Calendar: 1850-1851 Page 319

GENERAL LITERATURE AND SCIENCE 315 In Euclid 47 Book show if the adjacent corners of the squares be joined by lines II FD KE the sum of their squares is equal to six times the square of the hypothenuse The roduct of the terms of an arithmetic series is greater η than al and the sum of the terms of geometric series is 71 less than a- -l η being respectively the first the last term and the number of terms The three squares inscribed in circle its semicircle and quadrant are as the numbers 20 and 10 If be the sides of quadrilateral inscribed in circle and be the angle included by and and sum of the sides then hhall ta S-d S-c 11 person ascending mountain having reached an alti- tude of feet observes that the angle of depression of the visible horizon is twice as great as when he was feet high thence find the first angle of depression and the radius of the earth 12 If Ν be number of which the prime factors are and the number of integers prime to and less than 13 hexagon is inscribed in circle circle in that hexagon and so on show that the areas between the first two circles and first two hexagons are £ th respectively of the first circle and first hexagon and that the areas of all the interior circles are three times that of the original circle 14 If tan θ cos tan φ show that θ φ -tan sin φ -f-tan sin φ -f &c 15 Find the amount of an annuity to be continued η years and when η is considerable determine the increase of value if the payments be made half-yearly 16 Find number corresponding to logarithm not found exactly in the tables