ORDINATES

, in the Geometry of Curve Lines, are right lines drawn parallel to each other, and cutting the curve in a certain number of points.

The parallel Ordinates are usually all cut by some other line, which is called the absciss, and commonly the Ordinates are perpendicular to the abscissal line. When this line is a diameter of the curve, the property of the Ordinates is then the most remarkable; for, in the curves of the first kind, or the conic sections and circle, the Ordinates are all bisected by the diameter, making the part on one side of it equal to the part on the other side of it; and in the curves of the 2d order, which may be cut in three points by an Ordinate, then of the three parts of the Ordinate, lying between these three intersections of the curve and the intersection with the diameter, the part on one fide the diameter is equal to both the two parts on the other side of it. And so for curves of any order, whatever the number of intersections may be, the sum of the parts of any Ordinate, on one side of the diameter, is equal to the sum of the parts on the other side of it.

The use of Ordinates in a curve, and their abscisses, is to define or express the nature of a curve, by means of the general relation or equation between them; and the greatest number of factors, or the dimensions of the highest term, in such equation, is always the same as the order of the line; that equation being a quadratic, or its highest term of two dimensions, in the lines of the 2d order, being the circle and conic sections; and a cubic equation, or its highest term containing 3 dimensions, in the lines of the 3d order; and so on.|

Thus, y denoting an Ordinate BC, and x its absciss AB; also a, b, c, &c, given quantities: then is the general equation for the lines of the 2d order; and is the equation for the lines of the 3d order; and so on.