3. What is the area of the gable end of a house, beam 40 feet, and height 12 feet 6 inches?

Ans. 500 sqr. ft.

4. What is the superficial content of a piece of board, in form of figure first: the length of which is 16 feet 9 inches, and the wide end 1 foot 10 inches, and the narrow end coming to a point?

ft. in.

in. ft. in. ft. in!!

1 1011x16 915 4 3 Ans.

5. What is the content of the second figure, A B 20 feet, and C D 6 feet 4 inches?

Ans. 63 ft. 4 in.

N. B. The method of measuring every board with the pen, would be too tedious for common practice; I therefore shall show the method of making a board rule, and measuring boards with the same.

CASE IV.

TO MAKE A BOARD, RULE.

Prepare a rule 2 feet and 1 inch long, and about $ inches wide, and an inch thick; divide the sides of the rule into 6 divisions, or lines; and each line into two equal parts; or divide two feet of the rule in the middle; at the end of the rule (upon the odd inch, number the lines beginning with 10, and so on to 24; and then begin with the line numbered 10, and divide one foot, on that line, into 10 equal parts, and num-, ber each of those parts with 1, 2, 3, 4, &c. on to 20. Then begin with the line numbered 11 at the end, and divide each foot on that line into 11 equal parts, and number each of those parts 1, 2, 3, 4, &c. on to 22; and thus proceed to divide a foot on any line into as many equal parts, as are expressed by the number

at the end of the rule; and the rule will appear like the following figure.

4 5 6 7

One side of the rule.

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 8 9 10 11 12 13 14 15 16 117 118 119 210 211 212 213 214

0

1

1 2 3 4 5

6

7

1 2 3

11 12 13 14 15 16

2

N. B. At 1, 2, are steel points, and from 2 to A, and from 1 to B is two feet, and the feet are separated by the line 0, 0.

CASE V.

To measure boards with this rule.

RULE. Find first the length of the board, and then look on the end of the rule for the number corresponding to the length of the board, then apply that line of the rule to the middle of the board, and the width of the board will extend on that line to a number expressing its area. Examples.

1. What is the superficial content of a board, that is 11 feet long, and 12 inches. wide? Ans. 11 ft.

N. B. The board being li feet long, I look for the line numbered 11, at the end, and apply that line to the middle of the board, and the width extends to that division number, ed 11, which is its content. Ans. 11 ft.

CASE VI.

To measure boards with Gunter's sliding rule.

RULE. Bring 12 on the slider against 12 on the line above; then look along on the line above for the number expressing the length of the board; and against that number, on the slider, stands the number expressing the area of the board.

Example.

1. What is the content of a board that is 18 feet long and 10 inches wide? Ans. 15 feet.

N. B. I first slip the slider, so that 12 on the slider stands against 12 on the line above: I then look along on the line above, for the number expressing the length of the board, viz. 18 feet: and against that number (on the slider), stands the number expressing the superficial content of the board, viz. 15.

CASE VII.

To measure boards with Gunter's scale and dividers.

RULE.

On the line of numbers extend from 1 to the width, and that extent will reach from the length to the superficial content, or area.

Example.

1. What is the superficial content of a board that is 20 feet long and 14 feet wide?

Ans. 25 feet.

NOTE. On the line of numbers I extend from 1, to 2 tenths, or from 1 to 2; and that extent reaches from 20, (the length of the board) to the superficial content 25.

N. B. Any right angled parallelogram can be measur ed in the same way.

CASE VIII.

To measure joist, plank, &c.

Joists, are of different dimensions, sometimes 3 by 3; and 3 by 4, and 4 by 5, &c. they are sold by the thou sand, and are reduced to board measure: that is to say, a joist that is 4 inches wide and 3 thick would make 3 boards, that were 4 inches wide: therefore measure one of the sides in the same manner as if it were a board, by any of the preceding rules in board measure; and then multiply that content by the number of inches it is thick, and the product is the answer.

Example.

What is the superficial area, or board measure of a joist, that is 20 feet long 4 wide, and 3 thick? 20 ft. 0x0 ft. 4-6 ft. X3' thick equal 20 ft. Ans.

NOTE. Plank are sold by the thousand, and are reduced to board measure as joists, and are measured in the

same manner.

CASE IX.

To measure any irregular plane surface.

RULE. Divide the whole surface into triangles and measure each triangle separately, as taught in case third superficial measure.

Examples.

What is the superficial content of a plat of ground, in form of the following figure?

Divide it into 2 triangles by drawing the diagonal A B, and measure each triangle separately by case 3; diagonal A B 50 feet; Perpendiculars 12 and 24. 50X12+24=1800-900. Ans.

CASE X.

To measure the surface of a circle.

Circles are round figures bounded every where by a circular line called the periphery, or arch, or some times the circumference. The linc passing through the centre is called the diameter, half the diameter, or a line proceeding from the centre to the periphery is called the semi-diameter, or radius.

See the figure.

E

D

A EBD is the periphery or arc.
A B is the diameter of the same.
CD is the semi-diameter or radius.

PROBLEM I.

Diameter given to find the circumference.

RULE. AS 7 is to 22 so is the diameter to the circumference; or as 113 is to 355 so is the diameter to the cir-. cumference,