From Aroer on the rim of the Arnon Valley, along with the city in the valley, even as far as Gilead, not one city had walls too high for us. The LORD our God gave us all of them.
God having tried the self-denial of his people in forbidding them to meddle with the Moabites and Ammonites, and they having quietly passed by those rich countries, and, though superior in number, not made any attack upon them, here he recompenses them for their obedience by giving them possession of the country of Sihon king of the Amorites.
Commenting on Deuteronomy 2:24-37
From Aroer, which is by the brink of the river Arnon.... Upon the border of Moab, and the principal city of it; see Jer 48:19. and from the city that is by the river; or even the city that is in the midst of the river, the city Aroer, which seems to be meant; see Jos 12:2.
Deu 2:36 They proceeded this way with the whole of the kingdom of Sihon. “From Aroër on the edge of the Arnon valley (see at Num 32:34), and, in fact, from the city which is in the valley,” i.e., Ar, or Areopolis (see at Num 21:15), - Aroër being mentioned as the inclusive terminus a quo of the land that was taken, and the Moabitish...