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="355" file="0393" n="394" rhead="Conicor. Lib. VII."/>
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        <div xml:id="echoid-div1054" type="section" level="1" n="335">
          <head xml:id="echoid-head414" xml:space="preserve">Notæ in Propoſit. XXXXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s12273" xml:space="preserve">QVia ex hypotheſi duplum quadrati A C maius eſt quadrato ex C A F,
              <lb/>
            ergo duplum quadrati ex A H maius erit quadrato ex H G. </s>
            <s xml:id="echoid-s12274" xml:space="preserve">Fiat igitur
              <lb/>
            quadratum ex M H æquale ſemiquadrato G H, & </s>
            <s xml:id="echoid-s12275" xml:space="preserve">lateris C M fiant
              <lb/>
            duæ diametri Q P, & </s>
            <s xml:id="echoid-s12276" xml:space="preserve">q p, quarum erecta ſint P R, & </s>
            <s xml:id="echoid-s12277" xml:space="preserve">p r: </s>
            <s xml:id="echoid-s12278" xml:space="preserve">Dico duplum
              <lb/>
            quadrati Q P æquale eße quadrato ex ſumma laterum Q P R: </s>
            <s xml:id="echoid-s12279" xml:space="preserve">Quia Q P ad
              <lb/>
            P R eſt vt H M ad M G, & </s>
            <s xml:id="echoid-s12280" xml:space="preserve">antecedentes ad terminorum ſummas, & </s>
            <s xml:id="echoid-s12281" xml:space="preserve">eorum
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              <note position="right" xlink:label="note-0393-01" xlink:href="note-0393-01a" xml:space="preserve">Prop. 7.
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              huius.</note>
            quadrata proportionalia erunt, ſcilicet quadratum Q P ad quadratum ex Q P
              <lb/>
            R eandem proportionem habebit, quàm quadratum ex M H ad quadratum ex
              <lb/>
            H G: </s>
            <s xml:id="echoid-s12282" xml:space="preserve">erat autem quadratum M H ſubduplum quadrati ex H G, igitur qua-
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            dratum ex P Q ſubduplum eſt quadrati ex Q P R. </s>
            <s xml:id="echoid-s12283" xml:space="preserve">Eadem ratione quadra-
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            tum ex q p ſubduplum erit quadrati ex q p r, & </s>
            <s xml:id="echoid-s12284" xml:space="preserve">diametri Q P, & </s>
            <s xml:id="echoid-s12285" xml:space="preserve">q p æqua-
              <lb/>
            les erunt, cum æque recedant ab axi, & </s>
            <s xml:id="echoid-s12286" xml:space="preserve">habeant commune latus C M.</s>
            <s xml:id="echoid-s12287" xml:space="preserve"/>
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            <s xml:id="echoid-s12288" xml:space="preserve">Poſtea quia punctum E cadit inter M, & </s>
            <s xml:id="echoid-s12289" xml:space="preserve">A, erit duplum rectanguli M H
              <lb/>
            E maius duplo quadrati ex M H, ſeu maius quadrato G H, & </s>
            <s xml:id="echoid-s12290" xml:space="preserve">propterea du-
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            plum M H ad H G maiorem proportionem habebit, quàm G H ad H E, </s>
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