Sihon Is Defeated and His Land Possessed Up to The Borders of Ammon (Numbers 21:24).
‘And Israel smote him with the edge of the sword, and possessed his land from the Arnon to the Jabbok, even to the children of Ammon. For the border of the children of Ammon was strong.'
Israel defeated Sihon, and possessed his land. There would first be the initial battle and then the progressive taking of cities and seizure of the land which is described in summary. This is then followed by the history of Heshbon in poetic form.
“From the Arnon to the Jabbok.” The Arnon was the southern border of Sihon's land and formed the border with Moab. The River Jabbok was to the north and then curved round southward to form a border with Ammon.
Once Sihon determined to resist Israelite progress battle was inevitable. The border of Ammon, the only other possible route, was strong, guarded by a ring of fortresses to which archaeology bears witness. Thus it was defeat Sihon or retreat. And once the victory had been won the rest followed. Deuteronomy tells us that in fact all this was because Yahweh intended this land for Israel and therefore hardened Sihon's spirit in order to make him behave in the way in which he did (Deuteronomy 2:30). There the credit for the victory goes to Yahweh. And as the Amorites were basically ‘Canaanites' (related to inhabitants of Canaan) they were all to be put to the sword.