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="98" file="0136" n="136" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a" number="120">
                <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0136-01"/>
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            te ellipſis C B ducuntur à concurſu E duo breuiſecantes E I, E H; </s>
            <s xml:id="echoid-s3988" xml:space="preserve">igitur (ex
              <lb/>
            propoſitione 72. </s>
            <s xml:id="echoid-s3989" xml:space="preserve">huius) erit breuiſecans E I vertici A propinquior maximus om-
              <lb/>
            nium ramorum cadentium ex concurſu E ad ellipſis peripheriam C H; </s>
            <s xml:id="echoid-s3990" xml:space="preserve">& </s>
            <s xml:id="echoid-s3991" xml:space="preserve">pro-
              <lb/>
            pinquior maximo E I maior erit remotiore, ſed non omnium ramorũ cadentium
              <lb/>
            ad quadrantem C B, ſed eorum ſolummodo, qui inter verticem C, & </s>
            <s xml:id="echoid-s3992" xml:space="preserve">infimum
              <lb/>
            breuiſecantem E H, & </s>
            <s xml:id="echoid-s3993" xml:space="preserve">aliquorum propè ipſum; </s>
            <s xml:id="echoid-s3994" xml:space="preserve">nam rami ſecantes cadentes pro-
              <lb/>
            pè punctum H hinc inde ſucceſsiuè augentur, vt dictum eſt in notis propoſ. </s>
            <s xml:id="echoid-s3995" xml:space="preserve">67.
              <lb/>
            </s>
            <s xml:id="echoid-s3996" xml:space="preserve">in eiuſque Corollario.</s>
            <s xml:id="echoid-s3997" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3998" xml:space="preserve">Nec non, quia H M, G N ſunt duæ breuiſſimæ, conſtat, vt dictũ eſt, quod
              <lb/>
              <note position="right" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">c</note>
            G E ſit maximus ramorũ egredientiũ ex vtroque latere eius ad A H, &</s>
            <s xml:id="echoid-s3999" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4000" xml:space="preserve">Quorũ verborũ ſenſus hic eſt. </s>
            <s xml:id="echoid-s4001" xml:space="preserve">Quiaex concurſu E ducuntur duæ breuiſecantes E G
              <lb/>
            & </s>
            <s xml:id="echoid-s4002" xml:space="preserve">E H ad ſemiellipſim A B C, quarum E G ſecat vtrumq; </s>
            <s xml:id="echoid-s4003" xml:space="preserve">axim, at E H ſecat
              <lb/>
            tantummodo menſuram; </s>
            <s xml:id="echoid-s4004" xml:space="preserve">ergo, ſicuti in præcedenti propoſ. </s>
            <s xml:id="echoid-s4005" xml:space="preserve">74. </s>
            <s xml:id="echoid-s4006" xml:space="preserve">oſtenſum eſt, erit
              <lb/>
            ramus E G maximus omniũ cadentiũ ad peripheriam H A, &</s>
            <s xml:id="echoid-s4007" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4008" xml:space="preserve">At quia dubitari
              <lb/>
            poſſet de certitudine huius conſequentiæ, quandoquidem hypotheſes non ſunt om-
              <lb/>
            nino eædem; </s>
            <s xml:id="echoid-s4009" xml:space="preserve">in propoſitione enim 74. </s>
            <s xml:id="echoid-s4010" xml:space="preserve">non tres, ſed duo tantummodo breuiſecan-
              <lb/>
            tes ex concurſu E ad ſectionem C B A ducebãtur, hic vero etiam tertia breui-
              <lb/>
            ſecans ducitur: </s>
            <s xml:id="echoid-s4011" xml:space="preserve">ſed ſi conſideretur progreſſus Apollonij, eandem concluſionem ex
              <lb/>
            vtraque hypotheſi deduci poſſe percipitur; </s>
            <s xml:id="echoid-s4012" xml:space="preserve">nam (ex propoſitione 72. </s>
            <s xml:id="echoid-s4013" xml:space="preserve">huius) bre-
              <lb/>
            uiſecans E H, infra breuiſecantem, E I poſitus, minimus eſt omnium ramorum
              <lb/>
            cadentium ex E ad peripheriam H B ellipſis, & </s>
            <s xml:id="echoid-s4014" xml:space="preserve">propinquior minimo E H mi-
              <lb/>
            nor eſt remotiore, reliquorum vero ramorum cadentium ad quadrantem B A ma-
              <lb/>
            ximus eſt breuiſecans E G, vt oſtenſum eſt in præcedenti propoſit. </s>
            <s xml:id="echoid-s4015" xml:space="preserve">74. </s>
            <s xml:id="echoid-s4016" xml:space="preserve">ex Lemma-
              <lb/>
            te 12. </s>
            <s xml:id="echoid-s4017" xml:space="preserve">huius, & </s>
            <s xml:id="echoid-s4018" xml:space="preserve">ex Corollario propoſit. </s>
            <s xml:id="echoid-s4019" xml:space="preserve">67, atque propinquior ramus maximo
              <lb/>
            E G eorum, qui ad quadrantem B A cadunt maior eſt remotiore; </s>
            <s xml:id="echoid-s4020" xml:space="preserve">quapropter ra-
              <lb/>
            mus E G maximus eſt omnium ramorum ex E ad ellipſis peripheriam H A ca-
              <lb/>
            dentium.</s>
            <s xml:id="echoid-s4021" xml:space="preserve"/>
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