VAUBAN’S FIRST SYSTEM.[38]
To describe three Fronts of fortification, on a hexagon.—Vide [Plate.]
With a radius of 360 yards, the length of the exterior side of the fortification (taken from a scale of equal parts), describe a semicircle, which divide into three equal parts, and draw lines to the points of division; thus forming three exterior sides. Bisect each of these by perpendiculars drawn to the centre of the polygon, on which set off ⅙th of the exterior side, (if a hexagon,)[39] through which points draw the Lines of defence; on these set off 2/7ths of the exterior side, from the angles of the circumference, for the length of the faces of the bastions; with radius of the distance between the two faces describe arcs joining the lines of defence, and draw the cord of these arcs for the flanks of the bastions; a line joining the interior extremities of the flanks will give the length of the curtains.
Or, to describe one Front of fortification.
For the exterior side, draw a line 360 yards in length, at the ends of which, lines are to be directed to the centre of the polygon, at the angle required; (vide [Practical Geometry]—To find the angles at the centre, and circumference of a regular polygon,) then bisect the exterior side, and draw the perpendicular, &c., &c., as described for the construction on a hexagon.
Vauban’s 1st System.
J. W. Lowry, sc.
Main ditch.
From the salient angles of the bastions, with 38 yards as a radius, describe arcs, to which draw tangents, directed to the angles of the shoulders of the bastions.