SOLID

, in Physics, a body whose minute parts are connected together, so as not to give way, or slip from each other, on the smallest impression. The word is used in this sense, in contradistinction to fluid.

, in Geometry, is a magnitude extended in every possible direction, quite around. Though it is commonly said to be endued with three dimensions only, length, breadth, and depth or thickness.

Hence, as all bodies have these three dimensions, and nothing but bodies, Solid and body are often used indiscriminately.

The extremes of Solids are surfaces. That is, Solids are terminated either by one surface, as a globe, or by several, either plane or curved. And from the circumstances of these, Solids are distinguished into regular and irregular.

Regular Solids, are those that are terminated by regular and equal planes. These are the tetraedron, hexaedron, or cube, octaedron, dodecaedron, and icosaedron; nor can there possibly be more than these five regular Solids or bodies, unless perhaps the sphere or globe be considered as one of an infinite number of sides. See these articles severally, also the article Regular Body.

Irregular Solids, are all such as do not come under the definition of regular ones: such as cylinder, cone, prism, pyramid, &c.

Similar Solids are to one another in the triplicate ratio of their like sides, or as the cubes of the same. And all sorts of prisms, as also pyramids, are to one another in the compound ratio of their bases and altitudes.

Solid Angle, is that formed by three or more plane angles meeting in a point; like an angle of a die, or the point of a diamond well cut.

The sum of all the plane angles forming a Solid angle, is always less than 360°; otherwise they would constitute the plane of a circle, and not a Solid.

Atmosphere of Solids. See Atmosphere.

Solid Bastion. See Bastion.

Cubature of Solids. See Cubature and SOLIDITY. |

Measure of a Solid. See Measure.

Solid Foot. See Foot.

Solid Numbers, are those which arise from the multiplication of a plane number, by any other number whatever. Thus, 18 is a Solid number, produced from the plane number 6 and 3, or from 9 and 2.

Solid Place. See Locus.

Solid Problem, is one which cannot be constructed geometrically; but by the intersection of a circle and a conic section, or by the intersection of two conic sections. Thus, to describe an isosceles triangle on a given base, so that either angle at the base shall be triple of that at the vertex, is a Solid problem, resolved by the intersection of a parabola and circle, and it serves to inscribe a regular heptagon in a given circle.

In like manner, to describe an isosceles triangle having its angles at the base each equal to 4 times that at the vertex, is a Solid problem, effected by the intersection of an hyperbola and a parabola, and serves to inscribe a regular nonagon in a given circle.

And such a problem as this has four solutions, and no more; because two conic sections can intersect but in 4 points.

How all such problems are constructed, is shewn by Dr. Halley, in the Philos. Trans. num. 188.

Solid of Least Resistance. See Resistance.

Surfaces of Solids. See Area and SUPERFICIES.

Solid Theorem. See Theorem.