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-s8024" xml:space="preserve">
              <pb o="214" file="0252" n="252" rhead="Apollonij Pergæi"/>
            & </s>
            <s xml:id="echoid-s8025" xml:space="preserve">parallelæ erunt alicui recta lineæ ex L
              <lb/>
              <figure xlink:label="fig-0252-01" xlink:href="fig-0252-01a" number="291">
                <image file="0252-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0252-01"/>
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            diuidenti angulum H L M, eo quod paral-
              <lb/>
            lelæ erãt rectæ H g diuidenti angulum L H
              <lb/>
            G, & </s>
            <s xml:id="echoid-s8026" xml:space="preserve">prius B E vlterius, quàm C F ten-
              <lb/>
            debat ad partes asymptoti H I; </s>
            <s xml:id="echoid-s8027" xml:space="preserve">ergo è con-
              <lb/>
            tra C F vlterius tendet ad partes asymptoti
              <lb/>
            H G, & </s>
            <s xml:id="echoid-s8028" xml:space="preserve">educũtur ab asymptoto L M producta,
              <lb/>
            & </s>
            <s xml:id="echoid-s8029" xml:space="preserve">parallelæ ſunt rectæ lineæ ex L diuidenti
              <lb/>
            angulũ H L M, contentum à recta linea cen-
              <lb/>
            tra coniungente, & </s>
            <s xml:id="echoid-s8030" xml:space="preserve">a symptoto M L, in qua
              <lb/>
            illæ cadunt; </s>
            <s xml:id="echoid-s8031" xml:space="preserve">igitur ( ex prima parte huius propoſitionis) C F maior erit, quàm
              <lb/>
            B E; </s>
            <s xml:id="echoid-s8032" xml:space="preserve">& </s>
            <s xml:id="echoid-s8033" xml:space="preserve">è contra B E vlterius tendens ad partes asymptoti H I minor erit, quã
              <lb/>
            C F; </s>
            <s xml:id="echoid-s8034" xml:space="preserve">vt propoſitum fuerat.</s>
            <s xml:id="echoid-s8035" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8036" xml:space="preserve">Sint duæ æquales parabolæ A B, D E ad eaſdem partes cauæ, qua-
              <lb/>
              <note position="left" xlink:label="note-0252-01" xlink:href="note-0252-01a" xml:space="preserve">PROP. 4.
                <lb/>
              Addit.</note>
            rum diametri G I, H K ſint congruentes aut parallelæ inter ſe, nec nõ
              <lb/>
            ad eas ordinatim applicatæ B Z K, L X N
              <unsure/>
            ſint parallelæ alicui rectæ
              <lb/>
            diuidenti angulum G H K à recta linea G H vertices coniungenti, & </s>
            <s xml:id="echoid-s8037" xml:space="preserve">
              <lb/>
            diametro H K interioris ſectionis D H contentum, ſi diametri congruentes
              <lb/>
            non fuerint. </s>
            <s xml:id="echoid-s8038" xml:space="preserve">Dico quod, B E, L M portiones applicatarum à ſectioni-
              <lb/>
            bus ad eaſdem partes interceptæ, ſemper magis diminuentur, quo magis
              <lb/>
            à verticibus recedunt; </s>
            <s xml:id="echoid-s8039" xml:space="preserve">efficienturque minores quacumque recta linea pro-
              <lb/>
            poſita, ſi diametri ſunt congruentes: </s>
            <s xml:id="echoid-s8040" xml:space="preserve">ſi verò ſunt parallelæ nunquam mi-
              <lb/>
            nores erunt portione ordinatæ inter diametros intercepta. </s>
            <s xml:id="echoid-s8041" xml:space="preserve">At ſi paral-
              <lb/>
            lelæ fuerint alicui rectæ lineæ diuidenti angulum H G I à recta G H,
              <lb/>
            & </s>
            <s xml:id="echoid-s8042" xml:space="preserve">diametro I G exterioris ſectionis A G contentum, ſemper magis au-
              <lb/>
            gentur, ſed erunt ſemper minores ea quæ à diametris intercipitur. </s>
            <s xml:id="echoid-s8043" xml:space="preserve">Vel ſi
              <lb/>
            fuerint parallelæ diametris non congruentibus, ſemper magis augentur,
              <lb/>
            quo magis à concurſu recedunt.</s>
            <s xml:id="echoid-s8044" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8045" xml:space="preserve">Sit F G latus rectum diametri G I in,
              <lb/>
              <figure xlink:label="fig-0252-02" xlink:href="fig-0252-02a" number="292">
                <image file="0252-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0252-02"/>
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            parabola G B, ordinatim applicatæ B E K,
              <lb/>
            & </s>
            <s xml:id="echoid-s8046" xml:space="preserve">L M N ſecent diametrum G I in X, Z,
              <lb/>
            & </s>
            <s xml:id="echoid-s8047" xml:space="preserve">diametrum H K in N, K, & </s>
            <s xml:id="echoid-s8048" xml:space="preserve">ſecetur
              <lb/>
            abſciſſa G I æqualis H K, & </s>
            <s xml:id="echoid-s8049" xml:space="preserve">G R æqualis
              <lb/>
            H N; </s>
            <s xml:id="echoid-s8050" xml:space="preserve">ideoque R I æqualis erit N K, ſeu
              <lb/>
            X Z (propterea quod in parallelogrammo
              <lb/>
            N Z oppoſita latera æqualia ſunt) ducan-
              <lb/>
            turque ordinatæ O I, Q R, quæ erunt æqua-
              <lb/>
              <note position="left" xlink:label="note-0252-02" xlink:href="note-0252-02a" xml:space="preserve">ex 10.
                <lb/>
              ex 21.
                <lb/>
              huius.</note>
            les, & </s>
            <s xml:id="echoid-s8051" xml:space="preserve">congruentes ipſis E K, M N pro-
              <lb/>
            pter æqualitatem ſectionum, & </s>
            <s xml:id="echoid-s8052" xml:space="preserve">abſciſſarũ
              <lb/>
            ſimilium diametrorum; </s>
            <s xml:id="echoid-s8053" xml:space="preserve">ducanturque à pun-
              <lb/>
            ctis E, L, Q rectæ lineæ E S, L T, Q V
              <lb/>
            parallelæ diametris occurrentes ipſis B E,
              <lb/>
            & </s>
            <s xml:id="echoid-s8054" xml:space="preserve">O I in S, T, V: </s>
            <s xml:id="echoid-s8055" xml:space="preserve">manifeſtum eſt S </s>
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