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

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133121 coroll. propof. 4. ex ſinu recto cuiuſuis arcus noto cognoſcitur quoque ſinus
rectus dimidij illius arous; cognofcemus ex ſinu a rcus grad. 15. ſinum arcus
grad. 7. Min. 30. Atque ex hoc ſinum arcus grad. 3. Min. 45. qui arcus amplius
bifariam ſecari non poteſt ſine Secundis, (continet enim eius medietas grad. 1.
11Supputatia
ſinuum ac-
cuum gta-
dibus 3.
Min. 45. ſe-
ſe ſupetan-
tium. Min. 52. Sec. 30.) quæ in Sinuum tractatione negliguntur. Deinde quia per pro
poſ. 3. ex ſinu recto cuiuſlibet arcus cognito notus quoque efficitur ſinus
complementi illius arcus, cognoſcemus ex ſinu arcus grad. 7. Min. 30. ſi-
num arcus grad. 82. Min. 30. Ex hoc autem, per coroll. propoſ. 4. ſinum ar-
cus grad. 41. Min. 15. Atque ex hoc, per propof. 3. ſinum arcus grad. 48. Min.
45. Item ex ſinu arcus gra. 3. Min. 45. cognoſcemus, per propoſ. 3. ſinum arcus
grad. 86. Min. 15. Quòd ſi alij arcus, quorum ſinus in uenti funt, bifariam quo
que fecentur, & eorum medietates rurſus bifariam, & ita deinceps, donec ad
Minuta numero imparia, quæ amplius bifariã diuidi ſine Secundis nequeunt,
peruentum ſit; Itemque harum medietatum complementa accipiantur, quæ
rurſus, eodem modo continue bifariam ſecẽtur, donec ad Minuta numero im-
paria ſit peruentum; & medietatum complementa ſumantur, & c. cognoſce-
mus, per coroll. propoſ. 4. & per propof. 3. ſinus omnium harum medieta-
tum, & complementorum. Qui ſinus cum illis ſex primò inuentis conſtituent
ſinus 24. arcuum fefe ordine ſuperantium gradibus 3. Min. 45. vt in hac ta-
bula vides.

22
## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
G # M # # G # M # # G # M # # G # M
3 # 45 # 654031 # 26 # 15 # 4422887 # 48 # 45 # 7518398 # 71 # 15 # 9469301
7 # 30 # 1305262 # 30 # 0 # 5000000 # 52 # 30 # 7933533 # 75 # 0 # 9659258
11 # 15 # 1950903 # 33 # 45 # 5555702 # 56 # 15 # 8314696 # 78 # 45 # 9807853
15 # 0 # 2588190 # 37 # 30 # 6087614 # 60 # 0 # 8660254 # 82 # 30 # 9914449
18 # 45 # 3214395 # 41 # 15 # 6593458 # 63 # 45 # 8968727 # 86 # 15 # 9978589
22 # 30 # 3826834 # 45 # 0 # 7071068 # 67 # 30 # 9238795 # 90 # 0 # 10000000

POST hæc, per ea, quæ propof. 2. de inuentione lateris Decagoni, & pen-
33Supputatio
ſinus arcus
grad. 36. tagoniæquilateri in eodem circulo demon ſtrauimus, inquiremus ſinum arcus
grad. 36. hac ratione. Repetatur figura propoſitionis 2. vbi demonſtratum eſt,
DF, eſſe latus Decagoni, & BF, latus

130[Figure 130] Pentagoni ęquilateri. Et quoniam qua-
drata rectarum BD, DE, notarum (Eſt
enim BD, ſinus totus, & DE, eius me-
dietas.) nota ſunt, & æqualia quadrato
4447. primi. rectæ EB; notum erit quadratum rectæ
EB; ac propterea & ipſa recta EB, hoc
eſt, recta EF, illi æqualis, nota erit, nem
pe partium fere 11180339. Ex qua ſi
detrahatur recta ED, medietas ſinus to
tius partiũ 5000000. nota fiet recta DF,
partium 6180339. cuius quadratum ſi addatur quadrato ſinus totius BD, no
tum fiet aggregatum quadratorum ex rectis DF, BD, deſcriptorum;

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Scan	Original
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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
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