Geometrical constructions? If you have an accurate visual intuition of the properties of triangles and squares, then a diagram of the Pythagorean theorem pretty much is a proof of it. Euclidean geometry is an axiomatic system, but it isn't a formal system on strings of symbols; it's a formal system on abstract geometric figures.

Throughout most of history, math wasn't done in what we now think of as "mathematical notation", i.e. expressions written symbolically. That wasn't invented until the 1500s. Before then, math was done with proofs written in ordinary language, accompanied by diagrams.