Excerpt from Barlow's Tables of Squares, Cubes, Square Roots, Cube Roots, Reciprocals, of All Integer Numbers Up to 10, 000
The squares and cubes of all numbers under 1250 were of course examined as above described, and the square and cube roots by halving, &c., the proper roots of numbers above 1250. An error of a unit in the last place can therefore hardly exist in this part of the table, though it is barely po~sible in numbers not much below 1250. The reciprocals of numbers between 1000 and 1250 were examined by second differences, and those from 1 to 999 by the reciprocals of the corresponding decade.
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