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

Page concordance

< >
Scan Original
491 473
492 474
493 473
494 474
495 475
496 476
497 477
498 478
499 479
500 480
501 481
502 482
503 483
504 484
505 485
506 486
507 487
508 488
509 489
510 490
511 491
512 492
513 493
514 494
515 495
516 496
517 497
518 498
519 499
520 500
< >
page |< < (480) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1130" type="section" level="1" n="677">
          <p>
            <s xml:id="echoid-s12304" xml:space="preserve">
              <pb o="480" file="0500" n="500" rhead="GEOMETRIÆ"/>
              <figure xlink:label="fig-0500-01" xlink:href="fig-0500-01a" number="337">
                <image file="0500-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0500-01"/>
              </figure>
            A, ad parallelepipe-
              <lb/>
            dum ſub compoſita
              <lb/>
            ex ſexquialteraeiuſ-
              <lb/>
            dem tranſuerſi late-
              <lb/>
            ris, &</s>
            <s xml:id="echoid-s12305" xml:space="preserve">, KA, & </s>
            <s xml:id="echoid-s12306" xml:space="preserve">qua-
              <lb/>
            drato, KA. </s>
            <s xml:id="echoid-s12307" xml:space="preserve">Conus
              <lb/>
            verò, DAF, ad co-
              <lb/>
            num, MAI, vt cu-
              <lb/>
            bus, EA, ad cubum,
              <lb/>
            AK.</s>
            <s xml:id="echoid-s12308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12309" xml:space="preserve">Nunc intelliga-
              <lb/>
              <note position="left" xlink:label="note-0500-01" xlink:href="note-0500-01a" xml:space="preserve">F. H.
                <lb/>
              Cor. gen.
                <lb/>
              34. l. 2.</note>
            tur demptum à cy-
              <lb/>
            lindro, BF, hæmi-
              <lb/>
            ſphærium, vel hæ-
              <lb/>
            miſphæroides, DVATF. </s>
            <s xml:id="echoid-s12310" xml:space="preserve">Igitur per demonſtrata patet reliquum
              <lb/>
            cylindri ab abſciſſam ab eo portionem per ductum planum eſſe, vt
              <lb/>
              <note position="left" xlink:label="note-0500-02" xlink:href="note-0500-02a" xml:space="preserve">Coroll. 5.
                <lb/>
              34. l. 3.</note>
            cubus, AE, eſt ad cubum, EK. </s>
            <s xml:id="echoid-s12311" xml:space="preserve">Dempto autem conoide parabo-
              <lb/>
            lico ab eodem cylindro; </s>
            <s xml:id="echoid-s12312" xml:space="preserve">reliquum cylindri ab abſciſſam portionẽ
              <lb/>
            erit, vt quadratum, AE, ad quadratum, EK. </s>
            <s xml:id="echoid-s12313" xml:space="preserve">Dempto verò co-
              <lb/>
              <note position="left" xlink:label="note-0500-03" xlink:href="note-0500-03a" xml:space="preserve">Coroll. 9.
                <lb/>
              51. l. 4.</note>
            noide hyperbolico ab eodem cylindro, reliquum cylindri ad ab-
              <lb/>
            ſciſſam portionem erit, vt parallelepipedum ſub compoſita ex
              <lb/>
            ſexquialtera tranſuerſi lateris, & </s>
            <s xml:id="echoid-s12314" xml:space="preserve">dupla axis eiuſdem, & </s>
            <s xml:id="echoid-s12315" xml:space="preserve">ſub qua-
              <lb/>
            drato eiuſdem axis, ad parallelepipedum ſub compoſita ex ſex-
              <lb/>
              <note position="left" xlink:label="note-0500-04" xlink:href="note-0500-04a" xml:space="preserve">Coroll. 5.
