I add by way of note the sequel in the text. The refinements of scholasticism have their place in the history of human thought.
"Corporeity may be taken in two senses. In one way as it is the substantial form of a body, according as that body has its place in the genus of substance. Taken thus, the corporeity of any body is nothing else than its substantial form, in respect of which the body is classified according to genus and species: by virtue of this substantial form it is due to a bodily thing to exist in three dimensions. For there are not different substantial forms in one and the same thing; one form, to place it in the highest genus, say, of 'substance'; and another to place it in the proximate genus, say, of 'corporeal' or 'animal substance'; and a third to put it in the species, say, of 'man' or 'horse': for if the first form made it a substance, the forms that followed would supervene upon something that was already in actuality and subsisting in nature; and thus the latter forms would not make it an individual thing, but would be in a subject that was already an individual thing, as is the case with accidental forms. Corporeity, therefore, considered as the substantial form in man, can be no other than the rational soul, which requires in its matter the possession of three dimensions: for it is the actualising principle of a body. In another way corporeity is taken to mean the accidental form whereby a body is said to be in the genus of quantity; and taken thus, corporeity is nothing else than the three dimensions which make the essence of a body. Though then this corporeity falls away to nothing when the human body rots, that cannot hinder the body from rising again numerically the same, since corporeity in the first sense does not fall away to nothing, but remains the same."
Of God and His Creatures: 4.81