1,721,057 research outputs found
On the Sanpō Taisei, an interim version of the Taisei Sankei, established in ca.1695 (Study of the History of Mathematics 2021)
No full textThe Taisei Sankei is an encyclopaedic work of Japanese mathematics compiled by three mathematicians, Seki Takakazu and his disciples, the Tatebe brothers. The compilation project began in 1683 on the initiative of the younger Takebe, Katahiro, and was completed by the elder Takebe, Kata'akira, in 1710. An interim edition in twelve volumes, entitled Sanpō Taisei, was drafted by Katahiro around 1695, but no manuscript of this edition survives. However, it is important to study the Sanpō Taisei because it is considered to be the culmination of Seki Takakazu's mathematical works. By studying the mathematical manuscripts left behind by the three mathematicians, this paper deduces which volumes of the Taisei Sankei succeed the Sanpō Taisei and how the Sanpō Taisei was compiled. We also identify the author(s) of the four manuscripts Kyūketsu Henkeisōkai, Kyūseki, Kaihō Sanshiki and Kaihō whose contents are common to some parts of the Taisei Sankei
Cubic equations in the casus irreducibilis (Study of the History of Mathematics 2022)
No full textWhen a real cubic equation has three distinct real roots, it is called the casus irreducibilis or the case of irreducible. To find the roots of such equations using Cardano's formula, it is necessary to extract cube roots of imaginary binomials. In this paper we review remarkable works from Cardano to Euler on the solution of cubic equations in the casus irreducibilis and on the extraction of the cube roots of imaginary binomials. In it we give new proofs of Girard's method of constructing three real roots of a cubic equation and of Newton's method of extracting cube roots of imaginary binomials
On Kai Kendai no Ho (Study of the History of Mathematics)
No full text"Study of the History of Mathematics". August 27～30, 2012. edited by Tsukane Ogawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.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
On Kaihō Honhen no Hō edited by Seki Takakazu (II) (The study of the history of mathematics 2016)
No full text"The study of the history of mathematics 2016". August 29～September 1, 2016. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.We discuss tekijin-shokyū (method of vanishing a polynomial and its certain derivative), shokyū-taisū (in literal, replacement of each coefficient to obtain a root), and shishō-kyokusū (in literal, find the common root of a given polynomial and its derivative ) in Kaihō honhen no Hō (Methods of Equation Modifications) re-revised by Seki Takakazu in 1685. We show that the algorithm of taisū consists of five procedures of Kaihō honhen no Hō. We declare tekijin-renkyūhō, which has been considerd to be purposeless, is available to use taisū. We also demonstrate that tekijin-renkyūhō and tekijin-karenkyūhō provide useful information on roots of real cubic and quartic equations, respectively
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