Mercurial > hg > mpdl-xml-content

<?xml version="1.0"?>
<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></translator>
    <lang>la</lang>
    <cvs_file>marci_regul_062_la_1639.xml</cvs_file>
    <cvs_version></cvs_version>
    <locator>062.xml</locator>
  </info>
  <text>
    <front>
      <section>
        <pb xlink:href="062/01/001.jpg"></pb>
        <p id="N1001B" type="main">
          <s id="N1001D"><emph type="center"></emph>DE PROPORTIONE MOTUS<emph.end type="center"></emph.end></s>
        </p>
        <p id="N10024" type="main">
          <s id="N10026"><emph type="center"></emph><emph type="italics"></emph>seu <lb></lb>
Regula ſphyigmica <lb></lb>AD celeritatem et tarditatem pulſuum ex illius motu <lb></lb>
ponderibus geometricis librato <expan abbr="abſq;">abſque</expan> errore metiendam. </s>
          <lb></lb>
          <s id="N10038">
Authore <lb></lb>
Ionanne Marco Marci Phil:ae er Medic:ae Doctore et ordi<lb></lb>
nario Profeſſore eiuſdem Medic: facultatis in Vni<lb></lb>
uerſitate Pragenſi Phyſico Reg: Boh.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
        </p>
        <pb xlink:href="062/01/002.jpg"></pb>
        <p id="N10048" type="caption">
          <s id="N1004A">IOANNES MARCVS MARCI PHIL: &amp; MEDIC: DOCTOR <lb></lb><emph type="italics"></emph>et Profeſſor natus Landscronæ Hermundurarum in Boëmia <lb></lb>anno 1595, 13 Iunij.<emph.end type="italics"></emph.end></s>
        </p>
      </section>
      <section>
        <figure id="id.062.01.002.1.jpg" xlink:href="062/01/002/1.jpg"></figure>
        <pb xlink:href="062/01/003.jpg"></pb>
        <p id="N1005E" type="main">
          <s id="N10060"><emph type="center"></emph>DIVO <lb></lb>FERDINANDO <lb></lb>TERTIO<emph.end type="center"></emph.end></s>
        </p>
        <p id="N1006B" type="main">
          <s id="N1006D"><emph type="center"></emph>AUGUSTISSIMO ROMANORUM <lb></lb>IMPERATORI<emph.end type="center"></emph.end></s>
        </p>
        <p id="N10076" type="main">
          <s id="N10078"><emph type="center"></emph>Hungariæ &amp; Bohemiæ Regi &amp;c. <lb></lb><emph type="italics"></emph>Domino meo Clementiſſimo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
        </p>
        <p id="N10085" type="main">
          <s id="N10087"><emph type="center"></emph>Auguſtiſsime Cæſar<emph.end type="center"></emph.end></s>
        </p>
        <p id="N1008E" type="main">
          <s id="N10090">DVm ut annus hic nouus TUÆ Maje<lb></lb>ſtati auſpicatus ordiatur, vota conci<lb></lb>pio, &amp; à tenuitate meà munuſculum <lb></lb>TUÆ Maie: gratum e flagito: ecce ti<lb></lb>bi hunc ipſum, qui annum auſpicatur, <expan abbr="atq;">atque</expan> ſua in ve<lb></lb>ſtigia reuoluit, motum mihi ultrò, ut Mercurius ſit <lb></lb>&amp; munus, ſe offerentem: quid enim inquit extra <lb></lb>me quæris? in me ſunt omnia.</s>
          <s id="N100A5"> Abſit, in quam ego, <lb></lb>ut ad Cæſarem eas, qui tam inſtabilis es &amp; infidus,


<pb xlink:href="062/01/004.jpg"></pb><expan abbr="atq;">atque</expan> eadem, quæ dare videbaris, rurſum aufers. </s>
          <s id="N100B1">Nul<lb></lb>lum, inquit ille periculum ab inſtabilitate: hic enim <lb></lb>Senex, ut vides, me quadratum fecit: quòd ſi tibi ita <lb></lb>videtur, me vel cubum facias. </s>
          <s id="N100BA">Benè inquam res ha<lb></lb>bet, ad Cæſaremibis: verùm his ego te priùs circu<lb></lb>lis illigabo, <expan abbr="atq́">atque</expan>; his lineis ceu virgulis ſub leges Geo<lb></lb>metriæ cogam, ut non niſi ad nutum Cæſaris mo<lb></lb>uearis: ſis autem menſura &amp; ſimul cuſtos illius mo<lb></lb>tus, à quo Regalis vita pendet. </s>
          <s id="N100CB">Hunc ergo motum <lb></lb>Auguſtiſsime Cæſar modulis geometricis adſtri<lb></lb>ctum, &amp; nunc Medicinæ famulantem ad TUAM <lb></lb>Maieſtatem tanquam Primum Motorem remitto, <lb></lb>qui &amp; cores &amp; Sol Imperij &amp; Regnorum, Tuæque <lb></lb>benignitatis motu hunc in me motum commoui<lb></lb>ſti. </s>
          <s id="N100DA">Motum quidem hunc TUÆ Maieſtati vt Soli <lb></lb>&amp; Motori, at verò eidem Soli vt illuminatori Iri<lb></lb>dem votiuam, gratitudinis &amp; debitæ obſervantiæ <lb></lb>ergo à TUÆ Maieſtatis radijs conceptam hic idem <lb></lb>annus in proximo dabit: quam huc <expan abbr="uſq́">uſque</expan>; quantum<lb></lb>uis conſpici volentem, &amp; ſuà pulchritudine ambi<lb></lb>tioſam eadem fata, quæ pacem morantur, detinue<lb></lb>re: ut nimirum hoc demum anno pace é victorijs


<pb xlink:href="062/01/005.jpg"></pb>TUÆ Maieſtatis naſcente &amp; pluuiá ſanguinis ejuſ<lb></lb>dem radijs ſiccatá, Iris conſpicua veluti arcus trium <lb></lb>phalis TUÆ Maieſtatis ſequatur pompam trium<lb></lb>phalem. </s>
        </p>
        <p id="N100F9" type="main">
          <s id="N100FB">Auguſtiſsimæ Maieſtatis Tuæ </s>
        </p>
        <p id="N100FE" type="main">
          <s id="N10100"><emph type="center"></emph>humillimus Servus &amp; Cliens<emph.end type="center"></emph.end></s>
        </p>
        <p id="N10107" type="main">
          <s id="N10109"><emph type="italics"></emph>Joannes Marcus Marci.<emph.end type="italics"></emph.end></s>
        </p>
      </section>
    </front>
    <body>
      <chap id="N10111">
        <pb xlink:href="062/01/006.jpg"></pb>
        <p id="N10115" type="main">
          <s id="N10117"><emph type="center"></emph>Definitiones.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N1011E" type="main">
          <s id="N10120"><emph type="center"></emph>1.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N10127" type="main">
          <s id="N10129"><emph type="italics"></emph>Contraria dicuntur quæ tollunt, uel impediunt ſu<lb></lb>um contrarium.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10132" type="main">
          <s id="N10134">NAm contrariorum eſt natura, ut ſimul eſſe <lb></lb>non poſsint in uno ſubjecto: necesse ergo unum <lb></lb>ab altero tolli, aut quò minùs recipiatur in illo <lb></lb>ſubiecto impediri. </s>
          <s id="N1013D"> <expan abbr="Itaq́">Itaque</expan>; calori frigus contrarium di<lb></lb>cunt non totà ſuà latitudine, ſed ſecundùm illos gra<lb></lb>dus, qui ſimul eſſe non poſſunt in codem ſubjecto,<lb></lb>quatuor autem gradus caloris cum totidem gradibus <lb></lb>frigoris non eſſe contrarios, verúm inter ſe miſceri, <expan abbr="atq́">atque</expan>; <lb></lb>ex illis ita permixtis temperiem naſci. </s>
          <s id="N10152">Simili modo <lb></lb>motus motui dicet ut contrarius, qui à termino illius <lb></lb>idem mobile abducit, <expan abbr="nullamq́">nullamque</expan>; partem viæ ſeu acceſ<lb></lb>ſus ad illum terminum habet communem. </s>
          <s id="N1015F">Vt ſi in <lb></lb>fig: 1 ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> moveatur, erit motus contrarius, qui ex <lb></lb>eodem <emph type="italics"></emph>a<emph.end type="italics"></emph.end> idem mobilè in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> ab ducit. </s>
          <s id="N1017E">Motus verò ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <lb></lb><emph type="italics"></emph>d<emph.end type="italics"></emph.end> non erit contrarius abſolutè, propterea quòd hic mo<lb></lb>tus non abducit à termino motus <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> verùm ad hunc in <lb></lb>omni puncto propiùs accedit: quód ſi enim ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ducan<lb></lb>tur lineæ <emph type="italics"></emph>be. bf. bg,<emph.end type="italics"></emph.end> erit linea <emph type="italics"></emph>bf<emph.end type="italics"></emph.end> minor quam <emph type="italics"></emph>be,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> mi<lb></lb>nor quam <emph type="italics"></emph>bf.<emph.end type="italics"></emph.end> Hujuſmodi ergo motus dum inter ſe


<pb xlink:href="062/01/007.jpg"></pb>miſcentur, non ſe mutuó tollunt abſolutè, verúm in <lb></lb>eo in quo ſunt ſimiles, in motum medium coaleſcentes <lb></lb>vià mediá <expan abbr="vtriq́;">vtrique;</expan> termino propinquant: in quantum <lb></lb>verò contrarij, illam rectitudinem viæ tollunt. </s>
          <s id="N101CE">Con<lb></lb>traria ergo dicuntur quæ tollunt, vel impediunt ſuum <lb></lb>contrarium. </s>
        </p>
        <p id="N101D5" type="main">
          <s id="N101D7"><emph type="center"></emph>2.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N101DE" type="main">
          <s id="N101E0"><emph type="italics"></emph>Similia verò qua augent vel perficiunt ſuum ſimile.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N101E7" type="main">
          <s id="N101E9">VT ſi ad motum <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> alius ac cedat impulſus, qui per <lb></lb>eandem lineam <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> moveat idem mobile, erit hic <lb></lb>motus illi ſimilis, ac proinde eundem dicetur augere, <lb></lb>quemadmodum calor alium calorem ſibi ſimilem: ca<lb></lb>lor autem à luce, aut è contra, quia diſsimiles, non di<lb></lb>centur augeri. </s>
        </p>
        <p id="N10202" type="main">
          <s id="N10204"><emph type="center"></emph>3.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N1020B" type="main">
          <s id="N1020D"><emph type="italics"></emph>Et mixta à quibus actiones procedunt mixtœ.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10214" type="main">
          <s id="N10216">ILlarum nimirum qualitatum, quæ vim habent a<lb></lb>gendi, latiùs ſumpto nomine actionis, pro qualibet <lb></lb>actione etiam perfectiuà: <expan abbr="itaq́">itaque</expan>; illa <expan abbr="quoq́">quoque</expan>; mutatio, <lb></lb>quam dulcoacidum inducit, actio dicetur mixta: <lb></lb>quem admodum frigus calore temperatum actionem <lb></lb>efficere èx <expan abbr="utroq́">utroque</expan>; mixtam. </s>
          <s id="N1022F">Sic ergo motus dicetur


<pb xlink:href="062/01/008.jpg"></pb>mixtus, dum inpulſus <expan abbr="neq́">neque</expan>; in totum ſimilis, <expan abbr="neq́">neque</expan>; in to<lb></lb>tum eſt contrarius alteri impulſui. </s>
        </p>
        <p id="N10240" type="main">
          <s id="N10242"><emph type="center"></emph>4.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N10249" type="main">
          <s id="N1024B"><emph type="italics"></emph>Motus abſoluté contrarij, qui idem mòbile ducunt <lb></lb>ex eodem puncto ad partes oppoſitas ejusdem lineæ rectæ.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10254" type="main">
          <s id="N10256"><emph type="center"></emph>5.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N1025D" type="main">
          <s id="N1025F"><emph type="italics"></emph>Motus ſecundum quid contrarij, qui ex illo puncto, <lb></lb>ſeù principio motus angulum ducunt majorem a ut minorem recto <lb></lb>minorem verò duobus rectis.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1026A" type="main">
          <s id="N1026C"><emph type="center"></emph>6.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N10273" type="main">
          <s id="N10275"><emph type="italics"></emph>Motus qui ex eodem puncto tendunt ad eaſdem <lb></lb>partes lineæ rectæ inter ſe ſunt ſimiles.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1027E" type="main">
          <s id="N10280"><emph type="center"></emph>7.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N10287" type="main">
          <s id="N10289"><emph type="italics"></emph>Motus qui minori angulo abſiſtunt magis ſunt <lb></lb>ſimiles<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N10292" type="main">
          <s id="N10294"><emph type="center"></emph>8.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N1029B" type="main">
          <s id="N1029D"><emph type="italics"></emph>Motus perfectè mixti quorum principium eſt an<lb></lb>gulus rectus.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N102A6" type="main">
          <s id="N102A8">VT ſi in fig: 2. ex eodem puncto <emph type="italics"></emph>a<emph.end type="italics"></emph.end> moueatur idem <lb></lb>mobile ſimul in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>e,<emph.end type="italics"></emph.end> dicetur hic motus abſolutè <lb></lb>contrarius. </s>
          <s id="N102C1">Motus verò ex eodem puncto <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>d,<emph.end type="italics"></emph.end><lb></lb>aut in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> quorum hic major, ille minor ſit angulo re-


<pb xlink:href="062/01/009.jpg"></pb>cto, erunt motus ſecundùm quid contrarij: propterea <lb></lb>quòd non ex toto ſe impediunt aut tollunt: contrarie<lb></lb>tas enim motus ex acceſſu &amp; receſſu ad eundem termi<lb></lb>num prouenit: motus autem ſecundùm quid contrari; <lb></lb>dum inter ſe miſcentur, licet ſuos terminos non aſ<lb></lb>ſequantur, ijſdem tamen continuò fiunt propiores. <lb></lb>Quia verò lineæ motus quò minori angulo abſiſtunt, <lb></lb>eò propiùs accedunt ad terminum, erunt hi motus ma<lb></lb>gis ſimiles: perfecta autem ſimilitudo in eadem lineà <lb></lb>rectà, quæ ad eundem terminum perducit. </s>
          <s id="N102F9">Motus de<lb></lb>mum, quorum principium eſt angulus rectus, quia ex <lb></lb>illà mixtione propiores quidem fiunt termino motus, <lb></lb>intervallum autem in fine motus ſpatio inter principi<lb></lb>um &amp; terminum motus eſt æquale, nimirum in fig: 7. <lb></lb>dicentur motus perfectè mixti: tantùm enim con<lb></lb>trarij, quantùm ſimilitudinis ineſt; </s>
        </p>
      </chap>
      <chap id="N10308">
        <subchap1 id="N10309">
          <p id="N1030A" type="main">
            <s id="N1030C"><emph type="center"></emph>Poſitiones:<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10313" type="main">
            <s id="N10315"><emph type="center"></emph>I.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N1031C" type="main">
            <s id="N1031E"><emph type="italics"></emph>Simile &amp; æquale auget ſuum ſimile in eadem rati<lb></lb>one, totum quidem totum, pars verò partem ſibi æqualem.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10327" type="main">
            <s id="N10329">SIt linea <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> æqualis lineæ <emph type="italics"></emph>ef,<emph.end type="italics"></emph.end> &amp; diuidatur bifariam in <lb></lb><emph type="italics"></emph>b<emph.end type="italics"></emph.end>: quód ſi ergo tota linea <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> addatur toti <emph type="italics"></emph>e f,<emph.end type="italics"></emph.end> ſicuti tota <lb></lb>
<figure id="id.062.01.009.1.jpg" xlink:href="062/01/009/1.jpg"></figure><lb></lb>


<pb xlink:href="062/01/010.jpg"></pb>toti, &amp; ſemiſsis ſemiſsi, &amp; <expan abbr="triẽs">triens</expan> trienti eſt æqualis, ita to<lb></lb>ta totam, &amp; ſemiſsis ſemiſſem, &amp; triens trientem auge<lb></lb>bit in eadem ratione, in quà tota totam. </s>
            <s id="N10360">Si ergo ſemiſ<lb></lb>ſis <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> addatur toti <emph type="italics"></emph>ef,<emph.end type="italics"></emph.end> quia ut <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> ita <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> æqualis <emph type="italics"></emph>ad<emph.end type="italics"></emph.end><lb></lb> ad eandem <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> erit augmentum æquale ejuſdem ſemiſ<lb></lb>ſi: ſola ergo ſemiſsis lineæ <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> augetur à ſemiſſe lineæ <emph type="italics"></emph>ad<emph.end type="italics"></emph.end><lb></lb>in eà ratione, in quà tota auget totam. </s>
            <s id="N1039F">Et quia linea <lb></lb><emph type="italics"></emph>ad<emph.end type="italics"></emph.end> ad ſemiſſem <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> rationem habet duplam, habebit <lb></lb><expan abbr="quoq́">quoque</expan>, <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> ad illam ſemiſſem, hoc eſt ad ſuum augmen<lb></lb>tum rationem duplam. </s>
            <s id="N103BC">Simili modo ſi augmentum <emph type="italics"></emph>cd<emph.end type="italics"></emph.end><lb></lb> ſit triens lineæ <emph type="italics"></emph>ad,<emph.end type="italics"></emph.end> erit linea <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> ad illud augmentum in <lb></lb>ratione triplá. </s>
            <s id="N103D4">Simile ergo &amp; æquale auget ſuum ſi<lb></lb>mile in eadem ratione &amp;c. </s>
          </p>
          <p id="N103D9" type="main">
            <s id="N103DB"><emph type="center"></emph>II.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N103E2" type="main">
            <s id="N103E4"><emph type="italics"></emph>Contrarium æquale tollit vel impedit ſuum contra<lb></lb>rium in eadem ratione, totum quidem totum, pars verò partem <lb></lb>ſibi æqualem<emph.end type="italics"></emph.end></s>
            <figure id="id.062.01.010.1.jpg" xlink:href="062/01/010/1.jpg"></figure>
            <lb></lb>
          </p>
          <p id="N103F5" type="main">
            <s id="N103F7">Sit <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ipſi <emph type="italics"></emph>df<emph.end type="italics"></emph.end> contrarium &amp; æquale, &amp; diuidantur bi<lb></lb>fariam in <emph type="italics"></emph>c<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>e<emph.end type="italics"></emph.end>: quia ergo <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> totum eſt æquale ipſi <lb></lb><emph type="italics"></emph>df<emph.end type="italics"></emph.end> toti, erit <expan abbr="quoq́">quoque</expan> ſemiſsis <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> æqualis ſemiſsi <emph type="italics"></emph>cb<emph.end type="italics"></emph.end>: tollit <lb></lb>autem <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> totum <emph type="italics"></emph>df,<emph.end type="italics"></emph.end> tollet ergo &amp; <emph type="italics"></emph>eb<emph.end type="italics"></emph.end> totum <emph type="italics"></emph>ef:<emph.end type="italics"></emph.end> quod <lb></lb>idem de reliquis partibus, <expan abbr="quacunq́">quacunque</expan> ratione diuidan<lb></lb>tur, oſtendemus. </s>
            <s id="N10453">Dices calorem &amp; frigus eſſe contra<lb></lb>ria, <expan abbr="neq́">neque</expan>; tamen à calore totum frigus, <expan abbr="neq́">neque</expan>; à frigore to-


<pb xlink:href="062/01/011.jpg"></pb>tum calorem tolli &amp; expelli, verùm tantum illorum <lb></lb>exceſſus: partes verò mutilatas inter ſe miſceri, &amp; ami<lb></lb>cabili ſocietate in eodem ſubjecto coniungj</s>
            <s id="N10468">orùm <lb></lb>ſi in gradibus remiſsis deeſt illa proprietas contrari<lb></lb>orum, <expan abbr="neq́">neque</expan>; ſanè contrarietas inerit. </s>
            <s id="N10473">Quidquid tamen <lb></lb>ſit de illis qualitatibus, de quibus alio loco diſſeren<lb></lb>dum, conſtat ex illà, quæ in motu eſt contrarietate, ſi <lb></lb>æqualis ſit, nullum ſe qui motum: ſi major, hujus ex<lb></lb>ceſſui eſſe æqualem. </s>
            <s id="N1047E">Conſtituatur enim in bilance <emph type="italics"></emph>ab <lb></lb>c<emph.end type="italics"></emph.end> pondus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> 8. lib. quod vectem deprimet impulſu 8, li<lb></lb>
<figure id="id.062.01.011.1.jpg" xlink:href="062/01/011/1.jpg"></figure><lb></lb><lb></lb>
brali, <expan abbr="atq́">atque</expan>; hujus impulſus non niſi ab æquali totidem li<lb></lb>brarum ponderis <emph type="italics"></emph>b<emph.end type="italics"></emph.end> impulſu inhibetur. </s>
            <s id="N104A5">Quòd ſi pon<lb></lb>dus in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> lib. 5. eundem vectem ſurſum trahat, erit im<lb></lb>pulſus in <emph type="italics"></emph>a<emph.end type="italics"></emph.end> lib. 3. pondus ergo ſeu impulſus in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> contra<lb></lb>rius impulſui in <emph type="italics"></emph>a<emph.end type="italics"></emph.end> tollit partem ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> ſibi æqualem. </s>
            <s id="N104CC">Si<lb></lb>mili modo ſi duo globi æquali niſu, &amp; in eadem lineá <lb></lb>motus centri ſibi occurrentes collidantur, nullus ab il-


<pb xlink:href="062/01/012.jpg"></pb>lo contactu erit mótus: major verò impulſus minorem <lb></lb>reflectet, tantò verò minori velocitate mouebitur à <lb></lb>contactu, quantò major eſt reſiſtentia minoris: quia <lb></lb>nimirum impulſus minor à majori tollit partem ſibi <lb></lb>æqualem, ſimul verò occumbit erit ergò exceſſus ma<lb></lb>joris principium motus à contactu: &amp; cùm ſit agens <lb></lb>neceſſarium, motum producit ſibi a qualem. </s>
            <s id="N104E3">Dices in<lb></lb>terdum fieri ut duo globi ſibi occurrentes <expan abbr="uterq́">uterque</expan>; reſili<lb></lb>at: quod <expan abbr="nõ">non</expan> niſi ab æquali impulſu eſſe poteſt; propte<lb></lb>rea quód motus eſt æqualis exceſſui majoris. </s>
            <s id="N104F4"><expan abbr="Reſpõdeo">Reſpondeo</expan> <lb></lb>ſi motus, quo <expan abbr="centrũ">centrum</expan> <expan abbr="utriuſq́">utriuſque</expan>; globi mouetur, ſit in ea<lb></lb>dem lineà rectà, ab æquali impulſu nunquam reſilire: <lb></lb>ſi autem motus centri unius ſit extra lineam motus al<lb></lb>terius, quia lateraliter fit contactus, hujuſmodi quidem <lb></lb>motum poſſe reſilire: verùm non abſoluté, ſed tantùm <lb></lb>ſecundùm quid eſſe contrarium. </s>
            <s id="N1050E">Vt in figurà ſubjectà <lb></lb>ſi centrum <emph type="italics"></emph>a<emph.end type="italics"></emph.end>  ex <emph type="italics"></emph>h,<emph.end type="italics"></emph.end> &amp; centrum <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>l<emph.end type="italics"></emph.end> moueantur in ea<lb></lb>dem lineà rectà <emph type="italics"></emph>h fl<emph.end type="italics"></emph.end>: ſit autem impulſus ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> æqualis im<lb></lb>pulſui ex <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> àcontactu in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> nullus erit motus: propterea <lb></lb>quód impulſus æquales æqualiter reluctantur, <expan abbr="ſeq́">ſeque</expan>; im<lb></lb>pediunt à motu. </s>
            <s id="N1054F">Quód ſi verò centrum grauitatis <emph type="italics"></emph>a<emph.end type="italics"></emph.end><lb></lb>ex <emph type="italics"></emph>c<emph.end type="italics"></emph.end> in <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> &amp; centrum grauitatis <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>d<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> moueatur; quia <lb></lb>lineæ motus <emph type="italics"></emph>ac.db<emph.end type="italics"></emph.end> non coincidunt eidem lineæ rectæ, <lb></lb>dico hujuſmodi motum non abſoluté, ſed ſecundùm <lb></lb>quid eſſe contrarium.</s>
            <s id="N10583"> Ducantur enim ex puncto con-


<pb xlink:href="062/01/013.jpg"></pb>tactus <emph type="italics"></emph>f<emph.end type="italics"></emph.end> lineæ <emph type="italics"></emph>fg. fe<emph.end type="italics"></emph.end> motui centri parallelæ, lineæ nimi<lb></lb>rum hypomochlij, extra quas cadunt centra <emph type="italics"></emph>a<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>b:<emph.end type="italics"></emph.end> quia <lb></lb>ergo plaga non niſi per centrum fit grauitatis, erunt li<lb></lb>neæ <emph type="italics"></emph>fab. fbb<emph.end type="italics"></emph.end> lineæ motus à percuſsione: ſunt autem li<lb></lb>neæ <emph type="italics"></emph>ai.bk<emph.end type="italics"></emph.end> lineæ motus centri extra hypomochlium: <lb></lb>
<figure id="id.062.01.013.1.jpg" xlink:href="062/01/013/1.jpg"></figure><lb></lb>

quia ergo lineæ motus <emph type="italics"></emph>ab. ai,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>bl.bk<emph.end type="italics"></emph.end> angulos ducunt <lb></lb><emph type="italics"></emph>iah.lbk<emph.end type="italics"></emph.end> minores duobus rectis, <expan abbr="erũt">erunt</expan> per defini: 5 motus <lb></lb>ſecundùm quid contrarij, ac proinde inter ſemiſcentur <lb></lb>per prop: 31. </s>
            <s id="N105DA">Verùm de motu reflexo accuratiùs dice<lb></lb>mus à prop: 36. <expan abbr="uſq́">uſque</expan>; ad 40. </s>
          </p>
          <p id="N105E3" type="main">
            <s id="N105E5"><emph type="center"></emph>III.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N105EC" type="main">
            <s id="N105EE"><emph type="italics"></emph>Mixtarum virium mixtæ ſunt actiones in ea<lb></lb>dem ratione, in quà miſcentur miſcibilia.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N105F7" type="main">
            <s id="N105F9">CVm enim mixtum ſit ſua miſcibilia inter ſe unita, &amp; <lb></lb>neceſſariò agat, <expan abbr="actionemq́">actionemque</expan>; producat ſibi æqua<lb></lb>lem aget ſecundùm ſe totum, ac proinde ſecundúm il<lb></lb>las partes, quæ in illo toto miſcentur: actio ergo mixta


<pb xlink:href="062/01/014.jpg"></pb>quia toti æqualis, habet partes virtuales illis partibus, à <lb></lb>quibus producitur æquales. </s>
          </p>
          <p id="N1060C" type="main">
            <s id="N1060E"><emph type="center"></emph>IV.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10615" type="main">
            <s id="N10617"><emph type="italics"></emph>Virtus agendi &amp; actio inter ſe ſunt æquales, <expan abbr="eſtq́">eſtque</expan> <lb></lb>idem modus incrementi.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10624" type="main">
            <s id="N10626">VIrtutem enim agendi magnam aut paruam dici<lb></lb>mus, quæ multùm aut parum poteſt agere: <expan abbr="itaq́">itaque</expan>; <lb></lb>hujus molem ex actionum mole æſtimamus; actionem <lb></lb>verò ab effectu noſcimus: dupla ergo virtus, quæ actio<lb></lb>nem dupló, &amp; tripla quæ triplò majorem, aut magis <lb></lb>perfectam producit. </s>
            <s id="N10637">Et quia virtus naturalis non li<lb></lb>berè ſed ex neceſsitate agit, <expan abbr="actionemq́">actionemque</expan>; producit ſibi <lb></lb>æqualem, erit idem modus incrementi <expan abbr="utriuſq́">utriuſque</expan>;. </s>
          </p>
          <p id="N10646" type="main">
            <s id="N10648"><emph type="center"></emph>Lemma,<emph.end type="center"></emph.end></s>
          </p>
          <p id="N1064F" type="main">
            <s id="N10651"><emph type="italics"></emph>Si punctum æqualiter moueatur inplano motu ſi<lb></lb>mul recto &amp; laterali in eadem proportione <expan abbr="utriusq́ue">utriusque</expan> interualli, <lb></lb>deſcribet illo motu triangulum.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10660" type="main">
            <s id="N10662">MOueatur in fig: 3. punctum <emph type="italics"></emph>a<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> per lineam re<lb></lb>ctam <emph type="italics"></emph>af<emph.end type="italics"></emph.end> æqualiter in longum &amp; latum, ita nimi<lb></lb>rum ut in quolibet puncto longitudo excurſus lateralis <lb></lb>ſit æqualis <expan abbr="lõgitudini">longitudini</expan> motus recti inter idem punctum


<pb xlink:href="062/01/015.jpg"></pb>&amp; principium motus, ideſt <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ipſi <emph type="italics"></emph>bg,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> ipſi <emph type="italics"></emph>cb,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ad<emph.end type="italics"></emph.end><lb></lb>ipſi <emph type="italics"></emph>di,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> ipſi <emph type="italics"></emph>ek,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>af<emph.end type="italics"></emph.end> ipſi <emph type="italics"></emph>fl<emph.end type="italics"></emph.end> ſit æqualis, dico puncta <lb></lb><emph type="italics"></emph>aghikl<emph.end type="italics"></emph.end> cadere in latus <emph type="italics"></emph>al<emph.end type="italics"></emph.end> trianguli <emph type="italics"></emph>alf.<emph.end type="italics"></emph.end> Quòd ſi enim <lb></lb>punctum <emph type="italics"></emph>i, u:g<emph.end type="italics"></emph.end>: dicatur non in latus <emph type="italics"></emph>al,<emph.end type="italics"></emph.end> ſed extra illud ca<lb></lb><figure id="id.062.01.015.1.jpg" xlink:href="062/01/015/1.jpg"></figure>
<arrow.to.target n="fig5"></arrow.to.target><lb></lb>dere in <emph type="italics"></emph>r,<emph.end type="italics"></emph.end> ducatur linea <emph type="italics"></emph>ar,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; angulus <emph type="italics"></emph>rad<emph.end type="italics"></emph.end> major <lb></lb>angulo <emph type="italics"></emph>iad.<emph.end type="italics"></emph.end> quia ergo latus <emph type="italics"></emph>dr<emph.end type="italics"></emph.end> lateri <emph type="italics"></emph>da<emph.end type="italics"></emph.end> eſt æquale, &amp; an<lb></lb>gulus <emph type="italics"></emph>adr<emph.end type="italics"></emph.end> rectus, erunt anguli <emph type="italics"></emph>dar. dra<emph.end type="italics"></emph.end> inter ſe æqua<lb></lb>les, ac proinde ſemiſſes anguli recti. </s>
            <s id="N1072F">Similiter quia <lb></lb>latus <emph type="italics"></emph>fl<emph.end type="italics"></emph.end> eſt æquale lateri <emph type="italics"></emph>fa,<emph.end type="italics"></emph.end> &amp; angulus <emph type="italics"></emph>afl<emph.end type="italics"></emph.end> re<lb></lb>ctus, erunt anguli <emph type="italics"></emph>fal. fla<emph.end type="italics"></emph.end> inter ſe æquales; igitur &amp; an<lb></lb>gulus <emph type="italics"></emph>laf<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>rad<emph.end type="italics"></emph.end> erit æqualis pars toti, quod eſt ab<lb></lb>ſurdum: non ergo punctum <emph type="italics"></emph>i<emph.end type="italics"></emph.end> extra latus <emph type="italics"></emph>al<emph.end type="italics"></emph.end> cadit. </s>
            <s id="N1076A">Simi<lb></lb>li modo oſtendemus non cadere intra illud latus: ca<lb></lb>det ergò neceſſarió in ipſum latus. </s>
            <s id="N10771">Si ergo punctum <lb></lb>æqualiter moueatur in plano motu ſimul recto &amp; late<lb></lb>rali in eadem proportione &amp;c. </s>
          </p>
          <pb xlink:href="062/01/016.jpg"></pb>
          <p id="N1077B" type="main">
            <s id="N1077D"><emph type="center"></emph>V.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10784" type="main">
            <s id="N10786"><emph type="italics"></emph>Perfectio intenſiua augetur eo modo, quo triangu<lb></lb>lum ſibi ſimile manens.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N1078F" type="main">
            <s id="N10791">QVia perfectio intenſiua non <expan abbr="abſq́">abſque</expan>; motu fit, ac pro<lb></lb>inde in aliquo tempore: ſupponatur illud tempus, <lb></lb>quo calor verbi gratia perficitur in quo <expan abbr="cunq́">cunque</expan>; gradu, eſ<lb></lb>ſe æquale lineæ <emph type="italics"></emph>af<emph.end type="italics"></emph.end>: &amp; diuidatur æqualiter in minuta <emph type="italics"></emph>ab. <lb></lb>bc. cd. de. ef<emph.end type="italics"></emph.end>: quia ergo in ſingulis minutis majora fiunt <lb></lb>hujus perfectionis in crementa, ſi in primo minuto <emph type="italics"></emph>ab<emph.end type="italics"></emph.end><lb></lb>perfectio intenſiua ſit æqualis <emph type="italics"></emph>bg,<emph.end type="italics"></emph.end> erit in minuto ſecun<lb></lb>do <emph type="italics"></emph>bc<emph.end type="italics"></emph.end> major quam <emph type="italics"></emph>bg,<emph.end type="italics"></emph.end> &amp; in tertiò minuto <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> major <lb></lb>quam <emph type="italics"></emph>ch:<emph.end type="italics"></emph.end> dico hujuſmodi incrementa eſſe ſimilia inter <lb></lb>ſe, ac proinde eo modo augeri, quo triangulum ſibi ſi<lb></lb>mile manens. </s>
            <s id="N107DF">Quia enim hæc perfectio continuò au<lb></lb>getur, &amp; veluti lateſcit ex illo puncto quietis; natura <lb></lb>autem uniformiter agit, <expan abbr="ſibiq́">ſibique</expan>; ſemper eſt ſimilis, erunt <lb></lb><expan abbr="quoq́">quoque</expan>; ſimilia incrementa: Sicuti ergo perfectionem <lb></lb>ſummam in tempore <emph type="italics"></emph>af<emph.end type="italics"></emph.end> æqualem lineæ <emph type="italics"></emph>fl,<emph.end type="italics"></emph.end> ita in hujus <lb></lb>temporis ſemiſſe: perfectionis ſemiſſem producet: igi<lb></lb>tur ut tempus <emph type="italics"></emph>af<emph.end type="italics"></emph.end> ad perfectionem <emph type="italics"></emph>fl,<emph.end type="italics"></emph.end> ita tempus <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> ad <lb></lb>perfectionem <emph type="italics"></emph>ek<emph.end type="italics"></emph.end> hoc eſt ut latus <emph type="italics"></emph>af<emph.end type="italics"></emph.end> trianguli <emph type="italics"></emph>afl<emph.end type="italics"></emph.end> ad la<lb></lb>tus <emph type="italics"></emph>fl,<emph.end type="italics"></emph.end> ita latus <emph type="italics"></emph>ae<emph.end type="italics"></emph.end> trianguli <emph type="italics"></emph>aek<emph.end type="italics"></emph.end> ad latus <emph type="italics"></emph>ek;<emph.end type="italics"></emph.end> ac proinde <lb></lb>ſimilia erunt triangula <emph type="italics"></emph>afl. aek.<emph.end type="italics"></emph.end> perfectio ergo intenſi<lb></lb>ua augetur eo modo, quo <expan abbr="triangulũ">triangulum</expan> ſibi ſimile manens. </s>
          </p>
          <pb xlink:href="062/01/017.jpg"></pb>
          <p id="N10852" type="main">
            <s id="N10854"><emph type="center"></emph>VI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N1085B" type="main">
            <s id="N1085D"><emph type="italics"></emph>Impulſus grauitatis ducetur ſecundum rationem diſtantiæ, <lb></lb>quam habet centrum grauitatis ab hypomochlio.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10866" type="main">
            <s id="N10868">HVjus poſitionis veritatem probat Archimedes in <lb></lb>libro de æquiponderantibus: &amp; nos in libro de <lb></lb>Arcu cæleſti ejus rationem à priori dare enitemur; quæ <lb></lb>non niſi ex naturà impulſus priùs explicatà reddi po<lb></lb>teſt, hujus ergo demonſtrationem ſupponentes eà ve<lb></lb>luti <emph type="italics"></emph>j<emph.end type="italics"></emph.end>am demonſtratì in poſterum utemur. </s>
          </p>
        </subchap1>
        <subchap1 id="N1087B">
          <p id="N1087C" type="main">
            <s id="N1087E"><emph type="center"></emph>Propoſitio I.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10885" type="main">
            <s id="N10887"><emph type="italics"></emph>Impulſus eſt virtus ſeu qualitas, loco motiua, quæ <lb></lb>non niſi in tempore, &amp; per ſpatium mouet finitum.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10890" type="main">
            <s id="N10892">IMpulſus dicitur ab impellendo: impellitur autem <lb></lb>mobile, dum loco ſuo expulſum in alium transfer<lb></lb>tur, aut ſimpliciter; aut ſecundúm quid, ſeu per com<lb></lb>mutationem, dum loco totius immoto partium loca <lb></lb>permutantur: quod duobus modis fieri poteſt, incho<lb></lb>atiuè, &amp; perfectè. </s>
            <s id="N1089F">Inchoatiuè dico, quæ ſecundùm nul <lb></lb>lam partem ſenſibilem, ſed per atomos in ſenſiles vibra<lb></lb>tione quadam mouentur; cujuſmodi ſunt corpora ſo<lb></lb>nora, quæ dum ſonant, motu quodam tremulo ſubſul-


