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added amount appears arithmetical Assume becomes calculation called cent CHAP clear coefficient complete compound consequently consider consists contains continually crowns cube root decimal denominator determine difference divided dividend divisible divisor easily enabled equal equation evident example exponent expressed Extracting the root factors find the value formula four fourth fraction geometrical given gives greater greatest common measure Hence increased instance integer interest irrational known last term less lesser letters logarithm manner means method multiplied necessary negative number of terms observe obtain positive preceding present principal progression proportion proposed quadratic question quotient ratio reduced remainder represented resolved respect resulting rule second term shown side square root Substituting subtracted suppose surds taken third tion transposition true twice unity unknown quantity whence whole
Side 46 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Side 228 - There are three numbers in geometrical progression ; the sum of the first and second of which is 9, and the sum of the first and third is 15.
Side 36 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Side 248 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Side 58 - We call this new species of numbers, irrational numbers ; they occur whenever we endeavour to find the square root of a number which is not a square. Thus, 2 not being a perfect square, the square root of 2, or the number which, multiplied by itself, would produce 2, is an irrational quantity. These numbers are also called surd quantities, or incommensurables.
Side 243 - Find two numbers, such, that their sum, their product, and the difference of their squares shall be all equal to each other.
Side 77 - any quantity may be transferred from "one side of the equation to the other, by changing its sign ;" and and it is founded upon the axiom, that " if equals be added to " or subtracted from equals, the sums or remainders will be
Side 113 - Ans. 3 and 7 8. The difference of two numbers is 2, and the difference of their cubes is 98; required the numbers. Ans. 5 and 3 9.