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

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              <pb o="460" file="0480" n="480" rhead="GEOMETRIÆ"/>
              <figure xlink:label="fig-0480-01" xlink:href="fig-0480-01a" number="327">
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            ſint, ET, TY, YZ, & </s>
            <s xml:id="echoid-s11751" xml:space="preserve">per puncta, YZ, ducantur parabolæ axi æ-
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            quidiſtantes, YX, ZQ, curuæ eiuſdem indefinitè productæ occur-
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            rentes in punctis, X, Q, & </s>
            <s xml:id="echoid-s11752" xml:space="preserve">iungantur, EX, EQ. </s>
            <s xml:id="echoid-s11753" xml:space="preserve">Erit igitur ſectio,
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            EIX, ad ſectionem, E℟I, vt cubus, YE, ad cubum, ET, ſic enim
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            ſunt eorum tripla ſcilicet triangula, EIT, EXY, quod elicitur ex
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            prima Lib. </s>
            <s xml:id="echoid-s11754" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11755" xml:space="preserve">&</s>
            <s xml:id="echoid-s11756" xml:space="preserve">, diuidendo, trilineum, EXI, ad ſectionem, E℟I,
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            erit vt parallelepipedum ter ſub, ET, ac quadrato, TY, & </s>
            <s xml:id="echoid-s11757" xml:space="preserve">ter ſub,
              <lb/>
              <note position="left" xlink:label="note-0480-01" xlink:href="note-0480-01a" xml:space="preserve">38. l. 2.</note>
            YT, & </s>
            <s xml:id="echoid-s11758" xml:space="preserve">quadrato, TE, cum cubo, TY, ad cubum, TE, vel vt horũ
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            ſubtripla, ſcilicet, vt parallelepipedum ſemel ſub, YT, & </s>
            <s xml:id="echoid-s11759" xml:space="preserve">quadra-
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            to, TE, & </s>
            <s xml:id="echoid-s11760" xml:space="preserve">ſub, ET, & </s>
            <s xml:id="echoid-s11761" xml:space="preserve">quadrato, TY, ſcilicet ſub, YT, & </s>
            <s xml:id="echoid-s11762" xml:space="preserve">rectan-
              <lb/>
              <note position="left" xlink:label="note-0480-02" xlink:href="note-0480-02a" xml:space="preserve">36. l. 2.</note>
            gulo, YTE, cum {1/3}. </s>
            <s xml:id="echoid-s11763" xml:space="preserve">cubi, TY, ideſt cum parallelepipedo ſub, TY, & </s>
            <s xml:id="echoid-s11764" xml:space="preserve">
              <lb/>
            {1/3}. </s>
            <s xml:id="echoid-s11765" xml:space="preserve">quadrati, TY, ad {1/ }. </s>
            <s xml:id="echoid-s11766" xml:space="preserve">cubi, TE, ideſt ad parallelepipedum ſub, T
              <lb/>
            E, vel, TY, & </s>
            <s xml:id="echoid-s11767" xml:space="preserve">tertia parte quadrati, TE, nempé vt parallelepipe-
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            dum ſub, TY, & </s>
            <s xml:id="echoid-s11768" xml:space="preserve">quadr. </s>
            <s xml:id="echoid-s11769" xml:space="preserve">ET, & </s>
            <s xml:id="echoid-s11770" xml:space="preserve">rectangulo, YTE, & </s>
            <s xml:id="echoid-s11771" xml:space="preserve">tertia parte
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            quadrati, YT, quod conficit parallelepipedum ſub, YT, & </s>
            <s xml:id="echoid-s11772" xml:space="preserve">rectan-
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            gulo ſub, YET, & </s>
            <s xml:id="echoid-s11773" xml:space="preserve">ſub tertia parte quadrati, YT, ad parallelepi-
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              <note position="left" xlink:label="note-0480-03" xlink:href="note-0480-03a" xml:space="preserve">35. l. 2.</note>
            pedum ſub, YT, & </s>
            <s xml:id="echoid-s11774" xml:space="preserve">ſub t ertia parte quadrati, TE, & </s>
            <s xml:id="echoid-s11775" xml:space="preserve">quia horum
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            parallelepipedorum altitudines ſunt eædem, ideò erunt, vt baſes
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            ſcilicet, vt rectangulum ſub, YET, cum tertia parte quadrati, TY,
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              <note position="left" xlink:label="note-0480-04" xlink:href="note-0480-04a" xml:space="preserve">R. G. Cor.
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              4. gener.
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              34. l. 2.</note>
            ad, {1/ }. </s>
            <s xml:id="echoid-s11776" xml:space="preserve">quadrati, ET. </s>
            <s xml:id="echoid-s11777" xml:space="preserve">Eodem modo oſtendemus trilineum, EQX,
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            adtrilineum, EXI, eſſe vt exceſſus cubi, ZE, ſuper cubum, YE, ad
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            exceſſum cubi, YE, ſuper cubum, TE, .</s>
            <s xml:id="echoid-s11778" xml:space="preserve">i. </s>
            <s xml:id="echoid-s11779" xml:space="preserve">vt parallelepipedum ter
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            ſub, ZY, & </s>
            <s xml:id="echoid-s11780" xml:space="preserve">quadrato, YE, ter ſub EY, & </s>
            <s xml:id="echoid-s11781" xml:space="preserve">quadrato, YZ, cum cu-
              <lb/>
              <note position="left" xlink:label="note-0480-05" xlink:href="note-0480-05a" xml:space="preserve">38. l. 2.</note>
            bo, YZ, ad parallelepipedum ter ſub, ET, & </s>
            <s xml:id="echoid-s11782" xml:space="preserve">quadrato, TY, </s>
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