長岡工業高等専門学校研究紀要

論第48巻（2012）

文ਈ᧼౎ᐈችߩ⚗ᄬ▚㗵
1ᶗ↰ ๺⧐ ࡮ᄖᎹ ৻ੳ122৻⥸ᢎ⢒⑼㧙ᢙቇ㧔Liberal Arts-Mathematics, Nagaoka National College of Technology㧕㔚ሶ೙ᓮᎿቇ⑼㧔Department of Electronic Control Engineering, Nagaoka National College of Technology㧕

The Sangaku Lost from the Yoita Hachiman Shrine
Kazuyoshi WAKUTA 1 and Kazuhito TOGAWA 2Abstract
A mathematical tablet called sangaku was dedicated to the Yoita Hachiman Gǌʊthe Shinto shrine in
the Edo period of Japan. Although the sangaku was lost, fortunately it was recorded in a book “SaishiShinzan”ʊthe collection of sangaku problems. The sangaku is a historical work that shows thewasanʊthe traditional Japanese mathematics in the Edo period. Then, we try to restore the sangaku
dedicated in 1800 through the drawing by computer. Also, from the literature,we infer the solution in theEdo period to the sangaku problem.
Key Words : wasan, sangaku, restoration by computer, solution㧝㧚ߪߓ߼ߦᳯᚭᤨઍฦ࿾ߩ␹␠࡮੽㑑ߦ▚㗵߇ᄺឝߐࠇߚ㧚ߎࠇࠄࠍ㓸㍳ߒ㧘ኡ᡽ర㧔㧕ᐕߦ㧘⮮↰ཅ⸒✬ߩ‫␹ޡ‬ო▚ᴺ‫  ޢ‬㧘⛯޿ߡ‫ޡ‬Ⴧೞ␹ო▚ᴺ‫  ޢ‬㧘‫␹⛯ޡ‬ო▚ᴺ‫߇ ޢ‬ೀⴕߐࠇߚ㧚߹ߚ㧘ᄤ଻ 㧔㧕ᐕߩਛ᧛ᤨਁ✬‫߽ߦ ޢ▚␹␻⾽ޡ‬ᄙߊߩ▚㗵߇㓸㍳ߐࠇߚ㧚‫ߩޢ▚␹␻⾽ޡ‬ਛߦ㧘‫⿧ޟ‬ᓟᎺਃፉ㇭ਈ᧼౎ᐈች‫ࠅ޽ߣޠ‬㧘ኡ᡽ 㧔㧕ᐕ㧘ਃፉ㇭ᣂ଻᧛ ᩿❢⋇㧘หᄢ㊁᧛ේ᧛ᧄߩᄺឝߒߚ߽ߩ߇޽ࠆ㧚⃻࿷ߩㇺ㊁␹␠ߣᕁࠊࠇࠆ㧚ઁߦ㧘ᢥൻర㧔㧕ᐕ㧘ᢥൻ 㧔㧕ᐕߦਈ᧼౎ᐈችߦᄺឝߐࠇߚ  㕙ߩ▚㗵߽㓸㍳ߐࠇߡ޿ࠆ㧚޿ߕࠇ߽⃻ ࿷ ᄬ ࠊ ࠇ ߡ ߒ ߹ ߞ ߚ 㧚 ᧄ Ⓜ ߢ ߪ 㧘 ኡ ᡽ 㧔㧕ᐕߩ▚㗵ࠍ‫ޢ▚␹␻⾽ޡ‬㧔Ꮞਯੑ㧕ࠃࠅឬ↹࠰ࡈ࠻ࠍ↪޿ߡᓳరߔࠆ࿑ᒻߩ໧㗴߇  㗴ߢ޽ࠆ㧚╙৻໧ߦߟ޿ߡߪ㧘ห╬ߥ໧㗴ߩᒰᤨߩ⸃ᴺ߇

