The result is the number of square units in the area; and twice this, divided by either side, is the perpendicular distance of that side from its opposite vertex.
To find the radius of the internal circle which touches the three sides of a triangle. Divide the area, found in the last paragraph, by half the sum of the sides.
Given the two sides of a right-angled triangle, to find the hypothenuse. Add the squares of the sides, and extract the square root of the sum.
Given the hypothenuse and one of the sides, to find the other side. Multiply the sum of the given lines by their difference, and extract the square root of the product.
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,2 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