The Geometry of Tracing, a Possible Link Between Geometric Drawing and Euclid's Geometry?

In this chapter, the authors focus on the objects and practices of middle school geometry. They define what they have called the geometry of tracing, which corresponds to a kind of practical axiomatics based on the use of tracing instruments (excluding measuring instruments) around a fundamental situation, the reproduction of a geometric figure, seen as an action situation. In middle school, one of the objectives of teaching geometry is as an introduction into demonstration. For centuries, the foundation of geometry teaching was Euclid's axiomatics, reworked and completed by Clairaut in the 18th century, by Legendre and Lacroix at the end of the 18th century and the beginning of the 19th, and by Hadamard at the turn of the 20th century. The authors present some elements of a progression implemented in Julien Ribennes's 5th grade class in Chamalières.