Our progress through the 1870 Logic of Relatives brings us in sight of a critical transition point, one which turns on the teridentity relation.
The markup for Peirce’s “giver of a horse to an owner of it” is shown again in Figure 22.
The hypergraph picture of the abstract composition is given in Figure 23.
If we analyze this in accord with the spreadsheet model of relational composition then the core of it is a particular way of composing a triadic giving relation with a dyadic owning relation in such a way as to determine a specialized dyadic relation Table 24 schematizes the associated constraints on tuples.
So we see the notorious teridentity relation, which I left equivocally denoted by the same symbol as the identity relation is already implicit in Peirce’s discussion at this point.