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Updated: May 8, 2025
In saying that arithmetic began with Pythagoras we have to distinguish between the uses of that word then and now. It included definitions of the unit and of number, and the classification and definitions of the various classes of numbers, odd, even, prime, composite, and sub-divisions of these such as odd-even, even-times-even, &c.
"All things," they said, "as known have Number; and this number has two natures, the Odd and the Even; the known thing is the Odd-Even or union of the two." By a curious and somewhat fanciful development of this conception the Pythagoreans drew up two parallel columns of antithetical principles in nature, ten in each, thus:
This principle of union was God, ever-living, ever One, eternal, immovable, self-identical. This was the supreme reality, the Odd-Even or Many in One, One in Many, in whom was gathered up, as in an eternal harmony, all the contrarieties of lower existence.
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