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="256" xlink:href="015/01/275.jpg"/>
            <p type="margin">
              <s id="id004383">
                <margin.target id="marg883"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id004384">Propoſitio ducenteſima uigeſima tertia.</s>
            </p>
            <p type="main">
              <s id="id004385">Quantitates quæ actu æquales eſſe non poſſunt, in nulla pro­
                <lb/>
              portione actu eſſe poſſunt.
                <lb/>
                <arrow.to.target n="marg884"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004386">
                <margin.target id="marg884"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004387">Sint duæ quantitates quæ æquales eſſe non poſsint, ut in priore
                <lb/>
              exemplo a & b, dico quod non poſſunt eſſe in aliqua proportione
                <lb/>
              in actu, aliter ſint in proportione c, & ducatur cin b, fiat d, erunt er­
                <lb/>
              go d & a æquales, quod eſt contra ſuppoſitum, nam ſupponitur
                <lb/>
              quod nulla quantitas ex genere b ſit æqualis a, ſed d eſt ex genere </s>
            </p>
            <p type="main">
              <s id="id004388">
                <arrow.to.target n="marg885"/>
                <lb/>
              b & æquale a, & ideo ſuppoſitum non manet, igitur a & b non ſunt
                <lb/>
              in aliqua proportione in actu.</s>
            </p>
            <p type="margin">
              <s id="id004389">
                <margin.target id="marg885"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              9.
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004390">Propoſitio ducenteſima uigeſima quarta.</s>
            </p>
            <p type="main">
              <s id="id004391">Neque temporis totius ut imaginamur ipſum eſſe infinitum, neque
                <lb/>
              æui uitarum proportio ulla eſt ad tempus quod poteſtate eſt, ut po
                <lb/>
              tè diem uel menſem.
                <lb/>
                <arrow.to.target n="marg886"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004392">
                <margin.target id="marg886"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id004393">Tempus ipſum ut
                <expan abbr="infinitũ">infinitum</expan>
              eſt, aut in actu eſt, aut refert quippiam
                <lb/>
              in actu, pars autem temporis ſolùm eſt poteſtate, quia nullum tem­
                <lb/>
              pus in actu eſt, neque annus, neque menſis, neque dies, neque hora aut mo­
                <lb/>
              mentum, ſed ſi totum tempus non eſſet actu, nihil eſſet actu, neque to
                <lb/>
              tum neque partes. </s>
              <s id="id004394">Igitur
                <expan abbr="totũ">totum</expan>
              tempus, uel aliquid loco eius eſt actu,
                <lb/>
              partes autem poteſtate, ſed ut uiſum proportio infiniti nulla eſt, &
                <lb/>
              ad rem quæ actu non eſt, igitur tempus nullam habet proportio­
                <lb/>
              nem ad annos, neque menſes uel dies. </s>
              <s id="id004395">Quare qui dicunt, quod mille
                <lb/>
              anni ſunt unus dies, in philoſophia errant, ſecus apud Apoſtolum,
                <lb/>
              ubi de diuinitate agitur. </s>
              <s id="id004396">Ergo anni ſunt
                <expan abbr="longũ">longum</expan>
              tempus, & dies bre­
                <lb/>
              ue, quia dicuntur in comparatione inter ſe, & non ſecundum pro­
                <lb/>
              portionem ad infinitum. </s>
              <s id="id004397">Quia ſit infinitum a, & d uæ quantitates b
                <lb/>
              maior, & c minor, uel ergo proportio a ad b c, eſt una uel diuerſa, ſi </s>
            </p>
            <p type="main">
              <s id="id004398">
                <arrow.to.target n="marg887"/>
                <lb/>
              una, ergo b c erunt æquales, ſi maior eſt ad c quam ad b, ergo infi­
                <lb/>
              nitum eſt maius infinito, ergo non eſt infinitum, quod eſt con­
                <lb/>
                <arrow.to.target n="marg888"/>
                <lb/>
              tra petita.</s>
            </p>
            <p type="margin">
              <s id="id004399">
                <margin.target id="marg887"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              9.
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004400">
                <margin.target id="marg888"/>
              4. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004401">Propoſitio ducenteſima uigeſima quinta.</s>
            </p>
            <p type="main">
              <s id="id004402">Proportio media non eſt ex ratione agentis ſed patientis.</s>
            </p>
            <figure id="id.015.01.275.1.jpg" xlink:href="015/01/275/1.jpg" number="281"/>
            <p type="main">
              <s id="id004403">Proponatur a quantitas, quę debeat mutari ab uir­
                <lb/>
                <arrow.to.target n="marg889"/>
                <lb/>
              tute quæ non fit in materia, & palam eſt quod non po
                <lb/>
              terit permutari in inſtanti, quia ſimul eſſet, & non eſſet
                <lb/>
              ergo repugnaret, neque etiam poteſt non eſſe, ut demonſtratum eſt
                <lb/>
              in Hyperchen, quia repugnant neceſſario & eſſentiæ Dei, neque mo­
                <lb/>
              uetur à certa proportione, quia b caret omni quantitate, ergo ni­
                <lb/>
                <arrow.to.target n="marg890"/>
                <lb/>
              hil oſtendit uim ipſius b eſſe finitam, quod ergo moueatur tardè ce</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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