  We present the foundations of a projective geometric theory of elasticity, as
well as outline a few possible application possibilities. We give the
description of the Cauchy stress and infinitesimal strain tensors compatible
with coordinate description of projective geometry and derive their
transformation rules under projective transformations. We identify these
tensors with generalized conics and quadrics; which shows that the material law
cannot be directly given as a correlation, and that the absence of normal
stresses and normal strains are projective invariants. The transformation of
the graph of the Airy stress function is given in a point-wise projective three
dimensional way, which preserves Pucher's equation corresponding to a
unidirectionally loaded membrane shell. The paper closes with an example
considering tapered beams, showing how to find a statically possible stress
distribution in trapezioidal plates relying on the Euler-Bernoulli beam theory
for rectangular beams.
