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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd">
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink">
  <info>
    <author>Baldi, Bernardino</author>
    <title>In mechanica Aristotelis problemata exercitationes</title>
    <date>1621</date>
    <place>Mainz</place>
    <translator/>
    <lang>la</lang>
    <cvs_file>baldi_mecha_007_la_1621.xml</cvs_file>
    <cvs_version/>
    <locator>007.xml</locator>
  </info>
  <text>
    <front>
      <section>
        <pb xlink:href="007/01/001.jpg"/>
        <p type="head">
          <s id="s.000001">BERNARDINI<!-- REMOVE S--> BALDI VRBINATIS <lb/>GVASTALL&AElig; AB&shy;<lb/>BATIS <lb/><emph type="italics"/>IN<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000002">MECHANICA ARISTOTE&shy;<lb/>LIS PROBLEMATA <lb/>EXERCITATIONES:<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000003"><emph type="italics"/>ADIECTA SVCCINCTA NAR&shy;<lb/>ratione de autoris vita &amp; &longs;criptis.<emph.end type="italics"/></s>
        </p>
        <p type="head">
          <s id="s.000004"><emph type="italics"/>MOGVNTIAE.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000005">Typis &amp; Sumptibus Vidu&aelig; Ioannis Albini.<!-- KEEP S--></s>
        </p>
        <p type="head">
          <s id="s.000006"><lb/>M. D C. XXI.</s>
        </p>
        <pb xlink:href="007/01/002.jpg"/>
      </section>
      <section>
        <pb xlink:href="007/01/003.jpg"/>
        <p type="head">
          <s id="s.000007"><emph type="italics"/>NOBILISSIMO AC GENE&shy;<lb/>ROSO DOMINO<emph.end type="italics"/> D. ADAMO PHILIP&shy;<lb/>PO BARONI A CRON&shy;<lb/>BERG, EQVITI, SACR&AElig; C&AElig;SA&shy;<lb/>RE&AElig; MAIESTATIS, ET SERENISSIMI Principis Archiducis Alberti Camerario intimo &amp; c. <lb/><!-- KEEP S--></s>
          <s id="s.000008">Domino meo gratio&longs;i&longs;&longs;imo.</s>
        </p>
        <p type="main">
          <s id="s.000009">Opportune &longs;ub hoc ip&longs;um tem&shy;<lb/>pus, quo in Belgium ad Sere&shy;<lb/>ni&longs;&longs;imos Principes iter ador&shy;<lb/>nat.</s>
          <s id="s.000010"> Nobili&longs;&longs;ima &amp; Genero&longs;a <lb/>Dom. <!-- REMOVE S-->V.^&lcub;ra}, prodit no&longs;tris for&shy;<lb/>mis in publicum editus Com&shy;<lb/>mentarius Bernardini Baldi Vrbinatis Gua&shy;<lb/>&longs;tall&aelig; Abbatis in Ari&longs;totelis Mechanica. <!-- KEEP S--></s>
          <s id="s.000011">Is <lb/>vir in omni &longs;cienti&aelig; genere, at maxime in Ma&shy;<lb/>thematicis di&longs;ciplinis fuit ver&longs;ati&longs;&longs;imus, quod <lb/>multa ab eo pr&aelig;clare &longs;cripta te&longs;tantur opera, <lb/>ex quibus paucula edita, reliqua vero &longs;pera&shy;<pb xlink:href="007/01/004.jpg"/>mus &longs;uo tempore in publicam lucem produ&shy;<lb/>cenda. </s>
          <s id="s.000012"> Cum vero nemini &longs;it ob&longs;curum Nobi&shy;<lb/>li&longs;&longs;im&aelig; ac Genero&longs;&aelig; Dom. <!-- REMOVE S-->V.^&lcub;r&aelig;} id &longs;emper <lb/>extiti&longs;&longs;e familiari&longs;&longs;imum, vt tum dome&longs;ticum <lb/>otium, tum maxime peregrinationes, quibus <lb/>totam p&aelig;ne Europam &longs;umma cum laude <lb/>circum&longs;crip&longs;it, tum variarum linguarum per&shy;<lb/>fecto v&longs;u, tum Mathematicarum di&longs;ciplina&shy;<lb/>rum notitia &amp; exercitio redderet <expan abbr="iuc&utilde;diores">iucundiores</expan>, <lb/>nulla me tenet dubitatio quin &amp; Baldum Vr&shy;<lb/>binatem no&longs;tris typis loquentem in hoc iti&shy;<lb/>nere, quod &agrave; Deo felici&longs;&longs;imum Nobili&longs;&longs;im&aelig; <lb/>ac Genero&longs;&aelig; Dom. <!-- REMOVE S-->V.^&lcub;r&aelig;} precor, in &longs;uum comi&shy;<lb/>tatum ac tutelam beneuolo animo &longs;it admi&longs;&shy;<lb/>&longs;ura.</s>
          <s id="s.000013"> Id rogo humillime &longs;imulque precor, vt. <lb/></s>
          <s id="s.000014">hanc meam typographiam plurimis iam re&shy;<lb/>tro annis de inclyt&aelig; famili&aelig; Cronbergic&aelig; tu&shy;<lb/>tela gloriantem, &longs;uo fauore pro&longs;equatur, vi&shy;<lb/>du&aelig;que afflict&aelig; fortunis beneuole ad&longs;piret.</s>
          <s id="s.000015"> <lb/>Sic Deus Nobili&longs;&longs;. <!-- REMOVE S-->&amp; Genero&longs;am Dom. <!-- REMOVE S-->V.^&lcub;ram} <lb/>illu&longs;tret omnibus bonis, eamque R.^&lcub;mo} &amp; Ill.^&lcub;mo} <lb/>Principi ac Domino meo Clementi&longs;&longs;imo, D. <lb/><!-- REMOVE S-->Ioanni Suicardo Archiepi&longs;copo Mogunti&shy;<lb/>no Principi Electori ac per <emph type="italics"/>G<emph.end type="italics"/>ermaniam Ar-<pb xlink:href="007/01/005.jpg"/>chicancellario &amp;c. </s>
          <s id="s.000016">patruo &longs;uo optati&longs;&longs;imo <lb/>&longs;aluo florentique redhibeat &longs;aluum &longs;imili&shy;<lb/>ter florentem ac incolumem.</s>
          <s id="s.000017"> Mogunti&aelig; &egrave; <lb/>typographeio Vidu&aelig; Albinian&aelig;, honori No&shy;<lb/>bili&longs;&longs;im&aelig; ac <emph type="italics"/>G<emph.end type="italics"/>enero&longs;&aelig; Dom. <!-- REMOVE S-->Ve&longs;tr&aelig; perpe&shy;<lb/>tuum dicato. </s>
          <s id="s.000018">Anno 1621.26.Martij. <!-- KEEP S--></s>
        </p>
        <pb xlink:href="007/01/006.jpg"/>
      </section>
      <section>
        <p type="head">
          <s id="s.000019">PRAEFATIO.</s>
        </p>
        <p type="main">
          <s id="s.000020"><emph type="italics"/>Diligenter legenti mihi qu&aelig;&longs;tiones il&shy;<lb/>las, in quibus ea qu&aelig; ad Mecha&shy;<lb/>nicam facultatem pertinent, expli&shy;<lb/>cantur, multa in mentem venie&shy;<lb/>bant; &amp; primum quidem eorum, qu&aelig; ibi dispu&shy;<lb/>tantur, vtilitatem, &longs;ubtilitatem, copiam admi&shy;<lb/>rabar: Tum ex animo dolebam, aureum hunc li&shy;<lb/>bellum prop&egrave; negligi, &amp; ab iis qui pulcherrimis <lb/>hi&longs;ce &longs;tudiis dant operam, assidu&egrave; pr&aelig; manibus <lb/>non haberi: Multas autem Auctori ip&longs;i haben&shy;<lb/>das referendasque e&longs;&longs;e gratias, qui tam egregiam, <lb/>vtilem &amp; prob&egrave; in&longs;tructam &longs;upellectilem Archi&shy;<lb/>tectis, Mechanicis, &amp; omnibus fer&egrave; Artificibus <lb/>&longs;uppeditauerit. </s>
          <s id="s.000021">Ari&longs;totelis nomini a&longs;cribitur <lb/>Commentarius, licet nonnulli, &longs;itne Philo&longs;ophi <lb/>illius pr&aelig;clarissimi &amp; acutissimi labor, an non, <lb/>adfirmare &longs;ubdubitauerint. </s>
          <s id="s.000022">Ari&longs;totelis tamen <lb/>e&longs;&longs;e omnes fer&egrave; meliores con&longs;entiunt: Idque tum <lb/>ex phra&longs;i, &amp; explicatione, qu&aelig; Ari&longs;totelem &longs;a&shy;<lb/>piunt, tum iudicio &longs;ubtilitatis &amp; rationum, qui-<pb xlink:href="007/01/007.jpg"/>bus qu&aelig;&longs;tiones ip&longs;&aelig; ingenio&longs;issim&egrave; diluuntur. </s>
          <s id="s.000023">Vi&shy;<lb/>detur autem mihi, rem accuratius exploranti, &longs;a&shy;<lb/>tis veri&longs;imile &lpar;nullum enim habeo opinionis hu&shy;<lb/>ius a&longs;&longs;ertorem,&rpar; &longs;ectionem e&longs;&longs;e hanc, &amp; partem <lb/>quandam eius operis nobilissimi, quod idem au&shy;<lb/>ctor De Problematibus edidit, &amp; hanc, ne&longs;cio <lb/>quam ob cau&longs;am; ni&longs;i fort&egrave; quod tractatio mer&egrave; <lb/>Phy&longs;ica non &longs;it, &agrave; reliquo corpore di&longs;tractam at&shy;<lb/>que reuul&longs;am. </s>
          <s id="s.000024">Id cert&egrave; quod ad rem facit, prob&egrave; <lb/>nouimus, Diogenem La&euml;rtium inter c&aelig;tera Ari&shy;<lb/>&longs;totelici ingenij monumenta Mechanica quoque <lb/>adnumera&longs;&longs;e. </s>
          <s id="s.000025">Quibus con&longs;ideratis magnopere <lb/>&longs;ubit mirari, cur ij qui po&longs;t Ari&longs;totelem floru&ecirc;re <lb/>atque vixere, Mechanici, Archimedes, Athen&aelig;us, <lb/>Heron, Pappus, &amp; c&aelig;teri, nullam huius libelli fe&shy;<lb/>cerint commemorationem: &amp; &longs;an&egrave; debuerunt; <lb/>neque enim &agrave; vero est dissimile, ip&longs;os per hunc ali&shy;<lb/>quatenus profeci&longs;&longs;e. </s>
          <s id="s.000026">Verum enim uero cum inge&shy;<lb/>nui illi fuerint homines, &amp; nullatenus obtrecta&shy;<lb/>tores, credendum potius est, Comment ariolum i&shy;<lb/>&longs;tud, eorum &aelig;uo, paucis cognitum, alicubi in Bi&shy;<lb/>bliothecis latui&longs;&longs;e: etenim c&aelig;tera quoque Ari&longs;tote&shy;<lb/>lis &longs;cripta, po&longs;t vetu&longs;ta illa tempora, ante Ale&shy;<lb/>xandrum Aphrodi&longs;ien&longs;em, &agrave; multis fui&longs;&longs;e igno-<pb xlink:href="007/01/008.jpg"/>rata non dubitamus. </s>
          <s id="s.000027">Habemus &longs;iquidem, Stra&shy;<lb/>bone te&longs;te, lib. 13. Ari&longs;totelis, &amp; Theophra&longs;ti bi&shy;<lb/>bliothecam, po&longs;t ip&longs;ius Theophra&longs;ti dece&longs;&longs;um, ad <lb/>Neleum quendam Scep&longs;ium, Cori&longs;ci filium, qui <lb/>eius fuerat auditor, perueni&longs;&longs;e; po&longs;t h&aelig;c libros, <lb/>blattis olim, &amp; humore corruptos, Apelliconi Te&shy;<lb/>io venditos, &amp; ab eo Athenas translatos, tum <lb/>Athenis captis in Syll&aelig; pote&longs;tatem deueni&longs;&longs;e, eo&longs;&shy;<lb/>que tandem &agrave; Sylla acceptos, Tyrannionem <lb/>Grammaticum, vt potuit meli&ugrave;s emendatos, <lb/>promulga&longs;&longs;e. </s>
          <s id="s.000028">Ex quibus colligimus, mirum non <lb/>e&longs;&longs;e, Archimedi, Heroni, &amp; alijs qui ante Syllam <lb/>vix&ecirc;re, fui&longs;&longs;e incognitos. </s>
          <s id="s.000029">quicquid &longs;it, illud cer&shy;<lb/>tum est, Ari&longs;totelem eorum omnium quidem Me&shy;<lb/>chanicis commentaria edidere, e&longs;&longs;e long&egrave; vetu&shy;<lb/>&longs;tissimum. </s>
          <s id="s.000030">Pappus enim Herone iunior, Athe&shy;<lb/>n&aelig;us Archimedi &aelig;qualis, vterque enim &longs;ub Mar&shy;<lb/>cello, cui Athen&aelig;us &longs;uum de bellicis Machinis <lb/><expan abbr="libell&umacr;">libellum</expan> dedicauit. </s>
          <s id="s.000031">Archimedes ver&ograve; circa CXL. <lb/><!-- KEEP S--></s>
          <s id="s.000032">Olympiadem floruit, quamobrem po&longs;t Ari&longs;tote&shy;<lb/>lem Olympiadas XL. hoc est, annos fer&egrave; CLX. <lb/><!-- KEEP S--></s>
          <s id="s.000033">I&longs;th&aelig;c autem con&longs;iderantibus, facile e&longs;t cogno&longs;ce&shy;<lb/>re facultatis huius nobilitatem, atque dignitatem; <lb/>quippe quod &longs;ummus Philo&longs;ophus non modo eam <pb xlink:href="007/01/009.jpg"/>probauerit, &longs;ed etiam &longs;uis acutissimis lucubra&shy;<lb/>tionibus illu&longs;trauerit. </s>
          <s id="s.000034">Hanc porro tractationem <lb/>&longs;ubiecto quidem Phy&longs;icam e&longs;&longs;e, demon&longs;tratio&shy;<lb/>nibus ver&ograve; Geometricam, ip&longs;emet nos docuit <lb/>Ari&longs;toteles, cuius etiam natur&aelig; &longs;unt Per&longs;pecti&shy;<lb/>ua, Specularia, Mu&longs;ica, &amp; c&aelig;ter&aelig; eiu&longs;dem <lb/>modi facultates, quas quidem &longs;ubalternas Peri&shy;<lb/>patetici appellant. </s>
          <s id="s.000035">Vitruuius Architectur&aelig; <lb/>membrum, vt ita dicam, &amp; portionem quan&shy;<lb/>dam facit, ait enim Architectur&aelig; partes e&longs;&longs;e tres, <lb/>&AElig;dificationem, Gnomonicam, Machinatio&shy;<lb/>nem. </s>
          <s id="s.000036">Est autem Architectur&acirc; quidem inferior, <lb/>paret enim Architecto Mechanicus; attamen &longs;i <lb/>c&aelig;teras artes &longs;pectes, Architectonica; h&aelig;c enim <lb/>omnes fer&egrave; &longs;edentari&aelig;, &longs;ellulari&aelig;ue, quas banau&shy;<lb/>&longs;as Gr&aelig;ci appellant, ordine &longs;ubijciuntur, &amp; &longs;a&shy;<lb/>n&egrave; latissimos i&longs;th&aelig;c habet fines; pr&aelig;cipu&egrave; autem <lb/>circa eam ver&longs;atur cognitionem, eamque inter <lb/>c&aelig;teras fer&egrave; principem, quam dixere Centrobari&shy;<lb/>cam, qu&aelig; quidem ad Centri grauitatem, eiu&longs;que <lb/>&longs;peculationem pertinet: qu&agrave; in &longs;pecie inter vete&shy;<lb/>res primum &longs;ibi vindicauit locum Archimedes, <lb/>mox Heron, deinde Pappus; inter neotericos au-<emph.end type="italics"/><pb xlink:href="007/01/010.jpg"/><emph type="italics"/>tem Commandinus, qui librum de Centro gra&shy;<lb/>uitatis &longs;olidorum &longs;crip&longs;it, &amp; po&longs;t eum G. <!-- REMOVE S-->Vbal&shy;<lb/>dus &egrave; Marchion. <!-- REMOVE S-->Montis, qui non mod&ograve; ab&shy;<lb/>&longs;olutissimum Mechanicorum librum cum maxi&shy;<lb/>ma ingenij &longs;ui laude con&longs;crip&longs;it, &longs;ed &amp; Paraphra&shy;<lb/>&longs;in in librum &AElig;queponderantium Archimedis <lb/>egregi&egrave; concinnauit Centrobaricam hanc, igno&shy;<lb/>tam fui&longs;&longs;e Ari&longs;toteli, &longs;&aelig;tis patet. </s>
          <s id="s.000037">nunquam enim <lb/>in Mechanicis demon&longs;trationibus, quod tamen <lb/>est potissimum, grauitatis centrum nominat, e&shy;<lb/>iu&longs;ue naturam atque vim &longs;peculatur. </s>
          <s id="s.000038">Diuidi&shy;<lb/>tur autem Mechanice tota, te&longs;te Herone apud <lb/>Pappum libro octauo, in Rationalem, hoc est, <lb/>Theoricam &amp; Chirurgicam, id est, manu ope&shy;<lb/>ratricem, quam Praxim apt&egrave; dicere valemus. <lb/></s>
          <s id="s.000039">Rationalis, &longs;peculationi &amp; <expan abbr="dem&omacr;&longs;trationibus">demon&longs;trationibus</expan>, ex <lb/>Geometricis, Arithmeticis &amp; Phy&longs;icis rationi&shy;<lb/>bus, dat operam; Chirurgica vero materiam <lb/>tractat, &amp; &longs;e&longs;e in varias artes diffundit, &AElig;ra&shy;<lb/>riam, Lignariam, Sculptoriam, Pictoriam, &AElig;&shy;<lb/>dificatoriam, Machinariam &amp; Thaumaturgi&shy;<lb/>cam, c&aelig;terasque eiu&longs;modi. </s>
          <s id="s.000040">Machinatori&aelig; au&shy;<lb/>tem &longs;unt partes Manganaria, qua ingentia <emph.end type="italics"/><pb xlink:href="007/01/011.jpg"/><emph type="italics"/>transferuntur pondera, tum ip&longs;a Poliorcetica, <lb/>qu&aelig; bellicas Machinas ad vrbium expugnatio&shy;<lb/>nes, quod vel ip&longs;o nomine profitetur, &aelig;dificat. </s>
          <s id="s.000041">At&shy;<lb/>qui hac dere plura &longs;cribere &longs;uper&longs;edemus, ne a&shy;<lb/>ctum agamus: quis quis enim minut&egrave; magis h&aelig;c <lb/>cogno&longs;cere de&longs;iderat, is Pappum adeat libro cita&shy;<lb/>to, &amp; Guidum Vbaldum in Pr&aelig;fatione quam <lb/>&longs;uo Mechanicorum Operi pr&aelig;po&longs;uit. </s>
          <s id="s.000042">Vt autem <lb/>ad Ari&longs;totelis, de quo egimus, libellum reuerta&shy;<lb/>mur, pauci &longs;unt qui ei ante nos &longs;tilum &amp; operam <lb/>commodauerint: Leonicenus Latinum fecit &amp; <lb/>figuris tum breuissimis, &amp; parui &longs;ane ponderis, <lb/>marginalibus adnotatiunculis, in&longs;truxit. </s>
          <s id="s.000043">Po&longs;t <lb/>hunc Alexander Picolomineus luculentissima <lb/>Par&aelig;phra&longs;i illu&longs;trauit. </s>
          <s id="s.000044">Modo, vt audio, Simon <lb/>Sticinus Hollanden&longs;is qu&aelig;dam edidit, qu&aelig; ad <lb/>nos minime peruen&ecirc;re. </s>
          <s id="s.000045">Nos demum, omnium, <lb/>tum &longs;cientia, &amp; ingenio, tum &aelig;tate, po&longs;tremi huic <lb/>operi manum admouimus; Con&longs;iderantes enim <lb/>Ari&longs;totelem aliis fecerint Mechanici, demon&longs;tra&longs;&longs;e, <lb/>morem huiu&longs;ce facultatis &longs;tudio&longs;is ge&longs;turos nos <lb/>fore arbitrati &longs;umus, &longs;i ea&longs;dem illas qu&aelig;&longs;tiones <emph.end type="italics"/><pb xlink:href="007/01/012.jpg"/><emph type="italics"/>Mechanicis, hoc est, Archimedeis probationi&shy;<lb/>bus confirmaremus; dum per latissimos faculta&shy;<lb/>tis huius campos vagantes, alias quoque i&longs;tis af&shy;<lb/>fines dubitationes introducentes &longs;olueremus. <lb/></s>
          <s id="s.000046"><expan abbr="quicquidaut&emacr;&longs;ecerimus">quicquid autem fecerimus</expan> profecerimu&longs;ue, Lector <lb/>optime, boni con&longs;ule, &amp; quia fax per manus tra&shy;<lb/>ditur, tu interim de me accipe, vt alijs tradas.<emph.end type="italics"/></s>
        </p>
        <pb xlink:href="007/01/013.jpg"/>
      </section>
      <section>
        <p type="head">
          <s id="s.000047">DE VITA ET SCRI&shy;<lb/>PTIS BERNARDINI <lb/>BALDI VRBINATIS</s>
        </p>
        <p type="head">
          <s id="s.000048"><emph type="italics"/>EX LITERIS FABRITII SCHAR&shy;<lb/>loncini ad Illu&longs;trissimum &amp; Reuerendissimum <lb/>Dominum L&aelig;lium Ruinum Epi&longs;copum Bal&shy;<lb/>neoregien&longs;em ex-Nuntium Apo&longs;tolicum <lb/>ad Poloni&aelig; Regem &amp; c.<emph.end type="italics"/><!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000049">Natus e&longs;t Bern. <!-- REMOVE S-->Baldus Vrbini nobilibus <expan abbr="pa-r&emacr;tibus">pa&shy;<lb/>rentibus</expan> po&longs;tridie Non. <!-- KEEP S--></s>
          <s id="s.000050">Iunij anno MDLIII. <lb/></s>
          <s id="s.000051">Genus traxit, quod me &longs;&aelig;p&egrave; ab eo memini <lb/>audire, &agrave; familia Cantagallina, qu&aelig; inter <lb/>Peru&longs;inas illu&longs;tris: hoc autem cognomen, <lb/>Baldi accepto, vt in varietate temporum fit, <lb/>Abauus reliquit, &agrave; teneris vnguiculis <expan abbr="pietat&emacr;">pietatem</expan> erga Deum <lb/>pr&aelig;&longs;etulit; nam vt mater eius narrabat, &longs;anctorum imagi&shy;<lb/>nes &amp; Altariola non cum l&aelig;titia &longs;olum, &longs;ed cum venera&shy;<lb/>tione anniculus intuebatur. </s>
          <s id="s.000052">Pr&aelig;ceptoribus in adole&longs;cen&shy;<lb/>tia v&longs;us fuit laudati&longs;&longs;imis Io. <!-- REMOVE S-->And. <!-- REMOVE S-->Palatio, &amp; Io. <!-- REMOVE S-->Antonio <lb/>Turoneo, qui altero doctior, &amp; Paulo Manutio maxime <lb/>carus ob latin&aelig; &amp; gr&aelig;c&aelig; lingu&aelig; peritiam prop&egrave; &longs;ingula&shy;<lb/>rem: ad illorum autem &longs;edulitatem tantum animi ardo&shy;<lb/>rem attulit, tantam ingenij ac iudicij vim, vt non tantum <lb/>&aelig;qualis &longs;ed omnium vicerit expectationem. </s>
          <s id="s.000053">Puer adhuc <lb/>Arati apparitiones Italico carmme reddidit. </s>
          <s id="s.000054">Parens hac <lb/>filij laude &amp; gloria motus anno 1573. eum ad maiorem in&shy;<lb/>genij cultum cape&longs;&longs;endum Patauium mi&longs;it. </s>
          <s id="s.000055">H&icirc;c in Ema&shy;<lb/>nuelis Margunij familiaritatem &longs;tatim venit, cui porro <pb xlink:href="007/01/014.jpg"/>fuit in amoribus. </s>
          <s id="s.000056">Homeri Iliad. <!-- REMOVE S-->illo Doctore &amp; interpre&shy;<lb/>te diligentius quam feci&longs;&longs;et antea, euoluit. </s>
          <s id="s.000057">priuato autem <lb/>&longs;tudio Anacreonti, Pindaro, &AElig;&longs;chyli, Euripidi, Sophocli <lb/>operam dedit, &longs;ed pr&aelig; c&aelig;teris Theocriti Bucolica triuit, <lb/>ad quod &longs;criptionis genus natura magis ferri videbatur: <lb/>centenos gr&aelig;ci alicuius po&euml;t&aelig; ver&longs;us memoriter tenebat, <lb/>&longs;&aelig;peque habebat in ore, in oratoribus gr&aelig;cis ver&longs;andis <lb/>laborem &longs;e aliquem &longs;entire, in po&euml;tis nullum. </s>
          <s id="s.000058">Scrip&longs;it Pa&shy;<lb/>tauij libellum de Tormentis Bellicis, &amp; eorum inuentori&shy;<lb/>bus, &amp; cum in Tran&longs;alpinorum amicitias incidi&longs;&longs;et, &longs;ibi <lb/>ducebat dedecori ip&longs;os &longs;ua lingua loquentes non intelli&shy;<lb/>gere. </s>
          <s id="s.000059">quare incredibili celeritate Gallicam &amp; Germani&shy;<lb/>cam didicit. </s>
          <s id="s.000060">Pe&longs;tilentia ex eo Gymna&longs;io exactus in Pa&shy;<lb/>triam redijt, vbi quinquennium integrum Federico <expan abbr="C&omacr;-mandino">Com&shy;<lb/>mandino</expan> affixus omnes Mathe&longs;eos partes perdidicit, cui <lb/>viro in delineandis figuris ad Euclidis, Pappi, &amp; Heronis <lb/>monumenta manum commodauit: ex eiu&longs;dem obitu do&shy;<lb/>lorem vix con&longs;olabilem &longs;u&longs;tinuit, &longs;u&longs;ceptoque eius vitam <lb/>&longs;cribendi con&longs;ilio, &longs;ubinde ad omnium Mathematicorum <lb/>vitas con&longs;cribendas animum adplicuit, quod &amp; duode&shy;<lb/>cim annorum &longs;patio pr&aelig;&longs;titit felici&longs;&longs;im&egrave;. </s>
          <s id="s.000061">cum vero Ma&shy;<lb/>thematicarum di&longs;ciplinarum amore torqueretur, ami&longs;&longs;o <lb/>Commandino Pr&aelig;ceptore, amicum nactus fuit pr&aelig;&longs;tan&shy;<lb/>ti&longs;&longs;imum &amp; &longs;ymmy&longs;tam Guidum Vbaldum &egrave; Marchioni&shy;<lb/>bus Montis, in cuius &longs;e con&longs;uetudinem daret: quantum <lb/>profeci&longs;&longs;et, o&longs;tendunt ij commentarij quos anno 1582. in <lb/>Ari&longs;t. Mechanica &longs;crip&longs;it. </s>
          <s id="s.000062">Vt po&longs;tea &agrave; grauioribus &longs;tudijs <lb/>ad am&oelig;niora animum abduceret, de re nautica po&euml;ma I&shy;<lb/>talic&egrave; confecit. </s>
          <s id="s.000063">quo ab&longs;oluto Paradoxa multa Mathema&shy;<lb/>tica explicauit. </s>
          <s id="s.000064">Fama de Baldi virtutibus di&longs;&longs;ipata Ferran&shy;<lb/>dus Gonzaga Molfetr&aelig; Princeps &amp; Gua&longs;tall&aelig; Dominus <lb/>c&oelig;pit de illo in &longs;uam familiam a&longs;ci&longs;cendo cogitare, vt qui <lb/>ij&longs;dem caperetur artibus, quibus excellere Baldus inci-<pb xlink:href="007/01/015.jpg"/>piebat: Itaque opera Curtij Arditij honorifice fuit in au&shy;<lb/>lam euocatus, dum vitam non aulicam viueret totus in <lb/>litteras abditus precibus Ve&longs;pa&longs;iani Gonzag&aelig; Sablonet&aelig; <lb/>Ducis ad explanandos Vitruuij libros adactus fuit. </s>
          <s id="s.000065">quare <lb/><expan abbr="t&umacr;c">tunc</expan> natus de <expan abbr="Verbor&umacr;">Verborum</expan> Vitruuianorum &longs;ignificatione com&shy;<lb/>mentarius; in quo minime mirandum &longs;i minuta qu&aelig;dam <lb/>pro&longs;equutus fuit, qu&aelig; viro magno minus e&longs;&longs;e digna vi&shy;<lb/>deantur:illi enim Principi morem ge&longs;&longs;it. </s>
          <s id="s.000066">&longs;cio dixi&longs;&longs;e ali&shy;<lb/>quando Adrianum Romanum &egrave; Polonia reuer&longs;um, vbi <lb/>Vitruuium Palatino cuidam explicauerat, &longs;i commen&shy;<lb/>tarium Baldi in Polonia adhibere potui&longs;&longs;em, aurum quod <lb/>mecum attuli emunxi&longs;&longs;em, quia &longs;atis feci&longs;&longs;em muneri la&shy;<lb/>bore nullo. </s>
          <s id="s.000067">Cum Ferrando hero &longs;uo obueni&longs;&longs;et nece&longs;&longs;i&shy;<lb/>tas Hi&longs;panias adeundi, illud iter &longs;ine Baldo facere &longs;e po&longs;&shy;<lb/>&longs;e non putabat, non tam vt haberet, qui erudito eloquio <lb/>vi&aelig; t&aelig; dium leuaret, quam cui po&longs;&longs;et arcana committere, <lb/>atque adeo &agrave; quo iuuaretur con&longs;ilio. </s>
          <s id="s.000068">Vix vi&aelig; &longs;e dederant <lb/>cum Baldus grauem in morbum delap&longs;us itinere cogitur <lb/>de&longs;i&longs;tere: Mediolanum proinde diuertit, vbi &agrave; S. <!-- REMOVE S-->Carolo <lb/>Borrom&aelig;o &amp; benign&egrave; exceptus, &amp; tamdiu detentus do&shy;<lb/>nec valetudinem recuperaret. </s>
          <s id="s.000069">Gua&longs;tallam po&longs;tea &longs;e re&shy;<lb/>cepit, vbi cum ab&longs;ente Domino liberiori otio frueretur, <lb/>libros &longs;ex de Aula eruditi&longs;&longs;imos methodo analytica con&shy;<lb/>&longs;crip&longs;it. </s>
          <s id="s.000070">alios non commemoro, quod cum otium erit, o&shy;<lb/>mnium &longs;yllabum dabo. </s>
          <s id="s.000071">Anno 1586. ip&longs;o nihil po&longs;tulante <lb/>eligitur Gua&longs;tall&aelig; Abbas, &agrave; quo tempore Iuri Can. <!-- KEEP S--></s>
          <s id="s.000072">Con&shy;<lb/>cilijs, &amp; SS.Patribus totum &longs;e dedit. </s>
          <s id="s.000073">Hebre&aelig; &amp; Chald&aelig;&aelig; <lb/>linguarum di&longs;cendarum triennium po&longs;uit. </s>
          <s id="s.000074">Anno 1593. no&shy;<lb/>u&aelig; Gnomonices libros quinque compo&longs;uit. </s>
          <s id="s.000075">in&longs;equenti <lb/>Chald&aelig;am Onkeli paraphra&longs;in in Pentateuchum vertit <lb/>&amp; commentarios adiunxit; quo exant lato labore in Iob <lb/>ex Heb. <!-- REMOVE S-->fonte paraphra&longs;in texuit, quam &amp; &longs;cholijs illu&shy;<lb/>&longs;trauit. </s>
          <s id="s.000076">Tabulam Etru&longs;cam Eugubinam interptetatus <pb xlink:href="007/01/016.jpg"/>fuit:in ea autem diuinatione, vt aiebat, &longs;ubci&longs;iuas vnius <lb/>men&longs;is horas con&longs;ump&longs;it. </s>
          <s id="s.000077">De Firmamento &amp; aquis egre&shy;<lb/>gie &longs;crip&longs;it. </s>
          <s id="s.000078">Oeconomiam Tropologicam in S.Matth&aelig;um <lb/>Card. <!-- REMOVE S-->Baronius, qui non alia Baldi vidit, vehementer pro&shy;<lb/>babat. </s>
          <s id="s.000079">Rom&aelig; dum viueret, fere ne&longs;ciuit quid gereretur <lb/>in Aulis: Arabic&aelig; enim lingu&aelig; cum Io. <!-- REMOVE S-->Bapti&longs;ta Raimon&shy;<lb/>do diligenti&longs;&longs;ime &longs;tuduit, &amp; arcana indu&longs;tria Slauonic&aelig;, <lb/>quam perfecte callebat. </s>
          <s id="s.000080">Ex Arabico vertit Hortum Geo&shy;<lb/>graphicum Anonymi, quem ante &longs;excentos annos flo&shy;<lb/>rui&longs;&longs;e arbitrabatur. </s>
          <s id="s.000081">Hunc vero extru&longs;i&longs;&longs;et, vt alios Baldi <lb/>libros, Marcus Vel&longs;erus IIvir Aug. <!-- REMOVE S-->&longs;i eo paulo longior <lb/>huius lucis v&longs;ura contigi&longs;&longs;et. </s>
          <s id="s.000082">Compo&longs;uit &amp; Dictionarium <lb/>Arabicum. <!-- KEEP S--></s>
          <s id="s.000083">atque cum beati&longs;&longs;imam illam vbertatem in&shy;<lb/>genij a&longs;&longs;idue diffundi nece&longs;&longs;e e&longs;&longs;et, anno 1603. orbem vni&shy;<lb/>uer&longs;um de&longs;cribere aggre&longs;&longs;us fuit; atque ita quidem, vt <lb/>tam qu&aelig; ad Hi&longs;toriam, quam qu&aelig; ad Geographiam per&shy;<lb/>tinerent complecteretur: Neque illu&longs;trare &longs;olum voluit <lb/>qu&aelig; nouerunt antiqui, quemadmodum vi&longs;um Ortelio, <lb/>&longs;ed vel oppidula omnia &amp; pagos, de quibus aliqua in po&shy;<lb/>&longs;tremis &longs;criptoribus mentio. </s>
          <s id="s.000084">&amp; profecto totum opus ad <lb/>vmbilicum perduxit: non dige&longs;&longs;it tamen vniuer&longs;um. </s>
          <s id="s.000085">qua&shy;<lb/>tuor aut ni fallor quinque tantum Tomi fuerunt ordine <lb/>Alphabetico di&longs;po&longs;iti:&longs;upere&longs;&longs;ent &longs;eptem aut octo di&longs;po&shy;<lb/>nendi, quantum ex chartarum &amp; fa&longs;ciculorum mole con&shy;<lb/>ijcere licet. </s>
          <s id="s.000086">Anno 1617. quarto Idus Octob. <!-- KEEP S--></s>
          <s id="s.000087">po&longs;tea quam <lb/>dies 40. vehementi de&longs;tillatione vexatus fui&longs;&longs;et, &longs;piritum <lb/>Deo reddidit Sacramentis Eccle&longs;i&aelig; omnibus rite muni&shy;<lb/>tus. </s>
          <s id="s.000088">Statura procerus fuit, facie oblonga &amp; acribus oculis, <lb/>colore &longs;ubfu&longs;co. </s>
          <s id="s.000089">Membrorum ei fuit decens habitudo, &amp; <lb/>compactum corpus. </s>
          <s id="s.000090">Diebus fe&longs;tis omnibus &longs;acrum facie&shy;<lb/>bat, ieiunabat bis in hebdomada, eleemo&longs;yni&longs;que paupe&shy;<lb/>res &longs;ubleuabat. </s>
          <s id="s.000091">In &longs;tudijs &longs;ic a&longs;&longs;iduus fuit, vt &longs;&aelig;pe &amp; legeret <lb/>&amp; comederet. </s>
          <s id="s.000092">S.Augu&longs;tini libros de Ciuitate Dei ter in-<pb xlink:href="007/01/017.jpg"/>ter prandium euoluit. </s>
          <s id="s.000093">Statim &agrave; noctis meridie dum ei vi&shy;<lb/>res firmiores e&longs;&longs;ent ad lucubrandum &longs;urgebat. </s>
          <s id="s.000094">&agrave; prandio <lb/>Euclidem Arabice editum, vel libellum aliquem germa&shy;<lb/>nicum aut gallicum in manus &longs;umebat. </s>
          <s id="s.000095">Suauitate morum <lb/>&amp; mode&longs;tia, etiam &longs;i ceter&aelig; dotes abfui&longs;&longs;ent, quemlibet <lb/>ad amorem &longs;ui allicere potui&longs;&longs;et. </s>
          <s id="s.000096">Sermo modicus ei fuit, <lb/>itemque cultus. </s>
          <s id="s.000097">Nullos vnquam honores petijt, qui &agrave; <lb/>Clem. 8. ampli&longs;&longs;imi promi&longs;&longs;i fuerant; nullum emolumen&shy;<lb/>tum qu&aelig;&longs;iuit &longs;uo cen&longs;u contentus. </s>
          <s id="s.000098">facile parcendum e&longs;&longs;e <lb/>dicebat, ijs maxime qui in re leui impegi&longs;&longs;ent, quoniam &longs;i <lb/>quos cen&longs;emus optimos, nudos con&longs;piceremus, nullum <lb/>eorum non iudicaremus multis dignum verberibus. </s>
          <s id="s.000099">Bi&shy;<lb/>bliothecam habuit non locupletem, &longs;ed &longs;electis <expan abbr="in&longs;truct&atilde;">in&longs;tructam</expan> <lb/>codicibus. </s>
          <s id="s.000100">Verum ire per &longs;ingula longum e&longs;&longs;et. </s>
          <s id="s.000101">Satis mihi <lb/>de incomparabili Baldi doctrina, &amp; &longs;umma innocentia, &ocirc; <lb/>rarum connubium, pauca dixi&longs;&longs;e, qu&aelig; for&longs;itan ad imitan&shy;<lb/>dum nimis multa. </s>
        </p>
      </section>
      <section>
        <p type="head">
          <s id="s.000102">SYLLABVS LIBRORVM</s>
        </p>
        <p type="head">
          <s id="s.000103">omnium B.Abb.Baldi.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000104">Arati apparitiones &egrave; gr.in Ital. <!-- KEEP S--><!-- REMOVE S-->vertit. </s>
        </p>
        <p type="main">
          <s id="s.000105">De Tormentis Bellicis &amp; eorum Inuentoribus lib. <!-- REMOVE S-->Heronis automata vertit. </s>
        </p>
        <p type="main">
          <s id="s.000106">Vitas omnium Mathematicorum &longs;crip&longs;it, &amp; trib. </s>
          <s id="s.000107">in Tom. <lb/><!-- REMOVE S-->2.1.P^&lcub;s}.&agrave; Thalete ad Chri&longs;tum.2.&agrave; Chri&longs;to ad &longs;ua tem&shy;<lb/>pora. </s>
        </p>
        <p type="main">
          <s id="s.000108">Earumdem vitarum Epitomen Chronologicum confecit. </s>
        </p>
        <p type="main">
          <s id="s.000109">In Ari&longs;tot. Mechan. Commentar. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000110">De Re nautica Po&euml;mation. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000111">Paradoxorum Mathematicorum liber. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000112">De&longs;criptio Palatij Ducum Vrbinarum quod e&longs;t Vrbini. </s>
        </p>
        <p type="main">
          <s id="s.000113">Poema cui titulus, Lamus. <!-- KEEP S--></s>
        </p>
        <pb xlink:href="007/01/018.jpg"/>
        <p type="main">
          <s id="s.000114">Carmina pia, qu&aelig; in&longs;cribuntur, Anni Corona. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000115">De Verborum Vitruuianorum &longs;ignificatione. </s>
        </p>
        <p type="main">
          <s id="s.000116">Carmina varia &amp; eclog&aelig; mixt&aelig;. </s>
        </p>
        <p type="main">
          <s id="s.000117">Apologi centum, quos &longs;crip&longs;it &aelig;mulatus Leonem Bapt. <lb/><!-- REMOVE S-->Albertum. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000118">De Humanitate Dialogus qui in&longs;cribitur Go&longs;elinus. </s>
        </p>
        <p type="main">
          <s id="s.000119">Comparatio Vit&aelig; Mona&longs;tic&aelig; cum &longs;eculari. </s>
        </p>
        <p type="main">
          <s id="s.000120">De Aula libri &longs;ex. </s>
        </p>
        <p type="main">
          <s id="s.000121">De felicitate Principis Dialogus. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000122">De Dignitate Dial. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000123">Carmina Romana. </s>
        </p>
        <p type="main">
          <s id="s.000124">Mo&longs;&aelig;i fabulam vertit. </s>
        </p>
        <p type="main">
          <s id="s.000125">De Italici carminis natura Dial. <!-- REMOVE S-->qui in&longs;cribitur Ta&longs;&longs;us. </s>
        </p>
        <p type="main">
          <s id="s.000126">De vniuer&longs;ali Diluuio poemation. </s>
        </p>
        <p type="main">
          <s id="s.000127">Nou&aelig; Gnomonices lib. quin que. </s>
        </p>
        <p type="main">
          <s id="s.000128">Hieremi&aelig; Threnos vertit, &amp; ex Heb. <!-- REMOVE S-->fonte annotat. </s>
          <s id="s.000129">ad&shy;<lb/>iecit. </s>
        </p>
        <p type="main">
          <s id="s.000130">Poemation in&longs;criptum, Deiphobe, quod &longs;crip&longs;it &aelig;mula&shy;<lb/>tus Lycophonem in Ca&longs;&longs;andra. </s>
        </p>
        <p type="main">
          <s id="s.000131">Scala c&oelig;le&longs;tis.1.Sermones pij &amp; carmina. </s>
        </p>
        <p type="main">
          <s id="s.000132">Onkeli paraphra&longs;in Chald&aelig;am in Pentateuchum ver&shy;<lb/>tit &amp; vberes commentarios adiecit. </s>
        </p>
        <p type="main">
          <s id="s.000133">In Iob Paraphra&longs;is latina ex fonte Heb. <!-- REMOVE S-->additis Scholijs. </s>
        </p>
        <p type="main">
          <s id="s.000134">De &longs;camillis imparibus Vitruuij. </s>
        </p>
        <p type="main">
          <s id="s.000135">De firmamento &amp; aquis. </s>
        </p>
        <p type="main">
          <s id="s.000136">Quincti Calabri Paralipomena vertit. </s>
        </p>
        <p type="main">
          <s id="s.000137">Tabul&aelig; Etru&longs;c&aelig; Eugubin&aelig; Interpretatio. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000138">Oeconom&iacute;a Tropologicain S.Matth&aelig;um. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000139">Vrbini encomium. </s>
        </p>
        <p type="main">
          <s id="s.000140">Horti geographici ex Arab. <!-- REMOVE S-->ver&longs;io. </s>
        </p>
        <p type="main">
          <s id="s.000141">Aduer&longs;us Aulam Carmina. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000142">Luciani de mi&longs;erijs.Aulicorum ver&longs;io. </s>
        </p>
        <p type="main">
          <s id="s.000143">Oratio ad Rom&aelig; con&longs;eruatores pro antiquitatum eius <lb/>Vrbis cu&longs;todia. </s>
        </p>
        <pb xlink:href="007/01/019.jpg"/>
        <p type="main">
          <s id="s.000144">Vniuer&longs;i orbis geographica &amp; Hi&longs;torica de&longs;criptio con&shy;<lb/>texta ex &longs;eptingentis &amp; eo amplius &longs;criptoribus. </s>
        </p>
        <p type="main">
          <s id="s.000145">Federici Vrbini Ducis Vita. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000146">Guidi Vbaldi Vrbini Ducis Vita. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000147">Epigrammaton &amp; Odarum libri tres. </s>
        </p>
        <p type="main">
          <s id="s.000148">Aliorum Carminum liber. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000149">Sententiarum moralium liber. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000150">Dictionarium Arabicum. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000151">Pro Procopio contra Flauium Blondum. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000152">Horographium vniuer&longs;ale. </s>
        </p>
        <p type="main">
          <s id="s.000153">Epigrammata alia. </s>
        </p>
        <p type="main">
          <s id="s.000154">Heronis lib.  de Balli&longs;tis conuer&longs;io. </s>
        </p>
        <p type="main">
          <s id="s.000155">Exercitationes in Ari&longs;totelis Mechan. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000156">Templi Ezechielis noua de&longs;criptio. </s>
        </p>
        <p type="main">
          <s id="s.000157">Antiquitatum Gua&longs;tallen&longs;ium liber. <!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.000158">Hi&longs;tori&aelig; &longs;cribend&aelig; leges. </s>
        </p>
        <p type="main">
          <s id="s.000159">Et alia qu&aelig;dam. </s>
        </p>
        <pb xlink:href="007/01/020.jpg"/>
        <pb xlink:href="007/01/021.jpg"/>
      </section>
    </front>
    <body>
      <chap>
        <p type="head">
          <s id="s.000160">IN MECHANICA ARISTOTE&shy;<lb/>LIS PROBLEMATA<!-- REMOVE S--> EXERCITATIONES.<!-- KEEP S--></s>
        </p>
        <subchap1>
          <p type="head">
            <s id="s.000161"><emph type="italics"/>Mechanices de&longs;criptio, natura, finis.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000162">MECHANICE, facultas qu&aelig;dam e&longs;t, qu&aelig; <lb/>naturali materi&acirc;, Geometricisque; demon&shy;<lb/>&longs;trationibus v&longs;a, ex centrobaric&acirc;, &amp; <expan abbr="eor&umacr;">eorum</expan> <lb/>qu&aelig; ad vectem &amp; libram rediguntur, &longs;pe&shy;<lb/>culatione; human&aelig; con&longs;ulens nece&longs;&longs;itati, <lb/>commoditatiqueue, &longs;uapte vi, Naturam i&shy;<lb/>p&longs;am vel &longs;ecundans, vel &longs;uperans, varia, eaque mirabilia <lb/>operatur. </s>
            <s id="s.000163">Hac diffinitione de&longs;cription&eacute;ue breuiter ea fe&shy;<lb/>r&egrave; omnia complexi &longs;umus, qu&aelig; fu&longs;i&longs;&longs;im&egrave; ab Ari&longs;totele, <lb/>Pappo, Guido Vbaldo, &amp; alijs hac de re tradita fu&ecirc;re. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000164"><emph type="italics"/>Mechanices Obiectum.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000165">Con&longs;iderat autem Mechanicus Graue &amp; Leue. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000166">Graue duplex, Natur&acirc;, Violenti&acirc;. </s>
          </p>
          <p type="main">
            <s id="s.000167">Graue Natur&acirc; dicitur, quod in&longs;ita propen&longs;ione in <lb/>centrum mundi fertur. </s>
            <s id="s.000168">Graue autem Violenti&acirc;, quod im&shy;<lb/>pre&longs;&longs;o extrin&longs;ecus pondere ab impellente pellitur. </s>
          </p>
          <p type="main">
            <s id="s.000169">Leue contr&agrave;, qu&ograve;d Natur&acirc; &agrave; centro fertur. </s>
          </p>
          <p type="main">
            <s id="s.000170">C&aelig;ter&ugrave;m quicquid graue e&longs;t, &longs;ecundum punctum <lb/>e&longs;t, quod Grauitatis centrum dicitur, &amp; hoc duplex, vt <lb/>duplex e&longs;t grauitas, Natur&aelig;, Violenti&aelig;. <!-- KEEP S--></s>
          </p>
          <pb xlink:href="007/01/022.jpg"/>
          <p type="main">
            <s id="s.000171">Grauitatis centrum in triplici magnitudine con&longs;i&shy;<lb/>derari pote&longs;t, lineari, plan&agrave;, &longs;olid&acirc;. </s>
          </p>
          <p type="main">
            <s id="s.000172">De centro grauitatis linearum nemo &longs;crip&longs;it, &longs;impli&shy;<lb/>ci&longs;&longs;imi enim illud e&longs;t contemplationis. </s>
          </p>
          <p type="main">
            <s id="s.000173">De centro grauitatis linearum egregi&egrave; tractauit Ar&shy;<lb/>chimedes in libro &AElig;queponderantium, &amp; de quadratu&shy;<lb/>ra Parabole, tum in eo quem de his qu&aelig; vehuntur in&shy;<lb/>&longs;crip&longs;it. </s>
          </p>
          <p type="main">
            <s id="s.000174">De centro grauitatis &longs;olidorum ip&longs;emet olim &longs;cri&shy;<lb/>p&longs;erat Archimedes, &longs;ed ea qu&aelig; protulit, temporis iniuri&acirc; <lb/>deperdita, &longs;u&acirc; diligenti&acirc; re&longs;tituit Federicus Commandi&shy;<lb/>nus. </s>
          </p>
          <p type="main">
            <s id="s.000175">E&longs;&longs;e autem &amp; Leuitatis centrum in rerum natura, <lb/>palam e&longs;t. </s>
            <s id="s.000176">Punctum enim illud e&longs;t, &longs;ecundum quod leuia <lb/>rect&agrave; &agrave; centro &longs;ur&longs;um feruntur. </s>
            <s id="s.000177">Huius autem non memi&shy;<lb/>n&ecirc;re Mechanici, propterea quod aut nihil, aut parum ad <lb/>eorum rem faciat. </s>
          </p>
          <p type="main">
            <s id="s.000178">Porro Grauitatis centrum ita definit Heron, &amp; qui <lb/>ab Herone Pappus 1.8. Collectionum Mathematicarum. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000179">Centrum grauitatis <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> corporis e&longs;t pun&shy;<lb/>ctum quoddam intra po&longs;itum, &agrave; quo &longs;i graue, mente ap&shy;<lb/>pen&longs;um concipiatur, dum fertur, quie&longs;cit, &amp; &longs;eruat eam <lb/>quam in principio habuit po&longs;itionem; neque in ip&longs;a latio&shy;<lb/>ne circumuertitur. </s>
            <s id="s.000180">Commandinus ver&ograve; in lib. de centro <lb/>grauitatis &longs;olidorum hoc pacto: Centrum grauitatis v&shy;<lb/>niu&longs;cuiu&longs;que &longs;olid&aelig; figur&aelig;, e&longs;t punctum illud intra po&longs;i&shy;<lb/>tum, circa quod vndique partes &aelig;qualium momentorum <lb/>ad&longs;i&longs;tunt. </s>
            <s id="s.000181">Si enim per tale centrum ducatur planum, fi&shy;<lb/>guram quomodolibet &longs;ecans, in partes &aelig;qu&egrave; ponderantes <lb/>eam diuidit. </s>
            <s id="s.000182">Nos ver&ograve; qu&agrave;m breui&longs;&longs;im&egrave; dicimus: <expan abbr="Centr&umacr;">Centrum</expan> <lb/>grauitatis, <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> magnitudinis punctum e&longs;&longs;e intra <lb/>extraue magnitudinem po&longs;itum, per quod &longs;i plano linea <lb/>punctoue diuidatur, in partes &longs;ecatur &aelig;queponderantes. </s>
          </p>
          <pb xlink:href="007/01/023.jpg"/>
          <figure id="id.007.01.023.1.jpg" xlink:href="007/01/023/1.jpg"/>
          <p type="main">
            <s id="s.000183">Diximus, Magnitudinis vt line&aelig;, plani &longs;olidique; cen&shy;<lb/>trum complecteremur. </s>
            <s id="s.000184">Erit igitur, vt in pr&aelig;&longs;enti figura, li&shy;<lb/>ne&aelig; quidem centrum A, plani B, &longs;olidi ver&ograve; C. quod &longs;i ob&shy;<lb/>ijciat qui&longs;piam, lineam &amp; &longs;uperficiem nullam habere gra&shy;<lb/>uitatem; is &longs;ciat, <expan abbr="neq;">neque</expan> corpora Mathematica grauitatem <lb/>habere, Mechanicum ver&ograve; funes, ha&longs;tas, vectes pro lineis <lb/>&longs;umere; tabulas ver&ograve;, &amp; eiu&longs;modi plana ad &longs;uperficierum <lb/>naturam referre. </s>
          </p>
          <p type="main">
            <s id="s.000185">Diximus in&longs;uper, intra extraue. </s>
            <s id="s.000186">Aliquando enim <lb/>grauitatis centrum extra molem corporis cuius corporis <lb/>centrum e&longs;t, cadit, vt in &longs;equenti figura. </s>
          </p>
          <figure id="id.007.01.023.2.jpg" xlink:href="007/01/023/2.jpg"/>
          <p type="main">
            <s id="s.000187">E&longs;to corpus aliquod <lb/>&longs;uperficiesue ABCDE, <lb/>ducatur linea CF, <expan abbr="diuid&emacr;s">diuidens</expan> <lb/>figuras in partes hinc inde <lb/>&aelig;queponderantes ABC, <lb/>EDC. <!-- KEEP S--></s>
            <s id="s.000188">Ducatur &amp; GH. <lb/>diu&iacute;dens item in partes &aelig;&shy;<lb/>queponderantes GCH, &amp; GAB, EDH. &longs;ecent autem <lb/>&longs;eip&longs;as in I. erit igitur centrum I extra figur&aelig; terminos &amp; <lb/>molem ip&longs;am. </s>
            <s id="s.000189">Attamen licet hoc verum &longs;it, intra e&longs;&longs;e dici <lb/>pote&longs;t, quippe quod imaginario quodam, &amp; vt ita dicam, <lb/>virtuali ambitu ACDA contineatur. </s>
          </p>
          <p type="main">
            <s id="s.000190">Dicebamus, duplex e&longs;&longs;e grauitatis centrum, Natu&shy;<pb xlink:href="007/01/024.jpg"/>r&acirc;, Violenti&agrave;: affirmamus mod&ograve;, h&aelig;c re quidem vnum e&longs;&shy;<lb/>&longs;e, &amp; ratione &longs;olum, non autem re ip&longs;a ac &longs;i duo e&longs;&longs;ent con&shy;<lb/>&longs;iderari. </s>
          </p>
          <figure id="id.007.01.024.1.jpg" xlink:href="007/01/024/1.jpg"/>
          <p type="main">
            <s id="s.000191">E&longs;to enim grauitatis na&shy;<lb/>turalis centrum B, corporis A, <lb/>&longs;ecundum quod dimi&longs;&longs;um, &longs;ua&shy;<lb/>pte natur&acirc; cadet in C, &longs;i ver&ograve; <lb/>corpus violenter impellatur in <lb/>D, aliud acquiret centrum gra&shy;<lb/>uitatis ex violentia &longs;ecundum <lb/>quam fertur, motum, in D, <expan abbr="id&emacr;">idem</expan> <lb/>autem &longs;unt re, nempe vnum B, <lb/>duo autem &longs;i violentia &amp; natura &longs;eor&longs;um con&longs;ideren&shy;<lb/>tur. </s>
          </p>
          <p type="main">
            <s id="s.000192">H&aelig;c centra, duo motus &longs;equuntur, rectus vterque, <lb/>Naturalis videlicet, &amp; Violentus. </s>
            <s id="s.000193">Tertius ex his mixtus, &amp; <lb/>is quidem non rectus, &longs;ed curuus. </s>
          </p>
          <figure id="id.007.01.024.2.jpg" xlink:href="007/01/024/2.jpg"/>
          <p type="main">
            <s id="s.000194">Proijciatur enim violen&shy;<lb/>ter corpus graue A &longs;uperante <lb/>igitur violentia, rect&agrave; feretur <lb/>in B; ea autem elangue&longs;cente <lb/>paullatim per curuam &amp; mi&shy;<lb/>xtam <expan abbr="line&atilde;">lineam</expan> &longs;ecetur in C, qua&shy;<lb/>tenus enim ad anteriora fer&shy;<lb/>tur, violentia e&longs;t; quatenus ve&shy;<lb/>r&ograve; ad inferiores partes, natur&aelig;. </s>
            <s id="s.000195">Vbi ver&ograve; peruenit in C, <lb/>violenti&acirc; ce&longs;&longs;ante, natur&acirc; ver&ograve; manente, rect&agrave; deor&longs;um <lb/>fertur DCD. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000196">C&aelig;ter&ugrave;m h&aelig;c centra, hiqueue motus, naturalis nem&shy;<lb/>pe, &amp; violentus diuer&longs;imode &longs;e habent adinuicem. </s>
            <s id="s.000197">Si e&shy;<lb/>nim graue corpus extern&acirc; vi adhibita, centrum mundi <lb/>ver&longs;us impellatur, adiuuabunt &longs;e inuicem Natura, Vio&shy;<lb/>lentia, Si autem contra, altera alteri re&longs;i&longs;tet, in motibus <pb xlink:href="007/01/025.jpg"/>autem ad latus, eo magis pugnabunt, quo magis ab infe&shy;<lb/>rioribus ad &longs;uperiora fiet motus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000198"><emph type="italics"/>Mechanices pr&aelig;cipua in&longs;trumenta.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000199">Hic ira con&longs;titutis dicimus, in&longs;trumenta, quibus ad <lb/>varias operationes Mechanici vtuntur, e&longs;&longs;e inter &longs;e qui&shy;<lb/>dem diuer&longs;a, multiplicia, &amp; &longs;i varietatem &longs;pectes, pen&egrave; in&shy;<lb/>numerabilia; quod quamuis verum &longs;it, ea omnia Ari&longs;tote&shy;<lb/>les ad vectem re ducit, &amp; libram: quod etiam G. <!-- REMOVE S-->Vbaldus <lb/>in libris Mechanicorum fecit. </s>
            <s id="s.000200">C&aelig;terum qui po&longs;t Ari&longs;to&shy;<lb/>telem floruere Mechanici, omnia ad quinque, quas ap&shy;<lb/>pellant, Potentias, redeg&ecirc;re. </s>
            <s id="s.000201">Sunt autem ex Herone, Pap&shy;<lb/>po, Guido Vbaldo, qui eos &longs;ecutus e&longs;t, Vectis, Trochlea, <lb/>Axis in Peritrochio, Cuneus, Cochl&egrave;a. </s>
            <s id="s.000202">Videtur autem i&shy;<lb/>p&longs;e G. <!-- REMOVE S-->Vbaldus &longs;extam addere, nempe Libram, de qua &amp; <lb/>primus ip&longs;e Mechanicorum tractatum in&longs;tituit. </s>
            <s id="s.000203">Verum <lb/>enimuero idem fer&egrave; &longs;unt Vectis &amp; Libra, ni&longs;i forte quod <lb/>Libra tunc dicitur, cum brachia &longs;unt &aelig;qualia. </s>
            <s id="s.000204">Vectis vero <lb/>quomodocunque ea &longs;e habeant; quinque harum <expan abbr="Poten-tiar&umacr;">Poten&shy;<lb/>tiarum</expan> imagines ita ob oculos ponimus. </s>
            <s id="s.000205">Vectis A. <!-- KEEP S--></s>
            <s id="s.000206">Trochlea <lb/>B, Axis in Peritrochio C. <!-- KEEP S--></s>
            <s id="s.000207">Cuneus D. <!-- KEEP S--></s>
            <s id="s.000208">Cochlea vero E. <!-- KEEP S--></s>
          </p>
          <pb xlink:href="007/01/026.jpg"/>
          <figure id="id.007.01.026.1.jpg" xlink:href="007/01/026/1.jpg"/>
          <p type="main">
            <s id="s.000209">Porro, Cuneum ad libram reducere conatur Ari&shy;<lb/>&longs;toteles, quod facit &amp; G. Vbaldus, qui e&ograve; refert &amp; Co&shy;<lb/>chleam, quippe quod nihil aliud &longs;it Cochlea, qu&agrave;m Cu&shy;<lb/>neus Cylindro inuolutus. </s>
            <s id="s.000210">Nos autem duas tant&ugrave;m Po&shy;<lb/>tentias ad vectem reduci po&longs;&longs;e arbitramur, Trochleam <lb/>nempe, &amp; Axem in Peritrochio. <!-- KEEP S--></s>
            <s id="s.000211">Nequaquam autem Cu&shy;<lb/>neum &amp; Cochleam. </s>
            <s id="s.000212">quod lati&ugrave;s quidem o&longs;tendemus, <lb/>c&ugrave;m de Cuneo erit nobis &longs;ermo peculiaris. </s>
          </p>
          <p type="head">
            <s id="s.000213"><emph type="italics"/>De Vecte &amp; Libra &longs;ecundum Ari&shy;<lb/>&longs;totelem.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000214">Ari&longs;toteles in ip&longs;o Mechanicorum ingre&longs;&longs;u ita &longs;cri&shy;<lb/>bit, Mirum videri ab exigua virtute magnum pondus mo-<pb xlink:href="007/01/027.jpg"/>ueri, addito nimirum ponderi pondere, &longs;iquidem &amp; vectis <lb/>e&longs;t pondus. </s>
            <s id="s.000215">Duplex ergo illi admiratio, &longs;cilicet qu&ograve;d exi&shy;<lb/>gua potentia moueat ingens pondus, idqueue etiam addito <lb/>vectis ip&longs;ius pondere, fiat. </s>
            <s id="s.000216">Hoc &longs;ecundum adieci&longs;&longs;e vide&shy;<lb/>tur, amplificationis alicuius grati&acirc;. </s>
            <s id="s.000217">Etenim quatenus <lb/>ad rem pertinet, &longs;i mouendis ponderibus vectis ip&longs;ius <lb/>pondus compares, nullius fer&egrave; e&longs;&longs;e momenti procul du&shy;<lb/>bio affirmaueris. </s>
            <s id="s.000218">Sed &amp; illud quoque notandum, aliquan&shy;<lb/>do vectis pondus mouenti auxilium ferre, quod fit vbi <lb/>fulcimento inter potentiam mouentem, &amp; pondus ip&longs;um <lb/>collocato, vectis pars qu&aelig; &agrave; fulcimento ad potentiam e&longs;t, <lb/>premitur. </s>
            <s id="s.000219">Tunc enim, vt dicebamus, vectis pondere &longs;uo <lb/>potentiam adiuuat. </s>
            <s id="s.000220">Contra ver&ograve; accidit, cum pondus i&shy;<lb/>p&longs;um inter fulcimentum e&longs;t &amp; potentiam vel potentia i&shy;<lb/>p&longs;a inter fulcimentum &amp; pondus. </s>
            <s id="s.000221">tunc enim vectis vn&acirc; <lb/>cum pondere attollitur. </s>
            <s id="s.000222">qu&aelig; licet vera &longs;int, non tamen in&shy;<lb/>de &longs;equitur, vectis pondus, quicquam quod curandum &longs;it, <lb/>in operatione efficere, aut impedire. </s>
          </p>
          <p type="main">
            <s id="s.000223">Porr&ograve; vectem ita finire po&longs;&longs;umus, longitudinem e&longs;&shy;<lb/>&longs;e quandam inflexibilem, qu&aelig; fulcimento dato, dat&acirc; po&shy;<lb/>tenti&acirc; datum pondus mouetur. </s>
          </p>
          <p type="main">
            <s id="s.000224">Ip&longs;a quoque Libra, vt diximus, vectis e&longs;t: eius autem <lb/>natur&aelig;, vt &longs;emper fulcimentum medium obtineat locum <lb/>inter pondus &amp; pondus. </s>
            <s id="s.000225">Statera autem merus e&longs;t vectis, &longs;i <lb/>&longs;par&longs;um pro fulcimento; appendiculum ver&ograve; currens pro <lb/>potentia mouente deputaueris. </s>
          </p>
          <p type="head">
            <s id="s.000226"><emph type="italics"/>De Circulo eiusque natura Ari&longs;totelis doctri&shy;<lb/>na examinata.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000227">Ari&longs;toteles, quicquid mirum in Mechanicis opera&shy;<lb/>tur, id totum admirabili circuli natur&aelig; e&longs;&longs;e tribuendum <lb/>arbitratur. </s>
            <s id="s.000228">Ait autem, ab&longs;urdum nullatenus e&longs;&longs;e, &longs;i ex re <lb/>mirabili mirandum quippiam oriatur. </s>
            <s id="s.000229">In circulo autem <pb xlink:href="007/01/028.jpg"/>quatuor inueniri qualitates admiratione dignas. </s>
            <s id="s.000230"><expan abbr="Prim&atilde;">Primam</expan>, <lb/>quod ex contrarijs con&longs;tituatur, mouente videlicet &amp; <lb/>moto. </s>
            <s id="s.000231">Secundam, qu&ograve;d contraria in eius circumferentia <lb/>inueniantur, quippe qu&aelig; cum vnica linea &longs;it, concaua &longs;i&shy;<lb/>mul e&longs;t &amp; conuexa. </s>
            <s id="s.000232">Tertiam, quod contrarijs feratur mo&shy;<lb/>tionibus, antror&longs;um nimirum, retror&longs;um, &longs;ur&longs;um, atque <lb/>deor&longs;um. </s>
            <s id="s.000233">Quartam, quod vnic&acirc; exi&longs;tente &longs;emidiametro, <lb/>nullum in ea punctum &longs;umi po&longs;&longs;it, &aelig;qualis alteri, in latio&shy;<lb/>ne, velocitatis. </s>
            <s id="s.000234">Sit enim circulus AB, cuius centrum C, <lb/>&longs;emidiameter AC, &longs;umatur autem in ea punctum D, i&shy;<lb/>tem&qacute;ue punctum E. <!-- KEEP S--></s>
            <s id="s.000235">Erit itaque in ip&longs;a circulatione D <lb/>tardius E, ip&longs;um ver&ograve; E tardius A, &amp; ita citius id feretur <lb/>&longs;emper, quod remotius &agrave; mouente termino accipitur. </s>
          </p>
          <figure id="id.007.01.028.1.jpg" xlink:href="007/01/028/1.jpg"/>
          <p type="main">
            <s id="s.000236">H&aelig;c ex illo, quibus ne vltro a&longs;&shy;<lb/>&longs;en&longs;um pr&aelig;beamus non vnica de cau&shy;<lb/>&longs;a cohibemur. </s>
            <s id="s.000237">Dicimus igitur, videri <lb/>nobis, circulum non ex contrarijs <expan abbr="c&omacr;-&longs;titui">con&shy;<lb/>&longs;titui</expan>, puta ex manente &amp; moto, &longs;ed ex <lb/>moto &longs;impliciter. </s>
            <s id="s.000238">Nulla e&longs;t enim &longs;e&shy;<lb/>midiametri pars, qu&aelig; non moueatur. <lb/></s>
            <s id="s.000239">Punctum autem, quod &longs;tat, &longs;emidia&shy;<lb/>metri pars nulla e&longs;t. </s>
            <s id="s.000240">Et &longs;an&egrave; cur moto <lb/><expan abbr="&longs;emidiam&emacr;tro">&longs;emidiametro</expan> fiat circulus, non ideo accidit, quod <expan abbr="alter&umacr;">alterum</expan> <lb/>extremum &longs;tet, alterum ver&ograve; moueatur:sed ideo qu&ograve;d &longs;e&shy;<lb/>midiameter perpetu&ograve; eandem &longs;eruet longitudinem. </s>
            <s id="s.000241">Elli&shy;<lb/>p&longs;is &longs;an&egrave; centrum habet, &longs;ed ab eo ad circumferentiam <lb/>quatuor tant&ugrave;m &longs;emidiametri quomodolibet &longs;umpti du&shy;<lb/>cuntur &aelig;quales. </s>
            <s id="s.000242">Si quis igitur &longs;emidiametrum daret pro&shy;<lb/>portione cre&longs;centem &amp; decre&longs;centem, &longs;tante altero ex&shy;<lb/>tremorum Ellip&longs;is de&longs;criberetur. </s>
            <s id="s.000243">Pr&aelig;terea &amp; &longs;piralis li&shy;<lb/>nea, qu&aelig; mixta e&longs;t, altero &longs;emidiametri extremo manen&shy;<lb/>te, altero vero moto producitur. </s>
            <s id="s.000244">Legem itaque circulo <pb xlink:href="007/01/029.jpg"/>pr&aelig;&longs;cribit, non quidem qu&ograve;d h&aelig;c extremitas &longs;ter, illa ve&shy;<lb/>r&ograve; moueatur, &longs;ed quod &longs;ua circulatione &longs;emper &longs;emidia&shy;<lb/>meter eandem &longs;eruet longitudinem, quod vel ex ip&longs;a cir&shy;<lb/>culi definitione colligitur. </s>
          </p>
          <p type="main">
            <s id="s.000245">Ad &longs;ecundum miraculum, &longs;cilicet, qu&ograve;d in circulo <lb/>circum ferentia, qu&aelig; vacua linea e&longs;t, concaua &longs;imul &longs;it, &amp; <lb/>conuexa. </s>
            <s id="s.000246">Diceret qui&longs;piam id, &longs;i mod&ograve; mirabile e&longs;t non <lb/>circulari tantum, &longs;ed cuilibet curu&aelig; line&aelig; primo compe&shy;<lb/>tere, etenim &amp; Ellip&longs;is &amp; Hyperbole, &amp; Parabole, &amp; &longs;pi&shy;<lb/>ra, tum Cy&longs;&longs;ois, Conchois, &amp; infinit&aelig; ali&aelig; irregulares <lb/>concau&aelig; &longs;imul &longs;unt &amp; conuex&aelig;. </s>
            <s id="s.000247">Sed &amp; h&aelig;c in &longs;uperficie&shy;<lb/>bus quoque de&longs;iderantur. </s>
          </p>
          <p type="main">
            <s id="s.000248">Ad tertium, quod contrarijs feratur lationibus, an&shy;<lb/>tror&longs;um, retror&longs;um, &longs;ur&longs;um &amp; deor&longs;um. </s>
            <s id="s.000249">Dicimus, facil&egrave; <lb/>&longs;olui, Nullus enim, re bene per&longs;pect&acirc;, affirmauerit circu&shy;<lb/>lum contrarijs lationibus moueri. </s>
          </p>
          <figure id="id.007.01.029.1.jpg" xlink:href="007/01/029/1.jpg"/>
          <p type="main">
            <s id="s.000250">E&longs;to enim circulus ABCD, <lb/>circa centrum E; ponamus ro&shy;<lb/>tari, &amp; A ver&longs;us B, exempli gra&shy;<lb/>ti&acirc;, antror&longs;um, mouebitur <expan abbr="aut&emacr;">autem</expan> <lb/>&amp; B ver&longs;us C, &amp; C ver&longs;us D, tum <lb/>D ver&longs;us A. <!-- KEEP S--></s>
            <s id="s.000251">Non puto <expan abbr="quenqu&atilde;">quenquam</expan> <lb/>dicturum, circulum hunc an&shy;<lb/>tror&longs;um eodem tempore, &amp; re&shy;<lb/>tror&longs;um ferri nec &longs;ur&longs;um aut de&shy;<lb/>or&longs;um, &longs;i enim qui&longs;piam per eius circuli circumferentiam <lb/>ambularet, is cert&egrave; centrum ip&longs;um &longs;emper ad dexteram <lb/>haberet, vel ad &longs;ini&longs;tram, &longs;i ad dexteram, antror&longs;um ibit, &longs;i <lb/>ad &longs;ini&longs;tram, retror&longs;um. </s>
            <s id="s.000252">Sed nec &longs;ur&longs;um vel deor&longs;um, e&longs;t <lb/>manife&longs;tum. </s>
            <s id="s.000253">Nihil autem prohibet eundem motum va&shy;<lb/>rio re&longs;pectu contrarium dici po&longs;&longs;e, id tamen profect&ograve; fie&shy;<lb/>ri nequaquam pote&longs;t, nempe A moueri ver&longs;us B, hoc e&longs;t, <pb xlink:href="007/01/030.jpg"/>antror&longs;um, &amp; eandem eodem tempore ver&longs;us B, id e&longs;t, re&shy;<lb/>tror&longs;um; repugnat enim natur&aelig;. </s>
          </p>
          <p type="main">
            <s id="s.000254">De quarto circuli miraculo, ibi erit nobis &longs;ermo, vbi <lb/>ea perpenderimus prim&ograve;, qu&aelig; Philo&longs;ophus de Circuli <lb/>productione di&longs;&longs;erens in medium profert. </s>
            <s id="s.000255">Sunt autem e&shy;<lb/>iu&longs;modi: </s>
          </p>
          <p type="main">
            <s id="s.000256">Circulum quidem duplici notione produci, Natu&shy;<lb/>rali videlicet altera, &amp; altera qu&aelig; e&longs;t pr&aelig;ter naturam, &amp; <lb/>ideo circularem lineam in ter mixtas computari. </s>
          </p>
          <p type="main">
            <s id="s.000257">Motus mixtus ait, vel proportione &longs;eruata fit, aut <lb/>non; Si proportione &longs;eruat&acirc;, rectam lineam; ea ver&ograve; non <lb/>&longs;eruata, circularem lineam produci. </s>
          </p>
          <figure id="id.007.01.030.1.jpg" xlink:href="007/01/030/1.jpg"/>
          <p type="main">
            <s id="s.000258">E&longs;to enim rectangu&shy;<lb/>lum ABCD, cuius late&shy;<lb/>ra in dat&acirc; &longs;int proportio&shy;<lb/>ne, AD cum AB. <!-- KEEP S--></s>
            <s id="s.000259">Mo&shy;<lb/>ueatur A, duplici motu, <lb/>Altero quidem tendens <lb/>in B, altero vero ad mo&shy;<lb/>tum line&aelig; AB, feratur <lb/>ver&longs;us D, &longs;eruata inte&shy;<lb/>rim laterum proportione. </s>
            <s id="s.000260">Itaque ponatur ex motu ab A <lb/>ver&longs;us B, perueni&longs;&longs;e in E, ex motu autem quo proportio&shy;<lb/>naliter fertur cum linea AB, facta ip&longs;a AB, in FH, perue&shy;<lb/>ni&longs;&longs;e in G, &amp; EG connectatur. </s>
            <s id="s.000261">Erit igitur Parallelogram&shy;<lb/>mum AEGF, Parallelogrammo ABCD proportiona&shy;<lb/>le &longs;imile, &amp; circa eandem diametrum AGC. <!-- KEEP S--></s>
            <s id="s.000262">Semper igi&shy;<lb/>tur punctum A &longs;i duabus lationibus feratur, laterum pro&shy;<lb/>portione &longs;eruata, lineam producet rectam, diametrum <lb/>nempe AGC. <!-- KEEP S--></s>
            <s id="s.000263">Et hoc &longs;an&egrave; nullam habet dubitationem, <lb/>ex ijs qu&aelig; docet Euclides 1. 6. prop.  24. </s>
          </p>
          <p type="main">
            <s id="s.000264">His ita demon&longs;tratis hac vti videtur Philo&longs;ophus <pb xlink:href="007/01/031.jpg"/>argumentatione: Si mixtus motus proportione &longs;emot&acirc;, <lb/>rectam producit, &longs;i nunquam &longs;emota, efficiet circulum; &longs;i <lb/>enim modo &longs;eruaretur, modo non, partim recta partim <lb/>non recta produceretur. </s>
            <s id="s.000265">Ingenio&longs;a quidem argumenta&shy;<lb/>tio, ni vitium contineret. </s>
            <s id="s.000266">non enim mixtus motus, qui <lb/>nun quam &longs;eruat&acirc; proportione fit, &longs;emper ci, culum pro&shy;<lb/>ducit, &longs;ed &amp; Ellip&longs;im pote&longs;t, &amp; quamlibet aliam lineam, <lb/>cuius nulla pars &longs;it recta. </s>
            <s id="s.000267">Hanc difficultatem vidit Pico&shy;<lb/>lomineus in &longs;ua Paraphra&longs;i, &amp; eam &longs;oluere conatus e&longs;t, <lb/>&longs;ed qu&agrave;m bene, aliorum e&longs;to iudicium. </s>
            <s id="s.000268">C&aelig;ter&ugrave;m fal&longs;um <lb/>e&longs;t, a&longs;&longs;erere circulum ex mixto motu nunquam &longs;eruat&acirc; <lb/>proportione produci. </s>
            <s id="s.000269">&longs;eruat enim a&longs;&longs;idu&egrave; mixtus motus <lb/>quo producitur &lpar;&longs;i cum mixto motu producere velimus&rpar; <lb/>aliquam proportionem, &longs;ed non eandem. </s>
          </p>
          <figure id="id.007.01.031.1.jpg" xlink:href="007/01/031/1.jpg"/>
          <p type="main">
            <s id="s.000270">E&longs;to enim recta AB, cui ad rectos <lb/>angulos AC. <!-- KEEP S--></s>
            <s id="s.000271">Moueatur autem A, ver&shy;<lb/>&longs;us C per lineam AC, &amp; eodem tempo&shy;<lb/>re linea AC, ver&longs;us B, ita tamen, vt &longs;em&shy;<lb/>per ip&longs;i AB, &longs;it perpendicularis. </s>
            <s id="s.000272">feratur <lb/>autem e&acirc; lege, vt quam proportionem <lb/>habet motus line&aelig; AC ver&longs;us B, ad mo&shy;<lb/>tum puncti A ve, &longs;us C, eandem habeat <lb/>ip&longs;e motus ab A ver&longs;us C, ad re&longs;iduum <lb/>line&aelig; AB, dempt&acirc; nempe ea parte quam <lb/>peragrauit linea AC mota ver&longs;us B. <!-- KEEP S--></s>
            <s id="s.000273">Sit <lb/>autem, cum AC &longs;uo motu peruenerit <lb/>in D, punctum A, &longs;imiliter &longs;uo motu per eam latum perue&shy;<lb/>nitle in E erit ergo ex mixto motu, non quidem in D, nec <lb/>in E, &longs;ed in F, eritque punctum F in circum ferentia circu&shy;<lb/>li, cuius e&longs;t diameter ip&longs;a linea AB, quod quidem demon&shy;<lb/>&longs;tratur ex conuer&longs;a propo&longs;. </s>
            <s id="s.000274">13. lib. 6. Elem. <!-- KEEP S--></s>
            <s id="s.000275">E&longs;t enim AE <lb/>hoc e&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>&amp; DB. <!-- KEEP S--></s>
            <s id="s.000276">Iterum &longs;i fiat motus AC in GH, ad motum H per <pb xlink:href="007/01/032.jpg"/>lineam AC, v&longs;que in C, vt &longs;e habet proportio AG ad <lb/>GH &amp; GH ad GB, erit ex motu mixto A in H, nempe in <lb/>eiu&longs;dem circuli circum ferentia AFHB. ex quibus ha&shy;<lb/>bemus, circulum ex mixto motu fieri po&longs;&longs;e proportioni&shy;<lb/>bus quidem mediarum &longs;eruatis, &longs;ed nunquam ij&longs;dem. </s>
          </p>
          <p type="main">
            <s id="s.000277">Vera h&aelig;c procul dubio &longs;unt; nihilominus, veluti ad <lb/>rectam producendam mixtus motus non e&longs;t nece&longs;&longs;arius, <lb/>licet mixto motu produci po&longs;&longs;it, ita ne que ad circularem, <lb/>&amp; ideo verum non e&longs;&longs;e quod a&longs;&longs;erebat Philo&longs;ophus, cir&shy;<lb/>culum ex mixto motu proportione nunquam &longs;eruat&acirc; ne&shy;<lb/>ce&longs;&longs;ari&ograve; produci. </s>
          </p>
          <p type="main">
            <s id="s.000278">Conatur po&longs;t h&aelig;c Ari&longs;toteles rationem afferre, cur <lb/>circuli partes, qu&ograve; propiores centro fuerint, eo &longs;int tar&shy;<lb/>diores. </s>
            <s id="s.000279">Ait autem; &longs;i duobus ab eadem potentia latis hoc <lb/>quidem plus repellatur, illud ver&ograve; minus, &aelig;quum e&longs;t tar&shy;<lb/>di&ugrave;s id moueri quod plus repellitur, eo quod minus. </s>
            <s id="s.000280">De&shy;<lb/>trahi autem plus lineam, cuius extremum propius e&longs;t cen&shy;<lb/>tro illa qu&aelig; &longs;uum habet terminum &agrave; centro remotiorem. </s>
          </p>
          <figure id="id.007.01.032.1.jpg" xlink:href="007/01/032/1.jpg"/>
          <p type="main">
            <s id="s.000281">E&longs;to, inquit, circulus <lb/>BCDE &amp; alter in eo minor <lb/>MNOP circa idem centrum <lb/>A. Ducanturque; Diametri ma&shy;<lb/>ioris quidem CD, EB, mino&shy;<lb/>ris ver&ograve; MO, NP. </s>
            <s id="s.000282">Itaque vbi <lb/>AB circulata e&ograve; peruenerit <lb/>vnde e&longs;t gre&longs;&longs;a, ip&longs;a quoque <lb/>AM eo vnde moueri c&oelig;pe&shy;<lb/>rat, perueniet. </s>
            <s id="s.000283">Tardi&ugrave;s autem <lb/>fertur AM, quam AD, pro&shy;<lb/>pterea qu&ograve;d AM &agrave; centro <lb/>magis retrahatur qu&agrave;m ip&longs;a AB. <!-- KEEP S--></s>
            <s id="s.000284">Ducatur igitur ALF &amp; <lb/>&agrave; puncto L, ip&longs;i AB perpendicularis L q, cadens in mino-<pb xlink:href="007/01/033.jpg"/>ri circulo, &amp; rur&longs;us ab eodem L ip&longs;i AB, parallela duca&shy;<lb/>tur LS, Ab S ver&ograve; eidem perpendicularis ST, &amp; ab F i&shy;<lb/>tem FX. </s>
            <s id="s.000285">Sunt ergo q L, ST, quidem &aelig;quales, nempe ill&aelig;, <lb/>per qu&aelig;, &longs;ecundum naturam, mouentur puncta BM. <!-- KEEP S--></s>
            <s id="s.000286">Mo&shy;<lb/>tu ver&ograve; retractionis ad centrum, hoc e&longs;t, pr&aelig;ter naturam, <lb/>plus motum e&longs;t M qu&agrave;m B. <!-- KEEP S--></s>
            <s id="s.000287">Maior enim e&longs;t M q, ip&longs;a BT, <lb/>quod, ceu notum, &longs;uppo&longs;uit Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.000288">nos autem inf. </s>
            <s id="s.000289">&agrave; <lb/>demon&longs;trabimus. </s>
            <s id="s.000290">Si igitur fiat vt motus pr&aelig;ter naturam <lb/>ad motum pr&aelig;ter naturam, ita motus <expan abbr="&longs;ec&umacr;dum">&longs;ecundum</expan> naturam, <lb/>ad motum &longs;ecundum naturam, punctum B; cum M fuerit <lb/>in L, non erit in S, &longs;ed in F. tunc enim, vt e&longs;t FX motus &longs;e&shy;<lb/>cund&ugrave;m naturam ad XB, pr&aelig;ter naturam, ita e&longs;t q L &longs;e&shy;<lb/>cundum naturam ad q M pr&aelig;ter naturam; &longs;ed BF maior <lb/>e&longs;t ML, ergo proportione &longs;eruat&acirc;, veloci&ugrave;s mouetur B <lb/>qu&agrave;m M circa idem centrum A. <!-- KEEP S--></s>
            <s id="s.000291">H&aelig;c autem &longs;umma e&longs;t <lb/>eorum qu&aelig; pr&aelig;fert Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.000292">C&aelig;ter&ugrave;m nos parallelo&shy;<lb/>grammum, quod in figura eius habetur pr&aelig;termi&longs;imus, <lb/>quippe quod nihil ad eam qu&aelig; affertur, demon&longs;tratio&shy;<lb/>nem faciat. </s>
          </p>
          <p type="main">
            <s id="s.000293">Mod&ograve; quod pollicebamur, nempe minorem e&longs;&longs;e <lb/>BT, qu&agrave;m q M, ita demon&longs;tramus. </s>
            <s id="s.000294"><expan abbr="quoni&atilde;">quoniam</expan> ST. ex prop. 13. <lb/>1. 6. media proportionalis e&longs;t inter BT &amp; TE, erit qua&shy;<lb/>dratum TS &aelig;quale <expan abbr="parallelogr&atilde;mo">parallelogrammo</expan> &longs;eu rectangulo BT, <lb/>TE, item, quoniam q L media proportionalis e&longs;t inter <lb/>M q, &amp; q O. erit quadratum q L &aelig;quale rectangulo M q, <lb/>q O, &aelig;qualia ergo &longs;unt rectangula BTE, M q O, itaque <lb/>reciproca latera habent proportionalia. </s>
            <s id="s.000295">quare, vt TE, ad <lb/>q O, ita M q ad TB, &longs;ed TE maior e&longs;t ip&longs;a q O, quippe <lb/>qu&ograve;d pars &longs;it q O ip&longs;ius TE, maior ergo &amp; M q ip&longs;a TB, <lb/>quod o&longs;tendendum fuerat. </s>
          </p>
          <p type="main">
