A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
num 21:1ISRAEL ATTACKED BY THE CANAANITES. (Num. 21:1-35)
King Arad the Canaanite--rather, "the Canaanite king of Arad"--an ancient town on the southernmost borders of Palestine, not far from Kadesh. A hill called Tell Arad marks the spot.
heard tell that Israel came by the way of the spies--in the way or manner of spies, stealthily, or from spies sent by himself to ascertain the designs and motions of the Israelites. The Septuagint and others consider the Hebrew word "spies" a proper name, and render it: "Came by the way of Atharim towards Arad" [KENNICOTT].
he fought against Israel, and took some of them prisoners--This discomfiture was permitted to teach them to expect the conquest of Canaan not from their own wisdom and valor, but solely from the favor and help of God (Deu 9:4; Psa 44:3-4).
num 21:2Israel vowed a vow unto the Lord--Made to feel their own weakness, they implored the aid of Heaven, and, in anticipation of it, devoted the cities of this king to future destruction. The nature and consequence of such anathemas are described (Lev. 27:1-34; Deu. 13:1-18). This vow of extermination against Arad [Num 21:2] gave name to the place Hormah (slaughter and destruction) though it was not accomplished till after the passage of the Jordan. Others think Hormah the name of a town mentioned (Jos 12:14).
num 21:4they journeyed from mount Hor--On being refused the passage requested, they returned through the Arabah, "the way of the Red Sea," to Elath, at the head of the eastern gulf of the Red Sea, and thence passed up through the mountains to the eastern desert, so as to make the circuit of the land of Edom (Num 33:41-42).
the soul of the people was much discouraged because of the way--Disappointment on finding themselves so near the confines of the promised land without entering it; vexation at the refusal of a passage through Edom and the absence of any divine interposition in their favor; and above all, the necessity of a retrograde journey by a long and circuitous route through the worst parts of a sandy desert and the dread of being plunged into new and unknown difficulties--all this produced a deep depression of spirits. But it was followed, as usually, by a gross outburst of murmuring at the scarcity of water, and of expressions of disgust at the manna.
num 21:5our soul loatheth this light bread--that is, bread without substance or nutritious quality. The refutation of this calumny appears in the fact, that on the strength of this food they performed for forty years so many and toilsome journeys. But they had been indulging a hope of the better and more varied fare enjoyed by a settled people; and disappointment, always the more bitter as the hope of enjoyment seems near, drove them to speak against God and against Moses (Co1 10:9).
num 21:6The Lord sent fiery serpents among the people--That part of the desert where the Israelites now were--near the head of the gulf of Akaba--is greatly infested with venomous reptiles, of various kinds, particularly lizards, which raise themselves in the air and swing themselves from branches; and scorpions, which, being in the habit of lying in long grass, are particularly dangerous to the barelegged, sandaled people of the East. The only known remedy consists in sucking the wound, or, in the case of cattle, in the application of ammonia. The exact species of serpents that caused so great mortality among the Israelites cannot be ascertained. They are said to have been "fiery," an epithet applied to them either from their bright, vivid color, or the violent inflammation their bite occasioned.
num 21:7the people came to Moses, and said, We have sinned--The severity of the scourge and the appalling extent of mortality brought them to a sense of sin, and through the intercessions of Moses, which they implored, they were miraculously healed. He was directed to make the figure of a serpent in brass, to be elevated on a pole or standard, that it might be seen at the extremities of the camp and that every bitten Israelite who looked to it might be healed. This peculiar method of cure was designed, in the first instance, to show that it was the efficacy of God's power and grace, not the effect of nature or art, and also that it might be a type of the power of faith in Christ to heal all who look to Him because of their sins (Joh 3:14-15; see also on Kg2 18:4).
num 21:10the children of Israel set forward--along the eastern frontier of the Edomites, encamping in various stations.
num 21:12pitched in the valley--literally, the "woody brook-valley" of Zared (Deu 2:13; Isa 15:7; Amo 6:14). This torrent rises among the mountains to the east of Moab, and flowing west, empties itself into the Dead Sea. Ije-Abarim is supposed to have been its ford [CALMET].
num 21:13pitched on the other side of Arnon--now El-Mojib, a deep, broad, and rapid stream, dividing the dominions of the Moabites and Amorites.
num 21:14book of the wars of the Lord--A fragment or passage is here quoted from a poem or history of the wars of the Israelites, principally with a view to decide the position of Arnon.
num 21:15Ar--the capital of Moab.
num 21:16from thence they went to Beer--that is, a "well." The name was probably given to it afterwards [see Jdg 9:21], as it is not mentioned (Num. 33:1-56).
num 21:17Then Israel sang--This beautiful little song was in accordance with the wants and feelings of travelling caravans in the East, where water is an occasion both of prayer and thanksgiving. From the princes using their official rods only, and not spades, it seems probable that this well was concealed by the brushwood or the sand, as is the case with many wells in Idumea still. The discovery of it was seasonable, and owing to the special interposition of God.
num 21:21Israel sent messengers unto Sihon--The rejection of their respectful and pacific message was resented--Sihon was discomfited in battle--and Israel obtained by right of conquest the whole of the Amorite dominions.
num 21:24from Arnon unto Jabbok--now the Zurka. These rivers formed the southern and northern boundaries of his usurped territory.
for the border of . . . Ammon was strong--a reason stated for Sihon not being able to push his invasion further.
num 21:25Israel dwelt in all the cities--after exterminating the inhabitants who had been previously doomed (Deu 2:34).
num 21:26Heshbon-- (Sol 7:4) --situated sixteen English miles north of the Arnon, and from its ruins it appears to have been a large city.
num 21:27Wherefore they that speak in proverbs--Here is given an extract from an Amorite song exultingly anticipating an extension of their conquests to Arnon. The quotation from the poem of the Amorite bard ends at Num 21:28. The two following verses appear to be the strains in which the Israelites expose the impotence of the usurpers.
num 21:29people of Chemosh--the name of the Moabite idol (1Ki. 11:7-33; Kg2 23:13; Jer 48:46).
he--that is, their god, hath surrendered his worshippers to the victorious arms of Sihon.
num 21:33they turned and went up by the way of Bashan--a name given to that district from the richness of the soil--now Batanea or El-Bottein--a hilly region east of the Jordan lying between the mountains of Hermon on the north and those of Gilead on the south.
Og--a giant, an Amoritish prince, who, having opposed the progress of the Israelites, was defeated.
num 21:34The Lord said unto Moses, Fear him not--a necessary encouragement, for Og's gigantic stature (Deu 3:11) was calculated to inspire terror. He and all his were put to the sword.