4. On the Solution of Perigal's Problem concerning the contact of Epicycloidal Curves

Extract

If the centre of a revolving wheel be carried with a uniform velocity, along a line; and if a tracing-point be fixed to an arm of the wheel, that point will trace out a curved line; to which the general name cycloid or trochoid has been given; the former appellation being often restricted to those cases in which the centre of the wheel moves in a straight line, while the name epicycloid is given when the same centre moves along the circumference of a circle.