From Latin 'dominari' (to rule), from 'dominus' (lord), from 'domus' (house) — the lord of the house became the model for all authority.
To have a commanding influence on; to exercise control over; to be the most important or conspicuous element.
From Latin 'dominātus,' past participle of 'dominārī' (to rule, to exercise lordship over, to be master), from 'dominus' (lord, master of the household), from 'domus' (house, home), from PIE *dem- / *dom- (house, to build). The evolution is telling: the house-owner (domus-owner → dominus) became the authority figure, and 'dominārī' expressed the exercise of that authority at any scale — over a household, a province, or an empire. The root *dem- is widely attested: Greek 'despotēs' (master, from *dems-poti-s, house-lord), Sanskrit 'dampati-' (lord of the house), Avestan 'dəmāna-' (house). In Latin, 'dominus' was also the standard translation
The word 'danger' is a hidden relative of 'dominate.' Old French 'dangier' originally meant 'power of a lord, dominion, authority,' from Vulgar Latin *dominiarium (power of a lord), from 'dominus.' To be 'in danger' originally meant to be 'in someone's power' — under a lord's dominion. The shift from 'under authority' to 'at risk of harm' occurred because being under a lord's arbitrary power was, historically, genuinely dangerous.