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

Page concordance

< >
Scan Original
441 421
442 422
443 423
444 424
445 425
446 426
447 427
448 428
449 429
450 428
451 429
452 432
453 433
454 434
455 435
456 436
457 437
458 438
459 439
460 440
461 441
462 442
463 443
464 444
465 445
466 446
467 447
468 448
469 449
470 450
< >
page |< < (320) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div764" type="section" level="1" n="450">
          <pb o="320" file="0340" n="340" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div765" type="section" level="1" n="451">
          <head xml:id="echoid-head471" xml:space="preserve">THEOREMA XXVI. PROPOS. XXVIII.</head>
          <p>
            <s xml:id="echoid-s7693" xml:space="preserve">SI intra curuam parabolicam duæ vtcunque ductæ fue-
              <lb/>
            rint rectæ lineæ in eandem terminantes, quarum vna
              <lb/>
            rectè, altera obliquè ſecet axim; </s>
            <s xml:id="echoid-s7694" xml:space="preserve">omnia quadrata conſtitu-
              <lb/>
            tæ parabolæ per eam, quæ axim rectè ſecat, regula eadem,
              <lb/>
            ad rectangula ſub parabola conſtituta per obliquè ſecantem
              <lb/>
            axem, regula huius baſi, & </s>
            <s xml:id="echoid-s7695" xml:space="preserve">ſub ſigura diſtantiarum eiuſ-
              <lb/>
            dem parabolæ, erunt vt quadratum axis primò dictæ para.
              <lb/>
            </s>
            <s xml:id="echoid-s7696" xml:space="preserve">bolæ ad quadratum diametriſecundò dictæ parabolæ.</s>
            <s xml:id="echoid-s7697" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7698" xml:space="preserve">Sintigitur intra curuam parabolicam, ADH, duæ ductæ rectæ
              <lb/>
            lineæ in eadem terminantes, quarum vna rectè, altera obliquè ſecet
              <lb/>
            axim, ſi ergo conſtitutarum ab ijſdem parabolarum diametri ſunt
              <lb/>
            æquales, pater veritas Propoſitionis ex antecedenti Theor. </s>
            <s xml:id="echoid-s7699" xml:space="preserve">non ſint
              <lb/>
            autem conſtitutarum parabolarum diametri æquales, ſint autem
              <lb/>
            duæ parabolas conſtituentes, AH, rectè ſecans axem, DO, & </s>
            <s xml:id="echoid-s7700" xml:space="preserve">C
              <lb/>
              <figure xlink:label="fig-0340-01" xlink:href="fig-0340-01a" number="229">
                <image file="0340-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0340-01"/>
              </figure>
            G, obliquè ipſum diuidens, exiſtatq;
              <lb/>
            </s>
            <s xml:id="echoid-s7701" xml:space="preserve">axis, DO, maior diametro parabo-
              <lb/>
            læ, CEG, quæ ſit, EM, & </s>
            <s xml:id="echoid-s7702" xml:space="preserve">ſit du-
              <lb/>
            cta linea, ER, & </s>
            <s xml:id="echoid-s7703" xml:space="preserve">conſtituta, ER
              <lb/>
            G, figura diſtantiarum parabolæ, C
              <lb/>
            EG. </s>
            <s xml:id="echoid-s7704" xml:space="preserve">Dico ergo omnia quadrata
              <lb/>
            parabolæ, ADH, regula, AH,
              <lb/>
            ad rectangula ſub parabola, CEG,
              <lb/>
            & </s>
            <s xml:id="echoid-s7705" xml:space="preserve">trilineo, ERG regula, CG,
              <lb/>
            eſſe vt quadratum, DO, ad quadratum, EM, abſcindatur ergo
              <lb/>
            ab, OD, DN, æqualis ipſi, EM, & </s>
            <s xml:id="echoid-s7706" xml:space="preserve">per, N, ducatur ipſi, AH,
              <lb/>
            parallela, BF. </s>
            <s xml:id="echoid-s7707" xml:space="preserve">Omnia ergo quadrata parabolæ, ADH, ad omnia
              <lb/>
            quadrata parabolæ, BDF, regula communi, AH, vel, BF, ſunt
              <lb/>
            vt qúadratum, OD, ad quadratum, DN, vel ad quadratum, E
              <lb/>
            M, ſedomnia quadrata parabolæ, BDF, regula, BF, ſunt æqua-
              <lb/>
              <note position="left" xlink:label="note-0340-01" xlink:href="note-0340-01a" xml:space="preserve">22. huius.</note>
            lia rectangulis ſub parabola, CEG, & </s>
            <s xml:id="echoid-s7708" xml:space="preserve">trilineo, ERG, regula, C
              <lb/>
            G, ergo omnia quadrata parabolæ, ADH, regula, AH ad re-
              <lb/>
            ctangula ſub parabola, CEG, & </s>
            <s xml:id="echoid-s7709" xml:space="preserve">trilineo, ERG, regula, CG,
              <lb/>
              <note position="left" xlink:label="note-0340-02" xlink:href="note-0340-02a" xml:space="preserve">Ex antec.</note>
            erunt vt quadratum, OD, ad quadratum, EM, quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s7710" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum