Etymology
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laugh (n.)
1680s, "action of laughing," from laugh (v.). The older noun form is laughter. Meaning "a cause of laughter" is from 1895; ironic use (in that's a laugh) attested from 1930. Laugh track "pre-recorded laughter on a TV program" is from 1961.
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laugh (v.)

late 14c., from Old English (Anglian) hlæhhan, earlier hliehhan, hlihhan "to laugh, laugh at; rejoice; deride," from Proto-Germanic *klakhjan (source also of Old Norse hlæja, Danish le, Old Frisian hlakkia, Old Saxon hlahhian, Middle Dutch and Dutch lachen, Old High German hlahhan, German lachen, Gothic hlahjan), from PIE *kleg-, of imitative origin (compare Latin cachinnare "to laugh aloud," Sanskrit kakhati "laughs," Old Church Slavonic chochotati "laugh," Lithuanian klagėti "to cackle," Greek kakhazein).

Originally with a "hard" -gh- sound, as in Scottish loch; the spelling remained after the pronunciation shifted to "-f."

If laugh were written as it is pronounced, laaff, there would be nothing in the word itself to put us in mind of the thing signified. The imitation begins to be felt in the guttural ach of G. lachen, and is clearly indicated in the reduplicate form of the Du. lachachen, to hawhaw or laugh loud, preserved by Kilian. [Hensleigh Wedgwood, introduction to "A Dictionary of English Etymology," 1878] 

To laugh in one's sleeve is to laugh inwardly so as not to be observed:

If I coveted nowe to avenge the injuries that you have done me, I myght laughe in my slyve. [John Daus, "Sleidanes Commentaries," 1560]

"The phrase generally implies some degree of contempt, and is used rather of a state of feeling than of actual laughter" [Century Dictionary]. Related: Laughed; laugher; laughing.

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laughable (adj.)
"fitted to excite laughter," 1590s, from laugh (v.) + -able. Related: Laughably. In this sense Old English had hleaterlic "laughterly."
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larf 
representing a colloquial pronunciation of laugh, by 1836. Also see R.
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laughter (n.)
late 14c., from Old English hleahtor "laughter; jubilation; derision," from Proto-Germanic *hlahtraz (source also of Old Norse hlatr, Danish latter, Old High German lahtar, German Gelächter); see laugh (v.).
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laughing (n.)

mid-14c., verbal noun from laugh (v.). Laughing matter (usually with negative) is from 1560s. Nitrous oxide has been called laughing gas since 1842 (for its exhilarating effects). Humphry Davy, experimenting with the gas, discovered these as far back as 1779: "When I took the bag from my mouth, I immediately laughed. The laughter was involuntary, but highly pleasurable, accompanied by a thrill all through me."

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though (adv., conj.)

c. 1200, from Old English þeah "though, although, even if, however, nevertheless, still, yet;" and in part from Old Norse þo "though," both from Proto-Germanic *thaukh (source also of Gothic þauh, Old Frisian thach, Middle Dutch, Dutch doch, Old High German doh, German doch), from PIE demonstrative pronoun *to- (see that). The evolution of the terminal sound did not follow laugh, tough, etc., though a tendency to end the word in "f" existed c. 1300-1750 and persists in dialects.

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yuck (2)
"laugh," 1938, yock, probably imitative.
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deride (v.)

"laugh at in contempt, mock, ridicule, scorn by laughter," 1520s, from French derider, from Latin deridere "to ridicule, laugh to scorn," from de "down" (see de-) + ridere "to laugh" (see risible). Related: Derided; deriding.

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smile (v.)

c. 1300, perhaps from Middle Low German *smilen or a Scandinavian source (such as Danish smile "smile," Swedish smila "smile, smirk, simper, fawn"), from Proto-Germanic *smil-, extended form of PIE root *smei- "to laugh, smile" (source also of Sanskrit smayate "smiles;" Latvian smiêt "to laugh;" Latin mirus "wonderful," mirari "to wonder;" Old English smerian "to laugh at, scorn," Old High German smieron "to smile"). Related: Smiled; smiling.

It gradually pushed the usual Old English word, smearcian (modern smirk), into a specific, unpleasant sense. Of the eyes, from 1759. Figuratively, as indicating favor or encouragement, from c. 1400. Romance, Celtic, and Slavic languages tend to use a diminutive of the word for "laugh" to mean "smile" (such as Latin ridere "laugh;" subridere "smile"), perhaps literally "small laugh" or "low laugh."

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