長岡工業高等専門学校研究紀要

論第49巻（2013）文୕᮲ᮏᡂᑎࡢ⣮ኻ⟬㢠
1ᾛ⏣ ࿴ⰾ ࣭እᕝ ୍ோ122୍⯡ᩍ⫱⛉㸫ᩘᏛ㸦Liberal Arts-Mathematics, Nagaoka National College of Technology㸧㟁ᏊไᚚᕤᏛ⛉㸦Department of Electronic Control Engineering, Nagaoka National College of Technology㸧

The Sangaku Lost from the Honjyǀji Temple in SanjyǀKazuyoshi WAKUTA 1 and Kazuhito TOGAWA 2Abstract
A mathematical tablet called sangaku was dedicated to the Honjyǀjiʊa Buddhist temple in Sanjyǀ in1800. Although the sangaku was lost, fortunately it was recorded in a book “Zoku Sinpeki Sanpǀ”ʊthecollection of sangaku problems. The sangaku is a historical work that shows the wasanʊthe traditional
Japanese mathematics in the Edo period. Then, we try to restore the sangaku through the drawing bycomputer. Also, we show the solution described in a book “ Zoku Sinpeki Sanpǀ Kaigi”.
Key Words : wasan, sangaku, restoration by computer, solution࿴⟬ࡣ㸪᫂἞௨ᚋ㸪⛉Ꮫྐࡢ❧ሙ࠿ࡽ◊✲ࡀ⾜ࢃࢀ㸪ᾏእ࡟ࡶ⤂௓ࡉࢀ཯㡪ࢆ࿧ࢇࡔ  㹼 㸬㏆ᖺࡣ㸪㸯㸬ࡣࡌࡵ࡟Ụᡞ᫬௦ྛᆅࡢ⚄♫࣭௖㛶࡟⟬㢠ࡀዊᥖࡉࢀࡓ㸬ࡇࢀࡽࢆ㞟㘓ࡋ㸪ᐶᨻඖ㸦㸧ᖺ࡟⸨⏣჆ゝ⦅ࡢࠗ⚄ቨ⟬ἲ࠘  㸪⥆࠸࡚ࠗቑ้⚄ቨ⟬ἲ࠘  㸪ࠗ⥆⚄ቨ⟬ἲ࠘ ࡀห⾜ࡉࢀࡓ㸬ࠗ⥆⚄ቨ⟬ἲ࠘ࡢ୰࡟㸪ࠕᡤᠱன໭㉺ⵦཎ㒆୕༑␒⚄⪅୍஦ࠖ࡜࠶ࡾ㸪ᐶᨻ㸦㸧ᖺ㸪Ụᡞᮏ㒓ࡢᯇୗΎභ㑻⯅ᫀࡢዊᥖࡋࡓࡶࡢࡀ࠶ࡿ㸬㐨⬥⩏ṇ㸪ඵ⏣೺஧ⴭࠗ᪂₲ࡢ⟬㢠࠘ ࡛ࡣ㸪ࡇࡢ⟬㢠ࡣ୕᮲ᕷࡢᮏᡂᑎ࡟ᥖ㢠ࡉࢀࡓࡶࡢ࡛⌧Ꮡࡋ࡞࠸࡜ࡉࢀ࡚࠸ࡿ㸬ࡑࡢᚋ࡟⦅⧩ࡉࢀࡓ୕᮲ᕷྐୖᕳ  㸦S㸧࡛ࡣ㸪ࡇࡢ⟬㢠ࡀ⌧Ꮡࡋ࡚࠸ࡿ࡜࠶ࡿࡀ㸬ṧᛕ࡞ࡀࡽ⌧ᅾࡣ୙࡛᫂࠶ࡿ㸬ᮏ✏࡛ࡣ㸪ࠗ⥆⚄ቨ⟬ἲ࠘ࡼࡾᥥ⏬ࢯࣇࢺࢆ⏝࠸࡚㸪ࡇࡢ⟬㢠ࢆ᚟ඖࡍࡿ㸬ࡲࡓ㸪ⓑ▼㛗ᛅ㸪ᚚ⢛Ᏻᮏⴭࠗ⥆⚄ቨ⟬ἲゎ⩏࠘ ࡢ෗ᮏࡀṧࡉࢀ࡚࠾ࡾ㸪ࡑࡢ୰࡟㸪ࡇࡢゎἲࡀグࡉࢀ࡚࠸ࡿࡢ࡛㸪ࡇࢀࢆ⤂௓ࡍࡿ㸬Ꮫ⾡ⓗ࡞◊✲ࡔࡅ࡛࡞ࡃ㸪୍⯡ࡢேࠎ࡬ࡢ࿴⟬ࡢ⤂௓ࡸᩘᏛᩍ⫱ࡢ❧ሙ࠿ࡽࡢ◊✲ࡶ┒ࢇ࡛࠶ࡿ  㹼 㸬㸰㸬⟬㢠᚟ඖᅗࠗ⥆⚄ቨ⟬ἲ࠘࡟ㄝ᫂ᩥ࡜ᅗࡀ࠶ࡿࡢ࡛㸪ࡇࢀ࡟ᇶ࡙࠸࡚᚟ඖࡍࡿ㸬ࡓࡔࡋ㸪⟬㢠ࡢ኱ࡁࡉ㸪࠾ࡼࡧㄝ᫂ᩥ࡜ᅗࡢ㓄⨨➼ࡣ୙࡛᫂࠶ࡿ㸬₎Ꮠࡣཎ๎࡜ࡋ
࡚ᪧᏐࡢṇᏐࢆ⏝࠸ࡓ㸬ࡲࡓ㸪ᅗࡢᙬⰍ࡟ࡘ࠸࡚ࡣ㸪⌧Ꮡࡍࡿ௚ࡢ⟬㢠➼ࢆཧ⪃࡟ࡋࡓ㸬ࢯࣇࢺࡣ㸪ᥥ⏬
ࢶ࣮ࣝ $GREH,OOXVWUDWRUFV ࢆ⏝࠸ࡓ㸬సᡂࡋࡓ᚟ඖᅗࢆ♧ࡍ㸦ᅗ㸫㸧㸬

