Complete Secondary AlgebraMacmillan Company, 1901 |
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Common terms and phrases
a₁ arithmetical means arithmetical progression assume b₁ b₂ C₁ coefficient colog column common logarithms continued fraction convergent series corresponding d₁ d₂ decimal places denominator depressed equation determinant digits divergent series Dividing elements equal equation whose roots EXERCISES expansion factor figure Find the value finite number following equations Form the equation geometrical means geometrical progression given equation given series graph harmonical mean Hence increases indefinitely infinite series last term less limit logarithms mantissa method multiplying nth term number of combinations obtained partial fractions partial quotient permutations preceding article principle quadratic equation r₁ ratio real roots reciprocal equation recurring series result S₁ second member series is convergent solution Solve the equation Sturm's Theorem Substituting subtracted third U₁ unknown number variable variations of sign whence wherein x-axis α₁
Popular passages
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...