# Arithmetic-mean Sentence Examples

Mention may also be made of his chapter on inequalities, in which he proves that the

**arithmetic mean**is always greater than the geometric mean.These theorems, which hold for the motion of a single rigid body, are true generally for a flexible system, such as considered here for a liquid, with one or more rigid bodies swimming in it; and they express the statement that the work done by an impulse is the product of the impulse and the

**arithmetic mean**of the initial and final velocity; so that the kinetic energy is the work done by the impulse in starting the motion from rest.In the latter case the two sections are taken at distances t 2H/ A l 3 = = 2887H from the middle section, where H is the total internal length; and their

**arithmetic mean**is taken to be the mean section of the cask.The significance of the word "mean," i.e., middle, is seen by considering 3 instead of n quantities; these will be denoted by a, b, c. The

**arithmetic mean**b, is seen to be such that the terms a, b, c are in arithmetical progression,.The proper statement is that, if a and b are the sides, the area is equal to the area of a rectangle whose sides are a and tb; this being, in fact, a particular case of the proposition that the area of a trapezium is equal to the area of a rectangle whose sides are its breadth and the

**arithmetic mean**of the lengths of the two parallel sides.