## A treatise on the elements of algebra, by G. Ainsworth and J. Yeats1854 |

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A Treatise on the Elements of Algebra, by G. Ainsworth and J. Yeats G Ainsworth No preview available - 2016 |

### Common terms and phrases

a+b-c a+b+c a²+2ab+b² abcd added algebraic fraction arithmetical means arithmetical progression arithmetical series binomial Binomial Theorem brackets casks cent coefficients common difference compound cube root decimal denoted digits dividend divisible divisor equal equation example EXERCISE XXXI exponent expression factors feet find the number four numbers fourth geometrical progression geometrical series greatest common measure harmonical harmonical mean Hence least common multiple letters lowest terms multinomial multiplied negative number of terms number of variations numerator and denominator obtain permutations positive preceding proportion quadratic quan quotient ratio Reduce remainder Required the number rule second term Simplify square root subtracted suppose surd Theorem things taken third power unknown quantity whole number write x+y=a x²-y² x²+2xy

### Popular passages

Page 160 - 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 19 - 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 131 - 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 109 - 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 124 - 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 164 - 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 80 - 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 119 - 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 65 - The product of two or more fractions is the product of their numerators divided by the product of their denominators. Exam ¡île \. Example 2. IX f о. x Г...

Page 156 - 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.