Vilna Gaon - The Kingdom Of Yishmael Gets A One Day Reprieve
On Succos each day we bring Parim, oxen for a Korban. On the first day we start with 13 and bring one less each successive day, for a total of 70. We also bring other korbanos with them, including a Sa'ir or goat for a Chatos. On the first two days the Torah calls this goat a S'ir Izim. On the third just plain Sa'ir. The on the fourth once again it is called S'ir Izim with the rest of the days it only calls it a Sa'ir. Why the different term on these particular days?
It is said in the name of Vilna Gaon that we know the 70 oxen represent the seventy nations who will ultimately cease to hold power over us. The two chief nations are Yishmael and Edom which is Eisav. Each of them head a contingent of 35 nations apiece. Yishmael is called S'ir Izim and Eisav Sa'ir.
First we bring korbanos for the 35 nations of Yishmael since as the son of Avrohom Avinu he goes first. The first two days we bring 13 and 12 oxen respectively for a total of 25, and we also bring a S'ir izim. Being that Yishmael only has ten more left and the third day when we bring 11 which would be too many for Yishmael, we bring it for Eisav instead together with the Sa'ir. The fourth day we bring 10 oxen and a S'ir Izim to finish up Yishmael. The rest of the days are for Eisav and we a bring a Sa'ir.
May Hashem speedily redeem his beloved little lamb from among the nations Bimheira BiYameinu Amein.