            <s id="s.000296">C&aelig;ter&ugrave;m &longs;ubtilia &amp; ingenio&longs;a i&longs;th&aelig;c e&longs;&longs;e non nega&shy;<lb/>mus, &amp; long&egrave; faciliori &amp; explicatiori modo veritas h&aelig;c <lb/>demon&longs;trari pote&longs;t, reiectis nempe illis, &longs;ecund&ugrave;m, &amp; prae&shy;<pb xlink:href="007/01/034.jpg"/>ter naturam motibus, qui <expan abbr="quid&emacr;">quidem</expan> in &longs;implici circulo nece&longs;&shy;<lb/>&longs;ario non cadunt: caderent autem forta&longs;&longs;e, &longs;i de circulo <lb/>res e&longs;&longs;et &agrave; <expan abbr="p&omacr;deribus">ponderibus</expan> circumlatis ex &longs;tabili centro de&longs;cri&shy;<lb/>pto, qua de re agit G. <!-- REMOVE S-->Vbaldus in Mechanicis tractatu de <lb/>libra. </s>
            <s id="s.000297">tunc enim dici pote&longs;t, pondus quod ali&acirc;s rect&agrave; ad <lb/>mundi centrum tenderet, &agrave; circuli centro in circulatio&shy;<lb/>ne retrahi, &longs;ed h&aelig;c ad circuli naturam, quatenus circulus <lb/>e&longs;t, nequaquam &longs;pectant. </s>
          </p>
          <figure id="id.007.01.034.1.jpg" xlink:href="007/01/034/1.jpg"/>
          <p type="main">
            <s id="s.000298">E&longs;to igitur circumferentia <lb/>AFBH, cuius centrum C, dia&shy;<lb/>meter ACB, &longs;emidiameter AC. <lb/>&longs;umatur in AC punctum quod&shy;<lb/>libet, D, &amp; centro C, &longs;patio CD, <lb/>circumferentia de&longs;cribatur <lb/>DGEI. <!-- KEEP S--></s>
            <s id="s.000299">Dico punctum A velo&shy;<lb/>cius moueri puncto D e&acirc;dem <lb/>circulatione rotato. </s>
            <s id="s.000300">etenim vt <lb/>diameter ad diametrum, &amp; &longs;emidiameter ad &longs;emidiame&shy;<lb/>trum, ita circumferentia ad circumferentiam: igitur vt <lb/>AC ad CD, ita circumferentia AFHB ad circumferen&shy;<lb/>tiam DGEI. <!-- KEEP S--></s>
            <s id="s.000301">At mota linea CA circa centrum C mo&shy;<lb/>uetur &longs;imul &amp; CD, eodem igitur tempore rotationem <lb/>complent puncta AD, maius ergo &longs;patium eodem tem&shy;<lb/>pore metitur A, ip&longs;a D, quare velocior. </s>
            <s id="s.000302">Ita igitur &longs;e ha&shy;<lb/>bet velocitas ad velocitatem, vt circumferentia ad cir&shy;<lb/>cumferentiam, &amp; diameter ad diametrum, quare id quod <lb/>mouetur in puncto &agrave; centro remotiori, velocius illo mo&shy;<lb/>uetur quod ab eo di&longs;tat minus, quod fuerat <lb/>demon&longs;trandum. </s>
          </p>
          <pb xlink:href="007/01/035.jpg"/>
        </subchap1>
      </chap>
      <chap>
        <p type="head">
          <s id="s.000303">QV&AElig;STIONES <lb/>MECHANIC&AElig;.</s>
        </p>
        <subchap1>
          <p type="head">
            <s id="s.000304">QV&AElig;STIO I.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000305"><emph type="italics"/>Cur maiores libr&aelig; exactiores &longs;int mi&shy;<lb/>noribus?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000306">Prior&iacute;bus, ceu fundamentis quibu&longs;dam iactis, oppor&shy;<lb/>tun&egrave; ad qu&aelig;&longs;tiones proponendas, eas queue diluendas &longs;e <lb/>confert Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.000307">Porro in propo&longs;ita qu&aelig;&longs;tione vide&shy;<lb/>tur prima fronte cau&longs;&longs;am qu&aelig;ri de re qu&aelig; non e&longs;t: etenim <lb/>quis affirmauerit vnquam, lances quibus Apothecarij &amp; <lb/>Macellarij vtuntur, magnas eas quidem, illis exactiores <lb/>e&longs;&longs;e quibus Gemmatij, atque Argentarij &longs;iliquis, &amp; &longs;cru&shy;<lb/>pulis minuti&longs;&longs;ima appendunt, qu&aelig; tamen perexigu&aelig; &longs;unt, <lb/>&amp; &longs;i illis comparentur minim&aelig;? </s>
            <s id="s.000308">Veruntamen, ita pror&longs;us <lb/>res habet, vt a&longs;&longs;erit Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.000309">Non enim propterea <lb/>qu&ograve;d ill&aelig; magn&aelig; &longs;int, h&aelig; ver&ograve; exigu&aelig;, h&aelig; &longs;unt illis exa&shy;<lb/>ctiores; &longs;ed quoniam magn&aelig;, rudes &longs;unt, minores ver&ograve; ex&shy;<lb/>qui&longs;ita diligentia elaborat&aelig;, &amp; &agrave; materi&aelig; pertinacia libe&shy;<lb/>riores. </s>
            <s id="s.000310">C&aelig;teris ergo paribus, exactiores e&longs;&longs;e maiores, ex <lb/>Philo&longs;ophi mente, ita docebimus. </s>
          </p>
          <figure id="id.007.01.035.1.jpg" xlink:href="007/01/035/1.jpg"/>
          <p type="main">
            <s id="s.000311">E&longs;to libra maior AB, <lb/>cuius fulcimentum C. <lb/><!-- KEEP S--></s>
            <s id="s.000312">Minor ver&ograve; libra DE, <lb/>circa idem <expan abbr="fulcim&emacr;tum">fulcimentum</expan> <lb/>C, vn&agrave; cum maiori, ima&shy;<lb/>ginatione, conuer&longs;a. </s>
            <s id="s.000313">Ap&shy;<lb/>ponatur quoduis pon&shy;<lb/>dus maiori libr&aelig; in A, <lb/>declinetque; exempli grati&acirc; in F, erit queue minor libra in G, <lb/>in eadem enim linea &longs;unt CGF. <expan abbr="Vnaq;">Vnaque</expan> igitur ex eodem <pb xlink:href="007/01/036.jpg"/>centro C portionem circuli de&longs;cribet GD, AF, eritqueue <lb/>ACF &longs;ector circuli, cuius diameter AB, &longs;ed DCG &longs;e&shy;<lb/>ctor circuli, cuius diameter DE. <!-- KEEP S--></s>
            <s id="s.000314">Itaque vt diameter ad <lb/>diametrum, ita portio ad portionem: maior autem dia&shy;<lb/>meter AB diametro DE: maior ergo portio AF, portio&shy;<lb/>ne DG. quod autem maius e&longs;t, minus obtutum fallit, ex&shy;<lb/>qui&longs;itius itaque tractum ex maiori AB qu&agrave;m ex ip&longs;a mi&shy;<lb/>nori DE cogno&longs;cemus, quod fuerat o&longs;tendendum. </s>
          </p>
          <p type="main">
            <s id="s.000315">C&aelig;ter&ugrave;m hac eadem de cau&longs;&longs;a, A&longs;tronomica in&shy;<lb/>&longs;trumenta, puta A&longs;trolabia, Armill&aelig;, &amp; alia eiu&longs;modi, <lb/>quo ampliora e&ograve; exqui&longs;itiora, &amp; certiora probantur. </s>
          </p>
          <figure id="id.007.01.036.1.jpg" xlink:href="007/01/036/1.jpg"/>
          <p type="main">
            <s id="s.000316">E&longs;to enim A&shy;<lb/>&longs;trolabium magnum, <lb/>cuius diameter AB, <lb/>paruum autem CD, <lb/>circa idem centrum <lb/>E. <!-- KEEP S--></s>
            <s id="s.000317">Ducatur &agrave; centro <lb/>recta EF tangens ma&shy;<lb/>iorem circulum in F, <lb/><expan abbr="minor&emacr;">minorem</expan> ver&ograve; <expan abbr="&longs;ec&atilde;s">&longs;ecans</expan> in <lb/>G, vt igitur GD ad to&shy;<lb/>tum circulum GCD, <lb/>ita FB. ad totum cir&shy;<lb/>culum FAB, vt erg&ograve; <lb/>GD ad FB, ita gradus <lb/>&longs;ignati in GD, ad eos qui &longs;ignantur in BF, maiores ergo <lb/>&longs;unt qui in FB, &amp; minutarum partium capaciores. </s>
            <s id="s.000318">Hinc <lb/>itaque apparet, <expan abbr="in&longs;trum&emacr;ta">in&longs;trumenta</expan> qu&aelig;libet qu&ograve; maiora fuerint, <lb/>e&ograve; e&longs;&longs;e &amp; exqui&longs;itiora, quod propo&longs;uerat Ari&longs;toteles, in <lb/>hac qu&aelig;&longs;tione de Libra. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000319">Quod autem addit de fraudibus Purpurariorum, <lb/>inquiens; quamobrem machin&aacute;ntur ij qui purpuram ven&shy;<lb/>dunt, vt <expan abbr="p&emacr;dendo">pendendo</expan> defraudent, dum ad medium, &longs;partum, <pb xlink:href="007/01/037.jpg"/>non ponentes; tum plumbum in alterutram libr&aelig; partem <lb/>infundentes; aut ligni quod ad radicem vergebat, in eam <lb/>quam deferri volunt partem con&longs;tituentes, aut &longs;i nodum <lb/>habuerit, ligni enim grauior ea e&longs;t pars, in qua e&longs;t radix, <lb/>nodus ver&ograve; radix qu&aelig; dam e&longs;t. </s>
            <s id="s.000320">Hinc qu&aelig;ri po&longs;&longs;et: </s>
          </p>
          <p type="head">
            <s id="s.000321"><emph type="italics"/>Vtrum libr&aelig; qu&aelig; ponderibus vacu&aelig; &aelig;quilibrant, <lb/>omni pror&longs;us careant fraude?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000322">Videri cuipiam po&longs;&longs;et, libras, qu&aelig; ponderibus va&shy;<lb/>cu&aelig;, &aelig;quilibrant, omni pror&longs;us fraude carere, verunta&shy;<lb/>men ita non e&longs;t, quod diligenti&ugrave;s &lpar;res enim magni mo&shy;<lb/>menti e&longs;t&rpar; di&longs;quiremus. </s>
          </p>
          <figure id="id.007.01.037.1.jpg" xlink:href="007/01/037/1.jpg"/>
          <p type="main">
            <s id="s.000323">E&longs;to enim libra AB, ita diui&longs;a <lb/>in C, vt AC &longs;it partium IS, CB ve&shy;<lb/>r&ograve; earundem &longs;it 10. apponatur parti <lb/>A lanx ponderans 10, parti vero B <lb/>lanx ponderans 15. ex permutata i&shy;<lb/>gitur proportione libra &longs;u&longs;pen&longs;a in <lb/>C, aequ&egrave; ponderabit; &longs;i autem appo&shy;<lb/>natur lanci B &longs;acoma vnciarum 6, &amp; in lance A con&longs;titua&shy;<lb/>tur purpura, qu&aelig; ita &longs;e habeat ad vncias 6, vt 10 ad 15, ite&shy;<lb/>rum &aelig;queponderabit, &longs;ed vt 10 ad 15, ita 4 ad 6. Purpura&shy;<lb/>rius ergo fraudulentus, ponens in lance A vncias purpur&aelig; <lb/>4, facto &aelig;quilibrio petet pretium vnciarum 6, &amp; ita em&shy;<lb/>ptorem decipiet, quod &longs;an&egrave; innuerat, non autem demon&shy;<lb/>&longs;trauerat Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.000324">H&aelig;c autem faciliora fient ex ijs, <lb/>qu&aelig; in &longs;equentibus qu&aelig;&longs;tionibus, vbi de vecte agetur, ex&shy;<lb/>plicabuntur. </s>
          </p>
          <p type="main">
            <s id="s.000325">Detegitur autem fraus, &longs;i alternatim &longs;acoma in pon&shy;<lb/>derando, modo huic, mod&ograve; illi lanci apponatur. </s>
            <s id="s.000326">Si enim <lb/>in lance A con&longs;tituatur &longs;acoma, in B ver&ograve; purpura non fit <lb/>&aelig;quilibrium. </s>
          </p>
          <pb xlink:href="007/01/038.jpg"/>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000327">QV&AElig;STIO II.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000328"><emph type="italics"/>Cur, &longs;i &longs;ur&longs;um libr&aelig; fulcimentum &longs;it, appo&longs;ito ad alteram partem <lb/>pondere, de&longs;cendat libra, &amp; eo amoto, iterum a&longs;cendat, &amp; ad &aelig;qui&shy;<lb/>librium reuertatur. </s>
            <s id="s.000329">Si ver&ograve; deor&longs;um fulcimentum fuerit, de&shy;<lb/>pre&longs;&longs;a ad &aelig;quilibrium non reuertatur?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000330">Bimembrem proponit Philo&longs;ophus qu&aelig;&longs;tionem, quam <lb/>trimembrem debuit, triplici &longs;i quidem loco fulcimen&shy;<lb/>tum aptari pote&longs;t, &longs;uperiori, medio, inferiori. </s>
            <s id="s.000331">Nos de o&shy;<lb/>mnibus verba faciemus. </s>
          </p>
          <p type="head">
            <s id="s.000332">Prima Qu&aelig;&longs;tionis pars.</s>
          </p>
          <p type="head">
            <s id="s.000333"><emph type="italics"/>De Libra &longs;ur&longs;um fulcimentum habente.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000334">Ari&longs;toteles primam qu&aelig;&longs;tionis partem ita &longs;oluit: An <lb/>quia &longs;ur&longs;um parte quidem exi&longs;tente, plus libr&aelig; extra per&shy;<lb/>pendiculum &longs;it? </s>
            <s id="s.000335">Spartum enim perpendiculum e&longs;t: quare <lb/>nece&longs;&longs;e e&longs;t deor&longs;um ferri id quod plus e&longs;t, donec a&longs;cendat <lb/>qua bifariam libram diuidit ad ip&longs;um perpendiculum, <lb/>cum onus incumbat ad libr&aelig; partem &longs;ur&longs;us raptam. </s>
          </p>
          <figure id="id.007.01.038.1.jpg" xlink:href="007/01/038/1.jpg"/>
          <p type="main">
            <s id="s.000336">Sit libra recta &lpar;hoc e&longs;t, in &aelig;quilibrio con&longs;tituta&rpar; BC, <lb/>&longs;partum autem AD, <lb/>fulcimentum autem <lb/>D, de&longs;uper: &longs;parto au&shy;<lb/>tem deor&longs;um proie&shy;<lb/>cto ad M perpendicu&shy;<lb/>laris erit vbi ADM. <lb/></s>
            <s id="s.000337">Si igitur in ip&longs;o B po&shy;<lb/>natur onus, erit B qui&shy;<lb/>dem vbi E, C autem <lb/>vbi H, quamobrem <lb/>ea qu&aelig; bifariam <expan abbr="libr&atilde;">libram</expan> <lb/>&longs;ecat, primo quidem erit DM, ip&longs;ius perpendiculi; in<expan abbr="c&umacr;-bente">cum&shy;<lb/>bente</expan> <expan abbr="aut&emacr;">autem</expan> onere, erit DG. quare libr&aelig; ip&longs;ius EH, quod <pb xlink:href="007/01/039.jpg"/>extra perpendiculum, e&longs;t AM, vbi e&longs;t q P maius e&longs;t dimi&shy;<lb/>dio. </s>
            <s id="s.000338">Si igitur amoueatur onus ab E, nece&longs;&longs;e e&longs;t deor&longs;um <lb/>ferri H, minus e&longs;t enim E: &longs;iquidem igitur habuerit &longs;par&shy;<lb/>tum &longs;ur&longs;um, propter hoc a&longs;cendit libra. </s>
          </p>
          <p type="main">
            <s id="s.000339">Pe&longs;&longs;im&egrave; omnes &longs;chema hoc line&acirc;runt, ita vt difficil&shy;<lb/>limum &longs;it auctoris inde &longs;en&longs;um a&longs;&longs;equi. </s>
            <s id="s.000340">Nos autem cla&shy;<lb/>rius rem ob oculos ponimus. </s>
            <s id="s.000341">Id ergo &longs;ibi vult Ari&longs;toteles, <lb/>propterea qu&ograve;d pars iugi HDG maior e&longs;t parte ED q, <lb/>eam eleuatam nece&longs;&longs;e e&longs;t de&longs;cendere, &amp; iterum &agrave; perpen&shy;<lb/>diculari ADM bifariam diui&longs;am ad &aelig;quilibrium reuer&shy;<lb/>ti, Po&longs;&longs;umus nos idem &longs;impliciori figura demon&longs;trare. </s>
          </p>
          <figure id="id.007.01.039.1.jpg" xlink:href="007/01/039/1.jpg"/>
          <p type="main">
            <s id="s.000342">E&longs;to libra AB, bi&shy;<lb/>fariam, diui&longs;a in G, <lb/><expan abbr="fulciment&umacr;">fulcimentum</expan> ver&ograve; &longs;ur&shy;<lb/>&longs;um vbi D, produca&shy;<lb/>tur perpendicularis <lb/>DC in E. <!-- KEEP S--></s>
            <s id="s.000343">Stante igi&shy;<lb/>tur libra AB, in &aelig;qui&shy;<lb/>librio &aelig;qualis e&longs;t pars <lb/>CH, ip&longs;i parti CB <lb/>apponatur pondus in <lb/>B. <!-- KEEP S--></s>
            <s id="s.000344">Declinabit igitur <lb/>libra mota circa centrum D, fiat autem in FG, &longs;ecetqueue <lb/>perpendicularem in I. <!-- KEEP S--></s>
            <s id="s.000345">Punctum vero C eodem motu cir&shy;<lb/>ca idem centrum D erit in H. amoueatur pondus appo&longs;i&shy;<lb/>tum: Dico libram &agrave; &longs;itu FG declinaturam &amp; iterum re&shy;<lb/>uer&longs;uram in &longs;itum pri&longs;tinum ACB. quoniam enim parti <lb/>GH, qu&aelig; &aelig;qualis e&longs;t parti HF, additur pars IH, qu&aelig; &agrave; <lb/>perpendiculari e&longs;t v&longs;que ad H, ip&longs;i ver&ograve; HF eadem pars <lb/>detrahitur, erit IF minor GI. </s>
            <s id="s.000346">Superabitur ita que IF &agrave; <lb/>GI, de&longs;cendetque FI, a&longs;cendet ver&ograve; IF, donec iterum li&shy;<pb xlink:href="007/01/040.jpg"/>bra &iacute;n partes &aelig;quales, vt antea, diuidatur in C, &longs;iat que &aelig;&shy;<lb/>quilibrium. </s>
          </p>
          <p type="main">
            <s id="s.000347">H&aelig;c Philo&longs;ophi demon&longs;tratio e&longs;t vera illa quidem, <lb/>&longs;ed non ex Mechanicis principijs, hoc e&longs;t, ex centri graui&shy;<lb/>tatis &longs;peculatione; nos igitur clari&ugrave;s rem exponemus, his <lb/>qu&aelig; &longs;equuntur con&longs;ideratis. </s>
          </p>
          <p type="main">
            <s id="s.000348">Si pondus circa &longs;tabile centrum conuertatur, dimi&longs;&shy;<lb/>&longs;um non &longs;tabit, ni&longs;i &longs;ecundum grauitatis centrum fuerit <lb/>in perpendiculari, qu&aelig; per centrum, circa quod conuer&shy;<lb/>titur, ad mundi centrum cadit. </s>
            <s id="s.000349">Stabit autem in ea per&shy;<lb/>pendiculari in duobus punctis, altero &agrave; centro mundi <lb/>remoti&longs;&longs;imo; altero ver&ograve; eidem quantum licuerit pro&shy;<lb/>ximo. </s>
          </p>
          <figure id="id.007.01.040.1.jpg" xlink:href="007/01/040/1.jpg"/>
          <p type="main">
            <s id="s.000350">E&longs;to corpus A, cuius graui&shy;<lb/>tatis centrum B, nixum lineae in&shy;<lb/>flexibili BC, cum qua liber&egrave; <lb/>conuertatur circa centrum C. <lb/><!-- KEEP S--></s>
            <s id="s.000351">Ducatur autem per mundi cen&shy;<lb/>trum perpendicularis BCD. <lb/><!-- KEEP S--></s>
            <s id="s.000352">Sit igitur prim&ograve; pondus A <expan abbr="&longs;ec&umacr;-dum">&longs;ecun&shy;<lb/>dum</expan> gracilis B centrum, in per&shy;<lb/>pendiculari ip&longs;a &longs;upra centrum <lb/>C, puta in B. <!-- KEEP S--></s>
            <s id="s.000353">Moueatur &amp; <expan abbr="de&longs;c&emacr;-dat">de&longs;cen&shy;<lb/>dat</expan> in E. <!-- KEEP S--></s>
            <s id="s.000354">Po&longs;t h&aelig;c ver&ograve; in F, hoc <lb/>e&longs;t iterum in ip&longs;a perpendiculari <lb/>infra centrum C. <!-- KEEP S--></s>
            <s id="s.000355">De&longs;cribet er&shy;<lb/>go circulum ex centro C, nem&shy;<lb/>pe BEF &longs;ecantem perpendicu&shy;<lb/>larem in duobus punctis oppo&shy;<lb/>&longs;itis BF, dico, pondus libe &egrave; di-<pb xlink:href="007/01/041.jpg"/>mi&longs;&longs;um in duobus tantum punctis &longs;uapte natur&acirc; perman&shy;<lb/>&longs;urum, BF, in B, prim&ograve;, quoniam cum corpus ip&longs;um A &agrave; <lb/>perpendiculari, qu&aelig; &longs;uperficiei loco intelligitur ABCD <lb/>per centrum grauitatis diuidatur, in partes diuiditur &aelig;&shy;<lb/>queponderantes, quare in neutram partem inclinabit. <lb/></s>
            <s id="s.000356">Stabit igitur erectum, line&aelig; ip&longs;i fultum, inflexibili BC, <lb/>qu&aelig; nititur puncto C. <!-- KEEP S--></s>
            <s id="s.000357">In E ver&ograve; non &longs;tabit, quippe quod <lb/>eo &longs;itu centrum ip&longs;um grauitatis &longs;it extra perpendicula&shy;<lb/>rem, &amp; ideo extra fulcimentum &longs;tabile C. <!-- KEEP S--></s>
            <s id="s.000358">In F ver&ograve; ite&shy;<lb/>rum &longs;tabit, pendens &agrave; centro C, propterea qu&ograve;d &amp; ibi ab <lb/>eadem perpendiculari diuidatur per grauitatis centrum <lb/>in partes &aelig;queponderantes. </s>
            <s id="s.000359">E&longs;t igitur re&longs;pectu B, ip&longs;um <lb/>punctum C, fulcimentum deor&longs;um, re&longs;pectu ver&ograve; F, ful&shy;<lb/>cimentum &longs;ur&longs;um. </s>
            <s id="s.000360">At quia linea DFCB, &agrave; centro mundi, <lb/>quod e&longs;t extra circulum, BEF, circulum ip&longs;um per cen&shy;<lb/>trum C &longs;ecat, erit pars eius DF quidem breui&longs;&longs;ima, ip&longs;a <lb/>ver&ograve; DB longi&longs;&longs;ima, ex propo&longs;. 8. lib. 3. Elem. <!-- KEEP S--></s>
            <s id="s.000361">Pondus igi&shy;<lb/>tur A conuer&longs;um &longs;eu liber&egrave; motum circa centrum C, in <lb/>duobus tantum locis perpendicularis line&aelig; &longs;tabit remo&shy;<lb/>ti&longs;&longs;imo altero, vt e&longs;t B, altero ver&ograve; eidem quam proximo, <lb/>vt e&longs;t F. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000362">Hoc idem egregi&egrave; demon&longs;trauit G. Vbald. <!-- REMOVE S-->in &longs;uis <lb/>Mechanicis, Tractatu de Libra prop.1.</s>
          </p>
          <p type="main">
            <s id="s.000363">Ad h&aelig;c autem dubitare quis po&longs;&longs;et, cur experienti&acirc; <lb/>docente, pondera qu&aelig; infra fulcimentum habent, vt lan&shy;<lb/>cea &longs;ari&longs;&longs;aue ad planum horizontis perpendiculariter e&shy;<lb/>recta, licet eo ca&longs;u grauitatis centrum in ip&longs;a perpendicu&shy;<lb/>lari con&longs;tituatur, non &longs;tet quidem, &longs;ed altrin&longs;ecus ca&shy;<lb/>dat? </s>
          </p>
          <pb xlink:href="007/01/042.jpg"/>
          <figure id="id.007.01.042.1.jpg" xlink:href="007/01/042/1.jpg"/>
          <p type="main">
            <s id="s.000364">Sit enim horizontis <lb/>planum AB, cui in puncto <lb/>C perpendiculariter ere&shy;<lb/>cta &longs;tatuatur &longs;ari&longs;&longs;a DC, <lb/>cuius grauitatis centrum <lb/>E, in ip&longs;a perpendiculari. <lb/></s>
            <s id="s.000365">Stabit ergo, ex pr&aelig;mi&longs;&longs;is, <lb/>&amp; cert&egrave; &longs;tare debuit, &longs;ta&shy;<lb/>retqueue, ni vitium ob&longs;taret <lb/>materi&aelig;; non &longs;tat autem, <lb/>quia difficillimum e&longs;t gra&shy;<lb/>uitatis centrum, &longs;uapte natur&acirc; indiui&longs;ibile, ita ad amu&longs;&longs;im <lb/>&longs;i&longs;tere, vt in neutram partem &agrave; perpendiculari declinet. <lb/></s>
            <s id="s.000366">H&aelig;c igitur ex ijs &longs;peculationibus e&longs;t, qu&aelig; ad praxim, ma&shy;<lb/>teri&aelig; vitio impediente, aut vix aut nunquam rediguntur. </s>
          </p>
          <p type="main">
            <s id="s.000367">Hinc autem ea qu&aelig;&longs;tio &longs;oluitur, Cur ij qui &longs;ari&longs;&longs;am <lb/>erectam digito &longs;ummo &longs;u&longs;tinere conantur, non &longs;tent qui&shy;<lb/>dem, &longs;ed digiti motu, &longs;ari&longs;&longs;&aelig; motum &longs;equantur. </s>
          </p>
          <p type="main">
            <s id="s.000368">Id cert&egrave; agit, qui nutantis &longs;ari&longs;&longs;&aelig;, digito, motum &longs;e&shy;<lb/>quitur; vt in ip&longs;o motu digitum a&longs;&longs;idu&egrave; centro grauitatis <lb/>&longs;ari&longs;&longs;&aelig; &longs;upponat, vnde &longs;it vt nunquam extra fulcimentum <lb/>permanens, nunquam cadat. </s>
          </p>
          <p type="main">
            <s id="s.000369">Similis huic alia quoque dubitatio &longs;oluitur: Nempe, <lb/>Cur turbines, quibus pueri ludunt, dum quidem rotan&shy;<lb/>tur, &longs;tent erecti, rotatione vero ce&longs;&longs;ante, cadant. </s>
          </p>
          <figure id="id.007.01.042.2.jpg" xlink:href="007/01/042/2.jpg"/>
          <p type="main">
            <s id="s.000370">E&longs;to enim Turbo AB, cu&shy;<lb/>ius grauitatis centrum C, planum <lb/>horizontis DE, linea Horizonti <lb/>perpendicularis ABC, tran&longs;iens <lb/>per centrum grauitatis C, &longs;it au&shy;<lb/>tem fulcimentum in B. <expan abbr="Itaq;">Itaque</expan> cum <lb/>centrum grauitatis C &longs;it in ip&longs;a <lb/>perpendiculari, &longs;tabit ex demon-<pb xlink:href="007/01/043.jpg"/>&longs;tratis, at ex vitio materi&aelig; non &longs;tabit. </s>
            <s id="s.000371">Mod&ograve;, vt a&longs;&longs;olet, ra&shy;<lb/>pido motu rotetur. </s>
            <s id="s.000372">Dico, Turbinem, motu &longs;eu rotatione <lb/>durante &longs;tare. </s>
            <s id="s.000373">ea autem paullatim elangue&longs;cente &iacute;n ca&shy;<lb/>&longs;um vergere; ce&longs;&longs;ante ver&ograve; penitus cadere. </s>
            <s id="s.000374">fit enim ex in&shy;<lb/>&aelig;qualitate materi&aelig;, vel operis ruditate, vel ali&acirc; quauis <lb/>ex cau&longs;&longs;a, grauitatis centrum non e&longs;&longs;e in C, &longs;ed exempli <lb/>grati&acirc; vbi F, notentur autem hinc inde Turbinis latera <lb/>notis GH. <!-- KEEP S--></s>
            <s id="s.000375">Vtique cum F extra perpendicularem fuerit, <lb/>cadet Turbo ad partem G; at id ne &longs;iat, efficitur velocita&shy;<lb/>te motus, quo centrum F transfertur in contrariam par&shy;<lb/>tem, vbi I. non autem cadit ver&longs;us H, quoniam eadem ve&shy;<lb/>locitate iterum transfertur in F, quamobrem cum huius&shy;<lb/>cemodi centri a&longs;&longs;idua circa perpendicularem fiat trans&shy;<lb/>latio, ad nullam partem Turbo cadere pote&longs;t; elangue&shy;<lb/>&longs;cente ver&ograve; motu rotans, paullatim incipit inclinari, do&shy;<lb/>nec eo penitus ce&longs;&longs;ante, ad eam partem cadit, ad quam &agrave; <lb/>perpendiculari grauitatis centrum vergit. </s>
            <s id="s.000376">De&longs;cribit au&shy;<lb/>tem in rotatione grauitatis centrum, quod in medio non <lb/>e&longs;t paruum circulum, per cuius centrum ip&longs;a perpendi&shy;<lb/>cularis pertingit. </s>
          </p>
          <p type="main">
            <s id="s.000377">Mod&ograve; redeuntes ad libram, cuius fulcimentum e&longs;t <lb/>&longs;ur&longs;um, alio principio, nempe Mechanico, cur depre&longs;&longs;a <lb/>ad &aelig;qualitatem reuertatur, demon&longs;trabimus. </s>
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          <pb xlink:href="007/01/044.jpg"/>
          <figure id="id.007.01.044.1.jpg" xlink:href="007/01/044/1.jpg"/>
          <p type="main">
            <s id="s.000378">Sit igitur, vt &longs;u&shy;<lb/>peri&ugrave;s, libra AB, cu&shy;<lb/>ius centrum grauita&shy;<lb/>tis C, fulcimentum, <lb/>ver&ograve; &longs;ur&longs;um, in D li&shy;<lb/>br&aelig; quidem in C per&shy;<lb/>pendiculariter con&shy;<lb/>iunctum. </s>
            <s id="s.000379">Perpendi&shy;<lb/>cularis ver&ograve; qu&aelig; per <lb/>fulcimentum, &amp; gra&shy;<lb/>uitatis <expan abbr="c&emacr;trum">centrum</expan> tran&longs;&shy;<lb/>iens ad mundi cen&shy;<lb/>trum tendit DLE. &longs;tante igitur libr&acirc; in &longs;ua &aelig;qualitate, e&shy;<lb/>rit centrum grauitatis C in ip&longs;a perpendiculari infra qui&shy;<lb/>dem fulcimentum D. <!-- KEEP S--></s>
            <s id="s.000380">Loco ver&ograve;, mundi centro qu&agrave;m <lb/>proximo. </s>
            <s id="s.000381">Pondus po&longs;t h&aelig;c apponatur in B, Declinabit au&shy;<lb/>tem pars CB, in HF, eleuat&acirc; interim parte AC, in GH. <lb/><!-- KEEP S--></s>
            <s id="s.000382">Mota igitur libra tota, circa fulcimentum D mouebitur <lb/>circa idem centrum, &amp; grauitatis centrum C, de&longs;cribens <lb/>portionem circuli CH, fi etque; C in H, &amp; quoniam H, hoc <lb/>e&longs;t C, extra perpendicularem fit, amoto pondere, ex lan&shy;<lb/>ce B, cuius pre&longs;&longs;ione libra declinauerat, centrum grauita&shy;<lb/>tis per eandem circul&igrave; portionem HC, ad perpendicula&shy;<lb/>rem de&longs;cendet, donec iterum in ea quie&longs;cat, quo ca&longs;u li&shy;<lb/>bra AB ad &aelig;quilibrium reuertetur: quod fuerat demon&shy;<lb/>&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.000383">His ita declaratis, o&longs;tendemus, &lpar;quod nullus ante <lb/>nos animaduertit&rpar; harum librarum, qu&aelig; fulcimentum <lb/>habent &longs;ur&longs;um, eam e&longs;&longs;e naturam, vt non &agrave; quouis ponde&shy;<lb/>re appo&longs;ito moueantur, vel penitus declinent. </s>
          </p>
          <p type="main">
            <s id="s.000384">Ij&longs;dem enim &longs;tantibus, addatur quoduis pondus lan&shy;<lb/>ci B; Itaque &longs;i tale fuerit quod &longs;uperet re&longs;i&longs;tentiam, quam <pb xlink:href="007/01/045.jpg"/>illi facit centrum grauitatis contra naturam elatum in H <lb/>mouebitur qu&aelig;dam libra. </s>
            <s id="s.000385">Sin autem tam parui momenti <lb/>&longs;it, vt eam re&longs;i&longs;tentiam non vincat, &longs;tante circa locum in&shy;<lb/>fimum centro C, non mouebitur aut &longs;altem parum, ip&longs;a <lb/>libra. </s>
          </p>
          <p type="main">
            <s id="s.000386">Hinc colligimus fieri po&longs;&longs;e, libras illas, qu&aelig; non "<lb/>quouis, quantumuis paruo pondere declinant, eas fulci- "<lb/>mentum habere &longs;ur&longs;um. </s>
          </p>
          <p type="main">
            <s id="s.000387">His addimus, c&aelig;teris paribus, re&longs;i&longs;tentiam e&ograve; e&longs;&longs;e <lb/>maiorem, quo minus grauitatis centrum di&longs;tat &agrave; fulci&shy;<lb/>mento &longs;ur&longs;um, circa quod ip&longs;a libra aduertitur. </s>
          </p>
          <figure id="id.007.01.045.1.jpg" xlink:href="007/01/045/1.jpg"/>
          <p type="main">
            <s id="s.000388">E&longs;to libra AB, cuius gra&shy;<lb/>uitatis centrum C, &amp; prim&ograve; <lb/>quidem eius fulcimentum <lb/>&longs;ur&longs;um &longs;it vbi D, itaque &longs;i ap&shy;<lb/>po&longs;ito pondere declinauerit <lb/>libra ad partes B, punctum <lb/>C, dum a&longs;cendet de&longs;cribet <lb/>portionem circuli CE. fulciatur iterum &longs;ur&longs;um puncto F, <lb/>&amp; iterum declinet ad partes B, &amp; iterum punctum C, dum <lb/>a&longs;cendet, circuli portionem de&longs;cribet CG. <!-- KEEP S--></s>
            <s id="s.000389">E&longs;t autem <lb/>minor angulus contactus ACE, angulo ACG, magis er&shy;<lb/>go &longs;ur&longs;um, hoc e&longs;t, ad naturam &longs;ui feretur C, per CG, ex <lb/>centro F, qu&agrave;m per CE, ex centro D, quod fuerat de&shy;<lb/>mon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.000390">H&aelig;c autem re&longs;i&longs;tentia ex eodem fulcimento &amp; eo&shy;<lb/>dem pondere eo facili&ugrave;s &longs;uperabitur, quo longius bra&shy;<lb/>chium libr&aelig; fuerit. </s>
          </p>
          <p type="main">
            <s id="s.000391">E&longs;to enim iterum libra AB, cuius fulcimentum D, <lb/>centrum grauitatis C, &longs;it &amp; alia libra, cuius brachia bre&shy;<lb/>uiora EF, idem habens centrum C, &amp; eidem puncto &longs;u&shy;<lb/>&longs;pen&longs;a D. <!-- KEEP S--></s>
            <s id="s.000392">Dico igitur, eodem pondere appo&longs;ito, facili&ugrave;s <pb xlink:href="007/01/046.jpg"/><figure id="id.007.01.046.1.jpg" xlink:href="007/01/046/1.jpg"/><lb/>declinaturam libram ad <lb/>partes B, qu&agrave;m &longs;i idem ap&shy;<lb/>poneretur in F. <!-- KEEP S--></s>
            <s id="s.000393">Demit&shy;<lb/>tatur enim, &agrave; puncto B <lb/>horizonti perpendicula&shy;<lb/>ris BG, &amp; ab F item per&shy;<lb/>pendicularis FH, Tum <lb/>iuncta DB, centro D, eo&shy;<lb/>dem vero &longs;patio DB, circuli portio de&longs;cribatur BI, item <lb/>iuncta DF eodem centro D, &longs;patio DF, portio circuli de&shy;<lb/>&longs;cribatu: FK. e&longs;t autem maior DB ip&longs;a DF ex propo&longs;. <lb/></s>
            <s id="s.000394">21. lib.  1. Elem.  quare maioris circuli portio e&longs;t BI qu&agrave;m <lb/>FK. <!-- KEEP S--></s>
            <s id="s.000395">Obliquior autem, hoc e&longs;t, &agrave; perpendiculari remotior <lb/>e&longs;t motus per FK qu&agrave;m per BI. maior &longs;i quidem e&longs;t angu&shy;<lb/>lus KFH angulo IBG. quod nos ita probamus. </s>
            <s id="s.000396">Ducatur <lb/>perpendicularis ip&longs;i DF linea LF contingens circulum <lb/>FK in F, item ip&longs;i DB, perpendicularis MB, contingens <lb/>circulum BI in B, &amp; quia angulus contingenti&aelig; maioris <lb/>circuli minor e&longs;t angulo contingenti&aelig; minoris, erit KFL <lb/>maior IBM, Recti autem &longs;unt DFL, DBM, minor ergo <lb/>DFK re&longs;idua ip&longs;o DBI re&longs;iduo. </s>
            <s id="s.000397">Maior autem DFC ex <lb/>iam citata propo&longs;. </s>
            <s id="s.000398"><expan abbr="qu&atilde;">quam</expan> DBC, erit igitur re&longs;iduum CFK, <lb/>multo minus re&longs;iduo FBI, &longs;ed recti &longs;unt CFH, FBG, ex <lb/>quibus &longs;i detrahantur CFK, FBI, erit re&longs;iduum KFH, <lb/>maius re&longs;iduo IBG, plus ergo retrahitur &agrave; perpendicula&shy;<lb/>ri pondus de&longs;cendens per FK qu&agrave;m per BI, minus igitur <lb/>pr&aelig;ualebit re&longs;i&longs;tenti&aelig; in C pondus appen&longs;um in F, qu&agrave;m <lb/>&longs;i appendatur in B. quod fuerat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.000399">Po&longs;&longs;umus &amp; idem quoque aliter o&longs;tendere. </s>
          </p>
          <p type="main">
            <s id="s.000400">Sint enim &longs;eor&longs;um du&aelig; libr&aelig;, maior AB, m&iuml;nor EF, <lb/>qu&agrave;m commune grauitatis centrum C, fulcimentum ve&shy;<lb/>r&ograve; &longs;ur&longs;um D. <!-- KEEP S--></s>
            <s id="s.000401">Producatur perpendicularis DC, in G &amp; fiat <lb/>CG &aelig;qualis CB, CH ver&ograve; &aelig;qualis CF. <!-- KEEP S--></s>
            <s id="s.000402">Sunt igitur duo <pb xlink:href="007/01/047.jpg"/><figure id="id.007.01.047.1.jpg" xlink:href="007/01/047/1.jpg"/><lb/>vectes DG, DH, quo&shy;<lb/>rum quidem commu&shy;<lb/>ne fulcimentum D, <lb/>pondus ver&ograve; C, poten&shy;<lb/>ti&aelig; vbi HG. <!-- KEEP S--></s>
            <s id="s.000403">Sunt au&shy;<lb/>tem hi vectes eius na&shy;<lb/>tur&aelig;, in quibus <expan abbr="p&omacr;dus">pondus</expan> <lb/>e&longs;t inter fulcimentum <lb/>&amp; potentiam, itaque <lb/>vt &longs;e habet DC, ad <lb/>DG, ita potentia in G <lb/>ad pondus in C, item vt DC ad DH ita potentia in H ad <lb/>idem pondus C, &longs;ed minor e&longs;t propo&longs;itio DC, ad DG <lb/>qu&agrave;m DC ad DH. minor ergo potentia requiritur in G, <lb/>hoc e&longs;t, in B, qu&agrave;m in H, hoc e&longs;t in F. <!-- KEEP S--></s>
            <s id="s.000404">Data igitur ponderis <lb/>&aelig;qualitate facili&ugrave;s &longs;uperabitur re&longs;i&longs;tentia C in B, qu&agrave;m <lb/>in F: quod o&longs;tendendum fuerat. </s>
          </p>
          <p type="main">
            <s id="s.000405">Ad huius libr&aelig; naturam ill&aelig; quoque rediguntur, <lb/>quarum iugum non rectum quidem, &longs;ed curuum, vel ex <lb/>rectis &longs;ur&longs;um in angulum ad fulcimentum detinentibus, <lb/>nec refert vtrum curuitas &longs;it circuli portio qu&aelig;libet, aut <lb/>ellip&longs;is &longs;ecundum alterum diametrorum; quod ita de&shy;<lb/>mon&longs;tramus. </s>
          </p>
          <figure id="id.007.01.047.2.jpg" xlink:href="007/01/047/2.jpg"/>
          <p type="main">
            <s id="s.000406">E&longs;to libra, cuius iugum <lb/>curuum <expan abbr="angulat&umacr;ue">angulatumue</expan> ABC, <lb/>cuius fulcimentum B, &aelig;qua&shy;<lb/>lia autem brachia AB, BC, <lb/>&amp; pondera item <expan abbr="vtrinq;">vtrinque</expan> ap&shy;<lb/>pen&longs;a &aelig;qualia. </s>
            <s id="s.000407">Demittatur <lb/>ex puncto B ad mundi cen&shy;<lb/>trum perpendicularis BD. <lb/><!-- KEEP S--></s>
            <s id="s.000408">Stante igitur libra ABC in <lb/>&aelig;quilibrio, erit eius graui&shy;<pb xlink:href="007/01/048.jpg"/>tatis centrum in ip&longs;a perpendiculari BD, puta in E. <!-- KEEP S--></s>
            <s id="s.000409">Ap&shy;<lb/>ponatur pondus in C, declinabit autem libra, &longs;it autem <lb/>iuxta po&longs;itionem FBG. <!-- KEEP S--></s>
            <s id="s.000410">Centrum igitur grauitatis E per <lb/>portionem EH, erit in H. <!-- KEEP S--></s>
            <s id="s.000411">A&longs;cendit ergo centrum graui&shy;<lb/>tatis in H, hoc e&longs;t, &longs;ur&longs;um, id e&longs;t, contra eius naturam; a&shy;<lb/>moto igitur pondere ex C, grauitatis centrum extra per&shy;<lb/>pendicularem con&longs;titutum rur&longs;us de&longs;cendet, &amp; iterum <lb/>libra ABC ad &aelig;quilibrium reuertetur. </s>
            <s id="s.000412">Hoc idem egre&shy;<lb/>gi&egrave; o&longs;tendit G. Vbald. <!-- REMOVE S-->in tractatu de libra, propo&longs;. 4. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000413">Hinc ratio pendet earum imaguncularum, quas ex <lb/>contu&longs;a papyro ligneaue leui materia compingunt, per&shy;<lb/>queue manus earum ambas, ferreum filum trajicientes, v&shy;<lb/>trinque plumbea appendunt pondera &aelig;qualia, ea <expan abbr="quid&emacr;">quidem</expan> <lb/>lege, vt centrum grauitatis infra pedes imaguncula &longs;ta&shy;<lb/>tuatur. </s>
            <s id="s.000414">Tunc enim exten&longs;o filo imponentes ceu funam&shy;<lb/>bulos per illud, vltr&ograve; citroque; decurrere faciunt, imagun&shy;<lb/>cula interim erecta &amp; in neutram partem cadente, quod <lb/>vt figur&acirc; clarius fiat; </s>
          </p>
          <figure id="id.007.01.048.1.jpg" xlink:href="007/01/048/1.jpg"/>
          <p type="main">
            <s id="s.000415">E&longs;to imaguncu&shy;<lb/>la AB, per cuius ma&shy;<lb/>nus traijciatur filum <lb/>ferreum curuum <expan abbr="c&umacr;">cum</expan> <lb/>&aelig; qualibus ponderi&shy;<lb/>bus hinc inde <expan abbr="app&emacr;-&longs;is">appen&shy;<lb/>&longs;is</expan> CD. <!-- KEEP S--></s>
            <s id="s.000416">Nitatur au&shy;<lb/>tem pedibus filo HI <lb/>in <emph type="italics"/>B<emph.end type="italics"/>, &longs;itque; tot&igrave;us ma&shy;<lb/>chin&aelig; grauitatis <expan abbr="c&emacr;-trum">cen&shy;<lb/>trum</expan> E, &longs;itque <expan abbr="per-p&emacr;dicularis">per&shy;<lb/>pendicularis</expan> per gra&shy;<lb/>uitatis <expan abbr="centr&umacr;">centrum</expan> tran&longs;i&shy;<lb/>ens A<emph type="italics"/>B<emph.end type="italics"/> E. <!-- KEEP S--></s>
            <s id="s.000417">Itaque in&shy;<lb/>clinata imaguncula, &amp; conuer&longs;a circa punctum <emph type="italics"/>B<emph.end type="italics"/>, &longs;i de-<pb xlink:href="007/01/049.jpg"/>clinet ad partes I, centrum grauitatis eleuabitur in F. <!-- KEEP S--></s>
            <s id="s.000418">Si <lb/>ver&ograve; ad partes H eleuabitur in G. quare cum FG loca <lb/>&longs;int remotiora &agrave; mundi centro, qu&agrave;m &longs;it E, non &longs;tabit gra&shy;<lb/>uitatis centrum in punctis FG, &longs;ed ad infimum locum re&shy;<lb/>uertetur, hoc e&longs;t, in ip&longs;a perpendiculari in E, &amp; imagun&shy;<lb/>cula ad perpendiculum ip&longs;i H<emph type="italics"/>B<emph.end type="italics"/>E filo, hoc e&longs;t, ip&longs;i hori&shy;<lb/>zonti reuertetur. </s>
          </p>
          <p type="main">
            <s id="s.000419">Hinc etiam Arictum, Te&longs;tudinumqueue demolito&shy;<lb/>riarum Machinarum vis pendet, nempe ex ratione libra&shy;<lb/>rum, qu&aelig; fulcimentum habent &longs;ur&longs;um. </s>
          </p>
          <figure id="id.007.01.049.1.jpg" xlink:href="007/01/049/1.jpg"/>
          <p type="main">
            <s id="s.000420">E&longs;to enim Aries A<emph type="italics"/>B<emph.end type="italics"/> <lb/>funi appen&longs;us CD, cu&shy;<lb/>ius grauitatis centrum, <lb/>D, perpendicularis ver&ograve; <lb/>qu&aelig; ad mundi centrum <lb/>ip&longs;a CDE. <!-- KEEP S--></s>
            <s id="s.000421">Stante igitur <lb/>in &aelig;quilibrio machina, <lb/>centrum grauitatis erit <lb/>in ip&longs;a perpendiculari. <lb/></s>
            <s id="s.000422">Applicetur alicubi po&shy;<lb/>tentia retropellens, eleuabitur igitur centrum grauitatis <lb/>per circuli portionem DF, cuius &longs;emidiameter e&longs;t CD, <lb/>&longs;i etqueue iuxta po&longs;itionem CF. <!-- KEEP S--></s>
            <s id="s.000423">Aries ver&ograve; in GFH. </s>
            <s id="s.000424">Di&shy;<lb/>mi&longs;&longs;a itaque Machina centrum F vtpote graue, non &longs;tabit, <lb/>&longs;ed &longs;uapte natur&acirc; reuertetur in D. <!-- KEEP S--></s>
            <s id="s.000425">Quadruplici autem <lb/>de cau&longs;&longs;a motus Arietis violenti&longs;&longs;imus e&longs;t ex vi naturalis <lb/>ponderis, quo deor&longs;um fertur, tum velocitate naturalis <lb/>motus in de&longs;cendendo auct&aelig;, tum ex vi potenti&aelig; impel&shy;<lb/>lentis, &amp; naturalem motum adiuuantis, tum ex velocita&shy;<lb/>te ex motu violento deor&longs;um &amp; antror&longs;um impellente <lb/>acqui&longs;it&acirc;. </s>
            <s id="s.000426">Id etiam addimus, eo validiores fore ictus, qu&ograve; <lb/>grauior fuerit Machina, &amp; maius &longs;patium, quo retrotra&shy;<pb xlink:href="007/01/050.jpg"/>hitur, grauitate ip&longs;a &amp; &longs;patio tum virium vnione opera&shy;<lb/>tionem mirum in modum adiuuantibus. </s>
          </p>
          <p type="main">
            <s id="s.000427">H&aelig;c nos de Libra &longs;ur&longs;um fulcimentum habente, d&iacute;&shy;<lb/>cta voluimus, nunc de ea, cuius fulcimentum deor&longs;um, <lb/>e&longs;t, verba faciemus. </s>
          </p>
          <p type="head">
            <s id="s.000428">Altera qu&aelig;&longs;tionis pars:</s>
          </p>
          <p type="head">
            <s id="s.000429"><emph type="italics"/>De Libra cuius fulcimentum deor&longs;um e&longs;t.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000430">Si deor&longs;um fuerit, inquit Ari&longs;toteles, id quod &longs;ub&shy;<lb/>&longs;tat, contrarium facit illi qu&aelig; &longs;ur&longs;um habet, nempe ad &aelig;&shy;<lb/>quilibrium non reuertitur. </s>
            <s id="s.000431">Plus enim, ait, dimidio fit li&shy;<lb/>br&aelig;, qu&aelig; deor&longs;um e&longs;t pars, qu&agrave;m quod perpendiculum <lb/>&longs;ecet, quapropter non a&longs;cendit. </s>
            <s id="s.000432">eleuata enim pars leuior <lb/>e&longs;t. </s>
          </p>
          <p type="main">
            <s id="s.000433">H&aelig;c ille, qui &longs;chemate quoque rem aperit, at eo a&shy;<lb/>pud interpretes, &amp; Picolomineum Paraphra&longs;tem, ita <expan abbr="m&emacr;-dos&egrave;">men&shy;<lb/>dos&egrave;</expan> lineato, vt inde ob&longs;curitas lucis loco, legentibus of&shy;<lb/>fundatur. </s>
            <s id="s.000434">Nos, quod &amp; &longs;upr&agrave; quoque fecimus, no&longs;tra fi&shy;<lb/>gur&acirc;, &longs;ole ip&longs;o clariorem, ex Ari&longs;to telis ip&longs;ius mente rem <lb/>totam efficiemus. </s>
          </p>
          <figure id="id.007.01.050.1.jpg" xlink:href="007/01/050/1.jpg"/>
          <p type="main">
            <s id="s.000435">Sit libra recta, &lpar;hoc <lb/>e&longs;t, in &aelig;quilibrio con&shy;<lb/>&longs;tituta&rpar; vbi NG. </s>
            <s id="s.000436">Per&shy;<lb/>pendiculum autem &lpar;id <lb/>e&longs;t, perpendicularis <lb/>qu&aelig; ad mundi <expan abbr="centr&umacr;">centrum</expan>&rpar; <lb/>KLM. </s>
            <s id="s.000437">Bifariam igitur <lb/>&longs;ecatur NG. impo&longs;ito <lb/>po&longs;th&aelig;c onere in ip&longs;o <lb/>N, erit quidem N, vbi <lb/>O. ip&longs;um autem G vbi <lb/>R. KL autem vbi LP. <pb xlink:href="007/01/051.jpg"/>quare maius e&longs;t KO, quam LR, ip&longs;a parte PKL. </s>
            <s id="s.000438">Amoto <lb/>igitur onere nece&longs;&longs;e e&longs;t manere. </s>
            <s id="s.000439">Incumbit enim onus ex&shy;<lb/>ce&longs;&longs;us medietatis eius, vbi e&longs;t F. <!-- KEEP S--></s>
            <s id="s.000440">Sen&longs;us e&longs;t igitur, idcirco <lb/>partem iugi KLO inclinatam, ad &aelig;quilibrium non re&shy;<lb/>uerti, propterea qu&ograve;d maior &longs;it ip&longs;a KLO pars qu&aelig; tra&shy;<lb/>hit, ip&longs;a RKL, qu&aelig; trahitur &amp; eleuatur. </s>
          </p>
          <figure id="id.007.01.051.1.jpg" xlink:href="007/01/051/1.jpg"/>
          <p type="main">
            <s id="s.000441">Pote&longs;t hoc idem long&egrave; <lb/>&longs;impliciori themate demon&shy;<lb/>&longs;trari. </s>
            <s id="s.000442">E&longs;to enim libra AB, <lb/>cuius centrum C, fulcimen&shy;<lb/>tum vero deor&longs;um D, Per&shy;<lb/>pendicularis per centrum &amp; <lb/>fulcimentum tran&longs;iens EF. <lb/><!-- KEEP S--></s>
            <s id="s.000443">Apponatur pondus in B, de&shy;<lb/>clinabitque; puta ad GH, cen&shy;<lb/>trum ver&ograve; C, ex &longs;tabili fulci&shy;<lb/>mento D, circuli portionem de&longs;cribet CI, libra autem <lb/>&longs;ecabit EF perpendicularem in K. &AElig;quales autem &longs;unt <lb/>IG, IH, at ex parte HI de&longs;umpta e&longs;t KI, addita queue ip&longs;i <lb/>IG, maior e&longs;t ergo tota KG, tor&acirc; KH. </s>
            <s id="s.000444">Non igitur KH <lb/>habet KG, &longs;ed libra, ni&longs;i impedita fuerit, cum centro C <lb/>de&longs;cendente per I in M, ad ip&longs;am perpendicularem dela&shy;<lb/>ta, ad in feriorem partem, mutatis vicibus quie&longs;cet, facto <lb/>nempe fulcimento &longs;ur&longs;um, fietque; horizonti &aelig;que di&longs;tans <lb/>iuxta po&longs;itionem LMN. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000445">Demon&longs;tratio <expan abbr="quid&emacr;">quidem</expan> e&longs;t h&aelig;c, &longs;ed non ex proprijs prin&shy;<lb/>cipijs Mechanicis, <expan abbr="n&emacr;pe">nempe</expan> ex ratione <expan abbr="c&emacr;t">cent</expan>ri grauitatis petit&acirc;. <lb/></s>
            <s id="s.000446">Ii&longs;dem enim &longs;tantibus, <expan abbr="c&umacr;">cum</expan> centrum grauitatis C fiat extra <lb/>perpendicularem, de&longs;cendens ad I, nunquam reuertetur <lb/>in C, a&longs;cenderet enim; &longs;ed &longs;i liber&egrave; circa centrum D con&shy;<lb/>uerteretur, de&longs;cendens vt dictum e&longs;t per circulum CIM <lb/>pondus B, fieret in L, A vero in N adepta po&longs;itione <lb/>LMN. <!-- KEEP S--></s>
          </p>
          <pb xlink:href="007/01/052.jpg"/>
          <p type="main">
            <s id="s.000447">Cur autem huius libr&aelig;, qu&aelig; ali&agrave;s inutilis e&longs;t, memi&shy;<lb/>nerit Philo&longs;ophus, ea videtur cau&longs;&longs;a, qu&ograve;d inde vectis vir&shy;<lb/>tutem eliciat, vt &longs;uo loco videbimus. </s>
            <s id="s.000448">Id autem valde mi&shy;<lb/>rum, hominem acuti&longs;&longs;imum nihil pror&longs;us de ea libra egi&longs;&shy;<lb/>&longs;e, qu&aelig; fulcimentum nec &longs;ur&longs;um habet, nec deor&longs;um, &longs;ed <lb/>in ip&longs;o exqui&longs;it&egrave; medio, ita vt centrum grauitatis in ip&longs;o&shy;<lb/>met fulcimento con&longs;i&longs;tat. </s>
            <s id="s.000449">Nos igitur de hac quod oper&aelig; <lb/>pretium fuerit, &amp; ad rem, qua de agimus, vtile, in medium <lb/>proferemus. </s>
          </p>
          <p type="head">
            <s id="s.000450"><emph type="italics"/>De libra cuius fulcimentum est in medio.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000451">Dicimus itaque, libram, cuius fulcimentum nec &longs;ur&shy;<lb/>&longs;um e&longs;t, nec deor&longs;um, &longs;ed pror&longs;us in medio, nempe in ip&longs;o <lb/>grauitatis centro, vbi brachia &amp; pondera vtrinque appo&shy;<lb/>&longs;ita fuerint &aelig;qualia, &longs;i ab &aelig;quilibrio mouentur, quomo&shy;<lb/>docunque po&longs;ita, &longs;tare nec ab eo, quem adepta e&longs;t, &longs;itu di&shy;<lb/>moueri. </s>
          </p>
          <p type="main">
            <s id="s.000452">Qu&aelig;&longs;tionem hanc perperam tract&acirc;runt recentio&shy;<lb/>res quidam, Hieron. <!-- REMOVE S-->Cardanus, Nicolaus Tartalea, &amp; alij <lb/>nonnulli, qui Iordani Nemoracij a&longs;&longs;ertiones &longs;unt &longs;ecuti, <lb/>quorum demon&longs;trationes vel paralogi&longs;mos poti&ugrave;s egre&shy;<lb/>gi&egrave; confutauit in libr. </s>
            <s id="s.000453">Mechanicor. <!-- REMOVE S-->Tractatu de libra pro&shy;<lb/>po&longs;. </s>
            <s id="s.000454">4. Guid. <!-- REMOVE S-->Vbald. <!-- REMOVE S-->ad cuius probati&longs;&longs;ima &longs;cripta Lecto&shy;<lb/>rem ablegamus. </s>
            <s id="s.000455">fu&longs;i&longs;&longs;im&egrave; enim ibi hac de re &amp; ab&longs;oluti&longs;&longs;i&shy;<lb/>m&egrave; agit. </s>
            <s id="s.000456">Nos autem quidem paucis ea, qu&aelig; ad hanc co&shy;<lb/>gnitionem pertinent, explicabimus. </s>
          </p>
          <figure id="id.007.01.052.1.jpg" xlink:href="007/01/052/1.jpg"/>
          <p type="main">
            <s id="s.000457">E&longs;to enim libra A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius brachia &aelig;qualia, <lb/>&amp; centrum grauitatis <lb/>in C, brachijs ver&ograve; <lb/>AC, C<emph type="italics"/>B<emph.end type="italics"/> &aelig;qualibus, &aelig;&shy;<lb/>qualia pondera hinc <lb/>inde <expan abbr="appon&atilde;tur">apponantur</expan>. </s>
            <s id="s.000458">Tum <pb xlink:href="007/01/053.jpg"/>fulcimento in medio, hoc e&longs;t, vbi grauitatis centrum C <lb/>applicato per centrum ip&longs;um C ducatur perpendicularis, <lb/>qu&aelig; ad mundi centrum, DCE, &longs;itque primum libra &aelig;&shy;<lb/>quedi&longs;tans horizonti, con&longs;tituta. </s>
            <s id="s.000459">Tum ex altera parte <lb/>pre&longs;&longs;a moueatur &amp; fiat iuxta po&longs;itionem FCG. <!-- KEEP S--></s>
            <s id="s.000460">Dico eam <lb/>dimi&longs;&longs;am permanere, etenim cum grauitatis centrum &longs;it <lb/>in ip&longs;a perpendiculari, in neutram partem verget, &longs;ed nec <lb/>vergere pote&longs;t, quippe quod non circa fulcimentum ceu <lb/>centrum motus, moueatur grauitatis centrum, &longs;ed in ip&longs;o <lb/>&longs;it fulcimento; &longs;itum ergo non mutat. </s>
            <s id="s.000461">Pr&aelig;terea cum per&shy;<lb/>pendicularis DCE per grauitatis centrum ducatur, cor&shy;<lb/>pus ip&longs;um ex ponderibus &amp; libra con&longs;tans ab ea in partes <lb/>&ccedil;que ponderantes &longs;ecatur, &amp; ideo ex centri grauitatis dif&shy;<lb/>finitione, quam protulit Pappus, corpus ip&longs;um centro <lb/>grauitatis appen&longs;um, dum fertur quie&longs;cit, &amp; &longs;eruat eam, <lb/>quam &agrave; principio habuit po&longs;itione. </s>
            <s id="s.000462">Et &longs;an&egrave; &longs;i partes quo&shy;<lb/>modo libet libr&acirc; per grauitatis centrum diuis&acirc;, &longs;unt &aelig;&shy;<lb/>queponderantes nec trahent inuicem, nec trahentur, &longs;ta&shy;<lb/>bit ergo libra, &amp; quam adepta fuerat po&longs;itionem, eam &longs;er&shy;<lb/>uabit. </s>
            <s id="s.000463">Id tamen non negamus, difficile e&longs;&longs;e libras eiu&longs;ce&shy;<lb/>modi ex materia fabricare, quippe quod non omnia qu&aelig; <lb/>vera &longs;unt, &amp; euidenti&longs;&longs;imis demon&longs;trationibus patent, <lb/>commod&egrave; ad praxim, ex artis &amp; materi&aelig; imperfectione, <lb/>reducuntur. </s>
          </p>
          <p type="main">
            <s id="s.000464">C&aelig;ter&ugrave;m harum librarum ea e&longs;t virtus, vt vel mini&shy;<lb/>mo pondere altrin&longs;ecus appo&longs;ito, declinet; quod illis qu&aelig; <lb/>centrum &longs;ur&longs;um habent, non euenire, demon&longs;trauimus. </s>
          </p>
          <p type="main">
            <s id="s.000465">Circa h&aelig;c po&longs;&longs;et cuipiam oriri Dubium, num chor&shy;<lb/>dul&aelig;, quibus lances appenduntur, variationem aliquam <lb/>circa ea qu&aelig; demon&longs;trata &longs;unt, inducere valeant. </s>
          </p>
          <p type="main">
            <s id="s.000466">Dicimus nullam inde fieri: E&longs;to enim libra AB, cu&shy;<lb/>ius centrum &amp; fulcimentum C, ab cuius extremitate A <lb/>dependeat, funiculus AD, ab alia ver&ograve; <emph type="italics"/>B<emph.end type="italics"/>, funiculus <emph type="italics"/>B<emph.end type="italics"/>E, <pb xlink:href="007/01/054.jpg"/><figure id="id.007.01.054.1.jpg" xlink:href="007/01/054/1.jpg"/><lb/>quibus appen&longs;&aelig; &longs;int &aelig;&shy;<lb/>qualis ponderis lances <lb/>DE. <!-- KEEP S--></s>
            <s id="s.000467">Moueatur libra, <lb/>fiatque in ICH, funi&shy;<lb/>culi ver&ograve; in lancibus in <lb/>IK, HL. &longs;ecet autem fu&shy;<lb/>niculus IK libram A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>in M, LH ver&ograve; produ&shy;<lb/>catur &amp; eandem &longs;ecer <lb/>in N. quoniam igitur <lb/>IC, &aelig;qualis e&longs;t CH, pa&shy;<lb/>rallel&aelig; autem KI, LN &aelig;quales <expan abbr="er&umacr;t">erunt</expan> alterni anguli MIC, <lb/>NHC, &longs;ed &amp; anguli ad verticem ICH, BCH &aelig;quales <lb/>&longs;unt, quare triangulum IMC, &aelig;quale triangulo HNC, <lb/>&amp; latera lateribus, qu&aelig; &aelig;qualibus angulis &longs;ubtenduntur. <lb/></s>
            <s id="s.000468">&AElig;qualis e&longs;t igitur linea MC line&aelig; NC. </s>
            <s id="s.000469">Itaque &longs;i ponde&shy;<lb/>ra lancesue, KL mente concipiantur appen&longs;&aelig; in punctis <lb/>MN, ex brachiorum &amp; ponderum &aelig;qualitate &aelig;quepon&shy;<lb/>derabunt. </s>
            <s id="s.000470">quod fuerat demon&longs;trandum. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000471">QV&AElig;STIO III.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000472"><emph type="italics"/>Cur exigu&aelig; vires &lpar;quod etiam &agrave; principio dixerat&rpar; vecte magna <lb/>mouent pondera, vectes in&longs;uper onus accipientes, cum facilius <lb/>&longs;it, minorem mouere grauitatem, minor est au&shy;<lb/>tem &longs;ine vecte?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000473">Ari&longs;toteles ita qu&aelig;&longs;tionem proponit, vt eam Rheto&shy;<lb/>rico quodam fuco admirabiliorem faciat. </s>
            <s id="s.000474">Soluit au&shy;<lb/>tem hoc pacto, <expan abbr="inqui&emacr;s">inquiens</expan>, fieri po&longs;&longs;e eam e&longs;&longs;e cau&longs;&longs;am, quod <lb/>vectis &longs;it libra, eius nempe generis quod fulcimentum ha&shy;<lb/>bet deor&longs;um, atque id circo in ip&longs;a pre&longs;&longs;ione in partes in&shy;<lb/>&aelig;quales vectem diuidi. </s>
          </p>
          <pb xlink:href="007/01/055.jpg"/>
          <figure id="id.007.01.055.1.jpg" xlink:href="007/01/055/1.jpg"/>
          <p type="main">
            <s id="s.000475">Figura quam ex&shy;<lb/>hibet, vix fer&egrave; quid &longs;i&shy;<lb/>bi velit explicat. </s>
            <s id="s.000476">Nos <lb/>ad eius <expan abbr="m&emacr;tem">mentem</expan> aliam <lb/>proponemus <expan abbr="eamq;">eamque</expan> <lb/>long&egrave; clariorem. </s>
          </p>
          <p type="main">
            <s id="s.000477">E&longs;to vectis A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius fulcimentum, <lb/>deor&longs;um in C, pon&shy;<lb/>dus D, potentia ex vecte, pondus &longs;u&longs;tinens E. <!-- KEEP S--></s>
            <s id="s.000478">Perpendi&shy;<lb/>cularis per fulcimentum FCG. <!-- KEEP S--></s>
            <s id="s.000479">Itaque quoniam poten&shy;<lb/>tia in E non &longs;uperat pondus D, nec ab eo &longs;uperatur, &longs;tat <lb/>vectis cum potentia Horizonti &aelig;quidi&longs;tans, hoc e&longs;t, in &aelig;&shy;<lb/>quilibrio, vectis autem in puncto C diuiditur in partes &aelig;&shy;<lb/>queponderantes. </s>
            <s id="s.000480">Modo pr&aelig;ualeat potentia ponderi, &amp; <lb/>vectem deprimat, fiat autem in LCH, erit igitur <emph type="italics"/>B<emph.end type="italics"/>, in L, <lb/>A in H, D in K, &amp; CF, qu&aelig; vectem in partes &aelig;que ponde&shy;<lb/>rantes diuidebat, in CI. <!-- KEEP S--></s>
            <s id="s.000481">Iam igitur non &aelig;queponderant <lb/>partes, &longs;i quidem pars vectis FCI, aufertur parti HCI, &amp; <lb/>adiungitur parti ICL, qu&aelig; ideo &longs;it pondero&longs;ior, vnde &amp; <lb/>potentia ad ponderis eleuationem adiuuatur. </s>
            <s id="s.000482">Eadem i&shy;<lb/>gitur vtitur hic demon&longs;tratione, quam in explicando ef&shy;<lb/>fectu libr&aelig;, cuius fulcimentum deor&longs;um e&longs;t, adhibuerat. <lb/></s>
            <s id="s.000483">Nec alia de cau&longs;&longs;a, vt &longs;upr&agrave; notauimus, videtur eius libr&aelig; <lb/>in &longs;uperiori qu&aelig;&longs;tione, con&longs;iderationem introduxi&longs;&longs;e. </s>
            <s id="s.000484">Et <lb/>&longs;an&egrave; verum e&longs;t quod concludit, Veruntamen minimi e&longs;t <lb/>momenti ad tantam vim parua illa adiectio, qu&aelig; parti ve&shy;<lb/>ctis depre&longs;&longs;&aelig; in ip&longs;a depre&longs;&longs;ione adiungitur. </s>
            <s id="s.000485">Aliunde igi&shy;<lb/>tur tant&aelig; rei cau&longs;&longs;a e&longs;t petenda, quod &amp; nos deinceps fa&shy;<lb/>ciemus. </s>
            <s id="s.000486">Videtur autem ip&longs;e quoque Ari&longs;toteles non &longs;ibi <lb/>pror&longs;us in a&longs;&longs;ignata ratione &longs;atis feci&longs;&longs;e, &amp; ideo &longs;ubiungit: <lb/>quoniam ab &aelig;quali pondere celerius mouetur maior ca&shy;<lb/>rum qu&aelig; &agrave; centro &longs;unt duo ver&ograve; pondera; quod mouet &amp; <pb xlink:href="007/01/056.jpg"/>quod mouetur, quod igitur motum pondus ad mouens <lb/>longitudo patitur ad longitudinem, &longs;emper autem <expan abbr="qu&atilde;-tum">quan&shy;<lb/>tum</expan> ab hypomochlio &lpar;id e&longs;t, fulcimento&rpar; di&longs;tabit magis, <lb/>tanto facilius mouebit. </s>
            <s id="s.000487">Cau&longs;&longs;a autem est, qu&aelig; retro com&shy;<lb/>memorata e&longs;t, quoniam qu&aelig; plus &agrave; centro di&longs;tat <expan abbr="maior&emacr;">maiorem</expan> <lb/>de&longs;cribit circulum. </s>
            <s id="s.000488">quare ab eadem potentia plus &longs;upera&shy;<lb/>bitur id quod mouetur, qu&aelig; plus &agrave; fulcimento di&longs;tat. </s>
            <s id="s.000489">H&ucedil;c <lb/>ille, qui a&longs;&longs;erit duo pondera in vecte con&longs;iderari, Pondus <lb/>nempe motum, &amp; mouentem Potentiam &lpar;hanc enim <expan abbr="p&omacr;-deris">pon&shy;<lb/>deris</expan> habere vim <expan abbr="atq;">atque</expan> rationem certum e&longs;t&rpar; Vires autem <lb/>potentiam acquirere ex brachij longitudine, &amp; ex inde <lb/>con&longs;equenti velocitate, quo enim brachia longiora, eo <lb/>in extremitate velociora, atque idcirco ita &longs;e habere mo&shy;<lb/>tum pondus ad potentiam mouentem, vt brachij longi&shy;<lb/>tudo ad brachij longitudinem: brachia autem vocamus, <lb/>partes illas vectis, qu&aelig; &agrave; fulcimento ad vtranque vectis <lb/>extremitatem pertingunt, &amp; ideo quantum &agrave; fulcimento <lb/>potentia di&longs;tabit magis, eo facili&ugrave;s pondus mouebit. </s>
          </p>
          <p type="main">
            <s id="s.000490">Vera vtique &amp; explorati&longs;&longs;ima h&aelig;c a&longs;&longs;ertio e&longs;t. </s>
            <s id="s.000491">Ve&shy;<lb/>runtamen, cau&longs;&longs;am huiu&longs;ce mirabilis effectus, e&longs;&longs;e velo&shy;<lb/>citatem, qu&aelig; brachij longitudinem con&longs;equitur, non af&shy;<lb/>firmamus. </s>
            <s id="s.000492">qu&aelig; enim velocitas in re &longs;tante? </s>
            <s id="s.000493">Stant autem <lb/>vectis, &amp; libra dum manent in &aelig;quilibrio, &amp; nihilo &longs;ecius <lb/>parua potentia ingens &longs;u&longs;tinet pondus. </s>
          </p>
          <p type="main">
            <s id="s.000494">Dicet ad h&aelig;c qui&longs;piam, velocitatem in longiori bra&shy;<lb/>chio &longs;i non actu, &longs;altem potenti&acirc; e&longs;&longs;e maiorem. </s>
            <s id="s.000495">At qu&aelig;&longs;o <lb/>quid in re qu&aelig; e&longs;t actu, momenti habet potentia? </s>
            <s id="s.000496">actu e&shy;<lb/>nim &longs;u&longs;tinet, &longs;u&longs;tinens. </s>
            <s id="s.000497">Con&longs;equ&igrave;tur, &lpar;id vtique fatemur&rpar; <lb/>nece&longs;&longs;ari&ograve; velocitas maior motu brachij maioris; non ta&shy;<lb/>men cau&longs;&longs;a e&longs;t cur vis loco vbi velocitas maior &longs;it, appo&longs;i&shy;<lb/>ta magis moueat. </s>
            <s id="s.000498">San&egrave; ex velocitate, dum mouentur, <expan abbr="p&omacr;-dus">pon&shy;<lb/>dus</expan> acquirere corpora, tum proiecta, tum cadentia cer&shy;<lb/>tum e&longs;t, quod etiam in qu&aelig;&longs;tione 19. cum Philo&longs;opho <expan abbr="c&omacr;-">con-</expan><pb xlink:href="007/01/057.jpg"/>&longs;iderabimus. </s>
            <s id="s.000499">Sed hoc ex velocitate &amp; motu &longs;it, qu&aelig; &longs;unt <lb/>actu. </s>
            <s id="s.000500">At brachia in ip&longs;o &aelig;quilibrio &longs;u&longs;tinent actu quidem, <lb/>&longs;ed non mouentur. </s>
            <s id="s.000501">C&aelig;terum videtur Ari&longs;toteles id &longs;ub&shy;<lb/>odora&longs;&longs;e, quod po&longs;tea Archimedes, Mechanicorum prin&shy;<lb/>ceps, in propo&longs;. </s>
            <s id="s.000502">6. primi &AElig;queponderantium explicit&egrave; <lb/>protulit &amp; probauit: nempe in &aelig;quilibrio ita e&longs;&longs;e pondus <lb/>ad pondus, vt brachium ad brachium, ratione permutata. </s>
          </p>
          <figure id="id.007.01.057.1.jpg" xlink:href="007/01/057/1.jpg"/>
          <p type="main">
            <s id="s.000503">E&longs;to enim vectis <lb/>AB, quomodolibet <lb/>fulcimento diui&longs;us in <lb/>C. <expan abbr="app&emacr;datur">appendatur</expan> autem <lb/>in A, pondus D, in B <lb/>ver&ograve; pondus E, ita &longs;e <lb/>habens ad pondus D, vt ip&longs;a AC ad CB. <!-- KEEP S--></s>
            <s id="s.000504">Stabit igitur ve&shy;<lb/>ctis, &amp; neutram in partem verget, erit enim centrum gra&shy;<lb/>uitatis in C, diui&longs;o nempe ibi vecte in partes &aelig;que ponde&shy;<lb/>rantes. </s>
            <s id="s.000505">Hoc po&longs;t Archimedem, &amp; in&longs;ignes illos veteres <lb/>Mechanicos pr&aelig;clari&longs;&longs;im&egrave; demon&longs;trauit G. <!-- REMOVE S-->Vbaldus in <lb/>Mechanicis, Tractatu de Libra propo&longs;. </s>
            <s id="s.000506">6. nec non de Ve&shy;<lb/>cte propo&longs;. </s>
            <s id="s.000507">4. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000508">C&aelig;ter&ugrave;m vt aliquid interim, quod no&longs;trum &longs;it, affe&shy;<lb/>ramus, liceat nobis egregios illos viros interrogare, qu&aelig;&shy;<lb/>nam mirabilis eius effectionis &longs;it cau&longs;&longs;a? </s>
            <s id="s.000509">Dicent permu&shy;<lb/>tatam proportionem. </s>
            <s id="s.000510">Teneo, at nondum acquie&longs;co: pe&shy;<lb/>tam enim, Cur ea rationis permutatio mirabilem illum <lb/>effectum pariat. </s>
            <s id="s.000511">Hoc quod illi non docent, puto nos, i&shy;<lb/>gnoranti&aelig; &longs;omno &longs;epultos, &longs;omnia&longs;&longs;e. </s>
          </p>
          <figure id="id.007.01.057.2.jpg" xlink:href="007/01/057/2.jpg"/>
          <p type="main">
            <s id="s.000512">&AElig;qualitatem &longs;tatus <lb/>e&longs;&longs;e cau&longs;&longs;am, nemo, vt <lb/>puto, inficiabitur. </s>
            <s id="s.000513">res e&longs;t <lb/>enim per &longs;e clara. </s>
            <s id="s.000514">E&longs;to &longs;i&shy;<lb/>quidem linea qu&aelig;piam AB, applicetur extremitati A po&shy;<pb xlink:href="007/01/058.jpg"/>tentia qu&aelig;dam qu&aelig; lineam ad &longs;e trahat ad partes nempe <lb/>A, Tum in B qu&aelig;dam alia potentia ip&longs;i qu&aelig; in A potentiae, <lb/>&aelig;qualis, qu&aelig; lineam trahat &longs;imili modo ad partes B. <!-- KEEP S--></s>
            <s id="s.000515">Dat&acirc; <lb/>igitur harum potentiarum &aelig;qualitate, linea AB, nec ad <lb/>partes A, nec ad partes B transferetur, &longs;ed pror&longs;us immo&shy;<lb/>bilis &longs;tabit. </s>
          </p>
          <p type="main">
            <s id="s.000516">His ita con&longs;titutis, Dico vecte quomodolibet diui&longs;o, <lb/>ponderibu&longs;que vtrinque appo&longs;itis, permutat&acirc; propor&shy;<lb/>tione &longs;ibi inuicem re&longs;pondentibus, rem e&longs;&longs;e redactam ad <lb/>&aelig;qualitatem, &amp; inde &longs;tatum fieri, hoc e&longs;t, &aelig;quilibrium. </s>
          </p>
          <figure id="id.007.01.058.1.jpg" xlink:href="007/01/058/1.jpg"/>
          <p type="main">
            <s id="s.000517">E&longs;to enim vectis AB, quo modo libet diui&longs;us in C, &amp; <lb/>ip&longs;i quidem C fulcimentum &longs;upponatur. </s>
            <s id="s.000518">Appendantur <lb/>quoque vtrinque pondera ex ratione brachiorum AC, <lb/>CB, &longs;ibi inuicem permutatim re&longs;pondentia, &longs;intque; DE. <lb/><!-- KEEP S--></s>
            <s id="s.000519">Dico vectem ex &aelig;qualitate, in neutram partem <expan abbr="inclina-tur&umacr;">inclina&shy;<lb/>turum</expan>, &longs;ed perman&longs;urum in &aelig;quilibrio. </s>
            <s id="s.000520">quoniam enim <expan abbr="P&omacr;-dus">Pon&shy;<lb/>dus</expan> D idem pote&longs;t quod brachium CB, addatur in dire&shy;<lb/>ctum ip&longs;i AC, recta AF &aelig;qualis ip&longs;i CB, item quoniam <lb/>Pondus E id pote&longs;t quod brachium AC, rect&aelig; CB ad&shy;<lb/>datur in directum BG, ip&longs;i AC &aelig;qualis. </s>
            <s id="s.000521">Igitur cum par&shy;<lb/>tes CA, AF totius FC, &aelig;quales &longs;int partibus CB, BG, <lb/>totius CG, erit totum FC, toti CG &aelig;quale. </s>
            <s id="s.000522">Diui&longs;us ita-<pb xlink:href="007/01/059.jpg"/>que erit vectis FG in partes &aelig;quales FC, CG in puncto <lb/>fulcimenti C. <!-- KEEP S--></s>
            <s id="s.000523">Et quoniam &aelig;quale in &aelig;quale non agit, <lb/>&longs;tabit vectis &amp; in neutram partem inclinabit. </s>
            <s id="s.000524">Rur&longs;um <lb/>quoniam ad partem FC, du&aelig; &longs;unt brachiorum potenti&aelig; <lb/>FA, HC, appendantur puncto F, duo pondera H, I, ip&longs;is <lb/>DE &aelig;qualia, item puncto G, alia duo pondera ij&longs;dem DE <lb/>&aelig;qualia KL, iterum &aelig;queponderabit, quippe quod &aelig;&shy;<lb/>qualibus brachijs FCCG &aelig;qualia appen&longs;a &longs;int pondera <lb/>HI KL. <!-- KEEP S--></s>
            <s id="s.000525">Cur igitur &longs;eruata permutatim brachiorum &amp; <lb/>ponderum proportione fiat &aelig;quilibrium, ex his qu&aelig; de&shy;<lb/>mon&longs;trauimus, clar&egrave; patet. </s>
          </p>
          <p type="main">
            <s id="s.000526">Sed forte dicet qui&longs;piam, &longs;i brachia, pondera &longs;unt, <lb/>vel ponderibus &aelig;quipollentia, &longs;u&longs;tinenti duplicabitur <lb/>pondus. </s>
          </p>
          <figure id="id.007.01.059.1.jpg" xlink:href="007/01/059/1.jpg"/>
          <p type="main">
            <s id="s.000527">E&longs;to enim vectis AB, <lb/>ita diui&longs;us in C, vt pars <lb/>maior CB minori AC &longs;it <lb/>in proportione quintu&shy;<lb/>pla. </s>
            <s id="s.000528">Appendatur autem <lb/>in A pondus D, <expan abbr="quintupl&umacr;">quintuplum</expan> <lb/>ponderi E appen&longs;o in B. <!-- KEEP S--></s>
            <s id="s.000529">Si <lb/>igitur brachio AC, quod <lb/>e&longs;t vnum, ad datur pondus <lb/>D, quod e&longs;t quinque, fient &longs;ex, item &longs;i brachio CB, quod <lb/>e&longs;t quinque, addatur pondus E, quod e&longs;t vnum, fient &longs;ex. <lb/></s>
            <s id="s.000530">Fulcimentum igitur &longs;u&longs;tinebit duodecim, quod e&longs;t ab&shy;<lb/>&longs;urdum ex ijs qu&aelig; clar&egrave; demon&longs;trauit G. Vbald. <!-- REMOVE S-->in Me&shy;<lb/>chan. <!-- REMOVE S-->tractatu de Libra propo&longs;. </s>
            <s id="s.000531">5. His re&longs;pondemus, bra&shy;<lb/>chia quidem operari non pondere, &longs;ed potenti&acirc;, qu&aelig; vis <lb/>qu&aelig;dam e&longs;t, non autem pondus. </s>
            <s id="s.000532">Et&longs;i &amp; illud verum &longs;it, da&shy;<lb/>to vecte pondero&longs;o, fulcimentum rum ponderum appen&shy;<lb/>&longs;orum, tum vectis ip&longs;ius pondus &longs;u&longs;tinere. </s>
          </p>
          <p type="main">
            <s id="s.000533">Iacta huiu&longs;cemodi, quam diximus, &aelig;qualitate, &longs;e-<pb xlink:href="007/01/060.jpg"/>quitur nece&longs;&longs;ari&ograve;, centrum grauitatis ip&longs;ius vectis cum <lb/>appen&longs;is ponderibus, ac &longs;i vnum idemqueue e&longs;&longs;et corpus <lb/>cadere in perpendiculari qu&aelig; per centrum ip&longs;um &amp; ful&shy;<lb/>cimentum tran&longs;iens ad mundi centrum pertingit. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000534">QV&AElig;STIO IV.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000535"><emph type="italics"/>Qu&aelig;rit hic Ari&longs;toteles, cur ij qui in nauis medio &longs;unt remiges ma&shy;<lb/>xim&egrave; nauem moueant?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000536">Ait, ideo forta&longs;&longs;e fieri, qu&ograve;d remus vectis &longs;it, fulcimen&shy;<lb/>tum ver&ograve; &longs;calmus, &longs;tat enim. </s>
            <s id="s.000537">Pondus autem mare i&shy;<lb/>p&longs;um, quod &agrave; remo propellitur, mouens ver&ograve; ip&longs;um remi&shy;<lb/>gem, &longs;emper autem plus mouere ponderis qui mouet, <lb/>quo magis di&longs;tat&agrave; fulcimento. </s>
            <s id="s.000538">Ita enim maiorem fieri <lb/>qu&aelig; ex centro; Scalmum ver&ograve; centrum e&longs;&longs;e. </s>
            <s id="s.000539">C&aelig;ter&ugrave;m in <lb/>medio nauis plurimum remi intus e&longs;&longs;e. </s>
            <s id="s.000540">Ibi enim nauem <lb/>e&longs;&longs;e lati&longs;&longs;imam. </s>
            <s id="s.000541">Moueri autem nauim, quoniam <expan abbr="appell&emacr;-te">appellen&shy;<lb/>te</expan> mari remo, <expan abbr="extrem&umacr;">extremum</expan> illius quod intus e&longs;t anterius pro&shy;<lb/>mouetur, cuius motum nauis &longs;equitur, cui &longs;calmus alliga&shy;<lb/>tur. </s>
            <s id="s.000542">Vbi autem plurimum maris diuidit remus, eo maxim&egrave; <lb/>nece&longs;&longs;e e&longs;&longs;e propelli. </s>
            <s id="s.000543">Plurimum autem diuidi vbi plurima <lb/>pars remi &agrave; &longs;calmo e&longs;t. </s>
            <s id="s.000544">Rem facilem, eo quod verbis potu&shy;<lb/>erit, &longs;chemate non declarauit, nos autem apponemus. </s>
          </p>
          <figure id="id.007.01.060.1.jpg" xlink:href="007/01/060/1.jpg"/>
          <p type="main">
            <s id="s.000545">E&longs;to enim nauis AB, mare CD, <lb/>remorum alter, qui ad proram EF, cu&shy;<lb/>ius &longs;calmus G, alter ver&ograve; in medio na&shy;<lb/>uis, HI, circa &longs;calmum K. <!-- KEEP S--></s>
            <s id="s.000546">Ait igitur, <lb/>remos e&longs;&longs;e vectes, &longs;calmos ver&ograve; fulci&shy;<lb/>menta, pondus quod remo, ceu vecte, <lb/>mouetur mare ip&longs;um. </s>
            <s id="s.000547">Itaque quoniam <lb/>nauis lata e&longs;t in medio vbi Scalmus K <lb/>maior pars KH intra nauim e&longs;t, minor <lb/>ver&ograve; KI, extra. </s>
            <s id="s.000548">Contra autem remi ad <lb/>proram, nempe EF pars minor EG <pb xlink:href="007/01/061.jpg"/>intra nauim, pars ver&ograve; maior GF extra nauim e&longs;t. </s>
            <s id="s.000549">Pondus <lb/>autem e&ograve; facili&ugrave;s mouetur, quo maior e&longs;t vectis pars, qu&aelig; <lb/>&agrave; fulcimento e&longs;t ad mouentem potentiam. </s>
