Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

Scan	Original
51	39
52	40
53	41
54	42
55	43
56	44
57	45
58	46
59	47
60	48
61	49
62	50
63	51
64	52
65	53
66	54
67	55
68	56
69	57
70	58
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68

5139 circunferentias vero maximorum circulorum inter parallelos, nempe A E,
B F, C G, D H, æquales eſſe. Sintenim communes ſectiones circuli A I C, &
parallelorum rectæ A C, E G, quæ parallelæ erunt: communes vero ſectiones
1116. vndec. circuli B I D, & parallelorum eorundem, rectæ B D, F H, quæ ſimiliter pa-

57[Figure 57] rallelæ erũt. Et quia circuli maximi A I C,
B I D, per polos parallelorum deſcripti ſe-
cant parallelos bifariam; erunt A C, B D,
2215. 1. huius. diametri circuli A B C D, & punctum L, vbi
ſe interſecant, centrũ eiuſdem: Item E G,
F H, diametri circuli E F G H, & punctum
K, vbi ſe interſecant, centrum eiuſdẽ. Quo
niam igitur rectæ E K, K F, rectis A L, L B,
parallelæ ſunt, ſuntq́; in diuerſis planis, e-
runt anguli E K F, A L B, ad centra K, L,
3310. vndeo. æquales. Quare circunſerentiæ A B, E F,
per ea, quæ in ſcholio propoſ. 33. lib 6. Eu-
clid. oſtendimus, ſimiles erunt. Eodemq́;
modo ſimiles erunt B C, F G, & C D, G H, nec non D A, H E.

RVRSVS, quia rectæ ex polo I, ad puncta A, B, C, D, demiſſæ æquales
ſunt, ex defin. poli, erunt quoque arcus I A, I B, I C, I D, æquales: Et eo-
4428. tertij. dem modo æquales erunt arcus I E, I F, I G, I H. Reliquæ igitur circunfe-
rentiæ A E, B F, C G, D H, æquales inter ſe erunt. Quapropter, ſi ſint in
ſphæra paralleli circuli, & c. Quod erat demonſtrandum.

THEOR. 11. PROP. 11

5516.

SI in diametris circulorum æqualium æqua-
lia circulorum ſegmenta ad angulos rectos inſi-
ſtant, à quibus ſumantur æquales circunferentiæ,
quarum quælibet inchoata ab extremitate ſui ſe-
gmenti, ſit minor ſemiſſe circunferentiæ integri
ſegmenti, à punctis autem æquales circunferen-
tias terminantibus ducátur æquales rectæ lineę ad
circunferentias circulorum primo poſitorum; ip-
ſæ circulorum primo poſitorum circunferentiæ
interceptæ inter illas rectas lineas, & extremitates
diametrorum, erunt æquales.

Page concordance

Text layer

Text normalization

Search

Scan	Original
51	39
52	40
53	41
54	42
55	43
56	44
57	45
58	46
59	47
60	48
61	49
62	50
63	51
64	52
65	53
66	54
67	55
68	56
69	57
70	58
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68

Scan	Original
51	39
52	40
53	41
54	42
55	43
56	44
57	45
58	46
59	47
60	48
61	49
62	50
63	51
64	52
65	53
66	54
67	55
68	56
69	57
70	58
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68

Scan	Original
51	39
52	40
53	41
54	42
55	43
56	44
57	45
58	46
59	47
60	48
61	49
62	50
63	51
64	52
65	53
66	54
67	55
68	56
69	57
70	58
71	59
72	60
73	61
74	62
75	63
76	64
77	65
78	66
79	67
80	68