Luca Pacioli, algebra, and double entry

This paper proposes that Pacioli, an accomplished mathematician, recognised that the Venetian method of bookkeeping had an algebraic underpinning, although, when writing his treatise, he converted this algebra into rules. The algebra that he may have used is deduced from a combination of his own words - derived from the translation by Geijsbeek, checked against that of Von Gebsattel and other translations - with quotations from the literature. Perhaps this is the ‘buried treasure waiting to be rediscovered’ referred to by Macve in ‘Pacioli’s Legacy’(Macve, 1996, 22). Chapter 23 in the treatise is central to this paper. Here Pacioli advises a merchant on how to run a store, using an approach that is now known as ‘the entity theory’. Pacioli also advised the merchants to exclude information about their private possessions from the public domain and this paper describes how this could be achieved.  The paper ends with a presentation in the Appendix of the evolution of double entry expressed algebraically in tabular form, along with an illustration of a matrix method approach to recording transactions.