ಿ‫ࣞުࢥؖ‬൝୺࿝‫ܮݪࡄࢷڠ‬ါȁల57‫ے‬Ȫ3121ȫ

აȁȁ໲

᧛਄⠀㤥␹␠ߩ⚗ᄬ▚㗵ᶗ↰ ๺⧐ 1࡮ᄖᎹ ৻ੳ 2㧝৻⥸ᢎ⢒⑼㧙ᢙቇ㧔Liberal Arts-Mathematics, Nagaoka National College of Technology㧕
2 㔚ሶ೙ᓮᎿቇ⑼㧔Department of Electronic Control Engineering, Nagaoka National College of Technology㧕

THE SANGAKU LOST FROM THE HAGURO SHRINE IN MURAKAMIKazuyoshi WAKUTA 1 and Kazuhito TOGAWA 2Abstract
A mathematical tablet called sangaku was dedicated to the Haguro Jinjyaʊthe Shinto shrine inMurakami in 1791. Although the sangaku was lost, fortunately it was recorded in a book “ShinpekiSanpou”ʊthe collection of sangaku problems. The sangaku is a historical work that shows thewasanʊthe traditional Japanese mathematics in the Edo period of Japan. Then, we try to restore thesangaku through the drawing by computer. Also, we present the solution in the Edo period to the sangaku
