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="347" file="0385" n="386" rhead="Conicor. Lib. VII."/>
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        <div xml:id="echoid-div1039" type="section" level="1" n="329">
          <head xml:id="echoid-head407" xml:space="preserve">PROPOSITIO XXXXVIII.</head>
          <p>
            <s xml:id="echoid-s12090" xml:space="preserve">S It iam duplum quadrati A C maius quadrato C A F, erit duplum
              <lb/>
            quadrati A H maius quadrato G H: </s>
            <s xml:id="echoid-s12091" xml:space="preserve">ponatur duplum quadrati H M
              <lb/>
            æquale quadrato G H: </s>
            <s xml:id="echoid-s12092" xml:space="preserve">& </s>
            <s xml:id="echoid-s12093" xml:space="preserve">ducatur ad axim perpendicularis M N; </s>
            <s xml:id="echoid-s12094" xml:space="preserve">iun-
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            gaturque A N, eiuſque diameter P Q extendatur, erit H M ad M G,
              <lb/>
            vt P Q ad P R (7. </s>
            <s xml:id="echoid-s12095" xml:space="preserve">ex 7.)</s>
            <s xml:id="echoid-s12096" xml:space="preserve">; </s>
            <s xml:id="echoid-s12097" xml:space="preserve">ergo, & </s>
            <s xml:id="echoid-s12098" xml:space="preserve">quadratum H M ad quadratum H
              <lb/>
            G erit, vt quadratum P Q ad quadratum P R, & </s>
            <s xml:id="echoid-s12099" xml:space="preserve">quadratum H M ad
              <lb/>
            duo quadrata ex H M, & </s>
            <s xml:id="echoid-s12100" xml:space="preserve">ex M G eandem proportionẽ habebit, quàm
              <lb/>
            quadratum P Q ad quadratum diametri ſuæ figuræ: </s>
            <s xml:id="echoid-s12101" xml:space="preserve">educatur poſtea dia-
              <lb/>
            meter I L inter A, & </s>
            <s xml:id="echoid-s12102" xml:space="preserve">B, & </s>
            <s xml:id="echoid-s12103" xml:space="preserve">erectum illius ſit I K ad quàm ordinatim
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            ducta ſit A B, & </s>
            <s xml:id="echoid-s12104" xml:space="preserve">ad axim perpendicularis ſit B E erit quadratum M H,
              <lb/>
            nec non G H in H D æquale dimidio quadrati H G; </s>
            <s xml:id="echoid-s12105" xml:space="preserve">igitur G H ad </s>
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