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Ajima is credited with introducing calculus into Japanese mathematics. The significance of this innovation is diminished by a likelihood that he had access to European writings on the subject. Ajima also posed the question of inscribing three mutually tangent circles in a triangle; these circles are now known as Malfatti circles after the later work of Gian Francesco Malfatti, but two triangle centers derived from them, the Ajima-Malfatti points, are named after Ajima.
Ajima was an astronomer at the Shogun's Observatory (Bakufu Temmongaki).