<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd">
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink">
  <info>
    <author>Marci von Kronland, Johannes Marcus </author>
    <title>De proportione motus seu Regula sphygmica ad celeritatem et tarditatem pulsuum</title>
    <date>1639</date>
    <place>Prague</place>
    <translator/>
    <lang>la</lang>
    <cvs_file>marci_regul_062_la_1639.xml</cvs_file>
    <cvs_version/>
    <locator>062.xml</locator>
  </info>
  <text>
    <front>
      <section>
        <pb xlink:href="062/01/001.jpg"/>
        <p id="N1001B" type="main">
          <s id="N1001D"><emph type="center"/>DE PROPORTIONE MOTUS<emph.end type="center"/></s>
        </p>
        <p id="N10024" type="main">
          <s id="N10026"><emph type="center"/><emph type="italics"/>seu <lb/>
Regula &longs;phyigmica <lb/>AD celeritatem et tarditatem pul&longs;uum ex illius motu <lb/>
ponderibus geometricis librato <expan abbr="ab&longs;q;">ab&longs;que</expan> errore metiendam. </s>
          <lb/>
          <s id="N10038">
Authore <lb/>
Ionanne Marco Marci Phil:ae er Medic:ae Doctore et ordi<lb/>
nario Profe&longs;&longs;ore eiu&longs;dem Medic: facultatis in Vni<lb/>
uer&longs;itate Pragen&longs;i Phy&longs;ico Reg: Boh.<emph.end type="italics"/><emph.end type="center"/></s>
        </p>
        <pb xlink:href="062/01/002.jpg"/>
        <p id="N10048" type="caption">
          <s id="N1004A">IOANNES MARCVS MARCI PHIL: &amp; MEDIC: DOCTOR <lb/><emph type="italics"/>et Profe&longs;&longs;or natus Landscron&aelig; Hermundurarum in Bo&euml;mia <lb/>anno 1595, 13 Iunij.<emph.end type="italics"/></s>
        </p>
      </section>
      <section>
        <figure id="id.062.01.002.1.jpg" xlink:href="062/01/002/1.jpg"/>
        <pb xlink:href="062/01/003.jpg"/>
        <p id="N1005E" type="main">
          <s id="N10060"><emph type="center"/>DIVO <lb/>FERDINANDO <lb/>TERTIO<emph.end type="center"/></s>
        </p>
        <p id="N1006B" type="main">
          <s id="N1006D"><emph type="center"/>AUGUSTISSIMO ROMANORUM <lb/>IMPERATORI<emph.end type="center"/></s>
        </p>
        <p id="N10076" type="main">
          <s id="N10078"><emph type="center"/>Hungari&aelig; &amp; Bohemi&aelig; Regi &amp;c. <lb/><emph type="italics"/>Domino meo Clementi&longs;&longs;imo.<emph.end type="italics"/><emph.end type="center"/></s>
        </p>
        <p id="N10085" type="main">
          <s id="N10087"><emph type="center"/>Augu&longs;ti&longs;sime C&aelig;&longs;ar<emph.end type="center"/></s>
        </p>
        <p id="N1008E" type="main">
          <s id="N10090">DVm ut annus hic nouus TU&AElig; Maje&shy;<lb/>&longs;tati au&longs;picatus ordiatur, vota conci&shy;<lb/>pio, &amp; &agrave; tenuitate me&agrave; munu&longs;culum <lb/>TU&AElig; Maie: gratum e flagito: ecce ti&shy;<lb/>bi hunc ip&longs;um, qui annum au&longs;picatur, <expan abbr="atq;">atque</expan> &longs;ua in ve<lb/>&longs;tigia reuoluit, motum mihi ultr&ograve;, ut Mercurius &longs;it <lb/>&amp; munus, &longs;e offerentem: quid enim inquit extra <lb/>me qu&aelig;ris? in me &longs;unt omnia.</s>
          <s id="N100A5"> Ab&longs;it, in quam ego, <lb/>ut ad C&aelig;&longs;arem eas, qui tam in&longs;tabilis es &amp; infidus, 


<pb xlink:href="062/01/004.jpg"/><expan abbr="atq;">atque</expan> eadem, qu&aelig; dare videbaris, rur&longs;um aufers. </s>
          <s id="N100B1">Nul<lb/>lum, inquit ille periculum ab in&longs;tabilitate: hic enim <lb/>Senex, ut vides, me quadratum fecit: qu&ograve;d &longs;i tibi ita <lb/>videtur, me vel cubum facias. </s>
          <s id="N100BA">Ben&egrave; inquam res ha&shy;<lb/>bet, ad C&aelig;&longs;aremibis: ver&ugrave;m his ego te pri&ugrave;s circu&shy;<lb/>lis illigabo, <expan abbr="at&qacute;">atque</expan>; his lineis ceu virgulis &longs;ub leges Geo&shy;<lb/>metri&aelig; cogam, ut non ni&longs;i ad nutum C&aelig;&longs;aris mo&shy;<lb/>uearis: &longs;is autem men&longs;ura &amp; &longs;imul cu&longs;tos illius mo<lb/>tus, &agrave; quo Regalis vita pendet. </s>
          <s id="N100CB">Hunc ergo motum <lb/>Augu&longs;ti&longs;sime C&aelig;&longs;ar modulis geometricis ad&longs;tri&shy;<lb/>ctum, &amp; nunc Medicin&aelig; famulantem ad TUAM <lb/>Maie&longs;tatem tanquam Primum Motorem remitto, <lb/>qui &amp; cores &amp; Sol Imperij &amp; Regnorum, Tu&aelig;que <lb/>benignitatis motu hunc in me motum commoui&shy;<lb/>&longs;ti. </s>
          <s id="N100DA">Motum quidem hunc TU&AElig; Maie&longs;tati vt Soli <lb/>&amp; Motori, at ver&ograve; eidem Soli vt illuminatori Iri&shy;<lb/>dem votiuam, gratitudinis &amp; debit&aelig; ob&longs;ervanti&aelig; <lb/>ergo &agrave; TU&AElig; Maie&longs;tatis radijs conceptam hic idem <lb/>annus in proximo dabit: quam huc <expan abbr="u&longs;&qacute;">u&longs;que</expan>; quantum&shy;<lb/>uis con&longs;pici volentem, &amp; &longs;u&agrave; pulchritudine ambi&shy;<lb/>tio&longs;am eadem fata, qu&aelig; pacem morantur, detinue&shy;<lb/>re: ut nimirum hoc demum anno pace &eacute; victorijs 


<pb xlink:href="062/01/005.jpg"/>TU&AElig; Maie&longs;tatis na&longs;cente &amp; pluui&aacute; &longs;anguinis eju&longs;&shy;<lb/>dem radijs &longs;iccat&aacute;, Iris con&longs;picua veluti arcus trium <lb/>phalis TU&AElig; Maie&longs;tatis &longs;equatur pompam trium&shy;<lb/>phalem. </s>
        </p>
        <p id="N100F9" type="main">
          <s id="N100FB">Augu&longs;ti&longs;sim&aelig; Maie&longs;tatis Tu&aelig; </s>
        </p>
        <p id="N100FE" type="main">
          <s id="N10100"><emph type="center"/>humillimus Servus &amp; Cliens<emph.end type="center"/></s>
        </p>
        <p id="N10107" type="main">
          <s id="N10109"><emph type="italics"/>Joannes Marcus Marci.<emph.end type="italics"/></s>
        </p>
      </section>
    </front>
    <body>
      <chap id="N10111">
        <pb xlink:href="062/01/006.jpg"/>
        <p id="N10115" type="main">
          <s id="N10117"><emph type="center"/>Definitiones.<emph.end type="center"/></s>
        </p>
        <p id="N1011E" type="main">
          <s id="N10120"><emph type="center"/>1.<emph.end type="center"/></s>
        </p>
        <p id="N10127" type="main">
          <s id="N10129"><emph type="italics"/>Contraria dicuntur qu&aelig; tollunt, uel impediunt &longs;u&shy;<lb/>um contrarium.<emph.end type="italics"/></s>
        </p>
        <p id="N10132" type="main">
          <s id="N10134">NAm contrariorum e&longs;t natura, ut &longs;imul e&longs;&longs;e <lb/>non po&longs;sint in uno &longs;ubjecto: necesse ergo unum <lb/>ab altero tolli, aut qu&ograve; min&ugrave;s recipiatur in illo <lb/>&longs;ubiecto impediri. </s>
          <s id="N1013D"> <expan abbr="Ita&qacute;">Itaque</expan>; calori frigus contrarium di&shy;<lb/>cunt non tot&agrave; &longs;u&agrave; latitudine, &longs;ed &longs;ecund&ugrave;m illos gra&shy;<lb/>dus, qui &longs;imul e&longs;&longs;e non po&longs;&longs;unt in codem &longs;ubjecto,<lb/>quatuor autem gradus caloris cum totidem gradibus <lb/>frigoris non e&longs;&longs;e contrarios, ver&uacute;m inter &longs;e mi&longs;ceri, <expan abbr="at&qacute;">atque</expan>; <lb/>ex illis ita permixtis temperiem na&longs;ci. </s>
          <s id="N10152">Simili modo <lb/>motus motui dicet ut contrarius, qui &agrave; termino illius <lb/>idem mobile abducit, <expan abbr="nullam&qacute;">nullamque</expan>; partem vi&aelig; &longs;eu acce&longs;&shy;<lb/>&longs;us ad illum terminum habet communem. </s>
          <s id="N1015F">Vt &longs;i in <lb/>fig: 1 ex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> moveatur, erit motus contrarius, qui ex <lb/>eodem <emph type="italics"/>a<emph.end type="italics"/> idem mobil&egrave; in <emph type="italics"/>e<emph.end type="italics"/> ab ducit. </s>
          <s id="N1017E">Motus ver&ograve; ex <emph type="italics"/>a<emph.end type="italics"/> in <lb/><emph type="italics"/>d<emph.end type="italics"/> non erit contrarius ab&longs;olut&egrave;, propterea qu&ograve;d hic mo&shy;<lb/>tus non abducit &agrave; termino motus <emph type="italics"/>b,<emph.end type="italics"/> ver&ugrave;m ad hunc in <lb/>omni puncto propi&ugrave;s accedit: qu&oacute;d &longs;i enim ex <emph type="italics"/>b<emph.end type="italics"/> ducan<lb/>tur line&aelig; <emph type="italics"/>be. bf. bg,<emph.end type="italics"/> erit linea <emph type="italics"/>bf<emph.end type="italics"/> minor quam <emph type="italics"/>be,<emph.end type="italics"/> &amp; <emph type="italics"/>bg<emph.end type="italics"/> mi<lb/>nor quam <emph type="italics"/>bf.<emph.end type="italics"/> Huju&longs;modi ergo motus dum inter &longs;e 


<pb xlink:href="062/01/007.jpg"/>mi&longs;centur, non &longs;e mutu&oacute; tollunt ab&longs;olut&egrave;, ver&uacute;m in <lb/>eo in quo &longs;unt &longs;imiles, in motum medium coale&longs;centes <lb/>vi&agrave; medi&aacute; <expan abbr="vtri&qacute;;">vtrique;</expan> termino propinquant: in quantum <lb/>ver&ograve; contrarij, illam rectitudinem vi&aelig; tollunt. </s>
          <s id="N101CE">Con&shy;<lb/>traria ergo dicuntur qu&aelig; tollunt, vel impediunt &longs;uum <lb/>contrarium. </s>
        </p>
        <p id="N101D5" type="main">
          <s id="N101D7"><emph type="center"/>2.<emph.end type="center"/></s>
        </p>
        <p id="N101DE" type="main">
          <s id="N101E0"><emph type="italics"/>Similia ver&ograve; qua augent vel perficiunt &longs;uum &longs;imile.<emph.end type="italics"/></s>
        </p>
        <p id="N101E7" type="main">
          <s id="N101E9">VT &longs;i ad motum <emph type="italics"/>ac<emph.end type="italics"/> alius ac cedat impul&longs;us, qui per <lb/>eandem lineam <emph type="italics"/>ac<emph.end type="italics"/> moveat idem mobile, erit hic <lb/>motus illi &longs;imilis, ac proinde eundem dicetur augere, <lb/>quemadmodum calor alium calorem &longs;ibi &longs;imilem: ca&shy;<lb/>lor autem &agrave; luce, aut &egrave; contra, quia di&longs;similes, non di&shy;<lb/>centur augeri. </s>
        </p>
        <p id="N10202" type="main">
          <s id="N10204"><emph type="center"/>3.<emph.end type="center"/></s>
        </p>
        <p id="N1020B" type="main">
          <s id="N1020D"><emph type="italics"/>Et mixta &agrave; quibus actiones procedunt mixt&oelig;.<emph.end type="italics"/></s>
        </p>
        <p id="N10214" type="main">
          <s id="N10216">ILlarum nimirum qualitatum, qu&aelig; vim habent a&shy;<lb/>gendi, lati&ugrave;s &longs;umpto nomine actionis, pro qualibet <lb/>actione etiam perfectiu&agrave;: <expan abbr="ita&qacute;">itaque</expan>; illa <expan abbr="quo&qacute;">quoque</expan>; mutatio, <lb/>quam dulcoacidum inducit, actio dicetur mixta: <lb/>quem admodum frigus calore temperatum actionem <lb/>efficere &egrave;x <expan abbr="utro&qacute;">utroque</expan>; mixtam. </s>
          <s id="N1022F">Sic ergo motus dicetur 


<pb xlink:href="062/01/008.jpg"/>mixtus, dum inpul&longs;us <expan abbr="ne&qacute;">neque</expan>; in totum &longs;imilis, <expan abbr="ne&qacute;">neque</expan>; in to&shy;<lb/>tum e&longs;t contrarius alteri impul&longs;ui. </s>
        </p>
        <p id="N10240" type="main">
          <s id="N10242"><emph type="center"/>4.<emph.end type="center"/></s>
        </p>
        <p id="N10249" type="main">
          <s id="N1024B"><emph type="italics"/>Motus ab&longs;olut&eacute; contrarij, qui idem m&ograve;bile ducunt <lb/>ex eodem puncto ad partes oppo&longs;itas ejusdem line&aelig; rect&aelig;.<emph.end type="italics"/></s>
        </p>
        <p id="N10254" type="main">
          <s id="N10256"><emph type="center"/>5.<emph.end type="center"/></s>
        </p>
        <p id="N1025D" type="main">
          <s id="N1025F"><emph type="italics"/>Motus &longs;ecundum quid contrarij, qui ex illo puncto, <lb/>&longs;e&ugrave; principio motus angulum ducunt majorem a ut minorem recto <lb/>minorem ver&ograve; duobus rectis.<emph.end type="italics"/></s>
        </p>
        <p id="N1026A" type="main">
          <s id="N1026C"><emph type="center"/>6.<emph.end type="center"/></s>
        </p>
        <p id="N10273" type="main">
          <s id="N10275"><emph type="italics"/>Motus qui ex eodem puncto tendunt ad ea&longs;dem <lb/>partes line&aelig; rect&aelig; inter &longs;e &longs;unt &longs;imiles.<emph.end type="italics"/></s>
        </p>
        <p id="N1027E" type="main">
          <s id="N10280"><emph type="center"/>7.<emph.end type="center"/></s>
        </p>
        <p id="N10287" type="main">
          <s id="N10289"><emph type="italics"/>Motus qui minori angulo ab&longs;i&longs;tunt magis &longs;unt <lb/>&longs;imiles<emph.end type="italics"/></s>
        </p>
        <p id="N10292" type="main">
          <s id="N10294"><emph type="center"/>8.<emph.end type="center"/></s>
        </p>
        <p id="N1029B" type="main">
          <s id="N1029D"><emph type="italics"/>Motus perfect&egrave; mixti quorum principium e&longs;t an&shy;<lb/>gulus rectus.<emph.end type="italics"/></s>
        </p>
        <p id="N102A6" type="main">
          <s id="N102A8">VT &longs;i in fig: 2. ex eodem puncto <emph type="italics"/>a<emph.end type="italics"/> moueatur idem <lb/>mobile &longs;imul in <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>e,<emph.end type="italics"/> dicetur hic motus ab&longs;olut&egrave; <lb/>contrarius. </s>
          <s id="N102C1">Motus ver&ograve; ex eodem puncto <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>d,<emph.end type="italics"/><lb/>aut in <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>f,<emph.end type="italics"/> quorum hic major, ille minor &longs;it angulo re-


<pb xlink:href="062/01/009.jpg"/>cto, erunt motus &longs;ecund&ugrave;m quid contrarij: propterea <lb/>qu&ograve;d non ex toto &longs;e impediunt aut tollunt: contrarie&shy;<lb/>tas enim motus ex acce&longs;&longs;u &amp; rece&longs;&longs;u ad eundem termi&shy;<lb/>num prouenit: motus autem &longs;ecund&ugrave;m quid contrari; <lb/>dum inter &longs;e mi&longs;centur, licet &longs;uos terminos non a&longs;&shy;<lb/>&longs;equantur, ij&longs;dem tamen continu&ograve; fiunt propiores. <lb/>Quia ver&ograve; line&aelig; motus qu&ograve; minori angulo ab&longs;i&longs;tunt, <lb/>e&ograve; propi&ugrave;s accedunt ad terminum, erunt hi motus ma<lb/>gis &longs;imiles: perfecta autem &longs;imilitudo in eadem line&agrave; <lb/>rect&agrave;, qu&aelig; ad eundem terminum perducit. </s>
          <s id="N102F9">Motus de&shy;<lb/>mum, quorum principium e&longs;t angulus rectus, quia ex <lb/>ill&agrave; mixtione propiores quidem fiunt termino motus, <lb/>intervallum autem in fine motus &longs;patio inter principi&shy;<lb/>um &amp; terminum motus e&longs;t &aelig;quale, nimirum in fig: 7. <lb/>dicentur motus perfect&egrave; mixti: tant&ugrave;m enim con<lb/>trarij, quant&ugrave;m &longs;imilitudinis ine&longs;t; </s>
        </p>
      </chap>
      <chap id="N10308">
        <subchap1 id="N10309">
          <p id="N1030A" type="main">
            <s id="N1030C"><emph type="center"/>Po&longs;itiones:<emph.end type="center"/></s>
          </p>
          <p id="N10313" type="main">
            <s id="N10315"><emph type="center"/>I.<emph.end type="center"/></s>
          </p>
          <p id="N1031C" type="main">
            <s id="N1031E"><emph type="italics"/>Simile &amp; &aelig;quale auget &longs;uum &longs;imile in eadem rati&shy;<lb/>one, totum quidem totum, pars ver&ograve; partem &longs;ibi &aelig;qualem.<emph.end type="italics"/></s>
          </p>
          <p id="N10327" type="main">
            <s id="N10329">SIt linea <emph type="italics"/>ad<emph.end type="italics"/> &aelig;qualis line&aelig; <emph type="italics"/>ef,<emph.end type="italics"/> &amp; diuidatur bifariam in <lb/><emph type="italics"/>b<emph.end type="italics"/>: qu&oacute;d &longs;i ergo tota linea <emph type="italics"/>ad<emph.end type="italics"/> addatur toti <emph type="italics"/>e f,<emph.end type="italics"/> &longs;icuti tota <lb/>
<figure id="id.062.01.009.1.jpg" xlink:href="062/01/009/1.jpg"/><lb/>


<pb xlink:href="062/01/010.jpg"/>toti, &amp; &longs;emi&longs;sis &longs;emi&longs;si, &amp; <expan abbr="tri&etilde;s">triens</expan> trienti e&longs;t &aelig;qualis, ita to&shy;<lb/>ta totam, &amp; &longs;emi&longs;sis &longs;emi&longs;&longs;em, &amp; triens trientem auge&shy;<lb/>bit in eadem ratione, in qu&agrave; tota totam. </s>
            <s id="N10360">Si ergo &longs;emi&longs;&shy;<lb/>&longs;is <emph type="italics"/>ab<emph.end type="italics"/> addatur toti <emph type="italics"/>ef,<emph.end type="italics"/> quia ut <emph type="italics"/>ad<emph.end type="italics"/> ad <emph type="italics"/>ab,<emph.end type="italics"/> ita <emph type="italics"/>ef<emph.end type="italics"/> &aelig;qualis <emph type="italics"/>ad<emph.end type="italics"/><lb/> ad eandem <emph type="italics"/>ab,<emph.end type="italics"/> erit augmentum &aelig;quale eju&longs;dem &longs;emi&longs;&shy;<lb/>&longs;i: &longs;ola ergo &longs;emi&longs;sis line&aelig; <emph type="italics"/>ef<emph.end type="italics"/> augetur &agrave; &longs;emi&longs;&longs;e line&aelig; <emph type="italics"/>ad<emph.end type="italics"/><lb/>in e&agrave; ratione, in qu&agrave; tota auget totam. </s>
            <s id="N1039F">Et quia linea <lb/><emph type="italics"/>ad<emph.end type="italics"/> ad &longs;emi&longs;&longs;em <emph type="italics"/>ab<emph.end type="italics"/> rationem habet duplam, habebit <lb/><expan abbr="quo&qacute;">quoque</expan>, <emph type="italics"/>ef<emph.end type="italics"/> ad illam &longs;emi&longs;&longs;em, hoc e&longs;t ad &longs;uum augmen&shy;<lb/>tum rationem duplam. </s>
            <s id="N103BC">Simili modo &longs;i augmentum <emph type="italics"/>cd<emph.end type="italics"/><lb/> &longs;it triens line&aelig; <emph type="italics"/>ad,<emph.end type="italics"/> erit linea <emph type="italics"/>ef<emph.end type="italics"/> ad illud augmentum in <lb/>ratione tripl&aacute;. </s>
            <s id="N103D4">Simile ergo &amp; &aelig;quale auget &longs;uum &longs;i&shy;<lb/>mile in eadem ratione &amp;c. </s>
          </p>
          <p id="N103D9" type="main">
            <s id="N103DB"><emph type="center"/>II.<emph.end type="center"/></s>
          </p>
          <p id="N103E2" type="main">
            <s id="N103E4"><emph type="italics"/>Contrarium &aelig;quale tollit vel impedit &longs;uum contra&shy;<lb/>rium in eadem ratione, totum quidem totum, pars ver&ograve; partem <lb/>&longs;ibi &aelig;qualem<emph.end type="italics"/></s>
            <figure id="id.062.01.010.1.jpg" xlink:href="062/01/010/1.jpg"/>
            <lb/>
          </p>
          <p id="N103F5" type="main">
            <s id="N103F7">Sit <emph type="italics"/>ab<emph.end type="italics"/> ip&longs;i <emph type="italics"/>df<emph.end type="italics"/> contrarium &amp; &aelig;quale, &amp; diuidantur bi&shy;<lb/>fariam in <emph type="italics"/>c<emph.end type="italics"/> &amp; <emph type="italics"/>e<emph.end type="italics"/>: quia ergo <emph type="italics"/>ab<emph.end type="italics"/> totum e&longs;t &aelig;quale ip&longs;i <lb/><emph type="italics"/>df<emph.end type="italics"/> toti, erit <expan abbr="quo&qacute;">quoque</expan> &longs;emi&longs;sis <emph type="italics"/>ef<emph.end type="italics"/> &aelig;qualis &longs;emi&longs;si <emph type="italics"/>cb<emph.end type="italics"/>: tollit <lb/>autem <emph type="italics"/>ab<emph.end type="italics"/> totum <emph type="italics"/>df,<emph.end type="italics"/> tollet ergo &amp; <emph type="italics"/>eb<emph.end type="italics"/> totum <emph type="italics"/>ef:<emph.end type="italics"/> quod <lb/>idem de reliquis partibus, <expan abbr="quacun&qacute;">quacunque</expan> ratione diuidan&shy;<lb/>tur, o&longs;tendemus. </s>
            <s id="N10453">Dices calorem &amp; frigus e&longs;&longs;e contra<lb/>ria, <expan abbr="ne&qacute;">neque</expan>; tamen &agrave; calore totum frigus, <expan abbr="ne&qacute;">neque</expan>; &agrave; frigore to-


<pb xlink:href="062/01/011.jpg"/>tum calorem tolli &amp; expelli, ver&ugrave;m tantum illorum <lb/>exce&longs;&longs;us: partes ver&ograve; mutilatas inter &longs;e mi&longs;ceri, &amp; ami&shy;<lb/>cabili &longs;ocietate in eodem &longs;ubjecto coniungj</s>
            <s id="N10468">or&ugrave;m <lb/>&longs;i in gradibus remi&longs;sis dee&longs;t illa proprietas contrari&shy;<lb/>orum, <expan abbr="ne&qacute;">neque</expan>; &longs;an&egrave; contrarietas inerit. </s>
            <s id="N10473">Quidquid tamen <lb/>&longs;it de illis qualitatibus, de quibus alio loco di&longs;&longs;eren&shy;<lb/>dum, con&longs;tat ex ill&agrave;, qu&aelig; in motu e&longs;t contrarietate, &longs;i <lb/>&aelig;qualis &longs;it, nullum &longs;e qui motum: &longs;i major, hujus ex&shy;<lb/>ce&longs;&longs;ui e&longs;&longs;e &aelig;qualem. </s>
            <s id="N1047E">Con&longs;tituatur enim in bilance <emph type="italics"/>ab <lb/>c<emph.end type="italics"/> pondus <emph type="italics"/>a<emph.end type="italics"/> 8. lib. quod vectem deprimet impul&longs;u 8, li&shy;<lb/>
<figure id="id.062.01.011.1.jpg" xlink:href="062/01/011/1.jpg"/><lb/><lb/>
brali, <expan abbr="at&qacute;">atque</expan>; hujus impul&longs;us non ni&longs;i ab &aelig;quali totidem li&shy;<lb/>brarum ponderis <emph type="italics"/>b<emph.end type="italics"/> impul&longs;u inhibetur. </s>
            <s id="N104A5">Qu&ograve;d &longs;i pon&shy;<lb/>dus in <emph type="italics"/>e<emph.end type="italics"/> lib. 5. eundem vectem &longs;ur&longs;um trahat, erit im&shy;<lb/>pul&longs;us in <emph type="italics"/>a<emph.end type="italics"/> lib. 3. pondus ergo &longs;eu impul&longs;us in <emph type="italics"/>e<emph.end type="italics"/> contra&shy;<lb/>rius impul&longs;ui in <emph type="italics"/>a<emph.end type="italics"/> tollit partem ex <emph type="italics"/>a<emph.end type="italics"/> &longs;ibi &aelig;qualem. </s>
            <s id="N104CC">Si&shy;<lb/>mili modo &longs;i duo globi &aelig;quali ni&longs;u, &amp; in eadem line&aacute; <lb/>motus centri &longs;ibi occurrentes collidantur, nullus ab il-


<pb xlink:href="062/01/012.jpg"/>lo contactu erit m&oacute;tus: major ver&ograve; impul&longs;us minorem <lb/>reflectet, tant&ograve; ver&ograve; minori velocitate mouebitur &agrave; <lb/>contactu, quant&ograve; major e&longs;t re&longs;i&longs;tentia minoris: quia <lb/>nimirum impul&longs;us minor &agrave; majori tollit partem &longs;ibi <lb/>&aelig;qualem, &longs;imul ver&ograve; occumbit erit erg&ograve; exce&longs;&longs;us ma&shy;<lb/>joris principium motus &agrave; contactu: &amp; c&ugrave;m &longs;it agens <lb/>nece&longs;&longs;arium, motum producit &longs;ibi a qualem. </s>
            <s id="N104E3">Dices in&shy;<lb/>terdum fieri ut duo globi &longs;ibi occurrentes <expan abbr="uter&qacute;">uterque</expan>; re&longs;ili&shy;<lb/>at: quod <expan abbr="n&otilde;">non</expan> ni&longs;i ab &aelig;quali impul&longs;u e&longs;&longs;e pote&longs;t; propte<lb/>rea qu&oacute;d motus e&longs;t &aelig;qualis exce&longs;&longs;ui majoris. </s>
            <s id="N104F4"><expan abbr="Re&longs;p&otilde;deo">Re&longs;pondeo</expan> <lb/>&longs;i motus, quo <expan abbr="centr&utilde;">centrum</expan> <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>; globi mouetur, &longs;it in ea&shy;<lb/>dem line&agrave; rect&agrave;, ab &aelig;quali impul&longs;u nunquam re&longs;ilire: <lb/>&longs;i autem motus centri unius &longs;it extra lineam motus al&shy;<lb/>terius, quia lateraliter fit contactus, huju&longs;modi quidem <lb/>motum po&longs;&longs;e re&longs;ilire: ver&ugrave;m non ab&longs;olut&eacute;, &longs;ed tant&ugrave;m <lb/>&longs;ecund&ugrave;m quid e&longs;&longs;e contrarium. </s>
            <s id="N1050E">Vt in figur&agrave; &longs;ubject&agrave; <lb/>&longs;i centrum <emph type="italics"/>a<emph.end type="italics"/>  ex <emph type="italics"/>h,<emph.end type="italics"/> &amp; centrum <emph type="italics"/>b<emph.end type="italics"/> ex <emph type="italics"/>l<emph.end type="italics"/> moueantur in ea&shy;<lb/>dem line&agrave; rect&agrave; <emph type="italics"/>h fl<emph.end type="italics"/>: &longs;it autem impul&longs;us ex <emph type="italics"/>a<emph.end type="italics"/> &aelig;qualis im<lb/>pul&longs;ui ex <emph type="italics"/>b,<emph.end type="italics"/> &agrave;contactu in <emph type="italics"/>f<emph.end type="italics"/> nullus erit motus: propterea <lb/>qu&oacute;d impul&longs;us &aelig;quales &aelig;qualiter reluctantur, <expan abbr="&longs;e&qacute;">&longs;eque</expan>; im&shy;<lb/>pediunt &agrave; motu. </s>
            <s id="N1054F">Qu&oacute;d &longs;i ver&ograve; centrum grauitatis <emph type="italics"/>a<emph.end type="italics"/><lb/>ex <emph type="italics"/>c<emph.end type="italics"/> in <emph type="italics"/>a,<emph.end type="italics"/> &amp; centrum grauitatis <emph type="italics"/>b<emph.end type="italics"/> ex <emph type="italics"/>d<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> moueatur; quia <lb/>line&aelig; motus <emph type="italics"/>ac.db<emph.end type="italics"/> non coincidunt eidem line&aelig; rect&aelig;, <lb/>dico huju&longs;modi motum non ab&longs;olut&eacute;, &longs;ed &longs;ecund&ugrave;m <lb/>quid e&longs;&longs;e contrarium.</s>
            <s id="N10583"> Ducantur enim ex puncto con-


<pb xlink:href="062/01/013.jpg"/>tactus <emph type="italics"/>f<emph.end type="italics"/> line&aelig; <emph type="italics"/>fg. fe<emph.end type="italics"/> motui centri parallel&aelig;, line&aelig; nimi&shy;<lb/>rum hypomochlij, extra quas cadunt centra <emph type="italics"/>a<emph.end type="italics"/> &amp; <emph type="italics"/>b:<emph.end type="italics"/> quia <lb/>ergo plaga non ni&longs;i per centrum fit grauitatis, erunt li<lb/>ne&aelig; <emph type="italics"/>fab. fbb<emph.end type="italics"/> line&aelig; motus &agrave; percu&longs;sione: &longs;unt autem li<lb/>ne&aelig; <emph type="italics"/>ai.bk<emph.end type="italics"/> line&aelig; motus centri extra hypomochlium: <lb/>
<figure id="id.062.01.013.1.jpg" xlink:href="062/01/013/1.jpg"/><lb/>

quia ergo line&aelig; motus <emph type="italics"/>ab. ai,<emph.end type="italics"/> &amp; <emph type="italics"/>bl.bk<emph.end type="italics"/> angulos ducunt <lb/><emph type="italics"/>iah.lbk<emph.end type="italics"/> minores duobus rectis, <expan abbr="er&utilde;t">erunt</expan> per defini: 5 motus <lb/>&longs;ecund&ugrave;m quid contrarij, ac proinde inter &longs;emi&longs;centur <lb/>per prop: 31. </s>
            <s id="N105DA">Ver&ugrave;m de motu reflexo accurati&ugrave;s dice&shy;<lb/>mus &agrave; prop: 36. <expan abbr="u&longs;&qacute;">u&longs;que</expan>; ad 40. </s>
          </p>
          <p id="N105E3" type="main">
            <s id="N105E5"><emph type="center"/>III.<emph.end type="center"/></s>
          </p>
          <p id="N105EC" type="main">
            <s id="N105EE"><emph type="italics"/>Mixtarum virium mixt&aelig; &longs;unt actiones in ea&shy;<lb/>dem ratione, in qu&agrave; mi&longs;centur mi&longs;cibilia.<emph.end type="italics"/></s>
          </p>
          <p id="N105F7" type="main">
            <s id="N105F9">CVm enim mixtum &longs;it &longs;ua mi&longs;cibilia inter &longs;e unita, &amp; <lb/>nece&longs;&longs;ari&ograve; agat, <expan abbr="actionem&qacute;">actionemque</expan>; producat &longs;ibi &aelig;qua&shy;<lb/>lem aget &longs;ecund&ugrave;m &longs;e totum, ac proinde &longs;ecund&uacute;m il&shy;<lb/>las partes, qu&aelig; in illo toto mi&longs;centur: actio ergo mixta 


<pb xlink:href="062/01/014.jpg"/>quia toti &aelig;qualis, habet partes virtuales illis partibus, &agrave; <lb/>quibus producitur &aelig;quales. </s>
          </p>
          <p id="N1060C" type="main">
            <s id="N1060E"><emph type="center"/>IV.<emph.end type="center"/></s>
          </p>
          <p id="N10615" type="main">
            <s id="N10617"><emph type="italics"/>Virtus agendi &amp; actio inter &longs;e &longs;unt &aelig;quales, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan> <lb/>idem modus incrementi.<emph.end type="italics"/></s>
          </p>
          <p id="N10624" type="main">
            <s id="N10626">VIrtutem enim agendi magnam aut paruam dici&shy;<lb/>mus, qu&aelig; mult&ugrave;m aut parum pote&longs;t agere: <expan abbr="ita&qacute;">itaque</expan>; <lb/>hujus molem ex actionum mole &aelig;&longs;timamus; actionem <lb/>ver&ograve; ab effectu no&longs;cimus: dupla ergo virtus, qu&aelig; actio&shy;<lb/>nem dupl&oacute;, &amp; tripla qu&aelig; tripl&ograve; majorem, aut magis <lb/>perfectam producit. </s>
            <s id="N10637">Et quia virtus naturalis non li&shy;<lb/>ber&egrave; &longs;ed ex nece&longs;sitate agit, <expan abbr="actionem&qacute;">actionemque</expan>; producit &longs;ibi <lb/>&aelig;qualem, erit idem modus incrementi <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>;. </s>
          </p>
          <p id="N10646" type="main">
            <s id="N10648"><emph type="center"/>Lemma,<emph.end type="center"/></s>
          </p>
          <p id="N1064F" type="main">
            <s id="N10651"><emph type="italics"/>Si punctum &aelig;qualiter moueatur inplano motu &longs;i&shy;<lb/>mul recto &amp; laterali in eadem proportione <expan abbr="utrius&qacute;ue">utriusque</expan> interualli, <lb/>de&longs;cribet illo motu triangulum.<emph.end type="italics"/></s>
          </p>
          <p id="N10660" type="main">
            <s id="N10662">MOueatur in fig: 3. punctum <emph type="italics"/>a<emph.end type="italics"/> ex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>f<emph.end type="italics"/> per lineam re<lb/>ctam <emph type="italics"/>af<emph.end type="italics"/> &aelig;qualiter in longum &amp; latum, ita nimi&shy;<lb/>rum ut in quolibet puncto longitudo excur&longs;us lateralis <lb/>&longs;it &aelig;qualis <expan abbr="l&otilde;gitudini">longitudini</expan> motus recti inter idem punctum 


<pb xlink:href="062/01/015.jpg"/>&amp; principium motus, ide&longs;t <emph type="italics"/>ab<emph.end type="italics"/> ip&longs;i <emph type="italics"/>bg,<emph.end type="italics"/> &amp; <emph type="italics"/>ac<emph.end type="italics"/> ip&longs;i <emph type="italics"/>cb,<emph.end type="italics"/> &amp; <emph type="italics"/>ad<emph.end type="italics"/><lb/>ip&longs;i <emph type="italics"/>di,<emph.end type="italics"/> &amp; <emph type="italics"/>ac<emph.end type="italics"/> ip&longs;i <emph type="italics"/>ek,<emph.end type="italics"/> &amp; <emph type="italics"/>af<emph.end type="italics"/> ip&longs;i <emph type="italics"/>fl<emph.end type="italics"/> &longs;it &aelig;qualis, dico puncta <lb/><emph type="italics"/>aghikl<emph.end type="italics"/> cadere in latus <emph type="italics"/>al<emph.end type="italics"/> trianguli <emph type="italics"/>alf.<emph.end type="italics"/> Qu&ograve;d &longs;i enim <lb/>punctum <emph type="italics"/>i, u:g<emph.end type="italics"/>: dicatur non in latus <emph type="italics"/>al,<emph.end type="italics"/> &longs;ed extra illud ca&shy;<lb/><figure id="id.062.01.015.1.jpg" xlink:href="062/01/015/1.jpg"/>
<arrow.to.target n="fig5"/><lb/>dere in <emph type="italics"/>r,<emph.end type="italics"/> ducatur linea <emph type="italics"/>ar,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; angulus <emph type="italics"/>rad<emph.end type="italics"/> major <lb/>angulo <emph type="italics"/>iad.<emph.end type="italics"/> quia ergo latus <emph type="italics"/>dr<emph.end type="italics"/> lateri <emph type="italics"/>da<emph.end type="italics"/> e&longs;t &aelig;quale, &amp; an<lb/>gulus <emph type="italics"/>adr<emph.end type="italics"/> rectus, erunt anguli <emph type="italics"/>dar. dra<emph.end type="italics"/> inter &longs;e &aelig;qua&shy;<lb/>les, ac proinde &longs;emi&longs;&longs;es anguli recti. </s>
            <s id="N1072F">Similiter quia <lb/>latus <emph type="italics"/>fl<emph.end type="italics"/> e&longs;t &aelig;quale lateri <emph type="italics"/>fa,<emph.end type="italics"/> &amp; angulus <emph type="italics"/>afl<emph.end type="italics"/> re&shy;<lb/>ctus, erunt anguli <emph type="italics"/>fal. fla<emph.end type="italics"/> inter &longs;e &aelig;quales; igitur &amp; an&shy;<lb/>gulus <emph type="italics"/>laf<emph.end type="italics"/> angulo <emph type="italics"/>rad<emph.end type="italics"/> erit &aelig;qualis pars toti, quod e&longs;t ab&shy;<lb/>&longs;urdum: non ergo punctum <emph type="italics"/>i<emph.end type="italics"/> extra latus <emph type="italics"/>al<emph.end type="italics"/> cadit. </s>
            <s id="N1076A">Simi&shy;<lb/>li modo o&longs;tendemus non cadere intra illud latus: ca&shy;<lb/>det erg&ograve; nece&longs;&longs;ari&oacute; in ip&longs;um latus. </s>
            <s id="N10771">Si ergo punctum <lb/>&aelig;qualiter moueatur in plano motu &longs;imul recto &amp; late&shy;<lb/>rali in eadem proportione &amp;c. </s>
          </p>
          <pb xlink:href="062/01/016.jpg"/>
          <p id="N1077B" type="main">
            <s id="N1077D"><emph type="center"/>V.<emph.end type="center"/></s>
          </p>
          <p id="N10784" type="main">
            <s id="N10786"><emph type="italics"/>Perfectio inten&longs;iua augetur eo modo, quo triangu&shy;<lb/>lum &longs;ibi &longs;imile manens.<emph.end type="italics"/></s>
          </p>
          <p id="N1078F" type="main">
            <s id="N10791">QVia perfectio inten&longs;iua non <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; motu fit, ac pro&shy;<lb/>inde in aliquo tempore: &longs;upponatur illud tempus, <lb/>quo calor verbi gratia perficitur in quo <expan abbr="cun&qacute;">cunque</expan>; gradu, e&longs;&shy;<lb/>&longs;e &aelig;quale line&aelig; <emph type="italics"/>af<emph.end type="italics"/>: &amp; diuidatur &aelig;qualiter in minuta <emph type="italics"/>ab. <lb/>bc. cd. de. ef<emph.end type="italics"/>: quia ergo in &longs;ingulis minutis majora fiunt <lb/>hujus perfectionis in crementa, &longs;i in primo minuto <emph type="italics"/>ab<emph.end type="italics"/><lb/>perfectio inten&longs;iua &longs;it &aelig;qualis <emph type="italics"/>bg,<emph.end type="italics"/> erit in minuto &longs;ecun&shy;<lb/>do <emph type="italics"/>bc<emph.end type="italics"/> major quam <emph type="italics"/>bg,<emph.end type="italics"/> &amp; in terti&ograve; minuto <emph type="italics"/>cd<emph.end type="italics"/> major <lb/>quam <emph type="italics"/>ch:<emph.end type="italics"/> dico huju&longs;modi incrementa e&longs;&longs;e &longs;imilia inter <lb/>&longs;e, ac proinde eo modo augeri, quo triangulum &longs;ibi &longs;i&shy;<lb/>mile manens. </s>
            <s id="N107DF">Quia enim h&aelig;c perfectio continu&ograve; au&shy;<lb/>getur, &amp; veluti late&longs;cit ex illo puncto quietis; natura <lb/>autem uniformiter agit, <expan abbr="&longs;ibi&qacute;">&longs;ibique</expan>; &longs;emper e&longs;t &longs;imilis, erunt <lb/><expan abbr="quo&qacute;">quoque</expan>; &longs;imilia incrementa: Sicuti ergo perfectionem <lb/>&longs;ummam in tempore <emph type="italics"/>af<emph.end type="italics"/> &aelig;qualem line&aelig; <emph type="italics"/>fl,<emph.end type="italics"/> ita in hujus <lb/>temporis &longs;emi&longs;&longs;e: perfectionis &longs;emi&longs;&longs;em producet: igi&shy;<lb/>tur ut tempus <emph type="italics"/>af<emph.end type="italics"/> ad perfectionem <emph type="italics"/>fl,<emph.end type="italics"/> ita tempus <emph type="italics"/>ac<emph.end type="italics"/> ad <lb/>perfectionem <emph type="italics"/>ek<emph.end type="italics"/> hoc e&longs;t ut latus <emph type="italics"/>af<emph.end type="italics"/> trianguli <emph type="italics"/>afl<emph.end type="italics"/> ad la&shy;<lb/>tus <emph type="italics"/>fl,<emph.end type="italics"/> ita latus <emph type="italics"/>ae<emph.end type="italics"/> trianguli <emph type="italics"/>aek<emph.end type="italics"/> ad latus <emph type="italics"/>ek;<emph.end type="italics"/> ac proinde <lb/>&longs;imilia erunt triangula <emph type="italics"/>afl. aek.<emph.end type="italics"/> perfectio ergo inten&longs;i&shy;<lb/>ua augetur eo modo, quo <expan abbr="triangul&utilde;">triangulum</expan> &longs;ibi &longs;imile manens. </s>
          </p>
          <pb xlink:href="062/01/017.jpg"/>
          <p id="N10852" type="main">
            <s id="N10854"><emph type="center"/>VI.<emph.end type="center"/></s>
          </p>
          <p id="N1085B" type="main">
            <s id="N1085D"><emph type="italics"/>Impul&longs;us grauitatis ducetur &longs;ecundum rationem di&longs;tanti&aelig;, <lb/>quam habet centrum grauitatis ab hypomochlio.<emph.end type="italics"/></s>
          </p>
          <p id="N10866" type="main">
            <s id="N10868">HVjus po&longs;itionis veritatem probat Archimedes in <lb/>libro de &aelig;quiponderantibus: &amp; nos in libro de <lb/>Arcu c&aelig;le&longs;ti ejus rationem &agrave; priori dare enitemur; qu&aelig; <lb/>non ni&longs;i ex natur&agrave; impul&longs;us pri&ugrave;s explicat&agrave; reddi po&shy;<lb/>te&longs;t, hujus ergo demon&longs;trationem &longs;upponentes e&agrave; ve&shy;<lb/>luti <emph type="italics"/>j<emph.end type="italics"/>am demon&longs;trat&igrave; in po&longs;terum utemur. </s>
          </p>
        </subchap1>
        <subchap1 id="N1087B">
          <p id="N1087C" type="main">
            <s id="N1087E"><emph type="center"/>Propo&longs;itio I.<emph.end type="center"/></s>
          </p>
          <p id="N10885" type="main">
            <s id="N10887"><emph type="italics"/>Impul&longs;us e&longs;t virtus &longs;eu qualitas, loco motiua, qu&aelig; <lb/>non ni&longs;i in tempore, &amp; per &longs;patium mouet finitum.<emph.end type="italics"/></s>
          </p>
          <p id="N10890" type="main">
            <s id="N10892">IMpul&longs;us dicitur ab impellendo: impellitur autem <lb/>mobile, dum loco &longs;uo expul&longs;um in alium transfer&shy;<lb/>tur, aut &longs;impliciter; aut &longs;ecund&uacute;m quid, &longs;eu per com&shy;<lb/>mutationem, dum loco totius immoto partium loca <lb/>permutantur: quod duobus modis fieri pote&longs;t, incho&shy;<lb/>atiu&egrave;, &amp; perfect&egrave;. </s>
            <s id="N1089F">Inchoatiu&egrave; dico, qu&aelig; &longs;ecund&ugrave;m nul&shy; <lb/>lam partem &longs;en&longs;ibilem, &longs;ed per atomos in &longs;en&longs;iles vibra<lb/>tione quadam mouentur; cuju&longs;modi &longs;unt corpora &longs;o&shy;<lb/>nora, qu&aelig; dum &longs;onant, motu quodam tremulo &longs;ub&longs;ul-


<pb xlink:href="062/01/018.jpg"/>tant: &amp; <expan abbr="qu&aelig;cun&qacute;">qu&aelig;cunque</expan>; corpora minorem habent impul&shy;<lb/>&longs;um, quam ut loco moueantur: ut c&ugrave;m tellus, aut &longs;a&shy;<lb/>xum malleo percu&longs;&longs;um tremit quidem ex illo impul&longs;u, <lb/>&longs;ecund&ugrave;m nullam ver&ograve; partem &longs;en&longs;ibilem loco moue&shy;<lb/>tur. </s>
            <s id="N108B8">Qu&oacute;d &longs;i <expan abbr="ne&qacute;">neque</expan>; &longs;onum edant corpora, <expan abbr="ne&qacute;">neque</expan>; tremu&shy;<lb/>l&acirc; vibratione motum te&longs;tentur, non videntur recipere <lb/>impul&longs;um: ut &longs;i granum milij terr&aelig; incidat: minorem <lb/>enim habet proportionem hic impul&longs;us, quam ut ali&shy;<lb/>quam partem loco moueat, aut ab alijs auellat. </s>
            <s id="N108CB">Tre&shy;<lb/>mor autem a percu&longs;sione videtur non <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; di&longs;tractio&shy;<lb/>ne fieri atomorum: <expan abbr="d&utilde;">dum</expan> minor e&longs;t impul&longs;us, quam ut to&shy;<lb/>tum moueat: major ver&ograve; quam ilia vis partium unit&shy;<lb/>iua, qu&agrave; inter &longs;e continuantur. </s>
            <s id="N108DE">Illa ergo corpora, qu&aelig; <lb/>uniones habent &longs;olubiles <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; reunione, fragilia &longs;unt: <lb/>cuju&longs;modi vitrum, lapides, gemm&aelig;; qu&aelig; iteratis per&shy;<lb/>cu&longs;sionibus, ob plures uniones &longs;olutas, demum fran&shy;<lb/>guntur, &amp; di&longs;siliunt: metalla ver&ograve; tamet&longs;i tremunt <expan abbr="&longs;o-nant&qacute;">&longs;o&shy;<lb/>nantque</expan>; &agrave; percu&longs;sione, ob atomos tamen reunibiles non <lb/>ni&longs;i c&ugrave;m impetus longi&ugrave;s abduxit, franguntur. </s>
            <s id="N108F5">Sic a&shy;<lb/>qua in calice vitreo &longs;ub&longs;ultat, &amp; veluti &aelig;&longs;tu agitur ad <lb/>motum digiti per margines circumacti: motu ver&ograve; ac <lb/>celerato extra calicem &longs;alit, <expan abbr="&longs;u&aacute;q;">&longs;u&aacute;que</expan> a&longs;pergine etiam lon&shy;<lb/>gi&ugrave;s ad&longs;tantes attingit. </s>
            <s id="N10904"><expan abbr="Ita&qacute;">Itaque</expan>; hic impul&longs;us &acirc; principio <lb/>quidem non ni&longs;i &longs;ecund&ugrave;m quid, &amp; inchoatiu&egrave;, &longs;olum <lb/>tremorem inducendo: inde commutatione partium, 


