Definitions:

  1. A mass point is a pair, $(n,P)$ consisting of a positive number $n$, the weight, and a point P. It will be written as $nP$ for convenience.
  2. $nP$ = $mQ$ if and only if $n=m$ and $P=Q$. (Usual equality for ordered pairs)
  3. $nP + mQ = (n+m)R$ where $R$ is on $\overline{PQ}$ and $PR:RQ = m:n$. ( A weight of $n$ at $P$ and a weight of $m$ at $Q$ will balance iff the fulcrum is place at $R$ since $n(PR) = m(RQ)$.