DIVISIONS of an army, are the number of brigades and squadrons it contains.
The advance, the main, and the rear guards are composed out of the several brigades, and march in front, in the centre, and in the rear of an army. Each army has its right wing, its centre, and its left wing. When armies march they advance in column, that is, they are divided into several squadrons and battalions of a given depth, successively formed upon one another. If an army be drawn out or displayed in order of battle it is usually divided into the first line, which constitutes the front, the second line, which makes the main body, and the third line or reserve.
DODECAGON, in geometry, is a regular polygon, consisting of 12 equal sides and angles, capable of being regularly fortified with the same number of bastions.
DODECAHEDRON, is one of the platonic bodies, or five regular solids, and is contained under 12 equal and regular pentagons.
The solidity of a dodecahedron, is found by multiplying the area of one of the pentagonal faces of it by 12; and this latter product by ¹⁄₃d of the distance of the face from the centre of the dodecahedron, which is the same as the centre of the circumscribing sphere.
The side of a dodecahedron inscribed in a sphere, is the greater part of the side of a cube inscribed in that sphere, cut into extreme and mean proportion.
If the diameter of the sphere be 1,0000, the side of a dodecahedron inscribed in it will be .35682 nearly.
All dodecahedrons are similar, and are to one another as the cubes of the sides; and their surfaces are also similar, and therefore they are as the squares of their sides; whence as .509282 is to 10.51462, so is the square of the side of any dodecahedron to the superficies thereof; and as .3637 is to 2.78516, so is the cube of the side of any dodecahedron to the solidity of it.
DOG-Nails. See [Nails].
DOLPHINS. See [Cannon].