Since Person cannot exist apart from a nature and since natures are either substances or accidents and we see that a person cannot come into being among accidents (for who can say there is any person of white or black or size?), it therefore remains that Person is properly applied to substances. But of substances, some are corporeal and others incorporeal. And of corporeals, some are living and others the reverse; of living substances, some are sensitive and others insensitive; of sensitive substances, some are rational and others irrational. Similarly of incorporeal substances, some are rational, others the reverse (for instance the animating spirits of beasts); but of rational substances there is one which is immutable and impassible by nature, namely God, another which in virtue of its creation is mutable and passible except in that case where the Grace of the impassible substance has transformed it to the unshaken impassibility which belongs to angels and to the soul.
Now from all the definitions we have given it is clear that Person cannot be affirmed of bodies which have no life (for no one ever said that a stone had a person), nor yet of living things which lack sense (for neither is there any person of a tree), nor finally of that which is bereft of mind and reason (for there is no person of a horse or ox or any other of the animals which dumb and unreasoning live a life of sense alone), but we say there is a person of a man, of God, of an angel. Again, some substances are universal, others are particular. Universal terms are those which are predicated of individuals, as man, animal, stone, stock and other things of this kind which are either genera or species; for the term man is applied to individual men just as animal is to individual animals, and stone and stock to individual stones and stocks. But particulars are terms which are never predicated of other things, as Cicero, Plato, this stone from which this statue of Achilles was hewn, this piece of wood out of which this table was made. But in all these things person cannot in any case be applied to universals, but only to particulars and individuals; for there is no person of a man if animal or general; only the single persons of Cicero, Plato, or other single individuals are termed persons.
Wherefore if Person belongs to substances alone, and these rational, and if every nature is a substance, existing not in universals but in individuals, we have found the definition of Person, viz.: "The individual substance of a rational nature."
Boethius, Contra Eutychen et Nestorium, II & III (from here)