p><p type="head">

<s id="id.001444">COMMENTARIVS. </s></p><p type="main">

<s id="id.001445">Id etiam ip&longs;um.] <emph type="italics"/>Ari&longs;toteles a&longs;&longs;erit gubernaculum idem fa&shy;<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, &amp; alienum. </s>

<s id="id.001448">Et cum &longs;imili modo quo remus <lb/>veniat in v&longs;um, omnia qu&aelig; 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&shy;<lb/>&longs;picax fuerit Ari&longs;toteles, nec in hoc per&longs;picacior fui&longs;&longs;e putandus e&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001450">Ni&longs;i quod anterius.] <emph type="italics"/>Repetitio e&longs;t differenti&aelig; motuum remi <lb/>&amp; gubernaculi &longs;umpta ex diuer&longs;itate terminorum ad quos vterque <lb/>ducit de qua igitur ante. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001451">Vbi igitur guber.] <emph type="italics"/>Antea in gubernaculi &longs;imilitudine cum <lb/>vecte attulerat Ari&longs;toteles pondus mouendum mare, motorem eum <lb/>qui &longs;edet in puppi, quod erat tertium de centro, circa quod temo mo&shy;<lb/>uetur, pr&aelig;termi&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 &amp; circa cardi&shy;<lb/>nem gubernaculum vertitur, &longs;icut circa &longs;calmum remus. <emph.end type="italics"/></s></p></chap><chap><p type="main">

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

<s id="id.001455">7. Cau&longs;a pote&longs;tatis <lb/>Antemn&aelig;. </s></p><p type="main">

<s id="id.001456"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001457">Cur quant&ograve; antemna &longs;u&shy;<lb/>perior fuerit, tant&ograve; celerius <lb/>nauis feratur <expan abbr="eod&etilde;">eodem</expan> velo, <expan abbr="eo-demq;">eo&shy;<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, &amp; calx in qua in&shy;<lb/>figitur, pre&longs;&longs;io? </s>

<s id="id.001459">Quod vero <lb/>pondus mouere oportet, <lb/>e&longs;t nauis: &amp; ventus in <expan abbr="vel&utilde;">velum</expan>, <lb/>e&longs;t mouens. </s>

<s id="id.001460">Igitur &longs;i quan&shy;<lb/>to remotior fuerit pre&longs;&longs;io, <lb/>facilius &amp; celerius vis <expan abbr="ead&etilde;">eadem</expan> <lb/>pondus ip&longs;um mouet: an&shy;<lb/>temna &longs;ublimius po&longs;ita &agrave; <lb/>calce mali, qu&aelig; pre&longs;&longs;io e&longs;t, <lb/>magis di&longs;tare velum faciet. </s></p><p type="head">

<s id="id.001461">COMMENTARIVS. </s></p><p type="main">

<s id="id.001462">Antemn&aelig;.] <emph type="italics"/>Antemna lignum e&longs;t per tran&longs;uer&longs;um in malo <lb/>nauis po&longs;itum, &agrave; quo velum dependet. </s>

<s id="id.001463">Latini illius ligni extre&shy;<lb/>mas partes <expan abbr="voc&atilde;t">vocant</expan> cornua ob quod Bayfius putat antemnas dici Gr&aelig;&shy;<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 prop&egrave; 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&shy;<lb/>uer&longs;is appellationibus di&longs;tinct&aelig; &agrave; Macrobio in quinto Saturnalium <lb/>in h&aelig;c verba &longs;unt. </s>

<s id="id.001464">A&longs;clepiades autem vir inter Gr&aelig;cos apprim&egrave; <lb/>doctus ac diligens carche&longs;ia &agrave; 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, &amp; inde diffundi in vtrumque veli latus ea qu&aelig; 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&shy;<lb/>pul&longs;u nauis tran&longs;uehitur non aliter <expan abbr="qu&atilde;">quam</expan> antea diximus remis. </s>

<s id="id.001467">&AElig;olus <lb/>primus mortalium velis v&longs;us e&longs;&longs;e dicitur. </s>

<s id="id.001468">Et propterea deus vento&shy;<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&shy;<lb/>da/cai. </foreign><emph type="italics"/> </s>

<s>id e&longs;t in&longs;uper &amp; velorum v&longs;um nautis introduxi&longs;&longs;e, ratio&shy;<lb/>nemque vtendi docui&longs;&longs;e. </s>

<s id="id.001470">velorum autem apud veteres tria fuerunt <lb/>genera Artemo &amp; acatium, quod velum maius: dolo, quod minus <lb/>erat: &amp;<emph.end type="italics"/> <foreign lang="greek">e)po/dromos,</foreign> <emph type="italics"/>quod velum &agrave; tergo ponebatur. </s>

<s id="id.001471">vnde nauis &agrave; <lb/>Iulio polluce<emph.end type="italics"/> <foreign lang="greek">triar/menos,</foreign> <emph type="italics"/>Antigoni dicta, qu&aelig; 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;ti&szlig;im&utilde;">frequenti&szlig;imum</expan>. <lb/></s>

<s id="id.001472">quia inuenta pyxide nautica, inquit Cardanus, &amp; lapidis Herculis <lb/>auxilio pluribus locis vela dispo&longs;ita, melius dirigunt iter: antiquis <lb/>contr&agrave;, quoniam &longs;yderibus Cyno&longs;ura, &amp; Helice, vias dirigebant, &amp; <lb/>ob id non ad amu&szlig;im, nec ex lineis, cra&longs;&longs;a quidem Minerua: &longs;ed certa <lb/>deformatis malorum multitudo confu&longs;ionem in cur&longs;u, &amp; impedi&shy;<lb/>mentum, maiu&longs;que periculum attuli&longs;&longs;et. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001473">Cur quanto.] <emph type="italics"/>Quintum e&longs;t &longs;peciale problema de vecte con&longs;i&shy;<lb/>derato in malo nauis. </s>

<s id="id.001474">Cur &longs;cilicet antemna &longs;ublimiore mali loco po&shy;<lb/>&longs;ita, vt &longs;it idem velum, idemque ventus velo exceptus, nauis cele&shy;<lb/>rius feratur. </s>

<s id="id.001475">Id e&longs;t vt c&aelig;tera omnia &longs;int paria. </s>

<s id="id.001476">Nam nauis velocitas, <lb/>non &longs;olum pendet &agrave; ventorum impetu &amp; rectitudine, &amp; velorum <lb/>magnitudine: &longs;ed &amp; ex loco humiliore, vel &longs;ublimiore, ex c&aelig;li ab <lb/>Oriente in Occidentem conuer&longs;ione, nauis leuitate &amp; forma. </s>

<s id="id.001477">qu&aelig; <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 veloci&szlig;im&aelig;, &amp; longiores latis, po&longs;t eas, qu&aelig; carinam habent te&shy;<lb/>nuem, vt aquas facile diuidant, vltimo loco qu&aelig; qua&longs;i medi&aelig; ante <lb/>quidem tenues, po&longs;t latiores ad velocem cur&longs;um &amp; ferendum onera <lb/>apt&aelig;, &amp; humiles altis, &amp; leui ex ligno: &longs;ed &amp; parte intra aquam <lb/>polita l&aelig;uigata &amp; &longs;&aelig;uo illita. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001478">An quia malus e&longs;t.] <emph type="italics"/>Solutio e&longs;t problematis propo&longs;iti per re&shy;<lb/>ductionem mali ad vectem, &amp; eius calcis ad hypomochlium. </s>

<s id="id.001479">Syllo&shy;<lb/>gi&longs;mus h&icirc;c e&longs;t &longs;uis omnibus partibus ab&longs;olutus, &longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001480"><emph type="italics"/>Quant&ograve; pars ab hypomochlio ad caput vectis e&longs;t longior: tant&ograve; <lb/>vis mouens, ea e&longs;t ventus, onus, id e&longs;t nauim, facilius &amp; ce&shy;<lb/>lerius mouet. </s>

<s id="id.001481">Ex anteced. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001482"><emph type="italics"/>Qu&ograve; autem antemna, intellige cum velo expan&longs;o, &longs;uperior e&longs;t in <lb/>malo: e&ograve; pars ab hypomochlio ad caput vectis e&longs;t longior. ax. 9. <lb/></s>

<s id="id.001484">E&longs;t enim malus vectis, &amp; mali pterna &longs;eu calx e&longs;t hypo&shy;<lb/>mochlium. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001485"><emph type="italics"/>Ergo antemna cum &longs;uperior e&longs;t, ventus facilius &amp; celerius <lb/>mouet nauim. <emph.end type="italics"/><lb/><arrow.to.target n="marg22"/></s></p><p type="margin">


<s id="id.001486"><margin.target id="marg22"/>Cap. 8. lib <lb/>10. </s></p><p type="main">

<s id="id.001487"><emph type="italics"/>Eadem de hoc problemate fuit Vitruuij <expan abbr="&longs;ent&etilde;tia">&longs;ententia</expan> his verbis expre&longs;&longs;a. <lb/></s>

<s id="id.001488">Nauis onerari&aelig; vela cum &longs;int per altitudinem mediam mali penden&shy;<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 antemn&aelig; &longs;ubduct&aelig; &longs;unt, tunc vehementiori progreditur <lb/>impetu, quod non proxime calcem mali, qu&aelig; e&longs;t loco centri: &longs;ed in <lb/>&longs;ummo longius, &amp; ab eo progre&longs;&longs;a recipiunt in &longs;e vela ventum. </s>

<s id="id.001489">Ita&shy;<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&shy;<lb/>rem habent virtutem. </s>

<s id="id.001491">Qu&aelig; autem in capite mali &longs;ummo collocantur, <lb/>di&longs;cedentia longius &agrave; centro non acriore, &longs;ed eodem flatu pre&szlig;ione ca&shy;<lb/>cuminis vehementius cogunt progredi nauem. </s>

<s id="id.001492">Ex his etiam intelli&shy;<lb/>gere licet cur hodierni naut&aelig; &longs;olo &longs;&aelig;pe in procellis vtuntur dolone, <lb/>velo quidem non tam minimo magnitudine quam altitudine Trin&shy;<lb/>chetum appellant. </s>

<s id="id.001493">Solum enim &longs;u&longs;tinet nauim, qu&aelig; &agrave; ventis vel vn&shy;<lb/>dis mergi &longs;olet. </s>

<s id="id.001494">ab vndis quidem vbi humilior e&longs;t: &agrave; ventis vero ex <lb/>lateribus &amp; anteriore parte. </s>

<s id="id.001495">Siquidem velum illud humile &amp; exi&shy;<lb/>guum efficit, vt nauis anteriore parte leuis, nec mergatur prona &agrave; <lb/>ventis, nec aquas ea excipiat, nec tamen impelli pote&longs;t nauis in &longs;copu&shy;<lb/>los, nec euerti ob cau&longs;as dictas. </s>

<s id="id.001496">Quin &longs;i nimium adhuc venti &longs;&aelig;uiant, <lb/>dolonem demittant adhuc infra magis, quin &amp; ip&longs;um malum etiam <lb/>&longs;ublato velo, aut circa antemnam implexo &amp; inuoluto, &amp; ne nauis <lb/>obruatur, antror&longs;um. </s>

<s id="id.001497">H&aelig;c enim pars vim <expan abbr="ventor&utilde;">ventorum</expan> omnem excipit: <lb/>gubernatores etiam puppim multa arena, lapilli&longs;que onerare, &longs;i de&longs;it <lb/>aliud onus, &longs;olent. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001498"><foreign lang="greek">*dia\ ti/ o(/tan e)kkerai/as bou/&shy;<lb/>lwntai diadramei=n po/da poiou=si. </foreign></s></p><p type="main">

<s id="id.001499">8. Cur quando &egrave; cornu vo&shy;<lb/>lunt nauigare pedem fa&shy;<lb/>ciunt. </s></p><p type="main">

<s id="id.001500"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001501">Cur quando &egrave; cornu na&shy;<lb/>uigare voluerint vento &longs;e&shy;<lb/>cundo non exi&longs;tente, par&shy;<lb/>tem quidem veli ad guber&shy;<lb/>natorem &longs;pectantem con&shy;<lb/>trahunt: <expan abbr="part&etilde;">partem</expan> vero ad pro&shy;<lb/>ram <expan abbr="relax&atilde;t">relaxant</expan> pedem facien&shy;<lb/>tes. </s>

<s id="id.001502">An quia gubernacu&shy;<lb/>lum non pote&longs;t auertere, <lb/>cum multus exiftit ventus: <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.134.jpg" pagenum="95"/><foreign lang="greek"><gap/></foreign><lb/><expan abbr="c&utilde;">cum</expan> paucus ver&ograve; pote&longs;t. </s>

<s id="id.001503"><expan abbr="v&etilde;tus">ventus</expan> <lb/>igitur perpellit, quem &longs;e&shy;<lb/>cundum facit gubernacu&shy;<lb/>lum, auertens &amp; compel&shy;<lb/>lens mare, &longs;imul &amp; naut&aelig; <lb/>pugnant cum vento, &amp; in <lb/>contrariam nituntur par&shy;<lb/>tem. </s></p><p type="head">

<s id="id.001504">COMMENTARIVS. </s></p><p type="main">

<s id="id.001505">E Cornu volunt nauigare.] <emph type="italics"/>Diximus antemnarum extrema <lb/>appellari cornua. </s>

<s id="id.001506">Hinc &egrave; cornu nauigare e&longs;t cum vento cornu <lb/>antemnarum obijcitur. </s>

<s id="id.001507">Quod feci&longs;&longs;e &longs;ignificabat Troianos Virgi&shy;<emph.end type="italics"/><arrow.to.target n="marg23"/><lb/><emph type="italics"/>lius hoc ver&longs;u,<emph.end type="italics"/></s></p><p type="margin">

<s id="id.001508"><margin.target id="marg23"/>Lib. 3. <lb/>&AElig;neid. </s></p><p type="main">

<s id="id.001509">Cornua velatarum obuertimus antemnarum. </s></p><p type="main">

<s id="id.001510">Pedem faciunt.] <emph type="italics"/>Ex textu &amp; rei natura qu&aelig; in eo explica&shy;<lb/>tur ratiocinantes h&icirc;c pro<emph.end type="italics"/> <foreign lang="greek">ou(/tws poiou=oi</foreign> <emph type="italics"/>repo&longs;uimus<emph.end type="italics"/> <foreign lang="greek">po/da poiou=oi. </foreign><emph type="italics"/>E&longs;t <lb/>autem<emph.end type="italics"/> <foreign lang="greek">pou/s</foreign> <emph type="italics"/>Gr&aelig;cis, &amp; pes Latinis vari&aelig; admodum &longs;ignificationis. <lb/></s>

<s id="id.001511">Pr&aelig;ter c&aelig;teras h&icirc;c huius duas annotare licet. </s>

<s id="id.001512">Prior venit in men&shy;<lb/>tem ob duos locos apud Galenum &agrave; perpaucis intellectos. </s>

<s id="id.001513">Alter e&longs;t <lb/>cap. 9. lib. 2. de mu&longs;c. motu: alter com. 4. in lib. 6. <emph.end type="italics"/> <foreign lang="greek">e(pid. </foreign><emph type="italics"/>in Aph. 24. <lb/>vbi dicit tibicines, pr&aelig;cones, nuncupatum<emph.end type="italics"/> <foreign lang="greek">po/da,</foreign> <emph type="italics"/>id e&longs;t, pedem cane&shy;<lb/>re. </s>

<s id="id.001516">vbi dubium non e&longs;t Galenum &longs;ignificare volui&longs;&longs;e genus quod&shy;<lb/>dam vocis, qu&aelig; vehementi &amp; longa exufflatione opus habeat, vt <lb/><expan abbr="eti&atilde;">etiam</expan> &longs;en&longs;it Hieronymus Mercurialis, qui hos Galeni locos ob&longs;erua&shy;<lb/>uit. </s>

<s id="id.001517">Nos <expan abbr="eti&atilde;">etiam</expan> legimus in <expan abbr="c&otilde;ment">comment</expan>. </s>

<s id="id.001518">C&aelig;&longs;aris cum <expan abbr="pugnand&utilde;">pugnandum</expan> &longs;ibi foret, <lb/>iu&szlig;i&longs;&longs;e ab equis milites <expan abbr="de&longs;c&etilde;dere">de&longs;cendere</expan>, nequis <expan abbr="&longs;p&etilde;">&longs;pem</expan> fug&aelig; in <expan abbr="equor&utilde;">equorum</expan> celerita&shy;<lb/>te reponeret. </s>

<s id="id.001519">Qu&aelig; iu&szlig;io forta&longs;&longs;e erat,<emph.end type="italics"/> <foreign lang="greek">e)rei=n po/da,</foreign> <emph type="italics"/>dicere <expan abbr="ped&etilde;">pedem</expan>, vbi <expan abbr="St&etilde;-torea">Sten&shy;<lb/>torea</expan> voce opus erat, vt ab omnibus audiretur: contra hodie apud <lb/>Gallos, inituris pugnam iubetur a&longs;cendere in equos: po&longs;terior e&longs;t qua <lb/>ea pars in velo, qu&aelig; acutior &amp; inferior ad nauis latus, vel ad mali <lb/><expan abbr="ptern&atilde;">pternam</expan> religatur, mod&oacute;que <expan abbr="c&otilde;trahitur">contrahitur</expan> mod&ograve; relaxatur. </s>

<s id="id.001520">vnde Po&euml;ta:<emph.end type="italics"/><lb/><arrow.to.target n="marg24"/></s></p><p type="margin">

<s id="id.001521"><margin.target id="marg24"/>Lib. 5. <lb/>&AElig;neid. </s></p><p type="main">

<s id="id.001522">vna omnes fecere pedem. </s></p><p type="main">

<s id="id.001523"><emph type="italics"/>Alij tamen dicunt e&longs;&longs;e funem, quo id fit. </s>

<s id="id.001524">Interpres Apollonij Rho&shy;<lb/>dij funes veli id e&longs;t<emph.end type="italics"/> <foreign lang="greek">ka/lw</foreign> <emph type="italics"/>rudentes in tria genera diuidit. </s>

<s id="id.001525">Aut enim<arrow.to.target n="marg25"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.135.jpg" pagenum="96"/>detrahitur his velum, &amp; vocantur<emph.end type="italics"/> <foreign lang="greek">mesouri/ai</foreign>: <emph type="italics"/>aut intenditur vtrin&shy;<lb/>que ad proram, &amp; &longs;unt<emph.end type="italics"/> <foreign lang="greek">pro/tonoi</foreign>: <emph type="italics"/>aut conuertitur &amp; laxatur, hi <lb/>&longs;unt<emph.end type="italics"/> <foreign lang="greek">kata\ ta\s gwni/as</foreign> <emph type="italics"/>ad angulos, &amp; dicuntur<emph.end type="italics"/> <foreign lang="greek">po/des</foreign> <emph type="italics"/>&amp; ante hos<emph.end type="italics"/><lb/><foreign lang="greek">pro/podes</foreign> <emph type="italics"/>quo &longs;en&longs;u dixi&longs;&longs;e Plinius videtur lib. 2. cap. 47. </s>

<s>Ii&longs;dem <lb/>autem ventis in contrarium nauigatur prolatis pedibus vt noctu <lb/>plerumque vela concurrant. <emph.end type="italics"/></s></p><p type="margin">

<s id="id.001527"><margin.target id="marg25"/>Lib. 3. </s></p><p type="main">

<s id="id.001528">Cur quando.] <emph type="italics"/>Sextum e&longs;t problema &longs;peciale de vecte in naui&shy;<lb/>gatione obliqua, quod &longs;oluitur triplici ope nempe veli obliqui ex par&shy;<lb/>te contracti, parteque expan&longs;i gubernaculi tanquam vectis, &amp; re&shy;<lb/>migum renixus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001529">E cornu nauigare.] <emph type="italics"/>Pro<emph.end type="italics"/> <foreign lang="greek">e)k ou)ri/as</foreign> <emph type="italics"/>h&icirc;c legendum putamus vt <lb/>in titulo<emph.end type="italics"/> <foreign lang="greek">e)k kerai/as</foreign> <emph type="italics"/>nam h&aelig;c &longs;unt<emph.end type="italics"/> <foreign lang="greek">a)si/stata</foreign> <emph type="italics"/>velle nauigare<emph.end type="italics"/> <foreign lang="greek">e)k ou)ri/as</foreign><lb/><emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">mh\ ou)ri/ou pneu/ma/tos o(/ntos.</foreign> </s>

<s><emph type="italics"/>Quomodo enim nauigabitur vento <lb/>&longs;ecundo, &longs;i ventus &longs;ecundus non e&longs;t. </s>

<s id="id.001530">At cum ventus &longs;ecundus non <lb/>e&longs;t, antemnarum ope rectum nihilominus tenere cur&longs;um po&szlig;ibile e&longs;t, <lb/>Et id vt fiat &amp; quibus de cau&longs;is, explicatur h&icirc;c ab Ari&longs;torele. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001531">Vento &longs;ecundo.] <emph type="italics"/>Ventus &longs;ecundus e&longs;t cum vt ait Po&euml;ta,<emph.end type="italics"/></s></p><p type="main">

<s id="id.001532">A tergo comitatur euntes,</s></p><p type="main">

<s id="id.001533"><emph type="italics"/>Hic e&longs;t quem naut&aelig; &longs;ibi dari optant vnde e&longs;t illud,<emph.end type="italics"/></s></p><p type="main">

<s id="id.001534">Ferte viam facilem, venti &amp; &longs;pirate &longs;ecundi. </s></p><p type="main">

<s id="id.001535"><emph type="italics"/>Qui huic e&longs;t contrarius, dicitur aduer&longs;us, cum in proram inuehitur. <lb/></s>

<s id="id.001536">Nec eo &longs;ic flante nauis ni&longs;i remis agi pote&longs;t, idque magnis viribus <lb/>&amp; magno conatu. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001537">Non aliter quam qui aduer&longs;o vix flumine lembum</s></p><p type="main">

<s id="id.001538">Remigijs &longs;ubigit, &longs;i brachia forte remi&longs;it,</s></p><p type="main">

<s id="id.001539">Atque illum pr&aelig;ceps prono rapit alueus amne. </s></p><p type="main">

<s id="id.001540"><emph type="italics"/>Inter hos duo &longs;unt medij, vnus tran&longs;uer&longs;us ad latera nauis perpendi&shy;<lb/>culariter incidens: alter obliquus <lb/><figure id="id.035.01.135.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.135.1.jpg"/><lb/>qui medius e&longs;t inter &longs;ecundum &amp; <lb/>tran&longs;uer&longs;um, vel inter aduer&longs;um &amp; <lb/>tran&longs;uer&longs;um. </s>

<s id="id.001541">Vt e&longs;to nauis G H, <lb/>&amp; prora &longs;it G puppis H, ventus <lb/>ex B &longs;ecundus erit, ex A aduer&shy;<lb/>&longs;us, ex C vel D tran&longs;uer&longs;us, ex E <lb/>vel F obliquus. </s>

<s id="id.001542">Horum autem mo&shy;<lb/>tuum Galenus obliquos per pulchr&egrave; <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.136.jpg" pagenum="97"/><emph type="italics"/>declarauit &longs;umpta prim&ugrave;m hac propo&longs;itione. </s>

<s id="id.001543">In vniuer&longs;um quando <lb/>&agrave; duobus motibus ex tran&longs;uer&longs;o &longs;ibi inuicem occurrentibus trahitur <lb/>corpus, &longs;i mult&ograve; quidem &longs;upereminet alter, nece&longs;&longs;arium e&longs;t ob&longs;curari, <lb/>di&longs;parer&eacute;ue reliquum: pauca ver&ograve; cum e&longs;t exuperantia alterius: aut <lb/>ambo &aelig;qualiter po&longs;&longs;unt, mixtum ex vtri&longs;que fieri eum corporis mo&shy;<lb/>tum oportet. </s>

<s id="id.001544">Videntur autem omnia i&longs;ta propemodum quotidie in <lb/>&longs;excentis exemplis, exempli gratia in remigantibus, &longs;imul &amp; naui&shy;<lb/>bus ventum tran&longs;uer&longs;um habentibus. </s>

<s id="id.001545">Si enim &aelig;quipollet venti &amp; <lb/>remigantium robur, mixtum fieri motum nece&longs;&longs;e e&longs;t. </s>

<s id="id.001546">Cum neque <lb/>antror&longs;um &longs;olum, neque ad tran&longs;uer&longs;um naues ferantur, &longs;ed ad am&shy;<lb/>borum medium (vbi mal&egrave; legitur Medicum) &longs;i vero remigantium <lb/>robur maius fuerit, antror&longs;um magis, quam ad tran&longs;uer&longs;um. </s>

<s id="id.001547">Si au&shy;<lb/>tem venti violentia vincat, ad tran&longs;uer&longs;um magis, quam antror&shy;<lb/>&longs;um. </s>

<s id="id.001548">Multus autem &longs;i fuerit exce&longs;&longs;us, adeo vt alterius vires omnino <lb/>vincantur, nauigantium quidem ob&longs;curatis viribus, ad tran&longs;uer&shy;<lb/>&longs;um: venti vero, antror&longs;um magis naues ferentur. </s>

<s id="id.001549">Quid tandem &longs;i <lb/>tenuis omnino aura fuerit, nauis ver&ograve; pr&aelig;longa, &amp; leuis, quamplu&shy;<lb/>rimos habens nautas, poterit aliquando motus ab aura e&longs;&longs;e manife&shy;<lb/>&longs;tus? </s>

<s id="id.001550">Sed neque &longs;i maximus quidem &longs;uerit ventus, nauis autem &amp; <lb/>maxima &amp; grauis, &amp; duo &longs;olum aut tres remigent, remigum actio&shy;<lb/>nem apparere po&szlig;ibile e&longs;t. </s>

<s id="id.001551">cap. 19. lib. 1. de v&longs;. partium. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001553">An quia gubernaculum.] <emph type="italics"/>Solutio e&longs;t problematis propo&longs;iti, <lb/>quod &longs;ic fiet euidentius. </s>

<s id="id.001554">Cur qui &egrave; cornu nauigaturi vento &longs;cilicet <lb/>non &longs;ecundo exi&longs;tente: &longs;ed obliquo vel tran&longs;uer&longs;o eam veli partem, <lb/>qu&aelig; ver&longs;us gubernatorem e&longs;t, contrahunt id e&longs;t &longs;tringunt, &amp; circa <lb/>antemnam implicant. </s>

<s id="id.001555">Eam vero, qu&aelig; ad proram, relaxant, quod ap&shy;<lb/>pellant pedem facere. </s>

<s id="id.001556">Re&longs;pon&longs;io. </s>

<s id="id.001557">Quia obliqu&egrave; vel tran&longs;uer&longs;im naui&shy;<lb/>gari non pote&longs;t, ni&longs;i tunc gubernaculum auertat, atque obliquet na&shy;<lb/>uim. </s>

<s id="id.001558">E&ograve; enim fertur nauis, qu&ograve; prora dirigitur. </s>

<s id="id.001559">Obliquare autem <lb/>nauim vel tran&longs;uertere tant&ograve; facilius gubernaculum pote&longs;t: quant&ograve; <lb/>ventus paucior e&longs;t. </s>

<s id="id.001560">Paucior autem fit contracto velo, quod &longs;pectat ad <lb/>puppim, &amp; relaxato eo quod e&longs;t ad proram. </s>

<s id="id.001561">Sufficiens tamen pro&shy;<lb/>pellere. </s>

<s id="id.001562">Obliquus enim veli relaxati &longs;inubus totis excipitur. </s>

<s id="id.001563">Ideo <expan abbr="c&utilde;">cum</expan> <lb/>&amp; &longs;ufficiat gubernaculum auertere atque propellere mare, vocatis <lb/>ad id in auxilium, &longs;i opus e&longs;t, nautis in contrariam vento partem ni&shy;<lb/>tentibus, fit vt ex obliquo vel tran&longs;uer&longs;o vento feratur nauis. </s>

<s id="id.001564">Sic <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.137.jpg" pagenum="98"/><emph type="italics"/>enim quantum ventus exempli gratia dextror&longs;um propellit nauim: <lb/>tantum vi &longs;ua gubernaculum cum nautis &longs;ini&longs;tror&longs;um illam tor&shy;<lb/>quet, ac rapit. </s>

<s id="id.001565">Et ita neutra ex contrarijs viribus pr&aelig;ualente, e&ograve; fer&shy;<lb/>tur nauis, qu&ograve; vult gubernator, etiam&longs;i ventus minime &longs;ecundus &longs;it. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001566">Quem <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan>.] <emph type="italics"/>Ex hoc loco colligi pote&longs;t cau&longs;a, propter quam <lb/>quotidie naues ob&longs;eruantur non citra admirationem eodem vento in <lb/>contrarias partes nauigare, vt &amp; Plinius etiam recitat. </s>

<s id="id.001567">Ii&longs;dem <lb/>ventis in contrarium nauigatur prolatis pedibus (hi &longs;unt funes de <lb/>quibus ante) vt noctu plerumque vela concurrant. </s>

<s id="id.001568">Hoc autem vt <lb/>fiat geometric&egrave; demon&longs;tratur. <emph.end type="italics"/></s></p><figure id="id.035.01.137.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.137.1.jpg"/><p type="main">

<s id="id.001569"><emph type="italics"/>Sint naues A tendens ad G, &amp; B tendens ad H. </s>

<s>ventus ex <lb/>C recta feratur ad D, tanquam ad centrum. </s>

<s id="id.001570">Itaque vento pro&shy;<lb/>pul&longs;a nauis A, feretur in E, &amp; B in F. </s>

<s id="id.001571">Fiat igitur in naui per <lb/>temonem mutatum angulus G A K, qui &longs;it &aelig;qualis angulo G <lb/>A E: tum H B L &aelig;qualis angulo H B F. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001572"><emph type="italics"/>Quia igitur nauis A &agrave; vento fertur in E, &amp; per temonis muta&shy;<lb/>tionem in K, feretur recta in G, &amp; eadem ratione B in H. <lb/></s>

<s id="id.001573">Neuter enim cum &longs;uo impul&longs;u pr&aelig;ualeat, medium teneat A G ne&shy;<lb/>ce&longs;&longs;e e&longs;t, quod &longs;i ventus pr&aelig;ualet, adiungitur remigum renixus, qui <lb/>&longs;i non &longs;atis &longs;it, vento cedendum, aut anchora iacienda. </s>

<s id="id.001574">Tum autem <lb/>vix remiges re&longs;i&longs;tunt, <expan abbr="c&utilde;">cum</expan> nauis e&longs;t in centro, vel radio perpendicula&shy;<lb/>ri venti, quo in loco propter vim venti maiorem, &amp; anguli per te&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.138.jpg" pagenum="99"/><emph type="italics"/>monem faciendi magnitudinem, vt qui rectum &aelig;quare debeat, dif&shy;<lb/>ficillim&egrave; ad locum de&longs;tinatum dirigitur: at quant&ograve; fuerit remotior <lb/>&agrave; puncto D, velocius &amp; facilius feretur, quia ventus rectius tan&shy;<lb/>get puppim, minor enim erit &longs;emper angulus per temonem facien&shy;<lb/>dus, vt intelligitur ex G P Q minore: quam G A E, &amp; G I <lb/>M minore: quam G P q. </s>

<s>Sunt enim duo C A G &amp; G A E, <lb/>quia facti &agrave; recta G A in rectam C E duobus rectis &aelig;quales <lb/>prop. 13. lib. 1. &amp; per eandem etiam duo C P G &amp; G P Q duobus <lb/>rectis &aelig;quales. </s>

<s id="id.001575">Ergo duo C A G &amp; G A E duobus C P G &amp; <lb/>G P Q &longs;unt &aelig;quales axiom. 1. </s>

<s id="id.001576">E&longs;t autem C P G externus oppo&shy;<lb/>&longs;ito interno C A G maior, prop. 16. lib. 1. </s>

<s>Reliquus igitur G P Q <lb/>reliquo G A E minor erit, &amp; ita de c&aelig;teris. </s>

<s id="id.001577">Sicque nauis proce&longs;&longs;u <lb/>&longs;uo mutabit &longs;en&longs;im temonem, vt &amp; vela. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001578"><foreign lang="greek">*dia\ ti/ ta\ periferh= tw=n sxhma/twn eu)kinhto/tera. </foreign></s></p><p type="main">

<s id="id.001579">9. Cur &egrave; figuris rotund&aelig; <lb/>&longs;unt mobiliores. </s></p><p type="main">

<s id="id.001580"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001581">Cur qu&aelig; figurarum ro&shy;<lb/>tund&aelig; &amp; circulares exi&shy;<lb/>&longs;tunt, facilius mouentur. <lb/></s>

<s id="id.001582">Tribus vero modis con&shy;<lb/>tingit circulum volui. </s>

<s id="id.001583">vel <lb/>enim &longs;ecundum curuatu&shy;<lb/>ram vn&agrave; centro tran&longs;lato, <lb/>qualiter rota plau&longs;tri vol&shy;<lb/>uitur: vel circa centrum <lb/>tantum, quod ip&longs;um quie&longs;&shy;<lb/>cat, vt trochle&aelig; vel in pla&shy;<lb/>no, manente centro, vt fi&shy;<lb/>guli rota vertitur. </s>

<s id="id.001584">An igi&shy;<lb/>tur h&aelig;c celerrima fiunt, <lb/>quod parua &longs;ui parte <expan abbr="plan&utilde;">planum</expan> <lb/><expan abbr="atting&atilde;t">attingant</expan>, vt circulus in <expan abbr="p&utilde;-cto">pun&shy;<lb/>cto</expan>, &amp; quia non offen&longs;ant? <lb/></s>

<s id="id.001585">Di&longs;tat enim angulus &agrave; terra. <lb/></s>

<s id="id.001586">Et hoc <expan abbr="eti&atilde;">etiam</expan> cui occur&longs;ant, <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.139.jpg" pagenum="100"/><foreign lang="greek"><gap/></foreign><lb/>corpus rur&longs;us parum tan&shy;<lb/>gant. </s>

<s id="id.001587">At &longs;i recti lineum e&longs;&shy;<lb/>&longs;et, rectitudine &longs;ua mul&shy;<lb/>tum plani attingeret. </s></p><p type="head">

<s id="id.001588">COMMENTARIVS. </s></p><p type="main">

<s id="id.001589">Cvr qu&aelig; figurarum.] <emph type="italics"/>In hoc capite redit Ari&longs;toteles ad fi&shy;<lb/>guras rotundas, &amp; qu&aelig;rit generaliter cau&longs;as facilitatis motus <lb/>earum, ea&longs;que quinque a&szlig;ignat <expan abbr="modic&utilde;">modicum</expan> tactum, offen&longs;ationem exi&shy;<lb/>guam, nutum dimidi&aelig; partis, motum <expan abbr="perpetu&utilde;">perpetuum</expan>, motum naturalem. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001590">Tribus modis.] <emph type="italics"/>Rotundorum motus &longs;implex per &longs;pecies indu&shy;<lb/>citur: &longs;ed diminut&egrave;. </s>

<s id="id.001591">Perfect&egrave; autem &longs;ic. </s>

<s id="id.001592">Rotundum omne per &longs;e mo&shy;<lb/>uetur, vel ab alio. </s>

<s id="id.001593">Per &longs;e quidem vt c&aelig;lum, cuius nulla pars prim&ograve; <lb/>moueri dici pote&longs;t: omnes tamen &longs;imul in loco mouentur. </s>

<s id="id.001594">Ab alio <lb/>ver&ograve;, in quo etiam eius quod mouetur pars aliqua prim&ograve; mouetur, <lb/>&amp; quidem duobus modis progrediente axe: vel manente. </s>

<s id="id.001595">Progre&shy;<lb/>diente rur&longs;us duobus modis, priore cum motus incipit &agrave; circumfe&shy;<lb/>rentia, vt in rota &longs;uper planum volutata: po&longs;teriore <expan abbr="c&utilde;">cum</expan> ab axe, vt in <lb/>rota per axem currus circumducta. </s>

<s id="id.001596">Manente ver&ograve;, rur&longs;us duobus <lb/>modis, nemp&egrave; axe moto in &longs;uo loco: vel etiam immoto. </s>

<s id="id.001597">Et moto qui&shy;<lb/>dem rur&longs;us duobus modis, primo cum motus incipit &agrave; circumferen&shy;<lb/>tia, vt in &longs;uccula per collopes ver&longs;a: &longs;ecundo cum motus incipit ab <lb/>axe, vt in mola &amp; rota qua acuuntur gladij: immoto vero, vt in <lb/>trochlea, cuius <expan abbr="vert&etilde;tis">vertentis</expan> per funes motus incipit &agrave; circumferentia: &longs;ed <lb/>axe omnino immoto. </s>

<s id="id.001598">Sicque legitima diui&longs;ione &amp; experimento ro&shy;<lb/>tundorum motus &longs;ex &longs;pecies infim&aelig; reperiuntur, &egrave; quibus prima pr&aelig;&shy;<lb/>termi&longs;&longs;a e&longs;t ab Ari&longs;totele, quia nihil ad Mechanicen, &longs;ecunda pr&aelig;&shy;<lb/>termitti non debuit, ni&longs;i quia noti&szlig;ima. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001599">Vel enim.] <emph type="italics"/>Cum rota currui &longs;ubiecta e&longs;t, tracto curru axis vn&agrave; <lb/>progreditur. </s>

<s id="id.001600">Et cum rota quie&longs;cere nequeat, quia axis tractus pre&shy;<lb/>mit, &amp; pondus adijcit non ad perpendiculum: &longs;ic enim ad centrum <lb/>impelleret: &longs;ed ad latus, quo trahitur, &amp; pondere adiecto ad nutan&shy;<lb/>tem dimidia &longs;ui parte &longs;emper rotam, e&ograve; labitur. </s>

