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absolutely convergent algebraic sum arithmetical arithmetical means arithmetical progression binomial cents changed coefficients common logarithms Commutative Law complete divisor containing continued fraction convergent series corresponding cube root decimal denominator difference digits divided dividend divisible equal to zero established as follows Examples exponent expression Extracting the square Find the value finite formula function geometrical geometrical progression given equation Hence highest common divisor imaginary numbers l)th limit logarithm lowest common multiple mantissa monomial multiplied negative number nth root number of permutations number of terms numerically less obtained odd number partial fractions polynomial positive integer positive number positive root Principle probability proportion quadratic quadratic equation quadratic surd quotient radical real number reduced remainder represent second term Simplify Solve the equation Solve the following square root Substituting subtracted surd third Transposing twice units unknown number variable white balls
Page 212 - ... and if the number is divided by the sum of its digits, the quotient is 21 and the remainder 4.
Page 343 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".
Page 41 - A term may be transposed from one member of an equation to the other, provided its sign is changed.
Page 435 - The number of permutations of n different things taken r at a time is denoted by „Pr.
Page 424 - The logarithm of a quotient is found by subtracting the logarithm of the divisor from that of the dividend.
Page 40 - The process of changing a term from one member of an equation to the other is called Transposition.
Page 331 - PRINCIPLE 7. — If four numbers are in proportion, the. difference between the terms of the first ratio is to either term of the first ratio as the difference between the terms of the second ratio is to the corresponding term of the second ratio ; that is, the numbers are in proportion by Division.
Page 323 - A farmer has two cubical granaries. The side of one is 3 yards longer than the side of the other, and the difference in their solid contents is 117 cubic yards.