The fortresses, which, like that of La Roche-Pont, are situated at the extremity of a promontory and present only a narrow front to the besieger, assuredly give certain advantages to the defence, since they have scarcely to fear more than one attack and are accessible only on one side; but this position is not without its drawbacks, especially if, as in the present instance, a fan-shaped plateau spreads outside the fortress; for then the besiegers sweep the defences with converging fires, to which the besieged can oppose only a narrow front unprovided with considerable flankments. On the east side the large bastion, in the middle of which Vauban had left standing the fifteenth-century tower, which thus gave him a good revetted cavalier, sufficiently flanked the eastern brow of the outer plateau; but on the western side such a flankment failed entirely, on account of the outward bend caused by the promontory. To obviate these disadvantages Vauban inclined his capital some paces eastwards.[58] He had thought at first of suppressing the south flanks of the two extreme bastions, but in that case the exteriors of the east and west faces of these bastions would have been too slanting to sweep the crests of the plateau effectively, while the two curtains answered this object. Besides, the enemy could not then, without risk, commence his trenches on the slopes of the plateau and rapidly approach fronts insufficiently flanked. Vauban therefore set out the plan of the great outwork according to the following method (Fig. 68):--To the outside he gave a length of 180 toises, or 1,156 feet. To the western side, _a c_, 1,120 feet; to the eastern side, _b d_, 1,054 feet--that is, he placed the points _c_ and _d_ according with the edge of the plateau; the two angles _a_ and _b_ being equal to one another. On the centre of the side _a b_ of the polygon he erected the perpendicular, _e f_, having a length equal to one-sixth of _a b_. From this extreme point, _f_, were drawn the lines of defence, _a g_, _b h_, on which the lengths of the faces of the bastion, _a k_, _b i_, were set off equal to two-sevenths of the outer side, _a b_. To find the flanks of the bastion, according to the method usually adopted in these defences, points _k_ and _i_, he described arcs of a circle, _k l_, taking _i k_ as the radius. The point of intersection of this arc with the line _b h_ gave the length and the direction of the flank of the bastion; but, not having been able to trace a regular half-hexagon, and the angles _a_ and _b_ being less obtuse than those of a regular hexagon, by proceeding in this manner, the gorges of the bastion would have been too contracted. Therefore, to determine the flank of the bastion, from the points _i_ and _k_, he let fall perpendiculars to the lines of defence, _a g_, _b h_, and the point _h_ gave the re-entering angle in the curtain, _h g_, parallel to the side _a b_. This exposed the flanks a little too much, but enabled