Things Which Are Equal To The

This is Common Notion 1 from Euclid's Elements (c. 300 BC), the first of five self-evident truths that the Elements treats as foundations of all geometric reasoning. The principle of transitivity of equality — if A = C and B = C, then A = B — is axiomatic in modern logic and mathematics. It is the logical foundation underlying the vast majority of proofs in the Elements and remained unquestioned as a foundational truth for over two thousand years.