let "d′" be a curve congruent to "c′" and let "d′" roll without slipping, as in the definition of a roulette, on "c′" so that "d′" is always the reflection of "c′" with respect to the line to which they are mutually tangent. then when the curves touch at "r′" the point corresponding to "p" on the moving plane is "x", and so the roulette is the pedal curve. equivalently, the orthotomic of a curve is the roulette of the curve on its mirror image.