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π∑π“¿“…“∏√√¡‡≈à¡ ¯ : ®“° website kanlayanatam.com
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8. 8 : w w w. k a n l a y a n a t a m. c o m
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ÒÚı. ‡∑«¥“ΩÉ“¬‡∑æ-ΩÉ“¬¡“√ ....................................................................... ÒÛ
ÒÚˆ. ‡Àµÿ‡æ√“–√Ÿâ ‰¡à®√‘ß ...................................................................................... ÒÙ
ÒÚ˜. Õ‘∑∏‘∫“∑ Ù ·≈– —π‚¥… ......................................................................... ÒÙ
ÒÚ¯. °”≈—ß µ‘¬ßÕàÕπ ....................................................................................... Òı
—
ÒÚ˘. ‡Àµÿ‡æ√“–‡ÀÁπº‘¥ ........................................................................................ Òˆ
ÒÛ. ‰¡àµÕß≈“ÕÕ°®“°ß“π ............................................................................. Ò˜
â
ÒÛÒ. »’≈ - »√—∑∏“ - §«“¡‡æ’¬√ ................................................................. Ò˜
ÒÛÚ. ‰°à·™à‡À≈â“ ................................................................................................. Ò¯
ÒÛÛ. ‰¥â∫≠·µà ‰¥â ‰¡à¡“° ..................................................................................... Ò¯
ÿ
ÒÛÙ. ∑”‰¡®–„™â ‰¡à ‰¥â ....................................................................................... Ò˘
ÒÛı. ‰¥â∫≠„π à«π∑’¡ µ‘°”°—∫ ........................................................................ Ò˘
ÿ Ë ’
ÒÛˆ. Õ¬“°æâπ∑ÿ°¢å‚¥¬‡√Á« ............................................................................... ÒÒ
ÒÛ˜. ®µÿ§“¡œ Õ’°·≈â« ....................................................................................... ÒÒ
ÒÛ¯. ‡ÀµÿÕ¬Ÿ∑’Ë ‰Àπ ............................................................................................ ÒÒÒ
à
ÒÛ˘. ®”‡ªìπÀ√◊Õ‰¡à ................................................................................................ ÒÒÚ
ÒÙ. µâÕ߇√‘¡µâπ„À¡à ........................................................................................... ÒÒÚ
Ë
ÒÙÒ. √—∫‰¥â·µà«∏√∫µà“ß°—π ................................................................................ ÒÒÛ
‘ ’—
ÒÙÚ. ·µà≈–§π‰¡à‡À¡◊Õπ°—π ............................................................................... ÒÒÙ
ÒÙÛ. ‡®√‘≠«‘ª π“µàÕ ....................................................................................... ÒÒı
í
ÒÙÙ. √—∫®â“ß∑”«‘∑¬“π‘æπ∏å ................................................................................ ÒÒı
ÒÙı. æ‘®“√≥“ µ‘ªØ∞“π Ù .............................................................................. ÒÒˆ
í

10. Ò
10 : w w w. k a n l a y a n a t a m. c o m
ÒÙˆ. Õÿ∫“¬‡√’¬° µ‘°≈—∫ ..................................................................................... ÒÒ˜
ÒÙ˜. µ—¥°√√¡‰¥âÀ√◊Õ ........................................................................................... ÒÒ¯
ÒÙ¯. ¢Õ∑√“∫∑“ß≈—¥ ........................................................................................... ÒÒ¯
ÒÙ˘. §”∂“¡∑’§≈⓬°—π ........................................................................................ ÒÒ˘
Ë
Òı. ª√“√∂π“¡√√§º≈π‘ææ“π .................................................................. ÒÒ˘
ÒıÒ. ‰¡àÕ“®™’·π– .................................................................................................. ÒÚ
È
ÒıÚ. µâÕß∑”„À⥉¥â°Õπ ...................................................................................... ÒÚ
Ÿ à
ÒıÛ. πâÕ¬≈ß·µà ‰¡àÀ¡¥ ....................................................................................... ÒÚÒ
ÒıÙ. §«“¡øÿß´à“π ............................................................................................. ÒÚÚ
Ñ
Òıı. ‡ªìπ‡æ’¬ß¡“¬“ ........................................................................................... ÒÚÚ
Òıˆ. §√Ÿ∫“Õ“®“√¬å‡§¬æŸ¥‰«â ............................................................................ ÒÚÛ
Òı˜. ∫√√≈ÿÕ–‰√ .................................................................................................... ÒÚÙ
Òı¯. ∫√√≈ÿ§«“¡‡ªìπ‡∑æ ................................................................................ ÒÚı
Òı˘. ‡√‘¡®“°ßà“¬‰ªÀ“¬“° ................................................................................ ÒÚˆ
Ë
Òˆ. ‘ß∑’º√Ÿâ ‰¡à∑” ................................................................................................ ÒÚˆ
Ë Ë Ÿâ
ÒˆÒ. √Ÿ °‰¡à¥’ .......................................................................................................... ÒÚ˜
â ÷
ÒˆÚ. √Ÿ®µ-√ŸªØ‘ π∏‘¢Õß®‘µ ................................................................................ ÒÚ¯
â ÿ ‘ â
ÒˆÛ. Õ°ÿ»≈°√√¡„Àâº≈ ........................................................................................ ÒÚ¯
ÒˆÙ. ¢÷πÕ¬Ÿ°∫∫“√¡’ ............................................................................................. ÒÚ˘
È à —
Òˆı. ªØ‘∫µ∏√√¡‡À¡◊Õπ°—π .............................................................................. ÒÛ
— ‘
Òˆˆ. ‡§√◊Õß¡◊Õ √â“ßµ—≥À“ .......................................................................... ÒÛÒ
Ë
Òˆ˜. ™à«¬·≈⫵âÕ߉¡à‡∫’¬¥‡∫’¬πµ—«‡Õß ....................................................... ÒÛÚ
Òˆ¯. ·°â°√√¡Õ¬à“߉√ ....................................................................................... ÒÛÛ
Òˆ˘. æ√–‚æ∏‘ µ«å ................................................................................................. ÒÛÙ
—
Ò˜. ¬â“¬∞“π‡®¥’¬å ........................................................................................... ÒÛı
Ò˜Ò. Õ¡πÿ…¬å∑¡√ªπ“¡‡ªìπ∑‘æ¬å ..................................................................... ÒÛˆ
’Ë ’ Ÿ
Ò˜Ú. ª√– “∑À≈ÕπÀ√◊Շ撬π ......................................................................... ÒÛˆ
È
Ò˜Û. ‰¥â∫≠‰¡à‡∑à“°—π ....................................................................................... ÒÛ¯
ÿ
Ò˜Ù. ∫“ª‡°‘¥®“°§«“¡À«—ߥ’ ........................................................................... ÒÛ¯
Ò˜ı. ‡ªÑ“À¡“¬‡¥’¬«°—π ....................................................................................... ÒÛ˘
Ò˜ˆ. §«“¡‡™◊Õ¢Õߧπ‚∫√“≥ ......................................................................... ÒÙ
Ë
Ò˜˜. §«“¡‡ªìπÕπ—µµ“ ....................................................................................... ÒÙ
Ò˜¯. ∑”§«“¡¥’¬Õ¡¡’Õª √√§ ........................................................................ ÒÙÒ
à ÿ
Ò˜˘. ªØ‘∫µº¥µâÕß·°â ‰¢ .................................................................................... ÒÙÚ
— ‘ ‘
Ò¯. ‰ªÕ¬Ÿà„π∑’™Õ∫ .............................................................................................. ÒÙÙ
Ë
Ò¯Ò. »’≈¬—ß∫°æ√àÕß ....................................................................................... ÒÙÙ
Ò¯Ú. √à«¡Õ°ÿ»≈°√√¡ ........................................................................................... ÒÙı

11. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : 11
ÒÒ
Ò¯Û. ‡¡◊Õ ÿπ¢®Õ߇«√ .......................................................................................... ÒÙˆ
Ë —
Ò¯Ù. ‡¥Á°µ“¬„π§√√¿å .......................................................................................... ÒÙˆ
Ò¯ı. ∫“ª‡∑à“∑’∑”™—« ............................................................................................. ÒÙ˜
Ë Ë
Ò¯ˆ. ¡¥ÿ≈∑“ß‚≈°-∑“ß∏√√¡ .................................................................... ÒÙ¯
Ò¯˜. ∫ÿ≠ Ÿß ÿ¥ ........................................................................................................ ÒÙ˘
Ò¯¯. »’≈‰¡à∫√‘ ∑∏‘Ï ................................................................................................. Òı
ÿ
Ò¯˘. ªØ‘ª∑“ Ù ...................................................................................................... ÒıÒ
Ò˘. ‰¡à ªª“¬– .................................................................................................... ÒıÚ
—
Ò˘Ò. —߶∑“π∑’¥’ ................................................................................................... ÒıÚ
Ë
Ò˘Ú. ¿‘°…ÿ¡»≈æ√àÕß ........................................................................................... ÒıÛ
’ ’
Ò˘Û. ∑”„Àâ ߧ¡·µ°·¬° ................................................................................ ÒıÙ
—
Ò˘Ù. ¢Õ¢¡“µàÕæ√–æÿ∑∏√Ÿª .............................................................................. ÒıÙ
Ò˘ı. ‡®µπ“¢ÕߺŸ‡ πÕ ....................................................................................... Òıı
â
Ò˘ˆ. ¡‘‰¥â Õπ„Àâ „®·§∫ ............................................................................... Òıˆ
Ò˘˜. ‰¡à∫ßÕ“®≈–‡¡‘¥ .......................................................................................... Òıˆ
—
Ò˘¯. ªØ‘∫µµ“¡æ√–√“™¥”√— ..................................................................... Òı˜
— ‘
Ò˘˘. ¡’·µà√ª .......................................................................................................... Òı¯
Ÿ
Ú. 𓬮â“ß-≈Ÿ°®â“ß ........................................................................................... Òı¯
ÚÒ. ‡ªìπ‡À¡◊Õπ ‘ßπ—π ....................................................................................... Òı˘
Ë È
ÚÚ. „§√‡¢’¬π∫Õ°‰«â ....................................................................................... Òˆ
ÚÛ. «‘∏‡®√‘≠¨“π .............................................................................................. ÒˆÒ
’
ÚÙ. §«“¡®”¥’‡≈‘» ............................................................................................. ÒˆÚ
Úı. Õ“™’æ∑𓬧«“¡ ....................................................................................... ÒˆÚ
Úˆ. §ÿ≥∏√√¡¢Õß™“« «√√§å ....................................................................... ÒˆÛ
Ú˜. ∫“√¡’ ß¡“°‰À¡ ......................................................................................... ÒˆÙ
Ÿ
Ú¯. ∫ÿ≠§ÿ¡√—°…“ ................................................................................................ ÒˆÙ
â
Ú˘. °“√µ‘¥¨“π ................................................................................................... Òˆı
ÚÒ. ‡ÀÁπ·®âß·≈⫉¡à ß —¬ ............................................................................ Òˆˆ
ÚÒÒ. ‰¡à·µ°µà“ß°—π .............................................................................................. Òˆ˜
ÚÒÚ. ∑”µ—«‡Õß„Àâ·¡à»√—∑∏“ ........................................................................... Òˆ¯
ÚÒÛ. ‰¡à¡ ≠≠“„π ¡¡µ‘∫≠≠—µ‘ ................................................................... Òˆ¯
’ — —
ÚÒÙ. ‡≈◊Õ°∑“ß™’«µ¥â«¬µπ‡Õß ..................................................................... Òˆ˘
‘
ÚÒı. ‡«√√–ß—∫¥â«¬°“√‰¡à®Õ߇«√ .................................................................. Ò˜
ÚÒˆ. °“√‡¢â“π‘‚√∏ ¡“∫—µ‘ ................................................................................. Ò˜
ÚÒ˜. ∫ÿ≠°‘√¬“«—µ∂ÿ Ò ..................................................................................... Ò˜Ò
‘
ÚÒ¯. Õ“π‘ ß å¢Õß°“√Õÿ∑»∫ÿ≠ ....................................................................... Ò˜Ú
‘
ÚÒ˘. ∫ÿ≠Õ¬Ÿà„π„® ............................................................................................... Ò˜Ú

12. ÒÚ
12 : w w w. k a n l a y a n a t a m. c o m
ÚÚ. Õÿ∑»„Àâ ‰¥â ....................................................................................................... Ò˜Û
‘
ÚÚÒ. Õ¬“°‡°‘¥‡ªì𙓬 ....................................................................................... Ò˜Ù
ÚÚÚ. —¡º— ∑’À° .................................................................................................. Ò˜Ù
Ë
ÚÚÛ. —≠≠“‡°à“∑’∂°∫—π∑÷° ................................................................................ Ò˜ı
Ë Ÿ
ÚÚÙ. ‡°‘¥‡ªìπ°√–‡∑¬ ........................................................................................... Ò˜ˆ
ÚÚı. ‡°‘¥¡“º‘¥‡æ» ............................................................................................... Ò˜˜
ÚÚˆ. ‰¥â∫≠µà“ß°—π .............................................................................................. Ò˜¯
ÿ
ÚÚ˜. àß°√–· ®‘µ ................................................................................................ Ò˜¯
ÚÚ¯. µ“¬·≈â«øóπ ................................................................................................... Ò˜˘
ô
ÚÚ˘. ‰¡à¢π°—∫°“≈‡«≈“ ....................................................................................... Ò¯Ò
÷È
ÚÛ. ∫“ªÀ√◊Õ‰¡à∫“ª ....................................................................................... Ò¯Ú
ÚÛÒ. «‘ª π“≠“≥‰¡à§√∫ ................................................................................ Ò¯Ú
í
ÚÛÚ. ∂“¡À≈“¬‡√◊Õß ........................................................................................... Ò¯Û
Ë
ÚÛÛ. „§√∫“ª¡“°°«à“ .......................................................................................... Ò¯ı
ÚÛÙ. µ‘‡µÁ¡√âÕ¬ .................................................................................................. Ò¯ı
ÚÛı. √Ÿ·≈â«„™à«“°‘‡≈ ≈¥ ..................................................................................... Ò¯ˆ
â à
ÚÛˆ. √Ÿ«πµ“¬≈à«ßÀπâ“ ....................................................................................... Ò¯˜
â—
ÚÛ˜. §π¡’‡¡’¬πâÕ¬µ°π√°™—π‰Àπ ................................................................... Ò¯¯
È
ÚÛ¯. À“‡Àµÿ„Àâæ∫·≈â«¥—∫„Àâ ‰¥â ........................................................................ Ò¯˘
ÚÛ˘. µàÕµâ“πæ√–√—µπµ√—¬ ................................................................................. Ò˘
ÚÙ. æ≈– ı ™à«¬‰¥â ....................................................................................... Ò˘Ò
ÚÙÒ. ß“π¿“¬πÕ° - ß“π¿“¬„π ................................................................... Ò˘Ú
ÚÙÚ. ¬°‡≈‘°Õ∏‘…∞“π‡°à“ ................................................................................... Ò˘Û
ÚÙÛ. ‡§√’¬¥°—∫§”µÕ∫ ....................................................................................... Ò˘Ù
ÚÙÙ. ™à«¬‡®â“™“¬π‘∑√“ ....................................................................................... Ò˘ı
ÚÙı. ∑“π√–¥—∫‰Àπ ....................................................................................... Ò˘ˆ
ÚÙˆ. ™à«¬¥’°«à“‰¡à™«¬ ....................................................................................... Ò˘˜
à
ÚÙ˜. «‘ª πŸª°‘‡≈ ....................................................................................... Ò˘¯
í
ÚÙ¯. ∑”‰¥â·µà ‰¡à ¡§«√ ................................................................................ Ú
ÚÙ˘. µâÕß √â“ß∫ÿ≠„À≠à .............................................................................. ÚÒ
Úı. ‡™◊Õ·≈â«∑”µ“¡ ....................................................................................... ÚÚ
Ë
ÚıÒ. Õÿ∑»∫ÿ≠„™âÀπ’È ....................................................................................... ÚÛ
‘
ÚıÚ. ‡Àπ◊Õ§«“¡™Õ∫ - §«“¡æÕ„® ............................................................ ÚÙ
ÚıÛ. ∑”‰¥â·≈–‡°‘¥º≈¥’Õ°¥â«¬ ..................................................................... Úı
’
ÚıÙ. µâÕß°“√Ωñ°«‘ª π“œ ............................................................................... Úı
í
Úıı. √Ÿ·≈⫉¡à¬¥µ‘¥ ....................................................................................... Úˆ
â ÷

13. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : ÒÛ
13
§µ‘∏√√¡
○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○
Õÿ‡∫°¢“∏√√¡ §◊ÕÕ–‰√
Õÿ‡∫°¢“ „™à«à“ ª≈àÕ¬«“ßÀ¡¥
À≈—ߧ“√—Ë« °“¬ °ª√° ‰¡à·°â‰¢
Õÿ‡∫°¢“ Õ¬à“߇¥’¬« ‰¡à π„®
‚≈°∫√√≈—¬ ™à“ß‚≈° ‰¡à ‚»°‡Õ¬
Õÿ‡∫°¢“ ®÷ߪ√–°Õ∫ ¥â«¬ªí≠≠“
‡¡◊ËÕ∂÷ߧ√“ ·°â‰¥â ‰¡àπ߇©¬
‘Ë
≈Õß∑”¥Ÿ ‰¡àª≈àÕ¬ª≈– ≈–‡≈¬
§«“¡‡ ∫¬ ‡æ◊Õ à«π√«¡
Ë ®÷ߧ«√∑”
∑”‰ª·≈â« „§√®–µ‘ µ”Àπ‘«“ à
‰¡à ‚¡¶ ‚°√∏“ ≈ß‚∑…‡¢“
¡’·µà®‘µ §‘¥Õ¿—¬ „®®÷߇∫“
—𵑠¢ ÿ ‡ªìπ√ࡇߓ ‡¢â“∂÷ß∏√√¡
Õÿ‡∫°¢“ ‡ªìπ‡√◊Õß
Ë ªí≠≠“®‘µ
µâÕßæ‘π® ‘ æ‘®“√≥“ „Àâ‡À¡“– ¡
æÕ·°â‰¥â °Á·°â‰ª ‰¡à√–∑¡
‡¡◊ËÕ·°â·≈â« ‰¡à ¡ ‰¡à∑°¢å‡Õ¬.
ÿ
®“°Àπ—ß ◊Õ∑“ßæâπ∑ÿ°¢å ¢Õ߇¥Á°πâÕ¬„π·¥π∏√√¡

14. ÒÙ
14 : w w w. k a n l a y a n a t a m. c o m
Ò. °“√°√–∑” ”§—≠°«à“™◊ËÕ
§”∂“¡
Õ¬“°∑√“∫«à“‡¡◊ËÕ¡’„§√∑—°™◊ËÕ‡√“·≈–π“¡ °ÿ≈‰¡à¥’ „Àâ
‡ª≈’ˬπ·≈â«®–¥’ Õ“®“√¬å§‘¥«à“§«√®–‡ª≈’Ë¬πµ“¡‰À¡‡¢“«à“
™◊Õπ“¡ °ÿ≈¡’°√√¡‡°à“ ·≈â«„À⇪≈’¬π‰¥â ‰¡à‡°‘π Û §√—ß„™à ‰À¡§à–
Ë Ë È
§”µÕ∫
æÿ∑∏»“ 𓇪ìπ»“ π“¢ÕߺŸâ√Ÿâ®√‘ß ºŸâ√Ÿâ®√‘߉¡à ‰ ¥â „ Àâ
§«“¡ ”§—≠°—∫ ¡¡µ‘∫—≠≠—µ‘ ™◊ËÕ·≈–π“¡ °ÿ≈ ‡ªìπ ¡¡µ‘∑’˧π
µ—Èߢ÷Èπ¥—ßµ—«Õ¬à“ß ‡™àπ ∑—ææ– ·ª≈«à“ ‰¡â ‡Àµÿ∑’Ë°ÿ¡“√¡’™◊ËÕ«à“
∑—ææ–‡ªìπ‡æ√“–·¡àµ“¬ ®÷ß∂Ÿ°π”‰ª‡º“∫π‡™‘ßµ–°Õπ§√√¿å
·µ°ÕÕ°·≈–≈Ÿ°∑’ËÕ¬Ÿà„π§√√¿å ‰¥â≈Õ¬¡“µ°Õ¬Ÿà∫π°Õ߉¡â∑’ËÕ¬Ÿà
„°≈⇙‘ßµ–°Õπ °ÿ¡“√π—Èπ®÷߉¥â™◊ËÕ«à“∑—ææ– ·≈–Õ’°µ—«Õ¬à“ß
Àπ÷Ëߧ”«à“ ÕÀ‘ß °– ·ª≈«à“‰¡à‡∫’¬¥‡∫’¬π ÕÀ‘ß °–µàÕ¡“§◊Õ
‚®√Õߧÿ≈’¡“≈∑’Ë ‰≈à¶à“§π‡ªìπ®”π«π¡“° ∑’ˬ°¡“‡ªìπµ—«Õ¬à“ß
¢Õß∑—Èß Õß°√≥’ „π∑’Ë ÿ¥‰¥â∫√√≈ÿ∏√√¡¢—Èπ Ÿß‡ªìπæ√–Õ√À—πµå
∑’Ë™◊ËÕ«à“æ√–∑—ææ– ·≈–æ√–Õߧÿ≈’¡“≈ §π®–¥’®–‡≈«Õ¬Ÿà∑’Ë°“√
°√–∑” (°√√¡) ¡‘‰¥âÕ¬Ÿà∑’Ë™◊ËÕ·≈–π“¡ °ÿ≈ „π ¡—¬ªí®®ÿ∫—π§π∑’Ë
¡’™◊ËÕ∑’˧«“¡À¡“¬‰ª„π∑“ߥ’ ‡¡◊ËÕ‰¥âª√–惵‘°√√¡™—Ë« °√√¡
™—Ë«®÷ߺ≈—°¥—πµ—«‡Õß„À⇢ⓉªÕ¬Ÿà„π§ÿ°„πµ–√“߉¥â °√√¡™—Ë«¬—ß
º≈—°¥—π„Àâ«‘∫—µ‘‰¥â ¬—ߺ≈—°¥—π„À⇪ìπ‚√§µ“¬‰¥â œ≈œ

15. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : Òı
15
Ú. æ√–æÿ∑∏‡®â“¡’‰¥âÀ≈“¬Õߧå
§”∂“¡
∑”‰¡∂÷ß¡’æ√–æÿ∑∏‡®â“À≈“¬Õߧå
§”µÕ∫
‡Àµÿ∑’Ë¡’æ√–æÿ∑∏‡®â“‰¥âÀ≈“¬Õß§å ‡π◊ËÕß®“°°√√¡∑’Ë
∫ÿ§§≈°√–∑” ∫ÿ§§≈„¥¡’ªØ‘ª∑“µ“¡·π«∑“ߢÕßæ√–‚æ∏‘ —µ«å
‡¡◊ËÕ‡Àµÿªí®®—¬∂÷ßæ√âÕ¡ ∫ÿ§§≈π—Èπ “¡“√∂‡ªìπæ√–æÿ∑∏‡®â“‰¥â
ºŸâ∂“¡ªí≠À“À“°ª√“√∂π“®–‡ªìπæ√–æÿ∑∏‡®â“Õߧ儥ÕߧåÀπ÷Ëß
„πÕ𓧵 °Á ¬à Õ ¡ª√“√∂π“‰¥â ‡ ¡◊Ë Õ ‰¥â ª √–惵‘ ∂Ÿ ° µ√ßµ“¡
·π«∑“ߢÕßæ√–‚æ∏‘ —µ«å ·≈–‰¡à¡’°“≈‡«≈“‡ªìπ¢âÕ®”°—¥ ‡¡◊ËÕ
‡Àµÿªí®®—¬∂÷ßæ√âÕ¡§◊Õ¡’∫“√¡’‡µÁ¡ Û ∑—» ‰¥â√—∫°“√欓°√≥å
®“°æ√–æÿ∑∏‡®â“Õߧå°àÕπ ®‘µ«‘≠≠“≥‡¢â“ªØ‘ π∏‘„π§√√¿å¢Õß
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16 : w w w. k a n l a y a n a t a m. c o m
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18 : w w w. k a n l a y a n a t a m. c o m
ˆ. ‚æ∏‘ —µ«å „πÕ∫“¬¿Ÿ¡‘
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19. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : Ò˘
19
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20. Ú
20 : w w w. k a n l a y a n a t a m. c o m
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21. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : ÚÒ
21
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22. ÚÚ : w w w. k a n l a y a n a t a m. c o m
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23. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : 23
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24 : w w w. k a n l a y a n a t a m. c o m
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°√–∫«πÕ°ÿ»≈°√√¡‡¥’¬«°—π ®÷ßµâÕß√—∫Õ°ÿ»≈«‘∫“°∑—Èß Ú ΩÉ“¬
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Òı. ‰¡à¡’ª√– ∫°“√≥å
§”∂“¡
·¥ππ‘ææ“π‰¡à¡’√Ÿª‰¡à¡’π“¡·≈â«¡’·µà§«“¡«à“ß ®–Õ¬Ÿà
Õ¬à“߉√
§”µÕ∫
ºŸâµÕ∫ªí≠À“µâÕߢÕÕ¿—¬ ‡π◊ËÕß®“°‰¡à¡’ª√– ∫°“√≥å
„π·¥ππ‘ææ“π ®÷߉¡à¢ÕµÕ∫ªí≠À“∑’Ë∂“¡‰ª

25. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : 25
Úı
Òˆ. Õ¬Ÿà∑’Ë°√√¡„°≈ⵓ¬
§”∂“¡
§π∑’Ë ‰¡à‡§¬∑”∑“π√—°…“»’≈¡“‡≈¬ ·µà°àÕπ®–µ“¬‰¥â
∑” —߶∑“π À“°®‘µπâÕ¡„π —߶∑“π∑’Ë∑”®–‰ª‡°‘¥∑’Ë ‰Àπ
§”µÕ∫
‡ªìπ‡√◊ËÕߢÕß°√√¡„°≈ⵓ¬ (Õ“ —ππ°√√¡) ‡¡◊ËÕ®‘µ‰¥â
√–≈÷°∂÷ß —߶∑“π∑’∑”·≈â« ·≈–‰¡à¡°√√¡Õ◊π¡“™‘ß„Àâº≈µ—¥Àπâ“
Ë ’ Ë
µ“¬·≈⫉ª‡°‘¥„À¡à„π ÿ§µ‘¿æ
—ß‚¬™πå Ò §◊Õ °‘‡≈ Ò Õ¬à“ß∑’˺Ÿ°¡—¥„® —µ«å „ÀâµâÕ߇«’¬πµ“¬
‡«’¬π‡°‘¥Õ¬Ÿà „π«—Ø ß “√‰¥â·°à Ò. —°°“¬∑‘Ø∞‘ À¡“¬∂÷ß §«“¡
‡ÀÁπ«à“‡ªìπµ—«µπ ‡ªìπ¢Õßµπ Ú. «‘®°®©“ À¡“¬∂÷ß §«“¡≈—߇≈ ß —¬
‘‘
Û. ’≈—æ浪√“¡“ À¡“¬∂÷ß §«“¡¬÷¥¡—Ëπ∂◊Õ¡—Ëπ„π»’≈·≈– æ√µÀ√◊Õ
‡™◊ËÕ«à“§«“¡»—°¥‘Ï ‘∑∏‘Ï®–¡’‰¥â¥â«¬»’≈À√◊Õæ√µ Ù. °“¡√“§– À¡“¬∂÷ß
°“√¡’®‘µ‡ªìπ∑“ ¢Õß°“¡§ÿ≥ ı. ªØ‘¶– À¡“¬∂÷ß °“√∑’Ë®‘µ∂Ÿ°
°√–∑∫·≈⫇°‘¥‡ªì𧫓¡¢—¥„® ˆ. √Ÿª√“§– À¡“¬∂÷ß ®‘µ‡ÀÁπ√Ÿª
æ√À¡ «¬ß“¡ ®÷ßÕ¬“°‡°‘¥‡ªìπæ√À¡¡’√Ÿª À√◊Õ¡’®‘µÕ¬Ÿà„πÕ“√¡≥å
·Ààß√Ÿª¨“π ˜. Õ√Ÿª√“§– À¡“¬∂÷ß ®‘µ™Õ∫°“√‰¡à¡’√Ÿª®÷ßÕ¬“°
‡°‘¥‡ªìπÕ√Ÿªæ√À¡ À√◊Õ¡’®µµ‘¥Õ¬Ÿ„πÕ“√¡≥å·ÀàßÕ√Ÿª¨“π ¯. ¡“π–
‘ à
À¡“¬∂÷ß §«“¡∂◊Õµ—«∂◊Õµπ ∂◊Õµ—«‡Õß«à“‡ªìππ—Ëπ‡ªìππ’Ë ˘. Õÿ∑∏—®®–
À¡“¬∂÷ß §«“¡¡’®‘µøÿÑß´à“π Ò. Õ«‘™™“ À¡“¬∂÷ß √Ÿâ·µà‰¡à®√‘ß À√◊Õ
§«“¡‰¡à√Ÿâ®√‘ß„π √√æ ‘ËßÀ√◊Õ§◊Õ§«“¡À≈ß

26. Úˆ
26 : w w w. k a n l a y a n a t a m. c o m
Ò˜. §«“¡°≈—«
§”∂“¡
¢≥–∑’Ë ª Ø‘ ∫— µ‘ ∏ √√¡‡¥‘ π ®ß°√¡+π—Ë ß ¡“∏‘ § π‡¥’ ¬ «
Õÿ ª √√§∑’Ë „À≠à§◊Õ§«“¡°≈—« ®π∑”„Àâ ‰ ¡à Õ ¬“°ªØ‘ ∫— µ‘ À √◊ Õ
ªØ‘∫—µ‘‰¥â ‰¡àπ“π∫“ߧ√—Èß°”Àπ¥√Ÿâ°Á¬—߉¡àÀ“¬ √∫°«π·π–π”
¥â«¬§à–
§”µÕ∫
‡Àµÿ·Ààߧ«“¡°≈—« §◊Õ‰¡à√Ÿâ®√‘ß„π‡√◊ËÕß∑’Ë°≈—« ºŸâ∑’Ë√Ÿâ®√‘ß
„π √√æ ‘Ëß √√æª√“°Ø°“√≥å ®–‰¡à°≈—«„π ‘Ëß„¥ Ê °“√‡¢â“
∂÷ߧ«“¡®√‘ßµà“ß Ê ‰¥â µâÕßæ—≤π“®‘µ„À⇰‘¥ªí≠≠“‡ÀÁπ·®âß ·≈â«
§«“¡°≈—«®–À¡¥‰ª ¥—ßπ—ÈπµâÕߪؑ∫—µ‘∏√√¡‰ª‡√◊ËÕ¬ Ê ·¡â
ªØ‘∫—µ‘‰¥â ‰¡àπ“π°Á¬—ߥ’°«à“‰¡àªØ‘∫—µ‘ ∑ÿ°§√—Èß∑’Ë¡’°“√ªØ‘∫—µ‘∏√√¡
°√√¡¥’‰¥â∂Ÿ°‡°Á∫ —Ëß ¡‡æ‘Ë¡¢÷Èπ‡√◊ËÕ¬ Ê „π¥«ß®‘µ ‡¡◊ËÕ„¥∑’Ë°√√¡
¥’¡’¡“°æÕ∑’Ë®–· ¥ßº≈‰¥â «‘ªí π“≠“≥®–‡°‘¥¢÷Èπ ·≈â«
ªí≠À“‡√◊ËÕߧ«“¡°≈—«®–À¡¥‰ª
燡◊ËÕ¡’ ‚Õ°“ ∑”¥’ µâÕß∑”¥’ Õ¬à“∑”‡¥àπ
‡¡◊ËÕ„¥∑”‡¥à𠧫“¡¥’®–«‘ËßÀπ’‡√“é

27. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : Ú˜
27
Ò¯. °√√¡‡«√¡’¡“°
§”∂“¡
À“°‡√“¢ÕÕ‚À ‘°√√¡·≈–‰¥â√—∫°“√Õ‚À ‘°√√¡·≈â«
¬—ß®–¡’‡»…¢Õß°√√¡∑’ˇ√“µâÕß√—∫À√◊Õ‰¡àÕ¬à“߉√
§”µÕ∫
ºŸâ¡’ª√– ∫°“√≥å‡√◊ËÕ߇«’¬πµ“¬ - ‡«’¬π‡°‘¥ ¢Õßµ—«
‡Õߥ⫬ªÿæ‡æπ‘«“ “πÿ µ‘≠“≥ √Ÿ«“·µà≈–¿æ∑’‡°‘¥¡’√ªπ“¡ ≈â«π
âà Ë Ÿ
µà“߉¥âª√–°Õ∫°√√¡∑—Èߥ’ - ™—Ë« ‡√◊ËÕ¬¡“®π∂÷ßªí®®ÿ∫—𙓵‘ ·≈–
√Ÿ«“‡®â“°√√¡π“¬‡«√¡’®”π«π¡“°¡“¬ ‡°‘π∑’®–√–≈÷°‰¥â§√∫∂â«π
âà Ë
©–π—π‡¡◊Õ‡®â“°√√¡π“¬‡«√∑’√∫√Ÿ°“√¢Õ¢¡“°√√¡·≈–¬°‚∑…„Àâ
È Ë Ë— â
‡«√°√√¡π—Èπ¬àÕ¡À¡¥°—π‰ª à«π‡®â“°√√¡π“¬‡«√∑’Ë ‰¡à “¡“√∂
√—∫√Ÿâ°“√¢Õ¢¡“°√√¡ ‡™àπ‡®â“°√√¡π“¬‡«√∑’Ë ‰ª‡°‘¥‡ªìπ —µ«å
π√°À√◊Õ‡ª√µ∑’ËÕ¬ŸàÀà“߉°≈ ‡°‘π∑’Ë®– ◊ËÕ∂÷ß°—π‰¥â ‡¢“¬—ß¡‘‰¥â
Õ‚À ‘°√√¡„Àâ ‡»…‡«√°√√¡®–¬—ß¡’Õ¬Ÿà „π°√≥’π’È°“√ª≈¥Àπ’È„Àâ
À¡¥‰¥â°ÁµàÕ‡¡◊ËÕ µâÕßæ—≤π“®‘µµπ‡Õß®π “¡“√∂¥—∫√Ÿª¥—∫
π“¡¢Õßµπ‡Õ߉¥â‡¡◊ËÕ„¥·≈⫇«√°√√¡∑’ˇÀ≈◊Õ ®–¬°‡≈‘°°—π‰ª
‡æ√“–‰¡à¡’√Ÿªπ“¡¡“‡«’¬πµ“¬ - ‡«’¬π‡°‘¥Õ¬Ÿà„π —ß “√«—Ø„Àâ
µâÕß¡“√—∫°“√™¥„™âÀπ’ȇ«√°√√¡Õ’°µàÕ‰ª
ç∑’˧π∑”¥’·≈â«¡—°∫àπ«à“‰¡à‰¥â¥’ ‡æ√“–¥’πÈπ¡’ ‚∑…é
—

