A {\it partial abelian semigroup} (PAS) is a structure
$(L,\perp,\oplus)$, where $\oplus$ is a partial binary
operation on $L$ with domain $\perp$, which is commutative
and associative (whenever the corresponding elements exist).
A class of congruences on partial abelian semigroups are
studied such that the corresponding quotient is again a PAS.
If $M$ is a subset of a PAS $L$, we say that $x,y\in L$ are
perspective with respect to $M$, if there is $z\in L$ such
that $x\oplus z\in M$ and $y\oplus z \in M$. A subset $M$ is
called weakly algebraic if perspectivity with respect to $M$
is a congruence. Some conditions are shown under which a
congruence coincides with a perspectivity with respect to an
appropriate set $M$. Especially, conditions under which the
corresponding quotient is a D-poset are found. It is also
shown that every congruence of MV-algebras and orthomodular
lattices is given by a perspectivity with respect to an
appropriate set $M$.