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達朗貝爾 - 九章數學

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(1)

オ ᖖ ⹤ ᴬ

㄄ᗤ⺾ᵺ 枼-/5 '¶$OHPEHUW -HDQ /H 5RQG 1717 ࿰ 11 ᗙ 17 ᔐύᓴᧄିྟ㤫 柋1783 ࿰ 10 ᗙ 29 ᔐ࣯ᓴྟ㤫 ώᶗ Ẻฎ ύᓄฎ ώ

㄄ᗤ⺾ᵺל୅ݴⷍध㐩 7KH 0DF7XWRU +LVWRU\ RI 0DWKH PDWLFV DUFKLYH ┐⌴

?iiT,ffrrr@;`QmTbX/+bXbi@M/X+XmFf?BbiQ`vfSB+i.BbTHvf.^H2K#2`iX

?iKH

(2)

オ ᖖ ⹤ ᴬ

ᖨ ᵥ ⥩

ॠټೲ๾

㄄ᗤ⺾ᵺ 枼-/5 '¶$OHPEHUW -HDQ /H 5RQG 1717 ࿰ 11 ᗙ 17 ᔐύᓴᧄିྟ㤫 柋1783 ࿰ 10 ᗙ 29 ᔐ࣯ᓴྟ㤫 ώᶗ Ẻฎ ύᓄฎ ώ

ㆁᙖ⼹ᷱᖺ⌂ῳ๣ 栾᥺ⶏᄹ੯ൟ೵ڂ 0DGDPH GH 7HQFLQ ‧ ㅻ݇ഞ 栾‧ᗆᖺتۗ⦰ু⃞ᨎ㨷ഞىڂ 桍᳻٦ണ⠇တ⃞ু⻔⛘

ໜ࢖ῳسٍ⃞๒ࡁ㆝ᝮாဓ㦯⃞✃ ⻣ए㨷 6DLQW -HDQ OH 5RQG ᔢహ⃞⇔㔝ذ цᄞⳝتኘ⃘࡙Ἢ 栾⠅ᗆΌ⸋ᔢహ⃞ু๩ۦ᳻๒ ࡁ⃞ᔢু ц൥ᦧㆁᙖ⼹ᷱᖺڒ㒆ೲᄞ⠇တঝ⃞ цڒ⃞ᷫⶏু᳻

⺍῎㊞఑ &KHYDOLHU 栾൥ᄹᚇᤞ ± ॥ㄛ 'HWRXFKHV&DQRQ 栾ᖺ 㜯゙࡙ດ цڒᄣࢲ᪴ᆷᄞᄚᅚጮ๒ࡁጤ஗܊ 栾ຯ㚙ᕧဉुℛᝤ 5RXVVHDX ೵෇⬧ цㆁᙖ⼹ᷱী㚙ᷫ᥺⃞ሯᇭᄚദ 栾47 ᤺ڞࣆت Ωாڒݜວ ц

ㆁᙖ⼹ᷱ໦ၣᗆⳝᷫⶏㅉࡏتݗᔢᙈ๾ᜉ  ⿾ᖨ॒دᗆڜ⃞ᔢ

⃠㛦⪨ᚲࣝჃ 栾ى⵶๾⚫ত࡜ᕄ๾ х݇ㄖ๾ਘᔷ๾ цڒ໢ᔷ๾Ḛ ࢭᙌ⠜⿄ 栾᳻ᄞ܊዗᳻⦰ু⃞ᔷἱ⌋๾ວጆر٦ళ⊃ 桍㕐ᵃாᔢ ᙈ๾ᜉفঞࢲᄚ೬ຓᔢᔢ✹ 栾ےᄞ܊ڎس݅⊾ 栾዗᳻ছ໢ຓᔢ⃞

⦰ুટ⧙๾⛓ਘ ³⃚⌋ࡑᙀ᪆´ ⃞ى⵶㝸ၨ ц

ㆁᙖ⼹ᷱᨈᙌঞㅻᤳ⵾⃞ೲ๾ᔢ✹ 栾㖫⠇๾Ꮨᐙ٦ , ḅ㘢 1HZWRQ ਘ‧ڜ⦰ুᔷἱ⌋๾ວݜ⃞⦰ۦ ц1739 ၣ 7 ᙋ 栾ڒຌ

዗⏜ت␹๾ⲣ⹐ᕄ 栾ࡐຩᖺጟⷷ & 㕧⹱ 5H\QHDX ⊾ᷫ⃞ᔷ๾

ᔢ⌫ цڞᄞࡒၣࡐখ৅ဓ㦯⌋๾㓾ᐋٷ٦ٯ␹๾ⲣ౛৮ 栾ࡐຩᖺ

⇩⍭ᄴ࢛ᕥ⌫⃞⍕࢛ᕥᨷਘḎ㞓ாڍ⽶ࡐ⃞㓥໻ㅹऑ цㅚٲ౛৮

(3)

  $& ࠽⥿♭ &ODLUDXW 㓾ೕ஗⵺ ц╲ㅻၬᤄ✌☑ᄞ 栾ㆁᙖ⼹

ᷱᕧ 1741 ၣ 5 ᙋᤳ჎ㅪࡏ⌋๾㓾 ц‧ᗆ⌋๾㓾⃞✓⍄࢛கݗ⏯

┙ 桌᠕⻔㓾ೕ 栾঩ᙌ✏ᙘᄚ㞖⃞ڂᓁک 桍┸ゎ㓾ೕ 栾᥻ݗ๾㇩

‧ᗆᙌࡖݗ ঩ᙌدু 桍ࣚ㓾ೕ 栾ዜ⍄ㅛ⷇㓾ೕ 桍ࣾἱ㓾ೕ ц୽

᜝܊⺋঩ᙌࣆࡒ⍁ጁᖺᤳ჎㓾ೕ 栾ےᙌٲᕄỉفጮㅚக⍁╚⍄᳻㓾

ೕ цㆁᙖ⼹ᷱ࣍ㅪࡏ⌋๾㓾ᗆکೳᕄ๾ࣾἱ㓾ೕ 桍1746 ၣᐋ᳻ᔷ

๾ࣚ㓾ೕ 桍1754 ၣᐋ᳻┸ゎ㓾ೕ ц

ா 1741 ၣ⠌ 1743 ၣ㒙 栾ㆁᙖ⼹ᷱ໢ἱ⹐ࣸ๾⃞ೲ㊡⸵㙃ㅪ ⲟ٦⇩⍭ 栾ؿா 1743 ၣၸ࢖᷹٦᤼঱ᆄু⦰ъऑࣸ๾ы7UDLWp GH G\QDPLTXH 栾1744 ၣখ࢖᷹ъ᪉㞓⃞ၢⲫਘㅹऑы7UDLWp GH O¶HTXLOLEUH HW GX PRXYHPHQW GHV IOXLGHV ц1747 ၣ⃘ⲯ٦ࡒ␹㊟⵶

