PROPERTIES of the CIRCLE. 59 
equal to the fum of the other two, and fo on; and if, in the 
hexagon, the point D be taken in one of the three diameters, the 
perpendiculars drawn from it to the other two are equal. 
AGAIN, DP’ + DR 4 DS’ +DO +DP=Nxr+3r 
x GH + GM + GV — GN — GF + 37x 
GH +GM +Gv +GN +GF4GH4GM +GV — 
GN GF =Nxr$Nx3r-24 Gr + GM’ + 
Gv — GN’ — GF. But finceN X 7?-+N X37 aa = 
DP + DR’ + DS +DO'+DT GH + GM +GV = 
GN’ + GF. | 
Ir D be in a line perpendicular from G the centre, to a dia- 
meter drawn from any point of contact L, the odd chord GV 
vanifhes, (V coinciding with G), and GN = GM, GH = GF; 
and the expreflion for the fum of the cubes of the perpendicu- 
lars, drawn from D to the fides of the circum{fcribing figure, is 
ae 
D 
fimply NX r3+N x 37x 
Ir the figure circumfcribing the circle be a pentagon, a line 
drawn from G, bifecting the angle QG d nearer to G, is perpendi- 
cular to LG; alfo, if D be in the line G d, the point M coincides 
‘with D, GN = GF, GH = GV, and GM coincides with GD, and 
twice the cube on GF or GN is equal to the three cubes on GD, 
GH, GV, or to the cube on GD with twice the cube on GH or 
‘GY ; and the difference of the cubes on GF, GV, or on GN, GH, 
H2 P is 
