## The elements of algebra |

### Other editions - View all

### Common terms and phrases

2ab+b² a+b+c a²+2ab+b² a²+2ax a²x² annex arithmetical series ax² binomial binomial theorem common denominator common difference common ratio compound quantity consecutive numbers cube root deno denote the number Divide divisor double equal equation contains EXERCISES expressed Extract the square factor Find a number find the Greatest Find the number Find the sum following quantities geometric means GEOMETRICAL PROGRESSION given quantity Greatest Common Measure Hence Least Common Multiple letters miles per hour mixed quantities multiplied negative number of balls number of combinations number of permutations number of terms numbers whose sum numerator and denominator Prove QUADRATIC EQUATIONS quotient remainder shillings sign changed simple quantity square root subtracting surd t₁ things taken third total number transposing travelled unknown quantity

### Popular passages

Page 59 - 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 of the other part.

Page 86 - The fore-wheel of a carriage makes six 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 four revolutions more than the hind-wheel in going the same distance.

Page 58 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.

Page 16 - If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered.

Page 42 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.

Page 9 - A power of a quantity is divided by any other power of the same quantity by subtracting the index of the divisor from that of the dividend, the quotient being that power of the quantity whose index is the remainder so obtained.

Page 64 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.

Page 39 - ... be divided by the number of terms to that place, it will give the coefficient of the term next following.

Page 42 - Take the root of the first term, for the first term of the required root...

Page 38 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...