The Whetstone of Witte

''The Whetstone of Witte'' is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being ''The whetstone of , is the : The ''Coßike'' practise, with the rule of ''Equation'': and the of ''Surde Nombers. The book covers topics including whole numbers, the extraction of roots and irrational numbers. The work is notable for containing the first recorded use of the equals sign and also for being the first book in English to use the plus and minus signs.

Recordian notation for exponentiation, however, differed from the later Cartesian notation $p^q = p \times p \times p \cdots \times p$. Recorde expressed indices and surds larger than 3 in a systematic form based on the prime factorization of the exponent: a factor of two he termed a ''zenzic'', and a factor of three, a ''cubic''. Recorde termed the larger prime numbers appearing in this factorization ''sursolids'', distinguishing between them by use of ordinal numbers: that is, he defined 5 as the ''first sursolid'', written as ʃz and 7 as the ''second sursolid'', written as Bʃz.
He also devised symbols for these factors: a zenzic was denoted by z, and a cubic by &. For instance, he referred to ''p⁸=p^2×2×2'' as zzz (the zenzizenzizenzic), and ''q¹²=q^2×2×3'' as zz& (the zenzizenzicubic).

Later in the book he includes a chart of exponents all the way up to ''p⁸⁰=p^{2×2×2×2×5}'' written as zzzzʃz. There is an error in the chart, however, writing ''p⁶⁹'' as Sʃz, despite it not being a prime. It should be ''p^3×23'' or &Gʃz.

Page images have been made available by Victor Katz and Frank Swetz through ''Convergence'', a publication of Mathematical Association of America.Page images on ''Convergence''
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References

External links

''The Whetstone of Witte'' at The Internet Archive

{{DEFAULTSORT:Whetstone of Witte
Mathematics books
British non-fiction literature
1557 books
History of mathematics