"Few contemporaries were as profoundly read in the history of mathematics as was De Morgan. No subject was too insignificant to receive his attention. ...In [his] article "Induction (Mathematics)," first printed in 1838, occurs, apparently for the first time, the name "mathematical induction"; it was adopted and popularized by I. Todhunter in his Algebra. The term "induction" had been used by John Wallis in 1656, in his Arithmetica infinitorum; he used the induction known to natural science. In 1686 Jacob Bernoulli criticised him for using a process which was not binding logically and then advanced in place of it the proof from n to n + 1. This is one of the several origins of the process of mathematical induction. From Wallis to De Morgan, the term "induction" was used occasionally in mathematics, and in a double sense, (1) to indicate incomplete inductions of the kind known in natural science, (2) for the proof from n to n + 1. De Morgan's "mathematical induction" assigns a distinct name for the latter process. The Germans employ more commonly the name "vollständige Induktion," which became current among them after the use of it by R. Dedekind in his Was sind und was sollen die Zahlen, 1887."