Medicaid

"pertaining or relating to the art or profession of healing or those who practice it," 1640s, from French médical, from Late Latin medicalis "of a physician," from Latin medicus "physician, surgeon, medical man" (n.); "healing, medicinal" (adj.), from medeor "to cure, heal," originally "know the best course for," from an early specialization of PIE root *med- "take appropriate measures" (source also of Avestan vi-mad- "physician"). "The meaning of medeor is based on a semantic shift from 'measure' to 'distribute a cure, heal'" [de Vaan]. The earlier adjective in English in this sense was medicinal. Related: Medically.

early 15c., aide, "war-time tax," also "help, support, assistance," from Old French aide, earlier aiudha "aid, help, assistance," from Late Latin adiuta, noun use of fem. of adiutus, past participle of Latin adiuvare "to give help to," from ad "to" (see ad-) + iuvare "to help, give strength, support, sustain," which is from a PIE source perhaps related to the root of iuvenis "young person" (see young (adj.)).

The meaning "thing by which assistance is given" is recorded from 1590s; the sense of "person who assists, helper" is from 1560s. The meaning "material help given by one country to another" is from 1940.