To find the circumference of a circle from its radius, very nearly. Multiply twice the radius, or the diameter, by 3·1415927, taking as many decimal places as may be thought necessary. For a rough computation, multiply by 22 and divide by 7. For a very exact computation, in which decimals shall be avoided, multiply by 355 and divide by 113. See (131), last example.
To find the arc of a circular sector, very nearly, knowing the radius and the angle. Turn the angle into seconds,[78] multiply by the radius, and divide the product by 206265. The result will be the number of units in the arc.
To find the area of a circle from its radius, very nearly. Multiply the square of the radius by 3·1415927.
To find the area of a sector, very nearly, knowing the radius and the angle. Turn the angle into seconds, multiply by the square of the radius, and divide by 206265 × 2, or 412530.
To find the solid content of a rectangular parallelopiped. Multiply together three sides which meet: the result is the number of cubic units required. If the figure be not rectangular, multiply the area of one of its planes by the perpendicular distance between it and its opposite plane.
To find the solid content of a pyramid. Multiply the area of the base by the perpendicular let fall from the vertex upon the base, and divide by 3.
To find the solid content of a prism. Multiply the area of the base by the perpendicular distance between the opposite bases.
To find the surface of a sphere. Multiply 4 times the square of the radius by 3·1415927.
To find the solid content of a sphere. Multiply the cube of the radius by 3·1415927 × ⁴/₃, or 4·18879.
To find the surface of a right cone. Take half the product of the circumference of the base and slanting side. To find the solid content, take one-third of the product of the base and the altitude.