Elements of AlgebraLongman, Hurst, Rees, Orme, 1822 - 593 pàgines |
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Frases i termes més freqüents
Algebra already arithmetical progression ax² become a square bers biquadrates calculation CHAP coefficient common divisor consequently consider continued fraction crowns cube root cx² decimal fraction denominator determine difference divided divisible equal evident example exponent expressed factors farther formula ƒ² geometrical progression given number gives greater number greatest common divisor Hence infinite number integer numbers last term lastly less let us suppose letters likewise logarithm manner method multiplied negative number of terms numbers sought obtain positive number preceding prime numbers proposed question quotient ratio reduced remainder represented resolve rule second term shew solution square number square root substitute subtract tion transform unity unknown quantity whence wherefore whole numbers
Passatges populars
Pàgina 151 - Three, then, is based on the principle, that the product of the extremes is equal to the product of the means...
Pàgina 31 - 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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?
Pàgina 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.
Pàgina 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...
Pàgina 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.
Pàgina 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...