in the modern algebra, is used for finding an intermediate term of a series, its place in the series being given. See ALGEBRA and SERIES, Encycl.

The method of interpolation was first invented by Mr Briggs, and applied by him to the calculation of logarithms, &c., in his Arithmetica Logarithmica, and his Trigonometria Britannica; where he explains, and fully applies, the method of interpolation by differences. His principles were followed by Reginald and Mouton in France, and by Cotes and others in England. Wallis made use of the method of interpolation in various parts of his works; as his arithmetic of infinites, and his algebra, for quadratures, &c. The same was also happily applied by Newton in various ways: by it he investigated his binomial theorem, and quadratures of the circle, ellipse, and hyperbola. See Wallis's Algebra, chap. 85, &c. Newton also, in lemma 5, lib. 3, Principia, gave a most elegant solution of the problem for drawing a curve line through the extremities of any number of given ordinates; and in the subsequent proposition, applied the solution of this problem to that of finding, from certain observed places of a comet, its place at any given intermediate time. And Dr Waring, who adds, that a solution still more elegant, on some accounts, has been since discovered by Mr Nichol and Stirling, has also resolved the same problem, and rendered it more general, without having recourse to finding the successive differences. Philos. Intersectant Transf. vol. 60, part 1, art. 7.