Elements of Algebra with Exercises

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Macmillan Company, 1902 - 478 páginas

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Página 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 356 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Página 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Página 414 - C„.r. That is, the number of combinations of n dissimilar .things r at a time is equal to the number of combinations of the n things n — r at a time.
Página 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 326 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards; but if the circumference of each wheel...
Página 166 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions, and whose denominator is the product of the given denominators.
Página 472 - We therefore have : (i.) The characteristic of the logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part.
Página 418 - Thus, 16 x2, ± -^/(a? — ж2), etc., are functions of x; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.

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