 We can now redescribe Hilbert’s technique, in a nutshell, as follows: Given a set AX of sentences, Hilbert appeals to a background theory B to construct an interpretation of AX’s geometric terms under which the members of AX express theorems of B. This interpretation is, assuming the consistency of B, an n-tuple satisfying the relation \(R_{\textit{AX}}\) defined by AX. Its existence demonstrates the satisfiability of \(R_{\textit{AX}}\) and consequently the consistency of AX relative to that of B. Similarly for the independence of I from AX. 