which represents the area BDD´B´. This area is intermediate between those of two rectangles, having as a common base the segment BB´, and as heights the greatest and least ordinates of points on the arc DD´ of the curve. Let these heights be H and h. Then [Delta]A is intermediate between H[Delta][xi] and h[Delta][xi], and the quotient of differences [Delta]A/[Delta][xi] is intermediate between H and h. If the function [f](x) is continuous at B (see Function), then, as [Delta][xi] is diminished without limit, H and h tend to BD, or [f]([xi]), as a limit, and we have Entry: _
Through the points A and B on p draw parallels to p', which cut the projecting rays in C2, D2, B2 and A1, C1, D1, as indicated in fig. 6. The two triangles ACC2 and BCC1 will be similar, as will also be the triangles ADD2 and BDD1. Entry: AC