<s id="id.001601">Facilius autem cir&shy;<lb/>cumuertitur: quam trahatur, itaque procedit. </s>

<s id="id.001602">Et &longs;ic ibi quidem rota <lb/>ex circumferentia, quam ab&longs;idem h&icirc;c appellat, mouetur: &longs;ed ab axe <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.140.jpg" pagenum="101"/><emph type="italics"/>initium e&longs;t motus. </s>

<s id="id.001603">Plurimum itaque confert ad motus facilitatem, <lb/>vt tum axis, tum rota intus &longs;int l&aelig;ui&szlig;ima, vnde aurig&aelig; axungia <lb/>(qu&aelig; inde nomen traxit) ip&longs;a inungunt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001604">Quod parua &longs;ui.] <emph type="italics"/>Prima cau&longs;a e&longs;t facilitatis motus &longs;uper plano <lb/>in rotundis de modico contactu in omni &longs;ui po&longs;itione. </s>

<s id="id.001605">Contactus <lb/>enim multa parte &longs;ui facit h&aelig;rere, &amp; &longs;imul e&longs;&longs;e ea, qu&aelig; &longs;e&longs;e &longs;ic con&shy;<lb/>tingunt, &amp; quidem tant&ograve; magis, quant&ograve; maior e&longs;t hic contactus. <lb/></s>

<s id="id.001606">qu&ograve; igitur erit minor, e&ograve; minus h&aelig;rere, citiu&longs;que diuelli faciet. </s>

<s id="id.001607">Mul&shy;<lb/>ta autem pr&aelig;ter rotunda vt triangulum &aelig;quilaterum, &amp; tetra&euml;&shy;<lb/>dron planum in puncto contingere po&longs;&longs;unt, &longs;ed non in omni &longs;ui po&longs;i&shy;<lb/>tione, vt cum &longs;ecundum vnam &longs;ui aream &longs;uperiacent: at rotunda <lb/>&longs;iue &longs;ph&aelig;ra &longs;it, &longs;iue circulus planum in vno puncto quouis modo &longs;e&shy;<lb/>cundum curuaturam po&longs;ita attingunt. </s>

<s id="id.001608">quod demon&longs;tratum e&longs;t de <lb/>illo quidem &agrave; Theodo&longs;. prop. 2. lib. 1. de Sph&aelig;r. de hoc vero ab Eucli&shy;<lb/>de prop. 16. lib. 3. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001610">Et quia non off.] <emph type="italics"/>Secunda cau&longs;a e&longs;t de occur&longs;antibus, qu&aelig; <lb/>rur&longs;us cum minimam partem rotundorum attingant, &amp; atterant, <lb/>minus impediunt, quam qu&aelig; plus attingunt, pluribu&longs;que occur&longs;ant. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001611">Di&longs;tat enim angulus.] <emph type="italics"/>Cum rotundum incumbit plano ad <lb/>omnes rectas &agrave; quibus tangitur in ip&longs;o plano angulos facit contin&shy;<lb/>genti&aelig;, quorum &longs;inguli quia &longs;unt minores quouis acuto angulo re&shy;<lb/>ctilineo, vt e&longs;t demon&longs;tratum prop. 16. lib. 3. </s>

<s>procliues &longs;unt maxime <lb/>ad motum. </s>

<s id="id.001612">Latus enim curuum anguli vnius contactus &longs;emotum <lb/>quidem e&longs;t &agrave; plano: &longs;ed parum propter anguli angu&longs;tiam. </s>

<s id="id.001613">Et &longs;ic non <lb/>offen&longs;at, &amp; proximum e&longs;t ca&longs;ui. </s>

<s id="id.001614">Hinc etiam vna cau&longs;a colligi po&shy;<lb/>te&longs;t, cur rotunda maiora facilius moueantur minoribus, quod <lb/>angulos &longs;ui contactus tant&ograve; acutiores faciunt: quant&ograve; &longs;unt maiora, <lb/>vt in libello no&longs;tro de angulo contactus demon&longs;trauimus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001615">At &longs;i rectilineum e&longs;&longs;et.] <emph type="italics"/>Difficultas motus in mobili pendet <lb/>ab eius internis aut externis. </s>

<s id="id.001616">Interna e&longs;t naturalis cuiu&longs;que <expan abbr="prop&etilde;&longs;io">propen&longs;io</expan>, <lb/>qua extra locum exi&longs;tens, &longs;i liberum &longs;inatur mobile, ad <expan abbr="e&utilde;">eum</expan> per &longs;e fe&shy;<lb/>ratur. </s>

<s id="id.001617">Atque vt ibi vi retineatur, e&ograve; tamen quodam motu occulto <lb/>tendit, vt graue deor&longs;um, leue &longs;ur&longs;um, &amp; &longs;emper &longs;ecundum rectam <lb/>perpendicularem in qua e&longs;t centrum grauitatis mobilis: ali&ograve; nun&shy;<lb/>quam, ni&longs;i vi contraria nixus ille vincatur, vt cum graue &longs;ur&longs;um: <lb/>aut leue deor&longs;um: aut vtrumque ad latera propellitur. </s>

<s id="id.001618">Itaque prima <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.141.jpg" pagenum="102"/><emph type="italics"/>difficultas in <expan abbr="viol&etilde;tis">violentis</expan> pendet &egrave; renixu. </s>

<s id="id.001619">Externa vero &longs;unt <expan abbr="&longs;ubiect&utilde;">&longs;ubiectum</expan>, <lb/>&amp; occur&longs;ans, &amp; mobilis figura. </s>

<s id="id.001620">Subiectum appello, cui mobile &longs;u&shy;<lb/>perincumbit, aut primo in&longs;i&longs;tit, &amp; huic tant&ograve; magis qua &longs;i inh&aelig;ret <lb/>&amp; in&longs;i&longs;tit: quant&ograve; pluribus punctis ab eo &longs;imul tangitur. </s>

<s id="id.001621">Tot enim <lb/>&longs;unt line&aelig; in mobili ad rectos angulos in&longs;i&longs;tentes &longs;ubiecto, qu&aelig; vt <lb/>vires vnit&aelig; &longs;e mutuo &longs;tabiliunt, &amp; fulciunt, ne facile deijciantur: <lb/>contr&agrave; id, quod ant&egrave; de Sph&aelig;rico, vbi cum vna e&longs;&longs;et <expan abbr="t&atilde;tum">tantum</expan> qu&aelig; in&shy;<lb/>&longs;i&longs;teret plano ad rectos, facillima ab illo &longs;tatu erat deiectio. </s>

<s id="id.001622">Maior <lb/>igitur inh&aelig;rentia, maius e&longs;t impedimentum. </s>

<s id="id.001623">Occur&longs;ans autem dico <lb/>quodlibet corpus aliud, vel contra motum, vel cum locum ibi habe&shy;<lb/>at, minim&egrave; <expan abbr="ced&etilde;s">cedens</expan>. </s>

<s id="id.001624">Talia &longs;unt fortuita omnia, qu&aelig; vt &longs;ubiectum, qu&ograve; <lb/>pluribus mobilis punctis occurrunt propter eandem cau&longs;am, e&ograve; plus. <lb/></s>

<s id="id.001625">ne fiat inuer&longs;io vel volutatio, impediunt. </s>

<s id="id.001626">Tale quoque medium e&longs;t <lb/>nece&longs;&longs;arium, per quod fit motus, <expan abbr="rar&utilde;">rarum</expan>, den&longs;um, vtrumque impariter. <lb/></s>

<s id="id.001627">Hoc enim magis, illud minus: re&longs;i&longs;tit partibus obuijs. </s>

<s id="id.001628">Re&longs;i&longs;tens in&shy;<lb/>&longs;uper ob loci, in quo e&longs;t, <expan abbr="&longs;eru&atilde;di">&longs;eruandi</expan> cupiditatem naturalem, &amp; etiam, ne <lb/>admittatur vacuum. </s>

<s id="id.001629">Mobilis denique figura qu&aelig; qu&ograve; propius ac&shy;<lb/>cedit ad &longs;ph&aelig;ricam vt mobili&szlig;imam, e&ograve; ad motum pronior: contra <lb/>qu&ograve; remotior. </s>

<s id="id.001630">Atque ea &longs;unt impedimenta, quorum duo &longs;ublatis for&shy;<lb/>tuitis &egrave; figurarum &longs;uperficialibus rectiline&aelig;, &egrave; &longs;olidis cubo in&longs;unt. <lb/></s>

<s id="id.001631">Sit enim <lb/>ABCD <lb/><figure id="id.035.01.141.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.141.1.jpg"/><lb/><expan abbr="rectili-ne&utilde;">rectili&shy;<lb/>neum</expan> pla&shy;<lb/>no E F <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan>, <lb/>&amp; <expan abbr="qui-d&etilde;">qui&shy;<lb/>dem</expan> &longs;i na&shy;<lb/>turale e&longs;t <lb/>in&longs;ita grauitate verget ver&longs;us G, &amp; ad rectos in&longs;i&longs;tet rectis A C <lb/>&amp; B D &amp; omnibus inter illas interiectis vt H I, K L, M N, <lb/>&longs;icque totidem momentis ver&longs;us G contendit. </s>

<s id="id.001632">Pr&aelig;terea a&euml;r vel <lb/>aqua medium occurrens lateri A C, quantum in &longs;e, e&longs;t impedit tot <lb/>punctis, quot &longs;unt in A C. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001633"><emph type="italics"/>Sit &amp; cubus A D, planum K L, vna &longs;uperficierum &longs;uarum <lb/>E D attingens, tum habeat rectas A E, C F, B D, H G, ad<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.142.jpg" pagenum="103"/><emph type="italics"/>rectos in&longs;i&longs;ten&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.142.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.142.1.jpg"/><lb/><emph type="italics"/>tes, vt totidem <lb/>alias, quot &longs;unt <lb/>puncta in &longs;u&shy;<lb/>perficie E D <lb/>nixu naturali <lb/>coniunct&aelig;. </s>

<s id="id.001634">Tot <lb/>vires nullo <expan abbr="t&etilde;-poris">tem&shy;<lb/>poris</expan> momento alio inclinantes &longs;e &agrave; &longs;uo &longs;tatu dimoueri &longs;inent: medio <lb/>etiam obuio &longs;eu a&euml;re, &longs;eu aqua totidem ad latus punctis propter &aelig;qua&shy;<lb/>litatem &longs;uperficierum impediente. </s>

<s id="id.001635">Ex quo fit vt figurarum planum <lb/>pro vertice habentium &longs;tabili&szlig;ima dicatur cubus. </s>

<s id="id.001636">Et quia talis e&longs;t, <lb/>eius figuram Plato affinxit terr&aelig; in loco &longs;uo pror&longs;us immobili. </s>

<s id="id.001637">Ob id <lb/>etiam pictores <expan abbr="Virtut&etilde;">Virtutem</expan> qu&aelig; &longs;ola con&longs;tans e&longs;t animi &longs;tatus, vel etiam <lb/>Mercurium qui &longs;uos &longs;ectatores numquam de&longs;erit cubo in&longs;identem <lb/>repr&aelig;&longs;entant: &longs;icut ob contrariam cau&longs;am Fortunam. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001638">Qu&aelig; tant&ugrave;m con&longs;tans in leuitate &longs;ua e&longs;t. <lb/></s>

<s><emph type="italics"/>globo mobili&szlig;imo. </s>

<s id="id.001639">Sed quod ad figuram attinet quia pluribus planis <lb/>clauditur quam tetraedrum, vel pentaedrum, vt qui &longs;it hexaedrum, <lb/>&amp; ideo propius accedit ad &longs;ph&aelig;ram, ad volutationem adhuc procli&shy;<lb/>uior e&longs;t, quam illa &longs;int. </s>

<s id="id.001640">hinc te&longs;&longs;erarum talorumque in alueo per hanc <lb/><expan abbr="figur&atilde;">figuram</expan> planum vnum pro vertice, &amp; planum vnum pro ba&longs;i &longs;emper <lb/><expan abbr="&longs;eruant&etilde;">&longs;eruantem</expan> ludus. </s>

<s id="id.001641">Sed h&icirc;c non immerit&ograve; <emph.end type="italics"/><lb/><figure id="id.035.01.142.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.142.2.jpg"/><lb/><emph type="italics"/>qu&aelig;ri pote&longs;t. </s>

<s id="id.001642">cur terr&aelig; &longs;tare debenti na&shy;<lb/>tura figuram attribuit &longs;ph&aelig;ricam, vt <lb/><expan abbr="doc&etilde;t">docent</expan> a&longs;tronomi. </s>

<s id="id.001643">vnum enim e&longs;t ex <expan abbr="ar-gum&etilde;tis">ar&shy;<lb/>gumentis</expan> Copernici terram moueri pro&shy;<lb/>bare volentis. </s>

<s id="id.001644">Sed id nullum locum ha&shy;<lb/>bet, quia qu&aelig; hactenus dicta &longs;unt im&shy;<lb/>pedimenta figurarum, &longs;unt <expan abbr="figurar&utilde;">figurarum</expan> in <lb/>plano <expan abbr="n&otilde;">non</expan> <expan abbr="aut&etilde;">autem</expan> in concauo &longs;imili &amp; <expan abbr="c&otilde;-">con&shy;</expan><emph.end type="italics"/><lb/><figure id="id.035.01.142.3.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.142.3.jpg"/><lb/><emph type="italics"/>gruenti <expan abbr="exi&longs;tenti&utilde;">exi&longs;tentium</expan>, cuiu&longs;modi e&longs;t terra, <lb/>cuiu&longs;que omnes partes <expan abbr="rot&utilde;d&aelig;">rotund&aelig;</expan> exi&longs;ten&shy;<lb/>tis &aelig;quabilius coniuncto nixu ad cen&shy;<lb/>trum contendunt: quam &longs;i alterius e&longs;&longs;et <lb/>cuiu&longs;cunque figur&aelig;. </s>

<s id="id.001645">Sit enim cubica <lb/>cuius centrum A &amp; B punctum an&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.143.jpg" pagenum="104"/><emph type="italics"/>gulare, &amp; ita remotius quam C laterale, non tanto nixu contendet: <lb/>quam ip&longs;um C. </s>

<s id="id.001646">Qu&ograve; enim mobile naturale propius e&longs;t, e&ograve; obnixius <lb/>incumbit. </s>

<s id="id.001647">Eadem e&longs;t ratio cuiu&longs;cumque figur&aelig; pr&aelig;terquam &longs;ph&aelig;ri&shy;<lb/>c&aelig;, cuius puncta B, C, D, in eadem &longs;uperficie &aelig;qualiter &agrave; centro <lb/>&longs;emper di&longs;tant. </s>

<s id="id.001648">Itaque terra, vt medium vndiquaque obtineret, &amp; <lb/>vt qu&aelig; in ea omnia puncta &aelig;quali nixu ad eius centrum niteren&shy;<lb/>tur, debuit e&longs;&longs;e &longs;ph&aelig;rica: ob idque immobili&szlig;ima e&longs;t, nullibique <lb/>nutat, contr&agrave; quam dixit Po&euml;ta,<emph.end type="italics"/></s></p><p type="main">

<s id="id.001649">A&longs;pice nutantem conuexo pondere mundum. <lb/></s></p>

<p type="main"><s><emph type="italics"/>Nutus enim hic e&longs;t inclinatio ali&ograve; facta: quam id, &agrave; quo &longs;u&longs;penditur, <lb/>vel &longs;u&longs;tinetur, inclinet. </s>

<s id="id.001650">Cuiu&longs;modi nihil e&longs;t in mundo, aut in terra: <lb/>&longs;ed omne punctum e&ograve; fertur, qu&ograve; id &agrave; quo &longs;u&longs;tinetur, rect&agrave; &longs;cilicet ad <lb/>centrum, non vt D ad E, hoc enim e&longs;&longs;et contra naturam grauis, <lb/>quippe in diuer&longs;um per ambitum. </s>

<s id="id.001651">Qu&aelig;renti ver&ograve; cur igitur c&oelig;lum <lb/>exacte &longs;ph&aelig;ricum moueatur. </s>

<s id="id.001652">Re&longs;pondent moueri in loco non na&shy;<lb/>turaliter: &longs;ed voluntari&egrave;. </s>

<s id="id.001653">Omnis enim motus naturalis e&longs;t per rectam <lb/>de centro ad locum. </s>

<s id="id.001654">Voluntas illa e&longs;t intelligenti&aelig;, qu&aelig; c&oelig;lo vt mens <lb/>corpori pr&aelig;e&longs;t. </s>

<s id="id.001655">Et per &longs;e cum motum hunc creet &longs;ine defatigatione e&longs;t <lb/>hic motus in regulari&szlig;imo corpore regulari&szlig;imus, &amp; facillimo ad <lb/>motum veloci&szlig;imus, vt e&longs;t apud Ptolom&aelig;um concl. 1. lib. 1. <emph.end type="italics"/> <foreign lang="greek">meg. <lb/>suntac.</foreign> </s>

<s><emph type="italics"/>Velocitatem autem intelliget, qui intellexerit quot millia&shy;<lb/>ria, habeat circulus in c&oelig;lo extimo maximus, &amp; quot ex his vno&shy;<lb/>quoque momento conficiat. </s>

<s id="id.001656">Intelligetur quoque quomodo illius c&oelig;li <lb/>motus &longs;it omnium motuum <expan abbr="m&etilde;&longs;ura">men&longs;ura</expan>. </s>

<s id="id.001657">Nam cum men&longs;ura &longs;it in vno&shy;<lb/>quoque genere minimum, vt e&longs;t cap. 4. lib. 2. de C&oelig;l. </s>

<s>hic autem mo&shy;<lb/>tus minimus debet dici, qui per minimam lineam earum qu&aelig; &aelig;qua&shy;<lb/>les areas includunt fit, cuiu&longs;modi e&longs;t circularis, &longs;icque &longs;ecundum eam <lb/>motus erit celerrimus, quia minimus. <emph.end type="italics"/></s>

</p><p type="main">

<s id="id.001658">Multum plani.] <emph type="italics"/>Ex hoc loco intelligatur, quod mobile, quant&ograve; <lb/>latius e&longs;t: tant&ograve; difficilius moueri per planum. </s>

<s id="id.001659">Attritio enim per <lb/>contactum plani cum mobili, tanto maior erit. </s>

<s id="id.001660">Ideo tangens in pun&shy;<lb/>cto facillime mouetur, vt dictum e&longs;t. </s>

<s id="id.001661">Tangens in linea difficilius: <lb/>tangens per &longs;uperficiem difficillime. </s>

<s id="id.001662">Im&ograve; vero plana exqui&longs;ita iun&shy;<lb/>cta &longs;ine ferruminatione &longs;eparari nequeunt, &longs;i &longs;uperius leuiter ap&shy;<lb/>prehen&longs;um ab inferiore di&longs;iungere quis conetur. </s>

<s id="id.001663">Rationem &longs;i vis <lb/>aliquam, vide apud Scaligerum exercit. 333. <emph.end type="italics"/></s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.144.jpg" pagenum="105"/><chap><p type="main">

<s id="id.001665"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001666">Pr&aelig;terea qu&ograve; pondus <lb/>vergit, e&ograve; motor impellit. <lb/></s>

<s id="id.001667">Quum igitur diameter cir<lb/>culi rect&agrave; in&longs;i&longs;tit plano, cir&shy;<lb/>culo in puncto planum at&shy;<lb/>tingente, &aelig;qualiter vtrim&shy;<lb/>que diameter pondus di&shy;<lb/>&longs;terminat. </s>

<s id="id.001668">Quando ver&ograve; <lb/>mouetur &longs;tatim plus ad id <lb/>mouetur, veluti e&ograve; repens <lb/>motu facilius impellente <lb/>in anteriorem partem. </s>

<s id="id.001669">E&ograve; <lb/>enim, qu&ograve; vergit vnum&shy;<lb/>quodque, facilius moue&shy;<lb/>tur. </s>

<s id="id.001670">Quandoquidem &longs;i in <lb/>contrarium: quam qu&ograve; <lb/>vergat, moueatur, difficulter mouebitur. </s></p><p type="head">

<s id="id.001671">COMMENTARIVS. </s></p><p type="main">

<s id="id.001672">Pr&aelig;terea qu&ograve;.] <emph type="italics"/>Tertia cau&longs;a facilitatis e&longs;t motus, quando mo&shy;<lb/>bile in omni po&longs;itu &longs;uper plano dimidia &longs;ui parte quoquouer&longs;um <lb/>ad planum ip&longs;um acclinat, vt fit in rotundo, quod ip&longs;um tangit in <lb/>puncto, vt ante docuimus, &longs;icque quoquouer&longs;um vergit. </s>

<s id="id.001673">Hinc dico <lb/>&longs;ph&aelig;ricum ad latus moueri po&longs;&longs;e quacumque vi, qu&aelig; a&euml;rem impul&longs;u <lb/>vel tractu diuidere po&szlig;it. </s>

<s id="id.001674">Vnus enim a&euml;r circun&longs;tans impedit, quo <lb/>minus voluatur. </s>

<s id="id.001675">Non enim nixus a&longs;cendendi &longs;ur&longs;um, cum ob graui&shy;<lb/>tatem e&ograve; non nitatur: neque rur&longs;us deor&longs;um de&longs;cendendi, ob &aelig;qui&shy;<lb/>librium enim innixus pondus non adfert, quin potius dimidia &longs;ui <lb/>parte quoquouer&longs;um nutans nititur moueri, vt in circulo ad cen&shy;<lb/>trum: &agrave; contactu quoque, quia minimo, non impeditur. </s>

<s id="id.001676">Relinqui&shy;<lb/>tur erg&ograve; tantum impediri &agrave; medio circunstante. </s>

<s id="id.001677">Hoc &agrave; quacun&shy;<lb/>que vi vt oris flatu &longs;i diuidatur, &longs;ph&aelig;ricum in locum diui&longs;ionis pro&shy;<lb/>mouebitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001678">Rect&agrave; in&longs;i&longs;tit.] <emph type="italics"/>Diameter circuli rect&agrave; in&longs;i&longs;tere in plano di&shy;<lb/>citur cum ad omnes rectas lineas &agrave; quibus tangitur in ip&longs;o plano<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.145.jpg" pagenum="106"/><emph type="italics"/>rectos angulos ef&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.145.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.145.1.jpg"/><lb/><emph type="italics"/>ficit ex def. 3. lib. <lb/>11. vt A B dia&shy;<lb/>meter ad B O, B D, <lb/>B E, B F. </s>

<s id="id.001680">Et A B <lb/>quia diameter e&longs;t <lb/>circulum &longs;uum bi&shy;<lb/>fariam diuidit ex <lb/>def. 17. lib. 1. </s>

<s id="id.001681">Sic&shy;<lb/>que tanta pars e&longs;t <lb/>ad G, quanta ad H. </s>

<s id="id.001682">Similiter maximus in &longs;ph&aelig;ra circulus recta <lb/>in&longs;i&longs;tens &longs;ph&aelig;ram bifariam di&longs;pe&longs;cit. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001683"><foreign lang="greek"><gap/></foreign><lb/><arrow.to.target n="marg26"/></s></p><p type="margin">

<s id="id.001684"><margin.target id="marg26"/>*<foreign lang="greek">e)/xh</foreign></s></p><p type="main">

<s id="id.001685">Pr&aelig;terea nonnulli di&shy;<lb/>cunt lineam circuli in per&shy;<lb/>petuo motu e&longs;&longs;e, vt qu&aelig; <lb/>manent, propter renixum. <lb/></s>

<s id="id.001686">Vt maioribus circulis eue&shy;<lb/>nit re&longs;pectu minorum. </s>

<s id="id.001687">Ce&shy;<lb/>lerius enim ab &aelig;quali vi <lb/>maiores <expan abbr="mou&etilde;tur">mouentur</expan>, &amp; pon&shy;<lb/>dera mouent. </s>

<s id="id.001688">quia maioris <lb/>circuli angulus <expan abbr="nut&utilde;">nutum</expan> quen&shy;<lb/>dam habet ad minoris an&shy;<lb/>gulum. </s>

<s id="id.001689">Et e&longs;t vt diameter <lb/>ad <expan abbr="diametr&utilde;">diametrum</expan>: &longs;ic omnis ma&shy;<lb/>ior circulus ad minorem. <lb/></s>

<s id="id.001690">Infiniti autem &longs;unt mino&shy;<lb/>res. </s>

<s id="id.001691">Si ver&ograve; etiam circulus <lb/>nutum habet ad alterum. <lb/></s>

<s id="id.001692">Similiter ver&ograve; facile mobi&shy;<lb/>lis <expan abbr="ali&utilde;">alium</expan> <expan abbr="nut&utilde;">nutum</expan> habet circulus, <lb/>&amp; qu&aelig; &agrave; circulo <expan abbr="mou&etilde;tur">mouentur</expan>, <lb/><expan abbr="eti&atilde;&longs;i">etiam&longs;i</expan> &longs;ua curuatura <expan abbr="plan&utilde;">planum</expan> <lb/><expan abbr="n&otilde;">non</expan> <expan abbr="c&otilde;tingat">contingat</expan>: &longs;ed vel prop&egrave; <lb/>planitiem, vel vt trochle&aelig;. <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.146.jpg" pagenum="107"/><foreign lang="greek"><gap/></foreign><lb/>Etenim qu&aelig; &longs;ic &longs;e habent, <lb/>facillim&egrave; <expan abbr="mou&etilde;tur">mouentur</expan>, &amp; mo&shy;<lb/>uent pondus. </s>

<s id="id.001693">an non quia <lb/>parua &longs;ui parte tangunt &amp; <lb/>offen&longs;ant. </s>

<s id="id.001694">Sed ob <expan abbr="ali&atilde;">aliam</expan> cau&shy;<lb/>&longs;am. </s>

<s id="id.001695">H&aelig;c vero prius e&longs;t di&shy;<lb/>cta. </s>

<s id="id.001696">quod circulus ex dua&shy;<lb/>bus lationibus effectus e&longs;t. <lb/></s>

<s id="id.001697">Itaque vnam harum &longs;em&shy;<lb/>per habet nutantem. </s>

<s id="id.001698">Et <expan abbr="e&utilde;">eum</expan>, <lb/>qua&longs;i &longs;emper moueatur, <lb/>mouent motores, quando <lb/>quocunque illum &longs;ecun&shy;<lb/>dum <expan abbr="peripheri&atilde;">peripheriam</expan> mouerint. <lb/></s>

<s id="id.001699">Motam enim ip&longs;am mo&shy;<lb/>uent. </s>

<s id="id.001700">Eam &longs;iquidem, qua <lb/>mouetur in <expan abbr="obliqu&utilde;">obliquum</expan>, mo&shy;<lb/>tor impellit: illa ver&ograve;, qu&aelig; &longs;uper diametro efficitur, ip&longs;e&shy;<lb/>met &longs;e circulus mouet. </s></p><p type="head">

<s id="id.001701">COMMENTARIVS. </s></p><p type="main">

<s id="id.001702">Pr&aelig;terea nonnulli.] <emph type="italics"/>Quarta cau&longs;a e&longs;t de perpetuo motu con&shy;<lb/>firmata nonnullorum, &longs;ed innominatorum authoritate: &amp; &longs;imi&shy;<lb/>litudine e contrarijs &longs;ic. </s>

<s id="id.001703">quemadmodum qu&aelig; perpetu&ograve; manent, ma&shy;<lb/>nent propter contrarium motui renixum: &longs;ic in quibus e&longs;t ad mo&shy;<lb/>tum perpetua propen&longs;io, perpetu&ograve; moueri ea debent. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001704">Vt maioribus circulis.] <emph type="italics"/>Nutus &longs;eu perpetua propen&longs;io con&shy;<lb/>firmatur e&longs;&longs;e &longs;emper in circulo. </s>

<s id="id.001705">quia quicunque &longs;it &longs;emper in &longs;e habet <lb/>concentricos minores infinitos, &amp; maior tum celerius mouetur ab <lb/>&aelig;quali vi, &amp; cum eo etiam pondera: tum angulus maioris nutum <lb/>habet ad angulum &aelig;qualem, qui e&longs;t in minori circulo. </s>

<s id="id.001706">quia anguli <lb/>maioris crura maiora &longs;unt, &longs;emp&eacute;rque e&longs;t, vt diameter ad diame&shy;<lb/>trum. </s>

<s id="id.001707">Sunt enim circulorum &longs;emidiametri. </s>

<s id="id.001708">Partes autem cum pari&shy;<lb/>ter multiplicibus &longs;unt in eadem ratione prop. 15. lib. 5. </s>

<s>Diameter au&shy;<lb/>tem maior celerius mouetur, h&icirc;c autem notandum e&longs;t angulos non <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.147.jpg" pagenum="108"/><emph type="italics"/>&longs;umi pro inclinatione: &longs;ed pro crurum<emph.end type="italics"/><lb/><figure id="id.035.01.147.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.147.1.jpg"/><lb/><emph type="italics"/><expan abbr="l&otilde;gitudine">longitudine</expan>. </s>

<s id="id.001709">h&aelig;c autem figura hac cir&shy;<lb/>culorum concentricorum &amp; &agrave; cen&shy;<lb/>tris angulorum illu&longs;trantur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001710">Nutum habet.] <foreign lang="greek">ro/ph</foreign> <emph type="italics"/>Nutus <lb/>vis e&longs;t cuiu&longs;que impre&longs;&longs;a &agrave; Deo &amp; <lb/>natura, qua in loco &longs;uo naturali quie&longs;&shy;<lb/>cit, &amp; volenti ab eo di&longs;pellere, re&longs;i&longs;tit. <lb/></s>

<s id="id.001711">vnde<emph.end type="italics"/> <foreign lang="greek">a)nteirisis</foreign> <emph type="italics"/>renixus. </s>

<s id="id.001712">Extra locum ver&ograve; ad eum per breui&szlig;i&shy;<lb/>mam viam mouetur. </s>

<s id="id.001713">Deus enim ne omnia in omnibus e&longs;&longs;ent, vni&shy;<lb/>cuique ab initio proprium locum tribuit, in quo &amp; circa quem con&shy;<lb/>globatur, &amp; ibi h&aelig;ret. </s>

<s id="id.001714">Hinc etiam &longs;ingul&aelig; partes &longs;uis totis natura <lb/>inh&aelig;rent, &amp; in ijs certum quendam &longs;itum habent, &agrave; quo remot&aelig; ad <lb/>ip&longs;um redeunt, vt in arcubus &amp; balli&longs;tis videre licet. </s>

<s id="id.001715">Nutus autem <lb/>naturalis e&longs;t: vel non naturalis: vel mixtus. </s>

<s id="id.001716">Naturalis e&longs;t is, quo res <lb/>qu&aelig;libet natura &longs;ua mouetur: aut <expan abbr="mou&etilde;ti">mouenti</expan> re&longs;i&longs;tit habita ratione loci <lb/>&longs;ui naturalis, &amp; &longs;itus &longs;uarum partium. </s>

<s id="id.001717">Non naturalis e&longs;t is, quo nec <lb/>ratione loci naturalis, nec &longs;itus partium mouetur, vt fortuitus vel <lb/>voluntarius. </s>

<s id="id.001718">Ille vt ventorum, hic vt animalium. </s>

<s id="id.001719">Mixtus parti&shy;<lb/>ceps e&longs;t vtriu&longs;que. </s>

<s id="id.001720">Nutus voluntarij mille &longs;unt modi <expan abbr="n&otilde;">non</expan> aliter, quam <lb/>voluntatis decreto determinabiles. </s>

<s id="id.001721">At naturalis vnius tantum e&longs;t <lb/>&agrave; loco non naturali ad naturalem. </s>

<s id="id.001722">Hinc linea recta, qu&aelig; e&longs;t &agrave; termi&shy;<lb/>no &agrave; quo incipit moueri ad terminum in quo quie&longs;cit, linea nutus, <lb/>&amp; eadem in terminis contrarijs renixus dicitur, vt &longs;i ab eo in quo <lb/>quie&longs;cit aliena vis ad alium moueret: linea ver&ograve; ip&longs;am &longs;ecans ad an&shy;<lb/>gulos in&aelig;quales e&longs;t linea obliqui nutus, vel renixus: &amp; &longs;ecans ad <lb/>rectos nec ad nutum e&longs;t, nec ad renixum. </s>

<s id="id.001723">Nunc igitur hoc cum ve&shy;<lb/>rum e&longs;&longs;e experiamur, &amp; ratio conuincat, quant&ograve; quodque remotius <lb/>e&longs;t &agrave; loco, in quo naturaliter quie&longs;ceret, tant&ograve; ad eum magis conari, <lb/>remotioris maior erit nutus. </s>

<s id="id.001724">In peripheria maiori punctum A re&shy;<lb/>motius puncto D. </s>

<s id="id.001725">Magis igitur nutat. </s>

<s id="id.001726">E&longs;t enim linea A C maior <lb/>quam D E vt ex &longs;imilibus triangulis A B C, D B E demon&longs;trari <lb/>facile pote&longs;t. </s>

<s id="id.001727">Et &longs;ic angulus ad angulum nutare dicitur, cum in an&shy;<lb/>gulorum &aelig;qualitate crurum e&longs;t in&aelig;qualitas. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001728">Et e&longs;t vt diameter.] <emph type="italics"/>H&aelig;c analogia antea &agrave; nobis demon&longs;tra&shy;<lb/>ra e&longs;t. </s>

<s id="id.001729">Huc autem adducta confirmat in maioribus circulis maiorem <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.148.jpg" pagenum="109"/><emph type="italics"/>nutum ad motum ine&longs;&longs;e: quam in minoribus. </s>

<s id="id.001730">Sed cum omnis circu&shy;<lb/>lus habeat intra &longs;e infinitos concentricos, omnis peripheria nutum <lb/>habebit infinitum, &amp; ide&ograve; perpetuum ad motum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001731">Infiniti autem.] <emph type="italics"/>Quod infiniti circuli minores concentrici in&shy;<lb/>&longs;int in quouis dato circulo &longs;ic demon&longs;trabimus. </s>

<s id="id.001732">Sit circulus C B, <lb/>cuius &longs;emidiameter D B bifariam <emph.end type="italics"/><lb/><figure id="id.035.01.148.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.148.1.jpg"/><lb/><emph type="italics"/>&longs;ecetur, vt in puncto E prop. 10. <lb/>lib. 1. </s>

<s>Et centro D interuallo D E <lb/>de&longs;criptus circulus po&longs;t. 3. </s>

<s id="id.001733">Hic <lb/>erit concentricus &amp; minor ip&longs;o <lb/>C B def. 1. lib. 3. </s>

<s id="id.001734">Rur&longs;us recta D <lb/>E bifariam &longs;ecetur, vt in puncto <lb/>F, &amp; centro D eodem interuallo <lb/>D F de&longs;criptus circulus erit con&shy;<lb/>centricus &amp; minor. </s>

<s id="id.001735">Et eadem ra&shy;<lb/>tione deinceps ad infinitum, cum rectam lineam &longs;emper bi&longs;&longs;ecare li&shy;<lb/>ceat prop. 10. lib. 1. </s>

<s>Et &longs;ic infiniti erunt circuli concentrici minores <lb/>in quouis circulo. </s>

<s id="id.001736">quod erat demon&longs;trandum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001737">Etiam&longs;i curuatura.] <emph type="italics"/>Repetit cau&longs;am perpetui motus, aut nu&shy;<lb/>tus ad motum, qu&aelig; in circulo e&longs;t, cum &longs;ua ab&longs;ide id e&longs;t curuatura at&shy;<lb/>tingit planum, ine&longs;&longs;e, etiam&longs;i non attingat, vt fit in rotis figulorum, <lb/>&amp; in trochleis. </s>

<s>de quibus po&longs;tea. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001739">Sed ob aliam cau&longs;am.] <emph type="italics"/>Quinta cau&longs;a de naturali motu &longs;e&shy;<lb/>cundum peripheriam h&icirc;c leuiter attingitur, vel potius ex anteceden&shy;<lb/>tibus breuiter repetitur. </s>

<s id="id.001740">Naturalis autem i&longs;te motus intelligi debet, <lb/>dum fit circulus &agrave; rect&aelig; manente altero extremo, &amp; moto altero, <lb/>quod &longs;uo motu de&longs;cribit peripheriam. </s>

<s id="id.001741">In facto enim circulo, vel glo&shy;<lb/>bo naturali quatenus particeps e&longs;&longs;et grauitatis reuera motus natura&shy;<lb/>lis e&longs;t is, qu&ograve; rect&agrave; deor&longs;um fertur. </s>

<s id="id.001742">Sed eo impedito ob planum cui in&shy;<lb/>cumbit non cedens, per vim aliquam impul&longs;us globus ad motum cir&shy;<lb/>cularem &longs;e recipit. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001743"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001744">10. Cur maiores circuli <lb/>&longs;unt mouentiores. </s></p><p type="main">

<s id="id.001745"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001746">Cur per maiores circu&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.149.jpg" pagenum="110"/><foreign lang="greek"><gap/></foreign><lb/>los &longs;ublata &amp; tracta faci&shy;<lb/>lius mouemus, vt &longs;i tro&shy;<lb/>chle&aelig; &longs;int maiores minori&shy;<lb/>bus, &amp; &longs;cytal&aelig; &longs;imiliter. </s>

<s id="id.001747">An <lb/>quia quant&ograve; maior fuerit <lb/>radius in tempore &aelig;quali, <lb/>per maius mouetur <expan abbr="&longs;pati&utilde;">&longs;patium</expan>. <lb/></s>

