25 It is indeed sad that the ancient adversaries of the council of Chalcedon (also called Monophysites) should have rejected this doctrine, so lucid, so coherent and so complete, on the strength of certain badly understood expressions of ancient writers. While they rejected the absurd teaching of Eutyches about the mixture of natures in Christ, they obstinately clung to the well-known expression: 'One Incarnate nature of the Word God'. This expression had been used by Cyril of Alexandria (who took it from St. Athanasius) with a perfectly correct meaning, since he used the term 'nature' to signify 'person'. The Fathers of Chalcedon, therefore, totally removed what was ambiguous or liable to cause error in these expressions. For they applied the same terms as are used in the theology of the Trinity, to the exposition of our Lord's Incarnation. Thus they made 'nature' and 'essence' (essentia) the same, and likewise 'Person' and 'Hypostasis', and they treated the latter two names as totally different in meaning, from the former two. Their approach, on the other hand, had made 'nature' the equivalent of' Person' not of 'essence' ( essentia ).
Source: Sempiternus Rex Christus (Vatican.va)