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

Table of figures

< >
[Figure 221]
Page: 330
[Figure 222]
Page: 331
[Figure 223]
Page: 332
[Figure 224]
Page: 333
[Figure 225]
Page: 335
[Figure 226]
Page: 336
[Figure 227]
Page: 337
[Figure 228]
Page: 338
[Figure 229]
Page: 340
[Figure 230]
Page: 343
[Figure 231]
Page: 344
[Figure 232]
Page: 345
[Figure 233]
Page: 346
[Figure 234]
Page: 347
[Figure 235]
Page: 348
[Figure 236]
Page: 350
[Figure 237]
Page: 351
[Figure 238]
Page: 352
[Figure 239]
Page: 353
[Figure 240]
Page: 355
[Figure 241]
Page: 357
[Figure 242]
Page: 357
[Figure 243]
Page: 359
[Figure 244]
Page: 360
[Figure 245]
Page: 363
[Figure 246]
Page: 364
[Figure 247]
Page: 366
[Figure 248]
Page: 366
[Figure 249]
Page: 367
[Figure 250]
Page: 367
< >
page |< < (320) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div764" type="section" level="1" n="450">
          <pb o="320" file="0340" n="340" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div765" type="section" level="1" n="451">
          <head xml:id="echoid-head471" xml:space="preserve">THEOREMA XXVI. PROPOS. XXVIII.</head>
          <p>
            <s xml:id="echoid-s7693" xml:space="preserve">SI intra curuam parabolicam duæ vtcunque ductæ fue-
              <lb/>
            rint rectæ lineæ in eandem terminantes, quarum vna
              <lb/>
            rectè, altera obliquè ſecet axim; </s>
            <s xml:id="echoid-s7694" xml:space="preserve">omnia quadrata conſtitu-
              <lb/>
            tæ parabolæ per eam, quæ axim rectè ſecat, regula eadem,
              <lb/>
            ad rectangula ſub parabola conſtituta per obliquè ſecantem
              <lb/>
            axem, regula huius baſi, & </s>
            <s xml:id="echoid-s7695" xml:space="preserve">ſub ſigura diſtantiarum eiuſ-
              <lb/>
            dem parabolæ, erunt vt quadratum axis primò dictæ para.
              <lb/>
            </s>
            <s xml:id="echoid-s7696" xml:space="preserve">bolæ ad quadratum diametriſecundò dictæ parabolæ.</s>
            <s xml:id="echoid-s7697" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7698" xml:space="preserve">Sintigitur intra curuam parabolicam, ADH, duæ ductæ rectæ
              <lb/>
            lineæ in eadem terminantes, quarum vna rectè, altera obliquè ſecet
              <lb/>
            axim, ſi ergo conſtitutarum ab ijſdem parabolarum diametri ſunt
              <lb/>
            æquales, pater veritas Propoſitionis ex antecedenti Theor. </s>
            <s xml:id="echoid-s7699" xml:space="preserve">non ſint
              <lb/>
            autem conſtitutarum parabolarum diametri æquales, ſint autem
              <lb/>
            duæ parabolas conſtituentes, AH, rectè ſecans axem, DO, & </s>
            <s xml:id="echoid-s7700" xml:space="preserve">C
              <lb/>
              <figure xlink:label="fig-0340-01" xlink:href="fig-0340-01a" number="229">
                <image file="0340-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0340-01"/>
              </figure>
            G, obliquè ipſum diuidens, exiſtatq;
              <lb/>
            </s>
            <s xml:id="echoid-s7701" xml:space="preserve">axis, DO, maior diametro parabo-
              <lb/>
            læ, CEG, quæ ſit, EM, & </s>
            <s xml:id="echoid-s7702" xml:space="preserve">ſit du-
              <lb/>
            cta linea, ER, & </s>
            <s xml:id="echoid-s7703" xml:space="preserve">conſtituta, ER
              <lb/>
            G, figura diſtantiarum parabolæ, C
              <lb/>
            EG. </s>
            <s xml:id="echoid-s7704" xml:space="preserve">Dico ergo omnia quadrata
              <lb/>
            parabolæ, ADH, regula, AH,
              <lb/>
            ad rectangula ſub parabola, CEG,
              <lb/>
            & </s>
            <s xml:id="echoid-s7705" xml:space="preserve">trilineo, ERG regula, CG,
              <lb/>
            eſſe vt quadratum, DO, ad quadratum, EM, abſcindatur ergo
              <lb/>
            ab, OD, DN, æqualis ipſi, EM, & </s>
            <s xml:id="echoid-s7706" xml:space="preserve">per, N, ducatur ipſi, AH,
              <lb/>
            parallela, BF. </s>
            <s xml:id="echoid-s7707" xml:space="preserve">Omnia ergo quadrata parabolæ, ADH, ad omnia
              <lb/>
            quadrata parabolæ, BDF, regula communi, AH, vel, BF, ſunt
              <lb/>
            vt qúadratum, OD, ad quadratum, DN, vel ad quadratum, E
              <lb/>
            M, ſedomnia quadrata parabolæ, BDF, regula, BF, ſunt æqua-
              <lb/>
              <note position="left" xlink:label="note-0340-01" xlink:href="note-0340-01a" xml:space="preserve">22. huius.</note>
            lia rectangulis ſub parabola, CEG, & </s>
            <s xml:id="echoid-s7708" xml:space="preserve">trilineo, ERG, regula, C
              <lb/>
            G, ergo omnia quadrata parabolæ, ADH, regula, AH ad re-
              <lb/>
            ctangula ſub parabola, CEG, & </s>
            <s xml:id="echoid-s7709" xml:space="preserve">trilineo, ERG, regula, CG,
              <lb/>
              <note position="left" xlink:label="note-0340-02" xlink:href="note-0340-02a" xml:space="preserve">Ex antec.</note>
            erunt vt quadratum, OD, ad quadratum, EM, quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s7710" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum