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>
            <pb pagenum="95" xlink:href="015/01/114.jpg"/>
            <p type="head">
              <s id="id001723">SCHOLIVM.</s>
            </p>
            <p type="main">
              <s id="id001724">Et nota, quòd ſi res hæc eſſet naturalis, oſtenderet infinitum in
                <lb/>
              rebus ex regula dialectica, ſed quia ex
                <expan abbr="uolũtaria">uoluntaria</expan>
              , nullas habet uires.</s>
            </p>
            <p type="main">
              <s id="id001725">Propoſitio centeſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id001726">Proportionem motuum inuerſionis, & attractionis in plano
                <lb/>
              inuenire.</s>
            </p>
            <p type="main">
              <s id="id001727">Et ſit, ut aliquid inuertatur, declaratum autem eſt ſuprà, quid ſit </s>
            </p>
            <p type="main">
              <s id="id001728">
                <arrow.to.target n="marg351"/>
                <lb/>
              inuerſio, & quàm diuerſa ſit rurſus, & quòd attractio eſt dimidium
                <lb/>
                <arrow.to.target n="marg352"/>
                <lb/>
              ponderis eleuati. </s>
              <s id="id001729">Cum ergo conſtet in inuerſione, quanta ſit pro­
                <lb/>
              portio ponderis ſuſpenſi ad pondus inuerſum, & pondus ſuſpenſi
                <lb/>
                <arrow.to.target n="marg353"/>
                <lb/>
              ſit duplum ponderi attracti, ſequitur, ut diuiſa proportione ponde
                <lb/>
              ris ſuſpenſi ad pondus inuerſum per medium cognoſcatur propor
                <lb/>
              tio attractionis ad inuerſionem.</s>
            </p>
            <p type="margin">
              <s id="id001730">
                <margin.target id="marg351"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="margin">
              <s id="id001731">
                <margin.target id="marg352"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              89.</s>
            </p>
            <p type="margin">
              <s id="id001732">
                <margin.target id="marg353"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              62.</s>
            </p>
            <p type="main">
              <s id="id001733">Ex hoc ſequitur, quod aliquod pondus trahi poteſt, quod non
                <lb/>
                <arrow.to.target n="marg354"/>
                <lb/>
              poteſt inuerti, hoc autem indiget longa declaratione, quam doce­
                <lb/>
              bimus inferiùs: & tamen attigit hoc rarò.</s>
            </p>
            <p type="margin">
              <s id="id001734">
                <margin.target id="marg354"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001735">Propoſitio centeſima tertia.</s>
            </p>
            <p type="main">
              <s id="id001736">Proportionem eorundem in accliui demonſtrare.</s>
            </p>
            <p type="main">
              <s id="id001737">Dupliciter poteſt intelligi, uel deſcendendo, uel aſcendendo.
                <lb/>
                <arrow.to.target n="marg355"/>
                <lb/>
                <arrow.to.target n="marg356"/>
                <lb/>
              Sed ego nunc loquor de aſcenſu, contraria ratione intelliges de
                <lb/>
              deſcenſu, & circa inuerſionem demonſtrata eſt proportio eius
                <lb/>
              iuxta angulum aſcenſus, & ſimiliter declarabitur de proportione
                <lb/>
                <arrow.to.target n="marg357"/>
                <lb/>
              attractionis iuxta eundem angulum aſcenſus, & nuper declarata
                <lb/>
              eſt proportio inuerſionis in plano ad attractionem, ex quibus ſe­
                <lb/>
              quitur per ea, quæ dicam inferius, quòd proportio cuiuſuis mobi­
                <lb/>
              lis inuerſi ad attractum ſub quibuſcunque angulis nota erit.</s>
            </p>
            <p type="margin">
              <s id="id001738">
                <margin.target id="marg355"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001739">
                <margin.target id="marg356"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              72.</s>
            </p>
            <p type="margin">
              <s id="id001740">
                <margin.target id="marg357"/>
              I
                <emph type="italics"/>
              n ſequenti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001741">Propoſitio centeſima quarta.</s>
            </p>
            <p type="main">
              <s id="id001742">Proportionem motus attractionis in decliui ad motum in pla­
                <lb/>
              no determinare.</s>
            </p>
            <p type="main">
              <s id="id001743">Si ab accliue, ſeu decliue in quo d ad attra­
                <lb/>
                <arrow.to.target n="marg358"/>
                <lb/>
                <arrow.to.target n="marg359"/>
                <lb/>
                <figure id="id.015.01.114.1.jpg" xlink:href="015/01/114/1.jpg" number="108"/>
                <lb/>
              hendum, cuius nota eſt ex ſuperioribus dif­
                <lb/>
              ficultas in plano ratione figuræ conſtante, er­
                <lb/>
              go ea quæritur proportio aſcenſus, & quo­
                <lb/>
              niam terminus ad perpendiculum eſt dupla
                <lb/>
              proportio, & iam grauitas in plano eſt dimidium, ideò quicquid
                <lb/>
              acquiritur in eleuatione eſt in comparatione ad illud dimidium,
                <lb/>
              cum ergo attractio ſecundum eandem proportionem augeatur, er­
                <lb/>
              go ſemper maior difficultas augebitur, ergo ab initio minimum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>