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
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 |< < (87) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div339" type="section" level="1" n="111">
          <p style="it">
            <s xml:id="echoid-s3617" xml:space="preserve">
              <pb o="87" file="0125" n="125" rhead="Conicor. Lib. V."/>
            te O N angulum acutum L N O ver-
              <lb/>
              <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a" number="107">
                <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-01"/>
              </figure>
              <note position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">Lem. 11.</note>
            ticem A reſpicientem; </s>
            <s xml:id="echoid-s3618" xml:space="preserve">eſtque G C or-
              <lb/>
            dinatim applicata ad diametrum N
              <lb/>
              <note position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">5. lib. 2.</note>
            M parallela tangenti verticali O N;
              <lb/>
            </s>
            <s xml:id="echoid-s3619" xml:space="preserve">ergo angulus L P G externus æqua-
              <lb/>
            lis erit angulo L N O interno, & </s>
            <s xml:id="echoid-s3620" xml:space="preserve">op-
              <lb/>
            poſito, & </s>
            <s xml:id="echoid-s3621" xml:space="preserve">ad eaſdem partes conſtitu-
              <lb/>
            to; </s>
            <s xml:id="echoid-s3622" xml:space="preserve">& </s>
            <s xml:id="echoid-s3623" xml:space="preserve">ideo angulus G P L acutus
              <lb/>
            quoque erit, at in triangulo P M
              <lb/>
            L angulus internus L M P, & </s>
            <s xml:id="echoid-s3624" xml:space="preserve">oppo-
              <lb/>
            ſitus minor eſt externo L P G acuto; </s>
            <s xml:id="echoid-s3625" xml:space="preserve">
              <lb/>
            igitur angulus L M P acutus pariter
              <lb/>
            erit, & </s>
            <s xml:id="echoid-s3626" xml:space="preserve">L M C obtuſus; </s>
            <s xml:id="echoid-s3627" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s3628" xml:space="preserve">intrian-
              <lb/>
            gulis L M G, & </s>
            <s xml:id="echoid-s3629" xml:space="preserve">L M C circa an-
              <lb/>
            gulos inæquales, latera G M, M C
              <lb/>
            æqualia, & </s>
            <s xml:id="echoid-s3630" xml:space="preserve">L M commune; </s>
            <s xml:id="echoid-s3631" xml:space="preserve">ergo L
              <lb/>
            C maior eſt, quàm L G, quod erat
              <lb/>
            faciendum.</s>
            <s xml:id="echoid-s3632" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3633" xml:space="preserve">E contra fieri poteſt, vt infimus
              <lb/>
            breuiſecans ramus L C æqualis, aut
              <lb/>
            minor ſit ramo aliquo ſupra breuiſe-
              <lb/>
            cantem reliquum B L poſito. </s>
            <s xml:id="echoid-s3634" xml:space="preserve">Nam L C minor eſt, quàm B L, & </s>
            <s xml:id="echoid-s3635" xml:space="preserve">maior effici
              <lb/>
            poteſt ramo non vltra ſectionis verticem A collocato ex prima parte huius pro-
              <lb/>
            poſitionis, ſed rami à concurſu L educti cadentes inter puncta A, & </s>
            <s xml:id="echoid-s3636" xml:space="preserve">B ſucceſ-
              <lb/>
            ſiuè augentur quo magis à vertice A recedunt; </s>
            <s xml:id="echoid-s3637" xml:space="preserve">Ergo ramus L C æqualis,
              <lb/>
            aut minor erit aliquo ramo ab eodem concurſu L educto inter puncta
              <lb/>
            A, & </s>
            <s xml:id="echoid-s3638" xml:space="preserve">B cadente; </s>
            <s xml:id="echoid-s3639" xml:space="preserve">igitur manifeſtum eſt ramum breuiſecantem
              <lb/>
            C L infimum duorum breuiſecantium, non eſſe ſemper
              <lb/>
            minimum omnium ramorum cadentium ex concurſis
              <unsure/>
              <lb/>
            L ad peripheriam ſectionis A B C, ſed tan-
              <lb/>
            tummodo minorem eſſe eorum, qui inter
              <lb/>
            duo breuiſecantes B L, C L cadunt,
              <lb/>
            & </s>
            <s xml:id="echoid-s3640" xml:space="preserve">reliquorum infra ramum
              <lb/>
            C L cadentium, atque
              <lb/>
            aliquorum in pe-
              <lb/>
            pheria
              <lb/>
            A N exiſtentium propè maximum L B;
              <lb/>
            </s>
            <s xml:id="echoid-s3641" xml:space="preserve">quapropter exiſtimandum eſt, in-
              <lb/>
            curia alicuius verba illa non
              <lb/>
            ſine Apollonij iniuria
              <lb/>
            textui irrepſiſſe.</s>
            <s xml:id="echoid-s3642" xml:space="preserve"/>
          </p>
          <figure number="108">
            <image file="0125-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-02"/>
          </figure>
        </div>
      </text>
    </echo>
Impressum