48 INVESTIGATION of fome 
n 1.2.0. u 
Q to the fame, = 33" xm=mnax are x rs When P coin- 
cides with B, Oc is =7, and A++Bt++C+-+ &c. to + 
herons | 
terms, (when 2—1 isa 
terms, + a+ + 4++ c++ &c. to 
multiple of 2 by an even number) 1s = ab aae xX rt; and At+ 
12 
> terms, 
Bi + C++ &c. to - = terms, +a++ 5+-+ &c. to 
BS 
(when n—1 is a multiple of 2 by an odd number) is = 
gn 8 ind 
16 aaa 
In like manner is it demonftrated, that the fum of the fifth 
powers of perpendiculars drawn from P to the fides of any regu- 
lar circumfcribing figure of a greater number 2 of fides than 5, 
is equal to the fum of the fifth powers of perpendiculars drawn 
n2—T 
from Q to the fame; and that AS + B>+ Cs+ &c. to 
a— 
I ; 
terms, — 43 — 65 —cs — &c. to terms, (when ~—1 isa 
5 
multiple of 2 by an even number) is = = and AS-+ Bs+ Cs 
+ &c. to “it terms — a5 — bs — &c. to - 7 3 terms, (when 
: 5 
n—1is a multiple of 2 by an odd number) is = -. 
