''The Whetstone of Witte'' is the shortened title of

Robert Recorde Robert Recorde () was an Anglo-Welsh physician and mathematician. He invented the equals sign (=) and also introduced the pre-existing plus sign (+) to English speakers in 1557. Biography Born around 1512, Robert Recorde was the second and last ...

'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 The equals sign (British English, Unicode) or equal sign (American English), also known as the equality sign, is the mathematical symbol , which is used to indicate equality in some well-defined sense. In an equation, it is placed between two ...

and also for being the first book in English to use the

plus and minus signs The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents subtraction, result ...

. Recordian notation for

exponentiation Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to r ...

, 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 In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are su ...

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., p. 163.

References

External links

''The Whetstone of Witte'' at The Internet Archive
Mathematics books British non-fiction literature 1557 books History of mathematics {{Mathpublication-stub