The organization of Greek mathematics from Theaetetus to Archimedes. (L’organisation des mathématiques grecques de Théétète à Archimède.) (French) Zbl 0952.01005

Problèmes et Controverses. Paris: Librairie Philosphique J. Vrin. 311 p. (1997).
This book is composed of ten philosophical studies in the history of Greek geometry, covering the 4th and 3rd centuries B.C. It analyses (i) the vocabulary of geometry in Euclid and Hilbert, (ii)–(v) the implicit propositional logic, a comparison of theorems vs. problems, existence of geometric entities, as well as the role of figures in Euclid and Archimedes, (vi) the theory of magnitudes from Eudoxus to Archimedes, (vii)–(ix) Proposition 14 of Book V, the structure of Book XII, as well as the Eudoxean and Theaetetean influences (seen as the grande fracture) in Euclid’s Elements, and (x) the Greek origins of proof.
The author does not take into account any of the studies related to the above topics that were published in languages other than French after 1954. He cites only one article by O. Becker (1934), one by van der Waerden (1947) and one by K. von Fritz (1954) from the relevant literature in languages other than French. Bringing E. Neuenschwander [Arch. Hist. Exact Sci. 9, 325-380 (1973; Zbl 0263.01007); 14, 91-125 (1974; Zbl 0335.01001)], I. Mueller [Philosophy of mathematics and deductive structure in Euclid’s Elements (1981; Zbl 0582.01003)], E. Niebel [Untersuchungen über die Bedeutung der geometrischen Konstruktion in der Antike (1959; Zbl 0113.00108)], B. Artmann [Arch. Hist. Exact Sci. 33, 291-306 (1985; Zbl 0577.01003); 39, No. 2, 121-135 (1988; Zbl 0762.01001); Euclid’s Elements and its prehistory. Edmonton: Academic Printing and Publishing. Apeiron. 24(4), 1-47 (1992; Zbl 0925.01006)], and the references in this last contribution, in particular the work of W. R. Knorr, into his discussion would in some instances have spared the repetition of arguments also found elsewhere, in others put into effect necessary corrections, and would have emphasized points of agreement and disagreement.


01A20 History of Greek and Roman mathematics
03A05 Philosophical and critical aspects of logic and foundations