problem.
Key Words : wasan, sangaku, restoration by computer, solution㧝㧚ߪߓ߼ߦ ᳯᚭᤨઍߩᢙቇ̆๺▚ߩ⁛․ߥ㘑⠌ߢ޽ࠆ▚㗵ߩᄺ ឝ ߇ ᆎ ߹ ߞ ߡ ߆ ࠄ 㧘  ᐕ એ ਄ ⚻ ߞ ߚ ኡ ᡽ ర ᐕߦ㧘‫␹ޡ‬ო▚ᴺ‫߇ޢ‬ೀⴕߐࠇߚ㧚ߎࠇߪ๺▚ኅ⮮↰⽵⾗࡮ཅ⸒ῳሶ߇㧘ਥߦ㐷ੱࠄ߇␹␠੽㑑ߦឝߍߚ▚㗵ߦߟ޿ߡ㓸㍳ߒߚ߽ߩߢ޽ࠆ㧚ኡ᡽  ᐕߦߪ㓸㍳ᢙࠍჇ߿ߒ‫ޡ‬Ⴧೞ␹ო▚ᴺ‫ ޢ‬1)߇ೀⴕߐࠇߚ㧚ᦝߦ㧘ᢥൻ   ᐕߦߪ‫␹⛯ޡ‬ო2)▚ᴺ‫߇ ޢ‬ೀⴕߐࠇߚ㧚ኡ᡽  ᐕߩ‫ޡ‬Ⴧೞ␹ო▚ᴺ‫ߩޢ‬ਛߦ㧘‫ޟ‬ᚲ ੓⿧ᓟᎺ᧛਄⠀㤥ጊ⠪৻੐‫ࠅ޽ߣޠ‬㧘᧛਄Ꮢ⠀㤥↸ߩ⠀㤥␹␠ߦᄺឝߐࠇߚ▚㗵߇ឝタߐࠇߡ޿ࠆ㧚⠀㤥␹␠ߪ㧘ᳯᚭᤨઍߦߪ⠀㤥ጊᄢᮭ⃻ߣ๭߫ࠇߡ޿ߚ㧚▚㗵ߩᄺឝ⠪ߪ㧘᧛਄⮲ߩ๺▚ኅਣጊ࿃ᐔ⦟₵ߩ㐷ੱߩ㢬⷗༑૞ᱜ⋥ߢ޽ࠅ㧘ኡ᡽   ᐕߦឝ㗵ߒߚ߽ߩߢ޽ࠆ㧚ᱷᔨߥ߇ࠄ㧘ߎߩ▚㗵ߪ⃻࿷ᄬࠊࠇߡߒ߹ߞߚ㧚▚㗵ߪᒰᤨߩ๺▚ߩ᭽ሶࠍ⍮ࠆߎߣ߇ߢ߈ࠆ⾆㊀ߥ⾗ᢱߢ޽ࠆߩߢ㧘ߘߩᓳరࠍ⹜ߺ㧘‫ޡ‬Ⴧೞ␹ო▚ᴺ‫⸥ߦޢ‬タߐࠇߚ▚㗵ߩ⺑᣿ᢥߣ࿑߆ࠄ㧘ࠦࡦࡇࡘ࡯࠲ࠍ↪޿ߡ▚㗵ߩᓳర࿑ࠍ૞ᚑߒߚ㧚▚㗵ߩ໧޿ߪ㧘ኈⴚߣ޿߁࿑ᒻߩ໧㗴  㗴ߩߺߢ޽ࠆ㧚ߎߩ▚㗵ߩ໧㗴ߦߟ޿ߡߪ㧘ᣂᐣ⮲ߩ๺▚ኅ᧻᳗⋥⧷ 㧫㨪 ᐕ ߩ⪺ߒߚ‫␹ޡ‬ო▚ᴺ⸃‫ ޢ‬3) 㧘߹ߚ㧘ฬฎደ⮲ߩ๺▚ኅศ↰ὑᐘ  ᐕ㨪ᐕ ߩ⪺ߒߚ‫␹ޡ‬ო▚ᴺ⸃‫ ޢ‬4 ) ߥߤߦ㧘๺▚ኅߩ⸃ᴺ߇ᱷߐࠇߡ޿ࠆ㧚ᧄⓂߢߪ㧘᧻᳗⋥⧷ߩ⸃ᴺࠍ⚫
