Etymology
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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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maximist (n.)

"one who has a fondness for quoting or using maxims," by 1827, from maxim + -ist.

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aphorism (n.)

1520s, "concise statement of a principle" (especially in reference to the "Aphorisms of Hippocrates"), from French aphorisme (corrected from Old French aufforisme, 14c.), from Late Latin aphorismus, from Greek aphorismos "definition; short, pithy sentence," from aphorizein "to mark off, divide," from apo "from" (see apo-) + horizein "to bound" (see horizon).

General sense of "short, pithy statement containing a truth of general import" (e.g. "life is short, and art is long") is from 1580s in English. Distinguished from an axiom, which is a statement of self-evident truth; an epigram is like an aphorism, but lacking in general import. Maxim and saying can be used as synonyms for aphorism, but maxims tend to be practical and sayings tend to be more commonplace and have an author's name attached.

[F]or aphorisms, except they should be ridiculous, cannot be made but of the pith and heart of sciences ; for discourse of illustration is cut off ; recitals of examples are cut off ; discourse of connexion and order is cut off ; descriptions of practice are cut off. So there remaineth nothing to fill the aphorisms but some good quantity of observation : and therefore no man can suffice, nor in reason will attempt, to write aphorisms, but he that is sound and grounded. [Francis Bacon, "The Advancement of Learning," 1605] 
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gnome (n.2)

"short, pithy statement of general truth," 1570s, from Greek gnōmē "judgment, opinion; maxim, the opinion of wise men," from PIE root *gno- "to know."

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pom-pom (n.)
"Maxim automatic gun," 1899, of imitative origin, soldiers' slang from the Boer War. For the ornamental tuft, see pompom.
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dicte (n.)

also dict, "a saying, maxim, statement," late 14c., from Latin dictum "a thing said" (see dictum). A word long obsolete, but it figures in what is probably the first book printed in English, Caxton's issue of Anthony Woodville's "Dictes and Sayings of the Philosophers."

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dictate (n.)
Origin and meaning of dictate

1590s, "positive order or command;" 1610s "authoritative rule, maxim, or precept," from Latin dictatum "a thing said, something dictated," noun use of neuter past participle of dictare "say often, prescribe," frequentative of dicere "to say, speak" (from PIE root *deik- "to show," also "pronounce solemnly").

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saw (n.2)

[proverb, saying, maxim], Middle English saue, at first in a general sense, "what is said, talk, words," from Old English sagu "saying, discourse, speech, study, tradition, tale," from Proto-Germanic *saga-, *sagon- (source also of Middle Low German, Middle Dutch sage, zage, German Sage "legend, fable, saga, myth, tradition," Old Norse saga "story, tale, saga"), from PIE root *sek(w)- "to say, utter" (see say (v.)).

The surviving specific sense of "proverb, saying, maxim" is by late 13c. "[A] contemptuous term for an expression that is more common than wise" [Century Dictionary].

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gnomic (adj.)

"full of instructive sayings," 1784, from French gnomique (18c.) and directly from Late Latin gnomicus "concerned with maxims, didactic," from Greek gnōmikos, from gnōmē "a means of knowing, a mark, token; the mind (as the organ of knowing), thought, judgment, intelligence; (one's) mind, will, purpose; a judgment, opinion; maxim, the opinion of wise men," from root of gignōskein "to come to know," from PIE root *gno- "to know." Gnomical is attested from 1610s.

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precept (n.)

"commandment or direction given as a rule of action," especially "an injunction as to moral conduct," late 14c., from Old French percept, percet (12c.) and directly from Latin praeceptum "maxim, rule of conduct, order," noun use of neuter past participle of praecipere "give rules to, order, advise," literally "take beforehand," from prae "before" (see pre-) + capere (past participle captus) "to take," from PIE root *kap- "to grasp." For change of vowel, see biennial. Related: Preceptive; preceptory.

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