Algebra for Colleges and Schools |
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Common terms and phrases
a²b a²b² a²x a²x² a³b ab² ab³ algebraic arithmetic means arithmetical ascending powers ax² ax³ b₁ binomial Binomial Theorem bx² cents CHAPTER coefficient column compound expressions continued fraction convergent cube denote digits dimes Divide dividend divisible divisor equal equation EXAMPLES Find the highest find the number Find the square Find the sum find the value fraction harmonic means Hence highest common factor integer letters logarithm lowest common multiple miles an hour Multiply negative number of terms numerator and denominator obtain positive quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs Simplify Solve square root Subtract surd symbols unknown quantity whence whole number x²y x²y² x³y xy² xy³ yards zero
Popular passages
Page 167 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Page 264 - That is, if a quadratic equation be reduced to the form x?+px = q, the algebraic sum of the roots is equal to the coefficient of x with its sign changed, and the product of the roots is equal to the second member, with its sign changed.
Page 351 - The logarithm of a product is the sum of the logarithms of its factors.
Page 352 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Page 183 - The sixth root of an expression is found by taking the cube root of the square root, or the square root of the cube root.
Page 102 - ... remainder. The lowest common multiple of two or more algebraic expressions is the expression of lowest degree which will contain them all without a remainder.
Page 289 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 328 - A telegraph has 5 arms, and each arm has 4 distinct positions, including the position of rest: find the total number of signals that can be made.
Page 322 - From 7 Englishmen and 4 Americans a committee of 6 Is to be formed: in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans...
Page 290 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if a...