Quadratrix
In geometry, a quadratrix (from Latin quadrator 'squarer') is a curve that can be used for quadrature, constructing the area under another curve.
For instance, in integral calculus as developed by Gottfried Wilhelm Leibniz, the quadratrix of a curve (the graph of a function) was another curve, the graph of its indefinite integral: the area under the first curve could be constructed from the -coordinates of points on the quadratrix. The property of being an indefinite integral was expressed geometrically, as an equality between the -coordinates on the first curve and the subnormals of the second, the difference between the -coordinate of a point on the curve and the -coordinate of the point where a perpendicular line to the curve crosses the -axis.
Certain specific curves are called a quadratrix. The two most famous curves of this class are the quadratrix of Hippias and the quadratrix of E. W. Tschirnhaus, which can be used for squaring the circle, the construction of a square with the area of a given circle.