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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        <body>
          <chap>
            <p type="main">
              <s id="id003653">
                <pb pagenum="217" xlink:href="015/01/236.jpg"/>
              quadratum eſt æquale quadratis g h, h f & duplo g h in h f, & qua­</s>
            </p>
            <p type="main">
              <s id="id003654">
                <arrow.to.target n="marg673"/>
                <lb/>
              dratum fh eſt ęquale e ſuperficiei, erit quadratum h g minus ſuper­
                <lb/>
              ficie d in duplo g h in h f, quare productum a b in c erit ęquale qua­
                <lb/>
              drato g h in ſe & a, nam duplo g h in h f & iam duplum g h in h f eſt
                <lb/>
              ęquale producto g h in a, quia a eſt duplum h f, igitur qualis eſt pro
                <lb/>
                <arrow.to.target n="marg674"/>
                <lb/>
              portio a b ad g h, talis g h & a ad c, igitur per definitionem datam
                <lb/>
              g h & quantitas grauitatis auxiliaris æquale.</s>
            </p>
            <p type="margin">
              <s id="id003655">
                <margin.target id="marg673"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              4.
                <emph type="italics"/>
              primi.
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003656">
                <margin.target id="marg674"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              ſex
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003657">Ex hoc manifeſtum eſt, quod ſi fuerit datum pondus tertium au­
                <lb/>
                <arrow.to.target n="marg675"/>
                <lb/>
              xiliare, quod ſciemus quantum addendum uel detrahendum ut fi­
                <lb/>
              at pondus auxiliare æquale, nam inuenta g h ſi fuerit k maior adde­
                <lb/>
              mus quod deficit, & ſi minor quàm k detrahemus ex k quod eſt
                <lb/>
              ſuperfluum.</s>
            </p>
            <p type="margin">
              <s id="id003658">
                <margin.target id="marg675"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id003659">Et rurſus inuenta g h ut perficiamus pondus ęquale, augebimus
                <lb/>
                <arrow.to.target n="marg676"/>
                <lb/>
              aliquantiſper, ut fiat æqualis ad unguem difficultas in motu: iuxta
                <lb/>
                <arrow.to.target n="marg677"/>
                <lb/>
              doctrinam ſuperiùs datam.</s>
            </p>
            <p type="margin">
              <s id="id003660">
                <margin.target id="marg676"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="margin">
              <s id="id003661">
                <margin.target id="marg677"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              187.</s>
            </p>
            <p type="main">
              <s id="id003662">Propoſitio centeſima nonageſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id003663">Si ex medio diametri linea ad perpendiculum erigatur ad circu­
                <lb/>
              li peripheriam: ex eo puncto
                <expan abbr="autẽ">autem</expan>
              quotlibet lineæ ducantur ſeu in­
                <lb/>
              tus ad circumferentiam uſque, ſeu extra ad diametrum, erit proportio
                <lb/>
              totius lineæ ad totam, uelut mutuò partis ad partem.</s>
            </p>
            <p type="main">
              <s id="id003664">Ex media diametro a c. 1.
                <expan abbr="cẽtro">centro</expan>
              b, ducatur ad perpendiculum b d,
                <lb/>
                <arrow.to.target n="marg678"/>
                <lb/>
              & ex d lineæ d a d e d h, dico d e ad d a, ut d a ad d f, & d h ad d a ut
                <lb/>
              d a ad d g, & d e ad d h ut d g ad d f. </s>
              <s id="id003665">Quia n quod fit ex d em e f, æ­
                <lb/>
              quale eſt ei quod ex e c in e a, quod uerò ex e c in e a cum quadrato
                <lb/>
                <arrow.to.target n="marg679"/>
                <lb/>
              b d ſeu b a ęquale eſt quadrato b e, igitur ex
                <lb/>
                <figure id="id.015.01.236.1.jpg" xlink:href="015/01/236/1.jpg" number="229"/>
                <lb/>
              e d in e f cum quadrato d b æquale qua­
                <lb/>
                <arrow.to.target n="marg680"/>
                <lb/>
              drato b e, ex d e igitur in e f cum quadratis
                <lb/>
                <arrow.to.target n="marg681"/>
                <lb/>
              d b & b a æquale quadrato d e. </s>
              <s id="id003666">Quadratis
                <lb/>
                <arrow.to.target n="marg682"/>
                <lb/>
              autem a b & b d æquale quadratum d e:
                <lb/>
                <arrow.to.target n="marg683"/>
                <lb/>
              igitur ex d e in e f cum quadrato d a æqua­
                <lb/>
                <arrow.to.target n="marg684"/>
                <lb/>
              le quadrato d e. </s>
              <s id="id003667">At quadratum d e æquale
                <lb/>
              eſt his quæ ex d e in e f, & f d igitur detra­
                <lb/>
                <arrow.to.target n="marg685"/>
                <lb/>
              cto communi ex d e in e f, erit quadratum d
                <lb/>
              e æquale ei quod ex d e in d f, igitur d e ad
                <lb/>
                <arrow.to.target n="marg686"/>
                <lb/>
              d a, ut d a ad d f. </s>
              <s id="id003668">Similiter quod fit ex h d in
                <lb/>
                <arrow.to.target n="marg687"/>
                <lb/>
              d g, æquale eſt ei quod fit ex h g in g d cum
                <lb/>
              quadrato d g, at quod fit ex h g in g d eſt æquale ei quod fit ex c g in
                <lb/>
              g a, erit quod fit ex c g in g a cum quadrato d g ęquale ei quod fit ex
                <lb/>
              d h in d g. </s>
              <s id="id003669">Quadratum autem d g eſt æquale quadratis d b, b g igi­
                <lb/>
                <arrow.to.target n="marg688"/>
                <lb/>
              tur d h in d g æquale eſt ei quod fit ex g a in c g cum quadratis b d
                <lb/>
              b g, at quod fit ex a g in g c cum quadrato b g eſt æquale quadrato </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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