朝鮮?方程式論歷史

History and Pedagogy of Mathematics 2012
16 July – 20 July, 2012, DCC, Daejeon, Korea.
THEORY OF EQUATIONS IN THE HISTORY OF
CHOSUN MATHEMATICS
朝鮮?方程式論歷史
Sung Sa HONG
Department of Mathematics, Sogang University, Seoul, Korea
sshong@sogang.ac.kr
ABSTRACT
Theory of equations has been one of the most important subjects in the history of algebra. In
eastern mathematics, geometry was somehowcontained in the theory of equations and its number
systemwas restricted to the ?eld of rational numbers and hence its theory of equations has a com-
pletely di?erent history from the western counterpart. Chosun mathematics was strongly in?u-
enced by Chinese mathematics, but there were very fewChinese mathematics books available that
Chosun mathematicians could study. Despite such poor conditions, Chosun mathematicians suc-
ceeded in establishing a perfect theory of equations in the context of eastern mathematics, namely
the theory of polynomial equations and that of solving them.
This paper intends to illustrate this achievement of the theory of equations in Chosun dynasty
and its implications to the school mathematics.
Keywords: Chosun Mathematics, Theory of equations, TianYuanShu(天元術), ZengCheng-
KaiFangFa(增乘開方法), Park Yul(??, 朴繘, 1621–1668), Hong Jung Ha(???, 洪正夏, 1684–
?), Lee Sang Hyuk(???, 李尙爀, 1810–?), NamByung Gil(???, 南秉吉, 1820–1869).
1 Introduction and Chosun mathematics
In eastern mathematics, geometry for practical mensuration was carried out by the theory of right
triangles and areas of triangles so that it was studied in the setting of algebra. Unlike geometrical
algebra in ancient western mathematics, algebra got its position as a main subject in eastern mathe-
matics. Further, the theory of equations was a main area of the study of algebra. The other subjects like
mensuration including a good approximation of π, problems of ratios, extractions of square and cube
roots and systems of linear equations were completely settled in JiuZhang SuanShu(九章算術), which
was commented thoroughly by Liu Hui(劉徽) in the third century. Thus subsequent mathematicians
took interest mainly in the theory of equations. Theory of equations divides into two parts. One is
how to construct and represent equations fromgiven conditions and the other is how to solve them.
Both problems were resolved by mathematicians of Song(960–1279) and Yuan(1271–1368) dynasties.
For the former, they introduced TianYuanShu(天元術) for representing and operating polynomials
and then extended it to SiYuanShu(四元術) for polynomials with four indeterminates and hence they
could deal with polynomial equations together with systems of equations of higher degrees. For the
latter, the eastern mathematics has a completely di?erent approach from the western counterpart,