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-div519" type="section" level="1" n="170">
          <pb o="140" file="0178" n="178" rhead="Apollonij Pergæi"/>
          <figure number="179">
            <image file="0178-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0178-01"/>
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          <p>
            <s xml:id="echoid-s5467" xml:space="preserve">Quoniam facta conuenienti ſuperpoſitione axis A M ſuper axim D
              <lb/>
            O, cadet quoque ſectio A B ſuper ſectionem D E: </s>
            <s xml:id="echoid-s5468" xml:space="preserve">ſi enim non cadit ſu-
              <lb/>
            per illam, ſumatur (ſi fieri poteſt) eius punctum B, extra ſectionem.
              <lb/>
            </s>
            <s xml:id="echoid-s5469" xml:space="preserve">D E cadens; </s>
            <s xml:id="echoid-s5470" xml:space="preserve">& </s>
            <s xml:id="echoid-s5471" xml:space="preserve">producatur ad axim perpendicularis B L vſque ad P: </s>
            <s xml:id="echoid-s5472" xml:space="preserve">& </s>
            <s xml:id="echoid-s5473" xml:space="preserve">
              <lb/>
            perficiatur planum A P applicatum comparatum; </s>
            <s xml:id="echoid-s5474" xml:space="preserve">& </s>
            <s xml:id="echoid-s5475" xml:space="preserve">ſecetur D N æqua-
              <lb/>
            lis A L, & </s>
            <s xml:id="echoid-s5476" xml:space="preserve">erigatur per N ad axim perpendicularis N E, & </s>
            <s xml:id="echoid-s5477" xml:space="preserve">producatur
              <lb/>
            vſque ad R, perficiendo planum D R applicatum comparatum; </s>
            <s xml:id="echoid-s5478" xml:space="preserve">Et quia
              <lb/>
            A I æqualis eſt D K, & </s>
            <s xml:id="echoid-s5479" xml:space="preserve">A L æqualis D N: </s>
            <s xml:id="echoid-s5480" xml:space="preserve">erit planum I L, æquale pla-
              <lb/>
            no K N; </s>
            <s xml:id="echoid-s5481" xml:space="preserve">cumque G I, H K ſint duæ figuræ ſimiles, & </s>
            <s xml:id="echoid-s5482" xml:space="preserve">æquales, pariter-
              <lb/>
              <note position="right" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">b</note>
            que I P, K R; </s>
            <s xml:id="echoid-s5483" xml:space="preserve">ergo duo plana A P, D R ſunt æqualia: </s>
            <s xml:id="echoid-s5484" xml:space="preserve">& </s>
            <s xml:id="echoid-s5485" xml:space="preserve">propterea E
              <lb/>
            N, B L, quæ illa ſpatia poſſunt (13. </s>
            <s xml:id="echoid-s5486" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5487" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5488" xml:space="preserve">ſunt æquales. </s>
            <s xml:id="echoid-s5489" xml:space="preserve">Si autem
              <lb/>
              <note position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">12. 13.
                <lb/>
              lib. I.</note>
            ſuperponatur axis axi cadet B L ſuper E N, eoquod duo anguli N, & </s>
            <s xml:id="echoid-s5490" xml:space="preserve">L
              <lb/>
            ſunt æquales; </s>
            <s xml:id="echoid-s5491" xml:space="preserve">igitur B cadit ſuper E, quod prius cadere non concedeba-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s5492" xml:space="preserve">& </s>
            <s xml:id="echoid-s5493" xml:space="preserve">hoc eſt abſurdum. </s>
            <s xml:id="echoid-s5494" xml:space="preserve">Quapropter ſectio ſectioni æqualis eſt.</s>
            <s xml:id="echoid-s5495" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5496" xml:space="preserve">Deinde ponamus duas ſe-
              <lb/>
              <figure xlink:label="fig-0178-02" xlink:href="fig-0178-02a" number="180">
                <image file="0178-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0178-02"/>
              </figure>
            ctiones æquales, vtique con-
              <lb/>
            gruet ſectio A B ſectioni D E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5497" xml:space="preserve">axis A L axi D N, quia ſi
              <lb/>
            non cadit ſuper illum, eſſent
              <lb/>
              <note position="right" xlink:label="note-0178-03" xlink:href="note-0178-03a" xml:space="preserve">c</note>
            in hyperbola duo axes, & </s>
            <s xml:id="echoid-s5498" xml:space="preserve">in
              <lb/>
            ellipſi tres axes, quod eſt ab-
              <lb/>
            ſurdum (52. </s>
            <s xml:id="echoid-s5499" xml:space="preserve">53. </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s5501" xml:space="preserve">Et fi-
              <lb/>
              <note position="left" xlink:label="note-0178-04" xlink:href="note-0178-04a" xml:space="preserve">48. lib. 2.</note>
            at A L æqualis D N, & </s>
            <s xml:id="echoid-s5502" xml:space="preserve">reli-
              <lb/>
            qua perficiantur, vt prius ca-
              <lb/>
            dent duo puncta L, B ſuper
              <lb/>
            N, E; </s>
            <s xml:id="echoid-s5503" xml:space="preserve">ideoque B L æqualis
              <lb/>
              <note position="right" xlink:label="note-0178-05" xlink:href="note-0178-05a" xml:space="preserve">d</note>
            erit E N; </s>
            <s xml:id="echoid-s5504" xml:space="preserve">& </s>
            <s xml:id="echoid-s5505" xml:space="preserve">poterunt æqua-
              <lb/>
            lia rectangula A P, D R applicata ad æquales A L, D N (13. </s>
            <s xml:id="echoid-s5506" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5507" xml:space="preserve">ex 1.)
              <lb/>
            </s>
            <s xml:id="echoid-s5508" xml:space="preserve">
              <note position="left" xlink:label="note-0178-06" xlink:href="note-0178-06a" xml:space="preserve">12. 13.
                <lb/>
              lib. 1.</note>
            ergo L P æqualis eſt N R. </s>
            <s xml:id="echoid-s5509" xml:space="preserve">Similiter ponatur A M æqualis D O, & </s>
            <s xml:id="echoid-s5510" xml:space="preserve">edu-
              <lb/>
            cantur C M Q, F O S duæ ordinationes, oſtendetur, quod M Q æqua-
              <lb/>
            lis eſt O S, & </s>
            <s xml:id="echoid-s5511" xml:space="preserve">L M æqualis N O; </s>
            <s xml:id="echoid-s5512" xml:space="preserve">& </s>
            <s xml:id="echoid-s5513" xml:space="preserve">propterea duo plana P Q, R S ſunt
              <lb/>
            æqualia, & </s>
            <s xml:id="echoid-s5514" xml:space="preserve">ſimilia; </s>
            <s xml:id="echoid-s5515" xml:space="preserve">igitur duo plana G P, H R ſunt æqualia, & </s>
            <s xml:id="echoid-s5516" xml:space="preserve">ſimilia,
              <lb/>
            & </s>
            <s xml:id="echoid-s5517" xml:space="preserve">L P oſtenſa eſt æqualis N R: </s>
            <s xml:id="echoid-s5518" xml:space="preserve">ergo G L æqualis eſt H N, & </s>
            <s xml:id="echoid-s5519" xml:space="preserve">A L æ-
              <lb/>
            qualis D N; </s>
            <s xml:id="echoid-s5520" xml:space="preserve">& </s>
            <s xml:id="echoid-s5521" xml:space="preserve">propterea G A æqualis eſt D H, & </s>
            <s xml:id="echoid-s5522" xml:space="preserve">A I æqualis D K.</s>
            <s xml:id="echoid-s5523" xml:space="preserve"/>
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