## First Lessons in Algebra: Embracing the Elements of the Science |

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### Common terms and phrases

algebraic quantities arithmetical means arithmetical progression binomial Binomial Theorem called cents common denominator common difference complete equation completing the square composed contain contrary sign cube decimal denotes Divide dividend division divisor dollars double product enunciation equation involving EXAMPLES exponent extracting the square fifth power figure find a number Find the square Find the sum Find the values following RULE four quantities fourth power geometrical progression Give the rule given number greater greyhound Hence last term least common multiple minus mixed quantity monomial Multiply negative number expressed number of terms obtain ounces of silver perfect square polynomial question quotient radical sign ratio Reduce remainder second degree second power second term simplest form square root Substituting this value take the equation tens third three terms tion transposing trinomial twice the product unknown quantity values of x Verification whence yards

### Popular passages

Page 230 - 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 231 - Quantities are said to be in proportion by composition, when the sum of the antecedent and consequent is compared either with antecedent or consequent.

Page 155 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.

Page 233 - AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.

Page 175 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...

Page 138 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend But if any of the products should be greater than the dividend, diminish the last figure of the root.

Page 214 - A merchant bought cloth for which he paid £33 15s., which he sold again at £2 8s. per piece, and gained by the bargain as much as one piece cost him : how many pieces did he buy ? Ans.

Page 35 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.

Page 214 - To find a number such that if you subtract it from 10, and multiply the remainder by the number itself, the product shall be 21. Ans. 7 or 3.

Page 230 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order...