Illustration showing the periodic center of motion as it often happens when two positions of a line…

Illustration showing a centroid, "the curve passing through the successive positions of the instantaneous…

"Since these curves are not closed, one pair cannot be used for continuous motion; but a pair of such…

Illustration used to compare the surfaces of a cylinder and a sphere.

Illustration of a cylinder showing, "If a piece of paper is fitted to cover the convex surface of a…

"If two equal ellipses, each turning about one of its foci, are placed in contact in such a way that…

Illustration of the rolling of equal hyperbolas. If two equal hyperbolas are placed so that the distances…

Illustration of the rolling of equal parabolas. "The two parabolas may be considered as two ellipses…

Illustration of an irregular surface abdc projected upon the flat surface ABCD.

"A lens is a transparent body the two refracting surfaces of which are curved, or one of which is curved…

"The shape of the double convex lens, d, c, is that of two plano-convex lenses, placed with their plane…

Illustration showing how a rolling logarithmic spiral can be constructed by taking successive values…

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of…

Illustration of a pentagonal prism showing, "If a piece of paper is fitted to cover the convex surface…

Illustration showing a section of the rolling surfaces by a plane perpendicular to their straight line…

In this illustration, "the driven surface of the slide coincides with the tangent to the spiral, the…