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="id002292">
                <pb pagenum="127" xlink:href="015/01/146.jpg"/>
              g c dupla toti e a. </s>
              <s id="id002293">quare ut g c ad g d ut e a ad e b
                <expan abbr="permutãdo">permutando</expan>
              , & per
                <lb/>
              euerſam ut e a ad a b, ita g c ad c d, ut g c ad c d
                <expan abbr="cõponitur">componitur</expan>
              ex g e ad
                <lb/>
              f e, & f c ad c d, igitur e a ad c b componitur ex eiſdem. </s>
              <s id="id002294">Proportio
                <lb/>
              autem g c ad f c eſt minor, quam f c ad c d, igitur minor quàm du­
                <lb/>
              plicata f c ad c d. </s>
              <s id="id002295">conſtat uerò ex eiſdem, quod proportio c a ad a b
                <lb/>
              maior eſt duplicata g c ad f c.</s>
            </p>
            <p type="main">
              <s id="id002296">Propoſitio centeſima trigeſima tertia.</s>
            </p>
            <p type="main">
              <s id="id002297">Si fuerint duæ quantitates, quarum una alteri dupla ſit: minua­
                <lb/>
              tur à minore quædam
                <expan abbr="quãtitas">quantitas</expan>
              eademque maiori addatur, erit mino­
                <lb/>
              ris ad
                <expan abbr="reſiduũ">reſiduum</expan>
              maior proportio,
                <expan abbr="quã">quam</expan>
              aggregati ad
                <expan abbr="maiorẽ">maiorem</expan>
              duplicata.
                <lb/>
              </s>
              <s id="id002298">Si uerò minori addatur et à maiore detrahatur, erit aggregati ad mi
                <lb/>
              nore m minor proportio quàm maioris ad reſiduum duplicata.</s>
            </p>
            <p type="main">
              <s id="id002299">
                <arrow.to.target n="marg454"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002300">
                <margin.target id="marg454"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <figure id="id.015.01.146.1.jpg" xlink:href="015/01/146/1.jpg" number="139"/>
            <p type="main">
              <s id="id002301">Sit a b dupla c d, & addatur quæ­
                <lb/>
              dam ad b a, quę ſit a g, eadem detraha­
                <lb/>
              tur ex c d & ſit c h, dico, quod propor­
                <lb/>
              tio e d ad d h maior eſt, quam duplica­
                <lb/>
              ta g b ad a b, & rurſus ſi quædam ad c & minuatur ex a b utpotè
                <lb/>
              c f addatur c d, & a e minuatur ex a b, erit proportio f d ad c d mi­
                <lb/>
              nor duplicata a b ad g e. </s>
              <s id="id002302">
                <expan abbr="Primũ">Primum</expan>
              ſic reſecentur a n & k l æquales ſin­
                <lb/>
              gulæ c h, igitur a l dupla eſt e h & a b fuit dupla a d, c d igitur ut in
                <lb/>
              priore conſtitutioné præcedentis a b ad l b, ut c d ad h d & a b ad
                <lb/>
              b l maior, quam duplicata a b ad b k ut minor quàm k b ad b l. </s>
              <s id="id002303">hoc
                <lb/>
              enim demonſtratum eſt in fine, igitur c d ad h d maior, quàm du­
                <lb/>
              plicata a k ad k b, ſed a k ad k b maior eſt per uigeſimam tertiam, hu­
                <lb/>
              ius ſcilicet per demonſtrationem illius, quàm g b ad b a, igitur mul­
                <lb/>
              to maior c d ad d h, quàm duplicata g b ad b a, quod eſt primum.</s>
            </p>
            <p type="main">
              <s id="id002304">Secundum ſic per eadem, addito enim duplo f c ipſi
                <lb/>
                <figure id="id.015.01.146.2.jpg" xlink:href="015/01/146/2.jpg" number="140"/>
                <lb/>
              a b ut in ſecunda figura, & ſint a m, & m n erit f d ad c d,
                <lb/>
              ut n a ad a b, quare cum n a ad a b ſit minor duplicata per
                <lb/>
              præcedentem in b ad a b, & a b ad e b ſit maior, ut demon
                <lb/>
              ſtratum eſt in uigeſima tertia huius, quàm m b ad a b, erit
                <lb/>
              f d ad d c multo minor duplicata a b ad b e, quod eſt ſe­
                <lb/>
              cundum.</s>
            </p>
            <p type="main">
              <s id="id002305">Propoſitio centeſima trigeſima quarta.</s>
            </p>
            <p type="main">
              <s id="id002306">Si rectangula ſuperficies ſit cuius pars tertia quadrata ſit, corpus
                <lb/>
              quod ex latere quadratæ in reſiduum ſuperficiei conſtat maius eſt
                <lb/>
              quouis corpore ex eadem ſuperficies aliter diuiſa conſtituto.</s>
            </p>
            <p type="main">
              <s id="id002307">Sit rectangulum a c cuius tertia pars c e ſit quadrata, dico quod
                <lb/>
                <arrow.to.target n="marg455"/>
                <lb/>
              corpus, quod
                <expan abbr="cõſtat">conſtat</expan>
              ex e d in a b eſt maius omni corpore, quod fue
                <lb/>
              rit ex latere partis ſuperficiei a b in reliquam
                <expan abbr="partẽ">partem</expan>
              . </s>
              <s id="id002308">Si non diuidatur
                <lb/>
              uel ſupra uel infra, & primo in f erit
                <expan abbr="autẽ">autem</expan>
              proportio e d ad d f, ut e c ad </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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