rigidity (n.)

"stiff, unyielding, inflexible, firm, not easily bent," early 15c., from Latin rigidus "hard, stiff, rough, severe," from rigēre "be stiff" (from PIE root *reig- "stretch; be stretched; be stiff"). Related: Rigidly. As a verb, "to make rigid," rigidize is attested by 1944 in U.S. military and commercial use in reference to metals; earlier was rigidify (1842), rigidification.

late 14c., rigour, "harshness, severity in dealing with persons; force; cruelty," from Old French rigor "strength, hardness" (13c., Modern French rigueur), from Latin rigorem (nominative rigor) "numbness, stiffness, hardness, firmness; roughness, rudeness," from rigēre "be stiff" (from PIE root *reig- "stretch; be stretched; be stiff").

Also, in medieval medicine, "a sudden chill" (c. 1400). From early 15c. as "exactness, strictness without indulgence" (of discipline, the law, etc.). Compare rigidity. Rigorism "rigidity in principles or practice" (originally religious) is from 1704. Rigidist is by 1716.

Proto-Indo-European root meaning "stretch; be stretched; be stiff" 

It forms all or part of: reach; rigid; rigidity; rigor.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit rjyati "he stretches himself," riag "torture" (by racking); Greek oregein "to reach, extend;" Latin rigidus "hard, stiff, rough, severe," rigēre "be stiff;" Lithuanian raižytis "to stretch oneself;" Old Irish ringid "torture," rigim "I stretch;" Middle High German ric "band, string;" Old High German reihhon, Old English ræcan, ræcean "to reach, achieve," on notion of "to stretch out."