'Rim' in the Bible

Sihon king of the Amorites lived in Heshbon. He ruled over the territory from Aroer on the rim of the Arnon Valley, along the middle of the valley, and half of Gilead up to the Jabbok River (the border of the Ammonites),

From Aroer on the rim of the Arnon Valley, along with the city in the middle of the valley, all the Medeba plateau as far as Dibon,

this as their territory:From Aroer on the rim of the Arnon Valley, along with the city in the middle of the valley, to the whole plateau as far as Medeba,