Higher Algebra (Classic Reprint)

This work is designed as a text-book in universities, colleges, and technical schools, the first fifteen chapters being also adapted to use in high schools and academies by students who have some knowledge of elementary algebra. The demonstrations constitute one of the characteristic features of the book. While most of our text-books on Algebra state with great clearness the theorems and rules, few of them, especially in the earlier parts, give the demonstrations in a way that enables a student to reproduce them. Usually illustration, explanation, and general demonstration are so intermingled that the student is not able to gather up and give in logical form just what constitutes the proof. In this work the plan is that which gives so much definiteness to our teaching in Geometry: each general principle is followed by a concise, logical demonstration, containing only the reasoning necessary to establish it, while all illustrations and explanations by special cases are given in separate articles. The student thus soon learns to know what is demanded in a general proof, and to distinguish between rigorous demonstration and verification or illustration by a special case. Without any loss of conclusiveness in reasoning, the methods employed have permitted, in many cases, much shorter and more easily followed demonstrations than those usually given. A nother characteristic feature is the substitution of short processes for many of the long and tedious ones in common use. As mathematical operations, at best, involve much drudgery, all practical means of shortening the work should be made available to the student. The few short processes given in our text-books are reserved until the student has formed a habit of using the long processes, and, consequently, he never gains a practical use of even these few.
(Typographical errors above are due to OCR software and don't occur in the book.)

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