Undergrad Uncovering the 10 Classes of Ratios in Greek Mathematics

[Seneka]

In the book 'ZERO THE BIOGRAPHY OF A DANGEROUS IDEA' Charles Seife says, "Because ratios were the key to understanding nature, the Pythagoreans and later Greek Mathematicians spent much of their energy investigating their properties. Eventually, they categorized proportions into 10 different classes with names like harmonic mean."
What are the 10 different classes?

 

[berkeman]

In the book 'ZERO THE BIOGRAPHY OF A DANGEROUS IDEA' Charles Seife says, "Because ratios were the key to understanding nature, the Pythagoreans and later Greek Mathematicians spent much of their energy investigating their properties. Eventually, they categorized proportions into 10 different classes with names like harmonic mean."
What are the 10 different classes?

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