$\iota$ $\sim$ $(1909\cdot 1967)$ \beta \sim $\Gamma$ (1938) ( 16 (1941) ) 20 2 (1964) 4 \Gamma 5 \sim $\sim$ ( ) $T

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1 (Shigeru JOCHI) Graduate School of Japanese Studies, National Kaohsiung First Univers I ty of Science and Technology 1 1 \sim ( ) 1( 1299 ) 1( 1892 ) $\Gamma$ 1 ( ) 2 ( ) 1 (2005) 2 (1953) (1954)

$ty of Science and Technology 1 1 \sim ( ) 1( 1299 ) 1($

2 $\iota$ $\sim$ $(1909\cdot 1967)$ \beta \sim $\Gamma$ (1938) ( 16 (1941) ) 20 2 (1964) 4 \Gamma 5 \sim $\sim$ ( ) $T$ \beta J ( ) (1996) 4 (1964) \Gamma \sim I( 1712 ) 10 (1877) (\Gamma \sim ( 1781 ) ) ( (2005) :12) (1935) \Gamma \sim vol 1:2 7 \sim \sim

$\beta J ( 1795-1799 ) (1996) 4 (1964) \Gamma \sim 5 1712 7 I( 1712 ) 10$

3 \Gamma \sim \sim \sim 3 1 $t$ \Gamma \beta \sim \sim $\lceil$ ( : (1953) $:60_{\text{ }}$ )

$\beta \sim \sim $\lceil$$

4 4 1 \sim \Gamma \sim (1970) 8 $F$ \sim 5000 (1960) 4 $\Gamma$ (1958) 1 \Gamma ( ) \sim \Gamma \sim \Gamma \sim \beta 1 \beta $J\cdot f$ 2 (\Gamma ( 1712 ) $4$ $7$ ( )) 8 ($i$ (1970) 9 (1960) 10 (1958:1998) \langle \langle $\ovalbox{\tt\small REJECT}$ 11 $F$ \sim 4( ( ) ( ) (1974) \sim :349)

$(\Gamma ( 1712 ) $4$ $7$ ( )) 8 ($i$ (1970) 9 (1960) 10 (1958:1998) \langle$

5 $\iota\iota$ $I$? $\Gamma$ 5 $S$ $Jr$ (17 ) (17 ) 12 ( ) 13 ( ) 14 $(1533\cdot 1603)$ ( ) 15 (1950 ) 8 $T$ ( ) (? ) ( ) ( 16) 1 (1887 ) ( ) 17 2 (1439) 18 \Gamma $\Gamma$ (16 ) $\sim 19$ ( 1540 ) 11 $T$ \sim $I2$ (1970) $T$ $J47$ 13 \sim :109 \Gamma ( 1677 ) 4 ( ( ) ) \Gamma \sim (1675 ) ( : ) 15 (1980 ) ( ) 10 $ B$ ( ) \sim ( ) ht $tp;//www2$ ipcku kansai-u ac $in\gamma nikaldo/baichuan$ html

$) ( ) ( 16) 1 (1887 ) ( ) 17 2 (1439) 18 \Gamma $\Gamma$ (16 ) $\sim 19$ ( 1540 ) 11 $T$ \sim 1592 50 24$

6 $20_{\text{ }}$ 6 $2-$ \sim \sim 21 22

7 7 23 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 24

8 8 1 $\Gamma$ ( : ) \Gamma \sim 174cm 12cm ( ) 15cm 10cm 1 \Gamma \sim $\Gamma$ \sim \Gamma 1 \sim 1 2 \sim

$10cm 1 \Gamma \sim$

9 $\iota\iota$ 9 \beta 1\sim 3 ( ) ( ) $\Gamma$ ( ) 4 ( $\Gamma$ ) ( 1598 ) ( ) 10 ( ) : : g ? f$ 29 41

10 $:\iota$ ( ) \sim $\Gamma$ 1 1 (1578 ) (1373) 28 (1592) ( 1) ( 2\sim 9) : 11\sim 19 (1960) $72\div 18=4$ ( ) ( ) ( ) $0$ $7\cross 8=56$ 1 12 $6\cross 8=48$ $5\cross 8=40$ (1960) 1 29 (1960) o

$) ( ) 18 72 182 18 12 18 22 18 32 $0$ + 3 72 10 7 $7\cross 8=56$ 1 12$

11 \Gamma \Gamma (1912) ( ) ( ) 7 (1932) 13 (1938) \beta 1 16 (1941 ) \Gamma \sim 1 2 ( ) $t$ 1

$7 (1932) 13 (1938) \beta 1$

12 $\theta 1$ \sim ( 4) \beta \sim 13 ( 5) [ \sim ( ) \sim (1592?) 6 \Gamma (1676 ) 7 $\Gamma$ 1 (1716 ) il $l0$ ( ) 1800 ( ) 31 $\Gamma$ \sim $13$ $3$ 32 $\Gamma$ \sim 1 2 ( ( ) (1990) \sim :46) ( ) ( ) (1993) 7 \sim 2:

$) 6 \Gamma (1676 ) 7 $\Gamma$ 1 (1716 ) il $l0$ ( ) 1800 ( )$

13 $\Gamma$ 13 (1676 ) ( ) 7 ( 55 (1716) ) \Gamma \sim ( ) \beta 4 $\sim$ \beta ( ) \sim \Gamma 1 \sim (Unlcode ) 20 $\sim$ $\Gamma$ ( 1 ) \sim ( 1627 ) \Gamma

$1 20 5 \Gamma 1 \sim 21 1970 8 (Unlcode ) 20$

14 14 \sim $\Gamma$ \sim \Gamma \sim $\ovalbox{\tt\small REJECT}$ \sim $I$ ( ) ( ) 18 ( ) ( ) ( ) ( ) ( ) 11 (1958;1998) $rr$

$REJECT}$ \sim $I$ ( ) ( ) 18 ($

15 15 $\ovalbox{\tt\small \Gamma \sim 4 \sim \sim 7 REJECT}$ \sim 7 $\Gamma$ \sim 7 $\Gamma$ 4 7 \sim 7 5 \sim \sim \sim 8 # \sim 12 1 $\Gamma$ $\Gamma$ 4 $\Gamma$ 1 \sim 3 \Gamma 1 \Gamma \sim \Gamma

$\sim 2 7 1 2 \sim 2 4 2 4 5 \sim 8 # \sim 12 1 $\Gamma$ 4$

16 $\ell\epsilon$ 16 4 \sim 6 \Gamma ( (1439) 84 (1540) 86 ( ) 36 ( ) 37 ( ) $39$ 38 ( 40) $41$ (1898 ) ( $42$ 43) ( $u$ ) 46 ( ) 46 (1938;1941 ) ( ) 7 (1896: 1918, 1960, 1981) : (1912) The De ofma thena tics in China and Japan Chelsea Publishing $\gamma etopm\theta Ilt$ Co (1932-4) ( 20\sim 22, (1964) \Gamma 122, 23 (1947;1984;1999) 1 : 2 3 ( N101- (1)) ( 1592 ) $S4$ 35 ( ) (1999) 16: si2 2 A 081, $ws010185$ $18074$ (1970) \Gamma $J:47$ $S7$ \Gamma \sim $18cm$ 1910? $4-$ 41 $\Gamma$ $J2$ 1 $40942$ $ws010470_{\text{ }}$ $Jf$ $\ell 32$ 1 $16\cross 12cm$ ( $24$ ?) (7) ( $5F$ ) (3) $312$ ? $16cm_{\text{ }}$ ( ( ) :

$( N101- (1)) ( 1592 ) $S4$ 35 ( ) (1999) 16:485-486 si2 2 A 081, $ws010185$ $18074$ (1970) \Gamma $J:47$ $S7$ \Gamma \sim 2 1 180-62 38 2 1 39 2 1 $18cm$ 1910?$

17 17 (1925;1954) \sim : (1933;1954) $J1928-2: $ $(1928_{i}1954)$ (1930;1954) (1937) 1, : : 1-21 (1933;1954) $(1933_{i}1954)$ ( ) \sim, : ( ) J 4 : 2 (1954-5) 5 : (1958;1998) $rr$ \sim \sim 2: $8-18$ (1998) vol 10: (1976) \sim : ( ( )) (1998) 410 : $\ovalbox{\tt\small (1932:1979) ( ) (1963) REJECT}$ \sim : (1964) : : : (1966;1985) \beta : (1983) $\Gamma$ : ( ) $J2$ : (1940) \sim : (1973) \sim : (1937) $2$ \iota \sim : (1941) : ( ) (1944) \Gamma : ( ) (1963) : ( ) (1967) : ( ) (1970) : (1974) : (1979) \Gamma \sim : ( ) (1980) \sim : (1944) \beta 13-1: ( ) ( ) (1954; 1979) $5$ \sim : (1953) $J1953-9:57-63$ (1954) $J26:13-19$ (1954) I \sim 28:1-12

$(1964) : : : (1966;1985) \beta : (1983) $\Gamma$ : (1935-1948) $J2$ : (1940) \sim : (1973) \sim : (1937) $2$ \iota \sim : (1941) : ( ) (1944) \Gamma : ( ) (1963) : ( ) (1967) :$

18 $\ovalbox{\tt\small REJECT}$ 18 (1954) I Jl 29:8-18 (1955) \Gamma 434:12-22 (1955) 16 (1) 436:17-22 (1956) 16 (2) $\int$ 438:10-16 (1957) 16 (3) $J39:7-14$ (1967) 15-2: 1-39 Needham, J (1954-) Science and Civilization in China (7 vols Proi ec t) Cambridge: Cambr idge Univers $i$ X ( ) ty Press (1957) $J5$ : 3 (1956) (1964) (1959) 1 : (1980) 1 : (1993) \iota \sim : (1983) \Gamma \sim : ( ) (1974) $\sim$ : (1964) $\Gamma$ \sim : (1960) 17:40-44 ( ) 1 : ( ) ( ) (1990-) $+$ $\Gamma$ $J5$ vols (1966;1985) ( ) : : (1987) \sim $J4-1:1-19$ (1966) 7 I : (1970) \Gamma 4 : (1978) \Gamma : Lam Lay Yong ( ) (1977) $ACrItIcat$ Study Yang Hui Suan $Fa$ SlngaPore Unlversi $ty$ Press (1980) : ( 577) ( ) (1982) : ( ) (1985-8?) $J3$, : ( ) (1987) 1 : ( ) ( ) (1993) 1 :, : ( ) ( ) ( ) $J8$ : (1983) : (1984) : ( ) ( ) (1985) :

$: ( ) (1974) $\sim$ : (1964) $\Gamma$ \sim : (1960) 17:40-44 (1965-1970) 1 : ( ) ( ) (1990-) $+$ $\Gamma$ $J5$ vols (1966;1985) ( ) : : (1987) \sim $J4-1:1-19$ (1966) 7 I : (1970) \Gamma 4 : (1978)$

19 $\Gamma$ 19 $\ovalbox{\tt\small (1987) ( ) (1986) $\Gamma$ \sim : REJECT}$ \sim : $\beta$ (1988) \beta \sim \Gamma \sim ) \sim 7 $(1988)-4; $ (1990) \Gamma \sim : (1992;1995) : (1995) : $\beta$ ( ) (1989) : (1989) $J1989-1:85-93$ ( ) (1990) 1 : Martzlof, J -C (1990 A Survey of lapanese Publ icat ions on the His tory of Japanese Trad I $ti$ onal Mathemat ics (Wasan) fr0m the Las $t30$ Years Historia Ma $tpemsfics$ (17: $\Gamma$ ( ) (1990) 1 : (1993) The In fluence of Chinese Ma thema tical Arts on SekI Koma Ph D Thes ls of Univers $ity$ of London ( ) (1996) \sim, ( ) 4 \sim : ), ( (1999), ( )) \Gamma \sim : : ( ) (1999) ( )) \sim $,$ : (1999) ( )) $\Gamma$ \sim : : (2002) \Gamma 1317: :1-24 (2003) \Gamma (2005) : (1990) \sim : (1993) : ( ) ( ) (1993) 1 5 ( ( ) : ( ) (1994) 1 : (1999) : $(2002\cdot 3)$ ( ) ( ) 1 $8\cdot 4:63\cdot 81,9\cdot 1\ddagger 99\cdot 110_{\text{ }}$ (2005) ( )

$Historia Ma $tpemsfics$ (17: 366-373 $\Gamma$ ( ) (1990) 1 : (1993) The In fluence of Chinese Ma thema tical Arts on SekI Koma Ph D Thes ls of Univers $ity$ of London ( ) (1996) \sim, ( ) 4 \sim : ),$

20 20 Southem Chinese Mathematical Arts Transmitted into Japan The Suanfa Tbngzong and the $ZA\dot{m}\dot{w}g$ Suanfa to the Jinkok Shigeru J0CHI $t$ Nat i0na1 Kaohs iung Fi rs Univers Graduate School of lapanese Studies \ddagger ty of Science and Techno 10gy Abstract IaPanese mathematics in the Edo peri0d was established on S0uthern Chinese mathemat ics in the Ming dynas ty Southern Chinese mathemat icians used the abacus instead of c0unt ing r0ds in Northern Chinese But there are few $s$ tudies f0r history of mathemat ics in the Mlng dynasty EsPecially, there are few studies about the ZhimIng Suan $fa$ Thus the author $s$ tudied the lhiming Suan $fa$ $s$ based on Prof Takeda Kusuo $(1909\cdot 1967)$ studies Our method is that using the figures of mathematical arts $s$ because it was quite difficult to 8tudy figures Prof Takeda Kusuo days $s$ We can ind ome vers ions of the Zhiming Suanfa in Taiwan More, there \ddagger $s$ the $s$ 1938 version in Taiwan on the Iapanese rule age The Zhiming Suanta is only 2 chapters book, $s$ It is not the ame of the Jiuzhang Suan $fs$ and the Suanfa Tongzong, which has 9 chapters And we know the Jinkokf is als0 not 9 chapters The number of Suzhou-ma was dr0wn in the Zhiming Suan $fa$, Suzhou-ma unt il 1970 $s$ thus Taiwanese use the Key Words: the $lh$ imng Suanfa, Japanese mathemat ics, Chinese mathemat ics, Suzhou-ma

$ZhimIng Suan $fa$ Thus the author $s$ tudied the lhiming Suan $fa$ $s$ based on Prof Takeda Kusuo $(1909\cdot 1967)$ studies Our method is that using the figures of mathematical arts $s$ because it$

1. 1 1840-1919 2 1642 3 3 4 5 6 (1875-1950) 7 1879 8 1881-1946 9 10 1904-1998 11 12 1 2005 pp.17-19 2 1890 1959 p.21 3 1642 3 1893 11 1932 489,pp.340-

1. 1 1840-1919 2 1642 3 3 4 5 6 (1875-1950) 7 1879 8 1881-1946 9 10 1904-1998 11 12 1 2005 pp.17-19 2 1890 1959 p.21 3 1642 3 1893 11 1932 489,pp.340- * 12 Shigeru JOCHI ** 1642?-1708 300 1775-1849 1782-1838 1847-1931 12 1690-12 * 2007 8 21 ** (Graduate School of Japanese Studies, National Kaohsiung First University of Science and Technology) 1 1. 1