New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges |
From inside the book
Results 1-5 of 45
Page 9
... represent known quantities and determined values , and the letters , any quantity whatever , known or unknown . 8. KNOWN QUANTITIES , or those whose values are given DEFINITIONS AND NOTATION Symbols of Quantity Symbols of Operation ...
... represent known quantities and determined values , and the letters , any quantity whatever , known or unknown . 8. KNOWN QUANTITIES , or those whose values are given DEFINITIONS AND NOTATION Symbols of Quantity Symbols of Operation ...
Page 10
... represented by the first letters of the alphabet , as a , b , c . 9. UNKNOWN QUANTITIES , or those whose values are not given , are represented by the last letters of the alpha- bet , as x , y , z . 10. ZERO , or the absence of quantity ...
... represented by the first letters of the alphabet , as a , b , c . 9. UNKNOWN QUANTITIES , or those whose values are not given , are represented by the last letters of the alpha- bet , as x , y , z . 10. ZERO , or the absence of quantity ...
Page 19
... represents , is taken 3 times in the first term , 7 times in the second , and 8 times in the third , or in all 18 times , the sum of the terms is 18 a b . 2. Let it be required to find the sum of ADDITION . 19 Addition.
... represents , is taken 3 times in the first term , 7 times in the second , and 8 times in the third , or in all 18 times , the sum of the terms is 18 a b . 2. Let it be required to find the sum of ADDITION . 19 Addition.
Page 20
... represents , is taken 7 times in the first term , - 5 - times in the second , and - 6 times in the third , or in all 18 times , the sum - of the terms is 18 b . - CASE II . 52. When the terms are similar , and have different signs . 1 ...
... represents , is taken 7 times in the first term , - 5 - times in the second , and - 6 times in the third , or in all 18 times , the sum - of the terms is 18 b . - CASE II . 52. When the terms are similar , and have different signs . 1 ...
Page 45
... represented by the quantity , taken independently of the sign affecting it . Thus , 1 and 1 have the same abso- lute value . - — - In algebraic language , however , 1 is greater than 1 , and 2 than 3 . - 86. In general , of two negative ...
... represented by the quantity , taken independently of the sign affecting it . Thus , 1 and 1 have the same abso- lute value . - — - In algebraic language , however , 1 is greater than 1 , and 2 than 3 . - 86. In general , of two negative ...
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.