"a constitutional walk," 1829, probably originally among university students, and probably short for constitutional walk or exercise; from constitutional (adj.) in the "beneficial to bodily health" sense.
1530s, "a climax;" 1670s, "orderly arrangement or succession," from French gradation (16c.) and directly from Latin gradationem (nominative gradatio) "ascent by steps; a climax," noun of action from gradi "to walk, go, step" (from PIE root *ghredh- "to walk, go"). Meaning "gradual change" is from 1540s.
1560s, "a leisurely walk, a walk for pleasure or display," from French promenade "a walking, a public walk" (16c.), from se promener "go for a walk," from Late Latin prominare "to drive (animals) onward," from pro "forth" (see pro-) + minare "to drive (animals) with shouts," from minari "to threaten" (see menace (n.)).
Meaning "place for walking" is from 1640s; specifically "walkway by the sea" (from late 18c.); British sense of "music hall favored by 'loose women and the simpletons who run after them' " [The Observer, Jan. 18, 1863, in reference to the Alhambra in Leicester Square] is attested from 1863. Sense of "a dance given by or at a school" is from 1887.
"consisting of 100 degrees, divided into 100 equal parts," 1799, from French, from centi- "hundred" (see centi-) + second element from Latin gradi "to walk, go, step" (from PIE root *ghredh- "to walk, go"). The centigrade thermometer (see Celsius) divides the interval between the freezing and boiling points of water into 100 degrees.
mid-15c., perambulacioun, "a journey or tour of inspection," especially a walk around the borders of a property, parish, etc., to determine the boundaries, from Anglo-Latin (c. 1300) and Anglo-French perambulacion, from Medieval Latin perambulationem (nominative perambulatio), noun of action from past-participle stem of Latin perambulare "to walk through, go through, ramble through," from per "through" (from PIE root *per- (1) "forward," hence "through") + ambulare "to walk, go about" (see amble (v.)). Meaning "act of passing or wandering through or over" is by late 15c.