<pb xlink:href="062/01/019.jpg"/>qu&aacute; in gyrum aguntur, perfect&agrave;: demum motu &longs;impli&shy;<lb/>citer mouent. </s>
            <s id="N10914">Vt igitur impul&longs;us loco moueat mobi&shy;<lb/>le, nece&longs;&longs;e illam re&longs;i&longs;tentiam, qu&acirc; in loco &longs;uo aut alieno <lb/>detinetur, &longs;uperate. </s>
            <s id="N1091B">Secund&ugrave;m quid autem inchoa&shy;<lb/>tiu&egrave; mouetur, c&ugrave;m &aelig;quatis viribus inter &longs;e luctantur <lb/>virtus partium vnitiua &amp; impul&longs;us: qu&agrave; quidem ratio&shy;<lb/>ne cymbala, cord&aelig;, <expan abbr="at&qacute;">atque</expan>; &aelig;ra tinnula mouentur. </s>
            <s id="N10928">Lapi&shy;<lb/>des ver&ograve; &amp; qu&aelig; fragilia &longs;unt, quia ex impul&longs;u uniones <lb/>&longs;en&longs;im depereunt, <expan abbr="ne&qacute;">neque</expan>; reuniri po&longs;&longs;unt, demum &acirc; per<lb/>cu&longs;sione continuat&aacute; pluribus unionibus euer&longs;is, &longs;eu <lb/>quia impul&longs;ui necdum ex&longs;oluto alius &longs;uperuenit im&shy;<lb/>pul&longs;us, franguntur. </s>
            <s id="N10939">Manife&longs;tum ergo ex his Impul&shy;<lb/>&longs;um e&longs;&longs;e virtutem finitam, qu&aelig; non quamlibet mo&shy;<lb/>lem, &longs;ed finitam loco mouere &amp; impellere pote&longs;t. </s>
            <s id="N10940">Et <lb/>quia motus ex uno loco in alium non ni&longs;i per medium <lb/>interuallum defert mobile, eju&longs;modi motum non po&longs;&shy;<lb/>&longs;e fieri in in&longs;tanti, &longs;ed in aliquo tempore ita o&longs;tende&shy;<lb/>mus. </s>
            <s id="N1094B">Moueatur ex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>b,<emph.end type="italics"/> inter qu&aelig; mediant partes lo&shy;<lb/>ci <emph type="italics"/>cdefg<emph.end type="italics"/> &amp;c. per quas nece&longs;&longs;ari&oacute; tran&longs;it in <emph type="italics"/>b<emph.end type="italics"/>; propterea <lb/>qu&ograve;d nequit medium tran&longs;ilire: qu&ograve;d &longs;i ergo non ni&longs;i <lb/>in uno momento mouetur ex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>b,<emph.end type="italics"/> erit eodem <expan abbr="mom&etilde;-to">momen&shy;<lb/>to</expan> &longs;imul in <emph type="italics"/>cdef<emph.end type="italics"/> pluribus locis ad&aelig;quatis, quod null&acirc; <lb/>ratione fieri pote&longs;t. </s>
            <s id="N10986">Simili modo o&longs;tendemus alio <lb/>momento in <emph type="italics"/>g,<emph.end type="italics"/> alio in <emph type="italics"/>f,<emph.end type="italics"/> pri&uacute;s nimirum in parte priori <lb/>quam po&longs;teriori motum terminari: pluribus ergo mo-<pb xlink:href="062/01/020.jpg"/>mentis mouetur ex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>b,<emph.end type="italics"/> ac pro&icirc;nde motus nece&longs;&longs;ari&ograve; <lb/>fit in tempore. </s>
            <s id="N109AB">Sed <expan abbr="ne&qacute;">neque</expan>; tempore infinito per &longs;pati&shy;<lb/>um mou&eacute;tur finitum, &longs;i nimirum motus eju&longs;dem &longs;it <lb/>rationis &amp; &longs;ibi &longs;imilis; nam &longs;i velocitas proportionali&shy;<lb/>ter decre&longs;cat, non repugnat per &longs;patium finitum tem&shy;<lb/>pore moueri infinito; ut &longs;i per lineam conchoideos ac&shy;<lb/>ce&longs;&longs;us fiat ad alteram parallelam, &longs;patium interjectum <lb/>nullo in tempore tran&longs;ibit. </s>
            <s id="N109BE">Moueatur ergo mobile ex <lb/><emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>f<emph.end type="italics"/> motu &aelig;quali quantumuis lento: &amp; &longs;umatur tem&shy;<lb/>pus quodcunq; <emph type="italics"/>ik,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; mobile extra terminum <emph type="italics"/>a,<emph.end type="italics"/> in <lb/>quo quie&longs;cebat. aut igitur in <emph type="italics"/>ik<emph.end type="italics"/> aliquam partem ug: <emph type="italics"/>a <lb/>b,<emph.end type="italics"/> aut in&longs;en&longs;ibile punctum tran&longs;mi&longs;it. </s>
            <s id="N109F0">Si partem, meti&shy;<lb/>etur h&aelig;c &longs;patium <emph type="italics"/>af<emph.end type="italics"/> aliquo numero finito: igitur &amp; <lb/>tempus, quo totum &longs;patium decurrit, erit finitum. </s>
            <s id="N109FD">Si <lb/>
<figure id="id.062.01.020.1.jpg" xlink:href="062/01/020/1.jpg"/><lb/>non ni&longs;i punctum: quia tempus diuidi pote&longs;t, tran&longs;i&shy;<lb/>bit in hujus &longs;emi&longs;&longs;e interuallum puncto minus, quod <lb/>e&longs;t ab&longs;urdum: non igitur motus &aelig;qualis per &longs;patium <lb/>finitum tempore infinito e&longs;&longs;e pote&longs;t. </s>
            <s id="N10A0F">Sed <expan abbr="ne&qacute;">neque</expan>, in tem&shy;<lb/>pore finito per &longs;patium infinitum: <expan abbr="n&atilde;&qacute;">nanque</expan> in &longs;emi&longs;&longs;e tem&shy;<lb/>

poris, <expan abbr="at&qacute;">atque</expan>; hujus &longs;emi&longs;&longs;e &amp;c. nunquid &longs;patium peram&shy;<lb/>

bulabit infinitum? qu&oacute;d &longs;i motus ill&acirc; &longs;ectione <expan abbr="dem&utilde;">demum</expan> <lb/>

terminabit in aliqu&agrave; parte finit&acirc;, erit <expan abbr="quo&qacute;">quoque</expan>; totum fini&shy;<lb/>

tum. </s>
            <s id="N10A30">Deinde c&ugrave;m motus incipiat &agrave; termino, erit ne&shy;<lb/>

ce&longs;&longs;ari&ograve; finitus. moueatur enim ex <emph type="italics"/>a<emph.end type="italics"/> per &longs;patium <emph type="italics"/>bcde<emph.end type="italics"/>


<pb xlink:href="062/01/021.jpg"/><emph type="italics"/>f<emph.end type="italics"/> &amp;c. in infinitum in tempore <emph type="italics"/>ghikl<emph.end type="italics"/> finito: igitur par&shy;<lb/>

tem quidem <emph type="italics"/>b<emph.end type="italics"/> in aliqu&agrave; parte temporis tran&longs;ibit, qu&aelig; <lb/>

&longs;it <emph type="italics"/>g<emph.end type="italics"/>; men&longs;urabit proinde tempus aliquo numero fini&shy;<lb/>

to: &amp; c&uacute;m motum ponamus &longs;imilarem, qui in tempo&shy;<lb/>

re &aelig;quali partes conficit &aelig;quales, totidem partes erunt <lb/>

in &longs;patio <emph type="italics"/>bcdef,<emph.end type="italics"/> qu<gap/>on tempore <emph type="italics"/>ghikl,<emph.end type="italics"/> ac proinde to&shy;<lb/>

tum interuallum erit finitum. </s>
            <s id="N10A76">Igitur impul&longs;us e&longs;t vir&shy;<lb/>

tus finita, qu&aelig; non ni&longs;i in tempore &amp; per &longs;patium mo&shy;<lb/>

uet finitum. </s>
          </p>
        </subchap1>
        <subchap1 id="N10A7D">
          <p id="N10A7E" type="main">
            <s id="N10A80"><emph type="center"/>Propo&longs;itio II.<emph.end type="center"/></s>
          </p>
          <p id="N10A87" type="main">
            <s id="N10A89"><emph type="italics"/>Impul&longs;us e&longs;t agens nece&longs;&longs;arium, <expan abbr="motum&qacute;">motumque</expan>; producit <lb/>

&longs;ibi &aelig;qualem.<emph.end type="italics"/></s>
          </p>
          <p id="N10A96" type="main">
            <s id="N10A98">NEce&longs;&longs;arium dico non &longs;ol&ugrave;m qu&ograve; ad exercitium a&shy;<lb/>

ctus, quo modo omnia agentia, qu&aelig; non liber&egrave; a&shy;<lb/>

gunt, nece&longs;&longs;aria dicuntur; &longs;ed etiam qu&ograve; ad perfectio&shy;<lb/>

nem actus, hoc e&longs;t agere &longs;ecund&uacute;m totum po&longs;&longs;e, &longs;eu <lb/>

&longs;ummam perfectionem tribuere &longs;uo effectui: quod <lb/>

non faciunt reliqua agentia naturalia, qu&aelig; non ni&longs;i &agrave; le&shy;<lb/>

uibus initijs ad &longs;umma euadunt incrementa: ut ma&shy;<lb/>

nife&longs;tum in calefactione. </s>
            <s id="N10AA9">At ver&ograve; impul&longs;us &longs;tatim &agrave; <lb/>

principio motum veloci&longs;simum producit: qui demum <lb/>

&longs;patij tractu langue&longs;cit &amp; emoritur, Cujus ratio e&longs;t, 


<pb xlink:href="062/01/022.jpg"/>qu&ograve;d impul&longs;us &longs;it qualitas tran&longs;iens, qu&aelig; non pote&longs;t in <lb/>

&longs;ubjecto con&longs;eruari <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; motu: qu&oacute;d &longs;i enim mobile <lb/>

ad motum concitatum vel uno momento detineas, nul<lb/>

lus ex illo contactu &longs;equitur motus: ni&longs;i ergo &agrave; princi&shy;<lb/>

pio, priu&longs;quam virtus ex&longs;oluatur, agat, nunquam &longs;uum <lb/>

finem a&longs;&longs;equetur: unde &agrave; veloci&longs;simo &amp; &longs;ibi &aelig;quali <lb/>

motu exor&longs;us, quant&ugrave;m virium deperit, tantum de ce&shy;<lb/>

leritate remittit</s>
            <s id="N10AC6"><expan abbr="Ne&qacute;;">Neque;</expan> hic nobis aduer&longs;antur, qui ne&shy;<lb/>

&longs;cio quas morulas inducunt, veloci&ugrave;s moueri dicentes <lb/>

illud mobile, quod paucioribus morulis quie&longs;cit: nam <lb/>

ex illorum <expan abbr="quo&qacute;">quoque</expan>; &longs;ententi&agrave; impul&longs;us id quod pote&longs;t <lb/>

&longs;ummum operatur: &amp; &agrave; principio quidem pauciori&shy;<lb/>

bus morulis quie&longs;cit, inde veluti ex illo motu la&longs;&longs;atus <lb/>

longiora ducit interualla. </s>
          </p>
        </subchap1>
        <subchap1 id="N10ADC">
          <p id="N10ADD" type="main">
            <s id="N10ADF"><emph type="center"/>Propo&longs;itio III.<emph.end type="center"/></s>
          </p>
          <p id="N10AE6" type="main">
            <s id="N10AE8"><emph type="italics"/>Impul&longs;us non ni&longs;i per lineam rectam mouet &longs;uum mobile.<emph.end type="italics"/></s>
          </p>
          <p id="N10AEF" type="main">
            <s id="N10AF1">DEmotu quidem, qui procedit &agrave; grauitate, nullum <lb/>

e&longs;t dubium fieri per lineam rectam: &longs;ed etiam ea, <lb/>

qu&aelig; proijciuntur &longs;eu manu, &longs;eu machin&agrave;, rectitudinem <lb/>

&longs;eruare con&longs;tat; tant&ograve; enim metam feriunt ictu certio&shy;<lb/>re, quant&ograve; min&ugrave;s principium motus &agrave; line&agrave; rect&agrave; aber<lb/>

rauit. </s>
            <s id="N10AFE">At ver&ograve; qu&aelig; circulariter mouentur, dubitatio&shy;<lb/>

nem habent: propterea qu&ograve;d ex impul&longs;u non per line-


<pb xlink:href="062/01/023.jpg"/>am rectam, &longs;ed circularem moueri videantur. </s>
            <s id="N10B07">Nihilo&shy;<lb/>

minus etiam in his, qu&aelig; circulariter mouentur, impul&shy;<lb/>

&longs;um ad motum rectum inelinare, &amp; non ni&longs;i vi ab hy&shy;<lb/>

pomochlio illat&agrave; circumagi facile o&longs;tendemus. </s>
            <s id="N10B10">Ete&shy;<lb/>

nim e&agrave; ratione mouetur totum, qu&agrave; illius partes, c&uacute;m <lb/>

motus totius &longs;it &longs;uarum partium motus: at ver&ograve; partes <lb/>

&longs;ingul&aelig; dum circumaguntur, &longs;i non firmiter coh&aelig;rent <lb/>

&longs;uo hypomochlio, non in circulum, &longs;ed per lineam re&shy;<lb/>

ctam mouentur: quod quidem in ill&agrave; rot&agrave; ver&longs;atili, qu&agrave; <lb/>

gemm&aelig; poliuntur, aut in lapide molari licebit experiri: <lb/>

qu&ograve;d &longs;i enim in ill&agrave; planitie prop&egrave; centrum arenam, <lb/>aut quid &longs;imile con&longs;tituas, videbis ex ill&agrave; rotatione <lb/>

ad circulos &longs;en&longs;im majores &agrave; centro propelli, &amp; demum <lb/>

excuti. </s>
            <s id="N10B27">Obijcies globum fi&longs;tul&agrave; &longs;triat&agrave; emi&longs;&longs;um velo&shy;<lb/>

ci&longs;sim&egrave; gyrando, &amp; veluti a&euml;rem terebrando ad metam <lb/>

venire, <expan abbr="ne&qacute;">neque</expan>; ullum punctum, pr&aelig;terquam centrum, per <lb/>

lineam rectam, &longs;ed per lineam &longs;piralem moueri: quia <lb/>

nimirum ab illis &longs;ulcis, quibus fi&longs;tula intern&eacute; excaua&shy;<lb/>

tur, toto illo tractu reuolutus impul&longs;um colligit circu&shy;<lb/>

larem: non igitur impul&longs;us nece&longs;&longs;ari&ograve; ducit per lineam <lb/>

rectam. </s>
            <s id="N10B3C">Deinde &longs;i quis velociter currendo &longs;agittam ja&shy;<lb/>

culetur, aut lapidem proijciat, quantumuis principium <lb/>

motus per lineam fiat perpendicularem, non tamen il<lb/>

lud mobile per lineam rectam, &longs;ed arcuatim &longs;ur&longs;um elu<lb/>

ctatur: propterea qu&ograve;d non ad idem punctum, &acirc; quo 


<pb xlink:href="062/01/024.jpg"/>moueri cepit, fit relap&longs;us, ver&ugrave;m ad procur&longs;um jaculan&shy;<lb/>

tis in anteriora profertur. </s>
            <s id="N10B4D"><expan abbr="Ita&qacute;">Itaque</expan>; auem in volatu deijce&shy;<lb/>

re volentes, illius volatum tanti&longs;per oculis &amp; arcu in&shy;<lb/>

tentis &longs;equuntur, &amp; tum in ip&longs;o motu &longs;agittam ejacu&shy;<lb/>

lantur: qui motus non videtur fieri per lineam rectam. <lb/>

Vt &longs;i auis ex <emph type="italics"/>b<emph.end type="italics"/> in <emph type="italics"/>f<emph.end type="italics"/> feratur, &longs;agitta per lineas <emph type="italics"/>mb.oc<emph.end type="italics"/> illius <lb/>

volatum &longs;ecuta, in line&agrave; demum <emph type="italics"/>ad<emph.end type="italics"/> &agrave; neruo excu&longs;&longs;a ean <lb/>

dem figet in <emph type="italics"/>g.<emph.end type="italics"/> at ver&ograve; ex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>g<emph.end type="italics"/> non ni&longs;i arcuatim &amp; per <lb/>

lineam inflexam, cuju&longs;modi <emph type="italics"/>ahig<emph.end type="italics"/> euadit: propterea <lb/>

qu&ograve;d motus &longs;agitt&aelig; videtur compo&longs;itus ex illo motu, <lb/><figure id="id.062.01.024.1.jpg" xlink:href="062/01/024/1.jpg"/>

quo ad motum arcus, &amp; quo &agrave; neruo impul&longs;a mouetur: <lb/>

at ver&ograve; motus, quo cum arcu mouetur, e&longs;t circulatis ha&shy;<lb/>

bens centrum in oculo &longs;agittantis: motus ergo ab hoc 


<pb xlink:href="062/01/025.jpg"/>in &longs;agittam deriuatus, ac proinde motus ex <expan abbr="utro&qacute;">utroque</expan>; mix&shy;<lb/>

tus erit circularis. </s>
            <s id="N10BA8">De&longs;cribatur arcus <emph type="italics"/>mn,<emph.end type="italics"/> cujus centrum <lb/>

in oculo <emph type="italics"/>l,<emph.end type="italics"/> &longs;emidiameter ver&ograve; &longs;agitta <emph type="italics"/>al<emph.end type="italics"/>: qu&aelig; ubi per ar&shy;<lb/>

cum <emph type="italics"/>ma<emph.end type="italics"/> moueri c&aelig;pit, ab alio impul&longs;u &agrave; neruo deriuato <lb/>

per lineam agitur <emph type="italics"/>ad<emph.end type="italics"/>: dico motum ex <expan abbr="utroq;">utroque</expan> mixtum, <lb/>

nimirum ex motu <emph type="italics"/>man,<emph.end type="italics"/> &amp; ex motu <emph type="italics"/>ad<emph.end type="italics"/> non po&longs;&longs;e fieri <lb/>

per lineam rectam. </s>
            <s id="N10BE3">Sit enim motus in <emph type="italics"/>ad<emph.end type="italics"/> ad motum in <lb/>

<emph type="italics"/>man,<emph.end type="italics"/> ut linea recta <emph type="italics"/>ap<emph.end type="italics"/> ad arcum <emph type="italics"/>aq<emph.end type="italics"/>: &amp; a&longs;&longs;umatur linea <lb/>

<emph type="italics"/>qh<emph.end type="italics"/> &aelig;qualis line&aelig; <emph type="italics"/>ap,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; motus compo&longs;itus ex <emph type="italics"/>ap. aq<emph.end type="italics"/><lb/>

in <emph type="italics"/>h:<emph.end type="italics"/> &longs;imiliter o&longs;tendemus motum in <emph type="italics"/>i<emph.end type="italics"/> &amp; <emph type="italics"/>g<emph.end type="italics"/> componi ex <lb/>

motu recto &amp; circulari: dico per puncta <emph type="italics"/>hig<emph.end type="italics"/> non pos-<lb/>

&longs;e duci lineam rectam. </s>
            <s id="N10C35">Sit enim, &longs;i fieri pote&longs;t, linea <emph type="italics"/>ab <lb/>

ig<emph.end type="italics"/> recta, &amp; ex puncto <emph type="italics"/>q<emph.end type="italics"/> ducatur linea tangens circulum <lb/>

in <emph type="italics"/>q,<emph.end type="italics"/> qu&aelig; <expan abbr="utrim&qacute;">utrimque</expan>; producta &longs;ecet lineas <emph type="italics"/>lf. ld<emph.end type="italics"/> in punctis <lb/>

s. u: <expan abbr="erunt&qacute;">eruntque</expan>; line&aelig; <emph type="italics"/>qs. qu<emph.end type="italics"/> inter &longs;e &aelig;quales: quibus ex <lb/>

puncto <emph type="italics"/>i<emph.end type="italics"/> ducatur linea parallela <emph type="italics"/>ix,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; angulus <emph type="italics"/>ixq<emph.end type="italics"/> re <lb/>

ctus, quia ergo in triangulo <emph type="italics"/>hxi<emph.end type="italics"/> duo anguli <emph type="italics"/>hxi. xhi<emph.end type="italics"/> du&shy;<lb/>

obus angulis <emph type="italics"/>hqu.qhu<emph.end type="italics"/> trianguli <emph type="italics"/>hqu<emph.end type="italics"/> &longs;unt &aelig;quales, <expan abbr="uter&qacute;">uterque</expan>; <lb/>

<expan abbr="utri&qacute;">utrique</expan>, erunt &longs;imilia inter &longs;e; ac proinde ut <emph type="italics"/>hi<emph.end type="italics"/> ad <emph type="italics"/>hq,<emph.end type="italics"/> ita <lb/>

<emph type="italics"/>xi<emph.end type="italics"/> ad <emph type="italics"/>qu,<emph.end type="italics"/> hoc e&longs;t ad <emph type="italics"/>qs<emph.end type="italics"/> illi &aelig;qualem. e&longs;t autem linea <emph type="italics"/>hx<emph.end type="italics"/><lb/> &aelig;qualis line&aelig; <emph type="italics"/>hq:<emph.end type="italics"/> igitur &amp; linea <emph type="italics"/>xi<emph.end type="italics"/> erit &aelig;qualis line&aelig; <emph type="italics"/>qs,<emph.end type="italics"/><lb/>

quod e&longs;t ab&longs;urdum: &longs;equeretur enim lineas <emph type="italics"/>is. xq<emph.end type="italics"/> in <lb/>

centro <emph type="italics"/>l<emph.end type="italics"/> concurrentes e&longs;&longs;e parallelas. </s>
            <s id="N10CEA">Re&longs;pondeo ad <lb/>

primum, motum globuli, quo gyrando ad metam va&shy;<lb/>

dit, e&longs;&longs;e compo&longs;itum ex impul&longs;u recto, quem ip&longs;i con-


<pb xlink:href="062/01/026.jpg"/>fert puluis pyrius &agrave; tergo incen&longs;us, &amp; eximpul&longs;u latera <lb/>

li, quem viarum &longs;eu <expan abbr="eanaliculor&utilde;">canaliculorum</expan> anfractus globulo e&shy;<lb/>

rumpenti conciliant: partes enim globuli prominen&shy;<lb/>

tes &longs;ulcis impre&longs;&longs;&aelig;, eo&longs;dem ductus &longs;equendo, ill&agrave; gyra&shy;<lb/>

tione globulum reuoluunt; quem motum adjuuat ig&shy;<lb/>

nis eadem vi&aacute; pabulum &longs;equendo, &amp; globulum impel&shy;<lb/>

lendo: dico ergo hunc motum partim &longs;imilem illi mo&shy;<lb/>

tui, quo rota circumagitur, partim di&longs;similem: propter&shy;<lb/>

ea, qu&ograve;d globulus circa centrum mobile, rota autem <lb/>

circa immobile reuoluatur. </s>
            <s id="N10D0B">At ver&ograve; trochus <lb/>

aut turbo, dum gyrando in a&euml;re labitur, motu pror&longs;us <lb/>

&longs;imili fertur: nam ex impul&longs;u funiculi multis &longs;piris re&shy;<lb/>

uoluti &amp; retracti in gyrum agitur circa mobile cen&shy;<lb/>

trum: quod &longs;u&agrave; grauitate inter gyrandum de&longs;cendit. <lb/>

at ver&ograve; impul&longs;us, quo rota aut turbo circulariter moue<lb/>

tur, &longs;i non impediatur, non circulari, &longs;ed motu recto mo<lb/>

uebitur: quemadmodum exemplo illarum rerum, qu&aelig; <lb/>

ad motum rot&aelig; circumaguntur, o&longs;tendimus</s>
            <s id="N10D1E"><expan abbr="Ita&qacute;">Itaque</expan>; &longs;i ca&shy;<lb/>

tenula conuoluta un&agrave; extremitate in illius plano firme&shy;<lb/>

tur, videbis ex ill&acirc; vertigine &longs;en&longs;im reuolui, &amp; demum <lb/>

in lineam tangentem eju&longs;dem circuli extendi. </s>
            <s id="N10D2A">Ita tro&shy;<lb/>chus aut turbo aqu&agrave; con&longs;per&longs;us in motu re&longs;iccatur, dum <lb/>

aqu&aelig; guttul&aelig; ex illo impul&longs;u lineam rectam &longs;equendo <lb/>

auelluntur. </s>
            <s id="N10D33">Simili ergo modo impul&longs;us, qui globu&shy;<lb/>

lum reuoluit, &longs;i non impediatur, lateraliter, &amp; per line&shy;


<pb xlink:href="062/01/027.jpg"/>am rectam mouebit. quod quidem con&longs;tabit, &longs;i globu&shy;<lb/>

lum friabilem &longs;ub&longs;tituas: ex motu enim gyrationis in <lb/>

atomos infinitas di&longs;sipabitur. </s>
            <s id="N10D40">At ver&ograve; continuitas par&shy;<lb/>

tium globuli di&longs;&longs;olui nequit ob firmitatem, <expan abbr="ne&qacute;">neque</expan>; late&shy;<lb/>

raliter moueri ob <expan abbr="re&longs;i&longs;t&etilde;tiam">re&longs;i&longs;tentiam</expan> illarum partium, qu&aelig; im&shy;<lb/>

pul&longs;u contra io aguntur: qu&ograve;t enim line&aelig; tangentes, <lb/>

tot: dem ine&longs;&longs;e videntur impul&longs;us: <expan abbr="ita&qacute;">itaque</expan>; centrum glo&shy;<lb/>

buli tant&ograve; magis detinetur in line&agrave; rect&agrave;, quant&ograve; majori <lb/>

velocitate in gyrum mouetur. </s>
            <s id="N10D5B">Dices quam ob rem er&shy;<lb/>

go turbo, dum &longs;uper axe mouetur horizonti parallelo, <lb/>

non eandem firmitatem habet &longs;ui centri &agrave; partibus cir&shy;<lb/>

cumactis? <expan abbr="neq;">neque</expan> enim eidem puncto in&longs;i&longs;tit axis, ver&ugrave;m <lb/>

huc illuc incerto motu oberrat. </s>
            <s id="N10D6A">Re&longs;pondeo id ab in <lb/>

&aelig;quali illarum partium &longs;itu, quibus planum tangit, <lb/>

prouenite: c&ugrave;m non in <expan abbr="p&utilde;cto">puncto</expan> fiat <expan abbr="c&otilde;tactus">contactus</expan>. quia ergo in <lb/>

&longs;uperficie illius plani a&longs;per&agrave; &amp; in &aelig;quali partes ali&aelig; &longs;unt <lb/>

depre&longs;&longs;&aelig;, ali&aelig; prominentes &amp; verruco&longs;&aelig;, nece&longs;&longs;e muta&shy;<lb/>

tionem fieri in motu: dum vel &longs;ub&longs;idet in lacunas, vel <lb/>

ad tubercula offendit. </s>
            <s id="N10D81">Ad &longs;ecundam objectionem, di&shy;<lb/>

co &longs;agittam circulariter moueri ex illo motu, quo cum <lb/>

arcu mouetur; impul&longs;us enim &agrave; centro detinetur, qu&ograve; <lb/>

min&ugrave;s per lineam rectam moueat: at ver&ograve; motus &longs;agit&shy;<lb/>

t&aelig; &agrave; neruo excu&longs;&longs;&aelig;, quia &agrave; nullo detinetur, per lineam fit <lb/>

mediam inter tangentem &amp; lineam rectam, &longs;iu&egrave; per di&shy;<lb/>

a metrum parallelogrammi, cujus latera &longs;unt in propor&shy;


<pb xlink:href="062/01/028.jpg"/>tione illorum motuum. </s>
            <s id="N10D94">Deinde e&longs;to demus impul&longs;um <lb/>

lateraliter abducentem e&longs;&longs;e circularem, non tamen &longs;e&shy;<lb/>

quitur motum compo&longs;itum e&longs;&longs;e circularem: nam mo&shy;<lb/>

tus quidem compo&longs;itus ex motu recto <emph type="italics"/>ap<emph.end type="italics"/> &amp; circulari <emph type="italics"/>a <lb/>

q<emph.end type="italics"/> non in <emph type="italics"/>h,<emph.end type="italics"/> ut &longs;upponebatur, ver&ugrave;m in <emph type="italics"/>y<emph.end type="italics"/> abducit mobile, <lb/>

propterea qu&ograve;d interuallum motus circularis in fine <lb/>

motus compo&longs;iti &longs;it &aelig;quale arcui <emph type="italics"/><expan abbr="aq.">aque</expan><emph.end type="italics"/> &longs;imiliter dum ex <lb/>

<emph type="italics"/>y<emph.end type="italics"/> per lineam fertur <emph type="italics"/>yz<emph.end type="italics"/> &aelig;qualem line&aelig; <emph type="italics"/>ap,<emph.end type="italics"/> impul&longs;u cir&shy;<lb/>

culari &longs;patium tran&longs;mittit <emph type="italics"/>zt<emph.end type="italics"/> &aelig;quale &longs;patio <emph type="italics"/>py<emph.end type="italics"/> &longs;eu arcui <lb/>

<emph type="italics"/>qs:<emph.end type="italics"/> dico puncta <emph type="italics"/>ayt<emph.end type="italics"/> e&longs;&longs;e in line&agrave; rect&agrave;, ac proinde mo&shy;<lb/>

tum compo&longs;itum <emph type="italics"/>ayt<emph.end type="italics"/> rectum non ver&ograve; circularem. <lb/>

Ducantur enim diametri <emph type="italics"/>ay. y t:<emph.end type="italics"/> quia ergo an&shy;<lb/>

gulus <emph type="italics"/>zyt<emph.end type="italics"/> angulo <emph type="italics"/>pay,<emph.end type="italics"/> hic autem angulo alterno <emph type="italics"/>ayq<emph.end type="italics"/><lb/>

e&longs;t &aelig;qualis, erit eidem angulus <emph type="italics"/>zyt<emph.end type="italics"/> ad verticem &aelig;qua&shy;<lb/>

lis, ac proinde linea <emph type="italics"/>ayt<emph.end type="italics"/> recta. </s>
            <s id="N10E26">Ratio autem quamob&shy;<lb/>

rem impul&longs;us non ni&longs;i per lineam rectam moueat, e&longs;t <lb/>

h&aelig;c: quia c&ugrave;m motus &longs;it via ad conjunctionem &longs;eu uni<lb/>

onem cum &longs;uo termino, ad quem mouetur, erit non &longs;ui <lb/>

&longs;ed finis gratia, ac pro&icirc;nde &longs;icuti nihil deficere, ita nihil <lb/>

abundare debet: at ver&ograve; &longs;icuti in vi&agrave; rect&agrave; nihil de e&longs;t ad <lb/>

finem con&longs;equendum, ita omnes reliqu&aelig; abundant: a&shy;<lb/>

bundare enim dicitur, <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; quo finis pote&longs;t obtineri. <lb/>

Deinde c&ugrave;m impul&longs;us &longs;it agens nece&longs;&longs;arium, habebit &amp; <lb/>

actionem &amp; modum agendi determinatum; determi&shy;<lb/>

natio autem non ni&longs;i in line&agrave; rect&acirc; e&longs;&longs;e pote&longs;t, c&ugrave;m h&aelig;c 


<pb xlink:href="062/01/029.jpg"/>&longs;it una, line&aelig; ver&ograve; obliqu&aelig; infinit&aelig;. </s>
            <s id="N10E45">Confirmatur ex <lb/>

modo agendi reliquorum agentium naturalium, qu&aelig; <lb/>

non ni&longs;i per lineas rectas operantur. </s>
          </p>
        </subchap1>
        <subchap1 id="N10E4C">
          <p id="N10E4D" type="main">
            <s id="N10E4F"><emph type="center"/>Propo&longs;itio IV.<emph.end type="center"/></s>
          </p>
          <p id="N10E56" type="main">
            <s id="N10E58"><emph type="italics"/>Impul&longs;us in quolibet puncto circuli per lineam fit tangentem.<emph.end type="italics"/></s>
          </p>
          <p id="N10E5F" type="main">
            <s id="N10E61">QVia enim motus e&longs;t rectus per pro: 3. talis autem <lb/>

e&longs;&longs;e non pote&longs;t in circulo, igitur &longs;i incipiat ab ali&shy;<lb/>

quo puncto circuli, cadet immediat&eacute; po&longs;t illud pun&shy;<lb/>

ctum extra peripheriam illius circuli: non pote&longs;t au&shy;<lb/>

tem cadere intra circulum, cadet igitur extra circulum. <lb/>

Probatur, punctum circuli immediat&egrave; ante contactum <lb/>

verbi gratia <emph type="italics"/>a<emph.end type="italics"/> impellit <emph type="italics"/>o<emph.end type="italics"/> ad motum rectum: <expan abbr="punct&utilde;">punctum</expan> ergo <lb/>

immediat&egrave; po&longs;t illum contactum erit cum duobus pun<lb/>

ctis <emph type="italics"/>a<emph.end type="italics"/> &amp; <emph type="italics"/>o<emph.end type="italics"/> in line&agrave; rect&agrave;, aut cert&egrave; ad hujus rectitudinem <lb/>

quam proxim&egrave; fieri pote&longs;t, accedet: at ver&ograve; intra peri&shy;<lb/>

pheriam circuli nullum e&longs;&longs;e pote&longs;t punctum, quod cum <lb/>

duobus illis punctis <emph type="italics"/>a<emph.end type="italics"/> &amp; <emph type="italics"/>o<emph.end type="italics"/> &longs;it in line&agrave; rect&agrave;, aut ad natu&shy;<lb/>

ram line&aelig; rect&aelig; quam proxim&egrave; accedat, verum ad ma&shy;<lb/>

iorem curuitatem: c&ugrave;m nece&longs;&longs;ari&ograve; &longs;it in peripheria ali&shy;<lb/>

cujus circuli minoris. </s>
            <s id="N10EA8">Cadat enim, &longs;i fieri pote&longs;t, intra 


<pb xlink:href="062/01/030.jpg"/>circulum illud punctum, per quod ducitur linea recta, <lb/>

&amp; &longs;it <emph type="italics"/>b<emph.end type="italics"/>: de&longs;cribatur autem circulus minor <emph type="italics"/>afp<emph.end type="italics"/> tangens <lb/>

priorem in <emph type="italics"/>a<emph.end type="italics"/>: qu&oacute;d &longs;i ergo punctum <emph type="italics"/>b<emph.end type="italics"/> cadit extra pe&shy;<lb/>

ripheriam huj&ugrave;s circuli, erit angulus <emph type="italics"/>bae<emph.end type="italics"/> minor <expan abbr="quid&etilde;">quidem</expan> <lb/>

recto, major autem angulo &longs;emicirculi <emph type="italics"/>fae<emph.end type="italics"/> contra prop: <lb/>

16. tert: Ver&ugrave;m quia po&longs;&longs;et quis dicere illud punctum <lb/>
<figure id="id.062.01.030.1.jpg" xlink:href="062/01/030/1.jpg"/>

nece&longs;&longs;ari&ograve; cadere intra omnes circulos etiam in infini&shy;<lb/>

tum minores, propterea qu&ograve;d angulus &longs;emicirculi &longs;it <lb/>

major quouis angulo acuto: ali&agrave; ratione &icirc;dem o&longs;ten&shy;<lb/>

demus. producatur ergo linea <emph type="italics"/>ab<emph.end type="italics"/> <expan abbr="utrim&qacute;">utrimque</expan>; in <emph type="italics"/>g. i<emph.end type="italics"/> &longs;ecans <lb/>

circulum in <emph type="italics"/>g,<emph.end type="italics"/> arcus autem <emph type="italics"/>ag<emph.end type="italics"/> diuidatur bifariam in <emph type="italics"/>b,<emph.end type="italics"/> &amp; <lb/>

ducatur linea <emph type="italics"/>bal<emph.end type="italics"/>; <expan abbr="erit&qacute;">eritque</expan>; angulus <emph type="italics"/>hab,<emph.end type="italics"/> <expan abbr="at&qacute;">atque</expan>; huic ad verti&shy;


<pb xlink:href="062/01/031.jpg"/>cem &aelig;qualis angulus <emph type="italics"/>ial<emph.end type="italics"/> major angulo contactus <emph type="italics"/>cah,<emph.end type="italics"/><lb/>

<expan abbr="at&qacute;">atque</expan>; huic &aelig;quali angulo <emph type="italics"/>kad<emph.end type="italics"/>: multo ergo major angu&shy;<lb/>

lus <emph type="italics"/>gab,<emph.end type="italics"/> <expan abbr="at&qacute;">atque</expan>; angulus <emph type="italics"/>iad<emph.end type="italics"/> angulis contactus <emph type="italics"/>cah. kad<emph.end type="italics"/>: <lb/>

puncta ergo circa contactum circuli <emph type="italics"/>a<emph.end type="italics"/> majori inter&shy;<lb/>

uallo ab&longs;unt &agrave; line&agrave; quauis &longs;ecante, quam &agrave; line&agrave; conta&shy;<lb/>

ctus, ac cum illis punctis, qu&aelig; in linea &longs;unt tangente, <lb/>

magis accedunt ad naturam line&aelig; rect&aelig;, quam cum il&shy;<lb/>

lis punctis, qu&aelig; in line&agrave; &longs;unt &longs;ecante: motus erg&ograve; &agrave; con&shy;<lb/>

tactu per lineam fit tangentem. </s>
            <s id="N10F6E">Qu&aelig; igitur circulari&shy;<lb/>

ter mouentur, &longs;i in ill&agrave; gyratione ab hypomochlio libe&shy;<lb/>

rentur, motu deinceps recto feruntur, facto initio mo&shy;<lb/>

tus ab illo puncto circuli, in quo ab hypomochlio avel&shy;<lb/>

luntur. </s>
            <s id="N10F79">Ita ergo lapis fund&agrave; circumactus, ubi ex ill&agrave; ro&shy;<lb/>

tatione impul&longs;um collegit, laxat&agrave; haben&agrave; auolat motu <lb/>

recto per lineam tangentem circuli, cujus &longs;emidiame&shy;<lb/>

ter e&longs;t longitudo fund&aelig;. </s>
          </p>
        </subchap1>
        <subchap1 id="N10F82">
          <p id="N10F83" type="main">
            <s id="N10F85"><emph type="center"/>Propo&longs;itio V.<emph.end type="center"/></s>
          </p>
          <p id="N10F8C" type="main">
            <s id="N10F8E"><emph type="italics"/>Impul&longs;us &aelig;qualis eodem vel &aelig;quali tempore per &longs;patium mouet <lb/>

&aelig;quate.<emph.end type="italics"/></s>
          </p>
          <p id="N10F97" type="main">
            <s id="N10F99">MAgnitudo &longs;eu exten&longs;io ine&longs;t motui non per&longs;e, &longs;ed <lb/>

ratione loci in quo fit motus; motum enim mag<lb/>

num dicimus, qui magno, paruum qui paruo &longs;patio con<lb/>

tinetur; &longs;iu&egrave; actu habeat illam exten&longs;ionem, &longs;iu&egrave; virtu&shy;


<pb xlink:href="062/01/032.jpg"/>aliter tantum: ut c&ugrave;m idem &longs;patium currendo aut am&shy;<lb/>

bulando &longs;&aelig;pi&ugrave;s remetimur. </s>
            <s id="N10FA8">Quia ver&ograve; eju&longs;dem aut <lb/>

&aelig;qualis magnitudinis eadem e&longs;t men&longs;ura: e&longs;t autem <lb/>

men&longs;ura motus tempus: erit <expan abbr="quo&qacute;">quoque</expan>; eju&longs;dem aut &aelig;qua&shy;<lb/>

lis motus idem tempus. </s>
            <s id="N10FB5">Motus ergo &aelig;qualis in tempo&shy;<lb/>

re &aelig;quali per &longs;patium fit &aelig;quale: &amp; c&ugrave;m impul&longs;us &longs;it <lb/>

agens nece&longs;&longs;arium, <expan abbr="motum&qacute;">motumque</expan>; producat &longs;ibi &aelig;qualem, <lb/>

per prop: 2. &aelig;qualis impul&longs;us in eodem vel &aelig;quali tem<lb/>

pore per &longs;patium mouebit &aelig;quale. </s>
          </p>
          <p id="N10FC4" type="main">
            <s id="N10FC6"><emph type="center"/><emph type="italics"/>Definitio.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N10FD1" type="main">
            <s id="N10FD3"><emph type="italics"/>Impul&longs;us qui m&iacute;nori tempore per &longs;patium mouet &aelig;quale aut <lb/>

majus, dicatur velox: qui ver&ograve; majori tempore per &longs;patium mouet <lb/>

&aelig;quale aut minus, dicatur tardus.<emph.end type="italics"/></s>
          </p>
          <p id="N10FDE" type="main">
            <s id="N10FE0">VT &longs;i mobile <emph type="italics"/>H<emph.end type="italics"/> per &longs;patium <emph type="italics"/>de<emph.end type="italics"/> in tempore <emph type="italics"/>ab<emph.end type="italics"/> minori, <lb/>

mobile ver&ograve; <emph type="italics"/>K<emph.end type="italics"/> per idem &longs;patium <emph type="italics"/>de,<emph.end type="italics"/> aut huic &aelig;quale <lb/>

<emph type="italics"/>fg<emph.end type="italics"/> in tempore <emph type="italics"/>abc<emph.end type="italics"/> m&aacute;jori moueatur: impul&longs;us quo <emph type="italics"/>H<emph.end type="italics"/><lb/> mouetur velox, quo autem <emph type="italics"/>K<emph.end type="italics"/> mouetur dicetur tardus. <lb/>veloci&ugrave;s enim &longs;patium tran&longs;mitti dicimus, in quo mobi&shy;<lb/>


<figure id="id.062.01.032.1.jpg" xlink:href="062/01/032/1.jpg"/><lb/>

le min&ugrave;s immoratur, &longs;eu ut Atomi&longs;t&aelig; volunt, in quo <lb/>

paucioribus morulis interquie&longs;cit. </s>
            <s id="N1102B">Quod autem mi&shy;


<pb xlink:href="062/01/033.jpg"/>nori tempore per &longs;patium &aelig;quale, idem <expan abbr="quo&qacute;">quoque</expan>; minori <lb/>

tempore per &longs;patium majus mouetur. </s>
            <s id="N11038">Diuidatur enim <lb/>

exce&longs;&longs;us temporis bifariam in <emph type="italics"/>i<emph.end type="italics"/>: <expan abbr="at&qacute;">atque</expan>; hujus &longs;emi&longs;sis <emph type="italics"/>bi<emph.end type="italics"/> ad&shy;<lb/>

datur minori <emph type="italics"/>ab,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; tempus compo&longs;itum <emph type="italics"/>abi<emph.end type="italics"/> majus <lb/>

quidem minori <emph type="italics"/>ab,<emph.end type="italics"/> minus ver&ograve; tempore majori <emph type="italics"/>abc.<emph.end type="italics"/> in <lb/>

tempore erg&ograve; <emph type="italics"/>abi<emph.end type="italics"/> &longs;patium majus quam <emph type="italics"/>de,<emph.end type="italics"/> ac proinde <lb/>

in minori tempore &longs;patium majus perambulabit. </s>
            <s id="N1107D">Eo&shy;<lb/>

dem modo o&longs;tendemus, &longs;i quid &aelig;quali tempore per <lb/>

&longs;patium majus moueatur, idem in minori tempore per <lb/>

&longs;patium majus moueri: &longs;i nimirum huj&ugrave;s exce&longs;&longs;um bi&shy;<lb/>

fariam &longs;ecemus: nam &longs;patium illud &aelig;quale, <expan abbr="at&qacute;">atque</expan>; hujus <lb/>

&longs;emi&longs;&longs;em in minori tempore pertran&longs;ibit. </s>
          </p>
        </subchap1>
        <subchap1 id="N1108E">
          <p id="N1108F" type="main">
            <s id="N11091"><emph type="center"/>Propo&longs;itio VI.<emph.end type="center"/></s>
          </p>
          <p id="N11098" type="main">
            <s id="N1109A"><emph type="italics"/>Impul&longs;us major eodem vel &aelig;qualis tempore per &longs;patium majus, <lb/>

minori ver&ograve; tempore per &longs;patium mouet &aelig;quale.<emph.end type="italics"/></s>
          </p>
          <p id="N110A3" type="main">
            <s id="N110A5">IMpul&longs;um magnum dicimus non exten&longs;iu&eacute;, &longs;ed inten<lb/>

&longs;iu&eacute;, cujus perfectionem &longs;equitur velocitas motus. <lb/>

quia ergo major velocitas in minori tempore per &longs;pati&shy;<lb/>

um mouet &aelig;quale aut majus, per defin: impul&longs;us ver&ograve; <lb/>

major majorem velocitatem producit, propterea qu&ograve;d <lb/>

agens &longs;it nece&longs;&longs;arium, <expan abbr="motum&qacute;">motumque</expan>; producat &longs;ibi &aelig;qua-


<pb xlink:href="062/01/034.jpg"/>lem: mouebit &longs;ane eodem vel &aelig;quali tempore per &longs;pa&shy;<lb/>

tium majus, minori ver&ograve; tempore per &longs;patium &aelig;quale. </s>
          </p>
        </subchap1>
        <subchap1 id="N110BC">
          <p id="N110BD" type="main">
            <s id="N110BF"><emph type="center"/>Propo&longs;itio VII.<emph.end type="center"/></s>
          </p>
          <p id="N110C6" type="main">
            <s id="N110C8"><emph type="italics"/>Velocitas motus eandem rationem habet quam interualla, rati&shy;<lb/>

onem ver&ograve; &longs;uorum temporum reciprocam.<emph.end type="italics"/></s>
          </p>
          <p id="N110D1" type="main">
            <s id="N110D3">Sit velocitas <emph type="italics"/>H<emph.end type="italics"/> dupla velocitatis <emph type="italics"/>K:<emph.end type="italics"/> dico hujus interual<lb/>

<expan abbr="l&utilde;">lum</expan> in ratione <expan abbr="quo&qacute;">quoque</expan>; e&longs;&longs;e dupl&agrave; ad illud interuallum, <lb/>

<figure id="id.062.01.034.1.jpg" xlink:href="062/01/034/1.jpg"/><lb/>

per quod velocitas &longs;ubdupla eodem vel &aelig;quali tempo&shy;<lb/>

re mouetur: at ver&ograve; tempus, quo velocitas d&ugrave;pla per <lb/>

&longs;patium &aelig;quale mouetur, in ratione &longs;ubdupl&aacute; ad tem&shy;<lb/>

pus velocitatis minoris, Vt &longs;i velo citas <emph type="italics"/>H<emph.end type="italics"/> in tempore <emph type="italics"/>ab,<emph.end type="italics"/><lb/>

velo citas autem <emph type="italics"/>K<emph.end type="italics"/> in tempore <emph type="italics"/>abc<emph.end type="italics"/> per idem &longs;patium <emph type="italics"/>de,<emph.end type="italics"/><lb/>

aut illi &aelig;quale <emph type="italics"/>fg<emph.end type="italics"/> moueatur, erit ut velocitas <emph type="italics"/>H<emph.end type="italics"/> ad veloci&shy;<lb/>

tatem K, ita tempus <emph type="italics"/>abc<emph.end type="italics"/> minoris velocitatis ad <expan abbr="t&etilde;pus">tempus</expan> <emph type="italics"/>ab<emph.end type="italics"/><lb/>

majoris velocitatis. </s>
            <s id="N1113A">Quia enim velocitas motus &longs;umi&shy;<lb/>

tur &agrave; magnitudine interualli, erit in eadem ratione in <lb/>

qu&acirc; interuallum, ac proinde velo citas dupla per &longs;pati<lb/>

um mouebit duplum. </s>
            <s id="N11143">E&longs;t autem tempus men&longs;ura <expan abbr="cu-ju&longs;&qacute;">cu&shy;<lb/>

ju&longs;que</expan>; velocitatis, minor <expan abbr="quid&etilde;">quidem</expan> majoris, major autem mi <lb/>

noris; quot igitur magnitudines minoris interualli in 


<pb xlink:href="062/01/035.jpg"/>majori, totidem men&longs;ur&aelig; velocitatis majoris in men&longs;u&shy;<lb/>

r&acirc; velocitatis minoris continentur. </s>
          </p>
        </subchap1>
        <subchap1 id="N11158">
          <p id="N11159" type="main">
            <s id="N1115B"><emph type="center"/>Propo&longs;itio VIII.<emph.end type="center"/></s>
          </p>
          <p id="N11162" type="main">
            <s id="N11164"><emph type="italics"/>Velocitas &agrave; principio motus per lineam perpendicularem e&longs;t <lb/>

&aelig;qualis grauitati, minor ver&ograve; per lineam inclinatam.<emph.end type="italics"/></s>
          </p>
          <p id="N1116D" type="main">
            <s id="N1116F">IMpul&longs;us, qu&oacute; magis impeditur ab alio impul&longs;u, e&ograve; mi <lb/>

n&ugrave;s mouet: e&longs;t <expan abbr="aut&etilde;">autem</expan> grauitas impul&longs;us deor&longs;um &longs;eu <lb/>

ad mundi centrum mouens; in line&agrave; ergo perpendicu&shy;<lb/>

lari quia &acirc; nullo impeditur impul&longs;u, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; agens nece&longs;&longs;a&shy;<lb/>

rium, motum producet &longs;ibi &aelig;qualem, <expan abbr="eritq;">eritque</expan> velocitas <lb/>

motus &aelig;qualis grauitati. </s>
            <s id="N11188">In line&acirc; ver&ograve; inclinat&acirc;, quia <lb/>

grauitas impeditur ab hypomochlio, mouebit tant&ograve; <lb/>

min&uacute;s, quant&ograve; magis impeditur, per prop: 14. ac proin&shy;<lb/>

de velocitas erit minor grauitate. </s>
            <s id="N11191">Velocitas ergo a prin&shy;<lb/>

cipio motus per lineam perpendicularem e&longs;t &aelig;qualis <lb/>

grauitati, minor ver&ograve; per lineam inclinatam. </s>
          </p>
        </subchap1>
        <subchap1 id="N11198">
          <p id="N11199" type="main">
            <s id="N1119B"><emph type="center"/>Propo&longs;itio IX.<emph.end type="center"/></s>
          </p>
          <p id="N111A2" type="main">
            <s id="N111A4"><emph type="italics"/>Velocitas continu&ograve; augetur in motu naturali, minuitur in motu <lb/>

violento.<emph.end type="italics"/></s>
          </p>
          <p id="N111AD" type="main">
            <s id="N111AF">GRauia enim qu&ograve; ex loco altiori cadunt, majori vi&shy;<lb/>

olenti&agrave; incidunt: violentia autem major ex impul&shy;


<pb xlink:href="062/01/036.jpg"/>&longs;u majori, qui illo de&longs;cen&longs;u continu&ograve; majus ac majus <lb/>

capit augmentum. </s>
            <s id="N111BA"><expan abbr="Ita&qacute;">Itaque</expan>; videmus globos ferreos &agrave; ma<lb/>

chin&agrave; bellic&agrave; &amp; vi ignis alti&longs;sim&egrave; extolli, ut relap&longs;u lon&shy;<lb/>

giore impul&longs;um colligant majorem <expan abbr="ictu&qacute;">ictuque</expan>; violentiore <lb/>

urbium tecta d ruant. </s>
            <s id="N111CA">Sic etiam fi&longs;tucis alti&ugrave;s &longs;ublatis <lb/>

palos adigunt &amp; terr&aelig; magis infigunt. </s>
            <s id="N111CF">Similiter pon&shy;<lb/>

dus &egrave; filo pendulum, qu&ograve; magis dimouetur &acirc; &longs;ua &longs;tatio&shy;<lb/>

ne, majori vi recurrit, &amp; ultra &longs;tationem procurrit: qui <lb/>

excur&longs;us non ad grauitatem, &longs;ed ad impul&longs;um illo re&shy;<lb/>

cur&longs;u collectum referri pote&longs;t. </s>
            <s id="N111DA">At ver&ograve; impul&longs;us ma&shy;<lb/>

jor eodem vel &aelig;quali tempore per &longs;patium majus, mi&shy;<lb/>

nori ver&ograve; tempore per &longs;patium &aelig;quale aut etiam majus <lb/>

mouet per prop: 6. ac proinde per definitionem ma<emph type="italics"/>j<emph.end type="italics"/>o&shy;<lb/>

ri velocitate. velocitas ergo continu&ograve; augetur in motu <lb/>

naturali, quod prim&ograve; erat demon&longs;trandum. </s>
            <s id="N111ED">Qu&aelig; au&shy;<lb/>

tem motu violento mouentur, cuiu&longs;modi projecta &longs;eu <lb/>

manu, &longs;eu machin&agrave;, &agrave; principio quidem veloci&longs;sim&egrave;, in&shy;<lb/>

de min&ugrave;s velociter mouentur, impul&longs;u veluti &longs;ene&longs;cen&shy;<lb/>

te: quia nimirum hujus principium e&longs;t externum, &agrave; quo <lb/>

in motu <expan abbr="&longs;epar&atilde;tur">&longs;eparantur</expan>: virtus autem finita, qu&aelig; non ni&longs;i in <lb/>

tempore &amp; per &longs;patium mouet finitum: non igitur ex&shy;<lb/>

tra illud tempus mouere, ac proinde <expan abbr="ne&qacute;">neque</expan>; in &longs;ubiecto <lb/>

con&longs;eruari pote&longs;t. </s>
            <s id="N11208">Emoritur autem &longs;eu natur&acirc; &longs;u&agrave;, &longs;eu <lb/>

quia grauitas contraria hunc &longs;en&longs;im atterit <expan abbr="minuit&qacute;">minuitque</expan>: ad <lb/>

cuius decrementum grauitas magis ac magis inuale&longs;cit: 


<pb xlink:href="062/01/037.jpg"/>unde priusquam vincat, motu mixto ferri, demum ubi <lb/>

pr&aelig;ualuit, reuer&longs;ionem fieri videmus. </s>
            <s id="N11219">In motu ver&ograve; <lb/>

naturali principium motus e&longs;t internum, nimirum gra&shy;<lb/>

uitas, &amp; qui &agrave; grauitate na&longs;citur impul&longs;us: qui c&ugrave;m &longs;it <lb/>

agens nece&longs;&longs;arium, motum producet &longs;ibi &aelig;qualem, &amp; <lb/>

prius quam finiat hunc motum, continu&oacute; ex eadem ra&shy;<lb/>

dice alius <expan abbr="at&qacute;">atque</expan>; alius impul&longs;us rena&longs;cens velocitatem mo<lb/>

tus continuo augebit incremento. </s>
            <s id="N1122C">Dices quam ob rem <lb/>

ergo grauia, dum in hypomochlio quie&longs;cunt, nihilo ma<lb/>

gis grauitant, &longs;i continuo veluti fluxu inde na&longs;citur im&shy;<lb/>

pul&longs;us? Re&longs;pondeo impul&longs;um quidem continuo fluxu <lb/>

&agrave; grauitate rena&longs;ci, ver&ugrave;m quant&ugrave;m grauitas producit, <lb/>

tantundem re&longs;i&longs;tentia &amp; quies violenta in hypomo&shy;<lb/>

chlio ab&longs;umit: <expan abbr="quou&longs;&qacute;">quou&longs;que</expan>; ergo grauia quie&longs;cunt, idem <lb/>

manet impul&longs;us, qui nequit ab q motu in &longs;ubiecto <lb/>

con&longs;eruari. </s>
            <s id="N11243">Qui <expan abbr="opin&atilde;tur">opinantur</expan> grauia non &agrave; &longs;e ip&longs;is, ver&ugrave;m &agrave; <lb/>

&longs;uo magnete &longs;eu tellure moueri qu&aelig; opinio non caret <lb/>

probabilitate, dicent <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>; motus principium e&longs;&longs;e <lb/>

externum: ver&ugrave;m in his, qu&aelig; projiciuntur, in motu &longs;e&shy;<lb/>

parari, <expan abbr="at&qacute;">atque</expan> ita &longs;en&longs;im deficere impul&longs;um; ob retractio&shy;<lb/>

nem ver&ograve; magneticam, ubi jam pr&aelig;ualuit, non aliter <lb/>

quam &agrave; grauitate fieri conuer&longs;ionem motus. </s>
            <s id="N1125E">Qu&aelig; au&shy;<lb/>

tem moueri dicuntur &agrave; grauitate, habere impul&longs;um &agrave; <lb/>

tellure, <expan abbr="at&qacute;">atque</expan>; eo modo, quo ferrum ad &longs;uum magne&shy;<lb/>

tem moueri, at ver&ograve; velocitatem ex ill&agrave; tractione con&shy;


<pb xlink:href="062/01/038.jpg"/>tinuat&agrave; na&longs;ci, dum impul&longs;us &longs;ibi ip&longs;i in&longs;tat non aliter <lb/>

quam &longs;i &agrave; tergo impelleretur. </s>
          </p>
        </subchap1>
        <subchap1 id="N11271">
          <p id="N11272" type="main">
            <s id="N11274"><emph type="center"/>Propo&longs;itio X.<emph.end type="center"/></s>
          </p>
          <p id="N1127B" type="main">
            <s id="N1127D"><emph type="italics"/>Incrementa velocitatis eadem ratione fiunt in motu recto &amp; <lb/>

inclinato.<emph.end type="italics"/></s>
          </p>
          <p id="N11286" type="main">
            <s id="N11288">TAmet&longs;i grauitas in line&agrave; inclinat&acirc; deficiat ab illa <lb/>

perfectione, quam habet in line&agrave; perpendiculari, <lb/>

non tamen eo modo, quo in line&agrave; horizontali quie&longs;cit&shy;<lb/> tota: exce&longs;&longs;us enim illius partis, qu&aelig; cum centro extra <lb/>

hypomochlium cadit, &agrave; nullo impeditur: &amp; c&uacute;m &longs;it a&shy;<lb/>

gens nece&longs;&longs;arium, motum producit &longs;ibi &aelig;qualem. quia <lb/>

ver&ograve; velocitas continu&ograve; augetur in de&longs;cen&longs;u, &longs;icuti gra&shy;<lb/>

uitas perfecta in line&agrave; perpendiculari &longs;e habet ad &longs;uum <lb/>

augmentum, ita grauitas diminuta in line&agrave; inclinat&agrave; &longs;e <lb/>


<figure id="id.062.01.038.1.jpg" xlink:href="062/01/038/1.jpg"/><lb/>

habebit ad &longs;uum augmentum. </s>
            <s id="N112A4">Moueatur enim ex <emph type="italics"/>a<emph.end type="italics"/><lb/>

idem mobile per lineam perpendicularem <emph type="italics"/>abc<emph.end type="italics"/> &amp; per li&shy;


<pb xlink:href="062/01/039.jpg"/>neam inclinatam <emph type="italics"/>ade:<emph.end type="italics"/> quia ergo motus <emph type="italics"/>ad<emph.end type="italics"/> motui <emph type="italics"/>ab,<emph.end type="italics"/> &amp; <lb/>

motus <emph type="italics"/>ae<emph.end type="italics"/> motui <emph type="italics"/>ac<emph.end type="italics"/> e&longs;t &aelig;qualis ut prop: 13. o&longs;tendemus: <lb/>

&longs;unt autem duo triangula <emph type="italics"/>dab. eac<emph.end type="italics"/> &longs;imilia inter &longs;e, erit <lb/>

ut <emph type="italics"/>bc<emph.end type="italics"/> ad <emph type="italics"/>ba,<emph.end type="italics"/> ita <emph type="italics"/>de<emph.end type="italics"/> ad <emph type="italics"/>da,<emph.end type="italics"/> incrementa nimirum velocita&shy;<lb/>

tis motus in linea perpendiculari &amp; line&agrave; inclinata. </s>
            <s id="N112FC">In <lb/>

crementa ergo velocitatis eadem ratione fiunt &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N11301">
          <p id="N11302" type="main">
            <s id="N11304"><emph type="center"/>Propo&longs;itio XI.<emph.end type="center"/></s>
          </p>
          <p id="N1130B" type="main">
            <s id="N1130D"><emph type="italics"/>Impul&longs;us in quolibet motu &longs;eu recto, &longs;eu inclinato e&longs;t major gra&shy;<lb/>

uitate.<emph.end type="italics"/></s>
          </p>
          <p id="N11316" type="main">
            <s id="N11318">MOtum in quolibet puncto line&aelig; perpendicularis <lb/>

e&longs;&longs;e majorem &longs;u&agrave; grauitate nullum e&longs;t dubium: <lb/>

nam c&ugrave;m velocitas cum ip&longs;o motu incipiat augeri, &longs;icu<lb/>

ti &agrave; principio e&longs;t &aelig;qualis grauitati, ita in progre&longs;&longs;u erit <lb/>

major grauitate. </s>
            <s id="N11323">At ver&ograve; de motu per lineam inclina&shy;<lb/>

tam dubitari pote&longs;t: propterea qu&oacute;d &agrave; grauitate fiat im<lb/>

pedit&agrave;, ac proinde minori: id tamen hac ratione o&longs;ten&shy;<lb/>

demus. </s>
            <s id="N1132C">Grauitas in line&agrave; inclinat&agrave; e&ograve; magis impeditur <lb/>

&agrave; &longs;u&agrave; velocitate, qu&ograve; magis h&aelig;c inclinatur, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; &longs;inus an<lb/>

guli inclinationis idem qui grauitatis exce&longs;&longs;us: uti <lb/>

prop: 14. o&longs;tendemus: grauitas ergo per lineam perpen&shy;<lb/>

dicularem ad grauitatem per lineam inclinatam, ut &longs;i&shy;<lb/>

nus totus ad &longs;inum complementi anguli inclinationis, <lb/>

ac proinde ut linea <emph type="italics"/>ab<emph.end type="italics"/> ad linea <emph type="italics"/>ad.<emph.end type="italics"/> at ver&ograve; velocitas in <emph type="italics"/>b<emph.end type="italics"/>


<pb xlink:href="062/01/040.jpg"/>majorem rationem habet ad velocitatem in aliquo pun<lb/>

cto <emph type="italics"/>f,<emph.end type="italics"/> c&uacute;m omni magnitudine dat&agrave; minor a&longs;&longs;umi po&longs;sit: <lb/>

e&longs;t autem velocitas in <emph type="italics"/>f<emph.end type="italics"/> major &longs;u&agrave; grauitate: erit ergo <lb/>

velocitas in <emph type="italics"/>d<emph.end type="italics"/> major <expan abbr="quo&qacute;">quoque</expan>; eadem grauitate, c&ugrave;m majo&shy;<lb/>

rem rationem habeat velocitas in <emph type="italics"/>b<emph.end type="italics"/> ad velocitatem in <emph type="italics"/>f,<emph.end type="italics"/><lb/>

quam ad velocitatem in <emph type="italics"/>d.<emph.end type="italics"/> Idem de quouis alio pun&shy;<lb/>cto o&longs;tendemus. impul&longs;us ergo in quolibet motu &longs;eu re<lb/>

cto, &longs;eu inclinato e&longs;t major grauitate. </s>
          </p>
        </subchap1>
        <subchap1 id="N1138A">
          <p id="N1138B" type="main">
            <s id="N1138D"><emph type="center"/>Propo&longs;itio XII.<emph.end type="center"/></s>
          </p>
          <p id="N11394" type="main">
            <s id="N11396"><emph type="italics"/>Incrementa velocitatis rationem habent quam temporum <lb/>

quadrata.<emph.end type="italics"/></s>
          </p>
          <p id="N1139F" type="main">
            <s id="N113A1">QVia virtus loco motiua eo modo augetur, quo tri&shy;<lb/>

angulum &longs;ibi &longs;imile manens, per po&longs;it: 5. propte&shy;<lb/>

rea qu&ograve;d hujus augmentum &longs;it perfectio inten&longs;iua; <lb/>

c&ugrave;m ex illo puncto quietis veluti late&longs;cit, angulum con<lb/>

&longs;tituit &longs;ui augmenti, ma<emph type="italics"/>j<emph.end type="italics"/>orem minoremu&egrave; pro <expan abbr="cuiu&longs;&qacute;">cuiu&longs;que</expan>; <lb/>

perfectione, quam obtinet in principio motus, &longs;iu&egrave; ex <lb/>

natur&acirc; &longs;u&acirc;, &longs;iue ex impedimento: majori enim perfecti&shy;<lb/>

oni maior angulus debetur. </s>
            <s id="N113BC">Sit prim&ugrave;m angulus <emph type="italics"/>nag<emph.end type="italics"/><lb/>&longs;e mi&longs;sis anguli recti; tempus ver&ograve; <emph type="italics"/>ag<emph.end type="italics"/> in minuta <emph type="italics"/>ab. bc. <lb/>

cd. de. ef.fg<emph.end type="italics"/> &aelig;qualiter diui&longs;um: velocitas erg&ograve; motus <lb/>

augetur impul&longs;u auge&longs;cente in primo quidem minuto <lb/>

in <emph type="italics"/>hb,<emph.end type="italics"/> in 2. in <emph type="italics"/>ic,<emph.end type="italics"/> in 3. in <emph type="italics"/>kd,<emph.end type="italics"/> <expan abbr="at&qacute;">atque</expan>; it&aelig; con&longs;equenter &aelig;quat&agrave; 


<pb xlink:href="062/01/041.jpg"/>are&agrave; illius trianguli rectanguli, cujus longitudo nume&shy;<lb/>

rus minutorum, ba&longs;is ver&ograve; terminus augmenti. </s>
            <s id="N113F4">Quia <lb/>

ver&ograve; eadem e&longs;t ratio motus &amp; virtutis impul&longs;iu&aelig;, vir&shy;<lb/>


<figure id="id.062.01.041.1.jpg" xlink:href="062/01/041/1.jpg"/><lb/>

tus quidem dupla in eodem aut &aelig;quali tempore moue&shy;<lb/>

bit per &longs;patium duplum: qu&ograve;d &longs;i ergo in primo minu&shy;<lb/>

to <emph type="italics"/>ab<emph.end type="italics"/> virtus <emph type="italics"/>a<emph.end type="italics"/> late&longs;cens, cum qu&agrave; pariter cre&longs;cit veloci&shy;<lb/>

tas motus, terminum habet &longs;ui incrementi in <emph type="italics"/>hb,<emph.end type="italics"/> in &longs;e&shy;<lb/>

cundo minuto in <emph type="italics"/>ic,<emph.end type="italics"/> in 3. in <emph type="italics"/>kd<emph.end type="italics"/> &amp;c. erit ut triangulum re&shy;<lb/>

ctangulum <emph type="italics"/>iac<emph.end type="italics"/> ad triangulum rectangulum <emph type="italics"/>hab,<emph.end type="italics"/> ita <lb/>

&longs;patium decur&longs;um in duobus minutis ad &longs;patium decur<lb/>

&longs;um in uno minuto; at ver&ograve; duo triangula <emph type="italics"/>iac.hab<emph.end type="italics"/> &longs;unt <lb/>

&longs;emi&longs;&longs;es duorum quadratorum <emph type="italics"/>ipac. hoab.<emph.end type="italics"/> ac pro&shy;<lb/>

inde in e&agrave;dem ratione, nimirum duplicat&agrave; ejus, <expan abbr="qu&atilde;">quam</expan> ha&shy;<lb/>

bent latera <emph type="italics"/>ic.hb<emph.end type="italics"/>: igitur ut quadratum lateris <emph type="italics"/>ic<emph.end type="italics"/> ad qua&shy;<lb/>

dratum lateris <emph type="italics"/>hb,<emph.end type="italics"/> ita motus duorum minutorum ad 


<pb xlink:href="062/01/042.jpg"/>motum unius minuti; propterea qu&ograve;d latus <emph type="italics"/>ca<emph.end type="italics"/> ad latus <lb/>

<emph type="italics"/>ba<emph.end type="italics"/> eandem habeat rationem, quam latus <emph type="italics"/>ic<emph.end type="italics"/> ad latus <emph type="italics"/>hb,<emph.end type="italics"/><lb/>

ac proinde illorum quadrata in eadem <expan abbr="quo&qacute;">quoque</expan>, ratione, <lb/>

nimirum duplicata. </s>
            <s id="N11489"><expan abbr="Ita&qacute;">Itaque</expan>; &longs;i quadratum lateris <emph type="italics"/>ab,<emph.end type="italics"/> hoc <lb/>

e&longs;t primi minuti, &longs;ubtrahas &acirc; quadrato <emph type="italics"/>ac<emph.end type="italics"/> &longs;ecundi minu&shy;<lb/>

ti, numerus reliquus dabit velocitatem motus in eodem <lb/>

minuto: ut &longs;i cubitum unum <emph type="italics"/>vg.<emph.end type="italics"/> perambulet in primo <lb/>

minuto, hujus quadratum, ide&longs;t unum, ab illius quadra<lb/>

to, id, e&longs;t &acirc; quatuor &longs;ubtractum relinquit tria totidem <lb/>

cubitorum illi &longs;patio, per quod <emph type="italics"/>a<emph.end type="italics"/> mouetur in minuto 2. <lb/>

tribuenda. </s>
            <s id="N114B5">Similiter quia 3. minutis conficit cubitos 9. <lb/>

ablato ex his quadrato &longs;ecundi minuti, numerus reli&shy;<lb/>

quus dabit velocitatem 5. cubitorum, qui minuto 3. de&shy;<lb/>

bentur. </s>
            <s id="N114BE">Rur&longs;um &acirc; numero 4. minuti in &longs;e ducto, ide&longs;t <lb/>

16. ablatis 9. quadrato tertij minuti rem anet numerus 7. <lb/>

pro 4. minuto: totidem ergo cubitorum &longs;patium trans&shy;<lb/>

mittit mobile <emph type="italics"/>a<emph.end type="italics"/> in minuto quarto. </s>
            <s id="N114CD">Qu&oacute;d &longs;i angulus <lb/>

augmenti major &longs;it aut minor &longs;emi&longs;&longs;e anguli recti, ut <lb/>

angulus <emph type="italics"/>qag.<emph.end type="italics"/> aut <emph type="italics"/>rag,<emph.end type="italics"/> quod quidem contingit, c&ugrave;m vir&shy;<lb/>

tus impul&longs;iua magis aut min&ugrave;s e&longs;t inten&longs;a, tum quidem <lb/>illa virtus magis perfecta ex illo puncto continu&ograve; majo<lb/>

ra &longs;umit incrementa: eadem tamen demon&longs;tratio, <expan abbr="at&qacute;">atque</expan>; <lb/>

eadem e&longs;t proportio <expan abbr="utrobi&qacute;">utrobique</expan>;, propterea qu&ograve;d parallelo&shy;<lb/>

gramma in proportione <expan abbr="quo&qacute;">quoque</expan>; &longs;int duplicat&aacute; &longs;uorum <lb/>

laterum &longs;imul &longs;umptorum.&verbar; </s>
          </p>
        </subchap1>
        <subchap1 id="N114F8">
          <pb xlink:href="062/01/043.jpg"/>
          <p id="N114FC" type="main">
            <s id="N114FE"><emph type="center"/>Propo&longs;itio XIII.<emph.end type="center"/></s>
          </p>
          <p id="N11505" type="main">
            <s id="N11507"><emph type="italics"/>Motus per lineam perpendicularem &amp; lineam inclinatam, quo&shy;<lb/>

rum terminos conjungit linea recta perpendicularis ad lineam in&shy;<lb/>

clinatam, inter &longs;e &longs;unt &aelig;quales.<emph.end type="italics"/></s>
          </p>
          <p id="N11512" type="main">
            <s id="N11514">&AElig;Quales dico non velocitate, qu&aelig; minor e&longs;t in line&agrave; <lb/>

inclinat&agrave;, &longs;ed duratione: hoc e&longs;t &longs;i ex eodem puncto <lb/>

incipiat motus <emph type="italics"/>Vg.<emph.end type="italics"/> ex <emph type="italics"/>b,<emph.end type="italics"/> &amp; unum quidem mobile per li&shy;<lb/>

neam perpendicularem <emph type="italics"/>ba,<emph.end type="italics"/> alterum ver&ograve; huic &aelig;quale <lb/>

per lineam <emph type="italics"/>bf<emph.end type="italics"/> ad horizontem inclinatam moueatur: a&longs;&shy;<lb/>

&longs;umpto quolibet puncto in line&agrave; perpendiculari <emph type="italics"/>Vg. a,<emph.end type="italics"/><lb/>

linea ex hoc puncto educta perpendicularis ad lineam <lb/>

<emph type="italics"/>bf<emph.end type="italics"/> locum terminabit in <emph type="italics"/>f,<emph.end type="italics"/> ad quod mobile eodem tem&shy;<lb/>


<figure id="id.062.01.043.1.jpg" xlink:href="062/01/043/1.jpg"/><lb/>


<pb xlink:href="062/01/044.jpg"/>pore per lineam <emph type="italics"/>bf,<emph.end type="italics"/> quo alterum mobile per lineam <emph type="italics"/>ba <emph.end type="italics"/><lb/>

decurrit. </s>
            <s id="N11568">Ducatur enim ex puncto contactus <emph type="italics"/>f<emph.end type="italics"/> linea <emph type="italics"/>fe<emph.end type="italics"/><lb/>

parallela line&aelig; perpendiculari <emph type="italics"/>ba,<emph.end type="italics"/> &amp; producatur in <emph type="italics"/>g<emph.end type="italics"/>; ad <lb/>

quam ex centro grauitatis <emph type="italics"/>d<emph.end type="italics"/> educta &longs;it linea perpendicu<lb/>

laris <emph type="italics"/>dc,<emph.end type="italics"/> di&longs;tantia nimirum centri &agrave; line&agrave; hypomochlij <emph type="italics"/>f <lb/>

g:<emph.end type="italics"/> e&longs;t autem linea <emph type="italics"/>df<emph.end type="italics"/> &longs;emidiameter circuli, di&longs;tantia eju&longs;&shy;<lb/>

dem centri ab hypochlio, quam obtinet in line&acirc; perpen<lb/>

diculari <emph type="italics"/>ba.<emph.end type="italics"/> quia ergo impul&longs;us augetur in ratione di&shy;<lb/>

&longs;tanti&aelig; centri ab hypomochlio, per Po&longs;it: 6. <expan abbr="mot&utilde;&qacute;">motunque</expan>; pro <lb/>

ducit &longs;ibi &aelig;qualem, per prop: 2. velocitas autem motus <lb/>

eandem rationem habet quam interualla, per prop: 7. e&shy;<lb/>

rit ut <emph type="italics"/>fd<emph.end type="italics"/> impul&longs;us major ad <emph type="italics"/>dc<emph.end type="italics"/> impul&longs;um minorem, ita <lb/>

motus in <emph type="italics"/>ba<emph.end type="italics"/> ad motum in <emph type="italics"/>bf:<emph.end type="italics"/> propterea qu&oacute;d triangula <lb/>

<emph type="italics"/>abf.fdc<emph.end type="italics"/> &longs;int &longs;imilia, &amp; linea <emph type="italics"/>dc<emph.end type="italics"/> perpendicularis, ac proinde <lb/>

linea <expan abbr="quo&qacute;">quoque</expan>; <emph type="italics"/>af,<emph.end type="italics"/> &longs;imilis line&aelig; <expan abbr="perp&etilde;diculari">perpendiculari</expan> <emph type="italics"/>dc,<emph.end type="italics"/> perpendi&shy;<lb/>

cularis. </s>
          </p>
        </subchap1>
        <subchap1 id="N115F8">
          <p id="N115F9" type="main">
            <s id="N115FB"><emph type="center"/>Propo&longs;itio XIV:<emph.end type="center"/></s>
          </p>
          <p id="N11602" type="main">
            <s id="N11604"><emph type="italics"/>Motus per lineam min&ugrave;s inclinatam e&longs;t veloc&igrave;or motu per li&shy;<lb/>

neam magis inclinatam, in ratione, quam habent &longs;inus complemen&shy;<lb/>

ti illarum inclinationum.<emph.end type="italics"/></s>
          </p>
          <p id="N1160F" type="main">
            <s id="N11611">DVcantur ex puncto <emph type="italics"/>a<emph.end type="italics"/> l&icirc;ne&aelig; <emph type="italics"/>ab. ac. ad. ae. af,<emph.end type="italics"/> &amp; &longs;it li&shy;<lb/>

nea <emph type="italics"/>ab<emph.end type="italics"/> horizontalis, linea ver&ograve; <emph type="italics"/>at<emph.end type="italics"/> perpendicularis, <lb/>

reliqu&aelig; line&aelig; ad horizontem inclinat&aelig;: dico idem mo&shy;<lb/>

bile o verbi grat: in&aelig;qualiter moueri, veloci&ugrave;s quidem 


<pb xlink:href="062/01/045.jpg"/>in line&agrave; <emph type="italics"/>ae<emph.end type="italics"/> minus inclinat&agrave;, min&ugrave;s autem velociter in li&shy;<lb/>

ne&agrave; <emph type="italics"/>ad<emph.end type="italics"/> magis inclinat&agrave;, <expan abbr="e&longs;&longs;e&qacute;">e&longs;&longs;eque</expan>; rationem velocitatis in <emph type="italics"/>ae<emph.end type="italics"/><lb/> ad velocitatem in <emph type="italics"/>ad,<emph.end type="italics"/> ut &longs;inus anguli <emph type="italics"/>ats<emph.end type="italics"/> ad &longs;inum angu&shy;<lb/>

li <emph type="italics"/>atr.<emph.end type="italics"/> Ex punctis contactus <emph type="italics"/>qrs<emph.end type="italics"/> demittantur line&aelig; <lb/>

perpendiculares <emph type="italics"/>qt.rt.st:<emph.end type="italics"/> &amp; ali&aelig; line&aelig; perpendiculari <emph type="italics"/>at <emph.end type="italics"/><lb/>


<figure id="id.062.01.045.1.jpg" xlink:href="062/01/045/1.jpg"/><lb/>

parallel&aelig; <emph type="italics"/>qg.rh.si<emph.end type="italics"/> <expan abbr="&longs;ec&atilde;tes">&longs;ecantes</expan> mobile in <emph type="italics"/>k. n. u,<emph.end type="italics"/> ex centro au<lb/>

tem <emph type="italics"/>o<emph.end type="italics"/> ducantur line&aelig; perpendiculares ad lineam hypo&shy;<lb/>

mochlij <foreign lang="greek">oa. ob. og</foreign>, <expan abbr="erunt&qacute;">eruntque</expan>; line&aelig; <emph type="italics"/>qg. rh. si<emph.end type="italics"/> line&aelig; hypo&shy;<lb/>

mochlij. </s>
            <s id="N116A9">Quia ver&ograve; angulus <emph type="italics"/>tsi,<emph.end type="italics"/> hoc e&longs;t angulus <emph type="italics"/>sh<emph.end type="italics"/> ex&shy;


<pb xlink:href="062/01/046.jpg"/>ternus major e&longs;t angulo <emph type="italics"/>trh<emph.end type="italics"/> interno &amp; oppo&longs;ito, erit an<lb/>

gulus <foreign lang="greek">gso</foreign> angulo <foreign lang="greek">bgo</foreign>, &amp; latus <foreign lang="greek">go</foreign> latere <foreign lang="greek">bo</foreign> majus: &longs;unt <lb/>

autem latera <foreign lang="greek">go. bo</foreign> di&longs;tantia centri grauitatis. </s>
            <s id="N116DA">Quia er&shy;<lb/>

go maior impul&longs;us in <foreign lang="greek">go</foreign> maiori, quam in <foreign lang="greek">bo</foreign> minori di&shy;<lb/>

&longs;tanti&agrave;; erit per prop: 6. velocior motus in linea <emph type="italics"/>as<emph.end type="italics"/> mi&shy;<lb/>

n&uacute;s inclinat&aacute;, quam in line&agrave; <emph type="italics"/>ar<emph.end type="italics"/> magis inclinat&agrave;. </s>
            <s id="N116F7">Qu&ograve;d <lb/>

autem velocitas motus &longs;it in ratione, quam habent cor&shy;<lb/>

d&aelig;, &longs;eu &longs;inus complementi inclinationum, ita o&longs;tende&shy;<lb/>

mus: quia ut <foreign lang="greek">so</foreign> ad <foreign lang="greek">go</foreign>, ita corda <emph type="italics"/>at<emph.end type="italics"/> ad cordam <emph type="italics"/>as,<emph.end type="italics"/> &amp; ut <emph type="italics"/>r&ograve;<emph.end type="italics"/><lb/> &aelig;qualis <foreign lang="greek">so</foreign> ad <foreign lang="greek">ob</foreign>, ita eadem corda <emph type="italics"/>at<emph.end type="italics"/> ad cordam <emph type="italics"/>ar:<emph.end type="italics"/> erit <lb/>

<expan abbr="quo&qacute;">quoque</expan>; ut <foreign lang="greek">og</foreign> ad <foreign lang="greek">ob</foreign>, ita <emph type="italics"/>as<emph.end type="italics"/> ad <emph type="italics"/>ar.<emph.end type="italics"/> at ver&ograve; ut cord&aelig; <emph type="italics"/>as. ar,<emph.end type="italics"/><lb/>

ita illarum &longs;emi&longs;&longs;es <emph type="italics"/>al. am<emph.end type="italics"/> &longs;inus angulorum <emph type="italics"/>apl. apm <emph.end type="italics"/><lb/>

qui &aelig;quales &longs;unt angulis <emph type="italics"/>ats.atr<emph.end type="italics"/> angulis complementi <lb/>

inclinationis, ob parallelas <emph type="italics"/>ts. pl,<emph.end type="italics"/> &amp; <emph type="italics"/>tr. pm.<emph.end type="italics"/> <emph type="italics"/>Igitur ut <foreign lang="greek">og</foreign><lb/>

ad <foreign lang="greek">ob</foreign>, ita &longs;inus complementi angulorum inclinationis, <lb/>

quod erat o&longs;tendendum. </s>
          </p>
        </subchap1>
        <subchap1 id="N1177F">
          <p id="N11780" type="main">
            <s id="N11782"><emph type="center"/>Propo&longs;itio XV.<emph.end type="center"/></s>
          </p>
          <p id="N11789" type="main">
            <s id="N1178B"><emph type="italics"/>Motus ex eodem puncto per lineas &longs;ubten&longs;as &longs;unt &aelig;quales motui <lb/>

per diametrum eju&longs;dem circuli.<emph.end type="italics"/></s>
          </p>
          <p id="N11794" type="main">
            <s id="N11796">MOueatur ex puncto <emph type="italics"/>b<emph.end type="italics"/> mobile per lineas <emph type="italics"/>bi. bh.bg. <lb/>

bf.be<emph.end type="italics"/> ad horizontem inclinatas, hoc e&longs;t per cordas <lb/>

arcuum <emph type="italics"/>bes.beh.beg.bef.be<emph.end type="italics"/>: dico eodem tempore per 


<pb xlink:href="062/01/047.jpg"/>cordam <emph type="italics"/>bf,<emph.end type="italics"/> aut <emph type="italics"/>bg,<emph.end type="italics"/> quo per diametrum eiu&longs;dem circuli <lb/>

<emph type="italics"/>ba<emph.end type="italics"/> motum terminari. </s>
            <s id="N117C7">Qu&ograve;d &longs;i enim ex puncto <emph type="italics"/>a<emph.end type="italics"/> du<lb/>

cantur line&aelig; rect&aelig; <emph type="italics"/>af. ag,<emph.end type="italics"/> erunt anguli <emph type="italics"/>afb. agb<emph.end type="italics"/> in &longs;emi&shy;<lb/>

circulo recti; ac proinde ex iam demon&longs;tratis motus in <lb/>

<emph type="italics"/>ba<emph.end type="italics"/> motui in <emph type="italics"/>bf<emph.end type="italics"/> &amp; <emph type="italics"/>bg<emph.end type="italics"/> duratione &aelig;qualis. </s>
            <s id="N117F4">Simili modo &longs;i <lb/>

ex punctis <emph type="italics"/>befg<emph.end type="italics"/> in <emph type="italics"/>a<emph.end type="italics"/> terminetur motus, <expan abbr="er&utilde;t">erunt</expan> line&aelig; <emph type="italics"/>be.bf.<emph.end type="italics"/><lb/>


<figure id="id.062.01.047.1.jpg" xlink:href="062/01/047/1.jpg"/><lb/>

<emph type="italics"/>bg<emph.end type="italics"/> perpendiculares ad <emph type="italics"/>ae. af. ag,<emph.end type="italics"/> ac proinde motus in <emph type="italics"/>b <lb/>

a<emph.end type="italics"/> motui in <emph type="italics"/>ea. fa. ga<emph.end type="italics"/> &aelig;qualis. </s>
            <s id="N11831">At ver&ograve; &longs;i ex alio puncto <lb/>

Vg <foreign lang="greek">a</foreign> incipiat motus, <expan abbr="ne&qacute;">neque</expan>; ad idem cum diametro pun&shy;<lb/>

ctum terminetur, cuju&longs;modi linea <foreign lang="greek">ab</foreign>, er t motus hujus <lb/>

motui in diametro <emph type="italics"/>ba<emph.end type="italics"/> in&aelig;qualis. </s>
            <s id="N1184C">Ducatur enim ex <foreign lang="greek">a</foreign> in <lb/>

<emph type="italics"/>a<emph.end type="italics"/> linea <foreign lang="greek">a</foreign> <emph type="italics"/>a,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; motus hujus motui <emph type="italics"/>ba,<emph.end type="italics"/> ide&longs;t motui <foreign lang="greek">ad</foreign>


<pb xlink:href="062/01/048.jpg"/>&aelig;qualis: linea ver&ograve; <foreign lang="greek">gb</foreign> perpendicularis ad <foreign lang="greek">ab</foreign> motum ter&shy;<lb/>

minabit in <foreign lang="greek">b</foreign> &aelig;qualem motui <foreign lang="greek">ag</foreign>: e&longs;t autem linea <foreign lang="greek">ag</foreign> mi&shy;<lb/>

nor quam <foreign lang="greek">ad</foreign> motus ergo in <foreign lang="greek">ag</foreign>, ide&longs;t motus huic &aelig;qua <lb/>

lis in <foreign lang="greek">ab</foreign> minori fit tempore quam in <foreign lang="greek">a</foreign> a.</s>
          </p>
        </subchap1>
        <subchap1 id="N118A1">
          <p id="N118A2" type="main">
            <s id="N118A4"><emph type="center"/>Propo&longs;itio XVI.<emph.end type="center"/></s>
          </p>
          <p id="N118AB" type="main">
            <s id="N118AD"><emph type="italics"/>Motus grauitatis per lineam magis inclinatam in majori &agrave; <lb/>

centro di&longs;tanti&agrave;, tempore ver&ograve; &aelig;quali terminatur.<emph.end type="italics"/></s>
          </p>
          <p id="N118B6" type="main">
            <s id="N118B8">MOueatur mobile &agrave; puncto <emph type="italics"/>b<emph.end type="italics"/> per lineas <emph type="italics"/>ba. bi. bh. bg <lb/>

bf be<emph.end type="italics"/>; dico &longs;olam lineam perpendicularem <emph type="italics"/>ba<emph.end type="italics"/> in <lb/>

centro <emph type="italics"/>a,<emph.end type="italics"/> reliquas omnes extra centrum, <expan abbr="at&qacute;">atque</expan>; ex inclina&shy;<lb/>

tione majori ad majus interuallum terminari: ut quia <lb/>

angulus <emph type="italics"/>abh<emph.end type="italics"/> e&longs;t major angulo <emph type="italics"/>abi,<emph.end type="italics"/> erit terminus mo&shy;<lb/>


<figure id="id.062.01.048.1.jpg" xlink:href="062/01/048/1.jpg"/><lb/>


<pb xlink:href="062/01/049.jpg"/>tus, quem grauitas inducit in line&acirc; <emph type="italics"/>bh,<emph.end type="italics"/> remotior &agrave; cen&shy;<lb/>

tro, qu&agrave;m in line&acirc; <emph type="italics"/>bi.<emph.end type="italics"/> Ducantur enim &agrave; centro <emph type="italics"/>a<emph.end type="italics"/> line&aelig; <emph type="italics"/>ai. <lb/>

ab<emph.end type="italics"/> perpendiculares ad <emph type="italics"/>bi. bh,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; terminus motus gra&shy;<lb/>

uitatis in <emph type="italics"/>i<emph.end type="italics"/> &amp; <emph type="italics"/>h<emph.end type="italics"/> ob breui&longs;simam di&longs;tantiam, qu&aelig; e&longs;&longs;e po&shy;<lb/>

te&longs;t in illis lineis; qu&oacute;d &longs;i enim ex <emph type="italics"/>i<emph.end type="italics"/> moueatur in <emph type="italics"/>st,<emph.end type="italics"/> quia <lb/>

illo progre&longs;&longs;u line&aelig; &agrave; centro duct&aelig; fiunt majores, ma&shy;<lb/>

jor enim <emph type="italics"/>as<emph.end type="italics"/> angulo recto <emph type="italics"/>ais<emph.end type="italics"/> &longs;ubten&longs;a quam <emph type="italics"/>ai,<emph.end type="italics"/> mobile <lb/>

motu naturali &agrave; centro magis abduceretur, quod fieri <lb/>

nequit. </s>
            <s id="N11954">Quia ergo linea <foreign lang="greek">ag</foreign> major e&longs;t qu&agrave;m linea <emph type="italics"/>ai,<emph.end type="italics"/><lb/>

erit linea <emph type="italics"/>ab<emph.end type="italics"/>c dem mult&ograve; major: igitur punctum <emph type="italics"/>h<emph.end type="italics"/> ter&shy;<lb/>

minus motus in line&agrave; magis inclinat&agrave;, majori, punctum <lb/>

ver&ograve; <emph type="italics"/>i<emph.end type="italics"/> terminus motus in line&agrave; min&uacute;s inclinat&acirc;, minori <lb/>

&agrave; centro abe&longs;t interuallo. </s>
            <s id="N1197A">Quia vet&ograve; <expan abbr="uter&qacute;">uterque</expan>; motus tam <lb/>

per <expan abbr="line&atilde;">lineam</expan> <emph type="italics"/>ai<emph.end type="italics"/> <expan abbr="qu&atilde;">quam</expan> per <expan abbr="line&atilde;">lineam</expan> <emph type="italics"/>ah<emph.end type="italics"/> e&longs;t &aelig;qualis motui per <expan abbr="line&atilde;">lineam</expan> <lb/>

perpendicularem <emph type="italics"/>ab,<emph.end type="italics"/> propterea qu&ograve;d line&aelig; perpendi&shy;<lb/>

culares <emph type="italics"/>as. ah<emph.end type="italics"/> <expan abbr="utrum&qacute;">utrumque</expan>; <expan abbr="mot&utilde;">motum</expan> conjungunt per prop: 13. <lb/>

erit motus <emph type="italics"/>at<emph.end type="italics"/> motui <emph type="italics"/>ab<emph.end type="italics"/> &aelig;qualis, ac proinde in tempore <lb/>

&aelig;quali. </s>
          </p>
        </subchap1>
        <subchap1 id="N119C7">
          <p id="N119C8" type="main">
            <s id="N119CA"><emph type="center"/>Propo&longs;itio XVII.<emph.end type="center"/></s>
          </p>
          <p id="N119D1" type="main">
            <s id="N119D3"><emph type="italics"/>Motus grauitatis ex eodem puncto per lineas ad horizontem in&shy;<lb/>

clinatas in circulum terminatur, cuius diameter e&longs;t di&longs;tantia inter <lb/>

illud punctum &amp; mundi centrum.<emph.end type="italics"/></s>
          </p>
          <p id="N119DE" type="main">
            <s id="N119E0">MOueatur ex puncto <emph type="italics"/>b<emph.end type="italics"/> mobile eju&longs;dem rationis per <lb/>

line&agrave;s ad horizontem inclinat as <emph type="italics"/>bi. bh. bg. bf.<emph.end type="italics"/> &amp;c. 


<pb xlink:href="062/01/050.jpg"/>&longs;it autem mundi centrum <emph type="italics"/>a,<emph.end type="italics"/> &amp; linea perpendicularis <emph type="italics"/>ba,<emph.end type="italics"/><lb/>

dico motum per lineas <emph type="italics"/>bi. bh. bg. bf<emph.end type="italics"/> &amp;c. in circulum ter <lb/>

minari, cujus diameter linea perpendicularis <emph type="italics"/>ab<emph.end type="italics"/> di&longs;tan&shy;<lb/>

tia inter <emph type="italics"/>b<emph.end type="italics"/> &amp; mundi centrum <emph type="italics"/>a.<emph.end type="italics"/> Ducantur enim &agrave; cen&shy;<lb/>

tro <emph type="italics"/>a<emph.end type="italics"/> line&aelig; <emph type="italics"/>ai.ah.ag.af<emph.end type="italics"/> &amp;c. perpendiculares ad <emph type="italics"/>bi.bh.bg. <lb/>

bf,<emph.end type="italics"/> <expan abbr="erunt&qacute;">eruntque</expan>; puncta <emph type="italics"/>i.h.g.f<emph.end type="italics"/> termini motus &agrave; grauitate: <lb/>


<figure id="id.062.01.050.1.jpg" xlink:href="062/01/050/1.jpg"/><lb/>

propterea qu&ograve;d minima &longs;it h&aelig;c di&longs;tantia &agrave; mundi cen&shy;<lb/>

tro <emph type="italics"/>a.<emph.end type="italics"/> Quia ver&ograve; anguli <emph type="italics"/>aib.ahb.afb<emph.end type="italics"/> &longs;unt recti ean&shy;<lb/>

dem habentes ba&longs;im <emph type="italics"/>ab.<emph.end type="italics"/> erunt in eodem &longs;emicirculo <emph type="italics"/>bef <lb/>

g hia,<emph.end type="italics"/> cujus diameter linea <emph type="italics"/>ba<emph.end type="italics"/> perpendicularis, di&longs;tantia <lb/>

inter <emph type="italics"/>b<emph.end type="italics"/> &amp; mundi centrum. </s>
          </p>
        </subchap1>
        <subchap1 id="N11A73">
          <pb xlink:href="062/01/051.jpg"/>
          <p id="N11A77" type="main">
            <s id="N11A79"><emph type="center"/>Propo&longs;itio XVIII.<emph.end type="center"/></s>
          </p>
          <p id="N11A80" type="main">
            <s id="N11A82"><emph type="italics"/>Velocitas in fine motus &aelig;quali tempore per &longs;patium mouet du&shy;<lb/>

plum velocitatis eodem motu collect&aelig;.<emph.end type="italics"/></s>
          </p>
          <p id="N11A8B" type="main">
            <s id="N11A8D">VT in fig: 5. &longs;i velocitas motus <emph type="italics"/>a<emph.end type="italics"/> in tempore <emph type="italics"/>ac<emph.end type="italics"/> conti&shy;<lb/>

nu&ograve; augeatur; quia hujus augmentum e&longs;t perfe&shy;<lb/>

ctio inten&longs;iua, ac proinde eo modo augetur, quo trian&shy;<lb/>

gulum &longs;ibi &longs;imile manens per po&longs;it: 5. erit velocitas in <lb/>

fine motus, ut ba&longs;is eju&longs;dem trianguli <emph type="italics"/>bc.<emph.end type="italics"/> Moueatur er&shy;<lb/>

go h&aelig;c velocitas in <emph type="italics"/>e,<emph.end type="italics"/> &amp; &longs;it tempus <emph type="italics"/>ec<emph.end type="italics"/> &aelig;quale tempori <lb/>

<emph type="italics"/>ac,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; velocitas illo motu colecta quadratum <emph type="italics"/>bcde<emph.end type="italics"/><lb/> duplum trianguli <emph type="italics"/>abc,<emph.end type="italics"/> propterea qu&ograve;d eandem ba&longs;im <lb/>

<emph type="italics"/>bc,<emph.end type="italics"/> altitudinem ver&ograve; habet &aelig;qualem. </s>
            <s id="N11AD9">Quia ergo virtus <lb/>

dupla in eodem vel &aelig;quali tempore per &longs;patium mouet <lb/>

<expan abbr="dupl&utilde;">duplum</expan>, <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; <expan abbr="ead&etilde;">eadem</expan> ratio velocitatis &amp; interualli, velocitas <lb/>

in fine motus eodem vel &aelig;quali tempore per &longs;patium <lb/>

mouebit duplum &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N11AF0">
          <p id="N11AF1" type="main">
            <s id="N11AF3"><emph type="center"/>Propo&longs;itio XIX.<emph.end type="center"/></s>
          </p>
          <p id="N11AFA" type="main">
            <s id="N11AFC"><emph type="italics"/>Velocitas in motu grauium collecta ultra &longs;tationem defert mo&shy;<lb/>

bile.<emph.end type="italics"/></s>
          </p>
          <p id="N11B05" type="main">
            <s id="N11B07">STatio quidem grauium e&longs;t centrum terr&aelig;, ponderis <lb/>

ver&ograve; &egrave; filo penduli linea perpendicularis, in qu&agrave; de&shy;


<pb xlink:href="062/01/052.jpg"/>mum mobile ex ill&acirc; agitatione conquie&longs;cit. </s>
            <s id="N11B10">Qu&ograve;d &longs;i <lb/>

ergo &longs;eu corpus graue ad centrum, &longs;eu perpendiculum <lb/>

in &longs;uam &longs;tationem moueatur, non &longs;tatim conquie&longs;cit <lb/>

ex hoc motu &longs;iu&egrave; in centro, &longs;iu&egrave; in line&acirc; perpendiculari, <lb/>

ver&ugrave;m ultra hos limites procurrit &amp; recurrit, <expan abbr="at&qacute;">atque</expan>; e&ograve; ma&shy;<lb/>

gis, qu&ograve; circuli majores. </s>
            <s id="N11B21">Quod quidem in perpendicu&shy;<lb/>

lo experienti&agrave; con&longs;tat: de grauium ver&ograve; &agrave; centro excur<lb/>

&longs;u licet nulla experientia habeatur, id tamen &longs;imilitudo <lb/>

rationis euincit: non enim min&ugrave;s contra natu&shy;<lb/>

ram grauitatis e&longs;&longs;e videtur in circulo &agrave; line&acirc; &longs;tatio&shy;<lb/>

nis, quam in line&acirc; perpendiculari &egrave; centro efferi. </s>
            <s id="N11B2E">Hujus <lb/>

autem ratio h&aelig;c: quia impul&longs;us in quolibet puncto, ac <lb/>

proinde in fine motus e&longs;t major grauitate: per prop: 11. <lb/>

e&longs;t autem agens nece&longs;&longs;arium per prop: 2. &amp; non ni&longs;i per <lb/>

lineam rectam mouet <expan abbr="&longs;u&utilde;">&longs;uum</expan> mobile per prop: 3. &longs;uperabit <lb/>

ergo illam, qu&acirc; in centro firmatur, grauitatem, non mi&shy;<lb/>

n&ugrave;s, quam c&ugrave;m lapidem &longs;imilis impul&longs;us &agrave; centro lon&shy;<lb/>

gi&ugrave;s abducit. </s>
          </p>
        </subchap1>
        <subchap1 id="N11B43">
          <p id="N11B44" type="main">
            <s id="N11B46"><emph type="center"/>Propo&longs;itio XX.<emph.end type="center"/></s>
          </p>
          <p id="N11B4D" type="main">
            <s id="N11B4F"><emph type="italics"/>Velocitas in motu collecta per &aelig;qualia &longs;uo augmento decremen&shy;<lb/>

ta in quietem terminatur.<emph.end type="italics"/></s>
          </p>
          <p id="N11B58" type="main">
            <s id="N11B5A">PErpendiculum liber&egrave; dimi&longs;&longs;um in &longs;uam &longs;tationem <lb/>

recurrit, <expan abbr="at&qacute;">atque</expan>; eodem motu continuato ultra &longs;tatio&shy;


<pb xlink:href="062/01/053.jpg"/>nem excurrit. </s>
            <s id="N11B67">Qu&ograve;d &longs;i ergo impul&longs;us ex illo recur&longs;u <lb/>

collectus aut idem maneat, aut continu&ograve; augeatur, quia <lb/>

per prop: 18. </s>
            <s id="N11B6E">Velocitas in fine eodem vel &aelig;quali tempo&shy;<lb/>

re per &longs;patium mouet duplum velocitatis ex illo motu <lb/>

collect&aelig;, erit ex cur&longs;us major recur&longs;u: &amp; quia ex quoli&shy;<lb/>

bet recur&longs;u magis excurrit, erit motus perpendiculi in&shy;<lb/>

finitus. </s>
            <s id="N11B79">At ver&ograve; hic motus demum conquie&longs;cit: <expan abbr="n&otilde;">non</expan> ergo <lb/>

impul&longs;us augeri, aut idem e&longs;&longs;e pote&longs;t. </s>
            <s id="N11B82">Et quia per ar&shy;<lb/>

cus excurrit &amp; recurrit continu&ograve; minores, nece&longs;&longs;e im&shy;<lb/>

pul&longs;um minui in illo a&longs;cen&longs;u; quia nimirum inter &longs;e <lb/>

mi&longs;centur, &amp; in de&longs;cen&longs;u quidem per eandem lineam <lb/>

mouent grauitas &amp; impul&longs;us, quem &agrave; grauitate conti&shy;<lb/>nuo fluxu na&longs;ci dicebamus: &agrave; &longs;tatione ver&ograve; grauitas im<lb/>

pul&longs;ui reluctatur: quia nimirum contrarius impul&longs;us <lb/>

ab e&acirc;dem grauitate rena&longs;cens tollit partem &longs;ibi &aelig;qua&shy;<lb/>

lem, per po&longs;it: 2. <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; motus reliquus &aelig;qualis exce&longs;&longs;ui <lb/>

majoris ut Prop: 30. dicemus: &longs;icut ergo impul&longs;us conti&shy;<lb/>

nu&ograve; decre&longs;cit ij&longs;dem, quibus augebatur augmentis, ita <lb/>

uelocitas &agrave; &longs;ummo augmento ad finem <expan abbr="u&longs;&qacute;">u&longs;que</expan>; motus con&shy;<lb/>

tinu&ograve; fit minor; &longs;imul ver&ograve; &longs;umpta &aelig;qualis velocitati &agrave; <lb/>

principio motus ad finem <expan abbr="augm&etilde;ti">augmenti</expan> collect&aelig;: ut &longs;i in &longs;ig: 9. <lb/>

<expan abbr="perpendicul&utilde;">perpendiculum</expan> <emph type="italics"/>ae<emph.end type="italics"/> ex <emph type="italics"/>e<emph.end type="italics"/> recurrat in <emph type="italics"/>b,<emph.end type="italics"/> &amp; ex <emph type="italics"/>b<emph.end type="italics"/> excurrat in <emph type="italics"/>&longs;i<emph.end type="italics"/> a&longs;&shy;<lb/>

&longs;umantur autem arcus <emph type="italics"/>bc. bd,<emph.end type="italics"/> &amp; <emph type="italics"/>be.bf<emph.end type="italics"/> inter &longs;e &aelig;quales: <lb/>

dico augmentum velocitatis in <emph type="italics"/>e<emph.end type="italics"/> eju&longs;dem decremento <lb/>

in <emph type="italics"/>f,<emph.end type="italics"/> &amp; augmentum velocitatis in <emph type="italics"/>c<emph.end type="italics"/> eju&longs;dem decremento 


<pb xlink:href="062/01/054.jpg"/>in <emph type="italics"/>d<emph.end type="italics"/> e&longs;&longs;e &aelig;quale. </s>
            <s id="N11BFD">Ducantur enim line&aelig; tangentes <emph type="italics"/>eg fg,<emph.end type="italics"/><lb/>

&amp; <emph type="italics"/>cb. dh:<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; inclinatio <emph type="italics"/>eg<emph.end type="italics"/> inclinationi <emph type="italics"/>fg,<emph.end type="italics"/> &amp; inclina&shy;<lb/>

tio <emph type="italics"/>ch<emph.end type="italics"/> &aelig;qualis inclinationi <emph type="italics"/>dh<emph.end type="italics"/>: propterea qu&ograve;d <expan abbr="&atilde;guli">anguli</expan> <emph type="italics"/>ega.<lb/>

fga,<emph.end type="italics"/> &amp; anguli <emph type="italics"/>cha. dha<emph.end type="italics"/> &longs;unt &aelig;quales, impul&longs;us ergo gra&shy;<lb/>

uitatis in <emph type="italics"/>e<emph.end type="italics"/> eju&longs;dem impul&longs;ui in <emph type="italics"/>f,<emph.end type="italics"/> &amp; impul&longs;us grauitatis <lb/>

in <emph type="italics"/>c<emph.end type="italics"/> eju&longs;dem impul&longs;ui in <emph type="italics"/>d<emph.end type="italics"/> e&longs;t &aelig;qualis, ut con&longs;tat ex <lb/>

prop. 14. </s>
            <s id="N11C5B">Quia ergo impul&longs;us &aelig;quales in <emph type="italics"/>e<emph.end type="italics"/> quidem &amp; <emph type="italics"/>c<emph.end type="italics"/><lb/>

augent, in <emph type="italics"/>f<emph.end type="italics"/> ver&ograve; &amp; <emph type="italics"/>d<emph.end type="italics"/> minuunt velocitatem motus, <expan abbr="er&utilde;t">erunt</expan> <lb/>

&aelig;qualia velocitatis augmenta eju&longs;dem decremento; ac <lb/>

proinde velocitas in motu collecta per &aelig;qualia &longs;uo aug<lb/>

mento decrementa in quietem terminatur. </s>
            <s id="N11C81">Obijcies &longs;i <lb/>

velocitas excur&longs;us &longs;imul &longs;umpta e&longs;t &aelig;qualis velocitati in <lb/>

recur&longs;u collect&aelig;, quia velocitas &aelig;qualis eodem vel &aelig;&shy;<lb/>

quali tempore per &longs;patium mouet &aelig;quale, erunt excur&shy;<lb/>

&longs;us &amp; recur&longs;us inter &longs;e &aelig;quales: ac proinde motus per&shy;<lb/>

pendiculi infinitus. </s>
            <s id="N11C8E">Re&longs;pondent quidam excur&longs;um e&longs;&shy;<lb/>

&longs;e minorem recur&longs;u: propterea qu&oacute;d illius motus &agrave; fu&shy;<lb/>

niculo perturbetur, cujus partes in&aelig;qualiter mouen&shy;<lb/>

tur: veloci&ugrave;s quidem centro propiores, min&ugrave;s autem <lb/>

velociter &agrave; centro remotiores. </s>
            <s id="N11C99">Dum ergo h&aelig; re&longs;titant, <lb/>

&amp; minorum circulorum velocitatem morantur; ill&aelig; <lb/>

pr&aelig;currere fe&longs;tinant: nece&longs;&longs;e ex ill&agrave; luct&acirc; impul&longs;um mi&shy;<lb/>

nui, ut non ni&longs;i ad minus interuallum &longs;e extendat. </s>
            <s id="N11CA2">Hu&shy;<lb/>

jus autem &longs;ignum e&longs;&longs;e illos &longs;inus, in quos funis contor&shy;<lb/>

quetur, &amp; veluti fluctuat. </s>
            <s id="N11CA9">Ver&ugrave;m licet in fune, aut ca-


<pb xlink:href="062/01/055.jpg"/>ten&agrave;, cujus partes ex &longs;e &longs;unt pondero&longs;&aelig;, motus hic undo&shy;<lb/>

&longs;us &longs;ibi ip&longs;i &longs;it impedimento: non tamen h&aelig;c ratio lo&shy;<lb/>

cum habet in perquam &longs;ubtili &amp; tenui&longs;simo filo, cujus <lb/>

partes non ex &longs;e, ver&uacute;m ex impul&longs;u ponderis appen&longs;i <lb/>

<expan abbr="mou&etilde;tur">mouentur</expan>, <expan abbr="eo&qacute;">eoque</expan>; pr&aelig;ci&longs;o aut abrupto &agrave; motu <expan abbr="conquie&longs;c&utilde;t">conquie&longs;cunt</expan>. <lb/>

Deinde &longs;i ratio in&aelig;qualium circulorum perturbat il&shy;<lb/>

lum motum, quo perpendiculum &agrave; &longs;ua &longs;tatione procur<lb/>

rit, turbabit <expan abbr="quo&qacute;">quoque</expan>; rationem motus, quam ad &longs;e habent <lb/>

recur&longs;us: at ver&ograve; h&aelig;c in &aelig;qualitas nihil ob&longs;tat, qu&ograve; mi&shy;<lb/>

n&ugrave;s recur&longs;us inter &longs;e &longs;int &aelig;quales: nihil ergo ob&longs;tabit, <lb/>

qu&ograve; min&ugrave;s excur&longs;us <expan abbr="quo&qacute;">quoque</expan>; inter &longs;e &longs;int &aelig;quales. </s>
            <s id="N11CD8">Pr&aelig;te&shy;<lb/>

rea &longs;i funiculo <expan abbr="p&otilde;dus">pondus</expan> accedat medio inter <expan abbr="hypemochli&utilde;">hypomochlium</expan> <lb/>

loco, motum accelerabit; non igitur ex &longs;e motum aut <lb/>

pondus habet: propterea qu&ograve;d negant maius pondus <lb/>

velocitatem augere. </s>
            <s id="N11CEB">At ver&ograve; &longs;i pars illa fili, qu&aelig; ob pon<lb/>

dus acce&longs;&longs;orium veloci&ugrave;s mouetur, &longs;uo <expan abbr="quo&qacute;">quoque</expan>; pondere <lb/>

mouebatur, fiet &longs;an&egrave;, ut continu&agrave; hac ponderis noui ac&shy;<lb/>

ce&longs;sione velocitas in infinitum augeatur. </s>
            <s id="N11CF8">Dicendum <lb/>

erg&ograve; excur&longs;um perpendiculi continu&ograve; quidem mino&shy;<lb/>

rem fieri recur&longs;u; cau&longs;am ver&ograve; hujus in&aelig;qualitatis non <lb/>

in funiculo, &longs;ed in natur&agrave; circuli, in quo perpendiculum <lb/>

mouetur, &longs;itam e&longs;&longs;e. </s>
            <s id="N11D03">Quia enim velocitas motus conti&shy;<lb/>

nuo fluxu augetur &agrave; grauitate, qu&aelig; ex inclinatione ma&shy;<lb/>

iori ob maiorem <expan abbr="viol&etilde;ti&atilde;">violentiam</expan> hypomochlii min&ugrave;s grauitat, <lb/>

impul&longs;us, quo perpendiculum recurrit, continu&oacute; qui-


<pb xlink:href="062/01/056.jpg"/>dem maiora &longs;umit incrementa: quia tamen in quolibet <lb/>

puncto circuli per lineas fit tangentes, qu&aelig; in recur&longs;u <lb/>

continu&oacute; magis ac magis &longs;unt inclinat&aelig;; erunt in quo&shy;<lb/>

libet puncto recur&longs;us minora huius velocitatis incre&shy;<lb/>

menta: ita nimirum ut &longs;i arcus &longs;umantur &aelig;quales, ma&shy;<lb/>

jor &longs;it acce&longs;sio velocitatis in arcu primo, quam in arcu <lb/>

&longs;ecundo: &amp; velocitas in arcu circuli collecta minor ve&shy;<lb/>

locitate in line&agrave; rect&agrave; illi arcui &aelig;quali, qu&aelig; tangens &longs;it <lb/>

principii eiu&longs;dem motus circularis. </s>
            <s id="N11D24">Sicuti ver&ograve; in re&shy;<lb/>

cur&longs;u velocitas continu&oacute; &amp; in&aelig;qualiter cre&longs;cit, ita in <lb/>

excur&longs;u, quia motus violentus, proportionaliter decre&shy;<lb/>

&longs;cit, <expan abbr="fiunt&qacute;">fiuntque</expan>; huius decrementa &aelig;qualia illius incremen&shy;<lb/>

tis, prima nimirum ultimis; propterea qu&oacute;d <expan abbr="utra&qacute;">utraque</expan>; <expan abbr="fi&utilde;t">fiunt</expan> <lb/>

ab eadem grauitate, qu&aelig; &agrave; principio excur&longs;us per lineas <lb/>

grauitat magis inclinatas. </s>
            <s id="N11D3F">Qu&ograve;d &longs;i ergo &longs;ola grauitas <lb/>

minuat impul&longs;um, quia in &aelig;qualibus &agrave; &longs;tatione interual<lb/>

lis, ob &longs;imilem inclinationem, &aelig;qualiter grauitat; erunt <lb/>

ut arcus inter &longs;e, ita eiu&longs;dem grauitatis impul&longs;us: &amp; <lb/>

quia impul&longs;us contrarius tollit partem &longs;ibi &aelig;qualem, <lb/>

erunt excur&longs;us &amp; recur&longs;us inter &longs;e &aelig;quales. </s>
            <s id="N11D4C">At ver&ograve; <lb/>

quia non &longs;ola grauitas impul&longs;um minuit, &longs;ed etiam in&shy;<lb/>

clinatio motus; &longs;icuti enim grauitas extra lineam per&shy;<lb/>

pendicularem min&ugrave;s grauitat, ita impul&longs;us extra line&shy;<lb/>

am &longs;ui motus, cuius terminus e&longs;t veluti centrum, mi <lb/>

n&uacute;s impellit &longs;uum mobile: qu&oacute;d &longs;i enim funda lapidem 


<pb xlink:href="062/01/057.jpg"/>excutiat, ad majus feretur interuallum, quam ut &aelig;quale <lb/>

&longs;it illis rotationibus &longs;imul &longs;umptis, in quas idem lapis <lb/>

fund&aelig; alligatus reuoluitur. </s>
            <s id="N11D61">Quia ergo in illa gyratione <lb/>

perpendiculi inclinatio motus continu&ograve; &amp; &aelig;qualiter <lb/>

mutatur, velocitas in excur&longs;u collecta e&ograve; min&ugrave;s moue&shy;<lb/>

bit, qu&oacute; major portio ex ill&acirc; inclinatione eidem dece&shy;<lb/>

dit. </s>
            <s id="N11D6C">Impul&longs;us ergo &aelig;qualis quia magis decre&longs;cit in ex&shy;<lb/>

cur&longs;u, quam idem augeatur in recur&longs;u, ad minus moue&shy;<lb/>

bit interuallum: ac proinde excur&longs;us perpendiculi eju&longs;&shy;<lb/>

dem recur&longs;ibus erunt minores. </s>
          </p>
        </subchap1>
        <subchap1 id="N11D75">
          <p id="N11D76" type="main">
            <s id="N11D78"><emph type="center"/>Propo&longs;itio XXI.<emph.end type="center"/></s>
          </p>
          <p id="N11D7F" type="main">
            <s id="N11D81"><emph type="italics"/>Excur&longs;us grauium &agrave; termino motus in circulum terminatur, cu&shy;<lb/>

jus &longs;emidiameter e&longs;t di&longs;tanti&agrave; inter principium motus &amp; mundi <lb/>

centrum.<emph.end type="italics"/></s>
          </p>
          <p id="N11D8C" type="main">
            <s id="N11D8E">ATermino motus <emph type="italics"/>a.i.h.g.f.e<emph.end type="italics"/> in line&agrave; perpendiculari, &amp; <lb/>

lineis ad horizontem inclinatis producantur line&aelig; <lb/>

excur&longs;ui &aelig;quales lineis decur&longs;us, nimirum <emph type="italics"/>ap<emph.end type="italics"/> ip&longs;i <emph type="italics"/>ab, io<emph.end type="italics"/><lb/> ver&ograve; ip&longs;i <emph type="italics"/>ib<emph.end type="italics"/> &aelig;qualis, dico puncta <emph type="italics"/>po<emph.end type="italics"/> e&longs;&longs;e in peripheria cir&shy;<lb/>

culi, cujus &longs;emidiameter <emph type="italics"/>ab<emph.end type="italics"/> di&longs;tantia inter principium <lb/>

motus &amp; mundi centrum. </s>
            <s id="N11DBE">Ducatur enim linea <emph type="italics"/>ao:<emph.end type="italics"/> quia <lb/>

ergo line&aelig; <emph type="italics"/>bi. io<emph.end type="italics"/> inter &longs;e &longs;unt &aelig;quales, &amp; anguli <emph type="italics"/>bia. oia<emph.end type="italics"/><lb/> recti, erit angulus <emph type="italics"/>abi<emph.end type="italics"/> angulo <emph type="italics"/>aoi,<emph.end type="italics"/> &amp; latus <emph type="italics"/>ab<emph.end type="italics"/> lateri <emph type="italics"/>ao<emph.end type="italics"/><lb/>

&aelig;quale: e&longs;t autem linea <emph type="italics"/>ap<emph.end type="italics"/> &aelig;qualis eidem <emph type="italics"/>ab,<emph.end type="italics"/> puncta er&shy;


<pb xlink:href="062/01/058.jpg"/>go <emph type="italics"/>po<emph.end type="italics"/> &longs;unt in peripheri&agrave; circuli, cujus centrum <emph type="italics"/>a,<emph.end type="italics"/> &agrave; quo <lb/>

&aelig;qualiter ab&longs;i&longs;tunt ill&aelig; line&aelig;. </s>
            <s id="N11E0D">Simili modo o&longs;tende&shy;<lb/>

mus puncta <emph type="italics"/>n.m.l<emph.end type="italics"/> e&longs;&longs;e in peripheri&aacute; eju&longs;dem circuli, pro&shy;<lb/>


<figure id="id.062.01.058.1.jpg" xlink:href="062/01/058/1.jpg"/><lb/>

pterea qu&oacute;d line&aelig; <emph type="italics"/>an. am. al,<emph.end type="italics"/> ba&longs;es nimirum &aelig;qualium <lb/>

triangulorum, &longs;unt &aelig;quales line&aelig; <emph type="italics"/>ab.<emph.end type="italics"/> Excur&longs;us ergo <lb/>

grauium &agrave; termino motus in <expan abbr="circul&utilde;">circulum</expan> terminantur &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N11E35">
          <p id="N11E36" type="main">
            <s id="N11E38"><emph type="center"/>Propo&longs;itio XII.<emph.end type="center"/></s>
          </p>
          <p id="N11E3F" type="main">
            <s id="N11E41"><emph type="italics"/>Motus per arcus eju&longs;dem circuli rationem habet, quam &longs;inus an<lb/>

guli dupli illorum angulorum, qui complementa &longs;unt inclinationis <lb/>

cordarum.<emph.end type="italics"/></s>
          </p>
          <p id="N11E4C" type="main">
            <s id="N11E4E">AS&longs;umantur arcus <emph type="italics"/>bdi. bdc,<emph.end type="italics"/> &amp; <expan abbr="duc&atilde;tur">ducantur</expan> cord&aelig; <emph type="italics"/>bi. bc,<emph.end type="italics"/><lb/>

<expan abbr="erunt&qacute;">eruntque</expan>; anguli <emph type="italics"/>abi. abc<emph.end type="italics"/> anguli inclinationis corda-


<pb xlink:href="062/01/059.jpg"/>rum <emph type="italics"/>bi. bc,<emph.end type="italics"/> &amp; horum complementa <emph type="italics"/>bai. bac,<emph.end type="italics"/> propterea <lb/>

qu&oacute;d anguli <emph type="italics"/>aib. acb<emph.end type="italics"/> in &longs;emicirculo &longs;unt recti. </s>
            <s id="N11E84">Tan&shy;<lb/>

gant ergo circulum in punctis <emph type="italics"/>ic<emph.end type="italics"/> line&aelig; <emph type="italics"/>ib. cg:<emph.end type="italics"/> &amp; ex cen&shy;<lb/>

tro <emph type="italics"/>k<emph.end type="italics"/> educantur line&aelig; <emph type="italics"/>ki. kc<emph.end type="italics"/> perpendiculares ad <emph type="italics"/>ih.cg.<emph.end type="italics"/><lb/>

quia ergo anguli <emph type="italics"/>khi. kge<emph.end type="italics"/> &longs;unt anguli inclinationum, e&shy;<lb/>


<figure id="id.062.01.059.1.jpg" xlink:href="062/01/059/1.jpg"/><lb/>

runt anguli <emph type="italics"/>bki. gkc<emph.end type="italics"/> illorum complementa : angulo&shy;<lb/>

rum ver&ograve; <emph type="italics"/>bai. bac<emph.end type="italics"/> ad peripheriam dupli: dico velocita&shy;<lb/>

tem motus in <emph type="italics"/>i<emph.end type="italics"/> ad velocitatem motus in <emph type="italics"/>c<emph.end type="italics"/> e&longs;&longs;e ut &longs;inum <lb/>

anguli <emph type="italics"/>bki<emph.end type="italics"/> &longs;inum anguli <emph type="italics"/>bkc<emph.end type="italics"/> Quia enim motus in <lb/>

quolibet puncto circuli per lineam fit tangentem per 


<pb xlink:href="062/01/060.jpg"/>prop: 4. erit ratio velocitatis in <emph type="italics"/>i<emph.end type="italics"/> &amp; <emph type="italics"/>c<emph.end type="italics"/> qu&aelig; velocitas e&longs;t <lb/>

tangentium <emph type="italics"/>ih. cg<emph.end type="italics"/>: e&longs;t autem velocitas in <emph type="italics"/>ih<emph.end type="italics"/> ad veloci&shy;<lb/>

tatem in <emph type="italics"/>cg<emph.end type="italics"/> ut &longs;inus <emph type="italics"/>bl<emph.end type="italics"/> anguli <emph type="italics"/>bki<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>bm<emph.end type="italics"/> anguli <lb/>

<emph type="italics"/>bkc<emph.end type="italics"/> per prop: 14. velocitas ergo in arcu <emph type="italics"/>ib<emph.end type="italics"/> ad velocita&shy;<lb/>

tem in arcu <emph type="italics"/>cb<emph.end type="italics"/> ut &longs;inus anguli <emph type="italics"/>bki<emph.end type="italics"/> ad &longs;inum anguli <emph type="italics"/>bkc,<emph.end type="italics"/><lb/>

&longs;inus nimirum anguli dupli illorum angulorum, qui <lb/>

complementa &longs;unt inclinationis cordarum <emph type="italics"/>bi.bc,<emph.end type="italics"/> quod <lb/>

erat o&longs;tendendum. </s>
          </p>
        </subchap1>
        <subchap1 id="N11F4A">
          <p id="N11F4B" type="main">
            <s id="N11F4D"><emph type="center"/>Propo&longs;itio XXIII.<emph.end type="center"/></s>
          </p>
          <p id="N11F54" type="main">
            <s id="N11F56"><emph type="italics"/>Perpendiculum per arcus &aelig;quales eju&longs;dem circuli in&aelig;quali <lb/>

tempore mouetur: majori quidem prop&egrave; &longs;tationem, minori ver&ograve; per <lb/>

arcus, qui magis ab&longs;unt &agrave; &longs;tatione.<emph.end type="italics"/></s>
          </p>
          <p id="N11F61" type="main">
            <s id="N11F63">SInt duo arcus <emph type="italics"/>bd.d&longs;<emph.end type="italics"/> inter &longs;e &aelig;quales: <expan abbr="at&qacute;">atque</expan> <emph type="italics"/>bd<emph.end type="italics"/> propior, <lb/>

<emph type="italics"/>df<emph.end type="italics"/> ver&ograve; remotior &agrave; &longs;tatione <emph type="italics"/>b,<emph.end type="italics"/> dico motum in <emph type="italics"/>df<emph.end type="italics"/> e&longs;&longs;e <lb/>

velociorem motu in <emph type="italics"/>db.<emph.end type="italics"/> Quia enim motus per arcus e&shy;<lb/>

ju&longs;dem circuli rationem habent, quam &longs;inus, per prop. <lb/>

22. e&longs;t autem &longs;inus <emph type="italics"/>bg<emph.end type="italics"/> major &longs;inu <emph type="italics"/>bt,<emph.end type="italics"/> erit velocior motus <lb/>

in <emph type="italics"/>f<emph.end type="italics"/> quam in d: &amp; quia arcus <emph type="italics"/>bd.df<emph.end type="italics"/> &longs;unt &aelig;quales, minori <lb/>

tempore mouebitur in arcu <emph type="italics"/>df<emph.end type="italics"/> remotiore, quam in ar&shy;<lb/>

cu <emph type="italics"/>bd<emph.end type="italics"/> &longs;tationi propiore per prop. 6. </s>
            <s id="N11FC0">Dices velocitas mo&shy;<lb/>

tus ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>d<emph.end type="italics"/> augetur in&aelig;qualiter, <expan abbr="fiunt&qacute;">fiuntque</expan>; ad &longs;ingula pun&shy;<lb/>

cta minora incrementa; mutat&agrave; ergo velocitate non ea-


<pb xlink:href="062/01/061.jpg"/>dem erit ratio motus. </s>
            <s id="N11FDB">Re&longs;pondeo velocitatem ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>d<emph.end type="italics"/><lb/> in&aelig;qualiter quidem augeri, &amp; continu&oacute; minora fieri in&shy;<lb/>

crementa, per prop: 20. at ver&ograve; velocitatem ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>d<emph.end type="italics"/> col&shy;<lb/>


<figure id="id.062.01.061.1.jpg" xlink:href="062/01/061/1.jpg"/><lb/>

lectam e&longs;&longs;e majorem velocitate ex <emph type="italics"/>d<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> collect&agrave;. </s>
            <s id="N1200E">Quia <lb/>

enim velocitatis ex <emph type="italics"/>d<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> continu&ograve; <expan abbr="quo&qacute;">quoque</expan>; minora fiunt <lb/>

incrementa; velocitas inde collecta erit minor veloci<lb/>

tate ab &aelig;qualibus ip&longs;i <emph type="italics"/>d<emph.end type="italics"/> incrementis collect&aacute;: at ver&ograve; <lb/>

velocitas in <emph type="italics"/>f<emph.end type="italics"/> majora ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>d<emph.end type="italics"/> &longs;umit incrementa, quam <lb/>

ut &aelig;qualia &longs;int velocitati in <emph type="italics"/>d:<emph.end type="italics"/> velocitas ergo ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>d<emph.end type="italics"/> col&shy;<lb/>

lecta e&longs;t mult&oacute; major velocitate ex <emph type="italics"/>d<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> collecta, ac pro <lb/>

inde minori tempore illos arcus perambulat &aelig;quales. </s>
          </p>
          <pb xlink:href="062/01/062.jpg"/>
          <p id="N12068" type="main">
            <s id="N1206A"><emph type="center"/><emph type="italics"/>Lemma I.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N12075" type="main">
            <s id="N12077"><emph type="italics"/>Si a&longs;&longs;umantur arcus in ratione continu&agrave;, quam habent &longs;inus <lb/>

intercipientes illos arcus, major erit proportio inter arcus po&longs;terio&shy;<lb/>

res, quam inter arcus priores.<emph.end type="italics"/></s>
          </p>
          <p id="N12082" type="main">
            <s id="N12084">Sit arcus <emph type="italics"/>bd,<emph.end type="italics"/> &longs;inu <emph type="italics"/>ab<emph.end type="italics"/> &amp; <emph type="italics"/>cd<emph.end type="italics"/> interceptus, in eadem ratio&shy;<lb/>

ne ad arcum <emph type="italics"/>df<emph.end type="italics"/> &longs;inu <emph type="italics"/>cd<emph.end type="italics"/> &amp; <emph type="italics"/>ef<emph.end type="italics"/> interceptum, in qu&agrave; &longs;i&shy;<lb/>nus <emph type="italics"/>ab<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>cd:<emph.end type="italics"/> &amp; rur&longs;um arcus <emph type="italics"/>df<emph.end type="italics"/> &agrave;d arcum <emph type="italics"/>fh,<emph.end type="italics"/> ut <lb/>

&longs;inus <emph type="italics"/>cd<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>ef<emph.end type="italics"/>; dico proportionem tam inter &longs;i&shy;<lb/>

nus, quam inter arcus illis &longs;inubus interceptos conti&shy;<lb/>

nu&ograve; fieri majores, nimirum proportionem &longs;inus <emph type="italics"/>cd<emph.end type="italics"/> ad <lb/>

&longs;inum <emph type="italics"/>ef,<emph.end type="italics"/> &amp; arcus <emph type="italics"/>df<emph.end type="italics"/> ad arcum <emph type="italics"/>fh<emph.end type="italics"/> e&longs;&longs;e majorem, quam <lb/>

&longs;inus <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>cd,<emph.end type="italics"/> aut arcus <emph type="italics"/>bd<emph.end type="italics"/> ad <emph type="italics"/>df.<emph.end type="italics"/> A&longs;&longs;umatur enim ar&shy;<lb/>

cus <emph type="italics"/>bd<emph.end type="italics"/> grad: 9. <expan abbr="erit&qacute;">eritque</expan>; <emph type="italics"/>ab<emph.end type="italics"/> 100000. &longs;inus totus, <emph type="italics"/>cd<emph.end type="italics"/> autem <lb/>

<emph type="italics"/>98769.<emph.end type="italics"/> &longs;inus grad. <emph type="italics"/>81.<emph.end type="italics"/> qu&ograve;d &longs;i ergo fiat ut <emph type="italics"/>ab<emph.end type="italics"/> &longs;inus totus ad <lb/>

9, ita &longs;inus grad. <emph type="italics"/>81.<emph.end type="italics"/> ad aliud, prodibit arcus 8 in dat&acirc; ra&shy;<lb/>

tione, quam habet &longs;inus <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>cd,<emph.end type="italics"/> &longs;i minutias omittamus. <lb/>

Simili modo &longs;i fiat ut &longs;inus <emph type="italics"/>cd<emph.end type="italics"/> grad: <emph type="italics"/>81<emph.end type="italics"/> ad arcum <emph type="italics"/>df<emph.end type="italics"/> grad. <lb/>

8, ita &longs;inus <emph type="italics"/>ef<emph.end type="italics"/> grad.73 ad aliud, prodibit arcus <emph type="italics"/>fh<emph.end type="italics"/> grad. 7. <lb/>

<expan abbr="at&qacute;">atque</expan>; ita con&longs;equenter inuenientur arcus reliqui, quos di<lb/>

co majorem rationem habere ad arcus proxim&egrave; &longs;equen&shy;<lb/>

tes, quam ad hos habeant arcus proxim&egrave; antecedentes. <lb/>

E&longs;t enim major proportio grad. 8 ad 7, quam grad. 9 ad <lb/>

8: &amp; grad. 4 ad 3, quam grad. 5 ad 4. <expan abbr="at&qacute;">atque</expan>, eadem e&longs;t ratio 


<pb xlink:href="062/01/063.jpg"/>in arcubus reliquis. </s>
            <s id="N12187">Si ergo a&longs;&longs;umantur arcus in ratio&shy;<lb/>

ne continu&acirc;, quam habent &longs;inus intercipientes illos ar&shy;<lb/>


<figure id="id.062.01.063.1.jpg" xlink:href="062/01/063/1.jpg"/><lb/>

cus, major e&longs;t proportio inter arcus po&longs;teriores, quam <lb/>

inter arcus priores. </s>
          </p>
          <p id="N12197" type="main">
            <s id="N12199"><emph type="center"/><emph type="italics"/>Lemma II.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N121A4" type="main">
            <s id="N121A6"><emph type="italics"/>Si quadrans circuli diuidatur in quot libet arcus &aelig;quales, mino&shy;<lb/>

res ver&ograve; quam in ratione &longs;ubtripl&aacute; ad &longs;inum totum, habebunt &longs;inus <lb/>

proximi intercipientes illos arcus minorem rationem quam duplam.<emph.end type="italics"/></s>
          </p>
          <p id="N121B1" type="main">
            <s id="N121B3">IN fig: 6. </s>
            <s id="N121B6">Diuidatur quadrans circuli bifariam in <emph type="italics"/>h<emph.end type="italics"/> in <lb/>

arcum <emph type="italics"/>bh<emph.end type="italics"/> gra: 60, &amp; arcum <emph type="italics"/>ho<emph.end type="italics"/> grad: 30, <expan abbr="erit&qacute;">eritque</expan>, arcus <emph type="italics"/>bh<emph.end type="italics"/><lb/>

maior &longs;inu toto: propterea qu&ograve;d quadrans majo&shy;<lb/>

rem ad hunc, quam ad arcum grad. 60 habeat <expan abbr="ration&etilde;">rationem</expan>. <lb/>

Qu&ograve;d &longs;i ergo arcus <emph type="italics"/>bh<emph.end type="italics"/> &longs;ubdiuidatur in alios tres arcus 


<pb xlink:href="062/01/064.jpg"/><emph type="italics"/>bd. df.fh<emph.end type="italics"/> inter &longs;e &aelig;quales, minor erit proportio &longs;inus <emph type="italics"/>ab<emph.end type="italics"/><lb/>

ad arcum <emph type="italics"/>bd<emph.end type="italics"/> quam tripla, habebit ergo ad arcum mino&shy;<lb/>

rem, quam &longs;it <emph type="italics"/>bd,<emph.end type="italics"/> rationem triplam, qui &longs;it <emph type="italics"/>bq,<emph.end type="italics"/> <expan abbr="at&qacute;">atque</expan>; hunc <lb/>

intercipiens &longs;inus <emph type="italics"/>pq<emph.end type="italics"/> maior &longs;inu <emph type="italics"/>cd:<emph.end type="italics"/> dico &longs;inus proximos <lb/>

intercipientes illos arcus, nimirum <emph type="italics"/>ab<emph.end type="italics"/> &amp; <emph type="italics"/>cd,<emph.end type="italics"/> aut <emph type="italics"/>cd<emph.end type="italics"/> &amp; <emph type="italics"/>ef.<emph.end type="italics"/><lb/>

aut <emph type="italics"/>ef<emph.end type="italics"/> &amp; <emph type="italics"/>gh<emph.end type="italics"/> minorem rationem habere quam duplam. <lb/>

Erit enim &longs;inus <emph type="italics"/>cd.<emph.end type="italics"/> grad: 70, &amp; &longs;inus <emph type="italics"/>ef<emph.end type="italics"/> grad: 50. &amp; &longs;inus <emph type="italics"/>gh<emph.end type="italics"/><lb/>

gtad: 30. at ver&ograve; &longs;inus totus <emph type="italics"/>ab<emph.end type="italics"/> 100000. ad &longs;inum <emph type="italics"/>cd<emph.end type="italics"/> grad. <lb/>

70, nimirum ad 93969, &amp; &longs;inus <emph type="italics"/>ef<emph.end type="italics"/> grad: 50 ad &longs;inum <emph type="italics"/>gh<emph.end type="italics"/><lb/>

grad. 30 ide&longs;t. 76604. ad 50000 minorem habet <expan abbr="ration&etilde;">rationem</expan> <lb/>

quam duplam. </s>
            <s id="N12279">Quod idem de aliis &longs;inubus proxim&egrave; in&shy;<lb/>

tercipientibus illos arcus &aelig;quales, ex tabulis &longs;inuum <lb/>

con&longs;tabit. </s>
            <s id="N12280">Quia ver&ograve; &longs;inus propiores minorem ha&shy;<lb/>

bent rationem, erit minor proportio <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>pq<emph.end type="italics"/> quam ad <lb/>

<emph type="italics"/>cd.<emph.end type="italics"/> ac proinde minor quam dupla. </s>
            <s id="N12299">Si ergo quadrans cir&shy;<lb/>

culi diuidatur in quotlibet arcus &aelig;quales, minores ver&ograve; <lb/>

quam in ratione &longs;ubtripl&aacute; ad &longs;inum totum, habebunt &longs;i&shy;<lb/>

nus proximi intercipientes illos arcus minorem ratio&shy;<lb/>

nem quam duplam. </s>
          </p>
          <p id="N122A4" type="main">
            <s id="N122A6"><emph type="center"/><emph type="italics"/>Lemma III.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N122B1" type="main">
            <s id="N122B3"><emph type="italics"/>Si a&longs;&longs;umantur arcus in ratione continu&aacute;, quam habent &longs;inus <lb/>

intercipientes illos arcus, <expan abbr="habeat&qacute;">habeatque</expan>; &longs;inus primus ad arcum interce&shy;<lb/>

ptum majorem rationem quam triplam, habebunt &longs;inus proximi ra<lb/>

tionem ad &longs;e minorem quam duplam.<emph.end type="italics"/></s>
          </p>
          <pb xlink:href="062/01/065.jpg"/>
          <p id="N122C7" type="main">
            <s id="N122C9">VT &longs;i arcus <emph type="italics"/>bd<emph.end type="italics"/> ad arcum <emph type="italics"/>df<emph.end type="italics"/> &longs;it ut &longs;inus <emph type="italics"/>ab<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>cd:<emph.end type="italics"/><lb/>

&amp; rur&longs;um ut &longs;inus <emph type="italics"/>cd<emph.end type="italics"/> ad <emph type="italics"/>ef,<emph.end type="italics"/> ita arcus <emph type="italics"/>df<emph.end type="italics"/> ad <emph type="italics"/>fh,<emph.end type="italics"/> habeat <lb/>

ver&ograve; &longs;inus <emph type="italics"/>ab<emph.end type="italics"/> ad arcum <emph type="italics"/>bd<emph.end type="italics"/> majorem rationem quam tri<lb/>

plam, dico &longs;inus intercipientes illos arcus rationem ad <lb/>

&longs;e habere minorem quam duplam. </s>
            <s id="N1230F">Quia enim &longs;inus <emph type="italics"/>ab<emph.end type="italics"/><lb/>


<figure id="id.062.01.065.1.jpg" xlink:href="062/01/065/1.jpg"/><lb/>&gt;

e&longs;t major &longs;inu <emph type="italics"/>cd<emph.end type="italics"/> erit <expan abbr="quo&qacute;">quoque</expan>; arcus <emph type="italics"/>bd<emph.end type="italics"/> major arcu <emph type="italics"/>df<emph.end type="italics"/>: fiat <lb/>

ergo arcus <emph type="italics"/>bd<emph.end type="italics"/> &aelig;qualis arcui <emph type="italics"/>ds,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; &longs;inus <emph type="italics"/>rs<emph.end type="italics"/> minor &longs;inu <lb/>

<emph type="italics"/>cd<emph.end type="italics"/>: e&longs;t autem per Lemma 2. minor proportio eju&longs;dem <lb/>

&longs;inus <emph type="italics"/>cd<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>rs<emph.end type="italics"/> quam dupla; mult&ograve; ergo minor ad <lb/>

&longs;inum majorem <emph type="italics"/>ef<emph.end type="italics"/> quam dupla. </s>
            <s id="N1236C">Quod idem de aliis &longs;i&shy;<lb/>

nubus o&longs;tendemus. </s>
            <s id="N12371">Si ergo a&longs;&longs;umantur arcus in ratio&shy;<lb/>

ne continu&agrave; &amp;c. </s>
          </p>
          <p id="N12376" type="main">
            <s id="N12378"><emph type="center"/><emph type="italics"/>Lemma IV.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N12383" type="main">
            <s id="N12385"><emph type="italics"/>Si a&longs;&longs;umantur arcus in ratione continu&agrave;, quam habent &longs;inus in<emph.end type="italics"/>


<pb xlink:href="062/01/066.jpg"/><emph type="italics"/>tercipientes illos arcus, <expan abbr="habeat&qacute;">habeatque</expan>; &longs;inus primus ad arcum interce&shy;<lb/>

ptum majorem rationem quam triplam, erit &longs;inus &longs;ecundus major <lb/>

illo arcu intercepto.<emph.end type="italics"/></s>
          </p>
          <p id="N1239D" type="main">
            <s id="N1239F">QVia enim ut &longs;inus ita arcus intercepti; habent <expan abbr="aut&etilde;">autem</expan> <lb/>

