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

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            <s xml:id="echoid-s13160" xml:space="preserve">
              <pb o="510" file="0530" n="530" rhead="GEOMETRIÆ"/>
              <figure xlink:label="fig-0530-01" xlink:href="fig-0530-01a" number="352">
                <image file="0530-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0530-01"/>
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            cylindricum, FQ, ad fruſtum conici,
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            NISR, eandem rationem habere,
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            quam quadratum, PQ, ad rectan
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            gulem, ſub, PQ, LM, vna cum {1/3}.
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            </s>
            <s xml:id="echoid-s13161" xml:space="preserve">quadradifferentiæ earundem. </s>
            <s xml:id="echoid-s13162" xml:space="preserve">Idem
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            verò fruſtum ad conicum, OPQ, eſſe
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            vt rectangulum ſub, PQ, & </s>
            <s xml:id="echoid-s13163" xml:space="preserve">tripla,
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            LM, vna cum quadrato differentiæ
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            earundem, ad idem quadratum, P
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            Q. </s>
            <s xml:id="echoid-s13164" xml:space="preserve">Etenim cylindricus, FQ, ad fru-
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            ſtum conici, NISR, habet rationem
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            compoſitam ex ratione cylindrici,
              <lb/>
            FQ, ad cylindricum, AQ, ideſt ex
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            ratione, FP, ad, PA, vel, LP, ad, BP,
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              <note position="left" xlink:label="note-0530-01" xlink:href="note-0530-01a" xml:space="preserve">Annot. p.
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              5. huius.</note>
            vel exceſius, PQ, ſuper, LM, (qui
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            ſit, FX,) ad, PQ, & </s>
            <s xml:id="echoid-s13165" xml:space="preserve">ex ratione cylindri-
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            ci, AQ, ad conicum, BSR, ideſt ex
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            ea, quam habet, PQ, ad {1/3}. </s>
            <s xml:id="echoid-s13166" xml:space="preserve">PQ, & </s>
            <s xml:id="echoid-s13167" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0530-02" xlink:href="note-0530-02a" xml:space="preserve">8. huius.</note>
            tandem ex ratione conici, BSR, ad
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            fruſtum, ISRN, quæ eſt eadem ei, quam habet cubus, PQ, vel, F
              <lb/>
            H, ad parallelepipedum ter ſub, HX, & </s>
            <s xml:id="echoid-s13168" xml:space="preserve">quadrato, XF, ter ſub, F
              <lb/>
            X, & </s>
            <s xml:id="echoid-s13169" xml:space="preserve">quadrato, XH, cum cubo, FX, eſt enim conicus, BSR, ſimi-
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              <note position="left" xlink:label="note-0530-03" xlink:href="note-0530-03a" xml:space="preserve">Ex diff. 7.
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              l, 1.
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              Annot.p.
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              8. huius.</note>
            lis conico, BIN, & </s>
            <s xml:id="echoid-s13170" xml:space="preserve">ideò, BSR, ad, BIN, eſt vt cubus, PQ, vel, FH,
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            ad cubum, LM, ſeu ad cubum, XH, vnde cum cubus, FH, æquæ-
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            tur cubis, FX, XH, cum parallelepipedis ter ſub, FX, & </s>
            <s xml:id="echoid-s13171" xml:space="preserve">quadrato,
              <lb/>
            XH, & </s>
            <s xml:id="echoid-s13172" xml:space="preserve">ter ſub, HX, & </s>
            <s xml:id="echoid-s13173" xml:space="preserve">quadrato, XF, ideò per conuerſionem ra-
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            tionis conicus, BSR, ad fruſtum, ISRN, erit vt cubus, FH, ad
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            parallelepipedum ter ſub, FX, & </s>
            <s xml:id="echoid-s13174" xml:space="preserve">quadrato, XF, ter ſub, XF, & </s>
            <s xml:id="echoid-s13175" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0530-04" xlink:href="note-0530-04a" xml:space="preserve">38. lib. 2.</note>
            quadrato, HX, cum cubo, HX. </s>
            <s xml:id="echoid-s13176" xml:space="preserve">Duæ rationes autem nempè, quã
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            habet, FX, ad, PQ, &</s>
            <s xml:id="echoid-s13177" xml:space="preserve">, PQ, ad ſui {1/3}. </s>
            <s xml:id="echoid-s13178" xml:space="preserve">componunt rationem, FX, ad
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            {1/3}. </s>
            <s xml:id="echoid-s13179" xml:space="preserve">PQ, vel triplæ, FX, ad, PQ, ſeu, FH, vel, ſumpto pro communi
              <lb/>
            baſi quadrato, FH, componunt rationem parallelepipedi ſub tri-
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            pla, FX, & </s>
            <s xml:id="echoid-s13180" xml:space="preserve">ſub quadrato, FH, ad cubum, FH, quæ proportio cum
              <lb/>
            ea, quam d ximus habere cubum, FH, ad paralleiepipedum ter ſub
              <lb/>
            HX, & </s>
            <s xml:id="echoid-s13181" xml:space="preserve">quadrato, XF, ter ſub, XF, & </s>
            <s xml:id="echoid-s13182" xml:space="preserve">quadrato, HX, cum, cubo,
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            FX, componit rationem parallelepipedi ſub tripla, FX, & </s>
            <s xml:id="echoid-s13183" xml:space="preserve">quadra-
              <lb/>
            to, FH, ad parallelepipedum ter ſub, HX, & </s>
            <s xml:id="echoid-s13184" xml:space="preserve">quadrato, XF, ter
              <lb/>
            ſub, XF, & </s>
            <s xml:id="echoid-s13185" xml:space="preserve">quadrato, HX, cum cubo, XF, ergo cylindricus, FQ,
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            ad fruſtum, ISRN, erit vt parallelepipedum ſub tripla, FX, & </s>
            <s xml:id="echoid-s13186" xml:space="preserve">qua-
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            drato, FH, ad dicta ſex parailelepipeda cum cubo, FX, vel vt eo-
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            rum ſub tripla, idéſt vt parallelepipedum ſub, FX, & </s>
            <s xml:id="echoid-s13187" xml:space="preserve">quadrato, </s>
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