From Aroer, which is on the edge of the Valley of the Arnon, and from the city that is in the valley, as far as Gilead, there was not a city too high for us. The LORD our God gave all into our hands.
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...