Abstract

In the 17th century, Leibniz and Pascal assumed that geometry was the science of space itself instead of extended objects. Leibniz invented the geometry of situation while Pascal developed the study of perspective and the theory of conics. They both defended that geometry might be “pure”. Besides, Leibniz was the privileged reader of Pascal’s geometrical manuscripts and he started his own researches on the geometry of situation just after reading Pascal’s essays. Then, what kind of relation does exist between the new geometry invented by Leibniz and the geometry of conics and perspective presented by Pascal? And were they really pure geometries? Almost all Pascal’s papers on geometry of conics and perspective being nowadays lost, I thus deal in this essay with Leibniz’s notes on Pascal’s manuscripts in order to compare their geometries and to understand what a pure geometry consists in.

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