Things Which Coincide With One Another

This is Common Notion 4 from Euclid's Elements (c. 300 BC), asserting that figures which can be superimposed on one another — made to coincide exactly — are equal. It serves as the implicit justification for congruence arguments throughout the Elements, particularly in Book I's proofs about triangles. The notion is so fundamental that modern axiomatic geometry systems, such as Hilbert's Foundations of Geometry (1899), had to restate it more rigorously.