Frank Edgar Farley, An Advanced English Grammar with Exercises
“ She sleeps the sleep of death. Note. Cognate means “kindred” or “related.” The cognate object repeats the idea of the verb, often with some modification, and may be classed as an adverbial modifier. Its difference from the direct object may be seen by contrasting “The blacksmith struck the anvil” with “The blacksmith struck a mighty blow” (cf. “struck mightily”) . For the pronoun it as cognate object, see § 120. 5. Adverbial Objective 109. A noun, or a phrase consisting of a noun and its modifiers, may be used adverbially. Such a noun is called an adverbial objective. ”
