This section is from the book "The English And American Mechanic", by B. Frank Van Cleve. Also available from Amazon: The English And American Mechanic.
Fig. 19.

To find the radius of a circle for striking the side of a flaring vessel having the diameters and depth of side given.
As the difference between the large and small diameter is to the depth of the side, so is the small diameter to the radius of the circle by which it is struck.
Suppose A B C D to be the desired vessel, with a top diameter of 12 inches, bottom diameter 9 inches, depth of side 8 inches. Then as 12 - 9 = 3 : 8 : : 9 to the radius. 8X9 = 72/3 = 24 inches, answer.
 
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