  Boole’s final example (MAL, p. 78) was solving three equations in three unknowns for one of the unknowns in terms of the other two.  This example used a well known technique for handling side conditions in analysis called Lagrange Multipliers—this method (which reduced the three equations in the example to a single equation in five unknowns) reappeared in LT (p. 117), but was only used once.  It was superseded by the sum of squares reduction (LT, p. 121) which does not introduce new variables.  Using the Reduction and Elimination Theorems in LT one discovers that Boole’s constraint equations (3) (MAL, p. 80) for his three equation example are much too weak—each of the products should be 0, and there are additional constraint equations. 