  The explicit integrability of second order ordinary differential equations
invariant under time-translation and rescaling is investigated. Quadratic
systems generated from the linearisable version of this class of equations are
analysed to determine therelationship between the Painlev\'e and singularity
properties of the different systems. The transformation contains a parameter
and for critical values, intimately related to the possession of the Painlev\'e
Property in the parent second order equation, one finds a difference from the
generic behaviour. This study is a prelude to a full discussion of the class of
transformations which preserve the Painlev\'e Property in the construction of
quadratic systems from scalar nonlinear odes invariant under time translation
and rescaling.
