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4th power added Algebra algebraic quantities Answers arithmetical Belfast Academy binomial binomial theorem called coefficient common denominator common logarithms complete quotient compound quantity contained cube root cubic equation denote difference Divide dividend equal EXAMPLES FOR PRACTICE expressed extract the square factors Find the sum find the value follows fourth geometrical progression Given Equations gives greatest common measure Hence hypotenuse indicates infinite series integer involution last term least common multiple letters linear units logarithms means miles multiplied nature of division negative quantities number of terms odd number operations plain positive prime proportion quadratic quadratic equation quan quotient ratio rectangle Reduce remainder Required the number RULE second power second term sides solved square root substitution subtracted superficial units surds symbol taken third power tion tity transposing transposition triangle unknown quantities whence Art whole number
Page 249 - London, in order to distinguish his own from any he might meet on the road, pulled three feathers out of the tail of each turkey, and one out of the tail of each goose ; and, upon counting them, found that the number of turkey's feathers exceeded twice those of the geese by 15.
Page 242 - A vintner sold 7 dozen of sherry and 12 dozen of claret for £50, and finds that he has sold 3 dozen more of sherry for £10 than he has of claret for £6. Required the price of each.
Page 256 - In any proportion, the product of the means is equal to the product of the extremes.
Page 256 - In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2.
Page 294 - To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment.
Page 249 - ... feathers exceeded twice those of the geese by 15. Having bought 10 geese and sold 15 turkeys by the way, he was surprised to find, as he drove them into the poulterer's yard, that the number of geese exceeded the number of turkeys in the proportion of 7 to 3.
Page 246 - 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 250 - 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 1 Ans.