There’s a critical transition point in sight of Peirce’s 1870 Logic of Relatives and it’s a point that turns on the teridentity relation.

In taking up the next example of relational composition, let’s substitute the relation for Peirce’s relation simply for the sake of avoiding conflicts in the symbols we use.  In this way, Figure 17 is transformed into Figure 22.

(22)

The hypergraph picture of the abstract composition is given in Figure 23.

(23)

If we analyze this in accord with the spreadsheet model of relational composition, the core of it is a particular way of composing a triadic “giving” relation with a dyadic “taking” relation in such a way as to determine a certain dyadic relation   Table 24 schematizes the associated constraints on tuples.

So we see that the notorious teridentity relation, which I have left equivocally denoted by the same symbol as the identity relation is already implicit in Peirce’s discussion at this point.