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according added algebraic fraction arithmetical means arithmetical progression arithmetical series Binomial Theorem brackets casks cent coefficients common difference contain cube root decimal denoted digits Divide the number divisor equal equation example Exercise XXXI Expand and give expression Extract the square feet find the number Find the sum four numbers gallons geometrical progression geometrical series given fraction greatest common measure harmonical harmonical means Hence improper fraction least common multiple letters lowest terms middle term months multinomial multiplied number of terms number of variations numerator and denominator obtain piece preceding proportion quadratic quan quotient reduced remainder Required the number resolve rule second power second term sides Simplify solution solved square root substitute subtracted suppose things taken third power tity unknown quantity vulgar fraction whole number write x+y=a yards
Page 158 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 129 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Page 107 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Page 122 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 162 - To find a number consisting of three places, whose digits are in arithmetical progression; if this number be divided by the sum of its digits, the quotient will be 48 ; and if from the number be subtracted 198, the digits will be inverted.
Page 78 - RULE. Find an expression for the value of one of the unknown quantities in one of the equations, and substitute this value for the same unknown quantity in the other equation.
Page 117 - There are four numbers in arithmetical progression : the sum of the squares of the two first is 34 ; and the sum of the squares of the two last is 130. What are the numbers?
Page 63 - The product of two or more fractions is the product of their numerators divided by the product of their denominators. Exam °Óle \. Example 2. IX f о. x Г...