c.1200, perhaps from Old English bedecian "to beg," from Proto-Germanic *beth-; or possibly from Anglo-French begger, from Old French begart (see beggar). The Old English word for "beg" was wædlian, from wædl "poverty." Of trained dogs, 1816.
As a courteous mode of asking (beg pardon, etc.), first attested c.1600. To beg the question translates Latin petitio principii, and means "to assume something that hasn't been proven as a basis of one's argument," thus "asking" one's opponent to give something unearned, though more of the nature of taking it for granted without warrant.