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 triangle 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?

176. Can you fit an equilateral triangle about a circle?

177. Can you divide an equilateral triangle into four triangles, that shall be equal but dissimilar?

178. Group together seven hexagons so that each may touch the adjoining ones vertically at the angles.

179. Make an octagon, and place a square on each of its sides.

180. Can you convert a square into a rhomboid?

181. Can you convert a square into a rhombus?

182. Can you convert a rectangle into a rhomboid?

183. Can you convert a rectangle into a rhombus?

184. Can you divide any triangle into four equal and similar triangles?

185. Can you invent a method of dividing a line into three equal parts?

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186. Can you place a hexagon in an equilateral triangle, so that every other side of the hexagon may touch a side of the triangle?

187. Can you divide a line into two such. parts that one part may be twice the length of the other?

188. Can you divide a rectangular piece of paper into three equal strips by one cut of a knife or pair of scissors?

189. You have made one triangle similar to another, but not equal; can you make one rectangle similar to another, but not equal?

190. Can you make a square, and place four octagons round it in such a manner that each side of the square may form one side of one of the octagons?

191. Can you make two rhomboids that shall be similar, but not equal?

192. Can you place a circle, whose radius is 1 inch, so as to touch two points 2 inches asunder?

193. Can you place an octagon in a square,