University Algebra: Embracing a Logical Development of the Science, with Numerous Graded ExamplesA.S. Barnes and Company, 1870 |
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3x²y algebraic Arithmetic ax² Binomial Formula Clearing of fractions coefficients common difference containing contrary signs cube root Davies denominator denote the number distance Divide dividend divisible equal roots equation whose roots EXAMPLES exponent expressions extract the square factors Find the cube Find the fourth Find the greatest Find the square following RULE geometrical progression given equation greatest common divisor Hence imaginary indicated irreducible fraction last term least common multiple Let x denote logarithm Mathematics miles monomial Monteith's negative nth root number of terms operation polynomial positive preceding problem 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 third Transform the equation Transposing travels unknown quantity Whence whole number write X₁
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Page 36 - 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 : IV.
Page 136 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 36 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Page 236 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Page 258 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 230 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.
Page 230 - In any proportion, the product of the means is equal to the product of the extremes.
Page 255 - 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.