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
361 322
362 323
363 324
364 325
365 326
366 327
367 328
368 329
369 330
370 331
371 332
372 333
373 334
374 335
375 336
376 337
377 338
378 339
379 340
380 341
381 342
382 343
383 344
384 345
385 346
386 347
387 348
388 349
389 350
390 351
< >
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