ᱷߐࠇߡ߅ࠅ㧘ߎࠇࠍ⚫੺ߔࠆ㧚╙ੑ໧ߦߟ޿ߡߪ㧘๺▚ᦠ╬߆ࠄᒰᤨߩ⸃ᴺࠍផ᷹ߔࠆ㧚๺▚ߪ㧘᣿ᴦએᓟ㧘⑼ቇผߩ┙႐߆ࠄ⎇ⓥ߇ⴕࠊࠇ㧘ᶏᄖߦ߽⚫੺ߐࠇ෻㗀ࠍ๭ࠎߛ  㨪 㧚ㄭᐕߪ㧘ቇⴚ⊛ߥ⎇ⓥߛߌߢߥߊ㧘৻⥸ߩੱ‫ߩ߳ޘ‬๺▚ߩ⚫
੺߿ᢙቇᢎ⢒ߩ┙႐߆ࠄߩ⎇ⓥ߽⋓ࠎߢ޽ࠆ  㨪 㧚㧞㧚▚㗵ᓳర࿑‫ߪޢ▚␹␻⾽ޡ‬Ⓜᧄߢ޽ࠅ㧘ߘߩ౮ᧄߦ⺑᣿ᢥߣ࿑߇޽ࠆ㧚▚㗵ߩᄢ߈ߐ㧘߅ࠃ߮⺑᣿ᢥߣ࿑ߩ㈩⟎╬ߪਇ᣿ߢ޽ࠆ㧚ṽሼߪ౮ᧄߦࠃࠅ⇣ห߇޽ࠅ㧘ේೣߣߒߡᣥሼߩᱜሼࠍ↪޿ߚ㧚࿑ߩᓀ⦡ߦߟ޿ߡߪ㧘⃻ሽߔࠆઁߩ▚㗵ࠍෳ⠨ߦߒߚ㧚࠰ࡈ࠻ߪ㧘ឬ↹࠷࡯࡞㧔#FQDG+NNWUVTCVQTEU㧕ࠍ↪޿ߚ㧚૞ᚑߒߚᓳర࿑ࠍ␜ߔ㧔࿑㧙㧕㧚―1―涌田和芳・外川一仁㧟㧚㗵ᢥߩ⸃⺑㧟㧚㧝㗵ᢥߩᦠਅߒᢥ 㗵ᢥߩᦠਅߒᢥࠍ৻᩺ߣߒߡᦠ߈㧘ߘߩ⃻ઍ⺆⸶ࠍ␜ߔ㧚๺▚ߩ↪⺆ߦߟ޿ߡߪ⺑᣿ࠍߒߥ޿߇㧘⃻ઍ⺆⸶ߣᲧセߔࠇ߫㧘ߘߩᗧ๧߇ಽ߆ࠆ㧚╙৻໧੹㧘࿑ߩᅤߊ㧘ᄢዊ౞ߩ੤➱ߦ⚥౞ࠍኈࠆࠆ᦭ࠅ㧚ߘߩᢙࠍ⍮ࠄߕ㧚ฦ⚥౞ߪ㧘㓞౞ߣᄢ౞ߦಾߒ㧘઒ߦ✚౞৾▎ࠍ↹ߊ㧚ᄢ౞ᓘ৻චኸ㧘የ౞ᓘ৻ಽ㧚⥋ࠅߡᄙ߈✚ᢙ㧘ᐞ૗ߣ໧߰㧚╵߳ߡᦚߊ㧘✚ᢙ৻ච▎㧚ⴚߦᦚߊ㧘የ౞ᓘࠍએߡᄢ౞ᓘࠍ㒰ߒ㧘ᐔᣇߦ㐿ߊ㧚⧯ߒᏪಽߔࠇ߫ਅߪߎࠇࠍ෼߻㧚⥋ࠅߡᄙ߈✚౞ᢙࠍᓧߡ໧߭ߦวߔ㧚╙ੑ໧੹㧘࿑ߩᅤߊ㧘⋥ႆძߩ߁ߜߦᢳࠍኈࠆࠆ᦭ࠅ㧚ด੔߰㧘㐳ᐔߩᏅ৻ኸ㧘ᢳචਃኸ㧚Ⓧࠍߒߡ⥋ࠅߡᄙ߆ࠄߒ߼ࠎߣ᰼ߔ㧚㐳㧘ᐞ૗ߣ໧߰㧚╵߳ߡᦚߊ㧘㐳౎ኸ㧚ⴚߦᦚߊ㧘Ꮕߩඨࠍ⟎߈㧘ᭂߣฬߠߊ㧚ߎࠇࠍ⥄ߒߡએߡᢳߩ౹ࠍᷫߓ૛ࠅߣߔ㧚ਃߦߡߎࠇࠍ㒰ߒᐔᣇߦ㐿߈㧘ᭂࠍട߳㧘㐳ࠍᓧߡ໧߭ߦวߔ㧚㧟㧚㧞⃻ઍ⺆⸶╙৻໧࿑ߩࠃ߁ߦ㧘ᄢ౞ߣዊ౞ߩ㑆ߦ޿ߊߟ߆ߩ౞߇޽ࠆ㧚౞ߩ୘ᢙߪᧂ⍮ߢ޽ࠆ㧚ฦ౞ߪ㧘㓞౞ߣᄢ౞ߦធߒ㧘઒ߦ  ୘ߩ౞ࠍ↹ߊ㧚ᄢ౞ߩ⋥ᓘߪ  ኸ㧘የ౞ߩ⋥ᓘߪ  ኸߢ޽ࠆ㧚ᦨ߽ᄙߊߥࠆߣ߈ߩ౞ߩ✚ᢙߪ޿ߊࠄ߆㧚 ╵㧚✚ᢙ  ୘㧚ⴚ㧚የ౞ߩ⋥ᓘߢᄢ౞ߩ⋥ᓘࠍഀࠅ㧘ߘߩᐔᣇᩮࠍ᳞߼㧘✚౞ᢙࠍᓧࠆ㧚߽ߒᏪಽߔࠇ߫ಾࠅ਄ߍࠆ㧚╵߃ߪ㗴ᗧߦว߁㧚╙ੑ໧࿑ߩࠃ߁ߦ㧘⋥ᣇ૕ߦኻⷺ✢ࠍᒁߊ㧚㐳ߣᐔߩᏅߪ  ኸ㧚ኻⷺ✢ߪ  ኸߢ޽ࠆ㧚૕Ⓧࠍᦨᄢߦߔࠆ㐳ߪ޿ߊࠄ߆㧚╵㧚㐳ߪ  ኸ㧚ⴚ㧚㐳ߣᐔߩᏅߩ  ࠍᭂߣ޿߁㧚ߎࠇࠍ  ਸ਼ߒߡ㧘ኻⷺ✢ߩ  ਸ਼߆ࠄᒁߊ㧚ߎࠇࠍ  ߢഀࠅ㧘ᐔᣇᩮࠍ᳞߼㧘ᭂࠍട߃ߡ㐳ࠍᓧࠆ㧚╵߃ߪ㗴ᗧߦว߁㧚

