  We apply the methodology developed in \cite{Li2014,Li2015} to BOSS DR12
galaxies and derive cosmological constraints from the redshift dependence of
the Alcock-Paczynski (AP) effect. The apparent anisotropy in the distribution
of observed galaxies arise from two main sources, the redshift-space distortion
(RSD) effect due to the galaxy peculiar velocities, and the geometric
distortion when incorrect cosmological models are assumed for transforming
redshift to comoving distance, known as the AP effect. Anisotropies produced by
the RSD effect are, although large, maintaining a nearly uniform magnitude over
a large range of redshift, while the degree of anisotropies from the AP effect
varies with redshift by much larger magnitude. We split the DR12 galaxies into
six redshift bins, measure the 2-point correlation function in each bin, and
assess the redshift evolution of anisotropies. We obtain constraints of
$\Omega_m=0.290 \pm 0.053,\ \ w = -1.07 \pm 0.15$, which are comparable with
the current constraints from other cosmological probes such as type Ia
supernovae, cosmic microwave background, and baryon acoustic oscillation (BAO).
Combining these cosmological probes with our method yield tight constraints of
$ \Omega_m = 0.301 \pm 0.006,\ w=-1.054 \pm 0.025$. Our method is complementary
to the other large scale structure probes like BAO and topology. We expect this
technique will play an important role in deriving cosmological constraints from
large scale structure surveys.
