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="id000228">
                <pb pagenum="9 [=10]" xlink:href="015/01/029.jpg"/>
              quod etiam propor­
                <lb/>
                <figure id="id.015.01.029.1.jpg" xlink:href="015/01/029/1.jpg" number="14"/>
                <arrow.to.target n="marg24"/>
                <lb/>
              tio primi ad
                <expan abbr="quintũ">quintum</expan>
              .
                <lb/>
              </s>
              <s id="id000229">Nam tertium, & quin
                <lb/>
              tum, item que quartum,
                <lb/>
              & ſextum non
                <expan abbr="diffe­rũt">diffe­
                  <lb/>
                runt</expan>
              niſi ordine uolun
                <lb/>
              tario. </s>
              <s id="id000230">Ergo interpoſi­
                <lb/>
              to e inter a, & c per ſe­
                <lb/>
              cundam propoſitio­
                <lb/>
              nem proportio a ad c
                <lb/>
              producitur ex proportionibus a ad
                <lb/>
              e, & e ad c, ut ex demonſtratis in præ­
                <lb/>
              ſenti proportio a ad c producitur ex
                <lb/>
              c ad f & b ad d. </s>
              <s id="id000231">Proportio ergo a ad
                <lb/>
              c producitur ex proportionibus e
                <lb/>
              ad c & c ad f & b ad d, at e ad c & c ad
                <lb/>
              f producunt eam, quæ eſt e ad f per
                <lb/>
                <expan abbr="ſecũdam">ſecundam</expan>
              propoſitionem. </s>
              <s id="id000232">Igitur pro­
                <lb/>
              portio a ad c producitur ex propor­
                <lb/>
              tionibus b ad d ſecundi ad quartum,
                <lb/>
              & e ad f quinti ad ſextum. </s>
              <s id="id000233">Hæc Al­
                <lb/>
              chindus in ſuo libello: ſed licet inge­
                <lb/>
              nio ſa ualde: parum
                <expan abbr="tamẽ">tamen</expan>
              utilia olim
                <lb/>
                <expan abbr="erãt">erant</expan>
              neceſſaria ad intelligendum ma­
                <lb/>
              gnam
                <expan abbr="cõpoſitionem">compoſitionem</expan>
              Ptolemęi, nunc
                <lb/>
              poſtquam Heber has ſex quantita­
                <lb/>
              tes traduxit ad quatuor, prorſus hæc
                <lb/>
              ſcientia ulli uſui eſſe deſijt.
                <lb/>
                <arrow.to.target n="table9"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000234">
                <margin.target id="marg23"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id000235">
                <margin.target id="marg24"/>
              Modi qui
                <expan abbr="nõ">non</expan>
                <lb/>
              producuntur
                <lb/>
              pri. ad quartu
                <lb/>
              pri. ad ſextum
                <lb/>
              ſec. ad
                <expan abbr="tertiũ">tertium</expan>
                <lb/>
              ſec. ad
                <expan abbr="quintũ">quintum</expan>
                <lb/>
              tert. </s>
              <s id="id000236">ad quint.
                <lb/>
              </s>
              <s id="id000237">quart. </s>
              <s id="id000238">ad ſext.</s>
            </p>
            <table>
              <table.target id="table8"/>
              <row>
                <cell/>
                <cell>Primi ad ſecundum.</cell>
              </row>
              <row>
                <cell>1</cell>
                <cell>tertij ad
                  <expan abbr="quartũ">quartum</expan>
                , & quin</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad ſextum.</cell>
              </row>
              <row>
                <cell>2</cell>
                <cell>tertij ad ſextum, & quin</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad quartum.</cell>
              </row>
              <row>
                <cell/>
                <cell>Primi ad tertium.</cell>
              </row>
              <row>
                <cell>3</cell>
                <cell>ſecundi ad quartum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>quinti ad ſextum.</cell>
              </row>
              <row>
                <cell>4</cell>
                <cell>ſecundi ad ſextum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>quinti ad quartum.</cell>
              </row>
              <row>
                <cell/>
                <cell>Primi ad quintum.</cell>
              </row>
              <row>
                <cell>5</cell>
                <cell>ſecundi ad
                  <expan abbr="ſextũ">ſextum</expan>
                , & ter­</cell>
              </row>
              <row>
                <cell/>
                <cell>tij ad quartum.</cell>
              </row>
              <row>
                <cell>6</cell>
                <cell>ſecundi ad quartum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>tertij ad ſextum.</cell>
              </row>
              <row>
                <cell/>
                <cell>Secundi ad quartum.</cell>
              </row>
              <row>
                <cell>7</cell>
                <cell>primi ad tertium, & ſex</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad quintum.</cell>
