Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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          <p>
            <s xml:id="echoid-s9313" xml:space="preserve">
              <pb o="368" file="0388" n="388" rhead="GEOMETRIÆ"/>
            drata, AF, ſunt vt compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9314" xml:space="preserve">ON. </s>
            <s xml:id="echoid-s9315" xml:space="preserve">.</s>
            <s xml:id="echoid-s9316" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9317" xml:space="preserve">ex, BN, & </s>
            <s xml:id="echoid-s9318" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9319" xml:space="preserve">NE, ad,
              <lb/>
              <note position="left" xlink:label="note-0388-01" xlink:href="note-0388-01a" xml:space="preserve">11. l. 1.</note>
            OE, vel vt iſtorum tripla .</s>
            <s xml:id="echoid-s9320" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9321" xml:space="preserve">vt, XE, ad trip lam, OE. </s>
            <s xml:id="echoid-s9322" xml:space="preserve">Inſuper omnia
              <lb/>
              <note position="left" xlink:label="note-0388-02" xlink:href="note-0388-02a" xml:space="preserve">Corol. 39.
                <lb/>
              & Sch. 40.
                <lb/>
              l. 1.</note>
            quadrata, AF, ad omnia quadrata, CG, habent rationem compoſitã
              <lb/>
              <figure xlink:label="fig-0388-01" xlink:href="fig-0388-01a" number="265">
                <image file="0388-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0388-01"/>
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            ex ea, quã habet quadratu, DF, ad quadratũ,
              <lb/>
            HG, ideſt rectangulum, OEN, ad rectagulũ,
              <lb/>
            OMN, .</s>
            <s xml:id="echoid-s9323" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9324" xml:space="preserve">horũ tripla, .</s>
            <s xml:id="echoid-s9325" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9326" xml:space="preserve">rectangulum ſubtri-
              <lb/>
              <note position="left" xlink:label="note-0388-03" xlink:href="note-0388-03a" xml:space="preserve">EX antec.</note>
            pla, OE, &</s>
            <s xml:id="echoid-s9327" xml:space="preserve">, EN, ſola, ad rectã gulũ ſub tripla,
              <lb/>
            OM, & </s>
            <s xml:id="echoid-s9328" xml:space="preserve">ſola, MN, & </s>
            <s xml:id="echoid-s9329" xml:space="preserve">ex rñe, EN, ad, NM; </s>
            <s xml:id="echoid-s9330" xml:space="preserve">tã-
              <lb/>
            dem omnia quadrata, CG, ad omnia quadra-
              <lb/>
            ta hyperbolæ, HNG, ſunt vt, OM, ad cõpo-
              <lb/>
            ſitam ex, BN, & </s>
            <s xml:id="echoid-s9331" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9332" xml:space="preserve">NM, .</s>
            <s xml:id="echoid-s9333" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9334" xml:space="preserve">vt tripla, OM,
              <lb/>
            ad, MX, ideſt ſumpta, MN, communi alti-
              <lb/>
            tudine, vt rectangulũ ſub tripla, OM, & </s>
            <s xml:id="echoid-s9335" xml:space="preserve">ſub,
              <lb/>
            MN, ad rectãgulũ ſub, XM, MN, ergo omnia
              <lb/>
            quadrata hyperbolæ, DNF, ad omnia qua-
              <lb/>
            drata hyperbolæ, HNG, habent rationem
              <lb/>
            compoſitam ex ea, quam habet, XE, ad tri-
              <lb/>
            plam, EO, .</s>
            <s xml:id="echoid-s9336" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9337" xml:space="preserve">ſumpta, EN, communi altitudine, ex ea, quam ha-
              <lb/>
            bet rectangulum, XEN, ad rectangulum ſub, NE, & </s>
