宋元明代数学書と「阿蘭陀符帳」 : 蘇州号碼の日本伝来 (数学史の研究)

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1 $\backslash 4$ $\grave$ REJECT}$g$\mathscr{X}\mathscr{L}$ : Chinese Mathematical Arts in the Song, Yuan and Ming Dynasties and thedutch Numerals -The Suzhou Numerals Transmitted into Japan (JOCHI Shigeru) (LIU Bowen) 2 HAO (CHANG Hao) 3 lntemational Center, Osaka Kyoiku University Graduate lnstitute of Japanese Studies, National Kaohsiung First Univ of Sci And Tech Department of Applied Japanese, I-Shou University I $A$ (1275 ) ( 1299 ) 13 ( 1592 ) 16 ( ) 3 $\ovalbox{\tt\small REJECT}$lAjF$\not\in$X $\Re$ # $*\mathscr{z}$ $\varpi$f# $\ovalbox{\tt\small ( 1627 ) (C) $NSC S-327\cdot\omega 1-MY3$ 1 jochi\copyright ccosaka-kyom $\iota$acjp $hnp:/mw$osaka-kyoim$\iota$acjp $\sim$j $\alpha$h 2 lbw\copyright cmlsnkfistkedutw 3 ch3hao@gma com $i1$ 4 (199312) - ( ) (1993) Jl :6143 ( 1641 ) ( ) ( ) $([\alpha 1;1994) $ $:3$ Jl $178$ 004) Jl :15-22 ( 1673 ) ( ($MX\infty$ Ri$\alpha$i ) 1613 $)$ ( )

2 $10_{\text{ }}$ $\grave$ $\gravearrow$ 129 (1928;1954) (1930;1954) $**$ (1944) (1964) 5 ( ) ) $\circ$ $m$ $)$ ( 1592 ( ) ( ) ( 1675 ) 9 ( ) ( ( ) ( ) 1757 ) ( ) $ \grave $ ) 5 (1964) ( 1712 ) 10 (1877) J ( ( 1781 ) ) ( ( ) Jl :12) 7 (1935) $\underline{u}vol1:2$ [r 8 (2003) (2003) (2004) (2007) (2007) $\circ$ 9 10

3 $\mathscr{n}^{-\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}-}ffl^{13}$ $\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}$ $0^{1}$ 130 Big5 ( 1 ) $0$ $\sim$ 6 $8$ $9$ 5 $5\sim 9$ f$ =$ ( ) [ ( 1573 ) ( ) ( 1592 ) (?) H $ $ $\searrow$ 12 : $\ovalbox{\tt\small REJECT}$? J ( 1798 ) 1 ( ) ( )

4 131 ( ( ) 1893 ) $\Re^{m}) ) $ ( ) 14 ( 1524 ) $15$ $(1019\cdot 1086)$ $4$ $7$ ( ) $19152\div 56=19152\div 4\div 14=342$ $4788\div 14=342$ ( ) l\={o} (1944) : ( ) (1978;2008) 7 4 $(-)$ 17 ( ) (1993) I t 2:396

5 }*\subset)$ $\lrcorner r^{arrow}$ $\S^{\S}\S^{2}\frac{\prime}{;i}\backslash$ $\subset_{\bigwedge_{\vee}\cdot\bigwedge_{\prime}})k^{\gamma}\backslash ")_{:_{d^{l=}})}^{p_{t}\triangleleft}\re^{\searrow}:c^{\backslash }: _{-d^{t}}\{i\overline{\not\in}\backslash \iota^{t}[\theta \cdot$ $( \wedge \bigwedge_{-}r )\vee\cdot$ $\vee^{-}\phi^{\zeta j_{t})}\ovalbox{\tt\small REJECT}_{\vee}\}\^{\otimes 1}(rk^{\vee}$ $\{j\}_{-}:\ovalbox{\tt\small REJECT}_{\backslash }^{\wedge^{\otimes_{o_{\wedge}^{\rangle}}}}:_{\bigwedge,}$ $-$ $\{$ $)-\},\delta^{\theta\vee}$ $arrow\tau$ $\sim\backslash$ $i\downarrow$ $ $ $\Re^{-}$ $\#^{\_{t}}\wedge$ $\text{ _{}\overline{t}}:\overline{i}=/$ $ r\}j^{\gamma}j$ $\rangle$ $4788\div 14$ $($ $5\mathfrak{B}(47\cdot 12(3\cross 4))$ $(4\cross 4))$ ( ) $\ovalbox{\tt\small REJECT} \mathscr{x}^{-}4$ 5, $\frac{\text{ }}{}--$ $\vee\sim$ $\S\int$ $\ovalbox{\tt\small REJECT}$, $* )$ $i $ : $-$ $?$ $\sim$ 3 ( 418 $5^{}$ 6 $\mathfrak{u}i$ 721 ( ) ( 1573 ) ( ) $]$ 5 ( ) \={o} 5 ( 1439 ) 18 ( 1884 ) 19 ( ) $1$ $2$ 20 ( ) $2$ $1$ 21 ( 1898 ) (1953) (1954)

