Jon:

From his statement:
The angle of G1 is set at an angle that exhibits the following:
Half base width times the hypotenuse is equal to the square of the height.

Short form:
A right angle of base times the hypotenuse is equal to the square of the height.
a = base
b = height
c = hypotenuse

b^2 = a.c....1

Pythagoras b^2 = c^2-a^2....2

Sub 1-2, a.c = c^2-a^2.....3

From 3, c^2-a.c-a^2 = 0.....4

From 4, go for it...the rest of his statement is hogwash...!

Best.
Clive