<s id="id.001748"><expan abbr="Itaq;">Itaque</expan> &aelig;quali in&longs;i&longs;tente one&shy;<lb/>re, idem faciet, vt diximus <lb/>etiam libras maiores mi&shy;<lb/>noribus e&longs;&longs;e exactiores. </s>

<s id="id.001749">E&longs;t <lb/>enim agina <expan abbr="c&etilde;tr&utilde;">centrum</expan>. </s>

<s id="id.001750">Et line&aelig; <lb/>in librili, qu&aelig; &longs;unt ab agina <lb/>vtrimque, &longs;unt radij. </s></p><p type="head">

<s id="id.001751">COMMENTARIVS. </s></p><p type="main">

<s id="id.001752">Cvr per maiores.] <emph type="italics"/>In hoc capite tractatur problema de ma&shy;<lb/>ioribus circulis, &amp; &longs;ph&aelig;ricis. </s>

<s id="id.001753">cur &longs;cilicet facilius &amp; celerius <lb/>moueantur &amp; moueant. </s>

<s id="id.001754">Cui re&longs;pondetur ex line&aelig; &agrave; centro longitu&shy;<lb/>dine maiore. </s>

<s id="id.001755">Ratio &longs;ic di&longs;ponetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001756"><emph type="italics"/>Vbi line&aelig; &agrave; centro &longs;unt maiores: ibi per motum &aelig;quali tempore <lb/>maius &longs;patium conficitur, &amp; facilis etiam motio fit, tum an&shy;<lb/>nexa onera mouentur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001757"><emph type="italics"/>In circularibus &amp; &longs;ph&aelig;ricis maioribus line&aelig; &agrave; centro <lb/>&longs;unt maiores: quam in minoribus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001758"><emph type="italics"/>Ergo circuli &amp; &longs;ph&aelig;r&aelig; maiores &aelig;quali tempore maius &longs;patium <lb/>conficient, facilius mouebuntur, &amp; annexa onera moue&shy;<lb/>bunt: quam minores. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001759"><emph type="italics"/>Ex hoc colligimus maiores rotas in curribus vna volutatione tan&shy;<lb/>tam lineam cum conficiant: quanta orbit&aelig; re&longs;pondet, nec maiori tra&shy;<lb/>ctu egeant: quam minores, tant&ograve; commodiores e&longs;&longs;e ad celeritatem, &amp; <lb/>motus facilitatem: quant&ograve; maiores extiterint. </s>

<s id="id.001760">Et cum in facili tractu <lb/>biroti onerati &longs;arcina tendere debeat ad &aelig;quilibrium, vt neque tolla&shy;<lb/>tur de collo iugum pr&aelig; pondere po&longs;teriore, neque &longs;ic prematur, vt &longs;i&shy;<lb/>mul iumentum trahat, &amp; ge&longs;tet: &longs;ed potius trahat: quam ge&longs;tet: in<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.150.jpg" pagenum="111"/><emph type="italics"/>maioribus autem rotis &aelig;quilibrium illud facilius &longs;it, quia &longs;arcina al&shy;<lb/>tior, &amp; &longs;ic trahitur tantum: in paruis depre&szlig;ior, &longs;icque nonnihil le&shy;<lb/>uanda. </s>

<s id="id.001761">Vbi autem &longs;u&longs;tinere &amp; trahere opus e&longs;t, vt in bellicis tor&shy;<lb/>mentis vnus equus iugum &longs;u&longs;tinere, alij loris trahere debent. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001762">Vt &longs;i trochle&aelig;.] <emph type="italics"/>Problema illu&longs;tratur duobus exemplis Tro&shy;<lb/>chle&aelig; &amp; Scytal&aelig;. </s>

<s id="id.001763">E&longs;t autem Trochlea in&longs;trumentum tractorium ex <lb/>rotula circa axiculum fixum alicubi appen&longs;um per <expan abbr="fun&etilde;">funem</expan> ductarium, <lb/>in eius circumferentia circumuoluta. </s>

<s id="id.001764">Geminatur aliquando, tripli&shy;<lb/>catur, &amp; amplius multiplicatur. </s>

<s id="id.001765">Vnde &longs;unt illa tractoria infinita&shy;<lb/>rum propemodum virium Tri&longs;pa&longs;ton, Pente&longs;pa&longs;ton, Poly&longs;pa&longs;ton, in <lb/>quibus rotul&aelig; &longs;ibi inuicem &longs;ub&longs;eruientes, &amp; tanquam onus attra&shy;<lb/>hendum diuidentes &longs;umma facilitate ip&longs;um attrahunt, de quo qui <lb/>multa admirabilia videre volet, videat apud Guidum Vbaldum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001766">Et&longs;cytal&aelig;.] <emph type="italics"/>Scytala lignum e&longs;t cylindricum cuius pro duplici <lb/>v&longs;u duo genera &longs;tatuuntur. </s>

<s id="id.001767">Vnus v&longs;uum e&longs;t ad attrahendum, &amp; &longs;ic <lb/>in eius altera extremitate ferrum quoddam inflexum e&longs;t pro manu&shy;<lb/>brio, vbi annectitur potentia mouens: vel loco ferri vectes <expan abbr="emerg&utilde;t">emergunt</expan> <lb/>aliquot, qui vici&szlig;im per vim annexam mouentur: vel loco vectis <lb/>rota maior, quod idem e&longs;t: &longs;icque vel manubrio, vel vectibus, vel <lb/>rota mota vn&agrave; mouetur illud lignum cylindricum cum &longs;uo fune du&shy;<lb/>ctario. </s>

<s id="id.001768">Et cum eo pondus alligatum eleuatur. </s>

<s id="id.001769">Hoc genus &longs;cytal&aelig; e&longs;t <lb/>idem quod axis in peritrochio de quo po&longs;tea. </s>

<s id="id.001770">De hoc autem genere lo&shy;<lb/>cus hic intelligi debet. </s>

<s id="id.001771">De altero dicetur cap. 12. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001772">Vt diximus etiam.] <emph type="italics"/>Confirmatio e&longs;t propo&longs;itionis pr&aelig;ceden&shy;<lb/>tis &longs;yllogi&longs;mi per &longs;peciem libr&aelig;, qu&aelig; tant&ograve; exactior exi&longs;tit: quant&ograve; li&shy;<lb/>brile habet longius, &egrave; &longs;uperioribus repetitam. </s>

<s id="id.001773">C&aelig;terum pr&aelig;ter proble&shy;<lb/>ma huius capitis alia qu&aelig;ri po&longs;&longs;unt ad idem fer&egrave; pertinentia &longs;citu <lb/>digna, nec minus &longs;ubtilia, nemp&egrave;. </s>

<s id="id.001774">Quare bin&aelig; rot&aelig; quaternis facilio&shy;<lb/>res &longs;int. </s>

<s id="id.001775">Quare prioribus po&longs;teriores rotas maiores e&longs;&longs;e oporteat. <lb/></s>

<s id="id.001776">Quare maior &longs;arcina in anteriore plau&longs;tri parte poni debeat. </s>

<s id="id.001777">Soluitur <lb/>primum quia rota qu&aelig;libet, vt grauis, ad centrum &longs;pectat, &amp; arceri <lb/>de&longs;cen&longs;u e&longs;t contra eius naturam: arcetur &amp; cum tollitur &longs;ur&longs;um, &amp; <lb/>cum trahitur adlatus, quipp&egrave; in diuer&longs;um per <expan abbr="ambit&utilde;">ambitum</expan>. </s>

<s id="id.001778">Plures igitur <lb/>rot&aelig; augebunt onus, &amp; ideo trahentis laborem. </s>

<s id="id.001779">Itaque bin&aelig; rot&aelig; <lb/>quaternis faciliores erunt, vnde bellicis tormentis, licet immanibus <lb/>du&aelig; &longs;atis &longs;unt. </s>

<s id="id.001780">Quod autem quis obijceret per rotas plures pondus plus<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.151.jpg" pagenum="112"/><emph type="italics"/>di&longs;tribui, &amp; tanquam diuidi. </s>

<s id="id.001781">Id &longs;an&egrave; verum e&longs;t &amp; vtile ad facili&shy;<lb/>tatem &longs;u&longs;tentationis, non item ad tractum. </s>

<s id="id.001782">Et&longs;i biroti &longs;arcina in pe&shy;<lb/>toritum transferatur, eadem iumento grauior fiet tant&ograve;, quant&ograve; gra&shy;<lb/>uior currus. </s>

<s id="id.001783">Sed fallaci&aelig; cau&longs;a e&longs;t quod petorita birotis plus &longs;u&longs;tinent. <lb/></s>

<s id="id.001784">Secundum quia maiores tanquam altiores prioribus minoribus qua&longs;i <lb/>incumbunt, &longs;icque in proclinatiores iam partes onus recumbens &agrave; <lb/>facilius motis maioribus, vna quoque mouetur facilius. </s>

<s id="id.001785">Tertium ob <lb/>eandem cau&longs;am &longs;oluitur. </s>

<s id="id.001786">Sic enim impo&longs;ita &longs;arcina qua&longs;i inferiore <lb/>loco pendens adiuuat tractum. </s>

<s id="id.001787">Hinc e&longs;t quod quadrupedum omni <lb/>generi &longs;olis Gyraffis exceptis crura po&longs;teriora longiora &longs;unt. </s>

<s id="id.001788">Mouen&shy;<lb/>tur enim pul&longs;u primum, deinde tractu. </s>

<s id="id.001789">Commodius autem pellit, <lb/>quod grauius e&longs;t. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001790"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001791">11. Cur facilius mouetur li&shy;<lb/>brile ab&longs;que pondere. </s></p><p type="main">

<s id="id.001792"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001793">Cur librile quum fuerit <lb/>&longs;ine <expan abbr="p&otilde;dere">pondere</expan>, facilius moue&shy;<lb/>tur: <expan abbr="qu&atilde;">quam</expan> quum habet pon&shy;<lb/>dus. </s>

<s id="id.001794">Similiter ver&ograve; &amp; orbi&shy;<lb/>culus, vel aliud tale, gra&shy;<lb/>uius quidem, maius ver&ograve; <lb/>minore &amp; leuiore. </s>

<s id="id.001795">An quod <lb/>non &longs;olum in contrarium <lb/>id, quod graue e&longs;t: &longs;ed <expan abbr="eti&atilde;">etiam</expan> <lb/>in <expan abbr="obliqu&utilde;">obliquum</expan> difficulter mo&shy;<lb/>uetur. </s>

<s id="id.001796">Difficile enim e&longs;t <lb/>contr&agrave; propen&longs;ionem mo&shy;<lb/>uere. </s>

<s id="id.001797">At qu&ograve; propendet, fa&shy;<lb/>cile: non propendet aut&egrave;m in obliquum. </s></p><p type="head">

<s id="id.001798">COMMENTARIVS. </s></p><p type="main">

<s id="id.001799">Cvr librile.] <emph type="italics"/>In hoc capite &longs;peciale tractatur problema, quod <lb/>generale e&longs;&longs;e po&longs;&longs;et. </s>

<s id="id.001800">E&longs;t autem de librili. </s>

<s id="id.001801">cur qu&ograve; leuius, vel &longs;ine <lb/>pondere cum &longs;it, deprimitur facilius &amp; mouetur: quam cum graue <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.152.jpg" pagenum="113"/><emph type="italics"/>e&longs;t. </s>

<s id="id.001802">Exempli gratia vnum ligneum &longs;it, alterum ferreum, illud faci&shy;<lb/>lius moueatur: quam hoc, quod perinde e&longs;t de vecte, de rotis, de glo&shy;<lb/>bis, &amp; eiu&longs;modi contra naturam motis, &longs;uppo&longs;ita eadem firmitate. <lb/></s>

<s id="id.001803">Ratio erg&ograve; qu&aelig; redditur generalis e&longs;t, &amp; hoc &longs;yllogi&longs;mo compre&shy;<lb/>hendetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001804"><emph type="italics"/>Motum contra naturam e&ograve; difficilius fertur, qu&ograve; ip&longs;um grauius <lb/>e&longs;t. </s>

<s id="id.001805">Plus enim re&longs;i&longs;tit non &longs;olum in contrarium nutus &longs;ui, &longs;ed <lb/>&amp; in obliquum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001806"><emph type="italics"/>Librile moueri in obliquum (vt mouetur nece&longs;&longs;ari&ograve; propter <lb/>&longs;u&aelig; agin&aelig; &longs;eu centri immobilitatem: &longs;ic enim non rect&agrave; ad <lb/>centrum mundi quo natura fertur, de&longs;cendit: &longs;ed per ambi&shy;<lb/>tum circuli) e&longs;t contra naturam grauitatis &longs;u&aelig; moueri, vt <lb/>rotam &amp; eiu&longs;modi. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001807"><emph type="italics"/>Ergo librile qu&ograve; grauius, e&ograve; difficilius mouebitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001808"><emph type="italics"/>Hinc collige ex leuiori materia facta, dummodo firma, agiliora e&longs;&longs;e, <lb/>&amp; exactiora. </s>

<s id="id.001809">vnde petorita no&longs;tra rotis in orbita ferreis pr&aelig;dita <lb/>difficilius trahuntur, quam <emph.end type="italics"/><lb/><figure id="id.035.01.152.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.152.1.jpg"/><lb/><emph type="italics"/>nobilium Polonorum, qu&aelig; ex <lb/>ligno &longs;olo compacta &longs;unt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001810">Non propendet.] <emph type="italics"/>Linea <lb/>nutus grauis alicuius deor&shy;<lb/>&longs;um e&longs;t recta perpendicularis <lb/><expan abbr="in&longs;i&longs;t&etilde;s">in&longs;i&longs;tens</expan> plano horizontis, <expan abbr="h&atilde;c">hanc</expan> <lb/>qu&aelig; &longs;ecat ad in&aelig;quales an&shy;<lb/>gulos, e&longs;t obliqua, cuiu&longs;mo&shy;<lb/>di e&longs;t arcus B F ad rectam <lb/>B G lineam nutus puncti <lb/>B. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001811"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001812">12. Cur &longs;uper &longs;cytalis onera <lb/>facilius ge&longs;tantur: quam <lb/>&longs;uper curribus. </s></p><p type="main">

<s id="id.001813"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001814">Cur onera facilius ge&shy;<lb/>&longs;tantur &longs;cytalis: quam cur&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.153.jpg" pagenum="114"/><foreign lang="greek"><gap/></foreign><lb/>ribus etiam magnas rotas <lb/>habentibus, cum ip&longs;&aelig; par&shy;<lb/>uas habeant. </s>

<s id="id.001815">An quia one&shy;<lb/>ra in &longs;cytalis ad nihil offen&shy;<lb/>&longs;ant: in curribus vero ha&shy;<lb/>bent axem, ad quem offen&shy;<lb/>&longs;ant. </s>

<s id="id.001816">Supern&egrave; enim pre&shy;<lb/>munt ip&longs;um, &amp; in <expan abbr="obliqu&utilde;">obliquum</expan>. <lb/></s>

<s id="id.001817">In &longs;cytalis vero ad h&aelig;c <lb/>duo mouentur, &amp; infern&egrave; <lb/>&longs;cilicet &longs;ub&longs;trato &longs;patio, <lb/>&amp; onere &longs;uperimpo&longs;ito. </s>

<s id="id.001818">In <lb/>vtri&longs;que enim his locis re&shy;<lb/>uoluitur circulus, &amp; conci&shy;<lb/>tatus impellitur. </s></p><p type="head">

<s id="id.001819">COMMENTARIVS. </s></p><p type="main">

<s id="id.001820">Cvr onera.] <emph type="italics"/>Secundum genus &longs;cytal&aelig; e&longs;t lignum ferrumue <lb/>cylindricum oblongum in extremis rotulas habens intra annu&shy;<lb/>los currui <emph.end type="italics"/><lb/><figure id="id.035.01.153.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.153.1.jpg"/><lb/><emph type="italics"/>affixos <lb/>ver&longs;atile, <lb/>vt e&longs;t fi&shy;<lb/>gura A <lb/>B qu&aelig; <lb/>mota iu&shy;<lb/>go rotis annexo, contr&agrave;, quam in curribus, in quibus non rotis: &longs;ed <lb/>currui annectitur, omnibus &longs;uis partibus mouetur duobus motibus <lb/>&longs;imul, circumcirca, &amp; antror&longs;um. </s>

<s id="id.001821">quod cau&longs;a e&longs;t vt leuius vertatur, <lb/>quam rota in curru. </s>

<s id="id.001822">vt cuius axis procedendo tant&ugrave;m antror&longs;um <lb/>moueatur, non autem circum circa vertatur. </s>

<s id="id.001823">Vnde fit vt axis etiam <lb/>premat magis, &amp; veluti rotam affigat plano, &longs;icque remoretur: con&shy;<lb/>tra in &longs;cytala rot&aelig; dummodo maiores &longs;int, quam vt terra obruantur <lb/>&agrave; &longs;ubiecta planicie inferne ip&longs;am circunferentiam atterente impel&shy;<lb/>luntur. </s>

<s id="id.001824">Supern&egrave; etiam ab onere cylindricum premente. </s>

<s id="id.001825">Ob has itaque <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.154.jpg" pagenum="115"/><emph type="italics"/>cau&longs;as &longs;cytala commodior erit, &amp; expeditior ad onera conuehenda, <lb/>licet minores, quam currus habeat rotas, quod non repugnat ijs qu&aelig; <lb/>ante 10. cap. dicta <expan abbr="s&utilde;t">sunt</expan> de rotis maioribus. </s>

<s id="id.001826">Aliud enim facilius attol&shy;<lb/>lere, &amp; trahere qu&aelig;cunque pondera, aliud conuehere. </s>

<s id="id.001827">Scytala tamen <lb/>pote&longs;t e&longs;&longs;e illud curriculi genus quod Galli vocant<emph.end type="italics"/> Traineau, <emph type="italics"/>Itali <emph.end type="italics"/><lb/>Stra&longs;cino, <emph type="italics"/>apud quendam non ineruditum legi dici po&longs;&longs;e traham. <lb/></s>

<s id="id.001828">H&aelig;c autem annexa ligno cylindrico &longs;olas rotas habet ver&longs;atiles, qu&aelig; <lb/>quant&ograve; minores, tant&ograve; minus occur&longs;ant &longs;ubiecto pauimento. </s>

<s id="id.001829">vt enim <lb/>qu&ograve; circulus rot&aelig; maior e&longs;t, e&ograve; eius cum recta &agrave; qua tangitur in pla&shy;<lb/>no minor e&longs;t an&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.154.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.154.1.jpg"/><lb/><emph type="italics"/>gulus. </s>

<s id="id.001830">Et contr&agrave; <lb/>qu&ograve; circulus mi&shy;<lb/>nor, e&ograve; angulus <lb/>contactus maior <lb/>euadit. </s>

<s id="id.001831">vt angu&shy;<lb/>lus A B C ro&shy;<lb/>t&aelig; maioris mi&shy;<lb/>nor e&longs;t angulo <lb/>A B D rot&aelig; <lb/>minoris: &amp; con&shy;<lb/>tr&agrave; vtrolibet <lb/>maior e&longs;t angu&shy;<lb/>lus A B E rot&aelig; minoris. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001832"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001833">13. Cur mi&longs;&longs;ilia longius &agrave; <lb/>funda: quam &agrave; manu <lb/>proijciuntur. </s></p><p type="main">

<s id="id.001834"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001835">Cur mi&longs;&longs;ilia longius fe&shy;<lb/>runtur &agrave; funda, quam &agrave; <lb/>manu, etiam&longs;i proijciens <lb/>melius manu, comprehen&shy;<lb/>dat: quam &longs;u&longs;pendens &egrave; <lb/>fo&longs;&longs;a fund&aelig;? </s>

<s id="id.001836">Pr&aelig;terea &longs;ic <lb/>duo pondera moueat, fun&shy;<lb/>dam &longs;cilicet, &amp; mi&longs;&longs;ile: illo <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.155.jpg" pagenum="116"/><foreign lang="greek"><gap/></foreign><lb/>ver&ograve; modo mi&longs;&longs;ile dunta&shy;<lb/>xat. </s>

<s id="id.001837">An quia in funda mi&longs;&shy;<lb/>&longs;ile commotum proijciens <lb/>iacit. </s>

<s id="id.001838">In orbem enim volu&shy;<lb/>tans &longs;&aelig;pius, proijcit. </s>

<s id="id.001839">E ma&shy;<lb/>nu autem initium &agrave; quiete <lb/>capit. </s>

<s id="id.001840">At omnia commota <lb/>facilius: quam quie&longs;centia <lb/><expan abbr="mou&etilde;tur">mouentur</expan>. </s>

<s id="id.001841">An propter hoc: <lb/>&longs;ed &amp; quia in v&longs;u funda&shy;<lb/>rum manus quidem fit <expan abbr="c&etilde;-trum">cen&shy;<lb/>trum</expan>: funda vero linea ex <lb/>centro. </s>

<s id="id.001842">quant&ograve; autem fue&shy;<lb/>rit h&aelig;c maior, <expan abbr="t&atilde;t&ograve;">tant&ograve;</expan> celerius <lb/>mouetur. </s>

<s id="id.001843">At iactus &agrave; manu <lb/>re&longs;pectu fund&aelig; breuis e&longs;t. </s></p><p type="head">

<s id="id.001844">COMMENTARIVS. </s></p><p type="main">

<s id="id.001845">A Funda.] <emph type="italics"/>Funda e&longs;t funiculus duobus capitibus manu captus, <lb/>altero cum an&longs;ula digito circumuoluta ne exeat, altero &longs;ine an&shy;<lb/>&longs;ula, vt dimitti po&szlig;it. </s>

<s id="id.001846">In medio latior, &amp; paululum excauatus, vt <lb/>ibi mi&szlig;ile contineatur, quod aliquoties circumacto in orbem funicu&shy;<lb/>lo, &amp; ab vno capitum dimi&longs;&longs;o vehementer proijcitur. </s>

<s id="id.001847">Inuentam &agrave; <lb/>Phenicibus fui&longs;&longs;e refert Plinius cap. 56. lib. 7. ne manus iaculi a&longs;pe&shy;<lb/>rioris attrectatione l&aelig;deretur, &amp; vt longius atque validius proijce&shy;<lb/>retur. </s>

<s id="id.001848">Qu&aelig; cum intelligeret pa&longs;tor ille exilis, &longs;ed Deo dilectus Dauid <lb/>funda aduer&longs;us Goliathem immanem gigantem non aliter, quam <lb/>&longs;ummo impetu pro&longs;ternendum, prudenter &longs;e&longs;e armauit. </s>

<s id="id.001849">Erat autem <lb/>fund&aelig; v&longs;us ade&ograve; frequens Balearium in&longs;ularum populis, vt matres <lb/>filios non alijs auibus ve&longs;ci paterentur, quam quas funda &longs;ibi com&shy;<lb/>para&longs;&longs;ent. </s>

<s id="id.001850">Vnde &amp; funda balearis appellatur &agrave; Po&euml;ta,<emph.end type="italics"/></s></p><p type="main">

<s id="id.001851">Stuppea torquentur balearis verbera fund&aelig;. <lb/></s>

<s><emph type="italics"/>Nec &longs;olum lapides funda proijci&longs;olere: &longs;ed &amp; alia, vt plumbum, pa&shy;<lb/>tet ex Ouidio. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.156.jpg" pagenum="117"/><p type="main">

<s id="id.001852">Non &longs;ecus exar&longs;it quam cum balearica plumbum</s></p><p type="main">

<s id="id.001853">Funda iacit, volat illud, &amp; incande&longs;cit eundo. </s></p><p type="main">

<s id="id.001854"><emph type="italics"/>Et aduer&longs;um bellatores ca&szlig;idibus, cataphractis, lorici&longs;que munitos <lb/>teretes lapides de funda de&longs;tinatos &longs;agittis omnibus e&longs;&longs;e grauiores <lb/>&longs;crip&longs;it Vegetius. </s>

<s id="id.001855">Quandoquidem membris integris, lethale tamen <arrow.to.target n="marg27"/><lb/>vulnus importent, &amp; &longs;ine inuidia &longs;anguinis ho&longs;tis lapidis ictu in&shy;<lb/>tereat Qu&aelig; res ide&ograve;, inquit, ab vniuer&longs;is tyronibus frequenti exerci&shy;<lb/>tio di&longs;cenda e&longs;t, quia <expan abbr="fund&atilde;">fundam</expan> portare nullus labor. </s>

<s id="id.001857">Et interdum euenit, <lb/>vt in lapido&longs;is locis conflictus habeatur, vt aut mons aliquis &longs;it de&shy;<lb/>fendendus, aut collis, &amp; ab oppugnatione ca&longs;tellorum &longs;iue ciuitatum <lb/>lapidibus barbari fundi&longs;que &longs;int propellendi. <emph.end type="italics"/></s></p><p type="margin">


<s id="id.001858"><margin.target id="marg27"/>Cap. 16. lib <lb/>1. de re mili</s></p><p type="main">

<s id="id.001859">Cur mi&longs;&longs;ilia.] <emph type="italics"/>Qu&aelig;rit h&icirc;c Ari&longs;toteles cur iaculum mi&longs;&longs;um cum <lb/>funda longius proijcitur, quam &longs;i manu tantum. </s>

<s id="id.001860">Cui priu&longs;quam re&shy;<lb/>&longs;pondeat, duo repugnare dicit, alterum, quia proiectum &agrave; manu &longs;ola <lb/>melius comprehendatur: quam quod &agrave; funda &longs;u&longs;penditur, melior au&shy;<lb/>tem comprehen&longs;io conducit ad <expan abbr="longior&etilde;">longiorem</expan> iactum: alterum, quia proij&shy;<lb/>ciens cum funda duo &longs;imul proijcit fundam &longs;cilicet &amp; iaculum: ma&shy;<lb/>nu autem vnum tantum, nempe iaculum. </s>

<s id="id.001861">At difficilius duo mouere: <lb/>quam vnum. </s>

<s id="id.001862">His incommodis tamen neglectis &longs;oluit Ari&longs;toteles <lb/>problema dupliciter, priore modo &egrave; motu incitato, &amp; contraria quie&shy;<lb/>te. </s>

<s id="id.001863">Syllogi&longs;mus &longs;ic e&longs;t,<emph.end type="italics"/></s></p><p type="main">

<s id="id.001864"><emph type="italics"/>Qui initium proiectionis capit &agrave; motu longius iacit: quam &agrave; <lb/>quiete. </s>

<s id="id.001865">Quies enim vt contraria motui, ei repugnat, &amp; ip&longs;i re&shy;<lb/>nitens, ne fiat impedit. </s>

<s id="id.001866">Ide&oacute;que omnia commota facilius: quam <lb/>quie&longs;centia mouentur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001867"><emph type="italics"/>At proijciens cum funda initium capit &agrave; motu. </s>

<s id="id.001868">Ante vi&shy;<lb/>brationem enim funditor fundam &longs;&aelig;pius in circulum <lb/>circumagit: contr&agrave; cum manu, initium capit &agrave; quiete: aut <lb/>&longs;i &agrave; motu, mult&ograve; leuiore tamen. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001869"><emph type="italics"/>Igitur proiiciens cum funda longius iacit: quam cum manu &longs;ola. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001870">E fo&longs;&longs;a fund&aelig;.] <emph type="italics"/>In Gr&aelig;co vocabulum e&longs;t,<emph.end type="italics"/> <foreign lang="greek">to\ kai/ar,</foreign> <emph type="italics"/>&longs;ine vo&shy;<lb/>cabulo<emph.end type="italics"/> <foreign lang="greek">sfendo/nhs.</foreign> </s>

<s><emph type="italics"/>Significat <expan abbr="aut&etilde;">autem</expan><emph.end type="italics"/> <foreign lang="greek">kaiar</foreign> <emph type="italics"/>fo&longs;&longs;am terr&aelig; concu&longs;&longs;u <expan abbr="fact&atilde;">factam</expan> <lb/>qu&aelig; &longs;ignificatio quid ad rem pertineat non video, ni&longs;i per metapho&shy;<lb/>ram intelligamus eam fund&aelig; partem, qu&aelig; vt latior, ita &amp; in &longs;inum <lb/>leuiter excauatur ad iaculum continendum, &amp; &longs;ic conuenit rei pro&shy;<lb/>po&longs;it&aelig;: nonnulli tamen putarunt delendum<emph.end type="italics"/> <foreign lang="greek">to\ kai/ar</foreign> <emph type="italics"/>&amp; loco eius <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.157.jpg" pagenum="118"/><emph type="italics"/>reponendum<emph.end type="italics"/> <foreign lang="greek">o)i+/sto\n</foreign> <emph type="italics"/>id e&longs;t omne quod iaculamus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001871">At omnia commot&aelig;.] <emph type="italics"/>H&aelig;c cau&longs;a generalis erit trice&longs;imo <lb/>primo capiti huius libri. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001872">An propter hoc.] <emph type="italics"/>Alter e&longs;t modus &longs;olutionis problematis <lb/>&longs;umptus &egrave; funda tanquam radio longiore. </s>

<s id="id.001873">Syllog. &longs;ic e&longs;t. </s>

<s id="id.001874">Quant&ograve; li&shy;<lb/>nea &agrave; centro e&longs;t maior, tant&ograve; celerius mouet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001875"><emph type="italics"/>In proiectione cum funda manus e&longs;t centrum, funda ver&ograve; e&longs;t <lb/>linea &agrave; centro: &amp; longior manu. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001876"><emph type="italics"/>Igitur proiectio cum funda longior fiet. <emph.end type="italics"/><lb/><arrow.to.target n="marg28"/></s></p><p type="margin">

<s id="id.001877"><margin.target id="marg28"/>Cap 1. lib. 2. <lb/>de v&longs;. part. </s></p><p type="main">

<s id="id.001879">Manus quidem.] <emph type="italics"/>Manus apud veteres, vt videre e&longs;t apud <lb/>Gal. tres &longs;unt partes vna quidem brachium, alia vero<emph.end type="italics"/> <foreign lang="greek">ph/xus</foreign> <emph type="italics"/>id e&longs;t <lb/>cubitus, &amp; tertia<emph.end type="italics"/> <foreign lang="greek">a)kro/keiron</foreign> <emph type="italics"/>hoc e&longs;t &longs;umma extremave manus. <lb/></s>

<s id="id.001881">H&aelig;c et&longs;i commoueatur cum fundam rotat tanquam manens loco, <lb/>tamen &amp; centrum habetur, funda autem radius e&longs;t: at cum &longs;ine fun&shy;<lb/>da proiectio fit, articulus quo brachium cum humero connectitur, <lb/>videtur potius habere rationem centri, &amp; brachium cum cubito, &amp; <lb/>extrema manu rationem line&aelig; &agrave; centro. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001882"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001883">14. De collopibus &amp; &longs;uc&shy;<lb/>culis. </s></p><p type="main">

<s id="id.001884"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001885">Cur circa eandem erga&shy;<lb/>tam collopes maiores mi&shy;<lb/>noribus facilius <expan abbr="mou&etilde;tur">mouentur</expan>, <lb/>&amp; ip&longs;&aelig; &longs;uccul&aelig; graciliores <lb/>ab <expan abbr="ead&etilde;">eadem</expan> vi cra&longs;&longs;iotibus, An <lb/>quia &longs;uccula &amp; ergata cen&shy;<lb/>trum e&longs;t. </s>

<s id="id.001886">Longitudines au&shy;<lb/>tem di&longs;tantes &longs;unt line&aelig; ex <lb/>centro. </s>

<s id="id.001887">At &amp; celerius mo&shy;<lb/>uentur, &amp; plus ab eadem vi <lb/>line&aelig; <expan abbr="maior&utilde;">maiorum</expan> circulorum: <lb/>quam <expan abbr="minor&utilde;">minorum</expan>. </s>

<s id="id.001888">Ab eadem <lb/>enim vi extremum, quod <lb/>longi&ugrave;s e&longs;t &agrave; centro, plus <lb/>transfertur, ideo collopas <lb/>organa ad ergatas <expan abbr="adijci&utilde;t">adijciunt</expan>, <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.158.jpg" pagenum="119"/><foreign lang="greek"><gap/></foreign><lb/>quibus facilius vertunt. </s>

<s id="id.001889">In <lb/>&longs;ucculis vero tenuibus ma&shy;<lb/>ius fit id quod extra e&longs;t, li&shy;<lb/>gnum. </s>

<s id="id.001890">Et id linea e&longs;t qu&aelig; <lb/>ex centro. </s></p><p type="head">

<s id="id.001891">COMMENTARIVS. </s></p><p type="main">

<s id="id.001892">Cvr circa eandem.] <emph type="italics"/>In hoc capite continentur duo proble&shy;<lb/>mata vnum de ergatis, alterum de &longs;ucculis. </s>

<s id="id.001893">Illud cur ergat&aelig; &agrave; <lb/>maioribus collopibus facilius mouentur: quam &agrave; minoribus. </s>

<s id="id.001894">Hoc cur <lb/>&longs;uccul&aelig; graciliores etiam facilius <expan abbr="mou&etilde;tur">mouentur</expan>, quam cra&szlig;iores. </s>

<s id="id.001895">Vtrum&shy;<lb/>que &longs;oluitur ex line&aelig; &egrave; centro longitudine maiore. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001896"><emph type="italics"/>Maiores line&aelig; ex centro facilius &amp; celerius mouentur ab eadem <lb/>vi minoribus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001897"><emph type="italics"/>Ergata &amp; &longs;uccula collopibus ver&longs;at&aelig;, &longs;unt centrum, &amp; col&shy;<lb/>lopes &longs;unt line&aelig; ex centro, &amp; quidem tant&ograve; maiores, quan&shy;<lb/>t&ograve; &longs;uccula gracilior e&longs;t (pars enim quam cra&szlig;itudo tegeret <lb/>ob gracilitatem detegitur.)<emph.end type="italics"/></s></p><p type="main">

<s id="id.001898"><emph type="italics"/>Ergo ergata &amp; &longs;uccula gracilior &agrave; collopibus maioribus facilius <lb/>ab eadem vi mouebuntur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001899"><emph type="italics"/>C&aelig;terum quid h&icirc;c<emph.end type="italics"/> <foreign lang="greek">zugo\n</foreign> <emph type="italics"/>ergata differat &agrave; &longs;uccula,<emph.end type="italics"/> <foreign lang="greek">o)/non</foreign> <emph type="italics"/>Gr&aelig;ci vo&shy;<lb/>cant, &amp; &longs;cytal&aelig; primum genus, parum video, ni&longs;i fulcris, aut cra&szlig;i&shy;<lb/>tudine. </s>

<s id="id.001900">Horum enim vnumquodque axis e&longs;t circum quem voluitur <lb/>funis ductarius ad tollenda, vel trahenda onera tran&longs;uer&longs;as habens <lb/>collopas, id e&longs;t ligna oblonga in altera extremitate, vel vtraque, qu&aelig; <lb/>&longs;unt tanquam vectes &agrave; vi adiuncta deprimendi vici&szlig;im. </s>

<s id="id.001901">Differre <lb/>tamen po&longs;&longs;unt quod ergata erectum axem habeat, vel fulciatur dua&shy;<lb/>bus trabibus perpendiculariter erectis: &longs;uccula &longs;upinum habet axem <lb/>vel etiam quatuor tignis ex vtraque parte binis &longs;u&longs;tentetur, vnde<emph.end type="italics"/><lb/><foreign lang="greek">o)/nos</foreign> <emph type="italics"/>dicitur, tanquam ge&longs;tanti cuidam a&longs;ino &longs;imilis &longs;it. </s>

<s id="id.001902">Huius fecit <lb/>mentionem Hippocrates &longs;ect. 3. lib. de fract. </s>

<s id="id.001904">Ex vniuer&longs;is inquit, <lb/>machinationibus, qu&aelig; ab hominibus excogitat&aelig; &longs;unt, h&aelig; tres om&shy;<lb/>nium valenti&szlig;im&aelig;,<emph.end type="italics"/> <foreign lang="greek">o)/nou</foreign> <emph type="italics"/>id e&longs;t axis ver&longs;atio, impul&longs;us per vectem, &amp; <lb/>cuneus adactus. </s>

<s id="id.001905">Namque homines &longs;ine aliquo vno, vel &longs;ine omnibus <lb/>nullum opus, quod maximam vim po&longs;tulet, perficiunt. </s>

<s id="id.001906">H&aelig;c Hipp. <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.159.jpg" pagenum="120"/><emph type="italics"/>Succularum <expan abbr="tam&etilde;">tamen</expan> multa &longs;unt genera vt videre e&longs;t apud Vitruuium. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001907"><emph type="italics"/>Et Pappus lib. 8. Mathemat collectionum fabricam in&longs;trumenti <lb/>docet, quod huc referri debet, e&longs;t autem eiu&longs;modi. </s>

<s id="id.001908">vocat axem M B,<emph.end type="italics"/><lb/><figure id="id.035.01.159.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.159.1.jpg"/><lb/><emph type="italics"/><expan abbr="tympan&utilde;">tympanum</expan> C D, circa tympani <expan abbr="peripheri&atilde;">peripheriam</expan> &longs;cytalas vel collopes in fora&shy;<lb/>minibus tympani F G, H F, &amp;ct: ita, vt potentia qu&aelig; &longs;emper in <lb/>&longs;cytalis e&longs;t, vel in peripheria tympani vt in F, dum circumuertit <lb/>tympanum, &amp; axem &longs;ur&longs;um quoque mouet pondus K axi appen&longs;um <lb/>fune M circa axem reuoluto. </s>

<s id="id.001909">Qui amplius videre volet, cur ab <lb/>hoc in&longs;trumento, quod axis in peritrochio vocatur, magna pondera <lb/>ab exigua virtute, quo ve etiam modo moueantur, qu&aelig; ratio tempo&shy;<lb/>ris, &longs;patij, potenti&aelig;, ac moti ponderis inter &longs;e, &amp; vt v&longs;us ip&longs;ius ad ve&shy;<lb/>ctem referatur. </s>

<s id="id.001910">Videat apud Guidum Vbaldum in Mechanicis. </s>

<s id="id.001911">Ad <lb/>hoc genus etiam in&longs;trumenti referantur ingentes ill&aelig; rot&aelig; in vno <lb/>axe quarum vna labore vnius atque alterius hominis vertitur: alte&shy;<lb/>ra &longs;itulis quibus in &longs;ua circumferentia accommodate dispo&longs;itis con&shy;<lb/>ferta e&longs;t &longs;ui conuer&longs;ione ex vna parte aquam Sequan&aelig; &longs;eptis contra&shy;<lb/>ctam exhau&longs;it, ex altera ali&ograve; refudit, vt ex lapide quadrato firma <lb/><expan abbr="iacer&etilde;tur">iacerentur</expan> fundamenta illius eximij pontis, qui magno ornamento &amp; <lb/>commoditate celeberrim&aelig; vrbium Luteti&aelig;, iu&longs;&longs;u Henrici III. Regis<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.160.jpg" pagenum="121"/><emph type="italics"/>no&longs;tri Chri&longs;tiani&szlig;imi inchoatus, &amp; maiori iam ex parte con&longs;tru&shy;<lb/>ctus perfectionem ab Henrico IIII. </s>

<s id="id.001912">Rege nunc no&longs;tro magnifi&shy;<lb/>centi&szlig;imo de&longs;iderat, ea in parte, qua flumen &agrave; &longs;chola S. Germani <lb/>ad plateam Augu&longs;tinorum traducitur. </s>

<s id="id.001913">Hanc, vt &longs;pero, exorabit cla&shy;<lb/>ri&szlig;imus vir dominus Marlyius rationum regiarum pr&aelig;&longs;es, &amp; mer&shy;<lb/>catorum pr&aelig;fectus digni&szlig;imus. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001914"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001915">15. De fractura ligni. </s></p><p type="main">

<s id="id.001916"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001917">Cur lignum <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> ma&shy;<lb/>gnitudinis facilius &egrave; genu <lb/><expan abbr="fr&atilde;gitur">frangitur</expan>, &longs;i in extremis ma&shy;<lb/>nus &aelig;qualiter diductas ha&shy;<lb/>bens fregerit: quam &longs;i ad <lb/>genu propinquas habuerit. <lb/></s>

<s id="id.001918">Pr&aelig;terea &longs;i ad terram ap&shy;<lb/>plicans, &amp; pede impellens, <lb/>manu di&longs;tante frangat: <expan abbr="qu&atilde;">quam</expan> <lb/>propinqua. </s>

<s id="id.001919">An quia ill&icirc;c <lb/>genu quidem e&longs;t centrum: <lb/>h&icirc;c ver&ograve; pes. </s>

<s id="id.001920">quant&ograve; autem <lb/>quodque &agrave; centro fuerit <lb/>di&longs;tantius, id omne facilius <lb/>mouetur. </s>

<s id="id.001921">Quod frangitur autem moueri nece&longs;&longs;e e&longs;t. </s></p><p type="head">

<s id="id.001922">COMMENTARIVS. </s></p><p type="main">

<s id="id.001923"><emph type="italics"/>Mos e&longs;t ignem excitare in paruo foco volentium, baculos lon&shy;<lb/>giores bifariam frangere. </s>

<s id="id.001924">Itaque arreptos tracto&longs;que vtraque <lb/>manu per extrema medios ad genu applicantes, parua vi frangunt. <lb/></s>

<s id="id.001925">Idem faciunt &longs;i alterum extremorum ad terram applicent: alterum <lb/>eleuatum obliqu&egrave; manu teneant, &amp; medium pede conculcent. </s>

<s id="id.001926">Qu&aelig;&shy;<lb/>rit igitur Ari&longs;toteles cur fractio h&aelig;c facilior fit manibus ad extre&shy;<lb/>ma diductis: quam ad medium propius accedentibus. </s>

<s id="id.001927">Et &longs;oluit &egrave; ra&shy;<lb/>dijs maioribus, &longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001928"><emph type="italics"/>Quant&ograve; quidque &agrave; centro fuerit remotius, tant&ograve; facilius moue&shy;<lb/>tur, &amp; quia fractio e&longs;t motio, frangitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001929"><emph type="italics"/>In fractione ligni cum manus &longs;unt in extremis, remotiores<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.161.jpg" pagenum="122"/><emph type="italics"/>&longs;unt &agrave; centro (quod e&longs;t genu cum ad hoc applicatum e&longs;t li&shy;<lb/>gnum: vel pes, cum ip&longs;um pede conculcatur) quam cum <lb/>non &longs;unt in extremis. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001930"><emph type="italics"/>Ergo fractio ligni manibus in extremis exi&longs;tentibus facilior fiet <lb/>quam &longs;i propius exi&longs;tant. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001931"><emph type="italics"/>Qu&aelig;ri autem hic pote&longs;t, an qui &longs;ic fu&longs;tem frangunt, genu non offen&shy;<lb/>dant. </s>

<s id="id.001932">Et non offendere experientia comprobat. </s>

<s id="id.001933">Ratio tamen non ita <lb/>aperta e&longs;t. </s>

<s id="id.001934">E&longs;t autem vt arbitror, quia genu vt centrum, vel hypo&shy;<lb/>mochlium quie&longs;cit: partes vero fu&longs;tis, vbi fit ruptio, exterius mouen&shy;<lb/>tur. </s>

<s id="id.001935">Itaque &agrave; genu di&longs;cedunt. </s>

<s id="id.001936">Ob eandem cau&longs;am cyphi duo vitrei <lb/>&aelig;quales, &amp; aqua pleni fu&longs;tem oblongum extremis &longs;uis &longs;uper impo&longs;i&shy;<lb/>tum adacto celeriter per medium altero fu&longs;te frangi ip&longs;i infracti &amp; <lb/>&longs;ine aqu&aelig; effu&longs;ione tolerant. </s>

<s id="id.001937">In hoc tamen differentia e&longs;t, quod cyphi <lb/>hypomochlium &longs;unt, it&aacute; que in extremis, &amp; partes &agrave; cyphis ad me&shy;<lb/>dium &longs;unt line&aelig; &agrave; centro, &longs;icque impul&longs;&aelig; mouentur. </s>

<s id="id.001938">Vt &amp; cum cru&shy;<lb/>ris arietini os nudatum perio&longs;tio, &amp; manus eo, qui ad pollicem e&longs;t <lb/>monticulo atque hypothenare &longs;u&longs;tentum dor&longs;i gladij ad medium ce&shy;<lb/>leriter adacti vno ictu &longs;ine manus offen&longs;ione frangitur, contr&agrave;, <lb/>quam in fu&longs;te &egrave; genu fracto. </s>

<s id="id.001939">H&aelig;c vulgaria &longs;unt, &longs;ed cau&longs;a non vti&shy;<lb/>que vulgaris. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001940"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001941">16. Cur croc&aelig; rotund&aelig;. </s></p><p type="main">

<s id="id.001942"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001943">Cur circa littora croc&aelig;, <lb/>vt vocantur, rotund&aelig; &longs;unt, <lb/>&egrave; magnis qui erant &agrave; prin&shy;<lb/>cipio lapidibus, &amp; o&longs;treis <lb/>fact&aelig;. </s>

<s id="id.001944">An quia in motibus <lb/>magis &agrave; medio di&longs;tantia ce&shy;<lb/>lerius <expan abbr="fer&utilde;tur">feruntur</expan>. </s>

<s id="id.001945">Etenim me&shy;<lb/>dium quidem fit centrum: <lb/><expan abbr="interuall&utilde;">interuallum</expan> vero linea ex <expan abbr="c&etilde;-tro">cen&shy;<lb/>tro</expan>. </s>

<s id="id.001946">Semper <expan abbr="aut&etilde;">autem</expan> maior ab <lb/><expan abbr="ead&etilde;">eadem</expan> motione <expan abbr="maior&etilde;">maiorem</expan> de&shy;<lb/>&longs;cribit <expan abbr="circul&utilde;">circulum</expan>. </s>

<s id="id.001947">Et quod e&longs;t <lb/>maius <expan abbr="&longs;pati&utilde;">&longs;patium</expan> &aelig;quali <expan abbr="t&etilde;pore">tempore</expan> <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.162.jpg" pagenum="123"/><foreign lang="greek"><gap/></foreign><lb/><expan abbr="tr&atilde;fiens">tranfiens</expan> celerius fertur. </s>

<s id="id.001948">La&shy;<lb/>ta vero celerius in &aelig;quali <lb/>&longs;patio, vehementius pul&shy;<lb/>&longs;ant. </s>

<s id="id.001949">Et magis pul&longs;antia <lb/>magis etiam percutiuntur. <lb/></s>

<s id="id.001950">Ita que nece&longs;&longs;e e&longs;t plus di&shy;<lb/>&longs;tantia &agrave; medio &longs;emper at&shy;<lb/>teri. </s>

<s id="id.001951">Et qu&aelig; id patiuntur, <lb/><expan abbr="rot&utilde;da">rotunda</expan> fieri. </s>

<s id="id.001952">Crocis autem <lb/>propter maris motum, cum <lb/>quo etiam mouentur, con&shy;<lb/>tingit in perpetua motione <lb/>e&longs;&longs;e, &amp; in conuolutione of&shy;<lb/>fen&longs;are, &amp; nece&longs;&longs;e e&longs;t pr&aelig;&shy;<lb/>cipu&egrave; id contingere earum <lb/>extremitatibus. </s></p><p type="head">

<s id="id.001953">COMMENTARIVS. </s></p><p type="main">

<s id="id.001954">Cvr circa.] <emph type="italics"/>Credibile e&longs;t duo lumina &longs;apienti&aelig;, &amp; virtutis, <lb/>Pub. Scipionem Africanum minorem, &amp; Caium L&aelig;lium cum <lb/>propter actuo&longs;am vitam animi remi&szlig;ioni aliquando acquie&longs;centes, <lb/>&amp; ruri feriantes ad Caietam portum Campani&aelig;, Lucrinumque la&shy;<lb/>cum conchas id e&longs;t duriores te&longs;tas <expan abbr="pi&longs;ci&utilde;">pi&longs;cium</expan>, vt purpur&aelig;, muricis, o&longs;treo&shy;<lb/>rum, &amp; vmbilicos id e&longs;t rotundos calculos in &longs;peciem no&longs;tri vmbi&shy;<emph.end type="italics"/><arrow.to.target n="marg29"/><lb/><emph type="italics"/>lici puerorum more colligerent (vt recen&longs;ent Cicero &amp; Valerius <lb/>maximus) qu&aelig;&longs;i&longs;&longs;eidem quod h&icirc; Ari&longs;toteles. </s>

<s id="id.001956">Cur &longs;cilicet vmbilici <lb/>illi (crocas Ari&longs;toteles appellat) rotundi &longs;int, cum antea e&longs;&longs;ent lapi&shy;<lb/>des maiu&longs;culi minime <expan abbr="rot&utilde;di">rotundi</expan>, &longs;ed angulati, vt &amp; partes concharum <lb/>o&longs;treorum in&aelig;quales &amp; a&longs;per&aelig;. </s>

<s id="id.001957">Quod problema licet &longs;peciale &longs;it de <lb/>crocis, generale tamen fieri pote&longs;t de omnibus non rotundis. </s>

<s id="id.001958">Et cau&longs;a <lb/>generalis e&longs;&longs;et hoc modo: qu&aelig;cunque non &longs;unt rotunda frequenti, &amp; <lb/>celeri, &amp; maiori conuer&longs;ione eminentis vt anguli atteruntur, pul&shy;<lb/>&longs;ant enim ea parte magis occurrentia qu&aelig;libet &longs;iue liquida, &longs;iue &longs;oli&shy;<lb/>da, &amp; vici&szlig;im pul&longs;antur ab occurrentibus: &longs;icque &longs;ublatis per attri&shy;<lb/>tionem eminentijs &amp; angulis rotundantur. <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.163.jpg" pagenum="124"/><arrow.to.target n="marg30"/></s></p><p type="margin">

<s id="id.001959"><margin.target id="marg29"/>Lib. 2. de <lb/>Orat. cap. 8. <lb/>lib. 8. </s></p><p type="margin">

<s id="id.001960"><margin.target id="marg30"/>Cap. 11. lib. <lb/>1. de v&longs;u <lb/>part. </s></p><p type="main">

<s id="id.001961">Itaque nece&longs;&longs;e e&longs;t.] <emph type="italics"/>Ex his collige verum e&longs;&longs;e illud quod e&longs;t <lb/>apud Galenum, &longs;olam figurarum rotundam ad vix patiendum ex&shy;<lb/>qui&longs;it&egrave; comparatam e&longs;&longs;e, vt qu&aelig; nullum expo&longs;itum angulum frangi <lb/>potentem habeat, id e&longs;t, vt ex hoc capite interpretor, nullam partem <lb/>exteriorem &agrave; medio alteram altera di&longs;tantiorem. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001962">Semper atteri.] <emph type="italics"/>Vt Gutta &longs;&aelig;pius cadendo lapidem immotum <lb/>cauat: &longs;ic aqua in vertiginem commotum atterit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001963">Gutta cauat lapidem, con&longs;umitur annulus v&longs;u. </s></p></chap><chap><p type="main">

<s id="id.001964"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001965">17. Cur ligna longiora &longs;unt <lb/>imbecilliora. </s></p><p type="main">

<s id="id.001966"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001967"><arrow.to.target n="marg31"/></s></p><p type="margin">

<s id="id.001968"><margin.target id="marg31"/>[bis <expan abbr="dict&utilde;]">dictum]</expan> <lb/>fruftra. </s></p><p type="main">

<s id="id.001969">Cur quant&ograve; ligna fue&shy;<lb/>rint longiora, tant&ograve; fiunt <lb/>imbecilliora, &amp; &longs;ublata <lb/>magis <expan abbr="curu&atilde;tur">curuantur</expan>, licet breue <lb/>&longs;it quod tenue, vt <expan abbr="bicubi-t&utilde;">bicubi&shy;<lb/>tum</expan>, &amp; quod centum cubito&shy;<lb/>rum, cra&longs;&longs;um, An quia ligni <lb/>longitudo, dum attollitur, <lb/>fit vectis, pondus, &amp; <expan abbr="hypo-mochli&utilde;">hypo&shy;<lb/>mochlium</expan>? </s>

<s id="id.001970">prima enim ip&longs;ius <lb/>pars, quam manus attollit, <lb/>fit vt hypomochlium: qu&aelig; <lb/>autem in extremo, vt pon&shy;<lb/>dus. </s>

<s id="id.001971">Itaque quant&ograve; di&longs;tite&shy;<lb/>rit magis ab hypomochlio: <lb/>tant&ograve; magis curuari nece&longs;&shy;<lb/>&longs;e e&longs;t. </s>

<s id="id.001972">Nece&longs;&longs;e igitur extre&shy;<lb/>ma vectis eleuari. </s>

<s id="id.001973">Si ver&ograve; <lb/>flexilis vectis fuerit, nece&longs;&shy;<lb/>&longs;e erit ip&longs;um magis inflecti <lb/>cum attollitur: quod &amp; li&shy;<lb/>gnis longis contingit. </s>

<s id="id.001974">At in <lb/>breuibus <expan abbr="extrem&utilde;">extremum</expan> fit vici&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.164.jpg" pagenum="125"/><foreign lang="greek"><gap/></foreign><lb/>num hypomochlio quie&longs;&shy;<lb/>centi. </s></p><p type="head">

<s id="id.001975">COMMENTARIVS. </s></p><p type="main">

<s id="id.001976">Cvr quant&ograve;.] <emph type="italics"/>In exercitu &longs;&aelig;pe milites dum feriantur roboris <lb/>experiundi, vel exercendi gratia longas ha&longs;tas humi iacentes <lb/>vna manu, aut vtraque in alterum extremorum iniecta &amp; compre&shy;<lb/>hendente nituntur attollere, quou&longs;que perpendiculares fiant plano <lb/>horizontis: qua in &longs;ublatione videre licet ha&longs;tas illas longas vt cra&longs;&shy;<lb/>&longs;iores &longs;int, inflecti tamen magis medio &longs;ublationis tempore: quam <lb/>breues, licet tenuiores &longs;int. </s>

<s id="id.001977">Qu&aelig;rit igitur h&icirc; Ari&longs;toteles non &longs;olum <lb/>cur &longs;ic fiat, non in his tantum: &longs;ed &amp; in omnibus flexilibus. </s>

<s id="id.001978">Cau&longs;am <lb/>repetit ex eo quod flexilia illa &longs;int vectis, <expan abbr="p&otilde;dus">pondus</expan>, &amp; hypomochlium, <lb/>non eadem parte tamen: &longs;ed diuer&longs;is. </s>

<s id="id.001979">In extremo enim manu compre&shy;<lb/>hen&longs;o e&longs;t hypomochlium. </s>

<s id="id.001980">In altero e&longs;t pondus. </s>

<s id="id.001981">Longitudo vero inter <lb/>media e&longs;t vectis. </s>

<s id="id.001982">Ratio itaque &longs;ic di&longs;ponetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001983"><emph type="italics"/>Pondus qu&ograve; magis di&longs;titerit ab hypomochlio, e&ograve; magis vectem, <lb/>&longs;i flexilis e&longs;t, incuruat, dum attollitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001984"><emph type="italics"/>In longis lignis, vt flexilibus, pondus magis di&longs;tat ab hypo&shy;<lb/>mochlio: extremum &longs;cilicet ab extremo: quam in breuibus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001985"><emph type="italics"/>Ligna igitur longa magis incuruabuntur: quam breuia, dum &longs;ic <lb/>attolluntur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.001986"><emph type="italics"/>Sed &amp; ligna medio &longs;ui comprehen&longs;a, &amp; &longs;ic eleuata &longs;emper quo lon&shy;<lb/>giora, eo magis incuruabuntur. </s>

<s id="id.001987">At tunc hypomochlium erit in me&shy;<lb/>dio. </s>

<s id="id.001988">Pondera duo erunt in extremis. </s>

<s id="id.001989">Curuari autem magis imbecilli&shy;<lb/>tatis e&longs;t. </s>

<s id="id.001990">Curuatio enim &agrave; fractura non differt, ni&longs;i &longs;ecundum magis <lb/>&amp; minus. </s>

<s id="id.001991">Si plus enim curuatur: quam vnitas partium ferat, &longs;olui&shy;<lb/>tur continuum, &amp; &longs;ic frangitur. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.001992"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001993">18. Cau&longs;a pote&longs;tatis <lb/>cunei. </s></p><p type="main">

<s id="id.001994"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.001995">Cur &agrave; cuneo re parua ma&shy;<lb/>gn&aelig; moles, &amp; <expan abbr="corpor&utilde;">corporum</expan> ma&shy;<lb/>gnitudines <expan abbr="diuid&utilde;tur">diuiduntur</expan>, im&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.165.jpg" pagenum="126"/><foreign lang="greek"><gap/></foreign><lb/>pre&longs;&longs;ioque valida efficitur. <lb/></s>

<s id="id.001996">An quia cuneus vectes duo <lb/>&longs;unt &longs;ibi inuicem <expan abbr="c&otilde;trarij">contrarij</expan>, <lb/>vterque ver&ograve; habet &amp; pon&shy;<lb/>dus, &amp; <expan abbr="hypomochli&utilde;">hypomochlium</expan>, quod <lb/>diuellit, vel <expan abbr="c&otilde;primit">comprimit</expan>. </s>

<s id="id.001997">Pr&aelig;&shy;<lb/>terea percu&longs;&longs;io <expan abbr="p&otilde;dus">pondus</expan> quod <lb/>percutit, &amp; mouet <expan abbr="magn&utilde;">magnum</expan> <lb/>facit, &amp; quia motum mo&shy;<lb/>uet celeritate valentius e&longs;t. <lb/></s>

<s id="id.001998">Paruo vero exi&longs;tente vecte <lb/>magn&aelig; vires con&longs;equun&shy;<lb/>tur, ide&ograve; mouens latet pr&aelig;&shy;<lb/>ratione magnitudinis. </s></p><figure id="id.035.01.165.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.165.1.jpg"/><p type="main">

<s id="id.001999">E&longs;to cuneus vbi e&longs;t <foreign lang="greek">a b <lb/>g,</foreign> quod vero cuneo fin&shy;<lb/>ditur <foreign lang="greek">d n z.</foreign> </s>

<s>Vectis itaque <lb/>fiet <foreign lang="greek">a b,</foreign> pondus vero ip&longs;ius <lb/><foreign lang="greek">b</foreign> inferior pars: hypo&shy;<lb/>mochlium autem <foreign lang="greek">m &amp; n,</foreign><lb/>huic vero contrarius ve&shy;<lb/>ctis <foreign lang="greek">b g,</foreign> tum pars <foreign lang="greek">a g</foreign> per&shy;<lb/>cu&longs;&longs;a. </s>

<s id="id.002000"><expan abbr="vtroq;">vtroque</expan> illorum vecte vtitur. </s>

<s id="id.002001">diuellit enim ip&longs;um <foreign lang="greek">b. </foreign></s></p><p type="head">

<s id="id.002002">COMMENTARIVS. </s></p><p type="main">

<s id="id.002003">Cau&longs;a pote&longs;tatis cunei.] <emph type="italics"/>Cuneus e&longs;t in&longs;trumentum ex ma&shy;<lb/>teria firma in&longs;tar pyramidis &agrave; ba&longs;i lata in angu&longs;tum fa&longs;tigia&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.166.jpg" pagenum="127"/><figure id="id.035.01.166.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.166.1.jpg"/><lb/><emph type="italics"/>tum. </s>

<s id="id.002004">Vt A B C D E F. </s>

<s id="id.002005">In <lb/>hac forma duo con&longs;ideranda &longs;unt, <lb/>alterum e&longs;t ex amplitudine ba&longs;is, <lb/>qua cuneus ad &longs;u&longs;cipiendam &longs;u&longs;ti&shy;<lb/>nendamque percu&szlig;ionem apti&szlig;i&shy;<lb/>mus e&longs;t: alterum e&longs;t ex vertice acu&shy;<lb/>to, qui ob id facile intr&agrave; corpora penetrans &longs;ibi viam facit. </s>

<s id="id.002006">V&longs;us <lb/>eius e&longs;t ad magnos arborum truncos diuidendum, quod fit magna <lb/>cum facilitate <expan abbr="eti&atilde;">etiam</expan> &agrave; puero, beneficio ip&longs;ius cunei per rimulam prim&ograve; <lb/>factam, qua parte acutior e&longs;t, immi&longs;si &amp; qua parte oppo&longs;ita latior <lb/>e&longs;t &agrave; malleo percu&longs;si, quod &agrave; Milone licet athleta robu&longs;ti&longs;simo per &longs;e <lb/>fieri non potuit. </s>

<s id="id.002007">Hic enim cum aliquando conspiceret adole&longs;centem <lb/>cuneis immi&szlig;is findentem arbores, fertur &longs;ubri&longs;i&longs;&longs;e &amp; &longs;ubmoui&longs;&longs;e. <lb/></s>

<s id="id.002008">Tum non alio vtens in&longs;trumento, quam &longs;uis manibus au&longs;us e&longs;t trun&shy;<lb/>cum diducere. </s>

<s id="id.002009">Mox quicquid habebat roboris in primo impetu colli&shy;<lb/>gens, diduxit h&ucirc;c atque ill&ucirc;c partes, interim elap&longs;is cuneis, quoniam <lb/>reliquam arboris partem diducere non po&longs;&longs;et, di&ugrave; quidem obnixus e&longs;t, <lb/>tandem victus educere non potuit: &longs;ed ab arboris partibus in &longs;e&longs;e cele&shy;<lb/>riter co&euml;untibus comprehen&longs;&aelig;, primum quidem ip&longs;&aelig; contrit&aelig; &longs;unt, <lb/>mox &amp; ip&longs;i mi&longs;erandi exitij fuere cau&longs;a, vt refert Galenus in lib. de <lb/>exhort. ad bonas artes. </s>

<s id="id.002011">Hic e&longs;t de quo Iuuenalis,<emph.end type="italics"/></s></p><p type="main">

<s id="id.002012">Viribus ille</s></p><p type="main">

<s id="id.002013">Confi&longs;us perijt. </s></p><p type="main">

<s id="id.002014">Cur &agrave; cuneo.] <emph type="italics"/>Antea vectis con&longs;ideratus e&longs;t generaliter, dein&shy;<lb/>de &longs;pecialiter: &longs;ed &longs;implex vt in remo, gubernaculo, malo, collope: <lb/>nunc etiam idem &longs;pecialiter con&longs;ideratur, &longs;ed multiplex. </s>

<s id="id.002015">Et primum <lb/>quidem duplicatus, vt in cuneo. </s>

<s id="id.002016">Nam hic quod paruus exi&longs;tens ma&shy;<lb/>gnos arborum truncos penetrando diuidat, non aliunde habet quam <lb/>quia duplex e&longs;t vectis, &amp; &agrave; percu&longs;sione motus. </s>

<s id="id.002017">Ex hoc enim quod ve&shy;<lb/>ctis facile mouet. </s>

<s id="id.002018">Ex hoc quod e&longs;t duo vectes, cum hi ex aduer&longs;o &longs;ibi <lb/>inuicem contrarij &longs;int, &amp; mutuas operas &longs;ibi tradant, magis &amp; faci&shy;<lb/>lius mouet. </s>

<s id="id.002019">Ex hoc quod &agrave; percu&longs;sione, eaque celeri, qu&aelig; motus e&longs;t, ma&shy;<lb/>gis adhuc mouetur: &longs;icque &agrave; tribus ijs coniunctis effectus &agrave; cuneo ad&shy;<lb/>mirandi prodeuntis habetur cau&longs;a. </s>

<s id="id.002020">Notandum autem quod inter <lb/>cuneos, qui angulum ad verticem <expan abbr="acutior&etilde;">acutiorem</expan> habet facilius mouet, ac <lb/>&longs;cindit: quam qui obtu&longs;iorem. </s>

<s id="id.002021">Mouetur enim cuneus anguli maioris <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.167.jpg" pagenum="128"/><emph type="italics"/>per maius &longs;patium, quam minoris, &longs;iquidem maioris anguli maior e&longs;t <lb/>&longs;ubten&longs;a, cum anguli &longs;unt &aelig;quicruri prop. 26. lib. 1. </s>

<s>A potentia ver&ograve; <lb/>facilius eodem tempore mouetur aliquid per minus &longs;patium: quam <lb/>per maius cum c&aelig;tera paria &longs;unt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002022">An quia.] <emph type="italics"/>Prior cau&longs;a e&longs;t ad &longs;olutionem problematis, qu&aelig; hoc <lb/>&longs;yllogi&longs;mo concludetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002023"><emph type="italics"/>Duo vectes &longs;imul iuncti multum mouent, &amp; magnas moles <lb/>di&longs;trahunt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002024"><emph type="italics"/>Cuneus e&longs;t duo vectes, ijque &longs;ibi inuicem contrarij: &longs;ed <lb/>iuncti. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002025"><emph type="italics"/>Cuneus igitur multum mouet, &amp; magnas moles di&longs;trahet. <lb/></s>

<s id="id.002026">Syllogi&longs;mi propo&longs;itio confirmationem non habet: &longs;ed h&aelig;c repeti po&shy;<lb/>te&longs;t ex vnius vectis potentia ante&agrave; confirmata, qu&aelig; in duobus igitur <lb/>iunctis maior erit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002027">Vterque ver&ograve; habet.] <emph type="italics"/>Confirmatio e&longs;t a&longs;&longs;umptionis. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002028"><emph type="italics"/>Vbi e&longs;t longitudo duplex, hypomochlia duo, &amp; pondus, ibi &longs;unt <lb/>duo vectes. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002029"><emph type="italics"/>In cuneo e&longs;t vtrinque longitudo, labra rim&aelig; quam ingredi&shy;<lb/>tur cuneus, &longs;unt hypomochlia: truncus findendus e&longs;t <lb/>pondus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002030"><emph type="italics"/>E&longs;t igitur cuneus duo vectes. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002031">Pr&aelig;terea percu&longs;&longs;io.] <emph type="italics"/>Secunda e&longs;t cau&longs;a ad &longs;olutionem proble&shy;<lb/>matis, quod cuneus adigatur non &longs;implici pul&longs;u: &longs;ed percu&longs;&longs;u, qui ve&shy;<lb/>hemens &amp; celer e&longs;t motus: iam motum autem mouendum vehemen&shy;<lb/>tius mouet. </s>

<s id="id.002032">Percu&szlig;io autem duobus fit modis, vel ex eo ip&longs;o &longs;olo quod <lb/>percutit tanquam graui e loco &longs;uperiori deor&longs;um incidente: at que hoc <lb/>qu&ograve; grauius e&longs;t, e&ograve; maior fit percu&szlig;io: quin &amp; qu&ograve; longius di&longs;titerit <lb/>primum incidens, magis percutit. </s>

<s id="id.002033">Graue enim vnumquodque dum <lb/>mouetur grauitatis magis a&longs;&longs;umit motum: quam quie&longs;cens: &amp; adhuc <lb/>magis quo longius mouet. </s>

<s id="id.002034">quilibet enim a&euml;r addit &longs;uper motum iam <lb/>acqui&longs;itum. </s>

<s id="id.002035">Inde ca&longs;us lapidis aut ictus ab altiore loco grauius per&shy;<lb/>cutit: vel ex eo quidem quod percutit, &longs;ed recto atque moto, ab aliqua <lb/>potentia percutiente, vt &longs;i per manubrium mallei, quod vna vel du&aelig; <lb/>manus moueant. </s>

<s id="id.002036">Certum e&longs;t quod qu&ograve; grauior erit malleus, &amp; qu&ograve; <lb/>longius manubrium, e&ograve; maior fiet percu&longs;sio, vt ex pr&aelig;cedentibus &longs;atis <lb/>patere pote&longs;t, cum malleus tanquam pondus &agrave; centro, quod e&longs;t in ma&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.168.jpg" pagenum="129"/><emph type="italics"/>nubrio, vbi manus ip&longs;um comprehendunt, plus di&longs;tet. </s>

<s id="id.002037">Pr&aelig;terea cer&shy;<lb/>tum e&longs;t quod quant&ograve; potentia percutiens validior e&longs;t, validiori tant&ograve; <lb/>impellet pul&longs;u. </s>

<s id="id.002038">his adde quod e&longs;t ab Hippocrate<emph.end type="italics"/> <foreign lang="greek">e)n toi=s trw/masi</foreign><lb/><emph type="italics"/>annotatum. </s>

<s id="id.002039">Quant&ograve; impul&longs;us magis fiet<emph.end type="italics"/> <foreign lang="greek">kat' i)/cin</foreign> <emph type="italics"/>&egrave; directo, id e&longs;t vt <lb/>interpretor &egrave; perpendiculari. </s>

<s id="id.002040">C&aelig;terum percu&szlig;ionem vim habere ad <lb/>mouendum validi&szlig;imam docebit Ari&longs;toteles prob. 19. huius libri: <lb/>&longs;ed ex multis colligere id ita e&longs;&longs;e po&longs;&longs;umus. </s>

<s id="id.002042">Primum quod licet cuneo <lb/>ba&longs;i &longs;ua &longs;uper plano in&longs;i&longs;tenti, pondus alioqui valde ingens impona&shy;<lb/>tur, ip&longs;um non diuidet, aut par&ugrave;m, &longs;i ad diui&longs;ionem percu&szlig;ione fa&shy;<lb/>ctam compares. </s>

<s id="id.002043">Secundum &longs;i cuneo vel vectis vel cochlea vel aliud <lb/>aliquod in&longs;trumentum aptetur, vt ip&longs;e intimius propellatur, effectus <lb/>inde con&longs;equens parui erit momenti,<emph.end type="italics"/><lb/><figure id="id.035.01.168.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.168.1.jpg"/><lb/><emph type="italics"/>re&longs;pectu eius, qui &agrave; percu&szlig;ione pro&shy;<lb/>fici&longs;citur. </s>

<s id="id.002044">Guidus Vbaldus commo&shy;<lb/>de hoc adfert exemplum. </s>

<s id="id.002045">Sit A cor&shy;<lb/>pus lapideum ex quo angulus &longs;olidus <lb/>B &longs;it auferendus, mallei ferrei per&shy;<lb/>cu&longs;&longs;u facile id fit, &longs;ine percu&longs;&longs;u, nec <lb/>cum hoc, nec cum alio quouis in&longs;tru&shy;<lb/>mento, ni&longs;i cum maxima difficulta&shy;<lb/>te fieri poterit. </s>

<s id="id.002046">Percu&longs;sio igitur cau&longs;a e&longs;t, cur magna &longs;cindantur <lb/>pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002047">Paruo ver&ograve;.] <emph type="italics"/>Occurrit obiectioni, qu&aelig; fit propter exiguitatem <lb/>cunei, ob idque &amp; vectis, &longs;ed hanc dicit compen&longs;ari vehementia &amp; <lb/>celeritate percu&longs;sionis, &amp; quanquam ratione motus, motor exiguus <lb/>videatur, &amp; ita lateat, magnus e&longs;t tamen viribus. </s>

<s id="id.002048">Sic in rebus natu&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg32"/><lb/><emph type="italics"/>ralibus, vt e&longs;t apud Galenum, paru&aelig; molis res qu&aelig;dam &longs;olo tactu, <lb/>qu&aelig;dam exiguo mor&longs;u maximas corporibus inducunt alterationes. <lb/></s>

<s id="id.002049">Id quod in heraclio lapide, quem <expan abbr="magnet&etilde;">magnetem</expan> nominant, videre e&longs;t, fer&shy;<lb/>rum enim quod tetigerit, ei adh&aelig;ret vel nullo adhibito vinculo: dein&shy;<lb/>de &longs;i aliud id, quod primo tactum fuerit, tetigerit, &longs;imiliter vt pri&shy;<lb/>mum, illi inh&aelig;rebit, po&longs;tea tertium &longs;ecundo. </s>

<s id="id.002050">Pr&aelig;terea &agrave; Phalangij <lb/>ictu totum corpus affici videtur exiguo veneno per foramen iniecto: <lb/>&longs;ed long&egrave; maiori admiratione dignus e&longs;t Scorpionis ictus, qui breui <lb/>admodum tempore graui&szlig;ima infert accidentia. </s>

<s id="id.002051">H&aelig;c Galenus qu&aelig; <lb/>ideo attuli, vt intelligant mor&longs;us ab animalium dentibus inci&longs;orijs <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.169.jpg" pagenum="130"/><emph type="italics"/>maxillarum impetu adactis in rem mor&longs;am vt pondus diuidendum, <lb/>tanquam &agrave; cuneis e&longs;&longs;e factos, vt &amp; vulnera ab en&longs;ibus, ha&longs;tis, dola&shy;<lb/>bris, &longs;ecuribus &amp; id genus in&longs;trumentis. </s>

<s id="id.002052">Serra quoque &amp; lima ad <lb/>hoc genus, qu&ograve;d ad &longs;uos denticulos &longs;pectat reduci pote&longs;t, quot enim <lb/>denticuli tot cunei, &amp; ij alligati, aut continui &longs;uo vecti, id e&longs;t, manu&shy;<lb/>brio, quod pro vt longius, vel breuius e&longs;t, ita maiorem vim impul&longs;us <lb/>aut tractus obtinet. <emph.end type="italics"/></s></p><p type="margin">

<s id="id.002053"><margin.target id="marg32"/>Lib. 5. de <lb/>loc. aff. </s></p><p type="main">

<s id="id.002054">E&longs;to cuneus.] <emph type="italics"/>H&icirc;c e&longs;t demon&longs;tratio linearis ad ostenden&shy;<lb/>dum cuneum diuidendo ponderi duorum vectium vicem pror&longs;us ge&shy;<lb/>rere, eorumque &longs;ibi inuicem contrariorum. </s>

<s id="id.002055">Sed hanc &longs;ic paul&ograve; am&shy;<lb/>plius &amp; apertius repetemus. </s>

<s id="id.002056">Sit cuneus A B C cuius vertex B: <lb/>&amp; &longs;it A B &aelig;qualis B C, <lb/>quod autem diuidendum<emph.end type="italics"/><lb/><figure id="id.035.01.169.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.169.1.jpg"/><lb/><emph type="italics"/>e&longs;t, &longs;it D E F G, &longs;itque <lb/>pars cunei H B K intra <lb/>D E F G, &amp; H B &longs;it <lb/>&aelig;qualis ip&longs;i B K. </s>

<s>percu&shy;<lb/>tiatur vt fieri &longs;olet cuneus <lb/>in A C. </s>

<s id="id.002057">Dum cuneus in <lb/>A C percutitur, A B fit <lb/>vectis, cuius hypomoch&shy;<lb/>lium e&longs;t H, &amp; pondus in <lb/>B, eodemque modo C B <lb/>fit vectis, cuius hypomo&shy;<lb/>chlium e&longs;t K, &amp; pondus &longs;imiliter in B. </s>

<s id="id.002058">Sed dum percutitur cuneus <lb/>maiori adhuc ip&longs;ius portione, intra ip&longs;um D E F G ingreditur, <lb/>quam prius e&longs;&longs;et: &longs;it autem portio h&aelig;c M B L, &longs;itque M B ip&longs;i <lb/>B L &aelig;qualis. </s>

<s id="id.002059">Et cum M B, B L &longs;int ip&longs;is H B, B K maiores: <lb/>erit M L maior H K. </s>

