ORDINATES, in geometry, are right lines drawn parallel to each other, and cutting the curve in a certain number of points. Parallel ordinates are usually all cut by some other line, which is called an absciss. When this line is a diameter of the curve, the property of the ordi nates is then the most remarkable ; for, in the curves of the first kind, or ,the co nic 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 second order, which may be cut in three points by an ordinate, then of the three parts of the ordinate, lying be tween these three intersections of the curve and the intersection with the di ameter, the part on one side the diame ter is equal to both the two parts on the other side of it. And so for curves of any order, whatever the number of intersec tions 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 oth er 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 be.
tween them ; and the greatest number of factors, or the dimensions of the high est term, in such equation, is always the same as the order of the line ; that equa tion being a quadratic, or its highest term of two dimensions, in the lines of the second order, being the circle and conic sections ; and a cubic equation, or its highest term containing three dimen sions, in the lines of the third order, and so on. Thus, y denoting an ordi nate and x its absciss, also a b c, &c. given quantities : then y= = a x= b x + c is the general equation for the lines of the second order : and x y e y= a cx+dis the equation for the lines of the third order, and so on.