late 14c., "a deep place, deep water, the sea," also "distance or extension from the top down (opposed to height) or from without inward," apparently formed in Middle English on model of long/length, broad/breadth; from dēp "deep" (see deep (adj.)) + -th (2). Replaced older deopnes "deepness." Though the word is not recorded in Old English, the formation was in Proto-Germanic, *deupitho-, and corresponds to Old Saxon diupitha, Dutch diepte, Old Norse dypð, Gothic diupiþa.
From c. 1400 as "the part of anything most remote from the boundary or outer limit." From 1520s as "quality of extending a considerable distance downward or inward." Figurative use in reference to thought, ideas, etc., "profoundness," from 1580s.
early 15c., "fixed standard of measure" (surname Gageman is early 14c.), from Old North French gauge "gauging rod" (see gauge (v.)). Meaning "instrument for measuring" is from 1670s; meaning "distance between rails on a railway" is from 1841.
Railway-gage, the distance between perpendiculars on the insides of the heads of the two rails of a track. Standard gage is 4 feet 8 1/2 inches; anything less than this is narrow gage; anything broader is broad gage. The dimension was fixed for the United States by the wheels of the British locomotive imported from the Stephenson Works in 1829. [Century Dictionary]
early 15c., "bottom of the sea," from Old French profundite (Modern French profondité) and directly from Late Latin profunditatem (nominative profunditas) "depth, intensity, immensity," from profundus "deep, vast" (see profound). Meaning "depth of intellect, feeling, or spiritual mystery" in English is from c. 1500.