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

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        <div xml:id="echoid-div813" type="section" level="1" n="481">
          <p>
            <s xml:id="echoid-s8315" xml:space="preserve">
              <pb o="338" file="0358" n="358" rhead="GEOMETRIÆ"/>
            lelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8316" xml:space="preserve">dicti, ſpatijs, ideò omnia quadrata, AF,
              <lb/>
            ad omnia quadrata figuræ, CBHF, demptis omnibus quadratis
              <lb/>
            trilinei, BGE, erunt vt parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8317" xml:space="preserve">quadrato, H
              <lb/>
            F, ad reſiduum, dempta ſexta parte parallelepipedi ſub, BI, vel, C
              <lb/>
            E, exceſſu, BG, ſuper, EF, & </s>
            <s xml:id="echoid-s8318" xml:space="preserve">ſub quadrato, IE, à parallelepipedo
              <lb/>
            ſub, BG, & </s>
            <s xml:id="echoid-s8319" xml:space="preserve">dictis ſpatijs .</s>
            <s xml:id="echoid-s8320" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8321" xml:space="preserve">quadrato, FG, {1/2}. </s>
            <s xml:id="echoid-s8322" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8323" xml:space="preserve">re-
              <lb/>
            ctangulo ſub ſexquitertia, HG, & </s>
            <s xml:id="echoid-s8324" xml:space="preserve">ſub, GF.</s>
            <s xml:id="echoid-s8325" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div815" type="section" level="1" n="482">
          <head xml:id="echoid-head502" xml:space="preserve">THEOREMA XLII. PROPOS. XLIV.</head>
          <p>
            <s xml:id="echoid-s8326" xml:space="preserve">INeadem figura Prop. </s>
            <s xml:id="echoid-s8327" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8328" xml:space="preserve">ducta intra fruſtum parabolæ,
              <lb/>
            EBHF, recta, VR, parallela baſi, HM, oſtendemus
              <lb/>
            omnia quadrata figuræ, CBHF, ad omnia quadrata figu-
              <lb/>
            ræ, CBRV, eſſe vt parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8329" xml:space="preserve">his ſpa-
              <lb/>
            tijs .</s>
            <s xml:id="echoid-s8330" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8331" xml:space="preserve">quadrato, FG, {1/2}. </s>
            <s xml:id="echoid-s8332" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8333" xml:space="preserve">rectangulo ſub
              <lb/>
            ſexquitertia, HG, & </s>
            <s xml:id="echoid-s8334" xml:space="preserve">ſub, GF, ad parallelepipedum ſub, B
              <lb/>
            S, & </s>
            <s xml:id="echoid-s8335" xml:space="preserve">ſub his ſpatijs, ſcilicet quadrato, VS, 1. </s>
            <s xml:id="echoid-s8336" xml:space="preserve">quadrati, SR,
              <lb/>
            & </s>
            <s xml:id="echoid-s8337" xml:space="preserve">rectangulo ſub ſexquitertia, RS, & </s>
            <s xml:id="echoid-s8338" xml:space="preserve">ſub, SV.</s>
            <s xml:id="echoid-s8339" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8340" xml:space="preserve">Huius demonſtratio non eſt alia à demonſtratione Propoſ. </s>
            <s xml:id="echoid-s8341" xml:space="preserve">41.
              <lb/>
            </s>
            <s xml:id="echoid-s8342" xml:space="preserve">ideò ibi in ſecunda eiuſdem parte recolatur.</s>
            <s xml:id="echoid-s8343" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div816" type="section" level="1" n="483">
          <head xml:id="echoid-head503" xml:space="preserve">THEOREMA XLIII. PROP. XLV.</head>
          <p>
            <s xml:id="echoid-s8344" xml:space="preserve">INeodem Propoſ. </s>
            <s xml:id="echoid-s8345" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8346" xml:space="preserve">Schemate oſtendemus omnia qua-
              <lb/>
            drata figuræ, CBHF, demptis omnibus qua dratis trili-
              <lb/>
            nei, BCE, ad omnia quadrata ſemiparabolæ, BHG, eſſe
              <lb/>
            vt reliquum parallelepipedi ſub, BG, & </s>
            <s xml:id="echoid-s8347" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8348" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8349" xml:space="preserve">qua-
              <lb/>
            drato, FG, {1/2}. </s>
            <s xml:id="echoid-s8350" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8351" xml:space="preserve">rectangulo ſub, FG, & </s>
            <s xml:id="echoid-s8352" xml:space="preserve">ſex-
              <lb/>
            quitertia, GH, ab eodem dempta ſexta parte parallelepi-
              <lb/>
            pediſub, CE, & </s>
            <s xml:id="echoid-s8353" xml:space="preserve">quadrato, FG, ad dimidium parallelepi-
              <lb/>
            pediſub, BG, & </s>
            <s xml:id="echoid-s8354" xml:space="preserve">quadrato, GH.</s>
            <s xml:id="echoid-s8355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8356" xml:space="preserve">Etenim omnia quadrata figuræ, CBHF, demptis omnibus
              <lb/>
            quadratis trilinei, BCE, ad omnia quadrata, AF, conuertendo,
              <lb/>
            ſunt vt parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8357" xml:space="preserve">his ſpatijs, ſcilicet quadrato.
              <lb/>
            </s>
            <s xml:id="echoid-s8358" xml:space="preserve">FG, {1/2}. </s>
            <s xml:id="echoid-s8359" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s8360" xml:space="preserve">rectangulo ſub, FG, & </s>
            <s xml:id="echoid-s8361" xml:space="preserve">ſexquitertia, G
              <lb/>
            H, ab eodem dempto {1/6}. </s>
            <s xml:id="echoid-s8362" xml:space="preserve">parallelepipedi ſub, CE, & </s>
            <s xml:id="echoid-s8363" xml:space="preserve">quadrato, </s>
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