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="id000610">
                <pb pagenum="42 [=32]" xlink:href="015/01/051.jpg"/>
                <arrow.to.target n="marg103"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000611">
                <margin.target id="marg102"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id000612">
                <margin.target id="marg103"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id000613">Ex hoc liquet, quod oportet b planum eſſe ex duriſsima mate­
                <lb/>
              ria, quæ nullo modo cedat, aliter tanget pluſquàm in puncto.</s>
            </p>
            <p type="main">
              <s id="id000614">
                <arrow.to.target n="marg104"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000615">
                <margin.target id="marg104"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id000616">Vix fieri poteſt, utin elementaribus ſphæra tangat planum in
                <lb/>
              puncto. </s>
              <s id="id000617">Vel quia planum non erit exactè rectum, uel non durum,
                <lb/>
              ut prorſus non cedat, uel non ad æquilibrium poſitum, uel ſphæra
                <lb/>
              non erit exactè rotunda.</s>
            </p>
            <p type="main">
              <s id="id000618">Propoſitio quadrageſima prima.</s>
            </p>
            <p type="main">
              <s id="id000619">Si fuerint duæ quantitates ſumaturque totius aggregatum maio­
                <lb/>
              ris & minoris, quoties aggregatum minoris, & maioris, erit pro­
                <lb/>
              portio confuſa maioris aggregati ad minus, minor quàm multipli­
                <lb/>
              cis maioris ad multiplex minoris.</s>
            </p>
            <p type="main">
              <s id="id000620">
                <arrow.to.target n="marg105"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000621">
                <margin.target id="marg105"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000622">Sint duæ magnitudines a & b, & ſit a maior
                <lb/>
                <figure id="id.015.01.051.1.jpg" xlink:href="015/01/051/1.jpg" number="47"/>
                <lb/>
              b, & ſumatur exempli gratia a quater cum b ſe­
                <lb/>
              mel, & b quater cum a ſemel, dico, quod propor
                <lb/>
              tio (quam confuſam eſſe liquet) aggregati primi ad ſecundum, eſt </s>
            </p>
            <p type="main">
              <s id="id000623">
                <arrow.to.target n="marg106"/>
                <lb/>
              minor quàm quadrupla. </s>
              <s id="id000624">Conſtat enim quod proportio quadru­
                <lb/>
              pli a ad a eſt maior, quam b ad quadruplum b, cum una ſit quadru­
                <lb/>
              pla, alia ſub quadrupla, igitur per uigeſimam ſecundam huius ag­
                <lb/>
              gregati quadrupli a cum b ſemel, ad quadruplum b cum a ſemel mi
                <lb/>
                <arrow.to.target n="marg107"/>
                <lb/>
              nor, quàm quadrupli a ad a, & maior quàm b ad quadruplum b, &
                <lb/>
              eſt pro intellectu Archimedis.</s>
            </p>
            <p type="margin">
              <s id="id000625">
                <margin.target id="marg106"/>
              E
                <emph type="italics"/>
              x
                <emph.end type="italics"/>
              18.
                <emph type="italics"/>
              diff.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000626">
                <margin.target id="marg107"/>
              I
                <emph type="italics"/>
              n
                <emph.end type="italics"/>
              2.
                <emph type="italics"/>
              lib. de
                <emph.end type="italics"/>
                <lb/>
              A
                <emph type="italics"/>
              tqui pon­
                <lb/>
              deran.
                <emph.end type="italics"/>
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              10.</s>
            </p>
            <p type="main">
              <s id="id000627">Propoſitio quadrageſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id000628">Trahentium nauim, ut ferentium pondera proportiones in ſe in­
                <lb/>
              uicem, quomodo ducere oporteat conſiderare.
                <lb/>
                <arrow.to.target n="marg108"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000629">
                <margin.target id="marg108"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000630">Hoc quomodo non poſsit fieri ſuprà docuimus, nunc etiam ge­</s>
            </p>
            <p type="main">
              <s id="id000631">
                <arrow.to.target n="marg109"/>
                <lb/>
              neraliter dicam, cum conſiſtant hæc in duobus terminis, productio
                <lb/>
              uerò præſupponit quatuor terminos, ut in prima propoſitione, aut
                <lb/>
              ſaltem tres, atque in his medius habet rationem mouentis, & moti,
                <lb/>
              ergo cum in huiuſmodi
                <expan abbr="nõ">non</expan>
              ſint quatuor termini, nec tres, è quibus
                <lb/>
              unus ſit mouens, & motum proportio non poterit produci. </s>
              <s id="id000632">Illud
                <lb/>
              etiam patet exemplo, nam ſi eſſet lapis, aut nauis obſiſtens ut ſex, &
                <lb/>
              eſſent homines uiribus ſinguli, ut quatuor cum dimidio, tres mo­
                <lb/>
              uerent in proportione dupla ſexquiquarta perdicta ſuperius eo­
                <lb/>
              dem loco, at ſi proportio duci poſſet aliquorum hominum nume­
                <lb/>
              rus poſſet mouere in duplicata proportione ad unguem ſcilicet
                <lb/>
              5 1/16 ut eſſet uix hominum collectorum 30 3/8 at nullus eſt numerus ho
                <lb/>
              minum qui collectus faciat hunc numerum, nam ſex homines ex­
                <lb/>
              plent numerum 27, & ſeptem 31 1/2, & ideò non poteſt duci propor­
                <lb/>
              tio. </s>
              <s id="id000633">Et ideò maximus eſt error dicendo decem homines mouent na
                <lb/>
              uim proportione tripla, ergo triginta alij additis illis ſimiles robo­
                <lb/>
              re mouebunt à proportione uiginti ſeptupla ſcilicet ducta </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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