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

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            <s xml:id="echoid-s10351" xml:space="preserve">
              <pb o="399" file="0419" n="419" rhead="LIBER V."/>
            bolæ poſtremò dictæ, vna cum {1/3}. </s>
            <s xml:id="echoid-s10352" xml:space="preserve">quadrati eiuſdem axis,
              <lb/>
            vel diametri.</s>
            <s xml:id="echoid-s10353" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10354" xml:space="preserve">Sint oppoſitis ſectionibus, FAD, EVC, quorum latus tranſuer-
              <lb/>
            ſum, AV, centrum, O, circumſcripta parallelogramma vtcunque'
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              <figure xlink:label="fig-0419-01" xlink:href="fig-0419-01a" number="284">
                <image file="0419-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0419-01"/>
              </figure>
            FC, TN, quorum duo oppoſita latera
              <lb/>
            ſint baſes oppoſitarum hyperbolarum, F
              <lb/>
            D, EC, nempè hyperbolarum, FAD, EV
              <lb/>
            C, &</s>
            <s xml:id="echoid-s10355" xml:space="preserve">, TY, MN, hyperbolarum, TAY, M
              <lb/>
            VN, nempè ſint ad axim, vel diametrum
              <lb/>
            tranſuerſam, AV, ordinatim applicata, & </s>
            <s xml:id="echoid-s10356" xml:space="preserve">
              <lb/>
            reliqua latera, ad ſecundum axim, vel dia-
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            metrum, quæ ſit, XL, pariter ordinatim
              <lb/>
            applicata, regula autem vna dictarum ba-
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            ſinum, vt, EC. </s>
            <s xml:id="echoid-s10357" xml:space="preserve">Dico ergo omnia quadra.
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            </s>
            <s xml:id="echoid-s10358" xml:space="preserve">ta, FC, demptis omnibus quadratis oppo. </s>
            <s xml:id="echoid-s10359" xml:space="preserve">
              <lb/>
            ſitarum hyperbolarum, FAD, EVC, ad
              <lb/>
            omnia quadrata, FN, demptis omnibus
              <lb/>
            quadratis oppotitarum hyperbolarum, T
              <lb/>
            AY, MVN, eſſe vt parallelepipedum ſub
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            alcicudine, ZV, baſi rectangulo VOZ, cũ
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            {1/3}. </s>
            <s xml:id="echoid-s10360" xml:space="preserve">quadrati, ZV, ad parallelpipedu ſub altitudine, SV, baſi re-
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            ctangulo, VOS, cum {1/3}. </s>
            <s xml:id="echoid-s10361" xml:space="preserve">quadrati, SV: </s>
            <s xml:id="echoid-s10362" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s10363" xml:space="preserve">o. </s>
            <s xml:id="echoid-s10364" xml:space="preserve">quadrata, FC,
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            dempt somnibus quadratis oppoſitarum hyperbolarum, FAD, E
              <lb/>
            VC, ad omnia quadrata, TN, demp@ sommbus quadratis oppo-
              <lb/>
            ſitarum hyperbolarum, TAY, MVN, habentrationem compo-
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            fitam ex ea, quain habent omnia quadrata, FC, demptis omnibus
              <lb/>
            quadratis oppoſitarum hyperbolarum, FAD, EVC, ad omnia
              <lb/>
            quadrata, FC, & </s>
            <s xml:id="echoid-s10365" xml:space="preserve">ex ratione horum ad omnia quadrata, TN, & </s>
            <s xml:id="echoid-s10366" xml:space="preserve">
              <lb/>
            ex ratione iſtorum ad omnia eorundem quadrata, demptis omni-
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            bus quadratis oppoſitarum hyperbolarum, TAY, MVN; </s>
            <s xml:id="echoid-s10367" xml:space="preserve">verum
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            omnia quadrata, FC, demptis omnibus quadratis oppoſitarum
              <lb/>
            hyperbolarum, FAD, EVC, ad omnia quadrata, FC, ſunt vt re-
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            ctangulum, AOZ, b@s, cum {2/3}. </s>
            <s xml:id="echoid-s10368" xml:space="preserve">quadrati, ZV, ad rectangulum, A
              <lb/>
              <note position="right" xlink:label="note-0419-01" xlink:href="note-0419-01a" xml:space="preserve">20. huius,</note>
            ZO: </s>
            <s xml:id="echoid-s10369" xml:space="preserve">Omnia item quadrata, FC, ad omnia quadrata, TN, habẽt
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            rationem compoſitam ex ratione, FE, ad, TM, vel, EX, ad, MH,
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            ſiue, ZO, ad, OS, & </s>
            <s xml:id="echoid-s10370" xml:space="preserve">ex ratione quadrati, EC, ad quadratum, MN,
              <lb/>
              <note position="right" xlink:label="note-0419-02" xlink:href="note-0419-02a" xml:space="preserve">Defin. 12.
                <lb/>
              l. 1.</note>
            ſiue rectanguli, AZV, ad rectangulum, ASV: </s>
            <s xml:id="echoid-s10371" xml:space="preserve">@andem omnia
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            quadrata, TN ad eadem demptis omnibus quadratis oppoſitarũ
              <lb/>
            hyperbolarum, TAY, MVN, ſunt vt rectangulum, ASO, ad re-
              <lb/>
            ctangulum, AOS, bis, cum {2/3}. </s>
            <s xml:id="echoid-s10372" xml:space="preserve">quadrati, SV, habemus ergo has
              <lb/>
              <note position="right" xlink:label="note-0419-03" xlink:href="note-0419-03a" xml:space="preserve">20: huius.</note>
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