Objection 1. It would seem that love is not properly divided into love of friendship and love of concupiscence. For "love is a passion, while friendship is a habit," according to the Philosopher (Ethic. viii, 5). But habit cannot be the member of a division of passions. Therefore love is not properly divided into love of concupiscence and love of friendship.
Objection 2. Further, a thing cannot be divided by another member of the same division; for man is not a member of the same division as "animal." But concupiscence is a member of the same division as love, as a passion distinct from love. Therefore concupiscence is not a division of love.
Objection 3. Further, according to the Philosopher (Ethic. viii, 3) friendship is threefold, that which is founded on "usefulness," that which is founded on "pleasure," and that which is founded on "goodness." But useful and pleasant friendship are not without concupiscence. Therefore concupiscence should not be contrasted with friendship.
On the contrary, We are said to love certain things, because we desire them: thus "a man is said to love wine, on account of its sweetness which he desires"; as stated in Topic. ii, 3. But we have no friendship for wine and suchlike things, as stated in Ethic. viii, 2. Therefore love of concupiscence is distinct from love of friendship.
I answer that, As the Philosopher says (Rhet. ii, 4), "to love is to wish good to someone." Hence the movement of love has a twofold tendency: towards the good which a man wishes to someone (to himself or to another) and towards that to which he wishes some good. Accordingly, man has love of concupiscence towards the good that he wishes to another, and love of friendship towards him to whom he wishes good.
Now the members of this division are related as primary and secondary: since that which is loved with the love of friendship is loved simply and for itself; whereas that which is loved with the love of concupiscence, is loved, not simply and for itself, but for something else. For just as that which has existence, is a being simply, while that which exists in another is a relative being; so, because good is convertible with being, the good, which itself has goodness, is good simply; but that which is another's good, is a relative good. Consequently the love with which a thing is loved, that it may have some good, is love simply; while the love, with which a thing is loved, that it may be another's good, is relative love.
Reply to Objection 1. Love is not divided into friendship and concupiscence, but into love of friendship, and love of concupiscence. For a friend is, properly speaking, one to whom we wish good: while we are said to desire, what we wish for ourselves.
Hence the Reply to the Second Objection.
Reply to Objection 3. When friendship is based on usefulness or pleasure, a man does indeed wish his friend some good: and in this respect the character of friendship is preserved. But since he refers this good further to his own pleasure or use, the result is that friendship of the useful or pleasant, in so far as it is connected with love of concupiscence, loses the character to true friendship.
Source: Summa Theologica (New Advent)