declivity

Etymology

1610s, from French déclivité, from Latin declivitatem, dēclīvitās, from dēclivis (“a sloping downward”), from de (“down”) + clīvus (“a slope”), from Proto-Indo-European *ḱleywo-, from Proto-Indo-European *ḱley- (“to lean”) (English lean).

noun

1. (geomorphology) The downward slope of a curve.
   1780, Theodore Augustine Mann, A Treatise on Rivers and Canals, Philosophical Transactions of the Royal Society of London, Volume 69: For the Year 1779, Part II, 582, The velocity of flowing waters is very far from being in proportion to the quantity of declivity in their bed: […] .
   […]whoever takes the trouble of observing how the water runs longitudinally in the ruts on a convex road, although the declivity down the sides be incomparably greater than in the direction which it is compelled to take in the ruts, will soon see the propriety of constructing roads so as to have the water rim length-ways upon them, instead of attempting to gain a declivity, by making it run from the middle to the sides. 1809, Alexander Cumming, Observations on the Very Important and Contrary Effects which Carriage Wheels, with Rims of Cylindrical, and of Conical Shape, Have on the Roads, page 30
   […]a line was measured down the hill on the right of 420, and the angle of declivity is 23°, which shortens the line 33 links;[…]. 1812, John Ainslie, Comprehensive Treatise on Land Surveying, page 117
   1908 [Charles Griffin & Company], John Harvard Biles, The Design and Construction of Ships, Volume I: Calculations and Strength, 2009, Europāischer Hochschulverlag (Salzwasser-Verlag), page 216, The declivity of the keel blocks varies slightly with the size of the vessel. The larger the vessel, the less the declivity.
   Companion woodcut of "inclined plane on the railway from South Hetton to Seaham Harbour, showing the manner in which a loaded train of waggons pulls an empty one up the declivity" 1948 May and June, “The South Hetton Railway in 1835”, in Railway Magazine, page 184, image caption
2. A downward bend in a path.
3. (entomology) An inward curve of the exoskeleton of an insect, such as between body segments; a segment of an insect's body where the exoskeleton curves inward.
   1979, Entomology Circular, Issue 200, Part 366, Division of Plant Industry, page number not shown, Males of all species have more developed armature of the elytral declivity than females (Figs. S, 6, 8, 9, 11-14).
   Propodeum in profile with upper lobe of declivity elongate and narrow, subspiniform, almost as long as lower lobe. 2000, Barry Bolton, “The Ant Tribe Dacetini”, in American Entomological Institute, volume 65, number 2, page 500