What does it mean to prove theorem "synthetically"?

Question

no, I have a question that says "Prove theorem synthetically...".

Answer 1

1. synthetic proof: In certain contexts, a proof using the theorems and postulates mathematicians created for Euclidean geometry. This differs from analytic geometry proofs, which would use algebraic constructs, or transformational proofs, which would use transformations.
2. A geometrical proof without using any coordinates.
3. A proof which only uses previously proven or assumed facts and their implications. Contrasting with an analytic proof which requires equivalence of each pair of propositions in a chain of propositions (my wording)

I saw some synthetic proofs which were simply a single diagram.

Answer 2

I believe that you mean to provide a proof where all the steps are reversible. In this way, you START with what you want to prove (!) and end at something known to be true.
This isn't wrong, exactly because ALL steps are REVERSIBLE, so your proof can be read backwards, and each step is a valid step.

This was found in HallsofIvy's reply at the Forum in the Source. I am not sure about the definition, but at least this strategy is a valid proof technique.

Hope it helps.

Answer 3

Take a look at the link below. Perhaps you meant to ask about solving an equation synthetically instead?