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="id003226">
                <pb pagenum="186" xlink:href="015/01/205.jpg"/>
              mus, & eſt 252, & eſt coniugatio quinarij: hoc uolui dixiſſe,
                <lb/>
                <figure id="id.015.01.205.1.jpg" xlink:href="015/01/205/1.jpg" number="200"/>
                <arrow.to.target n="table24"/>
                <lb/>
              ut intelligeres rationes colligendi ſingulos ordines ſeor­
                <lb/>
              ſum. </s>
              <s id="id003227">Quod ergo attinet ad collectionem maximi numeri,
                <lb/>
              primus ordo ſeruit ſemper ultimo
                <expan abbr="relinquẽdo">relinquendo</expan>
              monadem,
                <lb/>
              & ſecundus penultimo, & tertius antepenultimo, & ita de
                <lb/>
                <figure id="id.015.01.205.2.jpg" xlink:href="015/01/205/2.jpg" number="201"/>
              alijs, nam ſi ſecundus uariatur 55 modis, &'pen­
                <lb/>
              ultimus uariabitur 55 modis. </s>
              <s id="id003228">Et ſi tertius uaria­
                <lb/>
              tur 165 modis, antepenultimus uariatur 165 mo
                <lb/>
              dis. </s>
              <s id="id003229">Et ita de alijs.
                <lb/>
                <arrow.to.target n="table25"/>
                <lb/>
                <arrow.to.target n="marg593"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003230">
                <margin.target id="marg592"/>
              C
                <emph type="italics"/>
              o.
                <emph.end type="italics"/>
              ^{m}</s>
            </p>
            <p type="margin">
              <s id="id003231">
                <margin.target id="marg593"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <table>
              <table.target id="table23"/>
              <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>
                <cell>9</cell>
                <cell>10</cell>
                <cell>11</cell>
              </row>
              <row>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
              </row>
              <row>
                <cell>2</cell>
                <cell>3</cell>
                <cell>4</cell>
                <cell>5</cell>
                <cell>6</cell>
                <cell>7</cell>
                <cell>8</cell>
                <cell>9</cell>
                <cell>10</cell>
                <cell>11</cell>
                <cell/>
              </row>
              <row>
                <cell>3</cell>
                <cell>6</cell>
                <cell>10</cell>
                <cell>15</cell>
                <cell>21</cell>
                <cell>28</cell>
                <cell>36</cell>
                <cell>45</cell>
                <cell>55</cell>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>4</cell>
                <cell>10</cell>
                <cell>20</cell>
                <cell>35</cell>
                <cell>56</cell>
                <cell>84</cell>
                <cell>120</cell>
                <cell>165</cell>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>5</cell>
                <cell>15</cell>
                <cell>35</cell>
                <cell>70</cell>
                <cell>126</cell>
                <cell>210</cell>
                <cell>330</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>6</cell>
                <cell>21</cell>
                <cell>56</cell>
                <cell>126</cell>
                <cell>252</cell>
                <cell>462</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>7</cell>
                <cell>28</cell>
                <cell>84</cell>
                <cell>210</cell>
                <cell>462</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>8</cell>
                <cell>36</cell>
                <cell>120</cell>
                <cell>330</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>9</cell>
                <cell>45</cell>
                <cell>165</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>10</cell>
                <cell>55</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
              <row>
                <cell>11</cell>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
                <cell/>
              </row>
            </table>
            <table>
              <table.target id="table24"/>
              <row>
                <cell>11</cell>
              </row>
              <row>
                <cell>55</cell>
              </row>
              <row>
                <cell>165</cell>
              </row>
              <row>
                <cell>330</cell>
              </row>
              <row>
                <cell>462</cell>
              </row>
              <row>
                <cell>462</cell>
              </row>
              <row>
                <cell>330</cell>
              </row>
              <row>
                <cell>165</cell>