੺ߔࠆ㧚ߎߩ▚㗵ߪ㧘ᦨ਄ᵹߩഃᆎ⠪ળ↰቟᣿ߩ⪺ߒߚ‫⿧ޡ‬ᓟ࿖⻉ၴ␠⻉ᵹᄺ㗵㓸‫ ޢ‬5 ) ߦ߽ឝタߐࠇߡ޿ࠆ㧚๺▚ߩ  ᄢᵹᵷߢ޽ࠆ㑐ᵹߣᦨ਄ᵹߩ㑆ߦ⺰੎ߩ޽ߞߚߎߣ߇⍮ࠄࠇߡ޿ࠆ 6 ) 㧚ߎߩ▚㗵߽ߘߩ⺰੎ߦᏎ߈ㄟ߹ࠇ㧘਄ឝᦠߦ߅޿ߡ㧘ળ↰ߪ㧘ታ㓙ߦ⸃ߌߚ߆ߤ߁߆ᕋߒ޿ߣઃ⸥ߢㅀߴߡ޿ࠆ㧚ᷓᎹ⧷ବ㧘࠳ࡦ࡮࠰ࠦࡠࡈࠬࠠ࡯⪺‫ޡ‬ᣣᧄߩᢙቇ̆૗㗴⸃ߌ߹ߔ߆㧫 ਄ ‫ ޢ‬7 ) ߦ߽㧘ߎߩ▚㗵ߣศ↰ὑᐘߩ⇛⸃߇⚫੺ߐࠇߡ޿ࠆ㧚߹ߚ㧘ߎߩ▚㗵ߩ໧㗴߆ࠄߪ㧘ᄢᄌ⟤ߒ޿⚿ᨐ߇ዉ߆ࠇࠆ㧚ᧄⓂߢߪ㧘᧻᳗⋥⧷ߩ⸃ᴺࠍ⚫੺ߔࠆ߇㧘ߘߩ⸘▚ജߦߪᢘ᦯ߔࠆ㧚๺▚ߦߟ޿ߡߪ㧘᣿ᴦએᓟ㧘⑼ቇผߩ┙႐߆ࠄ⎇ⓥ߇ⴕࠊࠇ㧘ߘߩᚑᨐߪᶏᄖߦ߽⚫੺ߐࠇ෻㗀ࠍ๭― 19 ―ငനȁგ༿Ȇ‫୼ٸ‬ȁ֚૾ࠎߛ 7 ) ~10 ) 㧚ㄭᐕߪ㧘ቇⴚ⊛ߥ⎇ⓥߛߌߢߥߊ㧘৻⥸ߩੱ‫ߩ߳ޘ‬๺▚ߩ⚫੺߿ᢙቇᢎ⢒ߩ┙႐߆ࠄߩ⎇ⓥ▚㗵ߩᄢ߈ߐߪਇ᣿ߢ޽ࠆ㧚⺑᣿ᢥߦߟ޿ߡߪ㧘‫ޡ‬Ⴧೞ␹ო▚ᴺ‫⸥ߩޢ‬ㅀߦᓥ޿㧘࿑ߦߟ޿ߡ߽ߘߎ
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޿ߚ㧚૞ᚑߒߚᓳర࿑ࠍ␜ߔ㧔࿑㧙㧕㧚߽⋓ࠎߢ޽ࠆ 11) ~ 20 ) 㧚㧞㧚▚㗵ᓳర࿑࿑᧛਄⠀㤥␹␠⚗ᄬ▚㗵ߩᓳర࿑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౞ߩౝߦᢳࠍ㓒ߡ྾౞ࠍኈࠆࠆ᦭ࠅ㧚ߘߩਛߩ➱ ߆ ߦ߹ߚ౞ࠍኈࠆ㧚ߔߥࠊߜ㧘྾౞ߦಾߔ㧚ධ౞ᓘੑኸ㧘᧲౞ᓘਃኸ㧘⷏౞ᓘ྾ኸ㧚ർ౞ᓘᐞ૗߆ߣ໧߰㧚 ╵ߦᦚߊ㧘ർ౞ᓘ৻චੑኸ㧚 ⴚߦᦚߊ㧘᧲౞ᓘࠍ⟎߈㧘⷏౞ᓘࠍਸ਼ߓᭂߣฬߠߊ㧚ධ౞ᓘࠍએߞߡߎࠇࠍ㒰ߒ㧘એߞߡ᧲⷏౞ᓘߩ๺ࠃࠅᷫߕ㧚૛ࠅࠍએߞߡᭂࠍ㒰ߒ㧘ർ౞ᓘࠍᓧߡ㧘໧߭ߦวߔ㧚㧟㧚㧞⃻ઍ⺆⸶࿑ߩࠃ߁ߦ㧘౞ߩਛߦᢳ✢ࠍ㓒ߡ  ౞߇޽ࠆ㧚ߘߩਛߩ‫ߚ߹ߦޠ߮߭ޟ‬౞߇޽ࠅ㧘 ౞ߦធߒߡ޿ࠆ㧚ධ౞ߩ⋥ᓘࠍ  ኸ㧘᧲౞ߩ⋥ᓘࠍ  ኸ㧘⷏౞ߩ⋥ᓘࠍ  ኸߣߔࠆ㧚ർ౞ߩ⋥ᓘߪ޿ߊࠄ߆㧚╵㧚ർ౞ߩ⋥ᓘߪ  ኸߢ޽ࠆ㧚⸃㧚᧲౞ߩ⋥ᓘߦ⷏౞ߩ⋥ᓘࠍਸ਼ߓߚ߽ߩࠍᭂߣ

― 20 ―ఆષֵࣱ૰২͈໰৐ॳ‫ڣ‬޿߁㧚ߎࠇࠍධ౞ߩ⋥ᓘߢഀࠅ㧘᧲⷏౞ߩ⋥ᓘߩ๺ࠃࠅᒁߊ㧚ߘߩ૛ࠅߢᭂࠍഀࠅ㧘ർ౞ߩ⋥ᓘࠍᓧࠆ㧚╵ߪ㗴ᗧߦว߁㧚㧟㧚㧟ᅏઃߦߟ޿ߡ▚㗵ᄺឝ⠪ߢ޽ࠆ㢬⷗༑૞ᱜ⋥ߦߟ޿ߡߪ㧘᧛਄ߩੱߢ޽ࠆએ਄ߩߎߣߪಽ߆ߞߡ޿ߥ޿㧚ߘߩᏧߩਣጊ࿃ᐔ⦟₵ ᐕ㨪ᐕ ߪ㧘᧛਄⮲჻ߢ޽ࠅ㧘㑐ᵹߩ⪺ฬߥ๺▚ኅ⮮↰⽵⾗ߩ㜞ᒉߢ޽ߞߚ 21) 㧚x2OE 㧘s2

t12tPE1 㧘 22PE2 

t32tPE3 㧘 42PE4 PE ߣ⟎ߊ㧚ᦨೋߦ㧘 'PO1E1 ў 'PO3 E3 ࠃࠅ *1 㧠㧚ⴚߩ⸃⺑ ੨๺   ᐕߦ㧘ᣂᐣ⮲ߩ๺▚ኅ᧻᳗⋥⧷ 㧫㨪 ᐕ ߦࠃࠅ⪺ߐࠇߚ‫␹ޡ‬ო▚ᴺ⸃‫ߩޢ‬౮ᧄ߇ᱷߐࠇߡ߅ࠅ㧘ߘߎߦ␜ߐࠇߡ޿ࠆ⸃ᴺࠍ⚫੺ߔࠆ㧚ߚߛߒ㧘ᓟඨߩౝ౞ߦ㑐ߔࠆㇱಽߪ㧘ේᢥߢߪ⚿ᨐߩߺߒ߆ᦠ߆ࠇߡ޿ߥ޿߇㧘⵬ߞߚ㧚⴫⸥ߪ⃻ઍᢙቇߦᓥ߁㧚

O

PF

B
ห᭽ߦ㧘 'PO2 E2 ў 'PO4 E4 ࠃࠅ  r2 : t 2

r4 : t 4 ߒߚ߇ߞߡ r2t 4r4t 2

    EO

r3t1   ߹ߚ㧘 'PO1E1 ў 'O2 PE2 ࠃࠅE EFO F

r3 : t3 ߒߚ߇ߞߡ r1t3

DA  r1 : t1

r1 : t1O

t 2 : r2 ߒߚ߇ߞߡ r1r2t1t 2   

E

ห᭽ߦ㧘 'PO1E1 ў 'O4 PE4 ࠃࠅEFO  r1 : t1

Ct 4 : r4 ߒߚ߇ߞߡ r1r4t1t 4            
ᰴߦ㧘 'OO1F1 ߦਃᐔᣇߩቯℂࠍㆡ↪ߒߡ *2 



࿑

(r1  x) 2  (t1  s) 2࿑ ߦ߅޿ߡ㧘 ⋥✢ AC ߣ BD ߩ੤ὐࠍ P 㧘ᄖ౞ߩਛᔃ O ߆ࠄ⋥✢ AC ߦᒁ޿ߚု✢ࠍ OE 㧘ὐ
O1 , O2 , O3 , O4 ߆ࠄ⋥✢ AC ߦᒁ޿ߚု✢ࠍ㧘ߘࠇߙࠇ㧘 O1 E1 , O2 E2 , O3 E3 , O4 E4 ߣߒ㧘߹ߚ㧘ὐ O ߆ࠄ⋥ߒߚ߇ߞߡx 2  2r1 x  ( s 2  2st1  t12  r 2  2r1r )✢ O1E1 , O2 E2 , O3 E3 , O4 E4 ߹ߚߪߘߩᑧ㐳਄ߦᒁ޿ߚ
ု✢ࠍ㧘ߘࠇߙࠇ㧘 OF1 , OF2 , OF3 , OF4 ߣߔࠆ㧚 r 㧦౞ O ߩ⋥ᓘ㧘 r1 㧦౞ O1 ߩ⋥ᓘ
r2 㧦౞ O 2 ߩ⋥ᓘ㧘 r3 㧦౞ O3 ߩ⋥ᓘ(r  r1 ) 2 ห᭽ߦ㧘 'OO2 F2 ߦߟ޿ߡ


r4 㧦౞ O4 ߩ⋥ᓘ― 21 ―0    ငനȁგ༿Ȇ‫୼ٸ‬ȁ֚૾
(r2  x ) 2  (t 2  s ) 2(r  r2 ) 2 ߎࠇࠄߢ਄ᑼࠍ⟎߈឵߃ߡ㧘 r1  r3 ߢഀࠅ r1 ࠍដߌߒߚ߇ߞߡࠆߣ
x 2  2r2 x  ( s 2  2st 2  t 2 2  r 2  2r2 r )0   

r1 x 2  r1s 2  r3t12  r1r 2 

4r12 r3r
r1  r30   ߎࠇࠍ╙㧝ᑼߣฬߠߌࠆ㧚ห᭽ߦ㧘 'OO3 F3 ߦߟ޿ߡ߹ߚ㧘  ߦ r4 㧘  ߦ r2 ࠍដߌߡട߃ࠆߣ

(r3  x) 2  (t3  s ) 2(r  r3 ) 2 (r2  r4 ) x 2  (r2  r4 ) s 2  2s (r2t 4  r4t 2 ) ߒߚ߇ߞߡ (r2t 4 2  r4t 2 2 )  (r2  r4 )r 2  4r2 r4 rx 2  2r3 x  ( s 2  2st3  t3 2  r 2  2r3r )0   ห᭽ߦ㧘 'OO4 F4 ߦߟ޿ߡߎߎߢ㧘  ߅ࠃ߮  㧘  ࠃࠅr2t 4  r4t 2 0 
(r4  x)  (t 4  s )220 

r2t 4 2  r4t 2 2(r  r4 ) 2

ߒߚ߇ߞߡ
r 2r 2r 2r 2r2  1 24  r4  1 22 
t1t1
r12 r2 r4t12x 2  2r4 x  ( s 2  2st 4  t 4 2  r 2  2r4 r )(r2  r4 ) 

0   ߎࠇࠄߢ਄ᑼࠍ⟎߈឵߃ߡ㧘 r2  r4 ߢഀࠅ t12 ࠍដએ਄ߩߎߣ߆ࠄ㧘  ߦ r3 㧘  ߦ r1 ࠍដߌߡട߃ߌࠆߣ
ࠆߣ
t12 x 2  t12 s 2  r12 r2 r4  t12 r 2 (r1  r3 ) x 2  (r1  r3 ) s 2  2s (r1t3  r3t1 ) 

 (r1t3 2  r3t12 )  (r1  r3 )r 2  4r1r3r

ߎߎߢ㧘  ࠃࠅ
r1t3  r3t1 0 
r1t3 2  r3t12

r3 2t12
 r3t12 
r1r rr3t12  1 3 
r10 

4r2 r4 rt12
r2  r40  ߎࠇࠍ╙  ᑼߣฬߠߌࠆ㧚╙  ᑼߦ t12 㧘╙  ᑼߦ r1 ࠍដߌߡ㧘╙  ᑼࠃࠅ╙  ᑼࠍᒁߊߣ
§ 4 r r r r 4r 2 r r · r3t14  ¨ 1 2 4  1 3 ¸ t12  r13r2 r4¨ r2  r4r1  r3 ¸¹©

0   
ߎࠇࠍ # ᑼߣฬߠߌࠆ㧚ᰴߦ㧘࿑ ߦ߅޿ߡ㧘ౝ౞ߩਛᔃࠍ O' 㧘ߘߩ⋥― 22 ―ఆષֵࣱ૰২͈໰৐ॳ‫ڣ‬ᓘࠍ r ' ߣߒ㧘࿑ ߣห᭽ߦฦု✢ࠍቯ⟵ߔࠆ㧚ߘߒߡ
x2O' E 㧘s2ห᭽ߦ㧘 'O' O3 F3 ߦߟ޿ߡ
PE ( r3  x ) 2  (t3  s ) 2ߣ⟎ߊ㧚(r ' r3 ) 2 ߒߚ߇ߞߡDAx 2  2r3 x  {s 2  2st3  t3 2  (r ' ) 2  2r3r ' } 0OO

