『三才発秘』(陳文、1697年)と「阿蘭陀符帳」 : Napier's Bonesの日本伝来 (数学史の研究)

Size: px

Start display at page:

Download "『三才発秘』(陳文、1697年)と「阿蘭陀符帳」 : Napier's Bonesの日本伝来 (数学史の研究)"

めぐのかくはり
5 years ago
Views:

$$*$ $\infty$ $ $ y_{\backslash }$ {1 1787 2012 105-115 105 * ( 1697 ) -Napier s Bones San Cai Fa Mi by CHEN Wen, 1697 and ffie Dutch Numerals -Napier s Bones Oansmitted into Japan (JOCHI Shigeru)$

1 $*$ $\infty$ $ $ y_{\backslash }$ { * ( 1697 ) -Napier s Bones San Cai Fa Mi by CHEN Wen, 1697 and ffie Dutch Numerals -Napier s Bones Oansmitted into Japan (JOCHI Shigeru) (LIU Bowen) 2 Hao (CHANG Hao) 3 Intemational Center, Osaka Kyoiku University Graduate Institute of Japanese Studies, National Kaohsiung First Univ. of Sci. and Tech. Center for General Education, I-Shou University 1 I. 21 $ $ $ $ 4 ) ( ) $(I_{A}ttioe$ muldplication 5 6 () ) 7 I. ( ) oe $ \downarrow $=\overline{\neg}rightarrow$ lk X $+$ $\cross$ ( Napier s Bone) (??) $=$ () 10 ($13$ 14 ) (C) 225(40962 $NSC9S-2511-S-327\cdot\{n$I-MY3 1 $h\mathbb{i}p://w\backslash jochi\copyright cc.o $\tilde$oi-ku.ac.jp w$.osaka-kyoiku.ac. $jp/\sim jochi/$ 2 lbw\copyright ccms.nkfilstedutw 3 ch3hao\copyright gnail.com 4 (1919-) 2001 ( ) (2005 ) 5 6 () (1954;1979) 2:3735: Unicode3.0 ( ) ( ) Unicode4.0 ( $r_{\re)\prime \backslash \rfloor}^{c}$ $)$ 9 26 (1893) ( (2011) $\lceil$ ) lo ( 60

$) $a1-khw\overline{a}rizm^{-}$ (825) $(Kit\overline{a}bd-J\overline{a}m awa7-$ $bil-his\overline{a}bd-h\dot{m}\delta l)$ (Robelt ofchester, 1150 18) ( Algor numero $lndomm$) $id\ell$ (Leonardo$

2 106 ( ) 11 ( 1592 ) $13$ ( ) 1675 ) 15 $14$ ( 1598 ) $16$ ( () () 1757 ) 17 $m$. (Napier s bones) 2 (Mu ammad ibn MQsa 780?-850?) $a1-khw\overline{a}rizm^{-}$ (825) $(Kit\overline{a}bd-J\overline{a}m awa7-$ $bil-his\overline{a}bd-h\dot{m}\delta l)$ (Robelt ofchester, ) ( Algor numero $lndomm$) $id\ell$ (Leonardo $F\iota b$ )$nacci$ Leonardo Pi-sano, $1170?-1250?)$ (Liber $Abaci$ 1202) 16 Matrakgl Nasuh (?-1564) $Umd\ell t-ul$ Hisab (John Napier, ) ( ) 1617 $19$ (R dolog Rabdology) $2\ovalbox{\tt\small REJECT}$ $\text{^{}\backslash }\mathscr{b}^{2}$ $ht\phi^{:}// REJECT} en60fficho.hm])$ $1I$ ( 1710 ) ( 2 (1790) $ $ $)$ $4]\alpha xn]051$ MF $2$ $19$ 21 ( ) $\ovalbox{\tt\small REJECT}$ 12 (1993) $\Gamma$ [12: ( ) (1986) : ( 9 (1883 ) : ) $\circ$ $1$ WW988& 15 9 J ( (2007) ) 16 ( ) (1986) : W9 (1883) ) $l7$ ( ) 20 Napier. J. (1617) RabdOlogy. $h\phi\sqrt{}/\psi lodwik\dot{m}\iota\propto 1ia\alpha ywi1\dot{q}\infty a/m/0/0yrabdoloy_{-}cov\sigma_{-}pagejpg$ 21 John Napier (1617; 1990) RabdOlogy: John Napier (1617; 1990) RabdOlogy: 15.

