Calendar: 1870-1871 Page 492

492 GENERAL LITERATURE AND SCIENCE Describe square equal to given rectangle Divide straight line into two parts so that the rectangle contained by the whole line and one of the parts may be equal to tbe square of the other part Solve this problem algebraically and show that the two solutions coincide What is meant by reduclio ad absurdum proof To what class of propositions is this mode of proof generally applied 10 Enunciate the 6th and 7th propositions of the second book Give the algebraical statements of equality which cor- respond to them 11 Produce straight line so that the rectangle contained by the whole line produced and the part produced may be equal to the square of given line 12 In the 24th proposition of the first book why are the two shorter of the given sides of the triangles applied to each other Can you give proof applying the two longer sides Π -Srftfcmttii anu SUgrbra Find the product of 45678 and 14112 by two lines only of multiplication Divide 203 tons 17 cwt qrs lbs 13 oz by 3J Find the cost of twenty dozen of wine at ז per bottle and if three bottles are spoiled what will be gained by selling the remainder at 5s 4d per bottle In what time will £229 10 amount to £258 3s 9d at per cent per annum simple interest What fraction of 5s is Is Reduce the result to decimal Add together 7125 of 3£ guineas and 03125 of £25 piece of cloth when measured by yard measure which is two-thirds of an inch short appears to be 10 yards long what is its real length and Β can build boat in 18 days and with the help of in 11 days in what time could do it alone