## The Elements of Algebra |

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### Common terms and phrases

added algebraic arithmetical binomial called cents changed coefficient common complete divisor containing cube decimal denominator difference digits Divide dividend divisible dollars equal equation EXAMPLE Exercise exponent expression Extract factors figures Find the number fourth fraction given gives greater Hence hour increased indicated integral less logarithm mantissa means method miles minus Multiply negative Note operation polynomial positive pounds Process quadratic quotient ratio Reduce remainder represent result second term Similarly simple Simplify Solution Solve square root Substitute Subtract surd taken term third Transpose travels trial divisor units unknown number Write x² y²

### Popular passages

Page 70 - 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 183 - To multiply a fraction by a fraction, multiply the numerators together for the numerator of the product, and the denominators together for the denominator of the product.

Page 121 - To the product of the numerical coefficients, annex each literal factor with an exponent equal to the sum of the exponents of that letter in both factors.

Page 214 - 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?

Page 77 - Observe that the sum of the same powers of two numbers is divisible by the sum of the numbers only when the powers are odd. PRINCIPLES. — 1. ж" — у" гя always divisible by x — y. 2. xn — у" is divisible by x + y only when n is even. 3. x" + y

Page 391 - A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms.

Page 214 - B sets out from the same place and travels in the same direction, at the rate of 5 miles in 3 hours.

Page 151 - Divide the greater number by the less, the divisor by the remainder, and thus continue to divide the last divisor by the last remainder until there is no remainder ; the last divisor will be the greatest common divisor.

Page 397 - In any proportion the terms are in proportion by division; that is, the difference of the first two terms is to the second term as the difference of the last two terms is to the fourth.

Page 100 - 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.