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>
        <front>
          <section>
            <pb xlink:href="015/01/008.jpg"/>
            <p type="head">
              <s id="id000040">TABVLA PRO­
                <lb/>
              POSITIONVM DE
                <lb/>
              PROPORTIONIBVS.
                <lb/>
                <arrow.to.target n="table1"/>
              </s>
            </p>
            <table>
              <table.target id="table1"/>
              <row>
                <cell>I.</cell>
                <cell>Proportionem
                  <emph type="italics"/>
                in proportionem duci, eſt ſuperiores numeros atque inferiores inuicem ducere.
                  <emph.end type="italics"/>
                </cell>
                <cell>
                  <emph type="italics"/>
                pagina
                  <emph.end type="italics"/>
                6</cell>
              </row>
              <row>
                <cell>II.</cell>
                <cell>P
                  <emph type="italics"/>
                roportio extremorum producitur ex intermedijs.
                  <emph.end type="italics"/>
                </cell>
                <cell>7</cell>
              </row>
              <row>
                <cell>III.</cell>
                <cell>S
                  <emph type="italics"/>
                i proportio ex duabus proportionibus in quatuor terminis producatur, ipſa uerò proportio inter duas alias quantitates fuerit conſtituta: conſurgent trecen­ti ſexaginta modi productionis proportionis.
                  <emph.end type="italics"/>
                </cell>
                <cell>7</cell>
              </row>
              <row>
                <cell>IIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerit proportio primi ad ſecundum, producta ex proportionibus tertij ad quartum, & quinti ad ſextum, producetur etiam ex proportione tertij ad ſextum, & quinti ad quartum.
                  <emph.end type="italics"/>
                </cell>
                <cell>8</cell>
              </row>
              <row>
                <cell>V.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerit proportio primi ad ſecundum, producta ex proportione tertij ad quartum, & quinti ad ſextum: erit proportio tertij ad ſextum, producta ex proportionibus primi ad ſecundum, & quarti ad quintum.
                  <emph.end type="italics"/>
                </cell>
                <cell>8</cell>
              </row>
              <row>
                <cell>VI.</cell>
                <cell>E
                  <emph type="italics"/>
                x trecentis ſexaginta modis producendarum proportionum triginta ſex tantum eſſe neceſſarios.
                  <emph.end type="italics"/>
                </cell>
                <cell>9</cell>
              </row>
              <row>
                <cell>VII.</cell>
                <cell>I
                  <emph type="italics"/>
                n modis qui neceſſariò producuntur ex duabus proportionibus, cum duæ quantitates ex illis quæ modos conficiunt, æquales fuerint: proportio producta ad quatuor quanti­tates omiologas reducetur.
                  <emph.end type="italics"/>
                </cell>
                <cell>10</cell>
              </row>
              <row>
                <cell>VIII.</cell>
                <cell>S
                  <emph type="italics"/>
                i duarum proportionum ſuperiores numeri alternatim cum inferioribus multiplicen­tur atque coniungantur, erit proportio aggregati ad productum ex inferioribus in­uicem proportio, ex primis proportionibus compoſita.
                  <emph.end type="italics"/>
                </cell>
                <cell>11</cell>
              </row>
              <row>
                <cell>IX.</cell>
                <cell>S
                  <emph type="italics"/>
                i duarum proportionum ſuperiores numeri alternatim cum inferioribus multiplicen­tur, minusque productum ex maiore detrahatur, erit reſidui ad productum ex inſe­rioribus proportio uelut illa, quæ relinquitur detracta minore proportione ex ma­iore.
                  <emph.end type="italics"/>
                </cell>
                <cell>11</cell>
              </row>
              <row>
                <cell>X.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerit alicuius quantitatis ad unam partem proportio, uelut alterius partis ad ſecun­dam quantitatem, erit proportio cuiuſuis quantitatis eiuſdem generis ad ſecundam compoſita proportio, ex proportionibus eiuſdem quantitatis, aſſumptæ ad utranque partem primæ quantitatis ſeorſum.
                  <emph.end type="italics"/>
                </cell>
                <cell>11</cell>
              </row>
              <row>
                <cell>XI.</cell>
                <cell>P
                  <emph type="italics"/>
                roportio aggregati quarumlibet duarum quantitatum ad aggregatum duarum æqua­lium
                  <expan abbr="quantitatũ">quantitatum</expan>
                eſt, compoſita ex proportionibus primis, & diuiſa per duplam.
                  <emph.end type="italics"/>
                </cell>
                <cell>12</cell>
              </row>
              <row>
                <cell>XII.</cell>
                <cell>P
                  <emph type="italics"/>
                ropoſitis duabus proportionibus unam alteri iungere abſque multiplicatione.
                  <emph.end type="italics"/>
                </cell>
                <cell>12</cell>
              </row>
              <row>
                <cell>XIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportio confuſa aggregata primæ & tertiæ quatuor quantitatum omiologarum ad aggregatum ſecundæ & quartæ, eſt uelut compoſita ex eiſdem diuiſa per du­plam.
                  <emph.end type="italics"/>
                </cell>
                <cell>13</cell>
              </row>
              <row>
                <cell>XIIII.</cell>
                <cell>P
                  <emph type="italics"/>
                roportiones confuſæ & coniunctæ in tribus quantitatibus inuicem commutantur.
                  <emph.end type="italics"/>
                </cell>
                <cell>13</cell>
              </row>
              <row>
                <cell>XV.</cell>
                <cell>S
                  <emph type="italics"/>
                i fuerint quatuor quantitates proportio confuſa, aggregati primæ & tertiæ, ad aggre­gatum ſecundæ & quartæ, erit ut monadis addito prouentu, qui fit diuiſa differentia, differentiarum primæ & ſecundæ, atque quartæ & tertiæ, per aggregatum tertiæ & quartæ ad ipſam monadem.
                  <emph.end type="italics"/>
                </cell>
                <cell>14</cell>
              </row>
              <row>
                <cell>XVI.</cell>
                <cell>O
                  <emph type="italics"/>
                mnium quatuor quantitatum propoſita prima, quæ non minorem habet proportio­nem ad ſuam correſpondentem quàm alia ad aliam, erit proportio confuſa illarum,
                  <emph.end type="italics"/>
                </cell>
                <cell/>
              </row>
            </table>
          </section>
        </front>
      </text>
    </archimedes>
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