<s id="id.002060">Dum igitur M L erit in &longs;itu H K, opor&shy;<lb/>tet vt fiat maior diui&longs;io, &amp; D moueatur ver&longs;us O: G autem ver&shy;<lb/>&longs;us N, &amp; qu&ograve; maior pars cunei intra D E F G ingredietur, e&ograve; <lb/>maior fiet diui&longs;io: &amp; D, G magis adhuc impellentur ver&longs;us O, <lb/>N. </s>

<s id="id.002061">Pars igitur K G eius quod diuiditur mouebitur &agrave; vecte A B, <lb/>cuius hypomochlium e&longs;t H, &amp; pondus in B, ita vt punctum B <lb/>ip&longs;ius vectis A B impellat partem k G: &amp; pars H D mouebi&shy;<lb/>tur &agrave; vecte C B, cuius hypomochlium e&longs;t k, ita vt B vecte C B <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.170.jpg" pagenum="131"/><emph type="italics"/>partem H D impellat. </s>

<s id="id.002062">Atque h&aelig;c e&longs;t &longs;ententia Ari&longs;totelis de du&shy;<lb/>plici vecte in cuneo. </s>

<s id="id.002063">Aliam habet Guidus Vbaldus, quam exi&longs;timat <lb/>meliorem. </s>

<s id="id.002064">E&longs;t autem eiu&longs;modi, vt figur&aelig; iam po&longs;it&aelig; vectis A B <lb/>habeat hypomochlium B, &amp; pondus mouendum H, &longs;icut vectis <lb/>C B, habeat item hypomochlium B &amp; pondus mouendum &longs;it K: it a <lb/>vt pars H D moueatur &agrave; vecte A B, &amp; pars k G &agrave; vecte C B. <lb/></s>

<s id="id.002065">Ratio e&longs;t, quia in&longs;trumenta mouent per contactum: vectis autem A <lb/>B tangit partem H D motam in H, non &longs;imiliter tangit in B. <lb/></s>

<s id="id.002066">Id ip&longs;um in&longs;uper comprobat ex cuneo inter duas moles &longs;eparatas in&shy;<lb/>terpo&longs;ito: &longs;ed quod pace tanti viri dixerim certum e&longs;t, quod ni&longs;i B <lb/>vertex cunei tangeret molem in B, &amp; ip&longs;am impelleret atque diui&shy;<lb/>deret, partes H D, K G non vtrinque cederent in O &amp; N. </s>

<s id="id.002067">Quod <lb/>igitur cedant motus is &longs;ecundarius e&longs;t, &amp; priorem qui e&longs;t in B con&shy;<lb/>&longs;equens. </s>

<s id="id.002068">Quod autem ad moles &longs;eparatas attinet, in his a&euml;r pondus e&longs;t <lb/>mouendum, quem &longs;i nequaquam cedere fingamus, non vltra ingre&shy;<lb/>diente cuneo, partes molium inter quas erit cuneus con&longs;i&longs;tent. </s>

<s id="id.002069">C&aelig;te&shy;<lb/>rum vt cuneus vectis e&longs;t multiplicatus: ita cochlea, cuius nullam <lb/><expan abbr="mention&etilde;">mentionem</expan> feci&longs;&longs;e <expan abbr="Ari&longs;totel&etilde;">Ari&longs;totelem</expan> totis his mechanicis miror, <expan abbr="c&umacr;">cum</expan> &longs;it cuneus <lb/>multiplicatus, vel vnus continuatus. </s>

<s id="id.002070">E&longs;t enim cochlea (vt de hac <lb/>pauca qu&aelig; ex Pappo, Vbaldo, Mun&longs;tero &longs;elegimus, dicamus) cuneus <lb/>cylindro circumuolutus helicis in&longs;tar, percu&szlig;ionis quidem expers, <lb/>&longs;ed per vectem cylindri axi annexum ver&longs;us, faciens motionem ma&shy;<lb/>gnorum ponderum. </s>

<s id="id.002071">Quod vt intelligatur. </s>

<s id="id.002072">Sit cuneus A B C circa<emph.end type="italics"/></s></p><figure id="id.035.01.170.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.170.1.jpg"/><p type="caption">

<s id="id.002073">Cochlea &longs;ine matrice. <lb/></s></p>

<p type="main"><s><emph type="italics"/>cylindrum D E, qui &longs;ine <expan abbr="impedim&etilde;to">impedimento</expan> verti po&szlig;it per vectem K F <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.171.jpg" pagenum="132"/><emph type="italics"/>cylindri axi an&shy;<emph.end type="italics"/></s></p><figure id="id.035.01.171.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.171.1.jpg"/><p type="caption">

<s id="id.002074">Cochlea cum matrice. <lb/></s></p><p type="main">

<s><emph type="italics"/>nexum: pondus <lb/>mouendum &longs;it <lb/>L M N O ex <lb/>parte M N im&shy;<lb/>mobile, vt in <lb/>his qu&aelig; <expan abbr="&longs;cind&umacr;-tur">&longs;cindun&shy;<lb/>tur</expan>, fieri &longs;olet: <lb/>cunei vero vertex A &longs;it intra rimam R S. </s>

<s id="id.002075">Itaque facile e&longs;t videre <lb/>quod dum K F circumuer&longs;us erit vbi K P, vertex A non erit <lb/>amplius intra R S: &longs;ed cunei pars alia vt T V: qu&aelig; cum maior <lb/>&longs;it, quam R S. </s>

<s id="id.002076">E&longs;t enim pars qu&aelig;que cunei remotior &agrave; vertice, latior <lb/>propinquiore: ergo vt T V &longs;it intra K S, oportet vt R cedat, mo&shy;<lb/>ueaturque ver&longs;us X, &amp; S ver&longs;us E vt faciunt ea qu&aelig; &longs;cindun&shy;<lb/>tur. </s>

<s id="id.002077">Totum ergo L M N O &longs;cindetur. </s>

<s id="id.002078">Nam dum rur&longs;us vectis K <lb/>P peruenerit ad K Q, tunc B C erit intra R S, erit R &longs;iquidem <lb/>in X &amp; S in E, vt X E &longs;it &aelig;qualis B C: &longs;emperque conti&shy;<lb/>nuato cuneo progredienteque A vertice vltr&agrave;, pondus L M N O, <lb/>&longs;cindetur, vel pondus G mobile impelletur, attrahetur, attolletur,<emph.end type="italics"/><lb/><figure id="id.035.01.171.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.171.2.jpg"/><lb/><emph type="italics"/>prout cylindrus cochle&aelig; po&longs;itus erit ad planum horizontis cum &longs;ua, <lb/>vel &longs;ine f&oelig;mina &longs;eu matrice. </s>

<s id="id.002079">Quod &longs;i rur&longs;us cochle&aelig; <expan abbr="tympan&utilde;">tympanum</expan> rect&egrave; <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.172.jpg" pagenum="133"/><emph type="italics"/>vel obliqu&egrave; denticulatum, ita vt helici facil&egrave; congruat, aptetur: ma&shy;<lb/>nife&longs;tum e&longs;t, quod ad motum cochle&aelig; etiam tympani C dentes &longs;uper <lb/>helicem cochle&aelig; ad infinitum <expan abbr="circumuert&etilde;tur">circumuertentur</expan>. </s>

<s id="id.002080">Vnde h&aelig;c cochlea di&shy;<lb/>citur infinita, id e&longs;t tandiu vertetur, quandiu quis volet. </s>

<s id="id.002081">Eodem enim <lb/>modo &longs;emper &longs;e habebit tympanum ad cochleam. </s>

<s id="id.002082">Porr&ograve; cochle&aelig; vi <lb/>&amp; beneficio admirabile cert&egrave; quanta pondera moueantur. </s>

<s id="id.002083">Refert <emph.end type="italics"/><lb/><arrow.to.target n="marg33"/><lb/><emph type="italics"/>Mun&longs;terus Ba&longs;ile&aelig; &longs;e vidi&longs;&longs;e longi&szlig;imas &longs;udes pr&aelig;acutis ferreis ro&shy;<lb/>&longs;tris munitas olim in fundum profundi&longs;sim&egrave; actas auelli. </s>

<s id="id.002084">Quinetiam <lb/>aliquando integras domos ex lignis compaginatas in &longs;ublime &longs;uble&shy;<lb/>uari &amp; cylindris aliquot &longs;ubmi&longs;sis ali&ograve; deferri: &longs;ed &amp; homi&nacute;um <lb/>v&longs;u propemodum immen&longs;o quotidie experimur, quantum valeat <lb/>torquendo &amp; premendo, dum vinum, oleum, &longs;uccos quo&longs;libet &agrave; <lb/>&longs;uis fructibus exprimimus, &amp; hone&longs;tam v&longs;uram dominis &longs;uis <lb/>per&longs;oluere cogimus, ita ad vltimum quadrantem v&longs;que, vt &agrave; pu&shy;<lb/>mice po&longs;tea aquam citius extrahas: quam &agrave; f&aelig;cibus reliquis &longs;uc&shy;<lb/>cum aliquem. </s>

<s id="id.002085">Immo ver&ograve;, qu&aelig; laudari nunquam &longs;atis pote&longs;t, &longs;ine <lb/>cochlea ars Typographica quid e&longs;&longs;e po&longs;&longs;et, Duo autem efficiunt vt <lb/>cochlea tanta po&longs;sit. </s>

<s id="id.002086">Primum quia e&longs;t helix circa cochleam, qu&aelig; qu&ograve; <lb/>e&longs;t vertex cunei acutioris, e&ograve; facilius: &longs;ed tardius mouet. </s>

<s id="id.002087">Alterum <lb/>quia e&longs;t vectis, quo cochlea circumuertitur, qui etiam qu&ograve; longior, e&ograve; <lb/>facilius: &longs;ed etiam tardius mouet. <emph.end type="italics"/></s></p><p type="margin">

<s id="id.002088"><margin.target id="marg33"/>Lib 1. Rud. <lb/>Math. </s></p></chap><chap><p type="main">

<s id="id.002089"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002090">19. Detrochleis. </s></p><p type="main">

<s id="id.002091"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002092">Quare &longs;i quis in duobus <lb/>tignis inter &longs;e <expan abbr="i&utilde;ctis&egrave;">iunctis&egrave;</expan> <expan abbr="c&otilde;tra-rio">contra&shy;<lb/>rio</expan> duas trochleas <expan abbr="c&otilde;pon&etilde;s">componens</expan> <lb/>ip&longs;is in circulo circum du&shy;<lb/>xerit funiculum, qui lorum <lb/>qu&ograve;d &longs;u&longs;pendatur ex altero <lb/>tignorum, &amp; alterum inni&shy;<lb/>tatur, aut appo&longs;itum &longs;it ad <lb/>trochleas, atque initium <lb/>funiculi traxerit, vt parua <lb/>vi trahat, magna tamen <lb/>pondera adducet. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.173.jpg" pagenum="134"/><p type="head">

<s id="id.002093">COMMENTARIVS. </s></p><p type="main">

<s id="id.002094">De trochleis.] <emph type="italics"/>Trochlea e&longs;t in&longs;trumentum vno aut pluribus <lb/>orbiculis circa &longs;uos axiculos mobilibus &amp; fune ductario con&shy;<lb/>&longs;tans ad trahendum, &amp; attollendum onera aptum. </s>

<s id="id.002095">Geminatur ali&shy;<lb/>quando, triplicatur, &amp; amplius multiplicatur. </s>

<s id="id.002096">Si duobus orbiculis <lb/>con&longs;ter<emph.end type="italics"/> <foreign lang="greek">di/spastos,</foreign> <emph type="italics"/>&longs;i tribus<emph.end type="italics"/> <foreign lang="greek">tri/spastos,</foreign> <emph type="italics"/>&longs;i quinque<emph.end type="italics"/> <foreign lang="greek">pente/spastos,</foreign> <emph type="italics"/>&longs;i plu&shy;<lb/>ribus<emph.end type="italics"/> <foreign lang="greek">polu/spastos</foreign> <emph type="italics"/>dicitur, ex quo &longs;unt illa tractoria in&longs;trumenta in&shy;<lb/>finitarum prope modum virium. </s>

<s id="id.002097">vt in quibus orbiculi plures &longs;ibi in&shy;<lb/>uicem &longs;ub&longs;eruientes, &amp; tanquam onus attrahendum diuidentes, &longs;um&shy;<lb/>ma facilitate ip&longs;um attrahunt. </s>

<s id="id.002098">Notandum etiam &longs;olum orbiculum <lb/>etiam aliquando trochleam appellari, &amp; ad v&longs;um vnam aliquando <lb/>trochleam, aliquando duas &amp; plures v&longs;urpari, quod vbi fit, &longs;i in vna <lb/>trochlea &longs;int plures orbiculi inferioris trochle&aelig; orbiculus &longs;uperior <lb/>debet &longs;emper e&longs;&longs;e minor inferiore: vt &amp; &longs;uperioris inferior, ne funes <lb/>ductarij inter &longs;e inuicem complicentur &amp; &longs;ibi ob&longs;int. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002099">Quare &longs;i quis.] <emph type="italics"/>Problema de trochleis cur duabus magna one&shy;<lb/>ra parua vi trahuntur, proponitur, apert&egrave; quidem, ni&longs;i vbi de alliga&shy;<lb/>tione ip&longs;arum agitur. </s>

<s id="id.002100">Tota enim particula contextus huius<emph.end type="italics"/> <foreign lang="greek">e)/xon to\ <lb/>a)/rthma e)k qate/rou tw=n cu/lwn, qa/teron de\ h)= proserhreime/non h)\ pro&shy;<lb/>steqeime/non kata\ ta\s troxali/as,</foreign> <emph type="italics"/>mendo&longs;a meo iudicio e&longs;t. </s>

<s id="id.002101">Quid enim <lb/>e&longs;t habere lorum quod dependeat, ab altero tignorum: alterum vero <lb/>e&longs;&longs;e infixum, &amp; appo&longs;itum ad trochleas, quid e&longs;t illud alterum, quod <lb/>dicitur infigi, &amp; apponi <emph.end type="italics"/><lb/><figure id="id.035.01.173.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.173.1.jpg"/><lb/><emph type="italics"/>ad trochleas, intelligi cert&egrave; <lb/>non pote&longs;t. </s>

<s id="id.002102">Si igitur quid <lb/>rei natura, &amp; v&longs;us o&longs;ten&shy;<lb/>dat, ponamus: illam parti&shy;<lb/>culam &longs;ic <expan abbr="c&otilde;mutabimus">commutabimus</expan>, <lb/>vt dicamus vnam &egrave; dua&shy;<lb/>bus trochleis habere <expan abbr="lor&utilde;">lorum</expan>, <lb/>quod dependeat ab altero <lb/>vel vtroque tignorum: al&shy;<lb/>teri vero infixum &amp; <expan abbr="ap-po&longs;it&utilde;">ap&shy;<lb/>po&longs;itum</expan> e&longs;&longs;e pondus trahen&shy;<lb/>dum vel attollendum. </s>

<s id="id.002103">Vt <lb/>&longs;int duo tigna &longs;e&longs;e ex ad&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.174.jpg" pagenum="135"/><emph type="italics"/>uer&longs;o fulcientia C D &amp; E F <emph.end type="italics"/><lb/><figure id="id.035.01.174.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.174.1.jpg"/><lb/><emph type="italics"/>(plura duobus vt tria, &amp; qua&shy;<lb/>tuor, vt &longs;e validius fulciant, vt <lb/>plurimum &longs;tatuuntur) &longs;int &amp; <lb/>du&aelig; trochle&aelig; A &amp; B, qua&shy;<lb/>rum altera A ad vtrumque ti&shy;<lb/>gnum reuinciatur loro H A, <lb/>alteri vero B appo&longs;itum &longs;it pon&shy;<lb/>dus G, tracto loro ab ini&shy;<lb/>tio vbi I, pondus G cum tro&shy;<lb/>chlea B attolletur ver&longs;us A. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002104"><emph type="italics"/>Vel etiam &longs;it trochlea in&shy;<lb/>ferior in qua orbiculi duo cui <lb/>pondus A per vncum apponi&shy;<lb/>tur, &longs;uperior in qua duo item or&shy;<lb/>biculi. </s>

<s id="id.002105">funis prim&ograve; alligari de&shy;<lb/>bet vnco, qui e&longs;t in ea, &amp; cir&shy;<lb/>cum agi circa &longs;uperiorem orbicu&shy;<lb/>lorum inferioris trochle&aelig;, ita vt <lb/>a&longs;cendens circum inferiorem &longs;u&shy;<lb/>perioris, deuoluatur po&longs;tea circa <lb/>inferiorem inferioris, &amp; reuol&shy;<lb/>uatur adhuc circa &longs;uperiorem &longs;u&shy;<lb/>perioris, habens tandem initium <lb/>&longs;ui in G vbi motor intelligitur. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002106"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002107">An quia <expan abbr="id&etilde;">idem</expan> pondus &agrave; mi&shy;<lb/>nore vi, &longs;i vecte moueatur, <lb/><expan abbr="tr&atilde;sfertur">transfertur</expan> magis: <expan abbr="qu&atilde;">quam</expan> &longs;i ma&shy;<lb/>nu. </s>

<s id="id.002108">Trochlea <expan abbr="aut&etilde;">autem</expan> id facit, <lb/>quod vectis. </s>

<s id="id.002109"><expan abbr="Itaq;">Itaque</expan> &longs;i vna fa&shy;<lb/>cilius trahat, &amp; ab vnico tra&shy;<lb/>ctu: <expan abbr="qu&atilde;">quam</expan> manu, grauius mult&ograve; <lb/>trahet. </s>

<s id="id.002110">Hoc vero du&aelig; tro&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.175.jpg" pagenum="136"/><foreign lang="greek"><gap/></foreign><lb/>chle&aelig; plus in dupla veloci&shy;<lb/>tate attollent. </s>

<s id="id.002111">Minus enim <lb/>altera trahit quam &longs;i ip&longs;a <lb/>per &longs;eip&longs;am traheret. </s>

<s id="id.002112">quo&shy;<lb/>niam iuxta <expan abbr="alter&atilde;">alteram</expan> iniectus <lb/>fuerit funiculus. </s>

<s id="id.002113">H&ecedil;c enim <lb/>in&longs;uper pondus minus effe&shy;<lb/>cit. </s>

<s id="id.002114">Et &longs;ic &longs;i in plures tro&shy;<lb/>chleas iniectus fuerit funi&shy;<lb/>culus, in paucis trochleis <lb/>multum intere&longs;t. </s>

<s id="id.002115">Itaque &agrave; <lb/>prima trahente <expan abbr="p&otilde;dus">pondus</expan> qua&shy;<lb/>tuor librarum, ab vltima <lb/>trahi multo minus. </s></p><p type="head">

<s id="id.002116">COMMENTARIVS. </s></p><p type="main">

<s id="id.002117">An quia idem.] <emph type="italics"/>Solutio e&longs;t propo&longs;iti problematis &longs;umpta &egrave; <lb/>vecte multiplicato. </s>

<s id="id.002118">Syllogi&longs;mus &longs;ic erit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002119"><emph type="italics"/>Quod &longs;olum magna moueret pondera parua vi, hoc etiam gemi&shy;<lb/>natum trahet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002120"><emph type="italics"/>Trochlea parua vi magna trahit pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002121"><emph type="italics"/>Trochlea ergo geminata parua vi magna trahet pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002122"><emph type="italics"/>Huius &longs;yllogi&longs;mi propo&longs;itio clara e&longs;t, ex eo quod vires bene compo&longs;i&shy;<lb/>t&aelig; &amp; multiplicat&aelig; plus po&longs;&longs;unt: quam &longs;ol&aelig; &amp; &longs;implices. </s>

<s id="id.002123">A&longs;&longs;umptio <lb/>ver&ograve; &longs;ic confirmatur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002124"><emph type="italics"/>Trochlea idem facit, quod vectis. </s>

<s id="id.002125">E&longs;t enim ip&longs;a vectis. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002126"><emph type="italics"/>Vectis parua vi magna mouet pondera. </s>

<s id="id.002127">ex anteced. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002128"><emph type="italics"/>Ergo trochlea parua vi magna trahet pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002129"><emph type="italics"/>Quod autem trochlea &longs;it vectis, patet. </s>

<s id="id.002130">quia hypomochlium e&longs;t in axi&shy;<lb/>culo immobili, diameter orbiculi e&longs;t longitudo vectis deor&longs;um vna <lb/>parte tracta per funem circumductum: altera &longs;ur&longs;um eleuata. </s>

<s id="id.002131"><expan abbr="Mou&etilde;s">Mouens</expan> <lb/><expan abbr="cut&etilde;">cutem</expan> e&longs;t virtus trahentis ad initium funis. </s>

<s id="id.002132">Et <expan abbr="p&otilde;dus">pondus</expan> quod e&longs;t vni tro&shy;<lb/>chlearum appo&longs;itum e&longs;t mobile. </s>

<s id="id.002133">Cum autem virtus trahit per plures <lb/>orbiculos, vt pluribus vectibus vtens vna opera, &amp; eodem temporis <lb/>momento facilius trahit &amp; minore vi, quandoquidem pondus, vt <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.176.jpg" pagenum="137"/><emph type="italics"/>pluribus diui&longs;um orbiculis, minus id e&longs;t leuius apparet. </s>

<s id="id.002134">Itaque quo&shy;<lb/>niam facilius e&longs;t mouere pondus vecte: quam manu, &amp; trochlea ve&shy;<lb/>ctis e&longs;t, facilius erit trochlea: quam manu. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002135">Plu&longs;quam in dupla.] <emph type="italics"/>Qu&ograve; plures &longs;unt orbiculi in trochleis, e&ograve; <lb/>quidem facilius, &amp; minore vi pondus trahitur, vt e&longs;t demon&longs;tra&shy;<lb/>tum &agrave; Guido Vbaldo prop. 3. &amp; aliquot &longs;equentibus in tractatu de <lb/>trochlea. </s>

<s id="id.002136">Sed etiam vbi &longs;unt plures, ibi lentior e&longs;t tractio, quia po&shy;<lb/>tentia in &aelig;quali tempore, &longs;patio &longs;ecundum duplum, triplum, &amp; &longs;ic <lb/>deinceps ampliori &longs;ine huiu&longs;modi trochleis idem pondus moueret: &longs;i <lb/>quidem per &longs;e &longs;ufficiat. </s>

<s id="id.002137">Vnde arbitror h&ucirc;c irrep&longs;i&longs;&longs;e mendum in vo&shy;<lb/>cabulo<emph.end type="italics"/> <foreign lang="greek">ta/xei</foreign> <emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">logw|</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">diplasi/w|. </foreign><emph type="italics"/>pro<emph.end type="italics"/> <foreign lang="greek">u(podiplasi/w|</foreign> <emph type="italics"/>tollendo<emph.end type="italics"/><lb/><foreign lang="greek">ple/on h)\</foreign> <emph type="italics"/>vel potius pro<emph.end type="italics"/> <foreign lang="greek">h)\</foreign> <emph type="italics"/>reponendo<emph.end type="italics"/> <foreign lang="greek">mh\</foreign> <emph type="italics"/>&longs;ic enim &longs;ententia vera erit. <emph.end type="italics"/> <lb/></s>

<s>Hoc vero du&aelig; trochle&aelig; plus non in dupla velocitate <expan abbr="at-toll&etilde;t">at&shy;<lb/>tollent</expan>. </s>

<s><emph type="italics"/><expan abbr="C&aelig;ter&utilde;">C&aelig;terum</expan> quomodo per trochleas, quanto <expan abbr="t&etilde;pore">tempore</expan>, &amp; &longs;patio, pon&shy;<lb/>dera moueantur, <expan abbr="quodn&atilde;">quodnam</expan> &longs;uperioris &amp; inferioris trochle&aelig; fuerit offi&shy;<lb/>cium, orbiculorum diametri vt moueantur, vt in omni ratione qu&aelig; <lb/>in numeris e&longs;t, pondus &amp; potentia &longs;tatui po&longs;sint, qu&aelig; omnia cert&egrave; <lb/>&longs;citu digni&longs;sima &longs;unt Geometric&egrave; demon&longs;trata, qui &longs;cire volet, vi&shy;<lb/>deat apud Guidum Vbaldum pr&aelig;dicto tractatu, ne maior pars il&shy;<lb/>lius pr&aelig;&longs;tanti&longs;simi operis, quod edidit de mechanicis, mihi &longs;it h&ucirc;c <lb/>transferenda. </s>

<s id="id.002138">Huic ver&ograve; loco non po&longs;&longs;um non in&longs;erere vnam ma&shy;<lb/>chinam e &longs;ex trochleis: &amp; funiculis quinque compo&longs;itam (&egrave; pluri&shy;<lb/>bus componi, &longs;i v&longs;us po&longs;tulet, nihil obe&longs;t) mira celeritate, &amp; funis <lb/>ductarij paucitate atque compendio pondus attollentem, quam mihi <lb/>communicauit Georgius Lhullierius vir &longs;ine honoris titulo <expan abbr="n&utilde;quam">nunquam</expan> <lb/>mihi nominandus, propter <expan abbr="&longs;u&utilde;">&longs;uum</expan> in artes mathematicas &amp; <expan abbr="mathema-t&utilde;">mathema&shy;<lb/>tum</expan> &longs;tudio&longs;os <expan abbr="qu&atilde;diu">quandiu</expan> vixit &longs;ingularem <expan abbr="amor&etilde;">amorem</expan>. </s>

<s id="id.002139">Machina e&longs;t eiu&longs;modi, <lb/>&longs;it tignum A B perpendiculariter in&longs;i&longs;tens, cui etiam ad rectos al&shy;<lb/>terum in &longs;i&longs;tat vt C D: &longs;int &longs;ex trochle&aelig; E, F, G, H, I, K, <lb/>funiculi quinque L A, N M, Q P, S R, B T, quorum pri&shy;<lb/>mus circumuoluitur circa duos orbiculos E &amp; F in extremis ti&shy;<lb/>gnorum circa &longs;uos axiculos mobiles reliquorum &longs;inguli circa &longs;ingu&shy;<lb/>los &agrave; proxim&egrave; antecedentibus funiculis &longs;u&longs;pen&longs;os. </s>

<s id="id.002140">In X autem &longs;it <lb/>harpago ad apprehendendum pondus E attollendum vel deprimen&shy;<lb/>dum. </s>

<s id="id.002141">Si enim extremum L ab harpagone V liberetur, &amp; ad A <lb/>traducatur, de&longs;cendet vno qua&longs;i nictu oculi pondus E, tantum <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.177.jpg" pagenum="138"/><figure id="id.035.01.177.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.177.1.jpg"/><lb/><emph type="italics"/>&longs;patij, quanti &longs;unt funiculi N M, Q P, <lb/>R S, B T. </s>

<s id="id.002142">Tanti erunt autem, <lb/>quantos loci, ad quem de&longs;cendere, vel <lb/>&egrave; quo educere volumus, profunditas, <lb/>po&longs;tulat. </s>

<s id="id.002143">Si autem attollere oporteat, <lb/>extremum L cum erit in A, traduce&shy;<lb/>tur ad harpagonem V. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002144"><emph type="italics"/>In hac machina igitur h&aelig;c duo in&shy;<lb/>&longs;unt, facilitas motionis ob multitudi&shy;<lb/>nem trochlearum, &amp; celeritas motio&shy;<lb/>nis. </s>

<s id="id.002145">quia quanto temporis &longs;patio extre&shy;<lb/>mum funiculi L ab A transfertur <lb/>ad harpagonem V, eodem pondus E <lb/>ex infimo loco &longs;ur&longs;um per decuplam <lb/>longitudinem &amp; amplius, &longs;i quis vo&shy;<lb/>let, euehitur, aut contra. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002146"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002147">Atque in ar&shy;<lb/>chitectura faci&shy;<lb/>le mouent ma&shy;<lb/>gna pondera, <lb/><expan abbr="Tr&atilde;sfer&utilde;t">Transferunt</expan> enim <lb/>ab ip&longs;a trochlea <lb/>ad <expan abbr="alter&atilde;">alteram</expan> &amp; rur&shy;<lb/>&longs;us ab ip&longs;a ad &longs;u&shy;<lb/>culas &amp; vectes, <lb/>quod <expan abbr="id&etilde;">idem</expan> e&longs;t ac <lb/>&longs;i multas <expan abbr="c&otilde;po-ner&etilde;t">compo&shy;<lb/>nerent</expan> trochleas. </s></p><p type="head">

<s id="id.002148">COMMENTARIVS. </s></p><p type="main">

<s id="id.002149">Atque in architect.] <emph type="italics"/>Vt funis <lb/>facilius trahatur in magnis ponde&shy;<lb/>ribus dimouendis ergata, aut &longs;ucula adhibetur ad tigna, vt &amp; rota <lb/>&amp; collopes. </s>

<s id="id.002150">qu&aelig; e&ograve; facilius trahunt, qu&ograve; longiores fuerint. </s>

<s id="id.002151">Atque<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.178.jpg" pagenum="139"/><emph type="italics"/>huius compo&longs;itionis qu&aelig; ad&aelig;quat multas trochleas, aut etiam lon&shy;<lb/>gi&szlig;imum vectem maximus e&longs;t v&longs;us. </s>

<s id="id.002152"><expan abbr="Quandoquid&etilde;">Quandoquidem</expan> cum materia ad <lb/>vectem, cuius longitudo vnius &longs;tadij requireretur, idonea <expan abbr="nu&longs;qu&atilde;">nu&longs;quam</expan> in&shy;<lb/>ueniri po&szlig;it, plurium tamen trochlearum, ergatarum, &longs;ucularum, <lb/>tympanorum, collopum compo&longs;itione apta proportionalium, fiet ma&shy;<lb/>china tractabilis, cuius vis maior e&longs;&longs;e pote&longs;t: quam vectis, cuius lon&shy;<lb/>gitudo e&longs;&longs;et &longs;tadij vnius. </s>

<s id="id.002153">Rei huius &longs;pecimen luculentum Rom&aelig; ex&shy;<lb/>hibitum e&longs;t &agrave; Dominico Fontana Mili in <expan abbr="Com&etilde;&longs;i">Comen&longs;i</expan> dioc&oelig;&longs;i orto, con&shy;<lb/>&longs;ilio, adhortatione, &longs;umptibus X i&longs;ti V. pontificis maximi, in tran&shy;<lb/>&longs;ponendo obeli&longs;co, qui Soli prim&ugrave;m &agrave; Pherone Rege &AElig;gypti, Helio&shy;<lb/>poli ant&egrave; Troiani belli tempora factus, &amp; dicatus: po&longs;tea &agrave; Caio Ca&shy;<lb/>ligula Romam tran&longs;uectus Augu&longs;to &amp; Tiberio C&aelig;&longs;aribus &longs;acer, <lb/>temporibus no&longs;tris p&aelig;n&egrave; obrutus ruderibus &aelig;dium, qu&aelig; circum eum <lb/>corruerant, parietinis &amp; c&oelig;mentis, nullam tamen iniuriam &agrave; tot <lb/>Romani nominis ho&longs;tibus pa&longs;&longs;us, nulla ex parte exe&longs;us, aut comminu&shy;<lb/>tus, magna omnium aduentantium admiratione parte adhuc &longs;ui ali&shy;<lb/>qua loco valde inepto con&longs;picuus, vi&longs;ebatur. </s>

<s id="id.002154">Vt totum hoc negotium <lb/>ge&longs;tum &longs;it, licet iam &agrave; multis doctis viris literarum monumentis <lb/>commendatum, inepti&szlig;imus tamen &longs;im, aut eorum, qu&aelig; mea &aelig;tate <lb/>fiunt maxime memorabilium, ignarus, &longs;i ip&longs;um in huius loci id <lb/>exempli maxime po&longs;tulantis illu&longs;tratione, pr&aelig;termittam, breuiter <lb/>ergo commemorabo. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002155"><emph type="italics"/>Primum &longs;cire oportet, quod obeli&longs;cus e&longs;t vnus ingenti magnitu&shy;<lb/>dine lapis, qui ab imo v&longs;que ad &longs;ummum rectis lineis in&longs;tar acus, aut <lb/>potius exigui veru in cu&longs;pidem terminatur. </s>

<s id="id.002156">Varia e&longs;t obeli&longs;corum <lb/>materia, forma, &amp; altitudo. </s>

<s id="id.002157">Hic de quo agitur ex vno lapide, eoque <lb/>duri&szlig;imo, qui pyrhop&aelig;cilos dicitur, quod punctis quibu&longs;dam ignei <lb/>coloris di&longs;tinctus &longs;it, ac varius vndique interluceat, &longs;ine notis hie&shy;<lb/>roglyphicis (quod alijs obeli&longs;cis frequens e&longs;t, per has regibus &AElig;gypti <lb/>&longs;uas res ge&longs;tas memori&aelig; commendantibus) &longs;emper eadem forma, ea&shy;<lb/>que quadrangulari ex infima &longs;ui parte minus ampla &amp; &longs;patio&longs;a, ob <lb/>idque pulcherrima, cuius cra&szlig;itudo, &longs;i Serlius antiquitatum Roma&shy;<lb/>narum &longs;criptor rect&egrave; metitus e&longs;t, pedibus 9. minuti&longs;que 24. altitu&shy;<lb/>do pedibus 85. &longs;ummaque demum cra&szlig;itudo pedibus 6. &amp; minutis<emph.end type="italics"/><lb/>8. <emph type="italics"/>comprehenditur, ad imanque ip&longs;ius radicem h&aelig; liter&aelig; in epitaphij <lb/>ordinem dige&longs;t&aelig; ac di&longs;tribut&aelig; legebantur. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.179.jpg" pagenum="140"/><p type="main">

<s id="id.002158">Diuo C&aelig;&longs;ari Diui Iulij. </s>

<s id="id.002159">F. Augu&longs;to: Ti.C&aelig;&longs;ari Diui Augu&longs;ti. </s></p><p type="main">

<s id="id.002160">F. Augu&longs;to &longs;acrum. </s></p><p type="main">

<s id="id.002162"><emph type="italics"/>Hic igitur cum ob &longs;itum (attingebat enim propemodum &longs;acrarium <lb/>ba&longs;ilic&aelig; S. Petri, quod ad meridiem vergit) &amp; eorum quibus &longs;acra&shy;<lb/>tus erat execrationem, &longs;ummo pontifici di&longs;plicui&longs;&longs;et, vt alijs nonnul&shy;<lb/>lis, qui ante eum in cathedra D. Petri &longs;ederunt: &longs;ed qui rem ob eius, vt <lb/>exi&longs;timabant,<emph.end type="italics"/> <foreign lang="greek">a)dunami/an</foreign>: <emph type="italics"/>aut ob &longs;umptuum magnitudinem ab ag&shy;<lb/>gre&szlig;ione deterriti, nunquam attentarunt. </s>

<s id="id.002164">Sanctitati vi&longs;um e&longs;t, vt in <lb/>media Vaticani area ante templi, quo nullum e&longs;t magnificentius, ve&shy;<lb/>&longs;tibulum, loco Rom&aelig; ampli&szlig;imo &amp; celeberrimo, &amp; pontificalibus <lb/>actionibus dedicato, collocaretur, &amp; &longs;igno crucis eius apici impo&longs;ito, <lb/>Chri&longs;to Chri&longs;tianorum duci vnico, &amp; &longs;eruatori, obliterata pror&longs;us <lb/>Paganorum con&longs;ecratione, con&longs;ecraretur, &amp; totus denique Chri&longs;tia&shy;<lb/>nos pr&aelig;moneret, vt quemadmodum eius quatuor latera ab infima <lb/>parte &longs;ur&longs;um ver&longs;us paulatim gracile&longs;cunt, quou&longs;que acuti&longs;simo <lb/>apice, in quo e&longs;t Chri&longs;tus, terminetur: &longs;ic di&longs;cant <expan abbr="m&etilde;tes">mentes</expan> &longs;uas ab hono&shy;<lb/>rum, diuitiarum, aliarum que rerum terre&longs;trium, quibus maxime pa&shy;<lb/>tent, cogitationibus &amp; cupiditatibus &longs;ubtrahere &amp; &longs;ubducere, nec <lb/>ante con&longs;i&longs;tant: quam ill&aelig; in altum paulatim erect&aelig;, &amp; acutiores <lb/>fact&aelig;, Chri&longs;tum, eumque crucifixum inueniant, &longs;olum ament, hunc <lb/>&longs;omnient, in &longs;olo quie&longs;cant, &amp; in eo &longs;e&longs;e noctes die&longs;que oblectent. <lb/></s>

<s id="id.002165">Hoc igitur vt fieret, ip&longs;um obeli&longs;cum &longs;ine offen&longs;ionis periculo pri&shy;<lb/>mum oportebat &egrave; &longs;uo &longs;tylobata auellere: deinde humi vel &longs;uper curri&shy;<lb/>culo reclinare: po&longs;tea tran&longs;uehere ad locum de&longs;tinatum, ab hoc mille <lb/>pedes di&longs;tantem per tumulum agge&longs;tum paulatim eminentiorem va&shy;<lb/>lidi&longs;simis trabibus per aliquot tignorum &longs;tatutiones religatis vndi&shy;<lb/>quaque coercitum, ne immen&longs;a vectur&aelig; mole fati&longs;ceret: po&longs;tea &longs;en&longs;im <lb/>in &longs;ublime &longs;ubrigere: po&longs;tremo perpendiculariter &longs;ubrectum &longs;uper <lb/>&longs;tylobata &longs;uo collocare: nunc qui vectes, qu&aelig; ferramenta, qu&aelig; machi&shy;<lb/>n&aelig;, quot oper&aelig;, qui modus tot molitionibus, quarum qu&aelig;libet factu <lb/>propemodum<emph.end type="italics"/> <foreign lang="greek">a)du/natos</foreign> <emph type="italics"/>iudicabatur, adhibita &longs;unt, dicam, vt ex qua&shy;<lb/>dam epistola familiari Roma in Hi&longs;paniam ad P.Velleium de hac <lb/>re mi&longs;&longs;a, &amp; aliorum doctorum <expan abbr="homin&utilde;">hominum</expan> &longs;criptis, breuiter collegimus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002166"><emph type="italics"/>Primum obeli&longs;cus validi&longs;simis octo columnis per latera circum&shy;<lb/>uallatus e&longs;t, h&aelig; concathenat&aelig;, atque alijs &longs;uccre&longs;centibus &amp; conne&shy;<lb/>xis apicem obeli&longs;ci ad &longs;ex palmos pr&aelig;cellebant. </s>

