## A Treatise on the Elements of Algebra: Designed for the Use of Eton School |

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added admits Algebraic amount Answer appears arithmetical becomes called cent co-efficient combinations compound consists continued cube root denotes difference digits Divide divisor equal equation EXAMPLES expression Extract the square find the numbers Find the sum find x formed four fraction geometrical give Given greater greatest common measure half Hence increased interest involving kind latter least common multiple length less Let x Logarithm manner means meet miles months multiplied number of permutations paid permutations person piece placed possible present progression proposed quadratic quantities question quotient raised ratio received remainder represent result rule shillings sides simple solve square root subtract successively Suppose taken term third tion travels unit unity whole number yards

### Popular passages

Page 30 - It is required to divide the number 14 into two such parts that the quotient of the greater divided by the less, may be to the quotient of the less divided by the greater as 16 to 9.

Page 12 - ... then find how often the first term of the divisor is contained in the first term of the dividend, and place the result in the quotient...

Page 22 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days : how many days would the man alone be in drinking it ? Ans.

Page 21 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Page 30 - If 248 men, in 5 days, of 11 hours each, can dig a trench 230 yards long, 3 wide, and 2 deep, in how many days, of 9 hours each, will 24 men dig a trench 420 yards long, 5 wide, and 3 deep ? Here the number of days, in which the proposed work can be done, depends on five circumstances, viz.

Page 70 - There are three numbers in geometrical progression, whose sum is 14; and the sum of the first and second is to the sum of the second and third as 1 to 2.

Page 52 - If there is a remainder, divide the first divisor by the first remainder, the second divisor by the second remainder, and so proceed until you obtain a quotient without a remainder.

Page 38 - What are the numbers ? Ans. 4, 12, and 36. 12. It is required to find two numbers, such, that their product shall be equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes.

Page 68 - 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.