⹐ᕄ 桌࡚فت␹㓊ᕧୖ᪉ছ໛⃞ᕄ⎮Ểᗣ㟹ೕ⌋๾㓾Ẩ㊣ 栾ᕄف 㛘࠻ாᔷ๾ḎἱفኩΌދᄴ࢛ᕥ⌫ 桍দت␹ᖺ㓊ᕧო᎕ऑ⃞ 栾࡚

ف⏜تᤄᤳ჎ᏪΌᩂऑᕥ⌫ ц1749 ၣখ⃘ⲯ٦ᙌ㓊ᖳ࢛㦼 х᤺ဎ ਘ⎮ऑ⃞⹐ᕄ 栾໢ೳ㞓ࣸ๾⃘།ۦ࢖㊟⵶⼽ỉ ц

ㆁᙖ⼹ᷱ⃞⇩⍭ဉۦਘ⹐ᕄ໎ۦㇺڞᅚㅠ✈ু цڒㅪࡏ⌋๾㓾 ᄞ 栾໴ڞ࠽⥿ᩨۦ᳻⎸ᷧ໢ጀ 栾࠽⥿ᩨ⇩⍭⃞᥻تݗ⸵㙃 栾ㆁᙖ

⼹ᷱၬْㇺ⵶⇩⍭ 栾⛘ظ№ᅚ⃘ⲯ ц೬ᔷᇭᨦر 栾ㆁᙖ⼹ᷱगㅻ ٦࠽⥿♭ цㅚ⍁⎸ᷧتΩࢲ࠽⥿♭ঔغ 1765 ᳻ᤲ ц

⠇ 1750 ၣ㒑൝ 栾ㆁᙖ⼹ᷱفᕣ٦ᔷἱ⇩⍭ဉۦ 栾ࣺࡏ٦ ³⃚

⌋ࡑᙀ᪆´ 栾⠛ટ⧙ㅹऑ዗ੌت⾨▮ャ࢖᷹ບߊટ⧙ᅼላ⃞ъ⃚

⌋ࡑᙀы ц  ' Ṏᄹ♭ 'LGHURW ى▮ 栾ㆁᙖ⼹ᷱک⌋๾ࣚى

▮ 栾ےဉۦထ⾰࢖⌋๾␷ர цㆁᙖ⼹ᷱ᳻ъ⃚⌋ࡑᙀы໎⃞㒆␹

ၷⷁ 栾዗᳻ટ⧙ㅹऑ⃞ى⵶ᕄڧ цாၷⷁف 栾ࡑ㖭ⷉ⹐٦⌋๾

ਘㆀᄹક㙃 栾ؿΌ੼Ḏى⚉⶜㦼㓎ᖣ٦⌋๾঱ਘਖ਼๾঱ ц㕐ᵃ ㆁᙖ⼹ᷱ᳻٦ኩڔᙀ࢟໌ᛦੌ 栾ণ㘲ጥ⸟ຓᔢ⃞⅂ἱᆄ 栾ےாၷ ⷁفڎᵃᖣ≌ᎁ࢖ 栾⌋๾⃞ళ⊃ᖺ້㔦⃞ሯঞ 桍ㆀᄹ⃞ళ⊃ᖺ᱋

ᇭ хীᇭਘߓ৅⏯ 栾⛘ㅚٲㇺᖺڂݜ⠇ゎ❫೮჈ᬑ⃞ цᤳங᳻ഫ

(4)

ᤴ 栾ၷⷁ࢖᷹ᄞ╲္ঞࢲᔍᒺ цᤴ೩ 栾ㆁᙖ⼹ᷱㆧᒪ໎٦س໦ᔷ

๾ਘ࡚຅⇉⺼᝗℠ 栾࢟ヅᕧъ⃚⌋ࡑᙀы ц

 ᕧḝ᪵ࢲ⃞⇉⺼㖭ᄚႵ 栾ㆁᙖ⼹ᷱாㅚၬၣࡐ⃞⦰ۦ⾰࢖٦ ᔷἱᕥ㖭⃞⇩⍭ ц1752 ၣ࢖᷹⃞ъ0 ፕ⤺ 5DPHDX উἱر⃞㘈 ᡍἱ⹐ਘ້Όళ⊃ы 栾༝ᕧᅂἱḎἱ๾㘥ఝ 桍1753 ၣ࢖᷹⃞ъᕄ

๾ਘਖ਼๾⹐ঢыࡒॲ㕃 栾ᖺ㓊ᕧ㘈ᡍ хᨷᄝਘຓᔢ⃞໤ਾᕄ㕃 ц 1757 ၣ 栾ㆁᙖ⼹ᷱⷛકۙாὭೕ⃞ᕄ๾ວ 0$ GH ڷᷱᩍ 9ROWDLUH ᄞ 栾໎٦تݗ ³ᖃࡐ῎´ ᝗℠ 栾࢟⃗ாъ⃚⌋ࡑᙀы⏜ج ॲذ цڒாᕄفⲯ㖭⻩♶ 栾້⽶ذᖺⷼਝㅚݗఖမ ц⛘ъ⃚⌋ࡑ ᙀыᤳദாὭೕ࢖᷹ 栾╁ᚶⳝ‧໾া㍅٦ъ⃚⌋ࡑᙀы⃞࢖᷹⷟ম

