ABSTRACT
Thomas Greenwood was a professor of philosophy at Montreal University in Quebec until his death. Maziarz first studied under Greenwood and then became a close personal friend. Greenwood’s professional writings focused on his feelings about the closeness of mathematics to philosophy. The assimilation of number and figure in a rational method of investigating nature called for a practical way of combining arithmetic and geometry. The generation of triangular and square numbers led naturally to the kind of numbers produced by adding the successive terms of the series of even numbers beginning with 2. The words “without the unit” are quite proper, provided their elliptic meaning is adequately understood. Aristotle surely refers to gnomons placed around the numbers beginning with the unit, and then around the numbers beginning without it, in other words, around any number other than the unit. The discovery of proportionals attributed to Pythagoras is a natural extension of his number theory.
