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From: Webster's Revised Unabridged Dictionary (1913)

 Eu·clid·i·an n. Related to Euclid, or to the geometry of Euclid.
 Euclidian space Geom., the kind of space to which the axioms and definitions of Euclid, relative to straight lines and parallel lines, apply; -- called also flat space, and homaloidal space.
 

From: Webster's Revised Unabridged Dictionary (1913)

 Flat a. [Compar. Flatter superl. Flattest ]
 1. Having an even and horizontal surface, or nearly so, without prominences or depressions; level without inclination; plane.
 Though sun and moon
 Were in the flat sea sunk.   --Milton.
 2. Lying at full length, or spread out, upon the ground; level with the ground or earth; prostrate; as, to lie flat on the ground; hence, fallen; laid low; ruined; destroyed.
    What ruins kingdoms, and lays cities flat!   --Milton.
    I feel . . . my hopes all flat.   --Milton.
 3. Fine Arts Wanting relief; destitute of variety; without points of prominence and striking interest.
    A large part of the work is, to me, very flat.   --Coleridge.
 4. Tasteless; stale; vapid; insipid; dead; as, fruit or drink flat to the taste.
 5. Unanimated; dull; uninteresting; without point or spirit; monotonous; as, a flat speech or composition.
 How weary, stale, flat, and unprofitable
 Seem to me all the uses of this world.   --Shak.
 6. Lacking liveliness of commercial exchange and dealings; depressed; dull; as, the market is flat.
 7. Clear; unmistakable; peremptory; absolute; positive; downright.
 Syn: -- flat-out.
    Flat burglary as ever was committed.   --Shak.
    A great tobacco taker too, -- that's flat.   --Marston.
 8. Mus. (a) Below the true pitch; hence, as applied to intervals, minor, or lower by a half step; as, a flat seventh; A flat. (b) Not sharp or shrill; not acute; as, a flat sound.
 9. Phonetics Sonant; vocal; -- applied to any one of the sonant or vocal consonants, as distinguished from a nonsonant (or sharp) consonant.
 10. Golf Having a head at a very obtuse angle to the shaft; -- said of a club.
 11.  Gram. Not having an inflectional ending or sign, as a noun used as an adjective, or an adjective as an adverb, without the addition of a formative suffix, or an infinitive without the sign to. Many flat adverbs, as in run fast, buy cheap, are from AS. adverbs in , the loss of this ending having made them like the adjectives. Some having forms in ly, such as exceeding, wonderful, true, are now archaic.
 12.  Hort. Flattening at the ends; -- said of certain fruits.
 Flat arch. Arch. See under Arch, n., 2. (b).
 Flat cap, cap paper, not folded. See under Paper.
 Flat chasing, in fine art metal working, a mode of ornamenting silverware, etc., producing figures by dots and lines made with a punching tool. --Knight.
 Flat chisel, a sculptor's chisel for smoothing.
 Flat file, a file wider than its thickness, and of rectangular section. See File.
 Flat nail, a small, sharp-pointed, wrought nail, with a flat, thin head, larger than a tack. --Knight.
 Flat paper, paper which has not been folded.
 Flat rail, a railroad rail consisting of a simple flat bar spiked to a longitudinal sleeper.
 Flat rods Mining, horizontal or inclined connecting rods, for transmitting motion to pump rods at a distance. --Raymond.
 Flat rope, a rope made by plaiting instead of twisting; gasket; sennit.
 Note: Some flat hoisting ropes, as for mining shafts, are made by sewing together a number of ropes, making a wide, flat band. --Knight.
 Flat space. Geom. See Euclidian space.
 Flat stitch, the process of wood engraving. [Obs.]
 Flat tint Painting, a coat of water color of one uniform shade.
 To fall flat (Fig.), to produce no effect; to fail in the intended effect; as, his speech fell flat.
 Of all who fell by saber or by shot,
 Not one fell half so flat as Walter Scott.   --Lord Erskine.