"The Divine and human natures cannot alternate, so that the Divine should become human or the human Divine; nor can they be so commingled as that a third should be produced from the two which is neither wholly Divine nor wholly human. For, granting that it were possible for either to be changed into the other, it would in that case be only God and not man, or man only and not God. Or, if they were so commingled that a third nature sprung from the combination of the two (as from two animals, a male and a female of different species, a third is produced, which does not preserve entire the species of either parent, but has a mixed nature derived from both), it would neither be God nor man. Therefore the God-man, whom we require to be of a nature both human and Divine, cannot be produced by a change from one into the other, nor by an imperfect commingling of both in a third; since these things cannot be, or, if they could be, would avail nothing to our purpose. Moreover, if these two complete natures are said to be joined somehow, in such a way that one may be Divine while the other is human, and yet that which is God not be the same with that which is man, it is impossible for both to do the work necessary to be accomplished. For God will not do it, because he has no debt to pay; and man will not do it, because he cannot. Therefore, in order that the God-man may perform this, it is necessary that the same being should perfect God and perfect man, in order to make this atonement. For he cannot and ought not to do it, unless he be very God and very man. Since, then, it is necessary that the God-man preserve the completeness of each nature, it is no less necessary that these two natures be united entire in one person, just as a body and a reasonable soul exist together in every human being; for otherwise it is impossible that the same being should be very God and very man."
From Cur Deus Homo , Book II, Chapter VII.