In this paper a straightforward method (based on quite traditional ideas) is presented for replacing an ''analytic'' formulation of a field-theory on a flat spacetime (in the style of Laplace) by a ''synthetic'' formulation (in the style of Archimedes). Real numbers are avoided by representing them by triples of points, and arbitrary choices of coordinate axes and scales of measurement are avoided by quantifying out parameters. The method thus permits a ''nominalistic'' and ''invariant'' interpretation of an important class of theories from mathematical physics. The method is briefly compared with that of Hartry Field.