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="63" xlink:href="015/01/082.jpg"/>
            <p type="main">
              <s id="id001203">Propoſitio ſeptuageſima prima.</s>
            </p>
            <p type="main">
              <s id="id001204">Proportionem leuitatis ponderis per uirgam torcularem attra­
                <lb/>
              cti ad rectam ſuſpenſionem inuenire.</s>
            </p>
            <figure id="id.015.01.082.1.jpg" xlink:href="015/01/082/1.jpg" number="78"/>
            <p type="main">
              <s id="id001205">Sit torcularis uirga, cuius ſpiræ a b per circui­
                <lb/>
                <arrow.to.target n="marg252"/>
                <lb/>
              tum ſint centuplæ ad altitudinem a b, & axis d c
                <lb/>
                <arrow.to.target n="marg253"/>
                <lb/>
              ſemidiametro b c centupla, & quoniam per ſupe­
                <lb/>
              rius aſſumpta, qualis eſt proportio ſpatij ad ſpa­
                <lb/>
              tium, talis leuitatis ad
                <expan abbr="leuitatẽ">leuitatem</expan>
              ,
                <expan abbr="igit̃">igitur</expan>
              e pondus aſcen
                <lb/>
              dens per a b leuius quam per b
                <expan abbr="crectã">c rectam</expan>
              centuplo, et
                <lb/>
              ſimiliter cum circuitus b c, & d c ſint in eodem tem
                <lb/>
              pore, & circuitus d c, ſit centuplus ad ſpiralem b c
                <lb/>
              per demonſtrata ab Euclide, ergo e erit centuplo
                <lb/>
              leuius circum ductum per d quàm b, ſed per b circumductum cen­
                <lb/>
              tuplo leuius eſt, quàm per rectam, igitur e ponderat ſolum particu­
                <lb/>
              lam ex decem millibus recti ponderis.</s>
            </p>
            <p type="margin">
              <s id="id001206">
                <margin.target id="marg252"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="margin">
              <s id="id001207">
                <margin.target id="marg253"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              45.</s>
            </p>
            <p type="main">
              <s id="id001208">Propoſitio ſeptuageſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id001209">Proportionem ponderis ſphęræ pendentis ad aſcendentem per
                <lb/>
              accliue planum inuenire</s>
            </p>
            <figure id="id.015.01.082.2.jpg" xlink:href="015/01/082/2.jpg" number="79"/>
            <p type="main">
              <s id="id001210">Sit ſphæra æqualis ponderi g in pun­
                <lb/>
                <arrow.to.target n="marg254"/>
                <lb/>
              cto b, quæ debeat trahi ſuper b c accli­
                <lb/>
              ue planum b e ad perpendiculum pla­
                <lb/>
                <arrow.to.target n="marg255"/>
                <lb/>
              ni b f. </s>
              <s id="id001211">Quia ergo in b e mouetur a, qua­
                <lb/>
              uis modica ui per dicta ſuperius, erit per
                <lb/>
              communem animi ſententiam uis, quæ
                <lb/>
              mouebit a per e b nulla: per dicta uerò
                <lb/>
              a mouebitur ad f ſemper, a conſtanti ui
                <lb/>
              æquali g, & per b c a conſtanti ui æqua­
                <lb/>
              li k, ſicut per b d a conſtanti æquali h, ergo per ultimam petitio­
                <lb/>
              nem, cum termini ſeruent, quo ad partes eandem rationem ſin­
                <lb/>
              guli per ſe, & motus per b e ſit a nulla ui, erit proportio g ad k, ue­
                <lb/>
              lut proportio uis, quæ mouet per b f ad uim, quæ mouet per
                <lb/>
              b c, & uelut anguli per e b f recti ad angulum e b c, & ita uis,
                <lb/>
              quæ mouet a per b f, & eſt, ut dictum eſt, g ad uim, quæ mouet
                <lb/>
              per b d, & eſt h ex ſuppoſito, ut c b f ad e b d, igitur proportio dif­
                <lb/>
              ficultatis motus a per b d ad idem a per b c, eſt uelut h ad k, quod
                <lb/>
              erat demonſtrandum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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