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

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        <div xml:id="echoid-div753" type="section" level="1" n="444">
          <p>
            <s xml:id="echoid-s7596" xml:space="preserve">
              <pb o="315" file="0335" n="335" rhead="LIBER IV."/>
            ita erit alia prædictæ parallela ad diſtantiam parallelarum
              <lb/>
            ductarum ab eiuſdem extremitate ſecundò dictæ.</s>
            <s xml:id="echoid-s7597" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7598" xml:space="preserve">Sit ergo intra curuam parabolicam, ABCDF, ducta vtcunque,
              <lb/>
            BF, obliquè ſecans axem, NR, in eandem curuam terminata,
              <lb/>
            agatur deinde intra portionem, BNF, reſectam à, BF, recta, C
              <lb/>
            D, parallela ipſi, BF; </s>
            <s xml:id="echoid-s7599" xml:space="preserve">ducantur inſuperà punctis, B, C, D, F, axi,
              <lb/>
            NR, parallelæ, BO, CV, DG, FH, & </s>
            <s xml:id="echoid-s7600" xml:space="preserve">à puncto, F, cadat
              <lb/>
              <figure xlink:label="fig-0335-01" xlink:href="fig-0335-01a" number="225">
                <image file="0335-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0335-01"/>
              </figure>
            ipſi, NR, perpendicularis, F
              <lb/>
            A, ſecans parallelas, DG
              <lb/>
            R, CV, BO, in punctis, G,
              <lb/>
            R, V, O, poterunt ergo dicta-
              <lb/>
            rum parallelarum diſtantiæ iumi
              <lb/>
            in ipſamet, AF, nam ipſa per-
              <lb/>
            pendiculariter dictas parallelas
              <lb/>
            ſecat, erit ergo, OF, diſtantia
              <lb/>
            parallelarum, BO, FH, ab
              <lb/>
            extremis punctis rectæ, BF, ductarum; </s>
            <s xml:id="echoid-s7601" xml:space="preserve">pariter, VG, erit diſtan-
              <lb/>
            tia parallelarum, CV, DG, ab extremis punctis, CD, ducta-
              <lb/>
            rum. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">Dico ergo, BF, ad, FO, eſſe vt, CD, ad, VG: </s>
            <s xml:id="echoid-s7603" xml:space="preserve">Ducan-
              <lb/>
            tur a puncto, D, ipſi, CV, perpendicularis, DX, ſecans, BF, in,
              <lb/>
            M, quoniam ergo anguli, BOF, CXD, ſunt recti, ideò iuntin-
              <lb/>
            terſe æ quales, item anguius, OBF, eſt æqualis angulo, VIF, & </s>
            <s xml:id="echoid-s7604" xml:space="preserve">V
              <lb/>
            IF, ipſi angulo, XCD, ergo angulus, OBF, erit æqualis angulo, X
              <lb/>
              <note position="right" xlink:label="note-0335-01" xlink:href="note-0335-01a" xml:space="preserve">46. Elem.</note>
            CD, & </s>
            <s xml:id="echoid-s7605" xml:space="preserve">ideò reliquus, OFB, reliquo, XDC, æqualis erit, & </s>
            <s xml:id="echoid-s7606" xml:space="preserve">trian-
              <lb/>
            guli, BOF, CXD, ſimiles erunt, vnde, BF, ad, FO, erit vt, C
              <lb/>
            D, ad, DX, . </s>
            <s xml:id="echoid-s7607" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7608" xml:space="preserve">ad, VG, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s7609" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div755" type="section" level="1" n="445">
          <head xml:id="echoid-head465" xml:space="preserve">PROBLEMA II. PROPOS. XXV.</head>
          <p>
            <s xml:id="echoid-s7610" xml:space="preserve">A Sſumpta iterum ſuperioris figura, dimiſſa axi, & </s>
            <s xml:id="echoid-s7611" xml:space="preserve">ei-
              <lb/>
            dem parallelis, BO, CV, DG, FH, & </s>
            <s xml:id="echoid-s7612" xml:space="preserve">ipſa, DX,
              <lb/>
            ſiguram plènam deſcribere cum portione, BCDF, com-
              <lb/>
            munem habens angulum mixtum ſub, BF, & </s>
            <s xml:id="echoid-s7613" xml:space="preserve">curua, FD
              <lb/>
            C, quifit ad punctum, F, ita vt quælibet in deſctipta figu-
              <lb/>
            ra recta linea ipſi, BF, æquidiſtanter ducta, ſit diſtantia pa-
              <lb/>
            rallelarum axi, quæ ab extremis punctis eiuſdem rectæ li-
              <lb/>
            neæ, productæ vſque ad curuam parabolicam, duci poſſunt:
              <lb/>
            </s>
            <s xml:id="echoid-s7614" xml:space="preserve">Vocetur autem hæc deſcripta figura; </s>
            <s xml:id="echoid-s7615" xml:space="preserve">figura diſtantiarum
              <lb/>
            portionis, ſiue parabolæ, BCDF.</s>
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