270 
NACHLASS. 
±U-!{( n+l -i m ) a ~i s ) 
(2 i) TO_1 sin -*-(a — b) sin \ (a — c) sin £ (a — d)... 
ubi signum superius vel inferius valet, prout m impar est vel par. Quam cum 
parte prima summae S n addendo, sive ab eadem subtrahendo, concludimus fieri 
primo pro valore impari ipsius m partem primam summae \[S n -j- T n ) 
cos ((w +1 — $m) a—s) 
(2 ¿) w_l sin a (a — h) sin £ (a — c) sin | (a — d). . . 
partem primam summae 
sin ({n +1—i m)a — *- s) 
(2 i) m 1 sin* (a — b) sin £ (a — c) sin£ (a — d)... 
secundo pro valore pari ipsius m partem primam summae T n ) 
sin ((n +1 — i'm) a — -J- s) 
2»»-i ¿»¿-s s j n a. ( a — 6) si n ^ ( a — c ) s in4 (a — d)... 
partem primam summae 
— cos ((n +1 — -\yri)a — \ s) 
# £ w y ^ 
Manifesto partes sequentes expressionum ±[S n -\- T n ), —— primae prorsus 
analogae erunt, atque inde per solam commutationem characteris a cum h,c,d... 
orientur. lam designando per k angulum arbitrarium ponendoque n-\-\ — = 
adiumento formularum 
cos(Xa-(-&) = cos (^-)~t 5 ) cos {^ a — ii s ) —sin (£-j—sin [Xa—-%-s) 
sin (Xa-f- k) = cos—|— 4--§■)sin(X— -|-s)-f-sin(A:-|-|-s) cos(Xa — -¡-s) 
haud difficile perveniemus ad summationem serierum sequentium 
cos (X a + k) 
sm \{a—b) sin^(a — c) sin% (a — d). . . 
cos (X b + k) 
sin-*-(6 — a)sin^-(& — c)sin-£(i — d) . . . 
cos (X c -j- k) 
sin J (c — a) sin (c — b) sin {c — d) . . . 
cos (X d + k) 
etc. = U K 
sin-J (d—a)sin£((i—b) sin£(d—c). . . 
atque