pass over the two theorems in Art. 74, until they become more familiar with algebraic reasoning. While the book has not been made simple by avoiding the legitimate use of the negative sign before a parenthesis or a fraction, the difficulty which is caused to beginners by the introduction of negative indices in simple division. has been obviated by deferring their introduction to the section on Powers and Roots, where they are fully explained. The utmost conciseness consistent with perspicuity has been studied throughout the work. It is hoped the book will commend itself to both teachers and pupils. W. F. B. CAMBRIDGE, MASS., May 17, 1868. 118 SECTION XVI. To reduce a Radical to its Simplest Form To reduce a Rational Quantity to the To reduce Radicals having different In- UNIV. OF ELEMENTARY ALGEBRA. SECTION I. DEFINITIONS. 1. MATHEMATICS is the science of quantity. 2. QUANTITY is that which can be measured; as distance, time, weight. 3. ARITHMETIC is the science of numbers. In Arithmetic quantities are represented by figures. 4. ALGEBRA is Universal Arithmetic. In Algebra quantities are represented by either letters or figures, and their relations by signs. ΝΟΤΑΤΙΟΝ. 5. ADDITION is denoted by the sign +, called plus; thus, 32, i. e. 3 plus 2, signifies that 2 is to be added to 3. called minus; 6. SUBTRACTION is denoted by the sign thus, 7 — 4, i. e. 7 minus 4, signifies that 4 is to be subtracted from 7. 7. MULTIPLICATION is denoted by the sign X; thus, 6 X 5 signifies that 6 and 5 are to be multiplied together. Between a figure and a letter, or between letters, the sign X is generally omitted; thus, 6 a b is the same as 6 × a × b. Multiplication is sometimes denoted by the period; thus, 8.6.4 is the same as 8 X 6 X 4. 8. DIVISION is denoted by the sign; thus, 9 3 signifies that 9 is to be divided by 3. Division is also indicated by the fractional form; thus, is the same as 9 ÷ 3. 9. EQUALITY is denoted by the sign; thus, $1100 cents, signifies that 1 dollar is equal to 100 cents. An expression in which the sign occurs is called an equation, and that portion which precedes the sign is called the first member, and that which follows, the second member. 10. INEQUALITY is denoted by the sign > or <, the smaller quantity always standing at the vertex; thus, 8 > 6 or 6 < 8 signifies that 8 is greater than 6. 11. THREE DOTS .. are sometimes used, meaning hence, therefore. 12. A PARENTHESIS ( ), or a Vinculum indicates that all the quantities included, or connected, are to be considered as a single quantity, or to be subjected to the same operation; thus, (8 + 4) × 3 = 12 X 3, or 24 +12 = 36; 21 6 3 15 ÷ 3, or 7 25., Without the parenthesis, these examples would stand thus: 84 × 3 = 8 + 12 = 20; 21 2= 19; the sign X, in the former, not nor the sign÷, in the latter, 21. 6 ÷ 3 = 21 affecting 8; × 14 how many? 4. (1413) X (52) how many? 5. 10+ (7 4) ÷ 3 X 4 how many? |