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added addition algebraic arithmetical arranged base binomial brackets called cents changed CHAPTER coefficients column combinations compound consider contains continued convergent corresponding cube definition denominator denote determinant difference digits Divide division divisor equal equation EXAMPLES expansion expression feet find the number Find the value four fraction function given gives greater Hence highest common factor increased integer less letters logarithm means method miles Multiply negative NOTE obtain places positive powers preceding present prove quadratic quantities quotient ratio reduces remainder respectively result rule rule of signs Show side simple Simplify solution Solve square root Substituting subtraction Suppose surd symbols taken term things third tion unity unknown whence write written yards zero
Página 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.
Página 351 - The logarithm of a product is the sum of the logarithms of its factors.
Página 352 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...