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-div960" type="section" level="1" n="302">
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            <s xml:id="echoid-s11317" xml:space="preserve">
              <pb o="317" file="0355" n="356" rhead="Conicor. Lib. VII."/>
            producto ex G E, & </s>
            <s xml:id="echoid-s11318" xml:space="preserve">G H in E H, erit M H in H E cum E G, atquè
              <lb/>
            G H in H E, nempe ſumma M G, G E, quæ eſt æqualis ipſi f in E H
              <lb/>
            minus erit, quàm quadratum H G cum aggregato E G, G H in E H,
              <lb/>
            quæ ſunt æqualia quadrato G E; </s>
            <s xml:id="echoid-s11319" xml:space="preserve">igitur f in E H minus eſt quadrato E
              <lb/>
            G. </s>
            <s xml:id="echoid-s11320" xml:space="preserve">Poſtea vti prius dictum eſt oſtendetur, quod quadratum A C ad
              <lb/>
            quadratum P R maiorem proportionem habet, quàm ad quadratum I K:
              <lb/>
            </s>
            <s xml:id="echoid-s11321" xml:space="preserve">& </s>
            <s xml:id="echoid-s11322" xml:space="preserve">propterea P R minor eſt, quàm I K. </s>
            <s xml:id="echoid-s11323" xml:space="preserve">Non aliter oſtendetur quod I K
              <lb/>
            minor ſit, quàm A F. </s>
            <s xml:id="echoid-s11324" xml:space="preserve">Ponatur poſtea diameter S T extra locum inter
              <lb/>
            P Q, A C compræhenſum, ducaturque C X ei parallela, & </s>
            <s xml:id="echoid-s11325" xml:space="preserve">ad axim
              <lb/>
            perpendicularis X V. </s>
            <s xml:id="echoid-s11326" xml:space="preserve">Igitur V H M maius erit quàm quadratum H G,
              <lb/>
              <figure xlink:label="fig-0355-01" xlink:href="fig-0355-01a" number="421">
                <image file="0355-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0355-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s11327" xml:space="preserve">eodem modo procedendo, tandem oſtendetur quod quadratum A C ad
              <lb/>
            quadratum S Z minorem proportionem habet, quàm ad quadratum P
              <lb/>
            R, & </s>
            <s xml:id="echoid-s11328" xml:space="preserve">ideo P R minor erit quàm S Z. </s>
            <s xml:id="echoid-s11329" xml:space="preserve">Non ſecus oſtendetur quod S Z
              <lb/>
            minor eſt erecto cuiuslibet inclinati cadentis ad partem S T extra illam.
              <lb/>
            </s>
            <s xml:id="echoid-s11330" xml:space="preserve">Itaque demonſtratum eſt, quod P R minor ſit erecto cuiuslibet diametri
              <lb/>
            ſectionis cadentis ad vtraſque partes ipſius P Q verſus A, & </s>
            <s xml:id="echoid-s11331" xml:space="preserve">X, & </s>
            <s xml:id="echoid-s11332" xml:space="preserve">ere-
              <lb/>
            cti proximiores diametro P Q minores ſunt remotioribus. </s>
            <s xml:id="echoid-s11333" xml:space="preserve">Et hoc erat
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s11334" xml:space="preserve"/>
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        <div xml:id="echoid-div962" type="section" level="1" n="303">
          <head xml:id="echoid-head376" xml:space="preserve">In Sectionem VI.</head>
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            <s xml:id="echoid-s11335" xml:space="preserve">IN Expoſitione ſequentium Propoſitionum difficultas, quæ à nimia prolixitate
              <lb/>
            oritur, ineuitabilis eſt, niſi Methodus in textu ſeruata aliquantisper relin-
              <lb/>
            quatur: </s>
            <s xml:id="echoid-s11336" xml:space="preserve">propterea non nulla lemmata præmittam, ex quibus ſemel demonſtra-
              <lb/>
            tis caſus omnes ſequentium propoſitionum facillime, & </s>
            <s xml:id="echoid-s11337" xml:space="preserve">breuiſſime deducnntur.</s>
            <s xml:id="echoid-s11338" xml:space="preserve"/>
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