"There are... in mathematics, some examples of so called induction, in which the conclusion does bear the appearance of a generalization grounded upon some of the particular cases included in it. A mathematician, when he has calculated a sufficient number of the terms of an algebraical or arithmetical series to have ascertained what is called the law of the series, does not hesitate to fill up any number of the succeeding terms without repeating the calculations. But I apprehend he only does so when it is apparent from à priori considerations (which might be exhibited in the form of demonstration) that the mode of formation of the subsequent terms, each from that which preceded it, must be similar to the formation of the terms which have been already calculated. And when the attempt has been hazarded without the sanction of such general considerations, there are instances upon record in which it has led to false results. ...Even, therefore, such cases as these, are but examples of what I have called induction by parity of reasoning, that is, not really induction, because not involving any inference of a general proposition from particular instances. ...I am happy to be able to refer, in confirmation of this view of what is called induction in mathematics, to the highest English authority on the philosophy of algebra, Mr. Peacock. See pp. 107-8 of his profound Treatise on Algebra."