                <lb/>
              30. l. 5.</note>
            quialtera eiuſdem tranſuerſi lateris, & </s>
            <s xml:id="echoid-s12316" xml:space="preserve">axibus vtriuſq; </s>
            <s xml:id="echoid-s12317" xml:space="preserve">portionis,
              <lb/>
            & </s>
            <s xml:id="echoid-s12318" xml:space="preserve">ſub quadrato exceſſus maioris axis ſuper minorem. </s>
            <s xml:id="echoid-s12319" xml:space="preserve">Tandem
              <lb/>
            dempto cono, DAF, à cylindro, BF, reſiduum cylindri ad abſciſsã
              <lb/>
            portionem erit, vt cubus, AE, ad parallelepipedum ſub ſexquialte-
              <lb/>
              <note position="left" xlink:label="note-0500-05" xlink:href="note-0500-05a" xml:space="preserve">Defin. 12.
                <lb/>
              l. 1.</note>
            ra, kE, & </s>
            <s xml:id="echoid-s12320" xml:space="preserve">ſub rectangulo, AKE, cum {2/3}. </s>
            <s xml:id="echoid-s12321" xml:space="preserve">quadrati, KE. </s>
            <s xml:id="echoid-s12322" xml:space="preserve">Nam cy-
              <lb/>
            lindrus, BF, ad reliquum cylindri, CF, dempto fruſto coni, DMIF,
              <lb/>
              <note position="left" xlink:label="note-0500-06" xlink:href="note-0500-06a" xml:space="preserve">C. Cor. 4.
                <lb/>
              gener. 34.
                <lb/>
              l. 2.</note>
            habet rationem compoſitam ex ea, quam habet cylindrus, BF, ad
              <lb/>
            cylindrum, CF, ideſt ex ea, quam habet, AE, ad, EK, & </s>
            <s xml:id="echoid-s12323" xml:space="preserve">ex ratio-
              <lb/>
              <note position="left" xlink:label="note-0500-07" xlink:href="note-0500-07a" xml:space="preserve">Collig. ex
                <lb/>
              L. Coroll.
                <lb/>
              4. gener.
                <lb/>
              34. l. 2.</note>
            ne cylindri, CF, ad reliquum, dempto à cylindro, CF, fruſto, DM
              <lb/>
            IF, quæ eſt ea, quam habet quadratum, DE, ad rectangulum, CM
              <lb/>
            K, cum {2/3}. </s>
            <s xml:id="echoid-s12324" xml:space="preserve">quadrati, CM, vel quadratum, EA, ad rectangulum, E
              <lb/>
            KA, cum {2/3}. </s>
            <s xml:id="echoid-s12325" xml:space="preserve">quadrati, EK, eſt autem reliquum cylindri, BF, dem-
              <lb/>
            pto cono, DAF, {2/3}. </s>
            <s xml:id="echoid-s12326" xml:space="preserve">eiuſdem cylindri, ergo reliquum cylindri, BF,
              <lb/>
            dempto cono, DAF, ad reliquum cylindri, CF, dempto fruſto, D
              <lb/>
            MIF, erit in ratione compoſita ex ea, quam habẽt {2/3}. </s>
            <s xml:id="echoid-s12327" xml:space="preserve">AE, ad, EK,
              <lb/>
            ideſt, AE, ad ſexquialteram, EK, & </s>
            <s xml:id="echoid-s12328" xml:space="preserve">quadratum, AE, ad rectangu-
              <lb/>
              <note position="left" xlink:label="note-0500-08" xlink:href="note-0500-08a" xml:space="preserve">D. G.
                <lb/>
              Cor. gen.
                <lb/>
              34. l. 2.</note>
            lum, AKE, cum {2/3}. </s>
            <s xml:id="echoid-s12329" xml:space="preserve">quadrati, kE, quæ duæ rationes componunt
              <lb/>
            rationem cubi, AE, ad parallelepipedum ſub ſexquialtera, Ek, &</s>
            <s xml:id="echoid-s12330" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum