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="id002308">
                <pb pagenum="128" xlink:href="015/01/147.jpg"/>
              e k, & f a ad a e, ut ſuperficierum ipſa­
                <lb/>
                <figure id="id.015.01.147.1.jpg" xlink:href="015/01/147/1.jpg" number="141"/>
                <lb/>
              rum per primam ſexti Elementorum: at
                <lb/>
              per præcedentem maior eſt proportio
                <lb/>
              e d ad d f, quàm a f ad a e, duplicata igi­
                <lb/>
              tur maior eſt proportio e d ad eam, quę
                <lb/>
              poteſt ſuper f c ſuperficiem, quam f a ad
                <lb/>
              a e, igitur maior, quàm a k ad a b ex pri­
                <lb/>
              ma ſexti Elementorum: igitur per trige
                <lb/>
              ſimam quartam undecimi. </s>
              <s id="id002309">Parallelipe­
                <lb/>
              dum ex e d in a b maius eſt parallelipedo ex ea, quæ poteſt in f c ſu­
                <lb/>
              perficiem in ipſam ſuperficiem a k. </s>
              <s id="id002310">Si uerò diuiſio facta fuerit in g,
                <lb/>
              conſtat ex præcedenti, quod minor eſt proportio g e ad e d, quàm
                <lb/>
              ſit duplicata e a ad a d a g, eam igitur minor proportio eius lineæ,
                <lb/>
              quæ poteſt in g e ſuperficiem ad e d quam a b ad a h, igitur paralle­
                <lb/>
              lipedum ex e d in a b eſt maius parallelipedo ex ea, quæ poteſt g c
                <lb/>
              in a h cum ſit a b ad a h, ut dictum eſt, uelut a e ad a g.
                <lb/>
                <arrow.to.target n="marg456"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002311">
                <margin.target id="marg455"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002312">
                <margin.target id="marg456"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002313">Manifeſtum eſt autem, quòd tale corpus eſt æquale duplo cubi
                <lb/>
              lateris partis tertiæ quadratæ.</s>
            </p>
            <p type="main">
              <s id="id002314">Propoſitio centeſima trigeſima quinta.</s>
            </p>
            <p type="main">
              <s id="id002315">Si linea in duas partes, quarum una ſit alteri dupla, diuidatur
                <lb/>
              erit, quod fit ex tertia parte in quadratum reſidui parallelipedum
                <lb/>
              maius omni parallelipedo, quod ex diuiſione eiuſdem lineæ crea­
                <lb/>
              ri poſsit.</s>
            </p>
            <p type="main">
              <s id="id002316">
                <arrow.to.target n="marg457"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002317">
                <margin.target id="marg457"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002318">Sit a c dupla b c, & ſit quadratum ad ipſius a c, dico parallelipe­
                <lb/>
                <figure id="id.015.01.147.2.jpg" xlink:href="015/01/147/2.jpg" number="142"/>
                <lb/>
              dum ex b c in a d maius eſſe quouis alio ex
                <lb/>
              diuiſione lineæ a b ſimiliter creato. </s>
              <s id="id002319">Secetur
                <lb/>
              primo in e, & fiat quadratum a f, eritque per
                <lb/>
              uigeſimam quintam. </s>
              <s id="id002320">Huius proportio c b
                <lb/>
              ad b c maior duplicata a e ad a c, quare ma­
                <lb/>
              ior, quam a f ad a d per uigeſimam ſexti Ele
                <lb/>
              mentorum, igitur per trigeſimam quartam
                <lb/>
              undecimi, Parallelipedum ex b c in a d maius eſt parallelipedo e b
                <lb/>
              in a f, quod eſt demonſtrandum. </s>
              <s id="id002321">Si uerò diuiſio cadat in g, fiat qua­
                <lb/>
              dratum a h, et erit per uigeſimamtertiam huius proportio g c ad c b
                <lb/>
              minor, quam duplicata c a ad a g: igitur minor, quàm a d ad a h, igi­
                <lb/>
              tur per eandem parallelipedum ex c b in a d maius eſt parallelipe­
                <lb/>
              do ex g b in a h.</s>
            </p>
            <p type="main">
              <s id="id002322">
                <arrow.to.target n="marg458"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002323">
                <margin.target id="marg458"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002324">Ex hoc liquet quòd parallelipedum illud erit quadruplum cu­
                <lb/>
              bo minoris partis, & dimidium cubi maioris.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>