What is the meaning of "va'Yachalosh Yehoshua ... "?
Rashi: It means that Yehoshua severed the heads of Amalek's strong men, keeping alive only the weak ones. He did not kill them all, due to a Divine command. 1
R. Bachye #1: Refer to 17:9:4:4*.
R. Bachye #2: With reference to the power of Amalek in the heaven, it implies that Hakadosh-Barcu-Hu only allowed Yehoshua to weaken Amalek, but not to destroy them ? since He never shuts down the celestisal system completely unless it is absolutely necessary, 2
R. Bachye #3: It means that Yehoshua did not kill Amalek, but he either weakened their guardian angel in Heaven, with his Tefilah or by raising his hands, or that he actually harnessed it to assist Yisrael.
Rashbam: It means that he vanquished Amalek. 3
Targum Yonasan: "Vayachalosh Yehoshua ... L'fi Charev" means tht he destroyed Amalek by the sword 4 - by severing their heads.
Gur Aryeh: The proof is, that if Yehoshua was powerful enough to behead their mighty warriors, certainly he should have been able to kill their weaker ones! Seeing as Yehoshua did not do so, it must be because that is what Hashem had commanded. (As for why Hashem did so, see the following question.)
See R. Bachye.
Rashbam: As in Sh'mos 32:18 "Kol Anos Chalushah".
Which is the regular death-penalty of a Nochri.
What are the connotations of " ? es Amalek ve'es Amo"?
Seforno: It means Amalek (the nation) and the nation or nations that joined him to fight Yisrael.
Targum Onkelos and TargmYonasan: It means 'Amalek and his nation'.
QUESTIONS ON RASHI
Rashi writes: "Yehoshua weakened [Amalek] - He left only the weak among them; he did not kill all of them.... He acted in accordance with the Word of the Shechinah." Why didn't Hashem allow Yehoshua to wipe out Amalek completely?
Maharal (Gevuros Hashem, end Ch. 42, p. 161): Bnei Yisrael had not yet reached the great level at which Hashem's Name would be whole (see Rashi to 17:16).
Lev Eliyahu (p. 97): Hashem makes a nation fall only after its angel has fallen, and the angel of Esav will not fall as long as the Yetzer ha'Ra is among us.
