The method of quarter-squares is a multiplication method which makes use of the identity ab = 1 ( (a + b) 4 2 − (a − b) 2) If we possess a table of squares, and wish to compute the product ab, it is then sufficient to compute a + b, a − b, to look up the table for these two values, to subtract the values read in the table, and to divide the result by 4. This seems complex, but for large numbers it is more efficient than to compute directly the product. 1 There have been a number of tables of squares around, in particular those of Ludolf published in 1690 , and those published by Séguin in 1801 and giving the squares up to 10000. But these authors did not have multiplications in mind. At the beginning of the 19th century, the method of quarter-squares was mentioned in passing by Laplace in 1809 [7, p. 261] and Gergonne in 1816 [9, pp. 159–160], but they did not produce tables
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