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a₁ a²b² ab² ab³ algebraic arithmetical arithmetical series arrangements b₁ binomial c₁ called cent coefficient cologarithm column common factor common logarithms Complete the square complex number contain continued fraction cube root decimal denominator denote determinant digits divided divisible divisor equal Exercise exponent expression Extract the square figures Find the H. C. F. Find the number Find the sum Find the value fraction given equation harmonical series Hence imaginary integers integral less letters limit logarithm miles monomial Multiply negative number number of terms obtained positive integer quadratic quadratic equation quotient ratio remainder represent Resolve into factors result selected Simplify square root Sturm's Theorem Subtract surd Theorem third trinomial unknown number variable whole number zero
Popular passages
Page 277 - For, if a : b = с : d, ,, ac then - = — bd Multiplying by bd, ad = be. The equation ad = be gives a — -£, b = — ; so that an d с 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.
Page 333 - 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 151 - 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 277 - 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 = be, then, dividing by bd, ad_ be bd~bd' ac or j- — -
Page 171 - 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 499 - 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 300 - 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 256 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 448 - 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 306 - 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.