28. Ú¯
28 : w w w. k a n l a y a n a t a m. c o m
Ò˘. —¡¿‡« ’À¡¥Õ“¬ÿ¢—¬
§”∂“¡
—¡¿‡« ’∑’ËÀ¡¥Õ“¬ÿ¢—¬·≈⫬—߉¡à ‰ª‡°‘¥¡’À√◊Õ‰¡à‡æ√“–
‡Àµÿ„¥
§”µÕ∫
‰¡à¡’ ‡¡◊ËÕ§√∫Õ“¬ÿ¢—¬·≈â« µâÕ߉ªªØ‘ π∏‘‡ªìπ —µ«å„π
√à“ß„À¡à µ“¡°Æ∏√√¡™“µ‘
Ú. ¬—ߪî¥Õ∫“¬¿Ÿ¡‘‰¡à ‰¥â
§”∂“¡
°“√‰ªπ¡— °“√ —߇«™π’¬ ∂“π¥â«¬®‘µ»√—∑∏“ “¡“√∂
À≈ÿ¥æâπ®“°Õ∫“¬¿Ÿ¡‘‰¥â„𙓵‘π’ÈÀ√◊Õ‰¡àÕ¬à“߉√
§”µÕ∫
—߇«™π’¬ ∂“π∂Ÿ° √â“ߢ÷Èπ ‡æ◊ËÕ„Àâ∫ÿ§§≈ºŸâ‡≈◊ËÕ¡„
»√—∑∏“‰¥â ‰ª°√“∫‰À«â∫Ÿ™“ √–≈÷°∂÷ßæ√–§ÿ≥¢ÕߺŸâ¡∫ÿ≠¡’∫“√¡’
’

29. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : 29
Ú˘
ªØ‘ ¡æ—π∏å°—∫ºŸâ¡’§≥∏√√¡ Ÿß ÿ¥‡™àππ’È ‡ªìπæ≈—ß°ÿ»≈°√√¡ ‡¡◊ËÕ
— ÿ
‰¥â∑”·≈â«®–∂Ÿ°‡°Á∫∫—π∑÷°‰«â „𮑵«‘≠≠“≥¢ÕߺŸâ°√–∑” ‡¡◊ËÕ
∂÷ß«“√–∑’Ë®‘µµâÕß ≈–∑‘Èß√Ÿª¢—π∏å æ≈—ß°ÿ»≈°√√¡®–º≈—°¥—𮑵
«‘≠≠“≥ ‰ª‰¥â√à“߇¢â“Õ¬ŸàÕ“»—¬„À¡à„π ÿ§µ‘¿æ ·µà‚Õ°“ ∑’Ë®–
≈߉ª‡°‘¥‡ªìπ —µ«å„πÕ∫“¬¿Ÿ¡‘„π¿æ∂—¥ Ê ‰ª¬—߇ªî¥√ÕÕ¬Ÿà
ÚÒ. °“√µ—Èߧ«“¡À«—ß
§”∂“¡
°“√∑”∫ÿ≠·≈â«À«—ߺ≈µÕ∫·∑π‡™àπÀ«—ß®–√«¬ À√◊Õ
®–‰¥â¢÷Èπ «√√§å∂◊Õ«à“‡ªì𰑇≈ À√◊Õ‰¡à·≈–®–‡ªìπ∫“ªÀ√◊Õ‰¡à
§”µÕ∫
∑”∫ÿ≠‰¥â∫ÿ≠µ“¡°Æ·Ààß°√√¡ À≈—ß®“°∑”∫ÿ≠·≈â«
À«—ß√«¬À«—ß®–‰¥â¢÷Èπ «√√§å “¡“√∂À«—߉¥â·µà®– ¡À«—ßÀ√◊Õ
‰¡àµâÕߥŸ∑’ˇÀµÿ∑’˺Ÿâπ—Èπ°√–∑” À“°µ—Èߧ«“¡À«—߉«â·≈⫉¡à √â“ß
‡Àµÿ„Àâ∂Ÿ°µ√ßµàÕ°“√√Ë”√«¬ µàÕ°“√‰¥â ‰ª‡°‘¥‡ªìπ™“«øÑ“™“«
«√√§å ®–∑”„À⺑¥À«—ß ‡°‘¥‡ªì𧫓¡‡»√â“À¡Õߢ÷Èπ„π¥«ß®‘µ
‡ªìπ∫“ª¥â«¬‡Àµÿ¡’µ—≥À“‡¢â“§√Õ∫ß”®‘µ

30. Û
30 : w w w. k a n l a y a n a t a m. c o m
ÚÚ. ∫ÿ≠∑’Ë „ÀâÕ“π‘ ß å Ÿß ÿ¥
§”∂“¡
∑”∫ÿ≠Õ¬à“߉√®÷ß®–¡’Õ“π‘ ß å Ÿß ÿ¥
§”µÕ∫
µâÕß∑”∫ÿ≠¥â«¬°“√ªØ‘∫—µ‘®‘µµ¿“«π“ ®π®‘µ “¡“√∂
æâπ‰ª®“°§«“¡√Ÿâ ‰¡à®√‘ß (Õ«‘™™“) ‰¥â‡¡◊ËÕ„¥·≈â« ºŸâ°√–∑”®–‰¥â
√—∫Õ“π‘ ß å Ÿß ÿ¥
ÚÛ. ™à«¬‡∑à“∑’˙૬‰¥â
§”∂“¡
‡§¬‡™‘≠™«π§π‡¢â“«—¥øíß∏√√¡∫â“ß·µà‡¢“‰¡à¬Õ¡‡≈¬
µ—Èß·µàÕ“¬ÿ Û ®π∂÷ß∫—¥π’È ˆ ªï·≈â«®–¡’«‘∏’™à«¬‡¢“Õ¬à“߉√
§”µÕ∫
™à«¬‡∑à“∑’˙૬‰¥â ºŸâ„¥‰¡à»√—∑∏“·≈⫉¡à∑”µ“¡¬àÕ¡™à«¬
‰¡à ‰¥â µâÕߪ≈àÕ¬«“ß ‡æ√“–™’«‘µ‡ªìπ¢Õ߇¢“ ‡¢“µâÕß∫√‘À“√
®—¥°“√‡≈◊Õ°¥â«¬µ—«¢Õ߇¢“‡Õß

31. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : ÛÒ
31
ÚÙ. °”Àπ¥√Ÿâ«—𵓬
§”∂“¡
ºŸâ∑’Ë «¥¡πµå‡ªìπª√–®” “¡“√∂°”À𥫗𵓬À√◊Õ≈–
—ߢ“√µπ‡Õ߉¥â®√‘ßÀ√◊Õ‰¡à
§”µÕ∫
‰¡à®√‘ß °“√ «¥¡πµå‡ªìπ‡æ’¬ß°“√ªØ‘∫µ∏√√¡‡∫◊Õßµâπ
— ‘ È
®‘µ‰¡à “¡“√∂¬°√–¥—∫‡¢â“ Ÿ§«“¡µ—ß¡—π Ÿß ÿ¥ (Õ—ªªπ“ ¡“∏‘) ‰¥â
à È Ë
‚Õ°“ ∑’Ë®–‰ª√Ÿâ«—𵓬¢Õßµπ‡Õ߬—߇ªìπ‰ª‰¡à ‰¥â ·µà∂Ⓡ¡◊ËÕ„¥
‡®√‘≠ ¡∂¿“«π“®π®‘µ‡¢â“∂÷ßÕ—ªªπ“ ¡“∏‘‰¥â Õߧ娓π®÷߇°‘¥
¢÷Èπ°—∫®‘µ¢ÕߺŸâ∑Ë’‡¢â“∂÷ß ·≈â«‚Õ°“ √Ÿâ«—𵓬¢Õßµ—«‡Õß®–‡ªìπ
‰ª‰¥â ¥—ßµ—«Õ¬à“ߢÕß¿‘°…ÿ≥Õ√À—πµå∑™Õ¡À“ª™“∫¥’ (‚§µ¡’) ‰¥â
’ ’Ë ◊Ë
‡¢â“¨“π·≈⫵√«®¥ŸÕ“¬ÿ —ߢ“√¢Õßµπ‡Õß ®÷ßæ∫«à“‡Àµÿªí®®—¬
∑’Ë®–∑”„Àâ¡’™’«‘µÕ¬ŸàµàÕ‰ª„°≈â®–À¡¥ ‘Èπ≈ß„π‡¬Áπ«—ππ’È ®÷߉¥â
∫Õ°≈“≠“µ‘∏√√¡·≈⫉ª°√“∫∑Ÿ≈≈“æ√–æÿ∑∏‡®â“ ‡æ◊ËÕ∑‘Èߢ—π∏å
≈“‚≈°‡¢â“ Ÿàπ‘ææ“π
ç∑ÿ°¢å°“¬°—∫∑ÿ°¢å „® ‡°’ˬ«‡π◊ËÕß°—π
‡À¡◊ÕπæàÕ·¡à≈Ÿ° 𓬰—∫≈Ÿ°πâÕß ¡¿“√°—∫≈Ÿ°«—¥
∑ÿ° à«π‡ªìπÕ«—¬«–‡¥’¬«°—π ÿ¢∑ÿ°¢å ‚¬ß∂÷ß°—πÀ¡¥
·µàæàÕ·¡à - 𓬠- ¡¿“√ ‰¥â√—∫§«“¡°√–‡∑◊Õπ„® Õ߇∑à“é

