Notes on Complete Book of Mathematics Vol.10: Geometry

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 39)


The Complete Book of Mathematics is the most comprehensive treatise of mathematics in the Edo Period of Japan. The 20 volume book is about 900 sheets or 1800 pages long. Seki Takakazu (1642?–1708), Takebe Kataakira (1661–1721) and Takebe Katahiro (1664–1739) spent 28 years (1683–1711) in writing it. Unfortunately, the Book has never been published as a whole. Except for Volume 4 we reproduce here only one volume, Volume 10 Geometry, which is the first volume on geometry in the treatise. They develop here the basics of the plain geometry as algebraic relations among line segments which specify the geometric objects in question. This is exactly the same standpoint as René Descartes’ (1596–1650) in his Géométrie (1637). At the end of the volume they discuss algebraic relations among the sides and diagonals in a general pentagon and hexagon by making use of Seki’s theory of resultants.


Algebraic Relation General Quadrilateral Pythagorean Theorem Section Foundation Gauss Integer 
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© Springer Japan 2013

Authors and Affiliations

  1. 1.Graduate School of Mathematical Sciencesthe University of TokyoTokyoJapan

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