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

Page concordance

< >
Scan Original
391 371
392 372
393 373
394 374
395 375
396 376
397 377
398 378
399 379
400 380
401 381
402 382
403 383
404 384
405 385
406 386
407 387
408 388
409 389
410 390
411 391
412 392
413 393
414 394
415 395
416 396
417 397
418 398
419 399
420 400
< >
page |< < (297) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div711" type="section" level="1" n="418">
          <pb o="297" file="0317" n="317" rhead="LIBER IV."/>
          <p>
            <s xml:id="echoid-s7192" xml:space="preserve">Hoc Problema ſoluetur methodo Propoſ. </s>
            <s xml:id="echoid-s7193" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7194" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s7195" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7196" xml:space="preserve">propterea circa
              <lb/>
            ipſum non immoror.</s>
            <s xml:id="echoid-s7197" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div712" type="section" level="1" n="419">
          <head xml:id="echoid-head439" xml:space="preserve">THEOREMAIX. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s7198" xml:space="preserve">SI ad baſim datæ parabolæ ordinatim applicentur vtcun-
              <lb/>
            que rectæ lineæ, triangula ſub ipſis, & </s>
            <s xml:id="echoid-s7199" xml:space="preserve">portionibus baſis
              <lb/>
            abijſdem abſciſſis, erunt vt parallelepipeda ſub baſibus qua-
              <lb/>
            dratis abſciſſarum à baſi, altitudinibus autem reſiduis ipſius
              <lb/>
            baſis demptis abſciſſis.</s>
            <s xml:id="echoid-s7200" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7201" xml:space="preserve">Sit parabola, HGA, cuius baſis, HA, axis, vel diameter, GO,
              <lb/>
            ſint autem ductæ duæ vtcunq; </s>
            <s xml:id="echoid-s7202" xml:space="preserve">ordinatim applicatæ adipſam baſim,
              <lb/>
            HA, ipſæ, ST, VX, & </s>
            <s xml:id="echoid-s7203" xml:space="preserve">iungantur, SH, VH. </s>
            <s xml:id="echoid-s7204" xml:space="preserve">Dico triangulum,
              <lb/>
            VHX, ad triangulum, HST, eſſe vt parallelepipedum ſub altitudi-
              <lb/>
            ne, AX, baſi quadrato, XH, ad parallelepipedum ſub altitudine, A
              <lb/>
            T, baſi quadrato, TH. </s>
            <s xml:id="echoid-s7205" xml:space="preserve">Quoniam enim triangula vnum angulum
              <lb/>
              <figure xlink:label="fig-0317-01" xlink:href="fig-0317-01a" number="211">
                <image file="0317-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0317-01"/>
              </figure>
            vni angulo æqualem habentia ratio-
              <lb/>
              <note position="right" xlink:label="note-0317-01" xlink:href="note-0317-01a" xml:space="preserve">6. Lib. 2.</note>
            nem habent ex ratione laterum illis
              <lb/>
            angulis circumſtãtium compoſitam,
              <lb/>
            ideò triangulum, VHX, ad triangu-
              <lb/>
              <note position="right" xlink:label="note-0317-02" xlink:href="note-0317-02a" xml:space="preserve">3. Huius.</note>
            lum, SHT, habebit rationem com-
              <lb/>
            poſitam ex ea, quam habet, VX, ad,
              <lb/>
            ST, ideſt rectangulum, AXH, ad
              <lb/>
              <note position="right" xlink:label="note-0317-03" xlink:href="note-0317-03a" xml:space="preserve">G. D Cor.
                <lb/>
              4. Gen. 34,
                <lb/>
              lib. 2.</note>
            rectangulum, ATH, & </s>
            <s xml:id="echoid-s7206" xml:space="preserve">ex ea, quam
              <lb/>
            habet, XH, ad, HT, ſed iſtæ duæ
              <lb/>
            rationes componunt rationem paral-
              <lb/>
            lelepipedi ſub altitudine, HX, baſi
              <lb/>
            rectangulo, AXH, ad parallelepi-
              <lb/>
            pedum ſub altitudine, HT, baſi re-
              <lb/>
            ctangulo, HTA, . </s>
            <s xml:id="echoid-s7207" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7208" xml:space="preserve">parallelepipedi
              <lb/>
              <note position="right" xlink:label="note-0317-04" xlink:href="note-0317-04a" xml:space="preserve">Schol. 35.
                <lb/>
              lib. 2.</note>
            ſub altitudine, AX, baſi quadrato, XH, ad parallelepipedum ſub
              <lb/>
            altitudine, AT, baſi quadrato, TH, ergo triangulum, VHX, ad
              <lb/>
            triangulum, SHT, erit vt parallelepipedum ſub altitudine, AX, baſi
              <lb/>
            quadrato, XH, ad parallelepipedum ſub altitudine, AT, baſi qua-
              <lb/>
            drato, TH, quod erat oſtendendum.</s>
            <s xml:id="echoid-s7209" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum