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added algebraic approaches arithmetical arranged assume base becomes called cent chance changed CHAPTER coefficients column common complete consists contains convergent corresponding cube decimal denominator determinant digits distance Divide divisible divisor equal equation event example Exercise exponent expression Extract factors feet figures Find the numbers four fraction function geometrical given gives greater Hence imaginary increased integral interest involving less letters limit logarithms means measure method Multiply negative obtained occur places positive problem progression quadratic quantities quotient ratio Reduce relation remainder represent respectively result selected Show side solution Solve square root Subtract Suppose surd taken term things third true unit unknown numbers variable write written zero
Page 21 - Divide the first term of the dividend by the first term of the divisor.
Page 20 - To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (Sab — 12ac) -i- 4a = 36 — 3c.
Page 27 - The square root of a number is one of the two equal factors of the number.
Page 155 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = be, then, dividing by bd, ad_ be bd~bd' ac or j- — -
Page 359 - Form all the possible products of n elements each that can be formed by taking one, and only one, element from each row, and one, and only one, element from each column...
Page 487 - The modulus of the product of two complex numbers is the product of their moduli, and the amplitude of the product is the sum of their amplitudes.
Page 157 - 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 155 - The equation ad = be gives a — -£, b = — ; so that an d с extreme may be found by dividing the product of the means by the other extreme ; and a mean may be found by dividing the product of the extremes by the other mean.
Page 173 - ... 16. The volume of a sphere varies as the cube of its diameter. Compare the volume of a sphere...
Page 67 - The coefficient of the second term is the same as the exponent of the power to which the binomial is raised.