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-s1016" xml:space="preserve">
              <pb o="11" file="0049" n="49" rhead="Conicor. Lib. V."/>
            D C, quad
              <unsure/>
            ratum igitur, &</s>
            <s xml:id="echoid-s1017" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1018" xml:space="preserve">Textum corruptum ſic corrigendum puto; </s>
            <s xml:id="echoid-s1019" xml:space="preserve">& </s>
            <s xml:id="echoid-s1020" xml:space="preserve">eſt
              <lb/>
            r C æqualis D C, atque γ F æqualis ſummæ in hyperbola, & </s>
            <s xml:id="echoid-s1021" xml:space="preserve">differentiæ in elli-
              <lb/>
            pſi laterum D C, & </s>
            <s xml:id="echoid-s1022" xml:space="preserve">C F.</s>
            <s xml:id="echoid-s1023" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1024" xml:space="preserve">Exemplar ſimile plano rectanguli C D in Y F in hyperbola, & </s>
            <s xml:id="echoid-s1025" xml:space="preserve">Y C in
              <lb/>
            ellipſi, &</s>
            <s xml:id="echoid-s1026" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1027" xml:space="preserve">Hæc poſtrema verba expungenda duxi, tanquam ſuperuacanea.</s>
            <s xml:id="echoid-s1028" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1029" xml:space="preserve">Poteſt etiam ad imitationem Euclidis reperiri multitudo ramorum inter ſe-
              <lb/>
            æqualium, qui ex origine duci poſſunt in eadem coniſectione. </s>
            <s xml:id="echoid-s1030" xml:space="preserve">Itaque quoties
              <lb/>
              <note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">PROP. I.
                <lb/>
              Additar.</note>
            menſura fuerit comparata, ſcilicet aqualis ſemiſsi lateris recti, tunc duo tan-
              <lb/>
            tum rami inter ſe æquales a puncto originis ad vtraſque partes axis duci poſ-
              <lb/>
            ſunt in qualibet coniſectione, eruntque illi, qui ad terminos L l cuiuslibet or-
              <lb/>
            dinatim applicatæ L l ducuntur ab origine
              <lb/>
              <figure xlink:label="fig-0049-01" xlink:href="fig-0049-01a" number="17">
                <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0049-01"/>
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            I, nam efſiciuntur duo triangula I M L, & </s>
            <s xml:id="echoid-s1031" xml:space="preserve">
              <lb/>
            I M l, quæ circa angulos æquales ad M, nẽ-
              <lb/>
            pe rectos, habent latera æqualia, ſcilicet L
              <lb/>
            M, & </s>
            <s xml:id="echoid-s1032" xml:space="preserve">l M medietates ordinatim applicatæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s1033" xml:space="preserve">ſegmentum axis I M inter ordinatam, & </s>
            <s xml:id="echoid-s1034" xml:space="preserve">
              <lb/>
            originem eſt latus commune; </s>
            <s xml:id="echoid-s1035" xml:space="preserve">ergobaſes, ſeu
              <lb/>
            rami I L, & </s>
            <s xml:id="echoid-s1036" xml:space="preserve">I l ſunt æquales. </s>
            <s xml:id="echoid-s1037" xml:space="preserve">Reliquiverò
              <lb/>
            rami ſupra, vel infra terminum eiuſdem ordinatim applicatæ minores, aut ma-
              <lb/>
            iores ſunt ramo ad eius terminum ducto; </s>
            <s xml:id="echoid-s1038" xml:space="preserve">quare duo tantum rami ad vtraſque
              <lb/>
            partes axis inter ſe æquales duci poſſunt.</s>
            <s xml:id="echoid-s1039" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1040" xml:space="preserve">Rurſus quadratum rami I A remotioris a comparata ſuperat quadratum ra-
              <lb/>
              <note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">PROP.
                <lb/>
              II.Add.</note>
            mì I L propinquioris (in parabola quidem) rectangulo ſub differentia, & </s>
            <s xml:id="echoid-s1041" xml:space="preserve">ſub
              <lb/>
            aggregato abſciſſarum eorundem ramorum; </s>
            <s xml:id="echoid-s1042" xml:space="preserve">in reliquis verò ſectionibus rectan-
              <lb/>
            gulo ſub differentia abſciſſarum, & </s>
            <s xml:id="echoid-s1043" xml:space="preserve">ſub recta linea, ad quam ſumma abſcißa-
              <lb/>
            rum eandem proportionem habet, quam latus tranſuerſum ad ſummam in hy-
              <lb/>
            perbola, & </s>
            <s xml:id="echoid-s1044" xml:space="preserve">ad differentiam in ellipſi laterum tranſuerſi, & </s>
            <s xml:id="echoid-s1045" xml:space="preserve">recti.</s>
            <s xml:id="echoid-s1046" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1047" xml:space="preserve">Et primò in parabola, quia quadratum I A æquale eſt quadrato I C cum qua-
              <lb/>
              <note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve">4. huius.</note>
            drato abſciſſæ C E; </s>
            <s xml:id="echoid-s1048" xml:space="preserve">pariterque quadratum I L æquale eſt quadrato eiuſdem I C
              <lb/>
            cum quadrato abſciſſæ C M; </s>
            <s xml:id="echoid-s1049" xml:space="preserve">ergo exceſſus quadrati I A ſupra quadratum I L
              <lb/>
              <note position="right" xlink:label="note-0049-04" xlink:href="note-0049-04a" xml:space="preserve">ibidem.</note>
            æqualis eſt differentiæ quadratorum E C, & </s>
            <s xml:id="echoid-s1050" xml:space="preserve">C M; </s>
            <s xml:id="echoid-s1051" xml:space="preserve">ſed exceſſus quadrati E C
              <lb/>
            ſupra quadratum M C æqualis eſt rectangulo, cuius baſis æqualis eſt ſummæ la-
              <lb/>
            terum E C, & </s>
            <s xml:id="echoid-s1052" xml:space="preserve">C M; </s>
            <s xml:id="echoid-s1053" xml:space="preserve">altitudo verò æqualis eſt E M differentiæ laterum eorun-
              <lb/>
            dem quadratorum (vt de-
              <lb/>
            ducitur ex elementis) igitur
              <lb/>
              <figure xlink:label="fig-0049-02" xlink:href="fig-0049-02a" number="18">
                <image file="0049-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0049-02"/>
              </figure>
            exceſſus quadrati I A ſupra
              <lb/>
            quadratum I L æqualis eſt
              <lb/>
            rectangulo, cuius baſis eſt
              <lb/>
            ſumma abſciſſarum E C, C
              <lb/>
            M, altitudo verò E M dif-
              <lb/>
            ferentia earundem abſciſſa-
              <lb/>
            rum.</s>
            <s xml:id="echoid-s1054" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1055" xml:space="preserve">Secundò in hyperbola, & </s>
            <s xml:id="echoid-s1056" xml:space="preserve">
              <lb/>
            ellipſi fiat exemplar N T ap-
              <lb/>
            plicatum ab abſciſſam C E.
              <lb/>
            </s>
            <s xml:id="echoid-s1057" xml:space="preserve">Et quia quadratum I A æ-
              <lb/>
            quale eſt quadrato </s>
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