Abū al-Wafā' Latinus? A study of method
The book titled \textit{Book on the geometric constructions needed by craftsmen} and written by the Moslem mathematician Abū al-Wafā' al-Būzjānī (940--997/998) is one of the oldest manuals on practical geometric constructions that were needed by artisans, builders, carpenters, and other craftsmen. The book consists of 171 constructions of varying difficulty and interest, and must have played a vital role in the development of Islamic decorative art. About two thirds of these constructions appeared later in the works of European scholars of the Renaissance, such as Cardan, Tartaglia, Benedetti, Marolois, Schwenter, and others. The author of the paper under review is concerned with comparing Abū al-Wafā's constructions with those of the Renaissance, and with investigating whether these later European constructions are original or borrowings from of those of Abū al-Wafā'. He starts with giving a brief but adequate exposition of opposing views of different historians on this matter. These include F. Woepcke (1855), who supported the thesis that the Renaissance geometers in Europe borrowed their constructions from Abū al-Wafā', C. Henry (1883), who believed in independent discoveries, and H. L'Huillier, who, in his earlier works in 1975, did not consider Renaissance constructions as borrowings from Abū al-Wafā', but who, later in 2003, endorses the opposite thesis. The author then expresses the feeling that the two opposing opinions are poorly supported and can be viewed, at best, as ``intimate convictions''. He also looks at the fact that Cardan, Tartaglia, and Benedetti used, in their constructions, fixed opening calipers (i.e., a rusty compass) instead of the ordinary compass, seemingly following the recommendation made by Abū al-Wafā', could simply have been a result of a universal constraint pertaining to need for precision, and that it does not provide evidence for possible borrowings. He supports this viewpoint by observing that Leonardo Da Vinci had already given instructions to use one opening of the compass. He then describes the methods generally used by historians in establishing borrowings. These include similarities in texts and in errors and in unnecessary complexities of arguments and procedures. He then suggests three new tests of his own based on defining the data suitably, on examining similarities in letterings of geometric figures, and on an \textit{index of independence} that he devised. He applies his tests to conclude that, in contradiction with Woepcke's belief, European constructions of the Renaissance are unlikely to have been borrowings from Abū al-Wafā'. He defends his tests by using them to establish Tartaglia's dependence on Fibonacci's \textit{Practica Geometriae}, thus showing that his tests do not always lead to negative results. He also has a section devoted to reply to possible anticipated criticisms of his tests. The paper contains the complete set of constructions of Abū al-Wafā' with more than one solution and with an extensive analysis of some of them. The author of the paper under review is to be commended for this interesting contribution, but the tests he introduced and the conclusions that he reached should be studied and tested further for reliability. It may sound strange that, after reading parts of the paper, this reviewer ended up forming a strong \textit{impression} that European constructions of the Renaissance must have borrowed fairly heavily from Abū al-Wafā'. However, this impression of the reviewer (an Arab), as well as the opposing conclusions of the author (a European), should be taken with a grain of skepticism because of possible intervention of national passions. Driven by such passions, ``today's Arabs'', writes the author, ``can claim for themselves the origin of these constructions, while Europeans may deny this heritage, having some political agenda in mind''. Besides, this reviewer admits that he is not a historian, and the author admits that his use of probability is based on ``drastic simplification'' of things.
scientific article; zbMATH DE number 5996995
scientific article