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according added algebraic quantities amount Answ ANSWER appears applied arise arithmetic becomes binomial called changed coefficient combinations common denominator compound consequently consisting contained cube root decimal difference digits divided dividend division divisor equal equation evident Exam EXAMPLE expressed Extract factors figure Find the value four fourth fraction geometric progression given gives greater greatest common measure Hence increase interest inversely known less lesser letters logarithm lowest terms manner means method Multiply negative number of terms observed operation period permutations person population positive proper proportional quadratic equation question quotient ratio Reduce relation remainder represent respect resulting Rule shillings side simple solution square root substitute subtracted Suppose taken Theor Theorem third units unknown quantities varies whole number
Side 216 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.
Side 36 - 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.
Side 55 - 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...
Side 90 - 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.
Side 121 - 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.
Side 62 - 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
Side 141 - 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.
Side 131 - 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.
Side 105 - 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.
Side 120 - 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.