The Circle in Homogeneous Coordinates

Extract

1. It is necessary to challenge Mr. F H. V Gulasekharam’s Note 1448 (May, 1940) in which he claims to give simpler methods than usual for dealing with the circle

S ≡ (Σlx)(Σx) − Σa²yz = 0.

Objection must be taken at the very beginning where he says “Suppose the circle cuts the sides of the triangle of reference ABC at D₁D₂” The arguments of §§ 1 and 2 are sound when these points are real, but it is asking too much of a young student to expect him to understand what is meant by the ratios D₁C/BD₁ and D₂C/BD₂ when D₁ and D₂ are imaginary Moreover the writer considers that the arguments of §§ 3 and 4 are not simple but very difficult.