figure (v.) Look up figure at
late 14c., "to represent" (in a picture); see figure (n.). Meaning "to shape into" is early 15c.; "to picture in the mind" is from c.1600; "to make an appearance" is c.1600. Meaning "work out a sum" is from 1833, American English. Related: Figured; figuring.
figure (n.) Look up figure at
c.1200, "numeral;" mid-13c. as "visible appearance of a person;" late 14c. as "form of anything," from Old French figure (10c.) "shape, body, form, figure; symbol, allegory," from Latin figura "a shape, form, figure," from PIE *dheigh- "to form, build" (see dough).

Philosophical and scientific senses are from Latin figura being used to translate Greek skhema. The rhetorical use of figure dates to late 14c.; hence figure of speech (1824). Figure eight as a shape was originally figure of eight (c.1600).