| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence |
| 1518 | Everything must involve numbers, or it couldn't be thought about or known |
| 473 | There is no falsehood in harmony and number, only in irrational things |
| 1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together |
| 469 | Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited |
| 476 | Self-created numbers make the universe stable |
| 1787 | Philolaus was the first person to say the earth moves in a circle |