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 |< < (65) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div252" type="section" level="1" n="84">
          <p style="it">
            <s xml:id="echoid-s2825" xml:space="preserve">
              <pb o="65" file="0103" n="103" rhead="Conicor. Lib. V."/>
            eorundẽ differen-
              <lb/>
              <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a" number="82">
                <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-01"/>
              </figure>
            tias in ellipſi ſci-
              <lb/>
            licet C L ad C E
              <lb/>
            erit vt D F ad D
              <lb/>
            E, & </s>
            <s xml:id="echoid-s2826" xml:space="preserve">propterea
              <lb/>
            K F ad E I erit,
              <lb/>
            vt D F ad D E,
              <lb/>
              <note position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">Lem. 3.</note>
            & </s>
            <s xml:id="echoid-s2827" xml:space="preserve">cõparando ho-
              <lb/>
            mologorum ſum-
              <lb/>
            mas in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s2828" xml:space="preserve">eorundem dif-
              <lb/>
            ferentias in elli-
              <lb/>
            pſi, K D ad D I
              <lb/>
            erit, vt D F ad D E, & </s>
            <s xml:id="echoid-s2829" xml:space="preserve">iterum comparando antecedentes ad differentias ter
              <lb/>
              <note position="right" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">Lem. 1.</note>
            minorum fiet D K ad K I, vt D F ad F E, ſeu vt latus tranſuer ſum ad rectum;
              <lb/>
            </s>
            <s xml:id="echoid-s2830" xml:space="preserve">igitur B I eſt linea breuiſsima.</s>
            <s xml:id="echoid-s2831" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Ex 9. 10.
            <lb/>
          huius.</note>
          <p>
            <s xml:id="echoid-s2832" xml:space="preserve">Si autem componamus proportionem in hyperbola deinde abſcinda-
              <lb/>
              <note position="left" xlink:label="note-0103-04" xlink:href="note-0103-04a" xml:space="preserve">d</note>
            mus, & </s>
            <s xml:id="echoid-s2833" xml:space="preserve">reijciamus oppoſitum ab oppoſito in ellipſi, deinde inuertamus
              <lb/>
            fiet K D ad K I, vt D F ad F E, &</s>
            <s xml:id="echoid-s2834" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">Sed textum mendoſum corrigi debere,
              <lb/>
            vt ſupra factum eſt conſtat ex præcedenti nota.</s>
            <s xml:id="echoid-s2836" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div257" type="section" level="1" n="85">
          <head xml:id="echoid-head118" xml:space="preserve">Notæ in Propoſit. LX.</head>
          <p style="it">
            <s xml:id="echoid-s2837" xml:space="preserve">DEinde ſit perpendicularis ex C, &</s>
            <s xml:id="echoid-s2838" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2839" xml:space="preserve">Siex puncto C extra hyperbolen po-
              <lb/>
              <note position="left" xlink:label="note-0103-05" xlink:href="note-0103-05a" xml:space="preserve">a</note>
            ſito perpendicularis ad axim ducta ad centrum eius D pertingat, duci de-
              <lb/>
            bet pariter ex puncto C recta linea ad ſectionem, cuius portio inter axim D F,
              <lb/>
            & </s>
            <s xml:id="echoid-s2840" xml:space="preserve">ſectionem A B ſit linea breuiſsima; </s>
            <s xml:id="echoid-s2841" xml:space="preserve">fiat C E ad E D, vt latus tranſuer ſum ad
              <lb/>
            rectum, & </s>
            <s xml:id="echoid-s2842" xml:space="preserve">ex E ducatur E B par allela axi, ſecans hyperbolen in B, & </s>
            <s xml:id="echoid-s2843" xml:space="preserve">ex B du-
              <lb/>
            catur B H perpendicularis ad axim, ſecans eum in H.</s>
            <s xml:id="echoid-s2844" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2845" xml:space="preserve">Et quia C E ad E D, nempe C B ad B G,
              <lb/>
              <figure xlink:label="fig-0103-02" xlink:href="fig-0103-02a" number="83">
                <image file="0103-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-02"/>
              </figure>
              <note position="left" xlink:label="note-0103-06" xlink:href="note-0103-06a" xml:space="preserve">b</note>
            &</s>
            <s xml:id="echoid-s2846" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2847" xml:space="preserve">Quia propter parallelas B E, F D eſt C E ad
              <lb/>
            E D, vt C B ad B G, & </s>
            <s xml:id="echoid-s2848" xml:space="preserve">propter parallelas D C,
              <lb/>
            H B, eſt D H ad H G, vt C B ad B G, quare D H
              <lb/>
            ad H G erit, vt C E ad E D: </s>
            <s xml:id="echoid-s2849" xml:space="preserve">poſita autem fuit C
              <lb/>
            E ad E D, vt latus tranſuer ſum ad rectum; </s>
            <s xml:id="echoid-s2850" xml:space="preserve">igi-
              <lb/>
            tur D H ex centro hyperboles ad H G eandem
              <lb/>
            proportionem habet, quàm latus tranſuerſum ad
              <lb/>
            rectum, & </s>
            <s xml:id="echoid-s2851" xml:space="preserve">propterea G B erit linea breuiſsima.</s>
            <s xml:id="echoid-s2852" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">9. huius.</note>
        </div>
        <div xml:id="echoid-div260" type="section" level="1" n="86">
          <head xml:id="echoid-head119" xml:space="preserve">Notæ in Propoſit. LXI.</head>
          <p style="it">
            <s xml:id="echoid-s2853" xml:space="preserve">SIt poſtea punctum C, & </s>
            <s xml:id="echoid-s2854" xml:space="preserve">perpendicularis C F, &</s>
            <s xml:id="echoid-s2855" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2856" xml:space="preserve">Si à puncto C extra
              <lb/>
              <note position="left" xlink:label="note-0103-08" xlink:href="note-0103-08a" xml:space="preserve">a</note>
            hyperbolen A B poſito, C F perpendicularis ad axim efficiat F A ſegmentũ
              <lb/>
            tranſuerſi axis maius ſemiſse eius D A, & </s>
            <s xml:id="echoid-s2857" xml:space="preserve">ponantur C E ad E F, atque D </s>
          </p>
        </div>
      </text>
    </echo>
Impressum