t . 



r — o^ 



Tî»2f5 



et hinc, singulis prodactis in factorcs simpllces resolutis, 

 Q'^'^'sin'mcosnm^i [sin (tt -f- u) m ^s\n(^ — n) m) 



— TT {sin (ir—o: H-n)m •♦- sin (tt — 2 — fi)m] 

 '"+" ^^â-^^iK-TT— 4-4-«)mH- sin (tt — 4 — /z)m] 



— etc. 



Comparatis deinde difierentialibus hujus seiici quartis, octa- 

 Vis, duodecimis etc., «rît 



1 , 3 . 3 . . if . 3 m'"' ' ■ 



(tt -H »2)''~*s.in(7r -h n)m -f- (TT—n)"^" 'sin(7r—n)m 

 TT [(tt — 2 H- /i)'^'~ ' sin (t — 2 -(- /?) >« 

 •4- (tt — 2 — n)"^" sin(7r— 2 — n)m] 

 •— .... 3..^.. ^ '-^♦^'^^:~U^~4-^") sin(7r-4H-/2)m S 



H- (tt— 4— •«)''""'sin(7r— 4 — «)«?] 

 ■ ^ , : ' - — - [(t — 6 H- n) sin'(7r — 6 -f «)m 

 H- (tt — 6 — ;/)'^~'sin'(7f— "6 — ;2)?JîjH-etc., 

 efTîin'C facîli negotio dedncitiir, posito t m ?i., 



sin/!C :=: sinnm ^- Yt^'^t^ 4- 0'" — sin (?i — i)m] 

 -f- 7"-"^a [(/i-4-2)sin(nH-2)»i — 2nsinnm-4^(»i — 2)sin(a— 2)7M] 

 TiEî S ('H-'3)'sin(/i4-3)iM — 3 (h— i>'sin(/i-f- i)m; 

 ""^3^' ^ -f- 3 (/V^ r)^ sin(n-i)m - (n- 3}* sin (n- 3) w^ 

 -f- etc. 

 IV. Substitmis niinc valôribns inventis quantitatis e 

 *(ex N°. II.) et sin »e'(ex N^ IJI.) , m acquatiône iS'o. L, 

 joullo fere negotio habebitar : 



