64 INVESTIGATION of fome 
circle, twice the fum of their cubes will be equal to2NX -~ 
Gs’ +2r.GS +2Nx 6rx Se, that is, equal to twice a 
multiple by the number of the fides of the figure of the cube on 
the fide of the infcribed decagon, together with four times a mul-. 
tiple, by the fame number of the folid which has the fquare of 
the fide of the decagon for its bafe, and 7 for its altitude, toge- 
ther with thrice a multiple by the fame number of the folid, 
which has the fquare of GP for its bafe, and 7 for its alti- 
tude. 
In like manner, may the fixth powers of lines earatiat from the 
angles of any regular infcribed figure of a greater number of 
fides than three, to any point either in, or not in the circumfer- 
ence, be exprefled in terms of the fide of an infcribed decagon, 
fince their fum is a multiple of the fum of the cubes of the ‘per- 
pendiculars, to the fides of the circumfcribing figure, by 8 73. 
Acain, fince r+ GS: 7r::7:GS:: GS:r—GS, we have 
2r+GS:r+GS::r+GS:r::r:GS::GS:r—Gs. 
eee er eae ee 
WHEREFORE 37 -4+ 2G5 2 pas =4X2r-+Gs, or 
26 r3 + 517°. GS + 337. GS +7G6S = 3273+ 487.GS + 
247. GS £65", for 37°. GS 97. GS + 3GS = 67°, or 
r-GS+ 37r-GS + co ego 
WueEreErorg, fince four times the fum of the cubes of the 
perpendiculars drawn from any point in the circumference of 
the circle to the fides of any regular circumfcribing figure, is 
NX.5 X27; four times the fum of thefe cubes is = N X 
g7r.GS+ 157. Gs +5GS = SN X77, Go + 37. GS +GS’;; 3 
that 