32. ÛÚ
32 : w w w. k a n l a y a n a t a m. c o m
Úı. ‡¢â“„Àâ∂÷ߧ«“¡®√‘ß·≈⫬ա√—∫
§”∂“¡
∫“ߧ√—Èß√Ÿâ ÷° —∫ π°—∫°“√¥”√ß™’«‘µ„πªí®®ÿ∫—π ∑’˵âÕß
¢«π¢«“¬¥‘Èπ√π∑–‡¬Õ∑–¬“π ‡æ◊ËÕ„Àâ ‰¥â „π∫“ß ‘Ëß∫“ßÕ¬à“ß∑’Ë
¡πÿ…¬åµâÕß°“√ „π¢≥–‡¥’¬«°—π‡¡◊ËÕ§”π÷ß∂÷ßÀ≈—°§” Õπ∑“ß
æÿ∑∏»“ π“∑’Ë„À⥔‡π‘π™’«‘µ„π∑“ß “¬°≈“ß∑’Ë ‰¡à¬÷¥µ‘¥°—∫«—µ∂ÿ
µà“ß Ê ‰¡à∑√“∫«à“Õ“®“√¬å®–¡’¢âÕ‡ πÕ·π–Õ¬à“߉√‡æ√“–„π
ªí®®ÿ∫—πºŸâ∂“¡‡Õß°Á¡‘„™à§π∑’Ë√Ë”√«¬Õ–‰√ ∑’Ë®– “¡“√∂ª≈àÕ¬
«“ßÕ–‰√ Ê ‰¥â
§”µÕ∫
∑ÿ°§π∑’ˇ°‘¥¡“≈â«π¡“µ—«‡ª≈à“ ¡‘‰¥âπ” ¡∫—µ‘„¥ Ê µ‘¥
µ—«¡“¥â«¬ §√—Èπ‡¡◊ËÕµ“¬‰ª°Á‰ªµ—«‡ª≈à“ ‰¡à¡’„§√·¡â —°§π‡¥’¬«
∑’Ë “¡“√∂π”¡πÿ … ¬å ¡∫— µ‘ µ‘ ¥ µ— « ‰ª‰¥â π’Ë §◊ Õ §«“¡®√‘ ß ºŸâ „ ¥
¬Õ¡√—∫§«“¡®√‘ß·≈–Õ¬Ÿà°—∫§«“¡®√‘ß ®–¥”‡π‘π™’«‘µÕ¬Ÿà„π∑“ß
“¬°≈“ß (æÕÕ¬ŸàæÕ°‘π) ¡‘‰¥âÕ¬ŸàÕ¬à“ߪ√–¡“∑ ‡¢“®– —Ëß ¡
∑√—æ¬å¿“¬„π (∫ÿ≠∫“√¡’) „Àâ°—∫®‘µ«‘≠≠“≥ ´÷Ë߇¡◊ËÕµ“¬‰ª·≈â«
∑√—æ¬å¿“¬„π “¡“√∂µ‘¥µ—«¢â“¡¿æ¢â“¡™“µ‘‰ª Ÿà¿æ„À¡à ‰¥â
ç ¡∫—µ‘ ∫√‘«“√ ¬» ¥Ÿ‡À¡◊Õπ„Àâ ÿ¢·°àµπ
·µà§«“¡®√‘ß ∑à“π„À≫â‡æ◊ËÕÕ”π«¬ ÿ¢·°à§πÕ◊Ëπé

33. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : ÛÛ
33
Úˆ. °√√¡µ—¥√Õπ„Àâº≈
§”∂“¡
¡’≠“µ‘‰ª¥ŸÀ¡Õ∫Õ°«à“¥’∑ÿ°Õ¬à“ßÕ“¬ÿ¬◊π ·µàÕ¬Ÿà¥’Ê °Á
‚¥πÕÿ∫—µ‘‡Àµÿ·≈–µ“¬‡æ√“–‡Àµÿ„¥·§àÕ“¬ÿ Ù °«à“
§”µÕ∫
‡Àµÿ‡æ√“–°√√¡µ—¥√Õπ (Õÿª¶“µ°√√¡) „Àâº≈
Ú˜. ¢“¥À√◊Õ‰¡à¢“¥Õ¬Ÿà∑Ë’ „®
§”∂“¡
æ√–∑’Ë∑”æ‘∏’ª≈ÿ°‡ °®µÿ§“¡®–∑”„À⢓¥®“°‰µ√ √≥
§¡πåÀ√◊Õ‰¡à
§”µÕ∫
§”«à“ 牵√ √≥§¡πåé À¡“¬∂÷ß°“√‡Õ“æ√–æÿ∑∏ æ√–
∏√√¡ æ√– ß¶å ‡ªìπ∑’Ëæ÷Ëß ∑’ˇ§“√æ∑’Ë°√“∫‰À«â∫Ÿ™“ ¿‘°…ÿ∑’Ë ‰ª∑”
æ‘∏ª≈ÿ°‡ °®µÿ§“¡œ À“°„®¢Õß¿‘°…ÿ√ªπ—π¬—߇Փæ√–æÿ∑∏ æ√–
’ Ÿ È
∏√√¡ æ√– ߶凪ìπ∑’Ëæ÷Ëß ∑’ˇ§“√æ∫Ÿ™“°√“∫‰À«â ¬—߉¡à∂◊Õ«à“
¢“¥®“°‰µ√ √≥§¡πå

34. ÛÙ
34 : w w w. k a n l a y a n a t a m. c o m
Ú¯. ‰¡à§«√∑”
§”∂“¡
º¡¡’§√Õ∫§√—«·≈–‰¥â √â“ß∫â“π·µà¡’Àπ’È ‘πÕ¬Ÿà¡“°∂â“
À“°º¡®–∑‘Èߧ√Õ∫§√—«·≈⫉ª∫«™µ≈Õ¥™’«‘µ®–‡ªìπ‚∑…À√◊Õ¡’
«‘∫“°°√√¡§√Õ∫§√—«À√◊Õ‰¡à ¥Ÿ·≈⫇À¡◊ÕπÀπ’‡Õ“µ—«√Õ¥§π
‡¥’¬«§«√∑”À√◊Õ‰¡à
§”µÕ∫
‰¡à§«√∑” ‡æ√“–∫√‘«“√¬—ß¡’Àπ’È ‘π ‡¡◊ËÕ„¥∑’Ë°√√¡„Àâ
º≈‡ªìπÕ°ÿ»≈«‘∫“° ºŸâ√à«¡°√–∫«π°√√¡ µâÕß√—∫º≈·Ààß«‘∫“°
π—π¥â«¬
È
Ú˘. ‰¡à‡ªìπ∫“ª
§”∂“¡
‰ª«—¥·≈â«æ√–∑à“π°≈à“««à“ 燙‘≠‰ª∑“π¢â“«é À≈—ß
®“°∑’Ë∑à“πµ—°Õ“À“√‰«â©π·≈â« æÕ‡√“°‘π„π«—¥‡ √Á®·≈⫪√“°Ø
—
«à“¡’Õ“À“√‡À≈◊Õ‡√“π”°≈—∫‰ª∑“πµàÕ∑’Ë∫â“π®–∫“ªÀ√◊Õ‰¡à

35. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : Ûı
35
§”µÕ∫
‡¡◊ËÕ∑à“πÕπÿ≠“µ·≈⫉¡à∂◊Õ‡ªìπ∫“ª
Û. µà“ß°—π∑’˧«“¡À¡“¬
§”∂“¡
°“√‡¢â “ π‘ ‚ √∏°√√¡°— ∫ °“√‡¢â “ π‘ ‚ √∏ ¡“∫— µ‘ µà “ ß°— π
Õ¬à“߉√
§”µÕ∫
π‘‚√∏ À¡“¬∂÷ß ¿“«–§«“¡¥—∫∑ÿ°¢å §◊Õæ√–π‘ææ“π
°√√¡ À¡“¬∂÷ß °“√°√–∑” π‘‚√∏°√√¡ À¡“¬∂÷ß°“√°√–∑”
„Àâ∂÷ß´÷Ëߧ«“¡¥—∫∑ÿ°¢å à«ππ‘‚√∏ ¡“∫—µ‘ À¡“¬∂÷ß ¿“«–°“√
¥—∫ —≠≠“ ·≈–¥—∫‡«∑π“´÷Ë߇ªìπ°“√¥—∫™—Ë«§√“« æ√–Õ𓧓¡’
À√◊Õæ√–Õ√À—πµåºŸâ‡¢â“∂÷ß ¨“π ¡“∫—µ‘ ¯ ·≈â«®÷ß®–¡’‚Õ°“
‡¢â“∂÷ßπ‘‚√∏ ¡“∫—µ‰¥â ·≈–„πÀâ«ß∑’Õ¬Ÿà„ππ‘‚√∏ ¡“∫—µ‘ °‘®°√√¡
‘ Ë
∑ÿ°Õ¬à“ߢÕß√à“ß°“¬À¬ÿ¥À¡¥
ç∫ÿ≠®–„Àâ§ÿ≥ µàÕ‡¡◊ËÕºŸâ „Àâ≈◊¡‰ª·≈â«é

36. Ûˆ
36 : w w w. k a n l a y a n a t a m. c o m
ÛÒ. ‡≈◊Õ°Õߧå∫√‘°√√¡„Àâµ√ß°—∫®√‘µ
§”∂“¡
¡’«‘∏’ªØ‘∫—µ‘Õ¬à“߉√∑’Ë∑”„Àâ‡√“¡’ µ‘·≈– ¡“∏‘
§”µÕ∫
µâÕ߇≈◊Õ°Õߧå∫√‘°√√¡Õ¬à“ß„¥Õ¬à“ßÀπ÷Ëß„π°√√¡∞“π
Ù ∑’ˇ¢â“°—π‰¥â¥’°—∫®√‘µ¢ÕߺŸâªØ‘∫—µ‘ ‡¡◊Ëժؑ∫—µ‘„À⬑Ëß Ê ¢÷Èπ·≈â«
§«“¡µ—Èß¡—Ëπ ( ¡“∏‘) ¢Õß®‘µ®÷ß®–¡’‚Õ°“ ‡°‘¥¢÷Èπ‰¥â
ÛÚ. ¬—߉¡à „™à ‘Ëß ”§—≠
§”∂“¡
§π∑’Ëπ—∫∂◊Õæÿ∑∏µàÕ¡“π—∫∂◊Õ§√‘ µå®–∫“ª‰À¡
§”µÕ∫
§”«à“∫“ª„π¢—Èπ‚≈°ÿµ√– À¡“¬∂÷ß¿“«–¢Õß®‘µ∑’ˬ—ß¡’
‘Ë߇»√â“À¡Õß (Õπÿ —¬ ˜ Àπâ“ Û˜ À√◊Õ —ß‚¬™πå Ò Àπâ“ Úı)
—Ëß ¡Õ¬Ÿà„π¥«ß®‘µ ¥—ßπ—Èπ°“√‡ª≈’Ë¬π§«“¡»√—∑∏“‡™◊ËÕ∂◊Õ®“°
»“ π“Àπ÷Ë߉ª»√—∑∏“‡™◊ËÕ∂◊Õ„πÕ’°»“ π“Àπ÷Ë߬—߉¡à„™à ‘Ëß ”§—≠
À“°®‘µ¬—ßµ°‡ªìπ∑“ ¢Õߧ«“¡‡»√â“À¡Õß∑’°≈à“«¢â“ßµâπ ∂◊Õ«à“
Ë
∫“ª∑—Èß°àÕπ‡ª≈’ˬπ·≈–À≈—߇ª≈’Ë¬π»“ π“

37. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : Û˜
37
ÛÛ. ‰¡à¡’ —≠≠“-‰¡à¡’§«“¡‡ÀÁπ
§”∂“¡
∑’Ë‚∫√“≥‡¢“«à“ Òˆ ™—ÈπøÑ“ Òı ™—Èπ¥‘ππ—È𠵓¡∑’˺¡‰¥â
»÷°…“∏√√¡–¡“ º¡§‘¥«à“‰¡àπ“®–„™à πà“®–‡ªìπ Úˆ ™—πøÑ“ ·≈–
à È
ı ™—Èπ¥‘π¢Õ„ÀâÕ“®“√¬å°√ÿ≥“∫Õ°„À⇢Ⓞ®¥â«¬§√—∫
§”µÕ∫
¢ÕÕ¿—¬ ‰¡à¡’ —≠≠“‡°’ˬ«°—∫ ¡¡µ‘∑’Ë∫Õ°‡≈à“‰ª®÷ß„Àâ
§«“¡‡ÀÁπ‰¡à ‰¥â
Õπÿ —¬ ˜ ®“°æ®π“πÿ°√¡æÿ∑∏»“ πå ª√–¡«≈∏√√¡ À¡«¥ ˜
(Ú˜Û) Õπÿ —¬ ˜ (°‘‡≈ ∑’ËπÕπ‡π◊ËÕßÕ¬Ÿà„π —π¥“π) ¡’¥—ßπ’È
Ò. °“¡√“§– (§«“¡°”Àπ—¥„π°“¡, §«“¡Õ¬“°‰¥âµ‘¥„®„π°“¡)
Ú. ªØ‘¶– (§«“¡¢—¥„®, §«“¡Àßÿ¥Àß‘¥¢—¥‡§◊Õߧ◊Õ‚∑ –)
Û. ∑‘Ø∞‘ (§«“¡‡ÀÁπº‘¥, °“√∂◊Õ§«“¡‡ÀÁπ ‡Õ“§«“¡§‘¥‡ÀÁπ
‡ªì𧫓¡®√‘ß)
Ù. «‘®‘°‘®©“ (§«“¡≈—߇≈, §«“¡ ß —¬)
ı. ¡“π– (§«“¡∂◊Õµ—«)
ˆ. ¿«√“§– (§«“¡°”À𗥄π¿æ, §«“¡Õ¬“°‡ªìπ Õ¬à“߬‘Ëß„À≠à
Õ¬“°¬—Ë߬◊π)
˜. Õ«‘™™“ (§«“¡‰¡à√Ÿâ®√‘ß §◊Õ ‚¡À–)

38. Û¯
38 : w w w. k a n l a y a n a t a m. c o m
ÛÙ. ¡À“ µ‘™à«¬‰¥â
§”∂“¡
∑”Õ¬à“߉√∂÷ß®–√–≈÷°∂÷ߧ«“¡µ“¬‰¥â „π∑ÿ°¢≥–®‘µ
(Õ“√¡≥å·∫∫æ√–‚ ¥“∫—π) «‘∏’°“√À√◊Õ°ÿ»‚≈∫“¬ ‚¥¬∑’Ë ‰¡àπ—∫
∂÷ß°“√®—∫≈¡À“¬„®‡¢â“-ÕÕ°
§”µÕ∫
µâÕßæ‘®“√≥“Õ ÿ¿°√√¡∞“π ®π°√–∑—Ëß®‘µ¡’°”≈—ߢÕß
µ‘°≈â“·¢Á߇ªìπ¡À“ µ‘‰¥â·≈â« ®÷ß®–√–≈÷°∂÷ߧ«“¡µ“¬‰¥â∑ÿ°
¢≥–®‘µ
Ûı. —µ«åπ√°√—∫∫ÿ≠‰¡à ‰¥â
§”∂“¡
‡§¬Õà “ πÀπ— ß ◊ Õ ¡“«à “ „ππ√°‰¡à “¡“√∂√— ∫ à « π∫ÿ ≠
à«π°ÿ»≈‰¥â®√‘ßÀ√◊Õ‰¡à§–
§”µÕ∫
®√‘ß ‡æ√“–‡ «¬Õ°ÿ»≈«‘∫“° ∑’Ë„Àâº≈‡ªì𧫓¡∑ÿ°¢å
≈â«πÕ¬à“߇¥’¬«

39. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : Û˘
39
Ûˆ. ®–∂Ÿ°√∫°«π®÷߉¡àµÕ∫
§”∂“¡
µ“¡∑’∑“π‡§¬°≈à“«‰«â„πÀπ—ß ◊Õµ“¡√Õ¬æàÕ«à“ çæ√–‡®â“
Ëà
¡À“π“¡–°—∫æ√–‡®â“«‘±Ÿ±¿–é ‰¥â°≈—∫¡“‡°‘¥„πª√–‡∑»‰∑¬
Õ¬“°∑√“∫«à“‡ªìπ∑à“π„¥§√—∫
§”µÕ∫
¢Õ ß«π‰¡àµÕ∫‡æ√“–®–‡ªìπ‡Àµÿ„Àâ∑à“π∑’Ë∂Ÿ°°≈à“«
π“¡∂Ÿ°√∫°«π ¥â«¬‡Àµÿ∑’Ë ‰¡à∑”„Àâæâπ‰ª®“°∑ÿ°¢å ‰¥â
Û˜. ∑”‰¥â ‰À¡
§”∂“¡
—¡¿‡« ’§◊Õ¥«ß«‘≠≠“≥∑’Ë√Õ‡°‘¥ Õ¬“°∑√“∫«à“‡¡◊ËÕ
∂÷߇«≈“‡°‘¥·≈â« ‡¢“¬—߉¡àÕ¬“°‰ª‡°‘¥®–∑”‰¥â ‰À¡
§”µÕ∫
∑”‰¡à ‰¥â ‡¡◊ËÕ‡Àµÿªí®®—¬≈ßµ—«µâÕ߉ª‡°‘¥µ“¡°Æ¢Õß
∏√√¡™“µ‘

40. Ù
40 : w w w. k a n l a y a n a t a m. c o m
Û¯. ∂Ⓡ≈‘°∑ÿ»’≈
§”∂“¡
‡§¬ª√–惵‘º‘¥»’≈¡“°àÕπ·µà „πªí®®ÿ∫—π‰¥â ”π÷°º‘¥
·≈â«·≈–‡ªìπ§π√—°…“»’≈ Õ¬“°∑√“∫«à“®–ªØ‘∫—µ‘°√√¡∞“π
‡®√‘≠°â“«ÀπⓉÀ¡
§”µÕ∫
À≠‘ßß“¡‡¡◊Õß∑’˪√–°Õ∫Õ“™’æ§â“ª√–‡«≥’ µàÕ¡“‰¥â
‡≈‘°Õ“™’æ∑’º¥»’≈ ·≈â«À—π¡“ª√–惵‘ªØ‘∫µ∏√√¡‰¥âº≈°â“«Àπâ“
Ë‘ — ‘
®π “¡“√∂‡¢â“∂÷ߧ«“¡‡ªìπÕ√‘¬∫ÿ§§≈‰¥â¥ß‡™àπ ‘√¡“ Õ—¡æª“≈’
— ‘
œ≈œ ‰¥â∑”„À⥟‡ªìπµ—«Õ¬à“ß·≈â«
Û˘. Õ¬“°‰¥â‡æ◊ËÕπ À√◊Õ‰¡àÕ¬“°‰¥â‡æ◊ËÕπ
§”∂“¡
Õ¬“°∑√“∫«à“‡«≈“‡√“ «¥¡πµå∏√√¡¥“∑ÿ°«—𮔇ªìπ
®–µâÕßÕ—≠‡™‘≠‡∑«¥“À√◊Õ‡ª≈à“
§”µÕ∫
°“√ «¥¡πµå‡ªìπ°“√∑”®‘µµ¿“«π“‡∫◊ÈÕßµâπ À“°

41. π ∑ π “ ¿ “ … “ ∏ √ √ ¡ ‡ ≈à ¡ ¯ : ÙÒ
41
ª√– ߧå„Àâ‡∑«¥“‰¥â∫ÿ≠ ª√– ߧå„Àâ‡∑«¥“‡ªìπ‡æ◊ËÕπ ®”‡ªìπ
µâÕ߇™‘≠‡∑«¥“¡“øíß «¥¡πµå ‰¡àÕ¬“°¡’‡∑«¥“‡ªìπ‡æ◊ËÕπ ‰¡à
Õ¬“°„Àâ‡∑«¥“‰¥â∫ÿ≠ °Á ‰¡à®”‡ªìπµâÕ߇™‘≠‡∑«¥“¡“øí߇ ’¬ß
«¥¡πµå¢Õߧÿ≥
Ù. ‰¡à „™â·≈–‰¡à™à«¬„ÀâÀ≈ÿ¥æâπ
§”∂“¡
Õ‘∑∏‘ƒ∑∏‘Ï ‡™à𠵓∑‘æ¬å ÀŸ∑‘æ¬å ∑‘欮—°…ÿ„™â·≈–™à«¬„π
°“√À≈ÿ¥æâπ‰¥âÕ¬à“߉√
§”µÕ∫
À“° ¡“∏‘ Ÿß∂÷ߢ—Èπ∑’ˇ°‘¥‚≈°‘¬Õ¿‘≠≠“ ‡™àπ ÀŸ∑‘æ¬å µ“
∑‘æ¬å ‰¡à “¡“√∂π”Õ¿‘≠≠“‡À≈à“π—Èπ¡“æ‘®“√≥“„À⮑µÀ≈ÿ¥æâπ
‰ª®“° —ß “√«—؉¥â µâÕß≈¥°”≈—ߢÕß µ‘≈ß¡“µ—Èß¡—ËπÕ¬Ÿà „π
√–¥—∫Õÿª®“√ ¡“∏‘ ·≈â«æ‘®“√≥“ µ‘ªíØ∞“π Ù „Àâ‡ÀÁπ‡ªìπ®√‘ß
µ“¡°Æ‰µ√≈—°…≥å ‰¥â ®÷ß®–¡’‚Õ°“ ∑”®‘µ„ÀâÀ≈ÿ¥æâπ®“°°‘‡≈ ∑’Ë
ºŸ°¡—¥„® —µ«å ( —ß‚¬™πå Ò Àπâ“ Úı) ‰¥â¥—ßµ—«Õ¬à“ߢÕßæ√–
Õ√À—πµå∑’ˇ¢â“√à«¡°√–∑”ª∞¡ —ߧ“¬π“æ√–‰µ√ªîÆ° ∑ÿ°Õߧå
≈â«π‡ªìπÕ√À—πµåÕ¿‘≠≠“ ˆ ∑—Èß ‘Èπ ´÷ËßÕ¿‘≠≠“µ—« ÿ¥∑⓬
(Õ“ «—°¢¬≠“≥) ∑”„Àâ ‘ÈπÕ“ «–

42. ÙÚ
42 : w w w. k a n l a y a n a t a m. c o m
ÙÒ. ™à«¬¥â“π»√—∑∏“ - ‰¡à™à«¬„ÀâÀ≈ÿ¥æâπ
§”∂“¡
°“√‡¥‘π∑“߉ªπ¡— °“√ ∂“π∑’Ë»—°¥‘Ï ‘∑∏‘χæ◊ËÕ„Àâ ‰¥âæ≈—ß
®”‡ªìπÀ√◊Õ‰¡à ™à«¬„π°“√À≈ÿ¥æâπÕ¬à“߉√
§”µÕ∫
™à«¬‰¥â∫â“ß„π‡√◊ËÕߢÕß°“√ √â“ß°”≈—ß„®¥â“π»√—∑∏“
„À⇰‘¥¢÷Èπ ·µà®µ®–À≈ÿ¥æâπ‡ªìπÕ‘ √–®“° ‘Ë߇»√â“À¡Õß∑—Èߪ«ß
‘
‰¥â µâÕßæ—≤π“®‘µ„À⇰‘¥ªí≠≠“‡ÀÁπ·®âߥ⫬µ—«‡Õ߇∑à“π—Èπ
ÙÚ. ‰¡à‡∫’¬¥‡∫’¬π ‰¡à∫“ª
§”∂“¡
ÀπŸ¡’Õ“™’梓¬√∂¡Õ‡µÕ√å ‰´¥å¢“¬‡ß‘πºàÕπ ‡°Á∫¥Õ°
‡∫’Ȭ·≈–√—∫®”π”∑–‡∫’¬π√∂ µâÕ߇≈’Ȭߧ√Õ∫§√—«∫√‘«“√
À≈“¬§π º‘¥∫“ª¡“°πâÕ¬·§à ‰Àπ®–·°â ‰¢Õ¬à“߉√ ‡æ√“–‡ªìπ
Õ“™’æ
§”µÕ∫
ª√–°Õ∫Õ“™’ æ ¥â « ¬§«“¡æÕ¥’ ¡‡Àµÿ º ≈ ‰¡à
‡∫’¬¥‡∫’¬πºŸâ´◊ÈÕ ºŸâ´◊ÈÕæÕ„®√—∫∫√‘°“√ ‡¡◊ËÕ´◊ÈÕ√∂‰ª·≈⫺Ÿâ´◊ÈÕ