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

Page concordance

< >
Scan Original
221 201
222 202
223 203
224 204
225 205
226 206
227 207
228 208
229 209
230 210
231 211
232 212
233 213
234 214
235 215
236 216
237 217
238 218
239 219
240 220
241 221
242 222
243 223
244 224
245 225
246 226
247 227
248 228
249 229
250 230
< >
page |< < (213) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div526" type="section" level="1" n="314">
          <pb o="213" file="0233" n="233" rhead="LIBER III."/>
        </div>
        <div xml:id="echoid-div528" type="section" level="1" n="315">
          <head xml:id="echoid-head332" xml:space="preserve">THEOREMAX. PROPOS. XI.</head>
          <p>
            <s xml:id="echoid-s5198" xml:space="preserve">C Irculus, vel ellipſis ad quemlibet circulum, vel ellipſim
              <lb/>
            habet eandem rationem, quam rectangulum ſub ipſius
              <lb/>
            coniugatis axibus, vel diametris, ad rectangulum ſub iſtius
              <lb/>
            coniugatis axibus, vel diametris, æquè tamen diametris ad
              <lb/>
            inuicem inclinatis.</s>
            <s xml:id="echoid-s5199" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5200" xml:space="preserve">Sit circulus, ABCD, cuius axes coniugati ſint, AC, BD, cen-
              <lb/>
            trum, O, ductis verò per puncta, A, C, parallelis ipſi, BD, FL, Q
              <lb/>
            G, & </s>
            <s xml:id="echoid-s5201" xml:space="preserve">per puncta, B, D, parallelis ipſi, AC, LG, FQ, vt ſit, FG,
              <lb/>
            rectangulum circulo, ABCD, circumſcriptum, ſit, STVI, qui-
              <lb/>
              <figure xlink:label="fig-0233-01" xlink:href="fig-0233-01a" number="145">
                <image file="0233-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0233-01"/>
              </figure>
            libet circulus, vel ellipſis, cuirectangu-
              <lb/>
            lum, ER, ſit circumſcriptum, habens
              <lb/>
            latera parallela coniugatis axibus, SV,
              <lb/>
            TI. </s>
            <s xml:id="echoid-s5202" xml:space="preserve">Dico circulum, ABCD, ad elli-
              <lb/>
            pſem, STVI, eſſe vt rectangulum, FG,
              <lb/>
            ad rectangulum, ER; </s>
            <s xml:id="echoid-s5203" xml:space="preserve">producatur, SV,
              <lb/>
            hinc inde, ita vt, NK, ſit æqualis, OA,
              <lb/>
            &</s>
            <s xml:id="echoid-s5204" xml:space="preserve">, NM, ipſi, OC, & </s>
            <s xml:id="echoid-s5205" xml:space="preserve">circa, KM, TI,
              <lb/>
            axes intelligatur, KT, MI, ellipſis, vel
              <lb/>
            circulus, & </s>
            <s xml:id="echoid-s5206" xml:space="preserve">productis tangentibus, TE,
              <lb/>
            IR, vt occurrantipſis, HK, MP, ſit
              <lb/>
            rectangulum, HP, circumſcriptum ipſi,
              <lb/>
            KTMI, ellipſi, vel circulo, habens la-
              <lb/>
            tera coniugatis axibus, KM, TI, paral-
              <lb/>
            lela: </s>
            <s xml:id="echoid-s5207" xml:space="preserve">Eſt ergo vt rectangulum, FG, ad
              <lb/>
              <note position="right" xlink:label="note-0233-01" xlink:href="note-0233-01a" xml:space="preserve">Exantec.</note>
            rectangulum, HP, ita circulus, ABC
              <lb/>
            D, ad circulum, vel ellipſim, KTMI,
              <lb/>
            quia ſunt ambo circa, AC, KM, axes
              <lb/>
              <note position="right" xlink:label="note-0233-02" xlink:href="note-0233-02a" xml:space="preserve">Exantec.</note>
            æquales; </s>
            <s xml:id="echoid-s5208" xml:space="preserve">item parallelogrammum, H
              <lb/>
            P, ad parallelogrammum, ER, eſt vt
              <lb/>
            circulus, vel ellipſis, KTMI, ad circu-
              <lb/>
            lum, vel ellipſim, STVI, ergo ex ęqua-
              <lb/>
            lirectangulum, FG, ad rectangulum, ER, erit vt circulus, ABC
              <lb/>
            D, ad circulum, vel ell pſim, STVI.</s>
            <s xml:id="echoid-s5209" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5210" xml:space="preserve">Sit nunc, ABCD, ellipſis, vt etiam, STVI, poterit eſſe, quod,
              <lb/>
            AC, BD, ſint non axes, ſed coniugatæ diametri, &</s>
            <s xml:id="echoid-s5211" xml:space="preserve">, FG, pa-
              <lb/>
            rallelogrammum, oportet autem ſumere in ellipſi, ST, VI,
              <lb/>
            coniugatas diametros, SV, TI, itavt æqualiter ſint inclinatæ
              <lb/>
            ac ipiæ, AC, BD, tunc enim circumſcripta </s>
          </p>
        </div>
      </text>
    </echo>
Impressum