<pb xlink:href="062/01/018.jpg"></pb>tant: &amp; <expan abbr="quæcunq́">quæcunque</expan>; corpora minorem habent impul<lb></lb>ſum, quam ut loco moueantur: ut cùm tellus, aut ſa<lb></lb>xum malleo percuſſum tremit quidem ex illo impulſu, <lb></lb>ſecundùm nullam verò partem ſenſibilem loco moue<lb></lb>tur. </s>
            <s id="N108B8">Quód ſi <expan abbr="neq́">neque</expan>; ſonum edant corpora, <expan abbr="neq́">neque</expan>; tremu<lb></lb>lâ vibratione motum teſtentur, non videntur recipere <lb></lb>impulſum: ut ſi granum milij terræ incidat: minorem <lb></lb>enim habet proportionem hic impulſus, quam ut ali<lb></lb>quam partem loco moueat, aut ab alijs auellat. </s>
            <s id="N108CB">Tre<lb></lb>mor autem a percuſsione videtur non <expan abbr="abſq́">abſque</expan>; diſtractio<lb></lb>ne fieri atomorum: <expan abbr="dũ">dum</expan> minor eſt impulſus, quam ut to<lb></lb>tum moueat: major verò quam ilia vis partium unit<lb></lb>iua, quà inter ſe continuantur. </s>
            <s id="N108DE">Illa ergo corpora, quæ <lb></lb>uniones habent ſolubiles <expan abbr="abſq́">abſque</expan>; reunione, fragilia ſunt: <lb></lb>cujuſmodi vitrum, lapides, gemmæ; quæ iteratis per<lb></lb>cuſsionibus, ob plures uniones ſolutas, demum fran<lb></lb>guntur, &amp; diſsiliunt: metalla verò tametſi tremunt <expan abbr="ſo-nantq́">ſo<lb></lb>nantque</expan>; à percuſsione, ob atomos tamen reunibiles non <lb></lb>niſi cùm impetus longiùs abduxit, franguntur. </s>
            <s id="N108F5">Sic a<lb></lb>qua in calice vitreo ſubſultat, &amp; veluti æſtu agitur ad <lb></lb>motum digiti per margines circumacti: motu verò ac <lb></lb>celerato extra calicem ſalit, <expan abbr="ſuáq;">ſuáque</expan> aſpergine etiam lon<lb></lb>giùs adſtantes attingit. </s>
            <s id="N10904"><expan abbr="Itaq́">Itaque</expan>; hic impulſus â principio <lb></lb>quidem non niſi ſecundùm quid, &amp; inchoatiuè, ſolum <lb></lb>tremorem inducendo: inde commutatione partium,


<pb xlink:href="062/01/019.jpg"></pb>quá in gyrum aguntur, perfectà: demum motu ſimpli<lb></lb>citer mouent. </s>
            <s id="N10914">Vt igitur impulſus loco moueat mobi<lb></lb>le, neceſſe illam reſiſtentiam, quâ in loco ſuo aut alieno <lb></lb>detinetur, ſuperate. </s>
            <s id="N1091B">Secundùm quid autem inchoa<lb></lb>tiuè mouetur, cùm æquatis viribus inter ſe luctantur <lb></lb>virtus partium vnitiua &amp; impulſus: quà quidem ratio<lb></lb>ne cymbala, cordæ, <expan abbr="atq́">atque</expan>; æra tinnula mouentur. </s>
            <s id="N10928">Lapi<lb></lb>des verò &amp; quæ fragilia ſunt, quia ex impulſu uniones <lb></lb>ſenſim depereunt, <expan abbr="neq́">neque</expan>; reuniri poſſunt, demum â per<lb></lb>cuſsione continuatá pluribus unionibus euerſis, ſeu <lb></lb>quia impulſui necdum exſoluto alius ſuperuenit im<lb></lb>pulſus, franguntur. </s>
            <s id="N10939">Manifeſtum ergo ex his Impul<lb></lb>ſum eſſe virtutem finitam, quæ non quamlibet mo<lb></lb>lem, ſed finitam loco mouere &amp; impellere poteſt. </s>
            <s id="N10940">Et <lb></lb>quia motus ex uno loco in alium non niſi per medium <lb></lb>interuallum defert mobile, ejuſmodi motum non poſ<lb></lb>ſe fieri in inſtanti, ſed in aliquo tempore ita oſtende<lb></lb>mus. </s>
            <s id="N1094B">Moueatur ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> inter quæ mediant partes lo<lb></lb>ci <emph type="italics"></emph>cdefg<emph.end type="italics"></emph.end> &amp;c. per quas neceſſarió tranſit in <emph type="italics"></emph>b<emph.end type="italics"></emph.end>; propterea <lb></lb>quòd nequit medium tranſilire: quòd ſi ergo non niſi <lb></lb>in uno momento mouetur ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> erit eodem <expan abbr="momẽ-to">momen<lb></lb>to</expan> ſimul in <emph type="italics"></emph>cdef<emph.end type="italics"></emph.end> pluribus locis adæquatis, quod nullâ <lb></lb>ratione fieri poteſt. </s>
            <s id="N10986">Simili modo oſtendemus alio <lb></lb>momento in <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> alio in <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> priús nimirum in parte priori <lb></lb>quam poſteriori motum terminari: pluribus ergo mo-<pb xlink:href="062/01/020.jpg"></pb>mentis mouetur ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> ac proînde motus neceſſariò <lb></lb>fit in tempore. </s>
            <s id="N109AB">Sed <expan abbr="neq́">neque</expan>; tempore infinito per ſpati<lb></lb>um mouétur finitum, ſi nimirum motus ejuſdem ſit <lb></lb>rationis &amp; ſibi ſimilis; nam ſi velocitas proportionali<lb></lb>ter decreſcat, non repugnat per ſpatium finitum tem<lb></lb>pore moueri infinito; ut ſi per lineam conchoideos ac<lb></lb>ceſſus fiat ad alteram parallelam, ſpatium interjectum <lb></lb>nullo in tempore tranſibit. </s>
            <s id="N109BE">Moueatur ergo mobile ex <lb></lb><emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> motu æquali quantumuis lento: &amp; ſumatur tem<lb></lb>pus quodcunq; <emph type="italics"></emph>ik,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; mobile extra terminum <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> in <lb></lb>quo quieſcebat. aut igitur in <emph type="italics"></emph>ik<emph.end type="italics"></emph.end> aliquam partem ug: <emph type="italics"></emph>a <lb></lb>b,<emph.end type="italics"></emph.end> aut inſenſibile punctum tranſmiſit. </s>
            <s id="N109F0">Si partem, meti<lb></lb>etur hæc ſpatium <emph type="italics"></emph>af<emph.end type="italics"></emph.end> aliquo numero finito: igitur &amp; <lb></lb>tempus, quo totum ſpatium decurrit, erit finitum. </s>
            <s id="N109FD">Si <lb></lb>
<figure id="id.062.01.020.1.jpg" xlink:href="062/01/020/1.jpg"></figure><lb></lb>non niſi punctum: quia tempus diuidi poteſt, tranſi<lb></lb>bit in hujus ſemiſſe interuallum puncto minus, quod <lb></lb>eſt abſurdum: non igitur motus æqualis per ſpatium <lb></lb>finitum tempore infinito eſſe poteſt. </s>
            <s id="N10A0F">Sed <expan abbr="neq́">neque</expan>, in tem<lb></lb>pore finito per ſpatium infinitum: <expan abbr="nãq́">nanque</expan> in ſemiſſe tem<lb></lb>

poris, <expan abbr="atq́">atque</expan>; hujus ſemiſſe &amp;c. nunquid ſpatium peram<lb></lb>

bulabit infinitum? quód ſi motus illâ ſectione <expan abbr="demũ">demum</expan> <lb></lb>

terminabit in aliquà parte finitâ, erit <expan abbr="quoq́">quoque</expan>; totum fini<lb></lb>

tum. </s>
            <s id="N10A30">Deinde cùm motus incipiat à termino, erit ne<lb></lb>

ceſſariò finitus. moueatur enim ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> per ſpatium <emph type="italics"></emph>bcde<emph.end type="italics"></emph.end>


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

tem quidem <emph type="italics"></emph>b<emph.end type="italics"></emph.end> in aliquà parte temporis tranſibit, quæ <lb></lb>

ſit <emph type="italics"></emph>g<emph.end type="italics"></emph.end>; menſurabit proinde tempus aliquo numero fini<lb></lb>

to: &amp; cúm motum ponamus ſimilarem, qui in tempo<lb></lb>

re æquali partes conficit æquales, totidem partes erunt <lb></lb>

in ſpatio <emph type="italics"></emph>bcdef,<emph.end type="italics"></emph.end> qu<gap></gap>on tempore <emph type="italics"></emph>ghikl,<emph.end type="italics"></emph.end> ac proinde to<lb></lb>

tum interuallum erit finitum. </s>
            <s id="N10A76">Igitur impulſus eſt vir<lb></lb>

tus finita, quæ non niſi in tempore &amp; per ſpatium mo<lb></lb>

uet finitum. </s>
          </p>
        </subchap1>
        <subchap1 id="N10A7D">
          <p id="N10A7E" type="main">
            <s id="N10A80"><emph type="center"></emph>Propoſitio II.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10A87" type="main">
            <s id="N10A89"><emph type="italics"></emph>Impulſus eſt agens neceſſarium, <expan abbr="motumq́">motumque</expan>; producit <lb></lb>

ſibi æqualem.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10A96" type="main">
            <s id="N10A98">NEceſſarium dico non ſolùm quò ad exercitium a<lb></lb>

ctus, quo modo omnia agentia, quæ non liberè a<lb></lb>

gunt, neceſſaria dicuntur; ſed etiam quò ad perfectio<lb></lb>

nem actus, hoc eſt agere ſecundúm totum poſſe, ſeu <lb></lb>

ſummam perfectionem tribuere ſuo effectui: quod <lb></lb>

non faciunt reliqua agentia naturalia, quæ non niſi à le<lb></lb>

uibus initijs ad ſumma euadunt incrementa: ut ma<lb></lb>

nifeſtum in calefactione. </s>
            <s id="N10AA9">At verò impulſus ſtatim à <lb></lb>

principio motum velociſsimum producit: qui demum <lb></lb>

ſpatij tractu langueſcit &amp; emoritur, Cujus ratio eſt,


<pb xlink:href="062/01/022.jpg"></pb>quòd impulſus ſit qualitas tranſiens, quæ non poteſt in <lb></lb>

ſubjecto conſeruari <expan abbr="abſq́">abſque</expan>; motu: quód ſi enim mobile <lb></lb>

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

lus ex illo contactu ſequitur motus: niſi ergo à princi<lb></lb>

pio, priuſquam virtus exſoluatur, agat, nunquam ſuum <lb></lb>

finem aſſequetur: unde à velociſsimo &amp; ſibi æquali <lb></lb>

motu exorſus, quantùm virium deperit, tantum de ce<lb></lb>

leritate remittit</s>
            <s id="N10AC6"><expan abbr="Neq́;">Neque;</expan> hic nobis aduerſantur, qui ne<lb></lb>

ſcio quas morulas inducunt, velociùs moueri dicentes <lb></lb>

illud mobile, quod paucioribus morulis quieſcit: nam <lb></lb>

ex illorum <expan abbr="quoq́">quoque</expan>; ſententià impulſus id quod poteſt <lb></lb>

ſummum operatur: &amp; à principio quidem pauciori<lb></lb>

bus morulis quieſcit, inde veluti ex illo motu laſſatus <lb></lb>

longiora ducit interualla. </s>
          </p>
        </subchap1>
        <subchap1 id="N10ADC">
          <p id="N10ADD" type="main">
            <s id="N10ADF"><emph type="center"></emph>Propoſitio III.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10AE6" type="main">
            <s id="N10AE8"><emph type="italics"></emph>Impulſus non niſi per lineam rectam mouet ſuum mobile.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10AEF" type="main">
            <s id="N10AF1">DEmotu quidem, qui procedit à grauitate, nullum <lb></lb>

eſt dubium fieri per lineam rectam: ſed etiam ea, <lb></lb>

quæ proijciuntur ſeu manu, ſeu machinà, rectitudinem <lb></lb>

ſeruare conſtat; tantò enim metam feriunt ictu certio<lb></lb>re, quantò minùs principium motus à lineà rectà aber<lb></lb>

rauit. </s>
            <s id="N10AFE">At verò quæ circulariter mouentur, dubitatio<lb></lb>

nem habent: propterea quòd ex impulſu non per line-


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

minus etiam in his, quæ circulariter mouentur, impul<lb></lb>

ſum ad motum rectum inelinare, &amp; non niſi vi ab hy<lb></lb>

pomochlio illatà circumagi facile oſtendemus. </s>
            <s id="N10B10">Ete<lb></lb>

nim eà ratione mouetur totum, quà illius partes, cúm <lb></lb>

motus totius ſit ſuarum partium motus: at verò partes <lb></lb>

ſingulæ dum circumaguntur, ſi non firmiter cohærent <lb></lb>

ſuo hypomochlio, non in circulum, ſed per lineam re<lb></lb>

ctam mouentur: quod quidem in illà rotà verſatili, quà <lb></lb>

gemmæ poliuntur, aut in lapide molari licebit experiri: <lb></lb>

quòd ſi enim in illà planitie propè centrum arenam, <lb></lb>aut quid ſimile conſtituas, videbis ex illà rotatione <lb></lb>

ad circulos ſenſim majores à centro propelli, &amp; demum <lb></lb>

excuti. </s>
            <s id="N10B27">Obijcies globum fiſtulà ſtriatà emiſſum velo<lb></lb>

ciſsimè gyrando, &amp; veluti aërem terebrando ad metam <lb></lb>

venire, <expan abbr="neq́">neque</expan>; ullum punctum, præterquam centrum, per <lb></lb>

lineam rectam, ſed per lineam ſpiralem moueri: quia <lb></lb>

nimirum ab illis ſulcis, quibus fiſtula interné excaua<lb></lb>

tur, toto illo tractu reuolutus impulſum colligit circu<lb></lb>

larem: non igitur impulſus neceſſariò ducit per lineam <lb></lb>

rectam. </s>
            <s id="N10B3C">Deinde ſi quis velociter currendo ſagittam ja<lb></lb>

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

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

lud mobile per lineam rectam, ſed arcuatim ſurſum elu<lb></lb>

ctatur: propterea quòd non ad idem punctum, â quo


<pb xlink:href="062/01/024.jpg"></pb>moueri cepit, fit relapſus, verùm ad procurſum jaculan<lb></lb>

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

re volentes, illius volatum tantiſper oculis &amp; arcu in<lb></lb>

tentis ſequuntur, &amp; tum in ipſo motu ſagittam ejacu<lb></lb>

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

Vt ſi auis ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> feratur, ſagitta per lineas <emph type="italics"></emph>mb.oc<emph.end type="italics"></emph.end> illius <lb></lb>

volatum ſecuta, in lineà demum <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> à neruo excuſſa ean <lb></lb>

dem figet in <emph type="italics"></emph>g.<emph.end type="italics"></emph.end> at verò ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>g<emph.end type="italics"></emph.end> non niſi arcuatim &amp; per <lb></lb>

lineam inflexam, cujuſmodi <emph type="italics"></emph>ahig<emph.end type="italics"></emph.end> euadit: propterea <lb></lb>

quòd motus ſagittæ videtur compoſitus ex illo motu, <lb></lb><figure id="id.062.01.024.1.jpg" xlink:href="062/01/024/1.jpg"></figure>

quo ad motum arcus, &amp; quo à neruo impulſa mouetur: <lb></lb>

at verò motus, quo cum arcu mouetur, eſt circulatis ha<lb></lb>

bens centrum in oculo ſagittantis: motus ergo ab hoc


<pb xlink:href="062/01/025.jpg"></pb>in ſagittam deriuatus, ac proinde motus ex <expan abbr="utroq́">utroque</expan>; mix<lb></lb>

tus erit circularis. </s>
            <s id="N10BA8">Deſcribatur arcus <emph type="italics"></emph>mn,<emph.end type="italics"></emph.end> cujus centrum <lb></lb>

in oculo <emph type="italics"></emph>l,<emph.end type="italics"></emph.end> ſemidiameter verò ſagitta <emph type="italics"></emph>al<emph.end type="italics"></emph.end>: quæ ubi per ar<lb></lb>

cum <emph type="italics"></emph>ma<emph.end type="italics"></emph.end> moueri cæpit, ab alio impulſu à neruo deriuato <lb></lb>

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

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

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

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

<emph type="italics"></emph>qh<emph.end type="italics"></emph.end> æqualis lineæ <emph type="italics"></emph>ap,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; motus compoſitus ex <emph type="italics"></emph>ap. aq<emph.end type="italics"></emph.end><lb></lb>

in <emph type="italics"></emph>h:<emph.end type="italics"></emph.end> ſimiliter oſtendemus motum in <emph type="italics"></emph>i<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>g<emph.end type="italics"></emph.end> componi ex <lb></lb>

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

ſe duci lineam rectam. </s>
            <s id="N10C35">Sit enim, ſi fieri poteſt, linea <emph type="italics"></emph>ab <lb></lb>

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

in <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> quæ <expan abbr="utrimq́">utrimque</expan>; producta ſecet lineas <emph type="italics"></emph>lf. ld<emph.end type="italics"></emph.end> in punctis <lb></lb>

s. u: <expan abbr="eruntq́">eruntque</expan>; lineæ <emph type="italics"></emph>qs. qu<emph.end type="italics"></emph.end> inter ſe æquales: quibus ex <lb></lb>

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

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

obus angulis <emph type="italics"></emph>hqu.qhu<emph.end type="italics"></emph.end> trianguli <emph type="italics"></emph>hqu<emph.end type="italics"></emph.end> ſunt æquales, <expan abbr="uterq́">uterque</expan>; <lb></lb>

<expan abbr="utriq́">utrique</expan>, erunt ſimilia inter ſe; ac proinde ut <emph type="italics"></emph>hi<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>hq,<emph.end type="italics"></emph.end> ita <lb></lb>

<emph type="italics"></emph>xi<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>qu,<emph.end type="italics"></emph.end> hoc eſt ad <emph type="italics"></emph>qs<emph.end type="italics"></emph.end> illi æqualem. eſt autem linea <emph type="italics"></emph>hx<emph.end type="italics"></emph.end><lb></lb> æqualis lineæ <emph type="italics"></emph>hq:<emph.end type="italics"></emph.end> igitur &amp; linea <emph type="italics"></emph>xi<emph.end type="italics"></emph.end> erit æqualis lineæ <emph type="italics"></emph>qs,<emph.end type="italics"></emph.end><lb></lb>

quod eſt abſurdum: ſequeretur enim lineas <emph type="italics"></emph>is. xq<emph.end type="italics"></emph.end> in <lb></lb>

centro <emph type="italics"></emph>l<emph.end type="italics"></emph.end> concurrentes eſſe parallelas. </s>
            <s id="N10CEA">Reſpondeo ad <lb></lb>

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

dit, eſſe compoſitum ex impulſu recto, quem ipſi con-


<pb xlink:href="062/01/026.jpg"></pb>fert puluis pyrius à tergo incenſus, &amp; eximpulſu latera <lb></lb>

li, quem viarum ſeu <expan abbr="eanaliculorũ">canaliculorum</expan> anfractus globulo e<lb></lb>

rumpenti conciliant: partes enim globuli prominen<lb></lb>

tes ſulcis impreſſæ, eoſdem ductus ſequendo, illà gyra<lb></lb>

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

nis eadem viá pabulum ſequendo, &amp; globulum impel<lb></lb>

lendo: dico ergo hunc motum partim ſimilem illi mo<lb></lb>

tui, quo rota circumagitur, partim diſsimilem: propter<lb></lb>

ea, quòd globulus circa centrum mobile, rota autem <lb></lb>

circa immobile reuoluatur. </s>
            <s id="N10D0B">At verò trochus <lb></lb>

aut turbo, dum gyrando in aëre labitur, motu prorſus <lb></lb>

ſimili fertur: nam ex impulſu funiculi multis ſpiris re<lb></lb>

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

trum: quod ſuà grauitate inter gyrandum deſcendit. <lb></lb>

at verò impulſus, quo rota aut turbo circulariter moue<lb></lb>

tur, ſi non impediatur, non circulari, ſed motu recto mo<lb></lb>

uebitur: quemadmodum exemplo illarum rerum, quæ <lb></lb>

ad motum rotæ circumaguntur, oſtendimus</s>
            <s id="N10D1E"><expan abbr="Itaq́">Itaque</expan>; ſi ca<lb></lb>

tenula conuoluta unà extremitate in illius plano firme<lb></lb>

tur, videbis ex illâ vertigine ſenſim reuolui, &amp; demum <lb></lb>

in lineam tangentem ejuſdem circuli extendi. </s>
            <s id="N10D2A">Ita tro<lb></lb>chus aut turbo aquà conſperſus in motu reſiccatur, dum <lb></lb>

aquæ guttulæ ex illo impulſu lineam rectam ſequendo <lb></lb>

auelluntur. </s>
            <s id="N10D33">Simili ergo modo impulſus, qui globu<lb></lb>

lum reuoluit, ſi non impediatur, lateraliter, &amp; per line


<pb xlink:href="062/01/027.jpg"></pb>am rectam mouebit. quod quidem conſtabit, ſi globu<lb></lb>

lum friabilem ſubſtituas: ex motu enim gyrationis in <lb></lb>

atomos infinitas diſsipabitur. </s>
            <s id="N10D40">At verò continuitas par<lb></lb>

tium globuli diſſolui nequit ob firmitatem, <expan abbr="neq́">neque</expan>; late<lb></lb>

raliter moueri ob <expan abbr="reſiſtẽtiam">reſiſtentiam</expan> illarum partium, quæ im<lb></lb>

pulſu contra io aguntur: quòt enim lineæ tangentes, <lb></lb>

tot: dem ineſſe videntur impulſus: <expan abbr="itaq́">itaque</expan>; centrum glo<lb></lb>

buli tantò magis detinetur in lineà rectà, quantò majori <lb></lb>

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

go turbo, dum ſuper axe mouetur horizonti parallelo, <lb></lb>

non eandem firmitatem habet ſui centri à partibus cir<lb></lb>

cumactis? <expan abbr="neq;">neque</expan> enim eidem puncto inſiſtit axis, verùm <lb></lb>

huc illuc incerto motu oberrat. </s>
            <s id="N10D6A">Reſpondeo id ab in <lb></lb>

æquali illarum partium ſitu, quibus planum tangit, <lb></lb>

prouenite: cùm non in <expan abbr="pũcto">puncto</expan> fiat <expan abbr="cõtactus">contactus</expan>. quia ergo in <lb></lb>

ſuperficie illius plani aſperà &amp; in æquali partes aliæ ſunt <lb></lb>

depreſſæ, aliæ prominentes &amp; verrucoſæ, neceſſe muta<lb></lb>

tionem fieri in motu: dum vel ſubſidet in lacunas, vel <lb></lb>

ad tubercula offendit. </s>
            <s id="N10D81">Ad ſecundam objectionem, di<lb></lb>

co ſagittam circulariter moueri ex illo motu, quo cum <lb></lb>

arcu mouetur; impulſus enim à centro detinetur, quò <lb></lb>

minùs per lineam rectam moueat: at verò motus ſagit<lb></lb>

tæ à neruo excuſſæ, quia à nullo detinetur, per lineam fit <lb></lb>

mediam inter tangentem &amp; lineam rectam, ſiuè per di<lb></lb>

a metrum parallelogrammi, cujus latera ſunt in propor


<pb xlink:href="062/01/028.jpg"></pb>tione illorum motuum. </s>
            <s id="N10D94">Deinde eſto demus impulſum <lb></lb>

lateraliter abducentem eſſe circularem, non tamen ſe<lb></lb>

quitur motum compoſitum eſſe circularem: nam mo<lb></lb>

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

q<emph.end type="italics"></emph.end> non in <emph type="italics"></emph>h,<emph.end type="italics"></emph.end> ut ſupponebatur, verùm in <emph type="italics"></emph>y<emph.end type="italics"></emph.end> abducit mobile, <lb></lb>

propterea quòd interuallum motus circularis in fine <lb></lb>

motus compoſiti ſit æquale arcui <emph type="italics"></emph><expan abbr="aq.">aque</expan><emph.end type="italics"></emph.end> ſimiliter dum ex <lb></lb>

<emph type="italics"></emph>y<emph.end type="italics"></emph.end> per lineam fertur <emph type="italics"></emph>yz<emph.end type="italics"></emph.end> æqualem lineæ <emph type="italics"></emph>ap,<emph.end type="italics"></emph.end> impulſu cir<lb></lb>

culari ſpatium tranſmittit <emph type="italics"></emph>zt<emph.end type="italics"></emph.end> æquale ſpatio <emph type="italics"></emph>py<emph.end type="italics"></emph.end> ſeu arcui <lb></lb>

<emph type="italics"></emph>qs:<emph.end type="italics"></emph.end> dico puncta <emph type="italics"></emph>ayt<emph.end type="italics"></emph.end> eſſe in lineà rectà, ac proinde mo<lb></lb>

tum compoſitum <emph type="italics"></emph>ayt<emph.end type="italics"></emph.end> rectum non verò circularem. <lb></lb>

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

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

eſt æqualis, erit eidem angulus <emph type="italics"></emph>zyt<emph.end type="italics"></emph.end> ad verticem æqua<lb></lb>

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

rem impulſus non niſi per lineam rectam moueat, eſt <lb></lb>

hæc: quia cùm motus ſit via ad conjunctionem ſeu uni<lb></lb>

onem cum ſuo termino, ad quem mouetur, erit non ſui <lb></lb>

ſed finis gratia, ac proînde ſicuti nihil deficere, ita nihil <lb></lb>

abundare debet: at verò ſicuti in vià rectà nihil de eſt ad <lb></lb>

finem conſequendum, ita omnes reliquæ abundant: a<lb></lb>

bundare enim dicitur, <expan abbr="abſq́">abſque</expan>; quo finis poteſt obtineri. <lb></lb>

Deinde cùm impulſus ſit agens neceſſarium, habebit &amp; <lb></lb>

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

natio autem non niſi in lineà rectâ eſſe poteſt, cùm hæc


<pb xlink:href="062/01/029.jpg"></pb>ſit una, lineæ verò obliquæ infinitæ. </s>
            <s id="N10E45">Confirmatur ex <lb></lb>

modo agendi reliquorum agentium naturalium, quæ <lb></lb>

non niſi per lineas rectas operantur. </s>
          </p>
        </subchap1>
        <subchap1 id="N10E4C">
          <p id="N10E4D" type="main">
            <s id="N10E4F"><emph type="center"></emph>Propoſitio IV.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10E56" type="main">
            <s id="N10E58"><emph type="italics"></emph>Impulſus in quolibet puncto circuli per lineam fit tangentem.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10E5F" type="main">
            <s id="N10E61">QVia enim motus eſt rectus per pro: 3. talis autem <lb></lb>

eſſe non poteſt in circulo, igitur ſi incipiat ab ali<lb></lb>

quo puncto circuli, cadet immediaté poſt illud pun<lb></lb>

ctum extra peripheriam illius circuli: non poteſt au<lb></lb>

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

Probatur, punctum circuli immediatè ante contactum <lb></lb>

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

immediatè poſt illum contactum erit cum duobus pun<lb></lb>

ctis <emph type="italics"></emph>a<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>o<emph.end type="italics"></emph.end> in lineà rectà, aut certè ad hujus rectitudinem <lb></lb>

quam proximè fieri poteſt, accedet: at verò intra peri<lb></lb>

pheriam circuli nullum eſſe poteſt punctum, quod cum <lb></lb>

duobus illis punctis <emph type="italics"></emph>a<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>o<emph.end type="italics"></emph.end> ſit in lineà rectà, aut ad natu<lb></lb>

ram lineæ rectæ quam proximè accedat, verum ad ma<lb></lb>

iorem curuitatem: cùm neceſſariò ſit in peripheria ali<lb></lb>

cujus circuli minoris. </s>
            <s id="N10EA8">Cadat enim, ſi fieri poteſt, intra


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

&amp; ſit <emph type="italics"></emph>b<emph.end type="italics"></emph.end>: deſcribatur autem circulus minor <emph type="italics"></emph>afp<emph.end type="italics"></emph.end> tangens <lb></lb>

priorem in <emph type="italics"></emph>a<emph.end type="italics"></emph.end>: quód ſi ergo punctum <emph type="italics"></emph>b<emph.end type="italics"></emph.end> cadit extra pe<lb></lb>

ripheriam hujùs circuli, erit angulus <emph type="italics"></emph>bae<emph.end type="italics"></emph.end> minor <expan abbr="quidẽ">quidem</expan> <lb></lb>

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

16. tert: Verùm quia poſſet quis dicere illud punctum <lb></lb>
<figure id="id.062.01.030.1.jpg" xlink:href="062/01/030/1.jpg"></figure>

neceſſariò cadere intra omnes circulos etiam in infini<lb></lb>

tum minores, propterea quòd angulus ſemicirculi ſit <lb></lb>

major quouis angulo acuto: alià ratione îdem oſten<lb></lb>

demus. producatur ergo linea <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> <expan abbr="utrimq́">utrimque</expan>; in <emph type="italics"></emph>g. i<emph.end type="italics"></emph.end> ſecans <lb></lb>

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

ducatur linea <emph type="italics"></emph>bal<emph.end type="italics"></emph.end>; <expan abbr="eritq́">eritque</expan>; angulus <emph type="italics"></emph>hab,<emph.end type="italics"></emph.end> <expan abbr="atq́">atque</expan>; huic ad verti


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

<expan abbr="atq́">atque</expan>; huic æquali angulo <emph type="italics"></emph>kad<emph.end type="italics"></emph.end>: multo ergo major angu<lb></lb>

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

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

uallo abſunt à lineà quauis ſecante, quam à lineà conta<lb></lb>

ctus, ac cum illis punctis, quæ in linea ſunt tangente, <lb></lb>

magis accedunt ad naturam lineæ rectæ, quam cum il<lb></lb>

lis punctis, quæ in lineà ſunt ſecante: motus ergò à con<lb></lb>

tactu per lineam fit tangentem. </s>
            <s id="N10F6E">Quæ igitur circulari<lb></lb>

ter mouentur, ſi in illà gyratione ab hypomochlio libe<lb></lb>

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

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

luntur. </s>
            <s id="N10F79">Ita ergo lapis fundà circumactus, ubi ex illà ro<lb></lb>

tatione impulſum collegit, laxatà habenà auolat motu <lb></lb>

recto per lineam tangentem circuli, cujus ſemidiame<lb></lb>

ter eſt longitudo fundæ. </s>
          </p>
        </subchap1>
        <subchap1 id="N10F82">
          <p id="N10F83" type="main">
            <s id="N10F85"><emph type="center"></emph>Propoſitio V.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N10F8C" type="main">
            <s id="N10F8E"><emph type="italics"></emph>Impulſus æqualis eodem vel æquali tempore per ſpatium mouet <lb></lb>

æquate.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10F97" type="main">
            <s id="N10F99">MAgnitudo ſeu extenſio ineſt motui non perſe, ſed <lb></lb>

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

num dicimus, qui magno, paruum qui paruo ſpatio con<lb></lb>

tinetur; ſiuè actu habeat illam extenſionem, ſiuè virtu


<pb xlink:href="062/01/032.jpg"></pb>aliter tantum: ut cùm idem ſpatium currendo aut am<lb></lb>

bulando ſæpiùs remetimur. </s>
            <s id="N10FA8">Quia verò ejuſdem aut <lb></lb>

æqualis magnitudinis eadem eſt menſura: eſt autem <lb></lb>

menſura motus tempus: erit <expan abbr="quoq́">quoque</expan>; ejuſdem aut æqua<lb></lb>

lis motus idem tempus. </s>
            <s id="N10FB5">Motus ergo æqualis in tempo<lb></lb>

re æquali per ſpatium fit æquale: &amp; cùm impulſus ſit <lb></lb>

agens neceſſarium, <expan abbr="motumq́">motumque</expan>; producat ſibi æqualem, <lb></lb>

per prop: 2. æqualis impulſus in eodem vel æquali tem<lb></lb>

pore per ſpatium mouebit æquale. </s>
          </p>
          <p id="N10FC4" type="main">
            <s id="N10FC6"><emph type="center"></emph><emph type="italics"></emph>Definitio.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N10FD1" type="main">
            <s id="N10FD3"><emph type="italics"></emph>Impulſus qui mínori tempore per ſpatium mouet æquale aut <lb></lb>

majus, dicatur velox: qui verò majori tempore per ſpatium mouet <lb></lb>

æquale aut minus, dicatur tardus.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N10FDE" type="main">
            <s id="N10FE0">VT ſi mobile <emph type="italics"></emph>H<emph.end type="italics"></emph.end> per ſpatium <emph type="italics"></emph>de<emph.end type="italics"></emph.end> in tempore <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> minori, <lb></lb>

mobile verò <emph type="italics"></emph>K<emph.end type="italics"></emph.end> per idem ſpatium <emph type="italics"></emph>de,<emph.end type="italics"></emph.end> aut huic æquale <lb></lb>

<emph type="italics"></emph>fg<emph.end type="italics"></emph.end> in tempore <emph type="italics"></emph>abc<emph.end type="italics"></emph.end> májori moueatur: impulſus quo <emph type="italics"></emph>H<emph.end type="italics"></emph.end><lb></lb> mouetur velox, quo autem <emph type="italics"></emph>K<emph.end type="italics"></emph.end> mouetur dicetur tardus. <lb></lb>velociùs enim ſpatium tranſmitti dicimus, in quo mobi<lb></lb>


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

le minùs immoratur, ſeu ut Atomiſtæ volunt, in quo <lb></lb>

paucioribus morulis interquieſcit. </s>
            <s id="N1102B">Quod autem mi


<pb xlink:href="062/01/033.jpg"></pb>nori tempore per ſpatium æquale, idem <expan abbr="quoq́">quoque</expan>; minori <lb></lb>

tempore per ſpatium majus mouetur. </s>
            <s id="N11038">Diuidatur enim <lb></lb>

exceſſus temporis bifariam in <emph type="italics"></emph>i<emph.end type="italics"></emph.end>: <expan abbr="atq́">atque</expan>; hujus ſemiſsis <emph type="italics"></emph>bi<emph.end type="italics"></emph.end> ad<lb></lb>

datur minori <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; tempus compoſitum <emph type="italics"></emph>abi<emph.end type="italics"></emph.end> majus <lb></lb>

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

tempore ergò <emph type="italics"></emph>abi<emph.end type="italics"></emph.end> ſpatium majus quam <emph type="italics"></emph>de,<emph.end type="italics"></emph.end> ac proinde <lb></lb>

in minori tempore ſpatium majus perambulabit. </s>
            <s id="N1107D">Eo<lb></lb>

dem modo oſtendemus, ſi quid æquali tempore per <lb></lb>

ſpatium majus moueatur, idem in minori tempore per <lb></lb>

ſpatium majus moueri: ſi nimirum hujùs exceſſum bi<lb></lb>

fariam ſecemus: nam ſpatium illud æquale, <expan abbr="atq́">atque</expan>; hujus <lb></lb>

ſemiſſem in minori tempore pertranſibit. </s>
          </p>
        </subchap1>
        <subchap1 id="N1108E">
          <p id="N1108F" type="main">
            <s id="N11091"><emph type="center"></emph>Propoſitio VI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11098" type="main">
            <s id="N1109A"><emph type="italics"></emph>Impulſus major eodem vel æqualis tempore per ſpatium majus, <lb></lb>

minori verò tempore per ſpatium mouet æquale.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N110A3" type="main">
            <s id="N110A5">IMpulſum magnum dicimus non extenſiué, ſed inten<lb></lb>

ſiué, cujus perfectionem ſequitur velocitas motus. <lb></lb>

quia ergo major velocitas in minori tempore per ſpati<lb></lb>

um mouet æquale aut majus, per defin: impulſus verò <lb></lb>

major majorem velocitatem producit, propterea quòd <lb></lb>

agens ſit neceſſarium, <expan abbr="motumq́">motumque</expan>; producat ſibi æqua-


<pb xlink:href="062/01/034.jpg"></pb>lem: mouebit ſane eodem vel æquali tempore per ſpa<lb></lb>

tium majus, minori verò tempore per ſpatium æquale. </s>
          </p>
        </subchap1>
        <subchap1 id="N110BC">
          <p id="N110BD" type="main">
            <s id="N110BF"><emph type="center"></emph>Propoſitio VII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N110C6" type="main">
            <s id="N110C8"><emph type="italics"></emph>Velocitas motus eandem rationem habet quam interualla, rati<lb></lb>

onem verò ſuorum temporum reciprocam.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N110D1" type="main">
            <s id="N110D3">Sit velocitas <emph type="italics"></emph>H<emph.end type="italics"></emph.end> dupla velocitatis <emph type="italics"></emph>K:<emph.end type="italics"></emph.end> dico hujus interual<lb></lb>

<expan abbr="lũ">lum</expan> in ratione <expan abbr="quoq́">quoque</expan>; eſſe duplà ad illud interuallum, <lb></lb>

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

per quod velocitas ſubdupla eodem vel æquali tempo<lb></lb>

re mouetur: at verò tempus, quo velocitas dùpla per <lb></lb>

ſpatium æquale mouetur, in ratione ſubduplá ad tem<lb></lb>

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

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

aut illi æquale <emph type="italics"></emph>fg<emph.end type="italics"></emph.end> moueatur, erit ut velocitas <emph type="italics"></emph>H<emph.end type="italics"></emph.end> ad veloci<lb></lb>

tatem K, ita tempus <emph type="italics"></emph>abc<emph.end type="italics"></emph.end> minoris velocitatis ad <expan abbr="tẽpus">tempus</expan> <emph type="italics"></emph>ab<emph.end type="italics"></emph.end><lb></lb>

majoris velocitatis. </s>
            <s id="N1113A">Quia enim velocitas motus ſumi<lb></lb>

tur à magnitudine interualli, erit in eadem ratione in <lb></lb>

quâ interuallum, ac proinde velo citas dupla per ſpati<lb></lb>

um mouebit duplum. </s>
            <s id="N11143">Eſt autem tempus menſura <expan abbr="cu-juſq́">cu<lb></lb>

juſque</expan>; velocitatis, minor <expan abbr="quidẽ">quidem</expan> majoris, major autem mi <lb></lb>

noris; quot igitur magnitudines minoris interualli in


<pb xlink:href="062/01/035.jpg"></pb>majori, totidem menſuræ velocitatis majoris in menſu<lb></lb>

râ velocitatis minoris continentur. </s>
          </p>
        </subchap1>
        <subchap1 id="N11158">
          <p id="N11159" type="main">
            <s id="N1115B"><emph type="center"></emph>Propoſitio VIII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11162" type="main">
            <s id="N11164"><emph type="italics"></emph>Velocitas à principio motus per lineam perpendicularem eſt <lb></lb>

æqualis grauitati, minor verò per lineam inclinatam.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N1116D" type="main">
            <s id="N1116F">IMpulſus, quó magis impeditur ab alio impulſu, eò mi <lb></lb>

nùs mouet: eſt <expan abbr="autẽ">autem</expan> grauitas impulſus deorſum ſeu <lb></lb>

ad mundi centrum mouens; in lineà ergo perpendicu<lb></lb>

lari quia â nullo impeditur impulſu, <expan abbr="eſtq́">eſtque</expan>; agens neceſſa<lb></lb>

rium, motum producet ſibi æqualem, <expan abbr="eritq;">eritque</expan> velocitas <lb></lb>

motus æqualis grauitati. </s>
            <s id="N11188">In lineâ verò inclinatâ, quia <lb></lb>

grauitas impeditur ab hypomochlio, mouebit tantò <lb></lb>

minús, quantò magis impeditur, per prop: 14. ac proin<lb></lb>

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

cipio motus per lineam perpendicularem eſt æqualis <lb></lb>

grauitati, minor verò per lineam inclinatam. </s>
          </p>
        </subchap1>
        <subchap1 id="N11198">
          <p id="N11199" type="main">
            <s id="N1119B"><emph type="center"></emph>Propoſitio IX.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N111A2" type="main">
            <s id="N111A4"><emph type="italics"></emph>Velocitas continuò augetur in motu naturali, minuitur in motu <lb></lb>

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

olentià incidunt: violentia autem major ex impul


<pb xlink:href="062/01/036.jpg"></pb>ſu majori, qui illo deſcenſu continuò majus ac majus <lb></lb>

capit augmentum. </s>
            <s id="N111BA"><expan abbr="Itaq́">Itaque</expan>; videmus globos ferreos à ma<lb></lb>

chinà bellicà &amp; vi ignis altiſsimè extolli, ut relapſu lon<lb></lb>

giore impulſum colligant majorem <expan abbr="ictuq́">ictuque</expan>; violentiore <lb></lb>

urbium tecta d ruant. </s>
            <s id="N111CA">Sic etiam fiſtucis altiùs ſublatis <lb></lb>

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

dus è filo pendulum, quò magis dimouetur â ſua ſtatio<lb></lb>

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

excurſus non ad grauitatem, ſed ad impulſum illo re<lb></lb>

curſu collectum referri poteſt. </s>
            <s id="N111DA">At verò impulſus ma<lb></lb>

jor eodem vel æquali tempore per ſpatium majus, mi<lb></lb>

nori verò tempore per ſpatium æquale aut etiam majus <lb></lb>

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

ri velocitate. velocitas ergo continuò augetur in motu <lb></lb>

naturali, quod primò erat demonſtrandum. </s>
            <s id="N111ED">Quæ au<lb></lb>

tem motu violento mouentur, cuiuſmodi projecta ſeu <lb></lb>

manu, ſeu machinà, à principio quidem velociſsimè, in<lb></lb>

de minùs velociter mouentur, impulſu veluti ſeneſcen<lb></lb>

te: quia nimirum hujus principium eſt externum, à quo <lb></lb>

in motu <expan abbr="ſeparãtur">ſeparantur</expan>: virtus autem finita, quæ non niſi in <lb></lb>

tempore &amp; per ſpatium mouet finitum: non igitur ex<lb></lb>

tra illud tempus mouere, ac proinde <expan abbr="neq́">neque</expan>; in ſubiecto <lb></lb>

conſeruari poteſt. </s>
            <s id="N11208">Emoritur autem ſeu naturâ ſuà, ſeu <lb></lb>

quia grauitas contraria hunc ſenſim atterit <expan abbr="minuitq́">minuitque</expan>: ad <lb></lb>

cuius decrementum grauitas magis ac magis inualeſcit:


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

præualuit, reuerſionem fieri videmus. </s>
            <s id="N11219">In motu verò <lb></lb>

naturali principium motus eſt internum, nimirum gra<lb></lb>

uitas, &amp; qui à grauitate naſcitur impulſus: qui cùm ſit <lb></lb>

agens neceſſarium, motum producet ſibi æqualem, &amp; <lb></lb>

prius quam finiat hunc motum, continuó ex eadem ra<lb></lb>

dice alius <expan abbr="atq́">atque</expan>; alius impulſus renaſcens velocitatem mo<lb></lb>

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

ergo grauia, dum in hypomochlio quieſcunt, nihilo ma<lb></lb>

gis grauitant, ſi continuo veluti fluxu inde naſcitur im<lb></lb>

pulſus? Reſpondeo impulſum quidem continuo fluxu <lb></lb>

à grauitate renaſci, verùm quantùm grauitas producit, <lb></lb>

tantundem reſiſtentia &amp; quies violenta in hypomo<lb></lb>

chlio abſumit: <expan abbr="quouſq́">quouſque</expan>; ergo grauia quieſcunt, idem <lb></lb>

manet impulſus, qui nequit ab q motu in ſubiecto <lb></lb>

conſeruari. </s>
            <s id="N11243">Qui <expan abbr="opinãtur">opinantur</expan> grauia non à ſe ipſis, verùm à <lb></lb>

ſuo magnete ſeu tellure moueri quæ opinio non caret <lb></lb>

probabilitate, dicent <expan abbr="utriuſq́">utriuſque</expan>; motus principium eſſe <lb></lb>

externum: verùm in his, quæ projiciuntur, in motu ſe<lb></lb>

parari, <expan abbr="atq́">atque</expan> ita ſenſim deficere impulſum; ob retractio<lb></lb>

nem verò magneticam, ubi jam præualuit, non aliter <lb></lb>

quam à grauitate fieri conuerſionem motus. </s>
            <s id="N1125E">Quæ au<lb></lb>

tem moueri dicuntur à grauitate, habere impulſum à <lb></lb>

tellure, <expan abbr="atq́">atque</expan>; eo modo, quo ferrum ad ſuum magne<lb></lb>

tem moueri, at verò velocitatem ex illà tractione con


<pb xlink:href="062/01/038.jpg"></pb>tinuatà naſci, dum impulſus ſibi ipſi inſtat non aliter <lb></lb>

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

inclinato.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N11286" type="main">
            <s id="N11288">TAmetſi grauitas in lineà inclinatâ deficiat ab illa <lb></lb>

perfectione, quam habet in lineà perpendiculari, <lb></lb>

non tamen eo modo, quo in lineà horizontali quieſcit<lb></lb> tota: exceſſus enim illius partis, quæ cum centro extra <lb></lb>

hypomochlium cadit, à nullo impeditur: &amp; cúm ſit a<lb></lb>

gens neceſſarium, motum producit ſibi æqualem. quia <lb></lb>

verò velocitas continuò augetur in deſcenſu, ſicuti gra<lb></lb>

uitas perfecta in lineà perpendiculari ſe habet ad ſuum <lb></lb>

augmentum, ita grauitas diminuta in lineà inclinatà ſe <lb></lb>


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

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

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


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

motus <emph type="italics"></emph>ae<emph.end type="italics"></emph.end> motui <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> eſt æqualis ut prop: 13. oſtendemus: <lb></lb>

ſunt autem duo triangula <emph type="italics"></emph>dab. eac<emph.end type="italics"></emph.end> ſimilia inter ſe, erit <lb></lb>

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

tis motus in linea perpendiculari &amp; lineà inclinata. </s>
            <s id="N112FC">In <lb></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"></emph>Propoſitio XI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N1130B" type="main">
            <s id="N1130D"><emph type="italics"></emph>Impulſus in quolibet motu ſeu recto, ſeu inclinato eſt major gra<lb></lb>

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

eſſe majorem ſuà grauitate nullum eſt dubium: <lb></lb>

nam cùm velocitas cum ipſo motu incipiat augeri, ſicu<lb></lb>

ti à principio eſt æqualis grauitati, ita in progreſſu erit <lb></lb>

major grauitate. </s>
            <s id="N11323">At verò de motu per lineam inclina<lb></lb>

tam dubitari poteſt: propterea quód à grauitate fiat im<lb></lb>

pedità, ac proinde minori: id tamen hac ratione oſten<lb></lb>

demus. </s>
            <s id="N1132C">Grauitas in lineà inclinatà eò magis impeditur <lb></lb>

à ſuà velocitate, quò magis hæc inclinatur, <expan abbr="eſtq́">eſtque</expan>; ſinus an<lb></lb>

guli inclinationis idem qui grauitatis exceſſus: uti <lb></lb>

prop: 14. oſtendemus: grauitas ergo per lineam perpen<lb></lb>

dicularem ad grauitatem per lineam inclinatam, ut ſi<lb></lb>

nus totus ad ſinum complementi anguli inclinationis, <lb></lb>

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


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

cto <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> cúm omni magnitudine datà minor aſſumi poſsit: <lb></lb>

eſt autem velocitas in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> major ſuà grauitate: erit ergo <lb></lb>

velocitas in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> major <expan abbr="quoq́">quoque</expan>; eadem grauitate, cùm majo<lb></lb>

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

quam ad velocitatem in <emph type="italics"></emph>d.<emph.end type="italics"></emph.end> Idem de quouis alio pun<lb></lb>cto oſtendemus. impulſus ergo in quolibet motu ſeu re<lb></lb>

cto, ſeu inclinato eſt major grauitate. </s>
          </p>
        </subchap1>
        <subchap1 id="N1138A">
          <p id="N1138B" type="main">
            <s id="N1138D"><emph type="center"></emph>Propoſitio XII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11394" type="main">
            <s id="N11396"><emph type="italics"></emph>Incrementa velocitatis rationem habent quam temporum <lb></lb>

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

angulum ſibi ſimile manens, per poſit: 5. propte<lb></lb>

rea quòd hujus augmentum ſit perfectio intenſiua; <lb></lb>

cùm ex illo puncto quietis veluti lateſcit, angulum con<lb></lb>

ſtituit ſui augmenti, ma<emph type="italics"></emph>j<emph.end type="italics"></emph.end>orem minoremuè pro <expan abbr="cuiuſq́">cuiuſque</expan>; <lb></lb>

perfectione, quam obtinet in principio motus, ſiuè ex <lb></lb>

naturâ ſuâ, ſiue ex impedimento: majori enim perfecti<lb></lb>

oni maior angulus debetur. </s>
            <s id="N113BC">Sit primùm angulus <emph type="italics"></emph>nag<emph.end type="italics"></emph.end><lb></lb>ſe miſsis anguli recti; tempus verò <emph type="italics"></emph>ag<emph.end type="italics"></emph.end> in minuta <emph type="italics"></emph>ab. bc. <lb></lb>

cd. de. ef.fg<emph.end type="italics"></emph.end> æqualiter diuiſum: velocitas ergò motus <lb></lb>

augetur impulſu augeſcente in primo quidem minuto <lb></lb>

in <emph type="italics"></emph>hb,<emph.end type="italics"></emph.end> in 2. in <emph type="italics"></emph>ic,<emph.end type="italics"></emph.end> in 3. in <emph type="italics"></emph>kd,<emph.end type="italics"></emph.end> <expan abbr="atq́">atque</expan>; itæ conſequenter æquatà


<pb xlink:href="062/01/041.jpg"></pb>areà illius trianguli rectanguli, cujus longitudo nume<lb></lb>

rus minutorum, baſis verò terminus augmenti. </s>
            <s id="N113F4">Quia <lb></lb>

verò eadem eſt ratio motus &amp; virtutis impulſiuæ, vir<lb></lb>


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

tus quidem dupla in eodem aut æquali tempore moue<lb></lb>

bit per ſpatium duplum: quòd ſi ergo in primo minu<lb></lb>

to <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> virtus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> lateſcens, cum quà pariter creſcit veloci<lb></lb>

tas motus, terminum habet ſui incrementi in <emph type="italics"></emph>hb,<emph.end type="italics"></emph.end> in ſe<lb></lb>

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

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

ſpatium decurſum in duobus minutis ad ſpatium decur<lb></lb>

ſum in uno minuto; at verò duo triangula <emph type="italics"></emph>iac.hab<emph.end type="italics"></emph.end> ſunt <lb></lb>

ſemiſſes duorum quadratorum <emph type="italics"></emph>ipac. hoab.<emph.end type="italics"></emph.end> ac pro<lb></lb>

inde in eàdem ratione, nimirum duplicatà ejus, <expan abbr="quã">quam</expan> ha<lb></lb>

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

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


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

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

ac proinde illorum quadrata in eadem <expan abbr="quoq́">quoque</expan>, ratione, <lb></lb>

nimirum duplicata. </s>
            <s id="N11489"><expan abbr="Itaq́">Itaque</expan>; ſi quadratum lateris <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> hoc <lb></lb>

eſt primi minuti, ſubtrahas â quadrato <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> ſecundi minu<lb></lb>

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

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

minuto, hujus quadratum, ideſt unum, ab illius quadra<lb></lb>

to, id, eſt â quatuor ſubtractum relinquit tria totidem <lb></lb>

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

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

ablato ex his quadrato ſecundi minuti, numerus reli<lb></lb>

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

bentur. </s>
            <s id="N114BE">Rurſum â numero 4. minuti in ſe ducto, ideſt <lb></lb>

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

pro 4. minuto: totidem ergo cubitorum ſpatium trans<lb></lb>

mittit mobile <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in minuto quarto. </s>
            <s id="N114CD">Quód ſi angulus <lb></lb>

augmenti major ſit aut minor ſemiſſe anguli recti, ut <lb></lb>

angulus <emph type="italics"></emph>qag.<emph.end type="italics"></emph.end> aut <emph type="italics"></emph>rag,<emph.end type="italics"></emph.end> quod quidem contingit, cùm vir<lb></lb>

tus impulſiua magis aut minùs eſt intenſa, tum quidem <lb></lb>illa virtus magis perfecta ex illo puncto continuò majo<lb></lb>

ra ſumit incrementa: eadem tamen demonſtratio, <expan abbr="atq́">atque</expan>; <lb></lb>

eadem eſt proportio <expan abbr="utrobiq́">utrobique</expan>;, propterea quòd parallelo<lb></lb>

gramma in proportione <expan abbr="quoq́">quoque</expan>; ſint duplicatá ſuorum <lb></lb>

laterum ſimul ſumptorum.| </s>
          </p>
        </subchap1>
        <subchap1 id="N114F8">
          <pb xlink:href="062/01/043.jpg"></pb>
          <p id="N114FC" type="main">
            <s id="N114FE"><emph type="center"></emph>Propoſitio XIII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11505" type="main">
            <s id="N11507"><emph type="italics"></emph>Motus per lineam perpendicularem &amp; lineam inclinatam, quo<lb></lb>

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

clinatam, inter ſe ſunt æquales.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N11512" type="main">
            <s id="N11514">ÆQuales dico non velocitate, quæ minor eſt in lineà <lb></lb>

inclinatà, ſed duratione: hoc eſt ſi ex eodem puncto <lb></lb>

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

neam perpendicularem <emph type="italics"></emph>ba,<emph.end type="italics"></emph.end> alterum verò huic æquale <lb></lb>

per lineam <emph type="italics"></emph>bf<emph.end type="italics"></emph.end> ad horizontem inclinatam moueatur: aſ<lb></lb>

ſumpto quolibet puncto in lineà perpendiculari <emph type="italics"></emph>Vg. a,<emph.end type="italics"></emph.end><lb></lb>

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

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


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


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

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

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

quam ex centro grauitatis <emph type="italics"></emph>d<emph.end type="italics"></emph.end> educta ſit linea perpendicu<lb></lb>

laris <emph type="italics"></emph>dc,<emph.end type="italics"></emph.end> diſtantia nimirum centri à lineà hypomochlij <emph type="italics"></emph>f <lb></lb>

g:<emph.end type="italics"></emph.end> eſt autem linea <emph type="italics"></emph>df<emph.end type="italics"></emph.end> ſemidiameter circuli, diſtantia ejuſ<lb></lb>

dem centri ab hypochlio, quam obtinet in lineâ perpen<lb></lb>

diculari <emph type="italics"></emph>ba.<emph.end type="italics"></emph.end> quia ergo impulſus augetur in ratione di<lb></lb>

ſtantiæ centri ab hypomochlio, per Poſit: 6. <expan abbr="motũq́">motunque</expan>; pro <lb></lb>

ducit ſibi æqualem, per prop: 2. velocitas autem motus <lb></lb>

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

rit ut <emph type="italics"></emph>fd<emph.end type="italics"></emph.end> impulſus major ad <emph type="italics"></emph>dc<emph.end type="italics"></emph.end> impulſum minorem, ita <lb></lb>

motus in <emph type="italics"></emph>ba<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>bf:<emph.end type="italics"></emph.end> propterea quód triangula <lb></lb>

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

linea <expan abbr="quoq́">quoque</expan>; <emph type="italics"></emph>af,<emph.end type="italics"></emph.end> ſimilis lineæ <expan abbr="perpẽdiculari">perpendiculari</expan> <emph type="italics"></emph>dc,<emph.end type="italics"></emph.end> perpendi<lb></lb>

cularis. </s>
          </p>
        </subchap1>
        <subchap1 id="N115F8">
          <p id="N115F9" type="main">
            <s id="N115FB"><emph type="center"></emph>Propoſitio XIV:<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11602" type="main">
            <s id="N11604"><emph type="italics"></emph>Motus per lineam minùs inclinatam eſt velocìor motu per li<lb></lb>

neam magis inclinatam, in ratione, quam habent ſinus complemen<lb></lb>

ti illarum inclinationum.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N1160F" type="main">
            <s id="N11611">DVcantur ex puncto <emph type="italics"></emph>a<emph.end type="italics"></emph.end> lîneæ <emph type="italics"></emph>ab. ac. ad. ae. af,<emph.end type="italics"></emph.end> &amp; ſit li<lb></lb>

nea <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> horizontalis, linea verò <emph type="italics"></emph>at<emph.end type="italics"></emph.end> perpendicularis, <lb></lb>

reliquæ lineæ ad horizontem inclinatæ: dico idem mo<lb></lb>

bile o verbi grat: inæqualiter moueri, velociùs quidem


<pb xlink:href="062/01/045.jpg"></pb>in lineà <emph type="italics"></emph>ae<emph.end type="italics"></emph.end> minus inclinatà, minùs autem velociter in li<lb></lb>

neà <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> magis inclinatà, <expan abbr="eſſeq́">eſſeque</expan>; rationem velocitatis in <emph type="italics"></emph>ae<emph.end type="italics"></emph.end><lb></lb> ad velocitatem in <emph type="italics"></emph>ad,<emph.end type="italics"></emph.end> ut ſinus anguli <emph type="italics"></emph>ats<emph.end type="italics"></emph.end> ad ſinum angu<lb></lb>

li <emph type="italics"></emph>atr.<emph.end type="italics"></emph.end> Ex punctis contactus <emph type="italics"></emph>qrs<emph.end type="italics"></emph.end> demittantur lineæ <lb></lb>

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


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

parallelæ <emph type="italics"></emph>qg.rh.si<emph.end type="italics"></emph.end> <expan abbr="ſecãtes">ſecantes</expan> mobile in <emph type="italics"></emph>k. n. u,<emph.end type="italics"></emph.end> ex centro au<lb></lb>

tem <emph type="italics"></emph>o<emph.end type="italics"></emph.end> ducantur lineæ perpendiculares ad lineam hypo<lb></lb>

mochlij <foreign lang="grc">οα. οβ. ογ</foreign>, <expan abbr="eruntq́">eruntque</expan>; lineæ <emph type="italics"></emph>qg. rh. si<emph.end type="italics"></emph.end> lineæ hypo<lb></lb>

mochlij. </s>
            <s id="N116A9">Quia verò angulus <emph type="italics"></emph>tsi,<emph.end type="italics"></emph.end> hoc eſt angulus <emph type="italics"></emph>sh<emph.end type="italics"></emph.end> ex


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

gulus <foreign lang="grc">γσο</foreign> angulo <foreign lang="grc">βγο</foreign>, &amp; latus <foreign lang="grc">γο</foreign> latere <foreign lang="grc">βο</foreign> majus: ſunt <lb></lb>

autem latera <foreign lang="grc">γο. βο</foreign> diſtantia centri grauitatis. </s>
            <s id="N116DA">Quia er<lb></lb>

go maior impulſus in <foreign lang="grc">γο</foreign> maiori, quam in <foreign lang="grc">βο</foreign> minori di<lb></lb>

ſtantià; erit per prop: 6. velocior motus in linea <emph type="italics"></emph>as<emph.end type="italics"></emph.end> mi<lb></lb>

nús inclinatá, quam in lineà <emph type="italics"></emph>ar<emph.end type="italics"></emph.end> magis inclinatà. </s>
            <s id="N116F7">Quòd <lb></lb>

autem velocitas motus ſit in ratione, quam habent cor<lb></lb>

dæ, ſeu ſinus complementi inclinationum, ita oſtende<lb></lb>

mus: quia ut <foreign lang="grc">σο</foreign> ad <foreign lang="grc">γο</foreign>, ita corda <emph type="italics"></emph>at<emph.end type="italics"></emph.end> ad cordam <emph type="italics"></emph>as,<emph.end type="italics"></emph.end> &amp; ut <emph type="italics"></emph>rò<emph.end type="italics"></emph.end><lb></lb> æqualis <foreign lang="grc">σο</foreign> ad <foreign lang="grc">οβ</foreign>, ita eadem corda <emph type="italics"></emph>at<emph.end type="italics"></emph.end> ad cordam <emph type="italics"></emph>ar:<emph.end type="italics"></emph.end> erit <lb></lb>

<expan abbr="quoq́">quoque</expan>; ut <foreign lang="grc">ογ</foreign> ad <foreign lang="grc">οβ</foreign>, ita <emph type="italics"></emph>as<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>ar.<emph.end type="italics"></emph.end> at verò ut cordæ <emph type="italics"></emph>as. ar,<emph.end type="italics"></emph.end><lb></lb>

ita illarum ſemiſſes <emph type="italics"></emph>al. am<emph.end type="italics"></emph.end> ſinus angulorum <emph type="italics"></emph>apl. apm <emph.end type="italics"></emph.end><lb></lb>

qui æquales ſunt angulis <emph type="italics"></emph>ats.atr<emph.end type="italics"></emph.end> angulis complementi <lb></lb>

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

ad <foreign lang="grc">οβ</foreign>, ita ſinus complementi angulorum inclinationis, <lb></lb>

quod erat oſtendendum. </s>
          </p>
        </subchap1>
        <subchap1 id="N1177F">
          <p id="N11780" type="main">
            <s id="N11782"><emph type="center"></emph>Propoſitio XV.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11789" type="main">
            <s id="N1178B"><emph type="italics"></emph>Motus ex eodem puncto per lineas ſubtenſas ſunt æquales motui <lb></lb>

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

bf.be<emph.end type="italics"></emph.end> ad horizontem inclinatas, hoc eſt per cordas <lb></lb>

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


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

<emph type="italics"></emph>ba<emph.end type="italics"></emph.end> motum terminari. </s>
            <s id="N117C7">Quòd ſi enim ex puncto <emph type="italics"></emph>a<emph.end type="italics"></emph.end> du<lb></lb>

cantur lineæ rectæ <emph type="italics"></emph>af. ag,<emph.end type="italics"></emph.end> erunt anguli <emph type="italics"></emph>afb. agb<emph.end type="italics"></emph.end> in ſemi<lb></lb>

circulo recti; ac proinde ex iam demonſtratis motus in <lb></lb>

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

ex punctis <emph type="italics"></emph>befg<emph.end type="italics"></emph.end> in <emph type="italics"></emph>a<emph.end type="italics"></emph.end> terminetur motus, <expan abbr="erũt">erunt</expan> lineæ <emph type="italics"></emph>be.bf.<emph.end type="italics"></emph.end><lb></lb>


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

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

a<emph.end type="italics"></emph.end> motui in <emph type="italics"></emph>ea. fa. ga<emph.end type="italics"></emph.end> æqualis. </s>
            <s id="N11831">At verò ſi ex alio puncto <lb></lb>

Vg <foreign lang="grc">α</foreign> incipiat motus, <expan abbr="neq́">neque</expan>; ad idem cum diametro pun<lb></lb>

ctum terminetur, cujuſmodi linea <foreign lang="grc">αβ</foreign>, er t motus hujus <lb></lb>

motui in diametro <emph type="italics"></emph>ba<emph.end type="italics"></emph.end> inæqualis. </s>
            <s id="N1184C">Ducatur enim ex <foreign lang="grc">α</foreign> in <lb></lb>

<emph type="italics"></emph>a<emph.end type="italics"></emph.end> linea <foreign lang="grc">α</foreign> <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; motus hujus motui <emph type="italics"></emph>ba,<emph.end type="italics"></emph.end> ideſt motui <foreign lang="grc">αδ</foreign>


<pb xlink:href="062/01/048.jpg"></pb>æqualis: linea verò <foreign lang="grc">γβ</foreign> perpendicularis ad <foreign lang="grc">αβ</foreign> motum ter<lb></lb>

minabit in <foreign lang="grc">β</foreign> æqualem motui <foreign lang="grc">αγ</foreign>: eſt autem linea <foreign lang="grc">αγ</foreign> mi<lb></lb>

nor quam <foreign lang="grc">αδ</foreign> motus ergo in <foreign lang="grc">αγ</foreign>, ideſt motus huic æqua <lb></lb>

lis in <foreign lang="grc">αβ</foreign> minori fit tempore quam in <foreign lang="grc">α</foreign> a.</s>
          </p>
        </subchap1>
        <subchap1 id="N118A1">
          <p id="N118A2" type="main">
            <s id="N118A4"><emph type="center"></emph>Propoſitio XVI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N118AB" type="main">
            <s id="N118AD"><emph type="italics"></emph>Motus grauitatis per lineam magis inclinatam in majori à <lb></lb>

centro diſtantià, tempore verò æquali terminatur.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N118B6" type="main">
            <s id="N118B8">MOueatur mobile à puncto <emph type="italics"></emph>b<emph.end type="italics"></emph.end> per lineas <emph type="italics"></emph>ba. bi. bh. bg <lb></lb>

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

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

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

angulus <emph type="italics"></emph>abh<emph.end type="italics"></emph.end> eſt major angulo <emph type="italics"></emph>abi,<emph.end type="italics"></emph.end> erit terminus mo<lb></lb>


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


<pb xlink:href="062/01/049.jpg"></pb>tus, quem grauitas inducit in lineâ <emph type="italics"></emph>bh,<emph.end type="italics"></emph.end> remotior à cen<lb></lb>

tro, quàm in lineâ <emph type="italics"></emph>bi.<emph.end type="italics"></emph.end> Ducantur enim à centro <emph type="italics"></emph>a<emph.end type="italics"></emph.end> lineæ <emph type="italics"></emph>ai. <lb></lb>

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

uitatis in <emph type="italics"></emph>i<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>h<emph.end type="italics"></emph.end> ob breuiſsimam diſtantiam, quæ eſſe po<lb></lb>

teſt in illis lineis; quód ſi enim ex <emph type="italics"></emph>i<emph.end type="italics"></emph.end> moueatur in <emph type="italics"></emph>st,<emph.end type="italics"></emph.end> quia <lb></lb>

illo progreſſu lineæ à centro ductæ fiunt majores, ma<lb></lb>

jor enim <emph type="italics"></emph>as<emph.end type="italics"></emph.end> angulo recto <emph type="italics"></emph>ais<emph.end type="italics"></emph.end> ſubtenſa quam <emph type="italics"></emph>ai,<emph.end type="italics"></emph.end> mobile <lb></lb>

motu naturali à centro magis abduceretur, quod fieri <lb></lb>

nequit. </s>
            <s id="N11954">Quia ergo linea <foreign lang="grc">αγ</foreign> major eſt quàm linea <emph type="italics"></emph>ai,<emph.end type="italics"></emph.end><lb></lb>

erit linea <emph type="italics"></emph>ab<emph.end type="italics"></emph.end>c dem multò major: igitur punctum <emph type="italics"></emph>h<emph.end type="italics"></emph.end> ter<lb></lb>

minus motus in lineà magis inclinatà, majori, punctum <lb></lb>

verò <emph type="italics"></emph>i<emph.end type="italics"></emph.end> terminus motus in lineà minús inclinatâ, minori <lb></lb>

à centro abeſt interuallo. </s>
            <s id="N1197A">Quia vetò <expan abbr="uterq́">uterque</expan>; motus tam <lb></lb>

per <expan abbr="lineã">lineam</expan> <emph type="italics"></emph>ai<emph.end type="italics"></emph.end> <expan abbr="quã">quam</expan> per <expan abbr="lineã">lineam</expan> <emph type="italics"></emph>ah<emph.end type="italics"></emph.end> eſt æqualis motui per <expan abbr="lineã">lineam</expan> <lb></lb>

perpendicularem <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> propterea quòd lineæ perpendi<lb></lb>

culares <emph type="italics"></emph>as. ah<emph.end type="italics"></emph.end> <expan abbr="utrumq́">utrumque</expan>; <expan abbr="motũ">motum</expan> conjungunt per prop: 13. <lb></lb>

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

æquali. </s>
          </p>
        </subchap1>
        <subchap1 id="N119C7">
          <p id="N119C8" type="main">
            <s id="N119CA"><emph type="center"></emph>Propoſitio XVII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N119D1" type="main">
            <s id="N119D3"><emph type="italics"></emph>Motus grauitatis ex eodem puncto per lineas ad horizontem in<lb></lb>

clinatas in circulum terminatur, cuius diameter eſt diſtantia inter <lb></lb>

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

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


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

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

minari, cujus diameter linea perpendicularis <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> diſtan<lb></lb>

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

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

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


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

propterea quòd minima ſit hæc diſtantia à mundi cen<lb></lb>

tro <emph type="italics"></emph>a.<emph.end type="italics"></emph.end> Quia verò anguli <emph type="italics"></emph>aib.ahb.afb<emph.end type="italics"></emph.end> ſunt recti ean<lb></lb>

dem habentes baſim <emph type="italics"></emph>ab.<emph.end type="italics"></emph.end> erunt in eodem ſemicirculo <emph type="italics"></emph>bef <lb></lb>

g hia,<emph.end type="italics"></emph.end> cujus diameter linea <emph type="italics"></emph>ba<emph.end type="italics"></emph.end> perpendicularis, diſtantia <lb></lb>

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

plum velocitatis eodem motu collectæ.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N11A8B" type="main">
            <s id="N11A8D">VT in fig: 5. ſi velocitas motus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in tempore <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> conti<lb></lb>

nuò augeatur; quia hujus augmentum eſt perfe<lb></lb>

ctio intenſiua, ac proinde eo modo augetur, quo trian<lb></lb>

gulum ſibi ſimile manens per poſit: 5. erit velocitas in <lb></lb>

fine motus, ut baſis ejuſdem trianguli <emph type="italics"></emph>bc.<emph.end type="italics"></emph.end> Moueatur er<lb></lb>

go hæc velocitas in <emph type="italics"></emph>e,<emph.end type="italics"></emph.end> &amp; ſit tempus <emph type="italics"></emph>ec<emph.end type="italics"></emph.end> æquale tempori <lb></lb>

<emph type="italics"></emph>ac,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; velocitas illo motu colecta quadratum <emph type="italics"></emph>bcde<emph.end type="italics"></emph.end><lb></lb> duplum trianguli <emph type="italics"></emph>abc,<emph.end type="italics"></emph.end> propterea quòd eandem baſim <lb></lb>

<emph type="italics"></emph>bc,<emph.end type="italics"></emph.end> altitudinem verò habet æqualem. </s>
            <s id="N11AD9">Quia ergo virtus <lb></lb>

dupla in eodem vel æquali tempore per ſpatium mouet <lb></lb>

<expan abbr="duplũ">duplum</expan>, <expan abbr="eſtq́">eſtque</expan>; <expan abbr="eadẽ">eadem</expan> ratio velocitatis &amp; interualli, velocitas <lb></lb>

in fine motus eodem vel æquali tempore per ſpatium <lb></lb>

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

bile.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N11B05" type="main">
            <s id="N11B07">STatio quidem grauium eſt centrum terræ, ponderis <lb></lb>

verò è filo penduli linea perpendicularis, in quà de


<pb xlink:href="062/01/052.jpg"></pb>mum mobile ex illâ agitatione conquieſcit. </s>
            <s id="N11B10">Quòd ſi <lb></lb>

ergo ſeu corpus graue ad centrum, ſeu perpendiculum <lb></lb>

in ſuam ſtationem moueatur, non ſtatim conquieſcit <lb></lb>

ex hoc motu ſiuè in centro, ſiuè in lineâ perpendiculari, <lb></lb>

verùm ultra hos limites procurrit &amp; recurrit, <expan abbr="atq́">atque</expan>; eò ma<lb></lb>

gis, quò circuli majores. </s>
            <s id="N11B21">Quod quidem in perpendicu<lb></lb>

lo experientià conſtat: de grauium verò à centro excur<lb></lb>

ſu licet nulla experientia habeatur, id tamen ſimilitudo <lb></lb>

rationis euincit: non enim minùs contra natu<lb></lb>

ram grauitatis eſſe videtur in circulo à lineâ ſtatio<lb></lb>

nis, quam in lineâ perpendiculari è centro efferi. </s>
            <s id="N11B2E">Hujus <lb></lb>

autem ratio hæc: quia impulſus in quolibet puncto, ac <lb></lb>

proinde in fine motus eſt major grauitate: per prop: 11. <lb></lb>

eſt autem agens neceſſarium per prop: 2. &amp; non niſi per <lb></lb>

lineam rectam mouet <expan abbr="ſuũ">ſuum</expan> mobile per prop: 3. ſuperabit <lb></lb>

ergo illam, quâ in centro firmatur, grauitatem, non mi<lb></lb>

nùs, quam cùm lapidem ſimilis impulſus à centro lon<lb></lb>

giùs abducit. </s>
          </p>
        </subchap1>
        <subchap1 id="N11B43">
          <p id="N11B44" type="main">
            <s id="N11B46"><emph type="center"></emph>Propoſitio XX.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11B4D" type="main">
            <s id="N11B4F"><emph type="italics"></emph>Velocitas in motu collecta per æqualia ſuo augmento decremen<lb></lb>

ta in quietem terminatur.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N11B58" type="main">
            <s id="N11B5A">PErpendiculum liberè dimiſſum in ſuam ſtationem <lb></lb>

recurrit, <expan abbr="atq́">atque</expan>; eodem motu continuato ultra ſtatio


<pb xlink:href="062/01/053.jpg"></pb>nem excurrit. </s>
            <s id="N11B67">Quòd ſi ergo impulſus ex illo recurſu <lb></lb>

collectus aut idem maneat, aut continuò augeatur, quia <lb></lb>

per prop: 18. </s>
            <s id="N11B6E">Velocitas in fine eodem vel æquali tempo<lb></lb>

re per ſpatium mouet duplum velocitatis ex illo motu <lb></lb>

collectæ, erit ex curſus major recurſu: &amp; quia ex quoli<lb></lb>

bet recurſu magis excurrit, erit motus perpendiculi in<lb></lb>

finitus. </s>
            <s id="N11B79">At verò hic motus demum conquieſcit: <expan abbr="nõ">non</expan> ergo <lb></lb>

impulſus augeri, aut idem eſſe poteſt. </s>
            <s id="N11B82">Et quia per ar<lb></lb>

cus excurrit &amp; recurrit continuò minores, neceſſe im<lb></lb>

pulſum minui in illo aſcenſu; quia nimirum inter ſe <lb></lb>

miſcentur, &amp; in deſcenſu quidem per eandem lineam <lb></lb>

mouent grauitas &amp; impulſus, quem à grauitate conti<lb></lb>nuo fluxu naſci dicebamus: à ſtatione verò grauitas im<lb></lb>

pulſui reluctatur: quia nimirum contrarius impulſus <lb></lb>

ab eâdem grauitate renaſcens tollit partem ſibi æqua<lb></lb>

lem, per poſit: 2. <expan abbr="eſtq́">eſtque</expan>; motus reliquus æqualis exceſſui <lb></lb>

majoris ut Prop: 30. dicemus: ſicut ergo impulſus conti<lb></lb>

nuò decreſcit ijſdem, quibus augebatur augmentis, ita <lb></lb>

uelocitas à ſummo augmento ad finem <expan abbr="uſq́">uſque</expan>; motus con<lb></lb>

tinuò fit minor; ſimul verò ſumpta æqualis velocitati à <lb></lb>

principio motus ad finem <expan abbr="augmẽti">augmenti</expan> collectæ: ut ſi in ſig: 9. <lb></lb>

<expan abbr="perpendiculũ">perpendiculum</expan> <emph type="italics"></emph>ae<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>e<emph.end type="italics"></emph.end> recurrat in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> &amp; ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> excurrat in <emph type="italics"></emph>ſi<emph.end type="italics"></emph.end> aſ<lb></lb>

ſumantur autem arcus <emph type="italics"></emph>bc. bd,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>be.bf<emph.end type="italics"></emph.end> inter ſe æquales: <lb></lb>

dico augmentum velocitatis in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> ejuſdem decremento <lb></lb>

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


<pb xlink:href="062/01/054.jpg"></pb>in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> eſſe æquale. </s>
            <s id="N11BFD">Ducantur enim lineæ tangentes <emph type="italics"></emph>eg fg,<emph.end type="italics"></emph.end><lb></lb>

