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

Table of figures

< >
< >
page |< < (513) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1182" type="section" level="1" n="706">
          <p>
            <s xml:id="echoid-s13302" xml:space="preserve">
              <pb o="513" file="0533" n="533" rhead="LIBER VII."/>
              <figure xlink:label="fig-0533-01" xlink:href="fig-0533-01a" number="353">
                <image file="0533-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0533-01"/>
              </figure>
            riter inſiſtunt, eidẽ,
              <lb/>
            LI, æquidiſtare, ex
              <lb/>
            quo concludemus
              <lb/>
            hæc omnia pariter
              <lb/>
            in ſuperficie cylin-
              <lb/>
            dracea coextendi,
              <lb/>
            quæ ſit, ACNR,
              <lb/>
            qua methodo pate
              <lb/>
            bit etiam ſuperficiẽ,
              <lb/>
            BSOD, eſſe cylin-
              <lb/>
            draceam, in qua
              <lb/>
            quidem iacent late-
              <lb/>
            ra rectangulorũ prę-
              <lb/>
            dictis oppoſita. </s>
            <s xml:id="echoid-s13303" xml:space="preserve">Nũc
              <lb/>
            ſi ducta intelligan-
              <lb/>
            tur oppoſita plana
              <lb/>
            ſolidum, AO, tan-
              <lb/>
            gentia, ac præfatis
              <lb/>
            ſecantibus planis æ-
              <lb/>
            quidiſtantia, contin-
              <lb/>
            gere poteſt, vt ipſo-
              <lb/>
            rũ planorũ cõtactus ſit ex vtraq; </s>
            <s xml:id="echoid-s13304" xml:space="preserve">parte, vel in puncto, vel in linea, vel
              <lb/>
            in plano, vel ex vna parte contactus in vno iſtorum, ex altera verò
              <lb/>
            in alio promiſcuè, vt conſideranti facilè innoteſcet, attamen quo-
              <lb/>
            modocunq; </s>
            <s xml:id="echoid-s13305" xml:space="preserve">res ſe habeat etiam ratione iſtorum contactuum fiet,
              <lb/>
            vt dictum ſolidum cylindraceis ſuperficiebus comprehendatur, ſi
              <lb/>
            enim contactus ex neutra parte fiat in plano, dictum ſolidum non
              <lb/>
            alijs ſuperficiebus cylindraceis, quam ijs, quæ dictæ ſunt compre-
              <lb/>
            hendetur, vt manifeſtum eſt, ſi vero contactus ſit in plano, illud
              <lb/>
            erit parallelogrammum rectangulum, vt, AD, RO, cum enim
              <lb/>
            hæc tangentia plana æquidiſtent planis ſecantibus, quę tranſeunt
              <lb/>
            per latera cylindrici, cuius, ACNR, BDOS, ſunt ſuperficies, etiam
              <lb/>
            ipſa per eiuſdem latera tranſibunt, ergo, AC, BD, ſicut etiam, R
              <lb/>
            N, SO, per quæ tranſeunt dicta tangentia plana, ipſis, EG, FH, æ-
              <lb/>
              <note position="right" xlink:label="note-0533-01" xlink:href="note-0533-01a" xml:space="preserve">9. l. 1.</note>
            quidiſtabunt, quo pacto oſtendemus etiam, AB, CD, RS, NO, ipſi,
              <lb/>
            EF, GH, pariter æquidiſtare, ergo plana contactuum, AD, RO,
              <lb/>
            erunt parallelogramma rectangula, ergo & </s>
            <s xml:id="echoid-s13306" xml:space="preserve">ipſa erunt ſuperficies
              <lb/>
            cylindraceæ, ergo etiam ratione contingentium planorum ſecan-
              <lb/>
            tibus planis æquidiſtantium præfatũ ſolidũ ſuperficiebus cylindra-
              <lb/>
            ceis comprehendi manifeſtum eſt, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s13307" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum