Cuthbert Tunstall (1474-1559), was born in Hackforth, in north Yorkshire. During his life Tunstall pursued many different careers. However, it seems that being a lawyer was his favourite as he stayed in this profession. He studied in Cambridge and Oxford universities and graduated as a Doctor of Law from Padua. He studied mathematics, theology and law and he was also an accomplished speaker of both Greek and Hebrew (Lee, 1909). He later became the Bishop of London and then Bishop of Durham. He died on 18 November 1559 in London at the age of eighty-five.

*De arte supputandi libri quatuor* was written by Cuthbert Tunstall in the early to mid-sixteenth century. The book was first published in 1522 (the second edition, which is part of Worth’s collection, was published in 1538), making it the first book to be published in England that was dedicated solely to mathematics (O’Connor and Robertson, 2007). It is believed to be based on the works of Luca Pacioli (1445-1517), specifically his book *Summa de Arithmetica* published in 1494 (Swetz, 2013), since Tunstall’s book differs little from Pacioli’s work. Tunstall begins by writing about addition and subtraction respectively.

Cuthbert Tunstall, *De arte supputandi libri quatuor* (Paris, 1538), p. 16.

Along with the handwritten sums and problems on the paper we see that he writes about the bigger addition problems such as 73005894+60103643=133209537 as seen at the bottom of the image above. As well as addition, Tunstall also discusses other aspects of arithmetic such as long multiplication and thereafter the much trickier process of dividing a given number by another (see below). Here he shows how to divide 2915410 by 47. The answer shown in the calculation is 62030; conveniently with no remainder.

Cuthbert Tunstall, *De arte supputandi libri quatuor* (Paris, 1538), p. 53.

His explanations can also be seen in the image above as he has a written summary after every line of the problem. Tunstall described many subtopics of basic arithmetic in great detail, from the easier arithmetic works to the somewhat harder ones, an example of which is the calculation below, showing the square root of 57836029 is approximately 7605. Radix means root and reliquum means remainder.

Cuthbert Tunstall, *De arte supputandi libri quatuor* (Paris, 1538), p. 65.

**Sources**

J J O’Connor and E F Robertson, Cuthbert Tunstall, *MacTutor History of Mathematics*, (University of St Andrews, July 2007).

Lee, Sidney (ed.), ‘Tunstall or Tonstall, Cuthbert (1474-1559)’, *Dictionary of National Biography*, Volume 19, (London, 1909).

Swetz, Frank J. (The Pennsylvania State University), ‘Mathematical Treasure: *De arte supputandi* by Cuthbert Tunstall’, *Convergence* (January 2013).

**Text:** Naoise Maughan and Fionnán Howard.