An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page vi
... common divisor of polynomials ( 43-47 ) , . Reduction of fractions to common denominator ( 48–50 ) , Least common multiple ( 51 ) , 9 9 13 13 14 14 18 21 22 25 25 26 26 26 34 36 SECTION II . Addition and Subtraction of Fractions ( 52 ...
... common divisor of polynomials ( 43-47 ) , . Reduction of fractions to common denominator ( 48–50 ) , Least common multiple ( 51 ) , 9 9 13 13 14 14 18 21 22 25 25 26 26 26 34 36 SECTION II . Addition and Subtraction of Fractions ( 52 ...
Page 25
... denominator of the fraction ; and the numerator and denominator of a ... common to the two terms of a quotient , which , as is evident from art . 30 ... Common Divisor . 41. The terms of a fraction 3 CH . II . § I. ] 25 REDUCTION OF ...
... denominator of the fraction ; and the numerator and denominator of a ... common to the two terms of a quotient , which , as is evident from art . 30 ... Common Divisor . 41. The terms of a fraction 3 CH . II . § I. ] 25 REDUCTION OF ...
Page 34
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Greatest Common Divisor . The suppression of ... denominator . Solution . Multiply both terms of each fraction by the product of all the other denominators . Common ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Greatest Common Divisor . The suppression of ... denominator . Solution . Multiply both terms of each fraction by the product of all the other denominators . Common ...
Page 35
... denominators , the fractions are all reduced to the same denominator . 49. But fractions can be reduced to a common denomi- nator which is smaller than their continued product , when- ever their denominators have a common multiple less ...
... denominators , the fractions are all reduced to the same denominator . 49. But fractions can be reduced to a common denomi- nator which is smaller than their continued product , when- ever their denominators have a common multiple less ...
Page 36
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Common Denominator . 1 denominator a2 3. Reduce a b ' - - b2 . a + b 1 , α b ' , a2 - c + d b2 to the common Ans . a2 + 2ab + b2 a2 — b2 - a b - a2 b2 - a2 b2 ' a2 ...
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Common Denominator . 1 denominator a2 3. Reduce a b ' - - b2 . a + b 1 , α b ' , a2 - c + d b2 to the common Ans . a2 + 2ab + b2 a2 — b2 - a b - a2 b2 - a2 b2 ' a2 ...
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Common terms and phrases
3d root 94 become zero arithmetical progression Binomial Theorem coefficient commensurable roots common difference continued fraction continued product Corollary deficient terms denote dividend divisible equal roots equation becomes factor Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum Free the equation gallons Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots integer last term least common multiple letter logarithm monomials negative roots number of real number of terms obtained places of decimals polynomial positive roots preceding article Problem proportion quantities in example Questions into Equations quotient radical quantities ratio real root reduced remainder required equation required root Scholium Second Degree Solution Solve the equation square root subtracted tained term multiplied unity unknown quantity whence
Popular passages
Page 149 - subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. Double the root now found for a new divisor and continue the operation as before, until all the periods are brought down. EXAMPLES. 1.
Page 149 - at the right of the divisor. Multiply the divisor, thus augmented, by the last figure of the root, subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. Double the
Page 203 - One hundred stones being placed on the ground, in a straight line, at a distance of 2 yards from each other; how far will a person travel, who shall bring them one by one to a basket, placed at 2 yards from the first stone? Ans. 11 miles, 840 yards.
Page 157 - Find three numbers such, that the product of the first and second is 6, that of the first and third is 10, and the sum of the squares of the second and third is 34. Ans. 2, 3, 5.
Page 262 - that is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 50 - A merchant adds yearly to his capital one third of it, but takes from it at the end of each year $1000 for his expenses. At the end of the third year, after deducting the last
Page 69 - A father gives to his five sons $1000, which they are to divide according to their ages, so that each elder son shall receive $20 more than his next younger brother. What is the share of the youngest? Ans. $160.
Page 95 - C compare their fortunes. A says to B, 'give me $700 of your money, and I shall have twice as much as you retain; ' B says to C, ' give me $1400, and I shall have thrice as much as you have remaining ;
Page 53 - A work is to be printed, so that each page may contain a certain number of lines, and each line a certain number of letters. If we wished each page to contain 3 lines more, and each line 4 letters more, then there would be 224 letters more on each page; but if
Page 262 - that is, the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root.