⺯ цㆁᙖ⼹ᷱㅚᡥۦㆂ❇٦ъ⃚⌋ࡑᙀы⃞▮ャᕥ㊬ 栾ঞࢲટ⧙

ㅹऑࡐ㇩ڂੌ⃞ᔍᒺ 栾⦰ুਖ਼๾ວ -- ℛᝤ 5RXVVHDX ᔍᒺᄣᙆ

঑຤ цㆁᙖ⼹ᷱდਚㄖঔࣚى▮✓क ц

1760 ၣڞᄞ 栾ㆁᙖ⼹ᷱ☟☪ᄨ٨ᔷἱ⇩⍭ 栾ى⵶ໝ⦰ᖺࡔ ॲဌ⦰ъᔷ๾ጀࡢы2SXVFXOHV 0DWKHPDWLTXHV 栾ࢲ 1780 ၣጁ࢖

㨊 ц1770 ၣڞᄞ⃘ⲯ⃞⹐ᕄس೬ 栾1777 ၣ⃘ⲯ⃞ᙌ㓊᪉㞓㓥໻⃞

⹐ᕄ 栾ᖺڞ়ۦ⛓ $ ᩂ⫱ %RVVXW ਘ -$ GH ๦೬౻ &RQGRUFHW

᳻ى ц

ㆁ ᙖ ⼹ ᷱ ┸ ῳ ᙣ ල 栾ے 㒆 ᙛ ⠛ ᨎ 㨷 ഞ ى ڂ - GH ए ⃷ ┌ ᕞ /HVSLQDVVH ாت⾨ цڒ⃞ῳ᪃⠛‧ᗆਖ਼๾ວݜتᡥ 栾ذॗࢲرॗ

ဉۦ 栾ᗓذঔᨎ㨷᪃ऑ цㆁᙖ⼹ᷱᄚ໦ᕮⲟ 栾ᙆ㒆⃞تᤄᖺ 1764

ၣኩᗣ㟹ೕமộ➛Ḛᴀِㆣ 栾ࢲᛕᚲộຢۙ٦دݗᙋ ц㕐ᵃமộ ࡣد⹈ڒ⌣༁ᄹம 栾໴کᗣ㟹ೕ⌋๾㓾㓾㒆 栾ㆁᙖ⼹ᷱڎනⷁ⺍

╆ 栾ؿᏰ⪥ / ᤦፕ (XOHU ᓁک 栾ےமộ൝┸ᙣ൦کᤦፕ ц1762

ၣ 栾ܭ⃠॥Ꮗὐ඘٩غᙄㆣ⹈ㆁᙖ⼹ᷱک⃠೴๣℗⻏ڂ 栾ⳝڒ

⺍╆ ц ᕧڒாᔷἱ๾⌋ف⃞㊟⵶⼽ỉ 栾1772 ၣⳝ㆛᳻ဓ㦯⌋

๾㓾⃞┸ゎ⌏ᙀ 栾዗᳻ᄉ㘐ᙆೲ⃞㓾ೕ 桍ᤦ᩺೬ᔷமວ⃞⌋๾㓾

✄⹈ڒ᳻ம೩㓾ೕ цㆁᙖ⼹ᷱㆧᖺ㖤ၣ⌋๾ວ⃞⡣ဳ℉ঙ 栾⦰ু

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⌋๾ວ -/ ፕ᜝ᙖᖃ /DJUDQJH ਘ 36 ፕᗣፕᕞ /DSODFH ா㖤

