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These values are computed with the "bc" program of the
UNIX operating system.
The approximate values in parens are taken from
Kepler, Mysterium Cosmographicum, 2nd edn.
(Duncan, 1981; p. 28). By the way, the term minor
refers to a root of a certain type of fourth order
algebraic equation, as defined in Euclid, Book X, Prop. 76
(Heath, 1960; v.3, pp. 163-164).
Note: Although there are five Platonic solids, there are only three harmonic ratios. Kepler knew this, but choose not emphasize it in his books. Rev'd 19 jan 2002 by ralph abraham |