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ᘋ 枼0 6 /LH 枼0DULXV 6RSKXV 1842 12 ᗙ 17 ᔐύᓴ ጟഛᵺ⣲ᵺჇ 1RUGIMRUGHLGH 柋1899 2 ᗙ 18ᔐ࣯
ᓴጟഛߐᓫ⥕บ .ULVWLDQLD 枼ಥᓫ㒌 ώᓄฎ ώ
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ᘋ 枼0 6 /LH 枼0DULXV 6RSKXV 1842 12 ᗙ 17 ᔐύᓴ ጟഛᵺ⣲ᵺჇ 1RUGIMRUGHLGH 柋1899 2 ᗙ 18ᔐ࣯
ᓴጟഛߐᓫ⥕บ .ULVWLDQLD 枼ಥᓫ㒌 ώᓄฎ ώ
ᙽாວفᖺࡖݗفᙆ⃞تݗ 栾ਘف“ᄞ 栾ᄨ 1859 ၣࢲ 1865 ၣ⻗ᕧ࠽㊞ᕞ⧏ຊٳೲ 栾⚫ᔷਘ⌋
ц“ᄞᓁکວႉᔢဳ 栾ㅚᗆڒೳᕄᙌٲ⠜⿄ 栾খላঔᢍ ᝧ 栾Ωࢲ 1868 ၣ 栾ாتݗ៰ިᵃ⃞ᢍᙈ 栾ڒℷࢲ٦ -9 㨸ᕞࢧ 3RQFHOHW ਘ -ᗣ২࠽ 3OFNHU ⃞⹐ᕄ 栾ጁ܃ڒ⾣ذ٦ᔷဉۦ
⃞ㆀ⿾ цᗣ২࠽ᐋ٦ᄉ⍰㒙⃞៷ᅡ 栾९ጆ⇿٦ߊ╚ 栾سΌ⍰
㒙ف⃞㦼⛘Ό⍰㒙فΩ▤࠶┟ 栾ᠫᕟ⃞⍰㒙 栾⇩⍭ݜ⃞ၬ
۟ᆄ⽶ цா‧ᗆ 栾ㅚ⍁ᕟ⃞ᅼላ 栾ᬂᬂৠდ٦ڒ 栾܃ᄣڒঔ
⛑ቦ࡚㙒௳⃞⍰㒙 栾ᄨ⛘ᙽ⚄ㅚݗ⌋⃞ࣝ൝ڂ цዷڞڒ 㕐ᵃᄨ܊ٜᨈᙌㅻᗣ২࠽ 栾ے◮ᖺ✏⍄⠇တᖺᗣ২࠽⃞ῳ ц
ᙽ⃞ᖆᙛဉۦ༝ᕧᄴ࢛ၬ۟′ цڒ⃞⏜ت⹐ᕄ 栾܃ᄣڒ Ểᄣ٦ம೩⃞Ẩ㊣ цா 1869 ၣ⌇ 栾ڒ܊ࢲᛕᚲ цாㆽⴂ 栾ڒ ਘ ) ࠽⥿ங .OHLQ ٷذ٦ᙎঙ ц࠽⥿ஙᙽج᤺ 栾ਘᙽت ᡥ 栾ٜᖺঞ٦ᗣ২࠽⃞ᄉ㘐⛘ၬ۟ሯ⠜⿄ 栾ےᖺᗣ২࠽ᖺ࠽
⥿ங⃞⛐ဳ ц ڒݜࡒڂ࡛ᙌㄵᵃسী⃞㙣 ц࠽⥿ஙᖺتݗڜ ᔷວ 栾ڒ္္ⳝㅀڂ⃞ક㙃⃞Ḛ᥉ᆄዷߓݝ 栾⛘ᙽॵᖺتݗ࢛
