1600–10; < Latincastīgātus literally, driven to be faultless (past participle of castigāre to chasten), equivalent to cast(us) pure, chaste + -īg-, combining form of agere to drive, incite + -ātus-ate1
Related formscas·ti·ga·tion, nouncas·ti·ga·tive, cas·ti·ga·to·ry[kas-ti-guh-tawr-ee, -tohr-ee]/ˈkæs tɪ gəˌtɔr i, -ˌtoʊr i/, adjectivecas·ti·ga·tor, nounnon·cas·ti·gat·ing, adjectivenon·cas·ti·ga·tion, nounself-cas·ti·gat·ing, adjectiveself-cas·ti·ga·tion, nounun·cas·ti·gat·ed, adjectiveun·cas·ti·ga·tive, adjective
c.1600, from Latin castigatus, past participle of castigare "to correct, set right; purify; chastise, punish," from castus "pure" (see caste) + agere "to do" (see act (n.)). The notion behind the word is "make someone pure by correcting or reproving him."
If thou didst put this soure cold habit on To castigate thy pride, 'twere well. [Shakespeare, "Timon" IV.iii (1607)]