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The Mathematical Works of Leon Battista Alberti

Kim Williams, Lionel March, Stephen R. Wassell, editors
Publication Date: 
Number of Pages: 
[Reviewed by
P. N. Ruane
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This book provides translations of, and commentaries upon, the four extant mathematical works of the renowned architect Leon Battista Alberti (1404–1472). Alberti is recognised for his contributions to the visual arts and ‘social writings’, but his mathematical works have not been readily available in English. Fortunately, this attractively presented and well-organized book rectifies the situation.

About two thirds of the book is devoted to ‘Ex ludis rerum mathematicarum’, which translates as ‘From games of mathematical things’. It is the longest of Alberti’s mathematical texts — but it is also his least mathematically innovative. Presented in the form of twenty practical activities, it was written for the amusement of Alberti’s patron, which may explain the strange use of the word ‘game’. Seventeen of the problems involve measuring distances and heights by means of similar triangles. Others concern ingenious methods for calculating weights of objects or the speed of ships.

‘Ex Ludis’ is of interest partly because it provides insight into the practical mathematics that was used in late medieval Italy. Its interest also stems from the fact that it gives a very good idea of the geometry that formed a basis for Alberti’s systematic approach to the visual arts and architecture. Moreover, it yields clues as to the range of the mathematicians who influenced Alberti’s own mathematical development (Fibonacci, Euclid, Archimedes etc). The complete text is presented in medieval Italian, and each of its pages is faced by a translated version. Alberti’s charmingly constructed illustrations are included, and much pleasurable insight can be gained simply by ‘looking at the pictures’. The translation, undertaken by Kim Williams, conveys Alberti’s most personable style of communicating mathematics. This attractive presentation of ‘Ex Ludis’ is complemented by Stephen Wassell’s extensively informative commentaries on its content, structure and raison d’être.

Similar comments apply to other aspects of Alberti’s work that are examined in this book. In particular, the ‘Elements of Painting’, which establishes him as the inventor of perspective drawing, was written without a single diagram (which was in total contrast to ‘Ex Ludis’). However, Stephen Wassell again clarifies Alberti’s way of thinking by converting his detailed written instructions into an understandable procedure for carrying out perspective drawing. In truth, perusal of Alberti’s written instructions is rather like reading a greatly extended version of Euclid’s definitions and postulates, which raises the question as to how understandable it was to those for whom it was intended (Italian painters of the Renaissance).

Perhaps the most mathematical aspects of Alberti’s work are represented in the last two ‘chapters’ of this book. The first of these is his innovative work on alphabetic ciphers, which Lionel March clarifies by means of modern mathematical notation. This is followed by the shortest of the books four ‘chapters’, in which Alberti’s methods for ‘Squaring the Lune’ are set against another helpful commentary by Lionel March.

All in all, this is a most pleasant book to read, and it is hard to imagine a better presentation of Alberti’s mathematical works. No small part of this achievement is due to Kim Williams, whose translations suggest that Alberti was of a warmly ingenuous disposition and that he was a man who aimed at a wide readership.

Peter Ruane spent his working years mainly on the training of teachers at the primary and secondary school levels.