185 



which in numberi5 gives OI, the supplemental chord of twice the 

 arch subtended by the side of the Polygon, = 



+ V |(s/34— Syr? + v'n — 1)1— i (^/34+2v/^7^^/ 17—1) = 

 (by reduction ^ (\/34— Sv^iT+^/rr— l) 



+i«/l7+3v/r7— n/34— 2v'17— 2\/34h-2^/T7=AR : 

 but by a well known Theorem, " If the supplemental chord of an 

 " arch be encreased by the number 3, ("the radius being unity) the 

 " square root of the sum will be the supplemental chord of half 

 " that arch," and hence 



AP =2+|-(^/ 34— 2^17+^17— 1) 



+7^17+3^/17— v/34—2v^T7—V3*+2^17, 

 and therefore 



KP' ( = AK— AP) = 2— l-Cv/34— 2^iT+ yi?— 1 ) 



~~i\Jl7+3^T7—^S4>—2Vr7 — 2y34+2v'r7 = 

 I ( 1 7— y 17— v/34— 2 v/ 17 — 

 2 Y 1 7 + Sy 17— ^34— 2 V 17— 2v/34+2 v^ r7), 



er 



KPrr V^K17— v/17— v'34--2v/17 



— 2vl 7 +3\/ 17— v'34— 2v/T7— 2v'34+2v/r7), 

 which, reduced to numbers, gives KP or AN, the side of the poly- 

 gon:^ .367499035633, &c. 



VOL. XIII. C C 



