Etymology
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*re- 

*rē-, Proto-Indo-European root meaning "to reason, count;" a variant of PIE root *ar-, also arə-, "to fit together." 

It forms all or part of: Alfred; arraign; arithmetic; Conrad; dread; Eldred; Ethelred; hatred; hundred; kindred; logarithm; Ralph; rate (n.) "estimated value or worth;" rathskeller; ratify; ratio; ration; read; reason; rede; rhyme; riddle (n.1) "word-game;" rite; ritual.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit radh- "to succeed, accomplish;" Greek arithmos "number, amount;" Latin reri "to consider, confirm, ratify," ritus "rite, religious custom;" Old Church Slavonic raditi "to take thought, attend to;" Old Irish im-radim "to deliberate, consider;" Old English rædan "to advise, counsel, persuade; read;" Old English, Old High German rim "number;" Old Irish rim "number," dorimu "I count."

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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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*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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*(s)pen- 

Proto-Indo-European root meaning "to draw, stretch, spin."

It forms all or part of: append; appendix; avoirdupois; compendium; compensate; compensation; counterpoise; depend; dispense; equipoise; expend; expense; expensive; hydroponics; impend; painter (n.2) "rope or chain that holds an anchor to a ship's side;" pansy; penchant; pend; pendant; pendentive; pending; pendular; pendulous; pendulum; pension; pensive; penthouse; perpendicular; peso; poise; ponder; ponderous; pound (n.1) "measure of weight;" prepend; prepense; preponderate; propensity; recompense; span (n.1) "distance between two objects;" span (n.2) "two animals driven together;" spangle; spanner; spend; spider; spin; spindle; spinner; spinster; stipend; suspend; suspension.

It is the hypothetical source of/evidence for its existence is provided by: Latin pendere "to hang, to cause to hang," pondus "weight" (perhaps the notion is the weight of a thing measured by how much it stretches a cord), pensare "to weigh, consider;" Greek ponos "toil," ponein "to toil;" Lithuanian spendžiu, spęsti "lay a snare;" Old Church Slavonic peti "stretch, strain," pato "fetter," pina "I span;" Old English spinnan "to spin," spannan "to join, fasten; stretch, span;" Armenian henum "I weave;" Greek patos "garment," literally "that which is spun;" Lithuanian pinu "I plait, braid," spandau "I spin;" Middle Welsh cy-ffiniden "spider;" Old English spinnan "draw out and twist fibers into thread," spiðra "spider," literally "spinner."

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