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

Page concordance

< >
Scan Original
421 401
422 402
423 403
424 404
425 405
426 406
427 407
428 408
429 409
430 410
431 411
432 412
433 413
434 414
435 415
436 416
437 417
438 418
439 419
440 420
441 421
442 422
443 423
444 424
445 425
446 426
447 427
448 428
449 429
450 428
< >
page |< < (315) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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>
        </div>
        <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>
            <s xml:id="echoid-s7616" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum