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="86" file="0124" n="124" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s3595" xml:space="preserve">Quod autem infimus ramus breuiſecans D C non ſit neceſſario minimus om-
              <lb/>
            nium ramorum cadentium ad peripheriam ſectionis A B, modò oſtendetur.</s>
            <s xml:id="echoid-s3596" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3597" xml:space="preserve">In coniſectione duos ramos hreuiſecantes, ducere, quorum infimus
              <lb/>
              <note position="left" xlink:label="note-0124-01" xlink:href="note-0124-01a" xml:space="preserve">PROB.6.
                <lb/>
              Addit.</note>
            maior ſit ramo ſecante poſito in peripheria à vertice, & </s>
            <s xml:id="echoid-s3598" xml:space="preserve">ſuprema bre-
              <lb/>
            uiſecante compræhenſa: </s>
            <s xml:id="echoid-s3599" xml:space="preserve">oportet autem in ellipſi, vt rami ſecantes ad
              <lb/>
            vnum eius quadrantem ducantur à concurſu, inter axim minorem, & </s>
            <s xml:id="echoid-s3600" xml:space="preserve">
              <lb/>
            verticem collocato.</s>
            <s xml:id="echoid-s3601" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3602" xml:space="preserve">In coniſectione A B C, cuius ver-
              <lb/>
              <figure xlink:label="fig-0124-01" xlink:href="fig-0124-01a" number="106">
                <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0124-01"/>
              </figure>
            tex A axis A D, & </s>
            <s xml:id="echoid-s3603" xml:space="preserve">in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s3604" xml:space="preserve">ellipſi centrum E ducatur quæli-
              <lb/>
              <note position="left" xlink:label="note-0124-02" xlink:href="note-0124-02a" xml:space="preserve">8. 9. 10.
                <lb/>
              huius.</note>
            bet breuiſsima F B: </s>
            <s xml:id="echoid-s3605" xml:space="preserve">poſtea ſecetur
              <lb/>
            F G ex axi, ita vt punctum G non
              <lb/>
            cadat ſupra verticem A, ſeceturque
              <lb/>
            F H non maior, quam F G, ducan-
              <lb/>
            turque rectæ H C, G G parallelæ ipſi
              <lb/>
            F B occurrentes ſectioni in C, & </s>
            <s xml:id="echoid-s3606" xml:space="preserve">
              <lb/>
            G, coniungaturque recta C G ſecans
              <lb/>
            F B in I: </s>
            <s xml:id="echoid-s3607" xml:space="preserve">patet, C I maiorem non
              <lb/>
            eſſe, quàm I G; </s>
            <s xml:id="echoid-s3608" xml:space="preserve">propterea quod G C,
              <lb/>
            G H à parallelis ſecantur proportio-
              <lb/>
            naliter; </s>
            <s xml:id="echoid-s3609" xml:space="preserve">Deinde ex C ducatur alia
              <lb/>
              <note position="left" xlink:label="note-0124-03" xlink:href="note-0124-03a" xml:space="preserve">8. 9. 10.
                <lb/>
              26. 27. 28.
                <lb/>
              huius.</note>
            breuiſsima C K, occurrens B F vl-
              <lb/>
            tra axim in L, iungaturque ramus
              <lb/>
            G L: </s>
            <s xml:id="echoid-s3610" xml:space="preserve">oſtendendum eſt L C maiorem
              <lb/>
            eſſe, quàm L G. </s>
            <s xml:id="echoid-s3611" xml:space="preserve">Secetur C G bifa-
              <lb/>
            riam in M, atque per M ducatur ſe-
              <lb/>
            ctionis diameter M N parallela axi
              <lb/>
            in parabola, & </s>
            <s xml:id="echoid-s3612" xml:space="preserve">per centrum exſten-
              <lb/>
            ſa in reliquis ſectionibus, occurrens
              <lb/>
            ſectioni in N, ducaturque O N ſe-
              <lb/>
            ctionem contingens in N, iungantur-
              <lb/>
              <note position="left" xlink:label="note-0124-04" xlink:href="note-0124-04a" xml:space="preserve">33. 34.
                <lb/>
              lib. 1.</note>
            que L M, & </s>
            <s xml:id="echoid-s3613" xml:space="preserve">L N, quæ ſecet G C in
              <lb/>
            P. </s>
            <s xml:id="echoid-s3614" xml:space="preserve">Quoniam G I æqualis, aut ma-
              <lb/>
            ior eſt, quàm I C, cadet punctum
              <lb/>
            M bipartitæ diuiſionis totius C G,
              <lb/>
            vel in I, vel inter I, G, & </s>
            <s xml:id="echoid-s3615" xml:space="preserve">in vtro-
              <lb/>
            que caſu punctum N cadet inter G,
              <lb/>
            & </s>
            <s xml:id="echoid-s3616" xml:space="preserve">B (eoquod diameter M N paral-
              <lb/>
            lela axi in parabola, aut ex centro
              <lb/>
            E educta in reliquis ſectionibus effi-
              <lb/>
            cit angulum N M L ad partes ver-
              <lb/>
            ticis A) & </s>
            <s xml:id="echoid-s3617" xml:space="preserve">ideo ramus L N cadens
              <lb/>
            ſupra duos breuiſecantes L C, L B
              <lb/>
            ad partes verticis efficit cum </s>
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