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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 treatise 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 everywhere studied.
[The figures in parentheses refer to the articles.]
Vertical and adjacent angles (23, 24),
Sum of angles about a point (25, 26),
Plane figure, polygon, and its perimeter (43); triangle, quadri-
Greater side of a triangle opposite the greater angle (62),
THE CIRCLE AND THE MEASURE OF ANGLES,
PROBLEMS RELATING TO THE FIRST EIGHT CHAPTERS,
A line parallel to one side of a triangle divides the other two
Intersections of lines drawn through the vertex of a triangle