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>
        <div xml:id="echoid-div350" type="section" level="1" n="113">
          <head xml:id="echoid-head156" xml:space="preserve">PROPOSITO LXXIV.</head>
          <p>
            <s xml:id="echoid-s3705" xml:space="preserve">DEinde ſint E H, E G duo breuiſecantes, & </s>
            <s xml:id="echoid-s3706" xml:space="preserve">E G ſecet
              <lb/>
            rectum B D. </s>
            <s xml:id="echoid-s3707" xml:space="preserve">Dico, quod E G eſt maximus ramorum,
              <lb/>
            egredientium ex E ad ſectioncm A B C, & </s>
            <s xml:id="echoid-s3708" xml:space="preserve">E C eſt minimus.</s>
            <s xml:id="echoid-s3709" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3710" xml:space="preserve">Producatur perpendicularis E F, quæ non cadet ſuper centrum; </s>
            <s xml:id="echoid-s3711" xml:space="preserve">ſi e-
              <lb/>
            nim per centrum duceretur, duci poſſet ex E, aut vnicus breuiſecans
              <lb/>
              <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">Ex 45.
                <lb/>
              huius.</note>
            tantum (44. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3713" xml:space="preserve">aut tres (45. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3715" xml:space="preserve">quod eſt contra hypotheſin; </s>
            <s xml:id="echoid-s3716" xml:space="preserve">er-
              <lb/>
              <note position="right" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">a</note>
            go E F per centrum non tranſit, cadat ſuper C D; </s>
            <s xml:id="echoid-s3717" xml:space="preserve">& </s>
            <s xml:id="echoid-s3718" xml:space="preserve">quia ducuntur ex
              <lb/>
            E duo breuiſecantes, erit C F maior dimidio erecti, & </s>
            <s xml:id="echoid-s3719" xml:space="preserve">E F æqualis Tru-
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            tinæ (52. </s>
            <s xml:id="echoid-s3720" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3721" xml:space="preserve">patet itaquè, vti antea demonſtrauimus, quod E G
              <lb/>
            maximus ſit ramorũ, & </s>
            <s xml:id="echoid-s3722" xml:space="preserve">E C minimus; </s>
            <s xml:id="echoid-s3723" xml:space="preserve">atquè propinquior maximo, maior
              <lb/>
            eſt, & </s>
            <s xml:id="echoid-s3724" xml:space="preserve">propinquior minimo, eſt minor.</s>
            <s xml:id="echoid-s3725" xml:space="preserve"/>
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        <div xml:id="echoid-div352" type="section" level="1" n="114">
          <head xml:id="echoid-head157" xml:space="preserve">PROPOSITO LXXV.</head>
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            <s xml:id="echoid-s3726" xml:space="preserve">POſtea educamus ex E tres breuiſecantes E G, E H, E I,
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              <note position="right" xlink:label="note-0128-03" xlink:href="note-0128-03a" xml:space="preserve">a</note>
            & </s>
            <s xml:id="echoid-s3727" xml:space="preserve">ſecent E I, E H menſuram, & </s>
            <s xml:id="echoid-s3728" xml:space="preserve">E G ſecet rectum in L.
              <lb/>
            </s>
            <s xml:id="echoid-s3729" xml:space="preserve">Dico, quod E G eſt maximus ramorum egredientium ex E
              <unsure/>
            ad
              <lb/>
            ſectionem A B C, & </s>
            <s xml:id="echoid-s3730" xml:space="preserve">ramorum inter A H cadentium propin-
              <lb/>
            quiores illi, maiores ſunt remotioribus, & </s>
            <s xml:id="echoid-s3731" xml:space="preserve">E I eſt maximus ra-
              <lb/>
            morum egredientium ad ſectionem H C, & </s>
            <s xml:id="echoid-s3732" xml:space="preserve">illi propinquiores
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            maiores ſunt remotioribus.</s>
            <s xml:id="echoid-s3733" xml:space="preserve"/>
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