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The first harmony is a 'square' number (Greek); the second

harmony is an 'oblong' number (Greek), i.e. a number representing

a figure of which the opposite sides only are equal. (Greek) =

'numbers squared from' or 'upon diameters'; (Greek) = 'rational,'

i.e. omitting fractions, (Greek), 'irrational,' i.e. including

fractions; e.g. 49 is a square of the rational diameter of a

figure the side of which = 5: 50, of an irrational diameter of

the same. For several of the explanations here given and for a

good deal besides I am indebted to an excellent article on the

Platonic Number by Dr. Donaldson (Proc. of the Philol. Society).