That the angels are incorporeal is proved from the perfection of the universe. This consists in assimilation to God, Who produces creatures by Intellect and Will; and since the act of understanding is not corporeal, one due to any bodily virtue, the perfection of the universe requires the existence of intellectual creatures, called by us Angels.
In this the ancients erred, not distinguishing between sense and intellect, for they esteemed every being to be corporeal, because body alone falls under the cognizance of the senses.
Nor are the angels composed of matter and form, as Avicebron taught that the matter of corporeal and spiritual things was the same: for if the same division of matter received both spiritual and corporeal forms, these forms would be the same, which is impossible; it remains, therefore, that one division of matter receives spiritual forms, and another corporeal ones. It does not befit matter, however, to be divided except as regards extension, which being removed, there remains only indivisible substance.
It is, moreover, evident that intellectual substances are not material, because everything operates according to the mode of its substance, and the act of understanding is an operation wholly immaterial. Hence, material things when present to our intellect are there in a more simple manner than in themselves. The angelic substances are, indeed, beyond our intellect, which cannot attain to comprehending them as they are: it can, nevertheless, do so after its own mode - that by which it apprehends composite things; and thus it also apprehends God.
Angels differ from each other in species, because, not being composed of matter and form, it is impossible they should be of the same species. For things which belong to the same species and differ numerically have the same form, but differ in regard of matter; while angels, not being composed of matter and form, it follows that no two can be of the same species. They are, moreover, by their nature incorruptible, for corruption takes place where form is separated from matter; but the angels are subsistent forms, wholly immaterial; therefore, they are not subject to corruption.
- text taken from Compendium of the Summa Theologica of Saint Thomas Aquinas, by Bishop Berardus Bongiovanni