C. F. Keil and Franz Delitzsch on Deuteronomy 2:36

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 capital Ar as the exclusive terminus, as in Jos 13:9 and Jos 13:16; “and as far as Gilead,” which rises on the north, near the Jabbok (or Zerka, see at Deu 3:4), “there was no town too high for us,” i.e., so strong that we could not take it.