The One Incarnate Word

Christ is Risen and Ascended!!!

I am very happy to find this forum. It always warms my heart to fellowship with Orthodox brethren. I have a question. Did St Cyril of Alexandria ever teach that Jesus Christ, Glory to Him, had ONE Composite Nature? This is the belief of the Coptics and other "Oriental Orthodox" that Our Lord Christ has one COMPOSITE nature where he is fully God and fully Human. They claim that St. Cyril taught this and that the Holy Ecumenical Council of Ephesus (431 A.D.) as well but that the Holy Council of Chalcedon (451 A.D.) had a Nestorian strain to it saying that Our Lord has 2 natures. They especially abhor the Tome of St.Leo I of Rome. Is this splitting hairs like saying 2+2=4 and 2x2=4? They both are saying the same thing: Jesus christ is Fully God and Fully Man. Any suggestions or insights will be deeply appreciated.