&longs;inus proximi rationem ad &longs;e minorem quam du&shy;<lb/>

plam, per Lemma 3; habebunt <expan abbr="quo&qacute;">quoque</expan>; arcus minorem <lb/>

rationem quam duplam. </s>
            <s id="N123B0">Et quia ut &longs;inus ad &longs;inum, ita <lb/>

arcus ad arcum, erit permutando ut &longs;inus primus ad ar&shy;<lb/>

cum primum, ita &longs;inus &longs;ecundus ad arcum &longs;ecundum: <lb/>

habet autem &longs;inus primus ad arcum primum majorem <lb/>

rationem quam triplam, habebit <expan abbr="quo&qacute;">quoque</expan>; &longs;inus &longs;ecundus <lb/>

ad arcum &longs;ecundum majorem rationem quam triplam. <lb/>

Quia ergo ad eundem arcum &longs;ecundum majorem rati&shy;<lb/>

onem habet &longs;inus &longs;ecundus, quam arcus primus, erit &longs;i&shy;<lb/>

nus &longs;ecundus major quam arcus primus, hoc e&longs;t quam <lb/>

arcus interceptus. </s>
          </p>
        </subchap1>
        <subchap1 id="N123C9">
          <p id="N123CA" type="main">
            <s id="N123CC"><emph type="center"/>Propo&longs;itio XXIV.<emph.end type="center"/></s>
          </p>
          <p id="N123D3" type="main">
            <s id="N123D5"><emph type="italics"/>Perpendiculum ex quolibet puncto eju&longs;dem circuli &aelig;quali tem&shy;<lb/>

pore recurrit in &longs;uam &longs;tationem.<emph.end type="italics"/></s>
          </p>
          <p id="N123DE" type="main">
            <s id="N123E0">IN circulo <emph type="italics"/>tuxb<emph.end type="italics"/> &longs;int duo perpendicula <emph type="italics"/>ab. ad<emph.end type="italics"/> extra &longs;u<lb/>

am &longs;tationem <emph type="italics"/>at,<emph.end type="italics"/> <expan abbr="habeat&qacute;">habeatque</expan>; &longs;inus totus <emph type="italics"/>ab<emph.end type="italics"/> ad interual&shy;<lb/>

lum <emph type="italics"/>bd<emph.end type="italics"/> majorem rationem quam tripl&aacute;, dico <expan abbr="utrum&qacute;">utrumque</expan>; 


<pb xlink:href="062/01/067.jpg"/><expan abbr="cod&etilde;">codem</expan> tempore recurrere in <emph type="italics"/>t.<emph.end type="italics"/> Erit enim velocitas in <emph type="italics"/>b<emph.end type="italics"/> ad <lb/>

velocitatem in <emph type="italics"/>d,<emph.end type="italics"/> ut &longs;inus <emph type="italics"/>ab<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>cd<emph.end type="italics"/> per prop: 22. <lb/>

qu&ograve;d &longs;i ergo in illo recur&longs;u eadem ratio velocitatis con&shy;<lb/>

&longs;taret, aut &longs;imilibus augeretur incrementis, quia major <lb/>

proportio arcus <emph type="italics"/>bt<emph.end type="italics"/> ad arcum <emph type="italics"/>dt,<emph.end type="italics"/> quam &longs;inus <emph type="italics"/>ab<emph.end type="italics"/> ad &longs;inum <lb/>

<emph type="italics"/>cd,<emph.end type="italics"/> quo quidem tempore perpendiculum <emph type="italics"/>ab<emph.end type="italics"/> recurrit <lb/>

in <emph type="italics"/>t,<emph.end type="italics"/> eodem perpendiculum <emph type="italics"/>cd<emph.end type="italics"/> procurreret extra <emph type="italics"/>t,<emph.end type="italics"/> tanto <lb/>

interuallo, quantus e&longs;t exce&longs;&longs;us hujus proportioni<emph type="italics"/>s.<emph.end type="italics"/> At <lb/>

ver&ograve; quia ad &longs;ingula puncta mutat&agrave; &longs;inuum ratione, <lb/>

mutatur <expan abbr="quo&qacute;">quoque</expan>; ratio velocitatis: major enim proportio <lb/>

<emph type="italics"/>cd<emph.end type="italics"/> ad <emph type="italics"/>ef,<emph.end type="italics"/> quam <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>cd<emph.end type="italics"/> per lem: 1. erit <expan abbr="quo&qacute;">quoque</expan>; major pro&shy;<lb/>

portio arcus <emph type="italics"/>df<emph.end type="italics"/> ad <emph type="italics"/>fh,<emph.end type="italics"/> quam arcus <emph type="italics"/>bd<emph.end type="italics"/> ad <emph type="italics"/>df.<emph.end type="italics"/> quia ergo <lb/>

cum hoc &longs;inuum &amp; arcuum decremento continu&oacute; au&shy;<lb/>

getur illorum proportio, minuitur ver&ograve; di&longs;tantia ter&shy;<lb/>

minorum motus, nece&longs;&longs;e demum ab&longs;umi &amp; deficere, <expan abbr="il-lo&qacute;">il&shy;<lb/>

loque</expan>; deficiente <expan abbr="mot&utilde;">motum</expan> co&aelig;quari: quod non ni&longs;i in pun&shy;<lb/>

cto <emph type="italics"/>t<emph.end type="italics"/> dico po&longs;&longs;e fieri. </s>
            <s id="N124CE">Concurrat enim, &longs;i fieri pote&longs;t, <lb/>

<expan abbr="utrum&qacute;">utrumque</expan>; perpendiculum in <emph type="italics"/>q<emph.end type="italics"/> minori, quam <emph type="italics"/>t,<emph.end type="italics"/> interuallo: <lb/>

&amp; quia non ante <emph type="italics"/>q<emph.end type="italics"/> fit concur&longs;us, &longs;i perpendiculum <emph type="italics"/>ab<emph.end type="italics"/><lb/>

&longs;tatuatur in <emph type="italics"/>m<emph.end type="italics"/>; erit perpendiculum <emph type="italics"/>ad<emph.end type="italics"/> inter <emph type="italics"/>m<emph.end type="italics"/> &amp; <emph type="italics"/>q<emph.end type="italics"/>: &longs;it er&shy;<lb/>

go in <emph type="italics"/>o.<emph.end type="italics"/> quia ver&ograve; ut <emph type="italics"/>lm<emph.end type="italics"/> ad <emph type="italics"/>no,<emph.end type="italics"/> ita velocitas motus in <emph type="italics"/>m<emph.end type="italics"/><lb/>

ad velocitatem motus in <emph type="italics"/>o<emph.end type="italics"/>: aut arcus <emph type="italics"/>mo<emph.end type="italics"/> ad arcum <emph type="italics"/>oq<emph.end type="italics"/><lb/> eandem habet rationem, quam &longs;inus <emph type="italics"/>lm<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>no,<emph.end type="italics"/><lb/>

aut non eandem, &longs;ed vel maiorem vel minorem: habe&shy;<lb/>

at prim&uacute;m eandem rationem. </s>
            <s id="N12547">Dum ergo perpendicu&shy;


<pb xlink:href="062/01/068.jpg"/>lum <emph type="italics"/>ad<emph.end type="italics"/> mouetur ex <emph type="italics"/>o<emph.end type="italics"/> in <emph type="italics"/>q,<emph.end type="italics"/> perpendiculum <emph type="italics"/>ab<emph.end type="italics"/> ex <emph type="italics"/>m<emph.end type="italics"/> in <emph type="italics"/>o<emph.end type="italics"/><lb/> promouebitur: non igitur concur&longs;us fit in <emph type="italics"/><expan abbr="q.">que</expan><emph.end type="italics"/> Simili mo <lb/>

do &longs;i <emph type="italics"/>mo<emph.end type="italics"/> ad <emph type="italics"/>oq<emph.end type="italics"/> majorem habeat rationem, perpendicu&shy;<lb/>


<figure id="id.062.01.068.1.jpg" xlink:href="062/01/068/1.jpg"/><lb/>

lum <emph type="italics"/>ad<emph.end type="italics"/> ex <emph type="italics"/>o<emph.end type="italics"/> majori quam <emph type="italics"/>oq<emph.end type="italics"/> interuallo abducetur. </s>
            <s id="N125A4">Si <lb/>

demum minorem habeat rationem, auferatur pars pro&shy;<lb/>

portionalis, <expan abbr="at&qacute;">atque</expan>; rur&longs;um alia, <expan abbr="quou&longs;&qacute;">quou&longs;que</expan>; in <emph type="italics"/>q<emph.end type="italics"/> &longs;it &aelig;qualis aut <lb/>

minor: &amp; tum rur&longs;um o&longs;tendemus perpendiculum <emph type="italics"/>ad<emph.end type="italics"/><lb/>

pr&aelig;currere: non igitur concur&longs;us in minori quam <emph type="italics"/>t<emph.end type="italics"/> in&shy;<lb/>

teruallo e&longs;&longs;e pote&longs;t. </s>
            <s id="N125CA">Qu&oacute;d &longs;i autem <emph type="italics"/>ad<emph.end type="italics"/> dicatur pr&aelig;cur&shy;<lb/>

rere in <emph type="italics"/>t,<emph.end type="italics"/> erit <emph type="italics"/>ab<emph.end type="italics"/> in aliquo puncto min&uacute;s remoto, verbi <lb/>

gratia<emph type="italics"/>s<emph.end type="italics"/>: igitur c&ugrave;m <emph type="italics"/>ab<emph.end type="italics"/> ferebatur in <emph type="italics"/>q, ad<emph.end type="italics"/> necdum atti&shy;<lb/>

git <emph type="italics"/>t<emph.end type="italics"/>: erit ergo in aliquo puncto inter <emph type="italics"/>t<emph.end type="italics"/> &amp; <emph type="italics"/>q,<emph.end type="italics"/> quod &longs;it <emph type="italics"/>s.<emph.end type="italics"/> Et <lb/>

quia ut &longs;inus <emph type="italics"/>pq<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>rs,<emph.end type="italics"/> ita motus in <emph type="italics"/>q<emph.end type="italics"/> ad motum in <lb/>

<emph type="italics"/>s<emph.end type="italics"/>: e&longs;t autem &longs;inus <emph type="italics"/>pq<emph.end type="italics"/> major quam <emph type="italics"/>rs,<emph.end type="italics"/> erit arcus proporti&shy;


<pb xlink:href="062/01/069.jpg"/>onalis minor qua <emph type="italics"/>qs:<emph.end type="italics"/> quia ver&ograve; &longs;inus <emph type="italics"/>rs<emph.end type="italics"/> e&longs;t maior arcu <emph type="italics"/>sq<emph.end type="italics"/><lb/> per Lemma 4. minor autem arcu <emph type="italics"/>ts,<emph.end type="italics"/> erit arcus <emph type="italics"/>ts<emph.end type="italics"/> mult&ograve; <lb/>

major arcu proportionali: po&longs;ito ergo perpendiculo <emph type="italics"/>ab<emph.end type="italics"/><lb/>

in <emph type="italics"/>s,<emph.end type="italics"/> perpendiculum <emph type="italics"/>ad<emph.end type="italics"/> necdum e&longs;&longs;e pote&longs;t in <emph type="italics"/>t.<emph.end type="italics"/> Quod <lb/>

idem de quouis alio puncto o&longs;tendemus. </s>
            <s id="N12677">Quia ergo <lb/>

perpendiculum <expan abbr="ne&qacute;">neque</expan>; propi&ugrave;s concurrere, <expan abbr="ne&qacute;">neque</expan>; pr&aelig;cur&shy;<lb/>

rere pote&longs;t, concurret nece&longs;&longs;ari&ograve; in <emph type="italics"/>t.<emph.end type="italics"/> Poterit eadem ra&shy;<lb/>

tio in hunc modum fieri: motus &longs;e habent ut &longs;inus <expan abbr="at&qacute;">atque</expan>; <lb/>

horum interualla, &longs;eu arcus &longs;inubus intercepti: h&aelig;c au&shy;<lb/>

tem interualla continu&ograve; fiunt minora, in puncto ver&ograve; <lb/>

<emph type="italics"/>t<emph.end type="italics"/> nulla: igitur &amp; motus continu&oacute; minori, in puncto ve&shy;<lb/>

r&ograve; <emph type="italics"/>t<emph.end type="italics"/> nullo <expan abbr="ab&longs;i&longs;t&utilde;t">ab&longs;i&longs;tunt</expan> interuallo, Qu&ograve;d &longs;i a&longs;&longs;umantur plura <lb/>

puncta <emph type="italics"/>b.d. f.h.k.m.<emph.end type="italics"/> &amp;c. eadem vi&agrave; o&longs;tendemus ex omni&shy;<lb/>

bus &longs;imul recurrere in <emph type="italics"/>t<emph.end type="italics"/>: &longs;icuti enim ex <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>d,<emph.end type="italics"/> ita ex <emph type="italics"/>d<emph.end type="italics"/> &amp; <emph type="italics"/>f,<emph.end type="italics"/><lb/>

&amp; ex <emph type="italics"/>f<emph.end type="italics"/> &amp; <emph type="italics"/>b, et<emph.end type="italics"/> ex <emph type="italics"/>h<emph.end type="italics"/> &amp; <emph type="italics"/>k<emph.end type="italics"/> &amp;c. &aelig;qualis fit recur&longs;us. </s>
            <s id="N126EB">Perpen&shy;<lb/>

diculum ergo ex <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>d<emph.end type="italics"/> &aelig;qualiter recurrens recurret <lb/>

<expan abbr="quo&qacute;">quoque</expan>; &aelig;qualiter ex <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>f<emph.end type="italics"/> &amp; <emph type="italics"/>h<emph.end type="italics"/> &amp; <emph type="italics"/>k<emph.end type="italics"/> &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N1271A">
          <p id="N1271B" type="main">
            <s id="N1271D"><emph type="center"/>Propo&longs;itio XXV.<emph.end type="center"/></s>
          </p>
          <p id="N12724" type="main">
            <s id="N12726"><emph type="italics"/>Excur&longs;us perpendiculi in eodem circulo &agrave; line&agrave; &longs;tationis &longs;unt in&shy;<lb/>

ter &longs;e &aelig;qualis.<emph.end type="italics"/></s>
          </p>
          <p id="N1272F" type="main">
            <s id="N12731">QVia &lpar;in fig: 8.&rpar; velocitas in <emph type="italics"/>eb<emph.end type="italics"/> velocitati in <emph type="italics"/>fb,<emph.end type="italics"/> &amp; <lb/>

velocitas in <emph type="italics"/>cb<emph.end type="italics"/> e&longs;t &aelig;qualis velocitati in <emph type="italics"/>db<emph.end type="italics"/> per prop. <lb/>

20. e&longs;t <expan abbr="aut&etilde;">autem</expan> velocitas in <emph type="italics"/>eb<emph.end type="italics"/> ad <expan abbr="velocitat&etilde;">velocitatem</expan> in <emph type="italics"/>cb,<emph.end type="italics"/> ut arcus <emph type="italics"/>e<emph.end type="italics"/>


<pb xlink:href="062/01/070.jpg"/><emph type="italics"/>b<emph.end type="italics"/> ad arcum <emph type="italics"/>cb:<emph.end type="italics"/> propterea qu&ograve;d perpendiculum ex <emph type="italics"/>c<emph.end type="italics"/> &amp; <emph type="italics"/>e<emph.end type="italics"/><lb/> &aelig;quali tempore recurrit in <emph type="italics"/>b<emph.end type="italics"/> per prop: 24. erit ut arcus <lb/>

<emph type="italics"/>fb<emph.end type="italics"/> ad arcum <emph type="italics"/>db,<emph.end type="italics"/> ita velocitas excur&longs;us in <emph type="italics"/>fb<emph.end type="italics"/> ad velocita&shy;<lb/>

tem excur&longs;us in <emph type="italics"/>db.<emph.end type="italics"/> At ver&ograve; ut idem arcus <emph type="italics"/>fb<emph.end type="italics"/> ad arcum <lb/>

<emph type="italics"/>db,<emph.end type="italics"/> ita violentia inclinationum in illis arcubus collecta: <lb/>

tollit autem violentia partem impul&longs;us &longs;ibi &aelig;qualem <lb/>

per po&longs;it: 2. igitur ut arcus <emph type="italics"/>fb<emph.end type="italics"/> ad arcum <emph type="italics"/>db,<emph.end type="italics"/> ita ablatum <lb/>

ad ablatum, hoc e&longs;t velocitatis decrementum, &amp; velo&shy;<lb/>

citas reliqua ad reliquam velocitatem habet autem ve&shy;<lb/>

locitas motus eandem rationem, quam interualla. </s>
            <s id="N127CC">Quia <lb/>

ergo excur&longs;us eandem rationem habent tum ad &longs;e, tum <lb/>

ad interualla, quam habent recur&longs;us ad &longs;e, &amp; &longs;ua inter&shy;<lb/>

ualla; fiunt autem recur&longs;us eodem vel &aelig;quali tempo&shy;<lb/>

re, erunt <expan abbr="quo&qacute;">quoque</expan>; excur&longs;us eodem vel &aelig;quali tempore, ac <lb/>

proinde inter &longs;e &aelig;quales. </s>
          </p>
        </subchap1>
        <subchap1 id="N127DD">
          <p id="N127DE" type="main">
            <s id="N127E0"><emph type="center"/>Propo&longs;itio XXVI.<emph.end type="center"/></s>
          </p>
          <p id="N127E7" type="main">
            <s id="N127E9"><emph type="italics"/>Motus per arcus &longs;imiles in&aelig;qualium circulorum rationem ha&shy;<lb/>

bent quam &longs;inus illorum arcuum.<emph.end type="italics"/></s>
          </p>
          <p id="N127F2" type="main">
            <s id="N127F4">AS&longs;umantur duo arcus, in circulo quidem maiori <emph type="italics"/>bd. <lb/>

bf,<emph.end type="italics"/> in circulo autem minori <emph type="italics"/>ce.cg<emph.end type="italics"/> inter &longs;e &longs;imiles: di&shy;<lb/>

co motum perpendiculi ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> ad motum ex <emph type="italics"/>g<emph.end type="italics"/> in <emph type="italics"/>c,<emph.end type="italics"/> &amp; <lb/>

motum ex <emph type="italics"/>d<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> ad motum ex <emph type="italics"/>e<emph.end type="italics"/> in <emph type="italics"/>c<emph.end type="italics"/> eandem rationem <lb/>

habere quam &longs;inus illorum arcuum. </s>
            <s id="N1283B">angant enim 


<pb xlink:href="062/01/071.jpg"/><expan abbr="utrum&qacute;">utrumque</expan>; circulum in punctis <emph type="italics"/>f.d.g.e<emph.end type="italics"/> line&aelig; <emph type="italics"/>fk. di,<emph.end type="italics"/> &amp; <emph type="italics"/>gb eh<emph.end type="italics"/>: <lb/>

<expan abbr="erit&qacute;">eritque</expan>; angulus <emph type="italics"/>akf<emph.end type="italics"/> angulo <emph type="italics"/>abg,<emph.end type="italics"/> &amp; angulus <emph type="italics"/>aid<emph.end type="italics"/> angulo <emph type="italics"/>ab <lb/>

e<emph.end type="italics"/> &aelig;qualis: propterea qu&oacute;d anguli <emph type="italics"/>afk. agb,<emph.end type="italics"/> &amp; anguli <emph type="italics"/>ad <lb/>

i. aeh<emph.end type="italics"/> &longs;int recti, anguli ver&ograve; <emph type="italics"/>kaf.iad<emph.end type="italics"/> communes: velo&shy;<lb/>

citas ergo in <emph type="italics"/>f<emph.end type="italics"/> velocitati in <emph type="italics"/>g,<emph.end type="italics"/> &amp; velocitas in <emph type="italics"/>d<emph.end type="italics"/> velocitati <lb/>


<figure id="id.062.01.071.1.jpg" xlink:href="062/01/071/1.jpg"/><lb/>

in <emph type="italics"/>e<emph.end type="italics"/> e&longs;t &aelig;qualis: igitur ut <emph type="italics"/>f<emph.end type="italics"/> ad <emph type="italics"/>d,<emph.end type="italics"/> ita <emph type="italics"/>g<emph.end type="italics"/> ad <emph type="italics"/>e<emph.end type="italics"/>: &longs;ed ut <emph type="italics"/>f<emph.end type="italics"/> ad <emph type="italics"/>d,<emph.end type="italics"/> ita <lb/>

&longs;inus arcu<emph type="italics"/>s fb<emph.end type="italics"/> ad &longs;inum arcus <emph type="italics"/>db<emph.end type="italics"/>; &amp; ut <emph type="italics"/>g<emph.end type="italics"/> ad <emph type="italics"/>e<emph.end type="italics"/> ita &longs;inus ar&shy;<lb/>

cus <emph type="italics"/>gc<emph.end type="italics"/> ad &longs;inum arcus <emph type="italics"/>ec<emph.end type="italics"/> per prop. 22. erit ergo permu&shy;<lb/>

tando motus in <emph type="italics"/>f<emph.end type="italics"/> ad motum in <emph type="italics"/>g,<emph.end type="italics"/> ut &longs;inus arcus <emph type="italics"/>fb<emph.end type="italics"/> ad &longs;i&shy;<lb/>

num arcus <emph type="italics"/>ge<emph.end type="italics"/>; &amp; motus in <emph type="italics"/>d<emph.end type="italics"/> ad motum in <emph type="italics"/>e,<emph.end type="italics"/> ut &longs;inus ar-


<pb xlink:href="062/01/072.jpg"/>cus <emph type="italics"/>db<emph.end type="italics"/> ad &longs;inum arcus <emph type="italics"/>ec.<emph.end type="italics"/> Motus ergo per arcus &longs;imiles <lb/>

in&aelig;qualium circulorum rationem habent quam &longs;inus <lb/>

illorum arcuum, </s>
          </p>
        </subchap1>
        <subchap1 id="N12936">
          <p id="N12937" type="main">
            <s id="N12939"><emph type="center"/>Propo&longs;itio XXVII.<emph.end type="center"/></s>
          </p>
          <p id="N12940" type="main">
            <s id="N12942"><emph type="italics"/>Motus in circulo minori e&longs;t velocior motu in circulo majori.<emph.end type="italics"/></s>
          </p>
          <p id="N12949" type="main">
            <s id="N1294B">IN circulo maiori <emph type="italics"/>dfb<emph.end type="italics"/> perpendiculum ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>b,<emph.end type="italics"/> in cir&shy;<lb/>

culo ver&ograve; minori <emph type="italics"/>mgc<emph.end type="italics"/> ex <emph type="italics"/>g<emph.end type="italics"/> in <emph type="italics"/>c<emph.end type="italics"/> moueatur: dico velo&shy;<lb/>

ci&ugrave;s ex <emph type="italics"/>g<emph.end type="italics"/> in <emph type="italics"/>c,<emph.end type="italics"/> quam ex <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> recurrere. </s>
            <s id="N1298E">Quia enim mo&shy;<lb/>

tus in <emph type="italics"/>fb<emph.end type="italics"/> ad motum in <emph type="italics"/>gc,<emph.end type="italics"/> ut &longs;inus <emph type="italics"/>bg<emph.end type="italics"/> ad <expan abbr="&longs;in&utilde;">&longs;inum</expan> <emph type="italics"/>cu<emph.end type="italics"/> per prop: <lb/>

25. &amp; ut <emph type="italics"/>bg<emph.end type="italics"/> ad <emph type="italics"/>cu,<emph.end type="italics"/> ita <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>ac,<emph.end type="italics"/> propterea qu&oacute;d line&aelig; <emph type="italics"/>bg cu<emph.end type="italics"/><lb/>

&longs;int parallel&aelig;, &amp; triangula <emph type="italics"/>bag. eau<emph.end type="italics"/> &longs;imilia: e&longs;t autem <lb/>

maior linea <emph type="italics"/>ab<emph.end type="italics"/> quam <emph type="italics"/>ac,<emph.end type="italics"/> erit <expan abbr="quo&qacute;">quoque</expan>; <emph type="italics"/>bg<emph.end type="italics"/> maior quam <emph type="italics"/>cu<emph.end type="italics"/><lb/> maior ergo motus ab eadem velocitate in <emph type="italics"/>bg,<emph.end type="italics"/> hoc e&longs;t in <lb/>

<emph type="italics"/>fb<emph.end type="italics"/> maiori, quam in <emph type="italics"/>cu,<emph.end type="italics"/> hoc e&longs;t in <emph type="italics"/>ge,<emph.end type="italics"/> minori interuallo <lb/>

per prop: 5. ac proinde in circulo minori e&longs;t velocior <lb/>

motus, hoc e&longs;t minori fit tempore, quam in circulo ma&shy;<lb/>

jori. </s>
          </p>
        </subchap1>
        <subchap1 id="N12A15">
          <p id="N12A16" type="main">
            <s id="N12A18"><emph type="center"/>Propo&longs;itio XXVIII.<emph.end type="center"/></s>
          </p>
          <p id="N12A1F" type="main">
            <s id="N12A21"><emph type="italics"/>Motus circulorum &longs;unt in ratione &longs;uorum temporum, quam ha&shy;<lb/>

bent diametri ad &longs;e duplicatam.<emph.end type="italics"/></s>
          </p>
          <p id="N12A2A" type="main">
            <s id="N12A2C">QVia enim ut &longs;inus <emph type="italics"/>bg<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>cu,<emph.end type="italics"/> ita motus in <emph type="italics"/>fb<emph.end type="italics"/><lb/>

ad motum in <emph type="italics"/>gc<emph.end type="italics"/> per prop. 25. e&longs;t autem ut <emph type="italics"/>bg<emph.end type="italics"/> ad <emph type="italics"/>cu<emph.end type="italics"/>


<pb xlink:href="062/01/073.jpg"/>ita motus in <emph type="italics"/>ab<emph.end type="italics"/> ad motum in <emph type="italics"/>ac<emph.end type="italics"/> propterea qu&ograve;d motus <lb/>

<emph type="italics"/>ab<emph.end type="italics"/> motui <emph type="italics"/>bg,<emph.end type="italics"/> &amp; motus <emph type="italics"/>ac<emph.end type="italics"/> motui <emph type="italics"/>cu<emph.end type="italics"/> e&longs;t &aelig;qualis per prop: <lb/>

13. erit motus in <emph type="italics"/>fb<emph.end type="italics"/> ad motum in <emph type="italics"/>gc,<emph.end type="italics"/> ut motus in <emph type="italics"/>ab<emph.end type="italics"/> ad <lb/>

motum in <emph type="italics"/>ac.<emph.end type="italics"/> At ver&ograve; motus in <emph type="italics"/>ab<emph.end type="italics"/> ad motum in <emph type="italics"/>ac,<emph.end type="italics"/> &amp; <lb/>


<figure id="id.062.01.073.1.jpg" xlink:href="062/01/073/1.jpg"/><lb/>

huius duplum <emph type="italics"/>lb<emph.end type="italics"/> ad <emph type="italics"/>mc<emph.end type="italics"/> rationem habent quam tempo&shy;<lb/>

rum quadrata per prop: 12. radices ergo quadrat&aelig; line&shy;<lb/>

arum <emph type="italics"/>bl. cm<emph.end type="italics"/> eandem rationem habent quam tempora <lb/>

motus circulorum, ac proinde illorum temporum rati&shy;<lb/>

onem habent diametri ad &longs;e duplicatam. </s>
          </p>
        </subchap1>
        <subchap1 id="N12AC9">
          <pb xlink:href="062/01/074.jpg"/>
          <p id="N12ACD" type="main">
            <s id="N12ACF"><emph type="center"/>Propo&longs;itio XXIX.<emph.end type="center"/></s>
          </p>
          <p id="N12AD6" type="main">
            <s id="N12AD8"><emph type="italics"/>Fieri pote&longs;t ut arcum circuli majoris minori tempore tran&longs;eat, <lb/>

quam arcum circuli minoris.<emph.end type="italics"/></s>
          </p>
          <p id="N12AE1" type="main">
            <s id="N12AE3">AS&longs;umatur in fig: 10. &longs;inus <emph type="italics"/>ou<emph.end type="italics"/> ad &longs;inum <emph type="italics"/>qm<emph.end type="italics"/> in e&agrave; rati&shy;<lb/>

one, in qu&agrave; diameter major <emph type="italics"/>ab<emph.end type="italics"/> ad minorem <emph type="italics"/>om,<emph.end type="italics"/> <expan abbr="e-tit&qacute;">e&shy;<lb/>

ritque</expan>; velocitas in <emph type="italics"/>o<emph.end type="italics"/> ad velocitatem in <emph type="italics"/>q,<emph.end type="italics"/> ut <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>om,<emph.end type="italics"/> hoc <lb/>

e&longs;t ut motus <emph type="italics"/>qb<emph.end type="italics"/> in circulo maiori ad motum <emph type="italics"/>tm<emph.end type="italics"/> in cir&shy;<lb/>

culo minori. </s>
            <s id="N12B2E">Qu&oacute;d &longs;i ergo &longs;umantur duo arcus <emph type="italics"/>op. qr<emph.end type="italics"/><lb/> inter &longs;e &aelig;quales, maior erit proportio motus in <emph type="italics"/>qr<emph.end type="italics"/> ad <lb/>

motum in <emph type="italics"/>op,<emph.end type="italics"/> quam ad motu in <emph type="italics"/>tm<emph.end type="italics"/>: velocior ergo mo&shy;<lb/>

tus in arcu <emph type="italics"/>op<emph.end type="italics"/> circuli maioris, quam in arcu <emph type="italics"/>tm<emph.end type="italics"/> circuli <lb/>

minoris. </s>
          </p>
        </subchap1>
        <subchap1 id="N12B5C">
          <p id="N12B5D" type="main">
            <s id="N12B5F"><emph type="center"/>Propo&longs;itio XXX.<emph.end type="center"/></s>
          </p>
          <p id="N12B66" type="main">
            <s id="N12B68"><emph type="italics"/>Ab impul&longs;u contrario &amp; &aelig;quali nullus e&longs;t motus: ab impul&longs;u <lb/>

ver&ograve; contrario &amp; in&aelig;quali motus e&longs;t &aelig;qualis exce&longs;&longs;ui majoris.<emph.end type="italics"/></s>
          </p>
          <p id="N12B71" type="main">
            <s id="N12B73">QVia enim contrarium &aelig;quale tollit vel impedit &longs;u<lb/>

um contrarium in eadem ratione, totum quidem <lb/>

totum, pars ver&ograve; partem &longs;ibi &aelig;qualem per po&longs;i: 2. </s>
            <s id="N12B7A">Su&shy;<lb/>

blato per contrarium &aelig;quale toto impul&longs;u nullus erit <lb/>

motus, qui e&longs;&longs;e non pote&longs;t <expan abbr="ab&longs;q;">ab&longs;que</expan> impul&longs;u.</s>
            <s id="N12B85">Qu&oacute;d &longs;i ve&shy;<lb/>

r&ograve; impul&longs;us &longs;int in&aelig;quales, quia minor &agrave; majori tollit <lb/>

partem &longs;ibi &aelig;qualem, erit reliquus exce&longs;&longs;us principium 


<pb xlink:href="062/01/075.jpg"/>motus. </s>
            <s id="N12B90">Ab impul&longs;u erg&ograve; contrario &amp; &aelig;quali nullus e&longs;t <lb/>

motus &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N12B95">
          <p id="N12B96" type="main">
            <s id="N12B98"><emph type="center"/>Propo&longs;itio XXXI.<emph.end type="center"/></s>
          </p>
          <p id="N12B9F" type="main">
            <s id="N12BA1"><emph type="italics"/>Motus &longs;ecund&ugrave;m quid contrarij per lineam fiunt mediam, cujus <lb/>

interuallam determinat &longs;inus complementi inclinationis, in ratione <lb/>

quam habent impul&longs;us.<emph.end type="italics"/></s>
          </p>
          <p id="N12BAC" type="main">
            <s id="N12BAE">VI in fig: 2 &longs;i mobile ex eodem puncto <emph type="italics"/>a<emph.end type="italics"/> moueatur <lb/>

per lineas <emph type="italics"/>ab. af,<emph.end type="italics"/> aut per lineas <emph type="italics"/>ab. ad,<emph.end type="italics"/> &amp; &longs;it angulus <lb/>

<emph type="italics"/>baf<emph.end type="italics"/> major, angulus ver&ograve; <emph type="italics"/>bad<emph.end type="italics"/> minor recto, erunt hi mo&shy;<lb/>

tus per definit: 5. &longs;ecund&ugrave;m quid contrarij, ac proinde <lb/>

in eo in quo &longs;unt contrarij, <expan abbr="toll&utilde;t">tollunt</expan> aut <expan abbr="impedi&utilde;t">impediunt</expan> <expan abbr="&longs;u&utilde;">&longs;uum</expan> con<lb/>

<expan abbr="trari&utilde;">trarium</expan>, per definit: 1. impul&longs;us ergo in <emph type="italics"/>af<emph.end type="italics"/> ab impul&longs;u in <emph type="italics"/>ab,<emph.end type="italics"/><lb/>

&amp; hic ab impul&longs;u in <emph type="italics"/>af<emph.end type="italics"/> retractus, quia <expan abbr="id&etilde;">idem</expan> mobile e&longs;&longs;e <expan abbr="n&otilde;">non</expan> <lb/>

pote&longs;t in pluribus locis, ac proinde <expan abbr="ne&qacute;">neque</expan>; pluribus moti&shy;<lb/>

bus agitari, mouebitur motu inter <expan abbr="utrum&qacute;">utrumque</expan>; medio, cu&shy;<lb/>

ju&longs;modi linea motus <emph type="italics"/>ad<emph.end type="italics"/>: dico huius line&aelig; interuallum &agrave;, <lb/>

lineis extremis <emph type="italics"/>ab. af<emph.end type="italics"/> e&longs;&longs;e &longs;inum complementi angulo&shy;<lb/>

rum <emph type="italics"/>faddab,<emph.end type="italics"/> in ratione quam habet impul&longs;us <emph type="italics"/>ab<emph.end type="italics"/> ad im&shy;<lb/>

pul&longs;um <emph type="italics"/>af.<emph.end type="italics"/> Quia enim velocitas motus per lineas incli&shy;<lb/>

natas e&longs;t in ratione &longs;inus complementi illarum inclina&shy;<lb/>

tionum, per prop: 14. ratio autem velocitatis e&longs;t eadem <lb/>

qu&aelig; impul&longs;us, propterea qu&ograve;d impul&longs;us e&longs;t agens ne&shy;<lb/>

ce&longs;&longs;arium, <expan abbr="motum&qacute;">motumque</expan>; producit &longs;ibi &aelig;qualem per prop: 2. 

<pb xlink:href="062/01/076.jpg"/>erit &longs;inus complementi anguli <emph type="italics"/>fad<emph.end type="italics"/> ad &longs;inum comple&shy;<lb/>

menti anguli <emph type="italics"/>dab,<emph.end type="italics"/> ut impul&longs;us in <emph type="italics"/>af<emph.end type="italics"/> ad impul&longs;um in <emph type="italics"/>ab,<emph.end type="italics"/><lb/>

Motus erg&ograve; &longs;ecund&ugrave;m quid contrarij per lineam fiunt <lb/>

mediam, cujus interuallum determinat &longs;inu<emph type="italics"/>s<emph.end type="italics"/> &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N12C69">
          <p id="N12C6A" type="main">
            <s id="N12C6C"><emph type="center"/>Propo&longs;itio XXXII.<emph.end type="center"/></s>
          </p>
          <p id="N12C73" type="main">
            <s id="N12C75"><emph type="italics"/>Motus perfect&egrave; mixtus fit per diametrum parallelogrammi, cu&shy;<lb/>

jus latera con&longs;tituit motus &longs;implex: &amp; ex impul&longs;u quidem &aelig;quali <lb/>

e&longs;t &aelig;qualis &longs;emis&longs;i, ex in&aelig;quali ver&ograve; major &longs;emi&longs;&longs;e eju&longs;dem motus.<emph.end type="italics"/></s>
          </p>
          <p id="N12C80" type="main">
            <s id="N12C82">MOtum perfect&egrave; mixtum con&longs;tituunt motus, qui &aelig;&shy;<lb/>

qualiter &longs;unt &longs;imiles &amp; contrarij: tant&ugrave;m enim hic <lb/>


<figure id="id.062.01.076.1.jpg" xlink:href="062/01/076/1.jpg"/><lb/>

illum auget, quant&ugrave;m &amp; minuit. </s>
            <s id="N12C90">Moueatur idem mobi<lb/>

le ex <emph type="italics"/>a<emph.end type="italics"/> in <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>c,<emph.end type="italics"/> &amp; &longs;it angulus <emph type="italics"/>bac<emph.end type="italics"/> rectus, <expan abbr="erit&qacute;">eritque</expan>; per defini&shy;<lb/>

tionem motus medius incipiens ab angulo recto per&shy;<lb/>

fect&egrave; mixtus: Dico hunc motum fieri per diametrum <lb/>

<emph type="italics"/>ad<emph.end type="italics"/> parallelogrammi <emph type="italics"/>abdc,<emph.end type="italics"/> cuius latera <emph type="italics"/>ab. ac<emph.end type="italics"/> &longs;unt mo&shy;<lb/>

tus, qui inter le <expan abbr="mi&longs;c&etilde;tur">mi&longs;centur</expan>: &amp; <expan abbr="&longs;iquid&etilde;">&longs;iquidem</expan> motus in <emph type="italics"/>ab<emph.end type="italics"/> &longs;it &aelig;qua <lb/>

lis motui in <emph type="italics"/>ac,<emph.end type="italics"/> <expan abbr="mot&utilde;">motum</expan> <expan abbr="mixt&utilde;">mixtum</expan> in <emph type="italics"/>ad<emph.end type="italics"/> e&longs;&longs;e <expan abbr="&aelig;qual&etilde;">&aelig;qualem</expan> &longs;emi&longs;si utri 


<pb xlink:href="062/01/077.jpg"/><expan abbr="u&longs;&qacute;">u&longs;que</expan>; motus &longs;imul &longs;umpti: &longs;i <expan abbr="aut&etilde;">autem</expan> motus fuerit in&aelig;qualis, <lb/>

<expan abbr="maior&etilde;">maiorem</expan> &longs;emi&longs;&longs;e. </s>
            <s id="N12D04">Sit prim&ograve; motus in <emph type="italics"/>ab<emph.end type="italics"/> &aelig;qualis motui in <lb/>

<emph type="italics"/>ac<emph.end type="italics"/>: &amp; ex <emph type="italics"/>bc<emph.end type="italics"/> termino <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>; motus demittantur line&aelig; <lb/>

perpendiculares <emph type="italics"/>be. ce,<emph.end type="italics"/> &longs;inus &aelig;qualium angulorum <emph type="italics"/>cde, <lb/>

edb.<emph.end type="italics"/> Quia ergo ut <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>ac,<emph.end type="italics"/> ita &longs;inus complementi <emph type="italics"/>eb<emph.end type="italics"/> ad <lb/>

<emph type="italics"/>ec,<emph.end type="italics"/> erit diameter <emph type="italics"/>ad<emph.end type="italics"/> linea motus mixti. </s>
            <s id="N12D4F">E&longs;t autem mo&shy;<lb/>

tus in <emph type="italics"/>ab<emph.end type="italics"/> &amp; <emph type="italics"/>ac<emph.end type="italics"/> duratione quidem &aelig;qualis motui in <emph type="italics"/>ae<emph.end type="italics"/><lb/>

per prop: 13. magnitudine ver&ograve; minor, cujus exce&longs;&longs;us <lb/>

quadratum <emph type="italics"/>eb.<emph.end type="italics"/> &amp; <emph type="italics"/>ec,<emph.end type="italics"/> &longs;eu <emph type="italics"/>ae<emph.end type="italics"/> &amp; <emph type="italics"/>ed<emph.end type="italics"/>: at ver&ograve; duo quadrata <emph type="italics"/>ae. <lb/>

ed<emph.end type="italics"/> &longs;unt &longs;emi&longs;sis quadrati <emph type="italics"/>ad,<emph.end type="italics"/> hoc e&longs;t motus in <emph type="italics"/>ab.ac,<emph.end type="italics"/> cui, <lb/>

&aelig;quale e&longs;t quadratum <emph type="italics"/>ad,<emph.end type="italics"/> propterea qu&ograve;d <emph type="italics"/>ad<emph.end type="italics"/> &longs;it dupla <lb/>

<emph type="italics"/>ae<emph.end type="italics"/> aut <emph type="italics"/>ed<emph.end type="italics"/>: igitur motus &aelig;qualiter mixtus fit per diame&shy;<lb/>

trum parallelogrammi, &amp; ab &aelig;quali impul&longs;u e&longs;t &aelig;qua&shy;<lb/>

lis &longs;emi&longs;si <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>; motus &longs;imul &longs;umpti. </s>
            <s id="N12DB9">Qu&oacute;d &longs;i mo&shy;<lb/>

tus &longs;it in&aelig;qualis, &amp; <emph type="italics"/>u.g.<emph.end type="italics"/> dupl&oacute; velocior in <emph type="italics"/>ef<emph.end type="italics"/> quam in <emph type="italics"/>eg,<emph.end type="italics"/><lb/>

dico motum mixtum fieri quidem per diametrum <emph type="italics"/>eb,<emph.end type="italics"/><lb/>

e&longs;&longs;e autem &longs;emi&longs;&longs;e maiorem. </s>
            <s id="N12DD8">De&longs;cripto enim centro <emph type="italics"/>b<emph.end type="italics"/><lb/> arcu <emph type="italics"/>mn,<emph.end type="italics"/> erit &longs;inus complementi <emph type="italics"/>ik<emph.end type="italics"/> ad &longs;inum comple&shy;<lb/>

menti <emph type="italics"/>ip,<emph.end type="italics"/> ut motus in <emph type="italics"/>ef<emph.end type="italics"/> ad motum in <emph type="italics"/>eg,<emph.end type="italics"/> ac proinde di&shy;<lb/>

ameter <emph type="italics"/>eh<emph.end type="italics"/> linea motus mixti: ad quam ex punctis <emph type="italics"/>fg<emph.end type="italics"/> du&shy;<lb/>

ct&aelig; line&aelig; perpendiculares <emph type="italics"/>fl. go<emph.end type="italics"/> metientur defectum <lb/>

motus in <emph type="italics"/>eh.<emph.end type="italics"/> Quia ergo ex angulo recto <emph type="italics"/>efh<emph.end type="italics"/> linea <emph type="italics"/>fl<emph.end type="italics"/> e&longs;t <lb/>

perpendicularis ad ba&longs;im <emph type="italics"/>eh,<emph.end type="italics"/> erit ut <emph type="italics"/>ef<emph.end type="italics"/> ad <emph type="italics"/>fh,<emph.end type="italics"/> ita <emph type="italics"/>el<emph.end type="italics"/> ad <emph type="italics"/>lf,<emph.end type="italics"/> &amp; <lb/>

<emph type="italics"/>lf<emph.end type="italics"/> ad <emph type="italics"/>lh:<emph.end type="italics"/> ponitur autem quadratum <emph type="italics"/>ef<emph.end type="italics"/> duplum quadrat <lb/>

<emph type="italics"/>fh,<emph.end type="italics"/> &longs;iue <emph type="italics"/>eg,<emph.end type="italics"/> erit ergo quadratum <emph type="italics"/>fl<emph.end type="italics"/> &longs;imiliter <expan abbr="dupl&utilde;">duplum</expan> quadra


<pb xlink:href="062/01/078.jpg"/>ti <emph type="italics"/>lh.<emph.end type="italics"/> quadratum ergo <emph type="italics"/>fh<emph.end type="italics"/> <expan abbr="utriq;">utrique</expan> &aelig;quale continebit tria <lb/>

quadrata, quorum &longs;ingula &longs;int &aelig;qualia quadrato <emph type="italics"/>lh.<emph.end type="italics"/> &amp; <lb/>

quia quadratum <emph type="italics"/>ef<emph.end type="italics"/> e&longs;t duplum quadrati <emph type="italics"/>fh,<emph.end type="italics"/> erit quadra&shy;<lb/>

tum <emph type="italics"/>eh<emph.end type="italics"/> &aelig;quale nouem quadratis <emph type="italics"/>lh<emph.end type="italics"/> &longs;imul &longs;umptis. </s>
            <s id="N12EB0">At <lb/>

ver&ograve; quadratum <emph type="italics"/>el<emph.end type="italics"/> duplum quadrati <emph type="italics"/>lf<emph.end type="italics"/> erit quadruplum <lb/>

quadrati <emph type="italics"/>lh,<emph.end type="italics"/> <expan abbr="a&longs;&longs;umpto&qacute;">a&longs;&longs;umptoque</expan>; quadrato <emph type="italics"/>eo,<emph.end type="italics"/> aut huic &aelig;quali <emph type="italics"/>lh<emph.end type="italics"/><lb/> erunt duo quadrata <emph type="italics"/>el. lh<emph.end type="italics"/> &longs;imul &longs;umpta &aelig;qualia <expan abbr="quin&qacute;">quinque</expan>; <lb/>

quadratis <emph type="italics"/>lh<emph.end type="italics"/>: Maiora ergo quam &longs;emi&longs;sis quadrati <emph type="italics"/>eh,<emph.end type="italics"/><lb/>

qu&ograve;d &aelig;quale ponitur nouem quadratis <emph type="italics"/>lh.<emph.end type="italics"/> Igitur mo&shy;<lb/>

tus perfect&egrave; mixtus fit per diametrum parallelogram&shy;<lb/>

mi, cujus latera con&longs;tituit motus &longs;implex &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N12EFD">
          <p id="N12EFE" type="main">
            <s id="N12F00"><emph type="center"/>Propo&longs;itio XXXIII.<emph.end type="center"/></s>
          </p>
          <p id="N12F07" type="main">
            <s id="N12F09"><emph type="italics"/>Motus mixtus incipiens ab angulo majori quam recto, e&longs;t minor <lb/>

&longs;emi&longs;&longs;e: incipiens ver&ograve; ab angulo minori quam recto, major &longs;emi&longs;&longs;e <lb/>

motus &longs;imul &longs;umpti.<emph.end type="italics"/></s>
          </p>
          <p id="N12F14" type="main">
            <s id="N12F16">Sit prim&ugrave;m in fig: 7. angulus <emph type="italics"/>dae<emph.end type="italics"/> maior recto, &amp; an&shy;<lb/>

gulus <emph type="italics"/>bac<emph.end type="italics"/> rectus, <expan abbr="erit&qacute;">eritque</expan>; quadratum <emph type="italics"/>bb<emph.end type="italics"/> &aelig;quale qua&shy;<lb/>

drato <emph type="italics"/>ab<emph.end type="italics"/>: e&longs;t autem quadratum <emph type="italics"/>db,<emph.end type="italics"/> ex ce&longs;&longs;us nimirum <lb/>

motus <emph type="italics"/>ad,<emph.end type="italics"/> quadrato <emph type="italics"/>bh,<emph.end type="italics"/> ac proinde quadrato <emph type="italics"/>ah<emph.end type="italics"/> maius: <lb/>

igitur quadratum <emph type="italics"/>ad<emph.end type="italics"/> &aelig;quale duobus quadratis <emph type="italics"/>dh. ah<emph.end type="italics"/> ad <lb/>

quadratum minus <emph type="italics"/>ah<emph.end type="italics"/> maiorem rationem habet quam <lb/>

duplam: motus ergo in <emph type="italics"/>ah<emph.end type="italics"/> mixtus e&longs;t minor &longs;emi&longs;&longs;e 


<pb xlink:href="062/01/079.jpg"/>motus in <emph type="italics"/>ad,<emph.end type="italics"/> <expan abbr="at&qacute;">atque</expan>; illius duplum minus quam motus in <emph type="italics"/>a <lb/>

d. ae<emph.end type="italics"/> &longs;imul &longs;umpti. </s>
            <s id="N12F87">Qu&ograve;d &longs;i angulus <emph type="italics"/>fag<emph.end type="italics"/> &longs;it minor recto, <lb/>

erit latus <emph type="italics"/>fh,<emph.end type="italics"/> &amp; huius quadratum minus quam <emph type="italics"/>ah:<emph.end type="italics"/> mo&shy;<lb/>

tus ergo in <emph type="italics"/>af<emph.end type="italics"/> ad motum in <emph type="italics"/>ah<emph.end type="italics"/> minorem rationem ha&shy;<lb/>

bet quam duplam, ac proinde motus in <emph type="italics"/>ah<emph.end type="italics"/> major &longs;emi&longs;&shy;<lb/>

&longs;e motus in <emph type="italics"/>af,<emph.end type="italics"/> &amp; illius duplum majus qu&aacute; motus in <emph type="italics"/>af. <lb/>

ag<emph.end type="italics"/> &longs;imul &longs;umpti. </s>
          </p>
        </subchap1>
        <subchap1 id="N12FC4">
          <p id="N12FC5" type="main">
            <s id="N12FC7"><emph type="center"/>Propo&longs;itio XXXIV.<emph.end type="center"/></s>
          </p>
          <p id="N12FCE" type="main">
            <s id="N12FD0"><emph type="italics"/>Motus mixtus e&longs;t nece&longs;&longs;ari&oacute; minor diametro quadrati aut <lb/>parallelogrammi, cujus latera &longs;unt motus &longs;implex.<emph.end type="italics"/></s>
          </p>
          <p id="N12FD9" type="main">
            <s id="N12FDB">NAm motus quidem in <emph type="italics"/>be<emph.end type="italics"/> mixtus &lpar;in fig: 4.&rpar; e&longs;t du&shy;<lb/>

plum quadrati eiu&longs;dem <emph type="italics"/>be<emph.end type="italics"/>: quadratum ver&ograve; <emph type="italics"/>db<emph.end type="italics"/> ad <lb/>

quadratum <emph type="italics"/>be<emph.end type="italics"/> e&longs;t quadruplum. </s>
            <s id="N12FFA">Cau&longs;a ver&ograve; hujus de&shy;<lb/>

&longs;ectus e&longs;t contrarietas illorum motuum, ex angulis pro&shy;<lb/>

ueniens, cum quibus augetur &amp; minuitur, <expan abbr="quou&longs;q;">quou&longs;que</expan> an&shy;<lb/>

gulus late&longs;cens &aelig;qualis fiat duobus rectis, in quo &longs;um&shy;<lb/>

ma e&longs;t contrarietas, ac proinde nullus e&longs;&longs;e pote&longs;t motus. <lb/>

Angulo ver&ograve; decre&longs;cente augetur &longs;imilitudo motus, <lb/>

<expan abbr="quou&longs;q;">quou&longs;que</expan> angulo deficiente &longs;int una linea motus, in qu&agrave; <lb/>

perfecta &longs;imilitudo, nulla autem e&longs;t contrarietas. <expan abbr="Itaq;">Itaque</expan> <lb/>

motus &aelig;qualis motum auget in eadem ratione, totus <lb/>

quidem totum, pars ver&ograve; partem &longs;ibi &aelig;qualem per <lb/>

po&longs;it. 1. </s>
          </p>
        </subchap1>
        <subchap1 id="N1301D">
          <pb xlink:href="062/01/080.jpg"/>
          <p id="N13021" type="main">
            <s id="N13023"><emph type="center"/>Propo&longs;itio XXXV.<emph.end type="center"/></s>
          </p>
          <p id="N1302A" type="main">
            <s id="N1302C"><emph type="center"/><emph type="italics"/>Problema I.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N13037" type="main">
            <s id="N13039"><emph type="italics"/>Lineam motus mixti, &amp; illius magnitudinem determinare.<emph.end type="italics"/></s>
          </p>
          <p id="N13040" type="main">
            <s id="N13042">SIt prim&ugrave;m motus <emph type="italics"/>pq. pr<emph.end type="italics"/> perfect&egrave; mixtus, incipiens ab <lb/>

angulo recto <emph type="italics"/>qpr<emph.end type="italics"/>: &amp; ex <emph type="italics"/>q<emph.end type="italics"/> &amp; <emph type="italics"/>r<emph.end type="italics"/> ducantur line&aelig; <emph type="italics"/>qs. rs<emph.end type="italics"/> pa<lb/>

rallel&aelig; ad <emph type="italics"/>pq. pr,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; per prop. 31. motus mixtus in di&shy;<lb/>

ametro <emph type="italics"/>ps<emph.end type="italics"/>: ad quam ex termino <expan abbr="utriu&longs;q;">utriu&longs;que</expan> motus <emph type="italics"/>q<emph.end type="italics"/> &amp; <emph type="italics"/>r<emph.end type="italics"/><lb/>


<figure id="id.062.01.080.1.jpg" xlink:href="062/01/080/1.jpg"/><lb/> demittantur line&aelig; perpendiculares <emph type="italics"/>qt.ru,<emph.end type="italics"/> <expan abbr="eritq;">eritque</expan> motus <lb/>

mixtus ex <emph type="italics"/>pqpr<emph.end type="italics"/> &aelig;qualis duobus quadratis <emph type="italics"/>pu.pt.<emph.end type="italics"/> ab&longs;cin&shy;


<pb xlink:href="062/01/081.jpg"/>datur ergo ex linea <emph type="italics"/>tq<emph.end type="italics"/> product&agrave; linea <emph type="italics"/>tx<emph.end type="italics"/> &aelig;qualis line&aelig; <emph type="italics"/>p <lb/>

u,<emph.end type="italics"/> &amp; ex puncto <emph type="italics"/>p,<emph.end type="italics"/> interuallo autem <emph type="italics"/>px<emph.end type="italics"/> de&longs;cribatur arcus <lb/>

<emph type="italics"/>xy,<emph.end type="italics"/> <expan abbr="connectantur&qacute;">connectanturque</expan>; linea <emph type="italics"/>px<emph.end type="italics"/>: dico quadratum <emph type="italics"/>py<emph.end type="italics"/> e&longs;&longs;e <lb/>

motum mixtum &amp; duratione &aelig;qualem motui <emph type="italics"/>pq. pr<emph.end type="italics"/> &longs;i&shy;<lb/>

mul &longs;umptis. </s>
            <s id="N130EF">Quia enim quadratum <emph type="italics"/>py<emph.end type="italics"/> quadrato <emph type="italics"/>px,<emph.end type="italics"/><lb/>

hoc autem duobus quadratis <emph type="italics"/>pt.tx,<emph.end type="italics"/> &longs;eu <emph type="italics"/>pu<emph.end type="italics"/> e&longs;t &aelig;quale: e&longs;t <lb/>

autem motus <emph type="italics"/>pt<emph.end type="italics"/> motui <emph type="italics"/>pq,<emph.end type="italics"/> &amp; <emph type="italics"/>pu<emph.end type="italics"/> motui <emph type="italics"/>pr<emph.end type="italics"/> &aelig;qualis dura&shy;<lb/>

tione per prop: 13. erit motus mixtus in <emph type="italics"/>py<emph.end type="italics"/> &longs;imiliter &aelig;&shy;<lb/>

qualis motibus <emph type="italics"/>pq<emph.end type="italics"/> &amp; <emph type="italics"/>pr<emph.end type="italics"/> &longs;imul &longs;umptis. </s>
            <s id="N1313B">Qu&ograve;d &longs;i ver&ograve; <lb/>

motus imperfect&egrave; mixtus &amp; in&aelig;qualis <emph type="italics"/>ab. ac<emph.end type="italics"/> ab angulo <lb/>

incipiat maiori aut minori quam recto <emph type="italics"/>bac<emph.end type="italics"/>: a&longs;&longs;uman&shy;<lb/>

tur duo puncta <emph type="italics"/>fg<emph.end type="italics"/> &aelig;qualiter remota ab <emph type="italics"/>a,<emph.end type="italics"/> &agrave; quibus pro&shy;<lb/>

tract&aelig; line&aelig; perpendiculares <emph type="italics"/>fh. gh<emph.end type="italics"/> &longs;e inter&longs;ecent in <emph type="italics"/>h,<emph.end type="italics"/> <expan abbr="e-rit&qacute;">e&shy;<lb/>

ritque</expan>; angulus <emph type="italics"/>fhg<emph.end type="italics"/> complementum anguli <emph type="italics"/>bac,<emph.end type="italics"/> &amp; &longs;imul <lb/>

&longs;umpti &aelig;quales duobus rectis. </s>
            <s id="N1317E">De&longs;cribatur ergo ex <emph type="italics"/>h<emph.end type="italics"/><lb/> arcus <emph type="italics"/>fig,<emph.end type="italics"/> <expan abbr="&longs;ecetur&qacute;">&longs;eceturque</expan>; bifariam in <emph type="italics"/>i<emph.end type="italics"/> e&agrave; ratione, ut &longs;inus <emph type="italics"/>ik<emph.end type="italics"/> ad <lb/>

&longs;inum <emph type="italics"/>il<emph.end type="italics"/> &longs;it, ut motus <emph type="italics"/>ab<emph.end type="italics"/> ad motum <emph type="italics"/>ac:<emph.end type="italics"/> dico lineam ex <emph type="italics"/>a<emph.end type="italics"/><lb/>

productam in <emph type="italics"/>i<emph.end type="italics"/> e&longs;&longs;e lineam motus mixti. </s>
            <s id="N131BF">Producatur e&shy;<lb/>

nim <emph type="italics"/>fh<emph.end type="italics"/> in <emph type="italics"/>p,<emph.end type="italics"/> <expan abbr="erit&qacute;">eritque</expan>; angulus <emph type="italics"/>fpa<emph.end type="italics"/> complementum anguli <emph type="italics"/>f <lb/>

ap,<emph.end type="italics"/> &amp; angulus <emph type="italics"/>aog<emph.end type="italics"/> complementum anguli <emph type="italics"/>oag<emph.end type="italics"/>: duo er&shy;<lb/>

go anguli <emph type="italics"/>hpo. aog<emph.end type="italics"/> hoc e&longs;t <emph type="italics"/>hop,<emph.end type="italics"/> &longs;imul &longs;umpti &longs;unt &aelig;qua&lt;l<lb/>

les duobus angulis <emph type="italics"/>fhi: thg<emph.end type="italics"/> &longs;imul &longs;umptis, propterea <lb/>

qu&oacute;d &longs;int complementa eju&longs;dem anguli <emph type="italics"/>fag,<emph.end type="italics"/> e&longs;t autem <lb/>

angulus <emph type="italics"/>hop<emph.end type="italics"/> externus major angulo <emph type="italics"/>iho<emph.end type="italics"/> interno quanti&shy;<lb/>

tate anguli <emph type="italics"/>bio,<emph.end type="italics"/> angulus ver&ograve; <emph type="italics"/>iph<emph.end type="italics"/> internus minor angu&shy;


<pb xlink:href="062/01/082.jpg"/>lo <emph type="italics"/>ihf<emph.end type="italics"/> externo, quantitate eju&longs;dem anguli <emph type="italics"/>hip:<emph.end type="italics"/> angulus <lb/>

ergo <emph type="italics"/>hop<emph.end type="italics"/> angulo <emph type="italics"/>fhi,<emph.end type="italics"/> &amp; angulus <emph type="italics"/>oph<emph.end type="italics"/> angulo <emph type="italics"/>tho<emph.end type="italics"/> &longs;eu <emph type="italics"/>ihg<emph.end type="italics"/><lb/>

e&longs;t &aelig;qualis, ac proinde <emph type="italics"/>ik. il<emph.end type="italics"/> &longs;unt &longs;inus complementi an&shy;<lb/>

gulorum <emph type="italics"/>iag.e ai.<emph.end type="italics"/> Et quia motus &longs;unt in ratione, quam <lb/>

habent &longs;inus complementi inclinationum, erit linea <emph type="italics"/>ai<emph.end type="italics"/><lb/> linea motus mixti ex <emph type="italics"/>ab.ac<emph.end type="italics"/>; ad quam ex termino <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>; <lb/>

motus <emph type="italics"/>b.c<emph.end type="italics"/> demittantur line&aelig; perpendiculares <emph type="italics"/>bd.ce:<emph.end type="italics"/><lb/>

<expan abbr="er&utilde;t&qacute;">eruntque</expan>, duo quadrata <emph type="italics"/>ad.ae<emph.end type="italics"/> &longs;imul &longs;umpta motus mix&shy;<lb/>

tus: ab&longs;cindatur ergo ex <emph type="italics"/>db<emph.end type="italics"/> producta <emph type="italics"/>dm<emph.end type="italics"/> &aelig;qualis <emph type="italics"/>ae,<emph.end type="italics"/> &amp; <lb/>

centro <emph type="italics"/>a<emph.end type="italics"/> ducatur arcus <emph type="italics"/>mn,<emph.end type="italics"/> dico quadratum <emph type="italics"/>an<emph.end type="italics"/> e&longs;&longs;e ma&shy;<lb/>

gnitudinem motus mixti. </s>
            <s id="N132BD">Erit enim quadratum <emph type="italics"/>am,<emph.end type="italics"/><lb/>

hoc e&longs;t <emph type="italics"/>an,<emph.end type="italics"/> &aelig;quale duobus quadratis <emph type="italics"/>ad. dm,<emph.end type="italics"/> &longs;eu <emph type="italics"/>ae,<emph.end type="italics"/> cui <lb/>

&aelig;qualis &longs;umebatur <emph type="italics"/>dm.<emph.end type="italics"/> Lineam ergo motus mixti &amp; il&shy;<lb/>

lius magnitudinem determinauimus, quod erat facien&shy;<lb/>

dum. </s>
          </p>
        </subchap1>
        <subchap1 id="N132E5">
          <p id="N132E6" type="main">
            <s id="N132E8"><emph type="center"/>Propo&longs;itio XXXVI.<emph.end type="center"/></s>
          </p>
          <p id="N132EF" type="main">
            <s id="N132F1"><emph type="italics"/>Mobile &longs;eu impul&longs;u, &longs;eu &agrave; grauitate moueatur, &longs;i planum occur&shy;<lb/>

rat, reflectit ab eodem plano per lineam rectam.<emph.end type="italics"/></s>
          </p>
          <p id="N132FA" type="main">
            <s id="N132FC">IMpul&longs;us &longs;it dum corpus unum alteri in currit &amp; alli<lb/>

dit, &longs;iue <expan abbr="utrum&qacute;">utrumque</expan>, &longs;iue unum ex illis moueatur, <expan abbr="at&qacute;">atque</expan>; eo <lb/>

magis mouet &amp; impellit, qu&ograve; magis ferit &amp; allidit: &amp; <lb/>

&longs;iquidem re&longs;i&longs;tentia minor e&longs;t impul&longs;u, in illam partem <lb/>

mouet illud mobile, in quam &longs;it plaga, eundem motum 


<pb xlink:href="062/01/083.jpg"/>continuando; velocitate tamen e&oacute; minori, qu&oacute; re&longs;i&shy;<lb/>

&longs;tentia e&longs;t maj&ograve;r. </s>
            <s id="N13315">Qu&oacute;d &longs;i re&longs;i&longs;tentia &longs;it major impul&shy;<lb/>

&longs;u, e&aacute;dem velocitate, qu&agrave; impulit, in partem auer&longs;am re <lb/>

pellitur: propterea qu&oacute;d illa plaga &aelig;qualem in <expan abbr="utro&qacute;">utroque</expan>; <lb/>

mobili impul&longs;um producit. </s>
            <s id="N13322">E&longs;t autem major plaga ex <lb/>

velociori &amp; magis violento incur&longs;u: igitur ab &aelig;quali <lb/>

plag&aacute; &aelig;qualis <expan abbr="quo&qacute;">quoque</expan>; recur&longs;us. </s>
            <s id="N1332D">Et quia per motum fit <lb/>

plaga, mouetur autem mobile ad motum &longs;ui centri, erit <lb/>

<expan abbr="quoq;">quoque</expan> plaga ab eodem centro. </s>
            <s id="N13338">Sed &amp; re&longs;i&longs;tentia fit &acirc; cen<lb/>

tro &longs;eu grauitatis, &longs;eu contrarij impul&longs;us: eadem ergo ra<lb/>


<figure id="id.062.01.083.1.jpg" xlink:href="062/01/083/1.jpg"/><lb/>

tione minor re&longs;i&longs;tentia impul&longs;um recipit, qu&agrave; major ei&shy;<lb/>

dem re&longs;i&longs;tit. </s>
            <s id="N13348">Vt &longs;i mobile ex <emph type="italics"/>a<emph.end type="italics"/> moueatur &agrave; grauitate qui <lb/>

dem in <emph type="italics"/>b,<emph.end type="italics"/> ex impul&longs;u ver&ograve; in <emph type="italics"/>f<emph.end type="italics"/>aut <emph type="italics"/>c:<emph.end type="italics"/> &longs;it autem major re&longs;i&shy;


<pb xlink:href="062/01/084.jpg"/>&longs;tenti&agrave; in <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>f,<emph.end type="italics"/> quam ut loco moueantur ex illo impul&shy;<lb/>

&longs;u, minor autem in <emph type="italics"/>c<emph.end type="italics"/>: motus quidem ex <emph type="italics"/>b<emph.end type="italics"/> &amp; <emph type="italics"/>f<emph.end type="italics"/> in <emph type="italics"/>a<emph.end type="italics"/> refle&shy;<lb/>

ctit, ex <emph type="italics"/>c<emph.end type="italics"/> ver&ograve; expul&longs;o illo mobili quie&longs;cit, &longs;i &longs;it &aelig;quale: <lb/>

eundem ver&ograve; motum continuat in <emph type="italics"/>d,<emph.end type="italics"/> &longs;i minus &longs;it percu&longs;&shy;<lb/>

&longs;um: quia tamen re&longs;i&longs;tentia impul&longs;um minuit, qu&oacute; ma&shy;<lb/>

jor re&longs;i&longs;tentia, e&ograve; minor velocitas motus. </s>
          </p>
        </subchap1>
        <subchap1 id="N133A3">
          <p id="N133A4" type="main">
            <s id="N133A6"><emph type="center"/>Propo&longs;itio XXXVII.<emph.end type="center"/></s>
          </p>
          <p id="N133AD" type="main">
            <s id="N133AF"><emph type="italics"/>Motus in &longs;e ip&longs;um reflectit, c&ugrave;m centrum grauitatis &amp; conta&shy;<lb/>

ctus &longs;unt in e&aacute;dem line&aacute; motus.<emph.end type="italics"/></s>
          </p>
          <p id="N133B8" type="main">
            <s id="N133BA">GLobus <emph type="italics"/>a<emph.end type="italics"/> occurrat plano in <emph type="italics"/>b,<emph.end type="italics"/> <expan abbr="&longs;itq;">&longs;itque</expan> centrum grauita<lb/>

tis aut impul&longs;us <emph type="italics"/>e<emph.end type="italics"/> in line&agrave; motus <emph type="italics"/>ab<emph.end type="italics"/> perpendiculari<lb/> ad contactum <emph type="italics"/>b,<emph.end type="italics"/> dico hunc motum in &longs;e ip&longs;um reflecti. <lb/>

Quia enim motus &amp; huius plaga ad motum fit &longs;ui cen&shy;<lb/>

tri, erit motus globi <emph type="italics"/>a,<emph.end type="italics"/> &amp; hujus plaga in line&acirc; <emph type="italics"/>ab<emph.end type="italics"/> &agrave; centro <lb/>

<emph type="italics"/>e<emph.end type="italics"/> duct&agrave; per contactum: &amp; quia eadem ratione impul&shy;<lb/>

&longs;um recipit &amp; impellit, <expan abbr="e&longs;tq;">e&longs;tque</expan> major re&longs;i&longs;tentia in <emph type="italics"/>b<emph.end type="italics"/> quam <lb/>

impul&longs;us ex <emph type="italics"/>e,<emph.end type="italics"/> erit motus reflexus in eadem line&agrave; <emph type="italics"/>ab.<emph.end type="italics"/><lb/>

Motus ergo in &longs;e ip&longs;um reflectit, c&uacute;m centrum grauita<lb/>

tis &amp; contactus &longs;unt in eadem line&agrave; motus. </s>
            <s id="N13418">Obijcies <lb/>

c&ugrave;m pila percutit planum, e&agrave;dem vi percutitur ab illo <lb/>

plano: e&longs;t autem &agrave; percu&longs;sione &aelig;quali impul&longs;us &aelig;qua&shy;<lb/>

lis, qu&oacute; enim violenti&ugrave;s incidit, e&oacute; magis impetuos&eacute; re&longs;i&shy;<lb/>

rit ab ill&aacute; plag&agrave;: impul&longs;us ergo, quem pila recipit &acirc; pla-


<pb xlink:href="062/01/085.jpg"/>no, e&longs;t &aelig;qualis impul&longs;ui, quod idem plano allidit. </s>
            <s id="N13427">Quia <lb/>

ver&ograve; hi impul&longs;us tendunt in partes oppo&longs;itas eju&longs;dem <lb/>

line&aelig; rect&aelig;, erunt per definit: 4. contrarij ab&longs;olut&egrave;: tol&shy;<lb/>

lit autem contrarium &aelig;quale &longs;uum contrarium in e&agrave;&shy;<lb/>

dem ratione, totum quidem totum, pars ver&ograve; partem <lb/>

&longs;ibi &aelig;qualem; &longs;ublato ergo per contrarium &aelig;quale im&shy;<lb/>

pul&longs;u nullus erit motus reflexus, c&ugrave;m linea motus e&longs;t <lb/>

perpendicularis ad illud planum. </s>
            <s id="N13438">Qu&oacute;d &longs;i &agrave; percu&longs;sio&shy;<lb/>

ne in plano, aut globo quie&longs;cente fact&aacute; morus reflectit, <lb/>

quid prohibet ab eodem plano, aut globo, &longs;i motu op&shy;<lb/>

po&longs;ito ferantur, &amp; violenti&agrave; &aelig;quali &longs;ibi occurant, &agrave; per&shy;<lb/>

cu&longs;sione &aelig;quali eundem motum reflecti? Vt in hac ob&shy;<lb/>


<arrow.to.target n="marg1"/><lb/>

&longs;curitate aliquam lucem con&longs;equamur, qu&aelig; non ni&longs;i ex <lb/>

natur&agrave; impul&longs;us pri&uacute;s cognit&aacute; eluce&longs;cit, de qu&acirc; in lib: de <lb/>

Arcu C&aelig;le&longs;ti lati&ugrave;s di&longs;&longs;eremus, <expan abbr="not&atilde;dum">notandum</expan> hic breuiter 1. <lb/>


<arrow.to.target n="marg2"/><lb/>

Impul&longs;um fieri &agrave; percu&longs;sione juxta determinationem il&shy;<lb/>

lius plag&aelig;, <expan abbr="qu&atilde;">quam</expan> centrum inducit percutientis, &amp; quam <lb/>

centrum recipit percu&longs;si; partes enim mobilis impul&shy;<lb/>


<arrow.to.target n="marg3"/><lb/>

&longs;um recipiunt per lineas motui centri parallelas. 2. <expan abbr="H&atilde;c">Hanc</expan> <lb/>

plagam, qu&aelig; fit &agrave; corpore percu&longs;&longs;o, aliter dum quie&longs;cit, <lb/>

aliter dum e&longs;t in motu impul&longs;um determinare: quia <lb/>

enim plaga ex impul&longs;u, percu&longs;&longs;um ver&ograve; quie&longs;cens nul&shy;<lb/>

lum ex &longs;e habet impul&longs;um, ver&ugrave;m &agrave; percutiente; e&aacute;dem <lb/>

plaga, qu&agrave; percutitur, impul&longs;um determinat in percuti<lb/>

ente: ab &aelig;quali ergo plag&agrave; &aelig;qualis impul&longs;us. </s>
            <s id="N13478">Cum au&shy;


<pb xlink:href="062/01/086.jpg"/>tem percutitur in motu, quia ex &longs;e impul&longs;um habet, <expan abbr="n&otilde;">non</expan> ex <lb/>

ill&agrave; plag&agrave;, quam recipit &agrave; percutiente, &longs;ed quam infert <lb/>

impul&longs;um determinat; licet ergo illorum corporum, <lb/>

qu&aelig; violenti&aacute; in&aelig;quali colliduntur, idem &longs;it contactus, <lb/>

non tamen eadem ab <expan abbr="utro&qacute;">utroque</expan>, ver&ugrave;m &acirc; majori major, &agrave; <lb/>


<arrow.to.target n="marg4"/><lb/>

minori impul&longs;u minor infertur plaga. </s>
            <s id="N13496">3. Corpora per&shy;<lb/>

cu&longs;&longs;a alia e&longs;&longs;e mollia, quorum partes percu&longs;sioni <expan abbr="ced&utilde;t">cedunt</expan>, <lb/>

inter &longs;e ver&ograve; unit&aelig; <expan abbr="man&etilde;t">manent</expan>; cuju&longs;modi argilla, cera, lana, <lb/>

plumbum, &amp;c. </s>
            <s id="N134A7">Alia dura; &amp; &longs;iquidem percu&longs;sioni nul&shy;<lb/>

lo modo cedunt, ab&longs;olut&egrave; dura; &longs;i autem percu&longs;sioni ce<lb/>

dunt, <expan abbr="ne&qacute;">neque</expan>; partes inter &longs;e unit&aelig; manent, fragilia dicun&shy;<lb/>

tur; ut vitrum, te&longs;ta, tophus, &amp;c. </s>
            <s id="N134B4">Corpora demum ab&longs;o&shy;<lb/>

lut&egrave; dura alia &longs;unt &longs;onora, quorum atomi vibratione <lb/>

quadam mouentur, ut propo: 1. dictum; alia &longs;urda, quo <lb/>


<arrow.to.target n="marg5"/><lb/>

rum atomi nullo aut in&longs;en&longs;ibili motu monentur. 4 <lb/>

Impul&longs;um natur&agrave; &longs;u&agrave; inclinare ad motum perfectum, <lb/>

quo mobile &longs;ecund&uacute;m &longs;e totum locum mutat. </s>
            <s id="N134C6">Qu&ograve;d <lb/>

&longs;i ergo impul&longs;us, quem plaga inducit, proportionem <lb/>

habeat ad illud mobile, eodem quo percutiens motu fe&shy;<lb/>

retur: &longs;i autem minor &longs;it impul&longs;us quam ut loco moue&shy;<lb/>

atur, habeat vor&ograve; idem mobile partes fragiles, aut in &longs;e <lb/>

cedentes, percutiens percu&longs;&longs;um perforabit, aut excaua&shy;<lb/>

bit; it a nimirum &longs;i major &longs;it &longs;oliditas percu&longs;si, quam ut <lb/>

impetus per omnes partes eluctetur, qui non prius iram <lb/>

ponit, quam continuat&agrave; illarum partium, cuas perrum&shy;


<pb xlink:href="062/01/087.jpg"/>pit, vel collidit, re&longs;i&longs;tentia vires ab&longs;umat. </s>
            <s id="N134DD">Ex huju&longs;mo&shy;<lb/>

di ergo corporibus nullo modo reflectit motus, ni&longs;i in <lb/>

progre&longs;&longs;u, pri&uacute;&longs;quam exoluatur, occurrant partes magis <lb/>

&longs;olid&aelig;: ita enim pila ubi calcem dera&longs;it &agrave;muro, ex oc&shy;<lb/>

cur&longs;u &longs;axi reflectit: quod non &longs;it &longs;i vi&aacute;, qu&agrave; irrupit &aacute; fi&longs;&shy;<lb/>

&longs;ur&agrave; rur&longs;um co&euml;at, quemadmodum in ligno viridi, cu&shy;<lb/>

jus vulnus ex partium fi&longs;&longs;arum coalitu mox &longs;olidatur. <lb/>

Corpora autem dura ab&longs;olut&eacute; quia <expan abbr="ne&qacute;">neque</expan>; perforantur, <lb/>

<expan abbr="ne&qacute;">neque</expan>; partes habent percu&longs;sioni cedentes, &aelig;qualem reci&shy;<lb/>

piunt <expan abbr="at&qacute;">atque</expan>; inferunt plagam, morum ver&ograve; ex ill&agrave; plag&acirc; re <lb/>

flectunt, <expan abbr="at&qacute;">atque</expan>; e&oacute; magis, qu&oacute; duritie magis pr&aelig;&longs;tant. </s>
            <s id="N13504">In&shy;<lb/>

de erg&ograve; fit qu&oacute;d vala vitrea aut cry&longs;tallina in&aelig;qualiter <lb/>

colliduntur, pro ut illa corpora, ad qu&aelig; offendunt, per&shy;<lb/>

cu&longs;sioni magis aut min&uacute;s cedunt: quia nimirum non <lb/>ex ill&agrave;, quam inferunt, &longs;ed ex ill&acirc;, quam recipiunt, plaga <lb/>

colliduntur. 5. </s>
            <s id="N13511">Impul&longs;um fieri per lineam rectam: &amp; &longs;i&shy;<lb/>


<arrow.to.target n="marg6"/><lb/>

cuti grauitas min&uacute;s mouet, qu&oacute; magis linea motus ad <lb/>

horizontem e&longs;t inclinata, quie&longs;cit ver&ograve; &agrave; motu in line&agrave; <lb/>

eidem parallel&aacute;s ita impul&longs;um ex inclinatione motus <lb/>

&longs;en&longs;im minui, &amp; demum in hypomochlio deficere. <lb/>

Qu&ograve;d &longs;i ergo mobile occurrat plano, it a ut contactus <lb/>

&longs;it in line&aacute; motus eiu&longs;dem centri, quia centrum hypo&shy;<lb/>

mochlio occurrit, totus ex ill&agrave; plag&agrave; emoritur impul&shy;<lb/>

&longs;us; propterea qu&ograve;d motui quies non min&ugrave;s e&longs;t contra<lb/>

ria, quam motus: at ver&ograve; &longs;i planum &longs;it inclinatum, in il&shy;


<pb xlink:href="062/01/088.jpg"/>l&agrave; tantum parte, qu&aelig; hypomochlio occurrit, motus <expan abbr="c&otilde;-quie&longs;cit">con&shy;<lb/>

quie&longs;cit</expan>, reliqu&agrave; parte, qu&aelig; cum centro extra hypomo&shy;<lb/>

chlium cadit, nihil impedit&agrave;: impul&longs;us ergo pil&aelig;, c&uacute;m <lb/>

motus centri e&longs;t perpendicularis ad planum, ubi percu&longs;&shy;<lb/>

&longs;it in hypomochlio &acirc; motu conquie&longs;cit: at vero <expan abbr="plan&utilde;">planum</expan> <lb/>

ex ill&agrave; plag&agrave; in percutiente nouum determinat impul&shy;<lb/>

&longs;um, juxta directionem plag&aelig;, quam infert; &agrave; quo <expan abbr="ead&etilde;">eadem</expan>, <lb/>

qu&agrave; venit, vi&agrave; retroagitur: &amp; &longs;iquidem duritie pr&aelig;&longs;tat, <lb/>

erit plaga &amp; qui hanc &longs;equitur impul&longs;us in <expan abbr="utro&qacute;">utroque</expan>; &aelig;qua&shy;<lb/>

lis, ac proinde motus reflexus &aelig;qualis motui recto: de&shy;<lb/>

ficiet autem motus reflexus &acirc; motu recto, &longs;i defectu du&shy;<lb/>

ritiei minorem recipiat, quam dedit plagam. </s>
            <s id="N13555">Qu&oacute;d &longs;i <lb/>

ergo duo globi violenti&aacute; &aelig;quali &longs;ibi occurrant, <expan abbr="&longs;it&qacute;">&longs;itque</expan>; mo&shy;<lb/>

tus centri <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>; in e&aacute;dem line&agrave; rect&agrave;; quia tum <expan abbr="uterq;">uterque</expan> <lb/>

alteri, non min&uacute;s quam planum, e&longs;t hypomochlij loco, <lb/>

ab ill&acirc; communi plag&agrave; in <expan abbr="utro&qacute;">utroque</expan>, emoritur, nouus ver&ograve; <lb/>

quo retro aguntur, impul&longs;us regeneratur. </s>
            <s id="N13572">Licet ver&ograve; <lb/>

po&longs;it: 2. inficiamur eju&longs;modi globos &longs;ibi occurrentes re<lb/>

&longs;ilire, id tamen exempli gratia ad naturam contrarij ma&shy;<lb/>

gis explicandam, &amp; ex &longs;uppo&longs;itione, &longs;i nimirum impul&shy;<lb/>

&longs;us ei ratione mi&longs;ceantur, &agrave; nobis dictum fuit: at ver&ograve; hi <lb/>

impul&longs;us non mi&longs;centur, ver&ugrave;m uni abolito alius &longs;uc&shy;<lb/>

cedit. </s>
            <s id="N13581">Qu&oacute;d &longs;i ver&ograve; <expan abbr="uter&qacute;">uterque</expan>; globus in motu percutiat vi&shy;<lb/>

olenti&agrave; in&aelig; quali, impul&longs;us quidem minoris, ubi percu&longs;&shy;<lb/>

&longs;it majus, ob hypomochlium &agrave; motu conquie&longs;cit, im&shy;


<pb xlink:href="062/01/089.jpg"/>pul&longs;um ver&ograve; &longs;ibi &longs;imilem &amp; &aelig;qualem producit, &longs;eu de&shy;<lb/>

terminat in majori ex illa, quam infert, plag&agrave;, hoc e&longs;t <lb/>

partem tollit &agrave; majori &longs;ibi &aelig;qualem. </s>
            <s id="N13594">At ver&ograve; majus, ubi <lb/>

percu&longs;sit, non videtur conquie&longs;cere &acirc; motu, propterea <lb/>

qu&ograve;d minus non habeat rationem hypomochlij ad ma <lb/>

jus, impul&longs;um ver&ograve; in minori producit &longs;ibi &aelig;qualem; ut <lb/>

&longs;i minor impul&longs;us ut 3. major ut 7. minor quidem &agrave; ma&shy;<lb/>

jori tollit partem &longs;ibi &aelig;qualem ide&longs;t 3. &amp; &longs;imul ob con&shy;<lb/>

trariam in hypomochlio quietem ex&longs;pirat; majus ver&ograve; <lb/>

quia tota vi percutit minus, impul&longs;um ut 7. producit ex <lb/>

ill&agrave; plag&agrave;, motum autem &agrave; percu&longs;sione non ni&longs;i partes 4. <lb/>

reliqu&aelig; perficiunt. <expan abbr="Ita&qacute;">Itaque</expan>; fit ut ex ill&agrave; in &aelig;quali plag&agrave;, ve <lb/>

locitate ferantur in&aelig;quali, minori quidem majus ob vi&shy;<lb/>

res &agrave; percu&longs;sione accitas &amp; mutilatas, majori ver&ograve; mi&shy;<lb/>

nus ob ea&longs;dem vires de integro acqui&longs;itas. </s>
            <s id="N135B3">Dices inter&shy;<lb/>

dum fieri ut in&aelig;quali violenti&agrave; &longs;ibi occurrant duo glo&shy;<lb/>

bi, &amp; tamen <expan abbr="uter&qacute;">uterque</expan>; re&longs;iliat. </s>
            <s id="N135BE">Re&longs;pondeo &longs;i contactus fi <lb/>

at in line&agrave; motus centri, videtur non po&longs;&longs;e fieri ut major <lb/>

re&longs;iliat, propterea, qu&oacute;d major violentia non detinetur <lb/>

&agrave; minori: at ver&oacute; &longs;i ex obliquo &longs;e percutiant, fieri po&longs;&longs;e <lb/>

ut etiam ille globus, qui magis percu&longs;sit, re&longs;iliat, aut in <lb/>

codem, quo percu&longs;sit, loco con&longs;i&longs;tat. </s>
            <s id="N135CB">In&longs;tabis hanc &longs;o&shy;<lb/>

lutionem non <expan abbr="u&longs;q;">u&longs;que</expan> <expan abbr="quaq;">quaque</expan> experienti&aelig; con&longs;onare: nam <lb/>

<expan abbr="quomodocunq;">quomodocunque</expan> duo globi inter &longs;e commicantur, <expan abbr="atq;">atque</expan> <lb/>

ade&ograve; in line&agrave; motus centri &longs;e percutiant violenti&acirc; in&shy;


<pb xlink:href="062/01/090.jpg"/>&aelig;quali, <expan abbr="uter&qacute;">uterque</expan> re&longs;ilit ab ill&agrave; plag&agrave;, magis quidem qui mi&shy;<lb/>

nus, min&ugrave;s ver&ograve; qui magis percu&longs;sit: non igitur exce&longs;&shy;<lb/>

&longs;us majoris e&longs;t principium morus reliqui &agrave; contactu. <lb/>

Vt objectioni &amp; experienti&aelig; &longs;atis fiat, dicendum &agrave; quo&shy;<lb/>

libet contactu impul&longs;um deficere &amp; ex&longs;pirare, nouum <lb/>

ver&ograve; &agrave; percu&longs;sione determinari, qui motu eidem plag&aelig; <lb/>

&aelig;quali retroagit illud mobile. </s>
            <s id="N135F8">C&ugrave;m enim impul&longs;us &acirc; <lb/>

percu&longs;sione fiat, juxta determinationem plag&aelig;, quam <lb/>

recipit &agrave; percutiente, nihil mirum &longs;i &acirc; determinatione <lb/>

nou&acirc; nouum impul&longs;um <expan abbr="c&otilde;&longs;equatur">con&longs;equatur</expan>: quomodo in acu <lb/>

nautic&agrave; fieri videmus, qu&aelig; quoties oppo&longs;itum polum <lb/>

tangit, directionem, qu&agrave; eidem polo &longs;e obuertit, &longs;orti&shy;<lb/>

tur nouam. </s>
            <s id="N1360B">Quod min&ugrave;s difficulter admittes, &longs;i per&shy;<lb/>

pendas qu&aacute; ratione va&longs;t&aelig; campan&aelig; ingens mugitus, &amp; <lb/>

qui hunc &longs;u&aacute; vibratione fouet in gyrum actus impul&longs;us <lb/>

ex leui&longs;simo tactu repente contice&longs;cat: quid ergo mi&shy;<lb/>

rum ex tactu pil&aelig; haud paulo majoris impul&longs;um cohi&shy;<lb/>

beri? In&longs;tabis an igitur globus ligneus, &longs;i ex oppo&longs;ito <lb/>

quantumuis motu lento moueatur, repercutiet pilam <lb/>

ferream <expan abbr="quacun&qacute;">quacunque</expan>; violenti&aacute; irruentem? Ad pleniorem <lb/>

hujus <expan abbr="at&qacute;">atque</expan>; aliarum obiectionum &longs;olutionem, notandum <lb/>

prim&ograve;: ut mobile moueatur, non &longs;ufficere quemlibet <lb/>

impul&longs;um, &longs;ed proportionatum illi mobili: impul&longs;us e&shy;<lb/>

nim, quo globus ligneus ad motum concitatur, haud <lb/>quaquam loco mouebit pilam ferream ejusdem molis <pb xlink:href="062/01/091.jpg"/>aut maiorem: at ver&ograve; &longs;i huius impul&longs;u moueatur glo&shy;<lb/>

bus ligneus, motu agit abitur mult&ograve; velociore. </s>
            <s id="N13634">Secund&ograve;: <lb/>


<arrow.to.target n="marg7"/><lb/>

hanc proportionem motus &amp; impul&longs;us non &aacute; mole, &longs;ed <lb/>

&aacute; grauitate illorum corporum determinari: <expan abbr="ita&qacute;">itaque</expan>; glo&shy;<lb/>

bus ligneus major, &amp; glans plumbea minor, &longs;i &aelig;quipon&shy;<lb/>

derant, ab impul&longs;u &aelig;quali &aelig;quali velocitate mouentur <lb/>

Simili modo &longs;i eandem rationem habeant impul&longs;us <lb/>

quam habent pondera, erit velocitas motus &aelig;qualis&apos; <lb/>

Terti&oacute; percu&longs;sionem &amp; qu&aelig; hanc &longs;equitur plagam non <lb/>


<arrow.to.target n="marg8"/><lb/>

uno in&longs;tanti, &longs;ed in aliquo tempore quantumuis imper&shy;<lb/>

ceptibili perfici: c&ugrave;m enim plaga proueniat non ex &longs;olo <lb/>

contactu, &longs;ed ex irruptione violent&aacute;, qu&aacute; veluti pene&shy;<lb/>

trat percutiens percu&longs;&longs;um, non e&longs;&longs;e pote&longs;t <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; motu; <lb/>

c&ugrave;m ergo percutiens tangit, necdum e&longs;t plaga, &longs;ed fit; <lb/>

cujus &longs;ignum fragor &acirc; percu&longs;sione non ni&longs;i in tempore <lb/>

proueniens. </s>
            <s id="N13665">Sicuti ergo plaga &longs;ua habet incrementa, ita <lb/>

determinatio impul&longs;us: &amp; &longs;i quod mobile non totam <lb/>

plagam recipit, deficiet <expan abbr="quo&qacute;">quoque</expan>; in eadem ratione impul&shy;<lb/>

&longs;us. </s>
            <s id="N13672">Quart&oacute;: impul&longs;um ex&longs;pirare ubi totam perfecit <lb/>


<arrow.to.target n="marg9"/><lb/>

plagam, partem ver&ograve; non ni&longs;i cum parte emori: re&longs;idu&shy;<lb/>

um ergo plag&aelig; &longs;eu impul&longs;us, &longs;i nihil e&longs;t quod recipiat il&shy;<lb/>

lam plagam, erit principium motus &aacute; percu&longs;sione con&shy;<lb/>

tinuati. </s>
            <s id="N13682">His &longs;uppo&longs;itis, ita rem tran&longs;igemus &longs;it ergo. </s>
          </p>
          <p id="N13685" type="margin">
            <s id="N13687"><margin.target id="marg1"/><emph type="italics"/>R<gap/><emph.end type="italics"/></s>
          </p>
          <p id="N13691" type="margin">
            <s id="N13693"><margin.target id="marg2"/><emph type="italics"/>No <lb/>

1.<emph.end type="italics"/></s>
          </p>
          <p id="N1369E" type="margin">
            <s id="N136A0"><margin.target id="marg3"/><emph type="italics"/>2.<emph.end type="italics"/></s>
          </p>
          <p id="N136A9" type="margin">
            <s id="N136AB"><margin.target id="marg4"/><emph type="italics"/>3<emph.end type="italics"/></s>
          </p>
          <p id="N136B4" type="margin">
            <s id="N136B6"><margin.target id="marg5"/><emph type="italics"/>4<emph.end type="italics"/></s>
          </p>
          <p id="N136BF" type="margin">
            <s id="N136C1"><margin.target id="marg6"/><emph type="italics"/>5<emph.end type="italics"/></s>
          </p>
          <p id="N136CA" type="margin">
            <s id="N136CC"><margin.target id="marg7"/>2</s>
          </p>
          <p id="N136D1" type="margin">
            <s id="N136D3"><margin.target id="marg8"/>3</s>
          </p>
          <p id="N136D8" type="margin">
            <s id="N136DA"><margin.target id="marg9"/>4</s>
          </p>
          <p id="N136DF" type="main">
            <s id="N136E1"><emph type="center"/><emph type="italics"/>Pori&longs;ma I.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <pb xlink:href="062/01/092.jpg"/>
          <p id="N136EF" type="main">
            <s id="N136F1"><emph type="italics"/>Si globus alium globum percutiat quie&longs;centem &amp; &aelig;qualem, illo <lb/>

expul&longs;o quie&longs;cit.<emph.end type="italics"/></s>
          </p>
          <p id="N136FA" type="main">
            <s id="N136FC">VT &longs;i duo globi lignei inter &longs;e &longs;int &aelig;quales, aut cum a&shy;<lb/>

lio quouis globo eju&longs;dem ponderis, <expan abbr="at&qacute;">atque</expan>; hic illum <lb/>

percutiat quie&longs;centem; quia impul&longs;us percutientis ad <lb/>

<expan abbr="utrum&qacute;">utrumque</expan>; globum eandem habet rationem ex notabili <lb/>

2. &aelig;qualis autem impul&longs;us non ni&longs;i &aacute; plag&aacute; &longs;it perfect&acirc;, e&shy;<lb/>

rit velocitas in percu&longs;&longs;o non ante illam plagam: non er&shy;<lb/>

go incipiente plag&aacute; pr&aelig;curret <expan abbr="&longs;e&qacute;">&longs;eque</expan>, auellet &agrave; <expan abbr="percuti&etilde;te">percutiente</expan>, <lb/>

&longs;ed plag&agrave; demum perfect&agrave; illam velocitatem con&longs;ecu&shy;<lb/>

tus. </s>
            <s id="N1371F">Et quia ex notabili 4. impul&longs;us, ubi plagam perfe&shy;<lb/>

cit, ex&longs;pirat; nullam ver&ograve; plagam inducit globus q&ugrave;ie&shy;<lb/>

&longs;cens, propterea qu&oacute;d <expan abbr="ne&qacute;">neque</expan>; irruptio violenta &longs;eu pene&shy;<lb/>

tratio fiat ab illo globo, qui e&agrave;dem velocitate, qu&agrave; percu<lb/>

titur, &longs;e abducit; quie&longs;cet globus percutiens ab illa, <lb/>

quam fecit, plag&agrave;. </s>
          </p>
          <p id="N13730" type="main">
            <s id="N13732"><emph type="center"/><emph type="italics"/>Pori&longs;ma II.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N1373D" type="main">
            <s id="N1373F"><emph type="italics"/>Si globus major percutiat minorem quie&longs;centem, minori expul&longs;o <lb/>

eundem motum continuat major.<emph.end type="italics"/></s>
          </p>
          <p id="N13748" type="main">
            <s id="N1374A">QVia enim minus pondus &aelig;quali celeritate mouetur <lb/>

a minori impul&longs;u; illam velocitatem motus qua <lb/>

pr&aelig;currit <expan abbr="&longs;e&qacute;">&longs;eque</expan>; auellit &agrave; percutiente, &agrave; minori plag&acirc; con&shy;


<pb xlink:href="062/01/093.jpg"/>&longs;equetur, quam ut totum impul&longs;um producat. </s>
            <s id="N13759">Et quia<lb/> impul&longs;us non ni&longs;i &agrave; plag&agrave; emoritur; impul&longs;us reliquus, <lb/>

qui nec dum percu&longs;sit, eundem motum continuabit. <lb/>

Habeat enim pondus <emph type="italics"/>de<emph.end type="italics"/> ad pondus <emph type="italics"/>fg<emph.end type="italics"/> eandem <expan abbr="ration&etilde;">rationem</expan>, <lb/>

quam habet impul&longs;us maioris <emph type="italics"/>ac<emph.end type="italics"/> ad impul&longs;um minoris <lb/>


<figure id="id.062.01.093.1.jpg" xlink:href="062/01/093/1.jpg"/><lb/>

<emph type="italics"/>ab,<emph.end type="italics"/> <expan abbr="percutiat&qacute;">percutiatque</expan>; <emph type="italics"/>de<emph.end type="italics"/> ip&longs;um <emph type="italics"/>fg<emph.end type="italics"/>: quia ergo plag&agrave; non ni&longs;i in <lb/>

aliquo tempore fit, &amp; &longs;icuti plaga, ita <expan abbr="quo&qacute;">quoque</expan>; impul&longs;us <lb/>

