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-div78" type="section" level="1" n="46">
          <p>
            <s xml:id="echoid-s1219" xml:space="preserve">
              <pb o="17" file="0055" n="55" rhead="Conicor. Lib. V."/>
            egredientium ex I, & </s>
            <s xml:id="echoid-s1220" xml:space="preserve">inſuper, propinquiores illi minores eſſe remotiori-
              <lb/>
            bus ramis ex vtraque parte, & </s>
            <s xml:id="echoid-s1221" xml:space="preserve">quod quadratum IN minus eſt quadrato
              <lb/>
            MI (exempli gratia) in parabola quadrato QH, in hyperbola, & </s>
            <s xml:id="echoid-s1222" xml:space="preserve">ellipſi
              <lb/>
            exemplari applicato ad QH. </s>
            <s xml:id="echoid-s1223" xml:space="preserve">Quoniam quadratum HN in parabola ęqua-
              <lb/>
              <note position="left" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">c</note>
            le eſt HI, nempe C G in HC bis (11. </s>
            <s xml:id="echoid-s1224" xml:space="preserve">ex primo) erit quadratum IN ęqua-
              <lb/>
            le IH in HC bis cum quadrato HI; </s>
            <s xml:id="echoid-s1225" xml:space="preserve">at ꝗuadratum M Q æquale eſt HI
              <lb/>
              <figure xlink:label="fig-0055-01" xlink:href="fig-0055-01a" number="25">
                <image file="0055-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0055-01"/>
              </figure>
            in QC bis (11. </s>
            <s xml:id="echoid-s1226" xml:space="preserve">ex primo)
              <lb/>
            igitur quadratum MI ęqua-
              <lb/>
            le eſt IH in QC bis cum
              <lb/>
            quadrato IQ; </s>
            <s xml:id="echoid-s1227" xml:space="preserve">hoc autem
              <lb/>
              <note position="left" xlink:label="note-0055-02" xlink:href="note-0055-02a" xml:space="preserve">d</note>
            eſt ęquale duobus quadra-
              <lb/>
            tis IH, HQ, & </s>
            <s xml:id="echoid-s1228" xml:space="preserve">IH in H
              <lb/>
            Q bis; </s>
            <s xml:id="echoid-s1229" xml:space="preserve">igitur quadratum I
              <lb/>
            M æquale eſt IH in HC
              <lb/>
            bis cum quadrato IH, quę
              <lb/>
            ſunt æqualia quadrato NI
              <lb/>
            vnà cum quadrato HQ.
              <lb/>
            </s>
            <s xml:id="echoid-s1230" xml:space="preserve">Quadratum igitur MI ex-
              <lb/>
            cedit quadratum NI qua-
              <lb/>
            drato HQ. </s>
            <s xml:id="echoid-s1231" xml:space="preserve">Et conſtat quo-
              <lb/>
            que, quadratum I L exce-
              <lb/>
            dere quadratum I N quadrato P H; </s>
            <s xml:id="echoid-s1232" xml:space="preserve">atque P H maior eſt, quàm Q H,
              <lb/>
            ergo I L maior eſt, quàm I M, & </s>
            <s xml:id="echoid-s1233" xml:space="preserve">I M, quàm N I. </s>
            <s xml:id="echoid-s1234" xml:space="preserve">Ponamus iam B I
              <lb/>
            perpendicularem ſuper C I, ergo quadratum B I ęquale eſt I C
              <lb/>
            in I H bis (11. </s>
            <s xml:id="echoid-s1235" xml:space="preserve">ex primo); </s>
            <s xml:id="echoid-s1236" xml:space="preserve">quadratum igitur I N minus eſt
              <lb/>
              <note position="left" xlink:label="note-0055-03" xlink:href="note-0055-03a" xml:space="preserve">e</note>
            quàm quadratum B I quadrato I H. </s>
            <s xml:id="echoid-s1237" xml:space="preserve">Et quia quadra-
              <lb/>
              <note position="left" xlink:label="note-0055-04" xlink:href="note-0055-04a" xml:space="preserve">f</note>
            tum O R ęquale eſt C R in I H bis excedet qua-
              <lb/>
            dratum I N (quod eſt ęquale quadrato I H,
              <lb/>
            & </s>
            <s xml:id="echoid-s1238" xml:space="preserve">I H in H C bis) duobus quadratis
              <lb/>
            HI, IR, & </s>
            <s xml:id="echoid-s1239" xml:space="preserve">IH in IR bis, nem-
              <lb/>
            pè quadrato R H; </s>
            <s xml:id="echoid-s1240" xml:space="preserve">atquè ſic
              <lb/>
            conſtat, quadratum.</s>
            <s xml:id="echoid-s1241" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1242" xml:space="preserve">A I excedere
              <lb/>
            quadratum I N quadrato D H; </s>
            <s xml:id="echoid-s1243" xml:space="preserve">eſtque
              <lb/>
            D H maior, quàm R H, igitur
              <lb/>
            I A maior eſt, quàm I O,
              <lb/>
            & </s>
            <s xml:id="echoid-s1244" xml:space="preserve">I O quàm I N. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">Et
              <lb/>
            hoc propofitum
              <lb/>
            fuerat.</s>
            <s xml:id="echoid-s1246" xml:space="preserve"/>
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