The following TABLES of Areas and Solidities will be found considerably to diminish the labour of calculation.

The numbers in the first column after the names represent the areas or solidities, when the length of the side or edge is 1, or unity; and the numbers in the other columns are multiples of those in the first, by the unit over each.

To find, therefore, the area of a Polygon, take the square of the length of the side, and seek in the proper columns the multipliers, which are to be ranged under each other as in common multiplication. The sum of these will be the area required.

EXAMPLE. To find the area of a Pentagon, whose side is 18 inches, the multiplier being the square of 18 324.

The number in the Table under 4 is

6.8819

3.4409

66 35.1614

Answer, the last four figures being

decimals

(the Area,) 5 5 7·4 3 0 9.

The same RULE is applicable to Table X., of the Solidities of Regular Bodies, using the cube instead of the square.

To find the Areas of Regular Polygons.

RULE.-Square the length of side of the Polygon, and take the products from the subjoined Table, as

directed in page 66.

12.0433
15.5884 18.1865 20.7846

1

2

3

4

5

6

7

8

9

Trigon....

•4330

⚫8660

2.1651

2.5981

3.0311

3.4641

3.8971

Pentagon

Hexagon.

8.6024
12.9903

1.2990 1.7320
1.7204 3.4409 5.1614 6.8819
2.5981 5.1961 7.7942 10.3923
3.6339
|
| |
7.2678 10.9017 14.5356 18-1695 21.8035 25-4374 29.0713 | 32.7052
4.8284 9.6568 14.4852 19.3137 24.1421 28.9706 33.7990 38.6274 43.4558
6.1818 12.363618-5455 24-7273 30.9091 37.0909 43.2728 49.4546 55.6364
7.6942 | 15-3884 23.0826 30.7768
46.1652
61.5537
46.1652 53.8595
69.2479
9.365618-7313 28.0969 37.4626
56.1938 65.5595 74.9251 84.2908
11.1961 22-3923 | 33.5884 44-7846
67.1769 78.3731 89.5692 100.7654

38.4710
38.4710
46.8282

To find the Areas of Circles and Spheres.

RULE.-Square the diameter, and take the products from the subjoined Table, as directed in page 66.
To find the circumference of a circle, take the products of the diameter only.

4
2.3562 3.1416 3.9270 4.7124 5.4978
|
9.4248 12.5664 15.7080 18.8496 21.9912

|

9.4248 12.5664 15.7080 18.8496 21.9912

25.1328 28.2744

To find the Areas of the Regular Bodies.

RULE.-Square the length of one of the edges, and take the products from the subjoined Table, as

directed in page 66.

1

2

3

Tetrahedron

....

4
1.7320
8.6603 10-3923 12.1244 13.8564 15.5885
3.4641 5.1962 6.9282
Hexahedron...... 6.0000 12.0000 18.0000 | 24-0000 30.0000 36.0000 | 42.0000 48.0000 54.0000
6.9282 10.3923 13.8564 17-3205| 20-7846 24.2487 27-7128 31.1769
Octahedron
3.4641
Dodecahedron ... 20-6457 41.2915 61.9372 82-5829 103.2287 123-8744 144-5201 165.1658 185.8116
| |
8.6603 17.3205 25.9808 34-6410 43.3013 51.9615 60-6218
Icosahedron....
69.2820 77.9423

5

6

7

8

9

To find the Solidities of the Regular Bodies.

RULE.-Cube the length of one of the edges, and take the products from the subjoined Table, as

directed in page 66.

•4714

.9428

1.4142 1.8856

2.2570

2.8281 3.2998

3.7712

4.2426

7·6631 | 15·3262 | 22.9894 | 30.6525 | 38.3156 45·9787

53.6418

61.3050 68.9681

2.1817 4.3634 6.5451

8.7268 10.9085 13.0901 15.2718

17.4535

19.6352

TABLE of Squares, Cubes, Square Roots, and Cube Roots.