296

Appendix.

Formnlae analyticae relolutioni triangalorum ſpk aericorum eblquangulorum infer- vientes ad radium= 1 canſtructae. 4, B., C ſant latera, et a, b, anguli his oppoſiti.

Formala gener alis trianguli fphaerici, culus quod-:0 4 vis 152, et quivis angulue 90° Iu pponitur, Signum competens. continens a ad fin. coſ. ſtang. cot.

tria Iatera— coſ. a In. B fin. C 4 † 1 (aMa. angulo 4 B Ca* coſ. B cof. C 9 199 1†+† † tres angulosX. 7 coſ.= cCol. A fin. 5 fin. c 0

Il.(cum latero)*el— coſ, 5 coſ.- † 90 † 18 b+48 †

quatuor par- cot. Alin. C= cot. a ſin. 5 5 5⁷0

III. C(tes aont Bae)45C² X col. C coſ. 5 t 180† 270%[4¼ 1¼

quatuor par- iin. 4 Hn. B—

WV.(An Seenee) Aa B5——([(270t 360 † †

fin. a ſin. 5 — 2——.— S Dantur Quaeritur Asf4ie d iugts e x 3

———

lat. 4B angulus a cof a=(coſ. 4— 26 B cof. C): ſin. B ſin. C 1

5 atus 7 coſ. 4A= coſ, a fin. B fin. 5+ coſ. B coſ. C; vel etiam

44 5 tert m fin. 44A[ün. B fin. C fin. 2+†ß ſin. 2 4(3— C)]

9 2 5 ag—

3 3 BCa 1u. N. 5cot. 5=(cot. B fin. C— coſ. a coſ. C): fin. a

8 8———

g. op.

3 5 15 5 ſcot. e=(cot. C ſin. B— coſ. a coſ. B): ſin, a In.

angulus 8 coſ. 5b ſin. B+† V(fin. 2 B— ſin, ² 5 ün. 2 C)

2 9 com- ſtang. ½2—

, henf a fin. 5 fin.(B+ C)

8 3 Prenen 12l tang. 5 coſ. C= tang. ꝙ; fin. 1. E 9 B tang. C ſin. ꝙ

4 BC5 laine cof. 5 ün. CV(fin. B— ſin.* 5 fin. ²2 C)— 5 beränm A tang. 14— cœoſ. B+. cof. C 5 8 vel, coſ.k Gng. eot. 93 ſin. ee zrtee ꝙ oeſ. B: coſ. O . 90 Ius— —— c fin. ce= ſin. C ün. 5 ſin. B IV. tres— b—— ang, 2bc latus Acoſ. 4=(coſ. a+ coſ. 5 coſ. c): ſin. 5 ſin.

a.———,—— 3 II.

55 angulus 5 coſ. a= coſ. A fin. 5 ſin.— cof. 5 coſ. o; vel etiam

3„ tertius in. Xa== V(ün. 5 fin. c Bn. 244+ coſ. 2 46+ c)]

S8——

a„lat. op.

5 5 ℳ aage 6 Beot. B(cot. b fin.+ coſ. c col. 4): Kn. 4

8—,—

8 8 lat. op.——

8 5 d cl C% cot. C=(cot. c ſin. 5+ coſ. à coſ. 4): fin. 4 III.

a. latus 3 2 coſ. B ſin. 5 tV(fin. 2 ⁵5— ſin. 2 B fin. 2 a2) 3 nmer- Cſtang. 1 C— 5 t ſin. B fin,(a— ³) 8 2 1Cept. el, tang. B coſ. a-=tang., fin.(—&= tung. a cot. P fin. n. S„ a 2 5— n 2

5 E. 4 angulus Hang. F 5 coſ. 8 ün. atY(En 5 bn.: B fin. ² 2) 2

8 ⁸ ertius 5 coſ. 5— cof. a—

5 1* vol, tang. a eoſ. Bcot. ꝙ; fin. P=n. ꝙ coſ. 5: coſ.

5 1—— V 1 datue 4 Hm. Ae Hn. a ün. B: fin. 5 IV.

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