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涌田

和芳・外川一仁㸱㸬㢠ᩥࡢゎㄝᅗ ᚟ඖᅗ㸱㸬㸯㢠ᩥࡢ᭩ୗࡋᩥ 㢠ᩥࡢ᭩ୗࡋᩥࢆ୍᱌࡜ࡋ࡚᭩ࡁ㸪ࡑࡢ⌧௦ㄒヂࢆ♧ࡍ㸬࿴⟬ࡢ⏝ㄒ࡟ࡘ࠸࡚ࡣㄝ᫂ࢆࡋ࡞࠸ࡀ㸪⌧௦ㄒヂ࡜ẚ㍑ࡍࢀࡤ㸪ࡑࡢព࿡ࡀศ࠿ࡿ㸬௒㸪ᅗࡢዴࡃ㸪⳻ࡢෆ࡟஧ᩳࢆ㝸࡚➼෇ᩘಶࢆᐜࡿࡿ᭷ࡾ㸬ࡍ࡞ࡣࡕ㸪ୖ෇୍ಶ㸪ୗ෇ᩘಶ㸬௬࡟෇ᩘ࡜ࡶ࡟ඵಶࢆ⏬ࡃ㸬⳻㛗ᅄᑍ㸪⳻ᖹ୕ᑍ㸪➼෇ಶᩘࡢ⥲ィ༑ಶ㸬➼෇ᚄ㸪ᗄఱ࡜ၥࡩ㸬⟅࡬࡚᭣ࡃ㸪➼෇ᚄ㸪ᅄศඵཊ㸬⾡࡟᭣ࡃ㸪⳻㛗ࢆ⨨ࡁ㸪ࡇࢀࢆ⮬ࡽࡋ࡚⳻ᖹࡢ࡭ࡁࢆຍ࡬㸪ᖹ᪉࡟ࡇࢀࢆ㛤ࡁ㸪ኳ࡜ྡ࡙ࡃ㸬⳻㛗ࢆ௨࡚ࡇࢀࢆ㝖ࡋ㸪ᆅ࡜ྡ࡙ࡃ㸬෇ᩘࡢ⥲ィࢆ⨨ࡁ㸪ࡇࢀࢆ༙ࡤࡋ㸪ෆ㸪୍ಶࢆῶࡌ㸪వࡾ࡟⳻ᖹࢆ஌ࡌ㸪ኳࢆ௨࡚ࡇࢀࢆ㝖ࡋ㸪ே࡜ྡ࡙ࡃ㸬ࡇࢀࢆ⮬ࡽࡋ୍࡚ಶࢆຍ࡬㸪ᖹ᪉࡟ࡇࢀࢆ㛤ࡁ㸪ᆅ࡜ேࢆຍ࡬㸪௨࡚⳻ᖹࢆ㝖ࡋ㸪➼෇ᚄࢆᚓ࡚ၥࡦ࡟ྜࡍ㸬㸱㸬㸰⌧௦ㄒヂᅗࡢࡼ࠺࡟㸪⳻ᙧࡢ୰࡟  ┤⥺ࢆ㝸࡚࡚➼෇ࡀᩘಶ࠶ࡿ㸬ୖ෇ࡀ  ಶ㸪ୗ෇ࡀᩘಶ࡛㸪௬࡟඲㒊࡛ ಶ࡜ࡋ࡚⏬ࡃ㸬⳻ᙧࡢ㛗࠸ᑐゅ⥺ࢆ  ᑍ㸪▷࠸ᑐゅ⥺ࢆ  ᑍ࡜ࡋ㸪➼෇ࡣ⥲ィ  ಶ࡜ࡍࡿ㸬➼෇ࡢ┤ᚄࡣ࠸ࡃࡽ࠿㸬⟅㸬➼෇ࡢ┤ᚄࡣ  ศ  ཊ㸬⾡㸬⳻ᙧࡢ㛗࠸ᑐゅ⥺ࢆ  ஌ࡋ࡚㸪⳻ᙧࡢ▷࠸ᑐゅ⥺ࡢ  ஌ࢆຍ࠼㸪ࡇࡢᖹ᪉᰿ࢆኳ࡜ࡍࡿ㸬⳻ᙧࡢ㛗࠸ᑐゅ⥺࡛ࡇࢀࢆ๭ࡗ࡚ᆅ࡜ࡍࡿ㸬෇ᩘࡢ⥲ィࡢ༙ศ࠿ࡽ  ࢆᘬࡁ㸪ࡑࡢ⤖ᯝ࡟⳻ᙧࡢ▷࠸ᑐゅ⥺ࢆ᥃ࡅ㸪ኳ࡛๭ࡗ࡚ே࡜ࡍࡿ㸬ࡇࢀࢆ  ஌ࡋ  ࢆ㊊ࡋ㸪ࡇࡢᖹ᪉᰿࡟ᆅ࡜ேࢆຍ࠼㸪⳻ᙧࡢ▷࠸ᑐゅ⥺ࢆ๭ࡗ࡚㸪➼෇ᚄࢆᚓࡿ㸬㸱㸬㸱ዟ௜࡟ࡘ࠸࡚⟬㢠ዊᥖ⪅࡛࠶ࡿᯇୗΎභ㑻⯅ᫀ࡟ࡘ࠸࡚ࡣỤᡞᮏ㒓ࡢே࡛࠶ࡿࡇ࡜௨እࡣศ࠿ࡽ࡞࠸ࠋࡑࡢᖌࡢ⚄㇂ᐃ௧ࡣ㸪㛵ὶࡢⴭྡ࡞࿴⟬ᐙ⸨⏣㈆㈨ࡢ㧗ᘵ࡛࠶ࡿ  㸬

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三条本成寺の紛失算額'AED ࡟ࡘ࠸࡚㸪බᘧࡼࡾ 㸲㸬⾡ࡢゎㄝࠗ⥆⚄ቨ⟬ἲゎ⩏࠘࡟࠶ࡿࡇࡢ⟬㢠ࡢゎἲࢆ♧ࡍ㸬ࡓࡔࡋ㸪⾲グࡣ㸪⌧௦ᩘᏛ࡟ᚑ࠺㸬 ᅗ ࡟࠾࠸࡚aBD 㸪 b

AC 㸪 cAB lAI 㸪 m

EH 㸪 nDI  (l  m  n ) r 2  4lmn

0    㸪  㸪  ࢆ  ࡟௦ධࡋ࡚㸪ᩚ⌮ࡍࡿ㸦 2a 3 ࢆ᥃ࡅ r ࡛๭ࡿ㸧㸬
4a 2 bc 2  2 Na 2 bcr  4a 2 bcr
 ( 4ab 2 cr  4a 3 cr )  ( Na 3 r 2  Nab 2 r 2 ) ( 2a 3 r 2  2ab 2 r 2 )  ( a 2 br 2  b 3 r 2 )0r 㸸➼෇ࡢ┤ᚄ㸪 N 㸸➼෇ࡢಶᩘ࡜࠾ࡃ㸬୍᪉㸪୕ᖹ᪉ࡢᐃ⌮ࡼࡾ 

