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

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          <pb o="200" file="0220" n="220" rhead="GEOMETRIÆ"/>
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        <div xml:id="echoid-div501" type="section" level="1" n="302">
          <head xml:id="echoid-head319" xml:space="preserve">THEOREMA II. PROPOS. II.</head>
          <p>
            <s xml:id="echoid-s4914" xml:space="preserve">SI à circulo, vel ellipſi per lineam ad eorum axim, vel dia-
              <lb/>
            metrum ordinatim applicatam vtcunque portio abſcin-
              <lb/>
            datur, ſit autem parallelogrammum in eadem altitudine cum
              <lb/>
            dicta portione, ſed in baſi æquali ſecundę diametro, & </s>
            <s xml:id="echoid-s4915" xml:space="preserve">regula
              <lb/>
            baſis ipſius portionis: </s>
            <s xml:id="echoid-s4916" xml:space="preserve">Omnia quadrata dicti parallelogram-
              <lb/>
            miad omnia quadrata dictę pottionis erunt, vt rectangulum
              <lb/>
            ſub dimidia eiuſdem axis, vel diametri, & </s>
            <s xml:id="echoid-s4917" xml:space="preserve">ſub eiuſdem dimi-
              <lb/>
            diæ tripla, ad rectangulum ſub axi, vel diametro abſciſſæ
              <lb/>
            portionis, & </s>
            <s xml:id="echoid-s4918" xml:space="preserve">ſub compoſita ex axe, vel diametro reliquę por-
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            tionis, & </s>
            <s xml:id="echoid-s4919" xml:space="preserve">dimidia totius axis, vel diametri.</s>
            <s xml:id="echoid-s4920" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4921" xml:space="preserve">Sit igitur circulus, vel ellipſis, BVOR, eius axis, vel diameter,
              <lb/>
            BO, ordinatim ad ipſum applicata, VR, vtcumq; </s>
            <s xml:id="echoid-s4922" xml:space="preserve">abſcindens por-
              <lb/>
            tionem, VBR, ſit verò ſecunda diameter, CF, & </s>
            <s xml:id="echoid-s4923" xml:space="preserve">producta, VR,
              <lb/>
            ita vt, PN, ſit æqualis ipſi, CF, &</s>
            <s xml:id="echoid-s4924" xml:space="preserve">, PM, ipſi, CA, in baſi, PN,
              <lb/>
            & </s>
            <s xml:id="echoid-s4925" xml:space="preserve">altitudine portionis, VBR, ſit parallelogrammum, DN, & </s>
            <s xml:id="echoid-s4926" xml:space="preserve">cir-
              <lb/>
            ca axim, vel diametrum, BM. </s>
            <s xml:id="echoid-s4927" xml:space="preserve">Dico ergo omnia quadrata paralle-
              <lb/>
            logrammi, DN, regula, VR, ad omnia quadrata portionis, VBR,
              <lb/>
            eſſe vt rectangulum ſub, BA, & </s>
            <s xml:id="echoid-s4928" xml:space="preserve">tripla, AO, ad rectangulum ſub, B
              <lb/>
              <figure xlink:label="fig-0220-01" xlink:href="fig-0220-01a" number="133">
                <image file="0220-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0220-01"/>
              </figure>
            M, & </s>
            <s xml:id="echoid-s4929" xml:space="preserve">ſub compoſita ex, MO, OA; </s>
            <s xml:id="echoid-s4930" xml:space="preserve">iun
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            gantur, VB, PB; </s>
            <s xml:id="echoid-s4931" xml:space="preserve">Omńia ergo quadrata
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            ſemiportionis, BCVM, ad omnia qua-
              <lb/>
            drata trianguli, BVM, ſunt vt, AO, O
              <lb/>
            M, ad, OM, .</s>
            <s xml:id="echoid-s4932" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4933" xml:space="preserve">ſumpta, BM, commu-
              <lb/>
              <note position="left" xlink:label="note-0220-01" xlink:href="note-0220-01a" xml:space="preserve">Exant.</note>
            ni altitudine, vt rectangulum ſub, BM,
              <lb/>
            MOA, ad rectangulum, BMO, omnia
              <lb/>
              <note position="left" xlink:label="note-0220-02" xlink:href="note-0220-02a" xml:space="preserve">5. Lib.2.</note>
            autem quadrata trianguli, BVM, ad
              <lb/>
              <note position="left" xlink:label="note-0220-03" xlink:href="note-0220-03a" xml:space="preserve">PerB.Co.
                <lb/>
              rollar.22.
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              lib.2.</note>
            omnia quadrata trianguli, BPM, ſunt
              <lb/>
            vt quadratum, VM, ad quadratum, P
              <lb/>
            M, velad quadratum, CA, .</s>
            <s xml:id="echoid-s4934" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4935" xml:space="preserve">vt rectan-
              <lb/>
              <note position="left" xlink:label="note-0220-04" xlink:href="note-0220-04a" xml:space="preserve">Ex 40. l.1.
                <lb/>
              & eiuſdẽ
                <lb/>
              Scholio.</note>
            gulum, OMB, ad rectangulum, OAB, ergo ex æquali, & </s>
            <s xml:id="echoid-s4936" xml:space="preserve">conuer-
              <lb/>
            tendo omnia quadrata trianguli, BPM, ad omnia quadrata ſemi-
              <lb/>
            portionis, BVM, erunt vt rectangulum, BAO, ad rectangulum
              <lb/>
              <note position="left" xlink:label="note-0220-05" xlink:href="note-0220-05a" xml:space="preserve">24. Lib. 2.</note>
            ſub, BM, &</s>
            <s xml:id="echoid-s4937" xml:space="preserve">, MOA, & </s>
            <s xml:id="echoid-s4938" xml:space="preserve">antecedentium tripla.</s>
            <s xml:id="echoid-s4939" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4940" xml:space="preserve">omnia quadrata
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            parallelogrammi, DM, ad omnia quadrata ſemiportionis, BVM,
              <lb/>
              <note position="left" xlink:label="note-0220-06" xlink:href="note-0220-06a" xml:space="preserve">8. Lib.2.</note>
            vel omnia quadrata parallelogrammi, DN, ad omnia quadrata
              <lb/>
            portionis, VBR, erunt vt rectangulum ſub, BA, & </s>
            <s xml:id="echoid-s4941" xml:space="preserve">tripla, </s>
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