Let a straight line A B be divided internally at C and externally at D in the same ratio, so that (A C)/(C B) = - (A D)/(D B). Then A B is said to be divided harmonically at C and D and the points A C B D are said to form a harmonic range. If C and D divide A B harmonically, then A and B divide C D harmonically. If O is the midpoint of A B, then O B^2 = O C×O D. Hardy uses the term harmonic system of points to refer to a harmonic range.
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