any error involved in the latter theory, it must not only be infinitely small, but must remain infinitely small after all the magnifying processes to which it could possibly be subjected. But there is no error; for, if we suppose that there be an error which we may represent by A, since the aggregate of all the quantities neglected in arriving at the result is infinitely small, that is, as small as we choose, we may choose it to be smaller than A; and, therefore, the error A is greater than the greatest possible error which could be obtained, a manifest absurdity, but one which cannot be avoided as long as A is any thing.

The term direction is introduced into this trea. tise without being defined; but it is regarded as a simple idea, and to be as incapable of definition as length, breadth, and thickness; and this innovation will probably be pardoned, when it is seen how much it contributes to the brevity and simplicity of demonstration, which I have every. where studied.