"Tirer d'eux leurs secrets": Leibniz on Artisanal Knowledge and "Secret" Geometry

What was Leibniz's approach to artisanal knowledge? And how did he consider it with respect to mathematical, and more concretely, to geometrical knowledge? On the one hand, Leibniz emphasizes several times in his writings that one should extract "secrets and inventions" from the artisans. On the other hand, Leibniz points out that such artisans cannot formulate by themselves the geometric principles at the base of their machines. In this paper, we examine these intricate relations between Leibniz's reflections on artisans, especially clockmakers and textile workers, as well as his thoughts on mechanical and geometric knowledge. Leibniz's considerations of various artisanal machines, like clocks and looms, lead us to discuss his wish to expand geometry, presenting these machines as embodying a "secret," "hidden," or even "deeper" or "more profound" geometry.