Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and CollegesWinthrop B. Smith & Company, 1852 - 396 σελίδες |
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Σελίδα v
... LEAST COMMON MULTIPLE . ALGEBRAIC THEOREMS - Square of the sum of two quantities . Square of the difference of two ... LEAST COMMON MULTIPLE 128 78 79 80 81 82 83 85 86 87 88 95 96-108 109-113 Definitions - CHAPTER III . ALGEBRAIC ...
... LEAST COMMON MULTIPLE . ALGEBRAIC THEOREMS - Square of the sum of two quantities . Square of the difference of two ... LEAST COMMON MULTIPLE 128 78 79 80 81 82 83 85 86 87 88 95 96-108 109-113 Definitions - CHAPTER III . ALGEBRAIC ...
Σελίδα 25
... least which contains the greatest num- ber of units . Thus , -3 is said to be less than -2 . But , of two negative quantities , that which contains the greatest number of units is said to be numerically the greatest ; thus , -3 is numer ...
... least which contains the greatest num- ber of units . Thus , -3 is said to be less than -2 . But , of two negative quantities , that which contains the greatest number of units is said to be numerically the greatest ; thus , -3 is numer ...
Σελίδα 48
... least two factors , one of which is the difference of the two quantities . ( See Art . 83 ) . Thus , am - bm = ( a — b ) ( am ̄1 + am - 2b .... + abm - 2 + bm - 1 , where a , b , and m , may be any quantities whatever . In this case ...
... least two factors , one of which is the difference of the two quantities . ( See Art . 83 ) . Thus , am - bm = ( a — b ) ( am ̄1 + am - 2b .... + abm - 2 + bm - 1 , where a , b , and m , may be any quantities whatever . In this case ...
Σελίδα 49
... least three factors , one of which is the sum , and another the difference of the quantities . ( See Art . 85. ) Thus , by Art . 84 , aa — ba , is divisible by a + b , and , by Art . 85 , it is divisible by a - b ; hence it is divisible ...
... least three factors , one of which is the sum , and another the difference of the quantities . ( See Art . 85. ) Thus , by Art . 84 , aa — ba , is divisible by a + b , and , by Art . 85 , it is divisible by a - b ; hence it is divisible ...
Σελίδα 52
... least exponent . 2. Find the greatest common divisor of 6a2xy , 9a3x3 , and 15a ^ x1y3 . OPERATION . 6a2xy = 3X2a2xy 9a3x3 3x3a3x3 15a3x1y3 = 3 × 5a1x1y3 Here we find that 3 is the only nu- merical factor , and a and x the only letters ...
... least exponent . 2. Find the greatest common divisor of 6a2xy , 9a3x3 , and 15a ^ x1y3 . OPERATION . 6a2xy = 3X2a2xy 9a3x3 3x3a3x3 15a3x1y3 = 3 × 5a1x1y3 Here we find that 3 is the only nu- merical factor , and a and x the only letters ...
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Άλλες εκδόσεις - Προβολή όλων
Ray's Algebra, Part Second: An Analytical Treatise, Designed for High ... Joseph Ray Πλήρης προβολή - 1857 |
Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic algebraic quantity arithmetical progression Binomial Theorem coëfficient 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
Δημοφιλή αποσπάσματα
Σελίδα 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.