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absolute value approaches the limit arithmetic means arithmetic progression assigned number Binomial Binomial Theorem coefficient column common factor Commutative Law complex number continued fraction cube root decimal degree denominator denote determinant digits Dividing divisible divisor equal equivalent example EXERCISE Expand exponent expression Find the number Find the value geometric progression given equation graph greater Hence indefinitely increased infinite series last term less letters linear equations logarithm method monomial Multiplying nth root nth term number of terms obtained partial fractions perfect square permutations polynomial positive integer positive number prove pure imaginary quadratic equation quotient radical sign rational and integral rational number real number remainder represented respectively result second member second term series is convergent solution Solve the equation square root Sturm's Theorem Substituting Subtracting surd Theorem third Transposing unknown numbers Whence zero
Page 56 - 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 43 - 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 201 - 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 41 - ... with an exponent equal to its exponent in the dividend minus its exponent in the divisor, omitting those letters whose exponents become zero.
Page 339 - 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 337 - 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 193 - 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 407 - The logarithm of a product is equal to the sum of the logarithms of its factors.