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

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

446Apollonij Pergæi

PROPOS. III.

9[Figure 9]

SI verò in ellipſi cadat B G infrà cen-
trum, poterit duplum differentię duo-
rum triangulorum D A F, & D G H, nem-
pè duplum plani G L. Et hoc erat pro-
poſitum.

Notæ in Propoſitionem primam.

VOcat in primo libro interpres ſectiones habentes centrum hyperbolem, &
ellipſim, & vocat erectum latus rectum ſectionis, vocat etiam ordina-
tionem axis eam, quam nos ordinatim ad axim applicatam appellamus.

Quia BG poteſt comparatum applicatum ad abſciſſam AG, & c. Vocat
11a inſuper parallelogrammum comparatum applicatum ad axis abſciſſam A G re-
ctangulum ipſum A G I, quod quidem adiacet lateri recto A E latitudinem ha-
2212. 13. lib.
primi. bens abſciſſam A G excedens in hyperbola, & deficiens in ellipſi rectangulo ſi-
mile ei, quod latere recto, & tranſuerſo continetur; ſcilicèt rectangulo C A E.

10[Figure 10]

Et planum G F dimidium eſt illius comparati, & c. Non erit inutile
33b paulo fuſius oſtendere id quod ob nimiam facilitatem Apollonius tantummodò in-
nuit. Ducatur recta linea F K parallela axi D A ſecans ordinatam B G produ-
ctam in K: quia figuræ latera C A, & A E ſunt ipſarum D A, A F duplicia
ergo C E, & D F H parallelæ ſunt, eſtque K H parallela A E, cum ambo poſitæ
ſint perpendiculares ad axim, & C A, F K ſunt quoquè æquidiſtantes, ergò
triangulum F K H ſimile eſt triangulo C A E, & proptereà parallelogramma
rectangula F K H, & C A E ſimilia erunt. Et quoniam quadratum ordinatæ
44Ibidem. B G æquale eſt rectangulo contento ſub latere recto E A, & abſciſſa A G

Page concordance

Text layer

Text normalization

Search

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72