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-div533" type="section" level="1" n="174">
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            <s xml:id="echoid-s5615" xml:space="preserve">
              <pb o="143" file="0181" n="181" rhead="Conicor. Lib. VI."/>
              <figure xlink:label="fig-0181-01" xlink:href="fig-0181-01a" number="184">
                <image file="0181-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0181-01"/>
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            æqualia ſunt inter ſe: </s>
            <s xml:id="echoid-s5616" xml:space="preserve">ſunt verò rectangula N K, & </s>
            <s xml:id="echoid-s5617" xml:space="preserve">L I æqualia quoque (cum
              <lb/>
            latera circa angulos rectos æqualia habeant, ſingula ſingulis) ergo duo rectangu-
              <lb/>
            la A P, & </s>
            <s xml:id="echoid-s5618" xml:space="preserve">D R æqualia ſunt inter ſe.</s>
            <s xml:id="echoid-s5619" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5620" xml:space="preserve">Quia, ſi non cadit ſuper illum, eſſent ſectioni hyperbolicæ duo axes,
              <lb/>
              <note position="left" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">C</note>
            & </s>
            <s xml:id="echoid-s5621" xml:space="preserve">in ellipſi tres axes, &</s>
            <s xml:id="echoid-s5622" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5623" xml:space="preserve">Q
              <unsure/>
            uoniam æquales ſectiones B A, E D ſibi mutuò
              <lb/>
            congruunt, & </s>
            <s xml:id="echoid-s5624" xml:space="preserve">vertices A, & </s>
            <s xml:id="echoid-s5625" xml:space="preserve">D coincidunt, ſiquidem axis A L non cadit ſuper
              <lb/>
            axim D N (cum ambo tamen axes ſint) haberet vnica ſectio, ſcilicet duæ ſe-
              <lb/>
            ctiones congruentes, duos axes A L, & </s>
            <s xml:id="echoid-s5626" xml:space="preserve">D N conuenientes in eodem puncto ver-
              <lb/>
              <figure xlink:label="fig-0181-02" xlink:href="fig-0181-02a" number="185">
                <image file="0181-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0181-02"/>
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            ticis, quod in hyperbola eſt im-
              <lb/>
              <note position="right" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">48. lib. 2.</note>
            poſſibile; </s>
            <s xml:id="echoid-s5627" xml:space="preserve">in ellipſi verò, in qua
              <lb/>
            ſemper duo axes reperiuntur ſe
              <lb/>
            ſe ſecantes in centro ad angulos
              <lb/>
            rectos, reperietur tertius axis,
              <lb/>
            ille nimirum, qui ab eodem ver-
              <lb/>
            tice A ducitur in eadem ſectione
              <lb/>
            A B, & </s>
            <s xml:id="echoid-s5628" xml:space="preserve">non coincidit cum axi
              <lb/>
            A L.</s>
            <s xml:id="echoid-s5629" xml:space="preserve"/>
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            <s xml:id="echoid-s5630" xml:space="preserve">Ideoque B L æqualis eſt N
              <lb/>
              <note position="left" xlink:label="note-0181-03" xlink:href="note-0181-03a" xml:space="preserve">d</note>
            E, & </s>
            <s xml:id="echoid-s5631" xml:space="preserve">poterunt A P, D R, ap-
              <lb/>
            plicata ad A L, D N æqualia
              <lb/>
            &</s>
            <s xml:id="echoid-s5632" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5633" xml:space="preserve">Q
              <unsure/>
            uia quadrata æqualium.
              <lb/>
            </s>
            <s xml:id="echoid-s5634" xml:space="preserve">B L, E N æqualia ſunt rectangulis A P, D R; </s>
            <s xml:id="echoid-s5635" xml:space="preserve">erunt illa æqualia, & </s>
            <s xml:id="echoid-s5636" xml:space="preserve">corum
              <lb/>
            latera A L, D N facta ſunt æqualia; </s>
            <s xml:id="echoid-s5637" xml:space="preserve">igitur reliqua duo latera L P, N R æ-
              <lb/>
            qualia quoque ſunt. </s>
            <s xml:id="echoid-s5638" xml:space="preserve">Simili modo oſtendetur, quod M Q æqualis eſt O S, ſeù L
              <lb/>
            T æqualis eſt N V, & </s>
            <s xml:id="echoid-s5639" xml:space="preserve">L M, ſeu T Q æqualis eſt N O, ſeu V S; </s>
            <s xml:id="echoid-s5640" xml:space="preserve">erant autem. </s>
            <s xml:id="echoid-s5641" xml:space="preserve">
              <lb/>
            prius L P, N R æquales; </s>
            <s xml:id="echoid-s5642" xml:space="preserve">igitur reſiduæ P T, & </s>
            <s xml:id="echoid-s5643" xml:space="preserve">R V æquales erunt, ſed quia
              <lb/>
            T Q, & </s>
            <s xml:id="echoid-s5644" xml:space="preserve">G L ſunt parallelæ pariterque V S, & </s>
            <s xml:id="echoid-s5645" xml:space="preserve">H N; </s>
            <s xml:id="echoid-s5646" xml:space="preserve">ergo vt T P ad P L ita
              <lb/>
            eſt Q T ad L G, ſimili modo vt V R ad R N ita eſt S V ad N H; </s>
            <s xml:id="echoid-s5647" xml:space="preserve">habent ve-
              <lb/>
            rò duæ æquales T P, & </s>
            <s xml:id="echoid-s5648" xml:space="preserve">V R ad duas æquales P L, & </s>
            <s xml:id="echoid-s5649" xml:space="preserve">R N eandem proportio-
              <lb/>
            nem, igitur duæ æquales Q T, & </s>
            <s xml:id="echoid-s5650" xml:space="preserve">S V eandem proportionem habent ad L G, & </s>
            <s xml:id="echoid-s5651" xml:space="preserve">
              <lb/>
            N H, & </s>
            <s xml:id="echoid-s5652" xml:space="preserve">propterea hæ erunt æquales, & </s>
            <s xml:id="echoid-s5653" xml:space="preserve">ablatis æqualibus A L, D N, erunt reliquæ
              <lb/>
            A G, & </s>
            <s xml:id="echoid-s5654" xml:space="preserve">D H inter ſe æquales, & </s>
            <s xml:id="echoid-s5655" xml:space="preserve">habet G A ad A I eandem proportionẽ, quàm
              <lb/>
            Q T ad T P, ſeu quàm S V ad V R; </s>
            <s xml:id="echoid-s5656" xml:space="preserve">pariterq; </s>
            <s xml:id="echoid-s5657" xml:space="preserve">H D ad D K eſt vt S V ad V R
              <lb/>
            (propter parallelas & </s>
            <s xml:id="echoid-s5658" xml:space="preserve">ſimilitudinẽ triangulorũ) igitur vt G A ad A I itaerit H </s>
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