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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        <body>
          <chap>
            <pb pagenum="140 [=139]" xlink:href="015/01/158.jpg"/>
            <p type="margin">
              <s id="id002451">
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              I
                <emph type="italics"/>
              d eſt per
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              eius demon­
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              ſtrationem.
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                <lb/>
              P
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              er
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              29.
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              un
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              decimi
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              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002452">Propoſitio centeſima quadrageſima quarta.</s>
            </p>
            <p type="main">
              <s id="id002453">Duplum cubi medietatis maius eſt aggregato corporum mutu­
                <lb/>
              orum cuiuslibet diuiſionis, quantum eſt, quod fit ex tota in quadra
                <lb/>
              tum differentiæ.
                <lb/>
                <arrow.to.target n="marg475"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002454">
                <margin.target id="marg475"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id002455">Sit a b diuiſa per æqualia in c, & per inæqua­
                <lb/>
              lia in d, dico, quòd duplum cubi a c eſt maius ag
                <lb/>
                <figure id="id.015.01.158.1.jpg" xlink:href="015/01/158/1.jpg" number="155"/>
                <lb/>
              gregato corporum ex a d in quadratum b d, & b d in quadratum
                <lb/>
              a cin eo quod fit ex a b in quadratum c d, nam per
                <expan abbr="præcedentẽ">præcedentem</expan>
              du­
                <lb/>
              plum cubi a c eſt æquale corpori ex a b in quadratum a c: aggrega­
                <lb/>
              tum quo que corporum ex a d in quadratum b d, & b d in quadra­
                <lb/>
              tum a d eſt ęquale ei, quod fit ex a b in
                <expan abbr="rectangulũ">rectangulum</expan>
              ex a d in d b. </s>
              <s id="id002456">
                <expan abbr="qua­dratũ">qua­
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                dratum</expan>
                <expan abbr="autẽ">autem</expan>
              a c eſt maius rectangulo a d in d b quadrato c d differen
                <lb/>
              tiæ, igitur duplum cubi a c excedit aggregatum
                <expan abbr="corporũ">corporum</expan>
                <expan abbr="mutuorũ">mutuorum</expan>
                <lb/>
              in corpore ex a b in quadratum c d differentię, quod eſt
                <expan abbr="propoſitũ">propoſitum</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id002457">
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              </s>
            </p>
            <p type="margin">
              <s id="id002458">
                <margin.target id="marg476"/>
              P
                <emph type="italics"/>
              er
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              5.
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              ſecun
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              di
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              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002459">Propoſitio centeſima quadrageſima quinta.</s>
            </p>
            <p type="main">
              <s id="id002460">Si line a in duas partes diuidatur quadrata ambarum partium
                <lb/>
              detracto eo quod fit ex una parte in alteram, ęqualia ſunt producto
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              unius in alteram cum quadrato differentiæ.</s>
            </p>
            <p type="main">
              <s id="id002461">
                <arrow.to.target n="marg477"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002462">
                <margin.target id="marg477"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002463">Sit linea a c diuiſa in b, & ſit differentia a b,
                <lb/>
              b c, b d, dico quod quadrata a b & b c detracto
                <lb/>
                <figure id="id.015.01.158.2.jpg" xlink:href="015/01/158/2.jpg" number="156"/>
                <lb/>
              eo quod fit ex a b in b c, æqualia ſunt producto a b in b c cum qua­
                <lb/>
              drato b d. </s>
              <s id="id002464">Quoniam. </s>
              <s id="id002465">n. </s>
              <s id="id002466">quadrata a b, b c æqualia quadratis a d d b
                <lb/>
              b c & productis ex a d in d b bis & quod fit ex a b in b c æquale eſt
                <lb/>
              ei quod fit ex a d in ſe cum eo quod fit ex a d in d b, quia a d eſt ęqua </s>
            </p>
            <p type="main">
              <s id="id002467">
                <arrow.to.target n="marg478"/>
                <lb/>
              lis b c ideo quadrata a b & b c detracto eo quod fit ex a b in b c ſunt
                <lb/>
              æqualia quadratis a d d b, & producto a d in d b ſemel: a c quadra­
                <lb/>
                <arrow.to.target n="marg479"/>
                <lb/>
              tum a d cum producto a d in d b eſt æquale producto a b in a d, &
                <lb/>
              ex conſequenti in b c, igitur reſiduum quadratorum a b & b c de­
                <lb/>
              tracto producti a b in b c eſt æquale a b in b c cum quadrato b d
                <lb/>
              quod fuit propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id002468">
                <margin.target id="marg478"/>
              P
                <emph type="italics"/>
              er
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              4.
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              ſecun
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              di
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              E
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              lem.
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              </s>
            </p>
            <p type="margin">
              <s id="id002469">
                <margin.target id="marg479"/>
              P
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              er
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              1.
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              ſecun
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              di
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              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002470">Propoſitio centeſima quadrageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id002471">Corpus quod fit ex linea diuiſa in ſuperficiem ęqualem quadra­
                <lb/>
              tis ambarum partium detracta ſuperficie unius partis in
                <expan abbr="alterã">alteram</expan>
              , eſt
                <lb/>
              æquale aggregato cuborum
                <expan abbr="ambarũ">ambarum</expan>
                <expan abbr="partiũ">partium</expan>
              .</s>
            </p>
            <figure id="id.015.01.158.3.jpg" xlink:href="015/01/158/3.jpg" number="157"/>
            <p type="main">
              <s id="id002472">Sic a b diuiſa in e quadrata partium e f &
                <lb/>
                <arrow.to.target n="marg480"/>
                <lb/>
              b d detrahatur ex e f, f g æqualis a d, dico cor
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              pus ex a b in ſuperficies b d, d g æquale eſ­
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              ſe cubis a c & c b pariter acceptis, quia. </s>
              <s id="id002473">n.
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              </s>
              <s id="id002474">ex a b in b d fiunt duo corpora cubus
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              b d & corpus ex a d in quadratum d b hoc
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              autem eſt æquale corpori ex b cin a d quia </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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