## Elements of Algebra |

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### Common terms and phrases

a b c a² b³ a³ b² algebraic algebraic quantities arithmetical binomial coefficient completing the square continued fraction decimal divide the number dividend division entire and positive entire number enunciation equal equation evident example exponent expression extract the root factors find the approximate find the greatest find the number find the square find the values formula Freeing from denominators geometrical progression given number gives greater greatest common divisor less letters logarithm manner monomial multiplied negative nth root number of terms obtain operations perfect square polynomials progression by quotient proportion question radical sign ratio reduced remainder Required the numbers resolve result second degree second power second term shillings solution square root subtract third power third root tion units unity unknown quantities values of x vulgar fraction whence yards

### Popular passages

Page 277 - 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 200 - 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 218 - 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 243 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 50 - 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 216 - 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 58 - 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 83 - 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 273 - 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 81 - 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.