Elliptic Trammels and Fagnano Points

Extract

22. To obtain a Fagnano pair of points on an ellipse whose axes are given, it may be considered sufficient to construct the corresponding Fagnano quadrilateral. That is, having drawn the line hk (Fig. 14) with the points p and z marked, and having described a circle on hk as diameter, it is only necessary to draw through z some chord c₁c₂ and to join the sides of the quadrilateral c₁hc₂k.