University Algebra: Embracing a Logical Development of the Science, with Numerous Graded Examples |
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algebraic ax² Binomial Formula called Clearing of fractions coefficients common difference containing contrary signs cube root denominator denote the number distance dividend divisible dollars equal roots equation whose roots EXAMPLES exponent expressions extracting the square factors Find the cube Find the fourth Find the greatest Find the square Find the sum following RULE geometrical progression given equation greatest common divisor Hence imaginary indicated irreducible fraction last term least common multiple Let x denote logarithm miles monomial Multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding proportion quotient radical sign real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root STURM'S THEOREM Substituting subtract Transform the equation Transposing travels unknown quantity Whence whole number write
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Page 130 - The SQUARE ROOT of a number is one of its two equal factors. Thus, 25 = 5 X 5 ; hence, 5 is the square root of 25 ; that is, \/25 = 5, or (25) ? = 5. The following table, verified by actual multiplication, is employed in finding the square root of any number less than 100. TABLE.
Page 53 - To reduce a fraction to its lowest terms. A fraction is in its lowest terms, when the numerator and denominator contain no common factors. It has been shown, that both terms of a fraction may be divided by the same quantity, without altering its value. Hence, if they have any common factors, we may strike them out.
Page 28 - Divide the first term of the remainder by the first term of the divisor, for the second term of the quotient. Multiply the divisor by this term, and subtract the product from the first remainder, and so on.
Page 73 - Every equation is composed of two parts, connected by the sign of equality. These parts are called members : the part on the left of the sign of equality, is called the first member; that on the right, the second member. Thus, in the equation, x + y = a — c, x
Page 234 - 1. If four quantities are in proportion, the product of the means is equal to the product of the extremes. Conversely, if we divide both members of ( 2 ) by
Page 31 - 2. TJie square of the difference of any two quantities, is equal to the square of the first, minus twice the product of the first and second, plus the square of the
Page 262 - That is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. If we extract any root
Page 259 - THE LOGARITHM of a number is the exponent of the power to which it is necessary to raise a fixed number to produce the given number. The fixed number is called the base of the system.
Page 239 - 8, &c., is an increasing arithmetical progression, in which the common difference is +2. The series, 18, 16, 14, 12, &c., is a decreasing arithmetical progression, in which the common difference is — 2. Although there are an infinite number • of terms in every progression, it is customary to speak of
Page 259 - If we denote any positive number, except 1, by a; any positive number whatever by n, and the exponent of the power to which it is necessary to raise a, in order to produce n± by x, we shall have the exponential equation, a