Duplicate Ratio

Duplicate Ratio, of two numbers, means the ratio of their squares. Thus the duplicate ratio of the numbers 5 and 6 is not 5: 6, but 25: 36. The duplicate ratio of two straight lines is the ratio of the areas of the squares described on them. This ratio is of importance in the theory of similar plane figures, for it is proved in geometry that the ratio of the areas of two such figures is equal to the duplicate ratio of any corresponding linear dimensions. If one square has its diagonal twice as great as that of another square, its area will bo four times that of the second. If the diameters of two circles are in the ratio of 3 to 4, their areas will be in the ratio of 9 to 16. The same r.ljle applies to any pair of similar plane figures. In the case of similar solids we find their volumes are in the triplicate ratio of corresponding linear dimensions - i.e. proportional to their cubes. Thus, if the diameters of two globes are in tl.c ratio of 1 to 2, their volumes will be as 1 to 8.