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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        <div xml:id="echoid-div374" type="section" level="1" n="120">
          <pb o="99" file="0137" n="137" rhead="Conicor. Lib. V."/>
          <note position="left" xml:space="preserve">d</note>
          <p style="it">
            <s xml:id="echoid-s4022" xml:space="preserve">Dico etiam, quod E G maior ſit, quàm E I, &</s>
            <s xml:id="echoid-s4023" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4024" xml:space="preserve">Ideſt: </s>
            <s xml:id="echoid-s4025" xml:space="preserve">Oſtendetur etiam,
              <lb/>
            quod ramus E G maximus etiam ſit omnium ramorũ cadentium ad peripheriam
              <lb/>
            C H, propterea quod E G oſtendetur maior E I maximo eorum, qui ad periphe-
              <lb/>
            riam C H duci poſſunt. </s>
            <s xml:id="echoid-s4026" xml:space="preserve">Ducatur ex puncto I recta I O parallela axi matori A
              <lb/>
            C, quæ ſecabit axim minorem, & </s>
            <s xml:id="echoid-s4027" xml:space="preserve">ſectionem, cum punctum I cadat inter ver-
              <lb/>
            tices C, & </s>
            <s xml:id="echoid-s4028" xml:space="preserve">B duorum axium; </s>
            <s xml:id="echoid-s4029" xml:space="preserve">ſecet igitur ſectionem in O, coniungaturque E O,
              <lb/>
            atque ex punctis I, O, G, E ducantur perpendiculares ad axim I P, O Q, G
              <lb/>
            R, E F S, quæ ſecent axim in P, Q, R, F, & </s>
            <s xml:id="echoid-s4030" xml:space="preserve">I O in S, & </s>
            <s xml:id="echoid-s4031" xml:space="preserve">quia G N, & </s>
            <s xml:id="echoid-s4032" xml:space="preserve">
              <lb/>
            I K ſunt breuiſsimæ; </s>
            <s xml:id="echoid-s4033" xml:space="preserve">ergo D R ad R N, atque D P ad P K eandem proportio-
              <lb/>
              <note position="right" xlink:label="note-0137-02" xlink:href="note-0137-02a" xml:space="preserve">15. huius.</note>
            nem habent, nimirum eam, quàm habet latus tranſuerſum ad rectum; </s>
            <s xml:id="echoid-s4034" xml:space="preserve">eſt verò
              <lb/>
            K F minor, quàm D K, atque R F maior, quàm D R; </s>
            <s xml:id="echoid-s4035" xml:space="preserve">igitur F P ad P K mi-
              <lb/>
            norem proportionem habet, quàm D P ad P K, ſeu quàm D R ad R N, & </s>
            <s xml:id="echoid-s4036" xml:space="preserve">mul-
              <lb/>
            to minorem, quàm F R ad R N; </s>
            <s xml:id="echoid-s4037" xml:space="preserve">quare diuidendo F K ad K P minorem pro-
              <lb/>
            portionem habebit, quàm F N ad N R, & </s>
            <s xml:id="echoid-s4038" xml:space="preserve">propter parallelas F E, I P, & </s>
            <s xml:id="echoid-s4039" xml:space="preserve">ſi-
              <lb/>
            militudinem triangulorum E K F, I K P eſt E F ad I P, vt F K ad K P; </s>
            <s xml:id="echoid-s4040" xml:space="preserve">igi-
              <lb/>
            tur E F ad I P minorem proportionem habet, quàm F N ad N R; </s>
            <s xml:id="echoid-s4041" xml:space="preserve">ſed propter
              <lb/>
            ſimilitudinem triangulorum E F N, G R N eſt E F ad G R, vt F N ad R N;
              <lb/>
            </s>
            <s xml:id="echoid-s4042" xml:space="preserve">igitur eadem E F ad I P minorem proportionem habet, quàm ad G R; </s>
            <s xml:id="echoid-s4043" xml:space="preserve">& </s>
            <s xml:id="echoid-s4044" xml:space="preserve">pro-
              <lb/>
            pterea I P, ſeu ei æqualis O Q (in parallegrammo rectangulo P O) maior erit,
              <lb/>
            quàm G R, & </s>
            <s xml:id="echoid-s4045" xml:space="preserve">propterea punctum O recedit à puncto G verſus B, ideoq; </s>
            <s xml:id="echoid-s4046" xml:space="preserve">ramus
              <lb/>
              <note position="right" xlink:label="note-0137-03" xlink:href="note-0137-03a" xml:space="preserve">74. huius.</note>
            E G maximus, maior erit ramo E O, &</s>
            <s xml:id="echoid-s4047" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4048" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div378" type="section" level="1" n="121">
          <head xml:id="echoid-head164" xml:space="preserve">Notæ in Propoſ. LXXVI.</head>
          <p>
            <s xml:id="echoid-s4049" xml:space="preserve">SI autem non educatur ex concurſu E ad rectum E B ellipſis A B C
              <lb/>
              <note position="left" xlink:label="note-0137-04" xlink:href="note-0137-04a" xml:space="preserve">a</note>
            breuiſecans præter tranſeuntem per centrum, vt E B, vtique erit ma-
              <lb/>
            ximus ramorum ſecantium egredientium ex concurſu ad ſectionem.</s>
            <s xml:id="echoid-s4050" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4051" xml:space="preserve">Si vero eductus fuerit ex illo alius
              <lb/>
              <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a" number="121">
                <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01"/>
              </figure>
            breuiſecans, ipſe erit ramus maximus,
              <lb/>
            &</s>
            <s xml:id="echoid-s4052" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4053" xml:space="preserve">Imperceptibilis eſt ſenſus huius textus,
              <lb/>
            quia, præter phraſis Arabicæ difficultatem,
              <lb/>
            nonnulla verba in textu deſiderantnr; </s>
            <s xml:id="echoid-s4054" xml:space="preserve">itaq;
              <lb/>
            </s>
            <s xml:id="echoid-s4055" xml:space="preserve">ſic legendum puto. </s>
            <s xml:id="echoid-s4056" xml:space="preserve">Si ex concurſu E in re-
              <lb/>
            cto E B poſito ellipſis A B C non educatur
              <lb/>
            breuiſecans præter E B tranſeuntem per cen-
              <lb/>
            trum, erit E B maximus ramorum ſecan-
              <lb/>
            tium ex concurſu ad ſectionem egredientiũ.</s>
            <s xml:id="echoid-s4057" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4058" xml:space="preserve">Si vero ex illo educatur alius breuiſe-
              <lb/>
            cans, erit æqualis vni breuiſecanti ex altera parte recti poſito, & </s>
            <s xml:id="echoid-s4059" xml:space="preserve">omnium re-
              <lb/>
            liquorum erit maximus: </s>
            <s xml:id="echoid-s4060" xml:space="preserve">Si enim hæc extrema verba non opponerentur, propo-
              <lb/>
            ſitio non eſſet vera, vt oſtendetur.</s>
            <s xml:id="echoid-s4061" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4062" xml:space="preserve">Quia breuiſſimæ egredientes ab extremitatibus reliquorum ramorum
              <lb/>
              <note position="left" xlink:label="note-0137-05" xlink:href="note-0137-05a" xml:space="preserve">b</note>
            abſcindunt cum A, vel B lineam maiorem, quàm ſecet ramus illius (49.
              <lb/>
            </s>
            <s xml:id="echoid-s4063" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4064" xml:space="preserve">demonſtratum ergo eſt in lineis tangentibus ad extremitatem il-
              <lb/>
            lius, quemadmodum antea, &</s>
            <s xml:id="echoid-s4065" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4066" xml:space="preserve">Mendoſe citatur quadrageſima nona huius,
              <lb/>
            debet potius legi 43. </s>
            <s xml:id="echoid-s4067" xml:space="preserve">in qua oſtenſum eſt, quod quotieſcunque ramus E B ad </s>
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