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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          <p style="it">
            <s xml:id="echoid-s7931" xml:space="preserve">
              <pb o="212" file="0250" n="250" rhead="Apollonij Pergæi"/>
            Rectæ lineæ parallelæ B E, C F ſe-
              <lb/>
              <figure xlink:label="fig-0250-01" xlink:href="fig-0250-01a" number="288">
                <image file="0250-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0250-01"/>
              </figure>
            cent æquidiſtantes aſymptotos H G,
              <lb/>
            L K in punctis N
              <unsure/>
            , O, P, Q. </s>
            <s xml:id="echoid-s7932" xml:space="preserve">De-
              <lb/>
            bent autem coniſectiones in eodem pla-
              <lb/>
            no collocari ſicuti aliæ omnes, quæ in.
              <lb/>
            </s>
            <s xml:id="echoid-s7933" xml:space="preserve">ſequentibus propoſitionibus 4. </s>
            <s xml:id="echoid-s7934" xml:space="preserve">5. </s>
            <s xml:id="echoid-s7935" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7936" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7937" xml:space="preserve">
              <lb/>
            8. </s>
            <s xml:id="echoid-s7938" xml:space="preserve">& </s>
            <s xml:id="echoid-s7939" xml:space="preserve">9. </s>
            <s xml:id="echoid-s7940" xml:space="preserve">vſurpantur ſemper in vno
              <lb/>
            plano poſitæ intelligi debent.</s>
            <s xml:id="echoid-s7941" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7942" xml:space="preserve">Et primo duæ rectæ B E, C F paralle-
              <lb/>
            læ ſint rectæ lineæ H L centra coniungen-
              <lb/>
            ti. </s>
            <s xml:id="echoid-s7943" xml:space="preserve">Quoniam hyperbolæ A B, D E æqua-
              <lb/>
            les ſunt, & </s>
            <s xml:id="echoid-s7944" xml:space="preserve">congruentes; </s>
            <s xml:id="echoid-s7945" xml:space="preserve">atque æquidiſtan-
              <lb/>
            tes asymptoti H N, L P æque inclinan-
              <lb/>
            tur ad æquales ſemiaxes tranſuerſos H
              <lb/>
            A, & </s>
            <s xml:id="echoid-s7946" xml:space="preserve">L D; </s>
            <s xml:id="echoid-s7947" xml:space="preserve">& </s>
            <s xml:id="echoid-s7948" xml:space="preserve">ſegmenta asymptotorum H N, L P æqualia ſunt in paralle-
              <lb/>
            logrammo H P, nec non duo anguli H N B, & </s>
            <s xml:id="echoid-s7949" xml:space="preserve">L P E æquales ſunt inter ſe, pro-
              <lb/>
            pter parallelas asymptotos: </s>
            <s xml:id="echoid-s7950" xml:space="preserve">igitur duæ figuræ A H N B A, & </s>
            <s xml:id="echoid-s7951" xml:space="preserve">D L P E D æquales
              <lb/>
            erunt, & </s>
            <s xml:id="echoid-s7952" xml:space="preserve">congruentes: </s>
            <s xml:id="echoid-s7953" xml:space="preserve">quapropter interpoſitæ rectæ lineæ N B & </s>
            <s xml:id="echoid-s7954" xml:space="preserve">P E congruẽ-
              <lb/>
            tes, & </s>
            <s xml:id="echoid-s7955" xml:space="preserve">æquales erunt; </s>
            <s xml:id="echoid-s7956" xml:space="preserve">& </s>
            <s xml:id="echoid-s7957" xml:space="preserve">addita vel ablata communi B P, erit N P æqualis
              <lb/>
            B E: </s>
            <s xml:id="echoid-s7958" xml:space="preserve">eſt verò N P æqualis H L, eo quod H P parallelogrammum eſt; </s>
            <s xml:id="echoid-s7959" xml:space="preserve">igitur
              <lb/>
            intercepta B E æqualis eſt rectæ lineæ H L centra coniungenti. </s>
            <s xml:id="echoid-s7960" xml:space="preserve">Eadem ratione