―2―࿑ᓳర࿑

与板八幡宮の紛失算額

T0 , T1 ,  , Tn ߣߒ㧟㧚㧟ᅏઃߦߟ޿ߡ▚㗵ᄺឝ⠪ߢ޽ࠆ ᩿❢⋇ߪਃፉ㇭ᣂ଻᧛ߩੱߢ
 r0 㧦౞ O ߩ⋥ᓘ㧘 rn 㧦౞ On ߩ⋥ᓘ޽ࠅ㧘ේ᧛ᧄߪਃፉ㇭ᄢ㊁᧛ߩੱߢ޽ࠆ㧚ߘߩᏧߩߣ߅ߊ㧚౏ᑼࠃࠅ ☨ ᜬ ⍱┨ ߪ㧘 ਃ ፉ㇭ ᣂ଻ ᧛ ߩੱ ߢ޽ ࠅ 㧘ኡ ᡽ 㧔㧕ᐕ㧘ᬁ⼱ⷰ㖸ၴߦ▚㗵ࠍᄺឝߒߡ޿ࠆ  㧚
T1T0
r0 r1 , T1T2
r1r2 , T2 T0
r2 r0   ࿑ࠃࠅ㧠㧚ⴚߩ⸃⺑

r1r2  r2 r0   

r0 r1‫␹⛯ޡ‬ო▚ᴺ‫ߦޢ‬㧘‫᧲ޟ‬ㇺ㤕↸ᐔᎹᄤḩች‫ߒߣޠ‬ߡ▚㗵߇  㕙㓸㍳ߐࠇߡ޿ࠆ㧚ኡ᡽ 㧔㧕ᐕߩ▚㗵ߩ໧㗴ߪ㧘ਈ᧼౎ᐈችߩ▚㗵ߩ╙৻໧ߩ࿑ߦ߅޿ߡ㧘ᄢ౞ߣ⚳౞㧔የ౞㧕ࠍਈ߃ߡ㧘ᄢ౞ߣዊ౞߅ࠃ߮⚥౞ߢ࿐߹ࠇߚ࿑ᒻߩ㕙Ⓧ߇ᦨᄢߦߥࠆߣ߈ߩዊ౞ᓘࠍ᳞߼ࠆ໧㗴ߢ޽ࠆ㧚ߚߛ㧘ᄢ౞ߣዊ౞ߩ૏⟎߇ㅒߦߥߞߡ޿ࠆ㧚㕙Ⓧ߇ᦨᄢߦߥࠆߩߪ㧘౞ᢙ߇ᦨ߽ᄙ޿ߣ߈ߢ޽ࠆߩߢ㧘ਈ᧼౎ᐈችߩ▚㗵ߩ╙৻໧ߪ㧘ߎࠇߣห╬ߢ޽ࠆ㧚‫␹⛯ޡ‬ო▚ᴺ⸃⟵‫ޢ‬ߦߘߩ⸃ᴺ߇޽ࠆߩߢ㧘ߎࠇࠍ⚫੺ߔࠆ㧚ਈ᧼౎ᐈችߩឝ㗵ߪኡ᡽  ᐕߢ޽ࠅ㧘ᐔᎹᄤḩችߩ▚㗵એᓟߢ޽ࠆ߇㧘‫␹⛯ޡ‬ო▚ᴺ‫߇⟵⸃ߩߘߣޢ‬಴ࠆએ೨ߩߎߣߢ޽ࠆ㧚╙ੑ໧ߩᒰᤨߩ⸃ᴺߪਇ᣿ߢ޽ࠆ㧚ᦨᄢᦨዊߩ໧㗴ߢ޽ࠆߩߢ㧘๺▚ߦ߅ߌࠆᭂ୯໧㗴ߩ⸃ᴺߢ޽ࠆ
ㆡዧᣇ⚖ᴺࠍ↪޿ߡߎࠇࠍ⸃ߊ㧚ߚߛߒ㧘⴫⸥ߪ㧘⃻ઍᢙቇߦᓥ߁㧚㧠㧚㧝 ╙৻໧ߦߟ޿ߡ
߇ᚑࠅ┙ߟ㧚ߎࠇ߆ࠄ㧘 r2 ߩᑼࠍዉߊ 㧚

§r1 ·¸
 r1  ¨1 r2¨r0 ¸¹©

0   ห᭽ߦ㧘 r3 ߩᑼࠍዉߊ㧚§r1 ·¸
 r1  ¨1 r3¨r2 ¸¹©

0    ࠃࠅr1

r11

r2

  r0 㧘  ࠃࠅ§r1 ·¸
 r1  ¨ 2 r
¨
¸ 3r0
©
¹0   ৻⥸ߦ㧘 rn ߩᑼߪ㧘ᰴߩࠃ߁ߦߥࠆ㧚§r1 ·¸
 r1  ¨ ( n  1) r¨¸ nr0©
¹0   

