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="83" file="0121" n="121" rhead="Conicor. Lib. V."/>
            ſunt D A V, D L G, D B I, D Q O, D C P, oſtenſus eſt ramus D A minor
              <lb/>
            quàm D B, & </s>
            <s xml:id="echoid-s3459" xml:space="preserve">D B propinquior vertici A, minor ramo D C remotiore.</s>
            <s xml:id="echoid-s3460" xml:space="preserve"/>
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        <div xml:id="echoid-div329" type="section" level="1" n="109">
          <head xml:id="echoid-head150" xml:space="preserve">Notæ in Propoſ. LXVII.</head>
          <p style="it">
            <s xml:id="echoid-s3461" xml:space="preserve">POſtea repetamus figuram vtrã-
              <lb/>
              <figure xlink:label="fig-0121-01" xlink:href="fig-0121-01a" number="102">
                <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0121-01"/>
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              <note position="left" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">a</note>
            que hyperboles, &</s>
            <s xml:id="echoid-s3462" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3463" xml:space="preserve">Lego;
              <lb/>
            </s>
            <s xml:id="echoid-s3464" xml:space="preserve">Repetamus figuras paraboles, & </s>
            <s xml:id="echoid-s3465" xml:space="preserve">hy-
              <lb/>
            perboles, & </s>
            <s xml:id="echoid-s3466" xml:space="preserve">ſupponantur denuo eædem
              <lb/>
            lineæ æductæ ex concurſu D ad ſectio-
              <lb/>
            nem; </s>
            <s xml:id="echoid-s3467" xml:space="preserve">& </s>
            <s xml:id="echoid-s3468" xml:space="preserve">perpendicularis D E, atque
              <lb/>
            Trutina F, & </s>
            <s xml:id="echoid-s3469" xml:space="preserve">omnium ramorum ſe-
              <lb/>
            cantium vnicus tantummodo D B ſit
              <lb/>
            breuiſecans.</s>
            <s xml:id="echoid-s3470" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3471" xml:space="preserve">Et illi propinquiores ſint maio-
              <lb/>
              <note position="left" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">b</note>
            res remotioribus, &</s>
            <s xml:id="echoid-s3472" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">Sed mendo-
              <lb/>
            sè; </s>
            <s xml:id="echoid-s3474" xml:space="preserve">legi debet: </s>
            <s xml:id="echoid-s3475" xml:space="preserve">Et illi propinquiores
              <lb/>
            ſint minores remotioribus.</s>
            <s xml:id="echoid-s3476" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3477" xml:space="preserve">Quia educitur ex D vnus tantum breuiſecans, &</s>
            <s xml:id="echoid-s3478" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3479" xml:space="preserve">Legi debet. </s>
            <s xml:id="echoid-s3480" xml:space="preserve">Quia
              <lb/>
              <note position="right" xlink:label="note-0121-03" xlink:href="note-0121-03a" xml:space="preserve">Conuerſ.
                <lb/>
              51. 52.
                <lb/>
              huius.</note>
              <note position="left" xlink:label="note-0121-04" xlink:href="note-0121-04a" xml:space="preserve">c</note>
            educitur ex concurſu D vnus tantum breuiſecans, erit menſura E A maior di-
              <lb/>
            midio erecti, & </s>
            <s xml:id="echoid-s3481" xml:space="preserve">D E perpendicularis ad axim æqualis erit Trutinæ F.</s>
            <s xml:id="echoid-s3482" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3483" xml:space="preserve">Inde conſtat D G maiorem eſſe, quàm D A, &</s>
            <s xml:id="echoid-s3484" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3485" xml:space="preserve">Quia ex concurſu D
              <lb/>
              <note position="left" xlink:label="note-0121-05" xlink:href="note-0121-05a" xml:space="preserve">d</note>
            ad ſectionem A C vnicus ramus D B breuiſecans ſupponitur igitur omnes rami
              <lb/>
            cadentes inter A, & </s>
            <s xml:id="echoid-s3486" xml:space="preserve">B præter infimum D B conſtituunt cum tangentibus ſectio-
              <lb/>
            nem, ab eorum terminis ductis, angulos reſpicientes verticem A acutos; </s>
            <s xml:id="echoid-s3487" xml:space="preserve">& </s>
            <s xml:id="echoid-s3488" xml:space="preserve">pro-
              <lb/>
              <note position="right" xlink:label="note-0121-06" xlink:href="note-0121-06a" xml:space="preserve">Lem. 10.</note>
            pterea ramus terminatus D A minor eſt quolibet ramo D G infra ipſum, & </s>
            <s xml:id="echoid-s3489" xml:space="preserve">ſu-
              <lb/>
            pra ramum D B poſito; </s>
            <s xml:id="echoid-s3490" xml:space="preserve">atque ramus D G minor eſt quolibet alio à vertice re-
              <lb/>
              <note position="right" xlink:label="note-0121-07" xlink:href="note-0121-07a" xml:space="preserve">Coro 11.
