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

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          <pb o="293" file="0313" n="313" rhead="LIBER IV."/>
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        <div xml:id="echoid-div703" type="section" level="1" n="413">
          <head xml:id="echoid-head433" xml:space="preserve">THEOREMA VI. PROPOS. VI.</head>
          <p>
            <s xml:id="echoid-s7123" xml:space="preserve">SI ad baſim datæ parabolæ ordinatim applicetur recta li-
              <lb/>
            nea, tota parabola ad abſciſſam portionem per ipſam or-
              <lb/>
            dinatim applicatam erit, vt parallelepipedum ſub altitudine
              <lb/>
            dimidia baſi, ſub baſi autem quadrato totius baſis, ad paral-
              <lb/>
            lelepipedum ſub altitudine linea compoſita ex dimidia baſi,
              <lb/>
            & </s>
            <s xml:id="echoid-s7124" xml:space="preserve">reliquo baſis, dempta abſciſſa ab eadem extremitate ba-
              <lb/>
            ſis, à qua portio parabolæ abſcinditur, & </s>
            <s xml:id="echoid-s7125" xml:space="preserve">ſub baſi quadrato
              <lb/>
            eiuſdem abſciſſæ per dictam ordinatim applicatam: </s>
            <s xml:id="echoid-s7126" xml:space="preserve">Vel erit,
              <lb/>
            vt cubus totius baſis ad parallelepipedum ſub baſi quadrato
              <lb/>
            abſciſſæ, altitudine tripla reliquæ, cum cubo dictæ abſciſſæ.</s>
            <s xml:id="echoid-s7127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7128" xml:space="preserve">Sit parabola, HG
              <lb/>
              <figure xlink:label="fig-0313-01" xlink:href="fig-0313-01a" number="207">
                <image file="0313-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0313-01"/>
              </figure>
            A, cuius baſis, HA,
              <lb/>
            & </s>
            <s xml:id="echoid-s7129" xml:space="preserve">axis, vel diameter,
              <lb/>
            GO; </s>
            <s xml:id="echoid-s7130" xml:space="preserve">ducatur deinde
              <lb/>
            ipſi, GO, vtcunque
              <lb/>
            parallela, ST. </s>
            <s xml:id="echoid-s7131" xml:space="preserve">Dico
              <lb/>
            parabolam, AGH,
              <lb/>
            ad vtramuis portio-
              <lb/>
            num, SHT, TSG
              <lb/>
            A, vt ad, SHT, eſſe
              <lb/>
            vt parallelepip. </s>
            <s xml:id="echoid-s7132" xml:space="preserve">ſub al-
              <lb/>
            titudine dimidia, H
              <lb/>
            A, quæ ſit, AX, illi
              <lb/>
            in directum conſtitu-
              <lb/>
            ta, baſi quadrato, A
              <lb/>
            H, ad parallelepipe-
              <lb/>
            dum ſub altitudine, X
              <lb/>
            T, baſi quadrato, T
              <lb/>
            H. </s>
            <s xml:id="echoid-s7133" xml:space="preserve">Producatur, GO,
              <lb/>
            in, M, & </s>
            <s xml:id="echoid-s7134" xml:space="preserve">circa ſemia-
              <lb/>
            xes, vel ſemidiame-
              <lb/>
            tros, HO, OM, in-
              <lb/>
            telligatur deſcriptus
              <lb/>
            ſemicirculus, vel ſe-
              <lb/>
            miellipſis, HMA,
              <lb/>
            deinde per puncta, G, M, ducantur ipſi, HA, parallelæ, B ℟, </s>
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