On the other side — Or rather, on this side of Arnon, for so it now was to the Israelites, who had not yet passed over it. Between Moab and the Amorites — Though formerly it and the land beyond it belonged to Moab, yet afterwards it had been taken from them by Sihon. This is added to reconcile two seemingly contrary commands of God, the one that of not meddling with the land of the Moabites, Deuteronomy 2:9, the other that of going over Arnon and taking possession of the land beyond it, Deuteronomy 2:24, because, saith he, it is not now the land of the Moabites, but of the Amorites.
Related Commentaries of Numbers 21:13
Numbers 21:13
13 From thence they removed, and pitched on the other side of Arnon, which is in the wilderness that cometh out of the coasts of the Amorites: for Arnon is the border of Moab, between Moab and the Amorites.