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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[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
[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)
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            niam, ſuperpoſita axi C H ſuper axim A G,
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            <s xml:id="echoid-s5559" xml:space="preserve">vt in textu habetur. </s>
            <s xml:id="echoid-s5560" xml:space="preserve">Si enim axis C H
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            ſuper axim A G applicatur, ita vt vertices A,
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            C coincidant, neceſſariò ſectio C D cadet ſu-
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            <s xml:id="echoid-s5562" xml:space="preserve">Præterea ponamus duas ſectiones æqua-
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            les, & </s>
            <s xml:id="echoid-s5563" xml:space="preserve">C F æqualis A E, &</s>
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            <s xml:id="echoid-s5565" xml:space="preserve">Textum cor-
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            ruptum ſic reſtituendum cenſeo. </s>
            <s xml:id="echoid-s5566" xml:space="preserve">Præterea ſup-
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            ponamus, duas illas ſectiones æquales eſſe in-
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            ter ſe, & </s>
            <s xml:id="echoid-s5567" xml:space="preserve">fiat C F æqualis A E, educamus ad
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            axes perpendiculares B E, D F, &</s>
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            <s xml:id="echoid-s5569" xml:space="preserve">Sic enim
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            <s xml:id="echoid-s5571" xml:space="preserve">Ergo ſectio A B cadit ſuper ſectionem.
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            C D, & </s>
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            <s xml:id="echoid-s5574" xml:space="preserve">alioqui eſſent ſe-
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            <s xml:id="echoid-s5577" xml:space="preserve">Quoniam (ex hypotheſi) ſectio-
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            <s xml:id="echoid-s5580" xml:space="preserve">Dico iam, axim A
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            E cadere ſuper axim C F: </s>
            <s xml:id="echoid-s5581" xml:space="preserve">alioquin in eadem parabola, ſcilicet in duabus pa-
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            rabolis ſibi congruentibus à communi vertice C, vel A, duo axes A E, & </s>
            <s xml:id="echoid-s5582" xml:space="preserve">C F
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            ducerentur: </s>
            <s xml:id="echoid-s5583" xml:space="preserve">quod eſt impoſſibile. </s>
            <s xml:id="echoid-s5584" xml:space="preserve">Quare axis A E cadit ſuper axim C F.</s>
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          <head xml:id="echoid-head228" xml:space="preserve">Notæ in Propoſit. II.</head>
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            <s xml:id="echoid-s5586" xml:space="preserve">SI fuerint figuræ duarum ſectionem hyperbolicarum, aut duarum elli-
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            pſium, vt duo plana G I, H K in A B, D E ſimiles, & </s>
            <s xml:id="echoid-s5587" xml:space="preserve">æquales;
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            <s xml:id="echoid-s5588" xml:space="preserve">vtique duæ ſectiones æquales erunt: </s>
            <s xml:id="echoid-s5589" xml:space="preserve">ſi vero duæ ſectiones ſint æquales
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            earum figuræ erunt æquales, ſimiles, &</s>
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            <s xml:id="echoid-s5591" xml:space="preserve">In duabus ſectionibus A B, & </s>
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            D E ſumi debent figuræ G I, & </s>
            <s xml:id="echoid-s5593" xml:space="preserve">H K, non qualeſcunque, ſed illæ, quæ ad axes
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            fiunt, nimirum debent eſſe G A, & </s>
            <s xml:id="echoid-s5594" xml:space="preserve">H D axes inclinati, ſeu tranſuerſi, & </s>
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            I, atque D K eorum latera recta; </s>
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            <s xml:id="echoid-s5603" xml:space="preserve">Cumque G I, H K ſint duæ figuræ ſimiles, & </s>
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            <s xml:id="echoid-s5607" xml:space="preserve">Quia rectangula
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            <s xml:id="echoid-s5609" xml:space="preserve">quare duo rectangula I P, & </s>
            <s xml:id="echoid-s5610" xml:space="preserve">K R
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            ſimilia ſunt duobus rectangulis G I, H K inter ſe ſimilibus; </s>
            <s xml:id="echoid-s5611" xml:space="preserve">& </s>
            <s xml:id="echoid-s5612" xml:space="preserve">ideo illa inter
              <lb/>
            ſe quoque ſimilia erunt, & </s>
            <s xml:id="echoid-s5613" xml:space="preserve">habent latera homologa æqualia, illa nimirum, quæ
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            opponuntur æqualibus abciſsis A L, & </s>
            <s xml:id="echoid-s5614" xml:space="preserve">D N, igitur rectangula P I, & </s>
            <s xml:id="echoid-s5615" xml:space="preserve">R </s>
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