Complete Book of Mathematics Vol. 4: Three Essentials, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Fumiaki Ozaki and Hikosaburo Komatsu

Abstract

Volume 4 is named Three Essentials [三要, san’yō] and composed of three sections. Each section starts with a general statement followed by problems, which serve as examples for the general statements. Section 1 is named Symbols and Figures [象形, shō-kei] and divided into (abstract) symbols [(抽) 象, (chū)shō] (Problems 1 – 6), (concrete) symbols [(表) 象, (hyō)shō] (Problems 7 – 11), planar figures [平形, heikei] (Problems 12 – 16), and solid figures [立形, ryūkei] (Problems 17 – 21). Section 2 is named Flow and Ebb [満干, man-kan] (Problems 22 – 37). Section 3 is named Numbers [数, sū] and divided into two subsections: the first subsection is named Provisional and Stationary [動静] numbers (Problems 38 – 47). The second subsection deals with two kinds of finitely presented numbers [整数], i.e., Whole [全] numbers (≒ finite decimal fractions) (Problems 48 – 52) and Complicated [繁] numbers (≒ fractions) (Problems 53 – 57), and two kinds of Inexhaustible numbers [不尽], i.e., Residual [畸] numbers (≒ algebraic numbers) (Problems 58 – 62) and Degraded [零] numbers (≒ transcendentals and observed constants) (Problems 63 – 67).