I think Quantity, Structure, Space etc... are highly abstract quantities.  I haven't understood what was meant till I looked at the article (where this explained by an exhaustive list of examples).  This sounds like a typical math book.  Vectorial analysis is the science of vectors.  Consider v and u, v and u are vectors if v+u is also a vector, etc...  I agree my suggestion is also abstract but one could give directly a simple example from naive basic geometry, algebra or even group theory which could be said in one line.  The object could be the tympan of the Accropolys it can be modeled by three line segments in a plane, a triangle; studying the properties of abstract triangles leads us to the understanding of all object which can be assumed to be triangles.  Or something alike. 
 : Do you have examples where mathematics is not a theorem prover except in the process of defining the object and guessing the theorem?  I don't but I would be interested if you could tell me one example.