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

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        <div xml:id="echoid-div516" type="section" level="1" n="309">
          <p>
            <s xml:id="echoid-s5136" xml:space="preserve">
              <pb o="209" file="0229" n="229" rhead="LIBER III."/>
            eſſe, vt parallelepipedum ſub baſi quadrato, AE, altitudine autem,
              <lb/>
              <figure xlink:label="fig-0229-01" xlink:href="fig-0229-01a" number="140">
                <image file="0229-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0229-01"/>
              </figure>
            EX, ad parallelepipedum ſub baſi quadrato, AM,
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            altitudine, MX. </s>
            <s xml:id="echoid-s5137" xml:space="preserve">Nam omnia quadrata portionis,
              <lb/>
              <note position="right" xlink:label="note-0229-01" xlink:href="note-0229-01a" xml:space="preserve">Ex antec.</note>
            BAF, ad omnia quadrata circuli, vel ellipſis, A
              <lb/>
            CND, ſunt vt parallelepipedum ſub baſi quadra-
              <lb/>
            to, AE, altitudine, EX, ad parallelepipedum ſub
              <lb/>
            baſi quadrato, AN, altitudine, NX, item om-
              <lb/>
            nia quadrata circuli, vel ellipſis, ACND, ad om-
              <lb/>
              <note position="right" xlink:label="note-0229-02" xlink:href="note-0229-02a" xml:space="preserve">Ex antec.</note>
            nia quadrata portionis, CAD, ſunt vt parallele-
              <lb/>
            pipedum ſub baſi quadrato, AN, altitudine, N
              <lb/>
            X, ad parallelepipedum ſub baſi quadrato, AM,
              <lb/>
            altitudine, MX, ergo ex æquali omnia quadrato portionis, BAF,
              <lb/>
            ad omnia quadrata portionis, CAD, erunt vt parallelepipedum ſub
              <lb/>
            baſi quadrato, AE, altitudine, EX, ad parallelepipedum ſub baſi
              <lb/>
            quadrato, AM, altitudine, MX, quod erat oſtendendum.</s>
            <s xml:id="echoid-s5138" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div518" type="section" level="1" n="310">
          <head xml:id="echoid-head327" xml:space="preserve">PROBLEMA I PROPOS. VIII.</head>
          <p>
            <s xml:id="echoid-s5139" xml:space="preserve">ADato circulo, vel ellipſi portionem abſcindere per li-
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            neam ad eiuſdem axim, vel diametrum ordinatim ap-
              <lb/>
            plicatam, cuiusomnia quadrata ad omnia quadrata trian-
              <lb/>
            guli in eadem baſi, & </s>
            <s xml:id="echoid-s5140" xml:space="preserve">altitudine cum ipſa portione, habeant
              <lb/>
            rationem datam; </s>
            <s xml:id="echoid-s5141" xml:space="preserve">oportet autem hanc eſſe maiorem ſexqui-
              <lb/>
            altera, exiſtente regula ipſa ordinatim applicata.</s>
            <s xml:id="echoid-s5142" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5143" xml:space="preserve">Sit circulus, vel ellipſis, ADME, axis, vel diameter, AM, cen-
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            trum, F, oportet igitur ad ipſum axim, vel diametrum, lineam or-
              <lb/>
              <figure xlink:label="fig-0229-02" xlink:href="fig-0229-02a" number="141">
                <image file="0229-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0229-02"/>
              </figure>
            dinatim applicare, quæ ab ipſo circulo,
              <lb/>
            vel ellipſi abſcindat, portionem, cuius
              <lb/>
            omnia quadrata (regula ipſa applicata)
              <lb/>
            ad omnia quadrata trianguli in eadem
              <lb/>
            baſi, & </s>
            <s xml:id="echoid-s5144" xml:space="preserve">altitudine cum ipſa habeant ra-
              <lb/>
            tionem datam; </s>
            <s xml:id="echoid-s5145" xml:space="preserve">hanc dico prius oporte-
              <lb/>
            re eſſe maiorem ſexquialtera, nam cu-
              <lb/>
            iuslibet abſciſſæ portionis (vt oſtenſum
              <lb/>
            eſt) omnia quadrata ad omnia quadrata
              <lb/>
            trianguli in eadem baſi, & </s>
            <s xml:id="echoid-s5146" xml:space="preserve">altitudine
              <lb/>
              <note position="right" xlink:label="note-0229-03" xlink:href="note-0229-03a" xml:space="preserve">1. Huius.</note>
            cum ipſa ſunt, vt compoſita ex dimidia
              <lb/>
            totius axis, vel diametri, & </s>
            <s xml:id="echoid-s5147" xml:space="preserve">ex diametro
              <lb/>
            reliquæ portionis, ad axim, vel diame-
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            trum reliquæ portionis, & </s>
            <s xml:id="echoid-s5148" xml:space="preserve">diuidendo exceſſus omnium </s>
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