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

13. dat AB, ſinum totum partium 100000. quid dabit BD, 5? inueniemusq́
ſinum BD, 38461. vt hic vides.

468.1.

337-01
19. primi.
17. primi.
Scholium
13. ſecundi.
9. huius.
AB. # AB. # BD. # # BD.
13. # 100000. # 5? # fit. # 38461.

Ex tabula ergo ſinuum dabitur angulus BAD,
grad. 22. Min. 37. atq; adeo eius complementum
B, grad. 67. Min. 23. qui eſt vnus angulorum quę-
ſitorum. Rurſus, quia poſito AC, ſinu toto, CD,
ſinus eſt anguli CAD, dicemus iterum per regu-
lam auream. Si AC, 20. dat AC, 100000. ſinum
totum, quid dabit CD, 16? Inueniemuſq; ſinum
CD, 80000. Vt hic patet.

468.1.

338-01
AC. # AC. # CD. # # CD.
20. # 100000. # 16? # fit # 80000.

Qui ſinus in tabula ſinuum monſtrat angulum
CAD, grad. 53. Min. 8. ac proinde eius comple-
mentum C, erit grad. 36. Min. 52. qui eſt vnus
etiam angulorum quæſitorum. Quòd ſi duo an-
guli duorum ſinuum inuentorum, nempe grad. 22. Min. 37. & grad. 53. Min. 8. ſimul componantur, fiet tertius angulus BAC, grad. 75. Min. 45. Vel cer-
te ſi ſumma duorum angulorum B, C, inuentorum ex grad. 180. auferatur,
reliquus fiet tertius angulus BAC, grad. 75. Min. 45.

468.1.

Praxis.

ITAQVE, (vt totam praxim complectamur) ſi fiat, vt maximum
latus (in quod perpendicularis ducta eſt) ad ſummam aliorum duorum,
ita differentia eorundem duorum ad aliud, reperietur numerus, qui ex
maximo latere ſubductus relinquet numerum, cuius ſemiſſis dabit minus
ſegmentum baſis, hoc autem ex baſi detractum relinquet maius ſegmen-
tum, vt conſtat ex ſecunda praxi propoſ. 9. Quòd ſi rurſum fiat, vt mi-
nimum latus ad ſinum totum, ita ſegmentum baſis minus ad aliud, inue-
nietur ſinus, cuius arcus complementum dabit angulum ſupra baſim me-
dio lateri oppoſitum. Deinde ſi rurſum fiat, vt medium latus ad ſinum
totum, ita maius ſegmentum baſis ad aliud, reperietur ſinus, cuius ar-
cus complementum dabit angulum ſupra baſim minimo lateri oppoſitum. Tertius vero angulus maximo lateri oppoſitus conflabitur ex duobus il-
lis arcubus duorum ſinuum inuentorum: vel certè relinquetur poſt de-
tractionem duorum angulorum inuentorum ex duobus rectis.

RVRSVS in poſteriori triangulo datum ſit latus AB, 11. AC, 13. & BC, 20. Demiſſa in maximum latus BC, perpendiculari AD, inuenietur
ſegmentum BD, 8 {4/5}. at CD, 11{@/5}. vt hic apparet ſecundum praxim poſte-
riorem propoſ. 9.

BC. # AB. AB. # Differ. inter # AB, AC.
20. # 24. # 2? # fit # 2 {2/5}.

Hic numerus ex baſe 20. ablatus relinquit 17 {3/5}. cuius ſemiſsis 8 {4/5}. dat ſeg-
mentum minus BD. Ergo maius CD, erit 11 {1/5}. Hinc inuenietur angulus

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