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 it frequently convenient to use both notations. Herschel, Peacock, and Babbage translated, in 1816, from the French, Lacroix's treatise on the differential and integral calculus, and added in 1820 two volumes of examples. Lacroix's was one of the best and most extensive works on the calculus of that time. Of the three founders of the "Analytical Society," Peacock afterwards did most work in pure mathematics. Babbage became famous for his invention of a calculating engine superior to Pascal's. It was never finished, owing to a misunderstanding with the government, and a consequent failure to secure funds. John Herschel, the eminent astronomer, displayed his mastery over higher analysis in memoirs communicated to the Royal Society on new applications of mathematical analysis, and in articles contributed to cyclopædias on light, on meteorology, and on the history of mathematics.

George Peacock (1791–1858) was educated at Trinity College, Cambridge, became Lowndean professor there, and later, dean of Ely. His chief publications are his Algebra, 1830 and 1842, and his Report on Recent Progress in Analysis, which was the first of several valuable summaries of scientific progress printed in the volumes of the British Association. He was one of the first to study seriously the fundamental principles of algebra, and to fully recognise its purely symbolic character. He advances, though somewhat imperfectly, the "principle of the permanence of equivalent forms." It assumes that the rules applying to the symbols of arithmetical algebra apply also in symbolical algebra. About this time D. F. Gregory wrote a paper "on the real nature of symbolical algebra," which brought out clearly the commutative and distributive laws. These laws had been noticed years before by the inventors of symbolic methods in the calculus. It was Servois who introduced the names commutative and distributive in 1813.