The first step is to find an expression for the distances λ, μ, of the centre of the oval from the guides. These distances are to be found separately, beginning with λ.

For this purpose it is indifferent whether we consider the oval as moving in contact with the guides, or whether we consider the guides as variable tangents moving round the circumference of the oval. On the latter supposition, the extremity of λ is evidently the locus of the foot of the perpendicular on the tangent of the oval, whose equation is given in the title.