He does not usually speak with me by day. As it is written (Bamidbar 22:8), “Spend this night here” and similarly, “Fallen, with opened eyes” (24:4), which according to the simple interpretation means, as Onkelos translates, that Hashem only appeared at night when he slept on his bed. (Gur Aryeh) For if not so, why did he say “perhaps” which implies a doubt, while above he said “I will know what he adds…” which implies that he was certain that Hashem would speak to him?

It denotes disgrace … as if to say “reluctantly and in humiliation.” Rashi says בקושי ["reluctantly"] in the sense of מקרה ועראי ["a chance or casual occurrence"] and בזיון ["in humiliation"] in the sense of קרי ["a seminal emission"].

But Avrohom only offered up a singe ram. For if not so, it should say, “I offered burnt-offerings”. Why does the Torah say “an ox and a ram”? Rather it was because “Avrohom only…”

With both names. Though the verse only states (22:6) [that Balak told him], “Curse…” it is logical that he instructed him so, given that this was what Bil’am said. We find a similar instance in the verse, “And you said: Let us send men […to spy out the land]” (Devarim 1:22) even though this [request] is not mentioned in the Torah.

When they deserved to have been cursed, they were not cursed. Thus the meaning of the verse is, “How can I curse when I know that Hashem will not agree to curse them through me?” And how do I know this? Because He never cursed them, even though they were deserving of a curse. One cannot say that it means that Hashem does not want to curse them, for if this were so what was meant by saying, “What Divine wrath can I evoke if Hashem has not been angry.” Surely if he had already said that Hashem did not want to curse them, even if he had been angry in those days he would not have been able to curse them.

But He was not angry during all those days… You might ask: Since he could only curse them at the moment when Hashem was angry, and Hashem was not angry during all of those days, why did Hashem tell him not to curse the people? Surely the curse would not have taken effect. The answer is that Hashem knew that they were destined to stumble with Baal Pe'or and that a plague would come upon them, thus if he has cursed them, people would have said that the plague came because of the curse.

And powerful like the mountains … because of the Patriarchs and Matriarchs. The Patriarchs are called “mountains” and the Matriarchs are called “hills.”

This was acquired for them by their forefathers. Meaning though the word הן ["behold"] refers to the beginning of the verse, “For [I view it] from the mountain peaks…” which refers to the Forefathers as Rashi explains. Thus it comes to teach what it was that was acquired for them by their Forefathers, as rendered by Targum Onkelos, “You are destined [to live] alone.” For if not so, what is the meaning of the term הן ["behold"]? But now it means the same as הנה ["here it is"], as if to say that when I said, “It was acquired for them by their forefathers,” this was that they would dwell alone.

Another interpretation: When they rejoice, no nation rejoices with them. According to the first reason there is the difficulty as to how one would think that He would annihilate them along with the nations, therefore Rashi brought the other interpretation. However, according to the other interpretation there is the difficulty as to how one would determine to differentiate between rejoicing and punishment, therefore he brought the first reason.

As Targum Onkelos interprets … of the four banners. Rashi explains that, “Who can count the dust…” is as Targum Onkelos interprets, and the Targum translates it as מארבע משרייתא [one] of the four camps"]. But since one might not know the meaning of this, therefore Rashi explains, “Of the four banners.”

Another interpretation … one cannot reckon the commandments which they perform with dust. Accordingly the sequence of the verse is reversed, as if it had said: “Who can count what Yaakov does with dust,” meaning the commandments which they perform with dust. “Or count the seed of Yisroel” refers to the seed which emanates during their intercourse. Thus, it as if the verse had said “Who can count the commandments of dust that Yisroel perform, or [who can] count the seed of Yisroel’s intercourse. But I do not know how they will explain the word את. The reason why Rashi brings another interpretation is because according to the first reason there is the difficulty as to how one could not have known the count of the four banners, for surely it was possible to count them. Therefore, he brought the other interpretation where he explains that it refers to reckoning their reward [for the number of mitzvos they perform with dust]. However according to the other interpretation one has to reverse the sequence of the verse, therefore he also brought the first reason.

