figure (v.) Look up figure at Dictionary.com
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 (see figure (n.)). 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.
figure (n.) Look up figure at Dictionary.com
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 *dheigh- "to form, build" (see dough).

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." The rhetorical use of figure, "peculiar use of words giving meaning different from usual," dates to late 14c.; hence figure of speech (by 1704). Figure-skating is from 1835. Figure eight as a shape was originally figure of eight (c.1600). From late 14c. as "a cut or diagram inserted in text."