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There are some words like "podiatry, podium" and "pedicure, pedestrian" which are etymologically cognate and very close in their semantics. At least, the first morpheme in all of them is the same. Why, then, is there a vowel change?

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The answer lies in the origins of the words. The first two are of Greek origin, the latter two are derived from Latin. Etymonline explains (with minor edits from me)

Greek origin

podiatry: 1914, formed from Greek pod-, stem of pous "foot" (from PIE root *ped- "foot")
podium: 1743, … from Latin podium "raised platform," from Greek podion "foot of a vase," diminutive of pous (genitive podos) "foot,…

Latin origin

pedicure: 1839, "one whose business is surgical care of feet" (removal of corns, bunions, etc.), from French pédicure, from Latin pes (genitive pedis) "foot" (from PIE root *ped- "foot") + curare "to care for," from cura "care".
pedestrian 1716, "prosaic, dull" (of writing), from Latin pedester (genitive pedestris) "plain, not versified, prosaic," literally "on foot" (sense contrasted with equester "on horseback"), from pedes "one who goes on foot," from pes (genitive pedis) "foot,"

  • I could expand this answer (why was Greek preferred instead of Latin and vice versa) but I lack the time to do the proper research. – Mari-Lou A May 7 '18 at 9:32

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