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 |< < (318) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div962" type="section" level="1" n="303">
          <pb o="318" file="0356" n="357" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div963" type="section" level="1" n="304">
          <head xml:id="echoid-head377" xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:id="echoid-s11339" xml:space="preserve">SI recta linea H G producatur in A & </s>
            <s xml:id="echoid-s11340" xml:space="preserve">E, ita vt A H, pariter-
              <lb/>
            que E H, non maior ſit H G: </s>
            <s xml:id="echoid-s11341" xml:space="preserve">Dico rectangulum ex A G E
              <lb/>
            ſumma inæqualium ſegmentorum in E H intermediam ſectionem, mi-
              <lb/>
            nus eſſe quadrato ex ſegmento intermedio minore E G.</s>
            <s xml:id="echoid-s11342" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11343" xml:space="preserve">Fiat H M æqualis H G, & </s>
            <s xml:id="echoid-s11344" xml:space="preserve">quia A
              <lb/>
            E æqualis, aut minor eſt, quàm M E;
              <lb/>
            </s>
            <s xml:id="echoid-s11345" xml:space="preserve">
              <figure xlink:label="fig-0356-01" xlink:href="fig-0356-01a" number="422">
                <image file="0356-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0356-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s11346" xml:space="preserve">E G maior, quàm E H, ergo A E
              <lb/>
            ad M E minorem proportionem babet,
              <lb/>
            quàm E G ad E H, & </s>
            <s xml:id="echoid-s11347" xml:space="preserve">permutando
              <lb/>
            A E ad E G minorem proportionem
              <lb/>
            habebit, quàm M E ad E H, & </s>
            <s xml:id="echoid-s11348" xml:space="preserve">cõ-
              <lb/>
            ponendo A G ad G E minorem proportionem habebit, quàm M H, ſeu ei æqua-
              <lb/>
            lis G H aà H E, & </s>
            <s xml:id="echoid-s11349" xml:space="preserve">iterum componendo A G E ad G E minorem proportionem
              <lb/>
            habebit, quàm G E ad E H: </s>
            <s xml:id="echoid-s11350" xml:space="preserve">quare rectangulum ex ſumma A G E in H E
              <lb/>
            minus erit quadrato ex intermedia G E, vt propoſitum fuerat.</s>
            <s xml:id="echoid-s11351" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div965" type="section" level="1" n="305">
          <head xml:id="echoid-head378" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s11352" xml:space="preserve">IIſdem poſitis ſint A H,
              <lb/>
            & </s>
            <s xml:id="echoid-s11353" xml:space="preserve">E H non minores
              <lb/>
              <figure xlink:label="fig-0356-02" xlink:href="fig-0356-02a" number="423">
                <image file="0356-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0356-02"/>
              </figure>
            quàm G H, vel H M:
              <lb/>
            </s>
            <s xml:id="echoid-s11354" xml:space="preserve">Dico rectangulum ex A G
              <lb/>
            E in E H maius eſſe quadrato ex E G.</s>
            <s xml:id="echoid-s11355" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11356" xml:space="preserve">Quia A G maior eſt quàm E G, & </s>
            <s xml:id="echoid-s11357" xml:space="preserve">G H non maior ipſa H E, ergo A G ad
              <lb/>
            G E maiorem proportionem habet, quàm G H ad H E, & </s>
            <s xml:id="echoid-s11358" xml:space="preserve">componendo A G E
              <lb/>
            ad E G maiorem proportionem habebit, quàm G E ad E H, & </s>
            <s xml:id="echoid-s11359" xml:space="preserve">ideo rectangu-
              <lb/>
            lum ex A G E in E H maius erit quadrato ex G E.</s>
            <s xml:id="echoid-s11360" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div967" type="section" level="1" n="306">
          <head xml:id="echoid-head379" xml:space="preserve">LEMMA IV.</head>
          <p style="it">
            <s xml:id="echoid-s11361" xml:space="preserve">IIſdem poſitis ſit A H ma-
              <lb/>
            ior, ſed E H minor ea-
              <lb/>
            dem M H ſemiſſe totius M
              <lb/>
              <figure xlink:label="fig-0356-03" xlink:href="fig-0356-03a" number="424">
                <image file="0356-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0356-03"/>
              </figure>
            G: </s>
            <s xml:id="echoid-s11362" xml:space="preserve">Dico quod ſi proportio ip-
              <lb/>
            ſius A G ad G E fuerit eadem
              <lb/>
            rationi G H ad H E, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum