Advanced Course in Algebra |
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a²b a²b² ab² ab³ absolute value approaches the limit arithmetic progression assigned number ax² b₁ balls Binomial Binomial Theorem coefficient common factor complex number continued fraction cube root degree denominator determinant digits Dividing divisible divisor equal equivalent EXERCISE exponent expression Find the number geometric geometric progression given equation graph Hence hold indefinitely increased infinite series last term letters linear equations logarithm method monomial Multiplying negative nth root nth term number of terms obtained perfect square polynomial positive integers prove pure imaginary quadratic equation quotient rational and integral rational number real number remainder represented respectively result series is convergent solution Solve the equation square root Sturm's Theorem Substituting Subtracting surd Theorem unknown numbers Whence zero
Popular passages
Page 54 - At what time between 3 and 4 o'clock are the hands of a watch opposite to each other ? Let x = the number of minute-spaces passed over by the minutehand from 3 o'clock to the required time.
Page 196 - Multiply the complete divisor by the term of the root last obtained, and subtract the product from the remainder. If...
Page 41 - 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 199 - Extract the cube root of the first term, write the result as the • first term of the root, and subtract its cube from the given expression; arranging the remainder in the same order of powers as the given expression.
Page 39 - ... with an exponent equal to its exponent in the dividend minus its exponent in the divisor, omitting those letters whose exponents become zero.
Page 337 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 335 - In any proportion, the terms are in proportion by Division ; that is, the difference of the first two terms is to the first term as the difference of the last two terms is to the third term. Let .the proportion be a : b = с : d.
Page 191 - Divide the first term of the remainder by three times the square of the root already found, and write the quotient for the next term of the root.
Page 405 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 172 - The number of terms is greater by 1 than the exponent of the binomial. 2. The exponent of a in the first term is the same as the exponent of the binomial, and decreases by 1 in each succeeding term.