Calendar: 1870-1871 Page 512

512 GENERAL LITERATURE AND SCIENCE About given circle describe triangle equiangular to given triangle Two equilateral triangles are described about the same circle show that their intersections will form an equilateral hexagon Inscribe regular quindecagon on given circle In circle inscribe triangle whose angles are as the numbers and 10 Similar triangles are to one another in tbe duplicate ratio of their homologous sides Bisect triangle by straight line drawn parallel to one of its sides 11 Equal triangles which have one angle in each equal have the sides about the equal angles reciprocally proportional Find point in the side of triangle from which two lines drawn one to the opposite angle and the other parallel to the base shall cut off towards the vertex and towards the base equal triangles 12 If the angle of triangle be divided into two equal angles by straight line which also cuts the base the segments of the the base have the same ratio which the other sides of the triangle have to one another If be three points in straight line and point at which AB BC subtend equal angles show that the locus of is circle 13 Draw straight line at right angles to plane from given point in the plane Prove that the shortest distance between two opposite edges of regular tetahedron is equal to half the diagonal of the square described on an edge 14 If be the middle point of chord QVQ' of parabola parallel to the tangent at show that V" SP PV If from the point of contact of tangent to parabola chord he drawn and line parallel to the axis meeting the chord the tangent and the curve show that this line will be divided by them in the saute ratio as it divides the chord 15 From the foci Sand Η of an ellipse ST and Ε Zare drawn at right angles to the tangent at Ρ prove that and Ζ are in the circumference of the circle whose diameter is the major axis