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according added already answers arithmetical become become a square begin bers calculation called CHAP common divisor consequently consider contains continued crowns cube denominator determine difference divided divisible easily easy equal equation evident example explained exponent expressed factors farther formula four fourth fraction given gives greater Hence immediately impossible infinite integer numbers kind known last term lastly least less letters likewise logarithm manner means method multiplied namely nature necessarily negative observed obtain perceive positive possible preceding present prime principal progression proportion proposed quantity question quotient ratio reason reduced relation remainder remark represented resolve result rule seen shew sides solution sought square root substitute subtract suppose Table taken third tion transform unity whence wherefore whole numbers write
Page 151 - Three, then, is based on the principle, that the product of the extremes is equal to the product of the means...
Page 203 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 137 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 203 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? 56.
Page 204 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Page 2 - The manner in which we generally calculate a person's property, is a good illustration of what has just been said. We denote what a man really possesses by positive numbers, using, or understanding the sign + ; whereas his debts are represented by negative numbers, or by using the sign — Thus, when it is said of any one that he has 100 crowns, but owes 50, this means that his property really amounts to 100 — 50 ; or, which is the same thing, + 100 — 50, that is to say 50.
Page 252 - The coefficient pt of the fourth term with its sign changed is equal to the sum of the products of the roots taken three by three ; and so on, the signs of the...
Page 221 - The general rule, therefore, which we deduce from this, in order to resolve the equation xx = — px + g, is founded on this consideration : That the unknown quantity x is equal to half the coefficient, or multiplier of x on the other side of the equation, plus or minus the square root of the square of this number, and the known quantity which forms the third term of the equation.
Page 24 - mb 90. In order therefore to reduce a given fraction to its least terms, it is required to find a number by which both the numerator and denominator may be divided. Such a number is called a common divisor, and so long as we can find a common divisor to the numerator and the denominator, it is certain that the fraction may be reduced to a lower form ; but, on the contrary, when we see that except unity no other common divisor can be found, this shews that the fraction is already in the simplest...