Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
ădăgĭum, i, n. [prob. ad and aio, but acc. to Paul. ex Fest. p. 12 Müll., “ad agendum apta,” applicable to life, suitable for use], a proverb, an adage: vetus adagium est, Nihil cum fidibus graculo, Gell. 1, praef.