CHECKING.
In a series of operations. multiplication takes pt•eeedenee over addition and subtraetion. E.g. 2 3 equals 2 18— 4. not 5 • 2. The operation of multiplication can be abbreviated by the use of logarithms (q.v.), the slide rule (q.v.), or tables of products and factors or of quarter squares. The plan of multiplication by means of Napier's rods (llabdologitr sire num( ra lionis per libri duo, Edinburgh, 1617) has been revived through the manufacture of sets of Itegletles ntrltipliedtriecs planned by l&enaille and Lucas I Paris. 1585). Growing out of the demand for a system by which prime numbers could be detected, there appeared, in the seven teenth century. numerous tables, of service in the theory of numbers. In 1728 Poitius pub lished a table of factors for numbers up to 1(10, 000. In 1770 Lambert arranged such a table in modern form for numbers up to 102,000. Burk hardt's table (1814.17) includes factors of num bers to 36,000, and Cloth.. Po-w, and have carried these to 9.000,000. The oldest of the large tables is that of Crelle (7th ed. with an in
troduction by Bremiker, Berlin, 1595). This gives the products to 1000 • 1000. lierhenta fel (Berlin, 1889) and Miller's I/ alfi plicationstabellen 1S!17) give t he products to 100 • and are well arranged. the products to 101) • inn. Ilrrpbr Had georliit isclu• 11illstiifeio 19111 ed.. Hanover. 1895) is one of the best. Products have also been tabulated by means of quarter squares. a relation known to the Arabs and doubt less of Hindu origin. The vonstruction of these tables depends upon the -F b12 — 4 (a — ' • thus the product of any two num hers is given by subtracting the quarter square of their difference from the quarter square of their sum. Among the various tables of this type. Laundy's 1850) contains the quarter nuares of all number. up to 1110.1010. Miter's \ it snag 1ti i. i , complete to 201000, is regarded a. the best. See CALCULATING 1\1.1(111-NES.