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 |< < (15) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div61" type="section" level="1" n="51">
          <p>
            <s xml:id="echoid-s537" xml:space="preserve">
              <pb o="15" file="0035" n="35" rhead="LIBER I."/>
            tinget figuram, ABC, contingatin ſitu ipſius, FG, & </s>
            <s xml:id="echoid-s538" xml:space="preserve">in pun-
              <lb/>
            cto, A, igitur, A, erit vertex figuræ, ABC, reſpectu ipſius, B
              <lb/>
              <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">A. Def. 1.</note>
            C, à nobis inuentus, qui in huius Problematis priori parte inue-
              <lb/>
            niendus proponebatur.</s>
            <s xml:id="echoid-s539" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s540" xml:space="preserve">Sit nunc figura ſolida, ſiue ſolidum, ADE, in quo reſpectu
              <lb/>
            plani, BECD, ſit vertex inueniendus, ſumpto igitur exrra pla-
              <lb/>
            num figuræ, vtcumque puncto, N, per ipſum agatur planum, K
              <lb/>
            HVX, ipſi, BECD, æquidiſtans, quod vel continget ſolidum,
              <lb/>
            BAC, vel non, ſi autem non contingat, moueatur accedendo,
              <lb/>
              <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">Poſtul. 2.</note>
            velrecedendo, à plano, BECD, tandem igitur contingetipſum,
              <lb/>
            tangatin, A, puncto, igitur punctum, A, erit vertex ſolidi, AD
              <lb/>
              <note position="right" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">A. Def. 2.</note>
            E, reſpectu plani, BECD, qui inueniendus proponebatur.</s>
            <s xml:id="echoid-s541" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div64" type="section" level="1" n="52">
          <head xml:id="echoid-head63" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s542" xml:space="preserve">_H_Inc manifeſtum eſt, ſi recta, BC, tangat planam figuram, AB
              <lb/>
              <note position="right" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">_B. Def. 1._</note>
            C, quod ductæ erunt oppoſitę tangentes ipſius figuræ, ABC,
              <lb/>
            reſpectu datæ rectæ lineæ, quæ fuit vna ex eiſdem tangentibus, nem-
              <lb/>
              <note position="right" xlink:label="note-0035-05" xlink:href="note-0035-05a" xml:space="preserve">_B. Def. 2._</note>
            pè, BC; </s>
            <s xml:id="echoid-s543" xml:space="preserve">& </s>
            <s xml:id="echoid-s544" xml:space="preserve">ita ſi figura, BDCE, tangit ſolidum, ADE, ducta erunt
              <lb/>
            oppoſita tangentia plana ſolidi, ADE, reſpectu plani, BECD, in
              <lb/>
              <note position="right" xlink:label="note-0035-06" xlink:href="note-0035-06a" xml:space="preserve">_A. Def. 2._</note>
            quibus puncta contactuum erunt oppoſiti vertices earumdem figura-
              <lb/>
            rum, boc pacto inuenti: </s>
            <s xml:id="echoid-s545" xml:space="preserve">Siverò recta linea, BC, ſecaret figuran, A
              <lb/>
            BC, vel planum, BECD, ſecaret ſolidum, ADE, eodem pacto ex
              <lb/>
            alia parte lineæ, BC, vel plani, BDCE, inueniemus verticem, vn-
              <lb/>
            de inuenti erun@ propoſitæ figuræ planæ oppoſiti vertices, & </s>
            <s xml:id="echoid-s546" xml:space="preserve">ductæ op-
              <lb/>
            poſitæ tangentes reſpectu datæ lineæ BC; </s>
            <s xml:id="echoid-s547" xml:space="preserve">& </s>
            <s xml:id="echoid-s548" xml:space="preserve">in ſolido iuuenti erunt
              <lb/>
            oppoſiti vertices, & </s>
            <s xml:id="echoid-s549" xml:space="preserve">ducta oppoſita tangentia plana reſpectu dati
              <lb/>
            plani, BDCE, quæ cum tangunt in figuris planis, figuræ contactuum
              <lb/>
              <note position="right" xlink:label="note-0035-07" xlink:href="note-0035-07a" xml:space="preserve">_C. Def. 2._</note>
            vocantur etiam oppoſitæ baſes, & </s>
            <s xml:id="echoid-s550" xml:space="preserve">earum ſingulæ baſes, & </s>
            <s xml:id="echoid-s551" xml:space="preserve">baſes li-
              <lb/>
            neares, ſi contactus fieret in lineis: </s>
            <s xml:id="echoid-s552" xml:space="preserve">binc ergo diſcimus inuenire op-
              <lb/>
              <note position="right" xlink:label="note-0035-08" xlink:href="note-0035-08a" xml:space="preserve">_A. B. Def._
                <lb/>
              _1. & 2._</note>
            poſitos vertices figuræ planæ, vel ſolidæ cuiuſcumque, & </s>
            <s xml:id="echoid-s553" xml:space="preserve">eorum op-
              <lb/>
            poſita tangentia ducere reſpectu datæ in figura plana rectæ lineæ, & </s>
            <s xml:id="echoid-s554" xml:space="preserve">
              <lb/>
            dati plani par@ter in ſolida figura.</s>
            <s xml:id="echoid-s555" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div66" type="section" level="1" n="53">
          <head xml:id="echoid-head64" xml:space="preserve">PROBLEMA II. PROPOS. II.</head>
          <p>
            <s xml:id="echoid-s556" xml:space="preserve">CVilibct figuræ planæ parallelogrammum circumſcri-
              <lb/>
            bere, cuius latera duabus datis rectis lineis, in pro-
              <lb/>
            poſitæ figuræ plano ſe ſecantibus, ſint parallela.</s>
            <s xml:id="echoid-s557" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum