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
401 362
402 363
403 364
404 365
405 366
406 367
407 368
408 369
409 370
410 371
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
< >
page |< < (316) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div958" type="section" level="1" n="301">
          <p>
            <s xml:id="echoid-s11288" xml:space="preserve">
              <pb o="316" file="0354" n="355" rhead="Apollonij Pergæi"/>
            Simili modo oſtendetur quod I K minor ſit, quam P R: </s>
            <s xml:id="echoid-s11289" xml:space="preserve">etenim ſi pona-
              <lb/>
            tur linea f æqualis ſummæ M G, G E: </s>
            <s xml:id="echoid-s11290" xml:space="preserve">cum G E non ſit maior duplo E
              <lb/>
            H, & </s>
            <s xml:id="echoid-s11291" xml:space="preserve">f maior ſit duplo G E; </s>
            <s xml:id="echoid-s11292" xml:space="preserve">igitur f in E H maius eſt quadrato G E.
              <lb/>
            </s>
            <s xml:id="echoid-s11293" xml:space="preserve">Poſtea oſtendetur (quemadmodum antea dictum eſt) quod M H ad H
              <lb/>
            E, nempe M H in H A ad E H in H A minorem proportionem habet
              <lb/>
              <figure xlink:label="fig-0354-01" xlink:href="fig-0354-01a" number="420">
                <image file="0354-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0354-01"/>
              </figure>
            quàm quadratum M G ad quadratum G E; </s>
            <s xml:id="echoid-s11294" xml:space="preserve">& </s>
            <s xml:id="echoid-s11295" xml:space="preserve">permutando M H in H A
              <lb/>
            ad quadratum M G, ſeu quadratum A C ad quadratum P R(15. </s>
            <s xml:id="echoid-s11296" xml:space="preserve">ex 7.)
              <lb/>
            </s>
            <s xml:id="echoid-s11297" xml:space="preserve">minorem proportionem habebit, quàm E H in H A ad quadratum G E,
              <lb/>
            nempe quàm quadratum A C ad quadratum I K: </s>
            <s xml:id="echoid-s11298" xml:space="preserve">& </s>
            <s xml:id="echoid-s11299" xml:space="preserve">propterea A C ad
              <lb/>
            P R minorem proportionem habebit, quàm ad I K; </s>
            <s xml:id="echoid-s11300" xml:space="preserve">ideoquè I K minor
              <lb/>
            eſt, quàm P R: </s>
            <s xml:id="echoid-s11301" xml:space="preserve">& </s>
            <s xml:id="echoid-s11302" xml:space="preserve">pariter P R minor, quàm S Z.</s>
            <s xml:id="echoid-s11303" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div960" type="section" level="1" n="302">
          <head xml:id="echoid-head375" xml:space="preserve">PROPOSITIO XXXV. &
            <lb/>
          XXXVI.</head>
          <p>
            <s xml:id="echoid-s11304" xml:space="preserve">S It poſtea A C minor dimidio A F; </s>
            <s xml:id="echoid-s11305" xml:space="preserve">erit A G maior duplo A H, & </s>
            <s xml:id="echoid-s11306" xml:space="preserve">
              <lb/>
            ideo H G maior eſt, quàm H A: </s>
            <s xml:id="echoid-s11307" xml:space="preserve">ponatur iam H M æqualis H G,
              <lb/>
            ducaturque ad axim perpendicularis N M ; </s>
            <s xml:id="echoid-s11308" xml:space="preserve">iungaturque N C, & </s>
            <s xml:id="echoid-s11309" xml:space="preserve">educa-
              <lb/>
            tur diameter P Q parallela N C. </s>
            <s xml:id="echoid-s11310" xml:space="preserve">Et quia M H medietas eſt ipſius M G,
              <lb/>
            erit P Q dimidium ipſius P R (6. </s>
            <s xml:id="echoid-s11311" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11312" xml:space="preserve">Inter duas diametros P Q, A C
              <lb/>
            ducatur diameter I I.</s>
            <s xml:id="echoid-s11313" xml:space="preserve">, & </s>
            <s xml:id="echoid-s11314" xml:space="preserve">C B ei parallela, & </s>
            <s xml:id="echoid-s11315" xml:space="preserve">ad axim perpendicularis
              <lb/>
            B E. </s>
            <s xml:id="echoid-s11316" xml:space="preserve">Quoniam M H in H E minus eſt quadrato H G; </s>
            <s xml:id="echoid-s11317" xml:space="preserve">addito </s>
          </p>
        </div>
      </text>
    </echo>
Impressum