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

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            <s xml:id="echoid-s10555" xml:space="preserve">
              <pb o="406" file="0426" n="426" rhead="GEOMETRIÆ"/>
            hyperbolæ, HTN, erunt vt parallelepipedum ſub, LO, & </s>
            <s xml:id="echoid-s10556" xml:space="preserve">triplo
              <lb/>
            quadrati, OG, ad reliquum, quod habetur, dempto parallelepipe-
              <lb/>
              <figure xlink:label="fig-0426-01" xlink:href="fig-0426-01a" number="288">
                <image file="0426-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0426-01"/>
              </figure>
            do ter ſub, OT, & </s>
            <s xml:id="echoid-s10557" xml:space="preserve">quadrato, TL,
              <lb/>
            cum cubo, TL, à parallelepipedo
              <lb/>
            ſub, LO, & </s>
            <s xml:id="echoid-s10558" xml:space="preserve">quadrato, LO, .</s>
            <s xml:id="echoid-s10559" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10560" xml:space="preserve">à cu-
              <lb/>
            bo, LO, & </s>
            <s xml:id="echoid-s10561" xml:space="preserve">parallelepipedo ſub, LO,
              <lb/>
            & </s>
            <s xml:id="echoid-s10562" xml:space="preserve">triplo quadrati, OT, verum, quia
              <lb/>
            cubus, LO, æquatur parallelepipe-
              <lb/>
            dis ter ſub, OT, & </s>
            <s xml:id="echoid-s10563" xml:space="preserve">quadrato, TL,
              <lb/>
            ter ſub, TL, & </s>
            <s xml:id="echoid-s10564" xml:space="preserve">quadrato, TO, cum
              <lb/>
            cubis, OT, TL, ideò ſi à cubo, OL,
              <lb/>
            dematur parallelepipedum ter ſub,
              <lb/>
            OT, & </s>
            <s xml:id="echoid-s10565" xml:space="preserve">quadrato, TL, cum cubo,
              <lb/>
              <note position="left" xlink:label="note-0426-01" xlink:href="note-0426-01a" xml:space="preserve">38. l. 2.</note>
            TL, remanebit parallelepipedum
              <lb/>
            ter ſub, LT, & </s>
            <s xml:id="echoid-s10566" xml:space="preserve">quadrato, TO, cum
              <lb/>
            cubo, TO, quod iungendum eſt pa-
              <lb/>
            rallelepipedo ſub, LO, & </s>
            <s xml:id="echoid-s10567" xml:space="preserve">triplo qua-
              <lb/>
            drati, TO, habebimus ergo pro
              <lb/>
            quæſito reſiduo parallelepipedum
              <lb/>
            ſub, LO, & </s>
            <s xml:id="echoid-s10568" xml:space="preserve">quadrato, OT, ter .</s>
            <s xml:id="echoid-s10569" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10570" xml:space="preserve">ſub, LT, & </s>
            <s xml:id="echoid-s10571" xml:space="preserve">quadrato, TO,
              <lb/>
            ter, cum tribus cubis, TO, & </s>
            <s xml:id="echoid-s10572" xml:space="preserve">adhuc parallelepipedum ſub, LT, & </s>
            <s xml:id="echoid-s10573" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0426-02" xlink:href="note-0426-02a" xml:space="preserve">3. 6. l. 2,</note>
            quadrato, TO, ter cum cubo, TO, .</s>
            <s xml:id="echoid-s10574" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10575" xml:space="preserve">habebimus parallelepipe-
              <lb/>
            dum ſub, LT, & </s>
            <s xml:id="echoid-s10576" xml:space="preserve">quadrato, TO, ſexies, cum quatuor cubis, TO,
              <lb/>
            pro quæſito reſiduo, igitur omnia quadrata, RC, ad omnia qua-
              <lb/>
            drata figuræ, DAVC, demptis omnibus quadratis hyperbolæ, HT
              <lb/>
            N, vel omnia quadrata, FC, ad omnia quadrata figuræ, FADCV
              <lb/>
            E, demptis omnibus quadratis oppoſitarum hyperbolarum, Y & </s>
            <s xml:id="echoid-s10577" xml:space="preserve">
              <lb/>
            B, HTN, erunt vt parallelepipedum ſub, LO, & </s>
            <s xml:id="echoid-s10578" xml:space="preserve">triplo quadrati,
              <lb/>
            OG, ad parallelepipedum ſexies ſub, LT, & </s>
            <s xml:id="echoid-s10579" xml:space="preserve">quadrato, TO, cum
              <lb/>
            quatuor cubis, TO, .</s>
            <s xml:id="echoid-s10580" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10581" xml:space="preserve">vt parallelepipedum ſub, LO, vel, ZC, & </s>
            <s xml:id="echoid-s10582" xml:space="preserve">
              <lb/>
            quadrato, OG, vel, ZS, ad parallelepipedum bis ſub, LT, & </s>
            <s xml:id="echoid-s10583" xml:space="preserve">qua-
              <lb/>
            drato, TO, cum cubo, TO, & </s>
            <s xml:id="echoid-s10584" xml:space="preserve">amplius eiuſdem cubi, TO, nam
              <lb/>
            hæc ſunt eorundem ſubtripla, vt conſideranti facilè patebit, quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s10585" xml:space="preserve"/>
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        <div xml:id="echoid-div956" type="section" level="1" n="569">
          <head xml:id="echoid-head594" xml:space="preserve">THEOREMA XXVII. PROPOS. XXVIII.</head>
          <p>
            <s xml:id="echoid-s10586" xml:space="preserve">SI, expoſitis ſectionibus coniugatis, parallelogrammũ
              <lb/>
            deſcribatur, habens latera earundem axibus, vel dia-
              <lb/>
            metris coniugatis parallela, in earum aſymptotis </s>
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