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### Contents

 Definitions 3 Subtraction 10 Division 17 Simple Equations 30 Evolution 38 Reduction 54 Multiplication 63
 Simple Equations continued 70 XII 97 XIII 110 XVI 131 XVIII 140 XXI 148 Miscellaneous Exercises 180

### Popular passages

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 17 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.
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 ��le \. Example 2. IX f о. x Г...
Page 154 - A certain number, consisting of two places, a unit and a ten, is four times the sum of its digits, and if 27 be added to it, the digits will be inverted. What is the number ? NOTE.