&longs;ua habet incrementa, erit impul&longs;us <emph type="italics"/>ab<emph.end type="italics"/> prior impul&longs;u <emph type="italics"/>ac.<emph.end type="italics"/><lb/>

e&longs;t autem <emph type="italics"/>ac<emph.end type="italics"/> ad <emph type="italics"/>al,<emph.end type="italics"/> ut <emph type="italics"/>de<emph.end type="italics"/> ad <emph type="italics"/>fg<emph.end type="italics"/>: &amp; permutando <emph type="italics"/>ac<emph.end type="italics"/> ad <emph type="italics"/>de,<emph.end type="italics"/><lb/>

ut <emph type="italics"/>ab<emph.end type="italics"/> ad <emph type="italics"/>fg<emph.end type="italics"/>; eadem erg&ograve; velocitas in <expan abbr="utro&qacute;">utroque</expan>;. </s>
            <s id="N137E3">Et quia e&aacute;&shy;<lb/>

dem velocitate mouentur, nulla &agrave; contactu erit plaga. <lb/>

Ita ergo pila ferrea dum murum percutit, quia minori <lb/>

impul&longs;u, ad motum concitantur partes in muro percu&longs;&shy;<lb/>

&longs;&aelig;, illam velocitatem motus, qu&acirc; pila ferrea mouetur, <lb/>

ab incipiente &amp; necdum perfect&agrave; plag&agrave; con&longs;equuntur: <lb/>

impul&longs;&aelig; ergo motum pil&aelig; anteuertunt, <expan abbr="&longs;uo&qacute;">&longs;uoque</expan>; impetu a&shy;<lb/>

liis in&longs;tant: &amp; &longs;icubi major vis ob&longs;tat, pila &agrave; tergo h&aelig;&shy;<lb/>

rentes nouo impul&longs;u urget, <expan abbr="quou&longs;&qacute;">quou&longs;que</expan>; ill&agrave; percu&longs;sione <expan abbr="c&otilde;">con</expan><lb/>

tinuat&agrave; totum impul&longs;um plaga hauriat &amp; ab&longs;umat <lb/>

Qu&oacute;d &longs;i major &longs;it impul&longs;us, quam ut &aelig;qualis &longs;it illi pla&shy;<lb/>

g&aelig;, qu&agrave; murum perforat, motum &agrave; ruptur&acirc; continuat li&shy;<lb/>

li exce&longs;&longs;ui &aelig;qualem. </s>
          </p>
          <pb xlink:href="062/01/094.jpg"/>
          <p id="N1380C" type="main">
            <s id="N1380E"><emph type="center"/><emph type="italics"/>Pori&longs;ma III.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N13819" type="main">
            <s id="N1381B"><emph type="italics"/>Si globus minor percutiat majorem quie&longs;centem, habeat ver&ograve; <lb/>

minorem rationem ad &longs;uum impul&longs;um, quam ad globum majorem, <lb/>

expul&longs;o majori minor quie&longs;cit aut reflectit.<emph.end type="italics"/></s>
          </p>
          <p id="N13826" type="main">
            <s id="N13828">HAbeat globus <emph type="italics"/>a<emph.end type="italics"/> maior ad minorem <emph type="italics"/>b<emph.end type="italics"/> rationem du&shy;<lb/>

plam, ide&longs;t grauitas &longs;eu pondus majoris &longs;it duplum <lb/>

ponderis minoris; impul&longs;us autem minoris ad eju&longs;dem <lb/>

grauitatem in ratione majori quam dupla. </s>
            <s id="N1383D">Quia ergo <lb/>

grauitas &amp; impul&longs;us inter &longs;e &longs;unt contraria, erit motus <lb/>

&aelig;qualis exce&longs;&longs;ui maioris; e&longs;t autem impul&longs;us minoris <lb/>

maior grauitate maioris, propterea qu&oacute;d ad grauitatem <lb/>

minoris maiorem habeat rationem; erit ergo huius ex&shy;<lb/>

ce&longs;&longs;us principium motus maiori. </s>
            <s id="N1384A">Igitur &longs;i globus mi&shy;<lb/>

nor percutiat maiorem, quia ab &aelig;quali impul&longs;u minor <lb/>

e&longs;t velocitas motus, non ante perfectam plagam auelli <lb/>

pote&longs;t &agrave; percutiente: &amp; quia &agrave; plag&agrave; perfect&acirc; emoritur <lb/>

impul&longs;us, minori autem velocitate maior &longs;e abducit ab <lb/>

ill&agrave; plag&agrave;, qu&agrave;m irruptio fiat minoris; repercutiet ma<lb/>

ior minorem, <expan abbr="erit&qacute;">eritque</expan>; huius plaga ad men&longs;uram illius tar&shy;<lb/>

ditatis. </s>
            <s id="N1385F">Globus ergo minor, ubi percu&longs;sit maiorem, illo <lb/>

expul&longs;o reflectit. </s>
            <s id="N13864">Qu&ograve;d &longs;i ob motum velociorem null&agrave; <lb/>

&agrave; percu&longs;&longs;o inducitur plaga, minor expul&longs;o maiori qui&shy;<lb/>

e&longs;cit. </s>
          </p>
          <pb xlink:href="062/01/095.jpg"/>
          <p id="N1386E" type="main">
            <s id="N13870"><emph type="center"/><emph type="italics"/>Pori&longs;ma IV.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N1387B" type="main">
            <s id="N1387D"><emph type="italics"/>Si globus minor percutiat majorem quie&longs;centem, habeat ver&ograve; <lb/>

majorem rationem ad &longs;uum impul&longs;um, quam ad globum majorem, <lb/>

illo immoto reflectit minor.<emph.end type="italics"/></s>
          </p>
          <p id="N13888" type="main">
            <s id="N1388A">VT &longs;i impul&longs;us, quo minor globus mouetur, ad illius <lb/>

grauitatem &longs;it in ratione dupl&agrave;; globus ver&oacute; major <lb/>

ad minorem rationem habeat maiorem quam duplam, <lb/>

erit impul&longs;us minoris minor grauitate maioris; non er&shy;<lb/>

g&ograve; <expan abbr="ill&atilde;">illam</expan> mouere valebit, propterea qu&oacute;d motus ab exce&longs;&shy;<lb/>

&longs;u fiat maioris. </s>
            <s id="N1389B">Qu&oacute;d &longs;i ergo minor globus percutiat <lb/>

maiorem, quia ex ill&agrave; plag&agrave; minor e&longs;t impul&longs;us, quam ut <lb/>

loco moueat; globus quidem maior &agrave; percu&longs;sione qui <lb/>

e&longs;cit, minor ver&ograve; quia &agrave; percu&longs;&longs;o quie&longs;cente nouam &amp; <lb/>

&aelig;qualem illi, quam dedit, plagam recipit, motum refle&shy;<lb/>

ctit. </s>
            <s id="N138A8">Ex iam definitis di&longs;&longs;oluemus &amp; hoc </s>
          </p>
          <p id="N138AB" type="main">
            <s id="N138AD"><emph type="center"/><emph type="italics"/>Problema I.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N138B8" type="main">
            <s id="N138BA"><emph type="italics"/>Globum in plano quie&longs;centem percutere alio globo <expan abbr="quacun&qacute;">quacunque</expan> vi&shy;<lb/>

olenti&agrave;, <expan abbr="ne&qacute;">neque</expan>; tamen loco mouere.<emph.end type="italics"/></s>
          </p>
          <p id="N138CB" type="main">
            <s id="N138CD">AS&longs;umatur globus <emph type="italics"/>a<emph.end type="italics"/> <expan abbr="cuiu&longs;cunq;">cuiu&longs;cunque</expan> molis &amp; ponderis, eius <lb/>

tamen firmitatis, qu&ograve; totum impetum &longs;ufferre vale&shy;<lb/>

at, <expan abbr="ne&qacute;">neque</expan>; di&longs;siliat ex illo ictu: <expan abbr="con&longs;tituatur&qacute;">con&longs;tituaturque</expan>; in plano <emph type="italics"/>AB<emph.end type="italics"/>


<pb xlink:href="062/01/096.jpg"/>liber&egrave;, &amp; <expan abbr="ab&longs;q;">ab&longs;que</expan> ullo nexu: <expan abbr="qu&etilde;">quem</expan> percuti volumus ab alio <lb/>

globo, &aelig;quali tamen aut minori, <expan abbr="quac&utilde;&qacute;">quacunque</expan> violentia, <expan abbr="at&qacute;">atque</expan>; <lb/>

ade&ograve; &agrave; machin&agrave; bellic&agrave; effulminato, <expan abbr="ne&qacute;">neque</expan>; tamen &longs;uo lo&shy;<lb/>

co moueri. quod quidem nullis machinis, aut retinacu&shy;<lb/>

lis, &longs;ed duntaxat unius globi appo&longs;itione con&longs;eque&shy;<lb/>


<figure id="id.062.01.096.1.jpg" xlink:href="062/01/096/1.jpg"/><lb/>

mur, qui iram illius fulminis &agrave; globo percu&longs;&longs;o hauriat &amp; <lb/>

ab&longs;umat. </s>
            <s id="N13917">Appone ergo &agrave; tergo alium globum illi &aelig;qua<lb/>

lem <emph type="italics"/>b,<emph.end type="italics"/> &amp; &longs;it linea motus pil&aelig; ad utrum <expan abbr="&qacute;">que</expan> globum perpen<lb/>

dicularis; dico globum <emph type="italics"/>a<emph.end type="italics"/> nulla ratione loco moueri a <lb/>

globo <emph type="italics"/>d.<emph.end type="italics"/> Quia enim globus <emph type="italics"/>a<emph.end type="italics"/> eodem momento, quo <lb/>

percutitur &agrave; globo <emph type="italics"/>d,<emph.end type="italics"/> percutit globum <emph type="italics"/>b<emph.end type="italics"/> &longs;ibi &aelig;qualem, <lb/>

inducet ill&agrave; percu&longs;sione plagam perfectam, ac proinde 


<pb xlink:href="062/01/097.jpg"/>per Pori&longs;: 1. &acirc; percu&longs;sione quie&longs;cet. </s>
            <s id="N13950">Qu&ograve;d &longs;i plures glo&shy;<lb/>

bi &aelig;quales &longs;e <expan abbr="conting&atilde;t">contingant</expan> in line&agrave; motus centri, ut <emph type="italics"/>f.g.h.i,<emph.end type="italics"/><lb/>

percu&longs;&longs;o <emph type="italics"/>f<emph.end type="italics"/> primo ab &aelig;quali <emph type="italics"/>e,<emph.end type="italics"/> ultimus <emph type="italics"/>i<emph.end type="italics"/> mouetur, reliquis <lb/>

<emph type="italics"/>f.g.h<emph.end type="italics"/> immotis; propterea qu&oacute;d per Pori&longs;. <emph type="italics"/>1.<emph.end type="italics"/> po&longs;terior <lb/>

prioris exhaurit plagam. </s>
            <s id="N13982">t ver&ograve; &longs;i unus &aelig;qualium po&longs;t <lb/>

fe habeat minores <expan abbr="quotcun&qacute;">quotcunque</expan>; ut <emph type="italics"/>o.p.q.<emph.end type="italics"/> percu&longs;&longs;o &agrave; <emph type="italics"/>k<emph.end type="italics"/> &aelig;qua&shy;<lb/>

li <emph type="italics"/>l,<emph.end type="italics"/> omnes cum <emph type="italics"/>l<emph.end type="italics"/> moto mouentur, ut con&longs;tat per Pori&longs;.2. <lb/>

Qu&ograve;d &longs;i demum percu&longs;sio incipiat &agrave; minori <emph type="italics"/>q<emph.end type="italics"/> ug: omni&shy;<lb/>

bus immotis aut reflexis ultimus mouetur, per Pori&longs;. 3. <lb/>

aut &longs;i minor e&longs;t impul&longs;us grauitate, quie&longs;cit, per Pori&longs;. <lb/>

4. </s>
            <s id="N139B3">Eadem vi&agrave; di&longs;&longs;oluemus hoc </s>
          </p>
          <p id="N139B6" type="main">
            <s id="N139B8"><emph type="center"/><emph type="italics"/>Problema II.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N139C3" type="main">
            <s id="N139C5"><emph type="italics"/>Globum in plano quie&longs;centem alio globo <expan abbr="quacun&qacute;">quacunque</expan> violenti&agrave; per<lb/>

cu&longs;&longs;um, ad imperatam di&longs;tantiam mouere.<emph.end type="italics"/></s>
          </p>
          <p id="N139D2" type="main">
            <s id="N139D4">VT &longs;i globum <emph type="italics"/>b<emph.end type="italics"/> ab alio globo &aelig;quali aut minori <expan abbr="qua-cun&qacute;">qua&shy;<lb/>

cunque</expan> violenti&acirc; percu&longs;&longs;um, ad locum determinatum <lb/>

vg: <emph type="italics"/>c<emph.end type="italics"/> mouere velis, <expan abbr="ne&qacute;">neque</expan>; limitem hunc pr&aelig;terire, quan&shy;<lb/>

tumuis effr&aelig;ni impetu feratur</s>
            <s id="N139F1">n eodem loco, quem <lb/>

terminum illi motui pr&aelig;fixi&longs;ti, globum con&longs;titue &aelig;qua&shy;<lb/>

lem, dico in eodem loco &agrave; motu quie&longs;cere globum <emph type="italics"/>b.<emph.end type="italics"/><lb/>

Quia enim globum <emph type="italics"/>c<emph.end type="italics"/> quie&longs;centem percutit globus &aelig;&shy;<lb/>

qualis <emph type="italics"/>b,<emph.end type="italics"/> per Pori&longs;. <emph type="italics"/>i<emph.end type="italics"/> quie&longs;cet ex illa, quam fecit, plag&acirc;. </s>
          </p>
          <pb xlink:href="062/01/098.jpg"/>
          <p id="N13A16" type="main">
            <s id="N13A18"><emph type="center"/><emph type="italics"/>Pori&longs;ma V.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N13A23" type="main">
            <s id="N13A25"><emph type="italics"/>Si duo globi eju&longs;dem molis &longs;eu ponderis &longs;e percutiant in motu, <lb/>

<expan abbr="uter&qacute;">uterque</expan>; reflectit.<emph.end type="italics"/></s>
          </p>
          <p id="N13A32" type="main">
            <s id="N13A34">NAm quia idem pondus <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>;, erit <expan abbr="quoq;">quoque</expan> velocitas <lb/>

motus, quam plaga inducit, &aelig;qualis; eadem ergo ve&shy;<lb/>

locitate reflectit percutiens, qu&agrave; percu&longs;&longs;um mouebatur. <lb/>

Ex quo fit manife&longs;tum illorum velocitatem, qu&aelig; in mo <lb/>

tu &longs;e percutiunt, &agrave; percu&longs;sione permutari: qu&aelig; enim ma<lb/>

gis percutiunt, min&ugrave;s; &amp; qu&aelig; min&ugrave;s percutiunt, magis <lb/>

impetuo&longs;&egrave; reflectunt. </s>
          </p>
          <p id="N13A4B" type="main">
            <s id="N13A4D"><emph type="center"/><emph type="italics"/>Pori&longs;ma VI.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N13A58" type="main">
            <s id="N13A5A"><emph type="italics"/>Si globus major in motu percutiat minorem, habeat ver&ograve; minor <lb/>

minorem rationem ad &longs;uum impul&longs;um, quam ad globum majorem, <lb/>

<expan abbr="uter&qacute;">uterque</expan>; reflectit.<emph.end type="italics"/></s>
          </p>
          <p id="N13A69" type="main">
            <s id="N13A6B">QVia enim major e&longs;t impul&longs;us minoris grauitate ma&shy;<lb/>

joris, ob minorem hujus quam illius ratio nem, &longs;i mi&shy;<lb/>

nor percutiat majorem, mouebitur ex ill&agrave; plag&agrave; major: <lb/>

reflectit autem &amp; minor &agrave; majori, propterea qu&oacute;d &agrave; qua<lb/>

<expan abbr="cun&qacute;">cunque</expan> hujus plag&acirc; mouetur minor. </s>
            <s id="N13A7A">Igitur &longs;i globus ma&shy;<lb/>

jor in motu percutiat minorem &amp;c. </s>
          </p>
          <p id="N13A7F" type="main">
            <s id="N13A81"><emph type="center"/><emph type="italics"/>Pori&longs;ma VII.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <pb xlink:href="062/01/099.jpg"/>
          <p id="N13A8F" type="main">
            <s id="N13A91"><emph type="italics"/>Si globus major in motu percutiat minorem, habeat ver&ograve; minor <lb/>

majorem rationem ad &longs;uum impul&longs;um, quam ad globum majorem, <lb/>

minori reflexo motum continuat major.<emph.end type="italics"/></s>
          </p>
          <p id="N13A9C" type="main">
            <s id="N13A9E">QVia enim minor e&longs;t impul&longs;us minoris grauitate ma<lb/>

joris, propterea qu&ograve;d minorem ad hanc quam ad im<lb/>

pul&longs;um habeat rationem, non poterit grauitas majoris <lb/>

moueri ex impul&longs;u minoris: licet ergo plaga fiat &agrave; mi&shy;<lb/>

nori, quia tamen minorem producit impul&longs;um, quam <lb/>

ut grauitatem majoris loco moueat, non pote&longs;t ex ill&agrave; <lb/>

plag&agrave; reflecti major. </s>
            <s id="N13AAD">Quia ver&ograve; &agrave; minori impul&longs;u &aelig;qua <lb/>

li velocitate mouetur minor, erit velocitas in minori &aelig;&shy;<lb/>

qualis velocitati majoris &agrave; plag&agrave; necdum perfect&agrave;: im&shy;<lb/>

pul&longs;us ergo reliquus, qui necdum percu&longs;sit, motum con&shy;<lb/>

tinuabit. </s>
            <s id="N13AB8">Si ergo globus major in motu percutiat mi&shy;<lb/>

norem &amp;c. </s>
          </p>
          <p id="N13ABD" type="main">
            <s id="N13ABF"><emph type="center"/><emph type="italics"/>Pori&longs;ma VIII.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N13ACA" type="main">
            <s id="N13ACC"><emph type="italics"/>Si globus major in motu percutiat minorem, hab&eacute;at ver&ograve; minor <lb/>

ad majorem eandem rationem, quam habet ad &longs;uum impul&longs;um, mi&shy;<lb/>

nori reflexo quie&longs;cit major.<emph.end type="italics"/></s>
          </p>
          <p id="N13AD7" type="main">
            <s id="N13AD9">MInorem quidem globem &agrave; majori reflecti con&longs;tat, <lb/>

propterea qu&oacute;d ex hujus plag&agrave; impul&longs;us quidem &aelig;&shy;<lb/>

qualis, maior autem velo citas in minori con&longs;equatur: &agrave;t <lb/>

ver&ograve; globum maiorem &acirc; percu&longs;sione quie&longs;cere, c&ugrave;m e&shy;


<pb xlink:href="062/01/100.jpg"/>andem habet rationem minor ad hunc, quam habet ad <lb/>

&longs;uum impul&longs;um, ita o&longs;tendemus: motus non ni&longs;i ab ex&shy;<lb/>

ce&longs;&longs;u fit maioris; at ver&ograve; impul&longs;us ex ill&agrave; plag&agrave;, quam in&shy;<lb/>

ducit minor in maiori, non maior &longs;ed &aelig;qualis e&longs;t eiu&longs;&shy;<lb/>

dem grauitati, ex &longs;uppo&longs;itione; non ergo ex illo impul&shy;<lb/>

&longs;u moueri pote&longs;t major. </s>
            <s id="N13AF0">Quia ver&ograve; &agrave; percu&longs;sione exol&shy;<lb/>

uitur, minor autem, quam ut mouere po&longs;sit, impul&longs;us <lb/>

regeneratur, quie&longs;cet ex ill&agrave; plag&agrave; globus maior. </s>
          </p>
        </subchap1>
        <subchap1 id="N13AF7">
          <p id="N13AF8" type="main">
            <s id="N13AFA"><emph type="center"/>Propo&longs;itio XXXVIII.<emph.end type="center"/></s>
          </p>
          <p id="N13B01" type="main">
            <s id="N13B03"><emph type="italics"/>C&ugrave;m centrum grauitatis cadit extra lineam hypomochlij, motus <lb/>

in illam partem, in qu&agrave; e&longs;t centrum, reflectit.<emph.end type="italics"/></s>
          </p>
          <p id="N13B0C" type="main">
            <s id="N13B0E">OCcurrat globus <emph type="italics"/>dcg<emph.end type="italics"/> plano <emph type="italics"/>ab<emph.end type="italics"/> non perpendiculari&shy;<lb/>

ter, &longs;ed ex obliquo, faciens angulum incidenti&aelig; <emph type="italics"/>adc<emph.end type="italics"/><lb/> acutum, <expan abbr="erit&qacute;">eritque</expan>; linea <emph type="italics"/>cd<emph.end type="italics"/> ducta per contactum linea hypo&shy;<lb/>

mochlii, &amp; motui centri parallela, centrum ver&ograve; <emph type="italics"/>e<emph.end type="italics"/> extra <lb/>

lineam hypomochlii: dico ex puncto contactus <emph type="italics"/>a<emph.end type="italics"/> mo&shy;<lb/>

tum reflexum fieri in illam partem, in qu&acirc; e&longs;t centrum <emph type="italics"/>e.<emph.end type="italics"/><lb/>

Quia enim motus &amp; plaga ad motum fit centri: <expan abbr="centr&utilde;">centrum</expan> <lb/>

ver&ograve; <emph type="italics"/>e<emph.end type="italics"/> plano occurrit per lineam <emph type="italics"/>ed,<emph.end type="italics"/> <expan abbr="e&longs;t&qacute;">e&longs;tque</expan>; maior re&longs;i&longs;ten<lb/>

tia in plano quam impul&longs;us, erit motus reflexus ad partes <lb/>

oppo&longs;itas illi plag&aelig;, ac proinde in partem in qu&agrave; e&longs;t cen&shy;<lb/>

trum. </s>
          </p>
        </subchap1>
        <subchap1 id="N13B65">
          <pb xlink:href="062/01/101.jpg"/>
          <p id="N13B69" type="main">
            <s id="N13B6B"><emph type="center"/>Propo&longs;itio XXXIX.<emph.end type="center"/></s>
          </p>
          <p id="N13B72" type="main">
            <s id="N13B74"><emph type="italics"/>Motus reflexus fit per lineam parallelam illi line&aelig;, qu&aelig; cum line&agrave; <lb/>

perpendiculari ad contactum angulum con&longs;tituit in centro, cujus &longs;i&shy;<lb/>

nus e&longs;t &aelig;qualis interuallo inter centrum grauitatis &amp; lineam hy&shy;<lb/>

pomochlij.<emph.end type="italics"/></s>
          </p>
          <p id="N13B81" type="main">
            <s id="N13B83">IN e&agrave;dem figur&agrave; ducatur ex <emph type="italics"/>e<emph.end type="italics"/> centro grauitatis &longs;eu im&shy;<lb/>

pul&longs;us linea <emph type="italics"/>ef<emph.end type="italics"/> perpendicularis ad lineam hypomo&shy;<lb/>

chlii <emph type="italics"/>cd,<emph.end type="italics"/> &amp; linea <emph type="italics"/>eg<emph.end type="italics"/> faciens cum line&agrave; <emph type="italics"/>dh<emph.end type="italics"/> perpendiculari <lb/>

ad contactum in eodem centro <emph type="italics"/>e<emph.end type="italics"/> angulum <emph type="italics"/>heg,<emph.end type="italics"/> cuius &longs;i&shy;<lb/>

nus <emph type="italics"/>hg<emph.end type="italics"/> &longs;it &aelig;qualis line&aelig; <emph type="italics"/>fe<emph.end type="italics"/> interuallo inter centrum gra&shy;<lb/>


<figure id="id.062.01.101.1.jpg" xlink:href="062/01/101/1.jpg"/><lb/>

uitatis <emph type="italics"/>e<emph.end type="italics"/> &amp; lineam hypomochlii: dico motum reflexum <lb/>

fieri per lineam <emph type="italics"/>di<emph.end type="italics"/> parallelam line&aelig; <emph type="italics"/>eg.<emph.end type="italics"/> Quia enim cen&shy;<lb/>

trum grauitatis, dum &longs;u&agrave; mole ferit planum in puncto <emph type="italics"/>d<emph.end type="italics"/>


<pb xlink:href="062/01/102.jpg"/> per lineam <emph type="italics"/>ed<emph.end type="italics"/> &longs;e ip&longs;um veluti partitur: illa quidem pars <lb/>

qu&aelig; hypomochlio in&longs;i&longs;tit, <expan abbr="atq&qacute;">atque</expan> illam plagam inducit, ea&shy;<lb/>

dem vi&agrave;, qu&aacute; impulit, &amp; impul&longs;u &aelig;quali retro agitur: re&shy;<lb/>

liqua ver&ograve;, qu&aelig; cum centro extra hypomochlium ca&shy;<lb/>

dit, per lineam fertur <emph type="italics"/>ek<emph.end type="italics"/> parallelam line&aelig; <emph type="italics"/>db,<emph.end type="italics"/> propterea <lb/>

qu&oacute;d h&aelig;c &longs;it proxima motui grauitatis ab hypomo&shy;<lb/>

chlio impedit&aelig;. </s>
            <s id="N13C0F">Quia ergo motus <emph type="italics"/>eh.ek,<emph.end type="italics"/> quibus cen&shy;<lb/>

trum grauitatis agitur, &longs;ecund&uacute;m quid &longs;unt contrarii, <lb/>

propterea qu&oacute;d angulus <emph type="italics"/>hek<emph.end type="italics"/> &longs;it minor duobus rectis, e&shy;<lb/>

rit motus mixtus per lineam mediam inter <emph type="italics"/>eh<emph.end type="italics"/> &amp; <emph type="italics"/>ek,<emph.end type="italics"/> cu&shy;<lb/>

jus interuallum determinat &longs;inus complementi inclina&shy;<lb/>

tionis, in ratione quam habent impul&longs;us per Prop; 31. e&longs;t <lb/>

autem interuallum <emph type="italics"/>fe,<emph.end type="italics"/> hoc e&longs;t &longs;inus <emph type="italics"/>dm<emph.end type="italics"/> anguli <emph type="italics"/>dem,<emph.end type="italics"/> men&shy;<lb/>

&longs;ura grauitatis extra hypomochlium; linea vero <emph type="italics"/>fd<emph.end type="italics"/> &longs;inus <lb/>

anguli reliqui men&longs;ura illius, qu&aelig; hypomochlio in&longs;i&longs;tit <lb/>

grauitatis: &longs;i fiat ut <emph type="italics"/>fd<emph.end type="italics"/> ad <emph type="italics"/>ef,<emph.end type="italics"/> ita <emph type="italics"/>kg<emph.end type="italics"/> &longs;inus complementi an<lb/>

guli <emph type="italics"/>heg<emph.end type="italics"/> ad<emph type="italics"/>hg<emph.end type="italics"/> &longs;inum complementi anguli <emph type="italics"/>keg<emph.end type="italics"/> erit li&shy;<lb/>

nea <emph type="italics"/>eg<emph.end type="italics"/> linea motus mixti ex <emph type="italics"/>eh<emph.end type="italics"/> &amp; <emph type="italics"/>ek<emph.end type="italics"/> per Prop: 31. </s>
            <s id="N13C8E">Vel &longs;ic <lb/>

motus reflexus fit per lineam <emph type="italics"/>de<emph.end type="italics"/> perpendicularem ad <lb/>

contactum; inclinatio autem motus reflexi augetur in <lb/>

ratione interualli inter centrum grauitatis &amp; hypomo&shy;<lb/>

chlium: Si igitur fiat ut &longs;inus totus nimirum motus re&shy;<lb/>

flexus, ad men&longs;uram hujus interu&agrave;lli, hoc e&longs;t grauitatem <lb/>

extra hypomochlium, ita linea motus <emph type="italics"/>eh<emph.end type="italics"/> &longs;inus nimirum <lb/>

anguli <emph type="italics"/>hek,<emph.end type="italics"/> hoc e&longs;t &longs;inus totus ad &longs;inum <emph type="italics"/>hg<emph.end type="italics"/> anguli incli&shy;


<pb xlink:href="062/01/103.jpg"/>nationis, erit eadem linea <emph type="italics"/>eg<emph.end type="italics"/> motus mixti. </s>
            <s id="N13CC1">Quia ergo <lb/>

mobile mouetur ad motum &longs;ui centri, erit motus ex <emph type="italics"/>d<emph.end type="italics"/><lb/> reflexus per lineam parallelam illi line&aelig;, qu&aelig; cum line&agrave; <lb/>

perpendiculari ad contactum angulum con&longs;tituit in <lb/>

centro, cujus &longs;inus e&longs;t &aelig;qualis interuallo inter centrum <lb/>

grauitatis &amp; lineam hypomochlij. </s>
          </p>
        </subchap1>
        <subchap1 id="N13CD3">
          <p id="N13CD4" type="main">
            <s id="N13CD6"><emph type="center"/>Propo&longs;itio XXXX.<emph.end type="center"/></s>
          </p>
          <p id="N13CDD" type="main">
            <s id="N13CDF"><emph type="italics"/>Anguli incidenti&aelig; &amp; reflexionis &longs;unt inter &longs;e &aelig;quales.<emph.end type="italics"/></s>
          </p>
          <p id="N13CE6" type="main">
            <s id="N13CE8">QVia enim duo latera <emph type="italics"/>eh.bg<emph.end type="italics"/> trianguli <emph type="italics"/>ehg<emph.end type="italics"/> &aelig;qualia <lb/>

&longs;unt duobus lateribus <emph type="italics"/>ef. fd<emph.end type="italics"/> trianguli <emph type="italics"/>efd,<emph.end type="italics"/> &amp; angu&shy;<lb/>

lus, qui adjacet uni &aelig;qualium laterum, rectus, erunt tri&shy;<lb/>

angula &aelig;qualia, &amp; angulus <emph type="italics"/>fde<emph.end type="italics"/> angulo <emph type="italics"/>heg<emph.end type="italics"/> &aelig;qualis: e&longs;t <lb/>

autem angulo <emph type="italics"/>heg<emph.end type="italics"/> &aelig;qualis angulus <emph type="italics"/>edi<emph.end type="italics"/> ob parallelas <emph type="italics"/>eg. <lb/>

di<emph.end type="italics"/>; idem ergo angulus <emph type="italics"/>edi<emph.end type="italics"/> e&longs;t &aelig;qualis angulo <emph type="italics"/>fde:<emph.end type="italics"/> &longs;unt <lb/>

ver&ograve; duo <expan abbr="quo&qacute;">quoque</expan>; anguli <emph type="italics"/>a.de.bde<emph.end type="italics"/> inter le &aelig;quales, nimi&shy;<lb/>

rum recti; ablatis ergo duobus angulis <emph type="italics"/>fde.edi<emph.end type="italics"/> &aelig;quali&shy;<lb/>

bus, erunt anguli reliqui <emph type="italics"/>adf.bdi,<emph.end type="italics"/> anguli nimirum inci&shy;<lb/>

denti&aelig; &amp; reflexionis inter &longs;e &aelig;quales. </s>
            <s id="N13D55">Priu&longs;quam de mo <lb/>

tu reflexo finiamus, unum <expan abbr="at&qacute;">atque</expan>; alterum Problema pro <lb/>

corollario adducemus, quorum &longs;olutio magis difficilis <lb/>

habetur, ex ijs autem, qu&aelig; hactenus &longs;unt demon&longs;trata, <lb/>

facil&egrave; di&longs;&longs;oluuntur. </s>
            <s id="N13D64">Sit ergo </s>
          </p>
          <pb xlink:href="062/01/104.jpg"/>
          <p id="N13D6A" type="main">
            <s id="N13D6C"><emph type="center"/><emph type="italics"/>Problema<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N13D77" type="main">
            <s id="N13D79"><emph type="italics"/>Tribus globis in <expan abbr="quacun&qacute;">quacunque</expan>; di&longs;tantia extra lineam rectam a&longs;&longs;um<lb/>

ptis, punctum determinare in globo &longs;ecundo, &agrave; quo reflexus primus <lb/>

percutiat tertium.<emph.end type="italics"/></s>
          </p>
          <p id="N13D88" type="main">
            <s id="N13D8A">IN figur&agrave; &longs;ubiect&agrave; a&longs;&longs;umantur globi <emph type="italics"/>s.p.r.<emph.end type="italics"/> in di&longs;tanti&acirc; <lb/>

<emph type="italics"/>sp.pr.rs:<emph.end type="italics"/> <expan abbr="oporteat&qacute;">oporteatque</expan>; in globo <emph type="italics"/>p<emph.end type="italics"/> punctum determina&shy;<lb/>

re, ad quod globus <emph type="italics"/>s<emph.end type="italics"/> allidens, <expan abbr="inde&qacute;">indeque</expan>; reflexus percutiat <lb/>

globum <emph type="italics"/>r.<emph.end type="italics"/> Tangant illos globos line&aelig; <emph type="italics"/>ac. bd<emph.end type="italics"/> in punctis <lb/>

<emph type="italics"/>a.c. b.d,<emph.end type="italics"/> &amp; diuidantur bifariam in punctis <emph type="italics"/>e<emph.end type="italics"/> &amp; <emph type="italics"/>f;<emph.end type="italics"/> &agrave; quibus in <lb/>

circulum <emph type="italics"/>p<emph.end type="italics"/> excurrant line&aelig; rect&aelig; <emph type="italics"/>eg.fg.<emph.end type="italics"/> &longs;e inter&longs;ecantes <lb/>

in puncto reflexionis <emph type="italics"/>g,<emph.end type="italics"/> eo modo, quo docent Optici in&shy;<lb/>

uento, &amp; producantur <expan abbr="utrin&qacute;">utrinque</expan> in <emph type="italics"/>k.l,<emph.end type="italics"/> &amp; <emph type="italics"/>h. i;<emph.end type="italics"/> dico <expan abbr="punct&utilde;">punctum</expan> <lb/>

<emph type="italics"/>g<emph.end type="italics"/> e&longs;&longs;e illud punctum, &acirc; quo globus <emph type="italics"/>s<emph.end type="italics"/> reflexus percutiat <lb/> globum<emph type="italics"/>r.<emph.end type="italics"/> Quia enim angulus <emph type="italics"/>egd<emph.end type="italics"/> angulo <emph type="italics"/>fgc<emph.end type="italics"/> per con&shy;<lb/>

&longs;tructionem, &amp; angulus <emph type="italics"/>egh<emph.end type="italics"/> angulo <emph type="italics"/>fgk<emph.end type="italics"/> ad verticem e&longs;t <lb/>

&aelig;quali<emph type="italics"/>s<emph.end type="italics"/>; ablatis ex his illis erunt anguli reliqui <emph type="italics"/>hgd. kge<emph.end type="italics"/><lb/> &aelig;quales: linea ergo &longs;ubten&longs;a <emph type="italics"/>hg<emph.end type="italics"/> e&longs;t &aelig;qualis line&aelig; <emph type="italics"/>kg.<emph.end type="italics"/> &amp; <lb/>

quia linea <emph type="italics"/>fd<emph.end type="italics"/> line&aelig; <emph type="italics"/>fb,<emph.end type="italics"/> &amp; angulus <emph type="italics"/>dfg<emph.end type="italics"/> e&longs;t &aelig;qualis angulo <lb/>

<emph type="italics"/>bfn,<emph.end type="italics"/> erit corda <emph type="italics"/>gh<emph.end type="italics"/> &aelig;qualis cord&aelig; <emph type="italics"/>ni.<emph.end type="italics"/> Similiter o&longs;tende&shy;<lb/>

mus cordam <emph type="italics"/>gk<emph.end type="italics"/> &aelig;qualem cord&aelig; <emph type="italics"/>ml.<emph.end type="italics"/> Ducatur ergo per <lb/>

contactum &acirc; centro <emph type="italics"/>p<emph.end type="italics"/> linea <emph type="italics"/>pq,<emph.end type="italics"/> <expan abbr="at&qacute;">atque</expan>, ex <emph type="italics"/>q<emph.end type="italics"/> circulus de&shy;<lb/>

&longs;cribatur &aelig;qualis circulo<emph type="italics"/>s,<emph.end type="italics"/> tangens priorem in <emph type="italics"/>g,<emph.end type="italics"/> <expan abbr="agatur&qacute;">agaturque</expan>; <lb/>

linea <emph type="italics"/>qr<emph.end type="italics"/> parallela line&aelig; <emph type="italics"/>gi<emph.end type="italics"/>: qu&ograve;d &longs;i ergo globus <emph type="italics"/>s<emph.end type="italics"/> motu &longs;ui 


<pb xlink:href="062/01/105.jpg"/>centri de&longs;cribat lineam <emph type="italics"/>sq,<emph.end type="italics"/> de&longs;cribet punctum <emph type="italics"/>m<emph.end type="italics"/> motu <lb/>

&longs;imili lineam <emph type="italics"/>mg<emph.end type="italics"/> illi parallelam, <expan abbr="tanget&qacute;">tangetque</expan>; globus <emph type="italics"/>s<emph.end type="italics"/> <expan abbr="glob&utilde;">globum</expan> <lb/>

<emph type="italics"/>p<emph.end type="italics"/> in puncto <emph type="italics"/>g<emph.end type="italics"/>: dico punctum <emph type="italics"/>m<emph.end type="italics"/> ex <emph type="italics"/>g<emph.end type="italics"/> per lineam <emph type="italics"/>gi,<emph.end type="italics"/> cen&shy;<lb/>

trum ver&oacute; <emph type="italics"/>q<emph.end type="italics"/> per lineam <emph type="italics"/>qr<emph.end type="italics"/> illi parallelam reflecti. </s>
            <s id="N13F12">rit <lb/>

enim <emph type="italics"/>gy<emph.end type="italics"/> linea hypomochlii, ad quam ex <emph type="italics"/><expan abbr="q.">que</expan><emph.end type="italics"/> cadat linea <lb/>

<figure id="id.062.01.105.1.jpg" xlink:href="062/01/105/1.jpg"/><lb/>

perpendicularis <emph type="italics"/>qt,<emph.end type="italics"/> <expan abbr="at&qacute;">atque</expan>; huic &aelig;qualis &longs;umatur in line&acirc; <lb/>

motus centri <emph type="italics"/>qz,<emph.end type="italics"/> &agrave; cujus termino <emph type="italics"/>z<emph.end type="italics"/> ducta linea perpendi&shy;<lb/>

cularis &longs;ecabit circulum in puncto <emph type="italics"/>x,<emph.end type="italics"/> per quod tran&longs;it li&shy;<lb/>

nea motus reflexi per Prop 39. tribus erg&ograve; globis extra <lb/>

lineam rectam a&longs;&longs;umptis punctum determinauimus in 


<pb xlink:href="062/01/106.jpg"/>globo &longs;ecundo, &agrave; quo reflexus primus tangit tertium: <lb/>

quod erat faciendum. </s>
            <s id="N13F58">Secundum Problema. </s>
          </p>
          <p id="N13F5B" type="main">
            <s id="N13F5D"><emph type="center"/>DE MOTV REFLEXO <expan abbr="LAPILLOR&utilde;">LAPILLORum</expan> EX AQVA.<emph.end type="center"/></s>
          </p>
          <p id="N13F68" type="main">
            <s id="N13F6A">QVi obliqu&egrave; incidentes illam minim&egrave; findunt, <lb/>

<expan abbr="ne&qacute;ue">neque</expan> merguntur; ver&ugrave;m inde reflexi, <expan abbr="at&qacute;">atque</expan>; ite&shy;<lb/>

rum relap&longs;i reciproc&agrave; alli&longs;ione, &amp; reli&longs;ione &longs;altu quodam <lb/>

progredi videntur. </s>
            <s id="N13F7B">E&longs;t autem prima difficultas, quam <lb/>

ob rem huju&longs;modi lapilli, <expan abbr="quacun&qacute;">quacunque</expan>; violenti&agrave; projecti, <lb/>

aquam molli&longs;simam non perrumpant, in qu&acirc; etiam pul&shy;<lb/>

ui&longs;culus &amp; leui&longs;sim&aelig; arenul&aelig; &longs;u&agrave; grauitate &longs;idunt. </s>
            <s id="N13F88">Se&shy;<lb/>

cunda qu&agrave; ratione &acirc; prim&acirc; reflexione alias inducant pla&shy;<lb/>

gas non perpendiculares: conuer&longs;io enim illa motus vi&shy;<lb/>

detur non ni&longs;i &acirc; grauitate na&longs;ci, quo modo in omnibus <lb/>

projectis fieri con&longs;tat: at ver&ograve; grauitas non ni&longs;i per line&shy;<lb/>

am mouet perpendicularem. </s>
            <s id="N13F95">In figur&agrave; &longs;ubject&agrave; lapillus <lb/>

&longs;eu globulus <emph type="italics"/>a<emph.end type="italics"/> &acirc; percu&longs;sione obliqu&agrave; <emph type="italics"/>ba<emph.end type="italics"/> reflectit in <emph type="italics"/>k<emph.end type="italics"/>: in <lb/>

de ver&ograve; non perpendiculariter in <emph type="italics"/>q,<emph.end type="italics"/> ver&ugrave;m obliqu&egrave; rela&shy;<lb/>

bitur in <emph type="italics"/>l,<emph.end type="italics"/> <expan abbr="noua&qacute;">nouaque</expan>; illat&agrave; &amp; relat&acirc; plag&agrave; reflectit in <emph type="italics"/>m<emph.end type="italics"/>: &longs;imi&shy;<lb/>

liter ex <emph type="italics"/>m<emph.end type="italics"/> in <emph type="italics"/>u,<emph.end type="italics"/> &amp; ex <emph type="italics"/>o<emph.end type="italics"/> in <emph type="italics"/>x<emph.end type="italics"/> ad nouam &longs;e ex obliquo vibrat <lb/>

plagam. </s>
            <s id="N13FE2">Hujus autem &longs;olutio pendet ex his, qu&aelig; de mo <lb/>

tu reflexo &acirc; nobis &longs;unt dicta. </s>
            <s id="N13FE7">Quia enim percu&longs;sio fit &aacute; <lb/>

centro, magnitudo autem plag&aelig; ab hypomochlio deter&shy;<lb/>

minatur; qu&oacute; enim major pars hypomochlio occurrit, <lb/>

e&oacute; majorem plagam inducit, unde ictus graui&longs;simus per


<pb xlink:href="062/01/107.jpg"/>pendiculatis; propterea qu&oacute;d cum centro part&egrave;s omnes <lb/>

coincidunt, <expan abbr="at&qacute;">atque</expan>; in illam plagam cooperantur: qu&oacute; ve&shy;<lb/>r&ograve; ictus magis e&longs;t obliquus, e&oacute; minorem plagam infert. <lb/>

Quia ergo lapilli obliqu&egrave; incidentes non ni&longs;i parte exi&shy;<lb/>

gu&agrave; feriunt, major autem vis extra hypomochlium ca&shy;<lb/>

dit. <expan abbr="ob&longs;tat&qacute;">ob&longs;tatque</expan>; qu&ograve; min&ugrave;s illa &longs;uo fulcro innitatur; inde fit <lb/>

ut non mergantur, <expan abbr="ne&qacute;">neque</expan>; findant quantumuis mollem a&shy;<lb/>


<figure id="id.062.01.107.1.jpg" xlink:href="062/01/107/1.jpg"/><lb/>

quam. </s>
            <s id="N14015">In globulo enim <emph type="italics"/>a<emph.end type="italics"/> &longs;ola pars <emph type="italics"/>dic<emph.end type="italics"/> hypomochlio oc<lb/>

currit, reliqua <emph type="italics"/>dghci<emph.end type="italics"/> cum centro <emph type="italics"/>a<emph.end type="italics"/> extra hypomochli&shy;<lb/>

um cadit, <expan abbr="at&qacute;">atque</expan>; ab ill&acirc; plag&agrave; idem mobile abducit. </s>
            <s id="N14038">Quia <lb/>

ver&ograve; minor e&longs;t plaga, quam ut perrumpat, recipiet &agrave; per<lb/>

cu&longs;&longs;o &aelig;qualem, qua re&longs;iliat, plagam, ac proinde mino <lb/>

rem, quam ut impul&longs;um producat illi &aelig;qualem, quo cen<lb/>

trum mouetur. </s>
            <s id="N14043">Motus erg&ograve; reflexus e&longs;t mixtus ex motu 


<pb xlink:href="062/01/108.jpg"/>centri <emph type="italics"/>ag<emph.end type="italics"/> &agrave; prim&agrave;, &amp; motu <emph type="italics"/>af<emph.end type="italics"/> &agrave; plag&acirc; &longs;ecund&agrave;, linea <emph type="italics"/>v<emph.end type="italics"/>er&ograve; <lb/>

motus reflexi <emph type="italics"/>ah<emph.end type="italics"/> per Prop: 39. quia ergo minor impul&longs;us <lb/>

&agrave; reflexione, impul&longs;u, quo centrum agitur, deficiet pri&shy;<lb/>

&ugrave;s, <expan abbr="illo&qacute;">illoque</expan>; deficiente motum continuabit major impul&shy;<lb/>

&longs;us; &amp; priu&longs;quam &longs;ui juris &longs;it, line&agrave; motus mixti &longs;inuo&shy;<lb/>

&longs;&egrave;, quomodo grauia &agrave; motu violento, &longs;e abducet; inde <lb/>

per tangentem arcus jam deficientis, ac proinde ex obli&shy;<lb/>

quo &longs;e deuoluet, ut nou&agrave; illat&agrave; &amp; relat&agrave; plag&acirc; &longs;e rur&longs;um <lb/>

attollat. </s>
            <s id="N14076">Quia ver&ograve; illo cur&longs;u &amp; recur&longs;u virtus elangue <lb/>

&longs;cit, quantumuis &aelig;quali parte feriat, minor tamen &acirc; per&shy;<lb/>

cu&longs;sione &longs;ecund&acirc; fit plaga, quam ut motus inde reflexus <lb/>

&longs;it &aelig;qualis primo: inde ergo fit ut &agrave; &longs;ecund&agrave; percu&longs;sione <lb/>

in <emph type="italics"/>d<emph.end type="italics"/> minor &longs;it altitudo motus reflexi in <emph type="italics"/>m<emph.end type="italics"/>; &amp; in <emph type="italics"/>o<emph.end type="italics"/> minor <lb/>

qu&agrave;m in <emph type="italics"/>m,<emph.end type="italics"/> <expan abbr="quou&longs;&qacute;">quou&longs;que</expan>; demum motus centri &agrave; percu&longs;sioni&shy;<lb/>

bus iteratis exoluatur: aut quia minor in fine altitudo <lb/>

motus reflexi, quam diameter illius lapilli &longs;eu globuli, <lb/>ob aquam motui reluctantem ictus emoritur; <expan abbr="at&qacute;">atque</expan>; inde <lb/>

fit, qu&ograve;d in fine motus ab huju&longs;modi lapillis aqua di&longs;per<lb/>

gatur: &agrave; <emph type="italics"/>p<emph.end type="italics"/> enim in <emph type="italics"/>q<emph.end type="italics"/> reflexus motus, ob altitudinem dia&shy;<lb/>

metro minorem, viam incedit <emph type="italics"/>pq<emph.end type="italics"/> ob aqu&aelig; grauitatem <lb/>

magis impeditam. </s>
            <s id="N140C3">Non &longs;ol&uacute;m ver&ograve; in aqu&agrave; ex huju&longs;mo&shy;<lb/>

di ictu obliquo fiunt repercu&longs;siones, verum in <expan abbr="quocun&qacute;">quocunque</expan> <lb/>

alio plano min&ugrave;s tamen &longs;en&longs;ibiles: cujus ratio e&longs;t mol&shy;<lb/>

lities aqu&aelig;, qu&aelig; pre&longs;&longs;a rea&longs;&longs;urgit, <expan abbr="ictu&qacute;">ictuque</expan>; geminato ferit. <lb/>

<expan abbr="Ita&qacute;">Itaque</expan>; videmus pilas lu&longs;orias magis re&longs;ilire, qu&aelig; &acirc; plag&agrave; ce


