Latin focus: hearth, fireplace, the home's center. Kepler used it in 1604 for the point where refracted light converges, the hearth of the lens, and mathematics kept it (foci of an ellipse). The abstract sense, center of attention, is 19th century. Fireplace, focal, fuel (through Old French fouaille) share the hearth.
The household logic: Rome's hearth was shrine, kitchen, and parliament, the family's converging point. When a culture needed a word for where things gather, it reached for the fireplace twice, once for light, once for attention.
The optical physics reversed: a lens focuses light to a point hot enough to burn, burning glasses were the ancient weapon-toy. Focus thus carries fire in both directions, the hearth that receives the family and the point that ignites, attention as combustion.
Why does every culture put its fire in the middle and call everything else peripheral?