The Principles of Elementary Algebra |
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... theorem or of undetermined 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 ...
... theorem or of undetermined 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 ...
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... THEOREM . TRANSFORMATION OF FUNC- TIONS . APPROXIMATION TO ROOTS ..... 176 XII . PROGRESSIONS . INTEREST AND ANNUITIES . 188 XIII . PERMUTATIONS , COMBINATIONS , BINOMIAL THEOREM 210 XIV . INEQUALITIES . 227 XV . UNDETERMINED ...
... THEOREM . TRANSFORMATION OF FUNC- TIONS . APPROXIMATION TO ROOTS ..... 176 XII . PROGRESSIONS . INTEREST AND ANNUITIES . 188 XIII . PERMUTATIONS , COMBINATIONS , BINOMIAL THEOREM 210 XIV . INEQUALITIES . 227 XV . UNDETERMINED ...
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... theorem : The sum of two numbers multiplied by their product is equal to the sum of the numbers formed by multiply- ing each number by the square of the other . It may be remarked that theorems like the foregoing cannot , in general ...
... theorem : The sum of two numbers multiplied by their product is equal to the sum of the numbers formed by multiply- ing each number by the square of the other . It may be remarked that theorems like the foregoing cannot , in general ...
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Nathan Fellowes Dupuis. 2. Interpret ii . and iii . of 1 as theorems in numbers . 3. By means of v . of 1 find two numbers such that the sum of their squares shall be a square . Make a table of such numbers . 4. Find the value of x in ...
Nathan Fellowes Dupuis. 2. Interpret ii . and iii . of 1 as theorems in numbers . 3. By means of v . of 1 find two numbers such that the sum of their squares shall be a square . Make a table of such numbers . 4. Find the value of x in ...
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... theorems in numbers 13. The difference between the square of the sum and the square of the difference of two numbers is the product of twice the numbers . 14. The sum of the squares of the sum and of the difference of two numbers is one ...
... theorems in numbers 13. The difference between the square of the sum and the square of the difference of two numbers is the product of twice the numbers . 14. The sum of the squares of the sum and of the difference of two numbers is one ...
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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.