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

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          <p>
            <s xml:id="echoid-s10608" xml:space="preserve">
              <pb o="408" file="0428" n="428" rhead="GEOMETRIÆ"/>
            {1/3}. </s>
            <s xml:id="echoid-s10609" xml:space="preserve">cubi eiuſdem reliquæ. </s>
            <s xml:id="echoid-s10610" xml:space="preserve">Producantur, FI, EO, hinc inde vſq; </s>
            <s xml:id="echoid-s10611" xml:space="preserve">ad
              <lb/>
            latera, TX, XV, VR, RT, quibus occurrant in punctis, &</s>
            <s xml:id="echoid-s10612" xml:space="preserve">, Z, Y,
              <lb/>
              <figure xlink:label="fig-0428-01" xlink:href="fig-0428-01a" number="289">
                <image file="0428-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0428-01"/>
              </figure>
            G, in quibus illa bifariam diui-
              <lb/>
            duntur, & </s>
            <s xml:id="echoid-s10613" xml:space="preserve">per, Q, ducatur, QK,
              <lb/>
            ęequidiſtans ipſi, RV: </s>
            <s xml:id="echoid-s10614" xml:space="preserve">Omnia
              <lb/>
            igitur quadrata parallelogram-
              <lb/>
            mi, SV, ad omnia quadrata ſigu
              <lb/>
            rę, SIQK, habent rationem com-
              <lb/>
            poſitam ex ea, quam habent om-
              <lb/>
            nia quadrata, SV, ad omnia qua-
              <lb/>
              <note position="left" xlink:label="note-0428-01" xlink:href="note-0428-01a" xml:space="preserve">Defin, 12.
                <lb/>
              11.</note>
            drata, SQ, .</s>
            <s xml:id="echoid-s10615" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10616" xml:space="preserve">ex ratione, YS, ad,
              <lb/>
            Sk, & </s>
            <s xml:id="echoid-s10617" xml:space="preserve">ex ratione omnium qua-
              <lb/>
            dratorum, SQ, ad omnia qua-
              <lb/>
            drata figurę, SIQk, .</s>
            <s xml:id="echoid-s10618" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10619" xml:space="preserve">ex ratione
              <lb/>
              <note position="left" xlink:label="note-0428-02" xlink:href="note-0428-02a" xml:space="preserve">10. l. 2,
                <lb/>
              21. huius.</note>
            quadrati, KQ, ad quadratum, SI,
              <lb/>
            cum {1/3}. </s>
            <s xml:id="echoid-s10620" xml:space="preserve">quadrati, kD, .</s>
            <s xml:id="echoid-s10621" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10622" xml:space="preserve">exra-
              <lb/>
            tione quadrati, YS, ad quadratũ
              <lb/>
            SO, cum {1/3}. </s>
            <s xml:id="echoid-s10623" xml:space="preserve">quadrati, SK, duę
              <lb/>
            autem rationes, YS, ad, Sk, & </s>
            <s xml:id="echoid-s10624" xml:space="preserve">
              <lb/>
            quadrati, YS, ad quadratum, SO, Cum {1/3}. </s>
            <s xml:id="echoid-s10625" xml:space="preserve">quadrati, Sk, componũt
              <lb/>
            rationem cubi, YS, ad parallelepipedum ſub, KS, & </s>
            <s xml:id="echoid-s10626" xml:space="preserve">compoſito ex
              <lb/>
            quadrato, SO, & </s>
            <s xml:id="echoid-s10627" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10628" xml:space="preserve">quadrati, Sk, ergo omnia quadrata, SV, ad
              <lb/>
            omnia quadrata figurę SIQk, erunt vt cubus, YS, ad parallelepi-
              <lb/>
            pedum ſub, kS, & </s>
            <s xml:id="echoid-s10629" xml:space="preserve">compoſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s10630" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10631" xml:space="preserve">quadrati, Sk:
              <lb/>
            </s>
            <s xml:id="echoid-s10632" xml:space="preserve">Omnia item quadrata, SV, ad omnia quadrata, kV, ſunt vt, SY,
              <lb/>
              <note position="left" xlink:label="note-0428-03" xlink:href="note-0428-03a" xml:space="preserve">10. l. 2.</note>
            ad, Yk, .</s>
            <s xml:id="echoid-s10633" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10634" xml:space="preserve">ſumpta communi baſi quadrato, SY, vt cubus, SY, ad
              <lb/>
            parallelepipedum ſub, Yk, & </s>
            <s xml:id="echoid-s10635" xml:space="preserve">quadrato, YS, ergo omnia quadrata’
              <lb/>
            SV, ad omnia quadrata figuræ, SIQk, & </s>
            <s xml:id="echoid-s10636" xml:space="preserve">parallelogrammi, kV, .</s>
            <s xml:id="echoid-s10637" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s10638" xml:space="preserve">ad omnia quadrata figuræ, SIQVY, erunt vt cubus, YS, ad paral-
              <lb/>
            lelepipedum ſub, kY, & </s>
            <s xml:id="echoid-s10639" xml:space="preserve">quadrato, YS, vna cum parallelepipedo
              <lb/>
            ſub, kS, & </s>
            <s xml:id="echoid-s10640" xml:space="preserve">compoſito ex quadrato, SO, & </s>
            <s xml:id="echoid-s10641" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10642" xml:space="preserve">quadrati, Sk: </s>
            <s xml:id="echoid-s10643" xml:space="preserve">Quo-
              <lb/>
            niam verò omnia quadrata, SV, ſunt tripla omnium quadratorũ
              <lb/>
              <note position="left" xlink:label="note-0428-04" xlink:href="note-0428-04a" xml:space="preserve">24. l. 2.</note>
            trianguli, SYV, hæc verò ad omnia quadrata ſemihyperbolæ, OY
              <lb/>
            N, ſunt vt cubus, SY, ad parallelepipedum ter ſub, SQ, & </s>
            <s xml:id="echoid-s10644" xml:space="preserve">quadra-
              <lb/>
            to, OY, cum cubo, OY, ideò omnia quadrata, SV, ad omnia qua-
              <lb/>
              <note position="left" xlink:label="note-0428-05" xlink:href="note-0428-05a" xml:space="preserve">9. huius.</note>
            drata ſemihyperbolæ, YON, erunt vt tres cubi, SY, ad parallele-
              <lb/>
            pipedum ter ſub, SO, & </s>
            <s xml:id="echoid-s10645" xml:space="preserve">quadrato, OY, cum cubo, OY, .</s>
            <s xml:id="echoid-s10646" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10647" xml:space="preserve">vt cu-
              <lb/>
            bus, SY, ad parallelepipedum ſub, SO, & </s>
            <s xml:id="echoid-s10648" xml:space="preserve">quadrato, OY, cum {1/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s10649" xml:space="preserve">cubi, OY; </s>
            <s xml:id="echoid-s10650" xml:space="preserve">erant autem omnia quadrata, SV, ad omnia quadrata
              <lb/>
            figuræ, SIQVY, vt cubus, SY, ad parallelepipedum ſub, kY, & </s>
            <s xml:id="echoid-s10651" xml:space="preserve">
              <lb/>
            quadrato, YS, vna cum parallelepipedo ſub, kS, & </s>
            <s xml:id="echoid-s10652" xml:space="preserve">compoſito </s>
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