Practical Geometry

PRACTICAL Geometry is an important branch of knowledge to all who are in any way engaged in the art of building. The workman, as well as the designer, requires its aid ; and unless he is acquainted with some of the leading principles of the science, he will frequently feel an uncertainty as to the results he may deduce from the problems which are presented to his notice.

Problem IV. Within A Given Circle To Describe A Regular Hexagon; That Is To Say, A Polygon Of Six Equal Sides

Let a b c be the given circle, and o the centre. With the radius of the circle divide it into parts, of which there will be six, and connect the points a d, d b, etc., and the figure a d b e c f will be a regular hexagon.

Fig. 33.

Problem IV Within A Given Circle To Describe A Reg 32

How To Multiply Numbers By The Rule

Set 1 on b opposite to the multiplier on a ; and against the number to be multiplied on b is the product on a. Multiply 6 by 4. Set 1 on b to 4 on a ; and against 6 on b is 24 on a.

The elide thus set, against 7 on b is 28 on a.

8 " 82 "

9 " 80 " 10 " 40 " 12 " 48 " 16 " 60 "

25 " 100 " etc.

How To Divide Numbers Upon The Rule

Set the divisor on b to 1 on a; and against the number to be divided on b is the quotient on a. Divide 63 by 8.

Set 8 on b to 1 on a ; and against 68 on B is 21 on a.

Proportion, Or Rule Of Three Direct. Rule

Set the first term on b to the second on a; and against the third upon B is the fourth upon a.

1. If 4 yards of cloth cost 38 cents, what will 80 yards cost at the same rate ?

Set 4 on b to 88 on a ; and against 80 on b is 286 cents on a.

2. Suppose I pay 81 dollars 60 cents for 8 cwt. of copper, at what rate is that per ton? 1 (on = 20 net.

Set 3 upon b to 31.5 upon a; and against 20 upon b is 210 upon a.

Of Engine Boilers

How many superficial feet are contained in a boiler 23 feet in length and 5 1/2 feet in width?

Set 1 on b to 28 on a ; and against 5.5 upon b is 126.5 square feet upon a.

If 5 square feet of boiler surface be sufficient for each horse-power, how many horses' power of engine is the boiler equal to?

Set 5 upon b to 126.5 upon a; and against 1 upon b is 25.5 upon a.

Non-Condensing Engine

d2 v

1000

= horse's power.

This is based upon a uniform steam pressure of 60 lbs. per square inch (steam gauge), cut off at one-half the stroke, deducting one sixth for friction and losses, with a mean velocity of piston of 250 feet per second.