Abstract
The solution of some ancient problems can be considered today as the solution of systems of linear equations. We come across such problems frequently in Babylonian and Egyptian mathematics, and also in Indian mathematics of the Middle Ages, as well in Islamic countries and in Europe [29]. It becomes quite difficult however to decide in which branch of mathematics we should place the corresponding algorithms for solving these problems. Their solution is given as a sequence of instructions, followed by a validation of the results, presented in ways that make their use quite general. However, in order to assess the validity of these algorithms, and to help our understanding, we shall consider them as belonging to the domain of algebra, as we understand the term today. Of course, describing these old problems as being problems about solving systems of linear equations involves an anachronism, since the idea of systems of equations is very much later. We have already seen such examples in Chapter 3, particularly with the text by Clavius, where we saw that he used the method of repeated double false position to solve, what we would now call a ‘system of order 3’ (see also [23]).
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Chabert, JL. (1999). Solving Systems of Linear Equations. In: Chabert, JL. (eds) A History of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18192-4_10
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