 Hilbert’s consistency demonstrations in FG are all demonstrations of relative consistency, which is to say that in each case the consistency of a set AX of geometric axioms is reduced to that of a familiar background theory B, demonstrating that AX is consistent if B is. The important technique Hilbert employs is the reinterpretation of the geometric terms appearing in AX in such a way that, as reinterpreted, the members of AX express theorems of B. For example, Hilbert’s first consistency-proof interprets the terms “point”, “line”, and “lies on” as standing respectively for a particular collection of ordered pairs of real numbers, for a collection of ratios of real numbers, and for an algebraically-defined relation between such pairs and ratios; under this reinterpretation, the geometric sentences in question express theorems of the background theory of real numbers.