ၣᗆڜ 栾ㇺᄣࢲڒ⃞㧠थਘᔆ፾ 栾ڒᏰ⪥ፕ᜝ᙖᖃঔᗣ㟹ೕ⌋๾

㓾 栾Ᏸ⪥ፕᗣፕᕞঔဓ㦯⌋๾㓾 栾ڞᄞㆧتΩㅪⲟ๾ⲣⷉ⹐ ц 1765 ၣ 栾ㆁᙖ⼹ᷱங⁙㕛㒑㚙ᷫ᥺⃞ວ 栾ۙࢲए⃷┌ᕞ໤ൢ

⬧ цாണ⃞ⓙᅂᵥᕍرᆪᄯ٦ޛ႒ 栾ڞᄞ໴☟☪ۙாㆽⴂ цک⌋

๾㓾⌏ᙀᄞ 栾ڒ┺☀▮ャਘ࢖᷹ဓ㦯⌋๾㓾ထᔓ㓾ೕ⃞ᕄ㕃 栾ے ங㓾ࡐሣ⵽࢛ᤷ⛘ㅪ།▯ቜ ц1776 ၣ 栾ए⃷┌ᕞ໤ൢঔغ 栾ㆁᙖ

⼹ᷱ㖪္ᇛ 桍ࡣࣺذဉۦ⃞س㘗ࢯ 栾ڒ⃞ᗓၣᖺா೺ᙘفႃㅻ

⃞ цㆁᙖ⼹ᷱঔغᄞⳝຊ⧀ாဓ㦯မ㇔ಟ௅ 栾 ᕧڒ⃞ছຓᔢⲯ Ἢ 栾ဓ㦯မᔐၽ፞╆᳻ڒ⠝ⲟ⧀⋲ ц

ㆁᙖ⼹ᷱᖺݗ೬῵⌋๾ວ 栾ڒ໢ࣸ๾ хᔷ๾ਘೳᕄ๾⃞ೲ

㊡⸵㙃ㅪⲟ٦⇩⍭ 桍⹐ᕄਘໝ⦰ᄚ೬ 栾ㆧᙌೲ㊡๾ⲣㅛ݅ цߘ 1805 ၣਘ 1821 ၣாဓ㦯࢖᷹⃞ㆁᙖ⼹ᷱъᕄ㕃ы2HXYUHV ໴ᙌ 23 ॲ ц

ㆁᙖ⼹ᷱۦ᳻ᔷ๾ວ 栾ী॒ࡔغ⓿࡚ڒᔷ๾ວتᡥ 栾⸟᳻᧌ⶫ

Ḏἱ ى⵶ᖺࣸ๾ 栾भ፩ೳ㞓ࣸ๾ ક㙃ᖺᔷ๾⃞℠ᡞ цᤳഫڒா

ъ⃚⌋ࡑᙀыၷⷁفዷ⸲ 桌⌋๾⬧ᕧᄨ॒جغ⓿⃞ᔷ๾ᗆڜࢲ॒ࡔ غ⓿⃞ࣸ๾ᗆڜ⃞ヷ⻝ 栾ࣸ๾ኩ⸋ᖺᔷ๾ວ⃞ى⵶⠜⿄ цڒ໢ࣸ

๾⃞⃘།ۦ࢖٦㊟ೲ⼽ỉ 栾ٜᖺᔷ๾࢛ᚬفتٲ㊟⵶࢛ᔆ⃞㒑፟

⛓ ц

1 ࡇහ୻↹℠⊤

(1) ࡟ࡇහ୻↹—င⋞ ḅ㘢ࣸ๾㞓⓼⃞Ⴣ⎧ 栾ᖺ॒ࡔغ⓿⃞

⌋๾ວݜຌ዗⃞ цㆁᙖ⼹ᷱᖺㅚጟ๾⛓⃞޵࢖ڜⲯِت цڒாࣸ

๾ళ⊃ذ⃞⼽ỉ 栾㕃فছᖯாڒ⃞ъऑࣸ๾ыف ц

ъऑࣸ๾ыᕧ 1743 ၣ࢖᷹ 栾1758 ၣࡣ᷹ цࡑᙀ࢛᳻ࡒ㇩࢛ 栾

ࣆ㖭ㆧᙌᄚ㒆⃞ਖ਼๾ၷⷁ ц⸋ᙀᖺڒ⃞⌋๾ဉۦفᙆᙌু⃞ۦ

ਾ ц

(6)

ாਖ਼๾ၷⷁⴂ 栾ڒ㛘࠻ᎁ࢖⌋๾㖰਍ထ╲⃘ῳ 栾㕮⵶ᄚ೬ڂ 㒆ᙛࣿࣸጁ❫ຌ዗ цڒ⠇တ⃞کकᖺጮࣸ๾ㅚ㒋ᕟ⌋๾⓼╚ऺਘ ࡕ჎ऺ цڒىღڞሯ⶘⹐⃞⸟⺼⹐ۦ᳻⌋๾⃞ళ⊃ 栾ےٜ݁‖٦ 5 ⏐॥ࡁ 'HVFDUWHV ⃞⶜㦼 桌⅂ἱ໴ᖺᖣ⃙ਘ⑹૕⃞ цၷⷁف

⃘ᐣ٦ڒ໢ࣸ๾⃞ਖ਼๾⶜㦼 栾შ⸾ళᙥ៷ᅡᅃ㘙⏘়ᖣ⃙ਘ⑹૕

⃞উࣁ цڒ⸟᳻ㅹऑᖺᗆ㒙ਘ⍰㒙៷ᅡ⃞ت⍁┺় 桍ڒ᜚ᓆḎ㞓 س❫٭℩⍴ㅓ⃞٨້ 栾ຖ⚉Ḏ⽶⃞سমࡏᆄ 栾⸟᳻Ḏ⽶ উ๣┺

዗ 栾উ๣ᖺ఼∙سমࡏ⃞ 栾উ๣㒙 ᛖ⍁ჯ⑾✌╁ цےㅚٲჯ⑾ ᖺڃ㦧" س⵽ᄣ᥿ḅ㘢Ό⃞ڞ೴ HWKHU ᘽ㞖ᖣ ц㓳ᕧ‧ᗆ⃞Ḏἱ๾

ᧃ᭭ 栾سম❫ᘽᬂࡏ٦ⶫḎ⽶⃞╁ᠫ ц

ъऑࣸ๾ы⏜ت㇩࢛ف 栾ㆁᙖ⼹ᷱᐋ࢖⠇တ⃞ㅹऑدೲຖᄝ 桌

⏜تຖᄝ⠛ḅ㘢⃞ቝᆄຖᄝ℩ী 栾ے═࢖تݗၬ۟๾⺯ᖣ 桍⏜

٩ຖᄝ᳻ㅹऑ⃞়዗ 栾═࢖تݗࢯΌၢⲟகㆬჽᨷࣁ⃞ᔷ๾⺯

ᖣ 桍⏜دຖᄝ᳻ၢⲫຖᄝ 栾ےسᖺ⺋ۦΌࣸ⠛ছۦΌࣸ 栾⛘ᖺΌ ऑ㊡ாᒝᒺࣆᄞ⃞ຉᆙ܊ⲯ⊡ 栾࡚فᒝᒺᗆ㒙᳻㕛ᔧ㒙㔡 цऑ㊡

ຉᆙف㔴৖⽶㊡ຖ⚉ 栾⛘سΌࣸ܊ຖ⚉⽶㊡ ц

ъऑࣸ๾ы⏜٩㇩࢛ف㓎ㄼ٦⦰ু⃞㄄ᗤ⺾ᵺछẺ 栾ؿΌسী

ჽ჎⃞܎๣܊⸲ᖣ цر㖭ڞἪڜ⸩ⷁਘ⏘⬭⑹ㄼᤴউἱ 桌 ۦΌᕧتݗḎ㞓⃞೩ࣸ⠛ऑࣸ⃞ছۦΌِࣸਘ⏯ᕧ㕦 ц९

F + (−ma) + N = 0 栾 (1)

࡚ف m хa ᳻Ḏ㞓⽶㊡ਘࣺㅠႃ 栾F ᳻Ḏ㞓ঞࢲ⃞ΩᏮ೩ࣸ 栾N

᳻Ḏ㞓ঞࢲ⃞┃ᚊছۦΌࣸ ٜᖺ೩ࣸ цாᨈᙌ┃ᚊᗆ 栾℩ኩᙌ N = 0 栾1 ჎዗᳻

F − ma = 0 栾 (2)

⠛ḅ㘢⃞ㅹऑ⏜٩ຖᄝت⠍ 栾঩ᖺㅪⲟ٦⌣㘖 цےㅚᖺ៷ᅡذ⃞

⻝ऺ 栾ᙌرࢧ㊟⵶ሣ⚉ 桌

1 Ό 2 ჎ⲯㆁ⃞ၢⲫ㓊ܫ 栾মڞጮऑࣸ๾ક㙃ヷऺ᳻㖩ࣸ

(7)

๾ક㙃܊⬧ἱ ц

2 ாᙌ┃ᚊᇭᨦر 栾Ό 1 ჎㖪္ᙌࢯ 桍຅⠛⬪ࣹউἱ╁়

ᄞ 栾মࢧ࢖ऑࣸ๾⃞ᗣㅺᕥ⌫ ц

3 Όᕧ࣍㞓⃞ၢ㖭ㅹऑᗆ 栾মࢯΌၢ㖭㖩ࣸ๾ᕥᨷ 栾܃ક 㙃⑹ऺ ц

້㔦ذ 栾ㆁᙖ⼹ᷱউἱㆧ᳻سٍᄞࣝ⎧⃞࢛ᚬࣸ๾ጆر٦ళ

⊃ ц

(2) ᧇ㚳ࡇහ℠⊤ ᪉㞓⃞ࣸ๾⇩⍭ᄨḅ㘢㒑൝ 栾ےۦ᳻

ت㒋๾⌋ ² ᪉㞓ࣸ๾ 栾ࣁᖺ ॒ࡔغ⓿⃞ᤦፕ х' ۄࣿࢯ

%HUQRXOOL х࠽⥿♭ਘㆁᙖ⼹ᷱጆر⃞ళ⊃ ц

ாᐋ࢖ㆁᙖ⼹ᷱউἱᄞ 栾ڒ⠇တ໴Όᕧ⇩⍭᪉㞓ㅹऑ⃞تٲى

⵶ક㙃 栾भ፩⏐॥ࡁᐋ࢖⃞ⲟᖮ⓼╚ㅹऑ⃞ᯙᬟἱ⹐ڞঘ࠽⥿♭⃞

ᙌ㓊௅ἮჽṊἱ⹐ ц

1752 ၣ⃘ⲯ⃞ ³᪉㞓㓥໻⃞ت⍁ᕟἱ⹐´ (VVDL G¶XQ QRXYHOOH WKpRULH GH OD UHVLVWDQFH GHV IOXLGHV تᕄ 栾⏜تᤄΌ᪉㞓ऑࣸ๾

⃞ᄴ࢛ᕥ⌫ⲯ⊡౞ 栾ؿᐋ࢖٦⦰ু⃞㄄ᗤ⺾ᵺⶌⷕ '¶$HPEHUW¶V

SDUDGR[ ц຅້㔦ذᖺ᪉㞓ࣸ๾ف⃞تݗຖἱ 桌Ḏ㞓ாೲ␷ர⃞

㖩ᤲዜऩㅠㅹऑ⃞سমೄ◟ хᴸⓄᆄ᪉㞓فۦ⏯ㅠㅹऑᗆ 栾຅ዷ ঞࢲ⃞೩ِࣸਘ᳻㕦 цㅚᖺㆁᙖ⼹ᷱᄨἱ⹐ذ໣࢖⃞╁ᚶ 栾ℷ⾨

܊ᙌ⇃℮ 栾ங᳻Ḏ㞓ா᪉㞓فㅹऑ◮ᙈঞࢲ㓥໻ 栾ㅚᖺت⍁⛢ᔧ

ࣸ 栾◮ਘسᙈ᳻㕦 цㆁᙖ⼹ᷱாᕄف໢ᤴᙣۦⶫ㊝ цᎃἪா⃞⶜

㦼 栾ㅚݗຖἱؿᨈᙌ㎟ 栾঩ᖺἪ້فس๪ாᴸⓄᆄ᪉㞓 ц९܃Ⓞ

ᆄ㖪္໤⃞᪉㞓 栾໢࡚فㅹऑ⃞Ḏ㞓ㇺᙈ⾨㊟⵶⃞ۦΌ 栾ங᳻Ⓞ

ᆄ܃᪉㞓ாḎ㞓ⲯ㖭῵ῳ࢜৅ኩࣸ 栾९ᑵᓎ㓥໻ ц

㕐ᵃᕄفㆧᙌٲ࡚຅ક㙃 栾ഫᙌٲރຖ⇿್٦ㅤ☪ᆄຖᄝ 栾ᄞ ڂڎࡕ⸟⸋⹐ᕄ໢᪉㞓ࣸ๾ళ⊃ἱ⹐ᙌ㊟ೲ⼽ỉ ц+ घᕞ 5RXVH ਘ 6 ⢿ᕞ ,QFH ᙄ⸲ 桌³ᖺㆁᙖ⼹ᷱ⏜تᤄდࡏ٦᪉㞓ㅠႃਘࣺㅠ

ႃ࢛㊡៷ᅡ ц´

(8)

ㆁᙖ⼹ᷱா᪉㞓ࣸ๾ذ⃞Ⴣᡮ 栾⠛‧ᗆᤦፕ х࠽⥿♭ хۄࢯ

ࣿ⏯㨊ু ц࡚فᤦፕ⃞⼽ỉᙆೲ 栾ے࡚㚣ၬݗڂᄚ㕜Ꮮুᤄ 栾ங

᳻ڒݜسᕣ௅℩٭ⷉ⹐ 栾ᄚ㕜⸲੔تݗላᨷᖺ⸴࠻ᐋ࢖܊⃞ ц (3) ఺㚳ࡇහ—ౘ୻★֘ղ ㆁᙖ⼹ᷱጮࣸ๾ἱ⹐Όᕧ⇩⍭

ೳ㞓ㅹऑ 栾዗᳻ೳ㞓ࣸ๾⃞഑ళ⛓ِت ц࡚⼽ỉى⵶㕃فாࡒ

㇩⦰ۦف 桌تᖺ 1749 ၣ࢖᷹⃞ъ࢛㦼᤺ဎਘ௅Ἦ⎮ऑ⃞⇩⍭ы 5HFKHUFKHV VXU OD SUpFHVVLRQ GHV HTXLQR[HV HW VXU OD QXWDWLRQ GH OD

WHUUH 栾ாᤴᙀف㕐ᵃᏪΌ٦⠛࠽⥿♭℩ی⃞ᕥᨷ 栾ےாㅹऑᕥ

⌫⃞⍕࢛ㅻ⌫ف 栾Ό٦ᘽ೬⃞ᓸऑ㘖 栾܃ᄣ╁ᚶᘽ⏘়⶜ᬣ 桍٩ ᖺъຈຕ㞓⓼⃞ၬݗ⵶㦼⇩⍭ы5HFKHUFKHV VXU GLIIHUpQV SRLQWV LPSRUWDQWV GX V\VWpPH GX PRQGH 栾ࡘ࢛دॲ 栾1754 ၣ࢖᷹ࣆࡒ ॲ 栾1756 ၣ࢖⏜دॲ ц࡚ف⼽ỉᙆೲ⃞ᖺر㖭ࡒݗ⸵㙃 桌

