Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Page concordance

< >
Scan Original
251 213
252 214
253 215
254 216
255 217
256 218
257 219
258 220
259 221
260 222
261 223
262 224
263 225
264 226
265 227
266 228
267 229
268 230
269 231
270 232
271 233
272 234
273 235
274 236
275 237
276 238
277 239
278 240
279 241
280 242
< >
page |< < (72) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div285" type="section" level="1" n="95">
          <pb o="72" file="0110" n="110" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s3066" xml:space="preserve">Patet ex hoc, quod ſi producantur ex duo-
              <lb/>
              <note position="right" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">d</note>
              <figure xlink:label="fig-0110-01" xlink:href="fig-0110-01a" number="91">
                <image file="0110-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0110-01"/>
              </figure>
            bus punctis contactus in ellipſi perpendiculares
              <lb/>
            E M, A L; </s>
            <s xml:id="echoid-s3067" xml:space="preserve">& </s>
            <s xml:id="echoid-s3068" xml:space="preserve">fuerit E M minor, exempli gra-
              <lb/>
            tia, tunc tangens educta ab eius extremitate,
              <lb/>
            quæ eſt in ſectione, minor quoque eſt, &</s>
            <s xml:id="echoid-s3069" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Si
              <lb/>
            enim ex punctis E, A contactuum in ellipſi ducan-
              <lb/>
            tur ad axim minorem K C perpendiculares E M,
              <lb/>
            & </s>
            <s xml:id="echoid-s3071" xml:space="preserve">A L ſecantes eum in M, & </s>
            <s xml:id="echoid-s3072" xml:space="preserve">L, fueritque E M
              <lb/>
            minor, quàm A L, tunc quidem punctum E magis
              <lb/>
            recedit à vertice B axis maioris, quàm punctum
              <lb/>
            A; </s>
            <s xml:id="echoid-s3073" xml:space="preserve">& </s>
            <s xml:id="echoid-s3074" xml:space="preserve">propterea, ex præmiſſa 70. </s>
            <s xml:id="echoid-s3075" xml:space="preserve">huius libri, erit
              <lb/>
            tangens E F minor, quàm A F. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">Expungo deter-
              <lb/>
            minationem ab aliquo incaute additam (quæ eſt in
              <lb/>
            ſectione) manifeſtum enim eſt ducinon poſſe contin-
              <lb/>
            gentem ellipſim à perpendicularis termino M in axi minori poſito, ſed à termi-
              <lb/>
            no E in ſectionis peripheria conſtituto.</s>
            <s xml:id="echoid-s3077" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div290" type="section" level="1" n="96">
          <head xml:id="echoid-head132" xml:space="preserve">SECTIO DVODECIMA</head>
          <head xml:id="echoid-head133" xml:space="preserve">Continens XXIX. XXX. XXXI.</head>
          <head xml:id="echoid-head134" xml:space="preserve">Propoſ. Appollonij.</head>
          <p>
            <s xml:id="echoid-s3078" xml:space="preserve">Q Vælibet linea recta A E D tangens fectionem aliquam A
              <lb/>
            F B in A extremitate lineæ breuiſſimæ A C eſt perpeudi-
              <lb/>
            cularis ſuper illam, nẽpe D A C eſt angulus rectus.
              <lb/>
            </s>
            <s xml:id="echoid-s3079" xml:space="preserve">Et ſi fuerit perpendicularis ſuper illam vtique tanget ſectio-
              <lb/>
            nem.</s>
            <s xml:id="echoid-s3080" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3081" xml:space="preserve">Alioquin producatur perpendicu-
              <lb/>
              <note position="right" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0110-02" xlink:href="fig-0110-02a" number="92">
                <image file="0110-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0110-02"/>
              </figure>
            laris C E ſuper A D, erit A C maior,
              <lb/>
            quàm E C, ergo maior eſt, quàm F
              <lb/>
            C; </s>
            <s xml:id="echoid-s3082" xml:space="preserve">ſed eſt minor, cũ ſit minor, quàm
              <lb/>
            C F, quod eſt abſurdum. </s>
            <s xml:id="echoid-s3083" xml:space="preserve">Igitur an-
              <lb/>
            gulus D A C, eſt rectus, quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s3084" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3085" xml:space="preserve">Si verò fuerit D A C rectus, erit
              <lb/>
              <note position="right" xlink:label="note-0110-03" xlink:href="note-0110-03a" xml:space="preserve">b</note>
            A D tangens, alioquin ſit tangens A
              <lb/>
            G; </s>
            <s xml:id="echoid-s3086" xml:space="preserve">ergo C A G erit rectus, ſed erat
              <lb/>
            C A D rectus, quod eſt abſurdum;
              <lb/>
            </s>
            <s xml:id="echoid-s3087" xml:space="preserve">ergo A D eſt tangens, & </s>
            <s xml:id="echoid-s3088" xml:space="preserve">hoc erat
              <lb/>
            probandum.</s>
            <s xml:id="echoid-s3089" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum