Total reaction cross sections have been measured for 50 and 65 MeV ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ on C, O, $^{18}\mathrm{O}$, S, Ca, and Zr. The motivation for this experiment is to obtain cross sections to act as constraints in optical model fits to elastic scattering data. Measurements using the ``poor geometry'' transmission method were made for exceptionally small angles with the aim of improving the accuracy of the extrapolation to zero solid angle. At these small solid angles the muon cone from pion decay contributes significantly and its effects were explicitly included. The accuracies of the elastic correction are evaluated by using error matrix techniques and an additional systematic error is included.