An Elementary Treatise on Algebra: For the Use of Students in High Schools and Colleges |
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Page iv
... factors , finding the divisors of quantities , and the substitution of numbers in algebraic for- mulæ . Most of the problems are original ; others have been selected , which seemed the most appropriate . Although this treatise is ...
... factors , finding the divisors of quantities , and the substitution of numbers in algebraic for- mulæ . Most of the problems are original ; others have been selected , which seemed the most appropriate . Although this treatise is ...
Page vi
... factors , XIV . Multiplication of fractions by integral quantities , XV . Division of fractions by integral quantities , - - 47 48 49 55 -b , - 56 58 ib . XVI . Factors and divisors of quantities- prime quantities , Separation of ...
... factors , XIV . Multiplication of fractions by integral quantities , XV . Division of fractions by integral quantities , - - 47 48 49 55 -b , - 56 58 ib . XVI . Factors and divisors of quantities- prime quantities , Separation of ...
Page vii
... factors , XLII . Roots of polynomials , XLIII . Simplification of irrational or radical quantities , 166 168 169 172 180 183 185 186 · ib . - 191 XLIV . Operations on irrational quantities with fractional exponents , 194 XLV ...
... factors , XLII . Roots of polynomials , XLIII . Simplification of irrational or radical quantities , 166 168 169 172 180 183 185 186 · ib . - 191 XLIV . Operations on irrational quantities with fractional exponents , 194 XLV ...
Page 30
... factors is unimportant , we may place the numerical factors next to each other , thus , 5 × 2 a b c d , or per- forming the multiplication of 5 by 2 , we have 10 a b c d . But we could not write 5 2 a b c d , as the product of 5 a b and ...
... factors is unimportant , we may place the numerical factors next to each other , thus , 5 × 2 a b c d , or per- forming the multiplication of 5 by 2 , we have 10 a b c d . But we could not write 5 2 a b c d , as the product of 5 a b and ...
Page 31
... factor . Thus , a a is written a2 ; aaa , a3 , and a a a a a , a3 . A product must always contain all the factors both of the mul- tiplicand and multiplier . In the present case , the letter a is twice a factor in the multiplicand , and ...
... factor . Thus , a a is written a2 ; aaa , a3 , and a a a a a , a3 . A product must always contain all the factors both of the mul- tiplicand and multiplier . In the present case , the letter a is twice a factor in the multiplicand , and ...
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Common terms and phrases
3d power a b c a² b² a² b³ abc2 added algebra ALGEBRAIC QUANTITIES arithmetical bought bushels cents change the signs coefficient contain cows decimal difference Divide dividend division equal example exponent expressed Extract Find the 3d Find the 4th Find the third following RULE formula fraction gallons given gives greater greatest common divisor Hence integral quantity last term least common multiple less Let the learner letter logarithm manner monomial mth power Multiply number of terms numerator and denominator obtain Operation polynomials preceding prime factors progression by quotient proportion quan question ratio remainder Required the number result rods second power second root SECTION separated shillings square Substitute subtracted Suppose tens third power third root tities twice unknown quantity whole number yards
Popular passages
Page 50 - 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.
Page 46 - ANOTHER. 1. Divide the coefficient of the dividend by the coefficient of the divisor. 2.
Page 23 - A shepherd in time of war was plundered by a party of soldiers, who took \ of his flock and \ of a sheep ; another party took from him \ of what he had left and \ of a sheep ; then a third party took \ of what now remained and J of a sheep.
Page 226 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 258 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 260 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 1 - Algebraic operations are based upon definitions and the following axioms : — 1. If the same quantity, or equal quantities, be added to equal quantities, the sums will be equal. 2. If the same quantity, or equal quantities, be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity, or equal quantities, the products will be equal.
Page 223 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 1 - If equal quantities be divided by the same or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be altered.
Page 137 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.