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="id002361">
                <pb pagenum="131" xlink:href="015/01/150.jpg"/>
              tato, & ita 64 habet rationem unius, & licet comparetur ad 2 rem,
                <lb/>
              & ſit ſextus ab eo, eo computato 4096 autem à 64 ſit ſeptimus, ta­
                <lb/>
              men non eſt eadem ratio, quia 64 non eſt quadratum 2.</s>
            </p>
            <p type="main">
              <s id="id002362">Propoſitio centeſima trigeſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id002363">Rationem numerorum ex progreſsione declarare.</s>
            </p>
            <p type="main">
              <s id="id002364">Michaël Stifelius rationem pulcherrimam tradidit ad inuentio­
                <lb/>
                <arrow.to.target n="marg462"/>
                <lb/>
                <arrow.to.target n="marg463"/>
                <lb/>
              nem numerorum, qui uocantur multiplicandi, & componitur hoc
                <lb/>
              modo. </s>
              <s id="id002365">Ex prima componitur 1 & 2, faciunt 3. 1. 2. 3 faciunt 6. 1. 2. 3. 4
                <lb/>
              faciunt 10, & ita prima tabula conſtituit ſecundam recta ſerie nu­
                <lb/>
              merorum iunctis o­
                <lb/>
              mnibus ab uno. </s>
              <s id="id002366">Ter
                <lb/>
                <figure id="id.015.01.150.1.jpg" xlink:href="015/01/150/1.jpg" number="143"/>
                <arrow.to.target n="table17"/>
                <lb/>
              tia fit ex ſecunda &
                <lb/>
              tertia, primò aſſumi
                <lb/>
              tur 10 in tertia, ut in
                <lb/>
              ſecunda, & ex 10 ſe­
                <lb/>
              cundæ, & 10 tertiæ
                <lb/>
              fit 20, & ex 15 ſecun­
                <lb/>
              dæ, & 20 tertiæ fit
                <lb/>
              35, & ex 21 ſecundæ,
                <lb/>
              & 35 tertiæ fit 56, &
                <lb/>
              ex 28, & 56 fit 84. Et
                <lb/>
              quanta fit ex tertia,
                <lb/>
              & ex ſe ipſa. </s>
              <s id="id002367">primum
                <lb/>
              aſſumendo 35 ex ter
                <lb/>
              tia, & ponitur pro
                <lb/>
              primo numero quartæ, & ex 35 tertiæ, & 35 quartæ fit 70 numerus
                <lb/>
              ſecundæ quartæ: & ita ex 56 & 70 fit 126, & ex 84, & 126. 210. & ita
                <lb/>
              quinta ex quarta & ſe ipſa, & ſic in infinitum.</s>
            </p>
            <p type="margin">
              <s id="id002368">
                <margin.target id="marg462"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="margin">
              <s id="id002369">
                <margin.target id="marg463"/>
              P
                <emph type="italics"/>
              rimæ ſuæ
                <emph.end type="italics"/>
                <lb/>
              A
                <emph type="italics"/>
              rith.
                <emph.end type="italics"/>
              </s>
            </p>
            <table>
              <table.target id="table17"/>
              <row>
                <cell>1</cell>
                <cell>2</cell>
                <cell>3</cell>
                <cell>4</cell>
                <cell>5</cell>
                <cell>6</cell>
                <cell>7</cell>
                <cell>8</cell>
              </row>
              <row>
                <cell>1</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>2</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>3</cell>
                <cell>3</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>4</cell>
                <cell>6</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>5</cell>
                <cell>10</cell>
                <cell>10</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>6</cell>
                <cell>15</cell>
                <cell>20</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>7</cell>
                <cell>21</cell>
                <cell>35</cell>
                <cell>35</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>8</cell>
                <cell>28</cell>
                <cell>56</cell>
                <cell>70</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>9</cell>
                <cell>36</cell>
                <cell>84</cell>
                <cell>126</cell>
                <cell>126</cell>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>10</cell>
                <cell>45</cell>
                <cell>120</cell>
                <cell>210</cell>
                <cell>252</cell>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>11</cell>
                <cell>55</cell>
                <cell>165</cell>
                <cell>330</cell>
                <cell>462</cell>
                <cell>462</cell>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>12</cell>
                <cell>66</cell>
                <cell>220</cell>
                <cell>495</cell>
                <cell>792</cell>
                <cell>924</cell>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>13</cell>
                <cell>78</cell>
                <cell>286</cell>
                <cell>715</cell>
                <cell>1297</cell>
                <cell>1716</cell>
                <cell>1716</cell>
                <cell/>
              </row>
              <row>
                <cell>14</cell>
                <cell>91</cell>
                <cell>364</cell>
                <cell>1001</cell>
                <cell>2002</cell>
                <cell>3003</cell>
                <cell>3432</cell>
                <cell/>
              </row>
              <row>
                <cell>15</cell>
                <cell>105</cell>
                <cell>455</cell>
                <cell>1365</cell>
                <cell>3003</cell>
                <cell>5005</cell>
                <cell>6435</cell>
                <cell>6435</cell>
              </row>
              <row>
                <cell>16</cell>
                <cell>120</cell>
                <cell>560</cell>
                <cell>1820</cell>
                <cell>4368</cell>
                <cell>8008</cell>
                <cell>11440</cell>
                <cell>12870</cell>
              </row>
              <row>
                <cell>17</cell>
                <cell>136</cell>
                <cell>680</cell>
                <cell>2380</cell>
                <cell>6188</cell>
                <cell>12376</cell>
                <cell>19448</cell>
                <cell>24310</cell>
              </row>
            </table>
            <p type="main">
              <s id="id002370">Regula ergo eſt, quòd binarius ſeruit <02> quadratæ, & quia nihil
                <lb/>
              eſt in eius directo, ſolus ipſe ſeruiet <02> quadratæ. </s>
              <s id="id002371">Ternarius autem
                <lb/>
              cubicæ, & quia in eius directo eſt alter ternarius, ille etiam ſeruiet
                <lb/>
              <02> cubicæ. </s>
              <s id="id002372">Quaternarius autem ſeruiet quadrato quadrati, & ſena­
                <lb/>
              rius, qui eſt in illius directo. </s>
              <s id="id002373">Ergo quinarius ſeruiet <02> relatę primę,
                <lb/>
              & duo ſequentes numeri ſcilicet 10 & 10, & eo dem modo ſenarius
                <lb/>
              numeri duo ſequentes 15 & 20 ſeruient cubo quadrati, & ita etiam
                <lb/>
              ſeptenarius cum tribus ſequentibus numeris 21. 35 & 35 ſeruient
                <lb/>
              rel. </s>
              <s id="id002374">ſecundi radici, & ita deinceps in infinitum.</s>
            </p>
            <p type="main">
              <s id="id002375">Propoſitio centeſima trigeſima octaua.</s>
            </p>
            <p type="main">
              <s id="id002376">Modos uſus horum numerorum declarare.</s>
            </p>
            <p type="main">
              <s id="id002377">In quouis numero denominationis oportet tot addere o, quo­
                <lb/>
                <arrow.to.target n="marg464"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum