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Ancient mathematics. A history of Greek mathematics, its problems and solutions. (Die antike Mathematik. Eine Geschichte der griechischen Mathematik, ihrer Probleme und Lösungen.) (German) Zbl 1284.01001

Heidelberg: Springer Spektrum (ISBN 978-3-642-37611-5/pbk; 978-3-642-37612-2/ebook). xi, 444 p. (2014).
The twenty-seven chapters of the book under review give a comprehensive survey of Greek mathematics from the very beginning (Thales) up to late antiquity (Proclus). Most of the chapters deal with certain mathematicians or authors and their mathematical achievements in chronological order, like Pythagoras, Hippocrates, Plato, Aristotle, Euclid, Archimedes, Eratosthenes, Apollonius, Hero, Ptolemy, Nicomachus, Theon from Smyrna, Diophantus, Pappus, Theon from Alexandria, Proclus. Some chapters deal with systematic issues like classical problems of Greek mathematics, beginnings of trigonometry etc. The modern mathematical explanations and descriptions are reliable and enriched by many fine, often coloured, illustrations that take into account also the cultural background. Very often the author adds modern proofs, modern constructions, and outlines later mathematical developments up to the 19th century. Hence the last chapter is entitled “What Euclid did not yet know”.
Unfortunately the author is not well acquainted with modern research literature so that old errors and mistakes are repeated that have been overcome in the meantime: the alleged prediction of a solar eclipse by Thales, the meaning of “ephodos” in the title of Archimedes’ letter to Eratosthenes, the Latin title of Kepler’s work “Harmony of the world” etc. But the most serious criticism concerns the Greek and Latin texts of the book. Nearly all Greek words are dramatically falsely written: there are no or false accents (p. 25, 29, 62, 187 etc.), false letters are used (epsilon instead of eta, omikron instead of omega, psi instead of ypsilon, p. 29, 62, 291 etc.), superfluous letters are inserted (p. 257, 291 etc.). Nearly always Latin words or titles are falsely used or misunderstood: opera ominia (p. 257), Philogus (p. 259), Geometrica, Metrica, Stereometrica are no feminine forms (p. 261, 263, 272), Vitae parallelae is a plural (p. 174) etc. etc. Too many proper names are wrong: Diophantosus (p. 7), Calvalieri (p. 263) etc. It is a great pity that no competent reader has corrected the manuscript before its publication.

MSC:

01-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to history and biography
01A20 History of Greek and Roman mathematics
00A09 Popularization of mathematics
00A30 Philosophy of mathematics
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