Elements of Algebra (Google eBook)

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Longman, Orme, 1822 - Algebra - 593 pages
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MBA 502

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A genius book. This old textbook truly depicts Leonhard Euler's genius. Too bad Euler's Identity was not mentioned in here!

Contents


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Page 153 - Three, then, is based on the principle, that the product of the extremes is equal to the product of the means...
Page 33 - Multiply the numerator of the dividend by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor ; the first product "will be the numerator of the quotient, and the second wiU be its denominator.
Page 205 - 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 139 - 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 205 - 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 206 - 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 4 - 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 254 - 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 223 - 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 26 - 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...

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