تᖺᙋἮㅹऑἱ⹐ цா॒ࡔغ⓿க॒ၣڜ 栾ᤦፕ х࠽⥿♭ਘ ㆁᙖ⼹ᷱၬْীᗆ⇩⍭ᙋἮㅹऑἱ⹐ 桍ங᳻ᎃḅ㘢ἱ⹐ 栾ထس

❫ⶫ㊝ᙋἮㅹऑ⃞Ἢ⼋ 栾⛘ظἱ⹐ⷆ␡ਘ⶜ᬣِ㒙⃞ဎም܊ም ೲ ц1747 ၣ 栾ㆁᙖ⼹ᷱ⠛࠽⥿♭ாীتೳ৅ဓ㦯⌋๾㓾ᐋٷ٦㓊 ᕧᙋἮㅹऑ⃞౛৮ цڒݜㇺⶫ㊝٦ᙋἮㄩ௅㦼⌣ऑ⃞Ἢ⼋ 栾ؿா

1749 ၣᐋܚ٦ᘽ⸌┨⃞╁ᚶ ц1754 ၣ 栾ڒݜࡒڂখၬْীᗆ⃘

ⲯ٦হ⠇⃞ᙋἮㅹऑᔷݽⲯ 栾዗᳻ᙆᖆ⃞ᙋἮᘟⲯِت цㆁᙖ⼹

ᷱ⃞ᙋἮㅹऑ⇩⍭዗ᚶ 栾ヅᕧъຈຕ㞓⓼⃞ၬݗ⵶㦼⇩⍭ы⏜د ॲ ц

٩ᖺ㓊ᕧ௅ἮჽṊਘ⠇ヷ⃞ἱ⹐ цㅚٜᖺㆁᙖ⼹ᷱী࠽⥿♭

⎸ᷧ⃞⸵㙃ِت 栾ᖺḅ㘢ᗆڜ໴๪ா⃞⛐⸵㙃 цㆁᙖ⼹ᷱ═࢖٦ ᪉㞓⠇ヷᗆၢⲫჽṊ⃞ت⠴╁ᚶ 栾࠽⥿♭⎧९Ό܊⇩⍭௅Ἦ⃞⠇

ヷ 栾㛘࠻ா1743 ၣ࢖᷹٦ъ௅Ἦ⃞ჽṊἱ⹐ы7KHRULH GH OD ILJXUH

GH OD 7HUUH цㆁᙖ⼹ᷱ໢࠽⥿♭㓊ᕧس௎ऩ᪉㞓⠇ヷᗆ⃞ჽṊἱ⹐

ㅪⲟᏰႵਘ⳾࠸ 栾⇩⍭╁ᚶヅᕧъຈຕ㞓⓼⃞ၬݗ⵶㦼⃞⇩⍭ы⏜

2 ॲ цڒڞᤴ᳻ళ⊃ 栾ᘽ᭭≌௅⇩⍭٦᤺ဎਘ⎮ऑἪ⼋ 栾ڞঘ℩

(9)

ی⃞ᙋἮೳၢऑ 栾᳻ೳ㞓ࣸ๾⃞഑ళۦ࢖⼽ỉ ц

2 ᑸහߪᗬ—㎳ኡ★

⠇ḅ㘢ਘ *0 ⥿ယ໻⣢ /HLEQL] ⃘Ἢᄴ⍕࢛ᄞ 栾ᔷ๾⃘།ࢲ تݗᕟ㔝ᥧ ц⢿மᔷ๾‐ ᕧ఼፾ၬ۟ᕥᨷ⛘ㅪ།▯ቜ 桍ᤦ᩺ೲ 㔎ᔷ๾ວॵ☟☪ா࢛ᚬᕥᨷذسᕣᏫ┡⛘ㄢㅠ⃘། 栾ㅪࡏᔷ๾࢛

