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="28" xlink:href="015/01/047.jpg"/>
            <p type="head">
              <s id="id000537">SCHOLIVM PRIMVM.</s>
            </p>
            <p type="main">
              <s id="id000538">Ne tamen ſine exemplo intelligas hanc duplicatam rationem,
                <lb/>
              proponatur c raritas quatuor, d unum, a pondus duodecim libra­
                <lb/>
                <figure id="id.015.01.047.1.jpg" xlink:href="015/01/047/1.jpg" number="40"/>
                <lb/>
              rum, tunc c reſiſtit ſolum ex quarta parte, & effi­
                <lb/>
              cit a quadruplo maioris actionis, ſcilicet ut qua­
                <lb/>
              draginta octo, tota igitur proportio, qua mo­
                <lb/>
              uebitur a in c, erit centum nonaginta duorum, & hoc diuidemus
                <lb/>
              per d, quod eſt unum, exibit
                <expan abbr="põdus">pondus</expan>
              b centum nonaginta duo. </s>
              <s id="id000539">Pro­
                <lb/>
              portio igitur b ad a eſt ſex de cupla, & hæc eſt duplicata quadruplæ
                <lb/>
              raritatis c ad raritatem d.</s>
            </p>
            <p type="main">
              <s id="id000540">Quòd ſi quis neget tantundem augere c actionem a, quanto mi­
                <lb/>
              nus reſiſtit, ſed aut magis aut minus, & ſit proportio b ad a dupli­
                <lb/>
              cata ipſi f, dico feſſe proportionem c ad d, nam proportio b ad a
                <lb/>
              eſt uelut actionis c ad d per decimam ſextam ſexti Elementorum,
                <lb/>
              ergo ex auxilio c in proportionem a ad c fit proportio b ad a, ſed ex
                <lb/>
              fin ſe fit proportio b ad a ex diffinitione proportionis duplicatæ.
                <lb/>
              </s>
              <s id="id000541">Sed ex duabus proportionibus a ad c, & actionis ex c ad a produ­
                <lb/>
              citur proportio b ad a, igitur per
                <expan abbr="decimamſeptimã">decimam ſeptimam</expan>
              ſexti Elemento­
                <lb/>
              rum proportio c ad d eſt media inter proportiones a ad c, & actio­
                <lb/>
              nis a in c, quare æqualis f, igitur proportio b ad a duplicata ei, quæ
                <lb/>
              eſt c ad d quod erat demonſtrandum.</s>
            </p>
            <p type="head">
              <s id="id000542">SCHOLIVM SECVNDVM.</s>
            </p>
            <p type="main">
              <s id="id000543">Si autem media fuerint diuerſarum rationum, ut aqua, & aër non
                <lb/>
              demonſtrat argumentum, quia pondera inter ſe non ſeruant ratio­
                <lb/>
              nem. </s>
              <s id="id000544">Nam lignum centum librarum ex ſalicis arbore, non magis
                <lb/>
              deſcendit, quàm lignum libræ unius. </s>
              <s id="id000545">Ideò nec in comparatione ad
                <lb/>
              medium aëris.</s>
            </p>
            <p type="main">
              <s id="id000546">Propoſitio trigeſima quarta.</s>
            </p>
            <p type="main">
              <s id="id000547">Proportio corporis cubi ad ſuam ſuperficiem quadratam, eſt ue­
                <lb/>
              lut eiuſdem ſuperficiei ad latus, eiuſdem uerò ad monadem.</s>
            </p>
            <p type="main">
              <s id="id000548">
                <arrow.to.target n="marg89"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000549">
                <margin.target id="marg89"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000550">Sit cubus a b c eius quadrata, ſuperficies a
                <lb/>
                <figure id="id.015.01.047.2.jpg" xlink:href="015/01/047/2.jpg" number="41"/>
                <lb/>
              c, latus a b, monas d, dico eas eſſe inuicem
                <lb/>
              analogas. </s>
              <s id="id000551">Quia enim proportio a b c ad a c
                <lb/>
              eſt, ut quoties aſſumitur a c in a b c, & toties
                <lb/>
              etiam aſſumitur a b in a c ex diffinitione Eucli </s>
            </p>
            <p type="main">
              <s id="id000552">
                <arrow.to.target n="marg90"/>
                <lb/>
              dis ſecundo Elementorum, ſi ergo monas eſt
                <lb/>
              in continua proportione, habeo intentum: ſi
                <lb/>
              non ponatur e media inter a e & d, erit ergo
                <lb/>
              per decimam noni Elementorum elatus a c,
                <lb/>
              ergo æqualis a b, igitur cum a c, e & d ſint analogæ, erunt & a b c,
                <lb/>
              a b, & d analogæ, quod fuit demonſtrandum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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