Limit

Use in the book

The brief notice on Philolaus names limit and the unlimited as principles without preserving a further exposition. Moderatus describes the monad as the point at which subtraction of whole units must stop. The arithmetic contrast between odd and even associates being bounded with a geometrical construction, but its wording is uncertain. These examples connect determination with number in different ways.

Places to read

1. I.10.12.8Limit is paired with the unlimited.
2. Arith.8The monad bounds the backward progression of quantity.
3. Arith.5bBeing bounded enters an obscure geometrical comparison.

Translation in this edition

“Limit” names the principle where appropriate; “boundary” can clarify a terminal condition. A brief heading or notice is not expanded into a lost proof.