EVOLUTE, in the higher geometry, a curve first proposed by Huyghens, and since much studied by mathematicians. It is any curve supposed to be evolved or opened, by having a thread wrapped close upon it, fastened at one end, and beginning to evolve or unwind the thread from the other end, keeping the part evolved or wound off tight stretched; then this end of the thread will describe another curve, called the involute. Or the same involute is described the contrary way, by wrapping the thread upon the evolute, keeping it always stretched. For the INVOLUTION and EVOLUTION of Curves, see INVOLUTION in this Supplement.
Imperfect Evolutes, a name given by M. Reaumur to a new kind of evolute. The mathematicians had hitherto only considered the perpendiculars let fall from the involute on the convex side of the evolute: but if other lines not perpendicular be drawn upon the same points, provided they be all drawn under the same angle, the effect will still be the same; that is, the oblique lines will all intersect in the curve, and by their intersections form the infinitely small sides of a new curve, to which they would be so many tangents. Such a curve is a kind of evolute, and has its radii; but it is an imperfect one, since the radii are not perpendicular to the first curve or involute.