## Elements of Algebra |

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### Contents

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### Common terms and phrases

added algebraic approximate arithmetical arrangements becomes binomial called coefficient consisting contain continued denominator determine difference divide dividend division entire number enunciation equal equation evident example exponent expression extract factors figure find the values formula four fourth fraction given gives greater greatest common divisor indicated interest less letters logarithm manner means miles multiplied necessary negative obtain operations performed persons pieces polynomials positive preceding principal problem progression proportion proposed question quotient radical raised ratio received reduced remainder represent resolve respectively result rule shillings sides simple solution sought square root Substituting subtract taken tens term third third power third root tion twice units unity unknown quantities values of x whence whole yards

### Popular passages

Page 273 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.

Page 196 - Powers of the same quantity are divided by subtracting the exponent of the divisor from that of the dividend ; the remainder is the exponent of the quotient.

Page 214 - Therefore, any term of the progression is equal to the first term multiplied by the ratio raised to a power 1 less than the number of the term.

Page 239 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 46 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.

Page 212 - A number consisting of three digits which are in arithmetical progression, being divided by the sum of its digits, gives a quotient 48 ; and if 198 be subtracted from the number, the digits will be inverted.

Page 54 - 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 79 - Two persons, A and B, can perform a piece of work in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. In what time could each do it separately? Ans. A in 24, B in 48 days.

Page 269 - A farmer has a stack of hay, from which he sells a quantity, which is to the quantity remaining in the proportion of 4 to 5. He then uses 15 loads, and finds that he has a quantity left, which is to the quantity sold as 1 to 2. How many loads did the stack at first contain ? 10. There are 3 pieces of cloth, whose lengths are in the proportion of 3, 5, and 7 ; and 8 yards being cut off" from each, the whole quantity is diminished in the proportion of 15 to 11.

Page 77 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.