          </p>
          <p type="main">
            <s id="s.000550">Acut&egrave; &longs;an&egrave; Philo&longs;ophus. <!-- KEEP S--></s>
            <s id="s.000551">Ego autem &longs;i per mode&longs;tiam <lb/>liceret, dicerem, non quidem e&longs;&longs;e fulcimentum <expan abbr="&longs;calm&umacr;">&longs;calmum</expan>, <lb/>&longs;ed mare ip&longs;um, pondus vero nauim, ad locum &longs;calmi, <expan abbr="n&emacr;-pe">nem&shy;<lb/>pe</expan> inter mouentem potentiam, &amp; fulcimentum po&longs;itum, <lb/>etenim &amp; eo pacto po&longs;&longs;umus vti vecte, quod ob&longs;eruat &amp; <lb/>demon&longs;trat G. <!-- REMOVE S-->Vbaldus tractatu de vecte propo&longs;. </s>
            <s id="s.000552">2. Erunt <lb/>igitur in de&longs;cripta figura puncta FI, qu&aelig; in mari &longs;unt, ful&shy;<lb/>cimenta, quibus remorum extrema in ip&longs;a impul&longs;ione ni&shy;<lb/>tuntur, pondera ver&ograve; &longs;eu pondus pluribus vectibus &amp; po&shy;<lb/>tentijs impul&longs;um nauis ip&longs;a, qu&aelig; &longs;calmis e&longs;t annexa. </s>
            <s id="s.000553">Re&longs;i&shy;<lb/>&longs;tente igitur mari, cedente autem impul&longs;ionibus &longs;calmo, <lb/>nauis eo transfertur, quo &longs;calmi ab ip&longs;a potentia mouen&shy;<lb/>te in anteriorem partem pelluntur. </s>
            <s id="s.000554">quoniam autem vt <lb/>FG ad FE ita potentia mouens in E ad pondus motum <lb/>in G. item vt IK ad IH ita potentia mouens in H ad pon&shy;<lb/>dus motum in K, maior autem e&longs;t proportio FG ad FE <lb/>qu&agrave;m proportio IK ad IH. </s>
            <s id="s.000555">Maiori indiget potentia vt <lb/>pellatur pondus in G qu&agrave;m pondus in K. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000556">H&aelig;c cert&egrave; vti diximus ita &longs;e habent. </s>
            <s id="s.000557">Philo&longs;ophi au&shy;<lb/>tem ratio tunc procederet, &longs;i &longs;tante naui immobili, vt fit <lb/>vbi &agrave; Remor&aelig; occulta vi aut ab alio impedimento reti&shy;<lb/>netur, remiges in ip&longs;o remigandi actu mare pul&longs;arent, <lb/>Tunc enim ver&egrave; &longs;calmus fieret fulcimentum, mare autem <lb/>pondus, remex ver&ograve; ip&longs;e mouens. </s>
          </p>
          <p type="main">
            <s id="s.000558">Addimus, fal&longs;um videri quod a&longs;&longs;erit Ari&longs;toteles, <lb/>nempe illos qui in media naui &longs;unt, remiges, maxim&egrave; na&shy;<lb/>uim mouere; facilius, melius dixi&longs;&longs;et. </s>
            <s id="s.000559">Si enim maxim&egrave;, <lb/>quod ait, denotat, maximo &longs;patio, &amp; velocius pror&longs;us fal&shy;<lb/>&longs;um, etenim tardius mouent &amp; minori &longs;patio, quod nos i&shy;<lb/>ta demon&longs;tramus. </s>
          </p>
          <pb xlink:href="007/01/062.jpg"/>
          <figure id="id.007.01.062.1.jpg" xlink:href="007/01/062/1.jpg"/>
          <p type="main">
            <s id="s.000560">E&longs;to enim Remus AB <lb/>qui mar&iacute; fulcitur in B, Scal&shy;<lb/>mus remi qui ad <expan abbr="pror&atilde;">proram</expan> pup&shy;<lb/>pimue C, qui in media naui <lb/>D, maior autem remi pars <lb/>e&longs;t &agrave; &longs;calmo Dad A quam i&shy;<lb/>p&longs;ius C 2d A, Pellantur remi &amp; &longs;tante ceu centro BA, in <lb/>E. eodem igitur tempore C eritin F, &amp; D in G, &longs;ed maius <lb/>e&longs;t &longs;patium CF &longs;patio DG, Ergo vnica impul&longs;ione, plus <lb/>mouit &longs;calmum, hoc e&longs;t, nauim, potentia ad puppim pro&shy;<lb/>ramue remigans, qu&agrave;m ea qu&aelig; operatur in media naui vt <lb/>&longs;entire videbatur &lpar;&longs;i modo is e&longs;t eius &longs;en&longs;us&rpar; Ari&longs;toteles. <lb/><!-- KEEP S--></s>
            <s id="s.000561">Nece&longs;&longs;arium igitur e&longs;t, quod ait, maxim&egrave; intelligendum, <lb/>facili&ugrave;s, Veritatem hanc cogno&longs;centes Triremium pr&aelig;&shy;<lb/>fecti robu&longs;tiores quidem remiges ad proram &amp; puppim, <lb/>inualidiores ver&ograve; circa mediam triremem collocant. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000562">QV&AElig;STIO V.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000563"><emph type="italics"/>Dubitatur, Cur paruum exi&longs;tens gubernaculum, &amp; in extremo <lb/>nauigio tantas habeat vires, vt ab exiguo temone, &amp; ab hominis <lb/>vnius viribus alioqui modic&egrave; vtentis magn&aelig; nauigiorum <lb/>moueantur moles?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000564">AN, inquit, quoniam gubernaculum vectis e&longs;t, onus <lb/>autem mare, Gubernator vero mouens e&longs;t? </s>
            <s id="s.000565">Non au&shy;<lb/>tem &longs;ecund&ugrave;m latitudinem veluti remus, mare accipit <lb/>gubernaculum; non enim in ante nauigium mouet, &longs;ed i&shy;<lb/>p&longs;um commotum mare accipiens inclinat obliqu&egrave;. </s>
            <s id="s.000566">quo&shy;<lb/>niam enim pondus e&longs;t mare contrario innixum modo na&shy;<lb/>uem inclinat. </s>
            <s id="s.000567">fulcimentum enim in contrarium ver&longs;atur, <lb/>mare vet&ograve; interius, &amp; illud exterius. </s>
            <s id="s.000568">illud autem &longs;equitur <lb/>nauis qu&aelig; illi e&longs;t alligata &amp; remus quidem &longs;ecundum la&shy;<lb/>titudinem onus propellens &amp; ab eodem repul&longs;us in re-<pb xlink:href="007/01/063.jpg"/>ctum propellit, Gubernaculum ver&ograve;, vt obliquum iacet <lb/>hinc inde in obliquum motionem facit. </s>
            <s id="s.000569">in extremo <expan abbr="aut&emacr;">autem</expan>, <lb/>non in medio iacet, quoniam mouenti facillimum e&longs;t mo&shy;<lb/>tum mouere: prima enim pars celerrim&egrave; fertur, &amp; quo&shy;<lb/>niam, quemadmodum in ijs qu&aelig; feruntur in fine deficit <lb/>latio, &longs;ic ip&longs;ius continui in finem, imbecillima e&longs;t latio. <lb/></s>
            <s id="s.000570">Imbecillima autem ad expellendum e&longs;t facilis. </s>
            <s id="s.000571">Propter <lb/>h&aelig;c igitur in puppi gubernaculum ponitur, nec minus, <lb/>quoniam parua ibi motione facta, multo maior fit in vlti&shy;<lb/>mo, quia &aelig;qualis angulus &longs;emper maiorem ad&longs;pectat, <expan abbr="t&atilde;-to">tan&shy;<lb/>to</expan> queue magis, quanto maiores fuerint ill&aelig;, qu&aelig; continent. <lb/></s>
            <s id="s.000572">Ex ijs etiam manife&longs;tum e&longs;t, quam ob cau&longs;&longs;am magis in <lb/>contrarium procedit nauigium, quam remi ip&longs;ius palmu&shy;<lb/>la, eadem enim magnitudo ij&longs;dem mota viribus in a&euml;re <lb/>plus qu&agrave;m in aqua progreditur. </s>
            <s id="s.000573">H&aelig;c Philo&longs;ophus, qui <lb/>haudquaquam ex more &longs;uo, quod duobus fer&egrave; poterat, <lb/>&longs;excentis verbis expo&longs;uit. </s>
            <s id="s.000574">Licebat enim id tantum dicere, <lb/>Gubernaculum &lpar;ita vocat id totum quod gubernaculo &amp; <lb/>temone con&longs;tat&rpar; e&longs;&longs;e ceu remum, quo nauis non antror&shy;<lb/>&longs;um, &longs;ed obliqu&egrave; &amp; ad latus mouetur. </s>
            <s id="s.000575">quamobrem omnia <lb/>fer&egrave; qu&aelig; de Temone dicenda fuerant, de remo loquens <lb/>proponit. </s>
            <s id="s.000576">Ait autem. <!-- KEEP S--></s>
          </p>
          <figure id="id.007.01.063.1.jpg" xlink:href="007/01/063/1.jpg"/>
          <p type="main">
            <s id="s.000577">Sit remus AB, <lb/>&longs;calmus vero C, remi <lb/>in nauigio <expan abbr="principi&umacr;">principium</expan> <lb/>A, palmula autem, <lb/>qu&aelig; in mari B. <!-- KEEP S--></s>
            <s id="s.000578">Si igi&shy;<lb/>tur A, vbi D transla&shy;<lb/>tum e&longs;t, non erit B v&shy;<lb/>bi E. &aelig;qualis enim, <lb/>BE ip&longs;i AD, &aelig;quale <lb/>igitur translatum erit, &longs;ed erat minus. </s>
            <s id="s.000579">erit igitur vbi F, mi&shy;<lb/>nor enim BF, ip&longs;a AD, quare ip&longs;o GF ip&longs;a DG. <!-- KEEP S--></s>
            <s id="s.000580">H&aelig;c <pb xlink:href="007/01/064.jpg"/>demon&longs;tratio licet vera videatur, rei ta men, de qua e&longs;t <lb/>&longs;ermo, minim&egrave; aptatur. </s>
            <s id="s.000581">Si enim aptaretur in ip&longs;ius remi <lb/>motu, cum palmula e&longs;&longs;et in F, &longs;calmus fieret in G, excur&shy;<lb/>reret ergo vel &longs;calmus per remum, vel remus per <expan abbr="&longs;calm&umacr;">&longs;calmum</expan>, <lb/>facta nempe eiu&longs;modi translatione de C in G, &amp; &longs;ic intra <lb/>nauim modo e&longs;&longs;et pars remi DC, mod&ograve; ver&ograve; GD, quod <lb/>tamen non fieri ips&acirc; experientia docemur. </s>
            <s id="s.000582">Illud quoque <lb/>fal&longs;um e&longs;t, nauim ip&longs;am tantum moueri in a&euml;re, quantum <lb/>e&longs;t &longs;patium AD, hoc e&longs;t, remi extremum quod e&longs;t in naui, <lb/>&longs;iquidem &longs;calmi motu, non autem manubrij remi, nauis <lb/>agatur. </s>
            <s id="s.000583">Aliter igitur res &longs;e habet, &amp; forte hoc pacto. </s>
          </p>
          <figure id="id.007.01.064.1.jpg" xlink:href="007/01/064/1.jpg"/>
          <p type="main">
            <s id="s.000584">Sit remus AB, cu&iacute;us <lb/>manubrium A, palmula <lb/>B, &longs;calmus C. <!-- KEEP S--></s>
            <s id="s.000585">Pellatur an&shy;<lb/>tror&longs;us A, fiatque; in D, tunc <lb/>&longs;i &aelig;qualiter mouerentur <lb/>manubrium &amp; palmula, i&shy;<lb/>p&longs;a palmula fieret in G, at <lb/>minus mouetur: fiet ergo <lb/>in E. ip&longs;e ver&ograve; &longs;calmus C <lb/>translatus erit in F, motaque; erit nauis &agrave; C in F, non autem <lb/>ab A in D. <!-- KEEP S--></s>
            <s id="s.000586">Po&longs;uit autem Ari&longs;toteles &longs;calmum ad medium <lb/>remi, &longs;ed non ad medium collocari &longs;olet, maior enim pars <lb/>in mare propendet puta HB, quo ca&longs;u translationis &longs;pa&shy;<lb/>tium fit maius, nempe ab H in I. fit autem motus &longs;calmi ex <lb/>centris qui &longs;unt in &longs;patio ip&longs;o BE, quatenus autem ad te&shy;<lb/>monem pertinet, quem remum ait, obliqu&egrave; puppim ip&longs;am <lb/>propellentem, ita &longs;e res habet. </s>
          </p>
          <p type="main">
            <s id="s.000587">E&longs;to nauis carina AB, prora A, puppis B, Temonis <lb/>ala BC, gubernaculum BD, cardo ver&ograve; fulcimentumue <lb/>B; facta itaque impul&longs;ione obliqu&acirc; gubernaculi &agrave; D in E, <lb/>minor fiet motus in mari &agrave; C in F, eritqueue temo vbi EGF, <pb xlink:href="007/01/065.jpg"/><figure id="id.007.01.065.1.jpg" xlink:href="007/01/065/1.jpg"/><lb/>cardo ver&ograve; vbi G, translata igitur e&shy;<lb/>rit eo motu, puppis ip&longs;a &agrave; B in G. facta <lb/>itaque paru&acirc; motione puppis ex B in <lb/>G, prora ip&longs;a qu&aelig; long&egrave; di&longs;tat &agrave; pup&shy;<lb/>pi B maiori &longs;patio &longs;uperato translata <lb/>erit in H facta pror&aelig; in contrariam <lb/>partem ab ea qu&aelig; facta e&longs;t guberna&shy;<lb/>culi motione. </s>
            <s id="s.000588">Porr&ograve; quod &amp; in pr&aelig;&shy;<lb/>cedente qu&aelig;&longs;tione adnotauimus, <expan abbr="l&omacr;-g&egrave;">lon&shy;<lb/>g&egrave;</expan> meli&ugrave;s procedet demon&longs;tratio &longs;i <lb/><expan abbr="fulciment&umacr;">fulcimentum</expan> mare intelligatur, qu&agrave;m <lb/>&longs;calmus, neque enim mare ceu pon&shy;<lb/>dus, &longs;ed &longs;calmus ip&longs;e Temonisuecardo, ponderum in&longs;tar <lb/>transferuntur. </s>
          </p>
          <p type="main">
            <s id="s.000589">C&aelig;ter&ugrave;m in hac &longs;peculatione liceat nobis aliquan&shy;<lb/>tulum &agrave; Philo&longs;opho di&longs;&longs;entire. </s>
            <s id="s.000590">Cert&egrave; &longs;i breuitas Temo&shy;<lb/>nis, &egrave; puppi eminentis, re&longs;pectu longitudinis totius nauis <lb/>con&longs;ideretur, &amp; parua motio, qu&aelig; temone guberna culo&shy;<lb/>ue moto fit, nullius fer&egrave; momenti erit ad eam qu&aelig; in pro. <lb/></s>
            <s id="s.000591">ra fit translationem. </s>
            <s id="s.000592">aliter ergo &longs;e rem habere non dubi&shy;<lb/>tamus, &amp; qu&aelig;&longs;tionis &longs;olutionem aliunde petendam. </s>
            <s id="s.000593">Na&shy;<lb/>ui non currente nullum fer&egrave;, aut qui vix curandus &longs;it ex <lb/>gubernaculi conuer&longs;ione nauis ad dextram &longs;ini&longs;tramue <lb/>motum fieri. </s>
            <s id="s.000594">at e&acirc; currente maximum, experienti&acirc; doce&shy;<lb/>mur. </s>
            <s id="s.000595">Obliqui igitur motus qui valid&egrave; in puppi &longs;it, cau&longs;&longs;a <lb/>e&longs;t non quidem ex conuer&longs;ione temonis percu&longs;&longs;io maris, <lb/>&longs;ed mare ip&longs;um, cuius fluctus naui currente obliquam te&shy;<lb/>monis alam ad eam partem qu&aelig; mari obuertitur, impel&shy;<lb/>lentes temonem cum puppi ad contrariam partem vali&shy;<lb/>di&longs;&longs;im&egrave; transferunt. </s>
          </p>
          <p type="main">
            <s id="s.000596">E&longs;to nauis carina AB, prora B, puppis A, Temo AC, <lb/>gubernaculum AD; Itaque currente naui, Temone in&shy;<lb/>terim &amp; guberna culo in eadem carin&aelig; linea exi&longs;tentibus, <pb xlink:href="007/01/066.jpg"/><figure id="id.007.01.066.1.jpg" xlink:href="007/01/066/1.jpg"/><lb/>Temo quidem mare &longs;ecat, nulla fa&shy;<lb/>ct&acirc; in puppi, nauis ad &longs;ini&longs;tram dex&shy;<lb/>tramue translatione. </s>
            <s id="s.000597">Si ver&ograve; mouea&shy;<lb/>tur gubernaculum &agrave; D in E, eo moto <lb/>mouebitur aliquantulum &amp; puppis <lb/>ad partes E, quod voluit Ari&longs;toteles. <lb/><!-- KEEP S--></s>
            <s id="s.000598">Sed minimi, vt diximus, ea res ad tan&shy;<lb/>tum effectum e&longs;t momenti. </s>
            <s id="s.000599">Temone <lb/>autem in obliquum <expan abbr="c&omacr;&longs;tituto">con&longs;tituto</expan> vt AF, <lb/>naui interim, ventorum aut remorum <lb/>vi pul&longs;a proram ver&longs;us currente te&shy;<lb/>monis latus &agrave; fluctibus obliquam par&shy;<lb/>tem alamue in ip&longs;o cur&longs;u ferientibus, <lb/>in contrariam partem transfertur, ad <lb/>eam nempe, ad quam ip&longs;um gubernaculum vergit. </s>
            <s id="s.000600">facta i&shy;<lb/>gitur nauis ceu circa centrum centraue qu&aelig; in carina in&shy;<lb/>ter puppim proramue con&longs;iderantur A, fertur in G, prora <lb/>ver&ograve; in H. ex quibus manife&longs;t&egrave; apparet, duo ad nauis ex <lb/>temone in puppi conuer&longs;ione motionem e&longs;&longs;e ne ce&longs;&longs;aria; <lb/>Temonis nempe obliquationem, &amp; nauis cur&longs;um, <expan abbr="quor&umacr;">quorum</expan> <lb/>&longs;i alterum &longs;ine altero adhibeatur, nullam fieri qu&aelig; alicu&shy;<lb/>ius momenti &longs;it, nauis conuer&longs;ionem. </s>
            <s id="s.000601">Illud quoque nota&shy;<lb/>mus, carinam in nauis conuer&longs;ione vectis in&longs;tar &longs;e habere, <lb/>cuius pars mota ad puppim, &amp; mouens potentia e&longs;t; fulci&shy;<lb/>mentum ver&ograve; circa proram, potentia autem mouens ma&shy;<lb/>re ip&longs;um, temonem in nauis cur&longs;u oblique feriens. </s>
            <s id="s.000602">Vnde <lb/>colligimus naues, quo longiores &longs;unt in mouente ad Te&shy;<lb/>monem adhibita maiori facilitate ad dextram &longs;ini&longs;tram&shy;<lb/>ue propelli: quod &longs;an&egrave; ip&longs;emet con&longs;iderauit Ari&longs;toteles, <lb/>qu&igrave; idcirco inquit, in extremo, non autem in medio temo&shy;<lb/>nem poni eo quod mouenti facilimum &longs;it ab extremo <lb/>motum mouere. </s>
          </p>
          <p type="main">
            <s id="s.000603">Ex hac no&longs;tr&acirc; &longs;peculatione ratio habetur eius ma-<pb xlink:href="007/01/067.jpg"/>chinationis, qu&acirc; in magnis fluminibus, ceu Pado, Abdua <lb/>&amp; &longs;imilibus, Portitores, equos, currus, viatore&longs;que; ip&longs;os, &egrave; <lb/>ripa in ripam transferunt. </s>
            <s id="s.000604">Pulcherrima enim res e&longs;t, &amp; <lb/>nobis per&longs;pecti&longs;&longs;ima, qui Gua&longs;tall&acirc; re&longs;identi&aelig; olim no&shy;<lb/>&longs;tr&aelig; oppido ad Padum, Mantuam pergentes &longs;&aelig;pi&longs;&longs;im&egrave; ad <lb/>Ca&longs;trum Borgi Iu&longs;is ea qua diximus machinatione lati&longs;&shy;<lb/>&longs;imum eiu&longs;dem Padi aluum tran&longs;iecimus. </s>
            <s id="s.000605">Habet autem <lb/>&longs;e hoc pacto. </s>
          </p>
          <figure id="id.007.01.067.1.jpg" xlink:href="007/01/067/1.jpg"/>
          <p type="main">
            <s id="s.000606">E&longs;to fluminis citerior <lb/>ripa AB, vlterior CD. <!-- KEEP S--></s>
            <s id="s.000607">Pon&shy;<lb/>tones duo tabulis &longs;trati, &amp; v&shy;<lb/>n&agrave; firmiter juncti EF, Temo <lb/>inter eorum puppes extans <lb/>GH, locus in ripa &longs;tabilis A, <lb/>funis, quo pontones, &amp; ma&shy;<lb/>china tota continetur AI. <lb/>fluuij decur&longs;us ver&longs;us BD, <lb/>&longs;tantibus itaque pontonibus <lb/>ad ripam citeriorem AB, Te&shy;<lb/>mone in <expan abbr="neutr&atilde;">neutram</expan> partem pul&shy;<lb/>&longs;o, cum aqua decurrens eum <lb/>re&longs;i&longs;tentem non inueniat, <lb/>&longs;cinditur quidem ab eo, &longs;ed <lb/>non propellit, eo autem con&shy;<lb/>uer&longs;o &amp; in GK con&longs;tituto, a&shy;<lb/>la eius GK ab aqua defluente propul&longs;a machinam &longs;ecum <lb/>trahit ver&longs;us ripam CD, fact&acirc; motione circa centrum &longs;eu <lb/>&longs;tabilem locum A, otio&longs;is interim portitoribus, donec per <lb/>circuli portionem ML deuenerit ad vlteriorem ripam in <lb/>L. <!-- KEEP S--></s>
            <s id="s.000608">Vnde iterum temone in contrariam partem conuer&longs;o, <lb/>aqu&acirc; &longs;imiliter temonem propellente, per eandem circuli <lb/>portionem ad ripam citeriorem reuertitur, &agrave; qua paullo <lb/>ant&egrave; di&longs;ce&longs;&longs;erat. </s>
            <s id="s.000609">Ex quibus apparet, motus cau&longs;&longs;am non <pb xlink:href="007/01/068.jpg"/>e&longs;&longs;e &longs;olam cam, qu&aelig; ab ala temonis fit, aqu&aelig; <expan abbr="percu&longs;&longs;ion&emacr;">percu&longs;&longs;ionem</expan>, <lb/>vt &longs;en&longs;erat Ari&longs;toteles, &longs;ed currentis a qu&aelig; temonis alam <lb/>ferientis impul&longs;ionem: nihil autem referre, vtrum &longs;tante <lb/>naui a qua currat, vel c&acirc; currente a qua &longs;tet, vt in mari fit, <lb/>idem enim vtroque modo temo patitur. </s>
            <s id="s.000610">Vt autem machi&shy;<lb/>n&aelig; huius &amp; totius negotij &longs;pecies facilius animo concipia&shy;<lb/>tur, &longs;chema hoc &longs;tudio&longs;orum oculis &longs;ubijciemus. </s>
          </p>
          <figure id="id.007.01.068.1.jpg" xlink:href="007/01/068/1.jpg"/>
          <p type="main">
            <s id="s.000611">Lembi nauicul&aelig;ue ideo appo&longs;it&aelig; &longs;unt, vt oblongum <lb/>funem &longs;u&longs;tineant; id etenim n&icirc; fieret, aqu&aelig; immer&longs;us a&shy;<lb/>quam &longs;cindens machin&aelig; motum impediret, ideo etiam <lb/>apponuntur, ne funis madens celeriter maceretur &amp; pu&shy;<lb/>tre&longs;cat. </s>
          </p>
          <p type="main">
            <s id="s.000612">Huic &longs;peculationi affinis e&longs;t ea, velorum eorum, <lb/>qu&aelig; obliqu&egrave; ventum, excipientia frumentarijs molis <lb/>dant motum, item verticillorum ex papyro, quibus con&shy;<lb/>tra ventum currentes per lu&longs;um pueri vtuntur. </s>
            <s id="s.000613">vnicum <pb xlink:href="007/01/069.jpg"/>enim horum omnium principium, &amp; eadem, ratio. </s>
          </p>
          <p type="main">
            <s id="s.000614">Diximus enim, Temonem currente naui, lateraliter <lb/>conuer&longs;um obuios fluctus excipientem puppim ip&longs;am ob&shy;<lb/>liqu&egrave; in alteram partem transferre. </s>
            <s id="s.000615">Porr&ograve; ea vela, de qui&shy;<lb/>bus loquimur, ventorum flatibus obliqu&egrave; oppo&longs;ita ean&shy;<lb/>dem ob cau&longs;&longs;am circulariter agitantur, quod vt figur&acirc; eui&shy;<lb/>dentius fiat, </s>
          </p>
          <figure id="id.007.01.069.1.jpg" xlink:href="007/01/069/1.jpg"/>
          <p type="main">
            <s id="s.000616">E&longs;to velum AB, brachio <lb/>CE obliqu&egrave; affixum, ita vt <lb/>angulus ACE maior &longs;it an&shy;<lb/>gulo BCE, ventus obliqu&egrave; <lb/>velum feriens FG. <expan abbr="Itaq;">Itaque</expan> quo&shy;<lb/>niam ventus in velum obli&shy;<lb/>quum incidit, elabitur velum, <lb/>&amp; circa centrum E vn&agrave; cum <lb/>brachio circumuertitur, in <lb/>cuius locum &longs;uccedit velum <lb/>HI, ex qua a&longs;&longs;idua velorum <lb/>&longs;ucce&longs;&longs;ione, brachiorum &amp; a&shy;<lb/>xis cui adh&aelig;rent, rotatio fit <lb/>perpetua. </s>
            <s id="s.000617">Sed enim de Te&shy;<lb/>mone agentes non e&longs;t interim cur de caudis auium pi&longs;ci&shy;<lb/>umque taceamus, in&longs;tar enim remonum &longs;unt &agrave; Natura i&shy;<lb/>p&longs;a opportunis animalium partibus, po&longs;tremis videlicet, <lb/>appo&longs;iti, quanquam nec &longs;olum Temonis v&longs;um pr&aelig;&longs;tent, <lb/>vt videbimus. </s>
          </p>
          <p type="main">
            <s id="s.000618">E&longs;to pi&longs;cis AB, cuius caput A, cauda ver&ograve; CB. <!-- KEEP S--></s>
            <s id="s.000619">Hac <lb/>igitur neutram in partem reflex&acirc;, pi&longs;cis pinnarum motu <lb/>rect&acirc; in anteriorem partem progreditur. </s>
            <s id="s.000620">Si autem nece&longs;&shy;<lb/>&longs;e ei fuerit ad dextram &longs;ini&longs;tramqueue conuerti non pote&shy;<lb/>rit, ni&longs;i cauda ip&longs;a iuuetur. </s>
            <s id="s.000621">Omnis enim motus progre&longs;&longs;i&shy;<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb xlink:href="007/01/070.jpg"/><figure id="id.007.01.070.1.jpg" xlink:href="007/01/070/1.jpg"/><lb/>pote&longs;t, quod in libris de ani&shy;<lb/>malium ince&longs;&longs;u docet ip&longs;e&shy;<lb/>met Philo&longs;ophus. <!-- KEEP S--></s>
            <s id="s.000622">Sit igitur, <lb/>pi&longs;cem conuerti velle, &amp; fie&shy;<lb/>ri capite in D, deflectet illi&shy;<lb/>co caudam in E, caque; aquam <lb/>ceu &longs;tabile quippiam <expan abbr="feri&emacr;s">feriens</expan> <lb/>eiqueue quoddammodo fultus, <lb/>reliquum corpus CA refle&shy;<lb/>ctet in D, &longs;i autem conuerti <lb/>velit in F, caudam deflectet in G, &amp; eadem ratione flecte&shy;<lb/>tur in F. <!-- KEEP S--></s>
            <s id="s.000623">Sed &amp; Temonis quoque v&longs;um pr&aelig;&longs;tat natatili&shy;<lb/>bus &amp; volatilibus cauda. </s>
            <s id="s.000624">Sit enim rectus pi&longs;cis, hoc e&longs;t, re&shy;<lb/>ct&acirc; pergens IKL, caudam obliquet in KM itaque ex a&shy;<lb/>qu&aelig; in ip&longs;o motu colli&longs;ione, eius po&longs;teriora pellentur vbi <lb/>INO. </s>
            <s id="s.000625">H&aelig;c itaque nos de Temone, quatenus ad hanc <lb/>qu&aelig;&longs;tionem pertinet, con&longs;idera&longs;&longs;e &longs;it &longs;atis. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000626">QV&AElig;STIO VI.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000627"><emph type="italics"/>Dubitatur, Cur quanto Antenna &longs;ublimior fuerit, &yuml;&longs;dem velis, &amp; <lb/>vento eodem celeri&ugrave;s ferantur nauigia?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000628">Soluit Philo&longs;ophus, inquiens: An quia malus quidem <lb/>&longs;it vectis, fulcimentum ver&ograve; mali &longs;edes, in qua colloca&shy;<lb/>tur, pondus autem quod moueri debet, ip&longs;um nauigium: <lb/>mouens ver&ograve; is, qui vela tendit &longs;piritus? </s>
            <s id="s.000629">Si igitur quanto <lb/>remotior fuerit fulcimentum facilius eadem potentia, &amp; <lb/>citi&ugrave;s idem mouet pondus, altius cert&egrave; &longs;ublat&acirc; antenn&acirc;, <lb/>velum &agrave; mali &longs;ede, quae fulcimentum e&longs;t remotius faciens, <lb/>id efficiet. </s>
            <s id="s.000630">H&aelig;c ille. <!-- KEEP S--></s>
            <s id="s.000631">qu&aelig; &longs;ic figur&acirc; explicamus. </s>
          </p>
          <pb xlink:href="007/01/071.jpg"/>
          <figure id="id.007.01.071.1.jpg" xlink:href="007/01/071/1.jpg"/>
          <p type="main">
            <s id="s.000632">E&longs;to nauis AB, malus CD, <lb/>mali &longs;edes D, locus antenn&aelig; <lb/>&longs;ublimior C, depre&longs;&longs;ior E: ita&shy;<lb/>que quoniam CD vectis e&longs;t, <lb/>quo mouens remotior fuerit &agrave; <lb/>fulcimento D, eo citi&ugrave;s &amp; vio&shy;<lb/>lenti&ugrave;s pellet, velocius ergo <lb/>nauis mouebitur antenna in <lb/>C, qu&agrave;m in E, con&longs;tituta. </s>
          </p>
          <p type="main">
            <s id="s.000633">Plau&longs;ibilia &longs;unt h&aelig;c, at cert&egrave; per veritatem ip&longs;am, <lb/>non vera. </s>
            <s id="s.000634">Rogo, Si fulcimentum dum vectis mouetur, <expan abbr="c&emacr;-trum">cen&shy;<lb/>trum</expan> e&longs;t, centrum vtique motus erit D. &longs;pirante igitur va&shy;<lb/>lid&egrave; vento inclinabitur malus, fietque; vbi FGD, qu&aelig; qui&shy;<lb/>dem inclinatio violentius fiet, vento pellente in F qu&agrave;m <lb/>in G, vtpote puncto &agrave; fulcimento remotiore. </s>
            <s id="s.000635">Impul&longs;o ma&shy;<lb/>lo, duo nece&longs;&longs;ari&ograve; <expan abbr="c&omacr;&longs;equentur">con&longs;equentur</expan>, vel enim ad ip&longs;am &longs;edem <lb/>D. frangetur vel puppis ip&longs;a circa D punctum conuer&longs;a, <lb/>vt mali &longs;equatur motum eleuabitur. </s>
            <s id="s.000636">Prora ver&ograve; &longs;ubmer&shy;<lb/>getur facta naui in HDI. </s>
            <s id="s.000637">Quod &longs;i qui&longs;piam funem ad ma&shy;<lb/>li &longs;ummitatem annexam ad ip&longs;am puppim alligauerit in <lb/>B, impedietur &longs;an&egrave; mali inclinatio ad partes F, &amp; ideo nul&shy;<lb/>la vis pror&longs;us fiet in D ex vectis ratione. </s>
            <s id="s.000638">Attamen nihilo <lb/>&longs;ecius, quo &longs;ublimior fuerit antenna, eo facili&ugrave;s &agrave; &longs;pirante <lb/>vento puppis eleuabitur. </s>
            <s id="s.000639">quatenus igitur malus vectis <lb/>e&longs;t, hoc tantum quod dicimus operatur. </s>
            <s id="s.000640">Quod &longs;i contr&agrave; <lb/>obiectum fuerit, experientiam docere, quo &longs;ublimior an&shy;<lb/>tenna fuerit, eo citi&ugrave;s nauigium, &longs;piritu flante moueri. <lb/></s>
            <s id="s.000641">Re&longs;pon&longs;io facilis, nempe, mirum non e&longs;&longs;e, &longs;i mali pars &longs;ub&shy;<lb/>limior validius &agrave; vento feriatur. </s>
            <s id="s.000642">Videmus enim, &amp; turres <lb/>quo &longs;ublimiores fuerint, eo magis &agrave; ventorum impetuo&longs;is <lb/>flatibus infe&longs;tari, quod &longs;an&egrave; ad vectis longitudinem refer&shy;<lb/>re, e&longs;&longs;et ridiculum. </s>
            <s id="s.000643">C&aelig;ter&ugrave;m quod ad puppis faciliorem <lb/>eleuationem ex mali ip&longs;ius altitudine pertinet, ad vectis <pb xlink:href="007/01/072.jpg"/>contemplationem reducimus. </s>
            <s id="s.000644">e&longs;t enim qu&aelig; dam vectium <lb/>&longs;pecies ab alijs non con&longs;iderata, cuius brachia in angu&shy;<lb/>lum de&longs;inunt, vt ip&longs;e angulus in operatione &longs;it fulcimen&shy;<lb/>tum. </s>
          </p>
          <figure id="id.007.01.072.1.jpg" xlink:href="007/01/072/1.jpg"/>
          <p type="main">
            <s id="s.000645">E&longs;to enim vectis, de quo agimus, <lb/>ABC, cuius brachia AB, BC. iuncta <lb/>ad angulum B, &longs;itqueue B in operatione <lb/>fulcimentum. </s>
            <s id="s.000646">Nec quicquam refert <lb/>quatenus ad v&longs;um pertinet, vtrum an&shy;<lb/>gulus ip&longs;e rectus &longs;it, acutus vel obtu&shy;<lb/>&longs;us. </s>
            <s id="s.000647">&longs;it autem mod&ograve; rectus. </s>
            <s id="s.000648">Ponatur i&shy;<lb/>gitur pondus aliquod in C, tum po&shy;<lb/>tentia qu&aelig;dam applicetur in A, quae i&shy;<lb/>p&longs;am vectis extremitatem A propel&shy;<lb/>lat in D. erit igitur AB in DB &amp; an&shy;<lb/>gulo &longs;eruato BC in BE. <!-- KEEP S--></s>
            <s id="s.000649">Pondus igi&shy;<lb/>tur cum parte vectis BC eleuabitur in E. <!-- KEEP S--></s>
            <s id="s.000650">In hoc autem <lb/>vectis genere attenditur proportio quam habet AB ad <lb/>BC. <!-- KEEP S--></s>
            <s id="s.000651">Si enim potentia qu&aelig; applicatur in A ita &longs;e habet ad <lb/>pondus in C vt CB, ip&longs;i BA, fiet &aelig;quilibrium. </s>
            <s id="s.000652">Si maior <lb/>autem fuerit proportio potenti&aelig; in A, ad pondus in C, ea <lb/>quam habet AB ad BC, &longs;uperat&acirc; ponderis re&longs;i&longs;tenti&acirc; fiet <lb/>motus. </s>
            <s id="s.000653">Res autem haud aliter &longs;e habet, ac &longs;i producta in <lb/>F, fieret BF &aelig;qualis BC. <!-- KEEP S--></s>
            <s id="s.000654">Tunc enim vectis ad rectitudi&shy;<lb/>nem, &longs;eruat&acirc; proportione, redigeretur, &amp; ita potentia in <lb/>A, fulcimento B operaretur in F, vt operabatur in C. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000655">Ad huius vectis naturam referuntur fabrorum mal&shy;<lb/>lei, quibus clauos reuellunt, forcipes item qu&aelig; tenaci <lb/>mor&longs;u clauorum capita vmbellasue apprendentes, vio&shy;<lb/>lenter &egrave; tabulis extrahunt. </s>
            <s id="s.000656">In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars qu&aelig; &agrave; fulcimento ad <lb/>potentiam; ac ver&ograve; qu&aelig; &agrave; fulcimento ad pondus, ponderi <pb xlink:href="007/01/073.jpg"/><figure id="id.007.01.073.1.jpg" xlink:href="007/01/073/1.jpg"/><lb/>&longs;iquidem &aelig;quiparatur re&longs;i&shy;<lb/>&longs;tentia quae fit in C. <!-- KEEP S--></s>
            <s id="s.000657">I dem ob&shy;<lb/>&longs;eruamus in forcipe, in quo <lb/>duo quidem brachia AD, <lb/>CB, quatenus ad appren&longs;io<lb/>nem pertinet, fulcimentum, <lb/>habent in ip&longs;o <expan abbr="c&emacr;tro">centro</expan> &longs;eu ver&shy;<lb/>tebra, &amp; ideo quo longiores <lb/>fuerint, eo tenaci&ugrave;s appre&shy;<lb/>hendunt &amp; retinent. </s>
            <s id="s.000658">quate&shy;<lb/>nus autem ad extractionem, <lb/>facit, pro vnico forceps totus habetur vecte, cuius <expan abbr="quid&emacr;">quidem</expan> <lb/>pars &agrave; potentia ad fulcimentum AB. qu&aelig; ver&ograve; &agrave; <expan abbr="fulcim&emacr;-to">fulcimen&shy;<lb/>to</expan> ad hoc e&longs;t clauum ip&longs;um qui reuellitur AC. <!-- KEEP S--></s>
            <s id="s.000659">Violenti&longs;&shy;<lb/>&longs;im&egrave; autem extrahunt forcipes, propterea quod maxima <lb/>&longs;it proportio longitudinis brachij BA, ad eam qu&aelig; e&longs;t ab <lb/>A ad C. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000660">His igitur hoc pacto examinatis, ad nauim &amp; malum <lb/>reuertentes, dicimus, tunc facillimam fieri puppis eleua&shy;<lb/>tionem, pror&aelig; ver&ograve; demer&longs;ionem, cum maxima fuerit <lb/>proportio, quam habet altitudo mali, ad eam nauis <expan abbr="part&emacr;">partem</expan> <lb/>qu&aelig; &agrave; malo ad ip&longs;am puppis extremitatem, pertingit. <lb/></s>
            <s id="s.000661">Quamobrem prudentes nauium fabri, vt huic difficultati <lb/>occurrant, malum non in medio quidem nauis, &longs;ed in ter&shy;<lb/>tia fer&egrave; parte longitudinis qu&aelig; &agrave; prora e&longs;t, puppim ver&longs;us <lb/>con&longs;tituunt. </s>
          </p>
          <figure id="id.007.01.073.2.jpg" xlink:href="007/01/073/2.jpg"/>
          <p type="main">
            <s id="s.000662">E&longs;to enim nauis AB; cuius <lb/>malus CD: prora A: puppis B; <expan abbr="v&emacr;-to">ven&shy;<lb/>to</expan> igitur velum impellente, <expan abbr="mal&umacr;">malum</expan> <lb/>ad partem contrariam vergit, pu&shy;<lb/>ta in FD. </s>
            <s id="s.000663">At <expan abbr="quoni&atilde;">quoniam</expan> catche&longs;ium <lb/>funi ad puppim vnitur in B, nauim, <lb/>hoc e&longs;t, ip&longs;am puppim trahat ne&shy;<pb xlink:href="007/01/074.jpg"/>ce&longs;&longs;e e&longs;t. </s>
            <s id="s.000664">non pote&longs;t autem; quoniam &longs;uburr&aelig; grauitas &amp; <lb/>onera, qu&aelig; naui impo&longs;ita inter D. &amp; <emph type="italics"/>B.<emph.end type="italics"/> grauitatis centrum <lb/>circa punctum E con&longs;tituunt, quod quidem vi ventorum <lb/>inclinante malo ab E, in G eleuaretur, quo igitur minor <lb/>fuerit proportio CD ad DE &amp; maius pondus ip&longs;um cu&shy;<lb/>ius grauitatis centrum in E minus pr&aelig;ualebit potentia <lb/>pellens in C ad eleuationem partis nauigij, qu&aelig; &agrave; mali &longs;e&shy;<lb/>de ad puppim intercedit, An igitur malus &longs;it vectis, pes ve&shy;<lb/>r&ograve; fulcimentum, pondus autem quod vecte mouetur, <expan abbr="ips&umacr;">ipsum</expan> <lb/>nauigium, vt placuit Ari&longs;toteli, &amp; qua item ratione malus <lb/>in nauim vt vectis operetur, ex ijs quae dicta &longs;unt, facil&egrave; pa&shy;<lb/>tet. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000665">QV&AElig;STIO VII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000666"><emph type="italics"/>Qu&aelig;ritur, Cur quando ex puppi nauigare voluerint, non flante ex <lb/>puppi vento, veli quidem partem, qu&aelig; ad gubernatorem vergit, <lb/>con&longs;tringunt; illam ver&ograve; qu&aelig; proram ver&longs;us e&longs;t, pedem <lb/>facientes, relaxant?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000667">Mirabilis huius effectionis cau&longs;&longs;am explicat Ari&longs;tote&shy;<lb/>les. </s>
            <s id="s.000668">inquit enim, An quia retrahere quidem multo <lb/>exi&longs;tente vento gubernaculum non pote&longs;t, pauco autem <lb/>pote&longs;t, quem con&longs;tringunt? </s>
            <s id="s.000669">propellit igitur quidem ip&longs;e <lb/>ventus, in puppim ver&ograve; illum con&longs;tituit gubernaculum, <lb/>retrahens, &amp; mare compellens: &longs;imul &amp; naut&aelig; ip&longs;i cum <lb/>vento contendunt; in contrariam enim &longs;e reclinant par&shy;<lb/>tem. </s>
            <s id="s.000670">H&aelig;c ille. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000671">Cuius &longs;en&longs;um breuitate &longs;ubob&longs;curum, mir&acirc; facilita&shy;<lb/>te explicat Picolomineus. <!-- KEEP S--></s>
            <s id="s.000672">Nos autem vt rem lucidiorem <lb/>faciamus, &longs;chema, quod nec ip&longs;e fecit, nec Philo&longs;ophus, <lb/>proponemus. </s>
          </p>
          <p type="main">
            <s id="s.000673">E&longs;to nauis A <emph type="italics"/>B<emph.end type="italics"/>, cuius prora A, puppis ver&ograve; D, guber&shy;<lb/>naculum C<emph type="italics"/>B<emph.end type="italics"/>, temonis ala <emph type="italics"/>B<emph.end type="italics"/>D, veli &longs;inus EF, velum vero <lb/>ita con&longs;titutum, vt direct&egrave; ex puppi flantem ventum exci-<pb xlink:href="007/01/075.jpg"/><figure id="id.007.01.075.1.jpg" xlink:href="007/01/075/1.jpg"/><lb/>piat. </s>
            <s id="s.000674">Hoc vbi euenerit, naui&shy;<lb/>gium, rect&acirc; &egrave; puppi mouetur <lb/>in proram; Si autem ventus la&shy;<lb/>teraliter &longs;pirat, puta &agrave; parte <lb/>G ver&longs;us H &amp; nihilo &longs;ecius na&shy;<lb/>uigium, ac &longs;i ventus ex pup&shy;<lb/>pi e&longs;&longs;et antror&longs;um propelle&shy;<lb/>re volunt, velum quidem obli&shy;<lb/>quant partem eius infimam, <lb/>pedem nempe, qu&aelig; e&longs;t in F <lb/>contrahentes, Cornu ver&ograve; <lb/>antenn&aelig; vbi E, proram ver&longs;us <lb/>laxantes ventumque; ip&longs;um obliqu&egrave; excipientes id <expan abbr="effici&umacr;t">efficiunt</expan>, <lb/>vt ventus minus violenter feriat, &amp; minori &longs;ui parte <expan abbr="vel&umacr;">velum</expan> <lb/>impleat, &amp; quoniam ventus velum pellit in partem con&shy;<lb/>trariam, nempe in H, ip&longs;i vt vento re&longs;i&longs;tant conuer&longs;o gu&shy;<lb/>bernaculo ex C in L, &amp; temone <emph type="italics"/>B<emph.end type="italics"/>D, in <emph type="italics"/>B<emph.end type="italics"/>M compellunt <lb/>proram ad partem &agrave; qua ventus ip&longs;e &longs;pirat. </s>
            <s id="s.000675">Sit igitur inter <lb/>ventum &amp; temonem pugna, illo proram in dextram, hoc <lb/>ver&ograve; eandem in &longs;ini&longs;tram pellente, <expan abbr="itaq;">itaque</expan> cum neuter pr&aelig;&shy;<lb/>ualeat, nece&longs;&longs;ario nauis mediam viam, qu&aelig; inter <expan abbr="vtramq;">vtramque</expan> <lb/>e&longs;t, &longs;uo cur&longs;u tenet. </s>
            <s id="s.000676">Naut&aelig; autem ideo in partem nauis <lb/>AE<emph type="italics"/>B<emph.end type="italics"/>, qu&aelig; ver&longs;us ventum e&longs;t, &longs;e conferunt, vt vento &aelig;qui&shy;<lb/>librium faciant, ne &longs;cilicet naui in <expan abbr="c&omacr;trariam">contrariam</expan> partem pel&shy;<lb/>lente &longs;piritu, eam demergat. </s>
            <s id="s.000677">C&aelig;ter&ugrave;m quod nec Ari&longs;to&shy;<lb/>teles nec Picolomineus animaduerterunt, velum obli&shy;<lb/>qu&egrave; con&longs;titutum &agrave; vento in anteriora impellitur eandem <lb/>ob cau&longs;&longs;am, quam retulimus, vbi de temone &amp; velis, qui&shy;<lb/>bus farinari&aelig; mol&aelig; <expan abbr="c&omacr;uertuntur">conuertuntur</expan>, verba faceremus. </s>
            <s id="s.000678">Quod <lb/>autem addit Picolomineus rem ad vectem reduci po&longs;&longs;e, <lb/>non e&longs;t cur &longs;ub &longs;ilentio pr&aelig;tereamus. </s>
            <s id="s.000679">Ventus, inquit, pon&shy;<lb/>deris gubernaculum mouentis vicem obtinet; centrum <lb/>ver&ograve; &lpar;fulcimentum intelligit&rpar; in medio nauis e&longs;t, quod ta-<pb xlink:href="007/01/076.jpg"/>men ad proram vergit, vt facili&ugrave;s ip&longs;i vento re&longs;i&longs;tere po&longs;&shy;<lb/>&longs;it. </s>
            <s id="s.000680">Tunc enim in rectum mouebitur nauis, cum &longs;ibi inui&shy;<lb/>cem &aelig;quat&aelig; vires, qua&longs;i libramentum con&longs;tituerint. </s>
            <s id="s.000681">H&aelig;c <lb/>ille, cuius &longs;en&longs;um figur&acirc; propo&longs;it&acirc; facil&egrave; aperiemus. </s>
          </p>
          <figure id="id.007.01.076.1.jpg" xlink:href="007/01/076/1.jpg"/>
          <p type="main">
            <s id="s.000682">E&longs;to carina AB, cuius prora <lb/>A, puppis, B temo BC, ventus ver&ograve; <lb/>obliqu&egrave; feriens H. <!-- KEEP S--></s>
            <s id="s.000683">Conuer&longs;us ita&shy;<lb/>que temo vt in BC vndarum vi cur&shy;<lb/>rente naui repul&longs;us &longs;it in EF ten&shy;<lb/>dens ver&longs;us I, quo ca&longs;u prora con&shy;<lb/>uertitur in D, nempe contra <expan abbr="vent&umacr;">ventum</expan> <lb/>qui &longs;pirat ex H. fit autem conuer&shy;<lb/>&longs;io circa punctum G, quod fulcimenti locum obtinet. </s>
            <s id="s.000684"><expan abbr="V&emacr;-tus">Ven&shy;<lb/>tus</expan> ver&ograve; ad contrariam <expan abbr="part&emacr;">partem</expan> proram impellit, repugnans <lb/>Temonis violenti&aelig; contra ip&longs;am proram dirigentis. </s>
            <s id="s.000685">E&longs;t i&shy;<lb/>gitur AB, &longs;eu DE carina, in&longs;tar vectis, cuius fulcimentum <lb/>G, vis mouens mare quo temo EF repellitur, pondus ve&shy;<lb/>ro, ventus premens in D; quo igitur remotior erit temo &agrave; <lb/>fulcimento G, D autem vbi pondus ei vicinius, eo magis <lb/>temo venti vim &longs;uperabit. </s>
            <s id="s.000686">H&aelig;c Picolominei ratio, quam <lb/>explicauimus, &longs;an&egrave; ingenio&longs;a e&longs;t, verum enimuero, quo&shy;<lb/>niam fulcimentum &longs;ui natur&acirc; &longs;tare debet, hic ver&ograve; <expan abbr="null&atilde;">nullam</expan> <lb/>habeat &longs;tabilitatem, difficultatem patitur. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000687">QV&AElig;STIO VIII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000688"><emph type="italics"/>Qu&aelig;ritur, Cur ex figuris omnibus rotund&aelig; facili&ugrave;s <lb/>moueantur?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000689">Trifariam, inquit Ari&longs;toteles, circulum rotari contin&shy;<lb/>git; Aut &longs;ecundum ab&longs;idem <expan abbr="c&emacr;tro">centro</expan> &longs;imul moto, quem&shy;<lb/>admodum plau&longs;tri vertitur rota; aut circa manens cen&shy;<lb/>trum, veluti trochle&aelig; puteorum, &longs;tante centro: Aut in pa&shy;<lb/>uimento manente centro, &longs;icuti figuli rota conuertitur. <pb xlink:href="007/01/077.jpg"/>Cau&longs;&longs;am ver&ograve; explicans, ait, celerrima eiu&longs;modi corpora <lb/>e&longs;&longs;e, eo quod paru&acirc; &longs;ui parte planum contingunt, vti cir&shy;<lb/>culus &longs;ecundum punctum, item quoniam non offen&longs;ant: <lb/>Non offen&longs;andi vero e&longs;&longs;e cau&longs;&longs;am, quod &longs;emotum &agrave; terra <lb/>habeant angulum. </s>
            <s id="s.000690">Item propterea quod corpus, cui fiunt <lb/>obuiam, &longs;ecundum pu&longs;illum tangunt. </s>
            <s id="s.000691">Rectilineo autem <lb/>aliter euenire, quippe quod rectitudine &longs;u&acirc;, multum pla&shy;<lb/>ni contingat. </s>
            <s id="s.000692">Ad h&aelig;c, quo nutat pondus eo mouentem <lb/>mouere. </s>
          </p>
          <p type="main">
            <s id="s.000693">H&aelig;c fer&egrave; Philo&longs;ophus, cuius rationes ad eum &longs;olum&shy;<lb/>modo circularem motum faciunt, qui fit &longs;ecundum ab&longs;i&shy;<lb/>dem, vt in carrorum rotis v&longs;u venit, nec aptantur rotis fi&shy;<lb/>gulorum trochlei&longs;queue, cuiu&longs;modi &longs;unt ill&aelig;, qu&aelig; &longs;upra <lb/>puteos appenduntur. </s>
            <s id="s.000694">Nos igitur, ad Ari&longs;totelis mentem, <lb/>primam rotationis &longs;peciem, qu&aelig; e&longs;t &longs;ecundum ab&longs;idem, <lb/>examinabimus. </s>
          </p>
          <figure id="id.007.01.077.1.jpg" xlink:href="007/01/077/1.jpg"/>
          <p type="main">
            <s id="s.000695">E&longs;to rota &longs;ph&aelig;&shy;<lb/>raue AB, cuius cen&shy;<lb/>trum C; Horizontis <lb/>planum DE; conta&shy;<lb/>ctus circuli in plano <lb/>B. <expan abbr="perp&emacr;dicularis">perpendicularis</expan> ho&shy;<lb/>rizonti &agrave; puncto <expan abbr="c&omacr;-tactus">con&shy;<lb/>tactus</expan> B ip&longs;a <emph type="italics"/>B<emph.end type="italics"/>CA, <lb/>tran&longs;iens per <expan abbr="centr&umacr;">centrum</expan> <lb/>C, partes rot&aelig; circa <lb/>perpendicularem AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, angulus contactus G<emph type="italics"/>B<emph.end type="italics"/>E. <lb/></s>
            <s id="s.000696">Primo itaque id con&longs;tat, circulum in puncto planum, &longs;eu <lb/>lineam contingere. </s>
            <s id="s.000697">At quoniam, vt Mechanici, de circulis <lb/>roti&longs;queue &longs;eu &longs;ph&aelig;ris agimus materialibus, rect&egrave; Philo&longs;o&shy;<lb/>phus non in puncto planum pr&aelig;cis&egrave; tangere dixit, &longs;ed &longs;e&shy;<lb/>cundum partem &longs;ui minimam. </s>
            <s id="s.000698">Angulum porro, quem &agrave; <lb/>terra &longs;emotum dicit, ip&longs;e angulus e&longs;t contingentiae. </s>
            <s id="s.000699">eleua&shy;<pb xlink:href="007/01/078.jpg"/>tur enim ex <emph type="italics"/>B<emph.end type="italics"/> in G. <!-- KEEP S--></s>
            <s id="s.000700">Si autem corpus quodpiam in plano <lb/>fuerit, puta HI in puncto illud tanget ci culus ei occur&shy;<lb/>rens, exempli grati&acirc; in K. <!-- KEEP S--></s>
            <s id="s.000701">H&aelig;c igitur accidunt circulari <lb/>figur&aelig;. </s>
            <s id="s.000702">In lateratis autem &longs;ecus fit, quippe qu&aelig; nec in <expan abbr="p&umacr;-cto">pun&shy;<lb/>cto</expan> &longs;eu &longs;ecundum paruam &longs;ui partem, planum tangunt, <lb/>nec &longs;emotum vt circulus &agrave; plano habent angulum, nec <lb/>impingentes offendiculum in puncto tangunt. </s>
            <s id="s.000703">C&aelig;ter&ugrave;m <lb/>poti&longs;&longs;imam facilitatis motus in rotatione qu&aelig; fit &longs;ecun&shy;<lb/>dum ab&longs;idem, e&longs;&longs;e cau&longs;&longs;am dixit, nempe qu&ograve; nutat pon&shy;<lb/>dus e&ograve; &agrave; mouente impelli ac moueri. </s>
            <s id="s.000704">Prim&ograve; igitur circu&shy;<lb/>laris &longs;ph&aelig;ricaue figura in &aelig;quilibrio &longs;tat; &aelig;quales enim <lb/>&longs;unt partes qu&aelig; circa perpendicularem: ceu &longs;unt AF<emph type="italics"/>B<emph.end type="italics"/>, <lb/>AG<emph type="italics"/>B.<emph.end type="italics"/> &longs;i enim impul&longs;us fiat ex parte F, pars oppo&longs;ita nuta&shy;<lb/>bit, &amp; propendet in partem G, &amp; &longs;uo nutu motuque; &longs;ecum <lb/>trahet partem AF<emph type="italics"/>B<emph.end type="italics"/>, fietqueue progre&longs;&longs;us. </s>
            <s id="s.000705">Si enim ducatur <lb/>FCG diameter, ip&longs;i horizonti &aelig; que di&longs;tans, erit veluti li&shy;<lb/>bra, cuius pondera vtrinque AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, brachia ver&ograve; <lb/>&aelig;qualia CF, CG. <!-- KEEP S--></s>
            <s id="s.000706">Potentia autem qu&acirc; trahitur pellitur&shy;<lb/>ue ad in&longs;tar ponderis &longs;e habet, quo addito partium alteri, <lb/>facto queue rece&longs;&longs;u ab &aelig;quilibrio, &longs;equetur motus. </s>
            <s id="s.000707">Putau&ecirc;re <lb/>quidam, vt refert Philo&longs;ophus, <expan abbr="circular&emacr;">circularem</expan> lineam, ita per&shy;<lb/>peti motu ver&longs;atum iri, vt manentia, propter contrarium <lb/>nixum, manent, neque enim circulus in plano contrarium <lb/>nixum habet, cum &longs;it, veluti dicebamus, in &aelig;quilibrio &amp; <lb/>facilis in vtramuis partem moueri. </s>
            <s id="s.000708">Veruntamen perpe&shy;<lb/>tuum e&longs;&longs;e non po&longs;&longs;e horum corporum motum, ea e&longs;t cau&longs;&shy;<lb/>&longs;a, quod violentum accidat natur&aelig;, &amp; ideo non durabile. <lb/></s>
            <s id="s.000709">Ad h&aelig;c, addit Philo&longs;ophus, Maiores circulos ad minores <lb/>nutum habere <expan abbr="qu&emacr;dam">quendam</expan>; &amp; nutum maioris ad minoris nu&shy;<lb/>tum, &longs;e habere vt angulos ad angulos, &amp; <expan abbr="diametr&umacr;">diametrum</expan> ad dia&shy;<lb/>metrum. </s>
            <s id="s.000710">Angulos autem h&icirc;c &longs;ectores ip&longs;os vocat; oportet <lb/>enim circulos tum maiores tum minores circa idem cen&shy;<lb/>trum e&longs;&longs;e con&longs;titutos. </s>
            <s id="s.000711">H&aelig;c autem non ab&longs;imili ab eo <lb/>quod &longs;upr&agrave; po&longs;uimus &longs;chemate explicantur. </s>
          </p>
          <pb xlink:href="007/01/079.jpg"/>
          <figure id="id.007.01.079.1.jpg" xlink:href="007/01/079/1.jpg"/>
          <p type="main">
            <s id="s.000712">E&longs;to enim circulus <lb/>AB circa centrum, C, <lb/>Horizontis planum DE, <lb/>tangens circulum in B, <lb/>linea ver&ograve; perpendicu&shy;<lb/>laris per centrum BCA. <lb/><!-- KEEP S--></s>
            <s id="s.000713">Sit autem circa idem <expan abbr="c&emacr;-trum">cen&shy;<lb/>trum</expan> C, minor circulus <lb/>FG, ducatur queue CH &longs;e&shy;<lb/>cus minorem circulum in I, tangens ver&ograve; maiorem in H, <lb/>con&longs;tituen&longs;queue cum AC linea angulum ACH, duos an&shy;<lb/>gulos, ex Ari&longs;totelis mente comprehendentem, hoc e&longs;t, <lb/>duos &longs;ectores ACH, FCI. quoniam igitur &longs;ector &longs;eu an&shy;<lb/>gulus ACH, &longs;uo &longs;patio &longs;uperat angulum &longs;eu &longs;ectorem <lb/>FGI, facil&egrave; ex nutu quem maior &longs;upra minorem habet, <lb/>maior ip&longs;e m&igrave;norem mouet. </s>
            <s id="s.000714">Videtur autem tacit&egrave; Philo&shy;<lb/>&longs;ophus h&aelig;c ad vectis naturam referre, cuius altera extre&shy;<lb/>mitatum in centro &longs;it, altera ver&ograve; in ab &longs;ide, &amp; ita &longs;e habe&shy;<lb/>re nutum maioris &longs;upra minorem, vt vectis ad vectem, hoc <lb/>e&longs;t, &longs;emidiameter ad &longs;emidiametrum, &longs;eu &longs;ector ad &longs;ecto&shy;<lb/>rem, quos quidem &longs;ectores, vt vidimus, angulos appellat. <lb/></s>
            <s id="s.000715">H&aelig;c autem qu&aelig; de nutu refert, licet &longs;ubtilia &longs;int, vera e&longs;&shy;<lb/>&longs;e non videntur. </s>
            <s id="s.000716">Si enim in figura producatur ad oppo&longs;i&shy;<lb/>tam partem &longs;emidiameter HC in K &longs;ecans minorem cir&shy;<lb/>culum in L, duos alios &longs;ectores angulosue habebimus, <expan abbr="n&emacr;-pe">nem&shy;<lb/>pe</expan> KCB, LCG, ip&longs;is ACHFCI &aelig;quales. </s>
            <s id="s.000717"><expan abbr="Itaq;">Itaque</expan> quan&shy;<lb/>tum adiuuat motum anguli ACH maioris nutus, in de&shy;<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus &lpar;vt ita appellem&rpar; in <expan abbr="a&longs;cend&emacr;-do">a&longs;cenden&shy;<lb/>do</expan> ad partes A. &amp; &longs;an&egrave; quatenus ad rei naturam pertinet <lb/>&amp; ad ip&longs;um &aelig;quilibrium, non differunt maiores circuli &agrave; <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex aliqua ratione minores videntur fore ad motum faci&shy;<pb xlink:href="007/01/080.jpg"/>liores, tum quia data materi&aelig; &aelig;qualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planum <lb/>circumferentiae minoris qu&agrave;m maioris circuli, vt in &longs;ubie&shy;<lb/><figure id="id.007.01.080.1.jpg" xlink:href="007/01/080/1.jpg"/><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i&shy;<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu&shy;<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>qu&aelig; tam in maioribus qu&agrave;m in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examinabimus. </s>
          </p>
          <p type="main">
            <s id="s.000718">C&aelig;ter&ugrave;m vt aliquid de motu qui &longs;ecundum ab&longs;idem <lb/>fit, ex no&longs;tro penu promamus, Dicimus, Circulos, rota&longs;ue, <lb/>qu&aelig; hoc pacto mouentur, vel per horizontis planum mo&shy;<lb/>ueri, vel per accliue, aut decliue. </s>
            <s id="s.000719">Si autem per horizontis <lb/>planum, ideo facilem e&longs;&longs;e motum, qu&ograve;d nunquam, c&aelig;te&shy;<lb/>ris paribus, centrum grauitatis ip&longs;ius corporis &agrave; centro <lb/>mundi, in ip&longs;a rotatione, fiat remotius. </s>
          </p>
          <figure id="id.007.01.080.2.jpg" xlink:href="007/01/080/2.jpg"/>
          <p type="main">
            <s id="s.000720">E&longs;to enim planum, <lb/>horizontis AB, cui circu&shy;<lb/>lus in&longs;i&longs;tat AD, circa cen&shy;<lb/>trum C, diui&longs;us per <expan abbr="centr&umacr;">centrum</expan> <lb/>ip&longs;um &agrave; perpendiculari <lb/>ACD; Ducatur autem per <lb/>centrum C recta linea ho&shy;<lb/>rizonti &aelig;quidi&longs;tans, ECFG: dum diuidatur circulus vt&shy;<lb/>cunque in partes AH, HF, FI, ID, &amp; CI, CH iungan&shy;<lb/>tur. </s>
            <s id="s.000721">Po&longs;th&aelig;c intelligatur circulum &longs;ecundum ab&longs;idem <lb/>moueri ad partes G, erit igitur aliquando punctum H, <lb/>tangens horizontis planum, tangat autem in K, tum F in <pb xlink:href="007/01/081.jpg"/>L, I in N. <!-- REMOVE S-->D ver&ograve; in O. <!-- KEEP S--></s>
            <s id="s.000722">Ducanturqueue KP, LQ, NR, OS <lb/>ip&longs;i AC parallel&aelig; horizonti autem perpendiculares. <lb/></s>
            <s id="s.000723">Centrum ergo circuli, quod idem &amp; grauitatis e&longs;t <expan abbr="centr&umacr;">centrum</expan>, <lb/>feretur per rectam CPQRS, &longs;unt enim KP, LQ, NR, <lb/>OS ip&longs;i AC &longs;emidiametro &aelig;quales, <expan abbr="n&umacr;quam">nunquam</expan> igitur cen&shy;<lb/>trum ip&longs;um C in circuli rotatione ab horizontis plano e&shy;<lb/>leuabitur, nec &agrave; mundi centro fiet remotius. </s>
          </p>
          <p type="main">
            <s id="s.000724">Hoc autem long&egrave; aliter c&aelig;teris figuris contingit, <lb/>quarum motus ideo in &aelig;qualis, qu&ograve;d non &longs;emper in rota&shy;<lb/>tione centrum grauitatis eandem &longs;eruet &agrave; mundi centro <lb/>di&longs;tantiam. </s>
          </p>
          <figure id="id.007.01.081.1.jpg" xlink:href="007/01/081/1.jpg"/>
          <p type="main">
            <s id="s.000725">E&longs;to enim Ellip&longs;is <lb/>ABCD, cuius <expan abbr="c&emacr;trum">centrum</expan> <lb/>E, diameter longior <lb/>BED, breuior AEC, <lb/>Horizontis planum, <lb/>FCG. locus contactus <lb/>C perpendicularis &agrave; <lb/>contactu per centrum i&shy;<lb/>p&longs;a CEA diuidens El&shy;<lb/>lip&longs;im in partes &aelig;quales, &amp; &aelig;queponderantes ABC, <lb/>ADC. <!-- KEEP S--></s>
            <s id="s.000726">Sumantur in quadrante CD, <expan abbr="p&umacr;cta">puncta</expan> HI, tum EH, <lb/>HI iungantur, erit autem EH longior ip&longs;a EC, tum EI, <lb/>ip&longs;a EH &amp; ED, p&longs;a EI. <!-- KEEP S--></s>
            <s id="s.000727">Rotetur ellip&longs;is &longs;ecun dum ab&longs;i&shy;<lb/>dem, fiet igitur punctum H in K, &amp; &agrave; puncto K horizonti <lb/>perpendicularis erigatur KL, qu&aelig; fiat &aelig;qualis EH. <!-- KEEP S--></s>
            <s id="s.000728">Po&longs;t <lb/>h&aelig;c punctum I erit in M, &amp; ab M perpendicularis, &aelig;qua&shy;<lb/>lis EI. rur&longs;us D fiat in O, &amp; ip&longs;i ED, &aelig;qualis perpendicu&shy;<lb/>laris OP. <!-- KEEP S--></s>
            <s id="s.000729">Mota igitur ellip&longs;i &agrave; C in K, haud ita difficilis e&shy;<lb/>rit motus, quippe quod haud multum EH &longs;uperet EC, at <lb/>difficilior erit translatio in M, difficillima ver&ograve; in O. Val<lb/>de enim &agrave; &longs;itu E, ibi attollitur grauitatis centrum, a&longs;cen&shy;<lb/>dens nempe vbi P. <!-- KEEP S--></s>
            <s id="s.000730">Videmus igitur ex his eandem poten&shy;<pb xlink:href="007/01/082.jpg"/>tiam in mouendo ellip&longs;im, haud pariter &longs;e habere, vt in <lb/>mouendo circulum. </s>
            <s id="s.000731">ibi enim centrum grauitatis fertur <lb/>per &aelig;quidi&longs;tantem horizonti, hic ver&ograve; mod&ograve; attollitur, <lb/>mod&ograve; deprimitur, quod &longs;an&egrave; mole&longs;tiam &amp; difficultatem <lb/>facit. </s>
            <s id="s.000732">Sed idem alijs figuris contingere, &amp; maxim&egrave; latera&shy;<lb/>tis, ita docebimus. </s>
          </p>
          <figure id="id.007.01.082.1.jpg" xlink:href="007/01/082/1.jpg"/>
          <p type="main">
            <s id="s.000733">E&longs;to enim triangulum <lb/>&aelig;quilaterum ABC, cuius <lb/>grauitatis centrum E hori&shy;<lb/>zontis planum BD. <!-- KEEP S--></s>
            <s id="s.000734">Demit&shy;<lb/>tatur &agrave; vertice A perpendi&shy;<lb/>cularis horizonti AF tran&longs;&shy;<lb/>ibit autem per centrum E, <lb/>&amp; bifariam diuidet ba&longs;im <lb/>BC in F. <!-- KEEP S--></s>
            <s id="s.000735">Sunt autem trianguli ABF, ACF, &aelig;quales &amp; <lb/>&aelig;queponderantes. </s>
            <s id="s.000736">angulus ver&ograve; AFC rectus. </s>
            <s id="s.000737">lungatur <lb/>EC, erit igitur maior EC, ip&longs;a EF. <!-- KEEP S--></s>
            <s id="s.000738">Rotetur iraque trian&shy;<lb/>gulum circa punctum C, fiatque; EC horizonti perpendi&shy;<lb/>cularis, &longs;itqueue GH, &amp; per E horizonti parallela ducatur <lb/>EK, moto igitur triangulo, centrum grauitatis E transla&shy;<lb/>tum erit in H, &longs;ed KC &aelig;qualis e&longs;t EF, minor autem ip&longs;a <lb/>CH, eleuatur ergo centrum grauitatis ab E in H, nempe <lb/>&longs;upra K, totum &longs;patium KH. ex qua eleuatione fit in mo&shy;<lb/>tu difficultas. </s>
            <s id="s.000739">Idem pror&longs;us eadem demon&longs;tratione o&longs;ten&shy;<lb/>deretur fieri in quadrato &amp; alijs lateratis figuris. </s>
            <s id="s.000740">Cur igi&shy;<lb/>tur in plano horizontis facillim&egrave; circularia, difficile <expan abbr="aut&emacr;">autem</expan> <lb/>laterata &amp; qu&aelig; in&aelig;quales habent &longs;emidiametros, mo&shy;<lb/>ueantur, ex dictis clar&egrave; patet. </s>
          </p>
          <p type="main">
            <s id="s.000741">Ad hanc qu&aelig;&longs;tionem illud quoque facit, cur per de&shy;<lb/>cliue planum grauiora corpora, &amp; rotunda maxim&egrave;; ma&shy;<lb/>gno impetu dimi&longs;&longs;a, delabantur. </s>
          </p>
          <p type="main">
            <s id="s.000742">E&longs;to enim rota &longs;ph&aelig;raue aut Cylindrus CD, cuius <lb/>centrum E, tangens decliue planum AB in D, qu&aelig;ritur <pb xlink:href="007/01/083.jpg"/>cur dimi&longs;&longs;a h&aelig;c magno impetu deferantur ad partes B, <lb/>Ducatur per grauitatis centrum E ad horizontem, BK <lb/>perpendicularis FEL &longs;ecans decliue planum in G, cir&shy;<lb/>cumferentiam ver&ograve; in H. opponitur autem EG angulo <lb/>recto EDG, maior ergo EG ip&longs;a ED, hoc e&longs;t, EH, inter <lb/><figure id="id.007.01.083.1.jpg" xlink:href="007/01/083/1.jpg"/><lb/>circumferentiam igitur &amp; pla&shy;<lb/>num decliue, &longs;patium interce&shy;<lb/>dit HG. <!-- KEEP S--></s>
            <s id="s.000743">Ducatur item DI ip&longs;i <lb/>FG &aelig;quidi&longs;tans. </s>
            <s id="s.000744">non tran&longs;ibit <lb/>igitur per centrum E. minor e&shy;<lb/>rit igitur diametro CD, quare <lb/>circulum in partes in&aelig;quales <lb/>&longs;ecabit, &amp; non per grauitatis <lb/>centrum, quod idem cum ma&shy;<lb/>gnitudinis &longs;eu figur&aelig; centro &longs;upponitur. </s>
            <s id="s.000745">Dimi&longs;&longs;a igitur <lb/>rota, contingit quidem planum decliue in puncto D. <!-- KEEP S--></s>
            <s id="s.000746">At <lb/>centrum grauitatis premit &longs;ecundam per lineam perpen&shy;<lb/>dicularem FG, non &longs;u&longs;tentatur autem in H, quippe quod <lb/>inter planum &amp; circum <expan abbr="ferenti&atilde;">ferentiam</expan> intercedat &longs;patium HG, <lb/>nec H locum habeat cui innitatur, corpus autem ita per <lb/>lineam DI e&longs;t diui&longs;um, vt long&egrave; maior &longs;it pars IFCHD <lb/>ip&longs;a DI, &amp; centrum in ea parte cadat qu&aelig; non fulcitur. </s>
            <s id="s.000747">i&shy;<lb/>taque &longs;uopte nutu, cum extra fulcimentum &longs;it D &amp; per&shy;<lb/>pendicularem DI ad inferiores partes rapid&egrave; rotans de&shy;<lb/>labitur. </s>
            <s id="s.000748">Ducatur autem perpendicularis GL, parallela <lb/>MN, &amp; quoniam BN breuior e&longs;t BL, erit MN ip&longs;a GL <lb/>breuior. </s>
            <s id="s.000749">E&longs;t igitur punctum M mundi centro propius <lb/>qu&agrave;m D &amp; G, quare e&ograve; non impedita rota ip&longs;a &longs;uo nutu <lb/>feretur, nec &longs;tabit donec in fimum <expan abbr="loc&umacr;">locum</expan> vbi quie&longs;cat nan&shy;<lb/>ci&longs;catur. </s>
            <s id="s.000750">Po&longs;&longs;umus etiam Rota &longs;ph&aelig;raue in plano decliui <lb/>collocata, datam potentiam inuenire, qu&aelig; extremitati <lb/>diametri ad eam partem qua vergit applicata ip&longs;am rotam <lb/>&longs;ph&aelig;ramue impediatne delabatur. </s>
          </p>
          <pb xlink:href="007/01/084.jpg"/>
          <figure id="id.007.01.084.1.jpg" xlink:href="007/01/084/1.jpg"/>
          <p type="main">
            <s id="s.000751">E&longs;to planum in clinatum <lb/>AB, cui Rota &longs;ph&aelig;raue in&longs;i&shy;<lb/>&longs;tat tangatque; illud in C. <!-- KEEP S--></s>
            <s id="s.000752">Rota <lb/>ver&ograve; ip&longs;a &longs;ph&aelig;raue DC, cu&shy;<lb/>ius centrum E, diameter ve&shy;<lb/>r&ograve; DEC ip&longs;i BA ad <expan abbr="punct&umacr;">punctum</expan> <lb/>contactus C, perpendicula&shy;<lb/>ris. </s>
            <s id="s.000753">Ducatur per C ip&longs;i hori&shy;<lb/>zonti perpendiculatis FCG <lb/>circulum <expan abbr="&longs;ec&atilde;s">&longs;ecans</expan> in G tum per <lb/>E ip&longs;i CG perpendicularis, ip&longs;i ver&ograve; BF horizonti &aelig;qui&shy;<lb/>di&longs;tans HEI ceu vectis, cuius fulcimentum I re&longs;pondens <lb/>ip&longs;i C, pondus ver&ograve; in E, vbi grauitatis e&longs;t centrum. </s>
            <s id="s.000754">Ap&shy;<lb/>plicata igitur potentia in H erit pondus inter fulcimen&shy;<lb/>tum &amp; potentiam, quare vt IE ad IH ita potentia &longs;u&longs;ti&shy;<lb/>nens in H ad pondus in E, quod demon&longs;trandum fuerat. </s>
          </p>
          <p type="main">
            <s id="s.000755">Quippiam &longs;imile o&longs;tendit Pappus 1. 8. prop. 9. alijs <lb/>tamen &longs;uppo&longs;itis &amp; con&longs;ideratis. </s>
            <s id="s.000756">Dico pr&aelig;terea, ij&longs;dem <lb/>&longs;tantibus angulum ECI &aelig;qualem e&longs;&longs;e angulo inclinatio&shy;<lb/>nis CBF. </s>
            <s id="s.000757">Producatur HI concurrens cum ip&longs;a AB in K, <lb/>concurret autem propterea, quod CIK rectus &longs;it, ICA <lb/>minor recto, &amp; quoniam HK parallela e&longs;t horizonti BF <lb/>alterni anguli IKC, CBF, &aelig;quales erunt. </s>
            <s id="s.000758">Similes autem <lb/>&longs;unt ECI, ECK, trianguli, e&longs;tqueue ECI angulus &aelig;qualis <lb/>angulo EKC, hoc e&longs;t, ip&longs;i CBF. vnde &longs;equitur, quo mi&shy;<lb/>nor fuerit inclinationis angulus, eo facilius rotam &longs;ph&aelig;&shy;<lb/>ramue in plano inclinato &longs;u&longs;tineri. </s>
            <s id="s.000759">quo enim minor fuerit <lb/>angulus ECI, eo minus latus EI &amp; minor proportio EI <lb/>ad IH, &amp; ideo minor potentia &longs;u&longs;tinens requiratur in H. <lb/><!-- KEEP S--></s>
            <s id="s.000760">C&aelig;ter&ugrave;m accliue &amp; decliue planum nihil differunt ni&longs;i <lb/>re&longs;pectu. </s>
          </p>
          <p type="main">
            <s id="s.000761">His ita con&longs;ideratis, admonet nos locus, vt pulcher&shy;<lb/>rimam dubitationem diluamus. </s>
            <s id="s.000762">Qu&aelig;ritur, Cur maiores <pb xlink:href="007/01/085.jpg"/>rotae impingentes, facilius offendicula &longs;uperent qu&agrave;m mi&shy;<lb/>nores. </s>
            <s id="s.000763">Neque enim &longs;atisfacere videtur quod ait Ari&longs;tote&shy;<lb/>les, ex contactu in puncto eo anguli &agrave; plano eleuatione id <lb/>fieri, alijs ergo principijs dubitatio &longs;oluitur. </s>
          </p>
          <figure id="id.007.01.085.1.jpg" xlink:href="007/01/085/1.jpg"/>
          <p type="main">
            <s id="s.000764">E&longs;to rota quidem maior <lb/>AB, circa centrum C minor <lb/>vero DB circa centrum, E, <lb/><expan abbr="t&atilde;gentes">tangentes</expan> horizontis planum <lb/>in B. <!-- KEEP S--></s>
            <s id="s.000765">Diameter maioris AB, <lb/>minoris DB, offendiculum, <lb/>horizonti perpendiculare <lb/>FG. <!-- KEEP S--></s>
            <s id="s.000766">Ducatur per F horizonti <lb/>parallela FK &longs;ecans minoris <lb/>rot&aelig; peripheriam in H, dia&shy;<lb/>metrum ver&ograve; AB in K, &amp; &agrave; <lb/>puncto H ad <expan abbr="plan&umacr;">planum</expan> horizon&shy;<lb/>tis perpendicularis demittatur HI: erit autem HI &aelig;qua&shy;<lb/>lis ip&longs;i offendiculo FG, &amp; iungantur BH, BF. <expan abbr="Itaq;">Itaque</expan> quo&shy;<lb/>niam BH ab extremo B cadit in triangulum KFB, erit <lb/>KHB angulus maior angulo KFB. </s>
            <s id="s.000767">Parallel&aelig; autem &longs;unt <lb/><emph type="italics"/>K<emph.end type="italics"/>F, BG, pares ergo anguli <emph type="italics"/>K<emph.end type="italics"/>HB, HBG, pares item <emph type="italics"/>K<emph.end type="italics"/>FB, <lb/>FBG, Maior ergo HBI, ip&longs;o FBC. <!-- KEEP S--></s>
            <s id="s.000768">At minoris rot&aelig; gra&shy;<lb/>uitatis centrum mouetur &longs;ecundum lineam BH, maius <lb/>ver&ograve; &longs;ecundum literam BF, difficilius ergo mouebitur, &amp; <lb/>&longs;uperabit offendiculum minor rota, qu&agrave;m maior: quod <lb/>fuerat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.000769">Po&longs;&longs;umus idem o&longs;tendere magis mechanic&egrave;, hoc <lb/>e&longs;t, tem ad vectem reducendo. </s>
            <s id="s.000770">E&longs;to horizontis planum <lb/>AB, rota maior CD planum tangens in D. rot&aelig; ver&ograve; ma&shy;<lb/>ioris centrum E. <!-- KEEP S--></s>
            <s id="s.000771">Rota ver&ograve; minor FD, tangens itidem <lb/>planum in D. rot&aelig; autem centrum G, offendiculi ver&ograve; re&shy;<lb/>ctitudo DH. <!-- KEEP S--></s>
            <s id="s.000772">Ducatur per H ip&longs;i AB horizonti &aelig;quidi&shy;<lb/>&longs;tans HI &longs;ecans minorem circulum in K, maiorem ver&ograve; <pb xlink:href="007/01/086.jpg"/><figure id="id.007.01.086.1.jpg" xlink:href="007/01/086/1.jpg"/><lb/>in I. <!-- KEEP S--></s>
            <s id="s.000773">Ducantur etiam dia&shy;<lb/>metri maioris quidem <lb/>LEM, minoris NGO, <lb/>Tum &agrave; puncto K perpen&shy;<lb/>dicularis ducatur ad <lb/>GO, ip&longs;a KP, item &agrave; pun&shy;<lb/>cto I ad EM perpendi&shy;<lb/>cularis <expan abbr="Iq.">Ique</expan> Dico EQ ad <lb/>QL, minorem habere <lb/>proportionem quam GP, <lb/>ad PN. <!-- KEEP S--></s>
            <s id="s.000774">Connectatur <lb/>GK, &amp; ei per E parallela <lb/>ducatur ER, &longs;ecans maiorem circulum in R, &amp; ab R ip&longs;i <lb/>EM perpendicularis ducatur RS. quoniam igitur ER <lb/>parallela e&longs;t ip&longs;i GK, erit GER angulus HGK angulo <lb/>&aelig;qualis. </s>
            <s id="s.000775">Recti autem &longs;unt HGP, GES reliqui ergo KGP, <lb/>RES ad inuicem &longs;unt &aelig;quales. </s>
            <s id="s.000776">Sed &amp; ESR, GPK recti <lb/>&longs;unt, quare ERSGKP anguli &aelig;quales &longs;unt, &amp; trianguli <lb/>GPKESR, per pr. <!-- REMOVE S-->diff. </s>
            <s id="s.000777">1.6. &longs;imiles. </s>
            <s id="s.000778">Vt ergo GK hoc e&longs;t <lb/>GN ad GP, ita ER hoc e&longs;t EL ad ES. <!-- KEEP S--></s>
            <s id="s.000779">Componendo igi&shy;<lb/>tur vt NP ad PG, ita LS ad SE. quamobrem &longs;i fulcimen&shy;<lb/>tum e&longs;&longs;et in S, pondus in E, <expan abbr="pot&emacr;tia">potentia</expan> in L, idem fieret ac fiat <lb/>fulcimento in P, pondere in G, potentia ver&ograve; in N con&longs;ti&shy;<lb/>tuta. </s>
            <s id="s.000780">&amp; id quidem &longs;i eiu&longs;dem ponderis vtraque rota &longs;up&shy;<lb/>ponatur. </s>
            <s id="s.000781">Rur&longs;us quoniam vt DK ad totum circulum DF, <lb/>ita DR ad totum DC. <!-- KEEP S--></s>
            <s id="s.000782">Minor e&longs;t autem proportio DI ad <lb/>totum circulum DC, ergo minor e&longs;t DI ip&longs;a DR. <!-- KEEP S--></s>
            <s id="s.000783">Maior <lb/>ergo MI ip&longs;a MR, maior ergo QI ip&longs;a SR, propius ergo <lb/>centro E e&longs;t Q ip&longs;o puncto S, minor e&longs;t igitur proportio <lb/>EG ad LQ qu&agrave;m ES ad SL. <!-- KEEP S--></s>
            <s id="s.000784">Minor ergo potentia requi&shy;<lb/>ritur in L ad &longs;u&longs;tinendum pondus E ex fulcimento Q hoc <lb/>e&longs;t I, qu&agrave;m requiratur in N ad &longs;u&longs;tinendum pondus G ex <lb/>fulcimento P, hoc e&longs;t K. <!-- KEEP S--></s>
            <s id="s.000785">Minor ergo potentia requiritur <pb xlink:href="007/01/087.jpg"/>ad transferendam maiorem retam CD vltra offendicu&shy;<lb/>lum IV, hoc e&longs;t, DH, qu&agrave;m requiratur ad trans ferendam <lb/>minorem vltra offendiculum KT, hoc e&longs;t HD, quod fue&shy;<lb/>rat o&longs;tendendum. </s>
          </p>
          <p type="main">
            <s id="s.000786">Ad h&aelig;c, qu&aelig;ri pote&longs;t, quo pacto plau&longs;trorum rot&aelig; <lb/>in ip&longs;a plau&longs;tri conuer&longs;ione &longs;e habeant, nempe qu&aelig; &longs;it li&shy;<lb/>nea illa curua, quam in conuer&longs;ione de&longs;cribunt. </s>
          </p>
          <figure id="id.007.01.087.1.jpg" xlink:href="007/01/087/1.jpg"/>
          <p type="main">
            <s id="s.000787">E&longs;to rotarum in <lb/>plano orbita, <expan abbr="d&umacr;">dum</expan> plau&shy;<lb/>&longs;trum rect&acirc; procedit <lb/>AB, CD, Sunt autem i&shy;<lb/>p&longs;&aelig; line&aelig;, quod o&longs;ten&shy;<lb/>demus po&longs;tea, &aelig;quedi&shy;<lb/>&longs;tantes. </s>
            <s id="s.000788">Sit itaque pun&shy;<lb/>ctum. </s>
            <s id="s.000789">B illud in quod <lb/>rota qu&aelig; per AB &longs;er&shy;<lb/>tur, e&ograve; delata planum <lb/>tangit. </s>
            <s id="s.000790">D ver&ograve; alterius rot&aelig; at que plani contactus. </s>
            <s id="s.000791">Igitur <lb/>dum plau&longs;tri fit conuer&longs;io, punctum D conuer&longs;ionis fit <lb/>centrum. </s>
            <s id="s.000792">Stat enim interim rota &amp; circa lineam conuer&shy;<lb/>titur, qu&aelig; &aring; puncto contactus D per rot&aelig; centrum ducta <lb/>horizontis plano e&longs;t perpendicularis. </s>
