New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges |
From inside the book
Results 1-5 of 31
Page 17
... whole of a quantity is equal to the sum of all its parts . ALGEBRAIC PROCESSES . 47. The PROCESSES of Algebra , in general , are only those of Arithmetic extended , or rendered more compre- hensive , by the aid of symbols . ( Art . 7 ...
... whole of a quantity is equal to the sum of all its parts . ALGEBRAIC PROCESSES . 47. The PROCESSES of Algebra , in general , are only those of Arithmetic extended , or rendered more compre- hensive , by the aid of symbols . ( Art . 7 ...
Page 31
... whole expression 2xy is to be multiplied by xy , each of its terms is to be taken x plus y times ; x times 2x y times 2x - y = 2x2 y = - xy ; 2xy - y2 , and the sum of these partial products is 2x2 + MULTIPLICATION . 21.
... whole expression 2xy is to be multiplied by xy , each of its terms is to be taken x plus y times ; x times 2x y times 2x - y = 2x2 y = - xy ; 2xy - y2 , and the sum of these partial products is 2x2 + MULTIPLICATION . 21.
Page 41
... the quotient . Multiply the whole divisor by this term , and subtract the prod- uct from the dividend . Regard the remainder as a new dividend , arrange it and find the next term of the quotient , in the 4 * DIVISION . 41.
... the quotient . Multiply the whole divisor by this term , and subtract the prod- uct from the dividend . Regard the remainder as a new dividend , arrange it and find the next term of the quotient , in the 4 * DIVISION . 41.
Page 46
... whole number of terms in their product will be mXn , or mn . By reduction of similar terms the whole number of terms in a product may be made often much less , but never less than two . ( Art . 73. ) USEFUL FORMULAS . 89. A FORMULA is ...
... whole number of terms in their product will be mXn , or mn . By reduction of similar terms the whole number of terms in a product may be made often much less , but never less than two . ( Art . 73. ) USEFUL FORMULAS . 89. A FORMULA is ...
Page 83
... whole , the negative exponent may be removed as in Art . 131 ; otherwise , both numerator and denominator must be multiplied by that letter or quantity with an equal posi- tive exponent , in accordance with Art . 139 . x2 + y - 3 19 ...
... whole , the negative exponent may be removed as in Art . 131 ; otherwise , both numerator and denominator must be multiplied by that letter or quantity with an equal posi- tive exponent , in accordance with Art . 139 . x2 + y - 3 19 ...
Contents
102 | |
106 | |
109 | |
119 | |
121 | |
126 | |
135 | |
141 | |
148 | |
155 | |
163 | |
169 | |
175 | |
181 | |
188 | |
196 | |
200 | |
206 | |
217 | |
280 | |
289 | |
296 | |
303 | |
311 | |
314 | |
321 | |
324 | |
327 | |
334 | |
340 | |
347 | |
358 | |
364 | |
372 | |
381 | |
388 | |
394 | |
Other editions - View all
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.