Complete Secondary Algebra

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Macmillan Company, 1901
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Page 316 - 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.
Page 354 - 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.
Page 351 - We will now derive a formula for the number of permutations of n things, taken all at a time, when some of them are alike.
Page 313 - 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...
Page 415 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 418 - 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.
Page 317 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Page 360 - As the body falls, the distance d and the time s are variables, and 16 is a constant. Again, time measured from a past date is a variable, while time measured between two fixed dates is a constant. 2. The constants in a mathematical investigation are, as a rule, general numbers, and are represented by the first letters of the alphabet, a, b, c, etc. ; variables are usually represented by the last letters, x, y, z, etc.
Page 310 - Two workmen can do a piece of work in 6 days. How long will it take each of them to do the work, if it takes one 5 days longer than the other ? 19.
Page 321 - One quantity is said to vary directly as a second and inversely as a third, when it varies jointly as the second and the reciprocal of the third. Thus...

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