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

Table of contents

< >
[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
[101.] PROPOSITIO LXXII.
Page: 115 (77)
[102.] MONITVM.
Page: 116 (78)
[103.] LEMMA IX.
Page: 116 (78)
[104.] LEMMA X.
Page: 116 (78)
[105.] LEMMA XI.
Page: 117 (79)
[106.] Notæ in Propoſ. LXIV. & LXV.
Page: 117 (79)
[107.] Notæ in Propoſ. LXVI.
Page: 120 (82)
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
Page: 120 (82)
[109.] Notæ in Propoſ. LXVII.
Page: 121 (83)
[110.] COROLLARIVM PROPOSIT. LXVII.
Page: 122 (84)
[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
< >
page |< < (84) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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"/>
              </figure>
            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"/>
          </p>
        </div>
        <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"/>
              </figure>
            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-
              <lb/>
            mi proximiores vertici ſectionis, minores erũt
              <lb/>
            remotioribus.</s>
            <s xml:id="echoid-s3542" xml:space="preserve"/>
          </p>
          <p style="it">
            <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-
              <lb/>
            nes rami D A, D L, D C, & </s>
            <s xml:id="echoid-s3545" xml:space="preserve">reliqui om-
              <lb/>
            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>
            <s xml:id="echoid-s3549" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum