In French we also have the word “pouvoir”, which is closer to the “top-down control and influence” meaning.

“In Renaissance humanism the triad esse–nosse–posse (being–knowing–having power)… became a force and symbol of resistance, in Bacon’s notion of inventio or experimentation, Campanella’s conception of love, and Spinoza’s usage of potentia… Posse refers to the power of the multitude and its telos, an embodied power of knowledge and being, always open to the possible [...] The mode of production of the multitude is posed against exploitation in the name of labor, against property in the name of cooperation, and against corruption in the name of freedom.” — pp. 407-408, Empire http://slash.autonomedia.org/article.pl?sid=01/08/07/1527205