makes it a good horse, and also good at galloping, at carrying its rider, and at facing the enemy. [3] If therefore this is true of all things, excellence or virtue in a man will be the disposition which renders him a good man and also which will cause him to perform his function well. [4] We have already indicated1 what this means; but it will throw more light on the subject if we consider what constitutes the specific nature of virtue.

Now of everything that is continuous2 and divisible, it is possible to take the larger part, or the smaller part, or an equal part, and these parts may be larger, smaller, and equal either with respect to the thing itself or relatively to us; the equal part being a mean between excess and deficiency.3 [5] By the mean of the thing I denote a point equally distant from either extreme, which is one and the same for everybody; by the mean relative to us, that amount which is neither too much nor too little, and this is not one and the same for everybody. [6] For example, let 10 be many and 2 few; then one takes the mean with respect to the thing if one takes 6; [7] since 6 —2 = 10 — 6, and this is the mean according to arithmetical proportion.4 But we cannot arrive by this method at the mean relative to us.

1 2.8 f.

2 i.e., without distinct parts, and so （if divisible at all）, divisible at any point, as opposed to what is διῃρημένον, ‘discrete,’ or made up of distinct parts and only divisible between them.

3 Greek comparatives, ‘larger’, ‘smaller’, etc., may also mean ‘too large’, ‘too small’, etc.; and there is the same ambiguity in the words translated ‘excess’ and ‘deficiency’. Again μέσον, ‘middle’ or ‘mean’, is used as a synonym for μέτριον ‘moderate’ or of the right amount, and ἴσον ‘equal’ can mean ‘equitable’. Hence ‘to take an equal part with respect to the thing itself’ means to take a part equal to the part left, viz. a half; ‘to take an equal part relatively to us,’ means to take what is a fair or suitable amount. The former is a mean as being exactly in the middle between all and none—if the thing in question is represented by a line, this is bisected at a point equidistant from its two ends; the latter is a mean in the sense of being the right amount for the recipient, and also of lying somewhere between any two other amounts that happen to be too much and too little for him.

4 We should rather call this an arithmetical progression.