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="364" file="0402" n="403" rhead="Apollonij Pergæi"/>
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            <s xml:id="echoid-s12487" xml:space="preserve">Tertio habeat H M ad M D maiorem proportionem quàm H E ad D E: </s>
            <s xml:id="echoid-s12488" xml:space="preserve">vt
              <lb/>
            prius permutando, ſumptis communibus altitudinibus H A, & </s>
            <s xml:id="echoid-s12489" xml:space="preserve">G H, & </s>
            <s xml:id="echoid-s12490" xml:space="preserve">denuo
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            permutando ex lem. </s>
            <s xml:id="echoid-s12491" xml:space="preserve">16. </s>
            <s xml:id="echoid-s12492" xml:space="preserve">& </s>
            <s xml:id="echoid-s12493" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s12494" xml:space="preserve">20. </s>
            <s xml:id="echoid-s12495" xml:space="preserve">huius, ſequitur quod idem quadratum
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              <figure xlink:label="fig-0402-01" xlink:href="fig-0402-01a" number="475">
                <image file="0402-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0402-01"/>
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            ex A C ad differentiam quadratorum ex P Q, & </s>
            <s xml:id="echoid-s12496" xml:space="preserve">ex P R maiorem proportio-
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            nem habet, quàm ad differentiam quadra orum ex I L, & </s>
            <s xml:id="echoid-s12497" xml:space="preserve">ex I K, quare dif-
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            ferentia quadratorum ex P Q, & </s>
            <s xml:id="echoid-s12498" xml:space="preserve">ex P R minor erit, quàm differentia qua-
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            dratorum ex I L, & </s>
            <s xml:id="echoid-s12499" xml:space="preserve">ex I K, ſiue minor, quàm diffi
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            rentia quadratorum ex
              <lb/>
            A C, & </s>
            <s xml:id="echoid-s12500" xml:space="preserve">ex A F, quæ erant oſtendenda.</s>
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          <head xml:id="echoid-head420" xml:space="preserve">LEMMA XVIII.</head>
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            <s xml:id="echoid-s12502" xml:space="preserve">IN ellipſi ſi diameter a b bifariam ſecuerit rectam lineam A O ter-
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            minos axium coniungentem, erit a b æqualis ſuo erecto a c.
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            </s>
            <s xml:id="echoid-s12503" xml:space="preserve">Zuia axis A C bifariam diuiditur in centro D ab axi O D perpendiculari
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            ad axim A C, quæ educitur à termino O ipſius A O ordinatim applicatæ ad
              <lb/>
            diametrum a b, habebit diameter a b ad eius erectũ a c eandem proportionem
              <lb/>
              <note position="left" xlink:label="note-0402-01" xlink:href="note-0402-01a" xml:space="preserve">Prop. 7.
                <lb/>
              huius.</note>
            æqualitatis quàm habet H D ad D G, igitur diameter a b æqualis eſt eius la-
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            teri recto a e, quod erat propoſitum.</s>
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