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

tio <emph type="italics"></emph>ch<emph.end type="italics"></emph.end> æqualis inclinationi <emph type="italics"></emph>dh<emph.end type="italics"></emph.end>: propterea quòd <expan abbr="ãguli">anguli</expan> <emph type="italics"></emph>ega.<lb></lb>

fga,<emph.end type="italics"></emph.end> &amp; anguli <emph type="italics"></emph>cha. dha<emph.end type="italics"></emph.end> ſunt æquales, impulſus ergo gra<lb></lb>

uitatis in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> ejuſdem impulſui in <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> &amp; impulſus grauitatis <lb></lb>

in <emph type="italics"></emph>c<emph.end type="italics"></emph.end> ejuſdem impulſui in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> eſt æqualis, ut conſtat ex <lb></lb>

prop. 14. </s>
            <s id="N11C5B">Quia ergo impulſus æquales in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> quidem &amp; <emph type="italics"></emph>c<emph.end type="italics"></emph.end><lb></lb>

augent, in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> verò &amp; <emph type="italics"></emph>d<emph.end type="italics"></emph.end> minuunt velocitatem motus, <expan abbr="erũt">erunt</expan> <lb></lb>

æqualia velocitatis augmenta ejuſdem decremento; ac <lb></lb>

proinde velocitas in motu collecta per æqualia ſuo aug<lb></lb>

mento decrementa in quietem terminatur. </s>
            <s id="N11C81">Obijcies ſi <lb></lb>

velocitas excurſus ſimul ſumpta eſt æqualis velocitati in <lb></lb>

recurſu collectæ, quia velocitas æqualis eodem vel æ<lb></lb>

quali tempore per ſpatium mouet æquale, erunt excur<lb></lb>

ſus &amp; recurſus inter ſe æquales: ac proinde motus per<lb></lb>

pendiculi infinitus. </s>
            <s id="N11C8E">Reſpondent quidam excurſum eſ<lb></lb>

ſe minorem recurſu: propterea quód illius motus à fu<lb></lb>

niculo perturbetur, cujus partes inæqualiter mouen<lb></lb>

tur: velociùs quidem centro propiores, minùs autem <lb></lb>

velociter à centro remotiores. </s>
            <s id="N11C99">Dum ergo hæ reſtitant, <lb></lb>

&amp; minorum circulorum velocitatem morantur; illæ <lb></lb>

præcurrere feſtinant: neceſſe ex illà luctâ impulſum mi<lb></lb>

nui, ut non niſi ad minus interuallum ſe extendat. </s>
            <s id="N11CA2">Hu<lb></lb>

jus autem ſignum eſſe illos ſinus, in quos funis contor<lb></lb>

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


<pb xlink:href="062/01/055.jpg"></pb>tenà, cujus partes ex ſe ſunt ponderoſæ, motus hic undo<lb></lb>

ſus ſibi ipſi ſit impedimento: non tamen hæc ratio lo<lb></lb>

cum habet in perquam ſubtili &amp; tenuiſsimo filo, cujus <lb></lb>

partes non ex ſe, verúm ex impulſu ponderis appenſi <lb></lb>

<expan abbr="mouẽtur">mouentur</expan>, <expan abbr="eoq́">eoque</expan>; præciſo aut abrupto à motu <expan abbr="conquieſcũt">conquieſcunt</expan>. <lb></lb>

Deinde ſi ratio inæqualium circulorum perturbat il<lb></lb>

lum motum, quo perpendiculum à ſua ſtatione procur<lb></lb>

rit, turbabit <expan abbr="quoq́">quoque</expan>; rationem motus, quam ad ſe habent <lb></lb>

recurſus: at verò hæc in æqualitas nihil obſtat, quò mi<lb></lb>

nùs recurſus inter ſe ſint æquales: nihil ergo obſtabit, <lb></lb>

quò minùs excurſus <expan abbr="quoq́">quoque</expan>; inter ſe ſint æquales. </s>
            <s id="N11CD8">Præte<lb></lb>

rea ſi funiculo <expan abbr="põdus">pondus</expan> accedat medio inter <expan abbr="hypemochliũ">hypomochlium</expan> <lb></lb>

loco, motum accelerabit; non igitur ex ſe motum aut <lb></lb>

pondus habet: propterea quòd negant maius pondus <lb></lb>

velocitatem augere. </s>
            <s id="N11CEB">At verò ſi pars illa fili, quæ ob pon<lb></lb>

dus acceſſorium velociùs mouetur, ſuo <expan abbr="quoq́">quoque</expan>; pondere <lb></lb>

mouebatur, fiet ſanè, ut continuà hac ponderis noui ac<lb></lb>

ceſsione velocitas in infinitum augeatur. </s>
            <s id="N11CF8">Dicendum <lb></lb>

ergò excurſum perpendiculi continuò quidem mino<lb></lb>

rem fieri recurſu; cauſam verò hujus inæqualitatis non <lb></lb>

in funiculo, ſed in naturà circuli, in quo perpendiculum <lb></lb>

mouetur, ſitam eſſe. </s>
            <s id="N11D03">Quia enim velocitas motus conti<lb></lb>

nuo fluxu augetur à grauitate, quæ ex inclinatione ma<lb></lb>

iori ob maiorem <expan abbr="violẽtiã">violentiam</expan> hypomochlii minùs grauitat, <lb></lb>

impulſus, quo perpendiculum recurrit, continuó qui-


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

puncto circuli per lineas fit tangentes, quæ in recurſu <lb></lb>

continuó magis ac magis ſunt inclinatæ; erunt in quo<lb></lb>

libet puncto recurſus minora huius velocitatis incre<lb></lb>

menta: ita nimirum ut ſi arcus ſumantur æquales, ma<lb></lb>

jor ſit acceſsio velocitatis in arcu primo, quam in arcu <lb></lb>

ſecundo: &amp; velocitas in arcu circuli collecta minor ve<lb></lb>

locitate in lineà rectà illi arcui æquali, quæ tangens ſit <lb></lb>

principii eiuſdem motus circularis. </s>
            <s id="N11D24">Sicuti verò in re<lb></lb>

curſu velocitas continuó &amp; inæqualiter creſcit, ita in <lb></lb>

excurſu, quia motus violentus, proportionaliter decre<lb></lb>

ſcit, <expan abbr="fiuntq́">fiuntque</expan>; huius decrementa æqualia illius incremen<lb></lb>

tis, prima nimirum ultimis; propterea quód <expan abbr="utraq́">utraque</expan>; <expan abbr="fiũt">fiunt</expan> <lb></lb>

ab eadem grauitate, quæ à principio excurſus per lineas <lb></lb>

grauitat magis inclinatas. </s>
            <s id="N11D3F">Quòd ſi ergo ſola grauitas <lb></lb>

minuat impulſum, quia in æqualibus à ſtatione interual<lb></lb>

lis, ob ſimilem inclinationem, æqualiter grauitat; erunt <lb></lb>

ut arcus inter ſe, ita eiuſdem grauitatis impulſus: &amp; <lb></lb>

quia impulſus contrarius tollit partem ſibi æqualem, <lb></lb>

erunt excurſus &amp; recurſus inter ſe æquales. </s>
            <s id="N11D4C">At verò <lb></lb>

quia non ſola grauitas impulſum minuit, ſed etiam in<lb></lb>

clinatio motus; ſicuti enim grauitas extra lineam per<lb></lb>

pendicularem minùs grauitat, ita impulſus extra line<lb></lb>

am ſui motus, cuius terminus eſt veluti centrum, mi <lb></lb>

nús impellit ſuum mobile: quód ſi enim funda lapidem


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

ſit illis rotationibus ſimul ſumptis, in quas idem lapis <lb></lb>

fundæ alligatus reuoluitur. </s>
            <s id="N11D61">Quia ergo in illa gyratione <lb></lb>

perpendiculi inclinatio motus continuò &amp; æqualiter <lb></lb>

mutatur, velocitas in excurſu collecta eò minùs moue<lb></lb>

bit, quó major portio ex illâ inclinatione eidem dece<lb></lb>

dit. </s>
            <s id="N11D6C">Impulſus ergo æqualis quia magis decreſcit in ex<lb></lb>

curſu, quam idem augeatur in recurſu, ad minus moue<lb></lb>

bit interuallum: ac proinde excurſus perpendiculi ejuſ<lb></lb>

dem recurſibus erunt minores. </s>
          </p>
        </subchap1>
        <subchap1 id="N11D75">
          <p id="N11D76" type="main">
            <s id="N11D78"><emph type="center"></emph>Propoſitio XXI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11D7F" type="main">
            <s id="N11D81"><emph type="italics"></emph>Excurſus grauium à termino motus in circulum terminatur, cu<lb></lb>

jus ſemidiameter eſt diſtantià inter principium motus &amp; mundi <lb></lb>

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

lineis ad horizontem inclinatis producantur lineæ <lb></lb>

excurſui æquales lineis decurſus, nimirum <emph type="italics"></emph>ap<emph.end type="italics"></emph.end> ipſi <emph type="italics"></emph>ab, io<emph.end type="italics"></emph.end><lb></lb> verò ipſi <emph type="italics"></emph>ib<emph.end type="italics"></emph.end> æqualis, dico puncta <emph type="italics"></emph>po<emph.end type="italics"></emph.end> eſſe in peripheria cir<lb></lb>

culi, cujus ſemidiameter <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> diſtantia inter principium <lb></lb>

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

ergo lineæ <emph type="italics"></emph>bi. io<emph.end type="italics"></emph.end> inter ſe ſunt æquales, &amp; anguli <emph type="italics"></emph>bia. oia<emph.end type="italics"></emph.end><lb></lb> recti, erit angulus <emph type="italics"></emph>abi<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>aoi,<emph.end type="italics"></emph.end> &amp; latus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> lateri <emph type="italics"></emph>ao<emph.end type="italics"></emph.end><lb></lb>

æquale: eſt autem linea <emph type="italics"></emph>ap<emph.end type="italics"></emph.end> æqualis eidem <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> puncta er


<pb xlink:href="062/01/058.jpg"></pb>go <emph type="italics"></emph>po<emph.end type="italics"></emph.end> ſunt in peripherià circuli, cujus centrum <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> à quo <lb></lb>

æqualiter abſiſtunt illæ lineæ. </s>
            <s id="N11E0D">Simili modo oſtende<lb></lb>

mus puncta <emph type="italics"></emph>n.m.l<emph.end type="italics"></emph.end> eſſe in peripheriá ejuſdem circuli, pro<lb></lb>


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

pterea quód lineæ <emph type="italics"></emph>an. am. al,<emph.end type="italics"></emph.end> baſes nimirum æqualium <lb></lb>

triangulorum, ſunt æquales lineæ <emph type="italics"></emph>ab.<emph.end type="italics"></emph.end> Excurſus ergo <lb></lb>

grauium à termino motus in <expan abbr="circulũ">circulum</expan> terminantur &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N11E35">
          <p id="N11E36" type="main">
            <s id="N11E38"><emph type="center"></emph>Propoſitio XII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11E3F" type="main">
            <s id="N11E41"><emph type="italics"></emph>Motus per arcus ejuſdem circuli rationem habet, quam ſinus an<lb></lb>

guli dupli illorum angulorum, qui complementa ſunt inclinationis <lb></lb>

cordarum.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N11E4C" type="main">
            <s id="N11E4E">ASſumantur arcus <emph type="italics"></emph>bdi. bdc,<emph.end type="italics"></emph.end> &amp; <expan abbr="ducãtur">ducantur</expan> cordæ <emph type="italics"></emph>bi. bc,<emph.end type="italics"></emph.end><lb></lb>

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


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

quód anguli <emph type="italics"></emph>aib. acb<emph.end type="italics"></emph.end> in ſemicirculo ſunt recti. </s>
            <s id="N11E84">Tan<lb></lb>

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

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

quia ergo anguli <emph type="italics"></emph>khi. kge<emph.end type="italics"></emph.end> ſunt anguli inclinationum, e<lb></lb>


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

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

rum verò <emph type="italics"></emph>bai. bac<emph.end type="italics"></emph.end> ad peripheriam dupli: dico velocita<lb></lb>

tem motus in <emph type="italics"></emph>i<emph.end type="italics"></emph.end> ad velocitatem motus in <emph type="italics"></emph>c<emph.end type="italics"></emph.end> eſſe ut ſinum <lb></lb>

anguli <emph type="italics"></emph>bki<emph.end type="italics"></emph.end> ſinum anguli <emph type="italics"></emph>bkc<emph.end type="italics"></emph.end> Quia enim motus in <lb></lb>

quolibet puncto circuli per lineam fit tangentem per


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

tangentium <emph type="italics"></emph>ih. cg<emph.end type="italics"></emph.end>: eſt autem velocitas in <emph type="italics"></emph>ih<emph.end type="italics"></emph.end> ad veloci<lb></lb>

tatem in <emph type="italics"></emph>cg<emph.end type="italics"></emph.end> ut ſinus <emph type="italics"></emph>bl<emph.end type="italics"></emph.end> anguli <emph type="italics"></emph>bki<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>bm<emph.end type="italics"></emph.end> anguli <lb></lb>

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

tem in arcu <emph type="italics"></emph>cb<emph.end type="italics"></emph.end> ut ſinus anguli <emph type="italics"></emph>bki<emph.end type="italics"></emph.end> ad ſinum anguli <emph type="italics"></emph>bkc,<emph.end type="italics"></emph.end><lb></lb>

ſinus nimirum anguli dupli illorum angulorum, qui <lb></lb>

complementa ſunt inclinationis cordarum <emph type="italics"></emph>bi.bc,<emph.end type="italics"></emph.end> quod <lb></lb>

erat oſtendendum. </s>
          </p>
        </subchap1>
        <subchap1 id="N11F4A">
          <p id="N11F4B" type="main">
            <s id="N11F4D"><emph type="center"></emph>Propoſitio XXIII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N11F54" type="main">
            <s id="N11F56"><emph type="italics"></emph>Perpendiculum per arcus æquales ejuſdem circuli inæquali <lb></lb>

tempore mouetur: majori quidem propè ſtationem, minori verò per <lb></lb>

arcus, qui magis abſunt à ſtatione.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N11F61" type="main">
            <s id="N11F63">SInt duo arcus <emph type="italics"></emph>bd.dſ<emph.end type="italics"></emph.end> inter ſe æquales: <expan abbr="atq́">atque</expan> <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> propior, <lb></lb>

<emph type="italics"></emph>df<emph.end type="italics"></emph.end> verò remotior à ſtatione <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> dico motum in <emph type="italics"></emph>df<emph.end type="italics"></emph.end> eſſe <lb></lb>

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

juſdem circuli rationem habent, quam ſinus, per prop. <lb></lb>

22. eſt autem ſinus <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> major ſinu <emph type="italics"></emph>bt,<emph.end type="italics"></emph.end> erit velocior motus <lb></lb>

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

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

cu <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> ſtationi propiore per prop. 6. </s>
            <s id="N11FC0">Dices velocitas mo<lb></lb>

tus ex <emph type="italics"></emph>f<emph.end type="italics"></emph.end> in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> augetur inæqualiter, <expan abbr="fiuntq́">fiuntque</expan>; ad ſingula pun<lb></lb>

cta minora incrementa; mutatà ergo velocitate non ea-


<pb xlink:href="062/01/061.jpg"></pb>dem erit ratio motus. </s>
            <s id="N11FDB">Reſpondeo velocitatem ex <emph type="italics"></emph>f<emph.end type="italics"></emph.end> in <emph type="italics"></emph>d<emph.end type="italics"></emph.end><lb></lb> inæqualiter quidem augeri, &amp; continuó minora fieri in<lb></lb>

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


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

lectam eſſe majorem velocitate ex <emph type="italics"></emph>d<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> collectà. </s>
            <s id="N1200E">Quia <lb></lb>

enim velocitatis ex <emph type="italics"></emph>d<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> continuò <expan abbr="quoq́">quoque</expan>; minora fiunt <lb></lb>

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

tate ab æqualibus ipſi <emph type="italics"></emph>d<emph.end type="italics"></emph.end> incrementis collectá: at verò <lb></lb>

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

ut æqualia ſint velocitati in <emph type="italics"></emph>d:<emph.end type="italics"></emph.end> velocitas ergo ex <emph type="italics"></emph>f<emph.end type="italics"></emph.end> in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> col<lb></lb>

lecta eſt multó major velocitate ex <emph type="italics"></emph>d<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> collecta, ac pro <lb></lb>

inde minori tempore illos arcus perambulat æquales. </s>
          </p>
          <pb xlink:href="062/01/062.jpg"></pb>
          <p id="N12068" type="main">
            <s id="N1206A"><emph type="center"></emph><emph type="italics"></emph>Lemma I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N12075" type="main">
            <s id="N12077"><emph type="italics"></emph>Si aſſumantur arcus in ratione continuà, quam habent ſinus <lb></lb>

intercipientes illos arcus, major erit proportio inter arcus poſterio<lb></lb>

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

ne ad arcum <emph type="italics"></emph>df<emph.end type="italics"></emph.end> ſinu <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> interceptum, in quà ſi<lb></lb>nus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>cd:<emph.end type="italics"></emph.end> &amp; rurſum arcus <emph type="italics"></emph>df<emph.end type="italics"></emph.end> àd arcum <emph type="italics"></emph>fh,<emph.end type="italics"></emph.end> ut <lb></lb>

ſinus <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>ef<emph.end type="italics"></emph.end>; dico proportionem tam inter ſi<lb></lb>

nus, quam inter arcus illis ſinubus interceptos conti<lb></lb>

nuò fieri majores, nimirum proportionem ſinus <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> ad <lb></lb>

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

ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>cd,<emph.end type="italics"></emph.end> aut arcus <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>df.<emph.end type="italics"></emph.end> Aſſumatur enim ar<lb></lb>

cus <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> grad: 9. <expan abbr="eritq́">eritque</expan>; <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> 100000. ſinus totus, <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> autem <lb></lb>

<emph type="italics"></emph>98769.<emph.end type="italics"></emph.end> ſinus grad. <emph type="italics"></emph>81.<emph.end type="italics"></emph.end> quòd ſi ergo fiat ut <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ſinus totus ad <lb></lb>

9, ita ſinus grad. <emph type="italics"></emph>81.<emph.end type="italics"></emph.end> ad aliud, prodibit arcus 8 in datâ ra<lb></lb>

tione, quam habet ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>cd,<emph.end type="italics"></emph.end> ſi minutias omittamus. <lb></lb>

Simili modo ſi fiat ut ſinus <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> grad: <emph type="italics"></emph>81<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>df<emph.end type="italics"></emph.end> grad. <lb></lb>

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

<expan abbr="atq́">atque</expan>; ita conſequenter inuenientur arcus reliqui, quos di<lb></lb>

co majorem rationem habere ad arcus proximè ſequen<lb></lb>

tes, quam ad hos habeant arcus proximè antecedentes. <lb></lb>

Eſt enim major proportio grad. 8 ad 7, quam grad. 9 ad <lb></lb>

8: &amp; grad. 4 ad 3, quam grad. 5 ad 4. <expan abbr="atq́">atque</expan>, eadem eſt ratio


<pb xlink:href="062/01/063.jpg"></pb>in arcubus reliquis. </s>
            <s id="N12187">Si ergo aſſumantur arcus in ratio<lb></lb>

ne continuâ, quam habent ſinus intercipientes illos ar<lb></lb>


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

cus, major eſt proportio inter arcus poſteriores, quam <lb></lb>

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

res verò quam in ratione ſubtriplá ad ſinum totum, habebunt ſinus <lb></lb>

proximi intercipientes illos arcus minorem rationem quam duplam.<emph.end type="italics"></emph.end></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"></emph>h<emph.end type="italics"></emph.end> in <lb></lb>

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

maior ſinu toto: propterea quòd quadrans majo<lb></lb>

rem ad hunc, quam ad arcum grad. 60 habeat <expan abbr="rationẽ">rationem</expan>. <lb></lb>

Quòd ſi ergo arcus <emph type="italics"></emph>bh<emph.end type="italics"></emph.end> ſubdiuidatur in alios tres arcus


<pb xlink:href="062/01/064.jpg"></pb><emph type="italics"></emph>bd. df.fh<emph.end type="italics"></emph.end> inter ſe æquales, minor erit proportio ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end><lb></lb>

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

rem, quam ſit <emph type="italics"></emph>bd,<emph.end type="italics"></emph.end> rationem triplam, qui ſit <emph type="italics"></emph>bq,<emph.end type="italics"></emph.end> <expan abbr="atq́">atque</expan>; hunc <lb></lb>

intercipiens ſinus <emph type="italics"></emph>pq<emph.end type="italics"></emph.end> maior ſinu <emph type="italics"></emph>cd:<emph.end type="italics"></emph.end> dico ſinus proximos <lb></lb>

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

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

Erit enim ſinus <emph type="italics"></emph>cd.<emph.end type="italics"></emph.end> grad: 70, &amp; ſinus <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> grad: 50. &amp; ſinus <emph type="italics"></emph>gh<emph.end type="italics"></emph.end><lb></lb>

gtad: 30. at verò ſinus totus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> 100000. ad ſinum <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> grad. <lb></lb>

70, nimirum ad 93969, &amp; ſinus <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> grad: 50 ad ſinum <emph type="italics"></emph>gh<emph.end type="italics"></emph.end><lb></lb>

grad. 30 ideſt. 76604. ad 50000 minorem habet <expan abbr="rationẽ">rationem</expan> <lb></lb>

quam duplam. </s>
            <s id="N12279">Quod idem de aliis ſinubus proximè in<lb></lb>

tercipientibus illos arcus æquales, ex tabulis ſinuum <lb></lb>

conſtabit. </s>
            <s id="N12280">Quia verò ſinus propiores minorem ha<lb></lb>

bent rationem, erit minor proportio <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>pq<emph.end type="italics"></emph.end> quam ad <lb></lb>

<emph type="italics"></emph>cd.<emph.end type="italics"></emph.end> ac proinde minor quam dupla. </s>
            <s id="N12299">Si ergo quadrans cir<lb></lb>

culi diuidatur in quotlibet arcus æquales, minores verò <lb></lb>

quam in ratione ſubtriplá ad ſinum totum, habebunt ſi<lb></lb>

nus proximi intercipientes illos arcus minorem ratio<lb></lb>

nem quam duplam. </s>
          </p>
          <p id="N122A4" type="main">
            <s id="N122A6"><emph type="center"></emph><emph type="italics"></emph>Lemma III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N122B1" type="main">
            <s id="N122B3"><emph type="italics"></emph>Si aſſumantur arcus in ratione continuá, quam habent ſinus <lb></lb>

intercipientes illos arcus, <expan abbr="habeatq́">habeatque</expan>; ſinus primus ad arcum interce<lb></lb>

ptum majorem rationem quam triplam, habebunt ſinus proximi ra<lb></lb>

tionem ad ſe minorem quam duplam.<emph.end type="italics"></emph.end></s>
          </p>
          <pb xlink:href="062/01/065.jpg"></pb>
          <p id="N122C7" type="main">
            <s id="N122C9">VT ſi arcus <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>df<emph.end type="italics"></emph.end> ſit ut ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>cd:<emph.end type="italics"></emph.end><lb></lb>

&amp; rurſum ut ſinus <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>ef,<emph.end type="italics"></emph.end> ita arcus <emph type="italics"></emph>df<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>fh,<emph.end type="italics"></emph.end> habeat <lb></lb>

verò ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> majorem rationem quam tri<lb></lb>

plam, dico ſinus intercipientes illos arcus rationem ad <lb></lb>

ſe habere minorem quam duplam. </s>
            <s id="N1230F">Quia enim ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end><lb></lb>


<figure id="id.062.01.065.1.jpg" xlink:href="062/01/065/1.jpg"></figure><lb></lb>&gt;

eſt major ſinu <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> erit <expan abbr="quoq́">quoque</expan>; arcus <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> major arcu <emph type="italics"></emph>df<emph.end type="italics"></emph.end>: fiat <lb></lb>

ergo arcus <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> æqualis arcui <emph type="italics"></emph>ds,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; ſinus <emph type="italics"></emph>rs<emph.end type="italics"></emph.end> minor ſinu <lb></lb>

<emph type="italics"></emph>cd<emph.end type="italics"></emph.end>: eſt autem per Lemma 2. minor proportio ejuſdem <lb></lb>

ſinus <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>rs<emph.end type="italics"></emph.end> quam dupla; multò ergo minor ad <lb></lb>

ſinum majorem <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> quam dupla. </s>
            <s id="N1236C">Quod idem de aliis ſi<lb></lb>

nubus oſtendemus. </s>
            <s id="N12371">Si ergo aſſumantur arcus in ratio<lb></lb>

ne continuà &amp;c. </s>
          </p>
          <p id="N12376" type="main">
            <s id="N12378"><emph type="center"></emph><emph type="italics"></emph>Lemma IV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N12383" type="main">
            <s id="N12385"><emph type="italics"></emph>Si aſſumantur arcus in ratione continuà, quam habent ſinus in<emph.end type="italics"></emph.end>


<pb xlink:href="062/01/066.jpg"></pb><emph type="italics"></emph>tercipientes illos arcus, <expan abbr="habeatq́">habeatque</expan>; ſinus primus ad arcum interce<lb></lb>

ptum majorem rationem quam triplam, erit ſinus ſecundus major <lb></lb>

illo arcu intercepto.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N1239D" type="main">
            <s id="N1239F">QVia enim ut ſinus ita arcus intercepti; habent <expan abbr="autẽ">autem</expan> <lb></lb>

ſinus proximi rationem ad ſe minorem quam du<lb></lb>

plam, per Lemma 3; habebunt <expan abbr="quoq́">quoque</expan>; arcus minorem <lb></lb>

rationem quam duplam. </s>
            <s id="N123B0">Et quia ut ſinus ad ſinum, ita <lb></lb>

arcus ad arcum, erit permutando ut ſinus primus ad ar<lb></lb>

cum primum, ita ſinus ſecundus ad arcum ſecundum: <lb></lb>

habet autem ſinus primus ad arcum primum majorem <lb></lb>

rationem quam triplam, habebit <expan abbr="quoq́">quoque</expan>; ſinus ſecundus <lb></lb>

ad arcum ſecundum majorem rationem quam triplam. <lb></lb>

Quia ergo ad eundem arcum ſecundum majorem rati<lb></lb>

onem habet ſinus ſecundus, quam arcus primus, erit ſi<lb></lb>

nus ſecundus major quam arcus primus, hoc eſt quam <lb></lb>

arcus interceptus. </s>
          </p>
        </subchap1>
        <subchap1 id="N123C9">
          <p id="N123CA" type="main">
            <s id="N123CC"><emph type="center"></emph>Propoſitio XXIV.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N123D3" type="main">
            <s id="N123D5"><emph type="italics"></emph>Perpendiculum ex quolibet puncto ejuſdem circuli æquali tem<lb></lb>

pore recurrit in ſuam ſtationem.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N123DE" type="main">
            <s id="N123E0">IN circulo <emph type="italics"></emph>tuxb<emph.end type="italics"></emph.end> ſint duo perpendicula <emph type="italics"></emph>ab. ad<emph.end type="italics"></emph.end> extra ſu<lb></lb>

am ſtationem <emph type="italics"></emph>at,<emph.end type="italics"></emph.end> <expan abbr="habeatq́">habeatque</expan>; ſinus totus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad interual<lb></lb>

lum <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> majorem rationem quam triplá, dico <expan abbr="utrumq́">utrumque</expan>;


<pb xlink:href="062/01/067.jpg"></pb><expan abbr="codẽ">codem</expan> tempore recurrere in <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> Erit enim velocitas in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ad <lb></lb>

velocitatem in <emph type="italics"></emph>d,<emph.end type="italics"></emph.end> ut ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> per prop: 22. <lb></lb>

quòd ſi ergo in illo recurſu eadem ratio velocitatis con<lb></lb>

ſtaret, aut ſimilibus augeretur incrementis, quia major <lb></lb>

proportio arcus <emph type="italics"></emph>bt<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>dt,<emph.end type="italics"></emph.end> quam ſinus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad ſinum <lb></lb>

<emph type="italics"></emph>cd,<emph.end type="italics"></emph.end> quo quidem tempore perpendiculum <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> recurrit <lb></lb>

in <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> eodem perpendiculum <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> procurreret extra <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> tanto <lb></lb>

interuallo, quantus eſt exceſſus hujus proportioni<emph type="italics"></emph>s.<emph.end type="italics"></emph.end> At <lb></lb>

verò quia ad ſingula puncta mutatà ſinuum ratione, <lb></lb>

mutatur <expan abbr="quoq́">quoque</expan>; ratio velocitatis: major enim proportio <lb></lb>

<emph type="italics"></emph>cd<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>ef,<emph.end type="italics"></emph.end> quam <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> per lem: 1. erit <expan abbr="quoq́">quoque</expan>; major pro<lb></lb>

portio arcus <emph type="italics"></emph>df<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>fh,<emph.end type="italics"></emph.end> quam arcus <emph type="italics"></emph>bd<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>df.<emph.end type="italics"></emph.end> quia ergo <lb></lb>

cum hoc ſinuum &amp; arcuum decremento continuó au<lb></lb>

getur illorum proportio, minuitur verò diſtantia ter<lb></lb>

minorum motus, neceſſe demum abſumi &amp; deficere, <expan abbr="il-loq́">il<lb></lb>

loque</expan>; deficiente <expan abbr="motũ">motum</expan> coæquari: quod non niſi in pun<lb></lb>

cto <emph type="italics"></emph>t<emph.end type="italics"></emph.end> dico poſſe fieri. </s>
            <s id="N124CE">Concurrat enim, ſi fieri poteſt, <lb></lb>

<expan abbr="utrumq́">utrumque</expan>; perpendiculum in <emph type="italics"></emph>q<emph.end type="italics"></emph.end> minori, quam <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> interuallo: <lb></lb>

&amp; quia non ante <emph type="italics"></emph>q<emph.end type="italics"></emph.end> fit concurſus, ſi perpendiculum <emph type="italics"></emph>ab<emph.end type="italics"></emph.end><lb></lb>

ſtatuatur in <emph type="italics"></emph>m<emph.end type="italics"></emph.end>; erit perpendiculum <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> inter <emph type="italics"></emph>m<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>q<emph.end type="italics"></emph.end>: ſit er<lb></lb>

go in <emph type="italics"></emph>o.<emph.end type="italics"></emph.end> quia verò ut <emph type="italics"></emph>lm<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>no,<emph.end type="italics"></emph.end> ita velocitas motus in <emph type="italics"></emph>m<emph.end type="italics"></emph.end><lb></lb>

ad velocitatem motus in <emph type="italics"></emph>o<emph.end type="italics"></emph.end>: aut arcus <emph type="italics"></emph>mo<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>oq<emph.end type="italics"></emph.end><lb></lb> eandem habet rationem, quam ſinus <emph type="italics"></emph>lm<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>no,<emph.end type="italics"></emph.end><lb></lb>

aut non eandem, ſed vel maiorem vel minorem: habe<lb></lb>

at primúm eandem rationem. </s>
            <s id="N12547">Dum ergo perpendicu


<pb xlink:href="062/01/068.jpg"></pb>lum <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> mouetur ex <emph type="italics"></emph>o<emph.end type="italics"></emph.end> in <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> perpendiculum <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>m<emph.end type="italics"></emph.end> in <emph type="italics"></emph>o<emph.end type="italics"></emph.end><lb></lb> promouebitur: non igitur concurſus fit in <emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end> Simili mo <lb></lb>

do ſi <emph type="italics"></emph>mo<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>oq<emph.end type="italics"></emph.end> majorem habeat rationem, perpendicu<lb></lb>


<figure id="id.062.01.068.1.jpg" xlink:href="062/01/068/1.jpg"></figure><lb></lb>

lum <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>o<emph.end type="italics"></emph.end> majori quam <emph type="italics"></emph>oq<emph.end type="italics"></emph.end> interuallo abducetur. </s>
            <s id="N125A4">Si <lb></lb>

demum minorem habeat rationem, auferatur pars pro<lb></lb>

portionalis, <expan abbr="atq́">atque</expan>; rurſum alia, <expan abbr="quouſq́">quouſque</expan>; in <emph type="italics"></emph>q<emph.end type="italics"></emph.end> ſit æqualis aut <lb></lb>

minor: &amp; tum rurſum oſtendemus perpendiculum <emph type="italics"></emph>ad<emph.end type="italics"></emph.end><lb></lb>

præcurrere: non igitur concurſus in minori quam <emph type="italics"></emph>t<emph.end type="italics"></emph.end> in<lb></lb>

teruallo eſſe poteſt. </s>
            <s id="N125CA">Quód ſi autem <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> dicatur præcur<lb></lb>

rere in <emph type="italics"></emph>t,<emph.end type="italics"></emph.end> erit <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> in aliquo puncto minús remoto, verbi <lb></lb>

gratia<emph type="italics"></emph>s<emph.end type="italics"></emph.end>: igitur cùm <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ferebatur in <emph type="italics"></emph>q, ad<emph.end type="italics"></emph.end> necdum atti<lb></lb>

git <emph type="italics"></emph>t<emph.end type="italics"></emph.end>: erit ergo in aliquo puncto inter <emph type="italics"></emph>t<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> quod ſit <emph type="italics"></emph>s.<emph.end type="italics"></emph.end> Et <lb></lb>

quia ut ſinus <emph type="italics"></emph>pq<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>rs,<emph.end type="italics"></emph.end> ita motus in <emph type="italics"></emph>q<emph.end type="italics"></emph.end> ad motum in <lb></lb>

<emph type="italics"></emph>s<emph.end type="italics"></emph.end>: eſt autem ſinus <emph type="italics"></emph>pq<emph.end type="italics"></emph.end> major quam <emph type="italics"></emph>rs,<emph.end type="italics"></emph.end> erit arcus proporti


<pb xlink:href="062/01/069.jpg"></pb>onalis minor qua <emph type="italics"></emph>qs:<emph.end type="italics"></emph.end> quia verò ſinus <emph type="italics"></emph>rs<emph.end type="italics"></emph.end> eſt maior arcu <emph type="italics"></emph>sq<emph.end type="italics"></emph.end><lb></lb> per Lemma 4. minor autem arcu <emph type="italics"></emph>ts,<emph.end type="italics"></emph.end> erit arcus <emph type="italics"></emph>ts<emph.end type="italics"></emph.end> multò <lb></lb>

major arcu proportionali: poſito ergo perpendiculo <emph type="italics"></emph>ab<emph.end type="italics"></emph.end><lb></lb>

in <emph type="italics"></emph>s,<emph.end type="italics"></emph.end> perpendiculum <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> necdum eſſe poteſt in <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> Quod <lb></lb>

idem de quouis alio puncto oſtendemus. </s>
            <s id="N12677">Quia ergo <lb></lb>

perpendiculum <expan abbr="neq́">neque</expan>; propiùs concurrere, <expan abbr="neq́">neque</expan>; præcur<lb></lb>

rere poteſt, concurret neceſſariò in <emph type="italics"></emph>t.<emph.end type="italics"></emph.end> Poterit eadem ra<lb></lb>

tio in hunc modum fieri: motus ſe habent ut ſinus <expan abbr="atq́">atque</expan>; <lb></lb>

horum interualla, ſeu arcus ſinubus intercepti: hæc au<lb></lb>

tem interualla continuò fiunt minora, in puncto verò <lb></lb>

<emph type="italics"></emph>t<emph.end type="italics"></emph.end> nulla: igitur &amp; motus continuó minori, in puncto ve<lb></lb>

rò <emph type="italics"></emph>t<emph.end type="italics"></emph.end> nullo <expan abbr="abſiſtũt">abſiſtunt</expan> interuallo, Quòd ſi aſſumantur plura <lb></lb>

puncta <emph type="italics"></emph>b.d. f.h.k.m.<emph.end type="italics"></emph.end> &amp;c. eadem vià oſtendemus ex omni<lb></lb>

bus ſimul recurrere in <emph type="italics"></emph>t<emph.end type="italics"></emph.end>: ſicuti enim ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>d,<emph.end type="italics"></emph.end> ita ex <emph type="italics"></emph>d<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>f,<emph.end type="italics"></emph.end><lb></lb>

&amp; ex <emph type="italics"></emph>f<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>b, et<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>h<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>k<emph.end type="italics"></emph.end> &amp;c. æqualis fit recurſus. </s>
            <s id="N126EB">Perpen<lb></lb>

diculum ergo ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>d<emph.end type="italics"></emph.end> æqualiter recurrens recurret <lb></lb>

<expan abbr="quoq́">quoque</expan>; æqualiter ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>f<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>h<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>k<emph.end type="italics"></emph.end> &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N1271A">
          <p id="N1271B" type="main">
            <s id="N1271D"><emph type="center"></emph>Propoſitio XXV.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12724" type="main">
            <s id="N12726"><emph type="italics"></emph>Excurſus perpendiculi in eodem circulo à lineà ſtationis ſunt in<lb></lb>

ter ſe æqualis.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N1272F" type="main">
            <s id="N12731">QVia (in fig: 8.) velocitas in <emph type="italics"></emph>eb<emph.end type="italics"></emph.end> velocitati in <emph type="italics"></emph>fb,<emph.end type="italics"></emph.end> &amp; <lb></lb>

velocitas in <emph type="italics"></emph>cb<emph.end type="italics"></emph.end> eſt æqualis velocitati in <emph type="italics"></emph>db<emph.end type="italics"></emph.end> per prop. <lb></lb>

20. eſt <expan abbr="autẽ">autem</expan> velocitas in <emph type="italics"></emph>eb<emph.end type="italics"></emph.end> ad <expan abbr="velocitatẽ">velocitatem</expan> in <emph type="italics"></emph>cb,<emph.end type="italics"></emph.end> ut arcus <emph type="italics"></emph>e<emph.end type="italics"></emph.end>


<pb xlink:href="062/01/070.jpg"></pb><emph type="italics"></emph>b<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>cb:<emph.end type="italics"></emph.end> propterea quòd perpendiculum ex <emph type="italics"></emph>c<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>e<emph.end type="italics"></emph.end><lb></lb> æquali tempore recurrit in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> per prop: 24. erit ut arcus <lb></lb>

<emph type="italics"></emph>fb<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>db,<emph.end type="italics"></emph.end> ita velocitas excurſus in <emph type="italics"></emph>fb<emph.end type="italics"></emph.end> ad velocita<lb></lb>

tem excurſus in <emph type="italics"></emph>db.<emph.end type="italics"></emph.end> At verò ut idem arcus <emph type="italics"></emph>fb<emph.end type="italics"></emph.end> ad arcum <lb></lb>

