Etymology
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utilitarianism (n.)

1827, from utilitarian + -ism. The doctrine that the end of all action should be the greatest happiness of the greatest number.

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maximum (adj.)

"greatest, at the maximum," 1834, from maximum (n.).

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happiness (n.)

1520s, "good fortune," from happy + -ness. Meaning "pleasant and contented mental state" is from 1590s. Phrase greatest happiness for the greatest number was in Francis Hutcheson (1725) but later was associated with Bentham.

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maxim (n.)

early 15c., maxime, "an axiom, statement of a self-evident truth," from Old French maxime, from Late Latin maxima, shortened from phrases such as maxima propositio (Boethius), maxima sententarium "axiom," literally "greatest or chief premise, greatest among propositions" (one which is general and absolute), from fem. of maximus "greatest," from PIE *mag-samo-, superlative form of root *meg- "great."

The modern meaning "summary statement of an established or accepted proposition serving as a rule or guide, a proposition ostensibly expressing some general truth" is from 1590s.

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maximal (adj.)

"of the highest or maximum value," 1872, from Latin maximus "greatest" (see maximum (n.)) + -al (1). Related: Maximally.

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Gautama 

surname of the Buddha, from Sanskrit Gotamah, properly a patronymic, literally "descendant of the greatest ox," from superlative of gauh "ox, bull, cow."

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maximum (n.)

"the greatest amount, quantity, or degree," 1740, from French maximum and directly from Latin maximum (plural maxima), neuter of maximus "greatest," which is superlative of magnus "great, large, big" (of size), "abundant" (of quantity), "great, considerable" (of value), "strong, powerful" (of force); of persons, "elder, aged," also, figuratively, "great, mighty, grand, important," from PIE *mag-samo-, superlative form of root *meg- "great."

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utmost (adj.)

Old English utmest (Anglian) "outermost," double superlative of ut "out" (see out (adv.)) + -most. Meaning "being of the greatest or highest degree" is from early 14c.

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anti-node (n.)

also antinode, 1872, "point of a vibrating string where the amplitude is greatest," from anti- + node. Later applied to other wave systems; at the anti-node the two waves cancel each other out.

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