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-div362" type="section" level="1" n="118">
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            <s xml:id="echoid-s3784" xml:space="preserve">
              <pb o="93" file="0131" n="131" rhead="Conicor. Lib. V."/>
            reſpicientem verticem C concurſui propinquiorem: </s>
            <s xml:id="echoid-s3785" xml:space="preserve">& </s>
            <s xml:id="echoid-s3786" xml:space="preserve">quilibet. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">ramus E
              <lb/>
            L inter breuiſecantem G E, & </s>
            <s xml:id="echoid-s3788" xml:space="preserve">axim maiorem poſitus efficit cum tan-
              <lb/>
            gente L M angulum E L M reſpicientem eundem verticem A acu-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s3789" xml:space="preserve"/>
          </p>
          <figure number="116">
            <image file="0131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0131-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s3790" xml:space="preserve">Ducatur E F perpendicularis ad axim maiorem, eum ſecans inter verticem
              <lb/>
            c, & </s>
            <s xml:id="echoid-s3791" xml:space="preserve">centrum D in F, & </s>
            <s xml:id="echoid-s3792" xml:space="preserve">ex concurſu axis minoris B H, & </s>
            <s xml:id="echoid-s3793" xml:space="preserve">breuiſsimæ G E,
              <lb/>
            scilicet ex H ducantur rectæ H K, & </s>
            <s xml:id="echoid-s3794" xml:space="preserve">H L; </s>
            <s xml:id="echoid-s3795" xml:space="preserve">pariterque ex punctis, K, & </s>
            <s xml:id="echoid-s3796" xml:space="preserve">L
              <lb/>
            ducantur ad axim maiorem A C lineæ breuiſsimæ K N, L O, ei occurrentes in
              <lb/>
            N, & </s>
            <s xml:id="echoid-s3797" xml:space="preserve">O. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">Luoniam (ex præmiſſo Lemmate 8.) </s>
            <s xml:id="echoid-s3799" xml:space="preserve">à concurſu H ducitur ramus
              <lb/>
            H K inter breuiſecantes H B, H G interceptus; </s>
            <s xml:id="echoid-s3800" xml:space="preserve">ergo H K cadit infra breuiſ-
              <lb/>
            ſimam K N ad partes verticis C; </s>
            <s xml:id="echoid-s3801" xml:space="preserve">eſt vero angulus N K P rectus à tangente,
              <lb/>
              <note position="right" xlink:label="note-0131-01" xlink:href="note-0131-01a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s3802" xml:space="preserve">breuiſsima contentus; </s>
            <s xml:id="echoid-s3803" xml:space="preserve">ergo angulus H K P erit acutus, cum H K cadat in-
              <lb/>
            ter N K, & </s>
            <s xml:id="echoid-s3804" xml:space="preserve">tangentem K P; </s>
            <s xml:id="echoid-s3805" xml:space="preserve">cadit vero E K infra ramum H K verſus C; </s>
            <s xml:id="echoid-s3806" xml:space="preserve">igi-
              <lb/>
            tur angulus E K P reſpiciens verticem C proximiorem concurſui E erit acutus.</s>
            <s xml:id="echoid-s3807" xml:space="preserve"/>
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            <s xml:id="echoid-s3808" xml:space="preserve">Similiter (ex eodem Lemmate 8.) </s>
            <s xml:id="echoid-s3809" xml:space="preserve">quia ramus H L ducitur inter breuiſecan-
              <lb/>
            tem H G, & </s>
            <s xml:id="echoid-s3810" xml:space="preserve">verticem A à concurſu E remotiorem, cadet ipſe ſupra breuiſsimã
              <lb/>
              <note position="right" xlink:label="note-0131-02" xlink:href="note-0131-02a" xml:space="preserve">Ibidem.</note>
            L O, eſtque angulus O L M ad partes verticis A rectus; </s>
            <s xml:id="echoid-s3811" xml:space="preserve">ergo H L M acutus erit,
              <lb/>
            cumque E L cadat ſupra H L verſus A; </s>
            <s xml:id="echoid-s3812" xml:space="preserve">igitur angulus E L M, verticem A re-
              <lb/>
            motiorem reſpiciens, erit acutus, quod erat oſtendendum.</s>
            <s xml:id="echoid-s3813" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3814" xml:space="preserve">Si à concurſu E non exiſtente ſuper recto ellipſis A C, producatur vni-
              <lb/>
              <note position="left" xlink:label="note-0131-03" xlink:href="note-0131-03a" xml:space="preserve">a</note>
            cus ramus ſecans ipſam A C, vt E G, cuius ſegmentum G I, & </s>
            <s xml:id="echoid-s3815" xml:space="preserve">A C ſit
              <lb/>
            breuiſsimum, vel duo breuiſecantes; </s>
            <s xml:id="echoid-s3816" xml:space="preserve">vtique maximus ſecantium ramorum
              <lb/>
            egredientium ex illo concurſu, eſt breuiſecans, qui rectum ſectionis ab-
              <lb/>
            ſcindit, nempe E G, &</s>
            <s xml:id="echoid-s3817" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3818" xml:space="preserve">Textum mendoſum ſic reſtituendum cenſeo. </s>
            <s xml:id="echoid-s3819" xml:space="preserve">Si </s>
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