            <s id="s.000793">ea autem &longs;tante, ro&shy;<lb/>ta qu&aelig; in B circa centrum D <expan abbr="&longs;emicircul&umacr;">&longs;emicirculum</expan> pertran&longs;it DEF, <lb/>vbi autem rota B, peruenerit in F, plau&longs;tro iam in oppo&longs;i&shy;<lb/>tam partem conuer&longs;o, rota qu&aelig; e&longs;t in D per lineam DC, <lb/>qu&aelig; ver&ograve; in F per rectam FG mouetur, plau&longs;triqueue fit re&shy;<lb/>gre&longs;&longs;us. </s>
            <s id="s.000794">Et quoniam vel D in ip&longs;a conuer&longs;ione &longs;tat omnino <lb/>nec quicquam progreditur, vt in prima figura, vel non &longs;tat <lb/>vt in &longs;ecunda, quo ca&longs;u portionem parui circuli de&longs;cribit, <lb/>ip&longs;i maiori circulo &amp; exteriori concentricam. </s>
            <s id="s.000795">Vnde col&shy;<lb/>ligimus, Plau&longs;trorum conuer&longs;iones flexione&longs;que &longs;emper <lb/>circa centrum, &amp; concentricorum circulorum portiones <lb/>fieri, <emph type="italics"/>H<emph.end type="italics"/>inc etiam di&longs;cimus, cur veteres, vt ex antiquis co&shy;<pb xlink:href="007/01/088.jpg"/>gno&longs;cimus ve&longs;tigijs, circos in quibus cur&longs;us quadrigarum <lb/>fiebant ea forma qu&aelig; apparet, efformauerint. </s>
            <s id="s.000796">Hoc etiam <lb/>theorema probamus. </s>
          </p>
          <p type="main">
            <s id="s.000797">Cylindros, quorum ba&longs;es axi &longs;unt perpendiculares, <lb/>dum in &aelig;quato plano conuoluuntur, rect&acirc; incedere &amp; <lb/>per parallelas, quarum di&longs;tantia axis &longs;eu latoris longitudi&shy;<lb/>ne pr&aelig;finitur. </s>
          </p>
          <figure id="id.007.01.088.1.jpg" xlink:href="007/01/088/1.jpg"/>
          <p type="main">
            <s id="s.000798">E&longs;to enim Cylin&shy;<lb/>drus ABCD, cuius a&shy;<lb/>xis GH, <expan abbr="horiz&omacr;tis">horizontis</expan> pla&shy;<lb/>no in&longs;i&longs;tens &longs;ecundum <lb/>latus AB, cui latus op&shy;<lb/>po&longs;itum &amp; aequale CD. <lb/><!-- KEEP S--></s>
            <s id="s.000799">Moueatur Cylindrus <lb/>rotans, donec latus <lb/>CD, in plano &longs;it vbi EF. <!-- KEEP S--></s>
            <s id="s.000800">De&longs;cribat autem circuli CB <expan abbr="line&atilde;">lineam</expan> <lb/>BF. <!-- KEEP S--></s>
            <s id="s.000801">Circulo ver&ograve; AD lineam AE. <!-- KEEP S--></s>
            <s id="s.000802">Dico eas rectas e&longs;&longs;e, &amp; <lb/>parallelas. </s>
            <s id="s.000803">Si enim &longs;uperficies ba&longs;ium DA, CB, extendan&shy;<lb/>tur ita vt horizontis planum &longs;ecent, illud &longs;ecabunt iuxta <lb/>lineas AE BF, recta ergo e&longs;t vtraque. </s>
            <s id="s.000804">Sed &amp; parallelas e&longs;&longs;e <lb/>ad inuicem ita o&longs;tendimus. </s>
            <s id="s.000805">quoniam &longs;emicirculus AD, <lb/>&aelig;qualis e&longs;t &longs;emicirculo BC, erit linea AE, &aelig;qualis line&aelig; <lb/>BF, &longs;ed &amp; AB, &aelig;qualis e&longs;t ip&longs;i DC, quare &amp; ip&longs;i EF. <!-- KEEP S--></s>
            <s id="s.000806">Oppo&shy;<lb/>&longs;ita igitur quadrilateri figura ABFE latera &aelig;qualia &longs;unt, <lb/>quare EF &aelig;quedi&longs;tat ip&longs;i AB, tum AE ip&longs;i BF, quod fue&shy;<lb/>rat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.000807">Probabimus etiam &longs;i cylindri ba&longs;es axi perpendicu&shy;<lb/>lares non fuerint, &amp; ideo ellip&longs;es in ip&longs;a rotatione perpla&shy;<lb/>num, parallelas quidem de&longs;cribere, &longs;ed non rectas. </s>
          </p>
          <p type="main">
            <s id="s.000808">E&longs;to enim Cylindrus ABCD, cuius ba&longs;es ellip&longs;es <expan abbr="inuic&emacr;">inuicem</expan> <lb/><expan abbr="&aelig;quedi&longs;t&atilde;tes">&aelig;quedi&longs;tantes</expan>, quarum axes longiores AB, CD, Commu&shy;<lb/>nis autem &longs;ectio cylindri &amp; plani ad axem &amp; horizontem <lb/>planum perpendicularis EHF. <!-- KEEP S--></s>
            <s id="s.000809">Diuidatur autem &longs;emicir-<pb xlink:href="007/01/089.jpg"/>culus EHF in partes &aelig;quales quatuor FI, IH, HG, GE. <lb/><figure id="id.007.01.089.1.jpg" xlink:href="007/01/089/1.jpg"/><lb/>Tum per diui&longs;ionum puncta lateri parallelae, rect&aelig; ducan&shy;<lb/>tur KGL, M<emph type="italics"/>H<emph.end type="italics"/>N, OIP, qu&aelig; quidem <expan abbr="c&umacr;">cum</expan> ba&longs;es AMB, DNC <lb/>parallel&aelig; &longs;int, erunt inuicem &aelig;quales, cumqueue circum&shy;<lb/>ferentia E<emph type="italics"/>H<emph.end type="italics"/>F &aelig;quales, eosqueue rectos angulos <expan abbr="c&omacr;&longs;tituent">con&longs;tituent</expan>. <lb/></s>
            <s id="s.000810">Ducatur po&longs;t h&aelig;c &longs;eor&longs;um recta QR, &amp; eidem perpendi&shy;<lb/>cularis ST eam &longs;ecans in V. applicetur autem rect&aelig; ST <lb/>&aelig;qualis Cylindri lateri BC, ip&longs;a <foreign lang="greek">hz. </foreign></s>
            <s id="s.000811">ita tamen vt punctum <lb/>E congruat puncto V, &longs;itqueue V<foreign lang="greek">h</foreign> &aelig;qualis EB, V<foreign lang="greek">z</foreign> ver&ograve; &aelig;&shy;<lb/>qualis EC. <!-- KEEP S--></s>
            <s id="s.000812">Tum fiant VX, XY, YZ, Z<foreign lang="greek">a</foreign> &aelig;quales ip&longs;is EG, <lb/>G<emph type="italics"/>H<emph.end type="italics"/>, <emph type="italics"/>H<emph.end type="italics"/>I, IF, &amp; per puncta X, Y, Z, <foreign lang="greek">a</foreign> &amp; paralleli ip&longs;i ST du&shy;<lb/>cantur <foreign lang="greek">o a p, n *z c, l g m, k x q</foreign>, tum &amp; his ex altera parte re&shy;<lb/>&longs;pondentes parallel&aelig; per puncta <foreign lang="greek">b, g, d, e. </foreign></s>
            <s id="s.000813">Sit autem <foreign lang="greek">o a</foreign> &aelig;&shy;<lb/>qualis AF, <foreign lang="greek">a</foreign> &lt;11&gt; &aelig;qualis FD, item <foreign lang="greek">e</foreign> &lt;10&gt;, &aelig;qualis EC, <foreign lang="greek">e s</foreign> &aelig;qualis <lb/>EB, &longs;ed &amp; <foreign lang="greek">n *z</foreign> aequalis OI, <foreign lang="greek">*z c</foreign> ip&longs;i P, <foreign lang="greek">l</foreign>y ip&longs;i MH, y <foreign lang="greek">m</foreign> ver&ograve; ip&longs;i <lb/>HN, <expan abbr="t&umacr;">tum</expan> <foreign lang="greek">k x</foreign> ip&longs;i KG. &amp; <foreign lang="greek">x q</foreign>, ip&longs;i GL &amp; ip&longs;is &aelig;quales &amp; aequa&shy;<lb/>liter po&longs;it&aelig; ad partes R, ali&aelig; parallel&aelig; <expan abbr="apt&emacr;tur">aptentur</expan> per <foreign lang="greek">b, g, d, c</foreign>, <pb xlink:href="007/01/090.jpg"/>quibus ita di&longs;po&longs;itis per puncta <foreign lang="greek">o, n, l, k, h</foreign>, item per <foreign lang="greek">p, c, m, q, z</foreign>. <lb/></s>
            <s id="s.000814">ducantur line&aelig; <foreign lang="greek">oh, pz</foreign>, curu&aelig; quidem &amp; eodem pacto a&shy;<lb/>li&aelig; curu&aelig; illis re&longs;pondentes <foreign lang="greek">h &lt;10&gt;, zs</foreign>, Erunt igitur <foreign lang="greek">o, h, &lt;10&gt;, <lb/>p, z, s</foreign>, parallel&aelig; quidem eo quod lineae qu&aelig; inter ip&longs;as du&shy;<lb/>cuntur, parallel&aelig; &longs;int &amp; &aelig;quales, non tamen rect&aelig; ill&aelig;, <lb/>&longs;ed curu&aelig;. </s>
            <s id="s.000815">Moto igitur Cylindro circulus EHF rectam <lb/>de&longs;cribet<foreign lang="greek">ae</foreign>, ellip&longs;is ver&ograve; AMB, curuam <foreign lang="greek">o h r</foreign>, ellip&longs;is au&shy;<lb/>rem DNC, ip&longs;am curuam <foreign lang="greek">pzs. </foreign></s>
            <s id="s.000816">In hoc <expan abbr="aut&emacr;">autem</expan> Cylindri mo&shy;<lb/>tu illud mirabile, velociores nempe, in ip&longs;a rotatione e&longs;&longs;e <lb/>ellip&longs;es ip&longs;o circulo EHF. <!-- KEEP S--></s>
            <s id="s.000817">Ducatur enim recta<foreign lang="greek">o&lt;10&gt;</foreign> qu&aelig; oc&shy;<lb/>currat ip&longs;i VS in S, &amp; <foreign lang="greek">oh</foreign> iungatur, fietqueue triangulum <lb/><foreign lang="greek">oh</foreign>S. e&longs;t autem, angulus <foreign lang="greek">o</foreign> S <foreign lang="greek">h</foreign> rectus, maior erg. <foreign lang="greek">oh</foreign> i&shy;<lb/>p&longs;a <foreign lang="greek">o</foreign> S, &longs;ed recta <foreign lang="greek">o</foreign> S &aelig;qualis e&longs;t ip&longs;i<foreign lang="greek">an</foreign>, hoc e&longs;t, &longs;emicircu&shy;<lb/>lo FHE. multo maior e&longs;t autem curua, <foreign lang="greek">o, n, l, k, h</foreign>, ip&longs;a recta <lb/><foreign lang="greek">oh</foreign>, &longs;ed eodem tempore quo &longs;emicirculus EHF conficit <lb/>in rotatione <expan abbr="&longs;pati&umacr;">&longs;patium</expan> <foreign lang="greek">a</foreign> V, eodem dimidia ellip&longs;is BMA me&shy;<lb/>titur curuam <foreign lang="greek">onlkh. </foreign></s>
            <s id="s.000818">velocior igitur e&longs;t ellip&longs;is ip&longs;o cir&shy;<lb/>culo. </s>
          </p>
          <p type="main">
            <s id="s.000819">H&aelig;c quoque &longs;peculatio ad motum qui &longs;ecundum <lb/>ab&longs;idem fit, manife&longs;t&egrave; pertinet. </s>
            <s id="s.000820">Coni, quorum ba&longs;es cir&shy;<lb/>culi &longs;unt, &longs;i in plano &longs;ecundum latus rotentur, ba&longs;i circu&shy;<lb/>lum de&longs;cribunt, cuius centrum immobile coni ip&longs;ius e&longs;t <lb/>vertex, &longs;emidiameter ver&ograve; ip&longs;um latus. </s>
          </p>
          <figure id="id.007.01.090.1.jpg" xlink:href="007/01/090/1.jpg"/>
          <p type="main">
            <s id="s.000821">E&longs;to conus ABC cu&shy;<lb/>ius vertex C ba&longs;is AB, axis <lb/>DC, ba&longs;is ver&ograve; centrum, <lb/>D, latus quo planum tan&shy;<lb/>git BC, &longs;ecatur itaque Co&shy;<lb/>nus per latus BC &amp; axem <lb/>DE &agrave; plano horizonti per&shy;<lb/>pendiculari, cuius &amp; coni <lb/>communis &longs;ectio e&longs;t ABC <lb/>triangulum, &amp; quoniam coni grauitatis centrum e&longs;t in <pb xlink:href="007/01/091.jpg"/>axe ip&longs;o, conus in partes &aelig;que <expan abbr="p&omacr;derantes">ponderantes</expan> &longs;ecatur AEBC, <lb/>AFBC, &longs;tat ergo conus &longs;ibimet &aelig;quilibris. </s>
            <s id="s.000822">Si autem &agrave; po&shy;<lb/>tentia quadam moueatur, puta ab A ver&longs;us F, trahitur &longs;e&shy;<lb/>micirculus BEA, &agrave; &longs;emicirculo AFB, &amp; ita fit rotatio. </s>
            <s id="s.000823">Ita&shy;<lb/>que &longs;i imaginemur, in finitos v&longs;que ad verticem parallelos <lb/>ba&longs;i circulos, eorum &longs;emicirculi in ip&longs;o motu &amp; trahent &amp; <lb/>trahentur; at cum ad verticem circuli de&longs;inant, nec ibi &longs;e&shy;<lb/>micirculi &longs;int qui trahant &amp; trahantur, motus rotationis <lb/>pror&longs;us ce&longs;&longs;at &amp; vertex ip&longs;e immobilis fit rotationis cen&shy;<lb/>trum. </s>
            <s id="s.000824">Quoniam igitur lateris BC, punctum C &longs;tat, B ver&ograve; <lb/>circa ip&longs;um mouetur, in ip&longs;o motu circulus de&longs;cribitur <lb/>BHIK, cuius &longs;emidiameter BC, &amp; eodem pacto alij cir&shy;<lb/>culi in cono, qui ba&longs;i HEBF &longs;unt &aelig;quedi&longs;tantes, circulos <lb/>in plano circa idem centrum de&longs;cribent, vt facile videre <lb/>e&longs;t in obiecto &longs;chemate. </s>
            <s id="s.000825">Huic &longs;imilem demon&longs;trationem <lb/>affert Heron in libello Automatum, quem nos Tyrones <lb/>adhuc vernacule &egrave; Gr&aelig;co translatum, Venetijs pr&aelig;lo <lb/>&longs;ubiecimus. </s>
          </p>
          <p type="main">
            <s id="s.000826">Porr&ograve; &longs;i conus rotundus pro ba&longs;i ellip&longs;im habeat, <lb/>&longs;ectionem videlicet per planum axi non perpendiculare, <lb/>in ip&longs;a rotatione, &longs;tante vertice, ellip&longs;is ba&longs;is, ellip&longs;im de&shy;<lb/>&longs;cribit in plano, cuius maior diameter &agrave; puncto quod co&shy;<lb/>ni vertex e&longs;t, ita diuiditur, vt diametri pars maior &aelig;qualis <lb/>&longs;it lateri maximo; minor ver&ograve; &aelig;qualis lateri minimo. </s>
            <s id="s.000827">Sed <lb/>h&aelig;c ad aliam pertinent &longs;peculationem. </s>
          </p>
          <p type="main">
            <s id="s.000828">His itaque de motu rotundorum, qui circa ab&longs;idem <lb/>fit, con&longs;ideratis, reliquum e&longs;&longs;et de motu trochlearum, qui <lb/>circa centrum &longs;it, opportun&egrave; agere, &longs;ed c&ugrave;m in &longs;equenti <lb/>qu&aelig;&longs;tione de hoc &longs;ermonem faciat Philo&longs;ophus, ad ea <lb/>qu&aelig; ibi di&longs;putabuntur, lectorem ablegamus. </s>
          </p>
          <p type="main">
            <s id="s.000829">Mod&ograve; de tertia motus &longs;pecie nobis erit &longs;ermo; in <lb/>qua quidem &longs;pecie nonnulla perpendemus, qu&aelig; omi&longs;it A&shy;<lb/>ri&longs;toteles. <!-- KEEP S--></s>
            <s id="s.000830">Agitur autem h&icirc;c de rotundorum corporum <pb xlink:href="007/01/092.jpg"/>motu, qui fit &ccedil;irca axem horizonti perpendicularem, axis <lb/>altera extremitate in eodem horizontis plano manente, <lb/>vti videre e&longs;t in ip&longs;is figulorum rotis. </s>
          </p>
          <p type="main">
            <s id="s.000831">Hanc motus &longs;peciem in extrema qu&aelig;&longs;tionis parte <lb/>cum duabus alijs &longs;peciebus comparans ait, eam qu&aelig; in <lb/>obliquo fit motionem &lpar;ita enim hanc, de qua agimus, ap&shy;<lb/>pellat&rpar; ip&longs;am impellere mouentem, hoc e&longs;t, nullum ex &longs;e <lb/>ad motum propen&longs;ionem habere, nutumue, &amp; omnia illi <lb/>e&longs;&longs;e &agrave; motore, &longs;ecundum ver&ograve; eam motionem, qu&aelig; &longs;upra <lb/>diametrum e&longs;t, &longs;e ip&longs;um mouere circulum. </s>
            <s id="s.000832">Dixerat enim, <lb/>ea referens qu&aelig; &longs;uperi&ugrave;s circa principium de circulo ver&shy;<lb/>ba faciens, examinauerat, circulum ex duabus fieri latio&shy;<lb/>nibus, altera pr&aelig;ter, altera ver&ograve; &longs;ecundum naturam, &amp; <lb/>ideo hanc &longs;emper nutum habere, &amp; ceu continuo motam <lb/>ab eo moueri qui mouet. </s>
            <s id="s.000833">Videtur autem clar&egrave; profiteri, <lb/>ideo difficiliorem e&longs;&longs;e huius terr&aelig; &longs;peciei motum, eo <lb/>qu&ograve;d nutu careat proprio &amp; tantum ab alieno, vt ita di&shy;<lb/>cam, motore, moueatur. </s>
          </p>
          <p type="main">
            <s id="s.000834">Veruntamen motum hunc facilitate alijs illis duo&shy;<lb/>bus nequaquam cedere, facil&egrave; ex &longs;equentibus o&longs;tende&shy;<lb/>mus. </s>
          </p>
          <p type="main">
            <s id="s.000835">Primo, quia pondus totum rotati corporis, ex graui&shy;<lb/>tatis centro quod in ip&longs;o axe e&longs;t &agrave; plano cui nititur, &longs;u&longs;ti&shy;<lb/>netur: minima quidem &longs;ui parte axe ip&longs;o tangente <expan abbr="plan&umacr;">planum</expan> <lb/>vnde fit, nullam fer&egrave; dum rotatur corpus, circa centrum <lb/>vbi nititur, frictionem partium fieri. </s>
            <s id="s.000836">Pr&aelig;terea grauitatis <lb/>centrum &longs;emper &longs;tat, nec minimum quidem in ip&longs;a rota&shy;<lb/>tione attollitur, quod &longs;an&egrave; cum natur&aelig; &longs;it repugnans, dif&shy;<lb/>ficultatem facit. </s>
            <s id="s.000837">Ad h&aelig;c circa axem ita libratur rota, vt <lb/>quantumuis exigua potentia alteri parti applicetur, alte&shy;<lb/>ra illico &longs;uperata moueatur. </s>
            <s id="s.000838">Licet enim propri&egrave; ea <expan abbr="tant&umacr;">tantum</expan> <lb/>corpora &aelig;quilibrare dicantur, qu&aelig; ob ponderis hinc in de <pb xlink:href="007/01/093.jpg"/>&aelig;qualitatem horizonti fiunt &aelig;quidi&longs;tantes, nihilominus <lb/>&amp; hic aliquam e&longs;&longs;e &aelig;quilibrij &longs;imilitudinem patebit. </s>
          </p>
          <figure id="id.007.01.093.1.jpg" xlink:href="007/01/093/1.jpg"/>
          <p type="main">
            <s id="s.000839">E&longs;to enim rota ABCD, <lb/>cuius axis horizonti perpendi&shy;<lb/>cularis FEG tran&longs;iens per cen&shy;<lb/>trum E, tangens autem planum <lb/>in puncto G. <!-- KEEP S--></s>
            <s id="s.000840">Ducatur diame&shy;<lb/>ter BED, Itaque &longs;i per diame&shy;<lb/>trum BED, &amp; axem FEG cor&shy;<lb/>pus diuidatur, eo qu&ograve;d <expan abbr="centr&umacr;">centrum</expan> <lb/>grauitatis in axe inueniatur, <lb/>corpus ip&longs;um in duas partes <expan abbr="t&umacr;">tum</expan> <lb/>mole tum <expan abbr="p&omacr;dere">pondere</expan> &aelig;quales &longs;ecabitur, nempe BAD, BCD. <lb/><!-- KEEP S--></s>
            <s id="s.000841">Nulla igitur adhibita vi extranea &longs;tabit corpus in <expan abbr="quod&atilde;">quodam</expan>, <lb/>vt diximus, &aelig;quilibrio. </s>
            <s id="s.000842">At alteri partium potenti&acirc; quauis <lb/>licet exigua appo&longs;it&acirc;, puta in C, pr&aelig;ualebit pars BCD, &amp; <lb/>partem BAD vel impellet vel rapiet, alter&acirc; interim eius <lb/>motui ob&longs;equente. </s>
            <s id="s.000843">Potentia igitur qu&aelig; in C, nullam rem <lb/>qu&aelig; impediat inueniens, veloci&longs;&longs;im&egrave; rotam mouet, quod <lb/>eo facili&ugrave;s velocius queue fit, quo magis rota e&longs;t in motu, e&shy;<lb/>ius ver&ograve; diameter maior &amp; potentia mouens &agrave; centro re&shy;<lb/>motior, &amp; &longs;an&egrave; motus <expan abbr="facilitat&emacr;">facilitatem</expan> inde cogno&longs;cimus, qu&ograve;d <lb/>ip&longs;o impul&longs;ore ab impul&longs;u ce&longs;&longs;ante, diuti&longs;&longs;im&egrave; rota im&shy;<lb/>pre&longs;&longs;um motum &longs;eruet, nec ni&longs;i po&longs;t longam rotationem <lb/>omnino quie&longs;cat. </s>
          </p>
          <p type="main">
            <s id="s.000844">C&aelig;ter&ugrave;m quia &longs;icco, vt aiunt, pede Ari&longs;toteles qu&aelig; <lb/>ad hunc motum <expan abbr="pertin&emacr;t">pertinent</expan> pertran&longs;ijt, nos qu&aelig;dam qu&aelig; ad <lb/>hanc rem faciunt, diligenti&ugrave;s expendemus. </s>
          </p>
          <p type="main">
            <s id="s.000845">Qu&aelig;rimus igitur prim&ograve;; Cur ea qu&aelig; hoc pacto <expan abbr="ro-t&atilde;tur">ro&shy;<lb/>tantur</expan>, in ip&longs;a rotatione locum non mutent, ni&longs;i extrin&longs;eca <lb/>aliqua id fiat ex cau&longs;&longs;a. </s>
          </p>
          <p type="main">
            <s id="s.000846">E&longs;to enim rota aut aliud quippiam rotundum ceu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho&shy;<pb xlink:href="007/01/094.jpg"/><figure id="id.007.01.094.1.jpg" xlink:href="007/01/094/1.jpg"/><lb/>rizonti perpendicularem mo&shy;<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. <!-- KEEP S--></s>
            <s id="s.000847">Mod&ograve; circa <lb/>centrum E in finiti imaginentur <lb/>circuli, alij alijs minores v&longs;que <lb/>ad <expan abbr="centr&umacr;">centrum</expan> ip&longs;um, vti &longs;unt FGH; <lb/>ibi enim circuli e&longs;&longs;e de&longs;inunt, <lb/>vbi nullum amplius e&longs;t &longs;patium. <lb/></s>
            <s id="s.000848">Applicetur itaque potentia in <lb/>B, qu&aelig; rotam v. <!-- REMOVE S-->geat ver&longs;us A. <lb/>eodem igitur tempore &amp; in&longs;imul A ver&longs;us D, D ver&longs;us C, <lb/>&amp; C ver&longs;us B mouebitur. </s>
            <s id="s.000849">quantum enim &longs;emicirculorum <lb/>&agrave; parte CBA tran&longs;it vltra diametrum AEC, tantundem <lb/>&longs;emicirculorum, qui &longs;unt ad partem ADC, tran&longs;ibit ad <lb/>partes CBA. <!-- KEEP S--></s>
            <s id="s.000850">At vbi de&longs;ierit motus, ibi de&longs;init rotatio; vbi <lb/>autem de&longs;init &longs;patium, de&longs;init motus, &longs;ed vbi de&longs;inunt cir&shy;<lb/>culi, de&longs;init &longs;patium, quare in centro cum non &longs;int circuli, <lb/>nec &longs;patium ibi de&longs;init motus. </s>
            <s id="s.000851">nulla enim ade&longs;t ratio, cur <lb/>ip&longs;um corpus alio &agrave; loco in quo e&longs;t, ex rotatione transfe&shy;<lb/>ratur. </s>
            <s id="s.000852">Stat ergo rotans, quod fuerat demon&longs;trandum. </s>
            <s id="s.000853">E&longs;t <lb/>autem h&aelig;c demon&longs;tratio ei &longs;imilis, quam &longs;upr&agrave; retuli&shy;<lb/>mus de coni in plano circa verticem rotatione, quam ab <lb/>Herone in Automatis excogitatam diximus. </s>
          </p>
          <p type="main">
            <s id="s.000854">Addimus in hoc rotationis genere corpus in ip&longs;o &shy;<lb/>motu fieri leuius, idqueue eo magis, quo rotatio velocior. <lb/></s>
            <s id="s.000855">Cau&longs;&longs;a e&longs;t, quod lateralis motus eum motum aliqualiter <lb/>impedit, qui ex naturali grauitate fit ad centrum, idcirco <lb/>experienti&acirc; docemur, leui&longs;&longs;imos e&longs;&longs;e turbines, quibus pu&shy;<lb/>eri ludunt, &longs;i manus teneantur palm&acirc;, dum citi&longs;&longs;ima rota&shy;<lb/>tione mouentur. </s>
          </p>
          <p type="main">
            <s id="s.000856">Ad h&aelig;c alia proponitur, &amp; &longs;oluitur qu&aelig;&longs;tio, Cur ro&shy;<lb/>tunda corpora huic motionis generi &longs;int aptiora. </s>
          </p>
          <p type="main">
            <s id="s.000857">Explorati&longs;&longs;imum e&longs;t, corporum, qu&aelig; ita mouentur, <pb xlink:href="007/01/095.jpg"/>partes eo e&longs;&longs;e velociores, quo magis &agrave; centro, circa quod <lb/>mouentur, fuerint remotiores. </s>
            <s id="s.000858">maius enim eodem tem&shy;<lb/>pore &longs;patium pertran&longs;eunt. </s>
            <s id="s.000859">quo igitur figura ijs partibus, <lb/>qu&aelig; longius &agrave; centro ab&longs;unt, abundauerit magis, eo faci&shy;<lb/>lius, &amp; velocius in circulum rotata mouebitur. </s>
            <s id="s.000860">Mod&ograve; o&shy;<lb/>&longs;tendemus, circularem c&aelig;teras omnes ea qua diximus <lb/>partium &agrave; centro remoti&longs;&longs;imarum copi&acirc; abundare. </s>
          </p>
          <figure id="id.007.01.095.1.jpg" xlink:href="007/01/095/1.jpg"/>
          <p type="main">
            <s id="s.000861">E&longs;to triangulum puta &aelig;qui&shy;<lb/>laterum, ABC circa centrum D. <lb/><!-- KEEP S--></s>
            <s id="s.000862">Ducantur Catheti per centrum ab <lb/>oppo&longs;itis angulis ad oppo&longs;ita late&shy;<lb/>ra ADG, BDF, CDE, erunt autem <lb/>lateribus perpendiculares. </s>
            <s id="s.000863"><expan abbr="quoni&atilde;">quoniam</expan> <lb/>igitur latera AD, DB, DC, rectis <lb/>angulis &longs;ubtenduntur, maiora <expan abbr="er&umacr;t">erunt</expan> <lb/>lateribus DE, DF, DG. tres igitur <lb/>line&aelig; in hoc triangulo &longs;unt longi&longs;&longs;im&aelig; DA; DB, DC. tres <lb/>ver&ograve; breui&longs;&longs;im&aelig; DE, DG, DF, quamobrem rotato &longs;uper <lb/>centrum D triangulo, tres tantum partes eius ABC velo&shy;<lb/>ci&longs;&longs;im&aelig; erunt, tres ver&ograve; tardi&longs;&longs;im&aelig; E, G, F. <!-- KEEP S--></s>
            <s id="s.000864">Minus igitur a&shy;<lb/>pta e&longs;t motui huic triangularis figura, quam quadrata, in <lb/>qua partes &agrave; centro remoti&longs;&longs;im&egrave;, &amp; ideo veloci&longs;&longs;im&egrave; &longs;unt <lb/>quatuor. </s>
            <s id="s.000865"><expan abbr="Itaq;">Itaque</expan> quo magis laterata figura angulis abunda&shy;<lb/>bit, eo magis erit ad hunc, &amp; c&aelig;teros omnes circulares <lb/>motus aptior. </s>
            <s id="s.000866">At circulus infinitas, vt ita dicam, partes &agrave; <lb/>centro remoti&longs;&longs;imas habet, itaque nulla figura e&longs;t circu&shy;<lb/>lari, in ip&longs;a rotatione, commodior atque velocior. </s>
            <s id="s.000867">Alia <lb/>quoque de cau&longs;&longs;a id fit, quod dum circularis figura mo&shy;<lb/>uetur, nullis eminentibus angulis a&euml;rem verberet <expan abbr="circ&umacr;-&longs;t&atilde;tem">circum&shy;<lb/>&longs;tantem</expan>, ex qua verberatione motus impeditus &longs;it tardior. <lb/></s>
            <s id="s.000868">Qu&aelig;ri etiam pote&longs;t, Num axe in clinato, rot&aelig; motus ali&shy;<lb/>qualiter impediatur? </s>
            <s id="s.000869">Nos negatiuam partem amplecti&shy;<lb/>mur. </s>
          </p>
          <pb xlink:href="007/01/096.jpg"/>
          <figure id="id.007.01.096.1.jpg" xlink:href="007/01/096/1.jpg"/>
          <p type="main">
            <s id="s.000870">E&longs;to enim tota ABCD, cuius cen&shy;<lb/>trum E axis inclinatus, circa quem <lb/>conuertitur EGF. <!-- KEEP S--></s>
            <s id="s.000871">Duobus aute pun&shy;<lb/>ctis fulcitur GF. </s>
            <s id="s.000872">Sit autem tum gra&shy;<lb/>uius tum figur&aelig; centrum E, Perpen&shy;<lb/>dicularis vero per inferius fulcimen&shy;<lb/>tum tran&longs;iens HFI. </s>
            <s id="s.000873">Conuer&longs;a igitur <lb/>rota, grauitatis centrum &longs;tabit nec &agrave; <lb/>&longs;uo &longs;itu &longs;ur&longs;um deor&longs;umue mouebi&shy;<lb/>tur. </s>
            <s id="s.000874">E&longs;t autem axis FEG, ceu vectis in <lb/>quo pondus in E, potenti&aelig; &longs;u&longs;tinentes GF; non enim hic <lb/>vt in axe perpendiculari pondus totum ab inferiori fulci&shy;<lb/>mento &longs;u&longs;tinetur. </s>
            <s id="s.000875">quo igitur minor erit proportio FE ad <lb/>FG, eo minori indigebit potenti&acirc; is qui pondus &longs;u&longs;tinet in <lb/>G. <!-- KEEP S--></s>
            <s id="s.000876">Et h&aelig;c &longs;an&egrave; ita &longs;e habent, grauitatis &ccedil;entro in axe ip&longs;o <lb/>con&longs;tituto, &longs;i enim extra fuerit motus impeditur &amp; moto&shy;<lb/>re ce&longs;&longs;ante cit&ograve; quie&longs;cit. </s>
            <s id="s.000877">E&longs;to enim grauitatis centrum in <lb/>K. <!-- KEEP S--></s>
            <s id="s.000878">Dum igitur circa axem fit motus, centrum circulatum <lb/>aliquando erit in L; Secet autem rot&aelig; diameter AC per&shy;<lb/>pendicularem Hl in M. <!-- KEEP S--></s>
            <s id="s.000879">Porr&ograve; &agrave; punctis LK ad ip&longs;am <expan abbr="per-p&emacr;dicularem">per&shy;<lb/>pendicularem</expan> ducantur ad rectos angulos line&aelig; LN, KO. <lb/></s>
            <s id="s.000880">Maior e&longs;t autem MK ip&longs;a ML, maior ergo MO, ip&longs;a MN. <lb/>magis igitur &agrave; mundi centro di&longs;tat punctum N puncto O. <lb/><!-- KEEP S--></s>
            <s id="s.000881">Centrum ergo grauitatis K &longs;i liber&egrave; dimittatur, requie&longs;cet <lb/>in K &amp; contranaturam transferetur in L. <!-- KEEP S--></s>
            <s id="s.000882">Ce&longs;&longs;ante igitur <lb/>violenti&acirc; &amp; pr&aelig;ualente natur&acirc; cit&ograve; rota &longs;u&acirc; &longs;ponte quie&shy;<lb/>&longs;cet, quod fuerat o&longs;tendendum. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000883">QV&AElig;STIO IX.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000884"><emph type="italics"/>Qu&aelig;ritur, Cur ea qu&aelig; per maiores circulos tolluntur, &amp; trahuntur <lb/>facili&ugrave;s, &amp; celeri&ugrave;s moueri contingat, veluti maioribus tro&shy;<lb/>chleis, &amp; &longs;cytalis &longs;imiliter?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000885">Re&longs;pondet ad h&aelig;c Philo&longs;ophus, forte id euenire, quo-<pb xlink:href="007/01/097.jpg"/>niam quanto maior fuerit illa qu&aelig; &agrave; centro e&longs;t, in &aelig;quali <lb/>tempore maius mouetur &longs;patium. </s>
            <s id="s.000886">quamobrem &aelig;quali <lb/>exi&longs;tente onere idem faciet. </s>
            <s id="s.000887">Ita enim dixerat de <expan abbr="librar&umacr;">librarum</expan> <lb/>natura, &amp; differentijs agens, maiores minoribus exactio&shy;<lb/>res e&longs;&longs;e. </s>
            <s id="s.000888">Circulos ver&ograve; libras, in quibus centrum &longs;partum, <lb/>&longs;emidiametri hinc in de &aelig;qualia brachia. </s>
          </p>
          <p type="main">
            <s id="s.000889">Quod vltimo loco affirmauit, trochleas e&longs;&longs;e in&longs;tar <lb/>librarum, verum e&longs;t. </s>
            <s id="s.000890">Quod autem dixit, facili&ugrave;s &amp; cele&shy;<lb/>rius mouere maiores libras ijs qu&aelig; minores &longs;unt, &longs;i &longs;impli&shy;<lb/>citer intelligatur, fal&longs;um, quippe quod facilitas motus, in <lb/>tractorijs machinis velocitati &longs;it contraria, quod demon&shy;<lb/>&longs;trauit Guid. <!-- REMOVE S-->Vbald. <!-- REMOVE S-->in tractatu de Trochlea in 2. Corol&shy;<lb/>lario propo&longs;itione vltima. </s>
          </p>
          <p type="main">
            <s id="s.000891">Ad id autem quod dixit, quo <expan abbr="maior&emacr;s">maiores</expan> fuerint tro&shy;<lb/>chle&aelig;, eo facili&ugrave;s mouere, non e&longs;t, vt dicebamus, &longs;impli&shy;<lb/>citer verum, quod facil&egrave; o&longs;tendemus. </s>
          </p>
          <figure id="id.007.01.097.1.jpg" xlink:href="007/01/097/1.jpg"/>
          <p type="main">
            <s id="s.000892">E&longs;to enim trochlea AB circa centrum C, appen&longs;a in <lb/>puncto D, perpendicularis qu&aelig; ad mundi centrum DCE, <lb/>pondera &aelig;qualia vtrinque appen&longs;a FG. <!-- KEEP S--></s>
            <s id="s.000893">E&longs;to item alia <lb/>Trochlea, eaque; maior HI, circa centrum K appen&longs;a in L, <lb/>perpendicularis, qu&aelig; ad mundi centrum LKM, &aelig;qualia <pb xlink:href="007/01/098.jpg"/>pondera vtrinque appen&longs;a N, O. <!-- KEEP S--></s>
            <s id="s.000894">Dico maiorem Hl ip&longs;a <lb/>minori DE facilius pondera non mouere, eo qu&ograve;d &longs;it ma&shy;<lb/>ior, illa ver&ograve; difficili&ugrave;s, propterea qu&ograve;d &longs;it minor. </s>
            <s id="s.000895">Et enim, <lb/>quoniam vtraque trochlea per centrum grauitatis &agrave; per&shy;<lb/>pendiculari diuiditur, erunt partes DAE, DBE, &aelig;que <expan abbr="p&omacr;-derantes">pon&shy;<lb/>derantes</expan>. </s>
            <s id="s.000896">Eadem ratione ip&longs;&aelig; quoque LHM, LIM &aelig;qu&egrave; <lb/>ponderabunt. </s>
            <s id="s.000897">Itaque &longs;i quantumuis pu&longs;illa pondera ad&shy;<lb/>das, <expan abbr="vtriq;">vtrique</expan> earum ad alteram partem tolletur <expan abbr="&aelig;quilibri&umacr;">&aelig;quilibrium</expan>, <lb/>nec minus requiritur pondus vt recedat ab &aelig;quilibrio <lb/>Trochlea minor, qu&agrave;m maior. </s>
            <s id="s.000898">Vnico autem verbo con&shy;<lb/>cludi pote&longs;t di&longs;putatio, <expan abbr="t&atilde;">tam</expan> in minori qu&agrave;m in maiori, bra&shy;<lb/>chia &longs;iqui dem bifariam diuiduntur, ergo in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> eadem <lb/>brachiorum proportio, &amp; eadem ponderum ratio. </s>
          </p>
          <p type="main">
            <s id="s.000899">Explorati&longs;&longs;ima &longs;unt h&aelig;c. </s>
            <s id="s.000900">Veruntamen c&ugrave;m res ip&longs;a <lb/>doceat, verum e&longs;&longs;e quod &longs;cribit Ari&longs;toteles, huius effe&shy;<lb/>ctus cau&longs;&longs;a aliunde &agrave; nobis, nempe &agrave; mechanicis princi&shy;<lb/>pijs, e&longs;t mutuanda. </s>
            <s id="s.000901">Dico igitur, Axium, circa quos tro&shy;<lb/>chle&aelig; rot&aelig;ue conuertuntur ad rotas ip&longs;as, varias habere <lb/>proportiones. </s>
            <s id="s.000902">O&longs;tendemus autem <expan abbr="rot&atilde;">rotam</expan> illam, trochleam&shy;<lb/>ue facili&ugrave;s moueri, &amp; mouere pondera, quo rot&aelig; diame&shy;<lb/>ter ad axis diametrum maiorem habuerit proportionem, <lb/>&amp; ideo fieri po&longs;&longs;e rotam maiorem ad &longs;uum axem <expan abbr="minor&emacr;">minorem</expan> <lb/>habere proportionem quam rotam minorem ad &longs;uum. </s>
          </p>
          <figure id="id.007.01.098.1.jpg" xlink:href="007/01/098/1.jpg"/>
          <p type="main">
            <s id="s.000903">E&longs;to enim <lb/>trochlea AB cir&shy;<lb/>ca centrum C, <lb/>cuius diameter <lb/>DCE &longs;it in ip&longs;a <lb/>qu&aelig; ad mundi <lb/>centrum <expan abbr="perp&emacr;-diculari">perpen&shy;<lb/>diculari</expan>: &longs;it au&shy;<lb/>tem appen&longs;a in D. <!-- KEEP S--></s>
            <s id="s.000904">Alia &longs;imiliter ei &aelig;qualis &longs;it trochlea F <lb/>G circa centrum H, cuius diameter IHK, conueniens <pb xlink:href="007/01/099.jpg"/>cum perpendiculari qu&aelig; ad mundi centrum. </s>
            <s id="s.000905">appendatur <lb/>autem in I. <!-- KEEP S--></s>
            <s id="s.000906">Habeant autem &amp; axes, circa quos conuertan&shy;<lb/>tur. </s>
            <s id="s.000907">Hi &longs;i &aelig;quales fuerint, proportione non mutat&acirc; idem <lb/>operabuntur. </s>
            <s id="s.000908">Mod&ograve; ponantur in&aelig;quales, &longs;itqueue axis ro&shy;<lb/>t&aelig; AB, cra&longs;&longs;ior axe rot&aelig; FG, &longs;itqueue cra&longs;&longs;ioris quidem &longs;emi&shy;<lb/>diameter CL, &longs;ubtilioris autem HM. </s>
            <s id="s.000909">Dico per trochleam <lb/>FG facilius attolli pondera &aelig;qualia qu&agrave;m per AB, licet <lb/>altera trochlearum alteri &longs;it &aelig;qualis. </s>
            <s id="s.000910">Quoniam enim me&shy;<lb/>chanica corpora &longs;ine materia &amp; pondere non &longs;unt, onera <lb/><expan abbr="app&emacr;&longs;a">appen&longs;a</expan> &amp; trochlearum ip&longs;arum grauitas ex &longs;uperiori par&shy;<lb/>te prement axes, vbi puncta L, M, qu&aelig;res, &longs;ecut&acirc; in uicem <lb/>corporum &longs;olidorum fricatione, motum ip&longs;um trochlea&shy;<lb/>rum difficiliorem &amp; a&longs;periorem facit. </s>
            <s id="s.000911">Succedit igitur im&shy;<lb/>pedimentum loco ponderis. </s>
            <s id="s.000912">Duos igitur habemus vectes <lb/>DC, IH, quorum fulcimenta contra ip&longs;a C, H. <!-- KEEP S--></s>
            <s id="s.000913">Pondera <lb/>ver&ograve; inter fulcimenta &amp; potentias in L, M. <!-- KEEP S--></s>
            <s id="s.000914">Intelligantur <lb/>autem potenti&aelig; applicat&aelig; punctis DI. <!-- KEEP S--></s>
            <s id="s.000915">Igitur ex natura e&shy;<lb/>iu&longs;modi vectis, in quo pondus inter fulcimentum e&longs;t &amp; <lb/>potentiam erit vt CL, ad CD, ita potentia in D ad <expan abbr="p&omacr;dus">pondus</expan>, <lb/>hoc e&longs;t, re&longs;i&longs;tentiam fricationis, qu&aelig; fit in L. <!-- KEEP S--></s>
            <s id="s.000916">Sed maior <lb/>e&longs;t proportio CL ad CD qu&agrave;m HM ad HI. <!-- KEEP S--></s>
            <s id="s.000917">Maior igitur <lb/>ad &longs;uperandum idem &longs;eu &aelig;quale impedimentum poten&shy;<lb/>tia requiritur in D, quam in I. <!-- KEEP S--></s>
            <s id="s.000918">Itaque cum vis tota in rota&shy;<lb/>rum &amp; axium, diametrorum proportione con&longs;i&longs;tat, fieri <lb/>pote&longs;t, quod dicebamus, minorem trochleam dari, qu&aelig; <lb/>maiorem habeat proportionem ad &longs;uum axem, qu&agrave;m, <lb/>maior ad &longs;uum, quo ca&longs;u minor rota facilius impedimen&shy;<lb/>tum, quod diximus, ip&longs;a maiori rota &longs;eu trochlea &longs;upera&shy;<lb/>bit. </s>
            <s id="s.000919">Veruntamen quoniam ex materia fiunt tum axes tum <lb/>rot&aelig;, nec rei natura patitur axes &longs;ubtiles, &amp; imbecilles <lb/>magna <expan abbr="p&omacr;dera">pondera</expan> &longs;u&longs;tinere po&longs;&longs;e, idcirco cra&longs;&longs;iores fiunt, qu&etail; <lb/>cra&longs;&longs;itudo cum proportione magis &agrave; magnarum rotarum <lb/>diametris &longs;uperetur; fit hinc maiores rotas dat&acirc; axium pa-<pb xlink:href="007/01/100.jpg"/>ritate facilius impedimentum &longs;uperare qu&agrave;m minores, &amp; <lb/>hoc videtur &longs;en&longs;i&longs;&longs;e Philo&longs;ophus in ip&longs;a qu&aelig;&longs;tionis huius <lb/>propo&longs;itione, Hinc aurig&aelig; vulgo axungi&acirc; &lpar;qu&aelig; inde no&shy;<lb/>men trahit&rpar; axium a&longs;peritates mitigant, vt minor in rotan&shy;<lb/>do, ex fricatione fiat re&longs;i&longs;tentia. </s>
            <s id="s.000920">Concludimus igitur, fa&shy;<lb/>cillim&egrave; trochleam illam pondus trahere, qu&aelig; cum maxi&shy;<lb/>ma &longs;it, axem habet minimum, cumqueue axungi&acirc; aliaue vn&shy;<lb/>ctuo&longs;a materia perfu&longs;um. </s>
            <s id="s.000921">De manubrijs, qu&aelig; rotarum a&shy;<lb/>xibus aptantur, nemo fer&egrave; verba fecit; nos igitur de his a&shy;<lb/>liquid; &longs;iquidem res ad &longs;peculationem, qua de agimus, <expan abbr="n&emacr;-pe">nem&shy;<lb/>pe</expan> Mechanicam pertinet. </s>
          </p>
          <p type="main">
            <s id="s.000922">Manubria vectes &longs;unt, &amp; ad vectium naturam redu&shy;<lb/>cuntur, eorum &longs;cilicet, in quibus fulcimentum e&longs;t inter <lb/>pondus &amp; potentiam. </s>
            <s id="s.000923">In his autem attenditur proportio, <lb/>quam habet manubrij longitudo ad ip&longs;um axis &longs;emidia&shy;<lb/>metrum, eo enim facili&ugrave;s mouent, quo eorum longitudo <lb/>ad axium &longs;emidiametros proportionem, habuerit ma&shy;<lb/>iorem. </s>
            <s id="s.000924">Duabus autem partibus con&longs;tant, alter&acirc;, qu&aelig; ab <lb/>axe ad angulum; qu&aelig; ver&egrave; vectis e&longs;t; alter&acirc;, cui manus i&shy;<lb/>p&longs;a admouetur, ex qua res tota manubrium dicitur. </s>
            <s id="s.000925">Fiunt <lb/>autem manubria h&aelig;c vt plurimum amouibilia, &longs;unt <expan abbr="tam&emacr;">tamen</expan> <lb/>ceu rotarum ip&longs;arum partes, &amp; rotis ip&longs;is commod&egrave; affi&shy;<lb/>gerentur, ni&longs;i in rotatione &agrave; tran&longs;uer&longs;arijs, quibus rot&aelig; &longs;u&shy;<lb/>&longs;tinentur, impedimentum fieret. </s>
          </p>
          <figure id="id.007.01.100.1.jpg" xlink:href="007/01/100/1.jpg"/>
          <p type="main">
            <s id="s.000926">E&longs;to enim rota AB, cu&shy;<lb/>ius axis E, terebretur autem <lb/>in F, ibiqueue paxillus affigatur <lb/>FK. <!-- KEEP S--></s>
            <s id="s.000927">Sit &amp; alia rota CD, cu&shy;<lb/>ius axis G, manubrium axi <lb/>appo&longs;itum GHI. <!-- KEEP S--></s>
            <s id="s.000928">Sint autem <lb/>rot&aelig; &aelig;quales &amp; axes &aelig;qua&shy;<lb/>les. </s>
            <s id="s.000929">Sint etiam &aelig;qualia ip&longs;a <lb/>&longs;patia EF, GH, hoc e&longs;t, ma-<pb xlink:href="007/01/101.jpg"/>nubrij GHI longitudo. </s>
            <s id="s.000930">Dico, e&acirc;dem facilitate moueri AB <lb/>rotam &agrave; potentia in FK, qu&acirc; mouetur CB, &agrave; potentia po&shy;<lb/>&longs;ita in HI, datis ip&longs;i nempe potentijs &aelig;qualibus. </s>
            <s id="s.000931">Produca&shy;<lb/>tur enim IH, v&longs;que ad rot&aelig; CD latus in L, &amp; LG ducatur, <lb/>&amp; FE in rota AB iungatur. </s>
            <s id="s.000932">Erunt igitur FE LG inter &longs;e &aelig;&shy;<lb/>quales. </s>
            <s id="s.000933">Sunt autem eorum circulorum &longs;emidiametri, qui <lb/>&agrave; punctis FL, in ip&longs;a rotatione de&longs;cribuntur. </s>
            <s id="s.000934">Ita igitur &longs;e <lb/>habebit potentia applicata in L ad diametrum &longs;emidia&shy;<lb/>metrumue axis rot&aelig; CD, vt &longs;e habet potentia applicata <lb/>in F, ad diametrum &longs;emidiametrumue axis E rot&aelig; AB, &longs;ed <lb/>&longs;patia &longs;unt &aelig;qualia &amp; potenti&aelig; &aelig;quales, quare nihil re&shy;<lb/>fert, vtrum manubrium lateri affigatur, vel axi &agrave; latere ro&shy;<lb/>t&aelig; &longs;eparatum applicetur. </s>
          </p>
          <figure id="id.007.01.101.1.jpg" xlink:href="007/01/101/1.jpg"/>
          <p type="main">
            <s id="s.000935">Duplex autem e&longs;t ma&shy;<lb/>nubriorum forma; altera e&shy;<lb/>nim rectis partibus con&longs;tat, <lb/>altera ver&ograve; curua e&longs;t tota, <lb/>&longs;ed rectis vtimur vt mani&shy;<lb/>bus apprendamus, curuis <lb/>ver&ograve; vt locum illis appona&shy;<lb/>mus, &amp; pedis pre&longs;&longs;ione ceu <lb/>in molis lapideis, quibus <lb/>gladij acuuntur, fieri a&longs;&longs;olet, conuertantur. </s>
            <s id="s.000936">Cur autem <lb/>manubria h&aelig;c curua fiant, ea videtur ratio, ne videlicet <lb/>manubrij capite &longs;upra centrum in linea qu&aelig; per centrum <lb/>tran&longs;it, <expan abbr="c&omacr;&longs;tituto">con&longs;tituto</expan>, fact&acirc; interim pre&longs;&longs;ione motus &agrave; centro, <lb/>ad quod direct&egrave; fieret pre&longs;&longs;io, impediretur. </s>
            <s id="s.000937">Curuitas <expan abbr="aut&emacr;">autem</expan> <lb/>facilitatem quandam habet, ex qua fact&acirc; modic&acirc; flexione <lb/>axis caput, dum premitur ab ip&longs;a perpendiculari linea le&shy;<lb/>niter abducitur. </s>
            <s id="s.000938">qu&aelig; cum ce&longs;&longs;ent in manubrijs qu&aelig; manu <lb/>aguntur, ideo alia forma, nempe ex rectis partibus pa&longs;&longs;im <lb/>fiunt. </s>
            <s id="s.000939">E&longs;to igitur illud quod ex rectis partibus AB, curuum <lb/>ver&ograve; CD, linea ver&ograve;, &longs;ecundum quam pede fit pre&longs;&longs;io <pb xlink:href="007/01/102.jpg"/>CDE. <!-- KEEP S--></s>
            <s id="s.000940">H&aelig;c itaque de manubrijs &longs;eu vectibus nos con&longs;i&shy;<lb/>dera&longs;&longs;e &longs;it &longs;atis. </s>
          </p>
          <p type="main">
            <s id="s.000941">Qu&aelig;ri interim po&longs;&longs;et, Cur duabus datis rotis &aelig;qua&shy;<lb/>lis magnitudinis in &aelig;qualis ponderis, circa &aelig;quales axes <lb/>con&longs;titutis leuior facili&ugrave;s moueatur &amp; citi&ugrave;s quie&longs;cat; <lb/>grauior ver&ograve; difficilius moueatur &amp; tardi&ugrave;s ce&longs;&longs;et &agrave; mo&shy;<lb/>tu, ea videtur ratio, quod grauior re&longs;i&longs;tens magis cum &longs;u&shy;<lb/>peratur impre&longs;&longs;am vim &longs;u&longs;cipit, &amp; diuti&ugrave;s retinet, quod <lb/>ce&longs;&longs;at in leuiore. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000942">QV&AElig;STIO X.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000943"><emph type="italics"/>Dubitat Ari&longs;toteles, Cur facili&ugrave;s, quando &longs;ine pondere est, mouea&shy;<lb/>tur libra, qu&agrave;m cum pondus habet. </s>
            <s id="s.000944">Simili modo rota, &amp; eiu&longs;modi <lb/>quidpiam, quod grauius quidem est, item quod maius &amp; <lb/>grauius minori, &amp; leuiori?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000945">Breuiter autem &longs;oluit, ait enim, An quia non &longs;olum in <lb/>contrarium quod graue e&longs;t, &longs;ed in obliquam etiam dif&shy;<lb/>ficulter mouetur? </s>
            <s id="s.000946">In contrarium enim ei ad quod vergit <lb/>onus mouere difficile e&longs;t, quo autem vergit, e&longs;t facile. </s>
            <s id="s.000947">In <lb/>obliquum autem haudquaquam vergit. </s>
            <s id="s.000948">Nos quod ip&longs;e <lb/>non fecit figur&acirc; ip&longs;a appo&longs;it&acirc; rem clariorem faciemus. </s>
          </p>
          <figure id="id.007.01.102.1.jpg" xlink:href="007/01/102/1.jpg"/>
          <p type="main">
            <s id="s.000949">E&longs;to libra AB, cuius ful&shy;<lb/>cimentum C, pondera vtrin&shy;<lb/>que appen&longs;a AB, quorum v&shy;<lb/>trumque ponderet 10. Item <lb/>libra DE, cuius fulcimentum <lb/>F pondere vero appen&longs;a D, E, <lb/>ip&longs;is A, B, dimidio leuiora, <expan abbr="n&emacr;-pe">nem&shy;<lb/>pe</expan> S. <!-- KEEP S--></s>
            <s id="s.000950">Addatur ponderi B pon&shy;<lb/>dus G, &amp; ponderi E pondus <lb/>H, quorum &longs;imiliter <expan abbr="vtrumq;">vtrumque</expan> <lb/>ponderet S, nutabunt igitur <lb/>libr&aelig; ponderibus appo&longs;itis, &amp; <pb xlink:href="007/01/103.jpg"/>BG &longs;ecetur in K, EH ver&ograve; in N, grauius e&longs;t autem GB, e&longs;t <lb/>enim IS, ip&longs;o EH, quod e&longs;t 10. Difficili&ugrave;s autem de&longs;cen&shy;<lb/>det BG, qu&agrave;m EH. hoc autem ex doctrina Ari&longs;totelis, <lb/>quia non &longs;olum in contrarium quod graue e&longs;t, &longs;ed in obli&shy;<lb/>quum etiam difficulter mouetur, in contrarium enim ei <lb/>ad quod vergit onus mouere difficile e&longs;t, qu&ograve; autem ver&shy;<lb/>git facil&egrave; in obliquum autem puta per lineas BK, EN non <lb/>vergit onus. </s>
            <s id="s.000951">Difficili&ugrave;s ergo in obliquum mouebitur pon&shy;<lb/>dus BG ip&longs;o pondere EH. vtrumque autem in de&longs;cen&longs;u <lb/>retrahitur nempe &agrave; perpendicularibus BI, EM &amp; retra&shy;<lb/>ctionis quidem anguli &longs;unt &aelig;quales &amp; &aelig;quales ip&longs;&aelig; retra&shy;<lb/>ctiones. </s>
            <s id="s.000952">Sed grauius e&longs;t pondus GB. quod autem grauius <lb/>e&longs;t, violentius <expan abbr="de&longs;c&emacr;dit">de&longs;cendit</expan> eo quod e&longs;t leuius. </s>
            <s id="s.000953">maiori igitur ni&shy;<lb/>&longs;u atque impetu cum c&aelig;tera paria &longs;int, de&longs;cendet pondus <lb/>BG, ip&longs;o EH, quod &egrave; diametro Ari&longs;totelis a&longs;&longs;ertioni e&longs;t <lb/>contrarium. </s>
            <s id="s.000954">ex alijs igitur principijs veritas ip&longs;a e&longs;t eruen&shy;<lb/>da. </s>
            <s id="s.000955">Dicimus autem id ex proportionum fieri in&aelig;qualita&shy;<lb/>te; quia enim is ad 10. proportionem habet &longs;e&longs;quialteram, <lb/>10. ver&ograve; ad 5. duplam, maiorem proportionem habet EH <lb/>ad oppo&longs;itum pondus D, qu&agrave;m BG ad pondus A, facilius <lb/>ergo trahet libra DE leuior pondus D, qu&agrave;m ip&longs;a AB, gra&shy;<lb/>uior pondus A, quod vtique fuerat o&longs;tendendum. </s>
            <s id="s.000956">Alia <lb/>quoque cau&longs;&longs;a &amp; h&aelig;c accidentalis ad hunc effectum pa&shy;<lb/>riendum concurrit, axium nempe ad fulcimenta, in qui&shy;<lb/>bus rotantur, fricatio. </s>
            <s id="s.000957">quo enim maius e&longs;t pondus c&aelig;teris <lb/>paribus, quod nos in pr&aelig; cedente qu&aelig;&longs;tione demon&longs;tra&shy;<lb/>uimus, e&ograve; mai&igrave;or fit ip&longs;a colli&longs;io. </s>
          </p>
          <p type="main">
            <s id="s.000958">Porr&ograve; huius <expan abbr="quoq;">quoque</expan> &longs;peculationis e&longs;t, Cur &aelig;qualia &amp; <lb/>&longs;imilia corpora in &aelig;qualibus &longs;imilibu&longs;queue ba&longs;ibus con&longs;ti&shy;<lb/>tuta eodem &longs;imiliqueue plano fulta, ponderibus tamen in&shy;<lb/>&aelig;qualia, non e&acirc;dem facilitate euertantur, &longs;ed horum gra&shy;<lb/>uiora difficilius. </s>
          </p>
          <pb xlink:href="007/01/104.jpg"/>
          <figure id="id.007.01.104.1.jpg" xlink:href="007/01/104/1.jpg"/>
          <p type="main">
            <s id="s.000959">Sit enim Pri&longs;ma &longs;eu <lb/>Cylindrus ABCD, cuius <lb/>grauitatis centrum E in <lb/>plano Cl, ba&longs;i fultus CD. <lb/><!-- KEEP S--></s>
            <s id="s.000960">Sit &amp; alter Cylindrus <lb/>FGHI, cuius grauitatis <lb/>centrum K fultus ba&longs;i HI <lb/>&aelig;qualis quidem &amp; &longs;imilis <lb/>ip&longs;i AD. <!-- KEEP S--></s>
            <s id="s.000961">Sit autem grauior FGHI, ip&longs;o ABCD. Dico, pari <lb/>potenti&acirc; vtrumque impellente, facilius euer&longs;um iri Cy&shy;<lb/>lindrum AD, ip&longs;o Fl. </s>
            <s id="s.000962">Ducantur EC, KH, &amp; &aelig;quales po&shy;<lb/>tenti&aelig; applicentur punctis BG, pellentes Cylindros ad <lb/>partes AF. <!-- KEEP S--></s>
            <s id="s.000963">Euer&longs;io autem non fiet donec facta corporis <lb/>conuer&longs;ione circa puncta CH, grauitatis centra E, K <expan abbr="tr&atilde;s-ferunturin">trans&shy;<lb/>feruntur in</expan> L, M, in ip&longs;is &longs;cilicet <expan abbr="perp&emacr;dicularibus">perpendicularibus</expan> ACFH. <lb/><!-- KEEP S--></s>
            <s id="s.000964">Demittantur EN, KO, perpendiculares ip&longs;is CD, HF. </s>
            <s id="s.000965">Et <lb/>quoniam CNE, HOK anguli recti &longs;unt, erunt EC KH i&shy;<lb/>p&longs;is EN, KO, maiores, quare &amp; LC, MH ip&longs;is EN KO, ma&shy;<lb/>iores attolluntur ergo in ip&longs;a euer&longs;ione, grauitatum cen&shy;<lb/>tra E in L, K in M. <!-- KEEP S--></s>
            <s id="s.000966">At quod grauius e&longs;t, difficilius contra <lb/>&longs;ui naturam mouetur, ideo difficilius euertetur corpus <lb/>FI, ip&longs;o AD, quod fuerat demon&longs;trandum. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.000967">QV&AElig;STIO XI.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.000968"><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;uper &longs;cytalas facilius portentur onera <lb/>qu&agrave;m &longs;uper currus, cum tamen ij magnas habeant rotas, <lb/>ill&aelig; ver&ograve; pu&longs;illas?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.000969">Optim&egrave; re&longs;pondet dubitationi. </s>
            <s id="s.000970">An, inquiens, quoniam <lb/>in &longs;cytalis nulla e&longs;t offen&longs;atio; in curribus ver&ograve; axis <lb/>e&longs;t, ad quem offen&longs;ant. </s>
            <s id="s.000971">De&longs;uper enim illum premunt, &amp; <lb/>&agrave; lateribus. </s>
            <s id="s.000972">quod autem e&longs;t in &longs;cytalis ad i&longs;th&aelig;c duo mo&shy;<lb/>uetur &amp; inferiori &longs;ub&longs;trato &longs;patio, &amp; onere &longs;uperimpo&longs;i-<pb xlink:href="007/01/105.jpg"/>to, in vtri&longs;que enim ijs reuoluitur locis circulus, &amp; motus <lb/>impellitur. </s>
            <s id="s.000973">Tam appo&longs;it&egrave; paucis verbis veritatem expli&shy;<lb/>cauit, vt fer&egrave; quicquid in&longs;uper ad datur, &longs;uperuacaneum <lb/>videri po&longs;&longs;it. </s>
            <s id="s.000974">quicquid tamen &longs;it, ad maiorem claritatem <lb/>aliquantulum in hac ip&longs;a qu&aelig;&longs;tione immorabimur. </s>
          </p>
          <p type="main">
            <s id="s.000975">Rotatas &longs;cytalas proponit h&icirc;c Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.000976">Coniun&shy;<lb/>ctas autem e&longs;&longs;e rotas ip&longs;is &longs;cytalis e&longs;t intelligendum, nem&shy;<lb/>pe, vt &longs;imul rot&aelig; cum &longs;cytalis conuertantur. </s>
            <s id="s.000977">Secus enim <lb/>axium &amp; Rotarum fieret offen&longs;atio, cuius offen&longs;ationis <lb/>vim &amp; effectum cum nouerit Ari&longs;toteles, vel hoc ip&longs;o lo&shy;<lb/>co te&longs;te, mirum e&longs;t, nihil de ea egi&longs;&longs;e qu&aelig;&longs;tione 9. vbi nos <lb/>hac de re fu&longs;i&longs;&longs;im&egrave; tractauimus. </s>
          </p>
          <p type="main">
            <s id="s.000978">C&aelig;ter&ugrave;m quod de rotatis &longs;cytalis &longs;cribit Philo&longs;o&shy;<lb/>phus, notandum, &agrave; Pappo quidem lib. 8. &amp; &agrave; no&longs;tris Me&shy;<lb/>chanicis pa&longs;&longs;im ab&longs;que rotis Cylindrica &longs;implici videli&shy;<lb/>cet, &amp; tereti form&acirc; ad v&longs;um adhiberi. </s>
            <s id="s.000979">E&longs;to igitur Ari&shy;<lb/><figure id="id.007.01.105.1.jpg" xlink:href="007/01/105/1.jpg"/><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi ver&ograve; &longs;eu vul&shy;<lb/>garis, &amp; communis CD. <lb/><!-- KEEP S--></s>
            <s id="s.000980">His non mod&ograve; lapicid&aelig; <lb/>pa&longs;&longs;im, &longs;ed &amp; naut&aelig; na&shy;<lb/>uiumqueue fabri &longs;ubdu&shy;<lb/>cendis &amp; mari inducen&shy;<lb/>dis nauibus vtuntur, quod varare dicunt vernacul&egrave;, Hi&shy;<lb/>&longs;panico, vt arbitror, vocabulo. </s>
            <s id="s.000981">ca enim natio teres lignum <lb/>baculumue appellat Varam. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.000982">Qu&aelig;ri autem po&longs;&longs;et, vtra harum formatum &longs;it vti&shy;<lb/>lior atque commodior? </s>
            <s id="s.000983">Nos rotatas laudamus magis in <lb/>plano duroqueue &longs;olo, minus enim tangunt &amp; minus offen&shy;<lb/>&longs;ant; in molliori autem &amp; minus duro proponimus non <lb/>rotatas, &longs;iquidem rot&aelig; &longs;ui natur&acirc; pondere pre&longs;&longs;&aelig; &longs;olum, <lb/>facillim&egrave; &longs;cindunt &amp; ab&longs;orbentur. </s>
          </p>
          <p type="main">
            <s id="s.000984">Quatenus autem ad v&longs;um pertinet. </s>
            <s id="s.000985">E&longs;to horizontis <pb xlink:href="007/01/106.jpg"/><figure id="id.007.01.106.1.jpg" xlink:href="007/01/106/1.jpg"/><lb/>planum AB, &longs;cytalae duae <lb/>CD, EF, Pondus ver&ograve; <lb/>eis impo&longs;itum G, tan&shy;<lb/>gens ip&longs;as in <expan abbr="p&umacr;ctis">punctis</expan> CE, <lb/>&longs;cytal&aelig; autem planum <lb/>in punctis D, F, Pellatur <lb/>&agrave; potentia quapiam <expan abbr="p&omacr;-dus">pon&shy;<lb/>dus</expan> G ad anteriora, <expan abbr="n&emacr;-pe">nen&shy;<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytal&aelig; &amp; pars qu&aelig;dam <lb/>&longs;cytal&aelig; D, in qua &longs;it contactus a&longs;cendet in I, C ver&ograve; de&shy;<lb/>&longs;cendet in H, nulla re motum impediente, quippe qu&ograve;d <lb/>nulla ponderis &longs;cytalarum, &amp; plani ad inuicem fiat offen&shy;<lb/>&longs;atio. </s>
            <s id="s.000986">Pr&aelig;terea cum &longs;cytalarum centra ab horizontis pla&shy;<lb/>no &aelig;qualiter di&longs;tent, pondus quidem horizonti &aelig;quidi&shy;<lb/>&longs;tanter mouetur, &amp; ideo eius centrum grauitatis nequa&shy;<lb/>quam, in motu qui &longs;it, eleuatur. </s>
          </p>
          <p type="main">
            <s id="s.000987">C&aelig;ter&ugrave;m materi&aelig; imperfectione remota nihil re&shy;<lb/>fert ad facilitatem, vtrum maioris minorisue diametri <lb/>&longs;int &longs;cytal&aelig;, vt ea po&longs;ita eo quod maiores circuli facili&ugrave;s <lb/>offendicula &longs;uperent, quod demon&longs;tratum e&longs;t in qu&aelig;&longs;tio&shy;<lb/>ne 8. eo vtiliores &longs;unt &longs;cytal&aelig;, quo cra&longs;&longs;iores. </s>
            <s id="s.000988">Quatenus <lb/>autem ad plau&longs;tri naturam &longs;pectat, cuius ad &longs;cytalas Phi&shy;<lb/>lo&longs;ophus fecit comparationem, vt o&longs;ten damus difficilius <lb/>ex eo moueri pondera. </s>
          </p>
          <figure id="id.007.01.106.2.jpg" xlink:href="007/01/106/2.jpg"/>
          <p type="main">
            <s id="s.000989">E&longs;to plau&longs;tri rota <lb/>KL, cuius centrum M, a&shy;<lb/>xis ver&ograve; NO circa quem <lb/>rota ip&longs;a conuertitur KL. <lb/><!-- KEEP S--></s>
            <s id="s.000990">Funis quo rota ex axis <lb/>centro M trahitur MP, <lb/>pondus vero QR. </s>
            <s id="s.000991">Quo&shy;<lb/>niam igitur pondus axem <lb/>premit in N, axis autem rot&aelig; modiolum in O, &amp; eodem, <pb xlink:href="007/01/107.jpg"/>tempore potentia qu&aelig; trahit in P, axem admouet modio&shy;<lb/>lo in parte V. duplex itaque fit ex fricatione &longs;eu offen&longs;a&shy;<lb/>tione impedimentum, infra nempe, vbi O, &amp; ad latus vbi <lb/>V. qu&aelig; quidem offen&longs;iones currus motum reddunt diffi&shy;<lb/>ciliorem, qu&aelig; quidem difficultas eo maior erit, quo ma&shy;<lb/>ior fuerit pondus axem premens, &amp; minor proportio &longs;e&shy;<lb/>midiametri rot&aelig; KM, ad axis &longs;emidiametrum MO. </s>
            <s id="s.000992">Cur <lb/>igitur &longs;cytalis facilius pondera transferantur quam plau&shy;<lb/>&longs;tris, apert&egrave; ex dictis ad Ari&longs;to telis mentem demon&longs;tra&shy;<lb/>uimus. </s>
          </p>
          <p type="main">
            <s id="s.000993">C&aelig;ter&ugrave;m quod ip&longs;e reticuit, nos dicemus, nempe <lb/>validi&longs;&longs;im&egrave; enormia pondera per &longs;cytalas moueri, &longs;i &longs;cy&shy;<lb/>talis ip&longs;is vectes adiungantur. </s>
            <s id="s.000994">Et &longs;an&egrave; motus erit tardi&longs;&longs;i&shy;<lb/>mus, veruntamen tarditas ip&longs;a facilitate, qu&aelig; in de fit, v&shy;<lb/>berrim&egrave; compen&longs;atur. </s>
          </p>
          <figure id="id.007.01.107.1.jpg" xlink:href="007/01/107/1.jpg"/>
          <p type="main">
            <s id="s.000995">E&longs;to igitur horizontis planum AB, &longs;cytal&aelig; CD, fo&shy;<lb/>ramina in &longs;cytalis EFGH, vectes foraminibus in&longs;erti IE, <lb/>KF, LG, MH. </s>
            <s id="s.000996">Pondus vero &longs;cytalis impo&longs;itum N. <!-- KEEP S--></s>
            <s id="s.000997">Appli&shy;<lb/>catis ig&igrave;tur quatuor potentijs extremitatibus vectium I, <lb/><emph type="italics"/>K<emph.end type="italics"/>, L, M, ij&longs;que in anteriora propul&longs;is, fiet &longs;cytalarum rota-<pb xlink:href="007/01/108.jpg"/>tio, &amp; ponderis N translatio ad anteriores partes B. <!-- KEEP S--></s>
            <s id="s.000998">E&longs;to <lb/>item &longs;eor&longs;um &longs;cytala PR, cuius centrum Q, vectis eidem <lb/>per centrum in&longs;ertus O, P, Q, R. facto igitur vectis motu <lb/>O P Q R fiet ex O; centro <expan abbr="aut&emacr;">autem</expan> Q circuli quadrans O T. <lb/>exi&longs;tente igitur O in T erit P in S. facta quart&aelig; partis ip&longs;ius <lb/>&longs;cytal&aelig; rotatione. </s>
            <s id="s.000999">Et quoniam ex eodem centro &longs;unt qua&shy;<lb/>drantes PSOT. erit vt OQ ad QP. ita quadrans OT, ad <lb/>quadrantem PS. <!-- KEEP S--></s>
            <s id="s.001000">Maxima autem e&longs;t proportio OQ, ad <lb/>QP. </s>
            <s id="s.001001">Maxima igitur proportio OT ad PS. <!-- KEEP S--></s>
            <s id="s.001002">Ex magno igitur <lb/>motu O ad T, paruus &longs;it &longs;cytal&aelig; motus &agrave; P in S. tardius i&shy;<lb/>gitur progreditur &longs;cytala, qu&aelig; longioribus vectibus rota&shy;<lb/>tur, vis tamen maxima, quippe quod vt &longs;e habet QP, hoc <lb/>e&longs;t, QR ad QO, ita potentia in O ad pondus quod premit <lb/>in P vel in V. <!-- KEEP S--></s>
            <s id="s.001003">Facillim&egrave; itaque pondera vectibus &amp; &longs;cyta&shy;<lb/>lis per horizontis planum transferri, exi&longs;tis patet. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001004">QVAESTIO XII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001005"><emph type="italics"/>Qu&aelig;ritur, Cur Mi&longs;&longs;ilia longius funda mittantur quam manu, <lb/>pr&aelig;&longs;ertim cum proijcienti fund&aelig; pondus addatur lapidis &longs;eu mi&longs;&longs;i&shy;<lb/>lis ponderi: &amp; minus mi&longs;&longs;ili, manu proiecto, com&shy;<lb/>prehendatur?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001006">Soluit Philo&longs;ophus, inquiens, fort&egrave; ita fieri, qu&ograve;d fun&shy;<lb/>ditor mi&longs;&longs;ile proijciat iam ex funda commotum, &longs;iqui&shy;<lb/>dem fundam circulo &longs;ubinde rotans, iaculatur, ex manu <lb/>autem &agrave; quiete e&longs;t initium. </s>
            <s id="s.001007">Omnia autem cum in motu <lb/>&longs;unt, qu&agrave;m cum quie&longs;cunt, facilius mouentur. </s>
            <s id="s.001008">Addit pr&aelig;&shy;<lb/>terea, An &amp; ob eam cau&longs;&longs;am e&longs;t, &longs;ed nec minus etiam, quia <lb/>infunde v&longs;u manus quidem fit centrum, funda ver&ograve; quod <lb/>&agrave; centro exit? </s>
            <s id="s.001009">quant&ograve; igitur productius fuerit quod &agrave; cen&shy;<lb/>tro e&longs;t, tanto citi&ugrave;s mouetur; iactus autem, qui manu fit, <lb/>fund&aelig; re&longs;pectu breuior e&longs;t. </s>
          </p>
          <p type="main">
            <s id="s.001010">H&aelig;c Philo&longs;ophus. <!-- KEEP S--></s>
            <s id="s.001011">Et &longs;an&egrave; perqu&agrave;m appo&longs;it&egrave;, <expan abbr="itaq;">itaque</expan> <pb xlink:href="007/01/109.jpg"/>illi pror&longs;us a&longs;&longs;entirer, ni&longs;i pro comperto haberem, in iactu <lb/>qui fund&acirc; fit, non e&longs;&longs;e manum ip&longs;am motus centium, &longs;ed <lb/>potius partem illam brachij, qu&aelig; humero iungitur, &amp; id&shy;<lb/>eo motum eo fieri velociorem, quo longior e&longs;t linea qu&aelig; <lb/>ab humero ad &longs;ummitatem fund&aelig; e&longs;t, ea qu&aelig; ab humero <lb/>ad manum ip&longs;am. </s>
            <s id="s.001012">Illud quoque mirabile e&longs;t, quod non <lb/>ob&longs;eruat Ari&longs;toteles, nempe &agrave; funditoribus in ip&longs;o eiacu&shy;<lb/>landi actu, tardam fieri circa caput fund&aelig; rotationem. <lb/></s>
            <s id="s.001013">Quamobrem con&longs;iderandum e&longs;t, quo pacto fiat &agrave; tardi&shy;<lb/>tate velocitas. </s>
            <s id="s.001014">Re&longs;pondemus, velocitatem acquiri non ex <lb/>&longs;implici, qu&aelig; circa funditoris caput &longs;it, rotatione, &longs;ed ex <lb/>eo impetu qui fit in ip&longs;a lapidis emi&longs;&longs;ione, qui quidem im&shy;<lb/>petus &longs;i ante vel po&longs;t illud tempus fiat, quod &agrave; funditore <lb/>captatur, ca&longs;&longs;a pror&longs;us &amp; inualida fit ip&longs;a iaculatio. </s>
          </p>
          <figure id="id.007.01.109.1.jpg" xlink:href="007/01/109/1.jpg"/>
          <p type="main">
            <s id="s.001015">E&longs;to funda AB, manus <lb/>B, brachium BC. <!-- KEEP S--></s>
            <s id="s.001016">Vt igitur &longs;e <lb/>habet CH, ad CB, ita veloci&shy;<lb/>tas AD ad velocitatem, BE; <lb/>Vidimus nos pueros, arundi&shy;<lb/>ni ad caput &longs;ci&longs;&longs;&aelig;, paruos la&shy;<lb/>pides in&longs;erentes, arundinem&shy;<lb/>queue manu rotantes longi&longs;&longs;i&shy;<lb/>m&egrave; lapides ip&longs;os proijcere; A&shy;<lb/>rundo FG, lapis F, manus G, <lb/>brachium GH. <!-- KEEP S--></s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001017">QV&AElig;STIO XIII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001018"><emph type="italics"/>Qu&aelig;ritur, Cur circa idem iugum, maiores collopes &lpar;vectes &longs;unt, <lb/>quos alij &longs;cytalas appellant, vt Pappus &amp; Heron&rpar; facili&ugrave;s qu&agrave;m mi&shy;<lb/>nores mouentur: &amp; item &longs;ucul&aelig;, qu&aelig; graciliores &longs;unt eadem <lb/>vi quam cra&longs;&longs;iores?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001019">Ideo hoc fieri po&longs;&longs;e docet Philo&longs;ophus, qu&ograve;d <expan abbr="tamiug&umacr;">tam iugum</expan> <lb/>quam &longs;ucula <expan abbr="c&emacr;trum">centrum</expan> &longs;it, prominentes autem collopum <pb xlink:href="007/01/110.jpg"/>longitudines e&aelig; line&aelig; qu&aelig; &longs;unt &agrave; centro. </s>
            <s id="s.001020">Celeri&ugrave;s autem <lb/>moueri &amp; plus ab eadem vi qu&aelig; maiorum &longs;unt <expan abbr="circulor&umacr;">circulorum</expan> <lb/>qu&agrave;m qu&aelig; minorum. </s>
            <s id="s.001021">quippe quod ab ea dem vi plus <expan abbr="tr&atilde;&longs;-feratur">tran&longs;&shy;<lb/>feratur</expan> illud extremum quod longius &agrave; centro di&longs;tat. </s>
            <s id="s.001022">In <lb/>gracilioribus ver&ograve; &longs;uculis dat&acirc; collopum paritate plus e&longs;&shy;<lb/>&longs;e id quod &agrave; ligno di&longs;tat. </s>
          </p>
          <figure id="id.007.01.110.1.jpg" xlink:href="007/01/110/1.jpg"/>
          <p type="main">
            <s id="s.001023">E&longs;to iugum &longs;ucu&shy;<lb/>laue maior, AB circa <lb/>centrum C, minor ver&ograve; <lb/>circa idem <expan abbr="centr&umacr;">centrum</expan> DE. <lb/><!-- KEEP S--></s>
            <s id="s.001024">Collops <expan abbr="aut&emacr;">autem</expan> AF, pon&shy;<lb/>dus quod per iugum at&shy;<lb/>tollitur G. <!-- KEEP S--></s>
            <s id="s.001025">A it igitur A&shy;<lb/>ri&longs;toteles, &longs;uculas, iu&shy;<lb/>gaue AB, DE ceu cen&shy;<lb/>tra e&longs;&longs;e, &agrave; quibus extat colops AB, ex maiori quidem, tot&acirc; <lb/>&longs;ui parte BF, ex minori autem EF. quo igitur, ait, longior <lb/>fuerit collops extans, eo maior, &amp; deo velocior ad <expan abbr="part&emacr;">partem</expan> <lb/>F per maiorem circulum FH, fiet collopis motus &amp; pon&shy;<lb/>deris eleuatio, at maior e&longs;t collops EF ip&longs;o BF, facil. </s>
            <s id="s.001026">us er&shy;<lb/>go mouebitur pondus per &longs;uculam DE, ex collope EF, ab <lb/>eadem vi, quam per &longs;uculam AB, &amp; collopem BF. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001027">H&aelig;c &longs;en&longs;i&longs;&longs;e videtur Ari&longs;to teles, qui cra&longs;&longs;a, vt aiunt, <lb/>Minerua rem pulchram &amp; &longs;ubtilem e&longs;t pro&longs;equutus. </s>
            <s id="s.001028">Di&shy;<lb/>cimus igitur prim&ograve;, in&longs;trumentum illud quod Latini &longs;u&shy;<lb/>culam, id e&longs;t, &longs;ero&longs;ulam, &agrave; &longs;tridore arbitror qui in conuer&shy;<lb/>&longs;ione fit, appellauere, Gr&aelig;ci ver&ograve; <foreign lang="greek">o&rpar;/non</foreign>, id e&longs;t, A &longs;inum, quip&shy;<lb/>pe quod ceu A &longs;inus pondera &longs;u&longs;tineat portetque. </s>
            <s id="s.001029">Hanc <lb/>eandem Machinam veteres Mechanici vocauere Axem <lb/>in Peritrochio, cuius nos imaginem, &egrave; P&agrave;ppo in 8. Col&shy;<lb/>lect. <!-- REMOVE S-->Mathematicarum de&longs;umptam in ip&longs;o huius no&longs;tri o&shy;<lb/>peris initio, inter quinque Potentias propo&longs;uimus. </s>
            <s id="s.001030">Huius <lb/>vim inter antiquos diligenti&longs;&longs;ime examinau&ecirc;re Heron, &amp; <pb xlink:href="007/01/111.jpg"/>ip&longs;emet Pappus, inter iuniores ver&ograve; Guilibaldus eo Tra&shy;<lb/>ctatu quem hac de Potentia Mechanicis &longs;uis in&longs;eruit. <lb/></s>
            <s id="s.001031">Summa e&longs;t, hanc Machinam ad vectem reduci. </s>
            <s id="s.001032">Nec ve&shy;<lb/>rum e&longs;t quod &longs;cribit Ari&longs;to teles, iugum &longs;uculamue cen&shy;<lb/>tra e&longs;&longs;e, h&aelig;c enim centrum habent, quod in figura &longs;upe&shy;<lb/>rius po&longs;ita notatur &longs;igno C. igitur vt &longs;e habet FC, ad CA, <lb/>ita pondus G ad potentiam in F; e&longs;t autem maior propor&shy;<lb/>tio FC ad CD, qu&agrave;m FC, ad CA. facili&ugrave;s ergo mouebit <lb/>potentia qu&aelig; in F, pondus in D, qu&agrave;m eadem potentia F, <lb/>pondus in A, hoc e&longs;t, G. <!-- KEEP S--></s>
            <s id="s.001033">Huius natur&aelig; &longs;unt quo que Erga&shy;<lb/>t&aelig;, quas machinas no&longs;tri, Gr&aelig;co luxato vocabulo Arga&shy;<lb/>nos appellant. </s>
            <s id="s.001034">Sucul&aelig; enim reuera &longs;unt, po&longs;itione <expan abbr="tant&umacr;">tantum</expan> <lb/>ab eis differentes, non enim plano horizontis ergat&aelig; &aelig;&shy;<lb/>quidi&longs;tant, ceu &longs;ucul&aelig; &amp; Axis in Peritrochio, &longs;ed eidem <lb/>fiunt perpendiculares. </s>
            <s id="s.001035">C&aelig;ter&ugrave;m facilitatem &agrave; velocitate <lb/>non oriri &longs;uperius demon&longs;trauimus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001036">QVAESTIO XIV.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001037"><emph type="italics"/>Proponitur dubitatio, Cur eiu&longs;dem magnitudinis lignum facilius <lb/>genu frangatur &longs;i qui&longs;piam &aelig;que diductis manibus extrema com&shy;<lb/>prehendens fregerit, qu&agrave;m &longs;i iuxta genu. </s>
            <s id="s.001038">Et &longs;i terr&aelig; applicans pede <lb/>&longs;uperpo&longs;ito manu hinc inde diducta confregerit <lb/>qu&agrave;m prop&egrave;.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001039">Soluitur &agrave; Philo&longs;opho paucis verbis, An quia ibi genu <lb/>centrum e&longs;t, hic ver&ograve; ip&longs;e pes? </s>
            <s id="s.001040">quanto autem remotius <lb/>&agrave; centro fuerit, facilius mouetur quodcunque: Moueri <lb/>autem quod frangitur nece&longs;&longs;e e&longs;t. </s>
          </p>
          <p type="main">
            <s id="s.001041">E&longs;to lignum quod frangi debet AB, genu vel pedis <lb/>locus C, manuum lat&egrave; diductarum &longs;itus DE, minus didu&shy;<lb/>ctarum FG; ltaque quoniam DE magis &agrave; centro C di&longs;tant <lb/>qu&agrave;m FG, velocius mouebuntur puncta DE ip&longs;is FG, er&shy;<lb/>go inde facilius fiet fractio quam ex FG. <!-- KEEP S--></s>
            <s id="s.001042">H&aelig;c ille ex &longs;uis <pb xlink:href="007/01/112.jpg"/><figure id="id.007.01.112.1.jpg" xlink:href="007/01/112/1.jpg"/><lb/>principijs. </s>
            <s id="s.001043">Nos dili&shy;<lb/>gentius, &longs;i fieri poterit, <lb/>effectus huius cau&longs;&longs;am <lb/>per&longs;crutemur. </s>
            <s id="s.001044">E&longs;to igi&shy;<lb/>tur in &longs;ecunda figura <lb/>lignum oblongum AB, <lb/>cuius medium C, linea <lb/>ducatur CD perpen&shy;<lb/>dicularis ip&longs;i AB. <!-- KEEP S--></s>
            <s id="s.001045">Ad&shy;<lb/>moueatur genu <expan abbr="p&umacr;cto">puncto</expan> <lb/>C, manus ver&ograve; diuari&shy;<lb/>centur in AB, facta i&shy;<lb/>gitur vtrinque impre&longs;&shy;<lb/>&longs;ione, lignum non <expan abbr="fr&atilde;-getur">fran&shy;<lb/>getur</expan>, ni&longs;i partium in CD coniunctarum &longs;eparatio fiat, <lb/>&longs;itqueue altera in E, altera ver&ograve; in F, fractum ergo erit <expan abbr="lign&umacr;">lignum</expan>, <lb/>&amp; centro C immobili permanente, partes facto angulo <lb/>GCH erunt in GC, HC: Mod&ograve; lignum &longs;u&aelig; integritati re&shy;<lb/>&longs;tituetur, &amp; denu&ograve; admoto genu puncto C, manus didu&shy;<lb/>cantur in I, K, qu&aelig; loca viciniora &longs;int ip&longs;i C, quam AB, Di&shy;<lb/>co hinc difficilius fractionem fieri quam ex AB. <!-- KEEP S--></s>
            <s id="s.001046">Con&longs;ide&shy;<lb/>ramus enim in integro ligno AB, duos vectes ACD, BCD, <lb/>quorum anguli concurrunt in commune fulcimentum C, <lb/>Sunt autem vectes angulati, &amp; eius natur&aelig;, quam exami&shy;<lb/>nauimus in qu&aelig;&longs;tiones. </s>
            <s id="s.001047">E&longs;t igitur re&longs;i&longs;tentia, qua ligni <lb/>partes vniuntur in D, loco ponderis: &longs;uperanda h&aelig;c e&longs;t, vt <lb/>ligni fiat fractio. </s>
            <s id="s.001048">Dico id facilius ce&longs;&longs;urum, &longs;i fiat ex pun&shy;<lb/>ctis A, B, remotioribus quam ex IK, ip&longs;i puncto C propio<lb/>ribus: etenim vt AC, ad CD, ita re&longs;i&longs;tentia qu&aelig; fit in D ad <lb/>potentiam in A, item vt &longs;e habet IC ad CD, ita re&longs;i&longs;tentia <lb/>in Dad potentiam in I, &longs;ed minor e&longs;t proportio IC ad CD, <lb/>quam AC ad CD. ergo facilius potentia qu&aelig; e&longs;t in A, re&shy;<lb/>&longs;i&longs;tentiam &longs;uperabit, qu&aelig; e&longs;t in D, quam ea qu&aelig; e&longs;t in I, <pb xlink:href="007/01/113.jpg"/>quod fuerat demon&longs;trandum. </s>
            <s id="s.001049">Idem autem <expan abbr="intelligend&umacr;">intelligendum</expan> <lb/>e&longs;t de parte CB; eadem enim e&longs;t ratio. </s>
            <s id="s.001050">Cur igitur longio&shy;<lb/>ra &amp; graciliora ligna facil&egrave; frangantur, ex i&longs;tis clare patet: <lb/>nempe quia maxima e&longs;t proportio longitudinis ad cra&longs;&longs;i&shy;<lb/>tudinem, cuius quidem cra&longs;&longs;itudinis &longs;patium loco partis <lb/>illius in vecte &longs;uccedit, qu&aelig; pertingit &agrave; fulcimento ad <expan abbr="p&omacr;-dus">pon&shy;<lb/>dus</expan>, hoc e&longs;t, ad ip&longs;am re&longs;i&longs;tentiam. </s>
            <s id="s.001051">Sed nos hac eadem de <lb/>re nonnulla in declaranda qu&aelig;&longs;tione 16. perpendemus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001052">QVAESTIO XV.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001053"><emph type="italics"/>Proponitur inuestigandum, Cur litterales croc&aelig; &lpar;glareas dicunt <lb/>Latini, vel calculos, quos vmbilicos appellat Cicero lib.  2. de Orat.&rpar; <lb/>rotund&acirc; &longs;int figur&acirc;, cum aliquando ex magnis &longs;int la&shy;<lb/>pidibus te&longs;tisue?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001054">A It Philo&longs;ophus, ideo forta&longs;&longs;e fieri, qu&ograve;d ca qu&aelig; &agrave; me&shy;<lb/>dio magis recedunt, in motionibus, celerius feran&shy;<lb/>tur; me dium e&longs;&longs;e centrum, interuallum vero qu&aelig; &agrave; cen&shy;<lb/>tro, &longs;emper autem maiorem ab &aelig;quali motione maiorem <lb/>de&longs;cribere circulum; quod autem maius in &aelig;quali tem&shy;<lb/>pore &longs;patium tran&longs;it, celerius ferri; qu&aelig; autem celerius ex <lb/>&aelig;quali feruntur &longs;patio vehementius impetere, qu&aelig; <expan abbr="aut&emacr;">autem</expan> <lb/>impetunt, impeti magis, &amp; ideo qu&aelig; magis &agrave; centro di&shy;<lb/>&longs;tant, nece&longs;&longs;e e&longs;&longs;e confringi, quod cum glare&aelig; &longs;eu croc&aelig; <lb/>patiantur, nece&longs;&longs;ari&ograve; rotundas fieri. </s>
            <s id="s.001055">Hactenus ille, &amp; &longs;an&egrave; <lb/>probabiliter. </s>
            <s id="s.001056">Verum enimuer&ograve; aliter &longs;eres habere vide&shy;<lb/>tur: &longs;iquidem enim &agrave; rotatione ex maiori &agrave; centro di&longs;tan&shy;<lb/>tia id fieret, maiores quidem glare&aelig; croc&aelig;ue e&longs;&longs;ent ro&shy;<lb/>tundiores, at nos non maximas mod&ograve;, &longs;ed &amp; minimas, <lb/>ea&longs;que magis angulis carere, &amp; ad rotunditatem accede&shy;<lb/>re videmus. </s>
            <s id="s.001057">Pr&aelig;terea non moueri eas circa centrum pa&shy;<lb/>lam e&longs;t, im&ograve; vt varia &longs;unt figura, ita varijs quoque motio&shy;<lb/>nibus, ex agitatione moueri. </s>
            <s id="s.001058">Id &longs;an&egrave; explorati&longs;&longs;imum e&longs;t, <pb xlink:href="007/01/114.jpg"/>angulos omnes, &amp; eminentias quaslibet in corporibus e&longs;&shy;<lb/>&longs;e infirmiores, offen&longs;ionibus enim expo&longs;it&aelig; &longs;unt, nec re&longs;i&shy;<lb/>&longs;tendi habent facultatem. </s>
            <s id="s.001059">Itaque in attritione qu&aelig; fit in <lb/>eorum agitatione perpetua, eminenti&aelig; contunduntur, &amp; <lb/>&longs;uperficies ip&longs;a paullatim leuigatur. </s>
          </p>
          <figure id="id.007.01.114.1.jpg" xlink:href="007/01/114/1.jpg"/>
          <p type="main">
            <s id="s.001060">E&longs;to angulatus lapis ABCD. <lb/><!-- KEEP S--></s>
            <s id="s.001061">Dum igitur perpeti motione <expan abbr="atq;">atque</expan> <lb/>a&longs;&longs;idu&acirc; ver&longs;atione agitatur, fer&shy;<lb/>turqueue, eminenti&aelig; anguliqueue, vt&shy;<lb/>pote debiles &amp; imbecilli, conte&shy;<lb/>runtur, &amp; inde figura fit qu&aelig;dam <lb/>irregularis, ad primam quidem la&shy;<lb/>pidis <expan abbr="form&atilde;">formam</expan> accedens, leuis tamen <lb/>&amp; quouis angulo carens, qualis e&longs;t E remotis ABCD, an&shy;<lb/>gularibus eminentijs. </s>
          </p>
          <p type="main">
            <s id="s.001062">Hanc eandem ob cau&longs;&longs;am, &longs;culptores antequam mar&shy;<lb/>moribus vltimum l&aelig;uorem inducant, dentato malleo pri&shy;<lb/>mum quidem vtuntur, tum demum eminentiores parti&shy;<lb/>culas radula facil&egrave; amouentes &longs;uperficiem ip&longs;am l&aelig;uem <lb/>&amp; ad&aelig;quatam reddunt. </s>
          </p>
          <p type="main">
            <s id="s.001063">Hinc etiam no&longs;trates Architecti, in arcium propu&shy;<lb/>gnaculis efformandis acutos angulos <expan abbr="deuit&atilde;t">deuitant</expan>, vtpote de&shy;<lb/>biliores, &amp; magis offen&longs;ionibus obnoxios. </s>
            <s id="s.001064">quod nec Vi&shy;<lb/>truuium latuit, qui ideo lib. 1. cap. 5. ita &longs;cribit: <emph type="italics"/>Turres itaque <lb/>rotund&aelig; aut polygoni&aelig; &longs;unt faciend&aelig;, quadratas enim machin&aelig; <lb/>celerius di&longs;&longs;ipant; &amp; angulos, Arietes tundendo frangunt, in ro&shy;<lb/>tundationibus autem, vti cuneos ad centrum adigendo l&aelig;dere non <lb/>po&longs;&longs;unt.<emph.end type="italics"/> H&aelig;c ille. <!-- KEEP S--></s>
            <s id="s.001065">Cur autem no&longs;tri rotundas figuras alias <lb/>vtiles reijciant, ab ijs petendum qui in ea facultate ver&shy;<lb/>&longs;antur. </s>
            <s id="s.001066">Porr&ograve; quod ad hanc eandem &longs;peculationem facit, <lb/>videmus, antiquas &longs;tatuas, vt &longs;&aelig;pius auribus, na&longs;o, digitis, <lb/>manibu&longs;ue atque pedibus carere, quippe quod imbecill&aelig; <lb/>&longs;int partes, &amp; facil&egrave; quouis occur&longs;u mutilentur. </s>
            <s id="s.001067">Qu&aelig; o-<pb xlink:href="007/01/115.jpg"/>mnia c&ugrave;m vera &longs;int, nemo, vt arbitror, dixerit, ab&longs;olut&egrave;, <lb/>quod voluit Ari&longs;toteles, id ex rotatione velociori &amp; par&shy;<lb/>tium &agrave; centro remotione, fieri. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001068">QVAESTIO XVI.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001069"><emph type="italics"/>Dubitatur, quare, qu&ograve; longiora &longs;unt ligna, <expan abbr="t&atilde;to">tanto</expan> imbecilliora fiant, <lb/>&amp; &longs;i tolluntur, inflectuntur magis: tamet&longs;i quod breue est ceu bi&shy;<lb/>cubitum fuerit, tenue, quod ver&ograve; cubitorum cen&shy;<lb/>tum cra&longs;&longs;um?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001070">Ex &longs;uis principijs &longs;oluit Ari&longs;toteles. </s>
            <s id="s.001071">Inquit enim: An <lb/>quia &amp; vectis &amp; onus &amp; hypomochlium, id e&longs;t, fulci&shy;<lb/>mentum in leuando, fit ip&longs;a ligni proceritas? </s>
            <s id="s.001072">Prior <expan abbr="namq;">namque</expan> <lb/>illius pars ceu hypomochlium fit, quod ver&ograve; in extremo <lb/>e&longs;t, pondus: quamobrem quanto exten&longs;ius fuerit id quod <lb/>&agrave; fulcimento e&longs;t, in flecti nece&longs;&longs;e e&longs;t magis; quo enim plus <lb/>&agrave; fulcimento di&longs;tat, eo magis incuruari nece&longs;&longs;e e&longs;t. </s>
            <s id="s.001073">Ne&shy;<lb/>ce&longs;&longs;ari&ograve; igitur extrema vectis eleuantur. </s>
            <s id="s.001074">Si igitur flexilis <lb/>fuerit vectis, ip&longs;um inflecti magis cum extollitur nece&longs;&longs;e <lb/>e&longs;t, quod longis accidit lignis, in breuibus autem quod vl&shy;<lb/>timum e&longs;t, quie&longs;centi hypomochlio deprop&egrave; fit. </s>
            <s id="s.001075">H&aelig;c <lb/>&longs;ubiect&acirc; figur&acirc; ob oculos ponimus. </s>
          </p>
          <figure id="id.007.01.115.1.jpg" xlink:href="007/01/115/1.jpg"/>
          <p type="main">
            <s id="s.001076">E&longs;to longum ac fle&shy;<lb/>xile lignum AB, manu ele&shy;<lb/>uetur in A, flectetur <expan abbr="itaq;">itaque</expan> <lb/>in B, &amp; declinabit in C. et&shy;<lb/>enim manus qu&aelig; &longs;u&longs;tinet <lb/>in A, fulcimenti loco &longs;uccedit: longitudo vero AB ponde&shy;<lb/>ris vices refert, at que vectis, quare quo longius abfuerit &agrave; <lb/>fulcimento, id e&longs;t, manu extremum B, eo magis flectetur; <lb/>&longs;i autem lignum breuius fuerit, nempe terminatum in D, <lb/>nequaquam flectetur, e&ograve; qu&ograve;d eius extremum D minus &agrave; <lb/>fulcimento quod e&longs;t in A &longs;it remotum. </s>
            <s id="s.001077">H&aelig;c igitur e&longs;t <expan abbr="m&emacr;s">mens</expan> <pb xlink:href="007/01/116.jpg"/>Ari&longs;totelis, cuius quidem &longs;ententiam non damnamus; <lb/>quippiam tamen addimus. </s>
            <s id="s.001078">Dicimus autem materiam, <lb/>quatenus ad hanc contemplationem &longs;pectat, in duplici <lb/>e&longs;&longs;e differentia. </s>
            <s id="s.001079">aut enim rarefactionis &amp; con&longs;tipationis <lb/>e&longs;t incapax, vt in chalybe videmus, nitro, metallo, mar&shy;<lb/>more, aut capax quidem, &amp; h&aelig;c duplex: Vel enim natura <lb/>nata e&longs;t ad rectitudinem quandam, vt arborum flagella <lb/>virg&aelig;que, aut non item, ceu &longs;tannum, plumbum, &amp; c&aelig;te&shy;<lb/>ra eiu&longs;modi. </s>
          </p>
          <figure id="id.007.01.116.1.jpg" xlink:href="007/01/116/1.jpg"/>
          <p type="main">
            <s id="s.001080">E&longs;to prim&ograve; vitreum <lb/>corpus gracile, procerum, <lb/>teres AB, manu capiatur in <lb/>A, <expan abbr="itaq.">itaque</expan> pondere ip&longs;ius cor&shy;<lb/>poris pr&aelig;ualente ad partes <lb/>B, quia in C puncto, quod <lb/>circa medium e&longs;t, ex parte <lb/>&longs;uperiori non fit rarefactio, <lb/>nec in in feriori con&longs;tipatio, <lb/>nec interim datur penetra&shy;<lb/>tio corporum, fit fractio &agrave; <lb/>&longs;uperiori parte, &amp; pars CB &agrave; <lb/>reliqua parte AC, auul&longs;a &amp; <lb/>&longs;eparata cadit in D, &longs;uccedit autem ip&longs;a &longs;eparatio rarefa&shy;<lb/>ctioni. </s>
            <s id="s.001081">Porr&ograve; quod materias ha&longs;ce non flexibiles diximus, <lb/>&longs;ed frangibiles, non ideo negamus vel &longs;en&longs;u docente, ali&shy;<lb/>quam in ijs fieri flexionem. </s>
            <s id="s.001082">Si autem lignea fuerit mate&shy;<lb/>ria, caque; flexibilis, vt EF, &longs;i manu eleuetur in E, pr&aelig;ualen&shy;<lb/>te pondere in F flectetur vbi G. ibi enim &agrave; parte &longs;uperiori <lb/>fit rarefactio, ab in feriori ver&ograve; con&longs;tipatio, &amp; pars GF de&shy;<lb/>clinabit in H, qu&aelig; declinatio e&ograve; v&longs;que procedet, quo ra&shy;<lb/>refactio &amp; con&longs;tipatio competens natur&aelig; illius materi&aelig;, <lb/>qu&aelig; flectitur ad &longs;ummam inten&longs;ionem deuenerint; tunc <lb/>&longs;i vis maior ingruerit, frangetur omnino: &longs;i &longs;ecus facta ibi <pb xlink:href="007/01/117.jpg"/>re&longs;i&longs;tentia, vbi rarefactio fit &amp; con&longs;tipatio per inclina&shy;<lb/>tionem &longs;ur&longs;um feretur pars in clinata &amp; nutans, tum in <lb/>contrariam partem tendens reflectetur, vt videre e&longs;t in <lb/>virga IN. </s>
            <s id="s.001083">Declinans enim in KL, repellente ea qu&aelig; infra <lb/>K fit materi&aelig; conden&longs;atione, impetu ex de&longs;cen&longs;u acqui&shy;<lb/>&longs;ito facta reflexione a&longs;cendit in KM, donec paullatim cir&shy;<lb/>ca pri&longs;tinam rectitudinem reuertatur, &amp; hic quidem mo&shy;<lb/>tus vibratio dicitur, agitatioue. </s>
            <s id="s.001084">Si autem virga plumbea <lb/>fuerit, natur&acirc; non fact&acirc; ad rectitudinem, puta OP, pro&shy;<lb/>prio vincente pondere, ad partes declinabit QS, fietque; in <lb/>QR rarefacta, nempe &longs;uperiori parte ea con&longs;tipata infe&shy;<lb/>riori in Q, nec reflectetur, quippe qu&ograve;d eius natura con&shy;<lb/>den&longs;ationem &amp; rarefactionem commod&egrave; patiatur, nec <lb/>facta &longs;it ad rectitudinem. </s>
          </p>
          <p type="main">
            <s id="s.001085">Porr&ograve; tripliciter fieri pote&longs;t horum oblongorum <lb/>corporum eleuatio, nempe vel extremorum alteio, aut &longs;i <lb/>ambobus, &longs;i vtrinque &longs;u&longs;pendatur, vel alicubi inter extre&shy;<lb/>ma. </s>
            <s id="s.001086">De priori modo iam egimus. </s>
            <s id="s.001087">Mod&ograve; &longs;u&longs;pendatur in <lb/>medio vt AB, in C. eo igitur ca&longs;u cum fulcimentum &longs;it in <lb/>C, <expan abbr="vtrinq;">vtrinque</expan> fit flexio in D, &amp; E, &amp; id quidem &longs;i materia fle&shy;<lb/>xionem patitur: &longs;in minus, fractio fit in C. <!-- KEEP S--></s>
            <s id="s.001088">Si autem ab ex&shy;<lb/><figure id="id.007.01.117.1.jpg" xlink:href="007/01/117/1.jpg"/><lb/>tremis fiat &longs;u&longs;pen&longs;io, vt in <lb/>AB, tunc ceu duo vectes <lb/>fient, quorum fulcimenta in <lb/>extremis AB. <!-- KEEP S--></s>
            <s id="s.001089">Pondera au&shy;<lb/>tem communia in medio vbi <lb/>C remoti&longs;&longs;ima enim ea pars e&longs;t ab extremis AB. <!-- KEEP S--></s>
            <s id="s.001090">Cedente <lb/><figure id="id.007.01.117.2.jpg" xlink:href="007/01/117/2.jpg"/><lb/>igitur materia &longs;uomet pon&shy;<lb/>deri, &longs;iquidem in flexibilis fu&shy;<lb/>erit, frangetur, &amp; fiet <expan abbr="parti&umacr;">partium</expan> <lb/>&longs;eparatio in C, duoque in de <lb/>corpora AD, BE. <!-- KEEP S--></s>
            <s id="s.001091">Si autem fle&shy;<lb/>xionis capax, vt AB in po&longs;tre&shy;<pb xlink:href="007/01/118.jpg"/>ma figura, facta ex contrario, nempe in in feriori parte cir&shy;<lb/>ca C rarefactione, in &longs;uperiori ver&ograve; conden&longs;atione, pon&shy;<lb/>dere pr&aelig;ualente curuabitur, fietque; lignum quidue aliud <lb/>huiu&longs;modi, vt ADB, nec amplius pondere &longs;uapte natur&acirc; <lb/>inferi&ugrave;s vergente ad rectitudinem reuertetur. </s>
          </p>
          <p type="main">
            <s id="s.001092">C&aelig;ter&ugrave;m cur oblonga &amp; graciliora corpora facilius <lb/>illis, qu&aelig; contrario &longs;e habent modo, frangantur, ex me&shy;<lb/>chanicis principijs in qu&aelig;&longs;tione 14. apert&egrave; demon&longs;traui&shy;<lb/>mus. </s>
            <s id="s.001093">Mod&ograve; vt ex hac contemplatione, qu&aelig; ali&agrave;s inutilis <lb/>videtur, aliquam vtilitatem capiamus, &amp; ex his qu&aelig; con&shy;<lb/>templabimur, Architecti prudentiores fiant, i&longs;th&aelig;c ip&longs;a, <lb/>de quibus agimus, ad rem &aelig;dificatoriam commod&egrave; apta&shy;<lb/>bimus. </s>
            <s id="s.001094">Transferamus igitur cogitationem ad eam <expan abbr="trabi&umacr;">trabium</expan> <lb/>compagem, qu&aelig; ad tecta &longs;u&longs;tinenda ex tran&longs;uer&longs;ario ar&shy;<lb/>rectarioque; &longs;it, &amp; duobus cauterijs, quam no&longs;tri &agrave; Latinis <lb/>detorto vocabulo Bi&longs;cauterium dicunt. </s>
            <s id="s.001095">Per&longs;crutabimur <lb/>enim, vnde illi tanta ad &longs;u&longs;tinendum vis, &amp; qu&aelig; compa&shy;<lb/>gem hanc con&longs;equantur pa&longs;&longs;iones. </s>
            <s id="s.001096">quamuis enim fabri <lb/>mer&aelig; praxi, quod vtile e&longs;t efficiant, nos meliorum inge&shy;<lb/>niorum grati&acirc;, rei ip&longs;ius cau&longs;&longs;as diligenter examinatas in <lb/>medium proferemus; nec de hac re tant&ugrave;m agemus, &longs;ed <lb/>de Cameris quoque, fornicibus eorumqueue vitijs &amp; virtu&shy;<lb/>tibus quatenus ad Mechanicum pertinet, &longs;ermonem ha&shy;<lb/>bebimus. </s>
            <s id="s.001097">Qu&aelig;rimus primo, cur perpendiculariter erectae <lb/>trabes &longs;uperimpo&longs;ita pondera validi&longs;&longs;ime &longs;u&longs;tineant? </s>
            <s id="s.001098">Et <lb/>&longs;ane hoc omnes norunt, &longs;ed non per cau&longs;&longs;as. </s>
          </p>
          <p type="main">
            <s id="s.001099">E&longs;to horizontis planum, illudqueue &longs;olidi&longs;&longs;imum, &amp; <lb/>impenetrabile AB, trabs eidem ad perpendiculum erecta <lb/>CD fulta ba&longs;i vbi C grauitatis centrum F. pondus &longs;uper&shy;<lb/>impo&longs;itum FG, cuius grauitatis centrum H: Sint autem <lb/>H &amp; E in eadem perpendiculari, qu&aelig; ad mundi centrum <lb/>HEC. </s>
            <s id="s.001100">Itaque eo quod tum penderis tum trabis centra <lb/>grauitent in perpendiculari, illa ver&ograve; fulciatur in C, to-<pb xlink:href="007/01/119.jpg"/><figure id="id.007.01.119.1.jpg" xlink:href="007/01/119/1.jpg"/><lb/>tius ponderis moles recumbet <lb/>in C: non de&longs;cendet autem in I, <lb/>propterea quod &longs;upponatur i&shy;<lb/>p&longs;um planum AB, impenetrabi&shy;<lb/>le. </s>
            <s id="s.001101">Igitur vt pondus H de&longs;cen&shy;<lb/>dat in C, alterum duorum e&longs;t <lb/>nece&longs;&longs;arium, nempe vel trabem <lb/>&longs;ubiectam comminui, aut eius <lb/>partes &longs;e&longs;e penetrare, &amp; plura <lb/>corpora e&longs;&longs;e in eodem loco, pu&shy;<lb/>ta KC, quorum hoc &longs;ecundum <lb/>natur&aelig; penitus repugnat, illud <lb/>vero primum, pen&egrave; impo&longs;&longs;ibile. </s>
            <s id="s.001102">Diuidatur enim trabs in <lb/>partes &aelig;quales tres, lineis KL, ip&longs;a igitur KC infima &longs;u&longs;ti&shy;<lb/>net mediam KL, h&aelig;c ver&ograve; &longs;upremam LD, h&aelig;c autem <expan abbr="p&omacr;-dus">pon&shy;<lb/>dus</expan>, ip&longs;um &longs;uperpo&longs;itum in H. <!-- KEEP S--></s>
            <s id="s.001103">Seigitur &longs;u&longs;tinent partes. <lb/></s>
            <s id="s.001104">Sed illud totum partibus con&longs;tat. </s>
            <s id="s.001105">ergo pondus totum &agrave; <lb/>trabe tota, hoc e&longs;t, &agrave; &longs;e toto &longs;u&longs;tinetur. </s>
          </p>
          <p type="main">
            <s id="s.001106">Pr&aelig;terea in pr&aelig;cedenti qu&aelig;&longs;tione mon&longs;trauimus <lb/>tunc facilem e&longs;&longs;e gracilis &amp; oblongi ligni fractionem, <expan abbr="c&umacr;">cum</expan> <lb/>maxima e&longs;t longitudinis ad cra&longs;&longs;itudinem proportio. </s>
            <s id="s.001107">H&icirc;c <lb/>ver&ograve; contr&agrave; accidit, etenim MD pars vectis qu&aelig; &agrave; fulci&shy;<lb/>mento e&longs;t ad potentiam minimam habet proportionem <lb/>ad rectam DC, qu&aelig; &agrave; fulcimento ad locum fractionis ex&shy;<lb/>tenditur, vbi C, quod vt euidentius pateat, </s>
          </p>
          <figure id="id.007.01.119.2.jpg" xlink:href="007/01/119/2.jpg"/>
          <p type="main">
            <s id="s.001108">E&longs;to &longs;eor&longs;um trabs AB, <lb/>cuius medium C. <!-- KEEP S--></s>
            <s id="s.001109">Sit autem <lb/>pondus D impo&longs;itum pun&shy;<lb/>cto C. facil&egrave; igitur frange&shy;<lb/>tur lignum AB, propterea <lb/>qu&ograve;d maxima &longs;it proportio <lb/>AC ad CE; re&longs;i&longs;tentia ver&ograve; <lb/>fiat in E, addatur vniaturque; <pb xlink:href="007/01/120.jpg"/>ligno AB lignum FH. <!-- KEEP S--></s>
            <s id="s.001110">Cra&longs;&longs;ius igitur e&longs;t totum AL, ip&longs;o <lb/>AH, &amp; ideo minor proportio AC ad CG qu&agrave;m AC, ad <lb/>CE. <!-- KEEP S--></s>
            <s id="s.001111">Addatur adhuc &amp; IM. </s>
            <s id="s.001112">Long&egrave; itaque difficilius fran&shy;<lb/>getur in K propterea qu&ograve;d long&egrave; minor &longs;it proportio AC <lb/>ad CK qu&agrave;m eiu&longs;dem ad CE &amp; CG. <!-- KEEP S--></s>
            <s id="s.001113">His igitur con&longs;ide&shy;<lb/>ratis, &amp; demon&longs;tratis concludimus, impo&longs;&longs;ibile e&longs;&longs;e ere&shy;<lb/>ctam trabem ponderi cedere, &amp; frangi. </s>
          </p>
          <p type="main">
            <s id="s.001114">Dicet autem qui&longs;piam, haec &longs;i vera &longs;unt, quo gracilius <lb/>fuerit fulcrum, eo validi&ugrave;s &longs;u&longs;tinebit, &amp; frangetur minus, <lb/>quod oppido fal&longs;um e&longs;t. </s>
            <s id="s.001115">Re&longs;pondemus, id non ex propor&shy;<lb/>tionum natur&acirc;, &longs;ed ex materi&aelig; ip&longs;ius infirmitate fieri. </s>
            <s id="s.001116">Ita <lb/>quoque invecte non materiam, quatenus ad vim pertinet, <lb/>&longs;ed proportiones partium con&longs;ideramus. </s>
            <s id="s.001117">Vtrumque igi&shy;<lb/>tur requiritur ad fulcri validitatem proportio longitudi&shy;<lb/>nis ad cra&longs;&longs;itudinem debita, &amp; materi&aelig; ip&longs;ius robur &amp; <lb/>fortitudo. </s>
            <s id="s.001118">Pr&aelig;terea, quoniam pondus, cui fulcrum re&longs;i&shy;<lb/>&longs;tit, vel ex natura premit, vel ex violentia, illud quidem <lb/>per lineam perpendicularem, qu&aelig; ad mundi <expan abbr="c&emacr;trum">centrum</expan>, hoc <lb/>autem lateraliter &amp; diuer&longs;i mod&egrave;, varia fit fulcrorum di&longs;&shy;<lb/>po&longs;itio. </s>
            <s id="s.001119">Cuius rei &longs;umma h&aelig;c e&longs;t, vt &longs;emper contra impe&shy;<lb/>tum &longs;upponantur. </s>
          </p>
          <figure id="id.007.01.120.1.jpg" xlink:href="007/01/120/1.jpg"/>
          <p type="main">
            <s id="s.001120">E&longs;to enim horizontis planum <lb/>AB, <expan abbr="eid&emacr;">eidem</expan> perpendiculares CADB, <lb/>&iacute;taque &longs;i naturaliter pondus pre&shy;<lb/>mat ex C, fulcrum &longs;upponetur AE. <lb/><!-- KEEP S--></s>
            <s id="s.001121">Si autem ex F ip&longs;um GE, &longs;i ver&ograve; ex <lb/>H, &longs;upponatur iuxta BE. <!-- KEEP S--></s>
            <s id="s.001122">Si ver&ograve; &longs;e&shy;<lb/>cundum I ponderi opponatur KE. <lb/></s>
            <s id="s.001123">H&aelig;c nos de arrectarijs fulcrisue; <lb/>nunc de tran&longs;uer&longs;arijs, &amp; inclinatis agemus, &amp; primum <lb/>de tran&longs;uer&longs;arijs, quatenus ad tectorum trabeationes &longs;pe&shy;<lb/>ctat. </s>
          </p>
          <p type="main">
            <s id="s.001124">E&longs;to tran&longs;uer&longs;aria trabs AB, muris <expan abbr="vtrinq;">vtrinque</expan> fulta CD, <pb xlink:href="007/01/121.jpg"/><figure id="id.007.01.121.1.jpg" xlink:href="007/01/121/1.jpg"/><lb/>cuius grauitatis centrum <lb/>E, in <expan abbr="perp&emacr;diculari">perpendiculari</expan> FEG, <lb/>qu&aelig; quidem ad mundi <lb/>centrum vergit. </s>
            <s id="s.001125"><expan abbr="Itaq;">Itaque</expan> eo&shy;<lb/>dem tendente grauitatis <lb/>centro, &longs;i pondus quod <lb/>premit in E, non pr&aelig;ua&shy;<lb/>leat vnioni <expan abbr="parti&umacr;">partium</expan> ip&longs;ius <lb/>materi&aelig; qu&aelig; e&longs;t in E, re&longs;i&longs;tet trabs &longs;uomet ponderi, nec <lb/>frangetur. </s>
            <s id="s.001126">Si autem vel in firmitate materi&aelig;, aut vitio, vel <lb/>maxima existente proportione AF ad FE, fractio fiet in E, <lb/>&amp; &longs;ecut&acirc; partium &longs;eparatione du&aelig; fient vtrin que trabes <lb/>AH, Bl, quorum grauitatis centra KL. <!-- KEEP S--></s>
            <s id="s.001127">Erunt igitur duo <lb/>vectes AE, BE, quorum fulcimenta MN, quamobrem &longs;i <lb/>proportio EM ad MH ita pr&aelig;ualeat, vt pondus quod e &longs;t <lb/>in E, &longs;uperet pondus muri O &longs;uperimpo&longs;iti, &amp; item muri <lb/>P, corruent quidem trabes, &amp; murorum fiet hinc inde di&longs;&shy;<lb/>&longs;ipatio. </s>
            <s id="s.001128">Si autem non pr&aelig;ualuerit ea, quam diximus, pro&shy;<lb/>portio, &longs;u&longs;pen&longs;&aelig; remanebunt vtrinque trabes vt AHBI. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001129">Huic difficultati egregi&egrave; occurrunt Architecti, ali&shy;<lb/>quando autem hoc modo: </s>
          </p>
          <figure id="id.007.01.121.2.jpg" xlink:href="007/01/121/2.jpg"/>
          <p type="main">
            <s id="s.001130">E&longs;to tran&longs;uer&longs;aria <lb/>trabs &longs;u&acirc; gracilitate, alia&shy;<lb/>ue de cau&longs;&longs;a imbecilla <lb/>AB, muri quibus <expan abbr="vtrinq;">vtrinque</expan> <lb/>&longs;u&longs;tinetur CD, Trabis i&shy;<lb/>p&longs;ius grauitatis centrum <lb/>G. <!-- KEEP S--></s>
            <s id="s.001131">Itaque adpactis trabi <lb/>lignis EF, capreolos ad&shy;<lb/>dunt muro vtrinque ful&shy;<lb/>tos CE, DF, eorum capita adpactis lignis admouentes EF, <lb/>&longs;ed &amp; tunc validi&longs;&longs;ima fit colligatio, &longs;i inter E &amp; F capreo&shy;<lb/>lorum capita integrum lignum trabi &longs;upponatur EF. <!-- KEEP S--></s>
            <s id="s.001132">Ra&shy;<pb xlink:href="007/01/122.jpg"/>tio autem validitatis patet; premente enim grauitatis <expan abbr="c&emacr;-tro">cen&shy;<lb/>tro</expan> in G, fulcra hinc inde &longs;uccurrunt CE, DF, qu&aelig; cum &longs;e&shy;<lb/>ip&longs;is fieri non valeant breuiora, ne corpori detur penetra&shy;<lb/>tio, re&longs;i&longs;tunt &amp; robu&longs;ti&longs;&longs;im&egrave; ip&longs;i ponderi &longs;uperimpo&longs;ito <lb/>contra nituntur. </s>
            <s id="s.001133">Videntur autem in hoc opere duo con&shy;<lb/>&longs;iderari vectes, GH, GB, quorum fulcimenta EF, potentia <lb/>premens vtrinque G. <!-- KEEP S--></s>
            <s id="s.001134">Pondera autem parietum partes ca&shy;<lb/>pitibus trabis impo&longs;it&aelig; in A &amp; B. <!-- KEEP S--></s>
            <s id="s.001135">Quoniam igitur parua <lb/>e&longs;t proportio GE ad EH, parua potentia premens in G, <lb/>maxim&egrave; autem pondus in A, fieri non pote&longs;t trabem fran&shy;<lb/>gi aut muros vtrinque di&longs;&longs;ipare in AB. <!-- KEEP S--></s>
            <s id="s.001136">Po&longs;&longs;unt etiam to&shy;<lb/>tius trabis tres partes con&longs;iderari AE, EF, FB, quarum ful&shy;<lb/>cimenta quatuor A, E, F, B, Diui&longs;o igitur pondere &amp; mul&shy;<lb/>tiplicatis fulcimentis impo&longs;&longs;ibile e&longs;t trabem conuelli &amp; <lb/>vitium facere. </s>
          </p>
          <p type="main">
            <s id="s.001137">Sed &amp; tectorum contignationes imbecillaque; tran&longs;&shy;<lb/>uer&longs;aria Mechanici corroborare &longs;olent, additis nempe <lb/>arrectaria trabe atque cauterijs. </s>
          </p>
          <figure id="id.007.01.122.1.jpg" xlink:href="007/01/122/1.jpg"/>
          <p type="main">
            <s id="s.001138">E&longs;to enim tran&longs;&shy;<lb/>uer&longs;aria trabs AB <lb/>parietibus vtrinque <lb/>fulta I, K, <expan abbr="arrectari&umacr;">arrectarium</expan> <lb/>CD. <!-- KEEP S--></s>
            <s id="s.001139">Cauterij vtrin&shy;<lb/>que AD, BD, ita <lb/>tran&longs;uer&longs;ari&aelig; trabi <lb/>in AB, &amp; arrectario <lb/>in D in&longs;erti, vt ne&shy;<lb/>quaquam inde ela&shy;<lb/>bi valeant. </s>
            <s id="s.001140">Tum ferrea fa&longs;cia EF mediam tran&longs;uer&longs;ariam <lb/>trabem AB, &agrave; parte inferiori ip&longs;i arrectario connectens, <lb/>Debet autem arrectarij pes vbi C, aliquantulum &agrave; tran&longs;&shy;<lb/>uer&longs;aria trabe di&longs;tare, ne deor&longs;um ex pondere vergente <lb/>paululum arrectario ip&longs;am tran&longs;uer&longs;ariam premat. </s>
            <s id="s.001141">His i-<pb xlink:href="007/01/123.jpg"/>gitur ita con&longs;titutis pondus quidem tran&longs;uer&longs;ari&aelig; trabis, <lb/>quod &longs;uapte natur&acirc; premit in medio vbi C, ferrea fa&longs;cia, <lb/>arrectari&aelig; trabi affixa di&longs;tinetur, Arrectariam cauterij &longs;u&shy;<lb/>&longs;tinent, hos ver&ograve; tran&longs;uer&longs;ari&aelig; capita AB, quibus indun&shy;<lb/>tur. </s>
            <s id="s.001142">Tota igitur eiu&longs;cemodi operis vis in eo con&longs;i&longs;tit, vt <lb/>prob&egrave; cauterij tran&longs;uersari&aelig; &amp; arrectari&aelig; trabi in&longs;eran&shy;<lb/>tur. </s>
            <s id="s.001143">fixis enim cauteriorum pedibus in AB, non <expan abbr="de&longs;cend&emacr;t">de&longs;cendent</expan> <lb/>&agrave; partibus &longs;eu capitibus D, ijs ver&ograve; &longs;tantibus &longs;tabit &amp; arre&shy;<lb/>ctarium, quo inde &longs;u&longs;pen&longs;o tran&longs;uer&longs;aria trabs ei ex ferrea <lb/>fa&longs;cia alligata nequaquam pendebit. </s>
            <s id="s.001144">Stabit ergo compa&shy;<lb/>ges tota &amp; &longs;uapte vi robu&longs;ti&longs;&longs;im&egrave; connexa totius tecti <lb/>pondus &longs;u&longs;tinebit. </s>
          </p>
          <p type="main">
            <s id="s.001145">Quoniam autem v&longs;u venire &longs;olet, cauterios nimia <lb/>longitudine debiles, aliquando tum proprio tum extra&shy;<lb/>neo cedentes ponderi deor&longs;um vergentes pandare, Ar&shy;<lb/>chitecti capreolis hinc inde &longs;uppo&longs;itis, ceu fulcris, huic <lb/>medentur infirmitati. </s>
          </p>
          <figure id="id.007.01.123.1.jpg" xlink:href="007/01/123/1.jpg"/>
          <p type="main">
            <s id="s.001146">Sint enim cauterij <lb/>debiles hinc inde AB, <lb/>AC, media trabs arre&shy;<lb/>ctaria, quam <expan abbr="Monach&umacr;">Monachum</expan> <lb/>dicimus AD. <!-- KEEP S--></s>
            <s id="s.001147">Cauterio&shy;<lb/>rum medi&aelig; partes E, F, <lb/>in punctis igitur EF, vtpote maxim&egrave; ab extremis di&longs;tanti&shy;<lb/>bus debiles cauterij valde laborant. </s>
            <s id="s.001148">Itaque &longs;uppo&longs;itis v&shy;<lb/>trinque arrectariolis EH, Fl, eorum capitibus E, F, duos <lb/>cauteriolos &longs;ibi ip&longs;is ad pedem arrectarij in D, re&longs;i&longs;tentes <lb/>apponunt. </s>
            <s id="s.001149">quibus ita con&longs;titutis nec E, nec F ad partes H, <lb/>I, de&longs;cendere valent. </s>
            <s id="s.001150">Capiatur enim inter EH, quoduis <lb/>punctum G, &amp; BG, DG, connectantur, erunt autem BG, <lb/>DG ip&longs;is BE ED breuiores ex 21. primi elem. </s>
            <s id="s.001151">Tunc igitur <lb/>punctum E fiet in G cum BE, ED fient in BG, DG, quod <lb/>non cedentibus B, D, &amp; &longs;ibi ip&longs;is breuioribus factis parti-<pb xlink:href="007/01/124.jpg"/>bus BE, ED, pror&longs;us e&longs;t impo&longs;&longs;ibile. </s>
            <s id="s.001152">&longs;tabunt igitur in eo&shy;<lb/>rum rectitudine cauterij AB, AC, nec pandabunt, quod <lb/>fieri querebatur. </s>
          </p>
          <p type="main">
            <s id="s.001153">H&icirc;c autem damnandi veniunt ij, qui tran&longs;uer&longs;ari&aelig; <lb/>quidem trabis capitibus cauteriorum pedes non <expan abbr="in&longs;er&umacr;t">in&longs;erunt</expan>, <lb/>&longs;ed ea vice tran&longs;uer&longs;ariolo quodam medios cauterios v&shy;<lb/>trinque connectunt ad in&longs;tar elementi A, quam compa&shy;<lb/>gem, capram, appellant. </s>
            <s id="s.001154">Sint enim cauterij hinc inde AB, <lb/>AC, quorum medias partes connectit tran&longs;uer&longs;ariolum, <lb/>DE. <!-- KEEP S--></s>
            <s id="s.001155">Dico igitur colligationem i&longs;tam magnopere impro&shy;<lb/>bandam. </s>
            <s id="s.001156">Sunt enim AB, AC vectes, quorum commune <lb/>fulcimentum A, potenti&aelig; hinc inde diuaricantes B, C, <lb/>pondera inter fulcimentum &amp; potentias DE. quoniam i&shy;<lb/>gitur vt DH ad AB, ita potentia in B, ad pondus in D, par&shy;<lb/>ua quidem potentia, pondus in D di&longs;trahet &amp; &longs;uperabit: <lb/>facillimaque; in de fiet tran&longs;uer&longs;ariol&igrave; &agrave; capreolis ip&longs;is vtrin&shy;<lb/>que reuul&longs;io: Et quoniam centrum quidem e&longs;t A, facta in <lb/>D, E, parua diuaricatione, maxima fit in BC, vtpote parti&shy;<lb/>bus ab ip&longs;o centro A quam remotis. </s>
            <s id="s.001157">Calcitrant igitur li&shy;<lb/>beri prope cauteriorum pedes, &amp; muros ip&longs;os &longs;ummos, <lb/>non &longs;ine magno operis totius vitio, &longs;ua calcitratione pro&shy;<lb/>pellunt. </s>
          </p>
          <p type="main">
            <s id="s.001158">H&aelig;c nos de trabeationibus, mod&ograve; ad fornicum ca&shy;<lb/>merarumque; naturam &longs;tilum transferemus; id enim &longs;uadet <lb/>vtilitas, imo &amp; nece&longs;&longs;itas ip&longs;a. </s>
            <s id="s.001159">Pauci enim ante nos h&aelig;c <lb/>tractarunt, &amp; &longs;an&egrave; his prob&egrave; non cognitis aut neglectis, <lb/>Architecti fabriqueue ingentes per&longs;&aelig;pe incurrunt, &amp; inex&shy;<lb/>plicabiles difficultates. </s>
            <s id="s.001160">Dicimus igitur prim&ograve;, coctiles la&shy;<lb/>teres, &amp; non cuneatos lapides ad rectam lineam di&longs;po&longs;i<lb/>tos, non &longs;tare. </s>
          </p>
          <p type="main">
            <s id="s.001161">Sint enim muri vtrinque AC, BD. <!-- KEEP S--></s>
            <s id="s.001162">Ducatur hori&shy;<lb/>zonti &aelig;quidi&longs;tans CD, iuxta quam lateres lapide&longs;ue non <lb/>cuneati, &longs;eriatim collocentur EF. <!-- KEEP S--></s>
            <s id="s.001163">Dicimus amoto arma&shy;<pb xlink:href="007/01/125.jpg"/><figure id="id.007.01.125.1.jpg" xlink:href="007/01/125/1.jpg"/><lb/>mento, hoc e&longs;t, pro&shy;<lb/>hibente ip&longs;o lateres <lb/>ruere. </s>
            <s id="s.001164">Producantur <lb/>enim AC in G, BD <lb/>ver&ograve; in H, cum ip&longs;is <lb/>CG, DH, &aelig;quales <lb/>fiant CI, DK, &amp; recta <lb/>IK iungatur, erit igi&shy;<lb/>tur GD &longs;patium ip&longs;i <lb/>CK &longs;patio &longs;imile qui&shy;<lb/>dem &amp; &aelig;quale, quod <lb/>c&ugrave;m ita &longs;it, nihil prohibet quin tota laterum GD moles in <lb/>&longs;patium CK transferatur, &amp; corruat. </s>
          </p>
          <p type="main">
            <s id="s.001165">Si autem cunei ip&longs;i latere&longs;ue, cuneatim di&longs;po&longs;iti, ita <lb/>&longs;int vt ad vnum centrum tendant, licet ad rectam lineam <lb/>collocentur, non delabentur, &longs;ed &longs;tabunt; quod ita o&longs;ten&shy;<lb/>demus. </s>
          </p>
          <figure id="id.007.01.125.2.jpg" xlink:href="007/01/125/2.jpg"/>
          <p type="main">
            <s id="s.001166">Sint cunei latere&longs;ue <lb/>cuneatim di&longs;po&longs;iti ABCD, <lb/>tendentes ad centrum, &longs;eu <lb/>commune punctum E, Du&shy;<lb/>cantur CAE, DBE, &longs;intqueue <lb/>muri vtrinque ponderi re&longs;i&shy;<lb/>&longs;tentes CL, DM, Demitta&shy;<lb/>tur perpendicularis, qu&aelig; ad <lb/>mundi centrum FGE &longs;ecans AB, in G. <!-- KEEP S--></s>
            <s id="s.001167">Tum fiat GK aequa&shy;<lb/>lis GF &amp; per K ip&longs;i AGB parallela ducatur, HKI claudens <lb/>&longs;patium AHIB. <!-- KEEP S--></s>
            <s id="s.001168">Quoniam igitur vt EC, ad EA, ita CD ad <lb/>AB per 4. propo&longs;. lib. 6. maior erit CD ip&longs;a AB, &amp; e&acirc;dem <lb/>de cau&longs;&longs;a maior AB, ip&longs;a HI, &amp; idcirco maius ABDC &longs;pa&shy;<lb/>tium, &longs;patio AHIB. <!-- KEEP S--></s>
            <s id="s.001169">Non igitur pote&longs;t linea CD, fieri in <lb/>AB, neque AB, in HI, neque &longs;patium totum CABD, tran&longs;&shy;<lb/>ferri in &longs;patium AHIB non data &lpar;quod natur&aelig; ip&longs;i repu&shy;<pb xlink:href="007/01/126.jpg"/>gnat&rpar; corporum penetratione. </s>
            <s id="s.001170">Stabunt ergo cunei, quod <lb/>fuerat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.001171">Verum enimuero, debilis h&aelig;c &longs;tructura e&longs;t, &amp; eo de&shy;<lb/>bilior, quo vani latitudo fuerit maior, cuneorum ver&ograve; al&shy;<lb/>titudo minor. </s>
            <s id="s.001172">Idem enim patitur quod epi&longs;tylia in &longs;pecie <lb/>Ar&aelig;os&longs;tyla, qu&aelig;, vt &longs;cribit Vitruuius lib.  3. c. <!-- REMOVE S-->2. propter in&shy;<lb/>teruallorum magnitudinem franguntur. </s>
            <s id="s.001173">Id quoque ha&shy;<lb/>bet vitij, quod cunei ita di&longs;po&longs;iti &longs;uo pondere incumbas <lb/>vtrinque violenti&longs;&longs;im&egrave; pellant. </s>
            <s id="s.001174">Vtilis tamen e&longs;&longs;e pote&longs;t <lb/>ad portarum &amp; fene&longs;trarum, qu&aelig; in medijs muris &longs;unt, &amp; <lb/>mediocri vano aperiuntur, &longs;uperliminaria. </s>
          </p>
          <p type="main">
            <s id="s.001175">Si ver&ograve; ad minorem circuli portionem curuetur Ca&shy;<lb/>mera, vtilior quidem erit &longs;tructura ea ip&longs;a, de qua locuti <lb/>&longs;umus; non tamen omnin&ograve; &longs;ine vitio. </s>
          </p>
          <figure id="id.007.01.126.1.jpg" xlink:href="007/01/126/1.jpg"/>
          <p type="main">
            <s id="s.001176">E&longs;to fornix ex minori <lb/>circuli portione AB, cuius in&shy;<lb/>cumb&aelig; AF, BH muris fult&aelig; <lb/>AC, BD. <!-- KEEP S--></s>
            <s id="s.001177">Con&longs;tet autem vel <lb/>ex lapidibus cuneatis, vel ex <lb/>coctilibus lateribus ad E <expan abbr="c&emacr;-trum">cen&shy;<lb/>trum</expan> tendentibus. </s>
            <s id="s.001178">Sitque; for&shy;<lb/>nicis linea exterior FGH, in&shy;<lb/>terior AIB. <!-- KEEP S--></s>
            <s id="s.001179">Ducantur EA, <lb/>ED, &amp; producantur in M, N. <lb/><!-- KEEP S--></s>
            <s id="s.001180">Quoniam igitur vt EM ad EA, ita MGN ad AIB, maior e&shy;<lb/>rit MGN linea ip&longs;a AIB, quamobrem fieri non pote&longs;t vt <lb/>aptetur line&aelig; AIB, &amp; in eius locum de&longs;cendat. </s>
            <s id="s.001181">Stabit igi&shy;<lb/>tur, incumbis vtrinque non cedentibus. </s>
            <s id="s.001182">Valid&egrave; autem <lb/>&longs;peciem hanc, loca quibus incumbit, propellere, ita o&shy;<lb/>&longs;tendemus. </s>
          </p>
          <p type="main">
            <s id="s.001183">Producatur in eadem figura CA in K, &amp; DB in L. <lb/><!-- KEEP S--></s>
            <s id="s.001184">Partes igitur qu&aelig; muris ad perpendiculum fulciuntur, <lb/>&longs;unt AKF, BLH, minim&aelig; ill&aelig; quidem, maxima ver&ograve; pars <pb xlink:href="007/01/127.jpg"/>e&longs;t extra fulcimenta, nempe tota AKLB qu&aelig; idcirc&oacute; &longs;uo&shy;<lb/>pte pondere deor&longs;um vergens &amp; in incumbas <expan abbr="vtrinq;">vtrinque</expan> pel&shy;<lb/>lens aperitur, &amp; facillim&egrave; vitium facit. </s>
            <s id="s.001185">Eiu&longs;dem fer&egrave; na&shy;<lb/>tur&aelig; ea &longs;pecies e&longs;t, qu&aelig; vel ex media, vel ex minori ellip&longs;is <lb/>&longs;ecundum maiorem diametrum fit &longs;egmento. </s>
            <s id="s.001186">Vtilior ta&shy;<lb/>men h&aelig;c e&longs;t, pr&aelig;cipu&egrave; circa incumbas, propterea quod <lb/>partes habeat erectiores, &amp; circulari illa de qua egimus, <lb/>magis fultas. </s>
            <s id="s.001187">circa medium autem pote&longs;t videri debilior, <lb/>quippe quod ellip&longs;is ibi circulo curuetur minus. </s>
          </p>
          <p type="main">
            <s id="s.001188">Ea ver&ograve; forma, qua mirum in modum delectati &longs;unt <lb/>Barbari, qui declinante imperio Italiam inua&longs;erunt, &amp; <lb/>bonam emendati&longs;&longs;imamqueue antiquorum &aelig;dificandi ra&shy;<lb/>tionem deturparunt, ex duobus con&longs;tat circuli portioni&shy;<lb/>bus, quamobrem Albertus lib. 3. ho&longs;ce arcus, compo&longs;itos, <lb/>appellat. </s>
            <s id="s.001189">Circinantur autem hoc pacto, diui&longs;a nempe <lb/>&longs;ubten&longs;a, in partes tres, ea&longs;que &aelig;quales, ponitur circini <lb/>pes in altero diui&longs;ionum puncto &amp; pars circuli de&longs;cribi&shy;<lb/>tur, mox in altero puncto circini pede collocato alia cir&shy;<lb/>culi portio lineatur, quibus arcus ip&longs;e integratur. </s>
            <s id="s.001190">Appel&shy;<lb/>lant autem tertium acutum, eo quod ex &longs;ubten&longs;a in tres <lb/>partes diui&longs;a, arcus non fiat rotundus, &longs;ed in acutum an&shy;<lb/>gulum ex duabus circuli portionibus de&longs;inens. </s>
          </p>
          <figure id="id.007.01.127.1.jpg" xlink:href="007/01/127/1.jpg"/>
          <p type="main">
            <s id="s.001191">Sint igitur muri <lb/>AC, BD, in quibus v&shy;<lb/>trinque incumb&aelig; KA, <lb/>BI. <!-- KEEP S--></s>
            <s id="s.001192">Ducatur itaque &longs;ub&shy;<lb/>ten&longs;a horizonti &aelig;quidi&shy;<lb/>&longs;tans AP, qu&aelig; in tres &aelig;&shy;<lb/>quales partes diuidatur <lb/>punctis E, F, tum centris <lb/>EF, circulorum portio&shy;<lb/>nes de&longs;cribantur hinc <lb/>AG, HK, inde ver&ograve; BG, <pb xlink:href="007/01/128.jpg"/>IH, ex quibus arcus totus integratur. </s>
            <s id="s.001193">Vtilis h&aelig;c quidem <lb/>&longs;pecies e&longs;t, licet inuenu&longs;ta, propterea quod haud violen&shy;<lb/>ter incumbas vtrinque repellat, &amp; in &longs;ummo magnis &longs;u&longs;ti&shy;<lb/>nendis oneribus &longs;it apta. </s>
            <s id="s.001194">Producantur CH in N, DB ver&ograve; <lb/>in O, &longs;itqueue centrum grauitatis AG in L, partis vero BG <lb/>in M. <!-- KEEP S--></s>
            <s id="s.001195">Quoniam igitur centra h&aelig;c ob elatam portionum <lb/>con&longs;titutionem quam proxima lineis AN, BO, fulcimen&shy;<lb/>torum fiunt, maxim&egrave; <expan abbr="&longs;u&longs;tin&emacr;tur">&longs;u&longs;tinentur</expan>, &amp; deor&longs;um potius quam <lb/>lateraliter incumbas ip&longs;as premunt. </s>
            <s id="s.001196">Si quid tamen <expan abbr="hab&emacr;t">habent</expan> <lb/>vitij, illud e&longs;t quod grauitatis centra momentum haben&shy;<lb/>tia ad interiorem partem ver&longs;us PQ vim faciant, &amp; ni&longs;i <lb/>partes magno &longs;uperimpo&longs;ito pondere comprimantur, <lb/>partes qu&aelig; &longs;unt circa HG, &longs;ur&longs;um pellentes aliquali &longs;ibi <lb/>rectitudine comparata corruunt, facta nempe circa L, M, <lb/>coniunctarum partium &longs;eparatione. </s>
          </p>
          <p type="main">
            <s id="s.001197">His hoc pacto explicatis de &longs;emicirculari fornice a&shy;<lb/>gemus, qu&aelig; c&aelig;teris omnibus vtilior e&longs;t, &amp; long&egrave; pulcher&shy;<lb/>rima, quamobrem Antiquis Architectis omnibus inpri&shy;<lb/>mis admodum familiaris: </s>
          </p>
          <figure id="id.007.01.128.1.jpg" xlink:href="007/01/128/1.jpg"/>
          <p type="main">
            <s id="s.001198">E&longs;to vanum <lb/>ABCD, muris v&shy;<lb/>trinque clau&longs;um. <lb/></s>
            <s id="s.001199">Ducatur per <expan abbr="s&umacr;-mitates">sum&shy;<lb/>mitates</expan> <expan abbr="muror&umacr;">murorum</expan> <lb/>horizonti &aelig;qui&shy;<lb/>di&longs;tans recta AD, <lb/>hac bifariam &longs;e&shy;<lb/>cta in E, eodem <lb/>centro E, &longs;patio <lb/>ver&ograve; EA &longs;emicir&shy;<lb/>culus de&longs;cribatur <lb/>AFD, concaua <lb/>nempe ip&longs;ius for-<pb xlink:href="007/01/129.jpg"/>nicis pars; tum eodem centro, &longs;patio ver&ograve; EG, circinetur <lb/>GHI eiu&longs;dem fornicis pars conuexa. </s>
            <s id="s.001200">Po&longs;t h&aelig;c productis <lb/>lineis BH, CD, in OP, &longs;ecetur fornix tota in tres &aelig;quales <lb/>partes AGKM, MNLK, NDIL, &amp; KME, LNE iungantur, <lb/>&longs;int autem partium ip&longs;arum grauitatis centra QRS. </s>
            <s id="s.001201">E&longs;t <lb/>autem R in ip&longs;a perpendiculari HE. </s>
            <s id="s.001202">Quoniam igitur <lb/>partium AGKM, DILN, qu&aelig; <expan abbr="vtrinq;">vtrinque</expan> &longs;unt grauitatis cen&shy;<lb/>tra QS, in ip&longs;is &longs;unt fulcimentorum lineis OH PD, &longs;u&acirc; <lb/>&longs;ponte fulcimentis eas &longs;u&longs;tinentibus partes ip&longs;&aelig; &longs;tabunt. <lb/></s>
            <s id="s.001203">Pars autem media KMNL deor&longs;um vergente per ip&longs;am <lb/>HE lineam grauitatis centro, &longs;i parumper vel incumb&aelig; <lb/>vel partes vtrinque AG<emph type="italics"/>K<emph.end type="italics"/>M, DILN cedant, vtpote qu&aelig; &agrave; <lb/>fulcimentis e&longs;t remoti&longs;&longs;ima, magno impetu &longs;uopte pon&shy;<lb/>dere deor&longs;um feretur. </s>
            <s id="s.001204">qu&aelig; igitur in his &longs;emicircularibus <lb/>fornicibus partes &longs;tabiliores &longs;int, qu&aelig; ver&ograve; ca&longs;ibus obno&shy;<lb/>xi&aelig;, ex his qu&aelig; diximus, clar&egrave; patet. </s>
          </p>
          <p type="main">
            <s id="s.001205">C&aelig;ter&ugrave;m cur incumbis manentibus fornix &longs;tet, ea <lb/>cau&longs;&longs;a e&longs;t, quod partes exteriores G<emph type="italics"/>K<emph.end type="italics"/>, <emph type="italics"/>K<emph.end type="italics"/>L, LI, maiores &longs;int <lb/>in ferioribus &amp; oppo&longs;itis AM, MN, NG; quod &longs;upr&agrave; de&shy;<lb/>mon&longs;trauimus. </s>
          </p>
          <p type="main">
            <s id="s.001206">Si quid autem vitij in hac &longs;pecie e&longs;t, illud quidem <lb/>e&longs;t, quod &longs;umma pars <emph type="italics"/>K<emph.end type="italics"/>MNL deor&longs;um vergens magn&acirc; vi <lb/>partes, qu&aelig; vtrinque &longs;unt, repellat, ex qua re &longs;olidarum <lb/>partium fit &longs;olutio, &amp; inde ruina. </s>
          </p>
          <p type="main">
            <s id="s.001207">Huic difficultati vt occurrerent peritiores Archite&shy;<lb/>cti, plura excogit&acirc;runt remedia. </s>
            <s id="s.001208">Primum enim parietes <lb/>hinc inde ita &longs;olidos, cra&longs;&longs;os &amp; firmos faciunt, vt &longs;uapte vi <lb/>re&longs;i&longs;tentes dimoueri loco nequeant, vel para&longs;tatas <expan abbr="add&umacr;t">addunt</expan> <lb/>vt in figura TX, VY. </s>
            <s id="s.001209">Pr&aelig;terea &amp; ferrea claui ex incumba <lb/>in incumbam ducta &amp; vtrinque firmata contrarias partes <lb/>validi&longs;&longs;im&egrave; connectunt, qu&aelig; calcitrantes &lpar;ita enim lo&shy;<lb/>quuntur no&longs;trates <emph type="italics"/>A<emph.end type="italics"/>rchitecti,&rpar; fornicis pedes cohibent, &amp; <lb/>&longs;olidum ne &longs;oluatur impediunt. </s>
            <s id="s.001210">qua in &longs;pecie dubitan<expan abbr="d&umacr;">dum</expan> <pb xlink:href="007/01/130.jpg"/>e&longs;&longs;et, an optimo loco &longs;it a &longs;it clauis, qu&aelig; per centrum? </s>
            <s id="s.001211">Et <lb/>&longs;an&egrave; videtur, quippe quod circa incumbas impetus fiat <lb/>maior. </s>
            <s id="s.001212">Ego autem vtilius ibi poni arbitror, vbi <expan abbr="punctaq.">punctaque</expan> <lb/>5. hoc e&longs;t, in medio tertiarum illarum partium, qu&aelig; vtrin&shy;<lb/>que incumbis in&longs;i&longs;tunt, propterea quod primus impul&longs;us <lb/>ex media parte qu&aelig; impendet, ibi fiat. </s>
            <s id="s.001213">Rar&ograve; tamen boni <lb/>Architecti eo loco aptare &longs;olent, eo qu&ograve;d eiu&longs;modi cla&shy;<lb/>ues vel pulcherrimis &aelig;dificijs minuant gratiam. </s>
            <s id="s.001214">Vnde fit <lb/>vt nunquam &longs;atis laudetur Lucianus ille Benuerardus <lb/>Lauranen&longs;is Dalmata, qui nullibi apparentes eas po&longs;uit <lb/>in admirabili illa Vrbini Aula, quam Federico Feltrio, fe&shy;<lb/>lici&longs;&longs;imo &aelig;qu&egrave; &amp; inuicti&longs;&longs;imo Duci, &aelig;dificauit. </s>
          </p>
          <p type="main">
            <s id="s.001215">Tertio denique modo huic infirmitati me dentur, <lb/>vt videre e&longs;t in &longs;equenti figura, in qua vanum ADBC, mu&shy;<lb/>ri vtrinque AF, BH, fornix ver&ograve; FGH. </s>
            <s id="s.001216">Itaque dum muros <lb/><figure id="id.007.01.130.1.jpg" xlink:href="007/01/130/1.jpg"/><lb/>ex&longs;truunt, arre&shy;<lb/>ctarias trabes, ro&shy;<lb/>bore aliaue mate&shy;<lb/>ria firmi&longs;&longs;ima, illis <lb/>in&longs;erunt, quales <lb/>&longs;unt IF<emph type="italics"/>K<emph.end type="italics"/> LHM, <lb/>ea proceritate vt <lb/>futuri fornicis &longs;u&shy;<lb/>perent &longs;ummita&shy;<lb/>tem. </s>
            <s id="s.001217">Con&longs;umma&shy;<lb/>to enim fornice, <lb/>nondum tamen, <lb/>exarmato, tran&longs;&shy;<lb/>uer&longs;ariam <expan abbr="trab&emacr;">trabem</expan> &agrave; <lb/>&longs;ummo fornicis <lb/>dor&longs;o parumper <lb/>eminentem in punctis I, L, arrectarijs trabibus validi&longs;&longs;i&shy;<lb/>mis clauibus connectunt, tum punctis NP, Oq, capreolos <pb xlink:href="007/01/131.jpg"/>tran&longs;uer&longs;ario, &amp; arrectarijs ferreis, clauis affigunt. </s>
            <s id="s.001218">Qui&shy;<lb/>bus ita concinnatis, facta fornicis valid&acirc; pre&longs;&longs;ione in G, <lb/>incumbi&longs;que F, H, ad exteriora repul&longs;is, AB &longs;patium non <lb/>fit maius. </s>
            <s id="s.001219">Repul&longs;is enim incumbis &amp; muros propelli ne&shy;<lb/>ce&longs;&longs;e e&longs;t, &amp; cum muris ip&longs;as in&longs;ertas trabes, I<emph type="italics"/>K<emph.end type="italics"/>, LM. </s>
            <s id="s.001220">At va&shy;<lb/>ricari non po&longs;&longs;unt, n&icirc; &longs;ecum trahant puncta PQ, quod fie&shy;<lb/>ri non pote&longs;t, propterea quod in punctis N, O, valid&egrave; di&longs;&shy;<lb/>tineantur. </s>
            <s id="s.001221">Itaque &longs;patio AB non dilatato nulla fit ip&longs;ius <lb/>fornicis di&longs;&longs;olutio, quod vtique &agrave; principio ceu propo&longs;i&shy;<lb/>tus finis qu&aelig;rebatur. </s>
            <s id="s.001222">Sed dicet qui&longs;piam, Nonne pende&shy;<lb/>bit tran&longs;uer&longs;aria trabs in ip&longs;a di&longs;tractione arrectariorum, <lb/>pre&longs;&longs;a in punctis N, O? aut parum dicimus, aut nihil. </s>
            <s id="s.001223">Cum <lb/>enim PQ proxima &longs;int punctis FH, qu&aelig; cum arrectarijs &agrave; <lb/>muro di&longs;tinentur, magna in ijs fit vtrobique re&longs;i&longs;tentia. </s>
          </p>
          <p type="main">
            <s id="s.001224">Rebus igitur ita &longs;e habentibus cum ob&longs;erua&longs;&longs;ent Ar&shy;<lb/>chitecti, ob enormitatem ponderis fornices in tertia illa <lb/><figure id="id.007.01.131.1.jpg" xlink:href="007/01/131/1.jpg"/><lb/>parte qu&aelig; &longs;umma e&longs;t <lb/>laborare, <expan abbr="qu&atilde;tum">quantum</expan> ter&shy;<lb/>tijs vtrinque partibus <lb/>&longs;oliditatis addunt, tan&shy;<lb/>tundem ex illa parte <lb/>&longs;uprema demere <expan abbr="&longs;ol&emacr;t">&longs;olent</expan>, <lb/>vt videre e&longs;t in &longs;ubie&shy;<lb/>cta figura, in qua par&shy;<lb/>tes A, B, &longs;olid&aelig; &amp; cra&longs;&shy;<lb/>&longs;iores, quibus h&aelig;rent <lb/>partes, qu&aelig; CE, DG <lb/>cra&longs;&longs;&aelig; quidem &amp; ill&aelig;, <lb/>tum vero &longs;umma EFG, <lb/>alijs &longs;ubtilior. </s>
            <s id="s.001225">Minus <lb/>igitur grauante ponde&shy;<lb/>re in F, minor fit ad incumbas pre&longs;&longs;io, aut &longs;i qua fit, &agrave; <expan abbr="parti&umacr;">partium</expan> <lb/>ACE, BDG &longs;oliditate haud inualid&egrave; &longs;u&longs;tinetur. </s>
          </p>
          <pb xlink:href="007/01/132.jpg"/>
          <p type="main">
            <s id="s.001226">C&aelig;ter&ugrave;m admonet nos locus, vt aliquid de forni&shy;<lb/>cum di&longs;&longs;olutionibus in medium afferamus: cau&longs;&longs;is enim <lb/>morborum cognitis, facilius periti medici adhibere &longs;o&shy;<lb/>lent remedia. </s>
          </p>
          <figure id="id.007.01.132.1.jpg" xlink:href="007/01/132/1.jpg"/>
          <p type="main">
            <s id="s.001227">E&longs;to enim &longs;emicircula&shy;<lb/>ris fornix ABC, cuius cen&shy;<lb/>trum E, perpendicularis ve&shy;<lb/>r&ograve; qu&aelig; per centrum DBE, &longs;e&shy;<lb/>micirculi ABC, diameter <lb/>AEC, incumb&aelig; <expan abbr="vtrinq;">vtrinque</expan> A, C. <lb/><!-- KEEP S--></s>
            <s id="s.001228">Itaque &longs;i nulla fiat incumba&shy;<lb/>rum repul&longs;io, &longs;tabit fornix; &longs;i ver&ograve; fiat, ruinam faciet. </s>
          </p>
          <p type="main">
            <s id="s.001229">Pellantur itaque ad exteriores partes, vt in &longs;ecunda <lb/><figure id="id.007.01.132.2.jpg" xlink:href="007/01/132/2.jpg"/><lb/>figura, H in F, &amp; C in G, <lb/>ex qua pul&longs;ione cum ma&shy;<lb/>ius fiat &longs;patium quod in&shy;<lb/>tegro fornice impleba&shy;<lb/>tur, iam di&longs;tractis <expan abbr="vtrinq;">vtrinque</expan> <lb/>fornicis partibus <expan abbr="n&omacr;">non</expan> im&shy;<lb/>pletur, Diuiditur igitur <lb/>locus maior factus in tres partes, quarum hinc inde duas <lb/>replent fornicis partes, tertiam ver&ograve; qu&aelig; media e&longs;t, re&shy;<lb/>plet in&longs;ertus, ne vacuum detur, a&euml;r, vt in figura videre e&longs;t, <lb/>in qua &longs;olut&aelig; vtrinque fornicis partes HIKF, PMNG, a&euml;r <lb/>autem medius &longs;patium replens IKMN. </s>
            <s id="s.001230">Diuidantur &longs;in&shy;<lb/>guli quadrantes FK, GN, in partes tres, quarum du&aelig; &longs;int <lb/>hinc inde FQ, GR, &amp; &agrave; centris, qu&aelig; &longs;eparatis quadranti&shy;<lb/>bus facta &longs;unt in ST, rect&aelig; ducantur SQV. TRX. <!-- KEEP S--></s>
            <s id="s.001231">Quo&shy;<lb/>niam igitur terti&aelig; partes vtrinque VIKQ MNRX pro&shy;<lb/>pria grauitate depre&longs;&longs;&aelig;, nullum quo &longs;u&longs;tineantur fulci&shy;<lb/>mentum habent, corruent quidem. </s>
            <s id="s.001232">Ducantur autem re&shy;<lb/>ct&aelig; QI, RM, con&longs;tituentes cum ip&longs;is QV, RX pares an&shy;<lb/>gulos VQI MRX. </s>
            <s id="s.001233">Itaque centris QR partes QIRM ad <pb xlink:href="007/01/133.jpg"/>inferiores partes deuoluentur, fientqueue QI, RM, vbi QZ, <lb/>RZ. </s>
            <s id="s.001234">Si autem QI, RM perpendicularibus qu&aelig; &agrave; punctis <lb/>QR ad perpendicularem DE ducuntur, fuerint maiores <lb/>conuenient alicubi in ip&longs;a perpendiculari, &amp; altera alte&shy;<lb/>ram &longs;u&longs;tinebit; &longs;i autem &aelig;quales tangent &longs;e &amp; nihilomi&shy;<lb/>nus fiet ruina, &longs;i minores nec &longs;e inuicem tangent, &amp; null&agrave; <lb/>re prohibente deor&longs;um corruent. </s>
            <s id="s.001235">tangant autem &longs;e in <expan abbr="p&umacr;-cto">pun&shy;<lb/>cto</expan> Z. quo pacto igitur fornices incumbis cedentibus in <lb/>medio aperti, <expan abbr="di&longs;&longs;olu&atilde;tur">di&longs;&longs;oluantur</expan> &amp; ruinam faciant, ex i&longs;tis patet. </s>
          </p>
          <p type="main">
            <s id="s.001236">Ex demon&longs;tratis qua&longs;i ex con&longs;ectario habemus for&shy;<lb/>nices quo fuerint cra&longs;&longs;iores dato pari incumbarum &longs;ece&longs;&shy;<lb/>&longs;u, ruin&aelig; minus e&longs;&longs;e obnoxios qu&agrave;m tenuiores, hoc e&longs;t, <lb/>maiori aperitione indigere ad ruinam cra&longs;&longs;iores quam te&shy;<lb/>nuiores, quod licet ex iam dictis re&longs;ultet, nos tamen cla&shy;<lb/>rius ex &longs;ubiecto &longs;chemate demon&longs;trabimus. </s>
          </p>
          <figure id="id.007.01.133.1.jpg" xlink:href="007/01/133/1.jpg"/>
          <p type="main">
            <s id="s.001237">E&longs;to enim cra&longs;&longs;ioris <lb/>fornicis pars <expan abbr="quid&emacr;">quidem</expan> ABCD, <lb/>tenuioris EFCD circa <expan abbr="id&emacr;">idem</expan> <lb/>centrum R. <!-- KEEP S--></s>
            <s id="s.001238">Ducatur au&shy;<lb/>tem RM, &longs;ecans CD in G. <lb/>EF in H AB, in M. <!-- KEEP S--></s>
            <s id="s.001239">Centro <lb/>igitur G fiet euer&longs;io portio&shy;<lb/>num fornicum, MD, HD, <lb/>Ducantur GA, GE &amp; producta AD in N ip&longs;i AN perpen&shy;<lb/>dicularis ducatur GN. quoniam igitur GE cadit in trian&shy;<lb/>gulo AGN erit ex 21. propo&longs;. lib. 1. elem. GA, maior GE. <lb/></s>
            <s id="s.001240">Corruente igitur maioris fornicis portione MD, recta <lb/>GA centro G punctum A de&longs;cribet portionem AI, mino&shy;<lb/>ris interim ex GE, de&longs;cribente EL, at cadenti angulo A <lb/>occurrit in perpendiculari IK in puncto I angulus oppo&shy;<lb/>&longs;it&aelig; portionis, O, ip&longs;i autem E cadenti per EL non occur&shy;<lb/>ret punctum P, cadens per Pq eo quod neutrum eorum <lb/>pertingat ad perpendicularem IK. <!-- REMOVE S-->Tenuioris ergo forni&shy;<pb xlink:href="007/01/134.jpg"/>cis partes &egrave; &longs;uis locis auul&longs;&aelig; ex eadem aperitione ruinam <lb/>facient, quod non contingit partibus cra&longs;&longs;ioris. </s>
            <s id="s.001241">quod &longs;a&shy;<lb/>n&egrave; fuerat de clarandum. </s>
          </p>
          <p type="main">
            <s id="s.001242">Qu&aelig;ritur adhuc, quare grauiores fornices in &longs;um&shy;<lb/>mis &aelig;dificijs non &longs;ine vitio fiant? </s>
          </p>
          <p type="main">
            <s id="s.001243">E&longs;to &aelig;dificium ABGH, cuius <expan abbr="vtrinq;">vtrinque</expan> muri ABCD, <lb/>EFGH, maiorum &longs;ummitates AD, EH, medi&aelig; murorum <lb/>partes KL, fornicum &longs;ummus quidem DIE, medius ver&ograve; <lb/><figure id="id.007.01.134.1.jpg" xlink:href="007/01/134/1.jpg"/><lb/>KML. Dico, magis cedere pul&shy;<lb/>&longs;os muros &longs;ummos circa DE, <lb/>quam in medio circa KL. <!-- KEEP S--></s>
            <s id="s.001244">Sunt <lb/>enim muri BA, GH ceu vectes <lb/>quidam, <expan abbr="quor&umacr;">quorum</expan> extremis par&shy;<lb/>tibus &agrave; fulcimentis BG remo&shy;<lb/>ti&longs;&longs;imis potentia admouetur, <lb/>hoc e&longs;t, ip&longs;ius fornicis DIE ad <lb/>DE incumbans repul&longs;io; lon&shy;<lb/>gior e&longs;t autem pars &agrave; <expan abbr="fulcim&emacr;-to">fulcimen&shy;<lb/>to</expan> ad potentiam AB, ip&longs;a BK. <lb/><!-- KEEP S--></s>
            <s id="s.001245">Data igitur paritate potentia&shy;<lb/>rum plus operabitur ea qu&aelig; in <lb/>D, illa qu&aelig; K. facilius ergo re&shy;<lb/>pellentur muri in DE qu&agrave;m in <lb/>KL. <!-- KEEP S--></s>
            <s id="s.001246">Alia quoque ratio intercedit, &longs;iquidem pondus muri <lb/>&longs;uperioris ADK, premens inferiorem murum KBC, cum <lb/>&longs;ua grauitate firmiorem, &amp; pul&longs;ionibus minus obnoxium <lb/>reddit. </s>
            <s id="s.001247">Difficilius enim propellitur id quod graue e&longs;t <expan abbr="qu&atilde;">quam</expan> <lb/>quod leue, vt nos qu&aelig;&longs;tione 10. demon&longs;trauimus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001248">QV&AElig;STIO XVII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001249"><emph type="italics"/>Qu&aelig;rit Ari&longs;toteles, Cur paruo exi&longs;tente cuneo magna &longs;cindantur <lb/>pondera &amp; corporum moles, validaque, fiat impre&longs;&longs;io?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001250">In parua re magnum negotium. </s>
            <s id="s.001251">Etenim qu&aelig;&longs;tio h&aelig;c <pb xlink:href="007/01/135.jpg"/>clari&longs;&longs;imorum virorum ingenia magnopere fatigauit. </s>
            <s id="s.001252">Ex <lb/>quibus Ari&longs;toteles inter veteres, Guid. <!-- REMOVE S-->Vbald. <!-- REMOVE S-->inter re&shy;<lb/>centiores ad vectis naturam &lpar;ne quid in Mechanicis ad <lb/>vectem non reduci putaretur&rpar; cuneum ip&longs;um trahere co&shy;<lb/><figure id="id.007.01.135.1.jpg" xlink:href="007/01/135/1.jpg"/><lb/>nati &longs;unt. </s>
            <s id="s.001253">Nos autem pro <lb/>veritate certantes, &longs;i in <lb/>horum &longs;ententiam vltr&ograve; <lb/>non tran&longs;ierimus, multa <lb/>venia digni &agrave; non iniquo <lb/>iudice exi&longs;timabimur. </s>
            <s id="s.001254">A&shy;<lb/>ri&longs;totelis mentem clar&egrave; <lb/>&amp; fus&egrave; explicat G. V&shy;<lb/>bald. <!-- REMOVE S-->in Mechan. vbi de <lb/>Cuneo peculiariter a&shy;<lb/>git. </s>
          </p>
          <p type="main">
            <s id="s.001255">E&longs;to igitur &longs;cindendum quippiam ABCD, Cuneus <lb/>EFG, cuius pars HFI &longs;ci&longs;&longs;ur&aelig; in&longs;erta HI, facta igitur vali&shy;<lb/>da percu&longs;&longs;ione in EG, fiet vt cum EG fuerit in NO, H &longs;it v&shy;<lb/>bi N, A vbi P, itemque I vbi O, D ver&ograve; vbi Q &amp; facta erit <lb/>&longs;ci&longs;&longs;io NSO, toti nempe cuneo EFG, &aelig;qualis. </s>
            <s id="s.001256">Vult igitur <lb/>Ari&longs;toteles, duos in cuneo vectes con&longs;iderari EF, GF, quo&shy;<lb/>rum alterius, nempe EF, fulcimentum &longs;it in H, pondus ve&shy;<lb/>ro in F; alterius autem, hoc e&longs;t, GF fulcimentum quidem <lb/>&longs;it in I, pondus ver&ograve; itidem &longs;it in F. <!-- KEEP S--></s>
            <s id="s.001257">His nequaquam con&shy;<lb/>&longs;entiens G. Vbald. <!-- REMOVE S-->aliam viam ingreditur. </s>
            <s id="s.001258">Ait enim EHF <lb/>vectes quidem e&longs;&longs;e, quorum commune fulcimentum F, <lb/>potentias ver&ograve; mouentes in EG. <!-- KEEP S--></s>
            <s id="s.001259">Pondera vtrinque inter <lb/>fulcimenta &amp; potentias, vbi HI, idemque; e&longs;&longs;e ac &longs;i EF, GF, <lb/>&longs;eor&longs;um &agrave; cuneo con&longs;iderati in puncto F, adinuicem fulti <lb/>atque di&longs;tracti pondera pellerent H in NP, I ver&ograve; in O, <lb/>Q.</s>
            <s id="s.001260"> Verum enimuer&ograve; quoniam cunei angulus non muta&shy;<lb/>tur, nec vertex ip&longs;e centri vllum pror&longs;us pr&aelig;bet v&longs;um, nec <lb/>eius latera vtrinque di&longs;tracta ad contrarias partes didu&shy;<pb xlink:href="007/01/136.jpg"/>cuntur, vectes in cuneo hoc pacto con&longs;iderare videtur &agrave; <lb/>veritate alienum. </s>
            <s id="s.001261">Ari&longs;totelis autem &longs;olutionem fal&longs;am e&longs;&shy;<lb/>&longs;e, clar&egrave; patet. </s>
            <s id="s.001262">quo pacto enim F pellet ex fulcimento H i&shy;<lb/>p&longs;am ligni partem OS, &amp; idem F ex fulcimento I pellet <lb/>oppo&longs;itam partem NS, &longs;i inuicem contendentes extrem&aelig; <lb/>vectium partes in F, altera alteri ne quicquam operentur, <lb/>e&longs;t impedimento? </s>
            <s id="s.001263">Et &longs;an&egrave; opinionis fal&longs;itas inde patet, <lb/>qu&ograve;d videamus materi&aelig; partes &longs;ci&longs;&longs;as, in ip&longs;o &longs;ci&longs;&longs;ionis a&shy;<lb/>ctu facta di&longs;tractione &agrave; cunei vertice nequaquam tangi. <lb/></s>
            <s id="s.001264">At eiu&longs;modi operationes per contactum fieri nulli e&longs;t i&shy;<lb/>gnotum. </s>
            <s id="s.001265">Solutio igitur i&longs;ta meo iudicio, tanto Philo&longs;o&shy;<lb/>pho pror&longs;us videtur indigna. </s>
          </p>
          <p type="main">
            <s id="s.001266">Porr&ograve; G. Vbald. <!-- REMOVE S-->ijs qu&aelig; de diuaricatis vectibus in <lb/>medium adduxerat non acquie&longs;cens alias qu&aelig;rit cau&longs;&longs;as, <lb/>cur cuneus minoris anguli validi&ugrave;s &longs;cindat. </s>
            <s id="s.001267">Idque; ex quo&shy;<lb/>dam lemmate demon&longs;trare conatur, figura autem eius ita <lb/>fer&egrave; &longs;e habet. </s>
          </p>
          <figure id="id.007.01.136.1.jpg" xlink:href="007/01/136/1.jpg"/>
          <p type="main">
            <s id="s.001268">E&longs;to cuneus ABC, <lb/>item alius DEF. <expan abbr="Dem&omacr;-&longs;trauit">Demon&shy;<lb/>&longs;trauit</expan> igitur ex a&longs;&longs;um&shy;<lb/>pto, quo acutior fuerit <lb/>angulus BIM, eo facilius <lb/>pondera moueri, &amp; ideo <lb/>facilius ceu vecte AB <lb/>moueri pondus I qu&agrave;m <lb/>vecte DE pondus Q.</s>
            <s id="s.001269"> In&shy;<lb/>genios&egrave; quidem. </s>
            <s id="s.001270">At ma&shy;<lb/>gnam h&aelig;c apud me ha&shy;<lb/>bent difficultatem. </s>
            <s id="s.001271">Si e&shy;<lb/>nim ita &longs;e habet AB, ad BI, vt DE, ad EQ &lpar;ip&longs;&aelig; enim DE, <lb/>EQ &longs;upponuntur &aelig;quales&rpar; ergo eadem &aelig;quali&longs;ue poten&shy;<lb/>tia &aelig;qualiter mouebit pondera I &amp; Q.</s>
            <s id="s.001272"> quod ip&longs;i eiu&longs;dem <lb/>demon&longs;trationi pror&longs;us concludit contrarium. </s>
            <s id="s.001273">Nec meo <pb xlink:href="007/01/137.jpg"/>quidem iudicio id &longs;equi videtur, propterea quod ex Pap&shy;<lb/>po ea qu&aelig; in planis inclinatis mouentur, redigantur ad li&shy;<lb/>bram. </s>
            <s id="s.001274">Ratio enim valde e&longs;t diuer&longs;a, &longs;iquidem pondera <lb/>qu&aelig; in planis inclinatis mouentur, certa habent fulci&shy;<lb/>menta &amp; determinatas tum brachiorum tum ponderum <lb/>proportiones, qu&aelig; omnia in cuneo, nec quidem mente <lb/>concipi po&longs;&longs;e, clar&egrave; patet. </s>
          </p>
          <p type="main">
            <s id="s.001275">His igitur difficultatibus con&longs;ideratis, Nos cunei <lb/>vim, ad alia e&longs;&longs;e principia referendam pro comperto ha&shy;<lb/>bemus. </s>
            <s id="s.001276">Ordimur igitur hoc pacto. </s>
            <s id="s.001277">Cuneo quidem res di&shy;<lb/>uidi certum e&longs;t. </s>
            <s id="s.001278">C&aelig;ter&ugrave;m qu&aelig; natura diuidere apta &longs;unt, <lb/>tria &longs;unt, punctum, linea, &longs;uperficies, Puncto enim linea, <lb/>line&acirc; &longs;uperficies, &longs;uperficie autem corpus ip&longs;um diuidi&shy;<lb/>tur. </s>
            <s id="s.001279">qu&aelig; omnia &agrave; Mathematico ab&longs;que materia con&longs;ide&shy;<lb/>rantur. </s>
            <s id="s.001280">De diui&longs;ione autem qu&aelig; fit ex puncto, nihil agit <lb/>Mechanicus, qui corporibus quidem vtitur, ad cuius na&shy;<lb/>turam non trahitur punctum, cuius partes &longs;unt null&aelig;. </s>
            <s id="s.001281">At <lb/>non lineis &amp; &longs;uperficiebus mod&ograve; corpora diuiduntur, &longs;ed <lb/>etiam corporibus, quod verum e&longs;t, at ea corpora ad linea&shy;<lb/>rum &amp; &longs;uperficierum naturam quodammodo aptari faci&shy;<lb/>l&egrave; docebimus. </s>
            <s id="s.001282">Dicimus igitur, duplicem e&longs;&longs;e Cuneorum <lb/>&longs;peciem, linearem vnam, &longs;uperficialem alteram. </s>
            <s id="s.001283">linearem <lb/>appello, qu&aelig; ad line&aelig; naturam magnopere accedit. </s>
            <s id="s.001284">Tales <lb/>&longs;unt orbiculares ill&aelig; cu&longs;pides, quibus ad perforandum v&shy;<lb/>timur, &amp; ideo vernacul&egrave; Pantirolos vocamus. </s>
            <s id="s.001285">Acus item <lb/>&longs;utorij, &amp; c&aelig;tera qu&aelig; non &longs;ecus ac linea in punctum de&longs;i&shy;<lb/>nunt, &amp; imaginariam quandam lineam ceu axem in eo <lb/>puncto de&longs;inentem continent. </s>
            <s id="s.001286">Ad lineam quoque refe&shy;<lb/>runtur laterat&aelig; cu&longs;pides oblong&aelig;, &amp; &longs;ubtiles ceu &longs;ubul&aelig;, <lb/>claui, en&longs;es, pugiones, &amp; his &longs;imilia, qu&aelig; cum adacta vali&shy;<lb/>dam faciant partium &longs;eparationem ad cunei naturam <expan abbr="n&omacr;">non</expan> <lb/>referre magn&aelig; videretur dementi&aelig;. </s>
            <s id="s.001287">Et tunc quanto ma&shy;<lb/>gis corpora h&aelig;c ad linearem naturam accedunt, eo ma&shy;<pb xlink:href="007/01/138.jpg"/>gis penetrant. </s>
            <s id="s.001288">Sed &amp; hoc idem in rebus non ab arte, &longs;ed <lb/>ab ip&longs;a natura productis facile e&longs;t cogno&longs;cere. </s>
            <s id="s.001289">Quis enim <lb/>non experitur, qu&agrave;m valid&egrave; culex, infirmi&longs;&longs;imum animal, <lb/>&amp; ea paruitate qua e&longs;t, hominum &amp; c&aelig;terorum <expan abbr="animali&umacr;">animalium</expan>, <lb/>cutes aculeata probo&longs;cide penetret? </s>
            <s id="s.001290">Id vtique non alia de <lb/>cau&longs;&longs;a fit, quod ad imaginari&aelig; line&aelig; &longs;ubtilitatem quam, <lb/>proxim&egrave; accedat. </s>
