Calendar: 1856-1857 Page 371

372 GENERAL LITERATURE AND SCIENCE To divide given straight line 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 Divide straight line into two parts so that the squares of the whole line and one of the parts three times the square of the other part BCD is parallelogram draw DFG meeting BC in and Β produced in join β then will the triangles Β CF be equal to one another sin Given in triangle show that tan Β -7--- a-b cos The rectangle contained by the diagonals of quadrilateral figure inscribed in circle is equal to both the rectangles con- tained by its opposite sides Every solid angle is contained by plane angles which together are less than four right angles Hence show that there can be but five regular solids Upon given straight line to describe segment of circle which shall contain an angle equal to given rectilineal angle Make an equilateral triangle equal to given triangle 10 straight line is divided into three parts Α Β Β CD so that from point Ο they appear of the same magnitude find the position of the point 11 If sin χ sin find χ in terms of the sines of the multiples of 12 If BCD be rectangle and Β be drawn LJ to the diagonal AC EG and Ε to CD and AD then shall EG EF AC 13 Sum sin sin θ sin &c to infinity 14 To inscribe an equilateral and equiangular pentagon in given circle and prove that the area of the triangle area of the pentagon