Using the language of Euclidean geometry one can talk about certain curves like the curves that had been studied before the invention of the Cartesian system. By talking about curves I mean I am not certain that for example a spiral had been precisely defined using only the language of euclidean geometry, rather they had been described by using terms like movement, time, velocity, etc.
Now my question is whether the graph of elementary functions can be defined as some loci using only the language of Euclidean geometry in any modern re-axiomatization of euclidean geometry like for example Hilbert's.