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="id003780">
                <pb pagenum="224" xlink:href="015/01/243.jpg"/>
              Quia ergo m eſt h
                <lb/>
              & e f,
                <expan abbr="igit̃">igitur</expan>
              cum n ſit
                <lb/>
              in linea e m, erit in
                <lb/>
              linea f h, ſed n eſt
                <lb/>
                <expan abbr="etiã">etiam</expan>
              in circulo a b,
                <lb/>
              igitur
                <expan abbr="cũ">cum</expan>
                <expan abbr="nullũ">nullum</expan>
              ſit
                <lb/>
                <expan abbr="punctũ">punctum</expan>
              aliud in li­
                <lb/>
              nea fh, et circulo g
                <lb/>
              q, <08> g eſt n
                <expan abbr="cõmu­nis">commu­
                  <lb/>
                nis</expan>
              ſectio, igitur n
                <lb/>
              peruenit in g. </s>
              <s id="id003781">Vi­
                <lb/>
              des ergo quod m
                <lb/>
                <figure id="id.015.01.243.1.jpg" xlink:href="015/01/243/1.jpg" number="237"/>
                <lb/>
              retroceſsit per angulum m g h, n autem anteceſsit per angulum n
                <lb/>
              g f, qui eſt æqualis angulo m g h. </s>
              <s id="id003782">Ex quo liquet cauſa dictorum, &
                <lb/>
              quod non intellexerunt quæſtionis fundamentum cum ferantur
                <lb/>
              ſingula puncta in una reuolutione æqualiter cum centro motu re­
                <lb/>
              cto: & motu circumuolutionis ſunt immobilia, quia tantum retro­
                <lb/>
              cedunt in una medietate, quantum procedunt in alia.</s>
            </p>
            <p type="margin">
              <s id="id003783">
                <margin.target id="marg710"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003784">Propoſitio centeſima nonageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id003785">Cur lances ad
                <expan abbr="locũ">locum</expan>
                <expan abbr="ſuũ">ſuum</expan>
                <expan abbr="ſuſpẽſi">ſuſpenſi</expan>
                <expan abbr="redeãt">redeant</expan>
                <expan abbr="impendẽtes">impendentes</expan>
                <expan abbr="nõ">non</expan>
              ,
                <expan abbr="demõſtrare">demonſtrare</expan>
              .
                <lb/>
                <arrow.to.target n="marg711"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003786">
                <margin.target id="marg711"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="main">
              <s id="id003787">Aliâs cum uiderem apud Ariſtotelem & eius expoſitores hoc </s>
            </p>
            <p type="main">
              <s id="id003788">
                <arrow.to.target n="marg712"/>
                <lb/>
              problema non ſum auſus, quia ex proprijs non mihi occurrebat
                <lb/>
              demonſtratio, rationem reddere, at confecta dialectica ſtatim appa
                <lb/>
              ruit modus. </s>
              <s id="id003789">Sit ergo libra a b appenſa ex trutina c d, & ſit per pon­
                <lb/>
                <figure id="id.015.01.243.2.jpg" xlink:href="015/01/243/2.jpg" number="238"/>
                <lb/>
              dus educta loco e f, & ſublato reuertitur
                <lb/>
              ad locum priorem: Et rurſus eadem ſi
                <lb/>
              immineat g d ſuſtentaculo
                <expan abbr="nõ">non</expan>
              mouetur:
                <lb/>
              igitur palam eſt quod in trutina d e gra­
                <lb/>
              uior eſt
                <expan abbr="quã">quam</expan>
              d f inſiſtens g d,
                <expan abbr="nõ">non</expan>
              eſt adeo
                <lb/>
              grauis, aut omnino non grauior. </s>
              <s id="id003790">Neque
                <lb/>
              poteſt id accidere quod in primo caſu
                <lb/>
              angulus e d c acutus, ſit in ſecundo obtu
                <lb/>
              ſus, nam ſi ob angulum e d c acutum
                <expan abbr="deſcẽdit">deſcendit</expan>
              in primo caſu e, in ſe­
                <lb/>
              cundo caſu deſcendet f, quia pariter f d g acutus eſt, & æqualis e d c,
                <lb/>
              hoc autem non contingit. </s>
              <s id="id003791">Mira ne dicam ſtultitia an audacia
                <expan abbr="eorũ">eorum</expan>
              ,
                <lb/>
              qui nihil intelligentes auſi ſunt, hæc pertractare, ſperantes in tot ſe­
                <lb/>
              culis nullum futurum, qui ignorantiam ſuam & impoſtura depre­
                <lb/>
              hendat, dicunt enim quod in primo caſu producta quadam recta
                <lb/>
              ad perpendiculum, & quæ ſit h k maiorem reddi d e quàm d f, neque
                <lb/>
              quomodo id fiat oſtendunt, & ſi (ut dixi) maior ſit
                <expan abbr="quã">quam</expan>
              d fin primo
                <lb/>
              caſu maior d f quam d e in
                <expan abbr="ſecũdo">ſecundo</expan>
              caſu: ergo ſi in primo caſu d e de­
                <lb/>
              ſcendit, in ſecundo deſcendet magis d f, at hoc non accidit ſed ſtat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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