              </row>
              <row>
                <cell>55</cell>
              </row>
              <row>
                <cell>11</cell>
              </row>
              <row>
                <cell>1</cell>
              </row>
              <row>
                <cell>----</cell>
              </row>
              <row>
                <cell>2047</cell>
              </row>
            </table>
            <table>
              <table.target id="table25"/>
              <row>
                <cell>10</cell>
              </row>
              <row>
                <cell>45</cell>
              </row>
              <row>
                <cell>120</cell>
              </row>
              <row>
                <cell>210</cell>
              </row>
              <row>
                <cell>252</cell>
              </row>
              <row>
                <cell>210</cell>
              </row>
              <row>
                <cell>120</cell>
              </row>
              <row>
                <cell>45</cell>
              </row>
              <row>
                <cell>10</cell>
              </row>
              <row>
                <cell>1</cell>
              </row>
              <row>
                <cell>----</cell>
              </row>
              <row>
                <cell>1023</cell>
              </row>
            </table>
            <p type="main">
              <s id="id003232">Hæc autem ratio ſatisfacit multum, & eſt ne­
                <lb/>
              ceſſaria in temperiebus corporis humani. </s>
              <s id="id003233">Vt in
                <lb/>
              ſecundo, De dentibus. </s>
              <s id="id003234">Et etiam ut quælibet di­
                <lb/>
              ſciplina quàm breuiſsimè tradi poſsit, ut gratia
                <lb/>
              exempli, medicina tota in una pagina, dico me­
                <lb/>
              dicina
                <expan abbr="nõ">non</expan>
              ſolum Græcorum, ſed etiam Arabum
                <lb/>
              & Latinorum, & etiam longè plus: nam ſi tradatur uiginti quatuor
                <lb/>
              regulis simplicibus, & ex illis fiant coniugationes 16777215, mani
                <lb/>
              feſtum eſt quod erunt regulæ omnes hæ multo plures, quàm con­
                <lb/>
              tineantur in omnibus libris Græcorum, & Arabum, & Latino­
                <lb/>
              rum, qui extant. </s>
              <s id="id003235">Et tamen perſpicuum eſt, uiginti quatuor regulas
                <lb/>
              una pagina commodiſsimè contineri. </s>
              <s id="id003236">Et hoc aliâs docui, quan­
                <lb/>
              quàm credam me erraſſe in ſupputatione, nam locum inuenire non
                <lb/>
              potui. </s>
              <s id="id003237">Vnum eſt id certum, quòd hæc ratio quàm nunc explicabo,
                <lb/>
              eſt uera & demonſtratiua, & facillima.</s>
            </p>
            <p type="main">
              <s id="id003238">Cum enim ſuperior ſit uera & demonſtratiua, non eſt tamen fa­
                <lb/>
              cilis, & præcipuè in magnis numeris. </s>
              <s id="id003239">Et ideò inueni hanc, quæ (ut
                <lb/>
              dixi) facillima eſt: adde numero propoſito monadem, in de confla­
                <lb/>
              ri inuenias numerum à monade in eodem ordine, & ab eo detra­
                <lb/>
              cta monade habes numerum coniugationum. </s>
              <s id="id003240">Exemplum, ſi ſint
                <lb/>
              10 adde 1 fit 11. Vndecimus ergo numerus in proportione dupla
                <lb/>
              eſt 1024, detrahe 1 & relinquantur 1023 numerus coniugationum,
                <lb/>
              ut in priore ſupputatione. </s>
              <s id="id003241">Item ſi ſint 11 numeri adde 1 fit 12, duo de­
                <lb/>
              cimus ergo numerus in proportione dupla eſt 2048, detrahe 1 re­
                <lb/>
              linquuntur 2047, coniugationes 11, ut prius in ſuprà ſcripto exem­
                <lb/>
              plo. </s>
              <s id="id003242">Et ita pro uiginti quatuor regulis adde 1 fit 25, uigeſimus quin­
                <lb/>
              tus igitur numerus in ordine duplæ proportionis à monade eſt
                <lb/>
              16777216, ergo detracta monade relinquitur numerus (ut dixi) re­
                <lb/>
              gularum & coniugationum uiginti quatuor regularum, quæ ta­
                <lb/>
              men non ſint contrariæ inuicem: nam tunc eſſent pauciores. </s>
              <s id="id003243">Et
                <lb/>
              quia in iſtis numeris duplicandis poſſes facile incidere in errorem,
                <lb/>
              diuide ultimum per 16, & ſi nihil ſupereſt, rectè proceſsit opus: ſin </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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