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-div329" type="section" level="1" n="109">
          <p style="it">
            <s xml:id="echoid-s3517" xml:space="preserve">
              <pb o="84" file="0122" n="122" rhead="Apollonij Pergæi"/>
            propoſitum deduci, nam duo rami D
              <lb/>
              <figure xlink:label="fig-0122-01" xlink:href="fig-0122-01a" number="103">
                <image file="0122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-01"/>
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            C, & </s>
            <s xml:id="echoid-s3518" xml:space="preserve">D N poſiti infra ſingularem
              <lb/>
            breuiſecantem D B efficiunt cum re-
              <lb/>
              <note position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">I em. 10.</note>
            ctis tangentibus ſectionẽ angulos ver-
              <lb/>
            ticem reſpicientes acutos; </s>
            <s xml:id="echoid-s3519" xml:space="preserve">igitur vt
              <lb/>
            in ſecunda parte propoſitionum 64.
              <lb/>
            </s>
            <s xml:id="echoid-s3520" xml:space="preserve">& </s>
            <s xml:id="echoid-s3521" xml:space="preserve">65. </s>
            <s xml:id="echoid-s3522" xml:space="preserve">demonſtratum eſt, eritramus
              <lb/>
            D N vertici propinquior minor re-
              <lb/>
            motiore ramo D C.</s>
            <s xml:id="echoid-s3523" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3524" xml:space="preserve">Et centro D, interuallo D O
              <lb/>
            circulus deſcriptus ſecabit ſectio-
              <lb/>
            nem exempli gratia in Q (56. </s>
            <s xml:id="echoid-s3525" xml:space="preserve">ex
              <lb/>
              <note position="right" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">g</note>
            5.) </s>
            <s xml:id="echoid-s3526" xml:space="preserve">& </s>
            <s xml:id="echoid-s3527" xml:space="preserve">iungamus, &</s>
            <s xml:id="echoid-s3528" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3529" xml:space="preserve">Videtur om-
              <lb/>
            nino expungenda citatio in textu appoſita; </s>
            <s xml:id="echoid-s3530" xml:space="preserve">(56. </s>
            <s xml:id="echoid-s3531" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3532" xml:space="preserve">nam circulum O Q ma-
              <lb/>
            nifeſtum eſt, ſecare coniſectionem alicubi, vt in Q, cum radius D O poſitus
              <lb/>
            ſit minor D B, & </s>
            <s xml:id="echoid-s3533" xml:space="preserve">maior D N; </s>
            <s xml:id="echoid-s3534" xml:space="preserve">poſtea, quia D Q propinquior eſt vertici A,
              <lb/>
            quàm D N, & </s>
            <s xml:id="echoid-s3535" xml:space="preserve">omnes rami à D ad peripheriam ſectionis N Q ducti, effici-
              <lb/>
              <note position="left" xlink:label="note-0122-03" xlink:href="note-0122-03a" xml:space="preserve">Lem. 10.
                <lb/>
              Coroll.
                <lb/>
              64. 65.
                <lb/>
              huius.</note>
            unt cum ſuis tangentibus angulos, verticem reſpicientes, acutos; </s>
            <s xml:id="echoid-s3536" xml:space="preserve">igitur D Q mi-
              <lb/>
            nor eſt, quàm D N, quod eſt abſurdum; </s>
            <s xml:id="echoid-s3537" xml:space="preserve">poſita enim fuit D O, ſeu ei æqualis
              <lb/>
            D Q, & </s>
            <s xml:id="echoid-s3538" xml:space="preserve">D P maior, quàm D N.</s>
            <s xml:id="echoid-s3539" xml:space="preserve"/>
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        <div xml:id="echoid-div337" type="section" level="1" n="110">
          <head xml:id="echoid-head151" xml:space="preserve">COROLLARIVM PROPOSIT.
            <lb/>
          LXVII.</head>
          <p style="it">
            <s xml:id="echoid-s3540" xml:space="preserve">A Ngulorum à ramis ſecantibus, qui à cõ-
              <lb/>
              <figure xlink:label="fig-0122-02" xlink:href="fig-0122-02a" number="104">
                <image file="0122-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0122-02"/>
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            curſu ad coniſectionem duci poſſunt,
              <lb/>
            cum tangentibus ab eorum terminis ductis cõ-
              <lb/>
            præhenſorum, ſi vnus tantnm rectus fuerit,
              <lb/>
            reliqui omnes verticem reſpicientes acuti; </s>
            <s xml:id="echoid-s3541" xml:space="preserve">ra-
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            mi proximiores vertici ſectionis, minores erũt
              <lb/>
            remotioribus.</s>
            <s xml:id="echoid-s3542" xml:space="preserve"/>
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            <s xml:id="echoid-s3543" xml:space="preserve">Ex eo enim, quod in propoſitione 67. </s>
            <s xml:id="echoid-s3544" xml:space="preserve">om-
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            nes rami D A, D L, D C, & </s>
            <s xml:id="echoid-s3545" xml:space="preserve">reliqui om-
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            nes, qui duci poſſunt ex concurſu D ad ſectio-
              <lb/>
            nem A B C, cum tangentibus ſectionem à ter-
              <lb/>
            minis A, L, C compræhenderunt angulos ver-
              <lb/>
            ticem reſpicientes D A V, D L G, D C P
              <lb/>
            acutos, & </s>
            <s xml:id="echoid-s3546" xml:space="preserve">tantummodo vnus D B I rectus fuit
              <lb/>
            oſtenſus eſt ramus D A minor, quàm D L, & </s>
            <s xml:id="echoid-s3547" xml:space="preserve">D L vertici A propinquior, mi-
              <lb/>
            nor, quàm D B, atq; </s>
            <s xml:id="echoid-s3548" xml:space="preserve">D B minor quolibet remotiore D C.</s>
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