Manual of AlgebraBarnes, 1875 - 331 páginas |
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Página 75
... corresponding nume- rators for new numerators . If there are any entire quantities , they may be regarded as frac- tions whose denominators are equal to 1 . Reduce each of the following groups of fractions to their least common ...
... corresponding nume- rators for new numerators . If there are any entire quantities , they may be regarded as frac- tions whose denominators are equal to 1 . Reduce each of the following groups of fractions to their least common ...
Página 90
... corresponding numerator , dropping the denominator . EXAMPLES . 1. Clear the equation , 214 ― 2x 3 - 5 of fractions . 6 ' The least common multiple of the denominators is 12. Multi- plying both members by 12 ( axiom 3o ) , and reducing ...
... corresponding numerator , dropping the denominator . EXAMPLES . 1. Clear the equation , 214 ― 2x 3 - 5 of fractions . 6 ' The least common multiple of the denominators is 12. Multi- plying both members by 12 ( axiom 3o ) , and reducing ...
Página 136
... corresponding powers of x in the formula ; we then raise the second term to its successive powers up to the nth , and substitute them in the formula for the corresponding powers of y , substituting for n the ex- ponent of the power ...
... corresponding powers of x in the formula ; we then raise the second term to its successive powers up to the nth , and substitute them in the formula for the corresponding powers of y , substituting for n the ex- ponent of the power ...
Página 139
... corresponding to the par- ticular power taken from the formula ; in the second line , we write the descending powers of the leading term down to the 0 power ; in the third line , we write the ascending powers of the following term from ...
... corresponding to the par- ticular power taken from the formula ; in the second line , we write the descending powers of the leading term down to the 0 power ; in the third line , we write the ascending powers of the following term from ...
Página 151
... corresponding numbers in the second line ; the less number of the two will be the entire part of the required cube root , that is , it is the cube root to within less than 1 . If the number is greater than 1000 , its cube root will be ...
... corresponding numbers in the second line ; the less number of the two will be the entire part of the required cube root , that is , it is the cube root to within less than 1 . If the number is greater than 1000 , its cube root will be ...
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Términos y frases comunes
algebraic Arithmetic ax² binomial formula called clearing of fractions coefficients common difference contain contrary signs cube root Davies denominator denote the number distance dividend divisible equa equal roots equation whose roots EXAMPLES exponent expression extracting the square factors Find the cube Find the greatest Find the least Find the square Find the sum following principle following rule geometrical geometrical progression given equation greatest common divisor hence imaginary indicated irreducible fraction least common multiple logarithm Mathematics miles minuend monomial multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quan quotient radical sign ratio real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root Sturm's Theorem substituting subtract third tion tity transposing travels unknown quantity V₁ whole number
Pasajes populares
Página 145 - 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.
Página 239 - 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.
Página 267 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 245 - 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.
Página 42 - ... the first term of the quotient ; multiply the divisor by this term and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Página 239 - In any proportion, the product of the means is equal to the product of the extremes.
Página 245 - That is, any term is equal to the first term, plus the product of the common difference by the number of preceding terms.
Página 41 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 264 - 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.