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annuity arithmetical mean Arithmetical Progression Binomial Theorem black balls coefficient common difference common measure complete quotient contains cube root digits divided divisible divisor equal event example expansion Extract the square factors find the chance find the number find the sum find the value Geometrical Progression given equations greater than unity harmonical mean Hence infinite continued fraction infinite series least common multiple less than unity logarithm miles multiply negative quantity number of combinations number of permutations number of terms obtain occur positive integers positive quantity preceding Article prime number problem proper fraction prove quadratic equation quadratic surd quotient radix ratio remainder respectively result scale series is convergent shew shewn shillings Similarly solution Solve square root student subtraction suppose supposition surd third trial unknown quantities white balls whole number zero
Page 69 - If the numerator and denominator of a fraction be multiplied by the same number, the value of the fraction is not altered.
Page vi - RESEARCHES IN THE CALCULUS OF VARIATIONS, principally on the Theory of Discontinuous Solutions: an Essay to which the Adams' Prize was awarded in the University of Cambridge in 1871.
Page 86 - By transposing we mean bringing the unknown quantities (x, y, z, etc.) to one side of the equation, and the known quantities to the other.
Page 26 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page x - PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples. New Edition, revised and enlarged.
Page 300 - The general formula for the number of combinations of n things taken r at a time is C(и,r) = n\ r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.
Page 71 - Multiply together the numerators for a new numerator, and the denominators for a new denominator.