Matthew Henry on Leviticus 3:6–end
Directions are here given concerning the peace-offering, if it was a sheep or a goat. Turtle-doves or young pigeons, which might be brought for whole burnt offerings, were not allowed for peace-offerings, because they have no fat considerable enough to be burnt upon the altar; and they would be next to nothing if they were to be divided according to the law of the peace-offerings. The laws concerning a lamb or goat offered for a peace offering are much the same with those concerning a bullock, and little now occurs here; but, 1. The rump of the mutton was to be burnt with the fat of the inwards upon the altar, the whole rump (Lev 3:9), because in those countries it was very fat and large. So…
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if his offering be a goat--Whether this or any of the other two animals were chosen, the same general directions were to be followed in the ceremony of offering.
Adam Clarke on Leviticus 3:12
A goat - Implying the whole species, he-goat, she-goat, and kid, as we have already seen.
John Gill on Leviticus 3:16
And the priest shall burn them upon the altar,.... Which shows that not the fat only, but the inwards and the kidneys, were burnt also; so Maimonides says (l), that the priest salted the parts, and burned them upon the altar; and the priests might not have the breast and shoulder (which were what belonged to them) until the parts were burnt:
it is the food of the offering made by fire; which the Lord ate of, or accepted of:
for a sweet savour; as a type of the sweet smelling sacrifice of Christ, with which he is well pleased:
all the fat is the Lord's; that is, all that was upon the parts mentioned in the several sacrifices of peace offerings, which was to be taken off and burnt: though t…
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