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Simplified etymology
Focus is Latin for “hearth” or “fireplace,” traditionally the center of a household. Johannes Kepler used it in Latin in 1604 as a geometrical term, perhaps likening the focus of a conic section to a source of light; English adopted this sense by the mid-17th century, followed soon afterward by the optical sense.
Etymology
Borrowed from Latin focus (“hearth, fireplace”); see there for more. Related to fuel. Kepler introduced the term into mathematics and the sciences in describing elliptical orbits of planets (quote from Nicholas Mee) : "One of the interesting properties of an ellipse is that if there were a light bulb at one focus, then all the light that it emits would reflect off the ellipse and converge at the other focus. This is why Kepler originally used the name focus for these points."