1 And if his oblation be a sacrifice of peace offering, if he offer it of the herd; whether it be a male or female, he shall offer it without blemish before the LORD.
2 And he shall lay his hand upon the head of his offering, and kill it at the door of the tabernacle of the congregation: and Aaron's sons the priests shall sprinkle the blood upon the altar round about.
3 And he shall offer of the sacrifice of the peace offering an offering made by fire unto the LORD; the fat that covereth the inwards, and all the fat that is upon the inwards,
4 And the two kidneys, and the fat that is on them, which is by the flanks, and the caul above the liver, with the kidneys, it shall he take away.
5 And Aaron's sons shall burn it on the altar upon the burnt sacrifice, which is upon the wood that is on the fire: it is an offering made by fire, of a sweet savour unto the LORD.
6 And if his offering for a sacrifice of peace offering unto the LORD be of the flock; male or female, he shall offer it without blemish.
7 If he offer a lamb for his offering, then shall he offer it before the LORD.
8 And he shall lay his hand upon the head of his offering, and kill it before the tabernacle of the congregation: and Aaron's sons shall sprinkle the blood thereof round about upon the altar.
9 And he shall offer of the sacrifice of the peace offering an offering made by fire unto the LORD; the fat thereof, and the whole rump, it shall he take off hard by the backbone; and the fat that covereth the inwards, and all the fat that is upon the inwards,
10 And the two kidneys, and the fat that is upon them, which is by the flanks, and the caul above the liver, with the kidneys, it shall he take away.
11 And the priest shall burn it upon the altar: it is the food of the offering made by fire unto the LORD.
12 And if his offering be a goat, then he shall offer it before the LORD.
13 And he shall lay his hand upon the head of it, and kill it before the tabernacle of the congregation: and the sons of Aaron shall sprinkle the blood thereof upon the altar round about.
14 And he shall offer thereof his offering, even an offering made by fire unto the LORD; the fat that covereth the inwards, and all the fat that is upon the inwards,
15 And the two kidneys, and the fat that is upon them, which is by the flanks, and the caul above the liver, with the kidneys, it shall he take away.
16 And the priest shall burn them upon the altar: it is the food of the offering made by fire for a sweet savour: all the fat is the LORD's.
17 It shall be a perpetual statute for your generations throughout all your dwellings, that ye eat neither fat nor blood.
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The Yahwist sacrifice, judging by the description in the book of Leviticus, included three elements. First of all, and every sacrifice began with this, came prayer. The person who wanted to offer a sacrifice laid his hands on the head of the sacrificial animal and said a prayer. In the case of the so-called sacrifice of reconciliation, or sacrifice of thanksgiving (the corresponding Hebrew word can mean both "peace" or "reconciliation" and "thanksgiving" in the sense of a return gift or payment), this was a prayer of praise or thanksgiving. Then the animal was slaughtered, after which the priest sprinkled the altar and all those taking part in the ritual with blood. The third element was the sacrificial meal itself, in which all those present also usually took part, at least when the sacrifice of reconciliation was involved (in the Synodal translation it is usually called a "peace offering"). During the meal, a separate, special portion of the sacrificial meat was intended for the priests and Levites taking part in the ritual.
This order becomes understandable if we remember that sacrifice was originally conceived as a form of communion with God and of human sanctification. By God's design, a human being is both a spiritual being and a natural one. As a spiritual being, he is the image of God, a self-aware person possessing freedom of will. Accordingly, for communion with God and for sanctification, a person must freely turn to God himself. That is why everything begins with prayer.
Without turning to God, at the level of ritual alone, sanctification is impossible for a person. On the other hand, a human being is not only spirit but also nature, animal nature, and after the fall he became much more animal than he had been before the fall. This human nature is sanctified through the sprinkling with blood and the eating of sanctified meat. By nature, after all, a person is closest precisely to animals, to those very animals God allowed him to eat after the fall.
God's presence sanctifies the animal placed on the altar, and the person, by then eating the sanctified meat, interacts with the nature sanctified by God on the bodily, and therefore natural, level. Animal nature acts on the bodily nature of fallen man, sanctifying it just as every sanctified nature acts on any other nature, sanctifying it in the process of interaction. If the fall had not happened, a person would not have needed such mediated action upon his bodily existence for its sanctification, but in the fallen state it is, as can be seen, the most adequate form of sanctifying human nature.