When a body has six equal and similar surfaces it is called a hexahedron.

143. Make of one piece of card a hollow hexahedron. Show on paper how you arrange the surfaces so as to fold together, and give a sketch of the hexahedron when finished; and say what other names a hexahedron has.

144. Can you make a right-angled triangle, whose base shall be 4 and perpendicular 6?

In a right-angled triangle, the side which faces the right angle is called the hypothen use.

145. Can you make a right-angled triangle, whose base shall be 4 and hypothenuse 6?

146. Can you make a rectangle, whose length shall be 5 and diagonal 6?

147. Divide a rectangle several ways into four equal and similar figures, and write upon each figure its proper name.

The term vertex means the crown, the top, the zenith; and yet the angle of an isosceles triangle which is contained by the equal sides is called the vertical angle, however such triangle may be placed; and the side opposite to suc

angle is still called the base, although it may not happen to be the lowermost side.

148. Place in different positions four isosceles triangles, and point out the vertex of each.

149. Construct an isosceles triangle, whose base shall be 1 inch, and each of the equal sides 2 inches, and place on the opposite side of the base another of the same dimensions.

150. Can you invent a method of dividing a circle into four equal and similar parts, having other boundaries rather than the radii?

You have made a square, and placed an equilateral triangle on each of its sides.

151. Can you make an equilateral triangle, and place a square on each of its sides?

152. Can you fit a square inside a circle, and another outside, in such positions with regard to cach other as shall show the ratio the inner one has to the outer?

153. Can you divide a hexagon into four equal and similar parts?

154. Can you divide a line into two such

parts that one part shall be three times the length of the other?

155. Can you divide a line into four equal parts, without using more than three circles?

156. Can you make a triangle whose sides shall be 2, 3, and 4 inches?

157. Make a scale having the end division to consist of ten equal parts of a unit of the scale, and with its assistance make a triangle whose sides shall have 25, 18, and 12 parts of that scale.

158. Can you construct a square on a line without using any other radius than the length of that line?

159. Can you make a circle so that the centre may not be marked, and find the centre by geometry?

160. Can you divide an equilateral trianglo into four equal and similar parts?

When a body has eight surfaces, whose sides and angles are all respectively equal, it is called an octahedron.

161. Make of one piece of card a hollow octahedron show how you arrange the surfaces so as to fold together correctly; and give a sketch of the octahedron.

162. Can you divide an angle into four equal angles, without using more than four circles?

163. In how many ways can you divide an equilateral triangle into three parts, that shall be equal to each other, and similar to each other?

164. Given an arc of a circle: it is required to find the centre of the circle of which it is an

arc.

165. Can you make a symmetrical trapezoid?

166. Can you make a symmetrical trapezium?

167. Is it possible to make a rhomboid without using more than one circle?

168. Is it possible to make a symmetrical trapezium, using no more than one circle?

169. Can you place a hexagon in an equilat

eral triangle, so that every other angle of the hexagon may touch the middle of a side of the equilateral triangle?

170. Can you construct a triangle, whose sides shall be 4, 5, and 9 inches?

171. Can you make an octagon, with one side given?

172. Is it possible that any triangle can be of such a form that, when divided in a certain way into two parts equal to each other, such parts shall have a form similar to that of the original triangle?

173. Show what is meant when it is said that triangles on equal bases, in the same line, and having the same vertex, are equal in surface.

174. Can you divide an isosceles triangle into two triangles that shall be equal to each other, but that shall not be similar to each other?

175. Can you divide an equilateral triangle into two figures that shall have equal surfaces, but no similarity in form?