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

6729Conicor. Lib. V.

SECTIO SEPTIMA

Continens XXVI. XXVII. XXVIII. Propoſ.
Apollonij.

PROPOSITIO XXVI. & XXVII.

ANgulorum ab axi ſectionis A H, & à lineis breuiſſimis F
B, H G contentorum proximiores vertici ſectionis mi-
nores ſunt remotioribus, nempe angulus AFB minor eſt AHG.

44[Figure 44]

SIt itaque centrum D, & ſemi inclinatus axis A D, ſiue ſemitranſuer-
ſus, & dimidium erecti A C: educamus itaque duas perpendiculares
11a GL, BI, & ſi ſectio fuerit parabole, erit FI æqualis LH, quia quælibet
earum æqualis eſt A C (13. ex quinto) & L G maior eſt, quàm BI; an-
22b gulus igitur F minor quàm H; ſi verò ſectio fuerit hyperbole, aut ellipſis,
erit FI ad ID, vt HL ad LD, quia quælibet earum eſt, vt AC ad AD
33c (14. 15. ex quinto) & permutando, erit I D ad L D nempe B I ad M L,
44d vt I F ad L H, & anguli I, & L ſunt recti; igitur duo triangula BIF, M
L H ſunt ſimilia, ideoque angulus A H G maior eſt, quàm angulus A F
B, & hoc erat propoſitum.

PROPOSITIO XXVIII.

Hinc patet, lineas breuiſſimas ſibi occurrere ad partes axis
ſectionis.

QVia angulus AFB minor eſt, quàm angulus AHG; quare ſibi oc-
5526. 27. h.66e currunt ad partes F, H, & hoc erat oſtendendum.

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