New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges |
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Page 11
... an exponent , it indi- cates that the quantity is to be used as a divisor . Thus , a2 a2 b - 1 c3 is the same as bc39 -2 and x2 is the same as * The root of a quantity is one of its equal DEFINITIONS AND NOTATION . 11.
... an exponent , it indi- cates that the quantity is to be used as a divisor . Thus , a2 a2 b - 1 c3 is the same as bc39 -2 and x2 is the same as * The root of a quantity is one of its equal DEFINITIONS AND NOTATION . 11.
Page 12
... equals , or equal to , indicates that the quantities between which it is written are equal . Thus , xy , indicates that the quantity x equals the quantity y . An expression in which quantities are connected by the sign is an equation ...
... equals , or equal to , indicates that the quantities between which it is written are equal . Thus , xy , indicates that the quantity x equals the quantity y . An expression in which quantities are connected by the sign is an equation ...
Page 13
... equal ratios . Thus , 30 : 6 = 25 : 5 is read the ratio of 30 to 6 equals the ratio of 25 to 5 , or 30 is to 6 as 25 to 5 . 24 . The SIGN OF INEQUALITY , > or < , read is greater than , or is less than , when placed between two ...
... equal ratios . Thus , 30 : 6 = 25 : 5 is read the ratio of 30 to 6 equals the ratio of 25 to 5 , or 30 is to 6 as 25 to 5 . 24 . The SIGN OF INEQUALITY , > or < , read is greater than , or is less than , when placed between two ...
Page 15
... equal terms affected by unlike signs , in an expression , cancel . Thus , abcdcd is the same as a b . Quantities independently additive or subtractive , may be regarded as added to , or subtracted from , 0 , the neu- tral point , or ...
... equal terms affected by unlike signs , in an expression , cancel . Thus , abcdcd is the same as a b . Quantities independently additive or subtractive , may be regarded as added to , or subtracted from , 0 , the neu- tral point , or ...
Page 17
... equal quantities , be added to equal quantities , the sums will be equal . 2. If the same quantity , or equal quantities , be sub- tracted from equal quantities , the remainders will be equal . 3. If equal quantities be multiplied by ...
... equal quantities , be added to equal quantities , the sums will be equal . 2. If the same quantity , or equal quantities , be sub- tracted from equal quantities , the remainders will be equal . 3. If equal quantities be multiplied by ...
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Common terms and phrases
a²x² algebraic arithmetical progression binomial factors bushels cent Clearing of fractions coefficient common difference common logarithm Completing the square cube root decimal degree denominator denote Divide dividend equal equation Art EXAMPLES exponent expression Extracting the square Find the cube Find the square Find the sum find the values formula given equation Given x² greatest common divisor Greenleaf's imaginary inequality infinite series last term least common multiple logarithm loge miles Multiply negative nth root number of terms obtain OPERATION permutations polynomial positive problem proportion quadratic equation quan quotient radical sign ratio Reduce remainder required root Required the number required to find result rods second term simplest form solution square root Subtracting tity Transposing and uniting unknown quantity Whence whole number α₁
Popular passages
Page 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.
Page 61 - The LEAST COMMON MULTIPLE of two or more quantities is the least quantity that can be divided by each of them without a remainder.
Page 157 - Subtract the square of the root from the left period, and to the remainder bring down the next period for a dividend. 3d. Double the root already found, and place it on the left for a divisor. Find how many times the divisor is contained...
Page 79 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 141 - Hence, for raising a monomial to any power, we have the following RULE. Raise the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Page 82 - A Complex Fraction is one having a fraction in its numerator, or denominator, or both. It may be regarded as a case in division, since its numerator answers to the dividend, and its denominator to the divisor.
Page 275 - ... travel over, who gathers them up singly, returning with them one by one to the basket ? Ans.
Page 165 - Find the cube root of the first term, write it as the first term of the root, and subtract its cube from the given polynomial.
Page 255 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 316 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.