This section is from the book "Manual Of Useful Information", by J. C Thomas. Also available from Amazon: Manual of useful Information.
Of all plane figures the circle is the most capacious, or has the greatest area within the same limits. It is geometrically demonstrable that it has the same area as a right-angled triangle with a base equal to its circumference, and a perpendicular equal to its radius, that is, half the product of the radius and circumference. It is obviously larger than any figure, of however many sides, inscribed within its perimeter, and smaller than any circumscribed polygon. As a result of laborious calculations on this basis (pushed in one instance to 600 places of decimals without reaching the end), it has been ascertained that the ratio of the diameter to the circumference of any circle (sufficiently exact for all practical purposes), is as 1: 3.1416 (3.141592653+) or in whole numbers, approximately, as 7: 22, or more nearly as 113: 355. Hence, to find the circumference or diameter, the other quantity being known, multiply or divide by 3.1416; and to find the area, multiply half the diameter by half the circumference, or the square of the diameter by .7854 (3.1416/4).
To find The Surface Of A Globe, multiply the square of the diameter by 3.1416.
To find The solidity Of A globe, multiply the cube of the diameter by .5236. ______
 
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