Participate
late 15th century: from Latin participat- ‘shared in’, from the verb participare, based on pars, part- ‘part’ + capere ‘take’.
wiktionary
From the participle stem of Latin participare(“to take part in, share in, give part in, impart”), from particeps(“taking part in, sharing in”), from pars(“part”) + capiō(“to take”); see part and capable.
etymonline
participate (v.)
1530s, "to partake, to share or share in," a back-formation from participation, or else from Latin participatus, past participle of participare "to share, share in, participate in; to impart," from particeps "partaking, sharing," from parti, past participle of partir "to divide" (from Latin partire, from pars "a part, piece," from PIE root *pere- (2) "to grant, allot") + Latin -cip-, weak form of stem of capere "to take" (from PIE root *kap- "to grasp"). Meaning "have features or characteristics in common with another or others" is by 1570s. Related: Participated; participating.