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-div290" type="section" level="1" n="96">
          <pb o="73" file="0111" n="111" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div293" type="section" level="1" n="97">
          <head xml:id="echoid-head135" xml:space="preserve">Notæ in Propoſit. XXIX. XXX.
            <lb/>
          & XXXI.</head>
          <p style="it">
            <s xml:id="echoid-s3090" xml:space="preserve">A Lioquin producatur perpendicularis C E, &</s>
            <s xml:id="echoid-s3091" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3092" xml:space="preserve">Exiſtente C A lineæ
              <lb/>
              <note position="left" xlink:label="note-0111-01" xlink:href="note-0111-01a" xml:space="preserve">a</note>
            breuiſsima, & </s>
            <s xml:id="echoid-s3093" xml:space="preserve">A D tangente, ſi C A non eſt perpendicularis ad tangen-
              <lb/>
            tem ducatur ex origine C recta C E perpendicularis ad tangentem A D, ſecans
              <lb/>
            eam in E, & </s>
            <s xml:id="echoid-s3094" xml:space="preserve">ſectionem in F, erit in triangulo A C E angulus C A E acutus,
              <lb/>
            & </s>
            <s xml:id="echoid-s3095" xml:space="preserve">minor angulo recto E, & </s>
            <s xml:id="echoid-s3096" xml:space="preserve">propterea C A ſubtendens maiorem angulum re-
              <lb/>
            ctum, maior erit quàm C E, quæ acutum ſubtendit: </s>
            <s xml:id="echoid-s3097" xml:space="preserve">cumque punctum E tan-
              <lb/>
            gentis cadat extra ſectionem, erit C F minor, quàm C E; </s>
            <s xml:id="echoid-s3098" xml:space="preserve">ideoque C A multo
              <lb/>
            maior eſt, quàm C F, quapropter C A non erit breuiſsima, quod eſt contra,
              <lb/>
            hypotheſin.</s>
            <s xml:id="echoid-s3099" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3100" xml:space="preserve">Si vero fuerit D A C rectus, &</s>
            <s xml:id="echoid-s3101" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3102" xml:space="preserve">Quia C A ſupponitur breuiſsima,
              <lb/>
              <note position="left" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">b</note>
              <note position="right" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">33. 34.
                <lb/>
              lib. 2.</note>
            & </s>
            <s xml:id="echoid-s3103" xml:space="preserve">angulus D A C rectus, erit A D tangens; </s>
            <s xml:id="echoid-s3104" xml:space="preserve">nam ſi hoc verum non eſt,
              <lb/>
            ducatur ex puncto A recta linea A G, contingens ſectionem in
              <lb/>
            A; </s>
            <s xml:id="echoid-s3105" xml:space="preserve">ſecabit vtique tangens A G ipſam D A, & </s>
            <s xml:id="echoid-s3106" xml:space="preserve">erit an-
              <lb/>
            gulus C A G rectus nimirum contentus à breuiſsima
              <lb/>
            C A, & </s>
            <s xml:id="echoid-s3107" xml:space="preserve">tangente A G, ex proxime demon-
              <lb/>
            ſtrata propoſitione; </s>
            <s xml:id="echoid-s3108" xml:space="preserve">ergo duo anguli recti
              <lb/>
            C A D, & </s>
            <s xml:id="echoid-s3109" xml:space="preserve">C A G æquales ſunt
              <lb/>
            inter ſe, pars, & </s>
            <s xml:id="echoid-s3110" xml:space="preserve">totum, quod
              <lb/>
            eſt abſurdum.</s>
            <s xml:id="echoid-s3111" xml:space="preserve"/>
          </p>
          <figure number="93">
            <image file="0111-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0111-01"/>
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