# (Where) does Plato define perfect number?

I've read several texts suggesting that Plato defines "perfect number" in his Republic, book VIII 546 b. However, there's no definition as we can see from - for example - this translation: "... Now that which is of divine birth has a period which is contained in a perfect number$$^1$$ but the period of human birth..."

"1: i.e. a cyclical number, such as 6, which is equal to the sum of its divisors 1, 2, 3, so that when the circle or time represented by 6 is completed, the lesser times or rotations represented by 1, 2, 3 are also completed."

So it's just the footnotes that explain what the perfect number is. Where does Plato himself define it?

• Did you read the Wikipedia article? "The introductory words mention (a period comprehended by) 'a perfect number' which is taken to be a reference to Plato's perfect year mentioned in his Timaeus (39d)". Dec 31, 2021 at 7:48
• I’m voting to close this question because it was answered in the comments. Dec 31, 2021 at 12:39

## 1 Answer

Plato does not define perfect numbers anywhere. The earliest extant definition is in Euclid VII, def. 22. Although Plato uses the term "perfect number" I do not think it certain that he understood this phrase in the same way as Euclid.

• Or, using perfect numbers for some numerological thing that has little to do with mathematics... Dec 31, 2021 at 1:07