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

Table of figures

< >
[Figure 31]
Page: 62
[Figure 32]
Page: 64
[Figure 33]
Page: 66
[Figure 34]
Page: 68
[Figure 35]
Page: 70
[Figure 36]
Page: 73
[Figure 37]
Page: 74
[Figure 38]
Page: 76
[Figure 39]
Page: 77
[Figure 40]
Page: 77
[Figure 41]
Page: 79
[Figure 42]
Page: 80
[Figure 43]
Page: 82
[Figure 44]
Page: 84
[Figure 45]
Page: 86
[Figure 46]
Page: 88
[Figure 47]
Page: 90
[Figure 48]
Page: 91
[Figure 49]
Page: 93
[Figure 50]
Page: 94
[Figure 51]
Page: 95
[Figure 52]
Page: 96
[Figure 53]
Page: 97
[Figure 54]
Page: 98
[Figure 55]
Page: 100
[Figure 56]
Page: 102
[Figure 57]
Page: 103
[Figure 58]
Page: 104
[Figure 59]
Page: 106
[Figure 60]
Page: 107
< >
page |< < (27) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div95" type="section" level="1" n="69">
          <pb o="27" file="0047" n="47" rhead="LIBER I."/>
        </div>
        <div xml:id="echoid-div97" type="section" level="1" n="70">
          <head xml:id="echoid-head81" xml:space="preserve">LEMMA PRO ANTECED. PROP.</head>
          <p>
            <s xml:id="echoid-s775" xml:space="preserve">DEſiderari tantum videtur huius euidentia, quod ſcilicet planum
              <lb/>
            inter oppoſita tangentia plana eiſdem a quidiſtanter ductum
              <lb/>
            tranſeat perlatera cylindrici, quod aſſumpra eiuſdem figura nunc
              <lb/>
              <figure xlink:label="fig-0047-01" xlink:href="fig-0047-01a" number="20">
                <image file="0047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0047-01"/>
              </figure>
            fiet manifeſtum; </s>
            <s xml:id="echoid-s776" xml:space="preserve">intelliga-
              <lb/>
            tur ergo in ambitu vtriuſuis
              <lb/>
            oppoſitarum baſium cylin-
              <lb/>
            drici, PN, ſumptum pun-
              <lb/>
            ctum, vt, O, in ambitu fi-
              <lb/>
            guræ, ZON. </s>
            <s xml:id="echoid-s777" xml:space="preserve">Dico pla-
              <lb/>
            num, quod tranſit per, O,
              <lb/>
            æquidiſtans planis tangen-
              <lb/>
            tibus, AG, VL, tranſire
              <lb/>
            per latera cylindrici, PN.
              <lb/>
            </s>
            <s xml:id="echoid-s778" xml:space="preserve">Ducatur ergo à puncto, O,
              <lb/>
            latus cylindrici, PO, & </s>
            <s xml:id="echoid-s779" xml:space="preserve">ab
              <lb/>
            eodem pundo, O, in baſi,
              <lb/>
            ZON, recta, ON, paral-
              <lb/>
            lela ipſi, XL, igitur pla-
              <lb/>
            num, quod tranſit per, P
              <lb/>
            O, ON, æquidiſtat plano,
              <lb/>
              <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">15. Vnde-
                <lb/>
              cimi Ele.</note>
            VL, nam, PO, ipſi, VX,
              <lb/>
            lateri cylindrici, &</s>
            <s xml:id="echoid-s780" xml:space="preserve">, ON,
              <lb/>
            ipſi, XL, ęquidiſtat, quod
              <lb/>
            ergo ducitur per, O, eidem plano tangenti æquidiſtans tranſit per
              <lb/>
            ipſas, PO, ON, ſi. </s>
            <s xml:id="echoid-s781" xml:space="preserve">n. </s>
            <s xml:id="echoid-s782" xml:space="preserve">non, erunt duo plana eidem plano, VL,
              <lb/>
            æquidiſtantia, & </s>
            <s xml:id="echoid-s783" xml:space="preserve">ideò inter ſe æquidiſtantia, quibus communis erit
              <lb/>
            punctus, O, igitur in eo concurrent, quod eſt abſurdum, non ergo
              <lb/>
            illa ſunt duo plana, ſed vnum tantum, illud nempè, quod ducitur
              <lb/>
            per punctum, O, ipſi plano, VL, æquidiſtans, tranſitque per, P
              <lb/>
            O, ON, neceſſariò: </s>
            <s xml:id="echoid-s784" xml:space="preserve">Siverò à punctis, I, M, N, erigantur latera
              <lb/>
            cylindrici, CI, ME, NK, erunt cuncta in plano per, PO, ON,
              <lb/>
            tranſeunte, ergo planum, quod ducitur per punctum, O, æquidi-
              <lb/>
            ſtans plano, VL, cylindricum tangenti tranſit per latera, PO, CI,
              <lb/>
            EM, KN, quod oſtendendum erat.</s>
            <s xml:id="echoid-s785" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div99" type="section" level="1" n="71">
          <head xml:id="echoid-head82" xml:space="preserve">THEOREMA IX. PROPOS. XII.</head>
          <p>
            <s xml:id="echoid-s786" xml:space="preserve">SI cylindricus planis ſecetur quomodocumque pet latera
              <lb/>
            ductis, eiuſdem oppoſitę baſes in figuras ſimiles, ęqua-
              <lb/>
            les, & </s>
            <s xml:id="echoid-s787" xml:space="preserve">ſimiliter poſitas diuiduntur, tales autem erunt, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum