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-s8129" xml:space="preserve">
              <pb o="216" file="0254" n="254" rhead="Apollonij Pergæi"/>
            B cadit inter verticem G, & </s>
            <s xml:id="echoid-s8130" xml:space="preserve">punctum
              <lb/>
              <figure xlink:label="fig-0254-01" xlink:href="fig-0254-01a" number="293">
                <image file="0254-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0254-01"/>
              </figure>
            C eiuſdem parabolæ G C; </s>
            <s xml:id="echoid-s8131" xml:space="preserve">igitur Z B
              <lb/>
            K ordinatim applicata ad diametrum
              <lb/>
            G I neceßario ſecabit diametrum G I
              <lb/>
            intra ſectionem in Z, & </s>
            <s xml:id="echoid-s8132" xml:space="preserve">producta
              <lb/>
            occurret K N extra eandem in K.
              <lb/>
            </s>
            <s xml:id="echoid-s8133" xml:space="preserve">Non ſecus oſtendetur, quod E N I or-
              <lb/>
            dinatim applicatæ ad diametrum H
              <lb/>
            N, punctum N cadit intra, & </s>
            <s xml:id="echoid-s8134" xml:space="preserve">I ex-
              <lb/>
            tra eandem ſectionem H E, & </s>
            <s xml:id="echoid-s8135" xml:space="preserve">pro-
              <lb/>
            pterea recta C H minor erit, quàm K
              <lb/>
            N, ſeu B E ei æqualis in parallelo-
              <lb/>
            grammo E K; </s>
            <s xml:id="echoid-s8136" xml:space="preserve">pariterque Z I, ſeu ei
              <lb/>
            æqualis B E minor erit, quàm G V. </s>
            <s xml:id="echoid-s8137" xml:space="preserve">
              <lb/>
            Cadat poſtea L M extra duas diame-
              <lb/>
            tros ad eaſdem partes. </s>
            <s xml:id="echoid-s8138" xml:space="preserve">Quoniam in parallelogrammo L S latera L O, M S æqua-
              <lb/>
            lia ſunt; </s>
            <s xml:id="echoid-s8139" xml:space="preserve">eſtque S R maior quàm M S, ſeu quàm O L; </s>
            <s xml:id="echoid-s8140" xml:space="preserve">ergo (vt in prima parte
              <lb/>
            huius propoſitionis oſtenſum eſt) rectangulum M S R, ſeu rectangulum ſub S V,
              <lb/>
            & </s>
            <s xml:id="echoid-s8141" xml:space="preserve">latere recto G F maius erit quadrato L O, ſeu rectãgulo O G F, & </s>
            <s xml:id="echoid-s8142" xml:space="preserve">propterea
              <lb/>
              <note position="left" xlink:label="note-0254-01" xlink:href="note-0254-01a" xml:space="preserve">II. lib. I.</note>
            S V maior erit, quàm O G, & </s>
            <s xml:id="echoid-s8143" xml:space="preserve">addita communi O V; </s>
            <s xml:id="echoid-s8144" xml:space="preserve">erit O S, ſeu ei æqualis
              <lb/>
            L M, in parallellogrammo L S, maior quàm G V. </s>
            <s xml:id="echoid-s8145" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s8146" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8147" xml:space="preserve">Idem omnino verificari in ellipſibus demonſtrari facile poſſet, quod breuitati
              <lb/>
              <note position="left" xlink:label="note-0254-02" xlink:href="note-0254-02a" xml:space="preserve">SCHO-
                <lb/>
              LIVM.</note>
            ſtudens libens omitto.</s>
            <s xml:id="echoid-s8148" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8149" xml:space="preserve">Si fuerint duæ quælibet coniſectiones A B C, D E F æquales, & </s>
            <s xml:id="echoid-s8150" xml:space="preserve">ſi-
              <lb/>
              <note position="left" xlink:label="note-0254-03" xlink:href="note-0254-03a" xml:space="preserve">PROP. 5.
                <lb/>
              Addit.</note>
            miles ad eaſdemque partes cauæ, quarum diametri B H, E I (æquè in-
              <lb/>
            clinatæ ad ordinatim ad eas applicatas) æquidiſtantes ſint inter ſe, vel
              <lb/>
            congruentes; </s>
            <s xml:id="echoid-s8151" xml:space="preserve">& </s>
            <s xml:id="echoid-s8152" xml:space="preserve">ducantur quælibet rectæ lineæ A D, K L à ſectionibus
              <lb/>
            interceptæ, parallelæ rectæ lineæ B E vertices coniungenti: </s>
            <s xml:id="echoid-s8153" xml:space="preserve">erunt illæ
              <lb/>
            æquales inter ſe.</s>
            <s xml:id="echoid-s8154" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8155" xml:space="preserve">Si enim hoc verum non eſt,
              <lb/>
              <figure xlink:label="fig-0254-02" xlink:href="fig-0254-02a" number="294">
                <image file="0254-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0254-02"/>
              </figure>
            ſit A D ſi fieri pote@t maior,
              <lb/>
            aut minor, quàm B E, & </s>
            <s xml:id="echoid-s8156" xml:space="preserve">ſe-
              <lb/>
            t@tur A R æqualis B E: </s>
            <s xml:id="echoid-s8157" xml:space="preserve">pa-
              <lb/>
            tet punctum R cadere intra,
              <lb/>
            aut extra ſectionem D E (ſed
              <lb/>
            in eius plano cum ſectiones in
              <lb/>
            eodem plano exiſtant) iungan-
              <lb/>
            turque rectæ lineæ A B, E
              <lb/>
            R, quæ æquales erunt, & </s>
            <s xml:id="echoid-s8158" xml:space="preserve">pa-
              <lb/>
            rallelæ inter ſe, cum ſint con-
              <lb/>
            iungentes æqualium, & </s>
            <s xml:id="echoid-s8159" xml:space="preserve">æqui-
              <lb/>
            diſtantium B E, & </s>
            <s xml:id="echoid-s8160" xml:space="preserve">A R. </s>
            <s xml:id="echoid-s8161" xml:space="preserve">Po-
              <lb/>
            ſtea ducatur A H ordinatim
              <lb/>
            applicata ad diametrum B H efficiens abſcißam H B; </s>
            <s xml:id="echoid-s8162" xml:space="preserve">ſeceturque abſciſſa E I in
              <lb/>
            altera ſectione æqualis B H; </s>
            <s xml:id="echoid-s8163" xml:space="preserve">iunganturque H I, I D, & </s>
            <s xml:id="echoid-s8164" xml:space="preserve">I R. </s>
            <s xml:id="echoid-s8165" xml:space="preserve">Et quoniam B </s>
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