The tabular area of the corresponding polygon multiplied by the square of the side of the given polygon, equals the area of the given polygon.
OF ELLIPSES, CONES, FRUSTRUMS, ETC.
1. The square root of half the sum of the squares of the two diameters of an ellipse multiplied by 3·1416 equals its circumference.
2. The product of the two axes of an ellipse multiplied by ·7854 equals its area.
3. The curve surface of a cone is equal to half the product of the circumference of its base multiplied by its slant side, to which, if the area of the base be added, the sum is the whole surface.
4. The solidity of a cone equals one-third of the product of its base multiplied by its altitude, or height.
5. The squares of the diameters of the two ends of the frustrum of a cone added to the product of the two diameters, and that sum multiplied by its height, and by ·2618, equals its solidity.
THE END.