They all started 'on' an equal 'footing' (with one another). = They all started 'on' the same 'footing'. [=none of them had an advantage when they started]
a nation that is 'on' a friendly 'footing' with its neighbors [=a nation that has friendly relations with its neighbors]
The loose stones made it difficult for me to maintain/keep my 'footing'. [=to avoid slipping or falling]
(..) The training is nothing! Will is everything! The will to act. Yield. You haven't beaten me. You have sacrificed sure footing for a killing stroke. DUCARD: Rub your chest. Your arms will take care of themselves. You are stronger than your father. (..)2005 Batman Begins