Text: The "doubling" of the roots is not a true doubling in the mathematical sense, but this doubling does "double" the value of all the other identities within the ellipse. Thus, the doubling of 1, 1, 2, 3 will give us 2, 1, 3, 4, but these two combinations are the roots of the 3, 4, 5, triangle and of the 6, 8, 10 triangle, which is a double of the first. The measurements of J, C/2, D, and K, along the major diameter of the same ellipse will be 2, 2, 4, 6 for the first roots and will be 6, 3, 9,12 for the second. This not a true doubling. The doubling occurs only in the triangle. A true doubling of the major diameter could not be because this ellipse is much more elliptical, but the triangle is truly doubled in its dimensions and quadrupled in its area. Along with that it is turned by ninety degrees in itself and within the ellipse which it represents.

See Also: OCTAVE

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