ᚬ⃞㒑፟ᗆᙛ цㆁᙖ⼹ᷱᖺ㊟⵶⃞㒑፟⛓ِت 栾࡚዗໴ߘᤄᕧᤦ

ፕ хፕ᜝ᙖᖃ хፕᗣፕᕞਘ ' ۄࣿࢯ %HUQRXOOL ц

ㆁᙖ⼹ᷱ⃞ᔷ๾዗ᚶᄞ܊ࡑ㇩ᔉࡏъᔷ๾ጀࡢы цر㖭ڍ┯࡚

ى⵶⼽ỉ ц

(1) ᜯ㐕᜶Ⴄ ㆁᙖ⼹ᷱாъ⃚⌋ࡑᙀы⃞ ³ᄴ࢛´ ᝗℠ف໎

ㆀ 桌³ᄴ࢛๾ᖺۦ᳻ᙆࢩ᥿ਘᙆ┸᥿⃞ᕥᨷ 栾९᧌࢖ㅚٲ᥿⃞៰ 㓳⃞ت⍁ᕥᨷ ц´ ᕄفㆧጮ໣ᔷℷ዗៰㓳 栾ؿ⹐⺯ 0

0 ম⏯ᕧک۟

㊡ ц

ா࡚຅تٲᕄ⎮ف 栾ڒ⸲៰㓳⹐ᖺᄴ⍕࢛๾⃞⅂ᤳፍ⼋ 栾س ᖺᄴ࢛๾فᴸ⎔໤㊡⃞تݗક㙃 栾⛘ᖺᙌ㓳㊡⃞ક㙃 цڒ═࢖٦

៰㓳⃞ダദຖ⚉ 桌³تݗ⻝㊡⿇ᕧتݗதຖ㊡ 栾⿇ㄩ⌫ႃ໤ᕧک۟

═ຖ㊡ 栾ظ⻝㊡ᧆㆉㆁسࢲதຖ㊡ ц´ ےڒᨈᙌጮㅚ⍁ⲯㆁࡕ჎

ऺ ц

ᤳഫ & ᩂ⛴ %R\HU ᎁ࢖ 桌ᨈᙌㅋ➄ߊ╚⃞ၬ۟ᕥᨷᄉ㘐 栾 سম❫ጮ៰㓳Ό୽᜝ჽ჎㓎ㄼ 桍ےڒᖺ‧ᗆၬْ੼تጮᄴ࢛ℷ዗ᖺ

ࢗᔷ៰㓳⃞ᔷ๾ວ ц

(2) ⑌ᑸṪ⵼ ᴸ⎔┙ᔷா॒ࡔغ⓿ف 栾ჽ჎ⷉ⹐۞ى໣௅

ۗ 栾ت⠴ㇺۦ᳻೬㘖჎⃞ᏰႵ 栾঩ᙌ໦ᔷڂ॑ࢭ㒑ᔉᕀ┙ᔷਘ⃘

ᔧ┙ᔷ цㆁᙖ⼹ᷱᖺ࡚فِت 栾ڒாъ⃚⌋ࡑᙀыف⃞ ³┙ᔷ´ ᝗

໎ㆀ 桌‧┙ᔷ⃞㘖ᔷತࣺ⛘┙ᔷݽም܊ም⿇৅ᛖᙌ㓳㊡ 栾ࣁ⍄ᤴ

┙ᔷ᳻ᔉᕀ┙ᔷ ц´ Ꮾ⦰ڒᐋ࢖٦تݗࢬࢭᴸ⎔┙ᔷ╆໢ᔉᕀ⃞ㄔ ᨷ 桌⢵┙ᔷ

(10)

u1 + u2 + u3 + · · · + un + · · ·

⃞℩㈩ࡒ㘖ِ᥿⃞╆໢ݽ |un+1

un

| 栾ா n ೲᕧᛖதຖᤳᔳᔷ N ᗆ 栾ᧆㆉ໤ᕧتݗ⠛ n ᴸ㓊⃞ᤳᔷ r 栾ظ r < 1 栾ࣁذㄼ┙ᔷ᳻

╆໢ᔉᕀ цㅚ໴ᖺ⠌ڌڎாኩΌ⃞⦰ু⃞㄄ᗤ⺾ᵺ࠾࠿ၜ ц

໢ᕧ⃘ᔧ┙ᔷ 栾‧ᗆت⠴ڂᵥᡥᏪΌ 栾ㆁᙖ⼹ᷱா 1768 ၣ࢖

᷹⃞ъᔷ๾ጀࡢы⏜ 5 ॲف⸲ 桌³ዷᙌళᕧسᔉᕀ┙ᔷ⃞Ᏸἱ 栾ா

ዘℷ܊ㇺᖺ॒࢛ম‹⃞ ц´ মᖺڒ⃞ℷᨷா‧ᗆؿᙣდ⾨㊟ⶁ ц

॒ࡔغ⓿ထ࢖Ἢد⶝┙ᔷ 栾ㆁᙖ⼹ᷱ໴ᖺ৑ዷᙌࢗᔷㇺ❫ⲯ⊡

᳻د⶝┙ᔷ⃞ક㙃 栾ীᤦፕਘፕ᜝ᙖᖃ⏯ㅪⲟ٦ᶒᴀ⃞ⷉ⹐ 栾᳻

॒ٚغ⓿Ⴣ⎧د⶝┙ᔷἱ⹐ጆر٦ళ⊃ ц

(3) ၷߪᒥ≢ 㔮⦰॒ࡔغ⓿ف⃞ࣸ๾ਘೳ㞓ࣸ๾⸵㙃⃞Ⴕᨼ

ᬂࡏ⇩⍭ 栾္ᄴ࢛ᕥ⌫ᄣࢲㄢㅠ⃘། цㆁᙖ⼹ᷱாㅚᕥ㖭⃞⼽ỉ 㕃فா᧌ⶫذ ц

ⶫ㞖㔝္ᄴ࢛ᕥ⌫⃞ت⍁ళᙥᕥᨷᖺ㓰㔝ᨷ 栾ㆁᙖ⼹ᷱ㛘࠻ጮ ٩㔝ᕥ⌫㓰㔝᳻ت⠴ჽ჎ᕥ⌫

dy

dx = a0(x) + a1(x)y + a2(x)y2 栾 (3) ؿظ਍ু᳻ ³㊞॥⧏ 5LFFDWL ᕥ⌫´1763 ц

ா္ᄴ࢛ᕥ⌫ംⶫ⃞ⷉ⹐ف 栾ㆁᙖ⼹ᷱ⃞⼽ỉᖺࣺშ٦ᤦፕா

1768 ၣᐋ࢖⃞ࢬࢭᨷ 栾९ாᙣ⇉ㅛⶫᗆ 栾ᄨتݗḚ᥉⍕࢛㑣ࢭം

ⶫ⃞ࢬࢭᨷ 1769 ц

ாㆁᙖ⼹ᷱڞࣆ 栾္ᄴ࢛ᕥ⌫⃞ⶫ঩Όࢩ⏯ࢗᔷⲯ⊡ 栾ᤦፕਘ ㆁᙖ⼹ᷱ㒑൝⇩⍭Ό᧌⍕ჽ჎⃞ࢗᔷۦ᳻ⶫ цㆁᙖ⼹ᷱா 1767 ၣ ᎁ࢖ 栾ᢐல⍕࢛মڞۦ᳻္ᄴ࢛ᕥ⌫⃞ⶫ ц