ߎࠇࠃࠅ

Or1

r1

rnr0

 ( n  1)   O10  r1  r0 ߥߩߢ㧘 0 
O3

T1

O2

T3 T2

ߥߌࠇ߫㧘

T0

r1
r0


࿑

r1

 1㧚

ߩዊᢙㇱಽ߇

rnr01 ߥߩߢ㧘

r1

r1n ߢ޽ࠆ㧚rnrn

ߦዊᢙㇱಽ߇޽ࠇ߫㧘᳞߼ࠆ n ߪ㧘

r1r1

ߩዊᢙㇱrn ࿑ ߦ߅޿ߡ㧘ᄢ౞ࠍ O1 㧘ዊ౞ࠍ O2 ߣߒ㧘ᄢ౞ߣዊ౞ߦធߔࠆⓨ౞ࠍ⠨߃ O ߣߔࠆ㧚ⓨ౞ O ߦ߅޿ ߡ 㧘 ⋥ ᓘ ߪ ᄢ ౞ O1 ߩ ⋥ ᓘ એ ਄ ߦ ߥ ࠆ 㧚 ౞O, O1 ,  , On ߣ ⋥ ✢ ߣ ߩ ធ ὐ ࠍ 㧘 ߘ ࠇ ߙ ࠇ 㧘ಽࠍಾࠅ਄ߍߚ߽ߩߦ╬ߒ޿㧚ⴚߪߎߩߎߣࠍㅀߴߡ޿ࠆ㧚
1ߥߩߢ㧘╵߃ߪ㧘 n 10 ߢ ੹㧘 r1 10 㧘 rn
10
޽ࠆ㧚

―3―

涌田和芳・外川一仁⸃ߩ౏ᑼࠃࠅ 㧠㧚㧞 ╙ੑ໧ߦߟ޿ߡ d  d2 xbc

4 2(c  d 2 )3
22d1 °­ 2 § d · °½®c  ¨ ¸ ¾  23 °̄
© 2 ¹ °¿a 㧘  ࠃࠅ x ߩ਄㒢ߪxx2  (x  d )2ࠍ⸃޿ߡ࿑xx 㧦㐳㧘 a 㧦ᐔ㧘 b 㧦㜞㧘 c 㧦ᢳ㧘 d 㧦㐳ߣᐔߩᏅd   x 2  a 2  b2

ࠍᦨᄢߦߔࠆ x ࠍ᳞߼ߚ޿㧚 㧘  㧘  ࠃࠅ^`( x  d ) 2 c 2  x 2  ( x  d ) 2 x 2    (c 2 d 2  d 4 ) x 2  y 22 ᵈ  012 x 5  30 dx 4  4( c 2  7d 2 ) x 3
 3(2c 2 d  4d 3 ) x 2  2( c 2 d 2  d 4 ) x  0ࠍḩߚߔ㧚 x ߢഀࠅ㧘ᑼࠍᄌᒻߒߡ dc2  d 2)( x 2  dx )23

 r2 ߦߟ޿ߡߩ  ᰴᣇ⒟ᑼߣߒߡ⴫ߒߡ޿ࠆ㧚 㧘  ߪ‫␹⛯ޡ‬ო▚ᴺ⸃⟵‫ߚߞ⵬ߊߥߪߦޢ‬㧚ㆡዧᣇ⚖ᴺߦࠃࠅ 㧘ᭂ୯ὐߩ୥⵬ߪ

0   x ! d ߥߩߢc2  d 231 2 §d ·c ¨ ¸2©2¹

 ๺▚ߢߪࠃߊ⍮ࠄࠇߚ౏ᑼߢ㧘ጊᧄ⾐೨✬‫▚ޡ‬ᴺഥⴚ‫ߦ╬ ޢ‬タߞߡ޿ࠆ㧚

2 x 6  6 dx 5  ( c 2  7d 2 ) x 4  ( 2c 2 d  4d 3 ) x 3x 2  dx   ߥߩߢ  ߩ⸃ߪ㧘 d  x  d ' ࠍḩߚߔ㧚 x d ߩߣ
߈ y 0 㧘 d  x  d ' ߩߣ߈ y ! 0 ߢ޽ࠅ㧘ᭂ୯ὐߩ୥⵬ߪߚߛ  ߟߢ޽ࠆߩߢ㧘  ߩὐߢᦨᄢ୯ࠍߣ
ࠆ㧚ߎߩ⸃߇㧘ⴚߢㅀߴࠄࠇߡ޿ࠆ㧚੹㧘 c 13 㧘 d 1 ߥߩߢ㧘╵߃ߪ㧘 x 8 ߢ޽ࠆ㧚ߎࠇࠍᦠ߈⋥ߔߣ12( x  d )( x 221 ­° 2 § d · °½ 1 22
®c  ¨ ¸ ¾  ( c  d )3 °̄
© 2 ¹ °¿ 6c 2   ߇ᚑࠅ┙ߟ㧚 c ߣ d ߇ਈ߃ࠄࠇߚߣ߈㧘⋥ᣇ૕ߩ૕Ⓧ
y abx   y2d
1 2 §d ·
c ¨ ¸22©2¹

