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

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[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)
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            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.
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              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-
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            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
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            ad peripheriam C B G. </s>
            <s xml:id="echoid-s3956" xml:space="preserve">Poſtremò, quia ramorum cadentium inter breuiſecan-
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            tem E G, & </s>
            <s xml:id="echoid-s3957" xml:space="preserve">remotiorem verticem A axis maioris, vnicus tantũ E G efficit cum
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              <note position="right" xlink:label="note-0135-03" xlink:href="note-0135-03a" xml:space="preserve">29. 30.
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              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">
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            A efficiunt cum ſuis tangentibus angulos, reſpicientes verticem A remotiorem,
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              <note position="right" xlink:label="note-0135-04" xlink:href="note-0135-04a" xml:space="preserve">I em. 12.
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              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
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            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
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            breuiſecans E G vtrumque axim abſcindens maximus eſt omnium ex E caden-
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            tium ad ſemiperipheriam ellipſis C B A, & </s>
            <s xml:id="echoid-s3965" xml:space="preserve">ramus E C, vt in præcedenti dictũ
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            eſt, minimus erit omnium, atque propinquiores maximo ex eadem parte maio-
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            res erunt remotioribus, & </s>
            <s xml:id="echoid-s3966" xml:space="preserve">cadentium ad peripheriam C B G minimo C E pro-
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          <head xml:id="echoid-head163" xml:space="preserve">Notæ in Propoſit. LXXV.</head>
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            <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-
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            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-
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            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-
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            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>
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            <s xml:id="echoid-s3981" xml:space="preserve">Quoniam I K, N M ſunt duæ breuiſſimæ conſtat, quod E I maximus ſit
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            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-
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            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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