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Netherlands in the latter half of the sixteenth century had relied on mere sketches to show them the way. Even Vauban, as great an expert on military geography as has ever lived, at various times produced estimates of the surface of France which differed from each other by as much as thirty percent. However, by the time von Bülow wrote the first map of a large country (France) to be based on triangulation rather than on guesswork had just been completed and submitted to the
depot de guerre
in Paris. Several other works aiming to cover other countries in a similar way were approaching completion.
    Strategy, then, was the art of conducting war not by means of
coup d’oiel
from behind a horse’s ears but in an office, on the surface of a map. Thus regarded, any army once deployed on the border would occupy a base, conceived by von Bülow not as a point but as a definite area with definite dimensions. Depending on geography and the general’s intent, a base could be either narrow or wide. Starting from it, the army was to advance upon its objective or objectives; between base and objective there stretched a line, or lines, of operations. Along these lines there flowed supplies and reinforcements in one direction and the wounded, the sick, and prisoners in the other. As of recent times, the growing role played by firearms had greatly increased the demand for ammunition and, in this way, the importance of the lines. It was in them that the key to strategy was to be found.
    For example, a general who contemplated an invasion of a neighboring country might advance in one line, two, or more. Depending on the extent of the base as well as the number and location of the objectives selected, these lines might either diverge, or converge, or run parallel to each other. The columns moving along each one might be made equally strong, or else different numbers of troops might be assigned to each. To obtain certainty in such questions (as in any others) it was necessary to resort to mathematics. That made von Bülow’s work resemble nothing so much as a textbook in Euclidean geometry. Definitions are provided and followed by propositions, which are then linked to each other by “proofs.”
    Various possibilities, such as diverging lines and parallel lines, are carefully eliminated. It having been determined that converging lines are best, the remaining question is how far away the objective ought to be. Like the power of gravity, that of the offensive diminishes the further into enemy territory it advances. If the advancing force is not to be cut off by a flanking attack, a definite relationship should be maintained between the length of the line of operations and the width of the base. Thus two lines, stretching from the flanks of the base, should meet at the objective in such a way that they should form a right angle. Proceed further than this—allow a sharp angle to be created—and you risk being cut off by a side-stroke. Thus the entire art of strategy was reduced to a single, simple, geometrical formula.
    Von Bülow was not entirely without forerunners. In particular, the British officer and writer Henry Lloyd deserves to be mentioned. However, in claiming that his system of strategy marked “an entirely new” way of looking at war he had right on his side. For centuries if not millenniums past its students had busied themselves with the best method for raising an army; disciplining it; arming and equipping it; building camps for it, provisioning it; adopting this or that marching order; and, when it came to confronting the enemy, either fighting him or tricking him by means of this stratagem or that. What von Bülow did was to shift the emphasis from what we today would have called the organizational, technical, and tactical aspects towards the larger operations of war. No wonder he was carried away by his own discovery. Thus, in the face of unfolding Napoleonic warfare with its numerous climactic battles, he insisted that the