Etymology
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Words related to scale

*skel- (1)
also *kel-, Proto-Indo-European root meaning "to cut."

It forms all or part of: coulter; cutlass; half; halve; scale (n.1) "skin plates on fish or snakes;" scale (n.2) "weighing instrument;" scalene; scallop; scalp; scalpel; school (n.2) "group of fish;" sculpture; shale; sheldrake; shelf; shell; shield; shoal (n.2) "large number;" skoal; skill.

It is the hypothetical source of/evidence for its existence is provided by: Latin culter "knife," scalpere "to cut, scrape;" Old Church Slavonic skolika "mussel, shell," Russian skala "rind, bark," Lithuanian skelti "split," Old English scell "shell," scalu "drinking cup, bowl, scale of a balance."
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scan (v.)
late 14c., "mark off verse in metric feet," from Late Latin scandere "to scan verse," originally, in classical Latin, "to climb, rise, mount" (the connecting notion is of the rising and falling rhythm of poetry), from PIE *skand- "to spring, leap, climb" (source also of Sanskrit skandati "hastens, leaps, jumps;" Greek skandalon "stumbling block;" Middle Irish sescaind "he sprang, jumped," sceinm "a bound, jump").

Missing -d in English is probably from confusion with suffix -ed (see lawn (n.1)). Sense of "look at closely, examine minutely (as one does when counting metrical feet in poetry)" first recorded 1540s. The (opposite) sense of "look over quickly, skim" is first attested 1926. Related: Scanned; scanning.
skull (n.)
"bony framework of the head," c. 1200, probably from Old Norse skalli "a bald head, skull," a general Scandinavian word (compare Swedish skulle, Norwegian skult), probably related to Old English scealu "husk" (see shell (n.)). But early prominence in southwestern texts suggests rather origin from a Dutch or Low German cognate (such as Dutch schol "turf, piece of ice," but the sense of "head bone framework" is wanting). Derivation from Old French escuelle seems unlikely on grounds of sound and sense. Old English words for skull include heafod-bolla.
scalable (adj.)
1570s, "able to be climbed;" see scale (v.1) + -able. From 1936 as "able to be graded by scale." Related: Scalably; scalability.
scalar (adj.)
"resembling a ladder," 1650s, from Latin scalaris "of or pertaining to a ladder," from scalae (plural) "ladder, steps, flight of steps" (see scale (n.2)). Mathematical sense first recorded 1846.
scale-pan (n.)
1830, from scale (n.2) + pan (n.).
downscale (v.)

"reduce in size or scale," 1945, American English, from down (adv.) + scale (v.). In business, especially, "to reduce the size of an operation." Related: Downscaled; downscaling. From 1966 as an adjective.

scaly (adj.)
also scaley, late 14c., from scale (n.1) + -y (2). Related: Scaliness.
upscale (adj.)
1966, "at the higher end of a scale, superior," a commercial word, from up (adv.) + scale (v.3).
large-scale (adj.)
1853, from large (adj.) + scale (n.3).