              </row>
              <row>
                <cell>8</cell>
                <cell>primi ad quintum, et ſex</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad tertium.</cell>
              </row>
              <row>
                <cell/>
                <cell>Secundi ad ſextum.</cell>
              </row>
              <row>
                <cell>9</cell>
                <cell>primi ad
                  <expan abbr="quintũ">quintum</expan>
                , & quar</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad tertium.</cell>
              </row>
              <row>
                <cell>10</cell>
                <cell>primi ad
                  <expan abbr="tertiũ">tertium</expan>
                , & quar­</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad quintum.</cell>
              </row>
              <row>
                <cell/>
                <cell>Tertij ad quartum.</cell>
              </row>
              <row>
                <cell>11</cell>
                <cell>primi ad ſecundum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>ſexti ad quintum.</cell>
              </row>
              <row>
                <cell>12</cell>
                <cell>primi ad quintum, & ſex</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad ſecundum.</cell>
              </row>
              <row>
                <cell/>
                <cell>Tertij ad ſextum.</cell>
              </row>
              <row>
                <cell>13</cell>
                <cell>primi ad ſecundum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>quarti ad quintum.</cell>
              </row>
              <row>
                <cell>14</cell>
                <cell>primi ad quintum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>quarti ad ſecundum.</cell>
              </row>
              <row>
                <cell/>
                <cell>Quarti ad quintum.</cell>
              </row>
              <row>
                <cell>15</cell>
                <cell>ſecundi ad primum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>tertij ad ſextum.</cell>
              </row>
              <row>
                <cell>16</cell>
                <cell>ſecundi ad ſextum, & ter</cell>
              </row>
              <row>
                <cell/>
                <cell>tij ad primum.</cell>
              </row>
              <row>
                <cell/>
                <cell>Quinti ad ſextum.</cell>
              </row>
              <row>
                <cell>17</cell>
                <cell>primi ad ſecundum, &</cell>
              </row>
              <row>
                <cell/>
                <cell>quarti ad tertium.</cell>
              </row>
              <row>
                <cell>18</cell>
                <cell>primi ad
                  <expan abbr="tertiũ">tertium</expan>
                , & quar­</cell>
              </row>
              <row>
                <cell/>
                <cell>ti ad ſecundum.</cell>
              </row>
            </table>
            <table>
              <table.target id="table9"/>
              <row>
                <cell>a</cell>
                <cell>e c</cell>
                <cell>a e</cell>
                <cell>e c</cell>
              </row>
              <row>
                <cell/>
                <cell/>
                <cell>c b</cell>
                <cell>e</cell>
              </row>
              <row>
                <cell/>
                <cell/>
                <cell>f d</cell>
                <cell>c</cell>
              </row>
              <row>
                <cell/>
                <cell/>
                <cell/>
                <cell>f</cell>
              </row>
            </table>
            <p type="main">
              <s id="id000239">Propoſitio ſeptima.</s>
            </p>
            <figure id="id.015.01.029.2.jpg" xlink:href="015/01/029/2.jpg" number="15"/>
            <p type="main">
              <s id="id000240">In modis qui neceſſariò produ­
                <lb/>
              cuntur ex duabus proportionibus,
                <lb/>
              cum duę quantitates ex illis, quę mo
                <lb/>
                <figure id="id.015.01.029.3.jpg" xlink:href="015/01/029/3.jpg" number="16"/>
              dos conficiunt, æquales fuerint: pro­
                <lb/>
                <arrow.to.target n="table10"/>
                <lb/>
              portio producta ad quatuor quanti­
                <lb/>
              tates omiologas reducetur.
                <lb/>
                <arrow.to.target n="marg25"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000241">
                <margin.target id="marg25"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <table>
              <table.target id="table10"/>
              <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>
            <p type="main">
              <s id="id000242">Sint ſex quantitates a b c d e f, &
                <lb/>
              producatur proportio a ad b ex pro­
                <lb/>
              portione c ad d, & e ad f, tu ſcis, quòd
                <lb/>
              modi recepti ſunt prima cum ſecunda, tertia uel quinta, & ſecunda
                <lb/>
              cum quarta, & ſexta, & tertia ſimiliter cum eiſdem, & quinta eodem
                <lb/>
              modo cum eiſdem: ſi igitur duę quantitates ex his, quę faciunt </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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