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 rhom. bus?

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 equilat eral 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

in such a position that every other side of the octagon may coincide with a side of the square?

194. Fit an equilateral triangle inside a circle, and another outside, in such positions with regard to each other as shall show the ratio the inner one has to the outer.

195. Can you place four octagons in a group to touch at their angles?

196. Can you fit a hexagon outside a circle?

197. Can you place four octagons to meet in one point, and to overlap each other to an equal extent ?

198. Can you let fall a perpendicular to a line from a point given above that line?

Those instruments by which an angle can be constructed so as to contain a certain number of degrees, or by which we can measure an angle, and determine how many degrees it contains, as also by which we can make an arc of a circle that shall subtend a certain number of degrees, or can measure an arc and determine how many degrees it subtends, are called protractors.

Protractors commonly extend to 180°; though there are protractors that include the whole circle, that is, which extend to 360°.

199. Make of a piece of card as accurate a protractor as you can.

200. Make by a protractor an angle of 45°, and prove by geometry whether it is accurate

or not.

201. Can you contrive to divide a square into two equal but dissimilar parts?

202. Make with a protractor an angle of 60°, and prove by geometry whether it is cor

rect or not.

203. Make an angle, and determine by the protractor the number of degrees it contains.

204. Make by geometry the arc of a quad