Hello, sjenkins!

We must show that . form a geometric progression.Descartes pointed out that the curves: .

intersect in a point such that and are the two mean proportionals

between and . .Show this.

From [1], we have: .

Substitute into [2]: .

Square both sides: .

. .

Disregarding the trivial solution, we have: .

Substitute into [3]: .

The progression is: .

. . The common ratio is: .