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-div562" type="section" level="1" n="183">
          <p style="it">
            <s xml:id="echoid-s5882" xml:space="preserve">
              <pb o="150" file="0188" n="188" rhead="Apollonij Pergæi"/>
            illo, & </s>
            <s xml:id="echoid-s5883" xml:space="preserve">ad angulos rectos, ſi intelligatur ſuperficies B I G, ſuperpoſita ſuperfi-
              <lb/>
            ciei B I H, itaut axis ſuper axim cadat, atque vertex B ſit communis neceſ-
              <lb/>
            ſario punctum I commune erit, atque recta I G cadet ſuper I H, cum anguli G
              <lb/>
            I B, & </s>
            <s xml:id="echoid-s5884" xml:space="preserve">H I B recti ſint, atque punctum G cadet in H, propter æqualitatem
              <lb/>
            duarum ordinatim applicatarum I G, I H: </s>
            <s xml:id="echoid-s5885" xml:space="preserve">eadem ratione quælibet alia puncta
              <lb/>
            ſectionis G B inter G, & </s>
            <s xml:id="echoid-s5886" xml:space="preserve">B ſumpta cadent ſuper B H; </s>
            <s xml:id="echoid-s5887" xml:space="preserve">& </s>
            <s xml:id="echoid-s5888" xml:space="preserve">ideo portio ſectionis
              <lb/>
            conicæ G B congruet portioni B H, & </s>
            <s xml:id="echoid-s5889" xml:space="preserve">eidem æqualis erit. </s>
            <s xml:id="echoid-s5890" xml:space="preserve">Simili modo conſtat,
              <lb/>
            portionem G C æqualem eße portioni H A, & </s>
            <s xml:id="echoid-s5891" xml:space="preserve">ſic
              <lb/>
              <figure xlink:label="fig-0188-01" xlink:href="fig-0188-01a" number="201">
                <image file="0188-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0188-01"/>
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            ſuperficies ipſæ. </s>
            <s xml:id="echoid-s5892" xml:space="preserve">Quod verò portio H A non con-
              <lb/>
            gruat alicui alteri ſegmento C K præter G C, con-
              <lb/>
            ſtat ex eo, quod ſi portiones K C, & </s>
            <s xml:id="echoid-s5893" xml:space="preserve">A H ſibi mu-
              <lb/>
            tuò congruunt, vt nimirum punctum C ſuper H, & </s>
            <s xml:id="echoid-s5894" xml:space="preserve">
              <lb/>
            punctum K ſuper A cadat: </s>
            <s xml:id="echoid-s5895" xml:space="preserve">& </s>
            <s xml:id="echoid-s5896" xml:space="preserve">concipiatur punctũ
              <lb/>
            C idem ac N, & </s>
            <s xml:id="echoid-s5897" xml:space="preserve">K idem ac O, & </s>
            <s xml:id="echoid-s5898" xml:space="preserve">portio O N L
              <lb/>
            æqualis immo eadem ſectio K C B, & </s>
            <s xml:id="echoid-s5899" xml:space="preserve">illius axis
              <lb/>
            L M omnino idem ac axis B D: </s>
            <s xml:id="echoid-s5900" xml:space="preserve">tunc quidem (ex
              <lb/>
            precedenti prop. </s>
            <s xml:id="echoid-s5901" xml:space="preserve">6.) </s>
            <s xml:id="echoid-s5902" xml:space="preserve">ſectiones ipſæ A B, & </s>
            <s xml:id="echoid-s5903" xml:space="preserve">K B, ſeu O L æquales erunt, & </s>
            <s xml:id="echoid-s5904" xml:space="preserve">ſi-
              <lb/>
            bi mutuò congruentes: </s>
            <s xml:id="echoid-s5905" xml:space="preserve">& </s>
            <s xml:id="echoid-s5906" xml:space="preserve">propterea H B cadet ſuper portionem maiorem C B
              <lb/>
            ſeu ei æqualem N B L (cum H B æqualis oſtenſa ſit ipſi G B) & </s>
            <s xml:id="echoid-s5907" xml:space="preserve">ideo vertices
              <lb/>
            B, & </s>
            <s xml:id="echoid-s5908" xml:space="preserve">L duarum axium B D, & </s>
            <s xml:id="echoid-s5909" xml:space="preserve">L M in duabus ſectionibus A B, & </s>
            <s xml:id="echoid-s5910" xml:space="preserve">K B ſeu
              <lb/>
            O N L inæqualibus non conuenient: </s>
            <s xml:id="echoid-s5911" xml:space="preserve">quapropter in duabus congruentibus, ſeu in
              <lb/>
            eadem ſectione duo axes B D, & </s>
            <s xml:id="echoid-s5912" xml:space="preserve">L M exiſtent, quod eſt abſurdum, quia eſt
              <lb/>
            contra propoſ: </s>
            <s xml:id="echoid-s5913" xml:space="preserve">48. </s>
            <s xml:id="echoid-s5914" xml:space="preserve">libri 2.</s>
            <s xml:id="echoid-s5915" xml:space="preserve"/>
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        <div xml:id="echoid-div565" type="section" level="1" n="184">
          <head xml:id="echoid-head238" xml:space="preserve">Notæ in Propoſit. IX.</head>
          <p>
            <s xml:id="echoid-s5916" xml:space="preserve">MAnifeſtum eſt ex demonſtratis, quod portiones ſectionum æqua-
              <lb/>
              <note position="right" xlink:label="note-0188-01" xlink:href="note-0188-01a" xml:space="preserve">a</note>
            lium non congruunt, &</s>
            <s xml:id="echoid-s5917" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5918" xml:space="preserve">Sicuti in propoſ. </s>
            <s xml:id="echoid-s5919" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5920" xml:space="preserve">dictum eſt, quod duæ
              <lb/>
            portiones non æqualiter à vertice axis diſtantes ſibi mutuò congruere nõ poſſunt,
              <lb/>
            ita hic in duabus quibuslibet æqualibus coniſectionibus idem verificari oſtendi-
              <lb/>
            tur, quod nimirum duæ portiones cuiuslibet ſectionis conicæ, vel duarum æqua-
              <lb/>
            lium ſectionum inæqualiter à vertice axis diſtantes non ſint congruentes. </s>
            <s xml:id="echoid-s5921" xml:space="preserve">Hoc
              <lb/>
            autem alia ratione demonſtrare ſuperuacaneum non erit, cum demonſtratio, quæ
              <lb/>
            in textu Arabico corrupto affertur non omnino ſufficiens videatur, ſed prius
              <lb/>
            oſtendendum eſt.</s>
            <s xml:id="echoid-s5922" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div567" type="section" level="1" n="185">
          <head xml:id="echoid-head239" xml:space="preserve">LEMMAI.</head>
          <p style="it">
            <s xml:id="echoid-s5923" xml:space="preserve">IN duabus æqualibus coniſectionibus A B C, & </s>
            <s xml:id="echoid-s5924" xml:space="preserve">D E F, quarum
              <lb/>
            axes A G, D H deſcribere duos circulos æquales contingentes coni-
              <lb/>
            cas ſectiones, quorum is, qui propinquior eſt vertici extrinſecùs, reli-
              <lb/>
            quus verò intrinſecùs ſectionem tangat.</s>
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