HEAa 2  b2I ࢆ⏝࠸࡚  ࢆᩚ⌮ࡋ㸪 2c ࡛๭ࡿ㸬FO14c 2   

2a 2 bc  Na 2 br  2a 2 br
 8ac 2 r  2 Nacr 2  4acr 2  2bcr 2

BO3J2DGO2X

2cJ5b  2'AO1 I ң 'ADG ࡼࡾ ࡇࡇ࡛㸪 Y

AG : DG br  2aࡲࡓNr r   2b  2 Zr  2Yr nDIbN b
2X X0b §N·¨  1¸ ࡜⨨ࡁ㸪X©2¹FIBJ 2§ b 2YZ · 2b  2(Y  Z ) r  ¨ 2 ¸rb ¹©aࡇࡇ࡛c  J2J5  lNrbrr  22aclc

2YZ 2 b 2r  2 rba0   ࡇࢀࡼࡾ㸪➼෇ࡢ┤ᚄࢆồࡵࡿ᪉⛬ᘧࢆᚓࡿ㸬

'FO1 I Ӈ 'BO 2 J 2 ࡼࡾcX㸪Za ࡑࢀࡒࢀ͆ᆅ͇㸪͆ே͇࡜ࡍࡿ㸬ḟࡢ᪉⛬ᘧࢆᚓࡿ㸬ࡍ࡞ࢃࡕ

EH  b §N·¨  1¸ r
X©2¹X2 X b §Nb·
 2   r    ¨  1¸ r 2  2  r 2ab a X©2a¹m0

ࡇࢀࢆ a 2 X ࡛๭ࡿ㸬Cᅗ

J2J5  a 2  b 2 ࡜⨨ࡁ㸪ࡇࢀࢆ͆ኳ͇࡜ࡍࡿ㸬

 2aX 2 r  ( NaXr 2  2aXr 2 )  bXr 2

AI : O1 I0a 2 bX  ( Na 2 br  2a 2 br )O4O5l  br   2a―9―§ b 2YZ ·(Y  Z ) 2  ¨ 2 ¸b b ¹
©aY2  Z2 b2a2



0   涌田2和芳・外川   (l  m  n ) r 2  4lmn2b§ 2c ·2¨ ¸ Z  2 a
© a ¹4c 2  b 2a2ࡀᡂࡾ❧ࡘ㸬  ࡇࢀࡣ㸪ḟࡢࡼ࠺࡟ࡋ࡚ᚓࡽࢀࡿ㸬Z lmnࡇࢀࢆ⏝࠸࡚0   ࢆᚓࡿ 㸬ࡋࡓࡀࡗ࡚b( Z 2  1  Y  Z ) r   ࡍ࡞ࢃࡕ
br  2Z 1 Y  Zࡇࢀࡀ⾡࡛㏙࡭ࡽࢀ࡚࠸ࡿ㸬 a 4, b 3, N 10࡜ࡍࡿ࡜㸪 c 5 / 2, X 5, Y 5 / 4, Z 12 / 5 ࡞ࡢ࡛㸪r

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0.48 㸬ࡇࢀࡀ⟅࡛࠶ࡿ㸬ὀ ┦ఝグྕࢆ⏝࠸࡚ㄝ᫂ࡋࡓࡀ㸪࿴⟬࡛ࡣ㸪┦ఝ࡜࠸࠺ᴫᛕࡣ⾲࡟ࡣฟࡉࡎ㸪┤᥋㸪ẚ౛㛵ಀࢆ㏙࡭ࡿ㸬ࠗ⥆⚄ቨ⟬ἲゎ⩏࡛࠘ࡣ㸪ࡇࡢㄝ᫂ࡣ࡞ࡃ㸪┤ࡕ࡟㸪  ࢆ㏙࡭࡚࠸ࡿ㸬
ᒣᮏ㈡๓⦅ࠗ⟬ἲຓ⾡࠘ ࡟㸪ḟࡢබᘧ  ࡀ࠶ࡿ㸬A

