Etymology
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Words related to sad

*sa- 
*sā-, Proto-Indo-European root meaning "to satisfy."

It forms all or part of: assets; hadron; sad; sate; satiate; satiety; satisfy; satire; saturate; saturation.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit a-sinvan "insatiable;" Greek hadros "thick, bulky;" Latin satis "enough, sufficient;" Old Church Slavonic sytu, Lithuanian sotus "satiated;" Old Irish saith "satiety," sathach "sated;" Old English sæd "sated, full, having had one's fill, weary of."
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sadden (v.)

"to make sorrowful," 1620s, from sad (adj.) + -en (1); earlier "to make solid or firm" (c. 1600). The earlier verb was simply sad, from Middle English saden "become weary or indifferent," also "make (something) hard or stiff," from Old English sadian, which also could be the source of the modern verb. The intransitive meaning "to become sorrowful" is from 1718. Related: Saddened; saddening.

sadder (adj.)

"more sad," Middle English saddere, comparative of sad (adj.).

sadly (adv.)

c. 1300, "heavily," also "solidly," from sad + -ly (2). The main modern meaning "sorrowfully" begins by mid-14c.

sadness (n.)

early 14c., sadnesse, "seriousness," from sad + -ness. Meaning "sorrowfulness, dejection of mind" is by c. 1500, perhaps c. 1400, but throughout Middle English the word usually referred to "solidness, firmness, thickness, toughness; permanence, continuance; maturity; sanity."

sate (v.)

"to satisfy, fill full, surfeit," c. 1600, probably an alteration (by influence of Latin satiare "satiate") of Middle English saden "become weary or indifferent; satiate," from Old English sadian "to satiate, fill; be sated, get wearied" (see sad (adj.)), ultimately from PIE root *sa- "to satisfy." Related: Sated; sating.