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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            <s xml:id="echoid-s11793" xml:space="preserve">
              <pb o="337" file="0375" n="376" rhead="Conicor. Lib. VII."/>
            guli ex ſumma extremorum, vel intermediorum in differentiam mini-
              <lb/>
            morum ſegmentorum, ſcilicet ex G A cum H E in E A.</s>
            <s xml:id="echoid-s11794" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11795" xml:space="preserve">Quia duplum rectanguli G A H cum duplo rectanguli G A E æquatur duplo
              <lb/>
            rectanguli ſub G A in H E, addito cõmuniter duplo rectanguli H E A erit du-
              <lb/>
            plum rectanguli G E H æquale duplo rectanguli G A H cum duplo rectanguli ex
              <lb/>
            ſumma G A, H E in E A; </s>
            <s xml:id="echoid-s11796" xml:space="preserve">& </s>
            <s xml:id="echoid-s11797" xml:space="preserve">addito communi quadrato G H, erit duplum
              <lb/>
            rectanguli G E H cum quadrato G H, ſcilicet duo quadrata ex G E, & </s>
            <s xml:id="echoid-s11798" xml:space="preserve">ex E
              <lb/>
              <figure xlink:label="fig-0375-01" xlink:href="fig-0375-01a" number="446">
                <image file="0375-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0375-01"/>
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            H, erunt æqualia illis om-
              <lb/>
            nibus ſpatijs, ſcilicet duplo
              <lb/>
            rectanguli ex ſumma G A,
              <lb/>
            H E in E A cum duplo re-
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            ctanguli G A H ſimul cum
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            quadrato ex G H: </s>
            <s xml:id="echoid-s11799" xml:space="preserve">ſed duplo
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            rectanguli G A H cum quadrato G H æqualia ſunt duo quadrata ex G A,
              <lb/>
            & </s>
            <s xml:id="echoid-s11800" xml:space="preserve">ex A H, ergo duo quadrata ex G E, & </s>
            <s xml:id="echoid-s11801" xml:space="preserve">ex E H æqualia erunt quadratis ex
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            G A, & </s>
            <s xml:id="echoid-s11802" xml:space="preserve">ex A H cum duplo rectanguli ex G A; </s>
            <s xml:id="echoid-s11803" xml:space="preserve">& </s>
            <s xml:id="echoid-s11804" xml:space="preserve">H E in E A, quod erat
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            oſtendendum.</s>
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        <div xml:id="echoid-div1018" type="section" level="1" n="323">
          <head xml:id="echoid-head400" xml:space="preserve">LEMM A XII.</head>
          <p style="it">
            <s xml:id="echoid-s11806" xml:space="preserve">IN hyperbola, cuius axis A C, erectus A F, præſectæ C G, H A,
              <lb/>
            centrum D, atque diameter I L, eiuſque erectus I K, & </s>
            <s xml:id="echoid-s11807" xml:space="preserve">latus
              <lb/>
            C E, pariterque altera diameter Q P, cuius erectus P R, & </s>
            <s xml:id="echoid-s11808" xml:space="preserve">latus
              <lb/>
            C O: </s>
            <s xml:id="echoid-s11809" xml:space="preserve">dico quod duplum rectanguli ex G E cũ O H in H E à duobus
              <lb/>
            quadratis ex G E, & </s>
            <s xml:id="echoid-s11810" xml:space="preserve">ex E H; </s>
            <s xml:id="echoid-s11811" xml:space="preserve">nec non quadrata Q P, & </s>
            <s xml:id="echoid-s11812" xml:space="preserve">P R late-
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            rum figuræ diametri Q P à quadratis ex L I, & </s>
            <s xml:id="echoid-s11813" xml:space="preserve">ex I K, vel ex C A,
              <lb/>
            & </s>
            <s xml:id="echoid-s11814" xml:space="preserve">ex A F, vna deficiunt, aut vna æqualia ſunt, vel vna exce-
              <lb/>
            dunt.</s>
            <s xml:id="echoid-s11815" xml:space="preserve"/>
          </p>
          <figure number="447">
            <image file="0375-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0375-02"/>
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