            <s id="s.001291">Ve&longs;p&aelig; quoque, Apes, Scorpiones a&shy;<lb/>culeis i&longs;tis ceu linearibus cuneis vtuntur. </s>
            <s id="s.001292">Nec refert, vt <lb/>diximus, vtrum laterati &longs;int, ceu &longs;ubul&aelig;, &amp; claui, vel ro&shy;<lb/>tundi &amp; vtrum plura paucioraue latera habeant, dummo&shy;<lb/>do in punctum &amp; aculeatam aciem de&longs;inant. </s>
            <s id="s.001293">Altera por&shy;<lb/>ro cuneorum &longs;pecies &longs;uperficiei naturam &longs;apit, acie &longs;iqui&shy;<lb/>dem in lineam de&longs;init, qu&aelig; &longs;uperficiei e&longs;t terminus, <expan abbr="qu&atilde;">quam</expan>obrem huc ea omnia referuntur, qu&aelig; acie ips&acirc; &longs;cindunt, <lb/>ceu &longs;unt cunei propri&egrave; dicti, de quibus hoc loco e&longs;t &longs;er&shy;<lb/>mo, cultra, en&longs;es, a&longs;ci&aelig;, &longs;ecures, &longs;calpra lata, &amp; c&aelig;tera e&shy;<lb/>iu&longs;modi, quibus corpora acie &longs;cinduntur. </s>
            <s id="s.001294">Quidam his ad&shy;<lb/>dunt &longs;erras, quibus haud pror&longs;us a&longs;&longs;entimur. </s>
            <s id="s.001295">Etenim alia <lb/>ratione diuidunt, &longs;icut &amp; lim&aelig; &longs;olent, deterendo enim, <expan abbr="n&omacr;">non</expan> <lb/>&longs;cindendo ferri, ligni, &amp; marmorum duritiem diuidunt &amp; <lb/>domant. </s>
            <s id="s.001296">His igitur <expan abbr="c&omacr;&longs;ideratis">con&longs;ideratis</expan>, &longs;i daretur ex materia qua&shy;<lb/>piam in frangibili cuneus, qui maxim&egrave; ad &longs;uperficiei natu&shy;<lb/>ram accederet, vel paruo labore tenaci&longs;&longs;ima ligna validi&longs;&shy;<lb/>&longs;im&egrave; &longs;cinderet, &amp; ideo optim&egrave; res gladijs illis diuiditur, <lb/>qui magis ad &longs;uperficiei naturam accedunt. </s>
            <s id="s.001297">Ex quibus o&shy;<lb/>mnibus, n&icirc; fallimur, clar&egrave; patet, cur acutiores angulo cu&shy;<lb/>nei obtu&longs;ioribus facilius &longs;cindant, qu&aelig; quidem ratio lon&shy;<lb/>g&egrave; ab ea di&longs;tat, ex qua c&aelig;teri fer&egrave; omnes Cuneum ad ve&shy;<lb/>ctis naturam referre hactenus contenderunt. </s>
          </p>
          <p type="main">
            <s id="s.001298">C&aelig;ter&ugrave;m vtramque eorum quos diximus, <expan abbr="cuneor&umacr;">cuneorum</expan> <lb/>&longs;peciem &longs;olerti&longs;&longs;ima cognouit Natura, &amp; ideo quoniam <lb/>res vel contu&longs;ione vel perforatione, vel &longs;ecatione confi&shy;<lb/>ciuntur, triplicem dentium qualitatem dentatis animali-<pb xlink:href="007/01/139.jpg"/><figure id="id.007.01.139.1.jpg" xlink:href="007/01/139/1.jpg"/><lb/>bus dedit, Molares, <lb/>qui &amp; Maxillares ap&shy;<lb/>pellantur, quibus <lb/>cibus contunditur, <lb/>Canini, quibus fit <lb/>perforatio, Anterio&shy;<lb/>res, quibus cibus <lb/>&longs;cinditur, quos ideo <lb/><foreign lang="greek">temnikou\s</foreign>, id e&longs;t, &longs;ecan&shy;<lb/>tes appellant Graeci. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001299">Molares KK, <lb/>Canini L, L, Temni&shy;<lb/>ci &longs;eu &longs;ecantes M. <!-- KEEP S--></s>
            <s id="s.001300">Cuneus orbicularis lineari&longs;queue AB, in <lb/>quo axis linea e&longs;t, ad cuius naturam accedit AB cuneus <lb/>&longs;uperficialis CD, accedens ad &longs;uperficiei naturam, quam <lb/>vitro imaginamur EFGD, in aciem cunei de&longs;inentem, <lb/>GD, Lateratus lineari&longs;que cuneus, clauus HI. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001301">Cunei autem omnes dupliciter &longs;unt efficaces, vel e&shy;<lb/>nim malleo, vt in ijs fit, quibus l&igrave;gna &longs;cinduntur &amp; &longs;calpris <lb/>fieri &longs;olet, adiguntur, vel impul&longs;u &amp; pre&longs;&longs;ione, vt in gla&shy;<lb/>dijs fit, pugionibus, c&aelig;latorum &longs;calpris, &longs;ubulis, &amp; c&aelig;teris <lb/>eiu&longs;modi. </s>
            <s id="s.001302">Quidam etiam &longs;unt, qui licet mallei ictu non <lb/>adigantur, malleum coniunctum habent, ceu &longs;unt &longs;ecu&shy;<lb/>res, ligones, A&longs;ci&aelig;, &amp; his &longs;imilia, qu&aelig; ex percu&longs;&longs;ione &longs;e&shy;<lb/>metip&longs;a &longs;cindendis rebus in&longs;erunt &amp; valid&egrave; penetrant. <lb/></s>
            <s id="s.001303">De vi autem &amp; efficacia ictus &longs;eu percu&longs;&longs;ionis hic &longs;uper&shy;<lb/>&longs;edemus aliquid, ea de re, in &longs;equenti qu&aelig;&longs;tione verba fa&shy;<lb/>cturi. </s>
          </p>
          <p type="main">
            <s id="s.001304">Multa h&icirc;c addere potui&longs;&longs;emus ad Cochleam &longs;pe&shy;<lb/>ctantia, quippe qu&ograve;d Cochlea cuneus &longs;it Cylindro inuo&shy;<lb/>lutus, qui quidem ad mallei, &longs;ed vectis virtute &longs;ibi adiun&shy;<lb/>ct&acirc;, validi&longs;&longs;im&egrave; operatur, &amp; &longs;excentis in&longs;eruit v&longs;ibus. </s>
            <s id="s.001305">Ve&shy;<lb/>runtamen c&ugrave;m de hac &longs;pecie egregi&egrave; di&longs;&longs;erat G. Vbaldus, <pb xlink:href="007/01/140.jpg"/>con&longs;ult&ograve; hanc di&longs;putationem omittimus; idque hac quo&shy;<lb/>que de cau&longs;&longs;a, quod nihil de cochlea, ac &longs;i eam non noui&longs;&shy;<lb/>&longs;et, locutus &longs;it Ari&longs;toteles. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001306">Po&longs;&longs;umus autem in actu &longs;ci&longs;&longs;ionis, qu&aelig; cuneo fit, a&shy;<lb/>li&acirc; tamen ratione vectem con&longs;iderare, nempe non in cu&shy;<lb/>neo quidem, &longs;ed in ip&longs;a re qu&aelig; &longs;cinditur. </s>
          </p>
          <figure id="id.007.01.140.1.jpg" xlink:href="007/01/140/1.jpg"/>
          <p type="main">
            <s id="s.001307">E&longs;to enim quip&shy;<lb/>piam &longs;ci&longs;&longs;ile ABCD, <lb/>cui alteri extremita&shy;<lb/>tum, puta BD, cuneus <lb/>adigatur EFG, <expan abbr="fiatq;">fiatque</expan> <lb/>&longs;ci&longs;&longs;io per longitudi&shy;<lb/>nem &longs;ecundum <expan abbr="line&atilde;">lineam</expan> <lb/>EH. facta igitur ex <lb/>cunei ingre&longs;&longs;u <expan abbr="parti&umacr;">partium</expan> &longs;eparatione B, expelletur in I, D ve&shy;<lb/>r&ograve; in K. fient igitur materi&aelig; &longs;ci&longs;&longs;&aelig; partes AIBH, CKDH, <lb/>ceu duo vectes, quorum hinc inde in corpore ip&longs;o fulci&shy;<lb/>menta L, M potenti&aelig; vtrinque dilatantes BD, pondus ve&shy;<lb/>r&ograve; materi&aelig; re&longs;i&longs;tentia, in &longs;eparationis loco vbi N. <!-- KEEP S--></s>
            <s id="s.001308">Duca&shy;<lb/>tur NL, quanto itaque BN maiorem habebit proportio&shy;<lb/>nem ad LN, eo facili&ugrave;s re&longs;i&longs;tentia qu&aelig; in N, &longs;uperabitur. <lb/></s>
            <s id="s.001309">Mutatur <expan abbr="aut&emacr;">autem</expan> a&longs;&longs;idu&egrave; in ip&longs;a &longs;ci&longs;&longs;ione fulcimentum, &amp; <expan abbr="c&umacr;">cum</expan> <lb/>fulcimento ip&longs;a proportio. </s>
            <s id="s.001310">Pertingente enim &longs;ci&longs;&longs;ione in <lb/>O, <expan abbr="fulcim&emacr;tum">fulcimentum</expan> fit in P. quo ca&longs;u &longs;ci&longs;&longs;ura e&longs;t facilior, quip&shy;<lb/>pe quod maiorem habeat proportionem BO ad OP, <expan abbr="qu&atilde;">quam</expan> <lb/>BN ad NL. </s>
            <s id="s.001311">Hoc autem experiuntur materiarij, qui primis <lb/>ictibus, &longs;ecuricul&acirc; nondum prob&egrave; adact&acirc;, &amp; nondum fa&shy;<lb/>ct&acirc; notabili &longs;ci&longs;&longs;ione difficultatem &longs;entiunt, mox <expan abbr="factai&atilde;">facta iam</expan> <lb/>&longs;eparatione facillima paullatim fit materi&aelig; totius &longs;epara&shy;<lb/>tio. </s>
            <s id="s.001312">Hoc idem &amp; nos ab&longs;que cunei v&longs;u experimur, cum ba&shy;<lb/>culum aut quippiam tale manibus diductis &longs;cindimus. </s>
            <s id="s.001313">&agrave; <lb/>principio enim difficultatem &longs;entimus, deinde ex ea <expan abbr="qu&atilde;">quam</expan> <lb/>diximus proportione &longs;ci&longs;&longs;io ip&longs;a fit apprime facilis. </s>
            <s id="s.001314">Vti-<pb xlink:href="007/01/141.jpg"/>mur etiam vecte cuneato ad &longs;cindendum &amp; aperiendum: <lb/>adacto enim &longs;ci&longs;&longs;ur&aelig; cuneo, idqueue manu malleoue, tum <lb/>ab altera extremitate pre&longs;&longs;o, valida fit ex vectis vi <expan abbr="c&omacr;tinui">continui</expan> <lb/><figure id="id.007.01.141.1.jpg" xlink:href="007/01/141/1.jpg"/><lb/>corporis &longs;eparatio. </s>
            <s id="s.001315">Ma&shy;<lb/>teria &longs;ci&longs;&longs;ilis AB <expan abbr="&longs;calpr&umacr;">&longs;calprum</expan> <lb/>ceu vectis cuneatus CD, <lb/>cuius fulcimentum, E, <lb/>pondus ver&ograve; vbi C, po&shy;<lb/>tentia vbi D, quo ca&longs;u <lb/>quo maior e&longs;t proportio <lb/>DE ad EC, eo e&longs;t ip&longs;a &longs;ci&longs;&longs;io leuior &amp; facilior. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001316">QVAESTIO XVIII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001317"><emph type="italics"/>Qu&aelig;rit hic Ari&longs;toteles, Cur per Trochleas ab exigua potentia in&shy;<lb/>gentia moueantur pondera?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001318">De Trochlea Pappus, &amp; veteres: inter recentiores e&shy;<lb/>gregi&egrave; admodum, vt omnia examinauit in Mechani&shy;<lb/>cis G. Vbaldus. <!-- KEEP S--></s>
            <s id="s.001319">Nos tamen interim po&longs;t clari&longs;&longs;imos illos <lb/>viros aliquid quod nouitatem &amp; &longs;ubtilitatem &longs;apiat, de <lb/>no&longs;tro penu promemus. </s>
            <s id="s.001320">Et &longs;an&egrave; inuentis quidem addere <lb/>res e&longs;t facilis, at quod inuentis addas inuenire haud adeo <lb/>facile. </s>
            <s id="s.001321">Sed nos primum Philo&longs;ophi ip&longs;ius dicta ad <expan abbr="trutin&atilde;">trutinam</expan> <lb/>reuocemus. </s>
            <s id="s.001322">Ita autem qu&aelig;&longs;tionem proponit; Cur &longs;i qui&longs;&shy;<lb/>piam Trochleas componens duas, in &longs;ignis duobus, ad &longs;e <lb/>inuicem iunctis contrario ad Trochleas modo circulo fu&shy;<lb/>nem circumduxerit, cuius alterum quidem caput tigno&shy;<lb/>rum appendatur alteri, alterum ver&ograve; Trochleis &longs;it <expan abbr="innix&umacr;">innixum</expan> <lb/>&amp; &agrave; funis initio trahere c&oelig;perit, magna trahit pondera, li&shy;<lb/>cet imbecillium fuerit virium? </s>
          </p>
          <p type="main">
            <s id="s.001323">Ob&longs;eueri&longs;&longs;ima expo&longs;itio, &amp; n&icirc; res e&longs;&longs;et vulg&ograve; per &longs;e <lb/>nota, dequeue ea Vitruuius &amp; Mechanici non egi&longs;&longs;ent, diffi&shy;<lb/>cile vtique e&longs;&longs;et ex eius verbis &longs;en&longs;um a&longs;&longs;equi. </s>
          </p>
          <pb xlink:href="007/01/142.jpg"/>
          <p type="main">
            <s id="s.001324">Tigna &longs;an&egrave; voca&longs;&longs;e videtur ea ligna, qu&aelig; &agrave; Vitruuio <lb/>Rechami dicuntur, in quibus nempe ip&longs;i in&longs;eruntur orbi&shy;<lb/>culi. </s>
            <s id="s.001325">Et&longs;i de tignis eiu&longs;modi aliud quippiam &longs;entire videa&shy;<lb/>tur Picolomineus. <!-- KEEP S--></s>
            <s id="s.001326">Gr&aelig;ca lectio pro tignis habet <foreign lang="greek">cu/la</foreign>, id <lb/>e&longs;t, ligna; item vbi Leoniceni ver&longs;io legit, ad &longs;e inuicem <lb/>iunctis, textus habet <foreign lang="greek">sumbai/nousin e&lpar;autoi=s e&rpar;nanti/ws</foreign>, hoc e&longs;t, in&shy;<lb/>uicem ex oppo&longs;ito concurrunt. </s>
            <s id="s.001327">Cert&egrave; locum totum ita <lb/>redderem: Cur &longs;i quis duas Trochleas fecerit, in duobus <lb/>lignis &longs;ibi ex oppo&longs;ito concurrentibus, ei&longs;queue Trochleis <lb/>circumpo&longs;uerit funem, cuius alterum caput alteri ligno&shy;<lb/>rum &longs;it annexum, alterum ver&ograve; Trochleis coh&aelig;reat, vel <lb/>apponatur. </s>
            <s id="s.001328">Si quis alterum funis principium trahat, ma&shy;<lb/>gna trahat pondera, et&longs;i trahens potentia &longs;it exigua? </s>
            <s id="s.001329">Nos <lb/>verbis figuram, &amp; figur&acirc; verba ip&longs;a elucidabimus. </s>
          </p>
          <figure id="id.007.01.142.1.jpg" xlink:href="007/01/142/1.jpg"/>
          <p type="main">
            <s id="s.001330">Sint duo ligna ex oppo&longs;ito concurrentia, <lb/>in quibus Trochle&aelig;, hoc e&longs;t, orbiculi AB, fu&shy;<lb/>nis ductarius DABC, cuius alterum caput re&shy;<lb/>ligatum e&longs;t ligno trochle&aelig; A, vbi e&longs;t C. <!-- KEEP S--></s>
            <s id="s.001331">Tro&shy;<lb/>chlea A loco &longs;tabili commendata, vbi E. <!-- KEEP S--></s>
            <s id="s.001332">Pon&shy;<lb/>dus alteri ligno Trochle&aelig; appen&longs;um F. <!-- KEEP S--></s>
            <s id="s.001333">Tra&shy;<lb/>cto itaque fune DABC, eleuatur &amp; trahitur <lb/>pondus F. <!-- KEEP S--></s>
            <s id="s.001334">Ex quibus clar&egrave; patet, <expan abbr="Philo&longs;oph&umacr;">Philo&longs;ophum</expan> <lb/>propo&longs;ui&longs;&longs;e Trochleam duobus tantum orbi&shy;<lb/>culis munitam, quod vtique &longs;atis erat ad ex&shy;<lb/>plicationem. </s>
            <s id="s.001335">Inquit autem, facili&ugrave;s vecte <expan abbr="qu&atilde;">quam</expan> <lb/>manu pondus moueri. </s>
            <s id="s.001336">Trochleam vero &lpar;id <lb/>e&longs;t, orbiculum; ita enim e&longs;t intelligendum&rpar; e&longs;&shy;<lb/>&longs;e vectem, aut vectis virtute operari. </s>
            <s id="s.001337">Ita autem <lb/>videtur argumentari. </s>
            <s id="s.001338">Si vnic&acirc; Trochle&acirc; plus trahitur <lb/>qu&agrave;m manu, multo faci ius &amp; velocius id fiet duobus, <lb/>quibus plus, vt ip&longs;e ait, qu&agrave;m in duplici velocitate pon&shy;<lb/>dus leuabitur. </s>
            <s id="s.001339">Summa dictorum e&longs;t, ex multiplicatione <lb/>orbiculorum pondus ip&longs;um imminui, &amp; minori difficul-<pb xlink:href="007/01/143.jpg"/>tate leuari, quod &longs;an&egrave; verum e&longs;t. </s>
            <s id="s.001340">Nos tamen nonnulla <expan abbr="c&omacr;-&longs;iderabimus">con&shy;<lb/>&longs;iderabimus</expan>. </s>
            <s id="s.001341">quod ait, vecte facilius moueri pondera <lb/>quam manu, &longs;emper non e&longs;t verum. </s>
            <s id="s.001342">Si enim vectis pars <lb/>qu&aelig; &agrave; fulcimento ad manum breuior fuerit ill&acirc;, qu&aelig; &agrave; <lb/>fulcimento ad pondus difficilius vecte pondus mouebi&shy;<lb/>tur quam manu. </s>
            <s id="s.001343">Idem quoque accidet, &longs;i eo modo vecte <lb/>vtamur, quem ob&longs;eruat Guidus Vbald. <!-- REMOVE S-->Tract. </s>
            <s id="s.001344">de Vecte <lb/>prop. 3. Po&longs;ita nempe inter fulcimentum &amp; pondus &longs;u&longs;ti&shy;<lb/>nente potenti&acirc;. </s>
            <s id="s.001345">Pr&aelig;terea quod a&longs;&longs;eruit Ari&longs;toteles, Tro&shy;<lb/>chleas ad vectem reduci, verum quidem e&longs;t, &longs;ed aptius di&shy;<lb/>xi&longs;&longs;et ad libram, etenim vectis vtcunque &agrave; fulcimento di&shy;<lb/>uiditur. </s>
            <s id="s.001346">Libra ver&ograve; quod &amp; orbiculis ex centro accidit, <lb/>&longs;emper bifariam. </s>
            <s id="s.001347">Ad h&aelig;c videtur ille ad orbiculorum <lb/>multiplicitatem Trochlearum vim referre. </s>
            <s id="s.001348">Si enim, ait, <lb/>vnic&acirc; Trochle&acirc; pondus facile trahitur, id multo validius <lb/>pluribus fiet. </s>
            <s id="s.001349">Veruntamen non ab&longs;olut&egrave; ex orbiculorum <lb/>multiplicatione id fieri ita o&longs;tendemus. </s>
          </p>
          <figure id="id.007.01.143.1.jpg" xlink:href="007/01/143/1.jpg"/>
          <p type="main">
            <s id="s.001350">Sint du&aelig; op&shy;<lb/>po&longs;it&aelig; lineae rectae, <lb/>vtpote trabes AB, <lb/>CD, <expan abbr="inuic&emacr;">inuicem</expan> &aelig;qui&shy;<lb/>di&longs;tantes &amp; ip&longs;&aelig; <lb/>&longs;tabiles: &longs;uperiori <lb/>tres appendantur <lb/>orbiculi ex <expan abbr="p&umacr;ctis">punctis</expan> <lb/>E, F, G, <expan abbr="n&emacr;pe">nempe</expan> ML, <lb/>PQ, TV. inferiori <lb/><expan abbr="aut&emacr;">autem</expan> duobus pun&shy;<lb/>ctis IH, nempe <lb/>NO, RS. </s>
            <s id="s.001351">Erunt i&shy;<lb/>gitur in vniuer&longs;um <lb/>quinque, indatur per eos funis ductarius KLMNOP <lb/>QRSTVX, ex cuius extremitate pendeat pondus X, <pb xlink:href="007/01/144.jpg"/>Trahatur funis in K. <!-- KEEP S--></s>
            <s id="s.001352">Dico ex multiplicatione <expan abbr="orbiculor&umacr;">orbiculorum</expan>, <lb/>trahenti pondus nequaquam minui. </s>
            <s id="s.001353">Sint autem orbicu&shy;<lb/>lorum diametri, LM, NO, PQ, RS, TV, applicetur poten&shy;<lb/>t&icirc;a in S. <!-- KEEP S--></s>
            <s id="s.001354">Erit igitur ad hoc vt &longs;u&longs;tineat &aelig;qualis ponderi X, <lb/>orbiculi enim TV &longs;emidiametri &longs;unt &aelig;quales. </s>
            <s id="s.001355">Transfe&shy;<lb/>ratur <expan abbr="pot&emacr;tia">potentia</expan> in q, &amp; ita deinceps donec perueniatur in K, <lb/>vbi funis ip&longs;ius e&longs;t principium, Idem e&longs;t igitur &longs;eruata &longs;em&shy;<lb/>per &longs;emidiametrorum &aelig;qualitate ac &longs;i potentia qu&aelig; e&longs;t in <lb/>K, applicata intelligatur in T vel in V. vbicunque enim <lb/>collocetur, ponderi erit &aelig;qualis. </s>
            <s id="s.001356">Nihil igitur rebus ita <lb/>di&longs;po&longs;itis, orbiculorum multiplicatio ad facilitatem ope&shy;<lb/>ratur. </s>
            <s id="s.001357">Alia itaque ratio qu&aelig;renda e&longs;t, quam non &longs;atis ex&shy;<lb/>plica&longs;&longs;e videtur Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.001358">Probabimus autem, nullam <lb/>ex &longs;uperioribus orbiculis fieri ponderum imminutionem, <lb/>&longs;ed totam vim in inferioribus con&longs;i&longs;tere. </s>
            <s id="s.001359">At nos interim <lb/>quippiam quod ad rem faciat, proponamus. </s>
          </p>
          <figure id="id.007.01.144.1.jpg" xlink:href="007/01/144/1.jpg"/>
          <p type="main">
            <s id="s.001360">E&longs;to punctum A, cui rect&aelig; ap&shy;<lb/>pendantur line&aelig; BAC, diui&longs;&aelig; qui&shy;<lb/>dem in A, &longs;it autem line&aelig; BA caput <lb/>B, ip&longs;ius ver&ograve; CA caput C. <!-- KEEP S--></s>
            <s id="s.001361">Mod&ograve; <lb/>intelligantur vnit&aelig; in A, &longs;itqueue vni&shy;<lb/>ca linea &agrave; puncto A ceu funiculus <lb/>dependens BAC; Appendatur capi&shy;<lb/>ti B pondus B. <!-- KEEP S--></s>
            <s id="s.001362">Capiti vero C, <expan abbr="p&omacr;dus">pondus</expan> <lb/>C, inter &longs;e &aelig;qualia. </s>
            <s id="s.001363">Potentia igitur <lb/>in A, duo &longs;u&longs;tinebit pondera BC. <lb/><!-- KEEP S--></s>
            <s id="s.001364">Pondera ver&ograve; ex &aelig;qualitate &aelig;que&shy;<lb/>ponderabunt. </s>
            <s id="s.001365">Quod &longs;i B potentia <lb/>dicatur &longs;u&longs;tinens pondus C, aut C <lb/>potentia &longs;u&longs;tinens pondus D, vel <lb/>du&aelig; potenti&aelig; inter &longs;e &aelig;quales, nihil <lb/>refert. </s>
            <s id="s.001366">Vtcunque enim id &longs;it, fiet &aelig;quilibrium. </s>
            <s id="s.001367">Habemus <lb/>igitur ex i&longs;tis ad &longs;u&longs;tinendum pondus ex &longs;uperiori parte <pb xlink:href="007/01/145.jpg"/>appen&longs;um potentiam requiri ip&longs;i ponderi &aelig;qualem. </s>
            <s id="s.001368">Ani&shy;<lb/>mo po&longs;th&aelig;c concipiatur alia recta linea DEF, cuius inte&shy;<lb/>gra longitudo &longs;i extenderetur, e&longs;&longs;et DE, EF. <!-- KEEP S--></s>
            <s id="s.001369">Appendatur <lb/>in E pondus E &aelig;quale alteri ponderum B vel, C, &longs;int autem <lb/>du&aelig; potenti&aelig; pondus E &longs;u&longs;tinentes D, F. <!-- KEEP S--></s>
            <s id="s.001370">Vtraque igitur <lb/>dimidium &longs;u&longs;tinebit ponderis E, &longs;ed potentia qu&aelig; &longs;u&longs;ti&shy;<lb/>nebat pondus B, in C erat ip&longs;i B &aelig;qualis, vbi appen&longs;io pon&shy;<lb/>deris erat in &longs;uperiori parte in A, h&icirc;c autem, vbi appen&longs;io <lb/>e&longs;t in parte in feriori, vtraque potentia dimidium &longs;u&longs;tinet <lb/>appen&longs;i ponderis. </s>
            <s id="s.001371">Videmus igitur illam appen&longs;ionem <lb/>quidem pondus nullatenus imminuere, hanc ver&ograve; pon&shy;<lb/>dus ip&longs;um, bifariam diui&longs;um, &longs;u&longs;tinentibus potentijs im&shy;<lb/>partiri. </s>
            <s id="s.001372">H&aelig;c in lineis, Mathematic&acirc; v&longs;i ab&longs;tractione, con&shy;<lb/>&longs;iderauimus, nunc ver&ograve; eadem mechanic&egrave; perpenda&shy;<lb/>mus. </s>
          </p>
          <figure id="id.007.01.145.1.jpg" xlink:href="007/01/145/1.jpg"/>
          <p type="main">
            <s id="s.001373">Sit igitur <lb/>punctum A, vt <lb/>in &longs;equenti figu&shy;<lb/>ra clauus paxil&shy;<lb/>lu&longs;ue, cui appen&shy;<lb/>&longs;us funiculus <lb/>BAC, &amp; funicu&shy;<lb/>li capitibus pon&shy;<lb/>dera BC, &longs;it quo&shy;<lb/>que anulus D, <lb/>per quem tra&igrave;e&shy;<lb/>ctus funiculus <lb/>EDF. <!-- KEEP S--></s>
            <s id="s.001374">Anulo au&shy;<lb/>tem <expan abbr="c&omacr;iunctum">coniunctum</expan> <lb/>pondus G. <!-- KEEP S--></s>
            <s id="s.001375">His igitur ita con&longs;titutis, eadem demon&longs;tra&shy;<lb/>buntur qu&aelig; &longs;uperius, nempe oportere vt fiat &aelig;quilibrium <lb/>B, C, e&longs;&longs;e &aelig;qualia, tum potentias, qu&aelig; &longs;unt in EF pondus <lb/>G inter eas diui&longs;um &longs;u&longs;tinere. </s>
            <s id="s.001376">Porr&ograve; volentes Mechanici <pb xlink:href="007/01/146.jpg"/>funiculos circa paxillum, &amp; anulum ad attollenda &amp; de&shy;<lb/>primenda pondera mouere incommod&egrave; illis vtique &longs;uc&shy;<lb/>cedebat, clauo &amp; anulo motum difficilem facientibus. <lb/></s>
            <s id="s.001377">Quamobrem vt difficultati occurrerent, ad locum claui <lb/>clauo ip&longs;i orbiculum circumpo&longs;uerunt, &amp; anuli itidem <lb/>loco orbiculum aptauerunt. </s>
            <s id="s.001378">H&aelig;c autem agentes rei i&shy;<lb/>p&longs;ius naturam non mutauerunt, &longs;ed &longs;ibi, vt diximus, ex or&shy;<lb/>biculis maximam commoditatem <expan abbr="atq;">atque</expan> facilitatem com&shy;<lb/>par&acirc;runt. </s>
          </p>
          <p type="main">
            <s id="s.001379">Ex his princip&icirc;js tota Trochlearum ratio pendet, <lb/>qu&aelig; tamen alia quoque con&longs;ideratione in idem tenden&shy;<lb/>te examinari pote&longs;t, quod quidem fecere veteres, &amp; ip&longs;e, <lb/>qui veteres optim&egrave; imitatus e&longs;t, Guid. <!-- KEEP S--></s>
            <s id="s.001380">Vbaldus. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001381">Vidimus vtique nos, &agrave; potentia qu&aelig; e&longs;t in B, pondus <lb/>par &longs;u&longs;tineri in C, Potentiam autem qu&aelig; e&longs;t in E <expan abbr="dimidi&umacr;">dimidium</expan> <lb/>&longs;u&longs;tinere ponderis quod e&longs;t in G. <!-- KEEP S--></s>
            <s id="s.001382">Nos igitur ij&longs;dem in&longs;i&shy;<lb/>&longs;tentes adiecta libra, vecteue, bifariam diui&longs;o rem ip&longs;am <lb/>ex &longs;ubiecto diagrammate lucidiorem faciemus. </s>
          </p>
          <p type="main">
            <s id="s.001383">E&longs;to linea qu&aelig;dam &longs;tabilis ceu trabs horizonti &aelig;&shy;<lb/>quedi&longs;tans AB, cui in A funiculus annectatur AC, cuius <lb/>extremum C vecti cuidam alligetur CD, in medio diui&longs;o <lb/>vbi E, tum alteri vectis eiu&longs;dem extremitati D, funiculus <lb/>nectatur DG, &amp; &agrave; puncto E pondus appendatur F. puta li&shy;<lb/>brarum mille, Tum puncto G in medio vectis HI, funis re&shy;<lb/>ligetur DG, &amp; ex altero vectis extremo alligato fune HK <lb/>commendetur loco &longs;tabili in K, &amp; ab alio capite vectis vbi <lb/>I ad medium vectis MN, vbi L, funis annectatur lL, tum <lb/>ex vectis capite M, funis commendetur MO, loco &longs;tabili <lb/>in O, &amp; alteri capiti N, funis, NP, qui alligetur medio ve&shy;<lb/>cti QR in P, &amp; ex Q, funis QS. </s>
            <s id="s.001384">Commendetur loco &longs;tabili <lb/>in S, &amp; alteri vectis extremo R funis alligetur RT, cui <lb/>quidem potentia &longs;u&longs;tinens applicetur in T. <!-- KEEP S--></s>
            <s id="s.001385">Dico igitur, <pb xlink:href="007/01/147.jpg"/><figure id="id.007.01.147.1.jpg" xlink:href="007/01/147/1.jpg"/><lb/>rebus ita di&longs;po&longs;itis, <lb/>potentiam in T ita <lb/>&longs;e habere ad pondus <lb/>F, vt vnum ad &longs;exde&shy;<lb/>cim, hoc e&longs;t, in pro&shy;<lb/>portione e&longs;&longs;e &longs;ub&shy;<lb/>&longs;exdecupla. </s>
            <s id="s.001386">Sunt <lb/>autem, hic vectes <lb/>quatuor in feriorum <lb/>cubiculorum, loco, <lb/>CD, HI, MN, QR, <lb/>quorum, centra E, <lb/>G, L, P. quoniam e&shy;<lb/>nim A hoc e&longs;t, C, v&shy;<lb/>n&agrave; cum potentia G, <lb/>hoc e&longs;t, D, &longs;u&longs;tinet <lb/>pondus F alterum, <lb/>ponderis dimidium <lb/>&longs;u&longs;tinebit C, <expan abbr="alter&umacr;">alterum</expan> <lb/>vero D. erunt igitur <lb/>vtrinque librae quin&shy;<lb/>gent&aelig;. </s>
            <s id="s.001387">Tum potentia in K, hoc e&longs;t, in H, vna cum poten&shy;<lb/>tia in L, hoc e&longs;t, in I &longs;u&longs;tinebunt quingenta. </s>
            <s id="s.001388">Quare <expan abbr="vtraq;">vtraque</expan> <lb/>ducenta quinquaginta, &longs;ed hoc totum bifariam diuiditur <lb/>inter potentias, O, id e&longs;t, M, &amp; P, id e&longs;t H. erunt igitur v&shy;<lb/>trinque centum viginti quinque. </s>
            <s id="s.001389">Ea autem &longs;umma <expan abbr="iter&umacr;">iterum</expan> <lb/>bifariam diu&igrave;ditur, hoc e&longs;t, inter potentias S, id e&longs;t, Q &amp; <lb/>T, id e&longs;t, R, quare vtraque &longs;u&longs;tinet &longs;exaginta duo cum di&shy;<lb/>midio. </s>
            <s id="s.001390">Sed numerus i&longs;te ad Millenarium ita &longs;e habet vt v&shy;<lb/>num ad &longs;exdecim. </s>
            <s id="s.001391">Hinc colligimus, pondus totum inter <lb/>loca &longs;tabilia diuidi, nempe A, K, O, S, &amp; ip&longs;am potentiam <lb/>qu&aelig; &longs;u&longs;tinet in T, &amp; locis ip&longs;is &longs;tabilibus quindecim par&shy;<lb/>tes integri ponderis, potentia ver&ograve; T &longs;extam decimam <pb xlink:href="007/01/148.jpg"/>tant&ugrave;m commendari. </s>
            <s id="s.001392">Itaque &longs;i ex puncto V appendere&shy;<lb/>tur AB, in X potentia, qu&aelig; in X &longs;u&longs;tineret mille, minus <lb/>&longs;exaginta duo cum dimidio, quod quidem &agrave; potentia in <lb/>T &longs;u&longs;tinetur; quod &longs;i alius adderetur orbiculus, &amp; fierent <lb/>quinque, potentia in T &longs;u&longs;tineret trige&longs;imam &longs;ecundam <lb/>partem integri ponderis, hoc e&longs;t, dimidium librarum &longs;e&shy;<lb/>xaginta duarum cum dimidio, nempe triginta &amp; vnam <lb/>cum quarta parte, &longs;i item textus adderetur, potentia in T <lb/>&longs;exage&longs;imam partem &longs;u&longs;tineret integri ponderis, hoc e&longs;t, <lb/>libras quindecim &amp; 5/8 libr&aelig; vnius. </s>
            <s id="s.001393">Vnde patet clar&egrave; pon&shy;<lb/>deris diminutionem fieri ex orbiculis inferioribus, non <lb/>autem ex &longs;uperioribus, &longs;uperiores autem addi non nece&longs;&shy;<lb/>&longs;itatis quidem, &longs;ed commoditatis grati&acirc;: neque enim ab&longs;&shy;<lb/>que &longs;uperioribus vnico ductario fune fieri po&longs;&longs;et attractio <lb/>&amp; ponderis ip&longs;ius eleuatio. </s>
            <s id="s.001394">Hactenus igitur nobis i&longs;th&aelig;c <lb/>de Trochle&aelig; natura &amp; vi po&longs;t alios, con&longs;idera&longs;&longs;e &longs;it &longs;atis. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001395">QV&AElig;STIO XIX.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001396"><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, de&longs;uperque magnum adijciat pondus, ligni quippiam quod <lb/>curandum &longs;it, non diuidit; &longs;i ver&ograve; &longs;ecurim extollens percutiat, illud <lb/>&longs;cindit, cum alioquin multo minus habeat ponderis id quod <lb/>percutit, quam illud quod &longs;uperiacet <lb/>&amp; premit?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001397">Poterat Ari&longs;toteles, n&icirc; fallimur, rem breuius &amp; vniuer&shy;<lb/>&longs;alius proponere. </s>
            <s id="s.001398">Scilicet cur motus ponderi addat <lb/>pondus &amp; efficacius ex motu quam ex immoto pondere <lb/>mota res operetur. </s>
            <s id="s.001399">Soluit autem. </s>
            <s id="s.001400">An, inquiens, ideo fit, <lb/>quia omnia cum motu fiunt, &amp; graue ip&longs;um grauitatis ma&shy;<lb/>gis a&longs;&longs;umit motum, dum mouetur quam dum quie&longs;cit? <lb/></s>
            <s id="s.001401">Incumbens igitur connatam graui motionem non moue&shy;<lb/>tur, motum ver&ograve; &amp; &longs;ecundum hanc mouetur &amp; &longs;ecun-<pb xlink:href="007/01/149.jpg"/>dum eam qu&aelig; e&longs;t <expan abbr="percuti&emacr;tis">percutientis</expan>? </s>
            <s id="s.001402">H&aelig;c pr&aelig;clar&egrave; quidem, c&aelig;&shy;<lb/>tera autem, qu&aelig; de cuneo iterat, nempe ad vectem eius o&shy;<lb/>perationem referri &longs;uperius confutauimus. </s>
            <s id="s.001403">Porr&ograve; effe&shy;<lb/>ctus huius, de quo agitur, di&longs;putatio illuc &longs;pectat, videli&shy;<lb/>cet ad cadentium atque proiectorum naturam. </s>
            <s id="s.001404">Ad maio&shy;<lb/>rem autem rei euidentiam h&aelig;c addimus. </s>
          </p>
          <figure id="id.007.01.149.1.jpg" xlink:href="007/01/149/1.jpg"/>
          <p type="main">
            <s id="s.001405">E&longs;to libra AB, cu&shy;<lb/>ius centrum C, libra&shy;<lb/>ta &aelig;qualibus ponde&shy;<lb/>ribus DE, apponatur <lb/>ponderi E pondus F, <lb/>item ponderi D pon&shy;<lb/>dus G ip&longs;i ponderi F <lb/>&aelig;quale, &aelig;quilibrabit <lb/>itidem, Mod&ograve; non apponatur &longs;impliciter pondus G &longs;ex <lb/>ex H in lancem A dimittatur, tunc &longs;an&egrave; non &aelig;quilibrabit, <lb/>&longs;ed libram deprimet. </s>
            <s id="s.001406">Duo enim in pondere dimi&longs;&longs;o con&shy;<lb/>&longs;iderantur pondera; naturale &longs;cilicet, &amp; quod motu ip&longs;i <lb/>moto, ponderi e&longs;t acqui&longs;itum. </s>
            <s id="s.001407">Itaque quo motus fuerit <lb/>maior, puta &longs;i cadat ex I, grauitas ex maiori motu fiet ma&shy;<lb/>ior. </s>
            <s id="s.001408">quod vtique efficacius fieret &longs;i pondus G non dimit&shy;<lb/>tetur modo remoto prohibente, &longs;ed proijceretur. </s>
            <s id="s.001409">Tunc <lb/>enim tria concurrerent, grauitas naturalis, grauitas ac&shy;<lb/>qui&longs;ita ex naturali motu, &amp; ea qu&aelig; naturali adijcitur ex <lb/>violentia. </s>
            <s id="s.001410">Pondus igitur &longs;ecuri impo&longs;itum &amp; &longs;ecuris ip&longs;ius <lb/>naturalis grauitas naturali tantum grauitate operantur, <lb/>&amp; ideo minus efficaciter. </s>
            <s id="s.001411">Huc autem ea fer&egrave; pertinent <lb/>qu&aelig; nos &agrave; principio de duobus centris retulimus, natura&shy;<lb/>lis nempe grauitatis, &amp; acqui&longs;it&aelig;. </s>
          </p>
          <p type="main">
            <s id="s.001412">C&aelig;ter&ugrave;m cur mallei &amp; &longs;ecuris ictus &longs;it violenti&longs;&longs;i&shy;<lb/>mus, ideo fit quod non ex vnico neque duplici, &longs;ed ex tri&shy;<lb/>plici grauitate operetur. </s>
            <s id="s.001413">E&longs;to enim &longs;ecuris A, cuius manu&shy;<lb/>brium AB, brachium vero &longs;ecuri vtentis BC, erit igitur C <pb xlink:href="007/01/150.jpg"/><figure id="id.007.01.150.1.jpg" xlink:href="007/01/150/1.jpg"/><lb/>locus vbi humero <lb/>brachium iungi&shy;<lb/>tur, motus ip&longs;ius <lb/>centrum, attollit <lb/>autem &longs;ecurim is <lb/>qui percutit, &amp; re&shy;<lb/>tro ad &longs;capulas re&shy;<lb/>ducens totis viri&shy;<lb/>bus ex centro C <lb/>&longs;ecurim vibrat, <lb/>portionem circuli <lb/>de&longs;cribens ADE <lb/>ictumqueue faciens <lb/>in E. <!-- KEEP S--></s>
            <s id="s.001414">Vires igitur acquirit &longs;ecuris, tum ex naturali grauita&shy;<lb/>te, cadens ex D, in E, tum ex proprio pondere, tum etiam <lb/>ex violentia eidem &agrave; percutiente impre&longs;&longs;a. </s>
            <s id="s.001415">Fiunt autem <lb/>motus tam naturalis qu&agrave;m violentus eo validiores, quo <lb/>maius e&longs;t &longs;patium, quo res mota mouetur, idqueue praecipu&egrave; <lb/>cum violentia ip&longs;am &longs;ecundat naturam. </s>
            <s id="s.001416">Itaque maior fit <lb/>ictus in E qu&agrave;m in F, &amp; in F maior qu&agrave;m in D. <!-- KEEP S--></s>
            <s id="s.001417">Item violen&shy;<lb/>tius feriret percutiens, &longs;i manubrium e&longs;&longs;et longius, puta <lb/>BG. <!-- KEEP S--></s>
            <s id="s.001418">Tunc enim maior e&longs;&longs;et circulus GH, &amp; motus tum <lb/>prolixior, tum velocior. </s>
            <s id="s.001419">quo igitur longiora habet bra&shy;<lb/>chia is qui &longs;ecuri malleoue vtitur, data virium paritate, ex <lb/>eadem ratione validius percellit. </s>
            <s id="s.001420">E&longs;t autem &longs;ecuris, vel <lb/>malleus cuneatus, vel cuneus malleatus manubrio in&longs;er&shy;<lb/>tus. </s>
            <s id="s.001421">An autem operetur efficacius cuneus malleo percu&longs;&shy;<lb/>&longs;us, aut cum manubrio motus, vt fit in &longs;ecuri, data aciei &amp; <lb/>ponderis &aelig;qualitate, difficile e&longs;t determinare. </s>
            <s id="s.001422">Cert&egrave; va&shy;<lb/>lidius, &amp; certius fieri &longs;ci&longs;&longs;ionem ex cuneo &amp; malleo, ea ra&shy;<lb/>tio e&longs;t, quod cuneus adactus, nec inde remotus eam inte<lb/>rim &longs;eruat, quam antea fecerat partium &longs;eparationem, <pb xlink:href="007/01/151.jpg"/>quod quidem &longs;ecuri non accidit, qu&aelig; adacta ad nouam <lb/>percu&longs;&longs;ionem faciendam extrahitur. </s>
          </p>
          <p type="main">
            <s id="s.001423">Hoc etiam con&longs;ideramus, &longs;ecuris in circulo motum, <lb/>ex A in D, e&longs;&longs;e videndum, id e&longs;t, non &longs;ecundum naturam, <lb/>&longs;ur&longs;um enim fertur quod e&longs;t graue, ex D ver&ograve; in F <expan abbr="mixt&umacr;">mixtum</expan>: <lb/>magis autem ad naturalem accedere qui fit ex F in E. <!-- KEEP S--></s>
            <s id="s.001424">Tar&shy;<lb/>dior ergo ex A in D, velocior ex D, in F, veloci&longs;&longs;imus ex F <lb/>in E; qu&aelig;dam qu&aelig; ad hanc rem faciunt, egregi&egrave; con&longs;ide&shy;<lb/>rat Guid, Vbald. <!-- REMOVE S-->in calce Tractatus, De Cuneo; ip&longs;um <lb/>con&longs;ule. </s>
          </p>
          <p type="main">
            <s id="s.001425">Ad h&aelig;c &longs;uccurrit nobis pulcherrima qu&aelig;&longs;tio. </s>
            <s id="s.001426">Du&shy;<lb/>bitari enim pote&longs;t, vtrum ictus ex en&longs;e efficacior &longs;it &agrave; par&shy;<lb/>te qu&aelig; e&longs;t circa aciem, aut circa medium en&longs;em, vel pro&shy;<lb/>pe manubrium capulumue; etenim hinc inde &longs;unt ra&shy;<lb/>tiones. </s>
          </p>
          <p type="main">
            <s id="s.001427">E&longs;to quidem en&longs;is AB, cuius capulus A, &longs;piculum ve <lb/>r&ograve; B, centrum grauitatis C, pars capulo proxima D. <!-- KEEP S--></s>
            <s id="s.001428">Libra&shy;<lb/>to itaque gladio tres fiunt circulorum portiones BE, CF, <lb/>DG, qu&aelig;ritur quo loco ictus &longs;it validior, nempe in E, in F, <lb/>velin G. <!-- KEEP S--></s>
            <s id="s.001429">Videtur validiorem futurum in E, quippe quod <lb/>ex maiori &longs;emidiametro AB, maioris &longs;it circuli portio BE, <lb/>&amp; ideo velocior motus ex B in E. <!-- KEEP S--></s>
            <s id="s.001430">Contra efficaciorem <lb/>futurum apparet in F, propterea quod ibi ex centro C to&shy;<lb/>tius fiat grauitatis impre&longs;&longs;io, fieri autem validi&longs;&longs;imum in <lb/>G, licet ibi motus &longs;it tardior inde videtur, quod &longs;i con&longs;ide&shy;<lb/>retur en&longs;is vt vectis, cuius fulcimentum e&longs;t A, potentia <lb/>premens in B, ponderis vero loco re&longs;i&longs;tentia rei qu&aelig; per&shy;<lb/>cutitur in D. <!-- KEEP S--></s>
            <s id="s.001431">Maior e&longs;t autem proportio BA, ad AD, quam <lb/>BA ad AC, &amp; ideo violentior fiet pre&longs;&longs;io ex ictu in D, <expan abbr="qu&atilde;">quam</expan> <lb/>in C. <!-- KEEP S--></s>
            <s id="s.001432">Hi&longs;ce hoc pacto con&longs;ideratis, putarem ictum effica&shy;<lb/>ciorem fieri in F ex medio C, quam ex extremis &amp; oppo&shy;<lb/>&longs;itis partibus EG. <!-- KEEP S--></s>
            <s id="s.001433">Licet enim in B velocitas &longs;it maior, dee&longs;t <lb/>ibi pondus. </s>
            <s id="s.001434">Si enim en&longs;is iterum vt vectis con&longs;ideretur, e&shy;<pb xlink:href="007/01/152.jpg"/>runt AB. duo fulcimenta &longs;u&longs;tinent&iacute;a pondus in C, vbi gra&shy;<lb/>uitatis e&longs;t centrum. </s>
            <s id="s.001435">Si igitur paria fuerint &longs;patia BC, CA, <lb/><figure id="id.007.01.152.1.jpg" xlink:href="007/01/152/1.jpg"/><lb/>in B erit d&igrave;midium <lb/>ponderis C, quantum <lb/>ergo velocitate pr&aelig;&shy;<lb/>ualet ictus in B, <expan abbr="tant&umacr;">tantum</expan> <lb/>ponderis amittit. </s>
            <s id="s.001436">D <lb/>ver&ograve; plus quidem de <lb/>pondere participat, <lb/>&longs;ed velocitatis habet <lb/>minimum, in C ver&ograve; <lb/>velocitas e&longs;t medio&shy;<lb/>cris, tota tamen ip&longs;ius <lb/>ex grauitatis centro <lb/>ponderis fit impre&longs;&shy;<lb/>&longs;io. </s>
          </p>
          <p type="main">
            <s id="s.001437">Quidam, quod huc pertinet, vt ex acie ip&longs;a qu&aelig; lon&shy;<lb/>gius &agrave; capulo abe&longs;t, violenti&longs;&longs;imum facerent ictum, Ar&shy;<lb/>gentum viuum, quod &longs;ui natur&acirc; graui&longs;&longs;imum quidem e&longs;t <lb/>&amp; mobili&longs;&longs;imum in canali &agrave; manubrio ad verticem exca&shy;<lb/>uato infundunt, quo in gladij de&longs;cen&longs;u ad verticem velo&shy;<lb/>ci&longs;&longs;im&egrave; delato illuc transfert grauitatem totam, quare <lb/>tum velocitate tum grauitate concurrentibus ictus fit <lb/>violenti&longs;&longs;imus &amp; long&egrave; validi&longs;&longs;imus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001438">QVAESTIO XX.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001439"><emph type="italics"/>Dubitatur, Cur &longs;tatera qua carnes ponderantur, paruo appendicu&shy;<lb/>lo, magna trutinet onera, cum alioqui tota, dimidiata exi&longs;tat <lb/>libra, altera vero parte &longs;ola &longs;it <lb/>&longs;tatera?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001440">Soluit Philo&longs;ophus, inquiens, &longs;tateram &longs;imul, &amp; vectem <lb/>e&longs;&longs;e &amp; libram, ip&longs;ius ver&ograve; libr&aelig; centra &longs;eu fulcimenta <pb xlink:href="007/01/153.jpg"/>e&longs;&longs;e ibi vbi fit &longs;u&longs;pen&longs;io. </s>
            <s id="s.001441">Pondera ver&ograve; hinc in de in lance <lb/>&amp; appendiculo, loco &longs;cilicet &aelig;quipondij, appendiculo <lb/>&longs;uccedente. </s>
            <s id="s.001442">Reducit autem demon&longs;trationem ad ea qu&aelig; <lb/>&longs;tatuit ip&longs;e Mechanica principia; nempe ad circulum &amp; <lb/>circuli virtutem. </s>
            <s id="s.001443">Ait igitur, appendiculum licet parui <expan abbr="p&omacr;-deris">pon&shy;<lb/>deris</expan> &longs;it, ideo maiori ponderi virtute &aelig;quari, quod lon&shy;<lb/>gius &agrave; centro, hoc e&longs;t, ab ip&longs;o fulcimento &longs;i&longs;tatur. </s>
            <s id="s.001444">quic&shy;<lb/>quid tamen &longs;it, &longs;tateram e&longs;&longs;e vectem, res e&longs;t explorati&longs;&shy;<lb/>&longs;ima. </s>
          </p>
          <figure id="id.007.01.153.1.jpg" xlink:href="007/01/153/1.jpg"/>
          <p type="main">
            <s id="s.001445">E&longs;to igitur &longs;tatera AB, <lb/>cuius appendiculum cur&shy;<lb/>rens F, fulcimentum cen&shy;<lb/>trumue C, lanx qu&aelig; cate&shy;<lb/>na &longs;u&longs;penditur E &longs;patium <lb/>&agrave; loco fulcimenti ad ap&shy;<lb/>pendiculum CF. quod ve&shy;<lb/>r&ograve; &agrave; fulcimento ad cate&shy;<lb/>nam, ex qua lanx appen&shy;<lb/>ditur AC. <!-- KEEP S--></s>
            <s id="s.001446">Intelligatur autem &amp; aliud fulcimentum D, &longs;it&shy;<lb/>queue maius &longs;patium AD, quam AC. <!-- KEEP S--></s>
            <s id="s.001447">Porr&ograve; ita &longs;e habeat <lb/>pondus in E ad appendiculi F pondus, vt CF &longs;patium, ad <lb/>&longs;patium AC, quo ca&longs;u &longs;eruata, permutatim, ponderum &amp; <lb/>brachiorum proportione, fiet aequilibrium. </s>
            <s id="s.001448">Si autem pon&shy;<lb/>deribus ita con&longs;titutis iterum &longs;u&longs;pendatur in D, non fiet <lb/>&aelig;quilibrium, propterea quod minor &longs;it proportio DF ad <lb/>DA, ea qu&aelig; e&longs;t FC ad CA. <!-- KEEP S--></s>
            <s id="s.001449">Minor ergo e&longs;t proportio FD <lb/>ad DA, quam ponderis E ad pondus F, &amp; idcirco facta <lb/>&longs;u&longs;pen&longs;ione pr&aelig;ualebit pondus E ponderi F. <!-- KEEP S--></s>
            <s id="s.001450">Ita que vt it e&shy;<lb/>rum fiat &aelig;quilibrium, nece&longs;&longs;e e&longs;t <expan abbr="iter&umacr;">iterum</expan> proportiones bra&shy;<lb/>chiorum &longs;eu &longs;patiorum proportionibus ponderum &aelig;qua&shy;<lb/>re. </s>
            <s id="s.001451">Transferatur igitur &lpar;lancis interim immoto pondere&rpar; <lb/>ip&longs;um appendiculum in B, fiatque vt FC ad CA, ita BD ad <lb/>DA. <!-- KEEP S--></s>
            <s id="s.001452">Stabit autem iterum &longs;tatera ad eam redacta quam <pb xlink:href="007/01/154.jpg"/>diximus brachiorum &amp; ponderum permutatam propor&shy;<lb/>tionem. </s>
          </p>
          <p type="main">
            <s id="s.001453">Nos &longs;tateris vtimur ex duplici fulcimento, altero <lb/>propiori, altero &agrave; lance &longs;eu loco, vbi lanx appenditur, re&shy;<lb/>motiori, illa grauiora appendimus pondera, &amp; non per <lb/>vncias &amp; libras, &longs;ed per libras tantum &amp; &longs;elibra ponde&shy;<lb/>ramus; &amp; hoc &longs;tater&aelig; latus eo quod minus minut&egrave; &longs;it di&shy;<lb/>ui&longs;um; vulgo no&longs;trates Gro&longs;&longs;um, hoc e&longs;t, rude &amp; cra&longs;&longs;um <lb/>appellant. </s>
            <s id="s.001454">Aliud ver&ograve;, cum fulcimentum e&longs;t loco appen&shy;<lb/>&longs;ionis lancis vicinius, &amp; per libras, &longs;elibras &amp; vncias diui&shy;<lb/>ditur, quo quidem minora appendimus pondera, e&ograve; quod <lb/><expan abbr="exqui&longs;itior&emacr;">exqui&longs;itiorem</expan> contineat diui&longs;ionem, &longs;ubtile dicunt. </s>
            <s id="s.001455">Rect&egrave; <lb/>igitur dicebat Philo&longs;ophus, in &longs;tatera plures e&longs;&longs;e libras, <lb/>quamquam &amp; ea quoque de cau&longs;&longs;a dici po&longs;&longs;it, quod, quot <lb/>&longs;unt appendiculi, &egrave; loco in locum translationes, totidem <lb/>ex proportionum variatione fiant libr&aelig;. </s>
            <s id="s.001456">Et hoc quidem <lb/>&longs;en&longs;i&longs;&longs;e videtur Ari&longs;toteles. <!-- KEEP S--></s>
          </p>
          <figure id="id.007.01.154.1.jpg" xlink:href="007/01/154/1.jpg"/>
          <p type="main">
            <s id="s.001457">Po&longs;&longs;emus &amp; alio <lb/>modo &longs;tatera vti, nempe <lb/>&longs;tabili appendiculo, mo&shy;<lb/>bili autem fulcimento. <lb/></s>
            <s id="s.001458">E&longs;to enim &longs;tatera AB, <lb/>cuius lanx C appen&longs;a in <lb/>A, appendiculum ver&ograve; <lb/>&longs;tabile D, appen&longs;um in <lb/>B, Apponatur ip&longs;i l&atail;nci <lb/>C, pondus E. <!-- KEEP S--></s>
            <s id="s.001459">Vnicum ergo fiet corpus CEABD con&longs;tans <lb/>ex lance, libra &amp; ponderibus. </s>
            <s id="s.001460">Habet ergo hoc totum gra&shy;<lb/>uitatis &longs;u&aelig; centrum, quod quidem vbi &longs;it e&longs;t ignotum. </s>
            <s id="s.001461">Ex <lb/>illo autem inuento &longs;i corpus totum appendatur, partes &aelig;&shy;<lb/>queponderabunt. </s>
            <s id="s.001462">Appendatur autem, puta in G, &longs;it <expan abbr="aut&emacr;">autem</expan> <lb/>grauitatis centrum in H. <!-- KEEP S--></s>
            <s id="s.001463">Quoniam igitur H e&longs;t extra ful&shy;<lb/>cimentum G, declinabit &longs;tater&aelig; pars GA, centro G per <pb xlink:href="007/01/155.jpg"/>circuli portionem Hl, &agrave; centro grauitatis in ip&longs;a de&longs;cen&shy;<lb/>&longs;ione de&longs;criptam. </s>
            <s id="s.001464">Si autem grauitatis centrum fuerit vbi <lb/>K, eo quod ibi quoque &longs;it extra fulcimentum G, de&longs;cen&shy;<lb/>det pars GB, de&longs;cribente interim grauitatis centro K, cir&shy;<lb/>culi portionem KL. ltaque &longs;i &longs;tateram totam eum ponde&shy;<lb/>ribus trahamus <expan abbr="pellamu&longs;q;">pellamu&longs;que</expan> vltro citroque;, immoto appen&shy;<lb/>diculo erit aliquando fulcimentum in ea linea perpendi&shy;<lb/>culari vel loco ip&longs;o, vbi e&longs;t grauitatis centrum, quo ca&longs;u <lb/>&longs;tatera &longs;tabit, &amp; tunc ita erit diui&longs;a, vt fiat brachiorum &amp; <lb/>ponderum eadem ratio, ordine permutato. </s>
            <s id="s.001465">Hic autem <lb/>modus ideo non e&longs;t in v&longs;u, quod mole&longs;tum &longs;it libram &longs;eu <lb/>&longs;tateram cum ponderibus vltro citroqueue transferre, qu&aelig; <lb/>difficultas commod&egrave; appendiculi mobilitate vitatur. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001466">QVAESTIO XXI.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001467"><emph type="italics"/>Qu&aelig;ritur, Cur facilius dentes extrahunt Chirurgi, denti forcipis <lb/>onere adiecto, quam &longs;i &longs;ola manu vtantur?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001468">Re&longs;pondet Philo&longs;ophus, An quia ex manu, magis quam <lb/>ex dentiforcipe lubrius elabitur dens? </s>
            <s id="s.001469">An ferro id po&shy;<lb/>tius accidit quam digitis, quoniam vndique dentem non <lb/>comprehendunt, quod mollis facit digitorum caro; ad&shy;<lb/>h&aelig;ret enim &amp; complectitur magis. </s>
            <s id="s.001470">H&aelig;c &longs;ecunda ratio <lb/>videtur primam de&longs;truere, &amp; contrarium pror&longs;us &longs;enten&shy;<lb/>ti&aelig;, qu&aelig; in problemate proponitur, a&longs;&longs;erere. </s>
            <s id="s.001471">Si Gr&aelig;ca ad <lb/>verbum reddas ita habent: An magis ip&longs;a manu labile e&longs;t <lb/>ferrum, &amp; ip&longs;um vndique &lpar;dentem nempe&rpar; non comple&shy;<lb/>ctitur, caro autem digitorum cum mollis &longs;it, adh&aelig;ret ma&shy;<lb/>gis, &amp; vndique congruit. </s>
            <s id="s.001472">Cert&egrave; vt &longs;ententia non &longs;it con&shy;<lb/>traria propo&longs;itioni, Gr&aelig;ca ver&longs;io ita videtur concinnan&shy;<lb/>da: Vel magis &egrave; manu elabitur, mollis enim e&longs;t digitorum <lb/>caro, ferrum autem circumplectitur, &amp; haeret magis. </s>
            <s id="s.001473">quic&shy;<lb/>quid &longs;it, Gr&aelig;cam lectionem contrarium ei quod qu&aelig;ri-<pb xlink:href="007/01/156.jpg"/>tur, affirmare certum e&longs;t. </s>
            <s id="s.001474">Picolomineus, Ideo, inquit, di&shy;<lb/>gitorum caro mollis minus apt&egrave; extrahit, quod dentem <lb/>totum comprehendere non pote&longs;t, quod ferrum ob &longs;uam <lb/>dur&iacute;tiem &amp; con&longs;tantiam commodi&longs;&longs;im&egrave; facit. </s>
            <s id="s.001475">Sen&longs;um ex <lb/>mente reddidit, quod ex verbis non poterat. </s>
            <s id="s.001476">Subiungit <lb/>denique Ari&longs;toteles, An quia dentiforcipes &longs;int duo con&shy;<lb/>trarij vectes vnicum habentes fulcimentum, ip&longs;am &longs;cili&shy;<lb/>cet in &longs;trumenti partium connexionem. </s>
            <s id="s.001477">Hoc igitur ad ex&shy;<lb/>tractionem vtuntur^&lcub;**}, vt facilius moueant. </s>
            <s id="s.001478">Figuram hoc <lb/>pacto proponit Philo&longs;ophus. <!-- KEEP S--></s>
          </p>
          <figure id="id.007.01.156.1.jpg" xlink:href="007/01/156/1.jpg"/>
          <p type="main">
            <s id="s.001479">E&longs;to dentiforcipis alterum <lb/>quidem extremum vbi A, alte&shy;<lb/>rum autem quod extrahit B, ve&shy;<lb/>ctis vbi ADF, alter vectis, vbi <lb/>BCE, fulcimentum ver&ograve; CGD <lb/>connexio vbi G. <!-- KEEP S--></s>
            <s id="s.001480">Dens autem pondus: vtroque igitur ve&shy;<lb/>cte B, &amp; F &longs;imul comprehendentes mouent, H&aelig;c ille. <!-- KEEP S--></s>
            <s id="s.001481">At&shy;<lb/>tamen rem ip&longs;am &longs;ubtilius con&longs;iderantibus aliter videtur <lb/>habere, ac ip&longs;e a&longs;&longs;erat. </s>
            <s id="s.001482">Et &longs;an&egrave; dentisforcipis brachia ve&shy;<lb/>ctes e&longs;&longs;e, quorum commune fulcimentum e&longs;t in ip&longs;o cen&shy;<lb/>tro vbi vertebra, nemo negauerit. </s>
            <s id="s.001483">Dentem autem e&longs;&longs;e <lb/>pondus, ego quidem ab&longs;olute non dixerim. </s>
            <s id="s.001484">Pondus <expan abbr="aut&emacr;">autem</expan> <lb/>h&icirc;c proprie e&longs;t ip&longs;a dentis durities, cuius re&longs;i&longs;tentia eo fa&shy;<lb/>cilius &longs;uperatur, quo maior e&longs;t proportio brachiorum &agrave; <lb/>manu ad vertebram, ad partem illam qu&aelig; &agrave; vertebra e&longs;t <lb/>ad dentem. </s>
            <s id="s.001485">At dentis ex con&longs;trictione fractio nihil facit <lb/>pror&longs;us ad extractionem: id tamen operatur brachio&shy;<lb/>rum longitudine dentiforceps, quod valide ex vectium <lb/>oppo&longs;itorum vi dentes con&longs;tringit &amp; extractioni commo&shy;<lb/>dum reddit &amp; facilem. </s>
            <s id="s.001486">Neque enim totus Dentiforceps <lb/>hic ceu vectis vnicus operatur, quod fit in forcipibus quas <lb/>Tenaleas vocamus, quibus &egrave; tabulis claui reuelluntur, <lb/>qua de re nos quae&longs;tione 6. verba fecimus. </s>
            <s id="s.001487">Quo pacto <expan abbr="aut&emacr;">autem</expan> <pb xlink:href="007/01/157.jpg"/>dentis ex Dentiforcipe extractio ad vectem reducatur, <lb/>&longs;ubtilius e&longs;t perpendendum, neque enim res e&longs;t in propa&shy;<lb/>tulo. </s>
          </p>
          <p type="main">
            <s id="s.001488">Dicimus igitur, tum dentem ip&longs;um, tum dentifor&shy;<lb/>cipem vectes e&longs;&longs;e, varia tamen ratione &amp; &longs;atis &longs;ane diuer&shy;<lb/>&longs;a. </s>
            <s id="s.001489">Dens enim fit vectis eius nempe natur&aelig; qu&aelig; fulcimen&shy;<lb/>tum habet in angulo, quo ca&longs;u ip&longs;ius Dentiforcipis <expan abbr="parti&umacr;">partium</expan>, <lb/>quibus Dens apprehenditur, ea qu&aelig; longior e&longs;t poten&shy;<lb/>ti&aelig; mouentis loco &longs;uccedit, breuior vero fulcimentum <lb/>facit, Dentis vero re&longs;i&longs;tentia ponderis vices refert. </s>
          </p>
          <figure id="id.007.01.157.1.jpg" xlink:href="007/01/157/1.jpg"/>
          <p type="main">
            <s id="s.001490">E&longs;to enim dens qui&shy;<lb/>dem A, cuius diameter <lb/>BC, longitudo v&longs;que ad <lb/>extremas radices CD, <lb/>pars dentiforcipis breui&shy;<lb/>or CG, longior BG. <!-- KEEP S--></s>
            <s id="s.001491">Fit <lb/>ergo vectis BCD, habens <lb/>fulcimentum in C. <!-- KEEP S--></s>
            <s id="s.001492">Den&shy;<lb/>te igitur apprehen&longs;o in BC, &amp; manu dentiforcipe ceu ve&shy;<lb/>cte ad inferiora compre&longs;&longs;o C, fit fulcimentum centrum&shy;<lb/>ue. </s>
            <s id="s.001493">Stante enim puncto C, trahente autem potentia qu&aelig; <lb/>e&longs;t in B, fit motus ip&longs;ius B, per circuli portionem BE, radi&shy;<lb/>cis vero D, fit motus per DF, &amp; inde ip&longs;ius dentis extra&shy;<lb/>ctio facilis. </s>
            <s id="s.001494">Quibus con&longs;ideratis vt rem ad proportiones <lb/>quatenus fieri pote&longs;t reducamus, dicimus, quo maior fu&shy;<lb/>erit proportio BC, ad CD, hoc e&longs;t, partis vectis, qu&aelig; &agrave; ful&shy;<lb/>cimento ad potentiam ad eam qu&aelig; &agrave; fulcimento e&longs;t ad <lb/>pondus, eo facilius fieri dentis auul&longs;ionem, quod vtique <lb/>demon&longs;trandum fuerat. </s>
          </p>
          <p type="main">
            <s id="s.001495">Porro quod in calce qu&aelig;&longs;tionis addit Philo&longs;ophus, <lb/>Dentes commotos facilius manu extrahi quam in&longs;tru&shy;<lb/>mento, nulla ratione probat. </s>
            <s id="s.001496">Ego autem arbitror, huc <lb/>pertinere ea verba, qu&aelig; &longs;uperius habentur, videlicet fer&shy;<pb xlink:href="007/01/158.jpg"/>rum quidem non vndique dentem <expan abbr="compreh&emacr;dere">comprehendere</expan>, quod <lb/>mollis facit digitorum caro, qu&aelig; id circo adh&aelig;ret &amp; com&shy;<lb/>plectitur magis. </s>
            <s id="s.001497">An autem ita &longs;it, alij videant, nobis enim <lb/>digito rem o&longs;tendi&longs;&longs;e fuerit &longs;atis. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001498">QV&AElig;STIO XXII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001499"><emph type="italics"/>H&icirc;c qu&aelig;rit Ari&longs;toteles, Cur nuces ab&longs;que ictu facile confringuntur <lb/>in&longs;trumentis qu&aelig; ad eum faciunt v&longs;um, &amp; hoc licet multum aufe&shy;<lb/>ratur virium, ce&longs;&longs;ante motu &amp; violentia, quod accidit dum mal&shy;<lb/>leo confringuntur. </s>
            <s id="s.001500">Addit pr&aelig;terea, citius fieri confractionem <lb/>graui, &amp; duro in&longs;trumento ferreo vide&shy;<lb/>licet qu&agrave;m ligneo.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001501">Soluit, inquiens, id fieri quod in&longs;trumentum duobus <lb/>vectibus con&longs;tet, co&euml;untibus in connexione &longs;eu verte&shy;<lb/>bra, &amp; idcirco eo violentius fieri confractionem, quo mi&shy;<lb/>nus e&longs;t &longs;patium &agrave; nuce, qu&aelig; frangitur, ad vertebram. </s>
            <s id="s.001502">ma&shy;<lb/>ius ver&ograve; quod &agrave; vertebra ad extremitates, qu&aelig; confrin&shy;<lb/>gentis manu comprimuntur. </s>
            <s id="s.001503">Ait igitur, &amp; id quam oppo&shy;<lb/>&longs;ite, vim ex vectibus ictus loco &longs;uccedere &amp; idem operari. </s>
          </p>
          <figure id="id.007.01.158.1.jpg" xlink:href="007/01/158/1.jpg"/>
          <p type="main">
            <s id="s.001504">E&longs;to igitur in &longs;trumentum, <lb/>de quo agimus CDBF, ex duo&shy;<lb/>bus vectibus con&longs;tans, quorum <lb/>alter CAF, alter vero DAB ver&shy;<lb/>tebra &longs;eu connexio A locus v&shy;<lb/>bi nux frangitur K, manubria <lb/>vero BF. quo igitur prolixiores <lb/>erunt AB, AF, breuiores vero ACAD, violentius fiet <expan abbr="c&omacr;-fractio">con&shy;<lb/>fractio</expan>. </s>
            <s id="s.001505">Erit autem nucis re&longs;i&longs;tentia loco ponderis A, ful&shy;<lb/>cimentum BF loco potenti&aelig;. </s>
            <s id="s.001506">Itaque n&icirc; maior &longs;it propor&shy;<lb/>tio potenti&aelig; ad re&longs;i&longs;tentiam, quam brachij &agrave; potentia ad <lb/>fulcimentum ad eam partem qu&aelig; &agrave; fulcimento e&longs;t ad nu&shy;<lb/>cem, non fiet confractio. </s>
            <s id="s.001507">eo autem magis &longs;uperabit, quo <pb xlink:href="007/01/159.jpg"/>maior fuerit pars vectis qu&aelig; &agrave; potentia ad fulcimentum. </s>
          </p>
          <p type="main">
            <s id="s.001508">Quod autem addit Ari&longs;toteles, eo maiorem fieri <lb/>vectium eleuationem, hoc e&longs;t, in&longs;trumenti aperitionem, <lb/>quo magis nux qu&aelig; frangitur, fuerit propior fulcimento, <lb/>hoc e&longs;t, ip&longs;i vertebr&aelig;, facile o&longs;tenditur ex conuer&longs;a 21. <lb/>propo&longs;. lib. 1. Elem. </s>
            <s id="s.001509">&longs;i enim ab extremitatibus vnius line&aelig; <lb/>ad ea&longs;dem partes con&longs;tituantur du&aelig; line&aelig; maiores con&shy;<lb/>currentes in angulo, &amp; ab ij&longs;dem extremitatibus du&aelig; a&shy;<lb/>li&aelig; minores, qu&aelig; intra triangulum &agrave; maioribus con&longs;titu&shy;<lb/>tum cadant, maiorem angulum continebunt. </s>
            <s id="s.001510">At talis e&longs;t <lb/>angulus qui fit in in &longs;trumento, cum partes vectis &agrave; verte&shy;<lb/>bra ad nucem fuerint breuiores. </s>
            <s id="s.001511">mag&igrave;s ergo dilatantur <lb/>vectes, &amp; magis dilatati magis comprimuntur, magis au&shy;<lb/>tem compre&longs;&longs;i validius frangunt, quod dixerat Ari&longs;to&shy;<lb/>teles. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001512">C&aelig;terum &amp; illud quod &longs;cribit, ex grauiori &amp; durio&shy;<lb/>ri materia in&longs;trumentum citius fractionem facere, quam <lb/>ex leuiori &amp; minus dura, ex parte quidem materi&aelig; verum <lb/>e&longs;t, nec pertinet ad proportionem, qu&aelig; &longs;ane in <expan abbr="huiu&longs;mod&imacr;">huiu&longs;modi</expan> <lb/>in&longs;trumentis form&aelig; fer&egrave; habent rationem. </s>
            <s id="s.001513">Nos hi&longs;ce in&shy;<lb/>&longs;trumentis non vtimur. </s>
            <s id="s.001514">Sunt autem &longs;imilia in&longs;trumentis <lb/>illis, quibus figuli cretaceas pilas ad chirobali&longs;tarum v&longs;um <lb/>facere &amp; efformare con&longs;ueuerunt. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001515">QV&AElig;STIO XXIII.<!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001516">Pvlcherrimam proponit hoc loco Philo&longs;ophus con&shy;<lb/>templationem, eamque ad mixtos motus <expan abbr="pertin&emacr;tem">pertinentem</expan>. <lb/></s>
            <s id="s.001517">Mixtorum autem motuum &longs;peculationem antiquis Me&shy;<lb/>chanicis fui&longs;&longs;e tum vtilem tum etiam familiarem, norunt <lb/>ij qui norunt qu&aelig; de lineis &longs;piralibus Helici&longs;ue, cy&longs;&longs;oidi&shy;<lb/>bus, conchoidibus &amp; alijs eiu&longs;cemodi &longs;cripta &amp; contem&shy;<lb/>plata reperiuntur, quibus tum ad duarum mediarum pro&shy;<pb xlink:href="007/01/160.jpg"/>portionalium inuentionem, tum ad circuli quadratio&shy;<lb/>nem vti &longs;olent. </s>
            <s id="s.001518">Quod autem h&icirc;c qu&aelig;rit Ari&longs;toteles, ita &longs;e <lb/>habet. </s>
          </p>
          <p type="head">
            <s id="s.001519"><emph type="italics"/>Cur &longs;i duo extrema in Rhombo puncta duabus ferantur lationibus, <lb/>haudquaquam &aelig;qualem vtrumque eorum pertran&longs;it rectam, &longs;ed <lb/>multo plus alteram? </s>
            <s id="s.001520">Item cur quod &longs;uper latus fertur, minus per&shy;<lb/>tran&longs;eat quam ip&longs;um latus. </s>
            <s id="s.001521">Illud enim diametrum pertran&longs;ire <lb/>certum est, hoc vero maius latus, licet hoc vnica, illud au&shy;<lb/>tem duabus feratur lationibus?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001522">Difficile hoc intellectu prima fronte, &amp; &longs;ane admi&shy;<lb/>rabile, itaque in tentam contemplationem requirit. </s>
            <s id="s.001523">Nos <lb/>primo cum Ari&longs;totele, rem totam explicabimus, tum ali&shy;<lb/>quid forta&longs;&longs;e non p&oelig;nitendum no&longs;tro de promptuario <lb/>proferemus. </s>
          </p>
          <figure id="id.007.01.160.1.jpg" xlink:href="007/01/160/1.jpg"/>
          <p type="main">
            <s id="s.001524">E&longs;to itaque Rhombus ABCD, <lb/>cuius latera AB, BD, DC, CA, diame&shy;<lb/>trorum maior AD, minor BC, &longs;ecan&shy;<lb/>tes &longs;e inuicem in puncto &longs;eu figur&aelig; <lb/>centro K. <!-- KEEP S--></s>
            <s id="s.001525">Sunt <expan abbr="aut&emacr;">autem</expan> ex ip&longs;ius Rhom&shy;<lb/>bi natura latera &aelig;qualia &amp; parallela, <lb/>Angulorum vero qui maiori diame&shy;<lb/>tro opponuntur, recto maiores, qui <lb/>vero minori minores. </s>
            <s id="s.001526">His igitur con&shy;<lb/>&longs;ideratis, intelligatur punctum A mo&shy;<lb/>ueri peculiari &amp; &longs;implici motu, per li&shy;<lb/>neam AB, ab A ver&longs;us B, &amp; eodem <expan abbr="t&emacr;-pore">tem&shy;<lb/>pore</expan> moueri totam lineam AB, ver&longs;us lineam DC, hac ta&shy;<lb/>men lege, vt &longs;emper eidem DC feratur parallela, &amp; eius <lb/>alterum extremorum feratur per AC, alterum vero per <lb/>BD, Intelligatur etiam punctum B moueri eodem tem&shy;<lb/>pore proprio motu, eoque &longs;implici, per eandem rectam <lb/>BA, ver&longs;us A, &amp; cum eadem, vt dictum e&longs;t, mota; ferri ver-<pb xlink:href="007/01/161.jpg"/>&longs;us CD. <!-- KEEP S--></s>
            <s id="s.001527">Erunt autem &longs;emper AB puncta in eadem linea <lb/>qu&aelig; mouetur, &longs;ibi inuicem ex contrarijs partibus occur&shy;<lb/>rentia. </s>
            <s id="s.001528">Itaque cum ex duobus motibus &longs;emper propor&shy;<lb/>tionalibus, hoc e&longs;t, laterum proportione &longs;eruata, recta <lb/>producatur, vt demon&longs;tratum e&longs;t &agrave; principio, vbi produ&shy;<lb/>ctio circuli ex Philo&longs;ophi mente e&longs;t declarata, <expan abbr="vtraq;">vtraque</expan> pun&shy;<lb/>cta qu&aelig; eandem laterum proportionem &longs;eruantia <expan abbr="mou&emacr;-tur">mouen&shy;<lb/>tur</expan>, rectas lineas <expan abbr="produc&emacr;t">producent</expan> A quidem AD, B autem ip&longs;am <lb/>BC. <!-- KEEP S--></s>
            <s id="s.001529">Feratur igitur A, tum mixto tum &longs;implici motu per <lb/>diametrum AD. <!-- KEEP S--></s>
            <s id="s.001530">B vero quoque tum mixto, tum proprio <lb/>per diametrum BC, &longs;upponitur autem motus omnes &longs;im&shy;<lb/>plices, tum punctorum, tum etiam lineae, &agrave; qua puncta ip&longs;a <lb/>feruntur, &aelig;quali velocitate fieri. </s>
            <s id="s.001531">Illud igitur mirabile e&longs;t, <lb/>cuius etiam ratio qu&aelig;ritur, quo pacto eodem tempore ea&shy;<lb/>dem que velocitate latum A quidem totam percurrat AD <lb/>maiorem, B vero totam BC, eamque longe minorem? <lb/></s>
            <s id="s.001532">Porro nece&longs;&longs;e fuit rem in Rhombo &longs;peculari, non autem <lb/>in quadrato &amp; altera parte longiori rectangulo, in quibus <lb/>diametri &lpar;quod Rhombo non accidit&rpar; &longs;unt &aelig;quales. </s>
            <s id="s.001533">Ima&shy;<lb/>ginemur igitur A, proprio motu percurri&longs;&longs;e &longs;patium AE, <lb/>nempe ip&longs;ius AB line&aelig; dimidium. </s>
            <s id="s.001534">Erit igitur in E, item li&shy;<lb/>neam totam AB eodem tempore pertran&longs;i&longs;&longs;e dimidia op&shy;<lb/>po&longs;itarum linearum, ACBD, &amp; e&longs;&longs;e translatam, vbi FKG. <lb/></s>
            <s id="s.001535">Quoniam igitur &aelig;quali celeritate line&aelig; AB extremitas <lb/>A, translata e&longs;t in F &amp; A, punctum per eam motum in E, e&shy;<lb/>rit &longs;patium AE, &aelig;quale &longs;patio AF. <!-- KEEP S--></s>
            <s id="s.001536">Ductis igitur lineis <lb/>FKG, EKH lateribus AB, AC &aelig;quidi&longs;tantibus, erit figura <lb/>AEKF. </s>
            <s id="s.001537">Rhombus &longs;imilis quidem Rhombo ABCD, recta <lb/>igitur FK &aelig;qualis erit oppo&longs;it&aelig; AE. quare A punctum <lb/>translatum erit ex mixto motu in K. <!-- KEEP S--></s>
            <s id="s.001538">Eodem pacto <expan abbr="quoni&atilde;">quoniam</expan> <lb/>punctum B. eadem velocitate mouetur ver&longs;us A, &amp; linea <lb/>AB ver&longs;us CD, cum B fuerit in E extremum line&aelig; mot&aelig; <lb/>BA, <expan abbr="n&emacr;pe">nempe</expan> B erit in G. &aelig;quales ergo &longs;unt BE, BG &amp; Rhom&shy;<pb xlink:href="007/01/162.jpg"/>bus EBGK, circa diametrum BKC ip&longs;i Rhombo ABCD <lb/>&longs;imilis, &amp; ideo GK &aelig;qualis oppo&longs;it&aelig; BE &amp; BG &aelig;qualis <lb/>EK. <!-- KEEP S--></s>
            <s id="s.001539">Cum ergo B confecerit &longs;patium BE, erit ex mixto <lb/>motu in K, &longs;uperato nempe &longs;patio BK, idque eodem tem&shy;<lb/>pore quo A percurrerat totum &longs;patium AK. <!-- KEEP S--></s>
            <s id="s.001540">Ex &aelig;quali i&shy;<lb/>gitur &longs;implicium motuum velocitate, in &aelig;qualia &longs;patia <lb/>AB puncta pertran&longs;ierunt, qu&aelig; res miraculo, cuius dilu&shy;<lb/>tio qu&aelig;ritur, pr&aelig;bet occa&longs;ionem. </s>
          </p>
          <p type="main">
            <s id="s.001541">Porro quod de dimidijs diametris demon&longs;tratum <lb/>e&longs;t, po&longs;&longs;umus &amp; de totis eadem ratione concludere, quip&shy;<lb/>pe quod eadem &longs;it proportio partium ad partes, qu&aelig; to&shy;<lb/>tius ad totum. </s>
            <s id="s.001542">H&aelig;c igitur prima e&longs;t pars propo&longs;it&aelig; qu&aelig;&shy;<lb/>&longs;tionis. </s>
            <s id="s.001543">Secunda vero dubitatio ita habet; Nempe mirum <lb/>videri punctum B, cum peruenerit in C, extremum line&aelig; <lb/>BA, videlicet ip&longs;um B, translatum e&longs;&longs;e in D, licet &aelig;quali&shy;<lb/>ter moueantur linea BA, per lineam BD, &amp; punctum B per <lb/>lineam BA. &longs;itque BC ip&longs;a BD maior. </s>
            <s id="s.001544">Primam dubitatio&shy;<lb/>nem hoc pacto &longs;oluit Philo&longs;ophus; A fertur tum proprio, <lb/>tum alieno motu, hoc e&longs;t, line&aelig; AB ver&longs;us oppo&longs;itam par&shy;<lb/>tem CD, Itaque cum vterque motus deor&longs;um vergat, mo&shy;<lb/>tus fit velocior. </s>
            <s id="s.001545">Contra vero B proprio quidem motu fer&shy;<lb/>tur ver&longs;us A, hoc e&longs;t, &longs;ur&longs;um, alieno vero, hoc e&longs;t, line&aelig; BA <lb/>ver&longs;us D, hoc e&longs;t, deor&longs;um, qui motus cum inuicem aduer&shy;<lb/>&longs;entur, motus ip&longs;e fit tardior, non igitur e&longs;t mirum, A eo&shy;<lb/>dem tempore maius &longs;patium pertran&longs;ire quam B. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001546">H&aelig;c &longs;olutio non modo vera videtur, &longs;ed mirabilis <lb/>&amp; ip&longs;omet Philo&longs;opho digni&longs;&longs;ima, cui quidem <expan abbr="temerari&umacr;">temerarium</expan> <lb/>iudicaremus contradicere, n&icirc; in genere ver&longs;aremur, in <lb/>quo non probabilia qu&aelig;runtur, &longs;ed demon&longs;trata, &longs;ed ve&shy;<lb/>ra. </s>
            <s id="s.001547">Futilem igitur e&longs;&longs;e rationem hanc ip&longs;ius Ari&longs;totelis <lb/>pace, hoc pacto o&longs;tendemus. </s>
          </p>
          <p type="main">
            <s id="s.001548">E&longs;to quadratum ABCD, cuius diametri ACBD &longs;e&shy;<lb/>cantes &longs;e&longs;e in E, moueatur eodem pacto BA, ver&longs;us CD, <pb xlink:href="007/01/163.jpg"/><figure id="id.007.01.163.1.jpg" xlink:href="007/01/163/1.jpg"/><lb/>item A, ver&longs;us B, &amp; B ver&longs;us A, ita&shy;<lb/>que punctum A tum proprio tum <lb/>alieno, hoc e&longs;t line&aelig; illud <expan abbr="defer&emacr;-tis">deferen&shy;<lb/>tis</expan> motu deor&longs;um trudet, hoc e&longs;t, <lb/>ver&longs;us CD. <!-- KEEP S--></s>
            <s id="s.001549">Motus ergo velocior <lb/>erit motu puncti B, quod lationi&shy;<lb/>bus fertur fer&egrave; contrarijs, hoc e&longs;t, <lb/>ex B ver&longs;us A &longs;ur&longs;um, cum linea <lb/>autem BA ver&longs;us C deor&longs;um. </s>
            <s id="s.001550">Ve&shy;<lb/>locius tamen non mouetur, quip&shy;<lb/>pe quod &aelig;quali tempore &aelig;quale <lb/>&longs;patium vtrum que punctum conficiat. </s>
            <s id="s.001551">Stante igitur cau&longs;&shy;<lb/>&longs;a &longs;equi debui&longs;&longs;et effectus; non &longs;equitur autem, Ari&longs;tote&shy;<lb/>lis igitur cau&longs;&longs;a non e&longs;t cau&longs;&longs;a. </s>
            <s id="s.001552">Rhombo quoque inuer&longs;o <lb/>idem clarius o&longs;tendemus hoc pacto: Sit Rhombus ABCD, <lb/><figure id="id.007.01.163.2.jpg" xlink:href="007/01/163/2.jpg"/><lb/>cuius diametri AC, BD &longs;ecan&shy;<lb/>tes &longs;e&longs;e in E. <!-- KEEP S--></s>
            <s id="s.001553">Mota igitur linea <lb/>AB ver&longs;us CD, nempe deor&longs;um <lb/>&amp; A quoque deor&longs;um ver&longs;us B, <lb/>contra vero B quidem &longs;ur&shy;<lb/>&longs;um ver&longs;us A, deor&longs;um vero <lb/>ver&longs;us C, erit B tardior A, &longs;ed <lb/>contrarium fit, quippe quod <lb/>longior &longs;it BD, per quam mouetur B ip&longs;a AC, per quam <lb/>mouetur A. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001554">His igitur non &longs;atisfacientibus veriorem &longs;i per im&shy;<lb/>becillitatem no&longs;tram licuerit, huius effectus cau&longs;&longs;am in&shy;<lb/>ue&longs;tigabimus. </s>
