# BODY

, in Geometry, is a figure conceived to be
extended in all directions, or what is usually said to consist
of length, breadth, and thickness; being otherwise
called a *Solid.* A body is conceived to be formed or
generated by the motion of a surface; like as a surface
by the motion of a line, and a line by the motion of
a point.—Similar bodies, or solids, are in proportion to
each other, as the cubes of their like sides, or linear
dimensions.

, in Physics, or Natural Philosophy, a solid, extended, palpable substance; of itself merely passive, being indifferent either to motion or rest, and capable of any sort of motion or figure.

Body is composed, according to the Peripatetics, of matter, form, and privation; according to the Epicureans and Corpuscularians, of an assemblage of hooked, heavy atoms; according to the Cartesians, of a certain extension; and according to the Newtonians, of a system or association of solid, massy, hard, impenetrable, moveable particles, ranged or disposed in this or that manner; from which arise bodies of this or that form, and distinguished by this or that name. These elementary or component particles of bodies, they assert, must be perfectly hard, so as never to wear or break in pieces; which, Newton observes, is necessary, in order to the world's persisting in the same state, and bodies continuing of the same nature and texture in several ages.

Body *of a piece of Ordnance,* the part contained between
the centre of the trunnions and the caseabel.
This should always be more fortified or stronger than
the rest. See Cannon.

Body *of the Place,* in Fortification, denotes either
the buildings inclosed, or more generally the inclosure
itself. Thus, to construct the body of the place, is to
fortify or inclose the place with bastions and curtains.

Body *of a Pump,* the thickest part of the barrel or
pipe of a pump, within which the piston moves.

, *Regular* or *Platonic,* are those which have
all their sides, angles, and planes, similar and equal.
Of these there are only 5; viz,
the *tetraedron,* contained by 4 equilateral triangles;
the *hexaedron* or *cube,* by 6 squares;
the *octaedron,* by 8 triangles;
the *dodecaedron,* by 12 pentagons; and
the *icosaedron,* by 20 triangles.

*To form the five Regular Bodies.*

Let the annexed sigures be exactly drawn on pasteboard, or stiff paper, and cut out from it by the extreme or bounding lines: then cut the others, or internal lines, only half through, so that the parts may be turned up by them, and then glued or otherwise fastened together with paste, sealing-wax, &c; so shall they form the respective body marked with the corresponding | number; viz, N° 1 the tetraedron, N° 2 the hexaedron or cube, N° 3 the octaedron, N° 4 the dodecaedron, and N° 5 the icosaedron.

*To find the Superficies or Solidity of the Regular Bodies.*

1. Multiply the proper tabular area (taken from the following table) by the square of the linear edge of the solid, for the superficies.

2. Multiply the tabular solidity by the cube of the linear edge, for the solid content.

Table of the Surfaces and Solidities of the five Regular Bodies, the linear edge being 1. | |||

No. of Faces | Names | Surfaces | Solidities |

4 | Tetraedron | 1.73205 | 0.11785 |

6 | Hexaedron | 6.00000 | 1.00000 |

8 | Octaedron | 3.46410 | 0.47140 |

12 | Dodecaedron | 20.64573 | 7.66312 |

20 | Icosaedron | 8.66025 | 2.18169 |

For more particular properties, see each respective
word. See also my large *Mensuration,* pa. 248, edit. 2.

These bodies were called *platonic,* because they were
said to have been invented, or first treated of, by *Plato,*
who conceived certain mysteries annexed to them.