Definitions for quadratrix
A curve having ordinates which are a measure of the area (or quadrature) of another curve.
Origin: Latin quadrator, squarer
a curve made use of in the quadrature of other curves; as the quadratrix, of Dinostratus, or of Tschirnhausen
In mathematics, a quadratrix is a curve having ordinates which are a measure of the area of another curve. The two most famous curves of this class are those of Dinostratus and E. W. Tschirnhausen, which are both related to the circle. The quadratrix of Dinostratus was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis. Dinostratus, a Greek geometer and disciple of Plato, discussed the curve, and showed how it affected a mechanical solution of squaring the circle. Pappus, in his Collections, treats its history, and gives two methods by which it can be generated. ⁕Let a helix be drawn on a right circular cylinder; a screw surface is then obtained by drawing lines from every point of this spiral perpendicular to its axis. The orthogonal projection of a section of this surface by a plane containing one of the perpendiculars and inclined to the axis is the quadratrix. ⁕A right cylinder having for its base an Archimedean spiral is intersected by a right circular cone which has the generating line of the cylinder passing through the initial point of the spiral for its axis. From every point of the curve of intersection, perpendiculars are drawn to the axis. Any plane section of the screw surface so obtained is the quadratrix.
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