1. The side of a square equals the square root of its area.

2. The area of a square equals the square of one of its sides. 8. The diagonal of a square equals the square root of twice the square of its side.

4. The side of a square is equal to the square root of half the square of its diagonal.

5. The side of a square equal to the diagonal of a given square contains double the area of a given square.

6. The area of a rectangle equals its length multiplied by its breadth.

7. The length of a rectangle equals the area divided by the breadth; or, the breadth equals the area divided by the length.

8. The side or end of a rectangle equals the square root of the sum of the diagonal and opposite side to that required, multiplied by their difference.

9. The diagonal in a rectangle equals the square root of the sum of the squares of the base and perpendicular.

10. The solidity of a cube equals the area of one of its sides, multiplied by the length or breadth of one of its sides.

11. The length or breadth of a side of a cube equals the cube root of its solidity.

12. The capacity of a 12-inch cube equals 7.4784 United States gallons.

Surfaces and Solidities of the Regular Bodies, each of whose Boundary Lines is 1.

The tabular surface multiplied by the square of one of the boundary lines equals the surface required; or,

The tabular solidity multiplied by the cube of one of the boundary lines equals the solidity required.