ᚬວ 栾ڒ္္ᒊ㒑Ḛ᥉ᇭᨦ 栾⛘ࣸழΌ‧⃞ت⠴ᆄ܊ἱⶫક 㙃 цᵃ⛘ڒݜࡒڂِ㒙⃞ঙ⸻ 栾ڒݜࡒڂாᔷذ⃞ㅪᤵॵᖺ 㖪္㓊㏋⃞ ц
1870 ၣೳ 栾ᙽਘ࠽⥿ஙتীࢲဓ㦯 栾ڒݜ╁⺼٦ * ㆁ ယ 'DUERX[ ਘ & و -RUGDQ цㅚᗆ 栾ᙽঞᨷம DQDOODJPDWLF
᪆ᅼላ⃞ᄉ㘐 栾⃘Ἢ٦ڒ⃞⦰ু⃞Ꮾⶻ⻝ᐔ цኩΌᕧᘻ㖭ᇭ ჽ 栾ㅚ⍁⻝ᐔໜΩ▤ᖯἮ 栾ໜى࢜ᘻ▤ᖯᘻổ▤ ц
ㅚၣ 7 ᙋ 栾ᨷமਘᗣ㟹ೕ㒙⃘᷑٦ይᷧ ц8 ᙋ 栾ڒ᧳ຖᤵⲟࢲ
⚉ೲࢯ 栾ےᖺா្و⃙㖔㓬ㄩ 栾ڒⳝ⸭ᙈ㒙⹕⛘ጴ٦⾨܊ 栾ㅻ ٦تݗᙋ 栾ጁⳝㆁယᶵᔛẢ 栾ڒヷㆀ⚉ೲࢯ 栾ࡣࢲᄹம ц
1871 ၣ 栾ᙽᄣࢲ٦࠽㊞ᕞ⧏ຊٳೲ⃞Ẩ㊣ 栾ীᗆாف
ᜉفސ✓ᔢੌ ц1872 ၣ 栾ڒா࠽㊞ᕞ⧏ຊٳೲỂᄣ٦ ॡೕۗ цㅚᙛ㒙 栾ڒਘ $ ㆤᷱ 0D\HU ীᗆẺ⎧Ⴣ⎧٦ދ ᄴ࢛ᕥ⌫⃞⍕࢛ἱ⹐ 栾ㅚݗἱ⹐Ἢாထ╲ᗣㅛᔢ⌋ᙀ⃞ࡐຩِ
ت 栾ாᙽỂᄣॡೕۗᄞ 栾ڒா࠽㊞ᕞ⧏ຊٳೲى٦تݗ ᔷ⺋ႄ ц
ೲ៷ா 1870 ၣညল 栾⚄⹐‧ᗆᔷ⇩⍭⃞ى᪉ِت цࢲ 1872 ၣ 栾࠽⥿ங⃘ⲯ٦ڒ⃞⦰ু⃞ᙖ▆㘥 栾९ၬ۟ᖺ⇩
⍭⍰㒙فழჽாتထ⇉⻝ᐔ⚄ِرس⻝⃞ᆄ⽶⃞⌋ цঞڒ⃞ᄉ 㘐 栾ᙽᄨ 1873 ၣ㒑൝ 栾ᄨ⇩⍭Ꮾⶻ⻝ᐔ⃞س⻝㊡ヷ٦⇩⍭⻝ᐔ
⚄ἱ⹐ цㅚᖺڒᙆᙌ⃞⇩⍭㘥ఝ цڒ⛑ቦ n ▂⍰㒙فܜ⽽ᕧ r ݗকᔷ⃞࠼ᮠᖯዷᠫ⃞⚄ 栾ڒুᙌ㓳ㅤ☪⚄ ᙌ㓳ᖺᎁ ܜ⽽ᕧᙌ㓳ݗকᔷ 栾ㅤ☪້㔦ذᎁ࠼ᮠ 栾ㅚݗἱ⹐ா॒ٚغ⓿ج
॒ၣڜထ╲ސദ٦ళဉۦ 栾ےᖺ⃘ⲯᄣダ㆕ ц
ா 1873 ၣ 栾ᙽㆧਘ 3/0 ♭ 6\ORZ ت⾨ 栾ᓁک٦ 1 㓨
⼹ᷱ $EHO ㆝⦰⃞▮ャဉۦ ц
ᙽா 1874 ၣਘຊ ۄം $QQD %LUFK ╁ල 栾ලᄞῳᙌ٩
تഞ ц
Ωࢲ 1876 ၣ 栾ڒখࢲᄴ࢛ၬ۟ᕥ㖭⃞⇩⍭ 栾ীၣڒਘ *2
⪨ᕞ 6DUV ঘ : ◷ए 0OOHU ت⾨ࣝჃ٦ ³$UFKLY I|U PDWKHPDWLN RJ QDWXUYLGHQVNDE´ ц
