Traditionally, history of mathematics had often neglected to consider the mathematical practices of engineers. In fact the mathematical needs of engineers seem very different from those of professional mathematicians. So engineers were often forced to imagine by themselves the operational methods and the calculation tools that mathematicians could not provide them. We are now knowing that mathematical knowledge and mathematical representations are part of various social groups in interaction, in which they find various legitimacies. Within this framework, history of mathematics should enrich itself by taking greater account of the engineering community, within which specific mathematical practices, original and fruitful, did exist. The military engineer André-Louis Cholesky offers us the occasion of a perfect case study. In fact, we have the chance that a great part of his personal papers has been kept by his family and recently donated to the École polytechnique. So it was a great opportunity for Claude Brezinski and me: we found there an exceptional set of archives deserving to be explored.