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‎An Essay towards the calculus of functions. Communicated by W.H. Wollaston. Read June 15, 1815. (+) An essay towards the calculus of functions. Part II. Communicated by W.H.Wollaston. Read March 14, 1816. (2 Papers).‎

‎(London, W. Bulmer and Co., 1815 and 1816). 4to. No wrappers as extracted from ""Philosophical Transactions"" 1815 - Part I. and 1816 - Part II. Having both titlepages to the parts. Pp. (2),389-446 and (2),179-256. First titlepage with a stamp on verso. Otherwise fine and clean.‎

‎First printings of Babbage's main mathematical contributions.""Babbage's major Contribution to mathematics was his calculus of functions, which he became interested in as early as 1809 and continued to develop during his years at Cambridge. Babbage presents his major ideas on the subject in the above two papers, published in the ""Philosophical Transactions"" in 1815 and 1816. ""It can be said with some assurance that no mathematician prior to Babbage had treated the calculus of functions in such systematic way...Babbage must be given full credit as the inventor of a distinct and importent branch of mathematics"" (Dubbey 1978, 90). Elsewhere Dubby states that his new scheme would serve as a generalized calculus to include all problems capable of analytical formulation, and it is possible to see here a hint of the inspiration for his concept of THE ANALYTICAL ENGINE. While the work on the engines and his other scientific, social and political activities caused him virtually to abandon mathematical research at the age of thirty, the calculus of functions was the area he often yearned to continue. In fact the calculus of functions was not taken up by other workers, and it is the aspect of Babbage's mathematical work that modern mathematicians find most fascinating (Dubbey 1989, 18-19)."" (Hook a. Norman No. 19).Charles Babbage, William Herschel and George Peacock founded in 1810 in Cambridge the ""Analytical Society"", at Trinity College in order to reform the notation and the teaching of mathematics in England, introducing Leibniz' differential notation instead of Newton's fluxions. The continental texts and papers then became accessible to English students.‎