Etymology
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may (v.1)

Old English mæg "am able" (infinitive magan, past tense meahte, mihte), from Proto-Germanic root *mag-, infinitive *maganan (Old Frisian mei/muga/machte "have power, may;" Old Saxon mag/mugan/mahte; Middle Dutch mach/moghen/mohte; Dutch mag/mogen/mocht; Old High German mag/magan/mahta; German mag/mögen/mochte; Old Norse ma/mega/matte; Gothic mag/magan/mahte "to be able"), from PIE root *magh- "to be able, have power." A present-preterit verb (with can, shall, etc.). Also used in Old English as a "auxiliary of prediction."

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machine (n.)

1540s, "structure of any kind," from Middle French machine "device, contrivance," from Latin machina "machine, engine, military machine; device, trick; instrument" (source also of Spanish maquina, Italian macchina), from Greek makhana, Doric variant of Attic mēkhanē "device, tool, machine;" also "contrivance, cunning," traditionally (Watkins) from PIE *magh-ana- "that which enables," from root *magh- "to be able, have power." But Beekes, on formal grounds, objects to the connection to words in Germanic and Slavic. He finds the Greek word isolated and is convinced that it is Pre-Greek.

Main modern sense of "device made of moving parts for applying mechanical power" (1670s) probably grew out of mid-17c. senses of "apparatus, appliance" and "military siege-tower."  It gradually came to be applied to an apparatus that works without the strength or skill of the workman.

From 17c.-19c. also "a vehicle; a stage- or mail-coach; a ship," and, from 1901, "a motor-car." Also in late 19c. slang the word was used for both "penis" and "vagina," one of the few so honored.

The political sense "a strict organization of the working members of a political party to secure a predominating influence for themselves and their associates" is U.S. slang, attested by 1876. Machine age, a time notable for the extensive use of mechanical devices, is attested by 1882, though there is this:

The idea of remodelling society at public meetings is one of the least reasonable which ever entered the mind of an agitator: and the notion that the relations of the sexes can be re-arranged and finally disposed of by preamble and resolution, is one of the latest, as it should have been the last, vagary of a machine age. ["The Literary World," Nov. 1, 1851]

Machine for living(in) "house" translates Le Corbusier's machine à habiter (1923).

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machismo (n.)

"male virility, masculine pride," 1940, from American Spanish machismo, from Spanish macho "male" (see macho) + ismo (see -ism).

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machinable (adj.)

"capable of being cut by machine-tools," 1896, from machine (v.) + -able. Related: Machinability.

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machinery (n.)

1680s; from machine (n.) + -ery. Originally theatrical, "devices for creating stage effects" (which also was a sense of Greek mēkhanē); meaning "machines or parts of machines considered collectively," is attested from 1731. Transferred meaning "any complex system of (non-mechanical) means to carry on a particular work" is by 1770. Middle English had machinament "a contrivance" (early 15c.).

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machete (n.)

"heavy knife or cutlass," used as a weapon and tool by the Spanish in the Americas, 1590s (in pseudo-Spanish form macheto), from Spanish machete "a chopping knife," probably a diminutive of macho "sledge hammer," alteration of mazo "club," which is probably [Barnhart] a dialectal variant of maza "mallet," from Vulgar Latin *mattea "war club" (see mace (n.1)). An alternative explanation traces macho to Latin marculus "a small hammer," diminutive of marcus "hammer," from a base parallel to that of Latin malleus (see mallet).

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macho 

1928 (n.) "tough guy," from Spanish macho "male animal," noun use of adjective meaning "masculine, virile," from Latin masculus (see masculine). As an adjective, "ostensibly manly and virile," attested in English by 1959 (Norman Mailer).

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machine-made (adj.)

"made by a machine or machinery" (opposed to man-made), by 1837, from machine (n.) + made.

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machine (v.)

mid-15c., "decide, resolve," from Old French and Latin usages, from Latin machina "machine, engine, military machine; device, trick; instrument," from Greek makhana, Doric variant of Attic mēkhanē "device, tool; contrivance, cunning" (see machine (n.)). Meaning "to apply machinery to, to make or form on or by the aid of a machine" is from 1878. Related: Machined; machining.

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machinist (n.)

1706, "engineer, mechanical inventor, constructor of machines and engines," a hybrid from machine (n.) + -ist. Meaning "machine operator" is attested from 1879; in  U.S. Navy ratings, "an engine-room artificer or attendant," by 1880.

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