# Does Euclid's Elements acknowledge a concept of 0, either directly or indirectly?

From what I understand Euclid avoided infinity, and so I'm wondering how Euclid might have dealt with the concept of 0 in the Elements.

• There's a difference between what is implicitly in the Elements and what is explicitly there. Implicitly, it contains the whole first-order theory of the reals.
– user466
Dec 25 '19 at 1:31
• There is very strong evidence that the Elements does not contain the first-order theory of the reals, or even first order logic (on any reasonable interpretation of "implicitly"). There are modern formalizations of Euclid that use much weaker means, like Euclidean fields, and his reasoning is much more closely reconstructed in (non-equivalent) diagrammatic alternatives to first order logic. He did not deal with $0$ or negatives because he had no need for them either. Dec 25 '19 at 6:35

He did not. There is no reference to $$0$$ in the Elements. As a matter of fact, for Euclid even $$1$$ was not a number. For him, the numbers are $$2,3,4,\ldots$$