"heedless disregard of duty, inactivity, indifference, habit of omitting to do things which ought to be done," mid-14c., necligence, from Old French negligence "negligence, sloth; injury, injustice" (12c.), and directly from Latin neclegentia, neglegentia "carelessness, heedlessness, neglect," from neglegentem (nominative neglegens) "heedless, careless, unconcerned," present participle of neglegere "to neglect" (see neglect (v.)).
"given to lying, speaking falsely; having the characteristics of a lie, false, untrue," 1610s, from French mendacieux and directly from Latin mendacium "a lie, untruth, falsehood, fiction," from mendax (genitive mendacis) "lying, deceitful," from menda "fault, defect, carelessness in writing," from PIE root *mend- "physical defect, fault" (see amend (v.)). The sense evolution of Latin mendax was influenced by mentiri "to speak falsely, lie, deceive." Related: Mendaciously; mendaciousness.
From mid-14c. with senses "lose one's footing," "slide out of place," "fall into error or fault." Sense of "pass unguarded or untaken" is from mid-15c. That of "slide, glide" is from 1520s. Transitive sense from 1510s; meaning "insert surreptitiously" is from 1680s. Related: Slipped; slipping. To slip up "make a mistake" is from 1855; to slip through the net "evade detection" is from 1902. To let (something) slip originally (1520s) was a reference to hounds on a leash; figurative use "allow to escape through carelessness" is from 1540s.