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
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82

215177Conicor. Lib. VI.

PROPOSITIO XVI.

SI ſectiones A B, C D ſimiles inter ſe, quæ ſint prius para-
bolæ, tangant lineæ A E, C F terminatæ ad earum axes
E B, F D, & contineant cum illis angulos æquales E, F, &
in qualibet earum educantur ordinationes G H, I K ad diame-
tros L A M, N C O tranſeuntes per puncta contactus axibus

239[Figure 239] æquidiſtantes, & fuerit proportio ſuarum abſciſſarum A M, C
O ad lineas tangentes A E, C F eadem; vtique ordinationes
abſcindent ex ſectionibus ſimilia ſegmenta, & ſimiliter poſita, vt
G A H, I C K. Si verò ordinationes ſecuerint ſimilia ſegmen-
ta; vtique ſectiones ſimiles erunt, & abſciſſarum ad lineas tan-
gentes proportio erit eadem, atque lineæ tangentes continebunt
cum axibus angulos æquales.

Educamus enim duas B L, D N ſuper duos axes B E, F D perpendi-
culares, quæ tangent ſectiones in B, D: & ponamus A P ad duplam A
1132. lib. 1. E, vt R A aſſumpta ad A L ei ſimilem, nec non C Q ad duplam C F,
vt aſſumpta S C ad C N; igitur P A, Q C ſunt erecti duarum diametro-
rum L M, N O (52. ex 1.) ergo G M poteſt P A in A M, (12. ex 1.)
2249 lib. 1.& ſimiliter I O poteſt O C in C Q, (12. ex 1.) & propter æquidiſtan-
3311. lib. 1.
lbidem. tiam E B, L A, atque F D, C N ſunt ſimilia E R B, R L A, atque D
S F, S N C; & duo anguli E, F ſuppoſiti ſunt æquales; igitur angulus R
A L æqualis eſt S C N, & N, L ſunt recti; quare R A ad A L, nempe
P A ad duplam A E eſt, vt S C ad N C, nempe vt Q C ad duplam
C F, & M A ad A E ſuppoſita eſt, vt O C ad C F: ergo M A ad A P
eſt, vt O C ad C Q, & angulus O æqualis eſt M. Oſtendetur igitur (vt
44a

Page concordance

Text layer

Text normalization

Search

Scan	Original
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82

Scan	Original
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82

Scan	Original
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
111	73
112	74
113	75
114	76
115	77
116	78
117	79
118	80
119	81
120	82