46 INVESTIGATION of fome 



terms, — a> — fo — &c. to — — terms, =; - . Thus, in the 



4 2 ' 



.4 



heptagon A + B — a = - , A* -f B* + a* = $— ; and A' -f B 3 — 



2 4 



# 3 = — . In the enneagon A -{- B — a — b = - , A a +■ B a + *' 



+ b l = 2£ an a A3 + B 3 — -a* — £J as - 3 , and fo on. But in 

 4 2 



the enneagon, A is the cofine of 20°, or the fine of 70% B is the 



fine of 30 == -, a is the fine of io°, and b the fine of 50°. 

 2 



Wherefore the fine of 70 * r= fine of io° -f the fine of 50 ; the 

 fquare of the fine of 70 ° -f- fquare of the fine of io° + fquare 



of the fine' of 50° = ^~ » an d the cube of the fine of 70 ° — 



2 



cube of the fine of io° — cube of the fine of 50 — ^rr, viz. 

 thrice the cube of half the radius. And fo on. 



r^Oc 4 — r*-~ 4^x0^ + 6/ xOc —^rxCk* 4* Oc\ 



a —3 1 



fZjQa = r* — 4r'xO^+ 6r*xOtf — 4 rX Oa +0«, 

 7=0| 4 = r+ — 4 r 3 x O k -f 6 r* X Ok — 4 r X O? + <3* 4 > 

 rFo2»* = r4+4/3X0*-+6r 1 -x6A , + 4'"X0i 3 + O^, 

 r+OJ 4 = r4-j- 4 r3XO^+ 6r*x0^ a + 4r x6df 3 + 0^ 4 , 



Sum = 5r+4-6r i X(^+(^+6i+C^ i 4-05 i 4-0^V^V0^+05 4 



But 



