  We describe a new approach for the determination of cosmological parameters
using gravitational lensing systems with multiple arcs, exploiting the fact
that a given cluster can produce multiple arcs from sources over a broad range
in redshift. The coupling between the critical radius of a single arc and the
projected mass density of the lensing cluster can be avoided by considering the
relative positions of two or more arcs. Cosmological sensitivity appears
through the angular size-redshift relation. We consider simulated data
constructed using a more general form for the potential, realistic sources, and
an assumed cosmology and present a method for simultaneously inverting the lens
and extracting the cosmological parameters. The input data required are the
image and measured redshifts for the arcs. The technique relies upon the
conservation of surface brightness in gravitationally lensed systems. We find
that for a simple lens model our approach can recover the cosmological
parameters assumed in the construction of the simulated images.
