The Whetstone of Witte
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| Author | Robert Recorde |
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| Genre | Mathematics |
Publication date | 1557 |
The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being The whetstone of , {{Not a typo|whiche o|seconde parte of Arithmeti e of Equation: and the woorkes of Surde Nombers. The book covers topics including whole numbers, the extraction of root rs.[1] The work is notable for containing the first recorded use of the equals sign[2] and also for being the first book in English to use the plus and minus signs.[3]
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.[4]
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).[5]
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.[7]
Page images have been made available by Victor Katz and Frank Swetz through Convergence, a publication of Mathematical Association of America.[8]
References
- ↑ 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, https://books.google.com/books?id=kJyXzvkXWBAC&pg=PT484.
- ↑ Cajori, Florian (2007), A History of Mathematical Notations, Cosimo, p. 164, ISBN 9781602066847, https://books.google.com/books?id=rhEh8jPGQOcC&pg=PA164.
- ↑ (Williams 2011), p. 147.
- ↑ (Williams 2011), p. 154.
- ↑ 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. London: Jhon Kyngstone. https://archive.org/download/TheWhetstoneOfWitte/TheWhetstoneOfWitte_text.pdf.. Page 238 in the pdf file.
- ↑ (Williams 2011), p. 163.
- ↑ Page images on Convergence
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