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

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            <s xml:id="echoid-s5700" xml:space="preserve">
              <pb o="232" file="0252" n="252" rhead="GEOMETRI Æ"/>
            drilineo, MTVN, bis ſumpta, ſunt ad omnia quadrata, HV, vt
              <lb/>
            portio, SMT, ad parallelogrammum, HV. </s>
            <s xml:id="echoid-s5701" xml:space="preserve">Omnia inſuper qua-
              <lb/>
              <note position="left" xlink:label="note-0252-01" xlink:href="note-0252-01a" xml:space="preserve">@o. l. 2.</note>
              <figure xlink:label="fig-0252-01" xlink:href="fig-0252-01a" number="157">
                <image file="0252-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0252-01"/>
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            drata, HV, ad omnia quadrata, VD,
              <lb/>
            ſunt vt, HR. </s>
            <s xml:id="echoid-s5702" xml:space="preserve">ad, RD, .</s>
            <s xml:id="echoid-s5703" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5704" xml:space="preserve">vt, HV,
              <lb/>
            ad, VD; </s>
            <s xml:id="echoid-s5705" xml:space="preserve">eodem deniq; </s>
            <s xml:id="echoid-s5706" xml:space="preserve">modo, quo ſu-
              <lb/>
            pra, oſtendemus omnia quadrata, RF,
              <lb/>
            ad omnia quadrata portionis, SET, cum
              <lb/>
            rectangulis bis ſub eidem, & </s>
            <s xml:id="echoid-s5707" xml:space="preserve">ſub trilineis,
              <lb/>
            TGV, GEF, eſſe vt, RF, ad portio-
              <lb/>
            nem, SET, ergo ex æquali, omnia
              <lb/>
            quadrata portionis, SMT, cum rectan-
              <lb/>
            gulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5708" xml:space="preserve">ſub quadrilineo,
              <lb/>
            MTVN, ad omnia quadrata portio-
              <lb/>
            nis, SET, cum rectangulis bis ſub eadem. </s>
            <s xml:id="echoid-s5709" xml:space="preserve">& </s>
            <s xml:id="echoid-s5710" xml:space="preserve">ſub trilineis, TGV,
              <lb/>
            GFE, erunt vt portio, SMT, ad portionem, SET. </s>
            <s xml:id="echoid-s5711" xml:space="preserve">quod oſten.
              <lb/>
            </s>
            <s xml:id="echoid-s5712" xml:space="preserve">dere opus erat.</s>
            <s xml:id="echoid-s5713" xml:space="preserve"/>
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        <div xml:id="echoid-div570" type="section" level="1" n="337">
          <head xml:id="echoid-head354" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5714" xml:space="preserve">_H_INC patet omniä quadrata parallelogrammorum in eadem al-
              <lb/>
            titudine cum portionibus, vel fruſtibus portionum exiſtentium,
              <lb/>
            ad omnia quadrata earundem ſimul cumrectangulis bis ſub ijſdem, & </s>
            <s xml:id="echoid-s5715" xml:space="preserve">
              <lb/>
            ſub quadrilineis, vel trilineis, quæ illis èregione reſpondent lateri,
              <lb/>
            NF, adiacentia, veluti ſupra fuerunt quadri ineum, MTVN, & </s>
            <s xml:id="echoid-s5716" xml:space="preserve">
              <lb/>
            trilineum, TGV, GEF, eſſe, vt eadem parallelogramma ad eaſdem
              <lb/>
            portiones, vel portionum fruſta, quod ex ſupra dictis clarè patet.</s>
            <s xml:id="echoid-s5717" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div571" type="section" level="1" n="338">
          <head xml:id="echoid-head355" xml:space="preserve">THEOREMA XIX. PROPOS. XX.</head>
          <p>
            <s xml:id="echoid-s5718" xml:space="preserve">EXpoſita adhuc figura Propoſ. </s>
            <s xml:id="echoid-s5719" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5720" xml:space="preserve">& </s>
            <s xml:id="echoid-s5721" xml:space="preserve">intra circulum, vel
              <lb/>
            ellipſim ducta quacunq; </s>
            <s xml:id="echoid-s5722" xml:space="preserve">regulæ parallela, RX, diui-
              <lb/>
            dente ipſum vtcunq; </s>
            <s xml:id="echoid-s5723" xml:space="preserve">in duas portiones, SMT, SET. </s>
            <s xml:id="echoid-s5724" xml:space="preserve">Di-
              <lb/>
            co omnia quadrata portionis, SMT, cum rectangulis bis
              <lb/>
            ſub eadem, & </s>
            <s xml:id="echoid-s5725" xml:space="preserve">ſub quadrilineo, MTXC, ad omnia quadra-
              <lb/>
            ta portionis, SET, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5726" xml:space="preserve">ſubqua-
              <lb/>
            drilineo, TGEOX, eſſe vt portio, SMT, ad portionem, SET.</s>
            <s xml:id="echoid-s5727" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Coroll. 1.
            <lb/>
          26. l. 2.</note>
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            <s xml:id="echoid-s5728" xml:space="preserve">Fiat prius, vt, MV, ad ſemiportionem, MYT, ſic, VY, ad,
              <lb/>
            YZ. </s>
            <s xml:id="echoid-s5729" xml:space="preserve">Omnia ergo quadrata, MX, ad rectangula ſub, MX, & </s>
            <s xml:id="echoid-s5730" xml:space="preserve">ſe-
              <lb/>
            miportione, MYT, ſunt vt, MX, ad, MYT, diuide rectangula
              <lb/>
              <note position="left" xlink:label="note-0252-03" xlink:href="note-0252-03a" xml:space="preserve">C. 23. l. 2.</note>
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