roundness n.

c. 1300 (early 13c. as a surname), "spherical in shape; circular in outline," of persons or animals, "well-fed;" from Anglo-French rounde, Old French roont (12c., Modern French rond), probably originally *redond, from Vulgar Latin *retundus (source also of Provençal redon, Spanish redondo, Old Italian ritondo), from Latin rotundus "like a wheel, circular, round," related to rota "wheel" (see rotary). The French word is the source of Middle Dutch ront (Dutch rond), Middle High German runt (German rund) and similar words in the Germanic languages. 

As an adverb from c. 1300. As a preposition from c. 1600, "so as to make a complete circuit" (as in round the world); 1715 as "throughout, all through" (as in round the clock); by 1743 as "so as to make a turn or partial circuit about" (as in round the corner). In many cases it is a shortened form of around (adv.).

Of numbers from mid-14c., "entire, full, complete, brought to completion," with the notion of symmetry extended to that of completeness. Round number for one only approximately correct, usually expressed in 10s, 100s, etc., is by 1640s. Compare round (v.). Round trip "an outward and return journey" is by 1844, originally of railways. A round-dance (1520s) is one in which the dancers move in a circle or ring. Round heels attested from 1926, in reference to incompetent boxers, 1927 in reference to loose women, implying in either case a tendency to end up flat on one's back.

word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).