<emph type="italics"></emph>db,<emph.end type="italics"></emph.end> ita violentia inclinationum in illis arcubus collecta: <lb></lb>

tollit autem violentia partem impulſus ſibi æqualem <lb></lb>

per poſit: 2. igitur ut arcus <emph type="italics"></emph>fb<emph.end type="italics"></emph.end> ad arcum <emph type="italics"></emph>db,<emph.end type="italics"></emph.end> ita ablatum <lb></lb>

ad ablatum, hoc eſt velocitatis decrementum, &amp; velo<lb></lb>

citas reliqua ad reliquam velocitatem habet autem ve<lb></lb>

locitas motus eandem rationem, quam interualla. </s>
            <s id="N127CC">Quia <lb></lb>

ergo excurſus eandem rationem habent tum ad ſe, tum <lb></lb>

ad interualla, quam habent recurſus ad ſe, &amp; ſua inter<lb></lb>

ualla; fiunt autem recurſus eodem vel æquali tempo<lb></lb>

re, erunt <expan abbr="quoq́">quoque</expan>; excurſus eodem vel æquali tempore, ac <lb></lb>

proinde inter ſe æquales. </s>
          </p>
        </subchap1>
        <subchap1 id="N127DD">
          <p id="N127DE" type="main">
            <s id="N127E0"><emph type="center"></emph>Propoſitio XXVI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N127E7" type="main">
            <s id="N127E9"><emph type="italics"></emph>Motus per arcus ſimiles inæqualium circulorum rationem ha<lb></lb>

bent quam ſinus illorum arcuum.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N127F2" type="main">
            <s id="N127F4">ASſumantur duo arcus, in circulo quidem maiori <emph type="italics"></emph>bd. <lb></lb>

bf,<emph.end type="italics"></emph.end> in circulo autem minori <emph type="italics"></emph>ce.cg<emph.end type="italics"></emph.end> inter ſe ſimiles: di<lb></lb>

co motum perpendiculi ex <emph type="italics"></emph>f<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ad motum ex <emph type="italics"></emph>g<emph.end type="italics"></emph.end> in <emph type="italics"></emph>c,<emph.end type="italics"></emph.end> &amp; <lb></lb>

motum ex <emph type="italics"></emph>d<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ad motum ex <emph type="italics"></emph>e<emph.end type="italics"></emph.end> in <emph type="italics"></emph>c<emph.end type="italics"></emph.end> eandem rationem <lb></lb>

habere quam ſinus illorum arcuum. </s>
            <s id="N1283B">angant enim


<pb xlink:href="062/01/071.jpg"></pb><expan abbr="utrumq́">utrumque</expan>; circulum in punctis <emph type="italics"></emph>f.d.g.e<emph.end type="italics"></emph.end> lineæ <emph type="italics"></emph>fk. di,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>gb eh<emph.end type="italics"></emph.end>: <lb></lb>

<expan abbr="eritq́">eritque</expan>; angulus <emph type="italics"></emph>akf<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>abg,<emph.end type="italics"></emph.end> &amp; angulus <emph type="italics"></emph>aid<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>ab <lb></lb>

e<emph.end type="italics"></emph.end> æqualis: propterea quód anguli <emph type="italics"></emph>afk. agb,<emph.end type="italics"></emph.end> &amp; anguli <emph type="italics"></emph>ad <lb></lb>

i. aeh<emph.end type="italics"></emph.end> ſint recti, anguli verò <emph type="italics"></emph>kaf.iad<emph.end type="italics"></emph.end> communes: velo<lb></lb>

citas ergo in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> velocitati in <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> &amp; velocitas in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> velocitati <lb></lb>


<figure id="id.062.01.071.1.jpg" xlink:href="062/01/071/1.jpg"></figure><lb></lb>

in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> eſt æqualis: igitur ut <emph type="italics"></emph>f<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>d,<emph.end type="italics"></emph.end> ita <emph type="italics"></emph>g<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>e<emph.end type="italics"></emph.end>: ſed ut <emph type="italics"></emph>f<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>d,<emph.end type="italics"></emph.end> ita <lb></lb>

ſinus arcu<emph type="italics"></emph>s fb<emph.end type="italics"></emph.end> ad ſinum arcus <emph type="italics"></emph>db<emph.end type="italics"></emph.end>; &amp; ut <emph type="italics"></emph>g<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>e<emph.end type="italics"></emph.end> ita ſinus ar<lb></lb>

cus <emph type="italics"></emph>gc<emph.end type="italics"></emph.end> ad ſinum arcus <emph type="italics"></emph>ec<emph.end type="italics"></emph.end> per prop. 22. erit ergo permu<lb></lb>

tando motus in <emph type="italics"></emph>f<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> ut ſinus arcus <emph type="italics"></emph>fb<emph.end type="italics"></emph.end> ad ſi<lb></lb>

num arcus <emph type="italics"></emph>ge<emph.end type="italics"></emph.end>; &amp; motus in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>e,<emph.end type="italics"></emph.end> ut ſinus ar-


<pb xlink:href="062/01/072.jpg"></pb>cus <emph type="italics"></emph>db<emph.end type="italics"></emph.end> ad ſinum arcus <emph type="italics"></emph>ec.<emph.end type="italics"></emph.end> Motus ergo per arcus ſimiles <lb></lb>

inæqualium circulorum rationem habent quam ſinus <lb></lb>

illorum arcuum, </s>
          </p>
        </subchap1>
        <subchap1 id="N12936">
          <p id="N12937" type="main">
            <s id="N12939"><emph type="center"></emph>Propoſitio XXVII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12940" type="main">
            <s id="N12942"><emph type="italics"></emph>Motus in circulo minori eſt velocior motu in circulo majori.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12949" type="main">
            <s id="N1294B">IN circulo maiori <emph type="italics"></emph>dfb<emph.end type="italics"></emph.end> perpendiculum ex <emph type="italics"></emph>f<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> in cir<lb></lb>

culo verò minori <emph type="italics"></emph>mgc<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>g<emph.end type="italics"></emph.end> in <emph type="italics"></emph>c<emph.end type="italics"></emph.end> moueatur: dico velo<lb></lb>

ciùs ex <emph type="italics"></emph>g<emph.end type="italics"></emph.end> in <emph type="italics"></emph>c,<emph.end type="italics"></emph.end> quam ex <emph type="italics"></emph>f<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> recurrere. </s>
            <s id="N1298E">Quia enim mo<lb></lb>

tus in <emph type="italics"></emph>fb<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>gc,<emph.end type="italics"></emph.end> ut ſinus <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> ad <expan abbr="ſinũ">ſinum</expan> <emph type="italics"></emph>cu<emph.end type="italics"></emph.end> per prop: <lb></lb>

25. &amp; ut <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>cu,<emph.end type="italics"></emph.end> ita <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>ac,<emph.end type="italics"></emph.end> propterea quód lineæ <emph type="italics"></emph>bg cu<emph.end type="italics"></emph.end><lb></lb>

ſint parallelæ, &amp; triangula <emph type="italics"></emph>bag. eau<emph.end type="italics"></emph.end> ſimilia: eſt autem <lb></lb>

maior linea <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> quam <emph type="italics"></emph>ac,<emph.end type="italics"></emph.end> erit <expan abbr="quoq́">quoque</expan>; <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> maior quam <emph type="italics"></emph>cu<emph.end type="italics"></emph.end><lb></lb> maior ergo motus ab eadem velocitate in <emph type="italics"></emph>bg,<emph.end type="italics"></emph.end> hoc eſt in <lb></lb>

<emph type="italics"></emph>fb<emph.end type="italics"></emph.end> maiori, quam in <emph type="italics"></emph>cu,<emph.end type="italics"></emph.end> hoc eſt in <emph type="italics"></emph>ge,<emph.end type="italics"></emph.end> minori interuallo <lb></lb>

per prop: 5. ac proinde in circulo minori eſt velocior <lb></lb>

motus, hoc eſt minori fit tempore, quam in circulo ma<lb></lb>

jori. </s>
          </p>
        </subchap1>
        <subchap1 id="N12A15">
          <p id="N12A16" type="main">
            <s id="N12A18"><emph type="center"></emph>Propoſitio XXVIII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12A1F" type="main">
            <s id="N12A21"><emph type="italics"></emph>Motus circulorum ſunt in ratione ſuorum temporum, quam ha<lb></lb>

bent diametri ad ſe duplicatam.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12A2A" type="main">
            <s id="N12A2C">QVia enim ut ſinus <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>cu,<emph.end type="italics"></emph.end> ita motus in <emph type="italics"></emph>fb<emph.end type="italics"></emph.end><lb></lb>

ad motum in <emph type="italics"></emph>gc<emph.end type="italics"></emph.end> per prop. 25. eſt autem ut <emph type="italics"></emph>bg<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>cu<emph.end type="italics"></emph.end>


<pb xlink:href="062/01/073.jpg"></pb>ita motus in <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> propterea quòd motus <lb></lb>

<emph type="italics"></emph>ab<emph.end type="italics"></emph.end> motui <emph type="italics"></emph>bg,<emph.end type="italics"></emph.end> &amp; motus <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> motui <emph type="italics"></emph>cu<emph.end type="italics"></emph.end> eſt æqualis per prop: <lb></lb>

13. erit motus in <emph type="italics"></emph>fb<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>gc,<emph.end type="italics"></emph.end> ut motus in <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <lb></lb>

motum in <emph type="italics"></emph>ac.<emph.end type="italics"></emph.end> At verò motus in <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>ac,<emph.end type="italics"></emph.end> &amp; <lb></lb>


<figure id="id.062.01.073.1.jpg" xlink:href="062/01/073/1.jpg"></figure><lb></lb>

huius duplum <emph type="italics"></emph>lb<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>mc<emph.end type="italics"></emph.end> rationem habent quam tempo<lb></lb>

rum quadrata per prop: 12. radices ergo quadratæ line<lb></lb>

arum <emph type="italics"></emph>bl. cm<emph.end type="italics"></emph.end> eandem rationem habent quam tempora <lb></lb>

motus circulorum, ac proinde illorum temporum rati<lb></lb>

onem habent diametri ad ſe duplicatam. </s>
          </p>
        </subchap1>
        <subchap1 id="N12AC9">
          <pb xlink:href="062/01/074.jpg"></pb>
          <p id="N12ACD" type="main">
            <s id="N12ACF"><emph type="center"></emph>Propoſitio XXIX.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12AD6" type="main">
            <s id="N12AD8"><emph type="italics"></emph>Fieri poteſt ut arcum circuli majoris minori tempore tranſeat, <lb></lb>

quam arcum circuli minoris.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12AE1" type="main">
            <s id="N12AE3">ASſumatur in fig: 10. ſinus <emph type="italics"></emph>ou<emph.end type="italics"></emph.end> ad ſinum <emph type="italics"></emph>qm<emph.end type="italics"></emph.end> in eà rati<lb></lb>

one, in quà diameter major <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad minorem <emph type="italics"></emph>om,<emph.end type="italics"></emph.end> <expan abbr="e-titq́">e<lb></lb>

ritque</expan>; velocitas in <emph type="italics"></emph>o<emph.end type="italics"></emph.end> ad velocitatem in <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> ut <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>om,<emph.end type="italics"></emph.end> hoc <lb></lb>

eſt ut motus <emph type="italics"></emph>qb<emph.end type="italics"></emph.end> in circulo maiori ad motum <emph type="italics"></emph>tm<emph.end type="italics"></emph.end> in cir<lb></lb>

culo minori. </s>
            <s id="N12B2E">Quód ſi ergo ſumantur duo arcus <emph type="italics"></emph>op. qr<emph.end type="italics"></emph.end><lb></lb> inter ſe æquales, maior erit proportio motus in <emph type="italics"></emph>qr<emph.end type="italics"></emph.end> ad <lb></lb>

motum in <emph type="italics"></emph>op,<emph.end type="italics"></emph.end> quam ad motu in <emph type="italics"></emph>tm<emph.end type="italics"></emph.end>: velocior ergo mo<lb></lb>

tus in arcu <emph type="italics"></emph>op<emph.end type="italics"></emph.end> circuli maioris, quam in arcu <emph type="italics"></emph>tm<emph.end type="italics"></emph.end> circuli <lb></lb>

minoris. </s>
          </p>
        </subchap1>
        <subchap1 id="N12B5C">
          <p id="N12B5D" type="main">
            <s id="N12B5F"><emph type="center"></emph>Propoſitio XXX.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12B66" type="main">
            <s id="N12B68"><emph type="italics"></emph>Ab impulſu contrario &amp; æquali nullus eſt motus: ab impulſu <lb></lb>

verò contrario &amp; inæquali motus eſt æqualis exceſſui majoris.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12B71" type="main">
            <s id="N12B73">QVia enim contrarium æquale tollit vel impedit ſu<lb></lb>

um contrarium in eadem ratione, totum quidem <lb></lb>

totum, pars verò partem ſibi æqualem per poſi: 2. </s>
            <s id="N12B7A">Su<lb></lb>

blato per contrarium æquale toto impulſu nullus erit <lb></lb>

motus, qui eſſe non poteſt <expan abbr="abſq;">abſque</expan> impulſu.</s>
            <s id="N12B85">Quód ſi ve<lb></lb>

rò impulſus ſint inæquales, quia minor à majori tollit <lb></lb>

partem ſibi æqualem, erit reliquus exceſſus principium


<pb xlink:href="062/01/075.jpg"></pb>motus. </s>
            <s id="N12B90">Ab impulſu ergò contrario &amp; æquali nullus eſt <lb></lb>

motus &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N12B95">
          <p id="N12B96" type="main">
            <s id="N12B98"><emph type="center"></emph>Propoſitio XXXI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12B9F" type="main">
            <s id="N12BA1"><emph type="italics"></emph>Motus ſecundùm quid contrarij per lineam fiunt mediam, cujus <lb></lb>

interuallam determinat ſinus complementi inclinationis, in ratione <lb></lb>

quam habent impulſus.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12BAC" type="main">
            <s id="N12BAE">VI in fig: 2 ſi mobile ex eodem puncto <emph type="italics"></emph>a<emph.end type="italics"></emph.end> moueatur <lb></lb>

per lineas <emph type="italics"></emph>ab. af,<emph.end type="italics"></emph.end> aut per lineas <emph type="italics"></emph>ab. ad,<emph.end type="italics"></emph.end> &amp; ſit angulus <lb></lb>

<emph type="italics"></emph>baf<emph.end type="italics"></emph.end> major, angulus verò <emph type="italics"></emph>bad<emph.end type="italics"></emph.end> minor recto, erunt hi mo<lb></lb>

tus per definit: 5. ſecundùm quid contrarij, ac proinde <lb></lb>

in eo in quo ſunt contrarij, <expan abbr="tollũt">tollunt</expan> aut <expan abbr="impediũt">impediunt</expan> <expan abbr="ſuũ">ſuum</expan> con<lb></lb>

<expan abbr="trariũ">trarium</expan>, per definit: 1. impulſus ergo in <emph type="italics"></emph>af<emph.end type="italics"></emph.end> ab impulſu in <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end><lb></lb>

&amp; hic ab impulſu in <emph type="italics"></emph>af<emph.end type="italics"></emph.end> retractus, quia <expan abbr="idẽ">idem</expan> mobile eſſe <expan abbr="nõ">non</expan> <lb></lb>

poteſt in pluribus locis, ac proinde <expan abbr="neq́">neque</expan>; pluribus moti<lb></lb>

bus agitari, mouebitur motu inter <expan abbr="utrumq́">utrumque</expan>; medio, cu<lb></lb>

juſmodi linea motus <emph type="italics"></emph>ad<emph.end type="italics"></emph.end>: dico huius lineæ interuallum à, <lb></lb>

lineis extremis <emph type="italics"></emph>ab. af<emph.end type="italics"></emph.end> eſſe ſinum complementi angulo<lb></lb>

rum <emph type="italics"></emph>faddab,<emph.end type="italics"></emph.end> in ratione quam habet impulſus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad im<lb></lb>

pulſum <emph type="italics"></emph>af.<emph.end type="italics"></emph.end> Quia enim velocitas motus per lineas incli<lb></lb>

natas eſt in ratione ſinus complementi illarum inclina<lb></lb>

tionum, per prop: 14. ratio autem velocitatis eſt eadem <lb></lb>

quæ impulſus, propterea quòd impulſus eſt agens ne<lb></lb>

ceſſarium, <expan abbr="motumq́">motumque</expan>; producit ſibi æqualem per prop: 2.

<pb xlink:href="062/01/076.jpg"></pb>erit ſinus complementi anguli <emph type="italics"></emph>fad<emph.end type="italics"></emph.end> ad ſinum comple<lb></lb>

menti anguli <emph type="italics"></emph>dab,<emph.end type="italics"></emph.end> ut impulſus in <emph type="italics"></emph>af<emph.end type="italics"></emph.end> ad impulſum in <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end><lb></lb>

Motus ergò ſecundùm quid contrarij per lineam fiunt <lb></lb>

mediam, cujus interuallum determinat ſinu<emph type="italics"></emph>s<emph.end type="italics"></emph.end> &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N12C69">
          <p id="N12C6A" type="main">
            <s id="N12C6C"><emph type="center"></emph>Propoſitio XXXII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12C73" type="main">
            <s id="N12C75"><emph type="italics"></emph>Motus perfectè mixtus fit per diametrum parallelogrammi, cu<lb></lb>

jus latera conſtituit motus ſimplex: &amp; ex impulſu quidem æquali <lb></lb>

eſt æqualis ſemisſi, ex inæquali verò major ſemiſſe ejuſdem motus.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12C80" type="main">
            <s id="N12C82">MOtum perfectè mixtum conſtituunt motus, qui æ<lb></lb>

qualiter ſunt ſimiles &amp; contrarij: tantùm enim hic <lb></lb>


<figure id="id.062.01.076.1.jpg" xlink:href="062/01/076/1.jpg"></figure><lb></lb>

illum auget, quantùm &amp; minuit. </s>
            <s id="N12C90">Moueatur idem mobi<lb></lb>

le ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>c,<emph.end type="italics"></emph.end> &amp; ſit angulus <emph type="italics"></emph>bac<emph.end type="italics"></emph.end> rectus, <expan abbr="eritq́">eritque</expan>; per defini<lb></lb>

tionem motus medius incipiens ab angulo recto per<lb></lb>

fectè mixtus: Dico hunc motum fieri per diametrum <lb></lb>

<emph type="italics"></emph>ad<emph.end type="italics"></emph.end> parallelogrammi <emph type="italics"></emph>abdc,<emph.end type="italics"></emph.end> cuius latera <emph type="italics"></emph>ab. ac<emph.end type="italics"></emph.end> ſunt mo<lb></lb>

tus, qui inter le <expan abbr="miſcẽtur">miſcentur</expan>: &amp; <expan abbr="ſiquidẽ">ſiquidem</expan> motus in <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ſit æqua <lb></lb>

lis motui in <emph type="italics"></emph>ac,<emph.end type="italics"></emph.end> <expan abbr="motũ">motum</expan> <expan abbr="mixtũ">mixtum</expan> in <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> eſſe <expan abbr="æqualẽ">æqualem</expan> ſemiſsi utri


<pb xlink:href="062/01/077.jpg"></pb><expan abbr="uſq́">uſque</expan>; motus ſimul ſumpti: ſi <expan abbr="autẽ">autem</expan> motus fuerit inæqualis, <lb></lb>

<expan abbr="maiorẽ">maiorem</expan> ſemiſſe. </s>
            <s id="N12D04">Sit primò motus in <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> æqualis motui in <lb></lb>

<emph type="italics"></emph>ac<emph.end type="italics"></emph.end>: &amp; ex <emph type="italics"></emph>bc<emph.end type="italics"></emph.end> termino <expan abbr="utriuſq́">utriuſque</expan>; motus demittantur lineæ <lb></lb>

perpendiculares <emph type="italics"></emph>be. ce,<emph.end type="italics"></emph.end> ſinus æqualium angulorum <emph type="italics"></emph>cde, <lb></lb>

edb.<emph.end type="italics"></emph.end> Quia ergo ut <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>ac,<emph.end type="italics"></emph.end> ita ſinus complementi <emph type="italics"></emph>eb<emph.end type="italics"></emph.end> ad <lb></lb>

<emph type="italics"></emph>ec,<emph.end type="italics"></emph.end> erit diameter <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> linea motus mixti. </s>
            <s id="N12D4F">Eſt autem mo<lb></lb>

tus in <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> duratione quidem æqualis motui in <emph type="italics"></emph>ae<emph.end type="italics"></emph.end><lb></lb>

per prop: 13. magnitudine verò minor, cujus exceſſus <lb></lb>

quadratum <emph type="italics"></emph>eb.<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ec,<emph.end type="italics"></emph.end> ſeu <emph type="italics"></emph>ae<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ed<emph.end type="italics"></emph.end>: at verò duo quadrata <emph type="italics"></emph>ae. <lb></lb>

ed<emph.end type="italics"></emph.end> ſunt ſemiſsis quadrati <emph type="italics"></emph>ad,<emph.end type="italics"></emph.end> hoc eſt motus in <emph type="italics"></emph>ab.ac,<emph.end type="italics"></emph.end> cui, <lb></lb>

æquale eſt quadratum <emph type="italics"></emph>ad,<emph.end type="italics"></emph.end> propterea quòd <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> ſit dupla <lb></lb>

<emph type="italics"></emph>ae<emph.end type="italics"></emph.end> aut <emph type="italics"></emph>ed<emph.end type="italics"></emph.end>: igitur motus æqualiter mixtus fit per diame<lb></lb>

trum parallelogrammi, &amp; ab æquali impulſu eſt æqua<lb></lb>

lis ſemiſsi <expan abbr="utriuſq́">utriuſque</expan>; motus ſimul ſumpti. </s>
            <s id="N12DB9">Quód ſi mo<lb></lb>

tus ſit inæqualis, &amp; <emph type="italics"></emph>u.g.<emph.end type="italics"></emph.end> dupló velocior in <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> quam in <emph type="italics"></emph>eg,<emph.end type="italics"></emph.end><lb></lb>

dico motum mixtum fieri quidem per diametrum <emph type="italics"></emph>eb,<emph.end type="italics"></emph.end><lb></lb>

eſſe autem ſemiſſe maiorem. </s>
            <s id="N12DD8">Deſcripto enim centro <emph type="italics"></emph>b<emph.end type="italics"></emph.end><lb></lb> arcu <emph type="italics"></emph>mn,<emph.end type="italics"></emph.end> erit ſinus complementi <emph type="italics"></emph>ik<emph.end type="italics"></emph.end> ad ſinum comple<lb></lb>

menti <emph type="italics"></emph>ip,<emph.end type="italics"></emph.end> ut motus in <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>eg,<emph.end type="italics"></emph.end> ac proinde di<lb></lb>

ameter <emph type="italics"></emph>eh<emph.end type="italics"></emph.end> linea motus mixti: ad quam ex punctis <emph type="italics"></emph>fg<emph.end type="italics"></emph.end> du<lb></lb>

ctæ lineæ perpendiculares <emph type="italics"></emph>fl. go<emph.end type="italics"></emph.end> metientur defectum <lb></lb>

motus in <emph type="italics"></emph>eh.<emph.end type="italics"></emph.end> Quia ergo ex angulo recto <emph type="italics"></emph>efh<emph.end type="italics"></emph.end> linea <emph type="italics"></emph>fl<emph.end type="italics"></emph.end> eſt <lb></lb>

perpendicularis ad baſim <emph type="italics"></emph>eh,<emph.end type="italics"></emph.end> erit ut <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>fh,<emph.end type="italics"></emph.end> ita <emph type="italics"></emph>el<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>lf,<emph.end type="italics"></emph.end> &amp; <lb></lb>

<emph type="italics"></emph>lf<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>lh:<emph.end type="italics"></emph.end> ponitur autem quadratum <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> duplum quadrat <lb></lb>

<emph type="italics"></emph>fh,<emph.end type="italics"></emph.end> ſiue <emph type="italics"></emph>eg,<emph.end type="italics"></emph.end> erit ergo quadratum <emph type="italics"></emph>fl<emph.end type="italics"></emph.end> ſimiliter <expan abbr="duplũ">duplum</expan> quadra


<pb xlink:href="062/01/078.jpg"></pb>ti <emph type="italics"></emph>lh.<emph.end type="italics"></emph.end> quadratum ergo <emph type="italics"></emph>fh<emph.end type="italics"></emph.end> <expan abbr="utriq;">utrique</expan> æquale continebit tria <lb></lb>

quadrata, quorum ſingula ſint æqualia quadrato <emph type="italics"></emph>lh.<emph.end type="italics"></emph.end> &amp; <lb></lb>

quia quadratum <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> eſt duplum quadrati <emph type="italics"></emph>fh,<emph.end type="italics"></emph.end> erit quadra<lb></lb>

tum <emph type="italics"></emph>eh<emph.end type="italics"></emph.end> æquale nouem quadratis <emph type="italics"></emph>lh<emph.end type="italics"></emph.end> ſimul ſumptis. </s>
            <s id="N12EB0">At <lb></lb>

verò quadratum <emph type="italics"></emph>el<emph.end type="italics"></emph.end> duplum quadrati <emph type="italics"></emph>lf<emph.end type="italics"></emph.end> erit quadruplum <lb></lb>

quadrati <emph type="italics"></emph>lh,<emph.end type="italics"></emph.end> <expan abbr="aſſumptoq́">aſſumptoque</expan>; quadrato <emph type="italics"></emph>eo,<emph.end type="italics"></emph.end> aut huic æquali <emph type="italics"></emph>lh<emph.end type="italics"></emph.end><lb></lb> erunt duo quadrata <emph type="italics"></emph>el. lh<emph.end type="italics"></emph.end> ſimul ſumpta æqualia <expan abbr="quinq́">quinque</expan>; <lb></lb>

quadratis <emph type="italics"></emph>lh<emph.end type="italics"></emph.end>: Maiora ergo quam ſemiſsis quadrati <emph type="italics"></emph>eh,<emph.end type="italics"></emph.end><lb></lb>

quòd æquale ponitur nouem quadratis <emph type="italics"></emph>lh.<emph.end type="italics"></emph.end> Igitur mo<lb></lb>

tus perfectè mixtus fit per diametrum parallelogram<lb></lb>

mi, cujus latera conſtituit motus ſimplex &amp;c. </s>
          </p>
        </subchap1>
        <subchap1 id="N12EFD">
          <p id="N12EFE" type="main">
            <s id="N12F00"><emph type="center"></emph>Propoſitio XXXIII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12F07" type="main">
            <s id="N12F09"><emph type="italics"></emph>Motus mixtus incipiens ab angulo majori quam recto, eſt minor <lb></lb>

ſemiſſe: incipiens verò ab angulo minori quam recto, major ſemiſſe <lb></lb>

motus ſimul ſumpti.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12F14" type="main">
            <s id="N12F16">Sit primùm in fig: 7. angulus <emph type="italics"></emph>dae<emph.end type="italics"></emph.end> maior recto, &amp; an<lb></lb>

gulus <emph type="italics"></emph>bac<emph.end type="italics"></emph.end> rectus, <expan abbr="eritq́">eritque</expan>; quadratum <emph type="italics"></emph>bb<emph.end type="italics"></emph.end> æquale qua<lb></lb>

drato <emph type="italics"></emph>ab<emph.end type="italics"></emph.end>: eſt autem quadratum <emph type="italics"></emph>db,<emph.end type="italics"></emph.end> ex ceſſus nimirum <lb></lb>

motus <emph type="italics"></emph>ad,<emph.end type="italics"></emph.end> quadrato <emph type="italics"></emph>bh,<emph.end type="italics"></emph.end> ac proinde quadrato <emph type="italics"></emph>ah<emph.end type="italics"></emph.end> maius: <lb></lb>

igitur quadratum <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> æquale duobus quadratis <emph type="italics"></emph>dh. ah<emph.end type="italics"></emph.end> ad <lb></lb>

quadratum minus <emph type="italics"></emph>ah<emph.end type="italics"></emph.end> maiorem rationem habet quam <lb></lb>

duplam: motus ergo in <emph type="italics"></emph>ah<emph.end type="italics"></emph.end> mixtus eſt minor ſemiſſe


<pb xlink:href="062/01/079.jpg"></pb>motus in <emph type="italics"></emph>ad,<emph.end type="italics"></emph.end> <expan abbr="atq́">atque</expan>; illius duplum minus quam motus in <emph type="italics"></emph>a <lb></lb>

d. ae<emph.end type="italics"></emph.end> ſimul ſumpti. </s>
            <s id="N12F87">Quòd ſi angulus <emph type="italics"></emph>fag<emph.end type="italics"></emph.end> ſit minor recto, <lb></lb>

erit latus <emph type="italics"></emph>fh,<emph.end type="italics"></emph.end> &amp; huius quadratum minus quam <emph type="italics"></emph>ah:<emph.end type="italics"></emph.end> mo<lb></lb>

tus ergo in <emph type="italics"></emph>af<emph.end type="italics"></emph.end> ad motum in <emph type="italics"></emph>ah<emph.end type="italics"></emph.end> minorem rationem ha<lb></lb>

bet quam duplam, ac proinde motus in <emph type="italics"></emph>ah<emph.end type="italics"></emph.end> major ſemiſ<lb></lb>

ſe motus in <emph type="italics"></emph>af,<emph.end type="italics"></emph.end> &amp; illius duplum majus quá motus in <emph type="italics"></emph>af. <lb></lb>

ag<emph.end type="italics"></emph.end> ſimul ſumpti. </s>
          </p>
        </subchap1>
        <subchap1 id="N12FC4">
          <p id="N12FC5" type="main">
            <s id="N12FC7"><emph type="center"></emph>Propoſitio XXXIV.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N12FCE" type="main">
            <s id="N12FD0"><emph type="italics"></emph>Motus mixtus eſt neceſſarió minor diametro quadrati aut <lb></lb>parallelogrammi, cujus latera ſunt motus ſimplex.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N12FD9" type="main">
            <s id="N12FDB">NAm motus quidem in <emph type="italics"></emph>be<emph.end type="italics"></emph.end> mixtus (in fig: 4.) eſt du<lb></lb>

plum quadrati eiuſdem <emph type="italics"></emph>be<emph.end type="italics"></emph.end>: quadratum verò <emph type="italics"></emph>db<emph.end type="italics"></emph.end> ad <lb></lb>

quadratum <emph type="italics"></emph>be<emph.end type="italics"></emph.end> eſt quadruplum. </s>
            <s id="N12FFA">Cauſa verò hujus de<lb></lb>

ſectus eſt contrarietas illorum motuum, ex angulis pro<lb></lb>

ueniens, cum quibus augetur &amp; minuitur, <expan abbr="quouſq;">quouſque</expan> an<lb></lb>

gulus lateſcens æqualis fiat duobus rectis, in quo ſum<lb></lb>

ma eſt contrarietas, ac proinde nullus eſſe poteſt motus. <lb></lb>

Angulo verò decreſcente augetur ſimilitudo motus, <lb></lb>

<expan abbr="quouſq;">quouſque</expan> angulo deficiente ſint una linea motus, in quà <lb></lb>

perfecta ſimilitudo, nulla autem eſt contrarietas. <expan abbr="Itaq;">Itaque</expan> <lb></lb>

motus æqualis motum auget in eadem ratione, totus <lb></lb>

quidem totum, pars verò partem ſibi æqualem per <lb></lb>

poſit. 1. </s>
          </p>
        </subchap1>
        <subchap1 id="N1301D">
          <pb xlink:href="062/01/080.jpg"></pb>
          <p id="N13021" type="main">
            <s id="N13023"><emph type="center"></emph>Propoſitio XXXV.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N1302A" type="main">
            <s id="N1302C"><emph type="center"></emph><emph type="italics"></emph>Problema I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N13037" type="main">
            <s id="N13039"><emph type="italics"></emph>Lineam motus mixti, &amp; illius magnitudinem determinare.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13040" type="main">
            <s id="N13042">SIt primùm motus <emph type="italics"></emph>pq. pr<emph.end type="italics"></emph.end> perfectè mixtus, incipiens ab <lb></lb>

angulo recto <emph type="italics"></emph>qpr<emph.end type="italics"></emph.end>: &amp; ex <emph type="italics"></emph>q<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>r<emph.end type="italics"></emph.end> ducantur lineæ <emph type="italics"></emph>qs. rs<emph.end type="italics"></emph.end> pa<lb></lb>

rallelæ ad <emph type="italics"></emph>pq. pr,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; per prop. 31. motus mixtus in di<lb></lb>

ametro <emph type="italics"></emph>ps<emph.end type="italics"></emph.end>: ad quam ex termino <expan abbr="utriuſq;">utriuſque</expan> motus <emph type="italics"></emph>q<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>r<emph.end type="italics"></emph.end><lb></lb>


<figure id="id.062.01.080.1.jpg" xlink:href="062/01/080/1.jpg"></figure><lb></lb> demittantur lineæ perpendiculares <emph type="italics"></emph>qt.ru,<emph.end type="italics"></emph.end> <expan abbr="eritq;">eritque</expan> motus <lb></lb>

mixtus ex <emph type="italics"></emph>pqpr<emph.end type="italics"></emph.end> æqualis duobus quadratis <emph type="italics"></emph>pu.pt.<emph.end type="italics"></emph.end> abſcin


<pb xlink:href="062/01/081.jpg"></pb>datur ergo ex linea <emph type="italics"></emph>tq<emph.end type="italics"></emph.end> productà linea <emph type="italics"></emph>tx<emph.end type="italics"></emph.end> æqualis lineæ <emph type="italics"></emph>p <lb></lb>

u,<emph.end type="italics"></emph.end> &amp; ex puncto <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> interuallo autem <emph type="italics"></emph>px<emph.end type="italics"></emph.end> deſcribatur arcus <lb></lb>

<emph type="italics"></emph>xy,<emph.end type="italics"></emph.end> <expan abbr="connectanturq́">connectanturque</expan>; linea <emph type="italics"></emph>px<emph.end type="italics"></emph.end>: dico quadratum <emph type="italics"></emph>py<emph.end type="italics"></emph.end> eſſe <lb></lb>

motum mixtum &amp; duratione æqualem motui <emph type="italics"></emph>pq. pr<emph.end type="italics"></emph.end> ſi<lb></lb>

mul ſumptis. </s>
            <s id="N130EF">Quia enim quadratum <emph type="italics"></emph>py<emph.end type="italics"></emph.end> quadrato <emph type="italics"></emph>px,<emph.end type="italics"></emph.end><lb></lb>

hoc autem duobus quadratis <emph type="italics"></emph>pt.tx,<emph.end type="italics"></emph.end> ſeu <emph type="italics"></emph>pu<emph.end type="italics"></emph.end> eſt æquale: eſt <lb></lb>

autem motus <emph type="italics"></emph>pt<emph.end type="italics"></emph.end> motui <emph type="italics"></emph>pq,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>pu<emph.end type="italics"></emph.end> motui <emph type="italics"></emph>pr<emph.end type="italics"></emph.end> æqualis dura<lb></lb>

tione per prop: 13. erit motus mixtus in <emph type="italics"></emph>py<emph.end type="italics"></emph.end> ſimiliter æ<lb></lb>

qualis motibus <emph type="italics"></emph>pq<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>pr<emph.end type="italics"></emph.end> ſimul ſumptis. </s>
            <s id="N1313B">Quòd ſi verò <lb></lb>

motus imperfectè mixtus &amp; inæqualis <emph type="italics"></emph>ab. ac<emph.end type="italics"></emph.end> ab angulo <lb></lb>

incipiat maiori aut minori quam recto <emph type="italics"></emph>bac<emph.end type="italics"></emph.end>: aſſuman<lb></lb>

tur duo puncta <emph type="italics"></emph>fg<emph.end type="italics"></emph.end> æqualiter remota ab <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> à quibus pro<lb></lb>

tractæ lineæ perpendiculares <emph type="italics"></emph>fh. gh<emph.end type="italics"></emph.end> ſe interſecent in <emph type="italics"></emph>h,<emph.end type="italics"></emph.end> <expan abbr="e-ritq́">e<lb></lb>

ritque</expan>; angulus <emph type="italics"></emph>fhg<emph.end type="italics"></emph.end> complementum anguli <emph type="italics"></emph>bac,<emph.end type="italics"></emph.end> &amp; ſimul <lb></lb>

ſumpti æquales duobus rectis. </s>
            <s id="N1317E">Deſcribatur ergo ex <emph type="italics"></emph>h<emph.end type="italics"></emph.end><lb></lb> arcus <emph type="italics"></emph>fig,<emph.end type="italics"></emph.end> <expan abbr="ſeceturq́">ſeceturque</expan>; bifariam in <emph type="italics"></emph>i<emph.end type="italics"></emph.end> eà ratione, ut ſinus <emph type="italics"></emph>ik<emph.end type="italics"></emph.end> ad <lb></lb>

ſinum <emph type="italics"></emph>il<emph.end type="italics"></emph.end> ſit, ut motus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad motum <emph type="italics"></emph>ac:<emph.end type="italics"></emph.end> dico lineam ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end><lb></lb>

productam in <emph type="italics"></emph>i<emph.end type="italics"></emph.end> eſſe lineam motus mixti. </s>
            <s id="N131BF">Producatur e<lb></lb>

nim <emph type="italics"></emph>fh<emph.end type="italics"></emph.end> in <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> <expan abbr="eritq́">eritque</expan>; angulus <emph type="italics"></emph>fpa<emph.end type="italics"></emph.end> complementum anguli <emph type="italics"></emph>f <lb></lb>

ap,<emph.end type="italics"></emph.end> &amp; angulus <emph type="italics"></emph>aog<emph.end type="italics"></emph.end> complementum anguli <emph type="italics"></emph>oag<emph.end type="italics"></emph.end>: duo er<lb></lb>

go anguli <emph type="italics"></emph>hpo. aog<emph.end type="italics"></emph.end> hoc eſt <emph type="italics"></emph>hop,<emph.end type="italics"></emph.end> ſimul ſumpti ſunt æqua&lt;l<lb></lb>

les duobus angulis <emph type="italics"></emph>fhi: thg<emph.end type="italics"></emph.end> ſimul ſumptis, propterea <lb></lb>

quód ſint complementa ejuſdem anguli <emph type="italics"></emph>fag,<emph.end type="italics"></emph.end> eſt autem <lb></lb>

angulus <emph type="italics"></emph>hop<emph.end type="italics"></emph.end> externus major angulo <emph type="italics"></emph>iho<emph.end type="italics"></emph.end> interno quanti<lb></lb>

tate anguli <emph type="italics"></emph>bio,<emph.end type="italics"></emph.end> angulus verò <emph type="italics"></emph>iph<emph.end type="italics"></emph.end> internus minor angu


