Calendar: 1861-1862 Page 503

504 APPLIED SCIENCES To describe circle about given square Describe circle which shall touch two given straight lines and pass through given point between 10 The sides about the equal angles of equiangular triangles are proportionals and those which are opposite to the equal angles are homologous sides that is are the antecedents or con- sequents of the ratios 11 Similar polygons may be divided into the same number of similar triangles having the same ratio to one another that the polygons have and the polygons have to one another the dupli- cate ratio of that which their homologous sides have 12 Β and AC are the sides of pentagon and decagon inscribed in the same circle on different sides of the point show if BC be joined that the difference between Β and is equal to the radius of the circle 13 If the corner of cube be cut off show that the area of the truncated portion of the cube is equal to the sum of the three areas of the triangle which form the part cut off 14 AB is the diameter of circle and any point in AB place in the circle line BD so that the square of BD equals the rectangle AB AC 15 The external angles Cof triangle ABC are bisected by lines meeting in and from lines are drawn parallel respectively to AB AC meeting AC AB in Μ show that the figure OMAN is Rhombus 16 Given the perimeter the vertical angle and the difference of the base angles construct it Department of tj&e gpplteu Sciences MIDDLE SCHOLARSHIPS -Conic Sections Π -C coru of Equations III -differential Calculus