If three quantities are in continued proportion; show that the ratio of the first to third is duplicate ratio of first to the second.

Let x, y and z be in continued proportion. ∴ x : y = y : z To prove : Substituting y 2 = xz in R.H.S. of above equation we get, = L.H.S. Hence, proved that ratio of the first to third is duplicate ratio of first to the second.