            <s id="s.001555">Rationibus igitur &amp; veritate contra aucto&shy;<lb/>ritatem &amp; probabilitatem e&longs;t nobis pugnandum: quod &amp; <lb/>intrepide faciemus. </s>
          </p>
          <p type="main">
            <s id="s.001556">Dicimus igitur, in quouis parallelogrammo &longs;it illud <lb/>quadratum aut altera parte longius, vel idem Rhombus <lb/>Rhomboi&longs;ue &longs;emper mixtos motus proportione &longs;eruata <pb xlink:href="007/01/164.jpg"/>fieri per diametros. </s>
            <s id="s.001557">C&aelig;terum d&iacute;ametrorum ad latera <lb/>proportiones e&longs;&longs;e varias &lpar;quadratis exceptis, in quibus ea&shy;<lb/>dem e&longs;t &longs;emper&rpar; explorati&longs;&longs;imum. </s>
            <s id="s.001558">Illud quoque certum <lb/>e&longs;t, in rectangulis nunquam dari po&longs;&longs;e diametros lateri&shy;<lb/>bus vtcunque captis &aelig;quales, &longs;emper enim diametri re&shy;<lb/>ctis angulis &longs;ubtruduntur. </s>
            <s id="s.001559">In Rhombis vero &amp; Rhombo&shy;<lb/>idibus diametrorum ad latera proportiones variant. </s>
            <s id="s.001560">Dari <lb/>enim po&longs;&longs;unt diametri lateribus longiores item &aelig;quales, <lb/>&amp; lateribus quoque ip&longs;is breuiores. </s>
          </p>
          <p type="main">
            <s id="s.001561">Itaque diametrorum &amp; laterum varia adinuicem <lb/>ratione &longs;e habentibus, attentis proportionibus, <expan abbr="mixtor&umacr;">mixtorum</expan> <lb/>&amp; &longs;implicium motuum diuer&longs;a fiet, &amp; varia comparatio. <lb/></s>
            <s id="s.001562">in quadratis motus mixtus, qui per diametros &longs;emper ve&shy;<lb/>locior erit &longs;implici qui per latera, Idem quoque in altera <lb/>parte longiori, in quo mixti quidem motus per diametros <lb/>erunt velociores, &longs;implices vero qui per latera, tardiores <lb/><expan abbr="quid&emacr;">quidem</expan>, &longs;ed ex illis tardior qui per latus breuius. </s>
            <s id="s.001563">In Rhom&shy;<lb/>bis autem mixtus motus qui fit per diametros in&aelig;qualis. <lb/></s>
            <s id="s.001564">Velocior enim qui per longiorem diametrum, tardior <lb/>qui per breuiorem. </s>
            <s id="s.001565">Itaque &longs;implices motus punctorum <lb/>per latera ad eum qui fit per diametros non eodem pacto <lb/>&longs;e habent. </s>
            <s id="s.001566">Porro cum Rhomboides vari&aelig; &longs;int <expan abbr="diametror&umacr;">diametrorum</expan> <lb/>ad latera habitudines, varia quoque dari pote&longs;t propor&shy;<lb/>tio. </s>
            <s id="s.001567">aliquando enim diametri dari po&longs;&longs;unt lateribus maio&shy;<lb/>res quando que, alter eorum minor. </s>
            <s id="s.001568">Si autem Rhombus in <lb/>duos &longs;oluatur triangulos, alter diametrorum datur &aelig;qua&shy;<lb/>lis &aelig;qualibus lateribus &aelig;quicrurium triangulorum; <expan abbr="itaq;">itaque</expan> <lb/>in i&longs;tis mixti motus per diametros aequeveloces erunt &longs;im&shy;<lb/>plicibus, qui per latera longiora, velociores autem illis <lb/>qui per latera breuiora. </s>
            <s id="s.001569">His igitur hoc pacto non perfun&shy;<lb/>ctori&egrave; con&longs;ideratis, facile ex proprijs cau&longs;&longs;is, n&icirc; fallimur, <lb/>hocce Ari&longs;totelicum &amp; mirabile Problema &longs;oluitur. </s>
          </p>
          <pb xlink:href="007/01/165.jpg"/>
          <figure id="id.007.01.165.1.jpg" xlink:href="007/01/165/1.jpg"/>
          <p type="main">
            <s id="s.001570">E&longs;to enim Rhombus ABDC, <lb/>cuius diameter longior AD maior &longs;it <lb/>tum lateribus, tum etiam altera dia&shy;<lb/>metro BC. &longs;ecent autem &longs;e inuicem <lb/>diametri in E. <!-- KEEP S--></s>
            <s id="s.001571">Ducatur queue ip&longs;is AB, <lb/>CD, parallela FG &longs;ecans longiorem <lb/>diametrum AD, in H, breuiorem ve&shy;<lb/>ro BC in I. &amp; per I ip&longs;is BD AC paral&shy;<lb/>lela ducatur KIL, Cum ergo B mixto <lb/>motu per diametrum BC erit in I &amp; <lb/>A per diametrum AD, mixto &longs;imili&shy;<lb/>ter motu erit in H, &amp; quia motus mi&shy;<lb/>xti fiunt per diametros, vt dictum e&longs;t, <lb/>vt &longs;e habet AD ad BC, ita AE ad EB, per 15. propos. 5. elem. <lb/></s>
            <s id="s.001572">item vt AE ad EB, ita per 4. propo&longs;. 6. AH ad BI. e&longs;t enim <lb/>IH ip&longs;i AB parallela. </s>
            <s id="s.001573">Longior e&longs;t autem AH ip&longs;a BI, quip&shy;<lb/>pe quod AE longior &longs;it ip&longs;a EB. motus igitur mixtus pun&shy;<lb/>cti A per diametrum AD v&longs;que ad H velocior e&longs;t motu B, <lb/>per diametrum BC v&longs;que ad I. <!-- KEEP S--></s>
            <s id="s.001574">Mota igitur linea AB mo&shy;<lb/>uebuntur communia eius &amp; diametrorum BC, AD pun&shy;<lb/>cta, quibus &longs;ecantur &longs;emper diametrorum proportione <lb/>&longs;eruata. </s>
            <s id="s.001575">Quibus ita &longs;e habentibus, nil mirum e&longs;t punctum <lb/>A motum per AD velociorem e&longs;&longs;e mixto motu puncti B, <lb/>quod per minorem diametrum fertur BC. quod fuerat <lb/>demon&longs;trandum. </s>
            <s id="s.001576">quatenus vero ad &longs;ecundam problema&shy;<lb/>tis partem pertinet, dicimus Propo&longs;itionem non e&longs;&longs;e vni&shy;<lb/>uer&longs;alem. </s>
            <s id="s.001577">Si enim Rhombus detur, ex duobus &aelig;quilateris <lb/>triangulis con&longs;tans, breuior diameter lateribus erit aequa&shy;<lb/>lis, quare non mouebitur citius motu &longs;implici punctum <lb/>per latus ac faciat mixto per minorem diametrum, quod <lb/>vt mirum propo&longs;uerat Ari&longs;toteles. </s>
            <s id="s.001578">Si autem latus ip&longs;um <lb/>breuiori diametro &longs;it <expan abbr="l&omacr;gius">longius</expan>, nec mirum quoque erit &longs;im&shy;<lb/>plici motu moueri velocius quam mixto, quippe quod, vt <pb xlink:href="007/01/166.jpg"/>dictum e&longs;t, motus i&longs;ti &agrave; proportionibus linearum, per quas <lb/>mouentur, legem velocitatis atque tarditatis accipiant. <lb/></s>
            <s id="s.001579">H&aelig;c igitur nos circa hoc mirabile Ari&longs;totelicum proble&shy;<lb/>ma con&longs;iderare &longs;it &longs;atis. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001580">QV&AElig;STIO XXIV.<!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001581">Mirabilem aliam qu&aelig;&longs;tionem proponit Ari&longs;toteles, <lb/>qu&aelig; itidem ad mixtos motus pertinet. </s>
          </p>
          <p type="main">
            <s id="s.001582"><emph type="italics"/>Dubitatio est, quam ob cau&longs;&longs;am maior circulus &aelig;qualem minori <lb/>circulo circumuoluitur lineam, quando circa idem centrum fue&shy;<lb/>rint po&longs;iti. </s>
            <s id="s.001583">Seor&longs;um autem reuoluti quemadmodum alterius ma&shy;<lb/>gnitudo ad alterius magnitudinem &longs;e habet, ita &amp; illorum adin&shy;<lb/>uicem fiunt line&aelig;? </s>
            <s id="s.001584">Pr&aelig;terea vno etiam &amp; eodem vtri&longs;que exi&longs;ten&shy;<lb/>te centro. </s>
            <s id="s.001585">Aliquando quidem tanta &longs;it linea, quam conuoluuntur, <lb/>quantum minor per &longs;e conuoluitur circulus, quandoque vero quan&shy;<lb/>tum maior.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001586">H&aelig;c ille, qui vt prober maiorem circulum in &longs;ua ro&shy;<lb/>tatione maiorem lineam pertran&longs;ire, minorem vero mi&shy;<lb/>norem; ait &longs;en&longs;u cogno&longs;ci angulum maioris circuli, id e&longs;t, <lb/>eius qui maiorem habet circumferentiam, e&longs;&longs;e maiorem, <lb/>eius vero qui minorem, minorem. </s>
            <s id="s.001587">Ita autem &longs;e habere cir&shy;<lb/>cumferentias vt &longs;e habent anguli, &amp; eandem <expan abbr="proportion&emacr;">proportionem</expan> <lb/>habere per quas tum maior, tum minor circulus circum&shy;<lb/>uoluuntur. </s>
            <s id="s.001588">Ad quorum clariorem intelligentiam ea re&shy;<lb/>uocare oportet in memoriam, qu&aelig; dixit de maiorum cir&shy;<lb/>culorum ad minores circulos nutu. </s>
            <s id="s.001589">Hic enim, quod ibi <lb/>quoque fecerat, &longs;ectorem ip&longs;um angulum appellauit, an&shy;<lb/>gulum vero maiorem maioris circuli &longs;ectorem, &amp; mino&shy;<lb/>rem angulum minoris ip&longs;ius circuli &longs;ectorem dixit. </s>
            <s id="s.001590">Clau&shy;<lb/>dit igitur dicens: quoniam circumferenti&aelig; &longs;e habent vt <lb/>anguli, hoc e&longs;t, vt &longs;ectores, maior erit circumferentia ma&shy;<lb/>ioris circuli, &amp; ex con&longs;equenti maior linea, per quam cir-<pb xlink:href="007/01/167.jpg"/>cumuoluitur, ea per quam minor. </s>
            <s id="s.001591">Demon&longs;trationem ve&shy;<lb/>ro ex &longs;en&longs;u petijt. </s>
            <s id="s.001592">Sat autem erat &longs;i dixi&longs;&longs;et, ita &longs;e habere <lb/>circumferentias vt &longs;e habent diametri &longs;eu &longs;emidiametri, <lb/>&amp; ideo lineas in rotatione de&longs;criptas inuicem &longs;e habere vt <lb/>diametros. </s>
            <s id="s.001593">Ob&longs;curiu&longs;cul&egrave;, h&aelig;c &longs;ua figura o&longs;tendit Ari&longs;to&shy;<lb/>teles. <!-- KEEP S--></s>
            <s id="s.001594">Nos igitur claritatem amantibus, no&longs;tram aliquan&shy;<lb/>to, n&icirc; fallimur, clariorem, proponemus. </s>
          </p>
          <figure id="id.007.01.167.1.jpg" xlink:href="007/01/167/1.jpg"/>
          <p type="main">
            <s id="s.001595">E&longs;to circulus <lb/>maior ABCD, mi&shy;<lb/>nor FGHI, circa i&shy;<lb/>dem, &amp; commune <lb/><expan abbr="c&emacr;trum">centrum</expan> E. <!-- KEEP S--></s>
            <s id="s.001596">Circum&shy;<lb/>uoluatur maior ad <lb/>partes D. <!-- KEEP S--></s>
            <s id="s.001597">Sint <expan abbr="aut&emacr;">autem</expan> <lb/>diametri, maioris <lb/><expan abbr="quid&emacr;">quidem</expan> AEC, BED, <lb/>minoris ver&ograve; FEH, <lb/>GEI, fitque CD, <lb/>quadrans maioris, <lb/>HI vero minoris circuli. </s>
            <s id="s.001598">Moto igitur maiori circulo <expan abbr="&longs;ec&umacr;-dum">&longs;ecun&shy;<lb/>dum</expan> ab&longs;idem, cum D fuerit in K erit CK ip&longs;i CD &aelig;qualis, <lb/>fietque; DE ex puncto K perpendicularis ip&longs;i CK, eritque vbi <lb/>KO, &amp; quia punctum I e&longs;t in linea DE, erit I facta <expan abbr="quadr&atilde;-tis">quadran&shy;<lb/>tis</expan> rotatione in linea KO vbi L, centrum vero E in ip&longs;a <lb/>KO, vbi O. <!-- KEEP S--></s>
            <s id="s.001599">Reuoluto igitur quadrante maioris, &amp; confe&shy;<lb/>cto &longs;patio CK minoris circuli quadrans HI conficiet &longs;pa&shy;<lb/>tium HL, quod ip&longs;i CK &longs;patio e&longs;t &aelig;quale. </s>
            <s id="s.001600">quod autem in <lb/>quadrantibus fit, in totis etiam fit circulis. </s>
            <s id="s.001601">Motus igitur <lb/>minor circulus circa centrum E, vnica rotatione &aelig;quauit <lb/>&longs;patium rotationis maioris circuli. </s>
            <s id="s.001602">Mirabile itaque e&longs;t mi&shy;<lb/>norem circulum eodem tempore &amp; circa idem centrum <lb/>circumuolutum, lineam pertran&longs;i&longs;&longs;e &aelig;qualem circumfe&shy;<lb/>renti&aelig; maioris circuli. </s>
            <s id="s.001603">Nec &longs;ecius admirationem facit ro&shy;<pb xlink:href="007/01/168.jpg"/>tato minori circulo, maiorem vna <expan abbr="circumuolut&umacr;">circumuolutum</expan> lineam <lb/>metiri circumferenti&aelig; minoris circuli &aelig;qualem. </s>
            <s id="s.001604">Rotetur <lb/>enim minoris circuli quadrans HI per rectam HL. erit i&shy;<lb/>gitur punctum I vbi M, &aelig;quali exi&longs;tente recta HM, ip&longs;i <lb/>curu&aelig; HI. <!-- KEEP S--></s>
            <s id="s.001605">Tunc autem facto motu centrum E erit vbi P, <lb/>exi&longs;tente EP, ip&longs;i HM &aelig;quali, demittatur autem ex P per <lb/>M, ip&longs;is HL CK perpendicularis PMN. </s>
            <s id="s.001606">Et quoniam in <lb/>eadem linea &longs;unt DIE, vbi E fuerit in PI erit in M, &amp; D in <lb/>N. quamobrem rotata quarta minoris circuli parte, ma&shy;<lb/>ioris interim circuli quadrans confecit &longs;patium CN &aelig;&shy;<lb/>quale ip&longs;i HM, hoc minus circuli quadranti HI, quod vti&shy;<lb/>que e&longs;t admirabile. </s>
          </p>
          <p type="main">
            <s id="s.001607">Porro cau&longs;&longs;am effectus huius mirifici diligenter qu&aelig;&shy;<lb/>rit Philo&longs;ophus, &amp; inueneram accurate explicat. </s>
            <s id="s.001608">Occur&shy;<lb/>rit autem primo ab&longs;urd&aelig; cuidam opinioni. </s>
            <s id="s.001609">Diceret enim <lb/>qui&longs;piam, ideo tardius moueri maiorem circulum, ad mo&shy;<lb/>tum minoris, quod interim <expan abbr="d&umacr;">dum</expan> minor moueretur, aliquas <lb/>inter rotandum moras interponeret, minor vero ad mo&shy;<lb/>tum maioris &longs;patia aliqua tran&longs;iliret, &amp; ita &longs;patiorum fieri <lb/>ad &aelig;quationem. </s>
            <s id="s.001610">Porro demon&longs;trationem aggre&longs;&longs;urus haec <lb/>a&longs;&longs;umit principia. </s>
            <s id="s.001611">Eandem aequalemue potentiam, <expan abbr="aliqu&atilde;">aliquam</expan> <lb/>magnitudinem tardius quidem mouere, aliquam vero <lb/>celerius. </s>
            <s id="s.001612">quod autem natum e&longs;t aptum moueri, tardius <lb/>moueri, &longs;i &longs;imul cum non apto nato moueri, moueatur, <lb/>quam &longs;i &longs;eparatim moueretur, celerius autem &longs;i non &longs;imul <lb/><figure id="id.007.01.168.1.jpg" xlink:href="007/01/168/1.jpg"/><lb/>cum eo moueatur. </s>
            <s id="s.001613">E&longs;to enim corpus A leue <lb/>quidem &amp; aptum natum moueri &longs;ur&longs;um, cui <lb/>connectatur B, aptum natum moueri deor&shy;<lb/>&longs;um, Si quis igitur mouere conetur corpus A <lb/>&longs;ur&longs;um difficilius mouebit, &amp; tardius <expan abbr="iunct&umacr;">iunctum</expan> <lb/>nempe ip&longs;i B, quam &longs;i ab ip&longs;o e&longs;&longs;et <expan abbr="&longs;ei&umacr;ctum">&longs;eiunctum</expan>. <lb/></s>
            <s id="s.001614">Praeterea quod non &longs;uo, &longs;ed alieno motu mo&shy;<lb/>uetur, impo&longs;&longs;ibile e&longs;&longs;e plus eo moueri qui <pb xlink:href="007/01/169.jpg"/>mouet, &longs;iquidem non &longs;uo, &longs;ed alieno motu mouetur. </s>
            <s id="s.001615">Mo&shy;<lb/>to igitur &longs;uo motu maiori circulo, minor non &longs;uo moue&shy;<lb/>tur, &longs;ed motu maioris circuli, &amp; ideo non plus mouetur <lb/>quam ille moueatur, mouetur autem maiori &longs;patio quam <lb/>ex &longs;e moueretur, propterea quod maior &longs;it maioris circu&shy;<lb/>li, &agrave; quo &longs;imul defertur, circumferentia. </s>
            <s id="s.001616">Item &longs;i minor &longs;uo <lb/>motu circumuoluatur, maiorem feret &longs;ecum, &amp; ideo non <lb/>plus in &longs;ua rotatione mouebitur maior, quam ip&longs;e minor <lb/>circulus moueatur. </s>
            <s id="s.001617">Summa rei haec e&longs;t, alterum ferri ab al&shy;<lb/>tero &amp; latum ad ferentis &longs;patium moueri. </s>
            <s id="s.001618">Licet enim al&shy;<lb/>tero moto, alter interim moueatur, nihil refert. </s>
            <s id="s.001619">E&longs;t enim <lb/>ac &longs;i is qui fertur, nullam habeat motionem, aut &longs;i eam ha&shy;<lb/>beat, ip&longs;a nequaquam vtatur. </s>
            <s id="s.001620">quod non fit &longs;i vterque &longs;e&shy;<lb/>paratim circa proprium centrum moueatur, tunc enim <lb/>magnus magnum, paruus vero paruum &longs;patium conficit. <lb/></s>
            <s id="s.001621">Hinc decipi ait Ari&longs;toteles illum, qui putat vtrum que cir&shy;<lb/>culum per &longs;e &longs;uper idem centrum in rotatione moueri, li&shy;<lb/>cet enim videatur, re vera non e&longs;t. </s>
            <s id="s.001622">Id enim vtique certum <lb/>e&longs;t, cum &agrave; maiori circulo minor fertur, circa maioris cen&shy;<lb/>trum motum fieri. </s>
            <s id="s.001623">Si vero maior &agrave; minori feratur circa mi&shy;<lb/>noris circuli centrum motum fieri. </s>
            <s id="s.001624">H&aelig;c fer&egrave; Philo&longs;ophi <lb/>e&longs;t mens, cuius &longs;olutionem e&longs;&longs;e certi&longs;&longs;imam, &amp; ex veris <lb/>cau&longs;&longs;is non dubitamus. </s>
          </p>
          <p type="main">
            <s id="s.001625">Hinc ad aliam eamqueue certam a&longs;&longs;ertionem tran&longs;i&shy;<lb/>mus. </s>
            <s id="s.001626">Dicimus enim, nullam materialem <expan abbr="rot&atilde;">rotam</expan> circa axem <lb/>eidem affixum, dum rotatur, po&longs;&longs;e eundem locum &longs;eruare, <lb/>ni&longs;i cauum fiat, quod axem ip&longs;um recipiat, in tran&longs;uer&longs;a&shy;<lb/>rijs quibus rota &longs;u&longs;tinetur &amp; progre&longs;&longs;iuum axis motum <lb/>impediat. </s>
          </p>
          <p type="main">
            <s id="s.001627">E&longs;to enim rota ABCD, cuius centrum E, diametri <lb/>AEC, BED, e&longs;to alia minor rota GH, item minor KL, tum <lb/>minor NO, &amp; adhuc minor QR, circa idem centrum E. <lb/><!-- KEEP S--></s>
            <s id="s.001628">Rotetur itaque &longs;ecundum ab&longs;idem integri quadrantis <pb xlink:href="007/01/170.jpg"/><figure id="id.007.01.170.1.jpg" xlink:href="007/01/170/1.jpg"/><lb/>&longs;patium CD, eritque <lb/>D, in F, item &longs;i ex rota <lb/>GH, ex quadrante <lb/>HT, erit T in I. <!-- KEEP S--></s>
            <s id="s.001629">Ex a&shy;<lb/>lijs item minoribus in <lb/>M, P, S. erit <expan abbr="itaq;">itaque</expan> <expan abbr="lon-gi&longs;&longs;im&umacr;">lon&shy;<lb/>gi&longs;&longs;imum</expan> &longs;patium CF, <lb/><expan abbr="breui&longs;&longs;im&umacr;">breui&longs;&longs;imum</expan> vero RS, <lb/>Mota igitur rota cir&shy;<lb/>ca <expan abbr="circul&umacr;">circulum</expan> &longs;eu axem, <lb/>QR, maior rota &longs;pa&shy;<lb/>tio mouebitur RS, <lb/>quod &longs;i intra QR, circa centrum E alij infiniti imaginen&shy;<lb/>tur circuli, quo propio es centro fuerint, eo maioris rot&aelig; <lb/>progre&longs;&longs;us erit minor, donec ad centrum deueniatur, vbi <lb/>cum non &longs;it circulus, nullus fiet progre&longs;&longs;iuus motus, &longs;ed <lb/>circa ip&longs;um centrum nulla facta loci mutatione rotabi&shy;<lb/>tur. </s>
            <s id="s.001630">At cum nulla materialis rota circa lineam punctumue <lb/>imaginarium conuerti po&longs;&longs;it, ideo axi ferreo alteriu&longs;ue <lb/>materi&aelig; circa quem &amp; cum quo circumuoluatur rota, ca&shy;<lb/>uum &longs;emirotundum incidere oportet, in quo in&longs;ertus axis <lb/>dum conuertitur &agrave; loco in quo conuertitur, non recedat. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001631">QV&AElig;STIO XXV.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001632"><emph type="italics"/>Qu&aelig;ritur, Cur lectulorum &longs;pondas &longs;ecundum duplam faciant pro&shy;<lb/>portionem, hanc quidem &longs;ex pedum, vel paulo ampliorem, illam <lb/>vero trium. </s>
            <s id="s.001633">Item cur vectes funesue non &longs;ecundum <lb/>diametrum extendantur?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001634">Primam qu&aelig;&longs;tionis partem ita diluit Philo&longs;ophus, for&shy;<lb/>ta&longs;&longs;e tant&aelig; fieri &longs;olitos magnitudinis lectulos vt corpo&shy;<lb/>ribus &longs;int proportionem habentes, &amp; ideo fieri &longs;ecundum <lb/>&longs;pondas dupli longitudine nempe cubitorum quatuor, <lb/>latitudine vero duorum. </s>
          </p>
          <pb xlink:href="007/01/171.jpg"/>
          <p type="main">
            <s id="s.001635">No&longs;trates alia vtuntur proportione, &longs;e&longs;quialtera, vi&shy;<lb/>delicet, quam Gr&aelig;ci Hemioliam dicunt, communiter e&shy;<lb/>nim pedes quatuor latos faciunt plus minu&longs;ue, longos ve&shy;<lb/>ro circiter &longs;ex. </s>
            <s id="s.001636">quod ideo fit vt in eis duo corpora commo&shy;<lb/>dius cubare po&longs;&longs;int. </s>
            <s id="s.001637">Lecturi autem, de quibus loquitur <lb/>Philo&longs;ophus, ad vnum tantummodo &longs;u&longs;tinendum facti <lb/>videntur, quicquid tamen &longs;it, nullam fer&egrave; habet res ex <lb/>hac parte dubitationem. </s>
          </p>
          <p type="main">
            <s id="s.001638">Secunda qu&aelig;&longs;tionis &longs;ectio ea erat, Cur non <expan abbr="&longs;ecund&umacr;">&longs;ecundum</expan> <lb/>diametros funes extendantur? </s>
            <s id="s.001639">Re&longs;tium funiumue in le&shy;<lb/>ctulis muniendis v&longs;us non e&longs;t apud nos. </s>
            <s id="s.001640">etenim feretra <lb/>tantum, &longs;eu &longs;andapilas, quibus defunctorum corpora ef&shy;<lb/>feruntur, funibus ad ea &longs;u&longs;tinenda inteximus. </s>
          </p>
          <p type="main">
            <s id="s.001641">C&aelig;terum lectos tabulis &longs;eu a&longs;&longs;eribus &longs;ternimus, qui&shy;<lb/>bus &longs;accos paleis plenos imponimus, &longs;accis vero culcitras, <lb/>&amp; tormenta, ne tabularum durities cubantes offendat. <lb/></s>
            <s id="s.001642">Atqui in re facili multum labora&longs;&longs;e videtur Ari&longs;toteles, <lb/>tum etiam ob&longs;cure &amp; inuolute nimis qu&aelig;&longs;tionem tracta&longs;&shy;<lb/>&longs;e. </s>
            <s id="s.001643">Difficilem enim apud eum habet h&aelig;c explicationem, <lb/>tum ea quam diximus de cau&longs;&longs;a, tum etiam quod Gr&aelig;ca <lb/>lectio &amp; Latina ver&longs;io corrupta, vt apparet, pr&aelig; manibus <lb/>habeantur. </s>
            <s id="s.001644">Sane vt veritatem hoc loco vindicaret in lu&shy;<lb/>cem, egregie laborauit Picolomineus nec parum profe&shy;<lb/>cit. </s>
            <s id="s.001645">C&aelig;terum currentes non &longs;ecundum diametrum extru&shy;<lb/>dantur, triplicem affert Philo&longs;ophus rationem. </s>
            <s id="s.001646">Prima e&longs;t <lb/>vt &longs;pondarum ligna, minus di&longs;trahantur. </s>
            <s id="s.001647">Secunda, vt <expan abbr="p&omacr;-dus">pon&shy;<lb/>dus</expan> inde commodius &longs;u&longs;tineatur. </s>
            <s id="s.001648">Tertia, vt in ip&longs;a textura <lb/>minus re&longs;tium funiumue ab&longs;umatur. </s>
          </p>
          <p type="main">
            <s id="s.001649">Ad primam, cur exten&longs;is diametraliter funibus <expan abbr="&longs;p&omacr;-d&aelig;">&longs;pon&shy;<lb/>d&aelig;</expan> ip&longs;&aelig; di&longs;trahantur di&longs;cindanturue, nec ille nec alij do&shy;<lb/>cent. </s>
            <s id="s.001650">Ego autem demon&longs;trarem hoc pacto. </s>
          </p>
          <p type="main">
            <s id="s.001651">E&longs;to &longs;ponda ABCD, cuius longitudo AB, cra&longs;&longs;itudo <lb/>AC, in ea foramen vtrinque pertinens EF, re&longs;tis per fora-<pb xlink:href="007/01/172.jpg"/><figure id="id.007.01.172.1.jpg" xlink:href="007/01/172/1.jpg"/><lb/>men inditus GFE, &longs;itque E pars &longs;eu ca&shy;<lb/>put exterius, quod nodo in E di&longs;tine&shy;<lb/>tur. </s>
            <s id="s.001652">Sit autem &longs;pond&aelig; lignum iuxta <lb/>longitudinem vt natura a&longs;&longs;olet &longs;ci&longs;&longs;ile. <lb/></s>
            <s id="s.001653">Vis qu&aelig;dam, fune ita extento applice&shy;<lb/>tur in G, quae funem ip&longs;um ad &longs;e violen&shy;<lb/>ter trahat. </s>
            <s id="s.001654">non di&longs;cindetur idcirco <lb/>&longs;ponda eo quod non diametraliter fu&shy;<lb/>nis extendatur. </s>
            <s id="s.001655">Modo facta capitis G <lb/>translatione in H, trahatur valide fu&shy;<lb/>nis, fiet autem pre&longs;&longs;io valida in F. ibi e&shy;<lb/>n&igrave;m impedimentum facit angulus, ne funis ip&longs;a dum tra&shy;<lb/>hitur, rectitudinem a&longs;&longs;equatur. </s>
            <s id="s.001656">Itaque vi pr&aelig;ualente, li&shy;<lb/>gno vero &longs;ci&longs;&longs;ili, minus re&longs;i&longs;tente, funis, a&longs;&longs;ecuta rectitudi&shy;<lb/>ne, fiet in HIE &longs;ci&longs;&longs;a &longs;ponda ad <expan abbr="qu&atilde;titatem">quantitatem</expan> trianguli FIE, <lb/>quod fuerat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.001657">Cur autem funes ab angulo in angulum exten&longs;&aelig; mi&shy;<lb/>nus commode pondus &longs;u&longs;tineant, &longs;atis patet. </s>
            <s id="s.001658">quo enim fu&shy;<lb/>nis <expan abbr="l&omacr;gior">longior</expan>, eo debilior, &amp; pre&longs;&longs;io qu&aelig; in medio fit, ea vide&shy;<lb/>licet parte qu&aelig; ab extremis e&longs;t remoti&longs;&longs;ima, magis funem <lb/>fatigat. </s>
            <s id="s.001659">Longiores autem funes &longs;unt qu&aelig; diametraliter <lb/>extenduntur. </s>
          </p>
          <figure id="id.007.01.172.2.jpg" xlink:href="007/01/172/2.jpg"/>
          <p type="main">
            <s id="s.001660">Quatenus ad <expan abbr="terti&atilde;">tertiam</expan> <lb/>rationem pertinet, hoc <lb/>pacto funes intexit <lb/>Philo&longs;oph^&lcub;9}. E&longs;to lectu&shy;<lb/>lus cum &longs;uis <expan abbr="&longs;p&omacr;dis">&longs;pondis</expan> AB <lb/>CD, cuius &longs;ponda AD, <lb/>&longs;it pedum &longs;ex, AB vero <lb/><expan abbr="tri&umacr;">trium</expan>, Diuidatur AD bi&shy;<lb/>far&iacute;am in E &amp; BC in F. item AE in tres AG, GH, HE &amp; in <lb/>totidem ED, nempe EL, LM, MD. </s>
            <s id="s.001661">Similiter medietas al&shy;<lb/>terius <expan abbr="&longs;p&omacr;d&aelig;">&longs;pond&aelig;</expan> BF in tres partes di&longs;tinguatur BN, NO, OF, <pb xlink:href="007/01/173.jpg"/>&amp; FC &longs;imiliter in tres FI, IK, KC, tum altero funis capite <lb/>in ducto per foramen A, ibique probe firmato, indatur per <lb/>F, inde per I, po&longs;tea per GHK CE, &amp; in E probe alligetur: <lb/>Erunt igitur funis quatuor partes &aelig;quales AF, IG, HK, <lb/>EC, quibus adijciuntur particul&aelig; cadentes extra, qu&aelig; <lb/>&longs;unt FI, GH, KC. </s>
            <s id="s.001662">Po&longs;t h&aelig;c alterius funis principium per <lb/>foramen traijcitur, quod e&longs;t in angulo B. <!-- KEEP S--></s>
            <s id="s.001663">Deinde per E, in&shy;<lb/>de per L, N, O, M, D, F &amp; in F probe vincitur, &amp; nodo fa&shy;<lb/>cto obfirmatur. </s>
            <s id="s.001664">Erunt igitur ali&aelig; quatuor alterius funis <lb/>partes, tum inter &longs;e, tum etiam &longs;upra dictis &aelig;quales, nem&shy;<lb/>pe BE, NL, OM, FD, quibus ill&aelig; pariter adijciuntur par&shy;<lb/>ticul&aelig;, qu&aelig; cadat extra, videlicet EL, NO, MD. <expan abbr="quoni&atilde;">quoniam</expan> <lb/>igitur quadratis ex BA, AE &aelig;quale e&longs;t quadratum BE, erit <lb/>BE quadratum 18. cuius latus radixue 4 1/3 quam proxime. <lb/></s>
            <s id="s.001665">Sunt autem huius longitudinis funes &aelig;quales octo. </s>
            <s id="s.001666">Ea&shy;<lb/>rum igitur &longs;imul &longs;umptarum longitudo erit pedum 34 2/3 vel <lb/>circiter, quibus &longs;i ad dantur pedes &longs;ex funium qui cadunt <lb/>extra, erit re&longs;tis totius longitudo expan&longs;a pedum 40 2/3 plus <lb/>minu&longs;ue. </s>
            <s id="s.001667">Picolomineus vero ait 34 2/3, omi&longs;it enim particu&shy;<lb/>las illas &longs;ex, qu&aelig;, vt diximus, cadunt extra. </s>
            <s id="s.001668">Idem rationem <lb/>funium diametraliter exten&longs;arum in idem, ait e&longs;&longs;e longi&shy;<lb/>tudinis pedum 40 1/2. Hic autem eas <expan abbr="quoq;">quoque</expan> particulas pr&aelig;&shy;<lb/>termittit, qu&aelig; extra cadunt. </s>
            <s id="s.001669">Itaque his additis clare pa&shy;<lb/>tet, plus re&longs;tium in&longs;umi diametraliter ip&longs;is, quam latera&shy;<lb/>liter exten&longs;is. </s>
            <s id="s.001670">C&aelig;terum ratio, qua Philo&longs;ophus h&aelig;c pro&shy;<lb/>bare conatur, adeo e&longs;t mutila, inuoluta, ob&longs;cura, vt Delio <lb/>pror&longs;us, vt aiunt, indigeat natatore. </s>
            <s id="s.001671">Huius loci in explica&shy;<lb/>bilem difficultatem, vidit Picolomineus, qui idcirco at&shy;<lb/>te&longs;tatus e&longs;t, interpretes in hac exponenda fui&longs;&longs;e halluci&shy;<lb/>natos. </s>
            <s id="s.001672">Certe Gr&aelig;ca lectio ver&longs;ione ip&longs;a Latina non e&longs;t <lb/>clarior. </s>
            <s id="s.001673">Nos interim ne inutilem fer&egrave; &longs;peculationem ni&shy;<lb/>mia diligentia, eaque forta&longs;&longs;e fru&longs;tranea pro&longs;equamur, a&shy;<lb/>lijs difficultatem hanc di&longs;&longs;oluendam aut ceu Gordij no&shy;<pb xlink:href="007/01/174.jpg"/>dum gladio &longs;cindendo relinquemus. </s>
            <s id="s.001674">Sed interim &longs;ubit <lb/>mirari, cur veteres vtiliori modo pr&aelig;termi&longs;&longs;o, <expan abbr="inutilioi&emacr;">inutiliorem</expan> <lb/>fuerint amplexati. </s>
            <s id="s.001675">Poterant enim reticulatim hoc per li&shy;<lb/>neas lateribus &aelig;quidi&longs;tantes intexere. </s>
          </p>
          <figure id="id.007.01.174.1.jpg" xlink:href="007/01/174/1.jpg"/>
          <p type="main">
            <s id="s.001676">E&longs;to enim lectulus <lb/>eiu&longs;dem dimen&longs;ionis <lb/>ABCD, in cuius latere <lb/>AD &longs;int foramina quin&shy;<lb/>que E, F, G, H, I, totidem <lb/>in latere oppo&longs;ito QP, <lb/>ONM. </s>
            <s id="s.001677">Duo vero in la&shy;<lb/>tere breuiori AB, nempe <lb/>RS, &amp; toti dem in oppo&longs;ito KL incipiatur exten&longs;io &agrave; fora&shy;<lb/>mine E, per QP, F, GON, HIM &amp; in M funis obfirmetur, <lb/>tum alterius funis caput in datur &longs;i lib et per K, &amp; inde per <lb/>S, R, L &amp; in L con&longs;tringatur. </s>
            <s id="s.001678">Sunt autem omnes EQ, FP, <lb/>GO, NN, IM, pedum quindecim, quibus &longs;i addantur KS, <lb/>RL, &longs;inguli pedum &longs;ex erunt pedum xxvii. </s>
            <s id="s.001679">quibus adiectis <lb/>particulis extra cadentibus QP, FG, ON, HI, &amp; RS, erit <lb/>integra &longs;umma pedum xxxii. </s>
            <s id="s.001680">Vide igitur quantum hinc <lb/>minus in&longs;umatur re&longs;tium quam eo modo, quem proba&shy;<lb/>uit, &amp; ceu vtiliorem propo&longs;uit Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.001681">Pr&aelig;terea vali&shy;<lb/>di&longs;&longs;imum e&longs;t hoc textur&aelig; opus nec ex eo fit vera &longs;ponda&shy;<lb/>rum di&longs;tractio &longs;ci&longs;&longs;ioue, quibus haud parum obnoxia e&longs;t <lb/>ea ratio, quam pr&aelig;fert ip&longs;e Philo&longs;ophus. <!-- KEEP S--></s>
            <s id="s.001682">Concludimus i&shy;<lb/>gitur, aut nos eius verba &amp; &longs;en&longs;um non intellexi&longs;&longs;e, aut <lb/>veteres ip&longs;os, quorum v&longs;um ip&longs;e explicat, rei, quam nos <lb/>proponimus, naturam &amp; commoditatem &lpar;quod ta&shy;<lb/>men vix credibile e&longs;t&rpar; igno&shy;<lb/>rare. </s>
          </p>
          <pb xlink:href="007/01/175.jpg"/>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001683">QV&AElig;STIO XXVI.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001684"><emph type="italics"/>Proponitur &agrave; Philo &longs;opho examinandum, Cur difficilius &longs;it, langa <lb/>ligna ab extremo &longs;uper humeros ferre, quam &longs;ecundum me&shy;<lb/>dium, &aelig;quali exi&longs;tente pondere?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001685">Dvo h&icirc;c con&longs;iderat, vibrationem, &amp; pondus. </s>
            <s id="s.001686">Ait enim <lb/>primo fieri po&longs;&longs;e, procera ligna vibratione impedien&shy;<lb/>te, difficilius ferri. </s>
            <s id="s.001687">Qu&aelig;rerer autem qui&longs;piam, &lpar;ip&longs;e enim <lb/>id reticet&rpar; cur vibratio h&aelig;c ferenti &longs;it nocua. </s>
            <s id="s.001688">Nos itaque <lb/>id expli&ccedil;are conabimur. </s>
          </p>
          <figure id="id.007.01.175.1.jpg" xlink:href="007/01/175/1.jpg"/>
          <p type="main">
            <s id="s.001689">E&longs;to igitur lignum <lb/>oblongum, flexile, &amp; vt <lb/>ita dicam, vibrabile <lb/>AB, imponatur hume&shy;<lb/>ro, eique h&aelig;reat in C, <lb/>manu vero &longs;u&longs;tineatur facta compre&longs;&longs;ione in B. <!-- KEEP S--></s>
            <s id="s.001690">Nutet i&shy;<lb/>gitur &amp; vibretur, in ip&longs;a vibratione, ad partem A. <!-- KEEP S--></s>
            <s id="s.001691">Sit au&shy;<lb/>tem centrum grauitatis eius D, Lignum igitur in ip&longs;a vi&shy;<lb/>bratione de&longs;cendet &longs;ua pre&longs;&longs;us grauitate in E, tum facta <lb/>ligni con&longs;tipatione in ea parte qu&aelig; e&longs;t inferius inter C &amp; <lb/>D, &amp; inde re&longs;i&longs;tentia, eodem fere impetu quo de&longs;cende&shy;<lb/>rat, repul&longs;um per D, nec enim in &longs;ua rectitudine &longs;tabit, a&shy;<lb/>&longs;cendet in F, facta iterum materi&aelig; con&longs;tipatione inter C <lb/>&amp; F. <!-- KEEP S--></s>
            <s id="s.001692">Mouebitur igitur lignum &longs;ua grauitate, motu fre&shy;<lb/>quenti&longs;&longs;imo, &longs;ur&longs;um deor&longs;um, &amp; is interim qui lignum hu&shy;<lb/>mero fert, procedit antror&longs;um, impedit igitur motus i&longs;te, <lb/>qui fit &longs;ur&longs;um deor&longs;um lationem, qu&aelig; fit ad anteriora; La&shy;<lb/>torem ip&longs;um quodammodo retrahens. </s>
            <s id="s.001693">Si autem medio <lb/>ligno &longs;upponatur humerus, eo quod vibratio &longs;it minor. <lb/></s>
            <s id="s.001694">breuiores enim partes &longs;unt, qu&aelig; &agrave; med&iacute;o ad extrema mi&shy;<lb/>nus &agrave; vibratione remorabitur ferens. </s>
          </p>
          <p type="main">
            <s id="s.001695">Quoniam autem non &longs;ola vibratio in hoc lationis <lb/>modo, nempe ex ligni extremitate difficultatem facit, ait <pb xlink:href="007/01/176.jpg"/>Philo&longs;ophus, forte id fieri, quoniam licet nihil inflecta&shy;<lb/>tur, neque multam habeat longitudinem, difficilius <expan abbr="tam&emacr;">tamen</expan> <lb/>&longs;it ad ferendum ab extremo, eo quod facilius eleuetur ex <lb/>medio quam ab extremis, &amp; ideo &longs;ic ferre &longs;it facilius. <lb/></s>
            <s id="s.001696">Cur autem ex medio facilius eleuetur, cau&longs;&longs;am e&longs;&longs;e ait, <lb/>quod eleuato medio ligno extrema &longs;e&longs;e inuicem &longs;u&longs;pen&shy;<lb/>dant, &amp; altera pars alteram bene &longs;ubleuet. </s>
            <s id="s.001697">Medium enim <lb/>fieri velut centrum, vbi is &longs;upponit humerum qui eleuat <lb/>aut fert. </s>
            <s id="s.001698">Extremorum autem interim altero depre&longs;&longs;o al&shy;<lb/>terum &longs;u&longs;tolli. </s>
            <s id="s.001699">Nos interim Mechanicis principijs, quod <lb/>ip&longs;e non fecit, rem clariorem efficiemus. </s>
          </p>
          <p type="main">
            <s id="s.001700">E&longs;to enim oblongum lignum AB, cui humerus &longs;up&shy;<lb/>ponatur in B, manus vero premendo &longs;u&longs;tinens in B. &longs;it au&shy;<lb/>tem ligni pars maxima AC, minima CB, inaioris autem ad <lb/>minorem proportio exempli gratia &longs;it &longs;excupla. </s>
            <s id="s.001701">Ad hoc i&shy;<lb/>gitur vt fiat &aelig;quilibrium inter potentiam &longs;u&longs;tinentem in <lb/>B, &amp; pondus comprimens in A, ita &longs;e habere oportet po&shy;<lb/>tentiam in B, ad pondus in A, vt &longs;e habet pars ligni AC ad <lb/><figure id="id.007.01.176.1.jpg" xlink:href="007/01/176/1.jpg"/><lb/>partem CD. <!-- KEEP S--></s>
            <s id="s.001702">E&longs;to igitur pon&shy;<lb/>dus in A, puta librarum &longs;ex. <lb/></s>
            <s id="s.001703">Erit igitur potentia qu&aelig; in B <lb/>ad hoc vt &longs;u&longs;tineat librarum <lb/>triginta &longs;ex, quas &longs;i addas <expan abbr="p&omacr;-deri">pon&shy;<lb/>deri</expan> in A, fiet humerus in C <lb/>&longs;u&longs;tinens pondus librarum quadraginta duo. </s>
            <s id="s.001704">Si autem <lb/>humerus medio ligno, hoc e&longs;t, in D &longs;upponatur, ad hoc vt <lb/>fiat &aelig;quilibrium, nece&longs;&longs;e erit potentiam in B e&longs;&longs;e &aelig;qua&shy;<lb/>lem ponderi in A, quod e&longs;t &longs;ex, quare humerus &longs;u&longs;tinebit <lb/>duodecim. </s>
            <s id="s.001705">Vnde patet, longe difficilius portari lignum <lb/>ex C extremo, quam ex D medio; quod Mechanice fue&shy;<lb/>rat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.001706">Po&longs;&longs;umus &amp; aliter idem o&longs;tendere. </s>
            <s id="s.001707">Intelligatur e&shy;<lb/>nim ij&longs;dem &longs;uppo&longs;itis, vectem quidem e&longs;&longs;e AB, cuius ful-<pb xlink:href="007/01/177.jpg"/>cimentum quidem B, pondus A, potentia &longs;u&longs;tinens in C, <lb/>nempe inter fulcimentum &amp; pondus. </s>
            <s id="s.001708">Res igitur ad eum <lb/>vectis v&longs;um reducitur, de quo G. <!-- REMOVE S-->Vbaldus tractatu de Ve&shy;<lb/>cte, propo&longs;. 3.</s>
            <s id="s.001709">Quare vtile o&longs;tendit, ita &longs;e habere oportet <lb/>potentiam &longs;u&longs;tinentem ad pondus, vt totus vectis ad par&shy;<lb/>tem eius qu&aelig; &agrave; potentia ad fulcimentum. </s>
            <s id="s.001710">Ita igitur &longs;e ha&shy;<lb/>bebit pre&longs;&longs;io, qu&aelig; fit in C ad pondus in A, vt totus vectis <lb/>AB ad partem eius CB, qu&aelig; &agrave; potentia ad fulcimentum. <lb/></s>
            <s id="s.001711">Erit igitur potentia &longs;eptupla ponderi, &amp; ideo &longs;u&longs;tinebit <lb/>pondus librarum quadraginta duarum. </s>
            <s id="s.001712">quod fuerat o&shy;<lb/>&longs;tendendum. </s>
          </p>
          <p type="main">
            <s id="s.001713">Hinc alia qu&aelig;&longs;tio huic affinis &longs;oluitur, Cur ha&longs;ta &longs;a&shy;<lb/>ri&longs;&longs;aue &longs;olo iacens manu ad alteram extremitatum ap&shy;<lb/>pren&longs;a difficillime extollatur? </s>
          </p>
          <figure id="id.007.01.177.1.jpg" xlink:href="007/01/177/1.jpg"/>
          <p type="main">
            <s id="s.001714">E&longs;to igitur &longs;ari&longs;&longs;a ha&shy;<lb/>&longs;taue iacens AB, cuius ex&shy;<lb/>tremitati A manus ad &longs;u&shy;<lb/>&longs;tollendum applicetur, &longs;it <lb/>autem pars qu&aelig; digitis capitur AC, qu&aelig;ritur cur pars re&shy;<lb/>liqua CB difficillime &longs;u&longs;tollatur? </s>
            <s id="s.001715">Facile dubitatio ex pr&aelig;&shy;<lb/>demon&longs;tratis &longs;oluitur. </s>
            <s id="s.001716">E&longs;t enim C fulcimentum, &longs;upponi&shy;<lb/>tur enim loco, pugno ad &longs;u&longs;tollendum clau&longs;o, digitus in&shy;<lb/>dex, potentia autem premens in A, vt &longs;uperet grauitatem <lb/>CB, e&longs;t manus ip&longs;ius corpus, hoc e&longs;t illa manus ip&longs;ius pars, <lb/>qua pondus facta &longs;uppre&longs;&longs;ione &longs;u&longs;tollitur. </s>
            <s id="s.001717">E&longs;t igitur AB <lb/>vectis, cuius fulcimentum C, pondus B, potentia A, <expan abbr="Itaq;">Itaque</expan> <lb/>quoniam maxima e&longs;t proportio BA ad AC, maximam e&longs;&shy;<lb/>&longs;e oportet potentiam pondus &longs;u&longs;tollentem in C. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001718">Huc etiam illud pertinet, Cur ha&longs;ta &longs;olo iacente, &longs;i <lb/>alterum extremorum manu &longs;u&longs;tollatur, alterum vero ve&shy;<lb/>loci&longs;&longs;ime &longs;ur&longs;um vibretur, &amp; eodem tempore manus ha&shy;<lb/>&longs;t&aelig; &longs;ic vibrat&aelig; &longs;upponatur, haud magna difficultate ha&longs;t&aelig; <lb/>ad perpendiculum fit erectio. </s>
          </p>
          <pb xlink:href="007/01/178.jpg"/>
          <figure id="id.007.01.178.1.jpg" xlink:href="007/01/178/1.jpg"/>
          <p type="main">
            <s id="s.001719">Sit enim ha&longs;ta AB, qu&aelig; <lb/>manu ex B capta eleuetur in <lb/>C, &amp; fiat in AC, tum facta ex <lb/>C partis A veloci vibratione, <lb/>ip&longs;a extremitas A transferatur <lb/>in D, &longs;itque vbi CD, tum velo&shy;<lb/>ci manus depre&longs;&longs;ione extremi&shy;<lb/>tas C transferatur in E, <expan abbr="fiatq;">fiatque</expan> <lb/>EF horizonti perpendicularis; <lb/>quod vbi factum fuerit, erunt <lb/>in eadem linea qu&aelig; ad centrum mundi, manus ip&longs;a qu&aelig; <lb/>&longs;u&longs;tinet, &amp; grauitatis ip&longs;ius centrum G, quare manus ip&longs;a <lb/>facta vibratione tantum portat, quantum pr&aelig;ci&longs;e ip&longs;ius <lb/>e&longs;t ha&longs;t&aelig; pondus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001720">QVAESTIO XXVII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001721"><emph type="italics"/>Dubitatur, Cur &longs;i valde procerum fuerit idem pondus, difficilius <lb/>&longs;uper humeros ge&longs;tatur, etiam&longs;i medium qui&longs;piam illud fe&shy;<lb/>rat quam &longs;i breuius &longs;it?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001722">Qv&aelig;&longs;tio h&aelig;c &longs;uperiori e&longs;t affinis. </s>
            <s id="s.001723">Ait autem Philo&longs;o&shy;<lb/>phus, cau&longs;&longs;am non e&longs;&longs;e id, quod in pr&aelig;cedenti qu&aelig;&shy;<lb/>&longs;tione dixerat, &longs;ed vibrationem: quo enim longiora &longs;unt <lb/>ligna, eo magis eorum extrema vibrantur, debiliora enim <lb/>&longs;unt &amp; &agrave; medio remotiora, quare &longs;uopte pondere facilius <lb/>nutant. </s>
            <s id="s.001724">Si autem breuiora &longs;int ea cau&longs;&longs;a ce&longs;&longs;ante minor <lb/>fit aut nulla vibratio, quare breuiora feruntur facilius. <lb/></s>
            <s id="s.001725">Dupliciter autem vibratione ip&longs;a, portans offenditur, <lb/>tum ex cau&longs;&longs;a quam in &longs;uperiori qu&aelig;&longs;tione con&longs;ideraui&shy;<lb/>mus, nempe quod motus &longs;ur&longs;um deor&longs;um a&longs;&longs;iduus, pro&shy;<lb/>gredientis motum impediat, tum etiam quod duplici <lb/>pre&longs;&longs;ione grauetur ferentis humerus, quod Philo&longs;ophus <lb/>non animaduertit. </s>
          </p>
          <p type="main">
            <s id="s.001726">Sit enim oblongum lignum AB, quod humero me-<pb xlink:href="007/01/179.jpg"/><figure id="id.007.01.179.1.jpg" xlink:href="007/01/179/1.jpg"/><lb/>dio loco &longs;u&longs;tineatur in C. <lb/>nutabunt ergo extrema AB, <lb/>&agrave; centro C, valde remota, <lb/>cadent autem &longs;imul A m D, <lb/>&amp; B in E trahere &longs;ecum conantes medium C, quare is qui <lb/>in C &longs;u&longs;tinet, non modo ligni &longs;u&longs;tinet pondus ex grauita&shy;<lb/>tis centro quod e&longs;t in C, &longs;ed impetum quoque in ip&longs;a ex&shy;<lb/>tremorum depre&longs;&longs;ione acqui&longs;itum ex ipsa violentia. </s>
            <s id="s.001727">Illud <lb/>autem &longs;ubtiliter con&longs;ideramus, portantem ex vibratione <lb/>per inter ualla deprimi &amp; &longs;ubleuari. </s>
            <s id="s.001728">fiat enim vibratum li&shy;<lb/>gnum ex contrario motu, vbi FCG. alleuiabit igitur eo <lb/>ca&longs;u portantem, &longs;iquidem impetus ex motu ip&longs;o acqui&longs;i&shy;<lb/>tus, medium C trahat ad &longs;uperiora. </s>
            <s id="s.001729"><expan abbr="Itaq;">Itaque</expan> cum e&longs;t in DCE <lb/>portans plus &longs;u&longs;tinet in ACD, &aelig;quale, in FCG minus, <lb/>quod vtique demon&longs;trandum fuerat. </s>
            <s id="s.001730">E&longs;t autem qu&aelig;&longs;tio <lb/>h&aelig;c illi familiaris, quam 16. loco explicauimus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001731">QVAESTIO XXVIII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001732"><emph type="italics"/>Qu&aelig;ritur, Cur iuxta puteos celonia faciunt eo quo vi&longs;untur mo&shy;<lb/>do? </s>
            <s id="s.001733">Ligno enim plumbi adiungunt pondus, cum alioquin vas <lb/>ip&longs;um &amp; plenum &amp; vacuum pon&shy;<lb/>dus habeat.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001734">Re&longs;pondet optime Philo&longs;ophus, hauriendi opus duo&shy;<lb/>bus temporibus diuidi, nempe dum vas ip&longs;um vacuum <lb/>demittitur, dum que extrahitur plenum: Contingere au&shy;<lb/>tem, vacuum facile demitti, plenum autem difficulter ex&shy;<lb/>trahi. </s>
            <s id="s.001735">Expedire nihilominus tardius, hoc e&longs;t difficilius di&shy;<lb/>mitti vt facilius extrahatur, plumbo nempe coadiuuante, <lb/>&amp; &longs;ane Philo&longs;ophi &longs;olutio e&longs;t lucidi&longs;&longs;ima. </s>
            <s id="s.001736">Nos autem luci <lb/>ip&longs;i lucem aliquam adhuc afferre conabimur. </s>
          </p>
          <p type="main">
            <s id="s.001737">E&longs;to Celomum &lpar;Latine Tolenonem appellant&rpar; ABC, <lb/>cuius arrectarium BD, tran&longs;uer&longs;um lignum AC, quod <pb xlink:href="007/01/180.jpg"/><figure id="id.007.01.180.1.jpg" xlink:href="007/01/180/1.jpg"/><lb/>conuertitur, circa <expan abbr="p&umacr;ctum">punctum</expan> &longs;eu <lb/>fulcimentum B, pondus, plum&shy;<lb/>bumue, vbi A, &longs;itula E, funi ap&shy;<lb/>pen&longs;a CE. <!-- KEEP S--></s>
            <s id="s.001738">Dico rebus ita con&shy;<lb/>&longs;titutis difficilem quidem e&longs;&longs;e <lb/>vacu&aelig; &longs;itul&aelig; demi&longs;&longs;ionem, fa&shy;<lb/>cile vero eiu&longs;dem extractio&shy;<lb/>nem. </s>
            <s id="s.001739">Vectis diui&longs;i, &longs;itul&aelig;, ac <lb/>ponderis, ad hoc vt fiat &aelig;quili&shy;<lb/>brium, ca debet e&longs;&longs;e propor&shy;<lb/>tio, vt quemadmodum &longs;e habet AB ad BC, ita &longs;e habeat <lb/>plen&aelig; &longs;itul&aelig; pondus E ad ip&longs;um pondus A, &longs;uperabit ergo <lb/>pondus in A &longs;itulam vacuam in E nec fiet &aelig;quilibrium, i&shy;<lb/>taque vt vacua &longs;itula demittatur, tanta vis adhibenda e&longs;t <lb/>quantum e&longs;t ip&longs;ius aqu&aelig;, qua &longs;itula impletur pondus, qu&aelig; <lb/>vis dum apponitur difficilem, vt dicebamus, efficit &longs;itul&aelig; <lb/>vacu&aelig; demi&longs;&longs;ionem. </s>
            <s id="s.001740">Plena vero &longs;itula &longs;it &aelig;quilibrium, vn&shy;<lb/>de quantumuis pu&longs;illa vi adhibita, &longs;itula extrahitur, qua&longs;i <lb/>ex &longs;emetip&longs;a ponderis appen&longs;i virtute a&longs;cendens. </s>
            <s id="s.001741">Quan&shy;<lb/>tum igitur pondus dum vacua demittitur impedit, tan&shy;<lb/>tundem plena dum extrahitur, adiuuat. </s>
            <s id="s.001742">Quae cum ita &longs;int, <lb/>&longs;i paria &longs;unt difficultas in demittendo, &amp; facilitas in ex&shy;<lb/>trahendo, qu&aelig; ratio hoc in negotio vtilitatis? </s>
            <s id="s.001743">Sane &longs;itula <lb/>vacua, manu per funem facile demittitur, plena vero dif&shy;<lb/>ficile extrahitur, v&longs;u autem Celonij res <expan abbr="permut&atilde;tur">permutantur</expan>. </s>
            <s id="s.001744">Cor&shy;<lb/>poris enim proprij pondere, dum premit, adiuuatur de&shy;<lb/>mittens, qui per funem &longs;implicem extrahendo, ab eodem <lb/>proprij corporis pondere impediebatur. </s>
            <s id="s.001745">quod quidem ex <lb/>corporis pondere, auxilium, ingentem parit in extrahen&shy;<lb/>do commoditatem. </s>
          </p>
          <p type="main">
            <s id="s.001746">Quippiam &longs;imile accidit, aquas &egrave; puteis extrahen&shy;<lb/>tibus v&longs;u trochle&aelig;. </s>
            <s id="s.001747">Sit enim trochlea puteo imminens <lb/>ABCD, cuius centrum E &longs;u&longs;pen&longs;a quidem in A, funis, cui <pb xlink:href="007/01/181.jpg"/>&longs;itula &longs;u&longs;penditur FCABG, &longs;itula vero G. <!-- KEEP S--></s>
            <s id="s.001748">E&longs;t igitur dia&shy;<lb/>meter CED, in&longs;tar libr&aelig;, quare vt fiat &aelig;quilibrium nece&longs;&shy;<lb/>&longs;e e&longs;t capiti funis F, potentiam applicare, qu&aelig; &longs;it &aelig;qualis <lb/><figure id="id.007.01.181.1.jpg" xlink:href="007/01/181/1.jpg"/><lb/>pondere &longs;itul&aelig; aqua plen&aelig;, itaque extra&shy;<lb/>hens proprijs viribus <expan abbr="corpor&imacr;s">corporis</expan> pondus ad&shy;<lb/>ijciens facile &longs;itulam aqua plenam extra&shy;<lb/>hit, ex qua re magna extrahentibus fit <lb/>commoditas. </s>
            <s id="s.001749">Patet autem diuer&longs;o modo <lb/>extrahentes iuuare Celonium. <!-- KEEP S--></s>
            <s id="s.001750">&amp; Tro&shy;<lb/>chleam, ibi enim corporis mole adiuuatur <lb/>demittens vacuam, hic vero qui extrahit <lb/>plenam aqua &longs;itulam. </s>
          </p>
          <p type="main">
            <s id="s.001751">C&aelig;terum Celonij partem BC, qui &agrave; <lb/>fulcimento ad funem longe maiorem e&longs;&shy;<lb/>&longs;e oportet, ip&longs;a AB, vt &longs;itula in profundum po&longs;&longs;it demitti, <lb/>quamobrem ita &longs;e debet habere pondus in A, ad pondus <lb/>&longs;itul&aelig; plen&aelig;, vt &longs;e habet brachium &longs;eu pars BC, ad par&shy;<lb/>tem BA. <!-- KEEP S--></s>
            <s id="s.001752">Tunc enim ex permutata proportione efficitur <lb/>&aelig;quilibrium. </s>
          </p>
          <p type="main">
            <s id="s.001753">Illud addimus, nouum non ae&longs;&longs;e Architectis Mecha&shy;<lb/>nici&longs;que, tum hominum tum animalium vt commodius <lb/>machinas moueant, adhibere pondera corporum. </s>
            <s id="s.001754">Nec e&shy;<lb/>nim alia ratione mouentur Rot&aelig; ill&aelig;, quas ob hanc cau&longs;&shy;<lb/>&longs;am ambulatorias vocant; quarum v&longs;us ad Mangana, ad <lb/>extrahendas &egrave; puteis aquas, &amp; ad farinarias quoque mo&shy;<lb/>las agitandas adhibetur. </s>
          </p>
          <p type="main">
            <s id="s.001755">Porro Tollenonem bellicam Machinam &agrave; Celonio <lb/>tum forma tum pote&longs;tate nihil differre, videre e&longs;t apud <lb/>veteres Mechanicos, Heronem Byzantium, &amp; alios. </s>
            <s id="s.001756">apud <lb/>neotericos vero hac de re agunt Daniel Barbarus in Vi&shy;<lb/>truuium, &amp; Iu&longs;tus Lip&longs;ius in librum quem de bellicis <lb/>machinis edidit, eleganti&longs;&longs;i&shy;<lb/>mum. </s>
          </p>
          <pb xlink:href="007/01/182.jpg"/>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001757">QVAESTIO XXIX.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001758"><emph type="italics"/>Dubitatur, Cur quando &longs;uper ligno, aut huiu&longs;modi quopiam, duo <lb/>portauerint homines, idem pondus non &aelig;qualiter premun&shy;<lb/>tur, &longs;ed ille magis cui vicinius fuerit <lb/>pondus?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001759">Soluit Ari&longs;toteles, inquiens, lignum e&longs;&longs;e vectem, pon&shy;<lb/>dus vero fulcimentum; res qu&aelig; mouetur is qui ponde&shy;<lb/>ri e&longs;t proximior: mouens vero qui remotior. </s>
            <s id="s.001760">Itaque quo <lb/>magis remotus e&longs;t &agrave; pondere, hoc e&longs;t, &agrave; fulcimento is qui <lb/>mouet, eo violentius is premitur qui altera vectis parte <lb/>eaque breuiori, mouetur. </s>
          </p>
          <figure id="id.007.01.182.1.jpg" xlink:href="007/01/182/1.jpg"/>
          <p type="main">
            <s id="s.001761">E&longs;to lignum AB, pondus <lb/>C appen&longs;um in E, vicinius ex&shy;<lb/>tremo B quam ip&longs;i A, &longs;it <expan abbr="aut&emacr;">autem</expan> <lb/><expan abbr="port&atilde;tium">portantium</expan> alter quidem AF, <lb/>alter vero BG, Imaginemur <lb/>itaque locum E &agrave; pondere ita <lb/>figi &amp; deprimi, vt &longs;ur&longs;um qui&shy;<lb/>dem ferri nequaquam po&longs;&longs;it, <lb/>circa vero punctum E, ceu <lb/>circa centrum fulcimentum&shy;<lb/>ne ip&longs;um vectem conuerti. </s>
            <s id="s.001762">Lignum ergo AB vectis: mo&shy;<lb/>uens potentia A, pars vectis &agrave; potentia ad fulcimentum <lb/>AE pars eiu&longs;dem qu&aelig; &agrave; fulcimento ad rem motam EB, &amp; <lb/>quoniam quanto longior e&longs;t pars vectis EA ip&longs;a EB, eo fa&shy;<lb/>cilius potentia qu&aelig; e&longs;t in A, operatur in id quod e&longs;t in B, &longs;i <lb/>res ad proportiones redigatur, erit potentia in A, ad id <lb/>quod mouetur &longs;eu premitur in B, vt pars vectis EB ad par&shy;<lb/>tem EA, &longs;ed maior e&longs;t AE ip&longs;a EB, ergo maiorem partem <lb/>&longs;u&longs;tinet ponderis, &amp; plus premitur is qui in E, &amp; qui mo&shy;<lb/>uet in A. <!-- KEEP S--></s>
            <s id="s.001763">H&aelig;c fere Philo&longs;ophi e&longs;t &longs;ententia: Picolomi&shy;<lb/>neus vero Paraphra&longs;tes appo&longs;ite duos vectes in vnico li-<pb xlink:href="007/01/183.jpg"/>gno con&longs;iderat, alterum AB, alterum BA, in primo A e&longs;t <lb/>mouens B, motum in &longs;ecundo B, mouens A vero motum <lb/>in quibus vectibus &longs;emper idem &amp; commune fulcimen&shy;<lb/>tum E. <!-- KEEP S--></s>
            <s id="s.001764">Et quoniam in propo&longs;ito diagrammate breuior e&longs;t <lb/>pars vectis EB, qu&aelig;que &agrave; mouente ad fulcimentum, parte <lb/>illa qu&aelig; ab eodem fulc&igrave;mento ad rem motam, minus o&shy;<lb/>peratur B in A, quam A in B, &amp; ideo qui in B mouetur plus <lb/>premitur, contra vero quia maior e&longs;t pars EA ip&longs;a parte <lb/>EB, magis operatur qui in A in ip&longs;um B, quam econtra. </s>
            <s id="s.001765">Et <lb/>&longs;ane con&longs;ideratio h&aelig;c &longs;ubtilis e&longs;t &amp; ingenio&longs;a, &amp; qu&aelig; &longs;i <lb/>recte intelligatur, quatenus ad proportiones &amp; effectum <lb/>ip&longs;um demon&longs;trandum pertinet, &agrave; veritate ip&longs;a non ab&shy;<lb/>horret, Quicquid tamen &longs;it, Mechanice magis hoc pacto <lb/>qu&aelig;&longs;tio diluetur. </s>
            <s id="s.001766">Dicimus enim, pondus quidem vere e&longs;&shy;<lb/>&longs;e pondus, non autem fulcimentum, vt &longs;ibi fingebat Ari&shy;<lb/>&longs;toteles: lignum vero vectem, duo autem qui pondus &longs;u&shy;<lb/>&longs;tinent pro duplici fulcimento haberi, vtri&longs;que enim ve&shy;<lb/>ctis cum appen&longs;o pondere innititur. </s>
            <s id="s.001767">Pote&longs;t etiam alter <lb/>eorum pro potentia mouente, alter vero pro fulcimen&shy;<lb/>to, &amp; &longs;ic vici&longs;&longs;im. </s>
            <s id="s.001768">E&longs;t autem, quomodocunque res accipia&shy;<lb/>tur, pondus inter fulcimentum. </s>
            <s id="s.001769">&amp; potentiam. </s>
            <s id="s.001770">Quare ex <lb/>ijs qu&aelig; demon&longs;trauit G. Vbald. <!-- REMOVE S-->de hoc vectis genere lo&shy;<lb/>quens, vt &longs;e habet AE pars ad AB vectem totum, ita po&shy;<lb/>tentia qu&aelig; &longs;u&longs;tinet in B, ad pondus appen&longs;um in E, &amp; vt <lb/>BE ad BA ita potentia qu&aelig; &longs;u&longs;tinet in A ad pondus quod <lb/>in E. <!-- KEEP S--></s>
            <s id="s.001771">At minor e&longs;t proportio BE, ad BA, quam AE ad AB, <lb/>quare magis &longs;uperatur pondus in E &agrave; potentia qu&aelig; in A, <lb/>quam &agrave; potentia qu&aelig; in B, &amp; ideo plus ponderis &longs;u&longs;tinet <lb/>ferens in B, quam ferens in A, quod fuerat demon&longs;tran&shy;<lb/>dum. </s>
          </p>
          <p type="main">
            <s id="s.001772">Hinc colligimus, pondere in medio vecte appen&longs;o <lb/>ferentes &aelig;qualiter &longs;u&longs;tinere, propterea quod totius vectis <lb/>ad partes ip&longs;as proportio &longs;it eadem, vel &aelig;qualis. </s>
          </p>
          <pb xlink:href="007/01/184.jpg"/>
          <p type="main">
            <s id="s.001773">Pulchre autem dubitari pote&longs;t, an idem pror&longs;us con&shy;<lb/>tingat, &longs;i alterum eorum qui &longs;u&longs;tinent, &longs;it &longs;tatura quidem <lb/>procerior, alter vero humilior. </s>
          </p>
          <figure id="id.007.01.184.1.jpg" xlink:href="007/01/184/1.jpg"/>
          <p type="main">
            <s id="s.001774">Sit enim vectis AB, in cuius <lb/>medio pondus H libere appen&shy;<lb/>&longs;um ex C, alter portantium pro&shy;<lb/>cerior AD, humilior vero BE. &longs;it <lb/>autem horizontis planum DE, <lb/>demittatur &agrave; puncto Cad <expan abbr="horiz&omacr;-tem">horizon&shy;<lb/>tem</expan> perpendicularis, ip&longs;is vero <lb/>AD, BE, &aelig;quidi&longs;tans CF. <!-- KEEP S--></s>
            <s id="s.001775">Tran&longs;i&shy;<lb/>bit autem per ip&longs;ius ponderis, <lb/>grauitatis centrum H. Dico igi&shy;<lb/>tur, nil referre quatenus ad pondus &longs;u&longs;tinendum perti&shy;<lb/>net, vtrum portantes &longs;int &longs;tatura pares velne. </s>
            <s id="s.001776">Ducatur e&shy;<lb/>nim horizonti &aelig;quidi&longs;tans GB, &longs;ecans perpendicularem <lb/>CF in I. <!-- KEEP S--></s>
            <s id="s.001777">Quoniam igitur AG &aelig;quidi&longs;tans e&longs;t ip&longs;i CI erit <lb/>vt AC ad CB per 4. &longs;exti elem, ita GI ad IB. <!-- KEEP S--></s>
            <s id="s.001778">Sunt ergo GI, <lb/>IB inter &longs;e &aelig;quales. </s>
            <s id="s.001779">Intelligatur itaque pondus H, <expan abbr="&longs;olut&umacr;">&longs;olutum</expan> <lb/>&agrave; puncto C appen&longs;um e&longs;&longs;e libere ex puncto I, hoc e&longs;t, ex <lb/>medio vectis GB, &aelig;qualiter ergo diui&longs;um erit pondus in&shy;<lb/>ter portantes, licet alter procerior, alter vero &longs;tatura pu&shy;<lb/>milior, quod fuerat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.001780">Si autem pondus ita vecti alligatum &longs;it vt libere non <lb/>pendeat, vecte ex vna parte eleuato, ex altera vero de&shy;<lb/>pre&longs;&longs;o, grauitatis centrum ad eam partem verget qu&aelig; <lb/>magis ab horizonte attollitur, &amp; ad eam ip&longs;am partem <lb/>vectis &agrave; pondere ad &longs;u&longs;tinentem fit breuior. </s>
          </p>
          <p type="main">
            <s id="s.001781">E&longs;to enim vectis AB, cuius medium C, pondus vecti <lb/>in C alligatum CFG, cuius grauitatis centrum H eorum <lb/>qui portant procerior AB, humilior BE, horizontis <expan abbr="plan&umacr;">planum</expan> <lb/>DE. <!-- KEEP S--></s>
            <s id="s.001782">Demittatur per centrum H horizonti perpendicu&shy;<lb/>laris IHK, &longs;ecans vectem quidem in I, horizontis vero pla-<pb xlink:href="007/01/185.jpg"/><figure id="id.007.01.185.1.jpg" xlink:href="007/01/185/1.jpg"/><lb/>num in K. <!-- KEEP S--></s>
            <s id="s.001783">Po&longs;t h&aelig;c intelligatur pon&shy;<lb/>dus &longs;olutum quidem &agrave; puncto C, ap&shy;<lb/>pen&longs;um vero ex puncto I. <!-- KEEP S--></s>
            <s id="s.001784">Stabit igitur <lb/>ex definitione centri grauitatis nec &longs;i&shy;<lb/>tu &longs;uo mouebitur. </s>
            <s id="s.001785">Dico autem par&shy;<lb/>tem AI ip&longs;a IB e&longs;&longs;e breuiorem, hoc e&longs;t, <lb/>punctum I cadere inter C &amp; A. <!-- KEEP S--></s>
            <s id="s.001786">Si e&shy;<lb/>nim non cadat, vel cadet in C, aut in&shy;<lb/>ter C &amp; B, cadat autem &longs;i fieri pote&longs;t <lb/>in C. <!-- KEEP S--></s>
            <s id="s.001787">Erit igitur CHK horizonti perpendicularis, &longs;ed ei&shy;<lb/>dem perpendicularis AD. <!-- KEEP S--></s>
            <s id="s.001788">Erunt igitur BCK BAD anguli <lb/>inter &longs;e &aelig;quales, &longs;ed ip&longs;i BAD angulo &aelig;qualis e&longs;t CIH, <lb/>quare &amp; BCH ip&longs;i CIH &aelig;qualis erit. </s>
            <s id="s.001789">Producto igitur la&shy;<lb/>tere IC trianguli ICH erit exterior angulus &aelig;qualis inte&shy;<lb/>riori ex oppo&longs;ito, quod e&longs;t ab&longs;urdum. </s>
            <s id="s.001790">non ergo I cadet in <lb/>C. <!-- KEEP S--></s>
            <s id="s.001791">Eadem autem ratione mon&longs;trabitur non cadere inter <lb/>CB, cadet ergo inter CA, &amp; ideo minor AI ip&longs;a IB. <!-- KEEP S--></s>
            <s id="s.001792">Itaque <lb/>vt &longs;e habet BI ad BA, ita potentia in A ad pondus in I, &longs;ed <lb/>maiorem proportionem habet BI ad BA, quam IA ad AB. <lb/><!-- KEEP S--></s>
            <s id="s.001793">Ergo minor potentia requiretur in B quam in A, &amp; &longs;ane <lb/>pars IB re&longs;pondet potenti&aelig; &longs;u&longs;tinenti in A, at IA potenti&aelig; <lb/>&longs;u&longs;tinenti in B, minor e&longs;t autem AI ip&longs;a IB, ergo maior po&shy;<lb/>tentia requiritur in B, quam in A, quod fuerat demon&shy;<lb/>&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.001794">Hoc item concludetur, &longs;i portantes &longs;tatura quidem <lb/>pares fuerint, &longs;ed per planum ambulent horizonti accliue <lb/>aut decliue. </s>
            <s id="s.001795">Si enim pondus libere pendeat, vectis <expan abbr="parti&umacr;">partium</expan> <lb/>proportio non mutabitur; &longs;r autem libere non pendeat, <lb/>is magis laborabit qui in a&longs;cen&longs;u pr&aelig;ibit, minus vero qui <lb/>in de&longs;cen&longs;u. </s>
          </p>
          <p type="main">
            <s id="s.001796">Hinc quoque Carrucarum ratio pendet, qu&aelig; dupli&shy;<lb/>ci manubrio vnica rota vulgo &longs;unt in v&longs;u, pro vecte enim <lb/>habentur, cuius fulcimentum ad contactum plani &amp; ro&shy;<pb xlink:href="007/01/186.jpg"/>t&aelig;; potenti&aelig; vero ad extremitatem duplicis manubrij. <lb/></s>
            <s id="s.001797">Reducitur enim ad idem genus vectis, in quo pondus in&shy;<lb/>ter fulcimentum e&longs;t &amp; potentiam. </s>
            <s id="s.001798">quo igitur minor fue&shy;<lb/>rit proportio partis vectis qu&aelig; &agrave; centro grauitatis ad i&shy;<lb/>p&longs;um fulcimentum, ad totum vectem eo facilius pondus <lb/>eleuabitur. </s>
          </p>
          <p type="main">
            <s id="s.001799">Cur autem difficilime h&aelig; per accliue horizonti pla&shy;<lb/>num pellantur, duplici fit de cau&longs;&longs;a, tum quia grauitatis <lb/>centrum ad ip&longs;um portantem &longs;eu pellentem vergit, &amp; id&shy;<lb/>eo pars qu&aelig; a fulcimento ad centrum grauitatis ponderis <lb/>fit maior, tum etiam quoniam ip&longs;um graue contra &longs;ui na&shy;<lb/>turam &longs;ur&longs;us pellitur ferturque. </s>
          </p>
          <p type="main">
            <s id="s.001800">Qu&aelig;rere ad h&aelig;c qui&longs;piam po&longs;&longs;et, Cur Baiuli ma&shy;<lb/>gna ferentes pondera, curui in cedant? </s>
            <s id="s.001801">Dixerit autem ali&shy;<lb/>quis, ponderis grauitate eos deprimentis id fieri. </s>
            <s id="s.001802">Nos au&shy;<lb/>tem duplici item de cau&longs;&longs;a id fieri putamus, tum ea quam <lb/>con&longs;iderauimus, tum etiam alia, nempe vt grauitatis cen&shy;<lb/>trum ip&longs;ius ponderis quod &longs;u&longs;tinent, in perpendiculari <lb/>collocent, ne &longs;i extra ponatur is qui fert &agrave; centro extra <lb/>fulcimentum po&longs;ito, ad eam partem ad quam vergit tra&shy;<lb/>hatur, &amp; pondere ip&longs;o opprimatur. </s>
          </p>
          <p type="main">
            <s id="s.001803">Eadem de cau&longs;&longs;a fit quoque vt ij qui magna ponde&shy;<lb/>ra &longs;ini&longs;tro ferunt humero, in dextram partem inclinentur, <lb/>qui vero dextro, contrario modo &longs;e habeant, &aelig;quatur e&shy;<lb/>nim pondus eo pacto, &amp; grauitatis centrum in ip&longs;a per&shy;<lb/>pendiculari collocatur. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001804">QV&AElig;STIO XXX.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001805"><emph type="italics"/>Cur a&longs;&longs;urgentes omnes f&oelig;mori tibiam ad acutum angulum con&longs;ti&shy;<lb/>tuamus &amp; pectori thoraciue &longs;imiliter f&oelig;mur, quod n&icirc; fiat <lb/>haudquaquam &longs;urgere poterunt?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001806">Ait Philo&longs;ophus, forte id fieri, quod &aelig;qualitas &longs;it o&shy;<lb/>mnino quietis cau&longs;&longs;a, rectum vero angulum quietis <pb xlink:href="007/01/187.jpg"/>angulum e&longs;&longs;e, &amp; &longs;tationem facere, nec alia de cau&longs;&longs;a &longs;tan&shy;<lb/>tem ip&longs;i terr&aelig; e&longs;&longs;e perpendicularem, &amp; ideo caput &amp; pe&shy;<lb/>des in eadem linea habere, &longs;edentem vero non item. </s>
            <s id="s.001807"><expan abbr="T&umacr;c">Tunc</expan> <lb/>autem &agrave; &longs;e&longs;&longs;ione &longs;urrectionem fieri, cum caput &amp; pedes in <lb/>vna linea collocantur, quod &longs;ane fit cum pectus &amp; crura <lb/>acutum cum ip&longs;o f&oelig;more angulum faciunt. </s>
          </p>
          <figure id="id.007.01.187.1.jpg" xlink:href="007/01/187/1.jpg"/>
          <p type="main">
            <s id="s.001808">E&longs;to enim &longs;tans AB hori&shy;<lb/>zonti IBK perpendicularis, c&ugrave;&shy;<lb/>ius caput A, pedes vero B, &longs;edeat <lb/>modo &longs;itque eius cum capite <lb/>Thorax CD, f&oelig;mur DE, crura <lb/>EF, &longs;intque CDE, DEF anguli <lb/>recti, quibus ita con&longs;titutis non <lb/>&longs;unt in eadem linea caput C &amp; <lb/>pedes F. <!-- KEEP S--></s>
            <s id="s.001809">Surgere itaque non po&shy;<lb/>terit &longs;edens, propterea quod <lb/>partes omnes corpor&igrave;s non &longs;int <lb/>horizonti perpendiculares. </s>
            <s id="s.001810">Ad <lb/>hoc autem vt &longs;urrectio fiat, nece&longs;&longs;e e&longs;t vt &longs;edens retrahat <lb/>quidem pedes in H, &amp; pectore in clinato acutum cum f&oelig;&shy;<lb/>more angulum con&longs;tituat GDE, quo ca&longs;u fient in eadem <lb/>recta linea, eaque horizonti perpendiculari caput in G, <lb/>&amp; pedes in H, ex cuius &longs;itus natura commoda fiet ab ip&longs;o <lb/>&longs;edente &longs;urrectio. </s>
            <s id="s.001811">H&aelig;c fere, licet alijs ab eo verbis expli&shy;<lb/>cata, ip&longs;ius e&longs;t Philo&longs;ophi &longs;ententia; qu&aelig; licet vera &longs;it, non <lb/>tamen ex proprijs, hoc e&longs;t, Mechanicis principijs e&longs;t peti&shy;<lb/>ta. </s>
            <s id="s.001812">quod quidem nos facere conabimur. </s>
          </p>
          <p type="main">
            <s id="s.001813">Dicimus autem primo, &longs;edentem non ideo quie&longs;ce&shy;<lb/>re, vt &longs;entit Ari&longs;toteles, quod rectus angulus quietis &longs;it <lb/>cau&longs;&longs;a, &longs;ed propterea quod eius thoracis tum etiam f&oelig;&shy;<lb/>morum pondus ab ip&longs;a &longs;ede &longs;u&longs;tineantur; crura vero &amp; <lb/>pedes ideo non laborent, quod partim &longs;u&longs;pen&longs;a &longs;int, par&shy;<lb/>tim &longs;olo ip&longs;i innitantur. </s>
            <s id="s.001814">Quare cum corpus totum nec &longs;e <pb xlink:href="007/01/188.jpg"/>&longs;u&longs;tineat, nec &agrave; pedibus &longs;u&longs;tineatur, fit quies &amp; la&longs;&longs;itudi&shy;<lb/>nis alleuatio. </s>
            <s id="s.001815">Natura autem ideo commodam hominibus <lb/>&longs;e&longs;&longs;ionem facere volui&longs;&longs;e inde apparet, quod clunes, qui&shy;<lb/>bus tota &longs;uperior pars, &amp; grauior nititur, carno&longs;am fece&shy;<lb/>rit, &amp; ceruicalis cuiu&longs;dam in&longs;tar mollem &amp; facilem. </s>
            <s id="s.001816">Sed <lb/>nos ad qu&aelig;&longs;tionem. </s>
          </p>
          <figure id="id.007.01.188.1.jpg" xlink:href="007/01/188/1.jpg"/>
          <p type="main">
            <s id="s.001817">E&longs;to enim &longs;tans AB, cuius caput A, <lb/>Thorax AC, f&oelig;mora CD, crura DB, pe&shy;<lb/>des vero B, centrum vero grauitatis in i&shy;<lb/>p&longs;o Thorace E. <!-- KEEP S--></s>
            <s id="s.001818">Modo &longs;edeat, &longs;itque ca&shy;<lb/>put in F, Thorax FG, f&oelig;mora GH, crura <lb/>HI, pedes I, grauitatis vero centrum vbi <lb/>K. <!-- KEEP S--></s>
            <s id="s.001819">Producatur recta FG in L, &longs;itque FL <lb/>horizonti perpendicularis. </s>
            <s id="s.001820">Centrum er&shy;<lb/>go grauitatis K fulcitur puncto G, hoc e&longs;t, <lb/>puncto L, in quo po&longs;teriores pedes ip&longs;ius <lb/>&longs;ed is &longs;olo h&aelig;rent. </s>
            <s id="s.001821">efficit autem &longs;edens <lb/>duos rectos angulos FGH, GHI. <!-- KEEP S--></s>
            <s id="s.001822">Rebus <lb/>igitur ita di&longs;po&longs;itis &longs;eruatis rectis angulis, non fiet &longs;urre&shy;<lb/>ctio, &amp; id quidem non ideo quod, vt ait Philo&longs;ophus, &aelig;&shy;<lb/>qualitas &amp; rectitudo angulorum quietis &longs;it cau&longs;&longs;a, &longs;ed <lb/>propterea quod centro grauitatis extra pedum <expan abbr="fulcim&emacr;-tum">fulcimen&shy;<lb/>tum</expan> con&longs;tituto, non habet centrum &longs;tabilem locum cui in <lb/>actu &longs;urrectionis h&aelig;reat, &amp; fulciatur, vnde fit vt &longs;i &longs;edenti <lb/>&longs;ubtrahatur &longs;edes remoto prohibente, &longs;edens pror&longs;us cor&shy;<lb/>ruat. </s>
            <s id="s.001823">Modo retrahat qui &longs;edet crura, &amp; pedes ponat in M, <lb/>&agrave; puncto autem M, horizonti perpendicularis erigatur <lb/>MN. erit ergo fulcimentum in M, &longs;ed adhuc &longs;urgere non <lb/>poterit, centro grauitatis adhuc extra lineam MN, qu&aelig; <lb/>per fulcimentum e&longs;t, con&longs;tituto. </s>
