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according added Algebra applied Arithmetic becomes binomial called CHAPTER coefficients common common measure complete compound quantity consequently consisting containing continued cube root DEFINITIONS denominator determine difference Divide dividend divisor equal equation EXAMPLE EXERCISE exponent expressed Extract factors former four fourth fraction geometrical progression given given quantity gives greater greatest Hence integer length less letters manner means merely method miles Multiply negative NOTE obtain positive possible preceding PROBLEM proportion proved quadratic quotient Raise ratio Reduce regarded remainder represent Resolve result RULE second term separately side simple sometimes square root subtract surd taken term THEOREM things third tion twice unknown quantity variations varies vinculum whole
Side 187 - ... fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 220 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 184 - When there is a series of quantities, such that the ratios of the first to the second, of the second to the third, of the third to the fourth, &c., are all equal ; the quantities are said to be in continued proportion.
Side 26 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Side 179 - Ratios tnat are equal to the same ratio are equal to one another.
Side 185 - If three quantities are proportional, the first is to the third, as the square of the first to the square of the second ; or as the square of the second, to the square of the third.
Side 184 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last.
Side 93 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Side 180 - Division, when the difference of the first and second is to the second as the difference of the third and fourth is to the fourth...