$$\backslash \hslash g\ovalbox{\tt\small REJECT} i,/\neq$ REJECT} IE2$ 2 (3 ) 1628 23 24 (Rho, Giacomo (Jacques), 1593-1638) ( 1645 25) ( )( 26.$

3 $\backslash \hslash g\ovalbox{\tt\small REJECT} i,/\neq$ REJECT} IE2$ 2 (3 ) (Rho, Giacomo (Jacques), ) ( ) ( )( 26. () ) 1645 ( ) ( m 5 ( ) 6 $( \alpha)$ ( ) ( ) ( 1678 ) 2S 29(1723; 1724; 1761 ) ( ) 31 ( ) 23 (1985) :56 ( ) 25 2(1645) $ f$ 21 ( ffrd) (1686) :368) ( ) (1993) $\mathscr{d}$ 8: Johann Adam Schall von Bell ( ) ( ) 27 () (1954,1979) 5: (1727) ( () (1954;1979) 5:427) $2S$ () (1954:1979) 5: $= $ $1-24$ ( $\ovalbox{\tt\small REJECT}$ $1723$ $))$ ( ) (( ( ) (1941; 1994) ) ( ) 1761 ( ) 30 $\ovalbox{\tt\small -514 Jl (1724) 1726 ( (i) (1954;1979) 5:427) $(1\infty )$ $( $ (1990) :84) 31 (1721) ( ) $(h\mathfrak{m}:// nvxtz\sqrt{}\dot{q}x\{\sqrt lswhmc/xjmr/2011/03/ hm)_{0}$ (1788)

$$\sim$ $\lceil$ $($ 1958; 108 IV ( 1450 ) 8 ( 1450 ) 32 33( 1573 ) ( ) 35 $5$ 2 $\lceil_{o}^{1}\rfloor$ $\lceil_{\text{}}^{1}\rfloor$ ( 1592 ) ( ) 38 11 3 2: $3\alpha 31$) $\rfloor$ 32 ( ( ) (1993)$

4 $\sim$ $\lceil$ $($ 1958; 108 IV ( 1450 ) 8 ( 1450 ) 32 33( 1573 ) ( ) 35 $5$ 2 $\lceil_{o}^{1}\rfloor$ $\lceil_{\text{}}^{1}\rfloor$ ( 1592 ) ( ) : $3\alpha 31$) $\rfloor$ 32 ( ( ) (1993) $M$ 33 $05G\alpha n5$ $(\{d!\ovalbox{\tt\small REJECT}$ (1993) 2: $1\mathfrak{B}8)$ REJECT} $ffl\ovalbox{\tt\small ff ( ) ( g$ $(2\alpha)7)$ 1) $\sqrt{} $ 35 (2011) $\mathfrak{x}$) $\backslash$ $A$ $11$ (1970) [ :6 ( ) (1993) 2: 1148

