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

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          <p>
            <s xml:id="echoid-s8562" xml:space="preserve">
              <pb o="343" file="0363" n="363" rhead="LIBER IV."/>
            rallelepipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8563" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8564" xml:space="preserve">f. </s>
            <s xml:id="echoid-s8565" xml:space="preserve">quadrato, PQ {1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s8566" xml:space="preserve">quadrati, QZ, & </s>
            <s xml:id="echoid-s8567" xml:space="preserve">rectangulo ſub ſexquitertia, ZQ, & </s>
            <s xml:id="echoid-s8568" xml:space="preserve">ſub, Q
              <lb/>
            P, ab eodem dempta {1/6}. </s>
            <s xml:id="echoid-s8569" xml:space="preserve">para llelepipedi ſub, CD, & </s>
            <s xml:id="echoid-s8570" xml:space="preserve">quadra-
              <lb/>
            to, QP,</s>
          </p>
          <p>
            <s xml:id="echoid-s8571" xml:space="preserve">Completo parallelogrammo, KP, omnia igitur quadrata trili-
              <lb/>
              <figure xlink:label="fig-0363-01" xlink:href="fig-0363-01a" number="245">
                <image file="0363-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0363-01"/>
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            nei, DPG, ad omnia qua-
              <lb/>
            drata figurę, CAZP, demp tis
              <lb/>
            omnibus quadratis trilinei, A
              <lb/>
            CD, habent rationem com-
              <lb/>
            poſitam ex ea, quam habent
              <lb/>
            omnia quadrata, DPG, ad
              <lb/>
            omnia quadrata, DG, .</s>
            <s xml:id="echoid-s8572" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8573" xml:space="preserve">ex
              <lb/>
            ratione compoſitæ ex {1/3}. </s>
            <s xml:id="echoid-s8574" xml:space="preserve">ZP,
              <lb/>
            & </s>
            <s xml:id="echoid-s8575" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s8576" xml:space="preserve">PG, ad, ZP, & </s>
            <s xml:id="echoid-s8577" xml:space="preserve">ex ratio-
              <lb/>
              <note position="right" xlink:label="note-0363-01" xlink:href="note-0363-01a" xml:space="preserve">47. huius.</note>
            ne omnium quadratorum, D
              <lb/>
            G, ad omnia quadrata, KP, .</s>
            <s xml:id="echoid-s8578" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8579" xml:space="preserve">ex ratione parallelepipedi ſub, D
              <lb/>
            P, & </s>
            <s xml:id="echoid-s8580" xml:space="preserve">quadrato, PG, ad parallel epipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8581" xml:space="preserve">quadrato, Z
              <lb/>
            P, & </s>
            <s xml:id="echoid-s8582" xml:space="preserve">tandem ex ratione omnium quadratorum, KP, ad omnia qua-
              <lb/>
            drata figuræ, CAZP, demptis omnibus quadratis trilinei, ACD,
              <lb/>
            .</s>
            <s xml:id="echoid-s8583" xml:space="preserve">f. </s>
            <s xml:id="echoid-s8584" xml:space="preserve">ex ratione parallelepipedi ſub, AQ, & </s>
            <s xml:id="echoid-s8585" xml:space="preserve">quadrato, ZP, ad paralle-
              <lb/>
            pipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8586" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8587" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8588" xml:space="preserve">quadrato, PQ, {1/2}. </s>
            <s xml:id="echoid-s8589" xml:space="preserve">quadrati,
              <lb/>
              <note position="right" xlink:label="note-0363-02" xlink:href="note-0363-02a" xml:space="preserve">34. huius.</note>
            QZ, & </s>
            <s xml:id="echoid-s8590" xml:space="preserve">rectangulo ſub, PQ, & </s>
            <s xml:id="echoid-s8591" xml:space="preserve">ſexquitertia, QZ, ab eodem dem-
              <lb/>
            pta {1/6}. </s>
            <s xml:id="echoid-s8592" xml:space="preserve">parallelepipedi ſub, CD, & </s>
            <s xml:id="echoid-s8593" xml:space="preserve">quadrato, PQ; </s>
            <s xml:id="echoid-s8594" xml:space="preserve">duæ autem ra-
              <lb/>
            tiones parallelepipedi ſub, DP, & </s>
            <s xml:id="echoid-s8595" xml:space="preserve">quadrato PG, ad parallelepipe-
              <lb/>
            dum ſub, AQ, & </s>
            <s xml:id="echoid-s8596" xml:space="preserve">quadrato, ZP, & </s>
            <s xml:id="echoid-s8597" xml:space="preserve">huius parallelepipedi ad paral-
              <lb/>
            lelepipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8598" xml:space="preserve">ſpatijs iam dictis, ab eodem dempta {1/6}. </s>
            <s xml:id="echoid-s8599" xml:space="preserve">pa-
              <lb/>
            rallelepipedi ſub, CD, & </s>
            <s xml:id="echoid-s8600" xml:space="preserve">quadrato, PQ, componunt rationem pa-
              <lb/>
            rallelepipedi ſub, DP, & </s>
            <s xml:id="echoid-s8601" xml:space="preserve">quadrato, PG, ad parallelepipedum ſub,
              <lb/>
              <note position="right" xlink:label="note-0363-03" xlink:href="note-0363-03a" xml:space="preserve">Defin. 12.
                <lb/>
              l. 1.</note>
            AQ, & </s>
            <s xml:id="echoid-s8602" xml:space="preserve">dictis ſpatijs ab eodem dempta {1/6}. </s>
            <s xml:id="echoid-s8603" xml:space="preserve">parallelepipedi ſub, CD,
              <lb/>
            & </s>
            <s xml:id="echoid-s8604" xml:space="preserve">quadrato, PQ, ergo omnia quadrata trilinei, DGP, ad omnia,
              <lb/>
            quadrata figuræ, CAZP, demptis omnibus quadratis trilinei, AC
              <lb/>
            D, erunt in ratione compoſita ex ea, quam habet {1/3}. </s>
            <s xml:id="echoid-s8605" xml:space="preserve">ZP, cum {1/6}. </s>
            <s xml:id="echoid-s8606" xml:space="preserve">P
              <lb/>
            G, ad, ZP, & </s>
            <s xml:id="echoid-s8607" xml:space="preserve">ex ea, quam habet parallelepipedum ſub, DP, & </s>
            <s xml:id="echoid-s8608" xml:space="preserve">qua-
              <lb/>
            drato, PG, ad parallelepipedum ſub, AQ, & </s>
            <s xml:id="echoid-s8609" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8610" xml:space="preserve">f. </s>
            <s xml:id="echoid-s8611" xml:space="preserve">quadra-
              <lb/>
            to, PQ, {1/2}. </s>
            <s xml:id="echoid-s8612" xml:space="preserve">quadrati, QZ, cum rectangulo ſub, PQ, & </s>
            <s xml:id="echoid-s8613" xml:space="preserve">ſexquitertia,
              <lb/>
            QZ, ab eodem parallelepipedo dempta {1/6}. </s>
            <s xml:id="echoid-s8614" xml:space="preserve">parallelepipedi ſub, CD,
              <lb/>
            & </s>
            <s xml:id="echoid-s8615" xml:space="preserve">quadrato, PQ, quod oſtendere opus erat.</s>
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