ா 1882 ၣ 栾 ᕧ *+ 㓨ᷱᕥ +DOSKHQ ਘࢯᷱ /HJXHUUH
ாᄴ࢛س⻝ᕥ㖭⃞ᕄ⎮ 栾ܬ܃ڒࡣᤄヷ⻝ᐔ⚄⃞⇩⍭ ц
ா࠽㊞ᕞ⧏ຊٳೲ⃞॒೬ၣف 栾ᙽ㖪္⎧ 栾ῳݜ
ڒ⃞⇩⍭ဉۦسሯ⠜⿄ цாம೩ 栾㔀٦࠽⥿ங хㆤᷱਘ &(
॥ 3LFDUG ೩ 栾ٜᨈᙌڂᩆሣڒ⃞ဉۦ 栾ഫ 栾ாъㅪ།ы
)RUWVFKULWWH 㕖⸞ف㓊ᕧᙽ⃞ဉۦ⃞ᖺ ᙽᙥڂ໎⃞ 栾ㅚ້㔦 ذᖺت⍁ছ္Ἢ⼋ цΩࢲ ) ᆱᷱ (QJHO ⃞ࢲ܊ 栾ጁㅔᯧጆ⇿
٦ㅚ⍁Ṋቊ ц࡚উஙாᕧ 栾ᙽ⃞ᅼላⳝ㔴⫅ாڒ⃞៰ⴜ㕖⃞ⲯㆁ ਘ␡ف 栾ᙽسળᕧፍ⼋ᐋᵌ 栾ٜᖺঞ٦‧ᗆᗆڜᰌ᪉⃞ᄉ㘐
ᬂِᔓ ц
1884 ၣ 栾ᆱᷱ࣍፼ࢲॡೕۗ 栾ᕧᖺ࠽⥿ஙਘㆤᷱधڒࢲ
࠽㊞ᕞ⧏ຊٳೲᙽ⚫⻝ᐔ⚄ 栾ؿظၛࣾᙽ໎تᙥ㓊ᕧ⻝ᐔ
⚄ᕥ㖭⃞╵়ᆄ⦰ۦ цᆱᷱாᙽ⬧ဉۦ٦ٚݗᙋ 栾 ᕧᆱᷱ
⃞ࣿࣸ 栾ㅚဌ⦰┸ᕧຌ٦ 栾ᄞ܊ 栾ᄨ 1888 ၣࢲ 1893 ၣ࢛د ॲ᷹ ц
ࢲ 1886 ၣ 栾࠽⥿ஙࢲثೲکᔢ 栾ாڒ⃞Ᏸ⪥ر 栾ᙽ ঞ✄ঔᄹம⥿㎜☟ک⺋ႄ✓क цாㅚⴂ 栾ᙽ⃞ဉۦ⃞ᄉ㘐ᓚೲ ٦ ц⛘࠽⥿ஙਘ -+ 㨸ࣺ⥿⏯ڂسᕣ㧠थῳࢲ⥿㎜⚫
ㅚ⍁ᕟᔷ цዷڞ☟ᆱᷱᄞ 栾খᙌ٦تጟῳ 栾࡚فِت
* ⠡⽒ᷱᕞ 6FKHIIHUV цᙽਘڒت⾨᷹٦ᙌ㓊⻝ᐔ⚄ хᄴ࢛ᕥ
⌫ਘᏮⶻ⻝ᐔ⃞ၬ۟ᕥ㖭⃞ᔢ⌋ᙀ цㅚᗆ 栾ᙽ⃞ဉۦᕥ
ٸ൘㕷⣪⍰㒙ક㙃 цㅚᖺ 1868 ၣ + YRQ ٸ൘㕷⣪ +ROPKROW]
ᐋ܊⃞ ц1890 ၣ 栾ᙽ⃘Ἢ٦ٸ൘㕷⣪⃞ᕄ⎮ᙌક㙃 栾╲ㅻᔌ ㅪ 栾٦Ἢா⃞ዷٸ൘㕷⣪ ± ᙽ⍰㒙ક㙃 ц
سၧ⃞ᖺ 栾ᙽா 1889 ၣᄣ٦‧ᗆ⍄ِ⊾╲ⲵფ⃞⁙ 栾ாⓙ
⊾⁙㊄㓾ᨠ₵ᄞ 栾ᄨ 1890 ၣ㒑൝☟☪ဉۦ цےᖺڒ⃞ᆄᙌ٦ᄚ ೲ⃞⻝ऺ 栾࠘ڒ⃞ুᙘ`㞖 栾ڒڎᵃ⻝ᄣᄚ೬‹ਘᔚሯ ц
