The ontological status of geometrical objects in the commentary on the Elements of Euclid of Jacques Peletier du Mans (1517-1582)

In Peletier’s commentary on the Elements (1557), the ontological status of the objects of geometry is defined, on one hand, through the assertion of their archetypal role in the constitution of the Universe and, on the other hand, through the description of their modes of apprehension in the frame of geometrical research. The first perspective, which is qualified by the statement of the limits of the human mind faced with the true genesis of geometrical objects, tends to give way to a more human representation of geometry, which is mainly fulfilled through the non-passive and rational study of the objects of Euclidean geometry.