Etymology
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figure (n.)

c. 1200, "numeral;" mid-13c., "visible appearance of a person;" late 14c., "visible and tangible form of anything," from Old French figure "shape, body; form of a word; figure of speech; symbol, allegory" (10c), from Latin figura "a shape, form, figure; quality, kind, style; figure of speech," in Late Latin "a sketch, drawing" (from PIE root *dheigh- "to form, build").

Philosophical and scientific senses are from use of Latin figura to translate Greek skhema. Meaning "lines forming a shape" is from mid-14c. From mid-14c. as "human body as represented by art;" late 15c. as "a body, the human form as a whole."  From late 14c. as "a cut or diagram inserted in text."

The rhetorical use of figure, "peculiar use of words giving meaning different from usual," dates to late 14c.; hence figure of speech (1550s). Figure-skating is from 1835, so called for the circular patterns skaters formerly made on the ice to demonstrate control; they were dropped from international competition in 1990, but the name remains. Figure eight as a shape was originally figure of eight (c. 1600).

figure (v.)

late 14c., "to represent" (in painting or sculpture), "make a likeness," also "to have a certain shape or appearance," from Old French figurer, from Latin figurare "to form, shape" (from PIE root *dheigh- "to form, build"). Meaning "to shape into" is c. 1400; from mid-15c. as "to cover or adorn with figures." Meaning "to picture in the mind" is from c. 1600. Intransitive meaning "make an appearance, make a figure, show oneself" is from c. 1600. Meaning "work out a sum" (by means of arithmetical figures) is from 1833, American English; hence colloquial sense "to calculate upon, expect" (1837). Related: Figured; figuring.

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Definitions of figure
1
figure (n.)
a diagram or picture illustrating textual material;
Synonyms: fig
figure (n.)
alternative names for the body of a human being;
Synonyms: human body / physical body / material body / soma / build / physique / anatomy / shape / bod / chassis / frame / form / flesh
figure (n.)
one of the elements that collectively form a system of numeration;
Synonyms: digit
figure (n.)
a model of a bodily form (especially of a person);
he made a figure of Santa Claus
figure (n.)
a well-known or notable person;
she is an important figure in modern music
Synonyms: name / public figure
figure (n.)
a combination of points and lines and planes that form a visible palpable shape;
figure (n.)
an amount of money expressed numerically;
a figure of $17 was suggested
figure (n.)
the impression produced by a person;
he cut a fine figure
a heroic figure
figure (n.)
the property possessed by a sum or total or indefinite quantity of units or individuals;
the figure was about a thousand
Synonyms: number
figure (n.)
language used in a figurative or nonliteral sense;
Synonyms: trope / figure of speech / image
figure (n.)
a unitary percept having structure and coherence that is the object of attention and that stands out against a ground;
figure (n.)
a decorative or artistic work;
Synonyms: design / pattern
figure (n.)
a predetermined set of movements in dancing or skating;
she made the best score on compulsory figures
2
figure (v.)
judge to be probable;
Synonyms: calculate / estimate / reckon / count on / forecast
figure (v.)
be or play a part of or in;
How do the elections figure in the current pattern of internal politics?
Elections figure prominently in every government program
Synonyms: enter
figure (v.)
imagine; conceive of; see in one's mind;
figure (v.)
make a mathematical calculation or computation;
Synonyms: calculate / cipher / cypher / compute / work out / reckon
figure (v.)
understand;
He didn't figure her
From wordnet.princeton.edu