In the second place it is asked, whether a line and a surface may really be distinguished from each other and from a body. And it seems that they are; for they are distinct species of quantity according to the philosopher in the Categories; therefore, they are really distinguished from each other and from a body.
As regards the opposite; as is the relation of a point to a line so is the relation of a line to a surface, and a surface to a body; but a point is not really distinct from a line, as was proved in the Categories; therefore, a line is not distinct from a surface nor a surface from a body, and consequently a line and a surface are not distinguished from each other or from a body.
With respect to that question, I say that a line and a surface are not things distinct from each other and from a body. For that a line may not be distinct from a surface can be proved through the first, third, and fourth reasons, and through other theological reasons through which it is proved that a point is not an indivisible thing really distinct from a line; for if a line were such another thing, it would be in some primary and adequate subject. Similarly, there would be infinite lines, none of which would be a part of another.
Similarly, God might not be able to divide one continuum unless He could create more absolute things, and could destroy some absolute things; nor would He be able to unite, unless He could very similarly corrupt and produce new things. Similarly, then it does not seem contradictory that there could be a surface without a line, and consequently there could be a surface not terminated, and yet it would be of finite length.
But that a surface could be distinct from a body can be proved through the first theological reason; for another primary and adequate subject can not be assigned to itself, as is evidently clear. Similarly, this can be proved through the third reason, for there would be surfaces infinite actually but potentially only finite; for the extreme surfaces alone of a body are actually; but the others are not except only potentially.
In opposition to those positing thus; either the parts of the body are joined to a surface, which is in the nature of things and is existent, or to a surface which is not in the nature of things but can be. If the first be granted; then that surface is actually, and consequently there are surfaces infinite actually. If the second be conceded, then those parts of a body are not actually continuous but only potentially; for no parts are actually continuous through that which is not in the nature of things.
And then I ask, how that potentiality may be reduced to actuality; whether when those parts are continuous or when they are not continuous. Not in the first mode, for then according to those writers a continuant surface always is potentially, not actually; nor in the second mode, for then they are not continuous. But it may be said that that surface is not indeed said to be potentially; for it is not in the nature of things; but because it is not separate from a body; as parts are said to be potentially, not because they are not in the nature of things, but because they are not separate from a whole.
On the contrary, this does not suffice. First, because according to this such an inconsistency follows; namely, that infinites are in the nature of things of the same quantity. In the second place, because everything, which is in the nature of things and is not part of another, is simply actually suitable to itself, but that surface is in the nature of things and is not a part of another; therefore, it simply is actually.
In the third place thus; for, as that intermediate surface is not separate from a body, so neither is the extreme separate from a body; therefore, as the extreme is actually, so that is actually. Thus, therefore, it is obvious that, if a surface be a thing other than a body; this inconsistency follows, that infinites of the same quantity, of which none is part of another, are actually.
However, the principal conclusion can be proved through four and five reasons and through other reasons which follow. For if a surface be a thing as regards itself as a whole distinct from a body, there does not appear any contradiction that God may make it without a body, or conversely; and consequently a body can be without any such surface, and yet it will be finite and continuous; therefore, a surface is needlessly posited.
Similarly, I ask how a surface and a body make one in the sacrament of the altar; whether they make one per se or one through accident or one only by aggregation. The first can not be granted; for then a surface would be part of a body or both would be essential parts of another, which can not be conceded. And if it be said that a surface, although it may not be a quantitative part of a body, is however an essential part of a body; it is not refuted by the philosopher, although it may be refuted, that a surface may be a quidditative part of a body.
On the contrary, whenever something is part of another, either it is of the same ground as another part or it is of another ground. Therefore, if a surface be a part of a body which is per se one, either it is of the same ground as another part of a body or it is of another ground, which also can not be conceded; for, whenever some parts of diverse grounds make one per se, one of them is matter or potentiality, and the other is actuality or form; but potentiality and actuality making one per se are never distinguished in place or situation, as is manifestly obvious; therefore, in no mode are body and surface potentiality and actuality, and consequently they do not make one per se.
The second also can not be granted; namely, that a surface and a body make one by accident; for then one would be the actuality of another, and consequently a surface would be subjectively in a body, or conversely; each of which is false according to the arguments set forth in the preceding question.
Nor can the third be conceded; namely, that they make one by aggregation, since it could not then be affirmed that a surface would otherwise be a terminus of a body than that a vase is a terminus of water. Then also no contradiction appears in the statement that God might be able to make a body in the same place and situation without a surface, as he can make water in the same place and situation without a vase; and yet a body would then be an infinite continuum without any surface; if this is conceded, it is obvious that such a surface is posited entirely in vain.
Similarly, then before transubstantiation a surface either would be without a substance or would be in another substance, as if in a primary and adequate subject, and not in the same substance in which a body is in a primary and adequate subject; as can be proved through the arguments set forth in the preceding question, and consequently there would be another substance there besides matter and form in which a body is posited, which is a quantity subjectively.
From the preceding statements it is obvious, that a line and a surface are not really distinguished from each other; and because it was proved that a surface is not distinguished from a body; therefore, neither is a line, and consequently they are not really distinguished from each other or from a body.
As regards the principal argument, I say that these concepts ‘line’ and ‘surface’ are distinct, and this suffices for a distinction of species; yet notwithstanding this, those, which are signified, are not distinct; for ‘place’ and ‘surface’ are thus distinct species, and yet they are not really distinct; but it suffices that they signify the same in diverse modes, as the commentator says in Book IV. of the Metaphysics concerning ‘entity’ and ‘one,’ where he states that ‘entity’ and ‘one’ signify the same, but in diverse modes.
Whence, as such diversity of modes of signifying the same thing vitiates the predication of one of another, although there may be only two such modes of signification, namely, ‘case’ and ‘number’; so a diversity of modes of signification suffices for the distinction of species, no matter how frequently one be truly predicated of another.
There are many arguments contrary to these which I pass over for the present; for I have spoken of them elsewhere in diverse places.