Publisher's Synopsis
Excerpt from A Course of Elementary Mathematics: Affording Aid to Candidates for Admission Into Either of the Military Colleges, to Applicants for Appointments in the Indian Civil Service, and to Students of Mathematics Generally
The preparation necessary for the profitable study of the following course of Mathematics - is a knowledge of common Arithmetic, and some acquaintance with the principles of Geometry, as taught in Euclid's Elements. A student ignorant of these initiatory, but most important departments of elementary science, would scarcely seek his first lessons therein from a book such as this. The Elements of Euclid is a work by itself; universally known and esteemed, and everywhere to be easily procured: - to transfer its pages to the present performance, could be of no possible advantage to the learner. And the same may be said of common Arithmetic: - both this and Euclid are more conveniently studied from the ordinary manuals in popular use. We shall therefore commence the volume now in the hands of the reader, with a treatise on Algebra - the indispensable foundation of the entire fabric of modern analytical science.
I. Algebra.
1. Preliminary Notions. - Algebra may be regarded simply as an extension of the principles of Arithmetic. In the latter science the symbols of quantity, to which its rules and operations are applied, are limited to the nine digits or figures 1, 2, 3, 4, 5, 6, 7, 8, 9, together with the cypher or zero, 0. And not only is the notation of Arithmetic limited to these ten symbols, but each symbol is employed by every computer in the same sense: - the character or symbol 4, for instance, stands for four, always; 6 for six; 8 for eight, and so on: the symbols of Arithmetic are thus fixed in meaning, as well as limited in number.
It is otherwise in Algebra: in this science the symbols of quantity comprehend not only the figures of arithmetic, but also the letters of the alphabet: - the figures being, as in arithmetic, of invariable signification, but the letters admitting of arbitrary interpretation. It is this latter circumstance - namely, the possession of a set of symbols which we may employ to represent anything we please - that gives to Algebra its peculiarity and its power.
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