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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[41.] MONITVM.
Page: 50 (12)
[42.] LEMMA I.
Page: 51 (13)
[43.] LEMMA II.
Page: 52 (14)
[44.] LEMMA III.
Page: 53 (15)
[45.] LEMMA IV.
Page: 53 (15)
[46.] SECTIO TERTIA Continens VIII. IX. X. Propoſ. Apollonij.
Page: 54 (16)
[47.] PROPOSITIO IX. & X.
Page: 56 (18)
[48.] Notæ in Propoſitionem VIII.
Page: 57 (19)
[49.] Notæ in Propoſitionem IX. & X.
Page: 59 (21)
[50.] SECTIO IV. Continens Propoſit. VII. & XII. Apollonij.
Page: 62 (24)
[51.] NOTÆ.
Page: 63 (25)
[52.] SECTIO QVINTA Continens XI. Propoſit. Apollonij.
Page: 64 (26)
[53.] NOTÆ.
Page: 64 (26)
[54.] SECTIO SEXTA Continens Propoſit. XIII. XIV. XV. Apollonij.
Page: 65 (27)
[55.] NOTÆ.
Page: 66 (28)
[56.] SECTIO SEPTIMA Continens XXVI. XXVII. XXVIII. Propoſ. Apollonij. PROPOSITIO XXVI. & XXVII.
Page: 67 (29)
[57.] PROPOSITIO XXVIII.
Page: 67 (29)
[58.] NOTÆ.
Page: 68 (30)
[59.] LEMMA V.
Page: 68 (30)
[60.] LEMMA. VI.
Page: 69 (31)
[61.] LEMMA VII.
Page: 69 (31)
[62.] SECTIO OCTAVA Continens Prop. IL. L. LI. LII. LIII. Apoll.
Page: 70 (32)
[63.] PROPOSITIO IL. & L.
Page: 71 (33)
[64.] PROPOSITIO LI.
Page: 72 (34)
[65.] PROPOSITIO LII. LIII.
Page: 73 (35)
[66.] PROPOSITIO LIV. LV.
Page: 77 (39)
[67.] PROPOSITIO LVI.
Page: 77 (39)
[68.] PROPOSITIO LVII.
Page: 78 (40)
[69.] Notæ in Propoſit. IL. L.
Page: 78 (40)
[70.] Notæ in Propoſit. LI.
Page: 79 (41)
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8143Conicor. Lib. V. 58[Figure 58]
Et ſimili modo conſtat, quod breuiſſima egrediens ex puncto L cadit
11f extra S L, & c. Ad vitandam confuſionem figuræ, & prolixitatem demonſtrationis
appoſui duas figuras, in quibus duo caſus ijſdem caracteribus notantur, itaque abſq;
nouo labore, ſi inſpiciatur ſecunda figura, ijſdem verbis prioris caſus, oſtendetur ca-
ſus ſecundus.
Pariter demonſtrabitur, quemadmodum iam oſtenſumeſt, & c. Pars ſecun-
22g da huius propoſitionis innuitur tantummodo pauciſsimis verbis; quare maioris cla-
ritatis gratia integram demonſtrationem hìc afferre libuit.
Demonſtratio ſecundæ partis.
PROPOSITIONIS LI.
Eſto E D æqualis trutinæ H: Dico ex concurſu E vnicum tantùm breui-
ſecantem ramum duci poſſe.
In eadem ſigura, quia ex conſtructione H ad B G eſt, vt G F ad F D, ponitur verò
E D æqualis H; ergo E D ad B G, ſeu D I ad I G (propter ſimilitudinem triangulo-
rum E D I, B G I) eſt, vt G F ad F D, & componendo D G ad G I eſt, vt eadem G D
ad D F; ideoque I G æqualis eſt D F, ſeu A C ſemierecto; igitur B I eſt breuiſsima.
338. huius.
Poſte a ducto quolibet ramo E K ſupra breuiſecantem E B (in prima figura, & in-
fra in ſecunda) occurrente axi in R, & ducta K M perpendiculari ad axim, quæ eum
ſecet in M, & tangentem O B in P. Quoniam (vt dictum eſt) O F ſecatur

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