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added addition already seen amount appears arithmetical Assume becomes calculation called changing CHAP clear coefficient common complete consequently consider consists contains continually crowns cube root determine difference divided dividend division 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 half Hence impossible increased instance integer interest irrational known less lesser letters logarithm manner means method multiplied nature necessary observe obtain positive preceding present principal progression proportion proposed quadratic question quotient radical sign ratio reduced remainder represented respect resulting rule second term shown side simple solution sought square root Substituting subtracted suppose surds taken third tion transposition true twice unity unknown quantity write
Página 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.
Página 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.
Página 36 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Página 248 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 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.
Página 243 - Find two numbers, such, that their sum, their product, and the difference of their squares shall be all equal to each other.
Página 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
Página 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.