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

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            <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"/>
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              <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"/>
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          <figure number="108">
            <image file="0125-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-02"/>
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