<pb xlink:href="062/01/082.jpg"></pb>lo <emph type="italics"></emph>ihf<emph.end type="italics"></emph.end> externo, quantitate ejuſdem anguli <emph type="italics"></emph>hip:<emph.end type="italics"></emph.end> angulus <lb></lb>

ergo <emph type="italics"></emph>hop<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>fhi,<emph.end type="italics"></emph.end> &amp; angulus <emph type="italics"></emph>oph<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>tho<emph.end type="italics"></emph.end> ſeu <emph type="italics"></emph>ihg<emph.end type="italics"></emph.end><lb></lb>

eſt æqualis, ac proinde <emph type="italics"></emph>ik. il<emph.end type="italics"></emph.end> ſunt ſinus complementi an<lb></lb>

gulorum <emph type="italics"></emph>iag.e ai.<emph.end type="italics"></emph.end> Et quia motus ſunt in ratione, quam <lb></lb>

habent ſinus complementi inclinationum, erit linea <emph type="italics"></emph>ai<emph.end type="italics"></emph.end><lb></lb> linea motus mixti ex <emph type="italics"></emph>ab.ac<emph.end type="italics"></emph.end>; ad quam ex termino <expan abbr="utriuſq́">utriuſque</expan>; <lb></lb>

motus <emph type="italics"></emph>b.c<emph.end type="italics"></emph.end> demittantur lineæ perpendiculares <emph type="italics"></emph>bd.ce:<emph.end type="italics"></emph.end><lb></lb>

<expan abbr="erũtq́">eruntque</expan>, duo quadrata <emph type="italics"></emph>ad.ae<emph.end type="italics"></emph.end> ſimul ſumpta motus mix<lb></lb>

tus: abſcindatur ergo ex <emph type="italics"></emph>db<emph.end type="italics"></emph.end> producta <emph type="italics"></emph>dm<emph.end type="italics"></emph.end> æqualis <emph type="italics"></emph>ae,<emph.end type="italics"></emph.end> &amp; <lb></lb>

centro <emph type="italics"></emph>a<emph.end type="italics"></emph.end> ducatur arcus <emph type="italics"></emph>mn,<emph.end type="italics"></emph.end> dico quadratum <emph type="italics"></emph>an<emph.end type="italics"></emph.end> eſſe ma<lb></lb>

gnitudinem motus mixti. </s>
            <s id="N132BD">Erit enim quadratum <emph type="italics"></emph>am,<emph.end type="italics"></emph.end><lb></lb>

hoc eſt <emph type="italics"></emph>an,<emph.end type="italics"></emph.end> æquale duobus quadratis <emph type="italics"></emph>ad. dm,<emph.end type="italics"></emph.end> ſeu <emph type="italics"></emph>ae,<emph.end type="italics"></emph.end> cui <lb></lb>

æqualis ſumebatur <emph type="italics"></emph>dm.<emph.end type="italics"></emph.end> Lineam ergo motus mixti &amp; il<lb></lb>

lius magnitudinem determinauimus, quod erat facien<lb></lb>

dum. </s>
          </p>
        </subchap1>
        <subchap1 id="N132E5">
          <p id="N132E6" type="main">
            <s id="N132E8"><emph type="center"></emph>Propoſitio XXXVI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N132EF" type="main">
            <s id="N132F1"><emph type="italics"></emph>Mobile ſeu impulſu, ſeu à grauitate moueatur, ſi planum occur<lb></lb>

rat, reflectit ab eodem plano per lineam rectam.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N132FA" type="main">
            <s id="N132FC">IMpulſus ſit dum corpus unum alteri in currit &amp; alli<lb></lb>

dit, ſiue <expan abbr="utrumq́">utrumque</expan>, ſiue unum ex illis moueatur, <expan abbr="atq́">atque</expan>; eo <lb></lb>

magis mouet &amp; impellit, quò magis ferit &amp; allidit: &amp; <lb></lb>

ſiquidem reſiſtentia minor eſt impulſu, in illam partem <lb></lb>

mouet illud mobile, in quam ſit plaga, eundem motum


<pb xlink:href="062/01/083.jpg"></pb>continuando; velocitate tamen eó minori, quó reſi<lb></lb>

ſtentia eſt majòr. </s>
            <s id="N13315">Quód ſi reſiſtentia ſit major impul<lb></lb>

ſu, eádem velocitate, quà impulit, in partem auerſam re <lb></lb>

pellitur: propterea quód illa plaga æqualem in <expan abbr="utroq́">utroque</expan>; <lb></lb>

mobili impulſum producit. </s>
            <s id="N13322">Eſt autem major plaga ex <lb></lb>

velociori &amp; magis violento incurſu: igitur ab æquali <lb></lb>

plagá æqualis <expan abbr="quoq́">quoque</expan>; recurſus. </s>
            <s id="N1332D">Et quia per motum fit <lb></lb>

plaga, mouetur autem mobile ad motum ſui centri, erit <lb></lb>

<expan abbr="quoq;">quoque</expan> plaga ab eodem centro. </s>
            <s id="N13338">Sed &amp; reſiſtentia fit â cen<lb></lb>

tro ſeu grauitatis, ſeu contrarij impulſus: eadem ergo ra<lb></lb>


<figure id="id.062.01.083.1.jpg" xlink:href="062/01/083/1.jpg"></figure><lb></lb>

tione minor reſiſtentia impulſum recipit, quà major ei<lb></lb>

dem reſiſtit. </s>
            <s id="N13348">Vt ſi mobile ex <emph type="italics"></emph>a<emph.end type="italics"></emph.end> moueatur à grauitate qui <lb></lb>

dem in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> ex impulſu verò in <emph type="italics"></emph>f<emph.end type="italics"></emph.end>aut <emph type="italics"></emph>c:<emph.end type="italics"></emph.end> ſit autem major reſi


<pb xlink:href="062/01/084.jpg"></pb>ſtentià in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>f,<emph.end type="italics"></emph.end> quam ut loco moueantur ex illo impul<lb></lb>

ſu, minor autem in <emph type="italics"></emph>c<emph.end type="italics"></emph.end>: motus quidem ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>f<emph.end type="italics"></emph.end> in <emph type="italics"></emph>a<emph.end type="italics"></emph.end> refle<lb></lb>

ctit, ex <emph type="italics"></emph>c<emph.end type="italics"></emph.end> verò expulſo illo mobili quieſcit, ſi ſit æquale: <lb></lb>

eundem verò motum continuat in <emph type="italics"></emph>d,<emph.end type="italics"></emph.end> ſi minus ſit percuſ<lb></lb>

ſum: quia tamen reſiſtentia impulſum minuit, quó ma<lb></lb>

jor reſiſtentia, eò minor velocitas motus. </s>
          </p>
        </subchap1>
        <subchap1 id="N133A3">
          <p id="N133A4" type="main">
            <s id="N133A6"><emph type="center"></emph>Propoſitio XXXVII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N133AD" type="main">
            <s id="N133AF"><emph type="italics"></emph>Motus in ſe ipſum reflectit, cùm centrum grauitatis &amp; conta<lb></lb>

ctus ſunt in eádem lineá motus.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N133B8" type="main">
            <s id="N133BA">GLobus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> occurrat plano in <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> <expan abbr="ſitq;">ſitque</expan> centrum grauita<lb></lb>

tis aut impulſus <emph type="italics"></emph>e<emph.end type="italics"></emph.end> in lineà motus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> perpendiculari<lb></lb> ad contactum <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> dico hunc motum in ſe ipſum reflecti. <lb></lb>

Quia enim motus &amp; huius plaga ad motum fit ſui cen<lb></lb>

tri, erit motus globi <emph type="italics"></emph>a,<emph.end type="italics"></emph.end> &amp; hujus plaga in lineâ <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> à centro <lb></lb>

<emph type="italics"></emph>e<emph.end type="italics"></emph.end> ductà per contactum: &amp; quia eadem ratione impul<lb></lb>

ſum recipit &amp; impellit, <expan abbr="eſtq;">eſtque</expan> major reſiſtentia in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> quam <lb></lb>

impulſus ex <emph type="italics"></emph>e,<emph.end type="italics"></emph.end> erit motus reflexus in eadem lineà <emph type="italics"></emph>ab.<emph.end type="italics"></emph.end><lb></lb>

Motus ergo in ſe ipſum reflectit, cúm centrum grauita<lb></lb>

tis &amp; contactus ſunt in eadem lineà motus. </s>
            <s id="N13418">Obijcies <lb></lb>

cùm pila percutit planum, eàdem vi percutitur ab illo <lb></lb>

plano: eſt autem à percuſsione æquali impulſus æqua<lb></lb>

lis, quó enim violentiùs incidit, eó magis impetuosé reſi<lb></lb>

rit ab illá plagà: impulſus ergo, quem pila recipit â pla-


<pb xlink:href="062/01/085.jpg"></pb>no, eſt æqualis impulſui, quod idem plano allidit. </s>
            <s id="N13427">Quia <lb></lb>

verò hi impulſus tendunt in partes oppoſitas ejuſdem <lb></lb>

lineæ rectæ, erunt per definit: 4. contrarij abſolutè: tol<lb></lb>

lit autem contrarium æquale ſuum contrarium in eà<lb></lb>

dem ratione, totum quidem totum, pars verò partem <lb></lb>

ſibi æqualem; ſublato ergo per contrarium æquale im<lb></lb>

pulſu nullus erit motus reflexus, cùm linea motus eſt <lb></lb>

perpendicularis ad illud planum. </s>
            <s id="N13438">Quód ſi à percuſsio<lb></lb>

ne in plano, aut globo quieſcente factá morus reflectit, <lb></lb>

quid prohibet ab eodem plano, aut globo, ſi motu op<lb></lb>

poſito ferantur, &amp; violentià æquali ſibi occurant, à per<lb></lb>

cuſsione æquali eundem motum reflecti? Vt in hac ob<lb></lb>


<arrow.to.target n="marg1"></arrow.to.target><lb></lb>

ſcuritate aliquam lucem conſequamur, quæ non niſi ex <lb></lb>

naturà impulſus priús cognitá eluceſcit, de quâ in lib: de <lb></lb>

Arcu Cæleſti latiùs diſſeremus, <expan abbr="notãdum">notandum</expan> hic breuiter 1. <lb></lb>


<arrow.to.target n="marg2"></arrow.to.target><lb></lb>

Impulſum fieri à percuſsione juxta determinationem il<lb></lb>

lius plagæ, <expan abbr="quã">quam</expan> centrum inducit percutientis, &amp; quam <lb></lb>

centrum recipit percuſsi; partes enim mobilis impul<lb></lb>


<arrow.to.target n="marg3"></arrow.to.target><lb></lb>

ſum recipiunt per lineas motui centri parallelas. 2. <expan abbr="Hãc">Hanc</expan> <lb></lb>

plagam, quæ fit à corpore percuſſo, aliter dum quieſcit, <lb></lb>

aliter dum eſt in motu impulſum determinare: quia <lb></lb>

enim plaga ex impulſu, percuſſum verò quieſcens nul<lb></lb>

lum ex ſe habet impulſum, verùm à percutiente; eádem <lb></lb>

plaga, quà percutitur, impulſum determinat in percuti<lb></lb>

ente: ab æquali ergo plagà æqualis impulſus. </s>
            <s id="N13478">Cum au


<pb xlink:href="062/01/086.jpg"></pb>tem percutitur in motu, quia ex ſe impulſum habet, <expan abbr="nõ">non</expan> ex <lb></lb>

illà plagà, quam recipit à percutiente, ſed quam infert <lb></lb>

impulſum determinat; licet ergo illorum corporum, <lb></lb>

quæ violentiá inæquali colliduntur, idem ſit contactus, <lb></lb>

non tamen eadem ab <expan abbr="utroq́">utroque</expan>, verùm â majori major, à <lb></lb>


<arrow.to.target n="marg4"></arrow.to.target><lb></lb>

minori impulſu minor infertur plaga. </s>
            <s id="N13496">3. Corpora per<lb></lb>

cuſſa alia eſſe mollia, quorum partes percuſsioni <expan abbr="cedũt">cedunt</expan>, <lb></lb>

inter ſe verò unitæ <expan abbr="manẽt">manent</expan>; cujuſmodi argilla, cera, lana, <lb></lb>

plumbum, &amp;c. </s>
            <s id="N134A7">Alia dura; &amp; ſiquidem percuſsioni nul<lb></lb>

lo modo cedunt, abſolutè dura; ſi autem percuſsioni ce<lb></lb>

dunt, <expan abbr="neq́">neque</expan>; partes inter ſe unitæ manent, fragilia dicun<lb></lb>

tur; ut vitrum, teſta, tophus, &amp;c. </s>
            <s id="N134B4">Corpora demum abſo<lb></lb>

lutè dura alia ſunt ſonora, quorum atomi vibratione <lb></lb>

quadam mouentur, ut propo: 1. dictum; alia ſurda, quo <lb></lb>


<arrow.to.target n="marg5"></arrow.to.target><lb></lb>

rum atomi nullo aut inſenſibili motu monentur. 4 <lb></lb>

Impulſum naturà ſuà inclinare ad motum perfectum, <lb></lb>

quo mobile ſecundúm ſe totum locum mutat. </s>
            <s id="N134C6">Quòd <lb></lb>

ſi ergo impulſus, quem plaga inducit, proportionem <lb></lb>

habeat ad illud mobile, eodem quo percutiens motu fe<lb></lb>

retur: ſi autem minor ſit impulſus quam ut loco moue<lb></lb>

atur, habeat vorò idem mobile partes fragiles, aut in ſe <lb></lb>

cedentes, percutiens percuſſum perforabit, aut excaua<lb></lb>

bit; it a nimirum ſi major ſit ſoliditas percuſsi, quam ut <lb></lb>

impetus per omnes partes eluctetur, qui non prius iram <lb></lb>

ponit, quam continuatà illarum partium, cuas perrum


<pb xlink:href="062/01/087.jpg"></pb>pit, vel collidit, reſiſtentia vires abſumat. </s>
            <s id="N134DD">Ex hujuſmo<lb></lb>

di ergo corporibus nullo modo reflectit motus, niſi in <lb></lb>

progreſſu, priúſquam exoluatur, occurrant partes magis <lb></lb>

ſolidæ: ita enim pila ubi calcem deraſit àmuro, ex oc<lb></lb>

curſu ſaxi reflectit: quod non ſit ſi viá, quà irrupit á fiſ<lb></lb>

ſurà rurſum coëat, quemadmodum in ligno viridi, cu<lb></lb>

jus vulnus ex partium fiſſarum coalitu mox ſolidatur. <lb></lb>

Corpora autem dura abſoluté quia <expan abbr="neq́">neque</expan>; perforantur, <lb></lb>

<expan abbr="neq́">neque</expan>; partes habent percuſsioni cedentes, æqualem reci<lb></lb>

piunt <expan abbr="atq́">atque</expan>; inferunt plagam, morum verò ex illà plagâ re <lb></lb>

flectunt, <expan abbr="atq́">atque</expan>; eó magis, quó duritie magis præſtant. </s>
            <s id="N13504">In<lb></lb>

de ergò fit quód vala vitrea aut cryſtallina inæqualiter <lb></lb>

colliduntur, pro ut illa corpora, ad quæ offendunt, per<lb></lb>

cuſsioni magis aut minús cedunt: quia nimirum non <lb></lb>ex illà, quam inferunt, ſed ex illâ, quam recipiunt, plaga <lb></lb>

colliduntur. 5. </s>
            <s id="N13511">Impulſum fieri per lineam rectam: &amp; ſi<lb></lb>


<arrow.to.target n="marg6"></arrow.to.target><lb></lb>

cuti grauitas minús mouet, quó magis linea motus ad <lb></lb>

horizontem eſt inclinata, quieſcit verò à motu in lineà <lb></lb>

eidem parallelás ita impulſum ex inclinatione motus <lb></lb>

ſenſim minui, &amp; demum in hypomochlio deficere. <lb></lb>

Quòd ſi ergo mobile occurrat plano, it a ut contactus <lb></lb>

ſit in lineá motus eiuſdem centri, quia centrum hypo<lb></lb>

mochlio occurrit, totus ex illà plagà emoritur impul<lb></lb>

ſus; propterea quòd motui quies non minùs eſt contra<lb></lb>

ria, quam motus: at verò ſi planum ſit inclinatum, in il


<pb xlink:href="062/01/088.jpg"></pb>là tantum parte, quæ hypomochlio occurrit, motus <expan abbr="cõ-quieſcit">con<lb></lb>

quieſcit</expan>, reliquà parte, quæ cum centro extra hypomo<lb></lb>

chlium cadit, nihil impedità: impulſus ergo pilæ, cúm <lb></lb>

motus centri eſt perpendicularis ad planum, ubi percuſ<lb></lb>

ſit in hypomochlio â motu conquieſcit: at vero <expan abbr="planũ">planum</expan> <lb></lb>

ex illà plagà in percutiente nouum determinat impul<lb></lb>

ſum, juxta directionem plagæ, quam infert; à quo <expan abbr="eadẽ">eadem</expan>, <lb></lb>

quà venit, vià retroagitur: &amp; ſiquidem duritie præſtat, <lb></lb>

erit plaga &amp; qui hanc ſequitur impulſus in <expan abbr="utroq́">utroque</expan>; æqua<lb></lb>

lis, ac proinde motus reflexus æqualis motui recto: de<lb></lb>

ficiet autem motus reflexus â motu recto, ſi defectu du<lb></lb>

ritiei minorem recipiat, quam dedit plagam. </s>
            <s id="N13555">Quód ſi <lb></lb>

ergo duo globi violentiá æquali ſibi occurrant, <expan abbr="ſitq́">ſitque</expan>; mo<lb></lb>

tus centri <expan abbr="utriuſq́">utriuſque</expan>; in eádem lineà rectà; quia tum <expan abbr="uterq;">uterque</expan> <lb></lb>

alteri, non minús quam planum, eſt hypomochlij loco, <lb></lb>

ab illâ communi plagà in <expan abbr="utroq́">utroque</expan>, emoritur, nouus verò <lb></lb>

quo retro aguntur, impulſus regeneratur. </s>
            <s id="N13572">Licet verò <lb></lb>

poſit: 2. inficiamur ejuſmodi globos ſibi occurrentes re<lb></lb>

ſilire, id tamen exempli gratia ad naturam contrarij ma<lb></lb>

gis explicandam, &amp; ex ſuppoſitione, ſi nimirum impul<lb></lb>

ſus ei ratione miſceantur, à nobis dictum fuit: at verò hi <lb></lb>

impulſus non miſcentur, verùm uni abolito alius ſuc<lb></lb>

cedit. </s>
            <s id="N13581">Quód ſi verò <expan abbr="uterq́">uterque</expan>; globus in motu percutiat vi<lb></lb>

olentià inæ quali, impulſus quidem minoris, ubi percuſ<lb></lb>

ſit majus, ob hypomochlium à motu conquieſcit, im


<pb xlink:href="062/01/089.jpg"></pb>pulſum verò ſibi ſimilem &amp; æqualem producit, ſeu de<lb></lb>

terminat in majori ex illa, quam infert, plagà, hoc eſt <lb></lb>

partem tollit à majori ſibi æqualem. </s>
            <s id="N13594">At verò majus, ubi <lb></lb>

percuſsit, non videtur conquieſcere â motu, propterea <lb></lb>

quòd minus non habeat rationem hypomochlij ad ma <lb></lb>

jus, impulſum verò in minori producit ſibi æqualem; ut <lb></lb>

ſi minor impulſus ut 3. major ut 7. minor quidem à ma<lb></lb>

jori tollit partem ſibi æqualem ideſt 3. &amp; ſimul ob con<lb></lb>

trariam in hypomochlio quietem exſpirat; majus verò <lb></lb>

quia tota vi percutit minus, impulſum ut 7. producit ex <lb></lb>

illà plagà, motum autem à percuſsione non niſi partes 4. <lb></lb>

reliquæ perficiunt. <expan abbr="Itaq́">Itaque</expan>; fit ut ex illà in æquali plagà, ve <lb></lb>

locitate ferantur inæquali, minori quidem majus ob vi<lb></lb>

res à percuſsione accitas &amp; mutilatas, majori verò mi<lb></lb>

nus ob eaſdem vires de integro acquiſitas. </s>
            <s id="N135B3">Dices inter<lb></lb>

dum fieri ut inæquali violentià ſibi occurrant duo glo<lb></lb>

bi, &amp; tamen <expan abbr="uterq́">uterque</expan>; reſiliat. </s>
            <s id="N135BE">Reſpondeo ſi contactus fi <lb></lb>

at in lineà motus centri, videtur non poſſe fieri ut major <lb></lb>

reſiliat, propterea, quód major violentia non detinetur <lb></lb>

à minori: at veró ſi ex obliquo ſe percutiant, fieri poſſe <lb></lb>

ut etiam ille globus, qui magis percuſsit, reſiliat, aut in <lb></lb>

codem, quo percuſsit, loco conſiſtat. </s>
            <s id="N135CB">Inſtabis hanc ſo<lb></lb>

lutionem non <expan abbr="uſq;">uſque</expan> <expan abbr="quaq;">quaque</expan> experientiæ conſonare: nam <lb></lb>

<expan abbr="quomodocunq;">quomodocunque</expan> duo globi inter ſe commicantur, <expan abbr="atq;">atque</expan> <lb></lb>

adeò in lineà motus centri ſe percutiant violentiâ in


<pb xlink:href="062/01/090.jpg"></pb>æquali, <expan abbr="uterq́">uterque</expan> reſilit ab illà plagà, magis quidem qui mi<lb></lb>

nus, minùs verò qui magis percuſsit: non igitur exceſ<lb></lb>

ſus majoris eſt principium morus reliqui à contactu. <lb></lb>

Vt objectioni &amp; experientiæ ſatis fiat, dicendum à quo<lb></lb>

libet contactu impulſum deficere &amp; exſpirare, nouum <lb></lb>

verò à percuſsione determinari, qui motu eidem plagæ <lb></lb>

æquali retroagit illud mobile. </s>
            <s id="N135F8">Cùm enim impulſus â <lb></lb>

percuſsione fiat, juxta determinationem plagæ, quam <lb></lb>

recipit à percutiente, nihil mirum ſi â determinatione <lb></lb>

nouâ nouum impulſum <expan abbr="cõſequatur">conſequatur</expan>: quomodo in acu <lb></lb>

nauticà fieri videmus, quæ quoties oppoſitum polum <lb></lb>

tangit, directionem, quà eidem polo ſe obuertit, ſorti<lb></lb>

tur nouam. </s>
            <s id="N1360B">Quod minùs difficulter admittes, ſi per<lb></lb>

pendas quá ratione vaſtæ campanæ ingens mugitus, &amp; <lb></lb>

qui hunc ſuá vibratione fouet in gyrum actus impulſus <lb></lb>

ex leuiſsimo tactu repente conticeſcat: quid ergo mi<lb></lb>

rum ex tactu pilæ haud paulo majoris impulſum cohi<lb></lb>

beri? Inſtabis an igitur globus ligneus, ſi ex oppoſito <lb></lb>

quantumuis motu lento moueatur, repercutiet pilam <lb></lb>

ferream <expan abbr="quacunq́">quacunque</expan>; violentiá irruentem? Ad pleniorem <lb></lb>

hujus <expan abbr="atq́">atque</expan>; aliarum obiectionum ſolutionem, notandum <lb></lb>

primò: ut mobile moueatur, non ſufficere quemlibet <lb></lb>

impulſum, ſed proportionatum illi mobili: impulſus e<lb></lb>

nim, quo globus ligneus ad motum concitatur, haud <lb></lb>quaquam loco mouebit pilam ferream ejusdem molis <pb xlink:href="062/01/091.jpg"></pb>aut maiorem: at verò ſi huius impulſu moueatur glo<lb></lb>

bus ligneus, motu agit abitur multò velociore. </s>
            <s id="N13634">Secundò: <lb></lb>


<arrow.to.target n="marg7"></arrow.to.target><lb></lb>

hanc proportionem motus &amp; impulſus non á mole, ſed <lb></lb>

á grauitate illorum corporum determinari: <expan abbr="itaq́">itaque</expan>; glo<lb></lb>

bus ligneus major, &amp; glans plumbea minor, ſi æquipon<lb></lb>

derant, ab impulſu æquali æquali velocitate mouentur <lb></lb>

Simili modo ſi eandem rationem habeant impulſus <lb></lb>

quam habent pondera, erit velocitas motus æqualis&#039; <lb></lb>

Tertió percuſsionem &amp; quæ hanc ſequitur plagam non <lb></lb>


<arrow.to.target n="marg8"></arrow.to.target><lb></lb>

uno inſtanti, ſed in aliquo tempore quantumuis imper<lb></lb>

ceptibili perfici: cùm enim plaga proueniat non ex ſolo <lb></lb>

contactu, ſed ex irruptione violentá, quá veluti pene<lb></lb>

trat percutiens percuſſum, non eſſe poteſt <expan abbr="abſq́">abſque</expan>; motu; <lb></lb>

cùm ergo percutiens tangit, necdum eſt plaga, ſed fit; <lb></lb>

cujus ſignum fragor â percuſsione non niſi in tempore <lb></lb>

proueniens. </s>
            <s id="N13665">Sicuti ergo plaga ſua habet incrementa, ita <lb></lb>

determinatio impulſus: &amp; ſi quod mobile non totam <lb></lb>

plagam recipit, deficiet <expan abbr="quoq́">quoque</expan>; in eadem ratione impul<lb></lb>

ſus. </s>
            <s id="N13672">Quartó: impulſum exſpirare ubi totam perfecit <lb></lb>


<arrow.to.target n="marg9"></arrow.to.target><lb></lb>

plagam, partem verò non niſi cum parte emori: reſidu<lb></lb>

um ergo plagæ ſeu impulſus, ſi nihil eſt quod recipiat il<lb></lb>

lam plagam, erit principium motus á percuſsione con<lb></lb>

tinuati. </s>
            <s id="N13682">His ſuppoſitis, ita rem tranſigemus ſit ergo. </s>
          </p>
          <p id="N13685" type="margin">
            <s id="N13687"><margin.target id="marg1"></margin.target><emph type="italics"></emph>R<gap></gap><emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13691" type="margin">
            <s id="N13693"><margin.target id="marg2"></margin.target><emph type="italics"></emph>No <lb></lb>

1.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N1369E" type="margin">
            <s id="N136A0"><margin.target id="marg3"></margin.target><emph type="italics"></emph>2.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N136A9" type="margin">
            <s id="N136AB"><margin.target id="marg4"></margin.target><emph type="italics"></emph>3<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N136B4" type="margin">
            <s id="N136B6"><margin.target id="marg5"></margin.target><emph type="italics"></emph>4<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N136BF" type="margin">
            <s id="N136C1"><margin.target id="marg6"></margin.target><emph type="italics"></emph>5<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N136CA" type="margin">
            <s id="N136CC"><margin.target id="marg7"></margin.target>2</s>
          </p>
          <p id="N136D1" type="margin">
            <s id="N136D3"><margin.target id="marg8"></margin.target>3</s>
          </p>
          <p id="N136D8" type="margin">
            <s id="N136DA"><margin.target id="marg9"></margin.target>4</s>
          </p>
          <p id="N136DF" type="main">
            <s id="N136E1"><emph type="center"></emph><emph type="italics"></emph>Poriſma I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <pb xlink:href="062/01/092.jpg"></pb>
          <p id="N136EF" type="main">
            <s id="N136F1"><emph type="italics"></emph>Si globus alium globum percutiat quieſcentem &amp; æqualem, illo <lb></lb>

expulſo quieſcit.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N136FA" type="main">
            <s id="N136FC">VT ſi duo globi lignei inter ſe ſint æquales, aut cum a<lb></lb>

lio quouis globo ejuſdem ponderis, <expan abbr="atq́">atque</expan>; hic illum <lb></lb>

percutiat quieſcentem; quia impulſus percutientis ad <lb></lb>

<expan abbr="utrumq́">utrumque</expan>; globum eandem habet rationem ex notabili <lb></lb>

2. æqualis autem impulſus non niſi á plagá ſit perfectâ, e<lb></lb>

rit velocitas in percuſſo non ante illam plagam: non er<lb></lb>

go incipiente plagá præcurret <expan abbr="ſeq́">ſeque</expan>, auellet à <expan abbr="percutiẽte">percutiente</expan>, <lb></lb>

ſed plagà demum perfectà illam velocitatem conſecu<lb></lb>

tus. </s>
            <s id="N1371F">Et quia ex notabili 4. impulſus, ubi plagam perfe<lb></lb>

cit, exſpirat; nullam verò plagam inducit globus qùie<lb></lb>

ſcens, propterea quód <expan abbr="neq́">neque</expan>; irruptio violenta ſeu pene<lb></lb>

tratio fiat ab illo globo, qui eàdem velocitate, quà percu<lb></lb>

titur, ſe abducit; quieſcet globus percutiens ab illa, <lb></lb>

quam fecit, plagà. </s>
          </p>
          <p id="N13730" type="main">
            <s id="N13732"><emph type="center"></emph><emph type="italics"></emph>Poriſma II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N1373D" type="main">
            <s id="N1373F"><emph type="italics"></emph>Si globus major percutiat minorem quieſcentem, minori expulſo <lb></lb>

eundem motum continuat major.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13748" type="main">
            <s id="N1374A">QVia enim minus pondus æquali celeritate mouetur <lb></lb>

a minori impulſu; illam velocitatem motus qua <lb></lb>

præcurrit <expan abbr="ſeq́">ſeque</expan>; auellit à percutiente, à minori plagâ con


<pb xlink:href="062/01/093.jpg"></pb>ſequetur, quam ut totum impulſum producat. </s>
            <s id="N13759">Et quia<lb></lb> impulſus non niſi à plagà emoritur; impulſus reliquus, <lb></lb>

qui nec dum percuſsit, eundem motum continuabit. <lb></lb>

Habeat enim pondus <emph type="italics"></emph>de<emph.end type="italics"></emph.end> ad pondus <emph type="italics"></emph>fg<emph.end type="italics"></emph.end> eandem <expan abbr="rationẽ">rationem</expan>, <lb></lb>

quam habet impulſus maioris <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> ad impulſum minoris <lb></lb>


<figure id="id.062.01.093.1.jpg" xlink:href="062/01/093/1.jpg"></figure><lb></lb>

<emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> <expan abbr="percutiatq́">percutiatque</expan>; <emph type="italics"></emph>de<emph.end type="italics"></emph.end> ipſum <emph type="italics"></emph>fg<emph.end type="italics"></emph.end>: quia ergo plagà non niſi in <lb></lb>

aliquo tempore fit, &amp; ſicuti plaga, ita <expan abbr="quoq́">quoque</expan>; impulſus <lb></lb>

ſua habet incrementa, erit impulſus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> prior impulſu <emph type="italics"></emph>ac.<emph.end type="italics"></emph.end><lb></lb>

eſt autem <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>al,<emph.end type="italics"></emph.end> ut <emph type="italics"></emph>de<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>fg<emph.end type="italics"></emph.end>: &amp; permutando <emph type="italics"></emph>ac<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>de,<emph.end type="italics"></emph.end><lb></lb>

ut <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>fg<emph.end type="italics"></emph.end>; eadem ergò velocitas in <expan abbr="utroq́">utroque</expan>;. </s>
            <s id="N137E3">Et quia eá<lb></lb>

dem velocitate mouentur, nulla à contactu erit plaga. <lb></lb>

Ita ergo pila ferrea dum murum percutit, quia minori <lb></lb>

impulſu, ad motum concitantur partes in muro percuſ<lb></lb>

ſæ, illam velocitatem motus, quâ pila ferrea mouetur, <lb></lb>

ab incipiente &amp; necdum perfectà plagà conſequuntur: <lb></lb>

impulſæ ergo motum pilæ anteuertunt, <expan abbr="ſuoq́">ſuoque</expan>; impetu a<lb></lb>

liis inſtant: &amp; ſicubi major vis obſtat, pila à tergo hæ<lb></lb>

rentes nouo impulſu urget, <expan abbr="quouſq́">quouſque</expan>; illà percuſsione <expan abbr="cõ">con</expan><lb></lb>

tinuatà totum impulſum plaga hauriat &amp; abſumat <lb></lb>

Quód ſi major ſit impulſus, quam ut æqualis ſit illi pla<lb></lb>

gæ, quà murum perforat, motum à rupturâ continuat li<lb></lb>

li exceſſui æqualem. </s>
          </p>
          <pb xlink:href="062/01/094.jpg"></pb>
          <p id="N1380C" type="main">
            <s id="N1380E"><emph type="center"></emph><emph type="italics"></emph>Poriſma III.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N13819" type="main">
            <s id="N1381B"><emph type="italics"></emph>Si globus minor percutiat majorem quieſcentem, habeat verò <lb></lb>

minorem rationem ad ſuum impulſum, quam ad globum majorem, <lb></lb>

expulſo majori minor quieſcit aut reflectit.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13826" type="main">
            <s id="N13828">HAbeat globus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> maior ad minorem <emph type="italics"></emph>b<emph.end type="italics"></emph.end> rationem du<lb></lb>

plam, ideſt grauitas ſeu pondus majoris ſit duplum <lb></lb>

ponderis minoris; impulſus autem minoris ad ejuſdem <lb></lb>

grauitatem in ratione majori quam dupla. </s>
            <s id="N1383D">Quia ergo <lb></lb>

grauitas &amp; impulſus inter ſe ſunt contraria, erit motus <lb></lb>

æqualis exceſſui maioris; eſt autem impulſus minoris <lb></lb>

maior grauitate maioris, propterea quód ad grauitatem <lb></lb>

minoris maiorem habeat rationem; erit ergo huius ex<lb></lb>

ceſſus principium motus maiori. </s>
            <s id="N1384A">Igitur ſi globus mi<lb></lb>

nor percutiat maiorem, quia ab æquali impulſu minor <lb></lb>

eſt velocitas motus, non ante perfectam plagam auelli <lb></lb>

poteſt à percutiente: &amp; quia à plagà perfectâ emoritur <lb></lb>

impulſus, minori autem velocitate maior ſe abducit ab <lb></lb>

illà plagà, quàm irruptio fiat minoris; repercutiet ma<lb></lb>

ior minorem, <expan abbr="eritq́">eritque</expan>; huius plaga ad menſuram illius tar<lb></lb>

ditatis. </s>
            <s id="N1385F">Globus ergo minor, ubi percuſsit maiorem, illo <lb></lb>

expulſo reflectit. </s>
            <s id="N13864">Quòd ſi ob motum velociorem nullà <lb></lb>

à percuſſo inducitur plaga, minor expulſo maiori qui<lb></lb>

eſcit. </s>
          </p>
          <pb xlink:href="062/01/095.jpg"></pb>
          <p id="N1386E" type="main">
            <s id="N13870"><emph type="center"></emph><emph type="italics"></emph>Poriſma IV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N1387B" type="main">
            <s id="N1387D"><emph type="italics"></emph>Si globus minor percutiat majorem quieſcentem, habeat verò <lb></lb>

majorem rationem ad ſuum impulſum, quam ad globum majorem, <lb></lb>

illo immoto reflectit minor.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13888" type="main">
            <s id="N1388A">VT ſi impulſus, quo minor globus mouetur, ad illius <lb></lb>

grauitatem ſit in ratione duplà; globus veró major <lb></lb>

ad minorem rationem habeat maiorem quam duplam, <lb></lb>

erit impulſus minoris minor grauitate maioris; non er<lb></lb>

gò <expan abbr="illã">illam</expan> mouere valebit, propterea quód motus ab exceſ<lb></lb>

ſu fiat maioris. </s>
            <s id="N1389B">Quód ſi ergo minor globus percutiat <lb></lb>

maiorem, quia ex illà plagà minor eſt impulſus, quam ut <lb></lb>

loco moueat; globus quidem maior à percuſsione qui <lb></lb>

eſcit, minor verò quia à percuſſo quieſcente nouam &amp; <lb></lb>

æqualem illi, quam dedit, plagam recipit, motum refle<lb></lb>

ctit. </s>
            <s id="N138A8">Ex iam definitis diſſoluemus &amp; hoc </s>
          </p>
          <p id="N138AB" type="main">
            <s id="N138AD"><emph type="center"></emph><emph type="italics"></emph>Problema I.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N138B8" type="main">
            <s id="N138BA"><emph type="italics"></emph>Globum in plano quieſcentem percutere alio globo <expan abbr="quacunq́">quacunque</expan> vi<lb></lb>

olentià, <expan abbr="neq́">neque</expan>; tamen loco mouere.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N138CB" type="main">
            <s id="N138CD">ASſumatur globus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> <expan abbr="cuiuſcunq;">cuiuſcunque</expan> molis &amp; ponderis, eius <lb></lb>

tamen firmitatis, quò totum impetum ſufferre vale<lb></lb>

at, <expan abbr="neq́">neque</expan>; diſsiliat ex illo ictu: <expan abbr="conſtituaturq́">conſtituaturque</expan>; in plano <emph type="italics"></emph>AB<emph.end type="italics"></emph.end>


