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On arithmetic and geometry. An Arabic critical edition and English translation of Epistles 1 and 2. Edited and translated by Nader El-Bizri. (English) Zbl 1262.01001
Epistles of the Brethren of Purity. Oxford: Oxford University Press in association with The Institute of Ismaili Studies (ISBN 978-0-19-965560-1/hbk). xxiii, 400 p., not consecutively paged. £ 50.00 (2012).
This volume is two books in one: An Arabic critical edition and an English introduction together with a translation, of the first two Epistles of the Encyclopedia known as the Epistles of the Brethren of Purity. The separation of the two texts makes for a rather difficult reading. The English introduction describes well the contents of the epistles, whose number theory in its elements, the theory of figurate numbers, and magic squares is dependent of Nicomachos’s Pythagorean explanations and whose more advanced topics, such as perfect numbers, together with algebra and geometry, are dependent on Euclid. There are no proofs. The translation gives the sense of the text quite well, but the technical terms are chosen for the convenience of the reader and not as translation from the Arabic. For example, for an integer $p$ the number $p^2$ in the translation is called “perfect square”, while in the Arabic it is “having a square root”, i.e., having an integer square root. The translation leaves out the correspondence between {\it abjad} and Hindoo numerals which is difficult to translate unless one uses Alexandrian numerals ($\alpha'= 1$, $\beta'=2$, $\gamma'= 3$, etc.). (The {\it abjad} magic square on p. 159 is derived from the numerical on p. 155 by reflection in the middle row.)
MSC:
 01-06 Proceedings of conferences, etc. (history) 01A30 Mathematics of Islam (Medieval) 11-03 Historical (number theory) 51-03 Historical (geometry)