Euler's Theorem may be looked upon as the result of a certain operator acting on a special kind of function. This function may depend on any number of variables, but for convenience it is usual to consider three, viz., x, y, z. A function is homogeneous in x, y, z and of the nth degree if it can be put into the form

It is a very convenient method to begin the study of Trigonometry with one or two lessons on Coordinates and the Coordinate Diagram. This leads to a general definition of the Sine and Cosine of any angle which the beginner has little difficulty in comprehending. With the help of the Coordinate Diagram the theorems on projection which are of so much importance can be proved with great precision. It is in such a course that the present proof of the Addition Theorems might find a place.