              <lb/>
            quælibet alia intercepta C F parallela ipſi H L eidem æqualis oſtendetur: </s>
            <s xml:id="echoid-s7961" xml:space="preserve">qua-
              <lb/>
            propter duæ interceptæ æquidiſtantes B E, & </s>
            <s xml:id="echoid-s7962" xml:space="preserve">C F inter ſe æquales erunt.</s>
            <s xml:id="echoid-s7963" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7964" xml:space="preserve">Secundo B E, C F parallelæ ſint alicui rectæ lineæ L f diuidenti angulum K
              <lb/>
            L H; </s>
            <s xml:id="echoid-s7965" xml:space="preserve">ideoque P L f N, & </s>
            <s xml:id="echoid-s7966" xml:space="preserve">Q L f O parallelogramma erunt: </s>
            <s xml:id="echoid-s7967" xml:space="preserve">ſecetur L T æqua-
              <lb/>
              <figure xlink:label="fig-0250-02" xlink:href="fig-0250-02a" number="289">
                <image file="0250-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0250-02"/>
              </figure>
            lis H N, atque L V æqualis H O; </s>
            <s xml:id="echoid-s7968" xml:space="preserve">ducan-
              <lb/>
            turque T X, V Z parallelæ ipſis N B, O
              <lb/>
            C ſecantes reliquam hyperbolen in X, Z;
              <lb/>
            </s>
            <s xml:id="echoid-s7969" xml:space="preserve">eritque ( vt in prima parte oſtenſum eſt)
              <lb/>
            T X æqualis N B, atque V Z æqualis O C. </s>
            <s xml:id="echoid-s7970" xml:space="preserve">
              <lb/>
            Et ſiquidem B E, C F cadunt infra cen-
              <lb/>
            tra H, L ad partes G, K, cadent quoque
              <lb/>
            infra L f eis parallelam per L ductam in-
              <lb/>
            fra centrum H incidentem, & </s>
            <s xml:id="echoid-s7971" xml:space="preserve">ideo N f,
              <lb/>
            ſeu ei æqualis P L in parallelogrãmo P f
              <lb/>
            minor erit, quàm H N; </s>
            <s xml:id="echoid-s7972" xml:space="preserve">eſtque L T æqua-
              <lb/>
            lis H N; </s>
            <s xml:id="echoid-s7973" xml:space="preserve">igitur L P minor erit, quàm L T ; </s>
            <s xml:id="echoid-s7974" xml:space="preserve">& </s>
            <s xml:id="echoid-s7975" xml:space="preserve">propterea punctum P propin-
              <lb/>
            quius erit centro L, quàm T: </s>
            <s xml:id="echoid-s7976" xml:space="preserve">Eadem ratione oſtendetur, quod punctum Q pro-
              <lb/>
            pinquius ſit centro L, quàm V, & </s>
            <s xml:id="echoid-s7977" xml:space="preserve">P propinquius centro quàm Q; </s>
            <s xml:id="echoid-s7978" xml:space="preserve">ergo quatuor
              <lb/>
              <note position="left" xlink:label="note-0250-01" xlink:href="note-0250-01a" xml:space="preserve">Def. add.</note>
            æquidiſtantium P E, Q F, T X, V Z cadentium infra centrum ad partes K,
              <lb/>
            duæ P E, T X vlterius ad partes centri, vel asymptoti L M tendunt, quàm,
              <lb/>
            duæ Q F, V Z. </s>
            <s xml:id="echoid-s7979" xml:space="preserve">At ſi B E, C F ſecent rectã lineam centra coniungentem inter
              <lb/>
            duo centra H, & </s>
            <s xml:id="echoid-s7980" xml:space="preserve">L, manifeſtum eſt puncta P, & </s>
            <s xml:id="echoid-s7981" xml:space="preserve">Q cadere ſupra centrum L,
              <lb/>
            atque duo puncta N, & </s>
            <s xml:id="echoid-s7982" xml:space="preserve">O cadere infra centrnm H alterius hyperboles, cumque
              <lb/>
            L T ſecta ſit æqualis ipſi H N ad eaſdem partes; </s>
            <s xml:id="echoid-s7983" xml:space="preserve">pariterque L V æqualis </s>
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