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In dividing any genus, we ought to divide it by that note which is fundamental, primary, and proximate. That note will act as the root of all other differences and will itself (virtually) encapsulate those differences.
An example can be found in the distinction within the genus animal between brute and man. If we were to make the distinction between man and brute to be "risibility" (ability to laugh), "ability to use language," etc., we would not be giving the most fundamental differences between men and brutes. Rather, we would be listing that which FOLLOWS FROM the fundamental, primary, and proximate difference in the genus animal.