15th Novembertagung on the History of Mathematics

15. Novembertagung zur Geschichte der Mathematik

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Comments on reconstruction based on an example: Stevin's attempt to clarify the notion of equation by an analogy to the 'rule of three'

Henk Bos

Universiteit Utrecht, The Netherlands

Abstract. In his Arithmétique of 1585 Simon Stevin proposed an analogy between equations (in one unknown, of degree 2--4) and problems solvable by the so-called 'rule of three'. The latter problems were of the type 'if 6 chicken cost 15 pennies, what do 14 chicken cost?'; they were solved by finding the fourth proportional of (in this case) 6, 15, and 14, that is, the number 35, because 6 : 15 = 14 : 35.
 
Stevin considered this analogy a great help in understanding the nature of equations. The idea has been short-lived in mathematics; one finds a few echos of it in early 17th century texts, but that is all. Historians have wondered what clarification Stevin saw in the analogy and this is indeed an intriguing question. I will use it as an example to discuss the role of 'reconstruction' in historians' attempts to understand past mathematics.

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S.H. © 27.Oct.2004