Etymology
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infuse (v.)
early 15c., "to pour in, introduce, soak (something in liquid)," from Latin infusus, past participle of infundere "to pour into, pour out; press in, crowd in; mix, mingle," from in- "in" (from PIE root *en "in") + fundere "to pour, melt" (from nasalized form of PIE root *gheu- "to pour"). Related: Infused; infusing; infusory; infusorial.
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infusion (n.)
c. 1400, "a liquid extract (obtained by soaking in water);" early 15c., "a pouring in; that which is poured in," from Old French infusion "injection" (13c.) or directly from Latin infusionem (nominative infusio) "a pouring in, a watering," noun of action from past participle stem of infundere "to pour into" (see infuse).
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infundibulum (n.)
1799, "funnel-shaped organ or body part," from a Modern Latin use of Latin infundibulum "a funnel," from infundere "to pour into" (see infuse) + -bulum, suffix forming names of instruments. In some cases a loan-translation into Latin of Greek khoane "funnel." Related: Infundibular.
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*gheu- 
Proto-Indo-European root meaning "to pour, pour a libation."

It forms all or part of: alchemy; chyle; chyme; confound; confuse; diffuse; diffusion; effuse; effusion; effusive; fondant; fondue; font (n.2) "complete set of characters of a particular face and size of type;" found (v.2) "to cast metal;" foundry; funnel; fuse (v.) "to melt, make liquid by heat;" fusible; fusion; futile; futility; geyser; gush; gust (n.) "sudden squall of wind;" gut; infuse; ingot; parenchyma; perfuse; perfusion; profuse; refund; refuse (v.) "reject, disregard, avoid;" refuse (n.) "waste material, trash;" suffuse; suffusion; transfuse; transfusion.

It is the hypothetical source of/evidence for its existence is provided by: Greek khein "to pour," khoane "funnel," khymos "juice;" Latin fundere (past participle fusus) "melt, cast, pour out;" Gothic giutan, Old English geotan "to pour;" Old English guttas (plural) "bowels, entrails;" Old Norse geysa "to gush;" German Gosse "gutter, drain."
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intellectualize (v.)
1819 (Coleridge), "infuse with intellectual quality," from intellectual + -ize. From 1827 as "exercise the mind, reason upon a matter of intellect." Related: Intellectualized; intellectualizing.
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inanimate (adj.)

early 15c., "without vital force, having lost life," from Late Latin inanimatus "lifeless," from in- "not" (see in- (1)) + animatus (see animation). The Latin word closest corresponding in form and sense is inanimalis. Meaning "lacking vivacity, without spirit, dull" is from 1734. Inanimate as a verb meant "infuse with life or vigor" (17c.), from the other in- (see in- (2)).

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aspire (v.)
"strive for, seek eagerly to attain, long to reach," c. 1400, from Old French aspirer "aspire to; inspire; breathe, breathe on" (12c.), from Latin aspirare "to breathe upon, blow upon, to breathe," also, in transferred senses, "to be favorable to, assist; to climb up to, to endeavor to obtain, to reach to, to seek to reach; infuse," from ad "to" (see ad-) + spirare "to breathe" (see spirit (n.)). The notion is of "panting with desire," or perhaps of rising smoke. Literal sense of "breathe, exhale" (1530s) is rare in English. Related: Aspired; aspiring.
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inspiration (n.)
Origin and meaning of inspiration

c. 1300, "immediate influence of God or a god," especially that under which the holy books were written, from Old French inspiracion "inhaling, breathing in; inspiration" (13c.), from Late Latin inspirationem (nominative inspiratio), noun of action from past-participle stem of Latin inspirare "blow into, breathe upon," figuratively "inspire, excite, inflame," from in- "in" (from PIE root *en "in") + spirare "to breathe" (see spirit (n.)). ,

And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. [Genesis ii.7]

The sense evolution seems to be from "breathe into" to "infuse animation or influence," thus "affect, rouse, guide or control," especially by divine influence. Inspire (v.) in Middle English also was used to mean "breath or put life or spirit into the human body; impart reason to a human soul." Literal sense "act of inhaling" attested in English from 1560s. Meaning "one who inspires others" is attested by 1867.

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in- (2)
Origin and meaning of in-

element meaning "into, in, on, upon" (also im-, il-, ir- by assimilation of -n- with following consonant), from Latin in- "in," from PIE root *en "in."

In Old French (and hence in Middle English) this often became en-, which in English had a strong tendency to revert to Latin in-, but not always, which accounts for pairs such as enquire/inquire. There was a native form, which in West Saxon usually appeared as on- (as in Old English onliehtan "to enlighten"), and some of those verbs survived into Middle English (such as inwrite "to inscribe"), but all now seem to be extinct.

Not related to in- (1) "not," which also was a common prefix in Latin, causing confusion: to the Romans impressus could mean "pressed" or "unpressed;" inaudire meant "to hear," but inauditus meant "unheard of;" in Late Latin investigabilis could mean "that may be searched into" or "that cannot be searched into." Latin invocatus was "uncalled, uninvited," but invocare was "to call, appeal to."

The trouble has continued in English; the hesitation over what is meant by inflammable being a commonly cited example. Implume (1610s) meant "to feather," but implumed (c. 1600) meant "unfeathered." Impliable can mean "capable of being implied" (1865) or "inflexible" (1734). Impartible in 17c. could mean "incapable of being divided" or "capable of being imparted." Impassionate can be "free from passion" or it can mean "strongly stirred by passion." Inanimate (adj.) is "lifeless," but Donne uses inanimate (v.) to mean "infuse with life or vigor." Irruption is "a breaking in," but irruptible is "unbreakable."

In addition to improve "use to one's profit," Middle English also had a verb improve meaning "to disprove" (15c.). To inculpate is "to accuse," but inculpable means "not culpable, free from blame." Infestive has meant "troublesome, annoying" (1560s, from infest) and "not festive" (1620s). In Middle English inflexible could mean "incapable of being bent" or "capable of being swayed or moved." In 17c., informed could mean "current in information," formed, animated," or "unformed, formless" ("This was an awkward use" [OED]). Inhabited has meant "dwelt in" (1560s) and "uninhabited" (1610s); inhabitable likewise has been used on opposite senses, a confusion that goes back to Late Latin.

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