III. TRUE GOD AND TRUE MAN
The Nestorian heresy regarded Christ as a human person joined to the divine person of God's Son. Opposing this heresy, St. Cyril of Alexandria and the third ecumenical council, at Ephesus in 431, confessed "that the Word, uniting to himself in his person the flesh animated by a rational soul, became man." Christ's humanity has no other subject than the divine person of the Son of God, who assumed it and made it his own, from his conception. For this reason the Council of Ephesus proclaimed in that Mary truly became the Mother of God by the human conception of the Son of God in her womb: "Mother of God, not that the nature of the Word or his divinity received the beginning of its existence from the holy Virgin, but that, since the holy body, animated by a rational soul, which the Word of God united to himself according to the hypostasis, was born from her, the Word is said to be born according to the flesh."
The Monophysites affirmed that the human nature had ceased to exist as such in Christ when the divine person of God's Son assumed it. Faced with this heresy, the fourth ecumenical council, at Chalcedon in 451, confessed:
Following the holy Fathers, we unanimously teach and confess one and the same Son, our Lord Jesus Christ: the same perfect in divinity and perfect in humanity, the same truly God and truly man, composed of rational soul and body; consubstantial with the Father as to his divinity and consubstantial with us as to his humanity; "like us in all things but sin". He was begotten from the Father before all ages as to his divinity and in these last days, for us and for our salvation, was born as to his humanity of the virgin Mary, the Mother of God.
We confess that one and the same Christ, Lord, and only-begotten Son, is to be acknowledged in two natures without confusion, change, division or separation. The distinction between the natures was never abolished by their union, but rather the character proper to each of the two natures was preserved as they came together in one person (prosopon) and one hypostasis.
Source: Catechism of the Catholic Church (Vatican.va)