An Elementary Treatise on AlgebraCadell and Davies, 1818 - 227 σελίδες |
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1st equation A=log algebraic quantities ANSW ANSWER antecedent arithmetic means arithmetic series coefficient common denominator common difference consequently cube root decimal digits divide the number divisor equal EXAM EXAMPLE expressed Extract the square Find the sum Find the value four quantities fourth geometric progression geometric series given number greater inequality greatest common measure Hence inversely last term least common multiple lesser inequality lesser number logarithm lowest terms means negative nth power nth root number of terms numerator and denominator quadratic equation quadratic surd quan quantities be proportional question quotient ratio of a b ratio of greater ratio of lesser Reduce remainder resulting ratio RULE solution square root subtracted surd quantity THEOR Theorem three numbers tities transposition unknown quantities whole number
Δημοφιλή αποσπάσματα
Σελίδα 214 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.
Σελίδα 34 - 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.
Σελίδα 53 - 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...
Σελίδα 88 - 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.
Σελίδα 119 - 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.
Σελίδα 60 - 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
Σελίδα 139 - 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.
Σελίδα 129 - 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.
Σελίδα 103 - 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.
Σελίδα 118 - 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.