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="id000633">
                <pb pagenum="33" xlink:href="015/01/052.jpg"/>
              pla in triplam. </s>
              <s id="id000634">Sed ſumpta proportione alio modo producitur. </s>
              <s id="id000635">Ve
                <lb/>
              lut ſi dicam, homines decem mouent nauim, aut
                <expan abbr="ferũt">ferunt</expan>
              pondus pro­
                <lb/>
              portione tripla, igitur quadraginta homines idem facient propor­
                <lb/>
              tione duodecupla ſcilicet quadrupla in triplam ducta. </s>
              <s id="id000636">Cum ergo
                <lb/>
              addo triginta homines, qui mouent in proportione nonupla, non
                <lb/>
              oportet ducere nonuplam in triplam, ſed totum numerum accipe­
                <lb/>
              re, & quam proportionem habet ad partem, tandem habet uis mo­
                <lb/>
              uens ad uim
                <expan abbr="mouẽtem">mouentem</expan>
              . </s>
              <s id="id000637">Vnde ſi duo moueant in proportione ſex­
                <lb/>
              quialtera, & ſex in proportione quadrupla cum dimidia, & iungan
                <lb/>
              tur, ut fiant octo, non oportebit ducere ſexquialteram, in quadru­
                <lb/>
              plam ſexquialteram, ſed cum octo ad duo ſit in proportione qua­
                <lb/>
              drupla, ſumemus quadruplam ad ſexquialteram, quę erit ſexcupla,
                <lb/>
              & octo mouebunt, aut pondus gerentin proportione ſexcupla.</s>
            </p>
            <p type="margin">
              <s id="id000638">
                <margin.target id="marg109"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              37.</s>
            </p>
            <p type="main">
              <s id="id000639">Propoſitio quadrageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id000640">Productionem ad additionem retrahere.
                <lb/>
                <arrow.to.target n="marg110"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000641">
                <margin.target id="marg110"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <figure id="id.015.01.052.1.jpg" xlink:href="015/01/052/1.jpg" number="48"/>
            <p type="main">
              <s id="id000642">Sit proportio a ad b dupla poteſtate li­
                <lb/>
              cet ſint quinque homines, & ſint quindecim
                <lb/>
              homines c, & habebunt ad b ſexcuplam
                <lb/>
              proportionem per præcedentem. </s>
              <s id="id000643">Iuncta
                <lb/>
              ergo a, & c per octauam huius
                <expan abbr="mouebũt">mouebunt</expan>
                <lb/>
              b proportione octupla, dico, quod ſi du­
                <lb/>
              xeris
                <expan abbr="proportionẽ">proportionem</expan>
              c ad a plus uno. </s>
              <s id="id000644">i. </s>
              <s id="id000645">qua­
                <lb/>
              druplam in proportionem a ad b, quæ eſt dupla, proueniet eadem
                <lb/>
              octupla. </s>
              <s id="id000646">Nam quia in coniunctione ſufficit iungere c cum a, & ſu­
                <lb/>
              mitur ſecundum proportionem a ad b, igitur cum proportio a ad
                <lb/>
              b comparata ad proportionem c & a ad b ſit, ſicut proportio c & a
                <lb/>
              ad a, & proportio c & a ad a ſit, ſicut proportio c ad a, & a ad a, &
                <lb/>
              proportio a ad a habet rationem unius, igitur proportio aggregati
                <lb/>
              c a ad b eſt producta ex proportione c ad a plus monade in propor
                <lb/>
              tionem a ad b, quod erat demonſtrandum.</s>
            </p>
            <p type="main">
              <s id="id000647">Propoſitio quadrageſima quarta.</s>
            </p>
            <p type="main">
              <s id="id000648">Si fuerit proportio motoris ad id, quod eſt maximum non mo­
                <lb/>
              uens & ſpatium, & tempus, nota erit etiam reliquorum nota.</s>
            </p>
            <p type="main">
              <s id="id000649">Sæpe contingit, ut quinque homines moueant nauim, & ſpatium
                <lb/>
              ad tempus notum, & etiam cognitum maximum, quod mouere
                <lb/>
              non poteſt. </s>
              <s id="id000650">Sit ergo a numerus hominum, b na­
                <lb/>
                <figure id="id.015.01.052.2.jpg" xlink:href="015/01/052/2.jpg" number="49"/>
                <lb/>
              uis, c maximum, quod non mouere poteſt, d
                <lb/>
              tempus, e ſpatium, f motor alius ſiue numerus
                <lb/>
              hominum notus, & g tempus, dico, quod h ſpatium notum erit, ſeu
                <lb/>
                <expan abbr="notũ">notum</expan>
              g tempus, & h ſpatium, dico, quod erit f motor, ſeu numerus </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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