Algebra for High Schools and Colleges: Containing a Systematic Exposition and Application of the Elementary and Higher Principles of the SciencePratt, Oakley & Company, 1859 - 306 páginas |
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Página vii
... changed , ( 67 ) .— Of a Factor which is common to all the Terms of the Dividend , ( 68 ) .— Of a Factor which is contained in all the Terms of the two Polynomials , ( 69 ) .— One Quantity a MULTIPLE of another . - A Common Multiple of ...
... changed , ( 67 ) .— Of a Factor which is common to all the Terms of the Dividend , ( 68 ) .— Of a Factor which is contained in all the Terms of the two Polynomials , ( 69 ) .— One Quantity a MULTIPLE of another . - A Common Multiple of ...
Página viii
... changed from Positive to Negative , ( 84 ) .— A Fraction reduced to lower Terms - How a binomial Common Measure may often be discovered , ( 85 ) . - RULE IX . To Reduce a Fraction to its Lowest Terms , ( 86 ) . When Two or more ...
... changed from Positive to Negative , ( 84 ) .— A Fraction reduced to lower Terms - How a binomial Common Measure may often be discovered , ( 85 ) . - RULE IX . To Reduce a Fraction to its Lowest Terms , ( 86 ) . When Two or more ...
Página xii
... changed , ( 235 ) .— Product of a Rational and an Irrational Factor , ( 236 ) .— How a Surd may be simplified , ( 237 ) .— How a Fractional may be reduced to an Integral Surd , ( 238 ) .— Surds of Different Roots reduced to the Same ...
... changed , ( 235 ) .— Product of a Rational and an Irrational Factor , ( 236 ) .— How a Surd may be simplified , ( 237 ) .— How a Fractional may be reduced to an Integral Surd , ( 238 ) .— Surds of Different Roots reduced to the Same ...
Página 14
... changed , and then proceed as in Alge- braic Addition . EXAMPLE . To subtract a2 + 2ab - 3x - z from 3a2-5ab + 5x - y . 3a2-5ab + 5x — y a2 + 2ab - 3x - z 2a2-7ab + 8x - y + z Having set the polynomial which is to be subtracted under ...
... changed , and then proceed as in Alge- braic Addition . EXAMPLE . To subtract a2 + 2ab - 3x - z from 3a2-5ab + 5x - y . 3a2-5ab + 5x — y a2 + 2ab - 3x - z 2a2-7ab + 8x - y + z Having set the polynomial which is to be subtracted under ...
Página 16
... changed , by changing the signs of all the terms of the Polynomial . The value of a Polynomial is therefore not affected by changing the signs of any or all of its terms , enclosing those terms in a ( ) , and prefixing the sign to the ...
... changed , by changing the signs of all the terms of the Polynomial . The value of a Polynomial is therefore not affected by changing the signs of any or all of its terms , enclosing those terms in a ( ) , and prefixing the sign to the ...
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Términos y frases comunes
acres added amount applied approximate Arithmetical become binomial cent changed coefficient complete consists containing corresponding cube root decimal denotes Derivative determined difference divided dividend division divisor equal equation equivalent evident example EXERCISES exponent expressed factors figures Find the cube Find the Product Find the square Find the value four fourth fraction Function given given Equation gives greater greatest common measure Hence imaginary increased Inequality integral interest known less letters logarithm manner means method miles multiplied negative obtained period permutations person places polynomial positive preceding principles problem progression proportion quotient ratio Reduce remainder represent Resolve respectively result rods Rule second term share side similar simplest form solution square root substituted subtracting successive Surds taken Theorem third twice units unknown quantity value of x whole yards
Pasajes populares
Página 299 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the...
Página 209 - A put four horses, and B as many as cost him 18 shillings a week. Afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired ? 49.
Página 105 - Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third.
Página 85 - 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 177 - A set out from C towards D, and travelled 7 miles a day. After he had gone 32 miles, B set out from D towards C, and went every day J^ of the whole journey; •and after he had travelled as many days as he went miles in a day, he met A. Required the distance from C to D.
Página 206 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Página 80 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.
Página 79 - What fraction is that, to the numerator of which if 1 be added, the value will be •£ ; but if 1 be adde.d to the denominator, its value will be | ? Let — denote the fraction.
Página 60 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Página 244 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log