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="224" file="0262" n="262" rhead="Apollonij Pergæi"/>
            Protorum coincidentium, vel propinquiorum, ad oppoſitas partes citra axim G A,
              <lb/>
            ſumantur duo puncta C, T, & </s>
            <s xml:id="echoid-s8392" xml:space="preserve">ab cis ducantur ad axim rami breuiſſimi O C,
              <lb/>
            Q T ſecantcs externam ſectionem in F, V, & </s>
            <s xml:id="echoid-s8393" xml:space="preserve">ab occurſu, vel communi asym-
              <lb/>
            ptoto, vel ab asymptotis vicinioribus I K, M N magis recedat A G, quàm C F,
              <lb/>
            & </s>
            <s xml:id="echoid-s8394" xml:space="preserve">C F, quàm T V; </s>
            <s xml:id="echoid-s8395" xml:space="preserve">Dico G A maiorem eſſe, quàm C F, & </s>
            <s xml:id="echoid-s8396" xml:space="preserve">C F maiorem,
              <lb/>
            quàm T V. </s>
            <s xml:id="echoid-s8397" xml:space="preserve">Ducantur interceptæ F a parallela G A, & </s>
            <s xml:id="echoid-s8398" xml:space="preserve">V b parallela C F.
              <lb/>
            </s>
            <s xml:id="echoid-s8399" xml:space="preserve">
              <figure xlink:label="fig-0262-01" xlink:href="fig-0262-01a" number="308">
                <image file="0262-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0262-01"/>
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            Et quia in parabola F a propinquior eſt occur ſui ſectionum, & </s>
            <s xml:id="echoid-s8400" xml:space="preserve">parallela eſt dia-
              <lb/>
              <note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve">Poſtr. pars
                <lb/>
              pr. 4. add.
                <lb/>
              huius.</note>
            metro G A; </s>
            <s xml:id="echoid-s8401" xml:space="preserve">at in hyperbola F a parallela eſt axi G A, vel D Y diuidenti an-
              <lb/>
            gulum M I H, & </s>
            <s xml:id="echoid-s8402" xml:space="preserve">F a vlterius tendit ad partes asymptoti I K, quàm G A; </s>
            <s xml:id="echoid-s8403" xml:space="preserve">ergo
              <lb/>
              <note position="left" xlink:label="note-0262-02" xlink:href="note-0262-02a" xml:space="preserve">Pars 3.</note>
            F a minor eſt, quàm G A: </s>
            <s xml:id="echoid-s8404" xml:space="preserve">eſtque C F productio rami breuiſſiimi minor quàm
              <lb/>
              <note position="left" xlink:label="note-0262-03" xlink:href="note-0262-03a" xml:space="preserve">prop. 3.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            F a; </s>
            <s xml:id="echoid-s8405" xml:space="preserve">ergo A G maior erit, quàm C F. </s>
            <s xml:id="echoid-s8406" xml:space="preserve">Eodem ratiocinio oſtendetur C F maior,
              <lb/>
            quàm T V.</s>
            <s xml:id="echoid-s8407" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">38. lib. 5.</note>
          <p style="it">
            <s xml:id="echoid-s8408" xml:space="preserve">Secundò angulus Y D A ſit acutus in parabolis, at in hyperbolis minor ſe-
              <lb/>
            mirecto, & </s>
            <s xml:id="echoid-s8409" xml:space="preserve">M I H ab asymptoto I H, & </s>
            <s xml:id="echoid-s8410" xml:space="preserve">recta linea centra coniungente con-
              <lb/>
            tentus ſit acutus: </s>
            <s xml:id="echoid-s8411" xml:space="preserve">Manifeſtum eſt duci poſſe ramum breuiſſimum, vt O B ad ſe-
              <lb/>
              <note position="left" xlink:label="note-0262-05" xlink:href="note-0262-05a" xml:space="preserve">Propoſ. 6.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            ctionem interiorem A B, qui parallelus ſit rectæ lineæ D A vertices coniungenti,
              <lb/>
            vel I M centra coniungenti; </s>
            <s xml:id="echoid-s8412" xml:space="preserve">& </s>
            <s xml:id="echoid-s8413" xml:space="preserve">ex vtraque parte ipſius rami O B præter axim
              <lb/>
            A G ducantur quilibet breuiſſimi rami Q P, d e, i l, O C, qui ſecent exter-
              <lb/>
              <note position="left" xlink:label="note-0262-06" xlink:href="note-0262-06a" xml:space="preserve">8. 9. & 10.
                <lb/>
              lib. 5.</note>
            nam peripheriam in R, f, m, F. </s>
            <s xml:id="echoid-s8414" xml:space="preserve">Oſtendendum modò eſt in eiſdem coniſectio-
              <lb/>
            nibus E B eſſe diſtantiam omnium maximam, & </s>
            <s xml:id="echoid-s8415" xml:space="preserve">R P propinquiorem maximæ
              <lb/>
            maiorem eſſe remotiore f e; </s>
            <s xml:id="echoid-s8416" xml:space="preserve">pariterque m l maiorem eſſe quàm G A. </s>
            <s xml:id="echoid-s8417" xml:space="preserve">Ducantur
              <lb/>
            interceptæ R g, m n parallelæ E B, & </s>
            <s xml:id="echoid-s8418" xml:space="preserve">f h parallela R P, nec non G S paral-
              <lb/>
            lela m l, & </s>
            <s xml:id="echoid-s8419" xml:space="preserve">F a parallela G a. </s>
            <s xml:id="echoid-s8420" xml:space="preserve">Quoniam interceptæ R g, m n parallelæ ſunt
              <lb/>
            eidem E B, & </s>
            <s xml:id="echoid-s8421" xml:space="preserve">recta linea D A vertices coniungens, vel I M centra coniun-
              <lb/>
              <note position="left" xlink:label="note-0262-07" xlink:href="note-0262-07a" xml:space="preserve">Propoſ. 5.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            gens parallela facta fuit eidem E B; </s>
            <s xml:id="echoid-s8422" xml:space="preserve">ergo E B, R g, m n erunt omnes inter
              <lb/>
            ſe æquales; </s>
            <s xml:id="echoid-s8423" xml:space="preserve">eſtque R P minor, quàm R g; </s>
            <s xml:id="echoid-s8424" xml:space="preserve">pariterque m l minor, quàm m n,
              <lb/>
              <note position="left" xlink:label="note-0262-08" xlink:href="note-0262-08a" xml:space="preserve">38. lib. 5.</note>
            quia iliæ ſunt productiones breuiſſimorum ramorum Q P, & </s>
            <s xml:id="echoid-s8425" xml:space="preserve">i l; </s>
            <s xml:id="echoid-s8426" xml:space="preserve">igitur quæ-
              <lb/>
            libet diſtantia R P, vel l m ex vtraque parte ipſius E B ſumpta minor eſt,
              <lb/>
            quàm E B; </s>
            <s xml:id="echoid-s8427" xml:space="preserve">ideoque E B erit omnium maxima. </s>
            <s xml:id="echoid-s8428" xml:space="preserve">Deinde quia O B parallela eſt
              <lb/>
            A D, vel M I, & </s>
            <s xml:id="echoid-s8429" xml:space="preserve">rami breuiſſimi O B, Q P ſe ſecant vltra axim A O; </s>
            <s xml:id="echoid-s8430" xml:space="preserve">ergo
              <lb/>
            recta linea R P Q producta ſecabit quoque reliquam parallelarum D A, vel
              <lb/>
              <note position="left" xlink:label="note-0262-09" xlink:href="note-0262-09a" xml:space="preserve">38. lib. 5.</note>
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