XIV. Observations on the analogy which subsists between the calculus of functions and other branches of analysis

Abstract

It is my intention in the following Paper to offer to the Royal Society some remarks on the utility of analogical reasoning in mathematical subjects, and to illustrate them by some striking facts which have occurred to me, when comparing the calculus of functions with other modes of calculation with which mathematicians have been long acquainted. The employment of such an instrument may, perhaps, create surprise in those who have been accustomed to view this science as one which is founded on the most perfect demonstration, and it may be imagined that the vagueness and errors which analogy , when unskilfully employed, has sometimes introduced into other sciences, would be transferred to this. It is, however, only as a guide to point out the road to discovery, that analogy should be used, and for this purpose it is admirably adapted.