Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and Colleges |
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Page 14
... consisting of three terms ; as , a + b — c . · Binomials and trinomials are polynomials . ART . 27. The numerical value of an algebraic expression 14 RAY'S ALGEBRA , PART SECOND . figures, letters, and signs The letters and signs are ...
... consisting of three terms ; as , a + b — c . · Binomials and trinomials are polynomials . ART . 27. The numerical value of an algebraic expression 14 RAY'S ALGEBRA , PART SECOND . figures, letters, and signs The letters and signs are ...
Page 45
... consists of two factors , b and am - 1b - 1 . it is evident , that if the second of these factors is divisible by a — b , then will the quantity a ” —bm be divisible by a — b . Thus , if a - b is contained c times in am - 1 - bm - 1 ...
... consists of two factors , b and am - 1b - 1 . it is evident , that if the second of these factors is divisible by a — b , then will the quantity a ” —bm be divisible by a — b . Thus , if a - b is contained c times in am - 1 - bm - 1 ...
Page 66
... consist of the product of the same factors ; that is , of all the denominators . Thus , a Xnxr mxn xr anr mnr b Xmxr bmr - mxmxr mnr cxmXn__cmn rxmxn mnr It is evident that the value of each fraction is not changed , and that they have ...
... consist of the product of the same factors ; that is , of all the denominators . Thus , a Xnxr mxn xr anr mnr b Xmxr bmr - mxmxr mnr cxmXn__cmn rxmxn mnr It is evident that the value of each fraction is not changed , and that they have ...
Page 75
... consists of an unlimited number of terms which observe the same law . The law of a series is a relation existing between its terms , so that , when some of them are known , the succeeding terms may be easily obtained . Thus , in the ...
... consists of an unlimited number of terms which observe the same law . The law of a series is a relation existing between its terms , so that , when some of them are known , the succeeding terms may be easily obtained . Thus , in the ...
Page 85
... consists of three steps , viz .: 1st . Clearing the equation of fractions . 2nd . Transposition . 3rd . Reducing like terms , and dividing by the coėfficient of x . Let this value of x be substituted instead of x in the original ...
... consists of three steps , viz .: 1st . Clearing the equation of fractions . 2nd . Transposition . 3rd . Reducing like terms , and dividing by the coėfficient of x . Let this value of x be substituted instead of x in the original ...
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Common terms and phrases
algebraic algebraic quantity arithmetical progression Binomial Theorem coėfficient continued fraction converging fraction cube root denominator denotes dividend divisible equa equal equation whose roots evident exactly divide EXAMPLES FOR PRACTICE exponent expressed extract the square Find the cube Find the greatest Find the number Find the square Find the sum find the value geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root nth term number of balls number of permutations number of terms operation perfect square polynomial positive root preceding proportion proposed equation quotient ratio real roots reduced remainder Required the numbers required to find result second degree second term square root Sturm's theorem substitute subtracted taken theorem third tion transformed transposing unknown quantity whence whole number zero
Popular passages
Page 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 42 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 39 - 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.
Page 128 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 43 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Page 140 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 220 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Page 183 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Page 28 - Multiply the coefficients of the two terms together, and to their product annex all the letters in both quantities, giving to each letter an exponent equal to the sum of its exponents in the two factors.