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a₁ added arithmetical assume b₁ balls base called changed coefficient column common Consequently contains continued fraction convergent correction corresponding d₁ decimal definite denominator determinant difference divergent Dividing division elements equal evidently example EXERCISES expansion expression factor figure Find Find the value finite four fourth fraction function geometrical give given equation given series graph greater Hence holds increases infinite integral layer less letters limit logarithms manner mantissa means method multiplying negative Observe obtained opposite partial positive powers preceding article principle progression proportion proved quadratic quotient ratio relation remaining result roots satisfy solution Solve the equation square Substituting subtracted taken term things third transformed variable variations whence wherein yards
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...