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-div884" type="section" level="1" n="271">
          <head xml:id="echoid-head340" xml:space="preserve">Notæ in Propoſit. IX.</head>
          <p>
            <s xml:id="echoid-s10515" xml:space="preserve">SIue ad quadratum differentiæ eius, quæ eſt inter I L, N O eſt vt C
              <lb/>
              <note position="right" xlink:label="note-0324-01" xlink:href="note-0324-01a" xml:space="preserve">c</note>
            G in H E ad quadratum E H, H V, &</s>
            <s xml:id="echoid-s10516" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10517" xml:space="preserve">Licet nouem ſubſequentes
              <lb/>
            propoſitiones facile ex octaua deducantur, nequeunt tamen omnes ſimul conglo-
              <lb/>
            batæ vnico bauſtu deuorari; </s>
            <s xml:id="echoid-s10518" xml:space="preserve">itaque opere prætium erit aliquantisper breuita-
              <lb/>
            tem nimiam Arabici Interpretis relinquere. </s>
            <s xml:id="echoid-s10519" xml:space="preserve">Tria demonſtrata ſunt in propoſi-
              <lb/>
            tione octaua, quæ in ſequentibus nouem propoſitionibus vſum babent. </s>
            <s xml:id="echoid-s10520" xml:space="preserve">Primò
              <lb/>
            quod quadratum A C ad quadratum I L eandem proportionem habeat, quàm
              <lb/>
            rectangulum C G in H E ad quudratum H E. </s>
            <s xml:id="echoid-s10521" xml:space="preserve">Secundò quod I L ad N O ean-
              <lb/>
            dem proportionem habeat, quàm H E intercepta comparata ad H V potentem
              <lb/>
            comparatam. </s>
            <s xml:id="echoid-s10522" xml:space="preserve">Tertio quod quadratum I L ad quadratum N O, ſeu L I ad eius
              <lb/>
              <note position="left" xlink:label="note-0324-02" xlink:href="note-0324-02a" xml:space="preserve">15. & 16.
                <lb/>
              lib. I.</note>
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                <image file="0324-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0324-01"/>
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            latus rectum I P, ſit vt H E ad E G, vel vt quadratum H E ad rectangulum
              <lb/>
            H E G, vel ad quadratũ H V. </s>
            <s xml:id="echoid-s10523" xml:space="preserve">Modo propoſitio nona ſic demonſtrabitur. </s>
            <s xml:id="echoid-s10524" xml:space="preserve">Quia
              <lb/>
            I L ad N O eandem rationem habet quàm H E ad H V, erunt antecedentes ad
              <lb/>
            differentias terminorum proportionales, ideſt I L ad differentiam ipſarum I L,
              <lb/>
            & </s>
            <s xml:id="echoid-s10525" xml:space="preserve">N O eandem proportionem habebit, quàm H E ad differentiam ipſarum E
              <lb/>
            H, & </s>
            <s xml:id="echoid-s10526" xml:space="preserve">H V: </s>
            <s xml:id="echoid-s10527" xml:space="preserve">atquè quadratum I L ad quadratum ex differentia ipſarum I L,
              <lb/>
            & </s>
            <s xml:id="echoid-s10528" xml:space="preserve">N O deſcriptum eandem proportionem habebit, quàm quadratum H E ad
              <lb/>
            quadratum ex differentia ipſarum E H, & </s>
            <s xml:id="echoid-s10529" xml:space="preserve">H V deſcriptum: </s>
            <s xml:id="echoid-s10530" xml:space="preserve">erat autem qua-
              <lb/>
              <note position="left" xlink:label="note-0324-03" xlink:href="note-0324-03a" xml:space="preserve">8. huius.</note>
            dratum A C ad quadratum I L, vt rectangulum C G in H E ad quadratum
              <lb/>
            E H; </s>
            <s xml:id="echoid-s10531" xml:space="preserve">ergo ex æquali ordinata quadratum A C ad quadratum ex differentia ip-
              <lb/>
            ſarum I L, & </s>
            <s xml:id="echoid-s10532" xml:space="preserve">N O deſcriptum eandem proportionem habebit, quàm rectangu-
              <lb/>
            lum C G in H E ad quadratum ex differentia ipſarum E H, & </s>
            <s xml:id="echoid-s10533" xml:space="preserve">H V.</s>
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