Ideas from 'On the Cosmos (lost)' by Philolaus [435 BCE], by Theme Structure

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9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
No things would be clear to us as entity or relationships unless there existed Number and its essence
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
Everything must involve numbers, or it couldn't be thought about or known
Harmony must pre-exist the cosmos, to bring the dissimilar sources together
There is no falsehood in harmony and number, only in irrational things
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
Self-created numbers make the universe stable
27. Natural Reality / E. Cosmology / 1. Cosmology
Philolaus was the first person to say the earth moves in a circle [Diog. Laertius]