Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="26" xlink:href="015/01/045.jpg"/>
            <p type="main">
              <s id="id000497">
                <arrow.to.target n="marg80"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000498">
                <margin.target id="marg80"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id000499">Motus uoluntarius non habet, quòd fatiget, & ſumma perfectio
                <lb/>
              eſt æqualitas, & natura quæ mouet non debilitatur, igitur perpe­
                <lb/>
              tuo perſeuerat æqualis. </s>
              <s id="id000500">neque enim eſt, ut dixi, per medium corpus.
                <lb/>
              </s>
              <s id="id000501">Naturalis quoque, & uiolentus cum ratione proportionis mouentis
                <lb/>
              ſupra mobile perſe non uarientur, & ab ęquali proportione ęqua­
                <lb/>
              lis uelo citas proueniat, igitur natura tales motus ſunt ęquales, nam
                <lb/>
              in utroque mouens, mouet ſecundum ultimam ſuam uim.</s>
            </p>
            <p type="main">
              <s id="id000502">Propoſitio trigeſima.</s>
            </p>
            <p type="main">
              <s id="id000503">In omni corpore mobili in medio, partes medij reſiſtunt obuiæ,
                <lb/>
              aliæ impellunt.</s>
            </p>
            <p type="main">
              <s id="id000504">
                <arrow.to.target n="marg81"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000505">
                <margin.target id="marg81"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000506">Sit mobile a cui partes ſubiaceant directæ b, & ſit graue. </s>
              <s id="id000507">Et pa­
                <lb/>
              tet ne diuidatur b reſiſtere, cum autem ſuperauerit, partes b deſcen­
                <lb/>
              dunt ante a, & trahunt partes c & d adhęrentes ſecum, atque ita e c d f
                <lb/>
                <figure id="id.015.01.045.1.jpg" xlink:href="015/01/045/1.jpg" number="36"/>
                <lb/>
              adiuuant ad deſcenſum partes etiam laterales
                <lb/>
              g & h cum a tranſit in b, ne detur uacuum, tran­
                <lb/>
              ſeunt in k uelo ci motu, ergo propellunt a maio
                <lb/>
              re impetu inferius.</s>
            </p>
            <p type="main">
              <s id="id000508">
                <arrow.to.target n="marg82"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000509">
                <margin.target id="marg82"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000510">Ex quo patet, quod in omni motu naturali,
                <lb/>
              uel uiolento fit augumentum uelocitatis ab initio ſaltem uſque
                <lb/>
              ad aliquid.</s>
            </p>
            <p type="main">
              <s id="id000511">
                <arrow.to.target n="marg83"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000512">
                <margin.target id="marg83"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000513">Et ideò etiam bellicæ machinæ cuiuſcunque generis certam exi­
                <lb/>
              gunt diſtantiam, ut uiolentius feriant.</s>
            </p>
            <p type="main">
              <s id="id000514">Propoſitio trigeſima prima.</s>
            </p>
            <p type="main">
              <s id="id000515">Omnis motus naturalis in æquali medio ualidior eſt in fine,
                <lb/>
              quàm in principio: uiolentus contrà.</s>
            </p>
            <p type="main">
              <s id="id000516">
                <arrow.to.target n="marg84"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000517">
                <margin.target id="marg84"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000518">Cùm enim ex præcedenti augeantur ſemper ob medium, & cau­
                <lb/>
              ſa, quæ mouet, ſit perpetua, & à principio æterno, quod per dictæ
                <lb/>
              æqualiter mouet, igitur motus ille fiet uelocior in fine quàm in alia
                <lb/>
              parte temporis. </s>
              <s id="id000519">In uiolento autem, cùm perueniat ad finem deſinit </s>
            </p>
            <p type="main">
              <s id="id000520">
                <arrow.to.target n="marg85"/>
                <lb/>
              uis illa neceſſariò, quæ mouet, & ſuperatur à ui naturali, quæ mo­
                <lb/>
              uet in contrarium, igitur antequam ceſſet motus fiet tardiſsimus
                <lb/>
              in fine.</s>
            </p>
            <p type="margin">
              <s id="id000521">
                <margin.target id="marg85"/>
              29. P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000522">Ex quo patet, quòd motus quadrifariam miſti dicuntur, aut ſpe­
                <lb/>
                <arrow.to.target n="marg86"/>
                <lb/>
              cie, ut cùm quis iacit lapidem è turri: uel ex occulto naturali, & uio­
                <lb/>
              lento manifeſto: uelut cùm quis iacit lapidem, & deſcendit poſt mo
                <lb/>
                <figure id="id.015.01.045.2.jpg" xlink:href="015/01/045/2.jpg" number="37"/>
                <lb/>
              dum ex b in c motu utroque manifeſto, ſed ex a
                <lb/>
              in b motu uiolento manifeſto, & naturali oc­
                <lb/>
              culto: uel ratione medij, & hoc modo omnis
                <lb/>
              motus naturalis etiam non ſolum uiolentus eſt
                <lb/>
              miſtus ex proportione uirtutis mouentis, cum motu medij, ad me­
                <lb/>
              dium ipſum, uel ſi uiolentus ſit ex proportione uirtutis mouentis, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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