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>
            <p type="main">
              <s id="id000449">
                <pb pagenum="24" xlink:href="015/01/043.jpg"/>
                <figure id="id.015.01.043.1.jpg" xlink:href="015/01/043/1.jpg" number="35"/>
                <lb/>
              non naturalis. </s>
              <s id="id000450">nam ſi uiolentus eſſet, non
                <lb/>
              eſſet perpetuus. </s>
              <s id="id000451">Omnia ergo aſtra feruntur
                <lb/>
              circa centrum mundi. </s>
              <s id="id000452">Sit modo rota e f g, di
                <lb/>
              co e non moueri motu circulari nam linea
                <lb/>
              e c
                <expan abbr="lõgior">longior</expan>
              eſt g c, ergo recta mouetur ad cen
                <lb/>
              trum non circa centrum. </s>
              <s id="id000453">Indicio etiam id
                <lb/>
              eſt: quòd ſi in e ponatur fruſtum aliquod
                <lb/>
              inſigne plumbi in motu ad g per f deſcen­
                <lb/>
              det raptim: at dum ex g in e magna cum dif­
                <lb/>
              ficultate, igitur motus hic non eſt naturalis,
                <lb/>
              nec circularis. </s>
              <s id="id000454">nihil etiam hoc modo ſponte mouetur. </s>
              <s id="id000455">Sed cum non
                <lb/>
              moueatur per rectam naturaliter, nec æquidiſtans à centro per cir­
                <lb/>
              culum relinquitur, ut moueatur motu uiolento, aut miſto, ſed non
                <lb/>
              ex uoluntario, cum nullo modo moueatur æquidiſtans à centro,
                <lb/>
              ſed ſemper ab e lineæ ad centrum fiant breuiores, liquet eſſe mo­
                <lb/>
              tum uiolentum: aut miſtum ex naturali, & uiolento.</s>
            </p>
            <p type="main">
              <s id="id000456">Propoſitio uigeſima quinta.</s>
            </p>
            <p type="main">
              <s id="id000457">Tres ſunt motus omnino ſimplices naturalis, uoluntarius &
                <lb/>
              uiolentus.
                <lb/>
                <arrow.to.target n="marg77"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000458">
                <margin.target id="marg77"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000459">Tres ſunt modi, quibus poſſunt moueri in comparatione ad cen
                <lb/>
              trum ſcilicet uel recta cum centro, uel æquidiſtando à centro, uel
                <lb/>
              neutro modo, igitur tres motus. </s>
              <s id="id000460">Rurſus uel à principio interiore
                <lb/>
              non intelligente, & eſt naturalis, uel intelligente & eſt uoluntarius:
                <lb/>
              uel exteriore & eſt uiolentus. </s>
              <s id="id000461">Hæc autem diuiſio eſt ſolum propria
                <lb/>
              non prima. </s>
              <s id="id000462">Nam eſt uiolentus in recta ad centrum: ideo omnis, qui
                <lb/>
              non eſt in recta ad centrum, nec æquidiſtat, uiolentus eſt: non ta­
                <lb/>
              men omnis uiolentus eſt extra rectam. </s>
              <s id="id000463">Attractio autem, quæ fit ob
                <lb/>
              raritatem corporum, ſeu, ut dicunt, à uacuo, uiolenta eſt non natu­
                <lb/>
              ralis niſi ratione finis, non agentis. </s>
              <s id="id000464">Sunt enim quatuor genera mo­</s>
            </p>
            <p type="main">
              <s id="id000465">
                <arrow.to.target n="marg78"/>
                <lb/>
              tus uiolenti ab Ariſtotele poſita, uectio, tractio, pulſio, & uolutio:
                <lb/>
              quanquam his non opus ſit in demonſtratiua ſcientia. </s>
              <s id="id000466">
                <expan abbr="cõſtat">conſtat</expan>
              enim
                <lb/>
              uolutionem ex tractione, & pulſione apud illum conſiſtere.</s>
            </p>
            <p type="margin">
              <s id="id000467">
                <margin.target id="marg78"/>
              7. P
                <emph type="italics"/>
              hyſ.
                <lb/>
              cap.
                <emph.end type="italics"/>
              2.</s>
            </p>
            <p type="main">
              <s id="id000468">Propoſitio uigeſima.</s>
            </p>
            <p type="main">
              <s id="id000469">Motus ergo compoſiti quatuor neceſſariò ſunt ſpecies.</s>
            </p>
            <p type="main">
              <s id="id000470">Si tantum ſunt tres ſpecies ſimplicium, conſtat ratione arithme­
                <lb/>
              tica quatuor eſſe compoſitorum. </s>
              <s id="id000471">Diſquiramus ergo an ſint natura­
                <lb/>
              liter tot ſpecies, forſan enim repugnabit aliquis alicui. </s>
              <s id="id000472">Porrò uidea­
                <lb/>
              mus primò, quot ſint uiolentorum ſpecies: Prima erit cum non ſe­
                <lb/>
              cundum rectam lineam fuerit: nec à centro æquidiſtantem. </s>
              <s id="id000473">Secun­
                <lb/>
              da cum fuerit ſecundum rectam, ſed non ad centrum. </s>
              <s id="id000474">Tertia cum
                <lb/>
              fuerit in recta ad centrum, ſed contrario modo, uelut terræ ſurſum. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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