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a₁ adding algebraic amount Assume b₁ balls base called chance changed coefficients column common compound constant containing continued convergent course denominator denote derivative determinant divided divisible divisor element equal equation equivalent event evidently EXAMPLE EXERCISE expansion exponent expression factors finite formula fraction function given graph greater happen Hence identity imaginary increases infinite integral interest known least less letters limit loga logarithms method Multiplying negative NOTE obtain pile places positive powers principle probability prove quadratic quantities quotient ratio real roots remainder respectively resulting roots Show solution Solve square Substituting Subtracting successive surd taken things third throwing tion transformed u₁ unknown quantities variable variations write written zero
Page 110 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 193 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 228 - From 12 books in how many ways can a selection of 5 be made, (1) when one specified book is always included, (2) when one specified book is always excluded ? (1) Since the specified book is to be included in every selection, we have only to choose 4 out of the remaining 11. Hence the number of ways...
Page 235 - In general, if an event may happen in a ways, and fail in b ways, and each of these ways is equally likely to occur, the probability of its happening is -, and the probability of its failing is...
Page 109 - D. That is : If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 116 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1 Ib.
Page 107 - A ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same quantity to both its terms.
Page 21 - To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (Sab — 12ac) -i- 4a = 36 — 3c.
Page 3 - To measure a quantity is to find how many times it contains another quantity of the same kind, called a unit of measurement.