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

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        <div xml:id="echoid-div746" type="section" level="1" n="440">
          <p>
            <s xml:id="echoid-s7508" xml:space="preserve">
              <pb o="312" file="0332" n="332" rhead="GEOMETRIÆ"/>
            mæ abſciſſarum, EM, magnitudines tertij ordinis collectæ iuxta
              <lb/>
            tertiam . </s>
            <s xml:id="echoid-s7509" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7510" xml:space="preserve">iuxta, ME, ad omnes abiciſſas ipſius, ME, magnitudi-
              <lb/>
            nes quarti ordinis collectas iuxta quartam . </s>
            <s xml:id="echoid-s7511" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7512" xml:space="preserve">iuxta, EN, ſumptis
              <lb/>
            maximisabſciſſarum, EM, & </s>
            <s xml:id="echoid-s7513" xml:space="preserve">eiuſdem omnibus abſciſſis, vel recti,
              <lb/>
              <note position="left" xlink:label="note-0332-01" xlink:href="note-0332-01a" xml:space="preserve">Coroll. 2.
                <lb/>
              19. 1. 2.</note>
            vel eiuſdem obliqui tranſitus; </s>
            <s xml:id="echoid-s7514" xml:space="preserve">ſunt autem maximæ abſciſſarum, E
              <lb/>
            M, duplæ omnium abſciſſarum, EM, recti, vel eiuſdem obliqui
              <lb/>
            tranſitus, ergo & </s>
            <s xml:id="echoid-s7515" xml:space="preserve">omnia quadrata, EF, erunt dupla omnium qua-
              <lb/>
            dratorum ſemiparabolæ, EMF, & </s>
            <s xml:id="echoid-s7516" xml:space="preserve">eorum quadrupla . </s>
            <s xml:id="echoid-s7517" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7518" xml:space="preserve">omnia
              <lb/>
            quadrata, AF, erunt dupla omnium quadratorum parabolæ, VE
              <lb/>
            F; </s>
            <s xml:id="echoid-s7519" xml:space="preserve">Quarum ergo partium omnia quadrata, AF, erunt ſex, earum
              <lb/>
            omnia quadrata parabolæ, VEF, erunt tres, ſed quarum partium
              <lb/>
            omnia quadrata, AF, ſunt ſex, earum omnia quadrata trianguli,
              <lb/>
            EVF, iunt duæ, quia omnia quadrata, AF, iunt tripla omnium
              <lb/>
              <note position="left" xlink:label="note-0332-02" xlink:href="note-0332-02a" xml:space="preserve">34. 1. 2.</note>
            quadratorum trianguli, EVF, ergo quarum partium omnia qua-
              <lb/>
            drata parabolæ, VEF, funttres, earum omnia quadrata triangu-
              <lb/>
            li, EVF, erunt duæ, ergo omnia quadrata parabolæ, VEF, erunt
              <lb/>
            ſexquialtera omnium quadratorum trianguli, VEF, quæ oſtende-
              <lb/>
            re oportebat.</s>
            <s xml:id="echoid-s7520" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div748" type="section" level="1" n="441">
          <head xml:id="echoid-head461" xml:space="preserve">THEOREMA XXI. PROPOS. XXII.</head>
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            <s xml:id="echoid-s7521" xml:space="preserve">SI ad eundem axim, vel diametrum parabolæ ordinatim
              <lb/>
            applicentur duæ rectæ lineæ parabolas conſtituentes,
              <lb/>
            quarum altera ſumatur pro regula, harum parabolarum
              <lb/>
            omnia quadrata erunt interſe, vt quadrata axium, vel dia-
              <lb/>
            metrorum earundem.</s>
            <s xml:id="echoid-s7522" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7523" xml:space="preserve">Sinr ergo ad eundem axim, vel diametrum, CG, parabolæ, F
              <lb/>
              <figure xlink:label="fig-0332-01" xlink:href="fig-0332-01a" number="223">
                <image file="0332-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0332-01"/>
              </figure>
            CH, duæ vtcunque ordinatim
              <lb/>
            applicatæ, FH, OM, parabo-
              <lb/>
            las, FCH, OCM, abſcinden-
              <lb/>
            tes, ſit autem regula altera ha-
              <lb/>
            rum ordinatim applicatarum, vt,
              <lb/>
            FH. </s>
            <s xml:id="echoid-s7524" xml:space="preserve">Dico omnia quadrata pa-
              <lb/>
            rabolæ, FCH, ad omnia qua-
              <lb/>
            drata parabolæ, OCM, eſſe vt
              <lb/>
            quadratum, GC, ad quadratum,
              <lb/>
            CI: </s>
            <s xml:id="echoid-s7525" xml:space="preserve">Conſtituantur parallelo-
              <lb/>
            grammum, AH, in baſi, FH,
              <lb/>
            & </s>
            <s xml:id="echoid-s7526" xml:space="preserve">circa axim, vel diametrum, CG, & </s>
            <s xml:id="echoid-s7527" xml:space="preserve">parallelogrammum, RM,
              <lb/>
            in baſi, OM, & </s>
            <s xml:id="echoid-s7528" xml:space="preserve">circa axim, vel diametrum, CI. </s>
            <s xml:id="echoid-s7529" xml:space="preserve">Quoniam </s>
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