Etymology
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module (n.)

1580s, "allotted measure," a sense now obsolete, from French module (1540s) or directly from Latin modulus "small measure," diminutive of modus "measure, manner" (from PIE root *med- "take appropriate measures").

Sense of "a standard measure to regulate proportions" is from 1620s. Meaning "interchangeable part" is recorded by 1955, via the notion of "length chosen as the basis for the dimensions of parts of a building, etc." (1936); that of "separate section of a spacecraft" is from 1961.

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-ule 
word-forming element meaning "small, little" (in capsule, module, etc.), from French -ule, from Latin diminutive suffix -ulus (fem. -ula, neuter -ulum), from PIE *-(o)lo-, from *-lo-, secondary suffix forming diminutives, which also is the source of the first element in native diminutive suffix -ling.
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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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LEM (n.)
acronym (initialism) for lunar excursion module, 1962, from the U.S. space program.
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