Full text: Bithynius, Theodosius: Theodosii Tripolitae Sphaericorum libri tres

ſtum eſt, ſinum grad. 54. hoc eſt. 8090170. componi præciſe ex ſinubus grad. 18. & 30. hoc eſt, ex 3090170. & 5000000. Et quia ſinus grad. 30. æqualis eſt ſemiſ-
ſi ſinus totius, vt ſupra oſtenſum eſt, liquet ſinum grad. 54. componi ad vngué
ex ſemiſſe ſinus totius, & ſinu recto grad. 18. Id quod propoſ. 6. à nobis eſt de-
monſtratum.

166.1.

Supputatio
ſinuum at-
cuum gra-
dibus 2.
Min. 15. ſe-
ſe ſuperan
tiũ, & alio-
rum quorũ
dam.
## 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
## 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
24 # 45 # 4186597 # 56 # 15 # 8314696 # 87 # 45 # 9992290 # 75 # 0 # 965925
27 # 0 # 4539905 # 58 # 30 # 8526402 # 3 # 45 # 654031 # 82 # 30 # 9914449
9 # 15 # 4886212 # 60 # 45 # 8724960 # 7 # 30 # 1305262 # 86 # 15 # 9978589
31 # 30 # 5224986 # 63 # 0 # 8910065 # 15 # 0 # 2588190 # 90 # 0 # 10000000

IAM vero ſinum arcus grad. 12. beneſicio ſinuum grad. 30. & 54. qui iam
noti facti ſunt, ita inueſtigabimus. Sit in quadrā
te ABC, arcus BD, grad. 30. & BE, grad. 54. at-
que adeò arcus DE, eorum differentia, grad. 24. ducanturque rectæ DF, EG, ad AB, perpendi-
culares, quæ ſinus recti erunt arcuum BD, BE; Item rectæ DH, EI, ad AC, perpendiculares,
quæ finus recti erunt arcuum CD, CE, grad. 60. & 36. qui complementa ſunt arcuum BD,
BE. Secet autem recta DH, rectam EG, in K. Et quoniam ſinus DF, hoc eſt, KG, illi æqua-
lis, & EG, noti ſunt; erit quoque eorum diffe-
rentia EK, nota. Similiter quia ſinus EI, hoc
eſt, KH, illi æqualis, & DH, noti quoque ſunt, per propof. 3. cum ſint ſinus
complementorum arcuum BE, BD; erit etiam eorum differentia DK, nota; ac proinde duo quadrata rectarum notarum Ek, DK, nota erunt: quæ cum
æqualia ſint quadrato rectæ DE, notum quoque erit quadratum rectæ DE,
proptereaque & ipſarecta DE, nota erit, nem pe chorda arcus grad. 24. Hinc
& eius medietas nota erit, nimirum ſinus rectus arcus grad. 12. continebitque
particulas 2079117. Hac eadem arte; ſi duorum arcuum quorumcumque ſinus
cogniti ſint, cognoſcetur etiam ſinus medietatis differentiæ illorum arcuum. Vt ſi ſinus arcuum BD, BE, quorumcumque etiam ſi non contineant grad. 30. & 54. noti ſint, erunt & ſinus complementorum CD, CE, per propof. 3. noti. Quare, vt modo demon ſtrauimus, nota ſiet chorda DE; ac proinde eius me-
dietas nota quoque erit, nempe ſinus medietatis arcus DE.

166.1.

Supputatio
ſinus arcus
grad. 12.
135-01
34. primi.
34. primi.
47. primi
Ex duorũ
arcuũ ſinu
bus notis
notus quo-
que ſit ſinꝰ
medietatis
differentiæ
arcuum.

Cae Tervm ex ſinu arcus grad. 12. (ſi hunc arcum bifariam ſecemus
continue, quoad poſſumus, medietatumq́; complementa accipiamus, vnà cum
ſinu complementi arcus grad. 12. quæ rurſus ſecemus bifariam continue, & c.) reperiemus per coroll. propof. 4. & per propoſ. 3. ſinus omnium hor um arcuũ,
qui in hac tabella continentur. Quos ſinus ſi cum ſinubus proxime antece-
dentis tabellæ in ordinem redigamus, habebimus ſinus arcuum numero 120.

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