Text-book of Algebra: With Exercises for Secondary Schools and Colleges, Part I, Part 1 |
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Common terms and phrases
a₁ a²b a²b² a²x a²x² a³b ab² ab³ absolute value arithmetical arithmetical means ax² binomial coefficient common factor Commutative Law complex number courier cube root definition denominator digits divided divisor equal equivalent exactly divisible EXERCISES exponent Find the values following expressions following principle fraction given equation given expression given number given system greater harmonical means inequality integer irrational number less m₁ means minuend monomial multinomial multiplied negative number number of dollars obtain parentheses positive integer positive number preceding problem quadratic equation quotient r₁ radicand rational number remainder required numbers result second member solution Solve the equation Solve the system square root Substituting subtracted summands surds trinomial unknown number whence x²y x²y² xy²
Popular passages
Page 362 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Page 437 - The trial divisor at any stage is three times the square of the part of the root already found ; as 27 in the preceding example.
Page 144 - 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 285 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions, and whose denominator is the product of the given denominators.
Page 187 - The square of the sum of two numbers is equal to the square \ (¿ of the first, plus twice the product of the first and second, plus the J square of the second.
Page 602 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Page 196 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Page 612 - The volume of a gas varies inversely as the pressure when the temperature is constant. When the pressure is 15, the volume is 20; what is the volume when the pressure is 20 ? Let v stand for the volume and p for the pressure. Then from pv = k we obtain k = 300. Therefore pv = 300. Consequently, when p = 20, 20 v = 300 ; whence v = 15. EXERCISES III.
Page 615 - It has been found by experiment that the weight of a body varies inversely as the square of its distance from the center of the earth. If...
Page 640 - Eg, in the series 1+3 + 5 + 7 + 9 + .- • (1) each, term after the first is formed by adding 2 to the preceding term. In the series 1 + 2 + 4 + 8 + ••• (2) each term after the first is formed by multiplying the preceding term by 2.