A New Introduction to the Science of Algebra ...F. J. Huntington, 1836 - 304 σελίδες |
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... exponents Division of quantities having fractional exponents . Formation of powers Extraction of roots • Of polynomials having radical terms Equations involving radical quantities • • 237 238 239 • 240 241 242 343 66 246 CHAPTER IV ...
... exponents Division of quantities having fractional exponents . Formation of powers Extraction of roots • Of polynomials having radical terms Equations involving radical quantities • • 237 238 239 • 240 241 242 343 66 246 CHAPTER IV ...
Σελίδα 65
... exponent of the required power ; or take two or more powers of the given number the sum of whose exponents is equal to the exponent of the required power , and multiply them together successively . EXAMPLES . 1. Involve 67 to the 2d ...
... exponent of the required power ; or take two or more powers of the given number the sum of whose exponents is equal to the exponent of the required power , and multiply them together successively . EXAMPLES . 1. Involve 67 to the 2d ...
Σελίδα 81
... exponent 1 less than the number of terms . For example , in the progression , 3 : 6 12:24 : 48 : 96 : 192 . : 2 $ 64 × 3 = 192 , the seventh term . = EXAMPLES . 1. In a geometrical series , the first 8 GEOMETRICAL PROPORTIONS . 81 ...
... exponent 1 less than the number of terms . For example , in the progression , 3 : 6 12:24 : 48 : 96 : 192 . : 2 $ 64 × 3 = 192 , the seventh term . = EXAMPLES . 1. In a geometrical series , the first 8 GEOMETRICAL PROPORTIONS . 81 ...
Σελίδα 96
... exponent is a number written to the right of a letter , and a little above , to denote the number of times it is taken as a factor ; or how many times + ONE it is multiplied by itself . Instead of writing a × a × a × a × a , or aaaaa ...
... exponent is a number written to the right of a letter , and a little above , to denote the number of times it is taken as a factor ; or how many times + ONE it is multiplied by itself . Instead of writing a × a × a × a × a , or aaaaa ...
Σελίδα 97
... exponents of the letters which enter into that term . An algebraic quan- tity which has all its terms of the same degree , is said to be homogeneous : 4a + 2a2b3-3abc3 + b'c , is therefore ho- mogeneous , and of the 5th degree . Similar ...
... exponents of the letters which enter into that term . An algebraic quan- tity which has all its terms of the same degree , is said to be homogeneous : 4a + 2a2b3-3abc3 + b'c , is therefore ho- mogeneous , and of the 5th degree . Similar ...
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2d power a²+2ab+b² a²b² a²x ab² added algebraic quantity Arith arithmetical progression ax² becomes Clearing of fractions coefficient common denominator common difference contained continued fraction cube root decimal fraction Divide the numerator dividend division equation evident EXAMPLES exponent expressed Extract the square extracting the root factors Find the greatest Find the sum find the value geometrical progression given number gives greater greatest common divisor hence improper fraction last term least common multiple letters logarithms lowest terms merator mixed number multiplicand Multiply nator nth root number of terms operation orders of units polynomials Prod quan quotient radical ratio remainder required to find result simple fraction square root subtractive terms tens tion tity unity unknown quantity vulgar fraction whence whole number writing written
Δημοφιλή αποσπάσματα
Σελίδα 117 - 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 178 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Σελίδα 70 - ... 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 161 - B with $96. A lost twice as much as B; and, upon settling their accounts, it appeared that A had three times as much remaining as B. How much did each lose ? Ans. A lost $96, and B lost $48.
Σελίδα 132 - 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.
Σελίδα 63 - To divide a Decimal by 10, 100, 1000, &c., remove the decimal point as many places to the left as there are ciphers in the divisor...
Σελίδα 73 - The first term of a ratio is called the antecedent, and the second term the consequent.
Σελίδα 78 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 262 - A and B hired a pasture, into which A put 4 horses, and B as many as cost him 18 shillings a week ; afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired? Ans.
Σελίδα 60 - Multiply as in whole numbers, and from the right hand of the product point off as many figures for decimals as there are decimal places in both factors.