On tablets with tables of reciprocals the signs are arranged in two columns. At first glance, it appears that the numbers in column i on the left, all less than sixty, all factors of some power of 60, when multiplied by values in the right column, yield a product of 60 or a power of 60 (for example, 2 . 30 = 60; 3. 20 = 60). However, there is another way to explain the use of this table. The reciprocal of column i (1/x where x's are the values in column 1) is equal to the value in column ii on the right (y) divided by 60, or an appropriate power of 60, or y/60n, where n = 1,2, 3 , . . . . Thus, 1/x = y/60n or ½. 60 = 30.

Column ii therefore gives the reciprocals of column i. If one thinks of time and angle; that is, hours/minutes, degrees/seconds, the meaning is clear: 1/2 hour = 1/2 . 60 minutes...