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-div962" type="section" level="1" n="303">
          <pb o="318" file="0356" n="357" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div963" type="section" level="1" n="304">
          <head xml:id="echoid-head377" xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:id="echoid-s11339" xml:space="preserve">SI recta linea H G producatur in A & </s>
            <s xml:id="echoid-s11340" xml:space="preserve">E, ita vt A H, pariter-
              <lb/>
            que E H, non maior ſit H G: </s>
            <s xml:id="echoid-s11341" xml:space="preserve">Dico rectangulum ex A G E
              <lb/>
            ſumma inæqualium ſegmentorum in E H intermediam ſectionem, mi-
              <lb/>
            nus eſſe quadrato ex ſegmento intermedio minore E G.</s>
            <s xml:id="echoid-s11342" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11343" xml:space="preserve">Fiat H M æqualis H G, & </s>
            <s xml:id="echoid-s11344" xml:space="preserve">quia A
              <lb/>
            E æqualis, aut minor eſt, quàm M E;
              <lb/>
            </s>
            <s xml:id="echoid-s11345" xml:space="preserve">
              <figure xlink:label="fig-0356-01" xlink:href="fig-0356-01a" number="422">
                <image file="0356-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0356-01"/>
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            & </s>
            <s xml:id="echoid-s11346" xml:space="preserve">E G maior, quàm E H, ergo A E
              <lb/>
            ad M E minorem proportionem babet,
              <lb/>
            quàm E G ad E H, & </s>
            <s xml:id="echoid-s11347" xml:space="preserve">permutando
              <lb/>
            A E ad E G minorem proportionem
              <lb/>
            habebit, quàm M E ad E H, & </s>
            <s xml:id="echoid-s11348" xml:space="preserve">cõ-
              <lb/>
            ponendo A G ad G E minorem proportionem habebit, quàm M H, ſeu ei æqua-
              <lb/>
            lis G H aà H E, & </s>
            <s xml:id="echoid-s11349" xml:space="preserve">iterum componendo A G E ad G E minorem proportionem
              <lb/>
            habebit, quàm G E ad E H: </s>
            <s xml:id="echoid-s11350" xml:space="preserve">quare rectangulum ex ſumma A G E in H E
              <lb/>
            minus erit quadrato ex intermedia G E, vt propoſitum fuerat.</s>
            <s xml:id="echoid-s11351" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div965" type="section" level="1" n="305">
          <head xml:id="echoid-head378" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s11352" xml:space="preserve">IIſdem poſitis ſint A H,
              <lb/>
            & </s>
            <s xml:id="echoid-s11353" xml:space="preserve">E H non minores
              <lb/>
              <figure xlink:label="fig-0356-02" xlink:href="fig-0356-02a" number="423">
                <image file="0356-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0356-02"/>
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            quàm G H, vel H M:
              <lb/>
            </s>
            <s xml:id="echoid-s11354" xml:space="preserve">Dico rectangulum ex A G
              <lb/>
            E in E H maius eſſe quadrato ex E G.</s>
            <s xml:id="echoid-s11355" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11356" xml:space="preserve">Quia A G maior eſt quàm E G, & </s>
            <s xml:id="echoid-s11357" xml:space="preserve">G H non maior ipſa H E, ergo A G ad
              <lb/>
            G E maiorem proportionem habet, quàm G H ad H E, & </s>
            <s xml:id="echoid-s11358" xml:space="preserve">componendo A G E
              <lb/>
            ad E G maiorem proportionem habebit, quàm G E ad E H, & </s>
            <s xml:id="echoid-s11359" xml:space="preserve">ideo rectangu-
              <lb/>
            lum ex A G E in E H maius erit quadrato ex G E.</s>
            <s xml:id="echoid-s11360" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div967" type="section" level="1" n="306">
          <head xml:id="echoid-head379" xml:space="preserve">LEMMA IV.</head>
          <p style="it">
            <s xml:id="echoid-s11361" xml:space="preserve">IIſdem poſitis ſit A H ma-
              <lb/>
            ior, ſed E H minor ea-
              <lb/>
            dem M H ſemiſſe totius M
              <lb/>
              <figure xlink:label="fig-0356-03" xlink:href="fig-0356-03a" number="424">
                <image file="0356-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0356-03"/>
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            G: </s>
            <s xml:id="echoid-s11362" xml:space="preserve">Dico quod ſi proportio ip-
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            ſius A G ad G E fuerit eadem
              <lb/>
            rationi G H ad H E, </s>
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