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1 2.8 f.
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.