An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page v
... factor and coefficient ( 5 ) , power ( 6 ) , Root and radical sign ( 7 ) , sign ( 8 ) , Sign = , and equation ( 9 ) , signs > and < ( 10 ) , Algebraic quantity ( 11 ) , monomial ( 12 ) , polynomial ( 13 ) , Dimension and degree of terms ...
... factor and coefficient ( 5 ) , power ( 6 ) , Root and radical sign ( 7 ) , sign ( 8 ) , Sign = , and equation ( 9 ) , signs > and < ( 10 ) , Algebraic quantity ( 11 ) , monomial ( 12 ) , polynomial ( 13 ) , Dimension and degree of terms ...
Page vi
... factors ( 27 ) , of sum and difference ( 28 ) , Product of homogeneous factors ( 29 ) , SECTION V. Division ( 30-38 ) , Quotient of monomials ( 30-33 ) , negative exponents ( 32 ) , Quotient of polynomial ( 34-36 , 38 ) , Taking out a ...
... factors ( 27 ) , of sum and difference ( 28 ) , Product of homogeneous factors ( 29 ) , SECTION V. Division ( 30-38 ) , Quotient of monomials ( 30-33 ) , negative exponents ( 32 ) , Quotient of polynomial ( 34-36 , 38 ) , Taking out a ...
Page vii
... factor ( 84 ) , Equation freed from fractions ( 85 , 86 ) , Transposition of terms ( 87 , 88 ) , SECTION III . Solution of Equations of the First Degree , with one Unknown Quantity ( 89-99 ) , • General form of equation ( 89 ) , • Its ...
... factor ( 84 ) , Equation freed from fractions ( 85 , 86 ) , Transposition of terms ( 87 , 88 ) , SECTION III . Solution of Equations of the First Degree , with one Unknown Quantity ( 89-99 ) , • General form of equation ( 89 ) , • Its ...
Page 2
... factor of a product is sometimes called its coefficient , and the numerical factor is called the nu- merical coefficient . When no coefficient is written , the coefficient may be considered to be unity . Thus in the expression 15 a b ...
... factor of a product is sometimes called its coefficient , and the numerical factor is called the nu- merical coefficient . When no coefficient is written , the coefficient may be considered to be unity . Thus in the expression 15 a b ...
Page 3
... factor in the given quantity . The sign is called the radical sign , and when prefixed to a quantity indicates that its root is to be extracted , the index of the root being placed to the left of the sign and a little above it . The ...
... factor in the given quantity . The sign is called the radical sign , and when prefixed to a quantity indicates that its root is to be extracted , the index of the root being placed to the left of the sign and a little above it . The ...
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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.