## An Elementary Treatise on Algebra |

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A=log ANsw ANswer arithmetic means arithmetic progression arithmetic series binomial surd Binomial Theorem CHAP coefficient common denominator common difference common ratio compound interest compound quantity consequently cube root decimal digits divide the number dividend divisor equal ExAM ExAMPLE expressed Extract the square figure find the greatest Find the sum Find the value four quantities fraction required geometric progression geometric series given number greatest common measure Hence improper fraction inversely irreducible surd last term least common multiple lesser number logarithm lowest terms Multiply nth root number of terms number required numerator and denominator odd number ºth quadratic equations quan quantity varies question quotient Reduce remainder REVERSION OF SERIES roots of quantities RULE side Simple Equations solution square root substitute subtracted surd quantities Theor three numbers tities transposition unknown quantities whole number

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Página 218 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.

Página 38 - One quantity is said to measure another, when it is contained in that other a certain number of times, without a remainder. 41. A quantity is said to be a multiple of another, when it contains that other quantity a certain number of times, without a remainder. 42.

Página 57 - To explain the division of the given number into periods consisting of two figures each, by placing a dot over every second figure beginning with the units, as exhibited in the foregoing operation. It must be observed, that, since the square root of 100 is 10 ; of 10000 is 100 ; of 1000000 is 1000 ; &c. &c. it follows, that the square root of a number less than 100 must consist of one figure ; of a number between 100 and 10000, of two figures ; of a number between 10000 and 1000000, of three figures...

Página 92 - There is a certain number, to the sum of whose digits if you add 7, the result will be three times the left-hand digit ; and if from the number itself you subtract 18, the digits will be inverted. What is the number ? ANSW.

Página 123 - If four quantities are proportional, the quotient of the first divided by the second, is equal to the quotient of the third divided by the fourth.

Página 64 - any quantity may be transferred from " one side of the equation to the other, by changing its sign ;" and it is founded upon the axiom, that "if equals be added to " or subtracted from equals, the sums от remainders will be

Página 143 - Mr3, ar3, ar*, &c., which will evidently be an increasing or decreasing series, according as r is a whole number, or a proper fraction. In the foregoing series, the index of r in any term is less by unity than the number which denotes the place of that term in the series. Hence, if the number of terms in the series be denoted by (n), the last term will be arn"1.

Página 133 - Prob. 6. If the number 20 be divided into two parts, which are to each other in the duplicate ratio of 3 to 1, what number is a mean proportional between those parts 1 Prob.

Página 107 - Prob. 13. A and B distributed 1200 dollars each, among a certain number of persons. A relieved 40 persons more than B, and B gave to each individual 5 dollars more than A. How many were relieved by A and B 1 Prob.

Página 122 - When the antecedent of a ra13 tio is greater than the consequent, it is called a ratio of greater inequality ; when the antecedent is less than the consequent, a ratio of lesser inequality ; and if the two terms of a ratio be the same, then it is said to be a ratio of equality.