  We present proofs of two classical theorems. The first one, due to Darboux
and Sauer, states that infinitesimal rigidity is a projective invariant; the
other one establishes relations (infinitesimal Pogorelov maps) between the
infinitesimal motions of a Euclidean framework and of its hyperbolic and
spherical images.
  The arguments use the static formulation of infinitesimal rigidity. The
duality between statics and kinematics is established through the principles of
virtual work. A geometric approach to statics, due essentially to Grassmann,
makes both theorems straightforward. Besides, it provides a simple derivation
of the formulas both for the Darboux-Sauer correspondence and for the
infinitesimal Pogorelov maps.
