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but the easiest and most simple is by spacing. Two dimensions, half the width of the building and the height of the roof, are divided into an equal number of parts. The width of half the building is called. the run and is usually divided into parts of 12 inches or a foot for convenience. The height is called the rise, and is divided into an equal number of parts. A glance at Figure 9 tells us that the run there shown is 10 inches rise to 12 inches run.

FIGURE 9

When the square is laid on the stick to be cut into a rafter, the 10-inch mark on the tongue and the 12-inch mark on the blade are held so that they come exactly even with the outside edge. The blade then takes a level position and the tongue a vertical position or plumb position. This gives the proper level for the cut at the top of the rafter and

the level cut at the top of the plate. As the square now lies on the stick make a fine mark and move the square along, marking another space. Mark as many of these spaces as the parts into which the rise and run were divided. This gives the length of a rafter from the ridge to a point exactly over the outside of the plate.

Where the rafter overhangs the plate, it is necessary to square down or in to form the notch for the plate. By studying Figure 9 you can readily see the different positions taken by the square, also, how and why the rise and run are divided into an equal number of spaces. By this method the length of the rafter is obtained without use of mathematics.

STAIR STRINGER

The stair stringer is laid out in much the same manner as the common rafter. The total rise of height to go up is divided into parts of about 72 inches, as near as possible. This makes the easiest step. The run is always divided into one less space than the rise. The reason for this can be easily understood by examining Figure 10. Lay the square on the stick to be used as a stair stringer, taking the numbers into which the rise and run have been divided, mark, and slide the square along until the required number of spaces are marked. A little experience, with allowance made for the surrounding conditions, and any handy mechanic can lay out stringers for an ordinary flight of stairs. To get an easy flight of stairs for the person of average size where plenty of room can be used, experience teaches that 71⁄2 inches rise and 10 Inches run or tread makes an easy flight.

From this some stair-building experts have put together the following rule, which works very well for the average stair: When the rise multiplied by the tread equals 75, the run will be an easy inches rise by 101⁄2 inches tread inches rise by 9 inches tread equals

one,

as 71⁄2 equals 75;

8

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75; 8 inches rise by 91⁄2 inches tread equals 76, which is very near the desired result. When the rise is 9 inches or over, the rule is not good, as the tread must be shortened up much more, and the rise should never be more than II inches-that is about the rise in an ordinary ladder leaning against a house.

THE 47TH PROBLEM OF EUCLID

The problem shown in Figure II is known as the 47th Problem of Euclid, and is an invention by an

FIGURE II

ancient Greek ge

ometer who sought

many years for a method of finding the length of the hypothenuse of a right angle triangle in mathematics, and when the method was discovered, history tells us there was great rejoicing. Pythagoras is

credited with hav

ing first proved the rule successfully applied to the

problem.

The rule is that the

square of the base

added to the square of the altitude equals the

square of the hypothenuse. The base of a right angle triangle is the side on which it rests, marked B in Figure II. The altitude is the height and is marked A in Figure 1I. The hypothenuse is the connecting side of the triangle, marked H in Figure 11. The base, 6, squared or multiplied by itself, equals 36. The altitude, 8, squared, equals 64. By adding these together we have 100, which is the square of the hypothenuse. It remains but to extract the square root of 100, which we know is 10, therefore 10 is the length of the hypothenuse or third side of this right angle triangle. All right angle triangles can be figured in the same manner, but only multiples of the

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He's a city chap now, but when he comes home, he proves that his early training has not been forgotten. Teach your boy to use tools and use them right.

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