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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              <pb o="320" file="0358" n="359" rhead="Apollonij Pergæi"/>
            G E, & </s>
            <s xml:id="echoid-s11382" xml:space="preserve">componendo O H ad E H, ſeu rectangulum O H A ad rectangulum
              <lb/>
            E H A, erit vt rectangulum ſub G E, & </s>
            <s xml:id="echoid-s11383" xml:space="preserve">G O in O E vna cum quadrato E
              <lb/>
            G, ſeu vt quadratum ex O G ad quadratum ex G E, & </s>
            <s xml:id="echoid-s11384" xml:space="preserve">permutando rectangu-
              <lb/>
            lum A H O ad quadratum O G, erit vt rectangulum E H A ad quadratum G
              <lb/>
            E, ſed vt rectangulum O H A ad quadratum O G, ita eſt quadratum A C ad
              <lb/>
              <note position="left" xlink:label="note-0358-01" xlink:href="note-0358-01a" xml:space="preserve">15. huius.
                <lb/>
              ex Def. &
                <lb/>
              15. huius.</note>
            quadratum P K, & </s>
            <s xml:id="echoid-s11385" xml:space="preserve">vt rectangulum E H A ad quadratnm ex G E, ſeu vt
              <lb/>
            quadratum A C ad quadratum A F, vel ex I K; </s>
            <s xml:id="echoid-s11386" xml:space="preserve">quapropter idem quadratum
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            A C ad quadratum ex P K, atque ad quadratum ex A F vel I K eandem pro-
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            portionem habet, & </s>
            <s xml:id="echoid-s11387" xml:space="preserve">ideo quadrata ipſa æqualia ſunt, & </s>
            <s xml:id="echoid-s11388" xml:space="preserve">eorum latera P K; </s>
            <s xml:id="echoid-s11389" xml:space="preserve">& </s>
            <s xml:id="echoid-s11390" xml:space="preserve">
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            A F, vel I K pariter æqualia erunt.</s>
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            <s xml:id="echoid-s11392" xml:space="preserve">Eodem modo quando rectangulum ſub O G E in E H maius eſt quadrato G
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            E, tunc quidem idem rectangulum, cuius altitudo O G E, baſis vero O E, ad
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            rectangulum, cuius altitudo O G E, baſis verò E H, ſeu O E ad E H, mino-
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            rem proportionem habebit, quàm ad quadratum E G, & </s>
            <s xml:id="echoid-s11393" xml:space="preserve">componendo, atque
              <lb/>
            permutando, vt prius factum eſt, habebit rectangulum O H A ad quadratum
              <lb/>
            O G, ſiue quadratum A C ad quadratum P K minorem proportionem, quàm
              <lb/>
            rectangulum E H A ad quadratum G E, ſeu quàm quadratum A C ad qua-
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              <note position="left" xlink:label="note-0358-02" xlink:href="note-0358-02a" xml:space="preserve">15. huius.</note>
            dratum A F, vel I K, & </s>
            <s xml:id="echoid-s11394" xml:space="preserve">propterea P K maior erit, quàm A F, vel I K.</s>
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            <s xml:id="echoid-s11396" xml:space="preserve">Quando verò rectangulum ſub E G O in E H minus eſt quadrato E G, tunc
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            quidem oſtendetur eodem progreſſu quadratum P K minus eſſe quadrato A F,
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            vel I K, quod erat propoſitum.</s>
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        <div xml:id="echoid-div973" type="section" level="1" n="308">
          <head xml:id="echoid-head381" xml:space="preserve">Notæ in Propof. XXXIII. & XXXIV.</head>
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            <s xml:id="echoid-s11398" xml:space="preserve">QVoniam ex hypoteſi C A minor non eſt medietate ipſius A F, eſtque A H
              <lb/>
            ad A G, vt C A, ad A F, ergo A H maior, aut æqualis eſt medietati
              <lb/>
              <note position="left" xlink:label="note-0358-03" xlink:href="note-0358-03a" xml:space="preserve">Def. 2.
                <lb/>
              huius.</note>
            ipſius A G, & </s>
            <s xml:id="echoid-s11399" xml:space="preserve">ideo A H maior, aut æqualis eſt reſiduo H G, </s>
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