<pb xlink:href="062/01/096.jpg"></pb>liberè, &amp; <expan abbr="abſq;">abſque</expan> ullo nexu: <expan abbr="quẽ">quem</expan> percuti volumus ab alio <lb></lb>

globo, æquali tamen aut minori, <expan abbr="quacũq́">quacunque</expan> violentia, <expan abbr="atq́">atque</expan>; <lb></lb>

adeò à machinà bellicà effulminato, <expan abbr="neq́">neque</expan>; tamen ſuo lo<lb></lb>

co moueri. quod quidem nullis machinis, aut retinacu<lb></lb>

lis, ſed duntaxat unius globi appoſitione conſeque<lb></lb>


<figure id="id.062.01.096.1.jpg" xlink:href="062/01/096/1.jpg"></figure><lb></lb>

mur, qui iram illius fulminis à globo percuſſo hauriat &amp; <lb></lb>

abſumat. </s>
            <s id="N13917">Appone ergo à tergo alium globum illi æqua<lb></lb>

lem <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> &amp; ſit linea motus pilæ ad utrum <expan abbr="q́">que</expan> globum perpen<lb></lb>

dicularis; dico globum <emph type="italics"></emph>a<emph.end type="italics"></emph.end> nulla ratione loco moueri a <lb></lb>

globo <emph type="italics"></emph>d.<emph.end type="italics"></emph.end> Quia enim globus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> eodem momento, quo <lb></lb>

percutitur à globo <emph type="italics"></emph>d,<emph.end type="italics"></emph.end> percutit globum <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ſibi æqualem, <lb></lb>

inducet illà percuſsione plagam perfectam, ac proinde


<pb xlink:href="062/01/097.jpg"></pb>per Poriſ: 1. â percuſsione quieſcet. </s>
            <s id="N13950">Quòd ſi plures glo<lb></lb>

bi æquales ſe <expan abbr="contingãt">contingant</expan> in lineà motus centri, ut <emph type="italics"></emph>f.g.h.i,<emph.end type="italics"></emph.end><lb></lb>

percuſſo <emph type="italics"></emph>f<emph.end type="italics"></emph.end> primo ab æquali <emph type="italics"></emph>e,<emph.end type="italics"></emph.end> ultimus <emph type="italics"></emph>i<emph.end type="italics"></emph.end> mouetur, reliquis <lb></lb>

<emph type="italics"></emph>f.g.h<emph.end type="italics"></emph.end> immotis; propterea quód per Poriſ. <emph type="italics"></emph>1.<emph.end type="italics"></emph.end> poſterior <lb></lb>

prioris exhaurit plagam. </s>
            <s id="N13982">t verò ſi unus æqualium poſt <lb></lb>

fe habeat minores <expan abbr="quotcunq́">quotcunque</expan>; ut <emph type="italics"></emph>o.p.q.<emph.end type="italics"></emph.end> percuſſo à <emph type="italics"></emph>k<emph.end type="italics"></emph.end> æqua<lb></lb>

li <emph type="italics"></emph>l,<emph.end type="italics"></emph.end> omnes cum <emph type="italics"></emph>l<emph.end type="italics"></emph.end> moto mouentur, ut conſtat per Poriſ.2. <lb></lb>

Quòd ſi demum percuſsio incipiat à minori <emph type="italics"></emph>q<emph.end type="italics"></emph.end> ug: omni<lb></lb>

bus immotis aut reflexis ultimus mouetur, per Poriſ. 3. <lb></lb>

aut ſi minor eſt impulſus grauitate, quieſcit, per Poriſ. <lb></lb>

4. </s>
            <s id="N139B3">Eadem vià diſſoluemus hoc </s>
          </p>
          <p id="N139B6" type="main">
            <s id="N139B8"><emph type="center"></emph><emph type="italics"></emph>Problema II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N139C3" type="main">
            <s id="N139C5"><emph type="italics"></emph>Globum in plano quieſcentem alio globo <expan abbr="quacunq́">quacunque</expan> violentià per<lb></lb>

cuſſum, ad imperatam diſtantiam mouere.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N139D2" type="main">
            <s id="N139D4">VT ſi globum <emph type="italics"></emph>b<emph.end type="italics"></emph.end> ab alio globo æquali aut minori <expan abbr="qua-cunq́">qua<lb></lb>

cunque</expan> violentiâ percuſſum, ad locum determinatum <lb></lb>

vg: <emph type="italics"></emph>c<emph.end type="italics"></emph.end> mouere velis, <expan abbr="neq́">neque</expan>; limitem hunc præterire, quan<lb></lb>

tumuis effræni impetu feratur</s>
            <s id="N139F1">n eodem loco, quem <lb></lb>

terminum illi motui præfixiſti, globum conſtitue æqua<lb></lb>

lem, dico in eodem loco à motu quieſcere globum <emph type="italics"></emph>b.<emph.end type="italics"></emph.end><lb></lb>

Quia enim globum <emph type="italics"></emph>c<emph.end type="italics"></emph.end> quieſcentem percutit globus æ<lb></lb>

qualis <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> per Poriſ. <emph type="italics"></emph>i<emph.end type="italics"></emph.end> quieſcet ex illa, quam fecit, plagâ. </s>
          </p>
          <pb xlink:href="062/01/098.jpg"></pb>
          <p id="N13A16" type="main">
            <s id="N13A18"><emph type="center"></emph><emph type="italics"></emph>Poriſma V.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N13A23" type="main">
            <s id="N13A25"><emph type="italics"></emph>Si duo globi ejuſdem molis ſeu ponderis ſe percutiant in motu, <lb></lb>

<expan abbr="uterq́">uterque</expan>; reflectit.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13A32" type="main">
            <s id="N13A34">NAm quia idem pondus <expan abbr="utriuſq́">utriuſque</expan>;, erit <expan abbr="quoq;">quoque</expan> velocitas <lb></lb>

motus, quam plaga inducit, æqualis; eadem ergo ve<lb></lb>

locitate reflectit percutiens, quà percuſſum mouebatur. <lb></lb>

Ex quo fit manifeſtum illorum velocitatem, quæ in mo <lb></lb>

tu ſe percutiunt, à percuſsione permutari: quæ enim ma<lb></lb>

gis percutiunt, minùs; &amp; quæ minùs percutiunt, magis <lb></lb>

impetuoſè reflectunt. </s>
          </p>
          <p id="N13A4B" type="main">
            <s id="N13A4D"><emph type="center"></emph><emph type="italics"></emph>Poriſma VI.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N13A58" type="main">
            <s id="N13A5A"><emph type="italics"></emph>Si globus major in motu percutiat minorem, habeat verò minor <lb></lb>

minorem rationem ad ſuum impulſum, quam ad globum majorem, <lb></lb>

<expan abbr="uterq́">uterque</expan>; reflectit.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13A69" type="main">
            <s id="N13A6B">QVia enim major eſt impulſus minoris grauitate ma<lb></lb>

joris, ob minorem hujus quam illius ratio nem, ſi mi<lb></lb>

nor percutiat majorem, mouebitur ex illà plagà major: <lb></lb>

reflectit autem &amp; minor à majori, propterea quód à qua<lb></lb>

<expan abbr="cunq́">cunque</expan> hujus plagâ mouetur minor. </s>
            <s id="N13A7A">Igitur ſi globus ma<lb></lb>

jor in motu percutiat minorem &amp;c. </s>
          </p>
          <p id="N13A7F" type="main">
            <s id="N13A81"><emph type="center"></emph><emph type="italics"></emph>Poriſma VII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <pb xlink:href="062/01/099.jpg"></pb>
          <p id="N13A8F" type="main">
            <s id="N13A91"><emph type="italics"></emph>Si globus major in motu percutiat minorem, habeat verò minor <lb></lb>

majorem rationem ad ſuum impulſum, quam ad globum majorem, <lb></lb>

minori reflexo motum continuat major.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13A9C" type="main">
            <s id="N13A9E">QVia enim minor eſt impulſus minoris grauitate ma<lb></lb>

joris, propterea quòd minorem ad hanc quam ad im<lb></lb>

pulſum habeat rationem, non poterit grauitas majoris <lb></lb>

moueri ex impulſu minoris: licet ergo plaga fiat à mi<lb></lb>

nori, quia tamen minorem producit impulſum, quam <lb></lb>

ut grauitatem majoris loco moueat, non poteſt ex illà <lb></lb>

plagà reflecti major. </s>
            <s id="N13AAD">Quia verò à minori impulſu æqua <lb></lb>

li velocitate mouetur minor, erit velocitas in minori æ<lb></lb>

qualis velocitati majoris à plagà necdum perfectà: im<lb></lb>

pulſus ergo reliquus, qui necdum percuſsit, motum con<lb></lb>

tinuabit. </s>
            <s id="N13AB8">Si ergo globus major in motu percutiat mi<lb></lb>

norem &amp;c. </s>
          </p>
          <p id="N13ABD" type="main">
            <s id="N13ABF"><emph type="center"></emph><emph type="italics"></emph>Poriſma VIII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N13ACA" type="main">
            <s id="N13ACC"><emph type="italics"></emph>Si globus major in motu percutiat minorem, habéat verò minor <lb></lb>

ad majorem eandem rationem, quam habet ad ſuum impulſum, mi<lb></lb>

nori reflexo quieſcit major.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13AD7" type="main">
            <s id="N13AD9">MInorem quidem globem à majori reflecti conſtat, <lb></lb>

propterea quód ex hujus plagà impulſus quidem æ<lb></lb>

qualis, maior autem velo citas in minori conſequatur: àt <lb></lb>

verò globum maiorem â percuſsione quieſcere, cùm e


<pb xlink:href="062/01/100.jpg"></pb>andem habet rationem minor ad hunc, quam habet ad <lb></lb>

ſuum impulſum, ita oſtendemus: motus non niſi ab ex<lb></lb>

ceſſu fit maioris; at verò impulſus ex illà plagà, quam in<lb></lb>

ducit minor in maiori, non maior ſed æqualis eſt eiuſ<lb></lb>

dem grauitati, ex ſuppoſitione; non ergo ex illo impul<lb></lb>

ſu moueri poteſt major. </s>
            <s id="N13AF0">Quia verò à percuſsione exol<lb></lb>

uitur, minor autem, quam ut mouere poſsit, impulſus <lb></lb>

regeneratur, quieſcet ex illà plagà globus maior. </s>
          </p>
        </subchap1>
        <subchap1 id="N13AF7">
          <p id="N13AF8" type="main">
            <s id="N13AFA"><emph type="center"></emph>Propoſitio XXXVIII.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N13B01" type="main">
            <s id="N13B03"><emph type="italics"></emph>Cùm centrum grauitatis cadit extra lineam hypomochlij, motus <lb></lb>

in illam partem, in quà eſt centrum, reflectit.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13B0C" type="main">
            <s id="N13B0E">OCcurrat globus <emph type="italics"></emph>dcg<emph.end type="italics"></emph.end> plano <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> non perpendiculari<lb></lb>

ter, ſed ex obliquo, faciens angulum incidentiæ <emph type="italics"></emph>adc<emph.end type="italics"></emph.end><lb></lb> acutum, <expan abbr="eritq́">eritque</expan>; linea <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> ducta per contactum linea hypo<lb></lb>

mochlii, &amp; motui centri parallela, centrum verò <emph type="italics"></emph>e<emph.end type="italics"></emph.end> extra <lb></lb>

lineam hypomochlii: dico ex puncto contactus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> mo<lb></lb>

tum reflexum fieri in illam partem, in quâ eſt centrum <emph type="italics"></emph>e.<emph.end type="italics"></emph.end><lb></lb>

Quia enim motus &amp; plaga ad motum fit centri: <expan abbr="centrũ">centrum</expan> <lb></lb>

verò <emph type="italics"></emph>e<emph.end type="italics"></emph.end> plano occurrit per lineam <emph type="italics"></emph>ed,<emph.end type="italics"></emph.end> <expan abbr="eſtq́">eſtque</expan>; maior reſiſten<lb></lb>

tia in plano quam impulſus, erit motus reflexus ad partes <lb></lb>

oppoſitas illi plagæ, ac proinde in partem in quà eſt cen<lb></lb>

trum. </s>
          </p>
        </subchap1>
        <subchap1 id="N13B65">
          <pb xlink:href="062/01/101.jpg"></pb>
          <p id="N13B69" type="main">
            <s id="N13B6B"><emph type="center"></emph>Propoſitio XXXIX.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N13B72" type="main">
            <s id="N13B74"><emph type="italics"></emph>Motus reflexus fit per lineam parallelam illi lineæ, quæ cum lineà <lb></lb>

perpendiculari ad contactum angulum conſtituit in centro, cujus ſi<lb></lb>

nus eſt æqualis interuallo inter centrum grauitatis &amp; lineam hy<lb></lb>

pomochlij.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13B81" type="main">
            <s id="N13B83">IN eàdem figurà ducatur ex <emph type="italics"></emph>e<emph.end type="italics"></emph.end> centro grauitatis ſeu im<lb></lb>

pulſus linea <emph type="italics"></emph>ef<emph.end type="italics"></emph.end> perpendicularis ad lineam hypomo<lb></lb>

chlii <emph type="italics"></emph>cd,<emph.end type="italics"></emph.end> &amp; linea <emph type="italics"></emph>eg<emph.end type="italics"></emph.end> faciens cum lineà <emph type="italics"></emph>dh<emph.end type="italics"></emph.end> perpendiculari <lb></lb>

ad contactum in eodem centro <emph type="italics"></emph>e<emph.end type="italics"></emph.end> angulum <emph type="italics"></emph>heg,<emph.end type="italics"></emph.end> cuius ſi<lb></lb>

nus <emph type="italics"></emph>hg<emph.end type="italics"></emph.end> ſit æqualis lineæ <emph type="italics"></emph>fe<emph.end type="italics"></emph.end> interuallo inter centrum gra<lb></lb>


<figure id="id.062.01.101.1.jpg" xlink:href="062/01/101/1.jpg"></figure><lb></lb>

uitatis <emph type="italics"></emph>e<emph.end type="italics"></emph.end> &amp; lineam hypomochlii: dico motum reflexum <lb></lb>

fieri per lineam <emph type="italics"></emph>di<emph.end type="italics"></emph.end> parallelam lineæ <emph type="italics"></emph>eg.<emph.end type="italics"></emph.end> Quia enim cen<lb></lb>

trum grauitatis, dum ſuà mole ferit planum in puncto <emph type="italics"></emph>d<emph.end type="italics"></emph.end>


<pb xlink:href="062/01/102.jpg"></pb> per lineam <emph type="italics"></emph>ed<emph.end type="italics"></emph.end> ſe ipſum veluti partitur: illa quidem pars <lb></lb>

quæ hypomochlio inſiſtit, <expan abbr="atqq́">atque</expan> illam plagam inducit, ea<lb></lb>

dem vià, quá impulit, &amp; impulſu æquali retro agitur: re<lb></lb>

liqua verò, quæ cum centro extra hypomochlium ca<lb></lb>

dit, per lineam fertur <emph type="italics"></emph>ek<emph.end type="italics"></emph.end> parallelam lineæ <emph type="italics"></emph>db,<emph.end type="italics"></emph.end> propterea <lb></lb>

quód hæc ſit proxima motui grauitatis ab hypomo<lb></lb>

chlio impeditæ. </s>
            <s id="N13C0F">Quia ergo motus <emph type="italics"></emph>eh.ek,<emph.end type="italics"></emph.end> quibus cen<lb></lb>

trum grauitatis agitur, ſecundúm quid ſunt contrarii, <lb></lb>

propterea quód angulus <emph type="italics"></emph>hek<emph.end type="italics"></emph.end> ſit minor duobus rectis, e<lb></lb>

rit motus mixtus per lineam mediam inter <emph type="italics"></emph>eh<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ek,<emph.end type="italics"></emph.end> cu<lb></lb>

jus interuallum determinat ſinus complementi inclina<lb></lb>

tionis, in ratione quam habent impulſus per Prop; 31. eſt <lb></lb>

autem interuallum <emph type="italics"></emph>fe,<emph.end type="italics"></emph.end> hoc eſt ſinus <emph type="italics"></emph>dm<emph.end type="italics"></emph.end> anguli <emph type="italics"></emph>dem,<emph.end type="italics"></emph.end> men<lb></lb>

ſura grauitatis extra hypomochlium; linea vero <emph type="italics"></emph>fd<emph.end type="italics"></emph.end> ſinus <lb></lb>

anguli reliqui menſura illius, quæ hypomochlio inſiſtit <lb></lb>

grauitatis: ſi fiat ut <emph type="italics"></emph>fd<emph.end type="italics"></emph.end> ad <emph type="italics"></emph>ef,<emph.end type="italics"></emph.end> ita <emph type="italics"></emph>kg<emph.end type="italics"></emph.end> ſinus complementi an<lb></lb>

guli <emph type="italics"></emph>heg<emph.end type="italics"></emph.end> ad<emph type="italics"></emph>hg<emph.end type="italics"></emph.end> ſinum complementi anguli <emph type="italics"></emph>keg<emph.end type="italics"></emph.end> erit li<lb></lb>

nea <emph type="italics"></emph>eg<emph.end type="italics"></emph.end> linea motus mixti ex <emph type="italics"></emph>eh<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>ek<emph.end type="italics"></emph.end> per Prop: 31. </s>
            <s id="N13C8E">Vel ſic <lb></lb>

motus reflexus fit per lineam <emph type="italics"></emph>de<emph.end type="italics"></emph.end> perpendicularem ad <lb></lb>

contactum; inclinatio autem motus reflexi augetur in <lb></lb>

ratione interualli inter centrum grauitatis &amp; hypomo<lb></lb>

chlium: Si igitur fiat ut ſinus totus nimirum motus re<lb></lb>

flexus, ad menſuram hujus interuàlli, hoc eſt grauitatem <lb></lb>

extra hypomochlium, ita linea motus <emph type="italics"></emph>eh<emph.end type="italics"></emph.end> ſinus nimirum <lb></lb>

anguli <emph type="italics"></emph>hek,<emph.end type="italics"></emph.end> hoc eſt ſinus totus ad ſinum <emph type="italics"></emph>hg<emph.end type="italics"></emph.end> anguli incli


<pb xlink:href="062/01/103.jpg"></pb>nationis, erit eadem linea <emph type="italics"></emph>eg<emph.end type="italics"></emph.end> motus mixti. </s>
            <s id="N13CC1">Quia ergo <lb></lb>

mobile mouetur ad motum ſui centri, erit motus ex <emph type="italics"></emph>d<emph.end type="italics"></emph.end><lb></lb> reflexus per lineam parallelam illi lineæ, quæ cum lineà <lb></lb>

perpendiculari ad contactum angulum conſtituit in <lb></lb>

centro, cujus ſinus eſt æqualis interuallo inter centrum <lb></lb>

grauitatis &amp; lineam hypomochlij. </s>
          </p>
        </subchap1>
        <subchap1 id="N13CD3">
          <p id="N13CD4" type="main">
            <s id="N13CD6"><emph type="center"></emph>Propoſitio XXXX.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N13CDD" type="main">
            <s id="N13CDF"><emph type="italics"></emph>Anguli incidentiæ &amp; reflexionis ſunt inter ſe æquales.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13CE6" type="main">
            <s id="N13CE8">QVia enim duo latera <emph type="italics"></emph>eh.bg<emph.end type="italics"></emph.end> trianguli <emph type="italics"></emph>ehg<emph.end type="italics"></emph.end> æqualia <lb></lb>

ſunt duobus lateribus <emph type="italics"></emph>ef. fd<emph.end type="italics"></emph.end> trianguli <emph type="italics"></emph>efd,<emph.end type="italics"></emph.end> &amp; angu<lb></lb>

lus, qui adjacet uni æqualium laterum, rectus, erunt tri<lb></lb>

angula æqualia, &amp; angulus <emph type="italics"></emph>fde<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>heg<emph.end type="italics"></emph.end> æqualis: eſt <lb></lb>

autem angulo <emph type="italics"></emph>heg<emph.end type="italics"></emph.end> æqualis angulus <emph type="italics"></emph>edi<emph.end type="italics"></emph.end> ob parallelas <emph type="italics"></emph>eg. <lb></lb>

di<emph.end type="italics"></emph.end>; idem ergo angulus <emph type="italics"></emph>edi<emph.end type="italics"></emph.end> eſt æqualis angulo <emph type="italics"></emph>fde:<emph.end type="italics"></emph.end> ſunt <lb></lb>

verò duo <expan abbr="quoq́">quoque</expan>; anguli <emph type="italics"></emph>a.de.bde<emph.end type="italics"></emph.end> inter le æquales, nimi<lb></lb>

rum recti; ablatis ergo duobus angulis <emph type="italics"></emph>fde.edi<emph.end type="italics"></emph.end> æquali<lb></lb>

bus, erunt anguli reliqui <emph type="italics"></emph>adf.bdi,<emph.end type="italics"></emph.end> anguli nimirum inci<lb></lb>

dentiæ &amp; reflexionis inter ſe æquales. </s>
            <s id="N13D55">Priuſquam de mo <lb></lb>

tu reflexo finiamus, unum <expan abbr="atq́">atque</expan>; alterum Problema pro <lb></lb>

corollario adducemus, quorum ſolutio magis difficilis <lb></lb>

habetur, ex ijs autem, quæ hactenus ſunt demonſtrata, <lb></lb>

facilè diſſoluuntur. </s>
            <s id="N13D64">Sit ergo </s>
          </p>
          <pb xlink:href="062/01/104.jpg"></pb>
          <p id="N13D6A" type="main">
            <s id="N13D6C"><emph type="center"></emph><emph type="italics"></emph>Problema<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N13D77" type="main">
            <s id="N13D79"><emph type="italics"></emph>Tribus globis in <expan abbr="quacunq́">quacunque</expan>; diſtantia extra lineam rectam aſſum<lb></lb>

ptis, punctum determinare in globo ſecundo, à quo reflexus primus <lb></lb>

percutiat tertium.<emph.end type="italics"></emph.end></s>
          </p>
          <p id="N13D88" type="main">
            <s id="N13D8A">IN figurà ſubiectà aſſumantur globi <emph type="italics"></emph>s.p.r.<emph.end type="italics"></emph.end> in diſtantiâ <lb></lb>

<emph type="italics"></emph>sp.pr.rs:<emph.end type="italics"></emph.end> <expan abbr="oporteatq́">oporteatque</expan>; in globo <emph type="italics"></emph>p<emph.end type="italics"></emph.end> punctum determina<lb></lb>

re, ad quod globus <emph type="italics"></emph>s<emph.end type="italics"></emph.end> allidens, <expan abbr="indeq́">indeque</expan>; reflexus percutiat <lb></lb>

globum <emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Tangant illos globos lineæ <emph type="italics"></emph>ac. bd<emph.end type="italics"></emph.end> in punctis <lb></lb>

<emph type="italics"></emph>a.c. b.d,<emph.end type="italics"></emph.end> &amp; diuidantur bifariam in punctis <emph type="italics"></emph>e<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>f;<emph.end type="italics"></emph.end> à quibus in <lb></lb>

circulum <emph type="italics"></emph>p<emph.end type="italics"></emph.end> excurrant lineæ rectæ <emph type="italics"></emph>eg.fg.<emph.end type="italics"></emph.end> ſe interſecantes <lb></lb>

in puncto reflexionis <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> eo modo, quo docent Optici in<lb></lb>

uento, &amp; producantur <expan abbr="utrinq́">utrinque</expan> in <emph type="italics"></emph>k.l,<emph.end type="italics"></emph.end> &amp; <emph type="italics"></emph>h. i;<emph.end type="italics"></emph.end> dico <expan abbr="punctũ">punctum</expan> <lb></lb>

<emph type="italics"></emph>g<emph.end type="italics"></emph.end> eſſe illud punctum, â quo globus <emph type="italics"></emph>s<emph.end type="italics"></emph.end> reflexus percutiat <lb></lb> globum<emph type="italics"></emph>r.<emph.end type="italics"></emph.end> Quia enim angulus <emph type="italics"></emph>egd<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>fgc<emph.end type="italics"></emph.end> per con<lb></lb>

ſtructionem, &amp; angulus <emph type="italics"></emph>egh<emph.end type="italics"></emph.end> angulo <emph type="italics"></emph>fgk<emph.end type="italics"></emph.end> ad verticem eſt <lb></lb>

æquali<emph type="italics"></emph>s<emph.end type="italics"></emph.end>; ablatis ex his illis erunt anguli reliqui <emph type="italics"></emph>hgd. kge<emph.end type="italics"></emph.end><lb></lb> æquales: linea ergo ſubtenſa <emph type="italics"></emph>hg<emph.end type="italics"></emph.end> eſt æqualis lineæ <emph type="italics"></emph>kg.<emph.end type="italics"></emph.end> &amp; <lb></lb>

quia linea <emph type="italics"></emph>fd<emph.end type="italics"></emph.end> lineæ <emph type="italics"></emph>fb,<emph.end type="italics"></emph.end> &amp; angulus <emph type="italics"></emph>dfg<emph.end type="italics"></emph.end> eſt æqualis angulo <lb></lb>

<emph type="italics"></emph>bfn,<emph.end type="italics"></emph.end> erit corda <emph type="italics"></emph>gh<emph.end type="italics"></emph.end> æqualis cordæ <emph type="italics"></emph>ni.<emph.end type="italics"></emph.end> Similiter oſtende<lb></lb>

mus cordam <emph type="italics"></emph>gk<emph.end type="italics"></emph.end> æqualem cordæ <emph type="italics"></emph>ml.<emph.end type="italics"></emph.end> Ducatur ergo per <lb></lb>

contactum â centro <emph type="italics"></emph>p<emph.end type="italics"></emph.end> linea <emph type="italics"></emph>pq,<emph.end type="italics"></emph.end> <expan abbr="atq́">atque</expan>, ex <emph type="italics"></emph>q<emph.end type="italics"></emph.end> circulus de<lb></lb>

ſcribatur æqualis circulo<emph type="italics"></emph>s,<emph.end type="italics"></emph.end> tangens priorem in <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> <expan abbr="agaturq́">agaturque</expan>; <lb></lb>

linea <emph type="italics"></emph>qr<emph.end type="italics"></emph.end> parallela lineæ <emph type="italics"></emph>gi<emph.end type="italics"></emph.end>: quòd ſi ergo globus <emph type="italics"></emph>s<emph.end type="italics"></emph.end> motu ſui


<pb xlink:href="062/01/105.jpg"></pb>centri deſcribat lineam <emph type="italics"></emph>sq,<emph.end type="italics"></emph.end> deſcribet punctum <emph type="italics"></emph>m<emph.end type="italics"></emph.end> motu <lb></lb>

ſimili lineam <emph type="italics"></emph>mg<emph.end type="italics"></emph.end> illi parallelam, <expan abbr="tangetq́">tangetque</expan>; globus <emph type="italics"></emph>s<emph.end type="italics"></emph.end> <expan abbr="globũ">globum</expan> <lb></lb>

<emph type="italics"></emph>p<emph.end type="italics"></emph.end> in puncto <emph type="italics"></emph>g<emph.end type="italics"></emph.end>: dico punctum <emph type="italics"></emph>m<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>g<emph.end type="italics"></emph.end> per lineam <emph type="italics"></emph>gi,<emph.end type="italics"></emph.end> cen<lb></lb>

trum veró <emph type="italics"></emph>q<emph.end type="italics"></emph.end> per lineam <emph type="italics"></emph>qr<emph.end type="italics"></emph.end> illi parallelam reflecti. </s>
            <s id="N13F12">rit <lb></lb>

enim <emph type="italics"></emph>gy<emph.end type="italics"></emph.end> linea hypomochlii, ad quam ex <emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end> cadat linea <lb></lb>

<figure id="id.062.01.105.1.jpg" xlink:href="062/01/105/1.jpg"></figure><lb></lb>

perpendicularis <emph type="italics"></emph>qt,<emph.end type="italics"></emph.end> <expan abbr="atq́">atque</expan>; huic æqualis ſumatur in lineâ <lb></lb>

motus centri <emph type="italics"></emph>qz,<emph.end type="italics"></emph.end> à cujus termino <emph type="italics"></emph>z<emph.end type="italics"></emph.end> ducta linea perpendi<lb></lb>

cularis ſecabit circulum in puncto <emph type="italics"></emph>x,<emph.end type="italics"></emph.end> per quod tranſit li<lb></lb>

nea motus reflexi per Prop 39. tribus ergò globis extra <lb></lb>

lineam rectam aſſumptis punctum determinauimus in


<pb xlink:href="062/01/106.jpg"></pb>globo ſecundo, à quo reflexus primus tangit tertium: <lb></lb>

quod erat faciendum. </s>
            <s id="N13F58">Secundum Problema. </s>
          </p>
          <p id="N13F5B" type="main">
            <s id="N13F5D"><emph type="center"></emph>DE MOTV REFLEXO <expan abbr="LAPILLORũ">LAPILLORum</expan> EX AQVA.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N13F68" type="main">
            <s id="N13F6A">QVi obliquè incidentes illam minimè findunt, <lb></lb>

<expan abbr="neq́ue">neque</expan> merguntur; verùm inde reflexi, <expan abbr="atq́">atque</expan>; ite<lb></lb>

rum relapſi reciprocà alliſione, &amp; reliſione ſaltu quodam <lb></lb>

progredi videntur. </s>
            <s id="N13F7B">Eſt autem prima difficultas, quam <lb></lb>

ob rem hujuſmodi lapilli, <expan abbr="quacunq́">quacunque</expan>; violentià projecti, <lb></lb>

aquam molliſsimam non perrumpant, in quâ etiam pul<lb></lb>

uiſculus &amp; leuiſsimæ arenulæ ſuà grauitate ſidunt. </s>
            <s id="N13F88">Se<lb></lb>

cunda quà ratione â primâ reflexione alias inducant pla<lb></lb>

gas non perpendiculares: conuerſio enim illa motus vi<lb></lb>

detur non niſi â grauitate naſci, quo modo in omnibus <lb></lb>

projectis fieri conſtat: at verò grauitas non niſi per line<lb></lb>

am mouet perpendicularem. </s>
            <s id="N13F95">In figurà ſubjectà lapillus <lb></lb>

ſeu globulus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> â percuſsione obliquà <emph type="italics"></emph>ba<emph.end type="italics"></emph.end> reflectit in <emph type="italics"></emph>k<emph.end type="italics"></emph.end>: in <lb></lb>

de verò non perpendiculariter in <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> verùm obliquè rela<lb></lb>

bitur in <emph type="italics"></emph>l,<emph.end type="italics"></emph.end> <expan abbr="nouaq́">nouaque</expan>; illatà &amp; relatâ plagà reflectit in <emph type="italics"></emph>m<emph.end type="italics"></emph.end>: ſimi<lb></lb>

liter ex <emph type="italics"></emph>m<emph.end type="italics"></emph.end> in <emph type="italics"></emph>u,<emph.end type="italics"></emph.end> &amp; ex <emph type="italics"></emph>o<emph.end type="italics"></emph.end> in <emph type="italics"></emph>x<emph.end type="italics"></emph.end> ad nouam ſe ex obliquo vibrat <lb></lb>

plagam. </s>
            <s id="N13FE2">Hujus autem ſolutio pendet ex his, quæ de mo <lb></lb>

tu reflexo â nobis ſunt dicta. </s>
            <s id="N13FE7">Quia enim percuſsio fit á <lb></lb>

centro, magnitudo autem plagæ ab hypomochlio deter<lb></lb>

minatur; quó enim major pars hypomochlio occurrit, <lb></lb>

eó majorem plagam inducit, unde ictus grauiſsimus per


<pb xlink:href="062/01/107.jpg"></pb>pendiculatis; propterea quód cum centro partès omnes <lb></lb>

coincidunt, <expan abbr="atq́">atque</expan>; in illam plagam cooperantur: quó ve<lb></lb>rò ictus magis eſt obliquus, eó minorem plagam infert. <lb></lb>

Quia ergo lapilli obliquè incidentes non niſi parte exi<lb></lb>

guà feriunt, major autem vis extra hypomochlium ca<lb></lb>

dit. <expan abbr="obſtatq́">obſtatque</expan>; quò minùs illa ſuo fulcro innitatur; inde fit <lb></lb>

ut non mergantur, <expan abbr="neq́">neque</expan>; findant quantumuis mollem a<lb></lb>


<figure id="id.062.01.107.1.jpg" xlink:href="062/01/107/1.jpg"></figure><lb></lb>

quam. </s>
            <s id="N14015">In globulo enim <emph type="italics"></emph>a<emph.end type="italics"></emph.end> ſola pars <emph type="italics"></emph>dic<emph.end type="italics"></emph.end> hypomochlio oc<lb></lb>

currit, reliqua <emph type="italics"></emph>dghci<emph.end type="italics"></emph.end> cum centro <emph type="italics"></emph>a<emph.end type="italics"></emph.end> extra hypomochli<lb></lb>

um cadit, <expan abbr="atq́">atque</expan>; ab illâ plagà idem mobile abducit. </s>
            <s id="N14038">Quia <lb></lb>

verò minor eſt plaga, quam ut perrumpat, recipiet à per<lb></lb>

cuſſo æqualem, qua reſiliat, plagam, ac proinde mino <lb></lb>

rem, quam ut impulſum producat illi æqualem, quo cen<lb></lb>

trum mouetur. </s>
            <s id="N14043">Motus ergò reflexus eſt mixtus ex motu


<pb xlink:href="062/01/108.jpg"></pb>centri <emph type="italics"></emph>ag<emph.end type="italics"></emph.end> à primà, &amp; motu <emph type="italics"></emph>af<emph.end type="italics"></emph.end> à plagâ ſecundà, linea <emph type="italics"></emph>v<emph.end type="italics"></emph.end>erò <lb></lb>

motus reflexi <emph type="italics"></emph>ah<emph.end type="italics"></emph.end> per Prop: 39. quia ergo minor impulſus <lb></lb>

à reflexione, impulſu, quo centrum agitur, deficiet pri<lb></lb>

ùs, <expan abbr="illoq́">illoque</expan>; deficiente motum continuabit major impul<lb></lb>

ſus; &amp; priuſquam ſui juris ſit, lineà motus mixti ſinuo<lb></lb>

ſè, quomodo grauia à motu violento, ſe abducet; inde <lb></lb>

per tangentem arcus jam deficientis, ac proinde ex obli<lb></lb>

quo ſe deuoluet, ut nouà illatà &amp; relatà plagâ ſe rurſum <lb></lb>

attollat. </s>
            <s id="N14076">Quia verò illo curſu &amp; recurſu virtus elangue <lb></lb>

ſcit, quantumuis æquali parte feriat, minor tamen â per<lb></lb>

cuſsione ſecundâ fit plaga, quam ut motus inde reflexus <lb></lb>

ſit æqualis primo: inde ergo fit ut à ſecundà percuſsione <lb></lb>

in <emph type="italics"></emph>d<emph.end type="italics"></emph.end> minor ſit altitudo motus reflexi in <emph type="italics"></emph>m<emph.end type="italics"></emph.end>; &amp; in <emph type="italics"></emph>o<emph.end type="italics"></emph.end> minor <lb></lb>

quàm in <emph type="italics"></emph>m,<emph.end type="italics"></emph.end> <expan abbr="quouſq́">quouſque</expan>; demum motus centri à percuſsioni<lb></lb>

bus iteratis exoluatur: aut quia minor in fine altitudo <lb></lb>

motus reflexi, quam diameter illius lapilli ſeu globuli, <lb></lb>ob aquam motui reluctantem ictus emoritur; <expan abbr="atq́">atque</expan>; inde <lb></lb>

fit, quòd in fine motus ab hujuſmodi lapillis aqua diſper<lb></lb>

gatur: à <emph type="italics"></emph>p<emph.end type="italics"></emph.end> enim in <emph type="italics"></emph>q<emph.end type="italics"></emph.end> reflexus motus, ob altitudinem dia<lb></lb>

metro minorem, viam incedit <emph type="italics"></emph>pq<emph.end type="italics"></emph.end> ob aquæ grauitatem <lb></lb>

magis impeditam. </s>
            <s id="N140C3">Non ſolúm verò in aquà ex hujuſmo<lb></lb>

di ictu obliquo fiunt repercuſsiones, verum in <expan abbr="quocunq́">quocunque</expan> <lb></lb>

alio plano minùs tamen ſenſibiles: cujus ratio eſt mol<lb></lb>

lities aquæ, quæ preſſa reaſſurgit, <expan abbr="ictuq́">ictuque</expan>; geminato ferit. <lb></lb>

<expan abbr="Itaq́">Itaque</expan>; videmus pilas luſorias magis reſilire, quæ â plagà ce


<pb xlink:href="062/01/109.jpg"></pb>dunt in ſe ipſas, &amp; veluti complanantur, <expan abbr="atq́">atque</expan>; ita plagam <lb></lb>

inducunt latiorem; mox verò â plagâ impulſu gemina<lb></lb>

to reaſſurgunt: idem enim ſit ſiuè planum, ſiuè mobile <lb></lb>

eidem plano alliſum eà ratione moueatur. </s>
            <s id="N140E8">Similes ictus <lb></lb>

repetiti fiunt in cauo ſphærico, cujuſmodi peluis: ab <lb></lb>


<figure id="id.062.01.109.1.jpg" xlink:href="062/01/109/1.jpg"></figure><lb></lb>

uno enim puncto reflexus globus in alia porro offendit <lb></lb>

&amp; allidit: ut ſi globus ex <emph type="italics"></emph>l<emph.end type="italics"></emph.end> demittatur in peluim <emph type="italics"></emph>msbp,<emph.end type="italics"></emph.end> a <lb></lb>

puncto <emph type="italics"></emph>m<emph.end type="italics"></emph.end> ad angulos reflectit æquales in <emph type="italics"></emph>n,<emph.end type="italics"></emph.end> ex<emph type="italics"></emph>n<emph.end type="italics"></emph.end> verò in <lb></lb>

<emph type="italics"></emph>b,<emph.end type="italics"></emph.end> ex <emph type="italics"></emph>b<emph.end type="italics"></emph.end> in <emph type="italics"></emph>o,<emph.end type="italics"></emph.end> tum in <emph type="italics"></emph>p,<emph.end type="italics"></emph.end> à quo extra peluim reflectit in <emph type="italics"></emph><expan abbr="q.">que</expan><emph.end type="italics"></emph.end> <expan abbr="Idẽ">Idem</expan> <lb></lb>

ex <emph type="italics"></emph>r<emph.end type="italics"></emph.end> delapſus in <emph type="italics"></emph>s<emph.end type="italics"></emph.end> maiori angulo reflectens, ob cordas ma<lb></lb>

iores, pauciores inducit plagas. </s>
            <s id="N1414E">Ex <emph type="italics"></emph>z<emph.end type="italics"></emph.end> demum in <emph type="italics"></emph>b<emph.end type="italics"></emph.end> refle<lb></lb>

xus quia nullibi offendit, quemadmodum <expan abbr="neq́">neque</expan>; in linea <lb></lb>

perpendiculari <emph type="italics"></emph>ab,<emph.end type="italics"></emph.end> nullam præterea inducit plagam. <lb></lb>

