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-div913" type="section" level="1" n="285">
          <head xml:id="echoid-head355" xml:space="preserve">Notæ in Propoſit. XIV. & XXV.</head>
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            <s xml:id="echoid-s10749" xml:space="preserve">QVoniam nedum in hyperbola, ſed etiam in ellipſi quadratum A C ad ſum-
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            mam quadratorum ex I L, & </s>
            <s xml:id="echoid-s10750" xml:space="preserve">ex N O eandem proportionem habet, quã
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            A H ad ſummam ipſarum H E, & </s>
            <s xml:id="echoid-s10751" xml:space="preserve">E G, atque quadratorum ex I
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            L, & </s>
            <s xml:id="echoid-s10752" xml:space="preserve">ex N O ſumma ad eorundem quadratorum differentiam eandem propor-
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            tionem habet, quàm ipſarum H E, & </s>
            <s xml:id="echoid-s10753" xml:space="preserve">E G ſumma ad earundem differentiam;
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            evgo ex æquali quadratum A C ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10755" xml:space="preserve">ex N O differen-
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            tiam eandem proportionem habet, quàm C G, ſiue H A ad ipſarum H E, & </s>
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            E G differentiam; </s>
            <s xml:id="echoid-s10757" xml:space="preserve">ſed in ellipſi ipſarum H E, & </s>
            <s xml:id="echoid-s10758" xml:space="preserve">E G differentia æqualis eſt
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            duplo E D; </s>
            <s xml:id="echoid-s10759" xml:space="preserve">igitur in ellipſi quadratum A C ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10760" xml:space="preserve">ex
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            N O differentiam eandem proportionem habebit, quàm præſecta C G ad duplum
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            inuerſæ E D.</s>
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          <head xml:id="echoid-head356" xml:space="preserve">Notæ in Propoſit. XXVII.</head>
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            <s xml:id="echoid-s10762" xml:space="preserve">ET oſtenſum iam eſt, quod I L in hyperbola maior eſt, quàm A C;
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            ergo differentia A C, & </s>
            <s xml:id="echoid-s10764" xml:space="preserve">illius coniugati maior eſt, quàm differen-
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            tia homologorum ſuorum à ſuis coniugatis, & </s>
            <s xml:id="echoid-s10765" xml:space="preserve">differentia proximioris ho-
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            mologi ad ſuam coniugatam maior eſt differentia remotioris à ſua coniu-
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            gata, &</s>
            <s xml:id="echoid-s10766" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10767" xml:space="preserve">Hoc autem ſic demonſtrabitur. </s>
            <s xml:id="echoid-s10768" xml:space="preserve">In diametris A C, & </s>
            <s xml:id="echoid-s10769" xml:space="preserve">I L produca-
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            tur A M æqualis Q R, & </s>
            <s xml:id="echoid-s10770" xml:space="preserve">I K æqualis N O, & </s>
            <s xml:id="echoid-s10771" xml:space="preserve">ab ijsdem ſecentur A S æqua-
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            lis Q R, & </s>
            <s xml:id="echoid-s10772" xml:space="preserve">I T æqualis N O. </s>
            <s xml:id="echoid-s10773" xml:space="preserve">Quoniam M S bifariam ſecatur in A, & </s>
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