### Notes and References

- Antonie Arnauld, The Art of Thinking: Port-Royal Logic, Translated by James Dickoff and Patricia James (New York: Bobbs-Merrill, 1964), p. 299. text
- Loomis, Elisha Scott, The Pythagorean Proposition, (Washington D. C.: National Council of Teachers of Mathematics, 1968), p. 224. text
- Loomis, p. 197. The proof given using figure 269 most closely conforms to the present demonstration. text
- Since B is the base of a triangle and H is its height, neither can be 1, and we needn't worry about division by zero. text
- Although C would be equal to 5 for continuous metric spaces, it is not 5 in the atomic case; C is 4 for the atomic case. Because the length of the side of the outer square formed by "adding" the lengths of the sides of the triangles is "shorter" (by 1) than it would be in continuous metrics, the size of the atomic inscribed square is smaller than its corresponding continuous analogue. text
- See Note 5 . text
- Loomis text
- Philip Wheelwright, Heraclitus, (Princeton: Princeton University Press, 1959; reprint, New York: Atheneum, March 1971), p. 90. text