EUCLID.--THE FAMOUS FORTY-SEVENTH. “_In any right-angled triangle, the square which is described upon the side opposite to the right-angle is equal to the squares described upon the sides which contain the right-angle._” Here is a simple way of proving this proposition. Although perhaps not exactly scholastic, it is none the less interesting. Draw an exact square, whose sides measure 7 in.; then divide it into 49 square inches. Having done this, cut the figure in following the big lines as shown by Fig 1. It will be observed that C is a complete square, and that A and B will form a square: but as D is 1 in. short of being a square, it is necessary to cut a square inch and add it on. [Illustration: Fig. 1.] [Illustration: Fig. 2.] Then construct a right-angled triangle as shown by Figure 2. We then see that the sum of the two small squares is equivalent to the large square. D contains 9 small squares. A & B do. 16 do. -- 25 And as we see that C has 25 small squares, it is thus proved that the sum of the squares upon the sides which contain the right angle are equal to the squares upon the side opposite the right angle. _Q.E.D._ THE GREAT FISH PROBLEM. 209. There is a fish the head of which is 9 in. long, the tail is as long as the head and half the back, and the back is as long as the head and tail together. What is the length of the fish? 210. How may 100 be expressed with four nines? 211. Two shepherds, A and B, meeting on the road, began talking of the number of sheep each had, when A said to B, “Give me one of your sheep, and I will have as many as you.” “Oh, no!” replied B; “give me one of yours, and I will have as many again as you.” How many sheep had each? A BRICK PUZZLE. ONE FOR BUILDERS, CONTRACTORS, &C. 212. Suppose the measurements of a brick to be:--Length, 9 in.; breadth, 4½ in.; depth, 3 in. How many “stretchers, headers and closures” can be cut out of one, and what would be the face area of same? For the benefit of the uninitiated we might say that “stretcher” = length of brick x depth “header” = breadth " “closure” = half-breadth " 213. A woman has a basket of 150 eggs; for every 1½ goose egg she has 2½ duck eggs and 3½ hen eggs. How many of each had she? The Great Chess Problem. THE KNIGHT MOVE. 214. Move the Knight over all the 64 squares of the chess board so as to successively cover each square and, of course, not enter any square twice. This problem has always proved to be an interesting one. Mathematicians throughout all ages have devoted a good deal of time to it. To chess players it should be especially attractive. [Illustration] 215. If 3 times a certain number be taken from 7 times the same number the remainder will be 8. What is the number? 216. Divide £27 among 3 persons, A, B and C, so that B may have twice as much as A, and C 3 times as much as B. ANSWER THIS.