Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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          <pb o="337" file="0357" n="357" rhead="LIBER IV."/>
          <p>
            <s xml:id="echoid-s8279" xml:space="preserve">Sit ergo parabola, HBM, cuius axis, vel diameter, BG, baſis,
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              <figure xlink:label="fig-0357-01" xlink:href="fig-0357-01a" number="241">
                <image file="0357-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0357-01"/>
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            HM, ducatur autem intra ipſam
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            eidem, BG, parallela, EF, ducta
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            verò tangente, AC, in termino,
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            B, quæ erit parallela baſi, HF, pro-
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            ducatur verſus, FE, illi productæ
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            occurrens in, C, & </s>
            <s xml:id="echoid-s8280" xml:space="preserve">compleatur pa-
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            rallelogrammum, AF, regula ve-
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            rò ſit, HM. </s>
            <s xml:id="echoid-s8281" xml:space="preserve">Dico ergo omnia qua-
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            drata, AF, ad omnia quadrata fi-
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            guræ, CBHF, eſſe vt quadratum, HF, ad quadratum, FG, {1/2}. </s>
            <s xml:id="echoid-s8282" xml:space="preserve">qua-
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            dtati, GH, & </s>
            <s xml:id="echoid-s8283" xml:space="preserve">rectangulum ſub ſexquitertia, HG, & </s>
            <s xml:id="echoid-s8284" xml:space="preserve">ſub, GF. </s>
            <s xml:id="echoid-s8285" xml:space="preserve">Hęc
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            autem erit conſimilis demonſtrationi ſecundæ partis Theor. </s>
            <s xml:id="echoid-s8286" xml:space="preserve">32.
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            </s>
            <s xml:id="echoid-s8287" xml:space="preserve">ideo inde colligatur.</s>
            <s xml:id="echoid-s8288" xml:space="preserve"/>
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        <div xml:id="echoid-div813" type="section" level="1" n="481">
          <head xml:id="echoid-head501" xml:space="preserve">THEOREMA XLI. PROPOS. XLIII.</head>
          <p>
            <s xml:id="echoid-s8289" xml:space="preserve">IN eadem anteced. </s>
            <s xml:id="echoid-s8290" xml:space="preserve">Propoſit. </s>
            <s xml:id="echoid-s8291" xml:space="preserve">figura oſtendemus omnia
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            quadrata, AF, ad omnia quadrata figuræ, CBHF, dem-
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            ptis omnibus quadratis trilinei, BCE, eſſe vt parallelepi-
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            peduw ſub, BG, & </s>
            <s xml:id="echoid-s8292" xml:space="preserve">quadrato, HF, ad reliquum parallelepi-
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            pedi ſub, BG, & </s>
            <s xml:id="echoid-s8293" xml:space="preserve">his ſpatis .</s>
            <s xml:id="echoid-s8294" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8295" xml:space="preserve">quadrato, FG, {1/2}. </s>
            <s xml:id="echoid-s8296" xml:space="preserve">quadrati,
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            GH, & </s>
            <s xml:id="echoid-s8297" xml:space="preserve">rectangulo ſub ſexquitertia, HG, & </s>
            <s xml:id="echoid-s8298" xml:space="preserve">ſub, GF, ab eo-
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            dem dempto {1/3}. </s>
            <s xml:id="echoid-s8299" xml:space="preserve">parallelepipedi ſub, CE, & </s>
            <s xml:id="echoid-s8300" xml:space="preserve">quadrato, FG.</s>
            <s xml:id="echoid-s8301" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8302" xml:space="preserve">Nam omnia quadrata, AF, ad omnia quadrata, BF, ducta per,
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              <note position="right" xlink:label="note-0357-01" xlink:href="note-0357-01a" xml:space="preserve">11.l. 2.</note>
            E, ipſa, EI, æquidiſtans, HM, ſunt vt parallelepipedum ſub, AH,
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            & </s>
            <s xml:id="echoid-s8303" xml:space="preserve">quadrato, HF, ad parallelepipedum ſub, BI, & </s>
            <s xml:id="echoid-s8304" xml:space="preserve">quadrato, IE,
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            ſuut autem omnia quadrata, BE, ſexcupla ommum quadratorum
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              <note position="right" xlink:label="note-0357-02" xlink:href="note-0357-02a" xml:space="preserve">30. huius.</note>
            trilinei, BCE, ideò omnia quadrata, AF, ad omnia quadrata tri-
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              <figure xlink:label="fig-0357-02" xlink:href="fig-0357-02a" number="242">
                <image file="0357-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0357-02"/>
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            linei, BCE, erunt vt parallelepi-
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            pedum ſub, AH, vel, BG, & </s>
            <s xml:id="echoid-s8305" xml:space="preserve">ſub
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            quadrato, HF, ad parallelepipedi
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            ſub, BI, & </s>
            <s xml:id="echoid-s8306" xml:space="preserve">quadrato, IE, ſextam
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            partem: </s>
            <s xml:id="echoid-s8307" xml:space="preserve">Quia verò omnia quadra-
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            ta, AF, ad omnia quadrata figuræ,
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              <note position="right" xlink:label="note-0357-03" xlink:href="note-0357-03a" xml:space="preserve">24. huius.</note>
            CBHF, ſunt vt quadratum, HF,
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            ad hæc ſpatia .</s>
            <s xml:id="echoid-s8308" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8309" xml:space="preserve">quadratum FG,
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            {1/2}. </s>
            <s xml:id="echoid-s8310" xml:space="preserve">quadrati, HG, & </s>
            <s xml:id="echoid-s8311" xml:space="preserve">rectangulum
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            ſub ſexquitertia, HG, & </s>
            <s xml:id="echoid-s8312" xml:space="preserve">ſub, GF, .</s>
            <s xml:id="echoid-s8313" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8314" xml:space="preserve">ſumpta, BG, communi alti-
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            tudine, vt parallelepipedum ſub, BG, & </s>
            <s xml:id="echoid-s8315" xml:space="preserve">quadrato, HF, ad </s>
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