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="id000261">
                <pb pagenum="12" xlink:href="015/01/031.jpg"/>
              dem tamen generis, cum illis dico quòd proportio e ad d eſt com­
                <lb/>
              poſita ex proportionibus e ad a c, & e ad b c. </s>
              <s id="id000262">Poſita ergo e tan<08> ſu­
                <lb/>
              periore numero, & a c & c b inferioribus, erit ex octaua propoſitio­
                <lb/>
              ne huius proportio productorum ex e in a c, & coniunctorum, &
                <lb/>
              ex conſequenti per primam ſecundi Elementorum producti ex e in
                <lb/>
              a b ad productum ex a c in c b compoſita ex proportionibus e ad
                <lb/>
              a c, & e ad c b: at quod fit ex a c in c b, eſt æquale ei quod fit ex a b in
                <lb/>
              d, eo quòd a b, a c, c b & d ſunt omiologæ per decimam ſextam ſexti
                <lb/>
                <expan abbr="Elemẽtorum">Elementorum</expan>
              : Proportio igitur producti ex e in a b ad productum
                <lb/>
              ex d in a b eſt compoſita ex proportionibus e ad a c, & e ad e b: At
                <lb/>
              proportio producti ex e in a b ad productum ex d in a b, eſt uelut e
                <lb/>
                <arrow.to.target n="marg32"/>
                <lb/>
              ad d. </s>
              <s id="id000263">per ſuppoſita igitur proportio e ad d eſt compoſita ex propor
                <lb/>
              tionibus e ad a c, & e ad b c, quod fuit demonſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id000264">
                <margin.target id="marg32"/>
              13. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000265">Propoſitio undecima.</s>
            </p>
            <p type="main">
              <s id="id000266">Proportio aggregati quarumlibet duarum quantitatum ad ag­
                <lb/>
              gregatum duarum æqualium quantitatum eſt compoſita ex pro­
                <lb/>
              portionibus primis, & diuiſa per duplam.
                <lb/>
                <arrow.to.target n="marg33"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000267">
                <margin.target id="marg33"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000268">Sit proportio a ad c, & b ad d, & ſint c & d
                <lb/>
                <figure id="id.015.01.031.1.jpg" xlink:href="015/01/031/1.jpg" number="19"/>
                <lb/>
              æquales, dico quòd proportio a b ad c d eſt
                <lb/>
              compoſita ex proportionibus a ad c, & b ad
                <lb/>
              d diuiſo compoſito per duplam. </s>
              <s id="id000269">Quia enim </s>
            </p>
            <p type="main">
              <s id="id000270">
                <arrow.to.target n="marg34"/>
                <lb/>
              c & d ſunt æquales, erit b ad c, ut b ad d, qua­
                <lb/>
              re ex diffinitione cùm proportio a b ad c d
                <lb/>
                <arrow.to.target n="marg35"/>
                <lb/>
              ſit compoſita ex proportionibus a ad c, & b
                <lb/>
              ad c, erit etiam compoſita ex dictis ex propoſitione a ad c, & b ad d,
                <lb/>
                <arrow.to.target n="marg36"/>
                <lb/>
              ſtatuatur ergo e æqualis c d media inter a b & c. </s>
              <s id="id000271">Et erit per ſecun­
                <lb/>
              dam propoſitionem proportio aggregati a b ad c producta ex
                <lb/>
                <arrow.to.target n="marg37"/>
                <lb/>
              proportione aggregati a b ad c, & e ad c, igitur proportio a b ad e
                <lb/>
              erit proportio a b ad c, diuiſa per proportionem e ad c, ſed e ad c eſt
                <lb/>
                <arrow.to.target n="marg38"/>
                <lb/>
              dupla: igitur proportio a b ad c d eſt proportio a b ad c diuiſa per
                <lb/>
              duplam.</s>
            </p>
            <p type="margin">
              <s id="id000272">
                <margin.target id="marg34"/>
              E
                <emph type="italics"/>
              x ſexta
                <emph.end type="italics"/>
              A
                <emph type="italics"/>
              nim.
                <lb/>
              com. </s>
              <s id="id000273">ſententia.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000274">
                <margin.target id="marg35"/>
              D
                <emph type="italics"/>
              ecimaquarta
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000275">
                <margin.target id="marg36"/>
              13. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000276">
                <margin.target id="marg37"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              2. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000277">
                <margin.target id="marg38"/>
              P
                <emph type="italics"/>
              er quintam
                <emph.end type="italics"/>
                <lb/>
              A
                <emph type="italics"/>
              nim. </s>
              <s id="id000278">com. </s>
              <s id="id000279">ſen
                <lb/>
              tentiam.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000280">Propoſitio duodecima.</s>
            </p>
            <p type="main">
              <s id="id000281">Propoſitis duabus proportionibus unam alteri iungere abſque
                <lb/>
              multiplicatione.
                <lb/>
                <arrow.to.target n="marg39"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000282">
                <margin.target id="marg39"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.
                <lb/>
              10. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000283">Sint propoſitæ proportiones a ad c &
                <lb/>
                <figure id="id.015.01.031.2.jpg" xlink:href="015/01/031/2.jpg" number="20"/>
                <lb/>
              b ad d, & aſſumo e ad c, iuxta ea quæ Eu­
                <lb/>
              clides demonſtrauit, ut b ad d, erit igitur </s>
            </p>
            <p type="main">
              <s id="id000284">
                <arrow.to.target n="marg40"/>
                <lb/>
              proportio a e ad c, compoſita ex proportionibus a ad c, & e ad c,
                <lb/>
              ſed proportio e ad c eſt, ut b ad d, igitur proportio a e ad c compo­
                <lb/>
              ſita eſt ex proportionibus a ad c, & b ad d.</s>
            </p>
            <p type="margin">
              <s id="id000285">
                <margin.target id="marg40"/>
              E
                <emph type="italics"/>
              x generali
                <lb/>
              com.
                <emph.end type="italics"/>
              A
                <emph type="italics"/>
              nim. ſen
                <lb/>
              tentia.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000286">Aliter ex b in c fiat f ex a in d, g ex c in d h coniunctum ex f g, k.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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