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="id001678">
                <pb pagenum="92" xlink:href="015/01/111.jpg"/>
              no de, & eleuetur ex a, & manifeſtum eſt, quod inſidebit per totam
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              lineam c f ipſi plano, & proportio grauitatis totius ſuſpenſi in com
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              paratione ad grauitatem eius, qui inuertit, eſt, uelut proportio par­
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              tis terminatæ ad lineam c f uerſus eum, qui eleuat ad partem, quæ
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              ultra eſt, cum uerò hæ partes notæ ſint iuxta perpendiculum ex
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              centro grauitatis, manifeſtum eſt, quod ſciemus pondus corporis
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              a b cf, dum inuertitur in quo cunque ſitu ad pondus eius, dum ſu­
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              ſpenditur, & clarum eſt, quòd cùm centrum, & medium grauitatis
                <lb/>
              fuerint in una linea per c f, tunc nulla erit grauitas.</s>
            </p>
            <p type="margin">
              <s id="id001679">
                <margin.target id="marg339"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              40.</s>
            </p>
            <p type="main">
              <s id="id001680">Propoſitio nonageſima octaua.</s>
            </p>
            <p type="main">
              <s id="id001681">Proportionem ponderum æqualium per differentiam angulo­
                <lb/>
              rum inuenire.
                <lb/>
                <arrow.to.target n="marg340"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001682">
                <margin.target id="marg340"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001683">Sit a b, quæ ſi appenſa eſſet ad æquidi­
                <lb/>
                <figure id="id.015.01.111.1.jpg" xlink:href="015/01/111/1.jpg" number="106"/>
                <lb/>
              ſtantem terræ ſuperficiei, nulla ui poſſet ele</s>
            </p>
            <p type="main">
              <s id="id001684">
                <arrow.to.target n="marg341"/>
                <lb/>
              uari, inflectatur ergo ad c punctum, omiſſa
                <lb/>
              c g, & manifeſtum eſt, quod ſi b c inſiſteret
                <lb/>
                <arrow.to.target n="marg342"/>
                <lb/>
              ad perpendiculum, ponderaret a c ſi eſſet in
                <lb/>
              æquilibrio, ponatur ergo accliuis in c d per
                <lb/>
              notum angulum. </s>
              <s id="id001685">Quia igitur b c ad c a no­
                <lb/>
              ta eſt, erit dicta ſuperiùs notum pondus
                <lb/>
              b h, poſita h c æquali c a, quare totius a b,
                <lb/>
              & iam fuit e k notum, & punctus d notus:
                <lb/>
              hoc enim infrà demonſtrabitur, qualis igitur proportio lineæ
                <lb/>
                <arrow.to.target n="marg343"/>
                <lb/>
              tranſuerſæ dl ad lineam deſcendentem d m, talis differentiæ pon­
                <lb/>
              derum c m, & c e, id eſt partis ad partem. </s>
              <s id="id001686">hæc autem inferiùs de­
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              monſtrabuntur. </s>
              <s id="id001687">Neque enim abſurdum eſt in materijs miſtis, ali­
                <lb/>
                <arrow.to.target n="marg344"/>
                <lb/>
              quando uti nondum demonſtratis cum fuerint mathematica, quia
                <lb/>
              obtinent principij rationem, quod etiam facit Archimedes. </s>
              <s id="id001688">Ma­
                <lb/>
              nifeſtum eſt autem, quod in angulo m c d recti dimidio, propor­
                <lb/>
              tio media erit. </s>
              <s id="id001689">Sed hoc bifariam contingere poteſt ſcilicet, ut ſit
                <lb/>
              media, per quantitatem, & per proportionem, eſt autem media, ut
                <lb/>
                <arrow.to.target n="marg345"/>
                <lb/>
              demonſtrabitur infrà ſecundum proportionem l d ad l e, propo­
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              natur ergo c e b, erit latus quadrati <02> 72, igitur latus octogoni eſt
                <lb/>
              <02> v: 72 m: <02> 2592, & latus reſidui <02> v: 72 p: <02> 2592. quadrata er­
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              go partium baſis differunt in <02> 10368. Quare partes baſis ſunt
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              6 p: <02> 18, & 6 m: <02> 18 ſcilicet l e, l d autem eſt <02> 18, igitur differen­
                <lb/>
              tia, & proportio eſt, qualis <02> 18 ad 6 m: <02> 18 fermê, ut 17 ad 7, & ta­
                <lb/>
              lis eſt proportio ponderis c d ad pondus c e ratione in crementi,
                <lb/>
              ſeu differentiæ. </s>
              <s id="id001690">Vt ſi pondus in c e eſſet decem librarum in c in </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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