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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              <pb o="217" file="0255" n="255" rhead="Conicor. Lib. VI."/>
            E I ſunt æquales, & </s>
            <s xml:id="echoid-s8166" xml:space="preserve">parallelæ; </s>
            <s xml:id="echoid-s8167" xml:space="preserve">ergo H I æqualis erit, & </s>
            <s xml:id="echoid-s8168" xml:space="preserve">parallela ipſi B E (vel
              <lb/>
            quia additur communis H E, vel propter parallelogrammum B I) ſed prius A
              <lb/>
            R æqualis erat, & </s>
            <s xml:id="echoid-s8169" xml:space="preserve">parallela eidem B E; </s>
            <s xml:id="echoid-s8170" xml:space="preserve">igitur A R, & </s>
            <s xml:id="echoid-s8171" xml:space="preserve">H I æquales ſunt inter
              <lb/>
            ſe, & </s>
            <s xml:id="echoid-s8172" xml:space="preserve">æquidiſtantes; </s>
            <s xml:id="echoid-s8173" xml:space="preserve">ideoque coniungentes A H, R I erunt æquales, & </s>
            <s xml:id="echoid-s8174" xml:space="preserve">paral-
              <lb/>
            lelæ; </s>
            <s xml:id="echoid-s8175" xml:space="preserve">ſuntque anguli A H B, & </s>
            <s xml:id="echoid-s8176" xml:space="preserve">R I E æquales inter ſe, cum ab æqualibus la-
              <lb/>
            teribus in triangulis A B H, & </s>
            <s xml:id="echoid-s8177" xml:space="preserve">R E I æquilateris inter ſe contineantur; </s>
            <s xml:id="echoid-s8178" xml:space="preserve">ergo
              <lb/>
            R I ordinatim quoque applicata eſt ad àiametrum E I; </s>
            <s xml:id="echoid-s8179" xml:space="preserve">atque in ſectionibus æ-
              <lb/>
            qualibus abſciſsæ B H, E I
              <lb/>
              <figure xlink:label="fig-0255-01" xlink:href="fig-0255-01a" number="295">
                <image file="0255-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0255-01"/>
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            diametrorum ſimilium, ſci-
              <lb/>
            licet æque inclinatarum ad
              <lb/>
            ſuas ordinatas æquales ſunt
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s8180" xml:space="preserve">nec non ordinatæ A
              <lb/>
            H, I R æquales ſunt oſten-
              <lb/>
            sæ; </s>
            <s xml:id="echoid-s8181" xml:space="preserve">igitur ſicut punctum A in
              <lb/>
              <note position="left" xlink:label="note-0255-01" xlink:href="note-0255-01a" xml:space="preserve">ex 10.
                <lb/>
              huius.</note>
            ſectione A B cadit, ita pun-
              <lb/>
            ctum R in ſectione E D exi-
              <lb/>
            ſtit; </s>
            <s xml:id="echoid-s8182" xml:space="preserve">ſed poſitus fuit intra,
              <lb/>
            aut extra ipſam, quod eſt ab-
              <lb/>
            ſurdũ: </s>
            <s xml:id="echoid-s8183" xml:space="preserve">Non igitur recta linea
              <lb/>
            A D maior, aut minor eſſe
              <lb/>
            poteſt, quàm B E; </s>
            <s xml:id="echoid-s8184" xml:space="preserve">ideoque ei
              <lb/>
            quælibet alia intercepta K L æqualis omnino erit. </s>
            <s xml:id="echoid-s8185" xml:space="preserve">Simili ratiocinio oſtendetur
              <lb/>
            æquidiſtans ipſi B E eidem
              <lb/>
              <figure xlink:label="fig-0255-02" xlink:href="fig-0255-02a" number="296">
                <image file="0255-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0255-02"/>
              </figure>
            æqualis; </s>
            <s xml:id="echoid-s8186" xml:space="preserve">quapropter interce-
              <lb/>
            ptæ A D, K L, & </s>
            <s xml:id="echoid-s8187" xml:space="preserve">B E æqua-
              <lb/>
            les erunt inter ſe: </s>
            <s xml:id="echoid-s8188" xml:space="preserve">Quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s8189" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8190" xml:space="preserve">Si duæ parabolæ B A C,
              <lb/>
            F D E æquales ad eaſdem
              <lb/>
              <note position="right" xlink:label="note-0255-02" xlink:href="note-0255-02a" xml:space="preserve">SCHO-
                <lb/>
              LIVM.</note>
            partes cauæ, conſtitutæ ſue-
              <lb/>
            rint circa axes A K, D G
              <lb/>
            æquidiſtantes, & </s>
            <s xml:id="echoid-s8191" xml:space="preserve">non con-
              <lb/>
            gruentes ſe mutuo ſecabunt.</s>
            <s xml:id="echoid-s8192" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8193" xml:space="preserve">Ex vertice D axis G D ducatur D H perpendicularis ad axim A K, eum ſe-
              <lb/>
            cans in H, & </s>
            <s xml:id="echoid-s8194" xml:space="preserve">deſcribatur alia parabolæ I H L æqualis prioribus B A, vel E
              <lb/>
            D, cuius axis ſit K H, & </s>
            <s xml:id="echoid-s8195" xml:space="preserve">ver-
              <lb/>
              <figure xlink:label="fig-0255-03" xlink:href="fig-0255-03a" number="297">
                <image file="0255-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0255-03"/>
              </figure>
            tex H, & </s>
            <s xml:id="echoid-s8196" xml:space="preserve">ſicuti in propoſi-
              <lb/>
            tione 4. </s>
            <s xml:id="echoid-s8197" xml:space="preserve">additarum factum
              <lb/>
            eſt, reperiatur B F C ordina-
              <lb/>
            tim ad axes applicata ſecans
              <lb/>
            parabolas in E, B, I, & </s>
            <s xml:id="echoid-s8198" xml:space="preserve">axes
              <lb/>
            in G, K, ita vt intercepta
              <lb/>
            B I æqualis ſit D H, ſen G
              <lb/>
            K, quæ in parallelogrammo
              <lb/>
            D K ei æqualis eſt. </s>
            <s xml:id="echoid-s8199" xml:space="preserve">Quoniā
              <lb/>
            parabolæ E D, & </s>
            <s xml:id="echoid-s8200" xml:space="preserve">I H </s>
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