DICT.TW Dictionary Taiwan

 Prob·lem n.
 1. A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt.
 2. Math. Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
 Note: ☞ Problem differs from theorem in this, that a problem is something to be done, as to bisect a triangle, to describe a circle, etc.; a theorem is something to be proved, as that all the angles of a triangle are equal to two right angles.
 Plane problem Geom., a problem that can be solved by the use of the rule and compass.
 Solid problem Geom., a problem requiring in its geometric solution the use of a conic section or higher curve.
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 Sol·id a.
 1. Having the constituent parts so compact, or so firmly adhering, as to resist the impression or penetration of other bodies; having a fixed form; hard; firm; compact; -- opposed to fluid and liquid or to plastic, like clay, or to incompact, like sand.
 2. Not hollow; full of matter; as, a solid globe or cone, as distinguished from a hollow one; not spongy; dense; hence, sometimes, heavy.
 3. Arith. Having all the geometrical dimensions; cubic; as, a solid foot contains 1,728 solid inches.
 Note: ☞ In this sense, cubics now generally used.
 4. Firm; compact; strong; stable; unyielding; as, a solid pier; a solid pile; a solid wall.
 5. Applied to a compound word whose parts are closely united and form an unbroken word; -- opposed to hyphened.
 6. Fig.: Worthy of credit, trust, or esteem; substantial, as opposed to frivolous or fallacious; weighty; firm; strong; valid; just; genuine.
    The solid purpose of a sincere and virtuous answer.   --Milton.
    These, wanting wit, affect gravity, and go by the name of solid men.   --Dryden.
    The genius of the Italians wrought by solid toil what the myth-making imagination of the Germans had projected in a poem.   --J. A. Symonds.
 7. Sound; not weakly; as, a solid constitution of body.
 8. Bot. Of a fleshy, uniform, undivided substance, as a bulb or root; not spongy or hollow within, as a stem.
 9. Metaph. Impenetrable; resisting or excluding any other material particle or atom from any given portion of space; -- applied to the supposed ultimate particles of matter.
 10. Print. Not having the lines separated by leads; not open.
 11. United; without division; unanimous; as, the delegation is solid for a candidate. [Polit. Cant. U.S.]
 Solid angle. Geom. See under Angle.
 Solid color, an even color; one not shaded or variegated.
 Solid green. See Emerald green (a), under Green.
 Solid measure Arith., a measure for volumes, in which the units are each a cube of fixed linear magnitude, as a cubic foot, yard, or the like; thus, a foot, in solid measure, or a solid foot, contains 1,728 solid inches.
 Solid newel Arch., a newel into which the ends of winding stairs are built, in distinction from a hollow newel. See under Hollow, a.
 Solid problem Geom., a problem which can be construed geometrically, only by the intersection of a circle and a conic section or of two conic sections. --Hutton.
 Solid square Mil., a square body or troops in which the ranks and files are equal.
 Syn: -- Hard; firm; compact; strong; substantial; stable; sound; real; valid; true; just; weighty; profound; grave; important.
 Usage: Solid, Hard. These words both relate to the internal constitution of bodies; but hardnotes a more impenetrable nature or a firmer adherence of the component parts than solid. Hard is opposed to soft, and solid to fluid, liquid, open, or hollow. Wood is usually solid; but some kinds of wood are hard, and others are soft.
 Repose you there; while I [return] to this hard house,
 More harder than the stones whereof 't is raised.   --Shak.
 I hear his thundering voice resound,
 And trampling feet than shake the solid ground.   --Dryden.