1826 (adj.), "eight-footed or eight-armed;" 1835 (n.) "an eight-footed or eight-armed animal," especially an octopus, from Latinized form of Greek oktōpod-, stem of oktōpous (see octopus).
"a four-footed animal," especially "a four-footed mammal," 1640s, from French quadrupède (16c.), from Latin quadrupes (genitive quadrupedis) "four-footed, on all fours," also, as a noun, "a four-footed animal," from quadri- "four" (from PIE root *kwetwer- "four") + pes "foot" (from PIE root *ped- "foot").
The adjective is attested from 1741, "four-footed, having four limbs fitted for sustaining the body and locomotion, habitually going on all fours." Related: Quadrupedal (1610s). In zoology, quadrumane (from Latin manus "hand") was "a four-handed animal," in reference to monkeys, apes, lemurs, etc.; attested by 1786.
"a fin-footed mammal," one having feet like fins or flippers, especially of the group of fin-footed aquatic carnivorous quadruped mammals that includes seals, sea-lions, and walruses, 1842, from Modern Latin Pinnipedia, suborder of aquatic carnivorous mammals (seals and walruses), literally "having feet as fins," from Latin pinna in its secondary sense "fin" (see pin (n.)) + pes, genitive pedis "foot" (from PIE root *ped- "foot").
"long-tailed, ten-footed shrimp-like crustacean, abundant on the shores of the British Isles," early 15c., prayne, a word of unknown origin. "No similar name found in other langs." [OED].