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

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          <p>
            <s xml:id="echoid-s5116" xml:space="preserve">
              <pb o="208" file="0228" n="228" rhead="GEOMETRIÆ"/>
            pedum ſub baſi quadrato, AC, altitudine, CO, vel, CX, (quod
              <lb/>
              <note position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve">Per C. Co
                <lb/>
              rollar. 4
                <lb/>
              G@n. 34.
                <lb/>
              lib. 2.</note>
            eſt dimidium cubi, AC,) ad parallelepipedum ſub baſi quadrato, A
              <lb/>
            E, altitudine, EX, (quæ eſt dimidia altitudinis parallelepipedi ſub
              <lb/>
            baſi quadrato, AE, altitudine dupla, EC, & </s>
            <s xml:id="echoid-s5117" xml:space="preserve">ipſa, CA, ſimul) pa-
              <lb/>
            tet ergo, quod omnia quadrata circuli, vel ellipſis, ABCD, ad om-
              <lb/>
            nia quadrata portionis, BAD, erunt vt parallelepipedum ſub baſi
              <lb/>
            quadrato, AC, altitudine, CX, ad parallelepipedum ſub baſi qua-
              <lb/>
            drato, AE, altitudine, EX, vel (vt probauimus) vt cubus, AC, ad
              <lb/>
            parallelepipedum ſub baſi quadrato, AE, altitudine linea compo-
              <lb/>
            ſita ex dupla, EC, & </s>
            <s xml:id="echoid-s5118" xml:space="preserve">ex, AC, .</s>
            <s xml:id="echoid-s5119" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5120" xml:space="preserve">ad parallelepipedum ſub baſi qua-
              <lb/>
            drato, AE, altitudine tripla, EC, cum cubo, AE, quæ erant de-
              <lb/>
            monſtranda.</s>
            <s xml:id="echoid-s5121" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div515" type="section" level="1" n="308">
          <head xml:id="echoid-head325" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5122" xml:space="preserve">HInc etiam patet portionis, BCD, omnia quadrata ad omnia qua-
              <lb/>
            drata portionis, BAD, eſſe vt parallelepipedum ſub baſi qua-
              <lb/>
            drato, CE, altitudine autem, EAO, ad parallelepipedum ſub baſi qua-
              <lb/>
            drato, AE, altitudine autem, ECO, patet ergo ſi circulus, vel ellipſis
              <lb/>
            per applicatam ad eorum axim, vel di@metrum in duas portiones vt-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s5123" xml:space="preserve">diuidantur, quæq; </s>
            <s xml:id="echoid-s5124" xml:space="preserve">ſumatur pro regula, quod nota erit ratio om-
              <lb/>
            nium quadratorum vtriuſque portionis inter ſe.</s>
            <s xml:id="echoid-s5125" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div516" type="section" level="1" n="309">
          <head xml:id="echoid-head326" xml:space="preserve">THEOREMA VII. PROPOS. VII.</head>
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            <s xml:id="echoid-s5126" xml:space="preserve">SI in circulo, vel ellipſi duæ ad eundem axim, vel diame-
              <lb/>
            trum ordinatim applicentur rectæ lineæ; </s>
            <s xml:id="echoid-s5127" xml:space="preserve">Omnia qua-
              <lb/>
            drata vnius portionis (regula baſi) ad omnia quadrata alte-
              <lb/>
            rius portionis erunt, vt parallelepipedum ſub baſi quadrato
              <lb/>
            axis, vel diametri illius, & </s>
            <s xml:id="echoid-s5128" xml:space="preserve">ſub compoſita ex axi, vel dia-
              <lb/>
            metro reliquæ portionis, & </s>
            <s xml:id="echoid-s5129" xml:space="preserve">dimidia totius, ad parallelepi-
              <lb/>
            pedum ſub baſi quadrato axis, vel diametri alterius portio-
              <lb/>
            nis, & </s>
            <s xml:id="echoid-s5130" xml:space="preserve">ſub compoſita ex axi, vel diametro reliquæ portio-
              <lb/>
            nis, & </s>
            <s xml:id="echoid-s5131" xml:space="preserve">dimidia totius.</s>
            <s xml:id="echoid-s5132" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5133" xml:space="preserve">Sit circulus, vel ellipſis, ACND, cuius axis, vel diameter, AN,
              <lb/>
            centrum, O, duæ ad ipſum vtcunq; </s>
            <s xml:id="echoid-s5134" xml:space="preserve">ordinatim applicatæ ſint, BF,
              <lb/>
            CD, ſit autem producta, AN, in, X, ita vt, XN, ſit æqualis, N
              <lb/>
            O; </s>
            <s xml:id="echoid-s5135" xml:space="preserve">regula vero alterutra applicatarum, vt, CD. </s>
            <s xml:id="echoid-s5136" xml:space="preserve">Dico ergo omnia
              <lb/>
            quadrata portionis, BAF, ad omnia quadrata portionis, </s>
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