            <s xml:id="echoid-s9338" xml:space="preserve">tripla, EO, & </s>
            <s xml:id="echoid-s9339" xml:space="preserve">
              <lb/>
            ex ea, quam habet rectangulum ſub tripla; </s>
            <s xml:id="echoid-s9340" xml:space="preserve">OE, & </s>
            <s xml:id="echoid-s9341" xml:space="preserve">ſub, EN, ad re-
              <lb/>
            ctangulum ſub tripla, OM, & </s>
            <s xml:id="echoid-s9342" xml:space="preserve">ſub, MN, & </s>
            <s xml:id="echoid-s9343" xml:space="preserve">rectangulum ſub tripla,
              <lb/>
            OM, & </s>
            <s xml:id="echoid-s9344" xml:space="preserve">ſub, MN, ad rectangulum ſub, MN, & </s>
            <s xml:id="echoid-s9345" xml:space="preserve">MX, & </s>
            <s xml:id="echoid-s9346" xml:space="preserve">tandem ex
              <lb/>
            ea, quam habet, EN, ad, NM; </s>
            <s xml:id="echoid-s9347" xml:space="preserve">porrò iſtæ rationes .</s>
            <s xml:id="echoid-s9348" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9349" xml:space="preserve">quam habet
              <lb/>
            rectangulum ſub, XE, &</s>
            <s xml:id="echoid-s9350" xml:space="preserve">, EN, ad rectangulum ſub tripla, OE, &</s>
            <s xml:id="echoid-s9351" xml:space="preserve">,
              <lb/>
            EN, item quam habet rectangulum ſub tripla, OE, &</s>
            <s xml:id="echoid-s9352" xml:space="preserve">, EN, ad re-
              <lb/>
            ctangulum ſub tripla, OM, & </s>
            <s xml:id="echoid-s9353" xml:space="preserve">MN, & </s>
            <s xml:id="echoid-s9354" xml:space="preserve">quam habet rectangulum
              <lb/>
            ſubtripla, OM, &</s>
            <s xml:id="echoid-s9355" xml:space="preserve">, MN, ad rectangulum, XMN, conficiunt ratio-
              <lb/>
            nem rectanguli, XEN, ad rectangulum, XMN, quæ ſimul cum ra-
              <lb/>
            tione: </s>
            <s xml:id="echoid-s9356" xml:space="preserve">quam habet, EN, ad, NM, conficit rationem parallelepipe-
              <lb/>
            di ſub, NE, & </s>
            <s xml:id="echoid-s9357" xml:space="preserve">rectangulo, NEX, .</s>
            <s xml:id="echoid-s9358" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9359" xml:space="preserve">ſub, XE, & </s>
            <s xml:id="echoid-s9360" xml:space="preserve">quadrato, EN, ad
              <lb/>
              <note position="left" xlink:label="note-0388-04" xlink:href="note-0388-04a" xml:space="preserve">36. l. 2.</note>
            parallelepipedum ſub, NM, & </s>
            <s xml:id="echoid-s9361" xml:space="preserve">rectangu o, NMX, .</s>
            <s xml:id="echoid-s9362" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9363" xml:space="preserve">ſub, XM & </s>
            <s xml:id="echoid-s9364" xml:space="preserve">
              <lb/>
            quadrato, MN, ergo omnia quadrata hyperbolæ, DNF, ad omnia
              <lb/>
            quadrata hyperbolæ, HNG, erunt vt parallelepipedum ſub, XE,
              <lb/>
            & </s>
            <s xml:id="echoid-s9365" xml:space="preserve">quadrato, EN, ad parallelepipedum ſub, XM, & </s>
            <s xml:id="echoid-s9366" xml:space="preserve">quadrato, M
              <lb/>
            N, quod oſtendere oportebat.</s>
            <s xml:id="echoid-s9367" xml:space="preserve"/>
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        <div xml:id="echoid-div895" type="section" level="1" n="536">
          <head xml:id="echoid-head560" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s9368" xml:space="preserve">IN eadem antecedentis figura, ſi producatur, HG, hinc
              <lb/>
            inde vſque ad curuam hyperbolicam, cui incidat </s>
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