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

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13512311
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
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.

IAM vero ſinum arcus grad. 12. beneſicio ſinuum grad. 30. & 54. qui iam
22Supputatio
ſinus arcus
grad. 12. noti facti ſunt, ita inueſtigabimus. Sit in quadrā

131[Figure 131] 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-
3334. primi. 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
4434. primi. 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,
5547. primi proptereaque & ipſarecta DE, nota erit, nem pe chorda arcus grad. 24. Hinc
& eius medietas nota erit, nimirum ſinus rectus arcus grad. 12. continebitque
66Ex duorũ
arcuũ ſinu
bus notis
notus quo-
que ſit ſinꝰ
medietatis
differentiæ
arcuum. 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.

CaeTervm ex ſinu arcus grad. 12. (ſi hunc arcum bifariam ſecemus
77Supputatio
ſinuu ar-
cuum Mi-
nutis 45. ſe
ſe ſupeian-
tium. 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.
88
## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
G # M # # G # M # # G # M # # G # M
12 # 0 # 2079117 # 42 # 0 # 6691306 # 12 # 45 # 2206974 # 33 # 0 # 5446390
78 # 0 # 9781476 # 48 # 0 # 7431448 # 77 # 15 # 9753423 # 57 # 0 # 8386706

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