The Liber mahameleth. A 12th century mathematical treatise. 3 volume set
This is the definitive Latin edition, English translation, and mathematical commentary of a 12th century mathematical treatise, the \textit{Liber mahameleth}, written by an author who had access to Arabic algebraic treatises, living in the still Arabic part of Spain, but himself not an Arab. The treatise exists in four manuscripts, two of which contain only a very small part of the entire treatise. Both in the introduction and on every page of the Latin text, the editor is very careful to mention all the variations that occur in different manuscripts. Each individual manuscript is presented in detail in the introduction, as are the (scant) traces of this work in medieval times, all the way to 1484. The reader of the \textit{Liber mahameleth} was supposed to have been acquainted with Euclid's \textit{Elements} and with Abū Kāmil's \textit{Algebra}. The mathematics dealt with include proportions and operations with them, linear equations (determinate and indeterminate ones), quadratic equations, summation of arithmetic series, some practical geometry, as well as metrology. Throughout the text, there are no numerical symbols in the text (they do occur in some illustrations, but without any explanation nor mention of their Indian origin), nor signs for arithmetical operations, nor for the main unknown (the \(x\)), which is simply \textit{res}, so that the book is a \(100\%\) language book (a typical sentence reading as ``Converte tertiam in quintas, et fient quinta et due tertie unius quinte.''). What's more unusual is that there is no method for the exact determination of the square root of non-square integers, only approximation methods, although the book had all the needed tools to provide the algorithm. The mathematical commentary on the text (Volume 3) offers an invaluable tool by presenting the content of the Latin text not only in English (which Volume 2 already did, but without any actual formula, i.e., as a purely English language text), but also with today's algebraic notation. The edition by \textit{A.-M. Vlasschaert} (ed.) [The Liber mahameleth. Critical edition with commentary. Stuttgart: Franz Steiner Verlag (2010; Zbl 1225.01018)] is mentioned only in a footnote on page xv of Volume 1 (where it is mentioned that the influence of the \textit{Liber mahameleth} on the applications of mathematics to daily and commercial life was ``negligible'' and that the book ``fell into oblivion right up until the present time'') with the sentence ``Her edition differs in many respects from ours'' as the only comparison.
scientific article; zbMATH DE number 6243679