In just proportional exchange, under Aristotle's theory of reciprocal justice, superior sharers in a community materially assist the weaker, and receive honour as a reward. Aristotle's economic thought is represented with a system of 18 formulae. Explained are: (1) What Aristotle means when he says that it is impossible for two sharers or their erga to be commensurable; (2) The extent to which the variables in Aristotle's proportions can be quantified. (3) What diagonal pairing ( ?ατ δ? ??τ?o? σ ??????) (...) is; (4) How need makes sharers and their erga ?sufficiently' commensurable; and (5) Aristotle's theory of what is just in exchange. (shrink)