286 
NACHLASS. 
resp. mutantur in 
vel in 
Tunc erit 
a, 
A, 
b, 
B, 
c, 
a 
d, 
D 
etc. 
c, 
c, 
d, 
D, 
e. 
f 
F 
etc. 
d, 
D, 
e. 
F, 
/ 
F, 
9. 
G 
etc. 
etc. 
A — - 
A — B 
sin £ (a — b) ’ 
B’ = . 
sin£(6 — c) ’ 
C' = y 
C—D 
etc. 
sin — d) 
J5'cos£(5 — d)— C 
A" 
A" 
A 
A' 
etc 
sin a (a — c) ’ 
A"cos£(a — c) + .4'sin(a— c) —B " 
B"' = 
sin£(6— d) 
B"cos${b — d) + B'smi{h—d)—C" 
sin-La — d) 
sin -k{b — e) 
A'"cos £ [a — e) — B 
B"" = 
B'"coH{h-f)-C" . 
sin \ (a — e) 
• /7 ^ • 
sm i (b —/) 
A!'"cos a (a — e) + -4 "'sin £ (a — e)— B "" 
11 
K| 
B ""cos${b-f) + B '"sin {(b—f)—C "" 
sin i (a—/) 
sin £ (h — g) 
A v cos \{a — g) — B y 
II 
ici 
B y cos x {b-h)-C y 
sin i[a — g) 
sin f (a — h) 1 
etc. 
Lex formationis hic satis obvia est, si modo observetur, numeratores in valori- 
bus pro A", A", A"’, A v , A n etc. (valor pro A ab hac regula excipiendus est) 
alternis vicibus e duabus vel tribus partibus constare. 
13. 
Theorema. Si X est functio arcus x formae (F) 
oc-|-a'cos 1 r-j-of , cos 2;r-|-ft w cos 3o?+ etc. 
-f-ö'sin#-j-6"sin2£c-|-6'"sin3 ( 27-l- etc. 
vel huius formae [G) 
y COS-^-j-V 008 %-X-\~Y cosf x-\~ e ^ c - 
-f-Ssin^o?-]-8'sin|-a?+ 8"sin-jf-a?-f- etc, 
positoque x — a, valor functionis X fit — 0: erit X divisibilis per sinj {x— a), 
quotiensque in casu priore formae G, in posteriore formae F. 
Demonstratio. Casus prior. Si in functione X pro quavis parte cos n x 
substituitur cos nx—cos na, pro quavis parte sin na? autem sin no?—sin na,