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-s5700" xml:space="preserve">
              <pb o="145" file="0183" n="183" rhead="Conicor. Lib. VI."/>
            ſectiones æquales eſſe. </s>
            <s xml:id="echoid-s5701" xml:space="preserve">Sumatur quodlibet punctum B in ſectione B A ducaturque
              <lb/>
            ordinatim applicata B E, ſeceturque C F æqualis A E, & </s>
            <s xml:id="echoid-s5702" xml:space="preserve">ducatur ordinatim
              <lb/>
            D F. </s>
            <s xml:id="echoid-s5703" xml:space="preserve">Maniſeſtum eſt, rectangula E A I, & </s>
            <s xml:id="echoid-s5704" xml:space="preserve">F C N æqualia eße (cum latera
              <lb/>
            ſint æqualia, ſingula ſingulis); </s>
            <s xml:id="echoid-s5705" xml:space="preserve">his verò rectangulis æqualia ſunt quadrata or-
              <lb/>
              <note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">11. lib. 1.</note>
            dinatim applicatarum B E, D F; </s>
            <s xml:id="echoid-s5706" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s5707" xml:space="preserve">quadrata ſunt æqualia, atque eorum
              <lb/>
            latera B E, D F æqualia quoque. </s>
            <s xml:id="echoid-s5708" xml:space="preserve">Si igitur parabolæ ſuperponantur ita, vt
              <lb/>
            punctum E ſuper F, & </s>
            <s xml:id="echoid-s5709" xml:space="preserve">diameter A E ſuper C F cadat, neceſſariò punctum A
              <lb/>
            ſuper C cadet (propter æqualitatem abſcißarum) atque punctum B ſuper punctũ
              <lb/>
            D incidet (propterea quod anguli E, & </s>
            <s xml:id="echoid-s5710" xml:space="preserve">F æquales ſunt, pariterque rectæ B E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5711" xml:space="preserve">D F ſunt æquales), & </s>
            <s xml:id="echoid-s5712" xml:space="preserve">quia quodlibet punctum B parabolæ A B cadit ſemper
              <lb/>
            ſuper ſectionem C D; </s>
            <s xml:id="echoid-s5713" xml:space="preserve">ergo duæ ſectiones B A, & </s>
            <s xml:id="echoid-s5714" xml:space="preserve">D C ſibi mutuò congruunt, & </s>
            <s xml:id="echoid-s5715" xml:space="preserve">
              <lb/>
            ideo æquales ſunt. </s>
            <s xml:id="echoid-s5716" xml:space="preserve">Non ſecus conuerſum huius propoſitionis demonſtrari poteſt.</s>
            <s xml:id="echoid-s5717" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5718" xml:space="preserve">Altera verò pars propoſitionis breuius de-
              <lb/>
              <figure xlink:label="fig-0183-01" xlink:href="fig-0183-01a" number="188">
                <image file="0183-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0183-01"/>
              </figure>
            monſtrabitur hac ratione. </s>
            <s xml:id="echoid-s5719" xml:space="preserve">In duabus hyperbo-
              <lb/>
            lis, aut ellipſibus efficiant ordinatim applicatæ
              <lb/>
            B E, D F cum diametris A E, & </s>
            <s xml:id="echoid-s5720" xml:space="preserve">C F angu-
              <lb/>
            los æquales, & </s>
            <s xml:id="echoid-s5721" xml:space="preserve">non rectos; </s>
            <s xml:id="echoid-s5722" xml:space="preserve">ſintque tranſuerſa
              <lb/>
            latera G A, & </s>
            <s xml:id="echoid-s5723" xml:space="preserve">H C æqualia, pariterque late-
              <lb/>
            ra recta A I, & </s>
            <s xml:id="echoid-s5724" xml:space="preserve">C N æqualia. </s>
            <s xml:id="echoid-s5725" xml:space="preserve">Dico, ſectiones
              <lb/>
            B A, C D æquales eſſe. </s>
            <s xml:id="echoid-s5726" xml:space="preserve">Sumatur quodlibet
              <lb/>
            punctum B ſectionis B A, ducaturque ad A E
              <lb/>
            diametrum ordinatim applicata B E, ſecetur-
              <lb/>
            que C F æqualis abſciſſæ A E, ducaturque F D
              <lb/>
            ad H C F diametrũ ordinatim applicata. </s>
            <s xml:id="echoid-s5727" xml:space="preserve">Erit
              <lb/>
            rectangulum G E A ad quadr atum B E, vt la-
              <lb/>
            tus tranſuerſum G A ad rectum A I; </s>
            <s xml:id="echoid-s5728" xml:space="preserve">pariter-
              <lb/>
            que rectangulum H F C ad quadratum F D
              <lb/>
            erit, vt H C ad C N: </s>
            <s xml:id="echoid-s5729" xml:space="preserve">habent vero duæ æqua-
              <lb/>
            les G A, & </s>
            <s xml:id="echoid-s5730" xml:space="preserve">H C eandem proportionem ad duas
              <lb/>
            æquales A I, & </s>
            <s xml:id="echoid-s5731" xml:space="preserve">C N; </s>
            <s xml:id="echoid-s5732" xml:space="preserve">igitur rectangulum G E
              <lb/>
            A ad quadratum B E eandem proportionem ha-
              <lb/>
              <figure xlink:label="fig-0183-02" xlink:href="fig-0183-02a" number="189">
                <image file="0183-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0183-02"/>
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            bebit, quàm rectangulum.
              <lb/>
            </s>
            <s xml:id="echoid-s5733" xml:space="preserve">H F C ad quadratum D F,
              <lb/>
            ſunt verò rectangula G E
              <lb/>
            A, H F C æqualia inter, ſe
              <lb/>
            (quandoquidem eorum la-
              <lb/>
            tera A E, C F facta ſunt
              <lb/>
            æqualia) quæ addita ipſis
              <lb/>
            A G, & </s>
            <s xml:id="echoid-s5734" xml:space="preserve">C H æqualibus eſ-
              <lb/>
            eſſiciunt latera E G, & </s>
            <s xml:id="echoid-s5735" xml:space="preserve">F
              <lb/>
            H æqualia; </s>
            <s xml:id="echoid-s5736" xml:space="preserve">ergo quadrat a
              <lb/>
            d a um B E, & </s>
            <s xml:id="echoid-s5737" xml:space="preserve">D F æqua-
              <lb/>
            lia ſunt inter ſe; </s>
            <s xml:id="echoid-s5738" xml:space="preserve">& </s>
            <s xml:id="echoid-s5739" xml:space="preserve">ideo ordinatim applicatæ B E, & </s>
            <s xml:id="echoid-s5740" xml:space="preserve">D F æquales erunt. </s>
            <s xml:id="echoid-s5741" xml:space="preserve">
              <lb/>
            Quare facta, vt prius, intellectuali ſuperpoſitione; </s>
            <s xml:id="echoid-s5742" xml:space="preserve">nedum veriex A ſuper C,
              <lb/>
            ſed etiam quodlibet punctum B ſectionis A B ſuper ſectionem C D cadet; </s>
            <s xml:id="echoid-s5743" xml:space="preserve">ideo-
              <lb/>
            que ſectiones ſibi mutuò congruent, & </s>
            <s xml:id="echoid-s5744" xml:space="preserve">æquales erunt.</s>
            <s xml:id="echoid-s5745" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5746" xml:space="preserve">E conuerſo, ſi ſectiones B A, & </s>
            <s xml:id="echoid-s5747" xml:space="preserve">C D æquales ſupponantur, ſibi mutuò </s>
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