( $?^{-\mathrm{b}}$ 17 ( C 152) km ( ) 14 ( ) 5 ( ) $(?^{-}219)$ $\mathrm{m}$ 247 ( ) 6 1 5km

Size: px

Start display at page:

Download "( $?^{-\mathrm{b}}$ 17 ( C 152) km ( ) 14 ( ) 5 ( ) $(?^{-}219)$ $\mathrm{m}$ 247 ( ) 6 1 5km"

しまなこうじょう
7 years ago
Views:

1 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 ( ) : * ( ) National Kaohsiung First University of Science and Technology, Kaohsiung, Taiwan 824 jochi@cemsnkfustedutw

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

2 ( $?^{-\mathrm{b}}$ 17 ( C 152) km ( ) 14 ( ) 5 ( ) $(?^{-}219)$ $\mathrm{m}$ 247 ( ) 6 1 5km L79 $\mathrm{k}\mathrm{n}$ ( ) ( ) ( ) ( ) r (, 1\gamma \mbox{\boldmath $\theta$}: ) 3, 1986a, 1986b 1988 \breve 4, 2000, ( 3 )

$^{-}219)$ $\mathrm{m}$ 247 ( ) 6 1 5km 2000 2 9 1 L79 $\mathrm{k}\mathrm{n}$ 7 2900$

3 $347_{\text{ }}\mathrm{p}$ (BC 186 ) 7 $\ltimes$ ( ) 8, $-\text{ }$ + \mp,, \mp ( ) 10 ( 50 ) 1 2 $A$ 3 r r 200 ( ) 180 7, 1 5, \sim 2 ) ( $3-6$ ) p p ( 3 ) r ( ) $(\mathrm{r}$ $131$ 2000 $2_{\text{ }}$ 12 p 16 $69$ $\mathrm{p} 2815)_{\epsilon}$ 10997

$$(\mathrm{r}$ $131$ 2000 $2_{\text{ }}$ 12 p 16 $69$ $\mathrm{p}$

4 $ffl J\backslash \backslash \backslash$ $(_{J\mathrm{J}}^{/\backslash }\ovalbox{\tt\small REJECT}_{JJ}^{J\backslash }/ff_{\overline{\mathrm{i}}}\backslash )$ 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 $\mathrm{k}\mathrm{b}ffi \mathrm{j}_{\mathrm{p}}^{-}*\mathrm{g}$ $\mathrm{k}\mathrm{b}\psi \mathrm{j}_{\mathrm{p}}^{-}*\mathrm{f}$ $\mathrm{t}^{\backslash }A\mathrm{A}\emptyset \mathrm{m}\mathrm{e}$ $\vdash^{\backslash ^{\backslash }}\sigma)\xi \oplus\backslash \not\in\backslash$ $13\text{ }$ 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 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 $\Re R$ 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 $(\overline{\mathrm{z}},\leftrightarrow\backslash$ $3\backslash 22 $\otimes\backslash $r\mathrm{u}\mathfrak{b}\mathrm{e}_{\backslash 25 REJECT}\Phi$ $\mathrm{r}$ $ffi\downarrow$, $\mathrm{r}$ $ffi\downarrow$, $\overline{ff}^{/}a$ 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

$\mathfrak{n}$ ffi REJECT}_{J\mathrm{J}}^{\prime\backslash }$ $\mathrm{g}$ $1$ 12\sim REJECT}^{\backslash }*$ $g$ $g$ REJECT}\ovalbox{\tt\small $\overline{\ovalbox{\tt\small REJECT}}_{J7}^{/\backslash$

5 14 2\otimes

6 155 r ( ) $\bigwedge_{\urcorner}$,,,,,,,,, 1516 ${ }$ $?-\mathrm{a}$ $\bigwedge_{\urcorner}$ ( D 83) (A D ) \leq ( 1 ) \supset \sim 2 B C 186 $\mathfrak{j}_{\sqrt}\mathrm{a}$ [ [ 15r 10 J ( $w$ :707) $\backslash$ 16 r \sim [ [ r / ( $\theta$ 1 ) 9 r r ( (, 2001) $\backslash \cdot\backslash$ ) [

$4 \sim 2 B C 186 $\mathfrak{j}_{\sqrt}\mathrm{a}$ [ [ 15r 10 J ( $w$ :707)$

7 $\mathrm{f}\mathrm{f}\mathrm{l}\not\in l\grave{\grave{>}}\mathrm{p}\urcorner_{\mathrm{h}^{1}\mathrm{b}}^{\mathrm{z}\mathrm{g}}t^{\vee}\hslash o_{0}$ $10\text{ }$ $\rfloor$ ) 156 (1) ( ) ( ) $?\sim 349 ( \mathrm{b}$c 338) (B C 403 $=$ ) i 65 $22$ $23$ $\mathrm{f}\mathrm{i}**1937:76$ 14 \sim (, 198\epsilon : 5-3% 2\mbox{\boldmath $\alpha$}\mbox{\boldmath $\alpha$} 4 ) 20 $l$ (1 ) (1 ) 9 3/5 1 ( ) ( ) f ( \sim $\text{ _{}1}$ ( ) ( ) 6/8 4/7 ) 16/21 3/7 2/4 1 1/6 [ 23 6 r r ( ) ( ) 1( ) 1/3 ( $=$ ) ( ) ( ) r (480 ) ( $=$ ) 1/3 1 6 $3_{\text{ }}1/3$ /11 1/4 $6_{\text{ }}1/3$ $4_{\text{ }}1/4$ 5/5 1

$\sim 349 ( \mathrm{b}$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$

8 / ( ) ( ) $\mathrm{z} \mathrm{f}\mathrm{f}\backslash \overline{\mathrm{t}}^{25}$ ( $=$ ) ( ) 1/ / /137 $20_{\backslash }1/4$ $15_{\backslash }1/5$ 1 $30_{\backslash }$ T[ 1/ $1/3$ $20_{\backslash }1/4$ 15 1/ } 97 1/147 $12_{\backslash }1/6$ $210_{\backslash }1/3$ 1/ / } /1089 $140_{\backslash }1/4$ $105_{\backslash }1/5$ $70_{\backslash }1/7$ 1 1/ g $420_{\backslash }1/3$ $280_{\text{ }}1/4$ $210_{\text{ }}1/5$ $168_{\backslash }1/6$ $140_{\text{ }}1/7$ $120_{\text{ }}1/8$ / / $1/3$ $840_{\text{ }}$ $1/4$ $630_{\backslash }1/5$ $504_{\backslash }1/6$ $420_{\text{ }}$ $1/7$ $360_{\backslash }1/8$ $315_{\backslash }$ $1/9$ 280 } / / $1/6$ $420_{\text{ }}$ $1/7$ 360, 1/8 315, 1/9 252 [ $280_{\backslash }1/10$ / ( 9) 612/ $1+1/2+\cdots+1/\mathrm{n}$ 1 r 1/10 r 1 1/ [ ( ) (375 ) ( $=$ )

$140_{\backslash }1/4$ $105_{\backslash }1/5$ $70_{\backslash }1/7$ 1 1/8 1 840 105 2283 g $420_{\backslash }1/3$ $280_{\text{ }}1/4$ $210_{\text{ }}1/5$ $168_{\backslash }1/6$ $140_{\text{ }}1/7$

9 158 ( ) $\mathrm{x}16\dagger 16\cross 15=480$ 15\dagger $16=31$ $480\div 31=15$ 15/31 $(=\mathrm{o} )$ ( $\mathrm{y}=f_{\mathrm{x}}$) 1 $26\text{ }$ $-$ ( ) $s$ 7 $11_{\text{ }}$ ( $1\mathfrak{B}3:229$) \kappa ( 1 ) j

$483871)$ ( $\mathrm{y}=f_{\mathrm{x}}$) 1 $26\text{ }$ $-$ 1 100 10 1 240 ($

10 159 (2) 4- (1) / $29\text{ }$ 1/30 ( ) (B CA ) 30 B C ( B C ) ( B C ) ( B C ) 168 1/30 1/10 1/ $3+^{\text{ }}\backslash 1$ 31 $\bigwedge_{\urcorner}$ / (24 ) r :,,,,,, ( ) 30 L67: /10 \Phi (B C $246?/7?-195$ (, 1978:276 ) B C $2\%^{-}195$ )

$$3+^{\text{ }}\backslash 1$ 31 $\bigwedge_{\urcorner}$ 1 7 23/3132 1 3 1 (24 ) 10 29 r$

11 /10 31/300 ( 10 3%) % ( $=$ ) 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 ) ( ) $?-\mathrm{b}$ ( 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 $\tau$}-

$-\mathrm{b}$ ( C 152) (B C $1\mathrm{c}$) M247 { 32 23/37 2\mbox{\boldmath $\alpha$} 78 23/31$

12 (B C 221) B C 223 B C A D B C $\text{ }1$ (2000 ), ( ) 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 ( ), 1986:16

$(1967 ) $\dot{\text{ }}$,, : $\dagger\pm$, (1978 ),, : (1974 ) ( ) \neq \mathrm{t}$,$

13 )$ 162, \sim, : (1983 ),, $1985-1:1-8$, (1985 ),, :9-15, (1985 ) $\text{ }1$,, $1985-1:46-47$, (1985 ),, : , (1985 ),, :49, (1986 ), 2, :41, (1986 ) ( ) : (1986 ),, 1JI (1987 $\rangle$, $\mathrm{p}$ ,, 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 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 ( ( )), : : , (2001 ) 7, no 3: (1988 $\text{ }\mathrm{v}\mathrm{o}\mathrm{l}$,, ),, : (1990 ),, : (1990 ) $\mathrm{o}$,, : : (1992;1995 ) ( ), [ 5, : (1993 ) $l\mathrm{b}\text{ }$, : (1999 ),, :78-84 (2000 ),, :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, ( )

$of Mathematics Across Cultures -The History of Non-Western mathematics-, Amherst: Kluwer Academic Pub, Helaine Selin et al $(\mathrm{e}\mathrm{d}\mathrm{s}, \sim, \sim ( ( )), : :157-168, (2001 ) 7,$

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}