Duncan Gregory: Calculus

“The chief object of the present work is, as its title indicates, to furnish to the student examples by which to illustrate the processes of the Differential and Integral Calculus. In this respect it will be seen to agree with Professor Peacock's Collection of Examples; and indeed if a second edition of that excellent work had been published I should not have undertaken the task of making this compilation. But as Professor Peacock informed me that he had not leisure to superintend the publication of a second edition of his "Examples" which had been long out of print, I thought that I should do a service to students by preparing a work on a similar plan, but with such modifications as seemed called for by the increased cultivation of Analysis in this University.”

Duncan Gregory

p. iii http://books.google.com/books?id=h7JT-QDuAHoC&pg=PR3; Lead paragraph of the Preface; Highlighted section cited in: Patricia R. Allaire and Robert E. Bradley. " Symbolical algebra as a foundation for calculus: DF Gregory's contribution http://poncelet.math.nthu.edu.tw/disk5/js/history/gregory.pdf." Historia Mathematica 29.4 (2002): p. 408
Examples of the processes of the differential and integral calculus, (1841)

Universe

“In this chapter I shall collect those Theorems in the Differential Calculus which, depending only on the laws of combination of the symbols of differentiation, and not on the functions which are operated on by these symbols, may be proved by the method of the separation of the symbols : but as the principles of this method have not as yet found a place in the elementary works on the Calculus, I shall first state? briefly the theory on which it is founded.”

Duncan Gregory

Source: Examples of the processes of the differential and integral calculus, (1841), p. 237; Lead paragraph of Ch. XV, On General Theorems in the Differential Calculus,; Cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52

Law , Dependency

“It has always appeared to me that we sacriﬁce many of the advantages and more of the pleasures of studying any science by omitting all reference to the history of its progress: I have therefore occasionally introduced historical notices of those problems which are interesting either from the nature of the questions involved, or from their bearing on the history of the Calculus. …[T]hese digressions may serve to relieve the dryness of a mere collection of Examples.”

Duncan Gregory

p. vi http://books.google.com/books?id=h7JT-QDuAHoC&pg=PR6, as cited in: Patricia R. Allaire and Robert E. Bradley. " Symbolical algebra as a foundation for calculus: DF Gregory's contribution http://poncelet.math.nthu.edu.tw/disk5/js/history/gregory.pdf." Historia Mathematica 29.4 (2002): p. 409.
Examples of the processes of the differential and integral calculus, (1841)

Pleasure , History , Question , Nature