ߎࠇࠍ d ' ߣ߅ߊߣ㧘 x ߩቯ⟵ၞߪ㧘 d  x  d ' 㧚ߣ߅ߊ㧚ߎߎߢ
xac 2   

0   ―4―ㆡዧᣇ⚖ᴺߪ㧘๺▚ߦ߅ߌࠆᭂ୯໧㗴ߩ⸃ᴺߢ
޽ࠆ㧚ߎࠇߦߟ޿ߡ㧘᭎⇛ࠍ೨⪺  ߢ␜ߒߚ㧚๺▚ߢߪ㧘ᑼߩฦ㗄ࠍᏁߺߦ⚵วࠊߖ㧘౒ㅢ࿃ᢙࠍ⷗ߟߌ಴ߒߡ࿃ᢙಽ⸃ࠍߒߡ޿ࠆ㧚଀߃߫㧘‫ޡ‬ᣣᧄߩᢙቇ㧙૗㗴⸃ߌ߹ߔ߆㧫㧔ਅ㧕‫଀ߩޢ‬㗴 ߦ૒ਭ㑆➡⪺‫▚ޡ‬ᴺ⿠Ḯ㓸‫ࠆ޽߇଀ߩ ޢ‬㧚 ߦߟ޿ߡ߽ห᭽ߥᣇᴺߢ࿃ᢙࠍ⷗ߟߌ಴ߔߎߣ߇ߢ߈ߚߣ⠨߃ࠄࠇࠆ㧚๺▚ߢߪ㧘ὐ┒ⴚߦࠃࠅᣇ⒟ᑼࠍ┙ߡ㧘ߎࠇࠍ⸃ߊߦߪ▚ᧁࠍ↪޿ߚ㧚 ᰴᣇ⒟ᑼߩ႐วߪ㧘ᒻߦ⋧⇣ߪ޽ࠆ߇㧘⃻ઍߩ⸃ߩ౏ᑼߣหߓ߽ߩ߇↪
޿ࠄࠇ㧘ߘࠈ߫ࠎࠍ૶ߞߡ⸃ࠍᓧߚ㧚ߎࠇߪᣧ޿ᤨᦼ߆ࠄⴕࠊࠇ㧘▚㗰ⴚߣ๭߫ࠇߚ㧚与板八幡宮の紛失算額ෳ⠨ᢥ₂ ⮮↰ཅ⸒㧦␹ო▚ᴺ㧘ኡ᡽ర㧔㧕ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ⮮↰ཅ⸒㧦Ⴧೞ␹ო▚ᴺ㧘ኡ᡽ 㧔㧕ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ⮮↰ཅ⸒㧦⛯␹ო▚ᴺ㧘ᢥൻ 㧔㧕ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ਛ᧛ᤨਁ㧦⾽␻␹▚㧘ᄤ଻ 㧔㧕ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ਃ਄⟵ᄦᢥൻผ਄ࠃࠅ⷗ߚࠆᣣᧄߩᢙቇ㧘ጤᵄᢥᐶ㧘 ᐕ㧔 ᐕೋ಴㧕㧚 ᷓᎹ⧷ବ㧘࠳ࡦ࡮ࡍ࠼࡯ᣣᧄߩᐞ૗㧙૗㗴⸃ߌ߹ߔ߆㧫㧘᫪ർ಴ 㧘 ᐕ㧚 ᷓᎹ⧷ବ㧘࠳ࡦ࡮࠰ࠦࡠࡈࠬࠠ࡯ᣣᧄߩᢙቇ㧙૗㗴⸃ߌ߹ߔ߆㧫㧔਄㧕 ਅ 㧘᫪ർ಴ 㧘 ᐕ㧚 ᷓᎹ⧷ବ㧘6QP[4QVJOCP5CETGF/CVJGOCVKEU㧙,CRCPGUG 