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-div371" type="section" level="1" n="119">
          <p style="it">
            <s xml:id="echoid-s3950" xml:space="preserve">
              <pb o="97" file="0135" n="135" rhead="Conicor. Lib. V."/>
            rectum, & </s>
            <s xml:id="echoid-s3951" xml:space="preserve">reliqui omnes rami cadentes ſuper totum arcũ G B, conſtituunt cum
              <lb/>
              <note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">Lem. 12.</note>
            ſuis tangentibus angulos acutos, reſpicientes verticem C; </s>
            <s xml:id="echoid-s3952" xml:space="preserve">igitur quilibet ramus
              <lb/>
              <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">Coroll.
                <lb/>
              prop. 67.
                <lb/>
              huius.</note>
            E B propinquior vertici C minor eſt quolibet remotiore ramo E K, & </s>
            <s xml:id="echoid-s3953" xml:space="preserve">E K mi-
              <lb/>
            nor eſt remotiore E G: </s>
            <s xml:id="echoid-s3954" xml:space="preserve">& </s>
            <s xml:id="echoid-s3955" xml:space="preserve">propterea ramus E G maximus eſt omnium cadentium
              <lb/>
            ad peripheriam C B G. </s>
            <s xml:id="echoid-s3956" xml:space="preserve">Poſtremò, quia ramorum cadentium inter breuiſecan-
              <lb/>
            tem E G, & </s>
            <s xml:id="echoid-s3957" xml:space="preserve">remotiorem verticem A axis maioris, vnicus tantũ E G efficit cum
              <lb/>
              <note position="right" xlink:label="note-0135-03" xlink:href="note-0135-03a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            ſua tangente angulum E G N rectum; </s>
            <s xml:id="echoid-s3958" xml:space="preserve">reliqui vero omnes cadentes inter G, & </s>
            <s xml:id="echoid-s3959" xml:space="preserve">
              <lb/>
            A efficiunt cum ſuis tangentibus angulos, reſpicientes verticem A remotiorem,
              <lb/>
              <note position="right" xlink:label="note-0135-04" xlink:href="note-0135-04a" xml:space="preserve">I em. 12.
                <lb/>
              huius.</note>
            acutos; </s>
            <s xml:id="echoid-s3960" xml:space="preserve">igitur (ex Corollario propoſ. </s>
            <s xml:id="echoid-s3961" xml:space="preserve">67. </s>
            <s xml:id="echoid-s3962" xml:space="preserve">huius) ramus E G maior eſt quolibet
              <lb/>
            ramo E O vertici A propinquiore, & </s>
            <s xml:id="echoid-s3963" xml:space="preserve">E O maior eſt, quàm E A: </s>
            <s xml:id="echoid-s3964" xml:space="preserve">quapropter
              <lb/>
            breuiſecans E G vtrumque axim abſcindens maximus eſt omnium ex E caden-
              <lb/>
            tium ad ſemiperipheriam ellipſis C B A, & </s>
            <s xml:id="echoid-s3965" xml:space="preserve">ramus E C, vt in præcedenti dictũ
              <lb/>
            eſt, minimus erit omnium, atque propinquiores maximo ex eadem parte maio-
              <lb/>
            res erunt remotioribus, & </s>
            <s xml:id="echoid-s3966" xml:space="preserve">cadentium ad peripheriam C B G minimo C E pro-
              <lb/>
            pinquiores, minores erunt remotioribus, quod erat oſtendendum.</s>
            <s xml:id="echoid-s3967" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div374" type="section" level="1" n="120">
          <head xml:id="echoid-head163" xml:space="preserve">Notæ in Propoſit. LXXV.</head>
          <note position="left" xml:space="preserve">a</note>
          <p>
            <s xml:id="echoid-s3968" xml:space="preserve">POſtea ducamus ex E tres breuiſecantes E G, E I, E H, & </s>
            <s xml:id="echoid-s3969" xml:space="preserve">ſecent E
              <lb/>
            I menſuram, & </s>
            <s xml:id="echoid-s3970" xml:space="preserve">E G ſecet rectum in L, &</s>
            <s xml:id="echoid-s3971" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3972" xml:space="preserve">Ideſt: </s>
            <s xml:id="echoid-s3973" xml:space="preserve">Poſtea ſi ex concur-
              <lb/>
            ſu E ducti fuerint tres breuiſecantes E G, E I, E H; </s>
            <s xml:id="echoid-s3974" xml:space="preserve">quorum duo E I, E H ſe-
              <lb/>
            cent menſuram in K, & </s>
            <s xml:id="echoid-s3975" xml:space="preserve">M: </s>
            <s xml:id="echoid-s3976" xml:space="preserve">E G vero ſecet axim rectum in L, & </s>
            <s xml:id="echoid-s3977" xml:space="preserve">axim ma-
              <lb/>
            iorem A C in N. </s>
            <s xml:id="echoid-s3978" xml:space="preserve">Dico, &</s>
            <s xml:id="echoid-s3979" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3980" xml:space="preserve"/>
          </p>
          <figure number="119">
            <image file="0135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0135-01"/>
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          <p>
            <s xml:id="echoid-s3981" xml:space="preserve">Quoniam I K, N M ſunt duæ breuiſſimæ conſtat, quod E I maximus ſit
              <lb/>
              <note position="left" xlink:label="note-0135-06" xlink:href="note-0135-06a" xml:space="preserve">b</note>
            ramorum egredientium ad illius ſectionem (52. </s>
            <s xml:id="echoid-s3982" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3983" xml:space="preserve">& </s>
            <s xml:id="echoid-s3984" xml:space="preserve">reliquorum ra-
              <lb/>
            morum propinquior illi, maior eſt remotiore, &</s>
            <s xml:id="echoid-s3985" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3986" xml:space="preserve">Ideſt: </s>
            <s xml:id="echoid-s3987" xml:space="preserve">Quia in </s>
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