centre_, or _one of the extremities of the enemy's line of defence_;
unless our forces be infinitely superior in number, it would be absurd
to act against the front and extremities at the same time.

If the configuration of the theatre of operations be favorable to a
movement against the extremity of the enemy's line of defence, this
direction maybe best calculated to lead to important results. (Fig. 4.)

In 1800 the army of the Rhine was directed against the extreme left of
the line of the Black Forest; the army of reserve was directed by the
St. Bernard and Milan on the extreme right and rear of Melas's line of
defence: both operations were most eminently successful. (Fig. 5.)

It may be well to remark that it is not enough merely to gain the
extremity and rear of the enemy, for in that case it may be possible for
him to throw himself on our communications and place us in the very
dilemma in which we had hoped to involve him. To avoid this danger it is
necessary to give such a direction to the line of operations that our
army shall preserve its communications and be able to reach its base.

Thus, if Napoleon, in 1800, after crossing the Alps, had marched by
Turin on Alexandria and received battle at Marengo, without having first
secured Lombardy and the left of the Po, his own line of retreat would
have been completely cut off by Melas; whereas, by the direction which
he gave to his line of operations he had, in case of reverse, every
means for reaching either the Var or the Valois. (Fig. 6.) Again, in
1806, if he had marched directly from Gera to Leipsic, he would have
been cut off from his base on the Rhine; whereas, by turning from Gera
towards Weimar, he not only cut off the Prussians from the Elbe, but at
the same time secured to himself the roads of Saalfield, Schleitz, and