The Principles of Elementary Algebra |
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... coefficients , both of which are amply dealt with . Probably the most distinctive feature of the work is the importance attached to the interpretation of alge- braic expressions and results . Algebra is an unspoken language written in ...
... coefficients , both of which are amply dealt with . Probably the most distinctive feature of the work is the importance attached to the interpretation of alge- braic expressions and results . Algebra is an unspoken language written in ...
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... COEFFICIENTS AND THEIR APPLICA- TIONS .... 231 XVI . CONTINUED FRACTIONS .. 244 XVII . LOGARITHMS AND EXPONENTIALS . 255 XVIII . SERIES AND INTERPOLATION .... 274 XIX . ELEMENTARY DETERMINANTS .. 296 For a more detailed statement ...
... COEFFICIENTS AND THEIR APPLICA- TIONS .... 231 XVI . CONTINUED FRACTIONS .. 244 XVII . LOGARITHMS AND EXPONENTIALS . 255 XVIII . SERIES AND INTERPOLATION .... 274 XIX . ELEMENTARY DETERMINANTS .. 296 For a more detailed statement ...
Page 10
... coefficient of x . Similarly , x a and ax + bc are both linear in x , although the first is of one dimension , and the second of two , in regard to all the letters . An expression which is of the same dimensions in every term is ...
... coefficient of x . Similarly , x a and ax + bc are both linear in x , although the first is of one dimension , and the second of two , in regard to all the letters . An expression which is of the same dimensions in every term is ...
Page 23
... coefficient of a3 is 1-1 or 0 ; The coefficient of a2b is 3 + 1 or 4 ; The coefficient of abc is 6 2 or 4 - and the expansion is 4 Za2b + 4 abc . .. m = 0 . .. n = 4 . ; .. p = 4 , - EXERCISE II . b . 1. Write out the type ...
... coefficient of a3 is 1-1 or 0 ; The coefficient of a2b is 3 + 1 or 4 ; The coefficient of abc is 6 2 or 4 - and the expansion is 4 Za2b + 4 abc . .. m = 0 . .. n = 4 . ; .. p = 4 , - EXERCISE II . b . 1. Write out the type ...
Page 27
... coefficients of the several terms in these and higher powers are exhibited in the following table , which may be extended at pleasure - The coefficients form the diagonals , up to the 8th power . 1 1 ----- --1 -15- 7 ----- -21-- -28 ...
... coefficients of the several terms in these and higher powers are exhibited in the following table , which may be extended at pleasure - The coefficients form the diagonals , up to the 8th power . 1 1 ----- --1 -15- 7 ----- -21-- -28 ...
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Common terms and phrases
a₁ ab² arithmetic ax² b₁ becomes binomial binomial theorem c₁ coefficients complete square continued fraction convergent cube root decimal denominator denote diagonal difference dimensions Divide divisor elementary algebra equal equate coefficients equation EXERCISE expansion expression find the L. C. M. find the nth Find the value finite geometric geometric series given gives graph Hence imaginary independent term integer integral function inversions letters linear factors logarithms mantissa matrix miles monomial Multiply negative nth root nth term number of terms numerical quantity operation permutations positive integers proper fraction quadratic quantitative symbol R₁ rationalizing factor recurring series relation remainder result sides signs Similarly solution square root substituting subtract suffixes surd theorem tion triangle U₂ variable Whence zero
Popular passages
Page 90 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 254 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 336 - ... University of Ohio, of Pennsylvania, of Michigan, of Wisconsin, of Kansas, of California, of Missouri, Stanford University, etc., etc. "Those acquainted with Mr. Smith's text-books on conic sections and solid geometry will form a high expectation of this work, and we do not think they will be disappointed. Its style is clear and neat, it gives alternative proofs of most of the fundamental theorems, and abounds in practical hints, among which we may notice those on the resolution of expressions...
Page 254 - ... that the logarithm of the product of two numbers is the sum of the logarithms of the numbers.
Page 74 - Multiply together the numerators for a new numerator, and the denominators for a new denominator.