EF EFP EO' ห᭽ߦ㧘 'O' O4 F4 ߦߟ޿ߡO

E
E

(r4  x) 2  (t 4  s ) 2FFߒߚ߇ߞߡ
O
B(r ' r4 ) 2 

Cx 2  2r4 x  {s 2  2st 4  t 4 2  (r ' ) 2  2r4 r ' } 0 ╙  ᑼߣห᭽ߦ㧘  㧘  ࠃࠅ࿑


r1 x 2  r1s 2  r3t12  r1 (r ' ) 2 'O' O1F1 ߦਃᐔᣇߩቯℂࠍㆡ↪ߒߡ
(r1  x) 2  (t1  s ) 20   ߎࠇࠍ╙  ᑼߣฬߠߌࠆ㧚߹ߚ㧘╙  ᑼߣห᭽ߦ㧘  㧘  ࠃࠅ(r ' r1 ) 2 ߒߚ߇ߞߡ
t12 x 2  t12 s 2  r12 r2 r4  t12 (r ' ) 2 x 2  2r1 x  {s 2  2 st1  t12  (r ' ) 2  2r1r ' } 0   

4r2 r4 r ' t12r2  r40

 0

 
ߎࠇࠍ╙  ᑼߣฬߠߌࠆ㧚
# ᑼߣห᭽ߦ㧘╙  ᑼߣ╙  ᑼࠃࠅ

ห᭽ߦ㧘 'O' O2 F2 ߦߟ޿ߡ
(r2  x) 2  (t 2  s ) 2

4r12 r3 (r ' )r1  r3§ 4r r r r ' 4r 2 r r ' · r3t14  ¨ 1 2 4  1 3 ¸ t12  r13r2 r4¨ r2  r4r1  r3 ¸¹©

(r ' r2 ) 2 ߒߚ߇ߞߡ
x 2  2r2 x  {s 2  2st 2  t 2 2  (r ' ) 2  2r2 r ' } 0   ߎࠇࠍ $ ᑼߣฬߠߌࠆ㧚ᦨᓟߦ㧘# ᑼࠃࠅ $ ᑼࠍᒁߊߣ


― 23 ―

ငനȁგ༿Ȇ‫୼ٸ‬ȁ֚૾
­° 4r1r2 r4 (r  r ' ) 4r12 r3 (r  r ' ) ½° 2

¾t1®
r2  r4r1  r3°¿°̄㗴⸃ߌ߹ߔ߆㧫㧔਄㧕 ਅ 㧘᫪ർ಴

0    ਃ਄⟵ᄦᢥൻผ਄ࠃࠅ⷗ߚࠆᣣᧄߩᢙቇ㧘ጤᵄᢥᐶ㧘 ᐕ㧚ߒߚ߇ߞߡ ᷓᎹ⧷ବ㧘࠳ࡦ࡮ࡍ࠼࡯ᣣᧄߩᐞ૗㧙૗㗴⸃ߌ߹ߔ߆㧫㧘᫪ർ಴㧘 ᐕ㧚  ᷓ Ꮉ ⧷ ବ 㧘 6QP[ 4QVJOCP5CETGF /CVJGOCVKEU 㧙(r1  r3 )r2 r4  (r2  r4 )r1r30   ᡿ߦr1㧘 ᐕ㧚

,CRCPGUG6GORNG)GQOGVT[㧘2TKPEGVQP7PKX㧚  2TGUU㧘 ᐕ㧚 ㇌⸶ ⡛ߥࠆᢙቇ㧦▚㗵㧘᫪ർ಴㧘 ᐕ㧚 ዊୖ㊄ਯഥᣣᧄߩᢙቇ㧘ጤᵄᣂᦠ㧘 ᐕ㧚 ᄢ⍫⌀৻๺▚౉㐷㧘ᣣᧄ⹏⺰␠㧘 ᐕ㧚

r2 r4rr(r2  r4 )  2 4r3   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಴ߎࠇ߇㧘ⴚߢㅀߴߡ޽ࠆᑼߢ޽ࠆ㧚 r2r44 㧘 r3㧘 ᐕ㧚

