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

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            <s xml:id="echoid-s10685" xml:space="preserve">
              <pb o="410" file="0430" n="430" rhead="GEOMETRIÆ"/>
            ΦΙΛ, 9F7, à parallelogrammo, βΩ, ablatis ab ijſdem om-
              <lb/>
            nibus quadratis oppoſitarum hyperbolarum, LΕΓ, ΣΟ3,
              <lb/>
            quæ dicatur figura parallelogrammi, βΩ, eſſe vt paralle-
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            lepipedum ſub, QV, & </s>
            <s xml:id="echoid-s10686" xml:space="preserve">quadrato. </s>
            <s xml:id="echoid-s10687" xml:space="preserve">VZ, vna cum parallelepi-
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            pedo ſub, QZ, & </s>
            <s xml:id="echoid-s10688" xml:space="preserve">compoſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s10689" xml:space="preserve">@. </s>
            <s xml:id="echoid-s10690" xml:space="preserve">quadra-
              <lb/>
            ti, QZ, ab his dempto parallelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s10691" xml:space="preserve">quadra-
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            to, OY, & </s>
            <s xml:id="echoid-s10692" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10693" xml:space="preserve">cubi, OY, ad parallelepipedum ſub, ΛΩ, & </s>
            <s xml:id="echoid-s10694" xml:space="preserve">
              <lb/>
            quadrato, Ω4, vna cum parallelepipedo ſub, Λ4, & </s>
            <s xml:id="echoid-s10695" xml:space="preserve">com-
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            poſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s10696" xml:space="preserve">@. </s>
            <s xml:id="echoid-s10697" xml:space="preserve">quadrati, Λ4, dempto paral-
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            lelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s10698" xml:space="preserve">quadrato, O6, cum {1/3}. </s>
            <s xml:id="echoid-s10699" xml:space="preserve">cubi, O6.</s>
            <s xml:id="echoid-s10700" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s10701" xml:space="preserve">Nam omnia quadrata figuræ parallelogrammi, TV, demptis
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            iam dictis, ad omnia quadrata figuræ parallelogrammi, βΩ, dem-
              <lb/>
            ptis iam dictis, habent rationem compoſitam ex ratione omniũ
              <lb/>
            quadratorum primo dictæ figuræ, demptis, &</s>
            <s xml:id="echoid-s10702" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10703" xml:space="preserve">ad omnia qua-
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            drata, TV, .</s>
            <s xml:id="echoid-s10704" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10705" xml:space="preserve">ex ea, quam habet parallelepipedum ſub, QV, & </s>
            <s xml:id="echoid-s10706" xml:space="preserve">
              <lb/>
            quadrato, VZ, vna cum parallelepipedo ſub, QZ, & </s>
            <s xml:id="echoid-s10707" xml:space="preserve">compoſita
              <lb/>
              <note position="left" xlink:label="note-0430-01" xlink:href="note-0430-01a" xml:space="preserve">Exantec.</note>
            ex quadrato, OS, & </s>
            <s xml:id="echoid-s10708" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10709" xml:space="preserve">quadrati, QZ, dempto ab his parallelepi-
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            pedo ſub, SO, & </s>
            <s xml:id="echoid-s10710" xml:space="preserve">quadrato, OY, & </s>
            <s xml:id="echoid-s10711" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10712" xml:space="preserve">cubi, OY, ad cubum, ZV, itẽ
              <lb/>
            ex ratione omnium quadratorum, TV, ad omnia quadrata, βΩ,
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            ideſt ex ratione cubi, VZ, ad cubum, Ω4, quia parallelogramma,
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              <note position="left" xlink:label="note-0430-02" xlink:href="note-0430-02a" xml:space="preserve">3. l. 2.</note>
            TV, βΩ, ſunt ſimilia, cum ſint circa eandem diametrum, & </s>
            <s xml:id="echoid-s10713" xml:space="preserve">tandẽ
              <lb/>
            ex ratione omnium quadratorum, βΩ, ad omnia quadrata figuræ
              <lb/>
            parallelogrammi, βΩ, demptis iam dictis, .</s>
            <s xml:id="echoid-s10714" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10715" xml:space="preserve">ex ratione cubi, Ω4,
              <lb/>
              <note position="left" xlink:label="note-0430-03" xlink:href="note-0430-03a" xml:space="preserve">Exantec.</note>
            ad parallelepipedum ſub, ΛΩ, & </s>
            <s xml:id="echoid-s10716" xml:space="preserve">quadrato, Ω4, vna cum paralle-
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            lepipedo ſub, Λ4, & </s>
            <s xml:id="echoid-s10717" xml:space="preserve">compoſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s10718" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10719" xml:space="preserve">quadrati,
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            Λ4, ab his dempto parallelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s10720" xml:space="preserve">quadrato, O6, vna
              <lb/>
            cum {1/3}. </s>
            <s xml:id="echoid-s10721" xml:space="preserve">cubi, O6, rationes autem parallelepipedorum primò dicto-
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            rum, dempto parallelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s10722" xml:space="preserve">quadrato, OY, cum {1/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s10723" xml:space="preserve">cubi, OY, ad cubum, ZV, cubi, ZV, ad cubum, Ω4, & </s>
            <s xml:id="echoid-s10724" xml:space="preserve">cubi, Ω4,
              <lb/>
            ad parallelepipeda poſtremò dicta, dempto parallerepipedo ſub, S
              <lb/>
            O, & </s>
            <s xml:id="echoid-s10725" xml:space="preserve">quadrato, O6, cum {1/3}. </s>
            <s xml:id="echoid-s10726" xml:space="preserve">cubi, O6, componunt rationem pa-
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            rallelepipedorum primò dictorum, dempto iam dicto ad parallele-
              <lb/>
              <note position="left" xlink:label="note-0430-04" xlink:href="note-0430-04a" xml:space="preserve">Deſin. 12.
                <lb/>
              l. 1.</note>
            pipeda poſtremò dicta, dempto iam dicto, ergo omnia quadrata
              <lb/>
            figuræ parallelogrammi, TV, demptis omnibus quadratis oppoſi-
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            tarum hyperbolarum, AEC, MON, ad omnia quadrata figuræ
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            parallelogrammi, βΩ, demptis omnibus quadratis oppoſitarum
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            hyperbolarum, LEI, ΣΟ3, erunt vt parallelepipedum ſub, QV,
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            & </s>
            <s xml:id="echoid-s10727" xml:space="preserve">quadrato, VZ, vna cum parallelepipedo ſub, QZ, & </s>
            <s xml:id="echoid-s10728" xml:space="preserve">compoſi-
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            to ex quadrato, SO, & </s>
            <s xml:id="echoid-s10729" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10730" xml:space="preserve">quadrati, QZ, ab his dempto </s>
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