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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              <s id="id002474">
                <pb pagenum="140" xlink:href="015/01/159.jpg"/>
              fíunt ex æqualibus lineis: at corpus quod fit ex a b in d g æquale eſt
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              corporibus quæ fiunt ex a c, c b in ſuperficiem d g at cubus a c con­
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              tinet duo corpora quę fiunt & a c in d g & g f, igitur cubus a c ſupe­
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              rat productum ex a b in d g in producto ex a c in f g & ſuperatur ab
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              eo in producto ex b c in d g, ſuperabatur etiam, ut uiſum eſt, cubus
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              b c à producto b a in d b in producto b cin c f, igitur cubi a c c b ſu­
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              perantur à producto a b in ad in producto b c in c f & in d g, quare
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              in producto b c in f e: ſi quidem f e & f g ſunt æqualia ex ſuppoſito
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              ſuperant autem in producto ex c b in e f, igitur tantum eſt in in quo
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              ſuperantur quantum eſt id in quo ſuperant: ergo ſunt æqualia.</s>
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              C
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              o
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              m.</s>
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            <p type="main">
              <s id="id002476">Propoſitio centeſima quadrageſima ſeptima.</s>
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            <p type="main">
              <s id="id002477">Propoſita linea diuiſa duas ei lineas adijcere, ut proportio addita­
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              rum ſingularum & partium ſimul iunctarum ad additas ſit mutua.
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              C
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              ^{m}.</s>
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              <s id="id002479">Sit linea a b diuiſa in c uolo eius
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                <figure id="id.015.01.159.1.jpg" xlink:href="015/01/159/1.jpg" number="158"/>
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              partibus addere lineas, ut propoſi­</s>
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              tum eſt, ſtatuo mediam c d inter a e &
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              c b quæ ſit c d, & facio ut c d ad c a ita
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              c a ad a e, & ut d c ad c b ita c b ad b f, quia ergo d e media eſt inter
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              a c & c b, & ut ea ad a cita d c a c b ad c f erunt omnes in continua
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                <arrow.to.target n="marg485"/>
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              proportione, quare proportio e c ad c a ut c f ad b f & e c ad ea ut
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              c f ad c b quod eſt propoſitum.</s>
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            <p type="margin">
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              P
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              er
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              13.
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              ſex
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              ti
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              E
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              lem.
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              </s>
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            <p type="margin">
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              er
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              11.
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              ſex
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              ti
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              E
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              lement.
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              </s>
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            <p type="margin">
              <s id="id002483">
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              P
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              er
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              11.
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                <emph type="italics"/>
              quinti
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              E
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              lem.
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              </s>
            </p>
            <p type="margin">
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              P
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              er
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              quinti
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              E
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              lem.
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              </s>
            </p>
            <p type="main">
              <s id="id002485">Propoſitio centeſima quadrageſima octaua.</s>
            </p>
            <p type="main">
              <s id="id002486">Propoſitis tribus lineis primam ſic diuidere, ut adiectis duabus
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              alijs lineis ſecundum rationem mutuam ſingularum ſingulis ag­
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              gregatum ex una adiectarum & parte ad aggregatum ex alia parte
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              & adiecta ſe habeat, ut ſecunda ad tertiam.
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                <arrow.to.target n="marg486"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002487">
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              C
                <emph type="italics"/>
              o
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              m.</s>
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            <p type="main">
              <s id="id002488">Sit a, b, c, d, propoſitæ lineę,
                <lb/>
                <figure id="id.015.01.159.2.jpg" xlink:href="015/01/159/2.jpg" number="159"/>
                <lb/>
              uolo diuidere a b ita in e ut
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              ſumpta ſecundum proportio­
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              nem alicuius quantitatis, puta
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              g ad a e ſic b f ad e b & ut g ad
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              e b ſic g a ad a e ut ſit propor­
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              tio g e ad e f ut c ad d. </s>
              <s id="id002489">Sint ergo
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              omnia
                <expan abbr="cõſtituta">conſtituta</expan>
              & ſit g rectan­
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              gulum ex a e in e b, cum ergo
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              g a contineat a e ut g continet e b, g autem continet e b ſecundum
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              a e, igitur g a continet a e ſecundum a c, ergo ex diffinitione qua­</s>
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            <p type="main">
              <s id="id002490">
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              drati a g eſt quadratum a e. </s>
              <s id="id002491">Pari ratione b f eſt quadratum b e. </s>
              <s id="id002492">pro­
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              portio igitur g e ad e f cum ſit ut c ad e ex ſuppoſito erit ut ipſi pro­
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              portioni addamus, & detrahamus ex duplo a b & dimidium reſi­
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              dui ducamus in ſe, & addamus aggregato quadrati a b cum ipſa </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>