Etymology
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Lancaster 
1086, Loncastre, literally "Roman Fort on the River Lune," a Celtic river name probably meaning "healthy, pure." In English history, the Lancastrians or House of Lancaster in the War of the Roses were the branch of the Plantagenets descended from John of Gaunt, Duke of Lancaster. Lancastrian (1650s) is the usual adjective with places of that name; Lancasterian (1807) was used of the teaching methods popularized early 19c. by educator Joseph Lancaster (1778-1838).
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firm (adj.)

late 14c., ferm, "strong, steady" (of things), "permanent, enduring" (of agreements), "steadfast, steady" (of persons), "sound, well-founded" (of arguments), from Old French ferm "strong, vigorous; healthy, sound; steadfast, loyal, faithful" (12c.), from Latin firmus "strong, steadfast, enduring, stable," figuratively "constant, steadfast, trusty, faithful," from suffixed form of PIE root *dher- "to hold firmly, support." The spelling return to -i- in late 1500s was modeled on Latin. Related: Firmly; firmness.

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sanatorium (n.)

"place to which people go for the sake of health or to regain health; hospital, usually private, for the treatment of patients not beyond hope of a cure," 1839, Modern Latin, noun use of neuter of Late Latin adjective sanitorius "health-giving," from Latin sanat-, past participle stem of sanare "to heal," from sanus "well, healthy, sane" (see sane). Latin sanare is the source of Italian sanare, Spanish sanar. Century Dictionary [1895] notes it was "specifically applied to military stations on the mountains or tablelands of tropical countries, with climates suited to the health of Europeans." 

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rosy (adj.)

c. 1200, "rose-colored, having a pink hue," of a color, from rose (n.1) + -y (2), probably modeled on Old French rose. By 1580s as "resembling a rose" in some sense, especially "fragrant." From 1590s of healthy complexions. The meaning "promising" is by 1887. Similar formation in Middle Dutch rosich, Dutch rozig, German rosig. The Homeric rosy-fingered was in "Faerie Queene" (1590). For figurative senses, see rose-colored.

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hale (adj.)

"in good health, robust," Old English hal "healthy, sound, safe; entire; uninjured; genuine, straightforward," from Proto-Germanic *hailaz(source also of Old Frisian hel"complete, full; firm" (of ground), Old High German heil, Old Norse heill "hale, sound," Gothic hails "hale"), from PIE *kailo- "whole, uninjured, of good omen" (see health). The Scottish and northern English form of whole and with a more etymological spelling. It later acquired a literary sense of "free from infirmity" (1734), especially in reference to the aged. Related: Haleness.

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whole (adj.)
Old English hal "entire, whole; unhurt, uninjured, safe; healthy, sound; genuine, straightforward," from Proto-Germanic *haila- "undamaged" (source also of Old Saxon hel, Old Norse heill, Old Frisian hal, Middle Dutch hiel, Dutch heel, Old High German, German heil "salvation, welfare"), from PIE *kailo- "whole, uninjured, of good omen" (source also of Old Church Slavonic celu "whole, complete;" see health).

The spelling with wh- developed early 15c. The sense in whole number is from early 14c. Whole milk is from 1782. On the whole "considering all facts or circumstances" is from 1690s. For phrase whole hog, see hog (n.).
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health (n.)

Old English hælþ "wholeness, a being whole, sound or well," from Proto-Germanic *hailitho, from PIE *kailo- "whole, uninjured, of good omen" (source also of Old English hal "hale, whole;" Old Norse heill "healthy;" Old English halig, Old Norse helge "holy, sacred;" Old English hælan "to heal"). With Proto-Germanic abstract noun suffix *-itho (see -th (2)).

Of physical health in Middle English, but also "prosperity, happiness, welfare; preservation, safety." An abstract noun to whole, not to heal. Meaning "a salutation" (in a toast, etc.) wishing one welfare or prosperity is from 1590s. Health food is from 1848.

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sage (n.1)

kind of shrubby, aromatic herb (Salvia officinalis), esteemed formerly as a medicine, also used as a condiment, early 14c., from Old French sauge (13c.), from Latin salvia, from salvus "healthy" (from PIE root *sol- "whole, well-kept"). So called for the healing or preserving qualities attributed to it (sage was used to keep teeth clean and relieve sore gums and boiled in water to make a drink to alleviate arthritis). In English folklore, sage, like parsley, is said to grow best where the wife is dominant. The word was in late Old English as salvie, directly from Latin. Compare German Salbei, also from Latin.

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clean-living (adj.)

"of upright character and healthful habits, mentally and morally healthy," 1874, from the noun phrase; see clean (adj.) + living (n.).

Clean Living is opposed to anything and everything which speaks for physical and mental disorder, dirt, disease, distress and discontent. Clean Living stands for babies, better born and better bred, better clothed and better fed; happier, healthier babies with normal play, normal environment and a normal chance to live and develop. Clean Living stands for youth, the critical time, the unfolding time, the time when muscle, mind, morals and manners of the boy and girl shall start right or wrong, for health and success or disease and failure. [Clean Living, vol. I, no. 1, April 1916, Chicago]
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*sol- 

also solə-, Proto-Indo-European root meaning "whole, well-kept." 

It forms all or part of: catholic; consolidate; consolidation; holism; holo-; holocaust; Holocene; hologram; holograph; insouciant; safe; safety; sage (n.1) kind of herb; salubrious; salutary; salute; salvage; salvific; salvo "simultaneous discharge of guns;" save (v.) "deliver from danger;" save (prep.) "except;" solder; soldier; solemn; solicit; solicitous; solid; solidarity; solidity; sou.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit sarvah "uninjured, intact, whole;" Avestan haurva- "uninjured, intact;" Old Persian haruva-; Greek holos "whole;" Latin salvus "uninjured, in good health, safe," salus "good health," solidus "solid;" Armenian olj "whole, healthy."  

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