Sympathetic
mid 17th century (in the sense ‘relating to an affinity or paranormal influence’, as in sympathetic magic): from sympathy, on the pattern of pathetic .
wiktionary
Mid 17th century in the sense “relating to an affinity or paranormal influence”, from sympathy + -etic(“pertaining to”), on the pattern of pathetic.
etymonline
sympathetic (adj.)
1640s, "pertaining to sympathy," from Modern Latin sympatheticus, from late Greek sympathetikos "having sympathy," from sympathein, from sympathes "having a fellow feeling, affected by like feelings" (see sympathy). In English, the meaning "having fellow feeling, susceptible to altruistic feelings" is recorded from 1718.
In the anatomical sense, "subject to a common nervous influence," the word is attested from 1769, from Modern Latin (nervus) sympathicus, coined by Jacques-Benigne Winslow (1669-1760), Danish anatomist living in Paris. Related: Sympathetical (1630s); Sympathetically (1620s).