What the word does in English now
In present-day English, figure is a crowded word. As a noun it can be a written numeral, an amount of money, a geometric shape, a diagram in a book, the outline of a human body, a well-known person, or a marked way of using language. The verb is no narrower. You can figure a likeness in clay, figure in an event, figure that rain is coming, or figure out a bill. Those uses look unrelated until the older idea of a made form is put back at the center.
A medieval borrowing, not a native survival
English did not inherit figure from Old English. It entered during the Middle English centuries as a loan, chiefly through Old French figure, itself from Latin figūra. Historical dictionaries do not agree on a single first year. One standard etymological account places English uses around 1200, with the written numeral among the earliest senses. The Oxford English Dictionary’s earliest citation is a little later, about 1225, in the religious guide known as the Ancrene Riwle. The gap is small. What is not in dispute is the period: this is a thirteenth-century import, not a Germanic word that had been in the language all along.
The OED also treats the noun as having more than one immediate parent: partly French, partly Latin. That split is ordinary for medieval learned vocabulary. A clerk who already knew Latin figūra from school or from the Church could take the French form in everyday prose, or lean on the Latin he had already met. Old French had already widened the word. By the tenth century it could mean a shape or a body, the form of a word, a symbol or allegory, and a figure of speech.
The English verb is later. Evidence for figure as a verb begins in the late fourteenth century, including the early Wycliffite Bible. It comes from Old French figurer and Latin figūrāre, to form or shape: first to represent in painting or sculpture, and also to have a certain appearance.
The origin of the word figure, then, is a Romance path into Middle English, with Latin standing behind French and sometimes beside it.
A result noun from a verb of molding
Latin figūra is not a primitive root. It is a result noun on the verb fingere (first person fingō, perfect fīnxī, participle fictus), which meant to shape, fashion, or knead, the work of a potter or a modeler as much as of a writer who invents. The suffix is the familiar -ūra that names the product of an action, so the noun is, in outline, the thing obtained by shaping. Late Latin also used it for a sketch or drawing.
Behind fingere lies a reconstructed Proto-Indo-European root, given in handbooks as dheigh- or dʰeyǵʰ-, with the sense to form, build, or knead. That reconstruction is a scholarly hypothesis, not a chain of documents, but the Latin, Greek, and Germanic descendants line up in a consistent way. From the same Latin verb, on other routes, English later took fiction, figment, feign, and effigy. Those are siblings of figure, not children of the noun. A native English cousin is dough, from Old English dāg, the mass that is worked by hand. Greek teîkhos, a wall, and Sanskrit deha, the body as something formed, are usually listed in the same family.
Medieval scholars also used Latin figura as a standing equivalent when they translated Greek schēma. That habit helped English pick up technical senses in geometry, rhetoric, logic, and, once printing spread, the labeled diagram in a text.
From a made shape to numbers, bodies, and speech
The numeral sense is old in English, which can surprise anyone who first hears a person’s physique. Arabic numerals were moving through Western Europe in the same centuries. A written character for a number is a made shape that stands for something else, so the leap from form to digit is smaller than it looks. From the digit came the amount (a large figure) and, much later, an American English verb meaning to work a sum, recorded in the 1830s. From that arithmetic use came the colloquial sense, a few years later, of calculating or expecting an outcome: you figure it will cost more.
The bodily and pictorial cluster is almost as old. By the mid-thirteenth century the word could mean a person’s visible appearance. By the late fourteenth it named the tangible form of a thing, a cut or diagram inserted in a text, and a human body as art represents it. The later everyday sense of physique, and the public sense of a notable person, grow from that same outline that can be seen and judged. To cut a figure is to make an appearance of a certain kind. Figurehead, first the carved ornament under a ship’s bowsprit in the eighteenth century, later named a leader who is displayed rather than in charge.
Rhetoric took the word in the late fourteenth century for a marked way of using language. The compound figure of speech is recorded in the mid-sixteenth century. Geometry kept the older idea of lines that compose a shape. Ice skating borrowed it in the nineteenth century from the patterns, including the figure eight, that skaters traced to show control. Compulsory figures later left international competition, but the name figure skating stayed.
What looks like a jumble of dictionary senses is mostly one Latin idea stretched: a form produced by making, whether the product is clay, a digit, a body, a diagram, or a turn of phrase.
The kitchen cognate
The most concrete reminder of that history is not the French loan itself but its Germanic cousin dough. At a long distance both names point to a mass that has been worked into a form. Figure kept the abstract side of that craft; dough kept the kitchen. Once that pair is in view, the path from a molded shape to a numeral, and from a numeral to figuring a total, reads less like a pile of accidents and more like a single word doing more and more of the same job.