Etymology
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stratum (n.)
"horizontal layer," 1590s, from Modern Latin special use of Latin stratum "thing spread out, coverlet, bedspread, horse-blanket; pavement," noun uses of neuter of stratus "prostrate, prone," past participle of sternere "to spread out, lay down, stretch out," from nasalized form of PIE root *stere- "to spread."
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expand (v.)

early 15c., "spread out, open out, spread flat, extend widely;" also transitive, "cause to grow larger;" from Anglo-French espaundre, Old French espandre "spread, spread out, be spilled," and directly from Latin expandere "to spread out, unfold, expand," from ex "out" (see ex-) + pandere "to spread, stretch" (from nasalized form of PIE root *pete- "to spread"). Related: Expanded; expanding.

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substrate (n.)
1810, from Modern Latin substratum, noun use of neuter singular past participle of Latin substernere "to spread underneath," from sub "under, below, beneath" (see sub-) + sternere "to spread out, lay down, stretch out," from nasalized form of PIE root *stere- "to spread."
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expend (v.)

"to spend, pay out; to consume by use, spend in using," early 15c., expenden, from Latin expendere "pay out, weigh out money," from ex "out, out of" (see ex-) + pendere "to hang, cause to hang; weigh; pay" (from PIE root *(s)pen- "to draw, stretch, spin"). For the financial sense of the Latin verb, see pound (n.1). Related: Expended; expending.

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substratum (n.)
1630s, from Modern Latin substratum (plural substrata), noun use of neuter singular past participle of Latin substernere "to spread underneath," from sub "under, below, beneath" (see sub-) + sternere "to spread out, lay down, stretch out," from nasalized form of PIE root *stere- "to spread."
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*reig- 

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." 

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reach (v.)

Middle English rēchen, from Old English ræcan, reccan "to reach out, stretch or extend outward, hold forth, extend in continuity or scope," also "to succeed in touching, succeed in striking;" also "to address, speak to," also "to offer, present, give, grant."

This is proposed to be from Proto-West Germanic *raikejanan "stretch out the hand" (source also of Old Frisian reka "to give, pay," Middle Dutch reken, reiken, Old High German reihhen, reichen "give, reach out, get," Dutch reiken,  German reichen "to reach, to pass, to hand, to give; to be sufficient"), from Proto-Germanic *raikijanau, which is probably from PIE root *reig- "to stretch, stretch out, be stretched; be stiff."

Sometimes 16c. spelled retch. As "to hand (someone something), give" from c. 1300. The meaning "arrive at, succeed in getting to" is early 14c.; that of "succeed in influencing" is from 1660s. Related: Reached; reaching. Shakespeare uses the now-obsolete past tense form raught (Old English ræhte).

Colloquial reach-me-down "ready-made" (of clothes) is recorded from 1862, from notion of being on the rack in a finished state.

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spread (v.)

c. 1200, "to stretch out, to lay out; diffuse, disseminate" (transitive), also "to advance over a wide area" (intransitive); probably from Old English sprædan "to spread, stretch forth, extend" (especially in tosprædan "to spread out," and gesprædung "spreading"), from Proto-Germanic *spreit- (source also of Danish sprede, Old Swedish spreda, Middle Dutch spreiden, Old High German and German spreiten "to spread"), extended form of PIE root *sper- (4) "to strew" (see sprout (v.)).

Reflexive sense of "to be outspread" is from c. 1300; that of "to extend, expand" is attested from mid-14c. Transitive sense of "make (something) wide" is from late 14c. As an adjective from 1510s. Related: Spreading.

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spawn (v.)
c. 1400, intransitive, from Anglo-French espaundre, Old French espandre "to spread out, pour out, scatter, strew, spawn (of fish)" (Modern French épandre), from Latin expandere "to spread out, unfold, expand," from ex "out" (see ex-) + pandere "to spread, stretch" (from nasalized form of PIE root *pete- "to spread"). The notion is of a "spreading out" of fish eggs released in water. The transitive meaning "to engender, give rise to" is attested from 1590s. Related: Spawned; spawning.
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svelte (adj.)

"slender, lithe," 1817, from French svelte "slim, slender" (17c.), from Italian svelto "slim, slender," originally "pulled out, lengthened," past participle of svellere "to pluck or root out," from Vulgar Latin *exvellere, from Latin ex- "out" (see ex-) + vellere "to pluck, stretch," from PIE *wel-no-, suffixed form of *uelh- "to strike" (source also of Hittite ualh- "to hit, strike," Greek aliskomai "to be caught").

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