a42- 



^.jit + i.jn+i.eiî'j !!«« 



= [(«-!- i^'cos^i-f.Ox— (rc— ly+'cosfa— r)rl 

 4_„ ■[(«— i ) ,+, cos (»»— i)x — (/J — Sr^'cos^— 3)x] 

 -f ;z J(/î — 3)." + ' cos (n — 3) x — (;» — 5/" T " ' cos (a — 5) x] 

 -h etc. 



Posito autem x — ço — w, ont - 



cos(/i-hi)x — sin (/z -f- 1 ) m 

 cos (n — 1) x — — sin (n — 1) m 

 gos (n — 3) x rr sin (n — 3) m 

 etc. 



III. Substitutis denique valoribus inventis in aequatione? 





Ezpr [sin" m (t — cos m)J 

 ubi signum 2 indicat , pro 11 ordine naturali ponendos 

 esse numéros o, 1, 2, 3 etc. eiït expressio nostra quaesita,, 

 omnibus scilicet rite reductis;, 



tg t *= '&? (' + e ) tg f -f- O f -7X7n^- * 



(n^iy 1- *" sin(fw-i) m— 2 n n ~*~ T sin nm 

 -(n-i)* +a S in(n— 1) m-t-2 (n-G) 71 " 1 "' sin (n- 2) m 



(n-3) n+2 . £ . sin (»- 3) m - 2 («-4)^' sin(n-4)w 

 _ (n-S)* 4 " 2 . f%£t sin (m- 5) m-t- 2 (n-ô)^' sw(n-6) m 

 |ï (rc-?)"^^??- sin (n-7) m - 2 (11- Bf* sin (n-8) w 

 — etc. 

 nbi n ~ o, i, 2> 3 etc. 



! 

 ) 



