Decapitation is tricky enough when the victim is bound and has his head on the block. It seems to have gone wrong so often that mr. Guillotin thought his fail-safe execution device was a humane invention, since it saved the victim the agony of an imperfectly carried-out decapitation. In order words: no way it was as quick and easy as in that video, and I doubt most soldiers would have bothered when the opponent is already down. Dismemberment, on the other hand, is quite possible with the heavy chopping swords of the Greeks and Dacians. However, since your average heavy infantryman of the era would have been covered by a large shield and only briefly exposed their weapons-arm when attempting a strike, I doubt it was practical in face-to-face melee combat.
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