D
F
O



BCEHᅗ ᅗ ࡟࠾࠸࡚a BC 㸪 b CA 㸪 c AB l AD 㸪 m BE 㸪 n CF r ෆ᥋෇ O ࡢ┤ᚄ㸪 S  'ABC ࡢ㠃✚ ࡜࠾ࡃ࡜

a  b  c
㸪m2

lZ 2  1   b  ( Z  1  Y  Z )r0     S 2   (l  m  n )lmn

2

2一仁

abc
㸪n
2abc
2abc2 ࡞ࡢ࡛㸪  ࡣ㸪࣊ࣟࣥࡢබᘧ࡛࠶ࡿ㸬බᘧ ࡟㸪వᘻᐃ⌮࡟┦ᙜࡍࡿබᘧࡀ࠶ࡿ㸬ࡍ࡞ࢃࡕ㸪A ࠿ࡽ BC ࡟ᘬ࠸ࡓᆶ⥺ࢆ AH ࡜ࡍࡿ࡜㸪ḟࡀᡂࡾ❧ࡘ㸬  BHc 2  a 2  b2
㸪 CH2aa 2  b2  c2
  2a

  ࡣ㸪  ࡼࡾ AH ࢆồࡵ࡚ᚓࡽࢀࡿ㸬   ࡣ(l  m  n ) rr
  (a  b  c)42ࢆ  ࡟௦ධࡋ࡚ᚓࡽࢀࡿ㸬୕ᖹ᪉ࡢᐃ⌮ࡣ㸪㕍⫤ᘻࡢ⾡㸦⌮㸧࡜ࡋ࡚㸪࿴⟬࡛ࡣࡼࡃ▱ࡽࢀࡓබᘧ࡛࠶ࡿ㸬 ḟ᪉⛬ᘧ c  bx  ax 2 0 ࡢゎࢆᚓࡿᘧ࡜ࡋ࡚㸪ḟࡢࡼ࠺࡞ࡶࡢࡀ▱ࡽࢀ࡚࠸ࡓ㸬S2§·§b·¨b
¸rac
¨¸
¨¨ 2
¸¸  ax©2¹©
¹0   2§·§b·¨b¸c  ¨ # ¨ ¸  ac ¸ x
¨2
¸
©2¹
©
¹0    ࡀ▱ࡽࢀ࡚࠸ࡓ㸬ࡇࢀࢆゎࡅࡤ

2xb§b·r ¨ ¸  ac
2
©2¹ac2  b§b·# ¨ ¸  ac2
©2¹

  ࡣ㸪  ࡢ」ྕࡀ㸩ࡢሙྜ࡛࠶ࡿ㸬㸫ࡢሙྜࡣ㸪㢟ព࡟ࡼࡾ୙㐺ᙜ࡛࠶ࡿ㸬ཧ⪃ᩥ⊩ ⸨⏣჆ゝ⚄ቨ⟬ἲ㸪ᐶᨻඖ㸦㸧ᖺ㸪ᮾ໭኱Ꮫ࿴⟬㈨ᩱࢹ࣮ࢱ࣮࣋ࢫⶶ㸬 ⸨⏣჆ゝቑ้⚄ቨ⟬ἲ㸪ᐶᨻ 㸦㸧ᖺ㸪ᮾ໭

