Etymology
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*spek- 
Proto-Indo-European root meaning "to observe."

It forms all or part of: aspect; auspex; auspices; auspicious; bishop; circumspect; conspicuous; despicable; despise; episcopal; especial; espionage; espy; expect; frontispiece; gyroscope; haruspex; horoscope; inspect; inspection; inspector; introspect; introspection; perspective; perspicacious; perspicacity; prospect; prospective; respect; respite; retrospect; scope; -scope; scopophilia; -scopy; skeptic; species; specimen; specious; spectacle; spectacular; spectrum; speculate; speculation; speculum; spice; spy; suspect; suspicion; suspicious; telescope.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit spasati "sees;" Avestan spasyeiti "spies;" Greek skopein "behold, look, consider," skeptesthai "to look at," skopos "watcher, one who watches;" Latin specere "to look at;" Old High German spehhon "to spy," German spähen "to spy."
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*mendh- 

Proto-Indo-European root meaning "to learn." It forms all or part of: chrestomathy; mathematic; mathematical; mathematics; opsimathy; polymath.

It is the hypothetical source of/evidence for its existence is provided by: Greek menthere "to care," manthanein "to learn," mathēma "science, knowledge, mathematical knowledge;" Lithuanian mandras "wide-awake;" Old Church Slavonic madru "wise, sage;" Gothic mundonsis "to look at," German munter "awake, lively."

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*keu- 

also *skeu- Proto-Indo-European root meaning "to see, observe, perceive." 

It forms all or part of: Anschauung; caution; cautious; caveat; kudos; precaution; scavenger; scone; sheen; show.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kavih "wise, sage; seer, poet;" Avestan kauui- "seer, poet, wise man;" Middle Iranian škoh "splendor, majesty;" Latin cautio "care, foresight," cautus "careful, heedful," cavere "beware, take heed;" Greek kydos "glory, fame;" Lithuanian kavoti "tend, safeguard;" Armenian cucanem "I show;" Old Church Slavonic čudo "wonder;" Czech (z)koumati "to perceive, be aware of;" Serbian čuvati "watch, heed;" Old English sceawian "to look at," Middle Dutch schoon "beautiful, bright," properly "showy," Old High German scouwon "to watch."

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