  Every schoolboy knows which is the famous geometrical theorem, commonly called the Asses’ Bridge, and which is propounded as follows: The square constructed on the hypotenuse of a right angled triangle is equivalent to the sum of the squares constructed on the two other sides. If we had only to propound this terrible theorem, it would be an easy matter, but the question is to prove it by A and B, and by means of the triangles, similar angles, equivalents, etc. Well, instead of all this, we give here a very Trace on a piece of cardboard or thick paper a square, and divide into 49 parts. This done, cut it out in following the big lines. Take out on the center one division, which add to the small square, and then construct the figure 2. Fig. 2. The right-angled triangle A C D will be found by the sides of the three squares, and the sum of the two small squares constructed on the two sides of the triangle will be equivalent to the great square constructed on the hypotenuse. Effectively:
And the square No. 3 has also 25 divisions. Therefore the theorem is proved. |
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