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-div80" type="section" level="1" n="47">
          <p>
            <s xml:id="echoid-s1264" xml:space="preserve">
              <pb o="19" file="0057" n="57" rhead="Conicor. Lib. V."/>
            nempe ad QH. </s>
            <s xml:id="echoid-s1265" xml:space="preserve">Eodem modo conſtat, quod quadratum IL excedit qua-
              <lb/>
            dratum I N quantitate exemplaris applicati ad H P, & </s>
            <s xml:id="echoid-s1266" xml:space="preserve">quod quadratum
              <lb/>
            B I excedit quadratum I N exemplari applicato ad I H, & </s>
            <s xml:id="echoid-s1267" xml:space="preserve">quod quadra-
              <lb/>
            tum I O excedit quadratum I N exemplari applicato ad R H (eo quod
              <lb/>
              <note position="left" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve">m</note>
            quadratum R I æquale eſt duplo trianguli R V I, & </s>
            <s xml:id="echoid-s1268" xml:space="preserve">quadratum O R ęqua-
              <lb/>
              <note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">Prop. 1. h.</note>
            le eſt duplo trapezij R G, at in ellipſi quando O R cadit infra centrum F
              <lb/>
            æquale eſt duplo trapezij R K; </s>
            <s xml:id="echoid-s1269" xml:space="preserve">quadratum igitur O I in ellipſi æquale eſt
              <lb/>
              <note position="right" xlink:label="note-0057-03" xlink:href="note-0057-03a" xml:space="preserve">Prop. 3. h.</note>
            duplo trianguli K E F, quod eſt æquale F C G cum duplo trapezij V F,
              <lb/>
              <note position="left" xlink:label="note-0057-04" xlink:href="note-0057-04a" xml:space="preserve">n</note>
            igitur quadratum O I in hyperbola, & </s>
            <s xml:id="echoid-s1270" xml:space="preserve">ellipſi excedit duplum trapezij I G
              <lb/>
            (quod eſt æquale quadrato N I) duplo trianguli V S
              <emph style="sub">0</emph>
            , quod eſt æquale
              <lb/>
              <note position="left" xlink:label="note-0057-05" xlink:href="note-0057-05a" xml:space="preserve">o</note>
            exemplari applicato ad R H: </s>
            <s xml:id="echoid-s1271" xml:space="preserve">& </s>
            <s xml:id="echoid-s1272" xml:space="preserve">ſimiliter patet, quod quadratum A I ex-
              <lb/>
            cedit quadratum N I exemplari applicato ad D H, eſtque D H maior
              <lb/>
            quàm R H, & </s>
            <s xml:id="echoid-s1273" xml:space="preserve">R H maior quàm I H; </s>
            <s xml:id="echoid-s1274" xml:space="preserve">quare A I maior eſt, quàm O I, & </s>
            <s xml:id="echoid-s1275" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0057-06" xlink:href="note-0057-06a" xml:space="preserve">p</note>
            O I maior, quàm B I, & </s>
            <s xml:id="echoid-s1276" xml:space="preserve">B I, quàm N I, & </s>
            <s xml:id="echoid-s1277" xml:space="preserve">quodlibet horum duorum ex-
              <lb/>
            cedit N I poteſtate plano iam dicto, & </s>
            <s xml:id="echoid-s1278" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s1279" xml:space="preserve"/>
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        <div xml:id="echoid-div82" type="section" level="1" n="48">
          <head xml:id="echoid-head74" xml:space="preserve">Notæ in Propoſitionem VIII.</head>
          <p>
            <s xml:id="echoid-s1280" xml:space="preserve">S I menſura fuerit maior comparata, dummodò in ellipſi ſit portio tran-
              <lb/>
              <note position="left" xlink:label="note-0057-07" xlink:href="note-0057-07a" xml:space="preserve">a</note>
            ſuerſæ, non maior medietate ipſius, tunc minimus, &</s>
            <s xml:id="echoid-s1281" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1282" xml:space="preserve">Sic puto le-
              <lb/>
            gendum: </s>
            <s xml:id="echoid-s1283" xml:space="preserve">Si menſura fuerit maior comparata, dummodo in ellipſi minor ſit me-
              <lb/>
            dietate axis tranſuerſi, tunc minimus, &</s>
            <s xml:id="echoid-s1284" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1285" xml:space="preserve">Nam ſi menſura ſumi poſſet æqua-
              <lb/>
            lis ſemitranſuerſo, tunc qui-
              <lb/>
              <figure xlink:label="fig-0057-01" xlink:href="fig-0057-01a" number="28">
                <image file="0057-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0057-01"/>
              </figure>
            dem origo eßet in centro elli-
              <lb/>
            pſis, quare undecima propo-
              <lb/>
            ſitio huius eſſet ſuperflua, in
              <lb/>
            qua ſupponitur origo in ipſo-
              <lb/>
            met centro ellipſis. </s>
            <s xml:id="echoid-s1286" xml:space="preserve">Animad-
              <lb/>
            uertendum eſt quod in hac
              <lb/>
            propoſitione menſura neceſſa-
              <lb/>
            riò ſumi debet in axe maiori
              <lb/>
            ellipſis; </s>
            <s xml:id="echoid-s1287" xml:space="preserve">quandoquidem menſu-
              <lb/>
            ra I C ponitur maior, quàm
              <lb/>
            C G, & </s>
            <s xml:id="echoid-s1288" xml:space="preserve">C F maior quàm C I,
              <lb/>
            ergo C F maior eſt quàm C G,
              <lb/>
            & </s>
            <s xml:id="echoid-s1289" xml:space="preserve">illius duplum ſcilicet axis
              <lb/>
            E C maior erit duplo huius, ſed ut E C ad duplum C G, ita eſt quadratum E C
              <lb/>
            ad quadratum Recti axis eiuſdem ellipſis: </s>
            <s xml:id="echoid-s1290" xml:space="preserve">ergo E C eſt maior duorum axium
              <lb/>
            ellipſis A B C.</s>
            <s xml:id="echoid-s1291" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1292" xml:space="preserve">Et educta ex H perpendiculari H N, &</s>
            <s xml:id="echoid-s1293" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1294" xml:space="preserve">Ideſt ex H educta H N per-
              <lb/>
              <note position="left" xlink:label="note-0057-08" xlink:href="note-0057-08a" xml:space="preserve">b</note>
            pendiculari ad axim C I, quæ ſecet ſectionem in N, & </s>
            <s xml:id="echoid-s1295" xml:space="preserve">iuncta recta N I, pari-
              <lb/>
            terque ductis reliquis ramis I M, I L, I B, I A, atque ab eorum terminis ad
              <lb/>
            axim extenſis perpendicularibus, vt in propoſitionibus quarta, quinta, ſexta
              <lb/>
            factum eſt.</s>
            <s xml:id="echoid-s1296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1297" xml:space="preserve">Quadratum H N in parabola æquale eſt H I nempè C G in H C bis
              <lb/>
              <note position="left" xlink:label="note-0057-09" xlink:href="note-0057-09a" xml:space="preserve">c</note>
            (prima ex quinto) &</s>
            <s xml:id="echoid-s1298" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1299" xml:space="preserve">Hoc deduci non poteſt ex prima propoſitione huius </s>
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