<s id="id.002167">His totidem fa&longs;tigia <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.180.jpg" pagenum="141"/><emph type="italics"/>&longs;uperimpo&longs;ita, &agrave; quibus perpetu&aelig; intr&agrave; extr&aacute; que &longs;uccedentes fulctu&shy;<lb/>r&aelig; &longs;tatuta tigna &longs;u&longs;tentabant, &longs;ic enim ca&longs;ui &amp; inflexionibus pro&shy;<lb/>&longs;pectum. </s>

<s id="id.002168">Tota h&aelig;c machina validi&longs;simis laminis, ferrei&longs;que clauis &agrave; <lb/>vertice ad calcem religata, plurimis &amp; retinaculis, &amp; ductarijs fu&shy;<lb/>nibus vndequaque &longs;uffulta. </s>

<s id="id.002169">Quadraginta trochle&aelig; &agrave; totidem ergatis <lb/>mouend&aelig; fa&longs;tigijs dictis alligat&aelig; erant. </s>

<s id="id.002170">Horum &longs;ingulis homines <lb/>quindecim, equi duo de&longs;tinati &longs;unt, qui ad nutum pr&aelig;fecti (pr&aelig;erat <lb/>autem, cuique ergat&aelig; vnus) pr&aelig;&longs;to e&longs;&longs;ent. </s>

<s id="id.002171">Pr&aelig;fecti ad &longs;ignum tub&aelig; <lb/>vrgebant molitionem, cymbali &longs;i&longs;tebant. </s>

<s id="id.002172">Vectes adiuncti &longs;unt quin&shy;<lb/>que &longs;eptuaginta palmorum longitudine ex validi&longs;simis trabibus <lb/>compacti, tres ab obeli&longs;ci fronte: duo &agrave; tergo. </s>

<s id="id.002173">Primo impetu ferrea <lb/>qu&aelig;dam lamina, qu&aelig; machinam obeli&longs;cum ambientem religabat, <lb/>di&longs;rupta e&longs;t, &longs;ed hac vnius hor&aelig; &longs;patio re&longs;tituta, decem demum im&shy;<lb/>pul&longs;ibus duos palmos, ac <expan abbr="dimidi&umacr;">dimidium</expan> in altum obeli&longs;cus eleuatur, ne ta&shy;<lb/>men tanta pendente mole &longs;ini&longs;trum quid accideret, cunei &longs;tatim ac <lb/>tignorum c&aelig;&longs;ur&aelig;, quibus obniteretur, &longs;uppo&longs;it&aelig;. </s>

<s id="id.002174">Tum deinde a&longs;&longs;eri&shy;<lb/>bus ac cylindris, cubi quidam, quibus in&longs;idebat, dimoti, &amp; qu&aelig;dam <lb/>traha &longs;uppo&longs;ita. </s>

<s id="id.002175">Hoc facto, qu&aelig; prima ad auellendum molitio acer&shy;<lb/>rima fuit, &longs;u&longs;tenta tamen magnum ad reliquas aggrediendas adiecit <lb/>animum. </s>

<s id="id.002176">Itaque ergat&aelig;, trabes, funes ductarij, c&aelig;teraque, vt conue&shy;<lb/>niebat, mutata, atque in diuer&longs;am formam compo&longs;ita: &amp; ima pars <lb/>obeli&longs;ci quatuor ergatarum viribus, qu&aelig; &agrave; tergo mouebantur, c&aelig;teris <lb/>qu&aelig; &agrave; fronte erant, funes remittentibus, trahi paulatim c&oelig;pit. </s>

<s id="id.002177">Ip&longs;e <lb/>vero apex clementi&longs;sim&egrave; vergebat, quou&longs;que famo&longs;i&longs;sima moles om&shy;<lb/>nino integra, ac &longs;ine vlla iactura humi decubuit. </s>

<s id="id.002178">Atque h&aelig;c &longs;ecun&shy;<lb/>da molitio fuit. </s>

<s id="id.002179">Po&longs;tea per dictum tumulum &longs;ex ergatarum vi trahi <lb/>c&oelig;pta e&longs;t, &amp; quia huic &longs;pectaculo intererat ip&longs;e &longs;ummus pontifex, <lb/>huius tanti tant&aelig; molitionis curatoris exactori&longs;que in&longs;tigante <lb/>operarum moras pr&aelig;&longs;entia, breuius quidem, quam cogitari pote&longs;t, <lb/>pertracta e&longs;t. </s>

<s id="id.002180">Atque h&aelig;c tertia molitio fuit. </s>

<s id="id.002181">po&longs;tquam ad aliquot <lb/>dies, ne funes nimio calore conflagrarent, ob motum, &amp; a&euml;ris &aelig;&longs;tuo&shy;<lb/>&longs;am tunc temporis con&longs;titutionem, ce&longs;&longs;atum e&longs;t, tandem eadem ma&shy;<lb/>china, qua auul&longs;us: &longs;ed altiore propter loci eminentiam, externo in&shy;<lb/>ternoque chomate muniti&longs;sima, adhibitis ergatis quadraginta &longs;ex, <lb/>equis centum quadraginta, hominibus &longs;excentis, ex ergati&longs;que qua&shy;<lb/>tuor imam obeli&longs;ci partem <expan abbr="trah&etilde;tibus">trahentibus</expan>. </s>

<s id="id.002182">Reliqu&aelig; &agrave; cu&longs;pide ad medium <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.181.jpg" pagenum="142"/><emph type="italics"/>religatum erexerunt, atque tandem quadraginta &longs;eptem ni&longs;ibus &longs;te&shy;<lb/>tit moles. </s>

<s id="id.002183">Cubi, quibus antea in&longs;idebat, &longs;uppo&longs;iti, &amp; in omnis &longs;eculi <lb/>memoriam iam quinquaginta &longs;ex &amp; amplius doctorum hominum <lb/>&longs;criptis editis celebrata, ad perpendiculum collocata e&longs;t. </s>

<s id="id.002184">H&aelig;c quarta <lb/>&amp; quinta &longs;unt molitio. </s>

<s id="id.002185">Po&longs;tquam vice&longs;ima &longs;exta men&longs;is dicti glo&shy;<lb/>rio&longs;i&szlig;imo huic triumpho &agrave; pontifice delecta per B <expan abbr="Feratin&umacr;">Feratinum</expan> Epi&longs;co&shy;<lb/>pum <expan abbr="Amerin&umacr;">Amerinum</expan> &amp; cancellari&aelig; Apo&longs;tolic&aelig; <expan abbr="regent&etilde;">regentem</expan> &longs;olemni prius ad <lb/>Petri altare &longs;acrificio facto, &amp; circ&agrave; obeli&longs;cum frequenti &longs;upplicatio&shy;<lb/>ne peracta, multaque &longs;uper &longs;ancti&szlig;im&aelig; Crucis <expan abbr="&longs;tatu&atilde;">&longs;tatuam</expan> &aelig;ream, &longs;ed affa&shy;<lb/>br&egrave; inauratam, <expan abbr="precat&umacr;">precatum</expan>, tradita e&longs;t Crux Diacono &longs;acris adhuc ve&longs;ti&shy;<lb/>bus induto, &agrave; quo denique in mucrone obeli&longs;ci collocata e&longs;t. </s>

<s id="id.002186">quo tem&shy;<lb/>poris momento cuncta tormentorum genera, qu&aelig; in Sancti Angeli <lb/>arce erant, a&longs;siduos edidere bombos. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002187"><emph type="italics"/>Itaque quod pri&longs;cis illis natur&aelig; miraculis qu&aelig; &agrave; Leone decimo ad <lb/>Paulum III. orbis tulit, desperatum plan&egrave; opus <expan abbr="iudicat&umacr;">iudicatum</expan> erat. </s>

<s id="id.002188">Id <expan abbr="n&umacr;c">nunc</expan> <lb/>Sixti V. Pontificis cura &amp; magnificentia, Dominici Fontan&aelig; ope&shy;<lb/>ra &amp; indu&longs;tria, &amp;<emph.end type="italics"/> <foreign lang="greek">tw=n mhxanikw=n</foreign> <emph type="italics"/>auxilia <expan abbr="perfecer&umacr;t">perfecerunt</expan>, atque ab&longs;ol&shy;<lb/>uerunt tanto &longs;pectantium applau&longs;u, vt cum Fontana perfecto opere <lb/>domum reductus e&longs;t, diceres Camillum vel Fabium magnum in ca&shy;<lb/>pitolium triumphantem duci. </s>

<s id="id.002190">Area vero Vaticani in qua obeli&longs;cus, <lb/>qualem in &longs;equenti pagina tibi cum &longs;uis titulis repr&aelig;&longs;entamus, licet <lb/>ampli&longs;sima, hominum ad rei miraculum confluentium per multos <lb/>po&longs;tea dies concur&longs;um vix capere potuit. <emph.end type="italics"/></s></p><p type="head">

<s id="id.002191">E MVLTIS EPIGRAMMIS DE <lb/>obeli&longs;co, Cruce, &amp; Sixto &longs;ummo Pontifice <lb/>hoc &longs;electum h&icirc;c in&longs;crip&longs;imus. </s></p><p type="main">

<s id="id.002192">&AElig;nea &longs;erpentis Mo&longs;es &longs;imulachra &longs;acerdos <lb/>Extulit, &aelig;grotis vt medicina foret</s></p><p type="main">

<s id="id.002193">Nunc alter Mo&longs;es obeli&longs;ci in vertice Sixtus <lb/>Erigit &aelig;grotis &aelig;rea &longs;igna Crucis</s></p><p type="main">

<s id="id.002194">Vos &ocirc; Romani &longs;u&longs;tollite ad &aelig;thera vultus, <lb/>A Cruce nam vobis ve&longs;tra petenda &longs;alus. </s></p><p type="main">

<s id="id.002195"><emph type="italics"/>Gulielmus Blancus Albien&longs;i. I. C. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.182.jpg" pagenum="143"/><figure id="id.035.01.182.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.182.1.jpg"/><p type="caption">

<s id="id.002197">Sancti&longs;&longs;im&aelig; Cruci &longs;acra&shy;<lb/>uit Sixtus V. Pont. Max. <lb/>&egrave; priore &longs;ede auul&longs;um &amp; <lb/>C&aelig;&longs;aribus Aug. &amp; Tib. <lb/>11.ablatum. </s></p><p type="caption">

<s id="id.002198"><emph type="italics"/>Faciata &agrave; leuante. <emph.end type="italics"/></s></p><p type="caption">

<s id="id.002199">Ecce Crux Domini <lb/>fugite partes aduer&longs;&aelig; <lb/>vincit leo de Tribu <lb/>Iuda. </s></p><p type="caption">

<s id="id.002200"><emph type="italics"/>Faciata &agrave; Tramontana. <emph.end type="italics"/></s></p><p type="caption">

<s id="id.002201">Sixtus V. Pontif. Max. Cruci <lb/>inuict&aelig; obeli&longs;cum vaticanum <lb/>ab impura &longs;uper&longs;titione expia&shy;<lb/>tum Iu&longs;tius &amp; Felicius con&longs;e&shy;<lb/>crauit Ann. M. D. LXXXVI. <lb/>Pont. II. </s></p><p type="caption">

<s id="id.002202">Diuo C&aelig;&longs;. Diui <lb/>Iulij F. Augu&longs;to Ti. <lb/>C&aelig;&longs;. Diui Augu&longs;t. <lb/>F. Augu&longs;t. &longs;acrum. </s></p><p type="caption">

<s id="id.002204"><emph type="italics"/>Faciata in ver&longs;o pietro. <emph.end type="italics"/></s></p><p type="caption">

<s id="id.002205">Chri&longs;tus vincit, <lb/>Chri&longs;tus regnat, <lb/>Chri&longs;tus imperat, <lb/>Chri&longs;tus ab omni malo <lb/>plebem &longs;uam defendat. </s></p><p type="caption">

<s id="id.002209"><emph type="italics"/>Della faciata &agrave; mezzo giorne. <emph.end type="italics"/></s></p><p type="caption">

<s id="id.002210">Sixtus V. Pont. Max. obeli <lb/>vaticanum, <lb/>di&longs;. gentium. <lb/></s>

<s id="id.002212">Impio cultu dicatum ad Apo&longs;tolo&shy; <lb/>rum limina opero&longs;o labore <lb/></s>

<s>Tran&longs;tulit. </s>

<s id="id.002213">Ann. M.D. LXXXV. Pont. II. </s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.183.jpg" pagenum="144"/><chap><p type="main">

<s id="id.002214"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002215">20. Cur &longs;ecuris feriens di&shy;<lb/>uidit: premens vero non <lb/>item. </s></p><p type="main">

<s id="id.002216"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002217">Cur &longs;i quis magnam &longs;e&shy;<lb/>curim &longs;uper lignum impo&shy;<lb/>&longs;uerit, &amp; illi in&longs;uper ma&shy;<lb/>gnum pondus, lignum non <lb/>diuidit, quod &longs;it effatu di&shy;<lb/>gnum: at &longs;i quis &longs;ecurim at&shy;<lb/>tollens percu&longs;&longs;erit, ip&longs;um <lb/>diuidit, ip&longs;o percutiente <lb/>mult&ograve; minus pondus ha&shy;<lb/>bente: quam &longs;it id, quod <lb/>impo&longs;itum erat, &amp; preme&shy;<lb/>bat. </s>

<s id="id.002218">An quia omnia motio&shy;<lb/>ne fiunt: &amp; graue commo&shy;<lb/>tum magis: quam <expan abbr="quie&longs;c&etilde;s">quie&longs;cens</expan> <lb/>motionem grauitatis acci&shy;<lb/>pit. </s>

<s id="id.002219">Impo&longs;itum igitur non <lb/>mouetur, ni&longs;i motione gra&shy;<lb/>uitatis [propri&aelig;]: commotum vero &amp; ip&longs;a &amp; motione <lb/>percutientis. </s></p><p type="head">

<s id="id.002220">COMMENTARIVS. </s></p><p type="main">

<s id="id.002221">Cvr&longs;i quis.] <emph type="italics"/>Problema de &longs;ecuri, qu&aelig; &longs;ecat dum percutit, non <lb/>autem dum &longs;impliciter incumbit, duobus modis &longs;oluitur. </s>

<s id="id.002222">Prior <lb/>&longs;umptus e&longs;t &egrave; communi &longs;ententia phy&longs;icorum a&longs;&longs;erentium, omnia <lb/>motione fieri. </s>

<s id="id.002223">Syllogi&longs;mus igitur &longs;ic e&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002224"><emph type="italics"/>Cum omnia motione fiant, proinde &amp; &longs;ectio, quod duplici mo&shy;<lb/>tione commotum erit, magis mouebit: quam id, quod vna. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002225"><emph type="italics"/>Sed graue commotum, vt magna &longs;ecuris feriens, duplici <lb/>motione mouetur, vna grauitatis propri&aelig;: altera percu&shy;<lb/>tientis. </s>

<s id="id.002226">Graue autem impo&longs;itum vna tantum mouetur, <lb/>nempe grauitatis propri&aelig;. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.184.jpg" pagenum="145"/><p type="main">

<s id="id.002227"><emph type="italics"/>Ergo magna &longs;ecuris feriens &longs;ecabit: impo&longs;ita vero minim&egrave;. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002228">Motione grauitatis.] <foreign lang="greek">ki/nhsis tou= ba/rous</foreign> <emph type="italics"/>e&longs;t motus cuique <lb/>graui occultus inh&aelig;rens. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002229"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002230">Pr&aelig;terea &longs;ecuris fit cu&shy;<lb/>neus. </s>

<s id="id.002231">Cuneus <expan abbr="aut&etilde;">autem</expan> paruus <lb/><expan abbr="exi&longs;t&etilde;s">exi&longs;tens</expan> magna diuidit. </s>

<s id="id.002232">quia <lb/>ex duobus vectibus con&longs;ti&shy;<lb/>tutus e&longs;t contrario modo <lb/>collocatis. </s></p><p type="head">

<s id="id.002233">COMMENTARIVS. </s></p><p type="main">

<s id="id.002234">Pr&aelig;terea &longs;ecuris.] <emph type="italics"/>Altera e&longs;t problematis propo&longs;iti &longs;olutio <lb/>&longs;umpta &egrave; cunei forma, qu&aelig; in &longs;ecuri propter aciem acutam, &amp; &longs;u&shy;<lb/>perioris partis latitudinem con&longs;picua e&longs;t. </s>

<s id="id.002235">Comprehendetur hoc &longs;yl&shy;<lb/>logi&longs;mo. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002236"><emph type="italics"/>Cuneus paruus cum &longs;it, magna diuidit. (ex anteced.)<emph.end type="italics"/></s></p><p type="main">

<s id="id.002237"><emph type="italics"/>Securis feriens e&longs;t cuneus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002238"><emph type="italics"/>Ergo &longs;ecuris feriens magna diuidet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002239"><emph type="italics"/>Sed hic obijci pote&longs;t, quod &longs;ecuris impo&longs;ita etiam e&longs;t cuneus. </s>

<s id="id.002240">Et ita <lb/>e&longs;t, &longs;ed non actu. </s>

<s id="id.002241">Quia opus e&longs;t malleo percutiente, tanquam motore <lb/>vectium. </s>

<s id="id.002242">Securis autem feriens e&longs;t cuneus annexus malleo, &amp; ideo <lb/>actu cuneus. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002243"><emph type="italics"/>Cardanus propo&longs;itum problema aliter &longs;oluit, cau&longs;amque putat. <lb/></s>

<s id="id.002244">quia a&euml;r non pote&longs;t in ictu effugere. </s>

<s id="id.002245">quanquam enim acuta cu&longs;pide &longs;it <lb/>&longs;ecuris, momento tamen tam paruo temporis effugere nequit. </s>

<s id="id.002246">Ne igi&shy;<lb/>tur nimis den&longs;etur, cogitur in poros ingredi &longs;ubiecti ligni, at que cu&shy;<lb/>nei vice diuidere illud. </s>

<s id="id.002247">Indicio e&longs;t, inquit, quod paulo tardior ictus <emph.end type="italics"/><lb/><arrow.to.target n="marg34"/><lb/><emph type="italics"/>maximum in diuidendo di&longs;crimen adfert dilabente a&euml;re. </s>

<s id="id.002248">Solutionem <lb/>hanc reprehendit Scaliger, con&longs;entitque cum Ari&longs;totele motum mo&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg35"/><lb/><emph type="italics"/>uere, &amp; &longs;ecurim, &longs;i comprimatur manu, &longs;ecare propter nixum: multo <lb/>magis &longs;i ictu adigatur, &amp; ex Ioanne Iucundo proponit aliud proble&shy;<lb/>ma dignum qu&aelig;&longs;itu. </s>

<s id="id.002249">Quot pondo proportionem habeat pugnus ho&shy;<lb/>minis ferientis, cum &longs;eip&longs;o non feriente comparatus. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.185.jpg" pagenum="146"/><p type="margin">

<s id="id.002250"><margin.target id="marg34"/>Lib. 17. de <lb/>&longs;ubt. </s></p><p type="margin">

<s id="id.002251"><margin.target id="marg35"/>Exerc. 331. </s></p></chap><chap><p type="main">

<s id="id.002252"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002253">21. De &longs;tateris. </s></p><p type="main">

<s id="id.002254"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002255">Cur &longs;tater&aelig; paruo &aelig;qui&shy;<lb/>pondio carnium magna <lb/>pondera expendunt, cum <lb/>tot&aelig; dimidia &longs;int libra. </s>

<s id="id.002256">Vbi <lb/>enim pondus apponitur, <lb/>appen&longs;a e&longs;t duntaxat lanx. <lb/></s>

<s id="id.002257">Ex altera vero parte &longs;olum <lb/>e&longs;t &longs;tater&aelig; &longs;capus. </s>

<s id="id.002258">An quia <lb/>contingit &longs;tateram &longs;imul <lb/>e&longs;&longs;e libram &amp; vectem. </s>

<s id="id.002259">Li&shy;<lb/>bra <expan abbr="quid&etilde;">quidem</expan> e&longs;t, vbi vnaqu&aelig;&shy;<lb/>que an&longs;arum fit centrum <lb/>&longs;tater&aelig;. </s>

<s id="id.002260">Igitur in alter a par&shy;<lb/>te habet lancem: in altera <lb/>pro lance &aelig;quipondium, <lb/>quod libr&aelig; incumbit. <lb/></s>

<s id="id.002261">Quemadmodum &longs;i quis al&shy;<lb/>teram lancem &amp; pondus <lb/>in eius &longs;ummitate impo&shy;<lb/>neret. </s>

<s id="id.002262">Clarum enim e&longs;t, <lb/>quod hoc pondus in altera <lb/>lance &longs;itum trahit. </s>

<s id="id.002263">Vt au&shy;<lb/>tem vna libra mult&aelig; libr&aelig; <lb/>&longs;int in tali libra, mult&aelig; an&longs;&ecedil; <lb/>adiect&aelig; &longs;unt, &egrave; quibus vna&shy;<lb/>qu&aelig;que ad eas partes, vbi <lb/>e&longs;t &aelig;quipondium, dimi&shy;<lb/>dium e&longs;t &longs;tater&aelig;. </s></p><p type="head">

<s id="id.002264">COMMENTARIVS. </s></p><p type="main">

<s id="id.002265">De &longs;tateris.] <foreign lang="greek">fa/lagc</foreign> <emph type="italics"/>apud Gr&aelig;cos multa &longs;ignificat vt in&shy;<lb/>ternodium in digitis, ordinem &amp; agmem militare longius <lb/>quam latius, ligna teretia, quibus naues in mare deuoluuntur: &longs;ed h&icirc;c <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.186.jpg" pagenum="147"/><emph type="italics"/>&longs;ignificat libr&aelig; genus, quod trutina, ab alijs &longs;tatera appellatur. </s>

<s id="id.002266">Huius <lb/>partes quatuor &longs;unt A B &longs;capus, C D an&longs;a, A E harpago vel <lb/>lanx, F G<emph.end type="italics"/><lb/><figure id="id.035.01.186.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.186.1.jpg"/><lb/><emph type="italics"/><expan abbr="&aelig;quip&otilde;dium">&aelig;quipondium</expan> <lb/>Gr&aelig;cis di&shy;<lb/>ctum<emph.end type="italics"/> <foreign lang="greek">sfai/&shy;<lb/>rwma</foreign> <emph type="italics"/>no&longs;tris <lb/>Marcum vel <lb/><expan abbr="Roman&utilde;">Romanum</expan>. </s>

<s id="id.002267">Vi<lb/>truuius dixit inuentam fui&longs;&longs;e &longs;tateram, vt ab iniquitate iu&longs;tis mori&shy;<lb/>bus hominum vita vindicetur. </s>

<s id="id.002268">Vnde e&longs;t apud &longs;apientem &longs;tatera do&shy;<lb/>lo&longs;a abhominatio e&longs;t apud Deum, &amp; pondus &aelig;quum voluntas eius. <lb/></s>

<s id="id.002269">In rebus autem pretio&longs;is licet libra, non &longs;tatera v&longs;urpetur, quia tam <lb/>exacta e&longs;&longs;e non pote&longs;t: in vilioribus tamen, quia iniquitatis parua ia&shy;<lb/>ctura e&longs;t, frequenti&szlig;im&egrave; v&longs;urpatur, propter operis commoditatem. <lb/></s>

<s id="id.002270">Nam libra vti non po&longs;&longs;umus, ni&longs;i paria pondera pen&longs;ionibus &longs;emper <lb/>habeantur, quarum apparatus atque tractatio e&longs;t magis opero&longs;a &amp; <lb/>mole&longs;ta. </s>

<s id="id.002271">In &longs;tateris autem quicquid appenderis &longs;eu magnum, &longs;eu par&shy;<lb/>uum vnico pondere, hoc e&longs;t &aelig;quipondio: distinctione tamen puncto&shy;<lb/>rum in &longs;capo examinatur. </s>

<s id="id.002272">Id enim in &longs;capo ita impo&longs;itum e&longs;t, vt mo&shy;<lb/>d&ograve; ad an&longs;am, mod&ograve; ab an&longs;a remoueatur, vt maiora &amp; minora pon&shy;<lb/>dera libret, &amp; vi mouenti re&longs;pondeat. </s>

<s id="id.002273">Nam velut aliqua manus va&shy;<lb/>lida longiorem &longs;tater&aelig; &longs;capum deprimit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002274">Cur &longs;tater&aelig;.] <emph type="italics"/>Problema e&longs;t de &longs;tatera, qu&aelig; paruo &aelig;quipondio <lb/>magna appendit pondera. </s>

<s id="id.002275">Et problematis difficultas hinc o&longs;tenditur, <lb/>quod &longs;tatera videatur tantum e&longs;&longs;e dimidia libra, vt in cuius vna <lb/>parte lanx e&longs;t vna dependens, ex altera vero &longs;capus. </s>

<s id="id.002276">Rationi igitur <lb/>con&longs;entaneum e&longs;tne tanta pendat, quanta libra integra. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002277">An quia contingit.] <emph type="italics"/>Solutio problematis petitur ex libra, &amp; <lb/>vecte, ex libra dupliciter. </s>

<s id="id.002278">Syllogi&longs;mus prior &longs;ic erit. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002279"><emph type="italics"/>Libra expendit magna pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002280"><emph type="italics"/>Statera e&longs;t libra, vt in cuius vna parte vna e&longs;t lanx, in altera <lb/>vice alterius lancis, e&longs;t &aelig;quipondium, quod pro &longs;ua grauitate <lb/>deprimit &longs;capum, &amp; facit &aelig;quilibrium, &amp; extremum an&longs;&aelig; <lb/>e&longs;t centrum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002281"><emph type="italics"/>Ergo &amp; &longs;tatera magna expendet pondera. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.187.jpg" pagenum="148"/><p type="main">

<s id="id.002282">Vt autem vna libra.] <emph type="italics"/>Syllogi&longs;mus po&longs;terior &longs;ic e&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002283"><emph type="italics"/>Mult&aelig; &longs;imul libr&aelig; magna expendunt pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002284"><emph type="italics"/>Statera, cui plures an&longs;&aelig; adiect&aelig; &longs;unt, vel vna, &longs;ed per plura <lb/>puncta mobilis, e&longs;t mult&aelig; libr&aelig; &longs;imul. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002285"><emph type="italics"/>Ergo &longs;tatera magna expendet pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002286"><emph type="italics"/>Statera certe mult&aelig; &longs;unt libr&aelig; actu &amp; pote&longs;tate. </s>

<s id="id.002287">Et primum actu <lb/>cum an&longs;&aelig; (&longs;ic enim<emph.end type="italics"/> <foreign lang="greek">ta\ spa/rtia</foreign> <emph type="italics"/>exprimi debere declarant multi <lb/>huius contextus loci inter &longs;e comparati) plures &longs;unt in vno &longs;capo, vt <lb/>du&aelig;, quod frequenti&szlig;imum, vel tres, quod rarius: cuiu&longs;modi &longs;unt in <lb/>A B &longs;capo<emph.end type="italics"/><lb/><figure id="id.035.01.187.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.187.1.jpg"/><lb/><emph type="italics"/>du&aelig; C D, E F <lb/>quarum pro&shy;<lb/>piore lanci, <lb/>qui vtuntur, <lb/>pondera ad <lb/><expan abbr="cra&szlig;ior&etilde;">cra&szlig;iorem</expan> tru&shy;<lb/>tinam &longs;e ex&shy;<lb/>pendere dicunt. </s>

<s id="id.002288">quod huius not&aelig; longius inter &longs;e di&longs;tent: qui vero re&shy;<lb/>motiore, ad &longs;ubtiliorem, vt in qua not&aelig; minus di&longs;tent in lateribus <lb/>&longs;capi &longs;ignat&aelig;. </s>

<s id="id.002289">Deinde pote&longs;tate plures &longs;unt, cum an&longs;a vna e&longs;t, &longs;ed mi&shy;<lb/>nim&egrave; fixa, verum libero modo propius A, modo remotius colloca&shy;<lb/>tur. </s>

<s id="id.002290">Semper autem in aliquo puncto inter A &amp; B intermedio. <lb/></s>

<s id="id.002291">Vnde e&longs;t quod h&icirc;c dicat Ari&longs;toteles an&longs;am ad partes, vbi e&longs;t &aelig;qui&shy;<lb/>pondium, e&longs;&longs;e dimidium &longs;tater&aelig;, non &longs;umendo dimidium exact&egrave;, <lb/>quandoquidem extremo, &agrave; quo lanx <expan abbr="dep&etilde;det">dependet</expan> &longs;emper propior &longs;it. </s>

<s id="id.002292">Hinc <lb/>elicitur pulchra regula &egrave; qua po&longs;tea fer&egrave; omnia, qu&aelig; ad &longs;tater&aelig; ratio&shy;<lb/>nem pertinent, deducuntur. </s>

<s id="id.002293">qu&aelig; e&longs;t eiu&longs;modi. </s>

<s id="id.002294">Cum &longs;capus integer ad <lb/>pondus appen&longs;um, rationem eam habet: quam duplum partis, qu&aelig; e&longs;t <lb/>ab an&longs;a ver&longs;us lancem ad reliquum: tunc <expan abbr="p&otilde;dus">pondus</expan> &longs;capum vniformem, <lb/>&amp; omnibus &longs;uis partibus &aelig;qualem in &aelig;quilubrio con&longs;tituit. </s>

<s id="id.002295">Vt e&longs;to <lb/>&longs;capus A B duodecim vnciarum, &amp; pars A F <expan abbr="duar&utilde;">duarum</expan>: huius partis <lb/>duplum e&longs;t 4. &amp; reliquum 8. </s>

<s>Quemadmodum ergo 4. ad 8. &longs;ic &longs;ca&shy;<lb/>pus rotus id e&longs;t 12. erit ad pondus, quod per regulam trium inuenie&shy;<lb/>tur e&longs;&longs;e 4. vnciarum. </s>

<s id="id.002296">Rur&longs;us &longs;it an&longs;a in D &amp; A D &longs;it vna vn&shy;<lb/>cia. </s>

<s id="id.002297">Huius duplum e&longs;t 2. </s>

<s>Reliquum e&longs;t 10. </s>

<s>Vt igitur 2. ad 10. &longs;ic 12. <lb/>totus &longs;capus erit ad pondus: quod per regulam trium inuenietur e&longs;&longs;e<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.188.jpg" pagenum="149"/>60. <emph type="italics"/>vnciarum. </s>

<s id="id.002298">Vbi notandum lancem in hoc numero pro &longs;uo pon&shy;<lb/>dere includi. </s>

<s id="id.002299">Notandum etiam pondus impo&longs;itum lanci e&longs;&longs;e perinde <lb/>atque &longs;i in puncto A imponeretur. </s>

<s id="id.002300">Sed de his qui mult&ograve; plura vide&shy;<lb/>re volet, videat apud Cardanum lib. 1. de &longs;ubtilitate. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002301"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002302">Et &aelig;quipondium ab an&shy;<lb/>&longs;ulis inuicem commotis, vt <lb/>commetiatur quantum &longs;it <lb/>pondus, trahit id, quod e&longs;t <lb/>in lance po&longs;itum. </s>

<s id="id.002303"><expan abbr="Atq;">Atque</expan> co&shy;<lb/>gno&longs;cere licet, <expan abbr="quant&utilde;">quantum</expan> pon&shy;<lb/>dus lanx habeat, quando <lb/>&longs;tater&aelig; &longs;capus ad an&longs;am re&shy;<lb/>ctus fuerit. </s>

<s id="id.002304">Omnino qui&shy;<lb/>dem hoc e&longs;t libra habens <lb/>vnam lancem, in qua pon&shy;<lb/>dus appenditur, &amp; ex alte&shy;<lb/>ra parte in &longs;tatera equipon&shy;<lb/>dium. </s>

<s id="id.002305">Propterea altera pars <lb/>&longs;tater&aelig; e&longs;t &aelig;quipondium. <lb/></s>

<s id="id.002306">Et talis exi&longs;tens mult&aelig; &longs;unt <lb/>libr&aelig;, &amp; quidem tot, quot <lb/>&longs;unt an&longs;&aelig;. </s></p><p type="head">

<s id="id.002307">COMMENTARIVS. </s></p><p type="main">

<s id="id.002308">Et &aelig;quipondium.] <emph type="italics"/>Hic textus interiectus quidem e&longs;&longs;e vide&shy;<lb/>tur, non ita tamen inutilis, vt totus reijciendus &longs;it, quod aliquis <lb/>interpres fecit. </s>

<s id="id.002309">Indicat enim modum, quo cogno&longs;catur <expan abbr="p&otilde;derationis">ponderationis</expan> <lb/>&aelig;quilibrium. </s>

<s id="id.002310">quod e&longs;t vbi in appendendo &longs;capus &longs;tater&aelig; cum an&longs;a <lb/>rectos con&longs;tituit angulos, tuncque e&longs;t parallellus plano horizontis. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002311"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002312">Semper autem an&longs;a pro&shy;<lb/>pinquior lanci, ponderan&shy;<lb/>doque oneri, trahit maius <lb/>pondus. </s>

<s id="id.002313">quia &longs;tatera effici&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.189.jpg" pagenum="150"/><foreign lang="greek"><gap/></foreign>tur vectis inuer&longs;us. </s>

<s id="id.002315">E&longs;t enim <lb/>an&longs;a qu&aelig;libet &longs;upern&egrave; exi&shy;<lb/>&longs;tens hypomochlium. </s>

<s id="id.002316">Et <lb/>pondus id quod e&longs;t in lan&shy;<lb/>ce. </s>

<s id="id.002317">Quant&ograve; autem longi&shy;<lb/>tudo vectis maior fuerit ab <lb/>hypomochlio: tant&ograve; ibi fa&shy;<lb/>cilius mouet. </s>

<s id="id.002318">H&icirc;c autem <lb/>&longs;acoma facit &amp; ponderat <lb/>ad &aelig;quipondium pondus <lb/>&longs;tater&aelig;. </s></p><p type="head">

<s id="id.002319">COMMENTARIVS. </s></p><p type="main">

<s id="id.002320">Omnino quidem.] <emph type="italics"/>Repetitio e&longs;t a&longs;&longs;umptionum pr&aelig;ceden&shy;<lb/>tium &longs;yllogi&longs;morum &longs;cilicet,<emph.end type="italics"/></s></p><p type="main">

<s id="id.002321"><emph type="italics"/>Statera e&longs;t omnino libra. <lb/></s>

<s id="id.002322">&amp; <lb/>Statera mult&aelig; &longs;unt libr&aelig;. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002323">Semper autem.] <emph type="italics"/>Po&longs;tquam o&longs;ten&longs;um e&longs;t &longs;tateram magna pon&shy;<lb/>derare pondera: nunc qu&aelig;ritur quare tant&ograve; maiora ponderet: quant&ograve; <lb/>an&longs;am lanci habet propinquiorem. </s>

<s id="id.002324">Ratio e&longs;t quia vectis e&longs;t, &amp; &longs;ic <lb/>concluditur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002325"><emph type="italics"/>Qu&ograve; vectis habet hypomochlium propius ponderi mouendo, e&ograve; <lb/>maius mouet. </s>

<s id="id.002326">Reliquum enim ab hypomochlio longius e&longs;t. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002327"><emph type="italics"/>Statera e&longs;t vectis inuer&longs;us. </s>

<s id="id.002328">Nam an&longs;a e&longs;t hypomochlium &longs;u&shy;<lb/>perne exi&longs;tens, &amp; id quod lanci imponitur e&longs;t pondus <lb/>mouendum, vis mouens e&longs;t &aelig;quipondium. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002329"><emph type="italics"/>Ergo qu&ograve; an&longs;a erit propior ponderi, e&ograve; &longs;tatera maiora pondera&shy;<lb/>bit pondera. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002330">H&icirc;c autem &longs;acoma.] <emph type="italics"/>Hic locus &egrave; Gr&aelig;co in Latinum verbo <lb/>ad verbum ver&longs;us difficilem, ne dicam nullum &longs;en&longs;um habet. </s>

<s id="id.002331">Vide&shy;<lb/>tur tamen Ari&longs;toteles &amp; appo&longs;it&egrave; volui&longs;&longs;e &longs;ignificare &aelig;quipondium <lb/>e&longs;&longs;e in &longs;tatera, vim mouentem, &amp; vnum actu cum &longs;it, quia tamen <lb/>per varias notas di&longs;currere pote&longs;t in &longs;tatera, pr&aelig;&longs;tare ad diuer&longs;a pon&shy;<lb/>dera pendenda, quod in altera libr&aelig; lance diuer&longs;a &longs;acomata. </s>

<s id="id.002332">E&longs;t enim<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.190.jpg" pagenum="151"/><foreign lang="greek">sh/kwma,</foreign> <emph type="italics"/>vt annotauit Bud&aelig;us in Pandect. quod apponitur in libra <lb/>ad &aelig;quilibrium faciendum. </s>

