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
431 392
432 393
433 394
434 395
435 396
436 397
437 398
438 399
439 400
440 401
441 402
442 403
443 404
444 405
445 406
446 407
447 408
448 409
449 410
450 411
451 412
452 413
453 414
454 415
455
456
457
< >
page |< < (343) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1032" type="section" level="1" n="326">
          <pb o="343" file="0381" n="382" rhead="Conicor. Lib. VII."/>
        </div>
        <div xml:id="echoid-div1035" type="section" level="1" n="327">
          <head xml:id="echoid-head405" xml:space="preserve">PROPOSITIO XXXXI.</head>
          <p>
            <s xml:id="echoid-s11978" xml:space="preserve">IN ellipſi A B C ſit A C axis maior, & </s>
            <s xml:id="echoid-s11979" xml:space="preserve">y O minor, & </s>
            <s xml:id="echoid-s11980" xml:space="preserve">ſint P
              <lb/>
            Q, & </s>
            <s xml:id="echoid-s11981" xml:space="preserve">S T duæ aliæ diametri, ſitque A F erectus ipſius A
              <lb/>
            C, & </s>
            <s xml:id="echoid-s11982" xml:space="preserve">P R erectus ipſius P Q, & </s>
            <s xml:id="echoid-s11983" xml:space="preserve">O f ipſius y O. </s>
            <s xml:id="echoid-s11984" xml:space="preserve">Dico quod
              <lb/>
            C F minor eſt, quàm Q R, & </s>
            <s xml:id="echoid-s11985" xml:space="preserve">Q R, quàm T Z, & </s>
            <s xml:id="echoid-s11986" xml:space="preserve">T Z,
              <lb/>
            quàm y f.</s>
            <s xml:id="echoid-s11987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11988" xml:space="preserve">Ducantur A N, A X ordinatim applicatæ ad diametros P Q, S T,
              <lb/>
            & </s>
            <s xml:id="echoid-s11989" xml:space="preserve">duæ ad axim perpendiculares N M, X V, & </s>
            <s xml:id="echoid-s11990" xml:space="preserve">interceptæ A G, C H.
              <lb/>
            </s>
            <s xml:id="echoid-s11991" xml:space="preserve">Quia quadratum A C ad quadratum y O, nempe A C ad A F eandem,
              <lb/>
              <note position="left" xlink:label="note-0381-01" xlink:href="note-0381-01a" xml:space="preserve">b</note>
            proportionem habet, quàm C G ad G A, ſeu ad C H habebit quadra-
              <lb/>
              <note position="right" xlink:label="note-0381-02" xlink:href="note-0381-02a" xml:space="preserve">Defin. 1.
                <lb/>
              huius.</note>
            tum C A ad quadratum C F ſummæ ipſius C A, eiuſque erecti eandem
              <lb/>
            proportionem, quàm quadratum C G, nempe C G in A H ad quadra-
              <lb/>
            tum G H: </s>
            <s xml:id="echoid-s11992" xml:space="preserve">& </s>
            <s xml:id="echoid-s11993" xml:space="preserve">quadratum A C ad quadratum y O eandem proportionem,
              <lb/>
            habet, quàm G C in C H ad quadratum C H: </s>
            <s xml:id="echoid-s11994" xml:space="preserve">eſtquè quadratum y O ad
              <lb/>
            quadratum ſummæ y f, vt quadra-
              <lb/>
              <figure xlink:label="fig-0381-01" xlink:href="fig-0381-01a" number="452">
                <image file="0381-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0381-01"/>
              </figure>
            tum C H ad quadratum H G; </s>
            <s xml:id="echoid-s11995" xml:space="preserve">er-
              <lb/>
            go quadratum A C ad quadratum
              <lb/>
            y f eſt, vt C G in C H minorem
              <lb/>
            ad quadratum H G; </s>
            <s xml:id="echoid-s11996" xml:space="preserve">ſed quadra-
              <lb/>
            tum A C ad quadratum C F ean-
              <lb/>
            dem proportionem habet, quàm.
              <lb/>
            </s>
            <s xml:id="echoid-s11997" xml:space="preserve">G C in maiorem A H ad quadra-
              <lb/>
            tum G H; </s>
            <s xml:id="echoid-s11998" xml:space="preserve">igitur A C ad C F ma-
              <lb/>
            iorem proportionem habet, quàm
              <lb/>
            ad y f: </s>
            <s xml:id="echoid-s11999" xml:space="preserve">& </s>
            <s xml:id="echoid-s12000" xml:space="preserve">propterea C F ſumma,
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s12001" xml:space="preserve">erecti illius minor eſt,
              <lb/>
            quàm y f, quæ eſt ſumma y O, & </s>
            <s xml:id="echoid-s12002" xml:space="preserve">
              <lb/>
            erecti illius. </s>
            <s xml:id="echoid-s12003" xml:space="preserve">Et quoniam C G in,
              <lb/>
            M H, quod minus eſt, quàm C G
              <lb/>
            in A H ad quadratum H G eandem
              <lb/>
            proportionem habet, quàm qua-
              <lb/>
            dratum A C ad quadratum Q R
              <lb/>
            ſummæ diametri, & </s>
            <s xml:id="echoid-s12004" xml:space="preserve">erecti ipſius
              <lb/>
            P Q (16. </s>
            <s xml:id="echoid-s12005" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s12006" xml:space="preserve">quare quadratum
              <lb/>
            A C ad quadratnm C F maiorem
              <lb/>
            proportionem babebit, quàm ad
              <lb/>
            quadratum Q R, & </s>
            <s xml:id="echoid-s12007" xml:space="preserve">propterea C F
              <lb/>
            minor erit, quam Q R. </s>
            <s xml:id="echoid-s12008" xml:space="preserve">Et quoniam
              <lb/>
            C G in V H ad quadratum H G eſt vt quadratum A C ad quadratum
              <lb/>
            T Z ad quàm ordinatim applicatur A X (16. </s>
            <s xml:id="echoid-s12009" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s12010" xml:space="preserve">erit C F minor quàm
              <lb/>
            T Z: </s>
            <s xml:id="echoid-s12011" xml:space="preserve">cumque C G in H M ad quadratum H G maiorem proportionem,
              <lb/>
            habeat, quàm G C in V H ad quadratum idipſum H G habebit </s>
          </p>
        </div>
      </text>
    </echo>
Impressum