Objection 1. It would seem that consanguinity is unfittingly distinguished by degrees and lines. For a line of consanguinity is described as "the ordered series of persons related by blood, and descending from a common ancestor in various degrees." Now consanguinity is nothing else but a series of such persons. Therefore a line of consanguinity is the same as consanguinity. Now a thing ought not to be distinguished by itself. Therefore consanguinity is not fittingly distinguished into lines.
Objection 2. Further, that by which a common thing is divided should not be placed in the definition of that common thing. Now descent is placed in the above definition of consanguinity. Therefore consanguinity cannot be divided into ascending, descending and collateral lines.
Objection 3. Further, a line is defined as being between two points. But two points make but one degree. Therefore one line has but one degree, and for this reason it would seem that consanguinity should not be divided into lines and degrees.
Objection 4. Further, a degree is defined as "the relation between distant persons, whereby is known the distance between them." Now since consanguinity is a kind of propinquity, distance between persons is opposed to consanguinity rather than a part thereof.
Objection 5. Further, if consanguinity is distinguished and known by its degrees, those who are in the same degree ought to be equally related. But this is false since a man's great-uncle and great-nephew are in the same degree, and yet they are not equally related according to a Decretal (cap. Porro; cap. Parenteloe, 35, qu. v). Therefore consanguinity is not rightly divided into degrees.
Objection 6. Further, in ordinary things a different degree results from the addition of one thing to another, even as every additional unity makes a different species of number. Yet the addition of one person to another does not always make a different degree of consanguinity, since father and uncle are in the same degree of consanguinity, for they are side by side. Therefore consanguinity is not rightly divided into degrees.
Objection 7. Further, if two persons be akin to one another there is always the same measure of kinship between them, since the distance from one extreme to the other is the same either way. Yet the degrees of consanguinity are not always the same on either side, since sometimes one relative is in the third and the other in the fourth degree. Therefore the measure of consanguinity cannot be sufficiently known by its degrees.
I answer that, Consanguinity as stated (1) is a certain propinquity based on the natural communication by the act of procreation whereby nature is propagated. Wherefore according to the Philosopher (Ethic. viii, 12) this communication is threefold. one corresponds to the relationship between cause and effect, and this is the consanguinity of father to son, wherefore he says that "parents love their children as being a part of themselves." Another corresponds to the relation of effect to cause, and this is the consanguinity of son to father, wherefore he says that "children love their parents as being themselves something which owes its existence to them." The third corresponds to the mutual relation between things that come from the same cause, as brothers, "who are born of the same parents," as he again says (Ethic. viii, 12). And since the movement of a point makes a line, and since a father by procreation may be said to descend to his son, hence it is that corresponding to these three relationships there are three lines of consanguinity, namely the "descending" line corresponding to the first relationship, the "ascending" line corresponding to the second, and the "collateral" line corresponding to the third. Since however the movement of propagation does not rest in one term but continues beyond, the result is that one can point to the father's father and to the son's son, and so on, and according to the various steps we take we find various degrees in one line. And seeing that the degrees of a thing are parts of that thing, there cannot be degrees of propinquity where there is no propinquity. Consequently identity and too great a distance do away with degrees of consanguinity; since no man is kin to himself any more than he is like himself: for which reason there is no degree of consanguinity where there is but one person, but only when one person is compared to another.
Nevertheless there are different ways of counting the degrees in various lines. For the degree of consanguinity in the ascending and descending line is contracted from the fact that one of the parties whose consanguinity is in question, is descended from the other. Wherefore according to the canonical as well as the legal reckoning, the person who occupies the first place, whether in the ascending or in the descending line, is distant from a certain one, say Peter, in the first degree--for instance father and son; while the one who occupies the second place in either direction is distant in the second degree, for instance grandfather, grandson and so on. But the consanguinity that exists between persons who are in collateral lines is contracted not through one being descended from the other, but through both being descended from one: wherefore the degrees of consanguinity in this line must be reckoned in relation to the one principle whence it arises. Here, however, the canonical and legal reckonings differ: for the legal reckoning takes into account the descent from the common stock on both sides, whereas the canonical reckoning takes into account only one, that namely on which the greater number of degrees are found. Hence according to the legal reckoning brother and sister, or two brothers, are related in the second degree, because each is separated from the common stock by one degree; and in like manner the children of two brothers are distant from one another in the fourth degree. But according to the canonical reckoning, two brothers are related in the first degree, since neither is distant more than one degree from the common stock: but the children of one brother are distant in the second degree from the other brother, because they are at that distance from the common stock. Hence, according to the canonical reckoning, by whatever degree a person is distant from some higher degree, by so much and never by less is he distant from each person descending from that degree, because "the cause of a thing being so is yet more so." Wherefore although the other descendants from the common stock be related to some person on account of his being descended from the common stock, these descendants of the other branch cannot be more nearly related to him than he is to the common stock. Sometimes, however, a person is more distantly related to a descendant from the common stock, than he himself is to the common stock, because this other person may be more distantly related to the common stock than he is: and consanguinity must be reckoned according to the more distant degree.
Reply to Objection 1. This objection is based on a false premise: for consanguinity is not the series but a mutual relationship existing between certain persons, the series of whom forms a line of consanguinity.
Reply to Objection 2. Descent taken in a general sense attaches to every line of consanguinity, because carnal procreation whence the tie of consanguinity arises is a kind of descent: but it is a particular kind of descent, namely from the person whose consanguinity is in question, that makes the descending line.
Reply to Objection 3. A line may be taken in two ways. Sometimes it is taken properly for the dimension itself that is the first species of continuous quantity: and thus a straight line contains actually but two points which terminate it, but infinite points potentially, any one of which being actually designated, the line is divided, and becomes two lines. But sometimes a line designates things which are arranged in a line, and thus we have line and figure in numbers, in so far as unity added to unity involves number. Thus every unity added makes a degree in a particular line: and it is the same with the line of consanguinity: wherefore one line contains several degrees.
Reply to Objection 4. Even as there cannot be likeness without a difference, so there is no propinquity without distance. Hence not every distance is opposed to consanguinity, but such as excludes the propinquity of blood-relationship.
Reply to Objection 5. Even as whiteness is said to be greater in two ways, in one way through intensity of the quality itself, in another way through the quantity of the surface, so consanguinity is said to be greater or lesser in two ways. First, intensively by reason of the very nature of consanguinity: secondly, extensively as it were, and thus the degree of consanguinity is measured by the persons between whom there is the propagation of a common blood, and in this way the degrees of consanguinity are distinguished. Wherefore it happens that of two persons related to one person in the same degree of consanguinity, one is more akin to him than the other, if we consider the quantity of consanguinity in the first way: thus a man's father and brother are related to him in the first degree of consanguinity, because in neither case does any person come in between; and yet from the point of view of intensity a man's father is more closely related to him than his brother, since his brother is related to him only because he is of the same father. Hence the nearer a person is to the common ancestor from whom the consanguinity descends, the greater is his consanguinity although he be not in a nearer degree. In this way a man's great-uncle is more closely related to him than his great-nephew, although they are in the same degree.
Reply to Objection 6. Although a man's father and uncle are in the same degree in respect of the root of consanguinity, since both are separated by one degree from the grandfather, nevertheless in respect of the person whose consanguinity is in question, they are not in the same degree, since the father is in the first degree, whereas the uncle cannot be nearer than the second degree, wherein the grandfather stands.
Reply to Objection 7. Two persons are always related in the same degree to one another, although they are not always distant in the same number of degrees from the common ancestor, as explained above.
Source: Summa Theologica (New Advent)