Etymology
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pneuma (n.)

a word used in English in various sense from late 19c. ("breath;" "spirit;" "soul;" "a breathing;" also as a technical term), from Greek pneuma "a blowing, a wind, blast; breeze; influence; breathed air, breath; odor, scent; spirit of a person; inspiration, a spirit, ghost," from pnein "to blow, to breathe," from PIE root *pneu- "to breathe," of imitative origin (compare Greek pnoe "breath," pnoia "breathing;" Old English fnora "sneezing," fnæran "to snort").

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pneumato- 
before vowels pneumat-, word-forming element meaning "wind, air, spirit, presence of air," from Greek pneuma (genitive pneumatos) "the wind," also "breath" (see pneuma).
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tachypnea (n.)
"hysterical rapid breathing," 1896, from tachy- "swift" + -pnea, from pnein "to breathe" (see pneuma). Related: Tachypneic.
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pneumatic (adj.)

"moved or played by means of air; of or pertaining to air or gases," 1650s, from Latin pneumaticus "of the wind, belonging to the air," from Greek pneumatikos "of wind or air" (which is attested mainly as "of spirit, spiritual"), from pneuma (genitive pneumatos) "the wind," also "breath" (see pneuma). Earlier was pneumatical (c. 1600). The pneumatic-dispatch tube was so called by 1859 (in Paris, pneumatique).

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apnea (n.)
in pathology, "suspension of breathing," originally, and until recently most commonly, apnoea, 1719, Modern Latin, from Greek apnoia "absence of respiration," from apnoos "without breathing, without wind," from a- "not, without" (see a- (3)) + pnein "to breathe" (see pneuma).
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spirit (n.)
Origin and meaning of spirit

mid-13c., "animating or vital principle in man and animals," from Anglo-French spirit, Old French espirit "spirit, soul" (12c., Modern French esprit) and directly from Latin spiritus "a breathing (respiration, and of the wind), breath; breath of a god," hence "inspiration; breath of life," hence "life;" also "disposition, character; high spirit, vigor, courage; pride, arrogance," related to spirare "to breathe," perhaps from PIE *(s)peis- "to blow" (source also of Old Church Slavonic pisto "to play on the flute"). But de Vaan says "Possibly an onomatopoeic formation imitating the sound of breathing. There are no direct cognates."

Meaning "supernatural immaterial creature; angel, demon; an apparition, invisible corporeal being of an airy nature" is attested from mid-14c.; from late 14c. as "a ghost" (see ghost (n.)). From c. 1500 as "a nature, character"; sense of "essential principle of something" (in a non-theological context, as in Spirit of St. Louis) is attested from 1680s, common after 1800; Spirit of '76 in reference to the qualities that sparked and sustained the American Revolution is attested by 1797 in William Cobbett's "Porcupine's Gazette and Daily Advertiser."

From late 14c. in alchemy as "volatile substance; distillate;" from c. 1500 as "substance capable of uniting the fixed and the volatile elements of the philosopher's stone." Hence spirits "volatile substance;" sense narrowed to "strong alcoholic liquor" by 1670s. This also is the sense in spirit level (1768). Also from mid-14c. as "character, disposition; way of thinking and feeling, state of mind; source of a human desire;" in Middle English freedom of spirit meant "freedom of choice." From late 14c. as "divine substance, divine mind, God;" also "Christ" or His divine nature; "the Holy Ghost; divine power;" also, "extension of divine power to man; inspiration, a charismatic state; charismatic power, especially of prophecy." Also "essential nature, essential quality." From 1580s in metaphoric sense "animation, vitality."

According to Barnhart and OED, originally in English mainly from passages in Vulgate, where the Latin word translates Greek pneuma and Hebrew ruah. Distinction between "soul" and "spirit" (as "seat of emotions") became current in Christian terminology (such as Greek psykhe vs. pneuma, Latin anima vs. spiritus) but "is without significance for earlier periods" [Buck]. Latin spiritus, usually in classical Latin "breath," replaces animus in the sense "spirit" in the imperial period and appears in Christian writings as the usual equivalent of Greek pneuma. Spirit-rapping is from 1852.

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pneumatics (n.)

"the branch of physics which treats of the mechanical properties of gases, especially of atmospheric air," 1650s, from pneumatic. Also see -ics.

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psyche (n.)

1640s, "animating spirit, the human spirit or mind," from Latin psyche, from Greek psykhē "the soul, mind, spirit; life, one's life, the invisible animating principle or entity which occupies and directs the physical body; understanding, the mind (as the seat of thought), faculty of reason," also "ghost, spirit of a dead person;" probably akin to psykhein "to blow, breathe," also "to cool, to make dry."

These are sometimes traced to a PIE root *bhes- "to blow, to breathe" (source also of Sanskrit bhas-), "Probably imitative" [Watkins]. Beekes finds this tempting but not convincing and doubts the existence of the PIE verb based on scant evidence.

Personified by the Greeks as Psykhē, the beloved of Eros, often represented as a fair young girl; the butterfly was her symbol.  Also in ancient Greek, "departed soul, spirit, ghost," seen as a winged creature and often represented symbolically as a butterfly or moth.

The word had extensive sense development in Platonic philosophy and Jewish-influenced theological writing of St. Paul (compare spirit (n.)). Thus in Biblical use the Greek word was "the soul as the seat of feelings, desires, affections, etc.," also "the soul regarded as a moral being designed for everlasting life," and "the soul as an essence which differs from the body and is not dissolved by death." In English, the meaning "human soul" is from 1650s; the psychological sense of "mind" is attested by 1910.

In the Jewish-Alexandrine Pauline, and Neo-Platonist psychology, the psyche is in general treated as the animating principle in close relation to the body, whereas the pneuma (as representing the divine breath breathed into man), the nous, and the Logos (q.v.) stand for higher entities. They are the more universal, the more divine, the ethically purer. By this more explicit separation of the intellectual and ethical activities from the physiological the conception of the mental or psychical (in the modern sense) was at length reached. ["Dictionary of Philosophy and Psychology," J.M. Baldwin, ed., London, 1902]
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