## Essentials of Algebra for Secondary Schools |

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### Common terms and phrases

9 x² a²b a²b² a³b ab² ab³ algebraic arithmetic means arithmetic progression 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 formulæ geometric geometric progression greater Hence highest common factor last term less logarithm 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 278 - 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 39 - 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 130 - 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 276 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.

Page 57 - 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 135 - A person has a hours at his disposal. How far may he ride in a coach which travels b miles an hour, so as to return home in time, walking back at the rate of с miles an hour ? 43.

Page 279 - 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:b = c:d = e:f.

Page 277 - 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 = bc.

Page 129 - Find the fraction. 30. The second digit of a number exceeds the first by 4 ; and if the number, increased by 39, be divided by the sum of its digits, the quotient is 7. Find the number. 31. I paid a certain sum for a horse, and seven-tenths as much for a carriage. If the horse had cost...

Page 135 - A banker has two kinds of money ; it takes a pieces of the first to make a crown, and b of the second to make the same sum. Some one offers him a crown for c pieces. How many of each kind must the banker give him ? Ans.