1. At $18 per M., what will be the cost of a pile of bricks 20 ft. long, 15 ft. wide, 6 ft. high? A brick measures 8 in. by 4 in. by 2 in.

2. Find the cost of a silver pitcher, weighing 5 lb. 5 oz. 12 pwt. 12 gr., at 48 cents per ounce troy.

3. How many pounds and ounces avoirdupois does the above pitcher weigh?

4. How many 5-grain pills can be made from an avoirdupois pound of quinine? From a pound apothecaries' weight?

5. How many spoons weighing 18 pwt. 16 gr. each, can be made from 11 oz. 4 pwt. of silver?

CANCELLATION.

834. Indicate operations, and cancel where possible. Terms compared

should be of the same denomination.

1. If 90 tons of coal cost $472.50, what will be the cost of 132 tons?

2. If 3 lb. and 4 oz. of tea cost $1.95, what will 12 oz. cost? 3. A party of men can build 16 rd. 2 ft. of wall in 20 days. How long will it take them to build 4 yd. and 6 in. ?

4. What will be the cost of 3 bu. 2 pk. 7 qt. 1 pt. of oats if 7 bu. 1 qt. cost $4.50?

5. By traveling at the rate of 20 miles a day, a person can complete a journey in 18 days. At what rate must he travel tɔ finish it in 15 days?

REVIEW.

841. Add across :

1. 13+16+83

2. 4+53 +27
3. 191+35+35
4. 81++ 14층
5. 23+51 +3212

6. 599+3+4
7. 75+183+40
8. 35+51 +8,7%
9. 37+9+25
10. 66+8+143

843. Multiply. Do not reduce to improper fractions:

845. Miscellaneous.

1. Find the value of (a) (6.125 +8.75-9.1235) + .0125; (b) (1,708.4592.00024) x .003.

4.

of 71% of 48

?

of 15 1 × 11

5. Add 85++§+&+§.

6. Find the value of 728-1-8-J.

10. A person owning of a factory sells 75 per cent of his share for $1,710. What is the value of the whole factory?

11. Find of 2 days 5 hours 45 minutes.

12. What is the interest on $760 for 5 months at 31% ?

13. If a piece of cloth is 20 yd. long and yd. broad, how broad is another piece which is 12 yd. long and contains as many square yards as the first?

15. A merchant insures property worth $20,000 for of its value. How much does he pay, the rate being 11%?

16. If 7 men can do a piece of work in 10 days, how long will it take 8 men and 5 boys to do the same work, each boy doing one-half as much as a man?

ANGLES, TRIANGLES, QUADRILATERALS.

846. The following may be drawn free hand, the compasses being reserved for the geometrical problems in Chapter XVI.

1. Draw two lines meeting at a point. These lines make an angle.

2. Draw two lines that will make four angles.

3. Draw two lines so as to make two angles. Two such angles are called adjacent angles.

4. Make two equal adjacent angles.

Equal adjacent angles are called right angles. A line making a right angle with another line is said to be perpendicular to it.

5. Draw two lines so as to make one right angle.

Is the right angle made by two lines, each 10 ft. long, any larger than a right angle made by two lines, each 1 inch long?

6. What is the smallest number of straight lines that will enclose a space? Draw a figure enclosed by the smallest possible number of straight lines. What is its name? Why?

7. Make a triangle having one right angle.

8. Can you draw a triangle having two right angles? Why? What name is given to lines that will not meet, no matter how far they are extended?

9. An angle less than a right angle is called an acute angle.

Draw a triangle containing an acute angle.

10. Can you draw a triangle containing two acute angles? Three acute angles?

11. An angle greater than a right angle is called an obtuse angle. Draw a triangle containing an obtuse angle.

12. Can you draw a triangle containing three obtuse angles? Containing two?

13. Draw a triangle with sides 2 inches, 3 inches, 4 inches, respectively.

A triangle having no two sides equal is called a scalene triangle.

14. Draw a triangle having two equal sides.

This is called an isosceles triangle. The unequal side is called the base.

15. Draw an isosceles triangle with the base uppermost. With the base on the left. On the right.

16. Draw a triangle having three equal sides (an equilateral triangle).

17. Draw a square. Draw a rectangle 4 in. by 3 in.

How many right angles in each?

18. Draw a four-sided figure having its opposite sides parallel, but containing no right angle (rhomboid).

What kinds of angles does it contain? How many of each? Write name in each angle.

19. Draw a four-sided figure, having all its sides equal, but containing no right angle (rhombus).

20. Draw a quadrilateral (four-sided figure) having only two parallel sides (trapezoid).

21. Draw a quadrilateral having no parallel sides (trapezium). 22. Draw a rhombus, each side 2 inches. A square, each side 2 inches.

What is the difference between them? Which is larger?

23. A parallelogram is a quadrilateral that has its opposite sides parallel.

Name the parallelograms that have four equal sides (equilateral). Those that have four equal angles (equiangular).

24. The height of a parallelogram is called its altitude. Draw a rectangle, base 3 inches, altitude 2 inches. Draw a rhomboid, base 3 inches, altitude 2 inches. Draw several rhomboids of the above dimensions, all differing in shape.