SECT. III.
The two diameters (cd and ef) of an Ellipsis, being given, to find the Area or Content in Ale-Gallons.
As the Square of the Diameter of a Circle is to the Area of that circle; so is the Rect-Angle or Product of the greater and lesser Diameters of an Ellipsis, to the Area thereof. Therefore multiply the greater Diameter by the lesser Diameter, then that Product multiplied or divided by the fixed Multiplicators or Divisors given (in pages 46, and 47,) gives the Area in Inches, Gallons or Barrels, according to the Number made use of.
Or thus, (by Problem VIII. Sect. I) find a Geometrical Mean Proportion between the greater and lesser Diameters, for this Mean is the Diameter of a Circle, whose Area is equal to the Area of the Ellipsis.
Example. Fig. 2.
Let the greater Diameter cd be 72 Inches, and the lesser ef, 50; by the foregoing Rule, the Geometrical Mean between them will be found to be 60, the Diameter of a Circle equal to the Ellipsis, and the Area of a Circle, whose Diameter is 60, will be found to be 10.02 Ale-Gallons. But the Area of an Ellipsis may be more easily found by the rule, thus;
Set 359.05 upon B, to one of the Diameters (suppose 50) upon A; then against the other Diameter 72 upon B, you have the Area upon A, which in this Example will be 10.02, Ale-Gallons, the Content of this Ellipsis at one Inch deep: The like may be done for Wine-Gallons, if instead of 359.05, you take 294.11.
This page was last updated on 29 March 2000.