Full Idea
The relations in an abstraction principle are always constituted by possession of a common property (which is imprecise as it relies on 'predicate'), ..so we say a common property of two terms is any third term to which both have the same relation.
Gist of Idea
Abstraction principles identify a common property, which is some third term with the right relation
Source
Bertrand Russell (The Principles of Mathematics [1903], §157)
Book Reference
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.166
A Reaction
This brings out clearly the linguistic approach of the modern account of abstraction, where the older abstractionism was torn between the ontology and the epistemology (that is, the parts of objects, or the appearances of them in the mind).