What does "Es ha'Cheilev Al he'Chazeh" incorporate?
Chulin, 45a: It incorporates the part of the chest that faces the ground, the lower end up to the neck, the upper end up to the stomach, 1 including two ribs, one on either side
See Torah Temimah, note 129.
What are the connotatons of "es ha?Cheilev al he'Chazeh Yevi'enu". Who brings it and from where?
Menachos, 42a: The Kohen brings the Chalavim together with the Chazeh from the Beis-ha'Mitbachayim.
Why does the Torah repeat "Eis he'Chazeh"?
Sifra: To teach us that, even if all the Chalavim have become Tamei, he performs Tenufah on the Chazeh alone..
Why does the Torah insert the two (superfluous) words "Lehanif oso Tenufah"?
Sifra: It adds "Oso", to teach us that, even if only one kidney (besides the Chazeh) remains, then the Kohen performs Tenufah on it, and not two Tenufos on the Chazeh, and "Tenufah", to extrapolate "Tenufah", 've'Lo Tenufos' - the Chazeh does require a second Tenufah 1
See Malbim
How will we reconcile this Pasuk, which requires the owner to perform the Tenufah, with the Pasuk in Ki Savo Devarim, 26:4, in connection with Bikurim, which places the obligation on the Kohen?
Rashi: In fact, both the owner and the Kohen perform the Tenufah - the owner's hands on top, the hands of the Kohen underneath. 1
Since, based on a Gezeirah Shavah "Yadav" "Yadecha," we apply what is written here to there, and vice-versa.
How will we reconcile this Pasuk, which refers to "the Cheilev on the chest", with the Pasuk in Shemini, 10:15, which refers to "the calf ... and the chest on the ... Chalavim"?
Rashi: The current Pasuk is referring to when the Kohen brings the Korban from the Beis ha'Mitbachayim, 1 the latter Pasuk to when he places them into the hands of a second Kohen who performs the Tenufah - turning them upside-down in the process. 2
Ramban: The chest is waved together with the Chalavim, first on its own, then together with the right calf.
The slaughterhouse that was situated in the Azarah, north of the Mizbe'ach.
And the reason that the Pasuk here mentions only the chest - adding "Lehanif Oso" (in the singular) - and not the right calf, is to teach us that if one of them became Tamei, then they perform Tenufah with the remaining one (Ramban, citing the Sifra).
How will we reconcile Pasuk 10:15 in Shemini, "the calf ... and the chest on the ... Chalavim with the Pasuk there 9:20 "and they shall place the Chalavim on the chests and burn the Chalavim on the Mizbe'ach"?
Rashi: Refer to 7:30:2:1. The earlier Pasuk discusses after Tenufah where the second Kohen places them into the hands of a third Kohen, who carries them to the Mizbe'ach in order to burn them. 1
Even though it could all have been done by one Kohen - in fulfillment of the Pasuk in Mishlei, 14:28 "be'Rov Am Hadras Melech" (Sifsei Chachamim). See also Torah Temimah, note 127.
What is the purpose of the Tenufah?
