Latin petitio principii is a calque for Greek en archei aiteisthai. Both have a meaning closer to 'request for the beginning' than to 'begging the question'. That's what I meant earlier by poor translation. Because both beg and question have common meanings in English, most speakers who are unaware of this logical term from Aristotle have reanlyzed the phrase according to English. Greek aiteo 'to beg, ask' has a specialized meaning of 'to assume, postulate' in Aristotle. Latin principium means 'beginning, commencement'. I'd use petitio principii for the logical term and let begging the question go its own sweet way.
