1257 2002 150-162 150 Abstract When was the Suanshushu edited? * JOCHI Shigeru The oldest mathematical book in China whose name is the Suanshushu was unearthed in the Zhangjiashan ruins, Jiangsha City, Hubei province, China from December 1983 to January 1984 Some parts of the Suanshushu were opened, but the detafl had not been opened yet The Suanshushu was written about 186 BC at least, and it must be the oldest mathematical art in China And it was about 200 years before of the Jiu Zhang Suan Shu Then, in September 2000, we can read whole book because the committee opened full text of it Therefore, the author consider the question of ufangtian (a square root method) and the others, then found that the field system at the Suanshushu was one Mu was two hundred and fourty Bu Thus the Suanshushu was edited in the Hun dynasty, not Qin dynasty KEY WORDS: Suanshushu, Zhangjiashan, Chinese mathematics, Jiu Zhang Suan Shu, field system 1983 12 1 17 200 2000 9 ( ) 1 240 : * ( ) National Kaohsiung First University of Science and Technology, Kaohsiung, Taiwan 824 jochi@cemsnkfustedutw
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$ffl J\backslash \backslash \backslash$ $(_{J\mathrm{J}}^{/\backslash }\ovalbox{\tt\small REJECT}_{JJ}^{J\backslash }/ff_{\overline{\mathrm{i}}}\backslash )$ REJECT}_{J} \not\simeq$ $\xi\not\in J\backslash \backslash \backslash$ J\backslash \backslash \backslash$ l\backslash \backslash \backslash$ ^{\backslash }\not\simeq$ $\kappa_{\backslash ^{\backslash }}J\prime JJ\backslash$ $g$ \mathfrak{n}$ ffi REJECT}_{J\mathrm{J}}^{\prime\backslash }$ $\mathrm{g}$ $1$ 12\sim REJECT}^{\backslash }*$ $g$ $g$ REJECT}\ovalbox{\tt\small $\overline{\ovalbox{\tt\small REJECT}}_{J7}^{/\backslash }$ kb \exists^{\backslash }*$ $\cdot$ REJECT}^{\backslash }*$ \mathrm{g}\backslash$ REJECT}^{\backslash }*$ }\backslash$ $\overline{\ovalbox{\tt\small REJECT}}_{JJ}^{/\backslash }$ $g$ $2$ $4$ $21$ $20$ $(\mathrm{f}\mathrm{h}\hat{*},\backslash l\mathrm{j}\ovalbox{\tt\small REJECT}^{\backslash }*)$ $=_{-}-f$ REJECT}\backslash \ovalbox{\tt\small \backslash \ovalbox{\tt\small REJECT} J\mathrm{J}\mathcal{D}ffl\#\mathrm{y}\mathrm{g}$ $/\backslash \backslash \ovalbox{\tt\small REJECT} JJ\mathrm{n}\overline{\mathrm{p}}\pm\emptyset ffl[] 2\ovalbox{\tt\small $\nearrow\backslash \backslash \ovalbox{\tt\small REJECT} J\mathrm{J}\lambda \mathrm{i}\phi\backslash \ \backslash$ $\nearrow\backslash \backslash \ovalbox{\tt\small REJECT} JJ\ovalbox{\tt\small REJECT}/\backslash \not\in\backslash$ /\backslash$ $\nearrow \mathrm{a}\backslash \ovalbox{\tt\small REJECT} \mathcal{d}\beta,*_{\backslash }\backslash \ae$ $\mathrm{j}*ff^{1}\mathrm{i}_{j\mathrm{j}}^{/\backslash }\mathrm{e}\mathrm{e}$ $\Leftrightarrow \mathrm{k}\ovalbox{\tt\small REJECT} F1\mathrm{J}$ $*\backslash \emptyset\grave{1}\ovalbox{\tt\small REJECT}^{\backslash }\not\in$ }\Xi \mathrm{e}$ }\Phi \mathrm{e}$ $\mathrm{k}\mathrm{b}ffi \mathrm{j}_{\mathrm{p}}^{-}\mp\ovalbox{\tt\small $\mathrm{k}\mathrm{b}ffi \mathrm{j}_{\mathrm{p}}^{-}*\mathrm{g}$ $\mathrm{k}\mathrm{b}\psi \mathrm{j}_{\mathrm{p}}^{-}*\mathrm{f}$ $\mathrm{t}^{\backslash }A\mathrm{A}\emptyset \mathrm{m}\mathrm{e}$ $\vdash^{\backslash ^{\backslash }}\sigma)\xi \oplus\backslash \not\in\backslash$ - 153 10 68 7000 $13\text{ }$ 1 10 REJECT}_{\mathrm{R}}7ffl$ REJECT}\ovalbox{\tt\small REJECT}\backslash \ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}\ovalbox{\tt\small $\emptyset*\mathrm{r},\gamma\backslash$ $\mathrm{f}\lambda_{\lrcorner}\not\in\ovalbox{\tt\small REJECT} ff\backslash \overline{\tau}4$ $q)*\pi \backslash$ $\mathrm{h}\overline,\epsilon^{\backslash }$ $ffl\ovalbox{\tt\small 1 $/+J\ovalbox{\tt\small 2 3 4 ffl $ffl $/t3^{\backslash 5 $/\mathrm{a}*\leftrightarrow$ 6 $\hslash_{j}^{j\nearrow}\backslash 7 $\bigwedge_{\square 8 $\prime 9 }4$ #\yen $(\oplus)$ $\mathbb{h}^{/}a$ $ffl 10 fflk $\mathrm{g}_{\backslash 11 $\mathfrak{w}ffl\ovalbox{\tt\small 12 13 $\Re R$ 14 $\#\ovalbox{\tt\small $ffl }/A$ $\mathrm{a}/\backslash \mathrm{d}j\mathrm{j}$ $\mathrm{g}$ $1$ ae 19\sim 21$ $\mathrm{f}$ $ffi J\cdot\backslash \backslash$ $(arrow\ovalbox{\tt\small REJECT}^{J}\mathrm{A})$ $/\backslash \ovalbox{\tt\small REJECT} J7^{\cdot}$ $\mathrm{g}\re\sigma)ffl\ovalbox{\tt\small REJECT}\gamma \mathrm{g}\emptyset ffi \rfloor$ $1\not\in 5-6$ $7\sim 9$ \mathrm{x}f\pm/\backslash J\mathrm{J}$ $\acute{\mathrm{f}}\pm JJ\mathrm{x}/\backslash$ $\mathrm{g}$ $1\not\in 17\sim 18$ }\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}\chi$ $\overline{ff}_{j7}^{\prime\backslash }$ $\mathrm{g}$ $3$ $1$ $\mathrm{e}$ $\mathrm{g}$ $3$ $\mathrm{g}$ $\mathrm{g}$ $3$ $/\backslash $5\not\in \mathit{0})$ $100$ $ J$ $\backslash $\mathrm{e}$ $/\mathrm{a}\ovalbox{\tt\small REJECT}\sigma)\mathbb{H}\backslash \not\in$ 14, 3 $\mathrm{e}$ $3\not\in 3$ $\mathrm{h}$ 15 $\# ffl$ $,ffl\backslash 16 $\mathrm{g}\backslash *$ $g$ $5$ 17 $k\mathrm{e}$ (ffl) 18 $\Phi 19 $(\overline{\mathrm{z}},\leftrightarrow\backslash$ 20 21 $3\backslash 22 $\otimes\backslash 23 24 $r\mathrm{u}\mathfrak{b}\mathrm{e}_{\backslash 25 REJECT}\Phi$ $\mathrm{r}$ $ffi\downarrow$, $\mathrm{r}$ $ffi\downarrow$, $\overline{ff}^{/}a$ kb REJECT}\phi\overline{\mathrm{g}}$ $\not\cong\backslash *$ \backslash \backslash$ $(arrow\overline{ff}_{j7}^{/\backslash })$ $\mathfrak{b}ffl$ $6$ ae $6$ $3$ 11 $\mathrm{e}$ $1$ $1$ $\mathrm{h}$ $\mathrm{f}$ $\Psi^{1}\mathrm{J}_{J7}^{\prime\backslash $\hslash^{1}\mathrm{j}_{jj}^{\prime\backslash $k$ $g\leftrightarrow\sigma)\mathrm{b}\mathrm{g}$ $\mathrm{k}\mathrm{b}ffi 1^{-\neq\ovalbox{\tt\small REJECT}}\mathrm{J}_{\mathrm{p}}^{-}$ $(\Leftrightarrow$ $3$ $10-20$ $\mathrm{h}\mathfrak{l}\mathrm{f}$ $\not\cong\backslash *$ $\emptyset \mathrm{f}_{\mathrm{b}}\#\mathrm{h}$ ) 26 $\mathfrak{b}\backslash \Phi$ $(\tau\backslash \mathrm{b}fl)$ REJECT} T\backslash \not\in 15$? 13 1 Q
14 2\otimes 167 61 62 154
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$\mathrm{f}\mathrm{f}\mathrm{l}\not\in l\grave{\grave{>}}\mathrm{p}\urcorner_{\mathrm{h}^{1}\mathrm{b}}^{\mathrm{z}\mathrm{g}}t^{\vee}\hslash o_{0}$ $10\text{ }$ $\rfloor$ ) 156 (1) ( ) 1 100 ( ) 1 100 10 $?\sim 349 ( \mathrm{b}$c 338) 1 240 18 (B C 403 $=$ ) 240 1 9 38 20 53 64 i 65 $22$ $23$ 66 68 24 6 1 240 18 $\mathrm{f}\mathrm{i}**1937:76$ 14 \sim 1 240 (, 198\epsilon : 5-3% 2\mbox{\boldmath $\alpha$}\mbox{\boldmath $\alpha$} 4 ) 20 $l$ (1 ) 10 1 2 4 2 5 (1 ) 9 3/5 1 ( ) ( ) f ( 1 240 21 1 \sim 8 30 240 $\text{ _{}1}$ 240 22 65 23 4 4 ( ) ( ) 6/8 4/7 ) 16/21 3/7 2/4 1 1/6 [ 23 6 r r ( ) ( ) 1( ) 1/3 ( $=$ ) 240 1 ( ) ( ) r 240 1 1 1 2 1 3 240 1 2 (480 ) 160 1 ( $=$ ) 1/3 1 6 $3_{\text{ }}1/3$ 1 2 11 130 10/11 1/4 $6_{\text{ }}1/3$ 1 12 3 25 115 $4_{\text{ }}1/4$ 5/5 1
157 53 1 15 15/31 15 15 ( ) ( ) $\mathrm{z} \mathrm{f}\mathrm{f}\backslash \overline{\mathrm{t}}^{25}$ 16 4 1 7 7 1-3 ( $=$ ) ( ) 1/5 1 60 30 1/3 12 137 105 15/137 $20_{\backslash }1/4$ $15_{\backslash }1/5$ 1 $30_{\backslash }$ T[ 1/6 1 60 $1/3$ $20_{\backslash }1/4$ 15 1/5 101 147 } 97 1/147 $12_{\backslash }1/6$ $210_{\backslash }1/3$ 1/7 1 420 84 1/6 60 1089 } 92 612/1089 $140_{\backslash }1/4$ $105_{\backslash }1/5$ $70_{\backslash }1/7$ 1 1/8 1 840 105 2283 g $420_{\backslash }1/3$ $280_{\text{ }}1/4$ $210_{\text{ }}1/5$ $168_{\backslash }1/6$ $140_{\text{ }}1/7$ $120_{\text{ }}1/8$ 88 696/2283 1 1/9 1 2520 $1/3$ $840_{\text{ }}$ $1/4$ $630_{\backslash }1/5$ $504_{\backslash }1/6$ $420_{\text{ }}$ $1/7$ $360_{\backslash }1/8$ $315_{\backslash }$ $1/9$ 280 } 7129 84 5964/7129 1 1/10 1 2520 $1/6$ $420_{\text{ }}$ $1/7$ 360, 1/8 315, 1/9 252 [ $280_{\backslash }1/10$ 7381 81 6939/7381 1 ( 9) 612/1089 1 1 $1+1/2+\cdots+1/\mathrm{n}$ 1 r 1/10 r 1 1/12 24 68 [ ( ) 1 1 3 5 3 3 75 (375 ) 3 5 3 220 350 28 8750-3 1 5 3 3 ( $=$ ) 25 3 1 1 3 75 1 240
158 ( ) 240 15 225 16 256 16 15 15 16-15 16 15 $\mathrm{x}16\dagger 16\cross 15=480$ 15\dagger $16=31$ $480\div 31=15$ 15/31 $(=\mathrm{o} 483871)$ ( $\mathrm{y}=f_{\mathrm{x}}$) 1 $26\text{ }$ $-$ 1 100 10 1 240 ( ) 27 28 26 $s$ 7 $11_{\text{ }}$ 12 19 ( $1\mathfrak{B}3:229$) \kappa 1998 27 28 ( 1 ) j
159 (2) 4- (1) 1 240 100 1 1/10 240 1 $29\text{ }$ 1/30 ( ) (B CA59-87 141-87) 30 B C 186 1 240 ( B C 202-195) ( B C 195-188) ( B C 180-157) 168 1/30 1/10 1/15 27 24 8 1 3 $3+^{\text{ }}\backslash 1$ 31 $\bigwedge_{\urcorner}$ 1 7 23/3132 1 3 1 (24 ) 10 29 r :,,,,,, ( ) 30 L67:153 31 1 3 1/10 \Phi (B C $246?/7?-195$ (, 1978:276 ) B C $2\%^{-}195$ )
160 1 3 24 8 1 1/10 31/300 ( 10 3%) 1 240 10% 24 37 ( $=$ ) 1 10 ( ) 1 10 1 10 ( ) ( $=$ ) # 38 ( 18 ) 24/300 (1/12 5 ) 25/300 (1/12 8 3%) 1/10 1/15 $\Delta$ 5 (A D 263 ) R (B C 213-212) ( ) $?-\mathrm{b}$ ( C 152) (B C $1\mathrm{c}$) M247 { 32 23/37 2\mbox{\boldmath $\alpha$} 78 23/31 $24\cross 10/31=7$23/31 2\mbox{\boldmath $\alpha$} 107 r { 1\infty : \mbox{\boldmath $\tau$}-
161 35 (B C 221) B C 223 B C 278 3 A D 25 36 37 200 B C 186 1 6 $\text{ }1$ 2000 9(2000 ), 78-84 4( ) 3 11 (11 $\text{ }\mathrm{h}\mathrm{p}\mathrm{m}$ ),, : (1937 ),, :, (1967 ) $\dot{\text{ }}$,, : $\dagger\pm$, (1978 ),, : (1974 ) ( ) \neq \mathrm{t}$, $x$ $\mapsto\backslash, (1980 ) ( ),, : (1982 ) ( ),, : : (1993 ) 35 \sim 987 36 ( ), 1986:16
)$ 162, \sim, : (1983 ),, $1985-1:1-8$, (1985 ),, 1985-1:9-15, (1985 ) $\text{ }1$,, $1985-1:46-47$, (1985 ),, 1985-12: 1124-1120, (1985 ),, 1986-3:49, (1986 ), 2, 1986-5:41, (1986 ) ( ) : (1986 ),, 1JI (1987 $\rangle$, $\mathrm{p}$ 220-222,, 4 117:21-25, (1988 ) Z \acute \acute ( (1989 ) TAN :The Davm of Wasan (Japanese Mathematics), ) $\text{ }1989-4:85-9$, 158:15-29 (1998 ) (2000) Pp 423-454 of Mathematics Across Cultures -The History of Non-Western mathematics-, Amherst: Kluwer Academic Pub, Helaine Selin et al $(\mathrm{e}\mathrm{d}\mathrm{s}, \sim, \sim ( ( )), : :157-168, (2001 ) 7, no 3:201-204(1988 $\text{ }\mathrm{v}\mathrm{o}\mathrm{l}$,, ),, : (1990 ),, : (1990 ) $\mathrm{o}$,, : : (1992;1995 ) ( ), [ 5, : (1993 ) $l\mathrm{b}\text{ }$, : (1999 ),, 2000 9:78-84 (2000 ),, 2000 9:85-90, (2000 ) $\text{ }\mathrm{h}\mathrm{p}\mathrm{m}$, r \sim, j vol 3, noll:2-20, (2000 ) $\text{ }\mathrm{v}\mathrm{o}\mathrm{l}$, $\mathrm{v}\mathrm{s}$ [r, 21:1-6, (2000 ) $\text{ }1$ 45:15-28, (2000 ) \sim, ( )