Page:Ferrier Works vol 2 1888 LECTURES IN GREEK PHILOSOPHY.pdf/130

Rh 17. The monad and the duad being the elements of number must be viewed as antecedent to number. There is thus a primary one which is the ground or root out of which all arithmetical numbers proceed. And there is also a primary duad from which numbers derive their diversity. These two enter into the composition of every number (even into the composition of the numerical one), the one of them giving to all numbers their unity, or agreement, or identity; the other of them giving to all numbers their diversity. The primitive numbers, the numbers antecedent, as we may say, to all arithmetical numbers, are the Pythagorean monad and the Pythagorean duad. Of these, the former expresses the invariable and universal in all number; the latter, the variable and particular. And inasmuch as the particular is inexhaustible and indefinite, the duad is called  or indeterminate. Better to hold them elements of number than numbers.

18. As an illustration of the spirit of this philosophy, let me show you how a solid, or rather the scheme of a solid, may be constructed on Pythagorean principles. Given a mathematical point and motion, the problem is to construct a geometrical solid, or a figure in space of three dimensions, that is, occupying length, breadth, and depth. Let the point move—move its minimum distance, whatever that may be; this movement generates the line. Now let the line move. When you are told to let the line move,