EN106
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2 revisions | jasirs94 at Nov 20, 2016 03:56 AM | |
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106G108 measured by the sum of the parallelograms into which it may be cut up, each parallelogram having its sides in the directions of E NE and N by W. Were that the sole method of measurement, nothing would be gained by combining the linear measures in the two directions, but rather the reverse. But in fact we may measure the area by parallelograms in any other two dimensions; and the ratio between the any two areas will be the same by any two such methods of measurement. Moreover, we may employ polar, in place of Cartesian, coordinates, and cut the area up into a circle and broken, concentric, and very thin rings. The area will be sum of the areas, each [of] which will be x x y where x is the difference of the two radii, while y is the proportion of their sum, the proportion being that of the entire ring which forms a part of the area. | 106 |