            <s id="s.001824">Reclinetur autem pe&shy;<lb/>ctus ad anteriora, &amp; cum f&oelig;more acutum angulum faciat <lb/>&longs;itque vbi GO, erit igitur grauitatis centrum vbi P, hoc <lb/>e&longs;t, in ip&longs;a perpendiculari NM, fiet igitur inde commoda <pb xlink:href="007/01/189.jpg"/>&longs;urrectio, propterea quod in eadem linea facta &longs;int, graui&shy;<lb/>tatis centrum P, &amp; fulcimentum ip&longs;um M. <!-- KEEP S--></s>
            <s id="s.001825">Acutum vero <lb/>angulum in &longs;urrectione nece&longs;&longs;arium e&longs;&longs;e clare patet, non <lb/>autem effectus ip&longs;ius e&longs;&longs;e cau&longs;&longs;am, vt videtur &longs;en&longs;i&longs;&longs;e Ari&shy;<lb/>&longs;toteles; nisi dicamus, cau&longs;&longs;am e&longs;&longs;e cau&longs;&longs;&aelig;, &longs;iquidem acuti <lb/>qui fiunt anguli centrum &amp; pedes in eadem linea collo&shy;<lb/>cant, quicquid tamen &longs;it, nos ideo &longs;urrectionem fieri dici&shy;<lb/>mus, quod immutatis angulis centrum grauitatis &longs;upra <lb/>fulcimentum, fulcimento vero &longs;ub ip&longs;o grauitatis centro <lb/>collocetur, &amp; h&aelig;c e&longs;t cau&longs;&longs;a proxima. </s>
            <s id="s.001826">H&aelig;c nos ad Ari&longs;to&shy;<lb/>telem. </s>
            <s id="s.001827">Modo qua&longs;dam alias qu&aelig;&longs;tiones, nec inutiles &longs;ed <lb/>&amp; eas non iniucundas quoque proponemus. </s>
          </p>
          <p type="main">
            <s id="s.001828">Primum igitur qu&aelig;rimus, Cur hominum &amp; c&aelig;tero&shy;<lb/>rum animalium, qu&aelig; aliquando erecto corpore incedunt, <lb/>pedes non quidem breues &longs;int &amp; rotundi, &longs;ed longiores <lb/>potius, &amp; in inferiorem partem porrecti? </s>
            <s id="s.001829">Item cur magis <lb/>ad digitos quam ad calcaneum porrigantur? </s>
          </p>
          <figure id="id.007.01.189.1.jpg" xlink:href="007/01/189/1.jpg"/>
          <p type="main">
            <s id="s.001830">E&longs;to homo animalue quodpiam &longs;tans <lb/>AB, cuius pes CD, pedis pars qu&aelig; ad digitos <lb/>BC. quae vero ad calcaneum BD f&oelig;moris ver&shy;<lb/>tebra E, centrum vero grauitatis ip&longs;ius cor&shy;<lb/>poris F. <!-- KEEP S--></s>
            <s id="s.001831">Primum igitur &longs;tatuendum e&longs;t, ho&shy;<lb/>minem &amp; c&aelig;tera fere animalia &agrave; Natura fa&shy;<lb/>cta e&longs;&longs;e vt ad anteriora moueantur, &amp; ideo o&shy;<lb/>mnes fere quod in &longs;enioribus manife&longs;te ap&shy;<lb/>paret, ad anteriora ex ip&longs;a corporis di&longs;po&longs;i&shy;<lb/>tione vergant. </s>
            <s id="s.001832">Itaque dum qui &longs;tat horizon&shy;<lb/>ti pror&longs;us e&longs;t perpendicularis, grauitatis centrum F in ip&longs;a <lb/>perpendiculari con&longs;tituitur qu&aelig; ad mundi centrum AB, <lb/>&amp; ideo corporis moles pondu&longs;que fulcitur puncto B. <!-- KEEP S--></s>
            <s id="s.001833">Mo&shy;<lb/>do fiat ex vertebra E thoracis AE, inclinatio in anteriora, <lb/>in GE &amp; grauitatis centrum D diluetur in H, &amp; per H per&shy;<lb/>pendicularis demittatur HI, non erit ** extra pedis ful&shy;<pb xlink:href="007/01/190.jpg"/>cimentum BC. <!-- KEEP S--></s>
            <s id="s.001834">Stabit ergo qui ita inclinatur, nec corruet: <lb/>&longs;i autem adhuc propendeat magis, fiatque in KE, centro <lb/>grauitatis con&longs;tituto in M, ducatur per M perpendicula&shy;<lb/>ris ML, quare quoniam linea ML extra pedis fulcimen&shy;<lb/>tum cadit, corruet qui eo pacto inclinatur nec &longs;u&longs;tinebi&shy;<lb/>tur. </s>
            <s id="s.001835">Cur igitur natura animalibus quae erecto corpore am&shy;<lb/>balant, pedes in anteriora porrectos fecerit, hinc clare <lb/>patet. </s>
          </p>
          <p type="main">
            <s id="s.001836">Hinc etiam ceu con&longs;ectarium habemus, cur homi&shy;<lb/>nes &longs;i impellantur, magis ad ca&longs;um in po&longs;teriora quam in <lb/>anteriora &longs;int proni. </s>
            <s id="s.001837">Nec non etiam cur &longs;imi&aelig;, vr&longs;i, &amp; &longs;i <lb/>qu&aelig; c&aelig;tera eiu&longs;modi animalia diutius erecto corpore <lb/>ambulare nequeant, nempe ideo quod eorum corporum <lb/>moles valde in anteriora propendeat, nec ita commodo, <lb/>vt humanis euenit corporibus, pedum ip&longs;orum ba&longs;ibus <lb/>fulciantur. </s>
          </p>
          <p type="main">
            <s id="s.001838">Qu&aelig;rere item haud importune po&longs;&longs;umus, Cur gral&shy;<lb/>latores non &longs;tent erecti, ni&longs;i a&longs;&longs;idue moueantur? </s>
            <s id="s.001839">Solutio <lb/>facilis. </s>
            <s id="s.001840">grall&aelig; etenim duobus tantum punctis &longs;olum tan&shy;<lb/>gunt, nec porrecti beneficio, quod ambulantibus accidit, <lb/>vti po&longs;&longs;unt. </s>
            <s id="s.001841">quamobrem grauitatis centrum fit extra ful&shy;<lb/>cimentum, &amp; ideo coguntur grallatores a&longs;&longs;iduo motu <lb/>grauitatis centro fulcimentum &longs;upponere, quod dum fit, <lb/>&agrave; ca&longs;u prohibentur. </s>
          </p>
          <p type="main">
            <s id="s.001842">Pote&longs;t autem id quod fulcitur, tripliciter fulciri, <expan abbr="n&emacr;-peaut">nem&shy;<lb/>pe aut</expan> puncto, aut linea, aut &longs;uperficie. </s>
          </p>
          <p type="main">
            <s id="s.001843">Quod puncto fulcitur, nulla reimpediente ad quam&shy;<lb/>uis partem cadere pote&longs;t, centrum &longs;iquidem, motus, pun&shy;<lb/>ctum e&longs;t. </s>
          </p>
          <p type="main">
            <s id="s.001844">Quod linea fulcitur ad duas tantum partes, ea&longs;que <lb/>oppo&longs;itas, habet ca&longs;um. </s>
            <s id="s.001845">&longs;it illud &longs;uperficies, corpu&longs;ue in <lb/>latus con&longs;titutum. </s>
          </p>
          <pb xlink:href="007/01/191.jpg"/>
          <figure id="id.007.01.191.1.jpg" xlink:href="007/01/191/1.jpg"/>
          <p type="main">
            <s id="s.001846">E&longs;to horizontis pla&shy;<lb/>num ABCD, cui ad re&shy;<lb/>ctos angulos in&longs;i&longs;tat &longs;u&shy;<lb/>perficies EFGH, &longs;ecun&shy;<lb/>dum latus FG. <!-- KEEP S--></s>
            <s id="s.001847">Sit autem <lb/>ip&longs;ius &longs;uperficiei grauita&shy;<lb/>tis centrum I. &agrave; quo ad <lb/>horizontis planum per&shy;<lb/>pendicularis demittatur IK. <!-- REMOVE S-->Cadet autem in lineam FG. <lb/>per propo&longs;. </s>
            <s id="s.001848">38. vndecimi elem. </s>
            <s id="s.001849">&amp; anguli IKG IKF recti e&shy;<lb/>runt. </s>
            <s id="s.001850">Itaque &longs;uperficie EFGH circa lineam FKG ceu cir&shy;<lb/>ca axem mota punctum I peripheriam de&longs;cribet LIM, &amp; <lb/>&longs;iquidem cadat ad partes CD, grauitatis centrum erit vbi <lb/>M. <!-- KEEP S--></s>
            <s id="s.001851">Si vero ad partes AB, fiet vbi L. <!-- KEEP S--></s>
            <s id="s.001852">Sunt autem LKM <expan abbr="p&umacr;-cta">pun&shy;<lb/>cta</expan> in recta LKM, qu&aelig; quidem communis &longs;ectio e&longs;t plani <lb/>horizontis, &amp; plani per IKLM, tran&longs;euntis. </s>
          </p>
          <figure id="id.007.01.191.2.jpg" xlink:href="007/01/191/2.jpg"/>
          <p type="main">
            <s id="s.001853">Idem quoque de cor&shy;<lb/>pore dicimus in latus col&shy;<lb/>locato. </s>
            <s id="s.001854">E&longs;to enim cubus <lb/>LO, cuius grauitatis cen&shy;<lb/>trum R, latus vero quo ful&shy;<lb/>citur, NO, Si enim ita col&shy;<lb/>locetur, vt interna &longs;uperfi&shy;<lb/>cies LNOQ ad rectos an&shy;<lb/>gulos horizonti &longs;it con&longs;ti&shy;<lb/>tuta, demi&longs;&longs;a perpendicu&shy;<lb/>laris &agrave; puncto R, ea det in S, in ip&longs;a linea NSO. <!-- KEEP S--></s>
            <s id="s.001855">Cadente i&shy;<lb/>gitur corpore fiet motus circa lineam NO, centro graui&shy;<lb/>tatis interim peripheriam TRV. de&longs;cribente. </s>
          </p>
          <p type="main">
            <s id="s.001856">Hinc animaduertere licet, Cur prouidi&longs;&longs;ima Natu&shy;<lb/>ra nulli animantium vnicum dederit pedem, &longs;ed aut qua&shy;<lb/>ternos, aut &longs;altem binos, &amp; binos quidem ip&longs;os virtute <lb/>quaternos, &longs;iquidem in quolibet animantium bipedum <pb xlink:href="007/01/192.jpg"/>pede duo &longs;altem puncta con&longs;iderantur, quibus ip&longs;um ani-<lb/>mal fulcitur. </s>
          </p>
          <figure id="id.007.01.192.1.jpg" xlink:href="007/01/192/1.jpg"/>
          <p type="main">
            <s id="s.001857">Sint enim humani pedis ve&shy;<lb/>&longs;tigia A, B, C, D, in vtroque igitur <lb/>duo puncta con&longs;iderantur, A, B, <lb/>C, D, illa quidem ad digitos, h&aelig;c <lb/>autem ad calcaneum. </s>
            <s id="s.001858">Idem quo&shy;<lb/>que in auium pedibus ob&longs;erua&shy;<lb/>tur, ex quibus concludimus, bi&shy;<lb/>pedum omnium fulcimentum e&longs;&shy;<lb/>&longs;e quadruplex. </s>
            <s id="s.001859">Porro quadrupe&shy;<lb/>dia eo quod tota corporis mole <lb/>ad in feriora vergant, quatuor ful&shy;<lb/>cimenta, eaque di&longs;tincta, &amp; commode ab inuicem remo&shy;<lb/>ta eademmet Natura pr&aelig;parauit. </s>
          </p>
          <p type="main">
            <s id="s.001860">Eadem quoque in artificialibus con&longs;ideramus. </s>
            <s id="s.001861">Sit <lb/>enim vas quodpiam ABC, cuius pes vnicus, i&longs;que rotun&shy;<lb/>dus BC, grauitatis vero centrum D. <!-- KEEP S--></s>
            <s id="s.001862">Quoniam igitur in <lb/>pedis ip&longs;ius peripheria, infinita puncta intelligantur, dici <lb/>quodammodo pote&longs;t vas ip&longs;um infinitis fere punctis, licet <lb/><figure id="id.007.01.192.2.jpg" xlink:href="007/01/192/2.jpg"/><lb/>pes vnicus &longs;it, &longs;u&longs;tineri. </s>
            <s id="s.001863">Non&shy;<lb/>nulla autem corpora artifi&shy;<lb/>cialia. </s>
            <s id="s.001864">quatuor pedibus &longs;u&shy;<lb/>&longs;tinentur, vt men&longs;&aelig; <expan abbr="qu&aelig;d&atilde;">qu&aelig;dam</expan>, <lb/>nonnulla etiam tribus, vt <lb/>tripodes, qui nomen ab ip&longs;o <lb/>pedum numero &longs;ortiuntur. <lb/></s>
            <s id="s.001865">Sit enim triangulum EFG, <lb/>cuius centrum grauitatis H, <lb/>nitatur autem tribus pun&shy;<lb/>ctis I, K, L, &longs;tabit igitur. </s>
            <s id="s.001866">Si <lb/>autem duobus tantum; non &longs;tabit. </s>
            <s id="s.001867">ducta enim IK &longs;i pun&shy;<lb/>ctis tantum IK innitatur, con&longs;tituto grauitatis centro <pb xlink:href="007/01/193.jpg"/>extra fulcimentum IK, verget cedens ver&longs;is partes, L, Si <lb/>autem innitatur punctis IL, cadet ad partes K. <!-- KEEP S--></s>
            <s id="s.001868">Sivero ip&longs;is <lb/>KL, cadet ad partes I.Ex quibus apparet, inanimata cor&shy;<lb/>pora aut vnico pede plurium virtutem habente, aut &longs;al&shy;<lb/>tem tribus actu, vt &longs;u&longs;tineantur, indigere. </s>
          </p>
          <p type="main">
            <s id="s.001869">Hinc etiam patet, cur &longs;enes, imbecilles, curui, &amp; pe&shy;<lb/>dibus capti, baculi baculorumue fulcimento egeant, ete&shy;<lb/>nim cum hi debiles &longs;int, &amp; in anteriorem partem magno&shy;<lb/>pere propendeant, ne grauitatis centrum extra fulcimen&shy;<lb/>tum fiat, baculo vel baculis indigent, quibus centrum i&shy;<lb/>p&longs;um fulciatur. </s>
          </p>
          <p type="main">
            <s id="s.001870">C&aelig;terum cur duplici genu ingeniculati difficile in <lb/>eo &longs;itu permaneant, ea cau&longs;&longs;a e&longs;t, quod grauitatis centrum <lb/>in thorace con&longs;titutum, duobus genibus fulciatur, eo&longs;&shy;<lb/>que premat. </s>
            <s id="s.001871">qu&aelig; quidem genua eo quod natura apta na&shy;<lb/>ta non &longs;int, veluti pedes, ad &longs;u&longs;tinendam corporis molem <lb/>laborant, idque eo magis, quod cum o&longs;&longs;ea &longs;int, cutem in&shy;<lb/>ter o&longs;&longs;ium &amp; plani duritiem con&longs;titutam, accidit arctari, <lb/>&amp; ideo dolorem &amp; mole&longs;tiam ingeniculatis facere. </s>
          </p>
          <p type="main">
            <s id="s.001872">Si autem vnico tantum genu qui&longs;piam nitatur, dif&shy;<lb/>ficultatem &longs;entiet longe minorem. </s>
            <s id="s.001873">Triplici enim fulci&shy;<lb/><figure id="id.007.01.193.1.jpg" xlink:href="007/01/193/1.jpg"/><lb/>mento eo ca&longs;u ingeniculatus <lb/>fulcitur. </s>
            <s id="s.001874">Sit enim ingenicula&shy;<lb/>tus ABCDE, cuius grauitatis <lb/>centrum F. dextrum vero ge&shy;<lb/>nu, cui nititur D, &longs;ini&longs;trum ve&shy;<lb/>ro, quod eleuatur B. <!-- KEEP S--></s>
            <s id="s.001875">Tribus ergo fulcimentis ingenicula&shy;<lb/>tus vt diximus, &longs;u&longs;tinetur, CDE. <!-- KEEP S--></s>
            <s id="s.001876">Diuiditur itaque pondus <lb/>in tres partes, &amp; ideo &longs;ingul&aelig; minus fatigantur. </s>
            <s id="s.001877">Magis ta&shy;<lb/>men laborat punctum D, vtpote illud, cui ad perpendicu&shy;<lb/>lum F grauitatis centrum innititur. </s>
          </p>
          <p type="main">
            <s id="s.001878">Vtique illud quoque mirabile e&longs;t, Aues dormientes <lb/>vnico tantum pede fulciri, &amp; quod magis mirum e&longs;t, dor&shy;<pb xlink:href="007/01/194.jpg"/>mientes po&longs;&longs;e, quod vel ip&longs;is vigilantibus e&longs;t difficile. </s>
            <s id="s.001879">Cur <lb/>id Natura docente faciant, eam puto e&longs;&longs;e cau&longs;&longs;am, quod <lb/>dum dormiunt, caput &longs;ini&longs;tr&aelig; al&aelig;, vt naturali calore iu&shy;<lb/>uentur, &longs;upponunt, quapropter ad eam partem declinan&shy;<lb/>tes, vt interim &aelig;quilibrium faciant, pedem &longs;ubleuant, &amp; <lb/>eo ca&longs;u ceu inutilem retrahunt atque &longs;u&longs;pendunt: addita <lb/>item alia cau&longs;&longs;a, nempe vt pedem ip&longs;um dormientes nati&shy;<lb/>uo calore confoueant. </s>
          </p>
          <p type="main">
            <s id="s.001880">Qu&aelig;ritur etiam, Cur ij qui inclinantur, vt <expan abbr="r&emacr;">rem</expan> quam&shy;<lb/>piam &agrave; &longs;olo &longs;u&longs;tollant, alterum crurium ad anteriora, <expan abbr="n&emacr;-pever&longs;us">nem&shy;<lb/>pe ver&longs;us</expan> manum ip&longs;am, quam porrigunt, extendant? </s>
          </p>
          <figure id="id.007.01.194.1.jpg" xlink:href="007/01/194/1.jpg"/>
          <p type="main">
            <s id="s.001881">E&longs;to enim qui&longs;piam ABCD, <lb/>cuius crura BC, BD, grauitatis <lb/>centrum E, velit autem quippiam <lb/>&agrave; &longs;olo tollere quod &longs;it in F. &longs;it per&shy;<lb/>pendicularis, qu&aelig; per grauitatis <lb/>centrum GEH. </s>
            <s id="s.001882">Dum igitur ad <lb/>anteriora &iacute;nclinatur, centrum a&shy;<lb/>mouet &agrave; perpendiculari, quam&shy;<lb/>obrem docente Natura, crus BC <lb/>ad centrum ip&longs;um fulciendum. <lb/></s>
            <s id="s.001883">ad anteriora, hoc e&longs;t, ver&longs;us rem <lb/>&longs;u&longs;tollendam porrigitur. </s>
          </p>
          <p type="main">
            <s id="s.001884">Huius quoque &longs;peculationis e&longs;t inue&longs;tigare, Cur <lb/>quadrupedia dum gradiuntur, pedes diametraliter mo&shy;<lb/>ueant. </s>
            <s id="s.001885">Cuius rei verba fecit ip&longs;e quoque Philo&longs;ophus lib. <lb/> de animalium ince&longs;&longs;u cap. 12. </s>
            <s id="s.001886">Nos autem ad maiorem de&shy;<lb/>clarationem, quod ip&longs;e Phy&longs;icis principijs fecit, mecha&shy;<lb/>nicis demon&longs;trabimus. </s>
          </p>
          <p type="main">
            <s id="s.001887">Sint du&aelig; in plano parallel&aelig; AB, CD, in quibus qua&shy;<lb/>drupedis pedes E, F, B, D, quorum EF, anteriores, BD vero <lb/>po&longs;teriores. </s>
            <s id="s.001888">iungantur BDEF, eritque EBDF parallelo&shy;<lb/>grammum altera parte longius, cuius diametri ducantur <pb xlink:href="007/01/195.jpg"/><figure id="id.007.01.195.1.jpg" xlink:href="007/01/195/1.jpg"/><lb/>ED, BF, &longs;ecantes &longs;e&longs;e in G, vbi &amp; grauitatis <lb/>centrum. </s>
            <s id="s.001889">Moto igitur po&longs;teriori &longs;ini&longs;tro pe&shy;<lb/>de B in K, &longs;i anteriorem E, eodem tempore <lb/>moueret in I, &longs;tantibus interim DF, ceu ful&shy;<lb/>cimentis, centrum G extra fulcimenta fieret <lb/>ad partes BE. <!-- KEEP S--></s>
            <s id="s.001890">Caderet igitur ad partes BE. <!-- KEEP S--></s>
            <s id="s.001891">Si <lb/>autem eodem tempore moueret dextros eo&shy;<lb/>dem pacto centrum extra fulcimenta po&longs;i&shy;<lb/>tum caderet ad partes ip&longs;as DF. <!-- KEEP S--></s>
            <s id="s.001892">Si autem <lb/>moto pede B in K, &amp; eodem tempore F in L, <lb/>&amp; D in H, E, in I, centrum erit in diametris HI, KL, hoc <lb/>e&longs;t, vbi M, fultum quidem ab ip&longs;is pedibus K, L, H, I. <!-- KEEP S--></s>
            <s id="s.001893">Hoc <lb/>igitur pacto transfertur vici&longs;&longs;im cum grauitatis centro &longs;i&shy;<lb/>mul translatis fulcimentis &longs;e&longs;e diametraliter re&longs;ponden&shy;<lb/>tibus; quod vtique demon&longs;trandum fuerat. </s>
          </p>
          <p type="main">
            <s id="s.001894">Sane &amp; bipedia quoque alternatim gradiendo gra&shy;<lb/>uitatis centrum transferunt. </s>
            <s id="s.001895">Dum enim dextrum crus e&shy;<lb/>leuatur, centrum &longs;ini&longs;tro fulcitur, &amp; econtra. </s>
          </p>
          <p type="main">
            <s id="s.001896">Naturalia i&longs;th&aelig;c &longs;unt; in artificialibus autem qu&aelig;ri <lb/>po&longs;&longs;et, Cur Architecti, Arcium muros non ad perpendi&shy;<lb/>culum erectos, &longs;ed intror&longs;um inclinatos con&longs;tituant? </s>
          </p>
          <figure id="id.007.01.195.2.jpg" xlink:href="007/01/195/2.jpg"/>
          <p type="main">
            <s id="s.001897">Vtique hoc faciunt, vt minus <lb/>&longs;int ad ruinam proni. </s>
            <s id="s.001898">E&longs;to enim <lb/>murus ad interiorem partem ver&shy;<lb/>gens ABCD, Cuius grauitatis cen&shy;<lb/>trum E ba&longs;is BC erigatur &agrave; puncto <lb/>B horizonti perpendicularis BF, &amp; <lb/>ad eundem &agrave; centro grauitatis E <lb/>demittatur EM, tum BE iungatur. <lb/></s>
            <s id="s.001899">Po&longs;t h&aelig;c &agrave; puncto BG angulum. <lb/></s>
            <s id="s.001900">cum linea horizontis BK faciens recto maiorem. </s>
            <s id="s.001901">Ita que <lb/>murus hoc pacto con&longs;titutus ad interiorem partem &longs;uo <lb/>pondere vergit, cadere autem non pote&longs;t, vel quod viu&aelig; <pb xlink:href="007/01/196.jpg"/>rupi, cui forte h&aelig;ret, fulciatur, vel anti&longs;tatis, quos no&shy;<lb/>&longs;trates &longs;perones &amp; contra fortes appellant, innitatur. </s>
            <s id="s.001902">Sed <lb/>nec in anteriora corruet, quandoquidem ruinam factu&shy;<lb/>ras, nece&longs;&longs;e e&longs;t vt grauitatis centrum &longs;ecum trahat in per&shy;<lb/>pendiculari BF, &amp; demum in eam qu&aelig; vltra perpendicu&shy;<lb/>larem e&longs;t BG, facta nempe circa B, ceu circa centrum, <expan abbr="c&omacr;-uer&longs;ione">con&shy;<lb/>uer&longs;ione</expan>. </s>
            <s id="s.001903">Moueatur autem &amp; ex &longs;emidiametro BE cen&shy;<lb/>tro B portio circuli de&longs;cribatur EH, qu&aelig; &longs;ecet BG in H, <lb/>&amp; BF in I; Et quia EM &longs;emidiametro BK perpendicularis <lb/>per B, centrum non tran&longs;it, erit EM ip&longs;a BK, hoc e&longs;t, BI <lb/>brevior. </s>
            <s id="s.001904">Ab&longs;cindatur ex BI, ip&longs;i EM &aelig;qualis LB. </s>
            <s id="s.001905">Erit igi&shy;<lb/>tur punctum L infra punctum I, hoc e&longs;t, ip&longs;o I, mundi cen&shy;<lb/>tro propius. </s>
            <s id="s.001906">Nece&longs;&longs;e igitur erit ad hoc vt murus corruat, <lb/>centrum grauitatis E facta circa B, conuer&longs;ione aliquan&shy;<lb/>do fieri in I, vt demum transferri po&longs;&longs;it in H, &longs;ed I remo&shy;<lb/>tius e&longs;t &agrave; mundi centro ip&longs;is E, L, a&longs;cendet igitur graue <lb/>contra &longs;ui naturam ex E in I, at hoc e&longs;t impo&longs;&longs;ibile; quod <lb/>fuerat demon&longs;trandum. </s>
          </p>
          <p type="main">
            <s id="s.001907">Ex his ij&longs;dem principijs alia &longs;oluitur qu&aelig;&longs;tio, Cur <lb/>&longs;cilicet Campanaria turris qu&aelig; Pi&longs;is vi&longs;itur, nec non alia <lb/>Bononi&aelig; in foro prope A&longs;ellorum turrim, quam &agrave; nobili <lb/>olim Cari&longs;endorum familia ex&longs;tructam, Cari&longs;endam vo&shy;<lb/>cant, cuius meminit &amp; Dantes Poeta &longs;ummus in &longs;ua Co&shy;<lb/>m&oelig;dia. </s>
            <s id="s.001908">Propendet autem h&aelig;c in latus, &amp; ita propendet <lb/>vt perpendicularis, qu&aelig; &agrave; &longs;ummo inclinat&aelig; partis in &longs;o&shy;<lb/>lum demittitur, longe cadat ab ip&longs;a, cui nititur, ba&longs;i, quod <lb/>&longs;ane mirabile videtur, muros nempe, in ruinam pronos, <lb/>ruinam non facere. </s>
          </p>
          <p type="main">
            <s id="s.001909">E&longs;to enim turris ABCD, ba&longs;i fulta BC, horizontis <lb/>planum BCF latera AB, DC, centrum vero grauitatis to&shy;<lb/>tius molis E. <!-- KEEP S--></s>
            <s id="s.001910">Propendeat autem ad partes DC ex angulo <lb/>DCF. <!-- KEEP S--></s>
            <s id="s.001911">Ita autem con&longs;tituta intelligatur vt perpendicula&shy;<lb/>ris ab A, in planum horizontis demi&longs;&longs;a per grauitatis cen-<pb xlink:href="007/01/197.jpg"/><figure id="id.007.01.197.1.jpg" xlink:href="007/01/197/1.jpg"/><lb/>trum E extra ba&longs;im BC, non cadat, <lb/>cadat autem in C. <!-- KEEP S--></s>
            <s id="s.001912">Quoniam igitur <lb/>ABCD moles per E grauitatis cen&shy;<lb/>trum diuiditur, in partes &longs;ecatur &aelig;&shy;<lb/>queponderantes, &longs;ed &amp; centrum. <lb/></s>
            <s id="s.001913">grauitatis extra fulcimentum non <lb/>cadit, quare nec pars ACD, trahet <lb/>partem ABC, nec centrum extra <lb/>fulcimentum po&longs;itum locum petet <lb/>centro mundi viciniorem. </s>
            <s id="s.001914">Cur igitur Cari&longs;enda &longs;tet, &amp; e&shy;<lb/>gregia illa turris campanaria qu&aelig; Pi&longs;is prope &longs;ummum <lb/>Templum marmoribus pr&aelig;clare ex&longs;tructa videtur, licet <lb/>ruinam minentur, &longs;tent &aelig;ternum, nec cadant, ex his qu&aelig; <lb/>con&longs;iderauimus, liquido patet. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001915">QVAESTIO XXXI<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001916"><emph type="italics"/>Cur facilius moueatur commotum quam manens, veluti currus <lb/>commotos citius agitant, quam moueri incipientes?<emph.end type="italics"/></s>
          </p>
          <p type="head">
            <s id="s.001917"><emph type="italics"/>Hoc qu&aelig;ritur.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001918">Problema hoc e&longs;t mere Phy&longs;icum; verumtamen quo&shy;<lb/>niam ad localem motum pertinet, de quo ip&longs;e quoque <lb/>Mechanicus agit, Hi&longs;ce qu&aelig;&longs;tionibus contemplatio h&aelig;c <lb/>inter&longs;eritur. </s>
            <s id="s.001919">Soluit autem Ari&longs;toteles inquiens, id forta&longs;&shy;<lb/>&longs;e ea de cau&longs;&longs;a fieri, quod difficillimum &longs;it pondus moue&shy;<lb/>re, quod in contrarium mouetur. </s>
            <s id="s.001920">Demit enim quippiam <lb/>de motoris potentia re&longs;i&longs;tens, licet mouens ip&longs;o moto &longs;it <lb/>longe potentius atque velocius. </s>
            <s id="s.001921">nece&longs;&longs;e enim e&longs;&longs;e id tar&shy;<lb/>dius moueri quod repellitur. </s>
            <s id="s.001922">H&aelig;c verba licet de ea po&shy;<lb/>tentia dicta videantur, qu&aelig; rem motam in contrariam. <lb/></s>
            <s id="s.001923">partem repellit, nihilominus illi quoque aptantur qu&aelig; <lb/>rem immobilem &agrave; principio mouere conatur. </s>
            <s id="s.001924">e&longs;t enim re&shy;<lb/>&longs;i&longs;tentia rei qu&aelig; &agrave; &longs;tatu ad motum transfertur ceu <expan abbr="quid&atilde;">quidam</expan> <pb xlink:href="007/01/198.jpg"/>contrarius motus. </s>
            <s id="s.001925">Contra autem accidit illi qui rem mo&shy;<lb/>tam mouet in ip&longs;o motu: eo enim ca&longs;u mouens ab ip&longs;o rei <lb/>motu magnopere iuuatur, cooperatur enim motus moto&shy;<lb/>ri, in ip&longs;am rem motam operanti. </s>
            <s id="s.001926">Auget autem res mota <lb/>quodammodo mouentis potentiam. </s>
            <s id="s.001927">quod enim &agrave; mouen&shy;<lb/>te pateretur, ex &longs;e ip&longs;a agit res qu&aelig; mouetur. </s>
          </p>
          <figure id="id.007.01.198.1.jpg" xlink:href="007/01/198/1.jpg"/>
          <p type="main">
            <s id="s.001928">E&longs;to horizontis pla&shy;<lb/>num AB, cui moles qu&aelig;&shy;<lb/>dam in&longs;i&longs;tat, CD. <!-- KEEP S--></s>
            <s id="s.001929">Modo <lb/>potentia qu&aelig;dam appli&shy;<lb/>cetur vbi E, qu&aelig; molem in <lb/>anteriora propellat, id <lb/>e&longs;t, ver&longs;us B. Primum igitur, quoniam &agrave; quiete ad motum <lb/>fit tran&longs;itus, re&longs;i&longs;tit &longs;ua quiere corpus graue, potenti&aelig; im&shy;<lb/>pellenti, &longs;uperata demum re&longs;i&longs;tentia moles qu&aelig; moueri <lb/>c&oelig;pit, fertur in F &amp; mouetur, quare potentia qu&aelig; &agrave; prin&shy;<lb/>cipio re&longs;i&longs;tentiam rei non mot&aelig; &longs;uperauerat, pellendo <lb/>rem motam pergens facilius pellit: Duo enim &longs;unt quo&shy;<lb/>dammodo motores, mouens videlicet ip&longs;e, &amp; motus quo <lb/>res mota mouetur. </s>
            <s id="s.001930">facilius ergo pelletur ex F in G, quam <lb/>ex D in F, &amp; ex G in B, quam ex F in G, &amp; eo motus fiet in <lb/>progre&longs;&longs;u facilior atque in ip&longs;a velocitate velocior, quo <lb/>magis in ip&longs;a motione mouetur. </s>
          </p>
          <p type="main">
            <s id="s.001931">Hinc &longs;oluitur ea qu&aelig;&longs;tio apud Phy&longs;icos difficillima, <lb/>Cur nempe in motu naturali velocitas v&longs;que augeatur; <lb/>etenim ibi Natura mouens e&longs;t, atque eadem in&longs;eparabilis <lb/>&agrave; remota, vrget igitur a&longs;&longs;idue, &agrave; principio quidem tar dius, <lb/>po&longs;t h&aelig;c autem ea quam diximus, de cau&longs;&longs;a v&longs;que &amp; v&longs;que <lb/>velocius. </s>
            <s id="s.001932">Motus ergo fit in motu, qui motus cum &longs;emper &agrave; <lb/>motore, &amp; motu ip&longs;o augeatur, cre&longs;cit ex progre&longs;&longs;u in im&shy;<lb/>men&longs;um. </s>
            <s id="s.001933">Certe cau&longs;&longs;am velocitatis auct&aelig; eam e&longs;&longs;e, quod <lb/>potentia mouens rem motam in motu ip&longs;o moueat, nemo <lb/>vt arbitror, inficias ibit, acquirit enim corpus motum <expan abbr="p&omacr;-dero&longs;itatem">pon-<pb xlink:href="007/01/199.jpg"/>dero&longs;itatem</expan> quandam accidentalem, qu&aelig; cum ex motu <lb/>perinde augeatur, ip&longs;um motum faciliorem, eoque velo&shy;<lb/>ciorem facit. </s>
            <s id="s.001934">Di&longs;putat h&aelig;c &amp; Simplicius lib. 7. Phy&longs;ic. <!-- REMOVE S-->c. <lb/><!-- REMOVE S-->11. Ari&longs;totelis de Natura libros exponens. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001935">QVAESTIO XXXII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001936"><emph type="italics"/>Qu&aelig;ritur hic, Cur ea qu&aelig; proijciuntur, ce&longs;&longs;ent <lb/>&agrave; latione?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001937">Hoc itidem problema e&longs;t mere Phy&longs;icum. <!-- KEEP S--></s>
            <s id="s.001938">Ad quod ea <lb/>pertinent qu&aelig; &agrave; Philo&longs;opho tractantur libro Natu&shy;<lb/>ralium 8. &amp; lib.  1. de C&oelig;lo. <!-- KEEP S--></s>
            <s id="s.001939">Tres autem affert &longs;ubdubitan&shy;<lb/>do rationes, An quia impellens de&longs;init potentia, vel pro&shy;<lb/>pter retractionem, vel propter rei proiect&aelig; in<expan abbr="clination&emacr;">clinationem</expan>, <lb/>quando ea valentior fuerit quam proijcientis vires? </s>
          </p>
          <p type="main">
            <s id="s.001940">Quicquid dicat Philo&longs;ophus, id vtique explorati&longs;&shy;<lb/>&longs;imum e&longs;t. </s>
            <s id="s.001941">Proiecta ideo &agrave; motu ce&longs;&longs;are, propterea quod <lb/>impre&longs;&longs;io, cuius impetu &amp; virtute feruntur, non &longs;it proie&shy;<lb/>ctus quidem naturalis, &longs;ed mere accidentalis &amp; violenta, <lb/>at nullum accidentale &amp; violentum quodque, non natu&shy;<lb/>rale e&longs;t, perpetuum e&longs;t. </s>
            <s id="s.001942">Ce&longs;&longs;at ergo accidentalis illa im&shy;<lb/>pre&longs;&longs;io, eaque paullatim ce&longs;&longs;ante proiecti motus elan&shy;<lb/>gue&longs;cit, donec quietem pror&longs;us adipi&longs;catur. </s>
            <s id="s.001943">Illud quoque <lb/>notamus, quod &agrave; multis vidimus non ob&longs;eruatum, nempe <lb/>violentum motum violentia pr&aelig;ualente non differre &agrave; <lb/>naturali, &amp; ideo tardiorem e&longs;&longs;e &agrave; principio po&longs;t h&aelig;c, in i&shy;<lb/>p&longs;o motu fieri velociorem, remittente demum paullatim <lb/>impre&longs;&longs;a violentia, tardiorem, donec impetus, &amp; cum im&shy;<lb/>petu motus euane&longs;cat, &amp; res ip&longs;a mota quietem adipi&longs;ca&shy;<lb/>tur. </s>
            <s id="s.001944">Vnde etiam experientia docemur, ictum ex proiectis <lb/>violentius fieri, &longs;i fiat paullo remotior &agrave; principio, &amp; tunc <lb/>demum e&longs;&longs;e innocenti&longs;&longs;imum, cum ibi fit, vbi proiectum <lb/>ex motu plene acqui&longs;ito, &longs;ummam adeptum e&longs;t velocita&shy;<pb xlink:href="007/01/200.jpg"/>tem. </s>
            <s id="s.001945">Hinc videmus, vel pueros ip&longs;os, docente Natura <expan abbr="c&umacr;">cum</expan> <lb/>nuces, vel aliud quippiam, parieti alli&longs;um frangere <expan abbr="con&atilde;-tur">conan&shy;<lb/>tur</expan>, &agrave; pariete moderato aliquo &longs;patio recedere. </s>
            <s id="s.001946">Si autem <lb/>eos interroges, cur id faciant, re&longs;pondebunt, vt inde ictus <lb/>valentius fiat atque efficacius. </s>
            <s id="s.001947">Eleganter ex Simplicij &amp; <lb/>Alexandri Aphrodi&longs;ien&longs;is doctrina, qu&aelig; lucidi&longs;&longs;ima e&longs;t, <lb/>qu&aelig;&longs;tionem hanc in &longs;ua Paraphra&longs;i explicat Picolomi&shy;<lb/>neus. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001948">QVAESTIO XXXIII.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001949"><emph type="italics"/>Dubitatur, Cur proiecta moueantur, licet impellens &agrave; proiectis &longs;e&shy;<lb/>paretur; vel vt verbis Philo&longs;ophi vtar, Cur quippiam non pecu&shy;<lb/>liarem &longs;ibi fertur lationem impul&longs;ore alioquin <lb/>non con&longs;equente?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001950">Soluit, inquiens, an videlicet, quoniam primum, id e&longs;t, <lb/>impellens ip&longs;e, id efficit vt alterum, nempe proiectum <lb/>ip&longs;um impellat, illud vero &lpar;hoc e&longs;t proiectum&rpar; alterum <lb/>impellat, hoc e&longs;t, a&euml;rem ip&longs;um mediumue, quod &agrave; proie&shy;<lb/>cto repelletur. </s>
            <s id="s.001951">Ce&longs;&longs;are autem motum, cum res eo deue&shy;<lb/>nit, vt motus eidem &agrave; proijciente impre&longs;&longs;us, non po&longs;&longs;it <lb/>amplius rem proiectam mouere, &amp; itidem rem ip&longs;am, a&euml;&shy;<lb/>rem videlicet non po&longs;&longs;it amplius repellere. </s>
            <s id="s.001952">Vel etiam <lb/>quando ip&longs;ius lati grauitas nutu &longs;uo declinat magis quam <lb/>impellentis in ante &longs;it potentia. </s>
            <s id="s.001953">Vtique res per &longs;e &longs;atis cla&shy;<lb/>ra. </s>
            <s id="s.001954">etenim motus impre&longs;&longs;us accidentalis e&longs;t, quod vero la&shy;<lb/>tioni violent&aelig; re&longs;i&longs;tit principium, naturale, &amp; ab ip&longs;o mo&shy;<lb/>to in&longs;eparabile, vincente igitur quod natura e&longs;t, paulla&shy;<lb/>tim remittitur quod ex accidenti e&longs;t, &amp; inde proiecti fit <lb/>quies. </s>
            <s id="s.001955">E&longs;t autem &amp; hoc quoque Problema pure phy&longs;icum, <lb/>&amp; &longs;uperiori, de quo immediate egimus, perquam familia&shy;<lb/>re, quamobrem ex ij&longs;dem pror&longs;us &longs;oluitur <lb/>principijs. </s>
          </p>
          <pb xlink:href="007/01/201.jpg"/>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.001956">QV&AElig;STIO XXXIV.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.001957"><emph type="italics"/>Cur neque parua multum, neque magna nimis longe proijci queunt, <lb/>&longs;ed proportionem quandam habere oportet proiecta ip&longs;a ad <lb/>eius vires qui proijcit?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.001958">Pvlchre dubitationem diluit, inquiens, An quia nece&longs;&shy;<lb/>&longs;e e&longs;t quod proijcitur, &amp; impellitur contraniti ei vnde <lb/>impellitur. </s>
            <s id="s.001959">Quod autem magnitudine &longs;ua nihil cedit, aut <lb/>imbecillitate nihil contra nititur, non efficit <expan abbr="proiection&emacr;">proiectionem</expan> <lb/>neque impul&longs;ionem. </s>
            <s id="s.001960">quod enim multo impellentis exce&shy;<lb/>dit vires, haud quaquam cedit. </s>
            <s id="s.001961">Quod vero e&longs;t multo im&shy;<lb/>becillius, nihil contranititur, &amp; impre&longs;&longs;ionem non &longs;u&longs;ci&shy;<lb/>pit. </s>
            <s id="s.001962">Aliam quoque adiungit rationem, videlicet, Tantum <lb/>ferri id quod fertur quantum a&euml;ris mouerit ad <expan abbr="profund&umacr;">profundum</expan> <lb/>&lpar;hoc e&longs;t, ad eam partem a&euml;ris remotiorem, ad quam fer&shy;<lb/>tur&rpar; etenim proiectum &agrave; principio dum fertur a&euml;rem pel&shy;<lb/>lit, non pellit autem &longs;i nihil mouetur. </s>
            <s id="s.001963">Accidit igitur vt <lb/>concludit Philo&longs;ophus, proiecta i&longs;th&aelig;c contrarijs ex cau&shy;<lb/>&longs;is minus moueri. </s>
            <s id="s.001964">quod enim valde paruum e&longs;t nihil mo&shy;<lb/>uet imbecillitate &longs;ua impediente. </s>
            <s id="s.001965">quod vero valde ma&shy;<lb/>gnum e&longs;t, ex contraria cau&longs;&longs;a nihil mouet, nempe quod <lb/>ob magnitudinem &longs;uam nihil moueatur. </s>
            <s id="s.001966">Vnde fit pro&shy;<lb/>portionem inter proiectum &amp; proijcientem e&longs;&longs;e inprimis <lb/>ad motum, nece&longs;&longs;ariam. </s>
            <s id="s.001967">H&aelig;c eadem pr&aelig;clare in &longs;ua Pa&shy;<lb/>raphra&longs;i explicat Picolomineus. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.001968">Huic nos, de proiectis qu&aelig;&longs;tioni, h&aelig;c addimus. </s>
          </p>
          <p type="main">
            <s id="s.001969">Cur proiecta corpora non &longs;ibimet ip&longs;is &longs;ecundum, <lb/>partes &aelig;quegrauia, &longs;i fuerint irregularis figur&aelig; in ip&longs;o mo&shy;<lb/>tu, &longs;ecundum grauiorem partem antror&longs;us inuiolento, &amp; <lb/>deor&longs;um in naturali ferantur, &amp; dum in latione conuer&shy;<lb/>tuntur, &longs;onitum edant. </s>
          </p>
          <p type="main">
            <s id="s.001970">E&longs;to pila ABCD, cuius centrum E concinnata ex <lb/>di&longs;pari materia leui, nempe BCD, &amp; graui ABD. non ergo <pb xlink:href="007/01/202.jpg"/><figure id="id.007.01.202.1.jpg" xlink:href="007/01/202/1.jpg"/><lb/>erit <expan abbr="centr&umacr;">centrum</expan> grauitatis &amp; cen&shy;<lb/>trum molis, &longs;it autem grauita&shy;<lb/>tis centrum F. <!-- KEEP S--></s>
            <s id="s.001971">De&longs;cendat cor&shy;<lb/>pus prohibente remoto per <lb/>rectam AG. <!-- KEEP S--></s>
            <s id="s.001972">Et quoniam gra&shy;<lb/>uiora deor&longs;um tendunt ma&shy;<lb/>gis, &longs;i &agrave; principio motus gra&shy;<lb/>uior pars fuerit &longs;upra in ip&longs;o <lb/>de&longs;cen&longs;u conuertet ir pila, &amp; <lb/>&longs;itum non &longs;eruabit donec &longs;u&shy;<lb/>perior pars ea qu&aelig; grauior, <lb/>deor&longs;um fiat, vt videre e&longs;t in <lb/>pila HIK, cuius centrum e&longs;t G. pars grauior HIK. </s>
            <s id="s.001973">Si au&shy;<lb/>tem eadem pila, laterali motu violenter feratur ver&longs;us <lb/>N, ad eam quoque partem conuertetur pars grauior. </s>
            <s id="s.001974">fa&shy;<lb/>cto enim molis &longs;eu magnitudinis centro vbi L, grauior <lb/>pars fiet in MNO; qu&aelig;cunque igitur &longs;unt corpora ita <expan abbr="c&omacr;-&longs;tituta">con&shy;<lb/>&longs;tituta</expan>, vt in illis non &longs;it idem molis &amp; grauitatis centrum <lb/>in ip&longs;a latione conuertentur, &amp; eorum pars grauior an&shy;<lb/>tror&longs;us fiet. </s>
            <s id="s.001975">Sonitus porro in ip&longs;o motu editi ea e&longs;t cau&longs;&longs;a, <lb/>quod irregulare corpus &agrave; principio incipit conuerti, &amp; in <lb/>ip&longs;a conuer&longs;ione dum fertur a&euml;rem verberat, &amp; ab eodem <lb/>vici&longs;&longs;im reuerberatur, ex qua reuerberatione fit corporis <lb/>rotatio dum fertur, &amp; ip&longs;e &longs;onitus, quem Gr&aelig;ci <foreign lang="greek">roi/zon</foreign><lb/>Rh&oelig;zum appellant. </s>
          </p>
          <p type="main">
            <s id="s.001976">Ad hanc quoque &longs;peculationem pertinet, Cur lapi&shy;<lb/>des ad &longs;uperficiem aqu&aelig; proiecti non &longs;tatim demergan&shy;<lb/>tur, &longs;ed aliquot vicibus a qu&aelig; &longs;uperficiem radentes, abea, <lb/>dem re&longs;iliant. </s>
          </p>
          <p type="main">
            <s id="s.001977">E&longs;to aqu&aelig; &longs;uperficies AB, lapis proiectus C, tangens <lb/>aqu&aelig; &longs;uperficiem in D, &amp; inde re&longs;iliens in E, mox iterum <lb/>eandem tangens in F, &amp; re&longs;iliens in G, donec <expan abbr="viol&emacr;to">violento</expan> mo&shy;<lb/>tu ce&longs;&longs;ante demergatur. </s>
            <s id="s.001978">Vtique lapis C, proiectus in D, <pb xlink:href="007/01/203.jpg"/><figure id="id.007.01.203.1.jpg" xlink:href="007/01/203/1.jpg"/><lb/>ni&longs;i medio den&longs;iori, aqua vi&shy;<lb/>delicet, repelleretur, pene&shy;<lb/>traret per D, in H. <!-- KEEP S--></s>
            <s id="s.001979">At eo re&longs;i&shy;<lb/>&longs;tente, &amp; adhuc vigente im&shy;<lb/>petu, fertur in E ad angulos <lb/>fere pares. </s>
            <s id="s.001980">Dico autem fere, <lb/>&longs;iquidem maior e&longs;t ADC ip&longs;o EDF, propterea quod vis <lb/>non &longs;it eadem, &longs;ed minor ea qu&aelig; ex D pellit in E. <!-- KEEP S--></s>
            <s id="s.001981">Durante <lb/>igitur impetu quo pellitur antror&longs;um, fiunt ip&longs;&aelig; re&longs;ilitio&shy;<lb/>nes, &amp; eo ce&longs;&longs;ante, re&longs;ilitiones ce&longs;&longs;ant, &amp; lapis &longs;uapte gra&shy;<lb/>uitate demergitur. </s>
          </p>
          <p type="main">
            <s id="s.001982">Huc quoque &longs;pectat, Cur pila lu&longs;oria in horizontis <lb/>planum proiecta ad pares re&longs;iliat, angulos nempe rectos? </s>
          </p>
          <figure id="id.007.01.203.2.jpg" xlink:href="007/01/203/2.jpg"/>
          <p type="main">
            <s id="s.001983">E&longs;to horizontis planum <lb/>AB, in quod &agrave; puncto C per <lb/>lineam perpendicularem CE <lb/>cadat proijciaturue pila DE, <lb/>cuius grauitatis centrum F. <lb/><!-- KEEP S--></s>
            <s id="s.001984">Tangit autem planum in <expan abbr="p&umacr;-cto">pun&shy;<lb/>cto</expan> E. <!-- KEEP S--></s>
            <s id="s.001985">Perpendicularis ergo <lb/>EC, circulum DE per <expan abbr="centr&umacr;">centrum</expan> <lb/>&longs;ecat, hoc e&longs;t, in partes &aelig; qua&shy;<lb/>les &amp; &aelig;queponderantes, &longs;ed <lb/>dum pila cadit proijciturue, <lb/>agit in planum horizontis, vbi E, &amp; in eodem puncto re. <lb/></s>
            <s id="s.001986">petitur, quare cum cadens &amp; agens diuidatur in partes &aelig;&shy;<lb/>quales &amp; &aelig;queponderantes &amp; item repatiens &amp; re&longs;iliens <lb/>diuidatur item in partes &aelig;quales &amp; &aelig;queponderantes, ita <lb/>re&longs;ilit repatiendo, vti egerat in cadendo, hoc e&longs;t; ad angu&shy;<lb/>los pares; quod fuerat demon&longs;trandum. </s>
            <s id="s.001987">Modo &longs;it <expan abbr="plan&umacr;">planum</expan> <lb/>aliquod ita ad horizontem inclinatum, vt GH, &amp; in illud <lb/>cadat proijciaturue eadem pila. </s>
            <s id="s.001988">Dico eam ab eodem in&shy;<lb/>clinato plano ad pares angulos re&longs;ilire non tamen rectos. <pb xlink:href="007/01/204.jpg"/>Vtique pila cadens, planum non tanget in E. e&longs;&longs;et enim <lb/>GH, vbi AB, Tangat autem in I, &amp; &agrave; centro F ad contin&shy;<lb/>genti&aelig; punctum I, recta ducatur FI. </s>
            <s id="s.001989">Erit igitur FI &lpar;prop. <lb/>18. lib. 3. elem.&rpar; ip&longs;i GH plano perpendicularis. </s>
            <s id="s.001990">Ducatur <lb/>item peri, ip&longs;i EC, parallela IK, &longs;ecans pil&aelig; circumferen&shy;<lb/>tiam in K. <!-- KEEP S--></s>
            <s id="s.001991">Agit ergo &amp; repatitur pila in puncto Inon &aelig;. <lb/></s>
            <s id="s.001992">qualiter in&aelig;quales. </s>
            <s id="s.001993">etenim &longs;unt partes KDLEI, &amp; IK, eo <lb/>quod IK &longs;ecet circulum non per centrum. </s>
            <s id="s.001994">repellitur ergo <lb/>in repatiendo non &aelig;qualiter, &longs;ed iuxta in&aelig;qualitatem ea&shy;<lb/>rundem partium. </s>
            <s id="s.001995">Ducatur autem recta in circulo LI &aelig;&shy;<lb/>qualis ip&longs;i IK. <!-- REMOVE S-->Erit igitur LEI, &aelig;qualis IK, &amp; tota KDLI &aelig;&shy;<lb/>qualis toti IKDL. </s>
            <s id="s.001996">Vt igitur actio e&longs;t per de&longs;cen&longs;um iuxta <lb/>rectam KI, ita e&longs;t repa&longs;&longs;io per a&longs;cen&longs;um ex IL. </s>
            <s id="s.001997">Dico autem <lb/>angulos KIH, LIG e&longs;&longs;e &aelig;quales &amp; &longs;ingulos recto minores. <lb/></s>
            <s id="s.001998">Connectantur FL, FK. <!-- KEEP S--></s>
            <s id="s.001999">Quoniam igitur IK portio &aelig;qualis <lb/>e&longs;t portioni IEL, &amp; recta LI &aelig;qualis rect&aelig; IK, &amp; LF &aelig;qua&shy;<lb/>lis ip&longs;i FK, &amp; FI communis, triangulum LFI, &aelig;quale e&longs;t <lb/>triangulo IFK. </s>
            <s id="s.002000">Quare &amp; angulus FIL aequalis angulo FIK, <lb/>&longs;ed GIF, HIF recti &longs;unt, ergo re&longs;idui LIG, KIH &aelig;quales <lb/>&longs;unt inter &longs;e comparati, &amp; recto minores; quod fuerat o&shy;<lb/>&longs;tendendum. </s>
          </p>
          <p type="main">
            <s id="s.002001">Hinc colligimus, quo magis planum ab &aelig;quidi&longs;tan&shy;<lb/>tia horizontis rece&longs;&longs;erit, eo pilam in eo proiectam in par&shy;<lb/>tes in &aelig;qualiores diuidi &amp; ad minores ip&longs;i plano angulos <lb/>re&longs;ilire. </s>
            <s id="s.002002">Nihil autem refert, vtrum planum, in quod pila <lb/>cadit, ad horizontem &longs;it inclinatum, vel eodem horizonti <lb/>&aelig;quedi&longs;tante pila non ad perpendiculas, &longs;ed iuxta <expan abbr="aliqu&emacr;">aliquem</expan> <lb/>angulum in illud proijciatur. </s>
            <s id="s.002003">H&aelig;c &longs;ane ita ex demon&longs;tra&shy;<lb/>tione fieri o&longs;tenduntur. </s>
            <s id="s.002004">Veruntamen quoniam proiecta <lb/>pila materialis e&longs;t, &amp; ideo nec &aelig;qualis, nec &aelig;queponde&shy;<lb/>rans &amp; &longs;ua grauitate re&longs;i&longs;tens, non ad pares ex amu&longs;&longs;i re&longs;i&shy;<lb/>lit angulos, &longs;ed minores aliquantulum in re&longs;ilitione, re. <lb/></s>
            <s id="s.002005">mittente nimirum vi in ip&longs;a reactione. </s>
            <s id="s.002006">Et &longs;ane fieri non <pb xlink:href="007/01/205.jpg"/>pote&longs;t, pilam &agrave; plano re&longs;ilientem eo peruenire vnde &agrave; <lb/>principio di&longs;ce&longs;&longs;erat; Id enim &longs;i daretur, &aelig;terna quoque <lb/>pil&aelig; ip&longs;ius daretur re&longs;ilitio, &amp; paullatim vi &amp; impetu re&shy;<lb/>mittente per parua interualla motus e&longs;&longs;et, donec res qu&aelig; <lb/>mouebatur, omnino quie&longs;cat. </s>
          </p>
        </subchap1>
        <subchap1>
          <p type="head">
            <s id="s.002007">QV&AElig;STIO XXXV.<!-- KEEP S--></s>
          </p>
          <p type="head">
            <s id="s.002008"><emph type="italics"/>Qu&aelig;rit hoc vltimo Problemate Ari&longs;toteles, Cur ea qu&aelig; in vorti&shy;<lb/>co&longs;is feruntur aquis, ad medium tandem agan&shy;<lb/>tur omnia?<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.002009">Tribus rationibus &longs;oluit; quarum prima e&longs;t: Quicquid <lb/>fertur, magnitudinem habet, cuius extrema in duo&shy;<lb/>bus &longs;unt circulis, hoc in minori, illud in maiori. </s>
            <s id="s.002010">Et quo&shy;<lb/>niam maior velocior e&longs;t, magnitudo media, non &aelig;quali&shy;<lb/>ter fertur, &longs;ed &agrave; maiori quidem pellitur, &agrave; minori vero re&shy;<lb/>trahitur, vnde transuer&longs;us fit magnitudinis motus, &amp; ip&longs;a <lb/>magnitudo ad interiorem propellitur circulum, itaque <lb/>eodem pacto, &egrave; maiori in minorem propul&longs;a in centrum. <lb/></s>
            <s id="s.002011">tantum fertur, &amp; ibi quie&longs;cit. </s>
          </p>
          <figure id="id.007.01.205.1.jpg" xlink:href="007/01/205/1.jpg"/>
          <p type="main">
            <s id="s.002012">E&longs;to vortex AB, cuius cen&shy;<lb/>trum C, magnitudo qu&aelig; fer&shy;<lb/>tur AD, maior circulus AFB, <lb/>minor DHEG. <!-- KEEP S--></s>
            <s id="s.002013">Velocitas igi&shy;<lb/>tur in A maior e&longs;t velocitate <lb/>qu&aelig; in D, magnitudinis ergo <lb/>extremum A, velocius rapitur <lb/>in A quam eiu&longs;dem extremum <lb/>inferius D, in D. <!-- KEEP S--></s>
            <s id="s.002014">Velocitas igi&shy;<lb/>tur maioris circuli pellit Aver&shy;<lb/>&longs;us F. tarditas vero minoris cir&shy;<lb/>culi D retrahit ad partes G. conuertitur itaque magnitu&shy;<lb/>do inter pellentem &amp; retrahentem circulum, donec ex&shy;<pb xlink:href="007/01/206.jpg"/>tremitas A in circulo minori fuerit vbi H, D vero vbi I, &amp; <lb/>ita deinceps eadem ratione vbi KL, donec paullatim fe&shy;<lb/>ratur in centrum C, facto nempe &agrave; maiori in minorem cir&shy;<lb/>culum tran&longs;itu. </s>
          </p>
          <p type="main">
            <s id="s.002015">Secunda ratio ita habet, quia quod fertur, &longs;imili &longs;e <lb/>habet modo ad omnes circulos propter centrum, hoc e&longs;t, <lb/>in quouis circulo, qui circa idem centrum fertur. </s>
            <s id="s.002016">Omnes <lb/>autem circuli mouentur, centrum vero &longs;tat, nece&longs;&longs;e e&longs;t &agrave; <lb/>motu tandem id quod mouetur ad quietis locum, hoc e&longs;t, <lb/>in centrum ip&longs;um peruenire. </s>
          </p>
          <p type="main">
            <s id="s.002017">Tertia, quoniam circulorum, qui in vorticibus fiunt, <lb/>velocitas, &amp; ideo impetus non e&longs;t &aelig;qualis, &longs;ed &longs;emper ex&shy;<lb/>terior e&longs;t interiore velocior &amp; violentior, &AElig;qualis autem <lb/>&longs;emper in mota magnitudine, grauitas, diuer&longs;i mode &longs;e <lb/>habet ad circulos, &agrave; quibus mouetur, &amp; ideo modo vin&shy;<lb/>citur, modo vincit: vincitur autem &agrave; velocioribus circulis, <lb/>vincit autem tardiores. </s>
            <s id="s.002018">Ita que quoniam &longs;ua grauitate re&shy;<lb/>&longs;i&longs;tens, maioris circuli motum pror&longs;us non &longs;equitur, ad <lb/>tardiorem reijcitur, hoc e&longs;t, interiorem, &amp; &longs;ic deinceps, <lb/>donec tandem centrum ip&longs;um nanci&longs;catur, in quo nec &longs;u&shy;<lb/>perans, nec &longs;uperata quie&longs;cit. </s>
          </p>
          <p type="main">
            <s id="s.002019">H&aelig; &longs;unt rationes, licet ob&longs;curi&longs;&longs;ime propo&longs;it&aelig;, qui&shy;<lb/>bus, vt diximus, vtitur Ari&longs;toteles. <!-- KEEP S--></s>
            <s id="s.002020">acut&aelig; &longs;ane ill&aelig; <expan abbr="quid&emacr;">quidem</expan>, <lb/>attamen haudquaquam vltro admittend&aelig;. </s>
          </p>
          <p type="main">
            <s id="s.002021">Primo enim fal&longs;um videtur, quod a&longs;&longs;erit, vortices <lb/>circulos e&longs;&longs;e, &amp; circa idem centrum fieri atque rotari. </s>
            <s id="s.002022">Spi&shy;<lb/>r&aelig; enim potius &longs;unt, qu&aelig; ab exteriori parte <expan abbr="remotioreq;">remotioreque</expan> <lb/>incipientes &longs;piraliter circumuolut&aelig;, ad intimam tandem <lb/>partem, qu&aelig; media e&longs;t &amp; centri vices gerit, deueniunt. <lb/></s>
            <s id="s.002023">qua veritate cognita, omnis pror&longs;us difficultas tollitur, <lb/>Cum enim ea qu&aelig; feruntur, ab aqua ferantur, aqua vero <lb/>feratur &longs;piraliter, ea quoque &longs;piraliter ferri, e&longs;t nece&longs;&longs;a-<pb xlink:href="007/01/207.jpg"/>rium. </s>
            <s id="s.002024">H&aelig;c autem clariora erunt &longs;i quo pacto vortices <lb/>fiant, qui&longs;piam con&longs;iderauerit. </s>
          </p>
          <figure id="id.007.01.207.1.jpg" xlink:href="007/01/207/1.jpg"/>
          <p type="main">
            <s id="s.002025">E&longs;to fluminis cuiu&longs;piam curua <lb/>eademque profunda ripa ABCD. <lb/><!-- KEEP S--></s>
            <s id="s.002026">Aqu&aelig; vero moles rapida EFDC, <lb/>qu&aelig; quidem eo quod magno impe&shy;<lb/>tu deferatur in C, rip&aelig; ip&longs;ius <expan abbr="natur&atilde;">naturam</expan> <lb/>&longs;equens turbinatim circum uoluitur, <lb/>egre&longs;&longs;a autem extra locum &longs;eu ripam <lb/>B rotationis principium &longs;ecundans, <lb/>in &longs;eip&longs;am &longs;piraliter contorquetur, <lb/>&amp; vorticem efficit GHFIK, cuius <lb/>quidem centrum e&longs;t vbi K. <!-- KEEP S--></s>
          </p>
          <p type="main">
            <s id="s.002027">Alia quoque de cau&longs;&longs;a, ex quie&longs;cente nimirum, &amp; <lb/>mota aqua fiunt &longs;pir&aelig; vorticesue. </s>
            <s id="s.002028">E&longs;to enim fluminis ripa <lb/><figure id="id.007.01.207.2.jpg" xlink:href="007/01/207/2.jpg"/><lb/>ABC, &longs;inum efficiens, qui a quam ex <lb/>rip&aelig; ip&longs;ius obiectu contineat quie&shy;<lb/>&longs;centem, Cur&longs;us vero fluminis liber &amp; <lb/>rectus, &longs;it inter lineas AC, DE. <!-- KEEP S--></s>
            <s id="s.002029">Itaque <lb/>dum aqua AC rapide fertur ad partes <lb/>A, quie&longs;centem ABC iuxta lineam. <lb/></s>
            <s id="s.002030">CA lateraliter propellit, &amp; eius qui&shy;<lb/>dem partem quam tangit, &longs;ecum ra&shy;<lb/>pit, puta ex F in G. <!-- KEEP S--></s>
            <s id="s.002031">Delata igitur aqua <lb/>&amp; currente ex F ver&longs;us G quie&longs;cens <lb/>lateraliter eidem &longs;e&longs;e aliqualiter op&shy;<lb/>ponit, &amp; currentem repellit ex G in H. <!-- KEEP S--></s>
            <s id="s.002032">C&oelig;pto <expan abbr="itaq;">itaque</expan> &longs;pirali <lb/>motu aqua circumuoluitur &longs;ecundum lineam GHK, do&shy;<lb/>nec perueniat ad centrum I, vbi circumuolut&aelig; aqu&aelig; par&shy;<lb/>tes &longs;e&longs;e inuicem tangunt. </s>
            <s id="s.002033">Porro vortices i&longs;ti &longs;pir&aelig;ue, quod <lb/>nos per Padum, Abduam, &amp; magna flumina nauigantes <lb/>ob&longs;eruauimus, non eodem permanent loco, &longs;ed rapientis <lb/>aqu&aelig; motum &longs;ecundantes, paullatim in currentem <expan abbr="aqu&atilde;">aquam</expan> <pb xlink:href="007/01/208.jpg"/>delati euane&longs;cunt, fiunt etiam eiu&longs;cemodi vortices nau&shy;<lb/>tis quidem valde formidabiles etiam in mari, de quibus <lb/>Po&euml;ta libro &AElig;neidos primo. </s>
          </p>
          <p type="main">
            <s id="s.002034">&mdash; <emph type="italics"/>a&longs;t illam ter fluctus ibidem <lb/>Torquet agens circum, &amp; rapidus vorat &aelig;quore vortex.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.002035">Sed &amp; idem quoque de vorticibus, qui in fluminibus <lb/>fiunt libro 7. </s>
          </p>
          <p type="main">
            <s id="s.002036">&mdash; <emph type="italics"/>hunc inter fluuio Tiberinus am&oelig;no <lb/>Vorticibus rapidis, &amp; multa flauus arena <lb/>In mare prorumpit.<emph.end type="italics"/></s>
          </p>
          <p type="main">
            <s id="s.002037">Fiunt autem in mari partim occultis de cau&longs;&longs;is, partim <lb/>etiam ex violentia aquarum &longs;ibi inuicem obuiantium a&shy;<lb/>gitatione. </s>
            <s id="s.002038">Sed nos hi&longs;ce explicatis commode ad ea qu&aelig; <lb/>dixerat Ari&longs;toteles, reuertemur. </s>
          </p>
          <p type="main">
            <s id="s.002039">Dicimus igitur, primam eius rationem haud magni <lb/>videri ponderis, &longs;iquidem non per circulos actu di&longs;tinctos <lb/>aqua circumfertur, &longs;ed ip&longs;amet &longs;ua mole tota &longs;imul. </s>
          </p>
          <figure id="id.007.01.208.1.jpg" xlink:href="007/01/208/1.jpg"/>
          <p type="main">
            <s id="s.002040">E&longs;to enim vortex AB, cu&shy;<lb/>ius centrum C, &longs;emidiameter <lb/>CA, fiat autem rotatio totius a&shy;<lb/>qu&aelig; CA ad partes D, in linea <lb/>autem AC, &longs;it corpus aliquod a&shy;<lb/>qu&aelig; rotatione <expan abbr="circumlat&umacr;">circumlatum</expan> AE, <lb/>inter circulos maiorem ADB, <lb/>minorem EFG. velocius autem <lb/>mouetur ADB, ip&longs;o EFG, citius <lb/>ergo fertur pars &longs;uperior ip&longs;ius <lb/>corporis vbi A, quam inferior <lb/>vbi E. <!-- KEEP S--></s>
            <s id="s.002041">At id nec A repellit, nec E retrahit, &longs;iquidem eodem <lb/>tempore quo A permeauit <expan abbr="circul&umacr;">circulum</expan> ADB, eodem &amp; E per&shy;<lb/>currit circulum EFG. <expan abbr="Itaq;">Itaque</expan> A reuer&longs;o in A &amp; E, punctum <lb/>reuer&longs;um erit in E, nulla facta corporis E quoad &longs;itum, <lb/>muratione quod voluit Ari&longs;toteles. <!-- KEEP S--></s>
          </p>
          <pb xlink:href="007/01/209.jpg"/>
          <p type="main">
            <s id="s.002042">Ad &longs;ecundam vero dicimus, non ideo quod omnes <lb/>circuli &aelig;qualiter circa centrum &longs;erantur, ni&longs;i alia <expan abbr="qu&aelig;pi&atilde;">qu&aelig;piam</expan> <lb/>extranea vis interce&longs;&longs;erit, qu&aelig; ea ab exterioribus circulis <lb/>pellens agat in medium. </s>
          </p>
          <figure id="id.007.01.209.1.jpg" xlink:href="007/01/209/1.jpg"/>
          <p type="main">
            <s id="s.002043">Tertia quoque ratio la&shy;<lb/>borare videtur. </s>
          </p>
          <p type="main">
            <s id="s.002044">E&longs;to enim vortex AB, <lb/>cuius centrum C, &longs;it autem <lb/>corpus aliquod E, cuius na&shy;<lb/>tura apta &longs;it rotationi aliqua&shy;<lb/>tenus re&longs;i&longs;tere. </s>
            <s id="s.002045">Quoniam i&shy;<lb/>gitur eius re&longs;i&longs;tentia <expan abbr="aliqu&atilde;-tulum">aliquan&shy;<lb/>tulum</expan> ab aqua rapiente &longs;u&shy;<lb/>peratur in ip&longs;a rotatione, par&shy;<lb/>tim aquae impetum &longs;equetur, <lb/>partim &longs;uapte natura retardabitur. </s>
            <s id="s.002046">Quamobrem aqua <lb/>qu&aelig; e&longs;t in A, translata in H, corpus ip&longs;um non erit in H, <lb/>&longs;ed in G. <!-- KEEP S--></s>
            <s id="s.002047">Tardius igitur corpus quam aqua ip&longs;a, rotatio&shy;<lb/>nem complebit, non tamen propterea, ni&longs;i alia qu&aelig; piam <lb/>ad&longs;it cau&longs;&longs;a, feretur in medium. </s>
          </p>
          <p type="main">
            <s id="s.002048">C&aelig;terum horum vorticum effectum &amp; cau&longs;&longs;am ob&shy;<lb/>&longs;eruare licet, &longs;i va&longs;e quopiam aqua pleno aquam ip&longs;am <lb/>baculo manuue circulariter agitauerimus, fiet enim vor&shy;<lb/>tex, &amp; &longs;i quippiam quod leue &longs;it, in aquam motam proie&shy;<lb/>cerimus, ea quam diximus de cau&longs;&longs;a in motum ip&longs;um, hoc <lb/>e&longs;t, vorticis &longs;pir&aelig;ue, centrum feretur. </s>
          </p>
          <p type="main">
            <s id="s.002049">H&aelig;c nos, vt vera proponimus, &amp; forta&longs;&longs;e decipimur. <lb/></s>
            <s id="s.002050">Certe Philo&longs;opho tant&aelig; auctoritatis contradicere, ma&shy;<lb/>gn&aelig; videtur audaci&aelig;, aut potius in&longs;ani&aelig;. </s>
            <s id="s.002051">Quicquid ta&shy;<lb/>men &longs;it, pro pulcherrima veritate labora&longs;&longs;e, &agrave; parte <lb/>aliqua laudis non fuerit pror&longs;us, vt <lb/>arbitror, alienum. </s>
          </p>
          <pb xlink:href="007/01/210.jpg"/>
        </subchap1>
      </chap>
      <chap>
        <p type="head">
          <s id="s.002052">APPENDIX.<!-- KEEP S--></s>
        </p>
        <p type="main">
          <s id="s.002053">Modum inueniendarum duarum mediarum propor&shy;<lb/>tionalium non tantum vtilem e&longs;&longs;e, &longs;ed pror&longs;us nece&longs;&shy;<lb/>&longs;arium, illi norunt, qui in Mechanicis di&longs;ciplinis vel <expan abbr="par&umacr;">parum</expan> <lb/>fuerint ver&longs;ati. </s>
          <s id="s.002054">Nulla enim alia ratio e&longs;t, qua corporeae ma&shy;<lb/>gnitudines &longs;eruata figura &amp; &longs;imilitudine augeri propor&shy;<lb/>tionaliter imminuiue po&longs;&longs;int. </s>
          <s id="s.002055">Quamobrem factum e&longs;t vt <lb/>in his inueniendis tum vetu&longs;ti&longs;&longs;imo tum etiam in feriori &aelig;&shy;<lb/>uo, clari&longs;&longs;imi Viri magnopere laborauerint. </s>
          <s id="s.002056">Plato etenim, <lb/>Eudoxus &lpar;cuius modum repudiauit Eutocius&rpar; Heron A&shy;<lb/>lexandrinus, Philon Byzantius, Apollonius, clari&longs;&longs;imi <lb/>Geometr&aelig;, Diocles, Pappus, Sporus, Men&aelig;chmus, Ar&shy;<lb/>chytas Tarentinus, Platoni &aelig;qualis: Erato&longs;thenes, &amp; Ni&shy;<lb/>comedes ad has inueniendas varias rationes <expan abbr="excogitar&umacr;t">excogitarunt</expan>, <lb/>quorum omnium modos, &amp; in&longs;trumenta, <expan abbr="demon&longs;tratio-ne&longs;q;">demon&longs;tratio&shy;<lb/>ne&longs;que</expan> diligenti&longs;&longs;ime collegit, &amp; in illos <expan abbr="C&omacr;mentarios">Commentarios</expan> con&shy;<lb/>iecit idemmet Eutocius, quos eleganti&longs;&longs;imos in Archime&shy;<lb/>dis libros de Sph&aelig;ra &amp; Cylindro &longs;crip&longs;it. </s>
          <s id="s.002057">Nos autem ijs o&shy;<lb/>mnibus accurate per&longs;pectis, &amp; diligenti&longs;&longs;ime ponderatis, <lb/>inuenimus eos fere omnes tentando negotium ab&longs;olue&shy;<lb/>re, quod &longs;ane laborio&longs;um valde e&longs;t &amp; operantibus permo&shy;<lb/>le&longs;tum. </s>
          <s id="s.002058">Itaque cum modum praximue inueni&longs;&longs;emus, ex <lb/>qua is qui operatur tuti&longs;&longs;ime &amp; facillime ad qu&aelig; &longs;itas ip&longs;as <lb/>medias manu ducitur, hunc pulcherrim&aelig; huius facultatis <lb/>&longs;tudio &longs;is inuidere nefarium iudicauimus. </s>
          <s id="s.002059">Quod &longs;i <expan abbr="qui&longs;pi&atilde;">qui&longs;piam</expan> <lb/>dixerit, Balli&longs;tarum, Catapultarum, Scorpionum, &amp; c&aelig;&shy;<lb/>terarum eiu&longs;cemodi Machinarum v&longs;um, olim apud nos <lb/>de&longs;ij&longs;&longs;e, &amp; ideo Problema hoc videri &longs;uperuacaneum, Re&shy;<lb/>&longs;pondemus, nulla alia ratione &aelig;neorum tormentorum pi&shy;<lb/>las augeri imminuiue &longs;eruata ponderis ratione po&longs;&longs;e, in&shy;<lb/>numeraque e&longs;&longs;e, qu&aelig; vt rite perficiantur, h&aelig;c penitus in&shy;<lb/>digent &longs;peculatione. </s>
          <s id="s.002060">Nos rem Mechanicis vtilem, Me. <pb xlink:href="007/01/211.jpg"/>chanicis no&longs;tris Exercitationibus annectere, haud im&shy;<lb/>portunum iudicauimus. </s>
          <s id="s.002061">Sed tempus e&longs;t, vt his breuiter <lb/>pr&aelig;fatis, ad rem ip&longs;am <expan abbr="explicand&atilde;">explicandam</expan> commode accedamus. </s>
        </p>
        <p type="head">
          <s id="s.002062"><emph type="italics"/>Datis duabus proportionalibus prima, &amp; quarta duas inter eas <lb/>medias in continua proportione inuenire.<emph.end type="italics"/></s>
        </p>
        <p type="main">
          <s id="s.002063">Esto prima datarum AB, quarta BC, inter quas <expan abbr="&longs;ecund&atilde;">&longs;ecundam</expan> <lb/>&amp; tertiam oportet inuenire. </s>
          <s id="s.002064">Ducatur recta DE, cui &agrave; <lb/>puncto F, vtcunque &longs;umpto, perpendicularis demittatur <lb/>FG, Tum ab F ver&longs;us D duplicetur quarta BC, &longs;itque FH, <lb/>deinde ab H ip&longs;i FG parallela demittatur HI, &amp; ab HF <lb/>ab&longs;cindatur HK, ip&longs;ius BC quart&aelig; medietati &aelig;qualis. <lb/></s>
          <s id="s.002065">Po&longs;th&aelig;c puncto K &longs;patio autem medietati, prim&aelig; data&shy;<lb/>rum &aelig;quali, in linea HI notetur punctum L, &amp; ip&longs;i HL <lb/>fiat &aelig;qualis FM, &amp; KM iungatur. </s>
          <s id="s.002066">His ita con&longs;titutis pare&shy;<lb/>tur &longs;eor&longs;um &longs;cheda regulaue qu&aelig;piam NO, in cuius late&shy;<lb/>re accipiatur OP, &aelig;qualis medietati prim&aelig; datarum &longs;eu <lb/>ip&longs;i KL. <!-- KEEP S--></s>
          <s id="s.002067">Tum regul&aelig; latus aptetur puncto L, extremum <lb/>vero O, feratur a&longs;&longs;idue per rectam EK, ver&longs;us K, nunquam <lb/><figure id="id.007.01.211.1.jpg" xlink:href="007/01/211/1.jpg"/><pb xlink:href="007/01/212.jpg"/>interim regul&aelig; latere ON amoto &agrave; puncto L, idque do&shy;<lb/>nec punctum P, obuians incidat in lineam KM, puta vbi <lb/>Q extremum vero O inueniatur in R, notato igitur in li&shy;<lb/>nea EK puncto R habebitur, quod qu&aelig;rebatur. </s>
          <s id="s.002068">Erunt i&shy;<lb/>gitur AB prima, RK &longs;ecunda, QL tertia, BC quarta. </s>
        </p>
        <p type="main">
          <s id="s.002069">H&aelig;c praxis ij&longs;dem principijs demon&longs;tratur, quibus <lb/>&longs;uam ex Conchoide o&longs;tendit Nicomedes. </s>
          <s id="s.002070">Conficit ille <lb/>in&longs;trumentum, ex quo de&longs;cribit <expan abbr="Conchoid&emacr;">Conchoidem</expan>, ex qua po&longs;t&shy;<lb/>ea duas medias venatur. </s>
          <s id="s.002071">Nos autem nec in&longs;trumentum <lb/>con&longs;truimus nec Conchoidem de&longs;cribimus, &amp; duabus fe&shy;<lb/>re lineis rem ab&longs;oluimus, vt nemo fere non dixerit, hoci&shy;<lb/>&longs;tud quod docemus, &agrave; Nicomedea praxi e&longs;&longs;e pror&longs;us a&shy;<lb/>lienum. </s>
        </p>
        <p type="main">
          <s id="s.002072">Sed nos, vt eius, quam o&longs;tendimus, operationis de&shy;<lb/>mon&longs;tratio habeatur; ip&longs;ius Nicomedis ex Pappi libro 3. <lb/>propo&longs;. </s>
          <s id="s.002073">5. de&longs;umptam in medio afferemus, quippe quod <lb/>i&longs;th&aelig;c ea quam in &longs;uis in Archimedem commentarijs re&shy;<lb/>fert Eutocius, &longs;it lucidior. </s>
        </p>
        <p type="main">
          <s id="s.002074">Datis duabus rectis lineis CD, DA; du&aelig; medi&aelig; in <lb/>continua proportione hoc modo a&longs;&longs;umuntur. </s>
        </p>
        <p type="main">
          <s id="s.002075">Compleatur ABCD parallelogrammum, &amp; <expan abbr="vtraq;">vtraque</expan> <lb/>ip&longs;arum AB, BC, bifariam &longs;ecetur in punctis L, E, iuncta&shy;<lb/>que LD producatur; &amp; occurrat product&aelig; CB, in G, ip&longs;i <lb/>vero BC ad rectos angulos ducatur EF, &amp; CF iungatur, <lb/>qu&aelig; &longs;it &aelig;qualis AL. <!-- KEEP S--></s>
          <s id="s.002076">Iungatur pr&aelig;terea FG &amp; ip&longs;i paralle&shy;<lb/>la &longs;it CH, eritque angulus KCH, &aelig;qualis angulo CGF. <lb/></s>
          <s id="s.002077">Tum &agrave; dato puncto F ducatur FHK, quae faciat KH &aelig;qua&shy;<lb/>lem ip&longs;i AL vel CF. <!-- KEEP S--></s>
          <s id="s.002078">Hoc enim per lineam Conchoidem <lb/>fieri po&longs;&longs;e o&longs;tendit Nicomedes, &amp; iuncta KD producatur, <lb/>occurratque ip&longs;i BA, product&aelig; in puncto M. <!-- KEEP S--></s>
          <s id="s.002079">Dico vt DC <lb/>ad CK ita CK ad MA &amp; MA ad AD. <!-- KEEP S--></s>
          <s id="s.002080">Quoniam enim BC <lb/>bifariam &longs;ecta e&longs;t in E, &amp; ip&longs;i adijcitur CK. <!-- KEEP S--></s>
          <s id="s.002081">Rectangulum <lb/>BKC per 6. &longs;ecundi: vna cum quadrato ex CE, &aelig;quale e&longs;t <pb xlink:href="007/01/213.jpg"/><figure id="id.007.01.213.1.jpg" xlink:href="007/01/213/1.jpg"/><lb/>quadrato ex EK. commune apponatur ex EF quadratum, <lb/>ergo rectangulum BKC vna cum quadrato CF &aelig;quale <lb/>e&longs;t quadratis ex KE, EF, hoc e&longs;t, quadrato ex FK. <!-- KEEP S--></s>
          <s id="s.002082">Et quo&shy;<lb/>niam vt MA ad AB, ita e&longs;t MD ad DK, vt autem MD ad <lb/>DK per 2. &longs;exti, ita BC ad C<emph type="italics"/>K<emph.end type="italics"/> erit vt MA ad AB, ita BC <lb/>ad C<emph type="italics"/>K<emph.end type="italics"/>. <!-- KEEP S--></s>
          <s id="s.002083">Atque e&longs;t ip&longs;ius AB dimidia AL, &amp; ip&longs;ius BC, du&shy;<lb/>pla CG, e&longs;t igitur vt MA ad AL, ita GC ad C<emph type="italics"/>K<emph.end type="italics"/>. <!-- KEEP S--></s>
          <s id="s.002084">Sed vt GC <lb/>ad C<emph type="italics"/>K<emph.end type="italics"/>, ita FH ad H<emph type="italics"/>K<emph.end type="italics"/> propter lineas parallelas GF, CH. <lb/>quare &amp; componendo vt ML, ad LA, ita F<emph type="italics"/>K<emph.end type="italics"/> ad <emph type="italics"/>K<emph.end type="italics"/>H, &longs;ed <lb/>AL ponitur &aelig;qualis H<emph type="italics"/>K<emph.end type="italics"/>, quoniam &amp; ip&longs;i CF, ergo &amp; ML <lb/>per 9. lib.  5. &aelig;qualis erit F<emph type="italics"/>K<emph.end type="italics"/>, &amp; quadratum ex ML, &aelig;quale <lb/>quadrato ex F<emph type="italics"/>K<emph.end type="italics"/>. <!-- KEEP S--></s>
          <s id="s.002085">e&longs;t autem quadrato ex ML, &aelig;quale re&shy;<lb/>ctangulum BMA vna cum quadrato ex AL &amp; quadrato <lb/>ex Fk &aelig;quale o&longs;ten&longs;um e&longs;t rectangulum BkC vna cum. <pb xlink:href="007/01/214.jpg"/>quadrato ex CF, quorum quidem quadratum ex AL &aelig;&shy;<lb/>quale e&longs;t quadrato ex CF, ponitur enim AL, ip&longs;i CF &aelig;&shy;<lb/>qualis, ergo reliquum BMA rectangulum &aelig;quale e&longs;t reli&shy;<lb/>quo BkC. <!-- KEEP S--></s>
          <s id="s.002086">Vt igitur MB ad Bk, ita Ck ad MA. <!-- KEEP S--></s>
          <s id="s.002087">Sed vt MD <lb/>ad Bk, ita DC ad Ck. <!-- KEEP S--></s>
          <s id="s.002088">quare vt DC ad Ck, ita e&longs;t Ck ad <lb/>MA. vt autem MD ad Bk, ita MA, ad AD. <!-- KEEP S--></s>
          <s id="s.002089">Ergo vt DC, <lb/>prima, ad Ck &longs;ecundam, ita Ck &longs;ecunda ad MA tertiam, <lb/>&amp; MA tertia ad AD quartam, quod fuerat demon&longs;tran&shy;<lb/>dum. </s>
          <s id="s.002090">H&aelig;c Pappus. <!-- KEEP S--></s>
          <s id="s.002091">Quod autem in no&longs;tra Praxi diximus, <lb/>QL e&longs;&longs;e tertiam, ea ratio e&longs;t, quod LR vt in prima figura <lb/>e&longs;t, &longs;it &aelig;qualis ip&longs;i LM &longs;ecund&aelig; figur&aelig;, in demon&longs;tratio&shy;<lb/>ne Pappi, ex quibus demptis QR &amp; LA, qu&aelig; &longs;unt &aelig;qua&shy;<lb/>les, reliqua QL prim&aelig; figur&aelig; &aelig;qualis e&longs;t AM &longs;ecund&aelig; fi&shy;<lb/>gur&aelig;, hoc e&longs;t, ip&longs;i terti&aelig; proportionali: E&longs;t igitur, vt in pri&shy;<lb/>ma figura dicebamus, AB prima, kR &longs;ecunda, QL tertia, <lb/>BC quarta. </s>
        </p>
        <p type="main">
          <s id="s.002092">Vides igitur tu qui legis, nos ex Nicomedis demon&shy;<lb/>&longs;tratione &lpar;quatenus ad praxin pertinet&rpar; &longs;uperflua re&longs;eca&longs;&shy;<lb/>&longs;e, &amp; ab&longs;que Conchoidis in&longs;trumento lineaue rem ip&longs;am <lb/>confeci&longs;&longs;e, idque non tentantes, vt alij, &longs;ed progre&shy;<lb/>dientes, &amp; qua&longs;i manuductos qu&aelig;&longs;i&shy;<lb/>tum inue&longs;tiga&longs;&longs;e. </s>
        </p>
        <p type="head">
          <s id="s.002093">FINIS.<lb/> <!-- KEEP S--></s>
        </p>
      </chap>
    </body>
    <back/>
  </text>
</archimedes>