A third party can dominate two others by turning their combined strength against itself

Evidence

Its outline is that initially two elements are united or mutually dependent in regard to a third, and that this third element knows how to put the forces combined against him into action against one another. The outcome is that the two either keep each other balanced so that he, who is not interfered with by either, can pursue his advantages; or that they so weaken one another that neither of them can stand up against his superiority. — Georg Simmel, The Sociology of Georg Simmel, 4597

Categorization

• DEFINE: The divide-and-conquer triad is the conflict-form where the tertius himself manufactures the clash between two parties.
• XREF: Distinguishes this tertius gaudens variant, where the third deliberately creates conflict, from the other form at 4568 where the third merely profits from pre-existing discord.