ㆁᙖ⼹ٜᷱ᳻ދᄴ࢛ᕥ⌫⃞⸤ῳސ࢖٦㊟ೲ⼽ỉ цᖆா 1743

ၣ࢖᷹⃞ъऑࣸ๾ыف 栾ထ࢖Ἢދᄴ࢛ᕥ⌫ 桍1746 ၣ⃘ⲯ⃞ъღ

▛⃞ო᎕ऑᗆჽ዗⃞ᘻ▤⇩⍭ы5HFKHUFKHV GHV FRXUEHV IRUPp SDU

(11)

YLEUDWLRQ GH OD FRUGH WHQGXH ف 栾㛘࠻ᐋ࢖٦ᩂऑᕥ⌫

2y(t , x)

∂t2 = a22y(t , x)

∂x2 (4)

࡚ف a ᳻္ᔷ 栾⠛ო⃞ັႃਘღࣸᙌ㓊 цㆁᙖ⼹ᷱ⺯ᖣ٦຅⃞ⶫ

᳻ at + x ⃞ࢗᔷ⠛ at − x ⃞ࢗᔷِਘ 栾ؿⷉ⹐٦ㅚࡒݗࢗᔷாࢩ

൝᝗ڧر⃞㓊ܫ ц

1750 ၣ 栾ㆁᙖ⼹ᷱდࡏ٦࢛㕛⻝㊡⃞ᕥᨷ 栾ጮ 4 ჎⃞ⶫⲯ⊡

y(t, x) = g(t)h(x) (5)

ڜࡏ 4 ჎ᄞ 栾মऺ᳻ g(t) ਘ h(x) ⃞ࡒݗ္ᄴ࢛ᕥ⌫ 栾ؿ⺯ᖣா

ო᎕ऑ⃞ࢩ൝᝗ڧر 栾g(t) хh(x) ࢛ࢭ᳻ t ਘ x ⃞ㅩᙛࢗᔷ цㅚ ᖺἪாڎாᏪΌ⃞ت⍁ⶫދᄴ࢛ᕥ⌫⃞ళᙥᕥᨷ ц

1763 ၣ 栾ㆁᙖ⼹ᷱㅪتᤵⷉ⹐٦س௎ऩო⃞᎕ऑ 栾ᄣ࢖Ⴕ⚉

⃞ᩂऑᕥ⌫

2y(t, x)

∂t2 = A(x)∂2y(t, x)

∂x2 (6)

ாΌ࢛㕛⻝㊡᧌ⶫㅻ⌫ف 栾࢖Ἢ٦္ᄴ࢛ᕥ⌫⃞ㆬݽਘḚᄷݽક 㙃 栾ےᙣᬂࡏرঔ ц

ㆁᙖ⼹఼ᷱ፾ދᄴ࢛ᕥ⌫⃞ⶫᖺ⠇⻝㊡⃞ⶫᚬࢗᔷ 栾ㅚ໴໾

㓳٦ڒঝᄣᘽ೬⃞዗ᚶ 桍ڒ㛘࠻॑ࢭ٦ދᄴ࢛ᕥ⌫⃞Ḛⶫਘㅛ ⶫ 栾ے⸟᳻ㅛⶫᘽ㊟⵶ 栾ᨈᙌ⸟⺼ࢲாⶫ᧳້㔦ક㙃 ഫო᎕ऑ ᗆ 栾᮹⿏ࢩ൝ਘㆬ‐᝗ڧ⃞ḚⶫጁᙌۦΌ ц

ㆁᙖ⼹ᷱாᔷ๾ذㆧᙌᄚ೬࡚຅዗ᚶ 桌ڒᖺᖆᙛ⇩⍭ⴜᔷᆄ⽶

⃞ڂ 桍ㆧᖺ⺯ᖣڜᔷ๾ళᙥຖἱ⃞ᙆᖆᔷ๾ວِت 栾㕐ᵃ⺯ᖣس

ຌࡑ 桍ڒ໢៷ổ⹐ٜᙌ⇩⍭ ц

(12)

 ᕧ॒ࡔغ⓿⃞᤼঱Ḛ㦼 栾ㆁᙖ⼹ᷱী࡚ڒᔷ๾ວݜتᡥ 栾࠘

㊡ᄨࣸ๾ хೳᕄ๾ х࠼๾ਘ✏๾⃞হ⍁⸵㙃⇩⍭ف 栾㒑፟࢖ᔷ

๾࢛ᚬ⃞হ࢛ᔆ цےஙᙣ❫ᄨ୽ັਘ⓼╚ऺᕥ㖭ᬂࡏ 栾ᔓாᗓ

ၣীሣፕ᜝ᙖᖃ⃞ℷᨷ 栾⸟᳻ᔷ๾⃞ᅼላဎس೬ᅚ⎔№٦ ц້㔦 ذ 栾ாڒݜ⃞⼽ỉళ⊃ذ 栾॒ٚغ⓿⃞ᔷ๾⃘།ᄣᘽᅚ ц

ࣕತᒄḂ

[1] $ %DVWLHQ HGLWRU 2HXYUHV SKLORVRSKLTXHV KLVWRULTXHV HW OLW WHUDLUHV GH '¶$OHPEHUW 9ROV 1 ± 18 3DULV 1805 ц

[2] * %RVVDQJH HW / %pOLQ HGLWRUV2HXYUHV FRPSOpWHV GH '¶OHPEHUW 9ROV 1 ± 5 3DULV 1821 5HSULQWV 1967 ц

[3] -/5 '¶$OHPEHUW 2SXVFXOHV PDWKHPDWLTXHV 9ROV 1 ± 8 3DULV 1761 ± 1780 ц

℠⊤ᒄḂ

[4] - 0RUWRQ %ULJJV -HDQ /H 5RQG '¶$OHPEHUW'LFWLRQDU\ RI VFLHQWLILF ELRJUDSK\ 9RO 1 1976 110 ± 117 ц

[5] & %R\HU 7KH KLVWRU\ RI FDOFXOXV DQG LWV FRQFHSWLRQDO GHYHORS PHQW 1HZ <RUN 1949 ц

[6] 0 .OLQH 0DWKHPDWLFDO WKRXJKW IURP DQFLHQW WR PRUGHUQ WLPHV 2[IRUG 8QLYHUVLW\ 3UHVV 1972 ц

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