  This is an annotated translation from Latin of E327 'De motu rectilineo trium
corporum se mutuo attrahentium'. In this publication, Euler considers three
bodies lying on a straight line, which are attracted to each other by central
forces inversely proportional to the square of their separation distance
(inverse-square law). Although not explicitly mentioned by Euler, this is an
exact solution of three bodies that move around the common center of mass and
always line up. The solution given by Euler could represent a hypothetical
situation of Sun, Earth and Moon in perpetual alignment in syzygy, for which
the parameter that controls the distances among the planets was found to be
given by a quintic function.
