Manual of AlgebraA.S. Barnes, 1875 - 331 páginas |
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Página 4
... that every change made has been in the direc- tion of a closer resemblance to the great work whose spirit it would aspire to imitate . NEW YORK , June 17 , 1875 . CONTENTS . CHAPTER I. DEFINITIONS AND EXPLANATION OF SIGNS . 4 PREFACE .
... that every change made has been in the direc- tion of a closer resemblance to the great work whose spirit it would aspire to imitate . NEW YORK , June 17 , 1875 . CONTENTS . CHAPTER I. DEFINITIONS AND EXPLANATION OF SIGNS . 4 PREFACE .
Página 16
... tion of literal factors is the same in both . Thus , the terms 822yz and -7xyz , are similar , as are also the terms 25a2beds and 2a2bcd3 . In order that two terms may be similar , they must contain the same letters , and each letter ...
... tion of literal factors is the same in both . Thus , the terms 822yz and -7xyz , are similar , as are also the terms 25a2beds and 2a2bcd3 . In order that two terms may be similar , they must contain the same letters , and each letter ...
Página 69
... tion of changing its form without altering its value . FIRST TRANSFORMATION . To reduce an entire quan- tity to a fractional form having a given denominator . 61. Let a be the entire quantity , and b the given denominator . We have ...
... tion of changing its form without altering its value . FIRST TRANSFORMATION . To reduce an entire quan- tity to a fractional form having a given denominator . 61. Let a be the entire quantity , and b the given denominator . We have ...
Página 83
... for dividing one frac- tion by another : RULE . Invert the terms of the divisor , and multiply the dividend by the resulting fraction . After indicating the operation of multiplication strike out all the DIVISION OF FRACTIONS . 8883.
... for dividing one frac- tion by another : RULE . Invert the terms of the divisor , and multiply the dividend by the resulting fraction . After indicating the operation of multiplication strike out all the DIVISION OF FRACTIONS . 8883.
Página 90
... tion by it , reducing fractional to entire terms . The reduction will be effected , if we divide the least common multiple by each denominator , and then multiply the quotient by the corresponding numerator , dropping the denominator ...
... tion by it , reducing fractional to entire terms . The reduction will be effected , if we divide the least common multiple by each denominator , and then multiply the quotient by the corresponding numerator , dropping the denominator ...
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Términos y frases comunes
algebraic Arithmetic ax² binomial formula called clearing of fractions coefficients common difference containing contrary signs cube root 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 progression given equation greatest common divisor hence imaginary indicated least common multiple logarithms 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 required root 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 write
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 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 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 239 - In any proportion, the product of the means is equal to the product of the extremes.
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.
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 87 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Página 266 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.