  The ordered addition of two Lorentz boosts is normally shown to result in a
boost by utilizing concepts from group theory and non-Euclidian geometry. We
present a method for achieving this addition by performing a sequence of
spatial rotations and uni-dimensional Lorentz transformations. The method is
first developed for two-dimensional space and it is then extended to
three-dimensional space by utilizing the commutative property of the rotation
of the y-z plane and a boost along the x-axis. The method employs only matrix
multiplication and certain invariant quantities that are natural consequences
of spatial rotations and Lorentz transformations. The combining of two boosts
in different directions into a single boost cannot be expected a priori because
we show that the converse of this statement is not true. That is, two rotations
interspersed with a boost cannot always be reduced to a single rotation
preceded and followed by boosts.