2 㧘  ૒⮮ஜ৻ᣂ๺▚౉㐷㧘⎇ᚑ␠㧘 ᐕ㧚 ዊᎹ᧤㧘ᐔ㊁⪲৻⻠ᐳᢙቇߩ⠨߃ᣇ  ᢙቇߩᱧผ㧘

3 ࠍઍ౉ߒߡ㧘╵ r1 12 ࠍᓧࠆ㧚ᦺୖᦠᐫ㧘 ᐕ㧚⵬⿷  ᑼࠃࠅ
1 1 1 1  

r1 r3 r2 r4

 દ⮮ᵗ⟤ᚻߠߊࠅㆬᛯᢙቇ  ߅߽ߒࠈ๺▚㧘᣿ߣ޿߁⟤ߒ޿⚿ᨐ߇ᓧࠄࠇࠆ㧚 ㆙⮮೑⽵㧦Ⴧୃᣣᧄᢙቇผ㧘ᕡᤊ␠ෘ↢㑑㧘 ᐕ㧚ᴦ࿑ᦠ㧘 ᐕ㧚 ዊኹ⵨㧦ߛ߆ࠄᭉߒ޿ᳯᚭߩ▚㗵㧘⎇ᚑ␠㧘ᐕ㧚 ᪉੗ㅴ㧦ᳯᚭߩᢙቇᢎ⑼ᦠ㧘㓸⧷␠㧘 ᐕ㧚㩷㩿㪉㪇㪈㪇㪅㩷㪈㪇㪅㩷㪈㩷ฃઃ㪀ᵈ ⋧ૃ⸥ภࠍ↪޿ߡ⺑᣿ߒߚ߇㧘๺▚ߢߪ㧘৻⥸ߦ㧘⋧ૃߣ޿߁᭎ᔨߪ⴫ߦߪ಴ߐߕ⋥ធ  ߩࠃ߁ߥᲧ଀㑐ଥࠍㅀߴࠆ㧔એਅห᭽ߢ޽ࠆ㧕㧚ਃᐔᣇߩቯℂߪ㧘㋭⢆ᒏߩℂߣߒߡࠃߊ⍮ࠄࠇߡ޿ߚ㧚ෳ⠨ᢥ₂ ⮮↰⽵⾗㧘⮮↰ཅ⸒㧦Ⴧೞ␹ო▚ᴺ㧘ኡ᡽  ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ⮮↰⽵⾗㧘⮮↰ཅ⸒㧦⛯␹ო▚ᴺ㧘ᢥൻ   ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ᧻᳗⋥⧷㧦␹ო▚ᴺ⸃㧘੨๺   ᐕ㧘᧲ർᄢቇ๺▚⾗ᢱ࠺࡯࠲ࡌ࡯ࠬ⬿㧚 ศ↰ὑᐘ㧦␹ო▚ᴺ⸃㧔ᚑ┙ᐕਇ⹦㧕㧘ᣣᧄቇ჻㒮⬿㧚 ળ↰቟᣿㧦⿧ᓟ࿖⻉ၴ␠⻉ᵹᄺ㗵㓸 ᚑ┙ᐕਇ⹦ 㧘ጊᒻᄢቇ㒝ዻ࿑ᦠ㙚⬿ ૒ਭ㑆ᢥᐶ 㧘 ᐔጊ⺼㧦๺▚ߩᱧผ㧙ߘߩᧄ⾰ߣ⊒ዷ㧘ߜߊ߹ᢥᐶ㧘 ᐕ㧚 ᷓᎹ⧷ବ㧘࠳ࡦ࡮࠰ࠦࡠࡈࠬࠠ࡯ᣣᧄߩᢙቇ㧙૗― 24 ―