The seed… (Divrei Dovid) Explains this matter according to the teaching in the chapter [entitled] Kol Hayad (Niddah 16b) that the angel who is appointed over pregnancy is called Layla [“Night”]. He takes the drop [of seed] before Hashem and says “Creator of the Universe, what shall become of this drop? Will it be strong or weak, wise or foolish?” With this Bil’am mentioned the praise of Yisroel, that even a repulsive matter such as this was important for Hashem involve Himself with.

Among them. Not just a regular righteous [death], for if this was his intent, the blessing would not have been directed to Yisroel. Thus, how could Balak say, “I took you to curse my enemies but you have in fact blessed them” (v. 11)?

What is this placing and what would Scripture have been lacking. Rashi is asking two questions: Firstly, “What is this placing”? For the verse does not explain to what it refers. Furthermore, “What would Scripture have been lacking”? Meaning that it should have written, “Hashem chanced to appear to Bil’am and He stated, 'Return to Balak…'." For surely the verse would not have been lacking anything if it had not said [the phrase], “And placed the word in his mouth.” Re’m explains: “What is this placing”? for it is impossible to say that the statement “Return to Balak” is what was meant by “and placed the word in his mouth.” For if so, why was it necessary to say “He said”? Instead it should have said, “And placed the word in his mouth: Return to Balak and say as follows.”

He said to him “You will be forced to return to Balak.” You might ask: Why did Rashi not explain this above (v. 5)? For there also it is written “Hashem placed the word in Bil’am’s mouth and He said: Return to Balak and tell him as follows.” The answer is that above one could say that “Hashem placed in his mouth…” was in response to “I have set up the seven altars…” (v. 4). However, here the difficulty is that Bil’am had not said anything.

This denotes derision. For if not so, he should have inquired, “What do you [have to] say?” It was obvious that he had asked what Hashem had said. (Gur Aryeh) For if this were not so, why did he need to ask, given that he would certainly tell him what Hashem said, as he did at first? Rather, he intended to deride him.

The word denotes a question. As if to say, “Would Hashem say and not do [it], or speak and not fulfill it?

They retract then reconsider whether to change their minds. Meaning that the Targum translates ויתנחם ["He should change His mind"] as תייבין ומתמלכין, which according to Rashi’s explanation means, “Who retract and then reconsider whether to change their minds.” However, according to Targum’s translation this does not denote a question; [rather] it is a statement that people are accustomed to do so, but not Hashem.

I have received instructions from Him to bless them. With this Rashi informs us that “to bless” is not a continuation of “or speak and not fulfill it” which comes before (v. 19). Rather, it is associated with the statement “what did Hashem say” (v. 17). Rashi says קבלתי ["I have received"] instead of לקחתי [lit. "I have taken"], for he had not taken [anything] from him in the normal sense. Since the word ברך is a verb root Rashi adds a lamed because a verb root normally takes one of the letters beis, kaf, lamed or mem. In order to indicate from whom he received the [the instructions to] bless Rashi adds the word “from Him” and to indicate whom he should bless, he added the word “them”.

And I will not reverse… With this Rashi informs us that the word ברך ["bless"] is a verb, meaning that He had blessed them, not a noun meaning that He [had a blessing and] was ready to bless them. The words ולא אשיבנה ["I cannot reverse it"] are only appropriate when referring to a noun, implying that He had not yet blessed them and I will reverse His intention to bless them. However they are not appropriate for a verb. Thus, since He had already blessed them Rashi has to say “I will not reverse His blessing” as if the Torah had stated “He has blessed them with a blessing, and I cannot reverse it.”

The wickedness. באוניות ["wickedness"] is derived from the word און ["sin"].

Like the power [of his] loftiness. Rashi means that the word ראם is in the sense of רום ["loftiness"] not ראם ["ram"] which is an animal, for it is not proper to compare the power of Hashem to an animal. Thus the Torah is saying as follows: Just as when a builder constructs a high and mighty building, you recognize him and know that he is mighty. So too Hashem built His world and founded it upon His might. He brought them out with might, “like the power of His loftiness and elevation” meaning like the might of His world. Thus Rashi means that כתועפות ["like the power"] here and וכסף תועפות ["and silver [shall be] your strength"] both denote strength.