Tertium Problema. </s>
          </p>
          <pb xlink:href="062/01/110.jpg"></pb>
          <p id="N14170" type="main">
            <s id="N14172"><emph type="center"></emph>DE REFLEXIONE MOTVS CIRCVLARIS.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N14179" type="main">
            <s id="N1417B">VT ſi duo globi ab eodem hypomochlio filo ſuſpenſi, <lb></lb>

&amp; in ſuam ſtationem recurrentes ſe percutiant in il<lb></lb>

lo motu. </s>
            <s id="N14182">Quia enim hic motus diſcedit à lineà rectà, per <lb></lb>

quam ducit impulſus, neceſſe alio modo reflexionem fi<lb></lb>

eri, quám in motu recto. </s>
            <s id="N14189">Mouetur autem vel unus tan<lb></lb>

tum, vel <expan abbr="uterq́">uterque</expan>;, ac proinde hic illum percutit aut quies<lb></lb>

centem, aut commotum; &amp; ſiquidem percuſsio fiat in <lb></lb>

motu, <expan abbr="uterq́">uterque</expan>; reflectit: Si verò quieſcit alter, interdum <lb></lb>

reflectit ille qui percuſsit, interdum in ipſo ictu emori<lb></lb>

tur motus. </s>
            <s id="N1419E">Quod qua ratione fiat ſubjectà figurá pate<lb></lb>

fiet. </s>
            <s id="N141A3">Percutiant ergò ſe duo globi <foreign lang="grc">εγ</foreign> ab eodem hypomo<lb></lb>

chlio <foreign lang="grc">α</foreign> ſuſpenſi in ipſo motu, &amp; ducantur lineæ tangen<lb></lb>

tes <foreign lang="grc">βο. θξ</foreign> <expan abbr="atq́">atque</expan>; his parallelæ <foreign lang="grc">ψι.ψκ</foreign> lineæ hypomochlij; in <lb></lb>

lineà autem, <foreign lang="grc">γ</foreign> per <expan abbr="utrumq;">utrumque</expan> centrum ductà, &amp; <expan abbr="utrinq;">utrinque</expan> <lb></lb>

protractà ſumatur <foreign lang="grc">γπ</foreign> æqualis <foreign lang="grc">ψλ</foreign>, &amp; ex <foreign lang="grc">π</foreign> excitetur li<lb></lb>

nèa perpendicularis <foreign lang="grc">πμ</foreign>, <expan abbr="eritq;">eritque</expan> linea <foreign lang="grc">γμ</foreign>, ſi nihil impediat, <lb></lb>

linea motus reflexi, per Prop: 39. motus nimirum mix<lb></lb>

tus ex motu centri <foreign lang="grc">γω</foreign> &amp; motu à percusſione <foreign lang="grc">γν</foreign>. </s>
            <s id="N141F4">At verò <lb></lb>

huic motui obſtat funiculus, à quo globus detinetur, <lb></lb>

quò minùs extra <expan abbr="peripheriã">peripheriam</expan> circuli euagetur. </s>
            <s id="N141FF">Quia ve<lb></lb>

rò hic motus à reflexione &amp; motus à retractione funi<lb></lb>

culi angulum ducunt <foreign lang="grc">αγμ</foreign> minorem duobus rectis, erunt <lb></lb>

per definit: 5. ſecundùm quid contrarii, ac proinde inter


<pb xlink:href="062/01/111.jpg"></pb>ſe miſcentur. </s>
            <s id="N14210">Motus ergò ex <expan abbr="utroq;">utroque</expan> mixtus à percuſsio<lb></lb>

ne reflectit. </s>
            <s id="N14219">Simili modo oſtendemus globum <foreign lang="grc">ε</foreign> refle<lb></lb>

cti ex illà plagà. </s>
            <s id="N14222">Quòd ſi globus <emph type="italics"></emph>a<emph.end type="italics"></emph.end> percutiat globum <emph type="italics"></emph>b<emph.end type="italics"></emph.end><lb></lb> quieſcentem, &amp; minori filo ſuſpenſum, erit per Prop: 39 <lb></lb>

linea motus reflexi <emph type="italics"></emph><expan abbr="aq.">aque</expan><emph.end type="italics"></emph.end> &amp; quia hic motus in partes oppo<lb></lb>


<figure id="id.062.01.111.1.jpg" xlink:href="062/01/111/1.jpg"></figure><lb></lb>
ſitas tendit eiuſdem lineæ rectæ, per quam retrahitur ab <lb></lb>

hypomochlio, erunt motus abſolutè contrarii: globus <lb></lb>

ergò <emph type="italics"></emph>a<emph.end type="italics"></emph.end> ſi in illo ſitu percutiat <emph type="italics"></emph>b,<emph.end type="italics"></emph.end> â percuſsione quieſcet; <lb></lb>

tantò verò minùs reflectet, quantó maior fuerit angu


<pb xlink:href="062/01/112.jpg"></pb>lus <foreign lang="grc">α</foreign><emph type="italics"></emph>aq<emph.end type="italics"></emph.end> Si demum globus <emph type="italics"></emph>b<emph.end type="italics"></emph.end> percutiat globum <emph type="italics"></emph>a<emph.end type="italics"></emph.end> quie<lb></lb>

ſcentem &amp; longiori filo ſuſpenſum, erit linea motus re<lb></lb>

flexi <emph type="italics"></emph>br<emph.end type="italics"></emph.end> ad eaſdem partes cum retractione hypomo<lb></lb>

chlii, propterea quòd linea <emph type="italics"></emph>bp<emph.end type="italics"></emph.end> ſit motus centri, linea ve<lb></lb>

rò <emph type="italics"></emph>bn<emph.end type="italics"></emph.end> motus à percuſsione; globus ergo <emph type="italics"></emph>b<emph.end type="italics"></emph.end> percuſſo glo<lb></lb>

bo <emph type="italics"></emph>a<emph.end type="italics"></emph.end> reflectet in illo ſitu à percuſsione: Eadem via diſ <lb></lb>

ſoluemus &amp; illam quæſtionem. </s>
          </p>
          <p id="N1429A" type="main">
            <s id="N1429C"><emph type="center"></emph>DE IN ÆQVALIVM PONDERVM LAPSV<emph.end type="center"></emph.end></s>
          </p>
          <p id="N142A3" type="main">
            <s id="N142A5">MAgnis motibus &amp; animorum contentionibus a<lb></lb>

gitatam: dum hi quidem rationibus ſe tuentur, illi <lb></lb>

verò experientià eos urgent, <expan abbr="erroriſq́">erroriſque</expan>; manifeſti reos pe<lb></lb>

ragunt. </s>
            <s id="N142B2">Quorum opinio vulgi applauſu excepta pal<lb></lb>

mam tulit, judice magis ſenſu quam ratione. </s>
            <s id="N142B7">At verò <lb></lb>

qui opinantur inæqualia pondera æquali lapſu ruere, <lb></lb>

videntur magis id, quod motui per ſe ineſt, attendiſſe, <lb></lb>

impedimenta verò motus, quæ ab extra fiunt, veluti du<lb></lb>

biæ ſortis neglexiſſe. </s>
            <s id="N142C2">Vt verò hanc litem dirimamus, <lb></lb>

memoriá repetendum id, quod Prop: 37. notabili 4. di<lb></lb>

ximus, impulſum deficere à plagà perfecta, partem verò <lb></lb>

hujus cum parte æquali plagæ emori. </s>
            <s id="N142CB">Secundo â reſi<lb></lb>

ſtentiá majori plagam induci majorem: propterea quòd <lb></lb>

percutiens magis tum immoratur. </s>
            <s id="N142D2">Tertio omnia cor<lb></lb>

pora reſiſtere diuiſioni, <expan abbr="atq́">atque</expan>; eó magis, quó major eſt vir


<pb xlink:href="062/01/113.jpg"></pb>tus illarum partium unitiua, ut Prop: 1. dictum: quan<lb></lb>

tumuis ergo aër naturá ſuá ſit fluidus, <expan abbr="atq́">atque</expan>; omni <lb></lb>

aurá mobilis, non tamen <expan abbr="abſq́">abſque</expan>, violentiá, ac proinde <lb></lb>

non <expan abbr="abſq́">abſque</expan>; plagà findi poteſt. </s>
            <s id="N142F1">Quar<lb></lb>

to majorem diuiſionem fieri à majori plagà; multúm e<lb></lb>

nim aëris non eadem facilitate mouemus, <expan abbr="neq́">neque</expan>; eadem <lb></lb>

velocitate parte ferri latiore, quam in mucronem tenua<lb></lb>

ta hunc penetramus. </s>
            <s id="N14300">His ſuppoſitis: dico 1. motum qua <lb></lb>

tenus à grauitate procedit eiuſdem ſpeciei ſeu gradus, eà<lb></lb>

dem celeritate fieri in omnibus, quantumuis mole, figu<lb></lb>

rà, pondere à ſe differant: ratio, quia ut mobile mouea<lb></lb>

tur, non quilibet impulſus, ſed proportionatus eſſe debet <lb></lb>

ad illud mobile; ab eadem ergo proportione eadem ve<lb></lb>

locitas motus: at veró impulſus, quo totum mobile mo<lb></lb>

uetur, eandem rationem habet ad illud mobile, quam ſe<lb></lb>

miſsis illius impulſus ad ſemiſſem, &amp; triens ad trientem <lb></lb>

ejuſdem mobilis; eadem ergo velocitas motus. </s>
            <s id="N14315">Quod <lb></lb>

idem de qualibet particulá, <expan abbr="quacunq́">quacunque</expan>; factá diuiſione, di<lb></lb>

cendum; non minùs enim extra illud mobile, quam in <lb></lb>

mobili, &amp; alijs conjunctæ ſuo inpulſu mouentur. </s>
            <s id="N14322">Dices <lb></lb>

virtus collecta eſt fortior ſe ipſà diſperſà: major ergo im<lb></lb>

pulſus in partibus unitis, quam extra illam unionem. </s>
            <s id="N14329">Re <lb></lb>

ſpondeo illud axioma non in omnibus valere, ſed tan<lb></lb>

tum in ordine ad actionem, quæ extra illud ſubjectum <lb></lb>

terminatur; ita enim lux alteri conjuncta lumen longi


<pb xlink:href="062/01/114.jpg"></pb>ùs protendit, nihilo ex illa conjunctione luce auctà: ita <lb></lb>

ergo impulſus partium unitarum licet magis percutiat, <lb></lb>

non tamen in ordine ad motum, quo illius ſubjectum <lb></lb>

fertur, magis inualeſcit, quemadmodum cùm plures ſi<lb></lb>

mul vocem attollunt, licet magis audiatur, non tamen <lb></lb>

ex aliorum vociferatione ſingulorum clamor facilitatur. <lb></lb>

Plura quæ pro hac ſententià, &amp; <expan abbr="cõtra">contra</expan> afferri poſſunt, ſuo <lb></lb>

loco dicemus; nunc verò dato eſſe veram, illam inæqua<lb></lb>

litatem motus conſtare, <expan abbr="atq́">atque</expan>; ex alià radice naſci paucis o<lb></lb>

ſtendemus. </s>
            <s id="N14350">Dico ſecundò, illam inæqualitatem motus, <lb></lb>

quo inæqualia pondera mouentur, eſſe à medio, in quo <lb></lb>

fit motus; <expan abbr="atq́">atque</expan>; illa corpora, quorum grauitas ſeu impul<lb></lb>

ſus majorem rationem habet ad ſuam plagam, velociùs <lb></lb>

moueri. </s>
            <s id="N1435F">Quia enim aër reſiſtit diuiſioni ex notabili 3. <lb></lb>

erit plaga ad menſuram hujus reſiſtentiæ; deficiet ergò <lb></lb>

impulſus, ac proinde velocitas motus in eà ratione, in <lb></lb>

quâ magnitudo plagæ: igitur ut plaga ad plagam, ita ve<lb></lb>

locitatis decrementum. </s>
            <s id="N1436A">At verò grauitas illorum cor<lb></lb>

porum majorem rationem habet, quam illorum plaga: <lb></lb>

ſit enim globus <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> ad globum <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> in ratione duplà, <expan abbr="eritq́">eritque</expan>; <lb></lb>

illorum plaga æqualis circulo maximo ſuæ ſphæræ, pro<lb></lb>

pterea quód plaga inducitur non niſi à parte inferiore, <lb></lb>

quæ aërem findit, &amp; cui ſoli aër reſiſtit: habet autem cir<lb></lb>

culus maximus ſphæræ ſeu globi in ratione duplà ad ali<lb></lb>

am ſphæram, minorem rationem, quám duplam, ad hu-


<pb xlink:href="062/01/115.jpg"></pb>jus circulum maximum; globus ergo major plagam in<lb></lb>

ducit minorem, quàm ut ſit dupla ad plagam minoris <lb></lb>

globi: ut ſi globus major ſit duarum lib: erit ſemiſsis, id<lb></lb>

eſt lib: una, æqualis globo minori; hujus verò plaga ſe<lb></lb>

miſsis plagæ totius minor plagâ totá globi minoris. quia <lb></lb>

ergò plaga tollit partem ſibi æqualem, maius erit decre<lb></lb>

mentum velocitatis in librà unà, dum extra illud totum, <lb></lb>

ſeu globum maiorem &amp; per ſe, ideſt in globo minori mo<lb></lb>

uetur. </s>
            <s id="N1439F">Et quia in medio ſimilari eadem plaga continu<lb></lb>

atur, eadem ratio erit decrementi quæ interualli; ut ſi in <lb></lb>

toto motu deficiat cubitus unus, deficiet in ſemiſſe hu<lb></lb>

jus motus illius ſemiſsis: <expan abbr="atq;">atque</expan> inde ratio conſtat, quam ob <lb></lb>

rem à principio motus inæqualia pondera ſimul ferri <lb></lb>

<expan abbr="videãtur">videantur</expan>, inde verò magnis à ſe diſiungi interuallis. </s>
            <s id="N143B4">Ma<lb></lb>

lè ergo rationem huius inæqualitatis petunt à proporti<lb></lb>

one illorum ponderum, quæ á ratione creſcentis plagæ <lb></lb>

deſumi debet; ablatá enim á grauitate ſeu impulſu parte <lb></lb>

æquali ſuæ plagæ, reliquus impulſus dabit illam inæqua<lb></lb>

lem velocitatem. </s>
            <s id="N143C1">Obiicies fieri non poſsè ut eadem ratio <lb></lb>

maneat plagæ in illo motu inæquali continuatæ, propte<lb></lb>

rea quód aër percuſſus alium percutiat, <expan abbr="viamq;">viamque</expan> eá rati<lb></lb>

one aperiat ruenti globo, plagæ imminenti ſe <expan abbr="ſubducẽs">ſubducens</expan>, <lb></lb>

non aliter, quám cùm ultro cedentem trudimus: <expan abbr="itaq;">itaque</expan> in <lb></lb>

relapſu globi maioris, quem ignis in ſublime tulit, pri<lb></lb>

uſquam terram feriat, ab aëris percuſsione hiatum in il-


<pb xlink:href="062/01/116.jpg"></pb>lá fieri quidam aſſeuerant. </s>
            <s id="N143E0">Cùm ergò aër ab illo ictu ſe <lb></lb>

ſubducat, nullam inducet plagam, nullum proinde velo<lb></lb>

citatis decrementum; non aliter quam ſi globus per fiſ<lb></lb>

ſuram muri tranſuolet muro inoffenſo. </s>
            <s id="N143E9">Deinde cùm im<lb></lb>

pulſus continuò augeatur, erit continuó minor reſiſten<lb></lb>

tia. </s>
            <s id="N143F0">Reſpondeo aerem quidem impelli &amp; præcurrere, <lb></lb>

verùm minori celeritate, quàm ut plagam effugiat á ter<lb></lb>

go hærentem; major enim globi impetus, quâm ut ab <lb></lb>

aere fluido recipiatur: unde eadem reſiſtentia in aëre per <lb></lb>

forando, non minús, quàm ſi ſecundo flumine elucte<lb></lb>

mur motu velociori, quàm ſit defluxus; non minor e<lb></lb>

nim difficultas in perrumpendo, quam ſi in aquà fiat im<lb></lb>

motà. </s>
            <s id="N14401">Deinde licet aër percuſſus à plagà ſe ſubducat &amp; <lb></lb>

præcurrat, alius tamen in locum plagæ ſe infundit non <lb></lb>

minori vi findendus: <expan abbr="neq́">neque</expan>; enim aër diſcerpi poteſt eo <lb></lb>

modo, quo corpora magis denſa, in quibus perruptis cor<lb></lb>

pus magis ſubtile interceptum viam præſtat faciliorem; <lb></lb>

verùm <expan abbr="quacunq́">quacunque</expan>; plaga incidit, eadem aëris ſoliditas per<lb></lb>

rumpenda. </s>
            <s id="N14418">Ad ſecundam rationem, dico velocitatem <lb></lb>

motus continuò quidem augeri, ac proinde illam reſi<lb></lb>

ſtentiam medij auctà velocitate faciliùs perrumpi; pro<lb></lb>

pterea quód ablatà parte æquali major ſit exceſſus reli<lb></lb>

quus: nego autem â velociori plagà minus eſſe decre<lb></lb>

mentum. </s>
            <s id="N14425">An non velociùs vectem deprimunt libræ 10. <lb></lb>

aut 100, quam libra <emph type="italics"></emph>1?<emph.end type="italics"></emph.end> &amp; tamen granum unum aut deci-


<pb xlink:href="062/01/117.jpg"></pb>ma pars grani æqualem partem ex hoc, <expan abbr="atq́">atque</expan>, ex illis tollit. <lb></lb>

Verùm deceptio latet ob exiguitatem decrementi, que<lb></lb>

madmodum ſi ad deprimendum libras 100. unum <expan abbr="atq́">atque</expan>; <lb></lb>

alterum granum apponas. </s>
            <s id="N14442">Quia ergò retardatio motus <lb></lb>

eſt à medio, quó medium magis reſiſtit diuiſioni, eó mi<lb></lb>

nor velocitas motus, major autem exceſſus tarditatis in <lb></lb>

minori: propterea quód auctá reſiſtentiá eadem diffe<lb></lb>

rentia in minori interuallo. </s>
            <s id="N1444D">E contra minuitur exceſ<lb></lb>

ſus in medio magis raro; <expan abbr="itaq́">itaque</expan>; ſi detur corpus infinitæ ra<lb></lb>

ritatis, cuiuſmodi vacuum, quia nulla reſiſtentia, nulla <lb></lb>

<expan abbr="quoq́">quoque</expan>; erit inæqualitas motus. </s>
            <s id="N1445E">Quòd autem à ſolá reſi<lb></lb>

ſtentià medij procedat inæqualitas motus, ratio manife<lb></lb>

ſta: idem enim pondus ſe ipſo velociús, <expan abbr="atq́">atque</expan>; cum alio <lb></lb>

pondere <expan abbr="quocunq́">quocunque</expan>; exceſſu majori, eádem velocitate de<lb></lb>

ſcendit, ſi rationem plagæ &amp; reſiſtentiam medii in illâ <lb></lb>


<figure id="id.062.01.117.1.jpg" xlink:href="062/01/117/1.jpg"></figure><lb></lb>

proportione minuàs. </s>
            <s id="N1447A">Sit enim vas plumbeum, aut de <lb></lb>

alià materià graui, formá dimidiæ ſphæræ, cujuſmodi <foreign lang="grc">βγδ</foreign>


<pb xlink:href="062/01/118.jpg"></pb>habens cauitatem in parte ſuperiore, &amp; à plagâ auerſa, <lb></lb>

centrum verò grauitatis in <gap></gap> ne dum labitur ſe inuertat: <lb></lb>

quód ſi ergo alium globum <expan abbr="quocunq́">quocunque</expan>; exceſſu leuio<lb></lb>

rem conſtituas in illà cauitate, eádem cum illo vaſe ce<lb></lb>

leritate feretur. </s>
            <s id="N14495">At verò ſi inæqualitas motus eſſet <lb></lb>

à grauitate, oporteret illud vas magis ponderoſum <lb></lb>

præcurrere, globum verò leuiorem attolli, &amp; longo poſt <lb></lb>

tergum interuallo relinqui. </s>
            <s id="N1449E">Obiicies grauitas eſt impul<lb></lb>

ſus, impulſus verò per Prop: 2. motum producit ſibi æ<lb></lb>

qualem; à majori ergò grauitate major, ac proinde velo<lb></lb>

cior motus: quòd ſi ergò libra una in <expan abbr="quinq́">quinque</expan>; ſecundis <lb></lb>

per ſpatium mouet cubitorum 100, mouebit hujus du<lb></lb>

plum in eodem, vel æquali tempore per ſpatium <expan abbr="duplũ">duplum</expan>. <lb></lb>

Deinde plaga inducitur ex motu; non enim manus à la<lb></lb>

pide in eà quieſcente, ſed ubi iram ex motu concepit, vul<lb></lb>

neratur: at verò majus pondus æquali lapſu magis vulne<lb></lb>

rat, velocior ergo motus. </s>
            <s id="N144BB">Reſpondeo grauitatem eſſe <lb></lb>

impulſum, &amp; velocitatem motus in eá ratione, in quá eſt <lb></lb>

grauitas ſeu impulſus; dupla ergo grauitas in eodem, vel <lb></lb>

æquali tempore mouebit per ſpatium duplum. </s>
            <s id="N144C4">At verò <lb></lb>

cùm inferunt libras duas Vg: plumbi in duplà ferri celeri<lb></lb>

tate ad libram unam, falluntur; propterea quòd illa gra<lb></lb>

uitas in alio ſit ſubiecto, cuius partes omnes æquali gra<lb></lb>

uitate mouentur: ſicuti enim pars extra totum Vg. libra <lb></lb>

una â ſua grauitate mouetur cum tantà velocitate, ita


<pb xlink:href="062/01/119.jpg"></pb>partes librarum decem, aut centum in toto unitæ eádem <lb></lb>

velocitate <expan abbr="mouẽtur">mouentur</expan> á ſuá <expan abbr="cuiq;">cuique</expan> propria grauitate. </s>
            <s id="N144DF">Quód <lb></lb>

ſi grauitas librarum decem conſtituatur in ſubiecto uni<lb></lb>

us libræ, tum verò decupla velocitate mouebitur illud <lb></lb>

ſubiectum. </s>
            <s id="N144E8">Niſi ergò grauitas magis ſit intenſa, nihil <lb></lb>

proficiet ad velocitatem augendam illorum moles. <lb></lb>

Quód autem maior grauitas plagam inducat maiorem, <lb></lb>

ut ſi libræ decem percutiant libram unam, huius ratio <lb></lb>

eſt, quia totidem fiunt plagæ, quot in maiori continen<lb></lb>

tur partes æquales: quemadmodum ſi decem ictus ſi<lb></lb>

mul inferantur, aut ſi priuſquam vis emoriatur prioris <lb></lb>

plagæ, reliquæ ſequantur. </s>
            <s id="N144F9">Impulſus ergò in illo ſubie<lb></lb>

cto minori á maiori percuſſo magis eſt intenſus. <expan abbr="Atq;">Atque</expan> <lb></lb>

inde fit, quód globus minor accepta à maiori plaga præ<lb></lb>

currat; quód ſi enim globos <expan abbr="quotcunq;">quotcunque</expan> eà ſerie diſpo<lb></lb>

nas, ut continuò maiorem minor ſequatur, percuſſo pri<lb></lb>

mo videbis quaſi uno impetu omnes ad motum conci<lb></lb>

tari, verùm celeritate, pro ratione magnitudinis, inæ<lb></lb>

quali. </s>
          </p>
        </subchap1>
        <subchap1 id="N14512">
          <p id="N14513" type="main">
            <s id="N14515"><emph type="center"></emph>Propoſitio XXXXI.<emph.end type="center"></emph.end></s>
          </p>
          <p id="N1451C" type="main">
            <s id="N1451E"><emph type="center"></emph><emph type="italics"></emph>Problema II.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
          </p>
          <p id="N14529" type="main">
            <s id="N1452B"><emph type="italics"></emph>Regulam conſtruere ad celeritatem &amp; tarditatem pulſuum <expan abbr="abſq́">abſque</expan>; <lb></lb>

errore metiendam.<emph.end type="italics"></emph.end></s>
          </p>
          <pb xlink:href="062/01/120.jpg"></pb>
          <p id="N1453B" type="main">
            <s id="N1453D">REgula hæc nullo apparatu, ſed. hac arte ſimplici <lb></lb>

confit ſiue ex ligno, ſiue ex qualibet alià materià. </s>
            <s id="N14542">Hu<lb></lb>

ius longitudo <emph type="italics"></emph>ab<emph.end type="italics"></emph.end> unius cubiti, aut ad placitum: quó enim <lb></lb>

maior, eò plures differentias tarditatis indicabit: nam <lb></lb>

ad velocitatem ſummam indicandam quælibet magni<lb></lb>

tudo ſufficit. </s>
            <s id="N14553">Latitudo verò, quæ cordam ſeu filum ca<lb></lb>

piat cum numerorum notis eidem adſcriptis. </s>
            <s id="N14558">Filum <lb></lb>

porro eo modo, quo fidibus aptatur; parte ſuperiore <lb></lb>

trochleâ verſatili conuolutum, parte verò inferiore fora <lb></lb>

mine tranſmiſſum, globulum habens dependentem, qui <lb></lb>

eidem rectitudinem præſtat &amp; pondus. </s>
            <s id="N14563">Tota longitu<lb></lb>

do regulæ, quæ continetur inter foramen &amp; trochleam, <lb></lb>

æqualiter ſecetur in partes quotlibet Vg. 60, aut 100. <lb></lb>


<figure id="id.062.01.120.1.jpg" xlink:href="062/01/120/1.jpg"></figure><lb></lb>

quas trochleà laxatâ nodulus <emph type="italics"></emph>q,<emph.end type="italics"></emph.end> globulo interea deſcen


<pb xlink:href="062/01/121.jpg"></pb>dente, percurrit, <expan abbr="ſuoq́">ſuoque</expan> contactu quot ejuſmodi ſegmen<lb></lb>

ta contineat longitudo ejuſdem fili cum ſuo globulo à <lb></lb>

foramine penduli, oſtendit. </s>
            <s id="N14585">Cùm ergo per dictum in<lb></lb>

ſtrumentum pulſus celeritatem indagare voles, trochle<lb></lb>

am verſando filum eò <expan abbr="uſq́">uſque</expan>; laxa, dum globulus in <emph type="italics"></emph>e<emph.end type="italics"></emph.end> Vg. <lb></lb>

aut <emph type="italics"></emph>g<emph.end type="italics"></emph.end> deſcendat: quom ex <emph type="italics"></emph>g,<emph.end type="italics"></emph.end> in quo naturaliter à motu <lb></lb>

quieſcit, in <emph type="italics"></emph>l<emph.end type="italics"></emph.end> vel <emph type="italics"></emph>o<emph.end type="italics"></emph.end> dimotum inde recurrere ſinas; in<lb></lb>

terea, dum globulus per arcum <emph type="italics"></emph>cd<emph.end type="italics"></emph.end> ultra <expan abbr="citraq́">citraque</expan> <emph type="italics"></emph>g<emph.end type="italics"></emph.end> excurrit, <lb></lb>

<expan abbr="plureſq́">plureſque</expan>; recurſus facit, agitationem quidem arteriæ ma<lb></lb>

nu, motum verò perpendiculi viſu explora, <expan abbr="atq́">atque</expan>; unum <lb></lb>

alteri compara. </s>
            <s id="N145D2">Quód ſi tardior arteriæ motus, perpen<lb></lb>

diculum trochleá laxatá producas, ſi celerior contrahas <lb></lb>

Æquato demum <expan abbr="utriuſq́">utriuſque</expan>; motu, quænam ſit celeritatis <lb></lb>

ratio, ex numerorum diuiſione, quem nodulus cum filo <lb></lb>

depreſſus indicabit, facilè cognoſces. </s>
            <s id="N145E1">Quin &amp; quamli<lb></lb>

bet mutationem ad ſingula momenta ex collatione ad <lb></lb>

huiuſmodi numeros factâ conijcies. </s>
            <s id="N145E8">Vbi ergo menſu<lb></lb>

ram pulſus quam maximè naturalis hac vià deprehen<lb></lb>

des: diuiſionis interuallum, quod nodulus indicabit, <lb></lb>

diligenter nota; ad cuius motum reliquos pulſus com<lb></lb>

parando illorum exceſſus &amp;, defectus facilè obtinebis. <lb></lb>

Porro huiuſmodi regulam celeritatem &amp; tarditatem pul<lb></lb>

ſuum <expan abbr="abſq́">abſque</expan>; errore meti i, hac vià oſtendemus. </s>
            <s id="N145FB">Pulſus in <lb></lb>

ter ſe aut ſunt æquales, quorum eadem eſt velocitas mo<lb></lb>

tus, atque iſdem fiunt momentis: aut inæquales, cele


<pb xlink:href="062/01/122.jpg"></pb>ritate &amp; tarditate à ſe differentes, <expan abbr="quorũ">quorum</expan> inæqualia ſunt <lb></lb>

durationis momenta. </s>
            <s id="N1460C">Quia ergo motus perpendiculi <lb></lb>

eſt illorum menſura; erit quidem æqualium pulſuum æ<lb></lb>

qualis, inæqualium verò inæqualis in ea ratione, in quâ <lb></lb>

velocitas pulſuum. </s>
            <s id="N14615">At verò recurſus &amp; excurſus perpen<lb></lb>

diculi ex eadem productione inter ſe ſunt æquales: pro<lb></lb>

pterea quód perpendiculum ex quolibet puncto <expan abbr="eiuſdẽ">eiuſdem</expan> <lb></lb>

circuli æquali tempore recurrit in ſuam ſtationem per <lb></lb>

Prop: 24. ſunt autem excurſus <expan abbr="quoq́">quoque</expan>; inter ſe æquales per <lb></lb>

Prop: 25. excurſus ergo &amp; recurſus in unà circulatione <lb></lb>

ſimul ſumpti ſunt æquales excurſibus &amp; recurſibus o<lb></lb>

mnium circulationum ſimul <expan abbr="quoq́">quoque</expan>; ſumptis: &amp; quia uni <lb></lb>

æqualium pulſuum circulatio aſſumpta eſt æqualis, e<lb></lb>

runt reliquæ circulationes reliquis pulſibus æquales. <lb></lb>

Motus ergo perpendiculi ex eádem productione fili <lb></lb>

metitur pulſus inter ſe æquales. </s>
            <s id="N1463A">Quia verò motus per<lb></lb>

pendiculi per arcus ſimiles inæqualium circulorum ra<lb></lb>

tionem habent ad ſe quam ſinus illorum arcuum, hoc eſt <lb></lb>

lineæ ſubtenſæ arcus dupli, per Prop: 25. ac proinde <lb></lb>

quam habent motus per diametrum illorum circulo<lb></lb>

rum per Prop: 15. motus autem per diametrum ſe habent <lb></lb>

ut quadrata temporum per Prop: 12. </s>
            <s id="N14649">Si ſumatur radix <lb></lb>

quadrata illius proportionis, quam habent diametri ad <lb></lb>

ſe, erunt in eadem ratione tempora motus, in quà radices <lb></lb>

quadratæ: ut ſi diameter maioris circuli ad diametrum


<pb xlink:href="062/01/123.jpg"></pb>minoris circuli ſit quadrupla, huius radix quadrata, duo, <lb></lb>

dabit tempus in ratione duplá: ſi ergo motus per dia<lb></lb>

metrum minoris circuli ſit unius minuti, erit motus ma<lb></lb>

ioris diametri duorum minutorum. </s>
            <s id="N1465C">Sunt autem pro<lb></lb>

ductiones fili ſemidiametri illorum circulorum, in qui<lb></lb>

bus perpendiculum mouetur, æquales diuiſionum in<lb></lb>

teruallis, quæ globulus in productione fili percurrit: ea<lb></lb>

dem ergo proportio interualli, quæ motus illorum cir<lb></lb>

culorum. </s>
            <s id="N14669">Quia ergo motus inæqualium circulorum <lb></lb>

metiuntur pulſus inæquales, eoſdem metientur diuiſio<lb></lb>

num interualla: ac proinde regulam conſtruximus ad <lb></lb>

velocitatem &amp; tarditatem pulſuum <expan abbr="abſq;">abſque</expan> errore metien<lb></lb>

dam, quod erat faciendum. </s>
          </p>
        </subchap1>
      </chap>
      <chap id="N14678">
        <p id="N14679" type="main">
          <s id="N1467B"><emph type="center"></emph>Parergon.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N14682" type="main">
          <s id="N14684"><emph type="center"></emph><emph type="italics"></emph>Problema.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
        </p>
        <p id="N1468F" type="main">
          <s id="N14691"><emph type="italics"></emph>Horologium conſtruere, quod ſuo motu tempus numeret diuiſum <lb></lb>

in partes minores, quàm tertias unius ſecundi.<emph.end type="italics"></emph.end></s>
        </p>
        <p id="N1469A" type="main">
          <s id="N1469C">QVanti uſus &amp; utilitatis ſit tempus in quàm minimas <lb></lb>

partes diuiſum poſſe numerare, <expan abbr="norũt">norunt</expan> Aſtronomi, <lb></lb>

&amp; ex conatibus Tychonis Brahe ſatis conſtat; qui ad hu<lb></lb>

iuſmodi horologia fabricanda nihil intentatum reliquit: <lb></lb>

quam uis huius votum non niſi ad ſecunda numeranda


<pb xlink:href="062/01/124.jpg"></pb>le extendit. </s>
          <s id="N146AF">Aliquid ampliùs damus: &amp; non modó ſe<lb></lb>

cunda, verùm etiam huius triente minorem partem nu<lb></lb>

merabimus. </s>
          <s id="N146B6">Horologium autem hoc nullis rotulis cir<lb></lb>

cumagitur, nullis ponderibus libratur; verùm ſuâ nati<lb></lb>

uâ grauitate, à quà nuſquam aberrat, ad normam præ<lb></lb>

ſcriptam agitatur: illud inquam idem, quod ad celerita<lb></lb>

tem &amp; tarditatem pulſuum metiendam paulo ante con<lb></lb>

ſtruximus. </s>
          <s id="N146C3">Huius enim pondus à filo pendulum ſuo <lb></lb>

motu tempus in quotlibet partes diuiſum numerabit. <lb></lb>

Quòd autem hic motus minor eſſe poſsit, quâm tertia <lb></lb>

pars unius ſecundi, ita oſten demus: agitationes arteriæ, <lb></lb>

cuiuſmodi in me ipſo numeraui, ſpatio unius horæ fi<lb></lb>

unt 4850. motus autem perpendiculi his æquales fiunt â <lb></lb>

productione fili maiori quàm digitorum 5. </s>
          <s id="N146D2">Quia ergo <lb></lb>

motus circulorum ſunt in ratione ſuorum temporum, <lb></lb>

quam habent diametri ad ſe duplicatam, per Prop: 28. ſi <lb></lb>

ſumatur pars nona huius productionis pro ſemidiame<lb></lb>

tro circuli, erit hic motus triplo velocior illo, ac proinde <lb></lb>

huius recurſus ſpatio horæ unius 14550 multò plures, <lb></lb>

quàm 10800 partes tertiæ unius ſecundi. </s>
          <s id="N146E1">Et quia hic mo<lb></lb>

tus bifariam ſecari poteſt in excurſum &amp; recurſum, fient <lb></lb>

ſanè ſpatio unius horæ partes 29100. </s>
          <s id="N146E8">Horologium ergò <lb></lb>

conſtruximus, quod ſuo motu tempus numerat diuiſum <lb></lb>

in partes minores quàm tertias unius ſecundi. </s>
          <s id="N146EF">Quia ta<lb></lb>

men hic motus velociſsimus ob paruitatem circelli mi-


<pb xlink:href="062/01/125.jpg"></pb>nùs eſt diuturnus, ſufficiet filum producere, <expan abbr="quouſq́">quouſque</expan>; mo<lb></lb>

tus perpendiculi ſit æqualis uni ſecundo. </s>
          <s id="N146FE">Quod quidem <lb></lb>

hac ratione conſequemur: ſumatur <expan abbr="quæcunq́">quæcunque</expan>; produ<lb></lb>

ctio fili, aliquantó tamen longior, quò minùs citò à mo<lb></lb>

tu conquieſcat: <expan abbr="numerenturq́">numerenturque</expan>; huius excurſus per ſpati<lb></lb>

um unius horæ quadrantis, &amp; ſint Vg. 300. <expan abbr="eruntq́">eruntque</expan>; ſpa<lb></lb>

tio horæ unius 1200. </s>
          <s id="N14717">Quòd ſi ergò fiat ut quadratum <lb></lb>

temporis, nimirum trium ſecundorum, ideſt 9 ad 1, ita <lb></lb>

longitudo fili ad minorem, erit hujus motus æqualis <lb></lb>

uni ſecundo. <lb></lb>


<arrow.to.target n="fig38"></arrow.to.target></s>
        </p>
      </chap>
    </body>
    <back>
      <section>
        <pb xlink:href="062/01/126.jpg"></pb>
        <p id="N1472A" type="main">
          <s id="N1472C"><emph type="center"></emph>[Errata not transcribed.]<emph.end type="center"></emph.end></s>
        </p>
        <pb xlink:href="062/01/127.jpg"></pb>
        <p id="N14736" type="main">
          <s id="N14738"><emph type="center"></emph>PRAGÆ.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N1473F" type="main">
          <s id="N14741"><emph type="center"></emph>Typis Ioannis Bilinæ.<emph.end type="center"></emph.end></s>
        </p>
        <p id="N14748" type="main">
          <s id="N1474A"><emph type="center"></emph><emph type="italics"></emph>Anno<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
        </p>
        <p id="N14755" type="main">
          <s id="N14757"><emph type="center"></emph><emph type="italics"></emph>M. DC. XXXIX:<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s>
        </p>
        <pb xlink:href="062/01/128.jpg"></pb>
        <pb xlink:href="062/01/129.jpg"></pb>
      </section>
    </back>
  </text>
</archimedes>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Thu, 02 May 2013 11:08:12 +0200
parents	22d6a63640c6
children