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Archimedes. Transl. from the Dutch by C. Dikshoorn. With a new bibliographic essay by Wilbur R. Knorr. (Reprint). (English) Zbl 0646.01001

Princeton, New Jersey: Princeton University Press. 457 p.; $ 15.00 (1987).
In a field in which affordable access to the literature is so rare, the decision taken by Princeton University Press to print in paperback this modern classic and to ask Wilbur R. Knorr to add to it a new bibliographic essay must be lauded. Eduard Jan Dijksterhuis (1892-1965) was a major historian of the sciences. When he decided to write about Archimedes in the later 30’s and early 40’s, the comprehensive treatments of T. L. Heath and P. Ver Eecke were standing as definitive editions of his major works. As Dijksterhuis says in a sort of explanation of why he decided to work in a new translation of the works of Archimedes, he claims that both Heath and Ver Eecke have disadvantages, the first resulting from the incorporation of the symbolism of modern algebra into the translation and the second for sticking to a literal translation. So, when trying “to combine the advantages and avoid the disadvantages of the two methods [by following] the Greek text closely, but only the propositions are given in a literal translation; after that the proofs are set forth in a symbolical notation especially devised for the purpose” (p. 7), the author contributes with this scholarship to a new style of translating and editing the classics. Rightfully, this makes Dijksterhuis’s Archimedes a modern classic and “Thirty years after its publication [it] remains the best survey available in English”, as rightfully says Wilbur R. Knorr in his excellent essay entitled “Archimedes after Dijksterhuis: A guide to recent studies”, incorporated in this edition (p. 420). In this short essay (pp. 419-451), W. R. Knorr gives an appreciation of the importance of the treatment of Dijksterhuis in placing Archimedes views of rigor and the process of discovery as contrasted with Euclid and Apollonius. Then he proceeds, in the major part of his essay, to give a commented bibliography of over 230 titles on Archimedes’s scholarship, covering mainly the period after Dijksterhuis first published his book. This becomes a basic reading for those interested in going into Archimedean studies.
The main body of this important book consists of 9 chapters: I. The life of Archimedes (21 pages); II. The works of Archimedes. Manuscripts and editions (16 pages); III. The elements of the work of Archimedes (91 pages); IV. On the sphere and cylinder. Book I (41 pages); V. On the sphere and cylinder. Book II (34 pages); VI. Measurement of a circle (18 pages); VII. On conoids and spheroids (24 pages); VIII. On spirals (22 pages); IX. On the equilibrium of planes or centres of gravity of planes. Book I (27 pages); X. The method of mechanical theorems (23 pages); XI. Quadrature of the parabole (10 pages); XII. On the equilibrium of planes. Book II (14 pages); XIII. The sand-reckoner (13 pages); XIV. Floating bodies (25 pages); XV. Miscellaneous (21 pages); Bibliography (2 pages); Archimedes after Dijksterhuis: A guide to recent studies, by Wilbur R. Knorr (33 pages); Index of names (4 pages); Errata (2 pages).
Reviewer: U.d’Ambrosio

MSC:

01A20 History of Greek and Roman mathematics
01A70 Biographies, obituaries, personalia, bibliographies
01A75 Collected or selected works; reprintings or translations of classics

Biographic References:

Archimedes