## A Higher Algebra |

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### Common terms and phrases

algebraic arithmetical arithmetical series arrangements assigned value binomial binomial theorem called cent coefficient cologarithm column common factor common logarithms Complete the square complex number contain cube root decimal denominator denote determinant digits divided divisible divisor equal Exercise exponent expression Extract the square factors x figures Find the H. C. F. Find the number Find the sum Find the value geometrical series given equation given number greater harmonical series Hence imaginary infinite series integers last term less letters limit logarithm mantissa miles monomial Multiply negative number number of terms obtained perfect square positive integer quadratic equation quotient ratio real roots Reduce remainder Resolve into factors result second term Simplify square root Sturm's Theorem subtract surd Theorem things third trinomial unknown number variable whole number written yards zero

### Popular passages

Page 315 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.

Page 139 - A man leaves the half of his property to his wife, a sixth to each of his two children, a twelfth to his brother, and the remainder, amounting to $600, to his sister. What was the amount of his property ? 17.

Page 149 - A cask contains 12 gallons of wine and 18 gallons of water ; another cask contains 9 gallons of wine and 3 gallons of water. How many gallons must be drawn from each cask to produce a mixture containing 7 gallons of wine and 7 gallons of water?

Page 265 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = bc, then, dividing by bd, or / (л- с'- v / 316.

Page 169 - The sum of the two digits of a number is 6, and if the number is divided by the sum of the digits the quotient is 4. What is the number ? 19.

Page 475 - Form all the possible products of n elements each that can be formed by taking one, and only one, element from each row, and one, and only one, element from each column ; prefix to each of the products thus formed either...

Page 286 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? 24.

Page 290 - Of three numbers in geometrical progression, the sum of the first and second exceeds the third by 3, and the sum of the first and third exceeds the second by 21. What are the numbers ? 15.

Page 432 - The coefficient pt of the fourth term with its sign changed is equal to the sum of the products of the roots taken three...

Page 265 - The equation ad = be gives be ad a = -у, b — — ; a с so that an extreme may be found by dividing the product of the means by the other extreme ; and a mean may be found by dividing the product of the extremes by the other mean.