(continued from last post...)

There are two orders of number: odd and even. Because unity, or 1, always remains indivisible, the odd number cannot be divided equally. Thus, 9 is 4 + 1 + 4, the unity in the center being indivisible. Furthermore, if any odd number be divided into two parts, one part will always be odd and the other even. Thus 9 maybe 5 +4, 3+6, 7+2, or 8+1. The Pythagoreans considered the odd number - of which the monad was the prototype - to be deinite and masculine. They were not all agreed, however, as to the nature of unity, or 1. Some delcared it to be positive, because if added to an even (negative) number, it produces an odd (positive) number. Others demonstrated that if unity be added to an odd number, the latter becomes even, thereby making the masculine to be feminine. Unity, or 1, therefore, was considered an androgynous number, partaking of both the masculine and the feminine attributes; consequently both odd and even. For this reason the Pythagoreans called it evenly-odd. It was customary for the Pythagoreans to offer sacrifices of an uneven number of objects to the superior gods, while to the goddesses and subterranean spirits an even number was offered.

Any even number may be divided into two equal parts, which are always either both odd or both even. Thus, 10 by equal division gives 5+5, both odd numbers. The same principle holds true if the 10 be unequally divided. For example, in 6+4, both parts are even; in 7+3, both parts are odd; in 8+2, both parts are again even; and in 9+1, both parts are again odd. Thus, in the even number, however it may be divided, the parts will always be both odd or both even. The Pythagoreans considered the even number - of which the duad was the prototype - to be indefinite and feminine.

(to be continued...)