Essentials of Algebra for Secondary Schools |
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Common terms and phrases
a²b a²b² a²b³ a²x² a³b ab² ab³ Algebra arithmetic means arithmetic progression ascending powers ax² binomial Binomial Theorem cents change the sign coefficient cologarithm common factor cube root decimal degree denominator digits Divide dividend divisor equal EXAMPLES exponent Extracting the square Find the H. C. F. Find the number Find the value following rule geometric progression greater Hence highest common factor last term less logarithm m³n mantissa miles an hour monomial Multiplying negative number Note number of dollars number of terms partial fractions perfect square polynomial positive integer positive number proportion quadratic equation quotient radical sign ratio Reduce remainder result second term Solve the equation Solve the following square root Subtracting Transposing trial-divisor unknown quantities Whence x²y xy² xy³
Popular passages
Page 272 - In any proportion, the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
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.
Page 273 - 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 51 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 22 - From §§36 and 37, we have the following rule: To subtract one number from another, change the sign of the subtrahend, and add the result to the minuend.
Page 271 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = bс.
Page 61 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.
Page 334 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 272 - In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second term is to the fourth.
Page 273 - 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 to their difference.