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

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### Common terms and phrases

added addition affected algebraic antecedent arithmetical becomes binomial called cents changing coefficient common difference completing the square composed consequent considered contains cube decreasing denominator denotes diminished Divide dividend division divisor dollars double entire enunciation equal equation equation 22 EXAMPLES exponent expression extracting the square extremes factors figure Find the square Find the sum Find the values following RULE four fourth fraction gives greater half Hence increasing interest known last term less letter means method monomial Multiply negative number of terms obtain operations perfect square periods person polynomial positive progression proportion question quotient radical ratio received Reduce remainder represent result rule second degree second term similar simplest form square root subtract taken tens third tion transposing twice units unknown quantity values of x Verification whence write yards

### Popular passages

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 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 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 234 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.

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 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.

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 116 - A person bought a chaise, horse, and harness, for £60 ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and harness ; what did he give for each?

Page 116 - If A and B together can do a piece of work in 8 days, A and C together in 9 days, and B and C in ten days ; how many days would it take each to perform the same work alone ? 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.