## A Treatise on Algebra: Containing the Latest Improvements. Adapted to the Use of Schools and Colleges |

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### Contents

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### Common terms and phrases

45 cents algebraic arithmetical arithmetical progression becomes binomial binomial theorem cenu coefficients column common divisor consequently contain continued fraction cube root cubic equation denote derived functions determine difference divide dividend divisible elimination equa EXAMPLE exponent expression final equation formula give given equation given number greater greatest common divisor greatest common measure Hence imaginary roots indeterminate least common multiple letter logarithm manner method modulus monomial multiplied negative roots number of terms number of variations obtain odd number perfect square permutations polynomial positive roots prime number problem proposed equation quadratic quadratic equation quotient radical ratio real roots reduced remainder represent result rule second degree second term solution square number square root substituting subtract successive suppose symmetric functions theorem third tion transformed equation Transposing unity unknown quantity whence whole number

### Popular passages

Page 76 - Multiply the divisor thus increased, by the second term of the root, and subtract the product from the remainder.

Page 23 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 237 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.

Page 261 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 122 - Proportion is an equality of ratios. Thus, if a, b, c, d are four quantities, such that a, when divided by b, gives the same quotient as c when divided by d, then a, b, c, d are called proportionals, and we say that a is to b as c is to d...

Page 107 - There will be as many figures in the root as there are periods in the given number.

Page 236 - A's journey. How far did each travel ? A 72 miles. B 54 miles. 9. A company at a tavern had £8 15s. to pay for their reckoning ; but before the bill was settled, two of them left the room, and then those who remained had 10s. apiece more to pay than before : how many were there in the company ? Ans. 7.

Page 237 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately ? Ans.

Page 69 - To divide powers of the same base, subtract the exponent of the divisor from the exponent of the dividend.

Page 49 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.