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>
            <pb pagenum="7" xlink:href="015/01/026.jpg"/>
            <p type="main">
              <s id="id000176">Sit proportio lineæ a ad lineam b, ut anguli c ad angulum d, ſta­
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                <arrow.to.target n="marg6"/>
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              tuatur e monas in genere a
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                <figure id="id.015.01.026.1.jpg" xlink:href="015/01/026/1.jpg" number="5"/>
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              b, & fiat f ad e, ut c ad d, & du
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                <arrow.to.target n="marg7"/>
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              catur a in f & b in e, & pro­
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              ducantur g & h. </s>
              <s id="id000177">Quia ergo
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                <arrow.to.target n="marg8"/>
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              f eſt proportio ipſa, erit g ad
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                <arrow.to.target n="marg9"/>
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              a ut c ad d, ſed h eſt æqualis
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              b, igitur a ad h ut ad b. </s>
              <s id="id000178">Du­
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              cta ergo dicetur proportio a
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                <arrow.to.target n="marg10"/>
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              ad b in proportionem c ad d
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              ducendo terminos proportionis, ſeu quantitatis recta ſcilicet ſu­
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              periores cum ſuperioribus, & inferiores cum inferioribus. </s>
              <s id="id000179">Nam ſi
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                <arrow.to.target n="marg11"/>
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              rurſum conſtituantur f ad e ut a ad b cùm f ſit proportio, & k ad f ut
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                <arrow.to.target n="marg12"/>
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              c ad d, erit k ad e, ut g ad h, k autem fit ex ductu proportionis a ad b,
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              quæ eſt fin proportionem c ad d, liquet igitur propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id000180">
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              C
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              or
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              ^{m}.</s>
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              <s id="id000181">
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              er
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              9. P
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              etit.
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              </s>
            </p>
            <p type="margin">
              <s id="id000182">
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              er
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              10. P
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              et.
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              </s>
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            <p type="margin">
              <s id="id000183">
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              P
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              er
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              8. P
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              etit.
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              </s>
            </p>
            <p type="margin">
              <s id="id000184">
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              P
                <emph type="italics"/>
              er
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              2. A
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              ni­
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              mi ſentent.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000185">
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              P
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              er
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              11. P
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              et.
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              </s>
            </p>
            <p type="margin">
              <s id="id000186">
                <margin.target id="marg12"/>
              P
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              er
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              8. P
                <emph type="italics"/>
              etit.
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              </s>
            </p>
            <p type="main">
              <s id="id000187">Propoſitio
                <expan abbr="ſecũnda">ſecunda</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id000188">Proportio extremorum producitur ex intermedijs.
                <lb/>
                <arrow.to.target n="marg13"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000189">
                <margin.target id="marg13"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000190">Sint a b c quantitates dico proportio­
                <lb/>
                <figure id="id.015.01.026.2.jpg" xlink:href="015/01/026/2.jpg" number="6"/>
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              nem a ad c, produci ex proportione a ad b </s>
            </p>
            <p type="main">
              <s id="id000191">
                <arrow.to.target n="marg14"/>
                <lb/>
              & b ad c, ſtatuantur totidem à monade d e
                <lb/>
              f, erúntque ex demonſtrantis ab Euclide in
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              quinto
                <expan abbr="Elemẽtorum">Elementorum</expan>
              in eadem proportio­
                <lb/>
              ne, ſtatuatur ergo d prima quantitas e ſe­
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              cunda & tertia f quarta. </s>
              <s id="id000192">eritqúe per præce­
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                <arrow.to.target n="marg15"/>
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              dentem proportio productorum ex d in e
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              & ſit g, & in f & ſit h, producta ex propor­
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              tionibus d ad e & e ad f, quare ex propor­
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              tionibus a ad b & b ad e, ſed ex dictis cum
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              e ſit eadem, erit proportio d ad f, ut g ad h & proportio, d ad f per
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              æquam proportionem ab Euclide demonſtratam, ut a ad c, igitur
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                <arrow.to.target n="marg16"/>
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              proportio a ad c producitur ex proportionibus a ad b & b ad c, &
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              eſt proportio ipſa a ad c d numerus, ut oſtenſum eſt.</s>
            </p>
            <p type="margin">
              <s id="id000193">
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              P
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              er
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              6.
                <emph type="italics"/>
              &
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              9.
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              P
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              etit.
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              </s>
            </p>
            <p type="margin">
              <s id="id000194">
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              P
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              er
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              13. P
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              et.
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              </s>
            </p>
            <p type="margin">
              <s id="id000195">
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              P
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              er
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              13. P
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              et.
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              </s>
            </p>
            <p type="main">
              <s id="id000196">Ex hoc ſequitur, quòd cùm fuerit quantitas tertia monas ex pro­
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                <arrow.to.target n="marg17"/>
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              portionibus inuicem ductis producetur prima quantitas.
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                <arrow.to.target n="marg18"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000197">
                <margin.target id="marg17"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="margin">
              <s id="id000198">
                <margin.target id="marg18"/>
              C
                <emph type="italics"/>
              or
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              ^{m}. 3</s>
            </p>
            <p type="main">
              <s id="id000199">Ex hoc ſequitur, quòd conuerſa proportio producitur ex con­
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              uerſis proportionibus.</s>
            </p>
            <p type="main">
              <s id="id000200">Propoſitio tertia.</s>
            </p>
            <p type="main">
              <s id="id000201">Si proportio ex duabus proportionibus in quatuor terminis
                <lb/>
              producatur, ipſa uerò proportio inter duas alias quantitates </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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