Page 11 - Conclusion. Luckily the angle terms cancel out of the equation for a, and it is indeed shown to be a constant for any particular circle and perspective set up. The unknown curve is shown to be an ellipse.

No assumptions have been made about the distance of the eyepoint from the circle, so this result applies for near (wide angle) or far perspectives. From a greater distance, however, the centre of the ellipse will be closer to the centre of the circle.