#
*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 book covers topics including whole numbers, the extraction of roots and irrational numbers.[2] The work is notable for containing the first recorded use of the equals sign[3] and also for being the first book in English to use the plus and minus signs.[4]**

*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 NombersRecordian 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**.[5]
He also devised symbols for these factors: a zenzic was denoted by **z**, and a cubic by **&**. For instance, he referred to *p ^{8}=p^{2×2×2}* as

**zzz**(the zenzizenzizenzic), and

*q*as

^{12}=q^{2×2×3}**zz&**(the zenzizenzicubic).[6]

Later in the book he includes a chart of exponents all the way up to *p ^{80}=p^{2×2×2x2x5}* written as

**zzzzʃz**. There is an error in the chart, however, writing

*p*as

^{69}**Sʃz**, despite it not being a prime. It should be

*p*or

^{3x23}**&Gʃz**.[7]

## 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.