Three medieval collections of mathematical problems. Alkuin, Métrodóros, Abú Kámil (Q2784307)

Instead of the three items promised in the title, in fact, five collections are included in the book. Nonetheless, ``Propositiones ad acuendos iuvenes'' (known in English as Problems to sharpen the young or as whetstones for the budding intellect) attributed to \textit{Alcuin of York} are the main topic, and the remaining four collections are included because of their possible relations to Alcuin's (?) work. The Latin text of the \textit{Propositiones} reprinted according to \textit{M.\ Folkerts}' critical edition [Die älteste mathematische Aufgabensammlung in lateinischer Sprache: Die Alkuin zugeschriebenen `Propositiones ad acuendos iuvenes'. Österr. Akad. Wiss., Math.-Naturw. Kl., Denkschriften 116, Band 6, Abh., 13--78 (Springer-Verlag, Wien) (1978; Zbl 0469.01003)] is accompanied by its richly commented Czech translation. 53 problems are assorted according to their subjects into nine groups (transportation, sequences, geometrical problems, problems leading to linear and diophantine equations etc.). Alcuin's original solutions are shortly stated, then explained in detail and corrected when necessary. This part of the book is closed by a short biography of Alcuin and by another commented medieval collection of problems preceding Alcuin's one, namely ``De arithmeticis propositionibus'' attributed (incorrectly) to \textit{Bede the Venerable}. This collection is remarkable by the first known occurrence of negative numbers and calculations with them. NEWLINENEWLINEThe third collection contained in the book consists of 46 mathematical problems excerpted from the epigrams included in \textit{Anthologia Palatina} the authorship of which is attributed to the otherwise unknown Greek mathematician (or poet as the problems are in verses) \textit{Métrodóros} (IVth century). Because of the close relations between Charlemagne and the Byzantine court, the problems or the collection could have been known to Alcuin and, perhaps, could have served as an inspiration to him. The problems are much older; some of them are attributed to celebrities like \textit{Socrates, Euclid} or even \textit{Homer}. Widespread is also s.c.\ \textit{Diophantus}' epitaph. Solutions of all problems are given and usually shortly commented.NEWLINENEWLINEAlso the fourth collection of the six commented ``fowls'' problems -- ``Book of rare things in the art of calculation'' could be related to Alcuin's work, even though its author, \textit{Abú Kámil}, was born nearly 50 years after Alcuins' death. However, by his statement, the book contains well known problems, the knowledge of which by Alcuin can be reasonably expected; five of them lead to indeterminate equations of the type considered by Diophantus and included in the Propositiones.NEWLINENEWLINEFinally, the Appendix contains 41 problems collected in the manuscript (National Library, Prague), and written perhaps between 1711 and 1716 at the Jesuit Gymnasio Tricoronato, Köln am Rhein. At least one group of these problems is of the type considered by Alcuin and the whole collection is an interesting testimony on teaching mathematics at Jesuit schools in the 18th century.