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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page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <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
                <lb/>
              corporibus quæ fiunt ex a c, c b in ſuperficiem d g at cubus a c con­
                <lb/>
              tinet duo corpora quę fiunt & a c in d g & g f, igitur cubus a c ſupe­
                <lb/>
              rat productum ex a b in d g in producto ex a c in f g & ſuperatur ab
                <lb/>
              eo in producto ex b c in d g, ſuperabatur etiam, ut uiſum eſt, cubus
                <lb/>
              b c à producto b a in d b in producto b cin c f, igitur cubi a c c b ſu­
                <lb/>
              perantur à producto a b in ad in producto b c in c f & in d g, quare
                <lb/>
              in producto b c in f e: ſi quidem f e & f g ſunt æqualia ex ſuppoſito
                <lb/>
              ſuperant autem in producto ex c b in e f, igitur tantum eſt in in quo
                <lb/>
              ſuperantur quantum eſt id in quo ſuperant: ergo ſunt æqualia.</s>
            </p>
            <p type="margin">
              <s id="id002475">
                <margin.target id="marg480"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id002476">Propoſitio centeſima quadrageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id002477">Propoſita linea diuiſa duas ei lineas adijcere, ut proportio addita­
                <lb/>
              rum ſingularum & partium ſimul iunctarum ad additas ſit mutua.
                <lb/>
                <arrow.to.target n="marg481"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002478">
                <margin.target id="marg481"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002479">Sit linea a b diuiſa in c uolo eius
                <lb/>
                <figure id="id.015.01.159.1.jpg" xlink:href="015/01/159/1.jpg" number="158"/>
                <lb/>
              partibus addere lineas, ut propoſi­</s>
            </p>
            <p type="main">
              <s id="id002480">
                <arrow.to.target n="marg482"/>
                <lb/>
              tum eſt, ſtatuo mediam c d inter a e &
                <lb/>
                <arrow.to.target n="marg483"/>
                <lb/>
              c b quæ ſit c d, & facio ut c d ad c a ita
                <lb/>
              c a ad a e, & ut d c ad c b ita c b ad b f, quia ergo d e media eſt inter
                <lb/>
                <arrow.to.target n="marg484"/>
                <lb/>
              a c & c b, & ut ea ad a cita d c a c b ad c f erunt omnes in continua
                <lb/>
                <arrow.to.target n="marg485"/>
                <lb/>
              proportione, quare proportio e c ad c a ut c f ad b f & e c ad ea ut
                <lb/>
              c f ad c b quod eſt propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id002481">
                <margin.target id="marg482"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              13.
                <emph type="italics"/>
              ſex
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002482">
                <margin.target id="marg483"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              ſex
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002483">
                <margin.target id="marg484"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <lb/>
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002484">
                <margin.target id="marg485"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              18.
                <lb/>
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </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
                <lb/>
              alijs lineis ſecundum rationem mutuam ſingularum ſingulis ag­
                <lb/>
              gregatum ex una adiectarum & parte ad aggregatum ex alia parte
                <lb/>
              & adiecta ſe habeat, ut ſecunda ad tertiam.
                <lb/>
                <arrow.to.target n="marg486"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002487">
                <margin.target id="marg486"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <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
                <lb/>
              ſumpta ſecundum proportio­
                <lb/>
              nem alicuius quantitatis, puta
                <lb/>
              g ad a e ſic b f ad e b & ut g ad
                <lb/>
              e b ſic g a ad a e ut ſit propor­
                <lb/>
              tio g e ad e f ut c ad d. </s>
              <s id="id002489">Sint ergo
                <lb/>
              omnia
                <expan abbr="cõſtituta">conſtituta</expan>
              & ſit g rectan­
                <lb/>
              gulum ex a e in e b, cum ergo
                <lb/>
              g a contineat a e ut g continet e b, g autem continet e b ſecundum
                <lb/>
              a e, igitur g a continet a e ſecundum a c, ergo ex diffinitione qua­</s>
            </p>
            <p type="main">
              <s id="id002490">
                <arrow.to.target n="marg487"/>
                <lb/>
              drati a g eſt quadratum a e. </s>
              <s id="id002491">Pari ratione b f eſt quadratum b e. </s>
              <s id="id002492">pro­
                <lb/>
              portio igitur g e ad e f cum ſit ut c ad e ex ſuppoſito erit ut ipſi pro­
                <lb/>
              portioni addamus, & detrahamus ex duplo a b & dimidium reſi­
                <lb/>
              dui ducamus in ſe, & addamus aggregato quadrati a b cum ipſa </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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