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**"IT IS NOT POSSIBLE TO ASSESS THE IMPORTANCE OF CHARLES BABBAGE WITHOUT AN APPRECIATION OF HIS MATHEMATICAL WORK… IN THE CALCULUS OF FUNCTIONS"**

BABBAGE, Charles. **Observations on the Analogy which subsists between the Calculus of Functions and other Branches of Analysis… Read April 17, 1817. **(London: W. Bulmer), 1817. Tall quarto (8-3/4 by 11 inches), period-style marbled wrappers; pp. 197-216. $850.

*First publication in Philosophical Transactions (1817) of Babbage's seminal work on the calculus of functions, one of his "highly influential papers on the theory of functions."*

The legendary inventor of the modern computer, Babbage saw mathematics as "his first love… It is not possible to assess the importance of Charles Babbage without an appreciation of his mathematical work… His major mathematical work was in the calculus of functions… His results were published in three papers, *An essay towards the calculus of functions* (in two parts, published in 1815/16) and the present paper, which in many respects provides an introduction to and motivation for the other two" (Dubbey, *Mathematical Work of Charles Babbage*). His "highly original papers on the theory of functions" affirmed Babbage's election to the Royal Society of London, where this paper was read on April 17, 1817 and published the same year in *Philosophical Transactions* (Hyman, 36). Babbage moved from this signal paper to his work on the Difference and Analytical Engines. As he later observed in his *Passages from the Life of a Philosopher*: "This [i.e. the calculus of functions] was my earliest step, and is still one to which I would willingly recur if other demands on my time permitted… It is very remarkable that the Analytical Engine adapts itself with singular facility to the development and numerical working out of this vast department of analysis." Published in *Philosophical Transactions of the Royal Society for the year MDCCCXVII, Part II*: preceded only by the Society's same year prepublication offprint. See* Origins of Cyberspace* 21.

A fine wide-margined copy.