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 |< < (79) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div313" type="section" level="1" n="104">
          <p style="it">
            <s xml:id="echoid-s3299" xml:space="preserve">
              <pb o="79" file="0117" n="117" rhead="Conicor. Lib. V."/>
            (qui eſt D B) cadit ſupra breuiſsimam ex puncto I ad axim ductam, quæ per-
              <lb/>
              <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            pendicularis eſt ad tangentem L I H, & </s>
            <s xml:id="echoid-s3300" xml:space="preserve">propterea angulus D I L, verticem
              <lb/>
              <note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            A reſpiciens erit acutus, & </s>
            <s xml:id="echoid-s3301" xml:space="preserve">conſequens angulus D I H obtuſus.</s>
            <s xml:id="echoid-s3302" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div315" type="section" level="1" n="105">
          <head xml:id="echoid-head145" xml:space="preserve">LEMMA XI.</head>
          <p style="it">
            <s xml:id="echoid-s3303" xml:space="preserve">Iiſdem poſitis, ſi à concurſu D duo breuiſecantes D C, D B ad ſe-
              <lb/>
            ctionem A B duci poſſunt; </s>
            <s xml:id="echoid-s3304" xml:space="preserve">Dico, quod quilibet ramus ſecans D I poſi-
              <lb/>
            tus ſupra breuiſecantem D B vertici proximiorem, vel infra infimum
              <lb/>
            breuiſecantem D C, efficit cum recta L I H tangente ſectionem in I an-
              <lb/>
            gulum D I L, reſpicientem verticem A, acutum, & </s>
            <s xml:id="echoid-s3305" xml:space="preserve">conſequentem D
              <lb/>
            I H obtuſum, & </s>
            <s xml:id="echoid-s3306" xml:space="preserve">quilibet ramus D O inter breuiſecantes poſitus efficit
              <lb/>
            cum recta G O N ſectionem tangente in O angulum D O G verticem
              <lb/>
            reſpicientem obtuſum, conſequentem vero D O N acutum.</s>
            <s xml:id="echoid-s3307" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3308" xml:space="preserve">Quia (ex conuerſa propoſitione 51. </s>
            <s xml:id="echoid-s3309" xml:space="preserve">& </s>
            <s xml:id="echoid-s3310" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3311" xml:space="preserve">huius) perpendicularis D E mi-
              <lb/>
              <note position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            nor eſſe debet Trutina F, & </s>
            <s xml:id="echoid-s3312" xml:space="preserve">propterea quilibet ramus D I ſupra breuiſecantem
              <lb/>
            D B, vel infra breuiſecãtem D C cadit ſupra breuiſsimam ex puncto I ad axim
              <lb/>
              <note position="right" xlink:label="note-0117-04" xlink:href="note-0117-04a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            ductam, cum qua contingens L I angulum rectum conſtituit; </s>
            <s xml:id="echoid-s3313" xml:space="preserve">ergo angulus D I
              <lb/>
            L verticem reſpiciens, eſt acutus, & </s>
            <s xml:id="echoid-s3314" xml:space="preserve">conſequens D I H obtuſus; </s>
            <s xml:id="echoid-s3315" xml:space="preserve">Similiter qui-
              <lb/>
            libet ramus D O inter breuiſecantes poſitus cadit infra breuiſsimam ex puncto
              <lb/>
            O ad axim ductam, & </s>
            <s xml:id="echoid-s3316" xml:space="preserve">cum illa ſectionem contingens G O efſicit angulos rectos,
              <lb/>
              <note position="right" xlink:label="note-0117-05" xlink:href="note-0117-05a" xml:space="preserve">Ibidem.</note>
            igitur angulus D O G verticem reſpiciens, eſt obtuſus, & </s>
            <s xml:id="echoid-s3317" xml:space="preserve">conſequens D O N
              <lb/>
            acutus.</s>
            <s xml:id="echoid-s3318" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div317" type="section" level="1" n="106">
          <head xml:id="echoid-head146" xml:space="preserve">Notæ in Propoſ. LXIV.
            <lb/>
          & LXV.</head>
          <p style="it">
            <s xml:id="echoid-s3319" xml:space="preserve">ANtea Apollonius docuit qui nam rami ab origine ad coniſectionem ducti
              <lb/>
            eſſent minimi, & </s>
            <s xml:id="echoid-s3320" xml:space="preserve">quo ordine reliqui rami ſe ſe excederent, modo agit
              <lb/>
            de ramis axim ſecantibus à concurſu ductis, & </s>
            <s xml:id="echoid-s3321" xml:space="preserve">quærit qui minimus, & </s>
            <s xml:id="echoid-s3322" xml:space="preserve">qui
              <lb/>
            maximus ſit, & </s>
            <s xml:id="echoid-s3323" xml:space="preserve">quo ordine diſponantur.</s>
            <s xml:id="echoid-s3324" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3325" xml:space="preserve">Producamus perpendicularem D E ſuper axim, &</s>
            <s xml:id="echoid-s3326" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3327" xml:space="preserve">Si nullus ramus
              <lb/>
              <note position="right" xlink:label="note-0117-06" xlink:href="note-0117-06a" xml:space="preserve">a</note>
            breuiſecans à concurſu D ad ſectionem A C duci poteſt; </s>
            <s xml:id="echoid-s3328" xml:space="preserve">Dico, quod ramus ter-
              <lb/>
            minatus D A eſt minimus omnium ramorum ſecantium D B, D C, & </s>
            <s xml:id="echoid-s3329" xml:space="preserve">propin-
              <lb/>
            quiores vertici A minores ſunt remotioribus; </s>
            <s xml:id="echoid-s3330" xml:space="preserve">ducatur D E perpendicularis ad
              <lb/>
            axim eum ſecans in E, & </s>
            <s xml:id="echoid-s3331" xml:space="preserve">reperiatur Trutina F. </s>
            <s xml:id="echoid-s3332" xml:space="preserve">Et ſiquidem D A non eſt
              <lb/>
            minor quolibet alio ramo ſecante D B infra ipſum poſito erit æqualis, aut maior
              <lb/>
            illo; </s>
            <s xml:id="echoid-s3333" xml:space="preserve">ſitque prius D A æqualis D B, ſi fieri poteſt, & </s>
            <s xml:id="echoid-s3334" xml:space="preserve">ex puncto A verticis du-
              <lb/>
            catur A G perpendicularis ad axim A E, quæ continget ſectionem in A, pari-
              <lb/>
              <note position="right" xlink:label="note-0117-07" xlink:href="note-0117-07a" xml:space="preserve">17. lib. 1.
                <lb/>
              32. pr.</note>
            terque ducatur recta A H perpendicularis ad ramum A D inclinatum ad axim;</s>
            <s xml:id="echoid-s3335" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum