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

Page concordance

< >
Scan Original
341 321
342 322
343 323
344 324
345 325
346 326
347 327
348 328
349 329
350 330
351 331
352 332
353 333
354 334
355 335
356 336
357 337
358 338
359 339
360 340
361 341
362 342
363 343
364 344
365 345
366 346
367 347
368 348
369 349
370 350
< >
page |< < (326) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div784" type="section" level="1" n="465">
          <pb o="326" file="0346" n="346" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div786" type="section" level="1" n="466">
          <head xml:id="echoid-head486" xml:space="preserve">THEOREMA XXX. PROPOS. XXXII.</head>
          <p>
            <s xml:id="echoid-s7836" xml:space="preserve">SI parallelogrammum, & </s>
            <s xml:id="echoid-s7837" xml:space="preserve">parabola fuerint in eadem ba-
              <lb/>
            ſi, & </s>
            <s xml:id="echoid-s7838" xml:space="preserve">circa eundem axim, vel diametrum conſtituta,
              <lb/>
            baſiſque ſumatur pro regula: </s>
            <s xml:id="echoid-s7839" xml:space="preserve">Omnia quadrata dicti paral-
              <lb/>
            lelogrammi ad omnia quadrata figuræ compoſitæ ex para-
              <lb/>
            bola, & </s>
            <s xml:id="echoid-s7840" xml:space="preserve">alterutro trilineorum, qui fiunt extra parabolam,
              <lb/>
            demptis omnibus quadratis eiuſdem trilinei, erunt vt di-
              <lb/>
            ctum parallelogrammum ad dictam parabolam; </s>
            <s xml:id="echoid-s7841" xml:space="preserve">ad eadem
              <lb/>
            verò cum omnibus quadratis illius trilinci erunt, vt dictum
              <lb/>
            parallelogrammum ad dictam parabolam ſimul cum {@/2} {1/4}. </s>
            <s xml:id="echoid-s7842" xml:space="preserve">di-
              <lb/>
            ctiparallelogrammi .</s>
            <s xml:id="echoid-s7843" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7844" xml:space="preserve">vt 24. </s>
            <s xml:id="echoid-s7845" xml:space="preserve">ad 17.</s>
            <s xml:id="echoid-s7846" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7847" xml:space="preserve">Sit ergo parallelogrammum, AF, in eadem baſi, DF, & </s>
            <s xml:id="echoid-s7848" xml:space="preserve">circa
              <lb/>
            eundem axim, vel diametrum, BE, cum parabola, DBF, regula
              <lb/>
            ſit, DF. </s>
            <s xml:id="echoid-s7849" xml:space="preserve">Dico omnia quadrata, AF, ad omnia quadrat
              <unsure/>
            a figuræ,
              <lb/>
            CBDF, demptis omnibus quadratis trilinei, BCF, eſſe, vt, AF,
              <lb/>
            ad parabolam, DBF, eadem verò ad omnia quadrata fig. </s>
            <s xml:id="echoid-s7850" xml:space="preserve">CBD
              <lb/>
              <figure xlink:label="fig-0346-01" xlink:href="fig-0346-01a" number="233">
                <image file="0346-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0346-01"/>
              </figure>
            F, eſſe vt, AF, ad parabo-
              <lb/>
            lam, DBF, cum {@/2} {1/4}. </s>
            <s xml:id="echoid-s7851" xml:space="preserve">paral-
              <lb/>
            lelogrammi, AF; </s>
            <s xml:id="echoid-s7852" xml:space="preserve">quoniam
              <lb/>
            enim, BE, eſt axis, vel dia-
              <lb/>
            meter tum parabolæ, DBF,
              <lb/>
            tum parallelogrammi, AF,
              <lb/>
            ideò ſi ducatur intra paralle-
              <lb/>
            logrammum, AF, vtcunq-
              <lb/>
            recta linea parallelaipſi, D
              <lb/>
            F, portiones eiuſdem inclu-
              <lb/>
            ſæ trilineis, ADB, CFB, erunt inter ſe æquales, & </s>
            <s xml:id="echoid-s7853" xml:space="preserve">ideò para-
              <lb/>
            bola, DBF, erit figura, qualem poſtulat Prop. </s>
            <s xml:id="echoid-s7854" xml:space="preserve">29. </s>
            <s xml:id="echoid-s7855" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s7856" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7857" xml:space="preserve">quapro-
              <lb/>
            pter omnia quadrata, AF, ad omnia quadrata figuræ, CBDF,
              <lb/>
            demptis omnibus quadratis trilinei, BCF, erunt vt, AF, ad para-
              <lb/>
            bolam, DBF.</s>
            <s xml:id="echoid-s7858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7859" xml:space="preserve">Quoniam verò omnia quadrata, AF, ad omnia quadrata, BF,
              <lb/>
            ſunt vt quadratum, DF, ad quadratum, FE, .</s>
            <s xml:id="echoid-s7860" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7861" xml:space="preserve">quadrupla .</s>
            <s xml:id="echoid-s7862" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7863" xml:space="preserve">vt
              <lb/>
            24. </s>
            <s xml:id="echoid-s7864" xml:space="preserve">ad 6. </s>
            <s xml:id="echoid-s7865" xml:space="preserve">omnia verò quadrata, BF, ſunt ſexcupla omnium qua-
              <lb/>
            dratorum trilinei, BCF, .</s>
            <s xml:id="echoid-s7866" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7867" xml:space="preserve">vt 6. </s>
            <s xml:id="echoid-s7868" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7869" xml:space="preserve">igitur omnia quadrata, AF,
              <lb/>
              <note position="left" xlink:label="note-0346-01" xlink:href="note-0346-01a" xml:space="preserve">30. huius.</note>
            ad omnia quadrata trilinei, BCF, erunt vt 24. </s>
            <s xml:id="echoid-s7870" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7871" xml:space="preserve">ideſt vt, AF,
              <lb/>
            ad ſui ipſius {@/2} {1/4}. </s>
            <s xml:id="echoid-s7872" xml:space="preserve">ergo omnia quadrata, AF, ad omnia quadrata </s>
          </p>
        </div>
      </text>
    </echo>
Impressum