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Gérard Desargues, a seventeenth-century French architect, was one of the early pioneers of projective geometry.

He used the point at infinity to prove a number of important new theorems, but Desargues’s colleagues couldn’t understand his terminology and concluded that Desargues was nuts.

Though a few mathematicians, like Blaise Pascal, picked up on Desargues’s work, it was forgotten.

It has been proved28 that Desargues’s theorem cannot be deduced from axioms 1-5, that is, if the geometry be confined to two dimensions.

This is Desargues’ celebrated theorem if we state it thus:— Theorem of Desargues.—If each of two triangles has one vertex on each of three concurrent lines, then the intersections of corresponding sides lie in a line, those sides being called corresponding which are opposite to vertices on the same line.