24 1 



sin n (90 — m) z=z cos n m 

 sin (n — 2) (90 — m) = — cos(n — 2) m 

 sin (n — 4) (90 — m) = cos (n — 4) m 

 sin (n — 6) (90 — m) = — cos (n — 6) m 



etc. 

 unde demum concluditur fore 



dm" 



-^,[fi* 2 cosnm—n (« — 2) n a cos(n — 2) 



m 



-f- n o (n — 4) n s cos (n — 4) m — etc.] 

 et hinc per triplicem ditTerentiationem 



3 ^^- = - 2 n [»*+; ' sin n m - rr (n - 2)"+ ' sin (n- 2) m 

 _j_, z ( n — 4)"" 4 "sin.(» — 4) m — etc.] 



II. Pro altéra quantitate. 

 Multiplicata aequatione supra adhibita 

 2 n cos"x zzz cosnx -\~ n cos(n — 2)x-Hi cos(n — 4)x-+-etc. 

 per 2 . sin x, obtinebitur 



2 n ~ + " cos"xsin x z= [sin(n-f- i)x — sin(n — i)x] 

 -{- n [sin (n — 1) x — sin (n — 3) x] 

 -(- n n [sin (n — 3) x — sin (« — 5) x] 

 -f- etc. 

 unde saepius differentiando et, nti pro prima parte factum. 

 erat, non nisi casum primum, quo n~ 2(2p-f-i), adhi- 

 (bendo , id quod ad expressionem generalem eliciendam 

 •sufficit, facile habcbitur 



Mfmlres de l'Acad. -T '. VI, 3l 



