422 A Demonstration of 
Again, if in the diameter of a circle 
DH, two points F, G be taken such that 
FD:FH:: DG : GH, and from the 
points F and G, be inflected to any point 
of the circumference E, two lines FE, 
GE meeting the same again in h and bh’. 
8 Then Fh: FE:: Gh’: EG. Which is 
the eighth Proposition. 
Perpendicular to FE, draw Ee, cutting 
the diameter in c, and the circlein e ; then 
the angle EcF = FEf = FgG, and heE 
= h’H’E = FE; .-. h’ e is parallel to FH, 
9 and Fh = Fh’: FE : : Gh’: EG: :ce 
Ec. Which is the ninth Proposition. 
and H, and from the point G be drawn GK the same side 
of DG as F is of the diameter AB to make the angle DGK 
equal to the angle CFE, and let the line GK meet the cirche 
in L and the line CF in M; then I say that GM : ML:: 
GD: DH. 
Prop. XI. If from any point C in the diameter of a 
circle produced a perpendicular be raised and from any 
point D in the same a line be drawn to cut the circle in E 
and F; then I say the rectangle EDF is equal to the rect- 
angle ACB together with the square of CD. 
Prov. XII. If from any point C in the diameter of a 
circle produced a perpendicular be raised and thereon CD 
be taken whose square is equal the rectangle ACB, and CE 
be put equal CD, and from any point in DE as H a line 
be drawn to cut the cirele in Fand G; then I say twice the 
