$o INVESTIGATION of fome 



n— i is a multiple of 2 by an odd number. Thus, in the en- 

 neagon, or figure of nine fides, A is the cofine of 20 or the fine 

 of 70°, B is the eofine of 6o° or the fine of 30 , a is the cofine 

 of ioo° or the fine of io% and b is the cofine of 140 ° or the 



fine of 50, and A'" - or - j*. = 2 ~P± X r>\ And if p be 



any even number lefs than n, A p -f- B* -f C> -f &o to - *~" l 



4 

 terms or *8-£ terms + a P _+_ hP _j_ c p + &c tQ «--_i_ terms ^ 

 4 4 



— -I terms, (according as « — 1 is a multiple of 2 by an even 



or odd number) is =a n X T .'.3-5-7-- •/>— 1 x _J^__ _ g£ Con _ 



1.2.3.4...* ^" r " 8 2 



frequently, A> + a /> -f A'" — a m + B> + bP -f B™ — £« -f- &c. to 

 — ; — terms, is~»X •* d ' £ - X -— _ _i_ r — 



* 1. 2.3.4... £ 2-p 2 2 



2 



p-f-2 p+6 p+ IP 



X 



r^ »-** 



2.4. 6 . 



J> /-^ 2 



J T" "t" — (when 



• • 



2^~ * 2 



2 



— I is a multiple of 2 by an even number) e 



/>+2/> + 6 /> -f- *° ^ 2 /> — 2 

 ————— , — — _^_— ... to ' 



1 

 X 7+1, when r =z 1 ; 



2 . 4 . 6 ... to - 22 



2 



and when n — 1 is a multiple of 2 by an odd number A^ -f- A'" 



4. B^-j- B'" -f C> + O" + &c. to ^±-£ terms, -f- a' — of -f. 



4 



^ — b m 



