The Different Covenants & the Animal Sacrifices:
If there is one thing you cannot escape in the Old Testament, it is the animal sacrifices. They were present since Adam and Eve's time all the way to the rebuilding of the Temple after the exile (and even to the time of Jesus Christ). Why were they so important? Well, the means of atoning for sin in the Old Testament was in the shedding of the blood of animals. For without the shedding of blood there is no remission of sin (Hebrews 9:22). Yes, the OT (Old Testament) method of sacrifice was not meant to be a perfect and permanent solution for sin. For the blood of goats and bulls could never take away sin for good (Hebrews 10:4). Only Jesus Christ's one time perfect sacrifice could take away sin permanently; Meaning, Christ's shed blood can forever wash away our sins when we repent and accept Him and or when we confess of our sins.
Now, it is important to understand that all the Covenants (i.e. The Noadic, Abrahamic, Mosaic, and Davidic Covenants) in the Old Testament relate to Jesus Christ and His sacrifice (Which is typified in the Old Testament animal sacrifices). For if Jesus Christ did not go the cross, it would regulate all the Old Covenant Promises as meaningless rubbish whereby none of them could have been truly fulfilled (as they were intended to be).
The First Testament or Old Testament (Where all the later different Covenants fall under) was based on faith. It began with God dedicating that Testament in blood with an animal God sacrificed so as to provide coats of skins so as to cover Adam and Eve's nakedness (See Hebrews 9:18; Genesis 3:21). God did not accept their efforts in them trying to cover themselves with fig leaves. God clothed them, and Adam and Eve had to accept God's covering by faith. For Scripture speaks about how God clothes (covers) us with a robe of righteousness (Isaiah 61:10). Jesus is our robe of righteousness, so when we repent of our sins and accept Him as our Savior by faith, Christ imputes His righteousness to us. Christ covers our nakedness with His sacrifice. Just as God covered Adam and Eve's nakedness with an animal sacrifice. In fact, later we see one of Adam's children (Abel) making an animal sacrifice unto God as a part of doing what was good and right according to the Lord.
The Noadic Covenant (Which is under the First Testament) is based on a Promise. A promise made to Noah and all of creation which relates to Noah, the Ark, and Global Flood, which is a picture or symbol of baptism as mentioned in the New Testament by Peter (1 Peter 3:20-21). In Baptism: When we believers go down into the water, it is symbolic of being buried with Christ (with our sins being washed away) by His sacrifice and blood. The rising up out of the water is symbolic of Christ's resurrection and how we are resurrected to new life in Him. For the Promise that God would never destroy the world with the Condemnation with a Flood again is a symbolic picture of how God will never again visit our sins that have been forgiven under Christ's sacrifice at the cross. So just as Noah and all of creation were given a new promised life after the flood, we are resurrected in a new promised life in Christ. Which again, is not possible without Christ's sacrifice. A sacrifice that is typified in the animal sacrifices of the Old Testament.
The Abrahamic Covenant (Which is under the First Testament) was a Covenant based on a Promise. It was a Promise made to Abraham that His descendants would be as innumerable as the stars whereby all the nations of the Earth would be blessed. This is only made possible by the "Promised Seed" whose name is Jesus Christ (Who is Abraham's descendant). For when a believer in Jesus Christ dies, they will one day have a new resurrected body like Jesus. They will be of the seed of Abraham, not only spiritually when they accepted Christ in this life, but they will also one day physically be of the seed of Abraham by Jesus' resurrection (Because Jesus is a physical descendant of Abraham). So when we as believers make disciples of Jesus Christ of all nations as a part of the Great Commission given to us by our Lord, we are adding to Abraham's family in being as innumerable as the stars as a part of the Promise to him, which is only made possible by Jesus Christ and His sacrifice. A sacrifice that was typified in the animal sacrifices of the Old Testament.
The Mosaic Covenant (Which is under the First Testament) is based on the Law and the Priesthood (Involving animal sacrifices). The Law was a schoolmaster to bring us unto Christ. Meaning, when a person breaks the Law, they realize that they are a sinner in need of a Savior (i.e. Jesus Christ). For they cannot perfectly keep the Law alone on their own efforts or merits; And they had to keep bringing animal sacrifice to a priest to atone for sin over and over because they had to keep revisiting the same sins every year. So it was not a permanent solution for their sin problem. They needed a person who would be a righteous substitute who kept the Law perfectly and who could died in their place (As a sacrifice) once and for all. They needed a perfect and eternal Savior. They needed a Passover Lamb who would forever take away their sin. They needed a more perfect Priest who could intercede for them any time and any place. They needed Jesus Christ. For Jesus is our Passover Lamb; And Jesus is our eternal High Priest in Heaven acting on our behalf between God the Father and us (man). So if we slip up, we as believers can confess our sins and be cleansed of all unrighteousness (1 John 2:1; 1 John 1:9). For Jesus lives today so as to forever make intercession for us. This is only made possible by Jesus Christ and His sacrifice. A sacrifice that was typified in the animal sacrifices of the Old Testament (As clearly seen in the Law of Moses or the Mosaic Covenant).
The Davidic Covenant (Which is under the First Testament) is based on a Promise. It was a Promise made to David about how the Messiah would would one day come thru David's line and rule as King one day. A King who would rule over a Kingdom of peace and righteousness. A King and a Kingdom of which in both would have no end. Meaning, David's Kingdom would last forever because of Jesus Christ. For Jesus will one day purify this world, and rebuld a new world out of it's ashes, whereby He willl be King over His people here on this Earth. This is only made possible by Jesus Christ's sacrifice. For in order for Jesus to rule as King here on this Earth, he needs a people (that are His) so as to rule over. For how can one be a King without a Kingdom? So the Davidic Covenant is contingent upon Christ's sacrifice; Which again, is typified in the animal sacrifices in the Old Testament. For David had desired to rebuild the Temple so as to reinstitute the Temple sacrifices again. But God told David that his son Solomon was going to rebuild the Temple so as to do that. So the animal sacrifices were important. They were an important part of the Old Testament as a whole. For the rebuilding of the Temple and the sacrifices were shadows of Christ. For in the New Testament, Jesus would be our temple and our sacrifice for us so as to forever save us and rule over us (As King and Priest).
So in conclusion:
We see that the different covenants (i.e. the Noadic, Abrahamic, Mosaic, and Davidic Covenants) in the Old Testament were not separate from the Old Testament or separate from the First Testament. They were all a part of the Old Covenant or the Old Testament tied to the animal sacrifices (Which are of Type of Jesus Christ's sacrifice). For the First Testament was dedicated in blood by an animal sacrifice by God Himself with Adam and Eve and those sacrifices continued as a part of God's plan on all the way up to the time of Christ dedicated the New Testament with His own blood by His sacrifice upon the cross. For Jesus even Himself said, "no man puts new wine into old wine skins." This is a contrast between the Old Testament and the New Testament (Jesus was preparing people for). For There are only two major Covenants or Testaments. For that's why our Bible's are divided between the Old Testament and the New Testament. For Jesus (who is revealed to us in the New Testament) is the fulfillment of the Old Testament.
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