## Algebra: Adapted to the Course of Instruction Usually Pursued in the Colleges and Academies of the United States |

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### Common terms and phrases

2nd power 3x²y 3xy² 4th power algebraic arithmetical arithmetical mean arithmetical progression coefficient denominator difference Divide x² dividend equation whose roots equation x³ EXAMPLES exponent expression figure Find the 5th Find the equation Find the greatest Find the least Find the number Find the product Find the roots Find the value find x fractions geometrical mean geometrical progression given equation Given x² greatest common divisor last term least common multiple letters mantissa miles minuend mixed quantity monomials Multiply negative number of terms Operation problem Prop proportion px² quotient Reduce remainder root of x³ second member Simplify Solution Solve the equation square root subtract take the square transposed unknown quantity Va² Vide Def whence x²y x²y² x³y xy² xy³ y² x²

### Popular passages

Page 122 - 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.

Page 105 - Find the value of one of the unknown quantities, in terms of the other, from either of the given equations. II. Substitute this value for the same unknown quantity in the other equation.

Page 226 - 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 40 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 57 - 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 239 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.

Page 195 - A man travelled 105 miles, and then found that if he had not travelled so fast by 2 miles an hour, he should have been 6 hours longer in performing the journey.

Page 117 - C in ten days ; how many days would it take each to perform the same work alone ? Ans.

Page 223 - If the means of a proportion are equal, either mean is called a Mean Proportional between the first and last terms, and the last term is called a Third Proportional to the first and second terms.

Page 43 - To divide a polynomial by a monomial, divide each term of the dividend by the divisor and add the partial quotients.