Excerpt from Infinitesimal Analysis, Vol. 1

This volume has been written on what appeared, in the light of ten years' experience in teaching the Calculus, to be lines of least resistance. The aim has been, within a prescribed expense of time and energy, to penetrate as far as possible, and in as many directions, into the subject in hand, - that the student should attain as wide knowledge of the matter, as full comprehension of the methods, and as clear consciousness of the spirit and power of this analysis as the nature of the case would admit. Accordingly, what seemed to be natural suggestions and impulses towards near-lying extensions or generalizations have often been followed, and even allowed to direct the course of the discussion. Hereby, necessarily, the exposition has suffered in symmetry and in systematic character, but everything has the defects of its own qualities.

The aim already stated, no less than the plan of its pursuit, has excluded Weierstmssian rigor from many investigations and compelled the postponement of important discussions as too subtle for an early stage of study, in particular, no attempt has been made to deal with Series, unless the most familiar, or to follow in the wake of the masters of e-methods.

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