The generation of conic sections

Abstract

The essay contains significant results from the point of view of perspectivism that are relevant for Pascal’s epistemology. The first consequence of the sixth definition moves the abstract problem of conic sections into the area of the visual. Visual representation reveals the unity of diverse geometrical objects. If the conic sections that are either a circle, ellipsis, parabola or hyperbola are seen from the outside, their difference is not obvious. Yet, if “the eye is in the apex of the cone” then these forms are projected onto each other and will be similar. Therefore the apex of the cone determines a special perspective that enables one to see and understand similarity within difference. This epistemological model can be found throughout Pascal’s work and will be explicated philosophically in Pensées.