Ωࢲ 1898 ၣ 栾ڒ⃞᎑ඊᙎঙधڒ⊸மဉۦ 栾ڒᥲᵃᔏᝮ
ڒா‧ᗆغ‐ᔷفᅂ ± ᄹம⃞⏜ت᪉⃞⺋ႄ✓क 栾ா 9 ᙋࢲ ٦࠽㊞ᕞ⧏ຊٳೲۦتݗᗣㅛᔢᏕ цாㆽⴂ 栾ໝ㒋ڒⷝ⎧
٦تݗᔷ⺋ႄ ц1899 ၣ 栾ڒஙሄᆄ⽁ⲗ⛘ঔغ 栾ٻၣٯ॒ٯ
᤺ цڒ⃞ዷᙌ⦰ۦ ᆱᷱਘ 3 သࣺᄹ +HHJDDUG ▮ャࡢ 栾ؿ ظࣺذ٦ᄚദ⃞ⷤⶫ ц
ᙽ⚄ঘ࡚ᙽڜᔷᖺ٩॒غ⓿㊟⌋ِت цᙽ⚄ᖺتݗ⚄ 栾 খᖺتݗ࠼ᮠ᪉ჽ 栾ظٗᨷㅹ␡ਘঝㅎㅹ␡㓊ᕧ᪉ჽ╁ᠫ⛘ⷁᖺ
࠼ᮠ⃞ цᙽڜᔷᖺتݗ࡛ᙌᐔۗㅹ␡ ⷒۦ [ , ]) ⃞▤ᆄ⍰㒙 栾
়ڧ [a, b] = −[b, a] х[λa + µb, c] = λ[a, c] + µ[b, c] х [[a, b], c] + [[c, a], b] + [[b, c] хa] = 0 栾࡚ف a хb хc
㊡ 栾λ хµ ᔷ ц
ᕧா 1935 ၣ 栾+ ೩ᷱ :H\O ═᪉ჽ⃞ຖ⚉ࣆ 栾س ম❫Όࢭ⃞ㄔᨷἱⶫᙽ⚄ 栾້㔦ذ 栾ᙽ⃘Ἢ⃞ᖺᙽ⚄ 栾ڒ㛘
࠻Ⴣ⎧٦ᙽ⚄ਘ⃞ᙽڜᔷ㒙⃞دݗళᙥຖἱਘㅎຖἱ цⷒ U
n ▂⎧ᕥ㞓 栾U ف㦼 x ਘ y 㒙মຖ⚉ٗᨷ x · y = f(x, y) 栾
f(x, y) ∈ U цாຩᇭᨦرᙌ╁়ᄝ 栾খউ㦼ۗ࠶
┟ 栾ظ x ∈ U 栾ா y ∈ U ܃ᄣ f(x, y) = 0 цᕧᖺⷒ lji(x) =
∂fj(x, y)
∂yi y=0
栾1 ≤ i хj ≤ n 栾ࣁ⏜تళᙥຖἱ⸲ٗᨷᔷ
f(x, y) ়ᗣᨷ 3IDII ᕥ⌫┺
∂f(x, y)
∂y = L(xy)L(y)−1 栾 (1)
࡚ف L(x) = (lij(x)) ц⏜٩ళᙥຖἱ৮ⷠዘݜ 栾ⷒ Xi =
n
X
j=1
lji(x) ∂
∂xj 栾i = 1 х2 х· · · хn
ࣁᙌᨮ 3RLVVRQ ፩⬭
[Xi, Xj] =
n
X
k=1
ckijXk 栾 ९ n2 ݗᔷ lij(x) ়ᗣᨷᕥ⌫┺