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三条本成寺の紛失算額኱Ꮫ࿴⟬㈨ᩱࢹ࣮ࢱ࣮࣋ࢫⶶ㸬 ⸨⏣჆ゝ⥆⚄ቨ⟬ἲ㸪ᩥ໬ 㸦㸧ᖺ㸪ᮾ໭኱Ꮫ࿴⟬㈨ᩱࢹ࣮ࢱ࣮࣋ࢫⶶ㸬 㐨⬥⩏ṇ㸪ඵ⏣೺஧᪂₲ࡢ⟬㢠㸪⚾ᐙ∧㸪 ᖺ㸬 ୕᮲ᕷ⦅㸸୕᮲ᕷྐ㸪 ᖺ㸬 ⓑ▼㛗ᛅ㸪ᚚ⢛Ᏻᮏ⥆⚄ቨ⟬ἲゎ⩏㸪ᡂ❧ᖺ୙ヲ㸪ᮾ໭኱Ꮫ࿴⟬㈨ᩱࢹ࣮ࢱ࣮࣋ࢫⶶ ୕ୖ⩏ኵᩥ໬ྐୖࡼࡾぢࡓࡿ᪥ᮏࡢᩘᏛ㸪ᒾἼᩥᗜ㸪 ᖺ㸦 ᖺึฟ㸧㸬 ῝ᕝⱥಇ㸪ࢲ࣭ࣥ࣌ࢻ࣮᪥ᮏࡢᗄఱ㸫ఱ㢟ゎࡅࡲࡍ࠿㸽㸪᳃໭ฟ∧㸪 ᖺ㸬 ῝ᕝⱥಇ㸪ࢲ࣭ࣥࢯࢥࣟࣇࢫ࣮࢟᪥ᮏࡢᩘᏛ㸫ఱ㢟ゎࡅࡲࡍ࠿㸽㸦ୖ㸧㸦ୗ㸧㸪᳃໭ฟ∧㸪 ᖺ㸬 ῝ᕝⱥಇ㸪7RQ\5RWKPDQ6DFUHG0DWKHPDWLFV㸫-DSDQHVH 7HPSOH *HRPHWU\ 㸪 3ULQFHWRQ 8QLY 㸬3UHVV㸪 ᖺ㸬 㑥ヂ ⪷࡞ࡿᩘᏛ㸸⟬㢠㸪᳃໭ฟ∧㸪 ᖺ㸬 ᑠ಴㔠அຓ᪥ᮏࡢᩘᏛ㸪ᒾἼ᪂᭩㸪 ᖺ㸬 ᖹᒣㅉ࿴⟬ࡢṔྐ㸫ࡑࡢᮏ㉁࡜Ⓨᒎ㸪ࡕࡃࡲᩥᗜ㸪 ᖺ㸦 ᖺึฟ㸧㸬  ᖹ ᒣ ㅉ  ࿴ ⟬ ྐ ୖࡢ ேࠎ 㸪 ࡕ ࡃࡲ ᩥᗜ 㸪  ᖺ㸦 ᖺึฟ㸧㸬 ኱▮┿୍࿴⟬ධ㛛㸪᪥ᮏホㄽ♫㸪 ᖺ㸬 ᖹᒣㅉ࿴⟬ࡢㄌ⏕㸪ᜏᫍ♫ᜏᫍ㛶㸪 ᖺ㸬 బ⸨೺୍᪥ᮏே࡜ᩘỤᡞᗢẸࡢᩘᏛ㸪ᮾὒ᭩ᗑ㸪 ᖺ㸬 ῝ᕝⱥಇ᪥ᮏࡢᩘᏛ࡜⟬㢠㸪᳃໭ฟ∧㸪 ᖺ㸬 బ⸨೺୍᪂࿴⟬ධ㛛㸪◊ᡂ♫㸪 ᖺ㸬 ᑠᕝ᮰㸪ᖹ㔝ⴥ୍ㅮᗙᩘᏛࡢ⪃࠼᪉  ᩘᏛࡢṔྐ㸪ᮅ಴᭩ᗑ㸪 ᖺ㸬 ఀ⸨ὒ⨾ᡭ࡙ࡃࡾ㑅ᢥᩘᏛ࠾ࡶࡋࢁ࿴⟬㸪᫂἞ᅗ᭩㸪 ᖺ㸬 ᑠᑎ⿱ࡔ࠿ࡽᴦࡋ࠸Ụᡞࡢ⟬㢠㸪◊ᡂ♫㸪 ᖺ㸬 ᱜ஭㐍ỤᡞࡢᩘᏛᩍ⛉᭩㸪㞟ⱥ♫㸪 ᖺ㸬 ᑠᑎ⿱ỤᡞࡢᩘᏛ࿴⟬㸪ᢏ⾡ホㄽ♫㸪 ᖺ㸬 ᒣᮏ㈡๓⟬ἲຓ⾡㸪ኳಖ 㸦㸧ᖺ㸪ᮾ໭኱Ꮫ࿴⟬㈨ᩱࢹ࣮ࢱ࣮࣋ࢫⶶ㸬῝ᕝⱥಇᰯὀ⟬ἲຓ⾡㸦᚟้㸧㸪ᮅ᪥᪂⪺♫஦ᴗ㒊ྡྂᒇ௻⏬஦ᴗࢳ࣮࣒㸪 ᖺ㸬ཷ௜ ― 11 ―