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 |< < (398) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1136" type="section" level="1" n="365">
          <p style="it">
            <s xml:id="echoid-s13308" xml:space="preserve">
              <pb o="398" file="0436" n="437" rhead="Archimedis"/>
            ſuper oſtendit perpendicularem E O æqualem eſſe circuli diametro E F. </s>
            <s xml:id="echoid-s13309" xml:space="preserve">Itaque
              <lb/>
            in quadrato ſpatio E O P F, circuli diameter E F, ſiue O P media proportio-
              <lb/>
            nalis erit inter A O, & </s>
            <s xml:id="echoid-s13310" xml:space="preserve">P C. </s>
            <s xml:id="echoid-s13311" xml:space="preserve">Zuam ergo proportionem habent tres continuè
              <lb/>
            proportionales in eadem ratione A D ad D C ſimul ſumptæ ad illarum inter-
              <lb/>
              <figure xlink:label="fig-0436-01" xlink:href="fig-0436-01a" number="504">
                <image file="0436-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0436-01"/>
              </figure>
            mediam, eandem habebit diameter maioris ſemicirculi A C ad O P, ſiue E F.
              <lb/>
            </s>
            <s xml:id="echoid-s13312" xml:space="preserve">Zuæ deinde Pappus demonſtrat perpendiculares à centris circulorum in collate-
              <lb/>
            ralibus ſpatijs prædicti Arbeli exiſtentium eſſe multiplices diametrorum eorum
              <lb/>
            circulorum à quibus educuntur ſecundum ſeriem natur alem numerorum ab vni-
              <lb/>
            tate creſcentium, proprietas quidem eſt admirabilis, de qua in hac propoſitio-
              <lb/>
            ne Archimedis altum ſilentium, quod forte temporum iniuriæ tribuendum
              <lb/>
            eſt.</s>
            <s xml:id="echoid-s13313" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13314" xml:space="preserve">Poſſent in hiſce duabus propoſitionibus non pauca problemata ſuperaddi, quo-
              <lb/>
            modo nimirum in prædicto ſpatio à tribus ſemicirculis comprehenſo circuli in-
              <lb/>
            numerabiles deſcribi debeant, & </s>
            <s xml:id="echoid-s13315" xml:space="preserve">alia quamplurima facilia, quæ lectorum ſa-
              <lb/>
            gacitati relinquuntur.</s>
            <s xml:id="echoid-s13316" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1138" type="section" level="1" n="366">
          <head xml:id="echoid-head458" xml:space="preserve">PROPOSITIO VII.</head>
          <p>
            <s xml:id="echoid-s13317" xml:space="preserve">SI circulus circa quadratum deſcriptus fuerit, & </s>
            <s xml:id="echoid-s13318" xml:space="preserve">alius intra
              <lb/>
            illum, vtique erit circumſcriptus duplus inſcripti.</s>
            <s xml:id="echoid-s13319" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13320" xml:space="preserve">Sit itaque circulus compre-
              <lb/>
              <figure xlink:label="fig-0436-02" xlink:href="fig-0436-02a" number="505">
                <image file="0436-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0436-02"/>
              </figure>
            hendens quadratum A B, cir-
              <lb/>
            culus A B, & </s>
            <s xml:id="echoid-s13321" xml:space="preserve">inſcriptus C D,
              <lb/>
            & </s>
            <s xml:id="echoid-s13322" xml:space="preserve">ſit diameter quadrati A B, & </s>
            <s xml:id="echoid-s13323" xml:space="preserve">
              <lb/>
            eſt diameter circuli circumſcri-
              <lb/>
            pti, & </s>
            <s xml:id="echoid-s13324" xml:space="preserve">educamus C D diame-
              <lb/>
            trum circuli inſcripti parallelam
              <lb/>
            ipſi A E, quæ eſt ei æqualis.
              <lb/>
            </s>
            <s xml:id="echoid-s13325" xml:space="preserve">Et quia quadratum A B duplum
              <lb/>
            eſt quadrati A E, ſiue D C, & </s>
            <s xml:id="echoid-s13326" xml:space="preserve">
              <lb/>
            proportio quadratorum ex </s>
          </p>
        </div>
      </text>
    </echo>
Impressum