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
411 372
412 373
413 374
414
415
416
417
418 379
419 380
420 381
421 382
422 383
423
424 385
425 386
426 387
427 388
428 389
429 390
430 391
431 392
432 393
433 394
434 395
435 396
436 397
437 398
438 399
439 400
440 401
< >
page |< < (275) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div856" type="section" level="1" n="261">
          <p style="it">
            <s xml:id="echoid-s10231" xml:space="preserve">
              <pb o="275" file="0313" n="313" rhead="Conicor. Lib. VII."/>
            A F; </s>
            <s xml:id="echoid-s10232" xml:space="preserve">igitur rectangulum F D A æquale eſt
              <lb/>
              <figure xlink:label="fig-0313-01" xlink:href="fig-0313-01a" number="361">
                <image file="0313-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0313-01"/>
              </figure>
            rectangulo D A E vna cum quadrato D A;
              <lb/>
            </s>
            <s xml:id="echoid-s10233" xml:space="preserve">ſed quadratum ordinatim ad axim applicatæ
              <lb/>
              <note position="right" xlink:label="note-0313-01" xlink:href="note-0313-01a" xml:space="preserve">2 1. lib. 1.</note>
            B D æquale eſt rectangulo D A E ſub abſciſ-
              <lb/>
            ſa & </s>
            <s xml:id="echoid-s10234" xml:space="preserve">latere recto contento; </s>
            <s xml:id="echoid-s10235" xml:space="preserve">igitur rectangu-
              <lb/>
            lum F D A æquale eſt duobus quadratis B D,
              <lb/>
            & </s>
            <s xml:id="echoid-s10236" xml:space="preserve">D A: </s>
            <s xml:id="echoid-s10237" xml:space="preserve">eſtquè quadratum A B ſubtenden-
              <lb/>
            tis rectum angulum D æquale duobus quadra-
              <lb/>
            tis B D, & </s>
            <s xml:id="echoid-s10238" xml:space="preserve">D A; </s>
            <s xml:id="echoid-s10239" xml:space="preserve">igitur quadratum ſubten-
              <lb/>
            ſæ A B æquale eſt rectangulo A D E ſub ab-
              <lb/>
            ſciſſa D A, & </s>
            <s xml:id="echoid-s10240" xml:space="preserve">ſub D F, quæ æqualis eſt ei-
              <lb/>
            dem abſciſſæ cum latere recto.</s>
            <s xml:id="echoid-s10241" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div858" type="section" level="1" n="262">
          <head xml:id="echoid-head328" xml:space="preserve">Notæ in Propoſit. V. & XXIII.</head>
          <p style="it">
            <s xml:id="echoid-s10242" xml:space="preserve">ET diametri G C remotioris ab axe erectus C I maior eſt erecto B H
              <lb/>
              <note position="left" xlink:label="note-0313-02" xlink:href="note-0313-02a" xml:space="preserve">a</note>
            diametri propinquioris B F, &</s>
            <s xml:id="echoid-s10243" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10244" xml:space="preserve">Videtur hæc 23. </s>
            <s xml:id="echoid-s10245" xml:space="preserve">propoſitio deficiens;
              <lb/>
            </s>
            <s xml:id="echoid-s10246" xml:space="preserve">cum omnino inueriſimile ſit Apollonium non animaduertiſſe rem adeo facilem; </s>
            <s xml:id="echoid-s10247" xml:space="preserve">
              <lb/>
            quod nimirum diametri G C remotioris ab axe erectus C I maior ſit erecto B
              <lb/>
            H diametri B F proximioris quadruplo differentiæ axis abſciſſarum potentium
              <lb/>
            à terminis diametrorum ad axim ductorum.</s>
            <s xml:id="echoid-s10248" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10249" xml:space="preserve">Quare A E cum duplo K D, nempe cum quadruplo A D eſt æqualis
              <lb/>
              <note position="left" xlink:label="note-0313-03" xlink:href="note-0313-03a" xml:space="preserve">b</note>
            duplo K N, nempe dimidio B H, &</s>
            <s xml:id="echoid-s10250" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10251" xml:space="preserve">Zuoniam B H latus rectum diame-
              <lb/>
              <note position="right" xlink:label="note-0313-04" xlink:href="note-0313-04a" xml:space="preserve">49. lib. 1.</note>
            tri B F ad duplum contingentis B K eſt vt M B ad B L, ſed (propter æqui-
              <lb/>
            diſtantes, & </s>
            <s xml:id="echoid-s10252" xml:space="preserve">ſimilitudinem triangulorum L B M, & </s>
            <s xml:id="echoid-s10253" xml:space="preserve">K N B) vt M B ad B
              <lb/>
            L, ita eſt duplum N K ad duplum R B; </s>
            <s xml:id="echoid-s10254" xml:space="preserve">ergo latus rectum B H æquale eſt du-
              <lb/>
            plo K N; </s>
            <s xml:id="echoid-s10255" xml:space="preserve">ſed prius oſtenſum eſt quod D A æqualis eſt medietati ipſius D K, & </s>
            <s xml:id="echoid-s10256" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0313-05" xlink:href="note-0313-05a" xml:space="preserve">35. .lib. 1.</note>
            D N æqualis medietati ipſius A E; </s>
            <s xml:id="echoid-s10257" xml:space="preserve">igitur duplum K N æquale eſt duplo K D,
              <lb/>
            ſeu quadruplo A D cum duplo D N, ſeu cum A E.</s>
            <s xml:id="echoid-s10258" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10259" xml:space="preserve">Et A O maior eſt, quàm A D; </s>
            <s xml:id="echoid-s10260" xml:space="preserve">ergo erectus diametri C G remotioris
              <lb/>
              <note position="left" xlink:label="note-0313-06" xlink:href="note-0313-06a" xml:space="preserve">c</note>
            maior eſt quàm erectus B F proximioris, &</s>
            <s xml:id="echoid-s10261" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10262" xml:space="preserve">Addidi in bac concluſione
              <lb/>
            verba bæc (quadruplo D O differētiæ abſciſſarum) quæ videntur deficere. </s>
            <s xml:id="echoid-s10263" xml:space="preserve">Ma-
              <lb/>
            nifeſtum enim eſt, quod C I latus rectum diametri C G ab axe remotioris ſu-
              <lb/>
            perat latus rectum B H diametri F B axi propinguioris quadruplo D O diffe-
              <lb/>
            rentiæ abſeiſſarum axis ab ordinatis à verticibus earũdem diametrorum ductis;
              <lb/>
            </s>
            <s xml:id="echoid-s10264" xml:space="preserve">nam B H æqualis oſtenſa eſt E A vna cum quadruplo A D, eademque ratione
              <lb/>
            C I æqualis eſt eidem axis lateri recto E A cum quadruplo A O; </s>
            <s xml:id="echoid-s10265" xml:space="preserve">ergo exceſſus
              <lb/>
            C I ſupra B H erit æqualis quadruplo differentiæ D O.</s>
            <s xml:id="echoid-s10266" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum