From Aristotle's Rhetoric, Book 1, Chapter 7:
"Again, if the largest member of one class surpasses the largest member of another, then the one class surpasses the other; and if one class surpasses another, then the largest member of the one surpasses the largest member of the other. Thus, if the tallest man is taller than the tallest woman, then men in general are taller than women. Conversely, if men in general are taller than women, then the tallest man is taller than the tallest woman. For the superiority of class over class is proportionate to the superiority possessed by their largest specimens."
Fascinating. We no longer use that measure for the superiority of the class. Today, we would object "You cannot overgeneralize -- you cannot say 'men are taller than women' when some women are in fact taller than some men." You can say "This particular man is taller than this woman" or "The average height of all men is taller than the average height of all women."
I wonder if this type of thinking also resulted in the sexism of the Greeks. They looked around for the "strongest, smartest, most powerful person," and they found a man (for whatever reason). Using Aristotle's reasoning, men as a class are therefore stronger, smarter, and more powerful than women. Particular cases are not seen as particularly important -- that is, that a particular women may well be stronger, smarter, and more powerful than a particular man.
The overgeneralization is then enshrined into law and thought, and women are subordinated as a class. All based on a poor syllogism.