<s id="id.002333">Vnde &amp; apud Vitruuium legimus re&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg36"/><lb/><emph type="italics"/>demptorem ad tempus opus manufactum &longs;ubtiliter regi approba&shy;<lb/>ui&longs;&longs;e, &amp; ad &longs;acoma pondus coron&aelig; vi&longs;um e&longs;&longs;e pr&aelig;&longs;titi&longs;&longs;e. </s>

<s id="id.002334">C&aelig;terum <lb/>quam rationem habeat &aelig;quipondium ad &longs;e&longs;e pro varijs inter&longs;tit&uuml;s, <lb/>quibus remouetur ab an&longs;a, colligi pote&longs;t ex Vbaldo per corollarium <lb/>quod deduxit &egrave; prop. 6. tractatus de lib. in Mech. quod tale e&longs;t. </s>

<s id="id.002335">Ma&shy;<lb/>nife&longs;tum e&longs;t qu&ograve; pondus &agrave; centro libr&aelig; magis di&longs;tat, e&ograve; grauius e&longs;&longs;e, <lb/>&amp; per con&longs;equens velocius moueri. </s>

<s id="id.002336">Et &aelig;quipondij grauitatem in <lb/>vno loco ad grauitatem eiu&longs;dem in altero, eam rationem habere per <lb/>experientiam noui&longs;&longs;e &longs;e dicit Cardanus, quam habet remotio ad re&shy;<emph.end type="italics"/><lb/><arrow.to.target n="marg37"/><lb/><emph type="italics"/><expan abbr="motion&etilde;">motionem</expan>. <lb/> </s><emph.end type="italics"/><lb/><figure id="id.035.01.190.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.190.1.jpg"/>

<s><emph type="italics"/>vt &longs;i &aelig;qui <lb/><expan abbr="pondi&utilde;">pondium</expan> K <lb/>in D ele&shy;<lb/>uet libras <lb/>20. &amp; in <lb/>E 25. ele&shy;<lb/>uabit in F <lb/>30. In G 35. In H 40. </s>

<s>Sic &aelig;quali &longs;patio &aelig;quale <expan abbr="acquir&etilde;s">acquirens</expan> <expan abbr="augment&utilde;">augmentum</expan>. <emph.end type="italics"/></s></p><p type="margin">

<s id="id.002337"><margin.target id="marg36"/>Cap. 3. lib. <margin.target id="marg37"/>65. c. Arich</s></p><p type="main">

<s id="id.002338"><emph type="italics"/>Et quidem &longs;tater&aelig; ratio demon&longs;trari pote&longs;t. </s>

<s id="id.002339">Sit &longs;tater&aelig; &longs;capus <lb/>H B cu&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.190.2.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.190.2.jpg"/><lb/><emph type="italics"/>ius an&longs;a <lb/>&longs;it A C, <lb/>&amp; eius <lb/>&aelig;quipon&shy;<lb/>dium E, <lb/>appenda&shy;<lb/>tur vero <lb/>ex H <expan abbr="p&otilde;-dus">pon&shy;<lb/>dus</expan> D, <lb/>quod &aelig;quiponderet &aelig;quipondio E in F appen&longs;o. </s>

<s id="id.002340">Aliud quoque pon&shy;<lb/>dus G appendatur in H, quod etiam &aelig;quipondio in B appen&longs;o <lb/>&aelig;quiponderet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002342"><emph type="italics"/>Dico grauitatem ponderis D ad grauitatem ponderis G ita e&longs;&longs;e <lb/>vt C F ad C B. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.191.jpg" pagenum="152"/><p type="head">

<s id="id.002343">Demon&longs;t. </s></p><p type="main">

<s id="id.002344"><emph type="italics"/>Quia grauitas ponderis D e&longs;t &aelig;qualis grauitati ponderis E ex F <lb/>dependentis, &amp; grauitas ponderis G e&longs;t &aelig;qualis grauitati ponderis <lb/>E ex B, erit grauitas ponderis D ad grauitatem E ex F: vt gra&shy;<lb/>uitas ponderis G ad grauitatem ponderis E ex B, &amp; permutatim <lb/>prop. 16. lib. 5. </s>

<s>vt grauitas ponderis D ad grauitatem ponderis G: <lb/>ita grauitas ip&longs;ius E ex F ad ip&longs;um E ex B. </s>

<s id="id.002345">Grauitas autem pon&shy;<lb/>deris E ex F dependentis ad grauitatem ponderis E ex B e&longs;t: vt <lb/>C F ad C B, vt demon&longs;trat Vbaldus prop. 6. tract. delib. </s>

<s>vt igitur <lb/>grauitas ponderis D ad pondus G: ita e&longs;t C F ad C B. </s>



<s id="id.002346">Si ergo <lb/>pars &longs;capi C B diuidatur in partes &aelig;quales &longs;olo pondere E, &amp; pro&shy;<lb/>pius &amp; longius &agrave; puncto C po&longs;ito, ponderum grauitates ex puncto <lb/>H appen&longs;&aelig; not&aelig; erunt. </s>

<s id="id.002347">Exempli gratia &longs;it di&longs;tantia C B tripla ad <lb/>C F, erit pondus G triplum ponderis D. </s>

<s>quod demon&longs;trare oportebat. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002348"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002349">22. De dentiduco. </s></p><p type="main">

<s id="id.002350"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002351">Cur medici facilius den&shy;<lb/>tes <expan abbr="exim&utilde;t">eximunt</expan> <expan abbr="accipi&etilde;tes">accipientes</expan> pon&shy;<lb/>dus, <expan abbr="d&etilde;tiducum">dentiducum</expan>: <expan abbr="qu&atilde;">quam</expan> &longs;i &longs;ola <lb/>vtantur manu. </s>

<s id="id.002352">Vtrum quia <lb/>dens magis manum pr&aelig;&shy;<lb/>terlabitur, quam dentidu&shy;<lb/>cum? </s>

<s id="id.002353">vel ferrum quidem <lb/>magis labitur manu, neque <lb/>ip&longs;um vndique <expan abbr="compreh&etilde;-dit">comprehen&shy;<lb/>dit</expan>. </s>

<s id="id.002354">E&longs;t enim digitorum <lb/>caro mollis, &amp; adh&aelig;ret ma&shy;<lb/>gis, atque vndique con&shy;<lb/>gruit. </s>

<s id="id.002355">Verum quia denti&shy;<lb/>ducus e&longs;t duo vectes aduer&shy;<lb/>&longs;i, vnum <expan abbr="hypomochli&utilde;">hypomochlium</expan> ha&shy;<lb/>bentes in concur&longs;u com&shy;<lb/>mi&longs;&longs;ur&aelig;. </s>

<s id="id.002356">Igitur ad <expan abbr="ex&etilde;ptio-n&etilde;">exemptio&shy;<lb/>nem</expan>, vt facilius <expan abbr="dimoue&atilde;t">dimoueant</expan>, hoc <lb/>vtuntur organo. </s>

<s id="id.002357">Sit enim <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.192.jpg" pagenum="153"/><foreign lang="greek"><gap/></foreign><lb/>dentiduci extremum alte&shy;<lb/><figure id="id.035.01.192.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.192.1.jpg"/><lb/>rum <foreign lang="greek">a,</foreign> alterum <foreign lang="greek">b,</foreign> quod <lb/>eximit, vectis vero <foreign lang="greek">a q z,</foreign><lb/>&amp; alter vectis <foreign lang="greek">b g e</foreign>: hypo&shy;<lb/>mochlium ver&ograve; <foreign lang="greek">q</foreign> vbi e&longs;t <expan abbr="c&otilde;-mi&longs;&longs;ura">con&shy;<lb/>mi&longs;&longs;ura</expan>: <expan abbr="d&etilde;s">dens</expan> ver&ograve; <expan abbr="p&otilde;dus">pondus</expan> e&longs;t. <lb/></s>

<s id="id.002358">Vtroque igitur extremo <foreign lang="greek">b <lb/>&amp; z</foreign> &longs;imul capiens dimouet: <lb/>quando vero emotus fuerit, manu facilius: quam in&longs;tru&shy;<lb/>mento eximetur. </s></p><p type="head">

<s id="id.002359">COMMENTARIVS. </s></p><p type="main">

<s id="id.002360">De dentiduco.] <foreign lang="greek">o)donta/gran h)\ o)donta/gwgon</foreign> <emph type="italics"/>vertit C&aelig;lius <lb/>Aurelianus cap. 4. lib. 2. <emph.end type="italics"/> <foreign lang="greek">xroniw=n</foreign> <emph type="italics"/>pa&szlig;ionum dentiducum: Cel&shy;<lb/>&longs;us forficem, &amp; generaliter forcipem. </s>

<s id="id.002361">E&longs;t autem in&longs;trumentum, quo <lb/>dens eximitur. </s>

<s id="id.002362">Corro&longs;us enim aut vehementer dolens pr&aelig;&longs;cripto <lb/>medicorum eximi iubetur. </s>

<s id="id.002363">Refert tamen Era&longs;i&longs;tratus, vt e&longs;t apud <lb/>C&aelig;lium Aurelianum, plumbeum odontagogum apud Delphum in <lb/>templo Apollinis, o&longs;tentationis cau&longs;a propo&longs;itum, quo demon&longs;traba&shy;<lb/>tur oportere &longs;olos eos dentes auferri, qui &longs;int faciles, vel mobilitate <lb/>laxati, vel quibus &longs;ufficeret plumbei in&longs;trumenti conamen ad &longs;um&shy;<lb/>mum. </s>

<s id="id.002364">Et profect&ograve; dens integer, &amp; firmus, quid vtilis e&longs;t ad bene e&longs;&longs;e, <lb/>temer&egrave; eximi non debet, vt pa&szlig;im fit, &longs;ine iu&longs;&longs;u medicorum &agrave; vulga&shy;<lb/>ribus &amp; circumforaneis illis, qui ab hac &longs;ola chirurgica actione den&shy;<lb/>tiduci appellantur, propter quorum inpudentiam multi nobiles chi&shy;<lb/>rurgi operationem hanc, alioqui nece&longs;&longs;ariam aliquando, nec omnibus <lb/>facilem, dedignantur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002365">Cur medici.] <emph type="italics"/>Propo&longs;itio e&longs;t problematis de dente, cur facilius <lb/>dentiduco, quam &longs;ola manu eximatur, cui repugnantia ad augendam <lb/>difficultatem &longs;ed vnico ponderis vocabulo in &longs;inuata, opponitur, qua&shy;<lb/>&longs;i diceretur. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.193.jpg" pagenum="154"/><p type="main">

<s id="id.002366"><emph type="italics"/>Pondus adiectum ponderi non facilius mouet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002367"><emph type="italics"/>Dentiducus e&longs;t pondus, &amp; denti vt ponderi mouendo adij&shy;<lb/>citur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002368"><emph type="italics"/>Non igitur facilius mouet. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002369">Vtrum quia dens.] <emph type="italics"/>H&icirc;c continetur demon&longs;tratio problema&shy;<lb/>tis. </s>

<s id="id.002370">Vbi notandum dentem eximendum, vt melius eximatur, duo an&shy;<lb/>te exemptionem po&longs;tulare, prius, vt firm&egrave; apprehendatur: alterum <lb/>vt valid&egrave; dimoueatur. </s>

<s id="id.002371">In quo con&longs;i&longs;tit pr&aelig;cipu&egrave; pars exemptionis, <lb/>quandoquidem dens in gingiu&aelig; &longs;u&aelig; gynglimo e&longs;t, vt clauus ligno <lb/>infixus. </s>

<s id="id.002372">Horum autem prius primum quidem dentiduco attribuit, <lb/>vt minoris tamen momenti etiam relinquit digitis manus, vt quo&shy;<lb/>rum caro mollis vndiquaque dentem melius apprehendat, atque huic <lb/>congruat: &longs;ed alterum quod vim po&longs;tulat maiorem &longs;oli dentiduco <lb/><expan abbr="c&otilde;mittit">committit</expan>. </s>

<s id="id.002373">quia ip&longs;e &longs;it vectis duplicatus. </s>

<s id="id.002374">Ratio igitur &longs;ic concludetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002375"><emph type="italics"/>Pondus facilius vecte: quam manu &longs;ola mouetur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002376"><emph type="italics"/>Dentiducus e&longs;t duo vectes &longs;ibi inuicem oppo&longs;iti. </s>

<s id="id.002377">Habent <lb/>enim in commi&longs;&longs;ura hypomochlium, &amp; dens e&longs;t pondus <lb/>mouendum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002378"><emph type="italics"/>Ergo dens dentiduco facilius: quam manu &longs;ola mouebitur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002379">Sit enim dentiduci.] <emph type="italics"/>Lineari demon&longs;tratione o&longs;tenditur pr&aelig;&shy;<lb/>cedentis &longs;yllogi&longs;mi a&longs;&longs;umptio. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002380">Quando ver&ograve; emotus.] <emph type="italics"/>Factis ijs, qu&aelig; ante exemptionem <lb/>po&longs;tulabat fieri dens eximendus, vltimum quod e&longs;t exemptio melius <lb/>fieri &agrave; digitis: quam &agrave; dentiduco a&longs;&longs;erit Ari&longs;toteles, nulla tamen ra&shy;<lb/>tione adhibita, licet in clauis ferreis &egrave; ligno eximendis, totum per for&shy;<lb/>cipem melius ab&longs;oluatur negotium. </s>

<s id="id.002381">Sed res di&szlig;imilis videbitur dili&shy;<lb/>gentius attendenti. </s>

<s id="id.002382">Nam in clauo eximendo iam emoto forceps ex <lb/>eminentiori &longs;ui parte vt<emph.end type="italics"/> <foreign lang="greek">x</foreign> <emph type="italics"/>vel<emph.end type="italics"/> <foreign lang="greek">l</foreign> <emph type="italics"/>parietem, aut lignum attingit, &amp; <lb/>punctum contactus fit fulcimentum, &amp; huic totus vt vectis vnus <lb/>effectus innititur, vnde etiam clauus flectitur, &amp; contorquetur in <lb/>euul&longs;ione. </s>

<s id="id.002383">quia motus non fit &longs;ecundum rectam: at in dente eximen&shy;<lb/>do, non datur locus tali coaptationi propter gingiu&aelig; &longs;ubiect&aelig; molli&shy;<lb/>ciem, &amp; eiu&longs;dem l&aelig;&longs;ionis periculum, &amp; vt daretur dens potius &longs;ic <lb/>frangeretur: quam contorqueretur, &longs;icque &egrave; parte tantum eximeretur <lb/>magno dolor is augmento, &amp; reliqu&aelig; partis incommodo. </s>

<s id="id.002384">Itaque rect&agrave; <lb/>&longs;ur&longs;um educi po&longs;tulat, quod melius fit manu ob apprehen&longs;ionis vndi&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.194.jpg" pagenum="155"/><emph type="italics"/>quaque fact&aelig;, vt antea dictum e&longs;t, commoditatem <expan abbr="maior&etilde;">maiorem</expan>, &amp; rect&aelig; <lb/>eleuationis nullis propemodum viribus indig&aelig; opportunitatem. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002385"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002386">23. De in&longs;trumentis qu&aelig; <lb/>faciunt ad frangendum <lb/>nuces. </s></p><p type="main">

<s id="id.002387"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002388">Cur facilius in nucifran&shy;<lb/>gibulis nuces &longs;ine ictu <expan abbr="fr&atilde;-gunt">fran&shy;<lb/>gunt</expan>. </s>

<s id="id.002389">Multa enim vis illa&shy;<lb/>tionis &amp; <expan abbr="viol&etilde;ti&aelig;">violenti&aelig;</expan> demitur. <lb/></s>

<s id="id.002390">Pr&aelig;terea duro &amp; graui <expan abbr="c&otilde;-primens">con&shy;<lb/>primens</expan> velocius fregerit: <lb/>quam ligneo &amp; leui in&longs;tru&shy;<lb/>mento. </s>

<s id="id.002391">An quia &longs;ic vtrin&shy;<lb/>que &agrave; duobus vectibus nux <lb/><expan abbr="c&otilde;primitur">comprimitur</expan>, vecte vero fa&shy;<lb/>cile pondera diuelluntur, <lb/>in&longs;trumentum enim duo&shy;<lb/>bus con&longs;tat vectibus, Idem <lb/>hypomochlium <expan abbr="hab&etilde;tibus">habentibus</expan> <lb/>contactum vbi e&longs;t A. </s>

<s id="id.002392">Vt <lb/>igitur &longs;i line&aelig; E D, F C <lb/>diduct&aelig; e&longs;&longs;ent extremis C, <lb/>D motis, facile ab exigua <lb/>vi coadducerentur. </s>

<s id="id.002393">Quod <lb/>igitur ex ictu pondus feci&longs;&shy;<lb/>&longs;et, hoc valentius E D &amp; <lb/>F C vectes <expan abbr="c&utilde;">cum</expan> &longs;int, efficiunt. <lb/></s>

<s id="id.002394">Elatione enim in <expan abbr="aduers&utilde;">aduersum</expan> <lb/>tollunt, &amp; comprimentes <lb/>frangunt, quod e&longs;t vbi K. <lb/></s>

<s id="id.002395">Ob id quant&ograve; ip&longs;i K fuerit <lb/>propior commi&longs;&longs;ura A tan&shy;<lb/>t&ograve; citius conterit. </s>

<s id="id.002396">Quant&ograve; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.195.jpg" pagenum="156"/><foreign lang="greek"><gap/></foreign><lb/>enim plus di&longs;titerit vectis <lb/>ab hypomochlio, tant&ograve; fa&shy;<lb/>cilius ab eadem vi mouet. <lb/></s>

<s id="id.002397">E&longs;t igitur A <expan abbr="hypomochli&utilde;">hypomochlium</expan>, <lb/>&amp; E A D vectis, vt &amp; F A <lb/>C. </s>

<s id="id.002398">Quant&ograve; igitur ip&longs;um K <lb/>propius fuerit angulo A, <lb/>tant&ograve; propius fit commi&longs;&longs;u&shy;<lb/>r&aelig; A. </s>

<s id="id.002399">H&aelig;c ver&ograve; e&longs;t hypo&shy;<lb/>mochlium. </s>

<s id="id.002400">Nece&longs;&longs;e igitur <lb/>ab eadem vi coadducente <lb/>E, F plus extolli. </s>

<s id="id.002401">Et quia <lb/>eleuatio ex aduer&longs;o e&longs;t, ma&shy;<lb/>gis conteri nece&longs;&longs;e e&longs;t, ma&shy;<lb/>gis ver&ograve; contritum celerius <lb/>frangitur. </s></p><p type="head">

<s id="id.002402">COMMENTARIVS. </s></p><p type="main">

<s id="id.002403">De in&longs;trumentis.] <emph type="italics"/>In&longs;trumentum ad frangendum nuces <lb/>pote&longs;t appellari nucifrangibulum, &amp; hoc non differt &agrave; forcipe <lb/>ni&longs;i quia leuiter in extremis excauatur ad excipiendum nucem fran&shy;<lb/>gendam commodius, Huiu&longs;mo&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.195.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.195.1.jpg"/><lb/><emph type="italics"/>di e&longs;t F A C E A B. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002404">Cur facilius.] <emph type="italics"/>Qu&aelig;ritur <lb/>cur nucifrangibulum ab&longs;que ictu <lb/>facillim&egrave; frangat nucem. </s>

<s id="id.002405">Quod <lb/>problema, vt <expan abbr="anteced&etilde;s">antecedens</expan>, generale <lb/>e&longs;&longs;e pote&longs;t de quouis forcipe &amp; forfice, ad capiendum &longs;cindendum <lb/>frangendum qualibus multis chirurgi, &amp; quiuis manuales artifices <lb/>opera &longs;ua exercent &amp; perficiunt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002406">Multa enim vis.] <emph type="italics"/>Repugnantia e&longs;t ad augendam problematis <lb/>difficultatem &longs;ic,<emph.end type="italics"/></s></p><p type="main">

<s id="id.002407"><emph type="italics"/>Quod vim adfert motioni, plus valet ad frangendum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002408"><emph type="italics"/>Ictus motioni vim adfert. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002409"><emph type="italics"/>Ictus igitur ad frangendum plus valet. <emph.end type="italics"/></s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.196.jpg" pagenum="157"/><p type="main">

<s id="id.002410">Pr&aelig;terea duro.] <emph type="italics"/>Alterum e&longs;t qua&longs;i problema quod nuci&shy;<lb/>frangibulum durum &amp; graue facilius frangat: quam ligneum &amp; <lb/>leue. </s>

<s id="id.002411">Cum tamen contra euenire deberet. </s>

<s id="id.002412">Siquidem graue quod e&longs;t, <lb/>difficilius emoueatur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002413">An quia &longs;ic vtrinque.] <emph type="italics"/>Demon&longs;tratio e&longs;t problematis &longs;ic. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002414"><emph type="italics"/>Valide comprimentia compre&longs;&longs;um frangunt. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002415"><emph type="italics"/>Nucifrangibulum valid&egrave; nucem comprehen&longs;am comprimit. <lb/></s>

<s id="id.002416">quia duplicatus e&longs;t vectis, vnum hypomochlium, vt in A <lb/>commi&longs;&longs;ura habentibus. </s>

<s id="id.002417">Diductis enim B C extremis <lb/>vectium E A B &amp; F A C &agrave; viribus in E &amp; F. <lb/>alteris vectium extremis exi&longs;tentibus, &longs;i ip&longs;a compriman&shy;<lb/>tur etiam B &amp; C comprimentur. </s>

<s id="id.002418">Quare &amp; nux D in&shy;<lb/>terpo&longs;ita, &amp; valide compre&longs;&longs;a frangitur, tant&ograve; celerius: <lb/>quant&ograve; extrema B &amp; C minus di&longs;tabunt ab hypomoch&shy;<lb/>lio A. </s>

<s id="id.002419">Sic enim ali&aelig; partes vectium ab ip&longs;o di&longs;tantes <lb/>maiorem rationem habebunt. </s>

<s id="id.002420">Et proinde facilius moue&shy;<lb/>bunt pondus mouendum, vt ante &longs;&aelig;pius e&longs;t declaratum, <lb/>Quare quod percu&longs;sione, vel ictu pondus aliquod irruens <lb/>in nucem feci&longs;&longs;et, id vectes compre&szlig;i certius faciunt. </s>

<s id="id.002421">S&aelig;p&egrave; <lb/>enim ictum ob &longs;ui <expan abbr="rot&utilde;ditatem">rotunditatem</expan> nux eludit. </s>

<s id="id.002422">Nam cum nux <lb/>&longs;it rotunda, in&longs;i&longs;tat autem plano attingens ip&longs;am puncto, <lb/>&amp; &agrave; plano mallei in puncto attingatur, facile elabitur, ni&longs;i <lb/>ictus<emph.end type="italics"/> <foreign lang="greek">kat' i)/cin</foreign> <emph type="italics"/>incidat in rectam, qu&aelig; coniungit h&aelig;c duo <lb/>puncta. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002423"><emph type="italics"/>Itaque nucifrangibulum nucem facile &longs;ine ictu franget. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002424">Quant&ograve; igitur.] <emph type="italics"/>Repetitio e&longs;t eiu&longs;dem &longs;uperflua. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002425"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002426">24. Cur in Rhombo <expan abbr="alter&utilde;">alterum</expan> <lb/><expan abbr="p&utilde;ctorum">punctorum</expan> extremorum <lb/>non &aelig;qualem rectam <lb/>tran&longs;it. </s></p><p type="main">

<s id="id.002427"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002428">Cur amborum extremo&shy;<lb/>rum <expan abbr="p&utilde;ctorum">punctorum</expan> duabus la&shy;<lb/>tionibus in rhombo lato&shy;<lb/>rum, alterum non tran&longs;it <lb/>&aelig;qualem rectam. </s>

<s id="id.002429">&longs;ed alte&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.197.jpg" pagenum="158"/><foreign lang="greek"><gap/></foreign><lb/><arrow.to.target n="marg38"/><lb/>rum plus. </s>

<s id="id.002430">Idem e&longs;t &longs;ermo <lb/>quare motum &longs;uper latere <lb/>minorem tran&longs;it <expan abbr="rect&atilde;">rectam</expan>: <expan abbr="qu&atilde;">quam</expan> <lb/>latus. </s>

<s id="id.002431">Illud enim minorem <lb/>diametrum: hoc ver&ograve; latus <lb/>maius, licet &amp; hoc vna: illud <lb/>ver&ograve; duabus feratur latio&shy;<lb/>nibus. </s>

<s id="id.002432">Feratur enim &longs;uper <foreign lang="greek">a <lb/>b</foreign> <expan abbr="punct&utilde;">punctum</expan> <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">a</foreign> ver&longs;us <foreign lang="greek">b,</foreign><lb/>&amp; <foreign lang="greek">b</foreign> ver&longs;us <foreign lang="greek">a</foreign> <expan abbr="ead&etilde;">eadem</expan> celerita&shy;<lb/>te: feratur <expan abbr="eti&atilde;">etiam</expan> latus <foreign lang="greek">a b</foreign> &longs;u&shy;<lb/>per <foreign lang="greek">a g</foreign> parallelum ip&longs;i <foreign lang="greek">g d</foreign><lb/><expan abbr="ead&etilde;">eadem</expan> celeritate <expan abbr="c&utilde;">cum</expan> his pun&shy;<lb/>ctis. </s>

<s id="id.002433">Nece&longs;&longs;e igitur <expan abbr="p&utilde;ctum">punctum</expan> <lb/><expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">a</foreign> per <expan abbr="diametr&utilde;">diametrum</expan> <foreign lang="greek">a d</foreign><lb/>ferri: <foreign lang="greek">b</foreign> vero per <foreign lang="greek">b g,</foreign> &amp; &longs;i&shy;<lb/>mul vtranque pertran&longs;ii&longs;&longs;e. <lb/></s>

<s id="id.002434"><expan abbr="T&utilde;">Tum</expan> &amp; latus <foreign lang="greek">a b</foreign> ip&longs;um <foreign lang="greek">a g. </foreign><lb/>Latum <expan abbr="quid&etilde;">quidem</expan> &longs;it <expan abbr="p&utilde;ctum">punctum</expan> <foreign lang="greek">a</foreign><lb/>per <expan abbr="line&atilde;">lineam</expan> <foreign lang="greek">a e,</foreign> &amp; <foreign lang="greek">a b</foreign> per <foreign lang="greek">a z,</foreign><lb/>&amp; &longs;it deducta <foreign lang="greek">z h</foreign> parallela <lb/>ip&longs;i <foreign lang="greek">a b,</foreign> &amp; per <expan abbr="punct&utilde;">punctum</expan> <foreign lang="greek">e</foreign> <expan abbr="c&otilde;-pleatur">com&shy;<lb/>pleatur</expan>. </s>

<s id="id.002435">Simile igitur fi<emph type="italics"/>t<emph.end type="italics"/> <expan abbr="c&otilde;-pletum">com&shy;<lb/>pletum</expan> toti parallelogram&shy;<lb/>mo. </s>

<s id="id.002436">Igitur &aelig;qualis e&longs;t <foreign lang="greek">a z</foreign><lb/>ip&longs;i <foreign lang="greek">a e: a b</foreign> vero latus <expan abbr="lat&utilde;">latum</expan> <lb/>erit per <foreign lang="greek">a z. </foreign>Erit itaque in <lb/>diametro iuxta <foreign lang="greek">q,</foreign> &amp; &longs;emper <lb/>iuxta <expan abbr="diametr&utilde;">diametrum</expan> ferri nece&longs;&shy;<lb/>&longs;e e&longs;t. </s>

<s id="id.002437">Et &longs;imul atque latus <lb/><foreign lang="greek">a g</foreign> <expan abbr="eti&atilde;">etiam</expan> punctum <foreign lang="greek">a</foreign> tran&longs;it <lb/><expan abbr="diametr&utilde;">diametrum</expan> <foreign lang="greek">a d. </foreign>Similiter ve&shy;<lb/>r&ograve; demon&longs;trabitur etiam <foreign lang="greek">b</foreign><lb/><expan abbr="lat&utilde;">latum</expan> e&longs;&longs;e per <expan abbr="diametr&utilde;">diametrum</expan> <foreign lang="greek">b g. </foreign><lb/>&AElig;qualis enim e&longs;t linea <foreign lang="greek">b e</foreign><lb/>ip&longs;i <foreign lang="greek">b h. </foreign>Completum igitur <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.198.jpg" pagenum="159"/><foreign lang="greek"><gap/></foreign><lb/>per punctum <foreign lang="greek">h</foreign> intus <expan abbr="paral-lelogramm&utilde;">paral&shy;<lb/>lelogrammum</expan> &longs;imile e&longs;t toti, <lb/>&amp; <foreign lang="greek">b</foreign> erit in diametro iuxta <lb/><expan abbr="contact&utilde;">contactum</expan> laterum. </s>

<s id="id.002438">Et &longs;imul <lb/>atque latus pertran&longs;it latus <lb/>etiam ip&longs;um <foreign lang="greek">b,</foreign> ip&longs;um <foreign lang="greek">b g</foreign><lb/>diametrum. </s>

<s id="id.002439">Simile igitur <lb/>ip&longs;um <foreign lang="greek">a</foreign> ip&longs;am <foreign lang="greek">a d</foreign> mult&ograve; <lb/><expan abbr="maior&etilde;">maiorem</expan> ip&longs;a <foreign lang="greek">b g</foreign> pertran&longs;it, <lb/>&amp; latus <expan abbr="mot&utilde;">motum</expan> eadem celeri&shy;<lb/>tate <expan abbr="minor&etilde;">minorem</expan> <expan abbr="line&atilde;">lineam</expan> [tran&longs;it.] <lb/>Et latus <foreign lang="greek">b d</foreign> vna latione <lb/>motum pertran&longs;ijt lineam <lb/>maiorem: quam <foreign lang="greek">b g. </foreign><expan abbr="qu&atilde;t&ograve;">quant&ograve;</expan> <lb/>enim acutior e&longs;t Rhombus, <lb/>diameter <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">b g</foreign> fit mi&shy;<lb/>nor, <foreign lang="greek">a d</foreign> vero maior, <expan abbr="t&utilde;">tum</expan> &amp; la&shy;<lb/>tus <foreign lang="greek">a b</foreign> maius quam <foreign lang="greek">b g. </foreign></s></p><p type="margin">

<s id="id.002440"><margin.target id="marg38"/>Quidam le&shy;<lb/>gunt <foreign lang="greek">lo/gw</foreign><lb/>pro <foreign lang="greek">ta/xei. </foreign></s></p><p type="head">

<s id="id.002441">COMMENTARIVS. </s></p><p type="main">

<s id="id.002442">Cvr amborum.] <emph type="italics"/>In hoc capite duo continentur problemata, <lb/><expan abbr="eor&utilde;que">eorumque</expan> &longs;olutiones. </s>

<s id="id.002443">Prius e&longs;t cur &egrave; duobus <expan abbr="p&utilde;ctis">punctis</expan> in vno Rhom&shy;<lb/>bi latere extremis eadem motis celeritate duobus &longs;imul motibus, vno <lb/>per &longs;e; altero ad motum lateris &longs;ui vnum plus &longs;patij conficit, nempe id <lb/>quod ab acuto angulo di&longs;cedit, alterum minus, nempe. </s>

<s id="id.002444">id quod ab <lb/>obtu&longs;o. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002445">Idem e&longs;t &longs;ermo.] <emph type="italics"/>Po&longs;terius e&longs;t cur vnum &ecirc; dictis punctis mo&shy;<lb/>tum pr&aelig;dictis duobus motibus minus aliquando &longs;patij conficiat: <expan abbr="qu&atilde;">quam</expan> <lb/>latus &longs;uum. </s>

<s id="id.002446">Vtrumque problema vt intelligatur &longs;ciendum e&longs;t e def. <lb/>32. lib. 1. Eucl. </s>

<s id="id.002448">Rhombum e&longs;&longs;e quadrilaterum &aelig;quilaterum, &amp; mini&shy;<lb/>m&egrave; rectangulum: Et tamen omnes eius angulos &aelig;quales e&longs;&longs;e quatuor <lb/>rectis per coroll. prop. 32. li. 1. Eucl. </s>

<s id="id.002451"><expan abbr="Cumq;">Cumque</expan> oppo&longs;iti in <expan abbr="parallelogr&atilde;mo">parallelogrammo</expan> <lb/>&longs;int &aelig;quales prop. 34. lib. <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> duo &longs;unt acuti, reliqui obtu&longs;i, vt &longs;it <lb/><expan abbr="Rh&otilde;bus">Rhombus</expan><emph.end type="italics"/> <foreign lang="greek">a b d g,</foreign> <emph type="italics"/>cuius anguli oppo&longs;iti<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>&longs;int acuti:<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>vero<emph.end type="italics"/> <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.199.jpg" pagenum="160"/><emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">g</foreign> <emph type="italics"/>obtu&longs;i. </s>

<s id="id.002453">Concipiamus ergo<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>tan&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.199.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.199.1.jpg"/><lb/><emph type="italics"/>quam formicam ambulantem proprio <lb/>motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">b,</foreign> <emph type="italics"/>vt &amp;<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>proprio iti&shy;<lb/>dem motu ver&longs;us<emph.end type="italics"/> <foreign lang="greek">a. </foreign><emph type="italics"/></s>

<s>Tum ip&longs;um<emph.end type="italics"/> <foreign lang="greek">a b</foreign><lb/><emph type="italics"/>latus ver&longs;us<emph.end type="italics"/> <foreign lang="greek">g d,</foreign> <emph type="italics"/>eadem etiam celerita&shy;<lb/>te moueri &longs;eruando paralleli&longs;mum, cum <lb/>ip&longs;o<emph.end type="italics"/> <foreign lang="greek">g d</foreign> <emph type="italics"/>quou&longs;que coniungatur ei. </s>

<s id="id.002454">Ad <lb/>huius autem <expan abbr="mot&utilde;">motum</expan> moueri etiam<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ver&shy;<lb/>&longs;us<emph.end type="italics"/> <foreign lang="greek">g,</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ver&longs;us<emph.end type="italics"/> <foreign lang="greek">d. </foreign><emph type="italics"/>Sicque<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>mouebuntur duobus motibus, vno per &longs;e: <lb/>altero per accidens. </s>

<s id="id.002455">Et po&longs;ito quod mo&shy;<lb/>ueantur in Rhombo. </s>

<s id="id.002456">Id e&longs;t quod motus <lb/>illi &longs;int in ratione laterum quibus Rhombus continetur. </s>

<s id="id.002457">E&longs;t autem <lb/>i&longs;ta certa, quia e&longs;t ratio &aelig;qualitatis vt<emph.end type="italics"/> <foreign lang="greek">i</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">i,</foreign> <emph type="italics"/>&amp; in eadem celerita&shy;<lb/>te, id e&longs;t eodem tempore, non immerit&ograve; primum problema in medium <lb/>adducitur. </s>

<s id="id.002458">quia &longs;i verum &longs;it, cau&longs;am habet minim&egrave; vulgarem. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002459">Feratur enim.] <emph type="italics"/>Prioris problematis <expan abbr="veritat&etilde;">veritatem</expan> geometric&egrave; o&longs;ten&shy;<lb/>dit. </s>

<s id="id.002460">Sit enim vt<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>proce&longs;&longs;erit per &longs;e v&longs;que ad<emph.end type="italics"/> <foreign lang="greek">e,</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>v&longs;que ad<emph.end type="italics"/><lb/><foreign lang="greek">z</foreign>: <emph type="italics"/>tunc quia motus illi &longs;unt in ratione laterum Rhombi id e&longs;t in ra&shy;<lb/>tione &aelig;qualitatis<emph.end type="italics"/> <foreign lang="greek">a e</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">a z</foreign> <emph type="italics"/>erunt &aelig;quales. </s>

<s id="id.002461">Perficiatur <expan abbr="parallelo-gramm&utilde;">parallelo&shy;<lb/>grammum</expan> prop. 31. lib. 1. <expan abbr="n&etilde;p&egrave;">nemp&egrave;</expan><emph.end type="italics"/> <foreign lang="greek">a e q z. </foreign><emph type="italics"/></s>

<s>Hoc erit &longs;imile toti<emph.end type="italics"/> <foreign lang="greek">a b d g. </foreign><lb/><emph type="italics"/>prop. 24. lib. 6. </s>

<s>Ergo per conu <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> prop. &longs;unt circa <expan abbr="eand&etilde;">eandem</expan> <expan abbr="diametr&utilde;">diametrum</expan><emph.end type="italics"/><lb/><foreign lang="greek">a q d,</foreign> <emph type="italics"/>&amp; &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>duobus motibus motum pr&aelig;dictis delineauit<emph.end type="italics"/> <foreign lang="greek">a q</foreign><lb/><emph type="italics"/>cum<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="greek">z h. </foreign></s>

<s><emph type="italics"/>proinde &amp;<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>etiam delineauerit<emph.end type="italics"/> <foreign lang="greek">a d</foreign><lb/><emph type="italics"/>cum peruenerit<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">g d. </foreign><emph type="italics"/></s>

<s>Simili ratiocinatione conficitur<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>eo&shy;<lb/>dem tempore peragra&longs;&longs;e diametrum<emph.end type="italics"/> <foreign lang="greek">b g. </foreign><emph type="italics"/></s>

<s>E&longs;t autem<emph.end type="italics"/> <foreign lang="greek">b g</foreign> <emph type="italics"/>minor: <lb/>quam<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>quia ba&longs;es &longs;unt duorum triangulorum<emph.end type="italics"/> <foreign lang="greek">g a b,</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">a b d</foreign><lb/><emph type="italics"/>bina latera<emph.end type="italics"/> <foreign lang="greek">a g, a b</foreign> <emph type="italics"/>binis<emph.end type="italics"/> <foreign lang="greek">a b, b d</foreign> <emph type="italics"/>&aelig;qualia habentium. </s>

