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-div637" type="section" level="1" n="212">
          <p>
            <s xml:id="echoid-s6815" xml:space="preserve">
              <pb o="178" file="0216" n="216" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0216-01" xlink:href="fig-0216-01a" number="240">
                <image file="0216-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0216-01"/>
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            diximus in 11. </s>
            <s xml:id="echoid-s6816" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s6817" xml:space="preserve">quod ſi ad abſciſſas A M, C O egrediantur quælibet
              <lb/>
            potentes, ad ſua abſciſſa eandẽ proportionẽ habebunt ſi abſciſſæ ad abſciſ-
              <lb/>
            ſas ſint in cadem proportione, & </s>
            <s xml:id="echoid-s6818" xml:space="preserve">quod anguli à potentialibus, & </s>
            <s xml:id="echoid-s6819" xml:space="preserve">ab-
              <lb/>
              <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            ſciſſis contenti, erunt æquales in duabus ſectionibus: </s>
            <s xml:id="echoid-s6820" xml:space="preserve">quare erit ſegmen-
              <lb/>
            tum H A G ſimile ſegmento I C K atque ſimiliter poſitum.</s>
            <s xml:id="echoid-s6821" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6822" xml:space="preserve">Deinde ijſdem ſignis in eiſdem figuris manẽtibus, vt prius de-
              <lb/>
            ſignatis ſupponatur, ſegmentum H A G ſimile ipſi K C I. </s>
            <s xml:id="echoid-s6823" xml:space="preserve">Dico,
              <lb/>
            quod angulus E æqualis erit F, & </s>
            <s xml:id="echoid-s6824" xml:space="preserve">M A ad A E erit, vt O C ad
              <lb/>
            C F.</s>
            <s xml:id="echoid-s6825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6826" xml:space="preserve">Quoniam duo ſegmenta ſunt ſimilia erit angulus O æqualis M, & </s>
            <s xml:id="echoid-s6827" xml:space="preserve">duo
              <lb/>
              <note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">Defin. 7.</note>
            anguli E A L, F C N illis æquales, ſunt quoque inter ſe æquales; </s>
            <s xml:id="echoid-s6828" xml:space="preserve">ergo
              <lb/>
            duo anguli F, E, qui illis æquales ſunt, erunt inter ſe æquales, eoquod
              <lb/>
            A E, C F parallelæ ſunt G H, I K, & </s>
            <s xml:id="echoid-s6829" xml:space="preserve">anguli N, L ſunt recti; </s>
            <s xml:id="echoid-s6830" xml:space="preserve">ergo duo
              <lb/>
            triangula proportionis ſunt ſimilia, ideoque R A ad A L, nempe P A ad
              <lb/>
              <note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">49. lib. 1.
                <lb/>
              11. lib. 1.</note>
            duplam A E eſt, vt C S ad C N, nempe Q C ad duplam C F: </s>
            <s xml:id="echoid-s6831" xml:space="preserve">& </s>
            <s xml:id="echoid-s6832" xml:space="preserve">quia
              <lb/>
            G M poteſt P A in A M (12. </s>
            <s xml:id="echoid-s6833" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6834" xml:space="preserve">& </s>
            <s xml:id="echoid-s6835" xml:space="preserve">ſimiliter I O poteſt Q C in C O;
              <lb/>
            </s>
            <s xml:id="echoid-s6836" xml:space="preserve">
              <note position="right" xlink:label="note-0216-04" xlink:href="note-0216-04a" xml:space="preserve">b</note>
            ergo P A ad G M eſt, vt Q C ad O I, & </s>
            <s xml:id="echoid-s6837" xml:space="preserve">G M ad M A eſt, vt I O ad
              <lb/>
            O C; </s>
            <s xml:id="echoid-s6838" xml:space="preserve">quia duo ſegmenta ſunt ſimilia, & </s>
            <s xml:id="echoid-s6839" xml:space="preserve">E A ad A M eſt, vt C F ad C
              <lb/>
            O: </s>
            <s xml:id="echoid-s6840" xml:space="preserve">& </s>
            <s xml:id="echoid-s6841" xml:space="preserve">iam oſtenſum eſt, quod duo anguli E, F ſunt æquales. </s>
            <s xml:id="echoid-s6842" xml:space="preserve">Et hoc erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s6843" xml:space="preserve"/>
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        <div xml:id="echoid-div641" type="section" level="1" n="213">
          <head xml:id="echoid-head270" xml:space="preserve">PROPOSITIO XVII.</head>
          <p>
            <s xml:id="echoid-s6844" xml:space="preserve">DEinde ſectiones ſint hyperbolicæ, aut ellipticæ, & </s>
            <s xml:id="echoid-s6845" xml:space="preserve">reliqua
              <lb/>
              <note position="right" xlink:label="note-0216-05" xlink:href="note-0216-05a" xml:space="preserve">a</note>
            ſupponantur, vt prius.</s>
            <s xml:id="echoid-s6846" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6847" xml:space="preserve">Educamus C c perpendicularẽ ſuper axim D F, & </s>
            <s xml:id="echoid-s6848" xml:space="preserve">A a perpendicula-
              <lb/>
            rem ſuper axim B E; </s>
            <s xml:id="echoid-s6849" xml:space="preserve">atque V, Y ſint duo centra. </s>
            <s xml:id="echoid-s6850" xml:space="preserve">Ergo (propter ſimi-
              <lb/>
            litudinem duarum ſectionum) erit V a in a E ad quadratum A a </s>
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