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Johannes Faulhaber 1580-1635. Arithmetician in a world of radical changes. (Johannes Faulhaber 1580-1635. Rechenmeister in einer Welt des Umbruchs.) (German) Zbl 0786.01020

Vita Mathematica. 7. Basel: Birkhäuser. xiv, 271 p. DM 98.00; öS 764.40; sFr 88.00 /hc (1993).
This volume is devoted to life and work of Johannes Faulhaber (1580- 1635), an outstanding German mathematician, also known as a specialist in fortifications and as an alchymist.
Faulhaber was one of the brillant exponents of German mathematics developed in 16th and 17th centuries after the publication by Christoff Rudolff (ca. 1500-1545), in 1525, of “Coss”, the first German algebra textbook. The author narrates the life of Faulhaber and describes the scientific atmosphere in Germany in the times before and during Thirty Years’ War. He emphasizes on the main mathematical techniques developed by German algebrists of the time. There are precise references to mathematical works of Peter Roth, René Descartes, Daniel Lipstorp, Michael Stiefel, Francesco Maurolico and many others. The book contains relevant aspects from Faulhaber’s life, for example the prediction of the comet from 1618. There are discussed the main publications of Johannes Faulhaber. Special chapters are devoted to the problem book “Lustgardens” (1604) and its relationship with “Arithmetica Philosophica” of Peter Roth, to “Miracula Arithmetica” (1622), “Academia Algebræ” (1631) and “Ingenieurs-Schul” (two parts: 1630, 1633). In the final chapter there are presented Lipstorps’ allegations about a meeting of Faulhaber with Descartes around 1620 at Ulm. The author discusses Faulhaber’s researches about polynomial equations of degree three, his consideration of the solid geometry versions of the theorems of Pythagoras and Heron and relationship with “Cogitationes privates” of Descartes and the use of logarithms in the first volume of the compendium of practice of mathematics entitled “Ingenieurs-Schul” (Faulhaber was the first to introduce the logarithms in Germany). There are also described the studies about the magic of figured numbers. The numbers occuring in the Bible were also considered by other German mathematicians, among others, by Michael Stiefel (1847- 1567). There are reconstructed in a modern flavour the results about sums of powers of natural numbers in “Miracula Arithmetica” and “Academia Algebræ” (1631).
The volume also includes a chronological table, 442 commented notes, a list of the source material of the books, manuscripts and of the correspondence of Faulhaber. It also contains a detailed bibliography of publications about Faulhaber and a good index of names. The book under review is a very attractive mathematical biography of a key figure of early German mathematics.

MSC:

01A45 History of mathematics in the 17th century

Biographic References:

Faulhaber, Johannes
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