12. The capacity of a 12-inch cube equals 6·232 gallons.
| Surfaces, and solidities of the regular bodies, when the linear edge is 1. | |||
| No. of Sides. | Names. | Surfaces. | Solids. |
| 4 | Tetrahedron | 1·7320508 | 0·1178513 |
| 6 | Hexahedron | 6· | 1· |
| 8 | Octahedron | 3·4641016 | 0·4714045 |
| 12 | Dodecahedron | 20·6457788 | 7·6631189 |
| 20 | Icosahedron | 8·6602540 | 2·1816950 |
The tabular surface multiplied by the square of the linear edge, the product equals the surface required:
Or, the tabular solidity, multiplied by the cube of the linear edge, the product is the solidity required.
OF TRIANGLES, POLYGONS, ETC.
1. The complement of an angle is its defect from a right angle.
2. The supplement of an angle is its defect from two right angles.
3. The sine, tangent, and secant of an angle, are the cosine, cotangent and cosecant of the complement of that angle.
4. The hypothenuse of a right-angled triangle being made radii, its sides become the sines of the opposite angles, or the cosines of the adjacent angles.
5. The three angles of every triangle are equal to two right angles; hence the oblique angles of a right-angled triangle are each other’s complements.