<s id="id.002463">quia &longs;unt <lb/>latera eiu&longs;dem Rhombi, &amp; angulum<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>vtpote acutum minorem <lb/>angulo<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>vtpote obtu&longs;o. </s>

<s id="id.002464">Ergo prop. 24. lib. 1. ba&longs;is<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>maior e&longs;t <lb/>ba&longs;i<emph.end type="italics"/> <foreign lang="greek">b g. </foreign><emph type="italics"/></s>

<s>Et &longs;ic<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ab angulo acuto di&longs;cedens &longs;uis motibus maiorem <lb/>in Rhombo lineam tran&longs;it, quam<emph.end type="italics"/> <foreign lang="greek">b. </foreign></s></p><p type="main">

<s id="id.002465">Licet &amp; hoc.] <emph type="italics"/>Hoc additur ad augendam &longs;ecundi problematis <lb/>difficultatem. </s>

<s id="id.002466">Rationi enim con&longs;entaneum videtur, vt motum duo&shy;<lb/>bus motibus &longs;imul plus &longs;patij conficiat: quam quod vno tantum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002467">Nece&longs;&longs;e igitur.] <emph type="italics"/>Nam parallelogramma qu&aelig; toti &amp; inter &longs;e<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.200.jpg" pagenum="161"/><emph type="italics"/>&longs;unt &longs;imilia, &longs;unt circa eandem diametrum. </s>

<s id="id.002468">conu prop. 24. lib. 6. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002469">&AElig;qualis enim e&longs;t.] <emph type="italics"/>Quia in ratione &aelig;qualitatis motum e&longs;t<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">e</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">h. </foreign></s></p><p type="main">

<s id="id.002470">Mult&ograve; maiorem.] <emph type="italics"/>Quia<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>&longs;ubtendit mult&ograve; maiorem an&shy;<lb/>gulum, vtpote<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>obtu&longs;um, &amp; ide&ograve; maiorem recto: quam<emph.end type="italics"/> <foreign lang="greek">b g,</foreign> <emph type="italics"/>qu&aelig; <lb/>&longs;ubtendit<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>angulum acutum, &amp; ide&ograve; etiam minorem recto. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002471">Et latus <foreign lang="greek">b d. </foreign>] <emph type="italics"/>Attingit &longs;ecundum problema quod generaliter <lb/>verum non e&longs;t. </s>

<s id="id.002472">In Rhombo enim cuius, qui acutus e&longs;t angulus, maior <lb/>e&longs;t dimidio obtu&longs;i, vt in E<emph.end type="italics"/><lb/><figure id="id.035.01.200.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.200.1.jpg"/><lb/><emph type="italics"/>F G H: quia F H an&shy;<lb/>gulum E maiorem &longs;ubten&shy;<lb/>dit: quam E H, erit F H <lb/>maior E H prop. 18. lib. 1. <lb/></s>

<s>Sed verum e&longs;t in certo ca&shy;<lb/>&longs;u, eo nimirum (licet h&icirc;c <lb/>non &longs;it expre&longs;&longs;us) in quo <lb/>Rhombi acutus e&longs;&longs;et mi&shy;<lb/>nor: quam dimidius obtu&shy;<lb/>&longs;i, vt angulus A Rhombi <lb/>A B C D &longs;it minor: quam dimidius obtu&longs;i B, id e&longs;t quam A B C. <lb/></s>

<s id="id.002473">Dico latus A C maius e&longs;&longs;e diametro B C per eandem prop. 18. <lb/>&longs;ubtendit enim trianguli A B C maiorem angulum. </s>

<s id="id.002474">Po&longs;&longs;e autem <lb/>talem Rhombum con&longs;titui, patet. </s>

<s id="id.002475">quia angulus acutus &longs;eruata late&shy;<lb/>rum quorumuis a&longs;&longs;umptorum longitudine, infinit&egrave; minor fieri pote&longs;t, <lb/>prop. 9. lib. 1. </s>

<s>Ergo &amp; tandem dabitur minor dimidio obtu&longs;i. </s>

<s id="id.002476">Nam <lb/>&amp; dimidius recti, qui acutus e&longs;t, e&longs;t eo minor prop. 15. lib. 5. </s>

<s id="id.002477">Ergo in <lb/>tali Rhombo latus A B per A C vna latione motum, plus &longs;patij <lb/>confecit: quam B, quod peragrans B C duabus lationibus ferebatur. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002478"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002479">Ab&longs;urdum enim, vt <expan abbr="dict&utilde;">dictum</expan> <lb/>e&longs;t, quod duabus lationibus <lb/>fertur, tardius <expan abbr="nonnunqu&atilde;">nonnunquam</expan> <lb/>ferri eo, quod vna: &amp; <expan abbr="dato-r&utilde;">dato&shy;<lb/>rum</expan> <expan abbr="ambor&utilde;">amborum</expan> <expan abbr="punctor&utilde;">punctorum</expan> &aelig;qua&shy;<lb/>li celeritate <expan abbr="motor&utilde;">motorum</expan> <expan abbr="alter&utilde;">alterum</expan> <lb/><expan abbr="maior&etilde;">maiorem</expan> <expan abbr="tr&atilde;&longs;ire">tran&longs;ire</expan>. </s>

<s id="id.002480">Cau&longs;a ver&ograve; <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.201.jpg" pagenum="162"/><foreign lang="greek"><gap/></foreign><lb/>e&longs;t, quod amb&aelig; lationes <lb/>eius, quod ab obtu&longs;o angu<lb/>lo fertur fiunt fer&egrave; contra&shy;<lb/>ri&aelig;. </s>

<s id="id.002481">H&ecedil;c &longs;cilicet qua per &longs;e <lb/>fertur, &amp; h&aelig;c qua per latus <lb/>effertur. </s>

<s id="id.002482">Ei ver&ograve; quod ab <lb/>acuto, contingit ad idem <lb/>ferri, ob&longs;ecundat enim la&shy;<lb/>teris latio ei, qu&aelig; e&longs;t <expan abbr="&longs;ec&utilde;-dum">&longs;ecun&shy;<lb/>dum</expan> diametrum. </s>

<s id="id.002483">Et quan&shy;<lb/>t&ograve; hic angulus fuerit acu&shy;<lb/>tior, ille obtu&longs;ior vna latio <lb/>erit tardior: altera velo&shy;<lb/>cior. </s>

<s id="id.002484">Lationes enim magis <lb/><expan abbr="c&otilde;trari&aelig;">contrari&aelig;</expan> fiunt propter ob&shy;<lb/>tu&longs;iorem angulum: contra <lb/>ver&ograve; h&aelig; magis ad <expan abbr="id&etilde;">idem</expan> pro&shy;<lb/>pter <expan abbr="propinquitat&etilde;">propinquitatem</expan> linea&shy;<lb/>rum. </s>

<s id="id.002485">Ip&longs;um enim <foreign lang="greek">a</foreign> fere ad <lb/>idem fertur ex vtri&longs;que la&shy;<lb/>tionibus. </s>

<s id="id.002486"><expan abbr="Itaq;">Itaque</expan> altera coad&shy;<lb/>iuuatur. </s>

<s id="id.002487">Et <expan abbr="qu&atilde;t&ograve;">quant&ograve;</expan> acutior <lb/>fuerit angulus: tant&ograve; ma&shy;<lb/>gis: ip&longs;um ver&ograve; <foreign lang="greek">b</foreign> ad con&shy;<lb/>trarium. </s>

<s id="id.002488">Ip&longs;um enim ad <foreign lang="greek">a</foreign><lb/>fertur. </s>

<s id="id.002489">Latus ver&ograve; effertur <lb/>ver&longs;us ip&longs;um <foreign lang="greek">g. </foreign>Et quant&ograve; <lb/>fuerit angulus obtu&longs;ior <lb/>magis contrari&aelig; lationes <lb/>fiunt. </s>

<s id="id.002490">Rectior enim linea <lb/>fit, quod &longs;i omnin&ograve; recta <lb/>e&longs;&longs;et, e&longs;&longs;ent lationes omni&shy;<lb/>n&ograve; contrari&aelig;. </s>

<s id="id.002491">Latus vero <lb/>vno motu motum &agrave; nullo <lb/>impeditur. </s>

<s id="id.002492">&AElig;quum e&longs;t igitur, vt lineam maiorem tran&shy;<lb/>&longs;eat. </s></p><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.202.jpg" pagenum="163"/><p type="head">

<s id="id.002493">COMMENTARIVS. </s></p><p type="main">

<s id="id.002494">Ab&longs;urdum enim.] <emph type="italics"/>Repetitio e&longs;t eius, quod problematis &longs;ecun&shy;<lb/>di antea iam auxit difficultatem. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002495">Nonnunquam ferri.] <emph type="italics"/>Particula<emph.end type="italics"/> <foreign lang="greek">en)i/ote</foreign> <emph type="italics"/>nonnunquam indi&shy;<lb/>cat &longs;ecundum problema tantum verum e&longs;&longs;e &longs;pecialiter non in genere, <lb/>quod antea e&longs;t demon&longs;tratum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002496">Et datorum amborum.] <emph type="italics"/>Auget difficultatem problematis <lb/>primi. </s>

<s id="id.002497">Videbatur enim rationi con&longs;entaneum, vt duo totidem moti&shy;<lb/>bus mota, &amp; eadem celeritate id e&longs;t &aelig;quali tempore idem &longs;patium <lb/>conficerent. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002498">Cau&longs;a vero e&longs;t.] <emph type="italics"/>Po&longs;tquam problema primum verum e&longs;&longs;e geo&shy;<lb/>metrice demon&longs;tratum e&longs;t: nunc huius vtpote admirabilis cau&longs;am <lb/>adfert Phy&longs;icam. </s>

<s id="id.002499">quod &longs;cilicet mota duobus motibus, &longs;i ad eundem <lb/>terminum, ad quem tendent, celerius mouentur: &longs;i ad contrarios, tar&shy;<lb/>dius. </s>

<s id="id.002500">Illa enim &longs;ibi inuicem ob&longs;equuntur, &amp; vt clauus clauo pellitur: <lb/>ita motus motum adiuuat: h&aelig;c ver&ograve; &longs;ibi ob&longs;i&longs;tunt, &longs;e&longs;e impediunt, &amp; <lb/>remorantur, &amp; vt magis minu&longs;ve contrarij &longs;unt termini ad quos: <lb/>ita qu&aelig; &longs;ic mouentur, magis minu&longs;ve &longs;e accelerant, aut retardant. <lb/></s>

<s id="id.002501">Atqui<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ab angulo obtu&longs;o motum duorum motuum vno ad<emph.end type="italics"/> <foreign lang="greek">a,</foreign> <emph type="italics"/>alte&shy;<lb/>ro ad<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>tendens ad magis contrarios terminos tendit: quam<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>ten&shy;<lb/>dens dictis motibus ad<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">g. </foreign><emph type="italics"/>E&longs;t enim, vt antea demon&longs;tratum <lb/>e&longs;t,<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>diameter &amp; recta maior: quam<emph.end type="italics"/> <foreign lang="greek">g d. </foreign><emph type="italics"/>Et qu&ograve;<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>acutior <lb/>erit angulus, e&ograve;<emph.end type="italics"/> <foreign lang="greek">a d</foreign> <emph type="italics"/>maior erit ergo &aelig;quum e&longs;t, vt<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>tardius fera&shy;<lb/>tur: quam<emph.end type="italics"/> <foreign lang="greek">a. </foreign><emph type="italics"/>Et quidem tant&ograve; tardius: quant&ograve;<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>erit obtu&longs;ior angu&shy;<lb/>lus, &amp;<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>acutior ob cau&longs;am pr&aelig;dictam. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002502">Fere ad idem.] <emph type="italics"/>Particula<emph.end type="italics"/> <foreign lang="greek">sxedo\n</foreign> <emph type="italics"/>fer&egrave; ad&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.202.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.202.1.jpg"/><lb/><emph type="italics"/>iecta indicat non eundem e&longs;&longs;e terminum vtriu&longs;&shy;<lb/>que motionis, qua fertur<emph.end type="italics"/> <foreign lang="greek">a</foreign> <emph type="italics"/>: &longs;ed duos diuer&longs;os, ve&shy;<lb/>rum propiores, quam &longs;int termini ad quos<emph.end type="italics"/> <foreign lang="greek">b</foreign><lb/><emph type="italics"/>fertur. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002503">Rectior enim linea.] <emph type="italics"/>Id e&longs;t duo latera<emph.end type="italics"/> <foreign lang="greek">b a</foreign><lb/><emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">b d</foreign> <emph type="italics"/>magis accedunt ad rectam vnam, vtpo&shy;<lb/>te quia angulus obtu&longs;us &longs;i augeatur plu&longs;culum, <lb/>latera ip&longs;um continentia fient &egrave; directo: &amp; tunc <emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.203.jpg" pagenum="164"/><emph type="italics"/>erunt vna omnino recta, quod vbi e&longs;&longs;et, vt cum<emph.end type="italics"/> <foreign lang="greek">b a</foreign> <emph type="italics"/>peruenit ad<emph.end type="italics"/> <foreign lang="greek">b <lb/>l,</foreign> <emph type="italics"/>tunc lationes<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">l,</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>ad<emph.end type="italics"/> <foreign lang="greek">d</foreign> <emph type="italics"/>e&longs;&longs;ent ad contrarios omnino <lb/>terminos. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002504">Latus ver&ograve; vno.] <emph type="italics"/>Breuiter cau&longs;am attingit &longs;ecundi problema&shy;<lb/>tis, quod in motu &agrave; nullo impeditum &aelig;quum e&longs;t celerius moueri: quam <lb/>quod impeditur. </s>

<s id="id.002505">Latus autem in dicto Rhombo &agrave; nullo impeditur: <lb/>contra<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>impeditur. </s>

<s id="id.002506">Ergo<emph.end type="italics"/> <foreign lang="greek">l b</foreign> <emph type="italics"/>latus celerius feretur ip&longs;o<emph.end type="italics"/> <foreign lang="greek">b. </foreign></s></p><p type="main">

<s id="id.002507">&AElig;quum e&longs;t igitur.] <emph type="italics"/>Id nu&longs;quam in hoc problemate demon&shy;<lb/>&longs;tratum e&longs;t, pote&longs;t etiam fal&longs;um e&longs;&longs;e. </s>

<s id="id.002508">C&aelig;terum ex hoc problemate <lb/>collige, quod etiam Leonicus annotauit, quantum corporum confor&shy;<lb/>mationes &amp; figurarum in illis varietas peculiares illorum inclina&shy;<lb/>tiones, naturale&longs;que motus aut adiuuent, aut contra in&longs;igniter impe&shy;<lb/>diant. </s>

<s id="id.002509">Conglobata etenim exempli gratia plumbi ma&longs;&longs;a, &longs;i natur&aelig; <lb/>relinquatur &longs;u&aelig;, rect&agrave; citius deor&longs;um fertur: quam &longs;i eadem pondere <lb/>&longs;eruato exten&longs;a fuerit in laminam: imm&ograve; rur&longs;us inflexa &amp; in&longs;tar <lb/>carin&aelig; conformata fluitabit in aquis. </s>

<s id="id.002510">In rebus etiam artificialibus <lb/>gladius acuta &longs;ui acie facile &longs;ecat: obtu&longs;a non item. </s>

<s id="id.002511">H&aelig;c cum ita <lb/>&longs;int nemini ab&longs;urdum videri debet, duo puncta duabus motionibus <lb/>&aelig;quali celeritate mota non &aelig;quale pertran&longs;ire &longs;patium: &longs;ed mu&longs;t&ograve; <lb/>plus maiu&longs;que illorum alterum, vt ex Rhombi natura cert&ograve; demon&shy;<lb/>&longs;tratum e&longs;t. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002512"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002513">25. Cur maior circulus cum <lb/>minore per &aelig;qualem re&shy;<lb/>uoluitur. </s></p><p type="main">

<s id="id.002514"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002515"><expan abbr="Dubi&utilde;">Dubium</expan> e&longs;t cur maior cir&shy;<lb/>culus <expan abbr="&aelig;qual&etilde;">&aelig;qualem</expan> minori circu&shy;<lb/>lo orbitam volutione pera&shy;<lb/>gret, <expan abbr="qu&atilde;do">quando</expan> circa <expan abbr="id&etilde;">idem</expan> <expan abbr="c&etilde;tr&utilde;">centrum</expan> <lb/>po&longs;itus e&longs;t: At <expan abbr="c&utilde;">cum</expan> &longs;eor&longs;um <lb/>voluuntur, vt <expan abbr="hor&utilde;">horum</expan> magni&shy;<lb/>tudines &longs;e <expan abbr="hab&etilde;t">habent</expan> inter &longs;e, ita <lb/><expan abbr="eti&atilde;">etiam</expan> <expan abbr="eor&utilde;">eorum</expan> orbit&aelig;. </s>

<s id="id.002516">Pr&aelig;terea <lb/>vno &amp; eodem <expan abbr="exi&longs;t&etilde;te">exi&longs;tente</expan> cen&shy;<lb/>tro, <expan abbr="aliqu&atilde;do">aliquando</expan> quidem tan&shy;<pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.204.jpg" pagenum="165"/><foreign lang="greek"><gap/></foreign><lb/>ta fit orbita: quanta e&longs;t ea: <lb/>quam minor circulus pera&shy;<lb/>grat: aliquando ver&ograve; quam <lb/>maior. </s>

<s id="id.002517">Quod igitur maio&shy;<lb/>rem peragret maior mani&shy;<lb/>fe&longs;tum e&longs;t. </s>

<s id="id.002518">Angulus enim <lb/>videtur <expan abbr="euid&etilde;ter">euidenter</expan> e&longs;&longs;e peri&shy;<lb/>pheria cuiu&longs;que <expan abbr="c&utilde;">cum</expan> propria <lb/>diametro maioris circuli <lb/>maior [minoris minor.] Ita&shy;<lb/>que orbit&ecedil; <expan abbr="eand&etilde;">eandem</expan> rationem <lb/>euidenter habebunt inter <lb/>&longs;e. </s>

<s id="id.002519">Attamen quod circa <expan abbr="id&etilde;">idem</expan> <lb/><expan abbr="centr&utilde;">centrum</expan> po&longs;iti &aelig;qualem <expan abbr="or-bit&atilde;">or&shy;<lb/>bitam</expan> <expan abbr="c&otilde;ficiant">conficiant</expan> etiam <expan abbr="mani-fe&longs;t&utilde;">mani&shy;<lb/>fe&longs;tum</expan>. </s>

<s id="id.002520">At que ita vt aliquan&shy;<lb/>do orbita maioris circuli <lb/>&longs;it &aelig;qualis linea, aliquando <lb/>orbita minoris. </s>

<s id="id.002521">Sit enim <lb/>circulus maior <expan abbr="quid&etilde;">quidem</expan> <foreign lang="greek">d z g,</foreign><lb/>minor vero <foreign lang="greek">e h b,</foreign> &amp; <expan abbr="vtriu&longs;q;">vtriu&longs;que</expan> <lb/><expan abbr="centr&utilde;">centrum</expan> <foreign lang="greek">a.</foreign> </s>

<s>Atque ea quidem <lb/>per quam magnus circulus <lb/>per &longs;e voluitur <foreign lang="greek">z l,</foreign> &longs;it &amp; ea <lb/>per quam per &longs;e minor <foreign lang="greek">h k</foreign><lb/>&aelig;qualis <foreign lang="greek">z l.</foreign> </s>

<s>Si vero moueo <lb/><expan abbr="minor&etilde;">minorem</expan>, ip&longs;um <expan abbr="c&etilde;trum">centrum</expan> mo&shy;<lb/>ueo vbi e&longs;t <foreign lang="greek">a.</foreign> </s>

<s>Magnus au&shy;<lb/>tem connexus e&longs;to. </s>

<s id="id.002522">Quum <lb/>igitur <foreign lang="greek">a b</foreign> ad rectos fiet li&shy;<lb/>ne&aelig; <foreign lang="greek">h k,</foreign> &longs;imul etiam <foreign lang="greek">a g</foreign><lb/>ad rectos fiet line&aelig; <foreign lang="greek">z l. </foreign></s></p><p type="main">

<s id="id.002523">Quare per &aelig;qualem erit <lb/>tran&longs;latio, nemp&egrave; <foreign lang="greek">h k</foreign> in <lb/>qua e&longs;t <foreign lang="greek">z g. </foreign>Quod &longs;i quarta <lb/>pars per &ecedil;qualem voluitur, <pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.205.jpg" pagenum="166"/><gap/><lb/>quod totus circulus &aelig;qua&shy;<lb/>lem toti circulo reuolua&shy;<lb/>tur, manife&longs;tum e&longs;t. </s>

<s id="id.002524">Itaque <lb/>quando linea <foreign lang="greek">b h</foreign> peruene&shy;<lb/>rit ad <foreign lang="greek">k</foreign> etiam <foreign lang="greek">z g</foreign> peri&shy;<lb/>pheria erit in <foreign lang="greek">z l</foreign> &amp; circu&shy;<lb/>lus totus conuolutus. </s>

<s id="id.002525">Si&shy;<lb/>militer &longs;i maiorem moue&shy;<lb/>ro, cui &longs;it annexus minor <lb/><expan abbr="eod&etilde;">eodem</expan> centro exi&longs;tente, vna <lb/>cum <foreign lang="greek">a g</foreign> etiam <foreign lang="greek">a b</foreign> perpen&shy;<lb/>dicularis erit. </s>

<s id="id.002526">Illa quidem <lb/>ad <foreign lang="greek">z i</foreign> h&aelig;c ver&ograve; ad <foreign lang="greek">h q</foreign>. </s>

<s>Ita&shy;<lb/>que quando per &aelig;qualem <lb/>ip&longs;i <foreign lang="greek">h q</foreign> vel <foreign lang="greek">z i</foreign> rur&longs;um erit <lb/>tran&longs;latio etiam <foreign lang="greek">a g</foreign> per&shy;<lb/>pendicularis erit ad <foreign lang="greek">z i,</foreign> &amp; <lb/><foreign lang="greek">a b</foreign> ad <foreign lang="greek">h q,</foreign> vt ab initio <lb/>erunt in <foreign lang="greek">q, i</foreign>: atque id nul&shy;<lb/>la intercedente mora ma&shy;<lb/>ioris ad minorem, qua&longs;i ad <lb/>aliquod tempus in eodem <lb/>ip&longs;o puncto moueret. </s>

<s id="id.002527">vter&shy;<lb/>que enim vtroque modo <lb/>continu&egrave; mouetur. </s>

<s id="id.002528">Neque <lb/>minore vllum punctum <lb/>tran&longs;iliente, &amp; maiorem <lb/>minori &aelig;qualem tran&longs;ire, &amp; minorem maiori ab&longs;urdum. </s></p><p type="head">

<s id="id.002529">COMMENTARIVS. </s></p><p type="main">

<s id="id.002530">Dvbium e&longs;t.] <emph type="italics"/>Problema quod hoc capite proponitur, omnium <lb/>qu&aelig; ante propo&longs;ita &longs;unt, &amp; po&longs;tea proponentur forta&szlig;&egrave; e&longs;t &longs;ub&shy;<lb/>tili&szlig;imum. </s>

<s id="id.002531">E&longs;t autem eiu&longs;modi, cur circuli concentrici, &amp; in&aelig;quales <lb/>iuncti, &aelig;qualem tamen orbitam circumuolutione peragrent. </s>

<s id="id.002532">Et <expan abbr="qui-d&etilde;">qui&shy;<lb/>dem</expan> hoc euenire duobus modis ponitur. </s>

<s id="id.002533">Vno, vt orbita minoris ad&aelig;que&shy;<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.206.jpg" pagenum="167"/><emph type="italics"/>tur orbit&aelig;, quam &longs;eor&longs;um maior conficeret: altero, vt orbita maioris <lb/>ad&aelig;quetur orbit&aelig;, quam &longs;eor&longs;um minor conficeret. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002534">At cum &longs;eor&longs;im.] <emph type="italics"/>Problematis propo&longs;iti difficultas declara&shy;<lb/>tur ex orbita, quam &longs;inguli &longs;eor&longs;im voluti faciunt. </s>

<s id="id.002535">H&aelig;c enim &longs;em&shy;<lb/>per &egrave; maiore maior e&longs;t, &egrave; minore minor, &amp; quidem proportione re&shy;<lb/>&longs;pondens magnitudini peripheriarum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002536">Pr&aelig;terea vno.] <emph type="italics"/>Duo modi &aelig;quationis pr&aelig;dicti explicantur in <lb/>habentibus idem centrum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002537">Quod igitur maiorem.] <emph type="italics"/>Confirmatio e&longs;t difficultatis allat&aelig; <lb/>ex euidentia per &longs;en&longs;um. </s>

<s id="id.002538">Si quis enim notato puncto vt A circumuo&shy;<lb/>lutionis primo, &amp; quidem circulum maiorem &amp; minorem &longs;uper re&shy;<lb/>ctam plani circumuoluat, quou&longs;que redierit contactus in eodem pun&shy;<lb/>cto maioris circuli maior recta: minoris minor erit per agrata. </s>

<s id="id.002539">Sed <lb/>&amp; anguli &egrave; &longs;emidiametris con&longs;tituti (quos angulos circuli vocat <lb/>hic Ari&longs;toteles) ba&longs;es qu&aelig; &longs;unt peripheri&aelig;, euidenter in&aelig;quales &longs;unt. <lb/></s>

<s id="id.002540">In maiore circulo maior: in minore minor (Sed &amp; hanc euidentiam, <lb/>ne qua e&longs;&longs;et dubitatio, demon&longs;tratione primo capite huius libri de&shy;<lb/>mon&longs;trauimus.) </s>

<s>Erunt igitur &amp; orbit&aelig; in&aelig;quales &amp; proportione <lb/>re&longs;pondentes ba&longs;ibus angulorum &egrave; &longs;emidiametris con&longs;titutorum. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002541">Attamen quod circa.] <emph type="italics"/>Problematis propo&longs;iti veritas demon&shy;<lb/>&longs;tratur figura geometrica in vtroque modo. </s>

<s id="id.002542">Nam po&longs;ito quod<emph.end type="italics"/> <foreign lang="greek">a h z</foreign><lb/><emph type="italics"/>perpendiculariter in&longs;i&longs;tat pla&shy;<emph.end type="italics"/><lb/><figure id="id.035.01.206.1.jpg" xlink:href="http://archimedes.fas.harvard.edu/images/035-01-figures/035.01.206.1.jpg"/><lb/><emph type="italics"/>no, &amp; ad rectam<emph.end type="italics"/> <foreign lang="greek">z i. </foreign><emph type="italics"/>Tum<emph.end type="italics"/> <foreign lang="greek">h q</foreign><lb/><emph type="italics"/>rectos angulos faciat, &longs;icque il&shy;<lb/>las tangat in punctis<emph.end type="italics"/> <foreign lang="greek">h</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">z,</foreign><lb/><emph type="italics"/>cum quarta pars peripheri&aelig;<emph.end type="italics"/> <foreign lang="greek">h b</foreign><lb/><emph type="italics"/>erit reuoluta: ita vt<emph.end type="italics"/> <foreign lang="greek">a b</foreign> <emph type="italics"/>rur&shy;<lb/>&longs;us ad rectos &longs;it ad rectam<emph.end type="italics"/> <foreign lang="greek">h q,</foreign><lb/><emph type="italics"/>ip&longs;amque tangat, vt in puncto<emph.end type="italics"/><lb/><foreign lang="greek">k</foreign>: <emph type="italics"/>tunc &amp;<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>etiam ad re&shy;<lb/>ctos erit &longs;uper<emph.end type="italics"/> <foreign lang="greek">z i,</foreign> <emph type="italics"/>&amp; &longs;it vt <lb/>tangat in puncto<emph.end type="italics"/> <foreign lang="greek">l. </foreign><emph type="italics"/></s>

<s>Erunt pro <lb/>29. prop. lib. 1. </s>

<s>Du&aelig;<emph.end type="italics"/> <foreign lang="greek">z h</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">k l</foreign> <emph type="italics"/>parallel&aelig; &amp; &aelig;quales, ex hypoth. <lb/></s>

<s id="id.002543">Ergo qu&aelig; eas ad ea&longs;dem partes iungunt rect&aelig;<emph.end type="italics"/> <foreign lang="greek">z l</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">h k</foreign> <emph type="italics"/>erunt <lb/>&aelig;quales, prop 34. eiu&longs;dem. </s>

<s id="id.002544">Sunt autem orbit&aelig; ab vtri&longs;que confect&aelig; <lb/>eadem celeritate motis. </s>

<s id="id.002545">Eadem ratiocinatione cum<emph.end type="italics"/> <foreign lang="greek">a g</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.207.jpg" pagenum="168"/><emph type="italics"/>puncto<emph.end type="italics"/> <foreign lang="greek">i</foreign> <emph type="italics"/>ex reuolutione maioris, &amp;<emph.end type="italics"/> <foreign lang="greek">b</foreign> <emph type="italics"/>tanget in<emph.end type="italics"/> <foreign lang="greek">q</foreign>: <emph type="italics"/>&longs;icque<emph.end type="italics"/> <foreign lang="greek">q i</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">h <lb/>z</foreign> <emph type="italics"/>cum &longs;int &aelig;quales &amp; parallel&aelig;, du&aelig; rur&longs;us<emph.end type="italics"/> <foreign lang="greek">h q</foreign> <emph type="italics"/>&amp;<emph.end type="italics"/> <foreign lang="greek">z i</foreign> <emph type="italics"/>erunt pa&shy;<lb/>rallel&aelig;. </s>

<s id="id.002546">Qu&aelig; autem ratio e&longs;t quartarum circulorum inter &longs;e, eadem <lb/>e&longs;t totorum. </s>

<s id="id.002547">Partes enim cum pariter multiplicibus eandem ratio&shy;<lb/>nem habent prop. 15. lib. 5. </s>

<s>Igitur in vtroque modo orbit&aelig; concen&shy;<lb/>tricorum in&aelig;qualium &longs;unt &aelig;quales. <emph.end type="italics"/></s></p><p type="main">

<s id="id.002548">Atque id nulla.] <emph type="italics"/>Cau&longs;am admirabilis huius aduentus, qu&aelig; <lb/>adferri potui&longs;&longs;et, In prim&ograve; quidem modo ex tarditate &amp; mora <lb/>maioris circuli in quibu&longs;dam rect&aelig; line&aelig; punctis, dum minor <lb/>circulus ip&longs;am peragrat: In &longs;ecundo ver&ograve; modo ex tran&longs;ultu minoris <lb/>qua&longs;i exiliat, nec &longs;imul omnia puncta rect&aelig; attingat: &longs;ed tran&longs;iliat <lb/>minor, dum maior contra omnia attingat peragrando, reijcit, mo&shy;<lb/>ramque nullam in hoc intercedere, neque tran&longs;ultum in i&longs;to: &longs;ed <lb/>vtriu&longs;que continuas motiones e&longs;&longs;e dicit, quia vnica latio e&longs;t. <emph.end type="italics"/></s></p></chap><chap><p type="main">

<s id="id.002549"><foreign lang="greek"><gap/></foreign></s></p><p type="main">

<s id="id.002550">Pr&aelig;terea vnica latione <lb/><expan abbr="exi&longs;t&etilde;te">exi&longs;tente</expan> <expan abbr="centr&utilde;">centrum</expan> &longs;emper <expan abbr="c&otilde;-tinu&egrave;">con&shy;<lb/>tinu&egrave;</expan> motum, aliquando <lb/><expan abbr="quid&etilde;">quidem</expan> per <expan abbr="maior&etilde;">maiorem</expan>, aliquan&shy;<lb/>do ver&ograve; per minorem con&shy;<lb/>uolui e&longs;t admirabile. </s>

<s id="id.002551">I dem <lb/>enim eadem celeritate <expan abbr="lat&utilde;">latum</expan> <lb/>&aelig;qualem <expan abbr="tr&atilde;&longs;ire">tran&longs;ire</expan> natum e&longs;t. <lb/></s>

<s id="id.002552">Eadem <expan abbr="aut&etilde;">autem</expan> celeritate per <lb/><expan abbr="&aelig;qual&etilde;">&aelig;qualem</expan> vtro que modo mo&shy;<lb/>uere licet. </s>

<s id="id.002553">C&aelig;terum princi&shy;<lb/>pium &longs;umatur ex vtriu&longs;que <lb/>cau&longs;a, quod eadem vis, &amp; <lb/>&aelig;qualis vnam quidem <expan abbr="ma-gnitudin&utilde;">ma&shy;<lb/>gnitudinum</expan> tardius: alteram <lb/>celerius moueat. </s>

<s id="id.002554">Si quid <lb/>enim fuerit non &agrave; &longs;eip&longs;o <lb/>moueri <expan abbr="nat&utilde;">natum</expan>, &amp; <expan abbr="ips&utilde;">ipsum</expan> aliud <lb/>quod moueri <expan abbr="nat&utilde;">natum</expan> &longs;it mo&shy;<lb/>uerit, tardius mouebitur: <lb/><expan abbr="qu&atilde;">quam</expan> &longs;i <expan abbr="ips&utilde;">ipsum</expan> per &longs;e moueretur. </s><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.208.jpg" pagenum="169"/>

<s><foreign lang="greek"><gap/></foreign></s>

<s>Et &longs;i quidem <expan abbr="nat&utilde;">natum</expan> &longs;it mo&shy;<lb/>ueri, neque <expan abbr="aut&etilde;">autem</expan> &longs;imul mo&shy;<lb/>ueatur, &longs;imiliter &longs;e habebit. <lb/></s>

<s id="id.002555">Et vt plus moueatur: quam <lb/>quod mouet, fieri non po&shy;<lb/>te&longs;t. </s>

<s id="id.002556">Non enim &longs;uo ip&longs;ius <lb/>mouetur motu: &longs;ed <expan abbr="mou&etilde;-">mouen&shy;<lb/></expan><arrow.to.target n="marg39"/><lb/>tis. </s>

<s>[Sit igitur circulus maior <lb/><expan abbr="quid&etilde;">quidem</expan> vbi <foreign lang="greek">g,</foreign> at minor vbi <lb/>b.] </s>

<s>Si impellat minor <expan abbr="maio-r&etilde;">maio&shy;<lb/>rem</expan> ip&longs;o &longs;e minime <expan abbr="volu&etilde;te">voluente</expan>, <lb/>manife&longs;tum quod tantam <lb/><expan abbr="rect&atilde;">rectam</expan> maior tran&longs;it, ad <expan abbr="qu&atilde;-tam">quan&shy;<lb/>tam</expan> &agrave; minore impul&longs;us e&longs;t: <lb/>ad tantam ver&ograve; impul&longs;us <lb/>e&longs;t, ad quantam minor &longs;e <lb/>mouit. </s>

<s id="id.002557"><expan abbr="Rect&atilde;">Rectam</expan> igitur &aelig;qua&shy;<lb/>lem pertran&longs;ierunt. </s>

<s id="id.002558">Nece&longs;&shy;<lb/>&longs;e igitur &longs;i minor conuolu&shy;<lb/>tus impulerit, <expan abbr="maior&etilde;">maiorem</expan> con&shy;<lb/>uolui quidem cum impul&shy;<lb/>&longs;ione tantum: <expan abbr="qu&atilde;tum">quantum</expan> mi&shy;<lb/>nor conuolutus fuerit. </s>

<s id="id.002559">&longs;i <lb/><expan abbr="neutiqu&atilde;">neutiquam</expan> ip&longs;e proprio mo&shy;<lb/>tu moueatur. </s>

<s id="id.002560">quomodo <lb/>enim &amp; quantum mouit, <lb/><expan abbr="t&atilde;tundem">tantundem</expan> <expan abbr="mot&utilde;">motum</expan> e&longs;&longs;e, quod <lb/>ab illo mouebatur, nece&longs;&shy;<lb/>&longs;um e&longs;t. </s>

<s id="id.002561">Sed circulus &longs;olum <lb/>&longs;e mouerit circulariter pe&shy;<lb/>dem vnum. </s>

<s id="id.002562">Sit enim tan&shy;<lb/>tum quod <expan abbr="mot&utilde;">motum</expan> e&longs;t. </s>

<s id="id.002563">Etiam <lb/>magnus tantundem motus <lb/>erit. </s>

<s id="id.002564">Similiter &longs;i magnus <lb/><expan abbr="paru&utilde;">paruum</expan> mouerit: <expan abbr="tant&utilde;">tantum</expan> paruus, <expan abbr="quant&utilde;">quantum</expan> magnus motus erit. <lb/></s>

<s id="id.002565">per &longs;e <expan abbr="quid&etilde;">quidem</expan> motus vtrouis modo &longs;eu celeriter: &longs;eu tard&egrave;. </s></p></chap><pb xlink:href="http://archimedes.fas.harvard.edu/images/035-01-pageimg/035.01.209.jpg" pagenum="170"/><chap><p type="main">

<s><foreign lang="greek"><gap/></foreign></s>

<s><lb/>Eadem ver&ograve; celeritate &longs;ta&shy;<lb/>tim per quantam lineam <lb/>natus e&longs;t conuolui maior. </s></p><p type="margin">

<s id="id.002566"><margin.target id="marg39"/>H&aelig;c inter&shy;<lb/>po&longs;ita <expan abbr="vid&etilde;-tur">viden&shy;<lb/>tur</expan>. </s></p><p type="head">

<s id="id.002567">COMMENTARIVS. </s>