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="id001415">
                <pb pagenum="76" xlink:href="015/01/095.jpg"/>
              uaſe aqua pleno impoſitis ſenſim centum aureis coronatis nihil ef­
                <lb/>
              funditur, non quod quicquam abſumatur in metallo, ſed cauſa eſt
                <lb/>
              quod cum aurum ſit duplum pondere ferro, erit ex demonſtratis
                <lb/>
              ſex decuplum ad pondus aquæ. </s>
              <s id="id001416">Igitur cum ſit proportio ponderis
                <lb/>
              auri ad differentiam ſpatij eadem, ſi ſit uas aquæ ponderis libræ
                <lb/>
              unius & mediæ, erit pondus totum xxiij unciarum, igitur aqua de­
                <lb/>
              ficiet ſolum ex decimaoctaua parte ſeu creſcet ex impoſitione auri,
                <lb/>
              ſed illa pars in tumore aquæ abſumitur,
                <expan abbr="nõ">non</expan>
              ſolum, quia
                <lb/>
                <figure id="id.015.01.095.1.jpg" xlink:href="015/01/095/1.jpg" number="88"/>
                <lb/>
              dum aureos imponimus plana ſolum ſit, ſed quia non ex
                <lb/>
              quauis rotunditate defluit, aliter in urceo tam exiguo
                <lb/>
              non poſſet apparere rotunda: quod enim rotunditas to­
                <lb/>
              tius terræ, quæ etiam planam oſtendit totam unam re­
                <lb/>
              gionem ad rotunditatem quæ apparet in exiguo urceo
                <lb/>
              aquæ. </s>
              <s id="id001417">Eſt igitur rotunditas illa potius ob lentorem aquę qui auge­
                <lb/>
              tur à lentore argenti, & etiam magis auri, cum ſenſu digitorum per­
                <lb/>
              cipiatur.</s>
            </p>
            <p type="main">
              <s id="id001418">
                <arrow.to.target n="marg297"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001419">
                <margin.target id="marg297"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 3.</s>
            </p>
            <p type="main">
              <s id="id001420">Ex hoc apparet ratio quomodo Archimedes potuerit deprehen
                <lb/>
              dere coronam à Hierone propoſitam quantum auri & argenti con
                <lb/>
              tineret. </s>
              <s id="id001421">Sit ergo uas a b aqua
                <expan abbr="plenũ">plenum</expan>
              ponderis unciarum triginta, &
                <lb/>
              cum libra auri ſit ponderis unciarum quadraginta unius, & cum li­
                <lb/>
              bra argenti ponderis unciarum quadraginta cum dimidio, igitur
                <lb/>
              erit auri pondus ad aquæ pondus duodecuplum, argenti autem
                <lb/>
              ad idem octuplum, quare auri ad
                <expan abbr="argẽtum">argentum</expan>
              pondus ſexquialterum.
                <lb/>
              </s>
              <s id="id001422">Ponamus ergo quod corona impoſita ex auro & argento ſolo fa­
                <lb/>
              bricata (hoc enim ſupponere oportet) fuerit unciarum ſexaginta,
                <lb/>
              pondus autem aquæ contentę cum corona in uaſe unciarum uigin
                <lb/>
              ti quatuor cum dimidio, ſcilicet totum octuaginta quatuor cum di­
                <lb/>
              midia, erit ergo proportio ponderis coronæ ad pondus aquæ, ut
                <lb/>
              cxx ad xi, aurum igitur eſt proportione duodecuplum, argentum
                <lb/>
              autem octuplum, corona ut cxx ad xi. </s>
              <s id="id001423">Conſtituantur ſub eiſdem ra­
                <lb/>
              tionibus ducen do lxxxviij. </s>
              <s id="id001424">cxx. </s>
              <s id="id001425">cxxxij. </s>
              <s id="id001426">hoc eſt ac ſi dicamus, accipe
                <lb/>
              partes ex cxxxij & lxxxviij, tot ut faciant integrum & componant
                <lb/>
              cxx. </s>
              <s id="id001427">Et ideò reduces ad minores numeros, ſcilicet xxxiij. </s>
              <s id="id001428">xxij. </s>
              <s id="id001429">et xxx. </s>
            </p>
            <p type="main">
              <s id="id001430">
                <arrow.to.target n="marg298"/>
                <lb/>
              & operaberis per regulam de conſolatione monetarum, quas po­
                <lb/>
              nemus infrà, & fient auri partes octo & argen
                <lb/>
                <figure id="id.015.01.095.2.jpg" xlink:href="015/01/095/2.jpg" number="89"/>
                <lb/>
              ti partes iij, nam cum duxeris iij in octo pon­
                <lb/>
              dus argenti fiet xxiiij, & cum duxeris viij in
                <lb/>
              xij, pondus auri fiet xcvi, igitur totum pon­
                <lb/>
              dus erit cxx, diuidendum per xi, aggregatum
                <lb/>
              partium auri & argenti, ita uero uncia ad unciam, ut tota corona mi
                <lb/>
              ſta ad coronam puram auri & argenti.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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