Elementary Algebra (Classic Reprint)

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Excerpt from Elementary Algebra In that part of mathematics known as algebra, letters are used to represent numbers or quantities, the term quantity is used to designate any number involved in a mathematical process. The use of letters or symbols, in place of the actual numbers, simplifies the solution of mathematical problems and makes the calculations easier and more rapid. The simplest use made of letters to represent numbers is in formulas. A formula may be defined as a mathematical rule expressed by signs and symbols instead of in actual words. The object is to make it possible to condense into small space the information that otherwise would be imparted by long and cumbersome rules. The symbols used in formulas, as well as in algebra in general, are mainly the letters in the alphabet, and the signs are the ordinary signs used in arithmetic, in addition to a number of signs used for special purposes in algebraic expressions only. Letters from the Greek alphabet are frequently used to designate angles, and the Greek letter p (pi) is always used to indicate the ratio between the circumference and the diameter of a circle, p, therefore, is always, in mathematical expressions, equal to 3.1416. The Greek letters most generally used, besides p, are a (alpha), a (beta), ¿ (gamma), d (delta), ¿ (theta), µ (mu), f (phi), and ¿ (omega). Knowledge of algebra is not necessary in order to make successful use of formulas of the general type, such as are found in engineering handbooks, it is only necessary to thoroughly understand the use of letters or symbols in place of numbers, and to be well versed in the methods, rules and processes of ordinary arithmetic. Knowledge of algebra becomes necessary only in cases where a general rule or formula which gives the answer to a problem directly is not available. In other words, algebra is useful in developing or originating a general rule or formula, but the formula can be used without recourse to algebraic processes. No attempt should be made to study algebra before all the methods of arithmetic are well understood. Formulas As mentioned, the symbols or letters used in formulas designate or "stand for" actual figures or numerical values. The figures or values for a given problem are inserted in the formula according to the requirements in each specific case. When the values are thus inserted, in place of the letters, the result or answer is obtained by ordinary arithmetical methods. There are two reasons why a formula is preferable to a rule expressed in words. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.