Publisher's Synopsis
From the PREFACE.
One of the chief objects of this volume is to bring within the reach of students of ordinary abilities, and to enable them to make practical use of, some portions of what are generally, though with little reason, called "higher" Mathematics. Many mathematical rules, such as those studied under Mensuration to obtain the volume and surface of a sphere, may be obtained by so-called "elementary" methods, but these are frequently only roundabout and troublesome tricks, and are after all merely expedients to evade the simple notation of the Calculus and usually end by assuming the idea of a limit, a conception which my experience shows is quite as difficult for the student to grasp as the underlying principles of the Calculus. Or, take the problem of determining the moment of inertia of a rod: when once the student becomes familiar with the easy language of the Calculus, all the scaffolding, which has to be so carefully and tediously built up to obtain a result if Algebra alone is employed, may be at once discarded.
For these and similar reasons, and to keep the size of the book within reasonable limits, the rudiments of Mathematics- Arithmetic and simple Algebra-are taken for granted, though summaries of the more important elementary results are given at the beginning of each section. A student not already familiar with the proofs leading to these results and at home with illustrative examples on them should refer to my earlier books or some similar source. The summaries referred to are in every case followed by concrete numerical examples fully worked out and a set of exercises to enable the student to become possessed of the full meaning of each of the terms in the algebraic expressions representing the rules.
The order of treatment merely represents what I have found to be most advantageous in my own classes. Other teachers may find it better to vary the sequence to meet the particular requirements of their own students. Readers who are studying without the help of a teacher are recommended to omit the more difficult sections at the first reading. I should like to direct particular attention- to several portions of the book, for, so far as I am aware, the method of treatment therein is now published for the first time....