<pb xlink:href="062/01/109.jpg"/>dunt in &longs;e ip&longs;as, &amp; veluti complanantur, <expan abbr="at&qacute;">atque</expan>; ita plagam <lb/>

inducunt latiorem; mox ver&ograve; &acirc; plag&acirc; impul&longs;u gemina&shy;<lb/>

to rea&longs;&longs;urgunt: idem enim &longs;it &longs;iu&egrave; planum, &longs;iu&egrave; mobile <lb/>

eidem plano alli&longs;um e&agrave; ratione moueatur. </s>
            <s id="N140E8">Similes ictus <lb/>

repetiti fiunt in cauo &longs;ph&aelig;rico, cuju&longs;modi peluis: ab <lb/>


<figure id="id.062.01.109.1.jpg" xlink:href="062/01/109/1.jpg"/><lb/>

uno enim puncto reflexus globus in alia porro offendit <lb/>

&amp; allidit: ut &longs;i globus ex <emph type="italics"/>l<emph.end type="italics"/> demittatur in peluim <emph type="italics"/>msbp,<emph.end type="italics"/> a <lb/>

puncto <emph type="italics"/>m<emph.end type="italics"/> ad angulos reflectit &aelig;quales in <emph type="italics"/>n,<emph.end type="italics"/> ex<emph type="italics"/>n<emph.end type="italics"/> ver&ograve; in <lb/>

<emph type="italics"/>b,<emph.end type="italics"/> ex <emph type="italics"/>b<emph.end type="italics"/> in <emph type="italics"/>o,<emph.end type="italics"/> tum in <emph type="italics"/>p,<emph.end type="italics"/> &agrave; quo extra peluim reflectit in <emph type="italics"/><expan abbr="q.">que</expan><emph.end type="italics"/> <expan abbr="Id&etilde;">Idem</expan> <lb/>

ex <emph type="italics"/>r<emph.end type="italics"/> delap&longs;us in <emph type="italics"/>s<emph.end type="italics"/> maiori angulo reflectens, ob cordas ma<lb/>

iores, pauciores inducit plagas. </s>
            <s id="N1414E">Ex <emph type="italics"/>z<emph.end type="italics"/> demum in <emph type="italics"/>b<emph.end type="italics"/> refle&shy;<lb/>

xus quia nullibi offendit, quemadmodum <expan abbr="ne&qacute;">neque</expan>; in linea <lb/>

perpendiculari <emph type="italics"/>ab,<emph.end type="italics"/> nullam pr&aelig;terea inducit plagam. <lb/>

Tertium Problema. </s>
          </p>
          <pb xlink:href="062/01/110.jpg"/>
          <p id="N14170" type="main">
            <s id="N14172"><emph type="center"/>DE REFLEXIONE MOTVS CIRCVLARIS.<emph.end type="center"/></s>
          </p>
          <p id="N14179" type="main">
            <s id="N1417B">VT &longs;i duo globi ab eodem hypomochlio filo &longs;u&longs;pen&longs;i, <lb/>

&amp; in &longs;uam &longs;tationem recurrentes &longs;e percutiant in il&shy;<lb/>

lo motu. </s>
            <s id="N14182">Quia enim hic motus di&longs;cedit &agrave; line&agrave; rect&agrave;, per <lb/>

quam ducit impul&longs;us, nece&longs;&longs;e alio modo reflexionem fi&shy;<lb/>

eri, qu&aacute;m in motu recto. </s>
            <s id="N14189">Mouetur autem vel unus tan&shy;<lb/>

tum, vel <expan abbr="uter&qacute;">uterque</expan>;, ac proinde hic illum percutit aut quies<lb/>

centem, aut commotum; &amp; &longs;iquidem percu&longs;sio fiat in <lb/>

motu, <expan abbr="uter&qacute;">uterque</expan>; reflectit: Si ver&ograve; quie&longs;cit alter, interdum <lb/>

reflectit ille qui percu&longs;sit, interdum in ip&longs;o ictu emori&shy;<lb/>

tur motus. </s>
            <s id="N1419E">Quod qua ratione fiat &longs;ubject&agrave; figur&aacute; pate<lb/>

fiet. </s>
            <s id="N141A3">Percutiant erg&ograve; &longs;e duo globi <foreign lang="greek">eg</foreign> ab eodem hypomo<lb/>

chlio <foreign lang="greek">a</foreign> &longs;u&longs;pen&longs;i in ip&longs;o motu, &amp; ducantur line&aelig; tangen&shy;<lb/>

tes <foreign lang="greek">bo. qc</foreign> <expan abbr="at&qacute;">atque</expan>; his parallel&aelig; <foreign lang="greek">yi.yk</foreign> line&aelig; hypomochlij; in <lb/>

line&agrave; autem, <foreign lang="greek">g</foreign> per <expan abbr="utrumq;">utrumque</expan> centrum duct&agrave;, &amp; <expan abbr="utrinq;">utrinque</expan> <lb/>

protract&agrave; &longs;umatur <foreign lang="greek">gp</foreign> &aelig;qualis <foreign lang="greek">yl</foreign>, &amp; ex <foreign lang="greek">p</foreign> excitetur li&shy;<lb/>

n&egrave;a perpendicularis <foreign lang="greek">pm</foreign>, <expan abbr="eritq;">eritque</expan> linea <foreign lang="greek">gm</foreign>, &longs;i nihil impediat, <lb/>

linea motus reflexi, per Prop: 39. motus nimirum mix&shy;<lb/>

tus ex motu centri <foreign lang="greek">gw</foreign> &amp; motu &agrave; percus&longs;ione <foreign lang="greek">gn</foreign>. </s>
            <s id="N141F4">At ver&ograve; <lb/>

huic motui ob&longs;tat funiculus, &agrave; quo globus detinetur, <lb/>

qu&ograve; min&ugrave;s extra <expan abbr="peripheri&atilde;">peripheriam</expan> circuli euagetur. </s>
            <s id="N141FF">Quia ve&shy;<lb/>

r&ograve; hic motus &agrave; reflexione &amp; motus &agrave; retractione funi&shy;<lb/>

culi angulum ducunt <foreign lang="greek">agm</foreign> minorem duobus rectis, erunt <lb/>

per definit: 5. &longs;ecund&ugrave;m quid contrarii, ac proinde inter 


<pb xlink:href="062/01/111.jpg"/>&longs;e mi&longs;centur. </s>
            <s id="N14210">Motus erg&ograve; ex <expan abbr="utroq;">utroque</expan> mixtus &agrave; percu&longs;sio&shy;<lb/>

ne reflectit. </s>
            <s id="N14219">Simili modo o&longs;tendemus globum <foreign lang="greek">e</foreign> refle&shy;<lb/>

cti ex ill&agrave; plag&agrave;. </s>
            <s id="N14222">Qu&ograve;d &longs;i globus <emph type="italics"/>a<emph.end type="italics"/> percutiat globum <emph type="italics"/>b<emph.end type="italics"/><lb/> quie&longs;centem, &amp; minori filo &longs;u&longs;pen&longs;um, erit per Prop: 39 <lb/>

linea motus reflexi <emph type="italics"/><expan abbr="aq.">aque</expan><emph.end type="italics"/> &amp; quia hic motus in partes oppo&shy;<lb/>


<figure id="id.062.01.111.1.jpg" xlink:href="062/01/111/1.jpg"/><lb/>
&longs;itas tendit eiu&longs;dem line&aelig; rect&aelig;, per quam retrahitur ab <lb/>

hypomochlio, erunt motus ab&longs;olut&egrave; contrarii: globus <lb/>

erg&ograve; <emph type="italics"/>a<emph.end type="italics"/> &longs;i in illo &longs;itu percutiat <emph type="italics"/>b,<emph.end type="italics"/> &acirc; percu&longs;sione quie&longs;cet; <lb/>

tant&ograve; ver&ograve; min&ugrave;s reflectet, quant&oacute; maior fuerit angu&shy;


<pb xlink:href="062/01/112.jpg"/>lus <foreign lang="greek">a</foreign><emph type="italics"/>aq<emph.end type="italics"/> Si demum globus <emph type="italics"/>b<emph.end type="italics"/> percutiat globum <emph type="italics"/>a<emph.end type="italics"/> quie&shy;<lb/>

&longs;centem &amp; longiori filo &longs;u&longs;pen&longs;um, erit linea motus re&shy;<lb/>

flexi <emph type="italics"/>br<emph.end type="italics"/> ad ea&longs;dem partes cum retractione hypomo&shy;<lb/>

chlii, propterea qu&ograve;d linea <emph type="italics"/>bp<emph.end type="italics"/> &longs;it motus centri, linea ve&shy;<lb/>

r&ograve; <emph type="italics"/>bn<emph.end type="italics"/> motus &agrave; percu&longs;sione; globus ergo <emph type="italics"/>b<emph.end type="italics"/> percu&longs;&longs;o glo&shy;<lb/>

bo <emph type="italics"/>a<emph.end type="italics"/> reflectet in illo &longs;itu &agrave; percu&longs;sione: Eadem via di&longs; <lb/>

&longs;oluemus &amp; illam qu&aelig;&longs;tionem. </s>
          </p>
          <p id="N1429A" type="main">
            <s id="N1429C"><emph type="center"/>DE IN &AElig;QVALIVM PONDERVM LAPSV<emph.end type="center"/></s>
          </p>
          <p id="N142A3" type="main">
            <s id="N142A5">MAgnis motibus &amp; animorum contentionibus a<lb/>

gitatam: dum hi quidem rationibus &longs;e tuentur, illi <lb/>

ver&ograve; experienti&agrave; eos urgent, <expan abbr="errori&longs;&qacute;">errori&longs;que</expan>; manife&longs;ti reos pe<lb/>

ragunt. </s>
            <s id="N142B2">Quorum opinio vulgi applau&longs;u excepta pal&shy;<lb/>

mam tulit, judice magis &longs;en&longs;u quam ratione. </s>
            <s id="N142B7">At ver&ograve; <lb/>

qui opinantur in&aelig;qualia pondera &aelig;quali lap&longs;u ruere, <lb/>

videntur magis id, quod motui per &longs;e ine&longs;t, attendi&longs;&longs;e, <lb/>

impedimenta ver&ograve; motus, qu&aelig; ab extra fiunt, veluti du&shy;<lb/>

bi&aelig; &longs;ortis neglexi&longs;&longs;e. </s>
            <s id="N142C2">Vt ver&ograve; hanc litem dirimamus, <lb/>

memori&aacute; repetendum id, quod Prop: 37. notabili 4. di&shy;<lb/>

ximus, impul&longs;um deficere &agrave; plag&agrave; perfecta, partem ver&ograve; <lb/>

hujus cum parte &aelig;quali plag&aelig; emori. </s>
            <s id="N142CB">Secundo &acirc; re&longs;i&shy;<lb/>

&longs;tenti&aacute; majori plagam induci majorem: propterea qu&ograve;d <lb/>

percutiens magis tum immoratur. </s>
            <s id="N142D2">Tertio omnia cor&shy;<lb/>

pora re&longs;i&longs;tere diui&longs;ioni, <expan abbr="at&qacute;">atque</expan>; e&oacute; magis, qu&oacute; major e&longs;t vir&shy;


<pb xlink:href="062/01/113.jpg"/>tus illarum partium unitiua, ut Prop: 1. dictum: quan&shy;<lb/>

tumuis ergo a&euml;r natur&aacute; &longs;u&aacute; &longs;it fluidus, <expan abbr="at&qacute;">atque</expan>; omni <lb/>

aur&aacute; mobilis, non tamen <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>, violenti&aacute;, ac proinde <lb/>

non <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; plag&agrave; findi pote&longs;t. </s>
            <s id="N142F1">Quar&shy;<lb/>

to majorem diui&longs;ionem fieri &agrave; majori plag&agrave;; mult&uacute;m e&shy;<lb/>

nim a&euml;ris non eadem facilitate mouemus, <expan abbr="ne&qacute;">neque</expan>; eadem <lb/>

velocitate parte ferri latiore, quam in mucronem tenua&shy;<lb/>

ta hunc penetramus. </s>
            <s id="N14300">His &longs;uppo&longs;itis: dico 1. motum qua <lb/>

tenus &agrave; grauitate procedit eiu&longs;dem &longs;peciei &longs;eu gradus, e&agrave;&shy;<lb/>

dem celeritate fieri in omnibus, quantumuis mole, figu<lb/>

r&agrave;, pondere &agrave; &longs;e differant: ratio, quia ut mobile mouea&shy;<lb/>

tur, non quilibet impul&longs;us, &longs;ed proportionatus e&longs;&longs;e debet <lb/>

ad illud mobile; ab eadem ergo proportione eadem ve&shy;<lb/>

locitas motus: at ver&oacute; impul&longs;us, quo totum mobile mo&shy;<lb/>

uetur, eandem rationem habet ad illud mobile, quam &longs;e&shy;<lb/>

mi&longs;sis illius impul&longs;us ad &longs;emi&longs;&longs;em, &amp; triens ad trientem <lb/>

eju&longs;dem mobilis; eadem ergo velocitas motus. </s>
            <s id="N14315">Quod <lb/>

idem de qualibet particul&aacute;, <expan abbr="quacun&qacute;">quacunque</expan>; fact&aacute; diui&longs;ione, di&shy;<lb/>

cendum; non min&ugrave;s enim extra illud mobile, quam in <lb/>

mobili, &amp; alijs conjunct&aelig; &longs;uo inpul&longs;u mouentur. </s>
            <s id="N14322">Dices <lb/>

virtus collecta e&longs;t fortior &longs;e ip&longs;&agrave; di&longs;per&longs;&agrave;: major ergo im<lb/>

pul&longs;us in partibus unitis, quam extra illam unionem. </s>
            <s id="N14329">Re <lb/>

&longs;pondeo illud axioma non in omnibus valere, &longs;ed tan&shy;<lb/>

tum in ordine ad actionem, qu&aelig; extra illud &longs;ubjectum <lb/>

terminatur; ita enim lux alteri conjuncta lumen longi&shy;


<pb xlink:href="062/01/114.jpg"/>&ugrave;s protendit, nihilo ex illa conjunctione luce auct&agrave;: ita <lb/>

ergo impul&longs;us partium unitarum licet magis percutiat, <lb/>

non tamen in ordine ad motum, quo illius &longs;ubjectum <lb/>

fertur, magis inuale&longs;cit, quemadmodum c&ugrave;m plures &longs;i&shy;<lb/>

mul vocem attollunt, licet magis audiatur, non tamen <lb/>

ex aliorum vociferatione &longs;ingulorum clamor facilitatur. <lb/>

Plura qu&aelig; pro hac &longs;ententi&agrave;, &amp; <expan abbr="c&otilde;tra">contra</expan> afferri po&longs;&longs;unt, &longs;uo <lb/>

loco dicemus; nunc ver&ograve; dato e&longs;&longs;e veram, illam in&aelig;qua&shy;<lb/>

litatem motus con&longs;tare, <expan abbr="at&qacute;">atque</expan>; ex ali&agrave; radice na&longs;ci paucis o&shy;<lb/>

&longs;tendemus. </s>
            <s id="N14350">Dico &longs;ecund&ograve;, illam in&aelig;qualitatem motus, <lb/>

quo in&aelig;qualia pondera mouentur, e&longs;&longs;e &agrave; medio, in quo <lb/>

fit motus; <expan abbr="at&qacute;">atque</expan>; illa corpora, quorum grauitas &longs;eu impul&shy;<lb/>

&longs;us majorem rationem habet ad &longs;uam plagam, veloci&ugrave;s <lb/>

moueri. </s>
            <s id="N1435F">Quia enim a&euml;r re&longs;i&longs;tit diui&longs;ioni ex notabili 3. <lb/>

erit plaga ad men&longs;uram hujus re&longs;i&longs;tenti&aelig;; deficiet erg&ograve; <lb/>

impul&longs;us, ac proinde velocitas motus in e&agrave; ratione, in <lb/>

qu&acirc; magnitudo plag&aelig;: igitur ut plaga ad plagam, ita ve&shy;<lb/>

locitatis decrementum. </s>
            <s id="N1436A">At ver&ograve; grauitas illorum cor&shy;<lb/>

porum majorem rationem habet, quam illorum plaga: <lb/>

&longs;it enim globus <emph type="italics"/>ab<emph.end type="italics"/> ad globum <emph type="italics"/>cd<emph.end type="italics"/> in ratione dupl&agrave;, <expan abbr="erit&qacute;">eritque</expan>; <lb/>

illorum plaga &aelig;qualis circulo maximo &longs;u&aelig; &longs;ph&aelig;r&aelig;, pro<lb/>

pterea qu&oacute;d plaga inducitur non ni&longs;i &agrave; parte inferiore, <lb/>

qu&aelig; a&euml;rem findit, &amp; cui &longs;oli a&euml;r re&longs;i&longs;tit: habet autem cir&shy;<lb/>

culus maximus &longs;ph&aelig;r&aelig; &longs;eu globi in ratione dupl&agrave; ad ali&shy;<lb/>

am &longs;ph&aelig;ram, minorem rationem, qu&aacute;m duplam, ad hu-


<pb xlink:href="062/01/115.jpg"/>jus circulum maximum; globus ergo major plagam in&shy;<lb/>

ducit minorem, qu&agrave;m ut &longs;it dupla ad plagam minoris <lb/>

globi: ut &longs;i globus major &longs;it duarum lib: erit &longs;emi&longs;sis, id&shy;<lb/>

e&longs;t lib: una, &aelig;qualis globo minori; hujus ver&ograve; plaga &longs;e&shy;<lb/>

mi&longs;sis plag&aelig; totius minor plag&acirc; tot&aacute; globi minoris. quia <lb/>

erg&ograve; plaga tollit partem &longs;ibi &aelig;qualem, maius erit decre<lb/>

mentum velocitatis in libr&agrave; un&agrave;, dum extra illud totum, <lb/>

&longs;eu globum maiorem &amp; per &longs;e, ide&longs;t in globo minori mo<lb/>

uetur. </s>
            <s id="N1439F">Et quia in medio &longs;imilari eadem plaga continu&shy;<lb/>

atur, eadem ratio erit decrementi qu&aelig; interualli; ut &longs;i in <lb/>

toto motu deficiat cubitus unus, deficiet in &longs;emi&longs;&longs;e hu&shy;<lb/>

jus motus illius &longs;emi&longs;sis: <expan abbr="atq;">atque</expan> inde ratio con&longs;tat, quam ob <lb/>

rem &agrave; principio motus in&aelig;qualia pondera &longs;imul ferri <lb/>

<expan abbr="vide&atilde;tur">videantur</expan>, inde ver&ograve; magnis &agrave; &longs;e di&longs;iungi interuallis. </s>
            <s id="N143B4">Ma&shy;<lb/>

l&egrave; ergo rationem huius in&aelig;qualitatis petunt &agrave; proporti&shy;<lb/>

one illorum ponderum, qu&aelig; &aacute; ratione cre&longs;centis plag&aelig; <lb/>

de&longs;umi debet; ablat&aacute; enim &aacute; grauitate &longs;eu impul&longs;u parte <lb/>

&aelig;quali &longs;u&aelig; plag&aelig;, reliquus impul&longs;us dabit illam in&aelig;qua&shy;<lb/>

lem velocitatem. </s>
            <s id="N143C1">Obiicies fieri non po&longs;s&egrave; ut eadem ratio <lb/>

maneat plag&aelig; in illo motu in&aelig;quali continuat&aelig;, propte<lb/>

rea qu&oacute;d a&euml;r percu&longs;&longs;us alium percutiat, <expan abbr="viamq;">viamque</expan> e&aacute; rati&shy;<lb/>

one aperiat ruenti globo, plag&aelig; imminenti &longs;e <expan abbr="&longs;ubduc&etilde;s">&longs;ubducens</expan>, <lb/>

non aliter, qu&aacute;m c&ugrave;m ultro cedentem trudimus: <expan abbr="itaq;">itaque</expan> in <lb/>

relap&longs;u globi maioris, quem ignis in &longs;ublime tulit, pri&shy;<lb/>

u&longs;quam terram feriat, ab a&euml;ris percu&longs;sione hiatum in il-


<pb xlink:href="062/01/116.jpg"/>l&aacute; fieri quidam a&longs;&longs;euerant. </s>
            <s id="N143E0">C&ugrave;m erg&ograve; a&euml;r ab illo ictu &longs;e <lb/>

&longs;ubducat, nullam inducet plagam, nullum proinde velo&shy;<lb/>

citatis decrementum; non aliter quam &longs;i globus per fi&longs;&shy;<lb/>

&longs;uram muri tran&longs;uolet muro inoffen&longs;o. </s>
            <s id="N143E9">Deinde c&ugrave;m im<lb/>

pul&longs;us continu&ograve; augeatur, erit continu&oacute; minor re&longs;i&longs;ten&shy;<lb/>

tia. </s>
            <s id="N143F0">Re&longs;pondeo aerem quidem impelli &amp; pr&aelig;currere, <lb/>

ver&ugrave;m minori celeritate, qu&agrave;m ut plagam effugiat &aacute; ter&shy;<lb/>

go h&aelig;rentem; major enim globi impetus, qu&acirc;m ut ab <lb/>

aere fluido recipiatur: unde eadem re&longs;i&longs;tentia in a&euml;re per <lb/>

forando, non min&uacute;s, qu&agrave;m &longs;i &longs;ecundo flumine elucte&shy;<lb/>

mur motu velociori, qu&agrave;m &longs;it defluxus; non minor e&shy;<lb/>

nim difficultas in perrumpendo, quam &longs;i in aqu&agrave; fiat im&shy;<lb/>

mot&agrave;. </s>
            <s id="N14401">Deinde licet a&euml;r percu&longs;&longs;us &agrave; plag&agrave; &longs;e &longs;ubducat &amp; <lb/>

pr&aelig;currat, alius tamen in locum plag&aelig; &longs;e infundit non <lb/>

minori vi findendus: <expan abbr="ne&qacute;">neque</expan>; enim a&euml;r di&longs;cerpi pote&longs;t eo <lb/>

modo, quo corpora magis den&longs;a, in quibus perruptis cor<lb/>

pus magis &longs;ubtile interceptum viam pr&aelig;&longs;tat faciliorem; <lb/>

ver&ugrave;m <expan abbr="quacun&qacute;">quacunque</expan>; plaga incidit, eadem a&euml;ris &longs;oliditas per&shy;<lb/>

rumpenda. </s>
            <s id="N14418">Ad &longs;ecundam rationem, dico velocitatem <lb/>

motus continu&ograve; quidem augeri, ac proinde illam re&longs;i&shy;<lb/>

&longs;tentiam medij auct&agrave; velocitate facili&ugrave;s perrumpi; pro&shy;<lb/>

pterea qu&oacute;d ablat&agrave; parte &aelig;quali major &longs;it exce&longs;&longs;us reli&shy;<lb/>

quus: nego autem &acirc; velociori plag&agrave; minus e&longs;&longs;e decre&shy;<lb/>

mentum. </s>
            <s id="N14425">An non veloci&ugrave;s vectem deprimunt libr&aelig; 10. <lb/>

aut 100, quam libra <emph type="italics"/>1?<emph.end type="italics"/> &amp; tamen granum unum aut deci-



<pb xlink:href="062/01/117.jpg"/>ma pars grani &aelig;qualem partem ex hoc, <expan abbr="at&qacute;">atque</expan>, ex illis tollit. <lb/>

Ver&ugrave;m deceptio latet ob exiguitatem decrementi, que&shy;<lb/>

madmodum &longs;i ad deprimendum libras 100. unum <expan abbr="at&qacute;">atque</expan>; <lb/>

alterum granum apponas. </s>
            <s id="N14442">Quia erg&ograve; retardatio motus <lb/>

e&longs;t &agrave; medio, qu&oacute; medium magis re&longs;i&longs;tit diui&longs;ioni, e&oacute; mi&shy;<lb/>

nor velocitas motus, major autem exce&longs;&longs;us tarditatis in <lb/>

minori: propterea qu&oacute;d auct&aacute; re&longs;i&longs;tenti&aacute; eadem diffe&shy;<lb/>

rentia in minori interuallo. </s>
            <s id="N1444D">E contra minuitur exce&longs;<lb/>

&longs;us in medio magis raro; <expan abbr="ita&qacute;">itaque</expan>; &longs;i detur corpus infinit&aelig; ra&shy;<lb/>

ritatis, cuiu&longs;modi vacuum, quia nulla re&longs;i&longs;tentia, nulla <lb/>

<expan abbr="quo&qacute;">quoque</expan>; erit in&aelig;qualitas motus. </s>
            <s id="N1445E">Qu&ograve;d autem &agrave; &longs;ol&aacute; re&longs;i&shy;<lb/>

&longs;tenti&agrave; medij procedat in&aelig;qualitas motus, ratio manife&shy;<lb/>

&longs;ta: idem enim pondus &longs;e ip&longs;o veloci&uacute;s, <expan abbr="at&qacute;">atque</expan>; cum alio <lb/>

pondere <expan abbr="quocun&qacute;">quocunque</expan>; exce&longs;&longs;u majori, e&aacute;dem velocitate de&shy;<lb/>

&longs;cendit, &longs;i rationem plag&aelig; &amp; re&longs;i&longs;tentiam medii in ill&acirc; <lb/>


<figure id="id.062.01.117.1.jpg" xlink:href="062/01/117/1.jpg"/><lb/>

proportione minu&agrave;s. </s>
            <s id="N1447A">Sit enim vas plumbeum, aut de <lb/>

ali&agrave; materi&agrave; graui, form&aacute; dimidi&aelig; &longs;ph&aelig;r&aelig;, cuju&longs;modi <foreign lang="greek">bgd</foreign>


<pb xlink:href="062/01/118.jpg"/>habens cauitatem in parte &longs;uperiore, &amp; &agrave; plag&acirc; auer&longs;a, <lb/>

centrum ver&ograve; grauitatis in <gap/> ne dum labitur &longs;e inuertat: <lb/>

qu&oacute;d &longs;i ergo alium globum <expan abbr="quocun&qacute;">quocunque</expan>; exce&longs;&longs;u leuio&shy;<lb/>

rem con&longs;tituas in ill&agrave; cauitate, e&aacute;dem cum illo va&longs;e ce&shy;<lb/>

leritate feretur. </s>
            <s id="N14495">At ver&ograve; &longs;i in&aelig;qualitas motus e&longs;&longs;et <lb/>

&agrave; grauitate, oporteret illud vas magis pondero&longs;um <lb/>

pr&aelig;currere, globum ver&ograve; leuiorem attolli, &amp; longo po&longs;t <lb/>

tergum interuallo relinqui. </s>
            <s id="N1449E">Obiicies grauitas e&longs;t impul<lb/>

&longs;us, impul&longs;us ver&ograve; per Prop: 2. motum producit &longs;ibi &aelig;<lb/>

qualem; &agrave; majori erg&ograve; grauitate major, ac proinde velo&shy;<lb/>

cior motus: qu&ograve;d &longs;i erg&ograve; libra una in <expan abbr="quin&qacute;">quinque</expan>; &longs;ecundis <lb/>

per &longs;patium mouet cubitorum 100, mouebit hujus du&shy;<lb/>

plum in eodem, vel &aelig;quali tempore per &longs;patium <expan abbr="dupl&utilde;">duplum</expan>. <lb/>

Deinde plaga inducitur ex motu; non enim manus &agrave; la&shy;<lb/>

pide in e&agrave; quie&longs;cente, &longs;ed ubi iram ex motu concepit, vul<lb/>

neratur: at ver&ograve; majus pondus &aelig;quali lap&longs;u magis vulne<lb/>

rat, velocior ergo motus. </s>
            <s id="N144BB">Re&longs;pondeo grauitatem e&longs;&longs;e <lb/>

impul&longs;um, &amp; velocitatem motus in e&aacute; ratione, in qu&aacute; e&longs;t <lb/>

grauitas &longs;eu impul&longs;us; dupla ergo grauitas in eodem, vel <lb/>

&aelig;quali tempore mouebit per &longs;patium duplum. </s>
            <s id="N144C4">At ver&ograve; <lb/>

c&ugrave;m inferunt libras duas Vg: plumbi in dupl&agrave; ferri celeri<lb/>

tate ad libram unam, falluntur; propterea qu&ograve;d illa gra&shy;<lb/>

uitas in alio &longs;it &longs;ubiecto, cuius partes omnes &aelig;quali gra&shy;<lb/>

uitate mouentur: &longs;icuti enim pars extra totum Vg. libra <lb/>

una &acirc; &longs;ua grauitate mouetur cum tant&agrave; velocitate, ita 


<pb xlink:href="062/01/119.jpg"/>partes librarum decem, aut centum in toto unit&aelig; e&aacute;dem <lb/>

velocitate <expan abbr="mou&etilde;tur">mouentur</expan> &aacute; &longs;u&aacute; <expan abbr="cuiq;">cuique</expan> propria grauitate. </s>
            <s id="N144DF">Qu&oacute;d <lb/>

&longs;i grauitas librarum decem con&longs;tituatur in &longs;ubiecto uni&shy;<lb/>

us libr&aelig;, tum ver&ograve; decupla velocitate mouebitur illud <lb/>

&longs;ubiectum. </s>
            <s id="N144E8">Ni&longs;i erg&ograve; grauitas magis &longs;it inten&longs;a, nihil <lb/>

proficiet ad velocitatem augendam illorum moles. <lb/>

Qu&oacute;d autem maior grauitas plagam inducat maiorem, <lb/>

ut &longs;i libr&aelig; decem percutiant libram unam, huius ratio <lb/>

e&longs;t, quia totidem fiunt plag&aelig;, quot in maiori continen&shy;<lb/>

tur partes &aelig;quales: quemadmodum &longs;i decem ictus &longs;i&shy;<lb/>

mul inferantur, aut &longs;i priu&longs;quam vis emoriatur prioris <lb/>

plag&aelig;, reliqu&aelig; &longs;equantur. </s>
            <s id="N144F9">Impul&longs;us erg&ograve; in illo &longs;ubie&shy;<lb/>

cto minori &aacute; maiori percu&longs;&longs;o magis e&longs;t inten&longs;us. <expan abbr="Atq;">Atque</expan> <lb/>

inde fit, qu&oacute;d globus minor accepta &agrave; maiori plaga pr&aelig;&shy;<lb/>

currat; qu&oacute;d &longs;i enim globos <expan abbr="quotcunq;">quotcunque</expan> e&agrave; &longs;erie di&longs;po&shy;<lb/>

nas, ut continu&ograve; maiorem minor &longs;equatur, percu&longs;&longs;o pri&shy;<lb/>

mo videbis qua&longs;i uno impetu omnes ad motum conci&shy;<lb/>

tari, ver&ugrave;m celeritate, pro ratione magnitudinis, in&aelig;&shy;<lb/>

quali. </s>
          </p>
        </subchap1>
        <subchap1 id="N14512">
          <p id="N14513" type="main">
            <s id="N14515"><emph type="center"/>Propo&longs;itio XXXXI.<emph.end type="center"/></s>
          </p>
          <p id="N1451C" type="main">
            <s id="N1451E"><emph type="center"/><emph type="italics"/>Problema II.<emph.end type="italics"/><emph.end type="center"/></s>
          </p>
          <p id="N14529" type="main">
            <s id="N1452B"><emph type="italics"/>Regulam con&longs;truere ad celeritatem &amp; tarditatem pul&longs;uum <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; <lb/>

errore metiendam.<emph.end type="italics"/></s>
          </p>
          <pb xlink:href="062/01/120.jpg"/>
          <p id="N1453B" type="main">
            <s id="N1453D">REgula h&aelig;c nullo apparatu, &longs;ed. hac arte &longs;implici <lb/>

confit &longs;iue ex ligno, &longs;iue ex qualibet ali&agrave; materi&agrave;. </s>
            <s id="N14542">Hu<lb/>

ius longitudo <emph type="italics"/>ab<emph.end type="italics"/> unius cubiti, aut ad placitum: qu&oacute; enim <lb/>

maior, e&ograve; plures differentias tarditatis indicabit: nam <lb/>

ad velocitatem &longs;ummam indicandam qu&aelig;libet magni&shy;<lb/>

tudo &longs;ufficit. </s>
            <s id="N14553">Latitudo ver&ograve;, qu&aelig; cordam &longs;eu filum ca&shy;<lb/>

piat cum numerorum notis eidem ad&longs;criptis. </s>
            <s id="N14558">Filum <lb/>

porro eo modo, quo fidibus aptatur; parte &longs;uperiore <lb/>

trochle&acirc; ver&longs;atili conuolutum, parte ver&ograve; inferiore fora <lb/>

mine tran&longs;mi&longs;&longs;um, globulum habens dependentem, qui <lb/>

eidem rectitudinem pr&aelig;&longs;tat &amp; pondus. </s>
            <s id="N14563">Tota longitu&shy;<lb/>

do regul&aelig;, qu&aelig; continetur inter foramen &amp; trochleam, <lb/>

&aelig;qualiter &longs;ecetur in partes quotlibet Vg. 60, aut 100. <lb/>


<figure id="id.062.01.120.1.jpg" xlink:href="062/01/120/1.jpg"/><lb/>

quas trochle&agrave; laxat&acirc; nodulus <emph type="italics"/>q,<emph.end type="italics"/> globulo interea de&longs;cen&shy;


<pb xlink:href="062/01/121.jpg"/>dente, percurrit, <expan abbr="&longs;uo&qacute;">&longs;uoque</expan> contactu quot eju&longs;modi &longs;egmen&shy;<lb/>

ta contineat longitudo eju&longs;dem fili cum &longs;uo globulo &agrave; <lb/>

foramine penduli, o&longs;tendit. </s>
            <s id="N14585">C&ugrave;m ergo per dictum in&shy;<lb/>

&longs;trumentum pul&longs;us celeritatem indagare voles, trochle&shy;<lb/>

am ver&longs;ando filum e&ograve; <expan abbr="u&longs;&qacute;">u&longs;que</expan>; laxa, dum globulus in <emph type="italics"/>e<emph.end type="italics"/> Vg. <lb/>

aut <emph type="italics"/>g<emph.end type="italics"/> de&longs;cendat: quom ex <emph type="italics"/>g,<emph.end type="italics"/> in quo naturaliter &agrave; motu <lb/>

quie&longs;cit, in <emph type="italics"/>l<emph.end type="italics"/> vel <emph type="italics"/>o<emph.end type="italics"/> dimotum inde recurrere &longs;inas; in&shy;<lb/>

terea, dum globulus per arcum <emph type="italics"/>cd<emph.end type="italics"/> ultra <expan abbr="citra&qacute;">citraque</expan> <emph type="italics"/>g<emph.end type="italics"/> excurrit, <lb/>

<expan abbr="plure&longs;&qacute;">plure&longs;que</expan>; recur&longs;us facit, agitationem quidem arteri&aelig; ma&shy;<lb/>

nu, motum ver&ograve; perpendiculi vi&longs;u explora, <expan abbr="at&qacute;">atque</expan>; unum <lb/>

alteri compara. </s>
            <s id="N145D2">Qu&oacute;d &longs;i tardior arteri&aelig; motus, perpen&shy;<lb/>

diculum trochle&aacute; laxat&aacute; producas, &longs;i celerior contrahas <lb/>

&AElig;quato demum <expan abbr="utriu&longs;&qacute;">utriu&longs;que</expan>; motu, qu&aelig;nam &longs;it celeritatis <lb/>

ratio, ex numerorum diui&longs;ione, quem nodulus cum filo <lb/>

depre&longs;&longs;us indicabit, facil&egrave; cogno&longs;ces. </s>
            <s id="N145E1">Quin &amp; quamli&shy;<lb/>

bet mutationem ad &longs;ingula momenta ex collatione ad <lb/>

huiu&longs;modi numeros fact&acirc; conijcies. </s>
            <s id="N145E8">Vbi ergo men&longs;u&shy;<lb/>

ram pul&longs;us quam maxim&egrave; naturalis hac vi&agrave; deprehen&shy;<lb/>

des: diui&longs;ionis interuallum, quod nodulus indicabit, <lb/>

diligenter nota; ad cuius motum reliquos pul&longs;us com<lb/>

parando illorum exce&longs;&longs;us &amp;, defectus facil&egrave; obtinebis. <lb/>

Porro huiu&longs;modi regulam celeritatem &amp; tarditatem pul<lb/>

&longs;uum <expan abbr="ab&longs;&qacute;">ab&longs;que</expan>; errore meti i, hac vi&agrave; o&longs;tendemus. </s>
            <s id="N145FB">Pul&longs;us in <lb/>

ter &longs;e aut &longs;unt &aelig;quales, quorum eadem e&longs;t velocitas mo&shy;<lb/>

tus, atque i&longs;dem fiunt momentis: aut in&aelig;quales, cele&shy;


<pb xlink:href="062/01/122.jpg"/>ritate &amp; tarditate &agrave; &longs;e differentes, <expan abbr="quor&utilde;">quorum</expan> in&aelig;qualia &longs;unt <lb/>

durationis momenta. </s>
            <s id="N1460C">Quia ergo motus perpendiculi <lb/>

e&longs;t illorum men&longs;ura; erit quidem &aelig;qualium pul&longs;uum &aelig;&shy;<lb/>

qualis, in&aelig;qualium ver&ograve; in&aelig;qualis in ea ratione, in qu&acirc; <lb/>

velocitas pul&longs;uum. </s>
            <s id="N14615">At ver&ograve; recur&longs;us &amp; excur&longs;us perpen<lb/>

diculi ex eadem productione inter &longs;e &longs;unt &aelig;quales: pro&shy;<lb/>

pterea qu&oacute;d perpendiculum ex quolibet puncto <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> <lb/>

circuli &aelig;quali tempore recurrit in &longs;uam &longs;tationem per <lb/>

Prop: 24. &longs;unt autem excur&longs;us <expan abbr="quo&qacute;">quoque</expan>; inter &longs;e &aelig;quales per <lb/>

Prop: 25. excur&longs;us ergo &amp; recur&longs;us in un&agrave; circulatione <lb/>

&longs;imul &longs;umpti &longs;unt &aelig;quales excur&longs;ibus &amp; recur&longs;ibus o&shy;<lb/>

mnium circulationum &longs;imul <expan abbr="quo&qacute;">quoque</expan>; &longs;umptis: &amp; quia uni <lb/>

&aelig;qualium pul&longs;uum circulatio a&longs;&longs;umpta e&longs;t &aelig;qualis, e&shy;<lb/>

runt reliqu&aelig; circulationes reliquis pul&longs;ibus &aelig;quales. <lb/>

Motus ergo perpendiculi ex e&aacute;dem productione fili <lb/>

metitur pul&longs;us inter &longs;e &aelig;quales. </s>
            <s id="N1463A">Quia ver&ograve; motus per&shy;<lb/>

pendiculi per arcus &longs;imiles in&aelig;qualium circulorum ra&shy;<lb/>

tionem habent ad &longs;e quam &longs;inus illorum arcuum, hoc e&longs;t <lb/>

line&aelig; &longs;ubten&longs;&aelig; arcus dupli, per Prop: 25. ac proinde <lb/>

quam habent motus per diametrum illorum circulo&shy;<lb/>

rum per Prop: 15. motus autem per diametrum &longs;e habent <lb/>

ut quadrata temporum per Prop: 12. </s>
            <s id="N14649">Si &longs;umatur radix <lb/>

quadrata illius proportionis, quam habent diametri ad <lb/>

&longs;e, erunt in eadem ratione tempora motus, in qu&agrave; radices <lb/>

quadrat&aelig;: ut &longs;i diameter maioris circuli ad diametrum 


<pb xlink:href="062/01/123.jpg"/>minoris circuli &longs;it quadrupla, huius radix quadrata, duo, <lb/>

dabit tempus in ratione dupl&aacute;: &longs;i ergo motus per dia&shy;<lb/>

metrum minoris circuli &longs;it unius minuti, erit motus ma&shy;<lb/>

ioris diametri duorum minutorum. </s>
            <s id="N1465C">Sunt autem pro&shy;<lb/>

ductiones fili &longs;emidiametri illorum circulorum, in qui&shy;<lb/>

bus perpendiculum mouetur, &aelig;quales diui&longs;ionum in&shy;<lb/>

teruallis, qu&aelig; globulus in productione fili percurrit: ea&shy;<lb/>

dem ergo proportio interualli, qu&aelig; motus illorum cir&shy;<lb/>

culorum. </s>
            <s id="N14669">Quia ergo motus in&aelig;qualium circulorum <lb/>

metiuntur pul&longs;us in&aelig;quales, eo&longs;dem metientur diui&longs;io&shy;<lb/>

num interualla: ac proinde regulam con&longs;truximus ad <lb/>

velocitatem &amp; tarditatem pul&longs;uum <expan abbr="ab&longs;q;">ab&longs;que</expan> errore metien<lb/>

dam, quod erat faciendum. </s>
          </p>
        </subchap1>
      </chap>
      <chap id="N14678">
        <p id="N14679" type="main">
          <s id="N1467B"><emph type="center"/>Parergon.<emph.end type="center"/></s>
        </p>
        <p id="N14682" type="main">
          <s id="N14684"><emph type="center"/><emph type="italics"/>Problema.<emph.end type="italics"/><emph.end type="center"/></s>
        </p>
        <p id="N1468F" type="main">
          <s id="N14691"><emph type="italics"/>Horologium con&longs;truere, quod &longs;uo motu tempus numeret diui&longs;um <lb/>

in partes minores, qu&agrave;m tertias unius &longs;ecundi.<emph.end type="italics"/></s>
        </p>
        <p id="N1469A" type="main">
          <s id="N1469C">QVanti u&longs;us &amp; utilitatis &longs;it tempus in qu&agrave;m minimas <lb/>

partes diui&longs;um po&longs;&longs;e numerare, <expan abbr="nor&utilde;t">norunt</expan> A&longs;tronomi, <lb/>

&amp; ex conatibus Tychonis Brahe &longs;atis con&longs;tat; qui ad hu<lb/>

iu&longs;modi horologia fabricanda nihil intentatum reliquit: <lb/>

quam uis huius votum non ni&longs;i ad &longs;ecunda numeranda 


<pb xlink:href="062/01/124.jpg"/>le extendit. </s>
          <s id="N146AF">Aliquid ampli&ugrave;s damus: &amp; non mod&oacute; &longs;e&shy;<lb/>

cunda, ver&ugrave;m etiam huius triente minorem partem nu&shy;<lb/>

merabimus. </s>
          <s id="N146B6">Horologium autem hoc nullis rotulis cir&shy;<lb/>

cumagitur, nullis ponderibus libratur; ver&ugrave;m &longs;u&acirc; nati&shy;<lb/>

u&acirc; grauitate, &agrave; qu&agrave; nu&longs;quam aberrat, ad normam pr&aelig;&shy;<lb/>

&longs;criptam agitatur: illud inquam idem, quod ad celerita&shy;<lb/>

tem &amp; tarditatem pul&longs;uum metiendam paulo ante con&shy;<lb/>

&longs;truximus. </s>
          <s id="N146C3">Huius enim pondus &agrave; filo pendulum &longs;uo <lb/>

motu tempus in quotlibet partes diui&longs;um numerabit. <lb/>

Qu&ograve;d autem hic motus minor e&longs;&longs;e po&longs;sit, qu&acirc;m tertia <lb/>

pars unius &longs;ecundi, ita o&longs;ten demus: agitationes arteri&aelig;, <lb/>

cuiu&longs;modi in me ip&longs;o numeraui, &longs;patio unius hor&aelig; fi&shy;<lb/>

unt 4850. motus autem perpendiculi his &aelig;quales fiunt &acirc; <lb/>

productione fili maiori qu&agrave;m digitorum 5. </s>
          <s id="N146D2">Quia ergo <lb/>

motus circulorum &longs;unt in ratione &longs;uorum temporum, <lb/>

quam habent diametri ad &longs;e duplicatam, per Prop: 28. &longs;i <lb/>

&longs;umatur pars nona huius productionis pro &longs;emidiame&shy;<lb/>

tro circuli, erit hic motus triplo velocior illo, ac proinde <lb/>

huius recur&longs;us &longs;patio hor&aelig; unius 14550 mult&ograve; plures, <lb/>

qu&agrave;m 10800 partes terti&aelig; unius &longs;ecundi. </s>
          <s id="N146E1">Et quia hic mo&shy;<lb/>

tus bifariam &longs;ecari pote&longs;t in excur&longs;um &amp; recur&longs;um, fient <lb/>

&longs;an&egrave; &longs;patio unius hor&aelig; partes 29100. </s>
          <s id="N146E8">Horologium erg&ograve; <lb/>

con&longs;truximus, quod &longs;uo motu tempus numerat diui&longs;um <lb/>

in partes minores qu&agrave;m tertias unius &longs;ecundi. </s>
          <s id="N146EF">Quia ta&shy;<lb/>

men hic motus veloci&longs;simus ob paruitatem circelli mi-


<pb xlink:href="062/01/125.jpg"/>n&ugrave;s e&longs;t diuturnus, &longs;ufficiet filum producere, <expan abbr="quou&longs;&qacute;">quou&longs;que</expan>; mo<lb/>

tus perpendiculi &longs;it &aelig;qualis uni &longs;ecundo. </s>
          <s id="N146FE">Quod quidem <lb/>

hac ratione con&longs;equemur: &longs;umatur <expan abbr="qu&aelig;cun&qacute;">qu&aelig;cunque</expan>; produ&shy;<lb/>

ctio fili, aliquant&oacute; tamen longior, qu&ograve; min&ugrave;s cit&ograve; &agrave; mo&shy;<lb/>

tu conquie&longs;cat: <expan abbr="numerentur&qacute;">numerenturque</expan>; huius excur&longs;us per &longs;pati&shy;<lb/>

um unius hor&aelig; quadrantis, &amp; &longs;int Vg. 300. <expan abbr="erunt&qacute;">eruntque</expan>; &longs;pa&shy;<lb/>

tio hor&aelig; unius 1200. </s>
          <s id="N14717">Qu&ograve;d &longs;i erg&ograve; fiat ut quadratum <lb/>

temporis, nimirum trium &longs;ecundorum, ide&longs;t 9 ad 1, ita <lb/>

longitudo fili ad minorem, erit hujus motus &aelig;qualis <lb/>

uni &longs;ecundo. <lb/>


<arrow.to.target n="fig38"/></s>
        </p>
      </chap>
    </body>
    <back>
      <section>
        <pb xlink:href="062/01/126.jpg"/>
        <p id="N1472A" type="main">
          <s id="N1472C"><emph type="center"/>&lsqb;Errata not transcribed.&rsqb;<emph.end type="center"/></s>
        </p>
        <pb xlink:href="062/01/127.jpg"/>
        <p id="N14736" type="main">
          <s id="N14738"><emph type="center"/>PRAG&AElig;.<emph.end type="center"/></s>
        </p>
        <p id="N1473F" type="main">
          <s id="N14741"><emph type="center"/>Typis Ioannis Bilin&aelig;.<emph.end type="center"/></s>
        </p>
        <p id="N14748" type="main">
          <s id="N1474A"><emph type="center"/><emph type="italics"/>Anno<emph.end type="italics"/><emph.end type="center"/></s>
        </p>
        <p id="N14755" type="main">
          <s id="N14757"><emph type="center"/><emph type="italics"/>M. DC. XXXIX:<emph.end type="italics"/><emph.end type="center"/></s>
        </p>
        <pb xlink:href="062/01/128.jpg"/>
        <pb xlink:href="062/01/129.jpg"/>
      </section>
    </back>
  </text>
</archimedes>