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

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134122 adeo & quadratum rectæ BF, quod illis duobus æquale eſt, cognitum erit; cu-
1147. primi. ius radix quadrata notam reddet rectam BF: quæ cũ fubtendat grad. 72. in cir
culo ABC, vtpote quintam partem circunferentiæ, quòd ſit latus pentago-
ni, nota erit chorda arcus grad. 72. cuius medietas partium 5877852. dabit ſi-
num rectum arcus grad. 36. qui illius dimidium eſt.

PORRO ex hoc ſinu arcus grad. 36. inueniemus, per propof. 3. ſinum eius
22Supputatio
ſinuum at-
cuum gra-
dibus 2.
Min. 15. ſe-
ſe ſuperan
tiũ, & alio-
rum quorũ
dam. complementi, hoc eſt, ſinum arcus grad. 54. Quos duos arcus ſi biſariam fece-
mus, eorumq́ue medietates rurſus bifariam, & ita deinceps, donec ad minuta
numero imparia veniamus, quæ amplius diuidi nequeunt, reperiemus quoque
per coroll. propof. 4. harum medietatum ſinus, nec non, per propoſ. 3. ſinus ea-
rum complementorum: quæ complementa ſi rurſus bifariam ſecemus, quoad
poſſumus, & harum medietatum complementa accipiamus, quæ rurſus ſece-
mus bifariam, & c. inueniemus eodem modo ſinus omnium ar cuum in hac ta-
bella contentorum. Quos ſinus ſi cum præcedentibus hactenus inuentis in or-
33
## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
G # M # # G # M # # G # M # # G # M
36 # 0 # 5877852 # 12 # 15 # 392598 # 40 # 30 # 6494480 # 15 # 45 # 2714405
54 # 0 # 8090170 # 87 # 45 # 9992290 # 49 # 30 # 7604060 # 74 # 15 # 9624552
18 # 0 # 3090170 # 27 # 0 # 4539905 # 20 # 15 # 3461171 # 38 # 15 # 6190940
72 # 0 # 9510565 # 63 # 0 # 8910065 # 69 # 45 # 9381913 # 51 # 45 # 7853169
9 # 0 # 1564345 # 13 # 30 # 2334454 # 42 # 45 # 6788007 # 24 # 45 # 4186597
81 # 0 # 9876883 # 76 # 30 # 9723699 # 47 # 15 # 7343225 # 65 # 15 # 9081432
4 # 30 # 784591 # 6 # 45 # 1175374 # 31 # 30 # 5224986 # 29 # 15 # 4886212
85 # 30 # 9969173 # 83 # 15 # 9930665 # 58 # 30 # 8526402 # 60 # 45 # 8724960
dinem redigamus, habebimus ſinus rectos omnium arcuum ſeſe ordine ſupe-
rantium gradibus 2. & Min. 15. initio facto ab arcu grad. 2. Min. 15. vſque ad
arcum grad. 87. Min. 45. incluſiue; & inſuper ſinus aliorum 17. arcuum, qui
non ſeruant huiuſmodi incrementum. Vt in hac tabella appparet. Vbi manife
44
## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
G # M # # G # M # # G # M # # G # M
2 # 15 # 392598 # 33 # 45 # 5555702 # 65 # 15 # 9081432 # 18 # 45 # 3214395
4 # 30 # 784591 # 36 # 0 # 5877852 # 67 # 30 # 9238795 # 26 # 15 # 4422887
6 # 45 # 1175374 # 38 # 15 # 6190940 # 69 # 45 # 9381913 # 30 # 0 # 5000000
9 # 0 # 1564345 # 40 # 30 # 6494480 # 72 # 0 # 9510565 # 37 # 30 # 6087614
11 # 15 # 1950903 # 42 # 45 # 6788007 # 74 # 15 # 9624552 # 41 # 15 # 6593458
13 # 30 # 2334454 # 45 # 0 # 7071068 # 76 # 30 # 9723699 # 48 # 45 # 7518398
15 # 45 # 2714405 # 47 # 15 # 7343225 # 78 # 45 # 9807853 # 52 # 30 # 7933533
18 # 0 # 3090170 # 49 # 30 # 7604060 # 81 # 0 # 9876883 # 60 # 0 # 8660254
20 # 15 # 3461171 # 51 # 45 # 7853169 # 83 # 15 # 9930685 # 63 # 45 # 8968727
22 # 30 # 3826834 # 54 # 0 # 8090170 # 85 # 30 # 9969173 # 71 # 15 # 9469301

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Scan	Original
101	89
102	90
103	91
104	92
105	93
106	94
107	95
108	96
109
110
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118

Scan	Original
101	89
102	90
103	91
104	92
105	93
106	94
107	95
108	96
109
110
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118

Scan	Original
101	89
102	90
103	91
104	92
105	93
106	94
107	95
108	96
109
110
111	99
112	100
113	101
114	102
115	103
116	104
117	105
118	106
119	107
120	108
121	109
122	110
123	111
124	112
125	113
126	114
127	115
128	116
129	117
130	118