5 $1$ $ i $ $ ^{x_{1^{1}\mathfrak{l}}^{\backslash }} \bigwedge_{l-}$ $\int\overline{\}_{\backslash \cdot\cdot\cdot=-}^{\bigwedge_{-}cc\wedge}}\overline{\approx\cdot}/\backslash w--\check{i\cdot}$ $\underline{\subset }L\ddot{A}_{-\frac{j.a\underline{=}\wedge.-}{}\simeq 1^{--)}-}^{-}\wedge.\cdot=$ $\frac{c^{---}}{\prime\iota L\prime c_{\vee}z,arrow-\vee-,\prime\backslash \backslash R_{-arrow\Delta }^{\underline{=}}x\backslash Y^{\sum_{\backslash }^{-\vee}}}\approx.\varpi_{l}\underline{\leftrightarrow Y}_{-,--}^{-\underline{\underline{1}}}- $ $\mapsto\wedge^{--\urcorner}m_{-\grave{\dot{\perp}}}^{\wedge^{---\backslash \ulcorner}}\triangleright\mapsto_{-}\cdot-=\backslash \equiv^{---.\overline{-\backslash }\backslash }-\backslash \backslash \prime A\underline{r\backslash }\approx.\overline{\cdot\tilde{g}}$ $@^{\overline{e}^{-}<^{s^{\approx},\sim.arrow-=}} arrow\cdot\leq X^{--\cdot\cdot\overline{/_{\backslash }}}\cdot L\infty.-c_{\underline{L^{\backslash \backslash ---\triangleleft_{-}}}}-\backslash \cdot..\bigwedge_{\underline{\llcorner\}}}^{-.\cdot\cdot.--\epsilon_{1}}=--arrow-.--\gamma_{\underline{a}\backslash }-\perp -\simeq$ $\varpi:^{\backslash _{=}}.-\underline{w}^{-\sigma_{--}^{-}}arrow\dot{rightarrow}^{\infty\backslash ^{\backslash }}--\underline{--\sim}..-\eta_{r_{-}}$ $: arrow\bigwedge_{--}rightarrow\cdot\overline{.\vee}\vee_{arrow}..\backslash \overline{=}l\equiv.\backslash -i_{\delta}\cdot\underline{\cdot\vee\backslash }\searrow\mapsto\vee..-x\pi_{a}.oe\overline{\frac{\prime}{-\ddot{a}--}\backslash =-\cdot p}_{-}$ $,L\cdot\backslash \cdot$ $\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}_{46\text{}}$ $[j$ (17 ) $\sim$ (12 ) 4142 V. ( ) ( ) ( 1248 ) 43 ( 1247 ) ( 1275 ) $\cross$ $19$ $-\circ$$3$ $x-$ $x1$ 44 VL $)$ ( $45$ ( 1725 $ _{\wedge^{-\equiv}}^{\overline{\prime}} \wedge^{-\lambda^{-\backslash }rightarrow\backslash \Phi\backslash v.\cong^{-}}\wedge\varpi\underline{=}-.\grave{g}.-\gamma r\cdot\backslash.\frac{-\cdot\approx-\overline{c_{\underline{\underline{--}}=<fl}^{-.\backslash _{-}.\supset}}}{}===-\cdot\backslash$. $\ovalbox{\tt\small REJECT}\prime_{-carrow-A\overline{-\cdot\dot{r}^{k}}}-\cdot$ $t=v_{!^{5}}r\searrow_{:}:_{s}$ 1 $\mathfrak{s}\check$ $!)4^{--}\cong$ $\downarrow_{--\frac{=\underline{-=}\wedge n\wedge\backslash \lrcorner\backslash }{}\dot{r}\backslash Y^{-}\backslash }^{\overline{x}_{j\backslash }\frac{=}{\equiv}=\mathscr{a}}--\backslash -<..\cdot\infty \text{_{}\tilde{\frac{}{c\phi}}(arrow}\sim\urcorner^{-=}-.l^{\cdot}\cdot$. $e^{\vee}-$ $\Gamma_{-}A--\backslash \underline{*\dashv}$ 14 ( )47 ( ) 10 ( ) 38 (1970) :22 ( ) (1993) $\Gamma$ 2: $( g\oint\ovalbox{\tt\small REJECT}\gamma$ 39 (1970) :22 (1993) 2: $17$ $4$ ( ) (1993) 2: $12$ $3$ (1592; 1986) : : 528 9(1883) () (1954;1979) 4: ( ) ( ) 44 (2011) -) [ ( $+ $ ) $A$ $\backslash _{o}$ 5 $\circ$ E (9633 ) 9633 [j ( ) () (1954;1979) 5:437) ( ) 46 ( () (1954;1979) 5:433) $\sim$210 4

