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="id000201">
                <pb pagenum="8" xlink:href="015/01/027.jpg"/>
              rit conſtituta: conſurgent trecenti ſexaginta modi productionis
                <lb/>
              proportionis.</s>
            </p>
            <p type="main">
              <s id="id000202">
                <arrow.to.target n="marg19"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000203">
                <margin.target id="marg19"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000204">Hęc propoſitio ut præcedens &
                <expan abbr="ſequẽtes">ſequentes</expan>
              tres ab Alchindo ſum­
                <lb/>
              ptæ ſunt, & ab eo demonſtrantur. </s>
              <s id="id000205">Sit ergo proportio a ad b, pro­
                <lb/>
                <arrow.to.target n="table2"/>
                <lb/>
                <figure id="id.015.01.027.1.jpg" xlink:href="015/01/027/1.jpg" number="7"/>
              ducta ex proportione c ad d & e ad f, conſtat
                <lb/>
              quòd cum ſint ſex quantitates, quòd fieri pote­
                <lb/>
              runt quindecim coniugationes, quas poſui à la­
                <lb/>
              tere facilitatis gratia, quibus reſpondent totidem
                <lb/>
                <arrow.to.target n="table3"/>
                <lb/>
              conuerſæ: erunt ergo triginta. </s>
              <s id="id000206">Singulæ autem ha
                <lb/>
              rum produci poſſunt duodecim modis: ductis
                <lb/>
                <figure id="id.015.01.027.2.jpg" xlink:href="015/01/027/2.jpg" number="8"/>
              duodecim in triginta, fiunt trecenti ſexaginta mo
                <lb/>
              di. </s>
              <s id="id000207">Et hoc eſt clarum perſe, modo
                <expan abbr="demõſtremus">demonſtremus</expan>
              ,
                <lb/>
              quod ſinguli horum modorum poſsint produ­
                <lb/>
              ci duodecim modis, & capiamus ab primam quę
                <lb/>
              poteſt produci ex c d & e f: Item ambabus con­
                <lb/>
              uerſis d c & fe: & rurſus altera recta altera con­
                <lb/>
              uerſa: & hoc bifariam c d & f e, & d c & e f, ſunt er­
                <lb/>
              go iam quatuor modi. </s>
              <s id="id000208">Totidem ex c e & d f, toti­
                <lb/>
              demque ex c f & d e, igitur erunt duodecim mo­
                <lb/>
              di, quibus produci poſſe intelligitur propor­
                <lb/>
              tio a ad b.</s>
            </p>
            <table>
              <table.target id="table2"/>
              <row>
                <cell>a</cell>
                <cell>b</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
              <row>
                <cell>c</cell>
                <cell>d</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
              <row>
                <cell>e</cell>
                <cell>f</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
            </table>
            <table>
              <table.target id="table3"/>
              <row>
                <cell>a b</cell>
                <cell>b a</cell>
              </row>
              <row>
                <cell>a c</cell>
                <cell>c a</cell>
              </row>
              <row>
                <cell>a d</cell>
                <cell>d a</cell>
              </row>
              <row>
                <cell>a e</cell>
                <cell>e a</cell>
              </row>
              <row>
                <cell>a f</cell>
                <cell>f a</cell>
              </row>
              <row>
                <cell>b c</cell>
                <cell>c b</cell>
              </row>
              <row>
                <cell>b d</cell>
                <cell>d b</cell>
              </row>
              <row>
                <cell>b e</cell>
                <cell>e b</cell>
              </row>
              <row>
                <cell>b f</cell>
                <cell>f b</cell>
              </row>
              <row>
                <cell>c d</cell>
                <cell>d c</cell>
              </row>
              <row>
                <cell>c e</cell>
                <cell>e c</cell>
              </row>
              <row>
                <cell>c f</cell>
                <cell>f c</cell>
              </row>
              <row>
                <cell>d e</cell>
                <cell>e d</cell>
              </row>
              <row>
                <cell>d f</cell>
                <cell>f d</cell>
              </row>
              <row>
                <cell>e f</cell>
                <cell>f e</cell>
              </row>
              <row>
                <cell>direc.</cell>
                <cell>conuer.</cell>
              </row>
            </table>
            <p type="main">
              <s id="id000209">Propoſitio quarta.</s>
            </p>
            <p type="main">
              <s id="id000210">Si fuerit proportio primi ad ſecundum produ­
                <lb/>
              cta ex proportionibus tertij ad quartum, & quin
                <lb/>
              ti ad ſextum, producetur etiam ex proportione
                <lb/>
              tertij ad ſextum, & quinti ad quartum.</s>
            </p>
            <p type="main">
              <s id="id000211">Sit proportio a b producta ex proportioni­
                <lb/>
                <arrow.to.target n="table4"/>
                <lb/>
                <figure id="id.015.01.027.3.jpg" xlink:href="015/01/027/3.jpg" number="9"/>
              bus c ad d, & e ad f, dico quod etiam erit produ­</s>
            </p>
            <table>
              <table.target id="table4"/>
              <row>
                <cell>a</cell>
                <cell>b</cell>
                <cell/>
              </row>
              <row>
                <cell>c</cell>
                <cell>e</cell>
                <cell>g</cell>
              </row>
              <row>
                <cell>d</cell>
                <cell>f</cell>
                <cell>h</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
                <cell>---</cell>
              </row>
              <row>
                <cell>c</cell>
                <cell>e</cell>
                <cell>g</cell>
              </row>
              <row>
                <cell>f</cell>
                <cell>d</cell>
                <cell>h</cell>
              </row>
            </table>
            <p type="main">
              <s id="id000212">
                <arrow.to.target n="marg20"/>
                <lb/>
              cta ex proportionibus c ad f, & e ad d, diſponan­
                <lb/>
              tur ut in figura & fiat ex c in e g, & ex d in fh, ergo
                <lb/>
                <arrow.to.target n="marg21"/>
                <lb/>
              per primam harum g ad h ut a ad b, ſed per præ­
                <lb/>
              ſuppoſita in ſecunda productione etiam prode­
                <lb/>
              unt g & h, igitur per primam propoſitionem ha­
                <lb/>
              rum a ad b proportio producitur ex proportionibus c ad f tertiæ
                <lb/>
              ſcilicet ad ſextam, & e ad d quintę ad quartam, quod fuit
                <expan abbr="propoſitũ">propoſitum</expan>
              .</s>
            </p>
            <p type="margin">
              <s id="id000213">
                <margin.target id="marg20"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              petit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000214">
                <margin.target id="marg21"/>
              I
                <emph type="italics"/>
              n
                <emph.end type="italics"/>
              13.
                <emph type="italics"/>
              petit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000215">Propoſitio quinta.</s>
            </p>
            <p type="main">
              <s id="id000216">Si fuerit proportio primi ad ſecundum producta ex proportio­
                <lb/>
              ne tertij ad quartum, & quinta ad ſextum: erit proportio tertij ad
                <lb/>
              ſextum producta ex proportionibus primi ad ſecundum, & quar­
                <lb/>
              ti ad quintum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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