6 $\} _{l}^{)}$ $0$ 1 2 $ $ 1766) $\sim$ VI 1930 % 2 $Q$ $i$ $t$; $\aleph$ ff V 3) $\cdot$ (1706 (1953) (1970) (20074) (20079) ! (20079) 25 ( ) (1924) I Jl : (2002) $htt\mathfrak{v}://www$ntledu aso? $\mathfrak{v}$id $=$3&mkev $tw/\mathfrak{v}\iota iblish/\mathfrak{v}ublish$ $=39_{o}$ $(0028X]912$ $2$ $20$ $)$ ht $://www$libkobe-u$ac\cdot/roducts/okeisho/mokurokuhtml$)

7 $( \mathscr{h}_{\ovalbox{\tt\small REJECT}}^{\underline{ }}g^{\underline{\langle}}\frac{\dot h_{l}^{*}}{\ovalbox{\tt\small REJECT}}27$ 134 $\mathscr{n}^{\lambda}\mathscr{h}^{\lambda}\mathscr{n}\dot{\text{ }}B^{-}4$ $10$ (1798) ) 9 ( 1798 ) ( ( ) 1893 ) $\backslash$ 5 ( ) $\ovalbox{\tt\small REJECT}$ & $\backslash$ $=$ W $\nearrow\backslash$ J $\backslash$ $(1824?-1898)$ ( ) ( ) 3

8 $\dagger\pm$ $arrow$ $\equiv$ 135 VI $+)) \iota $ (5 ) 5 (1720) 5 (1788 ) 8(1788) 2 ( ) 1789 ) ( ) $\sim$ ( ) ( ) ( ) Jl (1721 ) ) 5 (1720) ( 10 (1798) ) ( ) (2010) - (1658) 1677 p31 5 p34 (1896: $\overline{\mathbb{r}}$ 1918, 1960, 1981) [ : (1947;1984:1999) (1925;1954) k $*$ :82-88 (1933;1954) : (1928;1954) (1933:1954) (1930;1954) :1-21 (1933;1954) $($1958: $1\mathfrak{B}8)$ j 2:8-18 (IOP8) vol10:3\ o2-373 (1976) $\ovalbox{\tt\small REJECT}$ 4 ( ) (1998) $\sim$ $ $r $10$ : ( ) 2 : $\sim$ (1937) 2 :

