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
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
441 402
442 403
443 404
444 405
445 406
446 407
447 408
448 409
449 410
450 411
< >
page |< < (390) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1119" type="section" level="1" n="356">
          <p style="it">
            <s xml:id="echoid-s13080" xml:space="preserve">
              <pb o="390" file="0428" n="429" rhead="Archimedis"/>
            ipſius A B, eſtque nota A D medietas differentiæ inter diametrum A C, & </s>
            <s xml:id="echoid-s13081" xml:space="preserve">chor-
              <lb/>
            dam differentiæ F C; </s>
            <s xml:id="echoid-s13082" xml:space="preserve">at propoſitio Archimedea verificatur in quolibet circuli
              <lb/>
            ſegmento ſiue maiori, ſiue minori; </s>
            <s xml:id="echoid-s13083" xml:space="preserve">ex datis enim circumferentijs A C, A B,
              <lb/>
              <figure xlink:label="fig-0428-01" xlink:href="fig-0428-01a" number="493">
                <image file="0428-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0428-01"/>
              </figure>
            A F, & </s>
            <s xml:id="echoid-s13084" xml:space="preserve">F C vna cum cordis A C, & </s>
            <s xml:id="echoid-s13085" xml:space="preserve">F C, haberi quidem poteſt chorda A B
              <lb/>
            paulo difficilius, ſi nimirum ex chorda A C tollatur chorda F C, & </s>
            <s xml:id="echoid-s13086" xml:space="preserve">differen-
              <lb/>
            tia A E bifariam ſecetur in D, & </s>
            <s xml:id="echoid-s13087" xml:space="preserve">ex arcu cognito B C datur angulus A, atque
              <lb/>
            angulus D rectus eſt, ergo triangulum A B D ſpecie notum erit, & </s>
            <s xml:id="echoid-s13088" xml:space="preserve">propterea
              <lb/>
            proportio D A ad A B cognita erit, eſtque D A longitudine data, igitur A B
              <lb/>
            longitudine innoteſcet.</s>
            <s xml:id="echoid-s13089" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13090" xml:space="preserve">Notandum eſt quod figura appoſita in hac propoſ. </s>
            <s xml:id="echoid-s13091" xml:space="preserve">non exprimit omnes caſus
              <lb/>
            propoſitionis, quandoquidem ſemicirculus eſt A B C, & </s>
            <s xml:id="echoid-s13092" xml:space="preserve">propterea ex præceden-
              <lb/>
            tibus erroribus Arabici expoſitoris ſuſpicari licet non ritè eum percepiſſe Archi-
              <lb/>
            medis mentem.</s>
            <s xml:id="echoid-s13093" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1121" type="section" level="1" n="357">
          <head xml:id="echoid-head449" xml:space="preserve">PROPOSITIO IV.</head>
          <p>
            <s xml:id="echoid-s13094" xml:space="preserve">A B C ſemicirculus, & </s>
            <s xml:id="echoid-s13095" xml:space="preserve">fiant ſuper
              <lb/>
              <figure xlink:label="fig-0428-02" xlink:href="fig-0428-02a" number="494">
                <image file="0428-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0428-02"/>
              </figure>
            A C diametrum duo ſemicirculi, quo-
              <lb/>
            rum vnus A D, alter vero D C, & </s>
            <s xml:id="echoid-s13096" xml:space="preserve">
              <lb/>
            D B perpendicularis, vtique figura pro-
              <lb/>
            ueniens, quam vocat Archimedes AR-
              <lb/>
            BELON, eſt ſuperficies comprehenſa ab
              <lb/>
            arcu ſemicirculi maioris, & </s>
            <s xml:id="echoid-s13097" xml:space="preserve">duabus cir-
              <lb/>
            cumferentijs ſemicirculorum minorum, eſt æqualis circulo, cuius
              <lb/>
            diameter eſt perpendicularis D B.</s>
            <s xml:id="echoid-s13098" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13099" xml:space="preserve">Demonſtratio. </s>
            <s xml:id="echoid-s13100" xml:space="preserve">Quia linea D B media proportionalis eſt inter duas li-
              <lb/>
            neas D A, D C, erit planum A D in D C æquale quadrato D B, & </s>
            <s xml:id="echoid-s13101" xml:space="preserve">
              <lb/>
            ponamus A D in D C cum duobus quadratis A D, D C communiter,
              <lb/>
            fiet planum A D in D C bis cum duobus quadratis A D, D C, nempe
              <lb/>
            quadratum A C, æquale duplo quadrati D B cum duobus quadratis A
              <lb/>
            D, D C, & </s>
            <s xml:id="echoid-s13102" xml:space="preserve">proportio circulorum eadem eſt, ac proportio </s>
          </p>
        </div>
      </text>
    </echo>
Impressum