OBSERVE the buttresses on the church in the picture. They are not prisms such as we have been studying, for their upper surfaces are inclined to their bases, but they are what are called truncated prisms, truncated meaning "lopped off." A truncated prism is one from which a part has been cut off by a plane inclined to the base. We will now make a model of a truncated square prism or cube. The diagram will need paper 19 cm. X 17 cm. (or 71⁄2 in. × 61⁄2 in.). A, B, C, and D are squares with edges 5 cm. (or 2 in.) long. L is a rectangle with the shorter edges 2 cm. 5 mm. (or 1 in.) long. From two corners of A lines X are drawn to the middle points of the outer edges of two adjoining squares. E is a rectangle with the longer edges equal to X. The base of the truncated prism is the base of the prism of which it was a part. The face formed by the cutting plane is called the inclined section. The other faces are called lateral or side faces. 1. What are the shapes of the lateral faces of this figure? 2. If you were to place the figure upon one of its lateral faces as a base, what should you then call the figure? 3. How does it happen that this figure has different names according to its position? 4. Supposing the original figure to have been a cube, can you see what the shape of the part cut off must have been? 5. Can you place two of these truncated prisms together so as to form a rectangular parallelopiped? 6. What would be the volume of that parallelopiped? 7. What, then, is the volume of your truncated prism? I. IN the above picture you see a very ancient geometric form, supposed to have been invented by the Egyptians. This is the pyramid (pyr'-a-mid), a word whose original meaning is uncertain, though some writers trace a connection. between it and a word meaning "fire." A pyramid has all its faces, except one, triangles which meet at a point called the apex (a'-pex), a word meaning "a top or summit." The other face, which may have any number of edges, is called the base; and a pyramid takes a |