How does the covenant of circumcision with Abraham relate to the New Covenant?

Catechism or other references appreciated. Thank you.

CCC 527 Jesus’ circumcision, on the eighth day after his birth, [209] is the sign of his incorporation into Abraham’s descendants, into the people of the covenant. It is the sign of his submission to the Law [210] and his deputation to Israel’s worship, in which he will participate throughout his life. This sign prefigures that “circumcision of Christ” which is Baptism. [211]

[209] Cf. Lk 2:21.
[210] Cf. Gal 4:4.
[211] Cf. Col 2:11-13.

CCC 1150 Signs of the covenant. The Chosen People received from God distinctive signs and symbols that marked its liturgical life. These are no longer solely celebrations of cosmic cycles and social gestures, but signs of the covenant, symbols of God’s mighty deeds for his people. Among these liturgical signs from the Old Covenant are circumcision, anointing and consecration of kings and priests, laying on of hands, sacrifices, and above all the Passover. The Church sees in these signs a prefiguring of the sacraments of the New Covenant.

Baptism replaces circumcision.

See Colossians 2:6-12

The requested sacrifice of Abraham’s son Isaac prefigures the voluntary sacrifice of Jesus on the cross. In the first case, Isaac is spared when God shows his mercy. In the second case, we are all spared when Jesus shows us his loving mercy on the cross.

If this is a question that interests you, you may like listening to Jeff Cavins and Scott Hahn in Our Father’s Plan…

ewtn.com/vondemand/audio/seriessearchprog.asp?seriesID=-306548622

He does cover covenants and I really got a lot out of the series.

The 2nd program in the series describes the covenants…

Adam: marriage covenant
Noah: household covenant
Moses: National covenant
David: National kingdom covenant
Christ came and established a world wide covenant in the Catholic Church, which all the others were leading up to.

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