Maxim, n.
Etymology: [F. maxime, L. maxima (sc. sententia), the greatest sentence, proposition, or axiom, i. e., of the greatest weight or authority, fem. fr. maximus greatest, superl. of magnus great. See Magnitude, and cf. Maximum.]
1. An established principle or proposition; a condensed proposition of important practical truth; an axiom of practical wisdom; an adage; a proverb; an aphorism. 'T is their maxim, Love is love's reward. Dryden.
2. (Mus.)
The longest note formerly used, equal to two longs, or four breves; a large.
Syn. -- Axiom; aphorism; apothegm; adage; proverb; saying. See Axiom.
Shades of meaning
Fernald has no entry of its own for maxim; he lists it under proverb.
Where he writes about it:
Precept is a command to duty; motto or maxim is a brief statement of cherished truth, the maxim being more uniformly and directly practical; "God is love" may be a motto, "Fear God and fear naught," a maxim. — from proverb