A Source Book in Mathematics

David Eugene Smith’s A Source Book In Mathematics was one of the first mathematical source books to be published, and it continues to be reprinted by Dover Publications. It contains 100 or so extracts, classified under ‘number’; ‘algebra’; ‘geometry’; ‘probability’; and ‘calculus, functions, quaternions.’ To the modern reader the last seems a somewhat strange combination of topics, as does the description of all the headings as ‘fields’.

Within each ‘field’ the order of extracts is more or less random, jumping from De Moivre to Clavius to Gauss, for example in ‘The field of geometry’. Occasionally the jumps are dizzying, as when we are whisked from Stevin to Dedekind in ‘The field of number’.

Because of the age of the book a few extracts that must have once seemed up-to-date have now become obscure, most notably perhaps d’Ocagne on nomography, but most have stood the test of time fairly well. The same cannot be said of all the translations, some of which could be better, but that can always be said of translations. There are also some anachronisms that now grate: ascribing to Cavalieri an ‘approach to the calculus’, for example, or translating a geometric statement by Roger Cotes into the modern formula log (cos x + i sin x) = ix.

Most of these are blemishes that readers can cope with for themselves. A more pertinent reason for not buying an old source book is that so many sources are now readily available online in the original form; the modern reader is no longer dependent on print versions. Having said that, this book contains a few valuable sources, some reproduced at length, that remain difficult to find elsewhere. For myself, I am particularly pleased to have extracts from Bombelli and Cataldi, Cavalieri, Rolle, and Saccheri, the originals of which take some effort to come by. Other readers will no doubt find their own favourites.

Finally, for historians, a source book from 1929 is a historical source in its own right, giving us an insight into early twentieth-century views of the history of mathematics. Rather against my own expectations, I find it is not quite time yet to remove D E Smith from our shelves. 

Jackie Stedall is Lecturer in History of Mathematics at the Mathematical Institute, University of Oxford. She is the author of several books, including A Discourse Concerning Algebra: English Algebra to 1685, The Greate Invention of Algebra: Thomas Harriot's Treatise on Equations, and Mathematics Emerging: A Sourcebook 1540-1900..