[207.] Place four florins alternately with four pennies, and in four moves, moving two adjacent coins each time, bring the florins together and the pence together. When finished there must be no spaces between the coins.
[208.] If 2 be added to the numerator of a certain fraction, it is made equal to one-fifth, whilst if 2 be taken from the denominator it becomes equal to one-sixth. Find the fraction.
EUCLID.—The Famous Forty-Seventh.
Fig. 1.
“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.