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(15) 4 to 9 is duplicate of the ratio 2 to 3. For 2/3 x 2/3 = 4/9. So aa/b" is duplicate of a/b. And the ratio a/b is said to be underline subduplicate /underline of the ratio aa/bb/

72. A underline triplicate ratio /underline is that which is compounded of three equal ratios. Thus the ratio of 8/27 is triplicate of ^ addition the /addition ratio 2 to 3. For 2/3 x 2/3 x 2/3 = 8 /27. So deletion unclear /deletion a3/b3 is triplicate of unclear addition a/b /addition & the ratio a/b is said said to be underline subtriplicate /underline if the ratio a3/b3 deletion unclear. /deletion Hence the meaning of underline quadruplicate, quintuplicate, subquadrulicate & subquintuplicate & c. /underline may be understood.

73. In a continued arithmetic proportion the sum of the extremes is double of the mean. Thus in the continued arithmetic