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[7] since 6 —2 = 10 — 6, and this is the mean according to arithmetical proportion.1 But we cannot arrive by this method at the mean relative to us. Suppose that 10 lb. of food is a large ration for anybody and 2 lb. a small one: it does not follow that a trainer will prescribe 6 lb., for perhaps even this will be a large ration, or a small one, for the particular athlete who is to receive it; it is a small ration for a Milo,2 but a large one for a man just beginning to go in for athletics. And similarly with the amount of running or wrestling exercise to be taken.

1 We should rather call this an arithmetical progression.

2 A famous wrestler.

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