A precision measurement of absolute pi+p and pi-p elastic differential
cross sections at incident pion laboratory kinetic energies
from T_pi = 141.15 to 267.3 MeV is described. Data were obtained
detecting the scattered pion and recoil proton in coincidence
at 12 laboratory pion angles from 55 to 155 degrees for pi+p,
and six angles from 60 to 155 degrees for pi-p.
Single arm measurements were also obtained for pi+p energies
up to 218.1 MeV, with the scattered pi+ detected at six angles
from 20 to 70 degrees. A flat-walled, super-cooled liquid hydrogen target
as well as solid CH2 targets were used. The data are characterized
by small uncertainties, ~1-2% statistical and ~1-1.5% normalization.
The reliability of the cross section results was ensured by carrying out
the measurements under a variety of experimental conditions to identify
and quantify the sources of instrumental uncertainty. Our lowest and
highest energy data are consistent with overlapping results from TRIUMF
and LAMPF. In general, the Virginia Polytechnic Institute SM95 partial
wave analysis solution describes our data well, but the older
Karlsruhe-Helsinki PWA solution KH80 does not.