$1767 $\text{^{}\ovalbox{\tt\small REJECT}_{\text{ }}\iota\backslash }$ 110 $ $101J [ 1 $=$ 7 ( ) ( ) (1726 ( ) 1720 1 ( 1697 ) $ae$ ( ) $\mathfrak{s}$9) 15 51 52( 53 ) $\grave$ ( ) ( ) 48 (168&1752)$

6 1767 $\text{^{}\ovalbox{\tt\small REJECT}_{\text{ }}\iota\backslash }$ 110 $ $101J [ 1 $=$ 7 ( ) ( ) (1726 ( ) ( 1697 ) $ae$ ( ) $\mathfrak{s}$9) ( 53 ) $\grave$ ( ) ( ) 48 (168&1752) ( ) $\llcorner$ ( ) n L Jl $($ $h\mathfrak{m}:$$wwwl7.om.nejy\dashv 1!udm\mathfrak{w}u/n\alpha layamahbn)$ 49 (1967) : (1720) (1967) $:45)_{\kappa}$ 12 (1699) ( (1967) $:3\eta_{0}$ (1697) $169-28$ $\supset$-2030 (1) Y$\triangleright$ () (1697; 1936: 1972) : : 3 (1697;1997) : : 1997 pp. p.127 $12\downarrow 125$ 52 $152_{o}$ ( () 1936 ) 53 ( ) ( () (1954;1979) 5:433) 1768 ( ) O $ $ j $:3794$ http $flwww.g\infty cmeajynmyoubitom/2\pi i.w_{\text{}}$

$H 111 54( 1764 ) ) $+ $ ( $\lceil$ ) ( 1726 ) $\circ$ ) 5 1 1 16 ( 1775;1812 $)$ 56 57 $\circ$ 1775 58 $(1904-1998)$ 1812 59 0( 1798 ) 1798 1775 ( 1858 ) ( ) 54 $1012$ $1013$ 55 () $152$ 41$

7 H ( 1764 ) ) $+ $ ( $\lceil$ ) ( 1726 ) $\circ$ ) ( 1775;1812 $)$ $\circ$ $( )$ ( 1798 ) ( 1858 ) ( ) 54 $1012$ $1013$ 55 () $152$ 41 $(X)006584$ MF $102306$ $5$ ( $f\emptyset$ ( () 1936 ) $ ^{f}$ 56 (1896; 1981) :356 () (1954;1979) 5: ( ) ( ) (1812) $602$ $603$ (1811) 60 ( (2010) $\lceil$ J :36)

$\backslash$ 112 13 T 61 14 $\mathscr{z}$(1858 ) V ( ) ( ) ( ) $(\lceil \mathfrak{b}\rfloor)$ ( ) $rg$ $\grave$ $d$ 1 Jl (1936 ) $A$

8 $\backslash$ T $\mathscr{z}$(1858 ) V ( ) ( ) ( ) $(\lceil \mathfrak{b}\rfloor)$ ( ) $rg$ $\grave$ $d$ 1 Jl (1936 ) $A$ $\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}$ $\grave $ $\mathscr{x}$ (1812) : $02_{-}045\Re$)

$113 63 [ ( 1573 ) $1:11B-12A_{o}$ 64 65 2 66 () (1954;1979) 4:157 12 12?$

9 [ ( 1573 ) $1:11B-12A_{o}$ () (1954;1979) 4: ? ( 1592 ) $17:4B_{o}$ () (1954;1979) j 4:158 ( ) (1896; 1918, 1960, 1981) :362 ( (1941; 1994) :28) 70 W ( ) ( ( ) ) ( () $(2\alpha)8\cdot 10$) $2$ $ $ ) $\neg$,to$\backslash$ ( ) ( 1774 ) $n$ -P 73 ( (1941; $:65\ovalbox{\tt\small 1994) REJECT}$) 74 () (1954;1979) $5:432$ ( 1710 ) $2:20A_{o}$ 75 ( () (1954;1979) 5:438) 76 $156$ $ $ MF $3656$ $4100\alpha$)$6583$ M[ () (1954;1979) 5: () (1954;1979) 5:

