Page:Early Greek philosophy by John Burnet, 3rd edition, 1920.djvu/117

Rh It showed at a glance that 1+2+3+4=10. Speusippos tells us of several properties which the Pythagoreans discovered in the dekad. It is, for instance, the first number that has in it an equal number of prime and composite numbers. How much of this goes back to Pythagoras himself, we cannot tell; but we are probably justified in referring to him the conclusion that it is "according to nature" that all Hellenes and barbarians count up to ten and then begin over again.

It is obvious that the tetraktys may be indefinitely extended so as to exhibit the sums of the series of successive integers in a graphic form, and these sums are accordingly called "triangular numbers."

For similar reasons, the sums of the series of successive odd numbers are called "square numbers," and those of successive even numbers "oblong." If odd numbers are added in the form of gnomons, the result is always a similar figure, namely a square, while, if even numbers are added, we get a series of rectangles, as shown by the figure: