『解見題之法』について (数学史の研究)

Abstract

Unsolved problems of Kai Kendai no Ho (Methods of Solving Explicit Problems) and Kai Indai no Ho (Methods of Solving Implicit Problems) are discussed. It is shown as follows: 1. Seki Takakazu finished off the editing of Kai Kendai no Ho between September 1683 to June 1685 and the editing of Kai Indai no Ho between June to August 1685 according to the lunisolar calendar. 2. Seki edited both manuscripts in order to prepare for compiling Sanpo Taisei (Complete Collection of Mathematics) which was projected by Seki and his pupils Takebe Katahiro and Takebe Kata-akira. 3. Takebe Katahiro used both manuscripts for editing Sanpo Taisei, which was assembled in around 1695. 4. Yamaji Nushizumi probably transcribed manuscripts of Kai Kendai no Ho and Kai Indai no Ho in April 1726. Yamaji did not edit both manuscripts. These manuscripts were probably brought to Yamaji by his master Nakane Genkei who was a pupil of Takebe Katahiro. 5. The subject of Kai kendai no Ho is not to propose bosho ho (byscript method =Seki's notation system) but to apply ken dai (using not equations but addition, subtraction and multiplication) to the length, the area and the volume of figures.