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>
            <pb pagenum="9" xlink:href="015/01/028.jpg"/>
            <p type="main">
              <figure id="id.015.01.028.1.jpg" xlink:href="015/01/028/1.jpg" number="10"/>
              <s id="id000217">Sit proportio a ad b producta ex proportio­
                <lb/>
                <arrow.to.target n="marg22"/>
                <lb/>
                <arrow.to.target n="table5"/>
                <lb/>
              nibus c ad d, & e ad f, dico quod proportio c ad
                <lb/>
              f producitur ex proportione a ad b & d ad e. </s>
              <s id="id000218">In­
                <lb/>
              terponam d e inter c & f, eritque ex ſecunda pro­
                <lb/>
              poſitione repetita proportio c ad f producta ex
                <lb/>
              tribus proportionibus c ad d, d ad e, e ad f, ſed
                <lb/>
              proportiones c ad d, & e ad f producunt pro­
                <lb/>
                <figure id="id.015.01.028.2.jpg" xlink:href="015/01/028/2.jpg" number="11"/>
              portionem a ad b, igitur proportio c ad f produ
                <lb/>
              citur ex proportionibus a ad b, & e ad f.
                <lb/>
                <arrow.to.target n="table6"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000219">
                <margin.target id="marg22"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <table>
              <table.target id="table5"/>
              <row>
                <cell>a</cell>
                <cell>b</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
              <row>
                <cell>c</cell>
                <cell>e</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
              <row>
                <cell>d</cell>
                <cell>f</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
            </table>
            <table>
              <table.target id="table6"/>
              <row>
                <cell>c</cell>
              </row>
              <row>
                <cell>-----</cell>
              </row>
              <row>
                <cell>d</cell>
              </row>
              <row>
                <cell>-----</cell>
              </row>
              <row>
                <cell>e</cell>
              </row>
              <row>
                <cell>-----</cell>
              </row>
              <row>
                <cell>f</cell>
              </row>
              <row>
                <cell>-----</cell>
              </row>
            </table>
            <p type="main">
              <s id="id000220">Propoſitio ſexta.</s>
            </p>
            <p type="main">
              <s id="id000221">Ex trecentis ſexaginta modis producenda­
                <lb/>
              rum proportionum triginta ſex tantum eſſe ne­
                <lb/>
              ceſſarios.
                <lb/>
                <arrow.to.target n="table7"/>
              </s>
            </p>
            <table>
              <table.target id="table7"/>
              <row>
                <cell>c</cell>
                <cell>p</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
              <row>
                <cell>a</cell>
                <cell>d</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
              <row>
                <cell>b</cell>
                <cell>e</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
            </table>
            <p type="main">
              <figure id="id.015.01.028.3.jpg" xlink:href="015/01/028/3.jpg" number="12"/>
              <s id="id000222">Per quartam enim proportio a ad b produ­
                <lb/>
                <arrow.to.target n="marg23"/>
                <lb/>
              citur bifariam, & ex c ad d, & e ad f, & ex c ad f, &
                <lb/>
              e ad d. </s>
              <s id="id000223">& per præcedentem c ad f producitur ex
                <lb/>
              a ad b, & d ad e, & per quartam rurſus ex a ad e,
                <lb/>
              & d ad b. </s>
              <s id="id000224">Et per præcedentem rurſus a ad e ex c
                <lb/>
              ad f & b ad d, igitur per quartam eadem produ­
                <lb/>
              cetur ex c ad d & b ad f. </s>
              <s id="id000225">Quare per præceden­
                <lb/>
              tem c ad f ex a ad e, & d ad b, & ita diſponemus
                <lb/>
              hos modos in tabula. </s>
              <s id="id000226">Vides etiam
                <lb/>
                <arrow.to.target n="table8"/>
                <lb/>
                <figure id="id.015.01.028.4.jpg" xlink:href="015/01/028/4.jpg" number="13"/>
              aliquos modos non produci, ut pri­
                <lb/>
              mi ad quartum nec ad ſextum, & li­
                <lb/>
              quet, quòd cùm ſint quindecim o­
                <lb/>
              mnes modi qui produci poſſe intelli­
                <lb/>
              guntur, & nouem tantum producan­
                <lb/>
              tur ſex eſſe, qui non producuntur, quos
                <lb/>
              ſeorſum in tabula coniunxi. </s>
              <s id="id000227">Et con­
                <lb/>
              ſtat etiam, quod totidem conuerſi ſci­
                <lb/>
              licet decem octo
                <expan abbr="producũtur">producuntur</expan>
              , de qui­
                <lb/>
              bus diximus, ut ſint omnes triginta
                <lb/>
              ſex, qui conſtat ex duabus propoſi­
                <lb/>
              tionibus præmiſsis, & hac tertia,
                <expan abbr="quã">quam</expan>
                <lb/>
              adiungemus ſcilicet, quòd propor­
                <lb/>
              tio primi ad tertium producatur ex
                <lb/>
              proportionibus
                <expan abbr="ſecũdi">ſecundi</expan>
              ad quartum,
                <lb/>
              & quinti ad
                <expan abbr="ſextũ">ſextum</expan>
              . </s>
              <s id="id000228">Hoc enim ex præ­
                <lb/>
              cedentibus non liquet: benè liquet
                <lb/>
              permutatis ordinibus, quod ſi pro­
                <lb/>
              portio primi ad tertium producitur, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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