62 INVESTIGATION Of Jome 
Ie V be as much on the other fide of the centre G, towards L, 
as it is towards C, the lines GN, GM, exchange their values or 
magnitudes, as alfo do the lines GH, GF; and the perpendicu- 
lars to the fides of the circumfcribing figure then become 
r— GM, r — GH, 7+ GN, 7+ GF, r— GV; and the fum of 
their cubes NX73-+NX 37. ae af EN Giaeis Males 
anys, a3. 1: 7 GD <3 
GH — GV"; which added to N X3-4+N xX aitpracott GM 
Go a Gy 2 EN oe GF yiehe fum of their cubes before 
found, and the aggregate divided by 2, gives N X7r3-++-N X 3r. 
_——2 
ae the fum of their cubes, when D is in the line drawn from 
the centre G perpendicular to LG. 
LET a circle, (Pl. III. Fig. 7.), be defcribed on BC, with the 
centre G, and let BF be a fquare on the diameter BC ; draw EGD 
from E, through the centre G, to meet the circle in D, and join 
DF. 
THEN, fince BG X CS, or CG X CS = Gs, GC is cut in ex- 
treme and mean proportion in the point S, and GS is the fide of 
a regular decagon, infcribed in the circle. And fince the per- 
pendicular from G to the fide of a regular infcribed pentagon, is 
S } ass 
= Bes a G , BS is twice that perpendicular. But et. 
3 = 3 li “a 
an ae —S2 =5. Confequently BS’— GS’, or 7 GS" 
— -GS’=,4r. Therefore 37° = 31° x GS+ 37 x GS» and 
r? 