                <unsure/>
                <lb/>
              64. 65.
                <lb/>
              huius.</note>
            motiore ducto ex D ad peripheriam A B. </s>
            <s xml:id="echoid-s3491" xml:space="preserve">Dico iam, quod ramus D B maior
              <lb/>
            eſt quolibet ramo D G, poſito infra verticem A, & </s>
            <s xml:id="echoid-s3492" xml:space="preserve">ſupra breuiſecantem D B;
              <lb/>
            </s>
            <s xml:id="echoid-s3493" xml:space="preserve">Si enim hoc verum non eſt, erit D B æqualis, aut minor, quàm D G, & </s>
            <s xml:id="echoid-s3494" xml:space="preserve">tunc
              <lb/>
            ducto quolibet ramo D H ad ſectionem G B infra ramum D G, erit D H re-
              <lb/>
              <note position="right" xlink:label="note-0121-08" xlink:href="note-0121-08a" xml:space="preserve">Ibidem.</note>
            motior à vertice A maior propinquiore D G, & </s>
            <s xml:id="echoid-s3495" xml:space="preserve">propterea ramus D B adhuc
              <lb/>
            minor erit ramo D H.</s>
            <s xml:id="echoid-s3496" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s3497" xml:space="preserve">Ergo D M nempe D I, &</s>
            <s xml:id="echoid-s3498" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3499" xml:space="preserve">Quia D M, vt remotior à vertice A, eſt ma-
              <lb/>
              <note position="left" xlink:label="note-0121-09" xlink:href="note-0121-09a" xml:space="preserve">e</note>
            ior, quàm propinquior D H eſt vero D L, atque D I æqualis D M cum ſint
              <lb/>
              <note position="right" xlink:label="note-0121-10" xlink:href="note-0121-10a" xml:space="preserve">Ibidem.</note>
            radij eiuſdem circuli; </s>
            <s xml:id="echoid-s3500" xml:space="preserve">ergo D I portio maior eſt, quàm totum D H, quod eſt
              <lb/>
            abſurdum; </s>
            <s xml:id="echoid-s3501" xml:space="preserve">quare D B maior eſt quolibet ramo D G infra verticem A, & </s>
            <s xml:id="echoid-s3502" xml:space="preserve">ſu-
              <lb/>
            pra ramum D B poſito; </s>
            <s xml:id="echoid-s3503" xml:space="preserve">& </s>
            <s xml:id="echoid-s3504" xml:space="preserve">propterea D B multo maior erit, quàm D A.</s>
            <s xml:id="echoid-s3505" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3506" xml:space="preserve">Ergo D N minor eſt, quàm D C, &</s>
            <s xml:id="echoid-s3507" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3508" xml:space="preserve">Dubitare quis poſſet, an ramus
              <lb/>
              <note position="left" xlink:label="note-0121-11" xlink:href="note-0121-11a" xml:space="preserve">f</note>
            D N, quia propinquior eſt vertici A ſit minor remotiore ramo D C, vt in pro-
              <lb/>
            poſitione 64. </s>
            <s xml:id="echoid-s3509" xml:space="preserve">& </s>
            <s xml:id="echoid-s3510" xml:space="preserve">65. </s>
            <s xml:id="echoid-s3511" xml:space="preserve">verificabatur; </s>
            <s xml:id="echoid-s3512" xml:space="preserve">& </s>
            <s xml:id="echoid-s3513" xml:space="preserve">ratio eſt, quia hypotheſes ſunt diuerſæ,
              <lb/>
            nam ibi nullus ramus breuiſecans à concurſu D ad ſectionem A C duci poſſe
              <lb/>
            ſupponebatur, in hac vero propoſitione 67. </s>
            <s xml:id="echoid-s3514" xml:space="preserve">ponitur vnicus breuiſecans D B, at
              <lb/>
            ſcrupulus omnis tolletur, ſi dicatur, non quidem ex propoſitionibus 64. </s>
            <s xml:id="echoid-s3515" xml:space="preserve">& </s>
            <s xml:id="echoid-s3516" xml:space="preserve">65.
              <lb/>
            </s>
            <s xml:id="echoid-s3517" xml:space="preserve">ſed ex demonſtratione ibi allata, ſeu ex Corollario in fine notarum </s>
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