  We illustrate methods for deriving properties of thermonuclear, or Type Ia,
supernovae, including synthesized $^{56}$Ni mass, total ejecta mass, ejecta
kinetic energy, and $^{56}$Ni distribution in velocity, from gamma-ray line
observations. We simulate data from a small number of published SN Ia models
for a simple gamma-ray instrument, and measure their underlying properties from
straightforward analyses. Assuming spherical symmetry and homologous expansion,
we calculate exact line profiles for all $^{56}$Co and $^{56}$Ni lines at all
times, requiring only the variation of mass density and $^{56}$Ni mass fraction
with expansion velocity as input. By parameterizing these quantities, we
iterate the parameters to fit the simulated data. We fit the full profiles of
multiple lines, or we integrate over the lines and fit line fluxes only versus
time. Line profile fits are more robust, but in either case, we can recover
accurately the values of the aforementioned properties of the models simulated,
given sufficient signal-to-noise in the lines. A future gamma-ray mission with
line sensitivity approaching 10$^{-6}$ photons cm$^{-2}$ s$^{-1}$ would measure
these properties for many SN Ia, and with unprecedented precision and accuracy
for a few per year. Our analyses applied to the reported $^{56}$Co lines from
SN 2014J favor a low $^{56}$Ni mass and low ejecta mass, relative to other
estimates.
