quadratrix

In geometry, a quadratrix () 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 y-coordinates of points on the quadratrix. The property of being an indefinite integral was expressed geometrically, as an equality between the y-coordinates on the first curve and the subnormals of the second, the difference between the x-coordinate of a point on the curve and the x-coordinate of the point where a perpendicular line to the curve crosses the x-axis.