Etymology
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medusa (n.)

"jellyfish," 1758, as genus name, from Medusa, the name of one of the three Gorgons with snakes for hair, whose glance turned to stone whomever looked upon it (attested in English from late 14c.). Her name is from Greek Medousa, literally "guardian," fem. present participle of the verb medein "to protect, rule over" (from PIE root *med- "take appropriate measures"). The zoological name was chosen by Linnæus, suggested by the creature's long tentacles. Related: Medusoid.

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*med- 

Proto-Indo-European root meaning "take appropriate measures."

It forms all or part of: accommodate; accommodation; commode; commodious; commodity; empty; immoderate; immodest; Medea; medical; medicament; medicaster; medicate; medication; medicine; medico; medico-; meditate; meditation; Medusa; meet (adj.) "proper, fitting;" mete (v.) "to allot;" modal; mode; model; moderate; modern; modest; modicum; modify; modular; modulate; module; modulation; mold (n.1) "hollow shape;" mood (n.2) "grammatical form indicating the function of a verb;" must (v.); premeditate; premeditation; remedial; remediation; remedy.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit midiur "I judge, estimate;" Avestan vi-mad- "physician;" Greek mēdomai "be mindful of," medesthai "think about," medein "to rule," medon "ruler;" Latin meditari "think or reflect on, consider," modus "measure, manner," modestus "moderate," modernus "modern," mederi "to heal, give medical attention to, cure;" Irish miduir "judge;" Welsh meddwl "mind, thinking;" Gothic miton, Old English metan "to measure out."

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Perseus 

Greek hero, son of Zeus and Danaë, slayer of the gorgon Medusa, from Greek Perseus, a name of unknown origin. Also the name of an ancient northern constellation representing him.

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jellyfish (n.)
also jelly-fish, popular name of the medusa and similar sea-creatures, 1796, from jelly (n.) + fish (n.). So called for its soft structure. Figuratively, "person of weak character," 1883. Earlier it had been used of a type of actual fish (1707).
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gorgon (n.)

"female monster with a petrifying look," late 14c., in Greek legend, any of the three hideous sisters, with writhing serpents for hair, whose look turned beholders to stone, from Greek Gorgones (plural; singular Gorgō) "the grim ones," from gorgos, of a look or gaze, "grim, fierce, terrible," later also "vigorous, lively," a word of unknown origin. Beekes' sources reject the proposed connections to Old Irish garg "raw, wild," Old Church Slavonic groza "shiver," Armenian karcr "hard."

Transferred sense of "terrifyingly ugly person" is from 1520s. Their names were Medusa, Euryale, and Stheino, but when only one is mentioned, Medusa usually is meant. Slain by Perseus, her head was fixed on the aegis of Athena.

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pneumo- 

before vowels pneum-, word-forming element meaning "lung," from Greek pneumōn "lung," altered (probably by influence of pnein "to breathe") from pleumōn (which was an alternative form in Attic), literally "floater," probably cognate with Latin pulmo "lung(s)," from PIE root *pleu- "to flow." The notion perhaps is from the fact that, when thrown into a pot of water, lungs of a slaughtered animal float, while the heart, liver, etc., do not (compare Middle English lights "the lungs," literally "the light (in weight) organs").  Greek pneumōn also meant "jellyfish, medusa," "perhaps from its rhythmical pulsation, as if breathing" [Thompson].

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Pegasus 

famous winged horse in Greek mythology, also the name of an ancient northern constellation, late 14c., Pegase, from Latin, from Greek Pēgasos, usually said to be from pēgē "fountain, spring; a well fed by a spring" (plural pēgai), especially in reference to the "springs of Ocean," near which Medusa was said to have been killed by Perseus (Pegasus sprang from her blood). But this may be folk etymology, and the ending of the word suggests non-Greek origin.

Advances since the 1990s in the study of the Luwians, neighbors of the Hittites in ancient Anatolia, show a notable convergence of the Greek name with Pihaššašši, the name of a Luwian weather-god: "the mythological figure of Pegasus carrying the lightning and thunderbolt of Zeus, ... is likely to represent an avatar of the Luwian Storm-God of Lightning ...." [Alice Mouton, et al., eds., "Luwian Identities," 2013]

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