$(1697;1997) : ( ) () (1697; 1936; 1972) : : 3 (1896; 1918, 1960, 1981) : (1928;1954) $\mathfrak{w}$ 1928-2:189-195.$

10 114 1 John Napier (1617; 1990) Rabdology. Trs. by William Frank Richardson; Intr. by Robin E. Rider. MIT Press. (1697;1997) : ( ) () (1697; 1936; 1972) : : 3 (1896; 1918, 1960, 1981) : (1928;1954) $\mathfrak{w}$ : (1933;1954) (1930;1954) ] $1930-1:1-21$ (1933;1954) $(1\mathfrak{B}8)$ (1958;1998) [f J-] $2:8-18$ m vol.10: (1976) ( ()) (1998) 10 : ( ) 2 : (1940) 15(2): (1941; 1994) $\pm$ () (1970) : (1944) J13-1: $\mathscr{x}$ () j () [ ) (1954;1979) 5 : (1953) ;5743. $(]954)$ 126: $\underline{q}28:$ (1954) I ] $-12$. (1954) I J-129:8-18. (1955) $m$ Jl 34: (1955) 16 $(])$ J136: (1956) 16 (2) $ f$ 38: (1957) 16 (3) j 39:7-14. (1967) 5-2:1-39. (1964) : (1966) : (1970) : $($ $)$ (1985) () : () (1686) : (1990) Jl 124: 1-9. $(1\mathfrak{M})$ J1174: (2002) 1-221: $25\mathfrak{B}$ $\grave$ 11 (1936) 86 ( 1770 ) ( )( )

11 115 (2011) J] 259: (2002) 1317: (2003) 1:1-24. (2004) Jl 1392: ( ) : (2007) $1546:]-20$. (2007) J132: (2011) -tj$=$)fl i $\Phi ZU1739: $. $\dagger\pm$ ( ) (1993) 5 ( ( )) : (1996) j 149: $(2\mathfrak{W}2-3)$ () () 4 $8A:63-81$ 9-1: ()(2007) : () ( ) 3 Sancai Fami (CHEN Wen, 1697) and the Dutch Numerals -Napier s Bones Transmitted into Japan JOCHI Shigeru, LIU Bowen and CHANG Hao Abstract Japanese medical doctors and military scientists at the Edo period introduced the Suzhou Numelals fom the Sancai Fami (Chen Wen, 1697) in Chen Wen introduced the Lattice Multiplication system and Napiar s bones from Westem mathematical alts, and he used Suzhou Numerals. But Japanese mathematicians at the Edo period already smdied the Lamice Multiplication system of Xie Suan (or Pudijin ) and Suzhou Numerals by Chinese mathematical arts at the Ming dynasty such as the Suanfa Tongzong (Cheng Dawei, 1592) before Westem mathematics amived into China. Japanese medical doctors had never smdied Chinese mathematical arts at the Ming dynasty, therefore Senno, medical doctor at $Ka\omega_{1\dot{u}O}$ $Takama\ddagger su,$ described the Ou NumelalS $S$ On $Napiar s\ltimes$)$nes$. Then Vamamom Hifiuni named the St.p Ou Numerals on the Dutch Numerals Key $WoMs$; the Suzhou Numerals, the Dutch Numerals, the Sancai Fanu (CHEN Wen, 1697), the Chusan Shinan (SENNO Katahiro, 1767), the Hayazan Tebikishu (YAMAMOTO Hifumi, $177\mathfrak{D}$

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)

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) $\backslash 4$ $\grave$ REJECT}$g$\mathscr{X}\mathscr{L}$ 1739 2011 128-137 128 : Chinese Mathematical Arts in the Song, Yuan and Ming Dynasties and thedutch Numerals -The Suzhou Numerals Transmitted into