n
P
s=1
lis(x)∂ljt(x)
∂xs − ljs(x)∂lit(x)
∂xs
=
n
P
k=1
ckijltk(x) 栾 1 ≤ i хj хt ≤ n
(2)
⏜دళᙥຖἱ⸲ ckij n3 ݗ္ᔷ 栾ݜ়
−ckij = ckji хX
s
(csijctsk + cskictsj + csjkctsi) = 0 ц
ᤴ९ڞ X1 х· · · хXn ళِ n ▂▤ᆄ⍰㒙ாᛕ፩⬭رᠫᙽ ڜᔷ цᕧᖺᙽდㅪ٦ᙽ⚄ U ⃞ᙽڜᔷ цছِ 栾دݗళᙥຖἱ
ِㅎᖺ៰࡚ڂሣᕍِ೩⃞ ц৮ⷠዘݜ 栾㔮ܨ═تݗᙌ㓳▂
ᙽڜᔷ 栾९═়ڧ⃞ n3 ݗᔷ ckij 栾ࣁᅃா n2 ݗⶫᚬᔷ lji(x) ়ᗣᨷᕥ⌫┺ 2 ц ㅚ┺ⶫ L(x) = (lij(x)) 栾ࣁᅃா
ⶫᚬᔷ㊡ f(x, y) ়ᗣᨷᕥ⌫┺ 1 栾ظ f(x, y) ຖ⚉٦ تݗᙽ⚄ цዷڞᙽ⃞ళᙥຖἱ═٦ᙽ⚄ਘᙽڜᔷ㒙⃞࠸
࢛ᅃ㓊ܫ цΌἪڜ⸩ⷁ܊⸲ 栾ᙽڜᔷຌࡑ᧳ຖ٦ᙽ⚄⃞ᆄ
⽶ цᄨㅚݗళᙥຖἱ⃘ 栾ጮᙽ⚄⃞ક㙃 栾ऺ┓ⓔظ℩
⑹⃞ڜᔷક㙃 ц
້㔦ذ 栾ᙽ⚄ἱ⹐⃞⏜تᤵᖺᬑਘ⃞ᙽڜᔷ⃞㓊ܫ 栾დ ㅪকᔷ⚄ цዷڞᙽ⃞ళᆄဉۦ 栾܃ᄣㅚݗ⌋❫೮Ⴣ⎧⾨
܊ цᙽ⃞দتݗဉۦᖺသᙘჃ⎧ᄴ࢛ᕥ⌫ⶫ⃞ۍ♭῎ *DORLV ἱ
⹐ 栾㕐ᵃڒᙣ❫ࣹ 栾ےᖺڒ═٦⦰ু⃞ᙽຖἱ 桌▤ᆄমⶫᙽ ڜᔷ⃞کتⲯ⊡ᙌࡕࡘḚᄷ㊡ ц
ᙽ້㔦ذᖺᄴ࢛ၬ۟ਘދᄴ࢛ᕥ⌫ວ цڒ࡛ᙌၬ۟Ω⃞ೳ
⽳ цᙽாᙽ⻝ᐔ⚄ᕥ㖭⃞ဉۦ 栾═ᔷ།㒑٦تݗᕟ⃞ೳ цᄨ ت㒑൝ 栾ᙽ⚄ਘ࢛ᚬ хڜᔷঘၬ۟ັ࢜℩㓊 ц
ᙽாᙽ⻝ᐔ⚄ᕥ㖭⃞ဉۦ 栾 ڒ⃞ῳᆱᷱ х: ళ㖡 .LOOLQJ х⠡⽒ᷱᕞ х⠤ᷱ 6FKXU х( ‧ &DUWDQ ☟ጥਘ⃘
། цḚࢭᖺ‧ 栾☟ጥ٦ᙽ⃞হݗᕥ 栾٩॒غ⓿ᙆ⦰ু⃞
ၬ۟ວِت цࢲ 1922 ± 1923 ၣ 栾೩ᷱா▛ᙽ⚄ᕥ㖭⃞⓼╚ဉ ۦ 栾ڞঘா೩ᷱᖣ≌ᐋ᪉ჽ⃞៷ᅡᄞ 栾ᙽ⚄ጁ⃘།‧ڜ㊟
