References
W. Burkert, Lore and Science in Ancient Pythagoreanism, tr. E. L. Minar, Jr., Harvard University Press, 1972.
Euclid, Opera Omnia, ed. J: L. Heiberg & H. Menge, Teubner, Leipzig, 9 vol.; esp. I-VI: Elementa, 1883–96, rev. E. S. Stamatis, 1969–77; and IX: Anaritii Commentarii, ed. M. Curtze, 1896.
Euclid's Elements, ed. and tr. T. L. Heath, Cambridge University Press, 3 vol., 1926; repr. Dover, New York, 1956.
D. H. Fowler, Ratio in Early Greek Mathematics, Bulletin of the American Mathematical Society (New Series), 1 (1979) pp. 807–846.
D. H. Fowler, Equations, Neusis-constructions, and Euclid's Elements: an Anthyphairetic Interpretation, to appear.
D. H. Fowler, A Generalisation of the Golden Section, to appear.
J. Hintikka & U. Remes, The Method of Analysis, Reidel, Dordrecht, 1974.
T. L. Heath, A History of Greek Mathematics, 2 vol., Clarendon Press, Oxford, 1921.
W. R. Knorr, The Evolution of the Euclidean Elements, Reidel, Dordrecht, 1975.
W. R. Knorr, Archimedes' Neusis-Constructions in Spiral Lines, Centaurus, 22 (1978) pp. 77–98.
E. A. Neuenschwander, Die ersten vier Bücher der Elemente Euklids, Archive for History of Exact Sciences, 9 (1973) pp. 325–380.
Proclus, A Commentary on the First Book of Euclid's Elements, tr. G. N. Morrow, Princeton University Press, 1970.
I. Thomas [= I. Bulmer-Thomas], ed. and tr., Selections Illustrating the History of Greek Mathematics, 2 vol., Loeb Classical Library series, Heinemann, London/Harvard University Press, 1939–41.
C. J. de Vogel, Pythagoras and Early Pythagoreanism, van Gorcum, Assen, 1966.
H. G. Zeuthen, Sur la constitution des livres arithmétiques des Eléments d'Euclide et leur rapport à la question d'irrationalité, Oversigt over det k. Danske Videnskabernes Selskabs Forhandlinger 1910, pp. 395–435.
Author information
Authors and Affiliations
Additional information
Communicated by B.L. van der Waerden
To Ivor Bulmer-Thomas, for his seventy-fifth birthday, November 1980.
Rights and permissions
About this article
Cite this article
Fowler, D.H. Book II of Euclid's Elements and a pre-Eudoxan theory of ratio. Arch. Rational Mech. 22, 5–36 (1980). https://doi.org/10.1007/BF00327868
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00327868