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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