''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 las ...

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 tw ...

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, resul ...

. 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 re ...

, 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 Zenzizenzizenzic is an obsolete form of mathematical notation representing the eighth power of a number (that is, the zenzizenzizenzic of ''x'' is ''x''8), dating from a time when powers were written out in words rather than as superscript numbers. ...

), 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