What are Euclid’s five common notions?

In his foundational work, the Elements, Euclid established a rigorous logical framework for geometry by beginning with definitions, five postulates, and five common notions. While postulates were specific to geometric principles, common notions were considered intuitive, self-evident truths applicable to all sciences concerned with quantity.12

Euclid’s five common notions are as follows:

• Things equal to the same thing are equal.
• If equals are added to equals, the wholes are equal.
• If equals are subtracted from equals, the remainders are equal.
• Things that coincide with one another are equal.
• The whole is greater than a part.1

These principles, alongside his axioms, provided the essential logical foundation for the proofs and theorems developed throughout the Elements.31