
The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being The whetstone of witte, whiche is the seconde parte of Arithmetike: containyng thextraction of Rootes: The Coßike practise, with the rule of Equation: and the woorkes 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 . 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=p2×2×2 as zzz (the zenzizenzizenzic), and q12=q2×2×3 as zz& (the zenzizenzicubic).
Later in the book he includes a chart of exponents all the way up to p80=p2×2×2×2×5 written as zzzzʃz. There is an error in the chart, however, writing p69 as Sʃz, despite it not being a prime. It should be p3×23 or &Gʃz.
Page images have been made available by Victor Katz and Frank Swetz through Convergence, a publication of Mathematical Association of America.
References
- Robert Recorde (1557). The whetstone of witte, whiche is the seconde parte of Arithmetike: containyng thextraction of Rootes: The Coßike practise, with the rule of Equation: and the woorkes of Surde Nombers (PDF). London: Jhon Kyngstone.. Page 238 in the pdf file.
- Williams, Jack (2011), "The Whetstone of Witte", Robert Recorde: Tudor Polymath, Expositor and Practitioner of Computation, History of Computing, Springer, pp. 173–196, doi:10.1007/978-0-85729-862-1_10, ISBN 9780857298621.
- Atkins, Peter (2004), Galileo's Finger:The Ten Great Ideas of Science, Oxford University Press, p. 484, ISBN 9780191622502.
- Cajori, Florian (2007), A History of Mathematical Notations, Cosimo, p. 164, ISBN 9781602066847.
- Williams (2011), p. 147.
- Williams (2011), p. 154.
- Williams (2011), p. 163.
- Page images on Convergence
External links
- The Whetstone of Witte at The Internet Archive
The Whetstone of Witte is the shortened title of Robert Recorde s mathematics book published in 1557 the full title being The whetstone of witte whiche is the seconde parte of Arithmetike containyng thextraction of Rootes TheCossikepractise with the rule ofEquation and the woorkes ofSurde 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 The passage in The Whetstone of Witte introducing the equals sign Recordian notation for exponentiation however differed from the later Cartesian notation pq p p p p displaystyle 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 amp For instance he referred to p8 p2 2 2 as zzz the zenzizenzizenzic and q12 q2 2 3 as zz amp the zenzizenzicubic Later in the book he includes a chart of exponents all the way up to p80 p2 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 p3 23 or amp Gʃz Page images have been made available by Victor Katz and Frank Swetz through Convergence a publication of Mathematical Association of America ReferencesRobert Recorde 1557 The whetstone of witte whiche is the seconde parte of Arithmetike containyng thextraction of Rootes The Cossike practise with the rule of Equation and the woorkes of Surde Nombers PDF London Jhon Kyngstone Page 238 in the pdf file Williams Jack 2011 The Whetstone of Witte Robert Recorde Tudor Polymath Expositor and Practitioner of Computation History of Computing Springer pp 173 196 doi 10 1007 978 0 85729 862 1 10 ISBN 9780857298621 Atkins Peter 2004 Galileo s Finger The Ten Great Ideas of Science Oxford University Press p 484 ISBN 9780191622502 Cajori Florian 2007 A History of Mathematical Notations Cosimo p 164 ISBN 9781602066847 Williams 2011 p 147 Williams 2011 p 154 Williams 2011 p 163 Page images on ConvergenceExternal linksThe Whetstone of Witte at The Internet Archive