dʰeh₁-mn̥
“that which is set down, law”law, statute, theme
Nominal derivative of *dheh1-, yielding Greek thema/themis (law), English doom.
Discussion
The PIE form *dʰeh₁-mn̥ (that which is set down, established custom, law) is a nominal derivative of *dʰeh₁- (to put, to place, to set), formed with the suffix *-mn̥- producing a result noun: "the thing placed/established" — law, custom, judgment.
Greek thémis (θέμις, "divine law, established custom, right") is the most culturally significant reflex. Thémis was personified as a Titan goddess — the daughter of Earth and Sky, the divine embodiment of the laws that gods and humans alike must obey. She sat beside Zeus as his counsellor, and her judgments were the foundation of cosmic order. The word thémis in common Greek meant "that which is laid down as right" — natural law, the way things should be. English themis appears in legal and philosophical contexts.
The related Greek théma (θέμα, "that which is placed, a proposition") gave English theme — a subject placed before an audience for consideration. The mathematical term theorem (theṓrēma, "a thing observed/contemplated") is from a different formation of the same root.
Latin facere (to do, to make — from *dʰeh₁-k-) continues the root through a different suffixation, giving the massive English fac-/fec-/fic- family: fact, factor, factory, facility, faculty, feasible, affair, effect, perfect, sufficient, deficit, and scores more.
Sanskrit dhā́man- ("established rule, law, dwelling") continues the root in Indo-Iranian with the same *-mn̥ suffix and the same meaning: what has been laid down as rule.
The root's legal significance is immense: law conceived as something "laid down" — placed, established, set in position — is the foundational metaphor of Western jurisprudence. The judge who "lays down the law" performs, in modern English, the same speech act that the PIE speakers named with *dʰeh₁-.
Notes
Pokorny 235-239. English doom, deem, theme from this nominal form.