THEORIA INTERPOLATIONIS METHODO NOVA TRACTATA. 
315 
in casu tertio 
L cos -|-|u a cos cos — L sh+pacos(A: + £)pa cotgpa cos £ \icc 
-|- L sin p a cos (k + -f) p a cosec p a cos 4- \ioc 
quae expressio in omnibus tribus casibus reducitur ad 
L sin (k +1) ¡a a cos \'x — L sin k\xa cos (fx — X') x 
sin|>. a 
Quoties autem = 0, habemus in X' simpliciter Lcosk\xa, qui termi 
nus sine variatione in X" retinetur. 
33. 
Sit secundo X functio formae 
Ì)'sin<2?-f-?)"sin2a?"sin3a? + etc. + l5 w sinnx 
unde esse debebit p — n. Hic fit, ex art. 30, coefficiens ipsius A in formula 
secunda art. 16 pro T 
— —^— X ^ (sinua+ 2 sin(p—l)acos i4- 2 sin(p— 2)acos 2 i4- etc. 
[a sm [x a sm a V ^ 1 V1 ' 1 M ' 1 
+ 2 sin a COS (jU — l)t) 
= - s ~/ (2 cos (p — 1 ) a sin t 2 cos (p— 2)a sin 21-\- 2 cos (p— 3) a sin 3 i+ etc. 
+ 2 cos a sin (p—1 ) t -j- sin p t ) 
Prorsus similes expressiones pro coefficientibus ipsorum B, C, D etc. prodeunt, 
mutato tantummodo arcu a in 6, c, d etc. Quamobrem faciendo 
C = 1A cos (p—1 )a -j- B cos (p—1)6-J- Ccos(p—1)c + jDcos (p—l)d + etc. | 
C" = - gi ^ a j A cos (fi—2)a + i?cos(p—2) b -f- Ceos (p—2)c + Hcos (p—2)c? —j— etc. j 
C"' = j A cos (p—3)a + J5cos(p—3)6+ (7cos(p—3)c + X)cos(p—3)d + etc.j 
etc. 
^~ 1 = —-1A cos a + B cos 6 + C cos c + D cos d + etc. j 
^=Ur>+ £ +P+i>H-etc.| 
erit 
T = C'sini + C"sin 2/ + C"'sin3i + etc. + C |X sinpi 
Quum haec formula generaliter pro valore quocunque ipsius t valeat, necessario 
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