9 $\dagger\pm$ 136 (1941) : ( ) (1944) (r : I $\ovalbox{\tt\small REJECT})$ (1970) : ( ) $\dagger\pm$ (1980) : $ffi\gamma$ (1944) j 3-1: j $\sim$ ( ) (1954:1979) I 5 : (1953) :5743 (1954) m 26:13-19 $\varpi$f $\ovalbox{\tt\small REJECT}$ $28:1-12$ (1954) I j 29:818 (1954) II (1955) $m$ M 34:12-22 (1955) 16 (1) j j 36:17-22 (1956) 16 (2) M $38:1\alpha 16$ (1957) 16 (3) j 39:7-14 (1967) - M 5 $\sim$2:1-39 NeedhamJ (1993) $\mathbb{f}$oe (1954-) SCtence and Cyiltzaoin in Chum Cambridge: Cambndge University Pless : $(19\mathfrak{B})$ : $\approx ffi$ ) (1974) $\sim$ : (1964) [ - : (1960) j $7:4\alpha 44$ (1%5-1970) fftll : (1966:1985) ( ) : (1987) $*1:1-19$ (1966) : (1970) : (1978) : ( ) (197$2 8) : $\infty$ (1980) : ( 577) ( ) (1982) $\dagger\pm$ : (1983) ffiffl] : $\dagger\pm$ (1987) : (1988) ) : ( (1990) : (1993) ne Irjluence ofchunese MathemattcalArts on Seki Kowa PhD Thesis ofunivqsity oflondon $\dagger\pm$ $7(1\Re 8)A:$ 32&334 (1996) ( ) 4 : 3346 ( ) 28 P 12

10 137 (1999) $)$ ( ) (1(9993) $)$ [ ( ) : : (2002) Jl 1317:71-79 (20033) 1:1-24 (20049) ( ) $1392:4G59_{O}$ $(2\alpha)5:2(W)$ : (20074) - ( ) $\sim$ 1546: 1-20 $(2\omega 79)$ $32:65\mathfrak{X}2$ g l ( ) (1993) $\mathscr{q}$ 5 ( ( ) : (1993) - [ ) $ $ ( ) (1994) J186: : $(2\alpha)2\cdot 3)$ ( ) ( ) $48\cdot 4:63-8l9\cdot 1:99\cdot 110$ (2005) ( ) (2007) : Chinese Mathematical Arts in tbe Song Yuan and Ming Dynasties and the Duoeh Numerals -The Suzhou Numerals Transmitted into Japan JOCHI Shigeru, LIU Bowen, CHANG Hao Abstract Yang Hui $(13_{C})$ used the Suzhou Numerals at the Yang $Hui$ Simra in 1275 Chinese mathematicians used the counting rods, then Chinese scientists developed the Suzhou Numerals fiom them Then Chinese mathematicians in the Ming dynasty, Xu Xinlu (about 1573), Cheng Dawei ( ) used two $\Psi pes$ ofthe Suzhou Numerals, then Chinese merchants used them for their business Chinese melchants in the $20^{th}$ century in main land, Taiwan and Hong Kong used Cheng Dawei s type Then Japanese mathematicians used the similar to Xu Xinlu s ype in the century, and their name was the $18^{th}$ $:D\mathfrak{W}h$ Numerals in the &$\nu\nu$o Yorozu Toriatslme Nikki (Shike Fukufusa, 1798) Japanese merchants used them in the $19^{ffi}$ century at least $TheIefo\ddagger e$ the author conclude tha$\ddagger$ the influenoe of Cheng Dawei, that is to say, the Suanfa Tongzong (Cheng Dawei, 1592) was limited in the end ofedo period Key Words; the Suzhou Numerals, the Dutch Numerals, the Yang HuiSuanfa(Yang Hui, 1275),, the Suanfa Tongzong(Cheng Dawei, $1592h$ the Sanyo Yorozu Tonalsume Nikki (Shike Fukufhsa, 1798)

42 1 ( ) 7 ( ) $\mathrm{s}17$ $-\supset$ 2 $(1610?\sim 1624)$ 8 (1622) (3 ), 4 (1627?) 5 (1628) ( ) 6 (1629) ( ) 8 (1631) (2 ) $\text{ }$ ( ) $\text{

$42 1 ( ) 7 ( ) $\mathrm{s}17$ $-\supset$ 2 $(1610?\sim 1624)$ 8 (1622) (3 ), 4 (1627?) 5 (1628) ( ) 6 (1629) ( ) 8 (1631) (2 ) $\text{ }$ ( ) $\text{$ 26 [\copyright 0 $\perp$ $\perp$ 1064 1998 41-62 41 REJECT}$ $=\underline{\not\equiv!}\xi*$ $\iota_{arrow}^{-}\approx 1,$ $\ovalbox{\tt\small ffl $\mathrm{y}