Seki, Founder of Modern Mathematics in Japan: A Commemoration on His Tercentenary

Front Matter....Pages i-xxvi
Front Matter....Pages 1-1
Seki Takakazu, His Life and Bibliography....Pages 3-20
Some Reflections on Main Lines of Mathematical Development....Pages 21-30
Babylonian Number Theory and Trigonometric Functions: Trigonometric Table and Pythagorean Triples in the Mathematical Tablet Plimpton 322....Pages 31-47
Archimedes in China: Archimedes and His Works in Chinese Literature of the Ming and Qing Dynasties....Pages 49-62
The Nine Chapters on the Mathematical Procedures and Liu Hui’s Mathematical Theory....Pages 63-88
On the Alternative Algorithm of the 7th Problem in the Sea Island Mathematical Canon....Pages 89-92
A Comparative Study on Traditional Mathematics of Korea and Japan....Pages 93-104
The Axes of Mathematical Methodology in the Song and Yuan Dynasties: The Construction of Mathematical Models....Pages 105-117
The Suanxue Qimeng and Its Influence on Japanese Mathematics....Pages 119-132
Power Series Expansions in India Around A. D. 1400....Pages 133-147
An Early Japanese Work on Chinese Mathematics in Vietnam: Yoshio Mikami’s Study of the Vietnamese Mathematical Treatise Chi Minh Toan Phap ....Pages 149-172
The Jinkōki of Yoshida Mitsuyoshi....Pages 173-186
Résumé of Works on Mathematics of Seki Takakazu....Pages 187-192
Seki Takakazu’s Measuring Process of the Volume of Solids Derived from Spheres....Pages 193-206
Seki Takakazu’s Method on the Remainder Problem....Pages 207-218
Seki Takakazu’s Method of Calculating the Volume of Solids of Revolution and His Mathematical Object....Pages 219-228
Leibniz’s Theory of Elimination and Determinants....Pages 229-244
Algebra, Elimination and the Complete Book of Mathematics....Pages 245-274
Some Questions and Observations Around the Mathematics of Seki Takakazu....Pages 275-297
Ming Antu and His Power Series Expansions....Pages 299-310
Front Matter....Pages 1-1
Standing on the Shoulders of the Giant Influence of Seki Takakazu on Takebe Katahiro’s Mathematical Achievements....Pages 311-329
Takebe Katahiro’s Algorithms for Finding the Circular Arc Length....Pages 331-342
The Method of Successive Divisions by Takebe Katahiro and Nakane Genkei....Pages 343-352
Manuscripts in the Edo Period: Preliminary Study on Manuscripts Written by Seki Takakazu....Pages 353-355
Influence of European Mathematics on Pre-Meiji Japan....Pages 357-374
On Contemporary Mathematics in Vietnam....Pages 375-383
Front Matter....Pages 385-385
Notes on Complete Book of Mathematics Vol. 4: Three Essentials....Pages 387-392
Complete Book of Mathematics Vol. 4: Three Essentials, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Fumiaki Ozaki and Hikosaburo Komatsu....Pages 393-435
Seki’s Trilogy: Methods of Solving Explicit Problems, Methods of Solving Implicit Problems and Methods of Solving Concealed Problems....Pages 437-440
Methods of Solving Explicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu....Pages 441-456
Methods of Solving Implicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu....Pages 457-468
Methods of Solving Concealed Problems, by Seki Takakazu, collated by Hikosaburo Komatsu....Pages 469-494
Notes on Complete Book of Mathematics Vol.10: Geometry....Pages 495-498
Complete Book of Mathematics Vol. 10: Geometry, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Hikosaburo Komatsu....Pages 499-551
Seki’s Theory of Elimination as Compared with the Others’....Pages 553-574
Back Matter....Pages 575-588