Notations and definition in an old paper of S Lefschetz

Question

I am reading an old short paper of S. Lefschetz

Lefschetz, S., Continuous transformations of manifolds., Nat. Acad. Proc. 9, 90-93 (1923). ZBL49.0409.01.

The above paragraph of the paper is vague to me. what does he mean by $+$ and $-$ signs? In modern Algebraic Topology words, does it mean positive and negative orientation of an oriented $k$-simplex?

In the next paragraph I also don't understand his notations:

Can you elaborate these by a very simple example?

Answer 1

The source of such notations and definitions is

Veblen, Oswald, The Cambridge Colloquium 1916. Part II: Analysis Situs, Colloquium Publications. American Mathematical Society 5, Part II. New York: American Mathematical Society. VII u. 150 S. (8^0) (1922). ZBL48.0647.10.