## An Elementary Treatise on Algebra, Theoretical and Practical: With Attempts to Simplify Some of the More Difficult Parts of the Science, Particularly the Demonstration of the Binomial Theorem in Its Most General Form, [etc.] |

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according added addition arithmetical assumed becomes binomial called changed chapter Clear coefficient column completing the square compound consequently consist containing denominator difference Divide dividend division divisor equal equation evidently EXAMPLES expansion expression extracting the root factors figure find the values four fourth fraction gallons geometrical Given gives greater greatest hence increased integer interest known last term least less logarithms manner means method Multiply negative obtained operation performed positive preceding PROBLEM progression proportion proposed quadratic QUESTION quotient radicals ratio Reduce remainder represented Required the sum required to find respectively result rule side similar solutions square root substituting subtracting Suppose surd taken THEOREM third tion transposing transposition unknown quantity values of x whence whole

### Popular passages

Page 83 - В can perform a piece of work in 8 days, A and С together in 9 days, and В and С together in 10 days ; in how many days can each alone perform the same work ? Let...

Page 146 - PROBLEM I. To reduce a rational quantity to the form of a surd. RULE. Raise the quantity to a power...

Page 116 - The plate of a looking-glass is 18 inches by 12, and it is to be surrounded by a plain frame of uniform width/ having a surface equal to that of the glass.

Page 99 - The sum of the first and third of four numbers in geometrical progression is 148, and the sum of the second and fourth is 888.

Page 99 - 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 equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?

Page 75 - There is a number consisting of two digits, which is equal to four times the sum of those digits; and if 18 be added to it, the digits will be inverted. What is the number?

Page 67 - Ans. 16 and 24. 42. It is required to find a number such, that if it be increased by 7, the square root of the sum shall be equal to the square root of the number itself, and 1 more. Ans. 9.

Page 52 - An equation of the third, fourth, &c. degree, is one in which the highest power of the unknown quantity is the third, fourth, &c.

Page 114 - It is required to find two numbers, such, that their sum, product, and difference of their squares, shall be all equal.

Page 145 - The fore-wheel of a carriage makes 6 revolutions more than the hind- wheel in going 120 yards; but if the circumference of each wheel be increased one yard, it will make only 4 revolutions more than the hind-wheel in the same distance.