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The excerpt represents the core issue or deciding factor on which you must meditate, and is drawn from The Republic by Plato: applied either to the parts or factors of a single number or to the
relation of one number to another. 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).
The Republic |
