(continued from last post...)

The odd numbers are divided by a mathematical contrivance - called "the Sieve of Eratosthenes" - into three general classes: incomposite, composite, and incomposite-composite.

The incomposite numbers are those which have no divisor other than themselves and unity, such as 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and so forth. For example, 7 is divisible only by 7, which goes into itself once, and unity, which goes into 7 seven times.

The composite numbers are those which are divisible not only by themselves and unity but also by some other number, such as 9, 15, 21, 25, 27, 33, 39, 45, 51, 57, and so forth. For example, 21 is divisible not only by itself and by unity, but also by 3 and by 7.

The incomposite-composite numbers are those which have no common divisor, although each of itself is capable of division, such as 9 and 25. For example, 9 is divisible by 3 and 25 by 5, but neither is divisible by the divisor of the other; thus they have no common divisor. Because they have individual divisors, they are called composite; and because they have no common divisor, they are called incomposite. Accordingly, the term incomposite-composite was created to describe their properties.

(to be continued...)