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="213" file="0251" n="251" rhead="Conicor. Lib. VI."/>
            H O cadent puncta T, & </s>
            <s xml:id="echoid-s7984" xml:space="preserve">V infra centrum L; </s>
            <s xml:id="echoid-s7985" xml:space="preserve">& </s>
            <s xml:id="echoid-s7986" xml:space="preserve">P vlterius tendit quàm Q ad
              <lb/>
            partes, eiuſdem centri L. </s>
            <s xml:id="echoid-s7987" xml:space="preserve">igitur in tali caſit quatuor æquidiſtantium duæ P E,
              <lb/>
              <note position="right" xlink:label="note-0251-01" xlink:href="note-0251-01a" xml:space="preserve">Def. add.</note>
            T X vlterius tendent ad partes centri, & </s>
            <s xml:id="echoid-s7988" xml:space="preserve">asymptoti L M, quàm duæ aliæ æqui-
              <lb/>
            diſtantes Q F, V Z. </s>
            <s xml:id="echoid-s7989" xml:space="preserve">Quando verò B E, & </s>
            <s xml:id="echoid-s7990" xml:space="preserve">C F cadunt vltra centra H, & </s>
            <s xml:id="echoid-s7991" xml:space="preserve">
              <lb/>
            L in productionibus æquidiſtantium asymptotorum G H, K L: </s>
            <s xml:id="echoid-s7992" xml:space="preserve">quia N P cadit
              <lb/>
              <figure xlink:label="fig-0251-01" xlink:href="fig-0251-01a" number="290">
                <image file="0251-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0251-01"/>
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            ſupra, & </s>
            <s xml:id="echoid-s7993" xml:space="preserve">L f infra centrũ H, ergo in parallelogrammo P f recta N f, ſeu ei æ-
              <lb/>
            qualis L P maior erit quàm N H: </s>
            <s xml:id="echoid-s7994" xml:space="preserve">facta autem fuit L T æqualis H N; </s>
            <s xml:id="echoid-s7995" xml:space="preserve">igitur
              <lb/>
            L T minor eſt, quàm L P; </s>
            <s xml:id="echoid-s7996" xml:space="preserve">Eadem ratione L V minor erit, quàm L Q, at-
              <lb/>
            que P vlterius tendit quàm Q ad partes centri L, & </s>
            <s xml:id="echoid-s7997" xml:space="preserve">ab ijſdem punctis caden-
              <lb/>
            tibus ſupra centrum L in productione asymptoti K L ducuntur quatuor rectæ
              <lb/>
            lineæ inter ſe æquidiſtantes vſque ad hyperbolen D Z; </s>
            <s xml:id="echoid-s7998" xml:space="preserve">igitur duæ P E, T X vl-
              <lb/>
              <note position="right" xlink:label="note-0251-02" xlink:href="note-0251-02a" xml:space="preserve">Ibidem.</note>
            terius tendunt ad partes centri, vel asymptoti L M, quàm duæ Q F, V Z.
              <lb/>
            </s>
            <s xml:id="echoid-s7999" xml:space="preserve">Secetur poſtea P a æqualis N B, atque Q b æqualis O C. </s>
            <s xml:id="echoid-s8000" xml:space="preserve">Et quia T X æqua-
              <lb/>
            lis oſtenſa fuit N B erit P a æqualis ipſi T X; </s>
            <s xml:id="echoid-s8001" xml:space="preserve">eſtque P E maior quàm T X; </s>
            <s xml:id="echoid-s8002" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0251-03" xlink:href="note-0251-03a" xml:space="preserve">Coroll.
                <lb/>
              Propoſ. 2.
                <lb/>
              addit.</note>
            propterea quod illa vlterius tendit ad partes cẽtri L, quàm T X; </s>
            <s xml:id="echoid-s8003" xml:space="preserve">igitur P E ma-
              <lb/>
            ior erit, quàm P a, & </s>
            <s xml:id="echoid-s8004" xml:space="preserve">earum differentia erit E a. </s>
            <s xml:id="echoid-s8005" xml:space="preserve">Simili modo oſtendetur Q
              <lb/>
            b æqualis V Z, & </s>
            <s xml:id="echoid-s8006" xml:space="preserve">minor quàm Q F, quarum differentia F b: </s>
            <s xml:id="echoid-s8007" xml:space="preserve">cumque Q P
              <lb/>
            æqualis ſit ipſi N O, propterea quod ſunt latera oppoſita eiuſdem parallelogram-
              <lb/>
            mi; </s>
            <s xml:id="echoid-s8008" xml:space="preserve">igitur T V, quæ oſtenſa fuit æqualis O N erit quoque æqualis Q P, & </s>
            <s xml:id="echoid-s8009" xml:space="preserve">sũ-
              <lb/>
            pta communiter Q T erit Q V æqualis T P, atque à terminis æqualium ſeg-
              <lb/>
            mentorum eiuſdem asymptoti L K ducuntur vſque ad hyperbolen E Z quatuor
              <lb/>
            rectæ lineæ inter ſe æquidiſtantes, & </s>
            <s xml:id="echoid-s8010" xml:space="preserve">earum binæ P E, T X vlterius tendunt
              <lb/>
            ad partes centri, & </s>
            <s xml:id="echoid-s8011" xml:space="preserve">asymptoti L M, quàm binæ Q F, V Z; </s>
            <s xml:id="echoid-s8012" xml:space="preserve">igitur differentia
              <lb/>
              <note position="right" xlink:label="note-0251-04" xlink:href="note-0251-04a" xml:space="preserve">Propoſ. 2.
                <lb/>
              addit.</note>
            priorum, ſcilicet E a maior erit poſteriorum differentia F b; </s>
            <s xml:id="echoid-s8013" xml:space="preserve">eſtque B a æqua-
              <lb/>
            lis N P, propterea quod æqualibus N B, & </s>
            <s xml:id="echoid-s8014" xml:space="preserve">P a ponitur communiter B P; </s>
            <s xml:id="echoid-s8015" xml:space="preserve">pa-
              <lb/>
            riterque O Q æqualis eſt C b; </s>
            <s xml:id="echoid-s8016" xml:space="preserve">ſuntque N P, & </s>
            <s xml:id="echoid-s8017" xml:space="preserve">O Q æquales inter ſe, nempe
              <lb/>
            latera oppoſita eiuſdem parallelogrammi; </s>
            <s xml:id="echoid-s8018" xml:space="preserve">igitur B a, & </s>
            <s xml:id="echoid-s8019" xml:space="preserve">C b æquales ſunt inter
              <lb/>
            ſe: </s>
            <s xml:id="echoid-s8020" xml:space="preserve">ijs verò adduntur exceßus inæquales E a, F b efficietur E B vlterius ten-
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            dens ad partes asymptoti H I maior, quàm F C. </s>
            <s xml:id="echoid-s8021" xml:space="preserve">Quod erat primum.</s>
            <s xml:id="echoid-s8022" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8023" xml:space="preserve">Tertio ijſdem poſitis N E, O F ſint parallelæ alicui rectæ lineæ H g diuidẽti
              <lb/>
            angulum L H G, & </s>
            <s xml:id="echoid-s8024" xml:space="preserve">propterea extensæ productionem asymptoti M L </s>
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