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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        <div xml:id="echoid-div814" type="section" level="1" n="248">
          <pb o="265" file="0303" n="303" rhead="Conicor. Lib. VI."/>
          <p style="it">
            <s xml:id="echoid-s9956" xml:space="preserve">Si fuerint quotcunque coni
              <lb/>
              <note position="right" xlink:label="note-0303-01" xlink:href="note-0303-01a" xml:space="preserve">PROP.
                <lb/>
              17.
                <lb/>
              Addit.</note>
              <figure xlink:label="fig-0303-01" xlink:href="fig-0303-01a" number="350">
                <image file="0303-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0303-01"/>
              </figure>
            ſuper circulum communem ba-
              <lb/>
            ſis deſcripti, habentes latus com-
              <lb/>
            mune indefinitè extenſum in-
              <lb/>
            triangulis per axes ad baſes
              <lb/>
            perpendicularibus, atque per ter-
              <lb/>
            minum lateris communis duca-
              <lb/>
            tur planum efficiens coni ſectio-
              <lb/>
            nes tangentes baſim: </s>
            <s xml:id="echoid-s9957" xml:space="preserve">habebunt
              <lb/>
            illæ latera recta æqualia inter
              <lb/>
            ſe, eritquè ſectio ſingularis, ſi
              <lb/>
            fuerit par abole, vel circulus:
              <lb/>
            </s>
            <s xml:id="echoid-s9958" xml:space="preserve">ſi verò fuerit ellipſis, aut hy-
              <lb/>
            perbole erunt infinitæ.</s>
            <s xml:id="echoid-s9959" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9960" xml:space="preserve">Sit conus A D C ſingularis, & </s>
            <s xml:id="echoid-s9961" xml:space="preserve">
              <lb/>
            A B C ſit multiplex, habentes cir-
              <lb/>
            culum A C baſeos communem, & </s>
            <s xml:id="echoid-s9962" xml:space="preserve">
              <lb/>
            latus A B D productum commu-
              <lb/>
            ne ſumptum ſit in triangulis per
              <lb/>
            axes conorum perpendicularibus ad
              <lb/>
            circulum baſis B C, atque à ter-
              <lb/>
            mino A ducatur planũ ſecans cir-
              <lb/>
            culi A C planum in recta linea,
              <lb/>
            quæ perpendicularis ſit ad diame-
              <lb/>
            trum C A, quod efficiat in cono
              <lb/>
            quidem A B C ſectionem A N,
              <lb/>
            cuius latus rectum ſit X, & </s>
            <s xml:id="echoid-s9963" xml:space="preserve">latus
              <lb/>
            tranſuerſum A F: </s>
            <s xml:id="echoid-s9964" xml:space="preserve">in cono verò
              <lb/>
            A D C efficiat ſectionem A M, cu-
              <lb/>
            ius latus rectum Z, & </s>
            <s xml:id="echoid-s9965" xml:space="preserve">diameter
              <lb/>
            communis A E; </s>
            <s xml:id="echoid-s9966" xml:space="preserve">ſitque ſectio A N
              <lb/>
            hyperbole, circulus, aut ellipſis
              <lb/>
            circa axim maiorem, aut mino-
              <lb/>
            rem; </s>
            <s xml:id="echoid-s9967" xml:space="preserve">Sectio verò ſingularis A M in cono D A C ſit parabole, & </s>
            <s xml:id="echoid-s9968" xml:space="preserve">ducatur B H
              <lb/>
            parallela diametro ſectionis A E ſecans circuli diametrum A C in H: </s>
            <s xml:id="echoid-s9969" xml:space="preserve">& </s>
            <s xml:id="echoid-s9970" xml:space="preserve">du-
              <lb/>
            catur C O parallela D A ſecans A E in O. </s>
            <s xml:id="echoid-s9971" xml:space="preserve">Dico latus rectum Z paraboles A M
              <lb/>
            æquale eſſe lateri recto X cuiuſlibet alterius ſectionis A N; </s>
            <s xml:id="echoid-s9972" xml:space="preserve">& </s>
            <s xml:id="echoid-s9973" xml:space="preserve">ſupponantur tres
              <lb/>
            parabolæ A M inter ſe æquales earumq; </s>
            <s xml:id="echoid-s9974" xml:space="preserve">latera recta Z æqualia, quæ in tribus fi-
              <lb/>
            guris apponẽtur, vt confuſio euitetur. </s>
            <s xml:id="echoid-s9975" xml:space="preserve">Quoniam vt latus rectum X ad tran-
              <lb/>
            ſuerſum A F ſectionis A N, ita eſt rectangulum A H C ad quadratum B H:
              <lb/>
            </s>
            <s xml:id="echoid-s9976" xml:space="preserve">
              <note position="right" xlink:label="note-0303-02" xlink:href="note-0303-02a" xml:space="preserve">12. & 13
                <lb/>
              lib. I.</note>
            hæc verò proportio componitur ex ratione C H ad H B, & </s>
            <s xml:id="echoid-s9977" xml:space="preserve">ex ratione A H ad
              <lb/>
            H B: </s>
            <s xml:id="echoid-s9978" xml:space="preserve">eſtque C A ad A F, vt C H ad H B (propter parallelas F A, H B, & </s>
            <s xml:id="echoid-s9979" xml:space="preserve">
              <lb/>
            ſimilitudinem triangulorum) & </s>
            <s xml:id="echoid-s9980" xml:space="preserve">vt A H ad H B, ita eſt A C ad C D, ſeu </s>
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