⃞⌋ِت цாᔷ⃞হݗ࢛ᔆ 栾ாἱ⹐Ḏἱঘ࡚⅙೬⌋
ف 栾ㇺᄣࢲ٦ೲ㊡⃞ኩΌ ц
ᒄ Ḃ
ࣕತᒄḂ
[1] 6 /LH *HVDPPHOWH $EKDQGOXQJHQ ) (QJHO DQG 3 +HHJDDUG HGV 6 9ROV /HLS]LJ2VOR 1922 ± 1937 ц
[2] 6 /LH DQG ) (QJHO 7KHRULH GHU 7UDQVIRUPDWLRQVJUXSSHQ 1 2 1888 31893 /HLS]LJ ц
[3] 6 /LH DQG * 6FKHIIHUV 9RUOHVXQJHQ hEHU 'LIIHUHQWLDOJOHLFKXQ JHQ PLW EHNDQQWHQ LQ ILQLWIHVLPDOHQ 7UDQVIRUPDWLRQHQ /HLS]LJ 1891 ц
[4] 6 /LH DQG * 6FKHIIHUV 9RUOHVXQJHQQ EHU FRQWLQXLHUOLFKH *UXS SHQ PLW JHRPHWVLVFKHQ XQG DQGHUHQ $QZHQGXQJHQ /HLS]LJ 1893 [5] 6 /LH DQG * 6FKHIIHUV *HRPHWULH GHU %HUKUXQJVWUDQVIRUPD
WLRQHQ /HLS]LJ 1896 ц
℠⊤ᒄḂ
[6] ( (QJHO6RSKXV /LH -DKUHVEHULFKWH GHU 'HXWVFKHQ 0DWHPDWLNHU 9HUHLQLJXQJ 81900 30 ± 46 ц
[7] 0 1RHWKHU 6RSKXV /LH 0DWKHPDWLVFKH $QQDOHQ 531900 1 ± 41 ц
[8] + )UHXGHQWKDO 6RSKXV /LH 'LFWLRQDU\ RI VFLHQWLILF ELRJUD SK\ 9RO 8 323 ± 327 ц
