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="id001690">
                <pb pagenum="93" xlink:href="015/01/112.jpg"/>
              quadraginta erit in c d triginta unius cum quarta, ſed proportionis
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              ratione eſſet uiginti octo cum tertia.</s>
            </p>
            <p type="margin">
              <s id="id001691">
                <margin.target id="marg341"/>
              P
                <emph type="italics"/>
              er
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              C
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              or
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              ^{m}. 2.
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              45. P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001692">
                <margin.target id="marg342"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              86.
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001693">
                <margin.target id="marg343"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              99.</s>
            </p>
            <p type="margin">
              <s id="id001694">
                <margin.target id="marg344"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              97.</s>
            </p>
            <p type="margin">
              <s id="id001695">
                <margin.target id="marg345"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              98.</s>
            </p>
            <p type="main">
              <s id="id001696">Propoſitio nonageſima nona.</s>
            </p>
            <p type="main">
              <s id="id001697">Proportionem grauitatum per multitudinem ſuppoſitorum or
                <lb/>
              bium oſtendere.
                <lb/>
                <arrow.to.target n="marg346"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001698">
                <margin.target id="marg346"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001699">Omne, quod mouetur, mouetur ſecundum naturam ponderis,
                <lb/>
              quæ in attractione, ut demonſtratum eſt, æqualis eſt dimidio ſu­
                <lb/>
              ſpenſi, cum ergo diuidatur in multiplices partes motus uniuſcuiuſ­
                <lb/>
              que, eſt ſecundum dimidium illius partis, ut, ſi ſint ſex rotæ in cur­
                <lb/>
              ru det, quod uehitur, ſit pondus ſexaginta librarum, unaquæque </s>
            </p>
            <p type="main">
              <s id="id001700">
                <arrow.to.target n="marg347"/>
                <lb/>
              rota habet pondus quinque librarum, ſcilicet diuiſo triginta per
                <lb/>
              ſex, & quia quod cunque mouetur ſphæricè non habet pondus,
                <lb/>
              niſi quantum premitur axis, ideò pondus ſexaginta librarum in
                <lb/>
              uehendo redditur læſus, quanto proportio producta minor eſt
                <lb/>
              additione. </s>
              <s id="id001701">Exemplum, ſit deductum pondus ſexaginta librarum
                <lb/>
              per ſex rotas ad uiginti quatuor, quia ſi rotæ poſſent circumduci,
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              ut in inuerſione dictum eſt, & eſſent æquales, & in ſolido æquali,
                <lb/>
              ac duro, nulla ui mouerentur, ſed quaſi per ſe, ergo ſuppoſito pon­
                <lb/>
              dere uiginti quatuor librarum aſſumemus unamquamque partem,
                <lb/>
              & ducemus eam in ſe ipſam, ſcilicet detraham quintam partem ex
                <lb/>
              toto 30, fit 24, duc 30 in ſe, fit 900, duc 24 in ſe, fit 576, proportio ut
                <lb/>
              25 ad 16, at diuiſo 30 in ſex partes, fit 5, detrahe quintam partem, fit
                <lb/>
              4, duc in ſe, fit 16, duc in ſex, fit 96, igitur proportio 900 ad 96 eſt ut
                <lb/>
              25 ad 2 2/3, quod ergo erat 16 factum eſt 2 2/3, proportio ergo de­
                <lb/>
              creſcentis maior eſt diuiſo per plura. </s>
              <s id="id001702">Sed plerunque additis ro­
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              tis creſcit pondus nihilo ſecius, redditur etiam leuius. </s>
              <s id="id001703">Sed & de
                <lb/>
              hoc in ſequenti.</s>
            </p>
            <p type="margin">
              <s id="id001704">
                <margin.target id="marg347"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              40.</s>
            </p>
            <p type="main">
              <s id="id001705">Propoſitio centeſima.</s>
            </p>
            <p type="main">
              <s id="id001706">Proportionem grauitatis ponderum attractorum per trochlea­
                <lb/>
              rum numerum inueſtigare.
                <lb/>
                <arrow.to.target n="marg348"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001707">
                <margin.target id="marg348"/>
              C
                <emph type="italics"/>
              om.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001708">Ariſtoteles in Mechanicis cenſet cauſam leuitatis trochlearum </s>
            </p>
            <p type="main">
              <s id="id001709">
                <arrow.to.target n="marg349"/>
                <lb/>
              eſſe in pondere eleuando, quòd pondera auxilio uectium facilius
                <lb/>
              mouentur, quàm manibus. </s>
              <s id="id001710">Rotulæ uerò in trochleis uectes ſunt,
                <lb/>
              & axis miſta hypomochlij, ergo facilius pondus trahitur per u­
                <lb/>
              nam rotulam, quàm ſi manu traheretur, at uerò per duas tres,
                <lb/>
              unde tris paſſus longe facilius, & etiam facilius per quinque, unde
                <lb/>
              pentas paſſus, nam quinque orbiculis, quaſi totidem uectibus
                <lb/>
              diuiſum pondus manifeſtè fit leuius, & ut dictum eſt, tanquam
                <lb/>
              totidem uectibus pondus eleuatur, eſtqúe proportio </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>