Calendar: 1874-1875 Page 549

GENERAL LITERATURE AND SCIENCE 549 23 Of the two squares that can be inscribed in right-angled triangle which is the larger 24 Find the ratio between the sides the areas of an equilateral triangle and square inscribed in the same circle 25 The distances of the centre of the circle inscribed in triangle from the centres of the three escribed circles are respectively Β β sec ο sec csec 26 AB CD is horizontal straight line At point imnie- diately above AB and BC subtend the same angle If Β BC then the height of the observer's station above is 2ab tan bf 2t n2a' IV -algebra anil 3Df eorD of equations Find the number of homogeneous products of η things of dimensions Without assuming the form of the result show ά priori that the number ought to coincide with the number of combinations of η -J- things taken together Prove that the sum of the products of the η quantities c2 cn taken at time is e" e- ί2 If bz cy cx az ay bx prove that χ ζ s3 ζ and 2xyz where ί ύ