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
341 302
342 303
343 304
344 305
345 306
346 307
347 308
348 309
349 310
350 311
351 312
352 313
353 314
354 315
355 316
356 317
357 318
358 319
359 320
360 321
361 322
362 323
363 324
364 325
365 326
366 327
367 328
368 329
369 330
370 331
< >
page |< < (64) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div248" type="section" level="1" n="83">
          <pb o="64" file="0102" n="102" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div252" type="section" level="1" n="84">
          <head xml:id="echoid-head117" xml:space="preserve">Notæ in Propoſit. LIX. LXII. & LXIII.</head>
          <p style="it">
            <s xml:id="echoid-s2796" xml:space="preserve">E T lineis, atque ſignis eodem ſtatu manentibus, &</s>
            <s xml:id="echoid-s2797" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2798" xml:space="preserve">Ideſt punctum
              <lb/>
              <note position="right" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">a</note>
            C extra, aut intra ſectionem ponatur, dummodo non ſit in axi, ducaturq;
              <lb/>
            </s>
            <s xml:id="echoid-s2799" xml:space="preserve">C E perpendicularis ad axim, ſecans eum in E, & </s>
            <s xml:id="echoid-s2800" xml:space="preserve">vt latus tranſuerſum ad re-
              <lb/>
            ctum, ita ſiat D F ad F E, atque C L ad L E, & </s>
            <s xml:id="echoid-s2801" xml:space="preserve">per L producatur O L M pa-
              <lb/>
            rallela A I, & </s>
            <s xml:id="echoid-s2802" xml:space="preserve">per F ducatur F M G parallela C E, quæ ſecet O M in M, & </s>
            <s xml:id="echoid-s2803" xml:space="preserve">per
              <lb/>
            C deſcribatur hyperbole H C B circa aſymptotos G M O, quæ in ellipſi per eius
              <lb/>
              <note position="left" xlink:label="note-0102-02" xlink:href="note-0102-02a" xml:space="preserve">4. lib. 2.</note>
            centrum D tranſibit, & </s>
            <s xml:id="echoid-s2804" xml:space="preserve">ideo eam ſecabit ſicuti oſtenſum eſt in 56. </s>
            <s xml:id="echoid-s2805" xml:space="preserve">huius.</s>
            <s xml:id="echoid-s2806" xml:space="preserve"/>
          </p>
          <figure number="81">
            <image file="0102-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0102-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s2807" xml:space="preserve">Eo quod O M parallela axi D A inclinato ſubtendit, &</s>
            <s xml:id="echoid-s2808" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2809" xml:space="preserve">Quoniam
              <lb/>
              <note position="right" xlink:label="note-0102-03" xlink:href="note-0102-03a" xml:space="preserve">b</note>
            in hyperbola O M parallela axi ſecat vtrãque linearum continentium angulum,
              <lb/>
            qui deinceps eſt ei, qui hyperbolen continet ſectioni occurret, & </s>
            <s xml:id="echoid-s2810" xml:space="preserve">producta ſectio-
              <lb/>
              <note position="left" xlink:label="note-0102-04" xlink:href="note-0102-04a" xml:space="preserve">11. lib. 2.</note>
            nem A B ſecabit, & </s>
            <s xml:id="echoid-s2811" xml:space="preserve">ideo O M cadit intra ſectionem A B, atque hyperbole A B
              <lb/>
            producta ſemper magis, ac magis recedit tum ab M O parallela axi, cum ab M
              <lb/>
            G parallela tangenti verticali, & </s>
            <s xml:id="echoid-s2812" xml:space="preserve">ſectio H C B, & </s>
            <s xml:id="echoid-s2813" xml:space="preserve">asymptoti O M G ad ſe ip-
              <lb/>
              <note position="left" xlink:label="note-0102-05" xlink:href="note-0102-05a" xml:space="preserve">14. lib. 2.</note>
            ſas jemper propius accedunt, igitur ſectiones A B, B C conueniunt; </s>
            <s xml:id="echoid-s2814" xml:space="preserve">ſecent ſe
              <lb/>
            ſe in B, & </s>
            <s xml:id="echoid-s2815" xml:space="preserve">ducamus per B, C lineam occurrentem axi in I, ipſi M O in O, & </s>
            <s xml:id="echoid-s2816" xml:space="preserve">
              <lb/>
            M G in G.</s>
            <s xml:id="echoid-s2817" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2818" xml:space="preserve">Et quia B O æqualis eſt ipſi C G, &</s>
            <s xml:id="echoid-s2819" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">Cum lineæ rectæ O M, O G ſe ſe-
              <lb/>
              <note position="right" xlink:label="note-0102-06" xlink:href="note-0102-06a" xml:space="preserve">c</note>
            cantes in O, ſecentur à parallelis E C, K B, F G proportionaliter, erit O N
              <lb/>
            æqualis M L, ſicuti O B æqualis erat C G, & </s>
            <s xml:id="echoid-s2821" xml:space="preserve">O L, æqualis erit N M, ſicuti
              <lb/>
            O C æqualis erat B G, cumque triangula O C L, & </s>
            <s xml:id="echoid-s2822" xml:space="preserve">I C E ſint ſimilia propter
              <lb/>
              <note position="left" xlink:label="note-0102-07" xlink:href="note-0102-07a" xml:space="preserve">8. lib. 2.</note>
            parallelas O L, I E, erit O L ad E I, vt L C ad C E; </s>
            <s xml:id="echoid-s2823" xml:space="preserve">eſt vero M N, ſeu F
              <lb/>
            K æqualis ipſi L O, igitur F K ad E I eſt, vt L C ad E C, ſed ex conſtru-
              <lb/>
            ctione erat D F ad F E, vt C L ad L E, ſciluet vt latus tranſuerſum ad
              <lb/>
            rectum; </s>
            <s xml:id="echoid-s2824" xml:space="preserve">ergo antecedentes ad ſummas terminorum in hyperbola, & </s>
            <s xml:id="echoid-s2825" xml:space="preserve">ad
              <lb/>
              <note position="left" xlink:label="note-0102-08" xlink:href="note-0102-08a" xml:space="preserve">Lem. 1.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum