Review of The Differential Calculus [From North American Review 103.2 (July 1866):233.] ³⁰

The Differential Calculus: with Unusual and Particular Analysis of its Elementary Principles, and Copious Illustrations of its Practical Application. By John Spare, A. M., M. D. Boston: Bradley, Dayton, &Co. 1865. 12mo. pp. xix., 244.

An eccentric work, written in execrable English, and meant to help the tyro over the elementary difficulties of the Calculus by a profusion of practical problems, in which “the work aims at cultivating and prolonging the enthusiasm of the student, by clothing his conceptions of quantity in the garb of romance, or something of a supposable human experience. These conceptions may, with the more interest, be erratic and fanciful as to economical life, without ever filling or exhausting the generality of pure mathematical conception.”

The difficulties which this work is fitted to overcome are so idiosyncratic, that it will fail, we think, to meet the common needs of the student, who will find superadded to the difficulties of “pure mathematical conception” the perplexities of the author’s practical problems.

“The present treatise on the Differential Calculus is believed to be the first, of any character, that has been written and published in America as the special topic of a volume; and the first, so far as known to the author, ever published, that professes the character of the present one.” It must be conceded that there is a sort of negative merit in the self-restraint which has saved the Integral Calculus from the author’s romantic explanations. We can imagine no other reason why the limits of the work should be mentioned, but for the purpose of apologizing for them.

The author thinks he has proved that several American treatises are at fault in their treatment of certain elementary problems in the Calculus; but he is generous enough not to expose them by name.