Geometrical MEAN, commonly called a mean proportional, is the square root of the product of the two extremes; so that, to find a mean proportional between two given extremes, multiply these together, and extract the square root of the product. Thus, a mean proportional between 1 and 9, is \sqrt{1 \times 9} = \sqrt{9} = 3; a mean between 2 and 4\frac{1}{2} is \sqrt{2 \times 4\frac{1}{2}} = \sqrt{9} = 3 also; the mean between 4 and 6 is \sqrt{4 \times 6} = \sqrt{24}; and the mean between a and b is \sqrt{ab}.