Timeline

Computational Explanation

The Whetstone of Witte is best known as the text in which the modern symbol for the equal sign () was proposed:

A simple algebraic problem from The Whetstone of Witte is posed as follows. A captain marshalls his army in a square formation. When the square is of one size, he has 284 men too many. But when he arranges them in a square one more on a side than before, he lacks 25 men. How many men does he have?

The unique answer can be found simply by simultaneously solving two equations expressing these relations:

In[]:=

Solve[{n-

2

a

==284,

2

(a+1)

-n==25},{n,a}]

Out[]=

{{n24000,a154}}

… where n is the number of men and a is the side length of the original square.

In[]:=

Reduce[n-

2

a

==x&&n-

2

(a+1)

==y,{a,n,x,y},Integers]

Out[]=

a∈&&n∈&&x-

2

a

+n&&y-1-2a-

2

a

+n

Additional Reading

• Burton, D. M. The History of Mathematics: An Introduction, 6th ed. McGraw-Hill, pp. 316 and 347, 2007.
• Kaplan, E. "Robert Recorde: Studies in the Life and Works of a Tudor Scientist." Ph.D. Dissertation. New York University, 1960.
• Merzbach, U. C. and Boyer, C. B. "Robert Recorde." In A History of Mathematics, 3rd ed. Hoboken, NJ: Wiley, pp. 262–263, 2011.
• Recorde, R. 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, 1557. [archive.org]
• Roberts, G. Robert Recorde: Tudor Scholar and Mathematician. Cardiff, Wales: University of Wales Press, 2016.
• Scott, J. A History of Mathematics. London: Taylor and Francis, 1958.
• Sanford, V. A Short Story of Mathematics. Boston: Houghton Mifflin, 1930.
• Smith, D. Rara arithmetica. Boston: Ginn and Co., 1908.
• Williams, J. Robert Recorde: Tudor Polymath, Expositor and Practitioner of Computation. Heidelberg, Germany: Springer, 2011.

Additional Links

• Columbia University of New York: PLIMPTON 511 1557 R24
• Mathematical Treasures - Robert Recorde’s Whetstone of Witte
• Wikipedia: Robert Recorde
• Wikipedia: The Whetstone of Witte