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thus, without losing a man, his triumph will be complete.

[Owing to the double meanings in the Chinese text, the latter part of the sentence is susceptible of quite a different meaning: "And thus, the weapon not being blunted by use, its keenness remains perfect."]

This is the method of attacking by stratagem.

8. It is the rule in war, if our forces are ten to the enemy's one, to surround him; if five to one, to attack him;

[Straightway, without waiting for any further advantage.]

if twice as numerous, to divide our army into two.

[Tu Mu takes exception to the saying; and at first sight, indeed, it appears to violate a fundamental principle of war. Ts'ao Kung, however, gives a clue to Sun Tzu's meaning: "Being two to the enemy's one, we may use one part of our army in the regular way, and the other for some special diversion." Chang Yu thus further elucidates the point: "If our force is twice as numerous as that of the enemy, it should be split up into two divisions, one to meet the enemy in front, and one to fall upon his rear; if he replies to the frontal attack, he may be crushed from behind; if to the rearward attack, he may be crushed in front." This is what is meant by saying that 'one part may be used in the regular way, and the other for some special diversion.' Tu Mu does not understand that dividing one's army is simply an irregular, just as concentrating it is the regular, strategical method, and he is too hasty in calling this a mistake."]

9. If equally matched, we can offer battle;

[Li Ch`uan, followed by Ho Shih, gives the following paraphrase: "If attackers and attacked are equally matched in strength, only the able general will fight."]

if slightly inferior in numbers, we can avoid the enemy;

[The meaning, "we can WATCH the enemy," is certainly a great improvement on the above; but unfortunately there appears to be no very good authority for the variant. Chang Yu reminds us that the saying only applies if the other factors are e

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