Izeki Tomotoki (井関 知辰?) of Osaka publishes Sampo-Hakki (算法発揮), in which he gives the resultant and the Laplace formula of the determinant for the n×n case. At about this date, Tanaka Yoshizane (田中 由真?) also describes and applies the resultant, in Sampo-Funkai (算法紛解).
French physicist Denis Papin, while in Leipzig and having observed the mechanical power of atmospheric pressure on his 'digester', builds a working model of a reciprocatingsteam engine for pumping water, the first of its kind, though not efficient.