This is a great application of power. Meaning that Rashi wishes to give a reason as to why the power is referred to with the term תועפות. He answers that it is from the same derivation as עוף יעופף ["let birds fly"], because the fact that a bird flies is a great application of power. For it is the manner of anything that is made up of the four elements [of matter] that when one throws it in the air, it falls to the ground. Yet a bird flies in the air, which is [apparently] the opposite of its nature, thus it is certain that it has a great strength.

This refers to the demons and evil spirits. Meaning: Like the power of the demons which fly quickly from one end of the world to the other. According to the first reason there is the difficulty as to why the Torah had written ראם [according to that interpretation meaning ‘loftiness’] therefore Rashi brought the other interpretation because demons and evil spirits are called ראמים. However, according to the other interpretation there is the difficulty that the verse should have written ראמים, therefore he also brought the first reason. (Kitzur Mizrochi) One must explain why Rashi here mentions demons and evil spirits rather than angels. Gur Aryeh discusses this at length. But it is possible to say that it was because Bil’am’s principle acts were through demons and evil spirits, for originally he was a sorcerer. Thus since Balak was also a great sorcerer, as explained further on (Rashi to v. 28), he therefore scared Balak according to his understanding.

To be another time such as this. [Rashi knows this] because the [letter] kaf of comparison indicates that he is comparing another time to this time.

For they will be seated before Him… Given that above it is written (v. 21), “He has the King’s friendship,” which refers to endearment and friendship, [here] he is saying that there is destined to be another time such as this, when they will be seated before him in an endearing manner.

Rather they are told through their prophets. Meaning that כעת יאמר ["in due time it will be said"] is connected with כי לא נחש ביעקב ["for there no sorcery in Yaakov"]. According to the other interpretation the meaning of the kaf, which indicates a comparison, is as follows: “כעת” ["In due time"] as if to say if times arrive at which they need to speak in matters of sorcery or the occult, then “יאמר” ["He will say"] to them [what to do] through prophecy, and they will not need sorcery or the occult. Accordingly it is also understandable why Rashi brought two reasons.

Until he consumes and destroys… אוכל ["consumes"] is also an expression of destruction.

And strikes them dead. Referring to “and drinks the blood of its kill.”

Until he would strike the Midianite kings. According to the first interpretation, none of the verse is understood according to its plain meaning. However, according to other interpretation there is the difficulty that it explains לא ישכב ["he will not like down", i.e., die] as referring to Moshe, while simply speaking it refers to the people. Therefore Rashi also brings the first reason. Though there is no hint from here that Bil’am would be killed with them, nonetheless it is logical that heaven showed him his death as they showed him the deaths of the Midianites.

The first “also” is added to the second “also.” As if it had said, “Do not bless them and also do not curse them; do not curse them and also do not bless them.” You might ask: What is the reason that Balak said this to him? The answer is that Balak thought Bil’am might assume when he said, “Also do not curse them…” that if he wished he could bless them first and afterwards curse them. Therefore, he said, “Also [do not] curse them…” meaning that the first “also” refers to the second, and the second “also” refers to the first.

This is not a command. Because how could he command him to curse them immediately, for perhaps it would not be proper in the eyes of Hashem. Therefore he said וקבותו לי ["and you will curse them for me"] in the future tense, as if to say that once it is proper in the eyes of Hashem, then you should curse them.

It is similar with all the star gazers… (Nachalas Yaakov) Rashi here virtually repeats his comment above concerning the peak of the mountain (v. 14). However he adds that “it is similar with all [star] gazers…” Apparently it was understandable above that he saw there would be a breach at the peak of the mountain, since there indeed was one. For it states at the end of Parshas VeZos Habracha (Devarim 34:1), “Moshe went up… to the peak of the mountain… and Moshe died there…” However, there was no breach at the peak of Pe’or, so why did Balak take him there? And Rashi answers that nonetheless there was a breach through Pe’or. Rashi thus poses the difficulty that if so, Balak was not a sorcerer, for surely he erred. He answers, “It is similar with all [star] gazers…”