4. Octagonal redoubt.
Construct a square (vide [No. 1]), from the centre of each side of which erect perpendiculars outwards, in length proportional to the side as 13 to 60 (nearly 1 to 5); join the extremities, or termination of the perpendiculars, to the angles of the square, which will determine the sides of the octagon.
Note 1.—The directions for the construction of the pentagonal, and hexagonal redoubts are on a small scale; but the redoubts may be increased by the equal extension of the interior sides of the triangles, until the bases are sufficiently long for the periphery of the work required.
Note 2.—By means of the pocket sextant, prismatic compass, or reconnoitring protractor, the pentagonal, hexagonal, and octagonal redoubt may be thus traced on the ground. From a central point place pickets at the requisite distance from each other, and in the direction of lines drawn from the angle of the centre of the intended work. (Vide [Practical Geometry]. To find the angles at the centre, and circumference of a polygon.) Extend these radii equally until the relative distances between them are of the length required to form the sides of the proposed equilateral redoubt.
5. Front of fortification, for a Field fort.
Place pickets in a straight line, of the length required for the front of the proposed field work; from the centre of which drop a perpendicular inwards, making it for a square, pentagon, hexagon, or octagon, respectively one-eighth, one-fifth, one-fourth, or one-third of the exterior side. Direct the lines of defence from the termination of the exterior side to the end of the perpendicular, making the faces of the bastions two-sevenths of the exterior side, and constructing the flanks perpendicular to, and joining the lines of defence. Other fronts are traced by laying down the exterior sides, at the angle of the circumference of the intended polygon (Vide [Practical Geometry]) by means of the prismatic compass, &c., and then proceeding as directed for the former front.