6GORNG )GQOGVT[ 㧘 2TKPEGVQP 7PKX 㧚2TGUU㧘 ᐕ㧚㧔㇌⸶㧕⡛ߥࠆᢙቇ㧦▚㗵㧘᫪ർ಴ 㧘 ᐕ㧚 ዊୖ㊄ਯഥᣣᧄߩᢙቇ㧘ጤᵄᣂᦠ㧘 ᐕ㧚 ᐔጊ⺼㧦๺▚ߩᱧผ㧙ߘߩᧄ⾰ߣ⊒ዷ㧘ߜߊ߹ᢥᐶ㧘 ᐕ㧔 ᐕೋ಴㧕㧚  ᐔ ጊ ⺼ 㧦 ๺ ▚ ผ ਄ߩ ੱ‫ ޘ‬㧘 ߜ ߊ߹ ᢥᐶ 㧘  ᐕ㧔 ᐕೋ಴㧕㧚 ᄢ⍫⌀৻๺▚౉㐷㧘ᣣᧄ⹏⺰␠㧘 ᐕ㧚 ᐔጊ⺼㧦๺▚ߩ⺀↢㧘ᕡᤊ␠ᕡᤊ㑑㧘 ᐕ㧚 ૒⮮ஜ৻ᣣᧄੱߣᢙᳯᚭᐼ᳃ߩᢙቇ㧘᧲ᵗᦠᐫ㧘 ᐕ㧚 ᷓᎹ⧷ବᣣᧄߩᢙቇߣ▚㗵㧘᫪ർ಴ 㧘 ᐕ㧚 ૒⮮ஜ৻ᣂ๺▚౉㐷㧘⎇ᚑ␠㧘 ᐕ㧚 ዊᎹ᧤㧘ᐔ㊁⪲৻⻠ᐳᢙቇߩ⠨߃ᣇ  ᢙቇߩᱧผ㧘ᦺୖᦠᐫ㧘 ᐕ㧚 દ⮮ᵗ⟤ᚻߠߊࠅㆬᛯᢙቇ߅߽ߒࠈ๺▚㧘᣿ᴦ࿑ᦠ㧘 ᐕ㧚 ዊኹ⵨㧦ߛ߆ࠄᭉߒ޿ᳯᚭߩ▚㗵㧘⎇ᚑ␠㧘ᐕ㧚 ᪉੗ㅴ㧦ᳯᚭߩᢙቇᢎ⑼ᦠ㧘㓸⧷␠㧘 ᐕ㧚 ዊኹ⵨㧦ᳯᚭߩᢙቇ๺▚㧘ᛛⴚ⹏⺰␠㧘 ᐕ㧚 ᶗ↰๺⧐㧘ᄖᎹ৻ੳ㧦ᨰፒᬁ⼱ⷰ㖸ၴߩ▚㗵㧘㐳ጟᎿᬺ㜞╬ኾ㐷ቇᩞ♿ⷐ╙  Ꮞ╙  ภ㧘RR㧘 ᐕ㧚 ⊕⍹㐳ᔘ㧘ᓮ♄቟ᧄ㧦⛯␹ო▚ᴺ⸃⟵㧘ᚑ┙ᐕਇ⹦㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ጊᧄ⾐೨▚ᴺഥⴚ㧘ᄤ଻ 㧔㧕ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚ᷓᎹ⧷ବᩞᵈ㧦▚ᴺഥⴚ㧔ᓳೞ㧕㧘ᦺᣣᣂ⡞␠੐ᬺㇱฬฎደડ↹੐ᬺ࠴࡯ࡓ㧘 ᐕ㧚 ᶗ↰๺⧐㧘ᄖᎹ৻ੳ㧦⫷ᩊ␹␠ߩ▚㗵㧘㐳ጟᎿᬺ㜞╬ኾ㐷ቇᩞ♿ⷐ╙  Ꮞ╙  ภ㧘RR㧘 ᐕ㧚 ૒ਭ㑆➡▚ᴺ⿠Ḯ㓸㧘᣿ᴦ 㧔㧕ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 㪉㪇㪈㪉㪅㩷㪐㪅㪉㪋㩷ฃઃ ―5―