Objection 1. It seems that in this sacrament the dimensive quantity of the bread or wine is not the subject of the other accidents. For accident is not the subject of accident; because no form can be a subject, since to be a subject is a property of matter. But dimensive quantity is an accident. Therefore dimensive quantity cannot be the subject of the other accidents.
Objection 2. Further, just as quantity is individuated by substance, so also are the other accidents. If, then, the dimensive quantity of the bread or wine remains individuated according to the being it had before, in which it is preserved, for like reason the other accidents remain individuated according to the existence which they had before in the substance. Therefore they are not in dimensive quantity as in a subject, since every accident is individuated by its own subject.
Objection 3. Further, among the other accidents that remain, of the bread and wine, the senses perceive also rarity and density, which cannot be in dimensive quantity existing outside matter; because a thing is rare which has little matter under great dimensions. while a thing is dense which has much matter under small dimensions, as is said in Phys. iv. It does not seem, then, that dimensive quantity can be the subject of the accidents which remain in this sacrament.
Objection 4. Further, quantity abstract from matter seems to be mathematical quantity, which is not the subject of sensible qualities. Since, then, the remaining accidents in this sacrament are sensible, it seems that in this sacrament they cannot be subjected in the dimensive quantity of the bread and wine that remains after consecration.
On the contrary, Qualities are divisible only accidentally, that is, by reason of the subject. But the qualities remaining in this sacrament are divided by the division of dimensive quantity, as is evident through our senses. Therefore, dimensive quantity is the subject of the accidents which remain in this sacrament.
I answer that, It is necessary to say that the other accidents which remain in this sacrament are subjected in the dimensive quantity of the bread and wine that remains: first of all, because something having quantity and color and affected by other accidents is perceived by the senses; nor is sense deceived in such. Secondly, because the first disposition of matter is dimensive quantity, hence Plato also assigned "great" and "small" as the first differences of matter (Aristotle, Metaph. iv). And because the first subject is matter, the consequence is that all other accidents are related to their subject through the medium of dimensive quantity; just as the first subject of color is said to be the surface, on which account some have maintained that dimensions are the substances of bodies, as is said in Metaph. iii. And since, when the subject is withdrawn, the accidents remain according to the being which they had before, it follows that all accidents remain founded upon dimensive quantity.
Thirdly, because, since the subject is the principle of individuation of the accidents, it is necessary for what is admitted as the subject of some accidents to be somehow the principle of individuation: for it is of the very notion of an individual that it cannot be in several; and this happens in two ways. First, because it is not natural to it to be in any one; and in this way immaterial separated forms, subsisting of themselves, are also individuals of themselves. Secondly, because a form, be it substantial or accidental, is naturally in someone indeed, not in several, as this whiteness, which is in this body. As to the first, matter is the principle of individuation of all inherent forms, because, since these forms, considered in themselves, are naturally in something as in a subject, from the very fact that one of them is received in matter, which is not in another, it follows that neither can the form itself thus existing be in another. As to the second, it must be maintained that the principle of individuation is dimensive quantity. For that something is naturally in another one solely, is due to the fact that that other is undivided in itself, and distinct from all others. But it is on account of quantity that substance can be divided, as is said in Phys. i. And therefore dimensive quantity itself is a particular principle of individuation in forms of this kind, namely, inasmuch as forms numerically distinct are in different parts of the matter. Hence also dimensive quantity has of itself a kind of individuation, so that we can imagine several lines of the same species, differing in position, which is included in the notion of this quantity; for it belongs to dimension for it to be "quantity having position" (Aristotle, Categor. iv), and therefore dimensive quantity can be the subject of the other accidents, rather than the other way about.
Reply to Objection 1. One accident cannot of itself be the subject of another, because it does not exist of itself. But inasmuch as an accident is received in another thing, one is said to be the subject of the other, inasmuch as one is received in a subject through another, as the surface is said to be the subject of color. Hence when God makes an accident to exist of itself, it can also be of itself the subject of another.
Reply to Objection 2. The other accidents, even as they were in the substance of the bread, were individuated by means of dimensive quantity, as stated above. And therefore dimensive quantity is the subject of the other accidents remaining in this sacrament, rather than conversely.
Reply to Objection 3. Rarity and density are particular qualities accompanying bodies, by reason of their having much or little matter under dimensions; just as all other accidents likewise follow from the principles of substance. And consequently, as the accidents are preserved by Divine power when the substance is withdrawn, so, when matter is withdrawn, the qualities which go with matter, such as rarity and density, are preserved by Divine power.
Reply to Objection 4. Mathematical quantity abstracts not from intelligible matter, but from sensible matter, as is said in Metaph. vii. But matter is termed sensible because it underlies sensible qualities. And therefore it is manifest that the dimensive quantity, which remains in this sacrament without a subject, is not mathematical quantity.
Source: Summa Theologica (New Advent)