The problem of constructing three circles tangent to each other within a triangle was posed by the 18th-century Japanese mathematician Ajima Naonobu prior to the work of Malfatti, and included in an unpublished collection of Ajima's works made a year after Ajima's death by his student Kusaka Makoto. Even earlier, the same problem was considered in a 1384 manuscript by Gilio di Cecco da Montepulciano, now in the Municipal Library of Siena, Italy. studied a special case of the problem, for a specific isosceles triangle.