The Whetstone of Witte
Recorde’s, second book of arithmetic, the Whetstone of Witte, contains expositions on number theory and the roots of abstract and denominate numbers, the rule of Algeber and on surds The number theory described is that of Pythagoras as presented by Euclid, modified by Theon and Nichomacus, copied by Boethius, and modified further to deal with problems raised by the introduction of vulgar fractions. In defining the types of absolute numbers Recorde follows Euclid, whose method of finding perfect numbers he uses uncritically to make one of his few mistakes. The standard methods for derivation of square and cubic roots of numbers are given with special attention to improvement of accuracy of approximation. The greater part of the book is devoted to the arithmetic of denominate numbers of cossike and irrational forms, in which he draws on the works of Stifel, Scheubel and Cardano, but uses his own clearer order of presentation. He fell one step short of dispensing with cossike symbols in favour of a notation that used powers of numbers, but did introduce the sign for equality as part of his description and use of the Rule of Algeber. Whilst there has been wide acknowledgement of the value of the sign, it has to be be recognised that it was introduced specifically to ease the manipulation of equations, a means to an end and a basic feature of algebra rather than of arithmetic. The treatment of surds is both standard and incomplete. Recorde expected that this book would have limited appeal and he was right.